LMFDB - Embedded newform 9.52.a.b.1.3

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			1.3
Root			$644100.$ 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)

$f(q)$	$=$	$q+1.27049e7 q^{2} -2.09038e15 q^{4} +3.83602e17 q^{5} -2.02239e21 q^{7} -5.51672e22 q^{8} +O(q^{10})$	\(q+1.27049e7 q^{2} -2.09038e15 q^{4} +3.83602e17 q^{5} -2.02239e21 q^{7} -5.51672e22 q^{8} +4.87365e24 q^{10} +2.47031e25 q^{11} -1.34161e27 q^{13} -2.56944e28 q^{14} +4.00623e30 q^{16} -3.03892e31 q^{17} +7.39260e32 q^{19} -8.01876e32 q^{20} +3.13851e32 q^{22} +7.84569e34 q^{23} -2.96939e35 q^{25} -1.70450e34 q^{26} +4.22758e36 q^{28} -1.79754e37 q^{29} -9.27311e37 q^{31} +1.75124e38 q^{32} -3.86093e38 q^{34} -7.75794e38 q^{35} +6.86089e39 q^{37} +9.39226e39 q^{38} -2.11623e40 q^{40} +1.74971e41 q^{41} +5.07001e41 q^{43} -5.16389e40 q^{44} +9.96791e41 q^{46} +2.50083e42 q^{47} -8.49918e42 q^{49} -3.77259e42 q^{50} +2.80447e42 q^{52} -1.56292e44 q^{53} +9.47615e42 q^{55} +1.11570e44 q^{56} -2.28376e44 q^{58} +5.63890e44 q^{59} +3.98784e45 q^{61} -1.17814e45 q^{62} -6.79628e45 q^{64} -5.14643e44 q^{65} -1.33985e46 q^{67} +6.35251e46 q^{68} -9.85643e45 q^{70} -2.44343e47 q^{71} +1.85599e47 q^{73} +8.71673e46 q^{74} -1.54534e48 q^{76} -4.99593e46 q^{77} +1.63316e48 q^{79} +1.53680e48 q^{80} +2.22300e48 q^{82} -5.04167e48 q^{83} -1.16574e49 q^{85} +6.44142e48 q^{86} -1.36280e48 q^{88} -1.69379e48 q^{89} +2.71326e48 q^{91} -1.64005e50 q^{92} +3.17729e49 q^{94} +2.83582e50 q^{95} -6.10891e50 q^{97} -1.07982e50 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	1.27049e7	0.267737	0.133868	−	0.990999i	$-0.457260\pi$
$2$	1.27049e7	0.267737	0.133868	+	0.990999i	$0.457260\pi$
$3$	0	0
$3$	0	0
$4$	−2.09038e15	−0.928317
$5$	3.83602e17	0.575633	0.287817	−	0.957686i	$-0.407071\pi$
$5$	3.83602e17	0.575633	0.287817	+	0.957686i	$0.407071\pi$
$6$	0	0
$7$	−2.02239e21	−0.569988	−0.284994	−	0.958529i	$-0.591992\pi$
$7$	−2.02239e21	−0.569988	−0.284994	+	0.958529i	$0.591992\pi$
$8$	−5.51672e22	−0.516281
$9$	0	0
$10$	4.87365e24	0.154118
$11$	2.47031e25	0.0687444	0.0343722	−	0.999409i	$-0.489057\pi$
$11$	2.47031e25	0.0687444	0.0343722	+	0.999409i	$0.489057\pi$
$12$	0	0
$13$	−1.34161e27	−0.0527314	−0.0263657	−	0.999652i	$-0.508393\pi$
$13$	−1.34161e27	−0.0527314	−0.0263657	+	0.999652i	$0.508393\pi$
$14$	−2.56944e28	−0.152607
$15$	0	0
$16$	4.00623e30	0.790090
$17$	−3.03892e31	−1.27724	−0.638618	−	0.769524i	$-0.720494\pi$
$17$	−3.03892e31	−1.27724	−0.638618	+	0.769524i	$0.720494\pi$
$18$	0	0
$19$	7.39260e32	1.82214	0.911068	−	0.412257i	$-0.135259\pi$
$19$	7.39260e32	1.82214	0.911068	+	0.412257i	$0.135259\pi$
$20$	−8.01876e32	−0.534370
$21$	0	0
$22$	3.13851e32	0.0184054
$23$	7.84569e34	1.48106	0.740528	−	0.672026i	$-0.234576\pi$
$23$	7.84569e34	1.48106	0.740528	+	0.672026i	$0.234576\pi$
$24$	0	0
$25$	−2.96939e35	−0.668646
$26$	−1.70450e34	−0.0141181
$27$	0	0
$28$	4.22758e36	0.529129
$29$	−1.79754e37	−0.919451	−0.459726	−	0.888061i	$-0.652052\pi$
$29$	−1.79754e37	−0.919451	−0.459726	+	0.888061i	$0.652052\pi$
$30$	0	0
$31$	−9.27311e37	−0.865969	−0.432984	−	0.901401i	$-0.642539\pi$
$31$	−9.27311e37	−0.865969	−0.432984	+	0.901401i	$0.642539\pi$
$32$	1.75124e38	0.727817
$33$	0	0
$34$	−3.86093e38	−0.341963
$35$	−7.75794e38	−0.328104
$36$	0	0
$37$	6.86089e39	0.703456	0.351728	−	0.936102i	$-0.385594\pi$
$37$	6.86089e39	0.703456	0.351728	+	0.936102i	$0.385594\pi$
$38$	9.39226e39	0.487853
$39$	0	0
$40$	−2.11623e40	−0.297189
$41$	1.74971e41	1.30912	0.654559	−	0.756011i	$-0.272854\pi$
$41$	1.74971e41	1.30912	0.654559	+	0.756011i	$0.272854\pi$
$42$	0	0
$43$	5.07001e41	1.12606	0.563032	−	0.826435i	$-0.309635\pi$
$43$	5.07001e41	1.12606	0.563032	+	0.826435i	$0.309635\pi$
$44$	−5.16389e40	−0.0638166
$45$	0	0
$46$	9.96791e41	0.396533
$47$	2.50083e42	0.574895	0.287448	−	0.957796i	$-0.407193\pi$
$47$	2.50083e42	0.574895	0.287448	+	0.957796i	$0.407193\pi$
$48$	0	0
$49$	−8.49918e42	−0.675114
$50$	−3.77259e42	−0.179021
$51$	0	0
$52$	2.80447e42	0.0489515
$53$	−1.56292e44	−1.67843	−0.839215	−	0.543800i	$-0.816985\pi$
$53$	−1.56292e44	−1.67843	−0.839215	+	0.543800i	$0.816985\pi$
$54$	0	0
$55$	9.47615e42	0.0395716
$56$	1.11570e44	0.294274
$57$	0	0
$58$	−2.28376e44	−0.246171
$59$	5.63890e44	0.393068	0.196534	−	0.980497i	$-0.437031\pi$
$59$	5.63890e44	0.393068	0.196534	+	0.980497i	$0.437031\pi$
$60$	0	0
$61$	3.98784e45	1.18803	0.594014	−	0.804454i	$-0.297542\pi$
$61$	3.98784e45	1.18803	0.594014	+	0.804454i	$0.297542\pi$
$62$	−1.17814e45	−0.231852
$63$	0	0
$64$	−6.79628e45	−0.595226
$65$	−5.14643e44	−0.0303540
$66$	0	0
$67$	−1.33985e46	−0.364879	−0.182439	−	0.983217i	$-0.558399\pi$
$67$	−1.33985e46	−0.364879	−0.182439	+	0.983217i	$0.558399\pi$
$68$	6.35251e46	1.18568
$69$	0	0
$70$	−9.85643e45	−0.0878455
$71$	−2.44343e47	−1.51674	−0.758370	−	0.651824i	$-0.774004\pi$
$71$	−2.44343e47	−1.51674	−0.758370	+	0.651824i	$0.774004\pi$
$72$	0	0
$73$	1.85599e47	0.567339	0.283669	−	0.958922i	$-0.408448\pi$
$73$	1.85599e47	0.567339	0.283669	+	0.958922i	$0.408448\pi$
$74$	8.71673e46	0.188341
$75$	0	0
$76$	−1.54534e48	−1.69152
$77$	−4.99593e46	−0.0391835
$78$	0	0
$79$	1.63316e48	0.666097	0.333048	−	0.942910i	$-0.391923\pi$
$79$	1.63316e48	0.666097	0.333048	+	0.942910i	$0.391923\pi$
$80$	1.53680e48	0.454802
$81$	0	0
$82$	2.22300e48	0.350499
$83$	−5.04167e48	−0.583556	−0.291778	−	0.956486i	$-0.594247\pi$
$83$	−5.04167e48	−0.583556	−0.291778	+	0.956486i	$0.594247\pi$
$84$	0	0
$85$	−1.16574e49	−0.735220
$86$	6.44142e48	0.301489
$87$	0	0
$88$	−1.36280e48	−0.0354915
$89$	−1.69379e48	−0.0330685	−0.0165342	−	0.999863i	$-0.505263\pi$
$89$	−1.69379e48	−0.0330685	−0.0165342	+	0.999863i	$0.505263\pi$
$90$	0	0
$91$	2.71326e48	0.0300563
$92$	−1.64005e50	−1.37489
$93$	0	0
$94$	3.17729e49	0.153921
$95$	2.83582e50	1.04888
$96$	0	0
$97$	−6.10891e50	−1.32826	−0.664132	−	0.747615i	$-0.731199\pi$
$97$	−6.10891e50	−1.32826	−0.664132	+	0.747615i	$0.731199\pi$
$98$	−1.07982e50	−0.180753
$99$	0	0
$100$	6.20716e50	0.620716
$101$	6.28480e50	0.487636	0.243818	−	0.969821i	$-0.421600\pi$
$101$	6.28480e50	0.487636	0.243818	+	0.969821i	$0.421600\pi$
$102$	0	0
$103$	2.80053e51	1.31793	0.658963	−	0.752175i	$-0.270995\pi$
$103$	2.80053e51	1.31793	0.658963	+	0.752175i	$0.270995\pi$
$104$	7.40127e49	0.0272243
$105$	0	0
$106$	−1.98569e51	−0.449377
$107$	1.63322e50	0.0290910	0.0145455	−	0.999894i	$-0.495370\pi$
$107$	1.63322e50	0.0290910	0.0145455	+	0.999894i	$0.495370\pi$
$108$	0	0
$109$	−1.58683e51	−0.176260	−0.0881302	−	0.996109i	$-0.528089\pi$
$109$	−1.58683e51	−0.176260	−0.0881302	+	0.996109i	$0.528089\pi$
$110$	1.20394e50	0.0105948
$111$	0	0
$112$	−8.10217e51	−0.450341
$113$	−3.37912e52	−1.49728	−0.748640	−	0.662977i	$-0.769293\pi$
$113$	−3.37912e52	−1.49728	−0.748640	+	0.662977i	$0.769293\pi$
$114$	0	0
$115$	3.00962e52	0.852545
$116$	3.75754e52	0.853542
$117$	0	0
$118$	7.16419e51	0.105239
$119$	6.14589e52	0.728009
$120$	0	0
$121$	−1.28520e53	−0.995274
$122$	5.06653e52	0.318079
$123$	0	0
$124$	1.93844e53	0.803893
$125$	−2.84260e53	−0.960529
$126$	0	0
$127$	−3.62929e53	−0.818137	−0.409069	−	0.912504i	$-0.634146\pi$
$127$	−3.62929e53	−0.818137	−0.409069	+	0.912504i	$0.634146\pi$
$128$	−4.80692e53	−0.887181
$129$	0	0
$130$	−6.53852e51	−0.00812688
$131$	2.78824e53	0.285044	0.142522	−	0.989792i	$-0.454479\pi$
$131$	2.78824e53	0.285044	0.142522	+	0.989792i	$0.454479\pi$
$132$	0	0
$133$	−1.49507e54	−1.03859
$134$	−1.70227e53	−0.0976914
$135$	0	0
$136$	1.67649e54	0.659414
$137$	−2.86306e54	−0.934236	−0.467118	−	0.884195i	$-0.654708\pi$
$137$	−2.86306e54	−0.934236	−0.467118	+	0.884195i	$0.654708\pi$
$138$	0	0
$139$	3.12773e54	0.705264	0.352632	−	0.935762i	$-0.385287\pi$
$139$	3.12773e54	0.705264	0.352632	+	0.935762i	$0.385287\pi$
$140$	1.62171e54	0.304585
$141$	0	0
$142$	−3.10436e54	−0.406087
$143$	−3.31418e52	−0.00362499
$144$	0	0
$145$	−6.89539e54	−0.529267
$146$	2.35802e54	0.151897
$147$	0	0
$148$	−1.43419e55	−0.653030
$149$	−4.23740e55	−1.62499	−0.812493	−	0.582971i	$-0.801890\pi$
$149$	−4.23740e55	−1.62499	−0.812493	+	0.582971i	$0.801890\pi$
$150$	0	0
$151$	7.71079e54	0.210468	0.105234	−	0.994447i	$-0.466441\pi$
$151$	7.71079e54	0.210468	0.105234	+	0.994447i	$0.466441\pi$
$152$	−4.07829e55	−0.940734
$153$	0	0
$154$	−6.34730e53	−0.0104909
$155$	−3.55718e55	−0.498480
$156$	0	0
$157$	−1.17035e56	−1.18270	−0.591351	−	0.806414i	$-0.701405\pi$
$157$	−1.17035e56	−1.18270	−0.591351	+	0.806414i	$0.701405\pi$
$158$	2.07492e55	0.178339
$159$	0	0
$160$	6.71781e55	0.418956
$161$	−1.58671e56	−0.844183
$162$	0	0
$163$	−1.56667e56	−0.608405	−0.304203	−	0.952607i	$-0.598390\pi$
$163$	−1.56667e56	−0.608405	−0.304203	+	0.952607i	$0.598390\pi$
$164$	−3.65757e56	−1.21528
$165$	0	0
$166$	−6.40541e55	−0.156239
$167$	−4.64519e56	−0.972150	−0.486075	−	0.873917i	$-0.661572\pi$
$167$	−4.64519e56	−0.972150	−0.486075	+	0.873917i	$0.661572\pi$
$168$	0	0
$169$	−6.45508e56	−0.997219
$170$	−1.48106e56	−0.196846
$171$	0	0
$172$	−1.05983e57	−1.04534
$173$	−1.75769e57	−1.49543	−0.747714	−	0.664021i	$-0.768849\pi$
$173$	−1.75769e57	−1.49543	−0.747714	+	0.664021i	$0.768849\pi$
$174$	0	0
$175$	6.00526e56	0.381120
$176$	9.89661e55	0.0543142
$177$	0	0
$178$	−2.15195e55	−0.00885364
$179$	−3.24188e57	−1.15623	−0.578116	−	0.815955i	$-0.696212\pi$
$179$	−3.24188e57	−1.15623	−0.578116	+	0.815955i	$0.696212\pi$
$180$	0	0
$181$	8.53725e56	0.229358	0.114679	−	0.993403i	$-0.463416\pi$
$181$	8.53725e56	0.229358	0.114679	+	0.993403i	$0.463416\pi$
$182$	3.44718e55	0.00804717
$183$	0	0
$184$	−4.32825e57	−0.764641
$185$	2.63185e57	0.404933
$186$	0	0
$187$	−7.50706e56	−0.0878029
$188$	−5.22769e57	−0.533685
$189$	0	0
$190$	3.60289e57	0.280824
$191$	−9.24442e57	−0.630273	−0.315136	−	0.949046i	$-0.602050\pi$
$191$	−9.24442e57	−0.630273	−0.315136	+	0.949046i	$0.602050\pi$
$192$	0	0
$193$	−2.11389e57	−0.110502	−0.0552512	−	0.998472i	$-0.517596\pi$
$193$	−2.11389e57	−0.110502	−0.0552512	+	0.998472i	$0.517596\pi$
$194$	−7.76134e57	−0.355625
$195$	0	0
$196$	1.77666e58	0.626720
$197$	2.03837e58	0.631531	0.315765	−	0.948837i	$-0.397739\pi$
$197$	2.03837e58	0.631531	0.315765	+	0.948837i	$0.397739\pi$
$198$	0	0
$199$	−4.89566e58	−1.17235	−0.586176	−	0.810184i	$-0.699367\pi$
$199$	−4.89566e58	−1.17235	−0.586176	+	0.810184i	$0.699367\pi$
$200$	1.63813e58	0.345210
$201$	0	0
$202$	7.98480e57	0.130558
$203$	3.63532e58	0.524076
$204$	0	0
$205$	6.71194e58	0.753572
$206$	3.55806e58	0.352857
$207$	0	0
$208$	−5.37478e57	−0.0416626
$209$	1.82620e58	0.125262
$210$	0	0
$211$	1.53613e59	0.826467	0.413234	−	0.910625i	$-0.364399\pi$
$211$	1.53613e59	0.826467	0.413234	+	0.910625i	$0.364399\pi$
$212$	3.26711e59	1.55811
$213$	0	0
$214$	2.07500e57	0.00778872
$215$	1.94487e59	0.648200
$216$	0	0
$217$	1.87539e59	0.493591
$218$	−2.01606e58	−0.0471914
$219$	0	0
$220$	−1.98088e58	−0.0367350
$221$	4.07703e58	0.0673505
$222$	0	0
$223$	8.84276e59	1.16095	0.580475	−	0.814278i	$-0.302867\pi$
$223$	8.84276e59	1.16095	0.580475	+	0.814278i	$0.302867\pi$
$224$	−3.54171e59	−0.414847
$225$	0	0
$226$	−4.29315e59	−0.400877
$227$	1.84839e60	1.54218	0.771090	−	0.636726i	$-0.219712\pi$
$227$	1.84839e60	1.54218	0.771090	+	0.636726i	$0.219712\pi$
$228$	0	0
$229$	−1.13494e60	−0.757126	−0.378563	−	0.925576i	$-0.623582\pi$
$229$	−1.13494e60	−0.757126	−0.378563	+	0.925576i	$0.623582\pi$
$230$	3.82371e59	0.228258
$231$	0	0
$232$	9.91651e59	0.474696
$233$	1.75626e60	0.753376	0.376688	−	0.926340i	$-0.377063\pi$
$233$	1.75626e60	0.753376	0.376688	+	0.926340i	$0.377063\pi$
$234$	0	0
$235$	9.59324e59	0.330929
$236$	−1.17875e60	−0.364892
$237$	0	0
$238$	7.80832e59	0.194915
$239$	−7.46779e60	−1.67512	−0.837560	−	0.546346i	$-0.816018\pi$
$239$	−7.46779e60	−1.67512	−0.837560	+	0.546346i	$0.816018\pi$
$240$	0	0
$241$	−2.67830e60	−0.485763	−0.242882	−	0.970056i	$-0.578093\pi$
$241$	−2.67830e60	−0.485763	−0.242882	+	0.970056i	$0.578093\pi$
$242$	−1.63284e60	−0.266471
$243$	0	0
$244$	−8.33612e60	−1.10287
$245$	−3.26031e60	−0.388618
$246$	0	0
$247$	−9.91796e59	−0.0960838
$248$	5.11572e60	0.447083
$249$	0	0
$250$	−3.61151e60	−0.257169
$251$	−2.75172e61	−1.76980	−0.884900	−	0.465782i	$-0.845773\pi$
$251$	−2.75172e61	−1.76980	−0.884900	+	0.465782i	$0.845773\pi$
$252$	0	0
$253$	1.93813e60	0.101814
$254$	−4.61099e60	−0.219045
$255$	0	0
$256$	9.19670e60	0.357695
$257$	4.92610e59	0.0173464	0.00867318	−	0.999962i	$-0.497239\pi$
$257$	4.92610e59	0.0173464	0.00867318	+	0.999962i	$0.497239\pi$
$258$	0	0
$259$	−1.38754e61	−0.400961
$260$	1.07580e60	0.0281781
$261$	0	0
$262$	3.54245e60	0.0763169
$263$	1.45507e60	0.0284454	0.0142227	−	0.999899i	$-0.495473\pi$
$263$	1.45507e60	0.0284454	0.0142227	+	0.999899i	$0.495473\pi$
$264$	0	0
$265$	−5.99541e61	−0.966160
$266$	−1.89948e61	−0.278070
$267$	0	0
$268$	2.80080e61	0.338723
$269$	−8.25887e60	−0.0908318	−0.0454159	−	0.998968i	$-0.514461\pi$
$269$	−8.25887e60	−0.0908318	−0.0454159	+	0.998968i	$0.514461\pi$
$270$	0	0
$271$	8.46290e61	0.770553	0.385276	−	0.922801i	$-0.374106\pi$
$271$	8.46290e61	0.770553	0.385276	+	0.922801i	$0.374106\pi$
$272$	−1.21746e62	−1.00913
$273$	0	0
$274$	−3.63751e61	−0.250129
$275$	−7.33529e60	−0.0459657
$276$	0	0
$277$	−2.17621e62	−1.13362	−0.566808	−	0.823850i	$-0.691822\pi$
$277$	−2.17621e62	−1.13362	−0.566808	+	0.823850i	$0.691822\pi$
$278$	3.97376e61	0.188825
$279$	0	0
$280$	4.27984e61	0.169394
$281$	4.49759e62	1.62543	0.812715	−	0.582661i	$-0.197988\pi$
$281$	4.49759e62	1.62543	0.812715	+	0.582661i	$0.197988\pi$
$282$	0	0
$283$	5.28631e62	1.59440	0.797202	−	0.603713i	$-0.206313\pi$
$283$	5.28631e62	1.59440	0.797202	+	0.603713i	$0.206313\pi$
$284$	5.10770e62	1.40802
$285$	0	0
$286$	−4.21065e59	−0.000970543 0
$287$	−3.53861e62	−0.746181
$288$	0	0
$289$	3.57400e62	0.631334
$290$	−8.76056e61	−0.141704
$291$	0	0
$292$	−3.87973e62	−0.526670
$293$	1.35914e63	1.69099	0.845493	−	0.533987i	$-0.179307\pi$
$293$	1.35914e63	1.69099	0.845493	+	0.533987i	$0.179307\pi$
$294$	0	0
$295$	2.16309e62	0.226263
$296$	−3.78496e62	−0.363181
$297$	0	0
$298$	−5.38359e62	−0.435069
$299$	−1.05258e62	−0.0780982
$300$	0	0
$301$	−1.02535e63	−0.641843
$302$	9.79652e61	0.0563501
$303$	0	0
$304$	2.96165e63	1.43965
$305$	1.52974e63	0.683869
$306$	0	0
$307$	3.47883e63	1.31645	0.658226	−	0.752821i	$-0.271307\pi$
$307$	3.47883e63	1.31645	0.658226	+	0.752821i	$0.271307\pi$
$308$	1.04434e62	0.0363747
$309$	0	0
$310$	−4.51939e62	−0.133462
$311$	−9.88875e62	−0.268999	−0.134500	−	0.990914i	$-0.542943\pi$
$311$	−9.88875e62	−0.268999	−0.134500	+	0.990914i	$0.542943\pi$
$312$	0	0
$313$	−5.32344e63	−1.22974	−0.614868	−	0.788630i	$-0.710791\pi$
$313$	−5.32344e63	−1.22974	−0.614868	+	0.788630i	$0.710791\pi$
$314$	−1.48693e63	−0.316653
$315$	0	0
$316$	−3.41393e63	−0.618349
$317$	2.07710e63	0.347094	0.173547	−	0.984826i	$-0.444477\pi$
$317$	2.07710e63	0.347094	0.173547	+	0.984826i	$0.444477\pi$
$318$	0	0
$319$	−4.44046e62	−0.0632071
$320$	−2.60707e63	−0.342632
$321$	0	0
$322$	−2.01590e63	−0.226019
$323$	−2.24655e64	−2.32730
$324$	0	0
$325$	3.98375e62	0.0352587
$326$	−1.99044e63	−0.162892
$327$	0	0
$328$	−9.65269e63	−0.675873
$329$	−5.05766e63	−0.327683
$330$	0	0
$331$	−1.81346e63	−0.100669	−0.0503343	−	0.998732i	$-0.516029\pi$
$331$	−1.81346e63	−0.100669	−0.0503343	+	0.998732i	$0.516029\pi$
$332$	1.05390e64	0.541725
$333$	0	0
$334$	−5.90169e63	−0.260280
$335$	−5.13969e63	−0.210036
$336$	0	0
$337$	−1.27328e64	−0.447056	−0.223528	−	0.974698i	$-0.571757\pi$
$337$	−1.27328e64	−0.447056	−0.223528	+	0.974698i	$0.571757\pi$
$338$	−8.20115e63	−0.266992
$339$	0	0
$340$	2.43684e64	0.682518
$341$	−2.29074e63	−0.0595305
$342$	0	0
$343$	4.26491e64	0.954794
$344$	−2.79698e64	−0.581366
$345$	0	0
$346$	−2.23313e64	−0.400381
$347$	4.50582e64	0.750537	0.375269	−	0.926916i	$-0.377550\pi$
$347$	4.50582e64	0.750537	0.375269	+	0.926916i	$0.377550\pi$
$348$	0	0
$349$	6.10318e63	0.0878026	0.0439013	−	0.999036i	$-0.486021\pi$
$349$	6.10318e63	0.0878026	0.0439013	+	0.999036i	$0.486021\pi$
$350$	7.62966e63	0.102040
$351$	0	0
$352$	4.32611e63	0.0500334
$353$	6.21110e64	0.668211	0.334106	−	0.942536i	$-0.391566\pi$
$353$	6.21110e64	0.668211	0.334106	+	0.942536i	$0.391566\pi$
$354$	0	0
$355$	−9.37304e64	−0.873087
$356$	3.54067e63	0.0306980
$357$	0	0
$358$	−4.11879e64	−0.309566
$359$	2.08428e64	0.145898	0.0729488	−	0.997336i	$-0.476759\pi$
$359$	2.08428e64	0.145898	0.0729488	+	0.997336i	$0.476759\pi$
$360$	0	0
$361$	3.81904e65	2.32018
$362$	1.08465e64	0.0614076
$363$	0	0
$364$	−5.67175e63	−0.0279017
$365$	7.11962e64	0.326579
$366$	0	0
$367$	−1.66429e65	−0.664118	−0.332059	−	0.943259i	$-0.607743\pi$
$367$	−1.66429e65	−0.664118	−0.332059	+	0.943259i	$0.607743\pi$
$368$	3.14316e65	1.17017
$369$	0	0
$370$	3.34376e64	0.108415
$371$	3.16085e65	0.956684
$372$	0	0
$373$	3.79646e64	0.100185	0.0500925	−	0.998745i	$-0.484048\pi$
$373$	3.79646e64	0.100185	0.0500925	+	0.998745i	$0.484048\pi$
$374$	−9.53768e63	−0.0235081
$375$	0	0
$376$	−1.37964e65	−0.296808
$377$	2.41159e64	0.0484840
$378$	0	0
$379$	3.34355e65	0.587364	0.293682	−	0.955903i	$-0.405119\pi$
$379$	3.34355e65	0.587364	0.293682	+	0.955903i	$0.405119\pi$
$380$	−5.92795e65	−0.973695
$381$	0	0
$382$	−1.17450e65	−0.168747
$383$	−3.02479e65	−0.406561	−0.203281	−	0.979121i	$-0.565160\pi$
$383$	−3.02479e65	−0.406561	−0.203281	+	0.979121i	$0.565160\pi$
$384$	0	0
$385$	−1.91645e64	−0.0225553
$386$	−2.68569e64	−0.0295855
$387$	0	0
$388$	1.27700e66	1.23305
$389$	−3.96714e65	−0.358726	−0.179363	−	0.983783i	$-0.557404\pi$
$389$	−3.96714e65	−0.358726	−0.179363	+	0.983783i	$0.557404\pi$
$390$	0	0
$391$	−2.38424e66	−1.89166
$392$	4.68876e65	0.348549
$393$	0	0
$394$	2.58974e65	0.169084
$395$	6.26483e65	0.383428
$396$	0	0
$397$	1.53914e65	0.0828174	0.0414087	−	0.999142i	$-0.486815\pi$
$397$	1.53914e65	0.0828174	0.0414087	+	0.999142i	$0.486815\pi$
$398$	−6.21992e65	−0.313882
$399$	0	0
$400$	−1.18960e66	−0.528290
$401$	−3.72470e66	−1.55207	−0.776033	−	0.630693i	$-0.782771\pi$
$401$	−3.72470e66	−1.55207	−0.776033	+	0.630693i	$0.782771\pi$
$402$	0	0
$403$	1.24409e65	0.0456638
$404$	−1.31376e66	−0.452681
$405$	0	0
$406$	4.61866e65	0.140314
$407$	1.69485e65	0.0483586
$408$	0	0
$409$	1.18361e66	0.298033	0.149017	−	0.988835i	$-0.452389\pi$
$409$	1.18361e66	0.298033	0.149017	+	0.988835i	$0.452389\pi$
$410$	8.52749e65	0.201759
$411$	0	0
$412$	−5.85419e66	−1.22345
$413$	−1.14041e66	−0.224044
$414$	0	0
$415$	−1.93399e66	−0.335915
$416$	−2.34948e65	−0.0383789
$417$	0	0
$418$	2.32018e65	0.0335371
$419$	−9.81782e66	−1.33523	−0.667617	−	0.744505i	$-0.732686\pi$
$419$	−9.81782e66	−1.33523	−0.667617	+	0.744505i	$0.732686\pi$
$420$	0	0
$421$	4.41844e66	0.532201	0.266101	−	0.963945i	$-0.414265\pi$
$421$	4.41844e66	0.532201	0.266101	+	0.963945i	$0.414265\pi$
$422$	1.95165e66	0.221276
$423$	0	0
$424$	8.62222e66	0.866542
$425$	9.02372e66	0.854019
$426$	0	0
$427$	−8.06498e66	−0.677162
$428$	−3.41406e65	−0.0270056
$429$	0	0
$430$	2.47094e66	0.173547
$431$	9.31273e66	0.616463	0.308231	−	0.951311i	$-0.400263\pi$
$431$	9.31273e66	0.616463	0.308231	+	0.951311i	$0.400263\pi$
$432$	0	0
$433$	−5.53636e66	−0.325674	−0.162837	−	0.986653i	$-0.552064\pi$
$433$	−5.53636e66	−0.325674	−0.162837	+	0.986653i	$0.552064\pi$
$434$	2.38267e66	0.132153
$435$	0	0
$436$	3.31709e66	0.163626
$437$	5.80001e67	2.69868
$438$	0	0
$439$	3.50063e67	1.44978	0.724888	−	0.688867i	$-0.241891\pi$
$439$	3.50063e67	1.44978	0.724888	+	0.688867i	$0.241891\pi$
$440$	−5.22773e65	−0.0204301
$441$	0	0
$442$	5.17985e65	0.0180322
$443$	−3.49460e67	−1.14842	−0.574211	−	0.818707i	$-0.694691\pi$
$443$	−3.49460e67	−1.14842	−0.574211	+	0.818707i	$0.694691\pi$
$444$	0	0
$445$	−6.49741e65	−0.0190353
$446$	1.12347e67	0.310829
$447$	0	0
$448$	1.37447e67	0.339272
$449$	−3.38559e67	−0.789501	−0.394750	−	0.918788i	$-0.629169\pi$
$449$	−3.38559e67	−0.789501	−0.394750	+	0.918788i	$0.629169\pi$
$450$	0	0
$451$	4.32233e66	0.0899945
$452$	7.06365e67	1.38995
$453$	0	0
$454$	2.34838e67	0.412899
$455$	1.04081e66	0.0173014
$456$	0	0
$457$	−1.12417e68	−1.67096	−0.835482	−	0.549517i	$-0.814812\pi$
$457$	−1.12417e68	−1.67096	−0.835482	+	0.549517i	$0.814812\pi$
$458$	−1.44194e67	−0.202710
$459$	0	0
$460$	−6.29127e67	−0.791432
$461$	−3.19451e67	−0.380216	−0.190108	−	0.981763i	$-0.560884\pi$
$461$	−3.19451e67	−0.380216	−0.190108	+	0.981763i	$0.560884\pi$
$462$	0	0
$463$	1.31779e68	1.40453	0.702263	−	0.711918i	$-0.252173\pi$
$463$	1.31779e68	1.40453	0.702263	+	0.711918i	$0.252173\pi$
$464$	−7.20134e67	−0.726449
$465$	0	0
$466$	2.23131e67	0.201706
$467$	4.26431e67	0.364979	0.182490	−	0.983208i	$-0.441584\pi$
$467$	4.26431e67	0.364979	0.182490	+	0.983208i	$0.441584\pi$
$468$	0	0
$469$	2.70970e67	0.207976
$470$	1.21882e67	0.0886018
$471$	0	0
$472$	−3.11082e67	−0.202934
$473$	1.25245e67	0.0774106
$474$	0	0
$475$	−2.19515e68	−1.21836
$476$	−1.28473e68	−0.675823
$477$	0	0
$478$	−9.48779e67	−0.448491
$479$	−1.74665e68	−0.782801	−0.391401	−	0.920220i	$-0.628009\pi$
$479$	−1.74665e68	−0.782801	−0.391401	+	0.920220i	$0.628009\pi$
$480$	0	0
$481$	−9.20462e66	−0.0370942
$482$	−3.40277e67	−0.130057
$483$	0	0
$484$	2.68656e68	0.923930
$485$	−2.34339e68	−0.764593
$486$	0	0
$487$	−3.99057e68	−1.17232	−0.586161	−	0.810195i	$-0.699361\pi$
$487$	−3.99057e68	−1.17232	−0.586161	+	0.810195i	$0.699361\pi$
$488$	−2.19998e68	−0.613357
$489$	0	0
$490$	−4.14220e67	−0.104047
$491$	−1.41320e68	−0.336997	−0.168499	−	0.985702i	$-0.553892\pi$
$491$	−1.41320e68	−0.336997	−0.168499	+	0.985702i	$0.553892\pi$
$492$	0	0
$493$	5.46256e68	1.17436
$494$	−1.26007e67	−0.0257252
$495$	0	0
$496$	−3.71502e68	−0.684193
$497$	4.94157e68	0.864523
$498$	0	0
$499$	3.57937e68	0.565253	0.282626	−	0.959230i	$-0.408794\pi$
$499$	3.57937e68	0.565253	0.282626	+	0.959230i	$0.408794\pi$
$500$	5.94212e68	0.891675
$501$	0	0
$502$	−3.49604e68	−0.473840
$503$	4.56639e68	0.588287	0.294143	−	0.955761i	$-0.404966\pi$
$503$	4.56639e68	0.588287	0.294143	+	0.955761i	$0.404966\pi$
$504$	0	0
$505$	2.41086e68	0.280700
$506$	2.46238e67	0.0272594
$507$	0	0
$508$	7.58660e68	0.759491
$509$	−1.62918e69	−1.55119	−0.775596	−	0.631230i	$-0.782550\pi$
$509$	−1.62918e69	−1.55119	−0.775596	+	0.631230i	$0.782550\pi$
$510$	0	0
$511$	−3.75354e68	−0.323376
$512$	1.19926e69	0.982949
$513$	0	0
$514$	6.25858e66	0.00464426
$515$	1.07429e69	0.758643
$516$	0	0
$517$	6.17781e67	0.0395208
$518$	−1.76287e68	−0.107352
$519$	0	0
$520$	2.83914e67	0.0156712
$521$	1.25774e69	0.661040	0.330520	−	0.943799i	$-0.392776\pi$
$521$	1.25774e69	0.661040	0.330520	+	0.943799i	$0.392776\pi$
$522$	0	0
$523$	−1.98441e69	−0.945883	−0.472941	−	0.881094i	$-0.656808\pi$
$523$	−1.98441e69	−0.945883	−0.472941	+	0.881094i	$0.656808\pi$
$524$	−5.82850e68	−0.264612
$525$	0	0
$526$	1.84866e67	0.00761589
$527$	2.81802e69	1.10605
$528$	0	0
$529$	3.34927e69	1.19352
$530$	−7.61714e68	−0.258677
$531$	0	0
$532$	3.12528e69	0.964145
$533$	−2.34743e68	−0.0690317
$534$	0	0
$535$	6.26507e67	0.0167457
$536$	7.39158e68	0.188380
$537$	0	0
$538$	−1.04929e68	−0.0243190
$539$	−2.09956e68	−0.0464103
$540$	0	0
$541$	2.04153e69	0.410606	0.205303	−	0.978698i	$-0.434182\pi$
$541$	2.04153e69	0.410606	0.205303	+	0.978698i	$0.434182\pi$
$542$	1.07521e69	0.206305
$543$	0	0
$544$	−5.32189e69	−0.929595
$545$	−6.08712e68	−0.101461
$546$	0	0
$547$	−1.73926e69	−0.264050	−0.132025	−	0.991246i	$-0.542148\pi$
$547$	−1.73926e69	−0.264050	−0.132025	+	0.991246i	$0.542148\pi$
$548$	5.98490e69	0.867267
$549$	0	0
$550$	−9.31945e67	−0.0123067
$551$	−1.32885e70	−1.67536
$552$	0	0
$553$	−3.30289e69	−0.379667
$554$	−2.76486e69	−0.303511
$555$	0	0
$556$	−6.53815e69	−0.654709
$557$	−1.57782e70	−1.50921	−0.754604	−	0.656180i	$-0.772171\pi$
$557$	−1.57782e70	−1.50921	−0.754604	+	0.656180i	$0.772171\pi$
$558$	0	0
$559$	−6.80195e68	−0.0593790
$560$	−3.10801e69	−0.259232
$561$	0	0
$562$	5.71416e69	0.435188
$563$	−1.07629e70	−0.783370	−0.391685	−	0.920099i	$-0.628108\pi$
$563$	−1.07629e70	−0.783370	−0.391685	+	0.920099i	$0.628108\pi$
$564$	0	0
$565$	−1.29624e70	−0.861884
$566$	6.71623e69	0.426881
$567$	0	0
$568$	1.34797e70	0.783065
$569$	2.42046e70	1.34442	0.672210	−	0.740361i	$-0.265345\pi$
$569$	2.42046e70	1.34442	0.672210	+	0.740361i	$0.265345\pi$
$570$	0	0
$571$	−2.02012e70	−1.02602	−0.513012	−	0.858382i	$-0.671470\pi$
$571$	−2.02012e70	−1.02602	−0.513012	+	0.858382i	$0.671470\pi$
$572$	6.92791e67	0.00336514
$573$	0	0
$574$	−4.49579e69	−0.199780
$575$	−2.32969e70	−0.990302
$576$	0	0
$577$	2.07089e70	0.805699	0.402850	−	0.915266i	$-0.368020\pi$
$577$	2.07089e70	0.805699	0.402850	+	0.915266i	$0.368020\pi$
$578$	4.54075e69	0.169031
$579$	0	0
$580$	1.44140e70	0.491327
$581$	1.01962e70	0.332620
$582$	0	0
$583$	−3.86090e69	−0.115383
$584$	−1.02390e70	−0.292906
$585$	0	0
$586$	1.72678e70	0.452739
$587$	−4.82066e70	−1.21014	−0.605070	−	0.796173i	$-0.706855\pi$
$587$	−4.82066e70	−1.21014	−0.605070	+	0.796173i	$0.706855\pi$
$588$	0	0
$589$	−6.85524e70	−1.57791
$590$	2.74820e69	0.0605790
$591$	0	0
$592$	2.74863e70	0.555793
$593$	6.85044e70	1.32686	0.663428	−	0.748240i	$-0.269101\pi$
$593$	6.85044e70	1.32686	0.663428	+	0.748240i	$0.269101\pi$
$594$	0	0
$595$	2.35758e70	0.419067
$596$	8.85779e70	1.50850
$597$	0	0
$598$	−1.33730e69	−0.0209097
$599$	3.61715e70	0.541979	0.270990	−	0.962582i	$-0.412649\pi$
$599$	3.61715e70	0.541979	0.270990	+	0.962582i	$0.412649\pi$
$600$	0	0
$601$	6.55680e70	0.902387	0.451193	−	0.892426i	$-0.350998\pi$
$601$	6.55680e70	0.902387	0.451193	+	0.892426i	$0.350998\pi$
$602$	−1.30271e70	−0.171845
$603$	0	0
$604$	−1.61185e70	−0.195381
$605$	−4.93004e70	−0.572913
$606$	0	0
$607$	1.24140e71	1.32617	0.663086	−	0.748544i	$-0.269247\pi$
$607$	1.24140e71	1.32617	0.663086	+	0.748544i	$0.269247\pi$
$608$	1.29463e71	1.32618
$609$	0	0
$610$	1.94353e70	0.183097
$611$	−3.35513e69	−0.0303151
$612$	0	0
$613$	−7.66168e70	−0.636916	−0.318458	−	0.947937i	$-0.603165\pi$
$613$	−7.66168e70	−0.636916	−0.318458	+	0.947937i	$0.603165\pi$
$614$	4.41984e70	0.352462
$615$	0	0
$616$	2.75612e69	0.0202297
$617$	−8.27703e70	−0.582912	−0.291456	−	0.956584i	$-0.594140\pi$
$617$	−8.27703e70	−0.582912	−0.291456	+	0.956584i	$0.594140\pi$
$618$	0	0
$619$	−1.97805e71	−1.28270	−0.641350	−	0.767248i	$-0.721625\pi$
$619$	−1.97805e71	−1.28270	−0.641350	+	0.767248i	$0.721625\pi$
$620$	7.43588e70	0.462748
$621$	0	0
$622$	−1.25636e70	−0.0720210
$623$	3.42550e69	0.0188486
$624$	0	0
$625$	2.28244e70	0.115734
$626$	−6.76341e70	−0.329246
$627$	0	0
$628$	2.44649e71	1.09792
$629$	−2.08497e71	−0.898480
$630$	0	0
$631$	−1.41814e71	−0.563598	−0.281799	−	0.959473i	$-0.590931\pi$
$631$	−1.41814e71	−0.563598	−0.281799	+	0.959473i	$0.590931\pi$
$632$	−9.00968e70	−0.343893
$633$	0	0
$634$	2.63895e70	0.0929297
$635$	−1.39220e71	−0.470947
$636$	0	0
$637$	1.14026e70	0.0355997
$638$	−5.64159e69	−0.0169229
$639$	0	0
$640$	−1.84394e71	−0.510691
$641$	−3.78805e71	−1.00818	−0.504088	−	0.863652i	$-0.668171\pi$
$641$	−3.78805e71	−1.00818	−0.504088	+	0.863652i	$0.668171\pi$
$642$	0	0
$643$	−2.33505e71	−0.574006	−0.287003	−	0.957930i	$-0.592659\pi$
$643$	−2.33505e71	−0.574006	−0.287003	+	0.957930i	$0.592659\pi$
$644$	3.31683e71	0.783670
$645$	0	0
$646$	−2.85423e71	−0.623103
$647$	2.29082e71	0.480764	0.240382	−	0.970678i	$-0.422727\pi$
$647$	2.29082e71	0.480764	0.240382	+	0.970678i	$0.422727\pi$
$648$	0	0
$649$	1.39298e70	0.0270212
$650$	5.06133e69	0.00944004
$651$	0	0
$652$	3.27494e71	0.564793
$653$	−8.77846e71	−1.45590	−0.727951	−	0.685629i	$-0.759527\pi$
$653$	−8.77846e71	−1.45590	−0.727951	+	0.685629i	$0.759527\pi$
$654$	0	0
$655$	1.06958e71	0.164081
$656$	7.00976e71	1.03432
$657$	0	0
$658$	−6.42573e70	−0.0877329
$659$	−9.01191e71	−1.18369	−0.591846	−	0.806051i	$-0.701601\pi$
$659$	−9.01191e71	−1.18369	−0.591846	+	0.806051i	$0.701601\pi$
$660$	0	0
$661$	5.00776e71	0.608845	0.304422	−	0.952537i	$-0.401537\pi$
$661$	5.00776e71	0.608845	0.304422	+	0.952537i	$0.401537\pi$
$662$	−2.30399e70	−0.0269527
$663$	0	0
$664$	2.78135e71	0.301279
$665$	−5.73514e71	−0.597850
$666$	0	0
$667$	−1.41029e72	−1.36176
$668$	9.71022e71	0.902463
$669$	0	0
$670$	−6.52995e70	−0.0562345
$671$	9.85118e70	0.0816703
$672$	0	0
$673$	−8.23485e71	−0.632807	−0.316404	−	0.948625i	$-0.602475\pi$
$673$	−8.23485e71	−0.632807	−0.316404	+	0.948625i	$0.602475\pi$
$674$	−1.61770e71	−0.119693
$675$	0	0
$676$	1.34936e72	0.925736
$677$	1.48471e71	0.0980916	0.0490458	−	0.998797i	$-0.484382\pi$
$677$	1.48471e71	0.0980916	0.0490458	+	0.998797i	$0.484382\pi$
$678$	0	0
$679$	1.23546e72	0.757094
$680$	6.43104e71	0.379581
$681$	0	0
$682$	−2.91038e70	−0.0159385
$683$	9.71690e71	0.512625	0.256313	−	0.966594i	$-0.417492\pi$
$683$	9.71690e71	0.512625	0.256313	+	0.966594i	$0.417492\pi$
$684$	0	0
$685$	−1.09828e72	−0.537778
$686$	5.41855e71	0.255634
$687$	0	0
$688$	2.03116e72	0.889691
$689$	2.09683e71	0.0885060
$690$	0	0
$691$	1.49847e72	0.587431	0.293715	−	0.955893i	$-0.405108\pi$
$691$	1.49847e72	0.587431	0.293715	+	0.955893i	$0.405108\pi$
$692$	3.67424e72	1.38823
$693$	0	0
$694$	5.72462e71	0.200946
$695$	1.19980e72	0.405974
$696$	0	0
$697$	−5.31724e72	−1.67205
$698$	7.75405e70	0.0235080
$699$	0	0
$700$	−1.25533e72	−0.353800
$701$	4.77735e71	0.129831	0.0649153	−	0.997891i	$-0.479322\pi$
$701$	4.77735e71	0.129831	0.0649153	+	0.997891i	$0.479322\pi$
$702$	0	0
$703$	5.07199e72	1.28179
$704$	−1.67889e71	−0.0409185
$705$	0	0
$706$	7.89117e71	0.178905
$707$	−1.27103e72	−0.277947
$708$	0	0
$709$	3.39807e72	0.691439	0.345719	−	0.938338i	$-0.387635\pi$
$709$	3.39807e72	0.691439	0.345719	+	0.938338i	$0.387635\pi$
$710$	−1.19084e72	−0.233757
$711$	0	0
$712$	9.34416e70	0.0170726
$713$	−7.27539e72	−1.28255
$714$	0	0
$715$	−1.27133e70	−0.00208667
$716$	6.77678e72	1.07335
$717$	0	0
$718$	2.64807e71	0.0390621
$719$	−9.45409e72	−1.34596	−0.672981	−	0.739659i	$-0.734987\pi$
$719$	−9.45409e72	−1.34596	−0.672981	+	0.739659i	$0.734987\pi$
$720$	0	0
$721$	−5.66378e72	−0.751202
$722$	4.85207e72	0.621196
$723$	0	0
$724$	−1.78461e72	−0.212917
$725$	5.33758e72	0.614787
$726$	0	0
$727$	−9.75134e72	−1.04698	−0.523488	−	0.852033i	$-0.675370\pi$
$727$	−9.75134e72	−1.04698	−0.523488	+	0.852033i	$0.675370\pi$
$728$	−1.49683e71	−0.0155175
$729$	0	0
$730$	9.04544e71	0.0874373
$731$	−1.54073e73	−1.43825
$732$	0	0
$733$	−7.22486e72	−0.629040	−0.314520	−	0.949251i	$-0.601843\pi$
$733$	−7.22486e72	−0.629040	−0.314520	+	0.949251i	$0.601843\pi$
$734$	−2.11448e72	−0.177809
$735$	0	0
$736$	1.37397e73	1.07794
$737$	−3.30984e71	−0.0250834
$738$	0	0
$739$	2.75849e72	0.195091	0.0975456	−	0.995231i	$-0.468901\pi$
$739$	2.75849e72	0.195091	0.0975456	+	0.995231i	$0.468901\pi$
$740$	−5.50159e72	−0.375906
$741$	0	0
$742$	4.01584e72	0.256140
$743$	−1.34405e73	−0.828325	−0.414162	−	0.910203i	$-0.635925\pi$
$743$	−1.34405e73	−0.828325	−0.414162	+	0.910203i	$0.635925\pi$
$744$	0	0
$745$	−1.62548e73	−0.935396
$746$	4.82338e71	0.0268232
$747$	0	0
$748$	1.56926e72	0.0815089
$749$	−3.30301e71	−0.0165815
$750$	0	0
$751$	−3.23615e73	−1.51778	−0.758892	−	0.651216i	$-0.774259\pi$
$751$	−3.23615e73	−1.51778	−0.758892	+	0.651216i	$0.774259\pi$
$752$	1.00189e73	0.454219
$753$	0	0
$754$	3.06391e71	0.0129809
$755$	2.95788e72	0.121153
$756$	0	0
$757$	3.58779e73	1.37367	0.686834	−	0.726814i	$-0.259000\pi$
$757$	3.58779e73	1.37367	0.686834	+	0.726814i	$0.259000\pi$
$758$	4.24796e72	0.157259
$759$	0	0
$760$	−1.56444e73	−0.541518
$761$	−3.58257e73	−1.19918	−0.599592	−	0.800306i	$-0.704670\pi$
$761$	−3.58257e73	−1.19918	−0.599592	+	0.800306i	$0.704670\pi$
$762$	0	0
$763$	3.20920e72	0.100466
$764$	1.93244e73	0.585093
$765$	0	0
$766$	−3.84298e72	−0.108851
$767$	−7.56518e71	−0.0207271
$768$	0	0
$769$	5.92781e73	1.51975	0.759876	−	0.650068i	$-0.225259\pi$
$769$	5.92781e73	1.51975	0.759876	+	0.650068i	$0.225259\pi$
$770$	−2.43484e71	−0.00603889
$771$	0	0
$772$	4.41885e72	0.102581
$773$	5.75726e73	1.29312	0.646560	−	0.762863i	$-0.276207\pi$
$773$	5.75726e73	1.29312	0.646560	+	0.762863i	$0.276207\pi$
$774$	0	0
$775$	2.75354e73	0.579026
$776$	3.37011e73	0.685758
$777$	0	0
$778$	−5.04023e72	−0.0960441
$779$	1.29349e74	2.38539
$780$	0	0
$781$	−6.03601e72	−0.104267
$782$	−3.02916e73	−0.506466
$783$	0	0
$784$	−3.40497e73	−0.533400
$785$	−4.48950e73	−0.680803
$786$	0	0
$787$	1.39652e73	0.198469	0.0992344	−	0.995064i	$-0.468361\pi$
$787$	1.39652e73	0.198469	0.0992344	+	0.995064i	$0.468361\pi$
$788$	−4.26098e73	−0.586261
$789$	0	0
$790$	7.95943e72	0.102658
$791$	6.83390e73	0.853431
$792$	0	0
$793$	−5.35011e72	−0.0626465
$794$	1.95548e72	0.0221733
$795$	0	0
$796$	1.02338e74	1.08831
$797$	−9.83821e73	−1.01328	−0.506640	−	0.862158i	$-0.669112\pi$
$797$	−9.83821e73	−1.01328	−0.506640	+	0.862158i	$0.669112\pi$
$798$	0	0
$799$	−7.59982e73	−0.734277
$800$	−5.20012e73	−0.486652
$801$	0	0
$802$	−4.73222e73	−0.415545
$803$	4.58486e72	0.0390014
$804$	0	0
$805$	−6.08664e73	−0.485940
$806$	1.58060e72	0.0122259
$807$	0	0
$808$	−3.46715e73	−0.251758
$809$	2.22779e74	1.56742	0.783712	−	0.621125i	$-0.213324\pi$
$809$	2.22779e74	1.56742	0.783712	+	0.621125i	$0.213324\pi$
$810$	0	0
$811$	−7.69456e73	−0.508338	−0.254169	−	0.967160i	$-0.581802\pi$
$811$	−7.69456e73	−0.508338	−0.254169	+	0.967160i	$0.581802\pi$
$812$	−7.59922e73	−0.486509
$813$	0	0
$814$	2.15330e72	0.0129474
$815$	−6.00977e73	−0.350218
$816$	0	0
$817$	3.74806e74	2.05184
$818$	1.50377e73	0.0797944
$819$	0	0
$820$	−1.40305e74	−0.699554
$821$	−1.32614e74	−0.640971	−0.320486	−	0.947253i	$-0.603846\pi$
$821$	−1.32614e74	−0.640971	−0.320486	+	0.947253i	$0.603846\pi$
$822$	0	0
$823$	1.51804e73	0.0689585	0.0344792	−	0.999405i	$-0.489023\pi$
$823$	1.51804e73	0.0689585	0.0344792	+	0.999405i	$0.489023\pi$
$824$	−1.54498e74	−0.680421
$825$	0	0
$826$	−1.44888e73	−0.0599848
$827$	−3.58794e74	−1.44031	−0.720153	−	0.693815i	$-0.755928\pi$
$827$	−3.58794e74	−1.44031	−0.720153	+	0.693815i	$0.755928\pi$
$828$	0	0
$829$	−1.78233e74	−0.672741	−0.336370	−	0.941730i	$-0.609199\pi$
$829$	−1.78233e74	−0.672741	−0.336370	+	0.941730i	$0.609199\pi$
$830$	−2.45713e73	−0.0899367
$831$	0	0
$832$	9.11793e72	0.0313871
$833$	2.58283e74	0.862281
$834$	0	0
$835$	−1.78190e74	−0.559602
$836$	−3.81746e73	−0.116282
$837$	0	0
$838$	−1.24735e74	−0.357491
$839$	−6.85470e73	−0.190572	−0.0952859	−	0.995450i	$-0.530377\pi$
$839$	−6.85470e73	−0.190572	−0.0952859	+	0.995450i	$0.530377\pi$
$840$	0	0
$841$	−5.90927e73	−0.154609
$842$	5.61361e73	0.142490
$843$	0	0
$844$	−3.21110e74	−0.767224
$845$	−2.47618e74	−0.574033
$846$	0	0
$847$	2.59917e74	0.567294
$848$	−6.26143e74	−1.32611
$849$	0	0
$850$	1.14646e74	0.228652
$851$	5.38284e74	1.04186
$852$	0	0
$853$	2.78536e74	0.507787	0.253893	−	0.967232i	$-0.418289\pi$
$853$	2.78536e74	0.507787	0.253893	+	0.967232i	$0.418289\pi$
$854$	−1.02465e74	−0.181301
$855$	0	0
$856$	−9.01002e72	−0.0150191
$857$	9.69175e74	1.56816	0.784082	−	0.620658i	$-0.213134\pi$
$857$	9.69175e74	1.56816	0.784082	+	0.620658i	$0.213134\pi$
$858$	0	0
$859$	8.61964e74	1.31421	0.657103	−	0.753801i	$-0.271782\pi$
$859$	8.61964e74	1.31421	0.657103	+	0.753801i	$0.271782\pi$
$860$	−4.06552e74	−0.601735
$861$	0	0
$862$	1.18318e74	0.165050
$863$	9.32304e74	1.26265	0.631324	−	0.775519i	$-0.282512\pi$
$863$	9.32304e74	1.26265	0.631324	+	0.775519i	$0.282512\pi$
$864$	0	0
$865$	−6.74252e74	−0.860819
$866$	−7.03392e73	−0.0871949
$867$	0	0
$868$	−3.92028e74	−0.458209
$869$	4.03440e73	0.0457904
$870$	0	0
$871$	1.79755e73	0.0192406
$872$	8.75410e73	0.0910000
$873$	0	0
$874$	7.36888e74	0.722536
$875$	5.74885e74	0.547489
$876$	0	0
$877$	−9.43999e74	−0.848168	−0.424084	−	0.905623i	$-0.639404\pi$
$877$	−9.43999e74	−0.848168	−0.424084	+	0.905623i	$0.639404\pi$
$878$	4.44753e74	0.388158
$879$	0	0
$880$	3.79636e73	0.0312651
$881$	−5.77938e74	−0.462376	−0.231188	−	0.972909i	$-0.574261\pi$
$881$	−5.77938e74	−0.462376	−0.231188	+	0.972909i	$0.574261\pi$
$882$	0	0
$883$	2.23770e75	1.68968	0.844838	−	0.535022i	$-0.179697\pi$
$883$	2.23770e75	1.68968	0.844838	+	0.535022i	$0.179697\pi$
$884$	−8.52256e73	−0.0625227
$885$	0	0
$886$	−4.43987e74	−0.307475
$887$	−8.40500e74	−0.565568	−0.282784	−	0.959184i	$-0.591258\pi$
$887$	−8.40500e74	−0.565568	−0.282784	+	0.959184i	$0.591258\pi$
$888$	0	0
$889$	7.33984e74	0.466328
$890$	−8.25492e72	−0.00509645
$891$	0	0
$892$	−1.84848e75	−1.07773
$893$	1.84876e75	1.04754
$894$	0	0
$895$	−1.24359e75	−0.665566
$896$	9.72147e74	0.505682
$897$	0	0
$898$	−4.30137e74	−0.211378
$899$	1.66687e75	0.796216
$900$	0	0
$901$	4.74960e75	2.14375
$902$	5.49150e73	0.0240948
$903$	0	0
$904$	1.86416e75	0.773017
$905$	3.27491e74	0.132026
$906$	0	0
$907$	−4.85471e75	−1.85002	−0.925012	−	0.379937i	$-0.875946\pi$
$907$	−4.85471e75	−1.85002	−0.925012	+	0.379937i	$0.875946\pi$
$908$	−3.86385e75	−1.43163
$909$	0	0
$910$	1.32234e73	0.00463222
$911$	−1.08836e75	−0.370727	−0.185364	−	0.982670i	$-0.559346\pi$
$911$	−1.08836e75	−0.370727	−0.185364	+	0.982670i	$0.559346\pi$
$912$	0	0
$913$	−1.24545e74	−0.0401162
$914$	−1.42825e75	−0.447379
$915$	0	0
$916$	2.37246e75	0.702853
$917$	−5.63892e74	−0.162472
$918$	0	0
$919$	−1.86949e75	−0.509538	−0.254769	−	0.967002i	$-0.581999\pi$
$919$	−1.86949e75	−0.509538	−0.254769	+	0.967002i	$0.581999\pi$
$920$	−1.66033e75	−0.440153
$921$	0	0
$922$	−4.05860e74	−0.101798
$923$	3.27812e74	0.0799799
$924$	0	0
$925$	−2.03726e75	−0.470363
$926$	1.67424e75	0.376043
$927$	0	0
$928$	−3.14793e75	−0.669193
$929$	−7.68668e75	−1.58978	−0.794892	−	0.606751i	$-0.792473\pi$
$929$	−7.68668e75	−1.58978	−0.794892	+	0.606751i	$0.792473\pi$
$930$	0	0
$931$	−6.28311e75	−1.23015
$932$	−3.67125e75	−0.699372
$933$	0	0
$934$	5.41778e74	0.0977184
$935$	−2.87972e74	−0.0505423
$936$	0	0
$937$	5.84868e74	0.0972071	0.0486036	−	0.998818i	$-0.484523\pi$
$937$	5.84868e74	0.0972071	0.0486036	+	0.998818i	$0.484523\pi$
$938$	3.44266e74	0.0556829
$939$	0	0
$940$	−2.00536e75	−0.307207
$941$	−2.81919e75	−0.420328	−0.210164	−	0.977666i	$-0.567400\pi$
$941$	−2.81919e75	−0.420328	−0.210164	+	0.977666i	$0.567400\pi$
$942$	0	0
$943$	1.37277e76	1.93888
$944$	2.25907e75	0.310559
$945$	0	0
$946$	1.59123e74	0.0207257
$947$	6.56754e75	0.832680	0.416340	−	0.909209i	$-0.363313\pi$
$947$	6.56754e75	0.832680	0.416340	+	0.909209i	$0.363313\pi$
$948$	0	0
$949$	−2.49001e74	−0.0299166
$950$	−2.78892e75	−0.326201
$951$	0	0
$952$	−3.39051e75	−0.375858
$953$	−4.31977e74	−0.0466221	−0.0233110	−	0.999728i	$-0.507421\pi$
$953$	−4.31977e74	−0.0466221	−0.0233110	+	0.999728i	$0.507421\pi$
$954$	0	0
$955$	−3.54618e75	−0.362806
$956$	1.56106e76	1.55504
$957$	0	0
$958$	−2.21912e75	−0.209585
$959$	5.79024e75	0.532503
$960$	0	0
$961$	−2.86786e75	−0.250099
$962$	−1.16944e74	−0.00993149
$963$	0	0
$964$	5.59867e75	0.450942
$965$	−8.10894e74	−0.0636089
$966$	0	0
$967$	1.78694e76	1.32964	0.664820	−	0.747004i	$-0.268508\pi$
$967$	1.78694e76	1.32964	0.664820	+	0.747004i	$0.268508\pi$
$968$	7.09007e75	0.513842
$969$	0	0
$970$	−2.97727e75	−0.204710
$971$	−1.48969e76	−0.997715	−0.498857	−	0.866684i	$-0.666247\pi$
$971$	−1.48969e76	−0.997715	−0.498857	+	0.866684i	$0.666247\pi$
$972$	0	0
$973$	−6.32550e75	−0.401992
$974$	−5.07000e75	−0.313873
$975$	0	0
$976$	1.59762e76	0.938649
$977$	−3.67383e75	−0.210285	−0.105142	−	0.994457i	$-0.533530\pi$
$977$	−3.67383e75	−0.210285	−0.105142	+	0.994457i	$0.533530\pi$
$978$	0	0
$979$	−4.18417e73	−0.00227327
$980$	6.81529e75	0.360761
$981$	0	0
$982$	−1.79547e75	−0.0902265
$983$	2.53462e76	1.24108	0.620538	−	0.784176i	$-0.286914\pi$
$983$	2.53462e76	1.24108	0.620538	+	0.784176i	$0.286914\pi$
$984$	0	0
$985$	7.81924e75	0.363530
$986$	6.94016e75	0.314419
$987$	0	0
$988$	2.07324e75	0.0891962
$989$	3.97777e76	1.66776
$990$	0	0
$991$	−1.78337e76	−0.710173	−0.355086	−	0.934834i	$-0.615549\pi$
$991$	−1.78337e76	−0.710173	−0.355086	+	0.934834i	$0.615549\pi$
$992$	−1.62395e76	−0.630267
$993$	0	0
$994$	6.27824e75	0.231465
$995$	−1.87799e76	−0.674845
$996$	0	0
$997$	−6.38902e75	−0.218126	−0.109063	−	0.994035i	$-0.534785\pi$
$997$	−6.38902e75	−0.218126	−0.109063	+	0.994035i	$0.534785\pi$
$998$	4.54757e75	0.151339
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	9.52.a.b.1.3		4
3.2	odd	2		1.52.a.a.1.2	✓	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1.52.a.a.1.2	✓	4	3.2	odd	2
9.52.a.b.1.3		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)

\(f(q)\)	\(=\)	\(q+1.27049e7 q^{2} -2.09038e15 q^{4} +3.83602e17 q^{5} -2.02239e21 q^{7} -5.51672e22 q^{8} +O(q^{10})\)	\(q+1.27049e7 q^{2} -2.09038e15 q^{4} +3.83602e17 q^{5} -2.02239e21 q^{7} -5.51672e22 q^{8} +4.87365e24 q^{10} +2.47031e25 q^{11} -1.34161e27 q^{13} -2.56944e28 q^{14} +4.00623e30 q^{16} -3.03892e31 q^{17} +7.39260e32 q^{19} -8.01876e32 q^{20} +3.13851e32 q^{22} +7.84569e34 q^{23} -2.96939e35 q^{25} -1.70450e34 q^{26} +4.22758e36 q^{28} -1.79754e37 q^{29} -9.27311e37 q^{31} +1.75124e38 q^{32} -3.86093e38 q^{34} -7.75794e38 q^{35} +6.86089e39 q^{37} +9.39226e39 q^{38} -2.11623e40 q^{40} +1.74971e41 q^{41} +5.07001e41 q^{43} -5.16389e40 q^{44} +9.96791e41 q^{46} +2.50083e42 q^{47} -8.49918e42 q^{49} -3.77259e42 q^{50} +2.80447e42 q^{52} -1.56292e44 q^{53} +9.47615e42 q^{55} +1.11570e44 q^{56} -2.28376e44 q^{58} +5.63890e44 q^{59} +3.98784e45 q^{61} -1.17814e45 q^{62} -6.79628e45 q^{64} -5.14643e44 q^{65} -1.33985e46 q^{67} +6.35251e46 q^{68} -9.85643e45 q^{70} -2.44343e47 q^{71} +1.85599e47 q^{73} +8.71673e46 q^{74} -1.54534e48 q^{76} -4.99593e46 q^{77} +1.63316e48 q^{79} +1.53680e48 q^{80} +2.22300e48 q^{82} -5.04167e48 q^{83} -1.16574e49 q^{85} +6.44142e48 q^{86} -1.36280e48 q^{88} -1.69379e48 q^{89} +2.71326e48 q^{91} -1.64005e50 q^{92} +3.17729e49 q^{94} +2.83582e50 q^{95} -6.10891e50 q^{97} -1.07982e50 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 32756040 q^{2} + 79\!\cdots\!12 q^{4}+ \cdots + 13\!\cdots\!20 q^{8}+O(q^{10}) \) 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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