LMFDB - Embedded newform 9.48.a.c.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [9,48,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, 48, names="a")

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

chi := DirichletCharacter("9.1");

S:= CuspForms(chi, 48);

N := Newforms(S);

Level:	$ N $	$=$	$ 9 = 3^{2} $
Weight:	$ k $	$=$	$ 48 $
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:	$125.916896390$
Analytic rank:	$1$
Dimension:	$4$
Coefficient field:	$\mathbb{Q}[x]/(x^{4} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 832803191366x^{2} + 3710135215485780x + 13175318942671469337000 $ x^4 - x^3 - 832803191366x^2 + 3710135215485780x + 13175318942671469337000
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{20}\cdot 3^{11}\cdot 5^{3}\cdot 7^{2} $
Twist minimal:	no (minimal twist has level 1)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$-906006.$ of defining polynomial
Character	$\chi$	$=$	9.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.02978e7 q^{2} +2.71261e14 q^{4} +3.11682e16 q^{5} -1.26592e20 q^{7} +2.64934e21 q^{8} +O(q^{10})$	\(q+2.02978e7 q^{2} +2.71261e14 q^{4} +3.11682e16 q^{5} -1.26592e20 q^{7} +2.64934e21 q^{8} +6.32644e23 q^{10} +1.78518e23 q^{11} -1.12359e26 q^{13} -2.56953e27 q^{14} +1.55990e28 q^{16} -4.31126e28 q^{17} -7.19841e29 q^{19} +8.45472e30 q^{20} +3.62352e30 q^{22} -8.88061e30 q^{23} +2.60913e32 q^{25} -2.28064e33 q^{26} -3.43395e34 q^{28} -2.84937e34 q^{29} +1.11855e35 q^{31} -5.62362e34 q^{32} -8.75090e35 q^{34} -3.94564e36 q^{35} -9.87647e36 q^{37} -1.46112e37 q^{38} +8.25752e37 q^{40} +3.56038e37 q^{41} -3.37056e38 q^{43} +4.84250e37 q^{44} -1.80256e38 q^{46} +1.22952e39 q^{47} +1.07822e40 q^{49} +5.29595e39 q^{50} -3.04787e40 q^{52} +1.08443e39 q^{53} +5.56408e39 q^{55} -3.35385e41 q^{56} -5.78358e41 q^{58} +1.45567e40 q^{59} +4.79341e41 q^{61} +2.27041e42 q^{62} -3.33684e42 q^{64} -3.50203e42 q^{65} +3.35317e42 q^{67} -1.16948e43 q^{68} -8.00876e43 q^{70} -9.20990e42 q^{71} -5.22911e43 q^{73} -2.00470e44 q^{74} -1.95265e44 q^{76} -2.25989e43 q^{77} -7.68215e43 q^{79} +4.86194e44 q^{80} +7.22677e44 q^{82} +1.71031e45 q^{83} -1.34374e45 q^{85} -6.84147e45 q^{86} +4.72955e44 q^{88} +9.70124e45 q^{89} +1.42238e46 q^{91} -2.40897e45 q^{92} +2.49565e46 q^{94} -2.24361e46 q^{95} +5.35657e46 q^{97} +2.18854e47 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 5785560 q^{2} + 404807499161152 q^{4} + 31\!\cdots\!00 q^{5}+ \cdots - 23\!\cdots\!20 q^{8}+O(q^{10}) $ 4 * q - 5785560 * q^2 + 404807499161152 * q^4 + 31114680242272200 * q^5 - 39169218725888423200 * q^7 - 2392716988073784337920 * q^8	$ 4 q - 5785560 q^{2} + 404807499161152 q^{4} + 31\!\cdots\!00 q^{5}+ \cdots + 29\!\cdots\!20 q^{98}+O(q^{100}) $ 4 * q - 5785560 * q^2 + 404807499161152 * q^4 + 31114680242272200 * q^5 - 39169218725888423200 * q^7 - 2392716988073784337920 * q^8 + 161126302562215963534800 * q^10 + 1902165515717740404742512 * q^11 + 126959149195199610466858520 * q^13 - 3491363489769461659480835904 * q^14 + 124527684040554167211817897984 * q^16 - 210426285758836687099688769480 * q^17 - 1059119811802437301721159140240 * q^19 + 15129514318106701401937782249600 * q^20 - 79668451994083088127806382590880 * q^22 - 137531418344493639994288859179680 * q^23 + 1009909900344396506188154274977500 * q^25 - 2282338781897562472343866220387088 * q^26 - 36222097928665071743339635065479680 * q^28 + 22743132490172744184500850941726760 * q^29 + 75786540814706434901630981303934848 * q^31 - 1184674767018086471839527432906178560 * q^32 - 1261659118578465318749852382715620816 * q^34 + 1313148822925052387484546800067979200 * q^35 - 11291457045120157869429951769632191560 * q^37 - 29667542464851305273548614410680536480 * q^38 + 70753686685508718175919216681780352000 * q^40 - 130658126291089294119301677048020391528 * q^41 - 445357287738427943170332944488133090800 * q^43 + 1525898906718917337200010663037616115456 * q^44 + 1226146172325422687186041586267533291968 * q^46 - 2031912465958423919194866366997063590720 * q^47 + 9153745744156628626499502447643951451172 * q^49 + 19226200465513908889722489088356697935000 * q^50 - 55272350705889116147839999778699925596800 * q^52 - 29171719896619533806321793123448457437560 * q^53 + 192172580604633896452606078657416872901600 * q^55 - 276101696826518177934513744689489393111040 * q^56 - 732323136683092912071778597620095648941680 * q^58 - 478242858216320686410790860443879577596880 * q^59 + 626683213833907852009669690320782900857688 * q^61 + 6870459615610782098804391369236375065946880 * q^62 + 5525430481808418303700543890989262651523072 * q^64 - 12996735432890074297558542478104126872331600 * q^65 + 18701411419127220668869505853739529194216880 * q^67 + 27469024204738931095482995064729717598496640 * q^68 - 97207317904230285933067401805385458355395200 * q^70 - 22196594617762006008028198712153461686540768 * q^71 + 104911201720506650033573412943840886878191080 * q^73 - 187734656069700274526204928907842421165646544 * q^74 + 351694386032713991264839561028061045130100480 * q^76 + 263490744376507692433815778071300370399209600 * q^77 - 1327995310109394234162785254414226288730352960 * q^79 + 948349663264469859337474495994045561022259200 * q^80 + 3821513842864797430908620724480935919685390320 * q^82 + 1439130627532364606968733068855111784504073360 * q^83 - 1001895286410663502447652611446390227458237200 * q^85 - 9578145533777866709022895861637903827077656928 * q^86 - 15478856320702836436797993507832298416714229760 * q^88 + 7960590522674945421108320896849737731421281880 * q^89 + 5325194479227227497182497798631911205603381568 * q^91 - 13058297350229360275908546071900174502239009280 * q^92 + 3475860200879106349192555645858186353201354624 * q^94 - 75421152415106939771624998522249518123547668000 * q^95 + 95066248961258904822565865801364599382905757320 * q^97 + 296344663186266398350742083591017164797938217320 * q^98

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	2.02978e7	1.71097	0.855486	−	0.517825i	$-0.173258\pi$
$2$	2.02978e7	1.71097	0.855486	+	0.517825i	$0.173258\pi$
$3$	0	0
$3$	0	0
$4$	2.71261e14	1.92743
$5$	3.11682e16	1.16927	0.584637	−	0.811295i	$-0.301237\pi$
$5$	3.11682e16	1.16927	0.584637	+	0.811295i	$0.301237\pi$
$6$	0	0
$7$	−1.26592e20	−1.74824	−0.874122	−	0.485707i	$-0.838562\pi$
$7$	−1.26592e20	−1.74824	−0.874122	+	0.485707i	$0.838562\pi$
$8$	2.64934e21	1.58680
$9$	0	0
$10$	6.32644e23	2.00060
$11$	1.78518e23	0.0601110	0.0300555	−	0.999548i	$-0.490432\pi$
$11$	1.78518e23	0.0601110	0.0300555	+	0.999548i	$0.490432\pi$
$12$	0	0
$13$	−1.12359e26	−0.746346	−0.373173	−	0.927762i	$-0.621730\pi$
$13$	−1.12359e26	−0.746346	−0.373173	+	0.927762i	$0.621730\pi$
$14$	−2.56953e27	−2.99120
$15$	0	0
$16$	1.55990e28	0.787550
$17$	−4.31126e28	−0.523667	−0.261833	−	0.965113i	$-0.584327\pi$
$17$	−4.31126e28	−0.523667	−0.261833	+	0.965113i	$0.584327\pi$
$18$	0	0
$19$	−7.19841e29	−0.640511	−0.320256	−	0.947331i	$-0.603769\pi$
$19$	−7.19841e29	−0.640511	−0.320256	+	0.947331i	$0.603769\pi$
$20$	8.45472e30	2.25369
$21$	0	0
$22$	3.62352e30	0.102848
$23$	−8.88061e30	−0.0886826	−0.0443413	−	0.999016i	$-0.514119\pi$
$23$	−8.88061e30	−0.0886826	−0.0443413	+	0.999016i	$0.514119\pi$
$24$	0	0
$25$	2.60913e32	0.367202
$26$	−2.28064e33	−1.27698
$27$	0	0
$28$	−3.43395e34	−3.36961
$29$	−2.84937e34	−1.22573	−0.612866	−	0.790187i	$-0.709983\pi$
$29$	−2.84937e34	−1.22573	−0.612866	+	0.790187i	$0.709983\pi$
$30$	0	0
$31$	1.11855e35	1.00382	0.501911	−	0.864919i	$-0.332630\pi$
$31$	1.11855e35	1.00382	0.501911	+	0.864919i	$0.332630\pi$
$32$	−5.62362e34	−0.239327
$33$	0	0
$34$	−8.75090e35	−0.895980
$35$	−3.94564e36	−2.04418
$36$	0	0
$37$	−9.87647e36	−1.38631	−0.693156	−	0.720787i	$-0.743780\pi$
$37$	−9.87647e36	−1.38631	−0.693156	+	0.720787i	$0.743780\pi$
$38$	−1.46112e37	−1.09590
$39$	0	0
$40$	8.25752e37	1.85541
$41$	3.56038e37	0.447791	0.223896	−	0.974613i	$-0.428123\pi$
$41$	3.56038e37	0.447791	0.223896	+	0.974613i	$0.428123\pi$
$42$	0	0
$43$	−3.37056e38	−1.38418	−0.692091	−	0.721811i	$-0.743310\pi$
$43$	−3.37056e38	−1.38418	−0.692091	+	0.721811i	$0.743310\pi$
$44$	4.84250e37	0.115860
$45$	0	0
$46$	−1.80256e38	−0.151734
$47$	1.22952e39	0.624361	0.312181	−	0.950023i	$-0.398941\pi$
$47$	1.22952e39	0.624361	0.312181	+	0.950023i	$0.398941\pi$
$48$	0	0
$49$	1.07822e40	2.05635
$50$	5.29595e39	0.628273
$51$	0	0
$52$	−3.04787e40	−1.43853
$53$	1.08443e39	0.0327129	0.0163565	−	0.999866i	$-0.494793\pi$
$53$	1.08443e39	0.0327129	0.0163565	+	0.999866i	$0.494793\pi$
$54$	0	0
$55$	5.56408e39	0.0702863
$56$	−3.35385e41	−2.77412
$57$	0	0
$58$	−5.78358e41	−2.09719
$59$	1.45567e40	0.0353216	0.0176608	−	0.999844i	$-0.494378\pi$
$59$	1.45567e40	0.0353216	0.0176608	+	0.999844i	$0.494378\pi$
$60$	0	0
$61$	4.79341e41	0.531366	0.265683	−	0.964060i	$-0.414403\pi$
$61$	4.79341e41	0.531366	0.265683	+	0.964060i	$0.414403\pi$
$62$	2.27041e42	1.71751
$63$	0	0
$64$	−3.33684e42	−1.19703
$65$	−3.50203e42	−0.872683
$66$	0	0
$67$	3.35317e42	0.409919	0.204959	−	0.978770i	$-0.434294\pi$
$67$	3.35317e42	0.409919	0.204959	+	0.978770i	$0.434294\pi$
$68$	−1.16948e43	−1.00933
$69$	0	0
$70$	−8.00876e43	−3.49753
$71$	−9.20990e42	−0.288193	−0.144097	−	0.989564i	$-0.546028\pi$
$71$	−9.20990e42	−0.288193	−0.144097	+	0.989564i	$0.546028\pi$
$72$	0	0
$73$	−5.22911e43	−0.851805	−0.425903	−	0.904769i	$-0.640043\pi$
$73$	−5.22911e43	−0.851805	−0.425903	+	0.904769i	$0.640043\pi$
$74$	−2.00470e44	−2.37194
$75$	0	0
$76$	−1.95265e44	−1.23454
$77$	−2.25989e43	−0.105089
$78$	0	0
$79$	−7.68215e43	−0.195545	−0.0977724	−	0.995209i	$-0.531172\pi$
$79$	−7.68215e43	−0.195545	−0.0977724	+	0.995209i	$0.531172\pi$
$80$	4.86194e44	0.920862
$81$	0	0
$82$	7.22677e44	0.766158
$83$	1.71031e45	1.36377	0.681884	−	0.731460i	$-0.261161\pi$
$83$	1.71031e45	1.36377	0.681884	+	0.731460i	$0.261161\pi$
$84$	0	0
$85$	−1.34374e45	−0.612310
$86$	−6.84147e45	−2.36830
$87$	0	0
$88$	4.72955e44	0.0953844
$89$	9.70124e45	1.50024	0.750122	−	0.661299i	$-0.229995\pi$
$89$	9.70124e45	1.50024	0.750122	+	0.661299i	$0.229995\pi$
$90$	0	0
$91$	1.42238e46	1.30479
$92$	−2.40897e45	−0.170929
$93$	0	0
$94$	2.49565e46	1.06827
$95$	−2.24361e46	−0.748933
$96$	0	0
$97$	5.35657e46	1.09585	0.547925	−	0.836528i	$-0.315418\pi$
$97$	5.35657e46	1.09585	0.547925	+	0.836528i	$0.315418\pi$
$98$	2.18854e47	3.51837
$99$	0	0
$100$	7.07756e46	0.707756
$101$	−1.46056e47	−1.15602	−0.578011	−	0.816029i	$-0.696171\pi$
$101$	−1.46056e47	−1.15602	−0.578011	+	0.816029i	$0.696171\pi$
$102$	0	0
$103$	−3.94670e47	−1.97042	−0.985212	−	0.171342i	$-0.945190\pi$
$103$	−3.94670e47	−1.97042	−0.985212	+	0.171342i	$0.945190\pi$
$104$	−2.97678e47	−1.18430
$105$	0	0
$106$	2.20115e46	0.0559709
$107$	−5.84600e47	−1.19218	−0.596088	−	0.802919i	$-0.703279\pi$
$107$	−5.84600e47	−1.19218	−0.596088	+	0.802919i	$0.703279\pi$
$108$	0	0
$109$	−7.05835e47	−0.931494	−0.465747	−	0.884918i	$-0.654214\pi$
$109$	−7.05835e47	−0.931494	−0.465747	+	0.884918i	$0.654214\pi$
$110$	1.12938e47	0.120258
$111$	0	0
$112$	−1.97471e48	−1.37683
$113$	6.63621e47	0.375471	0.187736	−	0.982220i	$-0.439885\pi$
$113$	6.63621e47	0.375471	0.187736	+	0.982220i	$0.439885\pi$
$114$	0	0
$115$	−2.76792e47	−0.103694
$116$	−7.72923e48	−2.36251
$117$	0	0
$118$	2.95468e47	0.0604342
$119$	5.45771e48	0.915497
$120$	0	0
$121$	−8.78788e48	−0.996387
$122$	9.72955e48	0.909152
$123$	0	0
$124$	3.03420e49	1.93479
$125$	−1.40141e49	−0.739914
$126$	0	0
$127$	1.84983e49	0.672580	0.336290	−	0.941758i	$-0.390828\pi$
$127$	1.84983e49	0.672580	0.336290	+	0.941758i	$0.390828\pi$
$128$	−5.98158e49	−1.80876
$129$	0	0
$130$	−7.10834e49	−1.49314
$131$	−3.62008e49	−0.635100	−0.317550	−	0.948242i	$-0.602860\pi$
$131$	−3.62008e49	−0.635100	−0.317550	+	0.948242i	$0.602860\pi$
$132$	0	0
$133$	9.11260e49	1.11977
$134$	6.80618e49	0.701360
$135$	0	0
$136$	−1.14220e50	−0.830956
$137$	2.09650e50	1.28399	0.641994	−	0.766709i	$-0.278107\pi$
$137$	2.09650e50	1.28399	0.641994	+	0.766709i	$0.278107\pi$
$138$	0	0
$139$	−1.18819e50	−0.517653	−0.258826	−	0.965924i	$-0.583336\pi$
$139$	−1.18819e50	−0.517653	−0.258826	+	0.965924i	$0.583336\pi$
$140$	−1.07030e51	−3.94000
$141$	0	0
$142$	−1.86940e50	−0.493091
$143$	−2.00582e49	−0.0448636
$144$	0	0
$145$	−8.88096e50	−1.43322
$146$	−1.06139e51	−1.45742
$147$	0	0
$148$	−2.67910e51	−2.67202
$149$	−1.81480e51	−1.54508	−0.772540	−	0.634966i	$-0.781014\pi$
$149$	−1.81480e51	−1.54508	−0.772540	+	0.634966i	$0.781014\pi$
$150$	0	0
$151$	1.57042e51	0.977366	0.488683	−	0.872461i	$-0.337477\pi$
$151$	1.57042e51	0.977366	0.488683	+	0.872461i	$0.337477\pi$
$152$	−1.90710e51	−1.01637
$153$	0	0
$154$	−4.58708e50	−0.179804
$155$	3.48633e51	1.17374
$156$	0	0
$157$	3.70380e51	0.922584	0.461292	−	0.887248i	$-0.347386\pi$
$157$	3.70380e51	0.922584	0.461292	+	0.887248i	$0.347386\pi$
$158$	−1.55930e51	−0.334572
$159$	0	0
$160$	−1.75278e51	−0.279839
$161$	1.12421e51	0.155039
$162$	0	0
$163$	4.02579e51	0.415377	0.207688	−	0.978195i	$-0.433406\pi$
$163$	4.02579e51	0.415377	0.207688	+	0.978195i	$0.433406\pi$
$164$	9.65793e51	0.863085
$165$	0	0
$166$	3.47155e52	2.33337
$167$	−1.17072e52	−0.683308	−0.341654	−	0.939826i	$-0.610987\pi$
$167$	−1.17072e52	−0.683308	−0.341654	+	0.939826i	$0.610987\pi$
$168$	0	0
$169$	−1.00394e52	−0.442968
$170$	−2.72750e52	−1.04765
$171$	0	0
$172$	−9.14302e52	−2.66791
$173$	2.17798e52	0.554587	0.277293	−	0.960785i	$-0.410563\pi$
$173$	2.17798e52	0.554587	0.277293	+	0.960785i	$0.410563\pi$
$174$	0	0
$175$	−3.30295e52	−0.641959
$176$	2.78471e51	0.0473404
$177$	0	0
$178$	1.96913e53	2.56688
$179$	9.95625e52	1.13776	0.568879	−	0.822421i	$-0.307377\pi$
$179$	9.95625e52	1.13776	0.568879	+	0.822421i	$0.307377\pi$
$180$	0	0
$181$	−6.46484e52	−0.568998	−0.284499	−	0.958676i	$-0.591827\pi$
$181$	−6.46484e52	−0.568998	−0.284499	+	0.958676i	$0.591827\pi$
$182$	2.88711e53	2.23247
$183$	0	0
$184$	−2.35278e52	−0.140722
$185$	−3.07832e53	−1.62098
$186$	0	0
$187$	−7.69638e51	−0.0314781
$188$	3.33521e53	1.20341
$189$	0	0
$190$	−4.55403e53	−1.28140
$191$	−7.79937e53	−1.93988	−0.969942	−	0.243337i	$-0.921758\pi$
$191$	−7.79937e53	−1.93988	−0.969942	+	0.243337i	$0.921758\pi$
$192$	0	0
$193$	6.70136e52	0.130487	0.0652433	−	0.997869i	$-0.479218\pi$
$193$	6.70136e52	0.130487	0.0652433	+	0.997869i	$0.479218\pi$
$194$	1.08726e54	1.87497
$195$	0	0
$196$	2.92478e54	3.96348
$197$	1.22925e54	1.47804	0.739019	−	0.673685i	$-0.235289\pi$
$197$	1.22925e54	1.47804	0.739019	+	0.673685i	$0.235289\pi$
$198$	0	0
$199$	1.40028e54	1.32790	0.663952	−	0.747775i	$-0.268878\pi$
$199$	1.40028e54	1.32790	0.663952	+	0.747775i	$0.268878\pi$
$200$	6.91248e53	0.582678
$201$	0	0
$202$	−2.96460e54	−1.97792
$203$	3.60707e54	2.14288
$204$	0	0
$205$	1.10971e54	0.523591
$206$	−8.01092e54	−3.37134
$207$	0	0
$208$	−1.75270e54	−0.587785
$209$	−1.28505e53	−0.0385018
$210$	0	0
$211$	7.49292e53	0.179479	0.0897394	−	0.995965i	$-0.471397\pi$
$211$	7.49292e53	0.179479	0.0897394	+	0.995965i	$0.471397\pi$
$212$	2.94164e53	0.0630518
$213$	0	0
$214$	−1.18661e55	−2.03978
$215$	−1.05054e55	−1.61849
$216$	0	0
$217$	−1.41600e55	−1.75493
$218$	−1.43269e55	−1.59376
$219$	0	0
$220$	1.50932e54	0.135472
$221$	4.84410e54	0.390836
$222$	0	0
$223$	7.65012e54	0.499464	0.249732	−	0.968315i	$-0.419658\pi$
$223$	7.65012e54	0.499464	0.249732	+	0.968315i	$0.419658\pi$
$224$	7.11905e54	0.418402
$225$	0	0
$226$	1.34700e55	0.642421
$227$	−1.58232e55	−0.680277	−0.340138	−	0.940375i	$-0.610474\pi$
$227$	−1.58232e55	−0.680277	−0.340138	+	0.940375i	$0.610474\pi$
$228$	0	0
$229$	2.86045e55	1.00069	0.500347	−	0.865825i	$-0.333206\pi$
$229$	2.86045e55	1.00069	0.500347	+	0.865825i	$0.333206\pi$
$230$	−5.61827e54	−0.177418
$231$	0	0
$232$	−7.54894e55	−1.94500
$233$	3.61119e55	0.840980	0.420490	−	0.907297i	$-0.361858\pi$
$233$	3.61119e55	0.840980	0.420490	+	0.907297i	$0.361858\pi$
$234$	0	0
$235$	3.83219e55	0.730050
$236$	3.94866e54	0.0680798
$237$	0	0
$238$	1.10779e56	1.56639
$239$	−5.47124e55	−0.701027	−0.350514	−	0.936558i	$-0.613993\pi$
$239$	−5.47124e55	−0.701027	−0.350514	+	0.936558i	$0.613993\pi$
$240$	0	0
$241$	−8.92529e55	−0.940204	−0.470102	−	0.882612i	$-0.655783\pi$
$241$	−8.92529e55	−0.940204	−0.470102	+	0.882612i	$0.655783\pi$
$242$	−1.78374e56	−1.70479
$243$	0	0
$244$	1.30027e56	1.02417
$245$	3.36060e56	2.40444
$246$	0	0
$247$	8.08808e55	0.478043
$248$	2.96343e56	1.59287
$249$	0	0
$250$	−2.84456e56	−1.26597
$251$	−1.98048e56	−0.802487	−0.401244	−	0.915971i	$-0.631422\pi$
$251$	−1.98048e56	−0.802487	−0.401244	+	0.915971i	$0.631422\pi$
$252$	0	0
$253$	−1.58535e54	−0.00533080
$254$	3.75474e56	1.15077
$255$	0	0
$256$	−7.44508e56	−1.89771
$257$	1.71029e55	0.0397778	0.0198889	−	0.999802i	$-0.493669\pi$
$257$	1.71029e55	0.0397778	0.0198889	+	0.999802i	$0.493669\pi$
$258$	0	0
$259$	1.25028e57	2.42361
$260$	−9.49967e56	−1.68203
$261$	0	0
$262$	−7.34794e56	−1.08664
$263$	−3.32579e56	−0.449712	−0.224856	−	0.974392i	$-0.572191\pi$
$263$	−3.32579e56	−0.449712	−0.224856	+	0.974392i	$0.572191\pi$
$264$	0	0
$265$	3.37998e55	0.0382504
$266$	1.84965e57	1.91590
$267$	0	0
$268$	9.09585e56	0.790088
$269$	1.74613e57	1.38963	0.694815	−	0.719189i	$-0.255486\pi$
$269$	1.74613e57	1.38963	0.694815	+	0.719189i	$0.255486\pi$
$270$	0	0
$271$	1.96258e56	0.131235	0.0656174	−	0.997845i	$-0.479098\pi$
$271$	1.96258e56	0.131235	0.0656174	+	0.997845i	$0.479098\pi$
$272$	−6.72516e56	−0.412414
$273$	0	0
$274$	4.25542e57	2.19687
$275$	4.65777e55	0.0220729
$276$	0	0
$277$	1.40234e57	0.560503	0.280252	−	0.959927i	$-0.409582\pi$
$277$	1.40234e57	0.560503	0.280252	+	0.959927i	$0.409582\pi$
$278$	−2.41176e57	−0.885690
$279$	0	0
$280$	−1.04533e58	−3.24371
$281$	3.15409e57	0.900068	0.450034	−	0.893011i	$-0.351412\pi$
$281$	3.15409e57	0.900068	0.450034	+	0.893011i	$0.351412\pi$
$282$	0	0
$283$	6.43417e57	1.55422	0.777108	−	0.629368i	$-0.216686\pi$
$283$	6.43417e57	1.55422	0.777108	+	0.629368i	$0.216686\pi$
$284$	−2.49829e57	−0.555472
$285$	0	0
$286$	−4.07136e56	−0.0767604
$287$	−4.50715e57	−0.782848
$288$	0	0
$289$	−4.91926e57	−0.725773
$290$	−1.80264e58	−2.45219
$291$	0	0
$292$	−1.41845e58	−1.64179
$293$	7.47274e57	0.798162	0.399081	−	0.916916i	$-0.369329\pi$
$293$	7.47274e57	0.798162	0.399081	+	0.916916i	$0.369329\pi$
$294$	0	0
$295$	4.53705e56	0.0413006
$296$	−2.61661e58	−2.19981
$297$	0	0
$298$	−3.68363e58	−2.64359
$299$	9.97819e56	0.0661879
$300$	0	0
$301$	4.26685e58	2.41989
$302$	3.18760e58	1.67225
$303$	0	0
$304$	−1.12288e58	−0.504435
$305$	1.49402e58	0.621312
$306$	0	0
$307$	−2.04451e58	−0.729183	−0.364592	−	0.931168i	$-0.618791\pi$
$307$	−2.04451e58	−0.729183	−0.364592	+	0.931168i	$0.618791\pi$
$308$	−6.13022e57	−0.202551
$309$	0	0
$310$	7.07646e58	2.00824
$311$	−3.46247e58	−0.910997	−0.455499	−	0.890236i	$-0.650539\pi$
$311$	−3.46247e58	−0.910997	−0.455499	+	0.890236i	$0.650539\pi$
$312$	0	0
$313$	7.50527e58	1.69853	0.849267	−	0.527963i	$-0.177044\pi$
$313$	7.50527e58	1.69853	0.849267	+	0.527963i	$0.177044\pi$
$314$	7.51789e58	1.57852
$315$	0	0
$316$	−2.08387e58	−0.376898
$317$	9.59709e58	1.61156	0.805781	−	0.592213i	$-0.201746\pi$
$317$	9.59709e58	1.61156	0.805781	+	0.592213i	$0.201746\pi$
$318$	0	0
$319$	−5.08663e57	−0.0736800
$320$	−1.04003e59	−1.39966
$321$	0	0
$322$	2.28190e58	0.265267
$323$	3.10342e58	0.335414
$324$	0	0
$325$	−2.93160e58	−0.274060
$326$	8.17144e58	0.710698
$327$	0	0
$328$	9.43265e58	0.710556
$329$	−1.55647e59	−1.09154
$330$	0	0
$331$	−9.45783e58	−0.575219	−0.287610	−	0.957748i	$-0.592861\pi$
$331$	−9.45783e58	−0.575219	−0.287610	+	0.957748i	$0.592861\pi$
$332$	4.63942e59	2.62856
$333$	0	0
$334$	−2.37630e59	−1.16912
$335$	1.04512e59	0.479307
$336$	0	0
$337$	4.62637e59	1.84475	0.922375	−	0.386295i	$-0.126245\pi$
$337$	4.62637e59	1.84475	0.922375	+	0.386295i	$0.126245\pi$
$338$	−2.03778e59	−0.757906
$339$	0	0
$340$	−3.64505e59	−1.18018
$341$	1.99682e58	0.0603408
$342$	0	0
$343$	−7.01170e59	−1.84677
$344$	−8.92975e59	−2.19642
$345$	0	0
$346$	4.42080e59	0.948883
$347$	−4.68114e59	−0.938878	−0.469439	−	0.882965i	$-0.655544\pi$
$347$	−4.68114e59	−0.938878	−0.469439	+	0.882965i	$0.655544\pi$
$348$	0	0
$349$	−1.32904e59	−0.232884	−0.116442	−	0.993197i	$-0.537149\pi$
$349$	−1.32904e59	−0.232884	−0.116442	+	0.993197i	$0.537149\pi$
$350$	−6.70424e59	−1.09837
$351$	0	0
$352$	−1.00392e58	−0.0143862
$353$	7.06798e59	0.947523	0.473762	−	0.880653i	$-0.342896\pi$
$353$	7.06798e59	0.947523	0.473762	+	0.880653i	$0.342896\pi$
$354$	0	0
$355$	−2.87056e59	−0.336977
$356$	2.63157e60	2.89161
$357$	0	0
$358$	2.02090e60	1.94667
$359$	−8.86439e59	−0.799704	−0.399852	−	0.916580i	$-0.630939\pi$
$359$	−8.86439e59	−0.799704	−0.399852	+	0.916580i	$0.630939\pi$
$360$	0	0
$361$	−7.44875e59	−0.589745
$362$	−1.31222e60	−0.973541
$363$	0	0
$364$	3.85836e60	2.51490
$365$	−1.62982e60	−0.995994
$366$	0	0
$367$	−1.87716e60	−1.00890	−0.504451	−	0.863440i	$-0.668305\pi$
$367$	−1.87716e60	−1.00890	−0.504451	+	0.863440i	$0.668305\pi$
$368$	−1.38529e59	−0.0698420
$369$	0	0
$370$	−6.24829e60	−2.77345
$371$	−1.37280e59	−0.0571901
$372$	0	0
$373$	−2.92907e59	−0.107541	−0.0537703	−	0.998553i	$-0.517124\pi$
$373$	−2.92907e59	−0.107541	−0.0537703	+	0.998553i	$0.517124\pi$
$374$	−1.56219e59	−0.0538582
$375$	0	0
$376$	3.25742e60	0.990739
$377$	3.20153e60	0.914820
$378$	0	0
$379$	1.26439e60	0.319051	0.159525	−	0.987194i	$-0.449004\pi$
$379$	1.26439e60	0.319051	0.159525	+	0.987194i	$0.449004\pi$
$380$	−6.08605e60	−1.44352
$381$	0	0
$382$	−1.58310e61	−3.31909
$383$	−7.65652e60	−1.50959	−0.754797	−	0.655958i	$-0.772265\pi$
$383$	−7.65652e60	−1.50959	−0.754797	+	0.655958i	$0.772265\pi$
$384$	0	0
$385$	−7.04368e59	−0.122877
$386$	1.36023e60	0.223259
$387$	0	0
$388$	1.45303e61	2.11217
$389$	7.85479e60	1.07478	0.537389	−	0.843335i	$-0.319411\pi$
$389$	7.85479e60	1.07478	0.537389	+	0.843335i	$0.319411\pi$
$390$	0	0
$391$	3.82867e59	0.0464401
$392$	2.85656e61	3.26303
$393$	0	0
$394$	2.49511e61	2.52888
$395$	−2.39439e60	−0.228645
$396$	0	0
$397$	−1.21556e61	−1.03086	−0.515430	−	0.856932i	$-0.672368\pi$
$397$	−1.21556e61	−1.03086	−0.515430	+	0.856932i	$0.672368\pi$
$398$	2.84225e61	2.27201
$399$	0	0
$400$	4.06999e60	0.289190
$401$	−1.13229e61	−0.758692	−0.379346	−	0.925255i	$-0.623851\pi$
$401$	−1.13229e61	−0.758692	−0.379346	+	0.925255i	$0.623851\pi$
$402$	0	0
$403$	−1.25680e61	−0.749198
$404$	−3.96193e61	−2.22815
$405$	0	0
$406$	7.32154e61	3.66640
$407$	−1.76313e60	−0.0833327
$408$	0	0
$409$	−1.93004e61	−0.812958	−0.406479	−	0.913660i	$-0.633244\pi$
$409$	−1.93004e61	−0.812958	−0.406479	+	0.913660i	$0.633244\pi$
$410$	2.25245e61	0.895849
$411$	0	0
$412$	−1.07059e62	−3.79785
$413$	−1.84276e60	−0.0617507
$414$	0	0
$415$	5.33073e61	1.59462
$416$	6.31866e60	0.178621
$417$	0	0
$418$	−2.60835e60	−0.0658755
$419$	3.12082e60	0.0745141	0.0372571	−	0.999306i	$-0.488138\pi$
$419$	3.12082e60	0.0745141	0.0372571	+	0.999306i	$0.488138\pi$
$420$	0	0
$421$	6.12499e61	1.30760	0.653802	−	0.756666i	$-0.273173\pi$
$421$	6.12499e61	1.30760	0.653802	+	0.756666i	$0.273173\pi$
$422$	1.52089e61	0.307084
$423$	0	0
$424$	2.87303e60	0.0519090
$425$	−1.12487e61	−0.192292
$426$	0	0
$427$	−6.06807e61	−0.928957
$428$	−1.58579e62	−2.29783
$429$	0	0
$430$	−2.13236e62	−2.76919
$431$	7.83169e61	0.963030	0.481515	−	0.876438i	$-0.340087\pi$
$431$	7.83169e61	0.963030	0.481515	+	0.876438i	$0.340087\pi$
$432$	0	0
$433$	2.94510e61	0.324814	0.162407	−	0.986724i	$-0.448074\pi$
$433$	2.94510e61	0.324814	0.162407	+	0.986724i	$0.448074\pi$
$434$	−2.87416e62	−3.00263
$435$	0	0
$436$	−1.91466e62	−1.79539
$437$	6.39262e60	0.0568022
$438$	0	0
$439$	−8.39024e60	−0.0669666	−0.0334833	−	0.999439i	$-0.510660\pi$
$439$	−8.39024e60	−0.0669666	−0.0334833	+	0.999439i	$0.510660\pi$
$440$	1.47412e61	0.111530
$441$	0	0
$442$	9.83245e61	0.668711
$443$	7.70512e61	0.496926	0.248463	−	0.968641i	$-0.420075\pi$
$443$	7.70512e61	0.496926	0.248463	+	0.968641i	$0.420075\pi$
$444$	0	0
$445$	3.02370e62	1.75420
$446$	1.55280e62	0.854569
$447$	0	0
$448$	4.22417e62	2.09270
$449$	−1.71627e62	−0.806857	−0.403429	−	0.915011i	$-0.632182\pi$
$449$	−1.71627e62	−0.806857	−0.403429	+	0.915011i	$0.632182\pi$
$450$	0	0
$451$	6.35592e60	0.0269172
$452$	1.80015e62	0.723693
$453$	0	0
$454$	−3.21175e62	−1.16394
$455$	4.43329e62	1.52566
$456$	0	0
$457$	4.06573e62	1.26214	0.631070	−	0.775726i	$-0.282616\pi$
$457$	4.06573e62	1.26214	0.631070	+	0.775726i	$0.282616\pi$
$458$	5.80608e62	1.71216
$459$	0	0
$460$	−7.50831e61	−0.199863
$461$	−2.67924e62	−0.677704	−0.338852	−	0.940840i	$-0.610039\pi$
$461$	−2.67924e62	−0.677704	−0.338852	+	0.940840i	$0.610039\pi$
$462$	0	0
$463$	−5.44459e62	−1.24397	−0.621987	−	0.783027i	$-0.713675\pi$
$463$	−5.44459e62	−1.24397	−0.621987	+	0.783027i	$0.713675\pi$
$464$	−4.44474e62	−0.965325
$465$	0	0
$466$	7.32990e62	1.43889
$467$	−4.82071e62	−0.899839	−0.449919	−	0.893069i	$-0.648547\pi$
$467$	−4.82071e62	−0.899839	−0.449919	+	0.893069i	$0.648547\pi$
$468$	0	0
$469$	−4.24484e62	−0.716637
$470$	7.77849e62	1.24910
$471$	0	0
$472$	3.85656e61	0.0560484
$473$	−6.01705e61	−0.0832045
$474$	0	0
$475$	−1.87816e62	−0.235197
$476$	1.48047e63	1.76455
$477$	0	0
$478$	−1.11054e63	−1.19944
$479$	−1.74319e63	−1.79251	−0.896253	−	0.443543i	$-0.853721\pi$
$479$	−1.74319e63	−1.79251	−0.896253	+	0.443543i	$0.853721\pi$
$480$	0	0
$481$	1.10971e63	1.03467
$482$	−1.81163e63	−1.60866
$483$	0	0
$484$	−2.38381e63	−1.92046
$485$	1.66955e63	1.28135
$486$	0	0
$487$	−2.19497e63	−1.52932	−0.764661	−	0.644433i	$-0.777093\pi$
$487$	−2.19497e63	−1.52932	−0.764661	+	0.644433i	$0.777093\pi$
$488$	1.26994e63	0.843173
$489$	0	0
$490$	6.82127e63	4.11394
$491$	4.81659e62	0.276901	0.138451	−	0.990369i	$-0.455788\pi$
$491$	4.81659e62	0.276901	0.138451	+	0.990369i	$0.455788\pi$
$492$	0	0
$493$	1.22844e63	0.641875
$494$	1.64170e63	0.817918
$495$	0	0
$496$	1.74483e63	0.790560
$497$	1.16590e63	0.503832
$498$	0	0
$499$	−2.59805e63	−1.02161	−0.510805	−	0.859696i	$-0.670653\pi$
$499$	−2.59805e63	−1.02161	−0.510805	+	0.859696i	$0.670653\pi$
$500$	−3.80149e63	−1.42613
$501$	0	0
$502$	−4.01993e63	−1.37303
$503$	−5.26346e63	−1.71563	−0.857816	−	0.513958i	$-0.828179\pi$
$503$	−5.26346e63	−1.71563	−0.857816	+	0.513958i	$0.828179\pi$
$504$	0	0
$505$	−4.55229e63	−1.35171
$506$	−3.21790e61	−0.00912086
$507$	0	0
$508$	5.01787e63	1.29635
$509$	1.22138e63	0.301289	0.150644	−	0.988588i	$-0.451865\pi$
$509$	1.22138e63	0.301289	0.150644	+	0.988588i	$0.451865\pi$
$510$	0	0
$511$	6.61963e63	1.48916
$512$	−6.69351e63	−1.43817
$513$	0	0
$514$	3.47150e62	0.0680587
$515$	−1.23012e64	−2.30397
$516$	0	0
$517$	2.19492e62	0.0375310
$518$	2.53779e64	4.14673
$519$	0	0
$520$	−9.27808e63	−1.38478
$521$	9.22332e62	0.131583	0.0657916	−	0.997833i	$-0.479043\pi$
$521$	9.22332e62	0.131583	0.0657916	+	0.997833i	$0.479043\pi$
$522$	0	0
$523$	−1.18236e64	−1.54155	−0.770777	−	0.637105i	$-0.780132\pi$
$523$	−1.18236e64	−1.54155	−0.770777	+	0.637105i	$0.780132\pi$
$524$	−9.81987e63	−1.22411
$525$	0	0
$526$	−6.75060e63	−0.769444
$527$	−4.82238e63	−0.525668
$528$	0	0
$529$	−9.94900e63	−0.992135
$530$	6.86059e62	0.0654453
$531$	0	0
$532$	2.47190e64	2.15828
$533$	−4.00041e63	−0.334207
$534$	0	0
$535$	−1.82209e64	−1.39398
$536$	8.88369e63	0.650460
$537$	0	0
$538$	3.54426e64	2.37762
$539$	1.92481e63	0.123610
$540$	0	0
$541$	−1.28271e64	−0.755077	−0.377539	−	0.925994i	$-0.623229\pi$
$541$	−1.28271e64	−0.755077	−0.377539	+	0.925994i	$0.623229\pi$
$542$	3.98360e63	0.224539
$543$	0	0
$544$	2.42449e63	0.125328
$545$	−2.19996e64	−1.08917
$546$	0	0
$547$	3.21410e64	1.46001	0.730007	−	0.683440i	$-0.239517\pi$
$547$	3.21410e64	1.46001	0.730007	+	0.683440i	$0.239517\pi$
$548$	5.68699e64	2.47479
$549$	0	0
$550$	9.45422e62	0.0377661
$551$	2.05109e64	0.785095
$552$	0	0
$553$	9.72498e63	0.341860
$554$	2.84643e64	0.959006
$555$	0	0
$556$	−3.22310e64	−0.997738
$557$	1.16869e64	0.346819	0.173409	−	0.984850i	$-0.444522\pi$
$557$	1.16869e64	0.346819	0.173409	+	0.984850i	$0.444522\pi$
$558$	0	0
$559$	3.78713e64	1.03308
$560$	−6.15482e64	−1.60989
$561$	0	0
$562$	6.40209e64	1.53999
$563$	−9.31800e63	−0.214969	−0.107484	−	0.994207i	$-0.534280\pi$
$563$	−9.31800e63	−0.214969	−0.107484	+	0.994207i	$0.534280\pi$
$564$	0	0
$565$	2.06839e64	0.439029
$566$	1.30599e65	2.65922
$567$	0	0
$568$	−2.44002e64	−0.457306
$569$	−7.98965e64	−1.43678	−0.718388	−	0.695642i	$-0.755120\pi$
$569$	−7.98965e64	−1.43678	−0.718388	+	0.695642i	$0.755120\pi$
$570$	0	0
$571$	−7.20740e64	−1.19352	−0.596761	−	0.802419i	$-0.703546\pi$
$571$	−7.20740e64	−1.19352	−0.596761	+	0.802419i	$0.703546\pi$
$572$	−5.44100e63	−0.0864713
$573$	0	0
$574$	−9.14850e64	−1.33943
$575$	−2.31707e63	−0.0325645
$576$	0	0
$577$	3.11163e64	0.403047	0.201523	−	0.979484i	$-0.435411\pi$
$577$	3.11163e64	0.403047	0.201523	+	0.979484i	$0.435411\pi$
$578$	−9.98500e64	−1.24178
$579$	0	0
$580$	−2.40906e65	−2.76242
$581$	−2.16512e65	−2.38420
$582$	0	0
$583$	1.93591e62	0.00196641
$584$	−1.38537e65	−1.35165
$585$	0	0
$586$	1.51680e65	1.36563
$587$	1.26293e65	1.09241	0.546205	−	0.837652i	$-0.316072\pi$
$587$	1.26293e65	1.09241	0.546205	+	0.837652i	$0.316072\pi$
$588$	0	0
$589$	−8.05180e64	−0.642959
$590$	9.20919e63	0.0706642
$591$	0	0
$592$	−1.54063e65	−1.09179
$593$	1.16829e65	0.795726	0.397863	−	0.917445i	$-0.369752\pi$
$593$	1.16829e65	0.795726	0.397863	+	0.917445i	$0.369752\pi$
$594$	0	0
$595$	1.70107e65	1.07047
$596$	−4.92284e65	−2.97803
$597$	0	0
$598$	2.02535e64	0.113246
$599$	2.64716e65	1.42315	0.711573	−	0.702612i	$-0.247983\pi$
$599$	2.64716e65	1.42315	0.711573	+	0.702612i	$0.247983\pi$
$600$	0	0
$601$	−1.04245e65	−0.518208	−0.259104	−	0.965849i	$-0.583427\pi$
$601$	−1.04245e65	−0.518208	−0.259104	+	0.965849i	$0.583427\pi$
$602$	8.66075e65	4.14036
$603$	0	0
$604$	4.25994e65	1.88380
$605$	−2.73902e65	−1.16505
$606$	0	0
$607$	2.13825e65	0.841635	0.420818	−	0.907145i	$-0.361743\pi$
$607$	2.13825e65	0.841635	0.420818	+	0.907145i	$0.361743\pi$
$608$	4.04811e64	0.153292
$609$	0	0
$610$	3.03252e65	1.06305
$611$	−1.38148e65	−0.465990
$612$	0	0
$613$	−9.41515e64	−0.294108	−0.147054	−	0.989129i	$-0.546979\pi$
$613$	−9.41515e64	−0.294108	−0.147054	+	0.989129i	$0.546979\pi$
$614$	−4.14989e65	−1.24761
$615$	0	0
$616$	−5.98723e64	−0.166755
$617$	−3.62608e65	−0.972156	−0.486078	−	0.873916i	$-0.661573\pi$
$617$	−3.62608e65	−0.972156	−0.486078	+	0.873916i	$0.661573\pi$
$618$	0	0
$619$	−1.97673e65	−0.491154	−0.245577	−	0.969377i	$-0.578977\pi$
$619$	−1.97673e65	−0.491154	−0.245577	+	0.969377i	$0.578977\pi$
$620$	9.45706e65	2.26231
$621$	0	0
$622$	−7.02804e65	−1.55869
$623$	−1.22810e66	−2.62279
$624$	0	0
$625$	−6.22185e65	−1.23236
$626$	1.52340e66	2.90615
$627$	0	0
$628$	1.00470e66	1.77821
$629$	4.25801e65	0.725966
$630$	0	0
$631$	−1.83594e65	−0.290515	−0.145257	−	0.989394i	$-0.546401\pi$
$631$	−1.83594e65	−0.290515	−0.145257	+	0.989394i	$0.546401\pi$
$632$	−2.03526e65	−0.310291
$633$	0	0
$634$	1.94799e66	2.75734
$635$	5.76558e65	0.786431
$636$	0	0
$637$	−1.21148e66	−1.53475
$638$	−1.03247e65	−0.126064
$639$	0	0
$640$	−1.86435e66	−2.11494
$641$	−9.34817e64	−0.102226	−0.0511132	−	0.998693i	$-0.516277\pi$
$641$	−9.34817e64	−0.102226	−0.0511132	+	0.998693i	$0.516277\pi$
$642$	0	0
$643$	6.98717e65	0.710139	0.355070	−	0.934840i	$-0.384457\pi$
$643$	6.98717e65	0.710139	0.355070	+	0.934840i	$0.384457\pi$
$644$	3.04955e65	0.298826
$645$	0	0
$646$	6.29925e65	0.573885
$647$	−8.30387e65	−0.729508	−0.364754	−	0.931104i	$-0.618847\pi$
$647$	−8.30387e65	−0.729508	−0.364754	+	0.931104i	$0.618847\pi$
$648$	0	0
$649$	2.59863e63	0.00212321
$650$	−5.95049e65	−0.468909
$651$	0	0
$652$	1.09204e66	0.800609
$653$	7.01610e65	0.496176	0.248088	−	0.968737i	$-0.420198\pi$
$653$	7.01610e65	0.496176	0.248088	+	0.968737i	$0.420198\pi$
$654$	0	0
$655$	−1.12831e66	−0.742606
$656$	5.55385e65	0.352658
$657$	0	0
$658$	−3.15929e66	−1.86759
$659$	−2.56897e66	−1.46539	−0.732693	−	0.680559i	$-0.761737\pi$
$659$	−2.56897e66	−1.46539	−0.732693	+	0.680559i	$0.761737\pi$
$660$	0	0
$661$	1.01472e66	0.539028	0.269514	−	0.962996i	$-0.413137\pi$
$661$	1.01472e66	0.539028	0.269514	+	0.962996i	$0.413137\pi$
$662$	−1.91973e66	−0.984185
$663$	0	0
$664$	4.53120e66	2.16403
$665$	2.84023e66	1.30932
$666$	0	0
$667$	2.53041e65	0.108701
$668$	−3.17572e66	−1.31703
$669$	0	0
$670$	2.12136e66	0.820082
$671$	8.55710e64	0.0319409
$672$	0	0
$673$	1.27088e66	0.442334	0.221167	−	0.975236i	$-0.429013\pi$
$673$	1.27088e66	0.442334	0.221167	+	0.975236i	$0.429013\pi$
$674$	9.39049e66	3.15632
$675$	0	0
$676$	−2.72331e66	−0.853789
$677$	−2.17082e66	−0.657341	−0.328671	−	0.944445i	$-0.606601\pi$
$677$	−2.17082e66	−0.657341	−0.328671	+	0.944445i	$0.606601\pi$
$678$	0	0
$679$	−6.78098e66	−1.91581
$680$	−3.56003e66	−0.971616
$681$	0	0
$682$	4.05309e65	0.103241
$683$	−7.17341e64	−0.0176538	−0.00882692	−	0.999961i	$-0.502810\pi$
$683$	−7.17341e64	−0.0176538	−0.00882692	+	0.999961i	$0.502810\pi$
$684$	0	0
$685$	6.53440e66	1.50133
$686$	−1.42322e67	−3.15976
$687$	0	0
$688$	−5.25774e66	−1.09011
$689$	−1.21846e65	−0.0244151
$690$	0	0
$691$	−4.47891e66	−0.838374	−0.419187	−	0.907900i	$-0.637685\pi$
$691$	−4.47891e66	−0.838374	−0.419187	+	0.907900i	$0.637685\pi$
$692$	5.90801e66	1.06893
$693$	0	0
$694$	−9.50166e66	−1.60639
$695$	−3.70338e66	−0.605278
$696$	0	0
$697$	−1.53497e66	−0.234493
$698$	−2.69765e66	−0.398459
$699$	0	0
$700$	−8.95962e66	−1.23733
$701$	3.84070e66	0.512905	0.256452	−	0.966557i	$-0.417446\pi$
$701$	3.84070e66	0.512905	0.256452	+	0.966557i	$0.417446\pi$
$702$	0	0
$703$	7.10949e66	0.887949
$704$	−5.95686e65	−0.0719548
$705$	0	0
$706$	1.43464e67	1.62119
$707$	1.84895e67	2.02101
$708$	0	0
$709$	6.56172e64	0.00671168	0.00335584	−	0.999994i	$-0.498932\pi$
$709$	6.56172e64	0.00671168	0.00335584	+	0.999994i	$0.498932\pi$
$710$	−5.82659e66	−0.576558
$711$	0	0
$712$	2.57019e67	2.38059
$713$	−9.93343e65	−0.0890216
$714$	0	0
$715$	−6.25176e65	−0.0524579
$716$	2.70075e67	2.19294
$717$	0	0
$718$	−1.79927e67	−1.36827
$719$	2.12438e67	1.56352	0.781760	−	0.623580i	$-0.214322\pi$
$719$	2.12438e67	1.56352	0.781760	+	0.623580i	$0.214322\pi$
$720$	0	0
$721$	4.99620e67	3.44478
$722$	−1.51193e67	−1.00904
$723$	0	0
$724$	−1.75366e67	−1.09670
$725$	−7.43437e66	−0.450092
$726$	0	0
$727$	2.27873e67	1.29311	0.646554	−	0.762868i	$-0.276209\pi$
$727$	2.27873e67	1.29311	0.646554	+	0.762868i	$0.276209\pi$
$728$	3.76836e67	2.07045
$729$	0	0
$730$	−3.30816e67	−1.70412
$731$	1.45314e67	0.724850
$732$	0	0
$733$	−2.32774e66	−0.108891	−0.0544454	−	0.998517i	$-0.517339\pi$
$733$	−2.32774e66	−0.108891	−0.0544454	+	0.998517i	$0.517339\pi$
$734$	−3.81022e67	−1.72620
$735$	0	0
$736$	4.99412e65	0.0212242
$737$	5.98601e65	0.0246406
$738$	0	0
$739$	−1.90706e65	−0.00736579	−0.00368290	−	0.999993i	$-0.501172\pi$
$739$	−1.90706e65	−0.00736579	−0.00368290	+	0.999993i	$0.501172\pi$
$740$	−8.35028e67	−3.12432
$741$	0	0
$742$	−2.78648e66	−0.0978507
$743$	−3.96691e67	−1.34963	−0.674816	−	0.737986i	$-0.735777\pi$
$743$	−3.96691e67	−1.34963	−0.674816	+	0.737986i	$0.735777\pi$
$744$	0	0
$745$	−5.65639e67	−1.80662
$746$	−5.94536e66	−0.183999
$747$	0	0
$748$	−2.08773e66	−0.0606718
$749$	7.40056e67	2.08421
$750$	0	0
$751$	−4.47498e67	−1.18373	−0.591865	−	0.806037i	$-0.701608\pi$
$751$	−4.47498e67	−1.18373	−0.591865	+	0.806037i	$0.701608\pi$
$752$	1.91793e67	0.491716
$753$	0	0
$754$	6.49838e67	1.56523
$755$	4.89471e67	1.14281
$756$	0	0
$757$	1.35751e67	0.297845	0.148922	−	0.988849i	$-0.452420\pi$
$757$	1.35751e67	0.297845	0.148922	+	0.988849i	$0.452420\pi$
$758$	2.56643e67	0.545887
$759$	0	0
$760$	−5.94410e67	−1.18841
$761$	−3.22776e67	−0.625693	−0.312846	−	0.949804i	$-0.601283\pi$
$761$	−3.22776e67	−0.625693	−0.312846	+	0.949804i	$0.601283\pi$
$762$	0	0
$763$	8.93529e67	1.62848
$764$	−2.11567e68	−3.73899
$765$	0	0
$766$	−1.55410e68	−2.58288
$767$	−1.63558e66	−0.0263621
$768$	0	0
$769$	−6.92939e67	−1.05057	−0.525287	−	0.850925i	$-0.676042\pi$
$769$	−6.92939e67	−1.05057	−0.525287	+	0.850925i	$0.676042\pi$
$770$	−1.42971e67	−0.210240
$771$	0	0
$772$	1.81782e67	0.251504
$773$	−1.00550e68	−1.34947	−0.674733	−	0.738062i	$-0.735741\pi$
$773$	−1.00550e68	−1.34947	−0.674733	+	0.738062i	$0.735741\pi$
$774$	0	0
$775$	2.91845e67	0.368606
$776$	1.41914e68	1.73890
$777$	0	0
$778$	1.59435e68	1.83892
$779$	−2.56291e67	−0.286815
$780$	0	0
$781$	−1.64413e66	−0.0173236
$782$	7.77133e66	0.0794578
$783$	0	0
$784$	1.68191e68	1.61948
$785$	1.15441e68	1.07875
$786$	0	0
$787$	−2.41454e66	−0.0212534	−0.0106267	−	0.999944i	$-0.503383\pi$
$787$	−2.41454e66	−0.0212534	−0.0106267	+	0.999944i	$0.503383\pi$
$788$	3.33449e68	2.84881
$789$	0	0
$790$	−4.86007e67	−0.391206
$791$	−8.40090e67	−0.656415
$792$	0	0
$793$	−5.38584e67	−0.396583
$794$	−2.46732e68	−1.76377
$795$	0	0
$796$	3.79841e68	2.55944
$797$	2.29036e68	1.49842	0.749210	−	0.662332i	$-0.230433\pi$
$797$	2.29036e68	1.49842	0.749210	+	0.662332i	$0.230433\pi$
$798$	0	0
$799$	−5.30079e67	−0.326957
$800$	−1.46728e67	−0.0878815
$801$	0	0
$802$	−2.29830e68	−1.29810
$803$	−9.33490e66	−0.0512029
$804$	0	0
$805$	3.50397e67	0.181283
$806$	−2.55102e68	−1.28186
$807$	0	0
$808$	−3.86952e68	−1.83438
$809$	−7.74628e66	−0.0356700	−0.0178350	−	0.999841i	$-0.505677\pi$
$809$	−7.74628e66	−0.0356700	−0.0178350	+	0.999841i	$0.505677\pi$
$810$	0	0
$811$	−2.32748e68	−1.01134	−0.505669	−	0.862727i	$-0.668754\pi$
$811$	−2.32748e68	−1.01134	−0.505669	+	0.862727i	$0.668754\pi$
$812$	9.78458e68	4.13024
$813$	0	0
$814$	−3.57875e67	−0.142580
$815$	1.25476e68	0.485689
$816$	0	0
$817$	2.42626e68	0.886584
$818$	−3.91754e68	−1.39095
$819$	0	0
$820$	3.01020e68	1.00918
$821$	−4.26945e68	−1.39094	−0.695470	−	0.718556i	$-0.744804\pi$
$821$	−4.26945e68	−1.39094	−0.695470	+	0.718556i	$0.744804\pi$
$822$	0	0
$823$	1.89793e68	0.583961	0.291981	−	0.956424i	$-0.405686\pi$
$823$	1.89793e68	0.583961	0.291981	+	0.956424i	$0.405686\pi$
$824$	−1.04562e69	−3.12667
$825$	0	0
$826$	−3.74038e67	−0.105654
$827$	8.12864e67	0.223171	0.111586	−	0.993755i	$-0.464407\pi$
$827$	8.12864e67	0.223171	0.111586	+	0.993755i	$0.464407\pi$
$828$	0	0
$829$	−6.84615e68	−1.77589	−0.887943	−	0.459953i	$-0.847866\pi$
$829$	−6.84615e68	−1.77589	−0.887943	+	0.459953i	$0.847866\pi$
$830$	1.08202e69	2.72835
$831$	0	0
$832$	3.74925e68	0.893400
$833$	−4.64848e68	−1.07684
$834$	0	0
$835$	−3.64893e68	−0.798975
$836$	−3.48583e67	−0.0742094
$837$	0	0
$838$	6.33456e67	0.127492
$839$	4.43097e67	0.0867147	0.0433574	−	0.999060i	$-0.486195\pi$
$839$	4.43097e67	0.0867147	0.0433574	+	0.999060i	$0.486195\pi$
$840$	0	0
$841$	2.71501e68	0.502418
$842$	1.24324e69	2.23727
$843$	0	0
$844$	2.03254e68	0.345933
$845$	−3.12911e68	−0.517951
$846$	0	0
$847$	1.11247e69	1.74193
$848$	1.69161e67	0.0257630
$849$	0	0
$850$	−2.28322e68	−0.329006
$851$	8.77091e67	0.122942
$852$	0	0
$853$	1.15923e69	1.53768	0.768842	−	0.639439i	$-0.220833\pi$
$853$	1.15923e69	1.53768	0.768842	+	0.639439i	$0.220833\pi$
$854$	−1.23168e69	−1.58942
$855$	0	0
$856$	−1.54881e69	−1.89175
$857$	1.19885e69	1.42467	0.712334	−	0.701840i	$-0.247638\pi$
$857$	1.19885e69	1.42467	0.712334	+	0.701840i	$0.247638\pi$
$858$	0	0
$859$	−1.22015e69	−1.37269	−0.686345	−	0.727276i	$-0.740786\pi$
$859$	−1.22015e69	−1.37269	−0.686345	+	0.727276i	$0.740786\pi$
$860$	−2.84971e69	−3.11952
$861$	0	0
$862$	1.58966e69	1.64772
$863$	−5.27188e68	−0.531755	−0.265878	−	0.964007i	$-0.585662\pi$
$863$	−5.27188e68	−0.531755	−0.265878	+	0.964007i	$0.585662\pi$
$864$	0	0
$865$	6.78835e68	0.648464
$866$	5.97789e68	0.555748
$867$	0	0
$868$	−3.84105e69	−3.38249
$869$	−1.37140e67	−0.0117544
$870$	0	0
$871$	−3.76760e68	−0.305941
$872$	−1.87000e69	−1.47810
$873$	0	0
$874$	1.29756e68	0.0971871
$875$	1.77408e69	1.29355
$876$	0	0
$877$	−1.25938e69	−0.870296	−0.435148	−	0.900359i	$-0.643304\pi$
$877$	−1.25938e69	−0.870296	−0.435148	+	0.900359i	$0.643304\pi$
$878$	−1.70303e68	−0.114578
$879$	0	0
$880$	8.67943e67	0.0553539
$881$	−1.05379e69	−0.654365	−0.327182	−	0.944961i	$-0.606099\pi$
$881$	−1.05379e69	−0.654365	−0.327182	+	0.944961i	$0.606099\pi$
$882$	0	0
$883$	1.51174e69	0.890021	0.445010	−	0.895525i	$-0.353200\pi$
$883$	1.51174e69	0.890021	0.445010	+	0.895525i	$0.353200\pi$
$884$	1.31402e69	0.753309
$885$	0	0
$886$	1.56397e69	0.850227
$887$	−2.55796e69	−1.35422	−0.677108	−	0.735883i	$-0.736767\pi$
$887$	−2.55796e69	−1.35422	−0.677108	+	0.735883i	$0.736767\pi$
$888$	0	0
$889$	−2.34173e69	−1.17583
$890$	6.13743e69	3.00138
$891$	0	0
$892$	2.07518e69	0.962680
$893$	−8.85059e68	−0.399911
$894$	0	0
$895$	3.10318e69	1.33035
$896$	7.57219e69	3.16216
$897$	0	0
$898$	−3.48364e69	−1.38051
$899$	−3.18717e69	−1.23042
$900$	0	0
$901$	−4.67527e67	−0.0171307
$902$	1.29011e68	0.0460546
$903$	0	0
$904$	1.75816e69	0.595799
$905$	−2.01497e69	−0.665315
$906$	0	0
$907$	−1.67267e69	−0.524373	−0.262186	−	0.965017i	$-0.584443\pi$
$907$	−1.67267e69	−0.524373	−0.262186	+	0.965017i	$0.584443\pi$
$908$	−4.29221e69	−1.31118
$909$	0	0
$910$	8.99858e69	2.61037
$911$	2.16759e68	0.0612767	0.0306383	−	0.999531i	$-0.490246\pi$
$911$	2.16759e68	0.0612767	0.0306383	+	0.999531i	$0.490246\pi$
$912$	0	0
$913$	3.05322e68	0.0819775
$914$	8.25251e69	2.15949
$915$	0	0
$916$	7.75931e69	1.92876
$917$	4.58272e69	1.11031
$918$	0	0
$919$	−1.42756e69	−0.328610	−0.164305	−	0.986410i	$-0.552538\pi$
$919$	−1.42756e69	−0.328610	−0.164305	+	0.986410i	$0.552538\pi$
$920$	−7.33318e68	−0.164543
$921$	0	0
$922$	−5.43826e69	−1.15953
$923$	1.03482e69	0.215092
$924$	0	0
$925$	−2.57690e69	−0.509057
$926$	−1.10513e70	−2.12841
$927$	0	0
$928$	1.60238e69	0.293351
$929$	−8.84307e68	−0.157846	−0.0789231	−	0.996881i	$-0.525148\pi$
$929$	−8.84307e68	−0.157846	−0.0789231	+	0.996881i	$0.525148\pi$
$930$	0	0
$931$	−7.76144e69	−1.31712
$932$	9.79575e69	1.62093
$933$	0	0
$934$	−9.78496e69	−1.53960
$935$	−2.39882e68	−0.0368066
$936$	0	0
$937$	−4.16313e69	−0.607491	−0.303746	−	0.952753i	$-0.598237\pi$
$937$	−4.16313e69	−0.607491	−0.303746	+	0.952753i	$0.598237\pi$
$938$	−8.61607e69	−1.22615
$939$	0	0
$940$	1.03953e70	1.40712
$941$	−1.24869e70	−1.64853	−0.824266	−	0.566203i	$-0.808412\pi$
$941$	−1.24869e70	−1.64853	−0.824266	+	0.566203i	$0.808412\pi$
$942$	0	0
$943$	−3.16183e68	−0.0397113
$944$	2.27070e68	0.0278175
$945$	0	0
$946$	−1.22133e69	−0.142361
$947$	6.06340e69	0.689433	0.344716	−	0.938707i	$-0.387975\pi$
$947$	6.06340e69	0.689433	0.344716	+	0.938707i	$0.387975\pi$
$948$	0	0
$949$	5.87539e69	0.635741
$950$	−3.81224e69	−0.402416
$951$	0	0
$952$	1.44593e70	1.45271
$953$	3.62312e69	0.355140	0.177570	−	0.984108i	$-0.443176\pi$
$953$	3.62312e69	0.355140	0.177570	+	0.984108i	$0.443176\pi$
$954$	0	0
$955$	−2.43092e70	−2.26826
$956$	−1.48414e70	−1.35118
$957$	0	0
$958$	−3.53829e70	−3.06693
$959$	−2.65400e70	−2.24472
$960$	0	0
$961$	9.50929e67	0.00765858
$962$	2.25247e70	1.77029
$963$	0	0
$964$	−2.42109e70	−1.81217
$965$	2.08869e69	0.152575
$966$	0	0
$967$	2.47757e70	1.72387	0.861933	−	0.507023i	$-0.169254\pi$
$967$	2.47757e70	1.72387	0.861933	+	0.507023i	$0.169254\pi$
$968$	−2.32821e70	−1.58107
$969$	0	0
$970$	3.38880e70	2.19235
$971$	1.69313e70	1.06915	0.534574	−	0.845122i	$-0.320472\pi$
$971$	1.69313e70	1.06915	0.534574	+	0.845122i	$0.320472\pi$
$972$	0	0
$973$	1.50415e70	0.904983
$974$	−4.45530e70	−2.61663
$975$	0	0
$976$	7.47726e69	0.418477
$977$	1.88519e70	1.02999	0.514994	−	0.857193i	$-0.327794\pi$
$977$	1.88519e70	1.02999	0.514994	+	0.857193i	$0.327794\pi$
$978$	0	0
$979$	1.73185e69	0.0901812
$980$	9.11602e70	4.63439
$981$	0	0
$982$	9.77660e69	0.473770
$983$	−1.50691e69	−0.0712982	−0.0356491	−	0.999364i	$-0.511350\pi$
$983$	−1.50691e69	−0.0712982	−0.0356491	+	0.999364i	$0.511350\pi$
$984$	0	0
$985$	3.83136e70	1.72823
$986$	2.49345e70	1.09823
$987$	0	0
$988$	2.19398e70	0.921393
$989$	2.99326e69	0.122753
$990$	0	0
$991$	−3.55474e70	−1.39020	−0.695099	−	0.718914i	$-0.744639\pi$
$991$	−3.55474e70	−1.39020	−0.695099	+	0.718914i	$0.744639\pi$
$992$	−6.29032e69	−0.240242
$993$	0	0
$994$	2.36651e70	0.862043
$995$	4.36441e70	1.55268
$996$	0	0
$997$	−1.08915e70	−0.369618	−0.184809	−	0.982774i	$-0.559167\pi$
$997$	−1.08915e70	−0.369618	−0.184809	+	0.982774i	$0.559167\pi$
$998$	−5.27347e70	−1.74795
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	9.48.a.c.1.4		4
3.2	odd	2		1.48.a.a.1.1	✓	4
12.11	even	2		16.48.a.d.1.3		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1.48.a.a.1.1	✓	4	3.2	odd	2
9.48.a.c.1.4		4	1.1	even	1	trivial
16.48.a.d.1.3		4	12.11	even	2

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:	\( k \)	\(=\)	\( 48 \)
Character orbit:	\([\chi]\)	\(=\)	9.a (trivial)

\(f(q)\)	\(=\)	\(q+2.02978e7 q^{2} +2.71261e14 q^{4} +3.11682e16 q^{5} -1.26592e20 q^{7} +2.64934e21 q^{8} +O(q^{10})\)	\(q+2.02978e7 q^{2} +2.71261e14 q^{4} +3.11682e16 q^{5} -1.26592e20 q^{7} +2.64934e21 q^{8} +6.32644e23 q^{10} +1.78518e23 q^{11} -1.12359e26 q^{13} -2.56953e27 q^{14} +1.55990e28 q^{16} -4.31126e28 q^{17} -7.19841e29 q^{19} +8.45472e30 q^{20} +3.62352e30 q^{22} -8.88061e30 q^{23} +2.60913e32 q^{25} -2.28064e33 q^{26} -3.43395e34 q^{28} -2.84937e34 q^{29} +1.11855e35 q^{31} -5.62362e34 q^{32} -8.75090e35 q^{34} -3.94564e36 q^{35} -9.87647e36 q^{37} -1.46112e37 q^{38} +8.25752e37 q^{40} +3.56038e37 q^{41} -3.37056e38 q^{43} +4.84250e37 q^{44} -1.80256e38 q^{46} +1.22952e39 q^{47} +1.07822e40 q^{49} +5.29595e39 q^{50} -3.04787e40 q^{52} +1.08443e39 q^{53} +5.56408e39 q^{55} -3.35385e41 q^{56} -5.78358e41 q^{58} +1.45567e40 q^{59} +4.79341e41 q^{61} +2.27041e42 q^{62} -3.33684e42 q^{64} -3.50203e42 q^{65} +3.35317e42 q^{67} -1.16948e43 q^{68} -8.00876e43 q^{70} -9.20990e42 q^{71} -5.22911e43 q^{73} -2.00470e44 q^{74} -1.95265e44 q^{76} -2.25989e43 q^{77} -7.68215e43 q^{79} +4.86194e44 q^{80} +7.22677e44 q^{82} +1.71031e45 q^{83} -1.34374e45 q^{85} -6.84147e45 q^{86} +4.72955e44 q^{88} +9.70124e45 q^{89} +1.42238e46 q^{91} -2.40897e45 q^{92} +2.49565e46 q^{94} -2.24361e46 q^{95} +5.35657e46 q^{97} +2.18854e47 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 5785560 q^{2} + 404807499161152 q^{4} + 31\!\cdots\!00 q^{5}+ \cdots - 23\!\cdots\!20 q^{8}+O(q^{10}) \) 4 * q - 5785560 * q^2 + 404807499161152 * q^4 + 31114680242272200 * q^5 - 39169218725888423200 * q^7 - 2392716988073784337920 * q^8	\( 4 q - 5785560 q^{2} + 404807499161152 q^{4} + 31\!\cdots\!00 q^{5}+ \cdots + 29\!\cdots\!20 q^{98}+O(q^{100}) \) 4 * q - 5785560 * q^2 + 404807499161152 * q^4 + 31114680242272200 * q^5 - 39169218725888423200 * q^7 - 2392716988073784337920 * q^8 + 161126302562215963534800 * q^10 + 1902165515717740404742512 * q^11 + 126959149195199610466858520 * q^13 - 3491363489769461659480835904 * q^14 + 124527684040554167211817897984 * q^16 - 210426285758836687099688769480 * q^17 - 1059119811802437301721159140240 * q^19 + 15129514318106701401937782249600 * q^20 - 79668451994083088127806382590880 * q^22 - 137531418344493639994288859179680 * q^23 + 1009909900344396506188154274977500 * q^25 - 2282338781897562472343866220387088 * q^26 - 36222097928665071743339635065479680 * q^28 + 22743132490172744184500850941726760 * q^29 + 75786540814706434901630981303934848 * q^31 - 1184674767018086471839527432906178560 * q^32 - 1261659118578465318749852382715620816 * q^34 + 1313148822925052387484546800067979200 * q^35 - 11291457045120157869429951769632191560 * q^37 - 29667542464851305273548614410680536480 * q^38 + 70753686685508718175919216681780352000 * q^40 - 130658126291089294119301677048020391528 * q^41 - 445357287738427943170332944488133090800 * q^43 + 1525898906718917337200010663037616115456 * q^44 + 1226146172325422687186041586267533291968 * q^46 - 2031912465958423919194866366997063590720 * q^47 + 9153745744156628626499502447643951451172 * q^49 + 19226200465513908889722489088356697935000 * q^50 - 55272350705889116147839999778699925596800 * q^52 - 29171719896619533806321793123448457437560 * q^53 + 192172580604633896452606078657416872901600 * q^55 - 276101696826518177934513744689489393111040 * q^56 - 732323136683092912071778597620095648941680 * q^58 - 478242858216320686410790860443879577596880 * q^59 + 626683213833907852009669690320782900857688 * q^61 + 6870459615610782098804391369236375065946880 * q^62 + 5525430481808418303700543890989262651523072 * q^64 - 12996735432890074297558542478104126872331600 * q^65 + 18701411419127220668869505853739529194216880 * q^67 + 27469024204738931095482995064729717598496640 * q^68 - 97207317904230285933067401805385458355395200 * q^70 - 22196594617762006008028198712153461686540768 * q^71 + 104911201720506650033573412943840886878191080 * q^73 - 187734656069700274526204928907842421165646544 * q^74 + 351694386032713991264839561028061045130100480 * q^76 + 263490744376507692433815778071300370399209600 * q^77 - 1327995310109394234162785254414226288730352960 * q^79 + 948349663264469859337474495994045561022259200 * q^80 + 3821513842864797430908620724480935919685390320 * q^82 + 1439130627532364606968733068855111784504073360 * q^83 - 1001895286410663502447652611446390227458237200 * q^85 - 9578145533777866709022895861637903827077656928 * q^86 - 15478856320702836436797993507832298416714229760 * q^88 + 7960590522674945421108320896849737731421281880 * q^89 + 5325194479227227497182497798631911205603381568 * q^91 - 13058297350229360275908546071900174502239009280 * q^92 + 3475860200879106349192555645858186353201354624 * q^94 - 75421152415106939771624998522249518123547668000 * q^95 + 95066248961258904822565865801364599382905757320 * q^97 + 296344663186266398350742083591017164797938217320 * q^98

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