LMFDB - Embedded newform 9.62.a.a.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [9,62,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, 62, names="a")

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

chi := DirichletCharacter("9.1");

S:= CuspForms(chi, 62);

N := Newforms(S);

Level:	$ N $	$=$	$ 9 = 3^{2} $
Weight:	$ k $	$=$	$ 62 $
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:	$212.090564938$
Analytic rank:	$0$
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} - 180363795469121x^{2} + 166129321978984507920x + 2785609847439483545242446300 $ x^4 - x^3 - 180363795469121x^2 + 166129321978984507920x + 2785609847439483545242446300
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{28}\cdot 3^{10}\cdot 5^{2}\cdot 7 $
Twist minimal:	no (minimal twist has level 1)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$4.76281e6$ 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)

$f(q)$	$=$	$q+6.27881e8 q^{2} -1.91161e18 q^{4} -2.33985e20 q^{5} +6.25792e25 q^{7} -2.64806e27 q^{8} +O(q^{10})$	\(q+6.27881e8 q^{2} -1.91161e18 q^{4} -2.33985e20 q^{5} +6.25792e25 q^{7} -2.64806e27 q^{8} -1.46915e29 q^{10} +9.05394e31 q^{11} +7.79086e33 q^{13} +3.92923e34 q^{14} +2.74521e36 q^{16} +1.64134e37 q^{17} +1.45265e39 q^{19} +4.47288e38 q^{20} +5.68480e40 q^{22} +1.28631e41 q^{23} -4.28206e42 q^{25} +4.89173e42 q^{26} -1.19627e44 q^{28} -1.23922e44 q^{29} +2.17946e45 q^{31} +7.82966e45 q^{32} +1.03057e46 q^{34} -1.46426e46 q^{35} +5.13297e47 q^{37} +9.12091e47 q^{38} +6.19606e47 q^{40} -1.44082e49 q^{41} -4.68902e49 q^{43} -1.73076e50 q^{44} +8.07652e49 q^{46} +1.55786e51 q^{47} +3.60006e50 q^{49} -2.68862e51 q^{50} -1.48931e52 q^{52} -2.61505e52 q^{53} -2.11849e52 q^{55} -1.65713e53 q^{56} -7.78081e52 q^{58} -5.85447e53 q^{59} -6.99841e53 q^{61} +1.36844e54 q^{62} -1.41392e54 q^{64} -1.82294e54 q^{65} -5.65118e55 q^{67} -3.13760e55 q^{68} -9.19381e54 q^{70} +4.76482e56 q^{71} +4.87633e56 q^{73} +3.22289e56 q^{74} -2.77690e57 q^{76} +5.66589e57 q^{77} -6.21907e57 q^{79} -6.42337e56 q^{80} -9.04662e57 q^{82} +1.18158e58 q^{83} -3.84049e57 q^{85} -2.94414e58 q^{86} -2.39753e59 q^{88} +8.44939e58 q^{89} +4.87546e59 q^{91} -2.45893e59 q^{92} +9.78147e59 q^{94} -3.39899e59 q^{95} +8.57527e59 q^{97} +2.26041e59 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 1146312000 q^{2} + 44\!\cdots\!28 q^{4}+ \cdots - 97\!\cdots\!00 q^{8}+O(q^{10}) $ 4 * q - 1146312000 * q^2 + 4402997675828604928 * q^4 + 524125996020295237800 * q^5 - 63338569463385158773180000 * q^7 - 9767868387156674079031296000 * q^8	$ 4 q - 1146312000 q^{2} + 44\!\cdots\!28 q^{4}+ \cdots - 17\!\cdots\!00 q^{98}+O(q^{100}) $ 4 * q - 1146312000 * q^2 + 4402997675828604928 * q^4 + 524125996020295237800 * q^5 - 63338569463385158773180000 * q^7 - 9767868387156674079031296000 * q^8 - 1483353386285070117088509033600 * q^10 + 41554515064513200044500416014352 * q^11 + 10764994985103189070396812401291000 * q^13 + 211155135436541225684077605177122304 * q^14 + 10904646278227442826771588888892801024 * q^16 + 40906325415811699311242283170389539000 * q^17 - 356159749895948464708913853630763435120 * q^19 + 5071632401696432486275641956774663577600 * q^20 - 172062995599931314756360229299481569056000 * q^22 + 410968880183827232479513482663937487796000 * q^23 - 16739487717977510894946357652146107782722500 * q^25 + 49284147216613914166808777620995485562632832 * q^26 - 790757236315065917044952859738895406239744000 * q^28 - 6672429803576117328528976307882755467518520 * q^29 + 3262752943509002552517145952336046015034252928 * q^31 - 29552482936847865082009297897367834619543552000 * q^32 + 39802528145537101299701822666373970434557030016 * q^34 - 94932144900835792457443003213138857525722942400 * q^35 - 710312106544219153529408139748985993336062057000 * q^37 + 6572443117826428556368685861295549874330331616000 * q^38 - 6935278763126032494337494583468084555036360704000 * q^40 - 16359554122032268527799184148245398149035867491368 * q^41 + 75844732497959094206655920598930086763379517030000 * q^43 - 152692943245212279510621538861388707588508390670336 * q^44 - 150345409740296355038882940983341438053393810381312 * q^46 + 2164761335188781225334544122222333542985932701416000 * q^47 + 1523957834189526415441239854498433329172794287478628 * q^49 + 3735723416225956799610935352239535395426733934920000 * q^50 + 34115942043101628674837973043915515701891779834880000 * q^52 - 84459499120263342936174700173047508278523729350943000 * q^53 - 18917852463295959783361213875825060571992233753013600 * q^55 + 895534119833025861281009767571957442822737699977297920 * q^56 - 429363306259072204179262197105630766591459158948624000 * q^58 + 2147121767784312006347793068275982647255821920255956560 * q^59 + 4291528347018103219994434901020564652244372107292350648 * q^61 - 5191805357629316458585917076609024961942995611849984000 * q^62 + 19881300699476524526504677072626341971094030107078033408 * q^64 + 4054154514265281184405976695522203389642082195785626800 * q^65 - 151638661420806044794238226134660440129857438609787534000 * q^67 + 199797070973791372723379406738475848419062088637699072000 * q^68 + 164781406287311752350371419457017830072394299112015948800 * q^70 - 266771587169907679430401079119295396456876119234283837088 * q^71 + 436772697766954812846449565799176070423143504803837369000 * q^73 - 2727029156290392414014538532434064649250131670424597597056 * q^74 - 9182670231472830669367329606616577285345108294701612810240 * q^76 + 6239400117692696801885467207245334802759585122139865360000 * q^77 - 2171516124052566840962201891051143348431163494068568095680 * q^79 + 8149820448667982873535456900485215194289704343083732172800 * q^80 + 41751906507711557992784780576518459967807480604061450704000 * q^82 + 19301891587488226996497021336363284746717620338719475718000 * q^83 + 23823437828438802480990474713115034607148974715085027364400 * q^85 + 71538345696620408289043701603344533132955103857012068207872 * q^86 - 453611870852754620593515203785357874778152109551115829248000 * q^88 + 606362068644618673179710823370293144593411608656909401212440 * q^89 - 452168126000372891758634520948160370052422021946362710252352 * q^91 - 1607280224434271875135145612458728092411753130630908891136000 * q^92 + 6446155892605066539979931910636020289279531063064695408331776 * q^94 - 1105507768048183718212260841102299501129184381013780070972000 * q^95 - 8084830239737746227548751167926342536453719541548201116411000 * q^97 - 17015397362965438448003410858883076702895502959466609182344000 * 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 $

$2$	6.27881e8	0.413487	0.206744	−	0.978395i	$-0.433713\pi$
$2$	6.27881e8	0.413487	0.206744	+	0.978395i	$0.433713\pi$
$3$	0	0
$3$	0	0
$4$	−1.91161e18	−0.829028
$5$	−2.33985e20	−0.112358	−0.0561789	−	0.998421i	$-0.517892\pi$
$5$	−2.33985e20	−0.112358	−0.0561789	+	0.998421i	$0.517892\pi$
$6$	0	0
$7$	6.25792e25	1.04940	0.524699	−	0.851288i	$-0.324178\pi$
$7$	6.25792e25	1.04940	0.524699	+	0.851288i	$0.324178\pi$
$8$	−2.64806e27	−0.756280
$9$	0	0
$10$	−1.46915e29	−0.0464585
$11$	9.05394e31	1.56445	0.782223	−	0.622998i	$-0.214086\pi$
$11$	9.05394e31	1.56445	0.782223	+	0.622998i	$0.214086\pi$
$12$	0	0
$13$	7.79086e33	0.824732	0.412366	−	0.911018i	$-0.364702\pi$
$13$	7.79086e33	0.824732	0.412366	+	0.911018i	$0.364702\pi$
$14$	3.92923e34	0.433913
$15$	0	0
$16$	2.74521e36	0.516316
$17$	1.64134e37	0.485855	0.242927	−	0.970044i	$-0.421892\pi$
$17$	1.64134e37	0.485855	0.242927	+	0.970044i	$0.421892\pi$
$18$	0	0
$19$	1.45265e39	1.44603	0.723014	−	0.690834i	$-0.242756\pi$
$19$	1.45265e39	1.44603	0.723014	+	0.690834i	$0.242756\pi$
$20$	4.47288e38	0.0931477
$21$	0	0
$22$	5.68480e40	0.646879
$23$	1.28631e41	0.377266	0.188633	−	0.982048i	$-0.439594\pi$
$23$	1.28631e41	0.377266	0.188633	+	0.982048i	$0.439594\pi$
$24$	0	0
$25$	−4.28206e42	−0.987376
$26$	4.89173e42	0.341016
$27$	0	0
$28$	−1.19627e44	−0.869980
$29$	−1.23922e44	−0.309036	−0.154518	−	0.987990i	$-0.549382\pi$
$29$	−1.23922e44	−0.309036	−0.154518	+	0.987990i	$0.549382\pi$
$30$	0	0
$31$	2.17946e45	0.710915	0.355457	−	0.934692i	$-0.384325\pi$
$31$	2.17946e45	0.710915	0.355457	+	0.934692i	$0.384325\pi$
$32$	7.82966e45	0.969770
$33$	0	0
$34$	1.03057e46	0.200895
$35$	−1.46426e46	−0.117908
$36$	0	0
$37$	5.13297e47	0.758955	0.379478	−	0.925201i	$-0.376104\pi$
$37$	5.13297e47	0.758955	0.379478	+	0.925201i	$0.376104\pi$
$38$	9.12091e47	0.597914
$39$	0	0
$40$	6.19606e47	0.0849739
$41$	−1.44082e49	−0.930469	−0.465234	−	0.885188i	$-0.654030\pi$
$41$	−1.44082e49	−0.930469	−0.465234	+	0.885188i	$0.654030\pi$
$42$	0	0
$43$	−4.68902e49	−0.708425	−0.354213	−	0.935165i	$-0.615251\pi$
$43$	−4.68902e49	−0.708425	−0.354213	+	0.935165i	$0.615251\pi$
$44$	−1.73076e50	−1.29697
$45$	0	0
$46$	8.07652e49	0.155995
$47$	1.55786e51	1.56150	0.780751	−	0.624842i	$-0.214837\pi$
$47$	1.55786e51	1.56150	0.780751	+	0.624842i	$0.214837\pi$
$48$	0	0
$49$	3.60006e50	0.101235
$50$	−2.68862e51	−0.408267
$51$	0	0
$52$	−1.48931e52	−0.683726
$53$	−2.61505e52	−0.671531	−0.335765	−	0.941946i	$-0.608995\pi$
$53$	−2.61505e52	−0.671531	−0.335765	+	0.941946i	$0.608995\pi$
$54$	0	0
$55$	−2.11849e52	−0.175778
$56$	−1.65713e53	−0.793638
$57$	0	0
$58$	−7.78081e52	−0.127782
$59$	−5.85447e53	−0.570823	−0.285411	−	0.958405i	$-0.592130\pi$
$59$	−5.85447e53	−0.570823	−0.285411	+	0.958405i	$0.592130\pi$
$60$	0	0
$61$	−6.99841e53	−0.246854	−0.123427	−	0.992354i	$-0.539388\pi$
$61$	−6.99841e53	−0.246854	−0.123427	+	0.992354i	$0.539388\pi$
$62$	1.36844e54	0.293954
$63$	0	0
$64$	−1.41392e54	−0.115328
$65$	−1.82294e54	−0.0926650
$66$	0	0
$67$	−5.65118e55	−1.13988	−0.569938	−	0.821688i	$-0.693033\pi$
$67$	−5.65118e55	−1.13988	−0.569938	+	0.821688i	$0.693033\pi$
$68$	−3.13760e55	−0.402787
$69$	0	0
$70$	−9.19381e54	−0.0487534
$71$	4.76482e56	1.63933	0.819667	−	0.572841i	$-0.194159\pi$
$71$	4.76482e56	1.63933	0.819667	+	0.572841i	$0.194159\pi$
$72$	0	0
$73$	4.87633e56	0.719028	0.359514	−	0.933140i	$-0.382942\pi$
$73$	4.87633e56	0.719028	0.359514	+	0.933140i	$0.382942\pi$
$74$	3.22289e56	0.313818
$75$	0	0
$76$	−2.77690e57	−1.19880
$77$	5.66589e57	1.64173
$78$	0	0
$79$	−6.21907e57	−0.824326	−0.412163	−	0.911110i	$-0.635227\pi$
$79$	−6.21907e57	−0.824326	−0.412163	+	0.911110i	$0.635227\pi$
$80$	−6.42337e56	−0.0580121
$81$	0	0
$82$	−9.04662e57	−0.384737
$83$	1.18158e58	0.347202	0.173601	−	0.984816i	$-0.444460\pi$
$83$	1.18158e58	0.347202	0.173601	+	0.984816i	$0.444460\pi$
$84$	0	0
$85$	−3.84049e57	−0.0545895
$86$	−2.94414e58	−0.292925
$87$	0	0
$88$	−2.39753e59	−1.18316
$89$	8.44939e58	0.295414	0.147707	−	0.989031i	$-0.452811\pi$
$89$	8.44939e58	0.295414	0.147707	+	0.989031i	$0.452811\pi$
$90$	0	0
$91$	4.87546e59	0.865472
$92$	−2.45893e59	−0.312764
$93$	0	0
$94$	9.78147e59	0.645661
$95$	−3.39899e59	−0.162472
$96$	0	0
$97$	8.57527e59	0.217125	0.108563	−	0.994090i	$-0.465375\pi$
$97$	8.57527e59	0.217125	0.108563	+	0.994090i	$0.465375\pi$
$98$	2.26041e59	0.0418593
$99$	0	0
$100$	8.18562e60	0.818562
$101$	4.46035e59	0.0329281	0.0164641	−	0.999864i	$-0.494759\pi$
$101$	4.46035e59	0.0329281	0.0164641	+	0.999864i	$0.494759\pi$
$102$	0	0
$103$	1.96351e61	0.797074	0.398537	−	0.917152i	$-0.369518\pi$
$103$	1.96351e61	0.797074	0.398537	+	0.917152i	$0.369518\pi$
$104$	−2.06306e61	−0.623728
$105$	0	0
$106$	−1.64194e61	−0.277670
$107$	−1.32237e61	−0.167937	−0.0839687	−	0.996468i	$-0.526760\pi$
$107$	−1.32237e61	−0.167937	−0.0839687	+	0.996468i	$0.526760\pi$
$108$	0	0
$109$	−1.12679e62	−0.813455	−0.406728	−	0.913549i	$-0.633330\pi$
$109$	−1.12679e62	−0.813455	−0.406728	+	0.913549i	$0.633330\pi$
$110$	−1.33016e61	−0.0726819
$111$	0	0
$112$	1.71793e62	0.541821
$113$	6.52796e62	1.56995	0.784973	−	0.619530i	$-0.212677\pi$
$113$	6.52796e62	1.56995	0.784973	+	0.619530i	$0.212677\pi$
$114$	0	0
$115$	−3.00978e61	−0.0423888
$116$	2.36890e62	0.256199
$117$	0	0
$118$	−3.67591e62	−0.236028
$119$	1.02714e63	0.509855
$120$	0	0
$121$	4.84809e63	1.44749
$122$	−4.39417e62	−0.102071
$123$	0	0
$124$	−4.16628e63	−0.589369
$125$	2.01669e63	0.223297
$126$	0	0
$127$	9.36757e63	0.639166	0.319583	−	0.947558i	$-0.396457\pi$
$127$	9.36757e63	0.639166	0.319583	+	0.947558i	$0.396457\pi$
$128$	−1.89418e64	−1.01746
$129$	0	0
$130$	−1.14459e63	−0.0383158
$131$	−2.23839e63	−0.0593144	−0.0296572	−	0.999560i	$-0.509442\pi$
$131$	−2.23839e63	−0.0593144	−0.0296572	+	0.999560i	$0.509442\pi$
$132$	0	0
$133$	9.09058e64	1.51746
$134$	−3.54827e64	−0.471324
$135$	0	0
$136$	−4.34636e64	−0.367442
$137$	3.22204e64	0.217848	0.108924	−	0.994050i	$-0.465259\pi$
$137$	3.22204e64	0.217848	0.108924	+	0.994050i	$0.465259\pi$
$138$	0	0
$139$	−4.43557e65	−1.92752	−0.963758	−	0.266776i	$-0.914042\pi$
$139$	−4.43557e65	−1.92752	−0.963758	+	0.266776i	$0.914042\pi$
$140$	2.79909e64	0.0977490
$141$	0	0
$142$	2.99174e65	0.677843
$143$	7.05380e65	1.29025
$144$	0	0
$145$	2.89958e64	0.0347226
$146$	3.06175e65	0.297309
$147$	0	0
$148$	−9.81223e65	−0.629195
$149$	−1.19782e66	−0.625478	−0.312739	−	0.949839i	$-0.601246\pi$
$149$	−1.19782e66	−0.625478	−0.312739	+	0.949839i	$0.601246\pi$
$150$	0	0
$151$	−3.40521e66	−1.18399	−0.591994	−	0.805943i	$-0.701659\pi$
$151$	−3.40521e66	−1.18399	−0.591994	+	0.805943i	$0.701659\pi$
$152$	−3.84670e66	−1.09360
$153$	0	0
$154$	3.55750e66	0.678833
$155$	−5.09962e65	−0.0798768
$156$	0	0
$157$	6.21574e66	0.658496	0.329248	−	0.944243i	$-0.393205\pi$
$157$	6.21574e66	0.658496	0.329248	+	0.944243i	$0.393205\pi$
$158$	−3.90483e66	−0.340849
$159$	0	0
$160$	−1.83202e66	−0.108961
$161$	8.04965e66	0.395902
$162$	0	0
$163$	1.73234e67	0.584670	0.292335	−	0.956316i	$-0.405568\pi$
$163$	1.73234e67	0.584670	0.292335	+	0.956316i	$0.405568\pi$
$164$	2.75428e67	0.771385
$165$	0	0
$166$	7.41893e66	0.143564
$167$	−3.54014e67	−0.570385	−0.285193	−	0.958470i	$-0.592058\pi$
$167$	−3.54014e67	−0.570385	−0.285193	+	0.958470i	$0.592058\pi$
$168$	0	0
$169$	−2.85395e67	−0.319817
$170$	−2.41137e66	−0.0225721
$171$	0	0
$172$	8.96357e67	0.587304
$173$	1.75625e68	0.964231	0.482116	−	0.876108i	$-0.339869\pi$
$173$	1.75625e68	0.964231	0.482116	+	0.876108i	$0.339869\pi$
$174$	0	0
$175$	−2.67968e68	−1.03615
$176$	2.48549e68	0.807749
$177$	0	0
$178$	5.30521e67	0.122150
$179$	−4.59004e68	−0.890839	−0.445419	−	0.895322i	$-0.646945\pi$
$179$	−4.59004e68	−0.890839	−0.445419	+	0.895322i	$0.646945\pi$
$180$	0	0
$181$	4.08776e68	0.565312	0.282656	−	0.959221i	$-0.408784\pi$
$181$	4.08776e68	0.565312	0.282656	+	0.959221i	$0.408784\pi$
$182$	3.06121e68	0.357862
$183$	0	0
$184$	−3.40623e68	−0.285319
$185$	−1.20104e68	−0.0852745
$186$	0	0
$187$	1.48606e69	0.760094
$188$	−2.97801e69	−1.29453
$189$	0	0
$190$	−2.13416e68	−0.0671803
$191$	6.52737e69	1.75074	0.875368	−	0.483457i	$-0.160619\pi$
$191$	6.52737e69	1.75074	0.875368	+	0.483457i	$0.160619\pi$
$192$	0	0
$193$	3.40957e69	0.665582	0.332791	−	0.943001i	$-0.392010\pi$
$193$	3.40957e69	0.665582	0.332791	+	0.943001i	$0.392010\pi$
$194$	5.38425e68	0.0897785
$195$	0	0
$196$	−6.88191e68	−0.0839264
$197$	−5.81412e69	−0.607105	−0.303552	−	0.952815i	$-0.598173\pi$
$197$	−5.81412e69	−0.607105	−0.303552	+	0.952815i	$0.598173\pi$
$198$	0	0
$199$	−1.86375e70	−1.43011	−0.715055	−	0.699068i	$-0.753599\pi$
$199$	−1.86375e70	−1.43011	−0.715055	+	0.699068i	$0.753599\pi$
$200$	1.13391e70	0.746733
$201$	0	0
$202$	2.80057e68	0.0136154
$203$	−7.75493e69	−0.324301
$204$	0	0
$205$	3.37130e69	0.104545
$206$	1.23285e70	0.329580
$207$	0	0
$208$	2.13875e70	0.425822
$209$	1.31522e71	2.26223
$210$	0	0
$211$	1.02222e71	1.31501	0.657506	−	0.753449i	$-0.271611\pi$
$211$	1.02222e71	1.31501	0.657506	+	0.753449i	$0.271611\pi$
$212$	4.99895e70	0.556718
$213$	0	0
$214$	−8.30290e69	−0.0694400
$215$	1.09716e70	0.0795971
$216$	0	0
$217$	1.36389e71	0.746032
$218$	−7.07488e70	−0.336353
$219$	0	0
$220$	4.04972e70	0.145725
$221$	1.27874e71	0.400700
$222$	0	0
$223$	4.66041e71	1.10950	0.554748	−	0.832019i	$-0.312815\pi$
$223$	4.66041e71	1.10950	0.554748	+	0.832019i	$0.312815\pi$
$224$	4.89974e71	1.01767
$225$	0	0
$226$	4.09878e71	0.649153
$227$	4.66130e71	0.645236	0.322618	−	0.946529i	$-0.395437\pi$
$227$	4.66130e71	0.645236	0.322618	+	0.946529i	$0.395437\pi$
$228$	0	0
$229$	−8.29575e71	−0.878767	−0.439383	−	0.898300i	$-0.644803\pi$
$229$	−8.29575e71	−0.878767	−0.439383	+	0.898300i	$0.644803\pi$
$230$	−1.88978e70	−0.0175272
$231$	0	0
$232$	3.28152e71	0.233718
$233$	2.87441e72	1.79553	0.897767	−	0.440471i	$-0.145188\pi$
$233$	2.87441e72	1.79553	0.897767	+	0.440471i	$0.145188\pi$
$234$	0	0
$235$	−3.64515e71	−0.175447
$236$	1.11915e72	0.473228
$237$	0	0
$238$	6.44920e71	0.210818
$239$	5.74905e72	1.65371	0.826857	−	0.562412i	$-0.190127\pi$
$239$	5.74905e72	1.65371	0.826857	+	0.562412i	$0.190127\pi$
$240$	0	0
$241$	1.60687e72	0.358476	0.179238	−	0.983806i	$-0.442637\pi$
$241$	1.60687e72	0.358476	0.179238	+	0.983806i	$0.442637\pi$
$242$	3.04402e72	0.598520
$243$	0	0
$244$	1.33782e72	0.204649
$245$	−8.42361e70	−0.0113745
$246$	0	0
$247$	1.13174e73	1.19258
$248$	−5.77134e72	−0.537651
$249$	0	0
$250$	1.26624e72	0.0923305
$251$	2.02500e73	1.30730	0.653651	−	0.756796i	$-0.273236\pi$
$251$	2.02500e73	1.30730	0.653651	+	0.756796i	$0.273236\pi$
$252$	0	0
$253$	1.16462e73	0.590213
$254$	5.88172e72	0.264287
$255$	0	0
$256$	−8.63288e72	−0.305377
$257$	−1.08823e73	−0.341790	−0.170895	−	0.985289i	$-0.554666\pi$
$257$	−1.08823e73	−0.341790	−0.170895	+	0.985289i	$0.554666\pi$
$258$	0	0
$259$	3.21217e73	0.796446
$260$	3.48476e72	0.0768219
$261$	0	0
$262$	−1.40544e72	−0.0245258
$263$	1.14768e74	1.78307	0.891536	−	0.452950i	$-0.149628\pi$
$263$	1.14768e74	1.78307	0.891536	+	0.452950i	$0.149628\pi$
$264$	0	0
$265$	6.11883e72	0.0754517
$266$	5.70780e73	0.627449
$267$	0	0
$268$	1.08028e74	0.944989
$269$	−1.34285e72	−0.0104853	−0.00524267	−	0.999986i	$-0.501669\pi$
$269$	−1.34285e72	−0.0104853	−0.00524267	+	0.999986i	$0.501669\pi$
$270$	0	0
$271$	−3.00222e74	−1.87016	−0.935080	−	0.354437i	$-0.884673\pi$
$271$	−3.00222e74	−1.87016	−0.935080	+	0.354437i	$0.884673\pi$
$272$	4.50582e73	0.250855
$273$	0	0
$274$	2.02306e73	0.0900775
$275$	−3.87695e74	−1.54470
$276$	0	0
$277$	−8.70383e73	−0.278021	−0.139011	−	0.990291i	$-0.544392\pi$
$277$	−8.70383e73	−0.278021	−0.139011	+	0.990291i	$0.544392\pi$
$278$	−2.78501e74	−0.797004
$279$	0	0
$280$	3.87744e73	0.0891714
$281$	1.17276e74	0.241917	0.120959	−	0.992658i	$-0.461403\pi$
$281$	1.17276e74	0.241917	0.120959	+	0.992658i	$0.461403\pi$
$282$	0	0
$283$	−1.34561e74	−0.223580	−0.111790	−	0.993732i	$-0.535658\pi$
$283$	−1.34561e74	−0.223580	−0.111790	+	0.993732i	$0.535658\pi$
$284$	−9.10848e74	−1.35905
$285$	0	0
$286$	4.42894e74	0.533502
$287$	−9.01653e74	−0.976431
$288$	0	0
$289$	−8.71859e74	−0.763945
$290$	1.82059e73	0.0143573
$291$	0	0
$292$	−9.32164e74	−0.596095
$293$	−3.33052e74	−0.191889	−0.0959445	−	0.995387i	$-0.530587\pi$
$293$	−3.33052e74	−0.191889	−0.0959445	+	0.995387i	$0.530587\pi$
$294$	0	0
$295$	1.36986e74	0.0641364
$296$	−1.35924e75	−0.573983
$297$	0	0
$298$	−7.52090e74	−0.258627
$299$	1.00215e75	0.311144
$300$	0	0
$301$	−2.93435e75	−0.743419
$302$	−2.13807e75	−0.489564
$303$	0	0
$304$	3.98783e75	0.746607
$305$	1.63752e74	0.0277359
$306$	0	0
$307$	−1.19531e76	−1.65868	−0.829338	−	0.558748i	$-0.811282\pi$
$307$	−1.19531e76	−1.65868	−0.829338	+	0.558748i	$0.811282\pi$
$308$	−1.08310e76	−1.36104
$309$	0	0
$310$	−3.20195e74	−0.0330280
$311$	3.79842e75	0.355150	0.177575	−	0.984107i	$-0.443175\pi$
$311$	3.79842e75	0.355150	0.177575	+	0.984107i	$0.443175\pi$
$312$	0	0
$313$	1.65384e76	1.27172	0.635861	−	0.771804i	$-0.280645\pi$
$313$	1.65384e76	1.27172	0.635861	+	0.771804i	$0.280645\pi$
$314$	3.90274e75	0.272280
$315$	0	0
$316$	1.18884e76	0.683390
$317$	−2.82467e76	−1.47455	−0.737275	−	0.675592i	$-0.763888\pi$
$317$	−2.82467e76	−1.47455	−0.737275	+	0.675592i	$0.763888\pi$
$318$	0	0
$319$	−1.12198e76	−0.483470
$320$	3.30836e74	0.0129580
$321$	0	0
$322$	5.05422e75	0.163701
$323$	2.38429e76	0.702559
$324$	0	0
$325$	−3.33609e76	−0.814321
$326$	1.08770e76	0.241754
$327$	0	0
$328$	3.81537e76	0.703695
$329$	9.74894e76	1.63864
$330$	0	0
$331$	1.56426e75	0.0218553	0.0109276	−	0.999940i	$-0.496522\pi$
$331$	1.56426e75	0.0218553	0.0109276	+	0.999940i	$0.496522\pi$
$332$	−2.25872e76	−0.287840
$333$	0	0
$334$	−2.22279e76	−0.235847
$335$	1.32229e76	0.128074
$336$	0	0
$337$	4.48909e76	0.362615	0.181308	−	0.983426i	$-0.441967\pi$
$337$	4.48909e76	0.362615	0.181308	+	0.983426i	$0.441967\pi$
$338$	−1.79194e76	−0.132240
$339$	0	0
$340$	7.34152e75	0.0452563
$341$	1.97327e77	1.11219
$342$	0	0
$343$	−2.00012e77	−0.943162
$344$	1.24168e77	0.535768
$345$	0	0
$346$	1.10272e77	0.398697
$347$	2.97382e77	0.984615	0.492307	−	0.870421i	$-0.336154\pi$
$347$	2.97382e77	0.984615	0.492307	+	0.870421i	$0.336154\pi$
$348$	0	0
$349$	5.36967e77	1.49201	0.746005	−	0.665940i	$-0.231969\pi$
$349$	5.36967e77	1.49201	0.746005	+	0.665940i	$0.231969\pi$
$350$	−1.68252e77	−0.428435
$351$	0	0
$352$	7.08893e77	1.51715
$353$	7.22267e77	1.41765	0.708825	−	0.705384i	$-0.249226\pi$
$353$	7.22267e77	1.41765	0.708825	+	0.705384i	$0.249226\pi$
$354$	0	0
$355$	−1.11490e77	−0.184192
$356$	−1.61519e77	−0.244906
$357$	0	0
$358$	−2.88200e77	−0.368351
$359$	−7.97496e77	−0.936155	−0.468078	−	0.883687i	$-0.655053\pi$
$359$	−7.97496e77	−0.936155	−0.468078	+	0.883687i	$0.655053\pi$
$360$	0	0
$361$	1.10101e78	1.09099
$362$	2.56662e77	0.233750
$363$	0	0
$364$	−9.31997e77	−0.717500
$365$	−1.14099e77	−0.0807884
$366$	0	0
$367$	−2.30364e78	−1.38070	−0.690350	−	0.723476i	$-0.742543\pi$
$367$	−2.30364e78	−1.38070	−0.690350	+	0.723476i	$0.742543\pi$
$368$	3.53120e77	0.194789
$369$	0	0
$370$	−7.54109e76	−0.0352599
$371$	−1.63648e78	−0.704703
$372$	0	0
$373$	3.65569e77	0.133613	0.0668067	−	0.997766i	$-0.478719\pi$
$373$	3.65569e77	0.133613	0.0668067	+	0.997766i	$0.478719\pi$
$374$	9.33068e77	0.314289
$375$	0	0
$376$	−4.12529e78	−1.18093
$377$	−9.65457e77	−0.254872
$378$	0	0
$379$	−1.75228e78	−0.393647	−0.196823	−	0.980439i	$-0.563063\pi$
$379$	−1.75228e78	−0.393647	−0.196823	+	0.980439i	$0.563063\pi$
$380$	6.49753e77	0.134694
$381$	0	0
$382$	4.09841e78	0.723907
$383$	−1.06584e79	−1.73832	−0.869158	−	0.494534i	$-0.835339\pi$
$383$	−1.06584e79	−1.73832	−0.869158	+	0.494534i	$0.835339\pi$
$384$	0	0
$385$	−1.32573e78	−0.184461
$386$	2.14080e78	0.275210
$387$	0	0
$388$	−1.63926e78	−0.180003
$389$	−1.40497e79	−1.42628	−0.713140	−	0.701021i	$-0.752728\pi$
$389$	−1.40497e79	−1.42628	−0.713140	+	0.701021i	$0.752728\pi$
$390$	0	0
$391$	2.11128e78	0.183297
$392$	−9.53317e77	−0.0765618
$393$	0	0
$394$	−3.65057e78	−0.251030
$395$	1.45517e78	0.0926194
$396$	0	0
$397$	5.99515e78	0.327107	0.163553	−	0.986534i	$-0.447704\pi$
$397$	5.99515e78	0.327107	0.163553	+	0.986534i	$0.447704\pi$
$398$	−1.17021e79	−0.591333
$399$	0	0
$400$	−1.17551e79	−0.509798
$401$	−1.50995e79	−0.606818	−0.303409	−	0.952860i	$-0.598125\pi$
$401$	−1.50995e79	−0.606818	−0.303409	+	0.952860i	$0.598125\pi$
$402$	0	0
$403$	1.69799e79	0.586314
$404$	−8.52644e77	−0.0272983
$405$	0	0
$406$	−4.86917e78	−0.134094
$407$	4.64736e79	1.18735
$408$	0	0
$409$	−2.38844e79	−0.525476	−0.262738	−	0.964867i	$-0.584626\pi$
$409$	−2.38844e79	−0.525476	−0.262738	+	0.964867i	$0.584626\pi$
$410$	2.11677e78	0.0432282
$411$	0	0
$412$	−3.75347e79	−0.660796
$413$	−3.66368e79	−0.599020
$414$	0	0
$415$	−2.76473e78	−0.0390108
$416$	6.09998e79	0.799801
$417$	0	0
$418$	8.25802e79	0.935405
$419$	1.50267e80	1.58247	0.791233	−	0.611514i	$-0.209439\pi$
$419$	1.50267e80	1.58247	0.791233	+	0.611514i	$0.209439\pi$
$420$	0	0
$421$	6.15744e79	0.560785	0.280392	−	0.959885i	$-0.409535\pi$
$421$	6.15744e79	0.560785	0.280392	+	0.959885i	$0.409535\pi$
$422$	6.41833e79	0.543741
$423$	0	0
$424$	6.92480e79	0.507865
$425$	−7.02832e79	−0.479721
$426$	0	0
$427$	−4.37955e79	−0.259047
$428$	2.52785e79	0.139225
$429$	0	0
$430$	6.88886e78	0.0329124
$431$	−2.96244e80	−1.31854	−0.659269	−	0.751907i	$-0.729134\pi$
$431$	−2.96244e80	−1.31854	−0.659269	+	0.751907i	$0.729134\pi$
$432$	0	0
$433$	−2.82927e80	−1.09344	−0.546719	−	0.837316i	$-0.684123\pi$
$433$	−2.82927e80	−1.09344	−0.546719	+	0.837316i	$0.684123\pi$
$434$	8.56360e79	0.308475
$435$	0	0
$436$	2.15398e80	0.674377
$437$	1.86857e80	0.545537
$438$	0	0
$439$	6.24335e80	1.58580	0.792902	−	0.609349i	$-0.208569\pi$
$439$	6.24335e80	1.58580	0.792902	+	0.609349i	$0.208569\pi$
$440$	5.60987e79	0.132937
$441$	0	0
$442$	8.02899e79	0.165684
$443$	7.11121e80	1.36971	0.684857	−	0.728678i	$-0.259865\pi$
$443$	7.11121e80	1.36971	0.684857	+	0.728678i	$0.259865\pi$
$444$	0	0
$445$	−1.97703e79	−0.0331920
$446$	2.92618e80	0.458762
$447$	0	0
$448$	−8.84821e79	−0.121025
$449$	1.48296e81	1.89503	0.947514	−	0.319714i	$-0.103587\pi$
$449$	1.48296e81	1.89503	0.947514	+	0.319714i	$0.103587\pi$
$450$	0	0
$451$	−1.30451e81	−1.45567
$452$	−1.24789e81	−1.30153
$453$	0	0
$454$	2.92674e80	0.266797
$455$	−1.14078e80	−0.0972424
$456$	0	0
$457$	8.32281e80	0.620620	0.310310	−	0.950635i	$-0.399567\pi$
$457$	8.32281e80	0.620620	0.310310	+	0.950635i	$0.399567\pi$
$458$	−5.20874e80	−0.363359
$459$	0	0
$460$	5.75353e79	0.0351415
$461$	−1.90621e81	−1.08966	−0.544832	−	0.838545i	$-0.683406\pi$
$461$	−1.90621e81	−1.08966	−0.544832	+	0.838545i	$0.683406\pi$
$462$	0	0
$463$	−7.11693e80	−0.356511	−0.178255	−	0.983984i	$-0.557045\pi$
$463$	−7.11693e80	−0.356511	−0.178255	+	0.983984i	$0.557045\pi$
$464$	−3.40191e80	−0.159560
$465$	0	0
$466$	1.80479e81	0.742431
$467$	−1.96641e81	−0.757721	−0.378860	−	0.925454i	$-0.623684\pi$
$467$	−1.96641e81	−0.757721	−0.378860	+	0.925454i	$0.623684\pi$
$468$	0	0
$469$	−3.53646e81	−1.19618
$470$	−2.28872e80	−0.0725451
$471$	0	0
$472$	1.55030e81	0.431702
$473$	−4.24541e81	−1.10829
$474$	0	0
$475$	−6.22034e81	−1.42777
$476$	−1.96349e81	−0.422684
$477$	0	0
$478$	3.60972e81	0.683790
$479$	−2.12205e81	−0.377158	−0.188579	−	0.982058i	$-0.560388\pi$
$479$	−2.12205e81	−0.377158	−0.188579	+	0.982058i	$0.560388\pi$
$480$	0	0
$481$	3.99902e81	0.625935
$482$	1.00892e81	0.148225
$483$	0	0
$484$	−9.26765e81	−1.20001
$485$	−2.00649e80	−0.0243957
$486$	0	0
$487$	−6.70124e81	−0.718658	−0.359329	−	0.933211i	$-0.616994\pi$
$487$	−6.70124e81	−0.718658	−0.359329	+	0.933211i	$0.616994\pi$
$488$	1.85322e81	0.186690
$489$	0	0
$490$	−5.28902e79	−0.00470321
$491$	−8.10525e81	−0.677300	−0.338650	−	0.940912i	$-0.609970\pi$
$491$	−8.10525e81	−0.677300	−0.338650	+	0.940912i	$0.609970\pi$
$492$	0	0
$493$	−2.03398e81	−0.150147
$494$	7.10597e81	0.493119
$495$	0	0
$496$	5.98307e81	0.367057
$497$	2.98179e82	1.72031
$498$	0	0
$499$	6.93437e81	0.353949	0.176974	−	0.984215i	$-0.443369\pi$
$499$	6.93437e81	0.353949	0.176974	+	0.984215i	$0.443369\pi$
$500$	−3.85512e81	−0.185120
$501$	0	0
$502$	1.27146e82	0.540553
$503$	−4.44563e82	−1.77873	−0.889364	−	0.457200i	$-0.848853\pi$
$503$	−4.44563e82	−1.77873	−0.889364	+	0.457200i	$0.848853\pi$
$504$	0	0
$505$	−1.04366e80	−0.00369973
$506$	7.31243e81	0.244046
$507$	0	0
$508$	−1.79071e82	−0.529886
$509$	1.53808e82	0.428635	0.214317	−	0.976764i	$-0.431247\pi$
$509$	1.53808e82	0.428635	0.214317	+	0.976764i	$0.431247\pi$
$510$	0	0
$511$	3.05157e82	0.754546
$512$	3.82563e82	0.891187
$513$	0	0
$514$	−6.83276e81	−0.141326
$515$	−4.59433e81	−0.0895574
$516$	0	0
$517$	1.41047e83	2.44289
$518$	2.01686e82	0.329320
$519$	0	0
$520$	4.82726e81	0.0700807
$521$	1.18328e83	1.62009	0.810044	−	0.586369i	$-0.199443\pi$
$521$	1.18328e83	1.62009	0.810044	+	0.586369i	$0.199443\pi$
$522$	0	0
$523$	−9.45207e82	−1.15140	−0.575699	−	0.817662i	$-0.695270\pi$
$523$	−9.45207e82	−1.15140	−0.575699	+	0.817662i	$0.695270\pi$
$524$	4.27892e81	0.0491733
$525$	0	0
$526$	7.20603e82	0.737278
$527$	3.57724e82	0.345401
$528$	0	0
$529$	−9.97053e82	−0.857670
$530$	3.84189e81	0.0311983
$531$	0	0
$532$	−1.73776e83	−1.25801
$533$	−1.12252e83	−0.767387
$534$	0	0
$535$	3.09415e81	0.0188691
$536$	1.49646e83	0.862065
$537$	0	0
$538$	−8.43148e80	−0.00433555
$539$	3.25948e82	0.158376
$540$	0	0
$541$	1.48411e82	0.0644093	0.0322046	−	0.999481i	$-0.489747\pi$
$541$	1.48411e82	0.0644093	0.0322046	+	0.999481i	$0.489747\pi$
$542$	−1.88503e83	−0.773287
$543$	0	0
$544$	1.28511e83	0.471167
$545$	2.63651e82	0.0913980
$546$	0	0
$547$	3.24255e83	1.00525	0.502624	−	0.864505i	$-0.332368\pi$
$547$	3.24255e83	1.00525	0.502624	+	0.864505i	$0.332368\pi$
$548$	−6.15929e82	−0.180602
$549$	0	0
$550$	−2.43426e83	−0.638713
$551$	−1.80015e83	−0.446874
$552$	0	0
$553$	−3.89185e83	−0.865046
$554$	−5.46497e82	−0.114958
$555$	0	0
$556$	8.47908e83	1.59797
$557$	−4.33577e83	−0.773540	−0.386770	−	0.922176i	$-0.626409\pi$
$557$	−4.33577e83	−0.773540	−0.386770	+	0.922176i	$0.626409\pi$
$558$	0	0
$559$	−3.65315e83	−0.584261
$560$	−4.01970e82	−0.0608777
$561$	0	0
$562$	7.36355e82	0.100030
$563$	−8.30382e83	−1.06849	−0.534247	−	0.845328i	$-0.679405\pi$
$563$	−8.30382e83	−1.06849	−0.534247	+	0.845328i	$0.679405\pi$
$564$	0	0
$565$	−1.52744e83	−0.176396
$566$	−8.44882e82	−0.0924474
$567$	0	0
$568$	−1.26175e84	−1.23979
$569$	1.27745e84	1.18965	0.594826	−	0.803854i	$-0.297221\pi$
$569$	1.27745e84	1.18965	0.594826	+	0.803854i	$0.297221\pi$
$570$	0	0
$571$	8.91829e83	0.746243	0.373121	−	0.927783i	$-0.378288\pi$
$571$	8.91829e83	0.746243	0.373121	+	0.927783i	$0.378288\pi$
$572$	−1.34841e84	−1.06965
$573$	0	0
$574$	−5.66131e83	−0.403742
$575$	−5.50807e83	−0.372504
$576$	0	0
$577$	−1.15402e84	−0.702023	−0.351012	−	0.936371i	$-0.614162\pi$
$577$	−1.15402e84	−0.702023	−0.351012	+	0.936371i	$0.614162\pi$
$578$	−5.47424e83	−0.315882
$579$	0	0
$580$	−5.54287e82	−0.0287860
$581$	7.39425e83	0.364353
$582$	0	0
$583$	−2.36765e84	−1.05057
$584$	−1.29128e84	−0.543787
$585$	0	0
$586$	−2.09117e83	−0.0793437
$587$	1.26376e84	0.455200	0.227600	−	0.973755i	$-0.426912\pi$
$587$	1.26376e84	0.455200	0.227600	+	0.973755i	$0.426912\pi$
$588$	0	0
$589$	3.16600e84	1.02800
$590$	8.60108e82	0.0265196
$591$	0	0
$592$	1.40911e84	0.391861
$593$	2.81980e84	0.744818	0.372409	−	0.928069i	$-0.378532\pi$
$593$	2.81980e84	0.744818	0.372409	+	0.928069i	$0.378532\pi$
$594$	0	0
$595$	−2.40335e83	−0.0572861
$596$	2.28977e84	0.518539
$597$	0	0
$598$	6.29230e83	0.128654
$599$	−2.57638e84	−0.500602	−0.250301	−	0.968168i	$-0.580530\pi$
$599$	−2.57638e84	−0.500602	−0.250301	+	0.968168i	$0.580530\pi$
$600$	0	0
$601$	1.93837e84	0.340224	0.170112	−	0.985425i	$-0.445587\pi$
$601$	1.93837e84	0.340224	0.170112	+	0.985425i	$0.445587\pi$
$602$	−1.84242e84	−0.307395
$603$	0	0
$604$	6.50943e84	0.981559
$605$	−1.13438e84	−0.162637
$606$	0	0
$607$	9.64610e83	0.125054	0.0625269	−	0.998043i	$-0.480084\pi$
$607$	9.64610e83	0.125054	0.0625269	+	0.998043i	$0.480084\pi$
$608$	1.13738e85	1.40231
$609$	0	0
$610$	1.02817e83	0.0114684
$611$	1.21370e85	1.28782
$612$	0	0
$613$	1.07878e85	1.03607	0.518034	−	0.855360i	$-0.326664\pi$
$613$	1.07878e85	1.03607	0.518034	+	0.855360i	$0.326664\pi$
$614$	−7.50514e84	−0.685841
$615$	0	0
$616$	−1.50036e85	−1.24160
$617$	3.73172e84	0.293908	0.146954	−	0.989143i	$-0.453053\pi$
$617$	3.73172e84	0.293908	0.146954	+	0.989143i	$0.453053\pi$
$618$	0	0
$619$	−8.80827e84	−0.628529	−0.314265	−	0.949335i	$-0.601758\pi$
$619$	−8.80827e84	−0.628529	−0.314265	+	0.949335i	$0.601758\pi$
$620$	9.74847e83	0.0662201
$621$	0	0
$622$	2.38496e84	0.146850
$623$	5.28757e84	0.310006
$624$	0	0
$625$	1.80986e85	0.962287
$626$	1.03842e85	0.525841
$627$	0	0
$628$	−1.18821e85	−0.545912
$629$	8.42495e84	0.368742
$630$	0	0
$631$	1.68356e85	0.668856	0.334428	−	0.942421i	$-0.391457\pi$
$631$	1.68356e85	0.668856	0.334428	+	0.942421i	$0.391457\pi$
$632$	1.64684e85	0.623422
$633$	0	0
$634$	−1.77355e85	−0.609708
$635$	−2.19187e84	−0.0718152
$636$	0	0
$637$	2.80476e84	0.0834915
$638$	−7.04470e84	−0.199909
$639$	0	0
$640$	4.43209e84	0.114319
$641$	−6.42250e85	−1.57955	−0.789777	−	0.613394i	$-0.789804\pi$
$641$	−6.42250e85	−1.57955	−0.789777	+	0.613394i	$0.789804\pi$
$642$	0	0
$643$	−3.55027e84	−0.0794011	−0.0397005	−	0.999212i	$-0.512640\pi$
$643$	−3.55027e84	−0.0794011	−0.0397005	+	0.999212i	$0.512640\pi$
$644$	−1.53878e85	−0.328214
$645$	0	0
$646$	1.49705e85	0.290499
$647$	−8.24068e85	−1.52539	−0.762697	−	0.646755i	$-0.776125\pi$
$647$	−8.24068e85	−1.52539	−0.762697	+	0.646755i	$0.776125\pi$
$648$	0	0
$649$	−5.30061e85	−0.893022
$650$	−2.09467e85	−0.336711
$651$	0	0
$652$	−3.31155e85	−0.484708
$653$	−3.96464e85	−0.553799	−0.276899	−	0.960899i	$-0.589307\pi$
$653$	−3.96464e85	−0.553799	−0.276899	+	0.960899i	$0.589307\pi$
$654$	0	0
$655$	5.23749e83	0.00666443
$656$	−3.95534e85	−0.480416
$657$	0	0
$658$	6.12117e85	0.677555
$659$	8.56515e85	0.905169	0.452585	−	0.891721i	$-0.350502\pi$
$659$	8.56515e85	0.905169	0.452585	+	0.891721i	$0.350502\pi$
$660$	0	0
$661$	−1.49484e86	−1.44029	−0.720144	−	0.693825i	$-0.755924\pi$
$661$	−1.49484e86	−1.44029	−0.720144	+	0.693825i	$0.755924\pi$
$662$	9.82171e83	0.00903688
$663$	0	0
$664$	−3.12890e85	−0.262582
$665$	−2.12706e85	−0.170498
$666$	0	0
$667$	−1.59402e85	−0.116589
$668$	6.76737e85	0.472865
$669$	0	0
$670$	8.30241e84	0.0529569
$671$	−6.33632e85	−0.386189
$672$	0	0
$673$	9.30605e85	0.517972	0.258986	−	0.965881i	$-0.416612\pi$
$673$	9.30605e85	0.517972	0.258986	+	0.965881i	$0.416612\pi$
$674$	2.81861e85	0.149937
$675$	0	0
$676$	5.45563e85	0.265137
$677$	−1.12642e85	−0.0523293	−0.0261646	−	0.999658i	$-0.508329\pi$
$677$	−1.12642e85	−0.0523293	−0.0261646	+	0.999658i	$0.508329\pi$
$678$	0	0
$679$	5.36634e85	0.227851
$680$	1.01698e85	0.0412850
$681$	0	0
$682$	1.23898e86	0.459876
$683$	3.40704e86	1.20933	0.604666	−	0.796479i	$-0.293307\pi$
$683$	3.40704e86	1.20933	0.604666	+	0.796479i	$0.293307\pi$
$684$	0	0
$685$	−7.53910e84	−0.0244769
$686$	−1.25584e86	−0.389986
$687$	0	0
$688$	−1.28723e86	−0.365771
$689$	−2.03735e86	−0.553833
$690$	0	0
$691$	−4.85715e85	−0.120865	−0.0604326	−	0.998172i	$-0.519248\pi$
$691$	−4.85715e85	−0.120865	−0.0604326	+	0.998172i	$0.519248\pi$
$692$	−3.35727e86	−0.799375
$693$	0	0
$694$	1.86721e86	0.407126
$695$	1.03786e86	0.216571
$696$	0	0
$697$	−2.36487e86	−0.452073
$698$	3.37151e86	0.616927
$699$	0	0
$700$	5.12250e86	0.858997
$701$	9.30644e86	1.49411	0.747057	−	0.664759i	$-0.231466\pi$
$701$	9.30644e86	1.49411	0.747057	+	0.664759i	$0.231466\pi$
$702$	0	0
$703$	7.45642e86	1.09747
$704$	−1.28016e86	−0.180425
$705$	0	0
$706$	4.53497e86	0.586180
$707$	2.79125e85	0.0345547
$708$	0	0
$709$	−1.39697e87	−1.58663	−0.793316	−	0.608810i	$-0.791647\pi$
$709$	−1.39697e87	−1.58663	−0.793316	+	0.608810i	$0.791647\pi$
$710$	−7.00023e85	−0.0761610
$711$	0	0
$712$	−2.23745e86	−0.223415
$713$	2.80347e86	0.268204
$714$	0	0
$715$	−1.65048e86	−0.144970
$716$	8.77436e86	0.738530
$717$	0	0
$718$	−5.00732e86	−0.387088
$719$	1.38529e87	1.02639	0.513193	−	0.858273i	$-0.328463\pi$
$719$	1.38529e87	1.02639	0.513193	+	0.858273i	$0.328463\pi$
$720$	0	0
$721$	1.22875e87	0.836447
$722$	6.91304e86	0.451112
$723$	0	0
$724$	−7.81419e86	−0.468660
$725$	5.30641e86	0.305134
$726$	0	0
$727$	3.07878e85	0.0162772	0.00813860	−	0.999967i	$-0.497409\pi$
$727$	3.07878e85	0.0162772	0.00813860	+	0.999967i	$0.497409\pi$
$728$	−1.29105e87	−0.654539
$729$	0	0
$730$	−7.16405e85	−0.0334050
$731$	−7.69627e86	−0.344192
$732$	0	0
$733$	2.95619e87	1.21636	0.608178	−	0.793801i	$-0.291901\pi$
$733$	2.95619e87	1.21636	0.608178	+	0.793801i	$0.291901\pi$
$734$	−1.44641e87	−0.570902
$735$	0	0
$736$	1.00714e87	0.365862
$737$	−5.11654e87	−1.78328
$738$	0	0
$739$	−2.83483e87	−0.909646	−0.454823	−	0.890582i	$-0.650297\pi$
$739$	−2.83483e87	−0.909646	−0.454823	+	0.890582i	$0.650297\pi$
$740$	2.29592e86	0.0706950
$741$	0	0
$742$	−1.02751e87	−0.291386
$743$	−4.13337e87	−1.12498	−0.562491	−	0.826804i	$-0.690157\pi$
$743$	−4.13337e87	−1.12498	−0.562491	+	0.826804i	$0.690157\pi$
$744$	0	0
$745$	2.80273e86	0.0702773
$746$	2.29534e86	0.0552475
$747$	0	0
$748$	−2.84077e87	−0.630139
$749$	−8.27528e86	−0.176233
$750$	0	0
$751$	3.63538e87	0.713727	0.356863	−	0.934157i	$-0.383846\pi$
$751$	3.63538e87	0.713727	0.356863	+	0.934157i	$0.383846\pi$
$752$	4.27664e87	0.806229
$753$	0	0
$754$	−6.06192e86	−0.105386
$755$	7.96768e86	0.133030
$756$	0	0
$757$	−1.27239e87	−0.195972	−0.0979861	−	0.995188i	$-0.531240\pi$
$757$	−1.27239e87	−0.195972	−0.0979861	+	0.995188i	$0.531240\pi$
$758$	−1.10022e87	−0.162768
$759$	0	0
$760$	9.00071e86	0.122875
$761$	4.01227e87	0.526209	0.263104	−	0.964767i	$-0.415254\pi$
$761$	4.01227e87	0.526209	0.263104	+	0.964767i	$0.415254\pi$
$762$	0	0
$763$	−7.05135e87	−0.853638
$764$	−1.24778e88	−1.45141
$765$	0	0
$766$	−6.69219e87	−0.718772
$767$	−4.56113e87	−0.470776
$768$	0	0
$769$	−1.06276e87	−0.101317	−0.0506584	−	0.998716i	$-0.516132\pi$
$769$	−1.06276e87	−0.101317	−0.0506584	+	0.998716i	$0.516132\pi$
$770$	−8.32402e86	−0.0762721
$771$	0	0
$772$	−6.51777e87	−0.551787
$773$	1.73425e88	1.41136	0.705679	−	0.708532i	$-0.250642\pi$
$773$	1.73425e88	1.41136	0.705679	+	0.708532i	$0.250642\pi$
$774$	0	0
$775$	−9.33259e87	−0.701940
$776$	−2.27078e87	−0.164207
$777$	0	0
$778$	−8.82155e87	−0.589749
$779$	−2.09301e88	−1.34548
$780$	0	0
$781$	4.31404e88	2.56465
$782$	1.32563e87	0.0757909
$783$	0	0
$784$	9.88291e86	0.0522691
$785$	−1.45439e87	−0.0739871
$786$	0	0
$787$	7.10492e87	0.334449	0.167224	−	0.985919i	$-0.446520\pi$
$787$	7.10492e87	0.334449	0.167224	+	0.985919i	$0.446520\pi$
$788$	1.11143e88	0.503307
$789$	0	0
$790$	9.13673e86	0.0382970
$791$	4.08514e88	1.64750
$792$	0	0
$793$	−5.45236e87	−0.203588
$794$	3.76424e87	0.135255
$795$	0	0
$796$	3.56277e88	1.18560
$797$	2.01224e88	0.644467	0.322233	−	0.946660i	$-0.395566\pi$
$797$	2.01224e88	0.644467	0.322233	+	0.946660i	$0.395566\pi$
$798$	0	0
$799$	2.55697e88	0.758663
$800$	−3.35271e88	−0.957528
$801$	0	0
$802$	−9.48066e87	−0.250911
$803$	4.41500e88	1.12488
$804$	0	0
$805$	−1.88350e87	−0.0444827
$806$	1.06613e88	0.242434
$807$	0	0
$808$	−1.18113e87	−0.0249029
$809$	1.07349e88	0.217957	0.108978	−	0.994044i	$-0.465242\pi$
$809$	1.07349e88	0.217957	0.108978	+	0.994044i	$0.465242\pi$
$810$	0	0
$811$	−7.32258e87	−0.137888	−0.0689442	−	0.997621i	$-0.521963\pi$
$811$	−7.32258e87	−0.137888	−0.0689442	+	0.997621i	$0.521963\pi$
$812$	1.48244e88	0.268855
$813$	0	0
$814$	2.91799e88	0.490952
$815$	−4.05341e87	−0.0656922
$816$	0	0
$817$	−6.81151e88	−1.02440
$818$	−1.49965e88	−0.217278
$819$	0	0
$820$	−6.44461e87	−0.0866710
$821$	8.61776e88	1.11668	0.558339	−	0.829613i	$-0.311439\pi$
$821$	8.61776e88	1.11668	0.558339	+	0.829613i	$0.311439\pi$
$822$	0	0
$823$	−8.68150e87	−0.104448	−0.0522240	−	0.998635i	$-0.516631\pi$
$823$	−8.68150e87	−0.104448	−0.0522240	+	0.998635i	$0.516631\pi$
$824$	−5.19949e88	−0.602811
$825$	0	0
$826$	−2.30036e88	−0.247687
$827$	2.76062e88	0.286476	0.143238	−	0.989688i	$-0.454249\pi$
$827$	2.76062e88	0.286476	0.143238	+	0.989688i	$0.454249\pi$
$828$	0	0
$829$	−1.28246e88	−0.123632	−0.0618162	−	0.998088i	$-0.519689\pi$
$829$	−1.28246e88	−0.123632	−0.0618162	+	0.998088i	$0.519689\pi$
$830$	−1.73592e87	−0.0161305
$831$	0	0
$832$	−1.10157e88	−0.0951149
$833$	5.90893e87	0.0491854
$834$	0	0
$835$	8.28340e87	0.0640872
$836$	−2.51419e89	−1.87545
$837$	0	0
$838$	9.43495e88	0.654330
$839$	−1.98229e89	−1.32565	−0.662824	−	0.748776i	$-0.730642\pi$
$839$	−1.98229e89	−1.32565	−0.662824	+	0.748776i	$0.730642\pi$
$840$	0	0
$841$	−1.45440e89	−0.904497
$842$	3.86614e88	0.231878
$843$	0	0
$844$	−1.95409e89	−1.09018
$845$	6.67781e87	0.0359339
$846$	0	0
$847$	3.03390e89	1.51900
$848$	−7.17885e88	−0.346722
$849$	0	0
$850$	−4.41294e88	−0.198359
$851$	6.60261e88	0.286328
$852$	0	0
$853$	1.96594e89	0.793641	0.396821	−	0.917896i	$-0.370114\pi$
$853$	1.96594e89	0.793641	0.396821	+	0.917896i	$0.370114\pi$
$854$	−2.74983e88	−0.107113
$855$	0	0
$856$	3.50171e88	0.127008
$857$	−1.54952e89	−0.542353	−0.271177	−	0.962530i	$-0.587413\pi$
$857$	−1.54952e89	−0.542353	−0.271177	+	0.962530i	$0.587413\pi$
$858$	0	0
$859$	−2.29205e89	−0.747192	−0.373596	−	0.927592i	$-0.621875\pi$
$859$	−2.29205e89	−0.747192	−0.373596	+	0.927592i	$0.621875\pi$
$860$	−2.09734e88	−0.0659882
$861$	0	0
$862$	−1.86006e89	−0.545199
$863$	2.50671e89	0.709211	0.354606	−	0.935016i	$-0.384615\pi$
$863$	2.50671e89	0.709211	0.354606	+	0.935016i	$0.384615\pi$
$864$	0	0
$865$	−4.10937e88	−0.108339
$866$	−1.77645e89	−0.452123
$867$	0	0
$868$	−2.60722e89	−0.618482
$869$	−5.63071e89	−1.28961
$870$	0	0
$871$	−4.40275e89	−0.940092
$872$	2.98380e89	0.615200
$873$	0	0
$874$	1.17324e89	0.225573
$875$	1.26203e89	0.234327
$876$	0	0
$877$	2.61925e89	0.453617	0.226809	−	0.973939i	$-0.427171\pi$
$877$	2.61925e89	0.453617	0.226809	+	0.973939i	$0.427171\pi$
$878$	3.92008e89	0.655710
$879$	0	0
$880$	−5.81569e88	−0.0907568
$881$	7.15408e87	0.0107842	0.00539211	−	0.999985i	$-0.498284\pi$
$881$	7.15408e87	0.0107842	0.00539211	+	0.999985i	$0.498284\pi$
$882$	0	0
$883$	8.44585e89	1.18807	0.594035	−	0.804439i	$-0.297534\pi$
$883$	8.44585e89	1.18807	0.594035	+	0.804439i	$0.297534\pi$
$884$	−2.44446e89	−0.332192
$885$	0	0
$886$	4.46499e89	0.566359
$887$	6.84839e89	0.839302	0.419651	−	0.907686i	$-0.362153\pi$
$887$	6.84839e89	0.839302	0.419651	+	0.907686i	$0.362153\pi$
$888$	0	0
$889$	5.86215e89	0.670739
$890$	−1.24134e88	−0.0137245
$891$	0	0
$892$	−8.90887e89	−0.919803
$893$	2.26302e90	2.25797
$894$	0	0
$895$	1.07400e89	0.100093
$896$	−1.18536e90	−1.06772
$897$	0	0
$898$	9.31121e89	0.783570
$899$	−2.70083e89	−0.219698
$900$	0	0
$901$	−4.29219e89	−0.326267
$902$	−8.19076e89	−0.601901
$903$	0	0
$904$	−1.72864e90	−1.18732
$905$	−9.56474e88	−0.0635172
$906$	0	0
$907$	1.40576e90	0.872748	0.436374	−	0.899765i	$-0.356262\pi$
$907$	1.40576e90	0.872748	0.436374	+	0.899765i	$0.356262\pi$
$908$	−8.91058e89	−0.534919
$909$	0	0
$910$	−7.16276e88	−0.0402085
$911$	2.64352e90	1.43507	0.717534	−	0.696523i	$-0.245271\pi$
$911$	2.64352e90	1.43507	0.717534	+	0.696523i	$0.245271\pi$
$912$	0	0
$913$	1.06980e90	0.543179
$914$	5.22573e89	0.256618
$915$	0	0
$916$	1.58582e90	0.728522
$917$	−1.40076e89	−0.0622444
$918$	0	0
$919$	−4.96356e89	−0.206381	−0.103191	−	0.994662i	$-0.532905\pi$
$919$	−4.96356e89	−0.206381	−0.103191	+	0.994662i	$0.532905\pi$
$920$	7.97008e88	0.0320578
$921$	0	0
$922$	−1.19687e90	−0.450562
$923$	3.71221e90	1.35201
$924$	0	0
$925$	−2.19797e90	−0.749374
$926$	−4.46858e89	−0.147413
$927$	0	0
$928$	−9.70266e89	−0.299694
$929$	3.32635e90	0.994234	0.497117	−	0.867684i	$-0.334392\pi$
$929$	3.32635e90	0.994234	0.497117	+	0.867684i	$0.334392\pi$
$930$	0	0
$931$	5.22963e89	0.146388
$932$	−5.49475e90	−1.48855
$933$	0	0
$934$	−1.23467e90	−0.313308
$935$	−3.47716e89	−0.0854024
$936$	0	0
$937$	5.45798e90	1.25596	0.627978	−	0.778231i	$-0.283883\pi$
$937$	5.45798e90	1.25596	0.627978	+	0.778231i	$0.283883\pi$
$938$	−2.22048e90	−0.494606
$939$	0	0
$940$	6.96810e89	0.145450
$941$	2.34364e90	0.473595	0.236797	−	0.971559i	$-0.423902\pi$
$941$	2.34364e90	0.473595	0.236797	+	0.971559i	$0.423902\pi$
$942$	0	0
$943$	−1.85335e90	−0.351034
$944$	−1.60717e90	−0.294725
$945$	0	0
$946$	−2.66561e90	−0.458265
$947$	−4.24224e90	−0.706190	−0.353095	−	0.935588i	$-0.614871\pi$
$947$	−4.24224e90	−0.706190	−0.353095	+	0.935588i	$0.614871\pi$
$948$	0	0
$949$	3.79908e90	0.593006
$950$	−3.90563e90	−0.590366
$951$	0	0
$952$	−2.71992e90	−0.385593
$953$	−4.76356e90	−0.654031	−0.327015	−	0.945019i	$-0.606043\pi$
$953$	−4.76356e90	−0.654031	−0.327015	+	0.945019i	$0.606043\pi$
$954$	0	0
$955$	−1.52731e90	−0.196709
$956$	−1.09899e91	−1.37098
$957$	0	0
$958$	−1.33240e90	−0.155950
$959$	2.01633e90	0.228609
$960$	0	0
$961$	−4.64855e90	−0.494600
$962$	2.51091e90	0.258816
$963$	0	0
$964$	−3.07170e90	−0.297187
$965$	−7.97789e89	−0.0747833
$966$	0	0
$967$	1.00304e91	0.882699	0.441350	−	0.897335i	$-0.354500\pi$
$967$	1.00304e91	0.882699	0.441350	+	0.897335i	$0.354500\pi$
$968$	−1.28380e91	−1.09471
$969$	0	0
$970$	−1.25983e89	−0.0100873
$971$	−3.02928e90	−0.235046	−0.117523	−	0.993070i	$-0.537495\pi$
$971$	−3.02928e90	−0.235046	−0.117523	+	0.993070i	$0.537495\pi$
$972$	0	0
$973$	−2.77575e91	−2.02273
$974$	−4.20758e90	−0.297156
$975$	0	0
$976$	−1.92121e90	−0.127454
$977$	2.66487e91	1.71353	0.856764	−	0.515709i	$-0.172471\pi$
$977$	2.66487e91	1.71353	0.856764	+	0.515709i	$0.172471\pi$
$978$	0	0
$979$	7.65003e90	0.462159
$980$	1.61026e89	0.00942979
$981$	0	0
$982$	−5.08913e90	−0.280055
$983$	2.34161e91	1.24920	0.624601	−	0.780944i	$-0.285261\pi$
$983$	2.34161e91	1.24920	0.624601	+	0.780944i	$0.285261\pi$
$984$	0	0
$985$	1.36042e90	0.0682129
$986$	−1.27710e90	−0.0620837
$987$	0	0
$988$	−2.16344e91	−0.988687
$989$	−6.03155e90	−0.267265
$990$	0	0
$991$	3.94657e91	1.64427	0.822135	−	0.569292i	$-0.192783\pi$
$991$	3.94657e91	1.64427	0.822135	+	0.569292i	$0.192783\pi$
$992$	1.70645e91	0.689424
$993$	0	0
$994$	1.87221e91	0.711327
$995$	4.36090e90	0.160684
$996$	0	0
$997$	5.53684e91	1.91893	0.959466	−	0.281823i	$-0.0909390\pi$
$997$	5.53684e91	1.91893	0.959466	+	0.281823i	$0.0909390\pi$
$998$	4.35396e90	0.146353
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	9.62.a.a.1.3		4
3.2	odd	2		1.62.a.a.1.2	✓	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1.62.a.a.1.2	✓	4	3.2	odd	2
9.62.a.a.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:	\( k \)	\(=\)	\( 62 \)
Character orbit:	\([\chi]\)	\(=\)	9.a (trivial)

\(f(q)\)	\(=\)	\(q+6.27881e8 q^{2} -1.91161e18 q^{4} -2.33985e20 q^{5} +6.25792e25 q^{7} -2.64806e27 q^{8} +O(q^{10})\)	\(q+6.27881e8 q^{2} -1.91161e18 q^{4} -2.33985e20 q^{5} +6.25792e25 q^{7} -2.64806e27 q^{8} -1.46915e29 q^{10} +9.05394e31 q^{11} +7.79086e33 q^{13} +3.92923e34 q^{14} +2.74521e36 q^{16} +1.64134e37 q^{17} +1.45265e39 q^{19} +4.47288e38 q^{20} +5.68480e40 q^{22} +1.28631e41 q^{23} -4.28206e42 q^{25} +4.89173e42 q^{26} -1.19627e44 q^{28} -1.23922e44 q^{29} +2.17946e45 q^{31} +7.82966e45 q^{32} +1.03057e46 q^{34} -1.46426e46 q^{35} +5.13297e47 q^{37} +9.12091e47 q^{38} +6.19606e47 q^{40} -1.44082e49 q^{41} -4.68902e49 q^{43} -1.73076e50 q^{44} +8.07652e49 q^{46} +1.55786e51 q^{47} +3.60006e50 q^{49} -2.68862e51 q^{50} -1.48931e52 q^{52} -2.61505e52 q^{53} -2.11849e52 q^{55} -1.65713e53 q^{56} -7.78081e52 q^{58} -5.85447e53 q^{59} -6.99841e53 q^{61} +1.36844e54 q^{62} -1.41392e54 q^{64} -1.82294e54 q^{65} -5.65118e55 q^{67} -3.13760e55 q^{68} -9.19381e54 q^{70} +4.76482e56 q^{71} +4.87633e56 q^{73} +3.22289e56 q^{74} -2.77690e57 q^{76} +5.66589e57 q^{77} -6.21907e57 q^{79} -6.42337e56 q^{80} -9.04662e57 q^{82} +1.18158e58 q^{83} -3.84049e57 q^{85} -2.94414e58 q^{86} -2.39753e59 q^{88} +8.44939e58 q^{89} +4.87546e59 q^{91} -2.45893e59 q^{92} +9.78147e59 q^{94} -3.39899e59 q^{95} +8.57527e59 q^{97} +2.26041e59 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 1146312000 q^{2} + 44\!\cdots\!28 q^{4}+ \cdots - 97\!\cdots\!00 q^{8}+O(q^{10}) \) 4 * q - 1146312000 * q^2 + 4402997675828604928 * q^4 + 524125996020295237800 * q^5 - 63338569463385158773180000 * q^7 - 9767868387156674079031296000 * q^8	\( 4 q - 1146312000 q^{2} + 44\!\cdots\!28 q^{4}+ \cdots - 17\!\cdots\!00 q^{98}+O(q^{100}) \) 4 * q - 1146312000 * q^2 + 4402997675828604928 * q^4 + 524125996020295237800 * q^5 - 63338569463385158773180000 * q^7 - 9767868387156674079031296000 * q^8 - 1483353386285070117088509033600 * q^10 + 41554515064513200044500416014352 * q^11 + 10764994985103189070396812401291000 * q^13 + 211155135436541225684077605177122304 * q^14 + 10904646278227442826771588888892801024 * q^16 + 40906325415811699311242283170389539000 * q^17 - 356159749895948464708913853630763435120 * q^19 + 5071632401696432486275641956774663577600 * q^20 - 172062995599931314756360229299481569056000 * q^22 + 410968880183827232479513482663937487796000 * q^23 - 16739487717977510894946357652146107782722500 * q^25 + 49284147216613914166808777620995485562632832 * q^26 - 790757236315065917044952859738895406239744000 * q^28 - 6672429803576117328528976307882755467518520 * q^29 + 3262752943509002552517145952336046015034252928 * q^31 - 29552482936847865082009297897367834619543552000 * q^32 + 39802528145537101299701822666373970434557030016 * q^34 - 94932144900835792457443003213138857525722942400 * q^35 - 710312106544219153529408139748985993336062057000 * q^37 + 6572443117826428556368685861295549874330331616000 * q^38 - 6935278763126032494337494583468084555036360704000 * q^40 - 16359554122032268527799184148245398149035867491368 * q^41 + 75844732497959094206655920598930086763379517030000 * q^43 - 152692943245212279510621538861388707588508390670336 * q^44 - 150345409740296355038882940983341438053393810381312 * q^46 + 2164761335188781225334544122222333542985932701416000 * q^47 + 1523957834189526415441239854498433329172794287478628 * q^49 + 3735723416225956799610935352239535395426733934920000 * q^50 + 34115942043101628674837973043915515701891779834880000 * q^52 - 84459499120263342936174700173047508278523729350943000 * q^53 - 18917852463295959783361213875825060571992233753013600 * q^55 + 895534119833025861281009767571957442822737699977297920 * q^56 - 429363306259072204179262197105630766591459158948624000 * q^58 + 2147121767784312006347793068275982647255821920255956560 * q^59 + 4291528347018103219994434901020564652244372107292350648 * q^61 - 5191805357629316458585917076609024961942995611849984000 * q^62 + 19881300699476524526504677072626341971094030107078033408 * q^64 + 4054154514265281184405976695522203389642082195785626800 * q^65 - 151638661420806044794238226134660440129857438609787534000 * q^67 + 199797070973791372723379406738475848419062088637699072000 * q^68 + 164781406287311752350371419457017830072394299112015948800 * q^70 - 266771587169907679430401079119295396456876119234283837088 * q^71 + 436772697766954812846449565799176070423143504803837369000 * q^73 - 2727029156290392414014538532434064649250131670424597597056 * q^74 - 9182670231472830669367329606616577285345108294701612810240 * q^76 + 6239400117692696801885467207245334802759585122139865360000 * q^77 - 2171516124052566840962201891051143348431163494068568095680 * q^79 + 8149820448667982873535456900485215194289704343083732172800 * q^80 + 41751906507711557992784780576518459967807480604061450704000 * q^82 + 19301891587488226996497021336363284746717620338719475718000 * q^83 + 23823437828438802480990474713115034607148974715085027364400 * q^85 + 71538345696620408289043701603344533132955103857012068207872 * q^86 - 453611870852754620593515203785357874778152109551115829248000 * q^88 + 606362068644618673179710823370293144593411608656909401212440 * q^89 - 452168126000372891758634520948160370052422021946362710252352 * q^91 - 1607280224434271875135145612458728092411753130630908891136000 * q^92 + 6446155892605066539979931910636020289279531063064695408331776 * q^94 - 1105507768048183718212260841102299501129184381013780070972000 * q^95 - 8084830239737746227548751167926342536453719541548201116411000 * q^97 - 17015397362965438448003410858883076702895502959466609182344000 * q^98

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