LMFDB - Embedded newform 9.62.a.a.1.2

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			1.2
Root			$-3.61406e6$ 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)

$f(q)$	$=$	$q-9.80478e8 q^{2} -1.34451e18 q^{4} -1.59503e20 q^{5} +1.63507e25 q^{7} +3.57909e27 q^{8} +O(q^{10})$	\(q-9.80478e8 q^{2} -1.34451e18 q^{4} -1.59503e20 q^{5} +1.63507e25 q^{7} +3.57909e27 q^{8} +1.56389e29 q^{10} -1.92532e30 q^{11} -1.30898e34 q^{13} -1.60315e34 q^{14} -4.08993e35 q^{16} -2.98908e37 q^{17} -7.88343e38 q^{19} +2.14452e38 q^{20} +1.88773e39 q^{22} +4.50060e41 q^{23} -4.31137e42 q^{25} +1.28343e43 q^{26} -2.19837e43 q^{28} +5.51506e44 q^{29} +4.17012e45 q^{31} -7.85180e45 q^{32} +2.93073e46 q^{34} -2.60798e45 q^{35} -6.95142e47 q^{37} +7.72953e47 q^{38} -5.70874e47 q^{40} -1.25327e49 q^{41} +8.92745e49 q^{43} +2.58861e48 q^{44} -4.41273e50 q^{46} -1.21258e50 q^{47} -3.28881e51 q^{49} +4.22720e51 q^{50} +1.75994e52 q^{52} -5.55328e52 q^{53} +3.07094e50 q^{55} +5.85207e52 q^{56} -5.40740e53 q^{58} -4.29424e53 q^{59} +1.17661e53 q^{61} -4.08871e54 q^{62} +8.64159e54 q^{64} +2.08786e54 q^{65} -3.47829e55 q^{67} +4.01884e55 q^{68} +2.55707e54 q^{70} -3.07606e56 q^{71} +7.42117e56 q^{73} +6.81572e56 q^{74} +1.05993e57 q^{76} -3.14804e55 q^{77} -4.19454e57 q^{79} +6.52354e55 q^{80} +1.22880e58 q^{82} -3.40233e58 q^{83} +4.76766e57 q^{85} -8.75316e58 q^{86} -6.89089e57 q^{88} +3.77146e59 q^{89} -2.14028e59 q^{91} -6.05108e59 q^{92} +1.18890e59 q^{94} +1.25743e59 q^{95} -2.29644e60 q^{97} +3.22460e60 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−9.80478e8	−0.645688	−0.322844	−	0.946452i	$-0.604639\pi$
$2$	−9.80478e8	−0.645688	−0.322844	+	0.946452i	$0.604639\pi$
$3$	0	0
$3$	0	0
$4$	−1.34451e18	−0.583087
$5$	−1.59503e20	−0.0765919	−0.0382959	−	0.999266i	$-0.512193\pi$
$5$	−1.59503e20	−0.0765919	−0.0382959	+	0.999266i	$0.512193\pi$
$6$	0	0
$7$	1.63507e25	0.274187	0.137094	−	0.990558i	$-0.456224\pi$
$7$	1.63507e25	0.274187	0.137094	+	0.990558i	$0.456224\pi$
$8$	3.57909e27	1.02218
$9$	0	0
$10$	1.56389e29	0.0494545
$11$	−1.92532e30	−0.0332680	−0.0166340	−	0.999862i	$-0.505295\pi$
$11$	−1.92532e30	−0.0332680	−0.0166340	+	0.999862i	$0.505295\pi$
$12$	0	0
$13$	−1.30898e34	−1.38568	−0.692838	−	0.721094i	$-0.743640\pi$
$13$	−1.30898e34	−1.38568	−0.692838	+	0.721094i	$0.743640\pi$
$14$	−1.60315e34	−0.177039
$15$	0	0
$16$	−4.08993e35	−0.0769230
$17$	−2.98908e37	−0.884801	−0.442401	−	0.896818i	$-0.645873\pi$
$17$	−2.98908e37	−0.884801	−0.442401	+	0.896818i	$0.645873\pi$
$18$	0	0
$19$	−7.88343e38	−0.784748	−0.392374	−	0.919806i	$-0.628346\pi$
$19$	−7.88343e38	−0.784748	−0.392374	+	0.919806i	$0.628346\pi$
$20$	2.14452e38	0.0446597
$21$	0	0
$22$	1.88773e39	0.0214807
$23$	4.50060e41	1.31999	0.659995	−	0.751270i	$-0.270558\pi$
$23$	4.50060e41	1.31999	0.659995	+	0.751270i	$0.270558\pi$
$24$	0	0
$25$	−4.31137e42	−0.994134
$26$	1.28343e43	0.894714
$27$	0	0
$28$	−2.19837e43	−0.159875
$29$	5.51506e44	1.37534	0.687672	−	0.726021i	$-0.258633\pi$
$29$	5.51506e44	1.37534	0.687672	+	0.726021i	$0.258633\pi$
$30$	0	0
$31$	4.17012e45	1.36025	0.680123	−	0.733098i	$-0.261926\pi$
$31$	4.17012e45	1.36025	0.680123	+	0.733098i	$0.261926\pi$
$32$	−7.85180e45	−0.972512
$33$	0	0
$34$	2.93073e46	0.571306
$35$	−2.60798e45	−0.0210005
$36$	0	0
$37$	−6.95142e47	−1.02783	−0.513915	−	0.857841i	$-0.671805\pi$
$37$	−6.95142e47	−1.02783	−0.513915	+	0.857841i	$0.671805\pi$
$38$	7.72953e47	0.506703
$39$	0	0
$40$	−5.70874e47	−0.0782907
$41$	−1.25327e49	−0.809351	−0.404676	−	0.914460i	$-0.632616\pi$
$41$	−1.25327e49	−0.809351	−0.404676	+	0.914460i	$0.632616\pi$
$42$	0	0
$43$	8.92745e49	1.34877	0.674387	−	0.738378i	$-0.264408\pi$
$43$	8.92745e49	1.34877	0.674387	+	0.738378i	$0.264408\pi$
$44$	2.58861e48	0.0193981
$45$	0	0
$46$	−4.41273e50	−0.852303
$47$	−1.21258e50	−0.121541	−0.0607707	−	0.998152i	$-0.519356\pi$
$47$	−1.21258e50	−0.121541	−0.0607707	+	0.998152i	$0.519356\pi$
$48$	0	0
$49$	−3.28881e51	−0.924821
$50$	4.22720e51	0.641900
$51$	0	0
$52$	1.75994e52	0.807969
$53$	−5.55328e52	−1.42605	−0.713026	−	0.701138i	$-0.752676\pi$
$53$	−5.55328e52	−1.42605	−0.713026	+	0.701138i	$0.752676\pi$
$54$	0	0
$55$	3.07094e50	0.00254806
$56$	5.85207e52	0.280269
$57$	0	0
$58$	−5.40740e53	−0.888044
$59$	−4.29424e53	−0.418697	−0.209348	−	0.977841i	$-0.567134\pi$
$59$	−4.29424e53	−0.418697	−0.209348	+	0.977841i	$0.567134\pi$
$60$	0	0
$61$	1.17661e53	0.0415024	0.0207512	−	0.999785i	$-0.493394\pi$
$61$	1.17661e53	0.0415024	0.0207512	+	0.999785i	$0.493394\pi$
$62$	−4.08871e54	−0.878294
$63$	0	0
$64$	8.64159e54	0.704863
$65$	2.08786e54	0.106131
$66$	0	0
$67$	−3.47829e55	−0.701592	−0.350796	−	0.936452i	$-0.614089\pi$
$67$	−3.47829e55	−0.701592	−0.350796	+	0.936452i	$0.614089\pi$
$68$	4.01884e55	0.515916
$69$	0	0
$70$	2.55707e54	0.0135598
$71$	−3.07606e56	−1.05831	−0.529157	−	0.848524i	$-0.677492\pi$
$71$	−3.07606e56	−1.05831	−0.529157	+	0.848524i	$0.677492\pi$
$72$	0	0
$73$	7.42117e56	1.09427	0.547136	−	0.837044i	$-0.315718\pi$
$73$	7.42117e56	1.09427	0.547136	+	0.837044i	$0.315718\pi$
$74$	6.81572e56	0.663657
$75$	0	0
$76$	1.05993e57	0.457576
$77$	−3.14804e55	−0.00912165
$78$	0	0
$79$	−4.19454e57	−0.555978	−0.277989	−	0.960584i	$-0.589668\pi$
$79$	−4.19454e57	−0.555978	−0.277989	+	0.960584i	$0.589668\pi$
$80$	6.52354e55	0.00589168
$81$	0	0
$82$	1.22880e58	0.522588
$83$	−3.40233e58	−0.999758	−0.499879	−	0.866095i	$-0.666622\pi$
$83$	−3.40233e58	−0.999758	−0.499879	+	0.866095i	$0.666622\pi$
$84$	0	0
$85$	4.76766e57	0.0677686
$86$	−8.75316e58	−0.870888
$87$	0	0
$88$	−6.89089e57	−0.0340059
$89$	3.77146e59	1.31860	0.659302	−	0.751878i	$-0.270852\pi$
$89$	3.77146e59	1.31860	0.659302	+	0.751878i	$0.270852\pi$
$90$	0	0
$91$	−2.14028e59	−0.379934
$92$	−6.05108e59	−0.769669
$93$	0	0
$94$	1.18890e59	0.0784779
$95$	1.25743e59	0.0601053
$96$	0	0
$97$	−2.29644e60	−0.581457	−0.290728	−	0.956806i	$-0.593898\pi$
$97$	−2.29644e60	−0.581457	−0.290728	+	0.956806i	$0.593898\pi$
$98$	3.22460e60	0.597146
$99$	0	0
$100$	5.79666e60	0.579666
$101$	1.42955e61	1.05535	0.527675	−	0.849446i	$-0.323064\pi$
$101$	1.42955e61	1.05535	0.527675	+	0.849446i	$0.323064\pi$
$102$	0	0
$103$	−4.01328e61	−1.62916	−0.814581	−	0.580051i	$-0.803033\pi$
$103$	−4.01328e61	−1.62916	−0.814581	+	0.580051i	$0.803033\pi$
$104$	−4.68496e61	−1.41641
$105$	0	0
$106$	5.44486e61	0.920785
$107$	−4.31345e61	−0.547796	−0.273898	−	0.961759i	$-0.588313\pi$
$107$	−4.31345e61	−0.547796	−0.273898	+	0.961759i	$0.588313\pi$
$108$	0	0
$109$	−1.94980e62	−1.40761	−0.703805	−	0.710393i	$-0.748517\pi$
$109$	−1.94980e62	−1.40761	−0.703805	+	0.710393i	$0.748517\pi$
$110$	−3.01099e59	−0.00164525
$111$	0	0
$112$	−6.68733e60	−0.0210913
$113$	6.70205e61	0.161182	0.0805908	−	0.996747i	$-0.474319\pi$
$113$	6.70205e61	0.161182	0.0805908	+	0.996747i	$0.474319\pi$
$114$	0	0
$115$	−7.17857e61	−0.101101
$116$	−7.41504e62	−0.801945
$117$	0	0
$118$	4.21040e62	0.270347
$119$	−4.88737e62	−0.242601
$120$	0	0
$121$	−3.34559e63	−0.998893
$122$	−1.15364e62	−0.0267976
$123$	0	0
$124$	−5.60676e63	−0.793141
$125$	1.37941e63	0.152734
$126$	0	0
$127$	−2.06063e63	−0.140600	−0.0703002	−	0.997526i	$-0.522396\pi$
$127$	−2.06063e63	−0.140600	−0.0703002	+	0.997526i	$0.522396\pi$
$128$	9.63214e63	0.517391
$129$	0	0
$130$	−2.04710e63	−0.0685278
$131$	−6.07543e64	−1.60991	−0.804957	−	0.593333i	$-0.797812\pi$
$131$	−6.07543e64	−1.60991	−0.804957	+	0.593333i	$0.797812\pi$
$132$	0	0
$133$	−1.28900e64	−0.215168
$134$	3.41039e64	0.453010
$135$	0	0
$136$	−1.06982e65	−0.904426
$137$	1.12737e65	0.762238	0.381119	−	0.924526i	$-0.375539\pi$
$137$	1.12737e65	0.762238	0.381119	+	0.924526i	$0.375539\pi$
$138$	0	0
$139$	3.26131e65	1.41723	0.708616	−	0.705594i	$-0.249320\pi$
$139$	3.26131e65	1.41723	0.708616	+	0.705594i	$0.249320\pi$
$140$	3.50645e63	0.0122451
$141$	0	0
$142$	3.01600e65	0.683341
$143$	2.52021e64	0.0460986
$144$	0	0
$145$	−8.79667e64	−0.105340
$146$	−7.27630e65	−0.706559
$147$	0	0
$148$	9.34623e65	0.599314
$149$	2.77156e66	1.44725	0.723625	−	0.690194i	$-0.242475\pi$
$149$	2.77156e66	1.44725	0.723625	+	0.690194i	$0.242475\pi$
$150$	0	0
$151$	−1.14707e65	−0.0398836	−0.0199418	−	0.999801i	$-0.506348\pi$
$151$	−1.14707e65	−0.0398836	−0.0199418	+	0.999801i	$0.506348\pi$
$152$	−2.82155e66	−0.802154
$153$	0	0
$154$	3.08659e64	0.00588974
$155$	−6.65146e65	−0.104184
$156$	0	0
$157$	4.92931e66	0.522212	0.261106	−	0.965310i	$-0.415913\pi$
$157$	4.92931e66	0.522212	0.261106	+	0.965310i	$0.415913\pi$
$158$	4.11265e66	0.358988
$159$	0	0
$160$	1.25238e66	0.0744865
$161$	7.35880e66	0.361925
$162$	0	0
$163$	−5.45632e67	−1.84153	−0.920764	−	0.390121i	$-0.872433\pi$
$163$	−5.45632e67	−1.84153	−0.920764	+	0.390121i	$0.872433\pi$
$164$	1.68503e67	0.471922
$165$	0	0
$166$	3.33591e67	0.645532
$167$	−4.21801e67	−0.679603	−0.339801	−	0.940497i	$-0.610360\pi$
$167$	−4.21801e67	−0.679603	−0.339801	+	0.940497i	$0.610360\pi$
$168$	0	0
$169$	8.21065e67	0.920096
$170$	−4.67459e66	−0.0437574
$171$	0	0
$172$	−1.20030e68	−0.786453
$173$	−1.33954e68	−0.735443	−0.367721	−	0.929936i	$-0.619862\pi$
$173$	−1.33954e68	−0.735443	−0.367721	+	0.929936i	$0.619862\pi$
$174$	0	0
$175$	−7.04940e67	−0.272579
$176$	7.87443e65	0.00255907
$177$	0	0
$178$	−3.69784e68	−0.851408
$179$	1.01313e68	0.196630	0.0983150	−	0.995155i	$-0.468655\pi$
$179$	1.01313e68	0.196630	0.0983150	+	0.995155i	$0.468655\pi$
$180$	0	0
$181$	4.25098e67	0.0587885	0.0293943	−	0.999568i	$-0.490642\pi$
$181$	4.25098e67	0.0587885	0.0293943	+	0.999568i	$0.490642\pi$
$182$	2.09850e68	0.245319
$183$	0	0
$184$	1.61080e69	1.34927
$185$	1.10877e68	0.0787234
$186$	0	0
$187$	5.75494e67	0.0294355
$188$	1.63032e68	0.0708692
$189$	0	0
$190$	−1.23288e68	−0.0388093
$191$	5.32231e69	1.42752	0.713761	−	0.700389i	$-0.246990\pi$
$191$	5.32231e69	1.42752	0.713761	+	0.700389i	$0.246990\pi$
$192$	0	0
$193$	−2.00291e69	−0.390988	−0.195494	−	0.980705i	$-0.562631\pi$
$193$	−2.00291e69	−0.390988	−0.195494	+	0.980705i	$0.562631\pi$
$194$	2.25161e69	0.375440
$195$	0	0
$196$	4.42182e69	0.539251
$197$	2.47637e69	0.258580	0.129290	−	0.991607i	$-0.458730\pi$
$197$	2.47637e69	0.258580	0.129290	+	0.991607i	$0.458730\pi$
$198$	0	0
$199$	2.26238e70	1.73599	0.867994	−	0.496575i	$-0.165409\pi$
$199$	2.26238e70	1.73599	0.867994	+	0.496575i	$0.165409\pi$
$200$	−1.54308e70	−1.01618
$201$	0	0
$202$	−1.40164e70	−0.681427
$203$	9.01754e69	0.377102
$204$	0	0
$205$	1.99900e69	0.0619897
$206$	3.93493e70	1.05193
$207$	0	0
$208$	5.35364e69	0.106590
$209$	1.51781e69	0.0261070
$210$	0	0
$211$	−1.43805e70	−0.184995	−0.0924975	−	0.995713i	$-0.529485\pi$
$211$	−1.43805e70	−0.184995	−0.0924975	+	0.995713i	$0.529485\pi$
$212$	7.46642e70	0.831512
$213$	0	0
$214$	4.22924e70	0.353706
$215$	−1.42395e70	−0.103305
$216$	0	0
$217$	6.81846e70	0.372962
$218$	1.91174e71	0.908877
$219$	0	0
$220$	−4.12890e68	−0.00148574
$221$	3.91265e71	1.22605
$222$	0	0
$223$	−3.83507e71	−0.913009	−0.456504	−	0.889721i	$-0.650899\pi$
$223$	−3.83507e71	−0.913009	−0.456504	+	0.889721i	$0.650899\pi$
$224$	−1.28383e71	−0.266650
$225$	0	0
$226$	−6.57121e70	−0.104073
$227$	4.91476e71	0.680320	0.340160	−	0.940368i	$-0.389519\pi$
$227$	4.91476e71	0.680320	0.340160	+	0.940368i	$0.389519\pi$
$228$	0	0
$229$	1.61052e72	1.70602	0.853012	−	0.521891i	$-0.174773\pi$
$229$	1.61052e72	1.70602	0.853012	+	0.521891i	$0.174773\pi$
$230$	7.03842e70	0.0652794
$231$	0	0
$232$	1.97389e72	1.40585
$233$	2.97343e72	1.85739	0.928693	−	0.370850i	$-0.120934\pi$
$233$	2.97343e72	1.85739	0.928693	+	0.370850i	$0.120934\pi$
$234$	0	0
$235$	1.93409e70	0.00930908
$236$	5.77363e71	0.244136
$237$	0	0
$238$	4.79196e71	0.156645
$239$	5.09144e72	1.46455	0.732275	−	0.681009i	$-0.238458\pi$
$239$	5.09144e72	1.46455	0.732275	+	0.681009i	$0.238458\pi$
$240$	0	0
$241$	4.14476e72	0.924655	0.462327	−	0.886709i	$-0.347015\pi$
$241$	4.14476e72	0.924655	0.462327	+	0.886709i	$0.347015\pi$
$242$	3.28028e72	0.644974
$243$	0	0
$244$	−1.58196e71	−0.0241995
$245$	5.24573e71	0.0708338
$246$	0	0
$247$	1.03193e73	1.08741
$248$	1.49252e73	1.39042
$249$	0	0
$250$	−1.35248e72	−0.0986188
$251$	−3.22599e72	−0.208264	−0.104132	−	0.994563i	$-0.533206\pi$
$251$	−3.22599e72	−0.208264	−0.104132	+	0.994563i	$0.533206\pi$
$252$	0	0
$253$	−8.66509e71	−0.0439134
$254$	2.02040e72	0.0907840
$255$	0	0
$256$	−2.93702e73	−1.03894
$257$	4.70005e73	1.47619	0.738095	−	0.674697i	$-0.235726\pi$
$257$	4.70005e73	1.47619	0.738095	+	0.674697i	$0.235726\pi$
$258$	0	0
$259$	−1.13661e73	−0.281818
$260$	−2.80714e72	−0.0618838
$261$	0	0
$262$	5.95683e73	1.03950
$263$	−6.53435e73	−1.01520	−0.507601	−	0.861592i	$-0.669468\pi$
$263$	−6.53435e73	−1.01520	−0.507601	+	0.861592i	$0.669468\pi$
$264$	0	0
$265$	8.85762e72	0.109224
$266$	1.26383e73	0.138931
$267$	0	0
$268$	4.67659e73	0.409089
$269$	7.56525e73	0.590716	0.295358	−	0.955387i	$-0.404561\pi$
$269$	7.56525e73	0.590716	0.295358	+	0.955387i	$0.404561\pi$
$270$	0	0
$271$	−5.25878e73	−0.327583	−0.163792	−	0.986495i	$-0.552372\pi$
$271$	−5.25878e73	−0.327583	−0.163792	+	0.986495i	$0.552372\pi$
$272$	1.22251e73	0.0680615
$273$	0	0
$274$	−1.10537e74	−0.492168
$275$	8.30077e72	0.0330728
$276$	0	0
$277$	1.19304e72	0.00381085	0.00190543	−	0.999998i	$-0.499393\pi$
$277$	1.19304e72	0.00381085	0.00190543	+	0.999998i	$0.499393\pi$
$278$	−3.19764e74	−0.915090
$279$	0	0
$280$	−9.33420e72	−0.0214663
$281$	−5.85184e74	−1.20712	−0.603559	−	0.797319i	$-0.706251\pi$
$281$	−5.85184e74	−1.20712	−0.603559	+	0.797319i	$0.706251\pi$
$282$	0	0
$283$	1.48848e74	0.247318	0.123659	−	0.992325i	$-0.460537\pi$
$283$	1.48848e74	0.247318	0.123659	+	0.992325i	$0.460537\pi$
$284$	4.13578e74	0.617089
$285$	0	0
$286$	−2.47101e73	−0.0297653
$287$	−2.04919e74	−0.221914
$288$	0	0
$289$	−2.47798e74	−0.217127
$290$	8.62494e73	0.0680169
$291$	0	0
$292$	−9.97782e74	−0.638056
$293$	−7.53743e74	−0.434271	−0.217136	−	0.976141i	$-0.569671\pi$
$293$	−7.53743e74	−0.434271	−0.217136	+	0.976141i	$0.569671\pi$
$294$	0	0
$295$	6.84942e73	0.0320688
$296$	−2.48797e75	−1.05063
$297$	0	0
$298$	−2.71745e75	−0.934472
$299$	−5.89120e75	−1.82908
$300$	0	0
$301$	1.45970e75	0.369817
$302$	1.12468e74	0.0257523
$303$	0	0
$304$	3.22427e74	0.0603652
$305$	−1.87673e73	−0.00317875
$306$	0	0
$307$	−1.13968e76	−1.58147	−0.790735	−	0.612159i	$-0.790301\pi$
$307$	−1.13968e76	−1.58147	−0.790735	+	0.612159i	$0.790301\pi$
$308$	4.23256e73	0.00531871
$309$	0	0
$310$	6.52160e74	0.0672702
$311$	−1.39236e76	−1.30185	−0.650923	−	0.759144i	$-0.725618\pi$
$311$	−1.39236e76	−1.30185	−0.650923	+	0.759144i	$0.725618\pi$
$312$	0	0
$313$	−2.81704e75	−0.216616	−0.108308	−	0.994117i	$-0.534543\pi$
$313$	−2.81704e75	−0.216616	−0.108308	+	0.994117i	$0.534543\pi$
$314$	−4.83308e75	−0.337186
$315$	0	0
$316$	5.63958e75	0.324183
$317$	1.48589e76	0.775674	0.387837	−	0.921728i	$-0.373222\pi$
$317$	1.48589e76	0.775674	0.387837	+	0.921728i	$0.373222\pi$
$318$	0	0
$319$	−1.06183e75	−0.0457549
$320$	−1.37836e75	−0.0539867
$321$	0	0
$322$	−7.21514e75	−0.233690
$323$	2.35642e76	0.694346
$324$	0	0
$325$	5.64350e76	1.37755
$326$	5.34980e76	1.18905
$327$	0	0
$328$	−4.48556e76	−0.827303
$329$	−1.98265e75	−0.0333251
$330$	0	0
$331$	9.37638e76	1.31003	0.655015	−	0.755616i	$-0.272662\pi$
$331$	9.37638e76	1.31003	0.655015	+	0.755616i	$0.272662\pi$
$332$	4.57446e76	0.582946
$333$	0	0
$334$	4.13566e76	0.438811
$335$	5.54797e75	0.0537363
$336$	0	0
$337$	4.95449e76	0.400209	0.200105	−	0.979775i	$-0.435872\pi$
$337$	4.95449e76	0.400209	0.200105	+	0.979775i	$0.435872\pi$
$338$	−8.05036e76	−0.594095
$339$	0	0
$340$	−6.41015e75	−0.0395150
$341$	−8.02883e75	−0.0452526
$342$	0	0
$343$	−1.11920e77	−0.527761
$344$	3.19521e77	1.37869
$345$	0	0
$346$	1.31339e77	0.474867
$347$	4.94026e77	1.63569	0.817844	−	0.575440i	$-0.195169\pi$
$347$	4.94026e77	1.63569	0.817844	+	0.575440i	$0.195169\pi$
$348$	0	0
$349$	−3.62283e76	−0.100664	−0.0503318	−	0.998733i	$-0.516028\pi$
$349$	−3.62283e76	−0.100664	−0.0503318	+	0.998733i	$0.516028\pi$
$350$	6.91178e76	0.176001
$351$	0	0
$352$	1.51172e76	0.0323535
$353$	−1.78348e77	−0.350057	−0.175028	−	0.984563i	$-0.556002\pi$
$353$	−1.78348e77	−0.350057	−0.175028	+	0.984563i	$0.556002\pi$
$354$	0	0
$355$	4.90639e76	0.0810583
$356$	−5.07076e77	−0.768861
$357$	0	0
$358$	−9.93356e76	−0.126962
$359$	8.52288e77	1.00047	0.500237	−	0.865889i	$-0.333246\pi$
$359$	8.52288e77	1.00047	0.500237	+	0.865889i	$0.333246\pi$
$360$	0	0
$361$	−3.87698e77	−0.384170
$362$	−4.16799e76	−0.0379591
$363$	0	0
$364$	2.87762e77	0.221535
$365$	−1.18370e77	−0.0838124
$366$	0	0
$367$	−1.13900e77	−0.0682664	−0.0341332	−	0.999417i	$-0.510867\pi$
$367$	−1.13900e77	−0.0682664	−0.0341332	+	0.999417i	$0.510867\pi$
$368$	−1.84071e77	−0.101538
$369$	0	0
$370$	−1.08712e77	−0.0508308
$371$	−9.08002e77	−0.391005
$372$	0	0
$373$	2.11898e78	0.774476	0.387238	−	0.921980i	$-0.373429\pi$
$373$	2.11898e78	0.774476	0.387238	+	0.921980i	$0.373429\pi$
$374$	−5.64259e76	−0.0190062
$375$	0	0
$376$	−4.33991e77	−0.124237
$377$	−7.21912e78	−1.90578
$378$	0	0
$379$	1.08570e78	0.243902	0.121951	−	0.992536i	$-0.461085\pi$
$379$	1.08570e78	0.243902	0.121951	+	0.992536i	$0.461085\pi$
$380$	−1.69062e77	−0.0350466
$381$	0	0
$382$	−5.21841e78	−0.921734
$383$	6.68528e78	1.09033	0.545164	−	0.838329i	$-0.316467\pi$
$383$	6.68528e78	1.09033	0.545164	+	0.838329i	$0.316467\pi$
$384$	0	0
$385$	5.02121e75	0.000698644 0
$386$	1.96381e78	0.252456
$387$	0	0
$388$	3.08758e78	0.339040
$389$	−1.21345e79	−1.23185	−0.615926	−	0.787804i	$-0.711218\pi$
$389$	−1.21345e79	−1.23185	−0.615926	+	0.787804i	$0.711218\pi$
$390$	0	0
$391$	−1.34526e79	−1.16793
$392$	−1.17709e79	−0.945334
$393$	0	0
$394$	−2.42802e78	−0.166962
$395$	6.69039e77	0.0425834
$396$	0	0
$397$	1.96626e77	0.0107283	0.00536414	−	0.999986i	$-0.498293\pi$
$397$	1.96626e77	0.0107283	0.00536414	+	0.999986i	$0.498293\pi$
$398$	−2.21821e79	−1.12091
$399$	0	0
$400$	1.76332e78	0.0764717
$401$	1.33975e79	0.538417	0.269209	−	0.963082i	$-0.413238\pi$
$401$	1.33975e79	0.538417	0.269209	+	0.963082i	$0.413238\pi$
$402$	0	0
$403$	−5.45862e79	−1.88486
$404$	−1.92204e79	−0.615361
$405$	0	0
$406$	−8.84149e78	−0.243490
$407$	1.33837e78	0.0341938
$408$	0	0
$409$	5.24362e79	1.15364	0.576820	−	0.816871i	$-0.304293\pi$
$409$	5.24362e79	1.15364	0.576820	+	0.816871i	$0.304293\pi$
$410$	−1.95997e78	−0.0400260
$411$	0	0
$412$	5.39588e79	0.949942
$413$	−7.02139e78	−0.114801
$414$	0	0
$415$	5.42681e78	0.0765733
$416$	1.02779e80	1.34759
$417$	0	0
$418$	−1.48818e78	−0.0168570
$419$	1.15357e79	0.121483	0.0607417	−	0.998154i	$-0.480653\pi$
$419$	1.15357e79	0.121483	0.0607417	+	0.998154i	$0.480653\pi$
$420$	0	0
$421$	1.70015e80	1.54840	0.774201	−	0.632939i	$-0.218152\pi$
$421$	1.70015e80	1.54840	0.774201	+	0.632939i	$0.218152\pi$
$422$	1.40998e79	0.119449
$423$	0	0
$424$	−1.98757e80	−1.45768
$425$	1.28870e80	0.879611
$426$	0	0
$427$	1.92385e78	0.0113794
$428$	5.79946e79	0.319413
$429$	0	0
$430$	1.39615e79	0.0667029
$431$	3.88868e80	1.73080	0.865398	−	0.501085i	$-0.167066\pi$
$431$	3.88868e80	1.73080	0.865398	+	0.501085i	$0.167066\pi$
$432$	0	0
$433$	3.92018e80	1.51505	0.757523	−	0.652809i	$-0.226410\pi$
$433$	3.92018e80	1.51505	0.757523	+	0.652809i	$0.226410\pi$
$434$	−6.68535e79	−0.240817
$435$	0	0
$436$	2.62152e80	0.820759
$437$	−3.54801e80	−1.03586
$438$	0	0
$439$	−1.77739e80	−0.451455	−0.225727	−	0.974191i	$-0.572476\pi$
$439$	−1.77739e80	−0.451455	−0.225727	+	0.974191i	$0.572476\pi$
$440$	1.09912e78	0.00260457
$441$	0	0
$442$	−3.83627e80	−0.791644
$443$	5.81258e80	1.11958	0.559790	−	0.828635i	$-0.310882\pi$
$443$	5.81258e80	1.11958	0.559790	+	0.828635i	$0.310882\pi$
$444$	0	0
$445$	−6.01558e79	−0.100994
$446$	3.76020e80	0.589519
$447$	0	0
$448$	1.41296e80	0.193264
$449$	−2.43094e80	−0.310642	−0.155321	−	0.987864i	$-0.549641\pi$
$449$	−2.43094e80	−0.310642	−0.155321	+	0.987864i	$0.549641\pi$
$450$	0	0
$451$	2.41295e79	0.0269255
$452$	−9.01096e79	−0.0939828
$453$	0	0
$454$	−4.81881e80	−0.439275
$455$	3.41381e79	0.0290999
$456$	0	0
$457$	4.97936e80	0.371304	0.185652	−	0.982616i	$-0.440560\pi$
$457$	4.97936e80	0.371304	0.185652	+	0.982616i	$0.440560\pi$
$458$	−1.57908e81	−1.10156
$459$	0	0
$460$	9.65163e79	0.0589504
$461$	−1.47837e81	−0.845091	−0.422546	−	0.906342i	$-0.638863\pi$
$461$	−1.47837e81	−0.845091	−0.422546	+	0.906342i	$0.638863\pi$
$462$	0	0
$463$	−1.44774e80	−0.0725219	−0.0362610	−	0.999342i	$-0.511545\pi$
$463$	−1.44774e80	−0.0725219	−0.0362610	+	0.999342i	$0.511545\pi$
$464$	−2.25562e80	−0.105796
$465$	0	0
$466$	−2.91538e81	−1.19929
$467$	7.76500e78	0.00299210	0.00149605	−	0.999999i	$-0.499524\pi$
$467$	7.76500e78	0.00299210	0.00149605	+	0.999999i	$0.499524\pi$
$468$	0	0
$469$	−5.68727e80	−0.192368
$470$	−1.89633e79	−0.00601077
$471$	0	0
$472$	−1.53694e81	−0.427983
$473$	−1.71882e80	−0.0448710
$474$	0	0
$475$	3.39884e81	0.780145
$476$	6.57110e80	0.141457
$477$	0	0
$478$	−4.99204e81	−0.945643
$479$	−5.86941e81	−1.04318	−0.521592	−	0.853195i	$-0.674662\pi$
$479$	−5.86941e81	−1.04318	−0.521592	+	0.853195i	$0.674662\pi$
$480$	0	0
$481$	9.09929e81	1.42424
$482$	−4.06384e81	−0.597039
$483$	0	0
$484$	4.49817e81	0.582441
$485$	3.66288e80	0.0445348
$486$	0	0
$487$	−6.11323e81	−0.655597	−0.327799	−	0.944748i	$-0.606307\pi$
$487$	−6.11323e81	−0.655597	−0.327799	+	0.944748i	$0.606307\pi$
$488$	4.21120e80	0.0424230
$489$	0	0
$490$	−5.14332e80	−0.0457365
$491$	6.46236e81	0.540015	0.270008	−	0.962858i	$-0.412974\pi$
$491$	6.46236e81	0.540015	0.270008	+	0.962858i	$0.412974\pi$
$492$	0	0
$493$	−1.64850e82	−1.21691
$494$	−1.01178e82	−0.702125
$495$	0	0
$496$	−1.70555e81	−0.104634
$497$	−5.02958e81	−0.290176
$498$	0	0
$499$	1.13795e82	0.580838	0.290419	−	0.956900i	$-0.406205\pi$
$499$	1.13795e82	0.580838	0.290419	+	0.956900i	$0.406205\pi$
$500$	−1.85462e81	−0.0890574
$501$	0	0
$502$	3.16301e81	0.134474
$503$	−5.18866e80	−0.0207602	−0.0103801	−	0.999946i	$-0.503304\pi$
$503$	−5.18866e80	−0.0207602	−0.0103801	+	0.999946i	$0.503304\pi$
$504$	0	0
$505$	−2.28016e81	−0.0808312
$506$	8.49593e80	0.0283544
$507$	0	0
$508$	2.77053e81	0.0819822
$509$	5.17719e82	1.44279	0.721393	−	0.692526i	$-0.243502\pi$
$509$	5.17719e82	1.44279	0.721393	+	0.692526i	$0.243502\pi$
$510$	0	0
$511$	1.21342e82	0.300035
$512$	6.58667e81	0.153438
$513$	0	0
$514$	−4.60830e82	−0.953159
$515$	6.40128e81	0.124780
$516$	0	0
$517$	2.33460e80	0.00404344
$518$	1.11442e82	0.181966
$519$	0	0
$520$	7.47263e81	0.108485
$521$	1.12930e83	1.54617	0.773087	−	0.634300i	$-0.218712\pi$
$521$	1.12930e83	1.54617	0.773087	+	0.634300i	$0.218712\pi$
$522$	0	0
$523$	1.20266e83	1.46501	0.732506	−	0.680761i	$-0.238351\pi$
$523$	1.20266e83	1.46501	0.732506	+	0.680761i	$0.238351\pi$
$524$	8.16846e82	0.938720
$525$	0	0
$526$	6.40679e82	0.655504
$527$	−1.24648e83	−1.20355
$528$	0	0
$529$	8.63022e82	0.742376
$530$	−8.68470e81	−0.0705246
$531$	0	0
$532$	1.73307e82	0.125462
$533$	1.64051e83	1.12150
$534$	0	0
$535$	6.88006e81	0.0419567
$536$	−1.24491e83	−0.717154
$537$	0	0
$538$	−7.41756e82	−0.381418
$539$	6.33201e81	0.0307669
$540$	0	0
$541$	−4.18244e83	−1.81515	−0.907576	−	0.419889i	$-0.862069\pi$
$541$	−4.18244e83	−1.81515	−0.907576	+	0.419889i	$0.862069\pi$
$542$	5.15612e82	0.211517
$543$	0	0
$544$	2.34697e83	0.860480
$545$	3.10999e82	0.107811
$546$	0	0
$547$	2.73670e83	0.848426	0.424213	−	0.905563i	$-0.360551\pi$
$547$	2.73670e83	0.848426	0.424213	+	0.905563i	$0.360551\pi$
$548$	−1.51576e83	−0.444451
$549$	0	0
$550$	−8.13872e81	−0.0213547
$551$	−4.34776e83	−1.07930
$552$	0	0
$553$	−6.85837e82	−0.152442
$554$	−1.16975e81	−0.00246062
$555$	0	0
$556$	−4.38486e83	−0.826369
$557$	−6.78023e82	−0.120965	−0.0604826	−	0.998169i	$-0.519264\pi$
$557$	−6.78023e82	−0.120965	−0.0604826	+	0.998169i	$0.519264\pi$
$558$	0	0
$559$	−1.16859e84	−1.86896
$560$	1.06665e81	0.00161542
$561$	0	0
$562$	5.73760e83	0.779421
$563$	−6.36301e82	−0.0818760	−0.0409380	−	0.999162i	$-0.513035\pi$
$563$	−6.36301e82	−0.0818760	−0.0409380	+	0.999162i	$0.513035\pi$
$564$	0	0
$565$	−1.06899e82	−0.0123452
$566$	−1.45942e83	−0.159691
$567$	0	0
$568$	−1.10095e84	−1.08179
$569$	−1.58075e84	−1.47211	−0.736054	−	0.676923i	$-0.763313\pi$
$569$	−1.58075e84	−1.47211	−0.736054	+	0.676923i	$0.763313\pi$
$570$	0	0
$571$	−2.70603e83	−0.226429	−0.113214	−	0.993571i	$-0.536115\pi$
$571$	−2.70603e83	−0.226429	−0.113214	+	0.993571i	$0.536115\pi$
$572$	−3.38844e82	−0.0268795
$573$	0	0
$574$	2.00918e83	0.143287
$575$	−1.94037e84	−1.31225
$576$	0	0
$577$	2.52668e84	1.53705	0.768525	−	0.639820i	$-0.220991\pi$
$577$	2.52668e84	1.53705	0.768525	+	0.639820i	$0.220991\pi$
$578$	2.42961e83	0.140196
$579$	0	0
$580$	1.18272e83	0.0614225
$581$	−5.56306e83	−0.274121
$582$	0	0
$583$	1.06918e83	0.0474419
$584$	2.65610e84	1.11854
$585$	0	0
$586$	7.39028e83	0.280404
$587$	2.58255e84	0.930223	0.465112	−	0.885252i	$-0.346014\pi$
$587$	2.58255e84	0.930223	0.465112	+	0.885252i	$0.346014\pi$
$588$	0	0
$589$	−3.28749e84	−1.06745
$590$	−6.71570e82	−0.0207064
$591$	0	0
$592$	2.84308e83	0.0790637
$593$	7.02737e83	0.185620	0.0928100	−	0.995684i	$-0.470415\pi$
$593$	7.02737e83	0.185620	0.0928100	+	0.995684i	$0.470415\pi$
$594$	0	0
$595$	7.79548e82	0.0185813
$596$	−3.72638e84	−0.843872
$597$	0	0
$598$	5.77619e84	1.18101
$599$	9.83291e84	1.91057	0.955287	−	0.295679i	$-0.0955458\pi$
$599$	9.83291e84	1.91057	0.955287	+	0.295679i	$0.0955458\pi$
$600$	0	0
$601$	2.15831e84	0.378828	0.189414	−	0.981897i	$-0.439341\pi$
$601$	2.15831e84	0.378828	0.189414	+	0.981897i	$0.439341\pi$
$602$	−1.43121e84	−0.238786
$603$	0	0
$604$	1.54225e83	0.0232556
$605$	5.33630e83	0.0765071
$606$	0	0
$607$	−9.71024e83	−0.125885	−0.0629426	−	0.998017i	$-0.520049\pi$
$607$	−9.71024e83	−0.125885	−0.0629426	+	0.998017i	$0.520049\pi$
$608$	6.18991e84	0.763177
$609$	0	0
$610$	1.84009e82	0.00205248
$611$	1.58724e84	0.168417
$612$	0	0
$613$	−6.21883e84	−0.597261	−0.298630	−	0.954369i	$-0.596530\pi$
$613$	−6.21883e84	−0.597261	−0.298630	+	0.954369i	$0.596530\pi$
$614$	1.11743e85	1.02114
$615$	0	0
$616$	−1.12671e83	−0.00932397
$617$	−2.26334e85	−1.78259	−0.891297	−	0.453421i	$-0.850204\pi$
$617$	−2.26334e85	−1.78259	−0.891297	+	0.453421i	$0.850204\pi$
$618$	0	0
$619$	−1.15292e85	−0.822689	−0.411344	−	0.911480i	$-0.634941\pi$
$619$	−1.15292e85	−0.822689	−0.411344	+	0.911480i	$0.634941\pi$
$620$	8.94293e83	0.0607482
$621$	0	0
$622$	1.36518e85	0.840587
$623$	6.16662e84	0.361545
$624$	0	0
$625$	1.84776e85	0.982435
$626$	2.76204e84	0.139866
$627$	0	0
$628$	−6.62749e84	−0.304495
$629$	2.07784e85	0.909425
$630$	0	0
$631$	1.45194e84	0.0576838	0.0288419	−	0.999584i	$-0.490818\pi$
$631$	1.45194e84	0.0576838	0.0288419	+	0.999584i	$0.490818\pi$
$632$	−1.50126e85	−0.568310
$633$	0	0
$634$	−1.45688e85	−0.500844
$635$	3.28676e83	0.0107688
$636$	0	0
$637$	4.30499e85	1.28150
$638$	1.04110e84	0.0295434
$639$	0	0
$640$	−1.53635e84	−0.0396279
$641$	3.93288e85	0.967254	0.483627	−	0.875274i	$-0.339319\pi$
$641$	3.93288e85	0.967254	0.483627	+	0.875274i	$0.339319\pi$
$642$	0	0
$643$	−6.28047e85	−1.40461	−0.702307	−	0.711874i	$-0.747847\pi$
$643$	−6.28047e85	−1.40461	−0.702307	+	0.711874i	$0.747847\pi$
$644$	−9.89396e84	−0.211033
$645$	0	0
$646$	−2.31042e85	−0.448331
$647$	−8.04540e85	−1.48925	−0.744624	−	0.667484i	$-0.767371\pi$
$647$	−8.04540e85	−1.48925	−0.744624	+	0.667484i	$0.767371\pi$
$648$	0	0
$649$	8.26778e83	0.0139292
$650$	−5.53333e85	−0.889465
$651$	0	0
$652$	7.33606e85	1.07377
$653$	−2.27157e85	−0.317303	−0.158651	−	0.987335i	$-0.550715\pi$
$653$	−2.27157e85	−0.317303	−0.158651	+	0.987335i	$0.550715\pi$
$654$	0	0
$655$	9.69047e84	0.123306
$656$	5.12578e84	0.0622577
$657$	0	0
$658$	1.94395e84	0.0215176
$659$	1.63534e84	0.0172823	0.00864117	−	0.999963i	$-0.497249\pi$
$659$	1.63534e84	0.0172823	0.00864117	+	0.999963i	$0.497249\pi$
$660$	0	0
$661$	−1.97954e86	−1.90730	−0.953649	−	0.300920i	$-0.902706\pi$
$661$	−1.97954e86	−1.90730	−0.953649	+	0.300920i	$0.902706\pi$
$662$	−9.19333e85	−0.845871
$663$	0	0
$664$	−1.21772e86	−1.02193
$665$	2.05599e84	0.0164801
$666$	0	0
$667$	2.48211e86	1.81544
$668$	5.67114e85	0.396267
$669$	0	0
$670$	−5.43966e84	−0.0346969
$671$	−2.26536e83	−0.00138070
$672$	0	0
$673$	−2.07904e85	−0.115719	−0.0578594	−	0.998325i	$-0.518428\pi$
$673$	−2.07904e85	−0.115719	−0.0578594	+	0.998325i	$0.518428\pi$
$674$	−4.85777e85	−0.258410
$675$	0	0
$676$	−1.10393e86	−0.536496
$677$	−3.55563e86	−1.65182	−0.825909	−	0.563803i	$-0.809338\pi$
$677$	−3.55563e86	−1.65182	−0.825909	+	0.563803i	$0.809338\pi$
$678$	0	0
$679$	−3.75485e85	−0.159428
$680$	1.70639e85	0.0692717
$681$	0	0
$682$	7.87209e84	0.0292191
$683$	1.05935e86	0.376018	0.188009	−	0.982167i	$-0.439797\pi$
$683$	1.05935e86	0.376018	0.188009	+	0.982167i	$0.439797\pi$
$684$	0	0
$685$	−1.79819e85	−0.0583813
$686$	1.09735e86	0.340769
$687$	0	0
$688$	−3.65126e85	−0.103752
$689$	7.26914e86	1.97604
$690$	0	0
$691$	3.75049e86	0.933271	0.466635	−	0.884450i	$-0.345466\pi$
$691$	3.75049e86	0.933271	0.466635	+	0.884450i	$0.345466\pi$
$692$	1.80102e86	0.428827
$693$	0	0
$694$	−4.84381e86	−1.05614
$695$	−5.20188e85	−0.108548
$696$	0	0
$697$	3.74613e86	0.716115
$698$	3.55211e85	0.0649974
$699$	0	0
$700$	9.47797e85	0.158937
$701$	−1.21524e85	−0.0195103	−0.00975516	−	0.999952i	$-0.503105\pi$
$701$	−1.21524e85	−0.0195103	−0.00975516	+	0.999952i	$0.503105\pi$
$702$	0	0
$703$	5.48011e86	0.806587
$704$	−1.66378e85	−0.0234494
$705$	0	0
$706$	1.74866e86	0.226028
$707$	2.33741e86	0.289363
$708$	0	0
$709$	1.78732e86	0.202998	0.101499	−	0.994836i	$-0.467636\pi$
$709$	1.78732e86	0.202998	0.101499	+	0.994836i	$0.467636\pi$
$710$	−4.81060e85	−0.0523384
$711$	0	0
$712$	1.34984e87	1.34785
$713$	1.87680e87	1.79551
$714$	0	0
$715$	−4.01980e84	−0.00353078
$716$	−1.36217e86	−0.114652
$717$	0	0
$718$	−8.35649e86	−0.645994
$719$	1.18320e87	0.876651	0.438325	−	0.898816i	$-0.355572\pi$
$719$	1.18320e87	0.876651	0.438325	+	0.898816i	$0.355572\pi$
$720$	0	0
$721$	−6.56201e86	−0.446695
$722$	3.80129e86	0.248054
$723$	0	0
$724$	−5.71547e85	−0.0342788
$725$	−2.37775e87	−1.36728
$726$	0	0
$727$	7.32315e86	0.387167	0.193584	−	0.981084i	$-0.437989\pi$
$727$	7.32315e86	0.387167	0.193584	+	0.981084i	$0.437989\pi$
$728$	−7.66025e86	−0.388361
$729$	0	0
$730$	1.16059e86	0.0541166
$731$	−2.66849e87	−1.19340
$732$	0	0
$733$	−5.10204e86	−0.209929	−0.104965	−	0.994476i	$-0.533473\pi$
$733$	−5.10204e86	−0.209929	−0.104965	+	0.994476i	$0.533473\pi$
$734$	1.11676e86	0.0440788
$735$	0	0
$736$	−3.53378e87	−1.28371
$737$	6.69683e85	0.0233406
$738$	0	0
$739$	−2.70980e87	−0.869524	−0.434762	−	0.900545i	$-0.643168\pi$
$739$	−2.70980e87	−0.869524	−0.434762	+	0.900545i	$0.643168\pi$
$740$	−1.49075e86	−0.0459026
$741$	0	0
$742$	8.90275e86	0.252467
$743$	−6.18077e86	−0.168222	−0.0841112	−	0.996456i	$-0.526805\pi$
$743$	−6.18077e86	−0.168222	−0.0841112	+	0.996456i	$0.526805\pi$
$744$	0	0
$745$	−4.42071e86	−0.110848
$746$	−2.07762e87	−0.500070
$747$	0	0
$748$	−7.73756e85	−0.0171635
$749$	−7.05280e86	−0.150199
$750$	0	0
$751$	−5.20963e87	−1.02279	−0.511397	−	0.859344i	$-0.670872\pi$
$751$	−5.20963e87	−1.02279	−0.511397	+	0.859344i	$0.670872\pi$
$752$	4.95935e85	0.00934933
$753$	0	0
$754$	7.07819e87	1.23054
$755$	1.82961e85	0.00305476
$756$	0	0
$757$	2.22778e87	0.343121	0.171561	−	0.985174i	$-0.445119\pi$
$757$	2.22778e87	0.343121	0.171561	+	0.985174i	$0.445119\pi$
$758$	−1.06451e87	−0.157485
$759$	0	0
$760$	4.50044e86	0.0614385
$761$	−5.32204e87	−0.697985	−0.348992	−	0.937126i	$-0.613476\pi$
$761$	−5.32204e87	−0.697985	−0.348992	+	0.937126i	$0.613476\pi$
$762$	0	0
$763$	−3.18807e87	−0.385949
$764$	−7.15589e87	−0.832369
$765$	0	0
$766$	−6.55477e87	−0.704012
$767$	5.62108e87	0.580178
$768$	0	0
$769$	1.48822e88	1.41878	0.709389	−	0.704818i	$-0.248971\pi$
$769$	1.48822e88	1.41878	0.709389	+	0.704818i	$0.248971\pi$
$770$	−4.92318e84	−0.000451106 0
$771$	0	0
$772$	2.69293e87	0.227980
$773$	1.68328e87	0.136988	0.0684938	−	0.997652i	$-0.478181\pi$
$773$	1.68328e87	0.136988	0.0684938	+	0.997652i	$0.478181\pi$
$774$	0	0
$775$	−1.79789e88	−1.35227
$776$	−8.21916e87	−0.594354
$777$	0	0
$778$	1.18976e88	0.795392
$779$	9.88006e87	0.635137
$780$	0	0
$781$	5.92240e86	0.0352080
$782$	1.31900e88	0.754118
$783$	0	0
$784$	1.34510e87	0.0711400
$785$	−7.86238e86	−0.0399972
$786$	0	0
$787$	1.03317e88	0.486342	0.243171	−	0.969983i	$-0.421812\pi$
$787$	1.03317e88	0.486342	0.243171	+	0.969983i	$0.421812\pi$
$788$	−3.32949e87	−0.150775
$789$	0	0
$790$	−6.55978e86	−0.0274956
$791$	1.09584e87	0.0441939
$792$	0	0
$793$	−1.54016e87	−0.0575089
$794$	−1.92787e86	−0.00692712
$795$	0	0
$796$	−3.04178e88	−1.01223
$797$	3.51204e88	1.12481	0.562407	−	0.826861i	$-0.309876\pi$
$797$	3.51204e88	1.12481	0.562407	+	0.826861i	$0.309876\pi$
$798$	0	0
$799$	3.62449e87	0.107540
$800$	3.38520e88	0.966807
$801$	0	0
$802$	−1.31359e88	−0.347650
$803$	−1.42881e87	−0.0364042
$804$	0	0
$805$	−1.17375e87	−0.0277205
$806$	5.35205e88	1.21703
$807$	0	0
$808$	5.11647e88	1.07876
$809$	−4.70026e88	−0.954316	−0.477158	−	0.878818i	$-0.658333\pi$
$809$	−4.70026e88	−0.954316	−0.477158	+	0.878818i	$0.658333\pi$
$810$	0	0
$811$	7.07672e88	1.33259	0.666294	−	0.745689i	$-0.267880\pi$
$811$	7.07672e88	1.33259	0.666294	+	0.745689i	$0.267880\pi$
$812$	−1.21241e88	−0.219883
$813$	0	0
$814$	−1.31224e87	−0.0220785
$815$	8.70298e87	0.141046
$816$	0	0
$817$	−7.03789e88	−1.05845
$818$	−5.14125e88	−0.744892
$819$	0	0
$820$	−2.68767e87	−0.0361454
$821$	5.20477e88	0.674428	0.337214	−	0.941428i	$-0.390515\pi$
$821$	5.20477e88	0.674428	0.337214	+	0.941428i	$0.390515\pi$
$822$	0	0
$823$	4.31597e88	0.519258	0.259629	−	0.965708i	$-0.416400\pi$
$823$	4.31597e88	0.519258	0.259629	+	0.965708i	$0.416400\pi$
$824$	−1.43639e89	−1.66530
$825$	0	0
$826$	6.88432e87	0.0741258
$827$	1.50785e89	1.56473	0.782365	−	0.622821i	$-0.214013\pi$
$827$	1.50785e89	1.56473	0.782365	+	0.622821i	$0.214013\pi$
$828$	0	0
$829$	3.48420e88	0.335885	0.167942	−	0.985797i	$-0.446288\pi$
$829$	3.48420e88	0.335885	0.167942	+	0.985797i	$0.446288\pi$
$830$	−5.32086e87	−0.0494425
$831$	0	0
$832$	−1.13117e89	−0.976711
$833$	9.83051e88	0.818283
$834$	0	0
$835$	6.72783e87	0.0520520
$836$	−2.04071e87	−0.0152226
$837$	0	0
$838$	−1.13105e88	−0.0784404
$839$	−1.17215e89	−0.783872	−0.391936	−	0.919992i	$-0.628195\pi$
$839$	−1.17215e89	−0.783872	−0.391936	+	0.919992i	$0.628195\pi$
$840$	0	0
$841$	1.43362e89	0.891574
$842$	−1.66696e89	−0.999785
$843$	0	0
$844$	1.93347e88	0.107868
$845$	−1.30962e88	−0.0704719
$846$	0	0
$847$	−5.47029e88	−0.273884
$848$	2.27125e88	0.109696
$849$	0	0
$850$	−1.26354e89	−0.567954
$851$	−3.12855e89	−1.35673
$852$	0	0
$853$	−1.25601e89	−0.507045	−0.253523	−	0.967329i	$-0.581589\pi$
$853$	−1.25601e89	−0.507045	−0.253523	+	0.967329i	$0.581589\pi$
$854$	−1.88629e87	−0.00734756
$855$	0	0
$856$	−1.54382e89	−0.559947
$857$	1.93234e89	0.676347	0.338173	−	0.941084i	$-0.390191\pi$
$857$	1.93234e89	0.676347	0.338173	+	0.941084i	$0.390191\pi$
$858$	0	0
$859$	−4.33998e88	−0.141481	−0.0707403	−	0.997495i	$-0.522536\pi$
$859$	−4.33998e88	−0.141481	−0.0707403	+	0.997495i	$0.522536\pi$
$860$	1.91451e88	0.0602359
$861$	0	0
$862$	−3.81277e89	−1.11755
$863$	−1.76145e89	−0.498359	−0.249179	−	0.968457i	$-0.580161\pi$
$863$	−1.76145e89	−0.498359	−0.249179	+	0.968457i	$0.580161\pi$
$864$	0	0
$865$	2.13660e88	0.0563289
$866$	−3.84365e89	−0.978247
$867$	0	0
$868$	−9.16746e88	−0.217469
$869$	8.07583e87	0.0184963
$870$	0	0
$871$	4.55302e89	0.972179
$872$	−6.97851e89	−1.43883
$873$	0	0
$874$	3.47875e89	0.668843
$875$	2.25543e88	0.0418778
$876$	0	0
$877$	−1.31068e89	−0.226991	−0.113495	−	0.993539i	$-0.536205\pi$
$877$	−1.31068e89	−0.226991	−0.113495	+	0.993539i	$0.536205\pi$
$878$	1.74269e89	0.291499
$879$	0	0
$880$	−1.25599e86	−0.000196004 0
$881$	1.11397e90	1.67923	0.839614	−	0.543184i	$-0.182781\pi$
$881$	1.11397e90	1.67923	0.839614	+	0.543184i	$0.182781\pi$
$882$	0	0
$883$	2.93644e89	0.413067	0.206533	−	0.978440i	$-0.433782\pi$
$883$	2.93644e89	0.413067	0.206533	+	0.978440i	$0.433782\pi$
$884$	−5.26059e89	−0.714892
$885$	0	0
$886$	−5.69910e89	−0.722900
$887$	1.32601e90	1.62509	0.812544	−	0.582900i	$-0.198082\pi$
$887$	1.32601e90	1.62509	0.812544	+	0.582900i	$0.198082\pi$
$888$	0	0
$889$	−3.36928e88	−0.0385508
$890$	5.89814e88	0.0652109
$891$	0	0
$892$	5.15628e89	0.532363
$893$	9.55926e88	0.0953794
$894$	0	0
$895$	−1.61598e88	−0.0150603
$896$	1.57493e89	0.141862
$897$	0	0
$898$	2.38348e89	0.200578
$899$	2.29985e90	1.87081
$900$	0	0
$901$	1.65992e90	1.26177
$902$	−2.36584e88	−0.0173855
$903$	0	0
$904$	2.39872e89	0.164757
$905$	−6.78043e87	−0.00450272
$906$	0	0
$907$	1.13903e90	0.707150	0.353575	−	0.935406i	$-0.384966\pi$
$907$	1.13903e90	0.707150	0.353575	+	0.935406i	$0.384966\pi$
$908$	−6.60792e89	−0.396686
$909$	0	0
$910$	−3.34716e88	−0.0187894
$911$	4.40257e89	0.238999	0.119499	−	0.992834i	$-0.461871\pi$
$911$	4.40257e89	0.238999	0.119499	+	0.992834i	$0.461871\pi$
$912$	0	0
$913$	6.55058e88	0.0332599
$914$	−4.88215e89	−0.239746
$915$	0	0
$916$	−2.16536e90	−0.994760
$917$	−9.93378e89	−0.441418
$918$	0	0
$919$	−2.54886e90	−1.05980	−0.529898	−	0.848061i	$-0.677770\pi$
$919$	−2.54886e90	−1.05980	−0.529898	+	0.848061i	$0.677770\pi$
$920$	−2.56927e89	−0.103343
$921$	0	0
$922$	1.44950e90	0.545665
$923$	4.02650e90	1.46648
$924$	0	0
$925$	2.99701e90	1.02180
$926$	1.41947e89	0.0468266
$927$	0	0
$928$	−4.33032e90	−1.33754
$929$	−2.58810e90	−0.773575	−0.386788	−	0.922169i	$-0.626415\pi$
$929$	−2.58810e90	−0.773575	−0.386788	+	0.922169i	$0.626415\pi$
$930$	0	0
$931$	2.59271e90	0.725752
$932$	−3.99780e90	−1.08302
$933$	0	0
$934$	−7.61340e87	−0.00193196
$935$	−9.17928e87	−0.00225452
$936$	0	0
$937$	1.46131e90	0.336266	0.168133	−	0.985764i	$-0.446226\pi$
$937$	1.46131e90	0.336266	0.168133	+	0.985764i	$0.446226\pi$
$938$	5.57624e89	0.124209
$939$	0	0
$940$	−2.60040e88	−0.00542800
$941$	−1.30889e90	−0.264496	−0.132248	−	0.991217i	$-0.542220\pi$
$941$	−1.30889e90	−0.264496	−0.132248	+	0.991217i	$0.542220\pi$
$942$	0	0
$943$	−5.64046e90	−1.06834
$944$	1.75631e89	0.0322074
$945$	0	0
$946$	1.68527e89	0.0289727
$947$	−4.48696e90	−0.746927	−0.373464	−	0.927645i	$-0.621830\pi$
$947$	−4.48696e90	−0.746927	−0.373464	+	0.927645i	$0.621830\pi$
$948$	0	0
$949$	−9.71419e90	−1.51631
$950$	−3.33248e90	−0.503730
$951$	0	0
$952$	−1.74923e90	−0.247982
$953$	7.56718e90	1.03896	0.519482	−	0.854481i	$-0.326125\pi$
$953$	7.56718e90	1.03896	0.519482	+	0.854481i	$0.326125\pi$
$954$	0	0
$955$	−8.48923e89	−0.109337
$956$	−6.84547e90	−0.853960
$957$	0	0
$958$	5.75482e90	0.673572
$959$	1.84334e90	0.208996
$960$	0	0
$961$	7.99133e90	0.850268
$962$	−8.92165e90	−0.919614
$963$	0	0
$964$	−5.57266e90	−0.539154
$965$	3.19469e89	0.0299465
$966$	0	0
$967$	6.35826e90	0.559539	0.279770	−	0.960067i	$-0.409742\pi$
$967$	6.35826e90	0.559539	0.279770	+	0.960067i	$0.409742\pi$
$968$	−1.19742e91	−1.02105
$969$	0	0
$970$	−3.59137e89	−0.0287556
$971$	3.23669e90	0.251139	0.125570	−	0.992085i	$-0.459924\pi$
$971$	3.23669e90	0.251139	0.125570	+	0.992085i	$0.459924\pi$
$972$	0	0
$973$	5.33248e90	0.388587
$974$	5.99388e90	0.423311
$975$	0	0
$976$	−4.81226e88	−0.00319249
$977$	1.41204e90	0.0907953	0.0453977	−	0.998969i	$-0.485545\pi$
$977$	1.41204e90	0.0907953	0.0453977	+	0.998969i	$0.485545\pi$
$978$	0	0
$979$	−7.26128e89	−0.0438673
$980$	−7.05292e89	−0.0413022
$981$	0	0
$982$	−6.33620e90	−0.348681
$983$	8.68181e89	0.0463157	0.0231578	−	0.999732i	$-0.492628\pi$
$983$	8.68181e89	0.0463157	0.0231578	+	0.999732i	$0.492628\pi$
$984$	0	0
$985$	−3.94987e89	−0.0198051
$986$	1.61631e91	0.785742
$987$	0	0
$988$	−1.38743e91	−0.634052
$989$	4.01788e91	1.78037
$990$	0	0
$991$	1.85513e91	0.772907	0.386454	−	0.922309i	$-0.373700\pi$
$991$	1.85513e91	0.772907	0.386454	+	0.922309i	$0.373700\pi$
$992$	−3.27430e91	−1.32286
$993$	0	0
$994$	4.93139e90	0.187363
$995$	−3.60855e90	−0.132963
$996$	0	0
$997$	6.39525e90	0.221643	0.110822	−	0.993840i	$-0.464652\pi$
$997$	6.39525e90	0.221643	0.110822	+	0.993840i	$0.464652\pi$
$998$	−1.11573e91	−0.375040
$999$	0	0

Twists

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

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

\(f(q)\)	\(=\)	\(q-9.80478e8 q^{2} -1.34451e18 q^{4} -1.59503e20 q^{5} +1.63507e25 q^{7} +3.57909e27 q^{8} +O(q^{10})\)	\(q-9.80478e8 q^{2} -1.34451e18 q^{4} -1.59503e20 q^{5} +1.63507e25 q^{7} +3.57909e27 q^{8} +1.56389e29 q^{10} -1.92532e30 q^{11} -1.30898e34 q^{13} -1.60315e34 q^{14} -4.08993e35 q^{16} -2.98908e37 q^{17} -7.88343e38 q^{19} +2.14452e38 q^{20} +1.88773e39 q^{22} +4.50060e41 q^{23} -4.31137e42 q^{25} +1.28343e43 q^{26} -2.19837e43 q^{28} +5.51506e44 q^{29} +4.17012e45 q^{31} -7.85180e45 q^{32} +2.93073e46 q^{34} -2.60798e45 q^{35} -6.95142e47 q^{37} +7.72953e47 q^{38} -5.70874e47 q^{40} -1.25327e49 q^{41} +8.92745e49 q^{43} +2.58861e48 q^{44} -4.41273e50 q^{46} -1.21258e50 q^{47} -3.28881e51 q^{49} +4.22720e51 q^{50} +1.75994e52 q^{52} -5.55328e52 q^{53} +3.07094e50 q^{55} +5.85207e52 q^{56} -5.40740e53 q^{58} -4.29424e53 q^{59} +1.17661e53 q^{61} -4.08871e54 q^{62} +8.64159e54 q^{64} +2.08786e54 q^{65} -3.47829e55 q^{67} +4.01884e55 q^{68} +2.55707e54 q^{70} -3.07606e56 q^{71} +7.42117e56 q^{73} +6.81572e56 q^{74} +1.05993e57 q^{76} -3.14804e55 q^{77} -4.19454e57 q^{79} +6.52354e55 q^{80} +1.22880e58 q^{82} -3.40233e58 q^{83} +4.76766e57 q^{85} -8.75316e58 q^{86} -6.89089e57 q^{88} +3.77146e59 q^{89} -2.14028e59 q^{91} -6.05108e59 q^{92} +1.18890e59 q^{94} +1.25743e59 q^{95} -2.29644e60 q^{97} +3.22460e60 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 1146312000 q^{2} + 44\!\cdots\!28 q^{4}+ \cdots - 97\!\cdots\!00 q^{8}+O(q^{10}) \) 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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