LMFDB - Embedded newform 9.62.a.a.1.1

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			1.1
Root			$-1.33086e7$ of defining polynomial
Character	$\chi$	$=$	9.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.84183e9 q^{2} +5.77017e18 q^{4} +6.89620e20 q^{5} -9.80127e25 q^{7} -9.84504e27 q^{8} +O(q^{10})$	\(q-2.84183e9 q^{2} +5.77017e18 q^{4} +6.89620e20 q^{5} -9.80127e25 q^{7} -9.84504e27 q^{8} -1.95979e30 q^{10} +2.74880e31 q^{11} +2.74592e32 q^{13} +2.78536e35 q^{14} +1.46728e37 q^{16} +2.27394e37 q^{17} -1.42689e39 q^{19} +3.97923e39 q^{20} -7.81164e40 q^{22} -1.13228e41 q^{23} -3.86123e42 q^{25} -7.80343e41 q^{26} -5.65550e44 q^{28} -2.20574e44 q^{29} -7.87465e44 q^{31} -1.89967e46 q^{32} -6.46217e46 q^{34} -6.75915e46 q^{35} +5.41627e47 q^{37} +4.05499e48 q^{38} -6.78934e48 q^{40} -3.44353e48 q^{41} -2.45361e49 q^{43} +1.58611e50 q^{44} +3.21774e50 q^{46} -7.88915e50 q^{47} +6.05033e51 q^{49} +1.09730e52 q^{50} +1.58444e51 q^{52} -4.85762e52 q^{53} +1.89563e52 q^{55} +9.64938e53 q^{56} +6.26833e53 q^{58} +1.37665e54 q^{59} +4.54704e53 q^{61} +2.23784e54 q^{62} +2.01520e55 q^{64} +1.89364e53 q^{65} -8.79176e55 q^{67} +1.31210e56 q^{68} +1.92084e56 q^{70} -3.27010e56 q^{71} -6.07880e56 q^{73} -1.53921e57 q^{74} -8.23342e57 q^{76} -2.69418e57 q^{77} +1.23160e58 q^{79} +1.01187e58 q^{80} +9.78594e57 q^{82} +6.61561e58 q^{83} +1.56816e58 q^{85} +6.97276e58 q^{86} -2.70621e59 q^{88} +1.38088e59 q^{89} -2.69135e58 q^{91} -6.53342e59 q^{92} +2.24196e60 q^{94} -9.84014e59 q^{95} -3.96687e60 q^{97} -1.71940e61 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.84183e9	−1.87147	−0.935737	−	0.352699i	$-0.885264\pi$
$2$	−2.84183e9	−1.87147	−0.935737	+	0.352699i	$0.885264\pi$
$3$	0	0
$3$	0	0
$4$	5.77017e18	2.50241
$5$	6.89620e20	0.331150	0.165575	−	0.986197i	$-0.447052\pi$
$5$	6.89620e20	0.331150	0.165575	+	0.986197i	$0.447052\pi$
$6$	0	0
$7$	−9.80127e25	−1.64358	−0.821792	−	0.569787i	$-0.807026\pi$
$7$	−9.80127e25	−1.64358	−0.821792	+	0.569787i	$0.807026\pi$
$8$	−9.84504e27	−2.81172
$9$	0	0
$10$	−1.95979e30	−0.619738
$11$	2.74880e31	0.474971	0.237485	−	0.971391i	$-0.423677\pi$
$11$	2.74880e31	0.474971	0.237485	+	0.971391i	$0.423677\pi$
$12$	0	0
$13$	2.74592e32	0.0290680	0.0145340	−	0.999894i	$-0.495374\pi$
$13$	2.74592e32	0.0290680	0.0145340	+	0.999894i	$0.495374\pi$
$14$	2.78536e35	3.07592
$15$	0	0
$16$	1.46728e37	2.75966
$17$	2.27394e37	0.673112	0.336556	−	0.941663i	$-0.390738\pi$
$17$	2.27394e37	0.673112	0.336556	+	0.941663i	$0.390738\pi$
$18$	0	0
$19$	−1.42689e39	−1.42039	−0.710193	−	0.704007i	$-0.751393\pi$
$19$	−1.42689e39	−1.42039	−0.710193	+	0.704007i	$0.751393\pi$
$20$	3.97923e39	0.828674
$21$	0	0
$22$	−7.81164e40	−0.888895
$23$	−1.13228e41	−0.332088	−0.166044	−	0.986118i	$-0.553099\pi$
$23$	−1.13228e41	−0.332088	−0.166044	+	0.986118i	$0.553099\pi$
$24$	0	0
$25$	−3.86123e42	−0.890340
$26$	−7.80343e41	−0.0544000
$27$	0	0
$28$	−5.65550e44	−4.11293
$29$	−2.20574e44	−0.550066	−0.275033	−	0.961435i	$-0.588689\pi$
$29$	−2.20574e44	−0.550066	−0.275033	+	0.961435i	$0.588689\pi$
$30$	0	0
$31$	−7.87465e44	−0.256862	−0.128431	−	0.991718i	$-0.540994\pi$
$31$	−7.87465e44	−0.256862	−0.128431	+	0.991718i	$0.540994\pi$
$32$	−1.89967e46	−2.35290
$33$	0	0
$34$	−6.46217e46	−1.25971
$35$	−6.75915e46	−0.544273
$36$	0	0
$37$	5.41627e47	0.800843	0.400422	−	0.916331i	$-0.368864\pi$
$37$	5.41627e47	0.800843	0.400422	+	0.916331i	$0.368864\pi$
$38$	4.05499e48	2.65822
$39$	0	0
$40$	−6.78934e48	−0.931103
$41$	−3.44353e48	−0.222380	−0.111190	−	0.993799i	$-0.535466\pi$
$41$	−3.44353e48	−0.222380	−0.111190	+	0.993799i	$0.535466\pi$
$42$	0	0
$43$	−2.45361e49	−0.370696	−0.185348	−	0.982673i	$-0.559341\pi$
$43$	−2.45361e49	−0.370696	−0.185348	+	0.982673i	$0.559341\pi$
$44$	1.58611e50	1.18857
$45$	0	0
$46$	3.21774e50	0.621494
$47$	−7.88915e50	−0.790761	−0.395381	−	0.918517i	$-0.629387\pi$
$47$	−7.88915e50	−0.790761	−0.395381	+	0.918517i	$0.629387\pi$
$48$	0	0
$49$	6.05033e51	1.70137
$50$	1.09730e52	1.66625
$51$	0	0
$52$	1.58444e51	0.0727401
$53$	−4.85762e52	−1.24741	−0.623706	−	0.781659i	$-0.714374\pi$
$53$	−4.85762e52	−1.24741	−0.623706	+	0.781659i	$0.714374\pi$
$54$	0	0
$55$	1.89563e52	0.157287
$56$	9.64938e53	4.62131
$57$	0	0
$58$	6.26833e53	1.02943
$59$	1.37665e54	1.34226	0.671130	−	0.741340i	$-0.265809\pi$
$59$	1.37665e54	1.34226	0.671130	+	0.741340i	$0.265809\pi$
$60$	0	0
$61$	4.54704e53	0.160387	0.0801934	−	0.996779i	$-0.474446\pi$
$61$	4.54704e53	0.160387	0.0801934	+	0.996779i	$0.474446\pi$
$62$	2.23784e54	0.480710
$63$	0	0
$64$	2.01520e55	1.64373
$65$	1.89364e53	0.00962587
$66$	0	0
$67$	−8.79176e55	−1.77335	−0.886675	−	0.462393i	$-0.846991\pi$
$67$	−8.79176e55	−1.77335	−0.886675	+	0.462393i	$0.846991\pi$
$68$	1.31210e56	1.68440
$69$	0	0
$70$	1.92084e56	1.01859
$71$	−3.27010e56	−1.12508	−0.562538	−	0.826772i	$-0.690175\pi$
$71$	−3.27010e56	−1.12508	−0.562538	+	0.826772i	$0.690175\pi$
$72$	0	0
$73$	−6.07880e56	−0.896336	−0.448168	−	0.893949i	$-0.647923\pi$
$73$	−6.07880e56	−0.896336	−0.448168	+	0.893949i	$0.647923\pi$
$74$	−1.53921e57	−1.49876
$75$	0	0
$76$	−8.23342e57	−3.55439
$77$	−2.69418e57	−0.780654
$78$	0	0
$79$	1.23160e58	1.63246	0.816229	−	0.577729i	$-0.196061\pi$
$79$	1.23160e58	1.63246	0.816229	+	0.577729i	$0.196061\pi$
$80$	1.01187e58	0.913860
$81$	0	0
$82$	9.78594e57	0.416179
$83$	6.61561e58	1.94396	0.971981	−	0.235058i	$-0.0755280\pi$
$83$	6.61561e58	1.94396	0.971981	+	0.235058i	$0.0755280\pi$
$84$	0	0
$85$	1.56816e58	0.222901
$86$	6.97276e58	0.693749
$87$	0	0
$88$	−2.70621e59	−1.33549
$89$	1.38088e59	0.482793	0.241396	−	0.970427i	$-0.422395\pi$
$89$	1.38088e59	0.482793	0.241396	+	0.970427i	$0.422395\pi$
$90$	0	0
$91$	−2.69135e58	−0.0477757
$92$	−6.53342e59	−0.831021
$93$	0	0
$94$	2.24196e60	1.47989
$95$	−9.84014e59	−0.470361
$96$	0	0
$97$	−3.96687e60	−1.00441	−0.502204	−	0.864749i	$-0.667477\pi$
$97$	−3.96687e60	−1.00441	−0.502204	+	0.864749i	$0.667477\pi$
$98$	−1.71940e61	−3.18407
$99$	0	0
$100$	−2.22800e61	−2.22800
$101$	4.90481e60	0.362093	0.181047	−	0.983474i	$-0.442051\pi$
$101$	4.90481e60	0.362093	0.181047	+	0.983474i	$0.442051\pi$
$102$	0	0
$103$	−2.48884e61	−1.01033	−0.505163	−	0.863024i	$-0.668568\pi$
$103$	−2.48884e61	−1.01033	−0.505163	+	0.863024i	$0.668568\pi$
$104$	−2.70337e60	−0.0817312
$105$	0	0
$106$	1.38046e62	2.33450
$107$	1.15288e62	1.46413	0.732063	−	0.681237i	$-0.238558\pi$
$107$	1.15288e62	1.46413	0.732063	+	0.681237i	$0.238558\pi$
$108$	0	0
$109$	−6.30613e61	−0.455255	−0.227627	−	0.973748i	$-0.573097\pi$
$109$	−6.30613e61	−0.455255	−0.227627	+	0.973748i	$0.573097\pi$
$110$	−5.38706e61	−0.294358
$111$	0	0
$112$	−1.43812e63	−4.53573
$113$	−3.81996e62	−0.918685	−0.459343	−	0.888259i	$-0.651915\pi$
$113$	−3.81996e62	−0.918685	−0.459343	+	0.888259i	$0.651915\pi$
$114$	0	0
$115$	−7.80840e61	−0.109971
$116$	−1.27275e63	−1.37649
$117$	0	0
$118$	−3.91220e63	−2.51200
$119$	−2.22875e63	−1.10632
$120$	0	0
$121$	−2.59371e63	−0.774403
$122$	−1.29219e63	−0.300160
$123$	0	0
$124$	−4.54381e63	−0.642774
$125$	−5.65353e63	−0.625986
$126$	0	0
$127$	−2.01045e64	−1.37176	−0.685881	−	0.727714i	$-0.740583\pi$
$127$	−2.01045e64	−1.37176	−0.685881	+	0.727714i	$0.740583\pi$
$128$	−1.34654e64	−0.723296
$129$	0	0
$130$	−5.38141e62	−0.0180146
$131$	−1.95810e64	−0.518872	−0.259436	−	0.965760i	$-0.583537\pi$
$131$	−1.95810e64	−0.518872	−0.259436	+	0.965760i	$0.583537\pi$
$132$	0	0
$133$	1.39854e65	2.33453
$134$	2.49847e65	3.31878
$135$	0	0
$136$	−2.23871e65	−1.89261
$137$	−2.25308e65	−1.52335	−0.761673	−	0.647962i	$-0.775622\pi$
$137$	−2.25308e65	−1.52335	−0.761673	+	0.647962i	$0.775622\pi$
$138$	0	0
$139$	−1.19702e65	−0.520174	−0.260087	−	0.965585i	$-0.583751\pi$
$139$	−1.19702e65	−0.520174	−0.260087	+	0.965585i	$0.583751\pi$
$140$	−3.90014e65	−1.36200
$141$	0	0
$142$	9.29308e65	2.10555
$143$	7.54798e63	0.0138064
$144$	0	0
$145$	−1.52112e65	−0.182154
$146$	1.72749e66	1.67747
$147$	0	0
$148$	3.12528e66	2.00404
$149$	−8.52805e65	−0.445316	−0.222658	−	0.974897i	$-0.571473\pi$
$149$	−8.52805e65	−0.445316	−0.222658	+	0.974897i	$0.571473\pi$
$150$	0	0
$151$	−5.28415e65	−0.183729	−0.0918646	−	0.995772i	$-0.529283\pi$
$151$	−5.28415e65	−0.183729	−0.0918646	+	0.995772i	$0.529283\pi$
$152$	1.40478e67	3.99374
$153$	0	0
$154$	7.65640e66	1.46097
$155$	−5.43052e65	−0.0850598
$156$	0	0
$157$	7.85892e66	0.832575	0.416287	−	0.909233i	$-0.363331\pi$
$157$	7.85892e66	0.832575	0.416287	+	0.909233i	$0.363331\pi$
$158$	−3.49999e67	−3.05510
$159$	0	0
$160$	−1.31005e67	−0.779162
$161$	1.10977e67	0.545815
$162$	0	0
$163$	4.04897e67	1.36654	0.683270	−	0.730166i	$-0.260557\pi$
$163$	4.04897e67	1.36654	0.683270	+	0.730166i	$0.260557\pi$
$164$	−1.98698e67	−0.556487
$165$	0	0
$166$	−1.88004e68	−3.63807
$167$	−3.79481e67	−0.611417	−0.305708	−	0.952125i	$-0.598893\pi$
$167$	−3.79481e67	−0.611417	−0.305708	+	0.952125i	$0.598893\pi$
$168$	0	0
$169$	−8.91615e67	−0.999155
$170$	−4.45644e67	−0.417154
$171$	0	0
$172$	−1.41578e68	−0.927635
$173$	2.38020e67	0.130679	0.0653397	−	0.997863i	$-0.479187\pi$
$173$	2.38020e67	0.130679	0.0653397	+	0.997863i	$0.479187\pi$
$174$	0	0
$175$	3.78450e68	1.46335
$176$	4.03328e68	1.31076
$177$	0	0
$178$	−3.92423e68	−0.903534
$179$	−1.05792e68	−0.205323	−0.102661	−	0.994716i	$-0.532736\pi$
$179$	−1.05792e68	−0.205323	−0.102661	+	0.994716i	$0.532736\pi$
$180$	0	0
$181$	−4.17583e68	−0.577493	−0.288746	−	0.957406i	$-0.593238\pi$
$181$	−4.17583e68	−0.577493	−0.288746	+	0.957406i	$0.593238\pi$
$182$	7.64835e67	0.0894109
$183$	0	0
$184$	1.11473e69	0.933740
$185$	3.73517e68	0.265199
$186$	0	0
$187$	6.25062e68	0.319709
$188$	−4.55217e69	−1.97881
$189$	0	0
$190$	2.79640e69	0.880268
$191$	3.75239e69	1.00644	0.503222	−	0.864157i	$-0.332148\pi$
$191$	3.75239e69	1.00644	0.503222	+	0.864157i	$0.332148\pi$
$192$	0	0
$193$	−4.33214e69	−0.845678	−0.422839	−	0.906205i	$-0.638966\pi$
$193$	−4.33214e69	−0.845678	−0.422839	+	0.906205i	$0.638966\pi$
$194$	1.12732e70	1.87972
$195$	0	0
$196$	3.49114e70	4.25753
$197$	−1.20339e70	−1.25657	−0.628285	−	0.777983i	$-0.716243\pi$
$197$	−1.20339e70	−1.25657	−0.628285	+	0.777983i	$0.716243\pi$
$198$	0	0
$199$	−3.29217e69	−0.252618	−0.126309	−	0.991991i	$-0.540313\pi$
$199$	−3.29217e69	−0.252618	−0.126309	+	0.991991i	$0.540313\pi$
$200$	3.80140e70	2.50339
$201$	0	0
$202$	−1.39387e70	−0.677648
$203$	2.16190e70	0.904079
$204$	0	0
$205$	−2.37473e69	−0.0736412
$206$	7.07287e70	1.89080
$207$	0	0
$208$	4.02904e69	0.0802176
$209$	−3.92225e70	−0.674642
$210$	0	0
$211$	1.05468e68	0.00135677	0.000678387	−	1.00000i	$-0.499784\pi$
$211$	1.05468e68	0.00135677	0.000678387		1.00000i	$0.499784\pi$
$212$	−2.80293e71	−3.12154
$213$	0	0
$214$	−3.27629e71	−2.74007
$215$	−1.69206e70	−0.122756
$216$	0	0
$217$	7.71815e70	0.422174
$218$	1.79210e71	0.851997
$219$	0	0
$220$	1.09381e71	0.393596
$221$	6.24406e69	0.0195660
$222$	0	0
$223$	2.72351e71	0.648381	0.324191	−	0.945992i	$-0.394908\pi$
$223$	2.72351e71	0.648381	0.324191	+	0.945992i	$0.394908\pi$
$224$	1.86191e72	3.86718
$225$	0	0
$226$	1.08557e72	1.71929
$227$	2.72607e71	0.377354	0.188677	−	0.982039i	$-0.439580\pi$
$227$	2.72607e71	0.377354	0.188677	+	0.982039i	$0.439580\pi$
$228$	0	0
$229$	−1.01160e72	−1.07158	−0.535791	−	0.844351i	$-0.679986\pi$
$229$	−1.01160e72	−1.07158	−0.535791	+	0.844351i	$0.679986\pi$
$230$	2.21902e71	0.205808
$231$	0	0
$232$	2.17156e72	1.54663
$233$	−1.13228e72	−0.707291	−0.353646	−	0.935379i	$-0.615058\pi$
$233$	−1.13228e72	−0.707291	−0.353646	+	0.935379i	$0.615058\pi$
$234$	0	0
$235$	−5.44052e71	−0.261861
$236$	7.94349e72	3.35889
$237$	0	0
$238$	6.33374e72	2.07044
$239$	−2.78705e72	−0.801695	−0.400847	−	0.916145i	$-0.631284\pi$
$239$	−2.78705e72	−0.801695	−0.400847	+	0.916145i	$0.631284\pi$
$240$	0	0
$241$	2.43249e72	0.542664	0.271332	−	0.962486i	$-0.412536\pi$
$241$	2.43249e72	0.542664	0.271332	+	0.962486i	$0.412536\pi$
$242$	7.37088e72	1.44927
$243$	0	0
$244$	2.62372e72	0.401354
$245$	4.17243e72	0.563408
$246$	0	0
$247$	−3.91813e71	−0.0412878
$248$	7.75262e72	0.722225
$249$	0	0
$250$	1.60664e73	1.17152
$251$	−8.38055e72	−0.541033	−0.270517	−	0.962715i	$-0.587194\pi$
$251$	−8.38055e72	−0.541033	−0.270517	+	0.962715i	$0.587194\pi$
$252$	0	0
$253$	−3.11240e72	−0.157732
$254$	5.71335e73	2.56722
$255$	0	0
$256$	−8.20094e72	−0.290098
$257$	−2.92677e73	−0.919239	−0.459620	−	0.888116i	$-0.652014\pi$
$257$	−2.92677e73	−0.919239	−0.459620	+	0.888116i	$0.652014\pi$
$258$	0	0
$259$	−5.30863e73	−1.31625
$260$	1.09266e72	0.0240879
$261$	0	0
$262$	5.56459e73	0.971055
$263$	5.79108e73	0.899724	0.449862	−	0.893098i	$-0.351473\pi$
$263$	5.79108e73	0.899724	0.449862	+	0.893098i	$0.351473\pi$
$264$	0	0
$265$	−3.34991e73	−0.413080
$266$	−3.97441e74	−4.36900
$267$	0	0
$268$	−5.07300e74	−4.43765
$269$	1.60983e74	1.25700	0.628499	−	0.777810i	$-0.283670\pi$
$269$	1.60983e74	1.25700	0.628499	+	0.777810i	$0.283670\pi$
$270$	0	0
$271$	1.09220e74	0.680360	0.340180	−	0.940360i	$-0.389512\pi$
$271$	1.09220e74	0.680360	0.340180	+	0.940360i	$0.389512\pi$
$272$	3.33652e74	1.85756
$273$	0	0
$274$	6.40286e74	2.85090
$275$	−1.06138e74	−0.422885
$276$	0	0
$277$	2.91497e74	0.931112	0.465556	−	0.885018i	$-0.345854\pi$
$277$	2.91497e74	0.931112	0.465556	+	0.885018i	$0.345854\pi$
$278$	3.40172e74	0.973492
$279$	0	0
$280$	6.65441e74	1.53035
$281$	4.21232e74	0.868917	0.434458	−	0.900692i	$-0.356940\pi$
$281$	4.21232e74	0.868917	0.434458	+	0.900692i	$0.356940\pi$
$282$	0	0
$283$	−1.72539e74	−0.286682	−0.143341	−	0.989673i	$-0.545785\pi$
$283$	−1.72539e74	−0.286682	−0.143341	+	0.989673i	$0.545785\pi$
$284$	−1.88690e75	−2.81540
$285$	0	0
$286$	−2.14501e73	−0.0258384
$287$	3.37510e74	0.365501
$288$	0	0
$289$	−6.24177e74	−0.546920
$290$	4.32277e74	0.340897
$291$	0	0
$292$	−3.50757e75	−2.24300
$293$	−2.63304e75	−1.51703	−0.758517	−	0.651654i	$-0.774076\pi$
$293$	−2.63304e75	−1.51703	−0.758517	+	0.651654i	$0.774076\pi$
$294$	0	0
$295$	9.49364e74	0.444489
$296$	−5.33234e75	−2.25175
$297$	0	0
$298$	2.42353e75	0.833397
$299$	−3.10913e73	−0.00965313
$300$	0	0
$301$	2.40485e75	0.609271
$302$	1.50167e75	0.343844
$303$	0	0
$304$	−2.09366e76	−3.91978
$305$	3.13573e74	0.0531121
$306$	0	0
$307$	−1.01914e76	−1.41421	−0.707103	−	0.707110i	$-0.749998\pi$
$307$	−1.01914e76	−1.41421	−0.707103	+	0.707110i	$0.749998\pi$
$308$	−1.55458e76	−1.95352
$309$	0	0
$310$	1.54326e75	0.159187
$311$	1.92950e76	1.80406	0.902032	−	0.431669i	$-0.142075\pi$
$311$	1.92950e76	1.80406	0.902032	+	0.431669i	$0.142075\pi$
$312$	0	0
$313$	−1.21312e76	−0.932825	−0.466413	−	0.884567i	$-0.654454\pi$
$313$	−1.21312e76	−0.932825	−0.466413	+	0.884567i	$0.654454\pi$
$314$	−2.23337e76	−1.55814
$315$	0	0
$316$	7.10652e76	4.08508
$317$	1.56107e76	0.814918	0.407459	−	0.913224i	$-0.366415\pi$
$317$	1.56107e76	0.814918	0.407459	+	0.913224i	$0.366415\pi$
$318$	0	0
$319$	−6.06313e75	−0.261265
$320$	1.38973e76	0.544321
$321$	0	0
$322$	−3.15379e76	−1.02148
$323$	−3.24467e76	−0.956080
$324$	0	0
$325$	−1.06026e75	−0.0258804
$326$	−1.15065e77	−2.55744
$327$	0	0
$328$	3.39017e76	0.625272
$329$	7.73236e76	1.29968
$330$	0	0
$331$	6.24069e76	0.871924	0.435962	−	0.899965i	$-0.356408\pi$
$331$	6.24069e76	0.871924	0.435962	+	0.899965i	$0.356408\pi$
$332$	3.81732e77	4.86460
$333$	0	0
$334$	1.07842e77	1.14425
$335$	−6.06298e76	−0.587245
$336$	0	0
$337$	1.13017e77	0.912922	0.456461	−	0.889743i	$-0.349117\pi$
$337$	1.13017e77	0.912922	0.456461	+	0.889743i	$0.349117\pi$
$338$	2.53382e77	1.86989
$339$	0	0
$340$	9.04853e76	0.557791
$341$	−2.16459e76	−0.122002
$342$	0	0
$343$	−2.44461e77	−1.15276
$344$	2.41559e77	1.04230
$345$	0	0
$346$	−6.76413e76	−0.244563
$347$	−8.92703e76	−0.295568	−0.147784	−	0.989020i	$-0.547214\pi$
$347$	−8.92703e76	−0.295568	−0.147784	+	0.989020i	$0.547214\pi$
$348$	0	0
$349$	−2.05483e77	−0.570953	−0.285476	−	0.958386i	$-0.592152\pi$
$349$	−2.05483e77	−0.570953	−0.285476	+	0.958386i	$0.592152\pi$
$350$	−1.07549e78	−2.73862
$351$	0	0
$352$	−5.22181e77	−1.11756
$353$	−7.47126e77	−1.46644	−0.733222	−	0.679990i	$-0.761984\pi$
$353$	−7.47126e77	−1.46644	−0.733222	+	0.679990i	$0.761984\pi$
$354$	0	0
$355$	−2.25513e77	−0.372569
$356$	7.96791e77	1.20815
$357$	0	0
$358$	3.00645e77	0.384256
$359$	9.45141e77	1.10947	0.554736	−	0.832027i	$-0.312819\pi$
$359$	9.45141e77	1.10947	0.554736	+	0.832027i	$0.312819\pi$
$360$	0	0
$361$	1.02684e78	1.01750
$362$	1.18670e78	1.08076
$363$	0	0
$364$	−1.55295e77	−0.119554
$365$	−4.19206e77	−0.296822
$366$	0	0
$367$	−1.08283e78	−0.649002	−0.324501	−	0.945885i	$-0.605196\pi$
$367$	−1.08283e78	−0.649002	−0.324501	+	0.945885i	$0.605196\pi$
$368$	−1.66137e78	−0.916448
$369$	0	0
$370$	−1.06147e78	−0.496313
$371$	4.76109e78	2.05023
$372$	0	0
$373$	3.84170e78	1.40412	0.702059	−	0.712119i	$-0.252264\pi$
$373$	3.84170e78	1.40412	0.702059	+	0.712119i	$0.252264\pi$
$374$	−1.77632e78	−0.598326
$375$	0	0
$376$	7.76690e78	2.22340
$377$	−6.05677e76	−0.0159893
$378$	0	0
$379$	1.78001e78	0.399876	0.199938	−	0.979809i	$-0.435926\pi$
$379$	1.78001e78	0.399876	0.199938	+	0.979809i	$0.435926\pi$
$380$	−5.67793e78	−1.17704
$381$	0	0
$382$	−1.06637e79	−1.88353
$383$	−1.00847e79	−1.64475	−0.822374	−	0.568947i	$-0.807351\pi$
$383$	−1.00847e79	−1.64475	−0.822374	+	0.568947i	$0.807351\pi$
$384$	0	0
$385$	−1.85796e78	−0.258514
$386$	1.23112e79	1.58266
$387$	0	0
$388$	−2.28895e79	−2.51344
$389$	1.43823e78	0.146004	0.0730021	−	0.997332i	$-0.476742\pi$
$389$	1.43823e78	0.146004	0.0730021	+	0.997332i	$0.476742\pi$
$390$	0	0
$391$	−2.57473e78	−0.223533
$392$	−5.95657e79	−4.78378
$393$	0	0
$394$	3.41983e79	2.35164
$395$	8.49333e78	0.540588
$396$	0	0
$397$	1.30448e79	0.711751	0.355875	−	0.934533i	$-0.384183\pi$
$397$	1.30448e79	0.711751	0.355875	+	0.934533i	$0.384183\pi$
$398$	9.35580e78	0.472767
$399$	0	0
$400$	−5.66553e79	−2.45703
$401$	1.11670e79	0.448778	0.224389	−	0.974500i	$-0.427961\pi$
$401$	1.11670e79	0.448778	0.224389	+	0.974500i	$0.427961\pi$
$402$	0	0
$403$	−2.16231e77	−0.00746646
$404$	2.83016e79	0.906107
$405$	0	0
$406$	−6.14376e79	−1.69196
$407$	1.48883e79	0.380377
$408$	0	0
$409$	6.64811e79	1.46264	0.731320	−	0.682035i	$-0.238905\pi$
$409$	6.64811e79	1.46264	0.731320	+	0.682035i	$0.238905\pi$
$410$	6.74858e78	0.137818
$411$	0	0
$412$	−1.43610e80	−2.52825
$413$	−1.34929e80	−2.20612
$414$	0	0
$415$	4.56226e79	0.643743
$416$	−5.21632e78	−0.0683940
$417$	0	0
$418$	1.11464e80	1.26257
$419$	1.13113e80	1.19120	0.595602	−	0.803279i	$-0.296913\pi$
$419$	1.13113e80	1.19120	0.595602	+	0.803279i	$0.296913\pi$
$420$	0	0
$421$	−2.50575e78	−0.0228210	−0.0114105	−	0.999935i	$-0.503632\pi$
$421$	−2.50575e78	−0.0228210	−0.0114105	+	0.999935i	$0.503632\pi$
$422$	−2.99723e77	−0.00253916
$423$	0	0
$424$	4.78235e80	3.50738
$425$	−8.78022e79	−0.599299
$426$	0	0
$427$	−4.45667e79	−0.263609
$428$	6.65231e80	3.66385
$429$	0	0
$430$	4.80856e79	0.229735
$431$	4.22944e80	1.88246	0.941231	−	0.337763i	$-0.109670\pi$
$431$	4.22944e80	1.88246	0.941231	+	0.337763i	$0.109670\pi$
$432$	0	0
$433$	4.38659e80	1.69530	0.847650	−	0.530556i	$-0.178017\pi$
$433$	4.38659e80	1.69530	0.847650	+	0.530556i	$0.178017\pi$
$434$	−2.19337e80	−0.790087
$435$	0	0
$436$	−3.63874e80	−1.13924
$437$	1.61564e80	0.471693
$438$	0	0
$439$	1.27552e80	0.323981	0.161991	−	0.986792i	$-0.448209\pi$
$439$	1.27552e80	0.323981	0.161991	+	0.986792i	$0.448209\pi$
$440$	−1.86625e80	−0.442246
$441$	0	0
$442$	−1.77446e79	−0.0366173
$443$	3.94931e80	0.760691	0.380345	−	0.924845i	$-0.375805\pi$
$443$	3.94931e80	0.760691	0.380345	+	0.924845i	$0.375805\pi$
$444$	0	0
$445$	9.52283e79	0.159877
$446$	−7.73975e80	−1.21343
$447$	0	0
$448$	−1.97516e81	−2.70161
$449$	−3.41850e80	−0.436840	−0.218420	−	0.975855i	$-0.570090\pi$
$449$	−3.41850e80	−0.436840	−0.218420	+	0.975855i	$0.570090\pi$
$450$	0	0
$451$	−9.46559e79	−0.105624
$452$	−2.20418e81	−2.29893
$453$	0	0
$454$	−7.74704e80	−0.706207
$455$	−1.85601e79	−0.0158209
$456$	0	0
$457$	−1.01306e81	−0.755423	−0.377711	−	0.925923i	$-0.623289\pi$
$457$	−1.01306e81	−0.755423	−0.377711	+	0.925923i	$0.623289\pi$
$458$	2.87479e81	2.00544
$459$	0	0
$460$	−4.50558e80	−0.275193
$461$	3.55139e80	0.203011	0.101506	−	0.994835i	$-0.467634\pi$
$461$	3.55139e80	0.203011	0.101506	+	0.994835i	$0.467634\pi$
$462$	0	0
$463$	6.17959e80	0.309556	0.154778	−	0.987949i	$-0.450534\pi$
$463$	6.17959e80	0.309556	0.154778	+	0.987949i	$0.450534\pi$
$464$	−3.23644e81	−1.51799
$465$	0	0
$466$	3.21775e81	1.32368
$467$	2.32266e81	0.894997	0.447499	−	0.894285i	$-0.352315\pi$
$467$	2.32266e81	0.894997	0.447499	+	0.894285i	$0.352315\pi$
$468$	0	0
$469$	8.61704e81	2.91465
$470$	1.54610e81	0.490065
$471$	0	0
$472$	−1.35531e82	−3.77406
$473$	−6.74450e80	−0.176070
$474$	0	0
$475$	5.50957e81	1.26463
$476$	−1.28603e82	−2.76846
$477$	0	0
$478$	7.92034e81	1.50035
$479$	6.48492e81	1.15258	0.576290	−	0.817245i	$-0.304500\pi$
$479$	6.48492e81	1.15258	0.576290	+	0.817245i	$0.304500\pi$
$480$	0	0
$481$	1.48726e80	0.0232789
$482$	−6.91272e81	−1.01558
$483$	0	0
$484$	−1.49661e82	−1.93788
$485$	−2.73563e81	−0.332610
$486$	0	0
$487$	1.13904e82	1.22153	0.610765	−	0.791812i	$-0.290862\pi$
$487$	1.13904e82	1.22153	0.610765	+	0.791812i	$0.290862\pi$
$488$	−4.47658e81	−0.450964
$489$	0	0
$490$	−1.18573e82	−1.05440
$491$	8.43794e81	0.705101	0.352550	−	0.935793i	$-0.385315\pi$
$491$	8.43794e81	0.705101	0.352550	+	0.935793i	$0.385315\pi$
$492$	0	0
$493$	−5.01572e81	−0.370256
$494$	1.11347e81	0.0772690
$495$	0	0
$496$	−1.15543e82	−0.708850
$497$	3.20511e82	1.84916
$498$	0	0
$499$	4.77379e81	0.243667	0.121833	−	0.992551i	$-0.461123\pi$
$499$	4.77379e81	0.243667	0.121833	+	0.992551i	$0.461123\pi$
$500$	−3.26219e82	−1.56648
$501$	0	0
$502$	2.38161e82	1.01253
$503$	7.98855e81	0.319628	0.159814	−	0.987147i	$-0.448911\pi$
$503$	7.98855e81	0.319628	0.159814	+	0.987147i	$0.448911\pi$
$504$	0	0
$505$	3.38246e81	0.119907
$506$	8.84493e81	0.295191
$507$	0	0
$508$	−1.16006e83	−3.43271
$509$	−5.44275e82	−1.51679	−0.758396	−	0.651794i	$-0.774017\pi$
$509$	−5.44275e82	−1.51679	−0.758396	+	0.651794i	$0.774017\pi$
$510$	0	0
$511$	5.95800e82	1.47320
$512$	5.43549e82	1.26621
$513$	0	0
$514$	8.31740e82	1.72033
$515$	−1.71635e82	−0.334570
$516$	0	0
$517$	−2.16857e82	−0.375588
$518$	1.50862e83	2.46333
$519$	0	0
$520$	−1.86429e81	−0.0270653
$521$	−3.83339e82	−0.524847	−0.262424	−	0.964953i	$-0.584522\pi$
$521$	−3.83339e82	−0.524847	−0.262424	+	0.964953i	$0.584522\pi$
$522$	0	0
$523$	8.06645e82	0.982609	0.491305	−	0.870988i	$-0.336520\pi$
$523$	8.06645e82	0.982609	0.491305	+	0.870988i	$0.336520\pi$
$524$	−1.12986e83	−1.29843
$525$	0	0
$526$	−1.64573e83	−1.68381
$527$	−1.79065e82	−0.172897
$528$	0	0
$529$	−1.03431e83	−0.889718
$530$	9.51990e82	0.773069
$531$	0	0
$532$	8.06979e83	5.84195
$533$	−9.45564e80	−0.00646415
$534$	0	0
$535$	7.95048e82	0.484845
$536$	8.65553e83	4.98617
$537$	0	0
$538$	−4.57486e83	−2.35244
$539$	1.66312e83	0.808100
$540$	0	0
$541$	3.06629e83	1.33075	0.665375	−	0.746509i	$-0.268272\pi$
$541$	3.06629e83	1.33075	0.665375	+	0.746509i	$0.268272\pi$
$542$	−3.10385e83	−1.27328
$543$	0	0
$544$	−4.31973e83	−1.58376
$545$	−4.34883e82	−0.150758
$546$	0	0
$547$	1.45425e83	0.450842	0.225421	−	0.974261i	$-0.427624\pi$
$547$	1.45425e83	0.450842	0.225421	+	0.974261i	$0.427624\pi$
$548$	−1.30006e84	−3.81204
$549$	0	0
$550$	3.01626e83	0.791418
$551$	3.14735e83	0.781306
$552$	0	0
$553$	−1.20712e84	−2.68308
$554$	−8.28387e83	−1.74255
$555$	0	0
$556$	−6.90699e83	−1.30169
$557$	−3.06138e83	−0.546177	−0.273089	−	0.961989i	$-0.588045\pi$
$557$	−3.06138e83	−0.546177	−0.273089	+	0.961989i	$0.588045\pi$
$558$	0	0
$559$	−6.73742e81	−0.0107754
$560$	−9.91760e83	−1.50201
$561$	0	0
$562$	−1.19707e84	−1.62615
$563$	−2.96460e83	−0.381470	−0.190735	−	0.981642i	$-0.561087\pi$
$563$	−2.96460e83	−0.381470	−0.190735	+	0.981642i	$0.561087\pi$
$564$	0	0
$565$	−2.63432e83	−0.304223
$566$	4.90327e83	0.536518
$567$	0	0
$568$	3.21943e84	3.16340
$569$	7.76465e83	0.723099	0.361549	−	0.932353i	$-0.382248\pi$
$569$	7.76465e83	0.723099	0.361549	+	0.932353i	$0.382248\pi$
$570$	0	0
$571$	−3.44139e83	−0.287960	−0.143980	−	0.989581i	$-0.545990\pi$
$571$	−3.44139e83	−0.287960	−0.143980	+	0.989581i	$0.545990\pi$
$572$	4.35531e82	0.0345494
$573$	0	0
$574$	−9.59146e83	−0.684025
$575$	4.37198e83	0.295671
$576$	0	0
$577$	−1.84102e84	−1.11995	−0.559973	−	0.828511i	$-0.689189\pi$
$577$	−1.84102e84	−1.11995	−0.559973	+	0.828511i	$0.689189\pi$
$578$	1.77381e84	1.02355
$579$	0	0
$580$	−8.77712e83	−0.455825
$581$	−6.48413e84	−3.19507
$582$	0	0
$583$	−1.33526e84	−0.592484
$584$	5.98460e84	2.52025
$585$	0	0
$586$	7.48266e84	2.83909
$587$	5.03892e84	1.81500	0.907498	−	0.420057i	$-0.137990\pi$
$587$	5.03892e84	1.81500	0.907498	+	0.420057i	$0.137990\pi$
$588$	0	0
$589$	1.12363e84	0.364843
$590$	−2.69793e84	−0.831850
$591$	0	0
$592$	7.94720e84	2.21005
$593$	9.78641e82	0.0258497	0.0129248	−	0.999916i	$-0.495886\pi$
$593$	9.78641e82	0.0258497	0.0129248	+	0.999916i	$0.495886\pi$
$594$	0	0
$595$	−1.53699e84	−0.366357
$596$	−4.92083e84	−1.11436
$597$	0	0
$598$	8.83564e82	0.0180656
$599$	−8.94959e83	−0.173894	−0.0869471	−	0.996213i	$-0.527711\pi$
$599$	−8.94959e83	−0.173894	−0.0869471	+	0.996213i	$0.527711\pi$
$600$	0	0
$601$	−4.15804e84	−0.729822	−0.364911	−	0.931042i	$-0.618901\pi$
$601$	−4.15804e84	−0.729822	−0.364911	+	0.931042i	$0.618901\pi$
$602$	−6.83419e84	−1.14023
$603$	0	0
$604$	−3.04904e84	−0.459766
$605$	−1.78867e84	−0.256444
$606$	0	0
$607$	−1.10453e85	−1.43193	−0.715966	−	0.698135i	$-0.754014\pi$
$607$	−1.10453e85	−1.43193	−0.715966	+	0.698135i	$0.754014\pi$
$608$	2.71062e85	3.34202
$609$	0	0
$610$	−8.91122e83	−0.0993979
$611$	−2.16629e83	−0.0229858
$612$	0	0
$613$	4.37303e83	0.0419989	0.0209994	−	0.999779i	$-0.493315\pi$
$613$	4.37303e83	0.0419989	0.0209994	+	0.999779i	$0.493315\pi$
$614$	2.89622e85	2.64665
$615$	0	0
$616$	2.65243e85	2.19498
$617$	−1.63068e85	−1.28432	−0.642158	−	0.766572i	$-0.721961\pi$
$617$	−1.63068e85	−1.28432	−0.642158	+	0.766572i	$0.721961\pi$
$618$	0	0
$619$	2.95589e84	0.210923	0.105462	−	0.994423i	$-0.466368\pi$
$619$	2.95589e84	0.210923	0.105462	+	0.994423i	$0.466368\pi$
$620$	−3.13350e84	−0.212855
$621$	0	0
$622$	−5.48330e85	−3.37626
$623$	−1.35344e85	−0.793511
$624$	0	0
$625$	1.28466e85	0.683044
$626$	3.44747e85	1.74576
$627$	0	0
$628$	4.53473e85	2.08345
$629$	1.23163e85	0.539057
$630$	0	0
$631$	−2.00789e85	−0.797710	−0.398855	−	0.917014i	$-0.630592\pi$
$631$	−2.00789e85	−0.797710	−0.398855	+	0.917014i	$0.630592\pi$
$632$	−1.21251e86	−4.59002
$633$	0	0
$634$	−4.43629e85	−1.52510
$635$	−1.38644e85	−0.454259
$636$	0	0
$637$	1.66137e84	0.0494554
$638$	1.72304e85	0.488951
$639$	0	0
$640$	−9.28603e84	−0.239520
$641$	5.74852e85	1.41379	0.706897	−	0.707316i	$-0.250094\pi$
$641$	5.74852e85	1.41379	0.706897	+	0.707316i	$0.250094\pi$
$642$	0	0
$643$	1.81186e85	0.405219	0.202610	−	0.979260i	$-0.435058\pi$
$643$	1.81186e85	0.405219	0.202610	+	0.979260i	$0.435058\pi$
$644$	6.40358e85	1.36585
$645$	0	0
$646$	9.22082e85	1.78928
$647$	6.46742e84	0.119716	0.0598578	−	0.998207i	$-0.480935\pi$
$647$	6.46742e84	0.119716	0.0598578	+	0.998207i	$0.480935\pi$
$648$	0	0
$649$	3.78413e85	0.637534
$650$	3.01309e84	0.0484345
$651$	0	0
$652$	2.33632e86	3.41965
$653$	−5.18677e85	−0.724511	−0.362256	−	0.932079i	$-0.617993\pi$
$653$	−5.18677e85	−0.724511	−0.362256	+	0.932079i	$0.617993\pi$
$654$	0	0
$655$	−1.35035e85	−0.171825
$656$	−5.05264e85	−0.613693
$657$	0	0
$658$	−2.19741e86	−2.43232
$659$	1.56604e85	0.165500	0.0827501	−	0.996570i	$-0.473630\pi$
$659$	1.56604e85	0.165500	0.0827501	+	0.996570i	$0.473630\pi$
$660$	0	0
$661$	5.66912e85	0.546224	0.273112	−	0.961982i	$-0.411947\pi$
$661$	5.66912e85	0.546224	0.273112	+	0.961982i	$0.411947\pi$
$662$	−1.77350e86	−1.63178
$663$	0	0
$664$	−6.51309e86	−5.46589
$665$	9.64459e85	0.773078
$666$	0	0
$667$	2.49750e85	0.182670
$668$	−2.18967e86	−1.53002
$669$	0	0
$670$	1.72300e86	1.09901
$671$	1.24989e85	0.0761790
$672$	0	0
$673$	5.64478e85	0.314186	0.157093	−	0.987584i	$-0.449788\pi$
$673$	5.64478e85	0.314186	0.157093	+	0.987584i	$0.449788\pi$
$674$	−3.21177e86	−1.70851
$675$	0	0
$676$	−5.14477e86	−2.50030
$677$	3.08615e86	1.43371	0.716857	−	0.697220i	$-0.245580\pi$
$677$	3.08615e86	1.43371	0.716857	+	0.697220i	$0.245580\pi$
$678$	0	0
$679$	3.88803e86	1.65083
$680$	−1.54386e86	−0.626737
$681$	0	0
$682$	6.15139e85	0.228323
$683$	−2.92712e86	−1.03898	−0.519491	−	0.854476i	$-0.673879\pi$
$683$	−2.92712e86	−1.03898	−0.519491	+	0.854476i	$0.673879\pi$
$684$	0	0
$685$	−1.55377e86	−0.504456
$686$	6.94717e86	2.15736
$687$	0	0
$688$	−3.60015e86	−1.02299
$689$	−1.33386e85	−0.0362598
$690$	0	0
$691$	6.58507e86	1.63863	0.819313	−	0.573347i	$-0.194355\pi$
$691$	6.58507e86	1.63863	0.819313	+	0.573347i	$0.194355\pi$
$692$	1.37342e86	0.327014
$693$	0	0
$694$	2.53691e86	0.553148
$695$	−8.25487e85	−0.172256
$696$	0	0
$697$	−7.83039e85	−0.149687
$698$	5.83948e86	1.06852
$699$	0	0
$700$	2.18372e87	3.66190
$701$	1.19477e87	1.91817	0.959083	−	0.283124i	$-0.0913709\pi$
$701$	1.19477e87	1.91817	0.959083	+	0.283124i	$0.0913709\pi$
$702$	0	0
$703$	−7.72843e86	−1.13751
$704$	5.53940e86	0.780723
$705$	0	0
$706$	2.12321e87	2.74441
$707$	−4.80734e86	−0.595131
$708$	0	0
$709$	−8.38841e86	−0.952729	−0.476365	−	0.879248i	$-0.658046\pi$
$709$	−8.38841e86	−0.952729	−0.476365	+	0.879248i	$0.658046\pi$
$710$	6.40870e86	0.697253
$711$	0	0
$712$	−1.35948e87	−1.35748
$713$	8.91627e85	0.0853007
$714$	0	0
$715$	5.20524e84	0.00457200
$716$	−6.10441e86	−0.513803
$717$	0	0
$718$	−2.68593e87	−2.07635
$719$	1.44491e86	0.107055	0.0535277	−	0.998566i	$-0.482953\pi$
$719$	1.44491e86	0.107055	0.0535277	+	0.998566i	$0.482953\pi$
$720$	0	0
$721$	2.43938e87	1.66056
$722$	−2.91811e87	−1.90422
$723$	0	0
$724$	−2.40953e87	−1.44512
$725$	8.51686e86	0.489745
$726$	0	0
$727$	1.05896e87	0.559861	0.279931	−	0.960020i	$-0.409689\pi$
$727$	1.05896e87	0.559861	0.279931	+	0.960020i	$0.409689\pi$
$728$	2.64964e86	0.134332
$729$	0	0
$730$	1.19131e87	0.555494
$731$	−5.57938e86	−0.249520
$732$	0	0
$733$	6.14850e86	0.252987	0.126493	−	0.991967i	$-0.459628\pi$
$733$	6.14850e86	0.252987	0.126493	+	0.991967i	$0.459628\pi$
$734$	3.07723e87	1.21459
$735$	0	0
$736$	2.15095e87	0.781369
$737$	−2.41668e87	−0.842289
$738$	0	0
$739$	−1.06088e87	−0.340417	−0.170209	−	0.985408i	$-0.554444\pi$
$739$	−1.06088e87	−0.340417	−0.170209	+	0.985408i	$0.554444\pi$
$740$	2.15525e87	0.663638
$741$	0	0
$742$	−1.35302e88	−3.83694
$743$	7.11678e87	1.93698	0.968490	−	0.249054i	$-0.0801198\pi$
$743$	7.11678e87	1.93698	0.968490	+	0.249054i	$0.0801198\pi$
$744$	0	0
$745$	−5.88111e86	−0.147466
$746$	−1.09175e88	−2.62777
$747$	0	0
$748$	3.60672e87	0.800043
$749$	−1.12997e88	−2.40641
$750$	0	0
$751$	−2.75527e87	−0.540936	−0.270468	−	0.962729i	$-0.587178\pi$
$751$	−2.75527e87	−0.540936	−0.270468	+	0.962729i	$0.587178\pi$
$752$	−1.15756e88	−2.18223
$753$	0	0
$754$	1.72123e86	0.0299236
$755$	−3.64406e86	−0.0608419
$756$	0	0
$757$	−5.08599e87	−0.783342	−0.391671	−	0.920105i	$-0.628103\pi$
$757$	−5.08599e87	−0.783342	−0.391671	+	0.920105i	$0.628103\pi$
$758$	−5.05848e87	−0.748358
$759$	0	0
$760$	9.68766e87	1.32253
$761$	6.17119e87	0.809351	0.404675	−	0.914460i	$-0.367385\pi$
$761$	6.17119e87	0.809351	0.404675	+	0.914460i	$0.367385\pi$
$762$	0	0
$763$	6.18080e87	0.748250
$764$	2.16519e88	2.51854
$765$	0	0
$766$	2.86590e88	3.07810
$767$	3.78016e86	0.0390168
$768$	0	0
$769$	−9.88338e87	−0.942219	−0.471110	−	0.882075i	$-0.656146\pi$
$769$	−9.88338e87	−0.942219	−0.471110	+	0.882075i	$0.656146\pi$
$770$	5.28000e87	0.483801
$771$	0	0
$772$	−2.49972e88	−2.11623
$773$	−1.65349e88	−1.34563	−0.672816	−	0.739810i	$-0.734915\pi$
$773$	−1.65349e88	−1.34563	−0.672816	+	0.739810i	$0.734915\pi$
$774$	0	0
$775$	3.04058e87	0.228694
$776$	3.90540e88	2.82412
$777$	0	0
$778$	−4.08721e87	−0.273243
$779$	4.91355e87	0.315866
$780$	0	0
$781$	−8.98887e87	−0.534378
$782$	7.31695e87	0.418335
$783$	0	0
$784$	8.87755e88	4.69519
$785$	5.41967e87	0.275707
$786$	0	0
$787$	−3.40866e88	−1.60455	−0.802277	−	0.596952i	$-0.796378\pi$
$787$	−3.40866e88	−1.60455	−0.802277	+	0.596952i	$0.796378\pi$
$788$	−6.94377e88	−3.14446
$789$	0	0
$790$	−2.41366e88	−1.01170
$791$	3.74405e88	1.50994
$792$	0	0
$793$	1.24858e86	0.00466212
$794$	−3.70712e88	−1.33202
$795$	0	0
$796$	−1.89964e88	−0.632153
$797$	−5.14649e88	−1.64828	−0.824142	−	0.566384i	$-0.808342\pi$
$797$	−5.14649e88	−1.64828	−0.824142	+	0.566384i	$0.808342\pi$
$798$	0	0
$799$	−1.79395e88	−0.532271
$800$	7.33505e88	2.09488
$801$	0	0
$802$	−3.17346e88	−0.839876
$803$	−1.67094e88	−0.425733
$804$	0	0
$805$	7.65322e87	0.180747
$806$	6.14493e86	0.0139733
$807$	0	0
$808$	−4.82881e88	−1.01811
$809$	3.94596e88	0.801167	0.400583	−	0.916260i	$-0.368808\pi$
$809$	3.94596e88	0.801167	0.400583	+	0.916260i	$0.368808\pi$
$810$	0	0
$811$	5.01413e88	0.944189	0.472095	−	0.881548i	$-0.343498\pi$
$811$	5.01413e88	0.944189	0.472095	+	0.881548i	$0.343498\pi$
$812$	1.24745e89	2.26238
$813$	0	0
$814$	−4.23099e88	−0.711865
$815$	2.79225e88	0.452530
$816$	0	0
$817$	3.50105e88	0.526532
$818$	−1.88928e89	−2.73729
$819$	0	0
$820$	−1.37026e88	−0.184281
$821$	2.71849e88	0.352258	0.176129	−	0.984367i	$-0.443642\pi$
$821$	2.71849e88	0.352258	0.176129	+	0.984367i	$0.443642\pi$
$822$	0	0
$823$	1.12457e89	1.35299	0.676493	−	0.736449i	$-0.263499\pi$
$823$	1.12457e89	1.35299	0.676493	+	0.736449i	$0.263499\pi$
$824$	2.45027e89	2.84076
$825$	0	0
$826$	3.83445e89	4.12869
$827$	7.06235e88	0.732877	0.366439	−	0.930442i	$-0.380577\pi$
$827$	7.06235e88	0.732877	0.366439	+	0.930442i	$0.380577\pi$
$828$	0	0
$829$	−1.28843e89	−1.24207	−0.621035	−	0.783783i	$-0.713288\pi$
$829$	−1.28843e89	−1.24207	−0.621035	+	0.783783i	$0.713288\pi$
$830$	−1.29652e89	−1.20475
$831$	0	0
$832$	5.53358e87	0.0477799
$833$	1.37581e89	1.14521
$834$	0	0
$835$	−2.61697e88	−0.202471
$836$	−2.26320e89	−1.68823
$837$	0	0
$838$	−3.21449e89	−2.22931
$839$	−1.19830e89	−0.801355	−0.400678	−	0.916219i	$-0.631225\pi$
$839$	−1.19830e89	−0.801355	−0.400678	+	0.916219i	$0.631225\pi$
$840$	0	0
$841$	−1.12144e89	−0.697428
$842$	7.12093e87	0.0427089
$843$	0	0
$844$	6.08570e86	0.00339521
$845$	−6.14876e88	−0.330870
$846$	0	0
$847$	2.54216e89	1.27280
$848$	−7.12751e89	−3.44243
$849$	0	0
$850$	2.49519e89	1.12157
$851$	−6.13271e88	−0.265950
$852$	0	0
$853$	2.72024e89	1.09815	0.549075	−	0.835773i	$-0.314980\pi$
$853$	2.72024e89	1.09815	0.549075	+	0.835773i	$0.314980\pi$
$854$	1.26651e89	0.493338
$855$	0	0
$856$	−1.13501e90	−4.11672
$857$	4.40217e89	1.54082	0.770409	−	0.637549i	$-0.220052\pi$
$857$	4.40217e89	1.54082	0.770409	+	0.637549i	$0.220052\pi$
$858$	0	0
$859$	4.73420e89	1.54332	0.771659	−	0.636036i	$-0.219427\pi$
$859$	4.73420e89	1.54332	0.771659	+	0.636036i	$0.219427\pi$
$860$	−9.76348e88	−0.307186
$861$	0	0
$862$	−1.20194e90	−3.52298
$863$	2.92227e89	0.826781	0.413390	−	0.910554i	$-0.364344\pi$
$863$	2.92227e89	0.826781	0.413390	+	0.910554i	$0.364344\pi$
$864$	0	0
$865$	1.64143e88	0.0432745
$866$	−1.24660e90	−3.17271
$867$	0	0
$868$	4.45351e89	1.05645
$869$	3.38541e89	0.775369
$870$	0	0
$871$	−2.41415e88	−0.0515477
$872$	6.20841e89	1.28005
$873$	0	0
$874$	−4.59137e89	−0.882762
$875$	5.54118e89	1.02886
$876$	0	0
$877$	8.38175e89	1.45160	0.725800	−	0.687905i	$-0.241470\pi$
$877$	8.38175e89	1.45160	0.725800	+	0.687905i	$0.241470\pi$
$878$	−3.62482e89	−0.606322
$879$	0	0
$880$	2.78143e89	0.434057
$881$	4.60933e89	0.694820	0.347410	−	0.937713i	$-0.387061\pi$
$881$	4.60933e89	0.694820	0.347410	+	0.937713i	$0.387061\pi$
$882$	0	0
$883$	−1.05185e90	−1.47963	−0.739815	−	0.672810i	$-0.765087\pi$
$883$	−1.05185e90	−1.47963	−0.739815	+	0.672810i	$0.765087\pi$
$884$	3.60293e88	0.0489623
$885$	0	0
$886$	−1.12233e90	−1.42361
$887$	−1.61456e90	−1.97871	−0.989357	−	0.145510i	$-0.953518\pi$
$887$	−1.61456e90	−1.97871	−0.989357	+	0.145510i	$0.953518\pi$
$888$	0	0
$889$	1.97049e90	2.25461
$890$	−2.70623e89	−0.299205
$891$	0	0
$892$	1.57151e90	1.62252
$893$	1.12570e90	1.12319
$894$	0	0
$895$	−7.29566e88	−0.0679927
$896$	1.31978e90	1.18880
$897$	0	0
$898$	9.71480e89	0.817534
$899$	1.73694e89	0.141291
$900$	0	0
$901$	−1.10460e90	−0.839648
$902$	2.68996e89	0.197673
$903$	0	0
$904$	3.76077e90	2.58309
$905$	−2.87974e89	−0.191237
$906$	0	0
$907$	1.02664e90	0.637376	0.318688	−	0.947860i	$-0.396758\pi$
$907$	1.02664e90	0.637376	0.318688	+	0.947860i	$0.396758\pi$
$908$	1.57299e90	0.944295
$909$	0	0
$910$	5.27446e88	0.0296084
$911$	1.66692e90	0.904910	0.452455	−	0.891787i	$-0.350548\pi$
$911$	1.66692e90	0.904910	0.452455	+	0.891787i	$0.350548\pi$
$912$	0	0
$913$	1.81850e90	0.923325
$914$	2.87894e90	1.41375
$915$	0	0
$916$	−5.83708e90	−2.68154
$917$	1.91919e90	0.852810
$918$	0	0
$919$	1.08032e90	0.449188	0.224594	−	0.974452i	$-0.427894\pi$
$919$	1.08032e90	0.449188	0.224594	+	0.974452i	$0.427894\pi$
$920$	7.68740e89	0.309208
$921$	0	0
$922$	−1.00925e90	−0.379930
$923$	−8.97943e88	−0.0327037
$924$	0	0
$925$	−2.09135e90	−0.713022
$926$	−1.75614e90	−0.579326
$927$	0	0
$928$	4.19016e90	1.29425
$929$	−4.46225e90	−1.33375	−0.666875	−	0.745170i	$-0.732368\pi$
$929$	−4.46225e90	−1.33375	−0.666875	+	0.745170i	$0.732368\pi$
$930$	0	0
$931$	−8.63317e90	−2.41660
$932$	−6.53345e90	−1.76993
$933$	0	0
$934$	−6.60062e90	−1.67496
$935$	4.31055e89	0.105871
$936$	0	0
$937$	−2.19447e89	−0.0504978	−0.0252489	−	0.999681i	$-0.508038\pi$
$937$	−2.19447e89	−0.0504978	−0.0252489	+	0.999681i	$0.508038\pi$
$938$	−2.44882e91	−5.45469
$939$	0	0
$940$	−3.13927e90	−0.655283
$941$	4.73247e90	0.956321	0.478161	−	0.878272i	$-0.341304\pi$
$941$	4.73247e90	0.956321	0.478161	+	0.878272i	$0.341304\pi$
$942$	0	0
$943$	3.89902e89	0.0738498
$944$	2.01993e91	3.70417
$945$	0	0
$946$	1.91667e90	0.329510
$947$	6.68420e90	1.11269	0.556346	−	0.830951i	$-0.312203\pi$
$947$	6.68420e90	1.11269	0.556346	+	0.830951i	$0.312203\pi$
$948$	0	0
$949$	−1.66919e89	−0.0260547
$950$	−1.56573e91	−2.36672
$951$	0	0
$952$	2.19422e91	3.11066
$953$	8.38193e89	0.115083	0.0575414	−	0.998343i	$-0.481674\pi$
$953$	8.38193e89	0.115083	0.0575414	+	0.998343i	$0.481674\pi$
$954$	0	0
$955$	2.58772e90	0.333284
$956$	−1.60818e91	−2.00617
$957$	0	0
$958$	−1.84291e91	−2.15702
$959$	2.20830e91	2.50375
$960$	0	0
$961$	−8.77850e90	−0.934022
$962$	−4.22655e89	−0.0435658
$963$	0	0
$964$	1.40359e91	1.35797
$965$	−2.98753e90	−0.280046
$966$	0	0
$967$	5.11590e90	0.450209	0.225105	−	0.974335i	$-0.427728\pi$
$967$	5.11590e90	0.450209	0.225105	+	0.974335i	$0.427728\pi$
$968$	2.55351e91	2.17741
$969$	0	0
$970$	7.77421e90	0.622470
$971$	−5.40878e90	−0.419675	−0.209837	−	0.977736i	$-0.567293\pi$
$971$	−5.40878e90	−0.419675	−0.209837	+	0.977736i	$0.567293\pi$
$972$	0	0
$973$	1.17323e91	0.854950
$974$	−3.23695e91	−2.28606
$975$	0	0
$976$	6.67180e90	0.442612
$977$	1.46776e90	0.0943778	0.0471889	−	0.998886i	$-0.484974\pi$
$977$	1.46776e90	0.0943778	0.0471889	+	0.998886i	$0.484974\pi$
$978$	0	0
$979$	3.79577e90	0.229312
$980$	2.40756e91	1.40988
$981$	0	0
$982$	−2.39792e91	−1.31958
$983$	−3.29286e91	−1.75667	−0.878337	−	0.478041i	$-0.841347\pi$
$983$	−3.29286e91	−1.75667	−0.878337	+	0.478041i	$0.841347\pi$
$984$	0	0
$985$	−8.29882e90	−0.416113
$986$	1.42538e91	0.692924
$987$	0	0
$988$	−2.26083e90	−0.103319
$989$	2.77817e90	0.123104
$990$	0	0
$991$	1.54521e91	0.643785	0.321893	−	0.946776i	$-0.395681\pi$
$991$	1.54521e91	0.643785	0.321893	+	0.946776i	$0.395681\pi$
$992$	1.49592e91	0.604369
$993$	0	0
$994$	−9.10840e91	−3.46065
$995$	−2.27035e90	−0.0836543
$996$	0	0
$997$	−7.52005e90	−0.260626	−0.130313	−	0.991473i	$-0.541598\pi$
$997$	−7.52005e90	−0.260626	−0.130313	+	0.991473i	$0.541598\pi$
$998$	−1.35663e91	−0.456016
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	9.62.a.a.1.1		4
3.2	odd	2		1.62.a.a.1.4	✓	4

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 9 = 3^{2} \)
Weight:	\( k \)	\(=\)	\( 62 \)
Character orbit:	\([\chi]\)	\(=\)	9.a (trivial)

\(f(q)\)	\(=\)	\(q-2.84183e9 q^{2} +5.77017e18 q^{4} +6.89620e20 q^{5} -9.80127e25 q^{7} -9.84504e27 q^{8} +O(q^{10})\)	\(q-2.84183e9 q^{2} +5.77017e18 q^{4} +6.89620e20 q^{5} -9.80127e25 q^{7} -9.84504e27 q^{8} -1.95979e30 q^{10} +2.74880e31 q^{11} +2.74592e32 q^{13} +2.78536e35 q^{14} +1.46728e37 q^{16} +2.27394e37 q^{17} -1.42689e39 q^{19} +3.97923e39 q^{20} -7.81164e40 q^{22} -1.13228e41 q^{23} -3.86123e42 q^{25} -7.80343e41 q^{26} -5.65550e44 q^{28} -2.20574e44 q^{29} -7.87465e44 q^{31} -1.89967e46 q^{32} -6.46217e46 q^{34} -6.75915e46 q^{35} +5.41627e47 q^{37} +4.05499e48 q^{38} -6.78934e48 q^{40} -3.44353e48 q^{41} -2.45361e49 q^{43} +1.58611e50 q^{44} +3.21774e50 q^{46} -7.88915e50 q^{47} +6.05033e51 q^{49} +1.09730e52 q^{50} +1.58444e51 q^{52} -4.85762e52 q^{53} +1.89563e52 q^{55} +9.64938e53 q^{56} +6.26833e53 q^{58} +1.37665e54 q^{59} +4.54704e53 q^{61} +2.23784e54 q^{62} +2.01520e55 q^{64} +1.89364e53 q^{65} -8.79176e55 q^{67} +1.31210e56 q^{68} +1.92084e56 q^{70} -3.27010e56 q^{71} -6.07880e56 q^{73} -1.53921e57 q^{74} -8.23342e57 q^{76} -2.69418e57 q^{77} +1.23160e58 q^{79} +1.01187e58 q^{80} +9.78594e57 q^{82} +6.61561e58 q^{83} +1.56816e58 q^{85} +6.97276e58 q^{86} -2.70621e59 q^{88} +1.38088e59 q^{89} -2.69135e58 q^{91} -6.53342e59 q^{92} +2.24196e60 q^{94} -9.84014e59 q^{95} -3.96687e60 q^{97} -1.71940e61 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 1146312000 q^{2} + 44\!\cdots\!28 q^{4}+ \cdots - 97\!\cdots\!00 q^{8}+O(q^{10}) \) 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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more