LMFDB - Embedded newform 9.60.a.c.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [9,60,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, 60, names="a")

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

chi := DirichletCharacter("9.1");

S:= CuspForms(chi, 60);

N := Newforms(S);

Level:	$ N $	$=$	$ 9 = 3^{2} $
Weight:	$ k $	$=$	$ 60 $
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:	$198.412204959$
Analytic rank:	$1$
Dimension:	$5$
Coefficient field:	$\mathbb{Q}[x]/(x^{5} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - x^{4} + \cdots - 23\!\cdots\!36 $ x^5 - x^4 - 3976283494919360x^3 + 9065173660301515822976x^2 + 2677795447191606098169599438848*x - 23358185771581696169459363194340724736
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{39}\cdot 3^{19}\cdot 5^{3}\cdot 7^{2} $
Twist minimal:	no (minimal twist has level 1)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$9.74166e6$ 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)

$f(q)$	$=$	$q+3.23738e8 q^{2} -4.71654e17 q^{4} +7.71676e20 q^{5} -4.97804e24 q^{7} -3.39315e26 q^{8} +O(q^{10})$	\(q+3.23738e8 q^{2} -4.71654e17 q^{4} +7.71676e20 q^{5} -4.97804e24 q^{7} -3.39315e26 q^{8} +2.49821e29 q^{10} +5.41469e30 q^{11} -5.16559e32 q^{13} -1.61158e33 q^{14} +1.62041e35 q^{16} +9.94078e35 q^{17} -3.90272e37 q^{19} -3.63964e38 q^{20} +1.75294e39 q^{22} -2.19671e40 q^{23} +4.22011e41 q^{25} -1.67230e41 q^{26} +2.34792e42 q^{28} +1.47397e43 q^{29} -9.00895e43 q^{31} +2.48061e44 q^{32} +3.21821e44 q^{34} -3.84144e45 q^{35} -4.57851e45 q^{37} -1.26346e46 q^{38} -2.61841e47 q^{40} -1.81556e46 q^{41} -1.81438e48 q^{43} -2.55386e48 q^{44} -7.11158e48 q^{46} -9.84593e48 q^{47} -4.77936e49 q^{49} +1.36621e50 q^{50} +2.43637e50 q^{52} +4.04855e50 q^{53} +4.17839e51 q^{55} +1.68912e51 q^{56} +4.77181e51 q^{58} +2.73608e52 q^{59} -2.82665e52 q^{61} -2.91654e52 q^{62} -1.31036e52 q^{64} -3.98616e53 q^{65} -7.96736e53 q^{67} -4.68861e53 q^{68} -1.24362e54 q^{70} +2.85479e54 q^{71} +1.64698e55 q^{73} -1.48224e54 q^{74} +1.84074e55 q^{76} -2.69546e55 q^{77} -1.63561e56 q^{79} +1.25043e56 q^{80} -5.87766e54 q^{82} +4.71355e55 q^{83} +7.67106e56 q^{85} -5.87385e56 q^{86} -1.83729e57 q^{88} -1.35054e57 q^{89} +2.57145e57 q^{91} +1.03609e58 q^{92} -3.18751e57 q^{94} -3.01164e58 q^{95} +1.09114e58 q^{97} -1.54726e58 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q + 449691864 q^{2} + 17\!\cdots\!40 q^{4}+ \cdots + 34\!\cdots\!80 q^{8}+O(q^{10}) $ 5 * q + 449691864 * q^2 + 1738819379139544640 * q^4 - 179961612150086058390 * q^5 + 1498777546338193415604856 * q^7 + 345163648945131266751137280 * q^8	$ 5 q + 449691864 q^{2} + 17\!\cdots\!40 q^{4}+ \cdots + 10\!\cdots\!52 q^{98}+O(q^{100}) $ 5 * q + 449691864 * q^2 + 1738819379139544640 * q^4 - 179961612150086058390 * q^5 + 1498777546338193415604856 * q^7 + 345163648945131266751137280 * q^8 - 816306987485763512638039118160 * q^10 - 4258478353252041879297428322660 * q^11 - 845614914312482778669168084611378 * q^13 - 6292067851730037636066126264146880 * q^14 + 694835480494500010980166187386081280 * q^16 + 3408789133052869460614097222783941254 * q^17 + 64613555538305267315990967466483855900 * q^19 - 167758871278751870059053885614959950720 * q^20 + 16748450439811023159371198583524768270112 * q^22 - 26762219406239912352813565493381233364712 * q^23 + 626328164486171817149625807278273965801475 * q^25 - 2749973149308040923633652135036287227445360 * q^26 - 5611228561379710656820495758490486062705152 * q^28 + 17549046108593766297328008399864666159350850 * q^29 - 358583623042201488230225328552738568224907040 * q^31 + 1074522626525330530995966308544265757955293184 * q^32 + 1313186147384734516654444992913422917722864080 * q^34 - 8788755903389357061227741366680412802419085840 * q^35 + 12289654705391014078883644083969663074775614326 * q^37 + 45794685161100120795332322131326257673964677920 * q^38 - 623280493607240105129626720516519294122185241600 * q^40 + 1264600318837995850108850617547077064258140834590 * q^41 + 1362401402875616509759331175816257798295684833092 * q^43 - 10077075627927391677990061115125884792646469172480 * q^44 + 35794385229187598114442404877782400066811275005760 * q^46 - 58116315089138636393563553286549713195469724328016 * q^47 - 172418318747588613327122588406220961507566908720435 * q^49 + 233848387346081992883910872998391056418422012487400 * q^50 - 992097542005695911104987622381229757223139868049024 * q^52 - 2268101788488183861226576340546566132432064315777382 * q^53 + 900686393182056151569568156583842171451592208829880 * q^55 - 13057990199329560708452108630914154838760821091430400 * q^56 - 19935384508052610930909349257749128471453923297265680 * q^58 + 21931653365540795176945573682489794310901322601489100 * q^59 - 55594140754072322694181208673989737469003346813960290 * q^61 - 183475769536335462614566613996468524195162017418651392 * q^62 + 442992326944585087629292186411036974187652719990538240 * q^64 - 108239432655103548226552811908240865218465397888070180 * q^65 + 251728958220345096328034657219059743090559333983657196 * q^67 + 5807349046062465910161766073979061475602982250739804032 * q^68 - 5752977156560799367346480182820409713199133658156760960 * q^70 + 6369597660991167158573967320963521000612243175546832840 * q^71 + 12498734118021895660608582328454257591891310584798516162 * q^73 - 30430803441235884517255321866854090380478491767252508080 * q^74 + 44485052481827577410579765985045990814357967613276332800 * q^76 - 17284905559091020495400324815223194592508822902892800352 * q^77 - 195027743716001656833247333265450397879290980351117845200 * q^79 + 206704704480779086536260387174822452768748287935918120960 * q^80 - 900520634877949974377918733125010085392642066824246973168 * q^82 - 1340753017495815214930655712848265601901866175919407282652 * q^83 + 2489371886919081358504761029214476055227000571885198923340 * q^85 + 1480724029310290822922398160933917869023473589220972227040 * q^86 - 766253667564296029168711510940105999694943299571114997760 * q^88 - 4137994032714609594535072901976334293523151283735651174450 * q^89 + 2026135516273811264299668018701283385599128389353986522960 * q^91 + 40220109586116561836814028008941466356622877640185075490304 * q^92 - 11288243726815211032514455546739674300124940708563708661120 * q^94 - 87101339446452871712134322546432797479691690743389226486600 * q^95 + 116502743099592096760799908821840050224405365201122277495466 * q^97 + 100197653381373748947470486612022288330601696851398709875352 * 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 $

$2$	3.23738e8	0.426392	0.213196	−	0.977009i	$-0.431613\pi$
$2$	3.23738e8	0.426392	0.213196	+	0.977009i	$0.431613\pi$
$3$	0	0
$3$	0	0
$4$	−4.71654e17	−0.818190
$5$	7.71676e20	1.85276	0.926381	−	0.376587i	$-0.122902\pi$
$5$	7.71676e20	1.85276	0.926381	+	0.376587i	$0.122902\pi$
$6$	0	0
$7$	−4.97804e24	−0.584341	−0.292171	−	0.956366i	$-0.594378\pi$
$7$	−4.97804e24	−0.584341	−0.292171	+	0.956366i	$0.594378\pi$
$8$	−3.39315e26	−0.775262
$9$	0	0
$10$	2.49821e29	0.790003
$11$	5.41469e30	1.02918	0.514588	−	0.857438i	$-0.327945\pi$
$11$	5.41469e30	1.02918	0.514588	+	0.857438i	$0.327945\pi$
$12$	0	0
$13$	−5.16559e32	−0.710872	−0.355436	−	0.934701i	$-0.615668\pi$
$13$	−5.16559e32	−0.710872	−0.355436	+	0.934701i	$0.615668\pi$
$14$	−1.61158e33	−0.249159
$15$	0	0
$16$	1.62041e35	0.487624
$17$	9.94078e35	0.500239	0.250119	−	0.968215i	$-0.419530\pi$
$17$	9.94078e35	0.500239	0.250119	+	0.968215i	$0.419530\pi$
$18$	0	0
$19$	−3.90272e37	−0.738136	−0.369068	−	0.929402i	$-0.620323\pi$
$19$	−3.90272e37	−0.738136	−0.369068	+	0.929402i	$0.620323\pi$
$20$	−3.63964e38	−1.51591
$21$	0	0
$22$	1.75294e39	0.438833
$23$	−2.19671e40	−1.48184	−0.740920	−	0.671594i	$-0.765610\pi$
$23$	−2.19671e40	−1.48184	−0.740920	+	0.671594i	$0.765610\pi$
$24$	0	0
$25$	4.22011e41	2.43273
$26$	−1.67230e41	−0.303110
$27$	0	0
$28$	2.34792e42	0.478102
$29$	1.47397e43	1.06598	0.532989	−	0.846122i	$-0.321069\pi$
$29$	1.47397e43	1.06598	0.532989	+	0.846122i	$0.321069\pi$
$30$	0	0
$31$	−9.00895e43	−0.910970	−0.455485	−	0.890243i	$-0.650534\pi$
$31$	−9.00895e43	−0.910970	−0.455485	+	0.890243i	$0.650534\pi$
$32$	2.48061e44	0.983181
$33$	0	0
$34$	3.21821e44	0.213298
$35$	−3.84144e45	−1.08265
$36$	0	0
$37$	−4.57851e45	−0.250480	−0.125240	−	0.992126i	$-0.539970\pi$
$37$	−4.57851e45	−0.250480	−0.125240	+	0.992126i	$0.539970\pi$
$38$	−1.26346e46	−0.314736
$39$	0	0
$40$	−2.61841e47	−1.43638
$41$	−1.81556e46	−0.0480714	−0.0240357	−	0.999711i	$-0.507652\pi$
$41$	−1.81556e46	−0.0480714	−0.0240357	+	0.999711i	$0.507652\pi$
$42$	0	0
$43$	−1.81438e48	−1.17872	−0.589359	−	0.807871i	$-0.700620\pi$
$43$	−1.81438e48	−1.17872	−0.589359	+	0.807871i	$0.700620\pi$
$44$	−2.55386e48	−0.842061
$45$	0	0
$46$	−7.11158e48	−0.631845
$47$	−9.84593e48	−0.463842	−0.231921	−	0.972735i	$-0.574501\pi$
$47$	−9.84593e48	−0.463842	−0.231921	+	0.972735i	$0.574501\pi$
$48$	0	0
$49$	−4.77936e49	−0.658545
$50$	1.36621e50	1.03730
$51$	0	0
$52$	2.43637e50	0.581628
$53$	4.04855e50	0.551013	0.275506	−	0.961299i	$-0.411154\pi$
$53$	4.04855e50	0.551013	0.275506	+	0.961299i	$0.411154\pi$
$54$	0	0
$55$	4.17839e51	1.90682
$56$	1.68912e51	0.453017
$57$	0	0
$58$	4.77181e51	0.454524
$59$	2.73608e52	1.57396	0.786980	−	0.616978i	$-0.211643\pi$
$59$	2.73608e52	1.57396	0.786980	+	0.616978i	$0.211643\pi$
$60$	0	0
$61$	−2.82665e52	−0.608194	−0.304097	−	0.952641i	$-0.598355\pi$
$61$	−2.82665e52	−0.608194	−0.304097	+	0.952641i	$0.598355\pi$
$62$	−2.91654e52	−0.388430
$63$	0	0
$64$	−1.31036e52	−0.0684039
$65$	−3.98616e53	−1.31708
$66$	0	0
$67$	−7.96736e53	−1.07673	−0.538366	−	0.842711i	$-0.680958\pi$
$67$	−7.96736e53	−1.07673	−0.538366	+	0.842711i	$0.680958\pi$
$68$	−4.68861e53	−0.409290
$69$	0	0
$70$	−1.24362e54	−0.461632
$71$	2.85479e54	0.697354	0.348677	−	0.937243i	$-0.386631\pi$
$71$	2.85479e54	0.697354	0.348677	+	0.937243i	$0.386631\pi$
$72$	0	0
$73$	1.64698e55	1.77282	0.886410	−	0.462902i	$-0.153192\pi$
$73$	1.64698e55	1.77282	0.886410	+	0.462902i	$0.153192\pi$
$74$	−1.48224e54	−0.106803
$75$	0	0
$76$	1.84074e55	0.603936
$77$	−2.69546e55	−0.601390
$78$	0	0
$79$	−1.63561e56	−1.71270	−0.856349	−	0.516397i	$-0.827273\pi$
$79$	−1.63561e56	−1.71270	−0.856349	+	0.516397i	$0.827273\pi$
$80$	1.25043e56	0.903452
$81$	0	0
$82$	−5.87766e54	−0.0204973
$83$	4.71355e55	0.114959	0.0574797	−	0.998347i	$-0.481694\pi$
$83$	4.71355e55	0.114959	0.0574797	+	0.998347i	$0.481694\pi$
$84$	0	0
$85$	7.67106e56	0.926823
$86$	−5.87385e56	−0.502596
$87$	0	0
$88$	−1.83729e57	−0.797881
$89$	−1.35054e57	−0.420244	−0.210122	−	0.977675i	$-0.567386\pi$
$89$	−1.35054e57	−0.420244	−0.210122	+	0.977675i	$0.567386\pi$
$90$	0	0
$91$	2.57145e57	0.415392
$92$	1.03609e58	1.21243
$93$	0	0
$94$	−3.18751e57	−0.197779
$95$	−3.01164e58	−1.36759
$96$	0	0
$97$	1.09114e58	0.267987	0.133994	−	0.990982i	$-0.457220\pi$
$97$	1.09114e58	0.267987	0.133994	+	0.990982i	$0.457220\pi$
$98$	−1.54726e58	−0.280798
$99$	0	0
$100$	−1.99043e59	−1.99043
$101$	7.05413e58	0.525972	0.262986	−	0.964800i	$-0.415293\pi$
$101$	7.05413e58	0.525972	0.262986	+	0.964800i	$0.415293\pi$
$102$	0	0
$103$	1.13759e59	0.475648	0.237824	−	0.971308i	$-0.423566\pi$
$103$	1.13759e59	0.475648	0.237824	+	0.971308i	$0.423566\pi$
$104$	1.75276e59	0.551112
$105$	0	0
$106$	1.31067e59	0.234948
$107$	−8.55072e59	−1.16193	−0.580967	−	0.813927i	$-0.697325\pi$
$107$	−8.55072e59	−1.16193	−0.580967	+	0.813927i	$0.697325\pi$
$108$	0	0
$109$	8.25998e59	0.649976	0.324988	−	0.945718i	$-0.394640\pi$
$109$	8.25998e59	0.649976	0.324988	+	0.945718i	$0.394640\pi$
$110$	1.35270e60	0.813052
$111$	0	0
$112$	−8.06647e59	−0.284939
$113$	−2.15843e60	−0.586577	−0.293288	−	0.956024i	$-0.594750\pi$
$113$	−2.15843e60	−0.586577	−0.293288	+	0.956024i	$0.594750\pi$
$114$	0	0
$115$	−1.69515e61	−2.74550
$116$	−6.95205e60	−0.872172
$117$	0	0
$118$	8.85772e60	0.671124
$119$	−4.94856e60	−0.292310
$120$	0	0
$121$	1.63876e60	0.0592034
$122$	−9.15095e60	−0.259329
$123$	0	0
$124$	4.24911e61	0.745347
$125$	1.91791e62	2.65451
$126$	0	0
$127$	2.24486e61	0.194527	0.0972633	−	0.995259i	$-0.468991\pi$
$127$	2.24486e61	0.194527	0.0972633	+	0.995259i	$0.468991\pi$
$128$	−1.47239e62	−1.01235
$129$	0	0
$130$	−1.29047e62	−0.561591
$131$	−2.32590e62	−0.807399	−0.403699	−	0.914892i	$-0.632276\pi$
$131$	−2.32590e62	−0.807399	−0.403699	+	0.914892i	$0.632276\pi$
$132$	0	0
$133$	1.94279e62	0.431324
$134$	−2.57934e62	−0.459110
$135$	0	0
$136$	−3.37305e62	−0.387816
$137$	4.33788e62	0.401810	0.200905	−	0.979611i	$-0.435612\pi$
$137$	4.33788e62	0.401810	0.200905	+	0.979611i	$0.435612\pi$
$138$	0	0
$139$	−3.58922e62	−0.216802	−0.108401	−	0.994107i	$-0.534573\pi$
$139$	−3.58922e62	−0.216802	−0.108401	+	0.994107i	$0.534573\pi$
$140$	1.81183e63	0.885810
$141$	0	0
$142$	9.24205e62	0.297346
$143$	−2.79701e63	−0.731612
$144$	0	0
$145$	1.13743e64	1.97500
$146$	5.33191e63	0.755916
$147$	0	0
$148$	2.15947e63	0.204940
$149$	2.37342e63	0.184663	0.0923313	−	0.995728i	$-0.470568\pi$
$149$	2.37342e63	0.184663	0.0923313	+	0.995728i	$0.470568\pi$
$150$	0	0
$151$	−3.15470e64	−1.65630	−0.828150	−	0.560507i	$-0.810606\pi$
$151$	−3.15470e64	−1.65630	−0.828150	+	0.560507i	$0.810606\pi$
$152$	1.32425e64	0.572249
$153$	0	0
$154$	−8.72623e63	−0.256428
$155$	−6.95199e64	−1.68781
$156$	0	0
$157$	−7.08856e64	−1.17901	−0.589506	−	0.807764i	$-0.700678\pi$
$157$	−7.08856e64	−1.17901	−0.589506	+	0.807764i	$0.700678\pi$
$158$	−5.29510e64	−0.730281
$159$	0	0
$160$	1.91422e65	1.82160
$161$	1.09353e65	0.865900
$162$	0	0
$163$	−1.42919e65	−0.786243	−0.393122	−	0.919486i	$-0.628605\pi$
$163$	−1.42919e65	−0.786243	−0.393122	+	0.919486i	$0.628605\pi$
$164$	8.56317e63	0.0393316
$165$	0	0
$166$	1.52596e64	0.0490178
$167$	3.84006e64	0.103324	0.0516621	−	0.998665i	$-0.483548\pi$
$167$	3.84006e64	0.103324	0.0516621	+	0.998665i	$0.483548\pi$
$168$	0	0
$169$	−2.61196e65	−0.494662
$170$	2.48341e65	0.395190
$171$	0	0
$172$	8.55762e65	0.964415
$173$	−1.60962e66	−1.52885	−0.764423	−	0.644715i	$-0.776976\pi$
$173$	−1.60962e66	−1.52885	−0.764423	+	0.644715i	$0.776976\pi$
$174$	0	0
$175$	−2.10079e66	−1.42154
$176$	8.77402e65	0.501851
$177$	0	0
$178$	−4.37221e65	−0.179189
$179$	−1.29253e66	−0.449030	−0.224515	−	0.974471i	$-0.572080\pi$
$179$	−1.29253e66	−0.449030	−0.224515	+	0.974471i	$0.572080\pi$
$180$	0	0
$181$	7.40860e65	0.185446	0.0927231	−	0.995692i	$-0.470443\pi$
$181$	7.40860e65	0.185446	0.0927231	+	0.995692i	$0.470443\pi$
$182$	8.32478e65	0.177120
$183$	0	0
$184$	7.45376e66	1.14881
$185$	−3.53313e66	−0.464080
$186$	0	0
$187$	5.38263e66	0.514834
$188$	4.64388e66	0.379511
$189$	0	0
$190$	−9.74982e66	−0.583130
$191$	−1.84854e67	−0.946989	−0.473494	−	0.880797i	$-0.657008\pi$
$191$	−1.84854e67	−0.946989	−0.473494	+	0.880797i	$0.657008\pi$
$192$	0	0
$193$	−4.21306e67	−1.58729	−0.793647	−	0.608379i	$-0.791820\pi$
$193$	−4.21306e67	−1.58729	−0.793647	+	0.608379i	$0.791820\pi$
$194$	3.53244e66	0.114268
$195$	0	0
$196$	2.25421e67	0.538815
$197$	−5.58072e66	−0.114799	−0.0573993	−	0.998351i	$-0.518281\pi$
$197$	−5.58072e66	−0.114799	−0.0573993	+	0.998351i	$0.518281\pi$
$198$	0	0
$199$	−5.98440e67	−0.913808	−0.456904	−	0.889516i	$-0.651042\pi$
$199$	−5.98440e67	−0.913808	−0.456904	+	0.889516i	$0.651042\pi$
$200$	−1.43195e68	−1.88600
$201$	0	0
$202$	2.28369e67	0.224270
$203$	−7.33749e67	−0.622895
$204$	0	0
$205$	−1.40102e67	−0.0890649
$206$	3.68280e67	0.202813
$207$	0	0
$208$	−8.37038e67	−0.346638
$209$	−2.11321e68	−0.759672
$210$	0	0
$211$	−4.69123e68	−1.27337	−0.636685	−	0.771124i	$-0.719695\pi$
$211$	−4.69123e68	−1.27337	−0.636685	+	0.771124i	$0.719695\pi$
$212$	−1.90952e68	−0.450833
$213$	0	0
$214$	−2.76820e68	−0.495439
$215$	−1.40012e69	−2.18388
$216$	0	0
$217$	4.48469e68	0.532318
$218$	2.67407e68	0.277145
$219$	0	0
$220$	−1.97075e69	−1.56014
$221$	−5.13500e68	−0.355605
$222$	0	0
$223$	1.78943e69	0.949997	0.474998	−	0.879987i	$-0.342449\pi$
$223$	1.78943e69	0.949997	0.474998	+	0.879987i	$0.342449\pi$
$224$	−1.23486e69	−0.574513
$225$	0	0
$226$	−6.98768e68	−0.250112
$227$	−3.77818e68	−0.118719	−0.0593595	−	0.998237i	$-0.518906\pi$
$227$	−3.77818e68	−0.118719	−0.0593595	+	0.998237i	$0.518906\pi$
$228$	0	0
$229$	2.57281e69	0.624110	0.312055	−	0.950064i	$-0.398983\pi$
$229$	2.57281e69	0.624110	0.312055	+	0.950064i	$0.398983\pi$
$230$	−5.48784e69	−1.17066
$231$	0	0
$232$	−5.00140e69	−0.826412
$233$	−9.08473e69	−1.32225	−0.661123	−	0.750277i	$-0.729920\pi$
$233$	−9.08473e69	−1.32225	−0.661123	+	0.750277i	$0.729920\pi$
$234$	0	0
$235$	−7.59787e69	−0.859389
$236$	−1.29048e70	−1.28780
$237$	0	0
$238$	−1.60204e69	−0.124639
$239$	1.60292e70	1.10198	0.550992	−	0.834511i	$-0.314250\pi$
$239$	1.60292e70	1.10198	0.550992	+	0.834511i	$0.314250\pi$
$240$	0	0
$241$	−2.77243e70	−1.49059	−0.745294	−	0.666736i	$-0.767691\pi$
$241$	−2.77243e70	−1.49059	−0.745294	+	0.666736i	$0.767691\pi$
$242$	5.30529e68	0.0252439
$243$	0	0
$244$	1.33320e70	0.497618
$245$	−3.68812e70	−1.22013
$246$	0	0
$247$	2.01599e70	0.524720
$248$	3.05687e70	0.706240
$249$	0	0
$250$	6.20902e70	1.13186
$251$	−5.84246e70	−0.946719	−0.473360	−	0.880869i	$-0.656959\pi$
$251$	−5.84246e70	−0.946719	−0.473360	+	0.880869i	$0.656959\pi$
$252$	0	0
$253$	−1.18945e71	−1.52507
$254$	7.26746e69	0.0829446
$255$	0	0
$256$	−4.01133e70	−0.363253
$257$	−1.26421e70	−0.102045	−0.0510224	−	0.998698i	$-0.516248\pi$
$257$	−1.26421e70	−0.102045	−0.0510224	+	0.998698i	$0.516248\pi$
$258$	0	0
$259$	2.27920e70	0.146366
$260$	1.88009e71	1.07762
$261$	0	0
$262$	−7.52983e70	−0.344268
$263$	−9.45182e70	−0.386208	−0.193104	−	0.981178i	$-0.561855\pi$
$263$	−9.45182e70	−0.386208	−0.193104	+	0.981178i	$0.561855\pi$
$264$	0	0
$265$	3.12417e71	1.02090
$266$	6.28957e70	0.183913
$267$	0	0
$268$	3.75784e71	0.880971
$269$	6.14377e71	1.29045	0.645227	−	0.763991i	$-0.276763\pi$
$269$	6.14377e71	1.29045	0.645227	+	0.763991i	$0.276763\pi$
$270$	0	0
$271$	3.10484e71	0.524137	0.262068	−	0.965049i	$-0.415595\pi$
$271$	3.10484e71	0.524137	0.262068	+	0.965049i	$0.415595\pi$
$272$	1.61081e71	0.243928
$273$	0	0
$274$	1.40434e71	0.171329
$275$	2.28506e72	2.50371
$276$	0	0
$277$	2.42201e71	0.214300	0.107150	−	0.994243i	$-0.465827\pi$
$277$	2.42201e71	0.214300	0.107150	+	0.994243i	$0.465827\pi$
$278$	−1.16197e71	−0.0924426
$279$	0	0
$280$	1.30346e72	0.839334
$281$	−4.41465e71	−0.255894	−0.127947	−	0.991781i	$-0.540839\pi$
$281$	−4.41465e71	−0.255894	−0.127947	+	0.991781i	$0.540839\pi$
$282$	0	0
$283$	−4.82991e71	−0.227111	−0.113556	−	0.993532i	$-0.536224\pi$
$283$	−4.82991e71	−0.227111	−0.113556	+	0.993532i	$0.536224\pi$
$284$	−1.34647e72	−0.570568
$285$	0	0
$286$	−9.05499e71	−0.311954
$287$	9.03794e70	0.0280901
$288$	0	0
$289$	−2.96080e72	−0.749761
$290$	3.68229e72	0.842126
$291$	0	0
$292$	−7.76806e72	−1.45050
$293$	3.92066e72	0.661857	0.330929	−	0.943656i	$-0.392638\pi$
$293$	3.92066e72	0.661857	0.330929	+	0.943656i	$0.392638\pi$
$294$	0	0
$295$	2.11136e73	2.91617
$296$	1.55356e72	0.194188
$297$	0	0
$298$	7.68366e71	0.0787387
$299$	1.13473e73	1.05340
$300$	0	0
$301$	9.03208e72	0.688773
$302$	−1.02130e73	−0.706233
$303$	0	0
$304$	−6.32401e72	−0.359933
$305$	−2.18126e73	−1.12684
$306$	0	0
$307$	−3.54986e73	−1.51227	−0.756136	−	0.654415i	$-0.772915\pi$
$307$	−3.54986e73	−1.51227	−0.756136	+	0.654415i	$0.772915\pi$
$308$	1.27132e73	0.492051
$309$	0	0
$310$	−2.25062e73	−0.719669
$311$	−3.81419e73	−1.10910	−0.554551	−	0.832150i	$-0.687110\pi$
$311$	−3.81419e73	−1.10910	−0.554551	+	0.832150i	$0.687110\pi$
$312$	0	0
$313$	−4.16185e73	−1.00168	−0.500840	−	0.865540i	$-0.666975\pi$
$313$	−4.16185e73	−1.00168	−0.500840	+	0.865540i	$0.666975\pi$
$314$	−2.29484e73	−0.502722
$315$	0	0
$316$	7.71443e73	1.40131
$317$	−1.46541e73	−0.242499	−0.121250	−	0.992622i	$-0.538690\pi$
$317$	−1.46541e73	−0.242499	−0.121250	+	0.992622i	$0.538690\pi$
$318$	0	0
$319$	7.98110e73	1.09708
$320$	−1.01117e73	−0.126736
$321$	0	0
$322$	3.54018e73	0.369213
$323$	−3.87961e73	−0.369244
$324$	0	0
$325$	−2.17994e74	−1.72936
$326$	−4.62685e73	−0.335248
$327$	0	0
$328$	6.16047e72	0.0372679
$329$	4.90135e73	0.271042
$330$	0	0
$331$	−1.50576e74	−0.696353	−0.348177	−	0.937429i	$-0.613199\pi$
$331$	−1.50576e74	−0.696353	−0.348177	+	0.937429i	$0.613199\pi$
$332$	−2.22317e73	−0.0940586
$333$	0	0
$334$	1.24318e73	0.0440567
$335$	−6.14822e74	−1.99493
$336$	0	0
$337$	−2.34878e74	−0.639381	−0.319691	−	0.947522i	$-0.603579\pi$
$337$	−2.34878e74	−0.639381	−0.319691	+	0.947522i	$0.603579\pi$
$338$	−8.45590e73	−0.210920
$339$	0	0
$340$	−3.61809e74	−0.758317
$341$	−4.87807e74	−0.937549
$342$	0	0
$343$	5.99198e74	0.969157
$344$	6.15647e74	0.913815
$345$	0	0
$346$	−5.21096e74	−0.651888
$347$	1.16630e75	1.33996	0.669980	−	0.742379i	$-0.266303\pi$
$347$	1.16630e75	1.33996	0.669980	+	0.742379i	$0.266303\pi$
$348$	0	0
$349$	1.43487e74	0.139144	0.0695718	−	0.997577i	$-0.477837\pi$
$349$	1.43487e74	0.139144	0.0695718	+	0.997577i	$0.477837\pi$
$350$	−6.80106e74	−0.606135
$351$	0	0
$352$	1.34317e75	1.01187
$353$	1.70914e75	1.18419	0.592097	−	0.805866i	$-0.298300\pi$
$353$	1.70914e75	1.18419	0.592097	+	0.805866i	$0.298300\pi$
$354$	0	0
$355$	2.20297e75	1.29203
$356$	6.36987e74	0.343840
$357$	0	0
$358$	−4.18441e74	−0.191463
$359$	−2.00456e75	−0.844757	−0.422379	−	0.906420i	$-0.638805\pi$
$359$	−2.00456e75	−0.844757	−0.422379	+	0.906420i	$0.638805\pi$
$360$	0	0
$361$	−1.27239e75	−0.455155
$362$	2.39845e74	0.0790728
$363$	0	0
$364$	−1.21284e75	−0.339869
$365$	1.27094e76	3.28461
$366$	0	0
$367$	3.69368e75	0.812476	0.406238	−	0.913767i	$-0.366840\pi$
$367$	3.69368e75	0.812476	0.406238	+	0.913767i	$0.366840\pi$
$368$	−3.55957e75	−0.722581
$369$	0	0
$370$	−1.14381e75	−0.197880
$371$	−2.01539e75	−0.321980
$372$	0	0
$373$	2.06268e75	0.281203	0.140602	−	0.990066i	$-0.455096\pi$
$373$	2.06268e75	0.281203	0.140602	+	0.990066i	$0.455096\pi$
$374$	1.74256e75	0.219521
$375$	0	0
$376$	3.34087e75	0.359599
$377$	−7.61393e75	−0.757773
$378$	0	0
$379$	1.63106e76	1.38872	0.694359	−	0.719629i	$-0.255688\pi$
$379$	1.63106e76	1.38872	0.694359	+	0.719629i	$0.255688\pi$
$380$	1.42045e76	1.11895
$381$	0	0
$382$	−5.98443e75	−0.403788
$383$	1.67919e76	1.04891	0.524453	−	0.851440i	$-0.324270\pi$
$383$	1.67919e76	1.04891	0.524453	+	0.851440i	$0.324270\pi$
$384$	0	0
$385$	−2.08002e76	−1.11423
$386$	−1.36393e76	−0.676809
$387$	0	0
$388$	−5.14641e75	−0.219265
$389$	9.77054e75	0.385838	0.192919	−	0.981215i	$-0.438204\pi$
$389$	9.77054e75	0.385838	0.192919	+	0.981215i	$0.438204\pi$
$390$	0	0
$391$	−2.18370e76	−0.741273
$392$	1.62171e76	0.510545
$393$	0	0
$394$	−1.80669e75	−0.0489492
$395$	−1.26216e77	−3.17322
$396$	0	0
$397$	−2.20390e76	−0.477388	−0.238694	−	0.971095i	$-0.576719\pi$
$397$	−2.20390e76	−0.477388	−0.238694	+	0.971095i	$0.576719\pi$
$398$	−1.93738e76	−0.389640
$399$	0	0
$400$	6.83831e76	1.18626
$401$	8.57114e76	1.38127	0.690636	−	0.723202i	$-0.257331\pi$
$401$	8.57114e76	1.38127	0.690636	+	0.723202i	$0.257331\pi$
$402$	0	0
$403$	4.65365e76	0.647583
$404$	−3.32711e76	−0.430345
$405$	0	0
$406$	−2.37543e76	−0.265597
$407$	−2.47912e76	−0.257788
$408$	0	0
$409$	−1.18117e77	−1.06286	−0.531428	−	0.847104i	$-0.678344\pi$
$409$	−1.18117e77	−1.06286	−0.531428	+	0.847104i	$0.678344\pi$
$410$	−4.53565e75	−0.0379766
$411$	0	0
$412$	−5.36547e76	−0.389171
$413$	−1.36203e77	−0.919730
$414$	0	0
$415$	3.63733e76	0.212992
$416$	−1.28138e77	−0.698915
$417$	0	0
$418$	−6.84126e76	−0.323918
$419$	−8.82341e76	−0.389334	−0.194667	−	0.980869i	$-0.562363\pi$
$419$	−8.82341e76	−0.389334	−0.194667	+	0.980869i	$0.562363\pi$
$420$	0	0
$421$	4.95671e76	0.190052	0.0950258	−	0.995475i	$-0.469707\pi$
$421$	4.95671e76	0.190052	0.0950258	+	0.995475i	$0.469707\pi$
$422$	−1.51873e77	−0.542955
$423$	0	0
$424$	−1.37373e77	−0.427179
$425$	4.19512e77	1.21694
$426$	0	0
$427$	1.40712e77	0.355393
$428$	4.03298e77	0.950682
$429$	0	0
$430$	−4.53271e77	−0.931191
$431$	−8.16025e77	−1.56540	−0.782698	−	0.622402i	$-0.786157\pi$
$431$	−8.16025e77	−1.56540	−0.782698	+	0.622402i	$0.786157\pi$
$432$	0	0
$433$	5.70929e77	0.955408	0.477704	−	0.878521i	$-0.341469\pi$
$433$	5.70929e77	0.955408	0.477704	+	0.878521i	$0.341469\pi$
$434$	1.45187e77	0.226976
$435$	0	0
$436$	−3.89585e77	−0.531804
$437$	8.57314e77	1.09380
$438$	0	0
$439$	1.20511e78	1.34376	0.671881	−	0.740659i	$-0.265487\pi$
$439$	1.20511e78	1.34376	0.671881	+	0.740659i	$0.265487\pi$
$440$	−1.41779e78	−1.47828
$441$	0	0
$442$	−1.66240e77	−0.151627
$443$	9.08891e77	0.775536	0.387768	−	0.921757i	$-0.373246\pi$
$443$	9.08891e77	0.775536	0.387768	+	0.921757i	$0.373246\pi$
$444$	0	0
$445$	−1.04218e78	−0.778613
$446$	5.79308e77	0.405071
$447$	0	0
$448$	6.52302e76	0.0399712
$449$	2.07903e78	1.19287	0.596435	−	0.802661i	$-0.296583\pi$
$449$	2.07903e78	1.19287	0.596435	+	0.802661i	$0.296583\pi$
$450$	0	0
$451$	−9.83071e76	−0.0494740
$452$	1.01803e78	0.479931
$453$	0	0
$454$	−1.22314e77	−0.0506208
$455$	1.98433e78	0.769622
$456$	0	0
$457$	1.64014e78	0.558923	0.279462	−	0.960157i	$-0.409844\pi$
$457$	1.64014e78	0.558923	0.279462	+	0.960157i	$0.409844\pi$
$458$	8.32918e77	0.266116
$459$	0	0
$460$	7.99523e78	2.24634
$461$	−2.32024e78	−0.611441	−0.305721	−	0.952121i	$-0.598897\pi$
$461$	−2.32024e78	−0.611441	−0.305721	+	0.952121i	$0.598897\pi$
$462$	0	0
$463$	1.52939e78	0.354713	0.177357	−	0.984147i	$-0.443245\pi$
$463$	1.52939e78	0.354713	0.177357	+	0.984147i	$0.443245\pi$
$464$	2.38844e78	0.519797
$465$	0	0
$466$	−2.94108e78	−0.563796
$467$	7.17147e78	1.29051	0.645254	−	0.763968i	$-0.276752\pi$
$467$	7.17147e78	1.29051	0.645254	+	0.763968i	$0.276752\pi$
$468$	0	0
$469$	3.96619e78	0.629179
$470$	−2.45972e78	−0.366437
$471$	0	0
$472$	−9.28391e78	−1.22023
$473$	−9.82433e78	−1.21311
$474$	0	0
$475$	−1.64699e79	−1.79569
$476$	2.33401e78	0.239165
$477$	0	0
$478$	5.18928e78	0.469877
$479$	−1.52757e79	−1.30048	−0.650241	−	0.759728i	$-0.725332\pi$
$479$	−1.52757e79	−1.30048	−0.650241	+	0.759728i	$0.725332\pi$
$480$	0	0
$481$	2.36507e78	0.178059
$482$	−8.97542e78	−0.635575
$483$	0	0
$484$	−7.72928e77	−0.0484397
$485$	8.42006e78	0.496517
$486$	0	0
$487$	4.49651e78	0.234840	0.117420	−	0.993082i	$-0.462538\pi$
$487$	4.49651e78	0.234840	0.117420	+	0.993082i	$0.462538\pi$
$488$	9.59125e78	0.471509
$489$	0	0
$490$	−1.19398e79	−0.520253
$491$	−1.13413e79	−0.465326	−0.232663	−	0.972557i	$-0.574744\pi$
$491$	−1.13413e79	−0.465326	−0.232663	+	0.972557i	$0.574744\pi$
$492$	0	0
$493$	1.46524e79	0.533243
$494$	6.52652e78	0.223737
$495$	0	0
$496$	−1.45982e79	−0.444211
$497$	−1.42113e79	−0.407493
$498$	0	0
$499$	−2.74327e79	−0.698719	−0.349359	−	0.936989i	$-0.613601\pi$
$499$	−2.74327e79	−0.698719	−0.349359	+	0.936989i	$0.613601\pi$
$500$	−9.04592e79	−2.17189
$501$	0	0
$502$	−1.89143e79	−0.403674
$503$	5.28271e79	1.06317	0.531583	−	0.847006i	$-0.321597\pi$
$503$	5.28271e79	1.06317	0.531583	+	0.847006i	$0.321597\pi$
$504$	0	0
$505$	5.44350e79	0.974502
$506$	−3.85070e79	−0.650279
$507$	0	0
$508$	−1.05880e79	−0.159160
$509$	−1.13708e80	−1.61294	−0.806470	−	0.591275i	$-0.798625\pi$
$509$	−1.13708e80	−1.61294	−0.806470	+	0.591275i	$0.798625\pi$
$510$	0	0
$511$	−8.19875e79	−1.03593
$512$	7.18915e79	0.857459
$513$	0	0
$514$	−4.09272e78	−0.0435111
$515$	8.77847e79	0.881263
$516$	0	0
$517$	−5.33127e79	−0.477375
$518$	7.37865e78	0.0624093
$519$	0	0
$520$	1.35256e80	1.02108
$521$	1.18992e80	0.848797	0.424398	−	0.905476i	$-0.360486\pi$
$521$	1.18992e80	0.848797	0.424398	+	0.905476i	$0.360486\pi$
$522$	0	0
$523$	2.64671e80	1.68619	0.843097	−	0.537762i	$-0.180730\pi$
$523$	2.64671e80	1.68619	0.843097	+	0.537762i	$0.180730\pi$
$524$	1.09702e80	0.660606
$525$	0	0
$526$	−3.05992e79	−0.164676
$527$	−8.95559e79	−0.455702
$528$	0	0
$529$	2.62796e80	1.19585
$530$	1.01141e80	0.435302
$531$	0	0
$532$	−9.16327e79	−0.352905
$533$	9.37844e78	0.0341726
$534$	0	0
$535$	−6.59838e80	−2.15279
$536$	2.70344e80	0.834749
$537$	0	0
$538$	1.98897e80	0.550240
$539$	−2.58788e80	−0.677759
$540$	0	0
$541$	−1.23574e80	−0.290141	−0.145071	−	0.989421i	$-0.546341\pi$
$541$	−1.23574e80	−0.290141	−0.145071	+	0.989421i	$0.546341\pi$
$542$	1.00515e80	0.223488
$543$	0	0
$544$	2.46591e80	0.491825
$545$	6.37403e80	1.20425
$546$	0	0
$547$	−6.88700e80	−1.16789	−0.583947	−	0.811792i	$-0.698493\pi$
$547$	−6.88700e80	−1.16789	−0.583947	+	0.811792i	$0.698493\pi$
$548$	−2.04598e80	−0.328757
$549$	0	0
$550$	7.39762e80	1.06756
$551$	−5.75250e80	−0.786837
$552$	0	0
$553$	8.14214e80	1.00080
$554$	7.84097e79	0.0913760
$555$	0	0
$556$	1.69287e80	0.177385
$557$	1.64679e81	1.63648	0.818239	−	0.574878i	$-0.194951\pi$
$557$	1.64679e81	1.63648	0.818239	+	0.574878i	$0.194951\pi$
$558$	0	0
$559$	9.37237e80	0.837917
$560$	−6.22470e80	−0.527924
$561$	0	0
$562$	−1.42919e80	−0.109111
$563$	8.28386e80	0.600116	0.300058	−	0.953921i	$-0.402994\pi$
$563$	8.28386e80	0.600116	0.300058	+	0.953921i	$0.402994\pi$
$564$	0	0
$565$	−1.66561e81	−1.08679
$566$	−1.56363e80	−0.0968385
$567$	0	0
$568$	−9.68673e80	−0.540632
$569$	−1.62848e80	−0.0862919	−0.0431460	−	0.999069i	$-0.513738\pi$
$569$	−1.62848e80	−0.0862919	−0.0431460	+	0.999069i	$0.513738\pi$
$570$	0	0
$571$	2.39641e81	1.14497	0.572487	−	0.819914i	$-0.305979\pi$
$571$	2.39641e81	1.14497	0.572487	+	0.819914i	$0.305979\pi$
$572$	1.31922e81	0.598598
$573$	0	0
$574$	2.92593e79	0.0119774
$575$	−9.27035e81	−3.60491
$576$	0	0
$577$	−3.77209e81	−1.32402	−0.662012	−	0.749493i	$-0.730297\pi$
$577$	−3.77209e81	−1.32402	−0.662012	+	0.749493i	$0.730297\pi$
$578$	−9.58525e80	−0.319692
$579$	0	0
$580$	−5.36473e81	−1.61593
$581$	−2.34643e80	−0.0671755
$582$	0	0
$583$	2.19217e81	0.567089
$584$	−5.58846e81	−1.37440
$585$	0	0
$586$	1.26927e81	0.282211
$587$	8.21302e81	1.73652	0.868258	−	0.496113i	$-0.165240\pi$
$587$	8.21302e81	1.73652	0.868258	+	0.496113i	$0.165240\pi$
$588$	0	0
$589$	3.51594e81	0.672420
$590$	6.83529e81	1.24343
$591$	0	0
$592$	−7.41907e80	−0.122140
$593$	−7.94731e81	−1.24482	−0.622410	−	0.782691i	$-0.713846\pi$
$593$	−7.94731e81	−1.24482	−0.622410	+	0.782691i	$0.713846\pi$
$594$	0	0
$595$	−3.81869e81	−0.541581
$596$	−1.11943e81	−0.151089
$597$	0	0
$598$	3.67355e81	0.449160
$599$	−5.80570e81	−0.675715	−0.337857	−	0.941197i	$-0.609702\pi$
$599$	−5.80570e81	−0.675715	−0.337857	+	0.941197i	$0.609702\pi$
$600$	0	0
$601$	−7.35889e81	−0.776274	−0.388137	−	0.921602i	$-0.626881\pi$
$601$	−7.35889e81	−0.776274	−0.388137	+	0.921602i	$0.626881\pi$
$602$	2.92403e81	0.293687
$603$	0	0
$604$	1.48793e82	1.35517
$605$	1.26459e81	0.109690
$606$	0	0
$607$	−1.69742e82	−1.33574	−0.667870	−	0.744278i	$-0.732794\pi$
$607$	−1.69742e82	−1.33574	−0.667870	+	0.744278i	$0.732794\pi$
$608$	−9.68112e81	−0.725722
$609$	0	0
$610$	−7.06157e81	−0.480475
$611$	5.08601e81	0.329732
$612$	0	0
$613$	−1.34842e82	−0.793852	−0.396926	−	0.917851i	$-0.629923\pi$
$613$	−1.34842e82	−0.793852	−0.396926	+	0.917851i	$0.629923\pi$
$614$	−1.14923e82	−0.644820
$615$	0	0
$616$	9.14609e81	0.466235
$617$	3.18225e82	1.54640	0.773199	−	0.634163i	$-0.218655\pi$
$617$	3.18225e82	1.54640	0.773199	+	0.634163i	$0.218655\pi$
$618$	0	0
$619$	3.44849e82	1.52319	0.761596	−	0.648053i	$-0.224416\pi$
$619$	3.44849e82	1.52319	0.761596	+	0.648053i	$0.224416\pi$
$620$	3.27893e82	1.38095
$621$	0	0
$622$	−1.23480e82	−0.472912
$623$	6.72304e81	0.245566
$624$	0	0
$625$	7.47935e82	2.48544
$626$	−1.34735e82	−0.427108
$627$	0	0
$628$	3.34335e82	0.964656
$629$	−4.55140e81	−0.125300
$630$	0	0
$631$	−4.48510e82	−1.12436	−0.562181	−	0.827014i	$-0.690038\pi$
$631$	−4.48510e82	−1.12436	−0.562181	+	0.827014i	$0.690038\pi$
$632$	5.54987e82	1.32779
$633$	0	0
$634$	−4.74409e81	−0.103400
$635$	1.73230e82	0.360412
$636$	0	0
$637$	2.46882e82	0.468141
$638$	2.58379e82	0.467786
$639$	0	0
$640$	−1.13621e83	−1.87564
$641$	−3.38457e82	−0.533570	−0.266785	−	0.963756i	$-0.585961\pi$
$641$	−3.38457e82	−0.533570	−0.266785	+	0.963756i	$0.585961\pi$
$642$	0	0
$643$	−3.04533e82	−0.437936	−0.218968	−	0.975732i	$-0.570269\pi$
$643$	−3.04533e82	−0.437936	−0.218968	+	0.975732i	$0.570269\pi$
$644$	−5.15769e82	−0.708470
$645$	0	0
$646$	−1.25598e82	−0.157443
$647$	1.22434e83	1.46631	0.733157	−	0.680060i	$-0.238046\pi$
$647$	1.22434e83	1.46631	0.733157	+	0.680060i	$0.238046\pi$
$648$	0	0
$649$	1.48150e83	1.61988
$650$	−7.05729e82	−0.737384
$651$	0	0
$652$	6.74086e82	0.643296
$653$	−9.26564e82	−0.845156	−0.422578	−	0.906327i	$-0.638875\pi$
$653$	−9.26564e82	−0.845156	−0.422578	+	0.906327i	$0.638875\pi$
$654$	0	0
$655$	−1.79484e83	−1.49592
$656$	−2.94195e81	−0.0234408
$657$	0	0
$658$	1.58675e82	0.115570
$659$	−1.42910e83	−0.995275	−0.497638	−	0.867385i	$-0.665799\pi$
$659$	−1.42910e83	−0.995275	−0.497638	+	0.867385i	$0.665799\pi$
$660$	0	0
$661$	1.00439e83	0.639674	0.319837	−	0.947473i	$-0.396372\pi$
$661$	1.00439e83	0.639674	0.319837	+	0.947473i	$0.396372\pi$
$662$	−4.87472e82	−0.296920
$663$	0	0
$664$	−1.59938e82	−0.0891236
$665$	1.49921e83	0.799140
$666$	0	0
$667$	−3.23788e83	−1.57961
$668$	−1.81118e82	−0.0845389
$669$	0	0
$670$	−1.99041e83	−0.850622
$671$	−1.53054e83	−0.625939
$672$	0	0
$673$	2.95487e83	1.10686	0.553432	−	0.832894i	$-0.313318\pi$
$673$	2.95487e83	1.10686	0.553432	+	0.832894i	$0.313318\pi$
$674$	−7.60389e82	−0.272627
$675$	0	0
$676$	1.23194e83	0.404727
$677$	8.74198e81	0.0274944	0.0137472	−	0.999906i	$-0.495624\pi$
$677$	8.74198e81	0.0274944	0.0137472	+	0.999906i	$0.495624\pi$
$678$	0	0
$679$	−5.43174e82	−0.156596
$680$	−2.60290e83	−0.718531
$681$	0	0
$682$	−1.57922e83	−0.399763
$683$	−3.28450e83	−0.796267	−0.398134	−	0.917327i	$-0.630342\pi$
$683$	−3.28450e83	−0.796267	−0.398134	+	0.917327i	$0.630342\pi$
$684$	0	0
$685$	3.34744e83	0.744459
$686$	1.93983e83	0.413241
$687$	0	0
$688$	−2.94005e83	−0.574771
$689$	−2.09132e83	−0.391699
$690$	0	0
$691$	−6.66760e83	−1.14648	−0.573241	−	0.819387i	$-0.694314\pi$
$691$	−6.66760e83	−1.14648	−0.573241	+	0.819387i	$0.694314\pi$
$692$	7.59185e83	1.25089
$693$	0	0
$694$	3.77577e83	0.571349
$695$	−2.76971e83	−0.401682
$696$	0	0
$697$	−1.80481e82	−0.0240472
$698$	4.64523e82	0.0593297
$699$	0	0
$700$	9.90847e83	1.16309
$701$	−2.68462e83	−0.302135	−0.151068	−	0.988523i	$-0.548271\pi$
$701$	−2.68462e83	−0.302135	−0.151068	+	0.988523i	$0.548271\pi$
$702$	0	0
$703$	1.78687e83	0.184889
$704$	−7.09518e82	−0.0703996
$705$	0	0
$706$	5.53313e83	0.504931
$707$	−3.51158e83	−0.307347
$708$	0	0
$709$	−7.40264e83	−0.596105	−0.298053	−	0.954549i	$-0.596337\pi$
$709$	−7.40264e83	−0.596105	−0.298053	+	0.954549i	$0.596337\pi$
$710$	7.13187e83	0.550912
$711$	0	0
$712$	4.58258e83	0.325799
$713$	1.97900e84	1.34991
$714$	0	0
$715$	−2.15838e84	−1.35550
$716$	6.09627e83	0.367392
$717$	0	0
$718$	−6.48951e83	−0.360198
$719$	−1.09772e84	−0.584773	−0.292387	−	0.956300i	$-0.594449\pi$
$719$	−1.09772e84	−0.584773	−0.292387	+	0.956300i	$0.594449\pi$
$720$	0	0
$721$	−5.66295e83	−0.277941
$722$	−4.11922e83	−0.194074
$723$	0	0
$724$	−3.49430e83	−0.151730
$725$	6.22032e84	2.59323
$726$	0	0
$727$	4.10850e84	1.57913	0.789566	−	0.613666i	$-0.210306\pi$
$727$	4.10850e84	1.57913	0.789566	+	0.613666i	$0.210306\pi$
$728$	−8.72533e83	−0.322037
$729$	0	0
$730$	4.11451e84	1.40053
$731$	−1.80364e84	−0.589640
$732$	0	0
$733$	4.99365e84	1.50609	0.753045	−	0.657969i	$-0.228584\pi$
$733$	4.99365e84	1.50609	0.753045	+	0.657969i	$0.228584\pi$
$734$	1.19579e84	0.346433
$735$	0	0
$736$	−5.44917e84	−1.45692
$737$	−4.31408e84	−1.10815
$738$	0	0
$739$	−1.62337e83	−0.0384951	−0.0192476	−	0.999815i	$-0.506127\pi$
$739$	−1.62337e83	−0.0384951	−0.0192476	+	0.999815i	$0.506127\pi$
$740$	1.66641e84	0.379706
$741$	0	0
$742$	−6.52458e83	−0.137290
$743$	3.18863e84	0.644814	0.322407	−	0.946601i	$-0.395508\pi$
$743$	3.18863e84	0.644814	0.322407	+	0.946601i	$0.395508\pi$
$744$	0	0
$745$	1.83151e84	0.342136
$746$	6.67767e83	0.119903
$747$	0	0
$748$	−2.53874e84	−0.421232
$749$	4.25659e84	0.678966
$750$	0	0
$751$	−1.31852e85	−1.94405	−0.972026	−	0.234872i	$-0.924533\pi$
$751$	−1.31852e85	−1.94405	−0.972026	+	0.234872i	$0.924533\pi$
$752$	−1.59544e84	−0.226181
$753$	0	0
$754$	−2.46492e84	−0.323108
$755$	−2.43441e85	−3.06873
$756$	0	0
$757$	8.93658e84	1.04194	0.520970	−	0.853575i	$-0.325570\pi$
$757$	8.93658e84	1.04194	0.520970	+	0.853575i	$0.325570\pi$
$758$	5.28038e84	0.592138
$759$	0	0
$760$	1.02189e85	1.06024
$761$	5.17623e83	0.0516614	0.0258307	−	0.999666i	$-0.491777\pi$
$761$	5.17623e83	0.0516614	0.0258307	+	0.999666i	$0.491777\pi$
$762$	0	0
$763$	−4.11185e84	−0.379808
$764$	8.71872e84	0.774817
$765$	0	0
$766$	5.43618e84	0.447245
$767$	−1.41334e85	−1.11888
$768$	0	0
$769$	−2.04223e85	−1.49719	−0.748596	−	0.663026i	$-0.769272\pi$
$769$	−2.04223e85	−1.49719	−0.748596	+	0.663026i	$0.769272\pi$
$770$	−6.73382e84	−0.475100
$771$	0	0
$772$	1.98711e85	1.29871
$773$	1.06063e85	0.667221	0.333611	−	0.942711i	$-0.391733\pi$
$773$	1.06063e85	0.667221	0.333611	+	0.942711i	$0.391733\pi$
$774$	0	0
$775$	−3.80188e85	−2.21614
$776$	−3.70240e84	−0.207760
$777$	0	0
$778$	3.16310e84	0.164518
$779$	7.08563e83	0.0354833
$780$	0	0
$781$	1.54578e85	0.717700
$782$	−7.06947e84	−0.316073
$783$	0	0
$784$	−7.74453e84	−0.321123
$785$	−5.47007e85	−2.18443
$786$	0	0
$787$	−6.47255e84	−0.239784	−0.119892	−	0.992787i	$-0.538255\pi$
$787$	−6.47255e84	−0.239784	−0.119892	+	0.992787i	$0.538255\pi$
$788$	2.63217e84	0.0939270
$789$	0	0
$790$	−4.08610e85	−1.35304
$791$	1.07448e85	0.342761
$792$	0	0
$793$	1.46013e85	0.432348
$794$	−7.13487e84	−0.203555
$795$	0	0
$796$	2.82257e85	0.747668
$797$	−3.83924e85	−0.979997	−0.489998	−	0.871723i	$-0.663003\pi$
$797$	−3.83924e85	−0.979997	−0.489998	+	0.871723i	$0.663003\pi$
$798$	0	0
$799$	−9.78762e84	−0.232032
$800$	1.04684e86	2.39181
$801$	0	0
$802$	2.77480e85	0.588964
$803$	8.91790e85	1.82454
$804$	0	0
$805$	8.43851e85	1.60431
$806$	1.50657e85	0.276124
$807$	0	0
$808$	−2.39357e85	−0.407766
$809$	5.32062e85	0.873938	0.436969	−	0.899476i	$-0.356052\pi$
$809$	5.32062e85	0.873938	0.436969	+	0.899476i	$0.356052\pi$
$810$	0	0
$811$	3.55627e85	0.543100	0.271550	−	0.962424i	$-0.412464\pi$
$811$	3.55627e85	0.543100	0.271550	+	0.962424i	$0.412464\pi$
$812$	3.46076e85	0.509646
$813$	0	0
$814$	−8.02587e84	−0.109919
$815$	−1.10287e86	−1.45672
$816$	0	0
$817$	7.08104e85	0.870054
$818$	−3.82389e85	−0.453193
$819$	0	0
$820$	6.60799e84	0.0728720
$821$	−1.58053e84	−0.0168144	−0.00840719	−	0.999965i	$-0.502676\pi$
$821$	−1.58053e84	−0.0168144	−0.00840719	+	0.999965i	$0.502676\pi$
$822$	0	0
$823$	−1.35395e84	−0.0134063	−0.00670315	−	0.999978i	$-0.502134\pi$
$823$	−1.35395e84	−0.0134063	−0.00670315	+	0.999978i	$0.502134\pi$
$824$	−3.86000e85	−0.368752
$825$	0	0
$826$	−4.40941e85	−0.392166
$827$	2.09737e86	1.79996	0.899980	−	0.435930i	$-0.143581\pi$
$827$	2.09737e86	1.79996	0.899980	+	0.435930i	$0.143581\pi$
$828$	0	0
$829$	−2.20814e86	−1.76469	−0.882345	−	0.470603i	$-0.844037\pi$
$829$	−2.20814e86	−1.76469	−0.882345	+	0.470603i	$0.844037\pi$
$830$	1.17754e85	0.0908183
$831$	0	0
$832$	6.76877e84	0.0486264
$833$	−4.75106e85	−0.329430
$834$	0	0
$835$	2.96328e85	0.191435
$836$	9.96703e85	0.621556
$837$	0	0
$838$	−2.85647e85	−0.166009
$839$	−1.14299e86	−0.641307	−0.320654	−	0.947197i	$-0.603903\pi$
$839$	−1.14299e86	−0.641307	−0.320654	+	0.947197i	$0.603903\pi$
$840$	0	0
$841$	2.60617e85	0.136308
$842$	1.60468e85	0.0810365
$843$	0	0
$844$	2.21264e86	1.04186
$845$	−2.01558e86	−0.916490
$846$	0	0
$847$	−8.15782e84	−0.0345950
$848$	6.56032e85	0.268687
$849$	0	0
$850$	1.35812e86	0.518896
$851$	1.00577e86	0.371171
$852$	0	0
$853$	−2.96557e86	−1.02120	−0.510601	−	0.859818i	$-0.670577\pi$
$853$	−2.96557e86	−1.02120	−0.510601	+	0.859818i	$0.670577\pi$
$854$	4.55538e85	0.151537
$855$	0	0
$856$	2.90139e86	0.900803
$857$	−4.75436e86	−1.42612	−0.713062	−	0.701101i	$-0.752692\pi$
$857$	−4.75436e86	−1.42612	−0.713062	+	0.701101i	$0.752692\pi$
$858$	0	0
$859$	2.70859e86	0.758481	0.379240	−	0.925298i	$-0.376185\pi$
$859$	2.70859e86	0.758481	0.379240	+	0.925298i	$0.376185\pi$
$860$	6.60371e86	1.78683
$861$	0	0
$862$	−2.64179e86	−0.667472
$863$	−6.38040e86	−1.55786	−0.778932	−	0.627109i	$-0.784238\pi$
$863$	−6.38040e86	−1.55786	−0.778932	+	0.627109i	$0.784238\pi$
$864$	0	0
$865$	−1.24211e87	−2.83259
$866$	1.84831e86	0.407379
$867$	0	0
$868$	−2.11523e86	−0.435537
$869$	−8.85633e86	−1.76267
$870$	0	0
$871$	4.11561e86	0.765418
$872$	−2.80273e86	−0.503901
$873$	0	0
$874$	2.77545e86	0.466387
$875$	−9.54746e86	−1.55114
$876$	0	0
$877$	−1.05932e87	−1.60894	−0.804469	−	0.593995i	$-0.797550\pi$
$877$	−1.05932e87	−1.60894	−0.804469	+	0.593995i	$0.797550\pi$
$878$	3.90139e86	0.572970
$879$	0	0
$880$	6.77070e86	0.929811
$881$	3.34361e86	0.444045	0.222022	−	0.975042i	$-0.428734\pi$
$881$	3.34361e86	0.444045	0.222022	+	0.975042i	$0.428734\pi$
$882$	0	0
$883$	1.56798e87	1.94761	0.973803	−	0.227394i	$-0.0730204\pi$
$883$	1.56798e87	1.94761	0.973803	+	0.227394i	$0.0730204\pi$
$884$	2.42194e86	0.290953
$885$	0	0
$886$	2.94243e86	0.330682
$887$	1.35049e87	1.46806	0.734032	−	0.679115i	$-0.237636\pi$
$887$	1.35049e87	1.46806	0.734032	+	0.679115i	$0.237636\pi$
$888$	0	0
$889$	−1.11750e86	−0.113670
$890$	−3.37393e86	−0.331994
$891$	0	0
$892$	−8.43994e86	−0.777278
$893$	3.84260e86	0.342379
$894$	0	0
$895$	−9.97413e86	−0.831947
$896$	7.32964e86	0.591557
$897$	0	0
$898$	6.73061e86	0.508630
$899$	−1.32789e87	−0.971074
$900$	0	0
$901$	4.02458e86	0.275638
$902$	−3.18258e85	−0.0210953
$903$	0	0
$904$	7.32389e86	0.454750
$905$	5.71703e86	0.343588
$906$	0	0
$907$	−2.09556e87	−1.18001	−0.590003	−	0.807401i	$-0.700873\pi$
$907$	−2.09556e87	−1.18001	−0.590003	+	0.807401i	$0.700873\pi$
$908$	1.78200e86	0.0971346
$909$	0	0
$910$	6.42403e86	0.328161
$911$	−1.73916e87	−0.860096	−0.430048	−	0.902806i	$-0.641503\pi$
$911$	−1.73916e87	−0.860096	−0.430048	+	0.902806i	$0.641503\pi$
$912$	0	0
$913$	2.55224e86	0.118313
$914$	5.30975e86	0.238320
$915$	0	0
$916$	−1.21348e87	−0.510641
$917$	1.15784e87	0.471797
$918$	0	0
$919$	2.15988e87	0.825320	0.412660	−	0.910885i	$-0.364600\pi$
$919$	2.15988e87	0.825320	0.412660	+	0.910885i	$0.364600\pi$
$920$	5.75188e87	2.12848
$921$	0	0
$922$	−7.51149e86	−0.260714
$923$	−1.47467e87	−0.495729
$924$	0	0
$925$	−1.93218e87	−0.609350
$926$	4.95120e86	0.151247
$927$	0	0
$928$	3.65634e87	1.04805
$929$	−3.13437e87	−0.870336	−0.435168	−	0.900349i	$-0.643311\pi$
$929$	−3.13437e87	−0.870336	−0.435168	+	0.900349i	$0.643311\pi$
$930$	0	0
$931$	1.86525e87	0.486096
$932$	4.28485e87	1.08185
$933$	0	0
$934$	2.32168e87	0.550262
$935$	4.15364e87	0.953864
$936$	0	0
$937$	3.43491e87	0.740624	0.370312	−	0.928907i	$-0.379251\pi$
$937$	3.43491e87	0.740624	0.370312	+	0.928907i	$0.379251\pi$
$938$	1.28401e87	0.268277
$939$	0	0
$940$	3.58357e87	0.703143
$941$	−6.94454e87	−1.32053	−0.660267	−	0.751031i	$-0.729557\pi$
$941$	−6.94454e87	−1.32053	−0.660267	+	0.751031i	$0.729557\pi$
$942$	0	0
$943$	3.98826e86	0.0712341
$944$	4.43356e87	0.767501
$945$	0	0
$946$	−3.18051e87	−0.517260
$947$	2.62366e87	0.413603	0.206801	−	0.978383i	$-0.433695\pi$
$947$	2.62366e87	0.413603	0.206801	+	0.978383i	$0.433695\pi$
$948$	0	0
$949$	−8.50764e87	−1.26025
$950$	−5.33195e87	−0.765666
$951$	0	0
$952$	1.67912e87	0.226617
$953$	7.56122e86	0.0989353	0.0494676	−	0.998776i	$-0.484248\pi$
$953$	7.56122e86	0.0989353	0.0494676	+	0.998776i	$0.484248\pi$
$954$	0	0
$955$	−1.42647e88	−1.75455
$956$	−7.56026e87	−0.901632
$957$	0	0
$958$	−4.94534e87	−0.554515
$959$	−2.15942e87	−0.234794
$960$	0	0
$961$	−1.66391e87	−0.170133
$962$	7.65664e86	0.0759231
$963$	0	0
$964$	1.30763e88	1.21958
$965$	−3.25112e88	−2.94088
$966$	0	0
$967$	1.62324e87	0.138134	0.0690671	−	0.997612i	$-0.477998\pi$
$967$	1.62324e87	0.138134	0.0690671	+	0.997612i	$0.477998\pi$
$968$	−5.56056e86	−0.0458982
$969$	0	0
$970$	2.72590e87	0.211711
$971$	1.28331e88	0.966859	0.483430	−	0.875383i	$-0.339391\pi$
$971$	1.28331e88	0.966859	0.483430	+	0.875383i	$0.339391\pi$
$972$	0	0
$973$	1.78673e87	0.126686
$974$	1.45569e87	0.100134
$975$	0	0
$976$	−4.58033e87	−0.296570
$977$	−7.50188e87	−0.471281	−0.235641	−	0.971840i	$-0.575719\pi$
$977$	−7.50188e87	−0.471281	−0.235641	+	0.971840i	$0.575719\pi$
$978$	0	0
$979$	−7.31275e87	−0.432505
$980$	1.73952e88	0.998296
$981$	0	0
$982$	−3.67160e87	−0.198411
$983$	−2.00914e88	−1.05361	−0.526807	−	0.849985i	$-0.676611\pi$
$983$	−2.00914e88	−1.05361	−0.526807	+	0.849985i	$0.676611\pi$
$984$	0	0
$985$	−4.30650e87	−0.212694
$986$	4.74355e87	0.227371
$987$	0	0
$988$	−9.50849e87	−0.429321
$989$	3.98567e88	1.74667
$990$	0	0
$991$	−9.16723e87	−0.378500	−0.189250	−	0.981929i	$-0.560606\pi$
$991$	−9.16723e87	−0.378500	−0.189250	+	0.981929i	$0.560606\pi$
$992$	−2.23477e88	−0.895648
$993$	0	0
$994$	−4.60073e87	−0.173752
$995$	−4.61802e88	−1.69307
$996$	0	0
$997$	4.97874e88	1.72033	0.860167	−	0.510013i	$-0.170359\pi$
$997$	4.97874e88	1.72033	0.860167	+	0.510013i	$0.170359\pi$
$998$	−8.88101e87	−0.297928
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	9.60.a.c.1.3		5
3.2	odd	2		1.60.a.a.1.3	✓	5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1.60.a.a.1.3	✓	5	3.2	odd	2
9.60.a.c.1.3		5	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:	\( k \)	\(=\)	\( 60 \)
Character orbit:	\([\chi]\)	\(=\)	9.a (trivial)

\(f(q)\)	\(=\)	\(q+3.23738e8 q^{2} -4.71654e17 q^{4} +7.71676e20 q^{5} -4.97804e24 q^{7} -3.39315e26 q^{8} +O(q^{10})\)	\(q+3.23738e8 q^{2} -4.71654e17 q^{4} +7.71676e20 q^{5} -4.97804e24 q^{7} -3.39315e26 q^{8} +2.49821e29 q^{10} +5.41469e30 q^{11} -5.16559e32 q^{13} -1.61158e33 q^{14} +1.62041e35 q^{16} +9.94078e35 q^{17} -3.90272e37 q^{19} -3.63964e38 q^{20} +1.75294e39 q^{22} -2.19671e40 q^{23} +4.22011e41 q^{25} -1.67230e41 q^{26} +2.34792e42 q^{28} +1.47397e43 q^{29} -9.00895e43 q^{31} +2.48061e44 q^{32} +3.21821e44 q^{34} -3.84144e45 q^{35} -4.57851e45 q^{37} -1.26346e46 q^{38} -2.61841e47 q^{40} -1.81556e46 q^{41} -1.81438e48 q^{43} -2.55386e48 q^{44} -7.11158e48 q^{46} -9.84593e48 q^{47} -4.77936e49 q^{49} +1.36621e50 q^{50} +2.43637e50 q^{52} +4.04855e50 q^{53} +4.17839e51 q^{55} +1.68912e51 q^{56} +4.77181e51 q^{58} +2.73608e52 q^{59} -2.82665e52 q^{61} -2.91654e52 q^{62} -1.31036e52 q^{64} -3.98616e53 q^{65} -7.96736e53 q^{67} -4.68861e53 q^{68} -1.24362e54 q^{70} +2.85479e54 q^{71} +1.64698e55 q^{73} -1.48224e54 q^{74} +1.84074e55 q^{76} -2.69546e55 q^{77} -1.63561e56 q^{79} +1.25043e56 q^{80} -5.87766e54 q^{82} +4.71355e55 q^{83} +7.67106e56 q^{85} -5.87385e56 q^{86} -1.83729e57 q^{88} -1.35054e57 q^{89} +2.57145e57 q^{91} +1.03609e58 q^{92} -3.18751e57 q^{94} -3.01164e58 q^{95} +1.09114e58 q^{97} -1.54726e58 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q + 449691864 q^{2} + 17\!\cdots\!40 q^{4}+ \cdots + 34\!\cdots\!80 q^{8}+O(q^{10}) \) 5 * q + 449691864 * q^2 + 1738819379139544640 * q^4 - 179961612150086058390 * q^5 + 1498777546338193415604856 * q^7 + 345163648945131266751137280 * q^8	\( 5 q + 449691864 q^{2} + 17\!\cdots\!40 q^{4}+ \cdots + 10\!\cdots\!52 q^{98}+O(q^{100}) \) 5 * q + 449691864 * q^2 + 1738819379139544640 * q^4 - 179961612150086058390 * q^5 + 1498777546338193415604856 * q^7 + 345163648945131266751137280 * q^8 - 816306987485763512638039118160 * q^10 - 4258478353252041879297428322660 * q^11 - 845614914312482778669168084611378 * q^13 - 6292067851730037636066126264146880 * q^14 + 694835480494500010980166187386081280 * q^16 + 3408789133052869460614097222783941254 * q^17 + 64613555538305267315990967466483855900 * q^19 - 167758871278751870059053885614959950720 * q^20 + 16748450439811023159371198583524768270112 * q^22 - 26762219406239912352813565493381233364712 * q^23 + 626328164486171817149625807278273965801475 * q^25 - 2749973149308040923633652135036287227445360 * q^26 - 5611228561379710656820495758490486062705152 * q^28 + 17549046108593766297328008399864666159350850 * q^29 - 358583623042201488230225328552738568224907040 * q^31 + 1074522626525330530995966308544265757955293184 * q^32 + 1313186147384734516654444992913422917722864080 * q^34 - 8788755903389357061227741366680412802419085840 * q^35 + 12289654705391014078883644083969663074775614326 * q^37 + 45794685161100120795332322131326257673964677920 * q^38 - 623280493607240105129626720516519294122185241600 * q^40 + 1264600318837995850108850617547077064258140834590 * q^41 + 1362401402875616509759331175816257798295684833092 * q^43 - 10077075627927391677990061115125884792646469172480 * q^44 + 35794385229187598114442404877782400066811275005760 * q^46 - 58116315089138636393563553286549713195469724328016 * q^47 - 172418318747588613327122588406220961507566908720435 * q^49 + 233848387346081992883910872998391056418422012487400 * q^50 - 992097542005695911104987622381229757223139868049024 * q^52 - 2268101788488183861226576340546566132432064315777382 * q^53 + 900686393182056151569568156583842171451592208829880 * q^55 - 13057990199329560708452108630914154838760821091430400 * q^56 - 19935384508052610930909349257749128471453923297265680 * q^58 + 21931653365540795176945573682489794310901322601489100 * q^59 - 55594140754072322694181208673989737469003346813960290 * q^61 - 183475769536335462614566613996468524195162017418651392 * q^62 + 442992326944585087629292186411036974187652719990538240 * q^64 - 108239432655103548226552811908240865218465397888070180 * q^65 + 251728958220345096328034657219059743090559333983657196 * q^67 + 5807349046062465910161766073979061475602982250739804032 * q^68 - 5752977156560799367346480182820409713199133658156760960 * q^70 + 6369597660991167158573967320963521000612243175546832840 * q^71 + 12498734118021895660608582328454257591891310584798516162 * q^73 - 30430803441235884517255321866854090380478491767252508080 * q^74 + 44485052481827577410579765985045990814357967613276332800 * q^76 - 17284905559091020495400324815223194592508822902892800352 * q^77 - 195027743716001656833247333265450397879290980351117845200 * q^79 + 206704704480779086536260387174822452768748287935918120960 * q^80 - 900520634877949974377918733125010085392642066824246973168 * q^82 - 1340753017495815214930655712848265601901866175919407282652 * q^83 + 2489371886919081358504761029214476055227000571885198923340 * q^85 + 1480724029310290822922398160933917869023473589220972227040 * q^86 - 766253667564296029168711510940105999694943299571114997760 * q^88 - 4137994032714609594535072901976334293523151283735651174450 * q^89 + 2026135516273811264299668018701283385599128389353986522960 * q^91 + 40220109586116561836814028008941466356622877640185075490304 * q^92 - 11288243726815211032514455546739674300124940708563708661120 * q^94 - 87101339446452871712134322546432797479691690743389226486600 * q^95 + 116502743099592096760799908821840050224405365201122277495466 * q^97 + 100197653381373748947470486612022288330601696851398709875352 * q^98

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