LMFDB - Embedded newform 9.60.a.c.1.2

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			1.2
Root			$-3.26158e7$ of defining polynomial
Character	$\chi$	$=$	9.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-6.92842e8 q^{2} -9.64308e16 q^{4} -3.87033e20 q^{5} -7.47157e23 q^{7} +4.66207e26 q^{8} +O(q^{10})$	\(q-6.92842e8 q^{2} -9.64308e16 q^{4} -3.87033e20 q^{5} -7.47157e23 q^{7} +4.66207e26 q^{8} +2.68153e29 q^{10} -4.64881e30 q^{11} +1.02949e33 q^{13} +5.17661e32 q^{14} -2.67420e35 q^{16} -2.49454e36 q^{17} +3.24421e37 q^{19} +3.73219e37 q^{20} +3.22089e39 q^{22} -2.77809e40 q^{23} -2.36780e40 q^{25} -7.13271e41 q^{26} +7.20489e40 q^{28} +1.27852e43 q^{29} -1.14110e44 q^{31} -8.34708e43 q^{32} +1.72832e45 q^{34} +2.89174e44 q^{35} +2.85266e46 q^{37} -2.24773e46 q^{38} -1.80438e47 q^{40} +2.41356e47 q^{41} +1.26598e48 q^{43} +4.48289e47 q^{44} +1.92478e49 q^{46} +1.54116e49 q^{47} -7.20163e49 q^{49} +1.64051e49 q^{50} -9.92742e49 q^{52} -3.50384e50 q^{53} +1.79924e51 q^{55} -3.48330e50 q^{56} -8.85809e51 q^{58} -3.68928e51 q^{59} -9.17858e51 q^{61} +7.90602e52 q^{62} +2.11989e53 q^{64} -3.98445e53 q^{65} +4.08228e53 q^{67} +2.40550e53 q^{68} -2.00352e53 q^{70} +3.75256e52 q^{71} -2.19258e54 q^{73} -1.97644e55 q^{74} -3.12842e54 q^{76} +3.47339e54 q^{77} +1.38224e56 q^{79} +1.03500e56 q^{80} -1.67221e56 q^{82} -1.05696e56 q^{83} +9.65467e56 q^{85} -8.77123e56 q^{86} -2.16731e57 q^{88} +3.89442e57 q^{89} -7.69187e56 q^{91} +2.67894e57 q^{92} -1.06778e58 q^{94} -1.25562e58 q^{95} +7.21075e58 q^{97} +4.98959e58 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−6.92842e8	−0.912535	−0.456267	−	0.889843i	$-0.650814\pi$
$2$	−6.92842e8	−0.912535	−0.456267	+	0.889843i	$0.650814\pi$
$3$	0	0
$3$	0	0
$4$	−9.64308e16	−0.167281
$5$	−3.87033e20	−0.929250	−0.464625	−	0.885508i	$-0.653811\pi$
$5$	−3.87033e20	−0.929250	−0.464625	+	0.885508i	$0.653811\pi$
$6$	0	0
$7$	−7.47157e23	−0.0877040	−0.0438520	−	0.999038i	$-0.513963\pi$
$7$	−7.47157e23	−0.0877040	−0.0438520	+	0.999038i	$0.513963\pi$
$8$	4.66207e26	1.06518
$9$	0	0
$10$	2.68153e29	0.847973
$11$	−4.64881e30	−0.883604	−0.441802	−	0.897113i	$-0.645661\pi$
$11$	−4.64881e30	−0.883604	−0.441802	+	0.897113i	$0.645661\pi$
$12$	0	0
$13$	1.02949e33	1.41674	0.708372	−	0.705839i	$-0.249430\pi$
$13$	1.02949e33	1.41674	0.708372	+	0.705839i	$0.249430\pi$
$14$	5.17661e32	0.0800329
$15$	0	0
$16$	−2.67420e35	−0.804736
$17$	−2.49454e36	−1.25530	−0.627649	−	0.778497i	$-0.715983\pi$
$17$	−2.49454e36	−1.25530	−0.627649	+	0.778497i	$0.715983\pi$
$18$	0	0
$19$	3.24421e37	0.613590	0.306795	−	0.951776i	$-0.400743\pi$
$19$	3.24421e37	0.613590	0.306795	+	0.951776i	$0.400743\pi$
$20$	3.73219e37	0.155446
$21$	0	0
$22$	3.22089e39	0.806319
$23$	−2.77809e40	−1.87403	−0.937013	−	0.349294i	$-0.886421\pi$
$23$	−2.77809e40	−1.87403	−0.937013	+	0.349294i	$0.886421\pi$
$24$	0	0
$25$	−2.36780e40	−0.136494
$26$	−7.13271e41	−1.29283
$27$	0	0
$28$	7.20489e40	0.0146712
$29$	1.27852e43	0.924624	0.462312	−	0.886717i	$-0.347020\pi$
$29$	1.27852e43	0.924624	0.462312	+	0.886717i	$0.347020\pi$
$30$	0	0
$31$	−1.14110e44	−1.15386	−0.576931	−	0.816793i	$-0.695750\pi$
$31$	−1.14110e44	−1.15386	−0.576931	+	0.816793i	$0.695750\pi$
$32$	−8.34708e43	−0.330834
$33$	0	0
$34$	1.72832e45	1.14550
$35$	2.89174e44	0.0814990
$36$	0	0
$37$	2.85266e46	1.56063	0.780313	−	0.625390i	$-0.215060\pi$
$37$	2.85266e46	1.56063	0.780313	+	0.625390i	$0.215060\pi$
$38$	−2.24773e46	−0.559922
$39$	0	0
$40$	−1.80438e47	−0.989822
$41$	2.41356e47	0.639049	0.319524	−	0.947578i	$-0.396477\pi$
$41$	2.41356e47	0.639049	0.319524	+	0.947578i	$0.396477\pi$
$42$	0	0
$43$	1.26598e48	0.822445	0.411223	−	0.911535i	$-0.365102\pi$
$43$	1.26598e48	0.822445	0.411223	+	0.911535i	$0.365102\pi$
$44$	4.48289e47	0.147810
$45$	0	0
$46$	1.92478e49	1.71011
$47$	1.54116e49	0.726038	0.363019	−	0.931782i	$-0.381746\pi$
$47$	1.54116e49	0.726038	0.363019	+	0.931782i	$0.381746\pi$
$48$	0	0
$49$	−7.20163e49	−0.992308
$50$	1.64051e49	0.124556
$51$	0	0
$52$	−9.92742e49	−0.236994
$53$	−3.50384e50	−0.476876	−0.238438	−	0.971158i	$-0.576635\pi$
$53$	−3.50384e50	−0.476876	−0.238438	+	0.971158i	$0.576635\pi$
$54$	0	0
$55$	1.79924e51	0.821089
$56$	−3.48330e50	−0.0934209
$57$	0	0
$58$	−8.85809e51	−0.843751
$59$	−3.68928e51	−0.212230	−0.106115	−	0.994354i	$-0.533841\pi$
$59$	−3.68928e51	−0.212230	−0.106115	+	0.994354i	$0.533841\pi$
$60$	0	0
$61$	−9.17858e51	−0.197490	−0.0987450	−	0.995113i	$-0.531483\pi$
$61$	−9.17858e51	−0.197490	−0.0987450	+	0.995113i	$0.531483\pi$
$62$	7.90602e52	1.05294
$63$	0	0
$64$	2.11989e53	1.10663
$65$	−3.98445e53	−1.31651
$66$	0	0
$67$	4.08228e53	0.551691	0.275845	−	0.961202i	$-0.411042\pi$
$67$	4.08228e53	0.551691	0.275845	+	0.961202i	$0.411042\pi$
$68$	2.40550e53	0.209987
$69$	0	0
$70$	−2.00352e53	−0.0743706
$71$	3.75256e52	0.00916657	0.00458329	−	0.999989i	$-0.498541\pi$
$71$	3.75256e52	0.00916657	0.00458329	+	0.999989i	$0.498541\pi$
$72$	0	0
$73$	−2.19258e54	−0.236010	−0.118005	−	0.993013i	$-0.537650\pi$
$73$	−2.19258e54	−0.236010	−0.118005	+	0.993013i	$0.537650\pi$
$74$	−1.97644e55	−1.42412
$75$	0	0
$76$	−3.12842e54	−0.102642
$77$	3.47339e54	0.0774956
$78$	0	0
$79$	1.38224e56	1.44739	0.723694	−	0.690121i	$-0.242443\pi$
$79$	1.38224e56	1.44739	0.723694	+	0.690121i	$0.242443\pi$
$80$	1.03500e56	0.747801
$81$	0	0
$82$	−1.67221e56	−0.583154
$83$	−1.05696e56	−0.257783	−0.128892	−	0.991659i	$-0.541142\pi$
$83$	−1.05696e56	−0.257783	−0.128892	+	0.991659i	$0.541142\pi$
$84$	0	0
$85$	9.65467e56	1.16649
$86$	−8.77123e56	−0.750510
$87$	0	0
$88$	−2.16731e57	−0.941201
$89$	3.89442e57	1.21182	0.605909	−	0.795534i	$-0.292810\pi$
$89$	3.89442e57	1.21182	0.605909	+	0.795534i	$0.292810\pi$
$90$	0	0
$91$	−7.69187e56	−0.124254
$92$	2.67894e57	0.313489
$93$	0	0
$94$	−1.06778e58	−0.662535
$95$	−1.25562e58	−0.570179
$96$	0	0
$97$	7.21075e58	1.77098	0.885492	−	0.464655i	$-0.153822\pi$
$97$	7.21075e58	1.77098	0.885492	+	0.464655i	$0.153822\pi$
$98$	4.98959e58	0.905515
$99$	0	0
$100$	2.28329e57	0.0228329
$101$	−1.38211e58	−0.103053	−0.0515267	−	0.998672i	$-0.516409\pi$
$101$	−1.38211e58	−0.103053	−0.0515267	+	0.998672i	$0.516409\pi$
$102$	0	0
$103$	1.89666e59	0.793034	0.396517	−	0.918027i	$-0.370219\pi$
$103$	1.89666e59	0.793034	0.396517	+	0.918027i	$0.370219\pi$
$104$	4.79954e59	1.50909
$105$	0	0
$106$	2.42760e59	0.435166
$107$	−8.57892e59	−1.16577	−0.582883	−	0.812556i	$-0.698075\pi$
$107$	−8.57892e59	−1.16577	−0.582883	+	0.812556i	$0.698075\pi$
$108$	0	0
$109$	1.17707e60	0.926233	0.463117	−	0.886297i	$-0.346731\pi$
$109$	1.17707e60	0.926233	0.463117	+	0.886297i	$0.346731\pi$
$110$	−1.24659e60	−0.749272
$111$	0	0
$112$	1.99804e59	0.0705786
$113$	7.22546e60	1.96359	0.981796	−	0.189938i	$-0.0608286\pi$
$113$	7.22546e60	1.96359	0.981796	+	0.189938i	$0.0608286\pi$
$114$	0	0
$115$	1.07521e61	1.74144
$116$	−1.23288e60	−0.154672
$117$	0	0
$118$	2.55609e60	0.193667
$119$	1.86381e60	0.110095
$120$	0	0
$121$	−6.06869e60	−0.219244
$122$	6.35930e60	0.180217
$123$	0	0
$124$	1.10037e61	0.193019
$125$	7.63036e61	1.05609
$126$	0	0
$127$	−1.53871e62	−1.33336	−0.666680	−	0.745344i	$-0.732285\pi$
$127$	−1.53871e62	−1.33336	−0.666680	+	0.745344i	$0.732285\pi$
$128$	−9.87572e61	−0.679008
$129$	0	0
$130$	2.76059e62	1.20136
$131$	−1.44734e62	−0.502421	−0.251210	−	0.967933i	$-0.580829\pi$
$131$	−1.44734e62	−0.502421	−0.251210	+	0.967933i	$0.580829\pi$
$132$	0	0
$133$	−2.42394e61	−0.0538143
$134$	−2.82837e62	−0.503437
$135$	0	0
$136$	−1.16297e63	−1.33712
$137$	2.88977e62	0.267674	0.133837	−	0.991003i	$-0.457270\pi$
$137$	2.88977e62	0.267674	0.133837	+	0.991003i	$0.457270\pi$
$138$	0	0
$139$	5.60982e61	0.0338854	0.0169427	−	0.999856i	$-0.494607\pi$
$139$	5.60982e61	0.0338854	0.0169427	+	0.999856i	$0.494607\pi$
$140$	−2.78853e61	−0.0136332
$141$	0	0
$142$	−2.59993e61	−0.00836481
$143$	−4.78589e63	−1.25184
$144$	0	0
$145$	−4.94827e63	−0.859207
$146$	1.51911e63	0.215367
$147$	0	0
$148$	−2.75084e63	−0.261063
$149$	4.37262e62	0.0340210	0.0170105	−	0.999855i	$-0.494585\pi$
$149$	4.37262e62	0.0340210	0.0170105	+	0.999855i	$0.494585\pi$
$150$	0	0
$151$	−2.73644e63	−0.143670	−0.0718349	−	0.997417i	$-0.522885\pi$
$151$	−2.73644e63	−0.143670	−0.0718349	+	0.997417i	$0.522885\pi$
$152$	1.51248e64	0.653586
$153$	0	0
$154$	−2.40651e63	−0.0707175
$155$	4.41643e64	1.07223
$156$	0	0
$157$	9.42454e64	1.56755	0.783773	−	0.621047i	$-0.213292\pi$
$157$	9.42454e64	1.56755	0.783773	+	0.621047i	$0.213292\pi$
$158$	−9.57675e64	−1.32079
$159$	0	0
$160$	3.23059e64	0.307428
$161$	2.07567e64	0.164360
$162$	0	0
$163$	−9.60370e64	−0.528329	−0.264164	−	0.964478i	$-0.585096\pi$
$163$	−9.60370e64	−0.528329	−0.264164	+	0.964478i	$0.585096\pi$
$164$	−2.32741e64	−0.106901
$165$	0	0
$166$	7.32307e64	0.235236
$167$	3.29003e65	0.885245	0.442623	−	0.896708i	$-0.354048\pi$
$167$	3.29003e65	0.885245	0.442623	+	0.896708i	$0.354048\pi$
$168$	0	0
$169$	5.31813e65	1.00717
$170$	−6.68916e65	−1.06446
$171$	0	0
$172$	−1.22079e65	−0.137579
$173$	1.32471e65	0.125823	0.0629114	−	0.998019i	$-0.479961\pi$
$173$	1.32471e65	0.125823	0.0629114	+	0.998019i	$0.479961\pi$
$174$	0	0
$175$	1.76912e64	0.0119711
$176$	1.24318e66	0.711068
$177$	0	0
$178$	−2.69822e66	−1.10583
$179$	−3.36648e66	−1.16953	−0.584766	−	0.811202i	$-0.698814\pi$
$179$	−3.36648e66	−1.16953	−0.584766	+	0.811202i	$0.698814\pi$
$180$	0	0
$181$	−2.06923e66	−0.517952	−0.258976	−	0.965884i	$-0.583385\pi$
$181$	−2.06923e66	−0.517952	−0.258976	+	0.965884i	$0.583385\pi$
$182$	5.32925e65	0.113386
$183$	0	0
$184$	−1.29517e67	−1.99618
$185$	−1.10407e67	−1.45021
$186$	0	0
$187$	1.15966e67	1.10919
$188$	−1.48615e66	−0.121452
$189$	0	0
$190$	8.69944e66	0.520308
$191$	1.71430e67	0.878217	0.439108	−	0.898434i	$-0.355294\pi$
$191$	1.71430e67	0.878217	0.439108	+	0.898434i	$0.355294\pi$
$192$	0	0
$193$	−4.57672e67	−1.72430	−0.862152	−	0.506650i	$-0.830884\pi$
$193$	−4.57672e67	−1.72430	−0.862152	+	0.506650i	$0.830884\pi$
$194$	−4.99591e67	−1.61608
$195$	0	0
$196$	6.94459e66	0.165994
$197$	−2.68332e67	−0.551974	−0.275987	−	0.961161i	$-0.589005\pi$
$197$	−2.68332e67	−0.551974	−0.275987	+	0.961161i	$0.589005\pi$
$198$	0	0
$199$	9.84849e67	1.50385	0.751924	−	0.659250i	$-0.229126\pi$
$199$	9.84849e67	1.50385	0.751924	+	0.659250i	$0.229126\pi$
$200$	−1.10389e67	−0.145392
$201$	0	0
$202$	9.57584e66	0.0940397
$203$	−9.55251e66	−0.0810932
$204$	0	0
$205$	−9.34126e67	−0.593836
$206$	−1.31409e68	−0.723671
$207$	0	0
$208$	−2.75305e68	−1.14011
$209$	−1.50817e68	−0.542171
$210$	0	0
$211$	−3.01598e68	−0.818646	−0.409323	−	0.912390i	$-0.634235\pi$
$211$	−3.01598e68	−0.818646	−0.409323	+	0.912390i	$0.634235\pi$
$212$	3.37878e67	0.0797722
$213$	0	0
$214$	5.94384e68	1.06380
$215$	−4.89975e68	−0.764257
$216$	0	0
$217$	8.52581e67	0.101198
$218$	−8.15523e68	−0.845220
$219$	0	0
$220$	−1.73502e68	−0.137352
$221$	−2.56809e69	−1.77844
$222$	0	0
$223$	−3.24546e69	−1.72299	−0.861494	−	0.507767i	$-0.830471\pi$
$223$	−3.24546e69	−1.72299	−0.861494	+	0.507767i	$0.830471\pi$
$224$	6.23658e67	0.0290155
$225$	0	0
$226$	−5.00610e69	−1.79185
$227$	−4.06034e69	−1.27585	−0.637926	−	0.770098i	$-0.720207\pi$
$227$	−4.06034e69	−1.27585	−0.637926	+	0.770098i	$0.720207\pi$
$228$	0	0
$229$	−1.33796e69	−0.324560	−0.162280	−	0.986745i	$-0.551885\pi$
$229$	−1.33796e69	−0.324560	−0.162280	+	0.986745i	$0.551885\pi$
$230$	−7.44953e69	−1.58912
$231$	0	0
$232$	5.96053e69	0.984894
$233$	−1.30041e69	−0.189270	−0.0946348	−	0.995512i	$-0.530168\pi$
$233$	−1.30041e69	−0.189270	−0.0946348	+	0.995512i	$0.530168\pi$
$234$	0	0
$235$	−5.96478e69	−0.674671
$236$	3.55760e68	0.0355020
$237$	0	0
$238$	−1.29133e69	−0.100465
$239$	−1.00216e70	−0.688968	−0.344484	−	0.938792i	$-0.611946\pi$
$239$	−1.00216e70	−0.688968	−0.344484	+	0.938792i	$0.611946\pi$
$240$	0	0
$241$	−8.59826e69	−0.462283	−0.231142	−	0.972920i	$-0.574246\pi$
$241$	−8.59826e69	−0.462283	−0.231142	+	0.972920i	$0.574246\pi$
$242$	4.20465e69	0.200067
$243$	0	0
$244$	8.85097e68	0.0330363
$245$	2.78727e70	0.922102
$246$	0	0
$247$	3.33987e70	0.869300
$248$	−5.31990e70	−1.22908
$249$	0	0
$250$	−5.28664e70	−0.963716
$251$	−4.07048e70	−0.659586	−0.329793	−	0.944053i	$-0.606979\pi$
$251$	−4.07048e70	−0.659586	−0.329793	+	0.944053i	$0.606979\pi$
$252$	0	0
$253$	1.29148e71	1.65590
$254$	1.06608e71	1.21674
$255$	0	0
$256$	−5.37802e70	−0.487016
$257$	−2.69905e70	−0.217863	−0.108932	−	0.994049i	$-0.534743\pi$
$257$	−2.69905e70	−0.217863	−0.108932	+	0.994049i	$0.534743\pi$
$258$	0	0
$259$	−2.13138e70	−0.136873
$260$	3.84223e70	0.220227
$261$	0	0
$262$	1.00278e71	0.458476
$263$	−6.00409e69	−0.0245331	−0.0122666	−	0.999925i	$-0.503905\pi$
$263$	−6.00409e69	−0.0245331	−0.0122666	+	0.999925i	$0.503905\pi$
$264$	0	0
$265$	1.35610e71	0.443137
$266$	1.67940e70	0.0491074
$267$	0	0
$268$	−3.93657e70	−0.0922873
$269$	4.29641e71	0.902430	0.451215	−	0.892415i	$-0.350991\pi$
$269$	4.29641e71	0.902430	0.451215	+	0.892415i	$0.350991\pi$
$270$	0	0
$271$	−9.26809e71	−1.56457	−0.782287	−	0.622918i	$-0.785947\pi$
$271$	−9.26809e71	−1.56457	−0.782287	+	0.622918i	$0.785947\pi$
$272$	6.67088e71	1.01018
$273$	0	0
$274$	−2.00215e71	−0.244262
$275$	1.10075e71	0.120607
$276$	0	0
$277$	1.16877e72	1.03413	0.517067	−	0.855945i	$-0.327024\pi$
$277$	1.16877e72	1.03413	0.517067	+	0.855945i	$0.327024\pi$
$278$	−3.88672e70	−0.0309216
$279$	0	0
$280$	1.34815e71	0.0868114
$281$	2.43176e72	1.40957	0.704783	−	0.709423i	$-0.251045\pi$
$281$	2.43176e72	1.40957	0.704783	+	0.709423i	$0.251045\pi$
$282$	0	0
$283$	1.52233e72	0.715831	0.357915	−	0.933754i	$-0.383488\pi$
$283$	1.52233e72	0.715831	0.357915	+	0.933754i	$0.383488\pi$
$284$	−3.61863e69	−0.00153339
$285$	0	0
$286$	3.31586e72	1.14235
$287$	−1.80331e71	−0.0560471
$288$	0	0
$289$	2.27372e72	0.575772
$290$	3.42837e72	0.784056
$291$	0	0
$292$	2.11432e71	0.0394799
$293$	4.64053e72	0.783380	0.391690	−	0.920097i	$-0.371890\pi$
$293$	4.64053e72	0.783380	0.391690	+	0.920097i	$0.371890\pi$
$294$	0	0
$295$	1.42787e72	0.197215
$296$	1.32993e73	1.66235
$297$	0	0
$298$	−3.02954e71	−0.0310453
$299$	−2.86001e73	−2.65502
$300$	0	0
$301$	−9.45884e71	−0.0721317
$302$	1.89592e72	0.131104
$303$	0	0
$304$	−8.67566e72	−0.493778
$305$	3.55241e72	0.183518
$306$	0	0
$307$	9.50693e72	0.405003	0.202501	−	0.979282i	$-0.435093\pi$
$307$	9.50693e72	0.405003	0.202501	+	0.979282i	$0.435093\pi$
$308$	−3.34942e71	−0.0129635
$309$	0	0
$310$	−3.05989e73	−0.978444
$311$	3.66965e73	1.06707	0.533536	−	0.845778i	$-0.320863\pi$
$311$	3.66965e73	1.06707	0.533536	+	0.845778i	$0.320863\pi$
$312$	0	0
$313$	−2.59653e73	−0.624937	−0.312468	−	0.949928i	$-0.601156\pi$
$313$	−2.59653e73	−0.624937	−0.312468	+	0.949928i	$0.601156\pi$
$314$	−6.52972e73	−1.43044
$315$	0	0
$316$	−1.33291e73	−0.242120
$317$	−9.43841e73	−1.56189	−0.780945	−	0.624599i	$-0.785262\pi$
$317$	−9.43841e73	−1.56189	−0.780945	+	0.624599i	$0.785262\pi$
$318$	0	0
$319$	−5.94358e73	−0.817001
$320$	−8.20467e73	−1.02834
$321$	0	0
$322$	−1.43811e73	−0.149984
$323$	−8.09281e73	−0.770238
$324$	0	0
$325$	−2.43762e73	−0.193378
$326$	6.65384e73	0.482118
$327$	0	0
$328$	1.12522e74	0.680704
$329$	−1.15148e73	−0.0636765
$330$	0	0
$331$	2.42184e73	0.112000	0.0560002	−	0.998431i	$-0.482165\pi$
$331$	2.42184e73	0.112000	0.0560002	+	0.998431i	$0.482165\pi$
$332$	1.01924e73	0.0431222
$333$	0	0
$334$	−2.27947e74	−0.807817
$335$	−1.57997e74	−0.512659
$336$	0	0
$337$	4.16269e74	1.13316	0.566581	−	0.824006i	$-0.308266\pi$
$337$	4.16269e74	1.13316	0.566581	+	0.824006i	$0.308266\pi$
$338$	−3.68462e74	−0.919073
$339$	0	0
$340$	−9.31008e73	−0.195131
$341$	5.30476e74	1.01956
$342$	0	0
$343$	1.08032e74	0.174733
$344$	5.90209e74	0.876055
$345$	0	0
$346$	−9.17812e73	−0.114818
$347$	−3.03466e74	−0.348651	−0.174326	−	0.984688i	$-0.555775\pi$
$347$	−3.03466e74	−0.348651	−0.174326	+	0.984688i	$0.555775\pi$
$348$	0	0
$349$	−7.65470e74	−0.742297	−0.371149	−	0.928573i	$-0.621036\pi$
$349$	−7.65470e74	−0.742297	−0.371149	+	0.928573i	$0.621036\pi$
$350$	−1.22572e73	−0.0109241
$351$	0	0
$352$	3.88040e74	0.292327
$353$	−3.52861e73	−0.0244484	−0.0122242	−	0.999925i	$-0.503891\pi$
$353$	−3.52861e73	−0.0244484	−0.0122242	+	0.999925i	$0.503891\pi$
$354$	0	0
$355$	−1.45237e73	−0.00851804
$356$	−3.75542e74	−0.202714
$357$	0	0
$358$	2.33244e75	1.06724
$359$	1.13038e75	0.476363	0.238182	−	0.971221i	$-0.423449\pi$
$359$	1.13038e75	0.476363	0.238182	+	0.971221i	$0.423449\pi$
$360$	0	0
$361$	−1.74303e75	−0.623507
$362$	1.43365e75	0.472650
$363$	0	0
$364$	7.41733e73	0.0207853
$365$	8.48599e74	0.219312
$366$	0	0
$367$	−1.14489e75	−0.251834	−0.125917	−	0.992041i	$-0.540187\pi$
$367$	−1.14489e75	−0.251834	−0.125917	+	0.992041i	$0.540187\pi$
$368$	7.42916e75	1.50810
$369$	0	0
$370$	7.64947e75	1.32337
$371$	2.61791e74	0.0418240
$372$	0	0
$373$	−9.11728e75	−1.24295	−0.621476	−	0.783433i	$-0.713467\pi$
$373$	−9.11728e75	−1.24295	−0.621476	+	0.783433i	$0.713467\pi$
$374$	−8.03463e75	−1.01217
$375$	0	0
$376$	7.18498e75	0.773364
$377$	1.31621e76	1.30996
$378$	0	0
$379$	1.17838e76	1.00330	0.501648	−	0.865072i	$-0.332727\pi$
$379$	1.17838e76	1.00330	0.501648	+	0.865072i	$0.332727\pi$
$380$	1.21080e75	0.0953799
$381$	0	0
$382$	−1.18774e76	−0.801403
$383$	−8.81216e75	−0.550451	−0.275225	−	0.961380i	$-0.588753\pi$
$383$	−8.81216e75	−0.550451	−0.275225	+	0.961380i	$0.588753\pi$
$384$	0	0
$385$	−1.34432e75	−0.0720128
$386$	3.17094e76	1.57349
$387$	0	0
$388$	−6.95339e75	−0.296251
$389$	2.99716e76	1.18358	0.591789	−	0.806093i	$-0.298422\pi$
$389$	2.99716e76	1.18358	0.591789	+	0.806093i	$0.298422\pi$
$390$	0	0
$391$	6.93005e76	2.35246
$392$	−3.35745e76	−1.05699
$393$	0	0
$394$	1.85912e76	0.503695
$395$	−5.34973e76	−1.34498
$396$	0	0
$397$	−7.53563e76	−1.63230	−0.816149	−	0.577841i	$-0.803895\pi$
$397$	−7.53563e76	−1.63230	−0.816149	+	0.577841i	$0.803895\pi$
$398$	−6.82345e76	−1.37231
$399$	0	0
$400$	6.33196e75	0.109842
$401$	−2.27678e74	−0.00366913	−0.00183456	−	0.999998i	$-0.500584\pi$
$401$	−2.27678e74	−0.00366913	−0.00183456	+	0.999998i	$0.500584\pi$
$402$	0	0
$403$	−1.17475e77	−1.63473
$404$	1.33278e75	0.0172388
$405$	0	0
$406$	6.61838e75	0.0740004
$407$	−1.32615e77	−1.37898
$408$	0	0
$409$	−1.56193e77	−1.40548	−0.702740	−	0.711447i	$-0.748040\pi$
$409$	−1.56193e77	−1.40548	−0.702740	+	0.711447i	$0.748040\pi$
$410$	6.47201e76	0.541896
$411$	0	0
$412$	−1.82897e76	−0.132659
$413$	2.75647e75	0.0186134
$414$	0	0
$415$	4.09078e76	0.239545
$416$	−8.59321e76	−0.468708
$417$	0	0
$418$	1.04493e77	0.494750
$419$	−3.54180e77	−1.56282	−0.781411	−	0.624016i	$-0.785500\pi$
$419$	−3.54180e77	−1.56282	−0.781411	+	0.624016i	$0.785500\pi$
$420$	0	0
$421$	−6.31905e76	−0.242287	−0.121144	−	0.992635i	$-0.538656\pi$
$421$	−6.31905e76	−0.242287	−0.121144	+	0.992635i	$0.538656\pi$
$422$	2.08960e77	0.747042
$423$	0	0
$424$	−1.63351e77	−0.507961
$425$	5.90657e76	0.171341
$426$	0	0
$427$	6.85784e75	0.0173207
$428$	8.27272e76	0.195010
$429$	0	0
$430$	3.39475e77	0.697411
$431$	3.24391e77	0.622285	0.311142	−	0.950363i	$-0.399288\pi$
$431$	3.24391e77	0.622285	0.311142	+	0.950363i	$0.399288\pi$
$432$	0	0
$433$	2.56630e77	0.429451	0.214726	−	0.976674i	$-0.431114\pi$
$433$	2.56630e77	0.429451	0.214726	+	0.976674i	$0.431114\pi$
$434$	−5.90704e76	−0.0923470
$435$	0	0
$436$	−1.13506e77	−0.154941
$437$	−9.01273e77	−1.14988
$438$	0	0
$439$	6.93858e77	0.773690	0.386845	−	0.922145i	$-0.373565\pi$
$439$	6.93858e77	0.773690	0.386845	+	0.922145i	$0.373565\pi$
$440$	8.38820e77	0.874611
$441$	0	0
$442$	1.77928e78	1.62288
$443$	6.61525e77	0.564464	0.282232	−	0.959346i	$-0.408925\pi$
$443$	6.61525e77	0.564464	0.282232	+	0.959346i	$0.408925\pi$
$444$	0	0
$445$	−1.50727e78	−1.12608
$446$	2.24859e78	1.57229
$447$	0	0
$448$	−1.58389e77	−0.0970563
$449$	5.52670e77	0.317102	0.158551	−	0.987351i	$-0.449318\pi$
$449$	5.52670e77	0.317102	0.158551	+	0.987351i	$0.449318\pi$
$450$	0	0
$451$	−1.12202e78	−0.564666
$452$	−6.96757e77	−0.328471
$453$	0	0
$454$	2.81318e78	1.16426
$455$	2.97701e77	0.115463
$456$	0	0
$457$	−1.03722e78	−0.353464	−0.176732	−	0.984259i	$-0.556553\pi$
$457$	−1.03722e78	−0.353464	−0.176732	+	0.984259i	$0.556553\pi$
$458$	9.26993e77	0.296172
$459$	0	0
$460$	−1.03684e78	−0.291309
$461$	3.77107e78	0.993774	0.496887	−	0.867815i	$-0.334476\pi$
$461$	3.77107e78	0.993774	0.496887	+	0.867815i	$0.334476\pi$
$462$	0	0
$463$	−3.38674e78	−0.785495	−0.392747	−	0.919646i	$-0.628475\pi$
$463$	−3.38674e78	−0.785495	−0.392747	+	0.919646i	$0.628475\pi$
$464$	−3.41900e78	−0.744078
$465$	0	0
$466$	9.00979e77	0.172715
$467$	−1.56624e78	−0.281844	−0.140922	−	0.990021i	$-0.545007\pi$
$467$	−1.56624e78	−0.281844	−0.140922	+	0.990021i	$0.545007\pi$
$468$	0	0
$469$	−3.05010e77	−0.0483855
$470$	4.13265e78	0.615661
$471$	0	0
$472$	−1.71997e78	−0.226064
$473$	−5.88530e78	−0.726716
$474$	0	0
$475$	−7.68165e77	−0.0837516
$476$	−1.79729e77	−0.0184167
$477$	0	0
$478$	6.94339e78	0.628707
$479$	1.69803e78	0.144560	0.0722800	−	0.997384i	$-0.476972\pi$
$479$	1.69803e78	0.144560	0.0722800	+	0.997384i	$0.476972\pi$
$480$	0	0
$481$	2.93677e79	2.21101
$482$	5.95724e78	0.421849
$483$	0	0
$484$	5.85209e77	0.0366752
$485$	−2.79080e79	−1.64569
$486$	0	0
$487$	−1.96778e79	−1.02772	−0.513858	−	0.857875i	$-0.671784\pi$
$487$	−1.96778e79	−1.02772	−0.513858	+	0.857875i	$0.671784\pi$
$488$	−4.27912e78	−0.210363
$489$	0	0
$490$	−1.93114e79	−0.841450
$491$	2.71958e79	1.11583	0.557915	−	0.829898i	$-0.311601\pi$
$491$	2.71958e79	1.11583	0.557915	+	0.829898i	$0.311601\pi$
$492$	0	0
$493$	−3.18930e79	−1.16068
$494$	−2.31400e79	−0.793267
$495$	0	0
$496$	3.05153e79	0.928555
$497$	−2.80375e76	−0.000803945 0
$498$	0	0
$499$	−6.54096e79	−1.66600	−0.833000	−	0.553273i	$-0.813379\pi$
$499$	−6.54096e79	−1.66600	−0.833000	+	0.553273i	$0.813379\pi$
$500$	−7.35802e78	−0.176663
$501$	0	0
$502$	2.82020e79	0.601895
$503$	−5.77167e79	−1.16157	−0.580786	−	0.814056i	$-0.697255\pi$
$503$	−5.77167e79	−1.16157	−0.580786	+	0.814056i	$0.697255\pi$
$504$	0	0
$505$	5.34922e78	0.0957623
$506$	−8.94794e79	−1.51106
$507$	0	0
$508$	1.48379e79	0.223046
$509$	4.64283e79	0.658580	0.329290	−	0.944229i	$-0.393191\pi$
$509$	4.64283e79	0.658580	0.329290	+	0.944229i	$0.393191\pi$
$510$	0	0
$511$	1.63820e78	0.0206990
$512$	9.41908e79	1.12343
$513$	0	0
$514$	1.87002e79	0.198808
$515$	−7.34070e79	−0.736927
$516$	0	0
$517$	−7.16454e79	−0.641531
$518$	1.47671e79	0.124901
$519$	0	0
$520$	−1.85758e80	−1.40233
$521$	−9.43942e79	−0.673337	−0.336669	−	0.941623i	$-0.609300\pi$
$521$	−9.43942e79	−0.673337	−0.336669	+	0.941623i	$0.609300\pi$
$522$	0	0
$523$	1.03084e78	0.00656739	0.00328369	−	0.999995i	$-0.498955\pi$
$523$	1.03084e78	0.00656739	0.00328369	+	0.999995i	$0.498955\pi$
$524$	1.39568e79	0.0840453
$525$	0	0
$526$	4.15989e78	0.0223873
$527$	2.84652e80	1.44844
$528$	0	0
$529$	5.52023e80	2.51197
$530$	−9.39562e79	−0.404378
$531$	0	0
$532$	2.33742e78	0.00900210
$533$	2.48472e80	0.905369
$534$	0	0
$535$	3.32032e80	1.08329
$536$	1.90319e80	0.587652
$537$	0	0
$538$	−2.97673e80	−0.823499
$539$	3.34790e80	0.876808
$540$	0	0
$541$	−1.44420e80	−0.339085	−0.169542	−	0.985523i	$-0.554229\pi$
$541$	−1.44420e80	−0.339085	−0.169542	+	0.985523i	$0.554229\pi$
$542$	6.42132e80	1.42773
$543$	0	0
$544$	2.08221e80	0.415295
$545$	−4.55564e80	−0.860702
$546$	0	0
$547$	5.62958e80	0.954662	0.477331	−	0.878724i	$-0.341604\pi$
$547$	5.62958e80	0.954662	0.477331	+	0.878724i	$0.341604\pi$
$548$	−2.78662e79	−0.0447767
$549$	0	0
$550$	−7.62643e79	−0.110058
$551$	4.14778e80	0.567340
$552$	0	0
$553$	−1.03275e80	−0.126942
$554$	−8.09775e80	−0.943684
$555$	0	0
$556$	−5.40960e78	−0.00566838
$557$	1.07909e81	1.07233	0.536166	−	0.844113i	$-0.319872\pi$
$557$	1.07909e81	1.07233	0.536166	+	0.844113i	$0.319872\pi$
$558$	0	0
$559$	1.30331e81	1.16519
$560$	−7.73308e79	−0.0655852
$561$	0	0
$562$	−1.68483e81	−1.28628
$563$	−1.75793e81	−1.27351	−0.636756	−	0.771065i	$-0.719724\pi$
$563$	−1.75793e81	−1.27351	−0.636756	+	0.771065i	$0.719724\pi$
$564$	0	0
$565$	−2.79649e81	−1.82467
$566$	−1.05474e81	−0.653220
$567$	0	0
$568$	1.74947e79	0.00976408
$569$	−1.15567e81	−0.612380	−0.306190	−	0.951970i	$-0.599054\pi$
$569$	−1.15567e81	−0.612380	−0.306190	+	0.951970i	$0.599054\pi$
$570$	0	0
$571$	8.43971e80	0.403239	0.201619	−	0.979464i	$-0.435380\pi$
$571$	8.43971e80	0.403239	0.201619	+	0.979464i	$0.435380\pi$
$572$	4.61507e80	0.209409
$573$	0	0
$574$	1.24941e80	0.0511449
$575$	6.57797e80	0.255794
$576$	0	0
$577$	−7.28689e80	−0.255773	−0.127887	−	0.991789i	$-0.540819\pi$
$577$	−7.28689e80	−0.255773	−0.127887	+	0.991789i	$0.540819\pi$
$578$	−1.57533e81	−0.525412
$579$	0	0
$580$	4.77166e80	0.143729
$581$	7.89715e79	0.0226086
$582$	0	0
$583$	1.62887e81	0.421370
$584$	−1.02220e81	−0.251394
$585$	0	0
$586$	−3.21515e81	−0.714862
$587$	−5.13026e81	−1.08471	−0.542357	−	0.840148i	$-0.682468\pi$
$587$	−5.13026e81	−1.08471	−0.542357	+	0.840148i	$0.682468\pi$
$588$	0	0
$589$	−3.70197e81	−0.707998
$590$	−9.89289e80	−0.179965
$591$	0	0
$592$	−7.62856e81	−1.25589
$593$	6.47695e81	1.01451	0.507256	−	0.861796i	$-0.330660\pi$
$593$	6.47695e81	1.01451	0.507256	+	0.861796i	$0.330660\pi$
$594$	0	0
$595$	−7.21355e80	−0.102305
$596$	−4.21655e79	−0.00569106
$597$	0	0
$598$	1.98153e82	2.42279
$599$	−9.11251e81	−1.06059	−0.530294	−	0.847814i	$-0.677919\pi$
$599$	−9.11251e81	−1.06059	−0.530294	+	0.847814i	$0.677919\pi$
$600$	0	0
$601$	1.84804e82	1.94946	0.974730	−	0.223386i	$-0.0717110\pi$
$601$	1.84804e82	1.94946	0.974730	+	0.223386i	$0.0717110\pi$
$602$	6.55348e80	0.0658227
$603$	0	0
$604$	2.63877e80	0.0240332
$605$	2.34878e81	0.203732
$606$	0	0
$607$	−2.33831e82	−1.84008	−0.920039	−	0.391827i	$-0.871843\pi$
$607$	−2.33831e82	−1.84008	−0.920039	+	0.391827i	$0.871843\pi$
$608$	−2.70797e81	−0.202997
$609$	0	0
$610$	−2.46126e81	−0.167466
$611$	1.58660e82	1.02861
$612$	0	0
$613$	2.82036e81	0.166043	0.0830214	−	0.996548i	$-0.473543\pi$
$613$	2.82036e81	0.166043	0.0830214	+	0.996548i	$0.473543\pi$
$614$	−6.58680e81	−0.369579
$615$	0	0
$616$	1.61932e81	0.0825471
$617$	2.69137e82	1.30786	0.653929	−	0.756556i	$-0.273119\pi$
$617$	2.69137e82	1.30786	0.653929	+	0.756556i	$0.273119\pi$
$618$	0	0
$619$	1.45072e82	0.640779	0.320389	−	0.947286i	$-0.396186\pi$
$619$	1.45072e82	0.640779	0.320389	+	0.947286i	$0.396186\pi$
$620$	−4.25880e81	−0.179363
$621$	0	0
$622$	−2.54249e82	−0.973739
$623$	−2.90974e81	−0.106281
$624$	0	0
$625$	−2.54245e82	−0.844875
$626$	1.79899e82	0.570276
$627$	0	0
$628$	−9.08816e81	−0.262220
$629$	−7.11606e82	−1.95905
$630$	0	0
$631$	3.24958e82	0.814632	0.407316	−	0.913287i	$-0.366465\pi$
$631$	3.24958e82	0.814632	0.407316	+	0.913287i	$0.366465\pi$
$632$	6.44411e82	1.54173
$633$	0	0
$634$	6.53933e82	1.42528
$635$	5.95532e82	1.23903
$636$	0	0
$637$	−7.41398e82	−1.40585
$638$	4.11796e82	0.745542
$639$	0	0
$640$	3.82223e82	0.630968
$641$	−3.40514e81	−0.0536812	−0.0268406	−	0.999640i	$-0.508545\pi$
$641$	−3.40514e81	−0.0536812	−0.0268406	+	0.999640i	$0.508545\pi$
$642$	0	0
$643$	2.29625e82	0.330213	0.165107	−	0.986276i	$-0.447203\pi$
$643$	2.29625e82	0.330213	0.165107	+	0.986276i	$0.447203\pi$
$644$	−2.00159e81	−0.0274942
$645$	0	0
$646$	5.60704e82	0.702869
$647$	3.49095e82	0.418088	0.209044	−	0.977906i	$-0.432965\pi$
$647$	3.49095e82	0.418088	0.209044	+	0.977906i	$0.432965\pi$
$648$	0	0
$649$	1.71508e82	0.187527
$650$	1.68888e82	0.176464
$651$	0	0
$652$	9.26092e81	0.0883792
$653$	−2.13154e83	−1.94426	−0.972131	−	0.234437i	$-0.924675\pi$
$653$	−2.13154e83	−1.94426	−0.972131	+	0.234437i	$0.924675\pi$
$654$	0	0
$655$	5.60168e82	0.466874
$656$	−6.45432e82	−0.514266
$657$	0	0
$658$	7.97797e81	0.0581070
$659$	8.26273e82	0.575445	0.287722	−	0.957714i	$-0.407102\pi$
$659$	8.26273e82	0.575445	0.287722	+	0.957714i	$0.407102\pi$
$660$	0	0
$661$	−5.66974e82	−0.361094	−0.180547	−	0.983566i	$-0.557787\pi$
$661$	−5.66974e82	−0.361094	−0.180547	+	0.983566i	$0.557787\pi$
$662$	−1.67795e82	−0.102204
$663$	0	0
$664$	−4.92763e82	−0.274587
$665$	9.38143e81	0.0500070
$666$	0	0
$667$	−3.55184e83	−1.73277
$668$	−3.17260e82	−0.148085
$669$	0	0
$670$	1.09467e83	0.467819
$671$	4.26695e82	0.174503
$672$	0	0
$673$	8.50409e81	0.0318554	0.0159277	−	0.999873i	$-0.494930\pi$
$673$	8.50409e81	0.0318554	0.0159277	+	0.999873i	$0.494930\pi$
$674$	−2.88409e83	−1.03405
$675$	0	0
$676$	−5.12831e82	−0.168479
$677$	−3.74663e83	−1.17835	−0.589177	−	0.808004i	$-0.700548\pi$
$677$	−3.74663e83	−1.17835	−0.589177	+	0.808004i	$0.700548\pi$
$678$	0	0
$679$	−5.38756e82	−0.155322
$680$	4.50108e83	1.24252
$681$	0	0
$682$	−3.67536e83	−0.930381
$683$	−4.72123e83	−1.14458	−0.572288	−	0.820053i	$-0.693944\pi$
$683$	−4.72123e83	−1.14458	−0.572288	+	0.820053i	$0.693944\pi$
$684$	0	0
$685$	−1.11843e83	−0.248736
$686$	−7.48491e82	−0.159450
$687$	0	0
$688$	−3.38547e83	−0.661852
$689$	−3.60715e83	−0.675612
$690$	0	0
$691$	5.74414e83	0.987694	0.493847	−	0.869549i	$-0.335590\pi$
$691$	5.74414e83	0.987694	0.493847	+	0.869549i	$0.335590\pi$
$692$	−1.27743e82	−0.0210477
$693$	0	0
$694$	2.10254e83	0.318156
$695$	−2.17119e82	−0.0314880
$696$	0	0
$697$	−6.02071e83	−0.802196
$698$	5.30349e83	0.677372
$699$	0	0
$700$	−1.70597e81	−0.00200254
$701$	5.67798e83	0.639017	0.319508	−	0.947583i	$-0.396482\pi$
$701$	5.67798e83	0.639017	0.319508	+	0.947583i	$0.396482\pi$
$702$	0	0
$703$	9.25463e83	0.957584
$704$	−9.85497e83	−0.977827
$705$	0	0
$706$	2.44477e82	0.0223100
$707$	1.03265e82	0.00903819
$708$	0	0
$709$	−1.74026e83	−0.140136	−0.0700681	−	0.997542i	$-0.522322\pi$
$709$	−1.74026e83	−0.140136	−0.0700681	+	0.997542i	$0.522322\pi$
$710$	1.00626e82	0.00777300
$711$	0	0
$712$	1.81561e84	1.29081
$713$	3.17008e84	2.16237
$714$	0	0
$715$	1.85230e84	1.16327
$716$	3.24633e83	0.195640
$717$	0	0
$718$	−7.83174e83	−0.434698
$719$	2.89395e84	1.54166	0.770831	−	0.637040i	$-0.219842\pi$
$719$	2.89395e84	1.54166	0.770831	+	0.637040i	$0.219842\pi$
$720$	0	0
$721$	−1.41710e83	−0.0695523
$722$	1.20764e84	0.568972
$723$	0	0
$724$	1.99537e83	0.0866435
$725$	−3.02727e83	−0.126206
$726$	0	0
$727$	1.08709e84	0.417830	0.208915	−	0.977934i	$-0.433007\pi$
$727$	1.08709e84	0.417830	0.208915	+	0.977934i	$0.433007\pi$
$728$	−3.58601e83	−0.132354
$729$	0	0
$730$	−5.87945e83	−0.200130
$731$	−3.15803e84	−1.03241
$732$	0	0
$733$	−3.02062e84	−0.911021	−0.455511	−	0.890230i	$-0.650543\pi$
$733$	−3.02062e84	−0.911021	−0.455511	+	0.890230i	$0.650543\pi$
$734$	7.93228e83	0.229808
$735$	0	0
$736$	2.31890e84	0.619992
$737$	−1.89777e84	−0.487476
$738$	0	0
$739$	−5.50898e84	−1.30635	−0.653176	−	0.757206i	$-0.726564\pi$
$739$	−5.50898e84	−1.30635	−0.653176	+	0.757206i	$0.726564\pi$
$740$	1.06466e84	0.242592
$741$	0	0
$742$	−1.81380e83	−0.0381658
$743$	−3.77858e84	−0.764115	−0.382057	−	0.924139i	$-0.624784\pi$
$743$	−3.77858e84	−0.764115	−0.382057	+	0.924139i	$0.624784\pi$
$744$	0	0
$745$	−1.69235e83	−0.0316140
$746$	6.31683e84	1.13424
$747$	0	0
$748$	−1.11827e84	−0.185545
$749$	6.40980e83	0.102242
$750$	0	0
$751$	1.32327e85	1.95106	0.975530	−	0.219865i	$-0.0705617\pi$
$751$	1.32327e85	1.95106	0.975530	+	0.219865i	$0.0705617\pi$
$752$	−4.12135e84	−0.584270
$753$	0	0
$754$	−9.11928e84	−1.19538
$755$	1.05909e84	0.133505
$756$	0	0
$757$	−1.84701e82	−0.00215348	−0.00107674	−	0.999999i	$-0.500343\pi$
$757$	−1.84701e82	−0.00215348	−0.00107674	+	0.999999i	$0.500343\pi$
$758$	−8.16432e84	−0.915543
$759$	0	0
$760$	−5.85378e84	−0.607345
$761$	−1.43924e85	−1.43643	−0.718216	−	0.695820i	$-0.755041\pi$
$761$	−1.43924e85	−1.43643	−0.718216	+	0.695820i	$0.755041\pi$
$762$	0	0
$763$	−8.79455e83	−0.0812344
$764$	−1.65311e84	−0.146909
$765$	0	0
$766$	6.10544e84	0.502306
$767$	−3.79806e84	−0.300676
$768$	0	0
$769$	−1.22496e85	−0.898039	−0.449019	−	0.893522i	$-0.648227\pi$
$769$	−1.22496e85	−0.898039	−0.449019	+	0.893522i	$0.648227\pi$
$770$	9.31399e83	0.0657142
$771$	0	0
$772$	4.41337e84	0.288443
$773$	8.47270e84	0.533000	0.266500	−	0.963835i	$-0.414133\pi$
$773$	8.47270e84	0.533000	0.266500	+	0.963835i	$0.414133\pi$
$774$	0	0
$775$	2.70190e84	0.157496
$776$	3.36171e85	1.88642
$777$	0	0
$778$	−2.07656e85	−1.08006
$779$	7.83010e84	0.392114
$780$	0	0
$781$	−1.74450e83	−0.00809962
$782$	−4.80143e85	−2.14670
$783$	0	0
$784$	1.92586e85	0.798546
$785$	−3.64761e85	−1.45664
$786$	0	0
$787$	1.24322e85	0.460568	0.230284	−	0.973123i	$-0.426034\pi$
$787$	1.24322e85	0.460568	0.230284	+	0.973123i	$0.426034\pi$
$788$	2.58755e84	0.0923346
$789$	0	0
$790$	3.70652e85	1.22734
$791$	−5.39855e84	−0.172215
$792$	0	0
$793$	−9.44922e84	−0.279793
$794$	5.22100e85	1.48953
$795$	0	0
$796$	−9.49698e84	−0.251565
$797$	−1.49621e85	−0.381919	−0.190960	−	0.981598i	$-0.561160\pi$
$797$	−1.49621e85	−0.381919	−0.190960	+	0.981598i	$0.561160\pi$
$798$	0	0
$799$	−3.84447e85	−0.911394
$800$	1.97642e84	0.0451570
$801$	0	0
$802$	1.57745e83	0.00334820
$803$	1.01929e85	0.208539
$804$	0	0
$805$	−8.03353e84	−0.152731
$806$	8.13914e85	1.49175
$807$	0	0
$808$	−6.44350e84	−0.109771
$809$	−9.07918e85	−1.49130	−0.745651	−	0.666337i	$-0.767861\pi$
$809$	−9.07918e85	−1.49130	−0.745651	+	0.666337i	$0.767861\pi$
$810$	0	0
$811$	−8.14581e85	−1.24400	−0.621998	−	0.783019i	$-0.713679\pi$
$811$	−8.14581e85	−1.24400	−0.621998	+	0.783019i	$0.713679\pi$
$812$	9.21156e83	0.0135653
$813$	0	0
$814$	9.18810e85	1.25836
$815$	3.71694e85	0.490949
$816$	0	0
$817$	4.10711e85	0.504644
$818$	1.08217e86	1.28255
$819$	0	0
$820$	9.00785e84	0.0993373
$821$	−1.56347e85	−0.166329	−0.0831644	−	0.996536i	$-0.526503\pi$
$821$	−1.56347e85	−0.166329	−0.0831644	+	0.996536i	$0.526503\pi$
$822$	0	0
$823$	−2.10191e85	−0.208123	−0.104061	−	0.994571i	$-0.533184\pi$
$823$	−2.10191e85	−0.208123	−0.104061	+	0.994571i	$0.533184\pi$
$824$	8.84238e85	0.844727
$825$	0	0
$826$	−1.90980e84	−0.0169854
$827$	−4.67868e85	−0.401524	−0.200762	−	0.979640i	$-0.564342\pi$
$827$	−4.67868e85	−0.401524	−0.200762	+	0.979640i	$0.564342\pi$
$828$	0	0
$829$	−2.94227e85	−0.235139	−0.117569	−	0.993065i	$-0.537510\pi$
$829$	−2.94227e85	−0.235139	−0.117569	+	0.993065i	$0.537510\pi$
$830$	−2.83427e85	−0.218593
$831$	0	0
$832$	2.18240e86	1.56782
$833$	1.79647e86	1.24564
$834$	0	0
$835$	−1.27335e86	−0.822614
$836$	1.45434e85	0.0906947
$837$	0	0
$838$	2.45390e86	1.42613
$839$	8.27969e85	0.464554	0.232277	−	0.972650i	$-0.425382\pi$
$839$	8.27969e85	0.464554	0.232277	+	0.972650i	$0.425382\pi$
$840$	0	0
$841$	−2.77372e85	−0.145071
$842$	4.37811e85	0.221095
$843$	0	0
$844$	2.90833e85	0.136944
$845$	−2.05829e86	−0.935908
$846$	0	0
$847$	4.53427e84	0.0192285
$848$	9.36994e85	0.383760
$849$	0	0
$850$	−4.09232e85	−0.156355
$851$	−7.92495e86	−2.92465
$852$	0	0
$853$	1.96043e86	0.675080	0.337540	−	0.941311i	$-0.390405\pi$
$853$	1.96043e86	0.675080	0.337540	+	0.941311i	$0.390405\pi$
$854$	−4.75140e84	−0.0158057
$855$	0	0
$856$	−3.99956e86	−1.24176
$857$	4.95329e86	1.48580	0.742898	−	0.669405i	$-0.233451\pi$
$857$	4.95329e86	1.48580	0.742898	+	0.669405i	$0.233451\pi$
$858$	0	0
$859$	−4.22920e86	−1.18429	−0.592147	−	0.805830i	$-0.701720\pi$
$859$	−4.22920e86	−1.18429	−0.592147	+	0.805830i	$0.701720\pi$
$860$	4.72487e85	0.127846
$861$	0	0
$862$	−2.24752e86	−0.567856
$863$	−4.05433e86	−0.989921	−0.494961	−	0.868915i	$-0.664818\pi$
$863$	−4.05433e86	−0.989921	−0.494961	+	0.868915i	$0.664818\pi$
$864$	0	0
$865$	−5.12705e85	−0.116921
$866$	−1.77804e86	−0.391889
$867$	0	0
$868$	−8.22150e84	−0.0169285
$869$	−6.42578e86	−1.27892
$870$	0	0
$871$	4.20265e86	0.781605
$872$	5.48758e86	0.986609
$873$	0	0
$874$	6.24440e86	1.04931
$875$	−5.70108e85	−0.0926231
$876$	0	0
$877$	−9.27906e86	−1.40934	−0.704670	−	0.709535i	$-0.748905\pi$
$877$	−9.27906e86	−1.40934	−0.704670	+	0.709535i	$0.748905\pi$
$878$	−4.80734e86	−0.706019
$879$	0	0
$880$	−4.81153e86	−0.660760
$881$	−9.83973e86	−1.30675	−0.653377	−	0.757033i	$-0.726648\pi$
$881$	−9.83973e86	−1.30675	−0.653377	+	0.757033i	$0.726648\pi$
$882$	0	0
$883$	−9.21451e86	−1.14454	−0.572270	−	0.820065i	$-0.693937\pi$
$883$	−9.21451e86	−1.14454	−0.572270	+	0.820065i	$0.693937\pi$
$884$	2.47643e86	0.297498
$885$	0	0
$886$	−4.58332e86	−0.515093
$887$	2.01047e86	0.218550	0.109275	−	0.994012i	$-0.465147\pi$
$887$	2.01047e86	0.218550	0.109275	+	0.994012i	$0.465147\pi$
$888$	0	0
$889$	1.14966e86	0.116941
$890$	1.04430e87	1.02759
$891$	0	0
$892$	3.12962e86	0.288223
$893$	4.99984e86	0.445490
$894$	0	0
$895$	1.30294e87	1.08679
$896$	7.37871e85	0.0595517
$897$	0	0
$898$	−3.82913e86	−0.289366
$899$	−1.45891e87	−1.06689
$900$	0	0
$901$	8.74044e86	0.598621
$902$	7.77381e86	0.515277
$903$	0	0
$904$	3.36856e87	2.09159
$905$	8.00858e86	0.481307
$906$	0	0
$907$	1.04265e87	0.587118	0.293559	−	0.955941i	$-0.405160\pi$
$907$	1.04265e87	0.587118	0.293559	+	0.955941i	$0.405160\pi$
$908$	3.91542e86	0.213425
$909$	0	0
$910$	−2.06260e86	−0.105364
$911$	8.82970e86	0.436671	0.218335	−	0.975874i	$-0.429937\pi$
$911$	8.82970e86	0.436671	0.218335	+	0.975874i	$0.429937\pi$
$912$	0	0
$913$	4.91361e86	0.227779
$914$	7.18633e86	0.322548
$915$	0	0
$916$	1.29020e86	0.0542927
$917$	1.08139e86	0.0440643
$918$	0	0
$919$	−4.47608e86	−0.171037	−0.0855186	−	0.996337i	$-0.527255\pi$
$919$	−4.47608e86	−0.171037	−0.0855186	+	0.996337i	$0.527255\pi$
$920$	5.01272e87	1.85495
$921$	0	0
$922$	−2.61276e87	−0.906853
$923$	3.86321e85	0.0129867
$924$	0	0
$925$	−6.75452e86	−0.213017
$926$	2.34648e87	0.716791
$927$	0	0
$928$	−1.06719e87	−0.305897
$929$	−3.23475e87	−0.898208	−0.449104	−	0.893480i	$-0.648257\pi$
$929$	−3.23475e87	−0.898208	−0.449104	+	0.893480i	$0.648257\pi$
$930$	0	0
$931$	−2.33636e87	−0.608870
$932$	1.25400e86	0.0316612
$933$	0	0
$934$	1.08515e87	0.257193
$935$	−4.48828e87	−1.03071
$936$	0	0
$937$	4.49837e87	0.969923	0.484962	−	0.874535i	$-0.338834\pi$
$937$	4.49837e87	0.969923	0.484962	+	0.874535i	$0.338834\pi$
$938$	2.11324e86	0.0441534
$939$	0	0
$940$	5.75188e86	0.112860
$941$	6.41416e86	0.121968	0.0609840	−	0.998139i	$-0.480576\pi$
$941$	6.41416e86	0.121968	0.0609840	+	0.998139i	$0.480576\pi$
$942$	0	0
$943$	−6.70509e87	−1.19759
$944$	9.86585e86	0.170789
$945$	0	0
$946$	4.07758e87	0.663153
$947$	4.17909e87	0.658806	0.329403	−	0.944189i	$-0.393153\pi$
$947$	4.17909e87	0.658806	0.329403	+	0.944189i	$0.393153\pi$
$948$	0	0
$949$	−2.25723e87	−0.334366
$950$	5.32217e86	0.0764263
$951$	0	0
$952$	8.68922e86	0.117271
$953$	−1.20950e88	−1.58258	−0.791290	−	0.611441i	$-0.790590\pi$
$953$	−1.20950e88	−1.58258	−0.791290	+	0.611441i	$0.790590\pi$
$954$	0	0
$955$	−6.63489e87	−0.816083
$956$	9.66392e86	0.115251
$957$	0	0
$958$	−1.17647e87	−0.131916
$959$	−2.15911e86	−0.0234761
$960$	0	0
$961$	3.24108e87	0.331398
$962$	−2.03472e88	−2.01762
$963$	0	0
$964$	8.29137e86	0.0773311
$965$	1.77134e88	1.60231
$966$	0	0
$967$	−4.94615e87	−0.420907	−0.210454	−	0.977604i	$-0.567494\pi$
$967$	−4.94615e87	−0.420907	−0.210454	+	0.977604i	$0.567494\pi$
$968$	−2.82927e87	−0.233535
$969$	0	0
$970$	1.93358e88	1.50175
$971$	−1.84748e88	−1.39191	−0.695955	−	0.718085i	$-0.745019\pi$
$971$	−1.84748e88	−1.39191	−0.695955	+	0.718085i	$0.745019\pi$
$972$	0	0
$973$	−4.19142e85	−0.00297189
$974$	1.36336e88	0.937826
$975$	0	0
$976$	2.45453e87	0.158927
$977$	−2.10891e88	−1.32486	−0.662429	−	0.749125i	$-0.730474\pi$
$977$	−2.10891e88	−1.32486	−0.662429	+	0.749125i	$0.730474\pi$
$978$	0	0
$979$	−1.81044e88	−1.07077
$980$	−2.68778e87	−0.154250
$981$	0	0
$982$	−1.88424e88	−1.01823
$983$	2.64046e88	1.38468	0.692342	−	0.721569i	$-0.256579\pi$
$983$	2.64046e88	1.38468	0.692342	+	0.721569i	$0.256579\pi$
$984$	0	0
$985$	1.03853e88	0.512922
$986$	2.20968e88	1.05916
$987$	0	0
$988$	−3.22067e87	−0.145417
$989$	−3.51701e88	−1.54128
$990$	0	0
$991$	5.37825e87	0.222059	0.111030	−	0.993817i	$-0.464585\pi$
$991$	5.37825e87	0.222059	0.111030	+	0.993817i	$0.464585\pi$
$992$	9.52486e87	0.381737
$993$	0	0
$994$	1.94256e85	0.000733628 0
$995$	−3.81169e88	−1.39745
$996$	0	0
$997$	−1.80703e88	−0.624392	−0.312196	−	0.950018i	$-0.601065\pi$
$997$	−1.80703e88	−0.624392	−0.312196	+	0.950018i	$0.601065\pi$
$998$	4.53185e88	1.52028
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	9.60.a.c.1.2		5
3.2	odd	2		1.60.a.a.1.4	✓	5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1.60.a.a.1.4	✓	5	3.2	odd	2
9.60.a.c.1.2		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)

\(f(q)\)	\(=\)	\(q-6.92842e8 q^{2} -9.64308e16 q^{4} -3.87033e20 q^{5} -7.47157e23 q^{7} +4.66207e26 q^{8} +O(q^{10})\)	\(q-6.92842e8 q^{2} -9.64308e16 q^{4} -3.87033e20 q^{5} -7.47157e23 q^{7} +4.66207e26 q^{8} +2.68153e29 q^{10} -4.64881e30 q^{11} +1.02949e33 q^{13} +5.17661e32 q^{14} -2.67420e35 q^{16} -2.49454e36 q^{17} +3.24421e37 q^{19} +3.73219e37 q^{20} +3.22089e39 q^{22} -2.77809e40 q^{23} -2.36780e40 q^{25} -7.13271e41 q^{26} +7.20489e40 q^{28} +1.27852e43 q^{29} -1.14110e44 q^{31} -8.34708e43 q^{32} +1.72832e45 q^{34} +2.89174e44 q^{35} +2.85266e46 q^{37} -2.24773e46 q^{38} -1.80438e47 q^{40} +2.41356e47 q^{41} +1.26598e48 q^{43} +4.48289e47 q^{44} +1.92478e49 q^{46} +1.54116e49 q^{47} -7.20163e49 q^{49} +1.64051e49 q^{50} -9.92742e49 q^{52} -3.50384e50 q^{53} +1.79924e51 q^{55} -3.48330e50 q^{56} -8.85809e51 q^{58} -3.68928e51 q^{59} -9.17858e51 q^{61} +7.90602e52 q^{62} +2.11989e53 q^{64} -3.98445e53 q^{65} +4.08228e53 q^{67} +2.40550e53 q^{68} -2.00352e53 q^{70} +3.75256e52 q^{71} -2.19258e54 q^{73} -1.97644e55 q^{74} -3.12842e54 q^{76} +3.47339e54 q^{77} +1.38224e56 q^{79} +1.03500e56 q^{80} -1.67221e56 q^{82} -1.05696e56 q^{83} +9.65467e56 q^{85} -8.77123e56 q^{86} -2.16731e57 q^{88} +3.89442e57 q^{89} -7.69187e56 q^{91} +2.67894e57 q^{92} -1.06778e58 q^{94} -1.25562e58 q^{95} +7.21075e58 q^{97} +4.98959e58 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q + 449691864 q^{2} + 17\!\cdots\!40 q^{4}+ \cdots + 34\!\cdots\!80 q^{8}+O(q^{10}) \) 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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