LMFDB - Embedded newform 18.38.a.f.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [18,38,Mod(1,18)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(18, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0]))

N = Newforms(chi, 38, names="a")

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

chi := DirichletCharacter("18.1");

S:= CuspForms(chi, 38);

N := Newforms(S);

Level:	$ N $	$=$	$ 18 = 2 \cdot 3^{2} $
Weight:	$ k $	$=$	$ 38 $
Character orbit:	$[\chi]$	$=$	18.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:	$156.085268624$
Analytic rank:	$1$
Dimension:	$2$
Coefficient field:	$\mathbb{Q}[x]/(x^{2} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 756643680 $ x^2 - x - 756643680
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{8}\cdot 3^{4}\cdot 5 $
Twist minimal:	no (minimal twist has level 2)
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-27506.7$ of defining polynomial
Character	$\chi$	$=$	18.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+262144. q^{2} +6.87195e10 q^{4} +1.00278e13 q^{5} -3.32061e15 q^{7} +1.80144e16 q^{8} +O(q^{10})$	\(q+262144. q^{2} +6.87195e10 q^{4} +1.00278e13 q^{5} -3.32061e15 q^{7} +1.80144e16 q^{8} +2.62873e18 q^{10} +2.20179e19 q^{11} -2.47054e20 q^{13} -8.70479e20 q^{14} +4.72237e21 q^{16} -6.99239e22 q^{17} -8.30820e23 q^{19} +6.89105e23 q^{20} +5.77187e24 q^{22} +1.05566e25 q^{23} +2.77971e25 q^{25} -6.47638e25 q^{26} -2.28191e26 q^{28} +2.42517e26 q^{29} -1.93516e27 q^{31} +1.23794e27 q^{32} -1.83301e28 q^{34} -3.32984e28 q^{35} -8.55331e28 q^{37} -2.17794e29 q^{38} +1.80645e29 q^{40} -5.59412e29 q^{41} -3.15675e29 q^{43} +1.51306e30 q^{44} +2.76735e30 q^{46} -1.56788e30 q^{47} -7.53564e30 q^{49} +7.28684e30 q^{50} -1.69774e31 q^{52} -3.66286e31 q^{53} +2.20791e32 q^{55} -5.98189e31 q^{56} +6.35743e31 q^{58} -8.04503e32 q^{59} +1.21434e33 q^{61} -5.07292e32 q^{62} +3.24519e32 q^{64} -2.47741e33 q^{65} +1.45851e33 q^{67} -4.80513e33 q^{68} -8.72898e33 q^{70} +2.91230e34 q^{71} +3.11895e34 q^{73} -2.24220e34 q^{74} -5.70935e34 q^{76} -7.31130e34 q^{77} -8.04771e34 q^{79} +4.73549e34 q^{80} -1.46647e35 q^{82} -2.48909e35 q^{83} -7.01182e35 q^{85} -8.27523e34 q^{86} +3.96640e35 q^{88} +1.00339e36 q^{89} +8.20372e35 q^{91} +7.25443e35 q^{92} -4.11010e35 q^{94} -8.33129e36 q^{95} +2.19237e36 q^{97} -1.97542e36 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 524288 q^{2} + 137438953472 q^{4} + 13507530555540 q^{5} + 31\!\cdots\!56 q^{7}+ \cdots + 36\!\cdots\!68 q^{8}+O(q^{10}) $ 2 * q + 524288 * q^2 + 137438953472 * q^4 + 13507530555540 * q^5 + 3106174162962256 * q^7 + 36028797018963968 * q^8	$ 2 q + 524288 q^{2} + 137438953472 q^{4} + 13507530555540 q^{5} + 31\!\cdots\!56 q^{7}+ \cdots + 39\!\cdots\!76 q^{98}+O(q^{100}) $ 2 * q + 524288 * q^2 + 137438953472 * q^4 + 13507530555540 * q^5 + 3106174162962256 * q^7 + 36028797018963968 * q^8 + 3540918089951477760 * q^10 - 4002878661541032504 * q^11 - 417717305951174459972 * q^13 + 814264919775577636864 * q^14 + 9444732965739290427392 * q^16 - 924888511508274921636 * q^17 - 1502800666863954423438200 * q^19 + 928230431772240185917440 * q^20 - 1049330623851012424728576 * q^22 - 4977294427767526272845808 * q^23 - 32853923797109170328639650 * q^25 - 109502085451264677634899968 * q^26 + 213454663129649024038076416 * q^28 - 1174284943679786618741874780 * q^29 - 5529622970549622212915224256 * q^31 + 2475880078570760549798248448 * q^32 - 242453973960825221057347584 * q^34 - 10934908922823267414476448480 * q^35 - 115976327866820065024925346644 * q^37 - 393950178014384468377783500800 * q^38 + 243330038306502131297141391360 * q^40 - 479903809827585250071775594644 * q^41 - 3191808379897050809392290082952 * q^43 - 275075727058799801068047826944 * q^44 - 1304767870472690407268891492352 * q^46 + 11214072446606967601132239964704 * q^47 + 15205846893444101799554822389554 * q^49 - 8612458999869386346630912409600 * q^50 - 28705314688536327653923217211392 * q^52 - 53695242990369729463598618231628 * q^53 + 130245707009259764446614200122320 * q^55 + 55955859211458713757437503995904 * q^56 - 307831752275993983383470022328320 * q^58 - 58132414930279452353014089908760 * q^59 + 949379410209793628730917745257884 * q^61 - 1449557483991760165382448547364864 * q^62 + 649037107316853453566312041152512 * q^64 - 3071271884553430462753913899952040 * q^65 + 3280488273924335151706569871726696 * q^67 - 63557854549986566748857325060096 * q^68 - 2866520764664582613100514110341120 * q^70 + 36632636242259358919270327956284976 * q^71 - 10722559667485328549057125275606572 * q^73 - 30402498492319679125894030070644736 * q^74 - 103271675465402802078425678033715200 * q^76 - 240343208006950469127380344317189312 * q^77 + 41775981111170500771329248250783520 * q^79 + 63787509561819694706757832896675840 * q^80 - 125803904323442507794815541482356736 * q^82 - 173069025965519133350295483333594888 * q^83 - 461083992329885864995977782015209320 * q^85 - 836713415939732487377332491505369088 * q^86 - 72109451394102015051182329546407936 * q^88 + 770863557920750582452392321302299020 * q^89 - 276443184133973152010668401471277216 * q^91 - 342037068637192954123096291371122688 * q^92 + 2939701807443336914831209913307365376 * q^94 - 10669607994591022203853874284760756400 * q^95 - 6502221928957848822710145562502442044 * q^97 + 3986121528035010622142499360487243776 * 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 $

$2$	262144.	0.707107
$2$	262144.	0.707107
$3$	0	0
$3$	0	0
$4$	6.87195e10	0.500000
$5$	1.00278e13	1.17560	0.587801	−	0.809006i	$-0.299994\pi$
$5$	1.00278e13	1.17560	0.587801	+	0.809006i	$0.299994\pi$
$6$	0	0
$7$	−3.32061e15	−0.770734	−0.385367	−	0.922763i	$-0.625925\pi$
$7$	−3.32061e15	−0.770734	−0.385367	+	0.922763i	$0.625925\pi$
$8$	1.80144e16	0.353553
$9$	0	0
$10$	2.62873e18	0.831276
$11$	2.20179e19	1.19402	0.597010	−	0.802234i	$-0.296355\pi$
$11$	2.20179e19	1.19402	0.597010	+	0.802234i	$0.296355\pi$
$12$	0	0
$13$	−2.47054e20	−0.609313	−0.304656	−	0.952462i	$-0.598542\pi$
$13$	−2.47054e20	−0.609313	−0.304656	+	0.952462i	$0.598542\pi$
$14$	−8.70479e20	−0.544991
$15$	0	0
$16$	4.72237e21	0.250000
$17$	−6.99239e22	−1.20593	−0.602963	−	0.797769i	$-0.706013\pi$
$17$	−6.99239e22	−1.20593	−0.602963	+	0.797769i	$0.706013\pi$
$18$	0	0
$19$	−8.30820e23	−1.83048	−0.915241	−	0.402907i	$-0.868000\pi$
$19$	−8.30820e23	−1.83048	−0.915241	+	0.402907i	$0.868000\pi$
$20$	6.89105e23	0.587801
$21$	0	0
$22$	5.77187e24	0.844300
$23$	1.05566e25	0.678514	0.339257	−	0.940694i	$-0.389824\pi$
$23$	1.05566e25	0.678514	0.339257	+	0.940694i	$0.389824\pi$
$24$	0	0
$25$	2.77971e25	0.382040
$26$	−6.47638e25	−0.430849
$27$	0	0
$28$	−2.28191e26	−0.385367
$29$	2.42517e26	0.213983	0.106991	−	0.994260i	$-0.465878\pi$
$29$	2.42517e26	0.213983	0.106991	+	0.994260i	$0.465878\pi$
$30$	0	0
$31$	−1.93516e27	−0.497195	−0.248597	−	0.968607i	$-0.579970\pi$
$31$	−1.93516e27	−0.497195	−0.248597	+	0.968607i	$0.579970\pi$
$32$	1.23794e27	0.176777
$33$	0	0
$34$	−1.83301e28	−0.852718
$35$	−3.32984e28	−0.906077
$36$	0	0
$37$	−8.55331e28	−0.832535	−0.416268	−	0.909242i	$-0.636662\pi$
$37$	−8.55331e28	−0.832535	−0.416268	+	0.909242i	$0.636662\pi$
$38$	−2.17794e29	−1.29435
$39$	0	0
$40$	1.80645e29	0.415638
$41$	−5.59412e29	−0.815137	−0.407569	−	0.913175i	$-0.633623\pi$
$41$	−5.59412e29	−0.815137	−0.407569	+	0.913175i	$0.633623\pi$
$42$	0	0
$43$	−3.15675e29	−0.190579	−0.0952893	−	0.995450i	$-0.530378\pi$
$43$	−3.15675e29	−0.190579	−0.0952893	+	0.995450i	$0.530378\pi$
$44$	1.51306e30	0.597010
$45$	0	0
$46$	2.76735e30	0.479782
$47$	−1.56788e30	−0.182601	−0.0913003	−	0.995823i	$-0.529102\pi$
$47$	−1.56788e30	−0.182601	−0.0913003	+	0.995823i	$0.529102\pi$
$48$	0	0
$49$	−7.53564e30	−0.405969
$50$	7.28684e30	0.270143
$51$	0	0
$52$	−1.69774e31	−0.304656
$53$	−3.66286e31	−0.462080	−0.231040	−	0.972944i	$-0.574213\pi$
$53$	−3.66286e31	−0.462080	−0.231040	+	0.972944i	$0.574213\pi$
$54$	0	0
$55$	2.20791e32	1.40369
$56$	−5.98189e31	−0.272496
$57$	0	0
$58$	6.35743e31	0.151309
$59$	−8.04503e32	−1.39561	−0.697807	−	0.716286i	$-0.745841\pi$
$59$	−8.04503e32	−1.39561	−0.697807	+	0.716286i	$0.745841\pi$
$60$	0	0
$61$	1.21434e33	1.13694	0.568470	−	0.822704i	$-0.307536\pi$
$61$	1.21434e33	1.13694	0.568470	+	0.822704i	$0.307536\pi$
$62$	−5.07292e32	−0.351570
$63$	0	0
$64$	3.24519e32	0.125000
$65$	−2.47741e33	−0.716310
$66$	0	0
$67$	1.45851e33	0.240727	0.120364	−	0.992730i	$-0.461594\pi$
$67$	1.45851e33	0.240727	0.120364	+	0.992730i	$0.461594\pi$
$68$	−4.80513e33	−0.602963
$69$	0	0
$70$	−8.72898e33	−0.640693
$71$	2.91230e34	1.64421	0.822105	−	0.569336i	$-0.192800\pi$
$71$	2.91230e34	1.64421	0.822105	+	0.569336i	$0.192800\pi$
$72$	0	0
$73$	3.11895e34	1.05326	0.526629	−	0.850095i	$-0.323456\pi$
$73$	3.11895e34	1.05326	0.526629	+	0.850095i	$0.323456\pi$
$74$	−2.24220e34	−0.588691
$75$	0	0
$76$	−5.70935e34	−0.915241
$77$	−7.31130e34	−0.920272
$78$	0	0
$79$	−8.04771e34	−0.630334	−0.315167	−	0.949036i	$-0.602061\pi$
$79$	−8.04771e34	−0.630334	−0.315167	+	0.949036i	$0.602061\pi$
$80$	4.73549e34	0.293901
$81$	0	0
$82$	−1.46647e35	−0.576389
$83$	−2.48909e35	−0.781800	−0.390900	−	0.920433i	$-0.627836\pi$
$83$	−2.48909e35	−0.781800	−0.390900	+	0.920433i	$0.627836\pi$
$84$	0	0
$85$	−7.01182e35	−1.41769
$86$	−8.27523e34	−0.134759
$87$	0	0
$88$	3.96640e35	0.422150
$89$	1.00339e36	0.866470	0.433235	−	0.901281i	$-0.357372\pi$
$89$	1.00339e36	0.866470	0.433235	+	0.901281i	$0.357372\pi$
$90$	0	0
$91$	8.20372e35	0.469618
$92$	7.25443e35	0.339257
$93$	0	0
$94$	−4.11010e35	−0.129118
$95$	−8.33129e36	−2.15192
$96$	0	0
$97$	2.19237e36	0.385156	0.192578	−	0.981282i	$-0.438315\pi$
$97$	2.19237e36	0.385156	0.192578	+	0.981282i	$0.438315\pi$
$98$	−1.97542e36	−0.287063
$99$	0	0
$100$	1.91020e36	0.191020
$101$	−7.59676e36	−0.631950	−0.315975	−	0.948767i	$-0.602332\pi$
$101$	−7.59676e36	−0.631950	−0.315975	+	0.948767i	$0.602332\pi$
$102$	0	0
$103$	−1.64045e37	−0.949458	−0.474729	−	0.880132i	$-0.657454\pi$
$103$	−1.64045e37	−0.949458	−0.474729	+	0.880132i	$0.657454\pi$
$104$	−4.45053e36	−0.215425
$105$	0	0
$106$	−9.60197e36	−0.326740
$107$	−4.91223e37	−1.40501	−0.702504	−	0.711680i	$-0.747935\pi$
$107$	−4.91223e37	−1.40501	−0.702504	+	0.711680i	$0.747935\pi$
$108$	0	0
$109$	3.28303e37	0.666630	0.333315	−	0.942816i	$-0.391833\pi$
$109$	3.28303e37	0.666630	0.333315	+	0.942816i	$0.391833\pi$
$110$	5.78791e37	0.992561
$111$	0	0
$112$	−1.56812e37	−0.192684
$113$	1.12641e38	1.17421	0.587104	−	0.809512i	$-0.300268\pi$
$113$	1.12641e38	1.17421	0.587104	+	0.809512i	$0.300268\pi$
$114$	0	0
$115$	1.05859e38	0.797662
$116$	1.66656e37	0.106991
$117$	0	0
$118$	−2.10896e38	−0.986848
$119$	2.32190e38	0.929448
$120$	0	0
$121$	1.44750e38	0.425684
$122$	3.18331e38	0.803937
$123$	0	0
$124$	−1.32983e38	−0.248597
$125$	−4.50875e38	−0.726475
$126$	0	0
$127$	−2.82173e38	−0.338959	−0.169479	−	0.985534i	$-0.554209\pi$
$127$	−2.82173e38	−0.338959	−0.169479	+	0.985534i	$0.554209\pi$
$128$	8.50706e37	0.0883883
$129$	0	0
$130$	−6.49438e38	−0.506507
$131$	−3.02759e38	−0.204917	−0.102459	−	0.994737i	$-0.532671\pi$
$131$	−3.02759e38	−0.204917	−0.102459	+	0.994737i	$0.532671\pi$
$132$	0	0
$133$	2.75883e39	1.41081
$134$	3.82339e38	0.170220
$135$	0	0
$136$	−1.25964e39	−0.426359
$137$	−2.26804e39	−0.670377	−0.335189	−	0.942151i	$-0.608800\pi$
$137$	−2.26804e39	−0.670377	−0.335189	+	0.942151i	$0.608800\pi$
$138$	0	0
$139$	−4.94024e39	−1.11680	−0.558398	−	0.829573i	$-0.688584\pi$
$139$	−4.94024e39	−1.11680	−0.558398	+	0.829573i	$0.688584\pi$
$140$	−2.28825e39	−0.453038
$141$	0	0
$142$	7.63443e39	1.16263
$143$	−5.43962e39	−0.727532
$144$	0	0
$145$	2.43191e39	0.251559
$146$	8.17613e39	0.744767
$147$	0	0
$148$	−5.87779e39	−0.416268
$149$	5.44741e38	0.0340600	0.0170300	−	0.999855i	$-0.494579\pi$
$149$	5.44741e38	0.0340600	0.0170300	+	0.999855i	$0.494579\pi$
$150$	0	0
$151$	−3.86430e40	−1.88798	−0.943989	−	0.329976i	$-0.892959\pi$
$151$	−3.86430e40	−1.88798	−0.943989	+	0.329976i	$0.892959\pi$
$152$	−1.49667e40	−0.647173
$153$	0	0
$154$	−1.91661e40	−0.650731
$155$	−1.94054e40	−0.584503
$156$	0	0
$157$	−8.04588e40	−1.91175	−0.955873	−	0.293781i	$-0.905086\pi$
$157$	−8.04588e40	−1.91175	−0.955873	+	0.293781i	$0.905086\pi$
$158$	−2.10966e40	−0.445714
$159$	0	0
$160$	1.24138e40	0.207819
$161$	−3.50544e40	−0.522954
$162$	0	0
$163$	3.58379e40	0.425472	0.212736	−	0.977110i	$-0.431763\pi$
$163$	3.58379e40	0.425472	0.212736	+	0.977110i	$0.431763\pi$
$164$	−3.84425e40	−0.407569
$165$	0	0
$166$	−6.52500e40	−0.552816
$167$	2.31369e41	1.75409	0.877043	−	0.480411i	$-0.159513\pi$
$167$	2.31369e41	1.75409	0.877043	+	0.480411i	$0.159513\pi$
$168$	0	0
$169$	−1.03365e41	−0.628738
$170$	−1.83811e41	−1.00246
$171$	0	0
$172$	−2.16930e40	−0.0952893
$173$	−2.42959e41	−0.958693	−0.479346	−	0.877626i	$-0.659126\pi$
$173$	−2.42959e41	−0.958693	−0.479346	+	0.877626i	$0.659126\pi$
$174$	0	0
$175$	−9.23034e40	−0.294452
$176$	1.03977e41	0.298505
$177$	0	0
$178$	2.63032e41	0.612687
$179$	−1.97163e41	−0.414042	−0.207021	−	0.978336i	$-0.566377\pi$
$179$	−1.97163e41	−0.414042	−0.207021	+	0.978336i	$0.566377\pi$
$180$	0	0
$181$	−8.74626e41	−1.49544	−0.747719	−	0.664015i	$-0.768851\pi$
$181$	−8.74626e41	−1.49544	−0.747719	+	0.664015i	$0.768851\pi$
$182$	2.15056e41	0.332070
$183$	0	0
$184$	1.90171e41	0.239891
$185$	−8.57709e41	−0.978730
$186$	0	0
$187$	−1.53958e42	−1.43990
$188$	−1.07744e41	−0.0913003
$189$	0	0
$190$	−2.18400e42	−1.52164
$191$	−6.05957e41	−0.383111	−0.191555	−	0.981482i	$-0.561353\pi$
$191$	−6.05957e41	−0.383111	−0.191555	+	0.981482i	$0.561353\pi$
$192$	0	0
$193$	−1.72991e41	−0.0902016	−0.0451008	−	0.998982i	$-0.514361\pi$
$193$	−1.72991e41	−0.0902016	−0.0451008	+	0.998982i	$0.514361\pi$
$194$	5.74716e41	0.272346
$195$	0	0
$196$	−5.17845e41	−0.202984
$197$	7.91100e41	0.282232	0.141116	−	0.989993i	$-0.454931\pi$
$197$	7.91100e41	0.282232	0.141116	+	0.989993i	$0.454931\pi$
$198$	0	0
$199$	−2.54348e42	−0.752744	−0.376372	−	0.926469i	$-0.622828\pi$
$199$	−2.54348e42	−0.752744	−0.376372	+	0.926469i	$0.622828\pi$
$200$	5.00748e41	0.135072
$201$	0	0
$202$	−1.99145e42	−0.446856
$203$	−8.05304e41	−0.164924
$204$	0	0
$205$	−5.60967e42	−0.958277
$206$	−4.30035e42	−0.671368
$207$	0	0
$208$	−1.16668e42	−0.152328
$209$	−1.82929e43	−2.18563
$210$	0	0
$211$	1.20546e43	1.20761	0.603807	−	0.797131i	$-0.293650\pi$
$211$	1.20546e43	1.20761	0.603807	+	0.797131i	$0.293650\pi$
$212$	−2.51710e42	−0.231040
$213$	0	0
$214$	−1.28771e43	−0.993490
$215$	−3.16553e42	−0.224045
$216$	0	0
$217$	6.42593e42	0.383205
$218$	8.60626e42	0.471378
$219$	0	0
$220$	1.51727e43	0.701846
$221$	1.72750e43	0.734786
$222$	0	0
$223$	2.30674e43	0.830536	0.415268	−	0.909699i	$-0.363688\pi$
$223$	2.30674e43	0.830536	0.415268	+	0.909699i	$0.363688\pi$
$224$	−4.11072e42	−0.136248
$225$	0	0
$226$	2.95281e43	0.830290
$227$	3.57525e43	0.926463	0.463231	−	0.886237i	$-0.346690\pi$
$227$	3.57525e43	0.926463	0.463231	+	0.886237i	$0.346690\pi$
$228$	0	0
$229$	−6.86230e43	−1.51187	−0.755933	−	0.654649i	$-0.772817\pi$
$229$	−6.86230e43	−1.51187	−0.755933	+	0.654649i	$0.772817\pi$
$230$	2.77504e43	0.564033
$231$	0	0
$232$	4.36879e42	0.0756543
$233$	7.73057e43	1.23631	0.618154	−	0.786057i	$-0.287881\pi$
$233$	7.73057e43	1.23631	0.618154	+	0.786057i	$0.287881\pi$
$234$	0	0
$235$	−1.57224e43	−0.214666
$236$	−5.52850e43	−0.697807
$237$	0	0
$238$	6.08673e43	0.657219
$239$	8.60047e43	0.859332	0.429666	−	0.902988i	$-0.358631\pi$
$239$	8.60047e43	0.859332	0.429666	+	0.902988i	$0.358631\pi$
$240$	0	0
$241$	1.68453e44	1.44266	0.721328	−	0.692593i	$-0.243532\pi$
$241$	1.68453e44	1.44266	0.721328	+	0.692593i	$0.243532\pi$
$242$	3.79452e43	0.301004
$243$	0	0
$244$	8.34486e43	0.568470
$245$	−7.55659e43	−0.477258
$246$	0	0
$247$	2.05258e44	1.11534
$248$	−3.48608e43	−0.175785
$249$	0	0
$250$	−1.18194e44	−0.513695
$251$	1.93198e44	0.779899	0.389949	−	0.920836i	$-0.372492\pi$
$251$	1.93198e44	0.779899	0.389949	+	0.920836i	$0.372492\pi$
$252$	0	0
$253$	2.32434e44	0.810159
$254$	−7.39700e43	−0.239680
$255$	0	0
$256$	2.23007e43	0.0625000
$257$	6.84920e43	0.178598	0.0892991	−	0.996005i	$-0.471537\pi$
$257$	6.84920e43	0.178598	0.0892991	+	0.996005i	$0.471537\pi$
$258$	0	0
$259$	2.84023e44	0.641663
$260$	−1.70246e44	−0.358155
$261$	0	0
$262$	−7.93665e43	−0.144898
$263$	−3.42473e44	−0.582700	−0.291350	−	0.956617i	$-0.594104\pi$
$263$	−3.42473e44	−0.582700	−0.291350	+	0.956617i	$0.594104\pi$
$264$	0	0
$265$	−3.67304e44	−0.543222
$266$	7.23211e44	0.997597
$267$	0	0
$268$	1.00228e44	0.120364
$269$	−1.17310e45	−1.31497	−0.657486	−	0.753467i	$-0.728380\pi$
$269$	−1.17310e45	−1.31497	−0.657486	+	0.753467i	$0.728380\pi$
$270$	0	0
$271$	1.48009e45	1.44662	0.723311	−	0.690522i	$-0.242619\pi$
$271$	1.48009e45	1.44662	0.723311	+	0.690522i	$0.242619\pi$
$272$	−3.30206e44	−0.301481
$273$	0	0
$274$	−5.94552e44	−0.474028
$275$	6.12034e44	0.456164
$276$	0	0
$277$	−2.54630e45	−1.65972	−0.829858	−	0.557975i	$-0.811578\pi$
$277$	−2.54630e45	−1.65972	−0.829858	+	0.557975i	$0.811578\pi$
$278$	−1.29505e45	−0.789694
$279$	0	0
$280$	−5.99851e44	−0.320347
$281$	2.93334e45	1.46655	0.733273	−	0.679934i	$-0.237992\pi$
$281$	2.93334e45	1.46655	0.733273	+	0.679934i	$0.237992\pi$
$282$	0	0
$283$	4.02101e44	0.176314	0.0881568	−	0.996107i	$-0.471902\pi$
$283$	4.02101e44	0.176314	0.0881568	+	0.996107i	$0.471902\pi$
$284$	2.00132e45	0.822105
$285$	0	0
$286$	−1.42596e45	−0.514443
$287$	1.85759e45	0.628254
$288$	0	0
$289$	1.52725e45	0.454256
$290$	6.37510e44	0.177879
$291$	0	0
$292$	2.14332e45	0.526629
$293$	−5.50714e45	−1.27021	−0.635105	−	0.772426i	$-0.719043\pi$
$293$	−5.50714e45	−1.27021	−0.635105	+	0.772426i	$0.719043\pi$
$294$	0	0
$295$	−8.06739e45	−1.64069
$296$	−1.54083e45	−0.294346
$297$	0	0
$298$	1.42801e44	0.0240840
$299$	−2.60805e45	−0.413427
$300$	0	0
$301$	1.04824e45	0.146885
$302$	−1.01300e46	−1.33500
$303$	0	0
$304$	−3.92344e45	−0.457620
$305$	1.21771e46	1.33659
$306$	0	0
$307$	6.23539e45	0.606462	0.303231	−	0.952917i	$-0.401935\pi$
$307$	6.23539e45	0.606462	0.303231	+	0.952917i	$0.401935\pi$
$308$	−5.02429e45	−0.460136
$309$	0	0
$310$	−5.08702e45	−0.413306
$311$	−1.00705e46	−0.770872	−0.385436	−	0.922735i	$-0.625949\pi$
$311$	−1.00705e46	−0.770872	−0.385436	+	0.922735i	$0.625949\pi$
$312$	0	0
$313$	−2.62521e46	−1.78482	−0.892408	−	0.451230i	$-0.850985\pi$
$313$	−2.62521e46	−1.78482	−0.892408	+	0.451230i	$0.850985\pi$
$314$	−2.10918e46	−1.35181
$315$	0	0
$316$	−5.53034e45	−0.315167
$317$	−1.16596e46	−0.626741	−0.313371	−	0.949631i	$-0.601458\pi$
$317$	−1.16596e46	−0.626741	−0.313371	+	0.949631i	$0.601458\pi$
$318$	0	0
$319$	5.33971e45	0.255500
$320$	3.25421e45	0.146950
$321$	0	0
$322$	−9.18929e45	−0.369784
$323$	5.80942e46	2.20742
$324$	0	0
$325$	−6.86739e45	−0.232782
$326$	9.39468e45	0.300854
$327$	0	0
$328$	−1.00775e46	−0.288194
$329$	5.20632e45	0.140736
$330$	0	0
$331$	2.95352e46	0.713712	0.356856	−	0.934159i	$-0.383849\pi$
$331$	2.95352e46	0.713712	0.356856	+	0.934159i	$0.383849\pi$
$332$	−1.71049e46	−0.390900
$333$	0	0
$334$	6.06521e46	1.24033
$335$	1.46256e46	0.282999
$336$	0	0
$337$	−1.12287e46	−0.194615	−0.0973074	−	0.995254i	$-0.531023\pi$
$337$	−1.12287e46	−0.194615	−0.0973074	+	0.995254i	$0.531023\pi$
$338$	−2.70965e46	−0.444585
$339$	0	0
$340$	−4.81849e46	−0.708844
$341$	−4.26083e46	−0.593660
$342$	0	0
$343$	8.66606e46	1.08363
$344$	−5.68670e45	−0.0673797
$345$	0	0
$346$	−6.36901e46	−0.677898
$347$	3.38484e46	0.341541	0.170770	−	0.985311i	$-0.445374\pi$
$347$	3.38484e46	0.341541	0.170770	+	0.985311i	$0.445374\pi$
$348$	0	0
$349$	8.62093e46	0.782138	0.391069	−	0.920361i	$-0.372105\pi$
$349$	8.62093e46	0.782138	0.391069	+	0.920361i	$0.372105\pi$
$350$	−2.41968e46	−0.208209
$351$	0	0
$352$	2.72569e46	0.211075
$353$	1.39430e47	1.02453	0.512263	−	0.858828i	$-0.328807\pi$
$353$	1.39430e47	1.02453	0.512263	+	0.858828i	$0.328807\pi$
$354$	0	0
$355$	2.92040e47	1.93294
$356$	6.89523e46	0.433235
$357$	0	0
$358$	−5.16852e46	−0.292772
$359$	2.55899e47	1.37664	0.688321	−	0.725407i	$-0.258348\pi$
$359$	2.55899e47	1.37664	0.688321	+	0.725407i	$0.258348\pi$
$360$	0	0
$361$	4.84254e47	2.35066
$362$	−2.29278e47	−1.05743
$363$	0	0
$364$	5.63755e46	0.234809
$365$	3.12762e47	1.23821
$366$	0	0
$367$	−3.41199e47	−1.22091	−0.610457	−	0.792049i	$-0.709014\pi$
$367$	−3.41199e47	−1.22091	−0.610457	+	0.792049i	$0.709014\pi$
$368$	4.98521e46	0.169628
$369$	0	0
$370$	−2.24843e47	−0.692067
$371$	1.21629e47	0.356141
$372$	0	0
$373$	4.46224e47	1.18288	0.591438	−	0.806351i	$-0.298560\pi$
$373$	4.46224e47	1.18288	0.591438	+	0.806351i	$0.298560\pi$
$374$	−4.03591e47	−1.01816
$375$	0	0
$376$	−2.82444e46	−0.0645590
$377$	−5.99148e46	−0.130382
$378$	0	0
$379$	−7.46655e47	−1.47331	−0.736655	−	0.676268i	$-0.763596\pi$
$379$	−7.46655e47	−1.47331	−0.736655	+	0.676268i	$0.763596\pi$
$380$	−5.72522e47	−1.07596
$381$	0	0
$382$	−1.58848e47	−0.270900
$383$	6.01186e47	0.976858	0.488429	−	0.872604i	$-0.337570\pi$
$383$	6.01186e47	0.976858	0.488429	+	0.872604i	$0.337570\pi$
$384$	0	0
$385$	−7.33162e47	−1.08187
$386$	−4.53487e46	−0.0637822
$387$	0	0
$388$	1.50658e47	0.192578
$389$	−5.11575e47	−0.623508	−0.311754	−	0.950163i	$-0.600916\pi$
$389$	−5.11575e47	−0.623508	−0.311754	+	0.950163i	$0.600916\pi$
$390$	0	0
$391$	−7.38158e47	−0.818237
$392$	−1.35750e47	−0.143532
$393$	0	0
$394$	2.07382e47	0.199568
$395$	−8.07007e47	−0.741022
$396$	0	0
$397$	1.07709e48	0.900795	0.450398	−	0.892828i	$-0.351282\pi$
$397$	1.07709e48	0.900795	0.450398	+	0.892828i	$0.351282\pi$
$398$	−6.66759e47	−0.532270
$399$	0	0
$400$	1.31268e47	0.0955101
$401$	1.61629e48	1.12292	0.561458	−	0.827505i	$-0.310241\pi$
$401$	1.61629e48	1.12292	0.561458	+	0.827505i	$0.310241\pi$
$402$	0	0
$403$	4.78090e47	0.302947
$404$	−5.22045e47	−0.315975
$405$	0	0
$406$	−2.11106e47	−0.116619
$407$	−1.88326e48	−0.994064
$408$	0	0
$409$	−7.70085e47	−0.371242	−0.185621	−	0.982621i	$-0.559430\pi$
$409$	−7.70085e47	−0.371242	−0.185621	+	0.982621i	$0.559430\pi$
$410$	−1.47054e48	−0.677604
$411$	0	0
$412$	−1.12731e48	−0.474729
$413$	2.67144e48	1.07565
$414$	0	0
$415$	−2.49601e48	−0.919086
$416$	−3.05838e47	−0.107712
$417$	0	0
$418$	−4.79538e48	−1.54548
$419$	2.95178e47	0.0910175	0.0455087	−	0.998964i	$-0.485509\pi$
$419$	2.95178e47	0.0910175	0.0455087	+	0.998964i	$0.485509\pi$
$420$	0	0
$421$	6.03774e48	1.70473	0.852365	−	0.522947i	$-0.175167\pi$
$421$	6.03774e48	1.70473	0.852365	+	0.522947i	$0.175167\pi$
$422$	3.16005e48	0.853912
$423$	0	0
$424$	−6.59842e47	−0.163370
$425$	−1.94368e48	−0.460712
$426$	0	0
$427$	−4.03234e48	−0.876278
$428$	−3.37566e48	−0.702504
$429$	0	0
$430$	−8.29823e47	−0.158423
$431$	7.52239e48	1.37571	0.687854	−	0.725849i	$-0.258553\pi$
$431$	7.52239e48	1.37571	0.687854	+	0.725849i	$0.258553\pi$
$432$	0	0
$433$	−9.12185e48	−1.53129	−0.765644	−	0.643265i	$-0.777579\pi$
$433$	−9.12185e48	−1.53129	−0.765644	+	0.643265i	$0.777579\pi$
$434$	1.68452e48	0.270967
$435$	0	0
$436$	2.25608e48	0.333315
$437$	−8.77063e48	−1.24201
$438$	0	0
$439$	9.21085e48	1.19869	0.599344	−	0.800492i	$-0.295428\pi$
$439$	9.21085e48	1.19869	0.599344	+	0.800492i	$0.295428\pi$
$440$	3.97742e48	0.496280
$441$	0	0
$442$	4.52854e48	0.519572
$443$	1.02129e48	0.112377	0.0561887	−	0.998420i	$-0.482105\pi$
$443$	1.02129e48	0.112377	0.0561887	+	0.998420i	$0.482105\pi$
$444$	0	0
$445$	1.00618e49	1.01862
$446$	6.04698e48	0.587278
$447$	0	0
$448$	−1.07760e48	−0.0963418
$449$	−1.62214e49	−1.39165	−0.695825	−	0.718211i	$-0.744961\pi$
$449$	−1.62214e49	−1.39165	−0.695825	+	0.718211i	$0.744961\pi$
$450$	0	0
$451$	−1.23171e49	−0.973290
$452$	7.74062e48	0.587104
$453$	0	0
$454$	9.37230e48	0.655108
$455$	8.22652e48	0.552084
$456$	0	0
$457$	1.55439e49	0.961858	0.480929	−	0.876759i	$-0.340299\pi$
$457$	1.55439e49	0.961858	0.480929	+	0.876759i	$0.340299\pi$
$458$	−1.79891e49	−1.06905
$459$	0	0
$460$	7.27460e48	0.398831
$461$	−5.47057e48	−0.288115	−0.144057	−	0.989569i	$-0.546015\pi$
$461$	−5.47057e48	−0.288115	−0.144057	+	0.989569i	$0.546015\pi$
$462$	0	0
$463$	9.95251e48	0.483821	0.241910	−	0.970299i	$-0.422226\pi$
$463$	9.95251e48	0.483821	0.241910	+	0.970299i	$0.422226\pi$
$464$	1.14525e48	0.0534957
$465$	0	0
$466$	2.02652e49	0.874202
$467$	8.97489e48	0.372106	0.186053	−	0.982540i	$-0.440430\pi$
$467$	8.97489e48	0.372106	0.186053	+	0.982540i	$0.440430\pi$
$468$	0	0
$469$	−4.84314e48	−0.185537
$470$	−4.12152e48	−0.151791
$471$	0	0
$472$	−1.44926e49	−0.493424
$473$	−6.95051e48	−0.227555
$474$	0	0
$475$	−2.30944e49	−0.699318
$476$	1.59560e49	0.464724
$477$	0	0
$478$	2.25456e49	0.607640
$479$	2.92109e49	0.757421	0.378711	−	0.925515i	$-0.376368\pi$
$479$	2.92109e49	0.757421	0.378711	+	0.925515i	$0.376368\pi$
$480$	0	0
$481$	2.11313e49	0.507274
$482$	4.41589e49	1.02011
$483$	0	0
$484$	9.94711e48	0.212842
$485$	2.19846e49	0.452790
$486$	0	0
$487$	7.31257e48	0.139568	0.0697838	−	0.997562i	$-0.477769\pi$
$487$	7.31257e48	0.139568	0.0697838	+	0.997562i	$0.477769\pi$
$488$	2.18755e49	0.401969
$489$	0	0
$490$	−1.98091e49	−0.337472
$491$	1.60707e49	0.263649	0.131825	−	0.991273i	$-0.457916\pi$
$491$	1.60707e49	0.263649	0.131825	+	0.991273i	$0.457916\pi$
$492$	0	0
$493$	−1.69577e49	−0.258047
$494$	5.38071e49	0.788662
$495$	0	0
$496$	−9.13855e48	−0.124299
$497$	−9.67064e49	−1.26725
$498$	0	0
$499$	2.11587e49	0.257412	0.128706	−	0.991683i	$-0.458918\pi$
$499$	2.11587e49	0.257412	0.128706	+	0.991683i	$0.458918\pi$
$500$	−3.09839e49	−0.363237
$501$	0	0
$502$	5.06456e49	0.551472
$503$	3.29392e48	0.0345705	0.0172853	−	0.999851i	$-0.494498\pi$
$503$	3.29392e48	0.0345705	0.0172853	+	0.999851i	$0.494498\pi$
$504$	0	0
$505$	−7.61787e49	−0.742922
$506$	6.09312e49	0.572869
$507$	0	0
$508$	−1.93908e49	−0.169479
$509$	−2.11519e50	−1.78267	−0.891333	−	0.453349i	$-0.850229\pi$
$509$	−2.11519e50	−1.78267	−0.891333	+	0.453349i	$0.850229\pi$
$510$	0	0
$511$	−1.03568e50	−0.811783
$512$	5.84601e48	0.0441942
$513$	0	0
$514$	1.79548e49	0.126288
$515$	−1.64501e50	−1.11618
$516$	0	0
$517$	−3.45214e49	−0.218029
$518$	7.44548e49	0.453724
$519$	0	0
$520$	−4.46290e49	−0.253254
$521$	−2.89219e50	−1.58391	−0.791954	−	0.610581i	$-0.790936\pi$
$521$	−2.89219e50	−1.58391	−0.791954	+	0.610581i	$0.790936\pi$
$522$	0	0
$523$	−4.61612e49	−0.235503	−0.117751	−	0.993043i	$-0.537569\pi$
$523$	−4.61612e49	−0.235503	−0.117751	+	0.993043i	$0.537569\pi$
$524$	−2.08054e49	−0.102459
$525$	0	0
$526$	−8.97773e49	−0.412031
$527$	1.35314e50	0.599580
$528$	0	0
$529$	−1.30622e50	−0.539619
$530$	−9.62866e49	−0.384116
$531$	0	0
$532$	1.89586e50	0.705407
$533$	1.38205e50	0.496674
$534$	0	0
$535$	−4.92588e50	−1.65173
$536$	2.62741e49	0.0851099
$537$	0	0
$538$	−3.07520e50	−0.929826
$539$	−1.65919e50	−0.484735
$540$	0	0
$541$	4.12287e50	1.12473	0.562367	−	0.826888i	$-0.309891\pi$
$541$	4.12287e50	1.12473	0.562367	+	0.826888i	$0.309891\pi$
$542$	3.87996e50	1.02292
$543$	0	0
$544$	−8.65616e49	−0.213179
$545$	3.29215e50	0.783691
$546$	0	0
$547$	−3.85047e50	−0.856540	−0.428270	−	0.903651i	$-0.640877\pi$
$547$	−3.85047e50	−0.856540	−0.428270	+	0.903651i	$0.640877\pi$
$548$	−1.55858e50	−0.335189
$549$	0	0
$550$	1.60441e50	0.322557
$551$	−2.01488e50	−0.391691
$552$	0	0
$553$	2.67233e50	0.485820
$554$	−6.67497e50	−1.17360
$555$	0	0
$556$	−3.39490e50	−0.558398
$557$	5.73633e50	0.912668	0.456334	−	0.889809i	$-0.349162\pi$
$557$	5.73633e50	0.912668	0.456334	+	0.889809i	$0.349162\pi$
$558$	0	0
$559$	7.79889e49	0.116122
$560$	−1.57247e50	−0.226519
$561$	0	0
$562$	7.68958e50	1.03700
$563$	6.88670e50	0.898682	0.449341	−	0.893360i	$-0.351659\pi$
$563$	6.88670e50	0.898682	0.449341	+	0.893360i	$0.351659\pi$
$564$	0	0
$565$	1.12954e51	1.38040
$566$	1.05408e50	0.124673
$567$	0	0
$568$	5.24634e50	0.581316
$569$	4.67962e50	0.501919	0.250960	−	0.967998i	$-0.419254\pi$
$569$	4.67962e50	0.501919	0.250960	+	0.967998i	$0.419254\pi$
$570$	0	0
$571$	8.40413e50	0.844743	0.422371	−	0.906423i	$-0.361198\pi$
$571$	8.40413e50	0.844743	0.422371	+	0.906423i	$0.361198\pi$
$572$	−3.73808e50	−0.363766
$573$	0	0
$574$	4.86957e50	0.444243
$575$	2.93443e50	0.259220
$576$	0	0
$577$	2.43834e50	0.201996	0.100998	−	0.994887i	$-0.467796\pi$
$577$	2.43834e50	0.201996	0.100998	+	0.994887i	$0.467796\pi$
$578$	4.00360e50	0.321207
$579$	0	0
$580$	1.67119e50	0.125779
$581$	8.26531e50	0.602560
$582$	0	0
$583$	−8.06486e50	−0.551732
$584$	5.61860e50	0.372383
$585$	0	0
$586$	−1.44366e51	−0.898174
$587$	1.26888e51	0.764921	0.382460	−	0.923972i	$-0.375077\pi$
$587$	1.26888e51	0.764921	0.382460	+	0.923972i	$0.375077\pi$
$588$	0	0
$589$	1.60777e51	0.910105
$590$	−2.11482e51	−1.16014
$591$	0	0
$592$	−4.03919e50	−0.208134
$593$	−3.44917e51	−1.72267	−0.861335	−	0.508037i	$-0.830371\pi$
$593$	−3.44917e51	−1.72267	−0.861335	+	0.508037i	$0.830371\pi$
$594$	0	0
$595$	2.32836e51	1.09266
$596$	3.74343e49	0.0170300
$597$	0	0
$598$	−6.83685e50	−0.292337
$599$	1.03421e51	0.428759	0.214379	−	0.976750i	$-0.431227\pi$
$599$	1.03421e51	0.428759	0.214379	+	0.976750i	$0.431227\pi$
$600$	0	0
$601$	3.31491e50	0.129209	0.0646046	−	0.997911i	$-0.479421\pi$
$601$	3.31491e50	0.129209	0.0646046	+	0.997911i	$0.479421\pi$
$602$	2.74789e50	0.103864
$603$	0	0
$604$	−2.65552e51	−0.943989
$605$	1.45152e51	0.500436
$606$	0	0
$607$	−1.31827e51	−0.427577	−0.213788	−	0.976880i	$-0.568580\pi$
$607$	−1.31827e51	−0.427577	−0.213788	+	0.976880i	$0.568580\pi$
$608$	−1.02851e51	−0.323586
$609$	0	0
$610$	3.19216e51	0.945110
$611$	3.87351e50	0.111261
$612$	0	0
$613$	−4.00784e51	−1.08366	−0.541829	−	0.840489i	$-0.682268\pi$
$613$	−4.00784e51	−1.08366	−0.541829	+	0.840489i	$0.682268\pi$
$614$	1.63457e51	0.428833
$615$	0	0
$616$	−1.31709e51	−0.325365
$617$	3.89908e51	0.934731	0.467366	−	0.884064i	$-0.345203\pi$
$617$	3.89908e51	0.934731	0.467366	+	0.884064i	$0.345203\pi$
$618$	0	0
$619$	6.80067e51	1.53559	0.767794	−	0.640697i	$-0.221354\pi$
$619$	6.80067e51	1.53559	0.767794	+	0.640697i	$0.221354\pi$
$620$	−1.33353e51	−0.292251
$621$	0	0
$622$	−2.63991e51	−0.545089
$623$	−3.33186e51	−0.667818
$624$	0	0
$625$	−6.54378e51	−1.23609
$626$	−6.88182e51	−1.26206
$627$	0	0
$628$	−5.52909e51	−0.955873
$629$	5.98081e51	1.00398
$630$	0	0
$631$	8.58407e51	1.35878	0.679392	−	0.733776i	$-0.262244\pi$
$631$	8.58407e51	1.35878	0.679392	+	0.733776i	$0.262244\pi$
$632$	−1.44975e51	−0.222857
$633$	0	0
$634$	−3.05650e51	−0.443173
$635$	−2.82957e51	−0.398480
$636$	0	0
$637$	1.86171e51	0.247362
$638$	1.39977e51	0.180666
$639$	0	0
$640$	8.53070e50	0.103910
$641$	−4.76661e51	−0.564074	−0.282037	−	0.959404i	$-0.591010\pi$
$641$	−4.76661e51	−0.564074	−0.282037	+	0.959404i	$0.591010\pi$
$642$	0	0
$643$	−1.36823e52	−1.52846	−0.764231	−	0.644942i	$-0.776881\pi$
$643$	−1.36823e52	−1.52846	−0.764231	+	0.644942i	$0.776881\pi$
$644$	−2.40892e51	−0.261477
$645$	0	0
$646$	1.52290e52	1.56088
$647$	−2.16321e51	−0.215461	−0.107731	−	0.994180i	$-0.534358\pi$
$647$	−2.16321e51	−0.215461	−0.107731	+	0.994180i	$0.534358\pi$
$648$	0	0
$649$	−1.77135e52	−1.66639
$650$	−1.80025e51	−0.164602
$651$	0	0
$652$	2.46276e51	0.212736
$653$	8.05478e49	0.00676332	0.00338166	−	0.999994i	$-0.498924\pi$
$653$	8.05478e49	0.00676332	0.00338166	+	0.999994i	$0.498924\pi$
$654$	0	0
$655$	−3.03601e51	−0.240901
$656$	−2.64175e51	−0.203784
$657$	0	0
$658$	1.36481e51	0.0995157
$659$	−1.39232e52	−0.987098	−0.493549	−	0.869718i	$-0.664301\pi$
$659$	−1.39232e52	−0.987098	−0.493549	+	0.869718i	$0.664301\pi$
$660$	0	0
$661$	−1.05998e51	−0.0710511	−0.0355255	−	0.999369i	$-0.511311\pi$
$661$	−1.05998e51	−0.0710511	−0.0355255	+	0.999369i	$0.511311\pi$
$662$	7.74249e51	0.504670
$663$	0	0
$664$	−4.48395e51	−0.276408
$665$	2.76650e52	1.65856
$666$	0	0
$667$	2.56015e51	0.145190
$668$	1.58996e52	0.877043
$669$	0	0
$670$	3.83402e51	0.200111
$671$	2.67372e52	1.35753
$672$	0	0
$673$	1.75123e51	0.0841522	0.0420761	−	0.999114i	$-0.486603\pi$
$673$	1.75123e51	0.0841522	0.0420761	+	0.999114i	$0.486603\pi$
$674$	−2.94353e51	−0.137613
$675$	0	0
$676$	−7.10319e51	−0.314369
$677$	−3.00931e52	−1.29592	−0.647958	−	0.761676i	$-0.724377\pi$
$677$	−3.00931e52	−1.29592	−0.647958	+	0.761676i	$0.724377\pi$
$678$	0	0
$679$	−7.28000e51	−0.296853
$680$	−1.26314e52	−0.501229
$681$	0	0
$682$	−1.11695e52	−0.419781
$683$	−3.45300e52	−1.26303	−0.631515	−	0.775364i	$-0.717567\pi$
$683$	−3.45300e52	−1.26303	−0.631515	+	0.775364i	$0.717567\pi$
$684$	0	0
$685$	−2.27434e52	−0.788097
$686$	2.27175e52	0.766241
$687$	0	0
$688$	−1.49073e51	−0.0476446
$689$	9.04925e51	0.281551
$690$	0	0
$691$	5.56197e52	1.64015	0.820077	−	0.572253i	$-0.193931\pi$
$691$	5.56197e52	1.64015	0.820077	+	0.572253i	$0.193931\pi$
$692$	−1.66960e52	−0.479346
$693$	0	0
$694$	8.87315e51	0.241506
$695$	−4.95397e52	−1.31291
$696$	0	0
$697$	3.91163e52	0.982994
$698$	2.25992e52	0.553055
$699$	0	0
$700$	−6.34304e51	−0.147226
$701$	−2.61308e52	−0.590704	−0.295352	−	0.955389i	$-0.595437\pi$
$701$	−2.61308e52	−0.590704	−0.295352	+	0.955389i	$0.595437\pi$
$702$	0	0
$703$	7.10627e52	1.52394
$704$	7.14523e51	0.149253
$705$	0	0
$706$	3.65507e52	0.724450
$707$	2.52259e52	0.487066
$708$	0	0
$709$	−1.30761e52	−0.239620	−0.119810	−	0.992797i	$-0.538229\pi$
$709$	−1.30761e52	−0.239620	−0.119810	+	0.992797i	$0.538229\pi$
$710$	7.65565e52	1.36679
$711$	0	0
$712$	1.80754e52	0.306344
$713$	−2.04287e52	−0.337353
$714$	0	0
$715$	−5.45474e52	−0.855288
$716$	−1.35490e52	−0.207021
$717$	0	0
$718$	6.70823e52	0.973432
$719$	5.28485e52	0.747391	0.373695	−	0.927551i	$-0.378091\pi$
$719$	5.28485e52	0.747391	0.373695	+	0.927551i	$0.378091\pi$
$720$	0	0
$721$	5.44732e52	0.731780
$722$	1.26944e53	1.66217
$723$	0	0
$724$	−6.01038e52	−0.747719
$725$	6.74126e51	0.0817500
$726$	0	0
$727$	−8.62636e52	−0.994125	−0.497062	−	0.867715i	$-0.665588\pi$
$727$	−8.62636e52	−0.994125	−0.497062	+	0.867715i	$0.665588\pi$
$728$	1.47785e52	0.166035
$729$	0	0
$730$	8.19886e52	0.875549
$731$	2.20732e52	0.229823
$732$	0	0
$733$	−4.61809e52	−0.457129	−0.228565	−	0.973529i	$-0.573403\pi$
$733$	−4.61809e52	−0.457129	−0.228565	+	0.973529i	$0.573403\pi$
$734$	−8.94432e52	−0.863317
$735$	0	0
$736$	1.30684e52	0.119945
$737$	3.21133e52	0.287433
$738$	0	0
$739$	9.79613e52	0.833935	0.416968	−	0.908921i	$-0.363093\pi$
$739$	9.79613e52	0.833935	0.416968	+	0.908921i	$0.363093\pi$
$740$	−5.89413e52	−0.489365
$741$	0	0
$742$	3.18844e52	0.251829
$743$	−3.68344e52	−0.283766	−0.141883	−	0.989883i	$-0.545316\pi$
$743$	−3.68344e52	−0.283766	−0.141883	+	0.989883i	$0.545316\pi$
$744$	0	0
$745$	5.46255e51	0.0400409
$746$	1.16975e53	0.836419
$747$	0	0
$748$	−1.05799e53	−0.719950
$749$	1.63116e53	1.08289
$750$	0	0
$751$	−2.91686e53	−1.84322	−0.921610	−	0.388116i	$-0.873126\pi$
$751$	−2.91686e53	−1.84322	−0.921610	+	0.388116i	$0.873126\pi$
$752$	−7.40410e51	−0.0456501
$753$	0	0
$754$	−1.57063e52	−0.0921943
$755$	−3.87504e53	−2.21951
$756$	0	0
$757$	−2.14424e53	−1.16950	−0.584749	−	0.811214i	$-0.698807\pi$
$757$	−2.14424e53	−1.16950	−0.584749	+	0.811214i	$0.698807\pi$
$758$	−1.95731e53	−1.04179
$759$	0	0
$760$	−1.50083e53	−0.760818
$761$	−3.02873e53	−1.49846	−0.749228	−	0.662312i	$-0.769575\pi$
$761$	−3.02873e53	−1.49846	−0.749228	+	0.662312i	$0.769575\pi$
$762$	0	0
$763$	−1.09017e53	−0.513794
$764$	−4.16410e52	−0.191555
$765$	0	0
$766$	1.57597e53	0.690743
$767$	1.98756e53	0.850366
$768$	0	0
$769$	2.09535e53	0.854318	0.427159	−	0.904176i	$-0.359514\pi$
$769$	2.09535e53	0.854318	0.427159	+	0.904176i	$0.359514\pi$
$770$	−1.92194e53	−0.765000
$771$	0	0
$772$	−1.18879e52	−0.0451008
$773$	2.74843e53	1.01804	0.509018	−	0.860756i	$-0.330009\pi$
$773$	2.74843e53	1.01804	0.509018	+	0.860756i	$0.330009\pi$
$774$	0	0
$775$	−5.37919e52	−0.189948
$776$	3.94942e52	0.136173
$777$	0	0
$778$	−1.34106e53	−0.440887
$779$	4.64771e53	1.49209
$780$	0	0
$781$	6.41229e53	1.96322
$782$	−1.93504e53	−0.578581
$783$	0	0
$784$	−3.55861e52	−0.101492
$785$	−8.06824e53	−2.24745
$786$	0	0
$787$	−4.09272e53	−1.08762	−0.543812	−	0.839207i	$-0.683020\pi$
$787$	−4.09272e53	−1.08762	−0.543812	+	0.839207i	$0.683020\pi$
$788$	5.43640e52	0.141116
$789$	0	0
$790$	−2.11552e53	−0.523982
$791$	−3.74037e53	−0.905002
$792$	0	0
$793$	−3.00007e53	−0.692752
$794$	2.82352e53	0.636958
$795$	0	0
$796$	−1.74787e53	−0.376372
$797$	−3.09131e51	−0.00650374	−0.00325187	−	0.999995i	$-0.501035\pi$
$797$	−3.09131e51	−0.00650374	−0.00325187	+	0.999995i	$0.501035\pi$
$798$	0	0
$799$	1.09632e53	0.220203
$800$	3.44111e52	0.0675358
$801$	0	0
$802$	4.23700e53	0.794022
$803$	6.86728e53	1.25761
$804$	0	0
$805$	−3.51518e53	−0.614786
$806$	1.25329e53	0.214216
$807$	0	0
$808$	−1.36851e53	−0.223428
$809$	2.71214e53	0.432778	0.216389	−	0.976307i	$-0.430572\pi$
$809$	2.71214e53	0.432778	0.216389	+	0.976307i	$0.430572\pi$
$810$	0	0
$811$	−9.27510e52	−0.141395	−0.0706973	−	0.997498i	$-0.522522\pi$
$811$	−9.27510e52	−0.141395	−0.0706973	+	0.997498i	$0.522522\pi$
$812$	−5.53401e52	−0.0824619
$813$	0	0
$814$	−4.93686e53	−0.702909
$815$	3.59375e53	0.500186
$816$	0	0
$817$	2.62269e53	0.348850
$818$	−2.01873e53	−0.262508
$819$	0	0
$820$	−3.85494e53	−0.479138
$821$	9.54561e53	1.15999	0.579996	−	0.814619i	$-0.303054\pi$
$821$	9.54561e53	1.15999	0.579996	+	0.814619i	$0.303054\pi$
$822$	0	0
$823$	1.19456e54	1.38775	0.693873	−	0.720097i	$-0.255903\pi$
$823$	1.19456e54	1.38775	0.693873	+	0.720097i	$0.255903\pi$
$824$	−2.95518e53	−0.335684
$825$	0	0
$826$	7.00303e53	0.760598
$827$	1.05798e54	1.12364	0.561820	−	0.827260i	$-0.310102\pi$
$827$	1.05798e54	1.12364	0.561820	+	0.827260i	$0.310102\pi$
$828$	0	0
$829$	1.68391e54	1.71025	0.855124	−	0.518424i	$-0.173481\pi$
$829$	1.68391e54	1.71025	0.855124	+	0.518424i	$0.173481\pi$
$830$	−6.54314e53	−0.649892
$831$	0	0
$832$	−8.01737e52	−0.0761641
$833$	5.26921e53	0.489568
$834$	0	0
$835$	2.32012e54	2.06211
$836$	−1.25708e54	−1.09282
$837$	0	0
$838$	7.73792e52	0.0643591
$839$	3.78194e53	0.307693	0.153847	−	0.988095i	$-0.450834\pi$
$839$	3.78194e53	0.307693	0.153847	+	0.988095i	$0.450834\pi$
$840$	0	0
$841$	−1.22566e54	−0.954211
$842$	1.58276e54	1.20543
$843$	0	0
$844$	8.28387e53	0.603807
$845$	−1.03652e54	−0.739145
$846$	0	0
$847$	−4.80657e53	−0.328090
$848$	−1.72974e53	−0.115520
$849$	0	0
$850$	−5.09524e53	−0.325773
$851$	−9.02939e53	−0.564887
$852$	0	0
$853$	2.34797e54	1.40649	0.703244	−	0.710948i	$-0.251734\pi$
$853$	2.34797e54	1.40649	0.703244	+	0.710948i	$0.251734\pi$
$854$	−1.05705e54	−0.619622
$855$	0	0
$856$	−8.84908e53	−0.496745
$857$	−5.17381e53	−0.284227	−0.142114	−	0.989850i	$-0.545390\pi$
$857$	−5.17381e53	−0.284227	−0.142114	+	0.989850i	$0.545390\pi$
$858$	0	0
$859$	−2.26122e54	−1.18979	−0.594893	−	0.803805i	$-0.702806\pi$
$859$	−2.26122e54	−1.18979	−0.594893	+	0.803805i	$0.702806\pi$
$860$	−2.17533e53	−0.112022
$861$	0	0
$862$	1.97195e54	0.972773
$863$	1.13614e54	0.548572	0.274286	−	0.961648i	$-0.411558\pi$
$863$	1.13614e54	0.548572	0.274286	+	0.961648i	$0.411558\pi$
$864$	0	0
$865$	−2.43634e54	−1.12704
$866$	−2.39124e54	−1.08278
$867$	0	0
$868$	4.41587e53	0.191602
$869$	−1.77194e54	−0.752632
$870$	0	0
$871$	−3.60331e53	−0.146678
$872$	5.91418e53	0.235689
$873$	0	0
$874$	−2.29917e54	−0.878232
$875$	1.49718e54	0.559919
$876$	0	0
$877$	−3.53444e54	−1.26715	−0.633575	−	0.773682i	$-0.718413\pi$
$877$	−3.53444e54	−1.26715	−0.633575	+	0.773682i	$0.718413\pi$
$878$	2.41457e54	0.847600
$879$	0	0
$880$	1.04266e54	0.350923
$881$	2.74692e54	0.905300	0.452650	−	0.891688i	$-0.350479\pi$
$881$	2.74692e54	0.905300	0.452650	+	0.891688i	$0.350479\pi$
$882$	0	0
$883$	9.56723e53	0.302352	0.151176	−	0.988507i	$-0.451694\pi$
$883$	9.56723e53	0.302352	0.151176	+	0.988507i	$0.451694\pi$
$884$	1.18713e54	0.367393
$885$	0	0
$886$	2.67724e53	0.0794629
$887$	−2.37072e54	−0.689118	−0.344559	−	0.938765i	$-0.611972\pi$
$887$	−2.37072e54	−0.689118	−0.344559	+	0.938765i	$0.611972\pi$
$888$	0	0
$889$	9.36988e53	0.261247
$890$	2.63763e54	0.720276
$891$	0	0
$892$	1.58518e54	0.415268
$893$	1.30263e54	0.334247
$894$	0	0
$895$	−1.97711e54	−0.486749
$896$	−2.82487e53	−0.0681239
$897$	0	0
$898$	−4.25234e54	−0.984046
$899$	−4.69309e53	−0.106391
$900$	0	0
$901$	2.56121e54	0.557234
$902$	−3.22885e54	−0.688220
$903$	0	0
$904$	2.02916e54	0.415145
$905$	−8.77057e54	−1.75804
$906$	0	0
$907$	−3.89376e54	−0.749264	−0.374632	−	0.927174i	$-0.622231\pi$
$907$	−3.89376e54	−0.749264	−0.374632	+	0.927174i	$0.622231\pi$
$908$	2.45689e54	0.463231
$909$	0	0
$910$	2.15653e54	0.390383
$911$	−4.15122e54	−0.736353	−0.368177	−	0.929756i	$-0.620018\pi$
$911$	−4.15122e54	−0.736353	−0.368177	+	0.929756i	$0.620018\pi$
$912$	0	0
$913$	−5.48046e54	−0.933486
$914$	4.07475e54	0.680137
$915$	0	0
$916$	−4.71574e54	−0.755933
$917$	1.00535e54	0.157937
$918$	0	0
$919$	2.84350e54	0.429058	0.214529	−	0.976718i	$-0.431178\pi$
$919$	2.84350e54	0.429058	0.214529	+	0.976718i	$0.431178\pi$
$920$	1.90699e54	0.282016
$921$	0	0
$922$	−1.43408e54	−0.203728
$923$	−7.19497e54	−1.00184
$924$	0	0
$925$	−2.37757e54	−0.318062
$926$	2.60899e54	0.342113
$927$	0	0
$928$	3.00221e53	0.0378272
$929$	3.00016e53	0.0370555	0.0185278	−	0.999828i	$-0.494102\pi$
$929$	3.00016e53	0.0370555	0.0185278	+	0.999828i	$0.494102\pi$
$930$	0	0
$931$	6.26076e54	0.743118
$932$	5.31241e54	0.618154
$933$	0	0
$934$	2.35271e54	0.263119
$935$	−1.54386e55	−1.69275
$936$	0	0
$937$	5.72228e54	0.603096	0.301548	−	0.953451i	$-0.402497\pi$
$937$	5.72228e54	0.603096	0.301548	+	0.953451i	$0.402497\pi$
$938$	−1.26960e54	−0.131194
$939$	0	0
$940$	−1.08043e54	−0.107333
$941$	1.79388e55	1.74737	0.873684	−	0.486494i	$-0.161725\pi$
$941$	1.79388e55	1.74737	0.873684	+	0.486494i	$0.161725\pi$
$942$	0	0
$943$	−5.90549e54	−0.553082
$944$	−3.79916e54	−0.348904
$945$	0	0
$946$	−1.82203e54	−0.160905
$947$	1.24204e53	0.0107563	0.00537813	−	0.999986i	$-0.498288\pi$
$947$	1.24204e53	0.0107563	0.00537813	+	0.999986i	$0.498288\pi$
$948$	0	0
$949$	−7.70549e54	−0.641764
$950$	−6.05405e54	−0.494492
$951$	0	0
$952$	4.18277e54	0.328609
$953$	−8.24909e54	−0.635605	−0.317803	−	0.948157i	$-0.602945\pi$
$953$	−8.24909e54	−0.635605	−0.317803	+	0.948157i	$0.602945\pi$
$954$	0	0
$955$	−6.07641e54	−0.450386
$956$	5.91020e54	0.429666
$957$	0	0
$958$	7.65745e54	0.535578
$959$	7.53127e54	0.516683
$960$	0	0
$961$	−1.14041e55	−0.752798
$962$	5.53945e54	0.358697
$963$	0	0
$964$	1.15760e55	0.721328
$965$	−1.73472e54	−0.106041
$966$	0	0
$967$	−5.68031e54	−0.334182	−0.167091	−	0.985942i	$-0.553437\pi$
$967$	−5.68031e54	−0.334182	−0.167091	+	0.985942i	$0.553437\pi$
$968$	2.60758e54	0.150502
$969$	0	0
$970$	5.76313e54	0.320171
$971$	2.27277e55	1.23880	0.619399	−	0.785077i	$-0.287377\pi$
$971$	2.27277e55	1.23880	0.619399	+	0.785077i	$0.287377\pi$
$972$	0	0
$973$	1.64046e55	0.860753
$974$	1.91695e54	0.0986892
$975$	0	0
$976$	5.73454e54	0.284235
$977$	7.73374e54	0.376132	0.188066	−	0.982156i	$-0.439778\pi$
$977$	7.73374e54	0.376132	0.188066	+	0.982156i	$0.439778\pi$
$978$	0	0
$979$	2.20925e55	1.03458
$980$	−5.19285e54	−0.238629
$981$	0	0
$982$	4.21283e54	0.186428
$983$	−1.64593e55	−0.714777	−0.357389	−	0.933956i	$-0.616333\pi$
$983$	−1.64593e55	−0.714777	−0.357389	+	0.933956i	$0.616333\pi$
$984$	0	0
$985$	7.93299e54	0.331793
$986$	−4.44536e54	−0.182467
$987$	0	0
$988$	1.41052e55	0.557668
$989$	−3.33245e54	−0.129310
$990$	0	0
$991$	3.05470e54	0.114184	0.0570921	−	0.998369i	$-0.481817\pi$
$991$	3.05470e54	0.114184	0.0570921	+	0.998369i	$0.481817\pi$
$992$	−2.39562e54	−0.0878924
$993$	0	0
$994$	−2.53510e55	−0.896080
$995$	−2.55055e55	−0.884927
$996$	0	0
$997$	1.64945e55	0.551416	0.275708	−	0.961241i	$-0.411088\pi$
$997$	1.64945e55	0.551416	0.275708	+	0.961241i	$0.411088\pi$
$998$	5.54662e54	0.182018
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	18.38.a.f.1.2		2
3.2	odd	2		2.38.a.a.1.2	✓	2
12.11	even	2		16.38.a.a.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2.38.a.a.1.2	✓	2	3.2	odd	2
16.38.a.a.1.1		2	12.11	even	2
18.38.a.f.1.2		2	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:	\( N \)	\(=\)	\( 18 = 2 \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 38 \)
Character orbit:	\([\chi]\)	\(=\)	18.a (trivial)

\(f(q)\)	\(=\)	\(q+262144. q^{2} +6.87195e10 q^{4} +1.00278e13 q^{5} -3.32061e15 q^{7} +1.80144e16 q^{8} +O(q^{10})\)	\(q+262144. q^{2} +6.87195e10 q^{4} +1.00278e13 q^{5} -3.32061e15 q^{7} +1.80144e16 q^{8} +2.62873e18 q^{10} +2.20179e19 q^{11} -2.47054e20 q^{13} -8.70479e20 q^{14} +4.72237e21 q^{16} -6.99239e22 q^{17} -8.30820e23 q^{19} +6.89105e23 q^{20} +5.77187e24 q^{22} +1.05566e25 q^{23} +2.77971e25 q^{25} -6.47638e25 q^{26} -2.28191e26 q^{28} +2.42517e26 q^{29} -1.93516e27 q^{31} +1.23794e27 q^{32} -1.83301e28 q^{34} -3.32984e28 q^{35} -8.55331e28 q^{37} -2.17794e29 q^{38} +1.80645e29 q^{40} -5.59412e29 q^{41} -3.15675e29 q^{43} +1.51306e30 q^{44} +2.76735e30 q^{46} -1.56788e30 q^{47} -7.53564e30 q^{49} +7.28684e30 q^{50} -1.69774e31 q^{52} -3.66286e31 q^{53} +2.20791e32 q^{55} -5.98189e31 q^{56} +6.35743e31 q^{58} -8.04503e32 q^{59} +1.21434e33 q^{61} -5.07292e32 q^{62} +3.24519e32 q^{64} -2.47741e33 q^{65} +1.45851e33 q^{67} -4.80513e33 q^{68} -8.72898e33 q^{70} +2.91230e34 q^{71} +3.11895e34 q^{73} -2.24220e34 q^{74} -5.70935e34 q^{76} -7.31130e34 q^{77} -8.04771e34 q^{79} +4.73549e34 q^{80} -1.46647e35 q^{82} -2.48909e35 q^{83} -7.01182e35 q^{85} -8.27523e34 q^{86} +3.96640e35 q^{88} +1.00339e36 q^{89} +8.20372e35 q^{91} +7.25443e35 q^{92} -4.11010e35 q^{94} -8.33129e36 q^{95} +2.19237e36 q^{97} -1.97542e36 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 524288 q^{2} + 137438953472 q^{4} + 13507530555540 q^{5} + 31\!\cdots\!56 q^{7}+ \cdots + 36\!\cdots\!68 q^{8}+O(q^{10}) \) 2 * q + 524288 * q^2 + 137438953472 * q^4 + 13507530555540 * q^5 + 3106174162962256 * q^7 + 36028797018963968 * q^8	\( 2 q + 524288 q^{2} + 137438953472 q^{4} + 13507530555540 q^{5} + 31\!\cdots\!56 q^{7}+ \cdots + 39\!\cdots\!76 q^{98}+O(q^{100}) \) 2 * q + 524288 * q^2 + 137438953472 * q^4 + 13507530555540 * q^5 + 3106174162962256 * q^7 + 36028797018963968 * q^8 + 3540918089951477760 * q^10 - 4002878661541032504 * q^11 - 417717305951174459972 * q^13 + 814264919775577636864 * q^14 + 9444732965739290427392 * q^16 - 924888511508274921636 * q^17 - 1502800666863954423438200 * q^19 + 928230431772240185917440 * q^20 - 1049330623851012424728576 * q^22 - 4977294427767526272845808 * q^23 - 32853923797109170328639650 * q^25 - 109502085451264677634899968 * q^26 + 213454663129649024038076416 * q^28 - 1174284943679786618741874780 * q^29 - 5529622970549622212915224256 * q^31 + 2475880078570760549798248448 * q^32 - 242453973960825221057347584 * q^34 - 10934908922823267414476448480 * q^35 - 115976327866820065024925346644 * q^37 - 393950178014384468377783500800 * q^38 + 243330038306502131297141391360 * q^40 - 479903809827585250071775594644 * q^41 - 3191808379897050809392290082952 * q^43 - 275075727058799801068047826944 * q^44 - 1304767870472690407268891492352 * q^46 + 11214072446606967601132239964704 * q^47 + 15205846893444101799554822389554 * q^49 - 8612458999869386346630912409600 * q^50 - 28705314688536327653923217211392 * q^52 - 53695242990369729463598618231628 * q^53 + 130245707009259764446614200122320 * q^55 + 55955859211458713757437503995904 * q^56 - 307831752275993983383470022328320 * q^58 - 58132414930279452353014089908760 * q^59 + 949379410209793628730917745257884 * q^61 - 1449557483991760165382448547364864 * q^62 + 649037107316853453566312041152512 * q^64 - 3071271884553430462753913899952040 * q^65 + 3280488273924335151706569871726696 * q^67 - 63557854549986566748857325060096 * q^68 - 2866520764664582613100514110341120 * q^70 + 36632636242259358919270327956284976 * q^71 - 10722559667485328549057125275606572 * q^73 - 30402498492319679125894030070644736 * q^74 - 103271675465402802078425678033715200 * q^76 - 240343208006950469127380344317189312 * q^77 + 41775981111170500771329248250783520 * q^79 + 63787509561819694706757832896675840 * q^80 - 125803904323442507794815541482356736 * q^82 - 173069025965519133350295483333594888 * q^83 - 461083992329885864995977782015209320 * q^85 - 836713415939732487377332491505369088 * q^86 - 72109451394102015051182329546407936 * q^88 + 770863557920750582452392321302299020 * q^89 - 276443184133973152010668401471277216 * q^91 - 342037068637192954123096291371122688 * q^92 + 2939701807443336914831209913307365376 * q^94 - 10669607994591022203853874284760756400 * q^95 - 6502221928957848822710145562502442044 * q^97 + 3986121528035010622142499360487243776 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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