LMFDB - Embedded newform 27.7.b.c.26.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [27,7,Mod(26,27)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(27, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1]))

N = Newforms(chi, 7, names="a")

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

chi := DirichletCharacter("27.26");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 27 = 3^{3} $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	27.b (of order $2$, degree $1$, minimal)

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:	no
Analytic conductor:	$6.21146025774$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(i, \sqrt{41})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 21x^{2} + 100 $ x^4 + 21*x^2 + 100
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 3^{8} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			26.4
Root			$3.70156i$ of defining polynomial
Character	$\chi$	$=$	27.26
Dual form			27.7.b.c.26.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+14.1047i q^{2} -134.942 q^{4} -137.419i q^{5} -514.769 q^{7} -1000.62i q^{8} +O(q^{10})$	\(q+14.1047i q^{2} -134.942 q^{4} -137.419i q^{5} -514.769 q^{7} -1000.62i q^{8} +1938.25 q^{10} +1218.26i q^{11} -170.463 q^{13} -7260.65i q^{14} +5477.09 q^{16} -1574.10i q^{17} -11289.1 q^{19} +18543.6i q^{20} -17183.2 q^{22} +10572.6i q^{23} -3258.91 q^{25} -2404.32i q^{26} +69464.0 q^{28} -8665.42i q^{29} -26209.1 q^{31} +13213.2i q^{32} +22202.2 q^{34} +70738.9i q^{35} +21866.9 q^{37} -159229. i q^{38} -137504. q^{40} +38166.6i q^{41} +23895.1 q^{43} -164395. i q^{44} -149124. q^{46} -26698.7i q^{47} +147338. q^{49} -45965.9i q^{50} +23002.6 q^{52} +213997. i q^{53} +167412. q^{55} +515086. i q^{56} +122223. q^{58} -163689. i q^{59} +111078. q^{61} -369671. i q^{62} +164166. q^{64} +23424.8i q^{65} -381035. q^{67} +212412. i q^{68} -997750. q^{70} +675048. i q^{71} -762939. q^{73} +308426. i q^{74} +1.52337e6 q^{76} -627123. i q^{77} +515708. q^{79} -752655. i q^{80} -538328. q^{82} -903773. i q^{83} -216311. q^{85} +337033. i q^{86} +1.21901e6 q^{88} -644278. i q^{89} +87748.8 q^{91} -1.42669e6i q^{92} +376577. q^{94} +1.55133e6i q^{95} -616470. q^{97} +2.07815e6i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 194 q^{4} - 676 q^{7}+O(q^{10}) $ 4 * q - 194 * q^4 - 676 * q^7	$ 4 q - 194 q^{4} - 676 q^{7} + 3258 q^{10} - 3448 q^{13} + 10498 q^{16} - 3664 q^{19} - 58014 q^{22} + 17392 q^{25} + 152342 q^{28} - 153244 q^{31} + 65988 q^{34} + 128960 q^{37} - 338058 q^{40} + 126008 q^{43} - 116568 q^{46} + 121872 q^{49} - 71884 q^{52} + 54180 q^{55} + 567036 q^{58} + 167696 q^{61} - 28994 q^{64} + 8 q^{67} - 2104830 q^{70} - 1881676 q^{73} + 3764384 q^{76} + 1188728 q^{79} - 1366344 q^{82} - 176472 q^{85} + 27342 q^{88} - 373736 q^{91} + 1381140 q^{94} + 975212 q^{97}+O(q^{100}) $ 4 * q - 194 * q^4 - 676 * q^7 + 3258 * q^10 - 3448 * q^13 + 10498 * q^16 - 3664 * q^19 - 58014 * q^22 + 17392 * q^25 + 152342 * q^28 - 153244 * q^31 + 65988 * q^34 + 128960 * q^37 - 338058 * q^40 + 126008 * q^43 - 116568 * q^46 + 121872 * q^49 - 71884 * q^52 + 54180 * q^55 + 567036 * q^58 + 167696 * q^61 - 28994 * q^64 + 8 * q^67 - 2104830 * q^70 - 1881676 * q^73 + 3764384 * q^76 + 1188728 * q^79 - 1366344 * q^82 - 176472 * q^85 + 27342 * q^88 - 373736 * q^91 + 1381140 * q^94 + 975212 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/27\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$-1$

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 $

$2$	14.1047i	1.76309i	0.472104	+	0.881543i	$0.343495\pi$
$2$	14.1047i	1.76309i	−0.472104	+	0.881543i	$0.656505\pi$
$3$	0	0
$3$	0	0
$4$	−134.942	−2.10847
$5$	− 137.419i	− 1.09935i	−0.835379	−	0.549675i	$-0.814752\pi$
$5$	− 137.419i	− 1.09935i	0.835379	−	0.549675i	$-0.185248\pi$
$6$	0	0
$7$	−514.769	−1.50078	−0.750392	−	0.660993i	$-0.770135\pi$
$7$	−514.769	−1.50078	−0.750392	+	0.660993i	$0.770135\pi$
$8$	− 1000.62i	− 1.95433i
$9$	0	0
$10$	1938.25	1.93825
$11$	1218.26i	0.915298i	0.889133	+	0.457649i	$0.151308\pi$
$11$	1218.26i	0.915298i	−0.889133	+	0.457649i	$0.848692\pi$
$12$	0	0
$13$	−170.463	−0.0775888	−0.0387944	−	0.999247i	$-0.512352\pi$
$13$	−170.463	−0.0775888	−0.0387944	+	0.999247i	$0.512352\pi$
$14$	− 7260.65i	− 2.64601i
$15$	0	0
$16$	5477.09	1.33718
$17$	− 1574.10i	− 0.320395i	−0.987085	−	0.160197i	$-0.948787\pi$
$17$	− 1574.10i	− 0.320395i	0.987085	−	0.160197i	$-0.0512131\pi$
$18$	0	0
$19$	−11289.1	−1.64588	−0.822938	−	0.568131i	$-0.807667\pi$
$19$	−11289.1	−1.64588	−0.822938	+	0.568131i	$0.807667\pi$
$20$	18543.6i	2.31795i
$21$	0	0
$22$	−17183.2	−1.61375
$23$	10572.6i	0.868960i	0.900681	+	0.434480i	$0.143068\pi$
$23$	10572.6i	0.868960i	−0.900681	+	0.434480i	$0.856932\pi$
$24$	0	0
$25$	−3258.91	−0.208570
$26$	− 2404.32i	− 0.136796i
$27$	0	0
$28$	69464.0	3.16436
$29$	− 8665.42i	− 0.355300i	−0.984094	−	0.177650i	$-0.943150\pi$
$29$	− 8665.42i	− 0.355300i	0.984094	−	0.177650i	$-0.0568496\pi$
$30$	0	0
$31$	−26209.1	−0.879766	−0.439883	−	0.898055i	$-0.644980\pi$
$31$	−26209.1	−0.879766	−0.439883	+	0.898055i	$0.644980\pi$
$32$	13213.2i	0.403234i
$33$	0	0
$34$	22202.2	0.564884
$35$	70738.9i	1.64989i
$36$	0	0
$37$	21866.9	0.431701	0.215850	−	0.976426i	$-0.430748\pi$
$37$	21866.9	0.431701	0.215850	+	0.976426i	$0.430748\pi$
$38$	− 159229.i	− 2.90182i
$39$	0	0
$40$	−137504.	−2.14849
$41$	38166.6i	0.553774i	0.960903	+	0.276887i	$0.0893027\pi$
$41$	38166.6i	0.553774i	−0.960903	+	0.276887i	$0.910697\pi$
$42$	0	0
$43$	23895.1	0.300541	0.150270	−	0.988645i	$-0.451986\pi$
$43$	23895.1	0.300541	0.150270	+	0.988645i	$0.451986\pi$
$44$	− 164395.i	− 1.92988i
$45$	0	0
$46$	−149124.	−1.53205
$47$	− 26698.7i	− 0.257156i	−0.991699	−	0.128578i	$-0.958959\pi$
$47$	− 26698.7i	− 0.257156i	0.991699	−	0.128578i	$-0.0410413\pi$
$48$	0	0
$49$	147338.	1.25235
$50$	− 45965.9i	− 0.367727i
$51$	0	0
$52$	23002.6	0.163594
$53$	213997.i	1.43741i	0.695315	+	0.718705i	$0.255265\pi$
$53$	213997.i	1.43741i	−0.695315	+	0.718705i	$0.744735\pi$
$54$	0	0
$55$	167412.	1.00623
$56$	515086.i	2.93303i
$57$	0	0
$58$	122223.	0.626425
$59$	− 163689.i	− 0.797010i	−0.917166	−	0.398505i	$-0.869529\pi$
$59$	− 163689.i	− 0.797010i	0.917166	−	0.398505i	$-0.130471\pi$
$60$	0	0
$61$	111078.	0.489370	0.244685	−	0.969603i	$-0.421315\pi$
$61$	111078.	0.489370	0.244685	+	0.969603i	$0.421315\pi$
$62$	− 369671.i	− 1.55110i
$63$	0	0
$64$	164166.	0.626245
$65$	23424.8i	0.0852972i
$66$	0	0
$67$	−381035.	−1.26689	−0.633447	−	0.773786i	$-0.718361\pi$
$67$	−381035.	−1.26689	−0.633447	+	0.773786i	$0.718361\pi$
$68$	212412.i	0.675543i
$69$	0	0
$70$	−997750.	−2.90889
$71$	675048.i	1.88608i	0.332682	+	0.943039i	$0.392047\pi$
$71$	675048.i	1.88608i	−0.332682	+	0.943039i	$0.607953\pi$
$72$	0	0
$73$	−762939.	−1.96120	−0.980599	−	0.196025i	$-0.937197\pi$
$73$	−762939.	−1.96120	−0.980599	+	0.196025i	$0.937197\pi$
$74$	308426.i	0.761125i
$75$	0	0
$76$	1.52337e6	3.47028
$77$	− 627123.i	− 1.37366i
$78$	0	0
$79$	515708.	1.04598	0.522989	−	0.852340i	$-0.324817\pi$
$79$	515708.	1.04598	0.522989	+	0.852340i	$0.324817\pi$
$80$	− 752655.i	− 1.47003i
$81$	0	0
$82$	−538328.	−0.976350
$83$	− 903773.i	− 1.58061i	−0.612713	−	0.790306i	$-0.709922\pi$
$83$	− 903773.i	− 1.58061i	0.612713	−	0.790306i	$-0.290078\pi$
$84$	0	0
$85$	−216311.	−0.352226
$86$	337033.i	0.529879i
$87$	0	0
$88$	1.21901e6	1.78880
$89$	− 644278.i	− 0.913910i	−0.889490	−	0.456955i	$-0.848940\pi$
$89$	− 644278.i	− 0.913910i	0.889490	−	0.456955i	$-0.151060\pi$
$90$	0	0
$91$	87748.8	0.116444
$92$	− 1.42669e6i	− 1.83218i
$93$	0	0
$94$	376577.	0.453388
$95$	1.55133e6i	1.80939i
$96$	0	0
$97$	−616470.	−0.675455	−0.337728	−	0.941244i	$-0.609658\pi$
$97$	−616470.	−0.675455	−0.337728	+	0.941244i	$0.609658\pi$
$98$	2.07815e6i	2.20800i
$99$	0	0
$100$	439765.	0.439765
$101$	− 623027.i	− 0.604704i	−0.953196	−	0.302352i	$-0.902228\pi$
$101$	− 623027.i	− 0.604704i	0.953196	−	0.302352i	$-0.0977718\pi$
$102$	0	0
$103$	−750695.	−0.686992	−0.343496	−	0.939154i	$-0.611611\pi$
$103$	−750695.	−0.686992	−0.343496	+	0.939154i	$0.611611\pi$
$104$	170568.i	0.151634i
$105$	0	0
$106$	−3.01837e6	−2.53428
$107$	− 345428.i	− 0.281973i	−0.990012	−	0.140986i	$-0.954973\pi$
$107$	− 345428.i	− 0.281973i	0.990012	−	0.140986i	$-0.0450273\pi$
$108$	0	0
$109$	1.17208e6	0.905061	0.452530	−	0.891749i	$-0.350521\pi$
$109$	1.17208e6	0.905061	0.452530	+	0.891749i	$0.350521\pi$
$110$	2.36129e6i	1.77408i
$111$	0	0
$112$	−2.81944e6	−2.00682
$113$	− 2.45331e6i	− 1.70026i	−0.526569	−	0.850132i	$-0.676522\pi$
$113$	− 2.45331e6i	− 1.70026i	0.526569	−	0.850132i	$-0.323478\pi$
$114$	0	0
$115$	1.45288e6	0.955291
$116$	1.16933e6i	0.749141i
$117$	0	0
$118$	2.30878e6	1.40520
$119$	810297.i	0.480843i
$120$	0	0
$121$	287398.	0.162229
$122$	1.56672e6i	0.862802i
$123$	0	0
$124$	3.53671e6	1.85496
$125$	− 1.69933e6i	− 0.870058i
$126$	0	0
$127$	−1.53816e6	−0.750913	−0.375456	−	0.926840i	$-0.622514\pi$
$127$	−1.53816e6	−0.750913	−0.375456	+	0.926840i	$0.622514\pi$
$128$	3.16116e6i	1.50736i
$129$	0	0
$130$	−330399.	−0.150386
$131$	1.12723e6i	0.501416i	0.968063	+	0.250708i	$0.0806635\pi$
$131$	1.12723e6i	0.501416i	−0.968063	+	0.250708i	$0.919337\pi$
$132$	0	0
$133$	5.81126e6	2.47010
$134$	− 5.37438e6i	− 2.23364i
$135$	0	0
$136$	−1.57507e6	−0.626157
$137$	3.20599e6i	1.24681i	0.781899	+	0.623406i	$0.214251\pi$
$137$	3.20599e6i	1.24681i	−0.781899	+	0.623406i	$0.785749\pi$
$138$	0	0
$139$	−66685.5	−0.0248306	−0.0124153	−	0.999923i	$-0.503952\pi$
$139$	−66685.5	−0.0248306	−0.0124153	+	0.999923i	$0.503952\pi$
$140$	− 9.54566e6i	− 3.47874i
$141$	0	0
$142$	−9.52134e6	−3.32532
$143$	− 207668.i	− 0.0710169i
$144$	0	0
$145$	−1.19079e6	−0.390600
$146$	− 1.07610e7i	− 3.45776i
$147$	0	0
$148$	−2.95077e6	−0.910229
$149$	1.62846e6i	0.492288i	0.969233	+	0.246144i	$0.0791635\pi$
$149$	1.62846e6i	0.492288i	−0.969233	+	0.246144i	$0.920836\pi$
$150$	0	0
$151$	−365620.	−0.106194	−0.0530968	−	0.998589i	$-0.516909\pi$
$151$	−365620.	−0.106194	−0.0530968	+	0.998589i	$0.516909\pi$
$152$	1.12960e7i	3.21658i
$153$	0	0
$154$	8.84538e6	2.42189
$155$	3.60162e6i	0.967170i
$156$	0	0
$157$	−5.18926e6	−1.34093	−0.670465	−	0.741941i	$-0.733905\pi$
$157$	−5.18926e6	−1.34093	−0.670465	+	0.741941i	$0.733905\pi$
$158$	7.27390e6i	1.84415i
$159$	0	0
$160$	1.81574e6	0.443295
$161$	− 5.44246e6i	− 1.30412i
$162$	0	0
$163$	−3.00726e6	−0.694397	−0.347199	−	0.937792i	$-0.612867\pi$
$163$	−3.00726e6	−0.694397	−0.347199	+	0.937792i	$0.612867\pi$
$164$	− 5.15029e6i	− 1.16762i
$165$	0	0
$166$	1.27474e7	2.78675
$167$	4.78381e6i	1.02713i	0.858051	+	0.513564i	$0.171675\pi$
$167$	4.78381e6i	1.02713i	−0.858051	+	0.513564i	$0.828325\pi$
$168$	0	0
$169$	−4.79775e6	−0.993980
$170$	− 3.05100e6i	− 0.621005i
$171$	0	0
$172$	−3.22446e6	−0.633681
$173$	− 3.53596e6i	− 0.682918i	−0.939897	−	0.341459i	$-0.889079\pi$
$173$	− 3.53596e6i	− 0.682918i	0.939897	−	0.341459i	$-0.110921\pi$
$174$	0	0
$175$	1.67759e6	0.313019
$176$	6.67253e6i	1.22392i
$177$	0	0
$178$	9.08734e6	1.61130
$179$	8.57291e6i	1.49475i	0.664401	+	0.747376i	$0.268687\pi$
$179$	8.57291e6i	1.49475i	−0.664401	+	0.747376i	$0.731313\pi$
$180$	0	0
$181$	1.79208e6	0.302219	0.151110	−	0.988517i	$-0.451715\pi$
$181$	1.79208e6	0.302219	0.151110	+	0.988517i	$0.451715\pi$
$182$	1.23767e6i	0.205301i
$183$	0	0
$184$	1.05792e7	1.69824
$185$	− 3.00493e6i	− 0.474590i
$186$	0	0
$187$	1.91767e6	0.293257
$188$	3.60278e6i	0.542206i
$189$	0	0
$190$	−2.18810e7	−3.19012
$191$	1.01076e7i	1.45061i	0.688429	+	0.725304i	$0.258301\pi$
$191$	1.01076e7i	1.45061i	−0.688429	+	0.725304i	$0.741699\pi$
$192$	0	0
$193$	−7.64657e6	−1.06364	−0.531820	−	0.846857i	$-0.678492\pi$
$193$	−7.64657e6	−1.06364	−0.531820	+	0.846857i	$0.678492\pi$
$194$	− 8.69511e6i	− 1.19089i
$195$	0	0
$196$	−1.98821e7	−2.64055
$197$	− 4.94403e6i	− 0.646669i	−0.946285	−	0.323335i	$-0.895196\pi$
$197$	− 4.94403e6i	− 0.646669i	0.946285	−	0.323335i	$-0.104804\pi$
$198$	0	0
$199$	−1.96814e6	−0.249745	−0.124872	−	0.992173i	$-0.539852\pi$
$199$	−1.96814e6	−0.249745	−0.124872	+	0.992173i	$0.539852\pi$
$200$	3.26092e6i	0.407615i
$201$	0	0
$202$	8.78760e6	1.06615
$203$	4.46069e6i	0.533229i
$204$	0	0
$205$	5.24481e6	0.608791
$206$	− 1.05883e7i	− 1.21123i
$207$	0	0
$208$	−933639.	−0.103750
$209$	− 1.37530e7i	− 1.50647i
$210$	0	0
$211$	8.29966e6	0.883513	0.441756	−	0.897135i	$-0.354356\pi$
$211$	8.29966e6	0.883513	0.441756	+	0.897135i	$0.354356\pi$
$212$	− 2.88773e7i	− 3.03074i
$213$	0	0
$214$	4.87216e6	0.497142
$215$	− 3.28363e6i	− 0.330399i
$216$	0	0
$217$	1.34916e7	1.32034
$218$	1.65318e7i	1.59570i
$219$	0	0
$220$	−2.25909e7	−2.12161
$221$	268325.i	0.0248590i
$222$	0	0
$223$	9.37779e6	0.845641	0.422821	−	0.906213i	$-0.361040\pi$
$223$	9.37779e6	0.845641	0.422821	+	0.906213i	$0.361040\pi$
$224$	− 6.80172e6i	− 0.605167i
$225$	0	0
$226$	3.46031e7	2.99771
$227$	3.66419e6i	0.313257i	0.987658	+	0.156628i	$0.0500625\pi$
$227$	3.66419e6i	0.313257i	−0.987658	+	0.156628i	$0.949938\pi$
$228$	0	0
$229$	4.98904e6	0.415442	0.207721	−	0.978188i	$-0.433395\pi$
$229$	4.98904e6	0.415442	0.207721	+	0.978188i	$0.433395\pi$
$230$	2.04924e7i	1.68426i
$231$	0	0
$232$	−8.67077e6	−0.694374
$233$	5.00370e6i	0.395570i	0.980245	+	0.197785i	$0.0633749\pi$
$233$	5.00370e6i	0.395570i	−0.980245	+	0.197785i	$0.936625\pi$
$234$	0	0
$235$	−3.66890e6	−0.282705
$236$	2.20886e7i	1.68047i
$237$	0	0
$238$	−1.14290e7	−0.847768
$239$	− 1.89151e7i	− 1.38553i	−0.721163	−	0.692765i	$-0.756392\pi$
$239$	− 1.89151e7i	− 1.38553i	0.721163	−	0.692765i	$-0.243608\pi$
$240$	0	0
$241$	−1.52515e7	−1.08958	−0.544791	−	0.838572i	$-0.683391\pi$
$241$	−1.52515e7	−1.08958	−0.544791	+	0.838572i	$0.683391\pi$
$242$	4.05366e6i	0.286023i
$243$	0	0
$244$	−1.49891e7	−1.03182
$245$	− 2.02470e7i	− 1.37677i
$246$	0	0
$247$	1.92436e6	0.127702
$248$	2.62253e7i	1.71935i
$249$	0	0
$250$	2.39685e7	1.53399
$251$	1.44796e7i	0.915661i	0.889040	+	0.457830i	$0.151373\pi$
$251$	1.44796e7i	0.915661i	−0.889040	+	0.457830i	$0.848627\pi$
$252$	0	0
$253$	−1.28802e7	−0.795358
$254$	− 2.16952e7i	− 1.32392i
$255$	0	0
$256$	−3.40805e7	−2.03136
$257$	− 1.19468e7i	− 0.703807i	−0.936036	−	0.351904i	$-0.885534\pi$
$257$	− 1.19468e7i	− 0.703807i	0.936036	−	0.351904i	$-0.114466\pi$
$258$	0	0
$259$	−1.12564e7	−0.647889
$260$	− 3.16099e6i	− 0.179847i
$261$	0	0
$262$	−1.58992e7	−0.884040
$263$	− 1.51400e7i	− 0.832258i	−0.909306	−	0.416129i	$-0.863386\pi$
$263$	− 1.51400e7i	− 0.832258i	0.909306	−	0.416129i	$-0.136614\pi$
$264$	0	0
$265$	2.94073e7	1.58022
$266$	8.19659e7i	4.35500i
$267$	0	0
$268$	5.14177e7	2.67121
$269$	3.37864e7i	1.73574i	0.496789	+	0.867871i	$0.334512\pi$
$269$	3.37864e7i	1.73574i	−0.496789	+	0.867871i	$0.665488\pi$
$270$	0	0
$271$	−292052.	−0.0146741	−0.00733707	−	0.999973i	$-0.502335\pi$
$271$	−292052.	−0.0146741	−0.00733707	+	0.999973i	$0.502335\pi$
$272$	− 8.62149e6i	− 0.428426i
$273$	0	0
$274$	−4.52195e7	−2.19824
$275$	− 3.97021e6i	− 0.190904i
$276$	0	0
$277$	−1.18466e7	−0.557384	−0.278692	−	0.960381i	$-0.589901\pi$
$277$	−1.18466e7	−0.557384	−0.278692	+	0.960381i	$0.589901\pi$
$278$	− 940578.i	− 0.0437785i
$279$	0	0
$280$	7.07825e7	3.22442
$281$	− 2.67693e6i	− 0.120648i	−0.998179	−	0.0603238i	$-0.980787\pi$
$281$	− 2.67693e6i	− 0.120648i	0.998179	−	0.0603238i	$-0.0192133\pi$
$282$	0	0
$283$	−3.11101e7	−1.37260	−0.686298	−	0.727321i	$-0.740765\pi$
$283$	−3.11101e7	−1.37260	−0.686298	+	0.727321i	$0.740765\pi$
$284$	− 9.10925e7i	− 3.97674i
$285$	0	0
$286$	2.92909e6	0.125209
$287$	− 1.96470e7i	− 0.831094i
$288$	0	0
$289$	2.16598e7	0.897347
$290$	− 1.67957e7i	− 0.688660i
$291$	0	0
$292$	1.02953e8	4.13513
$293$	− 2.35392e6i	− 0.0935813i	−0.998905	−	0.0467906i	$-0.985101\pi$
$293$	− 2.35392e6i	− 0.0935813i	0.998905	−	0.0467906i	$-0.0148994\pi$
$294$	0	0
$295$	−2.24939e7	−0.876193
$296$	− 2.18804e7i	− 0.843686i
$297$	0	0
$298$	−2.29689e7	−0.867945
$299$	− 1.80224e6i	− 0.0674216i
$300$	0	0
$301$	−1.23004e7	−0.451046
$302$	− 5.15695e6i	− 0.187229i
$303$	0	0
$304$	−6.18312e7	−2.20083
$305$	− 1.52642e7i	− 0.537989i
$306$	0	0
$307$	3.99249e6	0.137984	0.0689920	−	0.997617i	$-0.478022\pi$
$307$	3.99249e6	0.137984	0.0689920	+	0.997617i	$0.478022\pi$
$308$	8.46254e7i	2.89633i
$309$	0	0
$310$	−5.07997e7	−1.70520
$311$	3.01385e7i	1.00194i	0.865465	+	0.500969i	$0.167023\pi$
$311$	3.01385e7i	1.00194i	−0.865465	+	0.500969i	$0.832977\pi$
$312$	0	0
$313$	−3.78911e7	−1.23568	−0.617838	−	0.786305i	$-0.711991\pi$
$313$	−3.78911e7	−1.23568	−0.617838	+	0.786305i	$0.711991\pi$
$314$	− 7.31928e7i	− 2.36417i
$315$	0	0
$316$	−6.95907e7	−2.20541
$317$	3.47444e7i	1.09070i	0.838207	+	0.545352i	$0.183604\pi$
$317$	3.47444e7i	1.09070i	−0.838207	+	0.545352i	$0.816396\pi$
$318$	0	0
$319$	1.05568e7	0.325206
$320$	− 2.25595e7i	− 0.688462i
$321$	0	0
$322$	7.67642e7	2.29928
$323$	1.77701e7i	0.527330i
$324$	0	0
$325$	555522.	0.0161827
$326$	− 4.24164e7i	− 1.22428i
$327$	0	0
$328$	3.81902e7	1.08226
$329$	1.37437e7i	0.385936i
$330$	0	0
$331$	3.66213e7	1.00983	0.504917	−	0.863168i	$-0.331523\pi$
$331$	3.66213e7	1.00983	0.504917	+	0.863168i	$0.331523\pi$
$332$	1.21957e8i	3.33267i
$333$	0	0
$334$	−6.74742e7	−1.81092
$335$	5.23614e7i	1.39276i
$336$	0	0
$337$	4.53144e7	1.18398	0.591992	−	0.805944i	$-0.298342\pi$
$337$	4.53144e7	1.18398	0.591992	+	0.805944i	$0.298342\pi$
$338$	− 6.76708e7i	− 1.75247i
$339$	0	0
$340$	2.91895e7	0.742659
$341$	− 3.19296e7i	− 0.805248i
$342$	0	0
$343$	−1.52829e7	−0.378724
$344$	− 2.39098e7i	− 0.587356i
$345$	0	0
$346$	4.98736e7	1.20404
$347$	− 2.92265e7i	− 0.699502i	−0.936843	−	0.349751i	$-0.886266\pi$
$347$	− 2.92265e7i	− 0.699502i	0.936843	−	0.349751i	$-0.113734\pi$
$348$	0	0
$349$	−9.61270e6	−0.226136	−0.113068	−	0.993587i	$-0.536068\pi$
$349$	−9.61270e6	−0.226136	−0.113068	+	0.993587i	$0.536068\pi$
$350$	2.36618e7i	0.551879i
$351$	0	0
$352$	−1.60971e7	−0.369079
$353$	3.01291e7i	0.684955i	0.939526	+	0.342478i	$0.111266\pi$
$353$	3.01291e7i	0.684955i	−0.939526	+	0.342478i	$0.888734\pi$
$354$	0	0
$355$	9.27643e7	2.07346
$356$	8.69403e7i	1.92695i
$357$	0	0
$358$	−1.20918e8	−2.63538
$359$	− 3.63910e7i	− 0.786521i	−0.919427	−	0.393260i	$-0.871347\pi$
$359$	− 3.63910e7i	− 0.786521i	0.919427	−	0.393260i	$-0.128653\pi$
$360$	0	0
$361$	8.03970e7	1.70891
$362$	2.52767e7i	0.532838i
$363$	0	0
$364$	−1.18410e7	−0.245519
$365$	1.04842e8i	2.15604i
$366$	0	0
$367$	5.05958e7	1.02357	0.511784	−	0.859114i	$-0.328985\pi$
$367$	5.05958e7	1.02357	0.511784	+	0.859114i	$0.328985\pi$
$368$	5.79073e7i	1.16196i
$369$	0	0
$370$	4.23836e7	0.836743
$371$	− 1.10159e8i	− 2.15724i
$372$	0	0
$373$	−9.44996e7	−1.82097	−0.910487	−	0.413538i	$-0.864293\pi$
$373$	−9.44996e7	−1.82097	−0.910487	+	0.413538i	$0.864293\pi$
$374$	2.70481e7i	0.517037i
$375$	0	0
$376$	−2.67152e7	−0.502568
$377$	1.47713e6i	0.0275673i
$378$	0	0
$379$	−5.62274e7	−1.03283	−0.516417	−	0.856337i	$-0.672734\pi$
$379$	−5.62274e7	−1.03283	−0.516417	+	0.856337i	$0.672734\pi$
$380$	− 2.09340e8i	− 3.81505i
$381$	0	0
$382$	−1.42565e8	−2.55755
$383$	2.12413e7i	0.378080i	0.981969	+	0.189040i	$0.0605376\pi$
$383$	2.12413e7i	0.378080i	−0.981969	+	0.189040i	$0.939462\pi$
$384$	0	0
$385$	−8.61785e7	−1.51014
$386$	− 1.07853e8i	− 1.87529i
$387$	0	0
$388$	8.31877e7	1.42418
$389$	9.62174e7i	1.63458i	0.576230	+	0.817288i	$0.304523\pi$
$389$	9.62174e7i	1.63458i	−0.576230	+	0.817288i	$0.695477\pi$
$390$	0	0
$391$	1.66424e7	0.278410
$392$	− 1.47429e8i	− 2.44751i
$393$	0	0
$394$	6.97339e7	1.14013
$395$	− 7.08679e7i	− 1.14990i
$396$	0	0
$397$	2.71686e7	0.434206	0.217103	−	0.976149i	$-0.430339\pi$
$397$	2.71686e7	0.434206	0.217103	+	0.976149i	$0.430339\pi$
$398$	− 2.77600e7i	− 0.440322i
$399$	0	0
$400$	−1.78494e7	−0.278896
$401$	− 1.53926e7i	− 0.238715i	−0.992851	−	0.119357i	$-0.961917\pi$
$401$	− 1.53926e7i	− 0.238715i	0.992851	−	0.119357i	$-0.0380834\pi$
$402$	0	0
$403$	4.46767e6	0.0682599
$404$	8.40727e7i	1.27500i
$405$	0	0
$406$	−6.29166e7	−0.940129
$407$	2.66397e7i	0.395135i
$408$	0	0
$409$	−3.26408e7	−0.477080	−0.238540	−	0.971133i	$-0.576669\pi$
$409$	−3.26408e7	−0.477080	−0.238540	+	0.971133i	$0.576669\pi$
$410$	7.39764e7i	1.07335i
$411$	0	0
$412$	1.01300e8	1.44850
$413$	8.42620e7i	1.19614i
$414$	0	0
$415$	−1.24195e8	−1.73765
$416$	− 2.25235e6i	− 0.0312864i
$417$	0	0
$418$	1.93982e8	2.65603
$419$	− 8.86249e7i	− 1.20480i	−0.798196	−	0.602398i	$-0.794212\pi$
$419$	− 8.86249e7i	− 1.20480i	0.798196	−	0.602398i	$-0.205788\pi$
$420$	0	0
$421$	9.51173e7	1.27472	0.637358	−	0.770568i	$-0.280027\pi$
$421$	9.51173e7	1.27472	0.637358	+	0.770568i	$0.280027\pi$
$422$	1.17064e8i	1.55771i
$423$	0	0
$424$	2.14130e8	2.80918
$425$	5.12985e6i	0.0668249i
$426$	0	0
$427$	−5.71793e7	−0.734439
$428$	4.66129e7i	0.594531i
$429$	0	0
$430$	4.63146e7	0.582522
$431$	− 8.05617e7i	− 1.00623i	−0.864220	−	0.503115i	$-0.832187\pi$
$431$	− 8.05617e7i	− 1.00623i	0.864220	−	0.503115i	$-0.167813\pi$
$432$	0	0
$433$	3.50511e7	0.431755	0.215878	−	0.976420i	$-0.430739\pi$
$433$	3.50511e7	0.431755	0.215878	+	0.976420i	$0.430739\pi$
$434$	1.90295e8i	2.32787i
$435$	0	0
$436$	−1.58163e8	−1.90829
$437$	− 1.19355e8i	− 1.43020i
$438$	0	0
$439$	−4.63062e7	−0.547325	−0.273663	−	0.961826i	$-0.588235\pi$
$439$	−4.63062e7	−0.547325	−0.273663	+	0.961826i	$0.588235\pi$
$440$	− 1.67515e8i	− 1.96651i
$441$	0	0
$442$	−3.78464e6	−0.0438286
$443$	− 1.19041e8i	− 1.36926i	−0.728893	−	0.684628i	$-0.759965\pi$
$443$	− 1.19041e8i	− 1.36926i	0.728893	−	0.684628i	$-0.240035\pi$
$444$	0	0
$445$	−8.85359e7	−1.00471
$446$	1.32271e8i	1.49094i
$447$	0	0
$448$	−8.45077e7	−0.939858
$449$	− 9.75546e7i	− 1.07773i	−0.842393	−	0.538864i	$-0.818854\pi$
$449$	− 9.75546e7i	− 1.07773i	0.842393	−	0.538864i	$-0.181146\pi$
$450$	0	0
$451$	−4.64970e7	−0.506868
$452$	3.31055e8i	3.58496i
$453$	0	0
$454$	−5.16822e7	−0.552298
$455$	− 1.20583e7i	− 0.128013i
$456$	0	0
$457$	−8.13740e6	−0.0852583	−0.0426292	−	0.999091i	$-0.513573\pi$
$457$	−8.13740e6	−0.0852583	−0.0426292	+	0.999091i	$0.513573\pi$
$458$	7.03688e7i	0.732460i
$459$	0	0
$460$	−1.96055e8	−2.01420
$461$	1.55318e8i	1.58533i	0.609659	+	0.792664i	$0.291306\pi$
$461$	1.55318e8i	1.58533i	−0.609659	+	0.792664i	$0.708694\pi$
$462$	0	0
$463$	7.62984e7	0.768728	0.384364	−	0.923182i	$-0.374421\pi$
$463$	7.62984e7	0.768728	0.384364	+	0.923182i	$0.374421\pi$
$464$	− 4.74613e7i	− 0.475101i
$465$	0	0
$466$	−7.05757e7	−0.697425
$467$	1.85842e8i	1.82470i	0.409408	+	0.912352i	$0.365735\pi$
$467$	1.85842e8i	1.82470i	−0.409408	+	0.912352i	$0.634265\pi$
$468$	0	0
$469$	1.96145e8	1.90133
$470$	− 5.17487e7i	− 0.498432i
$471$	0	0
$472$	−1.63790e8	−1.55762
$473$	2.91105e7i	0.275084i
$474$	0	0
$475$	3.67901e7	0.343281
$476$	− 1.09343e8i	− 1.01384i
$477$	0	0
$478$	2.66792e8	2.44281
$479$	− 1.23819e8i	− 1.12663i	−0.826243	−	0.563314i	$-0.809526\pi$
$479$	− 1.23819e8i	− 1.12663i	0.826243	−	0.563314i	$-0.190474\pi$
$480$	0	0
$481$	−3.72749e6	−0.0334951
$482$	− 2.15117e8i	− 1.92103i
$483$	0	0
$484$	−3.87821e7	−0.342055
$485$	8.47145e7i	0.742561i
$486$	0	0
$487$	−6.09360e7	−0.527578	−0.263789	−	0.964580i	$-0.584972\pi$
$487$	−6.09360e7	−0.527578	−0.263789	+	0.964580i	$0.584972\pi$
$488$	− 1.11146e8i	− 0.956391i
$489$	0	0
$490$	2.85577e8	2.42737
$491$	6.48068e7i	0.547490i	0.961802	+	0.273745i	$0.0882624\pi$
$491$	6.48068e7i	0.547490i	−0.961802	+	0.273745i	$0.911738\pi$
$492$	0	0
$493$	−1.36402e7	−0.113836
$494$	2.71425e7i	0.225149i
$495$	0	0
$496$	−1.43550e8	−1.17641
$497$	− 3.47494e8i	− 2.83060i
$498$	0	0
$499$	2.87096e7	0.231061	0.115530	−	0.993304i	$-0.463143\pi$
$499$	2.87096e7	0.231061	0.115530	+	0.993304i	$0.463143\pi$
$500$	2.29312e8i	1.83449i
$501$	0	0
$502$	−2.04230e8	−1.61439
$503$	− 1.12463e8i	− 0.883702i	−0.897088	−	0.441851i	$-0.854322\pi$
$503$	− 1.12463e8i	− 0.883702i	0.897088	−	0.441851i	$-0.145678\pi$
$504$	0	0
$505$	−8.56156e7	−0.664781
$506$	− 1.81672e8i	− 1.40228i
$507$	0	0
$508$	2.07562e8	1.58328
$509$	5.61786e7i	0.426008i	0.977051	+	0.213004i	$0.0683247\pi$
$509$	5.61786e7i	0.426008i	−0.977051	+	0.213004i	$0.931675\pi$
$510$	0	0
$511$	3.92737e8	2.94333
$512$	− 2.78380e8i	− 2.07410i
$513$	0	0
$514$	1.68506e8	1.24087
$515$	1.03160e8i	0.755245i
$516$	0	0
$517$	3.25260e7	0.235375
$518$	− 1.58768e8i	− 1.14228i
$519$	0	0
$520$	2.34392e7	0.166699
$521$	1.68861e8i	1.19403i	0.802230	+	0.597015i	$0.203647\pi$
$521$	1.68861e8i	1.19403i	−0.802230	+	0.597015i	$0.796353\pi$
$522$	0	0
$523$	−2.39748e8	−1.67591	−0.837955	−	0.545739i	$-0.816249\pi$
$523$	−2.39748e8	−1.67591	−0.837955	+	0.545739i	$0.816249\pi$
$524$	− 1.52111e8i	− 1.05722i
$525$	0	0
$526$	2.13545e8	1.46734
$527$	4.12557e7i	0.281872i
$528$	0	0
$529$	3.62552e7	0.244908
$530$	4.14780e8i	2.78606i
$531$	0	0
$532$	−7.84183e8	−5.20814
$533$	− 6.50598e6i	− 0.0429666i
$534$	0	0
$535$	−4.74683e7	−0.309986
$536$	3.81270e8i	2.47593i
$537$	0	0
$538$	−4.76547e8	−3.06026
$539$	1.79496e8i	1.14627i
$540$	0	0
$541$	1.85322e8	1.17040	0.585200	−	0.810889i	$-0.301016\pi$
$541$	1.85322e8	1.17040	0.585200	+	0.810889i	$0.301016\pi$
$542$	− 4.11930e6i	− 0.0258718i
$543$	0	0
$544$	2.07988e7	0.129194
$545$	− 1.61066e8i	− 0.994978i
$546$	0	0
$547$	2.52846e8	1.54488	0.772438	−	0.635090i	$-0.219037\pi$
$547$	2.52846e8	1.54488	0.772438	+	0.635090i	$0.219037\pi$
$548$	− 4.32624e8i	− 2.62887i
$549$	0	0
$550$	5.59986e7	0.336580
$551$	9.78245e7i	0.584780i
$552$	0	0
$553$	−2.65470e8	−1.56979
$554$	− 1.67093e8i	− 0.982715i
$555$	0	0
$556$	8.99869e6	0.0523546
$557$	1.01472e8i	0.587194i	0.955929	+	0.293597i	$0.0948524\pi$
$557$	1.01472e8i	0.587194i	−0.955929	+	0.293597i	$0.905148\pi$
$558$	0	0
$559$	−4.07322e6	−0.0233186
$560$	3.87443e8i	2.20620i
$561$	0	0
$562$	3.77573e7	0.212712
$563$	− 1.15852e8i	− 0.649202i	−0.945851	−	0.324601i	$-0.894770\pi$
$563$	− 1.15852e8i	− 0.649202i	0.945851	−	0.324601i	$-0.105230\pi$
$564$	0	0
$565$	−3.37130e8	−1.86919
$566$	− 4.38799e8i	− 2.42000i
$567$	0	0
$568$	6.75465e8	3.68602
$569$	7.30159e7i	0.396352i	0.980166	+	0.198176i	$0.0635017\pi$
$569$	7.30159e7i	0.396352i	−0.980166	+	0.198176i	$0.936498\pi$
$570$	0	0
$571$	−9.75143e7	−0.523793	−0.261897	−	0.965096i	$-0.584348\pi$
$571$	−9.75143e7	−0.523793	−0.261897	+	0.965096i	$0.584348\pi$
$572$	2.80232e7i	0.149737i
$573$	0	0
$574$	2.77115e8	1.46529
$575$	− 3.44553e7i	− 0.181239i
$576$	0	0
$577$	8.90080e7	0.463342	0.231671	−	0.972794i	$-0.425581\pi$
$577$	8.90080e7	0.463342	0.231671	+	0.972794i	$0.425581\pi$
$578$	3.05504e8i	1.58210i
$579$	0	0
$580$	1.60688e8	0.823568
$581$	4.65234e8i	2.37216i
$582$	0	0
$583$	−2.60705e8	−1.31566
$584$	7.63410e8i	3.83283i
$585$	0	0
$586$	3.32013e7	0.164992
$587$	1.26314e8i	0.624509i	0.949998	+	0.312255i	$0.101084\pi$
$587$	1.26314e8i	0.624509i	−0.949998	+	0.312255i	$0.898916\pi$
$588$	0	0
$589$	2.95876e8	1.44798
$590$	− 3.17270e8i	− 1.54480i
$591$	0	0
$592$	1.19767e8	0.577262
$593$	− 1.59275e8i	− 0.763805i	−0.924203	−	0.381902i	$-0.875269\pi$
$593$	− 1.59275e8i	− 0.763805i	0.924203	−	0.381902i	$-0.124731\pi$
$594$	0	0
$595$	1.11350e8	0.528615
$596$	− 2.19748e8i	− 1.03797i
$597$	0	0
$598$	2.54200e7	0.118870
$599$	− 1.42561e8i	− 0.663315i	−0.943400	−	0.331658i	$-0.892392\pi$
$599$	− 1.42561e8i	− 0.663315i	0.943400	−	0.331658i	$-0.107608\pi$
$600$	0	0
$601$	−1.18489e8	−0.545828	−0.272914	−	0.962038i	$-0.587987\pi$
$601$	−1.18489e8	−0.545828	−0.272914	+	0.962038i	$0.587987\pi$
$602$	− 1.73494e8i	− 0.795234i
$603$	0	0
$604$	4.93375e7	0.223906
$605$	− 3.94939e7i	− 0.178346i
$606$	0	0
$607$	−8.06041e7	−0.360405	−0.180203	−	0.983630i	$-0.557675\pi$
$607$	−8.06041e7	−0.360405	−0.180203	+	0.983630i	$0.557675\pi$
$608$	− 1.49164e8i	− 0.663673i
$609$	0	0
$610$	2.15296e8	0.948521
$611$	4.55113e6i	0.0199524i
$612$	0	0
$613$	−2.49459e8	−1.08297	−0.541486	−	0.840710i	$-0.682138\pi$
$613$	−2.49459e8	−1.08297	−0.541486	+	0.840710i	$0.682138\pi$
$614$	5.63128e7i	0.243278i
$615$	0	0
$616$	−6.27510e8	−2.68459
$617$	− 3.44285e8i	− 1.46576i	−0.680358	−	0.732880i	$-0.738176\pi$
$617$	− 3.44285e8i	− 1.46576i	0.680358	−	0.732880i	$-0.261824\pi$
$618$	0	0
$619$	4.59439e7	0.193712	0.0968558	−	0.995298i	$-0.469121\pi$
$619$	4.59439e7	0.193712	0.0968558	+	0.995298i	$0.469121\pi$
$620$	− 4.86011e8i	− 2.03925i
$621$	0	0
$622$	−4.25094e8	−1.76650
$623$	3.31654e8i	1.37158i
$624$	0	0
$625$	−2.84441e8	−1.16507
$626$	− 5.34443e8i	− 2.17860i
$627$	0	0
$628$	7.00249e8	2.82731
$629$	− 3.44207e7i	− 0.138315i
$630$	0	0
$631$	−2.71320e8	−1.07993	−0.539963	−	0.841689i	$-0.681562\pi$
$631$	−2.71320e8	−1.07993	−0.539963	+	0.841689i	$0.681562\pi$
$632$	− 5.16026e8i	− 2.04419i
$633$	0	0
$634$	−4.90059e8	−1.92300
$635$	2.11372e8i	0.825516i
$636$	0	0
$637$	−2.51156e7	−0.0971684
$638$	1.48900e8i	0.573366i
$639$	0	0
$640$	4.34402e8	1.65711
$641$	− 3.13515e8i	− 1.19037i	−0.803587	−	0.595187i	$-0.797078\pi$
$641$	− 3.13515e8i	− 1.19037i	0.803587	−	0.595187i	$-0.202922\pi$
$642$	0	0
$643$	5.94578e7	0.223654	0.111827	−	0.993728i	$-0.464330\pi$
$643$	5.94578e7	0.223654	0.111827	+	0.993728i	$0.464330\pi$
$644$	7.34418e8i	2.74970i
$645$	0	0
$646$	−2.50642e8	−0.929728
$647$	2.04779e8i	0.756089i	0.925787	+	0.378045i	$0.123403\pi$
$647$	2.04779e8i	0.756089i	−0.925787	+	0.378045i	$0.876597\pi$
$648$	0	0
$649$	1.99416e8	0.729502
$650$	7.83547e6i	0.0285315i
$651$	0	0
$652$	4.05806e8	1.46412
$653$	− 3.40035e7i	− 0.122119i	−0.998134	−	0.0610596i	$-0.980552\pi$
$653$	− 3.40035e7i	− 0.122119i	0.998134	−	0.0610596i	$-0.0194480\pi$
$654$	0	0
$655$	1.54902e8	0.551232
$656$	2.09042e8i	0.740495i
$657$	0	0
$658$	−1.93850e8	−0.680438
$659$	2.43145e8i	0.849590i	0.905290	+	0.424795i	$0.139654\pi$
$659$	2.43145e8i	0.849590i	−0.905290	+	0.424795i	$0.860346\pi$
$660$	0	0
$661$	4.51973e8	1.56498	0.782488	−	0.622665i	$-0.213950\pi$
$661$	4.51973e8	1.56498	0.782488	+	0.622665i	$0.213950\pi$
$662$	5.16532e8i	1.78042i
$663$	0	0
$664$	−9.04331e8	−3.08904
$665$	− 7.98575e8i	− 2.71551i
$666$	0	0
$667$	9.16164e7	0.308742
$668$	− 6.45538e8i	− 2.16567i
$669$	0	0
$670$	−7.38541e8	−2.45556
$671$	1.35322e8i	0.447920i
$672$	0	0
$673$	3.17560e8	1.04179	0.520896	−	0.853620i	$-0.325598\pi$
$673$	3.17560e8	1.04179	0.520896	+	0.853620i	$0.325598\pi$
$674$	6.39145e8i	2.08747i
$675$	0	0
$676$	6.47419e8	2.09578
$677$	− 6.70541e7i	− 0.216102i	−0.994145	−	0.108051i	$-0.965539\pi$
$677$	− 6.70541e7i	− 0.216102i	0.994145	−	0.108051i	$-0.0344610\pi$
$678$	0	0
$679$	3.17339e8	1.01371
$680$	2.16444e8i	0.688366i
$681$	0	0
$682$	4.50356e8	1.41972
$683$	− 1.51437e8i	− 0.475303i	−0.971350	−	0.237652i	$-0.923622\pi$
$683$	− 1.51437e8i	− 0.475303i	0.971350	−	0.237652i	$-0.0763777\pi$
$684$	0	0
$685$	4.40563e8	1.37068
$686$	− 2.15560e8i	− 0.667723i
$687$	0	0
$688$	1.30876e8	0.401877
$689$	− 3.64786e7i	− 0.111527i
$690$	0	0
$691$	9.46804e7	0.286963	0.143482	−	0.989653i	$-0.454170\pi$
$691$	9.46804e7	0.286963	0.143482	+	0.989653i	$0.454170\pi$
$692$	4.77150e8i	1.43991i
$693$	0	0
$694$	4.12231e8	1.23328
$695$	9.16384e6i	0.0272975i
$696$	0	0
$697$	6.00781e7	0.177426
$698$	− 1.35584e8i	− 0.398697i
$699$	0	0
$700$	−2.26377e8	−0.659991
$701$	7.92713e6i	0.0230124i	0.999934	+	0.0115062i	$0.00366262\pi$
$701$	7.92713e6i	0.0230124i	−0.999934	+	0.0115062i	$0.996337\pi$
$702$	0	0
$703$	−2.46857e8	−0.710526
$704$	1.99998e8i	0.573201i
$705$	0	0
$706$	−4.24962e8	−1.20763
$707$	3.20715e8i	0.907530i
$708$	0	0
$709$	−6.65474e8	−1.86721	−0.933603	−	0.358310i	$-0.883353\pi$
$709$	−6.65474e8	−1.86721	−0.933603	+	0.358310i	$0.883353\pi$
$710$	1.30841e9i	3.65569i
$711$	0	0
$712$	−6.44676e8	−1.78608
$713$	− 2.77099e8i	− 0.764481i
$714$	0	0
$715$	−2.85375e7	−0.0780724
$716$	− 1.15685e9i	− 3.15164i
$717$	0	0
$718$	5.13283e8	1.38670
$719$	− 4.90198e8i	− 1.31882i	−0.751784	−	0.659409i	$-0.770806\pi$
$719$	− 4.90198e8i	− 1.31882i	0.751784	−	0.659409i	$-0.229194\pi$
$720$	0	0
$721$	3.86434e8	1.03103
$722$	1.13397e9i	3.01295i
$723$	0	0
$724$	−2.41827e8	−0.637221
$725$	2.82398e7i	0.0741051i
$726$	0	0
$727$	−2.09307e8	−0.544730	−0.272365	−	0.962194i	$-0.587806\pi$
$727$	−2.09307e8	−0.544730	−0.272365	+	0.962194i	$0.587806\pi$
$728$	− 8.78030e7i	− 0.227570i
$729$	0	0
$730$	−1.47877e9	−3.80129
$731$	− 3.76133e7i	− 0.0962917i
$732$	0	0
$733$	−3.66672e8	−0.931034	−0.465517	−	0.885039i	$-0.654132\pi$
$733$	−3.66672e8	−0.931034	−0.465517	+	0.885039i	$0.654132\pi$
$734$	7.13638e8i	1.80464i
$735$	0	0
$736$	−1.39698e8	−0.350394
$737$	− 4.64201e8i	− 1.15959i
$738$	0	0
$739$	−6.11387e8	−1.51490	−0.757449	−	0.652895i	$-0.773554\pi$
$739$	−6.11387e8	−1.51490	−0.757449	+	0.652895i	$0.773554\pi$
$740$	4.05491e8i	1.00066i
$741$	0	0
$742$	1.55376e9	3.80340
$743$	2.10111e8i	0.512252i	0.966643	+	0.256126i	$0.0824461\pi$
$743$	2.10111e8i	0.512252i	−0.966643	+	0.256126i	$0.917554\pi$
$744$	0	0
$745$	2.23781e8	0.541196
$746$	− 1.33289e9i	− 3.21053i
$747$	0	0
$748$	−2.58774e8	−0.618324
$749$	1.77816e8i	0.423180i
$750$	0	0
$751$	5.05697e8	1.19391	0.596953	−	0.802276i	$-0.296378\pi$
$751$	5.05697e8	1.19391	0.596953	+	0.802276i	$0.296378\pi$
$752$	− 1.46231e8i	− 0.343864i
$753$	0	0
$754$	−2.08345e7	−0.0486036
$755$	5.02430e7i	0.116744i
$756$	0	0
$757$	4.19839e8	0.967822	0.483911	−	0.875117i	$-0.339216\pi$
$757$	4.19839e8	0.967822	0.483911	+	0.875117i	$0.339216\pi$
$758$	− 7.93070e8i	− 1.82097i
$759$	0	0
$760$	1.55229e9	3.53615
$761$	− 7.32156e8i	− 1.66131i	−0.556791	−	0.830653i	$-0.687968\pi$
$761$	− 7.32156e8i	− 1.66131i	0.556791	−	0.830653i	$-0.312032\pi$
$762$	0	0
$763$	−6.03350e8	−1.35830
$764$	− 1.36395e9i	− 3.05856i
$765$	0	0
$766$	−2.99601e8	−0.666588
$767$	2.79029e7i	0.0618390i
$768$	0	0
$769$	−2.53294e8	−0.556988	−0.278494	−	0.960438i	$-0.589835\pi$
$769$	−2.53294e8	−0.556988	−0.278494	+	0.960438i	$0.589835\pi$
$770$	− 1.21552e9i	− 2.66250i
$771$	0	0
$772$	1.03185e9	2.24266
$773$	7.82197e8i	1.69347i	0.532014	+	0.846735i	$0.321435\pi$
$773$	7.82197e8i	1.69347i	−0.532014	+	0.846735i	$0.678565\pi$
$774$	0	0
$775$	8.54131e7	0.183493
$776$	6.16850e8i	1.32006i
$777$	0	0
$778$	−1.35712e9	−2.88190
$779$	− 4.30865e8i	− 0.911443i
$780$	0	0
$781$	−8.22386e8	−1.72632
$782$	2.34736e8i	0.490861i
$783$	0	0
$784$	8.06983e8	1.67462
$785$	7.13101e8i	1.47415i
$786$	0	0
$787$	6.81837e8	1.39880	0.699401	−	0.714730i	$-0.253450\pi$
$787$	6.81837e8	1.39880	0.699401	+	0.714730i	$0.253450\pi$
$788$	6.67158e8i	1.36348i
$789$	0	0
$790$	9.99570e8	2.02736
$791$	1.26289e9i	2.55173i
$792$	0	0
$793$	−1.89346e7	−0.0379696
$794$	3.83205e8i	0.765543i
$795$	0	0
$796$	2.65585e8	0.526580
$797$	5.08452e7i	0.100433i	0.998738	+	0.0502163i	$0.0159911\pi$
$797$	5.08452e7i	0.100433i	−0.998738	+	0.0502163i	$0.984009\pi$
$798$	0	0
$799$	−4.20264e7	−0.0823915
$800$	− 4.30605e7i	− 0.0841026i
$801$	0	0
$802$	2.17108e8	0.420874
$803$	− 9.29460e8i	− 1.79508i
$804$	0	0
$805$	−7.47896e8	−1.43369
$806$	6.30151e7i	0.120348i
$807$	0	0
$808$	−6.23412e8	−1.18179
$809$	1.02851e7i	0.0194251i	0.999953	+	0.00971257i	$0.00309166\pi$
$809$	1.02851e7i	0.0194251i	−0.999953	+	0.00971257i	$0.996908\pi$
$810$	0	0
$811$	4.84952e8	0.909152	0.454576	−	0.890708i	$-0.349791\pi$
$811$	4.84952e8	0.909152	0.454576	+	0.890708i	$0.349791\pi$
$812$	− 6.01935e8i	− 1.12430i
$813$	0	0
$814$	−3.75744e8	−0.696657
$815$	4.13254e8i	0.763385i
$816$	0	0
$817$	−2.69753e8	−0.494653
$818$	− 4.60389e8i	− 0.841133i
$819$	0	0
$820$	−7.07746e8	−1.28362
$821$	4.96161e8i	0.896588i	0.893886	+	0.448294i	$0.147968\pi$
$821$	4.96161e8i	0.896588i	−0.893886	+	0.448294i	$0.852032\pi$
$822$	0	0
$823$	−3.21483e8	−0.576711	−0.288356	−	0.957523i	$-0.593109\pi$
$823$	−3.21483e8	−0.576711	−0.288356	+	0.957523i	$0.593109\pi$
$824$	7.51158e8i	1.34261i
$825$	0	0
$826$	−1.18849e9	−2.10890
$827$	− 7.54902e8i	− 1.33467i	−0.744757	−	0.667336i	$-0.767435\pi$
$827$	− 7.54902e8i	− 1.33467i	0.744757	−	0.667336i	$-0.232565\pi$
$828$	0	0
$829$	−5.82262e8	−1.02201	−0.511004	−	0.859578i	$-0.670726\pi$
$829$	−5.82262e8	−1.02201	−0.511004	+	0.859578i	$0.670726\pi$
$830$	− 1.75174e9i	− 3.06362i
$831$	0	0
$832$	−2.79842e7	−0.0485896
$833$	− 2.31924e8i	− 0.401247i
$834$	0	0
$835$	6.57385e8	1.12917
$836$	1.85586e9i	3.17634i
$837$	0	0
$838$	1.25003e9	2.12416
$839$	− 6.64141e8i	− 1.12454i	−0.826954	−	0.562270i	$-0.809928\pi$
$839$	− 6.64141e8i	− 1.12454i	0.826954	−	0.562270i	$-0.190072\pi$
$840$	0	0
$841$	5.19734e8	0.873762
$842$	1.34160e9i	2.24743i
$843$	0	0
$844$	−1.11997e9	−1.86286
$845$	6.59301e8i	1.09273i
$846$	0	0
$847$	−1.47943e8	−0.243470
$848$	1.17208e9i	1.92208i
$849$	0	0
$850$	−7.23550e7	−0.117818
$851$	2.31191e8i	0.375131i
$852$	0	0
$853$	7.87779e8	1.26928	0.634640	−	0.772808i	$-0.281148\pi$
$853$	7.87779e8	1.26928	0.634640	+	0.772808i	$0.281148\pi$
$854$	− 8.06497e8i	− 1.29488i
$855$	0	0
$856$	−3.45642e8	−0.551067
$857$	− 9.65175e8i	− 1.53343i	−0.641988	−	0.766715i	$-0.721890\pi$
$857$	− 9.65175e8i	− 1.53343i	0.641988	−	0.766715i	$-0.278110\pi$
$858$	0	0
$859$	−5.95457e8	−0.939444	−0.469722	−	0.882814i	$-0.655646\pi$
$859$	−5.95457e8	−0.939444	−0.469722	+	0.882814i	$0.655646\pi$
$860$	4.43101e8i	0.696638i
$861$	0	0
$862$	1.13630e9	1.77407
$863$	9.85551e8i	1.53337i	0.642024	+	0.766684i	$0.278095\pi$
$863$	9.85551e8i	1.53337i	−0.642024	+	0.766684i	$0.721905\pi$
$864$	0	0
$865$	−4.85907e8	−0.750766
$866$	4.94385e8i	0.761222i
$867$	0	0
$868$	−1.82059e9	−2.78389
$869$	6.28267e8i	0.957382i
$870$	0	0
$871$	6.49522e7	0.0982969
$872$	− 1.17280e9i	− 1.76879i
$873$	0	0
$874$	1.68347e9	2.52157
$875$	8.74763e8i	1.30577i
$876$	0	0
$877$	3.68680e8	0.546577	0.273288	−	0.961932i	$-0.411889\pi$
$877$	3.68680e8	0.546577	0.273288	+	0.961932i	$0.411889\pi$
$878$	− 6.53134e8i	− 0.964981i
$879$	0	0
$880$	9.16931e8	1.34552
$881$	7.29792e8i	1.06726i	0.845717	+	0.533632i	$0.179173\pi$
$881$	7.29792e8i	1.06726i	−0.845717	+	0.533632i	$0.820827\pi$
$882$	0	0
$883$	−7.12900e7	−0.103549	−0.0517746	−	0.998659i	$-0.516488\pi$
$883$	−7.12900e7	−0.103549	−0.0517746	+	0.998659i	$0.516488\pi$
$884$	− 3.62084e7i	− 0.0524146i
$885$	0	0
$886$	1.67903e9	2.41411
$887$	− 3.15305e8i	− 0.451814i	−0.974149	−	0.225907i	$-0.927465\pi$
$887$	− 3.15305e8i	− 0.451814i	0.974149	−	0.225907i	$-0.0725346\pi$
$888$	0	0
$889$	7.91795e8	1.12696
$890$	− 1.24877e9i	− 1.77139i
$891$	0	0
$892$	−1.26546e9	−1.78301
$893$	3.01403e8i	0.423247i
$894$	0	0
$895$	1.17808e9	1.64326
$896$	− 1.62726e9i	− 2.26222i
$897$	0	0
$898$	1.37598e9	1.90013
$899$	2.27113e8i	0.312581i
$900$	0	0
$901$	3.36853e8	0.460539
$902$	− 6.55825e8i	− 0.893652i
$903$	0	0
$904$	−2.45482e9	−3.32288
$905$	− 2.46266e8i	− 0.332245i
$906$	0	0
$907$	−5.70419e8	−0.764491	−0.382245	−	0.924061i	$-0.624849\pi$
$907$	−5.70419e8	−0.764491	−0.382245	+	0.924061i	$0.624849\pi$
$908$	− 4.94454e8i	− 0.660493i
$909$	0	0
$910$	1.70079e8	0.225697
$911$	− 3.43557e8i	− 0.454406i	−0.973847	−	0.227203i	$-0.927042\pi$
$911$	− 3.43557e8i	− 0.454406i	0.973847	−	0.227203i	$-0.0729581\pi$
$912$	0	0
$913$	1.10103e9	1.44673
$914$	− 1.14775e8i	− 0.150318i
$915$	0	0
$916$	−6.73231e8	−0.875947
$917$	− 5.80262e8i	− 0.752517i
$918$	0	0
$919$	7.92851e8	1.02152	0.510758	−	0.859725i	$-0.329365\pi$
$919$	7.92851e8	1.02152	0.510758	+	0.859725i	$0.329365\pi$
$920$	− 1.45378e9i	− 1.86695i
$921$	0	0
$922$	−2.19071e9	−2.79507
$923$	− 1.15070e8i	− 0.146339i
$924$	0	0
$925$	−7.12624e7	−0.0900400
$926$	1.07617e9i	1.35533i
$927$	0	0
$928$	1.14498e8	0.143269
$929$	− 1.82427e8i	− 0.227531i	−0.993508	−	0.113766i	$-0.963709\pi$
$929$	− 1.82427e8i	− 0.227531i	0.993508	−	0.113766i	$-0.0362913\pi$
$930$	0	0
$931$	−1.66331e9	−2.06121
$932$	− 6.75211e8i	− 0.834049i
$933$	0	0
$934$	−2.62124e9	−3.21711
$935$	− 2.63523e8i	− 0.322392i
$936$	0	0
$937$	−3.34488e8	−0.406594	−0.203297	−	0.979117i	$-0.565166\pi$
$937$	−3.34488e8	−0.406594	−0.203297	+	0.979117i	$0.565166\pi$
$938$	2.76656e9i	3.35222i
$939$	0	0
$940$	4.95090e8	0.596075
$941$	2.91160e8i	0.349433i	0.984619	+	0.174716i	$0.0559008\pi$
$941$	2.91160e8i	0.349433i	−0.984619	+	0.174716i	$0.944099\pi$
$942$	0	0
$943$	−4.03522e8	−0.481207
$944$	− 8.96540e8i	− 1.06575i
$945$	0	0
$946$	−4.10594e8	−0.484997
$947$	− 1.69634e8i	− 0.199739i	−0.995001	−	0.0998694i	$-0.968158\pi$
$947$	− 1.69634e8i	− 0.199739i	0.995001	−	0.0998694i	$-0.0318425\pi$
$948$	0	0
$949$	1.30053e8	0.152167
$950$	5.18912e8i	0.605234i
$951$	0	0
$952$	8.10797e8	0.939727
$953$	− 5.17958e8i	− 0.598434i	−0.954185	−	0.299217i	$-0.903275\pi$
$953$	− 5.17958e8i	− 0.598434i	0.954185	−	0.299217i	$-0.0967254\pi$
$954$	0	0
$955$	1.38898e9	1.59473
$956$	2.55245e9i	2.92135i
$957$	0	0
$958$	1.74643e9	1.98634
$959$	− 1.65034e9i	− 1.87119i
$960$	0	0
$961$	−2.00587e8	−0.226013
$962$	− 5.25751e7i	− 0.0590548i
$963$	0	0
$964$	2.05806e9	2.29735
$965$	1.05078e9i	1.16931i
$966$	0	0
$967$	−1.37422e9	−1.51976	−0.759881	−	0.650062i	$-0.774743\pi$
$967$	−1.37422e9	−1.51976	−0.759881	+	0.650062i	$0.774743\pi$
$968$	− 2.87575e8i	− 0.317048i
$969$	0	0
$970$	−1.19487e9	−1.30920
$971$	− 7.45510e8i	− 0.814321i	−0.913357	−	0.407160i	$-0.866519\pi$
$971$	− 7.45510e8i	− 0.814321i	0.913357	−	0.407160i	$-0.133481\pi$
$972$	0	0
$973$	3.43276e7	0.0372653
$974$	− 8.59483e8i	− 0.930166i
$975$	0	0
$976$	6.08383e8	0.654376
$977$	9.80224e8i	1.05109i	0.850764	+	0.525547i	$0.176139\pi$
$977$	9.80224e8i	1.05109i	−0.850764	+	0.525547i	$0.823861\pi$
$978$	0	0
$979$	7.84900e8	0.836501
$980$	2.73217e9i	2.90288i
$981$	0	0
$982$	−9.14080e8	−0.965272
$983$	− 1.01328e9i	− 1.06676i	−0.845875	−	0.533381i	$-0.820921\pi$
$983$	− 1.01328e9i	− 1.06676i	0.845875	−	0.533381i	$-0.179079\pi$
$984$	0	0
$985$	−6.79402e8	−0.710916
$986$	− 1.92391e8i	− 0.200703i
$987$	0	0
$988$	−2.59678e8	−0.269255
$989$	2.52634e8i	0.261158i
$990$	0	0
$991$	−1.85231e9	−1.90324	−0.951620	−	0.307279i	$-0.900582\pi$
$991$	−1.85231e9	−1.90324	−0.951620	+	0.307279i	$0.900582\pi$
$992$	− 3.46305e8i	− 0.354751i
$993$	0	0
$994$	4.90129e9	4.99058
$995$	2.70459e8i	0.274557i
$996$	0	0
$997$	1.25665e9	1.26803	0.634013	−	0.773322i	$-0.281407\pi$
$997$	1.25665e9	1.26803	0.634013	+	0.773322i	$0.281407\pi$
$998$	4.04941e8i	0.407380i
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	27.7.b.c.26.4	yes	4
3.2	odd	2	inner	27.7.b.c.26.1	✓	4
4.3	odd	2		432.7.e.j.161.1		4
9.2	odd	6		81.7.d.e.53.1		8
9.4	even	3		81.7.d.e.26.1		8
9.5	odd	6		81.7.d.e.26.4		8
9.7	even	3		81.7.d.e.53.4		8
12.11	even	2		432.7.e.j.161.4		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
27.7.b.c.26.1	✓	4	3.2	odd	2	inner
27.7.b.c.26.4	yes	4	1.1	even	1	trivial
81.7.d.e.26.1		8	9.4	even	3
81.7.d.e.26.4		8	9.5	odd	6
81.7.d.e.53.1		8	9.2	odd	6
81.7.d.e.53.4		8	9.7	even	3
432.7.e.j.161.1		4	4.3	odd	2
432.7.e.j.161.4		4	12.11	even	2

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:	\( N \)	\(=\)	\( 27 = 3^{3} \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	27.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+14.1047i q^{2} -134.942 q^{4} -137.419i q^{5} -514.769 q^{7} -1000.62i q^{8} +O(q^{10})\)	\(q+14.1047i q^{2} -134.942 q^{4} -137.419i q^{5} -514.769 q^{7} -1000.62i q^{8} +1938.25 q^{10} +1218.26i q^{11} -170.463 q^{13} -7260.65i q^{14} +5477.09 q^{16} -1574.10i q^{17} -11289.1 q^{19} +18543.6i q^{20} -17183.2 q^{22} +10572.6i q^{23} -3258.91 q^{25} -2404.32i q^{26} +69464.0 q^{28} -8665.42i q^{29} -26209.1 q^{31} +13213.2i q^{32} +22202.2 q^{34} +70738.9i q^{35} +21866.9 q^{37} -159229. i q^{38} -137504. q^{40} +38166.6i q^{41} +23895.1 q^{43} -164395. i q^{44} -149124. q^{46} -26698.7i q^{47} +147338. q^{49} -45965.9i q^{50} +23002.6 q^{52} +213997. i q^{53} +167412. q^{55} +515086. i q^{56} +122223. q^{58} -163689. i q^{59} +111078. q^{61} -369671. i q^{62} +164166. q^{64} +23424.8i q^{65} -381035. q^{67} +212412. i q^{68} -997750. q^{70} +675048. i q^{71} -762939. q^{73} +308426. i q^{74} +1.52337e6 q^{76} -627123. i q^{77} +515708. q^{79} -752655. i q^{80} -538328. q^{82} -903773. i q^{83} -216311. q^{85} +337033. i q^{86} +1.21901e6 q^{88} -644278. i q^{89} +87748.8 q^{91} -1.42669e6i q^{92} +376577. q^{94} +1.55133e6i q^{95} -616470. q^{97} +2.07815e6i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 194 q^{4} - 676 q^{7}+O(q^{10}) \) 4 * q - 194 * q^4 - 676 * q^7	\( 4 q - 194 q^{4} - 676 q^{7} + 3258 q^{10} - 3448 q^{13} + 10498 q^{16} - 3664 q^{19} - 58014 q^{22} + 17392 q^{25} + 152342 q^{28} - 153244 q^{31} + 65988 q^{34} + 128960 q^{37} - 338058 q^{40} + 126008 q^{43} - 116568 q^{46} + 121872 q^{49} - 71884 q^{52} + 54180 q^{55} + 567036 q^{58} + 167696 q^{61} - 28994 q^{64} + 8 q^{67} - 2104830 q^{70} - 1881676 q^{73} + 3764384 q^{76} + 1188728 q^{79} - 1366344 q^{82} - 176472 q^{85} + 27342 q^{88} - 373736 q^{91} + 1381140 q^{94} + 975212 q^{97}+O(q^{100}) \) 4 * q - 194 * q^4 - 676 * q^7 + 3258 * q^10 - 3448 * q^13 + 10498 * q^16 - 3664 * q^19 - 58014 * q^22 + 17392 * q^25 + 152342 * q^28 - 153244 * q^31 + 65988 * q^34 + 128960 * q^37 - 338058 * q^40 + 126008 * q^43 - 116568 * q^46 + 121872 * q^49 - 71884 * q^52 + 54180 * q^55 + 567036 * q^58 + 167696 * q^61 - 28994 * q^64 + 8 * q^67 - 2104830 * q^70 - 1881676 * q^73 + 3764384 * q^76 + 1188728 * q^79 - 1366344 * q^82 - 176472 * q^85 + 27342 * q^88 - 373736 * q^91 + 1381140 * q^94 + 975212 * q^97

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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