LMFDB - Embedded newform 27.7.b.c.26.3

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			26.3
Root			$2.70156i$ of defining polynomial
Character	$\chi$	$=$	27.26
Dual form			27.7.b.c.26.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+5.10469i q^{2} +37.9422 q^{4} +60.5813i q^{5} +176.769 q^{7} +520.383i q^{8} +O(q^{10})$	\(q+5.10469i q^{2} +37.9422 q^{4} +60.5813i q^{5} +176.769 q^{7} +520.383i q^{8} -309.248 q^{10} +2316.26i q^{11} -1553.54 q^{13} +902.349i q^{14} -228.092 q^{16} -2114.10i q^{17} +9457.06 q^{19} +2298.58i q^{20} -11823.8 q^{22} -17795.4i q^{23} +11954.9 q^{25} -7930.32i q^{26} +6706.99 q^{28} -31597.4i q^{29} -50412.9 q^{31} +32140.2i q^{32} +10791.8 q^{34} +10708.9i q^{35} +42613.1 q^{37} +48275.3i q^{38} -31525.4 q^{40} +28374.6i q^{41} +39108.9 q^{43} +87884.0i q^{44} +90839.7 q^{46} -61510.7i q^{47} -86401.8 q^{49} +61026.1i q^{50} -58944.6 q^{52} -77764.6i q^{53} -140322. q^{55} +91987.4i q^{56} +161295. q^{58} -330837. i q^{59} -27229.7 q^{61} -257342. i q^{62} -178663. q^{64} -94115.2i q^{65} +381039. q^{67} -80213.5i q^{68} -54665.4 q^{70} +127596. i q^{71} -177899. q^{73} +217526. i q^{74} +358821. q^{76} +409443. i q^{77} +78656.2 q^{79} -13818.1i q^{80} -144844. q^{82} +118033. i q^{83} +128075. q^{85} +199639. i q^{86} -1.20534e6 q^{88} +1.12789e6i q^{89} -274617. q^{91} -675195. i q^{92} +313993. q^{94} +572921. i q^{95} +1.10408e6 q^{97} -441054. i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	5.10469i	0.638086i	0.947740	+	0.319043i	$0.103361\pi$
$2$	5.10469i	0.638086i	−0.947740	+	0.319043i	$0.896639\pi$
$3$	0	0
$3$	0	0
$4$	37.9422	0.592847
$5$	60.5813i	0.484650i	0.970195	+	0.242325i	$0.0779100\pi$
$5$	60.5813i	0.484650i	−0.970195	+	0.242325i	$0.922090\pi$
$6$	0	0
$7$	176.769	0.515361	0.257680	−	0.966230i	$-0.417042\pi$
$7$	176.769	0.515361	0.257680	+	0.966230i	$0.417042\pi$
$8$	520.383i	1.01637i
$9$	0	0
$10$	−309.248	−0.309248
$11$	2316.26i	1.74024i	0.492838	+	0.870121i	$0.335960\pi$
$11$	2316.26i	1.74024i	−0.492838	+	0.870121i	$0.664040\pi$
$12$	0	0
$13$	−1553.54	−0.707118	−0.353559	−	0.935412i	$-0.615029\pi$
$13$	−1553.54	−0.707118	−0.353559	+	0.935412i	$0.615029\pi$
$14$	902.349i	0.328844i
$15$	0	0
$16$	−228.092	−0.0556865
$17$	− 2114.10i	− 0.430307i	−0.976580	−	0.215154i	$-0.930975\pi$
$17$	− 2114.10i	− 0.430307i	0.976580	−	0.215154i	$-0.0690252\pi$
$18$	0	0
$19$	9457.06	1.37878	0.689391	−	0.724390i	$-0.257878\pi$
$19$	9457.06	1.37878	0.689391	+	0.724390i	$0.257878\pi$
$20$	2298.58i	0.287323i
$21$	0	0
$22$	−11823.8	−1.11042
$23$	− 17795.4i	− 1.46259i	−0.682060	−	0.731296i	$-0.738916\pi$
$23$	− 17795.4i	− 1.46259i	0.682060	−	0.731296i	$-0.261084\pi$
$24$	0	0
$25$	11954.9	0.765114
$26$	− 7930.32i	− 0.451202i
$27$	0	0
$28$	6706.99	0.305530
$29$	− 31597.4i	− 1.29556i	−0.761827	−	0.647780i	$-0.775698\pi$
$29$	− 31597.4i	− 1.29556i	0.761827	−	0.647780i	$-0.224302\pi$
$30$	0	0
$31$	−50412.9	−1.69222	−0.846110	−	0.533009i	$-0.821061\pi$
$31$	−50412.9	−1.69222	−0.846110	+	0.533009i	$0.821061\pi$
$32$	32140.2i	0.980840i
$33$	0	0
$34$	10791.8	0.274573
$35$	10708.9i	0.249770i
$36$	0	0
$37$	42613.1	0.841274	0.420637	−	0.907229i	$-0.361807\pi$
$37$	42613.1	0.841274	0.420637	+	0.907229i	$0.361807\pi$
$38$	48275.3i	0.879781i
$39$	0	0
$40$	−31525.4	−0.492585
$41$	28374.6i	0.411698i	0.978584	+	0.205849i	$0.0659956\pi$
$41$	28374.6i	0.411698i	−0.978584	+	0.205849i	$0.934004\pi$
$42$	0	0
$43$	39108.9	0.491893	0.245946	−	0.969283i	$-0.420901\pi$
$43$	39108.9	0.491893	0.245946	+	0.969283i	$0.420901\pi$
$44$	87884.0i	1.03170i
$45$	0	0
$46$	90839.7	0.933259
$47$	− 61510.7i	− 0.592458i	−0.955117	−	0.296229i	$-0.904271\pi$
$47$	− 61510.7i	− 0.592458i	0.955117	−	0.296229i	$-0.0957291\pi$
$48$	0	0
$49$	−86401.8	−0.734403
$50$	61026.1i	0.488209i
$51$	0	0
$52$	−58944.6	−0.419212
$53$	− 77764.6i	− 0.522341i	−0.965293	−	0.261171i	$-0.915892\pi$
$53$	− 77764.6i	− 0.522341i	0.965293	−	0.261171i	$-0.0841085\pi$
$54$	0	0
$55$	−140322.	−0.843408
$56$	91987.4i	0.523799i
$57$	0	0
$58$	161295.	0.826679
$59$	− 330837.i	− 1.61086i	−0.592690	−	0.805431i	$-0.701934\pi$
$59$	− 330837.i	− 1.61086i	0.592690	−	0.805431i	$-0.298066\pi$
$60$	0	0
$61$	−27229.7	−0.119965	−0.0599824	−	0.998199i	$-0.519104\pi$
$61$	−27229.7	−0.119965	−0.0599824	+	0.998199i	$0.519104\pi$
$62$	− 257342.i	− 1.07978i
$63$	0	0
$64$	−178663.	−0.681547
$65$	− 94115.2i	− 0.342705i
$66$	0	0
$67$	381039.	1.26691	0.633454	−	0.773780i	$-0.281637\pi$
$67$	381039.	1.26691	0.633454	+	0.773780i	$0.281637\pi$
$68$	− 80213.5i	− 0.255106i
$69$	0	0
$70$	−54665.4	−0.159374
$71$	127596.i	0.356503i	0.983985	+	0.178251i	$0.0570440\pi$
$71$	127596.i	0.356503i	−0.983985	+	0.178251i	$0.942956\pi$
$72$	0	0
$73$	−177899.	−0.457303	−0.228652	−	0.973508i	$-0.573432\pi$
$73$	−177899.	−0.457303	−0.228652	+	0.973508i	$0.573432\pi$
$74$	217526.i	0.536805i
$75$	0	0
$76$	358821.	0.817406
$77$	409443.i	0.896852i
$78$	0	0
$79$	78656.2	0.159533	0.0797667	−	0.996814i	$-0.474582\pi$
$79$	78656.2	0.159533	0.0797667	+	0.996814i	$0.474582\pi$
$80$	− 13818.1i	− 0.0269885i
$81$	0	0
$82$	−144844.	−0.262699
$83$	118033.i	0.206428i	0.994659	+	0.103214i	$0.0329127\pi$
$83$	118033.i	0.206428i	−0.994659	+	0.103214i	$0.967087\pi$
$84$	0	0
$85$	128075.	0.208548
$86$	199639.i	0.313870i
$87$	0	0
$88$	−1.20534e6	−1.76873
$89$	1.12789e6i	1.59992i	0.600054	+	0.799960i	$0.295146\pi$
$89$	1.12789e6i	1.59992i	−0.600054	+	0.799960i	$0.704854\pi$
$90$	0	0
$91$	−274617.	−0.364421
$92$	− 675195.i	− 0.867093i
$93$	0	0
$94$	313993.	0.378039
$95$	572921.i	0.668226i
$96$	0	0
$97$	1.10408e6	1.20972	0.604858	−	0.796333i	$-0.293230\pi$
$97$	1.10408e6	1.20972	0.604858	+	0.796333i	$0.293230\pi$
$98$	− 441054.i	− 0.468612i
$99$	0	0
$100$	453595.	0.453595
$101$	264427.i	0.256650i	0.991732	+	0.128325i	$0.0409601\pi$
$101$	264427.i	0.256650i	−0.991732	+	0.128325i	$0.959040\pi$
$102$	0	0
$103$	−706437.	−0.646490	−0.323245	−	0.946315i	$-0.604774\pi$
$103$	−706437.	−0.646490	−0.323245	+	0.946315i	$0.604774\pi$
$104$	− 808434.i	− 0.718695i
$105$	0	0
$106$	396964.	0.333298
$107$	− 1.18702e6i	− 0.968961i	−0.874802	−	0.484480i	$-0.839009\pi$
$107$	− 1.18702e6i	− 0.968961i	0.874802	−	0.484480i	$-0.160991\pi$
$108$	0	0
$109$	−276000.	−0.213122	−0.106561	−	0.994306i	$-0.533984\pi$
$109$	−276000.	−0.213122	−0.106561	+	0.994306i	$0.533984\pi$
$110$	− 716300.i	− 0.538167i
$111$	0	0
$112$	−40319.5	−0.0286986
$113$	− 637251.i	− 0.441647i	−0.975314	−	0.220823i	$-0.929126\pi$
$113$	− 637251.i	− 0.441647i	0.975314	−	0.220823i	$-0.0708744\pi$
$114$	0	0
$115$	1.07807e6	0.708845
$116$	− 1.19888e6i	− 0.768068i
$117$	0	0
$118$	1.68882e6	1.02787
$119$	− 373707.i	− 0.221763i
$120$	0	0
$121$	−3.59351e6	−2.02844
$122$	− 138999.i	− 0.0765479i
$123$	0	0
$124$	−1.91278e6	−1.00323
$125$	1.67083e6i	0.855463i
$126$	0	0
$127$	878767.	0.429005	0.214503	−	0.976723i	$-0.431187\pi$
$127$	878767.	0.429005	0.214503	+	0.976723i	$0.431187\pi$
$128$	1.14495e6i	0.545955i
$129$	0	0
$130$	480429.	0.218675
$131$	− 1.19392e6i	− 0.531084i	−0.964099	−	0.265542i	$-0.914449\pi$
$131$	− 1.19392e6i	− 0.531084i	0.964099	−	0.265542i	$-0.0855508\pi$
$132$	0	0
$133$	1.67171e6	0.710570
$134$	1.94509e6i	0.808396i
$135$	0	0
$136$	1.10014e6	0.437353
$137$	4.07989e6i	1.58667i	0.608784	+	0.793336i	$0.291657\pi$
$137$	4.07989e6i	1.58667i	−0.608784	+	0.793336i	$0.708343\pi$
$138$	0	0
$139$	−3.70694e6	−1.38029	−0.690146	−	0.723670i	$-0.742454\pi$
$139$	−3.70694e6	−1.38029	−0.690146	+	0.723670i	$0.742454\pi$
$140$	406318.i	0.148075i
$141$	0	0
$142$	−651339.	−0.227479
$143$	− 3.59840e6i	− 1.23056i
$144$	0	0
$145$	1.91421e6	0.627893
$146$	− 908117.i	− 0.291799i
$147$	0	0
$148$	1.61683e6	0.498746
$149$	5.61278e6i	1.69676i	0.529392	+	0.848378i	$0.322420\pi$
$149$	5.61278e6i	1.69676i	−0.529392	+	0.848378i	$0.677580\pi$
$150$	0	0
$151$	3.53119e6	1.02563	0.512815	−	0.858499i	$-0.328603\pi$
$151$	3.53119e6	1.02563	0.512815	+	0.858499i	$0.328603\pi$
$152$	4.92129e6i	1.40136i
$153$	0	0
$154$	−2.09008e6	−0.572269
$155$	− 3.05408e6i	− 0.820134i
$156$	0	0
$157$	4.27374e6	1.10436	0.552178	−	0.833726i	$-0.313797\pi$
$157$	4.27374e6	1.10436	0.552178	+	0.833726i	$0.313797\pi$
$158$	401515.i	0.101796i
$159$	0	0
$160$	−1.94709e6	−0.475364
$161$	− 3.14566e6i	− 0.753763i
$162$	0	0
$163$	−5.66276e6	−1.30757	−0.653786	−	0.756680i	$-0.726820\pi$
$163$	−5.66276e6	−1.30757	−0.653786	+	0.756680i	$0.726820\pi$
$164$	1.07660e6i	0.244074i
$165$	0	0
$166$	−602521.	−0.131719
$167$	− 7.40827e6i	− 1.59062i	−0.606200	−	0.795312i	$-0.707307\pi$
$167$	− 7.40827e6i	− 1.59062i	0.606200	−	0.795312i	$-0.292693\pi$
$168$	0	0
$169$	−2.41333e6	−0.499985
$170$	653782.i	0.133072i
$171$	0	0
$172$	1.48388e6	0.291617
$173$	− 7.36260e6i	− 1.42198i	−0.703204	−	0.710989i	$-0.748248\pi$
$173$	− 7.36260e6i	− 1.42198i	0.703204	−	0.710989i	$-0.251752\pi$
$174$	0	0
$175$	2.11325e6	0.394310
$176$	− 528321.i	− 0.0969080i
$177$	0	0
$178$	−5.75754e6	−1.02089
$179$	− 2.05402e6i	− 0.358134i	−0.983837	−	0.179067i	$-0.942692\pi$
$179$	− 2.05402e6i	− 0.358134i	0.983837	−	0.179067i	$-0.0573079\pi$
$180$	0	0
$181$	−3.17869e6	−0.536059	−0.268029	−	0.963411i	$-0.586372\pi$
$181$	−3.17869e6	−0.536059	−0.268029	+	0.963411i	$0.586372\pi$
$182$	− 1.40183e6i	− 0.232532i
$183$	0	0
$184$	9.26040e6	1.48654
$185$	2.58155e6i	0.407724i
$186$	0	0
$187$	4.89681e6	0.748839
$188$	− 2.33385e6i	− 0.351236i
$189$	0	0
$190$	−2.92458e6	−0.426386
$191$	− 2.46769e6i	− 0.354153i	−0.984197	−	0.177077i	$-0.943336\pi$
$191$	− 2.46769e6i	− 0.354153i	0.984197	−	0.177077i	$-0.0566640\pi$
$192$	0	0
$193$	2.43466e6	0.338662	0.169331	−	0.985559i	$-0.445839\pi$
$193$	2.43466e6	0.338662	0.169331	+	0.985559i	$0.445839\pi$
$194$	5.63596e6i	0.771903i
$195$	0	0
$196$	−3.27827e6	−0.435388
$197$	5.37024e6i	0.702417i	0.936297	+	0.351209i	$0.114229\pi$
$197$	5.37024e6i	0.702417i	−0.936297	+	0.351209i	$0.885771\pi$
$198$	0	0
$199$	2.22880e6	0.282821	0.141411	−	0.989951i	$-0.454836\pi$
$199$	2.22880e6	0.282821	0.141411	+	0.989951i	$0.454836\pi$
$200$	6.22113e6i	0.777641i
$201$	0	0
$202$	−1.34982e6	−0.163765
$203$	− 5.58544e6i	− 0.667681i
$204$	0	0
$205$	−1.71897e6	−0.199529
$206$	− 3.60614e6i	− 0.412516i
$207$	0	0
$208$	354349.	0.0393769
$209$	2.19050e7i	2.39941i
$210$	0	0
$211$	8.93725e6	0.951386	0.475693	−	0.879611i	$-0.342197\pi$
$211$	8.93725e6	0.951386	0.475693	+	0.879611i	$0.342197\pi$
$212$	− 2.95056e6i	− 0.309668i
$213$	0	0
$214$	6.05936e6	0.618280
$215$	2.36927e6i	0.238396i
$216$	0	0
$217$	−8.91142e6	−0.872103
$218$	− 1.40889e6i	− 0.135990i
$219$	0	0
$220$	−5.32413e6	−0.500012
$221$	3.28433e6i	0.304278i
$222$	0	0
$223$	−1.40543e7	−1.26734	−0.633670	−	0.773603i	$-0.718452\pi$
$223$	−1.40543e7	−1.26734	−0.633670	+	0.773603i	$0.718452\pi$
$224$	5.68138e6i	0.505486i
$225$	0	0
$226$	3.25297e6	0.281809
$227$	− 3.68417e6i	− 0.314965i	−0.987522	−	0.157482i	$-0.949662\pi$
$227$	− 3.68417e6i	− 0.314965i	0.987522	−	0.157482i	$-0.0503377\pi$
$228$	0	0
$229$	−1.49162e7	−1.24208	−0.621042	−	0.783777i	$-0.713290\pi$
$229$	−1.49162e7	−1.24208	−0.621042	+	0.783777i	$0.713290\pi$
$230$	5.50319e6i	0.452304i
$231$	0	0
$232$	1.64428e7	1.31677
$233$	5.69069e6i	0.449881i	0.974373	+	0.224940i	$0.0722187\pi$
$233$	5.69069e6i	0.449881i	−0.974373	+	0.224940i	$0.927781\pi$
$234$	0	0
$235$	3.72640e6	0.287135
$236$	− 1.25527e7i	− 0.954993i
$237$	0	0
$238$	1.90766e6	0.141504
$239$	6.37450e6i	0.466930i	0.972365	+	0.233465i	$0.0750065\pi$
$239$	6.37450e6i	0.466930i	−0.972365	+	0.233465i	$0.924993\pi$
$240$	0	0
$241$	8.33550e6	0.595498	0.297749	−	0.954644i	$-0.403764\pi$
$241$	8.33550e6	0.595498	0.297749	+	0.954644i	$0.403764\pi$
$242$	− 1.83437e7i	− 1.29432i
$243$	0	0
$244$	−1.03316e6	−0.0711207
$245$	− 5.23433e6i	− 0.355929i
$246$	0	0
$247$	−1.46919e7	−0.974961
$248$	− 2.62340e7i	− 1.71993i
$249$	0	0
$250$	−8.52904e6	−0.545859
$251$	− 3.97558e6i	− 0.251408i	−0.992068	−	0.125704i	$-0.959881\pi$
$251$	− 3.97558e6i	− 0.251408i	0.992068	−	0.125704i	$-0.0401190\pi$
$252$	0	0
$253$	4.12187e7	2.54526
$254$	4.48583e6i	0.273742i
$255$	0	0
$256$	−1.72791e7	−1.02991
$257$	− 4.71491e6i	− 0.277763i	−0.990309	−	0.138881i	$-0.955649\pi$
$257$	− 4.71491e6i	− 0.277763i	0.990309	−	0.138881i	$-0.0443507\pi$
$258$	0	0
$259$	7.53266e6	0.433560
$260$	− 3.57094e6i	− 0.203171i
$261$	0	0
$262$	6.09461e6	0.338877
$263$	− 2.55263e7i	− 1.40320i	−0.712570	−	0.701601i	$-0.752469\pi$
$263$	− 2.55263e7i	− 1.40320i	0.712570	−	0.701601i	$-0.247531\pi$
$264$	0	0
$265$	4.71107e6	0.253153
$266$	8.53357e6i	0.453404i
$267$	0	0
$268$	1.44575e7	0.751082
$269$	2.34673e7i	1.20561i	0.797888	+	0.602805i	$0.205950\pi$
$269$	2.34673e7i	1.20561i	−0.797888	+	0.602805i	$0.794050\pi$
$270$	0	0
$271$	−1.86835e7	−0.938750	−0.469375	−	0.882999i	$-0.655521\pi$
$271$	−1.86835e7	−0.938750	−0.469375	+	0.882999i	$0.655521\pi$
$272$	482209.i	0.0239623i
$273$	0	0
$274$	−2.08266e7	−1.01243
$275$	2.76907e7i	1.33148i
$276$	0	0
$277$	−3.67724e7	−1.73014	−0.865072	−	0.501647i	$-0.832727\pi$
$277$	−3.67724e7	−1.73014	−0.865072	+	0.501647i	$0.832727\pi$
$278$	− 1.89228e7i	− 0.880745i
$279$	0	0
$280$	−5.57271e6	−0.253859
$281$	6.77022e6i	0.305129i	0.988293	+	0.152565i	$0.0487532\pi$
$281$	6.77022e6i	0.305129i	−0.988293	+	0.152565i	$0.951247\pi$
$282$	0	0
$283$	9.96580e6	0.439696	0.219848	−	0.975534i	$-0.429444\pi$
$283$	9.96580e6	0.439696	0.219848	+	0.975534i	$0.429444\pi$
$284$	4.84128e6i	0.211351i
$285$	0	0
$286$	1.83687e7	0.785200
$287$	5.01575e6i	0.212173i
$288$	0	0
$289$	1.96682e7	0.814836
$290$	9.77145e6i	0.400650i
$291$	0	0
$292$	−6.74986e6	−0.271111
$293$	− 1.51644e7i	− 0.602869i	−0.953487	−	0.301434i	$-0.902535\pi$
$293$	− 1.51644e7i	− 0.602869i	0.953487	−	0.301434i	$-0.0974654\pi$
$294$	0	0
$295$	2.00425e7	0.780704
$296$	2.21751e7i	0.855048i
$297$	0	0
$298$	−2.86515e7	−1.08268
$299$	2.76458e7i	1.03422i
$300$	0	0
$301$	6.91323e6	0.253502
$302$	1.80256e7i	0.654440i
$303$	0	0
$304$	−2.15708e6	−0.0767795
$305$	− 1.64961e6i	− 0.0581410i
$306$	0	0
$307$	−1.38326e7	−0.478066	−0.239033	−	0.971011i	$-0.576830\pi$
$307$	−1.38326e7	−0.478066	−0.239033	+	0.971011i	$0.576830\pi$
$308$	1.55351e7i	0.531696i
$309$	0	0
$310$	1.55901e7	0.523316
$311$	− 1.65344e7i	− 0.549677i	−0.961490	−	0.274839i	$-0.911376\pi$
$311$	− 1.65344e7i	− 0.549677i	0.961490	−	0.274839i	$-0.0886244\pi$
$312$	0	0
$313$	−2.05488e7	−0.670120	−0.335060	−	0.942197i	$-0.608757\pi$
$313$	−2.05488e7	−0.670120	−0.335060	+	0.942197i	$0.608757\pi$
$314$	2.18161e7i	0.704674i
$315$	0	0
$316$	2.98439e6	0.0945788
$317$	− 4.26456e6i	− 0.133874i	−0.997757	−	0.0669370i	$-0.978677\pi$
$317$	− 4.26456e6i	− 0.133874i	0.997757	−	0.0669370i	$-0.0213226\pi$
$318$	0	0
$319$	7.31879e7	2.25459
$320$	− 1.08236e7i	− 0.330312i
$321$	0	0
$322$	1.60576e7	0.480965
$323$	− 1.99932e7i	− 0.593300i
$324$	0	0
$325$	−1.85724e7	−0.541026
$326$	− 2.89066e7i	− 0.834343i
$327$	0	0
$328$	−1.47657e7	−0.418439
$329$	− 1.08732e7i	− 0.305329i
$330$	0	0
$331$	−5.49369e7	−1.51489	−0.757443	−	0.652901i	$-0.773552\pi$
$331$	−5.49369e7	−1.51489	−0.757443	+	0.652901i	$0.773552\pi$
$332$	4.47843e6i	0.122380i
$333$	0	0
$334$	3.78169e7	1.01495
$335$	2.30838e7i	0.614007i
$336$	0	0
$337$	4.07383e6	0.106442	0.0532210	−	0.998583i	$-0.483051\pi$
$337$	4.07383e6	0.106442	0.0532210	+	0.998583i	$0.483051\pi$
$338$	− 1.23193e7i	− 0.319033i
$339$	0	0
$340$	4.85944e6	0.123637
$341$	− 1.16770e8i	− 2.94487i
$342$	0	0
$343$	−3.60698e7	−0.893843
$344$	2.03516e7i	0.499946i
$345$	0	0
$346$	3.75837e7	0.907343
$347$	− 3.15668e7i	− 0.755514i	−0.925905	−	0.377757i	$-0.876696\pi$
$347$	− 3.15668e7i	− 0.755514i	0.925905	−	0.377757i	$-0.123304\pi$
$348$	0	0
$349$	−3.12730e7	−0.735688	−0.367844	−	0.929887i	$-0.619904\pi$
$349$	−3.12730e7	−0.735688	−0.367844	+	0.929887i	$0.619904\pi$
$350$	1.07875e7i	0.251604i
$351$	0	0
$352$	−7.44451e7	−1.70690
$353$	− 6.66535e7i	− 1.51530i	−0.652661	−	0.757650i	$-0.726347\pi$
$353$	− 6.66535e7i	− 1.51530i	0.652661	−	0.757650i	$-0.273653\pi$
$354$	0	0
$355$	−7.72994e6	−0.172779
$356$	4.27947e7i	0.948507i
$357$	0	0
$358$	1.04851e7	0.228520
$359$	6.87890e7i	1.48674i	0.668879	+	0.743371i	$0.266775\pi$
$359$	6.87890e7i	1.48674i	−0.668879	+	0.743371i	$0.733225\pi$
$360$	0	0
$361$	4.23901e7	0.901038
$362$	− 1.62262e7i	− 0.342051i
$363$	0	0
$364$	−1.04196e7	−0.216045
$365$	− 1.07773e7i	− 0.221632i
$366$	0	0
$367$	3.46386e7	0.700749	0.350374	−	0.936610i	$-0.386054\pi$
$367$	3.46386e7	0.700749	0.350374	+	0.936610i	$0.386054\pi$
$368$	4.05898e6i	0.0814466i
$369$	0	0
$370$	−1.31780e7	−0.260163
$371$	− 1.37463e7i	− 0.269194i
$372$	0	0
$373$	3.42743e7	0.660453	0.330227	−	0.943902i	$-0.392875\pi$
$373$	3.42743e7	0.660453	0.330227	+	0.943902i	$0.392875\pi$
$374$	2.49967e7i	0.477823i
$375$	0	0
$376$	3.20091e7	0.602158
$377$	4.90878e7i	0.916114i
$378$	0	0
$379$	−1.29759e7	−0.238352	−0.119176	−	0.992873i	$-0.538025\pi$
$379$	−1.29759e7	−0.238352	−0.119176	+	0.992873i	$0.538025\pi$
$380$	2.17379e7i	0.396156i
$381$	0	0
$382$	1.25968e7	0.225980
$383$	3.88636e7i	0.691747i	0.938281	+	0.345873i	$0.112417\pi$
$383$	3.88636e7i	0.691747i	−0.938281	+	0.345873i	$0.887583\pi$
$384$	0	0
$385$	−2.48046e7	−0.434660
$386$	1.24282e7i	0.216095i
$387$	0	0
$388$	4.18910e7	0.717176
$389$	− 5.97724e6i	− 0.101543i	−0.998710	−	0.0507717i	$-0.983832\pi$
$389$	− 5.97724e6i	− 0.101543i	0.998710	−	0.0507717i	$-0.0161681\pi$
$390$	0	0
$391$	−3.76212e7	−0.629364
$392$	− 4.49620e7i	− 0.746428i
$393$	0	0
$394$	−2.74134e7	−0.448203
$395$	4.76509e6i	0.0773179i
$396$	0	0
$397$	2.49239e7	0.398331	0.199166	−	0.979966i	$-0.436177\pi$
$397$	2.49239e7	0.398331	0.199166	+	0.979966i	$0.436177\pi$
$398$	1.13773e7i	0.180464i
$399$	0	0
$400$	−2.72682e6	−0.0426065
$401$	9.45291e7i	1.46599i	0.680232	+	0.732997i	$0.261879\pi$
$401$	9.45291e7i	1.46599i	−0.680232	+	0.732997i	$0.738121\pi$
$402$	0	0
$403$	7.83183e7	1.19660
$404$	1.00329e7i	0.152154i
$405$	0	0
$406$	2.85119e7	0.426038
$407$	9.87030e7i	1.46402i
$408$	0	0
$409$	−9.50341e7	−1.38902	−0.694512	−	0.719481i	$-0.744380\pi$
$409$	−9.50341e7	−1.38902	−0.694512	+	0.719481i	$0.744380\pi$
$410$	− 8.77481e6i	− 0.127317i
$411$	0	0
$412$	−2.68038e7	−0.383269
$413$	− 5.84816e7i	− 0.830174i
$414$	0	0
$415$	−7.15058e6	−0.100045
$416$	− 4.99309e7i	− 0.693569i
$417$	0	0
$418$	−1.11818e8	−1.53103
$419$	5.28519e7i	0.718486i	0.933244	+	0.359243i	$0.116965\pi$
$419$	5.28519e7i	0.718486i	−0.933244	+	0.359243i	$0.883035\pi$
$420$	0	0
$421$	−9.49015e6	−0.127182	−0.0635911	−	0.997976i	$-0.520255\pi$
$421$	−9.49015e6	−0.127182	−0.0635911	+	0.997976i	$0.520255\pi$
$422$	4.56219e7i	0.607066i
$423$	0	0
$424$	4.04673e7	0.530893
$425$	− 2.52739e7i	− 0.329234i
$426$	0	0
$427$	−4.81337e6	−0.0618252
$428$	− 4.50381e7i	− 0.574445i
$429$	0	0
$430$	−1.20944e7	−0.152117
$431$	− 4.75802e7i	− 0.594284i	−0.954833	−	0.297142i	$-0.903967\pi$
$431$	− 4.75802e7i	− 0.594284i	0.954833	−	0.297142i	$-0.0960335\pi$
$432$	0	0
$433$	1.15820e8	1.42666	0.713328	−	0.700830i	$-0.247187\pi$
$433$	1.15820e8	1.42666	0.713328	+	0.700830i	$0.247187\pi$
$434$	− 4.54900e7i	− 0.556477i
$435$	0	0
$436$	−1.04720e7	−0.126349
$437$	− 1.68292e8i	− 2.01660i
$438$	0	0
$439$	6.60638e7	0.780854	0.390427	−	0.920634i	$-0.372327\pi$
$439$	6.60638e7	0.780854	0.390427	+	0.920634i	$0.372327\pi$
$440$	− 7.30212e7i	− 0.857217i
$441$	0	0
$442$	−1.67655e7	−0.194155
$443$	1.07267e8i	1.23383i	0.787028	+	0.616917i	$0.211618\pi$
$443$	1.07267e8i	1.23383i	−0.787028	+	0.616917i	$0.788382\pi$
$444$	0	0
$445$	−6.83292e7	−0.775401
$446$	− 7.17426e7i	− 0.808672i
$447$	0	0
$448$	−3.15821e7	−0.351242
$449$	1.85732e7i	0.205186i	0.994723	+	0.102593i	$0.0327140\pi$
$449$	1.85732e7i	0.205186i	−0.994723	+	0.102593i	$0.967286\pi$
$450$	0	0
$451$	−6.57231e7	−0.716454
$452$	− 2.41787e7i	− 0.261829i
$453$	0	0
$454$	1.88065e7	0.200974
$455$	− 1.66366e7i	− 0.176616i
$456$	0	0
$457$	6.95969e7	0.729191	0.364596	−	0.931166i	$-0.381207\pi$
$457$	6.95969e7	0.729191	0.364596	+	0.931166i	$0.381207\pi$
$458$	− 7.61424e7i	− 0.792556i
$459$	0	0
$460$	4.09041e7	0.420237
$461$	− 2.56902e7i	− 0.262219i	−0.991368	−	0.131110i	$-0.958146\pi$
$461$	− 2.56902e7i	− 0.262219i	0.991368	−	0.131110i	$-0.0418540\pi$
$462$	0	0
$463$	−9.56494e6	−0.0963695	−0.0481847	−	0.998838i	$-0.515344\pi$
$463$	−9.56494e6	−0.0963695	−0.0481847	+	0.998838i	$0.515344\pi$
$464$	7.20711e6i	0.0721452i
$465$	0	0
$466$	−2.90492e7	−0.287062
$467$	7.22148e7i	0.709048i	0.935047	+	0.354524i	$0.115357\pi$
$467$	7.22148e7i	0.709048i	−0.935047	+	0.354524i	$0.884643\pi$
$468$	0	0
$469$	6.73558e7	0.652915
$470$	1.90221e7i	0.183216i
$471$	0	0
$472$	1.72162e8	1.63724
$473$	9.05865e7i	0.856012i
$474$	0	0
$475$	1.13058e8	1.05493
$476$	− 1.41792e7i	− 0.131472i
$477$	0	0
$478$	−3.25398e7	−0.297942
$479$	− 8.04747e7i	− 0.732239i	−0.930568	−	0.366120i	$-0.880686\pi$
$479$	− 8.04747e7i	− 0.732239i	0.930568	−	0.366120i	$-0.119314\pi$
$480$	0	0
$481$	−6.62010e7	−0.594880
$482$	4.25501e7i	0.379979i
$483$	0	0
$484$	−1.36346e8	−1.20256
$485$	6.68863e7i	0.586289i
$486$	0	0
$487$	−2.13387e8	−1.84748	−0.923742	−	0.383015i	$-0.874886\pi$
$487$	−2.13387e8	−1.84748	−0.923742	+	0.383015i	$0.874886\pi$
$488$	− 1.41699e7i	− 0.121929i
$489$	0	0
$490$	2.67196e7	0.227113
$491$	1.18371e8i	1.00000i	0.866025	+	0.500001i	$0.166667\pi$
$491$	1.18371e8i	1.00000i	−0.866025	+	0.500001i	$0.833333\pi$
$492$	0	0
$493$	−6.68001e7	−0.557489
$494$	− 7.49975e7i	− 0.622109i
$495$	0	0
$496$	1.14988e7	0.0942337
$497$	2.25550e7i	0.183727i
$498$	0	0
$499$	991441.	0.00797931	0.00398965	−	0.999992i	$-0.498730\pi$
$499$	991441.	0.00797931	0.00398965	+	0.999992i	$0.498730\pi$
$500$	6.33948e7i	0.507158i
$501$	0	0
$502$	2.02941e7	0.160420
$503$	1.83706e8i	1.44351i	0.692150	+	0.721753i	$0.256663\pi$
$503$	1.83706e8i	1.44351i	−0.692150	+	0.721753i	$0.743337\pi$
$504$	0	0
$505$	−1.60193e7	−0.124385
$506$	2.10409e8i	1.62410i
$507$	0	0
$508$	3.33423e7	0.254334
$509$	− 1.79117e8i	− 1.35826i	−0.734017	−	0.679131i	$-0.762357\pi$
$509$	− 1.79117e8i	− 1.35826i	0.734017	−	0.679131i	$-0.237643\pi$
$510$	0	0
$511$	−3.14469e7	−0.235676
$512$	− 1.49274e7i	− 0.111218i
$513$	0	0
$514$	2.40681e7	0.177236
$515$	− 4.27968e7i	− 0.313321i
$516$	0	0
$517$	1.42475e8	1.03102
$518$	3.84518e7i	0.276648i
$519$	0	0
$520$	4.89760e7	0.348316
$521$	6.66586e7i	0.471349i	0.971832	+	0.235675i	$0.0757300\pi$
$521$	6.66586e7i	0.471349i	−0.971832	+	0.235675i	$0.924270\pi$
$522$	0	0
$523$	−1.59361e8	−1.11398	−0.556991	−	0.830519i	$-0.688044\pi$
$523$	−1.59361e8	−1.11398	−0.556991	+	0.830519i	$0.688044\pi$
$524$	− 4.53001e7i	− 0.314851i
$525$	0	0
$526$	1.30304e8	0.895363
$527$	1.06578e8i	0.728174i
$528$	0	0
$529$	−1.68639e8	−1.13918
$530$	2.40486e7i	0.161533i
$531$	0	0
$532$	6.34284e7	0.421259
$533$	− 4.40811e7i	− 0.291119i
$534$	0	0
$535$	7.19111e7	0.469607
$536$	1.98286e8i	1.28765i
$537$	0	0
$538$	−1.19793e8	−0.769283
$539$	− 2.00129e8i	− 1.27804i
$540$	0	0
$541$	1.51696e8	0.958040	0.479020	−	0.877804i	$-0.340992\pi$
$541$	1.51696e8	0.958040	0.479020	+	0.877804i	$0.340992\pi$
$542$	− 9.53734e7i	− 0.599003i
$543$	0	0
$544$	6.79475e7	0.422063
$545$	− 1.67204e7i	− 0.103290i
$546$	0	0
$547$	2.50093e8	1.52806	0.764030	−	0.645181i	$-0.223218\pi$
$547$	2.50093e8	1.52806	0.764030	+	0.645181i	$0.223218\pi$
$548$	1.54800e8i	0.940653i
$549$	0	0
$550$	−1.41352e8	−0.849601
$551$	− 2.98819e8i	− 1.78629i
$552$	0	0
$553$	1.39040e7	0.0822172
$554$	− 1.87711e8i	− 1.10398i
$555$	0	0
$556$	−1.40649e8	−0.818301
$557$	− 1.71192e8i	− 0.990644i	−0.868709	−	0.495322i	$-0.835050\pi$
$557$	− 1.71192e8i	− 0.990644i	0.868709	−	0.495322i	$-0.164950\pi$
$558$	0	0
$559$	−6.07572e7	−0.347826
$560$	− 2.44261e6i	− 0.0139088i
$561$	0	0
$562$	−3.45599e7	−0.194699
$563$	− 2.68409e8i	− 1.50408i	−0.659115	−	0.752042i	$-0.729069\pi$
$563$	− 2.68409e8i	− 1.50408i	0.659115	−	0.752042i	$-0.270931\pi$
$564$	0	0
$565$	3.86055e7	0.214044
$566$	5.08723e7i	0.280564i
$567$	0	0
$568$	−6.63989e7	−0.362340
$569$	2.44299e8i	1.32612i	0.748564	+	0.663062i	$0.230743\pi$
$569$	2.44299e8i	1.32612i	−0.748564	+	0.663062i	$0.769257\pi$
$570$	0	0
$571$	1.49417e8	0.802587	0.401293	−	0.915950i	$-0.368561\pi$
$571$	1.49417e8	0.802587	0.401293	+	0.915950i	$0.368561\pi$
$572$	− 1.36531e8i	− 0.729531i
$573$	0	0
$574$	−2.56038e7	−0.135385
$575$	− 2.12742e8i	− 1.11905i
$576$	0	0
$577$	−1.88650e8	−0.982040	−0.491020	−	0.871148i	$-0.663376\pi$
$577$	−1.88650e8	−0.982040	−0.491020	+	0.871148i	$0.663376\pi$
$578$	1.00400e8i	0.519935i
$579$	0	0
$580$	7.26294e7	0.372244
$581$	2.08645e7i	0.106385i
$582$	0	0
$583$	1.80123e8	0.909000
$584$	− 9.25754e7i	− 0.464790i
$585$	0	0
$586$	7.74096e7	0.384682
$587$	7.92716e7i	0.391925i	0.980611	+	0.195963i	$0.0627832\pi$
$587$	7.92716e7i	0.391925i	−0.980611	+	0.195963i	$0.937217\pi$
$588$	0	0
$589$	−4.76758e8	−2.33320
$590$	1.02311e8i	0.498156i
$591$	0	0
$592$	−9.71969e6	−0.0468476
$593$	1.52784e8i	0.732678i	0.930481	+	0.366339i	$0.119389\pi$
$593$	1.52784e8i	0.732678i	−0.930481	+	0.366339i	$0.880611\pi$
$594$	0	0
$595$	2.26396e7	0.107478
$596$	2.12961e8i	1.00592i
$597$	0	0
$598$	−1.41123e8	−0.659924
$599$	− 2.72353e8i	− 1.26722i	−0.773654	−	0.633609i	$-0.781573\pi$
$599$	− 2.72353e8i	− 1.26722i	0.773654	−	0.633609i	$-0.218427\pi$
$600$	0	0
$601$	−3.56556e7	−0.164250	−0.0821248	−	0.996622i	$-0.526171\pi$
$601$	−3.56556e7	−0.164250	−0.0821248	+	0.996622i	$0.526171\pi$
$602$	3.52899e7i	0.161756i
$603$	0	0
$604$	1.33981e8	0.608041
$605$	− 2.17699e8i	− 0.983085i
$606$	0	0
$607$	7.72185e7	0.345267	0.172634	−	0.984986i	$-0.444772\pi$
$607$	7.72185e7	0.345267	0.172634	+	0.984986i	$0.444772\pi$
$608$	3.03952e8i	1.35236i
$609$	0	0
$610$	8.42075e6	0.0370989
$611$	9.55592e7i	0.418937i
$612$	0	0
$613$	4.11015e8	1.78433	0.892167	−	0.451706i	$-0.149184\pi$
$613$	4.11015e8	1.78433	0.892167	+	0.451706i	$0.149184\pi$
$614$	− 7.06110e7i	− 0.305047i
$615$	0	0
$616$	−2.13067e8	−0.911536
$617$	3.50920e8i	1.49401i	0.664821	+	0.747003i	$0.268508\pi$
$617$	3.50920e8i	1.49401i	−0.664821	+	0.747003i	$0.731492\pi$
$618$	0	0
$619$	−1.48013e8	−0.624062	−0.312031	−	0.950072i	$-0.601009\pi$
$619$	−1.48013e8	−0.624062	−0.312031	+	0.950072i	$0.601009\pi$
$620$	− 1.15878e8i	− 0.486214i
$621$	0	0
$622$	8.44030e7	0.350741
$623$	1.99376e8i	0.824536i
$624$	0	0
$625$	8.55748e7	0.350514
$626$	− 1.04895e8i	− 0.427594i
$627$	0	0
$628$	1.62155e8	0.654714
$629$	− 9.00883e7i	− 0.362006i
$630$	0	0
$631$	−1.37842e8	−0.548647	−0.274323	−	0.961638i	$-0.588454\pi$
$631$	−1.37842e8	−0.548647	−0.274323	+	0.961638i	$0.588454\pi$
$632$	4.09313e7i	0.162145i
$633$	0	0
$634$	2.17692e7	0.0854231
$635$	5.32368e7i	0.207917i
$636$	0	0
$637$	1.34228e8	0.519310
$638$	3.73601e8i	1.43862i
$639$	0	0
$640$	−6.93625e7	−0.264597
$641$	2.80331e8i	1.06438i	0.846625	+	0.532190i	$0.178631\pi$
$641$	2.80331e8i	1.06438i	−0.846625	+	0.532190i	$0.821369\pi$
$642$	0	0
$643$	−2.70884e8	−1.01894	−0.509472	−	0.860487i	$-0.670159\pi$
$643$	−2.70884e8	−1.01894	−0.509472	+	0.860487i	$0.670159\pi$
$644$	− 1.19353e8i	− 0.446866i
$645$	0	0
$646$	1.02059e8	0.378576
$647$	1.28121e8i	0.473052i	0.971625	+	0.236526i	$0.0760088\pi$
$647$	1.28121e8i	0.473052i	−0.971625	+	0.236526i	$0.923991\pi$
$648$	0	0
$649$	7.66305e8	2.80329
$650$	− 9.48063e7i	− 0.345221i
$651$	0	0
$652$	−2.14858e8	−0.775189
$653$	3.02662e8i	1.08697i	0.839419	+	0.543485i	$0.182896\pi$
$653$	3.02662e8i	1.08697i	−0.839419	+	0.543485i	$0.817104\pi$
$654$	0	0
$655$	7.23294e7	0.257390
$656$	− 6.47202e6i	− 0.0229260i
$657$	0	0
$658$	5.55041e7	0.194826
$659$	− 2.43959e8i	− 0.852434i	−0.904621	−	0.426217i	$-0.859846\pi$
$659$	− 2.43959e8i	− 0.852434i	0.904621	−	0.426217i	$-0.140154\pi$
$660$	0	0
$661$	−2.45903e8	−0.851452	−0.425726	−	0.904852i	$-0.639981\pi$
$661$	−2.45903e8	−0.851452	−0.425726	+	0.904852i	$0.639981\pi$
$662$	− 2.80435e8i	− 0.966627i
$663$	0	0
$664$	−6.14223e7	−0.209808
$665$	1.01274e8i	0.344378i
$666$	0	0
$667$	−5.62288e8	−1.89488
$668$	− 2.81086e8i	− 0.942996i
$669$	0	0
$670$	−1.17836e8	−0.391789
$671$	− 6.30712e7i	− 0.208768i
$672$	0	0
$673$	−4.47762e8	−1.46893	−0.734466	−	0.678645i	$-0.762567\pi$
$673$	−4.47762e8	−1.46893	−0.734466	+	0.678645i	$0.762567\pi$
$674$	2.07956e7i	0.0679192i
$675$	0	0
$676$	−9.15670e7	−0.296414
$677$	− 1.32514e8i	− 0.427067i	−0.976936	−	0.213533i	$-0.931503\pi$
$677$	− 1.32514e8i	− 0.427067i	0.976936	−	0.213533i	$-0.0684972\pi$
$678$	0	0
$679$	1.95166e8	0.623440
$680$	6.66479e7i	0.211963i
$681$	0	0
$682$	5.96072e8	1.87908
$683$	− 2.40688e8i	− 0.755428i	−0.925922	−	0.377714i	$-0.876710\pi$
$683$	− 2.40688e8i	− 0.755428i	0.925922	−	0.377714i	$-0.123290\pi$
$684$	0	0
$685$	−2.47165e8	−0.768980
$686$	− 1.84125e8i	− 0.570349i
$687$	0	0
$688$	−8.92042e6	−0.0273918
$689$	1.20810e8i	0.369357i
$690$	0	0
$691$	−6.01908e7	−0.182430	−0.0912149	−	0.995831i	$-0.529075\pi$
$691$	−6.01908e7	−0.182430	−0.0912149	+	0.995831i	$0.529075\pi$
$692$	− 2.79353e8i	− 0.843014i
$693$	0	0
$694$	1.61139e8	0.482083
$695$	− 2.24571e8i	− 0.668959i
$696$	0	0
$697$	5.99868e7	0.177157
$698$	− 1.59639e8i	− 0.469432i
$699$	0	0
$700$	8.01815e7	0.233765
$701$	− 1.85129e8i	− 0.537427i	−0.963220	−	0.268714i	$-0.913401\pi$
$701$	− 1.85129e8i	− 0.537427i	0.963220	−	0.268714i	$-0.0865986\pi$
$702$	0	0
$703$	4.02994e8	1.15993
$704$	− 4.13831e8i	− 1.18606i
$705$	0	0
$706$	3.40245e8	0.966892
$707$	4.67424e7i	0.132267i
$708$	0	0
$709$	−1.71954e8	−0.482473	−0.241237	−	0.970466i	$-0.577553\pi$
$709$	−1.71954e8	−0.482473	−0.241237	+	0.970466i	$0.577553\pi$
$710$	− 3.94589e7i	− 0.110248i
$711$	0	0
$712$	−5.86936e8	−1.62611
$713$	8.97116e8i	2.47503i
$714$	0	0
$715$	2.17996e8	0.596389
$716$	− 7.79339e7i	− 0.212318i
$717$	0	0
$718$	−3.51146e8	−0.948670
$719$	− 3.35794e8i	− 0.903414i	−0.892166	−	0.451707i	$-0.850815\pi$
$719$	− 3.35794e8i	− 0.903414i	0.892166	−	0.451707i	$-0.149185\pi$
$720$	0	0
$721$	−1.24876e8	−0.333175
$722$	2.16388e8i	0.574940i
$723$	0	0
$724$	−1.20606e8	−0.317801
$725$	− 3.77744e8i	− 0.991252i
$726$	0	0
$727$	−1.59856e8	−0.416032	−0.208016	−	0.978125i	$-0.566701\pi$
$727$	−1.59856e8	−0.416032	−0.208016	+	0.978125i	$0.566701\pi$
$728$	− 1.42906e8i	− 0.370387i
$729$	0	0
$730$	5.50149e7	0.141420
$731$	− 8.26801e7i	− 0.211665i
$732$	0	0
$733$	6.79164e8	1.72450	0.862249	−	0.506485i	$-0.169055\pi$
$733$	6.79164e8	1.72450	0.862249	+	0.506485i	$0.169055\pi$
$734$	1.76819e8i	0.447138i
$735$	0	0
$736$	5.71946e8	1.43457
$737$	8.82587e8i	2.20473i
$738$	0	0
$739$	2.06184e8	0.510883	0.255442	−	0.966824i	$-0.417779\pi$
$739$	2.06184e8	0.510883	0.255442	+	0.966824i	$0.417779\pi$
$740$	9.79497e7i	0.241717i
$741$	0	0
$742$	7.01708e7	0.171769
$743$	1.00505e8i	0.245031i	0.992467	+	0.122516i	$0.0390962\pi$
$743$	1.00505e8i	0.245031i	−0.992467	+	0.122516i	$0.960904\pi$
$744$	0	0
$745$	−3.40029e8	−0.822333
$746$	1.74960e8i	0.421426i
$747$	0	0
$748$	1.85796e8	0.443947
$749$	− 2.09828e8i	− 0.499364i
$750$	0	0
$751$	7.81034e7	0.184395	0.0921977	−	0.995741i	$-0.470611\pi$
$751$	7.81034e7	0.184395	0.0921977	+	0.995741i	$0.470611\pi$
$752$	1.40301e7i	0.0329919i
$753$	0	0
$754$	−2.50578e8	−0.584559
$755$	2.13924e8i	0.497072i
$756$	0	0
$757$	−4.11790e8	−0.949266	−0.474633	−	0.880184i	$-0.657419\pi$
$757$	−4.11790e8	−0.949266	−0.474633	+	0.880184i	$0.657419\pi$
$758$	− 6.62378e7i	− 0.152089i
$759$	0	0
$760$	−2.98138e8	−0.679167
$761$	− 3.07699e7i	− 0.0698187i	−0.999390	−	0.0349094i	$-0.988886\pi$
$761$	− 3.07699e7i	− 0.0698187i	0.999390	−	0.0349094i	$-0.0111143\pi$
$762$	0	0
$763$	−4.87881e7	−0.109835
$764$	− 9.36297e7i	− 0.209959i
$765$	0	0
$766$	−1.98387e8	−0.441394
$767$	5.13968e8i	1.13907i
$768$	0	0
$769$	4.01203e8	0.882237	0.441119	−	0.897449i	$-0.354582\pi$
$769$	4.01203e8	0.882237	0.441119	+	0.897449i	$0.354582\pi$
$770$	− 1.26619e8i	− 0.277350i
$771$	0	0
$772$	9.23763e7	0.200774
$773$	− 5.96520e7i	− 0.129148i	−0.997913	−	0.0645739i	$-0.979431\pi$
$773$	− 5.96520e7i	− 0.129148i	0.997913	−	0.0645739i	$-0.0205688\pi$
$774$	0	0
$775$	−6.02682e8	−1.29474
$776$	5.74542e8i	1.22952i
$777$	0	0
$778$	3.05119e7	0.0647934
$779$	2.68341e8i	0.567641i
$780$	0	0
$781$	−2.95546e8	−0.620401
$782$	− 1.92044e8i	− 0.401588i
$783$	0	0
$784$	1.97076e7	0.0408963
$785$	2.58909e8i	0.535227i
$786$	0	0
$787$	4.58088e8	0.939777	0.469889	−	0.882726i	$-0.344294\pi$
$787$	4.58088e8	0.939777	0.469889	+	0.882726i	$0.344294\pi$
$788$	2.03759e8i	0.416426i
$789$	0	0
$790$	−2.43243e7	−0.0493354
$791$	− 1.12646e8i	− 0.227607i
$792$	0	0
$793$	4.23024e7	0.0848293
$794$	1.27229e8i	0.254169i
$795$	0	0
$796$	8.45656e7	0.167670
$797$	− 5.83337e7i	− 0.115224i	−0.998339	−	0.0576122i	$-0.981651\pi$
$797$	− 5.83337e7i	− 0.115224i	0.998339	−	0.0576122i	$-0.0183487\pi$
$798$	0	0
$799$	−1.30040e8	−0.254939
$800$	3.84233e8i	0.750455i
$801$	0	0
$802$	−4.82541e8	−0.935430
$803$	− 4.12060e8i	− 0.795818i
$804$	0	0
$805$	1.90568e8	0.365311
$806$	3.99791e8i	0.763532i
$807$	0	0
$808$	−1.37603e8	−0.260852
$809$	− 1.96748e7i	− 0.0371591i	−0.999827	−	0.0185796i	$-0.994086\pi$
$809$	− 1.96748e7i	− 0.0371591i	0.999827	−	0.0185796i	$-0.00591440\pi$
$810$	0	0
$811$	6.36063e8	1.19244	0.596221	−	0.802820i	$-0.296668\pi$
$811$	6.36063e8	1.19244	0.596221	+	0.802820i	$0.296668\pi$
$812$	− 2.11924e8i	− 0.395832i
$813$	0	0
$814$	−5.03848e8	−0.934171
$815$	− 3.43057e8i	− 0.633715i
$816$	0	0
$817$	3.69855e8	0.678212
$818$	− 4.85119e8i	− 0.886316i
$819$	0	0
$820$	−6.52215e7	−0.118290
$821$	− 9.87886e8i	− 1.78516i	−0.450888	−	0.892581i	$-0.648893\pi$
$821$	− 9.87886e8i	− 1.78516i	0.450888	−	0.892581i	$-0.351107\pi$
$822$	0	0
$823$	1.39368e7	0.0250014	0.0125007	−	0.999922i	$-0.496021\pi$
$823$	1.39368e7	0.0250014	0.0125007	+	0.999922i	$0.496021\pi$
$824$	− 3.67618e8i	− 0.657075i
$825$	0	0
$826$	2.98530e8	0.529723
$827$	− 7.89957e8i	− 1.39665i	−0.715782	−	0.698324i	$-0.753929\pi$
$827$	− 7.89957e8i	− 1.39665i	0.715782	−	0.698324i	$-0.246071\pi$
$828$	0	0
$829$	6.29378e8	1.10471	0.552355	−	0.833609i	$-0.313729\pi$
$829$	6.29378e8	1.10471	0.552355	+	0.833609i	$0.313729\pi$
$830$	− 3.65015e7i	− 0.0638375i
$831$	0	0
$832$	2.77560e8	0.481934
$833$	1.82662e8i	0.316019i
$834$	0	0
$835$	4.48802e8	0.770896
$836$	8.31125e8i	1.42248i
$837$	0	0
$838$	−2.69792e8	−0.458456
$839$	− 2.67487e8i	− 0.452915i	−0.974021	−	0.226458i	$-0.927286\pi$
$839$	− 2.67487e8i	− 0.452915i	0.974021	−	0.226458i	$-0.0727145\pi$
$840$	0	0
$841$	−4.03574e8	−0.678477
$842$	− 4.84442e7i	− 0.0811532i
$843$	0	0
$844$	3.39099e8	0.564026
$845$	− 1.46203e8i	− 0.242318i
$846$	0	0
$847$	−6.35220e8	−1.04538
$848$	1.77375e7i	0.0290873i
$849$	0	0
$850$	1.29015e8	0.210080
$851$	− 7.58315e8i	− 1.23044i
$852$	0	0
$853$	−4.90055e8	−0.789582	−0.394791	−	0.918771i	$-0.629183\pi$
$853$	−4.90055e8	−0.789582	−0.394791	+	0.918771i	$0.629183\pi$
$854$	− 2.45707e7i	− 0.0394498i
$855$	0	0
$856$	6.17704e8	0.984825
$857$	− 8.18399e8i	− 1.30024i	−0.759833	−	0.650119i	$-0.774719\pi$
$857$	− 8.18399e8i	− 1.30024i	0.759833	−	0.650119i	$-0.225281\pi$
$858$	0	0
$859$	−9.34404e8	−1.47420	−0.737098	−	0.675786i	$-0.763804\pi$
$859$	−9.34404e8	−1.47420	−0.737098	+	0.675786i	$0.763804\pi$
$860$	8.98951e7i	0.141332i
$861$	0	0
$862$	2.42882e8	0.379204
$863$	2.86507e8i	0.445762i	0.974846	+	0.222881i	$0.0715462\pi$
$863$	2.86507e8i	0.445762i	−0.974846	+	0.222881i	$0.928454\pi$
$864$	0	0
$865$	4.46035e8	0.689161
$866$	5.91224e8i	0.910329i
$867$	0	0
$868$	−3.38119e8	−0.517023
$869$	1.82188e8i	0.277627i
$870$	0	0
$871$	−5.91959e8	−0.895853
$872$	− 1.43625e8i	− 0.216612i
$873$	0	0
$874$	8.59077e8	1.28676
$875$	2.95350e8i	0.440872i
$876$	0	0
$877$	−9.66122e8	−1.43230	−0.716149	−	0.697947i	$-0.754097\pi$
$877$	−9.66122e8	−1.43230	−0.716149	+	0.697947i	$0.754097\pi$
$878$	3.37235e8i	0.498252i
$879$	0	0
$880$	3.20063e7	0.0469665
$881$	− 3.33017e8i	− 0.487011i	−0.969900	−	0.243505i	$-0.921703\pi$
$881$	− 3.33017e8i	− 0.487011i	0.969900	−	0.243505i	$-0.0782973\pi$
$882$	0	0
$883$	5.33713e8	0.775221	0.387610	−	0.921823i	$-0.373301\pi$
$883$	5.33713e8	0.775221	0.387610	+	0.921823i	$0.373301\pi$
$884$	1.24615e8i	0.180390i
$885$	0	0
$886$	−5.47566e8	−0.787292
$887$	6.17923e8i	0.885449i	0.896658	+	0.442724i	$0.145988\pi$
$887$	6.17923e8i	0.885449i	−0.896658	+	0.442724i	$0.854012\pi$
$888$	0	0
$889$	1.55338e8	0.221092
$890$	− 3.48799e8i	− 0.494772i
$891$	0	0
$892$	−5.33249e8	−0.751339
$893$	− 5.81711e8i	− 0.816869i
$894$	0	0
$895$	1.24435e8	0.173570
$896$	2.02391e8i	0.281364i
$897$	0	0
$898$	−9.48105e7	−0.130926
$899$	1.59292e9i	2.19237i
$900$	0	0
$901$	−1.64402e8	−0.224767
$902$	− 3.35496e8i	− 0.457159i
$903$	0	0
$904$	3.31614e8	0.448878
$905$	− 1.92569e8i	− 0.259801i
$906$	0	0
$907$	7.78999e8	1.04403	0.522017	−	0.852935i	$-0.325180\pi$
$907$	7.78999e8	1.04403	0.522017	+	0.852935i	$0.325180\pi$
$908$	− 1.39785e8i	− 0.186726i
$909$	0	0
$910$	8.49248e7	0.112696
$911$	8.00263e8i	1.05847i	0.848476	+	0.529234i	$0.177521\pi$
$911$	8.00263e8i	1.05847i	−0.848476	+	0.529234i	$0.822479\pi$
$912$	0	0
$913$	−2.73395e8	−0.359235
$914$	3.55271e8i	0.465287i
$915$	0	0
$916$	−5.65952e8	−0.736365
$917$	− 2.11048e8i	− 0.273700i
$918$	0	0
$919$	4.75902e8	0.613156	0.306578	−	0.951846i	$-0.400816\pi$
$919$	4.75902e8	0.613156	0.306578	+	0.951846i	$0.400816\pi$
$920$	5.61007e8i	0.720451i
$921$	0	0
$922$	1.31140e8	0.167318
$923$	− 1.98225e8i	− 0.252089i
$924$	0	0
$925$	5.09435e8	0.643671
$926$	− 4.88260e7i	− 0.0614920i
$927$	0	0
$928$	1.01555e9	1.27074
$929$	1.18986e9i	1.48405i	0.670371	+	0.742026i	$0.266135\pi$
$929$	1.18986e9i	1.48405i	−0.670371	+	0.742026i	$0.733865\pi$
$930$	0	0
$931$	−8.17107e8	−1.01258
$932$	2.15917e8i	0.266710i
$933$	0	0
$934$	−3.68634e8	−0.452434
$935$	2.96655e8i	0.362925i
$936$	0	0
$937$	−1.06075e9	−1.28942	−0.644711	−	0.764427i	$-0.723022\pi$
$937$	−1.06075e9	−1.28942	−0.644711	+	0.764427i	$0.723022\pi$
$938$	3.43830e8i	0.416616i
$939$	0	0
$940$	1.41388e8	0.170227
$941$	− 1.48471e9i	− 1.78185i	−0.454146	−	0.890927i	$-0.650056\pi$
$941$	− 1.48471e9i	− 1.78185i	0.454146	−	0.890927i	$-0.349944\pi$
$942$	0	0
$943$	5.04937e8	0.602146
$944$	7.54612e7i	0.0897032i
$945$	0	0
$946$	−4.62416e8	−0.546209
$947$	5.11517e8i	0.602296i	0.953577	+	0.301148i	$0.0973699\pi$
$947$	5.11517e8i	0.602296i	−0.953577	+	0.301148i	$0.902630\pi$
$948$	0	0
$949$	2.76372e8	0.323367
$950$	5.77127e8i	0.673133i
$951$	0	0
$952$	1.94471e8	0.225394
$953$	− 7.30034e8i	− 0.843459i	−0.906722	−	0.421730i	$-0.861423\pi$
$953$	− 7.30034e8i	− 0.843459i	0.906722	−	0.421730i	$-0.138577\pi$
$954$	0	0
$955$	1.49496e8	0.171640
$956$	2.41862e8i	0.276818i
$957$	0	0
$958$	4.10798e8	0.467231
$959$	7.21197e8i	0.817708i
$960$	0	0
$961$	1.65396e9	1.86361
$962$	− 3.37935e8i	− 0.379584i
$963$	0	0
$964$	3.16267e8	0.353039
$965$	1.47495e8i	0.164132i
$966$	0	0
$967$	1.18887e9	1.31479	0.657394	−	0.753547i	$-0.271659\pi$
$967$	1.18887e9	1.31479	0.657394	+	0.753547i	$0.271659\pi$
$968$	− 1.87000e9i	− 2.06165i
$969$	0	0
$970$	−3.41433e8	−0.374103
$971$	4.35915e8i	0.476151i	0.971247	+	0.238075i	$0.0765165\pi$
$971$	4.35915e8i	0.476151i	−0.971247	+	0.238075i	$0.923484\pi$
$972$	0	0
$973$	−6.55271e8	−0.711348
$974$	− 1.08927e9i	− 1.17885i
$975$	0	0
$976$	6.21088e6	0.00668042
$977$	1.20441e9i	1.29149i	0.763553	+	0.645745i	$0.223453\pi$
$977$	1.20441e9i	1.29149i	−0.763553	+	0.645745i	$0.776547\pi$
$978$	0	0
$979$	−2.61250e9	−2.78425
$980$	− 1.98602e8i	− 0.211011i
$981$	0	0
$982$	−6.04247e8	−0.638087
$983$	− 8.76305e8i	− 0.922560i	−0.887255	−	0.461280i	$-0.847390\pi$
$983$	− 8.76305e8i	− 0.922560i	0.887255	−	0.461280i	$-0.152610\pi$
$984$	0	0
$985$	−3.25336e8	−0.340427
$986$	− 3.40994e8i	− 0.355726i
$987$	0	0
$988$	−5.57443e8	−0.578002
$989$	− 6.95957e8i	− 0.719439i
$990$	0	0
$991$	−8.74381e7	−0.0898421	−0.0449211	−	0.998991i	$-0.514304\pi$
$991$	−8.74381e7	−0.0898421	−0.0449211	+	0.998991i	$0.514304\pi$
$992$	− 1.62028e9i	− 1.65980i
$993$	0	0
$994$	−1.15136e8	−0.117234
$995$	1.35024e8i	0.137069i
$996$	0	0
$997$	1.33045e9	1.34250	0.671250	−	0.741231i	$-0.265758\pi$
$997$	1.33045e9	1.34250	0.671250	+	0.741231i	$0.265758\pi$
$998$	5.06099e6i	0.00509148i
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	27.7.b.c.26.3	yes	4
3.2	odd	2	inner	27.7.b.c.26.2	✓	4
4.3	odd	2		432.7.e.j.161.3		4
9.2	odd	6		81.7.d.e.53.2		8
9.4	even	3		81.7.d.e.26.2		8
9.5	odd	6		81.7.d.e.26.3		8
9.7	even	3		81.7.d.e.53.3		8
12.11	even	2		432.7.e.j.161.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
27.7.b.c.26.2	✓	4	3.2	odd	2	inner
27.7.b.c.26.3	yes	4	1.1	even	1	trivial
81.7.d.e.26.2		8	9.4	even	3
81.7.d.e.26.3		8	9.5	odd	6
81.7.d.e.53.2		8	9.2	odd	6
81.7.d.e.53.3		8	9.7	even	3
432.7.e.j.161.2		4	12.11	even	2
432.7.e.j.161.3		4	4.3	odd	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)

\(f(q)\)	\(=\)	\(q+5.10469i q^{2} +37.9422 q^{4} +60.5813i q^{5} +176.769 q^{7} +520.383i q^{8} +O(q^{10})\)	\(q+5.10469i q^{2} +37.9422 q^{4} +60.5813i q^{5} +176.769 q^{7} +520.383i q^{8} -309.248 q^{10} +2316.26i q^{11} -1553.54 q^{13} +902.349i q^{14} -228.092 q^{16} -2114.10i q^{17} +9457.06 q^{19} +2298.58i q^{20} -11823.8 q^{22} -17795.4i q^{23} +11954.9 q^{25} -7930.32i q^{26} +6706.99 q^{28} -31597.4i q^{29} -50412.9 q^{31} +32140.2i q^{32} +10791.8 q^{34} +10708.9i q^{35} +42613.1 q^{37} +48275.3i q^{38} -31525.4 q^{40} +28374.6i q^{41} +39108.9 q^{43} +87884.0i q^{44} +90839.7 q^{46} -61510.7i q^{47} -86401.8 q^{49} +61026.1i q^{50} -58944.6 q^{52} -77764.6i q^{53} -140322. q^{55} +91987.4i q^{56} +161295. q^{58} -330837. i q^{59} -27229.7 q^{61} -257342. i q^{62} -178663. q^{64} -94115.2i q^{65} +381039. q^{67} -80213.5i q^{68} -54665.4 q^{70} +127596. i q^{71} -177899. q^{73} +217526. i q^{74} +358821. q^{76} +409443. i q^{77} +78656.2 q^{79} -13818.1i q^{80} -144844. q^{82} +118033. i q^{83} +128075. q^{85} +199639. i q^{86} -1.20534e6 q^{88} +1.12789e6i q^{89} -274617. q^{91} -675195. i q^{92} +313993. q^{94} +572921. i q^{95} +1.10408e6 q^{97} -441054. i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 194 q^{4} - 676 q^{7}+O(q^{10}) \) 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

Fields

Representations

Groups

Database

Properties

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