LMFDB - Embedded newform 27.7.b.a.26.2

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:	$2$
Coefficient field:	$\Q(\sqrt{-10}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} + 10 $ x^2 + 10
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			26.2
Root			$3.16228i$ of defining polynomial
Character	$\chi$	$=$	27.26
Dual form			27.7.b.a.26.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+9.48683i q^{2} -26.0000 q^{4} +132.816i q^{5} -403.000 q^{7} +360.500i q^{8} +O(q^{10})$	\(q+9.48683i q^{2} -26.0000 q^{4} +132.816i q^{5} -403.000 q^{7} +360.500i q^{8} -1260.00 q^{10} -1498.92i q^{11} -961.000 q^{13} -3823.19i q^{14} -5084.00 q^{16} +9619.65i q^{17} +8021.00 q^{19} -3453.21i q^{20} +14220.0 q^{22} +10606.3i q^{23} -2015.00 q^{25} -9116.85i q^{26} +10478.0 q^{28} -2466.58i q^{29} +48854.0 q^{31} -25159.1i q^{32} -91260.0 q^{34} -53524.7i q^{35} +24167.0 q^{37} +76093.9i q^{38} -47880.0 q^{40} +70771.8i q^{41} -60802.0 q^{43} +38971.9i q^{44} -100620. q^{46} -26999.5i q^{47} +44760.0 q^{49} -19116.0i q^{50} +24986.0 q^{52} -137635. i q^{53} +199080. q^{55} -145281. i q^{56} +23400.0 q^{58} -97543.6i q^{59} +272999. q^{61} +463470. i q^{62} -86696.0 q^{64} -127636. i q^{65} -85579.0 q^{67} -250111. i q^{68} +507780. q^{70} +341754. i q^{71} -152737. q^{73} +229268. i q^{74} -208546. q^{76} +604065. i q^{77} -74059.0 q^{79} -675235. i q^{80} -671400. q^{82} +96576.0i q^{83} -1.27764e6 q^{85} -576818. i q^{86} +540360. q^{88} -1.19369e6i q^{89} +387283. q^{91} -275763. i q^{92} +256140. q^{94} +1.06531e6i q^{95} -1.19731e6 q^{97} +424631. i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 52 q^{4} - 806 q^{7}+O(q^{10}) $ 2 * q - 52 * q^4 - 806 * q^7	$ 2 q - 52 q^{4} - 806 q^{7} - 2520 q^{10} - 1922 q^{13} - 10168 q^{16} + 16042 q^{19} + 28440 q^{22} - 4030 q^{25} + 20956 q^{28} + 97708 q^{31} - 182520 q^{34} + 48334 q^{37} - 95760 q^{40} - 121604 q^{43} - 201240 q^{46} + 89520 q^{49} + 49972 q^{52} + 398160 q^{55} + 46800 q^{58} + 545998 q^{61} - 173392 q^{64} - 171158 q^{67} + 1015560 q^{70} - 305474 q^{73} - 417092 q^{76} - 148118 q^{79} - 1342800 q^{82} - 2555280 q^{85} + 1080720 q^{88} + 774566 q^{91} + 512280 q^{94} - 2394626 q^{97}+O(q^{100}) $ 2 * q - 52 * q^4 - 806 * q^7 - 2520 * q^10 - 1922 * q^13 - 10168 * q^16 + 16042 * q^19 + 28440 * q^22 - 4030 * q^25 + 20956 * q^28 + 97708 * q^31 - 182520 * q^34 + 48334 * q^37 - 95760 * q^40 - 121604 * q^43 - 201240 * q^46 + 89520 * q^49 + 49972 * q^52 + 398160 * q^55 + 46800 * q^58 + 545998 * q^61 - 173392 * q^64 - 171158 * q^67 + 1015560 * q^70 - 305474 * q^73 - 417092 * q^76 - 148118 * q^79 - 1342800 * q^82 - 2555280 * q^85 + 1080720 * q^88 + 774566 * q^91 + 512280 * q^94 - 2394626 * 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 $

$2$	9.48683i	1.18585i	0.805256	+	0.592927i	$0.202028\pi$
$2$	9.48683i	1.18585i	−0.805256	+	0.592927i	$0.797972\pi$
$3$	0	0
$3$	0	0
$4$	−26.0000	−0.406250
$5$	132.816i	1.06253i	0.847207	+	0.531263i	$0.178282\pi$
$5$	132.816i	1.06253i	−0.847207	+	0.531263i	$0.821718\pi$
$6$	0	0
$7$	−403.000	−1.17493	−0.587464	−	0.809251i	$-0.699873\pi$
$7$	−403.000	−1.17493	−0.587464	+	0.809251i	$0.699873\pi$
$8$	360.500i	0.704101i
$9$	0	0
$10$	−1260.00	−1.26000
$11$	− 1498.92i	− 1.12616i	−0.826402	−	0.563080i	$-0.809616\pi$
$11$	− 1498.92i	− 1.12616i	0.826402	−	0.563080i	$-0.190384\pi$
$12$	0	0
$13$	−961.000	−0.437415	−0.218707	−	0.975791i	$-0.570184\pi$
$13$	−961.000	−0.437415	−0.218707	+	0.975791i	$0.570184\pi$
$14$	− 3823.19i	− 1.39329i
$15$	0	0
$16$	−5084.00	−1.24121
$17$	9619.65i	1.95800i	0.203863	+	0.978999i	$0.434650\pi$
$17$	9619.65i	1.95800i	−0.203863	+	0.978999i	$0.565350\pi$
$18$	0	0
$19$	8021.00	1.16941	0.584706	−	0.811245i	$-0.301210\pi$
$19$	8021.00	1.16941	0.584706	+	0.811245i	$0.301210\pi$
$20$	− 3453.21i	− 0.431651i
$21$	0	0
$22$	14220.0	1.33546
$23$	10606.3i	0.871725i	0.900013	+	0.435863i	$0.143557\pi$
$23$	10606.3i	0.871725i	−0.900013	+	0.435863i	$0.856443\pi$
$24$	0	0
$25$	−2015.00	−0.128960
$26$	− 9116.85i	− 0.518710i
$27$	0	0
$28$	10478.0	0.477314
$29$	− 2466.58i	− 0.101135i	−0.998721	−	0.0505674i	$-0.983897\pi$
$29$	− 2466.58i	− 0.101135i	0.998721	−	0.0505674i	$-0.0161030\pi$
$30$	0	0
$31$	48854.0	1.63989	0.819946	−	0.572441i	$-0.194004\pi$
$31$	48854.0	1.63989	0.819946	+	0.572441i	$0.194004\pi$
$32$	− 25159.1i	− 0.767794i
$33$	0	0
$34$	−91260.0	−2.32190
$35$	− 53524.7i	− 1.24839i
$36$	0	0
$37$	24167.0	0.477109	0.238554	−	0.971129i	$-0.423326\pi$
$37$	24167.0	0.477109	0.238554	+	0.971129i	$0.423326\pi$
$38$	76093.9i	1.38675i
$39$	0	0
$40$	−47880.0	−0.748125
$41$	70771.8i	1.02685i	0.858133	+	0.513427i	$0.171624\pi$
$41$	70771.8i	1.02685i	−0.858133	+	0.513427i	$0.828376\pi$
$42$	0	0
$43$	−60802.0	−0.764738	−0.382369	−	0.924010i	$-0.624892\pi$
$43$	−60802.0	−0.764738	−0.382369	+	0.924010i	$0.624892\pi$
$44$	38971.9i	0.457503i
$45$	0	0
$46$	−100620.	−1.03374
$47$	− 26999.5i	− 0.260053i	−0.991510	−	0.130027i	$-0.958494\pi$
$47$	− 26999.5i	− 0.260053i	0.991510	−	0.130027i	$-0.0415063\pi$
$48$	0	0
$49$	44760.0	0.380454
$50$	− 19116.0i	− 0.152928i
$51$	0	0
$52$	24986.0	0.177700
$53$	− 137635.i	− 0.924488i	−0.886753	−	0.462244i	$-0.847044\pi$
$53$	− 137635.i	− 0.924488i	0.886753	−	0.462244i	$-0.152956\pi$
$54$	0	0
$55$	199080.	1.19657
$56$	− 145281.i	− 0.827267i
$57$	0	0
$58$	23400.0	0.119931
$59$	− 97543.6i	− 0.474944i	−0.971394	−	0.237472i	$-0.923681\pi$
$59$	− 97543.6i	− 0.474944i	0.971394	−	0.237472i	$-0.0763189\pi$
$60$	0	0
$61$	272999.	1.20274	0.601370	−	0.798971i	$-0.294622\pi$
$61$	272999.	1.20274	0.601370	+	0.798971i	$0.294622\pi$
$62$	463470.i	1.94467i
$63$	0	0
$64$	−86696.0	−0.330719
$65$	− 127636.i	− 0.464764i
$66$	0	0
$67$	−85579.0	−0.284540	−0.142270	−	0.989828i	$-0.545440\pi$
$67$	−85579.0	−0.284540	−0.142270	+	0.989828i	$0.545440\pi$
$68$	− 250111.i	− 0.795437i
$69$	0	0
$70$	507780.	1.48041
$71$	341754.i	0.954857i	0.878671	+	0.477428i	$0.158431\pi$
$71$	341754.i	0.954857i	−0.878671	+	0.477428i	$0.841569\pi$
$72$	0	0
$73$	−152737.	−0.392623	−0.196311	−	0.980542i	$-0.562896\pi$
$73$	−152737.	−0.392623	−0.196311	+	0.980542i	$0.562896\pi$
$74$	229268.i	0.565782i
$75$	0	0
$76$	−208546.	−0.475074
$77$	604065.i	1.32316i
$78$	0	0
$79$	−74059.0	−0.150209	−0.0751046	−	0.997176i	$-0.523929\pi$
$79$	−74059.0	−0.150209	−0.0751046	+	0.997176i	$0.523929\pi$
$80$	− 675235.i	− 1.31882i
$81$	0	0
$82$	−671400.	−1.21770
$83$	96576.0i	0.168902i	0.996428	+	0.0844510i	$0.0269136\pi$
$83$	96576.0i	0.168902i	−0.996428	+	0.0844510i	$0.973086\pi$
$84$	0	0
$85$	−1.27764e6	−2.08042
$86$	− 576818.i	− 0.906867i
$87$	0	0
$88$	540360.	0.792931
$89$	− 1.19369e6i	− 1.69325i	−0.532188	−	0.846626i	$-0.678630\pi$
$89$	− 1.19369e6i	− 1.69325i	0.532188	−	0.846626i	$-0.321370\pi$
$90$	0	0
$91$	387283.	0.513930
$92$	− 275763.i	− 0.354138i
$93$	0	0
$94$	256140.	0.308385
$95$	1.06531e6i	1.24253i
$96$	0	0
$97$	−1.19731e6	−1.31188	−0.655938	−	0.754815i	$-0.727727\pi$
$97$	−1.19731e6	−1.31188	−0.655938	+	0.754815i	$0.727727\pi$
$98$	424631.i	0.451163i
$99$	0	0
$100$	52390.0	0.0523900
$101$	884021.i	0.858022i	0.903299	+	0.429011i	$0.141138\pi$
$101$	884021.i	0.858022i	−0.903299	+	0.429011i	$0.858862\pi$
$102$	0	0
$103$	1.17413e6	1.07450	0.537249	−	0.843424i	$-0.319464\pi$
$103$	1.17413e6	1.07450	0.537249	+	0.843424i	$0.319464\pi$
$104$	− 346440.i	− 0.307984i
$105$	0	0
$106$	1.30572e6	1.09631
$107$	583839.i	0.476586i	0.971193	+	0.238293i	$0.0765879\pi$
$107$	583839.i	0.476586i	−0.971193	+	0.238293i	$0.923412\pi$
$108$	0	0
$109$	188786.	0.145777	0.0728887	−	0.997340i	$-0.476778\pi$
$109$	188786.	0.145777	0.0728887	+	0.997340i	$0.476778\pi$
$110$	1.88864e6i	1.41896i
$111$	0	0
$112$	2.04885e6	1.45833
$113$	− 1.64397e6i	− 1.13936i	−0.821868	−	0.569678i	$-0.807068\pi$
$113$	− 1.64397e6i	− 1.13936i	0.821868	−	0.569678i	$-0.192932\pi$
$114$	0	0
$115$	−1.40868e6	−0.926230
$116$	64131.0i	0.0410860i
$117$	0	0
$118$	925380.	0.563215
$119$	− 3.87672e6i	− 2.30051i
$120$	0	0
$121$	−475199.	−0.268237
$122$	2.58990e6i	1.42627i
$123$	0	0
$124$	−1.27020e6	−0.666206
$125$	1.80762e6i	0.925502i
$126$	0	0
$127$	3.10101e6	1.51388	0.756940	−	0.653484i	$-0.226693\pi$
$127$	3.10101e6	1.51388	0.756940	+	0.653484i	$0.226693\pi$
$128$	− 2.43265e6i	− 1.15998i
$129$	0	0
$130$	1.21086e6	0.551142
$131$	− 3.21494e6i	− 1.43007i	−0.699087	−	0.715037i	$-0.746410\pi$
$131$	− 3.21494e6i	− 1.43007i	0.699087	−	0.715037i	$-0.253590\pi$
$132$	0	0
$133$	−3.23246e6	−1.37397
$134$	− 811874.i	− 0.337423i
$135$	0	0
$136$	−3.46788e6	−1.37863
$137$	2.87848e6i	1.11944i	0.828682	+	0.559720i	$0.189091\pi$
$137$	2.87848e6i	1.11944i	−0.828682	+	0.559720i	$0.810909\pi$
$138$	0	0
$139$	−1.47662e6	−0.549824	−0.274912	−	0.961469i	$-0.588649\pi$
$139$	−1.47662e6	−0.549824	−0.274912	+	0.961469i	$0.588649\pi$
$140$	1.39164e6i	0.507158i
$141$	0	0
$142$	−3.24216e6	−1.13232
$143$	1.44046e6i	0.492599i
$144$	0	0
$145$	327600.	0.107458
$146$	− 1.44899e6i	− 0.465594i
$147$	0	0
$148$	−628342.	−0.193826
$149$	558812.i	0.168930i	0.996426	+	0.0844651i	$0.0269181\pi$
$149$	558812.i	0.168930i	−0.996426	+	0.0844651i	$0.973082\pi$
$150$	0	0
$151$	3.71739e6	1.07971	0.539855	−	0.841758i	$-0.318479\pi$
$151$	3.71739e6	1.07971	0.539855	+	0.841758i	$0.318479\pi$
$152$	2.89157e6i	0.823384i
$153$	0	0
$154$	−5.73066e6	−1.56907
$155$	6.48858e6i	1.74243i
$156$	0	0
$157$	1.23696e6	0.319637	0.159819	−	0.987146i	$-0.448909\pi$
$157$	1.23696e6	0.319637	0.159819	+	0.987146i	$0.448909\pi$
$158$	− 702585.i	− 0.178126i
$159$	0	0
$160$	3.34152e6	0.815801
$161$	− 4.27433e6i	− 1.02421i
$162$	0	0
$163$	6.87639e6	1.58781	0.793903	−	0.608044i	$-0.208046\pi$
$163$	6.87639e6	1.58781	0.793903	+	0.608044i	$0.208046\pi$
$164$	− 1.84007e6i	− 0.417159i
$165$	0	0
$166$	−916200.	−0.200293
$167$	− 1.91788e6i	− 0.411786i	−0.978575	−	0.205893i	$-0.933990\pi$
$167$	− 1.91788e6i	− 0.411786i	0.978575	−	0.205893i	$-0.0660099\pi$
$168$	0	0
$169$	−3.90329e6	−0.808668
$170$	− 1.21208e7i	− 2.46708i
$171$	0	0
$172$	1.58085e6	0.310675
$173$	− 3.82369e6i	− 0.738489i	−0.929332	−	0.369244i	$-0.879616\pi$
$173$	− 3.82369e6i	− 0.738489i	0.929332	−	0.369244i	$-0.120384\pi$
$174$	0	0
$175$	812045.	0.151519
$176$	7.62051e6i	1.39780i
$177$	0	0
$178$	1.13243e7	2.00795
$179$	1.60130e6i	0.279199i	0.990208	+	0.139600i	$0.0445815\pi$
$179$	1.60130e6i	0.279199i	−0.990208	+	0.139600i	$0.955418\pi$
$180$	0	0
$181$	570647.	0.0962347	0.0481174	−	0.998842i	$-0.484678\pi$
$181$	570647.	0.0962347	0.0481174	+	0.998842i	$0.484678\pi$
$182$	3.67409e6i	0.609446i
$183$	0	0
$184$	−3.82356e6	−0.613782
$185$	3.20976e6i	0.506940i
$186$	0	0
$187$	1.44191e7	2.20502
$188$	701988.i	0.105647i
$189$	0	0
$190$	−1.01065e7	−1.47346
$191$	4.14656e6i	0.595097i	0.954707	+	0.297549i	$0.0961691\pi$
$191$	4.14656e6i	0.595097i	−0.954707	+	0.297549i	$0.903831\pi$
$192$	0	0
$193$	−4.47238e6	−0.622109	−0.311054	−	0.950392i	$-0.600682\pi$
$193$	−4.47238e6	−0.622109	−0.311054	+	0.950392i	$0.600682\pi$
$194$	− 1.13587e7i	− 1.55569i
$195$	0	0
$196$	−1.16376e6	−0.154559
$197$	1.18772e7i	1.55351i	0.629801	+	0.776757i	$0.283137\pi$
$197$	1.18772e7i	1.55351i	−0.629801	+	0.776757i	$0.716863\pi$
$198$	0	0
$199$	902693.	0.114546	0.0572731	−	0.998359i	$-0.481759\pi$
$199$	902693.	0.114546	0.0572731	+	0.998359i	$0.481759\pi$
$200$	− 726407.i	− 0.0908009i
$201$	0	0
$202$	−8.38656e6	−1.01749
$203$	994030.i	0.118826i
$204$	0	0
$205$	−9.39960e6	−1.09106
$206$	1.11388e7i	1.27420i
$207$	0	0
$208$	4.88572e6	0.542924
$209$	− 1.20228e7i	− 1.31695i
$210$	0	0
$211$	5.67536e6	0.604151	0.302076	−	0.953284i	$-0.402320\pi$
$211$	5.67536e6	0.604151	0.302076	+	0.953284i	$0.402320\pi$
$212$	3.57851e6i	0.375573i
$213$	0	0
$214$	−5.53878e6	−0.565162
$215$	− 8.07546e6i	− 0.812553i
$216$	0	0
$217$	−1.96882e7	−1.92675
$218$	1.79098e6i	0.172871i
$219$	0	0
$220$	−5.17608e6	−0.486108
$221$	− 9.24448e6i	− 0.856457i
$222$	0	0
$223$	−5.64764e6	−0.509275	−0.254638	−	0.967037i	$-0.581956\pi$
$223$	−5.64764e6	−0.509275	−0.254638	+	0.967037i	$0.581956\pi$
$224$	1.01391e7i	0.902102i
$225$	0	0
$226$	1.55961e7	1.35111
$227$	− 1.25821e7i	− 1.07566i	−0.843052	−	0.537832i	$-0.819244\pi$
$227$	− 1.25821e7i	− 1.07566i	0.843052	−	0.537832i	$-0.180756\pi$
$228$	0	0
$229$	−6.51765e6	−0.542731	−0.271366	−	0.962476i	$-0.587475\pi$
$229$	−6.51765e6	−0.542731	−0.271366	+	0.962476i	$0.587475\pi$
$230$	− 1.33639e7i	− 1.09837i
$231$	0	0
$232$	889200.	0.0712091
$233$	− 8.32618e6i	− 0.658230i	−0.944290	−	0.329115i	$-0.893250\pi$
$233$	− 8.32618e6i	− 0.658230i	0.944290	−	0.329115i	$-0.106750\pi$
$234$	0	0
$235$	3.58596e6	0.276313
$236$	2.53613e6i	0.192946i
$237$	0	0
$238$	3.67778e7	2.72806
$239$	2.08241e7i	1.52536i	0.646778	+	0.762679i	$0.276116\pi$
$239$	2.08241e7i	1.52536i	−0.646778	+	0.762679i	$0.723884\pi$
$240$	0	0
$241$	4.62929e6	0.330722	0.165361	−	0.986233i	$-0.447121\pi$
$241$	4.62929e6	0.330722	0.165361	+	0.986233i	$0.447121\pi$
$242$	− 4.50813e6i	− 0.318090i
$243$	0	0
$244$	−7.09797e6	−0.488613
$245$	5.94483e6i	0.404242i
$246$	0	0
$247$	−7.70818e6	−0.511518
$248$	1.76119e7i	1.15465i
$249$	0	0
$250$	−1.71486e7	−1.09751
$251$	− 1.38242e7i	− 0.874215i	−0.899409	−	0.437107i	$-0.856003\pi$
$251$	− 1.38242e7i	− 0.874215i	0.899409	−	0.437107i	$-0.143997\pi$
$252$	0	0
$253$	1.58980e7	0.981702
$254$	2.94187e7i	1.79524i
$255$	0	0
$256$	1.75296e7	1.04485
$257$	6.86646e6i	0.404514i	0.979333	+	0.202257i	$0.0648276\pi$
$257$	6.86646e6i	0.404514i	−0.979333	+	0.202257i	$0.935172\pi$
$258$	0	0
$259$	−9.73930e6	−0.560568
$260$	3.31853e6i	0.188810i
$261$	0	0
$262$	3.04996e7	1.69586
$263$	1.40171e7i	0.770530i	0.922806	+	0.385265i	$0.125890\pi$
$263$	1.40171e7i	0.770530i	−0.922806	+	0.385265i	$0.874110\pi$
$264$	0	0
$265$	1.82801e7	0.982292
$266$	− 3.06658e7i	− 1.62933i
$267$	0	0
$268$	2.22505e6	0.115594
$269$	3.86044e6i	0.198326i	0.995071	+	0.0991630i	$0.0316165\pi$
$269$	3.86044e6i	0.198326i	−0.995071	+	0.0991630i	$0.968383\pi$
$270$	0	0
$271$	−9.15729e6	−0.460107	−0.230054	−	0.973178i	$-0.573890\pi$
$271$	−9.15729e6	−0.460107	−0.230054	+	0.973178i	$0.573890\pi$
$272$	− 4.89063e7i	− 2.43029i
$273$	0	0
$274$	−2.73076e7	−1.32749
$275$	3.02032e6i	0.145230i
$276$	0	0
$277$	−1.28498e7	−0.604586	−0.302293	−	0.953215i	$-0.597752\pi$
$277$	−1.28498e7	−0.604586	−0.302293	+	0.953215i	$0.597752\pi$
$278$	− 1.40084e7i	− 0.652012i
$279$	0	0
$280$	1.92956e7	0.878992
$281$	3.24867e7i	1.46415i	0.681223	+	0.732076i	$0.261449\pi$
$281$	3.24867e7i	1.46415i	−0.681223	+	0.732076i	$0.738551\pi$
$282$	0	0
$283$	−2.87816e6	−0.126986	−0.0634930	−	0.997982i	$-0.520224\pi$
$283$	−2.87816e6	−0.126986	−0.0634930	+	0.997982i	$0.520224\pi$
$284$	− 8.88560e6i	− 0.387910i
$285$	0	0
$286$	−1.36654e7	−0.584151
$287$	− 2.85210e7i	− 1.20648i
$288$	0	0
$289$	−6.84001e7	−2.83376
$290$	3.10789e6i	0.127430i
$291$	0	0
$292$	3.97116e6	0.159503
$293$	4.13692e6i	0.164465i	0.996613	+	0.0822327i	$0.0262051\pi$
$293$	4.13692e6i	0.164465i	−0.996613	+	0.0822327i	$0.973795\pi$
$294$	0	0
$295$	1.29553e7	0.504640
$296$	8.71220e6i	0.335933i
$297$	0	0
$298$	−5.30136e6	−0.200327
$299$	− 1.01926e7i	− 0.381305i
$300$	0	0
$301$	2.45032e7	0.898511
$302$	3.52662e7i	1.28038i
$303$	0	0
$304$	−4.07788e7	−1.45149
$305$	3.62585e7i	1.27794i
$306$	0	0
$307$	4.41342e6	0.152532	0.0762659	−	0.997088i	$-0.475700\pi$
$307$	4.41342e6	0.152532	0.0762659	+	0.997088i	$0.475700\pi$
$308$	− 1.57057e7i	− 0.537532i
$309$	0	0
$310$	−6.15560e7	−2.06626
$311$	− 1.33637e7i	− 0.444267i	−0.975016	−	0.222134i	$-0.928698\pi$
$311$	− 1.33637e7i	− 0.444267i	0.975016	−	0.222134i	$-0.0713021\pi$
$312$	0	0
$313$	6.00413e7	1.95802	0.979010	−	0.203814i	$-0.0653339\pi$
$313$	6.00413e7	1.95802	0.979010	+	0.203814i	$0.0653339\pi$
$314$	1.17349e7i	0.379043i
$315$	0	0
$316$	1.92553e6	0.0610225
$317$	− 5.85992e7i	− 1.83956i	−0.392434	−	0.919780i	$-0.628367\pi$
$317$	− 5.85992e7i	− 1.83956i	0.392434	−	0.919780i	$-0.371633\pi$
$318$	0	0
$319$	−3.69720e6	−0.113894
$320$	− 1.15146e7i	− 0.351397i
$321$	0	0
$322$	4.05499e7	1.21457
$323$	7.71592e7i	2.28971i
$324$	0	0
$325$	1.93642e6	0.0564090
$326$	6.52352e7i	1.88291i
$327$	0	0
$328$	−2.55132e7	−0.723008
$329$	1.08808e7i	0.305544i
$330$	0	0
$331$	1.09761e7	0.302665	0.151333	−	0.988483i	$-0.451644\pi$
$331$	1.09761e7	0.302665	0.151333	+	0.988483i	$0.451644\pi$
$332$	− 2.51097e6i	− 0.0686164i
$333$	0	0
$334$	1.81946e7	0.488318
$335$	− 1.13662e7i	− 0.302331i
$336$	0	0
$337$	8.51635e6	0.222517	0.111259	−	0.993791i	$-0.464512\pi$
$337$	8.51635e6	0.222517	0.111259	+	0.993791i	$0.464512\pi$
$338$	− 3.70298e7i	− 0.958963i
$339$	0	0
$340$	3.32186e7	0.845172
$341$	− 7.32282e7i	− 1.84678i
$342$	0	0
$343$	2.93743e7	0.727922
$344$	− 2.19191e7i	− 0.538452i
$345$	0	0
$346$	3.62747e7	0.875740
$347$	− 5.28212e7i	− 1.26421i	−0.774882	−	0.632106i	$-0.782191\pi$
$347$	− 5.28212e7i	− 1.26421i	0.774882	−	0.632106i	$-0.217809\pi$
$348$	0	0
$349$	4.99167e7	1.17427	0.587137	−	0.809487i	$-0.300255\pi$
$349$	4.99167e7	1.17427	0.587137	+	0.809487i	$0.300255\pi$
$350$	7.70374e6i	0.179679i
$351$	0	0
$352$	−3.77114e7	−0.864660
$353$	260850.i	0.00593016i	0.999996	+	0.00296508i	$0.000943816\pi$
$353$	260850.i	0.00593016i	−0.999996	+	0.00296508i	$0.999056\pi$
$354$	0	0
$355$	−4.53902e7	−1.01456
$356$	3.10359e7i	0.687884i
$357$	0	0
$358$	−1.51913e7	−0.331089
$359$	− 256884.i	− 0.00555206i	−0.999996	−	0.00277603i	$-0.999116\pi$
$359$	− 256884.i	− 0.00555206i	0.999996	−	0.00277603i	$-0.000883640\pi$
$360$	0	0
$361$	1.72906e7	0.367525
$362$	5.41363e6i	0.114120i
$363$	0	0
$364$	−1.00694e7	−0.208784
$365$	− 2.02859e7i	− 0.417172i
$366$	0	0
$367$	3.25689e7	0.658879	0.329439	−	0.944177i	$-0.393140\pi$
$367$	3.25689e7	0.658879	0.329439	+	0.944177i	$0.393140\pi$
$368$	− 5.39223e7i	− 1.08199i
$369$	0	0
$370$	−3.04504e7	−0.601157
$371$	5.54669e7i	1.08621i
$372$	0	0
$373$	8.33467e7	1.60606	0.803031	−	0.595938i	$-0.203219\pi$
$373$	8.33467e7	1.60606	0.803031	+	0.595938i	$0.203219\pi$
$374$	1.36791e8i	2.61483i
$375$	0	0
$376$	9.73332e6	0.183104
$377$	2.37038e6i	0.0442378i
$378$	0	0
$379$	−7.31011e7	−1.34278	−0.671392	−	0.741103i	$-0.734303\pi$
$379$	−7.31011e7	−1.34278	−0.671392	+	0.741103i	$0.734303\pi$
$380$	− 2.76982e7i	− 0.504778i
$381$	0	0
$382$	−3.93377e7	−0.705699
$383$	3.94507e7i	0.702195i	0.936339	+	0.351098i	$0.114191\pi$
$383$	3.94507e7i	0.702195i	−0.936339	+	0.351098i	$0.885809\pi$
$384$	0	0
$385$	−8.02292e7	−1.40589
$386$	− 4.24287e7i	− 0.737731i
$387$	0	0
$388$	3.11301e7	0.532949
$389$	7.50700e7i	1.27532i	0.770320	+	0.637658i	$0.220097\pi$
$389$	7.50700e7i	1.27532i	−0.770320	+	0.637658i	$0.779903\pi$
$390$	0	0
$391$	−1.02029e8	−1.70684
$392$	1.61360e7i	0.267878i
$393$	0	0
$394$	−1.12677e8	−1.84224
$395$	− 9.83620e6i	− 0.159601i
$396$	0	0
$397$	6.34586e7	1.01419	0.507095	−	0.861890i	$-0.330719\pi$
$397$	6.34586e7	1.01419	0.507095	+	0.861890i	$0.330719\pi$
$398$	8.56370e6i	0.135835i
$399$	0	0
$400$	1.02443e7	0.160067
$401$	− 7.64309e7i	− 1.18532i	−0.805452	−	0.592661i	$-0.798078\pi$
$401$	− 7.64309e7i	− 1.18532i	0.805452	−	0.592661i	$-0.201922\pi$
$402$	0	0
$403$	−4.69487e7	−0.717312
$404$	− 2.29845e7i	− 0.348571i
$405$	0	0
$406$	−9.43020e6	−0.140910
$407$	− 3.62244e7i	− 0.537301i
$408$	0	0
$409$	1.06247e8	1.55291	0.776456	−	0.630171i	$-0.217015\pi$
$409$	1.06247e8	1.55291	0.776456	+	0.630171i	$0.217015\pi$
$410$	− 8.91724e7i	− 1.29384i
$411$	0	0
$412$	−3.05275e7	−0.436515
$413$	3.93101e7i	0.558025i
$414$	0	0
$415$	−1.28268e7	−0.179463
$416$	2.41779e7i	0.335844i
$417$	0	0
$418$	1.14059e8	1.56171
$419$	− 3.77872e7i	− 0.513692i	−0.966452	−	0.256846i	$-0.917317\pi$
$419$	− 3.77872e7i	− 0.513692i	0.966452	−	0.256846i	$-0.0826833\pi$
$420$	0	0
$421$	−1.57456e7	−0.211014	−0.105507	−	0.994419i	$-0.533647\pi$
$421$	−1.57456e7	−0.211014	−0.105507	+	0.994419i	$0.533647\pi$
$422$	5.38412e7i	0.716435i
$423$	0	0
$424$	4.96174e7	0.650933
$425$	− 1.93836e7i	− 0.252504i
$426$	0	0
$427$	−1.10019e8	−1.41313
$428$	− 1.51798e7i	− 0.193613i
$429$	0	0
$430$	7.66105e7	0.963569
$431$	3.16419e7i	0.395212i	0.980282	+	0.197606i	$0.0633167\pi$
$431$	3.16419e7i	0.395212i	−0.980282	+	0.197606i	$0.936683\pi$
$432$	0	0
$433$	−6.50979e7	−0.801868	−0.400934	−	0.916107i	$-0.631314\pi$
$433$	−6.50979e7	−0.801868	−0.400934	+	0.916107i	$0.631314\pi$
$434$	− 1.86778e8i	− 2.28485i
$435$	0	0
$436$	−4.90844e6	−0.0592221
$437$	8.50730e7i	1.01941i
$438$	0	0
$439$	−3.15076e7	−0.372410	−0.186205	−	0.982511i	$-0.559619\pi$
$439$	−3.15076e7	−0.372410	−0.186205	+	0.982511i	$0.559619\pi$
$440$	7.17683e7i	0.842509i
$441$	0	0
$442$	8.77009e7	1.01563
$443$	− 1.41152e7i	− 0.162359i	−0.996699	−	0.0811796i	$-0.974131\pi$
$443$	− 1.41152e7i	− 0.162359i	0.996699	−	0.0811796i	$-0.0258687\pi$
$444$	0	0
$445$	1.58541e8	1.79912
$446$	− 5.35782e7i	− 0.603926i
$447$	0	0
$448$	3.49385e7	0.388571
$449$	4.88403e7i	0.539560i	0.962922	+	0.269780i	$0.0869509\pi$
$449$	4.88403e7i	0.539560i	−0.962922	+	0.269780i	$0.913049\pi$
$450$	0	0
$451$	1.06081e8	1.15640
$452$	4.27433e7i	0.462863i
$453$	0	0
$454$	1.19364e8	1.27558
$455$	5.14372e7i	0.546064i
$456$	0	0
$457$	−1.62942e8	−1.70720	−0.853600	−	0.520929i	$-0.825586\pi$
$457$	−1.62942e8	−1.70720	−0.853600	+	0.520929i	$0.825586\pi$
$458$	− 6.18319e7i	− 0.643600i
$459$	0	0
$460$	3.66257e7	0.376281
$461$	1.21133e8i	1.23640i	0.786019	+	0.618202i	$0.212139\pi$
$461$	1.21133e8i	1.23640i	−0.786019	+	0.618202i	$0.787861\pi$
$462$	0	0
$463$	−1.08239e8	−1.09053	−0.545267	−	0.838263i	$-0.683572\pi$
$463$	−1.08239e8	−1.09053	−0.545267	+	0.838263i	$0.683572\pi$
$464$	1.25401e7i	0.125530i
$465$	0	0
$466$	7.89890e7	0.780565
$467$	5.06445e7i	0.497258i	0.968599	+	0.248629i	$0.0799799\pi$
$467$	5.06445e7i	0.497258i	−0.968599	+	0.248629i	$0.920020\pi$
$468$	0	0
$469$	3.44883e7	0.334313
$470$	3.40194e7i	0.327667i
$471$	0	0
$472$	3.51644e7	0.334409
$473$	9.11373e7i	0.861217i
$474$	0	0
$475$	−1.61623e7	−0.150807
$476$	1.00795e8i	0.934581i
$477$	0	0
$478$	−1.97554e8	−1.80885
$479$	− 1.75967e8i	− 1.60112i	−0.599253	−	0.800560i	$-0.704535\pi$
$479$	− 1.75967e8i	− 1.60112i	0.599253	−	0.800560i	$-0.295465\pi$
$480$	0	0
$481$	−2.32245e7	−0.208694
$482$	4.39173e7i	0.392188i
$483$	0	0
$484$	1.23552e7	0.108971
$485$	− 1.59022e8i	− 1.39390i
$486$	0	0
$487$	1.32967e8	1.15121	0.575607	−	0.817726i	$-0.304766\pi$
$487$	1.32967e8	1.15121	0.575607	+	0.817726i	$0.304766\pi$
$488$	9.84160e7i	0.846850i
$489$	0	0
$490$	−5.63976e7	−0.479372
$491$	− 2.14361e8i	− 1.81093i	−0.424422	−	0.905464i	$-0.639523\pi$
$491$	− 2.14361e8i	− 1.81093i	0.424422	−	0.905464i	$-0.360477\pi$
$492$	0	0
$493$	2.37276e7	0.198022
$494$	− 7.31262e7i	− 0.606586i
$495$	0	0
$496$	−2.48374e8	−2.03545
$497$	− 1.37727e8i	− 1.12189i
$498$	0	0
$499$	−1.82123e8	−1.46576	−0.732880	−	0.680358i	$-0.761824\pi$
$499$	−1.82123e8	−1.46576	−0.732880	+	0.680358i	$0.761824\pi$
$500$	− 4.69982e7i	− 0.375985i
$501$	0	0
$502$	1.31148e8	1.03669
$503$	− 9.74226e7i	− 0.765519i	−0.923848	−	0.382759i	$-0.874974\pi$
$503$	− 9.74226e7i	− 0.765519i	0.923848	−	0.382759i	$-0.125026\pi$
$504$	0	0
$505$	−1.17412e8	−0.911670
$506$	1.50821e8i	1.16416i
$507$	0	0
$508$	−8.06262e7	−0.615014
$509$	− 2.58590e7i	− 0.196091i	−0.995182	−	0.0980455i	$-0.968741\pi$
$509$	− 2.58590e7i	− 0.196091i	0.995182	−	0.0980455i	$-0.0312591\pi$
$510$	0	0
$511$	6.15530e7	0.461303
$512$	1.06108e7i	0.0790569i
$513$	0	0
$514$	−6.51409e7	−0.479694
$515$	1.55943e8i	1.14168i
$516$	0	0
$517$	−4.04701e7	−0.292862
$518$	− 9.23951e7i	− 0.664752i
$519$	0	0
$520$	4.60127e7	0.327241
$521$	− 1.94679e8i	− 1.37659i	−0.725430	−	0.688296i	$-0.758359\pi$
$521$	− 1.94679e8i	− 1.37659i	0.725430	−	0.688296i	$-0.241641\pi$
$522$	0	0
$523$	6.83930e7	0.478086	0.239043	−	0.971009i	$-0.423166\pi$
$523$	6.83930e7	0.478086	0.239043	+	0.971009i	$0.423166\pi$
$524$	8.35883e7i	0.580967i
$525$	0	0
$526$	−1.32978e8	−0.913737
$527$	4.69958e8i	3.21091i
$528$	0	0
$529$	3.55427e7	0.240095
$530$	1.73420e8i	1.16485i
$531$	0	0
$532$	8.40440e7	0.558177
$533$	− 6.80117e7i	− 0.449161i
$534$	0	0
$535$	−7.75429e7	−0.506385
$536$	− 3.08512e7i	− 0.200345i
$537$	0	0
$538$	−3.66233e7	−0.235186
$539$	− 6.70916e7i	− 0.428452i
$540$	0	0
$541$	1.37627e8	0.869187	0.434593	−	0.900627i	$-0.356892\pi$
$541$	1.37627e8	0.869187	0.434593	+	0.900627i	$0.356892\pi$
$542$	− 8.68737e7i	− 0.545620i
$543$	0	0
$544$	2.42022e8	1.50334
$545$	2.50737e7i	0.154892i
$546$	0	0
$547$	1.38352e8	0.845324	0.422662	−	0.906287i	$-0.361096\pi$
$547$	1.38352e8	0.845324	0.422662	+	0.906287i	$0.361096\pi$
$548$	− 7.48404e7i	− 0.454773i
$549$	0	0
$550$	−2.86533e7	−0.172221
$551$	− 1.97844e7i	− 0.118268i
$552$	0	0
$553$	2.98458e7	0.176485
$554$	− 1.21904e8i	− 0.716951i
$555$	0	0
$556$	3.83921e7	0.223366
$557$	2.31331e8i	1.33866i	0.742967	+	0.669328i	$0.233418\pi$
$557$	2.31331e8i	1.33866i	−0.742967	+	0.669328i	$0.766582\pi$
$558$	0	0
$559$	5.84307e7	0.334507
$560$	2.72120e8i	1.54952i
$561$	0	0
$562$	−3.08196e8	−1.73627
$563$	− 1.91007e7i	− 0.107034i	−0.998567	−	0.0535172i	$-0.982957\pi$
$563$	− 1.91007e7i	− 0.107034i	0.998567	−	0.0535172i	$-0.0170432\pi$
$564$	0	0
$565$	2.18345e8	1.21059
$566$	− 2.73046e7i	− 0.150587i
$567$	0	0
$568$	−1.23202e8	−0.672315
$569$	5.23432e6i	0.0284134i	0.999899	+	0.0142067i	$0.00452229\pi$
$569$	5.23432e6i	0.0284134i	−0.999899	+	0.0142067i	$0.995478\pi$
$570$	0	0
$571$	2.94138e8	1.57995	0.789975	−	0.613139i	$-0.210093\pi$
$571$	2.94138e8	1.57995	0.789975	+	0.613139i	$0.210093\pi$
$572$	− 3.74520e7i	− 0.200118i
$573$	0	0
$574$	2.70574e8	1.43071
$575$	− 2.13717e7i	− 0.112418i
$576$	0	0
$577$	−1.42033e8	−0.739368	−0.369684	−	0.929158i	$-0.620534\pi$
$577$	−1.42033e8	−0.739368	−0.369684	+	0.929158i	$0.620534\pi$
$578$	− 6.48900e8i	− 3.36043i
$579$	0	0
$580$	−8.51760e6	−0.0436549
$581$	− 3.89201e7i	− 0.198448i
$582$	0	0
$583$	−2.06304e8	−1.04112
$584$	− 5.50616e7i	− 0.276446i
$585$	0	0
$586$	−3.92463e7	−0.195032
$587$	1.05535e7i	0.0521773i	0.999660	+	0.0260886i	$0.00830521\pi$
$587$	1.05535e7i	0.0521773i	−0.999660	+	0.0260886i	$0.991695\pi$
$588$	0	0
$589$	3.91858e8	1.91771
$590$	1.22905e8i	0.598430i
$591$	0	0
$592$	−1.22865e8	−0.592193
$593$	3.33771e8i	1.60061i	0.599596	+	0.800303i	$0.295328\pi$
$593$	3.33771e8i	1.60061i	−0.599596	+	0.800303i	$0.704672\pi$
$594$	0	0
$595$	5.14889e8	2.44435
$596$	− 1.45291e7i	− 0.0686279i
$597$	0	0
$598$	9.66958e7	0.452173
$599$	− 3.53033e8i	− 1.64261i	−0.570489	−	0.821305i	$-0.693246\pi$
$599$	− 3.53033e8i	− 1.64261i	0.570489	−	0.821305i	$-0.306754\pi$
$600$	0	0
$601$	−3.41276e8	−1.57211	−0.786055	−	0.618157i	$-0.787880\pi$
$601$	−3.41276e8	−1.57211	−0.786055	+	0.618157i	$0.787880\pi$
$602$	2.32458e8i	1.06550i
$603$	0	0
$604$	−9.66521e7	−0.438632
$605$	− 6.31139e7i	− 0.285009i
$606$	0	0
$607$	−2.29562e8	−1.02644	−0.513220	−	0.858257i	$-0.671547\pi$
$607$	−2.29562e8	−1.02644	−0.513220	+	0.858257i	$0.671547\pi$
$608$	− 2.01801e8i	− 0.897868i
$609$	0	0
$610$	−3.43979e8	−1.51545
$611$	2.59465e7i	0.113751i
$612$	0	0
$613$	−3.31047e8	−1.43717	−0.718586	−	0.695438i	$-0.755210\pi$
$613$	−3.31047e8	−1.43717	−0.718586	+	0.695438i	$0.755210\pi$
$614$	4.18694e7i	0.180880i
$615$	0	0
$616$	−2.17765e8	−0.931636
$617$	− 3.59055e8i	− 1.52864i	−0.644835	−	0.764321i	$-0.723074\pi$
$617$	− 3.59055e8i	− 1.52864i	0.644835	−	0.764321i	$-0.276926\pi$
$618$	0	0
$619$	−1.51131e7	−0.0637207	−0.0318603	−	0.999492i	$-0.510143\pi$
$619$	−1.51131e7	−0.0637207	−0.0318603	+	0.999492i	$0.510143\pi$
$620$	− 1.68703e8i	− 0.707861i
$621$	0	0
$622$	1.26779e8	0.526836
$623$	4.81057e8i	1.98945i
$624$	0	0
$625$	−2.71565e8	−1.11233
$626$	5.69602e8i	2.32193i
$627$	0	0
$628$	−3.21610e7	−0.129853
$629$	2.32478e8i	0.934179i
$630$	0	0
$631$	−1.91510e7	−0.0762259	−0.0381129	−	0.999273i	$-0.512135\pi$
$631$	−1.91510e7	−0.0762259	−0.0381129	+	0.999273i	$0.512135\pi$
$632$	− 2.66982e7i	− 0.105762i
$633$	0	0
$634$	5.55921e8	2.18145
$635$	4.11862e8i	1.60854i
$636$	0	0
$637$	−4.30144e7	−0.166416
$638$	− 3.50747e7i	− 0.135062i
$639$	0	0
$640$	3.23094e8	1.23251
$641$	− 7.52414e7i	− 0.285682i	−0.989746	−	0.142841i	$-0.954376\pi$
$641$	− 7.52414e7i	− 0.285682i	0.989746	−	0.142841i	$-0.0456238\pi$
$642$	0	0
$643$	−2.21573e8	−0.833457	−0.416728	−	0.909031i	$-0.636823\pi$
$643$	−2.21573e8	−0.833457	−0.416728	+	0.909031i	$0.636823\pi$
$644$	1.11133e8i	0.416087i
$645$	0	0
$646$	−7.31996e8	−2.71526
$647$	− 3.67765e8i	− 1.35787i	−0.734199	−	0.678934i	$-0.762442\pi$
$647$	− 3.67765e8i	− 1.35787i	0.734199	−	0.678934i	$-0.237558\pi$
$648$	0	0
$649$	−1.46210e8	−0.534864
$650$	1.83704e7i	0.0668928i
$651$	0	0
$652$	−1.78786e8	−0.645046
$653$	1.37694e8i	0.494509i	0.968951	+	0.247255i	$0.0795284\pi$
$653$	1.37694e8i	0.494509i	−0.968951	+	0.247255i	$0.920472\pi$
$654$	0	0
$655$	4.26994e8	1.51949
$656$	− 3.59804e8i	− 1.27454i
$657$	0	0
$658$	−1.03224e8	−0.362330
$659$	− 5.43046e7i	− 0.189750i	−0.995489	−	0.0948748i	$-0.969755\pi$
$659$	− 5.43046e7i	− 0.189750i	0.995489	−	0.0948748i	$-0.0302451\pi$
$660$	0	0
$661$	4.43002e8	1.53392	0.766958	−	0.641698i	$-0.221770\pi$
$661$	4.43002e8	1.53392	0.766958	+	0.641698i	$0.221770\pi$
$662$	1.04128e8i	0.358917i
$663$	0	0
$664$	−3.48156e7	−0.118924
$665$	− 4.29322e8i	− 1.45988i
$666$	0	0
$667$	2.61612e7	0.0881617
$668$	4.98648e7i	0.167288i
$669$	0	0
$670$	1.07830e8	0.358520
$671$	− 4.09204e8i	− 1.35448i
$672$	0	0
$673$	−5.25320e8	−1.72337	−0.861685	−	0.507443i	$-0.830591\pi$
$673$	−5.25320e8	−1.72337	−0.861685	+	0.507443i	$0.830591\pi$
$674$	8.07932e7i	0.263873i
$675$	0	0
$676$	1.01485e8	0.328522
$677$	− 1.01517e8i	− 0.327170i	−0.986529	−	0.163585i	$-0.947694\pi$
$677$	− 1.01517e8i	− 0.327170i	0.986529	−	0.163585i	$-0.0523058\pi$
$678$	0	0
$679$	4.82517e8	1.54136
$680$	− 4.60589e8i	− 1.46483i
$681$	0	0
$682$	6.94704e8	2.19001
$683$	5.87819e7i	0.184494i	0.995736	+	0.0922468i	$0.0294049\pi$
$683$	5.87819e7i	0.184494i	−0.995736	+	0.0922468i	$0.970595\pi$
$684$	0	0
$685$	−3.82307e8	−1.18943
$686$	2.78669e8i	0.863209i
$687$	0	0
$688$	3.09117e8	0.949201
$689$	1.32267e8i	0.404385i
$690$	0	0
$691$	2.05775e8	0.623675	0.311838	−	0.950135i	$-0.399055\pi$
$691$	2.05775e8	0.623675	0.311838	+	0.950135i	$0.399055\pi$
$692$	9.94159e7i	0.300011i
$693$	0	0
$694$	5.01106e8	1.49917
$695$	− 1.96118e8i	− 0.584202i
$696$	0	0
$697$	−6.80800e8	−2.01058
$698$	4.73552e8i	1.39252i
$699$	0	0
$700$	−2.11132e7	−0.0615544
$701$	1.77405e8i	0.515005i	0.966278	+	0.257502i	$0.0828995\pi$
$701$	1.77405e8i	0.515005i	−0.966278	+	0.257502i	$0.917100\pi$
$702$	0	0
$703$	1.93844e8	0.557937
$704$	1.29950e8i	0.372443i
$705$	0	0
$706$	−2.47464e6	−0.00703231
$707$	− 3.56260e8i	− 1.00811i
$708$	0	0
$709$	4.04116e7	0.113388	0.0566941	−	0.998392i	$-0.481944\pi$
$709$	4.04116e7	0.113388	0.0566941	+	0.998392i	$0.481944\pi$
$710$	− 4.30610e8i	− 1.20312i
$711$	0	0
$712$	4.30325e8	1.19222
$713$	5.18159e8i	1.42953i
$714$	0	0
$715$	−1.91316e8	−0.523399
$716$	− 4.16338e7i	− 0.113425i
$717$	0	0
$718$	2.43702e6	0.00658394
$719$	3.24675e8i	0.873498i	0.899583	+	0.436749i	$0.143870\pi$
$719$	3.24675e8i	0.873498i	−0.899583	+	0.436749i	$0.856130\pi$
$720$	0	0
$721$	−4.73176e8	−1.26246
$722$	1.64033e8i	0.435832i
$723$	0	0
$724$	−1.48368e7	−0.0390954
$725$	4.97015e6i	0.0130423i
$726$	0	0
$727$	5.43116e8	1.41348	0.706740	−	0.707473i	$-0.250165\pi$
$727$	5.43116e8	1.41348	0.706740	+	0.707473i	$0.250165\pi$
$728$	1.39615e8i	0.361859i
$729$	0	0
$730$	1.92449e8	0.494705
$731$	− 5.84894e8i	− 1.49736i
$732$	0	0
$733$	3.52488e8	0.895019	0.447510	−	0.894279i	$-0.352311\pi$
$733$	3.52488e8	0.895019	0.447510	+	0.894279i	$0.352311\pi$
$734$	3.08976e8i	0.781334i
$735$	0	0
$736$	2.66844e8	0.669305
$737$	1.28276e8i	0.320437i
$738$	0	0
$739$	−6.08455e8	−1.50763	−0.753816	−	0.657086i	$-0.771789\pi$
$739$	−6.08455e8	−1.50763	−0.753816	+	0.657086i	$0.771789\pi$
$740$	− 8.34537e7i	− 0.205945i
$741$	0	0
$742$	−5.26205e8	−1.28808
$743$	− 2.41845e8i	− 0.589618i	−0.955556	−	0.294809i	$-0.904744\pi$
$743$	− 2.41845e8i	− 0.589618i	0.955556	−	0.294809i	$-0.0952561\pi$
$744$	0	0
$745$	−7.42190e7	−0.179493
$746$	7.90697e8i	1.90455i
$747$	0	0
$748$	−3.74896e8	−0.895790
$749$	− 2.35287e8i	− 0.559954i
$750$	0	0
$751$	−4.98473e8	−1.17685	−0.588425	−	0.808551i	$-0.700252\pi$
$751$	−4.98473e8	−1.17685	−0.588425	+	0.808551i	$0.700252\pi$
$752$	1.37266e8i	0.322781i
$753$	0	0
$754$	−2.24874e7	−0.0524596
$755$	4.93727e8i	1.14722i
$756$	0	0
$757$	1.14551e8	0.264064	0.132032	−	0.991245i	$-0.457850\pi$
$757$	1.14551e8	0.264064	0.132032	+	0.991245i	$0.457850\pi$
$758$	− 6.93498e8i	− 1.59235i
$759$	0	0
$760$	−3.84045e8	−0.874867
$761$	3.91905e8i	0.889255i	0.895716	+	0.444628i	$0.146664\pi$
$761$	3.91905e8i	0.889255i	−0.895716	+	0.444628i	$0.853336\pi$
$762$	0	0
$763$	−7.60808e7	−0.171278
$764$	− 1.07811e8i	− 0.241758i
$765$	0	0
$766$	−3.74262e8	−0.832701
$767$	9.37394e7i	0.207748i
$768$	0	0
$769$	8.14384e7	0.179081	0.0895406	−	0.995983i	$-0.471460\pi$
$769$	8.14384e7	0.179081	0.0895406	+	0.995983i	$0.471460\pi$
$770$	− 7.61121e8i	− 1.66718i
$771$	0	0
$772$	1.16282e8	0.252732
$773$	− 7.23925e8i	− 1.56731i	−0.621196	−	0.783655i	$-0.713353\pi$
$773$	− 7.23925e8i	− 1.56731i	0.621196	−	0.783655i	$-0.286647\pi$
$774$	0	0
$775$	−9.84408e7	−0.211480
$776$	− 4.31631e8i	− 0.923692i
$777$	0	0
$778$	−7.12177e8	−1.51234
$779$	5.67660e8i	1.20082i
$780$	0	0
$781$	5.12261e8	1.07532
$782$	− 9.67929e8i	− 2.02406i
$783$	0	0
$784$	−2.27560e8	−0.472223
$785$	1.64288e8i	0.339623i
$786$	0	0
$787$	−8.81284e6	−0.0180797	−0.00903986	−	0.999959i	$-0.502878\pi$
$787$	−8.81284e6	−0.0180797	−0.00903986	+	0.999959i	$0.502878\pi$
$788$	− 3.08807e8i	− 0.631115i
$789$	0	0
$790$	9.33143e7	0.189264
$791$	6.62521e8i	1.33866i
$792$	0	0
$793$	−2.62352e8	−0.526096
$794$	6.02022e8i	1.20268i
$795$	0	0
$796$	−2.34700e7	−0.0465344
$797$	− 9.06857e8i	− 1.79128i	−0.444779	−	0.895640i	$-0.646718\pi$
$797$	− 9.06857e8i	− 1.79128i	0.444779	−	0.895640i	$-0.353282\pi$
$798$	0	0
$799$	2.59726e8	0.509184
$800$	5.06955e7i	0.0990147i
$801$	0	0
$802$	7.25088e8	1.40562
$803$	2.28940e8i	0.442156i
$804$	0	0
$805$	5.67698e8	1.08825
$806$	− 4.45394e8i	− 0.850628i
$807$	0	0
$808$	−3.18689e8	−0.604134
$809$	2.56667e8i	0.484757i	0.970182	+	0.242379i	$0.0779277\pi$
$809$	2.56667e8i	0.484757i	−0.970182	+	0.242379i	$0.922072\pi$
$810$	0	0
$811$	1.04558e8	0.196017	0.0980087	−	0.995186i	$-0.468753\pi$
$811$	1.04558e8	0.196017	0.0980087	+	0.995186i	$0.468753\pi$
$812$	− 2.58448e7i	− 0.0482731i
$813$	0	0
$814$	3.43655e8	0.637161
$815$	9.13292e8i	1.68708i
$816$	0	0
$817$	−4.87693e8	−0.894294
$818$	1.00795e9i	1.84153i
$819$	0	0
$820$	2.44390e8	0.443242
$821$	1.98313e8i	0.358361i	0.983816	+	0.179181i	$0.0573447\pi$
$821$	1.98313e8i	0.358361i	−0.983816	+	0.179181i	$0.942655\pi$
$822$	0	0
$823$	8.85085e7	0.158776	0.0793882	−	0.996844i	$-0.474703\pi$
$823$	8.85085e7	0.158776	0.0793882	+	0.996844i	$0.474703\pi$
$824$	4.23275e8i	0.756555i
$825$	0	0
$826$	−3.72928e8	−0.661736
$827$	− 9.40582e8i	− 1.66295i	−0.555560	−	0.831476i	$-0.687496\pi$
$827$	− 9.40582e8i	− 1.66295i	0.555560	−	0.831476i	$-0.312504\pi$
$828$	0	0
$829$	−4.25518e7	−0.0746886	−0.0373443	−	0.999302i	$-0.511890\pi$
$829$	−4.25518e7	−0.0746886	−0.0373443	+	0.999302i	$0.511890\pi$
$830$	− 1.21686e8i	− 0.212817i
$831$	0	0
$832$	8.33149e7	0.144661
$833$	4.30575e8i	0.744928i
$834$	0	0
$835$	2.54724e8	0.437533
$836$	3.12594e8i	0.535009i
$837$	0	0
$838$	3.58481e8	0.609164
$839$	3.62352e8i	0.613542i	0.951783	+	0.306771i	$0.0992486\pi$
$839$	3.62352e8i	0.613542i	−0.951783	+	0.306771i	$0.900751\pi$
$840$	0	0
$841$	5.88739e8	0.989772
$842$	− 1.49376e8i	− 0.250232i
$843$	0	0
$844$	−1.47559e8	−0.245437
$845$	− 5.18418e8i	− 0.859231i
$846$	0	0
$847$	1.91505e8	0.315159
$848$	6.99736e8i	1.14748i
$849$	0	0
$850$	1.83889e8	0.299432
$851$	2.56322e8i	0.415908i
$852$	0	0
$853$	1.14265e9	1.84106	0.920528	−	0.390676i	$-0.127759\pi$
$853$	1.14265e9	1.84106	0.920528	+	0.390676i	$0.127759\pi$
$854$	− 1.04373e9i	− 1.67577i
$855$	0	0
$856$	−2.10474e8	−0.335565
$857$	3.13910e8i	0.498727i	0.968410	+	0.249364i	$0.0802214\pi$
$857$	3.13910e8i	0.498727i	−0.968410	+	0.249364i	$0.919779\pi$
$858$	0	0
$859$	4.12608e8	0.650966	0.325483	−	0.945548i	$-0.394473\pi$
$859$	4.12608e8	0.650966	0.325483	+	0.945548i	$0.394473\pi$
$860$	2.09962e8i	0.330100i
$861$	0	0
$862$	−3.00181e8	−0.468664
$863$	− 7.45960e8i	− 1.16060i	−0.814402	−	0.580301i	$-0.802935\pi$
$863$	− 7.45960e8i	− 1.16060i	0.814402	−	0.580301i	$-0.197065\pi$
$864$	0	0
$865$	5.07846e8	0.784663
$866$	− 6.17573e8i	− 0.950899i
$867$	0	0
$868$	5.11892e8	0.782743
$869$	1.11008e8i	0.169160i
$870$	0	0
$871$	8.22414e7	0.124462
$872$	6.80573e7i	0.102642i
$873$	0	0
$874$	−8.07073e8	−1.20887
$875$	− 7.28471e8i	− 1.08740i
$876$	0	0
$877$	−8.19374e8	−1.21474	−0.607370	−	0.794419i	$-0.707775\pi$
$877$	−8.19374e8	−1.21474	−0.607370	+	0.794419i	$0.707775\pi$
$878$	− 2.98907e8i	− 0.441624i
$879$	0	0
$880$	−1.01212e9	−1.48520
$881$	− 1.15485e9i	− 1.68888i	−0.535653	−	0.844438i	$-0.679935\pi$
$881$	− 1.15485e9i	− 1.68888i	0.535653	−	0.844438i	$-0.320065\pi$
$882$	0	0
$883$	3.95346e8	0.574242	0.287121	−	0.957894i	$-0.407302\pi$
$883$	3.95346e8	0.574242	0.287121	+	0.957894i	$0.407302\pi$
$884$	2.40357e8i	0.347936i
$885$	0	0
$886$	1.33909e8	0.192534
$887$	− 7.42510e8i	− 1.06398i	−0.846752	−	0.531988i	$-0.821445\pi$
$887$	− 7.42510e8i	− 1.06398i	0.846752	−	0.531988i	$-0.178555\pi$
$888$	0	0
$889$	−1.24971e9	−1.77870
$890$	1.50405e9i	2.13350i
$891$	0	0
$892$	1.46839e8	0.206893
$893$	− 2.16563e8i	− 0.304110i
$894$	0	0
$895$	−2.12678e8	−0.296656
$896$	9.80359e8i	1.36289i
$897$	0	0
$898$	−4.63340e8	−0.639839
$899$	− 1.20502e8i	− 0.165850i
$900$	0	0
$901$	1.32400e9	1.81015
$902$	1.00637e9i	1.37132i
$903$	0	0
$904$	5.92652e8	0.802222
$905$	7.57909e7i	0.102252i
$906$	0	0
$907$	−1.22377e9	−1.64013	−0.820064	−	0.572271i	$-0.806062\pi$
$907$	−1.22377e9	−1.64013	−0.820064	+	0.572271i	$0.806062\pi$
$908$	3.27135e8i	0.436988i
$909$	0	0
$910$	−4.87977e8	−0.647552
$911$	− 7.85220e8i	− 1.03857i	−0.854601	−	0.519286i	$-0.826198\pi$
$911$	− 7.85220e8i	− 1.03857i	0.854601	−	0.519286i	$-0.173802\pi$
$912$	0	0
$913$	1.44760e8	0.190211
$914$	− 1.54580e9i	− 2.02449i
$915$	0	0
$916$	1.69459e8	0.220485
$917$	1.29562e9i	1.68023i
$918$	0	0
$919$	−5.58148e8	−0.719122	−0.359561	−	0.933121i	$-0.617074\pi$
$919$	−5.58148e8	−0.719122	−0.359561	+	0.933121i	$0.617074\pi$
$920$	− 5.07829e8i	− 0.652159i
$921$	0	0
$922$	−1.14917e9	−1.46620
$923$	− 3.28425e8i	− 0.417668i
$924$	0	0
$925$	−4.86965e7	−0.0615280
$926$	− 1.02684e9i	− 1.29321i
$927$	0	0
$928$	−6.20568e7	−0.0776507
$929$	− 6.71174e8i	− 0.837121i	−0.908189	−	0.418560i	$-0.862535\pi$
$929$	− 6.71174e8i	− 0.837121i	0.908189	−	0.418560i	$-0.137465\pi$
$930$	0	0
$931$	3.59020e8	0.444907
$932$	2.16481e8i	0.267406i
$933$	0	0
$934$	−4.80456e8	−0.589675
$935$	1.91508e9i	2.34289i
$936$	0	0
$937$	−4.07277e8	−0.495076	−0.247538	−	0.968878i	$-0.579621\pi$
$937$	−4.07277e8	−0.495076	−0.247538	+	0.968878i	$0.579621\pi$
$938$	3.27185e8i	0.396447i
$939$	0	0
$940$	−9.32350e7	−0.112252
$941$	1.47225e9i	1.76691i	0.468519	+	0.883454i	$0.344788\pi$
$941$	1.47225e9i	1.76691i	−0.468519	+	0.883454i	$0.655212\pi$
$942$	0	0
$943$	−7.50625e8	−0.895134
$944$	4.95912e8i	0.589506i
$945$	0	0
$946$	−8.64604e8	−1.02128
$947$	9.19598e8i	1.08280i	0.840765	+	0.541400i	$0.182105\pi$
$947$	9.19598e8i	1.08280i	−0.840765	+	0.541400i	$0.817895\pi$
$948$	0	0
$949$	1.46780e8	0.171739
$950$	− 1.53329e8i	− 0.178836i
$951$	0	0
$952$	1.39756e9	1.61979
$953$	9.44943e8i	1.09176i	0.837863	+	0.545880i	$0.183804\pi$
$953$	9.44943e8i	1.09176i	−0.837863	+	0.545880i	$0.816196\pi$
$954$	0	0
$955$	−5.50728e8	−0.632306
$956$	− 5.41425e8i	− 0.619676i
$957$	0	0
$958$	1.66937e9	1.89869
$959$	− 1.16003e9i	− 1.31526i
$960$	0	0
$961$	1.49921e9	1.68924
$962$	− 2.20327e8i	− 0.247481i
$963$	0	0
$964$	−1.20361e8	−0.134356
$965$	− 5.94002e8i	− 0.661007i
$966$	0	0
$967$	−8.95990e7	−0.0990886	−0.0495443	−	0.998772i	$-0.515777\pi$
$967$	−8.95990e7	−0.0990886	−0.0495443	+	0.998772i	$0.515777\pi$
$968$	− 1.71309e8i	− 0.188866i
$969$	0	0
$970$	1.50861e9	1.65296
$971$	− 3.70582e8i	− 0.404787i	−0.979304	−	0.202394i	$-0.935128\pi$
$971$	− 3.70582e8i	− 0.404787i	0.979304	−	0.202394i	$-0.0648720\pi$
$972$	0	0
$973$	5.95077e8	0.646004
$974$	1.26143e9i	1.36517i
$975$	0	0
$976$	−1.38793e9	−1.49285
$977$	− 1.44270e8i	− 0.154701i	−0.997004	−	0.0773505i	$-0.975354\pi$
$977$	− 1.44270e8i	− 0.154701i	0.997004	−	0.0773505i	$-0.0246460\pi$
$978$	0	0
$979$	−1.78925e9	−1.90687
$980$	− 1.54566e8i	− 0.164223i
$981$	0	0
$982$	2.03361e9	2.14750
$983$	− 4.37801e8i	− 0.460910i	−0.973083	−	0.230455i	$-0.925979\pi$
$983$	− 4.37801e8i	− 0.460910i	0.973083	−	0.230455i	$-0.0740214\pi$
$984$	0	0
$985$	−1.57748e9	−1.65065
$986$	2.25100e8i	0.234825i
$987$	0	0
$988$	2.00413e8	0.207804
$989$	− 6.44883e8i	− 0.666641i
$990$	0	0
$991$	−4.48947e8	−0.461290	−0.230645	−	0.973038i	$-0.574084\pi$
$991$	−4.48947e8	−0.461290	−0.230645	+	0.973038i	$0.574084\pi$
$992$	− 1.22912e9i	− 1.25910i
$993$	0	0
$994$	1.30659e9	1.33039
$995$	1.19892e8i	0.121708i
$996$	0	0
$997$	1.04433e9	1.05378	0.526892	−	0.849932i	$-0.323357\pi$
$997$	1.04433e9	1.05378	0.526892	+	0.849932i	$0.323357\pi$
$998$	− 1.72777e9i	− 1.73818i
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	27.7.b.a.26.2	yes	2
3.2	odd	2	inner	27.7.b.a.26.1	✓	2
4.3	odd	2		432.7.e.g.161.2		2
9.2	odd	6		81.7.d.c.53.1		4
9.4	even	3		81.7.d.c.26.1		4
9.5	odd	6		81.7.d.c.26.2		4
9.7	even	3		81.7.d.c.53.2		4
12.11	even	2		432.7.e.g.161.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
27.7.b.a.26.1	✓	2	3.2	odd	2	inner
27.7.b.a.26.2	yes	2	1.1	even	1	trivial
81.7.d.c.26.1		4	9.4	even	3
81.7.d.c.26.2		4	9.5	odd	6
81.7.d.c.53.1		4	9.2	odd	6
81.7.d.c.53.2		4	9.7	even	3
432.7.e.g.161.1		2	12.11	even	2
432.7.e.g.161.2		2	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)

\(f(q)\)	\(=\)	\(q+9.48683i q^{2} -26.0000 q^{4} +132.816i q^{5} -403.000 q^{7} +360.500i q^{8} +O(q^{10})\)	\(q+9.48683i q^{2} -26.0000 q^{4} +132.816i q^{5} -403.000 q^{7} +360.500i q^{8} -1260.00 q^{10} -1498.92i q^{11} -961.000 q^{13} -3823.19i q^{14} -5084.00 q^{16} +9619.65i q^{17} +8021.00 q^{19} -3453.21i q^{20} +14220.0 q^{22} +10606.3i q^{23} -2015.00 q^{25} -9116.85i q^{26} +10478.0 q^{28} -2466.58i q^{29} +48854.0 q^{31} -25159.1i q^{32} -91260.0 q^{34} -53524.7i q^{35} +24167.0 q^{37} +76093.9i q^{38} -47880.0 q^{40} +70771.8i q^{41} -60802.0 q^{43} +38971.9i q^{44} -100620. q^{46} -26999.5i q^{47} +44760.0 q^{49} -19116.0i q^{50} +24986.0 q^{52} -137635. i q^{53} +199080. q^{55} -145281. i q^{56} +23400.0 q^{58} -97543.6i q^{59} +272999. q^{61} +463470. i q^{62} -86696.0 q^{64} -127636. i q^{65} -85579.0 q^{67} -250111. i q^{68} +507780. q^{70} +341754. i q^{71} -152737. q^{73} +229268. i q^{74} -208546. q^{76} +604065. i q^{77} -74059.0 q^{79} -675235. i q^{80} -671400. q^{82} +96576.0i q^{83} -1.27764e6 q^{85} -576818. i q^{86} +540360. q^{88} -1.19369e6i q^{89} +387283. q^{91} -275763. i q^{92} +256140. q^{94} +1.06531e6i q^{95} -1.19731e6 q^{97} +424631. i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 52 q^{4} - 806 q^{7}+O(q^{10}) \) 2 * q - 52 * q^4 - 806 * q^7	\( 2 q - 52 q^{4} - 806 q^{7} - 2520 q^{10} - 1922 q^{13} - 10168 q^{16} + 16042 q^{19} + 28440 q^{22} - 4030 q^{25} + 20956 q^{28} + 97708 q^{31} - 182520 q^{34} + 48334 q^{37} - 95760 q^{40} - 121604 q^{43} - 201240 q^{46} + 89520 q^{49} + 49972 q^{52} + 398160 q^{55} + 46800 q^{58} + 545998 q^{61} - 173392 q^{64} - 171158 q^{67} + 1015560 q^{70} - 305474 q^{73} - 417092 q^{76} - 148118 q^{79} - 1342800 q^{82} - 2555280 q^{85} + 1080720 q^{88} + 774566 q^{91} + 512280 q^{94} - 2394626 q^{97}+O(q^{100}) \) 2 * q - 52 * q^4 - 806 * q^7 - 2520 * q^10 - 1922 * q^13 - 10168 * q^16 + 16042 * q^19 + 28440 * q^22 - 4030 * q^25 + 20956 * q^28 + 97708 * q^31 - 182520 * q^34 + 48334 * q^37 - 95760 * q^40 - 121604 * q^43 - 201240 * q^46 + 89520 * q^49 + 49972 * q^52 + 398160 * q^55 + 46800 * q^58 + 545998 * q^61 - 173392 * q^64 - 171158 * q^67 + 1015560 * q^70 - 305474 * q^73 - 417092 * q^76 - 148118 * q^79 - 1342800 * q^82 - 2555280 * q^85 + 1080720 * q^88 + 774566 * q^91 + 512280 * q^94 - 2394626 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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