LMFDB - Embedded newform 3024.2.t.e.289.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [3024,2,Mod(289,3024)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(3024, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 4, 2])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("3024.289"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 3024 = 2^{4} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3024.t (of order $3$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [2,0,0,0,2,0,1] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$24.1467615712$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{17}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 504)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			289.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	3024.289
Dual form			3024.2.t.e.1873.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{5} +(0.500000 - 2.59808i) q^{7} +3.00000 q^{11} +(-1.50000 - 2.59808i) q^{13} +(-2.50000 - 4.33013i) q^{17} +(3.50000 - 6.06218i) q^{19} +5.00000 q^{23} -4.00000 q^{25} +(-0.500000 + 0.866025i) q^{29} +(-4.00000 + 6.92820i) q^{31} +(0.500000 - 2.59808i) q^{35} +(-1.50000 + 2.59808i) q^{37} +(-2.50000 - 4.33013i) q^{41} +(-3.50000 + 6.06218i) q^{43} +(-4.00000 - 6.92820i) q^{47} +(-6.50000 - 2.59808i) q^{49} +(-0.500000 - 0.866025i) q^{53} +3.00000 q^{55} +(-5.00000 - 8.66025i) q^{61} +(-1.50000 - 2.59808i) q^{65} +(-6.00000 + 10.3923i) q^{67} +12.0000 q^{71} +(2.50000 + 4.33013i) q^{73} +(1.50000 - 7.79423i) q^{77} +(-4.00000 - 6.92820i) q^{79} +(7.50000 - 12.9904i) q^{83} +(-2.50000 - 4.33013i) q^{85} +(-2.50000 + 4.33013i) q^{89} +(-7.50000 + 2.59808i) q^{91} +(3.50000 - 6.06218i) q^{95} +(-3.50000 + 6.06218i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 2 q^{5} + q^{7} + 6 q^{11} - 3 q^{13} - 5 q^{17} + 7 q^{19} + 10 q^{23} - 8 q^{25} - q^{29} - 8 q^{31} + q^{35} - 3 q^{37} - 5 q^{41} - 7 q^{43} - 8 q^{47} - 13 q^{49} - q^{53} + 6 q^{55} - 10 q^{61}+ \cdots - 7 q^{97}+O(q^{100}) $ 2 * q + 2 * q^5 + q^7 + 6 * q^11 - 3 * q^13 - 5 * q^17 + 7 * q^19 + 10 * q^23 - 8 * q^25 - q^29 - 8 * q^31 + q^35 - 3 * q^37 - 5 * q^41 - 7 * q^43 - 8 * q^47 - 13 * q^49 - q^53 + 6 * q^55 - 10 * q^61 - 3 * q^65 - 12 * q^67 + 24 * q^71 + 5 * q^73 + 3 * q^77 - 8 * q^79 + 15 * q^83 - 5 * q^85 - 5 * q^89 - 15 * q^91 + 7 * q^95 - 7 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/3024\mathbb{Z}\right)^\times$.

$n$	$757$	$785$	$1135$	$2593$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$1$	$e\left(\frac{1}{3}\right)$

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 $

$2$		0			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	1.00000			0.447214			0.223607	−	0.974679i	$-0.428217\pi$
$5$	1.00000			0.447214			0.223607	+	0.974679i	$0.428217\pi$
$6$		0			0
$7$	0.500000	−	2.59808i	0.188982	−	0.981981i
$7$	0.500000	−	2.59808i	0.188982	−	0.981981i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	3.00000			0.904534			0.452267	−	0.891883i	$-0.350615\pi$
$11$	3.00000			0.904534			0.452267	+	0.891883i	$0.350615\pi$
$12$		0			0
$13$	−1.50000	−	2.59808i	−0.416025	−	0.720577i	0.579510	−	0.814965i	$-0.303244\pi$
$13$	−1.50000	−	2.59808i	−0.416025	−	0.720577i	−0.995535	+	0.0943882i	$0.969911\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−2.50000	−	4.33013i	−0.606339	−	1.05021i	−0.991838	−	0.127502i	$-0.959304\pi$
$17$	−2.50000	−	4.33013i	−0.606339	−	1.05021i	0.385499	−	0.922708i	$-0.374029\pi$
$18$		0			0
$19$	3.50000	−	6.06218i	0.802955	−	1.39076i	−0.114708	−	0.993399i	$-0.536593\pi$
$19$	3.50000	−	6.06218i	0.802955	−	1.39076i	0.917663	−	0.397360i	$-0.130073\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	5.00000			1.04257			0.521286	−	0.853382i	$-0.325452\pi$
$23$	5.00000			1.04257			0.521286	+	0.853382i	$0.325452\pi$
$24$		0			0
$25$	−4.00000			−0.800000
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−0.500000	+	0.866025i	−0.0928477	+	0.160817i	−0.908708	−	0.417432i	$-0.862930\pi$
$29$	−0.500000	+	0.866025i	−0.0928477	+	0.160817i	0.815861	+	0.578249i	$0.196264\pi$
$30$		0			0
$31$	−4.00000	+	6.92820i	−0.718421	+	1.24434i	0.243204	+	0.969975i	$0.421802\pi$
$31$	−4.00000	+	6.92820i	−0.718421	+	1.24434i	−0.961625	+	0.274367i	$0.911532\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	0.500000	−	2.59808i	0.0845154	−	0.439155i
$36$		0			0
$37$	−1.50000	+	2.59808i	−0.246598	+	0.427121i	−0.962580	−	0.270998i	$-0.912646\pi$
$37$	−1.50000	+	2.59808i	−0.246598	+	0.427121i	0.715981	+	0.698119i	$0.245980\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−2.50000	−	4.33013i	−0.390434	−	0.676252i	0.602072	−	0.798441i	$-0.294342\pi$
$41$	−2.50000	−	4.33013i	−0.390434	−	0.676252i	−0.992507	+	0.122189i	$0.961009\pi$
$42$		0			0
$43$	−3.50000	+	6.06218i	−0.533745	+	0.924473i	0.465478	+	0.885059i	$0.345882\pi$
$43$	−3.50000	+	6.06218i	−0.533745	+	0.924473i	−0.999223	+	0.0394140i	$0.987451\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−4.00000	−	6.92820i	−0.583460	−	1.01058i	−0.995066	−	0.0992202i	$-0.968365\pi$
$47$	−4.00000	−	6.92820i	−0.583460	−	1.01058i	0.411606	−	0.911362i	$-0.364968\pi$
$48$		0			0
$49$	−6.50000	−	2.59808i	−0.928571	−	0.371154i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−0.500000	−	0.866025i	−0.0686803	−	0.118958i	0.829640	−	0.558298i	$-0.188546\pi$
$53$	−0.500000	−	0.866025i	−0.0686803	−	0.118958i	−0.898321	+	0.439340i	$0.855212\pi$
$54$		0			0
$55$	3.00000			0.404520
$56$		0			0
$57$		0			0
$58$		0			0
$59$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$59$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$60$		0			0
$61$	−5.00000	−	8.66025i	−0.640184	−	1.10883i	−0.985391	−	0.170305i	$-0.945525\pi$
$61$	−5.00000	−	8.66025i	−0.640184	−	1.10883i	0.345207	−	0.938527i	$-0.387809\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−1.50000	−	2.59808i	−0.186052	−	0.322252i
$66$		0			0
$67$	−6.00000	+	10.3923i	−0.733017	+	1.26962i	0.222571	+	0.974916i	$0.428555\pi$
$67$	−6.00000	+	10.3923i	−0.733017	+	1.26962i	−0.955588	+	0.294706i	$0.904778\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	12.0000			1.42414			0.712069	−	0.702109i	$-0.247758\pi$
$71$	12.0000			1.42414			0.712069	+	0.702109i	$0.247758\pi$
$72$		0			0
$73$	2.50000	+	4.33013i	0.292603	+	0.506803i	0.974424	−	0.224716i	$-0.0721453\pi$
$73$	2.50000	+	4.33013i	0.292603	+	0.506803i	−0.681822	+	0.731519i	$0.738812\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	1.50000	−	7.79423i	0.170941	−	0.888235i
$78$		0			0
$79$	−4.00000	−	6.92820i	−0.450035	−	0.779484i	0.548352	−	0.836247i	$-0.315255\pi$
$79$	−4.00000	−	6.92820i	−0.450035	−	0.779484i	−0.998388	+	0.0567635i	$0.981922\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	7.50000	−	12.9904i	0.823232	−	1.42588i	−0.0800311	−	0.996792i	$-0.525502\pi$
$83$	7.50000	−	12.9904i	0.823232	−	1.42588i	0.903263	−	0.429087i	$-0.141165\pi$
$84$		0			0
$85$	−2.50000	−	4.33013i	−0.271163	−	0.469668i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−2.50000	+	4.33013i	−0.264999	+	0.458993i	−0.967563	−	0.252628i	$-0.918705\pi$
$89$	−2.50000	+	4.33013i	−0.264999	+	0.458993i	0.702564	+	0.711621i	$0.252038\pi$
$90$		0			0
$91$	−7.50000	+	2.59808i	−0.786214	+	0.272352i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	3.50000	−	6.06218i	0.359092	−	0.621966i
$96$		0			0
$97$	−3.50000	+	6.06218i	−0.355371	+	0.615521i	−0.987181	−	0.159602i	$-0.948979\pi$
$97$	−3.50000	+	6.06218i	−0.355371	+	0.615521i	0.631810	+	0.775123i	$0.282312\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	9.00000			0.895533			0.447767	−	0.894150i	$-0.352219\pi$
$101$	9.00000			0.895533			0.447767	+	0.894150i	$0.352219\pi$
$102$		0			0
$103$	15.0000			1.47799			0.738997	−	0.673709i	$-0.235300\pi$
$103$	15.0000			1.47799			0.738997	+	0.673709i	$0.235300\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	4.50000	−	7.79423i	0.435031	−	0.753497i	−0.562267	−	0.826956i	$-0.690071\pi$
$107$	4.50000	−	7.79423i	0.435031	−	0.753497i	0.997298	+	0.0734594i	$0.0234039\pi$
$108$		0			0
$109$	−3.50000	−	6.06218i	−0.335239	−	0.580651i	0.648292	−	0.761392i	$-0.275484\pi$
$109$	−3.50000	−	6.06218i	−0.335239	−	0.580651i	−0.983531	+	0.180741i	$0.942150\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	7.50000	+	12.9904i	0.705541	+	1.22203i	0.966496	+	0.256681i	$0.0826291\pi$
$113$	7.50000	+	12.9904i	0.705541	+	1.22203i	−0.260955	+	0.965351i	$0.584038\pi$
$114$		0			0
$115$	5.00000			0.466252
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−12.5000	+	4.33013i	−1.14587	+	0.396942i
$120$		0			0
$121$	−2.00000			−0.181818
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−9.00000			−0.804984
$126$		0			0
$127$	4.00000			0.354943			0.177471	−	0.984126i	$-0.443208\pi$
$127$	4.00000			0.354943			0.177471	+	0.984126i	$0.443208\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−7.00000			−0.611593			−0.305796	−	0.952097i	$-0.598923\pi$
$131$	−7.00000			−0.611593			−0.305796	+	0.952097i	$0.598923\pi$
$132$		0			0
$133$	−14.0000	−	12.1244i	−1.21395	−	1.05131i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−23.0000			−1.96502			−0.982511	−	0.186203i	$-0.940382\pi$
$137$	−23.0000			−1.96502			−0.982511	+	0.186203i	$0.940382\pi$
$138$		0			0
$139$	−4.50000	−	7.79423i	−0.381685	−	0.661098i	0.609618	−	0.792695i	$-0.291323\pi$
$139$	−4.50000	−	7.79423i	−0.381685	−	0.661098i	−0.991303	+	0.131597i	$0.957989\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−4.50000	−	7.79423i	−0.376309	−	0.651786i
$144$		0			0
$145$	−0.500000	+	0.866025i	−0.0415227	+	0.0719195i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	5.00000			0.409616			0.204808	−	0.978802i	$-0.434343\pi$
$149$	5.00000			0.409616			0.204808	+	0.978802i	$0.434343\pi$
$150$		0			0
$151$	5.00000			0.406894			0.203447	−	0.979086i	$-0.434786\pi$
$151$	5.00000			0.406894			0.203447	+	0.979086i	$0.434786\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−4.00000	+	6.92820i	−0.321288	+	0.556487i
$156$		0			0
$157$	3.00000	−	5.19615i	0.239426	−	0.414698i	−0.721124	−	0.692806i	$-0.756374\pi$
$157$	3.00000	−	5.19615i	0.239426	−	0.414698i	0.960550	+	0.278108i	$0.0897074\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	2.50000	−	12.9904i	0.197028	−	1.02379i
$162$		0			0
$163$	−2.50000	+	4.33013i	−0.195815	+	0.339162i	−0.947167	−	0.320740i	$-0.896069\pi$
$163$	−2.50000	+	4.33013i	−0.195815	+	0.339162i	0.751352	+	0.659901i	$0.229402\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	10.5000	+	18.1865i	0.812514	+	1.40732i	0.911099	+	0.412188i	$0.135235\pi$
$167$	10.5000	+	18.1865i	0.812514	+	1.40732i	−0.0985846	+	0.995129i	$0.531432\pi$
$168$		0			0
$169$	2.00000	−	3.46410i	0.153846	−	0.266469i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	1.00000	+	1.73205i	0.0760286	+	0.131685i	0.901533	−	0.432710i	$-0.142443\pi$
$173$	1.00000	+	1.73205i	0.0760286	+	0.131685i	−0.825505	+	0.564396i	$0.809109\pi$
$174$		0			0
$175$	−2.00000	+	10.3923i	−0.151186	+	0.785584i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−2.50000	−	4.33013i	−0.186859	−	0.323649i	0.757343	−	0.653018i	$-0.226497\pi$
$179$	−2.50000	−	4.33013i	−0.186859	−	0.323649i	−0.944201	+	0.329369i	$0.893164\pi$
$180$		0			0
$181$	2.00000			0.148659			0.0743294	−	0.997234i	$-0.476318\pi$
$181$	2.00000			0.148659			0.0743294	+	0.997234i	$0.476318\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−1.50000	+	2.59808i	−0.110282	+	0.191014i
$186$		0			0
$187$	−7.50000	−	12.9904i	−0.548454	−	0.949951i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−8.00000	−	13.8564i	−0.578860	−	1.00261i	−0.995610	−	0.0935936i	$-0.970165\pi$
$191$	−8.00000	−	13.8564i	−0.578860	−	1.00261i	0.416751	−	0.909021i	$-0.363169\pi$
$192$		0			0
$193$	9.00000	−	15.5885i	0.647834	−	1.12208i	−0.335805	−	0.941932i	$-0.609008\pi$
$193$	9.00000	−	15.5885i	0.647834	−	1.12208i	0.983639	−	0.180150i	$-0.0576584\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	6.00000			0.427482			0.213741	−	0.976890i	$-0.431435\pi$
$197$	6.00000			0.427482			0.213741	+	0.976890i	$0.431435\pi$
$198$		0			0
$199$	−9.50000	−	16.4545i	−0.673437	−	1.16643i	−0.976923	−	0.213591i	$-0.931484\pi$
$199$	−9.50000	−	16.4545i	−0.673437	−	1.16643i	0.303486	−	0.952836i	$-0.401849\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	2.00000	+	1.73205i	0.140372	+	0.121566i
$204$		0			0
$205$	−2.50000	−	4.33013i	−0.174608	−	0.302429i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	10.5000	−	18.1865i	0.726300	−	1.25799i
$210$		0			0
$211$	−6.50000	−	11.2583i	−0.447478	−	0.775055i	0.550743	−	0.834675i	$-0.314345\pi$
$211$	−6.50000	−	11.2583i	−0.447478	−	0.775055i	−0.998221	+	0.0596196i	$0.981011\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−3.50000	+	6.06218i	−0.238698	+	0.413437i
$216$		0			0
$217$	16.0000	+	13.8564i	1.08615	+	0.940634i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−7.50000	+	12.9904i	−0.504505	+	0.873828i
$222$		0			0
$223$	10.5000	−	18.1865i	0.703132	−	1.21786i	−0.264229	−	0.964460i	$-0.585118\pi$
$223$	10.5000	−	18.1865i	0.703132	−	1.21786i	0.967361	−	0.253401i	$-0.0815490\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	11.0000			0.730096			0.365048	−	0.930989i	$-0.381053\pi$
$227$	11.0000			0.730096			0.365048	+	0.930989i	$0.381053\pi$
$228$		0			0
$229$	−1.00000			−0.0660819			−0.0330409	−	0.999454i	$-0.510519\pi$
$229$	−1.00000			−0.0660819			−0.0330409	+	0.999454i	$0.510519\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	5.50000	−	9.52628i	0.360317	−	0.624087i	−0.627696	−	0.778459i	$-0.716002\pi$
$233$	5.50000	−	9.52628i	0.360317	−	0.624087i	0.988013	+	0.154371i	$0.0493352\pi$
$234$		0			0
$235$	−4.00000	−	6.92820i	−0.260931	−	0.451946i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	12.5000	+	21.6506i	0.808558	+	1.40046i	0.913863	+	0.406023i	$0.133085\pi$
$239$	12.5000	+	21.6506i	0.808558	+	1.40046i	−0.105305	+	0.994440i	$0.533582\pi$
$240$		0			0
$241$	−5.00000			−0.322078			−0.161039	−	0.986948i	$-0.551485\pi$
$241$	−5.00000			−0.322078			−0.161039	+	0.986948i	$0.551485\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−6.50000	−	2.59808i	−0.415270	−	0.165985i
$246$		0			0
$247$	−21.0000			−1.33620
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−20.0000			−1.26239			−0.631194	−	0.775625i	$-0.717435\pi$
$251$	−20.0000			−1.26239			−0.631194	+	0.775625i	$0.717435\pi$
$252$		0			0
$253$	15.0000			0.943042
$254$		0			0
$255$		0			0
$256$		0			0
$257$	21.0000			1.30994			0.654972	−	0.755653i	$-0.272680\pi$
$257$	21.0000			1.30994			0.654972	+	0.755653i	$0.272680\pi$
$258$		0			0
$259$	6.00000	+	5.19615i	0.372822	+	0.322873i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	27.0000			1.66489			0.832446	−	0.554107i	$-0.186940\pi$
$263$	27.0000			1.66489			0.832446	+	0.554107i	$0.186940\pi$
$264$		0			0
$265$	−0.500000	−	0.866025i	−0.0307148	−	0.0531995i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	1.50000	+	2.59808i	0.0914566	+	0.158408i	0.908124	−	0.418701i	$-0.137514\pi$
$269$	1.50000	+	2.59808i	0.0914566	+	0.158408i	−0.816668	+	0.577108i	$0.804181\pi$
$270$		0			0
$271$	11.5000	−	19.9186i	0.698575	−	1.20997i	−0.270385	−	0.962752i	$-0.587151\pi$
$271$	11.5000	−	19.9186i	0.698575	−	1.20997i	0.968960	−	0.247216i	$-0.0795156\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−12.0000			−0.723627
$276$		0			0
$277$	−5.00000			−0.300421			−0.150210	−	0.988654i	$-0.547995\pi$
$277$	−5.00000			−0.300421			−0.150210	+	0.988654i	$0.547995\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	13.5000	−	23.3827i	0.805342	−	1.39489i	−0.110717	−	0.993852i	$-0.535315\pi$
$281$	13.5000	−	23.3827i	0.805342	−	1.39489i	0.916060	−	0.401042i	$-0.131352\pi$
$282$		0			0
$283$	−2.00000	+	3.46410i	−0.118888	+	0.205919i	−0.919327	−	0.393494i	$-0.871266\pi$
$283$	−2.00000	+	3.46410i	−0.118888	+	0.205919i	0.800439	+	0.599414i	$0.204600\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−12.5000	+	4.33013i	−0.737852	+	0.255599i
$288$		0			0
$289$	−4.00000	+	6.92820i	−0.235294	+	0.407541i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	13.5000	+	23.3827i	0.788678	+	1.36603i	0.926777	+	0.375613i	$0.122568\pi$
$293$	13.5000	+	23.3827i	0.788678	+	1.36603i	−0.138098	+	0.990419i	$0.544099\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−7.50000	−	12.9904i	−0.433736	−	0.751253i
$300$		0			0
$301$	14.0000	+	12.1244i	0.806947	+	0.698836i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−5.00000	−	8.66025i	−0.286299	−	0.495885i
$306$		0			0
$307$	−4.00000			−0.228292			−0.114146	−	0.993464i	$-0.536413\pi$
$307$	−4.00000			−0.228292			−0.114146	+	0.993464i	$0.536413\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$311$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$312$		0			0
$313$	17.0000	+	29.4449i	0.960897	+	1.66432i	0.720257	+	0.693708i	$0.244024\pi$
$313$	17.0000	+	29.4449i	0.960897	+	1.66432i	0.240640	+	0.970614i	$0.422643\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−15.0000	−	25.9808i	−0.842484	−	1.45922i	−0.887788	−	0.460252i	$-0.847759\pi$
$317$	−15.0000	−	25.9808i	−0.842484	−	1.45922i	0.0453045	−	0.998973i	$-0.485574\pi$
$318$		0			0
$319$	−1.50000	+	2.59808i	−0.0839839	+	0.145464i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	−35.0000			−1.94745
$324$		0			0
$325$	6.00000	+	10.3923i	0.332820	+	0.576461i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−20.0000	+	6.92820i	−1.10264	+	0.381964i
$330$		0			0
$331$	4.00000	+	6.92820i	0.219860	+	0.380808i	0.954765	−	0.297361i	$-0.0961066\pi$
$331$	4.00000	+	6.92820i	0.219860	+	0.380808i	−0.734905	+	0.678170i	$0.762773\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−6.00000	+	10.3923i	−0.327815	+	0.567792i
$336$		0			0
$337$	6.50000	+	11.2583i	0.354078	+	0.613280i	0.986960	−	0.160968i	$-0.0514616\pi$
$337$	6.50000	+	11.2583i	0.354078	+	0.613280i	−0.632882	+	0.774248i	$0.718128\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−12.0000	+	20.7846i	−0.649836	+	1.12555i
$342$		0			0
$343$	−10.0000	+	15.5885i	−0.539949	+	0.841698i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	6.00000	−	10.3923i	0.322097	−	0.557888i	−0.658824	−	0.752297i	$-0.728946\pi$
$347$	6.00000	−	10.3923i	0.322097	−	0.557888i	0.980921	+	0.194409i	$0.0622790\pi$
$348$		0			0
$349$	−5.50000	+	9.52628i	−0.294408	+	0.509930i	−0.974847	−	0.222875i	$-0.928456\pi$
$349$	−5.50000	+	9.52628i	−0.294408	+	0.509930i	0.680439	+	0.732805i	$0.261789\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	21.0000			1.11772			0.558859	−	0.829263i	$-0.311239\pi$
$353$	21.0000			1.11772			0.558859	+	0.829263i	$0.311239\pi$
$354$		0			0
$355$	12.0000			0.636894
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−1.50000	+	2.59808i	−0.0791670	+	0.137121i	−0.902891	−	0.429870i	$-0.858559\pi$
$359$	−1.50000	+	2.59808i	−0.0791670	+	0.137121i	0.823724	+	0.566991i	$0.191893\pi$
$360$		0			0
$361$	−15.0000	−	25.9808i	−0.789474	−	1.36741i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	2.50000	+	4.33013i	0.130856	+	0.226649i
$366$		0			0
$367$	13.0000			0.678594			0.339297	−	0.940679i	$-0.389811\pi$
$367$	13.0000			0.678594			0.339297	+	0.940679i	$0.389811\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−2.50000	+	0.866025i	−0.129794	+	0.0449618i
$372$		0			0
$373$	−1.00000			−0.0517780			−0.0258890	−	0.999665i	$-0.508242\pi$
$373$	−1.00000			−0.0517780			−0.0258890	+	0.999665i	$0.508242\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	3.00000			0.154508
$378$		0			0
$379$	−36.0000			−1.84920			−0.924598	−	0.380945i	$-0.875599\pi$
$379$	−36.0000			−1.84920			−0.924598	+	0.380945i	$0.875599\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−3.00000			−0.153293			−0.0766464	−	0.997058i	$-0.524421\pi$
$383$	−3.00000			−0.153293			−0.0766464	+	0.997058i	$0.524421\pi$
$384$		0			0
$385$	1.50000	−	7.79423i	0.0764471	−	0.397231i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	17.0000			0.861934			0.430967	−	0.902368i	$-0.358172\pi$
$389$	17.0000			0.861934			0.430967	+	0.902368i	$0.358172\pi$
$390$		0			0
$391$	−12.5000	−	21.6506i	−0.632152	−	1.09492i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	−4.00000	−	6.92820i	−0.201262	−	0.348596i
$396$		0			0
$397$	8.50000	−	14.7224i	0.426603	−	0.738898i	−0.569966	−	0.821668i	$-0.693044\pi$
$397$	8.50000	−	14.7224i	0.426603	−	0.738898i	0.996569	+	0.0827707i	$0.0263769\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−3.00000			−0.149813			−0.0749064	−	0.997191i	$-0.523866\pi$
$401$	−3.00000			−0.149813			−0.0749064	+	0.997191i	$0.523866\pi$
$402$		0			0
$403$	24.0000			1.19553
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−4.50000	+	7.79423i	−0.223057	+	0.386346i
$408$		0			0
$409$	−3.00000	+	5.19615i	−0.148340	+	0.256933i	−0.930614	−	0.366002i	$-0.880726\pi$
$409$	−3.00000	+	5.19615i	−0.148340	+	0.256933i	0.782274	+	0.622935i	$0.214060\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$		0			0
$414$		0			0
$415$	7.50000	−	12.9904i	0.368161	−	0.637673i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−11.5000	−	19.9186i	−0.561812	−	0.973087i	−0.997338	−	0.0729107i	$-0.976771\pi$
$419$	−11.5000	−	19.9186i	−0.561812	−	0.973087i	0.435527	−	0.900176i	$-0.356562\pi$
$420$		0			0
$421$	−3.50000	+	6.06218i	−0.170580	+	0.295452i	−0.938623	−	0.344946i	$-0.887897\pi$
$421$	−3.50000	+	6.06218i	−0.170580	+	0.295452i	0.768043	+	0.640398i	$0.221231\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	10.0000	+	17.3205i	0.485071	+	0.840168i
$426$		0			0
$427$	−25.0000	+	8.66025i	−1.20983	+	0.419099i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	7.50000	+	12.9904i	0.361262	+	0.625725i	0.988169	−	0.153370i	$-0.0490126\pi$
$431$	7.50000	+	12.9904i	0.361262	+	0.625725i	−0.626907	+	0.779094i	$0.715679\pi$
$432$		0			0
$433$	−14.0000			−0.672797			−0.336399	−	0.941720i	$-0.609209\pi$
$433$	−14.0000			−0.672797			−0.336399	+	0.941720i	$0.609209\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	17.5000	−	30.3109i	0.837139	−	1.44997i
$438$		0			0
$439$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$439$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−10.0000	−	17.3205i	−0.475114	−	0.822922i	0.524479	−	0.851423i	$-0.324260\pi$
$443$	−10.0000	−	17.3205i	−0.475114	−	0.822922i	−0.999594	+	0.0285009i	$0.990927\pi$
$444$		0			0
$445$	−2.50000	+	4.33013i	−0.118511	+	0.205268i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−22.0000			−1.03824			−0.519122	−	0.854700i	$-0.673741\pi$
$449$	−22.0000			−1.03824			−0.519122	+	0.854700i	$0.673741\pi$
$450$		0			0
$451$	−7.50000	−	12.9904i	−0.353161	−	0.611693i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−7.50000	+	2.59808i	−0.351605	+	0.121800i
$456$		0			0
$457$	−11.0000	−	19.0526i	−0.514558	−	0.891241i	−0.999857	−	0.0168929i	$-0.994623\pi$
$457$	−11.0000	−	19.0526i	−0.514558	−	0.891241i	0.485299	−	0.874348i	$-0.338711\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−10.5000	+	18.1865i	−0.489034	+	0.847031i	−0.999920	−	0.0126168i	$-0.995984\pi$
$461$	−10.5000	+	18.1865i	−0.489034	+	0.847031i	0.510887	+	0.859648i	$0.329317\pi$
$462$		0			0
$463$	17.5000	+	30.3109i	0.813294	+	1.40867i	0.910546	+	0.413407i	$0.135661\pi$
$463$	17.5000	+	30.3109i	0.813294	+	1.40867i	−0.0972525	+	0.995260i	$0.531005\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−13.5000	+	23.3827i	−0.624705	+	1.08202i	0.363892	+	0.931441i	$0.381448\pi$
$467$	−13.5000	+	23.3827i	−0.624705	+	1.08202i	−0.988598	+	0.150581i	$0.951886\pi$
$468$		0			0
$469$	24.0000	+	20.7846i	1.10822	+	0.959744i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−10.5000	+	18.1865i	−0.482791	+	0.836218i
$474$		0			0
$475$	−14.0000	+	24.2487i	−0.642364	+	1.11261i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	7.00000			0.319838			0.159919	−	0.987130i	$-0.448877\pi$
$479$	7.00000			0.319838			0.159919	+	0.987130i	$0.448877\pi$
$480$		0			0
$481$	9.00000			0.410365
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−3.50000	+	6.06218i	−0.158927	+	0.275269i
$486$		0			0
$487$	18.5000	+	32.0429i	0.838315	+	1.45200i	0.891303	+	0.453409i	$0.149792\pi$
$487$	18.5000	+	32.0429i	0.838315	+	1.45200i	−0.0529875	+	0.998595i	$0.516874\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	10.5000	+	18.1865i	0.473858	+	0.820747i	0.999552	−	0.0299272i	$-0.00952753\pi$
$491$	10.5000	+	18.1865i	0.473858	+	0.820747i	−0.525694	+	0.850674i	$0.676194\pi$
$492$		0			0
$493$	5.00000			0.225189
$494$		0			0
$495$		0			0
$496$		0			0
$497$	6.00000	−	31.1769i	0.269137	−	1.39848i
$498$		0			0
$499$	−1.00000			−0.0447661			−0.0223831	−	0.999749i	$-0.507125\pi$
$499$	−1.00000			−0.0447661			−0.0223831	+	0.999749i	$0.507125\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	40.0000			1.78351			0.891756	−	0.452517i	$-0.149474\pi$
$503$	40.0000			1.78351			0.891756	+	0.452517i	$0.149474\pi$
$504$		0			0
$505$	9.00000			0.400495
$506$		0			0
$507$		0			0
$508$		0			0
$509$	21.0000			0.930809			0.465404	−	0.885098i	$-0.345909\pi$
$509$	21.0000			0.930809			0.465404	+	0.885098i	$0.345909\pi$
$510$		0			0
$511$	12.5000	−	4.33013i	0.552967	−	0.191554i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	15.0000			0.660979
$516$		0			0
$517$	−12.0000	−	20.7846i	−0.527759	−	0.914106i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	1.50000	+	2.59808i	0.0657162	+	0.113824i	0.897011	−	0.442007i	$-0.145733\pi$
$521$	1.50000	+	2.59808i	0.0657162	+	0.113824i	−0.831295	+	0.555831i	$0.812400\pi$
$522$		0			0
$523$	−12.5000	+	21.6506i	−0.546587	+	0.946716i	0.451918	+	0.892059i	$0.350740\pi$
$523$	−12.5000	+	21.6506i	−0.546587	+	0.946716i	−0.998505	+	0.0546569i	$0.982594\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	40.0000			1.74243
$528$		0			0
$529$	2.00000			0.0869565
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−7.50000	+	12.9904i	−0.324861	+	0.562676i
$534$		0			0
$535$	4.50000	−	7.79423i	0.194552	−	0.336974i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−19.5000	−	7.79423i	−0.839924	−	0.335721i
$540$		0			0
$541$	−15.5000	+	26.8468i	−0.666397	+	1.15423i	0.312507	+	0.949915i	$0.398831\pi$
$541$	−15.5000	+	26.8468i	−0.666397	+	1.15423i	−0.978905	+	0.204318i	$0.934502\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−3.50000	−	6.06218i	−0.149924	−	0.259675i
$546$		0			0
$547$	−17.5000	+	30.3109i	−0.748246	+	1.29600i	0.200417	+	0.979711i	$0.435770\pi$
$547$	−17.5000	+	30.3109i	−0.748246	+	1.29600i	−0.948663	+	0.316289i	$0.897563\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	3.50000	+	6.06218i	0.149105	+	0.258257i
$552$		0			0
$553$	−20.0000	+	6.92820i	−0.850487	+	0.294617i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	9.50000	+	16.4545i	0.402528	+	0.697199i	0.994030	−	0.109104i	$-0.0347983\pi$
$557$	9.50000	+	16.4545i	0.402528	+	0.697199i	−0.591502	+	0.806303i	$0.701465\pi$
$558$		0			0
$559$	21.0000			0.888205
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−2.00000	+	3.46410i	−0.0842900	+	0.145994i	−0.905088	−	0.425223i	$-0.860196\pi$
$563$	−2.00000	+	3.46410i	−0.0842900	+	0.145994i	0.820798	+	0.571218i	$0.193529\pi$
$564$		0			0
$565$	7.50000	+	12.9904i	0.315527	+	0.546509i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	15.0000	+	25.9808i	0.628833	+	1.08917i	0.987786	+	0.155815i	$0.0498003\pi$
$569$	15.0000	+	25.9808i	0.628833	+	1.08917i	−0.358954	+	0.933355i	$0.616866\pi$
$570$		0			0
$571$	16.0000	−	27.7128i	0.669579	−	1.15975i	−0.308443	−	0.951243i	$-0.599808\pi$
$571$	16.0000	−	27.7128i	0.669579	−	1.15975i	0.978022	−	0.208502i	$-0.0668588\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−20.0000			−0.834058
$576$		0			0
$577$	4.50000	+	7.79423i	0.187337	+	0.324478i	0.944362	−	0.328909i	$-0.106681\pi$
$577$	4.50000	+	7.79423i	0.187337	+	0.324478i	−0.757024	+	0.653387i	$0.773348\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−30.0000	−	25.9808i	−1.24461	−	1.07786i
$582$		0			0
$583$	−1.50000	−	2.59808i	−0.0621237	−	0.107601i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	17.5000	−	30.3109i	0.722302	−	1.25106i	−0.237773	−	0.971321i	$-0.576417\pi$
$587$	17.5000	−	30.3109i	0.722302	−	1.25106i	0.960075	−	0.279743i	$-0.0902494\pi$
$588$		0			0
$589$	28.0000	+	48.4974i	1.15372	+	1.99830i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−16.5000	+	28.5788i	−0.677574	+	1.17359i	0.298136	+	0.954524i	$0.403635\pi$
$593$	−16.5000	+	28.5788i	−0.677574	+	1.17359i	−0.975709	+	0.219069i	$0.929698\pi$
$594$		0			0
$595$	−12.5000	+	4.33013i	−0.512450	+	0.177518i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−8.00000	+	13.8564i	−0.326871	+	0.566157i	−0.981889	−	0.189456i	$-0.939328\pi$
$599$	−8.00000	+	13.8564i	−0.326871	+	0.566157i	0.655018	+	0.755613i	$0.272661\pi$
$600$		0			0
$601$	−3.50000	+	6.06218i	−0.142768	+	0.247281i	−0.928538	−	0.371237i	$-0.878934\pi$
$601$	−3.50000	+	6.06218i	−0.142768	+	0.247281i	0.785770	+	0.618519i	$0.212267\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−2.00000			−0.0813116
$606$		0			0
$607$	23.0000			0.933541			0.466771	−	0.884378i	$-0.345417\pi$
$607$	23.0000			0.933541			0.466771	+	0.884378i	$0.345417\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−12.0000	+	20.7846i	−0.485468	+	0.840855i
$612$		0			0
$613$	−21.5000	−	37.2391i	−0.868377	−	1.50407i	−0.863655	−	0.504084i	$-0.831830\pi$
$613$	−21.5000	−	37.2391i	−0.868377	−	1.50407i	−0.00472215	−	0.999989i	$-0.501503\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	13.5000	+	23.3827i	0.543490	+	0.941351i	0.998700	+	0.0509678i	$0.0162306\pi$
$617$	13.5000	+	23.3827i	0.543490	+	0.941351i	−0.455211	+	0.890384i	$0.650436\pi$
$618$		0			0
$619$	−15.0000			−0.602901			−0.301450	−	0.953482i	$-0.597471\pi$
$619$	−15.0000			−0.602901			−0.301450	+	0.953482i	$0.597471\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	10.0000	+	8.66025i	0.400642	+	0.346966i
$624$		0			0
$625$	11.0000			0.440000
$626$		0			0
$627$		0			0
$628$		0			0
$629$	15.0000			0.598089
$630$		0			0
$631$	40.0000			1.59237			0.796187	−	0.605050i	$-0.206847\pi$
$631$	40.0000			1.59237			0.796187	+	0.605050i	$0.206847\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	4.00000			0.158735
$636$		0			0
$637$	3.00000	+	20.7846i	0.118864	+	0.823516i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	17.0000			0.671460			0.335730	−	0.941958i	$-0.391017\pi$
$641$	17.0000			0.671460			0.335730	+	0.941958i	$0.391017\pi$
$642$		0			0
$643$	21.5000	+	37.2391i	0.847877	+	1.46857i	0.883099	+	0.469187i	$0.155453\pi$
$643$	21.5000	+	37.2391i	0.847877	+	1.46857i	−0.0352216	+	0.999380i	$0.511214\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−4.50000	−	7.79423i	−0.176913	−	0.306423i	0.763908	−	0.645325i	$-0.223278\pi$
$647$	−4.50000	−	7.79423i	−0.176913	−	0.306423i	−0.940822	+	0.338902i	$0.889945\pi$
$648$		0			0
$649$		0			0
$650$		0			0
$651$		0			0
$652$		0			0
$653$	13.0000			0.508729			0.254365	−	0.967108i	$-0.418134\pi$
$653$	13.0000			0.508729			0.254365	+	0.967108i	$0.418134\pi$
$654$		0			0
$655$	−7.00000			−0.273513
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−14.5000	+	25.1147i	−0.564840	+	0.978331i	0.432225	+	0.901766i	$0.357729\pi$
$659$	−14.5000	+	25.1147i	−0.564840	+	0.978331i	−0.997065	+	0.0765653i	$0.975605\pi$
$660$		0			0
$661$	23.0000	−	39.8372i	0.894596	−	1.54949i	0.0602929	−	0.998181i	$-0.480797\pi$
$661$	23.0000	−	39.8372i	0.894596	−	1.54949i	0.834303	−	0.551306i	$-0.185870\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−14.0000	−	12.1244i	−0.542897	−	0.470162i
$666$		0			0
$667$	−2.50000	+	4.33013i	−0.0968004	+	0.167663i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−15.0000	−	25.9808i	−0.579069	−	1.00298i
$672$		0			0
$673$	14.5000	−	25.1147i	0.558934	−	0.968102i	−0.438652	−	0.898657i	$-0.644544\pi$
$673$	14.5000	−	25.1147i	0.558934	−	0.968102i	0.997586	−	0.0694449i	$-0.0221228\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	9.00000	+	15.5885i	0.345898	+	0.599113i	0.985517	−	0.169580i	$-0.0542410\pi$
$677$	9.00000	+	15.5885i	0.345898	+	0.599113i	−0.639618	+	0.768693i	$0.720908\pi$
$678$		0			0
$679$	14.0000	+	12.1244i	0.537271	+	0.465290i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	19.5000	+	33.7750i	0.746147	+	1.29236i	0.949657	+	0.313291i	$0.101432\pi$
$683$	19.5000	+	33.7750i	0.746147	+	1.29236i	−0.203510	+	0.979073i	$0.565235\pi$
$684$		0			0
$685$	−23.0000			−0.878785
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−1.50000	+	2.59808i	−0.0571454	+	0.0989788i
$690$		0			0
$691$	−14.0000	−	24.2487i	−0.532585	−	0.922464i	−0.999276	−	0.0380440i	$-0.987887\pi$
$691$	−14.0000	−	24.2487i	−0.532585	−	0.922464i	0.466691	−	0.884420i	$-0.345446\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−4.50000	−	7.79423i	−0.170695	−	0.295652i
$696$		0			0
$697$	−12.5000	+	21.6506i	−0.473471	+	0.820076i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	2.00000			0.0755390			0.0377695	−	0.999286i	$-0.487975\pi$
$701$	2.00000			0.0755390			0.0377695	+	0.999286i	$0.487975\pi$
$702$		0			0
$703$	10.5000	+	18.1865i	0.396015	+	0.685918i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	4.50000	−	23.3827i	0.169240	−	0.879396i
$708$		0			0
$709$	19.0000	+	32.9090i	0.713560	+	1.23592i	0.963512	+	0.267664i	$0.0862517\pi$
$709$	19.0000	+	32.9090i	0.713560	+	1.23592i	−0.249952	+	0.968258i	$0.580415\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−20.0000	+	34.6410i	−0.749006	+	1.29732i
$714$		0			0
$715$	−4.50000	−	7.79423i	−0.168290	−	0.291488i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	10.5000	−	18.1865i	0.391584	−	0.678243i	−0.601075	−	0.799193i	$-0.705261\pi$
$719$	10.5000	−	18.1865i	0.391584	−	0.678243i	0.992659	+	0.120950i	$0.0385939\pi$
$720$		0			0
$721$	7.50000	−	38.9711i	0.279315	−	1.45136i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	2.00000	−	3.46410i	0.0742781	−	0.128654i
$726$		0			0
$727$	−3.50000	+	6.06218i	−0.129808	+	0.224834i	−0.923602	−	0.383353i	$-0.874769\pi$
$727$	−3.50000	+	6.06218i	−0.129808	+	0.224834i	0.793794	+	0.608186i	$0.208103\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	35.0000			1.29452
$732$		0			0
$733$	−29.0000			−1.07114			−0.535570	−	0.844491i	$-0.679903\pi$
$733$	−29.0000			−1.07114			−0.535570	+	0.844491i	$0.679903\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−18.0000	+	31.1769i	−0.663039	+	1.14842i
$738$		0			0
$739$	0.500000	+	0.866025i	0.0183928	+	0.0318573i	0.875075	−	0.483987i	$-0.160812\pi$
$739$	0.500000	+	0.866025i	0.0183928	+	0.0318573i	−0.856683	+	0.515844i	$0.827478\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	24.5000	+	42.4352i	0.898818	+	1.55680i	0.829007	+	0.559238i	$0.188906\pi$
$743$	24.5000	+	42.4352i	0.898818	+	1.55680i	0.0698106	+	0.997560i	$0.477761\pi$
$744$		0			0
$745$	5.00000			0.183186
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−18.0000	−	15.5885i	−0.657706	−	0.569590i
$750$		0			0
$751$	7.00000			0.255434			0.127717	−	0.991811i	$-0.459235\pi$
$751$	7.00000			0.255434			0.127717	+	0.991811i	$0.459235\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	5.00000			0.181969
$756$		0			0
$757$	−38.0000			−1.38113			−0.690567	−	0.723269i	$-0.742639\pi$
$757$	−38.0000			−1.38113			−0.690567	+	0.723269i	$0.742639\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−27.0000			−0.978749			−0.489375	−	0.872074i	$-0.662775\pi$
$761$	−27.0000			−0.978749			−0.489375	+	0.872074i	$0.662775\pi$
$762$		0			0
$763$	−17.5000	+	6.06218i	−0.633543	+	0.219466i
$764$		0			0
$765$		0			0
$766$		0			0
$767$		0			0
$768$		0			0
$769$	−15.5000	−	26.8468i	−0.558944	−	0.968120i	−0.997585	−	0.0694574i	$-0.977873\pi$
$769$	−15.5000	−	26.8468i	−0.558944	−	0.968120i	0.438641	−	0.898663i	$-0.355460\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−8.50000	−	14.7224i	−0.305724	−	0.529529i	0.671698	−	0.740825i	$-0.265565\pi$
$773$	−8.50000	−	14.7224i	−0.305724	−	0.529529i	−0.977422	+	0.211296i	$0.932232\pi$
$774$		0			0
$775$	16.0000	−	27.7128i	0.574737	−	0.995474i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−35.0000			−1.25401
$780$		0			0
$781$	36.0000			1.28818
$782$		0			0
$783$		0			0
$784$		0			0
$785$	3.00000	−	5.19615i	0.107075	−	0.185459i
$786$		0			0
$787$	26.0000	−	45.0333i	0.926800	−	1.60526i	0.138159	−	0.990410i	$-0.455881\pi$
$787$	26.0000	−	45.0333i	0.926800	−	1.60526i	0.788641	−	0.614855i	$-0.210785\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	37.5000	−	12.9904i	1.33335	−	0.461885i
$792$		0			0
$793$	−15.0000	+	25.9808i	−0.532666	+	0.922604i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−16.5000	−	28.5788i	−0.584460	−	1.01231i	−0.994943	−	0.100446i	$-0.967973\pi$
$797$	−16.5000	−	28.5788i	−0.584460	−	1.01231i	0.410483	−	0.911868i	$-0.365360\pi$
$798$		0			0
$799$	−20.0000	+	34.6410i	−0.707549	+	1.22551i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	7.50000	+	12.9904i	0.264669	+	0.458421i
$804$		0			0
$805$	2.50000	−	12.9904i	0.0881134	−	0.457851i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−16.5000	−	28.5788i	−0.580109	−	1.00478i	−0.995466	−	0.0951198i	$-0.969677\pi$
$809$	−16.5000	−	28.5788i	−0.580109	−	1.00478i	0.415357	−	0.909659i	$-0.363657\pi$
$810$		0			0
$811$	−12.0000			−0.421377			−0.210688	−	0.977553i	$-0.567571\pi$
$811$	−12.0000			−0.421377			−0.210688	+	0.977553i	$0.567571\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−2.50000	+	4.33013i	−0.0875712	+	0.151678i
$816$		0			0
$817$	24.5000	+	42.4352i	0.857146	+	1.48462i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−21.0000	−	36.3731i	−0.732905	−	1.26943i	−0.955636	−	0.294549i	$-0.904831\pi$
$821$	−21.0000	−	36.3731i	−0.732905	−	1.26943i	0.222731	−	0.974880i	$-0.428503\pi$
$822$		0			0
$823$	4.00000	−	6.92820i	0.139431	−	0.241502i	−0.787850	−	0.615867i	$-0.788806\pi$
$823$	4.00000	−	6.92820i	0.139431	−	0.241502i	0.927281	+	0.374365i	$0.122139\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	36.0000			1.25184			0.625921	−	0.779886i	$-0.284723\pi$
$827$	36.0000			1.25184			0.625921	+	0.779886i	$0.284723\pi$
$828$		0			0
$829$	12.5000	+	21.6506i	0.434143	+	0.751958i	0.997225	−	0.0744432i	$-0.0237179\pi$
$829$	12.5000	+	21.6506i	0.434143	+	0.751958i	−0.563082	+	0.826401i	$0.690385\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	5.00000	+	34.6410i	0.173240	+	1.20024i
$834$		0			0
$835$	10.5000	+	18.1865i	0.363367	+	0.629371i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	1.50000	−	2.59808i	0.0517858	−	0.0896956i	−0.838971	−	0.544177i	$-0.816842\pi$
$839$	1.50000	−	2.59808i	0.0517858	−	0.0896956i	0.890756	+	0.454481i	$0.150175\pi$
$840$		0			0
$841$	14.0000	+	24.2487i	0.482759	+	0.836162i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	2.00000	−	3.46410i	0.0688021	−	0.119169i
$846$		0			0
$847$	−1.00000	+	5.19615i	−0.0343604	+	0.178542i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−7.50000	+	12.9904i	−0.257097	+	0.445305i
$852$		0			0
$853$	26.5000	−	45.8993i	0.907343	−	1.57156i	0.0896015	−	0.995978i	$-0.471441\pi$
$853$	26.5000	−	45.8993i	0.907343	−	1.57156i	0.817741	−	0.575586i	$-0.195226\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	45.0000			1.53717			0.768585	−	0.639747i	$-0.220961\pi$
$857$	45.0000			1.53717			0.768585	+	0.639747i	$0.220961\pi$
$858$		0			0
$859$	23.0000			0.784750			0.392375	−	0.919805i	$-0.371654\pi$
$859$	23.0000			0.784750			0.392375	+	0.919805i	$0.371654\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−23.5000	+	40.7032i	−0.799949	+	1.38555i	0.119699	+	0.992810i	$0.461807\pi$
$863$	−23.5000	+	40.7032i	−0.799949	+	1.38555i	−0.919648	+	0.392743i	$0.871526\pi$
$864$		0			0
$865$	1.00000	+	1.73205i	0.0340010	+	0.0588915i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−12.0000	−	20.7846i	−0.407072	−	0.705070i
$870$		0			0
$871$	36.0000			1.21981
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−4.50000	+	23.3827i	−0.152128	+	0.790479i
$876$		0			0
$877$	−37.0000			−1.24940			−0.624701	−	0.780864i	$-0.714779\pi$
$877$	−37.0000			−1.24940			−0.624701	+	0.780864i	$0.714779\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−22.0000			−0.741199			−0.370599	−	0.928793i	$-0.620848\pi$
$881$	−22.0000			−0.741199			−0.370599	+	0.928793i	$0.620848\pi$
$882$		0			0
$883$	44.0000			1.48072			0.740359	−	0.672212i	$-0.234656\pi$
$883$	44.0000			1.48072			0.740359	+	0.672212i	$0.234656\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−3.00000			−0.100730			−0.0503651	−	0.998731i	$-0.516038\pi$
$887$	−3.00000			−0.100730			−0.0503651	+	0.998731i	$0.516038\pi$
$888$		0			0
$889$	2.00000	−	10.3923i	0.0670778	−	0.348547i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−56.0000			−1.87397
$894$		0			0
$895$	−2.50000	−	4.33013i	−0.0835658	−	0.144740i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−4.00000	−	6.92820i	−0.133407	−	0.231069i
$900$		0			0
$901$	−2.50000	+	4.33013i	−0.0832871	+	0.144257i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	2.00000			0.0664822
$906$		0			0
$907$	37.0000			1.22856			0.614282	−	0.789086i	$-0.289446\pi$
$907$	37.0000			1.22856			0.614282	+	0.789086i	$0.289446\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−6.50000	+	11.2583i	−0.215355	+	0.373005i	−0.953382	−	0.301765i	$-0.902424\pi$
$911$	−6.50000	+	11.2583i	−0.215355	+	0.373005i	0.738028	+	0.674771i	$0.235757\pi$
$912$		0			0
$913$	22.5000	−	38.9711i	0.744641	−	1.28976i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−3.50000	+	18.1865i	−0.115580	+	0.600572i
$918$		0			0
$919$	−20.5000	+	35.5070i	−0.676233	+	1.17127i	0.299874	+	0.953979i	$0.403055\pi$
$919$	−20.5000	+	35.5070i	−0.676233	+	1.17127i	−0.976107	+	0.217291i	$0.930278\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−18.0000	−	31.1769i	−0.592477	−	1.02620i
$924$		0			0
$925$	6.00000	−	10.3923i	0.197279	−	0.341697i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	17.0000	+	29.4449i	0.557752	+	0.966055i	0.997684	+	0.0680235i	$0.0216693\pi$
$929$	17.0000	+	29.4449i	0.557752	+	0.966055i	−0.439932	+	0.898031i	$0.644997\pi$
$930$		0			0
$931$	−38.5000	+	30.3109i	−1.26179	+	0.993399i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	−7.50000	−	12.9904i	−0.245276	−	0.424831i
$936$		0			0
$937$	−6.00000			−0.196011			−0.0980057	−	0.995186i	$-0.531246\pi$
$937$	−6.00000			−0.196011			−0.0980057	+	0.995186i	$0.531246\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−15.0000	+	25.9808i	−0.488986	+	0.846949i	−0.999920	−	0.0126715i	$-0.995966\pi$
$941$	−15.0000	+	25.9808i	−0.488986	+	0.846949i	0.510934	+	0.859620i	$0.329300\pi$
$942$		0			0
$943$	−12.5000	−	21.6506i	−0.407056	−	0.705042i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−26.0000	−	45.0333i	−0.844886	−	1.46339i	−0.885720	−	0.464220i	$-0.846335\pi$
$947$	−26.0000	−	45.0333i	−0.844886	−	1.46339i	0.0408333	−	0.999166i	$-0.486999\pi$
$948$		0			0
$949$	7.50000	−	12.9904i	0.243460	−	0.421686i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−46.0000			−1.49009			−0.745043	−	0.667016i	$-0.767571\pi$
$953$	−46.0000			−1.49009			−0.745043	+	0.667016i	$0.767571\pi$
$954$		0			0
$955$	−8.00000	−	13.8564i	−0.258874	−	0.448383i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−11.5000	+	59.7558i	−0.371354	+	1.92961i
$960$		0			0
$961$	−16.5000	−	28.5788i	−0.532258	−	0.921898i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	9.00000	−	15.5885i	0.289720	−	0.501810i
$966$		0			0
$967$	−10.5000	−	18.1865i	−0.337657	−	0.584839i	0.646334	−	0.763054i	$-0.276301\pi$
$967$	−10.5000	−	18.1865i	−0.337657	−	0.584839i	−0.983992	+	0.178215i	$0.942968\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−3.50000	+	6.06218i	−0.112320	+	0.194545i	−0.916705	−	0.399564i	$-0.869162\pi$
$971$	−3.50000	+	6.06218i	−0.112320	+	0.194545i	0.804385	+	0.594108i	$0.202495\pi$
$972$		0			0
$973$	−22.5000	+	7.79423i	−0.721317	+	0.249871i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	9.00000	−	15.5885i	0.287936	−	0.498719i	−0.685381	−	0.728184i	$-0.740364\pi$
$977$	9.00000	−	15.5885i	0.287936	−	0.498719i	0.973317	+	0.229465i	$0.0736978\pi$
$978$		0			0
$979$	−7.50000	+	12.9904i	−0.239701	+	0.415174i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	27.0000			0.861166			0.430583	−	0.902551i	$-0.358308\pi$
$983$	27.0000			0.861166			0.430583	+	0.902551i	$0.358308\pi$
$984$		0			0
$985$	6.00000			0.191176
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−17.5000	+	30.3109i	−0.556468	+	0.963830i
$990$		0			0
$991$	10.5000	+	18.1865i	0.333543	+	0.577714i	0.983204	−	0.182510i	$-0.0584223\pi$
$991$	10.5000	+	18.1865i	0.333543	+	0.577714i	−0.649660	+	0.760224i	$0.725089\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−9.50000	−	16.4545i	−0.301170	−	0.521642i
$996$		0			0
$997$	−17.0000			−0.538395			−0.269198	−	0.963085i	$-0.586759\pi$
$997$	−17.0000			−0.538395			−0.269198	+	0.963085i	$0.586759\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3024.2.t.e.289.1		2
3.2	odd	2		1008.2.t.a.961.1		2
4.3	odd	2		1512.2.t.b.289.1		2
7.4	even	3		3024.2.q.c.2881.1		2
9.4	even	3		3024.2.q.c.2305.1		2
9.5	odd	6		1008.2.q.d.625.1		2
12.11	even	2		504.2.t.b.457.1	yes	2
21.11	odd	6		1008.2.q.d.529.1		2
28.11	odd	6		1512.2.q.a.1369.1		2
36.23	even	6		504.2.q.b.121.1	yes	2
36.31	odd	6		1512.2.q.a.793.1		2
63.4	even	3	inner	3024.2.t.e.1873.1		2
63.32	odd	6		1008.2.t.a.193.1		2
84.11	even	6		504.2.q.b.25.1	✓	2
252.67	odd	6		1512.2.t.b.361.1		2
252.95	even	6		504.2.t.b.193.1	yes	2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.q.b.25.1	✓	2	84.11	even	6
504.2.q.b.121.1	yes	2	36.23	even	6
504.2.t.b.193.1	yes	2	252.95	even	6
504.2.t.b.457.1	yes	2	12.11	even	2
1008.2.q.d.529.1		2	21.11	odd	6
1008.2.q.d.625.1		2	9.5	odd	6
1008.2.t.a.193.1		2	63.32	odd	6
1008.2.t.a.961.1		2	3.2	odd	2
1512.2.q.a.793.1		2	36.31	odd	6
1512.2.q.a.1369.1		2	28.11	odd	6
1512.2.t.b.289.1		2	4.3	odd	2
1512.2.t.b.361.1		2	252.67	odd	6
3024.2.q.c.2305.1		2	9.4	even	3
3024.2.q.c.2881.1		2	7.4	even	3
3024.2.t.e.289.1		2	1.1	even	1	trivial
3024.2.t.e.1873.1		2	63.4	even	3	inner

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 3024 = 2^{4} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3024.t (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+1.00000 q^{5} +(0.500000 - 2.59808i) q^{7} +3.00000 q^{11} +(-1.50000 - 2.59808i) q^{13} +(-2.50000 - 4.33013i) q^{17} +(3.50000 - 6.06218i) q^{19} +5.00000 q^{23} -4.00000 q^{25} +(-0.500000 + 0.866025i) q^{29} +(-4.00000 + 6.92820i) q^{31} +(0.500000 - 2.59808i) q^{35} +(-1.50000 + 2.59808i) q^{37} +(-2.50000 - 4.33013i) q^{41} +(-3.50000 + 6.06218i) q^{43} +(-4.00000 - 6.92820i) q^{47} +(-6.50000 - 2.59808i) q^{49} +(-0.500000 - 0.866025i) q^{53} +3.00000 q^{55} +(-5.00000 - 8.66025i) q^{61} +(-1.50000 - 2.59808i) q^{65} +(-6.00000 + 10.3923i) q^{67} +12.0000 q^{71} +(2.50000 + 4.33013i) q^{73} +(1.50000 - 7.79423i) q^{77} +(-4.00000 - 6.92820i) q^{79} +(7.50000 - 12.9904i) q^{83} +(-2.50000 - 4.33013i) q^{85} +(-2.50000 + 4.33013i) q^{89} +(-7.50000 + 2.59808i) q^{91} +(3.50000 - 6.06218i) q^{95} +(-3.50000 + 6.06218i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{5} + q^{7} + 6 q^{11} - 3 q^{13} - 5 q^{17} + 7 q^{19} + 10 q^{23} - 8 q^{25} - q^{29} - 8 q^{31} + q^{35} - 3 q^{37} - 5 q^{41} - 7 q^{43} - 8 q^{47} - 13 q^{49} - q^{53} + 6 q^{55} - 10 q^{61}+ \cdots - 7 q^{97}+O(q^{100}) \) 2 * q + 2 * q^5 + q^7 + 6 * q^11 - 3 * q^13 - 5 * q^17 + 7 * q^19 + 10 * q^23 - 8 * q^25 - q^29 - 8 * q^31 + q^35 - 3 * q^37 - 5 * q^41 - 7 * q^43 - 8 * q^47 - 13 * q^49 - q^53 + 6 * q^55 - 10 * q^61 - 3 * q^65 - 12 * q^67 + 24 * q^71 + 5 * q^73 + 3 * q^77 - 8 * q^79 + 15 * q^83 - 5 * q^85 - 5 * q^89 - 15 * q^91 + 7 * q^95 - 7 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more