LMFDB - Embedded newform 2548.2.l.a.1537.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2548,2,Mod(373,2548)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2548, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2, 4]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("2548.373");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2548 = 2^{2} \cdot 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2548.l (of order $3$, degree $2$, not 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:	$20.3458824350$
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 52)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			1537.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	2548.1537
Dual form			2548.2.l.a.373.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q-3.00000 q^{3} +(1.00000 + 1.73205i) q^{5} +6.00000 q^{9} -5.00000 q^{11} +(1.00000 + 3.46410i) q^{13} +(-3.00000 - 5.19615i) q^{15} +(1.50000 + 2.59808i) q^{17} +3.00000 q^{19} +(0.500000 - 0.866025i) q^{23} +(0.500000 - 0.866025i) q^{25} -9.00000 q^{27} +(0.500000 + 0.866025i) q^{29} +(-4.00000 + 6.92820i) q^{31} +15.0000 q^{33} +(-1.50000 + 2.59808i) q^{37} +(-3.00000 - 10.3923i) q^{39} +(1.50000 + 2.59808i) q^{41} +(-0.500000 + 0.866025i) q^{43} +(6.00000 + 10.3923i) q^{45} +(2.00000 + 3.46410i) q^{47} +(-4.50000 - 7.79423i) q^{51} +(3.00000 - 5.19615i) q^{53} +(-5.00000 - 8.66025i) q^{55} -9.00000 q^{57} +(2.50000 + 4.33013i) q^{59} +5.00000 q^{61} +(-5.00000 + 5.19615i) q^{65} +7.00000 q^{67} +(-1.50000 + 2.59808i) q^{69} +(5.50000 - 9.52628i) q^{71} +(7.00000 - 12.1244i) q^{73} +(-1.50000 + 2.59808i) q^{75} +(2.00000 + 3.46410i) q^{79} +9.00000 q^{81} -12.0000 q^{83} +(-3.00000 + 5.19615i) q^{85} +(-1.50000 - 2.59808i) q^{87} +(-4.50000 + 7.79423i) q^{89} +(12.0000 - 20.7846i) q^{93} +(3.00000 + 5.19615i) q^{95} +(-0.500000 + 0.866025i) q^{97} -30.0000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 6 q^{3} + 2 q^{5} + 12 q^{9} - 10 q^{11} + 2 q^{13} - 6 q^{15} + 3 q^{17} + 6 q^{19} + q^{23} + q^{25} - 18 q^{27} + q^{29} - 8 q^{31} + 30 q^{33} - 3 q^{37} - 6 q^{39} + 3 q^{41} - q^{43} + 12 q^{45}+ \cdots - 60 q^{99}+O(q^{100}) $ 2 * q - 6 * q^3 + 2 * q^5 + 12 * q^9 - 10 * q^11 + 2 * q^13 - 6 * q^15 + 3 * q^17 + 6 * q^19 + q^23 + q^25 - 18 * q^27 + q^29 - 8 * q^31 + 30 * q^33 - 3 * q^37 - 6 * q^39 + 3 * q^41 - q^43 + 12 * q^45 + 4 * q^47 - 9 * q^51 + 6 * q^53 - 10 * q^55 - 18 * q^57 + 5 * q^59 + 10 * q^61 - 10 * q^65 + 14 * q^67 - 3 * q^69 + 11 * q^71 + 14 * q^73 - 3 * q^75 + 4 * q^79 + 18 * q^81 - 24 * q^83 - 6 * q^85 - 3 * q^87 - 9 * q^89 + 24 * q^93 + 6 * q^95 - q^97 - 60 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2548\mathbb{Z}\right)^\times$.

$n$	$197$	$885$	$1275$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$	$1$

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 $

$2$		0			0
$2$		0			0
$3$	−3.00000			−1.73205			−0.866025	−	0.500000i	$-0.833333\pi$
$3$	−3.00000			−1.73205			−0.866025	+	0.500000i	$0.833333\pi$
$4$		0			0
$5$	1.00000	+	1.73205i	0.447214	+	0.774597i	0.998203	−	0.0599153i	$-0.0190830\pi$
$5$	1.00000	+	1.73205i	0.447214	+	0.774597i	−0.550990	+	0.834512i	$0.685750\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$		0			0
$9$	6.00000			2.00000
$10$		0			0
$11$	−5.00000			−1.50756			−0.753778	−	0.657129i	$-0.771771\pi$
$11$	−5.00000			−1.50756			−0.753778	+	0.657129i	$0.771771\pi$
$12$		0			0
$13$	1.00000	+	3.46410i	0.277350	+	0.960769i
$13$	1.00000	+	3.46410i	0.277350	+	0.960769i
$14$		0			0
$15$	−3.00000	−	5.19615i	−0.774597	−	1.34164i
$16$		0			0
$17$	1.50000	+	2.59808i	0.363803	+	0.630126i	0.988583	−	0.150675i	$-0.0481447\pi$
$17$	1.50000	+	2.59808i	0.363803	+	0.630126i	−0.624780	+	0.780801i	$0.714811\pi$
$18$		0			0
$19$	3.00000			0.688247			0.344124	−	0.938924i	$-0.388176\pi$
$19$	3.00000			0.688247			0.344124	+	0.938924i	$0.388176\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	0.500000	−	0.866025i	0.104257	−	0.180579i	−0.809177	−	0.587565i	$-0.800087\pi$
$23$	0.500000	−	0.866025i	0.104257	−	0.180579i	0.913434	+	0.406986i	$0.133420\pi$
$24$		0			0
$25$	0.500000	−	0.866025i	0.100000	−	0.173205i
$26$		0			0
$27$	−9.00000			−1.73205
$28$		0			0
$29$	0.500000	+	0.866025i	0.0928477	+	0.160817i	0.908708	−	0.417432i	$-0.137070\pi$
$29$	0.500000	+	0.866025i	0.0928477	+	0.160817i	−0.815861	+	0.578249i	$0.803736\pi$
$30$		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
$33$	15.0000			2.61116
$34$		0			0
$35$		0			0
$36$		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
$39$	−3.00000	−	10.3923i	−0.480384	−	1.66410i
$40$		0			0
$41$	1.50000	+	2.59808i	0.234261	+	0.405751i	0.959058	−	0.283211i	$-0.0913998\pi$
$41$	1.50000	+	2.59808i	0.234261	+	0.405751i	−0.724797	+	0.688963i	$0.758066\pi$
$42$		0			0
$43$	−0.500000	+	0.866025i	−0.0762493	+	0.132068i	−0.901629	−	0.432511i	$-0.857628\pi$
$43$	−0.500000	+	0.866025i	−0.0762493	+	0.132068i	0.825380	+	0.564578i	$0.190961\pi$
$44$		0			0
$45$	6.00000	+	10.3923i	0.894427	+	1.54919i
$46$		0			0
$47$	2.00000	+	3.46410i	0.291730	+	0.505291i	0.974219	−	0.225605i	$-0.0724358\pi$
$47$	2.00000	+	3.46410i	0.291730	+	0.505291i	−0.682489	+	0.730896i	$0.739102\pi$
$48$		0			0
$49$		0			0
$50$		0			0
$51$	−4.50000	−	7.79423i	−0.630126	−	1.09141i
$52$		0			0
$53$	3.00000	−	5.19615i	0.412082	−	0.713746i	−0.583036	−	0.812447i	$-0.698135\pi$
$53$	3.00000	−	5.19615i	0.412082	−	0.713746i	0.995117	+	0.0987002i	$0.0314685\pi$
$54$		0			0
$55$	−5.00000	−	8.66025i	−0.674200	−	1.16775i
$56$		0			0
$57$	−9.00000			−1.19208
$58$		0			0
$59$	2.50000	+	4.33013i	0.325472	+	0.563735i	0.981608	−	0.190909i	$-0.0611434\pi$
$59$	2.50000	+	4.33013i	0.325472	+	0.563735i	−0.656136	+	0.754643i	$0.727810\pi$
$60$		0			0
$61$	5.00000			0.640184			0.320092	−	0.947386i	$-0.396286\pi$
$61$	5.00000			0.640184			0.320092	+	0.947386i	$0.396286\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−5.00000	+	5.19615i	−0.620174	+	0.644503i
$66$		0			0
$67$	7.00000			0.855186			0.427593	−	0.903971i	$-0.359362\pi$
$67$	7.00000			0.855186			0.427593	+	0.903971i	$0.359362\pi$
$68$		0			0
$69$	−1.50000	+	2.59808i	−0.180579	+	0.312772i
$70$		0			0
$71$	5.50000	−	9.52628i	0.652730	−	1.13056i	−0.329728	−	0.944076i	$-0.606957\pi$
$71$	5.50000	−	9.52628i	0.652730	−	1.13056i	0.982458	−	0.186485i	$-0.0597097\pi$
$72$		0			0
$73$	7.00000	−	12.1244i	0.819288	−	1.41905i	−0.0869195	−	0.996215i	$-0.527702\pi$
$73$	7.00000	−	12.1244i	0.819288	−	1.41905i	0.906208	−	0.422833i	$-0.138964\pi$
$74$		0			0
$75$	−1.50000	+	2.59808i	−0.173205	+	0.300000i
$76$		0			0
$77$		0			0
$78$		0			0
$79$	2.00000	+	3.46410i	0.225018	+	0.389742i	0.956325	−	0.292306i	$-0.0944227\pi$
$79$	2.00000	+	3.46410i	0.225018	+	0.389742i	−0.731307	+	0.682048i	$0.761089\pi$
$80$		0			0
$81$	9.00000			1.00000
$82$		0			0
$83$	−12.0000			−1.31717			−0.658586	−	0.752506i	$-0.728845\pi$
$83$	−12.0000			−1.31717			−0.658586	+	0.752506i	$0.728845\pi$
$84$		0			0
$85$	−3.00000	+	5.19615i	−0.325396	+	0.563602i
$86$		0			0
$87$	−1.50000	−	2.59808i	−0.160817	−	0.278543i
$88$		0			0
$89$	−4.50000	+	7.79423i	−0.476999	+	0.826187i	−0.999653	−	0.0263586i	$-0.991609\pi$
$89$	−4.50000	+	7.79423i	−0.476999	+	0.826187i	0.522654	+	0.852545i	$0.324942\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$	12.0000	−	20.7846i	1.24434	−	2.15526i
$94$		0			0
$95$	3.00000	+	5.19615i	0.307794	+	0.533114i
$96$		0			0
$97$	−0.500000	+	0.866025i	−0.0507673	+	0.0879316i	−0.890292	−	0.455389i	$-0.849500\pi$
$97$	−0.500000	+	0.866025i	−0.0507673	+	0.0879316i	0.839525	+	0.543321i	$0.182833\pi$
$98$		0			0
$99$	−30.0000			−3.01511
$100$		0			0
$101$	−19.0000			−1.89057			−0.945285	−	0.326245i	$-0.894217\pi$
$101$	−19.0000			−1.89057			−0.945285	+	0.326245i	$0.894217\pi$
$102$		0			0
$103$	−4.00000	−	6.92820i	−0.394132	−	0.682656i	0.598858	−	0.800855i	$-0.295621\pi$
$103$	−4.00000	−	6.92820i	−0.394132	−	0.682656i	−0.992990	+	0.118199i	$0.962288\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−5.50000	+	9.52628i	−0.531705	+	0.920940i	0.467610	+	0.883935i	$0.345115\pi$
$107$	−5.50000	+	9.52628i	−0.531705	+	0.920940i	−0.999315	+	0.0370053i	$0.988218\pi$
$108$		0			0
$109$	−5.00000	+	8.66025i	−0.478913	+	0.829502i	−0.999708	−	0.0241802i	$-0.992302\pi$
$109$	−5.00000	+	8.66025i	−0.478913	+	0.829502i	0.520794	+	0.853682i	$0.325636\pi$
$110$		0			0
$111$	4.50000	−	7.79423i	0.427121	−	0.739795i
$112$		0			0
$113$	−5.50000	+	9.52628i	−0.517396	+	0.896157i	0.482399	+	0.875951i	$0.339765\pi$
$113$	−5.50000	+	9.52628i	−0.517396	+	0.896157i	−0.999796	+	0.0202056i	$0.993568\pi$
$114$		0			0
$115$	2.00000			0.186501
$116$		0			0
$117$	6.00000	+	20.7846i	0.554700	+	1.92154i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	14.0000			1.27273
$122$		0			0
$123$	−4.50000	−	7.79423i	−0.405751	−	0.702782i
$124$		0			0
$125$	12.0000			1.07331
$126$		0			0
$127$	2.50000	+	4.33013i	0.221839	+	0.384237i	0.955366	−	0.295423i	$-0.0954607\pi$
$127$	2.50000	+	4.33013i	0.221839	+	0.384237i	−0.733527	+	0.679660i	$0.762127\pi$
$128$		0			0
$129$	1.50000	−	2.59808i	0.132068	−	0.228748i
$130$		0			0
$131$	−2.00000	−	3.46410i	−0.174741	−	0.302660i	0.765331	−	0.643637i	$-0.222575\pi$
$131$	−2.00000	−	3.46410i	−0.174741	−	0.302660i	−0.940072	+	0.340977i	$0.889242\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$	−9.00000	−	15.5885i	−0.774597	−	1.34164i
$136$		0			0
$137$	−7.50000	−	12.9904i	−0.640768	−	1.10984i	−0.985262	−	0.171054i	$-0.945283\pi$
$137$	−7.50000	−	12.9904i	−0.640768	−	1.10984i	0.344493	−	0.938789i	$-0.388051\pi$
$138$		0			0
$139$	−5.50000	+	9.52628i	−0.466504	+	0.808008i	−0.999268	−	0.0382553i	$-0.987820\pi$
$139$	−5.50000	+	9.52628i	−0.466504	+	0.808008i	0.532764	+	0.846264i	$0.321153\pi$
$140$		0			0
$141$	−6.00000	−	10.3923i	−0.505291	−	0.875190i
$142$		0			0
$143$	−5.00000	−	17.3205i	−0.418121	−	1.44841i
$144$		0			0
$145$	−1.00000	+	1.73205i	−0.0830455	+	0.143839i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−21.0000			−1.72039			−0.860194	−	0.509968i	$-0.829657\pi$
$149$	−21.0000			−1.72039			−0.860194	+	0.509968i	$0.829657\pi$
$150$		0			0
$151$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$151$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$152$		0			0
$153$	9.00000	+	15.5885i	0.727607	+	1.26025i
$154$		0			0
$155$	−16.0000			−1.28515
$156$		0			0
$157$	−11.0000	+	19.0526i	−0.877896	+	1.52056i	−0.0242497	+	0.999706i	$0.507720\pi$
$157$	−11.0000	+	19.0526i	−0.877896	+	1.52056i	−0.853646	+	0.520854i	$0.825614\pi$
$158$		0			0
$159$	−9.00000	+	15.5885i	−0.713746	+	1.23625i
$160$		0			0
$161$		0			0
$162$		0			0
$163$	−7.00000			−0.548282			−0.274141	−	0.961689i	$-0.588394\pi$
$163$	−7.00000			−0.548282			−0.274141	+	0.961689i	$0.588394\pi$
$164$		0			0
$165$	15.0000	+	25.9808i	1.16775	+	2.02260i
$166$		0			0
$167$	−4.50000	−	7.79423i	−0.348220	−	0.603136i	0.637713	−	0.770274i	$-0.279881\pi$
$167$	−4.50000	−	7.79423i	−0.348220	−	0.603136i	−0.985933	+	0.167139i	$0.946547\pi$
$168$		0			0
$169$	−11.0000	+	6.92820i	−0.846154	+	0.532939i
$170$		0			0
$171$	18.0000			1.37649
$172$		0			0
$173$	−11.0000			−0.836315			−0.418157	−	0.908375i	$-0.637324\pi$
$173$	−11.0000			−0.836315			−0.418157	+	0.908375i	$0.637324\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	−7.50000	−	12.9904i	−0.563735	−	0.976417i
$178$		0			0
$179$	−21.0000			−1.56961			−0.784807	−	0.619740i	$-0.787238\pi$
$179$	−21.0000			−1.56961			−0.784807	+	0.619740i	$0.787238\pi$
$180$		0			0
$181$	−18.0000			−1.33793			−0.668965	−	0.743294i	$-0.733262\pi$
$181$	−18.0000			−1.33793			−0.668965	+	0.743294i	$0.733262\pi$
$182$		0			0
$183$	−15.0000			−1.10883
$184$		0			0
$185$	−6.00000			−0.441129
$186$		0			0
$187$	−7.50000	−	12.9904i	−0.548454	−	0.949951i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	1.00000			0.0723575			0.0361787	−	0.999345i	$-0.488481\pi$
$191$	1.00000			0.0723575			0.0361787	+	0.999345i	$0.488481\pi$
$192$		0			0
$193$	11.0000			0.791797			0.395899	−	0.918294i	$-0.370433\pi$
$193$	11.0000			0.791797			0.395899	+	0.918294i	$0.370433\pi$
$194$		0			0
$195$	15.0000	−	15.5885i	1.07417	−	1.11631i
$196$		0			0
$197$	4.50000	+	7.79423i	0.320612	+	0.555316i	0.980614	−	0.195947i	$-0.0627782\pi$
$197$	4.50000	+	7.79423i	0.320612	+	0.555316i	−0.660003	+	0.751263i	$0.729445\pi$
$198$		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
$201$	−21.0000			−1.48123
$202$		0			0
$203$		0			0
$204$		0			0
$205$	−3.00000	+	5.19615i	−0.209529	+	0.362915i
$206$		0			0
$207$	3.00000	−	5.19615i	0.208514	−	0.361158i
$208$		0			0
$209$	−15.0000			−1.03757
$210$		0			0
$211$	6.50000	+	11.2583i	0.447478	+	0.775055i	0.998221	−	0.0596196i	$-0.0189888\pi$
$211$	6.50000	+	11.2583i	0.447478	+	0.775055i	−0.550743	+	0.834675i	$0.685655\pi$
$212$		0			0
$213$	−16.5000	+	28.5788i	−1.13056	+	1.95819i
$214$		0			0
$215$	−2.00000			−0.136399
$216$		0			0
$217$		0			0
$218$		0			0
$219$	−21.0000	+	36.3731i	−1.41905	+	2.45786i
$220$		0			0
$221$	−7.50000	+	7.79423i	−0.504505	+	0.524297i
$222$		0			0
$223$	−4.50000	−	7.79423i	−0.301342	−	0.521940i	0.675098	−	0.737728i	$-0.264101\pi$
$223$	−4.50000	−	7.79423i	−0.301342	−	0.521940i	−0.976440	+	0.215788i	$0.930768\pi$
$224$		0			0
$225$	3.00000	−	5.19615i	0.200000	−	0.346410i
$226$		0			0
$227$	10.5000	+	18.1865i	0.696909	+	1.20708i	0.969533	+	0.244962i	$0.0787754\pi$
$227$	10.5000	+	18.1865i	0.696909	+	1.20708i	−0.272623	+	0.962121i	$0.587891\pi$
$228$		0			0
$229$	−3.00000	−	5.19615i	−0.198246	−	0.343371i	0.749714	−	0.661762i	$-0.230191\pi$
$229$	−3.00000	−	5.19615i	−0.198246	−	0.343371i	−0.947960	+	0.318390i	$0.896858\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−11.0000	−	19.0526i	−0.720634	−	1.24817i	−0.960746	−	0.277429i	$-0.910518\pi$
$233$	−11.0000	−	19.0526i	−0.720634	−	1.24817i	0.240112	−	0.970745i	$-0.422816\pi$
$234$		0			0
$235$	−4.00000	+	6.92820i	−0.260931	+	0.451946i
$236$		0			0
$237$	−6.00000	−	10.3923i	−0.389742	−	0.675053i
$238$		0			0
$239$	24.0000			1.55243			0.776215	−	0.630468i	$-0.217137\pi$
$239$	24.0000			1.55243			0.776215	+	0.630468i	$0.217137\pi$
$240$		0			0
$241$	−10.5000	−	18.1865i	−0.676364	−	1.17150i	−0.976068	−	0.217465i	$-0.930221\pi$
$241$	−10.5000	−	18.1865i	−0.676364	−	1.17150i	0.299704	−	0.954032i	$-0.403112\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$		0			0
$246$		0			0
$247$	3.00000	+	10.3923i	0.190885	+	0.661247i
$248$		0			0
$249$	36.0000			2.28141
$250$		0			0
$251$	4.50000	−	7.79423i	0.284037	−	0.491967i	−0.688338	−	0.725390i	$-0.741659\pi$
$251$	4.50000	−	7.79423i	0.284037	−	0.491967i	0.972375	+	0.233423i	$0.0749927\pi$
$252$		0			0
$253$	−2.50000	+	4.33013i	−0.157174	+	0.272233i
$254$		0			0
$255$	9.00000	−	15.5885i	0.563602	−	0.976187i
$256$		0			0
$257$	1.50000	−	2.59808i	0.0935674	−	0.162064i	−0.815442	−	0.578838i	$-0.803506\pi$
$257$	1.50000	−	2.59808i	0.0935674	−	0.162064i	0.909010	+	0.416775i	$0.136840\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$	3.00000	+	5.19615i	0.185695	+	0.321634i
$262$		0			0
$263$	15.0000			0.924940			0.462470	−	0.886635i	$-0.346963\pi$
$263$	15.0000			0.924940			0.462470	+	0.886635i	$0.346963\pi$
$264$		0			0
$265$	12.0000			0.737154
$266$		0			0
$267$	13.5000	−	23.3827i	0.826187	−	1.43100i
$268$		0			0
$269$	7.50000	+	12.9904i	0.457283	+	0.792038i	0.998816	−	0.0486418i	$-0.0154893\pi$
$269$	7.50000	+	12.9904i	0.457283	+	0.792038i	−0.541533	+	0.840679i	$0.682156\pi$
$270$		0			0
$271$	−8.50000	+	14.7224i	−0.516338	+	0.894324i	0.483482	+	0.875354i	$0.339372\pi$
$271$	−8.50000	+	14.7224i	−0.516338	+	0.894324i	−0.999820	+	0.0189696i	$0.993961\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−2.50000	+	4.33013i	−0.150756	+	0.261116i
$276$		0			0
$277$	4.50000	+	7.79423i	0.270379	+	0.468310i	0.968959	−	0.247222i	$-0.0795177\pi$
$277$	4.50000	+	7.79423i	0.270379	+	0.468310i	−0.698580	+	0.715532i	$0.746184\pi$
$278$		0			0
$279$	−24.0000	+	41.5692i	−1.43684	+	2.48868i
$280$		0			0
$281$	−2.00000			−0.119310			−0.0596550	−	0.998219i	$-0.519000\pi$
$281$	−2.00000			−0.119310			−0.0596550	+	0.998219i	$0.519000\pi$
$282$		0			0
$283$	−19.0000			−1.12943			−0.564716	−	0.825285i	$-0.691014\pi$
$283$	−19.0000			−1.12943			−0.564716	+	0.825285i	$0.691014\pi$
$284$		0			0
$285$	−9.00000	−	15.5885i	−0.533114	−	0.923381i
$286$		0			0
$287$		0			0
$288$		0			0
$289$	4.00000	−	6.92820i	0.235294	−	0.407541i
$290$		0			0
$291$	1.50000	−	2.59808i	0.0879316	−	0.152302i
$292$		0			0
$293$	9.50000	−	16.4545i	0.554996	−	0.961281i	−0.442908	−	0.896567i	$-0.646053\pi$
$293$	9.50000	−	16.4545i	0.554996	−	0.961281i	0.997904	−	0.0647140i	$-0.0206135\pi$
$294$		0			0
$295$	−5.00000	+	8.66025i	−0.291111	+	0.504219i
$296$		0			0
$297$	45.0000			2.61116
$298$		0			0
$299$	3.50000	+	0.866025i	0.202410	+	0.0500835i
$300$		0			0
$301$		0			0
$302$		0			0
$303$	57.0000			3.27456
$304$		0			0
$305$	5.00000	+	8.66025i	0.286299	+	0.495885i
$306$		0			0
$307$	4.00000			0.228292			0.114146	−	0.993464i	$-0.463587\pi$
$307$	4.00000			0.228292			0.114146	+	0.993464i	$0.463587\pi$
$308$		0			0
$309$	12.0000	+	20.7846i	0.682656	+	1.18240i
$310$		0			0
$311$	−12.0000	+	20.7846i	−0.680458	+	1.17859i	0.294384	+	0.955687i	$0.404886\pi$
$311$	−12.0000	+	20.7846i	−0.680458	+	1.17859i	−0.974841	+	0.222900i	$0.928448\pi$
$312$		0			0
$313$	7.00000	+	12.1244i	0.395663	+	0.685309i	0.993186	−	0.116543i	$-0.0371814\pi$
$313$	7.00000	+	12.1244i	0.395663	+	0.685309i	−0.597522	+	0.801852i	$0.703848\pi$
$314$		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
$319$	−2.50000	−	4.33013i	−0.139973	−	0.242441i
$320$		0			0
$321$	16.5000	−	28.5788i	0.920940	−	1.59512i
$322$		0			0
$323$	4.50000	+	7.79423i	0.250387	+	0.433682i
$324$		0			0
$325$	3.50000	+	0.866025i	0.194145	+	0.0480384i
$326$		0			0
$327$	15.0000	−	25.9808i	0.829502	−	1.43674i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	17.0000			0.934405			0.467202	−	0.884150i	$-0.345262\pi$
$331$	17.0000			0.934405			0.467202	+	0.884150i	$0.345262\pi$
$332$		0			0
$333$	−9.00000	+	15.5885i	−0.493197	+	0.854242i
$334$		0			0
$335$	7.00000	+	12.1244i	0.382451	+	0.662424i
$336$		0			0
$337$	−10.0000			−0.544735			−0.272367	−	0.962193i	$-0.587807\pi$
$337$	−10.0000			−0.544735			−0.272367	+	0.962193i	$0.587807\pi$
$338$		0			0
$339$	16.5000	−	28.5788i	0.896157	−	1.55219i
$340$		0			0
$341$	20.0000	−	34.6410i	1.08306	−	1.87592i
$342$		0			0
$343$		0			0
$344$		0			0
$345$	−6.00000			−0.323029
$346$		0			0
$347$	−16.5000	−	28.5788i	−0.885766	−	1.53419i	−0.844833	−	0.535031i	$-0.820300\pi$
$347$	−16.5000	−	28.5788i	−0.885766	−	1.53419i	−0.0409337	−	0.999162i	$-0.513033\pi$
$348$		0			0
$349$	9.50000	+	16.4545i	0.508523	+	0.880788i	0.999951	+	0.00987003i	$0.00314178\pi$
$349$	9.50000	+	16.4545i	0.508523	+	0.880788i	−0.491428	+	0.870918i	$0.663525\pi$
$350$		0			0
$351$	−9.00000	−	31.1769i	−0.480384	−	1.66410i
$352$		0			0
$353$	−7.00000			−0.372572			−0.186286	−	0.982496i	$-0.559645\pi$
$353$	−7.00000			−0.372572			−0.186286	+	0.982496i	$0.559645\pi$
$354$		0			0
$355$	22.0000			1.16764
$356$		0			0
$357$		0			0
$358$		0			0
$359$	12.0000	+	20.7846i	0.633336	+	1.09697i	0.986865	+	0.161546i	$0.0516481\pi$
$359$	12.0000	+	20.7846i	0.633336	+	1.09697i	−0.353529	+	0.935423i	$0.615019\pi$
$360$		0			0
$361$	−10.0000			−0.526316
$362$		0			0
$363$	−42.0000			−2.20443
$364$		0			0
$365$	28.0000			1.46559
$366$		0			0
$367$	−23.0000			−1.20059			−0.600295	−	0.799779i	$-0.704950\pi$
$367$	−23.0000			−1.20059			−0.600295	+	0.799779i	$0.704950\pi$
$368$		0			0
$369$	9.00000	+	15.5885i	0.468521	+	0.811503i
$370$		0			0
$371$		0			0
$372$		0			0
$373$	23.0000			1.19089			0.595447	−	0.803394i	$-0.296975\pi$
$373$	23.0000			1.19089			0.595447	+	0.803394i	$0.296975\pi$
$374$		0			0
$375$	−36.0000			−1.85903
$376$		0			0
$377$	−2.50000	+	2.59808i	−0.128757	+	0.133808i
$378$		0			0
$379$	2.50000	+	4.33013i	0.128416	+	0.222424i	0.923063	−	0.384648i	$-0.125677\pi$
$379$	2.50000	+	4.33013i	0.128416	+	0.222424i	−0.794647	+	0.607072i	$0.792344\pi$
$380$		0			0
$381$	−7.50000	−	12.9904i	−0.384237	−	0.665517i
$382$		0			0
$383$	−9.00000			−0.459879			−0.229939	−	0.973205i	$-0.573853\pi$
$383$	−9.00000			−0.459879			−0.229939	+	0.973205i	$0.573853\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−3.00000	+	5.19615i	−0.152499	+	0.264135i
$388$		0			0
$389$	−3.00000	+	5.19615i	−0.152106	+	0.263455i	−0.932002	−	0.362454i	$-0.881939\pi$
$389$	−3.00000	+	5.19615i	−0.152106	+	0.263455i	0.779895	+	0.625910i	$0.215272\pi$
$390$		0			0
$391$	3.00000			0.151717
$392$		0			0
$393$	6.00000	+	10.3923i	0.302660	+	0.524222i
$394$		0			0
$395$	−4.00000	+	6.92820i	−0.201262	+	0.348596i
$396$		0			0
$397$	25.0000			1.25471			0.627357	−	0.778732i	$-0.284137\pi$
$397$	25.0000			1.25471			0.627357	+	0.778732i	$0.284137\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−13.5000	+	23.3827i	−0.674158	+	1.16768i	0.302556	+	0.953131i	$0.402160\pi$
$401$	−13.5000	+	23.3827i	−0.674158	+	1.16768i	−0.976714	+	0.214544i	$0.931173\pi$
$402$		0			0
$403$	−28.0000	−	6.92820i	−1.39478	−	0.345118i
$404$		0			0
$405$	9.00000	+	15.5885i	0.447214	+	0.774597i
$406$		0			0
$407$	7.50000	−	12.9904i	0.371761	−	0.643909i
$408$		0			0
$409$	−2.50000	−	4.33013i	−0.123617	−	0.214111i	0.797574	−	0.603220i	$-0.206116\pi$
$409$	−2.50000	−	4.33013i	−0.123617	−	0.214111i	−0.921192	+	0.389109i	$0.872783\pi$
$410$		0			0
$411$	22.5000	+	38.9711i	1.10984	+	1.92230i
$412$		0			0
$413$		0			0
$414$		0			0
$415$	−12.0000	−	20.7846i	−0.589057	−	1.02028i
$416$		0			0
$417$	16.5000	−	28.5788i	0.808008	−	1.39951i
$418$		0			0
$419$	7.50000	+	12.9904i	0.366399	+	0.634622i	0.989000	−	0.147918i	$-0.0472572\pi$
$419$	7.50000	+	12.9904i	0.366399	+	0.634622i	−0.622601	+	0.782540i	$0.713924\pi$
$420$		0			0
$421$	10.0000			0.487370			0.243685	−	0.969854i	$-0.421644\pi$
$421$	10.0000			0.487370			0.243685	+	0.969854i	$0.421644\pi$
$422$		0			0
$423$	12.0000	+	20.7846i	0.583460	+	1.01058i
$424$		0			0
$425$	3.00000			0.145521
$426$		0			0
$427$		0			0
$428$		0			0
$429$	15.0000	+	51.9615i	0.724207	+	2.50873i
$430$		0			0
$431$	3.00000			0.144505			0.0722525	−	0.997386i	$-0.476981\pi$
$431$	3.00000			0.144505			0.0722525	+	0.997386i	$0.476981\pi$
$432$		0			0
$433$	9.50000	−	16.4545i	0.456541	−	0.790752i	−0.542234	−	0.840227i	$-0.682422\pi$
$433$	9.50000	−	16.4545i	0.456541	−	0.790752i	0.998775	+	0.0494752i	$0.0157549\pi$
$434$		0			0
$435$	3.00000	−	5.19615i	0.143839	−	0.249136i
$436$		0			0
$437$	1.50000	−	2.59808i	0.0717547	−	0.124283i
$438$		0			0
$439$	−6.50000	+	11.2583i	−0.310228	+	0.537331i	−0.978412	−	0.206666i	$-0.933739\pi$
$439$	−6.50000	+	11.2583i	−0.310228	+	0.537331i	0.668184	+	0.743996i	$0.267072\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−6.00000	−	10.3923i	−0.285069	−	0.493753i	0.687557	−	0.726130i	$-0.258683\pi$
$443$	−6.00000	−	10.3923i	−0.285069	−	0.493753i	−0.972626	+	0.232377i	$0.925350\pi$
$444$		0			0
$445$	−18.0000			−0.853282
$446$		0			0
$447$	63.0000			2.97980
$448$		0			0
$449$	2.50000	−	4.33013i	0.117982	−	0.204351i	−0.800986	−	0.598684i	$-0.795691\pi$
$449$	2.50000	−	4.33013i	0.117982	−	0.204351i	0.918968	+	0.394332i	$0.129024\pi$
$450$		0			0
$451$	−7.50000	−	12.9904i	−0.353161	−	0.611693i
$452$		0			0
$453$		0			0
$454$		0			0
$455$		0			0
$456$		0			0
$457$	8.50000	−	14.7224i	0.397613	−	0.688686i	−0.595818	−	0.803120i	$-0.703172\pi$
$457$	8.50000	−	14.7224i	0.397613	−	0.688686i	0.993431	+	0.114433i	$0.0365053\pi$
$458$		0			0
$459$	−13.5000	−	23.3827i	−0.630126	−	1.09141i
$460$		0			0
$461$	−4.50000	+	7.79423i	−0.209586	+	0.363013i	−0.951584	−	0.307388i	$-0.900545\pi$
$461$	−4.50000	+	7.79423i	−0.209586	+	0.363013i	0.741998	+	0.670402i	$0.233878\pi$
$462$		0			0
$463$	40.0000			1.85896			0.929479	−	0.368875i	$-0.120257\pi$
$463$	40.0000			1.85896			0.929479	+	0.368875i	$0.120257\pi$
$464$		0			0
$465$	48.0000			2.22595
$466$		0			0
$467$	−8.00000	−	13.8564i	−0.370196	−	0.641198i	0.619400	−	0.785076i	$-0.287376\pi$
$467$	−8.00000	−	13.8564i	−0.370196	−	0.641198i	−0.989595	+	0.143878i	$0.954043\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$	33.0000	−	57.1577i	1.52056	−	2.63369i
$472$		0			0
$473$	2.50000	−	4.33013i	0.114950	−	0.199099i
$474$		0			0
$475$	1.50000	−	2.59808i	0.0688247	−	0.119208i
$476$		0			0
$477$	18.0000	−	31.1769i	0.824163	−	1.42749i
$478$		0			0
$479$	−3.00000			−0.137073			−0.0685367	−	0.997649i	$-0.521833\pi$
$479$	−3.00000			−0.137073			−0.0685367	+	0.997649i	$0.521833\pi$
$480$		0			0
$481$	−10.5000	−	2.59808i	−0.478759	−	0.118462i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−2.00000			−0.0908153
$486$		0			0
$487$	−14.5000	−	25.1147i	−0.657058	−	1.13806i	−0.981374	−	0.192109i	$-0.938467\pi$
$487$	−14.5000	−	25.1147i	−0.657058	−	1.13806i	0.324316	−	0.945949i	$-0.394866\pi$
$488$		0			0
$489$	21.0000			0.949653
$490$		0			0
$491$	−15.5000	−	26.8468i	−0.699505	−	1.21158i	−0.968638	−	0.248476i	$-0.920070\pi$
$491$	−15.5000	−	26.8468i	−0.699505	−	1.21158i	0.269133	−	0.963103i	$-0.413263\pi$
$492$		0			0
$493$	−1.50000	+	2.59808i	−0.0675566	+	0.117011i
$494$		0			0
$495$	−30.0000	−	51.9615i	−1.34840	−	2.33550i
$496$		0			0
$497$		0			0
$498$		0			0
$499$	−2.00000	−	3.46410i	−0.0895323	−	0.155074i	0.817781	−	0.575529i	$-0.195204\pi$
$499$	−2.00000	−	3.46410i	−0.0895323	−	0.155074i	−0.907314	+	0.420455i	$0.861871\pi$
$500$		0			0
$501$	13.5000	+	23.3827i	0.603136	+	1.04466i
$502$		0			0
$503$	−11.5000	+	19.9186i	−0.512760	+	0.888126i	0.487131	+	0.873329i	$0.338043\pi$
$503$	−11.5000	+	19.9186i	−0.512760	+	0.888126i	−0.999891	+	0.0147968i	$0.995290\pi$
$504$		0			0
$505$	−19.0000	−	32.9090i	−0.845489	−	1.46443i
$506$		0			0
$507$	33.0000	−	20.7846i	1.46558	−	0.923077i
$508$		0			0
$509$	−2.50000	+	4.33013i	−0.110811	+	0.191930i	−0.916097	−	0.400956i	$-0.868678\pi$
$509$	−2.50000	+	4.33013i	−0.110811	+	0.191930i	0.805287	+	0.592886i	$0.202011\pi$
$510$		0			0
$511$		0			0
$512$		0			0
$513$	−27.0000			−1.19208
$514$		0			0
$515$	8.00000	−	13.8564i	0.352522	−	0.610586i
$516$		0			0
$517$	−10.0000	−	17.3205i	−0.439799	−	0.761755i
$518$		0			0
$519$	33.0000			1.44854
$520$		0			0
$521$	3.00000	−	5.19615i	0.131432	−	0.227648i	−0.792797	−	0.609486i	$-0.791376\pi$
$521$	3.00000	−	5.19615i	0.131432	−	0.227648i	0.924229	+	0.381839i	$0.124709\pi$
$522$		0			0
$523$	7.50000	−	12.9904i	0.327952	−	0.568030i	−0.654153	−	0.756362i	$-0.726975\pi$
$523$	7.50000	−	12.9904i	0.327952	−	0.568030i	0.982105	+	0.188332i	$0.0603082\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−24.0000			−1.04546
$528$		0			0
$529$	11.0000	+	19.0526i	0.478261	+	0.828372i
$530$		0			0
$531$	15.0000	+	25.9808i	0.650945	+	1.12747i
$532$		0			0
$533$	−7.50000	+	7.79423i	−0.324861	+	0.337606i
$534$		0			0
$535$	−22.0000			−0.951143
$536$		0			0
$537$	63.0000			2.71865
$538$		0			0
$539$		0			0
$540$		0			0
$541$	17.0000	+	29.4449i	0.730887	+	1.26593i	0.956504	+	0.291718i	$0.0942267\pi$
$541$	17.0000	+	29.4449i	0.730887	+	1.26593i	−0.225617	+	0.974216i	$0.572440\pi$
$542$		0			0
$543$	54.0000			2.31736
$544$		0			0
$545$	−20.0000			−0.856706
$546$		0			0
$547$	28.0000			1.19719			0.598597	−	0.801050i	$-0.295725\pi$
$547$	28.0000			1.19719			0.598597	+	0.801050i	$0.295725\pi$
$548$		0			0
$549$	30.0000			1.28037
$550$		0			0
$551$	1.50000	+	2.59808i	0.0639021	+	0.110682i
$552$		0			0
$553$		0			0
$554$		0			0
$555$	18.0000			0.764057
$556$		0			0
$557$	−33.0000			−1.39825			−0.699127	−	0.714997i	$-0.746428\pi$
$557$	−33.0000			−1.39825			−0.699127	+	0.714997i	$0.746428\pi$
$558$		0			0
$559$	−3.50000	−	0.866025i	−0.148034	−	0.0366290i
$560$		0			0
$561$	22.5000	+	38.9711i	0.949951	+	1.64536i
$562$		0			0
$563$	−9.50000	−	16.4545i	−0.400377	−	0.693474i	0.593394	−	0.804912i	$-0.297788\pi$
$563$	−9.50000	−	16.4545i	−0.400377	−	0.693474i	−0.993771	+	0.111438i	$0.964454\pi$
$564$		0			0
$565$	−22.0000			−0.925547
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−3.50000	+	6.06218i	−0.146728	+	0.254140i	−0.930016	−	0.367519i	$-0.880207\pi$
$569$	−3.50000	+	6.06218i	−0.146728	+	0.254140i	0.783289	+	0.621658i	$0.213541\pi$
$570$		0			0
$571$	−6.00000	+	10.3923i	−0.251092	+	0.434904i	−0.963827	−	0.266529i	$-0.914123\pi$
$571$	−6.00000	+	10.3923i	−0.251092	+	0.434904i	0.712735	+	0.701434i	$0.247456\pi$
$572$		0			0
$573$	−3.00000			−0.125327
$574$		0			0
$575$	−0.500000	−	0.866025i	−0.0208514	−	0.0361158i
$576$		0			0
$577$	3.00000	−	5.19615i	0.124892	−	0.216319i	−0.796799	−	0.604245i	$-0.793475\pi$
$577$	3.00000	−	5.19615i	0.124892	−	0.216319i	0.921691	+	0.387926i	$0.126808\pi$
$578$		0			0
$579$	−33.0000			−1.37143
$580$		0			0
$581$		0			0
$582$		0			0
$583$	−15.0000	+	25.9808i	−0.621237	+	1.07601i
$584$		0			0
$585$	−30.0000	+	31.1769i	−1.24035	+	1.28901i
$586$		0			0
$587$	−12.5000	−	21.6506i	−0.515930	−	0.893617i	−0.999829	−	0.0184934i	$-0.994113\pi$
$587$	−12.5000	−	21.6506i	−0.515930	−	0.893617i	0.483899	−	0.875124i	$-0.339220\pi$
$588$		0			0
$589$	−12.0000	+	20.7846i	−0.494451	+	0.856415i
$590$		0			0
$591$	−13.5000	−	23.3827i	−0.555316	−	0.961835i
$592$		0			0
$593$	−17.0000	−	29.4449i	−0.698106	−	1.20916i	−0.969122	−	0.246581i	$-0.920693\pi$
$593$	−17.0000	−	29.4449i	−0.698106	−	1.20916i	0.271016	−	0.962575i	$-0.412640\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	28.5000	+	49.3634i	1.16643	+	2.02031i
$598$		0			0
$599$	10.0000	−	17.3205i	0.408589	−	0.707697i	−0.586143	−	0.810208i	$-0.699354\pi$
$599$	10.0000	−	17.3205i	0.408589	−	0.707697i	0.994732	+	0.102511i	$0.0326876\pi$
$600$		0			0
$601$	9.50000	+	16.4545i	0.387513	+	0.671192i	0.992114	−	0.125336i	$-0.0400009\pi$
$601$	9.50000	+	16.4545i	0.387513	+	0.671192i	−0.604601	+	0.796528i	$0.706668\pi$
$602$		0			0
$603$	42.0000			1.71037
$604$		0			0
$605$	14.0000	+	24.2487i	0.569181	+	0.985850i
$606$		0			0
$607$	27.0000			1.09590			0.547948	−	0.836512i	$-0.315409\pi$
$607$	27.0000			1.09590			0.547948	+	0.836512i	$0.315409\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−10.0000	+	10.3923i	−0.404557	+	0.420428i
$612$		0			0
$613$	11.0000			0.444286			0.222143	−	0.975014i	$-0.428695\pi$
$613$	11.0000			0.444286			0.222143	+	0.975014i	$0.428695\pi$
$614$		0			0
$615$	9.00000	−	15.5885i	0.362915	−	0.628587i
$616$		0			0
$617$	−3.50000	+	6.06218i	−0.140905	+	0.244054i	−0.927838	−	0.372985i	$-0.878334\pi$
$617$	−3.50000	+	6.06218i	−0.140905	+	0.244054i	0.786933	+	0.617039i	$0.211668\pi$
$618$		0			0
$619$	−10.0000	+	17.3205i	−0.401934	+	0.696170i	−0.993959	−	0.109749i	$-0.964995\pi$
$619$	−10.0000	+	17.3205i	−0.401934	+	0.696170i	0.592025	+	0.805919i	$0.298329\pi$
$620$		0			0
$621$	−4.50000	+	7.79423i	−0.180579	+	0.312772i
$622$		0			0
$623$		0			0
$624$		0			0
$625$	9.50000	+	16.4545i	0.380000	+	0.658179i
$626$		0			0
$627$	45.0000			1.79713
$628$		0			0
$629$	−9.00000			−0.358854
$630$		0			0
$631$	−18.5000	+	32.0429i	−0.736473	+	1.27561i	0.217601	+	0.976038i	$0.430177\pi$
$631$	−18.5000	+	32.0429i	−0.736473	+	1.27561i	−0.954074	+	0.299571i	$0.903156\pi$
$632$		0			0
$633$	−19.5000	−	33.7750i	−0.775055	−	1.34244i
$634$		0			0
$635$	−5.00000	+	8.66025i	−0.198419	+	0.343672i
$636$		0			0
$637$		0			0
$638$		0			0
$639$	33.0000	−	57.1577i	1.30546	−	2.26112i
$640$		0			0
$641$	2.50000	+	4.33013i	0.0987441	+	0.171030i	0.911165	−	0.412042i	$-0.135184\pi$
$641$	2.50000	+	4.33013i	0.0987441	+	0.171030i	−0.812421	+	0.583071i	$0.801851\pi$
$642$		0			0
$643$	−15.5000	+	26.8468i	−0.611260	+	1.05873i	0.379768	+	0.925082i	$0.376004\pi$
$643$	−15.5000	+	26.8468i	−0.611260	+	1.05873i	−0.991028	+	0.133652i	$0.957330\pi$
$644$		0			0
$645$	6.00000			0.236250
$646$		0			0
$647$	29.0000			1.14011			0.570054	−	0.821607i	$-0.306922\pi$
$647$	29.0000			1.14011			0.570054	+	0.821607i	$0.306922\pi$
$648$		0			0
$649$	−12.5000	−	21.6506i	−0.490668	−	0.849862i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−1.50000	+	2.59808i	−0.0586995	+	0.101671i	−0.893882	−	0.448303i	$-0.852029\pi$
$653$	−1.50000	+	2.59808i	−0.0586995	+	0.101671i	0.835182	+	0.549973i	$0.185362\pi$
$654$		0			0
$655$	4.00000	−	6.92820i	0.156293	−	0.270707i
$656$		0			0
$657$	42.0000	−	72.7461i	1.63858	−	2.83810i
$658$		0			0
$659$	−16.5000	+	28.5788i	−0.642749	+	1.11327i	0.342068	+	0.939675i	$0.388873\pi$
$659$	−16.5000	+	28.5788i	−0.642749	+	1.11327i	−0.984817	+	0.173598i	$0.944461\pi$
$660$		0			0
$661$	37.0000			1.43913			0.719567	−	0.694423i	$-0.244340\pi$
$661$	37.0000			1.43913			0.719567	+	0.694423i	$0.244340\pi$
$662$		0			0
$663$	22.5000	−	23.3827i	0.873828	−	0.908108i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	1.00000			0.0387202
$668$		0			0
$669$	13.5000	+	23.3827i	0.521940	+	0.904027i
$670$		0			0
$671$	−25.0000			−0.965114
$672$		0			0
$673$	−3.50000	−	6.06218i	−0.134915	−	0.233680i	0.790650	−	0.612268i	$-0.209743\pi$
$673$	−3.50000	−	6.06218i	−0.134915	−	0.233680i	−0.925565	+	0.378589i	$0.876409\pi$
$674$		0			0
$675$	−4.50000	+	7.79423i	−0.173205	+	0.300000i
$676$		0			0
$677$	−3.00000	−	5.19615i	−0.115299	−	0.199704i	0.802600	−	0.596518i	$-0.203449\pi$
$677$	−3.00000	−	5.19615i	−0.115299	−	0.199704i	−0.917899	+	0.396813i	$0.870116\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	−31.5000	−	54.5596i	−1.20708	−	2.09073i
$682$		0			0
$683$	5.50000	+	9.52628i	0.210452	+	0.364513i	0.951856	−	0.306546i	$-0.0991732\pi$
$683$	5.50000	+	9.52628i	0.210452	+	0.364513i	−0.741404	+	0.671059i	$0.765840\pi$
$684$		0			0
$685$	15.0000	−	25.9808i	0.573121	−	0.992674i
$686$		0			0
$687$	9.00000	+	15.5885i	0.343371	+	0.594737i
$688$		0			0
$689$	21.0000	+	5.19615i	0.800036	+	0.197958i
$690$		0			0
$691$	−2.50000	+	4.33013i	−0.0951045	+	0.164726i	−0.909652	−	0.415371i	$-0.863652\pi$
$691$	−2.50000	+	4.33013i	−0.0951045	+	0.164726i	0.814548	+	0.580097i	$0.196985\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−22.0000			−0.834508
$696$		0			0
$697$	−4.50000	+	7.79423i	−0.170450	+	0.295227i
$698$		0			0
$699$	33.0000	+	57.1577i	1.24817	+	2.16190i
$700$		0			0
$701$	42.0000			1.58632			0.793159	−	0.609015i	$-0.208435\pi$
$701$	42.0000			1.58632			0.793159	+	0.609015i	$0.208435\pi$
$702$		0			0
$703$	−4.50000	+	7.79423i	−0.169721	+	0.293965i
$704$		0			0
$705$	12.0000	−	20.7846i	0.451946	−	0.782794i
$706$		0			0
$707$		0			0
$708$		0			0
$709$	−1.00000			−0.0375558			−0.0187779	−	0.999824i	$-0.505978\pi$
$709$	−1.00000			−0.0375558			−0.0187779	+	0.999824i	$0.505978\pi$
$710$		0			0
$711$	12.0000	+	20.7846i	0.450035	+	0.779484i
$712$		0			0
$713$	4.00000	+	6.92820i	0.149801	+	0.259463i
$714$		0			0
$715$	25.0000	−	25.9808i	0.934947	−	0.971625i
$716$		0			0
$717$	−72.0000			−2.68889
$718$		0			0
$719$	−17.0000			−0.633993			−0.316997	−	0.948427i	$-0.602674\pi$
$719$	−17.0000			−0.633993			−0.316997	+	0.948427i	$0.602674\pi$
$720$		0			0
$721$		0			0
$722$		0			0
$723$	31.5000	+	54.5596i	1.17150	+	2.02909i
$724$		0			0
$725$	1.00000			0.0371391
$726$		0			0
$727$	8.00000			0.296704			0.148352	−	0.988935i	$-0.452603\pi$
$727$	8.00000			0.296704			0.148352	+	0.988935i	$0.452603\pi$
$728$		0			0
$729$	−27.0000			−1.00000
$730$		0			0
$731$	−3.00000			−0.110959
$732$		0			0
$733$	7.00000	+	12.1244i	0.258551	+	0.447823i	0.965854	−	0.259087i	$-0.0834217\pi$
$733$	7.00000	+	12.1244i	0.258551	+	0.447823i	−0.707303	+	0.706910i	$0.750088\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−35.0000			−1.28924
$738$		0			0
$739$	15.0000			0.551784			0.275892	−	0.961189i	$-0.411027\pi$
$739$	15.0000			0.551784			0.275892	+	0.961189i	$0.411027\pi$
$740$		0			0
$741$	−9.00000	−	31.1769i	−0.330623	−	1.14531i
$742$		0			0
$743$	14.5000	+	25.1147i	0.531953	+	0.921370i	0.999304	+	0.0372984i	$0.0118752\pi$
$743$	14.5000	+	25.1147i	0.531953	+	0.921370i	−0.467351	+	0.884072i	$0.654791\pi$
$744$		0			0
$745$	−21.0000	−	36.3731i	−0.769380	−	1.33261i
$746$		0			0
$747$	−72.0000			−2.63434
$748$		0			0
$749$		0			0
$750$		0			0
$751$	4.50000	−	7.79423i	0.164207	−	0.284415i	−0.772166	−	0.635421i	$-0.780827\pi$
$751$	4.50000	−	7.79423i	0.164207	−	0.284415i	0.936374	+	0.351005i	$0.114160\pi$
$752$		0			0
$753$	−13.5000	+	23.3827i	−0.491967	+	0.852112i
$754$		0			0
$755$		0			0
$756$		0			0
$757$	−1.50000	−	2.59808i	−0.0545184	−	0.0944287i	0.837478	−	0.546471i	$-0.184029\pi$
$757$	−1.50000	−	2.59808i	−0.0545184	−	0.0944287i	−0.891997	+	0.452042i	$0.850696\pi$
$758$		0			0
$759$	7.50000	−	12.9904i	0.272233	−	0.471521i
$760$		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
$763$		0			0
$764$		0			0
$765$	−18.0000	+	31.1769i	−0.650791	+	1.12720i
$766$		0			0
$767$	−12.5000	+	12.9904i	−0.451349	+	0.469055i
$768$		0			0
$769$	−10.5000	−	18.1865i	−0.378640	−	0.655823i	0.612225	−	0.790684i	$-0.290275\pi$
$769$	−10.5000	−	18.1865i	−0.378640	−	0.655823i	−0.990865	+	0.134860i	$0.956941\pi$
$770$		0			0
$771$	−4.50000	+	7.79423i	−0.162064	+	0.280702i
$772$		0			0
$773$	−0.500000	−	0.866025i	−0.0179838	−	0.0311488i	0.856893	−	0.515494i	$-0.172391\pi$
$773$	−0.500000	−	0.866025i	−0.0179838	−	0.0311488i	−0.874877	+	0.484345i	$0.839058\pi$
$774$		0			0
$775$	4.00000	+	6.92820i	0.143684	+	0.248868i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	4.50000	+	7.79423i	0.161229	+	0.279257i
$780$		0			0
$781$	−27.5000	+	47.6314i	−0.984027	+	1.70439i
$782$		0			0
$783$	−4.50000	−	7.79423i	−0.160817	−	0.278543i
$784$		0			0
$785$	−44.0000			−1.57043
$786$		0			0
$787$	−3.50000	−	6.06218i	−0.124762	−	0.216093i	0.796878	−	0.604140i	$-0.206483\pi$
$787$	−3.50000	−	6.06218i	−0.124762	−	0.216093i	−0.921640	+	0.388047i	$0.873150\pi$
$788$		0			0
$789$	−45.0000			−1.60204
$790$		0			0
$791$		0			0
$792$		0			0
$793$	5.00000	+	17.3205i	0.177555	+	0.615069i
$794$		0			0
$795$	−36.0000			−1.27679
$796$		0			0
$797$	13.5000	−	23.3827i	0.478195	−	0.828257i	−0.521493	−	0.853256i	$-0.674625\pi$
$797$	13.5000	−	23.3827i	0.478195	−	0.828257i	0.999687	+	0.0249984i	$0.00795805\pi$
$798$		0			0
$799$	−6.00000	+	10.3923i	−0.212265	+	0.367653i
$800$		0			0
$801$	−27.0000	+	46.7654i	−0.953998	+	1.65237i
$802$		0			0
$803$	−35.0000	+	60.6218i	−1.23512	+	2.13930i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−22.5000	−	38.9711i	−0.792038	−	1.37185i
$808$		0			0
$809$	−45.0000			−1.58212			−0.791058	−	0.611741i	$-0.790469\pi$
$809$	−45.0000			−1.58212			−0.791058	+	0.611741i	$0.790469\pi$
$810$		0			0
$811$	40.0000			1.40459			0.702295	−	0.711886i	$-0.252159\pi$
$811$	40.0000			1.40459			0.702295	+	0.711886i	$0.252159\pi$
$812$		0			0
$813$	25.5000	−	44.1673i	0.894324	−	1.54901i
$814$		0			0
$815$	−7.00000	−	12.1244i	−0.245199	−	0.424698i
$816$		0			0
$817$	−1.50000	+	2.59808i	−0.0524784	+	0.0908952i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−23.5000	+	40.7032i	−0.820156	+	1.42055i	0.0854103	+	0.996346i	$0.472780\pi$
$821$	−23.5000	+	40.7032i	−0.820156	+	1.42055i	−0.905566	+	0.424205i	$0.860553\pi$
$822$		0			0
$823$	1.50000	+	2.59808i	0.0522867	+	0.0905632i	0.890984	−	0.454034i	$-0.150016\pi$
$823$	1.50000	+	2.59808i	0.0522867	+	0.0905632i	−0.838697	+	0.544598i	$0.816682\pi$
$824$		0			0
$825$	7.50000	−	12.9904i	0.261116	−	0.452267i
$826$		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
$829$	−31.0000			−1.07667			−0.538337	−	0.842729i	$-0.680947\pi$
$829$	−31.0000			−1.07667			−0.538337	+	0.842729i	$0.680947\pi$
$830$		0			0
$831$	−13.5000	−	23.3827i	−0.468310	−	0.811136i
$832$		0			0
$833$		0			0
$834$		0			0
$835$	9.00000	−	15.5885i	0.311458	−	0.539461i
$836$		0			0
$837$	36.0000	−	62.3538i	1.24434	−	2.15526i
$838$		0			0
$839$	−21.5000	+	37.2391i	−0.742262	+	1.28564i	0.209200	+	0.977873i	$0.432914\pi$
$839$	−21.5000	+	37.2391i	−0.742262	+	1.28564i	−0.951463	+	0.307763i	$0.900419\pi$
$840$		0			0
$841$	14.0000	−	24.2487i	0.482759	−	0.836162i
$842$		0			0
$843$	6.00000			0.206651
$844$		0			0
$845$	−23.0000	−	12.1244i	−0.791224	−	0.417091i
$846$		0			0
$847$		0			0
$848$		0			0
$849$	57.0000			1.95623
$850$		0			0
$851$	1.50000	+	2.59808i	0.0514193	+	0.0890609i
$852$		0			0
$853$	−10.0000			−0.342393			−0.171197	−	0.985237i	$-0.554763\pi$
$853$	−10.0000			−0.342393			−0.171197	+	0.985237i	$0.554763\pi$
$854$		0			0
$855$	18.0000	+	31.1769i	0.615587	+	1.06623i
$856$		0			0
$857$	−1.00000	+	1.73205i	−0.0341593	+	0.0591657i	−0.882600	−	0.470125i	$-0.844209\pi$
$857$	−1.00000	+	1.73205i	−0.0341593	+	0.0591657i	0.848440	+	0.529291i	$0.177542\pi$
$858$		0			0
$859$	−14.0000	−	24.2487i	−0.477674	−	0.827355i	0.521999	−	0.852946i	$-0.325187\pi$
$859$	−14.0000	−	24.2487i	−0.477674	−	0.827355i	−0.999672	+	0.0255910i	$0.991853\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−8.00000	−	13.8564i	−0.272323	−	0.471678i	0.697133	−	0.716942i	$-0.254459\pi$
$863$	−8.00000	−	13.8564i	−0.272323	−	0.471678i	−0.969456	+	0.245264i	$0.921125\pi$
$864$		0			0
$865$	−11.0000	−	19.0526i	−0.374011	−	0.647806i
$866$		0			0
$867$	−12.0000	+	20.7846i	−0.407541	+	0.705882i
$868$		0			0
$869$	−10.0000	−	17.3205i	−0.339227	−	0.587558i
$870$		0			0
$871$	7.00000	+	24.2487i	0.237186	+	0.821636i
$872$		0			0
$873$	−3.00000	+	5.19615i	−0.101535	+	0.175863i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−45.0000			−1.51954			−0.759771	−	0.650191i	$-0.774689\pi$
$877$	−45.0000			−1.51954			−0.759771	+	0.650191i	$0.774689\pi$
$878$		0			0
$879$	−28.5000	+	49.3634i	−0.961281	+	1.66499i
$880$		0			0
$881$	25.5000	+	44.1673i	0.859117	+	1.48803i	0.872772	+	0.488127i	$0.162320\pi$
$881$	25.5000	+	44.1673i	0.859117	+	1.48803i	−0.0136556	+	0.999907i	$0.504347\pi$
$882$		0			0
$883$	−44.0000			−1.48072			−0.740359	−	0.672212i	$-0.765344\pi$
$883$	−44.0000			−1.48072			−0.740359	+	0.672212i	$0.765344\pi$
$884$		0			0
$885$	15.0000	−	25.9808i	0.504219	−	0.873334i
$886$		0			0
$887$	−26.5000	+	45.8993i	−0.889783	+	1.54115i	−0.0496513	+	0.998767i	$0.515811\pi$
$887$	−26.5000	+	45.8993i	−0.889783	+	1.54115i	−0.840132	+	0.542383i	$0.817522\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	−45.0000			−1.50756
$892$		0			0
$893$	6.00000	+	10.3923i	0.200782	+	0.347765i
$894$		0			0
$895$	−21.0000	−	36.3731i	−0.701953	−	1.21582i
$896$		0			0
$897$	−10.5000	−	2.59808i	−0.350585	−	0.0867472i
$898$		0			0
$899$	−8.00000			−0.266815
$900$		0			0
$901$	18.0000			0.599667
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−18.0000	−	31.1769i	−0.598340	−	1.03636i
$906$		0			0
$907$	3.00000			0.0996134			0.0498067	−	0.998759i	$-0.484139\pi$
$907$	3.00000			0.0996134			0.0498067	+	0.998759i	$0.484139\pi$
$908$		0			0
$909$	−114.000			−3.78114
$910$		0			0
$911$	−48.0000			−1.59031			−0.795155	−	0.606406i	$-0.792611\pi$
$911$	−48.0000			−1.59031			−0.795155	+	0.606406i	$0.792611\pi$
$912$		0			0
$913$	60.0000			1.98571
$914$		0			0
$915$	−15.0000	−	25.9808i	−0.495885	−	0.858898i
$916$		0			0
$917$		0			0
$918$		0			0
$919$	33.0000			1.08857			0.544285	−	0.838901i	$-0.316801\pi$
$919$	33.0000			1.08857			0.544285	+	0.838901i	$0.316801\pi$
$920$		0			0
$921$	−12.0000			−0.395413
$922$		0			0
$923$	38.5000	+	9.52628i	1.26724	+	0.313561i
$924$		0			0
$925$	1.50000	+	2.59808i	0.0493197	+	0.0854242i
$926$		0			0
$927$	−24.0000	−	41.5692i	−0.788263	−	1.36531i
$928$		0			0
$929$	21.0000			0.688988			0.344494	−	0.938789i	$-0.388051\pi$
$929$	21.0000			0.688988			0.344494	+	0.938789i	$0.388051\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$	36.0000	−	62.3538i	1.17859	−	2.04137i
$934$		0			0
$935$	15.0000	−	25.9808i	0.490552	−	0.849662i
$936$		0			0
$937$	18.0000			0.588034			0.294017	−	0.955800i	$-0.405008\pi$
$937$	18.0000			0.588034			0.294017	+	0.955800i	$0.405008\pi$
$938$		0			0
$939$	−21.0000	−	36.3731i	−0.685309	−	1.18699i
$940$		0			0
$941$	−25.0000	+	43.3013i	−0.814977	+	1.41158i	0.0943679	+	0.995537i	$0.469917\pi$
$941$	−25.0000	+	43.3013i	−0.814977	+	1.41158i	−0.909345	+	0.416044i	$0.863416\pi$
$942$		0			0
$943$	3.00000			0.0976934
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−13.5000	+	23.3827i	−0.438691	+	0.759835i	−0.997589	−	0.0694014i	$-0.977891\pi$
$947$	−13.5000	+	23.3827i	−0.438691	+	0.759835i	0.558898	+	0.829237i	$0.311224\pi$
$948$		0			0
$949$	49.0000	+	12.1244i	1.59061	+	0.393573i
$950$		0			0
$951$	45.0000	+	77.9423i	1.45922	+	2.52745i
$952$		0			0
$953$	0.500000	−	0.866025i	0.0161966	−	0.0280533i	−0.857814	−	0.513961i	$-0.828178\pi$
$953$	0.500000	−	0.866025i	0.0161966	−	0.0280533i	0.874010	+	0.485908i	$0.161511\pi$
$954$		0			0
$955$	1.00000	+	1.73205i	0.0323592	+	0.0560478i
$956$		0			0
$957$	7.50000	+	12.9904i	0.242441	+	0.419919i
$958$		0			0
$959$		0			0
$960$		0			0
$961$	−16.5000	−	28.5788i	−0.532258	−	0.921898i
$962$		0			0
$963$	−33.0000	+	57.1577i	−1.06341	+	1.84188i
$964$		0			0
$965$	11.0000	+	19.0526i	0.354103	+	0.613324i
$966$		0			0
$967$	32.0000			1.02905			0.514525	−	0.857475i	$-0.327968\pi$
$967$	32.0000			1.02905			0.514525	+	0.857475i	$0.327968\pi$
$968$		0			0
$969$	−13.5000	−	23.3827i	−0.433682	−	0.751160i
$970$		0			0
$971$	15.0000			0.481373			0.240686	−	0.970603i	$-0.422627\pi$
$971$	15.0000			0.481373			0.240686	+	0.970603i	$0.422627\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$	−10.5000	−	2.59808i	−0.336269	−	0.0832050i
$976$		0			0
$977$	39.0000			1.24772			0.623860	−	0.781536i	$-0.285563\pi$
$977$	39.0000			1.24772			0.623860	+	0.781536i	$0.285563\pi$
$978$		0			0
$979$	22.5000	−	38.9711i	0.719103	−	1.24552i
$980$		0			0
$981$	−30.0000	+	51.9615i	−0.957826	+	1.65900i
$982$		0			0
$983$	−8.00000	+	13.8564i	−0.255160	+	0.441951i	−0.964939	−	0.262474i	$-0.915462\pi$
$983$	−8.00000	+	13.8564i	−0.255160	+	0.441951i	0.709779	+	0.704425i	$0.248795\pi$
$984$		0			0
$985$	−9.00000	+	15.5885i	−0.286764	+	0.496690i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	0.500000	+	0.866025i	0.0158991	+	0.0275380i
$990$		0			0
$991$	27.0000			0.857683			0.428842	−	0.903380i	$-0.358922\pi$
$991$	27.0000			0.857683			0.428842	+	0.903380i	$0.358922\pi$
$992$		0			0
$993$	−51.0000			−1.61844
$994$		0			0
$995$	19.0000	−	32.9090i	0.602340	−	1.04328i
$996$		0			0
$997$	17.5000	+	30.3109i	0.554231	+	0.959955i	0.997963	+	0.0637961i	$0.0203207\pi$
$997$	17.5000	+	30.3109i	0.554231	+	0.959955i	−0.443732	+	0.896159i	$0.646346\pi$
$998$		0			0
$999$	13.5000	−	23.3827i	0.427121	−	0.739795i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2548.2.l.a.1537.1		2
7.2	even	3		2548.2.i.h.1745.1		2
7.3	odd	6		52.2.e.a.29.1	yes	2
7.4	even	3		2548.2.k.d.393.1		2
7.5	odd	6		2548.2.i.a.1745.1		2
7.6	odd	2		2548.2.l.h.1537.1		2
13.9	even	3		2548.2.i.h.165.1		2
21.17	even	6		468.2.l.a.289.1		2
28.3	even	6		208.2.i.d.81.1		2
35.3	even	12		1300.2.bb.f.549.2		4
35.17	even	12		1300.2.bb.f.549.1		4
35.24	odd	6		1300.2.i.f.601.1		2
56.3	even	6		832.2.i.a.705.1		2
56.45	odd	6		832.2.i.j.705.1		2
84.59	odd	6		1872.2.t.f.289.1		2
91.3	odd	6		676.2.a.e.1.1		1
91.9	even	3	inner	2548.2.l.a.373.1		2
91.10	odd	6		676.2.a.d.1.1		1
91.17	odd	6		676.2.e.a.529.1		2
91.24	even	12		676.2.d.d.337.2		2
91.31	even	12		676.2.h.b.361.1		4
91.38	odd	6		676.2.e.a.653.1		2
91.45	even	12		676.2.h.b.485.1		4
91.48	odd	6		2548.2.i.a.165.1		2
91.59	even	12		676.2.h.b.485.2		4
91.61	odd	6		2548.2.l.h.373.1		2
91.73	even	12		676.2.h.b.361.2		4
91.74	even	3		2548.2.k.d.1569.1		2
91.80	even	12		676.2.d.d.337.1		2
91.87	odd	6		52.2.e.a.9.1	✓	2
273.80	odd	12		6084.2.b.l.4393.2		2
273.101	even	6		6084.2.a.k.1.1		1
273.185	even	6		6084.2.a.f.1.1		1
273.206	odd	12		6084.2.b.l.4393.1		2
273.269	even	6		468.2.l.a.217.1		2
364.3	even	6		2704.2.a.b.1.1		1
364.87	even	6		208.2.i.d.113.1		2
364.115	odd	12		2704.2.f.a.337.2		2
364.171	odd	12		2704.2.f.a.337.1		2
364.283	even	6		2704.2.a.a.1.1		1
455.87	even	12		1300.2.bb.f.1049.2		4
455.178	even	12		1300.2.bb.f.1049.1		4
455.269	odd	6		1300.2.i.f.1101.1		2
728.269	odd	6		832.2.i.j.321.1		2
728.451	even	6		832.2.i.a.321.1		2
1092.815	odd	6		1872.2.t.f.1153.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
52.2.e.a.9.1	✓	2	91.87	odd	6
52.2.e.a.29.1	yes	2	7.3	odd	6
208.2.i.d.81.1		2	28.3	even	6
208.2.i.d.113.1		2	364.87	even	6
468.2.l.a.217.1		2	273.269	even	6
468.2.l.a.289.1		2	21.17	even	6
676.2.a.d.1.1		1	91.10	odd	6
676.2.a.e.1.1		1	91.3	odd	6
676.2.d.d.337.1		2	91.80	even	12
676.2.d.d.337.2		2	91.24	even	12
676.2.e.a.529.1		2	91.17	odd	6
676.2.e.a.653.1		2	91.38	odd	6
676.2.h.b.361.1		4	91.31	even	12
676.2.h.b.361.2		4	91.73	even	12
676.2.h.b.485.1		4	91.45	even	12
676.2.h.b.485.2		4	91.59	even	12
832.2.i.a.321.1		2	728.451	even	6
832.2.i.a.705.1		2	56.3	even	6
832.2.i.j.321.1		2	728.269	odd	6
832.2.i.j.705.1		2	56.45	odd	6
1300.2.i.f.601.1		2	35.24	odd	6
1300.2.i.f.1101.1		2	455.269	odd	6
1300.2.bb.f.549.1		4	35.17	even	12
1300.2.bb.f.549.2		4	35.3	even	12
1300.2.bb.f.1049.1		4	455.178	even	12
1300.2.bb.f.1049.2		4	455.87	even	12
1872.2.t.f.289.1		2	84.59	odd	6
1872.2.t.f.1153.1		2	1092.815	odd	6
2548.2.i.a.165.1		2	91.48	odd	6
2548.2.i.a.1745.1		2	7.5	odd	6
2548.2.i.h.165.1		2	13.9	even	3
2548.2.i.h.1745.1		2	7.2	even	3
2548.2.k.d.393.1		2	7.4	even	3
2548.2.k.d.1569.1		2	91.74	even	3
2548.2.l.a.373.1		2	91.9	even	3	inner
2548.2.l.a.1537.1		2	1.1	even	1	trivial
2548.2.l.h.373.1		2	91.61	odd	6
2548.2.l.h.1537.1		2	7.6	odd	2
2704.2.a.a.1.1		1	364.283	even	6
2704.2.a.b.1.1		1	364.3	even	6
2704.2.f.a.337.1		2	364.171	odd	12
2704.2.f.a.337.2		2	364.115	odd	12
6084.2.a.f.1.1		1	273.185	even	6
6084.2.a.k.1.1		1	273.101	even	6
6084.2.b.l.4393.1		2	273.206	odd	12
6084.2.b.l.4393.2		2	273.80	odd	12

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:	\( N \)	\(=\)	\( 2548 = 2^{2} \cdot 7^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2548.l (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q-3.00000 q^{3} +(1.00000 + 1.73205i) q^{5} +6.00000 q^{9} -5.00000 q^{11} +(1.00000 + 3.46410i) q^{13} +(-3.00000 - 5.19615i) q^{15} +(1.50000 + 2.59808i) q^{17} +3.00000 q^{19} +(0.500000 - 0.866025i) q^{23} +(0.500000 - 0.866025i) q^{25} -9.00000 q^{27} +(0.500000 + 0.866025i) q^{29} +(-4.00000 + 6.92820i) q^{31} +15.0000 q^{33} +(-1.50000 + 2.59808i) q^{37} +(-3.00000 - 10.3923i) q^{39} +(1.50000 + 2.59808i) q^{41} +(-0.500000 + 0.866025i) q^{43} +(6.00000 + 10.3923i) q^{45} +(2.00000 + 3.46410i) q^{47} +(-4.50000 - 7.79423i) q^{51} +(3.00000 - 5.19615i) q^{53} +(-5.00000 - 8.66025i) q^{55} -9.00000 q^{57} +(2.50000 + 4.33013i) q^{59} +5.00000 q^{61} +(-5.00000 + 5.19615i) q^{65} +7.00000 q^{67} +(-1.50000 + 2.59808i) q^{69} +(5.50000 - 9.52628i) q^{71} +(7.00000 - 12.1244i) q^{73} +(-1.50000 + 2.59808i) q^{75} +(2.00000 + 3.46410i) q^{79} +9.00000 q^{81} -12.0000 q^{83} +(-3.00000 + 5.19615i) q^{85} +(-1.50000 - 2.59808i) q^{87} +(-4.50000 + 7.79423i) q^{89} +(12.0000 - 20.7846i) q^{93} +(3.00000 + 5.19615i) q^{95} +(-0.500000 + 0.866025i) q^{97} -30.0000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 6 q^{3} + 2 q^{5} + 12 q^{9} - 10 q^{11} + 2 q^{13} - 6 q^{15} + 3 q^{17} + 6 q^{19} + q^{23} + q^{25} - 18 q^{27} + q^{29} - 8 q^{31} + 30 q^{33} - 3 q^{37} - 6 q^{39} + 3 q^{41} - q^{43} + 12 q^{45}+ \cdots - 60 q^{99}+O(q^{100}) \) 2 * q - 6 * q^3 + 2 * q^5 + 12 * q^9 - 10 * q^11 + 2 * q^13 - 6 * q^15 + 3 * q^17 + 6 * q^19 + q^23 + q^25 - 18 * q^27 + q^29 - 8 * q^31 + 30 * q^33 - 3 * q^37 - 6 * q^39 + 3 * q^41 - q^43 + 12 * q^45 + 4 * q^47 - 9 * q^51 + 6 * q^53 - 10 * q^55 - 18 * q^57 + 5 * q^59 + 10 * q^61 - 10 * q^65 + 14 * q^67 - 3 * q^69 + 11 * q^71 + 14 * q^73 - 3 * q^75 + 4 * q^79 + 18 * q^81 - 24 * q^83 - 6 * q^85 - 3 * q^87 - 9 * q^89 + 24 * q^93 + 6 * q^95 - q^97 - 60 * q^99

Introduction

L-functions

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Varieties

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Representations

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