LMFDB - Embedded newform 1620.2.x.d.53.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1620,2,Mod(53,1620)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1620, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 10, 9]))

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

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

chi := DirichletCharacter("1620.53");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1620 = 2^{2} \cdot 3^{4} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1620.x (of order $12$, degree $4$, 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:	$12.9357651274$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{12})$
Coefficient field:	16.0.1154223326374133760000.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 12x^{14} + 100x^{12} - 408x^{10} + 1191x^{8} - 2040x^{6} + 2500x^{4} - 1500x^{2} + 625 $ x^16 - 12x^14 + 100x^12 - 408x^10 + 1191x^8 - 2040x^6 + 2500x^4 - 1500*x^2 + 625
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 3^{4}\cdot 5^{2} $
Twist minimal:	no (minimal twist has level 540)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			53.1
Root			$-1.44919 - 0.836690i$ of defining polynomial
Character	$\chi$	$=$	1620.53
Dual form			1620.2.x.d.917.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.70289 - 1.44919i) q^{5} +(-0.307007 - 0.0822623i) q^{7} +O(q^{10})$	$q+(-1.70289 - 1.44919i) q^{5} +(-0.307007 - 0.0822623i) q^{7} +(2.41131 - 1.39217i) q^{11} +(1.67303 - 0.448288i) q^{13} +(2.78434 + 2.78434i) q^{17} +3.89898i q^{19} +(-2.26732 - 8.46177i) q^{23} +(0.799701 + 4.93563i) q^{25} +(-1.39217 - 2.41131i) q^{29} +(-0.224745 + 0.389270i) q^{31} +(0.403587 + 0.584996i) q^{35} +(3.67423 - 3.67423i) q^{37} +(-8.31779 - 4.80228i) q^{41} +(0.201501 - 0.752011i) q^{43} +(-5.97469 - 3.44949i) q^{49} +(6.19445 - 6.19445i) q^{53} +(-6.12372 - 1.12372i) q^{55} +(6.19445 - 10.7291i) q^{59} +(-6.39898 - 11.0834i) q^{61} +(-3.49865 - 1.66115i) q^{65} +(3.17499 + 11.8492i) q^{67} -9.60455i q^{71} +(-6.22474 - 6.22474i) q^{73} +(-0.854813 + 0.229046i) q^{77} +(8.00853 - 4.62372i) q^{79} +(-4.65829 - 1.24819i) q^{83} +(-0.706403 - 8.77647i) q^{85} +12.3889 q^{89} -0.550510 q^{91} +(5.65036 - 6.63955i) q^{95} +(6.52312 + 1.74786i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 8 q^{7}+O(q^{10}) $ 16 * q + 8 * q^7	$ 16 q + 8 q^{7} + 8 q^{25} + 16 q^{31} - 24 q^{43} - 24 q^{61} - 40 q^{67} - 80 q^{73} - 40 q^{85} - 48 q^{91} + 48 q^{97}+O(q^{100}) $ 16 * q + 8 * q^7 + 8 * q^25 + 16 * q^31 - 24 * q^43 - 24 * q^61 - 40 * q^67 - 80 * q^73 - 40 * q^85 - 48 * q^91 + 48 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1620\mathbb{Z}\right)^\times$.

$n$	$811$	$1297$	$1541$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{5}{6}\right)$

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
$5$	−1.70289	−	1.44919i	−0.761558	−	0.648097i
$5$	−1.70289	−	1.44919i	−0.761558	−	0.648097i
$6$		0			0
$7$	−0.307007	−	0.0822623i	−0.116038	−	0.0310922i	0.200333	−	0.979728i	$-0.435798\pi$
$7$	−0.307007	−	0.0822623i	−0.116038	−	0.0310922i	−0.316371	+	0.948636i	$0.602464\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	2.41131	−	1.39217i	0.727037	−	0.419755i	−0.0903001	−	0.995915i	$-0.528783\pi$
$11$	2.41131	−	1.39217i	0.727037	−	0.419755i	0.817337	+	0.576159i	$0.195449\pi$
$12$		0			0
$13$	1.67303	−	0.448288i	0.464016	−	0.124333i	−0.0192343	−	0.999815i	$-0.506123\pi$
$13$	1.67303	−	0.448288i	0.464016	−	0.124333i	0.483250	+	0.875482i	$0.339456\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	2.78434	+	2.78434i	0.675302	+	0.675302i	0.958933	−	0.283632i	$-0.0915393\pi$
$17$	2.78434	+	2.78434i	0.675302	+	0.675302i	−0.283632	+	0.958933i	$0.591539\pi$
$18$		0			0
$19$			3.89898i			0.894487i	0.894412	+	0.447244i	$0.147594\pi$
$19$			3.89898i			0.894487i	−0.894412	+	0.447244i	$0.852406\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−2.26732	−	8.46177i	−0.472770	−	1.76440i	−0.629748	−	0.776799i	$-0.716842\pi$
$23$	−2.26732	−	8.46177i	−0.472770	−	1.76440i	0.156978	−	0.987602i	$-0.449825\pi$
$24$		0			0
$25$	0.799701	+	4.93563i	0.159940	+	0.987127i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−1.39217	−	2.41131i	−0.258520	−	0.447769i	0.707326	−	0.706887i	$-0.249901\pi$
$29$	−1.39217	−	2.41131i	−0.258520	−	0.447769i	−0.965846	+	0.259119i	$0.916568\pi$
$30$		0			0
$31$	−0.224745	+	0.389270i	−0.0403654	+	0.0699149i	−0.885502	−	0.464635i	$-0.846186\pi$
$31$	−0.224745	+	0.389270i	−0.0403654	+	0.0699149i	0.845137	+	0.534550i	$0.179519\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	0.403587	+	0.584996i	0.0682187	+	0.0988823i
$36$		0			0
$37$	3.67423	−	3.67423i	0.604040	−	0.604040i	−0.337342	−	0.941382i	$-0.609528\pi$
$37$	3.67423	−	3.67423i	0.604040	−	0.604040i	0.941382	+	0.337342i	$0.109528\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−8.31779	−	4.80228i	−1.29902	−	0.749990i	−0.318785	−	0.947827i	$-0.603275\pi$
$41$	−8.31779	−	4.80228i	−1.29902	−	0.749990i	−0.980235	+	0.197837i	$0.936608\pi$
$42$		0			0
$43$	0.201501	−	0.752011i	0.0307286	−	0.114681i	−0.948858	−	0.315703i	$-0.897760\pi$
$43$	0.201501	−	0.752011i	0.0307286	−	0.114681i	0.979587	+	0.201022i	$0.0644264\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$		0			0		−0.965926	−	0.258819i	$-0.916667\pi$
$47$		0			0		0.965926	+	0.258819i	$0.0833333\pi$
$48$		0			0
$49$	−5.97469	−	3.44949i	−0.853527	−	0.492784i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	6.19445	−	6.19445i	0.850873	−	0.850873i	−0.139368	−	0.990241i	$-0.544507\pi$
$53$	6.19445	−	6.19445i	0.850873	−	0.850873i	0.990241	+	0.139368i	$0.0445071\pi$
$54$		0			0
$55$	−6.12372	−	1.12372i	−0.825723	−	0.151523i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	6.19445	−	10.7291i	0.806448	−	1.39681i	−0.108861	−	0.994057i	$-0.534720\pi$
$59$	6.19445	−	10.7291i	0.806448	−	1.39681i	0.915309	−	0.402752i	$-0.131946\pi$
$60$		0			0
$61$	−6.39898	−	11.0834i	−0.819305	−	1.41908i	−0.906195	−	0.422861i	$-0.861026\pi$
$61$	−6.39898	−	11.0834i	−0.819305	−	1.41908i	0.0868894	−	0.996218i	$-0.472307\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−3.49865	−	1.66115i	−0.433954	−	0.206041i
$66$		0			0
$67$	3.17499	+	11.8492i	0.387887	+	1.44761i	0.833566	+	0.552420i	$0.186296\pi$
$67$	3.17499	+	11.8492i	0.387887	+	1.44761i	−0.445679	+	0.895193i	$0.647038\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$		−	9.60455i		−	1.13985i	−0.821696	−	0.569925i	$-0.806972\pi$
$71$		−	9.60455i		−	1.13985i	0.821696	−	0.569925i	$-0.193028\pi$
$72$		0			0
$73$	−6.22474	−	6.22474i	−0.728551	−	0.728551i	0.241780	−	0.970331i	$-0.422269\pi$
$73$	−6.22474	−	6.22474i	−0.728551	−	0.728551i	−0.970331	+	0.241780i	$0.922269\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−0.854813	+	0.229046i	−0.0974149	+	0.0261023i
$78$		0			0
$79$	8.00853	−	4.62372i	0.901030	−	0.520210i	0.0234955	−	0.999724i	$-0.492520\pi$
$79$	8.00853	−	4.62372i	0.901030	−	0.520210i	0.877534	+	0.479514i	$0.159187\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−4.65829	−	1.24819i	−0.511314	−	0.137006i	−0.00606809	−	0.999982i	$-0.501932\pi$
$83$	−4.65829	−	1.24819i	−0.511314	−	0.137006i	−0.505246	+	0.862975i	$0.668598\pi$
$84$		0			0
$85$	−0.706403	−	8.77647i	−0.0766201	−	0.951942i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	12.3889			1.31322			0.656610	−	0.754230i	$-0.271990\pi$
$89$	12.3889			1.31322			0.656610	+	0.754230i	$0.271990\pi$
$90$		0			0
$91$	−0.550510			−0.0577092
$92$		0			0
$93$		0			0
$94$		0			0
$95$	5.65036	−	6.63955i	0.579715	−	0.681204i
$96$		0			0
$97$	6.52312	+	1.74786i	0.662322	+	0.177469i	0.574294	−	0.818649i	$-0.305277\pi$
$97$	6.52312	+	1.74786i	0.662322	+	0.177469i	0.0880285	+	0.996118i	$0.471943\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−15.5517	+	8.97879i	−1.54745	+	0.893423i	−0.549118	+	0.835745i	$0.685036\pi$
$101$	−15.5517	+	8.97879i	−1.54745	+	0.893423i	−0.998335	+	0.0576781i	$0.981630\pi$
$102$		0			0
$103$	8.50316	−	2.27841i	0.837841	−	0.224499i	0.185710	−	0.982605i	$-0.440542\pi$
$103$	8.50316	−	2.27841i	0.837841	−	0.224499i	0.652132	+	0.758106i	$0.273875\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−8.97879	−	8.97879i	−0.868012	−	0.868012i	0.124240	−	0.992252i	$-0.460351\pi$
$107$	−8.97879	−	8.97879i	−0.868012	−	0.868012i	−0.992252	+	0.124240i	$0.960351\pi$
$108$		0			0
$109$			11.3485i			1.08699i	0.839414	+	0.543493i	$0.182899\pi$
$109$			11.3485i			1.08699i	−0.839414	+	0.543493i	$0.817101\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−0.229046	−	0.854813i	−0.0215469	−	0.0804140i	0.954315	−	0.298802i	$-0.0965869\pi$
$113$	−0.229046	−	0.854813i	−0.0215469	−	0.0804140i	−0.975862	+	0.218388i	$0.929920\pi$
$114$		0			0
$115$	−8.40169	+	17.6953i	−0.783462	+	1.65009i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−0.625766	−	1.08386i	−0.0573639	−	0.0993572i
$120$		0			0
$121$	−1.62372	+	2.81237i	−0.147611	+	0.255670i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	5.79086	−	9.56378i	0.517950	−	0.855411i
$126$		0			0
$127$	9.89898	−	9.89898i	0.878392	−	0.878392i	−0.114976	−	0.993368i	$-0.536679\pi$
$127$	9.89898	−	9.89898i	0.878392	−	0.878392i	0.993368	+	0.114976i	$0.0366791\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	4.82262	+	2.78434i	0.421354	+	0.243269i	0.695657	−	0.718375i	$-0.255114\pi$
$131$	4.82262	+	2.78434i	0.421354	+	0.243269i	−0.274302	+	0.961644i	$0.588447\pi$
$132$		0			0
$133$	0.320739	−	1.19701i	0.0278116	−	0.103794i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−1.24819	+	4.65829i	−0.106640	+	0.397985i	−0.998526	−	0.0542749i	$-0.982715\pi$
$137$	−1.24819	+	4.65829i	−0.106640	+	0.397985i	0.891886	+	0.452260i	$0.149382\pi$
$138$		0			0
$139$	−16.6688	−	9.62372i	−1.41383	−	0.816274i	−0.418081	−	0.908410i	$-0.637297\pi$
$139$	−16.6688	−	9.62372i	−1.41383	−	0.816274i	−0.995746	+	0.0921361i	$0.970631\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	3.41011	−	3.41011i	0.285167	−	0.285167i
$144$		0			0
$145$	−1.12372	+	6.12372i	−0.0933202	+	0.508548i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−3.41011	+	5.90648i	−0.279367	+	0.483878i	−0.971228	−	0.238153i	$-0.923458\pi$
$149$	−3.41011	+	5.90648i	−0.279367	+	0.483878i	0.691861	+	0.722031i	$0.256791\pi$
$150$		0			0
$151$	−5.27526	−	9.13701i	−0.429294	−	0.743559i	0.567517	−	0.823362i	$-0.307904\pi$
$151$	−5.27526	−	9.13701i	−0.429294	−	0.743559i	−0.996811	+	0.0798027i	$0.974571\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	0.946842	−	0.337187i	0.0760522	−	0.0270835i
$156$		0			0
$157$	4.88588	+	18.2343i	0.389936	+	1.45526i	0.830238	+	0.557410i	$0.188205\pi$
$157$	4.88588	+	18.2343i	0.389936	+	1.45526i	−0.440302	+	0.897850i	$0.645129\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$			2.78434i			0.219437i
$162$		0			0
$163$	3.77526	+	3.77526i	0.295701	+	0.295701i	0.839327	−	0.543626i	$-0.182949\pi$
$163$	3.77526	+	3.77526i	0.295701	+	0.295701i	−0.543626	+	0.839327i	$0.682949\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	13.1201	−	3.51551i	1.01526	−	0.272038i	0.287435	−	0.957800i	$-0.407197\pi$
$167$	13.1201	−	3.51551i	1.01526	−	0.272038i	0.727826	+	0.685762i	$0.240531\pi$
$168$		0			0
$169$	−8.66025	+	5.00000i	−0.666173	+	0.384615i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−7.60696	−	2.03828i	−0.578346	−	0.154967i	−0.0422247	−	0.999108i	$-0.513445\pi$
$173$	−7.60696	−	2.03828i	−0.578346	−	0.154967i	−0.536122	+	0.844141i	$0.680111\pi$
$174$		0			0
$175$	0.160503	−	1.58106i	0.0121329	−	0.119517i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−9.60455			−0.717878			−0.358939	−	0.933361i	$-0.616861\pi$
$179$	−9.60455			−0.717878			−0.358939	+	0.933361i	$0.616861\pi$
$180$		0			0
$181$	11.2474			0.836016			0.418008	−	0.908443i	$-0.362728\pi$
$181$	11.2474			0.836016			0.418008	+	0.908443i	$0.362728\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−11.5815	+	0.932174i	−0.851489	+	0.0685348i
$186$		0			0
$187$	10.5902	+	2.83763i	0.774431	+	0.207508i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	10.7291	−	6.19445i	0.776330	−	0.448214i	−0.0587979	−	0.998270i	$-0.518727\pi$
$191$	10.7291	−	6.19445i	0.776330	−	0.448214i	0.835128	+	0.550055i	$0.185393\pi$
$192$		0			0
$193$	15.8093	−	4.23609i	1.13798	−	0.304920i	0.359841	−	0.933014i	$-0.382831\pi$
$193$	15.8093	−	4.23609i	1.13798	−	0.304920i	0.778138	+	0.628093i	$0.216164\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	6.82021	+	6.82021i	0.485920	+	0.485920i	0.907016	−	0.421096i	$-0.138354\pi$
$197$	6.82021	+	6.82021i	0.485920	+	0.485920i	−0.421096	+	0.907016i	$0.638354\pi$
$198$		0			0
$199$			9.24745i			0.655534i	0.944759	+	0.327767i	$0.106296\pi$
$199$			9.24745i			0.655534i	−0.944759	+	0.327767i	$0.893704\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	0.229046	+	0.854813i	0.0160759	+	0.0599961i
$204$		0			0
$205$	7.20491	+	20.2318i	0.503213	+	1.41305i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	5.42804	+	9.40165i	0.375466	+	0.650325i
$210$		0			0
$211$	6.62372	−	11.4726i	0.455996	−	0.789808i	−0.542749	−	0.839895i	$-0.682616\pi$
$211$	6.62372	−	11.4726i	0.455996	−	0.789808i	0.998745	+	0.0500868i	$0.0159498\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−1.43294	+	0.988583i	−0.0977257	+	0.0674208i
$216$		0			0
$217$	0.101021	−	0.101021i	0.00685772	−	0.00685772i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	5.90648	+	3.41011i	0.397313	+	0.229389i
$222$		0			0
$223$	4.68438	−	17.4823i	0.313689	−	1.17070i	−0.611515	−	0.791233i	$-0.709439\pi$
$223$	4.68438	−	17.4823i	0.313689	−	1.17070i	0.925204	−	0.379471i	$-0.123894\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	5.78284	−	21.5818i	0.383820	−	1.43244i	−0.456198	−	0.889878i	$-0.650789\pi$
$227$	5.78284	−	21.5818i	0.383820	−	1.43244i	0.840018	−	0.542558i	$-0.182544\pi$
$228$		0			0
$229$	−1.16781	−	0.674235i	−0.0771710	−	0.0445547i	0.460918	−	0.887443i	$-0.347520\pi$
$229$	−1.16781	−	0.674235i	−0.0771710	−	0.0445547i	−0.538089	+	0.842888i	$0.680854\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−15.1732	+	15.1732i	−0.994032	+	0.994032i	−0.999982	−	0.00595067i	$-0.998106\pi$
$233$	−15.1732	+	15.1732i	−0.994032	+	0.994032i	0.00595067	+	0.999982i	$0.498106\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−4.17651	+	7.23393i	−0.270156	+	0.467924i	−0.968902	−	0.247446i	$-0.920409\pi$
$239$	−4.17651	+	7.23393i	−0.270156	+	0.467924i	0.698746	+	0.715370i	$0.253742\pi$
$240$		0			0
$241$	−9.50000	−	16.4545i	−0.611949	−	1.05993i	−0.990912	−	0.134515i	$-0.957053\pi$
$241$	−9.50000	−	16.4545i	−0.611949	−	1.05993i	0.378963	−	0.925412i	$-0.376281\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	5.17531	+	14.5326i	0.330638	+	0.928452i
$246$		0			0
$247$	1.74786	+	6.52312i	0.111214	+	0.415056i
$248$		0			0
$249$		0			0
$250$		0			0
$251$			21.9934i			1.38821i	0.719872	+	0.694107i	$0.244201\pi$
$251$			21.9934i			1.38821i	−0.719872	+	0.694107i	$0.755799\pi$
$252$		0			0
$253$	−17.2474	−	17.2474i	−1.08434	−	1.08434i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−28.3340	+	7.59207i	−1.76743	+	0.473580i	−0.988201	−	0.153165i	$-0.951054\pi$
$257$	−28.3340	+	7.59207i	−1.76743	+	0.473580i	−0.779225	+	0.626745i	$0.784387\pi$
$258$		0			0
$259$	−1.43027	+	0.825765i	−0.0888725	+	0.0513106i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	16.9235	+	4.53465i	1.04355	+	0.279618i	0.739584	−	0.673064i	$-0.235022\pi$
$263$	16.9235	+	4.53465i	1.04355	+	0.279618i	0.303966	+	0.952683i	$0.401689\pi$
$264$		0			0
$265$	−19.5254	+	1.57157i	−1.19944	+	0.0965405i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−12.3889			−0.755364			−0.377682	−	0.925935i	$-0.623279\pi$
$269$	−12.3889			−0.755364			−0.377682	+	0.925935i	$0.623279\pi$
$270$		0			0
$271$	−21.0000			−1.27566			−0.637830	−	0.770178i	$-0.720168\pi$
$271$	−21.0000			−1.27566			−0.637830	+	0.770178i	$0.720168\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	8.79957	+	10.7880i	0.530634	+	0.650542i
$276$		0			0
$277$	18.9864	+	5.08738i	1.14078	+	0.305671i	0.779264	−	0.626695i	$-0.215593\pi$
$277$	18.9864	+	5.08738i	1.14078	+	0.305671i	0.361515	+	0.932366i	$0.382260\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	20.3743	−	11.7631i	1.21543	−	0.701729i	0.251494	−	0.967859i	$-0.419078\pi$
$281$	20.3743	−	11.7631i	1.21543	−	0.701729i	0.963937	+	0.266130i	$0.0857449\pi$
$282$		0			0
$283$	−3.82208	+	1.02412i	−0.227199	+	0.0608779i	−0.370623	−	0.928784i	$-0.620856\pi$
$283$	−3.82208	+	1.02412i	−0.227199	+	0.0608779i	0.143423	+	0.989661i	$0.454189\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	2.15857	+	2.15857i	0.127417	+	0.127417i
$288$		0			0
$289$		−	1.49490i		−	0.0879351i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	3.74456	+	13.9749i	0.218759	+	0.816421i	0.984809	+	0.173640i	$0.0555529\pi$
$293$	3.74456	+	13.9749i	0.218759	+	0.816421i	−0.766050	+	0.642781i	$0.777780\pi$
$294$		0			0
$295$	−26.0970	+	9.29360i	−1.51943	+	0.541094i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−7.58662	−	13.1404i	−0.438745	−	0.759929i
$300$		0			0
$301$	−0.123724	+	0.214297i	−0.00713135	+	0.0123519i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−5.16509	+	28.1471i	−0.295752	+	1.61170i
$306$		0			0
$307$	13.3485	−	13.3485i	0.761837	−	0.761837i	−0.214817	−	0.976654i	$-0.568915\pi$
$307$	13.3485	−	13.3485i	0.761837	−	0.761837i	0.976654	+	0.214817i	$0.0689155\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	1.08386	+	0.625766i	0.0614600	+	0.0354839i	0.530415	−	0.847738i	$-0.322036\pi$
$311$	1.08386	+	0.625766i	0.0614600	+	0.0354839i	−0.468955	+	0.883222i	$0.655369\pi$
$312$		0			0
$313$	5.04209	−	18.8173i	0.284996	−	1.06362i	−0.663846	−	0.747869i	$-0.731077\pi$
$313$	5.04209	−	18.8173i	0.284996	−	1.06362i	0.948842	−	0.315750i	$-0.102256\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−8.05016	+	30.0436i	−0.452142	+	1.68742i	0.244215	+	0.969721i	$0.421470\pi$
$317$	−8.05016	+	30.0436i	−0.452142	+	1.68742i	−0.696357	+	0.717696i	$0.745197\pi$
$318$		0			0
$319$	−6.71391	−	3.87628i	−0.375907	−	0.217030i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	−10.8561	+	10.8561i	−0.604049	+	0.604049i
$324$		0			0
$325$	3.55051	+	7.89898i	0.196947	+	0.438157i
$326$		0			0
$327$		0			0
$328$		0			0
$329$		0			0
$330$		0			0
$331$	−3.37628	−	5.84788i	−0.185577	−	0.321429i	0.758194	−	0.652029i	$-0.226082\pi$
$331$	−3.37628	−	5.84788i	−0.185577	−	0.321429i	−0.943771	+	0.330601i	$0.892749\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	11.7651	−	24.7791i	0.642796	−	1.35383i
$336$		0			0
$337$	2.35237	+	8.77915i	0.128142	+	0.478231i	0.999932	−	0.0116478i	$-0.00370770\pi$
$337$	2.35237	+	8.77915i	0.128142	+	0.478231i	−0.871791	+	0.489879i	$0.837041\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$			1.25153i			0.0677743i
$342$		0			0
$343$	3.12372	+	3.12372i	0.168665	+	0.168665i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	0.854813	−	0.229046i	0.0458887	−	0.0122959i	−0.235802	−	0.971801i	$-0.575772\pi$
$347$	0.854813	−	0.229046i	0.0458887	−	0.0122959i	0.281690	+	0.959505i	$0.409105\pi$
$348$		0			0
$349$	−11.2583	+	6.50000i	−0.602645	+	0.347937i	−0.770081	−	0.637946i	$-0.779784\pi$
$349$	−11.2583	+	6.50000i	−0.602645	+	0.347937i	0.167437	+	0.985883i	$0.446451\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	20.7270	+	5.55379i	1.10319	+	0.295598i	0.764062	−	0.645143i	$-0.223202\pi$
$353$	20.7270	+	5.55379i	1.10319	+	0.295598i	0.339126	+	0.940741i	$0.389869\pi$
$354$		0			0
$355$	−13.9188	+	16.3555i	−0.738734	+	0.868062i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	4.03587			0.213005			0.106503	−	0.994312i	$-0.466035\pi$
$359$	4.03587			0.213005			0.106503	+	0.994312i	$0.466035\pi$
$360$		0			0
$361$	3.79796			0.199893
$362$		0			0
$363$		0			0
$364$		0			0
$365$	1.57925	+	19.6209i	0.0826619	+	1.02701i
$366$		0			0
$367$	25.3715	+	6.79827i	1.32438	+	0.354867i	0.850617	−	0.525785i	$-0.176229\pi$
$367$	25.3715	+	6.79827i	1.32438	+	0.354867i	0.473763	+	0.880652i	$0.342895\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−2.41131	+	1.39217i	−0.125189	+	0.0722779i
$372$		0			0
$373$	5.90911	−	1.58334i	0.305962	−	0.0819822i	−0.102571	−	0.994726i	$-0.532707\pi$
$373$	5.90911	−	1.58334i	0.305962	−	0.0819822i	0.408533	+	0.912743i	$0.366040\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−3.41011	−	3.41011i	−0.175629	−	0.175629i
$378$		0			0
$379$		−	13.0000i		−	0.667765i	−0.942615	−	0.333883i	$-0.891641\pi$
$379$		−	13.0000i		−	0.667765i	0.942615	−	0.333883i	$-0.108359\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	8.61121	+	32.1375i	0.440012	+	1.64215i	0.728780	+	0.684748i	$0.240088\pi$
$383$	8.61121	+	32.1375i	0.440012	+	1.64215i	−0.288767	+	0.957399i	$0.593245\pi$
$384$		0			0
$385$	1.78759	+	0.848743i	0.0911039	+	0.0432560i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	8.35302	+	14.4679i	0.423515	+	0.733549i	0.996280	−	0.0861698i	$-0.0274628\pi$
$389$	8.35302	+	14.4679i	0.423515	+	0.733549i	−0.572765	+	0.819719i	$0.694129\pi$
$390$		0			0
$391$	17.2474	−	29.8735i	0.872241	−	1.51077i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	−20.3383	−	3.73215i	−1.02333	−	0.187785i
$396$		0			0
$397$	−16.1464	+	16.1464i	−0.810366	+	0.810366i	−0.984689	−	0.174323i	$-0.944226\pi$
$397$	−16.1464	+	16.1464i	−0.810366	+	0.810366i	0.174323	+	0.984689i	$0.444226\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−1.32745	−	0.766404i	−0.0662897	−	0.0382724i	0.466489	−	0.884527i	$-0.345519\pi$
$401$	−1.32745	−	0.766404i	−0.0662897	−	0.0382724i	−0.532779	+	0.846255i	$0.678852\pi$
$402$		0			0
$403$	−0.201501	+	0.752011i	−0.0100375	+	0.0374603i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	3.74456	−	13.9749i	0.185611	−	0.692709i
$408$		0			0
$409$	23.8113	+	13.7474i	1.17739	+	0.679768i	0.955410	−	0.295283i	$-0.0954140\pi$
$409$	23.8113	+	13.7474i	1.17739	+	0.679768i	0.221982	+	0.975051i	$0.428747\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−2.78434	+	2.78434i	−0.137008	+	0.137008i
$414$		0			0
$415$	6.12372	+	8.87628i	0.300602	+	0.435719i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−15.1732	+	26.2808i	−0.741261	+	1.28390i	0.210660	+	0.977559i	$0.432439\pi$
$419$	−15.1732	+	26.2808i	−0.741261	+	1.28390i	−0.951921	+	0.306342i	$0.900895\pi$
$420$		0			0
$421$	−5.62372	−	9.74058i	−0.274084	−	0.474727i	0.695820	−	0.718216i	$-0.255041\pi$
$421$	−5.62372	−	9.74058i	−0.274084	−	0.474727i	−0.969904	+	0.243490i	$0.921708\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−11.5158	+	15.9691i	−0.558600	+	0.774616i
$426$		0			0
$427$	1.05279	+	3.92907i	0.0509481	+	0.190141i
$428$		0			0
$429$		0			0
$430$		0			0
$431$		−	20.7419i		−	0.999103i	−0.866284	−	0.499551i	$-0.833498\pi$
$431$		−	20.7419i		−	0.999103i	0.866284	−	0.499551i	$-0.166502\pi$
$432$		0			0
$433$	2.79796	+	2.79796i	0.134461	+	0.134461i	0.771134	−	0.636673i	$-0.219690\pi$
$433$	2.79796	+	2.79796i	0.134461	+	0.134461i	−0.636673	+	0.771134i	$0.719690\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	32.9923	−	8.84025i	1.57823	−	0.422887i
$438$		0			0
$439$	−11.3851	+	6.57321i	−0.543383	+	0.313722i	−0.746449	−	0.665443i	$-0.768243\pi$
$439$	−11.3851	+	6.57321i	−0.543383	+	0.313722i	0.203066	+	0.979165i	$0.434909\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−9.31658	−	2.49637i	−0.442644	−	0.118606i	0.0306113	−	0.999531i	$-0.490255\pi$
$443$	−9.31658	−	2.49637i	−0.442644	−	0.118606i	−0.473256	+	0.880925i	$0.656921\pi$
$444$		0			0
$445$	−21.0970	−	17.9539i	−1.00009	−	0.851094i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−12.3889			−0.584668			−0.292334	−	0.956316i	$-0.594432\pi$
$449$	−12.3889			−0.584668			−0.292334	+	0.956316i	$0.594432\pi$
$450$		0			0
$451$	−26.7423			−1.25925
$452$		0			0
$453$		0			0
$454$		0			0
$455$	0.937461	+	0.797794i	0.0439489	+	0.0374011i
$456$		0			0
$457$	30.5286	+	8.18011i	1.42807	+	0.382649i	0.888338	−	0.459190i	$-0.151860\pi$
$457$	30.5286	+	8.18011i	1.42807	+	0.382649i	0.539728	+	0.841839i	$0.318527\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−25.1970	+	14.5475i	−1.17354	+	0.677543i	−0.954511	−	0.298175i	$-0.903622\pi$
$461$	−25.1970	+	14.5475i	−1.17354	+	0.677543i	−0.219028	+	0.975719i	$0.570289\pi$
$462$		0			0
$463$	−1.39704	+	0.374336i	−0.0649259	+	0.0173969i	−0.291136	−	0.956682i	$-0.594033\pi$
$463$	−1.39704	+	0.374336i	−0.0649259	+	0.0173969i	0.226210	+	0.974079i	$0.427366\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	16.4248	+	16.4248i	0.760048	+	0.760048i	0.976331	−	0.216283i	$-0.0693934\pi$
$467$	16.4248	+	16.4248i	0.760048	+	0.760048i	−0.216283	+	0.976331i	$0.569393\pi$
$468$		0			0
$469$		−	3.89898i		−	0.180038i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−0.561047	−	2.09385i	−0.0257970	−	0.0962755i
$474$		0			0
$475$	−19.2439	+	3.11802i	−0.882972	+	0.143065i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	2.01794	+	3.49517i	0.0922019	+	0.159698i	0.908437	−	0.418021i	$-0.137276\pi$
$479$	2.01794	+	3.49517i	0.0922019	+	0.159698i	−0.816235	+	0.577719i	$0.803943\pi$
$480$		0			0
$481$	4.50000	−	7.79423i	0.205182	−	0.355386i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−8.57520	−	12.4297i	−0.389380	−	0.564402i
$486$		0			0
$487$	18.6742	−	18.6742i	0.846210	−	0.846210i	−0.143448	−	0.989658i	$-0.545819\pi$
$487$	18.6742	−	18.6742i	0.846210	−	0.846210i	0.989658	+	0.143448i	$0.0458188\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	34.5986	+	19.9755i	1.56141	+	0.901482i	0.997115	+	0.0759113i	$0.0241866\pi$
$491$	34.5986	+	19.9755i	1.56141	+	0.901482i	0.564298	+	0.825571i	$0.309147\pi$
$492$		0			0
$493$	2.83763	−	10.5902i	0.127800	−	0.476958i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−0.790093	+	2.94867i	−0.0354405	+	0.132266i
$498$		0			0
$499$	0.778539	+	0.449490i	0.0348522	+	0.0201219i	0.517325	−	0.855789i	$-0.326928\pi$
$499$	0.778539	+	0.449490i	0.0348522	+	0.0201219i	−0.482473	+	0.875911i	$0.660261\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	18.5833	−	18.5833i	0.828590	−	0.828590i	−0.158732	−	0.987322i	$-0.550740\pi$
$503$	18.5833	−	18.5833i	0.828590	−	0.828590i	0.987322	+	0.158732i	$0.0507404\pi$
$504$		0			0
$505$	39.4949	+	7.24745i	1.75750	+	0.322507i
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−8.21238	+	14.2243i	−0.364007	+	0.630479i	−0.988616	−	0.150458i	$-0.951925\pi$
$509$	−8.21238	+	14.2243i	−0.364007	+	0.630479i	0.624609	+	0.780938i	$0.285258\pi$
$510$		0			0
$511$	1.39898	+	2.42310i	0.0618872	+	0.107192i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−17.7818	−	8.44279i	−0.783562	−	0.372034i
$516$		0			0
$517$		0			0
$518$		0			0
$519$		0			0
$520$		0			0
$521$			15.1732i			0.664751i	0.943147	+	0.332376i	$0.107850\pi$
$521$			15.1732i			0.664751i	−0.943147	+	0.332376i	$0.892150\pi$
$522$		0			0
$523$	27.9217	+	27.9217i	1.22093	+	1.22093i	0.967302	+	0.253628i	$0.0816240\pi$
$523$	27.9217	+	27.9217i	1.22093	+	1.22093i	0.253628	+	0.967302i	$0.418376\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−1.70963	+	0.458093i	−0.0744724	+	0.0199548i
$528$		0			0
$529$	−46.5422	+	26.8712i	−2.02358	+	1.16831i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−16.0687	−	4.30560i	−0.696014	−	0.186496i
$534$		0			0
$535$	2.27797	+	28.3019i	0.0984852	+	1.22360i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−19.2091			−0.827395
$540$		0			0
$541$	10.5505			0.453602			0.226801	−	0.973941i	$-0.427173\pi$
$541$	10.5505			0.453602			0.226801	+	0.973941i	$0.427173\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	16.4461	−	19.3252i	0.704473	−	0.827803i
$546$		0			0
$547$	32.2016	+	8.62840i	1.37684	+	0.368924i	0.869973	−	0.493100i	$-0.164136\pi$
$547$	32.2016	+	8.62840i	1.37684	+	0.368924i	0.506869	+	0.862023i	$0.330803\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	9.40165	−	5.42804i	0.400524	−	0.231242i
$552$		0			0
$553$	−2.83903	+	0.760717i	−0.120728	+	0.0323490i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−23.5263	−	23.5263i	−0.996839	−	0.996839i	0.00315559	−	0.999995i	$-0.498996\pi$
$557$	−23.5263	−	23.5263i	−0.996839	−	0.996839i	−0.999995	+	0.00315559i	$0.998996\pi$
$558$		0			0
$559$		−	1.34847i		−	0.0570342i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	3.05742	+	11.4104i	0.128855	+	0.480893i	0.999948	−	0.0102256i	$-0.00325496\pi$
$563$	3.05742	+	11.4104i	0.128855	+	0.480893i	−0.871093	+	0.491118i	$0.836588\pi$
$564$		0			0
$565$	−0.848743	+	1.78759i	−0.0357069	+	0.0752044i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	8.97879	+	15.5517i	0.376410	+	0.651962i	0.990537	−	0.137246i	$-0.0438250\pi$
$569$	8.97879	+	15.5517i	0.376410	+	0.651962i	−0.614127	+	0.789207i	$0.710492\pi$
$570$		0			0
$571$	4.72474	−	8.18350i	0.197724	−	0.342469i	−0.750066	−	0.661363i	$-0.769978\pi$
$571$	4.72474	−	8.18350i	0.197724	−	0.342469i	0.947790	+	0.318894i	$0.103312\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	39.9510	−	17.9576i	1.66607	−	0.748883i
$576$		0			0
$577$	−22.0227	+	22.0227i	−0.916817	+	0.916817i	−0.996797	−	0.0799794i	$-0.974515\pi$
$577$	−22.0227	+	22.0227i	−0.916817	+	0.916817i	0.0799794	+	0.996797i	$0.474515\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	1.32745	+	0.766404i	0.0550719	+	0.0317958i
$582$		0			0
$583$	6.31300	−	23.5605i	0.261458	−	0.975774i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−3.74456	+	13.9749i	−0.154554	+	0.576805i	0.844589	+	0.535416i	$0.179845\pi$
$587$	−3.74456	+	13.9749i	−0.154554	+	0.576805i	−0.999143	+	0.0413892i	$0.986822\pi$
$588$		0			0
$589$	−1.51775	−	0.876276i	−0.0625380	−	0.0361063i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	8.97879	−	8.97879i	0.368715	−	0.368715i	−0.498294	−	0.867008i	$-0.666040\pi$
$593$	8.97879	−	8.97879i	0.368715	−	0.368715i	0.867008	+	0.498294i	$0.166040\pi$
$594$		0			0
$595$	−0.505103	+	2.75255i	−0.0207072	+	0.112844i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	17.1912	−	29.7760i	0.702412	−	1.21661i	−0.265205	−	0.964192i	$-0.585440\pi$
$599$	17.1912	−	29.7760i	0.702412	−	1.21661i	0.967617	−	0.252422i	$-0.0812270\pi$
$600$		0			0
$601$	7.02270	+	12.1637i	0.286462	+	0.496167i	0.972963	−	0.230962i	$-0.0741874\pi$
$601$	7.02270	+	12.1637i	0.286462	+	0.496167i	−0.686501	+	0.727129i	$0.740854\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	6.84069	−	2.43609i	0.278114	−	0.0990412i
$606$		0			0
$607$	1.34486	+	5.01910i	0.0545863	+	0.203719i	0.987833	−	0.155517i	$-0.0497042\pi$
$607$	1.34486	+	5.01910i	0.0545863	+	0.203719i	−0.933247	+	0.359235i	$0.883038\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$		0			0
$612$		0			0
$613$	−31.2247	−	31.2247i	−1.26116	−	1.26116i	−0.950533	−	0.310622i	$-0.899463\pi$
$613$	−31.2247	−	31.2247i	−1.26116	−	1.26116i	−0.310622	−	0.950533i	$-0.600537\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−16.0687	+	4.30560i	−0.646903	+	0.173337i	−0.567328	−	0.823492i	$-0.692023\pi$
$617$	−16.0687	+	4.30560i	−0.646903	+	0.173337i	−0.0795746	+	0.996829i	$0.525356\pi$
$618$		0			0
$619$	1.43027	−	0.825765i	0.0574873	−	0.0331903i	−0.470981	−	0.882143i	$-0.656100\pi$
$619$	1.43027	−	0.825765i	0.0574873	−	0.0331903i	0.528468	+	0.848953i	$0.322767\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−3.80348	−	1.01914i	−0.152383	−	0.0408310i
$624$		0			0
$625$	−23.7210	+	7.89406i	−0.948838	+	0.315763i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	20.4606			0.815819
$630$		0			0
$631$	−35.4949			−1.41303			−0.706515	−	0.707698i	$-0.749734\pi$
$631$	−35.4949			−1.41303			−0.706515	+	0.707698i	$0.749734\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−31.2024	+	2.51143i	−1.23823	+	0.0996629i
$636$		0			0
$637$	−11.5422	−	3.09273i	−0.457319	−	0.122538i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−6.99034	+	4.03587i	−0.276102	+	0.159407i	−0.631657	−	0.775248i	$-0.717625\pi$
$641$	−6.99034	+	4.03587i	−0.276102	+	0.159407i	0.355556	+	0.934655i	$0.384292\pi$
$642$		0			0
$643$	17.1443	−	4.59381i	0.676106	−	0.181162i	0.0956021	−	0.995420i	$-0.469522\pi$
$643$	17.1443	−	4.59381i	0.676106	−	0.181162i	0.580504	+	0.814258i	$0.302856\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−13.0147	−	13.0147i	−0.511659	−	0.511659i	0.403375	−	0.915035i	$-0.367837\pi$
$647$	−13.0147	−	13.0147i	−0.511659	−	0.511659i	−0.915035	+	0.403375i	$0.867837\pi$
$648$		0			0
$649$		−	34.4949i		−	1.35404i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−8.05016	−	30.0436i	−0.315027	−	1.17570i	−0.923964	−	0.382479i	$-0.875071\pi$
$653$	−8.05016	−	30.0436i	−0.315027	−	1.17570i	0.608937	−	0.793218i	$-0.291596\pi$
$654$		0			0
$655$	−4.17738	−	11.7303i	−0.163224	−	0.458342i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−24.7778	−	42.9164i	−0.965206	−	1.67179i	−0.709062	−	0.705146i	$-0.750881\pi$
$659$	−24.7778	−	42.9164i	−0.965206	−	1.67179i	−0.256144	−	0.966639i	$-0.582452\pi$
$660$		0			0
$661$	0.500000	−	0.866025i	0.0194477	−	0.0336845i	−0.856138	−	0.516748i	$-0.827143\pi$
$661$	0.500000	−	0.866025i	0.0194477	−	0.0336845i	0.875585	+	0.483063i	$0.160476\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−2.28089	+	1.57358i	−0.0884490	+	0.0610208i
$666$		0			0
$667$	−17.2474	+	17.2474i	−0.667824	+	0.667824i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−30.8598	−	17.8169i	−1.19133	−	0.687815i
$672$		0			0
$673$	6.68734	−	24.9575i	0.257778	−	0.962041i	−0.708746	−	0.705464i	$-0.750739\pi$
$673$	6.68734	−	24.9575i	0.257778	−	0.962041i	0.966524	−	0.256577i	$-0.0825946\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	4.07656	−	15.2139i	0.156675	−	0.584718i	−0.842281	−	0.539038i	$-0.818788\pi$
$677$	4.07656	−	15.2139i	0.156675	−	0.584718i	0.998956	−	0.0456802i	$-0.0145455\pi$
$678$		0			0
$679$	−1.85886	−	1.07321i	−0.0713366	−	0.0411862i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−20.1161	+	20.1161i	−0.769723	+	0.769723i	−0.978058	−	0.208335i	$-0.933196\pi$
$683$	−20.1161	+	20.1161i	−0.769723	+	0.769723i	0.208335	+	0.978058i	$0.433196\pi$
$684$		0			0
$685$	8.87628	−	6.12372i	0.339145	−	0.233975i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	7.58662	−	13.1404i	0.289027	−	0.500610i
$690$		0			0
$691$	0.123724	+	0.214297i	0.00470670	+	0.00815224i	0.868369	−	0.495918i	$-0.165168\pi$
$691$	0.123724	+	0.214297i	0.00470670	+	0.00815224i	−0.863662	+	0.504071i	$0.831835\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	14.4386	+	40.5444i	0.547687	+	1.53794i
$696$		0			0
$697$	−9.78838	−	36.5307i	−0.370761	−	1.38370i
$698$		0			0
$699$		0			0
$700$		0			0
$701$		−	17.6763i		−	0.667625i	−0.942640	−	0.333812i	$-0.891665\pi$
$701$		−	17.6763i		−	0.667625i	0.942640	−	0.333812i	$-0.108335\pi$
$702$		0			0
$703$	14.3258	+	14.3258i	0.540306	+	0.540306i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	5.51310	−	1.47723i	0.207342	−	0.0555570i
$708$		0			0
$709$	−7.22999	+	4.17423i	−0.271528	+	0.156767i	−0.629582	−	0.776934i	$-0.716774\pi$
$709$	−7.22999	+	4.17423i	−0.271528	+	0.156767i	0.358054	+	0.933701i	$0.383440\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	3.80348	+	1.01914i	0.142441	+	0.0381671i
$714$		0			0
$715$	−10.7489	+	0.865163i	−0.401988	+	0.0323553i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	49.8369			1.85860			0.929300	−	0.369325i	$-0.120411\pi$
$719$	49.8369			1.85860			0.929300	+	0.369325i	$0.120411\pi$
$720$		0			0
$721$	−2.79796			−0.104201
$722$		0			0
$723$		0			0
$724$		0			0
$725$	10.7880	−	8.79957i	0.400657	−	0.326808i
$726$		0			0
$727$	18.9864	+	5.08738i	0.704165	+	0.188680i	0.593095	−	0.805132i	$-0.297906\pi$
$727$	18.9864	+	5.08738i	0.704165	+	0.188680i	0.111070	+	0.993813i	$0.464572\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	2.65490	−	1.53281i	0.0981951	−	0.0566929i
$732$		0			0
$733$	3.48406	−	0.933552i	0.128687	−	0.0344815i	−0.193901	−	0.981021i	$-0.562114\pi$
$733$	3.48406	−	0.933552i	0.128687	−	0.0344815i	0.322588	+	0.946540i	$0.395447\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	24.1520	+	24.1520i	0.889651	+	0.889651i
$738$		0			0
$739$		−	26.2474i		−	0.965528i	−0.875750	−	0.482764i	$-0.839633\pi$
$739$		−	26.2474i		−	0.965528i	0.875750	−	0.482764i	$-0.160367\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−12.5848	−	46.9672i	−0.461692	−	1.72306i	−0.667631	−	0.744493i	$-0.732691\pi$
$743$	−12.5848	−	46.9672i	−0.461692	−	1.72306i	0.205939	−	0.978565i	$-0.433975\pi$
$744$		0			0
$745$	14.3667	−	5.11622i	0.526354	−	0.187444i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	2.01794	+	3.49517i	0.0737338	+	0.127711i
$750$		0			0
$751$	−4.50000	+	7.79423i	−0.164207	+	0.284415i	−0.936374	−	0.351005i	$-0.885840\pi$
$751$	−4.50000	+	7.79423i	−0.164207	+	0.284415i	0.772166	+	0.635421i	$0.219173\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	−4.25805	+	23.2042i	−0.154966	+	0.844488i
$756$		0			0
$757$	19.7196	−	19.7196i	0.716723	−	0.716723i	−0.251210	−	0.967933i	$-0.580828\pi$
$757$	19.7196	−	19.7196i	0.716723	−	0.716723i	0.967933	+	0.251210i	$0.0808285\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−20.1307	−	11.6225i	−0.729739	−	0.421315i	0.0885878	−	0.996068i	$-0.471765\pi$
$761$	−20.1307	−	11.6225i	−0.729739	−	0.421315i	−0.818327	+	0.574753i	$0.805098\pi$
$762$		0			0
$763$	0.933552	−	3.48406i	0.0337968	−	0.126132i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	5.55379	−	20.7270i	0.200536	−	0.748409i
$768$		0			0
$769$	25.7576	+	14.8712i	0.928844	+	0.536268i	0.886446	−	0.462833i	$-0.153167\pi$
$769$	25.7576	+	14.8712i	0.928844	+	0.536268i	0.0423981	+	0.999101i	$0.486500\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	3.41011	−	3.41011i	0.122653	−	0.122653i	−0.643116	−	0.765769i	$-0.722359\pi$
$773$	3.41011	−	3.41011i	0.122653	−	0.122653i	0.765769	+	0.643116i	$0.222359\pi$
$774$		0			0
$775$	−2.10102	−	0.797959i	−0.0754709	−	0.0286635i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	18.7240	−	32.4309i	0.670856	−	1.16196i
$780$		0			0
$781$	−13.3712	−	23.1596i	−0.478458	−	0.828714i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	18.1049	−	38.1317i	0.646191	−	1.36098i
$786$		0			0
$787$	6.39527	+	23.8675i	0.227967	+	0.850783i	0.981194	+	0.193023i	$0.0618292\pi$
$787$	6.39527	+	23.8675i	0.227967	+	0.850783i	−0.753228	+	0.657760i	$0.771504\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$			0.281275i			0.0100010i
$792$		0			0
$793$	−15.6742	−	15.6742i	−0.556608	−	0.556608i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−30.0436	+	8.05016i	−1.06420	+	0.285151i	−0.748108	−	0.663577i	$-0.769037\pi$
$797$	−30.0436	+	8.05016i	−1.06420	+	0.285151i	−0.316092	+	0.948729i	$0.602371\pi$
$798$		0			0
$799$		0			0
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−23.6757	−	6.34388i	−0.835497	−	0.223871i
$804$		0			0
$805$	4.03504	−	4.74144i	0.142216	−	0.167114i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−1.25153			−0.0440015			−0.0220008	−	0.999758i	$-0.507004\pi$
$809$	−1.25153			−0.0440015			−0.0220008	+	0.999758i	$0.507004\pi$
$810$		0			0
$811$	−19.5505			−0.686511			−0.343256	−	0.939242i	$-0.611530\pi$
$811$	−19.5505			−0.686511			−0.343256	+	0.939242i	$0.611530\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−0.957803	−	11.8999i	−0.0335504	−	0.416836i
$816$		0			0
$817$	2.93208	+	0.785647i	0.102580	+	0.0274863i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	15.5517	−	8.97879i	0.542759	−	0.313362i	−0.203438	−	0.979088i	$-0.565211\pi$
$821$	15.5517	−	8.97879i	0.542759	−	0.313362i	0.746196	+	0.665726i	$0.231878\pi$
$822$		0			0
$823$	−42.3778	+	11.3551i	−1.47720	+	0.395814i	−0.905392	−	0.424576i	$-0.860423\pi$
$823$	−42.3778	+	11.3551i	−1.47720	+	0.395814i	−0.571805	+	0.820390i	$0.693757\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−6.82021	−	6.82021i	−0.237162	−	0.237162i	0.578512	−	0.815674i	$-0.303634\pi$
$827$	−6.82021	−	6.82021i	−0.237162	−	0.237162i	−0.815674	+	0.578512i	$0.803634\pi$
$828$		0			0
$829$			49.2474i			1.71043i	0.518270	+	0.855217i	$0.326576\pi$
$829$			49.2474i			1.71043i	−0.518270	+	0.855217i	$0.673424\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−7.03102	−	26.2401i	−0.243610	−	0.909167i
$834$		0			0
$835$	−27.4367	−	13.0269i	−0.949487	−	0.450815i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	12.3889	+	21.4582i	0.427712	+	0.740819i	0.996669	−	0.0815479i	$-0.0259864\pi$
$839$	12.3889	+	21.4582i	0.427712	+	0.740819i	−0.568957	+	0.822367i	$0.692653\pi$
$840$		0			0
$841$	10.6237	−	18.4008i	0.366335	−	0.634511i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	21.9934	+	4.03587i	0.756598	+	0.138838i
$846$		0			0
$847$	0.729847	−	0.729847i	0.0250779	−	0.0250779i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−39.4212	−	22.7599i	−1.35134	−	0.780198i
$852$		0			0
$853$	−1.27091	+	4.74310i	−0.0435152	+	0.162401i	−0.984264	−	0.176702i	$-0.943457\pi$
$853$	−1.27091	+	4.74310i	−0.0435152	+	0.162401i	0.940749	+	0.339103i	$0.110124\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−1.24819	+	4.65829i	−0.0426372	+	0.159124i	−0.983962	−	0.178377i	$-0.942915\pi$
$857$	−1.24819	+	4.65829i	−0.0426372	+	0.159124i	0.941325	+	0.337502i	$0.109582\pi$
$858$		0			0
$859$	4.54442	+	2.62372i	0.155054	+	0.0895203i	0.575519	−	0.817788i	$-0.304800\pi$
$859$	4.54442	+	2.62372i	0.155054	+	0.0895203i	−0.420466	+	0.907308i	$0.638133\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	10.8561	−	10.8561i	0.369545	−	0.369545i	−0.497766	−	0.867311i	$-0.665846\pi$
$863$	10.8561	−	10.8561i	0.369545	−	0.369545i	0.867311	+	0.497766i	$0.165846\pi$
$864$		0			0
$865$	10.0000	+	14.4949i	0.340010	+	0.492841i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	12.8740	−	22.2985i	0.436721	−	0.756423i
$870$		0			0
$871$	10.6237	+	18.4008i	0.359971	+	0.623488i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−2.56457	+	2.45978i	−0.0866984	+	0.0831558i
$876$		0			0
$877$	3.74252	+	13.9673i	0.126376	+	0.471641i	0.999885	−	0.0151668i	$-0.00482792\pi$
$877$	3.74252	+	13.9673i	0.126376	+	0.471641i	−0.873509	+	0.486808i	$0.838161\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$			2.78434i			0.0938068i	0.998899	+	0.0469034i	$0.0149353\pi$
$881$			2.78434i			0.0938068i	−0.998899	+	0.0469034i	$0.985065\pi$
$882$		0			0
$883$	22.9217	+	22.9217i	0.771376	+	0.771376i	0.978347	−	0.206971i	$-0.0663606\pi$
$883$	22.9217	+	22.9217i	0.771376	+	0.771376i	−0.206971	+	0.978347i	$0.566361\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−18.6332	+	4.99274i	−0.625641	+	0.167640i	−0.557691	−	0.830049i	$-0.688312\pi$
$887$	−18.6332	+	4.99274i	−0.625641	+	0.167640i	−0.0679499	+	0.997689i	$0.521646\pi$
$888$		0			0
$889$	−3.85337	+	2.22474i	−0.129238	+	0.0746155i
$890$		0			0
$891$		0			0
$892$		0			0
$893$		0			0
$894$		0			0
$895$	16.3555	+	13.9188i	0.546706	+	0.465255i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	1.25153			0.0417409
$900$		0			0
$901$	34.4949			1.14919
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−19.1532	−	16.2997i	−0.636675	−	0.541820i
$906$		0			0
$907$	−18.6794	−	5.00512i	−0.620238	−	0.166192i	−0.0650019	−	0.997885i	$-0.520705\pi$
$907$	−18.6794	−	5.00512i	−0.620238	−	0.166192i	−0.555236	+	0.831693i	$0.687372\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−3.73876	+	2.15857i	−0.123871	+	0.0715168i	−0.560655	−	0.828049i	$-0.689451\pi$
$911$	−3.73876	+	2.15857i	−0.123871	+	0.0715168i	0.436784	+	0.899566i	$0.356117\pi$
$912$		0			0
$913$	−12.9703	+	3.47537i	−0.429253	+	0.115018i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−1.25153	−	1.25153i	−0.0413292	−	0.0413292i
$918$		0			0
$919$		−	18.6515i		−	0.615257i	−0.951507	−	0.307629i	$-0.900465\pi$
$919$		−	18.6515i		−	0.615257i	0.951507	−	0.307629i	$-0.0995354\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−4.30560	−	16.0687i	−0.141721	−	0.528909i
$924$		0			0
$925$	21.0730	+	15.1964i	0.692875	+	0.499654i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−28.3285	−	49.0665i	−0.929429	−	1.60982i	−0.784279	−	0.620409i	$-0.786967\pi$
$929$	−28.3285	−	49.0665i	−0.929429	−	1.60982i	−0.145150	−	0.989410i	$-0.546367\pi$
$930$		0			0
$931$	13.4495	−	23.2952i	0.440789	−	0.763469i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	−13.9217	−	20.1794i	−0.455288	−	0.659936i
$936$		0			0
$937$	−9.77526	+	9.77526i	−0.319344	+	0.319344i	−0.848515	−	0.529171i	$-0.822503\pi$
$937$	−9.77526	+	9.77526i	−0.319344	+	0.319344i	0.529171	+	0.848515i	$0.322503\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−13.1404	−	7.58662i	−0.428365	−	0.247317i	0.270285	−	0.962780i	$-0.412882\pi$
$941$	−13.1404	−	7.58662i	−0.428365	−	0.247317i	−0.698650	+	0.715464i	$0.746215\pi$
$942$		0			0
$943$	−21.7766	+	81.2715i	−0.709145	+	2.64657i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−6.01188	+	22.4366i	−0.195360	+	0.729093i	0.796813	+	0.604225i	$0.206517\pi$
$947$	−6.01188	+	22.4366i	−0.195360	+	0.729093i	−0.992173	+	0.124868i	$0.960149\pi$
$948$		0			0
$949$	−13.2047	−	7.62372i	−0.428642	−	0.247477i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	23.5263	−	23.5263i	0.762090	−	0.762090i	−0.214610	−	0.976700i	$-0.568848\pi$
$953$	23.5263	−	23.5263i	0.762090	−	0.762090i	0.976700	+	0.214610i	$0.0688480\pi$
$954$		0			0
$955$	−27.2474	−	5.00000i	−0.881707	−	0.161796i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	0.766404	−	1.32745i	0.0247485	−	0.0428656i
$960$		0			0
$961$	15.3990	+	26.6718i	0.496741	+	0.860381i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−33.0605	−	15.6971i	−1.06425	−	0.505306i
$966$		0			0
$967$	−11.4660	−	42.7918i	−0.368723	−	1.37609i	−0.862304	−	0.506391i	$-0.830979\pi$
$967$	−11.4660	−	42.7918i	−0.368723	−	1.37609i	0.493581	−	0.869700i	$-0.335688\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$			2.50306i			0.0803272i	0.999193	+	0.0401636i	$0.0127879\pi$
$971$			2.50306i			0.0803272i	−0.999193	+	0.0401636i	$0.987212\pi$
$972$		0			0
$973$	4.32577	+	4.32577i	0.138678	+	0.138678i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	46.1123	−	12.3558i	1.47526	−	0.395296i	0.570532	−	0.821276i	$-0.306737\pi$
$977$	46.1123	−	12.3558i	1.47526	−	0.395296i	0.904733	+	0.425980i	$0.140070\pi$
$978$		0			0
$979$	29.8735	−	17.2474i	0.954760	−	0.551231i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	35.0861	+	9.40130i	1.11907	+	0.299855i	0.770509	−	0.637430i	$-0.220002\pi$
$983$	35.0861	+	9.40130i	1.11907	+	0.299855i	0.348565	+	0.937285i	$0.386669\pi$
$984$		0			0
$985$	−1.73033	−	21.4979i	−0.0551328	−	0.684980i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−6.82021			−0.216870
$990$		0			0
$991$	35.0454			1.11325			0.556627	−	0.830763i	$-0.312095\pi$
$991$	35.0454			1.11325			0.556627	+	0.830763i	$0.312095\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	13.4013	−	15.7474i	0.424850	−	0.499227i
$996$		0			0
$997$	0.137997	+	0.0369761i	0.00437040	+	0.00117104i	0.261004	−	0.965338i	$-0.415947\pi$
$997$	0.137997	+	0.0369761i	0.00437040	+	0.00117104i	−0.256633	+	0.966509i	$0.582613\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1620.2.x.d.53.1		16
3.2	odd	2	inner	1620.2.x.d.53.4		16
5.2	odd	4	inner	1620.2.x.d.377.1		16
9.2	odd	6	inner	1620.2.x.d.593.1		16
9.4	even	3		540.2.j.a.53.2	✓	8
9.5	odd	6		540.2.j.a.53.3	yes	8
9.7	even	3	inner	1620.2.x.d.593.4		16
15.2	even	4	inner	1620.2.x.d.377.4		16
36.23	even	6		2160.2.w.e.593.3		8
36.31	odd	6		2160.2.w.e.593.2		8
45.2	even	12	inner	1620.2.x.d.917.1		16
45.4	even	6		2700.2.j.j.593.2		8
45.7	odd	12	inner	1620.2.x.d.917.4		16
45.13	odd	12		2700.2.j.j.1457.2		8
45.14	odd	6		2700.2.j.j.593.1		8
45.22	odd	12		540.2.j.a.377.3	yes	8
45.23	even	12		2700.2.j.j.1457.1		8
45.32	even	12		540.2.j.a.377.2	yes	8
180.67	even	12		2160.2.w.e.1457.3		8
180.167	odd	12		2160.2.w.e.1457.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
540.2.j.a.53.2	✓	8	9.4	even	3
540.2.j.a.53.3	yes	8	9.5	odd	6
540.2.j.a.377.2	yes	8	45.32	even	12
540.2.j.a.377.3	yes	8	45.22	odd	12
1620.2.x.d.53.1		16	1.1	even	1	trivial
1620.2.x.d.53.4		16	3.2	odd	2	inner
1620.2.x.d.377.1		16	5.2	odd	4	inner
1620.2.x.d.377.4		16	15.2	even	4	inner
1620.2.x.d.593.1		16	9.2	odd	6	inner
1620.2.x.d.593.4		16	9.7	even	3	inner
1620.2.x.d.917.1		16	45.2	even	12	inner
1620.2.x.d.917.4		16	45.7	odd	12	inner
2160.2.w.e.593.2		8	36.31	odd	6
2160.2.w.e.593.3		8	36.23	even	6
2160.2.w.e.1457.2		8	180.167	odd	12
2160.2.w.e.1457.3		8	180.67	even	12
2700.2.j.j.593.1		8	45.14	odd	6
2700.2.j.j.593.2		8	45.4	even	6
2700.2.j.j.1457.1		8	45.23	even	12
2700.2.j.j.1457.2		8	45.13	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:	\( N \)	\(=\)	\( 1620 = 2^{2} \cdot 3^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1620.x (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.70289 - 1.44919i) q^{5} +(-0.307007 - 0.0822623i) q^{7} +O(q^{10})\)	\(q+(-1.70289 - 1.44919i) q^{5} +(-0.307007 - 0.0822623i) q^{7} +(2.41131 - 1.39217i) q^{11} +(1.67303 - 0.448288i) q^{13} +(2.78434 + 2.78434i) q^{17} +3.89898i q^{19} +(-2.26732 - 8.46177i) q^{23} +(0.799701 + 4.93563i) q^{25} +(-1.39217 - 2.41131i) q^{29} +(-0.224745 + 0.389270i) q^{31} +(0.403587 + 0.584996i) q^{35} +(3.67423 - 3.67423i) q^{37} +(-8.31779 - 4.80228i) q^{41} +(0.201501 - 0.752011i) q^{43} +(-5.97469 - 3.44949i) q^{49} +(6.19445 - 6.19445i) q^{53} +(-6.12372 - 1.12372i) q^{55} +(6.19445 - 10.7291i) q^{59} +(-6.39898 - 11.0834i) q^{61} +(-3.49865 - 1.66115i) q^{65} +(3.17499 + 11.8492i) q^{67} -9.60455i q^{71} +(-6.22474 - 6.22474i) q^{73} +(-0.854813 + 0.229046i) q^{77} +(8.00853 - 4.62372i) q^{79} +(-4.65829 - 1.24819i) q^{83} +(-0.706403 - 8.77647i) q^{85} +12.3889 q^{89} -0.550510 q^{91} +(5.65036 - 6.63955i) q^{95} +(6.52312 + 1.74786i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{7}+O(q^{10}) \) 16 * q + 8 * q^7	\( 16 q + 8 q^{7} + 8 q^{25} + 16 q^{31} - 24 q^{43} - 24 q^{61} - 40 q^{67} - 80 q^{73} - 40 q^{85} - 48 q^{91} + 48 q^{97}+O(q^{100}) \) 16 * q + 8 * q^7 + 8 * q^25 + 16 * q^31 - 24 * q^43 - 24 * q^61 - 40 * q^67 - 80 * q^73 - 40 * q^85 - 48 * q^91 + 48 * q^97

Introduction

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