LMFDB - Embedded newform 2880.2.u.a.719.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2880,2,Mod(719,2880)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2880, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1, 2, 2]))

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

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

chi := DirichletCharacter("2880.719");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2880 = 2^{6} \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2880.u (of order $4$, 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:	$22.9969157821$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$48$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 720)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			719.2
Character	$\chi$	$=$	2880.719
Dual form			2880.2.u.a.2159.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.22047 + 0.263678i) q^{5} -2.95946i q^{7} +O(q^{10})$	$q+(-2.22047 + 0.263678i) q^{5} -2.95946i q^{7} +(-1.04021 - 1.04021i) q^{11} +(-0.00780247 - 0.00780247i) q^{13} +2.00003 q^{17} +(-5.10608 - 5.10608i) q^{19} +6.49393 q^{23} +(4.86095 - 1.17098i) q^{25} +(5.45997 + 5.45997i) q^{29} -4.99178i q^{31} +(0.780345 + 6.57137i) q^{35} +(-3.74547 + 3.74547i) q^{37} -10.4245 q^{41} +(-3.52161 - 3.52161i) q^{43} +10.6419i q^{47} -1.75838 q^{49} +(-2.98006 - 2.98006i) q^{53} +(2.58404 + 2.03548i) q^{55} +(-5.47867 - 5.47867i) q^{59} +(-4.67845 + 4.67845i) q^{61} +(0.0193825 + 0.0152678i) q^{65} +(-2.29404 + 2.29404i) q^{67} +0.212315i q^{71} -16.4980 q^{73} +(-3.07847 + 3.07847i) q^{77} -4.54833i q^{79} +(-4.68359 - 4.68359i) q^{83} +(-4.44100 + 0.527365i) q^{85} +0.123094 q^{89} +(-0.0230911 + 0.0230911i) q^{91} +(12.6842 + 9.99152i) q^{95} +8.29464i q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q+O(q^{10}) $ 96 * q	$ 96 q + 16 q^{19} - 96 q^{49} - 64 q^{55} - 32 q^{61}+O(q^{100}) $ 96 * q + 16 * q^19 - 96 * q^49 - 64 * q^55 - 32 * q^61

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2880\mathbb{Z}\right)^\times$.

$n$	$577$	$641$	$901$	$2431$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{1}{4}\right)$	$-1$

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
$3$		0			0
$3$		0			0
$4$		0			0
$5$	−2.22047	+	0.263678i	−0.993023	+	0.117921i
$5$	−2.22047	+	0.263678i	−0.993023	+	0.117921i
$6$		0			0
$7$		−	2.95946i		−	1.11857i	−0.828976	−	0.559284i	$-0.811076\pi$
$7$		−	2.95946i		−	1.11857i	0.828976	−	0.559284i	$-0.188924\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−1.04021	−	1.04021i	−0.313636	−	0.313636i	0.532680	−	0.846317i	$-0.321185\pi$
$11$	−1.04021	−	1.04021i	−0.313636	−	0.313636i	−0.846317	+	0.532680i	$0.821185\pi$
$12$		0			0
$13$	−0.00780247	−	0.00780247i	−0.00216402	−	0.00216402i	0.706024	−	0.708188i	$-0.250487\pi$
$13$	−0.00780247	−	0.00780247i	−0.00216402	−	0.00216402i	−0.708188	+	0.706024i	$0.750487\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	2.00003			0.485079			0.242539	−	0.970142i	$-0.422020\pi$
$17$	2.00003			0.485079			0.242539	+	0.970142i	$0.422020\pi$
$18$		0			0
$19$	−5.10608	−	5.10608i	−1.17141	−	1.17141i	−0.981873	−	0.189542i	$-0.939300\pi$
$19$	−5.10608	−	5.10608i	−1.17141	−	1.17141i	−0.189542	−	0.981873i	$-0.560700\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	6.49393			1.35408			0.677039	−	0.735947i	$-0.263263\pi$
$23$	6.49393			1.35408			0.677039	+	0.735947i	$0.263263\pi$
$24$		0			0
$25$	4.86095	−	1.17098i	0.972189	−	0.234196i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	5.45997	+	5.45997i	1.01389	+	1.01389i	0.999902	+	0.0139895i	$0.00445315\pi$
$29$	5.45997	+	5.45997i	1.01389	+	1.01389i	0.0139895	+	0.999902i	$0.495547\pi$
$30$		0			0
$31$		−	4.99178i		−	0.896550i	−0.893896	−	0.448275i	$-0.852039\pi$
$31$		−	4.99178i		−	0.896550i	0.893896	−	0.448275i	$-0.147961\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	0.780345	+	6.57137i	0.131902	+	1.11076i
$36$		0			0
$37$	−3.74547	+	3.74547i	−0.615752	+	0.615752i	−0.944439	−	0.328687i	$-0.893394\pi$
$37$	−3.74547	+	3.74547i	−0.615752	+	0.615752i	0.328687	+	0.944439i	$0.393394\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−10.4245			−1.62803			−0.814017	−	0.580841i	$-0.802724\pi$
$41$	−10.4245			−1.62803			−0.814017	+	0.580841i	$0.802724\pi$
$42$		0			0
$43$	−3.52161	−	3.52161i	−0.537040	−	0.537040i	0.385618	−	0.922658i	$-0.373988\pi$
$43$	−3.52161	−	3.52161i	−0.537040	−	0.537040i	−0.922658	+	0.385618i	$0.873988\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$			10.6419i			1.55228i	0.630563	+	0.776138i	$0.282824\pi$
$47$			10.6419i			1.55228i	−0.630563	+	0.776138i	$0.717176\pi$
$48$		0			0
$49$	−1.75838			−0.251197
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−2.98006	−	2.98006i	−0.409342	−	0.409342i	0.472167	−	0.881509i	$-0.343472\pi$
$53$	−2.98006	−	2.98006i	−0.409342	−	0.409342i	−0.881509	+	0.472167i	$0.843472\pi$
$54$		0			0
$55$	2.58404	+	2.03548i	0.348432	+	0.274464i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−5.47867	−	5.47867i	−0.713262	−	0.713262i	0.253954	−	0.967216i	$-0.418269\pi$
$59$	−5.47867	−	5.47867i	−0.713262	−	0.713262i	−0.967216	+	0.253954i	$0.918269\pi$
$60$		0			0
$61$	−4.67845	+	4.67845i	−0.599014	+	0.599014i	−0.940050	−	0.341037i	$-0.889222\pi$
$61$	−4.67845	+	4.67845i	−0.599014	+	0.599014i	0.341037	+	0.940050i	$0.389222\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	0.0193825	+	0.0152678i	0.00240410	+	0.00189374i
$66$		0			0
$67$	−2.29404	+	2.29404i	−0.280261	+	0.280261i	−0.833213	−	0.552952i	$-0.813501\pi$
$67$	−2.29404	+	2.29404i	−0.280261	+	0.280261i	0.552952	+	0.833213i	$0.313501\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$			0.212315i			0.0251971i	0.999921	+	0.0125986i	$0.00401036\pi$
$71$			0.212315i			0.0251971i	−0.999921	+	0.0125986i	$0.995990\pi$
$72$		0			0
$73$	−16.4980			−1.93094			−0.965472	−	0.260505i	$-0.916111\pi$
$73$	−16.4980			−1.93094			−0.965472	+	0.260505i	$0.916111\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−3.07847	+	3.07847i	−0.350824	+	0.350824i
$78$		0			0
$79$		−	4.54833i		−	0.511727i	−0.966713	−	0.255863i	$-0.917640\pi$
$79$		−	4.54833i		−	0.511727i	0.966713	−	0.255863i	$-0.0823597\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−4.68359	−	4.68359i	−0.514090	−	0.514090i	0.401687	−	0.915777i	$-0.368424\pi$
$83$	−4.68359	−	4.68359i	−0.514090	−	0.514090i	−0.915777	+	0.401687i	$0.868424\pi$
$84$		0			0
$85$	−4.44100	+	0.527365i	−0.481694	+	0.0572008i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	0.123094			0.0130479			0.00652395	−	0.999979i	$-0.497923\pi$
$89$	0.123094			0.0130479			0.00652395	+	0.999979i	$0.497923\pi$
$90$		0			0
$91$	−0.0230911	+	0.0230911i	−0.00242060	+	0.00242060i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	12.6842	+	9.99152i	1.30138	+	1.02511i
$96$		0			0
$97$			8.29464i			0.842193i	0.907016	+	0.421096i	$0.138355\pi$
$97$			8.29464i			0.842193i	−0.907016	+	0.421096i	$0.861645\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−7.95152	+	7.95152i	−0.791205	+	0.791205i	−0.981690	−	0.190485i	$-0.938994\pi$
$101$	−7.95152	+	7.95152i	−0.791205	+	0.791205i	0.190485	+	0.981690i	$0.438994\pi$
$102$		0			0
$103$			6.14632i			0.605615i	0.953052	+	0.302808i	$0.0979240\pi$
$103$			6.14632i			0.605615i	−0.953052	+	0.302808i	$0.902076\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	5.83941	−	5.83941i	0.564517	−	0.564517i	−0.366070	−	0.930587i	$-0.619297\pi$
$107$	5.83941	−	5.83941i	0.564517	−	0.564517i	0.930587	+	0.366070i	$0.119297\pi$
$108$		0			0
$109$	10.9696	−	10.9696i	1.05070	−	1.05070i	0.0520513	−	0.998644i	$-0.483424\pi$
$109$	10.9696	−	10.9696i	1.05070	−	1.05070i	0.998644	−	0.0520513i	$-0.0165759\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	9.95287			0.936288			0.468144	−	0.883652i	$-0.344923\pi$
$113$	9.95287			0.936288			0.468144	+	0.883652i	$0.344923\pi$
$114$		0			0
$115$	−14.4196	+	1.71231i	−1.34463	+	0.159674i
$116$		0			0
$117$		0			0
$118$		0			0
$119$		−	5.91900i		−	0.542594i
$120$		0			0
$121$		−	8.83591i		−	0.803264i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−10.4848	+	3.88185i	−0.937790	+	0.347203i
$126$		0			0
$127$	0.542244			0.0481164			0.0240582	−	0.999711i	$-0.492341\pi$
$127$	0.542244			0.0481164			0.0240582	+	0.999711i	$0.492341\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−5.55272	+	5.55272i	−0.485143	+	0.485143i	−0.906770	−	0.421626i	$-0.861459\pi$
$131$	−5.55272	+	5.55272i	−0.485143	+	0.485143i	0.421626	+	0.906770i	$0.361459\pi$
$132$		0			0
$133$	−15.1112	+	15.1112i	−1.31031	+	1.31031i
$134$		0			0
$135$		0			0
$136$		0			0
$137$			5.80371i			0.495844i	0.968780	+	0.247922i	$0.0797477\pi$
$137$			5.80371i			0.495844i	−0.968780	+	0.247922i	$0.920252\pi$
$138$		0			0
$139$	−6.27873	+	6.27873i	−0.532555	+	0.532555i	−0.921332	−	0.388777i	$-0.872898\pi$
$139$	−6.27873	+	6.27873i	−0.532555	+	0.532555i	0.388777	+	0.921332i	$0.372898\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$			0.0162325i			0.00135743i
$144$		0			0
$145$	−13.5634	−	10.6840i	−1.12638	−	0.887259i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−12.6568	+	12.6568i	−1.03689	+	1.03689i	−0.0375933	+	0.999293i	$0.511969\pi$
$149$	−12.6568	+	12.6568i	−1.03689	+	1.03689i	−0.999293	+	0.0375933i	$0.988031\pi$
$150$		0			0
$151$	−17.1332			−1.39428			−0.697140	−	0.716935i	$-0.745544\pi$
$151$	−17.1332			−1.39428			−0.697140	+	0.716935i	$0.745544\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	1.31622	+	11.0841i	0.105722	+	0.890294i
$156$		0			0
$157$	4.80235	+	4.80235i	0.383269	+	0.383269i	0.872279	−	0.489009i	$-0.162642\pi$
$157$	4.80235	+	4.80235i	0.383269	+	0.383269i	−0.489009	+	0.872279i	$0.662642\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$		−	19.2185i		−	1.51463i
$162$		0			0
$163$	−0.778039	+	0.778039i	−0.0609407	+	0.0609407i	−0.736920	−	0.675980i	$-0.763721\pi$
$163$	−0.778039	+	0.778039i	−0.0609407	+	0.0609407i	0.675980	+	0.736920i	$0.263721\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−5.26638			−0.407525			−0.203763	−	0.979020i	$-0.565317\pi$
$167$	−5.26638			−0.407525			−0.203763	+	0.979020i	$0.565317\pi$
$168$		0			0
$169$		−	12.9999i		−	0.999991i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−8.51881	+	8.51881i	−0.647673	+	0.647673i	−0.952430	−	0.304757i	$-0.901425\pi$
$173$	−8.51881	+	8.51881i	−0.647673	+	0.647673i	0.304757	+	0.952430i	$0.401425\pi$
$174$		0			0
$175$	−3.46546	−	14.3858i	−0.261964	−	1.08746i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−10.2479	+	10.2479i	−0.765966	+	0.765966i	−0.977394	−	0.211428i	$-0.932189\pi$
$179$	−10.2479	+	10.2479i	−0.765966	+	0.765966i	0.211428	+	0.977394i	$0.432189\pi$
$180$		0			0
$181$	−0.590728	−	0.590728i	−0.0439085	−	0.0439085i	0.684812	−	0.728720i	$-0.259884\pi$
$181$	−0.590728	−	0.590728i	−0.0439085	−	0.0439085i	−0.728720	+	0.684812i	$0.759884\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	7.32909	−	9.30429i	0.538846	−	0.684065i
$186$		0			0
$187$	−2.08046	−	2.08046i	−0.152138	−	0.152138i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−15.2046			−1.10017			−0.550083	−	0.835110i	$-0.685404\pi$
$191$	−15.2046			−1.10017			−0.550083	+	0.835110i	$0.685404\pi$
$192$		0			0
$193$		−	12.4277i		−	0.894566i	−0.894392	−	0.447283i	$-0.852392\pi$
$193$		−	12.4277i		−	0.894566i	0.894392	−	0.447283i	$-0.147608\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−7.54210	−	7.54210i	−0.537352	−	0.537352i	0.385398	−	0.922750i	$-0.374064\pi$
$197$	−7.54210	−	7.54210i	−0.537352	−	0.537352i	−0.922750	+	0.385398i	$0.874064\pi$
$198$		0			0
$199$	−10.0231			−0.710517			−0.355258	−	0.934768i	$-0.615607\pi$
$199$	−10.0231			−0.710517			−0.355258	+	0.934768i	$0.615607\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	16.1585	−	16.1585i	1.13411	−	1.13411i
$204$		0			0
$205$	23.1473	−	2.74872i	1.61668	−	0.191979i
$206$		0			0
$207$		0			0
$208$		0			0
$209$			10.6228i			0.734796i
$210$		0			0
$211$	15.9950	+	15.9950i	1.10114	+	1.10114i	0.994273	+	0.106867i	$0.0340819\pi$
$211$	15.9950	+	15.9950i	1.10114	+	1.10114i	0.106867	+	0.994273i	$0.465918\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	8.74819	+	6.89104i	0.596621	+	0.469965i
$216$		0			0
$217$	−14.7729			−1.00285
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−0.0156052	−	0.0156052i	−0.00104972	−	0.00104972i
$222$		0			0
$223$	26.9611			1.80545			0.902724	−	0.430221i	$-0.141564\pi$
$223$	26.9611			1.80545			0.902724	+	0.430221i	$0.141564\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−4.80422	−	4.80422i	−0.318867	−	0.318867i	0.529465	−	0.848332i	$-0.322393\pi$
$227$	−4.80422	−	4.80422i	−0.318867	−	0.318867i	−0.848332	+	0.529465i	$0.822393\pi$
$228$		0			0
$229$	−3.77289	−	3.77289i	−0.249320	−	0.249320i	0.571372	−	0.820691i	$-0.306412\pi$
$229$	−3.77289	−	3.77289i	−0.249320	−	0.249320i	−0.820691	+	0.571372i	$0.806412\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$			12.2685i			0.803737i	0.915697	+	0.401868i	$0.131639\pi$
$233$			12.2685i			0.803737i	−0.915697	+	0.401868i	$0.868361\pi$
$234$		0			0
$235$	−2.80603	−	23.6299i	−0.183045	−	1.54145i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	12.4166			0.803164			0.401582	−	0.915823i	$-0.368460\pi$
$239$	12.4166			0.803164			0.401582	+	0.915823i	$0.368460\pi$
$240$		0			0
$241$	−16.6958			−1.07547			−0.537735	−	0.843114i	$-0.680720\pi$
$241$	−16.6958			−1.07547			−0.537735	+	0.843114i	$0.680720\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	3.90442	−	0.463646i	0.249444	−	0.0296212i
$246$		0			0
$247$			0.0796800i			0.00506992i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−18.3923	−	18.3923i	−1.16091	−	1.16091i	−0.984277	−	0.176634i	$-0.943479\pi$
$251$	−18.3923	−	18.3923i	−1.16091	−	1.16091i	−0.176634	−	0.984277i	$-0.556521\pi$
$252$		0			0
$253$	−6.75507	−	6.75507i	−0.424688	−	0.424688i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	29.8867			1.86428			0.932142	−	0.362094i	$-0.117938\pi$
$257$	29.8867			1.86428			0.932142	+	0.362094i	$0.117938\pi$
$258$		0			0
$259$	11.0846	+	11.0846i	0.688761	+	0.688761i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−17.6640			−1.08921			−0.544605	−	0.838693i	$-0.683320\pi$
$263$	−17.6640			−1.08921			−0.544605	+	0.838693i	$0.683320\pi$
$264$		0			0
$265$	7.40289	+	5.83134i	0.454756	+	0.358216i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	0.0280978	+	0.0280978i	0.00171315	+	0.00171315i	0.707963	−	0.706250i	$-0.249614\pi$
$269$	0.0280978	+	0.0280978i	0.00171315	+	0.00171315i	−0.706250	+	0.707963i	$0.749614\pi$
$270$		0			0
$271$		−	13.7422i		−	0.834779i	−0.908728	−	0.417390i	$-0.862945\pi$
$271$		−	13.7422i		−	0.834779i	0.908728	−	0.417390i	$-0.137055\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−6.27449	−	3.83836i	−0.378366	−	0.231462i
$276$		0			0
$277$	23.0188	−	23.0188i	1.38306	−	1.38306i	0.543937	−	0.839126i	$-0.316933\pi$
$277$	23.0188	−	23.0188i	1.38306	−	1.38306i	0.839126	−	0.543937i	$-0.183067\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−19.3294			−1.15309			−0.576547	−	0.817064i	$-0.695600\pi$
$281$	−19.3294			−1.15309			−0.576547	+	0.817064i	$0.695600\pi$
$282$		0			0
$283$	2.78511	+	2.78511i	0.165557	+	0.165557i	0.785023	−	0.619466i	$-0.212651\pi$
$283$	2.78511	+	2.78511i	0.165557	+	0.165557i	−0.619466	+	0.785023i	$0.712651\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$			30.8509i			1.82107i
$288$		0			0
$289$	−12.9999			−0.764699
$290$		0			0
$291$		0			0
$292$		0			0
$293$	17.8866	+	17.8866i	1.04495	+	1.04495i	0.998941	+	0.0460045i	$0.0146489\pi$
$293$	17.8866	+	17.8866i	1.04495	+	1.04495i	0.0460045	+	0.998941i	$0.485351\pi$
$294$		0			0
$295$	13.6098	+	10.7206i	0.792394	+	0.624178i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−0.0506687	−	0.0506687i	−0.00293025	−	0.00293025i
$300$		0			0
$301$	−10.4220	+	10.4220i	−0.600716	+	0.600716i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	9.15473	−	11.6219i	0.524198	−	0.665470i
$306$		0			0
$307$	−23.4113	+	23.4113i	−1.33615	+	1.33615i	−0.436397	+	0.899754i	$0.643746\pi$
$307$	−23.4113	+	23.4113i	−1.33615	+	1.33615i	−0.899754	+	0.436397i	$0.856254\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$			24.0385i			1.36310i	0.731772	+	0.681549i	$0.238693\pi$
$311$			24.0385i			1.36310i	−0.731772	+	0.681549i	$0.761307\pi$
$312$		0			0
$313$	17.7757			1.00474			0.502371	−	0.864652i	$-0.332461\pi$
$313$	17.7757			1.00474			0.502371	+	0.864652i	$0.332461\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−4.69302	+	4.69302i	−0.263586	+	0.263586i	−0.826509	−	0.562923i	$-0.809677\pi$
$317$	−4.69302	+	4.69302i	−0.263586	+	0.263586i	0.562923	+	0.826509i	$0.309677\pi$
$318$		0			0
$319$		−	11.3591i		−	0.635987i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	−10.2123	−	10.2123i	−0.568228	−	0.568228i
$324$		0			0
$325$	−0.0470639	−	0.0287909i	−0.00261064	−	0.00159703i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	31.4942			1.73633
$330$		0			0
$331$	−20.1568	+	20.1568i	−1.10792	+	1.10792i	−0.114494	+	0.993424i	$0.536525\pi$
$331$	−20.1568	+	20.1568i	−1.10792	+	1.10792i	−0.993424	+	0.114494i	$0.963475\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	4.48895	−	5.69873i	0.245258	−	0.311355i
$336$		0			0
$337$		−	22.5791i		−	1.22996i	−0.788542	−	0.614980i	$-0.789164\pi$
$337$		−	22.5791i		−	1.22996i	0.788542	−	0.614980i	$-0.210836\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−5.19252	+	5.19252i	−0.281191	+	0.281191i
$342$		0			0
$343$		−	15.5124i		−	0.837588i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	8.61782	−	8.61782i	0.462629	−	0.462629i	−0.436887	−	0.899516i	$-0.643919\pi$
$347$	8.61782	−	8.61782i	0.462629	−	0.462629i	0.899516	+	0.436887i	$0.143919\pi$
$348$		0			0
$349$	11.4945	−	11.4945i	0.615284	−	0.615284i	−0.329034	−	0.944318i	$-0.606723\pi$
$349$	11.4945	−	11.4945i	0.615284	−	0.615284i	0.944318	+	0.329034i	$0.106723\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	17.2352			0.917336			0.458668	−	0.888608i	$-0.348327\pi$
$353$	17.2352			0.917336			0.458668	+	0.888608i	$0.348327\pi$
$354$		0			0
$355$	−0.0559829	−	0.471438i	−0.00297126	−	0.0250213i
$356$		0			0
$357$		0			0
$358$		0			0
$359$		−	2.27145i		−	0.119882i	−0.998202	−	0.0599412i	$-0.980909\pi$
$359$		−	2.27145i		−	0.119882i	0.998202	−	0.0599412i	$-0.0190913\pi$
$360$		0			0
$361$			33.1441i			1.74442i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	36.6333	−	4.35017i	1.91747	−	0.227698i
$366$		0			0
$367$	−31.1335			−1.62516			−0.812579	−	0.582852i	$-0.801937\pi$
$367$	−31.1335			−1.62516			−0.812579	+	0.582852i	$0.801937\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−8.81934	+	8.81934i	−0.457877	+	0.457877i
$372$		0			0
$373$	−20.3199	+	20.3199i	−1.05212	+	1.05212i	−0.0535601	+	0.998565i	$0.517057\pi$
$373$	−20.3199	+	20.3199i	−1.05212	+	1.05212i	−0.998565	+	0.0535601i	$0.982943\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$		−	0.0852026i		−	0.00438816i
$378$		0			0
$379$	9.61527	−	9.61527i	0.493903	−	0.493903i	−0.415630	−	0.909534i	$-0.636439\pi$
$379$	9.61527	−	9.61527i	0.493903	−	0.493903i	0.909534	+	0.415630i	$0.136439\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$		−	1.17749i		−	0.0601668i	−0.999547	−	0.0300834i	$-0.990423\pi$
$383$		−	1.17749i		−	0.0601668i	0.999547	−	0.0300834i	$-0.00957728\pi$
$384$		0			0
$385$	6.02391	−	7.64736i	0.307007	−	0.389746i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	23.7967	−	23.7967i	1.20654	−	1.20654i	0.234403	−	0.972139i	$-0.424686\pi$
$389$	23.7967	−	23.7967i	1.20654	−	1.20654i	0.972139	−	0.234403i	$-0.0753137\pi$
$390$		0			0
$391$	12.9881			0.656834
$392$		0			0
$393$		0			0
$394$		0			0
$395$	1.19930	+	10.0994i	0.0603431	+	0.508156i
$396$		0			0
$397$	5.88396	+	5.88396i	0.295308	+	0.295308i	0.839173	−	0.543865i	$-0.183040\pi$
$397$	5.88396	+	5.88396i	0.295308	+	0.295308i	−0.543865	+	0.839173i	$0.683040\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$		−	15.4433i		−	0.771202i	−0.922666	−	0.385601i	$-0.873994\pi$
$401$		−	15.4433i		−	0.771202i	0.922666	−	0.385601i	$-0.126006\pi$
$402$		0			0
$403$	−0.0389482	+	0.0389482i	−0.00194015	+	0.00194015i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	7.79218			0.386244
$408$		0			0
$409$			8.72546i			0.431446i	0.976455	+	0.215723i	$0.0692109\pi$
$409$			8.72546i			0.431446i	−0.976455	+	0.215723i	$0.930789\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−16.2139	+	16.2139i	−0.797833	+	0.797833i
$414$		0			0
$415$	11.6347	+	9.16479i	0.571125	+	0.449882i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	4.83085	−	4.83085i	0.236003	−	0.236003i	−0.579190	−	0.815193i	$-0.696631\pi$
$419$	4.83085	−	4.83085i	0.236003	−	0.236003i	0.815193	+	0.579190i	$0.196631\pi$
$420$		0			0
$421$	20.2440	+	20.2440i	0.986633	+	0.986633i	0.999912	−	0.0132784i	$-0.00422678\pi$
$421$	20.2440	+	20.2440i	0.986633	+	0.986633i	−0.0132784	+	0.999912i	$0.504227\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	9.72204	−	2.34199i	0.471588	−	0.113603i
$426$		0			0
$427$	13.8456	+	13.8456i	0.670038	+	0.670038i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−6.63538			−0.319615			−0.159808	−	0.987148i	$-0.551087\pi$
$431$	−6.63538			−0.319615			−0.159808	+	0.987148i	$0.551087\pi$
$432$		0			0
$433$		−	2.17952i		−	0.104741i	−0.998628	−	0.0523706i	$-0.983322\pi$
$433$		−	2.17952i		−	0.104741i	0.998628	−	0.0523706i	$-0.0166777\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−33.1585	−	33.1585i	−1.58619	−	1.58619i
$438$		0			0
$439$	18.1795			0.867661			0.433830	−	0.900995i	$-0.357162\pi$
$439$	18.1795			0.867661			0.433830	+	0.900995i	$0.357162\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−20.1844	+	20.1844i	−0.958989	+	0.958989i	−0.999192	−	0.0402025i	$-0.987200\pi$
$443$	−20.1844	+	20.1844i	−0.958989	+	0.958989i	0.0402025	+	0.999192i	$0.487200\pi$
$444$		0			0
$445$	−0.273325	+	0.0324571i	−0.0129569	+	0.00153862i
$446$		0			0
$447$		0			0
$448$		0			0
$449$		−	31.3405i		−	1.47905i	−0.673129	−	0.739525i	$-0.735050\pi$
$449$		−	31.3405i		−	1.47905i	0.673129	−	0.739525i	$-0.264950\pi$
$450$		0			0
$451$	10.8437	+	10.8437i	0.510611	+	0.510611i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	0.0451843	−	0.0573616i	0.00211827	−	0.00268915i
$456$		0			0
$457$	15.6212			0.730727			0.365364	−	0.930865i	$-0.380945\pi$
$457$	15.6212			0.730727			0.365364	+	0.930865i	$0.380945\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−9.98698	−	9.98698i	−0.465140	−	0.465140i	0.435196	−	0.900336i	$-0.356679\pi$
$461$	−9.98698	−	9.98698i	−0.465140	−	0.465140i	−0.900336	+	0.435196i	$0.856679\pi$
$462$		0			0
$463$	27.8119			1.29253			0.646264	−	0.763114i	$-0.276330\pi$
$463$	27.8119			1.29253			0.646264	+	0.763114i	$0.276330\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−10.4295	−	10.4295i	−0.482620	−	0.482620i	0.423348	−	0.905967i	$-0.360855\pi$
$467$	−10.4295	−	10.4295i	−0.482620	−	0.482620i	−0.905967	+	0.423348i	$0.860855\pi$
$468$		0			0
$469$	6.78911	+	6.78911i	0.313492	+	0.313492i
$470$		0			0
$471$		0			0
$472$		0			0
$473$			7.32645i			0.336871i
$474$		0			0
$475$	−30.7995	−	18.8413i	−1.41318	−	0.864497i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	23.5450			1.07580			0.537900	−	0.843009i	$-0.319218\pi$
$479$	23.5450			1.07580			0.537900	+	0.843009i	$0.319218\pi$
$480$		0			0
$481$	0.0584478			0.00266499
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−2.18712	−	18.4180i	−0.0993119	−	0.836317i
$486$		0			0
$487$		−	15.4005i		−	0.697865i	−0.937148	−	0.348932i	$-0.886544\pi$
$487$		−	15.4005i		−	0.697865i	0.937148	−	0.348932i	$-0.113456\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−11.9089	−	11.9089i	−0.537443	−	0.537443i	0.385334	−	0.922777i	$-0.374086\pi$
$491$	−11.9089	−	11.9089i	−0.537443	−	0.537443i	−0.922777	+	0.385334i	$0.874086\pi$
$492$		0			0
$493$	10.9201	+	10.9201i	0.491817	+	0.491817i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	0.628336			0.0281847
$498$		0			0
$499$	−16.4502	−	16.4502i	−0.736411	−	0.736411i	0.235471	−	0.971881i	$-0.424337\pi$
$499$	−16.4502	−	16.4502i	−0.736411	−	0.736411i	−0.971881	+	0.235471i	$0.924337\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	11.4298			0.509632			0.254816	−	0.966990i	$-0.417985\pi$
$503$	11.4298			0.509632			0.254816	+	0.966990i	$0.417985\pi$
$504$		0			0
$505$	15.5594	−	19.7527i	0.692386	−	0.878985i
$506$		0			0
$507$		0			0
$508$		0			0
$509$	26.8748	+	26.8748i	1.19120	+	1.19120i	0.976730	+	0.214473i	$0.0688034\pi$
$509$	26.8748	+	26.8748i	1.19120	+	1.19120i	0.214473	+	0.976730i	$0.431197\pi$
$510$		0			0
$511$			48.8251i			2.15990i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−1.62065	−	13.6477i	−0.0714145	−	0.601390i
$516$		0			0
$517$	11.0698	−	11.0698i	0.486850	−	0.486850i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−18.0720			−0.791749			−0.395874	−	0.918305i	$-0.629558\pi$
$521$	−18.0720			−0.791749			−0.395874	+	0.918305i	$0.629558\pi$
$522$		0			0
$523$	10.2127	+	10.2127i	0.446571	+	0.446571i	0.894213	−	0.447642i	$-0.147736\pi$
$523$	10.2127	+	10.2127i	0.446571	+	0.446571i	−0.447642	+	0.894213i	$0.647736\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$		−	9.98371i		−	0.434897i
$528$		0			0
$529$	19.1711			0.833526
$530$		0			0
$531$		0			0
$532$		0			0
$533$	0.0813369	+	0.0813369i	0.00352309	+	0.00352309i
$534$		0			0
$535$	−11.4265	+	14.5059i	−0.494010	+	0.627147i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	1.82909	+	1.82909i	0.0787844	+	0.0787844i
$540$		0			0
$541$	−4.93323	+	4.93323i	−0.212096	+	0.212096i	−0.805157	−	0.593061i	$-0.797919\pi$
$541$	−4.93323	+	4.93323i	−0.212096	+	0.212096i	0.593061	+	0.805157i	$0.297919\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−21.4652	+	27.2500i	−0.919466	+	1.16726i
$546$		0			0
$547$	25.5794	−	25.5794i	1.09370	−	1.09370i	0.0985674	−	0.995130i	$-0.468574\pi$
$547$	25.5794	−	25.5794i	1.09370	−	1.09370i	0.995130	−	0.0985674i	$-0.0314260\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$		−	55.7581i		−	2.37538i
$552$		0			0
$553$	−13.4606			−0.572402
$554$		0			0
$555$		0			0
$556$		0			0
$557$	4.34156	−	4.34156i	0.183958	−	0.183958i	−0.609120	−	0.793078i	$-0.708477\pi$
$557$	4.34156	−	4.34156i	0.183958	−	0.183958i	0.793078	+	0.609120i	$0.208477\pi$
$558$		0			0
$559$			0.0549545i			0.00232433i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−16.4606	−	16.4606i	−0.693731	−	0.693731i	0.269320	−	0.963051i	$-0.413201\pi$
$563$	−16.4606	−	16.4606i	−0.693731	−	0.693731i	−0.963051	+	0.269320i	$0.913201\pi$
$564$		0			0
$565$	−22.1000	+	2.62436i	−0.929755	+	0.110408i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−27.5819			−1.15629			−0.578146	−	0.815933i	$-0.696224\pi$
$569$	−27.5819			−1.15629			−0.578146	+	0.815933i	$0.696224\pi$
$570$		0			0
$571$	−4.33390	+	4.33390i	−0.181368	+	0.181368i	−0.791952	−	0.610584i	$-0.790935\pi$
$571$	−4.33390	+	4.33390i	−0.181368	+	0.181368i	0.610584	+	0.791952i	$0.290935\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	31.5666	−	7.60425i	1.31642	−	0.317119i
$576$		0			0
$577$			32.4805i			1.35218i	0.736819	+	0.676090i	$0.236327\pi$
$577$			32.4805i			1.35218i	−0.736819	+	0.676090i	$0.763673\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−13.8609	+	13.8609i	−0.575046	+	0.575046i
$582$		0			0
$583$			6.19979i			0.256769i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	30.2712	−	30.2712i	1.24942	−	1.24942i	0.293450	−	0.955975i	$-0.405197\pi$
$587$	30.2712	−	30.2712i	1.24942	−	1.24942i	0.955975	−	0.293450i	$-0.0948033\pi$
$588$		0			0
$589$	−25.4884	+	25.4884i	−1.05023	+	1.05023i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−38.4245			−1.57790			−0.788952	−	0.614455i	$-0.789376\pi$
$593$	−38.4245			−1.57790			−0.788952	+	0.614455i	$0.789376\pi$
$594$		0			0
$595$	1.56071	+	13.1429i	0.0639830	+	0.538808i
$596$		0			0
$597$		0			0
$598$		0			0
$599$			20.1491i			0.823269i	0.911349	+	0.411635i	$0.135042\pi$
$599$			20.1491i			0.823269i	−0.911349	+	0.411635i	$0.864958\pi$
$600$		0			0
$601$			3.75831i			0.153305i	0.997058	+	0.0766524i	$0.0244232\pi$
$601$			3.75831i			0.153305i	−0.997058	+	0.0766524i	$0.975577\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	2.32984	+	19.6198i	0.0947214	+	0.797660i
$606$		0			0
$607$	−1.55683			−0.0631899			−0.0315949	−	0.999501i	$-0.510059\pi$
$607$	−1.55683			−0.0631899			−0.0315949	+	0.999501i	$0.510059\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	0.0830329	−	0.0830329i	0.00335915	−	0.00335915i
$612$		0			0
$613$	19.5306	−	19.5306i	0.788832	−	0.788832i	−0.192471	−	0.981303i	$-0.561650\pi$
$613$	19.5306	−	19.5306i	0.788832	−	0.788832i	0.981303	+	0.192471i	$0.0616501\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$		−	4.07636i		−	0.164108i	−0.996628	−	0.0820540i	$-0.973852\pi$
$617$		−	4.07636i		−	0.164108i	0.996628	−	0.0820540i	$-0.0261480\pi$
$618$		0			0
$619$	−5.05003	+	5.05003i	−0.202978	+	0.202978i	−0.801275	−	0.598297i	$-0.795844\pi$
$619$	−5.05003	+	5.05003i	−0.202978	+	0.202978i	0.598297	+	0.801275i	$0.295844\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$		−	0.364290i		−	0.0145950i
$624$		0			0
$625$	22.2576	−	11.3841i	0.890305	−	0.455365i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−7.49105	+	7.49105i	−0.298688	+	0.298688i
$630$		0			0
$631$	0.782254			0.0311411			0.0155705	−	0.999879i	$-0.495044\pi$
$631$	0.782254			0.0311411			0.0155705	+	0.999879i	$0.495044\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−1.20404	+	0.142978i	−0.0477807	+	0.00567391i
$636$		0			0
$637$	0.0137197	+	0.0137197i	0.000543593	+	0.000543593i
$638$		0			0
$639$		0			0
$640$		0			0
$641$			2.92420i			0.115499i	0.998331	+	0.0577495i	$0.0183925\pi$
$641$			2.92420i			0.115499i	−0.998331	+	0.0577495i	$0.981608\pi$
$642$		0			0
$643$	30.2222	−	30.2222i	1.19185	−	1.19185i	0.215301	−	0.976548i	$-0.430927\pi$
$643$	30.2222	−	30.2222i	1.19185	−	1.19185i	0.976548	−	0.215301i	$-0.0690732\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−48.8394			−1.92007			−0.960037	−	0.279871i	$-0.909708\pi$
$647$	−48.8394			−1.92007			−0.960037	+	0.279871i	$0.909708\pi$
$648$		0			0
$649$			11.3980i			0.447410i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−4.18933	+	4.18933i	−0.163941	+	0.163941i	−0.784310	−	0.620369i	$-0.786983\pi$
$653$	−4.18933	+	4.18933i	−0.163941	+	0.163941i	0.620369	+	0.784310i	$0.286983\pi$
$654$		0			0
$655$	10.8655	−	13.7938i	0.424550	−	0.538967i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	13.0512	−	13.0512i	0.508402	−	0.508402i	−0.405634	−	0.914036i	$-0.632949\pi$
$659$	13.0512	−	13.0512i	0.508402	−	0.508402i	0.914036	+	0.405634i	$0.132949\pi$
$660$		0			0
$661$	8.41832	+	8.41832i	0.327435	+	0.327435i	0.851610	−	0.524175i	$-0.175626\pi$
$661$	8.41832	+	8.41832i	0.327435	+	0.327435i	−0.524175	+	0.851610i	$0.675626\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	29.5694	−	37.5384i	1.14665	−	1.45568i
$666$		0			0
$667$	35.4567	+	35.4567i	1.37289	+	1.37289i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	9.73317			0.375745
$672$		0			0
$673$		−	8.96622i		−	0.345622i	−0.984955	−	0.172811i	$-0.944715\pi$
$673$		−	8.96622i		−	0.345622i	0.984955	−	0.172811i	$-0.0552850\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−16.5376	−	16.5376i	−0.635590	−	0.635590i	0.313874	−	0.949464i	$-0.398373\pi$
$677$	−16.5376	−	16.5376i	−0.635590	−	0.635590i	−0.949464	+	0.313874i	$0.898373\pi$
$678$		0			0
$679$	24.5476			0.942051
$680$		0			0
$681$		0			0
$682$		0			0
$683$	3.42707	−	3.42707i	0.131133	−	0.131133i	−0.638494	−	0.769627i	$-0.720442\pi$
$683$	3.42707	−	3.42707i	0.131133	−	0.131133i	0.769627	+	0.638494i	$0.220442\pi$
$684$		0			0
$685$	−1.53031	−	12.8869i	−0.0584702	−	0.492385i
$686$		0			0
$687$		0			0
$688$		0			0
$689$			0.0465036i			0.00177165i
$690$		0			0
$691$	−18.7477	−	18.7477i	−0.713195	−	0.713195i	0.254008	−	0.967202i	$-0.418251\pi$
$691$	−18.7477	−	18.7477i	−0.713195	−	0.713195i	−0.967202	+	0.254008i	$0.918251\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	12.2862	−	15.5973i	0.466040	−	0.591639i
$696$		0			0
$697$	−20.8493			−0.789725
$698$		0			0
$699$		0			0
$700$		0			0
$701$	−28.2156	−	28.2156i	−1.06569	−	1.06569i	−0.997685	−	0.0680026i	$-0.978337\pi$
$701$	−28.2156	−	28.2156i	−1.06569	−	1.06569i	−0.0680026	−	0.997685i	$-0.521663\pi$
$702$		0			0
$703$	38.2493			1.44260
$704$		0			0
$705$		0			0
$706$		0			0
$707$	23.5322	+	23.5322i	0.885018	+	0.885018i
$708$		0			0
$709$	10.7577	+	10.7577i	0.404013	+	0.404013i	0.879645	−	0.475631i	$-0.157780\pi$
$709$	10.7577	+	10.7577i	0.404013	+	0.404013i	−0.475631	+	0.879645i	$0.657780\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$		−	32.4162i		−	1.21400i
$714$		0			0
$715$	−0.00428015	−	0.0360437i	−0.000160069	−	0.00134796i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−1.68057			−0.0626748			−0.0313374	−	0.999509i	$-0.509977\pi$
$719$	−1.68057			−0.0626748			−0.0313374	+	0.999509i	$0.509977\pi$
$720$		0			0
$721$	18.1898			0.677422
$722$		0			0
$723$		0			0
$724$		0			0
$725$	32.9342	+	20.1471i	1.22314	+	0.748246i
$726$		0			0
$727$		−	33.3069i		−	1.23528i	−0.786460	−	0.617641i	$-0.788088\pi$
$727$		−	33.3069i		−	1.23528i	0.786460	−	0.617641i	$-0.211912\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−7.04332	−	7.04332i	−0.260507	−	0.260507i
$732$		0			0
$733$	−9.28476	−	9.28476i	−0.342941	−	0.342941i	0.514531	−	0.857472i	$-0.327966\pi$
$733$	−9.28476	−	9.28476i	−0.342941	−	0.342941i	−0.857472	+	0.514531i	$0.827966\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	4.77258			0.175800
$738$		0			0
$739$	24.0117	+	24.0117i	0.883286	+	0.883286i	0.993867	−	0.110581i	$-0.0352712\pi$
$739$	24.0117	+	24.0117i	0.883286	+	0.883286i	−0.110581	+	0.993867i	$0.535271\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	25.5380			0.936897			0.468448	−	0.883491i	$-0.344813\pi$
$743$	25.5380			0.936897			0.468448	+	0.883491i	$0.344813\pi$
$744$		0			0
$745$	24.7667	−	31.4414i	0.907382	−	1.15192i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−17.2815	−	17.2815i	−0.631451	−	0.631451i
$750$		0			0
$751$			38.6627i			1.41082i	0.708799	+	0.705411i	$0.249238\pi$
$751$			38.6627i			1.41082i	−0.708799	+	0.705411i	$0.750762\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	38.0437	−	4.51766i	1.38455	−	0.164414i
$756$		0			0
$757$	28.0622	−	28.0622i	1.01994	−	1.01994i	0.0201412	−	0.999797i	$-0.493588\pi$
$757$	28.0622	−	28.0622i	1.01994	−	1.01994i	0.999797	−	0.0201412i	$-0.00641158\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	12.1544			0.440597			0.220299	−	0.975432i	$-0.429297\pi$
$761$	12.1544			0.440597			0.220299	+	0.975432i	$0.429297\pi$
$762$		0			0
$763$	−32.4640	−	32.4640i	−1.17528	−	1.17528i
$764$		0			0
$765$		0			0
$766$		0			0
$767$			0.0854944i			0.00308702i
$768$		0			0
$769$	−0.0426731			−0.00153883			−0.000769416	−	1.00000i	$-0.500245\pi$
$769$	−0.0426731			−0.00153883			−0.000769416		1.00000i	$0.500245\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−4.96973	−	4.96973i	−0.178749	−	0.178749i	0.612061	−	0.790810i	$-0.290341\pi$
$773$	−4.96973	−	4.96973i	−0.178749	−	0.178749i	−0.790810	+	0.612061i	$0.790341\pi$
$774$		0			0
$775$	−5.84526	−	24.2648i	−0.209968	−	0.871616i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	53.2283	+	53.2283i	1.90710	+	1.90710i
$780$		0			0
$781$	0.220853	−	0.220853i	0.00790274	−	0.00790274i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−11.9297	−	9.39719i	−0.425791	−	0.335400i
$786$		0			0
$787$	16.8577	−	16.8577i	0.600911	−	0.600911i	−0.339643	−	0.940554i	$-0.610306\pi$
$787$	16.8577	−	16.8577i	0.600911	−	0.600911i	0.940554	+	0.339643i	$0.110306\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$		−	29.4551i		−	1.04730i
$792$		0			0
$793$	0.0730069			0.00259255
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−0.0286009	+	0.0286009i	−0.00101310	+	0.00101310i	−0.707613	−	0.706600i	$-0.750228\pi$
$797$	−0.0286009	+	0.0286009i	−0.00101310	+	0.00101310i	0.706600	+	0.707613i	$0.250228\pi$
$798$		0			0
$799$			21.2841i			0.752976i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	17.1615	+	17.1615i	0.605614	+	0.605614i
$804$		0			0
$805$	5.06750	+	42.6740i	0.178606	+	1.50406i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	1.19014			0.0418431			0.0209216	−	0.999781i	$-0.493340\pi$
$809$	1.19014			0.0418431			0.0209216	+	0.999781i	$0.493340\pi$
$810$		0			0
$811$	−13.9807	+	13.9807i	−0.490928	+	0.490928i	−0.908598	−	0.417671i	$-0.862847\pi$
$811$	−13.9807	+	13.9807i	−0.490928	+	0.490928i	0.417671	+	0.908598i	$0.362847\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	1.52246	−	1.93276i	0.0533294	−	0.0677017i
$816$		0			0
$817$			35.9632i			1.25819i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	13.0285	−	13.0285i	0.454699	−	0.454699i	−0.442212	−	0.896911i	$-0.645806\pi$
$821$	13.0285	−	13.0285i	0.454699	−	0.454699i	0.896911	+	0.442212i	$0.145806\pi$
$822$		0			0
$823$			44.1886i			1.54032i	0.637851	+	0.770160i	$0.279823\pi$
$823$			44.1886i			1.54032i	−0.637851	+	0.770160i	$0.720177\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−14.3077	+	14.3077i	−0.497528	+	0.497528i	−0.910668	−	0.413139i	$-0.864432\pi$
$827$	−14.3077	+	14.3077i	−0.497528	+	0.497528i	0.413139	+	0.910668i	$0.364432\pi$
$828$		0			0
$829$	−1.86701	+	1.86701i	−0.0648439	+	0.0648439i	−0.738785	−	0.673941i	$-0.764600\pi$
$829$	−1.86701	+	1.86701i	−0.0648439	+	0.0648439i	0.673941	+	0.738785i	$0.264600\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−3.51681			−0.121850
$834$		0			0
$835$	11.6938	−	1.38863i	0.404682	−	0.0480556i
$836$		0			0
$837$		0			0
$838$		0			0
$839$			11.8696i			0.409786i	0.978784	+	0.204893i	$0.0656846\pi$
$839$			11.8696i			0.409786i	−0.978784	+	0.204893i	$0.934315\pi$
$840$		0			0
$841$			30.6226i			1.05595i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	3.42779	+	28.8658i	0.117919	+	0.993014i
$846$		0			0
$847$	−26.1495			−0.898507
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−24.3228	+	24.3228i	−0.833775	+	0.833775i
$852$		0			0
$853$	−11.7299	+	11.7299i	−0.401626	+	0.401626i	−0.878806	−	0.477180i	$-0.841659\pi$
$853$	−11.7299	+	11.7299i	−0.401626	+	0.401626i	0.477180	+	0.878806i	$0.341659\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$			19.0655i			0.651266i	0.945496	+	0.325633i	$0.105577\pi$
$857$			19.0655i			0.651266i	−0.945496	+	0.325633i	$0.894423\pi$
$858$		0			0
$859$	22.2411	−	22.2411i	0.758858	−	0.758858i	−0.217256	−	0.976115i	$-0.569711\pi$
$859$	22.2411	−	22.2411i	0.758858	−	0.758858i	0.976115	+	0.217256i	$0.0697108\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$		−	39.9598i		−	1.36025i	−0.733097	−	0.680124i	$-0.761926\pi$
$863$		−	39.9598i		−	1.36025i	0.733097	−	0.680124i	$-0.238074\pi$
$864$		0			0
$865$	16.6695	−	21.1620i	0.566781	−	0.719529i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−4.73123	+	4.73123i	−0.160496	+	0.160496i
$870$		0			0
$871$	0.0357983			0.00121298
$872$		0			0
$873$		0			0
$874$		0			0
$875$	11.4882	+	31.0293i	0.388370	+	1.04898i
$876$		0			0
$877$	−24.1486	−	24.1486i	−0.815442	−	0.815442i	0.170002	−	0.985444i	$-0.445623\pi$
$877$	−24.1486	−	24.1486i	−0.815442	−	0.815442i	−0.985444	+	0.170002i	$0.945623\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$			31.7726i			1.07045i	0.844711	+	0.535223i	$0.179772\pi$
$881$			31.7726i			1.07045i	−0.844711	+	0.535223i	$0.820228\pi$
$882$		0			0
$883$	1.59278	−	1.59278i	0.0536012	−	0.0536012i	−0.679798	−	0.733399i	$-0.737933\pi$
$883$	1.59278	−	1.59278i	0.0536012	−	0.0536012i	0.733399	+	0.679798i	$0.237933\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	8.63569			0.289958			0.144979	−	0.989435i	$-0.453689\pi$
$887$	8.63569			0.289958			0.144979	+	0.989435i	$0.453689\pi$
$888$		0			0
$889$		−	1.60475i		−	0.0538215i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	54.3382	−	54.3382i	1.81836	−	1.81836i
$894$		0			0
$895$	20.0530	−	25.4573i	0.670298	−	0.850944i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	27.2550	−	27.2550i	0.909004	−	0.909004i
$900$		0			0
$901$	−5.96020	−	5.96020i	−0.198563	−	0.198563i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	1.46745	+	1.15593i	0.0487798	+	0.0384244i
$906$		0			0
$907$	12.8316	+	12.8316i	0.426068	+	0.426068i	0.887286	−	0.461219i	$-0.152588\pi$
$907$	12.8316	+	12.8316i	0.426068	+	0.426068i	−0.461219	+	0.887286i	$0.652588\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−52.5129			−1.73983			−0.869915	−	0.493202i	$-0.835826\pi$
$911$	−52.5129			−1.73983			−0.869915	+	0.493202i	$0.835826\pi$
$912$		0			0
$913$			9.74386i			0.322475i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	16.4330	+	16.4330i	0.542666	+	0.542666i
$918$		0			0
$919$	−43.7005			−1.44155			−0.720773	−	0.693172i	$-0.756213\pi$
$919$	−43.7005			−1.44155			−0.720773	+	0.693172i	$0.756213\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	0.00165658	−	0.00165658i	5.45270e−5	−	5.45270e-5i
$924$		0			0
$925$	−13.8207	+	22.5924i	−0.454421	+	0.742833i
$926$		0			0
$927$		0			0
$928$		0			0
$929$			11.4938i			0.377099i	0.982064	+	0.188550i	$0.0603786\pi$
$929$			11.4938i			0.377099i	−0.982064	+	0.188550i	$0.939621\pi$
$930$		0			0
$931$	8.97840	+	8.97840i	0.294255	+	0.294255i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	5.16816	+	4.07102i	0.169017	+	0.133137i
$936$		0			0
$937$	−53.9308			−1.76184			−0.880922	−	0.473261i	$-0.843077\pi$
$937$	−53.9308			−1.76184			−0.880922	+	0.473261i	$0.843077\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−6.98130	−	6.98130i	−0.227584	−	0.227584i	0.584099	−	0.811683i	$-0.301448\pi$
$941$	−6.98130	−	6.98130i	−0.227584	−	0.227584i	−0.811683	+	0.584099i	$0.801448\pi$
$942$		0			0
$943$	−67.6960			−2.20448
$944$		0			0
$945$		0			0
$946$		0			0
$947$	5.16523	+	5.16523i	0.167847	+	0.167847i	0.786032	−	0.618185i	$-0.212132\pi$
$947$	5.16523	+	5.16523i	0.167847	+	0.167847i	−0.618185	+	0.786032i	$0.712132\pi$
$948$		0			0
$949$	0.128725	+	0.128725i	0.00417860	+	0.00417860i
$950$		0			0
$951$		0			0
$952$		0			0
$953$			20.7891i			0.673424i	0.941608	+	0.336712i	$0.109315\pi$
$953$			20.7891i			0.673424i	−0.941608	+	0.336712i	$0.890685\pi$
$954$		0			0
$955$	33.7613	−	4.00912i	1.09249	−	0.129732i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	17.1758			0.554636
$960$		0			0
$961$	6.08216			0.196199
$962$		0			0
$963$		0			0
$964$		0			0
$965$	3.27692	+	27.5953i	0.105488	+	0.888325i
$966$		0			0
$967$		−	50.2701i		−	1.61658i	−0.588786	−	0.808289i	$-0.700394\pi$
$967$		−	50.2701i		−	1.61658i	0.588786	−	0.808289i	$-0.299606\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−19.7427	−	19.7427i	−0.633574	−	0.633574i	0.315388	−	0.948963i	$-0.397865\pi$
$971$	−19.7427	−	19.7427i	−0.633574	−	0.633574i	−0.948963	+	0.315388i	$0.897865\pi$
$972$		0			0
$973$	18.5816	+	18.5816i	0.595700	+	0.595700i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	29.6872			0.949779			0.474889	−	0.880045i	$-0.342488\pi$
$977$	29.6872			0.949779			0.474889	+	0.880045i	$0.342488\pi$
$978$		0			0
$979$	−0.128044	−	0.128044i	−0.00409229	−	0.00409229i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	0.250996			0.00800552			0.00400276	−	0.999992i	$-0.498726\pi$
$983$	0.250996			0.00800552			0.00400276	+	0.999992i	$0.498726\pi$
$984$		0			0
$985$	18.7357	+	14.7583i	0.596968	+	0.470238i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−22.8691	−	22.8691i	−0.727194	−	0.727194i
$990$		0			0
$991$			33.2980i			1.05775i	0.848701	+	0.528873i	$0.177385\pi$
$991$			33.2980i			1.05775i	−0.848701	+	0.528873i	$0.822615\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	22.2559	−	2.64287i	0.705559	−	0.0837845i
$996$		0			0
$997$	14.4987	−	14.4987i	0.459180	−	0.459180i	−0.439207	−	0.898386i	$-0.644740\pi$
$997$	14.4987	−	14.4987i	0.459180	−	0.459180i	0.898386	+	0.439207i	$0.144740\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2880.2.u.a.719.2		96
3.2	odd	2	inner	2880.2.u.a.719.47		96
4.3	odd	2		720.2.u.a.539.31	yes	96
5.4	even	2	inner	2880.2.u.a.719.23		96
12.11	even	2		720.2.u.a.539.18	yes	96
15.14	odd	2	inner	2880.2.u.a.719.26		96
16.3	odd	4	inner	2880.2.u.a.2159.26		96
16.13	even	4		720.2.u.a.179.32	yes	96
20.19	odd	2		720.2.u.a.539.17	yes	96
48.29	odd	4		720.2.u.a.179.17	✓	96
48.35	even	4	inner	2880.2.u.a.2159.23		96
60.59	even	2		720.2.u.a.539.32	yes	96
80.19	odd	4	inner	2880.2.u.a.2159.47		96
80.29	even	4		720.2.u.a.179.18	yes	96
240.29	odd	4		720.2.u.a.179.31	yes	96
240.179	even	4	inner	2880.2.u.a.2159.2		96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
720.2.u.a.179.17	✓	96	48.29	odd	4
720.2.u.a.179.18	yes	96	80.29	even	4
720.2.u.a.179.31	yes	96	240.29	odd	4
720.2.u.a.179.32	yes	96	16.13	even	4
720.2.u.a.539.17	yes	96	20.19	odd	2
720.2.u.a.539.18	yes	96	12.11	even	2
720.2.u.a.539.31	yes	96	4.3	odd	2
720.2.u.a.539.32	yes	96	60.59	even	2
2880.2.u.a.719.2		96	1.1	even	1	trivial
2880.2.u.a.719.23		96	5.4	even	2	inner
2880.2.u.a.719.26		96	15.14	odd	2	inner
2880.2.u.a.719.47		96	3.2	odd	2	inner
2880.2.u.a.2159.2		96	240.179	even	4	inner
2880.2.u.a.2159.23		96	48.35	even	4	inner
2880.2.u.a.2159.26		96	16.3	odd	4	inner
2880.2.u.a.2159.47		96	80.19	odd	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 2880 = 2^{6} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2880.u (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-2.22047 + 0.263678i) q^{5} -2.95946i q^{7} +O(q^{10})\)	\(q+(-2.22047 + 0.263678i) q^{5} -2.95946i q^{7} +(-1.04021 - 1.04021i) q^{11} +(-0.00780247 - 0.00780247i) q^{13} +2.00003 q^{17} +(-5.10608 - 5.10608i) q^{19} +6.49393 q^{23} +(4.86095 - 1.17098i) q^{25} +(5.45997 + 5.45997i) q^{29} -4.99178i q^{31} +(0.780345 + 6.57137i) q^{35} +(-3.74547 + 3.74547i) q^{37} -10.4245 q^{41} +(-3.52161 - 3.52161i) q^{43} +10.6419i q^{47} -1.75838 q^{49} +(-2.98006 - 2.98006i) q^{53} +(2.58404 + 2.03548i) q^{55} +(-5.47867 - 5.47867i) q^{59} +(-4.67845 + 4.67845i) q^{61} +(0.0193825 + 0.0152678i) q^{65} +(-2.29404 + 2.29404i) q^{67} +0.212315i q^{71} -16.4980 q^{73} +(-3.07847 + 3.07847i) q^{77} -4.54833i q^{79} +(-4.68359 - 4.68359i) q^{83} +(-4.44100 + 0.527365i) q^{85} +0.123094 q^{89} +(-0.0230911 + 0.0230911i) q^{91} +(12.6842 + 9.99152i) q^{95} +8.29464i q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q+O(q^{10}) \) 96 * q	\( 96 q + 16 q^{19} - 96 q^{49} - 64 q^{55} - 32 q^{61}+O(q^{100}) \) 96 * q + 16 * q^19 - 96 * q^49 - 64 * q^55 - 32 * q^61

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

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