LMFDB - Embedded newform 2880.2.bc.a.593.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2880,2,Mod(593,2880)]

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([0, 3, 2, 3]))

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

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

chi := DirichletCharacter("2880.593");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2880 = 2^{6} \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2880.bc (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			593.5
Character	$\chi$	$=$	2880.593
Dual form			2880.2.bc.a.1457.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.06437 + 0.859295i) q^{5} +(1.97431 + 1.97431i) q^{7} +O(q^{10})$	$q+(-2.06437 + 0.859295i) q^{5} +(1.97431 + 1.97431i) q^{7} +(1.52237 + 1.52237i) q^{11} -3.70335i q^{13} +(-4.66282 - 4.66282i) q^{17} +(-1.17040 + 1.17040i) q^{19} +(-4.63847 - 4.63847i) q^{23} +(3.52322 - 3.54780i) q^{25} +(3.24146 + 3.24146i) q^{29} -5.06721 q^{31} +(-5.77220 - 2.37918i) q^{35} -3.52053i q^{37} -4.37236 q^{41} +12.8222 q^{43} +(-3.76945 - 3.76945i) q^{47} +0.795764i q^{49} +3.29793i q^{53} +(-4.45090 - 1.83457i) q^{55} +(7.41584 - 7.41584i) q^{59} +(6.24030 + 6.24030i) q^{61} +(3.18227 + 7.64508i) q^{65} -8.99401 q^{67} -7.50552 q^{71} +(11.1892 - 11.1892i) q^{73} +6.01126i q^{77} -2.98622i q^{79} +8.94000 q^{83} +(13.6325 + 5.61903i) q^{85} +1.52146i q^{89} +(7.31155 - 7.31155i) q^{91} +(1.41041 - 3.42185i) q^{95} +(-2.70455 + 2.70455i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q+O(q^{10}) $ 96 * q	$ 96 q - 16 q^{19} - 64 q^{43} + 32 q^{61}+O(q^{100}) $ 96 * q - 16 * q^19 - 64 * q^43 + 32 * q^61

Display 100 coefficients 10 coefficients

Character values

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

$n$	$577$	$641$	$901$	$2431$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$-1$	$e\left(\frac{3}{4}\right)$	$1$

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
$5$	−2.06437	+	0.859295i	−0.923213	+	0.384289i
$5$	−2.06437	+	0.859295i	−0.923213	+	0.384289i
$6$		0			0
$7$	1.97431	+	1.97431i	0.746217	+	0.746217i	0.973767	−	0.227549i	$-0.0730713\pi$
$7$	1.97431	+	1.97431i	0.746217	+	0.746217i	−0.227549	+	0.973767i	$0.573071\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	1.52237	+	1.52237i	0.459012	+	0.459012i	0.898331	−	0.439319i	$-0.144780\pi$
$11$	1.52237	+	1.52237i	0.459012	+	0.459012i	−0.439319	+	0.898331i	$0.644780\pi$
$12$		0			0
$13$		−	3.70335i		−	1.02712i	−0.858052	−	0.513562i	$-0.828326\pi$
$13$		−	3.70335i		−	1.02712i	0.858052	−	0.513562i	$-0.171674\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−4.66282	−	4.66282i	−1.13090	−	1.13090i	−0.990028	−	0.140872i	$-0.955009\pi$
$17$	−4.66282	−	4.66282i	−1.13090	−	1.13090i	−0.140872	−	0.990028i	$-0.544991\pi$
$18$		0			0
$19$	−1.17040	+	1.17040i	−0.268508	+	0.268508i	−0.828499	−	0.559991i	$-0.810805\pi$
$19$	−1.17040	+	1.17040i	−0.268508	+	0.268508i	0.559991	+	0.828499i	$0.310805\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−4.63847	−	4.63847i	−0.967188	−	0.967188i	0.0322902	−	0.999479i	$-0.489720\pi$
$23$	−4.63847	−	4.63847i	−0.967188	−	0.967188i	−0.999479	+	0.0322902i	$0.989720\pi$
$24$		0			0
$25$	3.52322	−	3.54780i	0.704645	−	0.709560i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	3.24146	+	3.24146i	0.601924	+	0.601924i	0.940823	−	0.338898i	$-0.110054\pi$
$29$	3.24146	+	3.24146i	0.601924	+	0.601924i	−0.338898	+	0.940823i	$0.610054\pi$
$30$		0			0
$31$	−5.06721			−0.910098			−0.455049	−	0.890467i	$-0.650378\pi$
$31$	−5.06721			−0.910098			−0.455049	+	0.890467i	$0.650378\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−5.77220	−	2.37918i	−0.975680	−	0.402155i
$36$		0			0
$37$		−	3.52053i		−	0.578771i	−0.957213	−	0.289386i	$-0.906549\pi$
$37$		−	3.52053i		−	0.578771i	0.957213	−	0.289386i	$-0.0934510\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−4.37236			−0.682847			−0.341424	−	0.939909i	$-0.610909\pi$
$41$	−4.37236			−0.682847			−0.341424	+	0.939909i	$0.610909\pi$
$42$		0			0
$43$	12.8222			1.95537			0.977687	−	0.210067i	$-0.0673682\pi$
$43$	12.8222			1.95537			0.977687	+	0.210067i	$0.0673682\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−3.76945	−	3.76945i	−0.549830	−	0.549830i	0.376561	−	0.926392i	$-0.377106\pi$
$47$	−3.76945	−	3.76945i	−0.549830	−	0.549830i	−0.926392	+	0.376561i	$0.877106\pi$
$48$		0			0
$49$			0.795764i			0.113681i
$50$		0			0
$51$		0			0
$52$		0			0
$53$			3.29793i			0.453005i	0.974011	+	0.226502i	$0.0727291\pi$
$53$			3.29793i			0.453005i	−0.974011	+	0.226502i	$0.927271\pi$
$54$		0			0
$55$	−4.45090	−	1.83457i	−0.600160	−	0.247373i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	7.41584	−	7.41584i	0.965460	−	0.965460i	−0.0339629	−	0.999423i	$-0.510813\pi$
$59$	7.41584	−	7.41584i	0.965460	−	0.965460i	0.999423	+	0.0339629i	$0.0108128\pi$
$60$		0			0
$61$	6.24030	+	6.24030i	0.798988	+	0.798988i	0.982936	−	0.183948i	$-0.0588878\pi$
$61$	6.24030	+	6.24030i	0.798988	+	0.798988i	−0.183948	+	0.982936i	$0.558888\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	3.18227	+	7.64508i	0.394712	+	0.948255i
$66$		0			0
$67$	−8.99401			−1.09879			−0.549397	−	0.835562i	$-0.685142\pi$
$67$	−8.99401			−1.09879			−0.549397	+	0.835562i	$0.685142\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−7.50552			−0.890741			−0.445370	−	0.895346i	$-0.646928\pi$
$71$	−7.50552			−0.890741			−0.445370	+	0.895346i	$0.646928\pi$
$72$		0			0
$73$	11.1892	−	11.1892i	1.30960	−	1.30960i	0.387889	−	0.921706i	$-0.373204\pi$
$73$	11.1892	−	11.1892i	1.30960	−	1.30960i	0.921706	−	0.387889i	$-0.126796\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$			6.01126i			0.685046i
$78$		0			0
$79$		−	2.98622i		−	0.335976i	−0.985789	−	0.167988i	$-0.946273\pi$
$79$		−	2.98622i		−	0.335976i	0.985789	−	0.167988i	$-0.0537271\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	8.94000			0.981293			0.490646	−	0.871359i	$-0.336761\pi$
$83$	8.94000			0.981293			0.490646	+	0.871359i	$0.336761\pi$
$84$		0			0
$85$	13.6325	+	5.61903i	1.47865	+	0.609469i
$86$		0			0
$87$		0			0
$88$		0			0
$89$			1.52146i			0.161275i	0.996744	+	0.0806374i	$0.0256956\pi$
$89$			1.52146i			0.161275i	−0.996744	+	0.0806374i	$0.974304\pi$
$90$		0			0
$91$	7.31155	−	7.31155i	0.766458	−	0.766458i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	1.41041	−	3.42185i	0.144705	−	0.351074i
$96$		0			0
$97$	−2.70455	+	2.70455i	−0.274606	+	0.274606i	−0.830951	−	0.556345i	$-0.812203\pi$
$97$	−2.70455	+	2.70455i	−0.274606	+	0.274606i	0.556345	+	0.830951i	$0.312203\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−7.23795	−	7.23795i	−0.720203	−	0.720203i	0.248444	−	0.968646i	$-0.420081\pi$
$101$	−7.23795	−	7.23795i	−0.720203	−	0.720203i	−0.968646	+	0.248444i	$0.920081\pi$
$102$		0			0
$103$	1.71115	−	1.71115i	0.168605	−	0.168605i	−0.617761	−	0.786366i	$-0.711960\pi$
$103$	1.71115	−	1.71115i	0.168605	−	0.168605i	0.786366	+	0.617761i	$0.211960\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	0.521715			0.0504361			0.0252181	−	0.999682i	$-0.491972\pi$
$107$	0.521715			0.0504361			0.0252181	+	0.999682i	$0.491972\pi$
$108$		0			0
$109$	0.131968	−	0.131968i	0.0126403	−	0.0126403i	−0.700758	−	0.713399i	$-0.747155\pi$
$109$	0.131968	−	0.131968i	0.0126403	−	0.0126403i	0.713399	+	0.700758i	$0.247155\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	11.5524	−	11.5524i	1.08676	−	1.08676i	0.0909020	−	0.995860i	$-0.471025\pi$
$113$	11.5524	−	11.5524i	1.08676	−	1.08676i	0.995860	−	0.0909020i	$-0.0289750\pi$
$114$		0			0
$115$	13.5613	+	5.58969i	1.26460	+	0.521241i
$116$		0			0
$117$		0			0
$118$		0			0
$119$		−	18.4117i		−	1.68779i
$120$		0			0
$121$		−	6.36477i		−	0.578615i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−4.22461	+	10.3515i	−0.377861	+	0.925862i
$126$		0			0
$127$	−5.08928	+	5.08928i	−0.451600	+	0.451600i	−0.895885	−	0.444285i	$-0.853458\pi$
$127$	−5.08928	+	5.08928i	−0.451600	+	0.451600i	0.444285	+	0.895885i	$0.353458\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−6.96146	+	6.96146i	−0.608226	+	0.608226i	−0.942482	−	0.334256i	$-0.891515\pi$
$131$	−6.96146	+	6.96146i	−0.608226	+	0.608226i	0.334256	+	0.942482i	$0.391515\pi$
$132$		0			0
$133$	−4.62145			−0.400730
$134$		0			0
$135$		0			0
$136$		0			0
$137$	14.8383	−	14.8383i	1.26772	−	1.26772i	0.320464	−	0.947261i	$-0.396161\pi$
$137$	14.8383	−	14.8383i	1.26772	−	1.26772i	0.947261	−	0.320464i	$-0.103839\pi$
$138$		0			0
$139$	−8.57852	−	8.57852i	−0.727621	−	0.727621i	0.242524	−	0.970145i	$-0.422025\pi$
$139$	−8.57852	−	8.57852i	−0.727621	−	0.727621i	−0.970145	+	0.242524i	$0.922025\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	5.63788	−	5.63788i	0.471463	−	0.471463i
$144$		0			0
$145$	−9.47694	−	3.90619i	−0.787017	−	0.324392i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	9.74262	−	9.74262i	0.798147	−	0.798147i	−0.184656	−	0.982803i	$-0.559117\pi$
$149$	9.74262	−	9.74262i	0.798147	−	0.798147i	0.982803	+	0.184656i	$0.0591172\pi$
$150$		0			0
$151$		−	8.00428i		−	0.651379i	−0.945477	−	0.325690i	$-0.894404\pi$
$151$		−	8.00428i		−	0.651379i	0.945477	−	0.325690i	$-0.105596\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	10.4606	−	4.35423i	0.840214	−	0.349740i
$156$		0			0
$157$	2.83837			0.226526			0.113263	−	0.993565i	$-0.463870\pi$
$157$	2.83837			0.226526			0.113263	+	0.993565i	$0.463870\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$		−	18.3155i		−	1.44347i
$162$		0			0
$163$		−	14.0835i		−	1.10311i	−0.834139	−	0.551554i	$-0.814035\pi$
$163$		−	14.0835i		−	1.10311i	0.834139	−	0.551554i	$-0.185965\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−13.4355	+	13.4355i	−1.03967	+	1.03967i	−0.0404913	+	0.999180i	$0.512892\pi$
$167$	−13.4355	+	13.4355i	−1.03967	+	1.03967i	−0.999180	+	0.0404913i	$0.987108\pi$
$168$		0			0
$169$	−0.714807			−0.0549852
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−25.2772			−1.92179			−0.960894	−	0.276917i	$-0.910687\pi$
$173$	−25.2772			−1.92179			−0.960894	+	0.276917i	$0.910687\pi$
$174$		0			0
$175$	13.9604	−	0.0485279i	1.05530	−	0.00366836i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−13.2067	−	13.2067i	−0.987116	−	0.987116i	0.0128018	−	0.999918i	$-0.495925\pi$
$179$	−13.2067	−	13.2067i	−0.987116	−	0.987116i	−0.999918	+	0.0128018i	$0.995925\pi$
$180$		0			0
$181$	11.1015	−	11.1015i	0.825166	−	0.825166i	−0.161677	−	0.986844i	$-0.551690\pi$
$181$	11.1015	−	11.1015i	0.825166	−	0.825166i	0.986844	+	0.161677i	$0.0516904\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	3.02517	+	7.26766i	0.222415	+	0.534329i
$186$		0			0
$187$		−	14.1971i		−	1.03819i
$188$		0			0
$189$		0			0
$190$		0			0
$191$		−	9.83969i		−	0.711975i	−0.934491	−	0.355988i	$-0.884145\pi$
$191$		−	9.83969i		−	0.711975i	0.934491	−	0.355988i	$-0.115855\pi$
$192$		0			0
$193$	4.87902	+	4.87902i	0.351199	+	0.351199i	0.860556	−	0.509356i	$-0.170116\pi$
$193$	4.87902	+	4.87902i	0.351199	+	0.351199i	−0.509356	+	0.860556i	$0.670116\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	8.82127			0.628489			0.314245	−	0.949342i	$-0.398249\pi$
$197$	8.82127			0.628489			0.314245	+	0.949342i	$0.398249\pi$
$198$		0			0
$199$	22.8224			1.61784			0.808920	−	0.587918i	$-0.200052\pi$
$199$	22.8224			1.61784			0.808920	+	0.587918i	$0.200052\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$			12.7993i			0.898333i
$204$		0			0
$205$	9.02615	−	3.75715i	0.630414	−	0.262411i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−3.56356			−0.246497
$210$		0			0
$211$	−9.21097	−	9.21097i	−0.634109	−	0.634109i	0.314987	−	0.949096i	$-0.398000\pi$
$211$	−9.21097	−	9.21097i	−0.634109	−	0.634109i	−0.949096	+	0.314987i	$0.898000\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−26.4698	+	11.0181i	−1.80523	+	0.751428i
$216$		0			0
$217$	−10.0042	−	10.0042i	−0.679131	−	0.679131i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−17.2681	+	17.2681i	−1.16157	+	1.16157i
$222$		0			0
$223$	4.77474	+	4.77474i	0.319740	+	0.319740i	0.848667	−	0.528927i	$-0.177406\pi$
$223$	4.77474	+	4.77474i	0.319740	+	0.319740i	−0.528927	+	0.848667i	$0.677406\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$			7.33280i			0.486695i	0.969939	+	0.243347i	$0.0782455\pi$
$227$			7.33280i			0.486695i	−0.969939	+	0.243347i	$0.921754\pi$
$228$		0			0
$229$	6.94434	+	6.94434i	0.458895	+	0.458895i	0.898293	−	0.439398i	$-0.144808\pi$
$229$	6.94434	+	6.94434i	0.458895	+	0.458895i	−0.439398	+	0.898293i	$0.644808\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	3.36566	+	3.36566i	0.220492	+	0.220492i	0.808705	−	0.588214i	$-0.200169\pi$
$233$	3.36566	+	3.36566i	0.220492	+	0.220492i	−0.588214	+	0.808705i	$0.700169\pi$
$234$		0			0
$235$	11.0206	+	4.54245i	0.718904	+	0.296317i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−11.7475			−0.759883			−0.379941	−	0.925011i	$-0.624056\pi$
$239$	−11.7475			−0.759883			−0.379941	+	0.925011i	$0.624056\pi$
$240$		0			0
$241$	−24.7007			−1.59111			−0.795556	−	0.605880i	$-0.792821\pi$
$241$	−24.7007			−1.59111			−0.795556	+	0.605880i	$0.792821\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−0.683796	−	1.64275i	−0.0436862	−	0.104951i
$246$		0			0
$247$	4.33439	+	4.33439i	0.275791	+	0.275791i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	7.75581	+	7.75581i	0.489543	+	0.489543i	0.908162	−	0.418619i	$-0.137486\pi$
$251$	7.75581	+	7.75581i	0.489543	+	0.489543i	−0.418619	+	0.908162i	$0.637486\pi$
$252$		0			0
$253$		−	14.1230i		−	0.887903i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−11.0995	−	11.0995i	−0.692368	−	0.692368i	0.270384	−	0.962752i	$-0.412849\pi$
$257$	−11.0995	−	11.0995i	−0.692368	−	0.692368i	−0.962752	+	0.270384i	$0.912849\pi$
$258$		0			0
$259$	6.95060	−	6.95060i	0.431889	−	0.431889i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	21.1725	+	21.1725i	1.30555	+	1.30555i	0.924592	+	0.380960i	$0.124406\pi$
$263$	21.1725	+	21.1725i	1.30555	+	1.30555i	0.380960	+	0.924592i	$0.375594\pi$
$264$		0			0
$265$	−2.83389	−	6.80813i	−0.174085	−	0.418220i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−6.52888	−	6.52888i	−0.398073	−	0.398073i	0.479480	−	0.877553i	$-0.340825\pi$
$269$	−6.52888	−	6.52888i	−0.398073	−	0.398073i	−0.877553	+	0.479480i	$0.840825\pi$
$270$		0			0
$271$	−16.3978			−0.996095			−0.498048	−	0.867150i	$-0.665950\pi$
$271$	−16.3978			−0.996095			−0.498048	+	0.867150i	$0.665950\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	10.7647	−	0.0374195i	0.649138	−	0.00225648i
$276$		0			0
$277$			12.0598i			0.724600i	0.932061	+	0.362300i	$0.118008\pi$
$277$			12.0598i			0.724600i	−0.932061	+	0.362300i	$0.881992\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	8.54283			0.509622			0.254811	−	0.966991i	$-0.417987\pi$
$281$	8.54283			0.509622			0.254811	+	0.966991i	$0.417987\pi$
$282$		0			0
$283$	5.50898			0.327475			0.163737	−	0.986504i	$-0.447645\pi$
$283$	5.50898			0.327475			0.163737	+	0.986504i	$0.447645\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−8.63237	−	8.63237i	−0.509553	−	0.509553i
$288$		0			0
$289$			26.4838i			1.55787i
$290$		0			0
$291$		0			0
$292$		0			0
$293$		−	1.99524i		−	0.116563i	−0.998300	−	0.0582817i	$-0.981438\pi$
$293$		−	1.99524i		−	0.116563i	0.998300	−	0.0582817i	$-0.0185621\pi$
$294$		0			0
$295$	−8.93662	+	21.6814i	−0.520310	+	1.26234i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−17.1779	+	17.1779i	−0.993423	+	0.993423i
$300$		0			0
$301$	25.3150	+	25.3150i	1.45913	+	1.45913i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−18.2445	−	7.52000i	−1.04468	−	0.430594i
$306$		0			0
$307$	−9.21709			−0.526047			−0.263023	−	0.964789i	$-0.584720\pi$
$307$	−9.21709			−0.526047			−0.263023	+	0.964789i	$0.584720\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−6.41473			−0.363746			−0.181873	−	0.983322i	$-0.558216\pi$
$311$	−6.41473			−0.363746			−0.181873	+	0.983322i	$0.558216\pi$
$312$		0			0
$313$	−2.73400	+	2.73400i	−0.154535	+	0.154535i	−0.780140	−	0.625605i	$-0.784852\pi$
$313$	−2.73400	+	2.73400i	−0.154535	+	0.154535i	0.625605	+	0.780140i	$0.284852\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$		−	15.6531i		−	0.879166i	−0.898202	−	0.439583i	$-0.855126\pi$
$317$		−	15.6531i		−	0.879166i	0.898202	−	0.439583i	$-0.144874\pi$
$318$		0			0
$319$			9.86942i			0.552582i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	10.9147			0.607311
$324$		0			0
$325$	−13.1388	−	13.0477i	−0.728807	−	0.723758i
$326$		0			0
$327$		0			0
$328$		0			0
$329$		−	14.8841i		−	0.820586i
$330$		0			0
$331$	12.7366	−	12.7366i	0.700068	−	0.700068i	−0.264357	−	0.964425i	$-0.585160\pi$
$331$	12.7366	−	12.7366i	0.700068	−	0.700068i	0.964425	+	0.264357i	$0.0851598\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	18.5669	−	7.72851i	1.01442	−	0.422254i
$336$		0			0
$337$	23.8642	−	23.8642i	1.29996	−	1.29996i	0.371551	−	0.928413i	$-0.378826\pi$
$337$	23.8642	−	23.8642i	1.29996	−	1.29996i	0.928413	−	0.371551i	$-0.121174\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−7.71418	−	7.71418i	−0.417746	−	0.417746i
$342$		0			0
$343$	12.2491	−	12.2491i	0.661387	−	0.661387i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	25.3323			1.35991			0.679954	−	0.733255i	$-0.262000\pi$
$347$	25.3323			1.35991			0.679954	+	0.733255i	$0.262000\pi$
$348$		0			0
$349$	−25.4548	+	25.4548i	−1.36256	+	1.36256i	−0.491928	+	0.870636i	$0.663708\pi$
$349$	−25.4548	+	25.4548i	−1.36256	+	1.36256i	−0.870636	+	0.491928i	$0.836292\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	7.85111	−	7.85111i	0.417872	−	0.417872i	−0.466597	−	0.884470i	$-0.654520\pi$
$353$	7.85111	−	7.85111i	0.417872	−	0.417872i	0.884470	+	0.466597i	$0.154520\pi$
$354$		0			0
$355$	15.4941	−	6.44945i	0.822343	−	0.342302i
$356$		0			0
$357$		0			0
$358$		0			0
$359$		−	17.1835i		−	0.906911i	−0.891279	−	0.453456i	$-0.850191\pi$
$359$		−	17.1835i		−	0.906911i	0.891279	−	0.453456i	$-0.149809\pi$
$360$		0			0
$361$			16.2603i			0.855807i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−13.4838	+	32.7134i	−0.705773	+	1.71230i
$366$		0			0
$367$	−15.8145	+	15.8145i	−0.825508	+	0.825508i	−0.986892	−	0.161383i	$-0.948404\pi$
$367$	−15.8145	+	15.8145i	−0.825508	+	0.825508i	0.161383	+	0.986892i	$0.448404\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−6.51111	+	6.51111i	−0.338040	+	0.338040i
$372$		0			0
$373$	−3.11111			−0.161087			−0.0805437	−	0.996751i	$-0.525666\pi$
$373$	−3.11111			−0.161087			−0.0805437	+	0.996751i	$0.525666\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	12.0043	−	12.0043i	0.618252	−	0.618252i
$378$		0			0
$379$	4.55542	+	4.55542i	0.233996	+	0.233996i	0.814358	−	0.580362i	$-0.197089\pi$
$379$	4.55542	+	4.55542i	0.233996	+	0.233996i	−0.580362	+	0.814358i	$0.697089\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	16.8633	−	16.8633i	0.861672	−	0.861672i	−0.129860	−	0.991532i	$-0.541453\pi$
$383$	16.8633	−	16.8633i	0.861672	−	0.861672i	0.991532	+	0.129860i	$0.0414529\pi$
$384$		0			0
$385$	−5.16544	−	12.4094i	−0.263255	−	0.632443i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−14.8244	+	14.8244i	−0.751625	+	0.751625i	−0.974783	−	0.223157i	$-0.928364\pi$
$389$	−14.8244	+	14.8244i	−0.751625	+	0.751625i	0.223157	+	0.974783i	$0.428364\pi$
$390$		0			0
$391$			43.2567i			2.18759i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	2.56605	+	6.16466i	0.129112	+	0.310178i
$396$		0			0
$397$	0.627408			0.0314887			0.0157444	−	0.999876i	$-0.494988\pi$
$397$	0.627408			0.0314887			0.0157444	+	0.999876i	$0.494988\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$			26.6452i			1.33060i	0.746577	+	0.665299i	$0.231696\pi$
$401$			26.6452i			1.33060i	−0.746577	+	0.665299i	$0.768304\pi$
$402$		0			0
$403$			18.7657i			0.934784i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	5.35955	−	5.35955i	0.265663	−	0.265663i
$408$		0			0
$409$	−39.3391			−1.94519			−0.972596	−	0.232501i	$-0.925309\pi$
$409$	−39.3391			−1.94519			−0.972596	+	0.232501i	$0.925309\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	29.2823			1.44089
$414$		0			0
$415$	−18.4554	+	7.68210i	−0.905942	+	0.377100i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	16.2482	+	16.2482i	0.793778	+	0.793778i	0.982106	−	0.188328i	$-0.0603068\pi$
$419$	16.2482	+	16.2482i	0.793778	+	0.793778i	−0.188328	+	0.982106i	$0.560307\pi$
$420$		0			0
$421$	2.81579	−	2.81579i	0.137233	−	0.137233i	−0.635153	−	0.772386i	$-0.719063\pi$
$421$	2.81579	−	2.81579i	0.137233	−	0.137233i	0.772386	+	0.635153i	$0.219063\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−32.9709	+	0.114611i	−1.59932	+	0.00555944i
$426$		0			0
$427$			24.6405i			1.19244i
$428$		0			0
$429$		0			0
$430$		0			0
$431$			2.59871i			0.125176i	0.998039	+	0.0625878i	$0.0199354\pi$
$431$			2.59871i			0.125176i	−0.998039	+	0.0625878i	$0.980065\pi$
$432$		0			0
$433$	0.804663	+	0.804663i	0.0386696	+	0.0386696i	0.726177	−	0.687508i	$-0.241295\pi$
$433$	0.804663	+	0.804663i	0.0386696	+	0.0386696i	−0.687508	+	0.726177i	$0.741295\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	10.8577			0.519395
$438$		0			0
$439$	−5.61073			−0.267786			−0.133893	−	0.990996i	$-0.542748\pi$
$439$	−5.61073			−0.267786			−0.133893	+	0.990996i	$0.542748\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$			20.9879i			0.997166i	0.866842	+	0.498583i	$0.166146\pi$
$443$			20.9879i			0.997166i	−0.866842	+	0.498583i	$0.833854\pi$
$444$		0			0
$445$	−1.30739	−	3.14086i	−0.0619761	−	0.148891i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	15.8025			0.745765			0.372882	−	0.927879i	$-0.378370\pi$
$449$	15.8025			0.745765			0.372882	+	0.927879i	$0.378370\pi$
$450$		0			0
$451$	−6.65636	−	6.65636i	−0.313436	−	0.313436i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−8.81094	+	21.3765i	−0.413063	+	1.00215i
$456$		0			0
$457$	−8.41973	−	8.41973i	−0.393858	−	0.393858i	0.482202	−	0.876060i	$-0.339837\pi$
$457$	−8.41973	−	8.41973i	−0.393858	−	0.393858i	−0.876060	+	0.482202i	$0.839837\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	11.1111	−	11.1111i	0.517494	−	0.517494i	−0.399318	−	0.916812i	$-0.630753\pi$
$461$	11.1111	−	11.1111i	0.517494	−	0.517494i	0.916812	+	0.399318i	$0.130753\pi$
$462$		0			0
$463$	−26.7079	−	26.7079i	−1.24122	−	1.24122i	−0.959495	−	0.281725i	$-0.909094\pi$
$463$	−26.7079	−	26.7079i	−1.24122	−	1.24122i	−0.281725	−	0.959495i	$-0.590906\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$		−	19.6860i		−	0.910959i	−0.890246	−	0.455479i	$-0.849468\pi$
$467$		−	19.6860i		−	0.910959i	0.890246	−	0.455479i	$-0.150532\pi$
$468$		0			0
$469$	−17.7569	−	17.7569i	−0.819938	−	0.819938i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	19.5202	+	19.5202i	0.897541	+	0.897541i
$474$		0			0
$475$	0.0287681	+	8.27591i	0.00131997	+	0.379725i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−18.5711			−0.848537			−0.424269	−	0.905536i	$-0.639469\pi$
$479$	−18.5711			−0.848537			−0.424269	+	0.905536i	$0.639469\pi$
$480$		0			0
$481$	−13.0377			−0.594470
$482$		0			0
$483$		0			0
$484$		0			0
$485$	3.25918	−	7.90720i	0.147992	−	0.359048i
$486$		0			0
$487$	−25.6817	−	25.6817i	−1.16375	−	1.16375i	−0.983648	−	0.180101i	$-0.942358\pi$
$487$	−25.6817	−	25.6817i	−1.16375	−	1.16375i	−0.180101	−	0.983648i	$-0.557642\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	16.6211	+	16.6211i	0.750099	+	0.750099i	0.974497	−	0.224399i	$-0.0720417\pi$
$491$	16.6211	+	16.6211i	0.750099	+	0.750099i	−0.224399	+	0.974497i	$0.572042\pi$
$492$		0			0
$493$		−	30.2287i		−	1.36143i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−14.8182	−	14.8182i	−0.664686	−	0.664686i
$498$		0			0
$499$	−18.5750	+	18.5750i	−0.831529	+	0.831529i	−0.987726	−	0.156197i	$-0.950077\pi$
$499$	−18.5750	+	18.5750i	−0.831529	+	0.831529i	0.156197	+	0.987726i	$0.450077\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	−7.11756	−	7.11756i	−0.317356	−	0.317356i	0.530395	−	0.847751i	$-0.322044\pi$
$503$	−7.11756	−	7.11756i	−0.317356	−	0.317356i	−0.847751	+	0.530395i	$0.822044\pi$
$504$		0			0
$505$	21.1613	+	8.72225i	0.941666	+	0.388135i
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−5.38935	−	5.38935i	−0.238879	−	0.238879i	0.577507	−	0.816386i	$-0.304026\pi$
$509$	−5.38935	−	5.38935i	−0.238879	−	0.238879i	−0.816386	+	0.577507i	$0.804026\pi$
$510$		0			0
$511$	44.1817			1.95449
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−2.06206	+	5.00283i	−0.0908652	+	0.220451i
$516$		0			0
$517$		−	11.4770i		−	0.504758i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	23.5261			1.03070			0.515350	−	0.856980i	$-0.327662\pi$
$521$	23.5261			1.03070			0.515350	+	0.856980i	$0.327662\pi$
$522$		0			0
$523$	−36.1853			−1.58227			−0.791136	−	0.611641i	$-0.790510\pi$
$523$	−36.1853			−1.58227			−0.791136	+	0.611641i	$0.790510\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	23.6275	+	23.6275i	1.02923	+	1.02923i
$528$		0			0
$529$			20.0309i			0.870907i
$530$		0			0
$531$		0			0
$532$		0			0
$533$			16.1924i			0.701370i
$534$		0			0
$535$	−1.07701	+	0.448308i	−0.0465633	+	0.0193820i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−1.21145	+	1.21145i	−0.0521808	+	0.0521808i
$540$		0			0
$541$	23.0946	+	23.0946i	0.992913	+	0.992913i	0.999975	−	0.00706245i	$-0.00224807\pi$
$541$	23.0946	+	23.0946i	0.992913	+	0.992913i	−0.00706245	+	0.999975i	$0.502248\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−0.159031	+	0.385830i	−0.00681215	+	0.0165272i
$546$		0			0
$547$	25.3781			1.08509			0.542545	−	0.840027i	$-0.317461\pi$
$547$	25.3781			1.08509			0.542545	+	0.840027i	$0.317461\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−7.58760			−0.323243
$552$		0			0
$553$	5.89572	−	5.89572i	0.250711	−	0.250711i
$554$		0			0
$555$		0			0
$556$		0			0
$557$		−	1.43606i		−	0.0608478i	−0.999537	−	0.0304239i	$-0.990314\pi$
$557$		−	1.43606i		−	0.0608478i	0.999537	−	0.0304239i	$-0.00968572\pi$
$558$		0			0
$559$		−	47.4853i		−	2.00841i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	27.4330			1.15616			0.578081	−	0.815979i	$-0.303802\pi$
$563$	27.4330			1.15616			0.578081	+	0.815979i	$0.303802\pi$
$564$		0			0
$565$	−13.9215	+	33.7754i	−0.585683	+	1.42094i
$566$		0			0
$567$		0			0
$568$		0			0
$569$		−	7.65652i		−	0.320978i	−0.987038	−	0.160489i	$-0.948693\pi$
$569$		−	7.65652i		−	0.320978i	0.987038	−	0.160489i	$-0.0513071\pi$
$570$		0			0
$571$	14.0799	−	14.0799i	0.589225	−	0.589225i	−0.348196	−	0.937422i	$-0.613206\pi$
$571$	14.0799	−	14.0799i	0.589225	−	0.589225i	0.937422	+	0.348196i	$0.113206\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−32.7988	+	0.114012i	−1.36780	+	0.00475465i
$576$		0			0
$577$	−11.9686	+	11.9686i	−0.498261	+	0.498261i	−0.910896	−	0.412635i	$-0.864608\pi$
$577$	−11.9686	+	11.9686i	−0.498261	+	0.498261i	0.412635	+	0.910896i	$0.364608\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	17.6503	+	17.6503i	0.732258	+	0.732258i
$582$		0			0
$583$	−5.02067	+	5.02067i	−0.207935	+	0.207935i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	19.1663			0.791079			0.395540	−	0.918449i	$-0.370558\pi$
$587$	19.1663			0.791079			0.395540	+	0.918449i	$0.370558\pi$
$588$		0			0
$589$	5.93065	−	5.93065i	0.244368	−	0.244368i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	6.90109	−	6.90109i	0.283394	−	0.283394i	−0.551067	−	0.834461i	$-0.685779\pi$
$593$	6.90109	−	6.90109i	0.283394	−	0.283394i	0.834461	+	0.551067i	$0.185779\pi$
$594$		0			0
$595$	15.8211	+	38.0084i	0.648600	+	1.55819i
$596$		0			0
$597$		0			0
$598$		0			0
$599$			4.11930i			0.168310i	0.996453	+	0.0841551i	$0.0268191\pi$
$599$			4.11930i			0.168310i	−0.996453	+	0.0841551i	$0.973181\pi$
$600$		0			0
$601$			11.3938i			0.464765i	0.972625	+	0.232382i	$0.0746520\pi$
$601$			11.3938i			0.464765i	−0.972625	+	0.232382i	$0.925348\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	5.46921	+	13.1392i	0.222355	+	0.534185i
$606$		0			0
$607$	−5.12592	+	5.12592i	−0.208055	+	0.208055i	−0.803440	−	0.595385i	$-0.796999\pi$
$607$	−5.12592	+	5.12592i	−0.208055	+	0.208055i	0.595385	+	0.803440i	$0.296999\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−13.9596	+	13.9596i	−0.564744	+	0.564744i
$612$		0			0
$613$	−32.8335			−1.32613			−0.663067	−	0.748560i	$-0.730746\pi$
$613$	−32.8335			−1.32613			−0.663067	+	0.748560i	$0.730746\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−2.59691	+	2.59691i	−0.104548	+	0.104548i	−0.757446	−	0.652898i	$-0.773553\pi$
$617$	−2.59691	+	2.59691i	−0.104548	+	0.104548i	0.652898	+	0.757446i	$0.273553\pi$
$618$		0			0
$619$	−30.2892	−	30.2892i	−1.21743	−	1.21743i	−0.968530	−	0.248895i	$-0.919932\pi$
$619$	−30.2892	−	30.2892i	−1.21743	−	1.21743i	−0.248895	−	0.968530i	$-0.580068\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−3.00383	+	3.00383i	−0.120346	+	0.120346i
$624$		0			0
$625$	−0.173804	−	24.9994i	−0.00695216	−	0.999976i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−16.4156	+	16.4156i	−0.654532	+	0.654532i
$630$		0			0
$631$			46.6095i			1.85550i	0.373207	+	0.927748i	$0.378258\pi$
$631$			46.6095i			1.85550i	−0.373207	+	0.927748i	$0.621742\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	6.13294	−	14.8793i	0.243378	−	0.590468i
$636$		0			0
$637$	2.94699			0.116764
$638$		0			0
$639$		0			0
$640$		0			0
$641$			35.4584i			1.40052i	0.713886	+	0.700262i	$0.246934\pi$
$641$			35.4584i			1.40052i	−0.713886	+	0.700262i	$0.753066\pi$
$642$		0			0
$643$		−	5.53739i		−	0.218373i	−0.994021	−	0.109187i	$-0.965175\pi$
$643$		−	5.53739i		−	0.218373i	0.994021	−	0.109187i	$-0.0348246\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	14.5843	−	14.5843i	0.573367	−	0.573367i	−0.359701	−	0.933068i	$-0.617121\pi$
$647$	14.5843	−	14.5843i	0.573367	−	0.573367i	0.933068	+	0.359701i	$0.117121\pi$
$648$		0			0
$649$	22.5793			0.886317
$650$		0			0
$651$		0			0
$652$		0			0
$653$	27.2776			1.06746			0.533728	−	0.845656i	$-0.320791\pi$
$653$	27.2776			1.06746			0.533728	+	0.845656i	$0.320791\pi$
$654$		0			0
$655$	8.38906	−	20.3530i	0.327788	−	0.795256i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−30.1019	−	30.1019i	−1.17260	−	1.17260i	−0.981587	−	0.191015i	$-0.938822\pi$
$659$	−30.1019	−	30.1019i	−1.17260	−	1.17260i	−0.191015	−	0.981587i	$-0.561178\pi$
$660$		0			0
$661$	−7.68215	+	7.68215i	−0.298801	+	0.298801i	−0.840544	−	0.541743i	$-0.817765\pi$
$661$	−7.68215	+	7.68215i	−0.298801	+	0.298801i	0.541743	+	0.840544i	$0.317765\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	9.54036	−	3.97119i	0.369959	−	0.153996i
$666$		0			0
$667$		−	30.0709i		−	1.16435i
$668$		0			0
$669$		0			0
$670$		0			0
$671$			19.0001i			0.733491i
$672$		0			0
$673$	−20.7076	−	20.7076i	−0.798219	−	0.798219i	0.184596	−	0.982815i	$-0.440902\pi$
$673$	−20.7076	−	20.7076i	−0.798219	−	0.798219i	−0.982815	+	0.184596i	$0.940902\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	8.15198			0.313306			0.156653	−	0.987654i	$-0.449930\pi$
$677$	8.15198			0.313306			0.156653	+	0.987654i	$0.449930\pi$
$678$		0			0
$679$	−10.6792			−0.409831
$680$		0			0
$681$		0			0
$682$		0			0
$683$		−	8.82735i		−	0.337769i	−0.985636	−	0.168885i	$-0.945983\pi$
$683$		−	8.82735i		−	0.337769i	0.985636	−	0.168885i	$-0.0540165\pi$
$684$		0			0
$685$	−17.8813	+	43.3823i	−0.683208	+	1.65755i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	12.2134			0.465293
$690$		0			0
$691$	−12.1439	−	12.1439i	−0.461977	−	0.461977i	0.437326	−	0.899303i	$-0.355925\pi$
$691$	−12.1439	−	12.1439i	−0.461977	−	0.461977i	−0.899303	+	0.437326i	$0.855925\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	25.0807	+	10.3377i	0.951365	+	0.392133i
$696$		0			0
$697$	20.3875	+	20.3875i	0.772232	+	0.772232i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	6.05830	−	6.05830i	0.228819	−	0.228819i	−0.583380	−	0.812199i	$-0.698270\pi$
$701$	6.05830	−	6.05830i	0.228819	−	0.228819i	0.812199	+	0.583380i	$0.198270\pi$
$702$		0			0
$703$	4.12042	+	4.12042i	0.155405	+	0.155405i
$704$		0			0
$705$		0			0
$706$		0			0
$707$		−	28.5798i		−	1.07486i
$708$		0			0
$709$	−6.73535	−	6.73535i	−0.252951	−	0.252951i	0.569228	−	0.822180i	$-0.307242\pi$
$709$	−6.73535	−	6.73535i	−0.252951	−	0.252951i	−0.822180	+	0.569228i	$0.807242\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	23.5041	+	23.5041i	0.880236	+	0.880236i
$714$		0			0
$715$	−6.79405	+	16.4833i	−0.254083	+	0.616439i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−26.2837			−0.980216			−0.490108	−	0.871662i	$-0.663043\pi$
$719$	−26.2837			−0.980216			−0.490108	+	0.871662i	$0.663043\pi$
$720$		0			0
$721$	6.75667			0.251632
$722$		0			0
$723$		0			0
$724$		0			0
$725$	22.9205	−	0.0796743i	0.851245	−	0.00295903i
$726$		0			0
$727$	−29.4159	−	29.4159i	−1.09098	−	1.09098i	−0.995425	−	0.0955506i	$-0.969539\pi$
$727$	−29.4159	−	29.4159i	−1.09098	−	1.09098i	−0.0955506	−	0.995425i	$-0.530461\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−59.7878	−	59.7878i	−2.21133	−	2.21133i
$732$		0			0
$733$			19.9106i			0.735414i	0.929942	+	0.367707i	$0.119857\pi$
$733$			19.9106i			0.735414i	−0.929942	+	0.367707i	$0.880143\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−13.6922	−	13.6922i	−0.504360	−	0.504360i
$738$		0			0
$739$	−22.6162	+	22.6162i	−0.831949	+	0.831949i	−0.987783	−	0.155834i	$-0.950193\pi$
$739$	−22.6162	+	22.6162i	−0.831949	+	0.831949i	0.155834	+	0.987783i	$0.450193\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	5.62161	+	5.62161i	0.206237	+	0.206237i	0.802666	−	0.596429i	$-0.203414\pi$
$743$	5.62161	+	5.62161i	0.206237	+	0.206237i	−0.596429	+	0.802666i	$0.703414\pi$
$744$		0			0
$745$	−11.7406	+	28.4841i	−0.430141	+	1.04358i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	1.03003	+	1.03003i	0.0376363	+	0.0376363i
$750$		0			0
$751$	−46.4798			−1.69607			−0.848037	−	0.529938i	$-0.822215\pi$
$751$	−46.4798			−1.69607			−0.848037	+	0.529938i	$0.822215\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	6.87805	+	16.5238i	0.250318	+	0.601362i
$756$		0			0
$757$			9.88789i			0.359381i	0.983723	+	0.179691i	$0.0575097\pi$
$757$			9.88789i			0.359381i	−0.983723	+	0.179691i	$0.942490\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−19.0787			−0.691601			−0.345800	−	0.938308i	$-0.612393\pi$
$761$	−19.0787			−0.691601			−0.345800	+	0.938308i	$0.612393\pi$
$762$		0			0
$763$	0.521091			0.0188648
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−27.4635	−	27.4635i	−0.991648	−	0.991648i
$768$		0			0
$769$			2.45553i			0.0885488i	0.999019	+	0.0442744i	$0.0140976\pi$
$769$			2.45553i			0.0885488i	−0.999019	+	0.0442744i	$0.985902\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$			47.7795i			1.71851i	0.511548	+	0.859255i	$0.329072\pi$
$773$			47.7795i			1.71851i	−0.511548	+	0.859255i	$0.670928\pi$
$774$		0			0
$775$	−17.8529	+	17.9775i	−0.641295	+	0.645769i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	5.11740	−	5.11740i	0.183350	−	0.183350i
$780$		0			0
$781$	−11.4262	−	11.4262i	−0.408861	−	0.408861i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−5.85943	+	2.43900i	−0.209132	+	0.0870515i
$786$		0			0
$787$	−23.8622			−0.850595			−0.425297	−	0.905054i	$-0.639830\pi$
$787$	−23.8622			−0.850595			−0.425297	+	0.905054i	$0.639830\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	45.6161			1.62192
$792$		0			0
$793$	23.1100	−	23.1100i	0.820660	−	0.820660i
$794$		0			0
$795$		0			0
$796$		0			0
$797$			34.4506i			1.22030i	0.792284	+	0.610152i	$0.208892\pi$
$797$			34.4506i			1.22030i	−0.792284	+	0.610152i	$0.791108\pi$
$798$		0			0
$799$			35.1525i			1.24361i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	34.0682			1.20224
$804$		0			0
$805$	15.7384	+	37.8100i	0.554707	+	1.33263i
$806$		0			0
$807$		0			0
$808$		0			0
$809$			17.9062i			0.629547i	0.949167	+	0.314774i	$0.101929\pi$
$809$			17.9062i			0.629547i	−0.949167	+	0.314774i	$0.898071\pi$
$810$		0			0
$811$	−34.4309	+	34.4309i	−1.20903	+	1.20903i	−0.237690	+	0.971341i	$0.576390\pi$
$811$	−34.4309	+	34.4309i	−1.20903	+	1.20903i	−0.971341	+	0.237690i	$0.923610\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	12.1019	+	29.0736i	0.423911	+	1.01840i
$816$		0			0
$817$	−15.0071	+	15.0071i	−0.525033	+	0.525033i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−25.6054	−	25.6054i	−0.893633	−	0.893633i	0.101230	−	0.994863i	$-0.467722\pi$
$821$	−25.6054	−	25.6054i	−0.893633	−	0.893633i	−0.994863	+	0.101230i	$0.967722\pi$
$822$		0			0
$823$	23.3949	−	23.3949i	0.815496	−	0.815496i	−0.169956	−	0.985452i	$-0.554362\pi$
$823$	23.3949	−	23.3949i	0.815496	−	0.815496i	0.985452	+	0.169956i	$0.0543625\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−10.2367			−0.355966			−0.177983	−	0.984034i	$-0.556957\pi$
$827$	−10.2367			−0.355966			−0.177983	+	0.984034i	$0.556957\pi$
$828$		0			0
$829$	18.0390	−	18.0390i	0.626522	−	0.626522i	−0.320669	−	0.947191i	$-0.603908\pi$
$829$	18.0390	−	18.0390i	0.626522	−	0.626522i	0.947191	+	0.320669i	$0.103908\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	3.71050	−	3.71050i	0.128561	−	0.128561i
$834$		0			0
$835$	16.1908	−	39.2809i	0.560304	−	1.35937i
$836$		0			0
$837$		0			0
$838$		0			0
$839$		−	4.00169i		−	0.138154i	−0.997611	−	0.0690768i	$-0.977995\pi$
$839$		−	4.00169i		−	0.138154i	0.997611	−	0.0690768i	$-0.0220053\pi$
$840$		0			0
$841$		−	7.98584i		−	0.275374i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	1.47562	−	0.614231i	0.0507630	−	0.0211302i
$846$		0			0
$847$	12.5660	−	12.5660i	0.431773	−	0.431773i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−16.3299	+	16.3299i	−0.559781	+	0.559781i
$852$		0			0
$853$	35.2425			1.20668			0.603341	−	0.797483i	$-0.293836\pi$
$853$	35.2425			1.20668			0.603341	+	0.797483i	$0.293836\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−30.7194	+	30.7194i	−1.04936	+	1.04936i	−0.0506380	+	0.998717i	$0.516125\pi$
$857$	−30.7194	+	30.7194i	−1.04936	+	1.04936i	−0.998717	+	0.0506380i	$0.983875\pi$
$858$		0			0
$859$	9.92233	+	9.92233i	0.338545	+	0.338545i	0.855820	−	0.517274i	$-0.173053\pi$
$859$	9.92233	+	9.92233i	0.338545	+	0.338545i	−0.517274	+	0.855820i	$0.673053\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	1.61844	−	1.61844i	0.0550922	−	0.0550922i	−0.679024	−	0.734116i	$-0.737597\pi$
$863$	1.61844	−	1.61844i	0.0550922	−	0.0550922i	0.734116	+	0.679024i	$0.237597\pi$
$864$		0			0
$865$	52.1814	−	21.7206i	1.77422	−	0.738521i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	4.54614	−	4.54614i	0.154217	−	0.154217i
$870$		0			0
$871$			33.3080i			1.12860i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−28.7776	+	12.0963i	−0.972861	+	0.408928i
$876$		0			0
$877$	−25.1184			−0.848189			−0.424094	−	0.905618i	$-0.639408\pi$
$877$	−25.1184			−0.848189			−0.424094	+	0.905618i	$0.639408\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$			9.75591i			0.328685i	0.986403	+	0.164343i	$0.0525502\pi$
$881$			9.75591i			0.328685i	−0.986403	+	0.164343i	$0.947450\pi$
$882$		0			0
$883$			54.5578i			1.83602i	0.396562	+	0.918008i	$0.370203\pi$
$883$			54.5578i			1.83602i	−0.396562	+	0.918008i	$0.629797\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	8.67468	−	8.67468i	0.291267	−	0.291267i	−0.546314	−	0.837581i	$-0.683969\pi$
$887$	8.67468	−	8.67468i	0.291267	−	0.291267i	0.837581	+	0.546314i	$0.183969\pi$
$888$		0			0
$889$	−20.0956			−0.673984
$890$		0			0
$891$		0			0
$892$		0			0
$893$	8.82350			0.295267
$894$		0			0
$895$	38.6120	+	15.9150i	1.29066	+	0.531981i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−16.4252	−	16.4252i	−0.547810	−	0.547810i
$900$		0			0
$901$	15.3776	−	15.3776i	0.512303	−	0.512303i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−13.3781	+	32.4570i	−0.444702	+	1.07891i
$906$		0			0
$907$			33.1587i			1.10102i	0.834830	+	0.550508i	$0.185566\pi$
$907$			33.1587i			1.10102i	−0.834830	+	0.550508i	$0.814434\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$			38.6741i			1.28133i	0.767820	+	0.640666i	$0.221342\pi$
$911$			38.6741i			1.28133i	−0.767820	+	0.640666i	$0.778658\pi$
$912$		0			0
$913$	13.6100	+	13.6100i	0.450426	+	0.450426i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−27.4881			−0.907738
$918$		0			0
$919$	14.4705			0.477338			0.238669	−	0.971101i	$-0.423289\pi$
$919$	14.4705			0.477338			0.238669	+	0.971101i	$0.423289\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$			27.7956i			0.914902i
$924$		0			0
$925$	−12.4901	−	12.4036i	−0.410673	−	0.407828i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	11.9782			0.392992			0.196496	−	0.980505i	$-0.437044\pi$
$929$	11.9782			0.392992			0.196496	+	0.980505i	$0.437044\pi$
$930$		0			0
$931$	−0.931361	−	0.931361i	−0.0305241	−	0.0305241i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	12.1995	+	29.3080i	0.398966	+	0.958474i
$936$		0			0
$937$	1.06459	+	1.06459i	0.0347786	+	0.0347786i	0.724282	−	0.689504i	$-0.242171\pi$
$937$	1.06459	+	1.06459i	0.0347786	+	0.0347786i	−0.689504	+	0.724282i	$0.742171\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	30.6748	−	30.6748i	0.999970	−	0.999970i	−3.02358e−5	−	1.00000i	$-0.500010\pi$
$941$	30.6748	−	30.6748i	0.999970	−	0.999970i	1.00000		3.02358e-5i	$9.62437e-6\pi$
$942$		0			0
$943$	20.2811	+	20.2811i	0.660442	+	0.660442i
$944$		0			0
$945$		0			0
$946$		0			0
$947$		−	16.9667i		−	0.551342i	−0.961252	−	0.275671i	$-0.911100\pi$
$947$		−	16.9667i		−	0.551342i	0.961252	−	0.275671i	$-0.0889001\pi$
$948$		0			0
$949$	−41.4375	−	41.4375i	−1.34512	−	1.34512i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−0.216854	−	0.216854i	−0.00702459	−	0.00702459i	0.703586	−	0.710610i	$-0.251581\pi$
$953$	−0.216854	−	0.216854i	−0.00702459	−	0.00702459i	−0.710610	+	0.703586i	$0.751581\pi$
$954$		0			0
$955$	8.45520	+	20.3127i	0.273604	+	0.657305i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	58.5908			1.89200
$960$		0			0
$961$	−5.32339			−0.171722
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−14.2646	−	5.87957i	−0.459194	−	0.189270i
$966$		0			0
$967$	−24.0925	−	24.0925i	−0.774763	−	0.774763i	0.204172	−	0.978935i	$-0.434550\pi$
$967$	−24.0925	−	24.0925i	−0.774763	−	0.774763i	−0.978935	+	0.204172i	$0.934550\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	2.86886	+	2.86886i	0.0920660	+	0.0920660i	0.751640	−	0.659574i	$-0.229263\pi$
$971$	2.86886	+	2.86886i	0.0920660	+	0.0920660i	−0.659574	+	0.751640i	$0.729263\pi$
$972$		0			0
$973$		−	33.8732i		−	1.08593i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	30.6283	+	30.6283i	0.979886	+	0.979886i	0.999802	−	0.0199158i	$-0.00633982\pi$
$977$	30.6283	+	30.6283i	0.979886	+	0.979886i	−0.0199158	+	0.999802i	$0.506340\pi$
$978$		0			0
$979$	−2.31623	+	2.31623i	−0.0740271	+	0.0740271i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−43.5282	−	43.5282i	−1.38833	−	1.38833i	−0.828821	−	0.559513i	$-0.810988\pi$
$983$	−43.5282	−	43.5282i	−1.38833	−	1.38833i	−0.559513	−	0.828821i	$-0.689012\pi$
$984$		0			0
$985$	−18.2103	+	7.58008i	−0.580230	+	0.241521i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−59.4756	−	59.4756i	−1.89122	−	1.89122i
$990$		0			0
$991$	13.7500			0.436782			0.218391	−	0.975861i	$-0.429919\pi$
$991$	13.7500			0.436782			0.218391	+	0.975861i	$0.429919\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−47.1139	+	19.6112i	−1.49361	+	0.621718i
$996$		0			0
$997$			44.4639i			1.40819i	0.710108	+	0.704093i	$0.248646\pi$
$997$			44.4639i			1.40819i	−0.710108	+	0.704093i	$0.751354\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2880.2.bc.a.593.5		96
3.2	odd	2	inner	2880.2.bc.a.593.44		96
4.3	odd	2		720.2.bc.a.413.42	yes	96
5.2	odd	4		2880.2.bg.a.17.29		96
12.11	even	2		720.2.bc.a.413.7	yes	96
15.2	even	4		2880.2.bg.a.17.20		96
16.5	even	4		2880.2.bg.a.2033.20		96
16.11	odd	4		720.2.bg.a.53.18	yes	96
20.7	even	4		720.2.bg.a.557.31	yes	96
48.5	odd	4		2880.2.bg.a.2033.29		96
48.11	even	4		720.2.bg.a.53.31	yes	96
60.47	odd	4		720.2.bg.a.557.18	yes	96
80.27	even	4		720.2.bc.a.197.7	✓	96
80.37	odd	4	inner	2880.2.bc.a.1457.44		96
240.107	odd	4		720.2.bc.a.197.42	yes	96
240.197	even	4	inner	2880.2.bc.a.1457.5		96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
720.2.bc.a.197.7	✓	96	80.27	even	4
720.2.bc.a.197.42	yes	96	240.107	odd	4
720.2.bc.a.413.7	yes	96	12.11	even	2
720.2.bc.a.413.42	yes	96	4.3	odd	2
720.2.bg.a.53.18	yes	96	16.11	odd	4
720.2.bg.a.53.31	yes	96	48.11	even	4
720.2.bg.a.557.18	yes	96	60.47	odd	4
720.2.bg.a.557.31	yes	96	20.7	even	4
2880.2.bc.a.593.5		96	1.1	even	1	trivial
2880.2.bc.a.593.44		96	3.2	odd	2	inner
2880.2.bc.a.1457.5		96	240.197	even	4	inner
2880.2.bc.a.1457.44		96	80.37	odd	4	inner
2880.2.bg.a.17.20		96	15.2	even	4
2880.2.bg.a.17.29		96	5.2	odd	4
2880.2.bg.a.2033.20		96	16.5	even	4
2880.2.bg.a.2033.29		96	48.5	odd	4

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.bc (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-2.06437 + 0.859295i) q^{5} +(1.97431 + 1.97431i) q^{7} +O(q^{10})\)	\(q+(-2.06437 + 0.859295i) q^{5} +(1.97431 + 1.97431i) q^{7} +(1.52237 + 1.52237i) q^{11} -3.70335i q^{13} +(-4.66282 - 4.66282i) q^{17} +(-1.17040 + 1.17040i) q^{19} +(-4.63847 - 4.63847i) q^{23} +(3.52322 - 3.54780i) q^{25} +(3.24146 + 3.24146i) q^{29} -5.06721 q^{31} +(-5.77220 - 2.37918i) q^{35} -3.52053i q^{37} -4.37236 q^{41} +12.8222 q^{43} +(-3.76945 - 3.76945i) q^{47} +0.795764i q^{49} +3.29793i q^{53} +(-4.45090 - 1.83457i) q^{55} +(7.41584 - 7.41584i) q^{59} +(6.24030 + 6.24030i) q^{61} +(3.18227 + 7.64508i) q^{65} -8.99401 q^{67} -7.50552 q^{71} +(11.1892 - 11.1892i) q^{73} +6.01126i q^{77} -2.98622i q^{79} +8.94000 q^{83} +(13.6325 + 5.61903i) q^{85} +1.52146i q^{89} +(7.31155 - 7.31155i) q^{91} +(1.41041 - 3.42185i) q^{95} +(-2.70455 + 2.70455i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q+O(q^{10}) \) 96 * q	\( 96 q - 16 q^{19} - 64 q^{43} + 32 q^{61}+O(q^{100}) \) 96 * q - 16 * q^19 - 64 * q^43 + 32 * q^61

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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