LMFDB - Embedded newform 2880.2.bc.a.593.13

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			593.13
Character	$\chi$	$=$	2880.593
Dual form			2880.2.bc.a.1457.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.58807 - 1.57418i) q^{5} +(0.639411 + 0.639411i) q^{7} +O(q^{10})$	$q+(-1.58807 - 1.57418i) q^{5} +(0.639411 + 0.639411i) q^{7} +(1.32678 + 1.32678i) q^{11} +2.79581i q^{13} +(-1.99881 - 1.99881i) q^{17} +(4.39064 - 4.39064i) q^{19} +(-0.267176 - 0.267176i) q^{23} +(0.0439101 + 4.99981i) q^{25} +(1.05561 + 1.05561i) q^{29} -0.396013 q^{31} +(-0.00887869 - 2.02198i) q^{35} +8.19136i q^{37} -3.06941 q^{41} +3.93867 q^{43} +(-3.17684 - 3.17684i) q^{47} -6.18231i q^{49} +0.726400i q^{53} +(-0.0184233 - 4.19561i) q^{55} +(0.0466833 - 0.0466833i) q^{59} +(6.47373 + 6.47373i) q^{61} +(4.40111 - 4.43993i) q^{65} +14.4133 q^{67} +14.8770 q^{71} +(-9.00914 + 9.00914i) q^{73} +1.69672i q^{77} +12.8253i q^{79} +4.07140 q^{83} +(0.0277549 + 6.32073i) q^{85} -13.6250i q^{89} +(-1.78767 + 1.78767i) q^{91} +(-13.8843 + 0.0609673i) q^{95} +(4.98317 - 4.98317i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$5$	−1.58807	−	1.57418i	−0.710205	−	0.703995i
$5$	−1.58807	−	1.57418i	−0.710205	−	0.703995i
$6$		0			0
$7$	0.639411	+	0.639411i	0.241675	+	0.241675i	0.817543	−	0.575868i	$-0.195336\pi$
$7$	0.639411	+	0.639411i	0.241675	+	0.241675i	−0.575868	+	0.817543i	$0.695336\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	1.32678	+	1.32678i	0.400040	+	0.400040i	0.878247	−	0.478207i	$-0.158713\pi$
$11$	1.32678	+	1.32678i	0.400040	+	0.400040i	−0.478207	+	0.878247i	$0.658713\pi$
$12$		0			0
$13$			2.79581i			0.775419i	0.921782	+	0.387709i	$0.126734\pi$
$13$			2.79581i			0.775419i	−0.921782	+	0.387709i	$0.873266\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−1.99881	−	1.99881i	−0.484782	−	0.484782i	0.421873	−	0.906655i	$-0.361373\pi$
$17$	−1.99881	−	1.99881i	−0.484782	−	0.484782i	−0.906655	+	0.421873i	$0.861373\pi$
$18$		0			0
$19$	4.39064	−	4.39064i	1.00728	−	1.00728i	0.00730858	−	0.999973i	$-0.497674\pi$
$19$	4.39064	−	4.39064i	1.00728	−	1.00728i	0.999973	−	0.00730858i	$-0.00232641\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−0.267176	−	0.267176i	−0.0557101	−	0.0557101i	0.678703	−	0.734413i	$-0.262542\pi$
$23$	−0.267176	−	0.267176i	−0.0557101	−	0.0557101i	−0.734413	+	0.678703i	$0.762542\pi$
$24$		0			0
$25$	0.0439101	+	4.99981i	0.00878203	+	0.999961i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	1.05561	+	1.05561i	0.196022	+	0.196022i	0.798292	−	0.602270i	$-0.205737\pi$
$29$	1.05561	+	1.05561i	0.196022	+	0.196022i	−0.602270	+	0.798292i	$0.705737\pi$
$30$		0			0
$31$	−0.396013			−0.0711260			−0.0355630	−	0.999367i	$-0.511322\pi$
$31$	−0.396013			−0.0711260			−0.0355630	+	0.999367i	$0.511322\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−0.00887869	−	2.02198i	−0.00150077	−	0.341776i
$36$		0			0
$37$			8.19136i			1.34665i	0.739346	+	0.673325i	$0.235135\pi$
$37$			8.19136i			1.34665i	−0.739346	+	0.673325i	$0.764865\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−3.06941			−0.479362			−0.239681	−	0.970852i	$-0.577043\pi$
$41$	−3.06941			−0.479362			−0.239681	+	0.970852i	$0.577043\pi$
$42$		0			0
$43$	3.93867			0.600641			0.300320	−	0.953838i	$-0.402906\pi$
$43$	3.93867			0.600641			0.300320	+	0.953838i	$0.402906\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−3.17684	−	3.17684i	−0.463390	−	0.463390i	0.436375	−	0.899765i	$-0.356262\pi$
$47$	−3.17684	−	3.17684i	−0.463390	−	0.463390i	−0.899765	+	0.436375i	$0.856262\pi$
$48$		0			0
$49$		−	6.18231i		−	0.883187i
$50$		0			0
$51$		0			0
$52$		0			0
$53$			0.726400i			0.0997787i	0.998755	+	0.0498894i	$0.0158869\pi$
$53$			0.726400i			0.0997787i	−0.998755	+	0.0498894i	$0.984113\pi$
$54$		0			0
$55$	−0.0184233	−	4.19561i	−0.00248420	−	0.565736i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	0.0466833	−	0.0466833i	0.00607764	−	0.00607764i	−0.704061	−	0.710139i	$-0.748632\pi$
$59$	0.0466833	−	0.0466833i	0.00607764	−	0.00607764i	0.710139	+	0.704061i	$0.248632\pi$
$60$		0			0
$61$	6.47373	+	6.47373i	0.828877	+	0.828877i	0.987361	−	0.158485i	$-0.0506609\pi$
$61$	6.47373	+	6.47373i	0.828877	+	0.828877i	−0.158485	+	0.987361i	$0.550661\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	4.40111	−	4.43993i	0.545891	−	0.550706i
$66$		0			0
$67$	14.4133			1.76087			0.880434	−	0.474169i	$-0.157251\pi$
$67$	14.4133			1.76087			0.880434	+	0.474169i	$0.157251\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	14.8770			1.76558			0.882788	−	0.469772i	$-0.155664\pi$
$71$	14.8770			1.76558			0.882788	+	0.469772i	$0.155664\pi$
$72$		0			0
$73$	−9.00914	+	9.00914i	−1.05444	+	1.05444i	−0.0560094	+	0.998430i	$0.517838\pi$
$73$	−9.00914	+	9.00914i	−1.05444	+	1.05444i	−0.998430	+	0.0560094i	$0.982162\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$			1.69672i			0.193359i
$78$		0			0
$79$			12.8253i			1.44296i	0.692436	+	0.721480i	$0.256538\pi$
$79$			12.8253i			1.44296i	−0.692436	+	0.721480i	$0.743462\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	4.07140			0.446894			0.223447	−	0.974716i	$-0.428269\pi$
$83$	4.07140			0.446894			0.223447	+	0.974716i	$0.428269\pi$
$84$		0			0
$85$	0.0277549	+	6.32073i	0.00301045	+	0.685579i
$86$		0			0
$87$		0			0
$88$		0			0
$89$		−	13.6250i		−	1.44424i	−0.691767	−	0.722121i	$-0.743167\pi$
$89$		−	13.6250i		−	1.44424i	0.691767	−	0.722121i	$-0.256833\pi$
$90$		0			0
$91$	−1.78767	+	1.78767i	−0.187399	+	0.187399i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−13.8843	+	0.0609673i	−1.42450	+	0.00625511i
$96$		0			0
$97$	4.98317	−	4.98317i	0.505965	−	0.505965i	−0.407321	−	0.913285i	$-0.633537\pi$
$97$	4.98317	−	4.98317i	0.505965	−	0.505965i	0.913285	+	0.407321i	$0.133537\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−0.184452	−	0.184452i	−0.0183536	−	0.0183536i	0.697870	−	0.716224i	$-0.254131\pi$
$101$	−0.184452	−	0.184452i	−0.0183536	−	0.0183536i	−0.716224	+	0.697870i	$0.754131\pi$
$102$		0			0
$103$	−2.55342	+	2.55342i	−0.251596	+	0.251596i	−0.821625	−	0.570029i	$-0.806932\pi$
$103$	−2.55342	+	2.55342i	−0.251596	+	0.251596i	0.570029	+	0.821625i	$0.306932\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	18.4866			1.78716			0.893581	−	0.448901i	$-0.148185\pi$
$107$	18.4866			1.78716			0.893581	+	0.448901i	$0.148185\pi$
$108$		0			0
$109$	14.6471	−	14.6471i	1.40293	−	1.40293i	0.612339	−	0.790596i	$-0.290229\pi$
$109$	14.6471	−	14.6471i	1.40293	−	1.40293i	0.790596	−	0.612339i	$-0.209771\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−4.92200	+	4.92200i	−0.463023	+	0.463023i	−0.899645	−	0.436622i	$-0.856175\pi$
$113$	−4.92200	+	4.92200i	−0.463023	+	0.463023i	0.436622	+	0.899645i	$0.356175\pi$
$114$		0			0
$115$	0.00370994	+	0.844878i	0.000345954	+	0.0787853i
$116$		0			0
$117$		0			0
$118$		0			0
$119$		−	2.55612i		−	0.234319i
$120$		0			0
$121$		−	7.47930i		−	0.679936i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	7.80087	−	8.00915i	0.697731	−	0.716360i
$126$		0			0
$127$	9.66457	−	9.66457i	0.857592	−	0.857592i	−0.133462	−	0.991054i	$-0.542609\pi$
$127$	9.66457	−	9.66457i	0.857592	−	0.857592i	0.991054	+	0.133462i	$0.0426094\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	9.65468	−	9.65468i	0.843533	−	0.843533i	−0.145783	−	0.989317i	$-0.546570\pi$
$131$	9.65468	−	9.65468i	0.843533	−	0.843533i	0.989317	+	0.145783i	$0.0465702\pi$
$132$		0			0
$133$	5.61485			0.486869
$134$		0			0
$135$		0			0
$136$		0			0
$137$	12.7261	−	12.7261i	1.08726	−	1.08726i	0.0914551	−	0.995809i	$-0.470848\pi$
$137$	12.7261	−	12.7261i	1.08726	−	1.08726i	0.995809	−	0.0914551i	$-0.0291518\pi$
$138$		0			0
$139$	−5.85917	−	5.85917i	−0.496969	−	0.496969i	0.413524	−	0.910493i	$-0.364298\pi$
$139$	−5.85917	−	5.85917i	−0.496969	−	0.496969i	−0.910493	+	0.413524i	$0.864298\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−3.70943	+	3.70943i	−0.310198	+	0.310198i
$144$		0			0
$145$	−0.0146579	−	3.33810i	−0.00121727	−	0.277214i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−6.84655	+	6.84655i	−0.560891	+	0.560891i	−0.929561	−	0.368670i	$-0.879813\pi$
$149$	−6.84655	+	6.84655i	−0.560891	+	0.560891i	0.368670	+	0.929561i	$0.379813\pi$
$150$		0			0
$151$			13.8549i			1.12749i	0.825948	+	0.563747i	$0.190641\pi$
$151$			13.8549i			1.12749i	−0.825948	+	0.563747i	$0.809359\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	0.628895	+	0.623396i	0.0505141	+	0.0500724i
$156$		0			0
$157$	1.03844			0.0828765			0.0414382	−	0.999141i	$-0.486806\pi$
$157$	1.03844			0.0828765			0.0414382	+	0.999141i	$0.486806\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$		−	0.341671i		−	0.0269275i
$162$		0			0
$163$		−	6.30047i		−	0.493491i	−0.969080	−	0.246745i	$-0.920639\pi$
$163$		−	6.30047i		−	0.493491i	0.969080	−	0.246745i	$-0.0793612\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	9.01401	−	9.01401i	0.697525	−	0.697525i	−0.266351	−	0.963876i	$-0.585818\pi$
$167$	9.01401	−	9.01401i	0.697525	−	0.697525i	0.963876	+	0.266351i	$0.0858181\pi$
$168$		0			0
$169$	5.18344			0.398726
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−11.4001			−0.866734			−0.433367	−	0.901217i	$-0.642675\pi$
$173$	−11.4001			−0.866734			−0.433367	+	0.901217i	$0.642675\pi$
$174$		0			0
$175$	−3.16885	+	3.22501i	−0.239543	+	0.243788i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	16.4357	+	16.4357i	1.22846	+	1.22846i	0.964546	+	0.263913i	$0.0850133\pi$
$179$	16.4357	+	16.4357i	1.22846	+	1.22846i	0.263913	+	0.964546i	$0.414987\pi$
$180$		0			0
$181$	−2.34847	+	2.34847i	−0.174560	+	0.174560i	−0.788980	−	0.614419i	$-0.789390\pi$
$181$	−2.34847	+	2.34847i	−0.174560	+	0.174560i	0.614419	+	0.788980i	$0.289390\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	12.8947	−	13.0084i	0.948036	−	0.956398i
$186$		0			0
$187$		−	5.30397i		−	0.387864i
$188$		0			0
$189$		0			0
$190$		0			0
$191$		−	15.5529i		−	1.12537i	−0.826671	−	0.562686i	$-0.809768\pi$
$191$		−	15.5529i		−	1.12537i	0.826671	−	0.562686i	$-0.190232\pi$
$192$		0			0
$193$	9.72521	+	9.72521i	0.700036	+	0.700036i	0.964418	−	0.264382i	$-0.0851679\pi$
$193$	9.72521	+	9.72521i	0.700036	+	0.700036i	−0.264382	+	0.964418i	$0.585168\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−18.6066			−1.32566			−0.662832	−	0.748768i	$-0.730646\pi$
$197$	−18.6066			−1.32566			−0.662832	+	0.748768i	$0.730646\pi$
$198$		0			0
$199$	−1.38430			−0.0981302			−0.0490651	−	0.998796i	$-0.515624\pi$
$199$	−1.38430			−0.0981302			−0.0490651	+	0.998796i	$0.515624\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$			1.34994i			0.0947469i
$204$		0			0
$205$	4.87443	+	4.83181i	0.340445	+	0.337468i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	11.6508			0.805906
$210$		0			0
$211$	13.1821	+	13.1821i	0.907496	+	0.907496i	0.996070	−	0.0885732i	$-0.0282307\pi$
$211$	13.1821	+	13.1821i	0.907496	+	0.907496i	−0.0885732	+	0.996070i	$0.528231\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−6.25486	−	6.20017i	−0.426578	−	0.422848i
$216$		0			0
$217$	−0.253215	−	0.253215i	−0.0171894	−	0.0171894i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	5.58829	−	5.58829i	0.375909	−	0.375909i
$222$		0			0
$223$	11.1464	+	11.1464i	0.746421	+	0.746421i	0.973805	−	0.227384i	$-0.0730173\pi$
$223$	11.1464	+	11.1464i	0.746421	+	0.746421i	−0.227384	+	0.973805i	$0.573017\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$			19.8707i			1.31887i	0.751763	+	0.659433i	$0.229204\pi$
$227$			19.8707i			1.31887i	−0.751763	+	0.659433i	$0.770796\pi$
$228$		0			0
$229$	10.1284	+	10.1284i	0.669303	+	0.669303i	0.957555	−	0.288251i	$-0.0930739\pi$
$229$	10.1284	+	10.1284i	0.669303	+	0.669303i	−0.288251	+	0.957555i	$0.593074\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−3.94464	−	3.94464i	−0.258422	−	0.258422i	0.565990	−	0.824412i	$-0.308494\pi$
$233$	−3.94464	−	3.94464i	−0.258422	−	0.258422i	−0.824412	+	0.565990i	$0.808494\pi$
$234$		0			0
$235$	0.0441128	+	10.0460i	0.00287760	+	0.655327i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−9.06356			−0.586273			−0.293136	−	0.956071i	$-0.594699\pi$
$239$	−9.06356			−0.586273			−0.293136	+	0.956071i	$0.594699\pi$
$240$		0			0
$241$	−10.2661			−0.661295			−0.330648	−	0.943754i	$-0.607267\pi$
$241$	−10.2661			−0.661295			−0.330648	+	0.943754i	$0.607267\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−9.73207	+	9.81791i	−0.621759	+	0.627244i
$246$		0			0
$247$	12.2754	+	12.2754i	0.781065	+	0.781065i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−17.7486	−	17.7486i	−1.12028	−	1.12028i	−0.991699	−	0.128582i	$-0.958958\pi$
$251$	−17.7486	−	17.7486i	−1.12028	−	1.12028i	−0.128582	−	0.991699i	$-0.541042\pi$
$252$		0			0
$253$		−	0.708970i		−	0.0445725i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	10.3039	+	10.3039i	0.642742	+	0.642742i	0.951229	−	0.308487i	$-0.0998225\pi$
$257$	10.3039	+	10.3039i	0.642742	+	0.642742i	−0.308487	+	0.951229i	$0.599822\pi$
$258$		0			0
$259$	−5.23764	+	5.23764i	−0.325451	+	0.325451i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−11.4453	−	11.4453i	−0.705747	−	0.705747i	0.259891	−	0.965638i	$-0.416313\pi$
$263$	−11.4453	−	11.4453i	−0.705747	−	0.705747i	−0.965638	+	0.259891i	$0.916313\pi$
$264$		0			0
$265$	1.14348	−	1.15357i	0.0702437	−	0.0708633i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	5.28786	+	5.28786i	0.322406	+	0.322406i	0.849690	−	0.527283i	$-0.176789\pi$
$269$	5.28786	+	5.28786i	0.322406	+	0.322406i	−0.527283	+	0.849690i	$0.676789\pi$
$270$		0			0
$271$	−18.7985			−1.14193			−0.570964	−	0.820975i	$-0.693430\pi$
$271$	−18.7985			−1.14193			−0.570964	+	0.820975i	$0.693430\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−6.57539	+	6.69191i	−0.396511	+	0.403538i
$276$		0			0
$277$		−	9.66454i		−	0.580686i	−0.956923	−	0.290343i	$-0.906231\pi$
$277$		−	9.66454i		−	0.580686i	0.956923	−	0.290343i	$-0.0937694\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	10.1023			0.602653			0.301327	−	0.953521i	$-0.402571\pi$
$281$	10.1023			0.602653			0.301327	+	0.953521i	$0.402571\pi$
$282$		0			0
$283$	−13.7887			−0.819653			−0.409826	−	0.912164i	$-0.634411\pi$
$283$	−13.7887			−0.819653			−0.409826	+	0.912164i	$0.634411\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−1.96262	−	1.96262i	−0.115850	−	0.115850i
$288$		0			0
$289$		−	9.00953i		−	0.529972i
$290$		0			0
$291$		0			0
$292$		0			0
$293$			31.9232i			1.86497i	0.361207	+	0.932486i	$0.382365\pi$
$293$			31.9232i			1.86497i	−0.361207	+	0.932486i	$0.617635\pi$
$294$		0			0
$295$	−0.147624		0.000648231i	−0.00859500		3.77415e-5i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	0.746975	−	0.746975i	0.0431987	−	0.0431987i
$300$		0			0
$301$	2.51843	+	2.51843i	0.145160	+	0.145160i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−0.0898926	−	20.4715i	−0.00514723	−	1.17220i
$306$		0			0
$307$	31.2794			1.78521			0.892605	−	0.450840i	$-0.148875\pi$
$307$	31.2794			1.78521			0.892605	+	0.450840i	$0.148875\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−10.0681			−0.570911			−0.285455	−	0.958392i	$-0.592145\pi$
$311$	−10.0681			−0.570911			−0.285455	+	0.958392i	$0.592145\pi$
$312$		0			0
$313$	−9.01911	+	9.01911i	−0.509790	+	0.509790i	−0.914462	−	0.404672i	$-0.867386\pi$
$313$	−9.01911	+	9.01911i	−0.509790	+	0.509790i	0.404672	+	0.914462i	$0.367386\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$			21.5841i			1.21228i	0.795357	+	0.606141i	$0.207283\pi$
$317$			21.5841i			1.21228i	−0.795357	+	0.606141i	$0.792717\pi$
$318$		0			0
$319$			2.80113i			0.156833i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	−17.5521			−0.976625
$324$		0			0
$325$	−13.9785	+	0.122764i	−0.775389	+	0.00680975i
$326$		0			0
$327$		0			0
$328$		0			0
$329$		−	4.06262i		−	0.223979i
$330$		0			0
$331$	5.19560	−	5.19560i	0.285576	−	0.285576i	−0.549752	−	0.835328i	$-0.685278\pi$
$331$	5.19560	−	5.19560i	0.285576	−	0.285576i	0.835328	+	0.549752i	$0.185278\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−22.8893	−	22.6892i	−1.25058	−	1.23964i
$336$		0			0
$337$	−4.17667	+	4.17667i	−0.227518	+	0.227518i	−0.811655	−	0.584137i	$-0.801433\pi$
$337$	−4.17667	+	4.17667i	−0.227518	+	0.227518i	0.584137	+	0.811655i	$0.301433\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−0.525423	−	0.525423i	−0.0284533	−	0.0284533i
$342$		0			0
$343$	8.42891	−	8.42891i	0.455118	−	0.455118i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−9.49718			−0.509835			−0.254918	−	0.966963i	$-0.582048\pi$
$347$	−9.49718			−0.509835			−0.254918	+	0.966963i	$0.582048\pi$
$348$		0			0
$349$	18.8840	−	18.8840i	1.01084	−	1.01084i	0.0108954	−	0.999941i	$-0.496532\pi$
$349$	18.8840	−	18.8840i	1.01084	−	1.01084i	0.999941	−	0.0108954i	$-0.00346819\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−2.92573	+	2.92573i	−0.155721	+	0.155721i	−0.780667	−	0.624947i	$-0.785121\pi$
$353$	−2.92573	+	2.92573i	−0.155721	+	0.155721i	0.624947	+	0.780667i	$0.285121\pi$
$354$		0			0
$355$	−23.6257	−	23.4191i	−1.25392	−	1.24296i
$356$		0			0
$357$		0			0
$358$		0			0
$359$		−	7.14369i		−	0.377030i	−0.982070	−	0.188515i	$-0.939633\pi$
$359$		−	7.14369i		−	0.377030i	0.982070	−	0.188515i	$-0.0603673\pi$
$360$		0			0
$361$		−	19.5554i		−	1.02923i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	28.4891	−	0.125099i	1.49119	−	0.00654796i
$366$		0			0
$367$	−13.6207	+	13.6207i	−0.710993	+	0.710993i	−0.966743	−	0.255750i	$-0.917678\pi$
$367$	−13.6207	+	13.6207i	−0.710993	+	0.710993i	0.255750	+	0.966743i	$0.417678\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−0.464468	+	0.464468i	−0.0241140	+	0.0241140i
$372$		0			0
$373$	23.8485			1.23483			0.617415	−	0.786638i	$-0.288180\pi$
$373$	23.8485			1.23483			0.617415	+	0.786638i	$0.288180\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−2.95128	+	2.95128i	−0.151999	+	0.151999i
$378$		0			0
$379$	−18.8255	−	18.8255i	−0.966999	−	0.966999i	0.0324740	−	0.999473i	$-0.489661\pi$
$379$	−18.8255	−	18.8255i	−0.966999	−	0.966999i	−0.999473	+	0.0324740i	$0.989661\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−25.0604	+	25.0604i	−1.28053	+	1.28053i	−0.340160	+	0.940368i	$0.610481\pi$
$383$	−25.0604	+	25.0604i	−1.28053	+	1.28053i	−0.940368	+	0.340160i	$0.889519\pi$
$384$		0			0
$385$	2.67094	−	2.69450i	0.136124	−	0.137324i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	6.45890	−	6.45890i	0.327479	−	0.327479i	−0.524148	−	0.851627i	$-0.675616\pi$
$389$	6.45890	−	6.45890i	0.327479	−	0.327479i	0.851627	+	0.524148i	$0.175616\pi$
$390$		0			0
$391$			1.06807i			0.0540146i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	20.1893	−	20.3674i	1.01584	−	1.02480i
$396$		0			0
$397$	−22.3797			−1.12320			−0.561602	−	0.827407i	$-0.689815\pi$
$397$	−22.3797			−1.12320			−0.561602	+	0.827407i	$0.689815\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$			20.7140i			1.03441i	0.855863	+	0.517203i	$0.173027\pi$
$401$			20.7140i			1.03441i	−0.855863	+	0.517203i	$0.826973\pi$
$402$		0			0
$403$		−	1.10718i		−	0.0551525i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−10.8681	+	10.8681i	−0.538714	+	0.538714i
$408$		0			0
$409$	−24.0233			−1.18788			−0.593939	−	0.804510i	$-0.702428\pi$
$409$	−24.0233			−1.18788			−0.593939	+	0.804510i	$0.702428\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	0.0596996			0.00293762
$414$		0			0
$415$	−6.46565	−	6.40912i	−0.317386	−	0.314611i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	19.6957	+	19.6957i	0.962199	+	0.962199i	0.999311	−	0.0371121i	$-0.0118159\pi$
$419$	19.6957	+	19.6957i	0.962199	+	0.962199i	−0.0371121	+	0.999311i	$0.511816\pi$
$420$		0			0
$421$	−4.28387	+	4.28387i	−0.208783	+	0.208783i	−0.803750	−	0.594967i	$-0.797165\pi$
$421$	−4.28387	+	4.28387i	−0.208783	+	0.208783i	0.594967	+	0.803750i	$0.297165\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	9.90589	−	10.0814i	0.480506	−	0.489021i
$426$		0			0
$427$			8.27875i			0.400637i
$428$		0			0
$429$		0			0
$430$		0			0
$431$			6.09096i			0.293391i	0.989182	+	0.146696i	$0.0468638\pi$
$431$			6.09096i			0.293391i	−0.989182	+	0.146696i	$0.953136\pi$
$432$		0			0
$433$	24.6961	+	24.6961i	1.18682	+	1.18682i	0.977941	+	0.208880i	$0.0669817\pi$
$433$	24.6961	+	24.6961i	1.18682	+	1.18682i	0.208880	+	0.977941i	$0.433018\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−2.34615			−0.112232
$438$		0			0
$439$	−21.6754			−1.03451			−0.517254	−	0.855832i	$-0.673046\pi$
$439$	−21.6754			−1.03451			−0.517254	+	0.855832i	$0.673046\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$			7.59456i			0.360828i	0.983591	+	0.180414i	$0.0577438\pi$
$443$			7.59456i			0.360828i	−0.983591	+	0.180414i	$0.942256\pi$
$444$		0			0
$445$	−21.4481	+	21.6373i	−1.01674	+	1.02571i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	20.6462			0.974354			0.487177	−	0.873303i	$-0.338027\pi$
$449$	20.6462			0.974354			0.487177	+	0.873303i	$0.338027\pi$
$450$		0			0
$451$	−4.07244	−	4.07244i	−0.191764	−	0.191764i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	5.65306	−	0.0248232i	0.265020	−	0.00116373i
$456$		0			0
$457$	−16.3771	−	16.3771i	−0.766088	−	0.766088i	0.211327	−	0.977415i	$-0.432221\pi$
$457$	−16.3771	−	16.3771i	−0.766088	−	0.766088i	−0.977415	+	0.211327i	$0.932221\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	1.36758	−	1.36758i	0.0636946	−	0.0636946i	−0.674542	−	0.738237i	$-0.735659\pi$
$461$	1.36758	−	1.36758i	0.0636946	−	0.0636946i	0.738237	+	0.674542i	$0.235659\pi$
$462$		0			0
$463$	10.8367	+	10.8367i	0.503625	+	0.503625i	0.912562	−	0.408938i	$-0.134101\pi$
$463$	10.8367	+	10.8367i	0.503625	+	0.503625i	−0.408938	+	0.912562i	$0.634101\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$			14.1469i			0.654643i	0.944913	+	0.327321i	$0.106146\pi$
$467$			14.1469i			0.654643i	−0.944913	+	0.327321i	$0.893854\pi$
$468$		0			0
$469$	9.21604	+	9.21604i	0.425557	+	0.425557i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	5.22575	+	5.22575i	0.240280	+	0.240280i
$474$		0			0
$475$	22.1451	+	21.7596i	1.01609	+	0.998397i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	27.3249			1.24851			0.624254	−	0.781221i	$-0.285403\pi$
$479$	27.3249			1.24851			0.624254	+	0.781221i	$0.285403\pi$
$480$		0			0
$481$	−22.9015			−1.04422
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−15.7580	+	0.0691950i	−0.715535	+	0.00314199i
$486$		0			0
$487$	−10.0084	−	10.0084i	−0.453526	−	0.453526i	0.442997	−	0.896523i	$-0.353915\pi$
$487$	−10.0084	−	10.0084i	−0.453526	−	0.453526i	−0.896523	+	0.442997i	$0.853915\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	8.65233	+	8.65233i	0.390474	+	0.390474i	0.874856	−	0.484382i	$-0.160956\pi$
$491$	8.65233	+	8.65233i	0.390474	+	0.390474i	−0.484382	+	0.874856i	$0.660956\pi$
$492$		0			0
$493$		−	4.21992i		−	0.190056i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	9.51252	+	9.51252i	0.426695	+	0.426695i
$498$		0			0
$499$	16.4743	−	16.4743i	0.737491	−	0.737491i	−0.234600	−	0.972092i	$-0.575378\pi$
$499$	16.4743	−	16.4743i	0.737491	−	0.737491i	0.972092	+	0.234600i	$0.0753782\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	−10.6112	−	10.6112i	−0.473132	−	0.473132i	0.429795	−	0.902927i	$-0.358586\pi$
$503$	−10.6112	−	10.6112i	−0.473132	−	0.473132i	−0.902927	+	0.429795i	$0.858586\pi$
$504$		0			0
$505$	0.00256125	+	0.583282i	0.000113974	+	0.0259557i
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−12.7387	−	12.7387i	−0.564631	−	0.564631i	0.365989	−	0.930619i	$-0.380731\pi$
$509$	−12.7387	−	12.7387i	−0.564631	−	0.564631i	−0.930619	+	0.365989i	$0.880731\pi$
$510$		0			0
$511$	−11.5211			−0.509663
$512$		0			0
$513$		0			0
$514$		0			0
$515$	8.07456	−	0.0354562i	0.355808	−	0.00156239i
$516$		0			0
$517$		−	8.42996i		−	0.370749i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−28.4501			−1.24642			−0.623210	−	0.782054i	$-0.714172\pi$
$521$	−28.4501			−1.24642			−0.623210	+	0.782054i	$0.714172\pi$
$522$		0			0
$523$	−18.3803			−0.803714			−0.401857	−	0.915702i	$-0.631635\pi$
$523$	−18.3803			−0.803714			−0.401857	+	0.915702i	$0.631635\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	0.791554	+	0.791554i	0.0344807	+	0.0344807i
$528$		0			0
$529$		−	22.8572i		−	0.993793i
$530$		0			0
$531$		0			0
$532$		0			0
$533$		−	8.58150i		−	0.371706i
$534$		0			0
$535$	−29.3579	−	29.1012i	−1.26925	−	1.25815i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	8.20257	−	8.20257i	0.353310	−	0.353310i
$540$		0			0
$541$	−22.4042	−	22.4042i	−0.963231	−	0.963231i	0.0361167	−	0.999348i	$-0.488501\pi$
$541$	−22.4042	−	22.4042i	−0.963231	−	0.963231i	−0.999348	+	0.0361167i	$0.988501\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−46.3176	+	0.203385i	−1.98403	+	0.00871207i
$546$		0			0
$547$	−31.4047			−1.34277			−0.671383	−	0.741111i	$-0.734299\pi$
$547$	−31.4047			−1.34277			−0.671383	+	0.741111i	$0.734299\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	9.26960			0.394898
$552$		0			0
$553$	−8.20064	+	8.20064i	−0.348727	+	0.348727i
$554$		0			0
$555$		0			0
$556$		0			0
$557$			28.3634i			1.20180i	0.799326	+	0.600898i	$0.205190\pi$
$557$			28.3634i			1.20180i	−0.799326	+	0.600898i	$0.794810\pi$
$558$		0			0
$559$			11.0118i			0.465748i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−24.2909			−1.02374			−0.511870	−	0.859063i	$-0.671047\pi$
$563$	−24.2909			−1.02374			−0.511870	+	0.859063i	$0.671047\pi$
$564$		0			0
$565$	15.5646	−	0.0683456i	0.654807	−	0.00287532i
$566$		0			0
$567$		0			0
$568$		0			0
$569$			9.85838i			0.413285i	0.978417	+	0.206642i	$0.0662537\pi$
$569$			9.85838i			0.413285i	−0.978417	+	0.206642i	$0.933746\pi$
$570$		0			0
$571$	33.3984	−	33.3984i	1.39768	−	1.39768i	0.591028	−	0.806651i	$-0.298722\pi$
$571$	33.3984	−	33.3984i	1.39768	−	1.39768i	0.806651	−	0.591028i	$-0.201278\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	1.32410	−	1.34756i	0.0552187	−	0.0561972i
$576$		0			0
$577$	7.27346	−	7.27346i	0.302798	−	0.302798i	−0.539309	−	0.842108i	$-0.681315\pi$
$577$	7.27346	−	7.27346i	0.302798	−	0.302798i	0.842108	+	0.539309i	$0.181315\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	2.60330	+	2.60330i	0.108003	+	0.108003i
$582$		0			0
$583$	−0.963774	+	0.963774i	−0.0399155	+	0.0399155i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	21.6196			0.892337			0.446169	−	0.894949i	$-0.352788\pi$
$587$	21.6196			0.892337			0.446169	+	0.894949i	$0.352788\pi$
$588$		0			0
$589$	−1.73875	+	1.73875i	−0.0716440	+	0.0716440i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	2.36948	−	2.36948i	0.0973029	−	0.0973029i	−0.656780	−	0.754083i	$-0.728082\pi$
$593$	2.36948	−	2.36948i	0.0973029	−	0.0973029i	0.754083	+	0.656780i	$0.228082\pi$
$594$		0			0
$595$	−4.02380	+	4.05929i	−0.164960	+	0.166415i
$596$		0			0
$597$		0			0
$598$		0			0
$599$			45.4222i			1.85590i	0.372702	+	0.927951i	$0.378431\pi$
$599$			45.4222i			1.85590i	−0.372702	+	0.927951i	$0.621569\pi$
$600$		0			0
$601$		−	34.8860i		−	1.42303i	−0.702670	−	0.711516i	$-0.748009\pi$
$601$		−	34.8860i		−	1.42303i	0.702670	−	0.711516i	$-0.251991\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−11.7738	+	11.8776i	−0.478672	+	0.482894i
$606$		0			0
$607$	22.2622	−	22.2622i	0.903596	−	0.903596i	−0.0921488	−	0.995745i	$-0.529374\pi$
$607$	22.2622	−	22.2622i	0.903596	−	0.903596i	0.995745	+	0.0921488i	$0.0293735\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	8.88186	−	8.88186i	0.359322	−	0.359322i
$612$		0			0
$613$	0.808634			0.0326604			0.0163302	−	0.999867i	$-0.494802\pi$
$613$	0.808634			0.0326604			0.0163302	+	0.999867i	$0.494802\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−11.0391	+	11.0391i	−0.444417	+	0.444417i	−0.893493	−	0.449077i	$-0.851753\pi$
$617$	−11.0391	+	11.0391i	−0.444417	+	0.444417i	0.449077	+	0.893493i	$0.351753\pi$
$618$		0			0
$619$	−6.16606	−	6.16606i	−0.247835	−	0.247835i	0.572247	−	0.820082i	$-0.306072\pi$
$619$	−6.16606	−	6.16606i	−0.247835	−	0.247835i	−0.820082	+	0.572247i	$0.806072\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	8.71194	−	8.71194i	0.349037	−	0.349037i
$624$		0			0
$625$	−24.9961	+	0.439084i	−0.999846	+	0.0175634i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	16.3730	−	16.3730i	0.652833	−	0.652833i
$630$		0			0
$631$		−	20.3925i		−	0.811811i	−0.913915	−	0.405906i	$-0.866956\pi$
$631$		−	20.3925i		−	0.811811i	0.913915	−	0.405906i	$-0.133044\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−30.5618	+	0.134200i	−1.21281	+	0.00532555i
$636$		0			0
$637$	17.2846			0.684840
$638$		0			0
$639$		0			0
$640$		0			0
$641$		−	28.2619i		−	1.11628i	−0.829748	−	0.558138i	$-0.811516\pi$
$641$		−	28.2619i		−	1.11628i	0.829748	−	0.558138i	$-0.188484\pi$
$642$		0			0
$643$			6.36014i			0.250820i	0.992105	+	0.125410i	$0.0400246\pi$
$643$			6.36014i			0.250820i	−0.992105	+	0.125410i	$0.959975\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	6.41493	−	6.41493i	0.252197	−	0.252197i	−0.569674	−	0.821871i	$-0.692930\pi$
$647$	6.41493	−	6.41493i	0.252197	−	0.252197i	0.821871	+	0.569674i	$0.192930\pi$
$648$		0			0
$649$	0.123877			0.00486260
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−47.0503			−1.84122			−0.920611	−	0.390482i	$-0.872309\pi$
$653$	−47.0503			−1.84122			−0.920611	+	0.390482i	$0.872309\pi$
$654$		0			0
$655$	−30.5305	+	0.134062i	−1.19292	+	0.00523825i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−5.80037	−	5.80037i	−0.225950	−	0.225950i	0.585048	−	0.810999i	$-0.301076\pi$
$659$	−5.80037	−	5.80037i	−0.225950	−	0.225950i	−0.810999	+	0.585048i	$0.801076\pi$
$660$		0			0
$661$	−18.6096	+	18.6096i	−0.723831	+	0.723831i	−0.969383	−	0.245553i	$-0.921031\pi$
$661$	−18.6096	+	18.6096i	−0.723831	+	0.723831i	0.245553	+	0.969383i	$0.421031\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−8.91675	−	8.83878i	−0.345777	−	0.342753i
$666$		0			0
$667$		−	0.564068i		−	0.0218408i
$668$		0			0
$669$		0			0
$670$		0			0
$671$			17.1785i			0.663167i
$672$		0			0
$673$	−19.6012	−	19.6012i	−0.755570	−	0.755570i	0.219943	−	0.975513i	$-0.429413\pi$
$673$	−19.6012	−	19.6012i	−0.755570	−	0.755570i	−0.975513	+	0.219943i	$0.929413\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	21.0206			0.807888			0.403944	−	0.914784i	$-0.367639\pi$
$677$	21.0206			0.807888			0.403944	+	0.914784i	$0.367639\pi$
$678$		0			0
$679$	6.37259			0.244558
$680$		0			0
$681$		0			0
$682$		0			0
$683$			34.9901i			1.33886i	0.742875	+	0.669430i	$0.233462\pi$
$683$			34.9901i			1.33886i	−0.742875	+	0.669430i	$0.766538\pi$
$684$		0			0
$685$	−40.2431	+	0.176711i	−1.53761	+	0.00675179i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−2.03088			−0.0773703
$690$		0			0
$691$	−1.18062	−	1.18062i	−0.0449128	−	0.0449128i	0.684294	−	0.729206i	$-0.260111\pi$
$691$	−1.18062	−	1.18062i	−0.0449128	−	0.0449128i	−0.729206	+	0.684294i	$0.760111\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	0.0813590	+	18.5282i	0.00308612	+	0.702813i
$696$		0			0
$697$	6.13517	+	6.13517i	0.232386	+	0.232386i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	12.3704	−	12.3704i	0.467222	−	0.467222i	−0.433792	−	0.901013i	$-0.642825\pi$
$701$	12.3704	−	12.3704i	0.467222	−	0.467222i	0.901013	+	0.433792i	$0.142825\pi$
$702$		0			0
$703$	35.9653	+	35.9653i	1.35646	+	1.35646i
$704$		0			0
$705$		0			0
$706$		0			0
$707$		−	0.235881i		−	0.00887121i
$708$		0			0
$709$	−9.85164	−	9.85164i	−0.369986	−	0.369986i	0.497486	−	0.867472i	$-0.334257\pi$
$709$	−9.85164	−	9.85164i	−0.369986	−	0.369986i	−0.867472	+	0.497486i	$0.834257\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	0.105805	+	0.105805i	0.00396244	+	0.00396244i
$714$		0			0
$715$	11.7301	−	0.0515082i	0.438682	−	0.00192630i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	45.4889			1.69645			0.848225	−	0.529635i	$-0.177671\pi$
$719$	45.4889			1.69645			0.848225	+	0.529635i	$0.177671\pi$
$720$		0			0
$721$	−3.26537			−0.121609
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−5.23149	+	5.32419i	−0.194293	+	0.197736i
$726$		0			0
$727$	−26.5962	−	26.5962i	−0.986398	−	0.986398i	0.0135103	−	0.999909i	$-0.495699\pi$
$727$	−26.5962	−	26.5962i	−0.986398	−	0.986398i	−0.999909	+	0.0135103i	$0.995699\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−7.87264	−	7.87264i	−0.291180	−	0.291180i
$732$		0			0
$733$		−	1.35102i		−	0.0499010i	−0.999689	−	0.0249505i	$-0.992057\pi$
$733$		−	1.35102i		−	0.0499010i	0.999689	−	0.0249505i	$-0.00794281\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	19.1233	+	19.1233i	0.704417	+	0.704417i
$738$		0			0
$739$	−9.89011	+	9.89011i	−0.363814	+	0.363814i	−0.865215	−	0.501401i	$-0.832818\pi$
$739$	−9.89011	+	9.89011i	−0.363814	+	0.363814i	0.501401	+	0.865215i	$0.332818\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	19.1727	+	19.1727i	0.703378	+	0.703378i	0.965134	−	0.261756i	$-0.0843015\pi$
$743$	19.1727	+	19.1727i	0.703378	+	0.703378i	−0.261756	+	0.965134i	$0.584302\pi$
$744$		0			0
$745$	21.6505	−	0.0950693i	0.793212	−	0.00348307i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	11.8205	+	11.8205i	0.431912	+	0.431912i
$750$		0			0
$751$	−36.1877			−1.32051			−0.660255	−	0.751042i	$-0.729552\pi$
$751$	−36.1877			−1.32051			−0.660255	+	0.751042i	$0.729552\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	21.8101	−	22.0025i	0.793750	−	0.800751i
$756$		0			0
$757$		−	0.255640i		−	0.00929139i	−0.999989	−	0.00464570i	$-0.998521\pi$
$757$		−	0.255640i		−	0.00929139i	0.999989	−	0.00464570i	$-0.00147878\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−46.5158			−1.68620			−0.843098	−	0.537760i	$-0.819271\pi$
$761$	−46.5158			−1.68620			−0.843098	+	0.537760i	$0.819271\pi$
$762$		0			0
$763$	18.7310			0.678107
$764$		0			0
$765$		0			0
$766$		0			0
$767$	0.130518	+	0.130518i	0.00471272	+	0.00471272i
$768$		0			0
$769$			19.7021i			0.710478i	0.934776	+	0.355239i	$0.115600\pi$
$769$			19.7021i			0.710478i	−0.934776	+	0.355239i	$0.884400\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$		−	41.1583i		−	1.48036i	−0.672408	−	0.740180i	$-0.734740\pi$
$773$		−	41.1583i		−	1.48036i	0.672408	−	0.740180i	$-0.265260\pi$
$774$		0			0
$775$	−0.0173890	−	1.97999i	−0.000624631	−	0.0711233i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−13.4767	+	13.4767i	−0.482852	+	0.482852i
$780$		0			0
$781$	19.7385	+	19.7385i	0.706300	+	0.706300i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−1.64911	−	1.63469i	−0.0588593	−	0.0583446i
$786$		0			0
$787$	−13.5375			−0.482558			−0.241279	−	0.970456i	$-0.577567\pi$
$787$	−13.5375			−0.482558			−0.241279	+	0.970456i	$0.577567\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	−6.29436			−0.223802
$792$		0			0
$793$	−18.0993	+	18.0993i	−0.642726	+	0.642726i
$794$		0			0
$795$		0			0
$796$		0			0
$797$			44.4984i			1.57622i	0.615537	+	0.788108i	$0.288939\pi$
$797$			44.4984i			1.57622i	−0.615537	+	0.788108i	$0.711061\pi$
$798$		0			0
$799$			12.6998i			0.449287i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−23.9063			−0.843636
$804$		0			0
$805$	−0.537852	+	0.542596i	−0.0189568	+	0.0191240i
$806$		0			0
$807$		0			0
$808$		0			0
$809$			16.2919i			0.572794i	0.958111	+	0.286397i	$0.0924576\pi$
$809$			16.2919i			0.572794i	−0.958111	+	0.286397i	$0.907542\pi$
$810$		0			0
$811$	−8.98912	+	8.98912i	−0.315651	+	0.315651i	−0.847094	−	0.531443i	$-0.821650\pi$
$811$	−8.98912	+	8.98912i	−0.315651	+	0.315651i	0.531443	+	0.847094i	$0.321650\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−9.91808	+	10.0056i	−0.347415	+	0.350480i
$816$		0			0
$817$	17.2933	−	17.2933i	0.605015	−	0.605015i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−29.6118	−	29.6118i	−1.03346	−	1.03346i	−0.999420	−	0.0340398i	$-0.989163\pi$
$821$	−29.6118	−	29.6118i	−1.03346	−	1.03346i	−0.0340398	−	0.999420i	$-0.510837\pi$
$822$		0			0
$823$	8.23712	−	8.23712i	0.287128	−	0.287128i	−0.548816	−	0.835943i	$-0.684921\pi$
$823$	8.23712	−	8.23712i	0.287128	−	0.287128i	0.835943	+	0.548816i	$0.184921\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−7.28789			−0.253425			−0.126712	−	0.991940i	$-0.540443\pi$
$827$	−7.28789			−0.253425			−0.126712	+	0.991940i	$0.540443\pi$
$828$		0			0
$829$	4.99192	−	4.99192i	0.173377	−	0.173377i	−0.615085	−	0.788461i	$-0.710878\pi$
$829$	4.99192	−	4.99192i	0.173377	−	0.173377i	0.788461	+	0.615085i	$0.210878\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−12.3572	+	12.3572i	−0.428153	+	0.428153i
$834$		0			0
$835$	−28.5045	+	0.125166i	−0.986440	+	0.00433155i
$836$		0			0
$837$		0			0
$838$		0			0
$839$		−	24.5841i		−	0.848736i	−0.905490	−	0.424368i	$-0.860496\pi$
$839$		−	24.5841i		−	0.848736i	0.905490	−	0.424368i	$-0.139504\pi$
$840$		0			0
$841$		−	26.7714i		−	0.923151i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−8.23164	−	8.15967i	−0.283177	−	0.280701i
$846$		0			0
$847$	4.78235	−	4.78235i	0.164323	−	0.164323i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	2.18854	−	2.18854i	0.0750221	−	0.0750221i
$852$		0			0
$853$	−16.5183			−0.565576			−0.282788	−	0.959182i	$-0.591259\pi$
$853$	−16.5183			−0.565576			−0.282788	+	0.959182i	$0.591259\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−20.6068	+	20.6068i	−0.703915	+	0.703915i	−0.965249	−	0.261333i	$-0.915838\pi$
$857$	−20.6068	+	20.6068i	−0.703915	+	0.703915i	0.261333	+	0.965249i	$0.415838\pi$
$858$		0			0
$859$	−9.53453	−	9.53453i	−0.325314	−	0.325314i	0.525487	−	0.850801i	$-0.323883\pi$
$859$	−9.53453	−	9.53453i	−0.325314	−	0.325314i	−0.850801	+	0.525487i	$0.823883\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	5.00687	−	5.00687i	0.170436	−	0.170436i	−0.616735	−	0.787171i	$-0.711545\pi$
$863$	5.00687	−	5.00687i	0.170436	−	0.170436i	0.787171	+	0.616735i	$0.211545\pi$
$864$		0			0
$865$	18.1041	+	17.9458i	0.615559	+	0.610177i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−17.0164	+	17.0164i	−0.577241	+	0.577241i
$870$		0			0
$871$			40.2970i			1.36541i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	10.1091	−	0.133177i	0.341750	−	0.00450220i
$876$		0			0
$877$	−8.97858			−0.303185			−0.151593	−	0.988443i	$-0.548440\pi$
$877$	−8.97858			−0.303185			−0.151593	+	0.988443i	$0.548440\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$			2.40777i			0.0811197i	0.999177	+	0.0405599i	$0.0129141\pi$
$881$			2.40777i			0.0811197i	−0.999177	+	0.0405599i	$0.987086\pi$
$882$		0			0
$883$			15.2963i			0.514762i	0.966310	+	0.257381i	$0.0828595\pi$
$883$			15.2963i			0.514762i	−0.966310	+	0.257381i	$0.917140\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−20.5031	+	20.5031i	−0.688425	+	0.688425i	−0.961884	−	0.273458i	$-0.911832\pi$
$887$	−20.5031	+	20.5031i	−0.688425	+	0.688425i	0.273458	+	0.961884i	$0.411832\pi$
$888$		0			0
$889$	12.3593			0.414516
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−27.8968			−0.933530
$894$		0			0
$895$	−0.228221	−	51.9737i	−0.00762860	−	1.73729i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−0.418035	−	0.418035i	−0.0139422	−	0.0139422i
$900$		0			0
$901$	1.45193	−	1.45193i	0.0483710	−	0.0483710i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	7.42644	−	0.0326102i	0.246863	−	0.00108400i
$906$		0			0
$907$			23.9363i			0.794793i	0.917647	+	0.397397i	$0.130086\pi$
$907$			23.9363i			0.794793i	−0.917647	+	0.397397i	$0.869914\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$			53.6652i			1.77801i	0.457900	+	0.889004i	$0.348602\pi$
$911$			53.6652i			1.77801i	−0.457900	+	0.889004i	$0.651398\pi$
$912$		0			0
$913$	5.40186	+	5.40186i	0.178775	+	0.178775i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	12.3466			0.407721
$918$		0			0
$919$	28.1683			0.929188			0.464594	−	0.885524i	$-0.346200\pi$
$919$	28.1683			0.929188			0.464594	+	0.885524i	$0.346200\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$			41.5933i			1.36906i
$924$		0			0
$925$	−40.9552	+	0.359684i	−1.34660	+	0.0118263i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	10.4252			0.342041			0.171020	−	0.985267i	$-0.445294\pi$
$929$	10.4252			0.342041			0.171020	+	0.985267i	$0.445294\pi$
$930$		0			0
$931$	−27.1443	−	27.1443i	−0.889618	−	0.889618i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	−8.34940	+	8.42305i	−0.273055	+	0.275463i
$936$		0			0
$937$	26.2174	+	26.2174i	0.856484	+	0.856484i	0.990922	−	0.134438i	$-0.0429230\pi$
$937$	26.2174	+	26.2174i	0.856484	+	0.856484i	−0.134438	+	0.990922i	$0.542923\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	32.6937	−	32.6937i	1.06579	−	1.06579i	0.0681070	−	0.997678i	$-0.478304\pi$
$941$	32.6937	−	32.6937i	1.06579	−	1.06579i	0.997678	−	0.0681070i	$-0.0216959\pi$
$942$		0			0
$943$	0.820075	+	0.820075i	0.0267053	+	0.0267053i
$944$		0			0
$945$		0			0
$946$		0			0
$947$		−	14.6583i		−	0.476329i	−0.971225	−	0.238165i	$-0.923454\pi$
$947$		−	14.6583i		−	0.476329i	0.971225	−	0.238165i	$-0.0765458\pi$
$948$		0			0
$949$	−25.1879	−	25.1879i	−0.817632	−	0.817632i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	9.70954	+	9.70954i	0.314523	+	0.314523i	0.846659	−	0.532136i	$-0.178610\pi$
$953$	9.70954	+	9.70954i	0.314523	+	0.314523i	−0.532136	+	0.846659i	$0.678610\pi$
$954$		0			0
$955$	−24.4831	+	24.6991i	−0.792256	+	0.799244i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	16.2744			0.525528
$960$		0			0
$961$	−30.8432			−0.994941
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−0.135042	−	30.7535i	−0.00434715	−	0.989991i
$966$		0			0
$967$	28.0987	+	28.0987i	0.903593	+	0.903593i	0.995745	−	0.0921520i	$-0.0293746\pi$
$967$	28.0987	+	28.0987i	0.903593	+	0.903593i	−0.0921520	+	0.995745i	$0.529375\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−29.5510	−	29.5510i	−0.948336	−	0.948336i	0.0503938	−	0.998729i	$-0.483952\pi$
$971$	−29.5510	−	29.5510i	−0.948336	−	0.948336i	−0.998729	+	0.0503938i	$0.983952\pi$
$972$		0			0
$973$		−	7.49284i		−	0.240209i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−11.6829	−	11.6829i	−0.373769	−	0.373769i	0.495079	−	0.868848i	$-0.335139\pi$
$977$	−11.6829	−	11.6829i	−0.373769	−	0.373769i	−0.868848	+	0.495079i	$0.835139\pi$
$978$		0			0
$979$	18.0773	−	18.0773i	0.577754	−	0.577754i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−28.6164	−	28.6164i	−0.912721	−	0.912721i	0.0837648	−	0.996486i	$-0.473306\pi$
$983$	−28.6164	−	28.6164i	−0.912721	−	0.912721i	−0.996486	+	0.0837648i	$0.973306\pi$
$984$		0			0
$985$	29.5485	+	29.2901i	0.941494	+	0.933261i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−1.05232	−	1.05232i	−0.0334618	−	0.0334618i
$990$		0			0
$991$	1.25464			0.0398551			0.0199275	−	0.999801i	$-0.493656\pi$
$991$	1.25464			0.0398551			0.0199275	+	0.999801i	$0.493656\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	2.19836	+	2.17913i	0.0696926	+	0.0690832i
$996$		0			0
$997$		−	19.7940i		−	0.626883i	−0.949608	−	0.313441i	$-0.898518\pi$
$997$		−	19.7940i		−	0.626883i	0.949608	−	0.313441i	$-0.101482\pi$
$998$		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.593.13		96
3.2	odd	2	inner	2880.2.bc.a.593.36		96
4.3	odd	2		720.2.bc.a.413.25	yes	96
5.2	odd	4		2880.2.bg.a.17.12		96
12.11	even	2		720.2.bc.a.413.24	yes	96
15.2	even	4		2880.2.bg.a.17.37		96
16.5	even	4		2880.2.bg.a.2033.37		96
16.11	odd	4		720.2.bg.a.53.1	yes	96
20.7	even	4		720.2.bg.a.557.48	yes	96
48.5	odd	4		2880.2.bg.a.2033.12		96
48.11	even	4		720.2.bg.a.53.48	yes	96
60.47	odd	4		720.2.bg.a.557.1	yes	96
80.27	even	4		720.2.bc.a.197.24	✓	96
80.37	odd	4	inner	2880.2.bc.a.1457.36		96
240.107	odd	4		720.2.bc.a.197.25	yes	96
240.197	even	4	inner	2880.2.bc.a.1457.13		96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
720.2.bc.a.197.24	✓	96	80.27	even	4
720.2.bc.a.197.25	yes	96	240.107	odd	4
720.2.bc.a.413.24	yes	96	12.11	even	2
720.2.bc.a.413.25	yes	96	4.3	odd	2
720.2.bg.a.53.1	yes	96	16.11	odd	4
720.2.bg.a.53.48	yes	96	48.11	even	4
720.2.bg.a.557.1	yes	96	60.47	odd	4
720.2.bg.a.557.48	yes	96	20.7	even	4
2880.2.bc.a.593.13		96	1.1	even	1	trivial
2880.2.bc.a.593.36		96	3.2	odd	2	inner
2880.2.bc.a.1457.13		96	240.197	even	4	inner
2880.2.bc.a.1457.36		96	80.37	odd	4	inner
2880.2.bg.a.17.12		96	5.2	odd	4
2880.2.bg.a.17.37		96	15.2	even	4
2880.2.bg.a.2033.12		96	48.5	odd	4
2880.2.bg.a.2033.37		96	16.5	even	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)

\(f(q)\)	\(=\)	\(q+(-1.58807 - 1.57418i) q^{5} +(0.639411 + 0.639411i) q^{7} +O(q^{10})\)	\(q+(-1.58807 - 1.57418i) q^{5} +(0.639411 + 0.639411i) q^{7} +(1.32678 + 1.32678i) q^{11} +2.79581i q^{13} +(-1.99881 - 1.99881i) q^{17} +(4.39064 - 4.39064i) q^{19} +(-0.267176 - 0.267176i) q^{23} +(0.0439101 + 4.99981i) q^{25} +(1.05561 + 1.05561i) q^{29} -0.396013 q^{31} +(-0.00887869 - 2.02198i) q^{35} +8.19136i q^{37} -3.06941 q^{41} +3.93867 q^{43} +(-3.17684 - 3.17684i) q^{47} -6.18231i q^{49} +0.726400i q^{53} +(-0.0184233 - 4.19561i) q^{55} +(0.0466833 - 0.0466833i) q^{59} +(6.47373 + 6.47373i) q^{61} +(4.40111 - 4.43993i) q^{65} +14.4133 q^{67} +14.8770 q^{71} +(-9.00914 + 9.00914i) q^{73} +1.69672i q^{77} +12.8253i q^{79} +4.07140 q^{83} +(0.0277549 + 6.32073i) q^{85} -13.6250i q^{89} +(-1.78767 + 1.78767i) q^{91} +(-13.8843 + 0.0609673i) q^{95} +(4.98317 - 4.98317i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q+O(q^{10}) \) 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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