LMFDB - Embedded newform 560.3.v.a.447.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [560,3,Mod(223,560)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("560.223"); S:= CuspForms(chi, 3); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(560, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([2, 0, 3, 2])) N = Newforms(chi, 3, names="a")

Level:	$ N $	$=$	$ 560 = 2^{4} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	560.v (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [32] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$15.2588948042$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			447.2
Character	$\chi$	$=$	560.447
Dual form			560.3.v.a.223.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-3.74578 + 3.74578i) q^{3} +(3.76482 - 3.29031i) q^{5} +(-0.0261022 + 6.99995i) q^{7} -19.0618i q^{9} -5.33929i q^{11} +(13.8937 + 13.8937i) q^{13} +(-1.77738 + 26.4270i) q^{15} +(12.8989 - 12.8989i) q^{17} -25.2908i q^{19} +(-26.1225 - 26.3181i) q^{21} +(12.2842 + 12.2842i) q^{23} +(3.34766 - 24.7748i) q^{25} +(37.6891 + 37.6891i) q^{27} +13.3664i q^{29} +46.4474 q^{31} +(19.9998 + 19.9998i) q^{33} +(22.9338 + 26.4394i) q^{35} +(6.06076 + 6.06076i) q^{37} -104.086 q^{39} +80.3318i q^{41} +(-40.6508 - 40.6508i) q^{43} +(-62.7192 - 71.7640i) q^{45} +(19.3721 + 19.3721i) q^{47} +(-48.9986 - 0.365428i) q^{49} +96.6326i q^{51} +(-34.8178 + 34.8178i) q^{53} +(-17.5680 - 20.1015i) q^{55} +(94.7340 + 94.7340i) q^{57} +58.6144i q^{59} +14.4721i q^{61} +(133.431 + 0.497554i) q^{63} +(98.0219 + 6.59257i) q^{65} +(-36.9195 + 36.9195i) q^{67} -92.0282 q^{69} +24.3539i q^{71} +(30.9090 + 30.9090i) q^{73} +(80.2615 + 105.341i) q^{75} +(37.3748 + 0.139367i) q^{77} +135.635 q^{79} -110.795 q^{81} +(22.0590 - 22.0590i) q^{83} +(6.12052 - 91.0031i) q^{85} +(-50.0677 - 50.0677i) q^{87} -12.2861 q^{89} +(-97.6179 + 96.8926i) q^{91} +(-173.982 + 173.982i) q^{93} +(-83.2148 - 95.2153i) q^{95} +(46.1549 - 46.1549i) q^{97} -101.776 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 64 q^{21} + 72 q^{25} - 72 q^{37} - 272 q^{53} + 280 q^{57} + 376 q^{65} + 24 q^{77} - 528 q^{81} - 96 q^{85} - 552 q^{93}+O(q^{100}) $ 32 * q - 64 * q^21 + 72 * q^25 - 72 * q^37 - 272 * q^53 + 280 * q^57 + 376 * q^65 + 24 * q^77 - 528 * q^81 - 96 * q^85 - 552 * q^93

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/560\mathbb{Z}\right)^\times$.

$n$	$241$	$337$	$351$	$421$
$\chi(n)$	$-1$	$e\left(\frac{1}{4}\right)$	$-1$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	−3.74578	+	3.74578i	−1.24859	+	1.24859i	−0.292253	+	0.956341i	$0.594405\pi$
$3$	−3.74578	+	3.74578i	−1.24859	+	1.24859i	−0.956341	+	0.292253i	$0.905595\pi$
$4$		0			0
$5$	3.76482	−	3.29031i	0.752963	−	0.658063i
$5$	3.76482	−	3.29031i	0.752963	−	0.658063i
$6$		0			0
$7$	−0.0261022	+	6.99995i	−0.00372889	+	0.999993i
$7$	−0.0261022	+	6.99995i	−0.00372889	+	0.999993i
$8$		0			0
$9$		−	19.0618i		−	2.11797i
$10$		0			0
$11$		−	5.33929i		−	0.485390i	−0.970103	−	0.242695i	$-0.921969\pi$
$11$		−	5.33929i		−	0.485390i	0.970103	−	0.242695i	$-0.0780315\pi$
$12$		0			0
$13$	13.8937	+	13.8937i	1.06875	+	1.06875i	0.997456	+	0.0712908i	$0.0227118\pi$
$13$	13.8937	+	13.8937i	1.06875	+	1.06875i	0.0712908	+	0.997456i	$0.477288\pi$
$14$		0			0
$15$	−1.77738	+	26.4270i	−0.118492	+	1.76180i
$16$		0			0
$17$	12.8989	−	12.8989i	0.758756	−	0.758756i	−0.217340	−	0.976096i	$-0.569738\pi$
$17$	12.8989	−	12.8989i	0.758756	−	0.758756i	0.976096	+	0.217340i	$0.0697379\pi$
$18$		0			0
$19$		−	25.2908i		−	1.33110i	−0.746355	−	0.665548i	$-0.768198\pi$
$19$		−	25.2908i		−	1.33110i	0.746355	−	0.665548i	$-0.231802\pi$
$20$		0			0
$21$	−26.1225	−	26.3181i	−1.24393	−	1.25324i
$22$		0			0
$23$	12.2842	+	12.2842i	0.534098	+	0.534098i	0.921789	−	0.387692i	$-0.126727\pi$
$23$	12.2842	+	12.2842i	0.534098	+	0.534098i	−0.387692	+	0.921789i	$0.626727\pi$
$24$		0			0
$25$	3.34766	−	24.7748i	0.133907	−	0.990994i
$26$		0			0
$27$	37.6891	+	37.6891i	1.39589	+	1.39589i
$28$		0			0
$29$			13.3664i			0.460911i	0.973083	+	0.230456i	$0.0740217\pi$
$29$			13.3664i			0.460911i	−0.973083	+	0.230456i	$0.925978\pi$
$30$		0			0
$31$	46.4474			1.49830			0.749152	−	0.662398i	$-0.230461\pi$
$31$	46.4474			1.49830			0.749152	+	0.662398i	$0.230461\pi$
$32$		0			0
$33$	19.9998	+	19.9998i	0.606055	+	0.606055i
$34$		0			0
$35$	22.9338	+	26.4394i	0.655251	+	0.755412i
$36$		0			0
$37$	6.06076	+	6.06076i	0.163804	+	0.163804i	0.784250	−	0.620445i	$-0.213048\pi$
$37$	6.06076	+	6.06076i	0.163804	+	0.163804i	−0.620445	+	0.784250i	$0.713048\pi$
$38$		0			0
$39$	−104.086			−2.66886
$40$		0			0
$41$			80.3318i			1.95931i	0.200681	+	0.979657i	$0.435684\pi$
$41$			80.3318i			1.95931i	−0.200681	+	0.979657i	$0.564316\pi$
$42$		0			0
$43$	−40.6508	−	40.6508i	−0.945367	−	0.945367i	0.0532157	−	0.998583i	$-0.483053\pi$
$43$	−40.6508	−	40.6508i	−0.945367	−	0.945367i	−0.998583	+	0.0532157i	$0.983053\pi$
$44$		0			0
$45$	−62.7192	−	71.7640i	−1.39376	−	1.59476i
$46$		0			0
$47$	19.3721	+	19.3721i	0.412173	+	0.412173i	0.882495	−	0.470322i	$-0.155862\pi$
$47$	19.3721	+	19.3721i	0.412173	+	0.412173i	−0.470322	+	0.882495i	$0.655862\pi$
$48$		0			0
$49$	−48.9986	−	0.365428i	−0.999972	−	0.00745772i
$50$		0			0
$51$			96.6326i			1.89476i
$52$		0			0
$53$	−34.8178	+	34.8178i	−0.656940	+	0.656940i	−0.954655	−	0.297715i	$-0.903776\pi$
$53$	−34.8178	+	34.8178i	−0.656940	+	0.656940i	0.297715	+	0.954655i	$0.403776\pi$
$54$		0			0
$55$	−17.5680	−	20.1015i	−0.319417	−	0.365481i
$56$		0			0
$57$	94.7340	+	94.7340i	1.66200	+	1.66200i
$58$		0			0
$59$			58.6144i			0.993465i	0.867904	+	0.496732i	$0.165467\pi$
$59$			58.6144i			0.993465i	−0.867904	+	0.496732i	$0.834533\pi$
$60$		0			0
$61$			14.4721i			0.237247i	0.992939	+	0.118624i	$0.0378482\pi$
$61$			14.4721i			0.237247i	−0.992939	+	0.118624i	$0.962152\pi$
$62$		0			0
$63$	133.431	+	0.497554i	2.11796	+	0.00789768i
$64$		0			0
$65$	98.0219	+	6.59257i	1.50803	+	0.101424i
$66$		0			0
$67$	−36.9195	+	36.9195i	−0.551037	+	0.551037i	−0.926740	−	0.375703i	$-0.877401\pi$
$67$	−36.9195	+	36.9195i	−0.551037	+	0.551037i	0.375703	+	0.926740i	$0.377401\pi$
$68$		0			0
$69$	−92.0282			−1.33374
$70$		0			0
$71$			24.3539i			0.343013i	0.985183	+	0.171506i	$0.0548634\pi$
$71$			24.3539i			0.343013i	−0.985183	+	0.171506i	$0.945137\pi$
$72$		0			0
$73$	30.9090	+	30.9090i	0.423411	+	0.423411i	0.886376	−	0.462965i	$-0.153215\pi$
$73$	30.9090	+	30.9090i	0.423411	+	0.423411i	−0.462965	+	0.886376i	$0.653215\pi$
$74$		0			0
$75$	80.2615	+	105.341i	1.07015	+	1.40454i
$76$		0			0
$77$	37.3748	+	0.139367i	0.485387	+	0.00180997i
$78$		0			0
$79$	135.635			1.71690			0.858448	−	0.512901i	$-0.171429\pi$
$79$	135.635			1.71690			0.858448	+	0.512901i	$0.171429\pi$
$80$		0			0
$81$	−110.795			−1.36784
$82$		0			0
$83$	22.0590	−	22.0590i	0.265772	−	0.265772i	−0.561622	−	0.827394i	$-0.689823\pi$
$83$	22.0590	−	22.0590i	0.265772	−	0.265772i	0.827394	+	0.561622i	$0.189823\pi$
$84$		0			0
$85$	6.12052	−	91.0031i	0.0720061	−	1.07062i
$86$		0			0
$87$	−50.0677	−	50.0677i	−0.575491	−	0.575491i
$88$		0			0
$89$	−12.2861			−0.138046			−0.0690232	−	0.997615i	$-0.521988\pi$
$89$	−12.2861			−0.138046			−0.0690232	+	0.997615i	$0.521988\pi$
$90$		0			0
$91$	−97.6179	+	96.8926i	−1.07272	+	1.06475i
$92$		0			0
$93$	−173.982	+	173.982i	−1.87077	+	1.87077i
$94$		0			0
$95$	−83.2148	−	95.2153i	−0.875945	−	1.00227i
$96$		0			0
$97$	46.1549	−	46.1549i	0.475824	−	0.475824i	−0.427969	−	0.903793i	$-0.640771\pi$
$97$	46.1549	−	46.1549i	0.475824	−	0.475824i	0.903793	+	0.427969i	$0.140771\pi$
$98$		0			0
$99$	−101.776			−1.02804
$100$		0			0
$101$			102.763i			1.01745i	0.860928	+	0.508726i	$0.169883\pi$
$101$			102.763i			1.01745i	−0.860928	+	0.508726i	$0.830117\pi$
$102$		0			0
$103$	−18.2973	+	18.2973i	−0.177643	+	0.177643i	−0.790328	−	0.612684i	$-0.790090\pi$
$103$	−18.2973	+	18.2973i	−0.177643	+	0.177643i	0.612684	+	0.790328i	$0.290090\pi$
$104$		0			0
$105$	−184.941	−	13.1314i	−1.76134	−	0.125060i
$106$		0			0
$107$	1.83463	−	1.83463i	0.0171461	−	0.0171461i	−0.698482	−	0.715628i	$-0.746141\pi$
$107$	1.83463	−	1.83463i	0.0171461	−	0.0171461i	0.715628	+	0.698482i	$0.246141\pi$
$108$		0			0
$109$		−	129.856i		−	1.19134i	−0.803228	−	0.595672i	$-0.796886\pi$
$109$		−	129.856i		−	1.19134i	0.803228	−	0.595672i	$-0.203114\pi$
$110$		0			0
$111$	−45.4046			−0.409050
$112$		0			0
$113$	113.005	−	113.005i	1.00005	−	1.00005i	4.51785e−5	−	1.00000i	$-0.499986\pi$
$113$	113.005	−	113.005i	1.00005	−	1.00005i	1.00000		4.51785e-5i	$-1.43808e-5\pi$
$114$		0			0
$115$	86.6669	+	5.82889i	0.753626	+	0.0506860i
$116$		0			0
$117$	264.838	−	264.838i	2.26358	−	2.26358i
$118$		0			0
$119$	89.9547	+	90.6281i	0.755922	+	0.761580i
$120$		0			0
$121$	92.4919			0.764396
$122$		0			0
$123$	−300.906	−	300.906i	−2.44639	−	2.44639i
$124$		0			0
$125$	−68.9137	−	104.288i	−0.551310	−	0.834301i
$126$		0			0
$127$	−25.4533	+	25.4533i	−0.200420	+	0.200420i	−0.800180	−	0.599760i	$-0.795263\pi$
$127$	−25.4533	+	25.4533i	−0.200420	+	0.200420i	0.599760	+	0.800180i	$0.295263\pi$
$128$		0			0
$129$	304.538			2.36076
$130$		0			0
$131$	−110.052			−0.840091			−0.420045	−	0.907503i	$-0.637986\pi$
$131$	−110.052			−0.840091			−0.420045	+	0.907503i	$0.637986\pi$
$132$		0			0
$133$	177.035	+	0.660147i	1.33109	+	0.00496351i
$134$		0			0
$135$	265.902	+	17.8835i	1.96964	+	0.132471i
$136$		0			0
$137$	65.8786	+	65.8786i	0.480866	+	0.480866i	0.905408	−	0.424542i	$-0.139565\pi$
$137$	65.8786	+	65.8786i	0.480866	+	0.480866i	−0.424542	+	0.905408i	$0.639565\pi$
$138$		0			0
$139$		−	181.155i		−	1.30327i	−0.758531	−	0.651637i	$-0.774083\pi$
$139$		−	181.155i		−	1.30327i	0.758531	−	0.651637i	$-0.225917\pi$
$140$		0			0
$141$	−145.128			−1.02927
$142$		0			0
$143$	74.1826	−	74.1826i	0.518759	−	0.518759i
$144$		0			0
$145$	43.9797	+	50.3221i	0.303309	+	0.347049i
$146$		0			0
$147$	184.907	−	182.169i	1.25787	−	1.23925i
$148$		0			0
$149$		−	262.986i		−	1.76501i	−0.470306	−	0.882504i	$-0.655856\pi$
$149$		−	262.986i		−	1.76501i	0.470306	−	0.882504i	$-0.344144\pi$
$150$		0			0
$151$			16.4378i			0.108859i	0.998518	+	0.0544297i	$0.0173341\pi$
$151$			16.4378i			0.108859i	−0.998518	+	0.0544297i	$0.982666\pi$
$152$		0			0
$153$	−245.875	−	245.875i	−1.60703	−	1.60703i
$154$		0			0
$155$	174.866	−	152.827i	1.12817	−	0.985979i
$156$		0			0
$157$	−132.576	+	132.576i	−0.844435	+	0.844435i	−0.989432	−	0.144997i	$-0.953683\pi$
$157$	−132.576	+	132.576i	−0.844435	+	0.844435i	0.144997	+	0.989432i	$0.453683\pi$
$158$		0			0
$159$		−	260.840i		−	1.64050i
$160$		0			0
$161$	−86.3098	+	85.6685i	−0.536086	+	0.532102i
$162$		0			0
$163$	99.2255	+	99.2255i	0.608746	+	0.608746i	0.942618	−	0.333873i	$-0.108356\pi$
$163$	99.2255	+	99.2255i	0.608746	+	0.608746i	−0.333873	+	0.942618i	$0.608356\pi$
$164$		0			0
$165$	141.101	+	9.48994i	0.855160	+	0.0575148i
$166$		0			0
$167$	100.023	+	100.023i	0.598939	+	0.598939i	0.940030	−	0.341092i	$-0.110797\pi$
$167$	100.023	+	100.023i	0.598939	+	0.598939i	−0.341092	+	0.940030i	$0.610797\pi$
$168$		0			0
$169$			217.070i			1.28444i
$170$		0			0
$171$	−482.088			−2.81923
$172$		0			0
$173$	173.655	+	173.655i	1.00379	+	1.00379i	0.999993	+	0.00379621i	$0.00120837\pi$
$173$	173.655	+	173.655i	1.00379	+	1.00379i	0.00379621	+	0.999993i	$0.498792\pi$
$174$		0			0
$175$	173.335	+	24.0802i	0.990488	+	0.137601i
$176$		0			0
$177$	−219.557	−	219.557i	−1.24043	−	1.24043i
$178$		0			0
$179$	−235.460			−1.31542			−0.657708	−	0.753273i	$-0.728474\pi$
$179$	−235.460			−1.31542			−0.657708	+	0.753273i	$0.728474\pi$
$180$		0			0
$181$			50.8514i			0.280947i	0.990084	+	0.140473i	$0.0448625\pi$
$181$			50.8514i			0.280947i	−0.990084	+	0.140473i	$0.955138\pi$
$182$		0			0
$183$	−54.2092	−	54.2092i	−0.296225	−	0.296225i
$184$		0			0
$185$	42.7594	+	2.87584i	0.231132	+	0.0155451i
$186$		0			0
$187$	−68.8708	−	68.8708i	−0.368293	−	0.368293i
$188$		0			0
$189$	−264.806	+	262.838i	−1.40109	+	1.39068i
$190$		0			0
$191$			5.08193i			0.0266070i	0.999912	+	0.0133035i	$0.00423476\pi$
$191$			5.08193i			0.0266070i	−0.999912	+	0.0133035i	$0.995765\pi$
$192$		0			0
$193$	−119.528	+	119.528i	−0.619318	+	0.619318i	−0.945357	−	0.326038i	$-0.894286\pi$
$193$	−119.528	+	119.528i	−0.619318	+	0.619318i	0.326038	+	0.945357i	$0.394286\pi$
$194$		0			0
$195$	−391.863	+	342.474i	−2.00955	+	1.75628i
$196$		0			0
$197$	33.8459	+	33.8459i	0.171807	+	0.171807i	0.787773	−	0.615966i	$-0.211234\pi$
$197$	33.8459	+	33.8459i	0.171807	+	0.171807i	−0.615966	+	0.787773i	$0.711234\pi$
$198$		0			0
$199$		−	190.458i		−	0.957076i	−0.878067	−	0.478538i	$-0.841167\pi$
$199$		−	190.458i		−	0.957076i	0.878067	−	0.478538i	$-0.158833\pi$
$200$		0			0
$201$		−	276.585i		−	1.37604i
$202$		0			0
$203$	−93.5643	−	0.348893i	−0.460908	−	0.00171869i
$204$		0			0
$205$	264.317	+	302.435i	1.28935	+	1.47529i
$206$		0			0
$207$	234.159	−	234.159i	1.13120	−	1.13120i
$208$		0			0
$209$	−135.035			−0.646102
$210$		0			0
$211$		−	136.412i		−	0.646503i	−0.946313	−	0.323251i	$-0.895224\pi$
$211$		−	136.412i		−	0.646503i	0.946313	−	0.323251i	$-0.104776\pi$
$212$		0			0
$213$	−91.2244	−	91.2244i	−0.428283	−	0.428283i
$214$		0			0
$215$	−286.797	−	19.2888i	−1.33394	−	0.0897155i
$216$		0			0
$217$	−1.21238	+	325.130i	−0.00558701	+	1.49829i
$218$		0			0
$219$	−231.557			−1.05734
$220$		0			0
$221$	358.426			1.62184
$222$		0			0
$223$	26.3304	−	26.3304i	0.118073	−	0.118073i	−0.645601	−	0.763675i	$-0.723393\pi$
$223$	26.3304	−	26.3304i	0.118073	−	0.118073i	0.763675	+	0.645601i	$0.223393\pi$
$224$		0			0
$225$	−472.252	−	63.8124i	−2.09890	−	0.283611i
$226$		0			0
$227$	72.2282	+	72.2282i	0.318186	+	0.318186i	0.848070	−	0.529884i	$-0.177765\pi$
$227$	72.2282	+	72.2282i	0.318186	+	0.318186i	−0.529884	+	0.848070i	$0.677765\pi$
$228$		0			0
$229$	233.994			1.02181			0.510905	−	0.859637i	$-0.329310\pi$
$229$	233.994			1.02181			0.510905	+	0.859637i	$0.329310\pi$
$230$		0			0
$231$	−140.520	+	139.476i	−0.608311	+	0.603791i
$232$		0			0
$233$	−40.2994	+	40.2994i	−0.172959	+	0.172959i	−0.788278	−	0.615319i	$-0.789027\pi$
$233$	−40.2994	+	40.2994i	−0.172959	+	0.172959i	0.615319	+	0.788278i	$0.289027\pi$
$234$		0			0
$235$	136.673	+	9.19210i	0.581587	+	0.0391153i
$236$		0			0
$237$	−508.058	+	508.058i	−2.14370	+	2.14370i
$238$		0			0
$239$	−103.504			−0.433070			−0.216535	−	0.976275i	$-0.569476\pi$
$239$	−103.504			−0.433070			−0.216535	+	0.976275i	$0.569476\pi$
$240$		0			0
$241$		−	181.600i		−	0.753528i	−0.926309	−	0.376764i	$-0.877037\pi$
$241$		−	181.600i		−	0.753528i	0.926309	−	0.376764i	$-0.122963\pi$
$242$		0			0
$243$	75.8106	−	75.8106i	0.311978	−	0.311978i
$244$		0			0
$245$	−185.673	+	159.845i	−0.757850	+	0.652429i
$246$		0			0
$247$	351.383	−	351.383i	1.42261	−	1.42261i
$248$		0			0
$249$			165.257i			0.663681i
$250$		0			0
$251$	160.287			0.638592			0.319296	−	0.947655i	$-0.396554\pi$
$251$	160.287			0.638592			0.319296	+	0.947655i	$0.396554\pi$
$252$		0			0
$253$	65.5892	−	65.5892i	0.259246	−	0.259246i
$254$		0			0
$255$	317.952	+	363.804i	1.24687	+	1.42668i
$256$		0			0
$257$	73.6255	−	73.6255i	0.286481	−	0.286481i	−0.549206	−	0.835687i	$-0.685070\pi$
$257$	73.6255	−	73.6255i	0.286481	−	0.286481i	0.835687	+	0.549206i	$0.185070\pi$
$258$		0			0
$259$	−42.5832	+	42.2668i	−0.164414	+	0.163192i
$260$		0			0
$261$	254.788			0.976197
$262$		0			0
$263$	196.235	+	196.235i	0.746140	+	0.746140i	0.973752	−	0.227612i	$-0.0730916\pi$
$263$	196.235	+	196.235i	0.746140	+	0.746140i	−0.227612	+	0.973752i	$0.573092\pi$
$264$		0			0
$265$	−16.5211	+	245.644i	−0.0623438	+	0.926960i
$266$		0			0
$267$	46.0211	−	46.0211i	0.172364	−	0.172364i
$268$		0			0
$269$	−66.6418			−0.247739			−0.123870	−	0.992299i	$-0.539530\pi$
$269$	−66.6418			−0.247739			−0.123870	+	0.992299i	$0.539530\pi$
$270$		0			0
$271$	138.471			0.510965			0.255482	−	0.966814i	$-0.417766\pi$
$271$	138.471			0.510965			0.255482	+	0.966814i	$0.417766\pi$
$272$		0			0
$273$	2.71686	−	728.594i	0.00995188	−	2.66884i
$274$		0			0
$275$	−132.280	−	17.8742i	−0.481019	−	0.0649970i
$276$		0			0
$277$	−215.950	−	215.950i	−0.779602	−	0.779602i	0.200161	−	0.979763i	$-0.435853\pi$
$277$	−215.950	−	215.950i	−0.779602	−	0.779602i	−0.979763	+	0.200161i	$0.935853\pi$
$278$		0			0
$279$		−	885.370i		−	3.17337i
$280$		0			0
$281$	−104.952			−0.373493			−0.186747	−	0.982408i	$-0.559794\pi$
$281$	−104.952			−0.373493			−0.186747	+	0.982408i	$0.559794\pi$
$282$		0			0
$283$	322.376	−	322.376i	1.13914	−	1.13914i	0.150535	−	0.988605i	$-0.451901\pi$
$283$	322.376	−	322.376i	1.13914	−	1.13914i	0.988605	−	0.150535i	$-0.0480995\pi$
$284$		0			0
$285$	668.360	+	44.9513i	2.34512	+	0.157724i
$286$		0			0
$287$	−562.319	−	2.09684i	−1.95930	−	0.00730606i
$288$		0			0
$289$		−	43.7611i		−	0.151422i
$290$		0			0
$291$			345.772i			1.18822i
$292$		0			0
$293$	346.513	+	346.513i	1.18264	+	1.18264i	0.979058	+	0.203582i	$0.0652582\pi$
$293$	346.513	+	346.513i	1.18264	+	1.18264i	0.203582	+	0.979058i	$0.434742\pi$
$294$		0			0
$295$	192.860	+	220.672i	0.653762	+	0.748042i
$296$		0			0
$297$	201.233	−	201.233i	0.677554	−	0.677554i
$298$		0			0
$299$			341.347i			1.14163i
$300$		0			0
$301$	285.615	−	283.493i	0.948886	−	0.941836i
$302$		0			0
$303$	−384.927	−	384.927i	−1.27038	−	1.27038i
$304$		0			0
$305$	47.6177	+	54.4847i	0.156124	+	0.178638i
$306$		0			0
$307$	231.968	+	231.968i	0.755596	+	0.755596i	0.975518	−	0.219922i	$-0.0705802\pi$
$307$	231.968	+	231.968i	0.755596	+	0.755596i	−0.219922	+	0.975518i	$0.570580\pi$
$308$		0			0
$309$		−	137.075i		−	0.443609i
$310$		0			0
$311$	−518.189			−1.66620			−0.833102	−	0.553120i	$-0.813437\pi$
$311$	−518.189			−1.66620			−0.833102	+	0.553120i	$0.813437\pi$
$312$		0			0
$313$	22.9990	+	22.9990i	0.0734792	+	0.0734792i	0.742891	−	0.669412i	$-0.233454\pi$
$313$	22.9990	+	22.9990i	0.0734792	+	0.0734792i	−0.669412	+	0.742891i	$0.733454\pi$
$314$		0			0
$315$	503.982	−	437.158i	1.59994	−	1.38780i
$316$		0			0
$317$	−388.164	−	388.164i	−1.22449	−	1.22449i	−0.966018	−	0.258476i	$-0.916780\pi$
$317$	−388.164	−	388.164i	−1.22449	−	1.22449i	−0.258476	−	0.966018i	$-0.583220\pi$
$318$		0			0
$319$	71.3673			0.223722
$320$		0			0
$321$			13.7443i			0.0428170i
$322$		0			0
$323$	−326.223	−	326.223i	−1.00998	−	1.00998i
$324$		0			0
$325$	390.726	−	297.703i	1.20223	−	0.916009i
$326$		0			0
$327$	486.414	+	486.414i	1.48750	+	1.48750i
$328$		0			0
$329$	−136.110	+	135.098i	−0.413707	+	0.410633i
$330$		0			0
$331$			503.079i			1.51988i	0.649995	+	0.759938i	$0.274771\pi$
$331$			503.079i			1.51988i	−0.649995	+	0.759938i	$0.725229\pi$
$332$		0			0
$333$	115.529	−	115.529i	0.346933	−	0.346933i
$334$		0			0
$335$	−17.5183	+	260.472i	−0.0522936	+	0.777528i
$336$		0			0
$337$	−346.146	−	346.146i	−1.02714	−	1.02714i	−0.999621	−	0.0275189i	$-0.991239\pi$
$337$	−346.146	−	346.146i	−1.02714	−	1.02714i	−0.0275189	−	0.999621i	$-0.508761\pi$
$338$		0			0
$339$			846.585i			2.49730i
$340$		0			0
$341$		−	247.997i		−	0.727263i
$342$		0			0
$343$	3.83695	−	342.979i	0.0111865	−	0.999937i
$344$		0			0
$345$	−346.469	+	302.802i	−1.00426	+	0.877686i
$346$		0			0
$347$	−147.270	+	147.270i	−0.424410	+	0.424410i	−0.886719	−	0.462309i	$-0.847021\pi$
$347$	−147.270	+	147.270i	−0.424410	+	0.424410i	0.462309	+	0.886719i	$0.347021\pi$
$348$		0			0
$349$	−183.581			−0.526020			−0.263010	−	0.964793i	$-0.584715\pi$
$349$	−183.581			−0.526020			−0.263010	+	0.964793i	$0.584715\pi$
$350$		0			0
$351$			1047.28i			2.98371i
$352$		0			0
$353$	14.1827	+	14.1827i	0.0401777	+	0.0401777i	0.726910	−	0.686733i	$-0.240956\pi$
$353$	14.1827	+	14.1827i	0.0401777	+	0.0401777i	−0.686733	+	0.726910i	$0.740956\pi$
$354$		0			0
$355$	80.1320	+	91.6879i	0.225724	+	0.258276i
$356$		0			0
$357$	−676.424	−	2.52232i	−1.89474	−	0.00706534i
$358$		0			0
$359$	−362.363			−1.00937			−0.504683	−	0.863305i	$-0.668391\pi$
$359$	−362.363			−1.00937			−0.504683	+	0.863305i	$0.668391\pi$
$360$		0			0
$361$	−278.627			−0.771819
$362$		0			0
$363$	−346.455	+	346.455i	−0.954420	+	0.954420i
$364$		0			0
$365$	218.067	+	14.6663i	0.597444	+	0.0401818i
$366$		0			0
$367$	−219.352	−	219.352i	−0.597691	−	0.597691i	0.342007	−	0.939697i	$-0.388893\pi$
$367$	−219.352	−	219.352i	−0.597691	−	0.597691i	−0.939697	+	0.342007i	$0.888893\pi$
$368$		0			0
$369$	1531.27			4.14977
$370$		0			0
$371$	−242.814	−	244.632i	−0.654486	−	0.659386i
$372$		0			0
$373$	−215.361	+	215.361i	−0.577375	+	0.577375i	−0.934179	−	0.356804i	$-0.883866\pi$
$373$	−215.361	+	215.361i	−0.577375	+	0.577375i	0.356804	+	0.934179i	$0.383866\pi$
$374$		0			0
$375$	648.774	+	132.503i	1.73006	+	0.353341i
$376$		0			0
$377$	−185.709	+	185.709i	−0.492597	+	0.492597i
$378$		0			0
$379$	668.674			1.76431			0.882156	−	0.470958i	$-0.156092\pi$
$379$	668.674			1.76431			0.882156	+	0.470958i	$0.156092\pi$
$380$		0			0
$381$		−	190.685i		−	0.500485i
$382$		0			0
$383$	254.814	−	254.814i	0.665311	−	0.665311i	−0.291316	−	0.956627i	$-0.594093\pi$
$383$	254.814	−	254.814i	0.665311	−	0.665311i	0.956627	+	0.291316i	$0.0940931\pi$
$384$		0			0
$385$	141.168	−	122.450i	0.366670	−	0.318052i
$386$		0			0
$387$	−774.876	+	774.876i	−2.00226	+	2.00226i
$388$		0			0
$389$		−	307.853i		−	0.791395i	−0.918381	−	0.395698i	$-0.870503\pi$
$389$		−	307.853i		−	0.791395i	0.918381	−	0.395698i	$-0.129497\pi$
$390$		0			0
$391$	316.906			0.810500
$392$		0			0
$393$	412.230	−	412.230i	1.04893	−	1.04893i
$394$		0			0
$395$	510.640	−	446.281i	1.29276	−	1.12982i
$396$		0			0
$397$	−116.570	+	116.570i	−0.293627	+	0.293627i	−0.838511	−	0.544884i	$-0.816574\pi$
$397$	−116.570	+	116.570i	−0.293627	+	0.293627i	0.544884	+	0.838511i	$0.316574\pi$
$398$		0			0
$399$	−665.606	+	660.660i	−1.66819	+	1.65579i
$400$		0			0
$401$	399.186			0.995476			0.497738	−	0.867327i	$-0.334164\pi$
$401$	399.186			0.995476			0.497738	+	0.867327i	$0.334164\pi$
$402$		0			0
$403$	645.327	+	645.327i	1.60131	+	1.60131i
$404$		0			0
$405$	−417.122	+	364.549i	−1.02993	+	0.900122i
$406$		0			0
$407$	32.3602	−	32.3602i	0.0795090	−	0.0795090i
$408$		0			0
$409$	−381.063			−0.931693			−0.465847	−	0.884865i	$-0.654250\pi$
$409$	−381.063			−0.931693			−0.465847	+	0.884865i	$0.654250\pi$
$410$		0			0
$411$	−493.534			−1.20081
$412$		0			0
$413$	−410.298	−	1.52997i	−0.993458	−	0.00370452i
$414$		0			0
$415$	10.4670	−	155.629i	0.0252218	−	0.375011i
$416$		0			0
$417$	678.567	+	678.567i	1.62726	+	1.62726i
$418$		0			0
$419$		−	647.238i		−	1.54472i	−0.635184	−	0.772361i	$-0.719076\pi$
$419$		−	647.238i		−	1.54472i	0.635184	−	0.772361i	$-0.280924\pi$
$420$		0			0
$421$	102.049			0.242397			0.121198	−	0.992628i	$-0.461326\pi$
$421$	102.049			0.242397			0.121198	+	0.992628i	$0.461326\pi$
$422$		0			0
$423$	369.267	−	369.267i	0.872972	−	0.872972i
$424$		0			0
$425$	−276.386	−	362.748i	−0.650320	−	0.853525i
$426$		0			0
$427$	−101.304	−	0.377753i	−0.237246	−	0.000884668i
$428$		0			0
$429$			555.743i			1.29544i
$430$		0			0
$431$			355.282i			0.824321i	0.911111	+	0.412160i	$0.135226\pi$
$431$			355.282i			0.824321i	−0.911111	+	0.412160i	$0.864774\pi$
$432$		0			0
$433$	−564.434	−	564.434i	−1.30354	−	1.30354i	−0.925987	−	0.377555i	$-0.876765\pi$
$433$	−564.434	−	564.434i	−1.30354	−	1.30354i	−0.377555	−	0.925987i	$-0.623235\pi$
$434$		0			0
$435$	−353.234	−	23.7572i	−0.812033	−	0.0546142i
$436$		0			0
$437$	310.679	−	310.679i	0.710936	−	0.710936i
$438$		0			0
$439$		−	632.554i		−	1.44090i	−0.693508	−	0.720449i	$-0.743936\pi$
$439$		−	632.554i		−	1.44090i	0.693508	−	0.720449i	$-0.256064\pi$
$440$		0			0
$441$	−6.96571	+	934.000i	−0.0157953	+	2.11791i
$442$		0			0
$443$	−388.523	−	388.523i	−0.877026	−	0.877026i	0.116200	−	0.993226i	$-0.462929\pi$
$443$	−388.523	−	388.523i	−0.877026	−	0.877026i	−0.993226	+	0.116200i	$0.962929\pi$
$444$		0			0
$445$	−46.2550	+	40.4252i	−0.103944	+	0.0908432i
$446$		0			0
$447$	985.088	+	985.088i	2.20378	+	2.20378i
$448$		0			0
$449$			445.157i			0.991440i	0.868482	+	0.495720i	$0.165096\pi$
$449$			445.157i			0.991440i	−0.868482	+	0.495720i	$0.834904\pi$
$450$		0			0
$451$	428.915			0.951032
$452$		0			0
$453$	−61.5723	−	61.5723i	−0.135921	−	0.135921i
$454$		0			0
$455$	−48.7063	+	685.976i	−0.107047	+	1.50764i
$456$		0			0
$457$	35.6409	+	35.6409i	0.0779889	+	0.0779889i	0.745025	−	0.667036i	$-0.232437\pi$
$457$	35.6409	+	35.6409i	0.0779889	+	0.0779889i	−0.667036	+	0.745025i	$0.732437\pi$
$458$		0			0
$459$	972.294			2.11829
$460$		0			0
$461$		−	636.338i		−	1.38034i	−0.723646	−	0.690171i	$-0.757535\pi$
$461$		−	636.338i		−	1.38034i	0.723646	−	0.690171i	$-0.242465\pi$
$462$		0			0
$463$	482.511	+	482.511i	1.04214	+	1.04214i	0.999072	+	0.0430689i	$0.0137135\pi$
$463$	482.511	+	482.511i	1.04214	+	1.04214i	0.0430689	+	0.999072i	$0.486287\pi$
$464$		0			0
$465$	−82.5546	+	1227.47i	−0.177537	+	2.63971i
$466$		0			0
$467$	143.927	+	143.927i	0.308195	+	0.308195i	0.844209	−	0.536014i	$-0.180071\pi$
$467$	143.927	+	143.927i	0.308195	+	0.308195i	−0.536014	+	0.844209i	$0.680071\pi$
$468$		0			0
$469$	−257.471	−	259.398i	−0.548979	−	0.553088i
$470$		0			0
$471$		−	993.203i		−	2.10871i
$472$		0			0
$473$	−217.047	+	217.047i	−0.458872	+	0.458872i
$474$		0			0
$475$	−626.577	−	84.6653i	−1.31911	−	0.178243i
$476$		0			0
$477$	663.689	+	663.689i	1.39138	+	1.39138i
$478$		0			0
$479$			651.349i			1.35981i	0.733300	+	0.679905i	$0.237979\pi$
$479$			651.349i			1.35981i	−0.733300	+	0.679905i	$0.762021\pi$
$480$		0			0
$481$			168.413i			0.350130i
$482$		0			0
$483$	2.40214	−	644.193i	0.00497337	−	1.33373i
$484$		0			0
$485$	21.9005	−	325.629i	0.0451558	−	0.671400i
$486$		0			0
$487$	10.5862	−	10.5862i	0.0217375	−	0.0217375i	−0.696154	−	0.717892i	$-0.745107\pi$
$487$	10.5862	−	10.5862i	0.0217375	−	0.0217375i	0.717892	+	0.696154i	$0.245107\pi$
$488$		0			0
$489$	−743.354			−1.52015
$490$		0			0
$491$		−	385.151i		−	0.784421i	−0.919875	−	0.392211i	$-0.871710\pi$
$491$		−	385.151i		−	0.784421i	0.919875	−	0.392211i	$-0.128290\pi$
$492$		0			0
$493$	172.412	+	172.412i	0.349719	+	0.349719i
$494$		0			0
$495$	−383.169	+	334.876i	−0.774079	+	0.676517i
$496$		0			0
$497$	−170.476	−	0.635691i	−0.343010	−	0.00127906i
$498$		0			0
$499$	−569.287			−1.14086			−0.570428	−	0.821348i	$-0.693223\pi$
$499$	−569.287			−1.14086			−0.570428	+	0.821348i	$0.693223\pi$
$500$		0			0
$501$	−749.327			−1.49566
$502$		0			0
$503$	−647.047	+	647.047i	−1.28637	+	1.28637i	−0.349402	+	0.936973i	$0.613615\pi$
$503$	−647.047	+	647.047i	−1.28637	+	1.28637i	−0.936973	+	0.349402i	$0.886385\pi$
$504$		0			0
$505$	338.122	+	386.882i	0.669548	+	0.766104i
$506$		0			0
$507$	−813.097	−	813.097i	−1.60374	−	1.60374i
$508$		0			0
$509$	−194.701			−0.382517			−0.191258	−	0.981540i	$-0.561257\pi$
$509$	−194.701			−0.382517			−0.191258	+	0.981540i	$0.561257\pi$
$510$		0			0
$511$	−217.168	+	215.555i	−0.424987	+	0.421829i
$512$		0			0
$513$	953.190	−	953.190i	1.85807	−	1.85807i
$514$		0			0
$515$	−8.68207	+	129.090i	−0.0168584	+	0.250659i
$516$		0			0
$517$	103.434	−	103.434i	0.200065	−	0.200065i
$518$		0			0
$519$	−1300.95			−2.50665
$520$		0			0
$521$			563.976i			1.08249i	0.840866	+	0.541244i	$0.182046\pi$
$521$			563.976i			1.08249i	−0.840866	+	0.541244i	$0.817954\pi$
$522$		0			0
$523$	110.514	−	110.514i	0.211309	−	0.211309i	−0.593515	−	0.804823i	$-0.702260\pi$
$523$	110.514	−	110.514i	0.211309	−	0.211309i	0.804823	+	0.593515i	$0.202260\pi$
$524$		0			0
$525$	−739.475	+	559.077i	−1.40852	+	1.06491i
$526$		0			0
$527$	599.119	−	599.119i	1.13685	−	1.13685i
$528$		0			0
$529$		−	227.195i		−	0.429479i
$530$		0			0
$531$	1117.29			2.10413
$532$		0			0
$533$	−1116.11	+	1116.11i	−2.09401	+	2.09401i
$534$		0			0
$535$	0.870534	−	12.9436i	0.00162717	−	0.0241936i
$536$		0			0
$537$	881.980	−	881.980i	1.64242	−	1.64242i
$538$		0			0
$539$	−1.95113	+	261.618i	−0.00361991	+	0.485377i
$540$		0			0
$541$	−477.169			−0.882013			−0.441006	−	0.897504i	$-0.645378\pi$
$541$	−477.169			−0.882013			−0.441006	+	0.897504i	$0.645378\pi$
$542$		0			0
$543$	−190.478	−	190.478i	−0.350789	−	0.350789i
$544$		0			0
$545$	−427.269	−	488.886i	−0.783979	−	0.897038i
$546$		0			0
$547$	550.361	−	550.361i	1.00615	−	1.00615i	0.00616429	−	0.999981i	$-0.498038\pi$
$547$	550.361	−	550.361i	1.00615	−	1.00615i	0.999981	−	0.00616429i	$-0.00196217\pi$
$548$		0			0
$549$	275.863			0.502483
$550$		0			0
$551$	338.048			0.613518
$552$		0			0
$553$	−3.54037	+	949.436i	−0.00640211	+	1.71688i
$554$		0			0
$555$	−170.940	+	149.395i	−0.308000	+	0.269181i
$556$		0			0
$557$	−187.128	−	187.128i	−0.335957	−	0.335957i	0.518886	−	0.854843i	$-0.326347\pi$
$557$	−187.128	−	187.128i	−0.335957	−	0.335957i	−0.854843	+	0.518886i	$0.826347\pi$
$558$		0			0
$559$		−	1129.58i		−	2.02072i
$560$		0			0
$561$	515.950			0.919697
$562$		0			0
$563$	−553.472	+	553.472i	−0.983077	+	0.983077i	−0.999859	−	0.0167825i	$-0.994658\pi$
$563$	−553.472	+	553.472i	−0.983077	+	0.983077i	0.0167825	+	0.999859i	$0.494658\pi$
$564$		0			0
$565$	53.6210	−	797.266i	0.0949045	−	1.41109i
$566$		0			0
$567$	2.89199	−	775.558i	0.00510051	−	1.36783i
$568$		0			0
$569$			6.99633i			0.0122958i	0.999981	+	0.00614792i	$0.00195696\pi$
$569$			6.99633i			0.0122958i	−0.999981	+	0.00614792i	$0.998043\pi$
$570$		0			0
$571$			569.612i			0.997569i	0.866726	+	0.498784i	$0.166220\pi$
$571$			569.612i			0.997569i	−0.866726	+	0.498784i	$0.833780\pi$
$572$		0			0
$573$	−19.0358	−	19.0358i	−0.0332213	−	0.0332213i
$574$		0			0
$575$	345.464	−	263.217i	0.600807	−	0.457768i
$576$		0			0
$577$	81.9100	−	81.9100i	0.141958	−	0.141958i	−0.632556	−	0.774515i	$-0.717994\pi$
$577$	81.9100	−	81.9100i	0.141958	−	0.141958i	0.774515	+	0.632556i	$0.217994\pi$
$578$		0			0
$579$		−	895.455i		−	1.54655i
$580$		0			0
$581$	153.836	+	154.988i	0.264779	+	0.266761i
$582$		0			0
$583$	185.903	+	185.903i	0.318873	+	0.318873i
$584$		0			0
$585$	125.666	−	1868.47i	0.214814	−	3.19396i
$586$		0			0
$587$	−101.642	−	101.642i	−0.173155	−	0.173155i	0.615209	−	0.788364i	$-0.289072\pi$
$587$	−101.642	−	101.642i	−0.173155	−	0.173155i	−0.788364	+	0.615209i	$0.789072\pi$
$588$		0			0
$589$		−	1174.70i		−	1.99439i
$590$		0			0
$591$	−253.559			−0.429034
$592$		0			0
$593$	415.591	+	415.591i	0.700828	+	0.700828i	0.964588	−	0.263760i	$-0.0849628\pi$
$593$	415.591	+	415.591i	0.700828	+	0.700828i	−0.263760	+	0.964588i	$0.584963\pi$
$594$		0			0
$595$	636.858	+	45.2187i	1.07035	+	0.0759978i
$596$		0			0
$597$	713.414	+	713.414i	1.19500	+	1.19500i
$598$		0			0
$599$	461.719			0.770816			0.385408	−	0.922746i	$-0.374061\pi$
$599$	461.719			0.770816			0.385408	+	0.922746i	$0.374061\pi$
$600$		0			0
$601$			118.562i			0.197275i	0.995123	+	0.0986373i	$0.0314484\pi$
$601$			118.562i			0.197275i	−0.995123	+	0.0986373i	$0.968552\pi$
$602$		0			0
$603$	703.751	+	703.751i	1.16708	+	1.16708i
$604$		0			0
$605$	348.215	−	304.328i	0.575562	−	0.503021i
$606$		0			0
$607$	−191.896	−	191.896i	−0.316138	−	0.316138i	0.531144	−	0.847282i	$-0.321762\pi$
$607$	−191.896	−	191.896i	−0.316138	−	0.316138i	−0.847282	+	0.531144i	$0.821762\pi$
$608$		0			0
$609$	351.778	−	349.165i	0.577633	−	0.573341i
$610$		0			0
$611$			538.302i			0.881017i
$612$		0			0
$613$	−336.397	+	336.397i	−0.548772	+	0.548772i	−0.926086	−	0.377313i	$-0.876848\pi$
$613$	−336.397	+	336.397i	−0.548772	+	0.548772i	0.377313	+	0.926086i	$0.376848\pi$
$614$		0			0
$615$	−2122.93	−	142.780i	−3.45191	−	0.232162i
$616$		0			0
$617$	−17.8001	−	17.8001i	−0.0288495	−	0.0288495i	0.692535	−	0.721384i	$-0.256494\pi$
$617$	−17.8001	−	17.8001i	−0.0288495	−	0.0288495i	−0.721384	+	0.692535i	$0.756494\pi$
$618$		0			0
$619$			660.367i			1.06683i	0.845854	+	0.533414i	$0.179091\pi$
$619$			660.367i			1.06683i	−0.845854	+	0.533414i	$0.820909\pi$
$620$		0			0
$621$			925.965i			1.49109i
$622$		0			0
$623$	0.320695	−	86.0023i	0.000514759	−	0.138045i
$624$		0			0
$625$	−602.586	−	165.876i	−0.964138	−	0.265401i
$626$		0			0
$627$	505.813	−	505.813i	0.806719	−	0.806719i
$628$		0			0
$629$	156.354			0.248575
$630$		0			0
$631$		−	1159.21i		−	1.83709i	−0.395313	−	0.918547i	$-0.629364\pi$
$631$		−	1159.21i		−	1.83709i	0.395313	−	0.918547i	$-0.370636\pi$
$632$		0			0
$633$	510.970	+	510.970i	0.807219	+	0.807219i
$634$		0			0
$635$	−12.0776	+	179.576i	−0.0190199	+	0.282797i
$636$		0			0
$637$	−675.695	−	685.850i	−1.06075	−	1.07669i
$638$		0			0
$639$	464.228			0.726491
$640$		0			0
$641$	−888.588			−1.38625			−0.693127	−	0.720816i	$-0.743767\pi$
$641$	−888.588			−1.38625			−0.693127	+	0.720816i	$0.743767\pi$
$642$		0			0
$643$	431.429	−	431.429i	0.670963	−	0.670963i	−0.286975	−	0.957938i	$-0.592650\pi$
$643$	431.429	−	431.429i	0.670963	−	0.670963i	0.957938	+	0.286975i	$0.0926497\pi$
$644$		0			0
$645$	1146.53	−	1002.03i	1.77756	−	1.55353i
$646$		0			0
$647$	38.7344	+	38.7344i	0.0598677	+	0.0598677i	0.736407	−	0.676539i	$-0.236521\pi$
$647$	38.7344	+	38.7344i	0.0598677	+	0.0598677i	−0.676539	+	0.736407i	$0.736521\pi$
$648$		0			0
$649$	312.960			0.482218
$650$		0			0
$651$	−1213.32	−	1222.41i	−1.86379	−	1.87774i
$652$		0			0
$653$	746.810	−	746.810i	1.14366	−	1.14366i	0.155885	−	0.987775i	$-0.450177\pi$
$653$	746.810	−	746.810i	1.14366	−	1.14366i	0.987775	−	0.155885i	$-0.0498231\pi$
$654$		0			0
$655$	−414.325	+	362.105i	−0.632557	+	0.552833i
$656$		0			0
$657$	589.180	−	589.180i	0.896773	−	0.896773i
$658$		0			0
$659$	749.367			1.13713			0.568563	−	0.822639i	$-0.307499\pi$
$659$	749.367			1.13713			0.568563	+	0.822639i	$0.307499\pi$
$660$		0			0
$661$		−	1158.45i		−	1.75257i	−0.481793	−	0.876285i	$-0.660014\pi$
$661$		−	1158.45i		−	1.75257i	0.481793	−	0.876285i	$-0.339986\pi$
$662$		0			0
$663$	−1342.58	+	1342.58i	−2.02501	+	2.02501i
$664$		0			0
$665$	668.675	−	580.014i	1.00553	−	0.872202i
$666$		0			0
$667$	−164.196	+	164.196i	−0.246172	+	0.246172i
$668$		0			0
$669$			197.256i			0.294851i
$670$		0			0
$671$	77.2707			0.115158
$672$		0			0
$673$	−290.178	+	290.178i	−0.431171	+	0.431171i	−0.889027	−	0.457855i	$-0.848618\pi$
$673$	−290.178	+	290.178i	−0.431171	+	0.431171i	0.457855	+	0.889027i	$0.348618\pi$
$674$		0			0
$675$	1059.91	−	807.572i	1.57024	−	1.19640i
$676$		0			0
$677$	266.713	−	266.713i	0.393963	−	0.393963i	−0.482134	−	0.876097i	$-0.660138\pi$
$677$	266.713	−	266.713i	0.393963	−	0.393963i	0.876097	+	0.482134i	$0.160138\pi$
$678$		0			0
$679$	321.877	+	324.287i	0.474046	+	0.477595i
$680$		0			0
$681$	−541.102			−0.794570
$682$		0			0
$683$	−676.697	−	676.697i	−0.990771	−	0.990771i	0.00918636	−	0.999958i	$-0.497076\pi$
$683$	−676.697	−	676.697i	−0.990771	−	0.990771i	−0.999958	+	0.00918636i	$0.997076\pi$
$684$		0			0
$685$	464.782	+	31.2595i	0.678514	+	0.0456342i
$686$		0			0
$687$	−876.492	+	876.492i	−1.27583	+	1.27583i
$688$		0			0
$689$	−967.498			−1.40421
$690$		0			0
$691$	530.569			0.767827			0.383914	−	0.923369i	$-0.374576\pi$
$691$	530.569			0.767827			0.383914	+	0.923369i	$0.374576\pi$
$692$		0			0
$693$	2.65659	−	712.429i	0.00383346	−	1.02804i
$694$		0			0
$695$	−596.057	−	682.015i	−0.857636	−	0.981317i
$696$		0			0
$697$	1036.19	+	1036.19i	1.48664	+	1.48664i
$698$		0			0
$699$		−	301.905i		−	0.431910i
$700$		0			0
$701$	−551.968			−0.787401			−0.393701	−	0.919239i	$-0.628805\pi$
$701$	−551.968			−0.787401			−0.393701	+	0.919239i	$0.628805\pi$
$702$		0			0
$703$	153.282	−	153.282i	0.218039	−	0.218039i
$704$		0			0
$705$	−546.379	+	477.515i	−0.775005	+	0.677327i
$706$		0			0
$707$	−719.334	−	2.68233i	−1.01745	−	0.00379396i
$708$		0			0
$709$			721.903i			1.01820i	0.860708	+	0.509099i	$0.170021\pi$
$709$			721.903i			1.01820i	−0.860708	+	0.509099i	$0.829979\pi$
$710$		0			0
$711$		−	2585.44i		−	3.63634i
$712$		0			0
$713$	570.572	+	570.572i	0.800241	+	0.800241i
$714$		0			0
$715$	35.1997	−	523.368i	0.0492303	−	0.731983i
$716$		0			0
$717$	387.703	−	387.703i	0.540729	−	0.540729i
$718$		0			0
$719$			852.389i			1.18552i	0.805379	+	0.592760i	$0.201962\pi$
$719$			852.389i			1.18552i	−0.805379	+	0.592760i	$0.798038\pi$
$720$		0			0
$721$	−127.602	−	128.558i	−0.176980	−	0.178305i
$722$		0			0
$723$	680.235	+	680.235i	0.940851	+	0.940851i
$724$		0			0
$725$	331.151	+	44.7463i	0.456760	+	0.0617191i
$726$		0			0
$727$	235.912	+	235.912i	0.324501	+	0.324501i	0.850491	−	0.525990i	$-0.176305\pi$
$727$	235.912	+	235.912i	0.324501	+	0.324501i	−0.525990	+	0.850491i	$0.676305\pi$
$728$		0			0
$729$		−	429.213i		−	0.588769i
$730$		0			0
$731$	−1048.70			−1.43461
$732$		0			0
$733$	391.187	+	391.187i	0.533679	+	0.533679i	0.921665	−	0.387986i	$-0.126829\pi$
$733$	391.187	+	391.187i	0.533679	+	0.533679i	−0.387986	+	0.921665i	$0.626829\pi$
$734$		0			0
$735$	96.7462	−	1294.24i	0.131627	−	1.76087i
$736$		0			0
$737$	197.124	+	197.124i	0.267468	+	0.267468i
$738$		0			0
$739$	−420.950			−0.569621			−0.284811	−	0.958584i	$-0.591931\pi$
$739$	−420.950			−0.569621			−0.284811	+	0.958584i	$0.591931\pi$
$740$		0			0
$741$			2632.41i			3.55251i
$742$		0			0
$743$	−544.803	−	544.803i	−0.733248	−	0.733248i	0.238014	−	0.971262i	$-0.423504\pi$
$743$	−544.803	−	544.803i	−0.733248	−	0.733248i	−0.971262	+	0.238014i	$0.923504\pi$
$744$		0			0
$745$	−865.307	−	990.094i	−1.16149	−	1.32899i
$746$		0			0
$747$	−420.484	−	420.484i	−0.562897	−	0.562897i
$748$		0			0
$749$	12.7944	+	12.8902i	0.0170820	+	0.0172099i
$750$		0			0
$751$		−	468.863i		−	0.624319i	−0.950030	−	0.312159i	$-0.898948\pi$
$751$		−	468.863i		−	0.624319i	0.950030	−	0.312159i	$-0.101052\pi$
$752$		0			0
$753$	−600.399	+	600.399i	−0.797342	+	0.797342i
$754$		0			0
$755$	54.0854	+	61.8852i	0.0716363	+	0.0819671i
$756$		0			0
$757$	90.8925	+	90.8925i	0.120069	+	0.120069i	0.764588	−	0.644519i	$-0.222942\pi$
$757$	90.8925	+	90.8925i	0.120069	+	0.120069i	−0.644519	+	0.764588i	$0.722942\pi$
$758$		0			0
$759$			491.366i			0.647386i
$760$		0			0
$761$		−	1012.45i		−	1.33041i	−0.746659	−	0.665207i	$-0.768343\pi$
$761$		−	1012.45i		−	1.33041i	0.746659	−	0.665207i	$-0.231657\pi$
$762$		0			0
$763$	908.989	+	3.38954i	1.19134	+	0.00444239i
$764$		0			0
$765$	−1734.68	−	116.668i	−2.26755	−	0.152507i
$766$		0			0
$767$	−814.371	+	814.371i	−1.06176	+	1.06176i
$768$		0			0
$769$	−895.086			−1.16396			−0.581980	−	0.813203i	$-0.697722\pi$
$769$	−895.086			−1.16396			−0.581980	+	0.813203i	$0.697722\pi$
$770$		0			0
$771$			551.570i			0.715396i
$772$		0			0
$773$	−124.555	−	124.555i	−0.161132	−	0.161132i	0.621936	−	0.783068i	$-0.286346\pi$
$773$	−124.555	−	124.555i	−0.161132	−	0.161132i	−0.783068	+	0.621936i	$0.786346\pi$
$774$		0			0
$775$	155.490	−	1150.73i	0.200633	−	1.48481i
$776$		0			0
$777$	1.18516	−	317.830i	0.00152530	−	0.409047i
$778$		0			0
$779$	2031.66			2.60804
$780$		0			0
$781$	130.033			0.166495
$782$		0			0
$783$	−503.769	+	503.769i	−0.643383	+	0.643383i
$784$		0			0
$785$	−62.9075	+	935.343i	−0.0801370	+	1.19152i
$786$		0			0
$787$	−729.166	−	729.166i	−0.926513	−	0.926513i	0.0709660	−	0.997479i	$-0.477392\pi$
$787$	−729.166	−	729.166i	−0.926513	−	0.926513i	−0.997479	+	0.0709660i	$0.977392\pi$
$788$		0			0
$789$	−1470.11			−1.86325
$790$		0			0
$791$	788.081	+	793.980i	0.996309	+	1.00377i
$792$		0			0
$793$	−201.071	+	201.071i	−0.253557	+	0.253557i
$794$		0			0
$795$	−858.246	−	982.015i	−1.07955	−	1.23524i
$796$		0			0
$797$	−698.698	+	698.698i	−0.876660	+	0.876660i	−0.993187	−	0.116527i	$-0.962824\pi$
$797$	−698.698	+	698.698i	−0.876660	+	0.876660i	0.116527	+	0.993187i	$0.462824\pi$
$798$		0			0
$799$	499.757			0.625478
$800$		0			0
$801$			234.195i			0.292378i
$802$		0			0
$803$	165.032	−	165.032i	0.205520	−	0.205520i
$804$		0			0
$805$	−43.0641	+	606.512i	−0.0534958	+	0.753431i
$806$		0			0
$807$	249.626	−	249.626i	0.309325	−	0.309325i
$808$		0			0
$809$		−	1166.88i		−	1.44237i	−0.692742	−	0.721186i	$-0.743597\pi$
$809$		−	1166.88i		−	1.44237i	0.692742	−	0.721186i	$-0.256403\pi$
$810$		0			0
$811$	545.364			0.672458			0.336229	−	0.941780i	$-0.390848\pi$
$811$	545.364			0.672458			0.336229	+	0.941780i	$0.390848\pi$
$812$		0			0
$813$	−518.684	+	518.684i	−0.637987	+	0.637987i
$814$		0			0
$815$	700.049	+	47.0826i	0.858956	+	0.0577701i
$816$		0			0
$817$	−1028.09	+	1028.09i	−1.25838	+	1.25838i
$818$		0			0
$819$	1846.94	+	1860.77i	2.25512	+	2.27200i
$820$		0			0
$821$	48.9036			0.0595659			0.0297829	−	0.999556i	$-0.490518\pi$
$821$	48.9036			0.0595659			0.0297829	+	0.999556i	$0.490518\pi$
$822$		0			0
$823$	115.349	+	115.349i	0.140157	+	0.140157i	0.773704	−	0.633547i	$-0.218402\pi$
$823$	115.349	+	115.349i	0.140157	+	0.140157i	−0.633547	+	0.773704i	$0.718402\pi$
$824$		0			0
$825$	562.446	−	428.540i	0.681752	−	0.519442i
$826$		0			0
$827$	416.893	−	416.893i	0.504102	−	0.504102i	−0.408608	−	0.912710i	$-0.633986\pi$
$827$	416.893	−	416.893i	0.504102	−	0.504102i	0.912710	+	0.408608i	$0.133986\pi$
$828$		0			0
$829$	134.715			0.162503			0.0812514	−	0.996694i	$-0.474108\pi$
$829$	134.715			0.162503			0.0812514	+	0.996694i	$0.474108\pi$
$830$		0			0
$831$	1617.80			1.94681
$832$		0			0
$833$	−636.740	+	627.313i	−0.764394	+	0.753077i
$834$		0			0
$835$	705.673	+	47.4609i	0.845118	+	0.0568394i
$836$		0			0
$837$	1750.56	+	1750.56i	2.09147	+	2.09147i
$838$		0			0
$839$		−	199.958i		−	0.238329i	−0.992875	−	0.119165i	$-0.961978\pi$
$839$		−	199.958i		−	0.238329i	0.992875	−	0.119165i	$-0.0380216\pi$
$840$		0			0
$841$	662.339			0.787561
$842$		0			0
$843$	393.126	−	393.126i	0.466342	−	0.466342i
$844$		0			0
$845$	714.228	+	817.228i	0.845241	+	0.967134i
$846$		0			0
$847$	−2.41424	+	647.439i	−0.00285035	+	0.764391i
$848$		0			0
$849$			2415.10i			2.84464i
$850$		0			0
$851$			148.904i			0.174975i
$852$		0			0
$853$	632.422	+	632.422i	0.741409	+	0.741409i	0.972849	−	0.231440i	$-0.0743437\pi$
$853$	632.422	+	632.422i	0.741409	+	0.741409i	−0.231440	+	0.972849i	$0.574344\pi$
$854$		0			0
$855$	−1814.97	+	1586.22i	−2.12277	+	1.85523i
$856$		0			0
$857$	−373.070	+	373.070i	−0.435320	+	0.435320i	−0.890434	−	0.455113i	$-0.849599\pi$
$857$	−373.070	+	373.070i	−0.435320	+	0.435320i	0.455113	+	0.890434i	$0.349599\pi$
$858$		0			0
$859$		−	311.575i		−	0.362719i	−0.983417	−	0.181359i	$-0.941950\pi$
$859$		−	311.575i		−	0.362719i	0.983417	−	0.181359i	$-0.0580497\pi$
$860$		0			0
$861$	2114.18	−	2098.47i	2.45549	−	2.43725i
$862$		0			0
$863$	579.293	+	579.293i	0.671255	+	0.671255i	0.958005	−	0.286750i	$-0.0925751\pi$
$863$	579.293	+	579.293i	0.671255	+	0.671255i	−0.286750	+	0.958005i	$0.592575\pi$
$864$		0			0
$865$	1225.16	+	82.3997i	1.41637	+	0.0952597i
$866$		0			0
$867$	163.919	+	163.919i	0.189065	+	0.189065i
$868$		0			0
$869$		−	724.194i		−	0.833364i
$870$		0			0
$871$	−1025.90			−1.17784
$872$		0			0
$873$	−879.794	−	879.794i	−1.00778	−	1.00778i
$874$		0			0
$875$	731.807	−	479.670i	0.836351	−	0.548195i
$876$		0			0
$877$	−497.930	−	497.930i	−0.567765	−	0.567765i	0.363737	−	0.931502i	$-0.381501\pi$
$877$	−497.930	−	497.930i	−0.567765	−	0.567765i	−0.931502	+	0.363737i	$0.881501\pi$
$878$		0			0
$879$	−2595.93			−2.95327
$880$		0			0
$881$		−	1087.91i		−	1.23486i	−0.786625	−	0.617432i	$-0.788173\pi$
$881$		−	1087.91i		−	1.23486i	0.786625	−	0.617432i	$-0.211827\pi$
$882$		0			0
$883$	−974.771	−	974.771i	−1.10393	−	1.10393i	−0.993932	−	0.109999i	$-0.964915\pi$
$883$	−974.771	−	974.771i	−1.10393	−	1.10393i	−0.109999	−	0.993932i	$-0.535085\pi$
$884$		0			0
$885$	−1549.00	−	104.180i	−1.75028	−	0.117717i
$886$		0			0
$887$	−1012.26	−	1012.26i	−1.14121	−	1.14121i	−0.988229	−	0.152984i	$-0.951112\pi$
$887$	−1012.26	−	1012.26i	−1.14121	−	1.14121i	−0.152984	−	0.988229i	$-0.548888\pi$
$888$		0			0
$889$	−177.507	−	178.836i	−0.199671	−	0.201166i
$890$		0			0
$891$			591.566i			0.663935i
$892$		0			0
$893$	489.938	−	489.938i	0.548643	−	0.548643i
$894$		0			0
$895$	−886.462	+	774.736i	−0.990460	+	0.865627i
$896$		0			0
$897$	−1278.61	−	1278.61i	−1.42543	−	1.42543i
$898$		0			0
$899$			620.836i			0.690586i
$900$		0			0
$901$			898.221i			0.996915i
$902$		0			0
$903$	−7.94912	+	2131.75i	−0.00880301	+	2.36074i
$904$		0			0
$905$	167.317	+	191.446i	0.184881	+	0.211543i
$906$		0			0
$907$	−1067.07	+	1067.07i	−1.17649	+	1.17649i	−0.195853	+	0.980633i	$0.562748\pi$
$907$	−1067.07	+	1067.07i	−1.17649	+	1.17649i	−0.980633	+	0.195853i	$0.937252\pi$
$908$		0			0
$909$	1958.84			2.15494
$910$		0			0
$911$		−	581.817i		−	0.638658i	−0.947644	−	0.319329i	$-0.896543\pi$
$911$		−	581.817i		−	0.638658i	0.947644	−	0.319329i	$-0.103457\pi$
$912$		0			0
$913$	−117.780	−	117.780i	−0.129003	−	0.129003i
$914$		0			0
$915$	−382.453	−	25.7223i	−0.417982	−	0.0281118i
$916$		0			0
$917$	2.87260	−	770.358i	0.00313260	−	0.840085i
$918$		0			0
$919$	186.155			0.202562			0.101281	−	0.994858i	$-0.467706\pi$
$919$	186.155			0.202562			0.101281	+	0.994858i	$0.467706\pi$
$920$		0			0
$921$	−1737.80			−1.88686
$922$		0			0
$923$	−338.366	+	338.366i	−0.366593	+	0.366593i
$924$		0			0
$925$	170.444	−	129.865i	0.184264	−	0.140395i
$926$		0			0
$927$	348.778	+	348.778i	0.376244	+	0.376244i
$928$		0			0
$929$	−1007.18			−1.08415			−0.542076	−	0.840329i	$-0.682362\pi$
$929$	−1007.18			−1.08415			−0.542076	+	0.840329i	$0.682362\pi$
$930$		0			0
$931$	−9.24199	+	1239.22i	−0.00992695	+	1.33106i
$932$		0			0
$933$	1941.02	−	1941.02i	2.08041	−	2.08041i
$934$		0			0
$935$	−485.892	−	32.6793i	−0.519671	−	0.0349511i
$936$		0			0
$937$	664.204	−	664.204i	0.708862	−	0.708862i	−0.257434	−	0.966296i	$-0.582877\pi$
$937$	664.204	−	664.204i	0.708862	−	0.708862i	0.966296	+	0.257434i	$0.0828769\pi$
$938$		0			0
$939$	−172.298			−0.183491
$940$		0			0
$941$			947.407i			1.00681i	0.864051	+	0.503404i	$0.167919\pi$
$941$			947.407i			1.00681i	−0.864051	+	0.503404i	$0.832081\pi$
$942$		0			0
$943$	−986.816	+	986.816i	−1.04646	+	1.04646i
$944$		0			0
$945$	−132.124	+	1860.83i	−0.139814	+	1.96913i
$946$		0			0
$947$	−745.833	+	745.833i	−0.787575	+	0.787575i	−0.981096	−	0.193521i	$-0.938009\pi$
$947$	−745.833	+	745.833i	−0.787575	+	0.787575i	0.193521	+	0.981096i	$0.438009\pi$
$948$		0			0
$949$			858.881i			0.905038i
$950$		0			0
$951$	2907.96			3.05779
$952$		0			0
$953$	−148.533	+	148.533i	−0.155859	+	0.155859i	−0.780729	−	0.624870i	$-0.785152\pi$
$953$	−148.533	+	148.533i	−0.155859	+	0.155859i	0.624870	+	0.780729i	$0.285152\pi$
$954$		0			0
$955$	16.7211	+	19.1325i	0.0175091	+	0.0200341i
$956$		0			0
$957$	−267.326	+	267.326i	−0.279338	+	0.279338i
$958$		0			0
$959$	−462.867	+	459.427i	−0.482655	+	0.479069i
$960$		0			0
$961$	1196.37			1.24492
$962$		0			0
$963$	−34.9713	−	34.9713i	−0.0363149	−	0.0363149i
$964$		0			0
$965$	−56.7164	+	843.289i	−0.0587734	+	0.873874i
$966$		0			0
$967$	785.722	−	785.722i	0.812535	−	0.812535i	−0.172478	−	0.985013i	$-0.555177\pi$
$967$	785.722	−	785.722i	0.812535	−	0.812535i	0.985013	+	0.172478i	$0.0551774\pi$
$968$		0			0
$969$	2443.92			2.52211
$970$		0			0
$971$	574.407			0.591562			0.295781	−	0.955256i	$-0.404420\pi$
$971$	574.407			0.591562			0.295781	+	0.955256i	$0.404420\pi$
$972$		0			0
$973$	1268.08	+	4.72855i	1.30326	+	0.00485976i
$974$		0			0
$975$	−348.444	+	2578.70i	−0.357378	+	2.64482i
$976$		0			0
$977$	−327.396	−	327.396i	−0.335103	−	0.335103i	0.519417	−	0.854521i	$-0.326149\pi$
$977$	−327.396	−	327.396i	−0.335103	−	0.335103i	−0.854521	+	0.519417i	$0.826149\pi$
$978$		0			0
$979$			65.5993i			0.0670064i
$980$		0			0
$981$	−2475.29			−2.52323
$982$		0			0
$983$	573.336	−	573.336i	0.583252	−	0.583252i	−0.352544	−	0.935795i	$-0.614683\pi$
$983$	573.336	−	573.336i	0.583252	−	0.583252i	0.935795	+	0.352544i	$0.114683\pi$
$984$		0			0
$985$	238.788	+	16.0599i	0.242424	+	0.0163045i
$986$		0			0
$987$	3.78815	−	1015.89i	0.00383805	−	1.02927i
$988$		0			0
$989$		−	998.729i		−	1.00984i
$990$		0			0
$991$		−	682.946i		−	0.689149i	−0.938759	−	0.344574i	$-0.888023\pi$
$991$		−	682.946i		−	0.689149i	0.938759	−	0.344574i	$-0.111977\pi$
$992$		0			0
$993$	−1884.42	−	1884.42i	−1.89771	−	1.89771i
$994$		0			0
$995$	−626.667	−	717.039i	−0.629816	−	0.720643i
$996$		0			0
$997$	−479.397	+	479.397i	−0.480840	+	0.480840i	−0.905400	−	0.424560i	$-0.860429\pi$
$997$	−479.397	+	479.397i	−0.480840	+	0.480840i	0.424560	+	0.905400i	$0.360429\pi$
$998$		0			0
$999$			456.849i			0.457307i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	560.3.v.a.447.2	yes	32
4.3	odd	2	inner	560.3.v.a.447.15	yes	32
5.3	odd	4	inner	560.3.v.a.223.1	✓	32
7.6	odd	2	inner	560.3.v.a.447.16	yes	32
20.3	even	4	inner	560.3.v.a.223.16	yes	32
28.27	even	2	inner	560.3.v.a.447.1	yes	32
35.13	even	4	inner	560.3.v.a.223.15	yes	32
140.83	odd	4	inner	560.3.v.a.223.2	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
560.3.v.a.223.1	✓	32	5.3	odd	4	inner
560.3.v.a.223.2	yes	32	140.83	odd	4	inner
560.3.v.a.223.15	yes	32	35.13	even	4	inner
560.3.v.a.223.16	yes	32	20.3	even	4	inner
560.3.v.a.447.1	yes	32	28.27	even	2	inner
560.3.v.a.447.2	yes	32	1.1	even	1	trivial
560.3.v.a.447.15	yes	32	4.3	odd	2	inner
560.3.v.a.447.16	yes	32	7.6	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 560 = 2^{4} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	560.v (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-3.74578 + 3.74578i) q^{3} +(3.76482 - 3.29031i) q^{5} +(-0.0261022 + 6.99995i) q^{7} -19.0618i q^{9} -5.33929i q^{11} +(13.8937 + 13.8937i) q^{13} +(-1.77738 + 26.4270i) q^{15} +(12.8989 - 12.8989i) q^{17} -25.2908i q^{19} +(-26.1225 - 26.3181i) q^{21} +(12.2842 + 12.2842i) q^{23} +(3.34766 - 24.7748i) q^{25} +(37.6891 + 37.6891i) q^{27} +13.3664i q^{29} +46.4474 q^{31} +(19.9998 + 19.9998i) q^{33} +(22.9338 + 26.4394i) q^{35} +(6.06076 + 6.06076i) q^{37} -104.086 q^{39} +80.3318i q^{41} +(-40.6508 - 40.6508i) q^{43} +(-62.7192 - 71.7640i) q^{45} +(19.3721 + 19.3721i) q^{47} +(-48.9986 - 0.365428i) q^{49} +96.6326i q^{51} +(-34.8178 + 34.8178i) q^{53} +(-17.5680 - 20.1015i) q^{55} +(94.7340 + 94.7340i) q^{57} +58.6144i q^{59} +14.4721i q^{61} +(133.431 + 0.497554i) q^{63} +(98.0219 + 6.59257i) q^{65} +(-36.9195 + 36.9195i) q^{67} -92.0282 q^{69} +24.3539i q^{71} +(30.9090 + 30.9090i) q^{73} +(80.2615 + 105.341i) q^{75} +(37.3748 + 0.139367i) q^{77} +135.635 q^{79} -110.795 q^{81} +(22.0590 - 22.0590i) q^{83} +(6.12052 - 91.0031i) q^{85} +(-50.0677 - 50.0677i) q^{87} -12.2861 q^{89} +(-97.6179 + 96.8926i) q^{91} +(-173.982 + 173.982i) q^{93} +(-83.2148 - 95.2153i) q^{95} +(46.1549 - 46.1549i) q^{97} -101.776 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 64 q^{21} + 72 q^{25} - 72 q^{37} - 272 q^{53} + 280 q^{57} + 376 q^{65} + 24 q^{77} - 528 q^{81} - 96 q^{85} - 552 q^{93}+O(q^{100}) \) 32 * q - 64 * q^21 + 72 * q^25 - 72 * q^37 - 272 * q^53 + 280 * q^57 + 376 * q^65 + 24 * q^77 - 528 * q^81 - 96 * q^85 - 552 * q^93

Introduction

L-functions

Modular forms

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Database

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