LMFDB - Embedded newform 576.2.i.n.385.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [576,2,Mod(193,576)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(576, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 2]))

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

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

chi := DirichletCharacter("576.193");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 576 = 2^{6} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	576.i (of order $3$, 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:	$4.59938315643$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	8.0.170772624.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 3x^{7} + 5x^{6} - 6x^{5} + 6x^{4} - 12x^{3} + 20x^{2} - 24x + 16 $ x^8 - 3x^7 + 5x^6 - 6x^5 + 6x^4 - 12x^3 + 20x^2 - 24*x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{2}\cdot 3^{2} $
Twist minimal:	no (minimal twist has level 288)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			385.2
Root			$1.41203 + 0.0786378i$ of defining polynomial
Character	$\chi$	$=$	576.385
Dual form			576.2.i.n.193.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.637910 - 1.61030i) q^{3} +(-1.68614 - 2.92048i) q^{5} +(2.35143 - 4.07279i) q^{7} +(-2.18614 + 2.05446i) q^{9} +O(q^{10})$	\(q+(-0.637910 - 1.61030i) q^{3} +(-1.68614 - 2.92048i) q^{5} +(2.35143 - 4.07279i) q^{7} +(-2.18614 + 2.05446i) q^{9} +(-0.437696 + 0.758112i) q^{11} +(-0.686141 - 1.18843i) q^{13} +(-3.62725 + 4.57820i) q^{15} -2.37228 q^{17} +5.57825 q^{19} +(-8.05842 - 1.18843i) q^{21} +(2.35143 + 4.07279i) q^{23} +(-3.18614 + 5.51856i) q^{25} +(4.70285 + 2.20979i) q^{27} +(-2.68614 + 4.65253i) q^{29} +(-3.22682 - 5.58902i) q^{31} +(1.50000 + 0.221215i) q^{33} -15.8593 q^{35} -4.00000 q^{37} +(-1.47603 + 1.86301i) q^{39} +(-0.500000 - 0.866025i) q^{41} +(0.437696 - 0.758112i) q^{43} +(9.68614 + 2.92048i) q^{45} +(2.35143 - 4.07279i) q^{47} +(-7.55842 - 13.0916i) q^{49} +(1.51330 + 3.82009i) q^{51} +4.00000 q^{53} +2.95207 q^{55} +(-3.55842 - 8.98266i) q^{57} +(-4.26516 - 7.38747i) q^{59} +(-1.05842 + 1.83324i) q^{61} +(3.22682 + 13.7346i) q^{63} +(-2.31386 + 4.00772i) q^{65} +(4.26516 + 7.38747i) q^{67} +(5.05842 - 6.38458i) q^{69} -9.40571 q^{71} +10.3723 q^{73} +(10.9190 + 1.61030i) q^{75} +(2.05842 + 3.56529i) q^{77} +(3.22682 - 5.58902i) q^{79} +(0.558422 - 8.98266i) q^{81} +(1.47603 - 2.55657i) q^{83} +(4.00000 + 6.92820i) q^{85} +(9.20550 + 1.35760i) q^{87} +12.7446 q^{89} -6.45364 q^{91} +(-6.94158 + 8.76144i) q^{93} +(-9.40571 - 16.2912i) q^{95} +(-4.50000 + 7.79423i) q^{97} +(-0.600642 - 2.55657i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 2 q^{5} - 6 q^{9}+O(q^{10}) $ 8 * q - 2 * q^5 - 6 * q^9	$ 8 q - 2 q^{5} - 6 q^{9} + 6 q^{13} + 4 q^{17} - 30 q^{21} - 14 q^{25} - 10 q^{29} + 12 q^{33} - 32 q^{37} - 4 q^{41} + 66 q^{45} - 26 q^{49} + 32 q^{53} + 6 q^{57} + 26 q^{61} - 30 q^{65} + 6 q^{69} + 60 q^{73} - 18 q^{77} - 30 q^{81} + 32 q^{85} + 56 q^{89} - 90 q^{93} - 36 q^{97}+O(q^{100}) $ 8 * q - 2 * q^5 - 6 * q^9 + 6 * q^13 + 4 * q^17 - 30 * q^21 - 14 * q^25 - 10 * q^29 + 12 * q^33 - 32 * q^37 - 4 * q^41 + 66 * q^45 - 26 * q^49 + 32 * q^53 + 6 * q^57 + 26 * q^61 - 30 * q^65 + 6 * q^69 + 60 * q^73 - 18 * q^77 - 30 * q^81 + 32 * q^85 + 56 * q^89 - 90 * q^93 - 36 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/576\mathbb{Z}\right)^\times$.

$n$	$65$	$127$	$325$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$1$

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
$3$	−0.637910	−	1.61030i	−0.368298	−	0.929708i
$3$	−0.637910	−	1.61030i	−0.368298	−	0.929708i
$4$		0			0
$5$	−1.68614	−	2.92048i	−0.754065	−	1.30608i	−0.945838	−	0.324640i	$-0.894757\pi$
$5$	−1.68614	−	2.92048i	−0.754065	−	1.30608i	0.191773	−	0.981439i	$-0.438576\pi$
$6$		0			0
$7$	2.35143	−	4.07279i	0.888756	−	1.53937i	0.0474088	−	0.998876i	$-0.484904\pi$
$7$	2.35143	−	4.07279i	0.888756	−	1.53937i	0.841347	−	0.540495i	$-0.181763\pi$
$8$		0			0
$9$	−2.18614	+	2.05446i	−0.728714	+	0.684819i
$10$		0			0
$11$	−0.437696	+	0.758112i	−0.131970	+	0.228579i	−0.924436	−	0.381337i	$-0.875464\pi$
$11$	−0.437696	+	0.758112i	−0.131970	+	0.228579i	0.792466	+	0.609917i	$0.208797\pi$
$12$		0			0
$13$	−0.686141	−	1.18843i	−0.190301	−	0.329611i	0.755049	−	0.655669i	$-0.227613\pi$
$13$	−0.686141	−	1.18843i	−0.190301	−	0.329611i	−0.945350	+	0.326057i	$0.894280\pi$
$14$		0			0
$15$	−3.62725	+	4.57820i	−0.936551	+	1.18209i
$16$		0			0
$17$	−2.37228			−0.575363			−0.287681	−	0.957726i	$-0.592884\pi$
$17$	−2.37228			−0.575363			−0.287681	+	0.957726i	$0.592884\pi$
$18$		0			0
$19$	5.57825			1.27974			0.639869	−	0.768484i	$-0.278989\pi$
$19$	5.57825			1.27974			0.639869	+	0.768484i	$0.278989\pi$
$20$		0			0
$21$	−8.05842	−	1.18843i	−1.75849	−	0.259337i
$22$		0			0
$23$	2.35143	+	4.07279i	0.490307	+	0.849236i	0.999938	−	0.0111571i	$-0.00355150\pi$
$23$	2.35143	+	4.07279i	0.490307	+	0.849236i	−0.509631	+	0.860393i	$0.670218\pi$
$24$		0			0
$25$	−3.18614	+	5.51856i	−0.637228	+	1.10371i
$26$		0			0
$27$	4.70285	+	2.20979i	0.905065	+	0.425274i
$28$		0			0
$29$	−2.68614	+	4.65253i	−0.498804	+	0.863954i	−0.999999	−	0.00138070i	$-0.999561\pi$
$29$	−2.68614	+	4.65253i	−0.498804	+	0.863954i	0.501195	+	0.865334i	$0.332894\pi$
$30$		0			0
$31$	−3.22682	−	5.58902i	−0.579554	−	1.00382i	−0.995530	−	0.0944415i	$-0.969893\pi$
$31$	−3.22682	−	5.58902i	−0.579554	−	1.00382i	0.415976	−	0.909375i	$-0.363440\pi$
$32$		0			0
$33$	1.50000	+	0.221215i	0.261116	+	0.0385086i
$34$		0			0
$35$	−15.8593			−2.68072
$36$		0			0
$37$	−4.00000			−0.657596			−0.328798	−	0.944400i	$-0.606644\pi$
$37$	−4.00000			−0.657596			−0.328798	+	0.944400i	$0.606644\pi$
$38$		0			0
$39$	−1.47603	+	1.86301i	−0.236355	+	0.298320i
$40$		0			0
$41$	−0.500000	−	0.866025i	−0.0780869	−	0.135250i	0.824338	−	0.566099i	$-0.191548\pi$
$41$	−0.500000	−	0.866025i	−0.0780869	−	0.135250i	−0.902424	+	0.430848i	$0.858214\pi$
$42$		0			0
$43$	0.437696	−	0.758112i	0.0667481	−	0.115611i	−0.830720	−	0.556690i	$-0.812071\pi$
$43$	0.437696	−	0.758112i	0.0667481	−	0.115611i	0.897468	+	0.441079i	$0.145404\pi$
$44$		0			0
$45$	9.68614	+	2.92048i	1.44392	+	0.435360i
$46$		0			0
$47$	2.35143	−	4.07279i	0.342991	−	0.594078i	−0.641996	−	0.766708i	$-0.721893\pi$
$47$	2.35143	−	4.07279i	0.342991	−	0.594078i	0.984987	+	0.172630i	$0.0552266\pi$
$48$		0			0
$49$	−7.55842	−	13.0916i	−1.07977	−	1.87022i
$50$		0			0
$51$	1.51330	+	3.82009i	0.211905	+	0.534919i
$52$		0			0
$53$	4.00000			0.549442			0.274721	−	0.961524i	$-0.411414\pi$
$53$	4.00000			0.549442			0.274721	+	0.961524i	$0.411414\pi$
$54$		0			0
$55$	2.95207			0.398057
$56$		0			0
$57$	−3.55842	−	8.98266i	−0.471325	−	1.18978i
$58$		0			0
$59$	−4.26516	−	7.38747i	−0.555276	−	0.961767i	−0.997882	−	0.0650505i	$-0.979279\pi$
$59$	−4.26516	−	7.38747i	−0.555276	−	0.961767i	0.442606	−	0.896716i	$-0.354054\pi$
$60$		0			0
$61$	−1.05842	+	1.83324i	−0.135517	+	0.234722i	−0.925795	−	0.378026i	$-0.876603\pi$
$61$	−1.05842	+	1.83324i	−0.135517	+	0.234722i	0.790278	+	0.612749i	$0.209936\pi$
$62$		0			0
$63$	3.22682	+	13.7346i	0.406541	+	1.73040i
$64$		0			0
$65$	−2.31386	+	4.00772i	−0.286999	+	0.497097i
$66$		0			0
$67$	4.26516	+	7.38747i	0.521072	+	0.902523i	0.999700	+	0.0245053i	$0.00780106\pi$
$67$	4.26516	+	7.38747i	0.521072	+	0.902523i	−0.478628	+	0.878018i	$0.658866\pi$
$68$		0			0
$69$	5.05842	−	6.38458i	0.608962	−	0.768613i
$70$		0			0
$71$	−9.40571			−1.11625			−0.558126	−	0.829756i	$-0.688480\pi$
$71$	−9.40571			−1.11625			−0.558126	+	0.829756i	$0.688480\pi$
$72$		0			0
$73$	10.3723			1.21398			0.606992	−	0.794708i	$-0.292376\pi$
$73$	10.3723			1.21398			0.606992	+	0.794708i	$0.292376\pi$
$74$		0			0
$75$	10.9190	+	1.61030i	1.26082	+	0.185942i
$76$		0			0
$77$	2.05842	+	3.56529i	0.234579	+	0.406303i
$78$		0			0
$79$	3.22682	−	5.58902i	0.363046	−	0.628813i	−0.625415	−	0.780292i	$-0.715070\pi$
$79$	3.22682	−	5.58902i	0.363046	−	0.628813i	0.988460	+	0.151479i	$0.0484036\pi$
$80$		0			0
$81$	0.558422	−	8.98266i	0.0620469	−	0.998073i
$82$		0			0
$83$	1.47603	−	2.55657i	0.162016	−	0.280620i	−0.773576	−	0.633704i	$-0.781534\pi$
$83$	1.47603	−	2.55657i	0.162016	−	0.280620i	0.935592	+	0.353084i	$0.114867\pi$
$84$		0			0
$85$	4.00000	+	6.92820i	0.433861	+	0.751469i
$86$		0			0
$87$	9.20550	+	1.35760i	0.986933	+	0.145550i
$88$		0			0
$89$	12.7446			1.35092			0.675460	−	0.737396i	$-0.263945\pi$
$89$	12.7446			1.35092			0.675460	+	0.737396i	$0.263945\pi$
$90$		0			0
$91$	−6.45364			−0.676525
$92$		0			0
$93$	−6.94158	+	8.76144i	−0.719808	+	0.908519i
$94$		0			0
$95$	−9.40571	−	16.2912i	−0.965005	−	1.67144i
$96$		0			0
$97$	−4.50000	+	7.79423i	−0.456906	+	0.791384i	−0.998796	−	0.0490655i	$-0.984376\pi$
$97$	−4.50000	+	7.79423i	−0.456906	+	0.791384i	0.541890	+	0.840450i	$0.317709\pi$
$98$		0			0
$99$	−0.600642	−	2.55657i	−0.0603668	−	0.256945i
$100$		0			0
$101$	1.05842	−	1.83324i	0.105317	−	0.182414i	−0.808551	−	0.588426i	$-0.799748\pi$
$101$	1.05842	−	1.83324i	0.105317	−	0.182414i	0.913868	+	0.406012i	$0.133081\pi$
$102$		0			0
$103$	−2.35143	−	4.07279i	−0.231693	−	0.401304i	0.726613	−	0.687047i	$-0.241093\pi$
$103$	−2.35143	−	4.07279i	−0.231693	−	0.401304i	−0.958306	+	0.285742i	$0.907760\pi$
$104$		0			0
$105$	10.1168	+	25.5383i	0.987303	+	2.49229i
$106$		0			0
$107$	5.57825			0.539270			0.269635	−	0.962963i	$-0.413097\pi$
$107$	5.57825			0.539270			0.269635	+	0.962963i	$0.413097\pi$
$108$		0			0
$109$	5.48913			0.525763			0.262881	−	0.964828i	$-0.415327\pi$
$109$	5.48913			0.525763			0.262881	+	0.964828i	$0.415327\pi$
$110$		0			0
$111$	2.55164	+	6.44121i	0.242191	+	0.611372i
$112$		0			0
$113$	−8.68614	−	15.0448i	−0.817123	−	1.41530i	−0.907793	−	0.419418i	$-0.862234\pi$
$113$	−8.68614	−	15.0448i	−0.817123	−	1.41530i	0.0906698	−	0.995881i	$-0.471099\pi$
$114$		0			0
$115$	7.92967	−	13.7346i	0.739446	−	1.28076i
$116$		0			0
$117$	3.94158	+	1.18843i	0.364399	+	0.109870i
$118$		0			0
$119$	−5.57825	+	9.66181i	−0.511357	+	0.885696i
$120$		0			0
$121$	5.11684	+	8.86263i	0.465168	+	0.805694i
$122$		0			0
$123$	−1.07561	+	1.35760i	−0.0969842	+	0.122410i
$124$		0			0
$125$	4.62772			0.413916
$126$		0			0
$127$	11.1565			0.989979			0.494989	−	0.868899i	$-0.335172\pi$
$127$	11.1565			0.989979			0.494989	+	0.868899i	$0.335172\pi$
$128$		0			0
$129$	−1.50000	−	0.221215i	−0.132068	−	0.0194769i
$130$		0			0
$131$	−3.22682	−	5.58902i	−0.281929	−	0.488315i	0.689931	−	0.723875i	$-0.257641\pi$
$131$	−3.22682	−	5.58902i	−0.281929	−	0.488315i	−0.971860	+	0.235560i	$0.924307\pi$
$132$		0			0
$133$	13.1168	−	22.7190i	1.13737	−	1.96999i
$134$		0			0
$135$	−1.47603	−	17.4606i	−0.127037	−	1.50277i
$136$		0			0
$137$	−5.24456	+	9.08385i	−0.448073	+	0.776086i	−0.998261	−	0.0589556i	$-0.981223\pi$
$137$	−5.24456	+	9.08385i	−0.448073	+	0.776086i	0.550187	+	0.835041i	$0.314556\pi$
$138$		0			0
$139$	−9.84341	−	17.0493i	−0.834907	−	1.44610i	−0.894106	−	0.447855i	$-0.852188\pi$
$139$	−9.84341	−	17.0493i	−0.834907	−	1.44610i	0.0591995	−	0.998246i	$-0.481145\pi$
$140$		0			0
$141$	−8.05842	−	1.18843i	−0.678642	−	0.100084i
$142$		0			0
$143$	1.20128			0.100456
$144$		0			0
$145$	18.1168			1.50452
$146$		0			0
$147$	−16.2598	+	20.5226i	−1.34108	+	1.69267i
$148$		0			0
$149$	−8.68614	−	15.0448i	−0.711596	−	1.23252i	−0.964258	−	0.264966i	$-0.914639\pi$
$149$	−8.68614	−	15.0448i	−0.711596	−	1.23252i	0.252661	−	0.967555i	$-0.418694\pi$
$150$		0			0
$151$	−2.35143	+	4.07279i	−0.191356	+	0.331439i	−0.945700	−	0.325041i	$-0.894622\pi$
$151$	−2.35143	+	4.07279i	−0.191356	+	0.331439i	0.754344	+	0.656480i	$0.227955\pi$
$152$		0			0
$153$	5.18614	−	4.87375i	0.419275	−	0.394019i
$154$		0			0
$155$	−10.8817	+	18.8477i	−0.874043	+	1.51389i
$156$		0			0
$157$	7.05842	+	12.2255i	0.563323	+	0.975705i	0.997203	+	0.0747341i	$0.0238108\pi$
$157$	7.05842	+	12.2255i	0.563323	+	0.975705i	−0.433880	+	0.900971i	$0.642856\pi$
$158$		0			0
$159$	−2.55164	−	6.44121i	−0.202358	−	0.510821i
$160$		0			0
$161$	22.1168			1.74305
$162$		0			0
$163$	18.8114			1.47342			0.736712	−	0.676207i	$-0.236377\pi$
$163$	18.8114			1.47342			0.736712	+	0.676207i	$0.236377\pi$
$164$		0			0
$165$	−1.88316	−	4.75372i	−0.146603	−	0.370077i
$166$		0			0
$167$	3.22682	+	5.58902i	0.249699	+	0.432491i	0.963442	−	0.267916i	$-0.0863351\pi$
$167$	3.22682	+	5.58902i	0.249699	+	0.432491i	−0.713743	+	0.700407i	$0.753002\pi$
$168$		0			0
$169$	5.55842	−	9.62747i	0.427571	−	0.740575i
$170$		0			0
$171$	−12.1948	+	11.4603i	−0.932562	+	0.876388i
$172$		0			0
$173$	2.68614	−	4.65253i	0.204223	−	0.353725i	−0.745662	−	0.666325i	$-0.767866\pi$
$173$	2.68614	−	4.65253i	0.204223	−	0.353725i	0.949885	+	0.312599i	$0.101200\pi$
$174$		0			0
$175$	14.9840	+	25.9530i	1.13268	+	1.96186i
$176$		0			0
$177$	−9.17527	+	11.5807i	−0.689655	+	0.870461i
$178$		0			0
$179$	18.8114			1.40603			0.703016	−	0.711174i	$-0.251836\pi$
$179$	18.8114			1.40603			0.703016	+	0.711174i	$0.251836\pi$
$180$		0			0
$181$	−26.2337			−1.94993			−0.974967	−	0.222348i	$-0.928628\pi$
$181$	−26.2337			−1.94993			−0.974967	+	0.222348i	$0.928628\pi$
$182$		0			0
$183$	3.62725	+	0.534935i	0.268134	+	0.0395435i
$184$		0			0
$185$	6.74456	+	11.6819i	0.495870	+	0.858872i
$186$		0			0
$187$	1.03834	−	1.79846i	0.0759308	−	0.131516i
$188$		0			0
$189$	20.0584	−	13.9576i	1.45904	−	1.01527i
$190$		0			0
$191$	−8.80507	+	15.2508i	−0.637112	+	1.10351i	0.348951	+	0.937141i	$0.386538\pi$
$191$	−8.80507	+	15.2508i	−0.637112	+	1.10351i	−0.986063	+	0.166370i	$0.946795\pi$
$192$		0			0
$193$	−0.500000	−	0.866025i	−0.0359908	−	0.0623379i	0.847469	−	0.530845i	$-0.178125\pi$
$193$	−0.500000	−	0.866025i	−0.0359908	−	0.0623379i	−0.883460	+	0.468507i	$0.844792\pi$
$194$		0			0
$195$	7.92967	+	1.16944i	0.567856	+	0.0837456i
$196$		0			0
$197$	10.7446			0.765518			0.382759	−	0.923848i	$-0.374974\pi$
$197$	10.7446			0.765518			0.382759	+	0.923848i	$0.374974\pi$
$198$		0			0
$199$	−17.0606			−1.20940			−0.604698	−	0.796455i	$-0.706706\pi$
$199$	−17.0606			−1.20940			−0.604698	+	0.796455i	$0.706706\pi$
$200$		0			0
$201$	9.17527	−	11.5807i	0.647173	−	0.816842i
$202$		0			0
$203$	12.6325	+	21.8802i	0.886630	+	1.53569i
$204$		0			0
$205$	−1.68614	+	2.92048i	−0.117765	+	0.203975i
$206$		0			0
$207$	−13.5079	−	4.07279i	−0.938865	−	0.283079i
$208$		0			0
$209$	−2.44158	+	4.22894i	−0.168887	+	0.292522i
$210$		0			0
$211$	−7.92967	−	13.7346i	−0.545901	−	0.945529i	−0.998550	−	0.0538397i	$-0.982854\pi$
$211$	−7.92967	−	13.7346i	−0.545901	−	0.945529i	0.452648	−	0.891689i	$-0.350479\pi$
$212$		0			0
$213$	6.00000	+	15.1460i	0.411113	+	1.03779i
$214$		0			0
$215$	−2.95207			−0.201329
$216$		0			0
$217$	−30.3505			−2.06033
$218$		0			0
$219$	−6.61659	−	16.7025i	−0.447107	−	1.12865i
$220$		0			0
$221$	1.62772	+	2.81929i	0.109492	+	0.189646i
$222$		0			0
$223$	2.35143	−	4.07279i	0.157463	−	0.272734i	−0.776490	−	0.630130i	$-0.783002\pi$
$223$	2.35143	−	4.07279i	0.157463	−	0.272734i	0.933953	+	0.357395i	$0.116335\pi$
$224$		0			0
$225$	−4.37228	−	18.6101i	−0.291485	−	1.24068i
$226$		0			0
$227$	10.7188	−	18.5655i	0.711432	−	1.23224i	−0.252888	−	0.967496i	$-0.581380\pi$
$227$	10.7188	−	18.5655i	0.711432	−	1.23224i	0.964320	−	0.264740i	$-0.0852862\pi$
$228$		0			0
$229$	0.686141	+	1.18843i	0.0453415	+	0.0785337i	0.887805	−	0.460219i	$-0.152229\pi$
$229$	0.686141	+	1.18843i	0.0453415	+	0.0785337i	−0.842464	+	0.538753i	$0.818896\pi$
$230$		0			0
$231$	4.42810	−	5.58902i	0.291348	−	0.367730i
$232$		0			0
$233$	−25.8614			−1.69424			−0.847119	−	0.531404i	$-0.821665\pi$
$233$	−25.8614			−1.69424			−0.847119	+	0.531404i	$0.821665\pi$
$234$		0			0
$235$	−15.8593			−1.03455
$236$		0			0
$237$	−11.0584	−	1.63086i	−0.718322	−	0.105936i
$238$		0			0
$239$	−8.80507	−	15.2508i	−0.569552	−	0.986494i	−0.996610	−	0.0822694i	$-0.973783\pi$
$239$	−8.80507	−	15.2508i	−0.569552	−	0.986494i	0.427058	−	0.904224i	$-0.359550\pi$
$240$		0			0
$241$	−5.87228	+	10.1711i	−0.378267	+	0.655177i	−0.990810	−	0.135260i	$-0.956813\pi$
$241$	−5.87228	+	10.1711i	−0.378267	+	0.655177i	0.612543	+	0.790437i	$0.290147\pi$
$242$		0			0
$243$	−14.8210	+	4.83090i	−0.950768	+	0.309903i
$244$		0			0
$245$	−25.4891	+	44.1485i	−1.62844	+	2.82054i
$246$		0			0
$247$	−3.82746	−	6.62936i	−0.243536	−	0.421816i
$248$		0			0
$249$	−5.05842	−	0.746000i	−0.320564	−	0.0472758i
$250$		0			0
$251$	16.7347			1.05629			0.528144	−	0.849155i	$-0.322888\pi$
$251$	16.7347			1.05629			0.528144	+	0.849155i	$0.322888\pi$
$252$		0			0
$253$	−4.11684			−0.258824
$254$		0			0
$255$	8.60485	−	10.8608i	0.538857	−	0.680128i
$256$		0			0
$257$	−8.24456	−	14.2800i	−0.514282	−	0.890762i	−0.999863	−	0.0165703i	$-0.994725\pi$
$257$	−8.24456	−	14.2800i	−0.514282	−	0.890762i	0.485581	−	0.874192i	$-0.338608\pi$
$258$		0			0
$259$	−9.40571	+	16.2912i	−0.584442	+	1.01228i
$260$		0			0
$261$	−3.68614	−	15.6896i	−0.228166	−	0.971165i
$262$		0			0
$263$	8.80507	−	15.2508i	0.542944	−	0.940406i	−0.455790	−	0.890088i	$-0.650643\pi$
$263$	8.80507	−	15.2508i	0.542944	−	0.940406i	0.998733	−	0.0503185i	$-0.0160236\pi$
$264$		0			0
$265$	−6.74456	−	11.6819i	−0.414315	−	0.717615i
$266$		0			0
$267$	−8.12989	−	20.5226i	−0.497541	−	1.25596i
$268$		0			0
$269$	13.4891			0.822446			0.411223	−	0.911535i	$-0.365102\pi$
$269$	13.4891			0.822446			0.411223	+	0.911535i	$0.365102\pi$
$270$		0			0
$271$	22.3130			1.35542			0.677709	−	0.735330i	$-0.262973\pi$
$271$	22.3130			1.35542			0.677709	+	0.735330i	$0.262973\pi$
$272$		0			0
$273$	4.11684	+	10.3923i	0.249163	+	0.628971i
$274$		0			0
$275$	−2.78912	−	4.83090i	−0.168190	−	0.291314i
$276$		0			0
$277$	−2.05842	+	3.56529i	−0.123679	+	0.214218i	−0.921216	−	0.389052i	$-0.872803\pi$
$277$	−2.05842	+	3.56529i	−0.123679	+	0.214218i	0.797537	+	0.603270i	$0.206136\pi$
$278$		0			0
$279$	18.5367	+	5.58902i	1.10976	+	0.334606i
$280$		0			0
$281$	1.43070	−	2.47805i	0.0853486	−	0.147828i	−0.820191	−	0.572090i	$-0.806133\pi$
$281$	1.43070	−	2.47805i	0.0853486	−	0.147828i	0.905540	+	0.424262i	$0.139466\pi$
$282$		0			0
$283$	7.92967	+	13.7346i	0.471370	+	0.816437i	0.999464	−	0.0327491i	$-0.0104262\pi$
$283$	7.92967	+	13.7346i	0.471370	+	0.816437i	−0.528093	+	0.849186i	$0.677093\pi$
$284$		0			0
$285$	−20.2337	+	25.5383i	−1.19854	+	1.51276i
$286$		0			0
$287$	−4.70285			−0.277601
$288$		0			0
$289$	−11.3723			−0.668958
$290$		0			0
$291$	15.4217	+	2.27434i	0.904033	+	0.133324i
$292$		0			0
$293$	−7.31386	−	12.6680i	−0.427280	−	0.740071i	0.569350	−	0.822095i	$-0.307195\pi$
$293$	−7.31386	−	12.6680i	−0.427280	−	0.740071i	−0.996630	+	0.0820241i	$0.973862\pi$
$294$		0			0
$295$	−14.3833	+	24.9126i	−0.837429	+	1.45047i
$296$		0			0
$297$	−3.73369	+	2.59808i	−0.216651	+	0.150756i
$298$		0			0
$299$	3.22682	−	5.58902i	0.186612	−	0.323221i
$300$		0			0
$301$	−2.05842	−	3.56529i	−0.118645	−	0.205500i
$302$		0			0
$303$	−3.62725	−	0.534935i	−0.208380	−	0.0307312i
$304$		0			0
$305$	7.13859			0.408755
$306$		0			0
$307$	−20.8881			−1.19215			−0.596073	−	0.802930i	$-0.703273\pi$
$307$	−20.8881			−1.19215			−0.596073	+	0.802930i	$0.703273\pi$
$308$		0			0
$309$	−5.05842	+	6.38458i	−0.287764	+	0.363206i
$310$		0			0
$311$	13.5079	+	23.3964i	0.765964	+	1.32669i	0.939735	+	0.341903i	$0.111071\pi$
$311$	13.5079	+	23.3964i	0.765964	+	1.32669i	−0.173771	+	0.984786i	$0.555595\pi$
$312$		0			0
$313$	7.61684	−	13.1928i	0.430529	−	0.745699i	−0.566389	−	0.824138i	$-0.691660\pi$
$313$	7.61684	−	13.1928i	0.430529	−	0.745699i	0.996919	+	0.0784388i	$0.0249935\pi$
$314$		0			0
$315$	34.6708	−	32.5823i	1.95348	−	1.83581i
$316$		0			0
$317$	1.31386	−	2.27567i	0.0737937	−	0.127814i	−0.826767	−	0.562544i	$-0.809823\pi$
$317$	1.31386	−	2.27567i	0.0737937	−	0.127814i	0.900561	+	0.434730i	$0.143156\pi$
$318$		0			0
$319$	−2.35143	−	4.07279i	−0.131655	−	0.228033i
$320$		0			0
$321$	−3.55842	−	8.98266i	−0.198612	−	0.501363i
$322$		0			0
$323$	−13.2332			−0.736313
$324$		0			0
$325$	8.74456			0.485061
$326$		0			0
$327$	−3.50157	−	8.83915i	−0.193637	−	0.488806i
$328$		0			0
$329$	−11.0584	−	19.1537i	−0.609671	−	1.05598i
$330$		0			0
$331$	−4.97760	+	8.62146i	−0.273594	+	0.473879i	−0.969779	−	0.243983i	$-0.921546\pi$
$331$	−4.97760	+	8.62146i	−0.273594	+	0.473879i	0.696186	+	0.717862i	$0.254879\pi$
$332$		0			0
$333$	8.74456	−	8.21782i	0.479199	−	0.450334i
$334$		0			0
$335$	14.3833	−	24.9126i	0.785844	−	1.36112i
$336$		0			0
$337$	4.50000	+	7.79423i	0.245131	+	0.424579i	0.962168	−	0.272456i	$-0.0878358\pi$
$337$	4.50000	+	7.79423i	0.245131	+	0.424579i	−0.717038	+	0.697034i	$0.754502\pi$
$338$		0			0
$339$	−18.6857	+	23.5846i	−1.01487	+	1.28094i
$340$		0			0
$341$	5.64947			0.305936
$342$		0			0
$343$	−38.1723			−2.06111
$344$		0			0
$345$	−27.1753	−	4.00772i	−1.46307	−	0.215768i
$346$		0			0
$347$	4.26516	+	7.38747i	0.228966	+	0.396580i	0.957502	−	0.288427i	$-0.0931323\pi$
$347$	4.26516	+	7.38747i	0.228966	+	0.396580i	−0.728536	+	0.685007i	$0.759799\pi$
$348$		0			0
$349$	−2.94158	+	5.09496i	−0.157459	+	0.272727i	−0.933952	−	0.357399i	$-0.883664\pi$
$349$	−2.94158	+	5.09496i	−0.157459	+	0.272727i	0.776493	+	0.630126i	$0.216997\pi$
$350$		0			0
$351$	−0.600642	−	7.10524i	−0.0320599	−	0.379250i
$352$		0			0
$353$	−7.61684	+	13.1928i	−0.405404	+	0.702180i	−0.994368	−	0.105979i	$-0.966202\pi$
$353$	−7.61684	+	13.1928i	−0.405404	+	0.702180i	0.588965	+	0.808159i	$0.299536\pi$
$354$		0			0
$355$	15.8593	+	27.4692i	0.841727	+	1.45791i
$356$		0			0
$357$	19.1168	+	2.81929i	1.01177	+	0.149213i
$358$		0			0
$359$	33.4695			1.76645			0.883226	−	0.468948i	$-0.155367\pi$
$359$	33.4695			1.76645			0.883226	+	0.468948i	$0.155367\pi$
$360$		0			0
$361$	12.1168			0.637729
$362$		0			0
$363$	11.0074	−	13.8932i	0.577740	−	0.729205i
$364$		0			0
$365$	−17.4891	−	30.2921i	−0.915423	−	1.58556i
$366$		0			0
$367$	−15.5846	+	26.9933i	−0.813509	+	1.40904i	0.0968838	+	0.995296i	$0.469112\pi$
$367$	−15.5846	+	26.9933i	−0.813509	+	1.40904i	−0.910393	+	0.413744i	$0.864221\pi$
$368$		0			0
$369$	2.87228	+	0.866025i	0.149525	+	0.0450835i
$370$		0			0
$371$	9.40571	−	16.2912i	0.488320	−	0.845795i
$372$		0			0
$373$	0.0584220	+	0.101190i	0.00302498	+	0.00523941i	0.867534	−	0.497378i	$-0.165704\pi$
$373$	0.0584220	+	0.101190i	0.00302498	+	0.00523941i	−0.864509	+	0.502617i	$0.832370\pi$
$374$		0			0
$375$	−2.95207	−	7.45202i	−0.152444	−	0.384821i
$376$		0			0
$377$	7.37228			0.379692
$378$		0			0
$379$	−3.82746			−0.196604			−0.0983018	−	0.995157i	$-0.531341\pi$
$379$	−3.82746			−0.196604			−0.0983018	+	0.995157i	$0.531341\pi$
$380$		0			0
$381$	−7.11684	−	17.9653i	−0.364607	−	0.920391i
$382$		0			0
$383$	10.8817	+	18.8477i	0.556031	+	0.963074i	0.997823	+	0.0659564i	$0.0210098\pi$
$383$	10.8817	+	18.8477i	0.556031	+	0.963074i	−0.441791	+	0.897118i	$0.645657\pi$
$384$		0			0
$385$	6.94158	−	12.0232i	0.353776	−	0.612757i
$386$		0			0
$387$	0.600642	+	2.55657i	0.0305324	+	0.129958i
$388$		0			0
$389$	16.1753	−	28.0164i	0.820119	−	1.42049i	−0.0854750	−	0.996340i	$-0.527241\pi$
$389$	16.1753	−	28.0164i	0.820119	−	1.42049i	0.905594	−	0.424147i	$-0.139426\pi$
$390$		0			0
$391$	−5.57825	−	9.66181i	−0.282104	−	0.488619i
$392$		0			0
$393$	−6.94158	+	8.76144i	−0.350156	+	0.441956i
$394$		0			0
$395$	−21.7635			−1.09504
$396$		0			0
$397$	4.00000			0.200754			0.100377	−	0.994949i	$-0.467995\pi$
$397$	4.00000			0.200754			0.100377	+	0.994949i	$0.467995\pi$
$398$		0			0
$399$	−44.9519	−	6.62936i	−2.25041	−	0.331883i
$400$		0			0
$401$	8.98913	+	15.5696i	0.448895	+	0.777510i	0.998314	−	0.0580372i	$-0.0184842\pi$
$401$	8.98913	+	15.5696i	0.448895	+	0.777510i	−0.549419	+	0.835547i	$0.685151\pi$
$402$		0			0
$403$	−4.42810	+	7.66970i	−0.220580	+	0.382055i
$404$		0			0
$405$	−27.1753	+	13.5152i	−1.35035	+	0.671574i
$406$		0			0
$407$	1.75079	−	3.03245i	0.0867832	−	0.150313i
$408$		0			0
$409$	14.8723	+	25.7595i	0.735387	+	1.27373i	0.954553	+	0.298040i	$0.0963329\pi$
$409$	14.8723	+	25.7595i	0.735387	+	1.27373i	−0.219166	+	0.975688i	$0.570334\pi$
$410$		0			0
$411$	17.9733	+	2.65064i	0.886557	+	0.130747i
$412$		0			0
$413$	−40.1168			−1.97402
$414$		0			0
$415$	−9.95521			−0.488682
$416$		0			0
$417$	−21.1753	+	26.7268i	−1.03696	+	1.30882i
$418$		0			0
$419$	−7.92967	−	13.7346i	−0.387390	−	0.670979i	0.604708	−	0.796448i	$-0.293290\pi$
$419$	−7.92967	−	13.7346i	−0.387390	−	0.670979i	−0.992098	+	0.125468i	$0.959957\pi$
$420$		0			0
$421$	−8.31386	+	14.4000i	−0.405193	+	0.701814i	−0.994344	−	0.106208i	$-0.966129\pi$
$421$	−8.31386	+	14.4000i	−0.405193	+	0.701814i	0.589151	+	0.808023i	$0.299462\pi$
$422$		0			0
$423$	3.22682	+	13.7346i	0.156893	+	0.667799i
$424$		0			0
$425$	7.55842	−	13.0916i	0.366637	−	0.635034i
$426$		0			0
$427$	4.97760	+	8.62146i	0.240883	+	0.417222i
$428$		0			0
$429$	−0.766312	−	1.93443i	−0.0369979	−	0.0933952i
$430$		0			0
$431$	11.1565			0.537389			0.268695	−	0.963225i	$-0.413408\pi$
$431$	11.1565			0.537389			0.268695	+	0.963225i	$0.413408\pi$
$432$		0			0
$433$	−0.883156			−0.0424418			−0.0212209	−	0.999775i	$-0.506755\pi$
$433$	−0.883156			−0.0424418			−0.0212209	+	0.999775i	$0.506755\pi$
$434$		0			0
$435$	−11.5569	−	29.1736i	−0.554112	−	1.39877i
$436$		0			0
$437$	13.1168	+	22.7190i	0.627464	+	1.08680i
$438$		0			0
$439$	10.8817	−	18.8477i	0.519357	−	0.899553i	−0.480390	−	0.877055i	$-0.659505\pi$
$439$	10.8817	−	18.8477i	0.519357	−	0.899553i	0.999747	−	0.0224981i	$-0.00716196\pi$
$440$		0			0
$441$	43.4198	+	13.0916i	2.06761	+	0.623408i
$442$		0			0
$443$	−10.7188	+	18.5655i	−0.509265	+	0.882074i	0.490677	+	0.871342i	$0.336750\pi$
$443$	−10.7188	+	18.5655i	−0.509265	+	0.882074i	−0.999942	+	0.0107321i	$0.996584\pi$
$444$		0			0
$445$	−21.4891	−	37.2203i	−1.01868	−	1.76441i
$446$		0			0
$447$	−18.6857	+	23.5846i	−0.883805	+	1.11551i
$448$		0			0
$449$	−0.883156			−0.0416787			−0.0208394	−	0.999783i	$-0.506634\pi$
$449$	−0.883156			−0.0416787			−0.0208394	+	0.999783i	$0.506634\pi$
$450$		0			0
$451$	0.875393			0.0412206
$452$		0			0
$453$	8.05842	+	1.18843i	0.378618	+	0.0558373i
$454$		0			0
$455$	10.8817	+	18.8477i	0.510144	+	0.883595i
$456$		0			0
$457$	−9.98913	+	17.3017i	−0.467272	+	0.809338i	−0.999301	−	0.0373879i	$-0.988096\pi$
$457$	−9.98913	+	17.3017i	−0.467272	+	0.809338i	0.532029	+	0.846726i	$0.321430\pi$
$458$		0			0
$459$	−11.1565	−	5.24224i	−0.520741	−	0.244687i
$460$		0			0
$461$	−5.94158	+	10.2911i	−0.276727	+	0.479305i	−0.970569	−	0.240822i	$-0.922583\pi$
$461$	−5.94158	+	10.2911i	−0.276727	+	0.479305i	0.693842	+	0.720127i	$0.255916\pi$
$462$		0			0
$463$	0.274750	+	0.475881i	0.0127687	+	0.0221161i	0.872339	−	0.488901i	$-0.162602\pi$
$463$	0.274750	+	0.475881i	0.0127687	+	0.0221161i	−0.859570	+	0.511017i	$0.829269\pi$
$464$		0			0
$465$	37.2921	+	5.49972i	1.72938	+	0.255043i
$466$		0			0
$467$	9.73160			0.450325			0.225162	−	0.974321i	$-0.427709\pi$
$467$	9.73160			0.450325			0.225162	+	0.974321i	$0.427709\pi$
$468$		0			0
$469$	40.1168			1.85242
$470$		0			0
$471$	15.1842	−	19.1650i	0.699650	−	0.883076i
$472$		0			0
$473$	0.383156	+	0.663646i	0.0176175	+	0.0305145i
$474$		0			0
$475$	−17.7731	+	30.7839i	−0.815485	+	1.41246i
$476$		0			0
$477$	−8.74456	+	8.21782i	−0.400386	+	0.376268i
$478$		0			0
$479$	−2.35143	+	4.07279i	−0.107439	+	0.186091i	−0.914732	−	0.404061i	$-0.867599\pi$
$479$	−2.35143	+	4.07279i	−0.107439	+	0.186091i	0.807293	+	0.590151i	$0.200932\pi$
$480$		0			0
$481$	2.74456	+	4.75372i	0.125141	+	0.216751i
$482$		0			0
$483$	−14.1086	−	35.6148i	−0.641962	−	1.62053i
$484$		0			0
$485$	30.3505			1.37815
$486$		0			0
$487$	11.1565			0.505549			0.252775	−	0.967525i	$-0.418657\pi$
$487$	11.1565			0.505549			0.252775	+	0.967525i	$0.418657\pi$
$488$		0			0
$489$	−12.0000	−	30.2921i	−0.542659	−	1.36985i
$490$		0			0
$491$	20.1245	+	34.8567i	0.908206	+	1.57306i	0.816554	+	0.577268i	$0.195881\pi$
$491$	20.1245	+	34.8567i	0.908206	+	1.57306i	0.0916519	+	0.995791i	$0.470785\pi$
$492$		0			0
$493$	6.37228	−	11.0371i	0.286993	−	0.497087i
$494$		0			0
$495$	−6.45364	+	6.06490i	−0.290070	+	0.272597i
$496$		0			0
$497$	−22.1168	+	38.3075i	−0.992076	+	1.71833i
$498$		0			0
$499$	6.89134	+	11.9361i	0.308499	+	0.534335i	0.978034	−	0.208445i	$-0.0668402\pi$
$499$	6.89134	+	11.9361i	0.308499	+	0.534335i	−0.669536	+	0.742780i	$0.733507\pi$
$500$		0			0
$501$	6.94158	−	8.76144i	0.310127	−	0.391432i
$502$		0			0
$503$	31.7187			1.41427			0.707133	−	0.707080i	$-0.249988\pi$
$503$	31.7187			1.41427			0.707133	+	0.707080i	$0.249988\pi$
$504$		0			0
$505$	−7.13859			−0.317663
$506$		0			0
$507$	−19.0489	−	2.80927i	−0.845991	−	0.124764i
$508$		0			0
$509$	19.1753	+	33.2125i	0.849929	+	1.47212i	0.881271	+	0.472611i	$0.156688\pi$
$509$	19.1753	+	33.2125i	0.849929	+	1.47212i	−0.0313424	+	0.999509i	$0.509978\pi$
$510$		0			0
$511$	24.3897	−	42.2441i	1.07894	−	1.86877i
$512$		0			0
$513$	26.2337	+	12.3267i	1.15825	+	0.544239i
$514$		0			0
$515$	−7.92967	+	13.7346i	−0.349423	+	0.605219i
$516$		0			0
$517$	2.05842	+	3.56529i	0.0905293	+	0.156801i
$518$		0			0
$519$	−9.20550	−	1.35760i	−0.404076	−	0.0595919i
$520$		0			0
$521$	35.3505			1.54873			0.774367	−	0.632736i	$-0.218068\pi$
$521$	35.3505			1.54873			0.774367	+	0.632736i	$0.218068\pi$
$522$		0			0
$523$	12.9073			0.564396			0.282198	−	0.959356i	$-0.408936\pi$
$523$	12.9073			0.564396			0.282198	+	0.959356i	$0.408936\pi$
$524$		0			0
$525$	32.2337	−	40.6844i	1.40679	−	1.77561i
$526$		0			0
$527$	7.65492	+	13.2587i	0.333454	+	0.577559i
$528$		0			0
$529$	0.441578	−	0.764836i	0.0191990	−	0.0332537i
$530$		0			0
$531$	24.5015	+	7.38747i	1.06327	+	0.320589i
$532$		0			0
$533$	−0.686141	+	1.18843i	−0.0297201	+	0.0514766i
$534$		0			0
$535$	−9.40571	−	16.2912i	−0.406644	−	0.704329i
$536$		0			0
$537$	−12.0000	−	30.2921i	−0.517838	−	1.30720i
$538$		0			0
$539$	13.2332			0.569993
$540$		0			0
$541$	2.74456			0.117998			0.0589990	−	0.998258i	$-0.481209\pi$
$541$	2.74456			0.117998			0.0589990	+	0.998258i	$0.481209\pi$
$542$		0			0
$543$	16.7347	+	42.2441i	0.718157	+	1.81287i
$544$		0			0
$545$	−9.25544	−	16.0309i	−0.396459	−	0.686688i
$546$		0			0
$547$	5.14055	−	8.90370i	0.219794	−	0.380695i	−0.734951	−	0.678120i	$-0.762795\pi$
$547$	5.14055	−	8.90370i	0.219794	−	0.380695i	0.954745	+	0.297426i	$0.0961281\pi$
$548$		0			0
$549$	−1.45245	−	6.18220i	−0.0619892	−	0.263850i
$550$		0			0
$551$	−14.9840	+	25.9530i	−0.638338	+	1.10563i
$552$		0			0
$553$	−15.1753	−	26.2843i	−0.645318	−	1.11772i
$554$		0			0
$555$	14.5090	−	18.3128i	0.615872	−	0.777335i
$556$		0			0
$557$	7.25544			0.307423			0.153711	−	0.988116i	$-0.450877\pi$
$557$	7.25544			0.307423			0.153711	+	0.988116i	$0.450877\pi$
$558$		0			0
$559$	−1.20128			−0.0508089
$560$		0			0
$561$	−3.55842	−	0.524785i	−0.150237	−	0.0221564i
$562$		0			0
$563$	−3.38977	−	5.87125i	−0.142862	−	0.247444i	0.785711	−	0.618593i	$-0.212297\pi$
$563$	−3.38977	−	5.87125i	−0.142862	−	0.247444i	−0.928573	+	0.371150i	$0.878964\pi$
$564$		0			0
$565$	−29.2921	+	50.7354i	−1.23233	+	2.13446i
$566$		0			0
$567$	−35.2714	−	23.3964i	−1.48126	−	0.982557i
$568$		0			0
$569$	14.1277	−	24.4699i	0.592265	−	1.02583i	−0.401662	−	0.915788i	$-0.631567\pi$
$569$	14.1277	−	24.4699i	0.592265	−	1.02583i	0.993927	−	0.110045i	$-0.0350994\pi$
$570$		0			0
$571$	−20.1245	−	34.8567i	−0.842184	−	1.45871i	−0.888044	−	0.459758i	$-0.847936\pi$
$571$	−20.1245	−	34.8567i	−0.842184	−	1.45871i	0.0458596	−	0.998948i	$-0.485397\pi$
$572$		0			0
$573$	30.1753	+	4.45015i	1.26059	+	0.185908i
$574$		0			0
$575$	−29.9679			−1.24975
$576$		0			0
$577$	0.883156			0.0367663			0.0183831	−	0.999831i	$-0.494148\pi$
$577$	0.883156			0.0367663			0.0183831	+	0.999831i	$0.494148\pi$
$578$		0			0
$579$	−1.07561	+	1.35760i	−0.0447007	+	0.0564198i
$580$		0			0
$581$	−6.94158	−	12.0232i	−0.287985	−	0.498805i
$582$		0			0
$583$	−1.75079	+	3.03245i	−0.0725101	+	0.125591i
$584$		0			0
$585$	−3.17527	−	13.5152i	−0.131281	−	0.558783i
$586$		0			0
$587$	19.2491	−	33.3404i	0.794496	−	1.37611i	−0.128663	−	0.991688i	$-0.541068\pi$
$587$	19.2491	−	33.3404i	0.794496	−	1.37611i	0.923159	−	0.384419i	$-0.125598\pi$
$588$		0			0
$589$	−18.0000	−	31.1769i	−0.741677	−	1.28462i
$590$		0			0
$591$	−6.85407	−	17.3020i	−0.281939	−	0.711708i
$592$		0			0
$593$	39.7228			1.63122			0.815610	−	0.578602i	$-0.196401\pi$
$593$	39.7228			1.63122			0.815610	+	0.578602i	$0.196401\pi$
$594$		0			0
$595$	37.6228			1.54239
$596$		0			0
$597$	10.8832	+	27.4728i	0.445418	+	1.12439i
$598$		0			0
$599$	−15.5846	−	26.9933i	−0.636769	−	1.10292i	−0.986137	−	0.165931i	$-0.946937\pi$
$599$	−15.5846	−	26.9933i	−0.636769	−	1.10292i	0.349368	−	0.936986i	$-0.386396\pi$
$600$		0			0
$601$	18.6168	−	32.2453i	0.759397	−	1.31531i	−0.183762	−	0.982971i	$-0.558827\pi$
$601$	18.6168	−	32.2453i	0.759397	−	1.31531i	0.943159	−	0.332343i	$-0.107839\pi$
$602$		0			0
$603$	−24.5015	−	7.38747i	−0.997777	−	0.300841i
$604$		0			0
$605$	17.2554	−	29.8873i	0.701533	−	1.21509i
$606$		0			0
$607$	−0.274750	−	0.475881i	−0.0111518	−	0.0193154i	0.860396	−	0.509627i	$-0.170216\pi$
$607$	−0.274750	−	0.475881i	−0.0111518	−	0.0193154i	−0.871547	+	0.490311i	$0.836883\pi$
$608$		0			0
$609$	27.1753	−	34.2998i	1.10120	−	1.38990i
$610$		0			0
$611$	−6.45364			−0.261086
$612$		0			0
$613$	32.4674			1.31134			0.655672	−	0.755045i	$-0.272385\pi$
$613$	32.4674			1.31134			0.655672	+	0.755045i	$0.272385\pi$
$614$		0			0
$615$	5.77846	+	0.852189i	0.233010	+	0.0343636i
$616$		0			0
$617$	13.1277	+	22.7379i	0.528502	+	0.915392i	0.999448	+	0.0332302i	$0.0105794\pi$
$617$	13.1277	+	22.7379i	0.528502	+	0.915392i	−0.470946	+	0.882162i	$0.656087\pi$
$618$		0			0
$619$	5.14055	−	8.90370i	0.206616	−	0.357870i	−0.744030	−	0.668146i	$-0.767088\pi$
$619$	5.14055	−	8.90370i	0.206616	−	0.357870i	0.950646	+	0.310276i	$0.100422\pi$
$620$		0			0
$621$	2.05842	+	24.3499i	0.0826016	+	0.977128i
$622$		0			0
$623$	29.9679	−	51.9060i	1.20064	−	2.07957i
$624$		0			0
$625$	8.12772	+	14.0776i	0.325109	+	0.563105i
$626$		0			0
$627$	8.36737	+	1.23399i	0.334161	+	0.0492809i
$628$		0			0
$629$	9.48913			0.378356
$630$		0			0
$631$		0			0			−	1.00000i	$-0.5\pi$
$631$		0			0				1.00000i	$0.5\pi$
$632$		0			0
$633$	−17.0584	+	21.5306i	−0.678011	+	0.855765i
$634$		0			0
$635$	−18.8114	−	32.5823i	−0.746508	−	1.29299i
$636$		0			0
$637$	−10.3723	+	17.9653i	−0.410965	+	0.711812i
$638$		0			0
$639$	20.5622	−	19.3236i	0.813428	−	0.764430i
$640$		0			0
$641$	−1.12772	+	1.95327i	−0.0445422	+	0.0771494i	−0.887437	−	0.460929i	$-0.847516\pi$
$641$	−1.12772	+	1.95327i	−0.0445422	+	0.0771494i	0.842895	+	0.538078i	$0.180850\pi$
$642$		0			0
$643$	−1.31309	−	2.27434i	−0.0517832	−	0.0896911i	0.838972	−	0.544175i	$-0.183157\pi$
$643$	−1.31309	−	2.27434i	−0.0517832	−	0.0896911i	−0.890755	+	0.454484i	$0.849824\pi$
$644$		0			0
$645$	1.88316	+	4.75372i	0.0741492	+	0.187178i
$646$		0			0
$647$	4.15335			0.163285			0.0816426	−	0.996662i	$-0.473983\pi$
$647$	4.15335			0.163285			0.0816426	+	0.996662i	$0.473983\pi$
$648$		0			0
$649$	7.46738			0.293120
$650$		0			0
$651$	19.3609	+	48.8735i	0.758814	+	1.91550i
$652$		0			0
$653$	11.9416	+	20.6834i	0.467310	+	0.809405i	0.999302	−	0.0373444i	$-0.0118898\pi$
$653$	11.9416	+	20.6834i	0.467310	+	0.809405i	−0.531992	+	0.846749i	$0.678557\pi$
$654$		0			0
$655$	−10.8817	+	18.8477i	−0.425185	+	0.736442i
$656$		0			0
$657$	−22.6753	+	21.3094i	−0.884646	+	0.831359i
$658$		0			0
$659$	−20.2875	+	35.1389i	−0.790287	+	1.36882i	0.135502	+	0.990777i	$0.456735\pi$
$659$	−20.2875	+	35.1389i	−0.790287	+	1.36882i	−0.925789	+	0.378040i	$0.876598\pi$
$660$		0			0
$661$	7.05842	+	12.2255i	0.274541	+	0.475519i	0.970019	−	0.243028i	$-0.0781408\pi$
$661$	7.05842	+	12.2255i	0.274541	+	0.475519i	−0.695478	+	0.718547i	$0.744807\pi$
$662$		0			0
$663$	3.50157	−	4.41957i	0.135990	−	0.171642i
$664$		0			0
$665$	−88.4674			−3.43062
$666$		0			0
$667$	−25.2651			−0.978267
$668$		0			0
$669$	−8.05842	−	1.18843i	−0.311557	−	0.0459474i
$670$		0			0
$671$	−0.926535	−	1.60481i	−0.0357685	−	0.0619528i
$672$		0			0
$673$	14.1753	−	24.5523i	0.546416	−	0.946421i	−0.452100	−	0.891967i	$-0.649325\pi$
$673$	14.1753	−	24.5523i	0.546416	−	0.946421i	0.998516	−	0.0544536i	$-0.0173417\pi$
$674$		0			0
$675$	−27.1788	+	18.9123i	−1.04611	+	0.727934i
$676$		0			0
$677$	−25.1753	+	43.6048i	−0.967564	+	1.67587i	−0.265002	+	0.964248i	$0.585373\pi$
$677$	−25.1753	+	43.6048i	−0.967564	+	1.67587i	−0.702562	+	0.711622i	$0.747961\pi$
$678$		0			0
$679$	21.1628	+	36.6551i	0.812156	+	1.40669i
$680$		0			0
$681$	−36.7337	−	5.41737i	−1.40764	−	0.207594i
$682$		0			0
$683$	−9.73160			−0.372369			−0.186185	−	0.982515i	$-0.559612\pi$
$683$	−9.73160			−0.372369			−0.186185	+	0.982515i	$0.559612\pi$
$684$		0			0
$685$	35.3723			1.35151
$686$		0			0
$687$	1.47603	−	1.86301i	0.0563142	−	0.0710781i
$688$		0			0
$689$	−2.74456	−	4.75372i	−0.104560	−	0.181102i
$690$		0			0
$691$	9.13096	−	15.8153i	0.347358	−	0.601642i	−0.638421	−	0.769687i	$-0.720412\pi$
$691$	9.13096	−	15.8153i	0.347358	−	0.601642i	0.985779	+	0.168045i	$0.0537455\pi$
$692$		0			0
$693$	−11.8247	−	3.56529i	−0.449185	−	0.135434i
$694$		0			0
$695$	−33.1947	+	57.4950i	−1.25915	+	2.18091i
$696$		0			0
$697$	1.18614	+	2.05446i	0.0449283	+	0.0778181i
$698$		0			0
$699$	16.4973	+	41.6447i	0.623984	+	1.57515i
$700$		0			0
$701$	−23.2554			−0.878346			−0.439173	−	0.898403i	$-0.644728\pi$
$701$	−23.2554			−0.878346			−0.439173	+	0.898403i	$0.644728\pi$
$702$		0			0
$703$	−22.3130			−0.841550
$704$		0			0
$705$	10.1168	+	25.5383i	0.381022	+	0.961829i
$706$		0			0
$707$	−4.97760	−	8.62146i	−0.187202	−	0.324244i
$708$		0			0
$709$	13.8030	−	23.9075i	0.518382	−	0.897864i	−0.481390	−	0.876507i	$-0.659868\pi$
$709$	13.8030	−	23.9075i	0.518382	−	0.897864i	0.999772	−	0.0213574i	$-0.00679878\pi$
$710$		0			0
$711$	4.42810	+	18.8477i	0.166067	+	0.706845i
$712$		0			0
$713$	15.1753	−	26.2843i	0.568318	−	0.984356i
$714$		0			0
$715$	−2.02554	−	3.50833i	−0.0757507	−	0.131204i
$716$		0			0
$717$	−18.9416	+	23.9075i	−0.707386	+	0.892841i
$718$		0			0
$719$	15.3098			0.570961			0.285481	−	0.958385i	$-0.407847\pi$
$719$	15.3098			0.570961			0.285481	+	0.958385i	$0.407847\pi$
$720$		0			0
$721$	−22.1168			−0.823674
$722$		0			0
$723$	20.1245	+	2.96790i	0.748439	+	0.110377i
$724$		0			0
$725$	−17.1168	−	29.6472i	−0.635704	−	1.10107i
$726$		0			0
$727$	−10.0064	+	17.3315i	−0.371115	+	0.642790i	−0.989737	−	0.142898i	$-0.954358\pi$
$727$	−10.0064	+	17.3315i	−0.371115	+	0.642790i	0.618622	+	0.785689i	$0.287691\pi$
$728$		0			0
$729$	17.2337	+	20.7846i	0.638285	+	0.769800i
$730$		0			0
$731$	−1.03834	+	1.79846i	−0.0384043	+	0.0665183i
$732$		0			0
$733$	20.0584	+	34.7422i	0.740875	+	1.28323i	0.952097	+	0.305795i	$0.0989221\pi$
$733$	20.0584	+	34.7422i	0.740875	+	1.28323i	−0.211223	+	0.977438i	$0.567745\pi$
$734$		0			0
$735$	87.3521	+	12.8824i	3.22203	+	0.475175i
$736$		0			0
$737$	−7.46738			−0.275064
$738$		0			0
$739$	−7.32903			−0.269603			−0.134801	−	0.990873i	$-0.543040\pi$
$739$	−7.32903			−0.269603			−0.134801	+	0.990873i	$0.543040\pi$
$740$		0			0
$741$	−8.23369	+	10.3923i	−0.302472	+	0.381771i
$742$		0			0
$743$	−24.6644	−	42.7200i	−0.904850	−	1.56725i	−0.821119	−	0.570757i	$-0.806650\pi$
$743$	−24.6644	−	42.7200i	−0.904850	−	1.56725i	−0.0837309	−	0.996488i	$-0.526684\pi$
$744$		0			0
$745$	−29.2921	+	50.7354i	−1.07318	+	1.85880i
$746$		0			0
$747$	2.02554	+	8.62146i	0.0741105	+	0.315443i
$748$		0			0
$749$	13.1168	−	22.7190i	0.479279	−	0.830136i
$750$		0			0
$751$	10.8817	+	18.8477i	0.397081	+	0.687764i	0.993364	−	0.115010i	$-0.0366900\pi$
$751$	10.8817	+	18.8477i	0.397081	+	0.687764i	−0.596284	+	0.802774i	$0.703357\pi$
$752$		0			0
$753$	−10.6753	−	26.9480i	−0.389028	−	0.982039i
$754$		0			0
$755$	15.8593			0.577181
$756$		0			0
$757$	−34.4674			−1.25274			−0.626369	−	0.779527i	$-0.715460\pi$
$757$	−34.4674			−1.25274			−0.626369	+	0.779527i	$0.715460\pi$
$758$		0			0
$759$	2.62618	+	6.62936i	0.0953242	+	0.240630i
$760$		0			0
$761$	−7.31386	−	12.6680i	−0.265127	−	0.459214i	0.702470	−	0.711714i	$-0.252081\pi$
$761$	−7.31386	−	12.6680i	−0.265127	−	0.459214i	−0.967597	+	0.252500i	$0.918747\pi$
$762$		0			0
$763$	12.9073	−	22.3561i	0.467275	−	0.809344i
$764$		0			0
$765$	−22.9783	−	6.92820i	−0.830780	−	0.250490i
$766$		0			0
$767$	−5.85300	+	10.1377i	−0.211339	+	0.366051i
$768$		0			0
$769$	16.0584	+	27.8140i	0.579082	+	1.00300i	0.995585	+	0.0938645i	$0.0299220\pi$
$769$	16.0584	+	27.8140i	0.579082	+	1.00300i	−0.416503	+	0.909134i	$0.636745\pi$
$770$		0			0
$771$	−17.7358	+	22.3856i	−0.638740	+	0.806197i
$772$		0			0
$773$	7.25544			0.260960			0.130480	−	0.991451i	$-0.458348\pi$
$773$	7.25544			0.260960			0.130480	+	0.991451i	$0.458348\pi$
$774$		0			0
$775$	41.1244			1.47723
$776$		0			0
$777$	32.2337	+	4.75372i	1.15638	+	0.170539i
$778$		0			0
$779$	−2.78912	−	4.83090i	−0.0999307	−	0.173085i
$780$		0			0
$781$	4.11684	−	7.13058i	0.147312	−	0.255152i
$782$		0			0
$783$	−22.9136	+	15.9444i	−0.818866	+	0.569806i
$784$		0			0
$785$	23.8030	−	41.2280i	0.849565	−	1.47149i
$786$		0			0
$787$	4.42810	+	7.66970i	0.157845	+	0.273395i	0.934091	−	0.357034i	$-0.116212\pi$
$787$	4.42810	+	7.66970i	0.157845	+	0.273395i	−0.776246	+	0.630430i	$0.782879\pi$
$788$		0			0
$789$	−30.1753	−	4.45015i	−1.07427	−	0.158430i
$790$		0			0
$791$	−81.6993			−2.90489
$792$		0			0
$793$	2.90491			0.103156
$794$		0			0
$795$	−14.5090	+	18.3128i	−0.514581	+	0.649488i
$796$		0			0
$797$	−8.54755	−	14.8048i	−0.302770	−	0.524412i	0.673993	−	0.738738i	$-0.264578\pi$
$797$	−8.54755	−	14.8048i	−0.302770	−	0.524412i	−0.976762	+	0.214326i	$0.931245\pi$
$798$		0			0
$799$	−5.57825	+	9.66181i	−0.197344	+	0.341810i
$800$		0			0
$801$	−27.8614	+	26.1831i	−0.984434	+	0.925136i
$802$		0			0
$803$	−4.53991	+	7.86335i	−0.160210	+	0.277492i
$804$		0			0
$805$	−37.2921	−	64.5918i	−1.31437	−	2.27656i
$806$		0			0
$807$	−8.60485	−	21.7216i	−0.302905	−	0.764635i
$808$		0			0
$809$	−18.3723			−0.645935			−0.322968	−	0.946410i	$-0.604680\pi$
$809$	−18.3723			−0.645935			−0.322968	+	0.946410i	$0.604680\pi$
$810$		0			0
$811$	−50.2042			−1.76291			−0.881454	−	0.472269i	$-0.843435\pi$
$811$	−50.2042			−1.76291			−0.881454	+	0.472269i	$0.843435\pi$
$812$		0			0
$813$	−14.2337	−	35.9306i	−0.499197	−	1.26014i
$814$		0			0
$815$	−31.7187	−	54.9384i	−1.11106	−	1.92441i
$816$		0			0
$817$	2.44158	−	4.22894i	0.0854200	−	0.147952i
$818$		0			0
$819$	14.1086	−	13.2587i	0.492993	−	0.463297i
$820$		0			0
$821$	1.31386	−	2.27567i	0.0458540	−	0.0794215i	−0.842187	−	0.539185i	$-0.818732\pi$
$821$	1.31386	−	2.27567i	0.0458540	−	0.0794215i	0.888041	+	0.459763i	$0.152066\pi$
$822$		0			0
$823$	−10.8817	−	18.8477i	−0.379314	−	0.656991i	0.611649	−	0.791129i	$-0.290507\pi$
$823$	−10.8817	−	18.8477i	−0.379314	−	0.656991i	−0.990963	+	0.134139i	$0.957173\pi$
$824$		0			0
$825$	−6.00000	+	7.57301i	−0.208893	+	0.263658i
$826$		0			0
$827$	18.8114			0.654137			0.327069	−	0.945001i	$-0.393939\pi$
$827$	18.8114			0.654137			0.327069	+	0.945001i	$0.393939\pi$
$828$		0			0
$829$	−26.2337			−0.911134			−0.455567	−	0.890202i	$-0.650563\pi$
$829$	−26.2337			−0.911134			−0.455567	+	0.890202i	$0.650563\pi$
$830$		0			0
$831$	7.05428	+	1.04034i	0.244710	+	0.0360891i
$832$		0			0
$833$	17.9307	+	31.0569i	0.621262	+	1.07606i
$834$		0			0
$835$	10.8817	−	18.8477i	0.376578	−	0.652253i
$836$		0			0
$837$	−2.82473	−	33.4149i	−0.0976371	−	1.15499i
$838$		0			0
$839$	−3.22682	+	5.58902i	−0.111402	+	0.192954i	−0.916336	−	0.400411i	$-0.868868\pi$
$839$	−3.22682	+	5.58902i	−0.111402	+	0.192954i	0.804934	+	0.593365i	$0.202201\pi$
$840$		0			0
$841$	0.0692967	+	0.120025i	0.00238954	+	0.00413881i
$842$		0			0
$843$	−4.90307	−	0.723089i	−0.168871	−	0.0249045i
$844$		0			0
$845$	−37.4891			−1.28967
$846$		0			0
$847$	48.1275			1.65368
$848$		0			0
$849$	17.0584	−	21.5306i	0.585444	−	0.738929i
$850$		0			0
$851$	−9.40571	−	16.2912i	−0.322424	−	0.558454i
$852$		0			0
$853$	−1.94158	+	3.36291i	−0.0664784	+	0.115144i	−0.897349	−	0.441322i	$-0.854510\pi$
$853$	−1.94158	+	3.36291i	−0.0664784	+	0.115144i	0.830870	+	0.556466i	$0.187843\pi$
$854$		0			0
$855$	54.0317	+	16.2912i	1.84784	+	0.557146i
$856$		0			0
$857$	−9.54755	+	16.5368i	−0.326138	+	0.564888i	−0.981742	−	0.190217i	$-0.939081\pi$
$857$	−9.54755	+	16.5368i	−0.326138	+	0.564888i	0.655604	+	0.755105i	$0.272414\pi$
$858$		0			0
$859$	−1.31309	−	2.27434i	−0.0448020	−	0.0775994i	0.842755	−	0.538298i	$-0.180932\pi$
$859$	−1.31309	−	2.27434i	−0.0448020	−	0.0775994i	−0.887557	+	0.460698i	$0.847599\pi$
$860$		0			0
$861$	3.00000	+	7.57301i	0.102240	+	0.258088i
$862$		0			0
$863$	−37.6228			−1.28070			−0.640348	−	0.768085i	$-0.721210\pi$
$863$	−37.6228			−1.28070			−0.640348	+	0.768085i	$0.721210\pi$
$864$		0			0
$865$	−18.1168			−0.615991
$866$		0			0
$867$	7.25450	+	18.3128i	0.246376	+	0.621935i
$868$		0			0
$869$	2.82473	+	4.89258i	0.0958225	+	0.165970i
$870$		0			0
$871$	5.85300	−	10.1377i	0.198321	−	0.343502i
$872$		0			0
$873$	−6.17527	−	26.2843i	−0.209001	−	0.889590i
$874$		0			0
$875$	10.8817	−	18.8477i	0.367870	−	0.637170i
$876$		0			0
$877$	19.1753	+	33.2125i	0.647503	+	1.12151i	0.983717	+	0.179722i	$0.0575199\pi$
$877$	19.1753	+	33.2125i	0.647503	+	1.12151i	−0.336215	+	0.941785i	$0.609147\pi$
$878$		0			0
$879$	−15.7337	+	19.8586i	−0.530684	+	0.669812i
$880$		0			0
$881$	−30.2337			−1.01860			−0.509299	−	0.860589i	$-0.670095\pi$
$881$	−30.2337			−1.01860			−0.509299	+	0.860589i	$0.670095\pi$
$882$		0			0
$883$	32.0446			1.07839			0.539193	−	0.842182i	$-0.318729\pi$
$883$	32.0446			1.07839			0.539193	+	0.842182i	$0.318729\pi$
$884$		0			0
$885$	49.2921	+	7.26944i	1.65694	+	0.244360i
$886$		0			0
$887$	−10.8817	−	18.8477i	−0.365373	−	0.632845i	0.623463	−	0.781853i	$-0.285725\pi$
$887$	−10.8817	−	18.8477i	−0.365373	−	0.632845i	−0.988836	+	0.149008i	$0.952392\pi$
$888$		0			0
$889$	26.2337	−	45.4381i	0.879850	−	1.52394i
$890$		0			0
$891$	6.56544	+	4.35502i	0.219951	+	0.145899i
$892$		0			0
$893$	13.1168	−	22.7190i	0.438938	−	0.760264i
$894$		0			0
$895$	−31.7187	−	54.9384i	−1.06024	−	1.83639i
$896$		0			0
$897$	−11.0584	−	1.63086i	−0.369230	−	0.0544529i
$898$		0			0
$899$	34.6708			1.15633
$900$		0			0
$901$	−9.48913			−0.316129
$902$		0			0
$903$	−4.42810	+	5.58902i	−0.147358	+	0.185991i
$904$		0			0
$905$	44.2337	+	76.6150i	1.47038	+	2.54677i
$906$		0			0
$907$	17.1724	−	29.7435i	0.570201	−	0.987618i	−0.426343	−	0.904561i	$-0.640198\pi$
$907$	17.1724	−	29.7435i	0.570201	−	0.987618i	0.996545	−	0.0830565i	$-0.0264682\pi$
$908$		0			0
$909$	1.45245	+	6.18220i	0.0481748	+	0.205051i
$910$		0			0
$911$	−11.4312	+	19.7995i	−0.378734	+	0.655987i	−0.990878	−	0.134759i	$-0.956974\pi$
$911$	−11.4312	+	19.7995i	−0.378734	+	0.655987i	0.612144	+	0.790746i	$0.290307\pi$
$912$		0			0
$913$	1.29211	+	2.23800i	0.0427626	+	0.0740670i
$914$		0			0
$915$	−4.55378	−	11.4953i	−0.150543	−	0.380022i
$916$		0			0
$917$	−30.3505			−1.00226
$918$		0			0
$919$	26.4663			0.873044			0.436522	−	0.899694i	$-0.356210\pi$
$919$	26.4663			0.873044			0.436522	+	0.899694i	$0.356210\pi$
$920$		0			0
$921$	13.3247	+	33.6361i	0.439065	+	1.10835i
$922$		0			0
$923$	6.45364	+	11.1780i	0.212424	+	0.367929i
$924$		0			0
$925$	12.7446	−	22.0742i	0.419039	−	0.725796i
$926$		0			0
$927$	13.5079	+	4.07279i	0.443658	+	0.133768i
$928$		0			0
$929$	−15.3139	+	26.5244i	−0.502431	+	0.870237i	0.497565	+	0.867427i	$0.334228\pi$
$929$	−15.3139	+	26.5244i	−0.502431	+	0.870237i	−0.999996	+	0.00280985i	$0.999106\pi$
$930$		0			0
$931$	−42.1627	−	73.0280i	−1.38183	−	2.39340i
$932$		0			0
$933$	29.0584	−	36.6766i	0.951330	−	1.20074i
$934$		0			0
$935$	−7.00314			−0.229027
$936$		0			0
$937$	−22.2337			−0.726343			−0.363171	−	0.931722i	$-0.618306\pi$
$937$	−22.2337			−0.726343			−0.363171	+	0.931722i	$0.618306\pi$
$938$		0			0
$939$	−26.1032	−	3.84961i	−0.851845	−	0.125627i
$940$		0			0
$941$	8.54755	+	14.8048i	0.278642	+	0.482622i	0.971048	−	0.238886i	$-0.0767824\pi$
$941$	8.54755	+	14.8048i	0.278642	+	0.482622i	−0.692405	+	0.721509i	$0.743449\pi$
$942$		0			0
$943$	2.35143	−	4.07279i	0.0765730	−	0.132628i
$944$		0			0
$945$	−74.5842	−	35.0458i	−2.42622	−	1.14004i
$946$		0			0
$947$	−2.51437	+	4.35502i	−0.0817062	+	0.141519i	−0.903983	−	0.427569i	$-0.859370\pi$
$947$	−2.51437	+	4.35502i	−0.0817062	+	0.141519i	0.822277	+	0.569088i	$0.192704\pi$
$948$		0			0
$949$	−7.11684	−	12.3267i	−0.231023	−	0.400143i
$950$		0			0
$951$	−4.50264	−	0.664035i	−0.146008	−	0.0215328i
$952$		0			0
$953$	8.60597			0.278775			0.139387	−	0.990238i	$-0.455487\pi$
$953$	8.60597			0.278775			0.139387	+	0.990238i	$0.455487\pi$
$954$		0			0
$955$	59.3863			1.92170
$956$		0			0
$957$	−5.05842	+	6.38458i	−0.163516	+	0.206384i
$958$		0			0
$959$	24.6644	+	42.7200i	0.796456	+	1.37950i
$960$		0			0
$961$	−5.32473	+	9.22271i	−0.171766	+	0.297507i
$962$		0			0
$963$	−12.1948	+	11.4603i	−0.392973	+	0.369302i
$964$		0			0
$965$	−1.68614	+	2.92048i	−0.0542788	+	0.0940136i
$966$		0			0
$967$	24.6644	+	42.7200i	0.793154	+	1.37378i	0.924005	+	0.382381i	$0.124896\pi$
$967$	24.6644	+	42.7200i	0.793154	+	1.37378i	−0.130850	+	0.991402i	$0.541771\pi$
$968$		0			0
$969$	8.44158	+	21.3094i	0.271183	+	0.684556i
$970$		0			0
$971$	−57.5333			−1.84633			−0.923165	−	0.384404i	$-0.874407\pi$
$971$	−57.5333			−1.84633			−0.923165	+	0.384404i	$0.874407\pi$
$972$		0			0
$973$	−92.5842			−2.96811
$974$		0			0
$975$	−5.57825	−	14.0814i	−0.178647	−	0.450965i
$976$		0			0
$977$	−22.6168	−	39.1735i	−0.723577	−	1.25327i	−0.959557	−	0.281514i	$-0.909163\pi$
$977$	−22.6168	−	39.1735i	−0.723577	−	1.25327i	0.235980	−	0.971758i	$-0.424170\pi$
$978$		0			0
$979$	−5.57825	+	9.66181i	−0.178282	+	0.308793i
$980$		0			0
$981$	−12.0000	+	11.2772i	−0.383131	+	0.360052i
$982$		0			0
$983$	29.6932	−	51.4301i	0.947065	−	1.64036i	0.195502	−	0.980703i	$-0.437367\pi$
$983$	29.6932	−	51.4301i	0.947065	−	1.64036i	0.751563	−	0.659661i	$-0.229300\pi$
$984$		0			0
$985$	−18.1168	−	31.3793i	−0.577251	−	0.999827i
$986$		0			0
$987$	−23.7890	+	30.0258i	−0.757213	+	0.955731i
$988$		0			0
$989$	4.11684			0.130908
$990$		0			0
$991$	−7.00314			−0.222462			−0.111231	−	0.993795i	$-0.535479\pi$
$991$	−7.00314			−0.222462			−0.111231	+	0.993795i	$0.535479\pi$
$992$		0			0
$993$	17.0584	+	2.51572i	0.541333	+	0.0798340i
$994$		0			0
$995$	28.7666	+	49.8253i	0.911963	+	1.57957i
$996$		0			0
$997$	−5.17527	+	8.96382i	−0.163902	+	0.283887i	−0.936265	−	0.351295i	$-0.885742\pi$
$997$	−5.17527	+	8.96382i	−0.163902	+	0.283887i	0.772363	+	0.635182i	$0.219075\pi$
$998$		0			0
$999$	−18.8114	−	8.83915i	−0.595167	−	0.279658i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	576.2.i.n.385.2		8
3.2	odd	2		1728.2.i.n.1153.4		8
4.3	odd	2	inner	576.2.i.n.385.3		8
8.3	odd	2		288.2.i.f.97.2	✓	8
8.5	even	2		288.2.i.f.97.3	yes	8
9.2	odd	6		5184.2.a.cc.1.1		4
9.4	even	3	inner	576.2.i.n.193.2		8
9.5	odd	6		1728.2.i.n.577.4		8
9.7	even	3		5184.2.a.cf.1.3		4
12.11	even	2		1728.2.i.n.1153.3		8
24.5	odd	2		864.2.i.f.289.2		8
24.11	even	2		864.2.i.f.289.1		8
36.7	odd	6		5184.2.a.cf.1.4		4
36.11	even	6		5184.2.a.cc.1.2		4
36.23	even	6		1728.2.i.n.577.3		8
36.31	odd	6	inner	576.2.i.n.193.3		8
72.5	odd	6		864.2.i.f.577.2		8
72.11	even	6		2592.2.a.x.1.4		4
72.13	even	6		288.2.i.f.193.3	yes	8
72.29	odd	6		2592.2.a.x.1.3		4
72.43	odd	6		2592.2.a.u.1.2		4
72.59	even	6		864.2.i.f.577.1		8
72.61	even	6		2592.2.a.u.1.1		4
72.67	odd	6		288.2.i.f.193.2	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
288.2.i.f.97.2	✓	8	8.3	odd	2
288.2.i.f.97.3	yes	8	8.5	even	2
288.2.i.f.193.2	yes	8	72.67	odd	6
288.2.i.f.193.3	yes	8	72.13	even	6
576.2.i.n.193.2		8	9.4	even	3	inner
576.2.i.n.193.3		8	36.31	odd	6	inner
576.2.i.n.385.2		8	1.1	even	1	trivial
576.2.i.n.385.3		8	4.3	odd	2	inner
864.2.i.f.289.1		8	24.11	even	2
864.2.i.f.289.2		8	24.5	odd	2
864.2.i.f.577.1		8	72.59	even	6
864.2.i.f.577.2		8	72.5	odd	6
1728.2.i.n.577.3		8	36.23	even	6
1728.2.i.n.577.4		8	9.5	odd	6
1728.2.i.n.1153.3		8	12.11	even	2
1728.2.i.n.1153.4		8	3.2	odd	2
2592.2.a.u.1.1		4	72.61	even	6
2592.2.a.u.1.2		4	72.43	odd	6
2592.2.a.x.1.3		4	72.29	odd	6
2592.2.a.x.1.4		4	72.11	even	6
5184.2.a.cc.1.1		4	9.2	odd	6
5184.2.a.cc.1.2		4	36.11	even	6
5184.2.a.cf.1.3		4	9.7	even	3
5184.2.a.cf.1.4		4	36.7	odd	6

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:	\( N \)	\(=\)	\( 576 = 2^{6} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	576.i (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.637910 - 1.61030i) q^{3} +(-1.68614 - 2.92048i) q^{5} +(2.35143 - 4.07279i) q^{7} +(-2.18614 + 2.05446i) q^{9} +O(q^{10})\)	\(q+(-0.637910 - 1.61030i) q^{3} +(-1.68614 - 2.92048i) q^{5} +(2.35143 - 4.07279i) q^{7} +(-2.18614 + 2.05446i) q^{9} +(-0.437696 + 0.758112i) q^{11} +(-0.686141 - 1.18843i) q^{13} +(-3.62725 + 4.57820i) q^{15} -2.37228 q^{17} +5.57825 q^{19} +(-8.05842 - 1.18843i) q^{21} +(2.35143 + 4.07279i) q^{23} +(-3.18614 + 5.51856i) q^{25} +(4.70285 + 2.20979i) q^{27} +(-2.68614 + 4.65253i) q^{29} +(-3.22682 - 5.58902i) q^{31} +(1.50000 + 0.221215i) q^{33} -15.8593 q^{35} -4.00000 q^{37} +(-1.47603 + 1.86301i) q^{39} +(-0.500000 - 0.866025i) q^{41} +(0.437696 - 0.758112i) q^{43} +(9.68614 + 2.92048i) q^{45} +(2.35143 - 4.07279i) q^{47} +(-7.55842 - 13.0916i) q^{49} +(1.51330 + 3.82009i) q^{51} +4.00000 q^{53} +2.95207 q^{55} +(-3.55842 - 8.98266i) q^{57} +(-4.26516 - 7.38747i) q^{59} +(-1.05842 + 1.83324i) q^{61} +(3.22682 + 13.7346i) q^{63} +(-2.31386 + 4.00772i) q^{65} +(4.26516 + 7.38747i) q^{67} +(5.05842 - 6.38458i) q^{69} -9.40571 q^{71} +10.3723 q^{73} +(10.9190 + 1.61030i) q^{75} +(2.05842 + 3.56529i) q^{77} +(3.22682 - 5.58902i) q^{79} +(0.558422 - 8.98266i) q^{81} +(1.47603 - 2.55657i) q^{83} +(4.00000 + 6.92820i) q^{85} +(9.20550 + 1.35760i) q^{87} +12.7446 q^{89} -6.45364 q^{91} +(-6.94158 + 8.76144i) q^{93} +(-9.40571 - 16.2912i) q^{95} +(-4.50000 + 7.79423i) q^{97} +(-0.600642 - 2.55657i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 2 q^{5} - 6 q^{9}+O(q^{10}) \) 8 * q - 2 * q^5 - 6 * q^9	\( 8 q - 2 q^{5} - 6 q^{9} + 6 q^{13} + 4 q^{17} - 30 q^{21} - 14 q^{25} - 10 q^{29} + 12 q^{33} - 32 q^{37} - 4 q^{41} + 66 q^{45} - 26 q^{49} + 32 q^{53} + 6 q^{57} + 26 q^{61} - 30 q^{65} + 6 q^{69} + 60 q^{73} - 18 q^{77} - 30 q^{81} + 32 q^{85} + 56 q^{89} - 90 q^{93} - 36 q^{97}+O(q^{100}) \) 8 * q - 2 * q^5 - 6 * q^9 + 6 * q^13 + 4 * q^17 - 30 * q^21 - 14 * q^25 - 10 * q^29 + 12 * q^33 - 32 * q^37 - 4 * q^41 + 66 * q^45 - 26 * q^49 + 32 * q^53 + 6 * q^57 + 26 * q^61 - 30 * q^65 + 6 * q^69 + 60 * q^73 - 18 * q^77 - 30 * q^81 + 32 * q^85 + 56 * q^89 - 90 * q^93 - 36 * q^97

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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