LMFDB - Embedded newform 572.2.bc.a.197.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [572,2,Mod(197,572)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(572, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 6, 1]))

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

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

chi := DirichletCharacter("572.197");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 572 = 2^{2} \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	572.bc (of order $12$, degree $4$, 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:	$4.56744299562$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$14$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			197.9
Character	$\chi$	$=$	572.197
Dual form			572.2.bc.a.241.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.591694 + 1.02484i) q^{3} +(0.335170 - 0.335170i) q^{5} +(-0.719487 - 2.68516i) q^{7} +(0.799795 - 1.38529i) q^{9} +O(q^{10})$	\(q+(0.591694 + 1.02484i) q^{3} +(0.335170 - 0.335170i) q^{5} +(-0.719487 - 2.68516i) q^{7} +(0.799795 - 1.38529i) q^{9} +(-1.39509 - 3.00894i) q^{11} +(0.732998 - 3.53026i) q^{13} +(0.541815 + 0.145179i) q^{15} +(0.560760 - 0.971265i) q^{17} +(-1.88933 + 0.506244i) q^{19} +(2.32616 - 2.32616i) q^{21} +(0.906255 - 0.523227i) q^{23} +4.77532i q^{25} +5.44310 q^{27} +(3.57188 - 2.06222i) q^{29} +(-0.250321 + 0.250321i) q^{31} +(2.25823 - 3.21012i) q^{33} +(-1.14114 - 0.658835i) q^{35} +(-1.16759 + 4.35750i) q^{37} +(4.05168 - 1.33762i) q^{39} +(-0.673160 + 2.51227i) q^{41} +(-1.38997 + 2.40751i) q^{43} +(-0.196239 - 0.732373i) q^{45} +(-1.30884 - 1.30884i) q^{47} +(-0.630262 + 0.363882i) q^{49} +1.32719 q^{51} +7.61409 q^{53} +(-1.47610 - 0.540916i) q^{55} +(-1.63673 - 1.63673i) q^{57} +(-3.38868 + 0.907993i) q^{59} +(7.17698 + 4.14363i) q^{61} +(-4.29516 - 1.15089i) q^{63} +(-0.937556 - 1.42891i) q^{65} +(-2.02132 - 0.541611i) q^{67} +(1.07245 + 0.619181i) q^{69} +(-2.63710 - 9.84180i) q^{71} +(1.63496 - 1.63496i) q^{73} +(-4.89396 + 2.82553i) q^{75} +(-7.07576 + 5.91093i) q^{77} +1.70420i q^{79} +(0.821269 + 1.42248i) q^{81} +(2.86250 + 2.86250i) q^{83} +(-0.137589 - 0.513488i) q^{85} +(4.22692 + 2.44041i) q^{87} +(-0.700697 + 2.61504i) q^{89} +(-10.0067 + 0.571757i) q^{91} +(-0.404654 - 0.108427i) q^{93} +(-0.463568 + 0.802923i) q^{95} +(-1.29117 - 4.81873i) q^{97} +(-5.28403 - 0.473945i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q - 28 q^{9}+O(q^{10}) $ 56 * q - 28 * q^9	$ 56 q - 28 q^{9} + 4 q^{11} + 8 q^{15} - 12 q^{23} - 24 q^{27} - 4 q^{31} - 10 q^{33} - 12 q^{37} - 64 q^{45} - 8 q^{47} + 40 q^{53} + 22 q^{55} + 48 q^{59} - 36 q^{67} - 48 q^{71} + 120 q^{75} + 28 q^{81} + 28 q^{89} + 36 q^{91} + 20 q^{93} - 68 q^{97} - 44 q^{99}+O(q^{100}) $ 56 * q - 28 * q^9 + 4 * q^11 + 8 * q^15 - 12 * q^23 - 24 * q^27 - 4 * q^31 - 10 * q^33 - 12 * q^37 - 64 * q^45 - 8 * q^47 + 40 * q^53 + 22 * q^55 + 48 * q^59 - 36 * q^67 - 48 * q^71 + 120 * q^75 + 28 * q^81 + 28 * q^89 + 36 * q^91 + 20 * q^93 - 68 * q^97 - 44 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/572\mathbb{Z}\right)^\times$.

$n$	$287$	$353$	$365$
$\chi(n)$	$1$	$e\left(\frac{1}{12}\right)$	$-1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.591694	+	1.02484i	0.341615	+	0.591694i	0.984733	−	0.174073i	$-0.0556928\pi$
$3$	0.591694	+	1.02484i	0.341615	+	0.591694i	−0.643118	+	0.765767i	$0.722359\pi$
$4$		0			0
$5$	0.335170	−	0.335170i	0.149892	−	0.149892i	−0.628178	−	0.778070i	$-0.716199\pi$
$5$	0.335170	−	0.335170i	0.149892	−	0.149892i	0.778070	+	0.628178i	$0.216199\pi$
$6$		0			0
$7$	−0.719487	−	2.68516i	−0.271941	−	1.01490i	−0.957864	−	0.287222i	$-0.907268\pi$
$7$	−0.719487	−	2.68516i	−0.271941	−	1.01490i	0.685923	−	0.727674i	$-0.259399\pi$
$8$		0			0
$9$	0.799795	−	1.38529i	0.266598	−	0.461762i
$10$		0			0
$11$	−1.39509	−	3.00894i	−0.420634	−	0.907230i
$11$	−1.39509	−	3.00894i	−0.420634	−	0.907230i
$12$		0			0
$13$	0.732998	−	3.53026i	0.203297	−	0.979117i
$13$	0.732998	−	3.53026i	0.203297	−	0.979117i
$14$		0			0
$15$	0.541815	+	0.145179i	0.139896	+	0.0374850i
$16$		0			0
$17$	0.560760	−	0.971265i	0.136004	−	0.235566i	−0.789976	−	0.613137i	$-0.789907\pi$
$17$	0.560760	−	0.971265i	0.136004	−	0.235566i	0.925981	+	0.377571i	$0.123241\pi$
$18$		0			0
$19$	−1.88933	+	0.506244i	−0.433442	+	0.116140i	−0.468941	−	0.883229i	$-0.655364\pi$
$19$	−1.88933	+	0.506244i	−0.433442	+	0.116140i	0.0354996	+	0.999370i	$0.488698\pi$
$20$		0			0
$21$	2.32616	−	2.32616i	0.507610	−	0.507610i
$22$		0			0
$23$	0.906255	−	0.523227i	0.188967	−	0.109100i	−0.402532	−	0.915406i	$-0.631870\pi$
$23$	0.906255	−	0.523227i	0.188967	−	0.109100i	0.591499	+	0.806306i	$0.298536\pi$
$24$		0			0
$25$			4.77532i			0.955065i
$26$		0			0
$27$	5.44310			1.04753
$28$		0			0
$29$	3.57188	−	2.06222i	0.663281	−	0.382945i	−0.130245	−	0.991482i	$-0.541576\pi$
$29$	3.57188	−	2.06222i	0.663281	−	0.382945i	0.793526	+	0.608537i	$0.208243\pi$
$30$		0			0
$31$	−0.250321	+	0.250321i	−0.0449590	+	0.0449590i	−0.729229	−	0.684270i	$-0.760121\pi$
$31$	−0.250321	+	0.250321i	−0.0449590	+	0.0449590i	0.684270	+	0.729229i	$0.260121\pi$
$32$		0			0
$33$	2.25823	−	3.21012i	0.393108	−	0.558810i
$34$		0			0
$35$	−1.14114	−	0.658835i	−0.192887	−	0.111363i
$36$		0			0
$37$	−1.16759	+	4.35750i	−0.191950	+	0.716368i	0.801085	+	0.598551i	$0.204256\pi$
$37$	−1.16759	+	4.35750i	−0.191950	+	0.716368i	−0.993035	+	0.117817i	$0.962410\pi$
$38$		0			0
$39$	4.05168	−	1.33762i	0.648787	−	0.214191i
$40$		0			0
$41$	−0.673160	+	2.51227i	−0.105130	+	0.392350i	−0.998360	−	0.0572498i	$-0.981767\pi$
$41$	−0.673160	+	2.51227i	−0.105130	+	0.392350i	0.893230	+	0.449600i	$0.148434\pi$
$42$		0			0
$43$	−1.38997	+	2.40751i	−0.211969	+	0.367141i	−0.952331	−	0.305068i	$-0.901321\pi$
$43$	−1.38997	+	2.40751i	−0.211969	+	0.367141i	0.740362	+	0.672209i	$0.234654\pi$
$44$		0			0
$45$	−0.196239	−	0.732373i	−0.0292535	−	0.109176i
$46$		0			0
$47$	−1.30884	−	1.30884i	−0.190914	−	0.190914i	0.605177	−	0.796091i	$-0.293102\pi$
$47$	−1.30884	−	1.30884i	−0.190914	−	0.190914i	−0.796091	+	0.605177i	$0.793102\pi$
$48$		0			0
$49$	−0.630262	+	0.363882i	−0.0900374	+	0.0519831i
$50$		0			0
$51$	1.32719			0.185844
$52$		0			0
$53$	7.61409			1.04588			0.522938	−	0.852371i	$-0.324836\pi$
$53$	7.61409			1.04588			0.522938	+	0.852371i	$0.324836\pi$
$54$		0			0
$55$	−1.47610	−	0.540916i	−0.199037	−	0.0729371i
$56$		0			0
$57$	−1.63673	−	1.63673i	−0.216790	−	0.216790i
$58$		0			0
$59$	−3.38868	+	0.907993i	−0.441168	+	0.118211i	−0.472564	−	0.881296i	$-0.656671\pi$
$59$	−3.38868	+	0.907993i	−0.441168	+	0.118211i	0.0313958	+	0.999507i	$0.490005\pi$
$60$		0			0
$61$	7.17698	+	4.14363i	0.918918	+	0.530538i	0.883290	−	0.468827i	$-0.155323\pi$
$61$	7.17698	+	4.14363i	0.918918	+	0.530538i	0.0356284	+	0.999365i	$0.488657\pi$
$62$		0			0
$63$	−4.29516	−	1.15089i	−0.541140	−	0.144998i
$64$		0			0
$65$	−0.937556	−	1.42891i	−0.116290	−	0.177235i
$66$		0			0
$67$	−2.02132	−	0.541611i	−0.246944	−	0.0661683i	0.133224	−	0.991086i	$-0.457467\pi$
$67$	−2.02132	−	0.541611i	−0.246944	−	0.0661683i	−0.380168	+	0.924918i	$0.624134\pi$
$68$		0			0
$69$	1.07245	+	0.619181i	0.129108	+	0.0745406i
$70$		0			0
$71$	−2.63710	−	9.84180i	−0.312967	−	1.16801i	−0.925868	−	0.377848i	$-0.876664\pi$
$71$	−2.63710	−	9.84180i	−0.312967	−	1.16801i	0.612901	−	0.790160i	$-0.290002\pi$
$72$		0			0
$73$	1.63496	−	1.63496i	0.191357	−	0.191357i	−0.604925	−	0.796282i	$-0.706797\pi$
$73$	1.63496	−	1.63496i	0.191357	−	0.191357i	0.796282	+	0.604925i	$0.206797\pi$
$74$		0			0
$75$	−4.89396	+	2.82553i	−0.565106	+	0.326264i
$76$		0			0
$77$	−7.07576	+	5.91093i	−0.806357	+	0.673613i
$78$		0			0
$79$			1.70420i			0.191737i	0.995394	+	0.0958685i	$0.0305628\pi$
$79$			1.70420i			0.191737i	−0.995394	+	0.0958685i	$0.969437\pi$
$80$		0			0
$81$	0.821269	+	1.42248i	0.0912521	+	0.158053i
$82$		0			0
$83$	2.86250	+	2.86250i	0.314200	+	0.314200i	0.846534	−	0.532334i	$-0.178685\pi$
$83$	2.86250	+	2.86250i	0.314200	+	0.314200i	−0.532334	+	0.846534i	$0.678685\pi$
$84$		0			0
$85$	−0.137589	−	0.513488i	−0.0149236	−	0.0556956i
$86$		0			0
$87$	4.22692	+	2.44041i	0.453173	+	0.261640i
$88$		0			0
$89$	−0.700697	+	2.61504i	−0.0742738	+	0.277193i	−0.993068	−	0.117544i	$-0.962498\pi$
$89$	−0.700697	+	2.61504i	−0.0742738	+	0.277193i	0.918794	+	0.394738i	$0.129164\pi$
$90$		0			0
$91$	−10.0067	+	0.571757i	−1.04899	+	0.0599364i
$92$		0			0
$93$	−0.404654	−	0.108427i	−0.0419607	−	0.0112433i
$94$		0			0
$95$	−0.463568	+	0.802923i	−0.0475611	+	0.0823782i
$96$		0			0
$97$	−1.29117	−	4.81873i	−0.131099	−	0.489268i	0.868885	−	0.495015i	$-0.164837\pi$
$97$	−1.29117	−	4.81873i	−0.131099	−	0.489268i	−0.999983	+	0.00574708i	$0.998171\pi$
$98$		0			0
$99$	−5.28403	−	0.473945i	−0.531065	−	0.0476333i
$100$		0			0
$101$	−4.77124	−	8.26404i	−0.474757	−	0.822303i	0.524825	−	0.851210i	$-0.324131\pi$
$101$	−4.77124	−	8.26404i	−0.474757	−	0.822303i	−0.999582	+	0.0289073i	$0.990797\pi$
$102$		0			0
$103$		−	2.00827i		−	0.197881i	−0.995093	−	0.0989405i	$-0.968455\pi$
$103$		−	2.00827i		−	0.197881i	0.995093	−	0.0989405i	$-0.0315454\pi$
$104$		0			0
$105$		−	1.55932i		−	0.152174i
$106$		0			0
$107$	−14.9084	+	8.60735i	−1.44125	+	0.832103i	−0.997933	−	0.0642637i	$-0.979530\pi$
$107$	−14.9084	+	8.60735i	−1.44125	+	0.832103i	−0.443313	+	0.896367i	$0.646197\pi$
$108$		0			0
$109$	12.2879	+	12.2879i	1.17696	+	1.17696i	0.980514	+	0.196449i	$0.0629410\pi$
$109$	12.2879	+	12.2879i	1.17696	+	1.17696i	0.196449	+	0.980514i	$0.437059\pi$
$110$		0			0
$111$	−5.15661	+	1.38171i	−0.489444	+	0.131146i
$112$		0			0
$113$	7.61537	−	13.1902i	0.716393	−	1.24083i	−0.246026	−	0.969263i	$-0.579125\pi$
$113$	7.61537	−	13.1902i	0.716393	−	1.24083i	0.962420	−	0.271567i	$-0.0875418\pi$
$114$		0			0
$115$	0.128380	−	0.479119i	0.0119715	−	0.0446781i
$116$		0			0
$117$	−4.30417	−	3.83889i	−0.397920	−	0.354906i
$118$		0			0
$119$	−3.01147	−	0.806920i	−0.276061	−	0.0739702i
$120$		0			0
$121$	−7.10747	+	8.39547i	−0.646134	+	0.763224i
$122$		0			0
$123$	−2.97299	+	0.796610i	−0.268066	+	0.0718279i
$124$		0			0
$125$	3.27639	+	3.27639i	0.293049	+	0.293049i
$126$		0			0
$127$	4.78780	+	8.29272i	0.424849	+	0.735860i	0.996406	−	0.0847021i	$-0.0269939\pi$
$127$	4.78780	+	8.29272i	0.424849	+	0.735860i	−0.571557	+	0.820562i	$0.693661\pi$
$128$		0			0
$129$	−3.28976			−0.289647
$130$		0			0
$131$			17.3493i			1.51581i	0.652363	+	0.757907i	$0.273778\pi$
$131$			17.3493i			1.51581i	−0.652363	+	0.757907i	$0.726222\pi$
$132$		0			0
$133$	2.71870	+	4.70892i	0.235741	+	0.408315i
$134$		0			0
$135$	1.82436	−	1.82436i	0.157016	−	0.157016i
$136$		0			0
$137$	−12.1986	+	3.26862i	−1.04220	+	0.279257i	−0.739025	−	0.673678i	$-0.764713\pi$
$137$	−12.1986	+	3.26862i	−1.04220	+	0.279257i	−0.303175	+	0.952935i	$0.598047\pi$
$138$		0			0
$139$	13.5394	+	7.81698i	1.14840	+	0.663028i	0.948496	−	0.316788i	$-0.102605\pi$
$139$	13.5394	+	7.81698i	1.14840	+	0.663028i	0.199901	+	0.979816i	$0.435938\pi$
$140$		0			0
$141$	0.566926	−	2.11580i	0.0477438	−	0.178182i
$142$		0			0
$143$	−11.6449	+	2.71946i	−0.973798	+	0.227413i
$144$		0			0
$145$	0.505989	−	1.88838i	0.0420201	−	0.156821i
$146$		0			0
$147$	−0.745845	−	0.430614i	−0.0615163	−	0.0355164i
$148$		0			0
$149$	16.9072	−	4.53027i	1.38509	−	0.371134i	0.512123	−	0.858912i	$-0.328859\pi$
$149$	16.9072	−	4.53027i	1.38509	−	0.371134i	0.872968	+	0.487778i	$0.162192\pi$
$150$		0			0
$151$	−6.73027	+	6.73027i	−0.547701	+	0.547701i	−0.925775	−	0.378074i	$-0.876586\pi$
$151$	−6.73027	+	6.73027i	−0.547701	+	0.547701i	0.378074	+	0.925775i	$0.376586\pi$
$152$		0			0
$153$	−0.896987	−	1.55363i	−0.0725171	−	0.125603i
$154$		0			0
$155$			0.167800i			0.0134780i
$156$		0			0
$157$	−0.686360			−0.0547775			−0.0273888	−	0.999625i	$-0.508719\pi$
$157$	−0.686360			−0.0547775			−0.0273888	+	0.999625i	$0.508719\pi$
$158$		0			0
$159$	4.50521	+	7.80326i	0.357287	+	0.618839i
$160$		0			0
$161$	−2.05699	−	2.05699i	−0.162113	−	0.162113i
$162$		0			0
$163$	−16.9902	+	4.55250i	−1.33077	+	0.356580i	−0.853003	−	0.521905i	$-0.825221\pi$
$163$	−16.9902	+	4.55250i	−1.33077	+	0.356580i	−0.477770	+	0.878485i	$0.658555\pi$
$164$		0			0
$165$	−0.319043	−	1.83283i	−0.0248375	−	0.142685i
$166$		0			0
$167$	−5.57211	−	1.49304i	−0.431183	−	0.115535i	0.0366984	−	0.999326i	$-0.488316\pi$
$167$	−5.57211	−	1.49304i	−0.431183	−	0.115535i	−0.467881	+	0.883791i	$0.654983\pi$
$168$		0			0
$169$	−11.9254	−	5.17534i	−0.917341	−	0.398103i
$170$		0			0
$171$	−0.809783	+	3.02215i	−0.0619257	+	0.231110i
$172$		0			0
$173$	4.74266	−	8.21452i	0.360577	−	0.624538i	−0.627479	−	0.778634i	$-0.715913\pi$
$173$	4.74266	−	8.21452i	0.360577	−	0.624538i	0.988056	+	0.154095i	$0.0492463\pi$
$174$		0			0
$175$	12.8225	−	3.43578i	0.969291	−	0.259721i
$176$		0			0
$177$	−2.93561	−	2.93561i	−0.220654	−	0.220654i
$178$		0			0
$179$	−4.92236	+	2.84193i	−0.367914	+	0.212415i	−0.672547	−	0.740054i	$-0.734800\pi$
$179$	−4.92236	+	2.84193i	−0.367914	+	0.212415i	0.304633	+	0.952470i	$0.401466\pi$
$180$		0			0
$181$			17.8398i			1.32602i	0.748609	+	0.663012i	$0.230722\pi$
$181$			17.8398i			1.32602i	−0.748609	+	0.663012i	$0.769278\pi$
$182$		0			0
$183$			9.80706i			0.724958i
$184$		0			0
$185$	1.06916	+	1.85184i	0.0786062	+	0.136150i
$186$		0			0
$187$	−3.70479	−	0.332297i	−0.270921	−	0.0243000i
$188$		0			0
$189$	−3.91624	−	14.6156i	−0.284865	−	1.06313i
$190$		0			0
$191$	8.91353	−	15.4387i	0.644960	−	1.11710i	−0.339350	−	0.940660i	$-0.610207\pi$
$191$	8.91353	−	15.4387i	0.644960	−	1.11710i	0.984311	−	0.176444i	$-0.0564595\pi$
$192$		0			0
$193$	23.5949	+	6.32222i	1.69840	+	0.455084i	0.972535	−	0.232758i	$-0.0747751\pi$
$193$	23.5949	+	6.32222i	1.69840	+	0.455084i	0.725861	+	0.687842i	$0.241442\pi$
$194$		0			0
$195$	0.909667	−	1.80633i	0.0651426	−	0.129354i
$196$		0			0
$197$	0.979544	−	3.65571i	0.0697896	−	0.260458i	−0.922212	−	0.386685i	$-0.873620\pi$
$197$	0.979544	−	3.65571i	0.0697896	−	0.260458i	0.992001	+	0.126227i	$0.0402867\pi$
$198$		0			0
$199$	4.42003	+	2.55191i	0.313328	+	0.180900i	0.648415	−	0.761287i	$-0.275432\pi$
$199$	4.42003	+	2.55191i	0.313328	+	0.180900i	−0.335087	+	0.942187i	$0.608766\pi$
$200$		0			0
$201$	−0.640937	−	2.39201i	−0.0452082	−	0.168719i
$202$		0			0
$203$	−8.10733	−	8.10733i	−0.569023	−	0.569023i
$204$		0			0
$205$	0.616413	+	1.06766i	0.0430522	+	0.0745685i
$206$		0			0
$207$		−	1.67390i		−	0.116344i
$208$		0			0
$209$	4.15904	+	4.97863i	0.287686	+	0.344379i
$210$		0			0
$211$	−13.0305	+	7.52318i	−0.897058	+	0.517917i	−0.876245	−	0.481866i	$-0.839959\pi$
$211$	−13.0305	+	7.52318i	−0.897058	+	0.517917i	−0.0208137	+	0.999783i	$0.506626\pi$
$212$		0			0
$213$	8.52596	−	8.52596i	0.584189	−	0.584189i
$214$		0			0
$215$	0.341046	+	1.27280i	0.0232591	+	0.0868042i
$216$		0			0
$217$	0.852257	+	0.492051i	0.0578549	+	0.0334026i
$218$		0			0
$219$	2.64297	+	0.708182i	0.178595	+	0.0478545i
$220$		0			0
$221$	−3.01778	−	2.69156i	−0.202998	−	0.181054i
$222$		0			0
$223$	14.6833	+	3.93437i	0.983265	+	0.263465i	0.714419	−	0.699718i	$-0.246691\pi$
$223$	14.6833	+	3.93437i	0.983265	+	0.263465i	0.268846	+	0.963183i	$0.413358\pi$
$224$		0			0
$225$	6.61519	+	3.81928i	0.441013	+	0.254619i
$226$		0			0
$227$	16.2062	−	4.34244i	1.07564	−	0.288218i	0.322833	−	0.946456i	$-0.395365\pi$
$227$	16.2062	−	4.34244i	1.07564	−	0.288218i	0.752810	+	0.658238i	$0.228698\pi$
$228$		0			0
$229$	14.3617	+	14.3617i	0.949051	+	0.949051i	0.998764	−	0.0497125i	$-0.0158305\pi$
$229$	14.3617	+	14.3617i	0.949051	+	0.949051i	−0.0497125	+	0.998764i	$0.515831\pi$
$230$		0			0
$231$	−10.2445	−	3.75409i	−0.674037	−	0.247001i
$232$		0			0
$233$	−29.0568			−1.90358			−0.951788	−	0.306756i	$-0.900756\pi$
$233$	−29.0568			−1.90358			−0.951788	+	0.306756i	$0.900756\pi$
$234$		0			0
$235$	−0.877368			−0.0572332
$236$		0			0
$237$	−1.74654	+	1.00836i	−0.113450	+	0.0655002i
$238$		0			0
$239$	−13.7420	−	13.7420i	−0.888898	−	0.888898i	0.105519	−	0.994417i	$-0.466350\pi$
$239$	−13.7420	−	13.7420i	−0.888898	−	0.888898i	−0.994417	+	0.105519i	$0.966350\pi$
$240$		0			0
$241$	−0.780507	−	2.91289i	−0.0502769	−	0.187636i	0.936220	−	0.351413i	$-0.114299\pi$
$241$	−0.780507	−	2.91289i	−0.0502769	−	0.187636i	−0.986497	+	0.163777i	$0.947632\pi$
$242$		0			0
$243$	7.19278	−	12.4583i	0.461417	−	0.799197i
$244$		0			0
$245$	−0.0892825	+	0.333207i	−0.00570405	+	0.0212878i
$246$		0			0
$247$	0.402298	+	7.04089i	0.0255976	+	0.448001i
$248$		0			0
$249$	−1.23989	+	4.62734i	−0.0785749	+	0.293246i
$250$		0			0
$251$	9.56861	+	5.52444i	0.603966	+	0.348700i	0.770600	−	0.637319i	$-0.219957\pi$
$251$	9.56861	+	5.52444i	0.603966	+	0.348700i	−0.166634	+	0.986019i	$0.553290\pi$
$252$		0			0
$253$	−2.83866	−	1.99692i	−0.178465	−	0.125546i
$254$		0			0
$255$	0.444835	−	0.444835i	0.0278567	−	0.0278567i
$256$		0			0
$257$	6.03408	−	3.48378i	0.376396	−	0.217312i	−0.299853	−	0.953985i	$-0.596938\pi$
$257$	6.03408	−	3.48378i	0.376396	−	0.217312i	0.676249	+	0.736673i	$0.263604\pi$
$258$		0			0
$259$	12.5407			0.779238
$260$		0			0
$261$		−	6.59743i		−	0.408370i
$262$		0			0
$263$	8.32575	−	4.80687i	0.513388	−	0.296405i	−0.220837	−	0.975311i	$-0.570879\pi$
$263$	8.32575	−	4.80687i	0.513388	−	0.296405i	0.734225	+	0.678906i	$0.237546\pi$
$264$		0			0
$265$	2.55201	−	2.55201i	0.156769	−	0.156769i
$266$		0			0
$267$	−3.09461	+	0.829197i	−0.189387	+	0.0507460i
$268$		0			0
$269$	2.67591	−	4.63481i	0.163153	−	0.282589i	−0.772845	−	0.634595i	$-0.781167\pi$
$269$	2.67591	−	4.63481i	0.163153	−	0.282589i	0.935998	+	0.352006i	$0.114500\pi$
$270$		0			0
$271$	−3.26366	−	0.874495i	−0.198253	−	0.0531218i	0.158326	−	0.987387i	$-0.449390\pi$
$271$	−3.26366	−	0.874495i	−0.198253	−	0.0531218i	−0.356579	+	0.934265i	$0.616057\pi$
$272$		0			0
$273$	−6.50687	−	9.91701i	−0.393814	−	0.600205i
$274$		0			0
$275$	14.3687	−	6.66198i	0.866464	−	0.401733i
$276$		0			0
$277$	0.691575	−	1.19784i	0.0415527	−	0.0719714i	−0.844501	−	0.535554i	$-0.820103\pi$
$277$	0.691575	−	1.19784i	0.0415527	−	0.0719714i	0.886054	+	0.463582i	$0.153436\pi$
$278$		0			0
$279$	0.146561	+	0.546972i	0.00877437	+	0.0327464i
$280$		0			0
$281$	−1.96344	+	1.96344i	−0.117129	+	0.117129i	−0.763242	−	0.646113i	$-0.776394\pi$
$281$	−1.96344	+	1.96344i	−0.117129	+	0.117129i	0.646113	+	0.763242i	$0.276394\pi$
$282$		0			0
$283$	−11.2561	−	19.4962i	−0.669108	−	1.15893i	−0.978154	−	0.207882i	$-0.933343\pi$
$283$	−11.2561	−	19.4962i	−0.669108	−	1.15893i	0.309046	−	0.951047i	$-0.399990\pi$
$284$		0			0
$285$	−1.09716			−0.0649903
$286$		0			0
$287$	7.23018			0.426784
$288$		0			0
$289$	7.87110	+	13.6331i	0.463006	+	0.801949i
$290$		0			0
$291$	4.17447	−	4.17447i	0.244712	−	0.244712i
$292$		0			0
$293$	−4.81929	−	17.9858i	−0.281546	−	1.05074i	−0.951327	−	0.308184i	$-0.900279\pi$
$293$	−4.81929	−	17.9858i	−0.281546	−	1.05074i	0.669781	−	0.742559i	$-0.266388\pi$
$294$		0			0
$295$	−0.831450	+	1.44011i	−0.0484089	+	0.0838466i
$296$		0			0
$297$	−7.59360	−	16.3780i	−0.440625	−	0.950347i
$298$		0			0
$299$	−1.18284	−	3.58284i	−0.0684055	−	0.207201i
$300$		0			0
$301$	7.46462	+	2.00014i	0.430253	+	0.115286i
$302$		0			0
$303$	5.64624	−	9.77957i	0.324368	−	0.561822i
$304$		0			0
$305$	3.79432	−	1.01669i	0.217262	−	0.0582153i
$306$		0			0
$307$	19.4452	−	19.4452i	1.10979	−	1.10979i	0.116617	−	0.993177i	$-0.462795\pi$
$307$	19.4452	−	19.4452i	1.10979	−	1.10979i	0.993177	−	0.116617i	$-0.0372051\pi$
$308$		0			0
$309$	2.05817	−	1.18828i	0.117085	−	0.0675991i
$310$		0			0
$311$		−	8.41236i		−	0.477021i	−0.971140	−	0.238511i	$-0.923341\pi$
$311$		−	8.41236i		−	0.477021i	0.971140	−	0.238511i	$-0.0766591\pi$
$312$		0			0
$313$	−8.75366			−0.494786			−0.247393	−	0.968915i	$-0.579574\pi$
$313$	−8.75366			−0.494786			−0.247393	+	0.968915i	$0.579574\pi$
$314$		0			0
$315$	−1.82535	+	1.05387i	−0.102847	+	0.0593786i
$316$		0			0
$317$	4.93995	−	4.93995i	0.277455	−	0.277455i	−0.554637	−	0.832092i	$-0.687143\pi$
$317$	4.93995	−	4.93995i	0.277455	−	0.277455i	0.832092	+	0.554637i	$0.187143\pi$
$318$		0			0
$319$	−11.1882	−	7.87059i	−0.626418	−	0.440668i
$320$		0			0
$321$	−17.6424	−	10.1858i	−0.984702	−	0.568518i
$322$		0			0
$323$	−0.567763	+	2.11892i	−0.0315912	+	0.117900i
$324$		0			0
$325$	16.8581	+	3.50030i	0.935120	+	0.194162i
$326$		0			0
$327$	−5.32249	+	19.8638i	−0.294334	+	1.09847i
$328$		0			0
$329$	−2.57276	+	4.45615i	−0.141841	+	0.245676i
$330$		0			0
$331$	−3.55089	−	13.2521i	−0.195175	−	0.728402i	−0.992222	−	0.124484i	$-0.960272\pi$
$331$	−3.55089	−	13.2521i	−0.195175	−	0.728402i	0.797047	−	0.603917i	$-0.206394\pi$
$332$		0			0
$333$	5.10255	+	5.10255i	0.279618	+	0.279618i
$334$		0			0
$335$	−0.859016	+	0.495953i	−0.0469331	+	0.0270968i
$336$		0			0
$337$	−12.8194			−0.698318			−0.349159	−	0.937063i	$-0.613533\pi$
$337$	−12.8194			−0.698318			−0.349159	+	0.937063i	$0.613533\pi$
$338$		0			0
$339$	18.0239			0.978923
$340$		0			0
$341$	1.10242	+	0.403983i	0.0596995	+	0.0218769i
$342$		0			0
$343$	−12.3292	−	12.3292i	−0.665713	−	0.665713i
$344$		0			0
$345$	0.566984	−	0.151923i	0.0305254	−	0.00817925i
$346$		0			0
$347$	15.1088	+	8.72309i	0.811085	+	0.468280i	0.847332	−	0.531063i	$-0.178207\pi$
$347$	15.1088	+	8.72309i	0.811085	+	0.468280i	−0.0362476	+	0.999343i	$0.511541\pi$
$348$		0			0
$349$	32.8517	+	8.80258i	1.75851	+	0.471191i	0.986409	−	0.164308i	$-0.0525392\pi$
$349$	32.8517	+	8.80258i	1.75851	+	0.471191i	0.772101	+	0.635500i	$0.219206\pi$
$350$		0			0
$351$	3.98978	−	19.2156i	0.212959	−	1.02565i
$352$		0			0
$353$	4.91434	+	1.31679i	0.261564	+	0.0700858i	0.387218	−	0.921988i	$-0.373436\pi$
$353$	4.91434	+	1.31679i	0.261564	+	0.0700858i	−0.125654	+	0.992074i	$0.540103\pi$
$354$		0			0
$355$	−4.18255	−	2.41480i	−0.221987	−	0.128164i
$356$		0			0
$357$	−0.954900	−	3.56373i	−0.0505387	−	0.188613i
$358$		0			0
$359$	0.330174	−	0.330174i	0.0174259	−	0.0174259i	−0.698340	−	0.715766i	$-0.746078\pi$
$359$	0.330174	−	0.330174i	0.0174259	−	0.0174259i	0.715766	+	0.698340i	$0.246078\pi$
$360$		0			0
$361$	−13.1412	+	7.58708i	−0.691642	+	0.399320i
$362$		0			0
$363$	−12.8095	−	2.31651i	−0.672324	−	0.121585i
$364$		0			0
$365$		−	1.09597i		−	0.0573659i
$366$		0			0
$367$	12.9365	+	22.4067i	0.675280	+	1.16962i	0.976387	+	0.216029i	$0.0693107\pi$
$367$	12.9365	+	22.4067i	0.675280	+	1.16962i	−0.301107	+	0.953590i	$0.597356\pi$
$368$		0			0
$369$	2.94182	+	2.94182i	0.153145	+	0.153145i
$370$		0			0
$371$	−5.47824	−	20.4451i	−0.284416	−	1.06145i
$372$		0			0
$373$	23.6677	+	13.6645i	1.22546	+	0.707522i	0.966078	−	0.258251i	$-0.0831462\pi$
$373$	23.6677	+	13.6645i	1.22546	+	0.707522i	0.259387	+	0.965774i	$0.416480\pi$
$374$		0			0
$375$	−1.41917	+	5.29641i	−0.0732856	+	0.273506i
$376$		0			0
$377$	−4.66200	−	14.1212i	−0.240105	−	0.727281i
$378$		0			0
$379$	24.6962	+	6.61733i	1.26856	+	0.339909i	0.829478	−	0.558539i	$-0.188638\pi$
$379$	24.6962	+	6.61733i	1.26856	+	0.339909i	0.439080	+	0.898448i	$0.355304\pi$
$380$		0			0
$381$	−5.66584	+	9.81351i	−0.290270	+	0.502762i
$382$		0			0
$383$	−1.76712	−	6.59500i	−0.0902958	−	0.336989i	0.905968	−	0.423345i	$-0.139144\pi$
$383$	−1.76712	−	6.59500i	−0.0902958	−	0.336989i	−0.996264	+	0.0863566i	$0.972478\pi$
$384$		0			0
$385$	−0.390414	+	4.35274i	−0.0198974	+	0.221836i
$386$		0			0
$387$	2.22339	+	3.85102i	0.113021	+	0.195759i
$388$		0			0
$389$			34.1959i			1.73380i	0.498483	+	0.866899i	$0.333891\pi$
$389$			34.1959i			1.73380i	−0.498483	+	0.866899i	$0.666109\pi$
$390$		0			0
$391$		−	1.17362i		−	0.0593525i
$392$		0			0
$393$	−17.7803	+	10.2655i	−0.896898	+	0.517825i
$394$		0			0
$395$	0.571194	+	0.571194i	0.0287399	+	0.0287399i
$396$		0			0
$397$	−31.2866	+	8.38323i	−1.57023	+	0.420742i	−0.935885	−	0.352306i	$-0.885398\pi$
$397$	−31.2866	+	8.38323i	−1.57023	+	0.420742i	−0.634347	+	0.773048i	$0.718731\pi$
$398$		0			0
$399$	−3.21727	+	5.57248i	−0.161065	+	0.278973i
$400$		0			0
$401$	7.29106	−	27.2106i	0.364098	−	1.35883i	−0.504541	−	0.863388i	$-0.668338\pi$
$401$	7.29106	−	27.2106i	0.364098	−	1.35883i	0.868639	−	0.495446i	$-0.164995\pi$
$402$		0			0
$403$	0.700214	+	1.06718i	0.0348801	+	0.0531602i
$404$		0			0
$405$	0.752036	+	0.201507i	0.0373690	+	0.0100130i
$406$		0			0
$407$	14.7403	−	2.56588i	0.730652	−	0.127186i
$408$		0			0
$409$	−12.5466	+	3.36185i	−0.620388	+	0.166233i	−0.555304	−	0.831647i	$-0.687398\pi$
$409$	−12.5466	+	3.36185i	−0.620388	+	0.166233i	−0.0650841	+	0.997880i	$0.520732\pi$
$410$		0			0
$411$	−10.5677	−	10.5677i	−0.521266	−	0.521266i
$412$		0			0
$413$	4.87622	+	8.44586i	0.239943	+	0.415594i
$414$		0			0
$415$	1.91884			0.0941923
$416$		0			0
$417$			18.5011i			0.906001i
$418$		0			0
$419$	15.8796	+	27.5043i	0.775770	+	1.34367i	0.934361	+	0.356329i	$0.115972\pi$
$419$	15.8796	+	27.5043i	0.775770	+	1.34367i	−0.158591	+	0.987344i	$0.550695\pi$
$420$		0			0
$421$	−12.4545	+	12.4545i	−0.606994	+	0.606994i	−0.942159	−	0.335165i	$-0.891208\pi$
$421$	−12.4545	+	12.4545i	−0.606994	+	0.606994i	0.335165	+	0.942159i	$0.391208\pi$
$422$		0			0
$423$	−2.85993	+	0.766315i	−0.139054	+	0.0372595i
$424$		0			0
$425$	4.63810	+	2.67781i	0.224981	+	0.129893i
$426$		0			0
$427$	5.96258	−	22.2527i	0.288550	−	1.07688i
$428$		0			0
$429$	−9.67727	−	10.3252i	−0.467223	−	0.498503i
$430$		0			0
$431$	−7.71697	+	28.8001i	−0.371713	+	1.38725i	0.486374	+	0.873751i	$0.338319\pi$
$431$	−7.71697	+	28.8001i	−0.371713	+	1.38725i	−0.858088	+	0.513503i	$0.828348\pi$
$432$		0			0
$433$	−29.0808	−	16.7898i	−1.39753	−	0.806866i	−0.403399	−	0.915024i	$-0.632171\pi$
$433$	−29.0808	−	16.7898i	−1.39753	−	0.806866i	−0.994134	+	0.108159i	$0.965505\pi$
$434$		0			0
$435$	2.23469	−	0.598782i	0.107145	−	0.0287094i
$436$		0			0
$437$	−1.44733	+	1.44733i	−0.0692354	+	0.0692354i
$438$		0			0
$439$	1.13260	+	1.96173i	0.0540562	+	0.0936281i	0.891787	−	0.452455i	$-0.149452\pi$
$439$	1.13260	+	1.96173i	0.0540562	+	0.0936281i	−0.837731	+	0.546083i	$0.816118\pi$
$440$		0			0
$441$			1.16412i			0.0554345i
$442$		0			0
$443$	11.8475			0.562894			0.281447	−	0.959577i	$-0.409186\pi$
$443$	11.8475			0.562894			0.281447	+	0.959577i	$0.409186\pi$
$444$		0			0
$445$	0.641629	+	1.11133i	0.0304161	+	0.0526822i
$446$		0			0
$447$	14.6467	+	14.6467i	0.692766	+	0.692766i
$448$		0			0
$449$	−16.8010	+	4.50180i	−0.792886	+	0.212453i	−0.632458	−	0.774594i	$-0.717954\pi$
$449$	−16.8010	+	4.50180i	−0.792886	+	0.212453i	−0.160428	+	0.987048i	$0.551287\pi$
$450$		0			0
$451$	8.49839	−	1.47933i	0.400173	−	0.0696589i
$452$		0			0
$453$	−10.8797	−	2.91522i	−0.511175	−	0.136969i
$454$		0			0
$455$	−3.16231	+	3.54558i	−0.148251	+	0.166219i
$456$		0			0
$457$	−4.49406	+	16.7720i	−0.210223	+	0.784563i	0.777571	+	0.628796i	$0.216452\pi$
$457$	−4.49406	+	16.7720i	−0.210223	+	0.784563i	−0.987794	+	0.155768i	$0.950215\pi$
$458$		0			0
$459$	3.05228	−	5.28670i	0.142468	−	0.246762i
$460$		0			0
$461$	6.97079	−	1.86782i	0.324662	−	0.0869929i	−0.0928069	−	0.995684i	$-0.529584\pi$
$461$	6.97079	−	1.86782i	0.324662	−	0.0869929i	0.417469	+	0.908691i	$0.362917\pi$
$462$		0			0
$463$	6.28940	+	6.28940i	0.292293	+	0.292293i	0.837986	−	0.545692i	$-0.183733\pi$
$463$	6.28940	+	6.28940i	0.292293	+	0.292293i	−0.545692	+	0.837986i	$0.683733\pi$
$464$		0			0
$465$	−0.171969	+	0.0992864i	−0.00797488	+	0.00460430i
$466$		0			0
$467$			0.723225i			0.0334669i	0.999860	+	0.0167334i	$0.00532667\pi$
$467$			0.723225i			0.0334669i	−0.999860	+	0.0167334i	$0.994673\pi$
$468$		0			0
$469$			5.81726i			0.268616i
$470$		0			0
$471$	−0.406116	−	0.703413i	−0.0187128	−	0.0324116i
$472$		0			0
$473$	9.18318	+	0.823676i	0.422243	+	0.0378726i
$474$		0			0
$475$	−2.41748	−	9.02215i	−0.110922	−	0.413965i
$476$		0			0
$477$	6.08971	−	10.5477i	0.278829	−	0.482945i
$478$		0			0
$479$	33.4818	+	8.97141i	1.52982	+	0.409914i	0.922961	−	0.384894i	$-0.125762\pi$
$479$	33.4818	+	8.97141i	1.52982	+	0.409914i	0.606860	+	0.794808i	$0.292429\pi$
$480$		0			0
$481$	14.5272	+	7.31592i	0.662385	+	0.333577i
$482$		0			0
$483$	0.890985	−	3.32520i	0.0405412	−	0.151302i
$484$		0			0
$485$	−2.04785	−	1.18233i	−0.0929882	−	0.0536868i
$486$		0			0
$487$	−3.04206	−	11.3531i	−0.137849	−	0.514459i	−0.999970	−	0.00775668i	$-0.997531\pi$
$487$	−3.04206	−	11.3531i	−0.137849	−	0.514459i	0.862121	−	0.506702i	$-0.169136\pi$
$488$		0			0
$489$	−14.7186	−	14.7186i	−0.665598	−	0.665598i
$490$		0			0
$491$	−5.76198	−	9.98004i	−0.260034	−	0.450393i	0.706216	−	0.707996i	$-0.250401\pi$
$491$	−5.76198	−	9.98004i	−0.260034	−	0.450393i	−0.966251	+	0.257603i	$0.917067\pi$
$492$		0			0
$493$		−	4.62565i		−	0.208329i
$494$		0			0
$495$	−1.92990	+	1.61219i	−0.0867425	+	0.0724627i
$496$		0			0
$497$	−24.5295	+	14.1621i	−1.10030	+	0.635257i
$498$		0			0
$499$	−23.7515	+	23.7515i	−1.06327	+	1.06327i	−0.0654063	+	0.997859i	$0.520834\pi$
$499$	−23.7515	+	23.7515i	−1.06327	+	1.06327i	−0.997859	+	0.0654063i	$0.979166\pi$
$500$		0			0
$501$	−1.76685	−	6.59398i	−0.0789371	−	0.294597i
$502$		0			0
$503$	−21.4890	−	12.4067i	−0.958147	−	0.553186i	−0.0625445	−	0.998042i	$-0.519922\pi$
$503$	−21.4890	−	12.4067i	−0.958147	−	0.553186i	−0.895602	+	0.444856i	$0.853255\pi$
$504$		0			0
$505$	−4.36903	−	1.17068i	−0.194419	−	0.0520945i
$506$		0			0
$507$	−1.75229	−	15.2839i	−0.0778219	−	0.678783i
$508$		0			0
$509$	−30.8758	−	8.27314i	−1.36855	−	0.366701i	−0.501598	−	0.865101i	$-0.667254\pi$
$509$	−30.8758	−	8.27314i	−1.36855	−	0.366701i	−0.866947	+	0.498400i	$0.833921\pi$
$510$		0			0
$511$	−5.56645	−	3.21379i	−0.246245	−	0.142170i
$512$		0			0
$513$	−10.2838	+	2.75554i	−0.454041	+	0.121660i
$514$		0			0
$515$	−0.673112	−	0.673112i	−0.0296609	−	0.0296609i
$516$		0			0
$517$	−2.11229	+	5.76418i	−0.0928982	+	0.253508i
$518$		0			0
$519$	11.2248			0.492715
$520$		0			0
$521$	−7.72511			−0.338443			−0.169222	−	0.985578i	$-0.554125\pi$
$521$	−7.72511			−0.338443			−0.169222	+	0.985578i	$0.554125\pi$
$522$		0			0
$523$	−24.8951	+	14.3732i	−1.08859	+	0.628496i	−0.933200	−	0.359357i	$-0.882996\pi$
$523$	−24.8951	+	14.3732i	−1.08859	+	0.628496i	−0.155387	+	0.987854i	$0.549663\pi$
$524$		0			0
$525$	11.1082	+	11.1082i	0.484800	+	0.484800i
$526$		0			0
$527$	0.102758	+	0.383499i	0.00447621	+	0.0167055i
$528$		0			0
$529$	−10.9525	+	18.9702i	−0.476194	+	0.824793i
$530$		0			0
$531$	−1.45242	+	5.42050i	−0.0630296	+	0.235230i
$532$		0			0
$533$	8.37553	+	4.21792i	0.362784	+	0.182698i
$534$		0			0
$535$	−2.11191	+	7.88175i	−0.0913057	+	0.340758i
$536$		0			0
$537$	−5.82507	−	3.36310i	−0.251370	−	0.145129i
$538$		0			0
$539$	1.97417	+	1.38878i	0.0850335	+	0.0598188i
$540$		0			0
$541$	−17.5515	+	17.5515i	−0.754597	+	0.754597i	−0.975333	−	0.220737i	$-0.929154\pi$
$541$	−17.5515	+	17.5515i	−0.754597	+	0.754597i	0.220737	+	0.975333i	$0.429154\pi$
$542$		0			0
$543$	−18.2830	+	10.5557i	−0.784601	+	0.452989i
$544$		0			0
$545$	8.23703			0.352836
$546$		0			0
$547$		−	41.7372i		−	1.78455i	−0.451488	−	0.892277i	$-0.649107\pi$
$547$		−	41.7372i		−	1.78455i	0.451488	−	0.892277i	$-0.350893\pi$
$548$		0			0
$549$	11.4802	−	6.62811i	0.489964	−	0.282881i
$550$		0			0
$551$	−5.70446	+	5.70446i	−0.243018	+	0.243018i
$552$		0			0
$553$	4.57604	−	1.22615i	0.194593	−	0.0521411i
$554$		0			0
$555$	−1.26523	+	2.19145i	−0.0537061	+	0.0930217i
$556$		0			0
$557$	−6.44916	−	1.72805i	−0.273260	−	0.0732197i	0.119587	−	0.992824i	$-0.461843\pi$
$557$	−6.44916	−	1.72805i	−0.273260	−	0.0732197i	−0.392847	+	0.919604i	$0.628510\pi$
$558$		0			0
$559$	7.48027	+	6.67166i	0.316382	+	0.282181i
$560$		0			0
$561$	−1.85155	−	3.99345i	−0.0781725	−	0.168604i
$562$		0			0
$563$	−8.96014	+	15.5194i	−0.377625	+	0.654066i	−0.990716	−	0.135946i	$-0.956592\pi$
$563$	−8.96014	+	15.5194i	−0.377625	+	0.654066i	0.613091	+	0.790012i	$0.289926\pi$
$564$		0			0
$565$	−1.86852	−	6.97339i	−0.0786090	−	0.293373i
$566$		0			0
$567$	3.22870	−	3.22870i	0.135593	−	0.135593i
$568$		0			0
$569$	6.32937	+	10.9628i	0.265341	+	0.459584i	0.967653	−	0.252285i	$-0.0811822\pi$
$569$	6.32937	+	10.9628i	0.265341	+	0.459584i	−0.702312	+	0.711869i	$0.747849\pi$
$570$		0			0
$571$	7.23905			0.302945			0.151472	−	0.988461i	$-0.451599\pi$
$571$	7.23905			0.302945			0.151472	+	0.988461i	$0.451599\pi$
$572$		0			0
$573$	21.0963			0.881313
$574$		0			0
$575$	2.49858	+	4.32766i	0.104198	+	0.180476i
$576$		0			0
$577$	15.5971	−	15.5971i	0.649317	−	0.649317i	−0.303511	−	0.952828i	$-0.598159\pi$
$577$	15.5971	−	15.5971i	0.649317	−	0.649317i	0.952828	+	0.303511i	$0.0981590\pi$
$578$		0			0
$579$	7.48165	+	27.9219i	0.310927	+	1.16039i
$580$		0			0
$581$	5.62674	−	9.74580i	0.233436	−	0.404324i
$582$		0			0
$583$	−10.6223	−	22.9103i	−0.439931	−	0.948850i
$584$		0			0
$585$	−2.72931	+	0.155945i	−0.112843	+	0.00644755i
$586$		0			0
$587$	14.1446	+	3.79004i	0.583812	+	0.156432i	0.538623	−	0.842547i	$-0.318945\pi$
$587$	14.1446	+	3.79004i	0.583812	+	0.156432i	0.0451883	+	0.998978i	$0.485611\pi$
$588$		0			0
$589$	0.346216	−	0.599663i	0.0142656	−	0.0247087i
$590$		0			0
$591$	4.32612	−	1.15918i	0.177953	−	0.0476823i
$592$		0			0
$593$	−26.8155	+	26.8155i	−1.10118	+	1.10118i	−0.106910	+	0.994269i	$0.534096\pi$
$593$	−26.8155	+	26.8155i	−1.10118	+	1.10118i	−0.994269	+	0.106910i	$0.965904\pi$
$594$		0			0
$595$	−1.27981	+	0.738896i	−0.0524669	+	0.0302918i
$596$		0			0
$597$			6.03979i			0.247192i
$598$		0			0
$599$	−25.4269			−1.03892			−0.519458	−	0.854496i	$-0.673866\pi$
$599$	−25.4269			−1.03892			−0.519458	+	0.854496i	$0.673866\pi$
$600$		0			0
$601$	−17.4057	+	10.0492i	−0.709991	+	0.409914i	−0.811058	−	0.584966i	$-0.801108\pi$
$601$	−17.4057	+	10.0492i	−0.709991	+	0.409914i	0.101067	+	0.994880i	$0.467775\pi$
$602$		0			0
$603$	−2.36693	+	2.36693i	−0.0963888	+	0.0963888i
$604$		0			0
$605$	0.431696	+	5.19611i	0.0175510	+	0.211252i
$606$		0			0
$607$	20.7297	+	11.9683i	0.841394	+	0.485779i	0.857738	−	0.514087i	$-0.171869\pi$
$607$	20.7297	+	11.9683i	0.841394	+	0.485779i	−0.0163436	+	0.999866i	$0.505203\pi$
$608$		0			0
$609$	3.51169	−	13.1058i	0.142301	−	0.531074i
$610$		0			0
$611$	−5.57993	+	3.66117i	−0.225740	+	0.148115i
$612$		0			0
$613$	−2.64145	+	9.85801i	−0.106687	+	0.398161i	−0.998531	−	0.0541816i	$-0.982745\pi$
$613$	−2.64145	+	9.85801i	−0.106687	+	0.398161i	0.891844	+	0.452343i	$0.149412\pi$
$614$		0			0
$615$	−0.729456	+	1.26346i	−0.0294145	+	0.0509474i
$616$		0			0
$617$	−8.50645	−	31.7465i	−0.342457	−	1.27807i	−0.895555	−	0.444951i	$-0.853221\pi$
$617$	−8.50645	−	31.7465i	−0.342457	−	1.27807i	0.553098	−	0.833116i	$-0.313445\pi$
$618$		0			0
$619$	16.1040	+	16.1040i	0.647274	+	0.647274i	0.952333	−	0.305059i	$-0.0986763\pi$
$619$	16.1040	+	16.1040i	0.647274	+	0.647274i	−0.305059	+	0.952333i	$0.598676\pi$
$620$		0			0
$621$	4.93284	−	2.84798i	0.197948	−	0.114285i
$622$		0			0
$623$	7.52595			0.301521
$624$		0			0
$625$	−21.6803			−0.867213
$626$		0			0
$627$	−2.64144	+	7.20819i	−0.105489	+	0.287867i
$628$		0			0
$629$	3.57755	+	3.57755i	0.142646	+	0.142646i
$630$		0			0
$631$	45.2916	−	12.1359i	1.80303	−	0.483121i	0.808586	−	0.588378i	$-0.200233\pi$
$631$	45.2916	−	12.1359i	1.80303	−	0.483121i	0.994445	+	0.105257i	$0.0335664\pi$
$632$		0			0
$633$	−15.4202	−	8.90284i	−0.612897	−	0.353856i
$634$		0			0
$635$	4.38419	+	1.17474i	0.173981	+	0.0466182i
$636$		0			0
$637$	0.822616	+	2.49171i	0.0325932	+	0.0987252i
$638$		0			0
$639$	−15.7429	−	4.21829i	−0.622778	−	0.166873i
$640$		0			0
$641$	−7.01855	−	4.05216i	−0.277216	−	0.160051i	0.354946	−	0.934887i	$-0.384499\pi$
$641$	−7.01855	−	4.05216i	−0.277216	−	0.160051i	−0.632162	+	0.774836i	$0.717832\pi$
$642$		0			0
$643$	−1.28576	−	4.79851i	−0.0507053	−	0.189235i	0.935928	−	0.352192i	$-0.114563\pi$
$643$	−1.28576	−	4.79851i	−0.0507053	−	0.189235i	−0.986633	+	0.162957i	$0.947897\pi$
$644$		0			0
$645$	−1.10263	+	1.10263i	−0.0434159	+	0.0434159i
$646$		0			0
$647$	−11.9082	+	6.87520i	−0.468160	+	0.270292i	−0.715469	−	0.698645i	$-0.753787\pi$
$647$	−11.9082	+	6.87520i	−0.468160	+	0.270292i	0.247309	+	0.968937i	$0.420454\pi$
$648$		0			0
$649$	7.45960	+	8.92961i	0.292815	+	0.350518i
$650$		0			0
$651$			1.16457i			0.0456433i
$652$		0			0
$653$	0.591882	+	1.02517i	0.0231621	+	0.0401180i	0.877374	−	0.479807i	$-0.159293\pi$
$653$	0.591882	+	1.02517i	0.0231621	+	0.0401180i	−0.854212	+	0.519925i	$0.825960\pi$
$654$		0			0
$655$	5.81495	+	5.81495i	0.227209	+	0.227209i
$656$		0			0
$657$	−0.957252	−	3.57251i	−0.0373459	−	0.139377i
$658$		0			0
$659$	16.3859	+	9.46039i	0.638303	+	0.368524i	0.783961	−	0.620811i	$-0.213196\pi$
$659$	16.3859	+	9.46039i	0.638303	+	0.368524i	−0.145658	+	0.989335i	$0.546530\pi$
$660$		0			0
$661$	1.62514	−	6.06512i	0.0632107	−	0.235906i	−0.927092	−	0.374835i	$-0.877699\pi$
$661$	1.62514	−	6.06512i	0.0632107	−	0.235906i	0.990302	+	0.138929i	$0.0443661\pi$
$662$		0			0
$663$	0.972831	−	4.68534i	0.0377816	−	0.181963i
$664$		0			0
$665$	2.48951	+	0.667062i	0.0965391	+	0.0258676i
$666$		0			0
$667$	2.15802	−	3.73780i	0.0835589	−	0.144728i
$668$		0			0
$669$	4.65589	+	17.3760i	0.180007	+	0.671796i
$670$		0			0
$671$	2.45545	−	27.3758i	0.0947915	−	1.05683i
$672$		0			0
$673$	−11.7343	−	20.3244i	−0.452325	−	0.783450i	0.546205	−	0.837652i	$-0.316072\pi$
$673$	−11.7343	−	20.3244i	−0.452325	−	0.783450i	−0.998530	+	0.0542017i	$0.982739\pi$
$674$		0			0
$675$			25.9926i			1.00045i
$676$		0			0
$677$		−	26.5823i		−	1.02164i	−0.859688	−	0.510820i	$-0.829342\pi$
$677$		−	26.5823i		−	1.02164i	0.859688	−	0.510820i	$-0.170658\pi$
$678$		0			0
$679$	−12.0101	+	6.93403i	−0.460905	+	0.266103i
$680$		0			0
$681$	14.0394	+	14.0394i	0.537992	+	0.537992i
$682$		0			0
$683$	−24.1996	+	6.48427i	−0.925973	+	0.248114i	−0.690137	−	0.723679i	$-0.742450\pi$
$683$	−24.1996	+	6.48427i	−0.925973	+	0.248114i	−0.235836	+	0.971793i	$0.575783\pi$
$684$		0			0
$685$	−2.99307	+	5.18415i	−0.114359	+	0.198076i
$686$		0			0
$687$	−6.22080	+	23.2163i	−0.237338	+	0.885758i
$688$		0			0
$689$	5.58111	−	26.8797i	0.212623	−	1.02403i
$690$		0			0
$691$	31.2694	+	8.37861i	1.18954	+	0.318737i	0.798705	−	0.601722i	$-0.205519\pi$
$691$	31.2694	+	8.37861i	1.18954	+	0.318737i	0.390838	+	0.920459i	$0.372185\pi$
$692$		0			0
$693$	2.52917	+	14.5295i	0.0960753	+	0.551929i
$694$		0			0
$695$	7.15801	−	1.91798i	0.271519	−	0.0727532i
$696$		0			0
$697$	2.06260	+	2.06260i	0.0781264	+	0.0781264i
$698$		0			0
$699$	−17.1928	−	29.7787i	−0.650290	−	1.12634i
$700$		0			0
$701$	9.71849			0.367062			0.183531	−	0.983014i	$-0.441247\pi$
$701$	9.71849			0.367062			0.183531	+	0.983014i	$0.441247\pi$
$702$		0			0
$703$		−	8.82383i		−	0.332797i
$704$		0			0
$705$	−0.519134	−	0.899167i	−0.0195517	−	0.0338646i
$706$		0			0
$707$	−18.7574	+	18.7574i	−0.705446	+	0.705446i
$708$		0			0
$709$	−25.3448	+	6.79112i	−0.951844	+	0.255046i	−0.701144	−	0.713019i	$-0.747327\pi$
$709$	−25.3448	+	6.79112i	−0.951844	+	0.255046i	−0.250699	+	0.968065i	$0.580661\pi$
$710$		0			0
$711$	2.36080	+	1.36301i	0.0885369	+	0.0511168i
$712$		0			0
$713$	−0.0958802	+	0.357830i	−0.00359074	+	0.0134008i
$714$		0			0
$715$	−2.99155	+	4.81451i	−0.111877	+	0.180052i
$716$		0			0
$717$	5.95237	−	22.2145i	0.222295	−	0.829617i
$718$		0			0
$719$	−35.2649	−	20.3602i	−1.31516	−	0.759307i	−0.332213	−	0.943205i	$-0.607795\pi$
$719$	−35.2649	−	20.3602i	−1.31516	−	0.759307i	−0.982945	+	0.183898i	$0.941129\pi$
$720$		0			0
$721$	−5.39254	+	1.44493i	−0.200829	+	0.0538119i
$722$		0			0
$723$	2.52344	−	2.52344i	0.0938478	−	0.0938478i
$724$		0			0
$725$	9.84778	+	17.0569i	0.365737	+	0.633476i
$726$		0			0
$727$		−	44.9190i		−	1.66595i	−0.553308	−	0.832977i	$-0.686635\pi$
$727$		−	44.9190i		−	1.66595i	0.553308	−	0.832977i	$-0.313365\pi$
$728$		0			0
$729$	21.9513			0.813012
$730$		0			0
$731$	1.55888	+	2.70007i	0.0576574	+	0.0998656i
$732$		0			0
$733$	−18.2536	−	18.2536i	−0.674211	−	0.674211i	0.284473	−	0.958684i	$-0.408181\pi$
$733$	−18.2536	−	18.2536i	−0.674211	−	0.674211i	−0.958684	+	0.284473i	$0.908181\pi$
$734$		0			0
$735$	−0.394313	+	0.105656i	−0.0145445	+	0.00389718i
$736$		0			0
$737$	1.19024	+	6.83763i	0.0438430	+	0.251867i
$738$		0			0
$739$	38.1839	+	10.2313i	1.40462	+	0.376366i	0.880001	−	0.474972i	$-0.157542\pi$
$739$	38.1839	+	10.2313i	1.40462	+	0.376366i	0.524617	+	0.851338i	$0.324208\pi$
$740$		0			0
$741$	−6.97778	+	4.57835i	−0.256335	+	0.168190i
$742$		0			0
$743$	−6.39060	+	23.8501i	−0.234449	+	0.874974i	0.743948	+	0.668237i	$0.232951\pi$
$743$	−6.39060	+	23.8501i	−0.234449	+	0.874974i	−0.978397	+	0.206736i	$0.933716\pi$
$744$		0			0
$745$	4.14837	−	7.18518i	0.151984	−	0.263245i
$746$		0			0
$747$	6.25479	−	1.67597i	0.228851	−	0.0613204i
$748$		0			0
$749$	33.8385	+	33.8385i	1.23643	+	1.23643i
$750$		0			0
$751$	11.7995	−	6.81243i	0.430569	−	0.248589i	−0.269020	−	0.963135i	$-0.586700\pi$
$751$	11.7995	−	6.81243i	0.430569	−	0.248589i	0.699589	+	0.714545i	$0.253366\pi$
$752$		0			0
$753$			13.0751i			0.476484i
$754$		0			0
$755$			4.51156i			0.164192i
$756$		0			0
$757$	2.73547	+	4.73798i	0.0994224	+	0.172205i	0.911446	−	0.411420i	$-0.134967\pi$
$757$	2.73547	+	4.73798i	0.0994224	+	0.172205i	−0.812023	+	0.583625i	$0.801634\pi$
$758$		0			0
$759$	0.366916	−	4.09076i	0.0133182	−	0.148485i
$760$		0			0
$761$	−0.133683	−	0.498912i	−0.00484601	−	0.0180855i	0.963460	−	0.267850i	$-0.0863133\pi$
$761$	−0.133683	−	0.498912i	−0.00484601	−	0.0180855i	−0.968306	+	0.249765i	$0.919647\pi$
$762$		0			0
$763$	24.1539	−	41.8359i	0.874431	−	1.51456i
$764$		0			0
$765$	−0.821371	−	0.220086i	−0.0296967	−	0.00795721i
$766$		0			0
$767$	0.721557	+	12.6285i	0.0260539	+	0.455987i
$768$		0			0
$769$	5.55983	−	20.7496i	0.200493	−	0.748249i	−0.790284	−	0.612741i	$-0.790067\pi$
$769$	5.55983	−	20.7496i	0.200493	−	0.748249i	0.990776	−	0.135508i	$-0.0432666\pi$
$770$		0			0
$771$	7.14067	+	4.12267i	0.257165	+	0.148474i
$772$		0			0
$773$	−2.28106	−	8.51304i	−0.0820441	−	0.306193i	0.912694	−	0.408644i	$-0.133998\pi$
$773$	−2.28106	−	8.51304i	−0.0820441	−	0.306193i	−0.994738	+	0.102451i	$0.967331\pi$
$774$		0			0
$775$	−1.19536	−	1.19536i	−0.0429388	−	0.0429388i
$776$		0			0
$777$	7.42023	+	12.8522i	0.266199	+	0.461071i
$778$		0			0
$779$		−	5.08728i		−	0.182271i
$780$		0			0
$781$	−25.9344	+	21.6651i	−0.928007	+	0.775236i
$782$		0			0
$783$	19.4421	−	11.2249i	0.694804	−	0.401145i
$784$		0			0
$785$	−0.230047	+	0.230047i	−0.00821073	+	0.00821073i
$786$		0			0
$787$	−4.19348	−	15.6503i	−0.149481	−	0.557873i	−0.999515	−	0.0311438i	$-0.990085\pi$
$787$	−4.19348	−	15.6503i	−0.149481	−	0.557873i	0.850033	−	0.526729i	$-0.176582\pi$
$788$		0			0
$789$	9.85260	+	5.68840i	0.350762	+	0.202512i
$790$		0			0
$791$	−40.8970	−	10.9583i	−1.45413	−	0.389633i
$792$		0			0
$793$	19.8888	−	22.2993i	0.706272	−	0.791872i
$794$		0			0
$795$	4.12542	+	1.10540i	0.146314	+	0.0392046i
$796$		0			0
$797$	41.4393	+	23.9250i	1.46785	+	0.847466i	0.999352	−	0.0359955i	$-0.0114602\pi$
$797$	41.4393	+	23.9250i	1.46785	+	0.847466i	0.468503	+	0.883462i	$0.344794\pi$
$798$		0			0
$799$	−2.00518	+	0.537286i	−0.0709382	+	0.0190078i
$800$		0			0
$801$	3.06216	+	3.06216i	0.108196	+	0.108196i
$802$		0			0
$803$	−7.20039	−	2.63859i	−0.254096	−	0.0931136i
$804$		0			0
$805$	−1.37888			−0.0485991
$806$		0			0
$807$	6.33328			0.222942
$808$		0			0
$809$	6.34840	−	3.66525i	0.223198	−	0.128863i	−0.384232	−	0.923236i	$-0.625534\pi$
$809$	6.34840	−	3.66525i	0.223198	−	0.128863i	0.607430	+	0.794373i	$0.292200\pi$
$810$		0			0
$811$	−25.0691	−	25.0691i	−0.880296	−	0.880296i	0.113269	−	0.993564i	$-0.463868\pi$
$811$	−25.0691	−	25.0691i	−0.880296	−	0.880296i	−0.993564	+	0.113269i	$0.963868\pi$
$812$		0			0
$813$	−1.03487	−	3.86218i	−0.0362944	−	0.135453i
$814$		0			0
$815$	−4.16873	+	7.22045i	−0.146024	+	0.252921i
$816$		0			0
$817$	1.40733	−	5.25224i	0.0492363	−	0.183753i
$818$		0			0
$819$	−7.21126	+	14.3194i	−0.251982	+	0.500361i
$820$		0			0
$821$	11.7541	−	43.8668i	0.410220	−	1.53096i	−0.384001	−	0.923333i	$-0.625454\pi$
$821$	11.7541	−	43.8668i	0.410220	−	1.53096i	0.794221	−	0.607629i	$-0.207879\pi$
$822$		0			0
$823$	−0.934105	−	0.539306i	−0.0325609	−	0.0187990i	0.483631	−	0.875272i	$-0.339318\pi$
$823$	−0.934105	−	0.539306i	−0.0325609	−	0.0187990i	−0.516192	+	0.856473i	$0.672651\pi$
$824$		0			0
$825$	15.3294	+	10.7838i	0.533700	+	0.375444i
$826$		0			0
$827$	6.13970	−	6.13970i	0.213498	−	0.213498i	−0.592253	−	0.805752i	$-0.701762\pi$
$827$	6.13970	−	6.13970i	0.213498	−	0.213498i	0.805752	+	0.592253i	$0.201762\pi$
$828$		0			0
$829$	32.9079	−	18.9994i	1.14294	−	0.659875i	0.195781	−	0.980648i	$-0.437276\pi$
$829$	32.9079	−	18.9994i	1.14294	−	0.659875i	0.947156	+	0.320772i	$0.103942\pi$
$830$		0			0
$831$	1.63680			0.0567801
$832$		0			0
$833$			0.816202i			0.0282797i
$834$		0			0
$835$	−2.36803	+	1.36718i	−0.0819489	+	0.0473132i
$836$		0			0
$837$	−1.36253	+	1.36253i	−0.0470958	+	0.0470958i
$838$		0			0
$839$	10.2809	−	2.75476i	0.354937	−	0.0951050i	−0.0769448	−	0.997035i	$-0.524517\pi$
$839$	10.2809	−	2.75476i	0.354937	−	0.0951050i	0.431882	+	0.901930i	$0.357850\pi$
$840$		0			0
$841$	−5.99447	+	10.3827i	−0.206706	+	0.358025i
$842$		0			0
$843$	−3.17398	−	0.850466i	−0.109318	−	0.0292916i
$844$		0			0
$845$	−5.73166	+	2.26242i	−0.197175	+	0.0778297i
$846$		0			0
$847$	27.6569	+	13.0443i	0.950303	+	0.448207i
$848$		0			0
$849$	13.3204	−	23.0716i	0.457155	−	0.791815i
$850$		0			0
$851$	1.22183	+	4.55992i	0.0418837	+	0.156312i
$852$		0			0
$853$	−7.39401	+	7.39401i	−0.253166	+	0.253166i	−0.822267	−	0.569101i	$-0.807291\pi$
$853$	−7.39401	+	7.39401i	−0.253166	+	0.253166i	0.569101	+	0.822267i	$0.307291\pi$
$854$		0			0
$855$	0.741519	+	1.28435i	0.0253594	+	0.0439238i
$856$		0			0
$857$	−43.9435			−1.50108			−0.750540	−	0.660824i	$-0.770207\pi$
$857$	−43.9435			−1.50108			−0.750540	+	0.660824i	$0.770207\pi$
$858$		0			0
$859$	11.7377			0.400486			0.200243	−	0.979746i	$-0.435827\pi$
$859$	11.7377			0.400486			0.200243	+	0.979746i	$0.435827\pi$
$860$		0			0
$861$	4.27806	+	7.40981i	0.145796	+	0.252526i
$862$		0			0
$863$	7.88194	−	7.88194i	0.268304	−	0.268304i	−0.560112	−	0.828417i	$-0.689242\pi$
$863$	7.88194	−	7.88194i	0.268304	−	0.268304i	0.828417	+	0.560112i	$0.189242\pi$
$864$		0			0
$865$	−1.16366	−	4.34285i	−0.0395657	−	0.147661i
$866$		0			0
$867$	−9.31457	+	16.1333i	−0.316339	+	0.547916i
$868$		0			0
$869$	5.12783	−	2.37750i	0.173950	−	0.0806511i
$870$		0			0
$871$	−3.39365	+	6.73878i	−0.114989	+	0.228335i
$872$		0			0
$873$	−7.70799	−	2.06535i	−0.260876	−	0.0699015i
$874$		0			0
$875$	6.44032	−	11.1550i	0.217723	−	0.377107i
$876$		0			0
$877$	−9.84819	+	2.63881i	−0.332550	+	0.0891064i	−0.421230	−	0.906954i	$-0.638402\pi$
$877$	−9.84819	+	2.63881i	−0.332550	+	0.0891064i	0.0886807	+	0.996060i	$0.471735\pi$
$878$		0			0
$879$	15.5811	−	15.5811i	0.525539	−	0.525539i
$880$		0			0
$881$	22.6465	−	13.0750i	0.762981	−	0.440507i	−0.0673842	−	0.997727i	$-0.521465\pi$
$881$	22.6465	−	13.0750i	0.762981	−	0.440507i	0.830365	+	0.557220i	$0.188132\pi$
$882$		0			0
$883$		−	35.6047i		−	1.19819i	−0.800677	−	0.599097i	$-0.795527\pi$
$883$		−	35.6047i		−	1.19819i	0.800677	−	0.599097i	$-0.204473\pi$
$884$		0			0
$885$	−1.96786			−0.0661488
$886$		0			0
$887$	30.3908	−	17.5462i	1.02042	−	0.589143i	0.106198	−	0.994345i	$-0.466132\pi$
$887$	30.3908	−	17.5462i	1.02042	−	0.589143i	0.914227	+	0.405202i	$0.132799\pi$
$888$		0			0
$889$	18.8225	−	18.8225i	0.631288	−	0.631288i
$890$		0			0
$891$	3.13442	−	4.45563i	0.105007	−	0.149269i
$892$		0			0
$893$	3.13543	+	1.81024i	0.104923	+	0.0605774i
$894$		0			0
$895$	−0.697298	+	2.60235i	−0.0233081	+	0.0869870i
$896$		0			0
$897$	2.97197	−	3.33217i	0.0992313	−	0.111258i
$898$		0			0
$899$	−0.377898	+	1.41033i	−0.0126036	+	0.0470373i
$900$		0			0
$901$	4.26968	−	7.39530i	0.142244	−	0.246373i
$902$		0			0
$903$	2.36694	+	8.83354i	0.0787669	+	0.293962i
$904$		0			0
$905$	5.97936	+	5.97936i	0.198761	+	0.198761i
$906$		0			0
$907$	−12.6753	+	7.31810i	−0.420877	+	0.242994i	−0.695453	−	0.718572i	$-0.744796\pi$
$907$	−12.6753	+	7.31810i	−0.420877	+	0.242994i	0.274575	+	0.961566i	$0.411463\pi$
$908$		0			0
$909$	−15.2641			−0.506278
$910$		0			0
$911$	16.4109			0.543719			0.271859	−	0.962337i	$-0.412361\pi$
$911$	16.4109			0.543719			0.271859	+	0.962337i	$0.412361\pi$
$912$		0			0
$913$	4.61966	−	12.6065i	0.152888	−	0.417215i
$914$		0			0
$915$	3.28703	+	3.28703i	0.108666	+	0.108666i
$916$		0			0
$917$	46.5856	−	12.4826i	1.53839	−	0.412211i
$918$		0			0
$919$	−24.4167	−	14.0970i	−0.805433	−	0.465017i	0.0399344	−	0.999202i	$-0.487285\pi$
$919$	−24.4167	−	14.0970i	−0.805433	−	0.465017i	−0.845367	+	0.534185i	$0.820618\pi$
$920$		0			0
$921$	31.4339	+	8.42268i	1.03578	+	0.277537i
$922$		0			0
$923$	−36.6771	+	2.09563i	−1.20724	+	0.0689786i
$924$		0			0
$925$	−20.8084	−	5.57561i	−0.684178	−	0.183325i
$926$		0			0
$927$	−2.78203	−	1.60621i	−0.0913740	−	0.0527548i
$928$		0			0
$929$	12.1524	+	45.3534i	0.398707	+	1.48800i	0.815373	+	0.578937i	$0.196532\pi$
$929$	12.1524	+	45.3534i	0.398707	+	1.48800i	−0.416665	+	0.909060i	$0.636801\pi$
$930$		0			0
$931$	1.00656	−	1.00656i	0.0329886	−	0.0329886i
$932$		0			0
$933$	8.62136	−	4.97755i	0.282251	−	0.162958i
$934$		0			0
$935$	−1.35311	+	1.13036i	−0.0442514	+	0.0369666i
$936$		0			0
$937$		−	34.9016i		−	1.14019i	−0.821580	−	0.570093i	$-0.806907\pi$
$937$		−	34.9016i		−	1.14019i	0.821580	−	0.570093i	$-0.193093\pi$
$938$		0			0
$939$	−5.17949	−	8.97115i	−0.169026	−	0.292762i
$940$		0			0
$941$	−29.3802	−	29.3802i	−0.957768	−	0.957768i	0.0413756	−	0.999144i	$-0.486826\pi$
$941$	−29.3802	−	29.3802i	−0.957768	−	0.957768i	−0.999144	+	0.0413756i	$0.986826\pi$
$942$		0			0
$943$	0.704431	+	2.62897i	0.0229394	+	0.0856111i
$944$		0			0
$945$	−6.21132	−	3.58611i	−0.202054	−	0.116656i
$946$		0			0
$947$	−15.1556	+	56.5615i	−0.492491	+	1.83800i	0.0511583	+	0.998691i	$0.483709\pi$
$947$	−15.1556	+	56.5615i	−0.492491	+	1.83800i	−0.543650	+	0.839312i	$0.682958\pi$
$948$		0			0
$949$	−4.57340	−	6.97023i	−0.148459	−	0.226263i
$950$		0			0
$951$	7.98562	+	2.13974i	0.258951	+	0.0693858i
$952$		0			0
$953$	8.13440	−	14.0892i	0.263499	−	0.456394i	−0.703670	−	0.710527i	$-0.748457\pi$
$953$	8.13440	−	14.0892i	0.263499	−	0.456394i	0.967169	+	0.254133i	$0.0817901\pi$
$954$		0			0
$955$	−2.18703	−	8.16212i	−0.0707708	−	0.264120i
$956$		0			0
$957$	1.44615	−	16.1231i	0.0467473	−	0.521187i
$958$		0			0
$959$	17.5535	+	30.4036i	0.566833	+	0.981784i
$960$		0			0
$961$			30.8747i			0.995957i
$962$		0			0
$963$			27.5365i			0.887350i
$964$		0			0
$965$	10.0273	−	5.78926i	0.322790	−	0.186363i
$966$		0			0
$967$	−40.1415	−	40.1415i	−1.29086	−	1.29086i	−0.934253	−	0.356611i	$-0.883932\pi$
$967$	−40.1415	−	40.1415i	−1.29086	−	1.29086i	−0.356611	−	0.934253i	$-0.616068\pi$
$968$		0			0
$969$	−2.50751	+	0.671884i	−0.0805527	+	0.0215840i
$970$		0			0
$971$	20.3179	−	35.1917i	0.652033	−	1.12936i	−0.330595	−	0.943773i	$-0.607250\pi$
$971$	20.3179	−	35.1917i	0.652033	−	1.12936i	0.982629	−	0.185582i	$-0.0594172\pi$
$972$		0			0
$973$	11.2484	−	41.9797i	0.360608	−	1.34581i
$974$		0			0
$975$	6.38759	+	19.3481i	0.204567	+	0.619634i
$976$		0			0
$977$	−37.2344	−	9.97693i	−1.19123	−	0.319190i	−0.391860	−	0.920025i	$-0.628168\pi$
$977$	−37.2344	−	9.97693i	−1.19123	−	0.319190i	−0.799373	+	0.600834i	$0.794835\pi$
$978$		0			0
$979$	8.84603	−	1.53984i	0.282720	−	0.0492136i
$980$		0			0
$981$	26.8500	−	7.19443i	0.857253	−	0.229700i
$982$		0			0
$983$	−14.0601	−	14.0601i	−0.448446	−	0.448446i	0.446391	−	0.894838i	$-0.352709\pi$
$983$	−14.0601	−	14.0601i	−0.448446	−	0.448446i	−0.894838	+	0.446391i	$0.852709\pi$
$984$		0			0
$985$	−0.896968	−	1.55359i	−0.0285798	−	0.0495016i
$986$		0			0
$987$	−6.08915			−0.193820
$988$		0			0
$989$			2.90909i			0.0925036i
$990$		0			0
$991$	−0.881962	−	1.52760i	−0.0280164	−	0.0485259i	0.851677	−	0.524067i	$-0.175586\pi$
$991$	−0.881962	−	1.52760i	−0.0280164	−	0.0485259i	−0.879694	+	0.475541i	$0.842252\pi$
$992$		0			0
$993$	11.4803	−	11.4803i	0.364317	−	0.364317i
$994$		0			0
$995$	2.33678	−	0.626138i	0.0740809	−	0.0198499i
$996$		0			0
$997$	−42.7236	−	24.6665i	−1.35307	−	0.781196i	−0.364392	−	0.931245i	$-0.618723\pi$
$997$	−42.7236	−	24.6665i	−1.35307	−	0.781196i	−0.988678	+	0.150050i	$0.952057\pi$
$998$		0			0
$999$	−6.35530	+	23.7183i	−0.201073	+	0.750414i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	572.2.bc.a.197.9	✓	56
11.10	odd	2	inner	572.2.bc.a.197.10	yes	56
13.7	odd	12	inner	572.2.bc.a.241.10	yes	56
143.98	even	12	inner	572.2.bc.a.241.9	yes	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
572.2.bc.a.197.9	✓	56	1.1	even	1	trivial
572.2.bc.a.197.10	yes	56	11.10	odd	2	inner
572.2.bc.a.241.9	yes	56	143.98	even	12	inner
572.2.bc.a.241.10	yes	56	13.7	odd	12	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 572 = 2^{2} \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	572.bc (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.591694 + 1.02484i) q^{3} +(0.335170 - 0.335170i) q^{5} +(-0.719487 - 2.68516i) q^{7} +(0.799795 - 1.38529i) q^{9} +O(q^{10})\)	\(q+(0.591694 + 1.02484i) q^{3} +(0.335170 - 0.335170i) q^{5} +(-0.719487 - 2.68516i) q^{7} +(0.799795 - 1.38529i) q^{9} +(-1.39509 - 3.00894i) q^{11} +(0.732998 - 3.53026i) q^{13} +(0.541815 + 0.145179i) q^{15} +(0.560760 - 0.971265i) q^{17} +(-1.88933 + 0.506244i) q^{19} +(2.32616 - 2.32616i) q^{21} +(0.906255 - 0.523227i) q^{23} +4.77532i q^{25} +5.44310 q^{27} +(3.57188 - 2.06222i) q^{29} +(-0.250321 + 0.250321i) q^{31} +(2.25823 - 3.21012i) q^{33} +(-1.14114 - 0.658835i) q^{35} +(-1.16759 + 4.35750i) q^{37} +(4.05168 - 1.33762i) q^{39} +(-0.673160 + 2.51227i) q^{41} +(-1.38997 + 2.40751i) q^{43} +(-0.196239 - 0.732373i) q^{45} +(-1.30884 - 1.30884i) q^{47} +(-0.630262 + 0.363882i) q^{49} +1.32719 q^{51} +7.61409 q^{53} +(-1.47610 - 0.540916i) q^{55} +(-1.63673 - 1.63673i) q^{57} +(-3.38868 + 0.907993i) q^{59} +(7.17698 + 4.14363i) q^{61} +(-4.29516 - 1.15089i) q^{63} +(-0.937556 - 1.42891i) q^{65} +(-2.02132 - 0.541611i) q^{67} +(1.07245 + 0.619181i) q^{69} +(-2.63710 - 9.84180i) q^{71} +(1.63496 - 1.63496i) q^{73} +(-4.89396 + 2.82553i) q^{75} +(-7.07576 + 5.91093i) q^{77} +1.70420i q^{79} +(0.821269 + 1.42248i) q^{81} +(2.86250 + 2.86250i) q^{83} +(-0.137589 - 0.513488i) q^{85} +(4.22692 + 2.44041i) q^{87} +(-0.700697 + 2.61504i) q^{89} +(-10.0067 + 0.571757i) q^{91} +(-0.404654 - 0.108427i) q^{93} +(-0.463568 + 0.802923i) q^{95} +(-1.29117 - 4.81873i) q^{97} +(-5.28403 - 0.473945i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 28 q^{9}+O(q^{10}) \) 56 * q - 28 * q^9	\( 56 q - 28 q^{9} + 4 q^{11} + 8 q^{15} - 12 q^{23} - 24 q^{27} - 4 q^{31} - 10 q^{33} - 12 q^{37} - 64 q^{45} - 8 q^{47} + 40 q^{53} + 22 q^{55} + 48 q^{59} - 36 q^{67} - 48 q^{71} + 120 q^{75} + 28 q^{81} + 28 q^{89} + 36 q^{91} + 20 q^{93} - 68 q^{97} - 44 q^{99}+O(q^{100}) \) 56 * q - 28 * q^9 + 4 * q^11 + 8 * q^15 - 12 * q^23 - 24 * q^27 - 4 * q^31 - 10 * q^33 - 12 * q^37 - 64 * q^45 - 8 * q^47 + 40 * q^53 + 22 * q^55 + 48 * q^59 - 36 * q^67 - 48 * q^71 + 120 * q^75 + 28 * q^81 + 28 * q^89 + 36 * q^91 + 20 * q^93 - 68 * q^97 - 44 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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