LMFDB - Embedded newform 532.2.l.b.501.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [532,2,Mod(429,532)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(532, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2, 4]))

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

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

chi := DirichletCharacter("532.429");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 532 = 2^{2} \cdot 7 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	532.l (of order $3$, degree $2$, 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:	$4.24804138753$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			501.9
Character	$\chi$	$=$	532.501
Dual form			532.2.l.b.429.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.54342 q^{3} +(1.49792 - 2.59447i) q^{5} +(-2.55868 - 0.673181i) q^{7} -0.617840 q^{9} +(0.989466 - 1.71381i) q^{11} +(2.21473 - 3.83603i) q^{13} +(2.31193 - 4.00437i) q^{15} -5.18626 q^{17} +(4.31800 + 0.595698i) q^{19} +(-3.94913 - 1.03900i) q^{21} +8.30393 q^{23} +(-1.98753 - 3.44250i) q^{25} -5.58386 q^{27} +(-2.53342 + 4.38800i) q^{29} +(-0.243649 + 0.422013i) q^{31} +(1.52717 - 2.64513i) q^{33} +(-5.57924 + 5.63005i) q^{35} +(2.06507 + 3.57680i) q^{37} +(3.41827 - 5.92062i) q^{39} +(-3.74329 - 6.48356i) q^{41} +(4.69266 + 8.12792i) q^{43} +(-0.925475 + 1.60297i) q^{45} -1.94211 q^{47} +(6.09365 + 3.44491i) q^{49} -8.00460 q^{51} +(2.69978 + 4.67615i) q^{53} +(-2.96428 - 5.13429i) q^{55} +(6.66451 + 0.919414i) q^{57} +10.1794 q^{59} +8.78669 q^{61} +(1.58085 + 0.415918i) q^{63} +(-6.63498 - 11.4921i) q^{65} +(-1.17340 - 2.03239i) q^{67} +12.8165 q^{69} +(0.696823 + 1.20693i) q^{71} -6.19319 q^{73} +(-3.06760 - 5.31324i) q^{75} +(-3.68543 + 3.71898i) q^{77} +(4.89829 - 8.48408i) q^{79} -6.76475 q^{81} -6.01658 q^{83} +(-7.76860 + 13.4556i) q^{85} +(-3.91014 + 6.77256i) q^{87} -8.57570 q^{89} +(-8.24912 + 8.32423i) q^{91} +(-0.376055 + 0.651346i) q^{93} +(8.01354 - 10.3106i) q^{95} +(-3.34198 - 5.78849i) q^{97} +(-0.611332 + 1.05886i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 2 q^{3} - 6 q^{5} - 6 q^{7} + 30 q^{9} + q^{11} - 7 q^{13} - 2 q^{15} - 6 q^{17} + 17 q^{19} - 18 q^{21} - 16 q^{23} - 8 q^{25} + 20 q^{27} - 22 q^{29} - 7 q^{31} + 7 q^{33} - 21 q^{35} + 9 q^{37}+ \cdots - 27 q^{99}+O(q^{100}) $ 24 * q + 2 * q^3 - 6 * q^5 - 6 * q^7 + 30 * q^9 + q^11 - 7 * q^13 - 2 * q^15 - 6 * q^17 + 17 * q^19 - 18 * q^21 - 16 * q^23 - 8 * q^25 + 20 * q^27 - 22 * q^29 - 7 * q^31 + 7 * q^33 - 21 * q^35 + 9 * q^37 + 12 * q^39 - 11 * q^41 - 9 * q^43 - 28 * q^45 - 22 * q^47 - 32 * q^49 - 16 * q^51 - 7 * q^53 - 11 * q^55 + 11 * q^57 + 16 * q^59 + 12 * q^61 + 20 * q^63 + 3 * q^65 - 27 * q^67 + 108 * q^69 - 13 * q^71 + 20 * q^73 + 25 * q^75 + 2 * q^77 - 14 * q^79 + 80 * q^81 - 12 * q^83 - 19 * q^85 + 19 * q^87 + 74 * q^89 - 21 * q^91 + 5 * q^93 + 47 * q^95 - 21 * q^97 - 27 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/532\mathbb{Z}\right)^\times$.

$n$	$267$	$381$	$477$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$

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
$3$	1.54342			0.891097			0.445548	−	0.895258i	$-0.353009\pi$
$3$	1.54342			0.891097			0.445548	+	0.895258i	$0.353009\pi$
$4$		0			0
$5$	1.49792	−	2.59447i	0.669890	−	1.16028i	−0.308044	−	0.951372i	$-0.599675\pi$
$5$	1.49792	−	2.59447i	0.669890	−	1.16028i	0.977934	−	0.208912i	$-0.0669921\pi$
$6$		0			0
$7$	−2.55868	−	0.673181i	−0.967089	−	0.254439i
$7$	−2.55868	−	0.673181i	−0.967089	−	0.254439i
$8$		0			0
$9$	−0.617840			−0.205947
$10$		0			0
$11$	0.989466	−	1.71381i	0.298335	−	0.516732i	−0.677420	−	0.735597i	$-0.736902\pi$
$11$	0.989466	−	1.71381i	0.298335	−	0.516732i	0.975755	+	0.218865i	$0.0702353\pi$
$12$		0			0
$13$	2.21473	−	3.83603i	0.614256	−	1.06392i	−0.376259	−	0.926515i	$-0.622790\pi$
$13$	2.21473	−	3.83603i	0.614256	−	1.06392i	0.990515	−	0.137407i	$-0.0438770\pi$
$14$		0			0
$15$	2.31193	−	4.00437i	0.596937	−	1.03392i
$16$		0			0
$17$	−5.18626			−1.25785			−0.628927	−	0.777465i	$-0.716505\pi$
$17$	−5.18626			−1.25785			−0.628927	+	0.777465i	$0.716505\pi$
$18$		0			0
$19$	4.31800	+	0.595698i	0.990618	+	0.136662i
$19$	4.31800	+	0.595698i	0.990618	+	0.136662i
$20$		0			0
$21$	−3.94913	−	1.03900i	−0.861770	−	0.226729i
$22$		0			0
$23$	8.30393			1.73149			0.865744	−	0.500486i	$-0.166845\pi$
$23$	8.30393			1.73149			0.865744	+	0.500486i	$0.166845\pi$
$24$		0			0
$25$	−1.98753	−	3.44250i	−0.397506	−	0.688500i
$26$		0			0
$27$	−5.58386			−1.07462
$28$		0			0
$29$	−2.53342	+	4.38800i	−0.470444	+	0.814832i	−0.999429	−	0.0337990i	$-0.989239\pi$
$29$	−2.53342	+	4.38800i	−0.470444	+	0.814832i	0.528985	+	0.848631i	$0.322573\pi$
$30$		0			0
$31$	−0.243649	+	0.422013i	−0.0437607	+	0.0757958i	−0.887076	−	0.461623i	$-0.847267\pi$
$31$	−0.243649	+	0.422013i	−0.0437607	+	0.0757958i	0.843315	+	0.537419i	$0.180601\pi$
$32$		0			0
$33$	1.52717	−	2.64513i	0.265846	−	0.460458i
$34$		0			0
$35$	−5.57924	+	5.63005i	−0.943064	+	0.951652i
$36$		0			0
$37$	2.06507	+	3.57680i	0.339495	+	0.588023i	0.984338	−	0.176293i	$-0.0564105\pi$
$37$	2.06507	+	3.57680i	0.339495	+	0.588023i	−0.644843	+	0.764315i	$0.723077\pi$
$38$		0			0
$39$	3.41827	−	5.92062i	0.547361	−	0.948057i
$40$		0			0
$41$	−3.74329	−	6.48356i	−0.584603	−	1.01256i	−0.994925	−	0.100622i	$-0.967917\pi$
$41$	−3.74329	−	6.48356i	−0.584603	−	1.01256i	0.410322	−	0.911941i	$-0.365416\pi$
$42$		0			0
$43$	4.69266	+	8.12792i	0.715623	+	1.23950i	0.962719	+	0.270505i	$0.0871905\pi$
$43$	4.69266	+	8.12792i	0.715623	+	1.23950i	−0.247095	+	0.968991i	$0.579476\pi$
$44$		0			0
$45$	−0.925475	+	1.60297i	−0.137962	+	0.238957i
$46$		0			0
$47$	−1.94211			−0.283286			−0.141643	−	0.989918i	$-0.545239\pi$
$47$	−1.94211			−0.283286			−0.141643	+	0.989918i	$0.545239\pi$
$48$		0			0
$49$	6.09365	+	3.44491i	0.870522	+	0.492129i
$50$		0			0
$51$	−8.00460			−1.12087
$52$		0			0
$53$	2.69978	+	4.67615i	0.370843	+	0.642318i	0.989695	−	0.143189i	$-0.0457356\pi$
$53$	2.69978	+	4.67615i	0.370843	+	0.642318i	−0.618853	+	0.785507i	$0.712402\pi$
$54$		0			0
$55$	−2.96428	−	5.13429i	−0.399704	−	0.692307i
$56$		0			0
$57$	6.66451	+	0.919414i	0.882736	+	0.121779i
$58$		0			0
$59$	10.1794			1.32525			0.662625	−	0.748952i	$-0.269443\pi$
$59$	10.1794			1.32525			0.662625	+	0.748952i	$0.269443\pi$
$60$		0			0
$61$	8.78669			1.12502			0.562510	−	0.826790i	$-0.309836\pi$
$61$	8.78669			1.12502			0.562510	+	0.826790i	$0.309836\pi$
$62$		0			0
$63$	1.58085	+	0.415918i	0.199169	+	0.0524008i
$64$		0			0
$65$	−6.63498	−	11.4921i	−0.822968	−	1.42542i
$66$		0			0
$67$	−1.17340	−	2.03239i	−0.143354	−	0.248296i	0.785404	−	0.618984i	$-0.212455\pi$
$67$	−1.17340	−	2.03239i	−0.143354	−	0.248296i	−0.928758	+	0.370688i	$0.879122\pi$
$68$		0			0
$69$	12.8165			1.54292
$70$		0			0
$71$	0.696823	+	1.20693i	0.0826977	+	0.143237i	0.904408	−	0.426669i	$-0.140313\pi$
$71$	0.696823	+	1.20693i	0.0826977	+	0.143237i	−0.821710	+	0.569906i	$0.806980\pi$
$72$		0			0
$73$	−6.19319			−0.724858			−0.362429	−	0.932011i	$-0.618052\pi$
$73$	−6.19319			−0.724858			−0.362429	+	0.932011i	$0.618052\pi$
$74$		0			0
$75$	−3.06760	−	5.31324i	−0.354216	−	0.613520i
$76$		0			0
$77$	−3.68543	+	3.71898i	−0.419993	+	0.423818i
$78$		0			0
$79$	4.89829	−	8.48408i	0.551100	−	0.954534i	−0.447095	−	0.894486i	$-0.647541\pi$
$79$	4.89829	−	8.48408i	0.551100	−	0.954534i	0.998196	−	0.0600475i	$-0.0191252\pi$
$80$		0			0
$81$	−6.76475			−0.751639
$82$		0			0
$83$	−6.01658			−0.660405			−0.330203	−	0.943910i	$-0.607117\pi$
$83$	−6.01658			−0.660405			−0.330203	+	0.943910i	$0.607117\pi$
$84$		0			0
$85$	−7.76860	+	13.4556i	−0.842623	+	1.45947i
$86$		0			0
$87$	−3.91014	+	6.77256i	−0.419211	+	0.726094i
$88$		0			0
$89$	−8.57570			−0.909023			−0.454511	−	0.890741i	$-0.650186\pi$
$89$	−8.57570			−0.909023			−0.454511	+	0.890741i	$0.650186\pi$
$90$		0			0
$91$	−8.24912	+	8.32423i	−0.864743	+	0.872617i
$92$		0			0
$93$	−0.376055	+	0.651346i	−0.0389950	+	0.0675414i
$94$		0			0
$95$	8.01354	−	10.3106i	0.822172	−	1.05785i
$96$		0			0
$97$	−3.34198	−	5.78849i	−0.339327	−	0.587732i	0.644979	−	0.764200i	$-0.276866\pi$
$97$	−3.34198	−	5.78849i	−0.339327	−	0.587732i	−0.984306	+	0.176468i	$0.943533\pi$
$98$		0			0
$99$	−0.611332	+	1.05886i	−0.0614412	+	0.106419i
$100$		0			0
$101$	6.46677	+	11.2008i	0.643468	+	1.11452i	0.984653	+	0.174523i	$0.0558384\pi$
$101$	6.46677	+	11.2008i	0.643468	+	1.11452i	−0.341185	+	0.939996i	$0.610828\pi$
$102$		0			0
$103$	8.41439	+	14.5742i	0.829095	+	1.43603i	0.898749	+	0.438463i	$0.144477\pi$
$103$	8.41439	+	14.5742i	0.829095	+	1.43603i	−0.0696549	+	0.997571i	$0.522190\pi$
$104$		0			0
$105$	−8.61114	+	8.68955i	−0.840361	+	0.848014i
$106$		0			0
$107$	1.87075	+	3.24023i	0.180852	+	0.313245i	0.942171	−	0.335133i	$-0.108781\pi$
$107$	1.87075	+	3.24023i	0.180852	+	0.313245i	−0.761319	+	0.648378i	$0.775448\pi$
$108$		0			0
$109$	−19.9517			−1.91103			−0.955514	−	0.294946i	$-0.904698\pi$
$109$	−19.9517			−1.91103			−0.955514	+	0.294946i	$0.904698\pi$
$110$		0			0
$111$	3.18728	+	5.52053i	0.302523	+	0.523985i
$112$		0			0
$113$	−9.67021			−0.909697			−0.454849	−	0.890569i	$-0.650307\pi$
$113$	−9.67021			−0.909697			−0.454849	+	0.890569i	$0.650307\pi$
$114$		0			0
$115$	12.4386	−	21.5443i	1.15991	−	2.00902i
$116$		0			0
$117$	−1.36835	+	2.37005i	−0.126504	+	0.219111i
$118$		0			0
$119$	13.2700	+	3.49129i	1.21646	+	0.320046i
$120$		0			0
$121$	3.54191	+	6.13477i	0.321992	+	0.557707i
$122$		0			0
$123$	−5.77748	−	10.0069i	−0.520938	−	0.902291i
$124$		0			0
$125$	3.07057			0.274640
$126$		0			0
$127$	−5.15835	+	8.93452i	−0.457729	+	0.792810i	−0.998841	−	0.0481406i	$-0.984670\pi$
$127$	−5.15835	+	8.93452i	−0.457729	+	0.792810i	0.541111	+	0.840951i	$0.318004\pi$
$128$		0			0
$129$	7.24276	+	12.5448i	0.637689	+	1.10451i
$130$		0			0
$131$	9.59993	−	16.6276i	0.838750	−	1.45276i	−0.0521900	−	0.998637i	$-0.516620\pi$
$131$	9.59993	−	16.6276i	0.838750	−	1.45276i	0.890940	−	0.454121i	$-0.150047\pi$
$132$		0			0
$133$	−10.6474	−	4.43100i	−0.923243	−	0.384216i
$134$		0			0
$135$	−8.36418	+	14.4872i	−0.719874	+	1.24686i
$136$		0			0
$137$	0.495337	+	0.857950i	0.0423195	+	0.0732996i	0.886409	−	0.462902i	$-0.153192\pi$
$137$	0.495337	+	0.857950i	0.0423195	+	0.0732996i	−0.844090	+	0.536202i	$0.819859\pi$
$138$		0			0
$139$	−9.62528	+	16.6715i	−0.816406	+	1.41406i	0.0919085	+	0.995767i	$0.470703\pi$
$139$	−9.62528	+	16.6715i	−0.816406	+	1.41406i	−0.908314	+	0.418289i	$0.862630\pi$
$140$		0			0
$141$	−2.99750			−0.252435
$142$		0			0
$143$	−4.38280	−	7.59123i	−0.366508	−	0.634811i
$144$		0			0
$145$	7.58971	+	13.1458i	0.630291	+	1.09170i
$146$		0			0
$147$	9.40510	+	5.31695i	0.775719	+	0.438535i
$148$		0			0
$149$	6.81409	−	11.8024i	0.558232	−	0.966887i	−0.439412	−	0.898286i	$-0.644813\pi$
$149$	6.81409	−	11.8024i	0.558232	−	0.966887i	0.997644	−	0.0686010i	$-0.0218535\pi$
$150$		0			0
$151$	−6.76136	+	11.7110i	−0.550232	+	0.953030i	0.448026	+	0.894021i	$0.352127\pi$
$151$	−6.76136	+	11.7110i	−0.550232	+	0.953030i	−0.998257	+	0.0590089i	$0.981206\pi$
$152$		0			0
$153$	3.20428			0.259051
$154$		0			0
$155$	0.729935	+	1.26428i	0.0586298	+	0.101550i
$156$		0			0
$157$	5.72691			0.457057			0.228528	−	0.973537i	$-0.426609\pi$
$157$	5.72691			0.457057			0.228528	+	0.973537i	$0.426609\pi$
$158$		0			0
$159$	4.16690	+	7.21728i	0.330457	+	0.572368i
$160$		0			0
$161$	−21.2471	−	5.59005i	−1.67450	−	0.440558i
$162$		0			0
$163$	3.97027	+	6.87670i	0.310975	+	0.538625i	0.978574	−	0.205897i	$-0.0660111\pi$
$163$	3.97027	+	6.87670i	0.310975	+	0.538625i	−0.667599	+	0.744521i	$0.732678\pi$
$164$		0			0
$165$	−4.57515	−	7.92439i	−0.356175	−	0.616913i
$166$		0			0
$167$	9.05651	−	15.6863i	0.700814	−	1.21385i	−0.267367	−	0.963595i	$-0.586154\pi$
$167$	9.05651	−	15.6863i	0.700814	−	1.21385i	0.968181	−	0.250251i	$-0.0805130\pi$
$168$		0			0
$169$	−3.31006	−	5.73319i	−0.254620	−	0.441015i
$170$		0			0
$171$	−2.66783	−	0.368046i	−0.204014	−	0.0281452i
$172$		0			0
$173$	−0.704646	+	1.22048i	−0.0535732	+	0.0927916i	−0.891568	−	0.452886i	$-0.850394\pi$
$173$	−0.704646	+	1.22048i	−0.0535732	+	0.0927916i	0.837995	+	0.545678i	$0.183728\pi$
$174$		0			0
$175$	2.76802	+	10.1462i	0.209242	+	0.766981i
$176$		0			0
$177$	15.7112			1.18093
$178$		0			0
$179$	9.37453	−	16.2372i	0.700685	−	1.21362i	−0.267541	−	0.963547i	$-0.586211\pi$
$179$	9.37453	−	16.2372i	0.700685	−	1.21362i	0.968226	−	0.250076i	$-0.0804557\pi$
$180$		0			0
$181$	−9.00801	+	15.6023i	−0.669560	+	1.15971i	0.308468	+	0.951235i	$0.400184\pi$
$181$	−9.00801	+	15.6023i	−0.669560	+	1.15971i	−0.978027	+	0.208477i	$0.933149\pi$
$182$		0			0
$183$	13.5616			1.00250
$184$		0			0
$185$	12.3732			0.909698
$186$		0			0
$187$	−5.13163	+	8.88825i	−0.375262	+	0.649973i
$188$		0			0
$189$	14.2873	+	3.75895i	1.03925	+	0.273424i
$190$		0			0
$191$	0.0272510	+	0.0472001i	0.00197181	+	0.00341528i	0.867010	−	0.498291i	$-0.166039\pi$
$191$	0.0272510	+	0.0472001i	0.00197181	+	0.00341528i	−0.865038	+	0.501707i	$0.832706\pi$
$192$		0			0
$193$	−20.6905			−1.48933			−0.744666	−	0.667437i	$-0.767391\pi$
$193$	−20.6905			−1.48933			−0.744666	+	0.667437i	$0.767391\pi$
$194$		0			0
$195$	−10.2406	−	17.7372i	−0.733344	−	1.27019i
$196$		0			0
$197$	−19.8521			−1.41440			−0.707200	−	0.707013i	$-0.750042\pi$
$197$	−19.8521			−1.41440			−0.707200	+	0.707013i	$0.750042\pi$
$198$		0			0
$199$	3.45869	+	5.99062i	0.245180	+	0.424664i	0.962182	−	0.272407i	$-0.0878197\pi$
$199$	3.45869	+	5.99062i	0.245180	+	0.424664i	−0.717002	+	0.697071i	$0.754486\pi$
$200$		0			0
$201$	−1.81106	−	3.13684i	−0.127742	−	0.221256i
$202$		0			0
$203$	9.43611	−	9.52204i	0.662285	−	0.668316i
$204$		0			0
$205$	−22.4286			−1.56648
$206$		0			0
$207$	−5.13050			−0.356594
$208$		0			0
$209$	5.29343	−	6.81079i	0.366154	−	0.471113i
$210$		0			0
$211$	1.23851	+	2.14516i	0.0852624	+	0.147679i	0.905503	−	0.424340i	$-0.139494\pi$
$211$	1.23851	+	2.14516i	0.0852624	+	0.147679i	−0.820241	+	0.572019i	$0.806160\pi$
$212$		0			0
$213$	1.07549	+	1.86281i	0.0736917	+	0.127638i
$214$		0			0
$215$	28.1169			1.91756
$216$		0			0
$217$	0.907511	−	0.915775i	0.0616059	−	0.0621669i
$218$		0			0
$219$	−9.55872			−0.645918
$220$		0			0
$221$	−11.4862	+	19.8946i	−0.772643	+	1.33826i
$222$		0			0
$223$	1.60529	+	2.78044i	0.107498	+	0.186192i	0.914756	−	0.404007i	$-0.132383\pi$
$223$	1.60529	+	2.78044i	0.107498	+	0.186192i	−0.807258	+	0.590199i	$0.799049\pi$
$224$		0			0
$225$	1.22797	+	2.12691i	0.0818650	+	0.141794i
$226$		0			0
$227$	−1.11222	+	1.92643i	−0.0738209	+	0.127862i	−0.900573	−	0.434705i	$-0.856853\pi$
$227$	−1.11222	+	1.92643i	−0.0738209	+	0.127862i	0.826752	+	0.562567i	$0.190186\pi$
$228$		0			0
$229$	−9.53678	−	16.5182i	−0.630208	−	1.09155i	−0.987509	−	0.157563i	$-0.949636\pi$
$229$	−9.53678	−	16.5182i	−0.630208	−	1.09155i	0.357301	−	0.933989i	$-0.383697\pi$
$230$		0			0
$231$	−5.68818	+	5.73997i	−0.374255	+	0.377663i
$232$		0			0
$233$	7.67183	−	13.2880i	0.502598	−	0.870526i	−0.497397	−	0.867523i	$-0.665711\pi$
$233$	7.67183	−	13.2880i	0.502598	−	0.870526i	0.999995	−	0.00300290i	$-0.000955854\pi$
$234$		0			0
$235$	−2.90913	+	5.03875i	−0.189770	+	0.328692i
$236$		0			0
$237$	7.56014	−	13.0945i	0.491084	−	0.850582i
$238$		0			0
$239$	−2.34933			−0.151966			−0.0759828	−	0.997109i	$-0.524209\pi$
$239$	−2.34933			−0.151966			−0.0759828	+	0.997109i	$0.524209\pi$
$240$		0			0
$241$	−8.81904	−	15.2750i	−0.568084	−	0.983951i	−0.996755	−	0.0804901i	$-0.974351\pi$
$241$	−8.81904	−	15.2750i	−0.568084	−	0.983951i	0.428671	−	0.903461i	$-0.358982\pi$
$242$		0			0
$243$	6.31070			0.404832
$244$		0			0
$245$	18.0655	−	10.6496i	1.15416	−	0.680380i
$246$		0			0
$247$	11.8483	−	15.2447i	0.753891	−	0.969994i
$248$		0			0
$249$	−9.28613			−0.588485
$250$		0			0
$251$	2.21775	−	3.84126i	0.139983	−	0.242458i	−0.787507	−	0.616306i	$-0.788628\pi$
$251$	2.21775	−	3.84126i	0.139983	−	0.242458i	0.927490	+	0.373848i	$0.121962\pi$
$252$		0			0
$253$	8.21646	−	14.2313i	0.516564	−	0.894716i
$254$		0			0
$255$	−11.9903	+	20.7677i	−0.750859	+	1.30053i
$256$		0			0
$257$	−6.22168			−0.388098			−0.194049	−	0.980992i	$-0.562162\pi$
$257$	−6.22168			−0.388098			−0.194049	+	0.980992i	$0.562162\pi$
$258$		0			0
$259$	−2.87601	−	10.5420i	−0.178706	−	0.655051i
$260$		0			0
$261$	1.56525	−	2.71109i	0.0968863	−	0.167812i
$262$		0			0
$263$	−20.6266			−1.27189			−0.635946	−	0.771733i	$-0.719390\pi$
$263$	−20.6266			−1.27189			−0.635946	+	0.771733i	$0.719390\pi$
$264$		0			0
$265$	16.1762			0.993696
$266$		0			0
$267$	−13.2360			−0.810027
$268$		0			0
$269$	17.7867			1.08447			0.542237	−	0.840226i	$-0.317578\pi$
$269$	17.7867			1.08447			0.542237	+	0.840226i	$0.317578\pi$
$270$		0			0
$271$	9.38120	−	16.2487i	0.569867	−	0.987039i	−0.426711	−	0.904388i	$-0.640328\pi$
$271$	9.38120	−	16.2487i	0.569867	−	0.987039i	0.996579	−	0.0826512i	$-0.0263387\pi$
$272$		0			0
$273$	−12.7319	+	12.8478i	−0.770569	+	0.777586i
$274$		0			0
$275$	−7.86637			−0.474360
$276$		0			0
$277$	10.3030	−	17.8453i	0.619048	−	1.07222i	−0.370612	−	0.928788i	$-0.620852\pi$
$277$	10.3030	−	17.8453i	0.619048	−	1.07222i	0.989660	−	0.143434i	$-0.0458145\pi$
$278$		0			0
$279$	0.150536	−	0.260737i	0.00901238	−	0.0156099i
$280$		0			0
$281$	4.92982	−	8.53870i	0.294088	−	0.509376i	−0.680684	−	0.732577i	$-0.738317\pi$
$281$	4.92982	−	8.53870i	0.294088	−	0.509376i	0.974772	+	0.223201i	$0.0716507\pi$
$282$		0			0
$283$	−5.62800			−0.334550			−0.167275	−	0.985910i	$-0.553497\pi$
$283$	−5.62800			−0.334550			−0.167275	+	0.985910i	$0.553497\pi$
$284$		0			0
$285$	12.3683	−	15.9137i	0.732635	−	0.942646i
$286$		0			0
$287$	5.21325	+	19.1093i	0.307728	+	1.12798i
$288$		0			0
$289$	9.89731			0.582195
$290$		0			0
$291$	−5.15810	−	8.93409i	−0.302373	−	0.523726i
$292$		0			0
$293$	26.2347			1.53265			0.766324	−	0.642454i	$-0.222084\pi$
$293$	26.2347			1.53265			0.766324	+	0.642454i	$0.222084\pi$
$294$		0			0
$295$	15.2480	−	26.4103i	0.887771	−	1.53767i
$296$		0			0
$297$	−5.52504	+	9.56966i	−0.320596	+	0.555288i
$298$		0			0
$299$	18.3910	−	31.8541i	1.06358	−	1.84217i
$300$		0			0
$301$	−6.53543	−	23.9557i	−0.376696	−	1.38078i
$302$		0			0
$303$	9.98098	+	17.2876i	0.573392	+	0.993144i
$304$		0			0
$305$	13.1618	−	22.7968i	0.753640	−	1.30534i
$306$		0			0
$307$	−5.10646	−	8.84465i	−0.291441	−	0.504791i	0.682710	−	0.730690i	$-0.260801\pi$
$307$	−5.10646	−	8.84465i	−0.291441	−	0.504791i	−0.974151	+	0.225899i	$0.927468\pi$
$308$		0			0
$309$	12.9870	+	22.4941i	0.738803	+	1.27964i
$310$		0			0
$311$	8.29026	−	14.3592i	0.470098	−	0.814233i	−0.529318	−	0.848424i	$-0.677552\pi$
$311$	8.29026	−	14.3592i	0.470098	−	0.814233i	0.999415	+	0.0341907i	$0.0108854\pi$
$312$		0			0
$313$	3.93352			0.222336			0.111168	−	0.993802i	$-0.464541\pi$
$313$	3.93352			0.222336			0.111168	+	0.993802i	$0.464541\pi$
$314$		0			0
$315$	3.44708	−	3.47847i	0.194221	−	0.195990i
$316$		0			0
$317$	−11.6162			−0.652429			−0.326214	−	0.945296i	$-0.605773\pi$
$317$	−11.6162			−0.652429			−0.326214	+	0.945296i	$0.605773\pi$
$318$		0			0
$319$	5.01346	+	8.68357i	0.280700	+	0.486186i
$320$		0			0
$321$	2.88736	+	5.00106i	0.161157	+	0.279132i
$322$		0			0
$323$	−22.3943	−	3.08944i	−1.24605	−	0.171901i
$324$		0			0
$325$	−17.6074			−0.976680
$326$		0			0
$327$	−30.7940			−1.70291
$328$		0			0
$329$	4.96923	+	1.30739i	0.273963	+	0.0720789i
$330$		0			0
$331$	16.2515	+	28.1484i	0.893261	+	1.54717i	0.835942	+	0.548818i	$0.184922\pi$
$331$	16.2515	+	28.1484i	0.893261	+	1.54717i	0.0573193	+	0.998356i	$0.481745\pi$
$332$		0			0
$333$	−1.27588	−	2.20989i	−0.0699179	−	0.121101i
$334$		0			0
$335$	−7.03064			−0.384125
$336$		0			0
$337$	11.0884	+	19.2057i	0.604025	+	1.04620i	0.992205	+	0.124618i	$0.0397705\pi$
$337$	11.0884	+	19.2057i	0.604025	+	1.04620i	−0.388180	+	0.921584i	$0.626896\pi$
$338$		0			0
$339$	−14.9252			−0.810628
$340$		0			0
$341$	0.482166	+	0.835136i	0.0261107	+	0.0452251i
$342$		0			0
$343$	−13.2726	−	12.9165i	−0.716655	−	0.697427i
$344$		0			0
$345$	19.1981	−	33.2520i	1.03359	−	1.79023i
$346$		0			0
$347$	−19.7530			−1.06040			−0.530199	−	0.847873i	$-0.677883\pi$
$347$	−19.7530			−1.06040			−0.530199	+	0.847873i	$0.677883\pi$
$348$		0			0
$349$	28.4738			1.52417			0.762084	−	0.647478i	$-0.224176\pi$
$349$	28.4738			1.52417			0.762084	+	0.647478i	$0.224176\pi$
$350$		0			0
$351$	−12.3668	+	21.4198i	−0.660088	+	1.14331i
$352$		0			0
$353$	−7.92741	+	13.7307i	−0.421934	+	0.730810i	−0.996129	−	0.0879082i	$-0.971982\pi$
$353$	−7.92741	+	13.7307i	−0.421934	+	0.730810i	0.574195	+	0.818719i	$0.305315\pi$
$354$		0			0
$355$	4.17514			0.221594
$356$		0			0
$357$	20.4812	+	5.38855i	1.08398	+	0.285192i
$358$		0			0
$359$	−13.4994	+	23.3816i	−0.712470	+	1.23404i	0.251457	+	0.967869i	$0.419090\pi$
$359$	−13.4994	+	23.3816i	−0.712470	+	1.23404i	−0.963927	+	0.266166i	$0.914243\pi$
$360$		0			0
$361$	18.2903	+	5.14445i	0.962647	+	0.270760i
$362$		0			0
$363$	5.46668	+	9.46856i	0.286926	+	0.496971i
$364$		0			0
$365$	−9.27690	+	16.0681i	−0.485575	+	0.841041i
$366$		0			0
$367$	1.85091	+	3.20588i	0.0966169	+	0.167345i	0.910282	−	0.413988i	$-0.135864\pi$
$367$	1.85091	+	3.20588i	0.0966169	+	0.167345i	−0.813665	+	0.581334i	$0.802531\pi$
$368$		0			0
$369$	2.31275	+	4.00581i	0.120397	+	0.208534i
$370$		0			0
$371$	−3.75996	−	13.7822i	−0.195207	−	0.715536i
$372$		0			0
$373$	12.5477	+	21.7333i	0.649697	+	1.12531i	0.983195	+	0.182557i	$0.0584375\pi$
$373$	12.5477	+	21.7333i	0.649697	+	1.12531i	−0.333498	+	0.942751i	$0.608229\pi$
$374$		0			0
$375$	4.73919			0.244731
$376$		0			0
$377$	11.2217	+	19.4365i	0.577945	+	1.00103i
$378$		0			0
$379$	−5.87589			−0.301824			−0.150912	−	0.988547i	$-0.548221\pi$
$379$	−5.87589			−0.301824			−0.150912	+	0.988547i	$0.548221\pi$
$380$		0			0
$381$	−7.96152	+	13.7898i	−0.407881	+	0.706471i
$382$		0			0
$383$	9.86109	−	17.0799i	0.503878	−	0.872743i	−0.496112	−	0.868259i	$-0.665239\pi$
$383$	9.86109	−	17.0799i	0.503878	−	0.872743i	0.999990	−	0.00448393i	$-0.00142728\pi$
$384$		0			0
$385$	4.12833	+	15.1325i	0.210399	+	0.771223i
$386$		0			0
$387$	−2.89931	−	5.02175i	−0.147380	−	0.255270i
$388$		0			0
$389$	−13.8361	−	23.9649i	−0.701519	−	1.21507i	−0.967933	−	0.251208i	$-0.919172\pi$
$389$	−13.8361	−	23.9649i	−0.701519	−	1.21507i	0.266414	−	0.963859i	$-0.414161\pi$
$390$		0			0
$391$	−43.0664			−2.17796
$392$		0			0
$393$	14.8168	−	25.6634i	0.747407	−	1.29455i
$394$		0			0
$395$	−14.6745	−	25.4170i	−0.738353	−	1.27887i
$396$		0			0
$397$	2.08694	−	3.61469i	0.104741	−	0.181416i	−0.808891	−	0.587958i	$-0.799932\pi$
$397$	2.08694	−	3.61469i	0.104741	−	0.181416i	0.913632	+	0.406542i	$0.133265\pi$
$398$		0			0
$399$	−16.4334	−	6.83891i	−0.822699	−	0.342374i
$400$		0			0
$401$	−9.53082	+	16.5079i	−0.475947	+	0.824364i	−0.999620	−	0.0275553i	$-0.991228\pi$
$401$	−9.53082	+	16.5079i	−0.475947	+	0.824364i	0.523674	+	0.851919i	$0.324561\pi$
$402$		0			0
$403$	1.07924	+	1.86929i	0.0537605	+	0.0931160i
$404$		0			0
$405$	−10.1331	+	17.5510i	−0.503516	+	0.872115i
$406$		0			0
$407$	8.17326			0.405133
$408$		0			0
$409$	−4.34545	−	7.52654i	−0.214869	−	0.372164i	0.738363	−	0.674403i	$-0.235599\pi$
$409$	−4.34545	−	7.52654i	−0.214869	−	0.372164i	−0.953232	+	0.302240i	$0.902266\pi$
$410$		0			0
$411$	0.764516	+	1.32418i	0.0377108	+	0.0653170i
$412$		0			0
$413$	−26.0459	−	6.85260i	−1.28163	−	0.337195i
$414$		0			0
$415$	−9.01235	+	15.6098i	−0.442399	+	0.766257i
$416$		0			0
$417$	−14.8559	+	25.7312i	−0.727496	+	1.26006i
$418$		0			0
$419$	−2.18981			−0.106979			−0.0534895	−	0.998568i	$-0.517034\pi$
$419$	−2.18981			−0.106979			−0.0534895	+	0.998568i	$0.517034\pi$
$420$		0			0
$421$	4.50474	+	7.80244i	0.219548	+	0.380268i	0.954670	−	0.297667i	$-0.0962085\pi$
$421$	4.50474	+	7.80244i	0.219548	+	0.380268i	−0.735122	+	0.677935i	$0.762875\pi$
$422$		0			0
$423$	1.19991			0.0583418
$424$		0			0
$425$	10.3078	+	17.8537i	0.500004	+	0.866032i
$426$		0			0
$427$	−22.4823	−	5.91504i	−1.08799	−	0.286249i
$428$		0			0
$429$	−6.76452	−	11.7165i	−0.326594	−	0.565678i
$430$		0			0
$431$	9.65403	+	16.7213i	0.465018	+	0.805435i	0.999202	−	0.0399331i	$-0.0127145\pi$
$431$	9.65403	+	16.7213i	0.465018	+	0.805435i	−0.534184	+	0.845368i	$0.679381\pi$
$432$		0			0
$433$	−6.33241	+	10.9681i	−0.304316	+	0.527091i	−0.977109	−	0.212740i	$-0.931761\pi$
$433$	−6.33241	+	10.9681i	−0.304316	+	0.527091i	0.672793	+	0.739831i	$0.265095\pi$
$434$		0			0
$435$	11.7141	+	20.2895i	0.561650	+	0.972807i
$436$		0			0
$437$	35.8564	+	4.94663i	1.71524	+	0.236629i
$438$		0			0
$439$	−17.2578	+	29.8914i	−0.823671	+	1.42664i	0.0792591	+	0.996854i	$0.474745\pi$
$439$	−17.2578	+	29.8914i	−0.823671	+	1.42664i	−0.902930	+	0.429787i	$0.858589\pi$
$440$		0			0
$441$	−3.76490	−	2.12840i	−0.179281	−	0.101352i
$442$		0			0
$443$	−9.53039			−0.452803			−0.226401	−	0.974034i	$-0.572696\pi$
$443$	−9.53039			−0.452803			−0.226401	+	0.974034i	$0.572696\pi$
$444$		0			0
$445$	−12.8457	+	22.2494i	−0.608945	+	1.05472i
$446$		0			0
$447$	10.5170	−	18.2160i	0.497439	−	0.861590i
$448$		0			0
$449$	−1.22390			−0.0577596			−0.0288798	−	0.999583i	$-0.509194\pi$
$449$	−1.22390			−0.0577596			−0.0288798	+	0.999583i	$0.509194\pi$
$450$		0			0
$451$	−14.8154			−0.697631
$452$		0			0
$453$	−10.4357	+	18.0751i	−0.490310	+	0.849242i
$454$		0			0
$455$	9.24048	+	33.8712i	0.433201	+	1.58790i
$456$		0			0
$457$	−18.5292	−	32.0935i	−0.866759	−	1.50127i	−0.865290	−	0.501271i	$-0.832866\pi$
$457$	−18.5292	−	32.0935i	−0.866759	−	1.50127i	−0.00146815	−	0.999999i	$-0.500467\pi$
$458$		0			0
$459$	28.9594			1.35171
$460$		0			0
$461$	−12.1309	−	21.0113i	−0.564992	−	0.978596i	−0.997050	−	0.0767498i	$-0.975546\pi$
$461$	−12.1309	−	21.0113i	−0.564992	−	0.978596i	0.432058	−	0.901846i	$-0.357788\pi$
$462$		0			0
$463$	16.9873			0.789465			0.394732	−	0.918796i	$-0.370837\pi$
$463$	16.9873			0.789465			0.394732	+	0.918796i	$0.370837\pi$
$464$		0			0
$465$	1.12660	+	1.95133i	0.0522448	+	0.0904906i
$466$		0			0
$467$	−15.8206	−	27.4020i	−0.732088	−	1.26801i	−0.955989	−	0.293402i	$-0.905212\pi$
$467$	−15.8206	−	27.4020i	−0.732088	−	1.26801i	0.223901	−	0.974612i	$-0.428121\pi$
$468$		0			0
$469$	1.63419	+	5.99014i	0.0754597	+	0.276599i
$470$		0			0
$471$	8.83905			0.407282
$472$		0			0
$473$	18.5729			0.853983
$474$		0			0
$475$	−6.53146	−	16.0487i	−0.299684	−	0.736364i
$476$		0			0
$477$	−1.66803	−	2.88911i	−0.0763738	−	0.132283i
$478$		0			0
$479$	12.2523	+	21.2216i	0.559821	+	0.969638i	0.997511	+	0.0705119i	$0.0224633\pi$
$479$	12.2523	+	21.2216i	0.559821	+	0.969638i	−0.437690	+	0.899126i	$0.644203\pi$
$480$		0			0
$481$	18.2943			0.834147
$482$		0			0
$483$	−32.7933	−	8.62782i	−1.49214	−	0.392579i
$484$		0			0
$485$	−20.0241			−0.909247
$486$		0			0
$487$	−3.34790	+	5.79874i	−0.151708	+	0.262766i	−0.931855	−	0.362830i	$-0.881811\pi$
$487$	−3.34790	+	5.79874i	−0.151708	+	0.262766i	0.780147	+	0.625596i	$0.215144\pi$
$488$		0			0
$489$	6.12781	+	10.6137i	0.277109	+	0.479967i
$490$		0			0
$491$	−5.51655	−	9.55494i	−0.248958	−	0.431208i	0.714279	−	0.699861i	$-0.246755\pi$
$491$	−5.51655	−	9.55494i	−0.248958	−	0.431208i	−0.963237	+	0.268653i	$0.913422\pi$
$492$		0			0
$493$	13.1390	−	22.7573i	0.591749	−	1.02494i
$494$		0			0
$495$	1.83145	+	3.17217i	0.0823177	+	0.142578i
$496$		0			0
$497$	−0.970461	−	3.55724i	−0.0435311	−	0.159564i
$498$		0			0
$499$	2.46798	−	4.27466i	0.110482	−	0.191360i	−0.805483	−	0.592619i	$-0.798094\pi$
$499$	2.46798	−	4.27466i	0.110482	−	0.191360i	0.915965	+	0.401259i	$0.131427\pi$
$500$		0			0
$501$	13.9780	−	24.2107i	0.624493	−	1.08165i
$502$		0			0
$503$	−9.25993	+	16.0387i	−0.412880	+	0.715129i	−0.995203	−	0.0978284i	$-0.968810\pi$
$503$	−9.25993	+	16.0387i	−0.412880	+	0.715129i	0.582324	+	0.812957i	$0.302144\pi$
$504$		0			0
$505$	38.7468			1.72421
$506$		0			0
$507$	−5.10883	−	8.84875i	−0.226891	−	0.392987i
$508$		0			0
$509$	2.86837			0.127138			0.0635691	−	0.997977i	$-0.479752\pi$
$509$	2.86837			0.127138			0.0635691	+	0.997977i	$0.479752\pi$
$510$		0			0
$511$	15.8464	+	4.16914i	0.701002	+	0.184432i
$512$		0			0
$513$	−24.1111	−	3.32629i	−1.06453	−	0.146859i
$514$		0			0
$515$	50.4163			2.22161
$516$		0			0
$517$	−1.92165	+	3.32840i	−0.0845142	+	0.146383i
$518$		0			0
$519$	−1.08757	+	1.88372i	−0.0477389	+	0.0826863i
$520$		0			0
$521$	19.3005	−	33.4294i	0.845569	−	1.46457i	−0.0395568	−	0.999217i	$-0.512595\pi$
$521$	19.3005	−	33.4294i	0.845569	−	1.46457i	0.885126	−	0.465351i	$-0.154072\pi$
$522$		0			0
$523$	−35.9212			−1.57072			−0.785362	−	0.619037i	$-0.787523\pi$
$523$	−35.9212			−1.57072			−0.785362	+	0.619037i	$0.787523\pi$
$524$		0			0
$525$	4.27222	+	15.6599i	0.186455	+	0.683455i
$526$		0			0
$527$	1.26363	−	2.18867i	0.0550446	−	0.0953400i
$528$		0			0
$529$	45.9552			1.99805
$530$		0			0
$531$	−6.28926			−0.272931
$532$		0			0
$533$	−33.1615			−1.43638
$534$		0			0
$535$	11.2089			0.484604
$536$		0			0
$537$	14.4689	−	25.0608i	0.624378	−	1.08146i
$538$		0			0
$539$	11.9334	−	7.03472i	0.514006	−	0.303007i
$540$		0			0
$541$	8.80044			0.378361			0.189180	−	0.981942i	$-0.439417\pi$
$541$	8.80044			0.378361			0.189180	+	0.981942i	$0.439417\pi$
$542$		0			0
$543$	−13.9032	+	24.0810i	−0.596643	+	1.03342i
$544$		0			0
$545$	−29.8861	+	51.7642i	−1.28018	+	2.21733i
$546$		0			0
$547$	0.491535	−	0.851364i	0.0210165	−	0.0364017i	−0.855326	−	0.518090i	$-0.826643\pi$
$547$	0.491535	−	0.851364i	0.0210165	−	0.0364017i	0.876342	+	0.481689i	$0.159976\pi$
$548$		0			0
$549$	−5.42877			−0.231694
$550$		0			0
$551$	−13.5532	+	17.4383i	−0.577387	+	0.742895i
$552$		0			0
$553$	−18.2445	+	18.4106i	−0.775833	+	0.782898i
$554$		0			0
$555$	19.0971			0.810629
$556$		0			0
$557$	−2.07402	−	3.59232i	−0.0878793	−	0.152211i	0.818735	−	0.574171i	$-0.194676\pi$
$557$	−2.07402	−	3.59232i	−0.0878793	−	0.152211i	−0.906614	+	0.421960i	$0.861342\pi$
$558$		0			0
$559$	41.5719			1.75830
$560$		0			0
$561$	−7.92029	+	13.7183i	−0.334395	+	0.579189i
$562$		0			0
$563$	−18.4667	+	31.9852i	−0.778278	+	1.34802i	0.154655	+	0.987968i	$0.450573\pi$
$563$	−18.4667	+	31.9852i	−0.778278	+	1.34802i	−0.932933	+	0.360049i	$0.882760\pi$
$564$		0			0
$565$	−14.4852	+	25.0891i	−0.609397	+	1.05551i
$566$		0			0
$567$	17.3088	+	4.55391i	0.726902	+	0.191246i
$568$		0			0
$569$	−6.56492	−	11.3708i	−0.275216	−	0.476687i	0.694974	−	0.719035i	$-0.255416\pi$
$569$	−6.56492	−	11.3708i	−0.275216	−	0.476687i	−0.970190	+	0.242348i	$0.922083\pi$
$570$		0			0
$571$	−4.29911	+	7.44627i	−0.179912	+	0.311617i	−0.941850	−	0.336033i	$-0.890915\pi$
$571$	−4.29911	+	7.44627i	−0.179912	+	0.311617i	0.761938	+	0.647650i	$0.224248\pi$
$572$		0			0
$573$	0.0420598	+	0.0728498i	0.00175708	+	0.00304334i
$574$		0			0
$575$	−16.5043	−	28.5863i	−0.688276	−	1.19213i
$576$		0			0
$577$	−5.53040	+	9.57893i	−0.230233	+	0.398776i	−0.957877	−	0.287180i	$-0.907282\pi$
$577$	−5.53040	+	9.57893i	−0.230233	+	0.398776i	0.727643	+	0.685956i	$0.240616\pi$
$578$		0			0
$579$	−31.9342			−1.32714
$580$		0			0
$581$	15.3945	+	4.05025i	0.638670	+	0.168033i
$582$		0			0
$583$	10.6853			0.442542
$584$		0			0
$585$	4.09935	+	7.10029i	0.169487	+	0.293561i
$586$		0			0
$587$	11.4545	+	19.8398i	0.472779	+	0.818878i	0.999515	−	0.0311516i	$-0.00991746\pi$
$587$	11.4545	+	19.8398i	0.472779	+	0.818878i	−0.526735	+	0.850029i	$0.676584\pi$
$588$		0			0
$589$	−1.30347	+	1.67711i	−0.0537086	+	0.0691042i
$590$		0			0
$591$	−30.6402			−1.26037
$592$		0			0
$593$	−21.7893			−0.894780			−0.447390	−	0.894339i	$-0.647646\pi$
$593$	−21.7893			−0.894780			−0.447390	+	0.894339i	$0.647646\pi$
$594$		0			0
$595$	28.9354	−	29.1989i	1.18624	−	1.19704i
$596$		0			0
$597$	5.33822	+	9.24607i	0.218479	+	0.378417i
$598$		0			0
$599$	8.05995	+	13.9602i	0.329321	+	0.570400i	0.982377	−	0.186909i	$-0.0598469\pi$
$599$	8.05995	+	13.9602i	0.329321	+	0.570400i	−0.653056	+	0.757309i	$0.726514\pi$
$600$		0			0
$601$	−17.6762			−0.721028			−0.360514	−	0.932754i	$-0.617399\pi$
$601$	−17.6762			−0.721028			−0.360514	+	0.932754i	$0.617399\pi$
$602$		0			0
$603$	0.724974	+	1.25569i	0.0295232	+	0.0511357i
$604$		0			0
$605$	21.2220			0.862797
$606$		0			0
$607$	−6.97347	−	12.0784i	−0.283044	−	0.490247i	0.689089	−	0.724677i	$-0.258011\pi$
$607$	−6.97347	−	12.0784i	−0.283044	−	0.490247i	−0.972133	+	0.234430i	$0.924678\pi$
$608$		0			0
$609$	14.5639	−	14.6965i	0.590160	−	0.595534i
$610$		0			0
$611$	−4.30125	+	7.44999i	−0.174010	+	0.301394i
$612$		0			0
$613$	6.00636			0.242594			0.121297	−	0.992616i	$-0.461295\pi$
$613$	6.00636			0.242594			0.121297	+	0.992616i	$0.461295\pi$
$614$		0			0
$615$	−34.6168			−1.39588
$616$		0			0
$617$	4.05115	−	7.01680i	0.163093	−	0.282486i	−0.772883	−	0.634548i	$-0.781186\pi$
$617$	4.05115	−	7.01680i	0.163093	−	0.282486i	0.935977	+	0.352062i	$0.114520\pi$
$618$		0			0
$619$	0.396098	−	0.686062i	0.0159205	−	0.0275752i	−0.857955	−	0.513724i	$-0.828265\pi$
$619$	0.396098	−	0.686062i	0.0159205	−	0.0275752i	0.873876	+	0.486149i	$0.161599\pi$
$620$		0			0
$621$	−46.3680			−1.86068
$622$		0			0
$623$	21.9425	+	5.77300i	0.879106	+	0.231290i
$624$		0			0
$625$	14.5371	−	25.1790i	0.581484	−	1.00716i
$626$		0			0
$627$	8.17001	−	10.5119i	0.326279	−	0.419807i
$628$		0			0
$629$	−10.7100	−	18.5502i	−0.427035	−	0.739646i
$630$		0			0
$631$	3.27524	−	5.67288i	0.130385	−	0.225834i	−0.793440	−	0.608649i	$-0.791712\pi$
$631$	3.27524	−	5.67288i	0.130385	−	0.225834i	0.923825	+	0.382815i	$0.125045\pi$
$632$		0			0
$633$	1.91154	+	3.31089i	0.0759770	+	0.131596i
$634$		0			0
$635$	15.4536	+	26.7664i	0.613257	+	1.06219i
$636$		0			0
$637$	26.7105	−	15.7459i	1.05831	−	0.623874i
$638$		0			0
$639$	−0.430525	−	0.745692i	−0.0170313	−	0.0294991i
$640$		0			0
$641$	−37.1062			−1.46560			−0.732802	−	0.680441i	$-0.761788\pi$
$641$	−37.1062			−1.46560			−0.732802	+	0.680441i	$0.761788\pi$
$642$		0			0
$643$	−18.0377	−	31.2422i	−0.711337	−	1.23207i	−0.964356	−	0.264610i	$-0.914757\pi$
$643$	−18.0377	−	31.2422i	−0.711337	−	1.23207i	0.253019	−	0.967461i	$-0.418576\pi$
$644$		0			0
$645$	43.3963			1.70873
$646$		0			0
$647$	−3.12087	+	5.40550i	−0.122694	+	0.212512i	−0.920829	−	0.389966i	$-0.872487\pi$
$647$	−3.12087	+	5.40550i	−0.122694	+	0.212512i	0.798135	+	0.602478i	$0.205820\pi$
$648$		0			0
$649$	10.0722	−	17.4456i	0.395369	−	0.684798i
$650$		0			0
$651$	1.40068	−	1.41343i	0.0548968	−	0.0553967i
$652$		0			0
$653$	−20.7080	−	35.8673i	−0.810367	−	1.40360i	−0.912608	−	0.408837i	$-0.865935\pi$
$653$	−20.7080	−	35.8673i	−0.810367	−	1.40360i	0.102241	−	0.994760i	$-0.467399\pi$
$654$		0			0
$655$	−28.7599	−	49.8135i	−1.12374	−	1.94638i
$656$		0			0
$657$	3.82640			0.149282
$658$		0			0
$659$	8.73980	−	15.1378i	0.340454	−	0.589684i	−0.644063	−	0.764973i	$-0.722752\pi$
$659$	8.73980	−	15.1378i	0.340454	−	0.589684i	0.984517	+	0.175288i	$0.0560858\pi$
$660$		0			0
$661$	−2.75055	−	4.76410i	−0.106984	−	0.185302i	0.807563	−	0.589781i	$-0.200786\pi$
$661$	−2.75055	−	4.76410i	−0.106984	−	0.185302i	−0.914547	+	0.404479i	$0.867453\pi$
$662$		0			0
$663$	−17.7280	+	30.7059i	−0.688500	+	1.19252i
$664$		0			0
$665$	−27.4450	+	20.9870i	−1.06427	+	0.813842i
$666$		0			0
$667$	−21.0373	+	36.4377i	−0.814568	+	1.41087i
$668$		0			0
$669$	2.47764	+	4.29140i	0.0957911	+	0.165915i
$670$		0			0
$671$	8.69413	−	15.0587i	0.335633	−	0.581334i
$672$		0			0
$673$	−51.5038			−1.98533			−0.992663	−	0.120912i	$-0.961418\pi$
$673$	−51.5038			−1.98533			−0.992663	+	0.120912i	$0.961418\pi$
$674$		0			0
$675$	11.0981	+	19.2224i	0.427165	+	0.739872i
$676$		0			0
$677$	18.1552	+	31.4458i	0.697762	+	1.20856i	0.969241	+	0.246114i	$0.0791539\pi$
$677$	18.1552	+	31.4458i	0.697762	+	1.20856i	−0.271479	+	0.962444i	$0.587513\pi$
$678$		0			0
$679$	4.65436	+	17.0606i	0.178618	+	0.654727i
$680$		0			0
$681$	−1.71663	+	2.97330i	−0.0657815	+	0.113937i
$682$		0			0
$683$	−22.8728	+	39.6169i	−0.875204	+	1.51590i	−0.0186578	+	0.999826i	$0.505939\pi$
$683$	−22.8728	+	39.6169i	−0.875204	+	1.51590i	−0.856546	+	0.516071i	$0.827394\pi$
$684$		0			0
$685$	2.96790			0.113398
$686$		0			0
$687$	−14.7193	−	25.4946i	−0.561576	−	0.972678i
$688$		0			0
$689$	23.9171			0.911169
$690$		0			0
$691$	14.1093	+	24.4381i	0.536745	+	0.929669i	0.999077	+	0.0429622i	$0.0136795\pi$
$691$	14.1093	+	24.4381i	0.536745	+	0.929669i	−0.462332	+	0.886707i	$0.652987\pi$
$692$		0			0
$693$	2.27700	−	2.29774i	0.0864962	−	0.0872838i
$694$		0			0
$695$	28.8358	+	49.9451i	1.09380	+	1.89452i
$696$		0			0
$697$	19.4137	+	33.6255i	0.735345	+	1.27365i
$698$		0			0
$699$	11.8409	−	20.5090i	0.447864	−	0.775723i
$700$		0			0
$701$	−16.5309	−	28.6324i	−0.624365	−	1.08143i	−0.988663	−	0.150150i	$-0.952024\pi$
$701$	−16.5309	−	28.6324i	−0.624365	−	1.08143i	0.364298	−	0.931282i	$-0.381309\pi$
$702$		0			0
$703$	6.78628	+	16.6748i	0.255949	+	0.628902i
$704$		0			0
$705$	−4.49002	+	7.77694i	−0.169104	+	0.292896i
$706$		0			0
$707$	−9.00623	−	33.0125i	−0.338714	−	1.24156i
$708$		0			0
$709$	2.46788			0.0926834			0.0463417	−	0.998926i	$-0.485244\pi$
$709$	2.46788			0.0926834			0.0463417	+	0.998926i	$0.485244\pi$
$710$		0			0
$711$	−3.02636	+	5.24181i	−0.113497	+	0.196583i
$712$		0			0
$713$	−2.02325	+	3.50437i	−0.0757712	+	0.131240i
$714$		0			0
$715$	−26.2603			−0.982081
$716$		0			0
$717$	−3.62602			−0.135416
$718$		0			0
$719$	−5.95021	+	10.3061i	−0.221905	+	0.384351i	−0.955387	−	0.295358i	$-0.904561\pi$
$719$	−5.95021	+	10.3061i	−0.221905	+	0.384351i	0.733481	+	0.679710i	$0.237894\pi$
$720$		0			0
$721$	−11.7187	−	42.9550i	−0.436426	−	1.59973i
$722$		0			0
$723$	−13.6115	−	23.5758i	−0.506218	−	0.876795i
$724$		0			0
$725$	20.1409			0.748016
$726$		0			0
$727$	−11.4564	−	19.8431i	−0.424896	−	0.735941i	0.571515	−	0.820592i	$-0.306356\pi$
$727$	−11.4564	−	19.8431i	−0.424896	−	0.735941i	−0.996411	+	0.0846505i	$0.973023\pi$
$728$		0			0
$729$	30.0344			1.11238
$730$		0			0
$731$	−24.3373	−	42.1535i	−0.900149	−	1.55910i
$732$		0			0
$733$	16.2940	+	28.2220i	0.601832	+	1.04240i	0.992544	+	0.121891i	$0.0388957\pi$
$733$	16.2940	+	28.2220i	0.601832	+	1.04240i	−0.390711	+	0.920513i	$0.627771\pi$
$734$		0			0
$735$	27.8828	−	16.4369i	1.02847	−	0.606284i
$736$		0			0
$737$	−4.64416			−0.171070
$738$		0			0
$739$	46.7646			1.72026			0.860131	−	0.510073i	$-0.170381\pi$
$739$	46.7646			1.72026			0.860131	+	0.510073i	$0.170381\pi$
$740$		0			0
$741$	18.2870	−	23.5290i	0.671789	−	0.864359i
$742$		0			0
$743$	−16.7168	−	28.9543i	−0.613279	−	1.06223i	−0.990684	−	0.136182i	$-0.956517\pi$
$743$	−16.7168	−	28.9543i	−0.613279	−	1.06223i	0.377405	−	0.926048i	$-0.376817\pi$
$744$		0			0
$745$	−20.4139	−	35.3580i	−0.747909	−	1.29542i
$746$		0			0
$747$	3.71728			0.136008
$748$		0			0
$749$	−2.60538	−	9.55006i	−0.0951985	−	0.348952i
$750$		0			0
$751$	3.68057			0.134306			0.0671530	−	0.997743i	$-0.478608\pi$
$751$	3.68057			0.134306			0.0671530	+	0.997743i	$0.478608\pi$
$752$		0			0
$753$	3.42293	−	5.92869i	0.124739	−	0.216054i
$754$		0			0
$755$	20.2560	+	35.0844i	0.737190	+	1.27685i
$756$		0			0
$757$	10.2828	+	17.8103i	0.373735	+	0.647328i	0.990137	−	0.140104i	$-0.0447437\pi$
$757$	10.2828	+	17.8103i	0.373735	+	0.647328i	−0.616402	+	0.787432i	$0.711410\pi$
$758$		0			0
$759$	12.6815	−	21.9650i	0.460309	−	0.797278i
$760$		0			0
$761$	10.3375	+	17.9051i	0.374735	+	0.649060i	0.990287	−	0.139036i	$-0.0444004\pi$
$761$	10.3375	+	17.9051i	0.374735	+	0.649060i	−0.615553	+	0.788096i	$0.711067\pi$
$762$		0			0
$763$	51.0500	+	13.4311i	1.84813	+	0.486239i
$764$		0			0
$765$	4.79976	−	8.31342i	0.173536	−	0.300572i
$766$		0			0
$767$	22.5447	−	39.0486i	0.814042	−	1.40996i
$768$		0			0
$769$	−18.2913	+	31.6814i	−0.659600	+	1.14246i	0.321120	+	0.947039i	$0.395941\pi$
$769$	−18.2913	+	31.6814i	−0.659600	+	1.14246i	−0.980719	+	0.195422i	$0.937392\pi$
$770$		0			0
$771$	−9.60269			−0.345833
$772$		0			0
$773$	−11.7243	−	20.3072i	−0.421695	−	0.730398i	0.574410	−	0.818568i	$-0.305232\pi$
$773$	−11.7243	−	20.3072i	−0.421695	−	0.730398i	−0.996105	+	0.0881698i	$0.971898\pi$
$774$		0			0
$775$	1.93704			0.0695805
$776$		0			0
$777$	−4.43890	−	16.2709i	−0.159245	−	0.583714i
$778$		0			0
$779$	−12.3013	−	30.2259i	−0.440739	−	1.08296i
$780$		0			0
$781$	2.75793			0.0986866
$782$		0			0
$783$	14.1462	−	24.5020i	0.505546	−	0.875631i
$784$		0			0
$785$	8.57845	−	14.8583i	0.306178	−	0.530316i
$786$		0			0
$787$	−16.5356	+	28.6405i	−0.589431	+	1.02092i	0.404876	+	0.914371i	$0.367315\pi$
$787$	−16.5356	+	28.6405i	−0.589431	+	1.02092i	−0.994307	+	0.106553i	$0.966019\pi$
$788$		0			0
$789$	−31.8356			−1.13338
$790$		0			0
$791$	24.7430	+	6.50981i	0.879758	+	0.231462i
$792$		0			0
$793$	19.4602	−	33.7060i	0.691050	−	1.19693i
$794$		0			0
$795$	24.9667			0.885479
$796$		0			0
$797$	−7.89620			−0.279698			−0.139849	−	0.990173i	$-0.544662\pi$
$797$	−7.89620			−0.279698			−0.139849	+	0.990173i	$0.544662\pi$
$798$		0			0
$799$	10.0723			0.356332
$800$		0			0
$801$	5.29841			0.187210
$802$		0			0
$803$	−6.12795	+	10.6139i	−0.216251	+	0.374557i
$804$		0			0
$805$	−46.3296	+	46.7515i	−1.63291	+	1.64777i
$806$		0			0
$807$	27.4524			0.966370
$808$		0			0
$809$	−17.3919	+	30.1237i	−0.611468	+	1.05909i	0.379525	+	0.925182i	$0.376087\pi$
$809$	−17.3919	+	30.1237i	−0.611468	+	1.05909i	−0.990993	+	0.133913i	$0.957246\pi$
$810$		0			0
$811$	−10.9021	+	18.8829i	−0.382823	+	0.663069i	−0.991465	−	0.130376i	$-0.958382\pi$
$811$	−10.9021	+	18.8829i	−0.382823	+	0.663069i	0.608641	+	0.793445i	$0.291715\pi$
$812$		0			0
$813$	14.4792	−	25.0787i	0.507807	−	0.879547i
$814$		0			0
$815$	23.7886			0.833277
$816$		0			0
$817$	15.4211	+	37.8918i	0.539517	+	1.32567i
$818$		0			0
$819$	5.09664	−	5.14305i	0.178091	−	0.179713i
$820$		0			0
$821$	27.2445			0.950840			0.475420	−	0.879759i	$-0.342296\pi$
$821$	27.2445			0.950840			0.475420	+	0.879759i	$0.342296\pi$
$822$		0			0
$823$	8.92582	+	15.4600i	0.311134	+	0.538901i	0.978608	−	0.205733i	$-0.0659577\pi$
$823$	8.92582	+	15.4600i	0.311134	+	0.538901i	−0.667474	+	0.744633i	$0.732624\pi$
$824$		0			0
$825$	−12.1411			−0.422700
$826$		0			0
$827$	7.64224	−	13.2368i	0.265747	−	0.460287i	−0.702012	−	0.712165i	$-0.747715\pi$
$827$	7.64224	−	13.2368i	0.265747	−	0.460287i	0.967759	+	0.251878i	$0.0810482\pi$
$828$		0			0
$829$	13.2246	−	22.9057i	0.459310	−	0.795549i	−0.539614	−	0.841912i	$-0.681430\pi$
$829$	13.2246	−	22.9057i	0.459310	−	0.795549i	0.998925	+	0.0463634i	$0.0147632\pi$
$830$		0			0
$831$	15.9019	−	27.5429i	0.551631	−	0.955453i
$832$		0			0
$833$	−31.6033	−	17.8662i	−1.09499	−	0.619027i
$834$		0			0
$835$	−27.1319	−	46.9938i	−0.938937	−	1.62629i
$836$		0			0
$837$	1.36051	−	2.35646i	0.0470259	−	0.0814513i
$838$		0			0
$839$	11.0135	+	19.0760i	0.380230	+	0.658577i	0.991095	−	0.133157i	$-0.0425116\pi$
$839$	11.0135	+	19.0760i	0.380230	+	0.658577i	−0.610865	+	0.791735i	$0.709178\pi$
$840$		0			0
$841$	1.66361	+	2.88146i	0.0573658	+	0.0993605i
$842$		0			0
$843$	7.60880	−	13.1788i	0.262061	−	0.453903i
$844$		0			0
$845$	−19.8328			−0.682269
$846$		0			0
$847$	−4.93280	−	18.0813i	−0.169493	−	0.621279i
$848$		0			0
$849$	−8.68640			−0.298116
$850$		0			0
$851$	17.1482	+	29.7015i	0.587832	+	1.01815i
$852$		0			0
$853$	−24.2446	−	41.9928i	−0.830118	−	1.43781i	−0.897944	−	0.440109i	$-0.854940\pi$
$853$	−24.2446	−	41.9928i	−0.830118	−	1.43781i	0.0678269	−	0.997697i	$-0.478393\pi$
$854$		0			0
$855$	−4.95109	+	6.37032i	−0.169324	+	0.217860i
$856$		0			0
$857$	−31.3853			−1.07210			−0.536051	−	0.844186i	$-0.680084\pi$
$857$	−31.3853			−1.07210			−0.536051	+	0.844186i	$0.680084\pi$
$858$		0			0
$859$	9.73812			0.332260			0.166130	−	0.986104i	$-0.446873\pi$
$859$	9.73812			0.332260			0.166130	+	0.986104i	$0.446873\pi$
$860$		0			0
$861$	8.04626	+	29.4937i	0.274216	+	1.00514i
$862$		0			0
$863$	10.9453	+	18.9578i	0.372583	+	0.645332i	0.989962	−	0.141333i	$-0.0451389\pi$
$863$	10.9453	+	18.9578i	0.372583	+	0.645332i	−0.617379	+	0.786666i	$0.711806\pi$
$864$		0			0
$865$	2.11101	+	3.65637i	0.0717764	+	0.124320i
$866$		0			0
$867$	15.2758			0.518792
$868$		0			0
$869$	−9.69338	−	16.7894i	−0.328825	−	0.569542i
$870$		0			0
$871$	−10.3951			−0.352223
$872$		0			0
$873$	2.06481	+	3.57636i	0.0698833	+	0.121041i
$874$		0			0
$875$	−7.85659	−	2.06705i	−0.265601	−	0.0698790i
$876$		0			0
$877$	3.34241	−	5.78923i	0.112865	−	0.195488i	−0.804059	−	0.594549i	$-0.797330\pi$
$877$	3.34241	−	5.78923i	0.112865	−	0.195488i	0.916924	+	0.399061i	$0.130664\pi$
$878$		0			0
$879$	40.4913			1.36574
$880$		0			0
$881$	15.8968			0.535578			0.267789	−	0.963478i	$-0.413707\pi$
$881$	15.8968			0.535578			0.267789	+	0.963478i	$0.413707\pi$
$882$		0			0
$883$	−14.9113	+	25.8271i	−0.501804	+	0.869150i	0.498194	+	0.867066i	$0.333997\pi$
$883$	−14.9113	+	25.8271i	−0.501804	+	0.869150i	−0.999998	+	0.00208421i	$0.999337\pi$
$884$		0			0
$885$	23.5341	−	40.7623i	0.791090	−	1.37021i
$886$		0			0
$887$	−31.2869			−1.05051			−0.525256	−	0.850944i	$-0.676031\pi$
$887$	−31.2869			−1.05051			−0.525256	+	0.850944i	$0.676031\pi$
$888$		0			0
$889$	19.2131	−	19.3880i	0.644386	−	0.650254i
$890$		0			0
$891$	−6.69349	+	11.5935i	−0.224241	+	0.388396i
$892$		0			0
$893$	−8.38604	−	1.15691i	−0.280628	−	0.0387145i
$894$		0			0
$895$	−28.0846	−	48.6439i	−0.938764	−	1.62599i
$896$		0			0
$897$	28.3851	−	49.1644i	0.947750	−	1.64155i
$898$		0			0
$899$	−1.23453	−	2.13827i	−0.0411739	−	0.0713153i
$900$		0			0
$901$	−14.0017	−	24.2517i	−0.466466	−	0.807942i
$902$		0			0
$903$	−10.0869	−	36.9739i	−0.335672	−	1.23041i
$904$		0			0
$905$	26.9865	+	46.7421i	0.897063	+	1.55376i
$906$		0			0
$907$	−27.4907			−0.912813			−0.456406	−	0.889771i	$-0.650864\pi$
$907$	−27.4907			−0.912813			−0.456406	+	0.889771i	$0.650864\pi$
$908$		0			0
$909$	−3.99543	−	6.92029i	−0.132520	−	0.229532i
$910$		0			0
$911$	33.2850			1.10278			0.551391	−	0.834247i	$-0.314097\pi$
$911$	33.2850			1.10278			0.551391	+	0.834247i	$0.314097\pi$
$912$		0			0
$913$	−5.95320	+	10.3112i	−0.197022	+	0.341252i
$914$		0			0
$915$	20.3142	−	35.1852i	0.671566	−	1.16319i
$916$		0			0
$917$	−35.7565	+	36.0821i	−1.18078	+	1.19154i
$918$		0			0
$919$	−15.4208	−	26.7096i	−0.508686	−	0.881070i	−0.999949	−	0.0100587i	$-0.996798\pi$
$919$	−15.4208	−	26.7096i	−0.508686	−	0.881070i	0.491264	−	0.871011i	$-0.336535\pi$
$920$		0			0
$921$	−7.88144	−	13.6510i	−0.259702	−	0.449817i
$922$		0			0
$923$	6.17310			0.203190
$924$		0			0
$925$	8.20876	−	14.2180i	0.269902	−	0.467485i
$926$		0			0
$927$	−5.19875	−	9.00450i	−0.170749	−	0.295746i
$928$		0			0
$929$	18.8730	−	32.6889i	0.619202	−	1.07249i	−0.370430	−	0.928860i	$-0.620790\pi$
$929$	18.8730	−	32.6889i	0.619202	−	1.07249i	0.989632	−	0.143629i	$-0.0458771\pi$
$930$		0			0
$931$	24.2603	+	18.5051i	0.795099	+	0.606480i
$932$		0			0
$933$	12.7954	−	22.1623i	0.418902	−	0.725560i
$934$		0			0
$935$	15.3735	+	26.6278i	0.502769	+	0.870821i
$936$		0			0
$937$	−5.88110	+	10.1864i	−0.192127	+	0.332774i	−0.945955	−	0.324298i	$-0.894872\pi$
$937$	−5.88110	+	10.1864i	−0.192127	+	0.332774i	0.753828	+	0.657072i	$0.228205\pi$
$938$		0			0
$939$	6.07109			0.198122
$940$		0			0
$941$	−11.1677	−	19.3430i	−0.364056	−	0.630563i	0.624569	−	0.780970i	$-0.285275\pi$
$941$	−11.1677	−	19.3430i	−0.364056	−	0.630563i	−0.988624	+	0.150407i	$0.951942\pi$
$942$		0			0
$943$	−31.0840	−	53.8390i	−1.01223	−	1.75324i
$944$		0			0
$945$	31.1537	−	31.4374i	1.01343	−	1.02266i
$946$		0			0
$947$	−14.5346	+	25.1746i	−0.472311	+	0.818066i	−0.999498	−	0.0316832i	$-0.989913\pi$
$947$	−14.5346	+	25.1746i	−0.472311	+	0.818066i	0.527187	+	0.849749i	$0.323247\pi$
$948$		0			0
$949$	−13.7162	+	23.7572i	−0.445248	+	0.771192i
$950$		0			0
$951$	−17.9287			−0.581377
$952$		0			0
$953$	1.92366	+	3.33187i	0.0623133	+	0.107930i	0.895499	−	0.445063i	$-0.146819\pi$
$953$	1.92366	+	3.33187i	0.0623133	+	0.107930i	−0.833186	+	0.552993i	$0.813486\pi$
$954$		0			0
$955$	0.163279			0.00528359
$956$		0			0
$957$	7.73790	+	13.4024i	0.250131	+	0.433239i
$958$		0			0
$959$	−0.689853	−	2.52867i	−0.0222765	−	0.0816549i
$960$		0			0
$961$	15.3813	+	26.6411i	0.496170	+	0.859392i
$962$		0			0
$963$	−1.15582	−	2.00195i	−0.0372459	−	0.0645118i
$964$		0			0
$965$	−30.9926	+	53.6808i	−0.997689	+	1.72805i
$966$		0			0
$967$	−26.5599	−	46.0031i	−0.854109	−	1.47936i	−0.877469	−	0.479633i	$-0.840770\pi$
$967$	−26.5599	−	46.0031i	−0.854109	−	1.47936i	0.0233602	−	0.999727i	$-0.492564\pi$
$968$		0			0
$969$	−34.5639	−	4.76832i	−1.11035	−	0.153181i
$970$		0			0
$971$	−4.56618	+	7.90886i	−0.146536	+	0.253807i	−0.929945	−	0.367699i	$-0.880146\pi$
$971$	−4.56618	+	7.90886i	−0.146536	+	0.253807i	0.783409	+	0.621506i	$0.213479\pi$
$972$		0			0
$973$	35.8509	−	36.1774i	1.14933	−	1.15979i
$974$		0			0
$975$	−27.1756			−0.870316
$976$		0			0
$977$	−15.6610	+	27.1257i	−0.501040	+	0.867828i	0.498959	+	0.866626i	$0.333716\pi$
$977$	−15.6610	+	27.1257i	−0.501040	+	0.867828i	−0.999999	+	0.00120183i	$0.999617\pi$
$978$		0			0
$979$	−8.48537	+	14.6971i	−0.271194	+	0.469721i
$980$		0			0
$981$	12.3270			0.393570
$982$		0			0
$983$	−1.84399			−0.0588141			−0.0294071	−	0.999568i	$-0.509362\pi$
$983$	−1.84399			−0.0588141			−0.0294071	+	0.999568i	$0.509362\pi$
$984$		0			0
$985$	−29.7368	+	51.5056i	−0.947493	+	1.64111i
$986$		0			0
$987$	7.66964	+	2.01786i	0.244127	+	0.0642293i
$988$		0			0
$989$	38.9675	+	67.4936i	1.23909	+	2.14617i
$990$		0			0
$991$	−25.2241			−0.801269			−0.400635	−	0.916238i	$-0.631210\pi$
$991$	−25.2241			−0.801269			−0.400635	+	0.916238i	$0.631210\pi$
$992$		0			0
$993$	25.0829	+	43.4449i	0.795982	+	1.37868i
$994$		0			0
$995$	20.7233			0.656974
$996$		0			0
$997$	25.9690	+	44.9796i	0.822445	+	1.42452i	0.903856	+	0.427836i	$0.140724\pi$
$997$	25.9690	+	44.9796i	0.822445	+	1.42452i	−0.0814108	+	0.996681i	$0.525943\pi$
$998$		0			0
$999$	−11.5311	−	19.9724i	−0.364827	−	0.631898i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	532.2.l.b.501.9	yes	24
7.2	even	3		532.2.k.b.121.4	✓	24
19.11	even	3		532.2.k.b.277.4	yes	24
133.30	even	3	inner	532.2.l.b.429.9	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
532.2.k.b.121.4	✓	24	7.2	even	3
532.2.k.b.277.4	yes	24	19.11	even	3
532.2.l.b.429.9	yes	24	133.30	even	3	inner
532.2.l.b.501.9	yes	24	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 532 = 2^{2} \cdot 7 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	532.l (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+1.54342 q^{3} +(1.49792 - 2.59447i) q^{5} +(-2.55868 - 0.673181i) q^{7} -0.617840 q^{9} +(0.989466 - 1.71381i) q^{11} +(2.21473 - 3.83603i) q^{13} +(2.31193 - 4.00437i) q^{15} -5.18626 q^{17} +(4.31800 + 0.595698i) q^{19} +(-3.94913 - 1.03900i) q^{21} +8.30393 q^{23} +(-1.98753 - 3.44250i) q^{25} -5.58386 q^{27} +(-2.53342 + 4.38800i) q^{29} +(-0.243649 + 0.422013i) q^{31} +(1.52717 - 2.64513i) q^{33} +(-5.57924 + 5.63005i) q^{35} +(2.06507 + 3.57680i) q^{37} +(3.41827 - 5.92062i) q^{39} +(-3.74329 - 6.48356i) q^{41} +(4.69266 + 8.12792i) q^{43} +(-0.925475 + 1.60297i) q^{45} -1.94211 q^{47} +(6.09365 + 3.44491i) q^{49} -8.00460 q^{51} +(2.69978 + 4.67615i) q^{53} +(-2.96428 - 5.13429i) q^{55} +(6.66451 + 0.919414i) q^{57} +10.1794 q^{59} +8.78669 q^{61} +(1.58085 + 0.415918i) q^{63} +(-6.63498 - 11.4921i) q^{65} +(-1.17340 - 2.03239i) q^{67} +12.8165 q^{69} +(0.696823 + 1.20693i) q^{71} -6.19319 q^{73} +(-3.06760 - 5.31324i) q^{75} +(-3.68543 + 3.71898i) q^{77} +(4.89829 - 8.48408i) q^{79} -6.76475 q^{81} -6.01658 q^{83} +(-7.76860 + 13.4556i) q^{85} +(-3.91014 + 6.77256i) q^{87} -8.57570 q^{89} +(-8.24912 + 8.32423i) q^{91} +(-0.376055 + 0.651346i) q^{93} +(8.01354 - 10.3106i) q^{95} +(-3.34198 - 5.78849i) q^{97} +(-0.611332 + 1.05886i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 2 q^{3} - 6 q^{5} - 6 q^{7} + 30 q^{9} + q^{11} - 7 q^{13} - 2 q^{15} - 6 q^{17} + 17 q^{19} - 18 q^{21} - 16 q^{23} - 8 q^{25} + 20 q^{27} - 22 q^{29} - 7 q^{31} + 7 q^{33} - 21 q^{35} + 9 q^{37}+ \cdots - 27 q^{99}+O(q^{100}) \) 24 * q + 2 * q^3 - 6 * q^5 - 6 * q^7 + 30 * q^9 + q^11 - 7 * q^13 - 2 * q^15 - 6 * q^17 + 17 * q^19 - 18 * q^21 - 16 * q^23 - 8 * q^25 + 20 * q^27 - 22 * q^29 - 7 * q^31 + 7 * q^33 - 21 * q^35 + 9 * q^37 + 12 * q^39 - 11 * q^41 - 9 * q^43 - 28 * q^45 - 22 * q^47 - 32 * q^49 - 16 * q^51 - 7 * q^53 - 11 * q^55 + 11 * q^57 + 16 * q^59 + 12 * q^61 + 20 * q^63 + 3 * q^65 - 27 * q^67 + 108 * q^69 - 13 * q^71 + 20 * q^73 + 25 * q^75 + 2 * q^77 - 14 * q^79 + 80 * q^81 - 12 * q^83 - 19 * q^85 + 19 * q^87 + 74 * q^89 - 21 * q^91 + 5 * q^93 + 47 * q^95 - 21 * q^97 - 27 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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