LMFDB - Embedded newform 529.2.c.g.466.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [529,2,Mod(118,529)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("529.118"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(529, base_ring=CyclotomicField(22)) chi = DirichletCharacter(H, H._module([16])) N = Newforms(chi, 2, names="a")

Level:	$N$	$=$	$529 = 23^{2}$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	529.c (of order $11$ , degree $10$ , not minimal)

Newform invariants

comment:select newform

sage:traces = [10,4,4,-14,8,17,6] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$4.22408626693$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	$\Q(\zeta_{22})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$x^{10} - x^{9} + x^{8} - x^{7} + x^{6} - x^{5} + x^{4} - x^{3} + x^{2} - x + 1$ x^10 - x^9 + x^8 - x^7 + x^6 - x^5 + x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$1$
Twist minimal:	no (minimal twist has level 23)
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			466.1
Root			$0.959493 - 0.281733i$ of defining polynomial
Character	$\chi$	$=$	529.466
Dual form			529.2.c.g.487.1

$q$ -expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.915415 - 2.00448i) q^{2} +(2.41153 + 0.708089i) q^{3} +(-1.87023 - 2.15836i) q^{4} +(-1.04019 + 0.668491i) q^{5} +(3.62690 - 4.18567i) q^{6} +(0.337683 - 2.34863i) q^{7} +(-1.80972 + 0.531382i) q^{8} +(2.79032 + 1.79323i) q^{9} +(0.387769 + 2.69699i) q^{10} +(-0.794209 - 1.73907i) q^{11} +(-2.98181 - 6.52924i) q^{12} +(-0.0279611 - 0.194474i) q^{13} +(-4.39867 - 2.82685i) q^{14} +(-2.98181 + 0.875537i) q^{15} +(0.221378 - 1.53972i) q^{16} +(1.02152 - 1.17890i) q^{17} +(6.14880 - 3.95159i) q^{18} +(5.22871 + 6.03425i) q^{19} +(3.38825 + 0.994879i) q^{20} +(2.47737 - 5.42469i) q^{21} -4.21297 q^{22} -4.74046 q^{24} +(-1.44196 + 3.15744i) q^{25} +(-0.415415 - 0.121977i) q^{26} +(0.521521 + 0.601867i) q^{27} +(-5.70075 + 3.66365i) q^{28} +(-3.25945 + 3.76160i) q^{29} +(-0.974593 + 6.77845i) q^{30} +(-1.71047 + 0.502239i) q^{31} +(-6.05710 - 3.89266i) q^{32} +(-0.683838 - 4.75620i) q^{33} +(-1.42796 - 3.12680i) q^{34} +(1.21879 + 2.66877i) q^{35} +(-1.34811 - 9.37628i) q^{36} +(3.26678 + 2.09943i) q^{37} +(16.8820 - 4.95699i) q^{38} +(0.0702757 - 0.488779i) q^{39} +(1.52723 - 1.76252i) q^{40} +(0.358791 - 0.230581i) q^{41} +(-8.60586 - 9.93169i) q^{42} +(-4.27279 - 1.25460i) q^{43} +(-2.26820 + 4.96666i) q^{44} -4.10123 q^{45} -2.58842 q^{47} +(1.62412 - 3.55633i) q^{48} +(1.31440 + 0.385942i) q^{49} +(5.00904 + 5.78074i) q^{50} +(3.29819 - 2.11962i) q^{51} +(-0.367451 + 0.424061i) q^{52} +(-1.39745 + 9.71945i) q^{53} +(1.68384 - 0.494420i) q^{54} +(1.98869 + 1.27805i) q^{55} +(0.636911 + 4.42981i) q^{56} +(8.33640 + 18.2542i) q^{57} +(4.55631 + 9.97693i) q^{58} +(1.02736 + 7.14543i) q^{59} +(7.46639 + 4.79836i) q^{60} +(-7.12871 + 2.09318i) q^{61} +(-0.559061 + 3.88835i) q^{62} +(5.15389 - 5.94790i) q^{63} +(-10.7303 + 6.89594i) q^{64} +(0.159089 + 0.183599i) q^{65} +(-10.1597 - 2.98316i) q^{66} +(3.01861 - 6.60984i) q^{67} -4.45497 q^{68} +6.46519 q^{70} +(-0.303371 + 0.664289i) q^{71} +(-6.00260 - 1.76252i) q^{72} +(4.22014 + 4.87031i) q^{73} +(7.19872 - 4.62634i) q^{74} +(-5.71307 + 6.59323i) q^{75} +(3.24520 - 22.5709i) q^{76} +(-4.35264 + 1.27805i) q^{77} +(-0.915415 - 0.588302i) q^{78} +(0.808075 + 5.62029i) q^{79} +(0.799013 + 1.74960i) q^{80} +(-3.30214 - 7.23067i) q^{81} +(-0.133752 - 0.930267i) q^{82} +(-10.8435 - 6.96872i) q^{83} +(-16.3417 + 4.79836i) q^{84} +(-0.274495 + 1.90916i) q^{85} +(-6.42620 + 7.41623i) q^{86} +(-10.5238 + 6.76324i) q^{87} +(2.36141 + 2.72521i) q^{88} +(13.3372 + 3.91615i) q^{89} +(-3.75433 + 8.22083i) q^{90} -0.466190 q^{91} -4.48047 q^{93} +(-2.36948 + 5.18843i) q^{94} +(-9.47270 - 2.78144i) q^{95} +(-11.8505 - 13.6762i) q^{96} +(3.63739 - 2.33761i) q^{97} +(1.97683 - 2.28139i) q^{98} +(0.902465 - 6.27678i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$10 q + 4 q^{2} + 4 q^{3} - 14 q^{4} + 8 q^{5} + 17 q^{6} + 6 q^{7} - 7 q^{8} + 9 q^{9} + 12 q^{10} - 4 q^{11} + q^{12} - 14 q^{13} - 2 q^{14} + q^{15} + 12 q^{16} + 12 q^{17} + 19 q^{18} + 24 q^{19} - 9 q^{20}+ \cdots - 30 q^{99}+O(q^{100})$ 10 * q + 4 * q^2 + 4 * q^3 - 14 * q^4 + 8 * q^5 + 17 * q^6 + 6 * q^7 - 7 * q^8 + 9 * q^9 + 12 * q^10 - 4 * q^11 + q^12 - 14 * q^13 - 2 * q^14 + q^15 + 12 * q^16 + 12 * q^17 + 19 * q^18 + 24 * q^19 - 9 * q^20 + 20 * q^21 - 6 * q^22 - 38 * q^24 + 7 * q^25 + q^26 + 7 * q^27 - 15 * q^28 - 30 * q^29 + 7 * q^30 - 12 * q^31 - q^32 - 6 * q^33 - 4 * q^34 - 4 * q^35 - 17 * q^36 - 8 * q^37 + 36 * q^38 - 10 * q^39 + q^40 + 7 * q^41 - 14 * q^42 - 11 * q^43 - 12 * q^44 - 6 * q^45 - 18 * q^47 - 15 * q^48 - 7 * q^49 + 5 * q^50 + 18 * q^51 + 13 * q^52 + 7 * q^53 + 16 * q^54 - 34 * q^55 - 13 * q^56 + 14 * q^57 + 10 * q^58 + 34 * q^59 + 25 * q^60 - 19 * q^61 - 18 * q^62 + q^63 - 31 * q^64 + 2 * q^65 - 9 * q^66 - 21 * q^67 - 30 * q^68 + 38 * q^70 + 8 * q^71 - 3 * q^72 + 8 * q^73 + 10 * q^74 + 5 * q^75 - 38 * q^76 + 2 * q^77 - 4 * q^78 - 48 * q^79 + 36 * q^80 + 22 * q^81 + 5 * q^82 - 15 * q^83 - 39 * q^84 + 36 * q^85 - 33 * q^86 - 23 * q^87 - 28 * q^88 + 58 * q^89 + 24 * q^90 - 4 * q^91 + 4 * q^93 - 27 * q^94 - 16 * q^95 + 4 * q^96 - 34 * q^97 - 27 * q^98 - 30 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/529\mathbb{Z}\right)^\times$ .

$n$	$5$
$\chi(n)$	$e\left(\frac{9}{11}\right)$

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

)

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

$2$	0.915415	−	2.00448i	0.647296	−	1.41738i	−0.246605	−	0.969116i	$-0.579315\pi$
$2$	0.915415	−	2.00448i	0.647296	−	1.41738i	0.893901	−	0.448265i	$-0.147958\pi$
$3$	2.41153	+	0.708089i	1.39230	+	0.408815i	0.890032	−	0.455898i	$-0.150682\pi$
$3$	2.41153	+	0.708089i	1.39230	+	0.408815i	0.502265	+	0.864714i	$0.332500\pi$
$4$	−1.87023	−	2.15836i	−0.935116	−	1.07918i
$5$	−1.04019	+	0.668491i	−0.465188	+	0.298958i	−0.752160	−	0.658981i	$-0.770988\pi$
$5$	−1.04019	+	0.668491i	−0.465188	+	0.298958i	0.286972	+	0.957939i	$0.407351\pi$
$6$	3.62690	−	4.18567i	1.48068	−	1.70879i
$7$	0.337683	−	2.34863i	0.127632	−	0.887700i	−0.820912	−	0.571055i	$-0.806534\pi$
$7$	0.337683	−	2.34863i	0.127632	−	0.887700i	0.948544	−	0.316645i	$-0.102557\pi$
$8$	−1.80972	+	0.531382i	−0.639833	+	0.187872i
$9$	2.79032	+	1.79323i	0.930108	+	0.597744i
$10$	0.387769	+	2.69699i	0.122623	+	0.852863i
$11$	−0.794209	−	1.73907i	−0.239463	−	0.524351i	0.751299	−	0.659962i	$-0.229428\pi$
$11$	−0.794209	−	1.73907i	−0.239463	−	0.524351i	−0.990762	+	0.135611i	$0.956700\pi$
$12$	−2.98181	−	6.52924i	−0.860773	−	1.88483i
$13$	−0.0279611	−	0.194474i	−0.00775502	−	0.0539374i	0.985576	−	0.169231i	$-0.0541283\pi$
$13$	−0.0279611	−	0.194474i	−0.00775502	−	0.0539374i	−0.993331	+	0.115293i	$0.963219\pi$
$14$	−4.39867	−	2.82685i	−1.17559	−	0.755508i
$15$	−2.98181	+	0.875537i	−0.769899	+	0.226063i
$16$	0.221378	−	1.53972i	0.0553446	−	0.384930i
$17$	1.02152	−	1.17890i	0.247755	−	0.285925i	−0.618227	−	0.786000i	$-0.712149\pi$
$17$	1.02152	−	1.17890i	0.247755	−	0.285925i	0.865982	+	0.500075i	$0.166694\pi$
$18$	6.14880	−	3.95159i	1.44929	−	0.931399i
$19$	5.22871	+	6.03425i	1.19955	+	1.38435i	0.903171	+	0.429281i	$0.141233\pi$
$19$	5.22871	+	6.03425i	1.19955	+	1.38435i	0.296377	+	0.955071i	$0.404222\pi$
$20$	3.38825	+	0.994879i	0.757635	+	0.222462i
$21$	2.47737	−	5.42469i	0.540607	−	1.18376i
$22$	−4.21297			−0.898208
$23$		0			0
$23$		0			0
$24$	−4.74046			−0.967643
$25$	−1.44196	+	3.15744i	−0.288391	+	0.631488i
$26$	−0.415415	−	0.121977i	−0.0814696	−	0.0239216i
$27$	0.521521	+	0.601867i	0.100367	+	0.115829i
$28$	−5.70075	+	3.66365i	−1.07734	+	0.692364i
$29$	−3.25945	+	3.76160i	−0.605264	+	0.698512i	−0.972839	−	0.231482i	$-0.925643\pi$
$29$	−3.25945	+	3.76160i	−0.605264	+	0.698512i	0.367575	+	0.929994i	$0.380188\pi$
$30$	−0.974593	+	6.77845i	−0.177936	+	1.23757i
$31$	−1.71047	+	0.502239i	−0.307209	+	0.0902047i	−0.431703	−	0.902016i	$-0.642087\pi$
$31$	−1.71047	+	0.502239i	−0.307209	+	0.0902047i	0.124494	+	0.992220i	$0.460269\pi$
$32$	−6.05710	−	3.89266i	−1.07075	−	0.688132i
$33$	−0.683838	−	4.75620i	−0.119041	−	0.827948i
$34$	−1.42796	−	3.12680i	−0.244893	−	0.536241i
$35$	1.21879	+	2.66877i	0.206012	+	0.451104i
$36$	−1.34811	−	9.37628i	−0.224684	−	1.56271i
$37$	3.26678	+	2.09943i	0.537055	+	0.345144i	0.780886	−	0.624673i	$-0.214768\pi$
$37$	3.26678	+	2.09943i	0.537055	+	0.345144i	−0.243831	+	0.969818i	$0.578404\pi$
$38$	16.8820	−	4.95699i	2.73862	−	0.804130i
$39$	0.0702757	−	0.488779i	0.0112531	−	0.0782672i
$40$	1.52723	−	1.76252i	0.241477	−	0.278679i
$41$	0.358791	−	0.230581i	0.0560338	−	0.0360107i	−0.512324	−	0.858792i	$-0.671215\pi$
$41$	0.358791	−	0.230581i	0.0560338	−	0.0360107i	0.568358	+	0.822782i	$0.307579\pi$
$42$	−8.60586	−	9.93169i	−1.32791	−	1.53249i
$43$	−4.27279	−	1.25460i	−0.651594	−	0.191325i	−0.0608027	−	0.998150i	$-0.519366\pi$
$43$	−4.27279	−	1.25460i	−0.651594	−	0.191325i	−0.590791	+	0.806825i	$0.701184\pi$
$44$	−2.26820	+	4.96666i	−0.341944	+	0.748752i
$45$	−4.10123			−0.611375
$46$		0			0
$47$	−2.58842			−0.377559			−0.188780	−	0.982019i	$-0.560453\pi$
$47$	−2.58842			−0.377559			−0.188780	+	0.982019i	$0.560453\pi$
$48$	1.62412	−	3.55633i	0.234422	−	0.513312i
$49$	1.31440	+	0.385942i	0.187771	+	0.0551346i
$50$	5.00904	+	5.78074i	0.708385	+	0.817520i
$51$	3.29819	−	2.11962i	0.461839	−	0.296806i
$52$	−0.367451	+	0.424061i	−0.0509563	+	0.0588067i
$53$	−1.39745	+	9.71945i	−0.191954	+	1.33507i	0.634875	+	0.772615i	$0.281052\pi$
$53$	−1.39745	+	9.71945i	−0.191954	+	1.33507i	−0.826829	+	0.562454i	$0.809857\pi$
$54$	1.68384	−	0.494420i	0.229141	−	0.0672820i
$55$	1.98869	+	1.27805i	0.268154	+	0.172332i
$56$	0.636911	+	4.42981i	0.0851108	+	0.591959i
$57$	8.33640	+	18.2542i	1.10418	+	2.41782i
$58$	4.55631	+	9.97693i	0.598273	+	1.31003i
$59$	1.02736	+	7.14543i	0.133750	+	0.930255i	0.940605	+	0.339504i	$0.110259\pi$
$59$	1.02736	+	7.14543i	0.133750	+	0.930255i	−0.806854	+	0.590751i	$0.798832\pi$
$60$	7.46639	+	4.79836i	0.963907	+	0.619465i
$61$	−7.12871	+	2.09318i	−0.912737	+	0.268004i	−0.704193	−	0.710009i	$-0.748691\pi$
$61$	−7.12871	+	2.09318i	−0.912737	+	0.268004i	−0.208545	+	0.978013i	$0.566873\pi$
$62$	−0.559061	+	3.88835i	−0.0710008	+	0.493822i
$63$	5.15389	−	5.94790i	0.649329	−	0.749366i
$64$	−10.7303	+	6.89594i	−1.34129	+	0.861992i
$65$	0.159089	+	0.183599i	0.0197326	+	0.0227726i
$66$	−10.1597	−	2.98316i	−1.25057	−	0.367201i
$67$	3.01861	−	6.60984i	0.368782	−	0.807521i	−0.630721	−	0.776010i	$-0.717241\pi$
$67$	3.01861	−	6.60984i	0.368782	−	0.807521i	0.999503	−	0.0315110i	$-0.0100319\pi$
$68$	−4.45497			−0.540244
$69$		0			0
$70$	6.46519			0.772738
$71$	−0.303371	+	0.664289i	−0.0360035	+	0.0788366i	−0.926779	−	0.375606i	$-0.877434\pi$
$71$	−0.303371	+	0.664289i	−0.0360035	+	0.0788366i	0.890776	+	0.454443i	$0.150162\pi$
$72$	−6.00260	−	1.76252i	−0.707413	−	0.207715i
$73$	4.22014	+	4.87031i	0.493931	+	0.570026i	0.946912	−	0.321494i	$-0.104185\pi$
$73$	4.22014	+	4.87031i	0.493931	+	0.570026i	−0.452981	+	0.891520i	$0.649639\pi$
$74$	7.19872	−	4.62634i	0.836834	−	0.537801i
$75$	−5.71307	+	6.59323i	−0.659688	+	0.761321i
$76$	3.24520	−	22.5709i	0.372250	−	2.58906i
$77$	−4.35264	+	1.27805i	−0.496029	+	0.145647i
$78$	−0.915415	−	0.588302i	−0.103650	−	0.0666120i
$79$	0.808075	+	5.62029i	0.0909156	+	0.632332i	0.983427	+	0.181306i	$0.0580326\pi$
$79$	0.808075	+	5.62029i	0.0909156	+	0.632332i	−0.892511	+	0.451025i	$0.851058\pi$
$80$	0.799013	+	1.74960i	0.0893324	+	0.195611i
$81$	−3.30214	−	7.23067i	−0.366904	−	0.803408i
$82$	−0.133752	−	0.930267i	−0.0147705	−	0.102731i
$83$	−10.8435	−	6.96872i	−1.19023	−	0.764916i	−0.212993	−	0.977054i	$-0.568321\pi$
$83$	−10.8435	−	6.96872i	−1.19023	−	0.764916i	−0.977240	+	0.212137i	$0.931958\pi$
$84$	−16.3417	+	4.79836i	−1.78303	+	0.523544i
$85$	−0.274495	+	1.90916i	−0.0297732	+	0.207077i
$86$	−6.42620	+	7.41623i	−0.692955	+	0.799712i
$87$	−10.5238	+	6.76324i	−1.12827	+	0.725095i
$88$	2.36141	+	2.72521i	0.251727	+	0.290509i
$89$	13.3372	+	3.91615i	1.41374	+	0.415111i	0.897378	−	0.441262i	$-0.145469\pi$
$89$	13.3372	+	3.91615i	1.41374	+	0.415111i	0.516359	+	0.856372i	$0.327287\pi$
$90$	−3.75433	+	8.22083i	−0.395741	+	0.866552i
$91$	−0.466190			−0.0488700
$92$		0			0
$93$	−4.48047			−0.464603
$94$	−2.36948	+	5.18843i	−0.244393	+	0.535146i
$95$	−9.47270	−	2.78144i	−0.971879	−	0.285369i
$96$	−11.8505	−	13.6762i	−1.20949	−	1.39582i
$97$	3.63739	−	2.33761i	0.369321	−	0.237348i	−0.342795	−	0.939410i	$-0.611374\pi$
$97$	3.63739	−	2.33761i	0.369321	−	0.237348i	0.712116	+	0.702062i	$0.247737\pi$
$98$	1.97683	−	2.28139i	0.199690	−	0.230455i
$99$	0.902465	−	6.27678i	0.0907011	−	0.630840i
$100$	9.51169	−	2.79288i	0.951169	−	0.279288i
$101$	−1.53131	−	0.984116i	−0.152372	−	0.0979232i	0.462233	−	0.886758i	$-0.347048\pi$
$101$	−1.53131	−	0.984116i	−0.152372	−	0.0979232i	−0.614605	+	0.788835i	$0.710685\pi$
$102$	−1.22952	−	8.55149i	−0.121740	−	0.846724i
$103$	−6.36135	−	13.9294i	−0.626802	−	1.37250i	−0.910467	−	0.413582i	$-0.864278\pi$
$103$	−6.36135	−	13.9294i	−0.626802	−	1.37250i	0.283665	−	0.958923i	$-0.408450\pi$
$104$	0.153942	+	0.337086i	0.0150952	+	0.0330540i
$105$	1.04941	+	7.29882i	0.102412	+	0.712292i
$106$	18.2032	+	11.6985i	1.76805	+	1.13626i
$107$	−1.90779	+	0.560177i	−0.184433	+	0.0541543i	−0.372645	−	0.927974i	$-0.621549\pi$
$107$	−1.90779	+	0.560177i	−0.184433	+	0.0541543i	0.188212	+	0.982128i	$0.439731\pi$
$108$	0.323683	−	2.25126i	0.0311464	−	0.216628i
$109$	−10.2124	+	11.7857i	−0.978171	+	1.12887i	0.0134782	+	0.999909i	$0.495710\pi$
$109$	−10.2124	+	11.7857i	−0.978171	+	1.12887i	−0.991650	+	0.128961i	$0.958836\pi$
$110$	4.38230	−	2.81633i	0.417836	−	0.268527i
$111$	6.39135	+	7.37601i	0.606640	+	0.700100i
$112$	−3.54149	−	1.03987i	−0.334639	−	0.0982588i
$113$	−0.618239	+	1.35376i	−0.0581591	+	0.127351i	−0.936480	−	0.350721i	$-0.885937\pi$
$113$	−0.618239	+	1.35376i	−0.0581591	+	0.127351i	0.878321	+	0.478071i	$0.158664\pi$
$114$	44.2213			4.14171
$115$		0			0
$116$	14.2148			1.31981
$117$	0.270716	−	0.592786i	0.0250277	−	0.0548031i
$118$	15.2633	+	4.48171i	1.40510	+	0.412575i
$119$	−2.42385	−	2.79727i	−0.222194	−	0.256426i
$120$	4.93099	−	3.16896i	0.450136	−	0.289285i
$121$	4.80986	−	5.55087i	0.437260	−	0.504624i
$122$	−2.33000	+	16.2055i	−0.210948	+	1.46717i
$123$	1.02851	−	0.301997i	0.0927374	−	0.0272302i
$124$	4.28298	+	2.75251i	0.384623	+	0.247182i
$125$	−1.49066	−	10.3677i	−0.133328	−	0.927319i
$126$	−7.20450	−	15.7757i	−0.641828	−	1.40541i
$127$	2.49015	+	5.45267i	0.220965	+	0.483846i	0.987354	−	0.158531i	$-0.0506757\pi$
$127$	2.49015	+	5.45267i	0.220965	+	0.483846i	−0.766389	+	0.642377i	$0.777948\pi$
$128$	1.95074	+	13.5677i	0.172423	+	1.19923i
$129$	−9.41558	−	6.05102i	−0.828995	−	0.532763i
$130$	0.513652	−	0.150822i	0.0450503	−	0.0132279i
$131$	1.81719	−	12.6389i	0.158769	−	1.10426i	−0.742137	−	0.670248i	$-0.766188\pi$
$131$	1.81719	−	12.6389i	0.158769	−	1.10426i	0.900906	−	0.434014i	$-0.142903\pi$
$132$	−8.98666	+	10.3712i	−0.782189	+	0.902694i
$133$	15.9379	−	10.2427i	1.38199	−	0.888151i
$134$	−10.4860	−	12.1015i	−0.905853	−	1.04541i
$135$	−0.944825	−	0.277426i	−0.0813176	−	0.0238770i
$136$	−1.22222	+	2.67629i	−0.104805	+	0.229490i
$137$	0.697560			0.0595966			0.0297983	−	0.999556i	$-0.490514\pi$
$137$	0.697560			0.0595966			0.0297983	+	0.999556i	$0.490514\pi$
$138$		0			0
$139$	13.9559			1.18372			0.591862	−	0.806039i	$-0.298393\pi$
$139$	13.9559			1.18372			0.591862	+	0.806039i	$0.298393\pi$
$140$	3.48076	−	7.62179i	0.294178	−	0.644159i
$141$	−6.24204	−	1.83283i	−0.525675	−	0.154352i
$142$	1.05384	+	1.21620i	0.0884366	+	0.102061i
$143$	−0.315998	+	0.203079i	−0.0264251	+	0.0169824i
$144$	3.37879	−	3.89934i	0.281566	−	0.324945i
$145$	0.875855	−	6.09170i	0.0727358	−	0.505888i
$146$	13.6256	−	4.00084i	1.12766	−	0.331112i
$147$	2.89643	+	1.86142i	0.238893	+	0.153527i
$148$	−1.57830	−	10.9773i	−0.129735	−	0.902329i
$149$	−6.91210	−	15.1354i	−0.566262	−	1.23994i	−0.948764	−	0.315985i	$-0.897665\pi$
$149$	−6.91210	−	15.1354i	−0.566262	−	1.23994i	0.382502	−	0.923954i	$-0.375062\pi$
$150$	7.98617	+	17.4873i	0.652068	+	1.42783i
$151$	−1.87713	−	13.0557i	−0.152759	−	1.06246i	−0.911569	−	0.411147i	$-0.865128\pi$
$151$	−1.87713	−	13.0557i	−0.152759	−	1.06246i	0.758810	−	0.651312i	$-0.225781\pi$
$152$	−12.6690	−	8.14187i	−1.02759	−	0.660393i
$153$	4.96441	−	1.45768i	0.401349	−	0.117847i
$154$	−1.42265	+	9.89472i	−0.114640	+	0.797340i
$155$	1.44347	−	1.66586i	0.115943	−	0.133805i
$156$	−1.18639	+	0.762448i	−0.0949874	+	0.0610447i
$157$	−2.70371	−	3.12024i	−0.215779	−	0.249023i	0.637533	−	0.770423i	$-0.279955\pi$
$157$	−2.70371	−	3.12024i	−0.215779	−	0.249023i	−0.853312	+	0.521401i	$0.825410\pi$
$158$	12.0055	+	3.52513i	0.955104	+	0.280444i
$159$	−10.2522	+	22.4492i	−0.813053	+	1.78034i
$160$	8.90276			0.703825
$161$		0			0
$162$	−17.5166			−1.37623
$163$	−6.14370	+	13.4528i	−0.481212	+	1.05371i	0.500917	+	0.865496i	$0.332996\pi$
$163$	−6.14370	+	13.4528i	−0.481212	+	1.05371i	−0.982129	+	0.188211i	$0.939731\pi$
$164$	−1.16870	−	0.343161i	−0.0912601	−	0.0267964i
$165$	3.89080	+	4.49022i	0.302898	+	0.349563i
$166$	−23.8950	+	15.3564i	−1.85461	+	1.19189i
$167$	−0.870797	+	1.00495i	−0.0673843	+	0.0777656i	−0.788441	−	0.615111i	$-0.789111\pi$
$167$	−0.870797	+	1.00495i	−0.0673843	+	0.0777656i	0.721057	+	0.692876i	$0.243657\pi$
$168$	−1.60077	+	11.1336i	−0.123502	+	0.858977i
$169$	12.4364	−	3.65165i	0.956644	−	0.280896i
$170$	3.57559	+	2.29789i	0.274235	+	0.176240i
$171$	3.76897	+	26.2138i	0.288221	+	2.00462i
$172$	5.28321	+	11.5686i	0.402841	+	0.882099i
$173$	−7.03549	−	15.4056i	−0.534898	−	1.17126i	−0.963485	−	0.267763i	$-0.913715\pi$
$173$	−7.03549	−	15.4056i	−0.534898	−	1.17126i	0.428586	−	0.903501i	$-0.359012\pi$
$174$	3.92312	+	27.2859i	0.297411	+	2.06854i
$175$	6.92875	+	4.45284i	0.523764	+	0.336603i
$176$	−2.85351	+	0.837866i	−0.215091	+	0.0631565i
$177$	−2.58209	+	17.9589i	−0.194082	+	1.34987i
$178$	20.0589	−	23.1492i	1.50348	−	1.73510i
$179$	−1.20413	+	0.773846i	−0.0900007	+	0.0578400i	−0.584867	−	0.811129i	$-0.698853\pi$
$179$	−1.20413	+	0.773846i	−0.0900007	+	0.0578400i	0.494866	+	0.868969i	$0.335217\pi$
$180$	7.67025	+	8.85194i	0.571707	+	0.659785i
$181$	15.4779	+	4.54473i	1.15047	+	0.337807i	0.800721	−	0.599038i	$-0.204450\pi$
$181$	15.4779	+	4.54473i	1.15047	+	0.337807i	0.349745	+	0.936845i	$0.386268\pi$
$182$	−0.426757	+	0.934468i	−0.0316334	+	0.0692674i
$183$	−18.6732			−1.38037
$184$		0			0
$185$	−4.80153			−0.353015
$186$	−4.10149	+	8.98102i	−0.300736	+	0.658520i
$187$	−2.86149	−	0.840210i	−0.209253	−	0.0614422i
$188$	4.84094	+	5.58674i	0.353062	+	0.407455i
$189$	1.58967	−	1.02162i	0.115632	−	0.0743120i
$190$	−14.2468	+	16.4417i	−1.03357	+	1.19280i
$191$	2.95225	−	20.5333i	0.213617	−	1.48574i	−0.547325	−	0.836920i	$-0.684354\pi$
$191$	2.95225	−	20.5333i	0.213617	−	1.48574i	0.760942	−	0.648820i	$-0.224737\pi$
$192$	−30.7593	+	9.03176i	−2.21986	+	0.651811i
$193$	12.3263	+	7.92161i	0.887264	+	0.570210i	0.902988	−	0.429667i	$-0.141369\pi$
$193$	12.3263	+	7.92161i	0.887264	+	0.570210i	−0.0157239	+	0.999876i	$0.505005\pi$
$194$	−1.35597	−	9.43095i	−0.0973527	−	0.677103i
$195$	0.253644	+	0.555402i	0.0181638	+	0.0397732i
$196$	−1.62523	−	3.55875i	−0.116088	−	0.254196i
$197$	−1.66194	−	11.5590i	−0.118408	−	0.823547i	−0.959309	−	0.282358i	$-0.908883\pi$
$197$	−1.66194	−	11.5590i	−0.118408	−	0.823547i	0.840901	−	0.541189i	$-0.182026\pi$
$198$	−11.7555	−	7.55483i	−0.835430	−	0.536898i
$199$	5.49157	−	1.61247i	0.389287	−	0.114305i	−0.0812311	−	0.996695i	$-0.525885\pi$
$199$	5.49157	−	1.61247i	0.389287	−	0.114305i	0.470518	+	0.882390i	$0.344067\pi$
$200$	0.931729	−	6.48032i	0.0658832	−	0.458228i
$201$	11.9598	−	13.8024i	0.843581	−	0.973545i
$202$	−3.37443	+	2.16861i	−0.237424	+	0.152583i
$203$	7.73397	+	8.92548i	0.542818	+	0.626446i
$204$	−10.7433	−	3.15451i	−0.752180	−	0.220860i
$205$	−0.219070	+	0.479697i	−0.0153005	+	0.0335035i
$206$	−33.7445			−2.35109
$207$		0			0
$208$	−0.305626			−0.0211913
$209$	6.34133	−	13.8856i	0.438639	−	0.960485i
$210$	15.5910	+	4.57793i	1.07588	+	0.315907i
$211$	9.21241	+	10.6317i	0.634208	+	0.731916i	0.978340	−	0.207006i	$-0.0663720\pi$
$211$	9.21241	+	10.6317i	0.634208	+	0.731916i	−0.344131	+	0.938922i	$0.611827\pi$
$212$	23.5916	−	15.1614i	1.62028	−	1.04129i
$213$	−1.20196	+	1.38714i	−0.0823572	+	0.0950453i
$214$	−0.623554	+	4.33691i	−0.0426253	+	0.296465i
$215$	5.28321	−	1.55129i	0.360312	−	0.105797i
$216$	−1.26363	−	0.812085i	−0.0859791	−	0.0552554i
$217$	0.601980	+	4.18686i	0.0408650	+	0.284223i
$218$	14.2757	+	31.2594i	0.966872	+	2.11715i
$219$	6.72839	+	14.7331i	0.454663	+	0.995572i
$220$	−0.960806	−	6.68255i	−0.0647775	−	0.450538i
$221$	−0.257828	−	0.165696i	−0.0173434	−	0.0111459i
$222$	20.6358	−	6.05921i	1.38498	−	0.406668i
$223$	0.598233	−	4.16080i	0.0400606	−	0.278628i	−0.959938	−	0.280212i	$-0.909595\pi$
$223$	0.598233	−	4.16080i	0.0400606	−	0.278628i	0.999999	+	0.00158434i	$0.000504311\pi$
$224$	−11.1878	+	12.9114i	−0.747517	+	0.862681i
$225$	−9.68555	+	6.22452i	−0.645703	+	0.414968i
$226$	2.14763	+	2.47850i	0.142858	+	0.164867i
$227$	−17.6842	−	5.19255i	−1.17374	−	0.344641i	−0.363983	−	0.931406i	$-0.618583\pi$
$227$	−17.6842	−	5.19255i	−1.17374	−	0.344641i	−0.809758	+	0.586764i	$0.800402\pi$
$228$	23.8081	−	52.1325i	1.57673	−	3.45256i
$229$	10.9247			0.721923			0.360961	−	0.932581i	$-0.382449\pi$
$229$	10.9247			0.721923			0.360961	+	0.932581i	$0.382449\pi$
$230$		0			0
$231$	−11.4015			−0.750163
$232$	3.89984	−	8.53947i	0.256037	−	0.560644i
$233$	−3.99612	−	1.17337i	−0.261795	−	0.0768699i	0.148201	−	0.988957i	$-0.452652\pi$
$233$	−3.99612	−	1.17337i	−0.261795	−	0.0768699i	−0.409996	+	0.912087i	$0.634470\pi$
$234$	−0.940409	−	1.08529i	−0.0614765	−	0.0709476i
$235$	2.69245	−	1.73033i	0.175636	−	0.112875i
$236$	13.5010	−	15.5810i	0.878841	−	1.01424i
$237$	−2.03097	+	14.1257i	−0.131925	+	0.917561i
$238$	−7.82590	+	2.29789i	−0.507278	+	0.148950i
$239$	−18.9426	−	12.1737i	−1.22530	−	0.787450i	−0.242145	−	0.970240i	$-0.577851\pi$
$239$	−18.9426	−	12.1737i	−1.22530	−	0.787450i	−0.983152	+	0.182790i	$0.941487\pi$
$240$	0.687975	+	4.78497i	0.0444086	+	0.308869i
$241$	2.46305	+	5.39333i	0.158659	+	0.347415i	0.972222	−	0.234063i	$-0.0752021\pi$
$241$	2.46305	+	5.39333i	0.158659	+	0.347415i	−0.813562	+	0.581478i	$0.802475\pi$
$242$	−6.72359	−	14.7226i	−0.432209	−	0.946405i
$243$	−3.18325	−	22.1400i	−0.204206	−	1.42028i
$244$	17.8502	+	11.4716i	1.14274	+	0.734394i
$245$	−1.62523	+	0.477209i	−0.103832	+	0.0304878i
$246$	0.336164	−	2.33807i	0.0214331	−	0.149070i
$247$	1.02730	−	1.18557i	0.0653658	−	0.0754361i
$248$	2.82859	−	1.81782i	0.179616	−	0.115432i
$249$	−21.2150	−	24.4835i	−1.34445	−	1.55158i
$250$	−22.1465	−	6.50280i	−1.40067	−	0.411273i
$251$	−0.644148	+	1.41049i	−0.0406582	+	0.0890291i	−0.928871	−	0.370403i	$-0.879220\pi$
$251$	−0.644148	+	1.41049i	−0.0406582	+	0.0890291i	0.888213	+	0.459432i	$0.151947\pi$
$252$	−22.4767			−1.41590
$253$		0			0
$254$	13.2093			0.828824
$255$	−2.01381	+	4.40962i	−0.126110	+	0.276141i
$256$	4.50498	+	1.32278i	0.281561	+	0.0826739i
$257$	−17.9811	−	20.7513i	−1.12163	−	1.29443i	−0.951033	−	0.309089i	$-0.899976\pi$
$257$	−17.9811	−	20.7513i	−1.12163	−	1.29443i	−0.170596	−	0.985341i	$-0.554569\pi$
$258$	−20.7483	+	13.3341i	−1.29173	+	0.830147i
$259$	6.03393	−	6.96352i	0.374930	−	0.432692i
$260$	0.0987388	−	0.686743i	0.00612352	−	0.0425900i
$261$	−15.8403	+	4.65114i	−0.980492	+	0.287899i
$262$	−23.6708	−	15.2123i	−1.46239	−	0.939821i
$263$	1.84165	+	12.8090i	0.113561	+	0.789836i	0.964407	+	0.264421i	$0.0851807\pi$
$263$	1.84165	+	12.8090i	0.113561	+	0.789836i	−0.850846	+	0.525415i	$0.823910\pi$
$264$	3.76492	+	8.24402i	0.231715	+	0.507384i
$265$	−5.04375	−	11.0443i	−0.309835	−	0.678444i
$266$	−5.94142	−	41.3235i	−0.364292	−	2.53370i
$267$	29.3900	+	18.8878i	1.79864	+	1.15591i
$268$	−19.9119	+	5.84667i	−1.21631	+	0.357142i
$269$	1.42282	−	9.89590i	0.0867506	−	0.603364i	−0.899352	−	0.437226i	$-0.855961\pi$
$269$	1.42282	−	9.89590i	0.0867506	−	0.603364i	0.986102	−	0.166138i	$-0.0531298\pi$
$270$	−1.42100	+	1.63992i	−0.0864793	+	0.0998025i
$271$	3.71110	−	2.38498i	0.225433	−	0.144877i	−0.423049	−	0.906107i	$-0.639040\pi$
$271$	3.71110	−	2.38498i	0.225433	−	0.144877i	0.648483	+	0.761230i	$0.275404\pi$
$272$	−1.58903	−	1.83384i	−0.0963492	−	0.111193i
$273$	−1.12423	−	0.330104i	−0.0680416	−	0.0199788i
$274$	0.638557	−	1.39824i	0.0385766	−	0.0844710i
$275$	6.63624			0.400180
$276$		0			0
$277$	−30.8042			−1.85085			−0.925423	−	0.378935i	$-0.876290\pi$
$277$	−30.8042			−1.85085			−0.925423	+	0.378935i	$0.876290\pi$
$278$	12.7755	−	27.9743i	0.766221	−	1.67779i
$279$	−5.67339	−	1.66586i	−0.339657	−	0.0997323i
$280$	−3.62380	−	4.18209i	−0.216563	−	0.249927i
$281$	−3.01111	+	1.93512i	−0.179627	+	0.115440i	−0.627365	−	0.778726i	$-0.715866\pi$
$281$	−3.01111	+	1.93512i	−0.179627	+	0.115440i	0.447737	+	0.894165i	$0.352230\pi$
$282$	−9.38793	+	10.8342i	−0.559043	+	0.645170i
$283$	−2.10347	+	14.6300i	−0.125038	+	0.869661i	0.826676	+	0.562678i	$0.190229\pi$
$283$	−2.10347	+	14.6300i	−0.125038	+	0.869661i	−0.951715	+	0.306984i	$0.900680\pi$
$284$	2.00115	−	0.587591i	0.118746	−	0.0348671i
$285$	−20.8742	−	13.4150i	−1.23648	−	0.794638i
$286$	0.117799	+	0.819313i	0.00696562	+	0.0484470i
$287$	−0.420393	−	0.920532i	−0.0248150	−	0.0543373i
$288$	−9.92082	−	21.7236i	−0.584590	−	1.28007i
$289$	2.07306	+	14.4184i	0.121945	+	0.848143i
$290$	−11.4089	−	7.33207i	−0.669955	−	0.430554i
$291$	10.4269	−	3.06161i	0.611236	−	0.179475i
$292$	2.61924	−	18.2172i	0.153279	−	1.06608i
$293$	−14.0883	+	16.2588i	−0.823048	+	0.949848i	−0.999405	−	0.0344778i	$-0.989023\pi$
$293$	−14.0883	+	16.2588i	−0.823048	+	0.949848i	0.176357	+	0.984326i	$0.443569\pi$
$294$	6.38262	−	4.10186i	0.372242	−	0.239225i
$295$	−5.84530	−	6.74584i	−0.340327	−	0.392758i
$296$	−7.02756	−	2.06348i	−0.408468	−	0.119937i
$297$	0.632495	−	1.38497i	0.0367011	−	0.0803642i
$298$	−36.6660			−2.12401
$299$		0			0
$300$	24.9153			1.43849
$301$	−4.38945	+	9.61155i	−0.253004	+	0.554001i
$302$	−27.8883	−	8.18873i	−1.60479	−	0.471208i
$303$	−2.99597	−	3.45753i	−0.172114	−	0.198630i
$304$	10.4486	−	6.71490i	0.599267	−	0.385126i
$305$	6.01596	−	6.94278i	0.344473	−	0.397543i
$306$	1.62260	−	11.2854i	0.0927580	−	0.645146i
$307$	−13.5720	+	3.98509i	−0.774593	+	0.227441i	−0.645058	−	0.764134i	$-0.723167\pi$
$307$	−13.5720	+	3.98509i	−0.774593	+	0.227441i	−0.129535	+	0.991575i	$0.541349\pi$
$308$	10.8989	+	7.00432i	0.621025	+	0.399108i
$309$	−5.47732	−	38.0956i	−0.311594	−	2.16718i
$310$	−2.01780	−	4.41836i	−0.114603	−	0.250946i
$311$	0.236844	+	0.518617i	0.0134302	+	0.0294081i	0.916228	−	0.400657i	$-0.131218\pi$
$311$	0.236844	+	0.518617i	0.0134302	+	0.0294081i	−0.902798	+	0.430065i	$0.858491\pi$
$312$	0.132549	+	0.921896i	0.00750409	+	0.0521921i
$313$	−17.7780	−	11.4252i	−1.00487	−	0.645792i	−0.0688107	−	0.997630i	$-0.521920\pi$
$313$	−17.7780	−	11.4252i	−1.00487	−	0.645792i	−0.936061	+	0.351838i	$0.885557\pi$
$314$	−8.72948	+	2.56321i	−0.492633	+	0.144650i
$315$	−1.38491	+	9.63229i	−0.0780311	+	0.542718i
$316$	10.6193	−	12.2554i	0.597384	−	0.689418i
$317$	−7.41324	+	4.76420i	−0.416369	+	0.267584i	−0.732009	−	0.681295i	$-0.761417\pi$
$317$	−7.41324	+	4.76420i	−0.416369	+	0.267584i	0.315640	+	0.948879i	$0.397781\pi$
$318$	35.6140	+	41.1007i	1.99713	+	2.30481i
$319$	9.13039	+	2.68092i	0.511204	+	0.150103i
$320$	6.55169	−	14.3462i	0.366251	−	0.801977i
$321$	−4.99734			−0.278924
$322$		0			0
$323$	12.4550			0.693015
$324$	−9.43065	+	20.6502i	−0.523925	+	1.14724i
$325$	0.654359	+	0.192137i	0.0362973	+	0.0106578i
$326$	21.3419	+	24.6298i	1.18202	+	1.36412i
$327$	−32.9729	+	21.1904i	−1.82340	+	1.17183i
$328$	−0.526785	+	0.607943i	−0.0290869	+	0.0335680i
$329$	−0.874064	+	6.07925i	−0.0481887	+	0.335160i
$330$	12.5623	−	3.68861i	0.691529	−	0.203051i
$331$	25.3953	+	16.3206i	1.39585	+	0.897061i	0.999776	−	0.0211559i	$-0.00673464\pi$
$331$	25.3953	+	16.3206i	1.39585	+	0.897061i	0.396078	+	0.918217i	$0.370371\pi$
$332$	5.23891	+	36.4374i	0.287522	+	1.99976i
$333$	5.35060	+	11.7162i	0.293211	+	0.642043i
$334$	1.21727	+	2.66544i	0.0666059	+	0.145847i
$335$	1.27868	+	8.89342i	0.0698618	+	0.485900i
$336$	−7.80407	−	5.01537i	−0.425747	−	0.273611i
$337$	4.75502	−	1.39620i	0.259023	−	0.0760559i	−0.149643	−	0.988740i	$-0.547812\pi$
$337$	4.75502	−	1.39620i	0.259023	−	0.0760559i	0.408666	+	0.912684i	$0.365994\pi$
$338$	4.06479	−	28.2712i	0.221095	−	1.53775i
$339$	−2.44948	+	2.82685i	−0.133038	+	0.153534i
$340$	4.63402	−	2.97811i	0.251315	−	0.161510i
$341$	2.23190	+	2.57575i	0.120864	+	0.139485i
$342$	55.9952	+	16.4417i	3.02787	+	0.889064i
$343$	8.25012	−	18.0652i	0.445465	−	0.975432i
$344$	8.39923			0.452856
$345$		0			0
$346$	−37.3205			−2.00636
$347$	−2.81110	+	6.15544i	−0.150908	+	0.330441i	−0.969955	−	0.243284i	$-0.921775\pi$
$347$	−2.81110	+	6.15544i	−0.150908	+	0.330441i	0.819047	+	0.573726i	$0.194502\pi$
$348$	34.2795	+	10.0654i	1.83757	+	0.539560i
$349$	−6.60875	−	7.62691i	−0.353759	−	0.408259i	0.550780	−	0.834650i	$-0.314330\pi$
$349$	−6.60875	−	7.62691i	−0.353759	−	0.408259i	−0.904539	+	0.426391i	$0.859785\pi$
$350$	15.2683	−	9.81234i	0.816125	−	0.524492i
$351$	0.102465	−	0.118251i	0.00546919	−	0.00631178i
$352$	−1.95903	+	13.6253i	−0.104417	+	0.726233i
$353$	−23.4781	+	6.89379i	−1.24961	+	0.366919i	−0.838619	−	0.544719i	$-0.816636\pi$
$353$	−23.4781	+	6.89379i	−1.24961	+	0.366919i	−0.410994	+	0.911638i	$0.634818\pi$
$354$	33.6345	+	21.6156i	1.78765	+	1.14885i
$355$	−0.128507	−	0.893789i	−0.00682047	−	0.0474374i
$356$	−16.4911	−	36.1105i	−0.874028	−	1.91385i
$357$	−3.86447	−	8.46200i	−0.204529	−	0.447857i
$358$	0.448882	+	3.12204i	0.0237241	+	0.165005i
$359$	0.352328	+	0.226427i	0.0185952	+	0.0119504i	0.549905	−	0.835227i	$-0.314664\pi$
$359$	0.352328	+	0.226427i	0.0185952	+	0.0119504i	−0.531310	+	0.847177i	$0.678300\pi$
$360$	7.42209	−	2.17932i	0.391178	−	0.114860i
$361$	−6.36881	+	44.2960i	−0.335201	+	2.33137i
$362$	23.2785	−	26.8649i	1.22349	−	1.41199i
$363$	15.5296	−	9.98028i	0.815093	−	0.523829i
$364$	0.871883	+	1.00621i	0.0456991	+	0.0527396i
$365$	−7.64552	−	2.24493i	−0.400185	−	0.117505i
$366$	−17.0938	+	37.4301i	−0.893505	+	1.95650i
$367$	28.5682			1.49125			0.745624	−	0.666367i	$-0.232151\pi$
$367$	28.5682			1.49125			0.745624	+	0.666367i	$0.232151\pi$
$368$		0			0
$369$	1.41463			0.0736426
$370$	−4.39539	+	9.62456i	−0.228505	+	0.500357i
$371$	22.3555	+	6.56417i	1.16064	+	0.340795i
$372$	8.37952	+	9.67048i	0.434458	+	0.501391i
$373$	12.1206	−	7.78943i	0.627580	−	0.403321i	−0.187833	−	0.982201i	$-0.560146\pi$
$373$	12.1206	−	7.78943i	0.627580	−	0.403321i	0.815413	+	0.578880i	$0.196510\pi$
$374$	−4.30364	+	4.96666i	−0.222536	+	0.256820i
$375$	3.74652	−	26.0576i	0.193470	−	1.34561i
$376$	4.68431	−	1.37544i	0.241575	−	0.0709328i
$377$	0.822672	+	0.528699i	0.0423698	+	0.0272294i
$378$	−0.592608	−	4.12168i	−0.0304804	−	0.211996i
$379$	−2.33759	−	5.11861i	−0.120074	−	0.262925i	0.840045	−	0.542516i	$-0.182528\pi$
$379$	−2.33759	−	5.11861i	−0.120074	−	0.262925i	−0.960119	+	0.279591i	$0.909801\pi$
$380$	11.7128	+	25.6474i	0.600854	+	1.31569i
$381$	2.14410	+	14.9125i	0.109845	+	0.763991i
$382$	−38.4561	−	24.7143i	−1.96759	−	1.26449i
$383$	−0.222276	+	0.0652662i	−0.0113578	+	0.00333495i	−0.287407	−	0.957809i	$-0.592793\pi$
$383$	−0.222276	+	0.0652662i	−0.0113578	+	0.00333495i	0.276049	+	0.961144i	$0.410975\pi$
$384$	−4.90286	+	34.1002i	−0.250198	+	1.74017i
$385$	3.67322	−	4.23912i	0.187204	−	0.216045i
$386$	27.1623	−	17.4562i	1.38253	−	0.888496i
$387$	−9.67266	−	11.1628i	−0.491689	−	0.567439i
$388$	−11.8482	−	3.47893i	−0.601499	−	0.176616i
$389$	−12.5330	+	27.4434i	−0.635448	+	1.39144i	0.268285	+	0.963340i	$0.413543\pi$
$389$	−12.5330	+	27.4434i	−0.635448	+	1.39144i	−0.903733	+	0.428097i	$0.859184\pi$
$390$	1.34548			0.0681311
$391$		0			0
$392$	−2.58378			−0.130500
$393$	13.3316	−	29.1922i	0.672493	−	1.47255i
$394$	−24.6912	−	7.24999i	−1.24393	−	0.365249i
$395$	−4.59767	−	5.30599i	−0.231334	−	0.266973i
$396$	−15.2354	+	9.79118i	−0.765607	+	0.492025i
$397$	8.54283	−	9.85896i	0.428753	−	0.494807i	−0.499731	−	0.866181i	$-0.666568\pi$
$397$	8.54283	−	9.85896i	0.428753	−	0.494807i	0.928483	+	0.371374i	$0.121113\pi$
$398$	1.79490	−	12.4838i	0.0899703	−	0.625757i
$399$	45.6874	−	13.4150i	2.28723	−	0.671592i
$400$	4.54236	+	2.91920i	0.227118	+	0.145960i
$401$	3.03497	+	21.1087i	0.151559	+	1.05412i	0.913608	+	0.406597i	$0.133285\pi$
$401$	3.03497	+	21.1087i	0.151559	+	1.05412i	−0.762048	+	0.647520i	$0.775806\pi$
$402$	−16.7184	−	36.6081i	−0.833837	−	1.82585i
$403$	0.145499	+	0.318598i	0.00724782	+	0.0158705i
$404$	0.739834	+	5.14566i	0.0368081	+	0.256006i
$405$	8.26850	+	5.31384i	0.410865	+	0.264047i
$406$	24.9707	−	7.33207i	1.23928	−	0.363884i
$407$	1.05656	−	7.34856i	0.0523719	−	0.364254i
$408$	−4.84248	+	5.58852i	−0.239739	+	0.276673i
$409$	−7.69665	+	4.94634i	−0.380575	+	0.244581i	−0.716916	−	0.697160i	$-0.754447\pi$
$409$	−7.69665	+	4.94634i	−0.380575	+	0.244581i	0.336341	+	0.941740i	$0.390810\pi$
$410$	0.761003	+	0.878244i	0.0375833	+	0.0433734i
$411$	1.68219	+	0.493934i	0.0829761	+	0.0243640i
$412$	−18.1675	+	39.7813i	−0.895049	+	1.95988i
$413$	17.1289			0.842859
$414$		0			0
$415$	15.9379			0.782360
$416$	−0.587658	+	1.28679i	−0.0288123	+	0.0630901i
$417$	33.6551	+	9.88203i	1.64810	+	0.483925i
$418$	−22.0284	−	25.4221i	−1.07744	−	1.24344i
$419$	−7.54957	+	4.85182i	−0.368821	+	0.237027i	−0.711902	−	0.702279i	$-0.752166\pi$
$419$	−7.54957	+	4.85182i	−0.368821	+	0.237027i	0.343081	+	0.939306i	$0.388530\pi$
$420$	13.7909	−	15.9155i	0.672925	−	0.776597i
$421$	−4.47897	+	31.1519i	−0.218292	+	1.51825i	0.526050	+	0.850454i	$0.323673\pi$
$421$	−4.47897	+	31.1519i	−0.218292	+	1.51825i	−0.744342	+	0.667799i	$0.767237\pi$
$422$	29.7442	−	8.73368i	1.44792	−	0.425149i
$423$	−7.22252	−	4.64163i	−0.351171	−	0.225684i
$424$	−2.63575	−	18.3321i	−0.128003	−	0.890284i
$425$	2.24931	+	4.92531i	0.109108	+	0.238913i
$426$	1.68020	+	3.67912i	0.0814058	+	0.178254i
$427$	2.50887	+	17.4496i	0.121413	+	0.844443i
$428$	4.77707	+	3.07003i	0.230908	+	0.148396i
$429$	−0.905836	+	0.265977i	−0.0437342	+	0.0128415i
$430$	1.72680	−	12.0102i	0.0832737	−	0.579181i
$431$	14.4740	−	16.7039i	0.697188	−	0.804598i	−0.291182	−	0.956668i	$-0.594049\pi$
$431$	14.4740	−	16.7039i	0.697188	−	0.804598i	0.988370	+	0.152070i	$0.0485940\pi$
$432$	1.04216	−	0.669756i	0.0501410	−	0.0322237i
$433$	−8.31362	−	9.59443i	−0.399527	−	0.461079i	0.519965	−	0.854188i	$-0.325945\pi$
$433$	−8.31362	−	9.59443i	−0.399527	−	0.461079i	−0.919492	+	0.393109i	$0.871400\pi$
$434$	8.94354	+	2.62606i	0.429304	+	0.126055i
$435$	6.42562	−	14.0701i	0.308085	−	0.674611i
$436$	44.5375			2.13296
$437$		0			0
$438$	35.6915			1.70541
$439$	7.65236	−	16.7563i	0.365227	−	0.799736i	−0.634415	−	0.772993i	$-0.718759\pi$
$439$	7.65236	−	16.7563i	0.365227	−	0.799736i	0.999642	−	0.0267436i	$-0.00851377\pi$
$440$	−4.27810	−	1.25616i	−0.203950	−	0.0598852i
$441$	2.97551	+	3.43392i	0.141691	+	0.163520i
$442$	−0.568153	+	0.365130i	−0.0270243	+	0.0173675i
$443$	9.11093	−	10.5146i	0.432874	−	0.499563i	−0.496842	−	0.867841i	$-0.665507\pi$
$443$	9.11093	−	10.5146i	0.432874	−	0.499563i	0.929716	+	0.368278i	$0.120053\pi$
$444$	3.96680	−	27.5897i	0.188256	−	1.30935i
$445$	−16.4911	+	4.84223i	−0.781755	+	0.229544i
$446$	−7.79260	−	5.00800i	−0.368990	−	0.237136i
$447$	−5.95153	−	41.3938i	−0.281498	−	1.95786i
$448$	12.5726	+	27.5302i	0.594000	+	1.30068i
$449$	12.5009	+	27.3731i	0.589952	+	1.29182i	0.935471	+	0.353403i	$0.114976\pi$
$449$	12.5009	+	27.3731i	0.589952	+	1.29182i	−0.345519	+	0.938412i	$0.612297\pi$
$450$	3.61063	+	25.1125i	0.170207	+	1.18381i
$451$	−0.685953	−	0.440835i	−0.0323003	−	0.0207581i
$452$	4.07814	−	1.19745i	0.191820	−	0.0563234i
$453$	4.71786	−	32.8134i	0.221664	−	1.54171i
$454$	−26.5967	+	30.6943i	−1.24825	+	1.44055i
$455$	0.484927	−	0.311644i	0.0227337	−	0.0146101i
$456$	−24.7865	−	28.6051i	−1.16073	−	1.33956i
$457$	−36.5064	−	10.7192i	−1.70770	−	0.501425i	−0.725331	−	0.688401i	$-0.758313\pi$
$457$	−36.5064	−	10.7192i	−1.70770	−	0.501425i	−0.982364	+	0.186976i	$0.940131\pi$
$458$	10.0006	−	21.8983i	0.467298	−	1.02324i
$459$	1.24228			0.0579849
$460$		0			0
$461$	8.76016			0.408001			0.204001	−	0.978971i	$-0.434606\pi$
$461$	8.76016			0.408001			0.204001	+	0.978971i	$0.434606\pi$
$462$	−10.4371	+	22.8541i	−0.485578	+	1.06327i
$463$	26.7091	+	7.84251i	1.24128	+	0.364472i	0.835496	−	0.549497i	$-0.185181\pi$
$463$	26.7091	+	7.84251i	1.24128	+	0.364472i	0.405783	+	0.913970i	$0.366999\pi$
$464$	5.07025	+	5.85138i	0.235380	+	0.271643i
$465$	4.66055	−	2.99516i	0.216128	−	0.138897i
$466$	−6.01010	+	6.93603i	−0.278413	+	0.321305i
$467$	2.47149	−	17.1896i	0.114367	−	0.795439i	−0.849219	−	0.528040i	$-0.822927\pi$
$467$	2.47149	−	17.1896i	0.114367	−	0.795439i	0.963586	−	0.267398i	$-0.0861640\pi$
$468$	−1.78575	+	0.524343i	−0.0825462	+	0.0242378i
$469$	−14.5048	−	9.32165i	−0.669768	−	0.430434i
$470$	−1.00371	−	6.98094i	−0.0462976	−	0.322007i
$471$	−4.31066	−	9.43903i	−0.198625	−	0.434927i
$472$	−5.65618	−	12.3853i	−0.260347	−	0.570080i
$473$	1.21164	+	8.42711i	0.0557111	+	0.387479i
$474$	26.4555	+	17.0019i	1.21514	+	0.780923i
$475$	−26.5924	+	7.80822i	−1.22014	+	0.358266i
$476$	−1.50437	+	10.4631i	−0.0689525	+	0.479575i
$477$	−21.3285	+	24.6144i	−0.976567	+	1.12702i
$478$	−41.7423	+	26.8261i	−1.90925	+	1.22700i
$479$	16.6844	+	19.2548i	0.762330	+	0.879775i	0.995702	−	0.0926121i	$-0.0295216\pi$
$479$	16.6844	+	19.2548i	0.762330	+	0.879775i	−0.233373	+	0.972387i	$0.574976\pi$
$480$	21.4693	+	6.30394i	0.979933	+	0.287734i
$481$	0.316942	−	0.694005i	0.0144513	−	0.0316439i
$482$	13.0655			0.595119
$483$		0			0
$484$	−20.9763			−0.953469
$485$	−2.22091	+	4.86312i	−0.100846	+	0.220823i
$486$	−47.2932	−	13.8865i	−2.14526	−	0.629906i
$487$	4.03464	+	4.65623i	0.182827	+	0.210994i	0.839764	−	0.542952i	$-0.182693\pi$
$487$	4.03464	+	4.65623i	0.182827	+	0.210994i	−0.656936	+	0.753946i	$0.728148\pi$
$488$	11.7887	−	7.57614i	0.533649	−	0.342956i
$489$	−24.3415	+	28.0916i	−1.10076	+	1.27035i
$490$	−0.531200	+	3.69458i	−0.0239972	+	0.166904i
$491$	31.3252	−	9.19790i	1.41368	−	0.415095i	0.516324	−	0.856393i	$-0.327300\pi$
$491$	31.3252	−	9.19790i	1.41368	−	0.415095i	0.897361	+	0.441298i	$0.145482\pi$
$492$	−2.57536	−	1.65509i	−0.116106	−	0.0746171i
$493$	1.10495	+	7.68511i	0.0497646	+	0.346120i
$494$	−1.43604	−	3.14450i	−0.0646107	−	0.141478i
$495$	3.25723	+	7.13235i	0.146402	+	0.320575i
$496$	0.394647	+	2.74483i	0.0177202	+	0.123246i
$497$	1.45773	+	0.936826i	0.0653881	+	0.0420224i
$498$	−68.4971	+	20.1126i	−3.06943	+	0.901266i
$499$	1.22016	−	8.48642i	0.0546220	−	0.379904i	−0.944113	−	0.329622i	$-0.893079\pi$
$499$	1.22016	−	8.48642i	0.0546220	−	0.379904i	0.998735	−	0.0502825i	$-0.0160122\pi$
$500$	−19.5895	+	22.6075i	−0.876068	+	1.01104i
$501$	−2.81155	+	1.80687i	−0.125611	+	0.0807251i
$502$	2.23763	+	2.58236i	0.0998702	+	0.115256i
$503$	−6.48189	−	1.90325i	−0.289013	−	0.0848619i	0.134012	−	0.990980i	$-0.457214\pi$
$503$	−6.48189	−	1.90325i	−0.289013	−	0.0848619i	−0.423026	+	0.906118i	$0.639032\pi$
$504$	−6.16649	+	13.5027i	−0.274677	+	0.601460i
$505$	2.25073			0.100156
$506$		0			0
$507$	32.5764			1.44677
$508$	7.11167	−	15.5724i	0.315530	−	0.690913i
$509$	−39.3129	−	11.5433i	−1.74251	−	0.511648i	−0.753242	−	0.657743i	$-0.771511\pi$
$509$	−39.3129	−	11.5433i	−1.74251	−	0.511648i	−0.989270	+	0.146096i	$0.953329\pi$
$510$	6.99553	+	8.07327i	0.309767	+	0.357490i
$511$	12.8636	−	8.26696i	0.569054	−	0.365709i
$512$	−11.1772	+	12.8992i	−0.493967	+	0.570069i
$513$	−0.904937	+	6.29397i	−0.0399539	+	0.277886i
$514$	−58.0557	+	17.0467i	−2.56073	+	0.751897i
$515$	15.9287	+	10.2368i	0.701903	+	0.451085i
$516$	4.54901	+	31.6390i	0.200259	+	1.39283i
$517$	2.05574	+	4.50145i	0.0904115	+	0.197974i
$518$	−8.43469	−	18.4694i	−0.370599	−	0.811499i
$519$	−6.05777	−	42.1327i	−0.265907	−	1.84942i
$520$	−0.385468	−	0.247725i	−0.0169039	−	0.0108635i
$521$	17.9683	−	5.27596i	0.787204	−	0.231144i	0.136666	−	0.990617i	$-0.456361\pi$
$521$	17.9683	−	5.27596i	0.787204	−	0.231144i	0.650539	+	0.759473i	$0.274543\pi$
$522$	−5.17736	+	36.0094i	−0.226607	+	1.57609i
$523$	−15.4311	+	17.8085i	−0.674757	+	0.778711i	−0.985113	−	0.171910i	$-0.945006\pi$
$523$	−15.4311	+	17.8085i	−0.674757	+	0.778711i	0.310356	+	0.950620i	$0.399552\pi$
$524$	−30.6778	+	19.7154i	−1.34017	+	0.861272i
$525$	13.5559	+	15.6443i	0.591627	+	0.682774i
$526$	27.3612	+	8.03398i	1.19301	+	0.350298i
$527$	−1.15519	+	2.52951i	−0.0503209	+	0.110187i
$528$	−7.47461			−0.325291
$529$		0			0
$530$	−26.7551			−1.16217
$531$	−9.94674	+	21.7803i	−0.431652	+	0.945186i
$532$	−51.9149	−	15.2436i	−2.25080	−	0.660893i
$533$	−0.0548742	−	0.0633282i	−0.00237687	−	0.00274305i
$534$	64.7643	−	41.6215i	2.80262	−	1.80114i
$535$	1.60999	−	1.85803i	0.0696060	−	0.0803296i
$536$	−1.95050	+	13.5660i	−0.0842487	+	0.585962i
$537$	−3.45174	+	1.01352i	−0.148954	+	0.0437367i
$538$	−18.5337	−	11.9109i	−0.799043	−	0.513514i
$539$	−0.372724	−	2.59236i	−0.0160544	−	0.111661i
$540$	1.16826	+	2.55812i	0.0502737	+	0.110084i
$541$	0.396010	+	0.867141i	0.0170258	+	0.0372813i	0.917954	−	0.396687i	$-0.129840\pi$
$541$	0.396010	+	0.867141i	0.0170258	+	0.0372813i	−0.900928	+	0.433968i	$0.857113\pi$
$542$	−1.38344	−	9.62207i	−0.0594240	−	0.413303i
$543$	34.1074	+	21.9195i	1.46369	+	0.940656i
$544$	−10.7765	+	3.16427i	−0.462039	+	0.135667i
$545$	2.74420	−	19.0863i	0.117549	−	0.817569i
$546$	−1.69082	+	1.95132i	−0.0723606	+	0.0835086i
$547$	25.0576	−	16.1035i	1.07138	−	0.688537i	0.118833	−	0.992914i	$-0.462085\pi$
$547$	25.0576	−	16.1035i	1.07138	−	0.688537i	0.952552	+	0.304377i	$0.0984482\pi$
$548$	−1.30460	−	1.50559i	−0.0557297	−	0.0643155i
$549$	−23.6449	−	6.94278i	−1.00914	−	0.296311i
$550$	6.07491	−	13.3022i	0.259035	−	0.567208i
$551$	−39.7412			−1.69303
$552$		0			0
$553$	13.4729			0.572925
$554$	−28.1986	+	61.7464i	−1.19805	+	2.62335i
$555$	−11.5790	−	3.39991i	−0.491502	−	0.144318i
$556$	−26.1008	−	30.1219i	−1.10692	−	1.27745i
$557$	−5.05485	+	3.24856i	−0.214181	+	0.137646i	−0.643333	−	0.765587i	$-0.722449\pi$
$557$	−5.05485	+	3.24856i	−0.214181	+	0.137646i	0.429152	+	0.903232i	$0.358813\pi$
$558$	−8.53268	+	9.84724i	−0.361217	+	0.416867i
$559$	−0.124516	+	0.866026i	−0.00526645	+	0.0366290i
$560$	4.37897	−	1.28578i	0.185045	−	0.0543342i
$561$	−6.30563	−	4.05238i	−0.266224	−	0.171092i
$562$	1.12250	+	7.80714i	0.0473497	+	0.329324i
$563$	0.0370509	+	0.0811301i	0.00156151	+	0.00341923i	0.910411	−	0.413705i	$-0.135765\pi$
$563$	0.0370509	+	0.0811301i	0.00156151	+	0.00341923i	−0.908850	+	0.417124i	$0.863038\pi$
$564$	7.71816	+	16.9004i	0.324993	+	0.711635i
$565$	−0.261885	−	1.82145i	−0.0110176	−	0.0766291i
$566$	27.3999	+	17.6089i	1.15170	+	0.740155i
$567$	−18.0973	+	5.31384i	−0.760014	+	0.223160i
$568$	0.196025	−	1.36338i	0.00822503	−	0.0572063i
$569$	27.0848	−	31.2575i	1.13545	−	1.31038i	0.191053	−	0.981580i	$-0.438810\pi$
$569$	27.0848	−	31.2575i	1.13545	−	1.31038i	0.944399	−	0.328802i	$-0.106645\pi$
$570$	−45.9987	+	29.5616i	−1.92667	+	1.23820i
$571$	−16.8892	−	19.4911i	−0.706790	−	0.815679i	0.282863	−	0.959160i	$-0.408716\pi$
$571$	−16.8892	−	19.4911i	−0.706790	−	0.815679i	−0.989653	+	0.143481i	$0.954170\pi$
$572$	1.02931	+	0.302232i	0.0430375	+	0.0126370i
$573$	21.6589	−	47.4263i	0.904812	−	1.98126i
$574$	−2.23002			−0.0930793
$575$		0			0
$576$	−42.3070			−1.76279
$577$	11.2761	−	24.6912i	0.469431	−	1.02791i	−0.515805	−	0.856706i	$-0.672507\pi$
$577$	11.2761	−	24.6912i	0.469431	−	1.02791i	0.985236	−	0.171204i	$-0.0547657\pi$
$578$	30.7991	+	9.04345i	1.28108	+	0.376158i
$579$	24.1159	+	27.8313i	1.00222	+	1.15663i
$580$	−14.7861	+	9.50248i	−0.613961	+	0.394569i
$581$	−20.0286	+	23.1143i	−0.830928	+	0.958942i
$582$	3.40800	−	23.7032i	0.141266	−	0.982527i
$583$	18.0127	−	5.28901i	0.746010	−	0.219048i
$584$	−10.2253	−	6.57139i	−0.423125	−	0.271926i
$585$	0.114675	+	0.797583i	0.00474123	+	0.0329760i
$586$	19.6937	+	43.1233i	0.813541	+	1.78141i
$587$	13.1416	+	28.7760i	0.542411	+	1.18771i	0.960237	+	0.279186i	$0.0900648\pi$
$587$	13.1416	+	28.7760i	0.542411	+	1.18771i	−0.417826	+	0.908527i	$0.637208\pi$
$588$	−1.39937	−	9.73283i	−0.0577090	−	0.401375i
$589$	−11.9742	−	7.69533i	−0.493387	−	0.317081i
$590$	−18.8728	+	5.54154i	−0.776979	+	0.228142i
$591$	4.17701	−	29.0518i	0.171819	−	1.19503i
$592$	3.95573	−	4.56516i	0.162580	−	0.187627i
$593$	−21.6589	+	13.9193i	−0.889424	+	0.571598i	−0.903636	−	0.428301i	$-0.859112\pi$
$593$	−21.6589	+	13.9193i	−0.889424	+	0.571598i	0.0142122	+	0.999899i	$0.495476\pi$
$594$	−2.19715	−	2.53565i	−0.0901502	−	0.104039i
$595$	4.39122	+	1.28938i	0.180023	+	0.0528594i
$596$	−19.7404	+	43.2255i	−0.808599	+	1.77059i
$597$	14.3849			0.588733
$598$		0			0
$599$	16.9434			0.692289			0.346144	−	0.938181i	$-0.387491\pi$
$599$	16.9434			0.692289			0.346144	+	0.938181i	$0.387491\pi$
$600$	6.83553	−	14.9677i	0.279060	−	0.611055i
$601$	9.26386	+	2.72012i	0.377881	+	0.110956i	0.465157	−	0.885228i	$-0.345998\pi$
$601$	9.26386	+	2.72012i	0.377881	+	0.110956i	−0.0872758	+	0.996184i	$0.527816\pi$
$602$	15.2480	+	17.5971i	0.621462	+	0.717205i
$603$	20.2759	−	13.0305i	0.825698	−	0.530644i
$604$	−24.6683	+	28.4687i	−1.00374	+	1.15838i
$605$	−1.29247	+	8.98932i	−0.0525463	+	0.365468i
$606$	−9.67311	+	2.84028i	−0.392943	+	0.115378i
$607$	2.73009	+	1.75453i	0.110811	+	0.0712140i	0.594873	−	0.803820i	$-0.297203\pi$
$607$	2.73009	+	1.75453i	0.110811	+	0.0712140i	−0.484061	+	0.875034i	$0.660839\pi$
$608$	−8.18151	−	56.9036i	−0.331804	−	2.30775i
$609$	12.3307	+	27.0004i	0.499664	+	1.09411i
$610$	−8.40957	−	18.4144i	−0.340493	−	0.745577i
$611$	0.0723751	+	0.503380i	0.00292798	+	0.0203646i
$612$	−12.4308	−	7.98879i	−0.502485	−	0.322928i
$613$	31.5810	−	9.27303i	1.27555	−	0.374534i	0.427287	−	0.904116i	$-0.359469\pi$
$613$	31.5810	−	9.27303i	1.27555	−	0.374534i	0.848259	+	0.529582i	$0.177651\pi$
$614$	−4.43596	+	30.8527i	−0.179021	+	1.24512i
$615$	−0.867963	+	1.00168i	−0.0349996	+	0.0403917i
$616$	7.19793	−	4.62583i	0.290013	−	0.186380i
$617$	−1.98058	−	2.28571i	−0.0797350	−	0.0920191i	0.714480	−	0.699656i	$-0.246663\pi$
$617$	−1.98058	−	2.28571i	−0.0797350	−	0.0920191i	−0.794215	+	0.607636i	$0.792118\pi$
$618$	−81.3758	−	23.8941i	−3.27341	−	0.961161i
$619$	4.32961	−	9.48053i	0.174022	−	0.381055i	−0.802444	−	0.596728i	$-0.796467\pi$
$619$	4.32961	−	9.48053i	0.174022	−	0.381055i	0.976466	+	0.215673i	$0.0691945\pi$
$620$	−6.29515			−0.252819
$621$		0			0
$622$	1.25637			0.0503758
$623$	13.7013	−	30.0017i	0.548932	−	1.20199i
$624$	−0.737025	−	0.216410i	−0.0295046	−	0.00866334i
$625$	−2.88419	−	3.32853i	−0.115367	−	0.133141i
$626$	−39.1759	+	25.1768i	−1.56578	+	1.00627i
$627$	25.1245	−	28.9952i	1.00338	−	1.15796i
$628$	−1.67806	+	11.6712i	−0.0669618	+	0.465730i
$629$	5.81210	−	1.70659i	0.231743	−	0.0680460i
$630$	18.0400	+	11.5936i	0.718729	+	0.461899i
$631$	−4.85312	−	33.7542i	−0.193200	−	1.34373i	−0.823471	−	0.567359i	$-0.807965\pi$
$631$	−4.85312	−	33.7542i	−0.193200	−	1.34373i	0.630271	−	0.776375i	$-0.282944\pi$
$632$	−4.44891	−	9.74176i	−0.176968	−	0.387506i
$633$	14.6878	+	32.1618i	0.583788	+	1.27832i
$634$	2.76355	+	19.2209i	0.109755	+	0.763360i
$635$	−6.23529	−	4.00718i	−0.247440	−	0.159020i
$636$	67.6275	−	19.8572i	2.68161	−	0.787390i
$637$	0.0383036	−	0.266408i	0.00151765	−	0.0105555i
$638$	13.7320	−	15.8475i	0.543653	−	0.627409i
$639$	−2.03773	+	1.30957i	−0.0806112	+	0.0518057i
$640$	−11.0990	−	12.8089i	−0.438727	−	0.506318i
$641$	8.64087	+	2.53719i	0.341294	+	0.100213i	0.447888	−	0.894090i	$-0.352176\pi$
$641$	8.64087	+	2.53719i	0.341294	+	0.100213i	−0.106594	+	0.994303i	$0.533995\pi$
$642$	−4.57464	+	10.0171i	−0.180547	+	0.395342i
$643$	−22.9522			−0.905146			−0.452573	−	0.891727i	$-0.649494\pi$
$643$	−22.9522			−0.905146			−0.452573	+	0.891727i	$0.649494\pi$
$644$		0			0
$645$	13.8391			0.544913
$646$	11.4015	−	24.9658i	0.448586	−	0.982266i
$647$	43.1334	+	12.6651i	1.69575	+	0.497916i	0.979756	−	0.200193i	$-0.0641570\pi$
$647$	43.1334	+	12.6651i	1.69575	+	0.497916i	0.715991	+	0.698110i	$0.245975\pi$
$648$	9.81820	+	11.3308i	0.385695	+	0.445116i
$649$	11.6105	−	7.46161i	0.455752	−	0.292894i
$650$	0.984145	−	1.13576i	0.0386013	−	0.0445483i
$651$	−1.51298	+	10.5230i	−0.0592983	+	0.412429i
$652$	40.5262	−	11.8996i	1.58713	−	0.466023i
$653$	−24.7020	−	15.8750i	−0.966665	−	0.621238i	−0.0408304	−	0.999166i	$-0.513000\pi$
$653$	−24.7020	−	15.8750i	−0.966665	−	0.621238i	−0.925835	+	0.377928i	$0.876637\pi$
$654$	12.2918	+	85.4915i	0.480648	+	3.34298i
$655$	6.55873	+	14.3616i	0.256271	+	0.561155i
$656$	−0.275602	−	0.603484i	−0.0107604	−	0.0235621i
$657$	3.04198	+	21.1574i	0.118679	+	0.825430i
$658$	11.3856	+	7.31707i	0.443857	+	0.285249i
$659$	38.5272	−	11.3126i	1.50081	−	0.440677i	0.574835	−	0.818269i	$-0.305066\pi$
$659$	38.5272	−	11.3126i	1.50081	−	0.440677i	0.925972	+	0.377593i	$0.123248\pi$
$660$	2.41483	−	16.7955i	0.0939971	−	0.653764i
$661$	−6.52673	+	7.53225i	−0.253861	+	0.292971i	−0.868347	−	0.495956i	$-0.834818\pi$
$661$	−6.52673	+	7.53225i	−0.253861	+	0.292971i	0.614487	+	0.788927i	$0.289363\pi$
$662$	55.9616	−	35.9643i	2.17501	−	1.39779i
$663$	−0.504432	−	0.582145i	−0.0195905	−	0.0226087i
$664$	23.3268	+	6.84938i	0.905257	+	0.265807i
$665$	−9.73134	+	21.3087i	−0.377365	+	0.826315i
$666$	28.3829			1.09981
$667$		0			0
$668$	3.79764			0.146935
$669$	4.38887	−	9.61029i	0.169684	−	0.371555i
$670$	18.9972	+	5.57808i	0.733926	+	0.215500i
$671$	9.30187	+	10.7349i	0.359095	+	0.414418i
$672$	−36.1222	+	23.2143i	−1.39344	+	0.895512i
$673$	22.3024	−	25.7384i	0.859695	−	0.992141i	−0.140303	−	0.990109i	$-0.544808\pi$
$673$	22.3024	−	25.7384i	0.859695	−	0.992141i	0.999998	−	0.00203243i	$-0.000646944\pi$
$674$	1.55416	−	10.8094i	0.0598642	−	0.416364i
$675$	−2.65237	+	0.778806i	−0.102090	+	0.0299763i
$676$	−31.1405	−	20.0128i	−1.19771	−	0.769722i
$677$	3.55660	+	24.7367i	0.136691	+	0.950710i	0.936553	+	0.350525i	$0.113997\pi$
$677$	3.55660	+	24.7367i	0.136691	+	0.950710i	−0.799862	+	0.600184i	$0.795094\pi$
$678$	3.42408	+	7.49768i	0.131501	+	0.287947i
$679$	−4.26190	−	9.33226i	−0.163557	−	0.358139i
$680$	−0.517732	−	3.60091i	−0.0198541	−	0.138088i
$681$	−38.9692	−	25.0440i	−1.49330	−	0.959687i
$682$	7.20615	−	2.11592i	0.275938	−	0.0810226i
$683$	−4.90647	+	34.1253i	−0.187741	+	1.30577i	0.650099	+	0.759850i	$0.274728\pi$
$683$	−4.90647	+	34.1253i	−0.187741	+	1.30577i	−0.837840	+	0.545917i	$0.816182\pi$
$684$	49.5300	−	57.1607i	1.89383	−	2.18559i
$685$	−0.725596	+	0.466312i	−0.0277236	+	0.0178169i
$686$	−28.6591	−	33.0744i	−1.09421	−	1.26279i
$687$	26.3452	+	7.73564i	1.00513	+	0.295133i
$688$	−2.87764	+	6.30115i	−0.109709	+	0.240229i
$689$	1.92925			0.0734987
$690$		0			0
$691$	−21.2259			−0.807470			−0.403735	−	0.914876i	$-0.632288\pi$
$691$	−21.2259			−0.807470			−0.403735	+	0.914876i	$0.632288\pi$
$692$	−20.0928	+	43.9971i	−0.763814	+	1.67252i
$693$	−14.4371	−	4.23912i	−0.548421	−	0.161031i
$694$	9.76513	+	11.2696i	0.370679	+	0.427787i
$695$	−14.5168	+	9.32940i	−0.550655	+	0.353884i
$696$	15.4513	−	17.8317i	0.585680	−	0.675910i
$697$	0.0946811	−	0.658522i	0.00358630	−	0.0249433i
$698$	−21.3377	+	6.26532i	−0.807645	+	0.237146i
$699$	−8.80592	−	5.65922i	−0.333070	−	0.214051i
$700$	−3.34753	−	23.2826i	−0.126525	−	0.879999i
$701$	−10.0224	−	21.9459i	−0.378539	−	0.828886i	−0.999003	−	0.0446501i	$-0.985783\pi$
$701$	−10.0224	−	21.9459i	−0.378539	−	0.828886i	0.620463	−	0.784235i	$-0.286945\pi$
$702$	−0.143234	−	0.313638i	−0.00540601	−	0.0118375i
$703$	4.41254	+	30.6899i	0.166422	+	1.15749i
$704$	20.5146	+	13.1840i	0.773175	+	0.496889i
$705$	7.71816	−	2.26626i	0.290683	−	0.0853521i
$706$	−7.67374	+	53.3720i	−0.288805	+	2.00868i
$707$	−2.82843	+	3.26418i	−0.106374	+	0.122762i
$708$	43.5908	−	28.0141i	1.63824	−	1.05284i
$709$	−4.60821	−	5.31816i	−0.173065	−	0.199728i	0.662590	−	0.748982i	$-0.269457\pi$
$709$	−4.60821	−	5.31816i	−0.173065	−	0.199728i	−0.835655	+	0.549255i	$0.814912\pi$
$710$	−1.90922	−	0.560598i	−0.0716517	−	0.0210388i
$711$	−7.82369	+	17.1315i	−0.293411	+	0.642481i
$712$	−26.2175			−0.982544
$713$		0			0
$714$	−20.4995			−0.767175
$715$	0.192942	−	0.422483i	0.00721561	−	0.0158000i
$716$	3.92224	+	1.15167i	0.146581	+	0.0430400i
$717$	−37.0607	−	42.7703i	−1.38406	−	1.59729i
$718$	0.776395	−	0.498959i	0.0289748	−	0.0186210i
$719$	−17.3985	+	20.0789i	−0.648855	+	0.748818i	−0.980914	−	0.194440i	$-0.937711\pi$
$719$	−17.3985	+	20.0789i	−0.648855	+	0.748818i	0.332060	+	0.943258i	$0.392256\pi$
$720$	−0.907924	+	6.31475i	−0.0338363	+	0.235337i
$721$	−34.8632	+	10.2368i	−1.29837	+	0.381237i
$722$	82.9604	+	53.3154i	3.08747	+	1.98419i
$723$	2.12076	+	14.7502i	0.0788720	+	0.548567i
$724$	−19.1381	−	41.9067i	−0.711263	−	1.55745i
$725$	−7.17707	−	15.7156i	−0.266550	−	0.583662i
$726$	−5.78922	−	40.2649i	−0.214858	−	1.49437i
$727$	−4.39770	−	2.82623i	−0.163102	−	0.104819i	0.456544	−	0.889701i	$-0.349087\pi$
$727$	−4.39770	−	2.82623i	−0.163102	−	0.104819i	−0.619645	+	0.784882i	$0.712724\pi$
$728$	0.843674	−	0.247725i	0.0312686	−	0.00918130i
$729$	4.60681	−	32.0410i	0.170622	−	1.18670i
$730$	−11.4987	+	13.2702i	−0.425587	+	0.491154i
$731$	−5.84379	+	3.75557i	−0.216140	+	0.138905i
$732$	34.9233	+	40.3036i	1.29080	+	1.48966i
$733$	25.6078	+	7.51913i	0.945846	+	0.277725i	0.718056	−	0.695985i	$-0.245032\pi$
$733$	25.6078	+	7.51913i	0.945846	+	0.277725i	0.227789	+	0.973710i	$0.426850\pi$
$734$	26.1518	−	57.2644i	0.965279	−	2.11367i
$735$	−4.25719			−0.157029
$736$		0			0
$737$	−13.8924			−0.511734
$738$	1.29497	−	2.83559i	0.0476686	−	0.104380i
$739$	2.14883	+	0.630954i	0.0790460	+	0.0232100i	0.321016	−	0.947074i	$-0.395976\pi$
$739$	2.14883	+	0.630954i	0.0790460	+	0.0232100i	−0.241970	+	0.970284i	$0.577794\pi$
$740$	8.97996	+	10.3634i	0.330110	+	0.380967i
$741$	3.31686	−	2.13162i	0.121848	−	0.0783070i
$742$	33.6223	−	38.8022i	1.23431	−	1.42448i
$743$	−2.58161	+	17.9555i	−0.0947101	+	0.658723i	0.886062	+	0.463567i	$0.153431\pi$
$743$	−2.58161	+	17.9555i	−0.0947101	+	0.658723i	−0.980772	+	0.195156i	$0.937479\pi$
$744$	8.10841	−	2.38084i	0.297269	−	0.0872860i
$745$	17.3078	+	11.1230i	0.634108	+	0.407517i
$746$	−4.51838	−	31.4260i	−0.165430	−	1.15059i
$747$	−17.7604	−	38.8900i	−0.649821	−	1.42291i
$748$	3.53817	+	7.74752i	0.129368	+	0.283277i
$749$	0.671424	+	4.66985i	0.0245333	+	0.170633i
$750$	−48.8024	−	31.3634i	−1.78201	−	1.14523i
$751$	−27.0833	+	7.95238i	−0.988284	+	0.290186i	−0.735640	−	0.677373i	$-0.763118\pi$
$751$	−27.0833	+	7.95238i	−0.988284	+	0.290186i	−0.252644	+	0.967559i	$0.581300\pi$
$752$	−0.573020	+	3.98544i	−0.0208959	+	0.145334i
$753$	−2.55213	+	2.94532i	−0.0930048	+	0.107333i
$754$	1.81285	−	1.16505i	0.0660202	−	0.0424286i
$755$	10.6802	+	12.3256i	0.388692	+	0.448575i
$756$	−5.17809	−	1.52042i	−0.188325	−	0.0552973i
$757$	0.0506863	−	0.110987i	0.00184222	−	0.00403391i	−0.908709	−	0.417431i	$-0.862931\pi$
$757$	0.0506863	−	0.110987i	0.00184222	−	0.00403391i	0.910551	+	0.413397i	$0.135658\pi$
$758$	−12.4000			−0.450389
$759$		0			0
$760$	18.6210			0.675453
$761$	−11.0938	+	24.2921i	−0.402151	+	0.880587i	0.594897	+	0.803802i	$0.297193\pi$
$761$	−11.0938	+	24.2921i	−0.402151	+	0.880587i	−0.997048	+	0.0767852i	$0.975534\pi$
$762$	31.8546	+	9.35335i	1.15397	+	0.338836i
$763$	24.2319	+	27.9651i	0.877252	+	1.01240i
$764$	−49.8398	+	32.0301i	−1.80314	+	1.15881i
$765$	−4.18949	+	4.83493i	−0.151471	+	0.174807i
$766$	−0.0726502	+	0.505294i	−0.00262496	+	0.0182570i
$767$	1.36087	−	0.399588i	0.0491383	−	0.0144283i
$768$	9.92725	+	6.37985i	0.358219	+	0.230213i
$769$	1.11732	+	7.77113i	0.0402916	+	0.280234i	1.00000		0.000764719i	$-0.000243418\pi$
$769$	1.11732	+	7.77113i	0.0402916	+	0.280234i	−0.959708	+	0.280999i	$0.909334\pi$
$770$	−5.13471	−	11.2434i	−0.185042	−	0.405185i
$771$	−28.6682	−	62.7745i	−1.03246	−	2.26077i
$772$	−5.95526	−	41.4198i	−0.214335	−	1.49073i
$773$	−28.8396	−	18.5341i	−1.03729	−	0.666624i	−0.0929732	−	0.995669i	$-0.529637\pi$
$773$	−28.8396	−	18.5341i	−1.03729	−	0.666624i	−0.944314	+	0.329044i	$0.893273\pi$
$774$	−31.2302	+	9.17001i	−1.12255	+	0.329609i
$775$	0.880629	−	6.12491i	0.0316331	−	0.220013i
$776$	−5.34050	+	6.16326i	−0.191713	+	0.221248i
$777$	19.4818	−	12.5202i	0.698905	−	0.449159i
$778$	43.5369	+	50.2443i	1.56087	+	1.80134i
$779$	3.26740	+	0.959395i	0.117067	+	0.0343739i
$780$	0.724387	−	1.58619i	0.0259372	−	0.0567946i
$781$	1.39619			0.0499596
$782$		0			0
$783$	−3.96386			−0.141657
$784$	0.885223	−	1.93837i	0.0316151	−	0.0692274i
$785$	4.89823	+	1.43825i	0.174825	+	0.0513333i
$786$	−46.3112	−	53.4460i	−1.65187	−	1.90636i
$787$	13.4706	−	8.65702i	0.480175	−	0.308590i	−0.278069	−	0.960561i	$-0.589694\pi$
$787$	13.4706	−	8.65702i	0.480175	−	0.308590i	0.758243	+	0.651972i	$0.226058\pi$
$788$	−21.8404	+	25.2051i	−0.778031	+	0.897896i
$789$	−4.62870	+	32.1933i	−0.164786	+	1.14611i
$790$	−14.8445	+	4.35874i	−0.528144	+	0.155077i
$791$	2.97071	+	1.90916i	0.105626	+	0.0678818i
$792$	1.70216	+	11.8388i	0.0604836	+	0.420673i
$793$	0.606395	+	1.32782i	0.0215337	+	0.0471523i
$794$	−11.9418	−	26.1490i	−0.423800	−	0.927992i
$795$	−4.34282	−	30.2050i	−0.154024	−	1.07126i
$796$	−13.7508	−	8.83710i	−0.487384	−	0.313223i
$797$	−20.6519	+	6.06393i	−0.731526	+	0.214796i	−0.626222	−	0.779645i	$-0.715400\pi$
$797$	−20.6519	+	6.06393i	−0.731526	+	0.214796i	−0.105304	+	0.994440i	$0.533582\pi$
$798$	14.9328	−	103.860i	0.528615	−	3.67660i
$799$	−2.64412	+	3.05148i	−0.0935423	+	0.107954i
$800$	21.0249	−	13.5119i	0.743343	−	0.477718i
$801$	30.1925	+	34.8440i	1.06680	+	1.23115i
$802$	45.0902	+	13.2397i	1.59219	+	0.467509i
$803$	5.11815	−	11.2072i	0.180616	−	0.395493i
$804$	−52.1582			−1.83948
$805$		0			0
$806$	0.771816			0.0271860
$807$	10.4383	−	22.8568i	0.367447	−	0.804596i
$808$	3.29420	+	0.967263i	0.115889	+	0.0340282i
$809$	−15.7986	−	18.2325i	−0.555449	−	0.641022i	0.406695	−	0.913564i	$-0.366681\pi$
$809$	−15.7986	−	18.2325i	−0.555449	−	0.641022i	−0.962144	+	0.272542i	$0.912136\pi$
$810$	18.2206	−	11.7097i	0.640206	−	0.411436i
$811$	−9.38958	+	10.8362i	−0.329713	+	0.380509i	−0.896266	−	0.443516i	$-0.853731\pi$
$811$	−9.38958	+	10.8362i	−0.329713	+	0.380509i	0.566554	+	0.824025i	$0.308276\pi$
$812$	4.80010	−	33.3854i	0.168450	−	1.17160i
$813$	10.6382	−	3.12366i	0.373098	−	0.109551i
$814$	−13.7628	−	8.84484i	−0.482387	−	0.310011i
$815$	−2.60246	−	18.1005i	−0.0911604	−	0.634034i
$816$	−2.53347	−	5.54753i	−0.0886893	−	0.194203i
$817$	−14.7706	−	32.3430i	−0.516756	−	1.13154i
$818$	2.86920	+	19.9557i	0.100319	+	0.697735i
$819$	−1.30082	−	0.835987i	−0.0454544	−	0.0292117i
$820$	1.44507	−	0.424312i	0.0504641	−	0.0148176i
$821$	−2.02207	+	14.0638i	−0.0705709	+	0.490831i	0.923629	+	0.383287i	$0.125208\pi$
$821$	−2.02207	+	14.0638i	−0.0705709	+	0.490831i	−0.994200	+	0.107545i	$0.965701\pi$
$822$	2.52998	−	2.91975i	0.0882432	−	0.101838i
$823$	13.4795	−	8.66274i	0.469866	−	0.301964i	−0.284198	−	0.958766i	$-0.591727\pi$
$823$	13.4795	−	8.66274i	0.469866	−	0.301964i	0.754064	+	0.656801i	$0.228091\pi$
$824$	18.9141	+	21.8280i	0.658904	+	0.760416i
$825$	16.0035	+	4.69905i	0.557170	+	0.163600i
$826$	15.6801	−	34.3345i	0.545579	−	1.19465i
$827$	35.1240			1.22138			0.610690	−	0.791870i	$-0.290892\pi$
$827$	35.1240			1.22138			0.610690	+	0.791870i	$0.290892\pi$
$828$		0			0
$829$	−2.29604			−0.0797447			−0.0398723	−	0.999205i	$-0.512695\pi$
$829$	−2.29604			−0.0797447			−0.0398723	+	0.999205i	$0.512695\pi$
$830$	14.5898	−	31.9472i	0.506419	−	1.10890i
$831$	−74.2853	−	21.8121i	−2.57693	−	0.756654i
$832$	1.64111	+	1.89394i	0.0568953	+	0.0656607i
$833$	1.79767	−	1.15529i	0.0622856	−	0.0400285i
$834$	50.6167	−	58.4148i	1.75271	−	2.02274i
$835$	0.233994	−	1.62746i	0.00809770	−	0.0563207i
$836$	−41.8298	+	12.2823i	−1.44671	+	0.424794i
$837$	−1.19433	−	0.767547i	−0.0412819	−	0.0265303i
$838$	2.81437	+	19.5744i	0.0972209	+	0.676186i
$839$	16.0399	+	35.1224i	0.553758	+	1.21256i	0.955005	+	0.296590i	$0.0958496\pi$
$839$	16.0399	+	35.1224i	0.553758	+	1.21256i	−0.401247	+	0.915970i	$0.631423\pi$
$840$	−5.77761	−	12.6512i	−0.199346	−	0.436508i
$841$	0.601470	+	4.18332i	0.0207403	+	0.144252i
$842$	58.3433	+	37.4950i	2.01064	+	1.29216i
$843$	−8.63161	+	2.53447i	−0.297288	+	0.0872917i
$844$	5.71769	−	39.7674i	0.196811	−	1.36885i
$845$	−10.4951	+	12.1120i	−0.361043	+	0.416666i
$846$	−15.9157	+	10.2284i	−0.547192	+	0.351659i
$847$	−11.4128	−	13.1710i	−0.392147	−	0.452562i
$848$	14.6559	+	4.30335i	0.503285	+	0.147778i
$849$	−15.4319	+	33.7911i	−0.529621	+	1.15971i
$850$	11.9317			0.409255
$851$		0			0
$852$	5.24190			0.179584
$853$	−15.9641	+	34.9566i	−0.546602	+	1.19689i	0.411749	+	0.911297i	$0.364918\pi$
$853$	−15.9641	+	34.9566i	−0.546602	+	1.19689i	−0.958351	+	0.285594i	$0.907809\pi$
$854$	37.2739	+	10.9446i	1.27549	+	0.374517i
$855$	−21.4441	−	24.7479i	−0.733374	−	0.846359i
$856$	3.15489	−	2.02753i	0.107832	−	0.0692995i
$857$	33.3255	−	38.4597i	1.13838	−	1.31376i	0.195468	−	0.980710i	$-0.437377\pi$
$857$	33.3255	−	38.4597i	1.13838	−	1.31376i	0.942910	−	0.333048i	$-0.108077\pi$
$858$	−0.296070	+	2.05921i	−0.0101076	+	0.0703002i
$859$	−8.77658	+	2.57704i	−0.299453	+	0.0879274i	−0.428008	−	0.903775i	$-0.640784\pi$
$859$	−8.77658	+	2.57704i	−0.299453	+	0.0879274i	0.128555	+	0.991702i	$0.458966\pi$
$860$	−13.2291	−	8.50180i	−0.451107	−	0.289909i
$861$	−0.361971	−	2.51757i	−0.0123360	−	0.0857984i
$862$	−20.2329	−	44.3038i	−0.689134	−	1.50899i
$863$	5.12575	+	11.2238i	0.174482	+	0.382063i	0.976588	−	0.215119i	$-0.0690141\pi$
$863$	5.12575	+	11.2238i	0.174482	+	0.382063i	−0.802105	+	0.597183i	$0.796287\pi$
$864$	−0.816039	−	5.67567i	−0.0277622	−	0.193090i
$865$	17.6167	+	11.3216i	0.598987	+	0.384946i
$866$	−26.8422	+	7.88159i	−0.912137	+	0.267827i
$867$	−5.21029	+	36.2384i	−0.176951	+	1.23072i
$868$	7.91092	−	9.12969i	0.268514	−	0.309882i
$869$	9.13232	−	5.86899i	0.309793	−	0.199092i
$870$	−22.3212	−	25.7600i	−0.756759	−	0.873347i
$871$	−1.36985	−	0.402223i	−0.0464155	−	0.0136288i
$872$	12.2189	−	26.7556i	0.413783	−	0.906059i
$873$	14.3414			0.485381
$874$		0			0
$875$	−24.8534			−0.840199
$876$	19.2158	−	42.0767i	0.649240	−	1.42164i
$877$	−2.21374	−	0.650013i	−0.0747527	−	0.0219494i	0.244142	−	0.969739i	$-0.421494\pi$
$877$	−2.21374	−	0.650013i	−0.0747527	−	0.0219494i	−0.318895	+	0.947790i	$0.603312\pi$
$878$	−26.5826	−	30.6780i	−0.897121	−	1.03533i
$879$	−45.4871	+	29.2328i	−1.53424	+	0.985996i
$880$	2.40809	−	2.77909i	0.0811768	−	0.0936830i
$881$	5.06646	−	35.2380i	0.170693	−	1.18720i	−0.706731	−	0.707483i	$-0.749831\pi$
$881$	5.06646	−	35.2380i	0.170693	−	1.18720i	0.877424	−	0.479716i	$-0.159260\pi$
$882$	9.60706	−	2.82089i	0.323486	−	0.0949842i
$883$	25.6368	+	16.4758i	0.862747	+	0.554454i	0.895526	−	0.445009i	$-0.146799\pi$
$883$	25.6368	+	16.4758i	0.862747	+	0.554454i	−0.0327790	+	0.999463i	$0.510436\pi$
$884$	0.124566	+	0.866375i	0.00418961	+	0.0291394i
$885$	−9.31946	−	20.4068i	−0.313270	−	0.685966i
$886$	−12.7360	−	27.8879i	−0.427873	−	0.936912i
$887$	−2.95889	−	20.5795i	−0.0993498	−	0.690993i	−0.977241	−	0.212133i	$-0.931959\pi$
$887$	−2.95889	−	20.5795i	−0.0993498	−	0.690993i	0.877891	−	0.478860i	$-0.158950\pi$
$888$	−15.4860	−	9.95227i	−0.519677	−	0.333976i
$889$	13.6472	−	4.00718i	0.457713	−	0.134397i
$890$	−5.39007	+	37.4888i	−0.180676	+	1.25663i
$891$	−9.95209	+	11.4853i	−0.333408	+	0.384773i
$892$	−10.0993	+	6.49045i	−0.338151	+	0.217316i
$893$	−13.5341	−	15.6192i	−0.452901	−	0.522675i
$894$	−88.4212	−	25.9628i	−2.95725	−	0.868326i
$895$	0.735215	−	1.60990i	0.0245755	−	0.0538129i
$896$	32.5243			1.08656
$897$		0			0
$898$	66.3122			2.21287
$899$	3.68596	−	8.07113i	0.122934	−	0.269187i
$900$	31.5490	+	9.26362i	1.05163	+	0.308787i
$901$	10.0307	+	11.5761i	0.334172	+	0.385655i
$902$	−1.51158	+	0.971431i	−0.0503300	+	0.0323451i
$903$	−17.3911	+	20.0704i	−0.578740	+	0.667902i
$904$	0.399480	−	2.77844i	0.0132865	−	0.0924096i
$905$	−19.1381	+	5.61946i	−0.636173	+	0.186797i
$906$	−61.4550	−	39.4947i	−2.04171	−	1.31212i
$907$	3.23223	+	22.4806i	0.107324	+	0.746457i	0.970421	+	0.241419i	$0.0776127\pi$
$907$	3.23223	+	22.4806i	0.107324	+	0.746457i	−0.863097	+	0.505039i	$0.831478\pi$
$908$	21.8661	+	47.8801i	0.725653	+	1.58896i
$909$	−2.50811	−	5.49200i	−0.0831889	−	0.182158i
$910$	−0.180774	−	1.25731i	−0.00599260	−	0.0416794i
$911$	0.701642	+	0.450918i	0.0232464	+	0.0149396i	0.552212	−	0.833703i	$-0.313784\pi$
$911$	0.701642	+	0.450918i	0.0232464	+	0.0149396i	−0.528966	+	0.848643i	$0.677420\pi$
$912$	29.9518	−	8.79465i	0.991804	−	0.291220i
$913$	−3.50709	+	24.3923i	−0.116068	+	0.807269i
$914$	−54.9049	+	63.3637i	−1.81609	+	2.09588i
$915$	19.4238	−	12.4829i	0.642130	−	0.412672i
$916$	−20.4317	−	23.5794i	−0.675081	−	0.779085i
$917$	−29.0704	−	8.53584i	−0.959990	−	0.281878i
$918$	1.13721	−	2.49013i	0.0375334	−	0.0821866i
$919$	−45.3320			−1.49537			−0.747683	−	0.664056i	$-0.768834\pi$
$919$	−45.3320			−1.49537			−0.747683	+	0.664056i	$0.768834\pi$
$920$		0			0
$921$	−35.5510			−1.17145
$922$	8.01918	−	17.5596i	0.264098	−	0.578293i
$923$	0.137670	+	0.0404234i	0.00453145	+	0.00133055i
$924$	21.3234	+	24.6085i	0.701489	+	0.809562i
$925$	−11.3394	+	7.28737i	−0.372836	+	0.239607i
$926$	40.1701	−	46.3587i	1.32007	−	1.52344i
$927$	7.22844	−	50.2749i	0.237413	−	1.65124i
$928$	34.3855	−	10.0965i	1.12876	−	0.331433i
$929$	−14.8963	−	9.57324i	−0.488730	−	0.314088i	0.272964	−	0.962024i	$-0.411996\pi$
$929$	−14.8963	−	9.57324i	−0.488730	−	0.314088i	−0.761695	+	0.647936i	$0.775632\pi$
$930$	−1.73739	−	12.0838i	−0.0569712	−	0.396243i
$931$	4.54373	+	9.94939i	0.148915	+	0.326078i
$932$	4.94112	+	10.8195i	0.161852	+	0.354406i
$933$	0.203930	+	1.41837i	0.00667638	+	0.0464353i
$934$	−32.1937	−	20.6896i	−1.05341	−	0.676986i
$935$	3.53817	−	1.03890i	0.115711	−	0.0339757i
$936$	−0.174925	+	1.21663i	−0.00571761	+	0.0397668i
$937$	15.2753	−	17.6286i	0.499022	−	0.575902i	−0.449232	−	0.893415i	$-0.648302\pi$
$937$	15.2753	−	17.6286i	0.499022	−	0.575902i	0.948254	+	0.317513i	$0.102848\pi$
$938$	−31.9629	+	20.5413i	−1.04363	+	0.670698i
$939$	−34.7821	−	40.1407i	−1.13507	−	1.30994i
$940$	−8.77019	−	2.57516i	−0.286052	−	0.0839925i
$941$	4.82495	−	10.5652i	0.157289	−	0.344414i	−0.814538	−	0.580110i	$-0.803010\pi$
$941$	4.82495	−	10.5652i	0.157289	−	0.344414i	0.971827	+	0.235696i	$0.0757368\pi$
$942$	−22.8664			−0.745027
$943$		0			0
$944$	11.2294			0.365486
$945$	−0.970622	+	2.12537i	−0.0315743	+	0.0691382i
$946$	18.0011	+	5.28560i	0.585267	+	0.171850i
$947$	−3.92781	−	4.53294i	−0.127637	−	0.147301i	0.688334	−	0.725394i	$-0.258342\pi$
$947$	−3.92781	−	4.53294i	−0.127637	−	0.147301i	−0.815971	+	0.578093i	$0.803797\pi$
$948$	34.2867	−	22.0347i	1.11358	−	0.715655i
$949$	0.829148	−	0.956887i	0.0269153	−	0.0310619i
$950$	−8.69163	+	60.4516i	−0.281994	+	1.96131i
$951$	−21.2507	+	6.23977i	−0.689102	+	0.202339i
$952$	5.87291	+	3.77429i	0.190342	+	0.122326i
$953$	2.54838	+	17.7244i	0.0825503	+	0.574150i	0.988553	+	0.150877i	$0.0482097\pi$
$953$	2.54838	+	17.7244i	0.0825503	+	0.574150i	−0.906002	+	0.423273i	$0.860881\pi$
$954$	29.8147	+	65.2851i	0.965286	+	2.11368i
$955$	10.6554	+	23.3322i	0.344802	+	0.755011i
$956$	9.15187	+	63.6527i	0.295993	+	2.05867i
$957$	20.1199	+	12.9303i	0.650383	+	0.417976i
$958$	53.8690	−	15.8174i	1.74043	−	0.511036i
$959$	0.235554	−	1.63831i	0.00760643	−	0.0529039i
$960$	25.9580	−	29.9571i	0.837790	−	0.966862i
$961$	−23.4054	+	15.0417i	−0.755013	+	0.485217i
$962$	−1.10099	−	1.27061i	−0.0354972	−	0.0409660i
$963$	−6.32787	−	1.85803i	−0.203913	−	0.0598742i
$964$	7.03428	−	15.4029i	0.226559	−	0.496095i
$965$	−18.1172			−0.583213
$966$		0			0
$967$	33.5068			1.07751			0.538753	−	0.842464i	$-0.318896\pi$
$967$	33.5068			1.07751			0.538753	+	0.842464i	$0.318896\pi$
$968$	−5.75487	+	12.6014i	−0.184968	+	0.405024i
$969$	30.0356	+	8.81925i	0.964882	+	0.283315i
$970$	7.71497	+	8.90355i	0.247713	+	0.285876i
$971$	49.8746	−	32.0524i	1.60055	−	1.02861i	0.633596	−	0.773664i	$-0.281578\pi$
$971$	49.8746	−	32.0524i	1.60055	−	1.02861i	0.966955	−	0.254947i	$-0.0820580\pi$
$972$	−41.8327	+	48.2776i	−1.34179	+	1.54850i
$973$	4.71267	−	32.7773i	0.151081	−	1.05079i
$974$	13.0267	−	3.82498i	0.417402	−	0.122560i
$975$	1.44196	+	0.926688i	0.0461795	+	0.0296778i
$976$	1.64477	+	11.4396i	0.0526477	+	0.366173i
$977$	−5.25166	−	11.4995i	−0.168016	−	0.367903i	0.806830	−	0.590783i	$-0.201181\pi$
$977$	−5.25166	−	11.4995i	−0.168016	−	0.367903i	−0.974846	+	0.222881i	$0.928454\pi$
$978$	34.0265	+	74.5075i	1.08805	+	2.38249i
$979$	−3.78203	−	26.3046i	−0.120874	−	0.840698i
$980$	4.06954	+	2.61533i	0.129997	+	0.0835438i
$981$	−49.6305	+	14.5728i	−1.58458	+	0.465275i
$982$	10.2385	−	71.2105i	0.326725	−	2.27242i
$983$	38.2210	−	44.1093i	1.21906	−	1.40687i	0.333238	−	0.942843i	$-0.391859\pi$
$983$	38.2210	−	44.1093i	1.21906	−	1.40687i	0.885821	−	0.464027i	$-0.153596\pi$
$984$	−1.70084	+	1.09306i	−0.0542207	+	0.0348455i
$985$	9.45585	+	10.9126i	0.301288	+	0.347705i
$986$	16.4161	+	4.82021i	0.522796	+	0.153507i
$987$	−6.41248	+	14.0414i	−0.204111	+	0.446942i
$988$	−4.48019			−0.142534
$989$		0			0
$990$	17.2784			0.549142
$991$	−19.0223	+	41.6530i	−0.604263	+	1.32315i	0.322166	+	0.946683i	$0.395589\pi$
$991$	−19.0223	+	41.6530i	−0.604263	+	1.32315i	−0.926429	+	0.376469i	$0.877138\pi$
$992$	12.3155	+	3.61616i	0.391018	+	0.114813i
$993$	49.6852	+	57.3397i	1.57671	+	1.81962i
$994$	3.21228	−	2.06440i	0.101887	−	0.0654789i
$995$	−4.63437	+	5.34835i	−0.146919	+	0.169554i
$996$	−13.1671	+	91.5794i	−0.417217	+	2.90181i
$997$	37.7581	−	11.0868i	1.19581	−	0.351121i	0.377560	−	0.925985i	$-0.376763\pi$
$997$	37.7581	−	11.0868i	1.19581	−	0.351121i	0.818249	+	0.574864i	$0.194945\pi$
$998$	−15.8939	−	10.2144i	−0.503113	−	0.323331i
$999$	0.440114	+	3.06106i	0.0139246	+	0.0968477i

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

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	529.2.c.g.466.1		10
23.2	even	11		529.2.a.i.1.5		5
23.3	even	11		23.2.c.a.8.1	yes	10
23.4	even	11	inner	529.2.c.g.487.1		10
23.5	odd	22		529.2.c.h.334.1		10
23.6	even	11		529.2.c.b.170.1		10
23.7	odd	22		529.2.c.c.501.1		10
23.8	even	11		529.2.c.d.177.1		10
23.9	even	11		23.2.c.a.3.1	✓	10
23.10	odd	22		529.2.c.h.255.1		10
23.11	odd	22		529.2.c.e.266.1		10
23.12	even	11		529.2.c.d.266.1		10
23.13	even	11		529.2.c.i.255.1		10
23.14	odd	22		529.2.c.a.118.1		10
23.15	odd	22		529.2.c.e.177.1		10
23.16	even	11		529.2.c.b.501.1		10
23.17	odd	22		529.2.c.c.170.1		10
23.18	even	11		529.2.c.i.334.1		10
23.19	odd	22		529.2.c.f.487.1		10
23.20	odd	22		529.2.c.a.399.1		10
23.21	odd	22		529.2.a.j.1.5		5
23.22	odd	2		529.2.c.f.466.1		10
69.2	odd	22		4761.2.a.bo.1.1		5
69.26	odd	22		207.2.i.c.100.1		10
69.32	odd	22		207.2.i.c.118.1		10
69.44	even	22		4761.2.a.bn.1.1		5
92.3	odd	22		368.2.m.c.353.1		10
92.55	odd	22		368.2.m.c.49.1		10
92.67	even	22		8464.2.a.bt.1.5		5
92.71	odd	22		8464.2.a.bs.1.5		5
115.3	odd	44		575.2.p.b.399.2		20
115.9	even	22		575.2.k.b.26.1		10
115.32	odd	44		575.2.p.b.49.2		20
115.49	even	22		575.2.k.b.376.1		10
115.72	odd	44		575.2.p.b.399.1		20
115.78	odd	44		575.2.p.b.49.1		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
23.2.c.a.3.1	✓	10	23.9	even	11
23.2.c.a.8.1	yes	10	23.3	even	11
207.2.i.c.100.1		10	69.26	odd	22
207.2.i.c.118.1		10	69.32	odd	22
368.2.m.c.49.1		10	92.55	odd	22
368.2.m.c.353.1		10	92.3	odd	22
529.2.a.i.1.5		5	23.2	even	11
529.2.a.j.1.5		5	23.21	odd	22
529.2.c.a.118.1		10	23.14	odd	22
529.2.c.a.399.1		10	23.20	odd	22
529.2.c.b.170.1		10	23.6	even	11
529.2.c.b.501.1		10	23.16	even	11
529.2.c.c.170.1		10	23.17	odd	22
529.2.c.c.501.1		10	23.7	odd	22
529.2.c.d.177.1		10	23.8	even	11
529.2.c.d.266.1		10	23.12	even	11
529.2.c.e.177.1		10	23.15	odd	22
529.2.c.e.266.1		10	23.11	odd	22
529.2.c.f.466.1		10	23.22	odd	2
529.2.c.f.487.1		10	23.19	odd	22
529.2.c.g.466.1		10	1.1	even	1	trivial
529.2.c.g.487.1		10	23.4	even	11	inner
529.2.c.h.255.1		10	23.10	odd	22
529.2.c.h.334.1		10	23.5	odd	22
529.2.c.i.255.1		10	23.13	even	11
529.2.c.i.334.1		10	23.18	even	11
575.2.k.b.26.1		10	115.9	even	22
575.2.k.b.376.1		10	115.49	even	22
575.2.p.b.49.1		20	115.78	odd	44
575.2.p.b.49.2		20	115.32	odd	44
575.2.p.b.399.1		20	115.72	odd	44
575.2.p.b.399.2		20	115.3	odd	44
4761.2.a.bn.1.1		5	69.44	even	22
4761.2.a.bo.1.1		5	69.2	odd	22
8464.2.a.bs.1.5		5	92.71	odd	22
8464.2.a.bt.1.5		5	92.67	even	22

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Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
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Newspace parameters

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Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	529.2.c.g.466.1

Level	$529$
Weight	$2$
Character	529.466
Analytic conductor	$4.224$
Analytic rank	$0$
Dimension	$10$
Inner twists	$2$