LMFDB - Embedded newform 23.2.c.a.8.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [23,2,Mod(2,23)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(23, base_ring=CyclotomicField(22)) chi = DirichletCharacter(H, H._module([2])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("23.2"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$N$	$=$	$23$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	23.c (of order $11$ , degree $10$ , minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$0.183655924649$
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:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			8.1
Root			$0.142315 - 0.989821i$ of defining polynomial
Character	$\chi$	$=$	23.8
Dual form			23.2.c.a.3.1

$q$ -expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.313607 + 2.18119i) q^{2} +(-1.04408 - 2.28621i) q^{3} +(-2.74024 - 0.804606i) q^{4} +(0.809721 + 0.934468i) q^{5} +(5.31408 - 1.56036i) q^{6} +(-1.99611 - 1.28282i) q^{7} +(0.783524 - 1.71568i) q^{8} +(-2.17208 + 2.50672i) q^{9} +(-2.29218 + 1.47310i) q^{10} +(0.272084 + 1.89238i) q^{11} +(1.02152 + 7.10483i) q^{12} +(0.165284 - 0.106222i) q^{13} +(3.42408 - 3.95159i) q^{14} +(1.29098 - 2.82685i) q^{15} +(-1.30862 - 0.840996i) q^{16} +(1.49672 - 0.439476i) q^{17} +(-4.78644 - 5.52384i) q^{18} +(7.66103 + 2.24948i) q^{19} +(-1.46695 - 3.21217i) q^{20} +(-0.848710 + 5.90291i) q^{21} -4.21297 q^{22} +(-4.66752 - 1.10192i) q^{23} -4.74046 q^{24} +(0.493992 - 3.43579i) q^{25} +(0.179855 + 0.393828i) q^{26} +(0.764125 + 0.224367i) q^{27} +(4.43766 + 5.12133i) q^{28} +(-4.77570 + 1.40227i) q^{29} +(5.76103 + 3.70239i) q^{30} +(0.740552 - 1.62158i) q^{31} +(4.71506 - 5.44146i) q^{32} +(4.04231 - 2.59784i) q^{33} +(0.489198 + 3.40244i) q^{34} +(-0.417537 - 2.90404i) q^{35} +(7.96894 - 5.12133i) q^{36} +(-2.54297 + 2.93475i) q^{37} +(-7.30909 + 16.0047i) q^{38} +(-0.415415 - 0.266971i) q^{39} +(2.23768 - 0.657043i) q^{40} +(-0.279295 - 0.322324i) q^{41} +(-12.6092 - 3.70239i) q^{42} +(1.84991 + 4.05075i) q^{43} +(0.777050 - 5.40450i) q^{44} -4.10123 q^{45} +(3.86725 - 9.83517i) q^{46} -2.58842 q^{47} +(-0.556399 + 3.86984i) q^{48} +(-0.569072 - 1.24609i) q^{49} +(7.33918 + 2.15498i) q^{50} +(-2.56743 - 2.96297i) q^{51} +(-0.538385 + 0.158084i) q^{52} +(8.26060 + 5.30876i) q^{53} +(-0.729022 + 1.59634i) q^{54} +(-1.54806 + 1.78656i) q^{55} +(-3.76492 + 2.41956i) q^{56} +(-2.85592 - 19.8634i) q^{57} +(-1.56092 - 10.8565i) q^{58} +(-6.07293 + 3.90283i) q^{59} +(-5.81210 + 6.70752i) q^{60} +(3.08639 - 6.75826i) q^{61} +(3.30473 + 2.12382i) q^{62} +(7.55141 - 2.21729i) q^{63} +(8.35283 + 9.63968i) q^{64} +(0.233095 + 0.0684429i) q^{65} +(4.39867 + 9.63174i) q^{66} +(-1.03413 + 7.19254i) q^{67} -4.45497 q^{68} +(2.35404 + 11.8214i) q^{69} +6.46519 q^{70} +(0.103930 - 0.722850i) q^{71} +(2.59884 + 5.69067i) q^{72} +(6.18330 + 1.81558i) q^{73} +(-5.60373 - 6.46705i) q^{74} +(-8.37071 + 2.45786i) q^{75} +(-19.1831 - 12.3282i) q^{76} +(1.88449 - 4.12645i) q^{77} +(0.712591 - 0.822373i) q^{78} +(-4.77671 + 3.06980i) q^{79} +(-0.273730 - 1.90383i) q^{80} +(1.13126 + 7.86810i) q^{81} +(0.790638 - 0.508112i) q^{82} +(8.44098 - 9.74141i) q^{83} +(7.07518 - 15.4925i) q^{84} +(1.62260 + 1.04278i) q^{85} +(-9.41558 + 2.76466i) q^{86} +(8.19209 + 9.45418i) q^{87} +(3.45991 + 1.01592i) q^{88} +(-5.77436 - 12.6441i) q^{89} +(1.28618 - 8.94555i) q^{90} -0.466190 q^{91} +(11.9035 + 6.77503i) q^{92} -4.48047 q^{93} +(0.811746 - 5.64582i) q^{94} +(4.10123 + 8.98044i) q^{95} +(-17.3632 - 5.09830i) q^{96} +(-2.83147 - 3.26769i) q^{97} +(2.89643 - 0.850468i) q^{98} +(-5.33466 - 3.42838i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$10 q - 7 q^{2} - 7 q^{3} - 3 q^{4} - 3 q^{5} + 6 q^{6} - 5 q^{7} + 4 q^{8} - 2 q^{9} + q^{10} + 7 q^{11} + 12 q^{12} - 3 q^{13} + 9 q^{14} + 12 q^{15} + q^{16} - 10 q^{17} - 14 q^{18} + 2 q^{19} - 9 q^{20}+ \cdots - 30 q^{99}+O(q^{100})$ 10 * q - 7 * q^2 - 7 * q^3 - 3 * q^4 - 3 * q^5 + 6 * q^6 - 5 * q^7 + 4 * q^8 - 2 * q^9 + q^10 + 7 * q^11 + 12 * q^12 - 3 * q^13 + 9 * q^14 + 12 * q^15 + q^16 - 10 * q^17 - 14 * q^18 + 2 * q^19 - 9 * q^20 - 2 * q^21 - 6 * q^22 - 12 * q^23 - 38 * q^24 - 4 * q^25 + 12 * q^26 - 4 * q^27 + 7 * q^28 + 14 * q^29 + 7 * q^30 + 10 * q^31 + 21 * q^32 + 16 * q^33 + 29 * q^34 + 7 * q^35 + 27 * q^36 - 19 * q^37 - 8 * q^38 + q^39 + q^40 + 7 * q^41 - 25 * q^42 - 11 * q^43 - 34 * q^44 - 6 * q^45 - 29 * q^46 - 18 * q^47 + 18 * q^48 - 18 * q^49 + 16 * q^50 + 7 * q^51 - 20 * q^52 + 29 * q^53 - 6 * q^54 - q^55 - 2 * q^56 - 8 * q^57 - 23 * q^58 - 21 * q^59 + 25 * q^60 + 3 * q^61 + 4 * q^62 + 34 * q^63 + 24 * q^64 + 2 * q^65 + 2 * q^66 + 45 * q^67 - 30 * q^68 + 26 * q^69 + 38 * q^70 - 14 * q^71 + 19 * q^72 + 19 * q^73 + 10 * q^74 - 28 * q^75 - 16 * q^76 + 2 * q^77 - 4 * q^78 - 15 * q^79 - 52 * q^80 - 44 * q^81 + 16 * q^82 + 18 * q^83 - 17 * q^84 - 19 * q^85 - 11 * q^86 - 23 * q^87 + 27 * q^88 + 25 * q^89 - 20 * q^90 - 4 * q^91 + 52 * q^92 + 4 * q^93 + 17 * q^94 + 6 * q^95 - 51 * q^96 - 34 * q^97 + 17 * q^98 - 30 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/23\mathbb{Z}\right)^\times$ .

$n$	$5$
$\chi(n)$	$e\left(\frac{3}{11}\right)$

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

)

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

$2$	−0.313607	+	2.18119i	−0.221754	+	1.54233i	0.509647	+	0.860384i	$0.329776\pi$
$2$	−0.313607	+	2.18119i	−0.221754	+	1.54233i	−0.731401	+	0.681948i	$0.761133\pi$
$3$	−1.04408	−	2.28621i	−0.602799	−	1.31995i	−0.927392	−	0.374091i	$-0.877955\pi$
$3$	−1.04408	−	2.28621i	−0.602799	−	1.31995i	0.324593	−	0.945854i	$-0.394773\pi$
$4$	−2.74024	−	0.804606i	−1.37012	−	0.402303i
$5$	0.809721	+	0.934468i	0.362118	+	0.417907i	0.907348	−	0.420380i	$-0.138103\pi$
$5$	0.809721	+	0.934468i	0.362118	+	0.417907i	−0.545230	+	0.838287i	$0.683558\pi$
$6$	5.31408	−	1.56036i	2.16947	−	0.637013i
$7$	−1.99611	−	1.28282i	−0.754460	−	0.484862i	0.106009	−	0.994365i	$-0.466193\pi$
$7$	−1.99611	−	1.28282i	−0.754460	−	0.484862i	−0.860469	+	0.509503i	$0.829829\pi$
$8$	0.783524	−	1.71568i	0.277017	−	0.606584i
$9$	−2.17208	+	2.50672i	−0.724028	+	0.835573i
$10$	−2.29218	+	1.47310i	−0.724852	+	0.465834i
$11$	0.272084	+	1.89238i	0.0820363	+	0.570575i	0.988835	+	0.149012i	$0.0476093\pi$
$11$	0.272084	+	1.89238i	0.0820363	+	0.570575i	−0.906799	+	0.421563i	$0.861482\pi$
$12$	1.02152	+	7.10483i	0.294888	+	2.05099i
$13$	0.165284	−	0.106222i	0.0458416	−	0.0294606i	−0.517519	−	0.855672i	$-0.673144\pi$
$13$	0.165284	−	0.106222i	0.0458416	−	0.0294606i	0.563361	+	0.826211i	$0.309508\pi$
$14$	3.42408	−	3.95159i	0.915123	−	1.05611i
$15$	1.29098	−	2.82685i	0.333330	−	0.729890i
$16$	−1.30862	−	0.840996i	−0.327154	−	0.210249i
$17$	1.49672	−	0.439476i	0.363008	−	0.106589i	−0.0951421	−	0.995464i	$-0.530331\pi$
$17$	1.49672	−	0.439476i	0.363008	−	0.106589i	0.458150	+	0.888875i	$0.348512\pi$
$18$	−4.78644	−	5.52384i	−1.12817	−	1.30198i
$19$	7.66103	+	2.24948i	1.75756	+	0.516066i	0.991883	−	0.127157i	$-0.0405853\pi$
$19$	7.66103	+	2.24948i	1.75756	+	0.516066i	0.765678	+	0.643224i	$0.222403\pi$
$20$	−1.46695	−	3.21217i	−0.328020	−	0.718263i
$21$	−0.848710	+	5.90291i	−0.185204	+	1.28812i
$22$	−4.21297			−0.898208
$23$	−4.66752	−	1.10192i	−0.973246	−	0.229765i
$23$	−4.66752	−	1.10192i	−0.973246	−	0.229765i
$24$	−4.74046			−0.967643
$25$	0.493992	−	3.43579i	0.0987984	−	0.687158i
$26$	0.179855	+	0.393828i	0.0352725	+	0.0772359i
$27$	0.764125	+	0.224367i	0.147056	+	0.0431795i
$28$	4.43766	+	5.12133i	0.838638	+	0.967840i
$29$	−4.77570	+	1.40227i	−0.886825	+	0.260395i	−0.693256	−	0.720691i	$-0.743825\pi$
$29$	−4.77570	+	1.40227i	−0.886825	+	0.260395i	−0.193569	+	0.981087i	$0.562006\pi$
$30$	5.76103	+	3.70239i	1.05182	+	0.675961i
$31$	0.740552	−	1.62158i	0.133007	−	0.291245i	−0.831397	−	0.555680i	$-0.812458\pi$
$31$	0.740552	−	1.62158i	0.133007	−	0.291245i	0.964404	+	0.264435i	$0.0851854\pi$
$32$	4.71506	−	5.44146i	0.833512	−	0.961924i
$33$	4.04231	−	2.59784i	0.703677	−	0.452226i
$34$	0.489198	+	3.40244i	0.0838967	+	0.583514i
$35$	−0.417537	−	2.90404i	−0.0705767	−	0.490872i
$36$	7.96894	−	5.12133i	1.32816	−	0.853555i
$37$	−2.54297	+	2.93475i	−0.418062	+	0.482469i	−0.925246	−	0.379369i	$-0.876141\pi$
$37$	−2.54297	+	2.93475i	−0.418062	+	0.482469i	0.507184	+	0.861838i	$0.330687\pi$
$38$	−7.30909	+	16.0047i	−1.18569	+	2.59630i
$39$	−0.415415	−	0.266971i	−0.0665196	−	0.0427496i
$40$	2.23768	−	0.657043i	0.353809	−	0.103888i
$41$	−0.279295	−	0.322324i	−0.0436186	−	0.0503386i	0.733521	−	0.679667i	$-0.237876\pi$
$41$	−0.279295	−	0.322324i	−0.0436186	−	0.0503386i	−0.777140	+	0.629328i	$0.783330\pi$
$42$	−12.6092	−	3.70239i	−1.94564	−	0.571291i
$43$	1.84991	+	4.05075i	0.282109	+	0.617733i	0.996643	−	0.0818677i	$-0.0260885\pi$
$43$	1.84991	+	4.05075i	0.282109	+	0.617733i	−0.714534	+	0.699601i	$0.753361\pi$
$44$	0.777050	−	5.40450i	0.117145	−	0.814759i
$45$	−4.10123			−0.611375
$46$	3.86725	−	9.83517i	0.570195	−	1.45012i
$47$	−2.58842			−0.377559			−0.188780	−	0.982019i	$-0.560453\pi$
$47$	−2.58842			−0.377559			−0.188780	+	0.982019i	$0.560453\pi$
$48$	−0.556399	+	3.86984i	−0.0803092	+	0.558563i
$49$	−0.569072	−	1.24609i	−0.0812960	−	0.178013i
$50$	7.33918	+	2.15498i	1.03792	+	0.304760i
$51$	−2.56743	−	2.96297i	−0.359512	−	0.414898i
$52$	−0.538385	+	0.158084i	−0.0746605	+	0.0219223i
$53$	8.26060	+	5.30876i	1.13468	+	0.729215i	0.966532	−	0.256547i	$-0.0825848\pi$
$53$	8.26060	+	5.30876i	1.13468	+	0.729215i	0.168149	+	0.985762i	$0.446221\pi$
$54$	−0.729022	+	1.59634i	−0.0992074	+	0.217234i
$55$	−1.54806	+	1.78656i	−0.208741	+	0.240899i
$56$	−3.76492	+	2.41956i	−0.503108	+	0.323328i
$57$	−2.85592	−	19.8634i	−0.378276	−	2.63097i
$58$	−1.56092	−	10.8565i	−0.204959	−	1.42552i
$59$	−6.07293	+	3.90283i	−0.790628	+	0.508106i	−0.872545	−	0.488533i	$-0.837532\pi$
$59$	−6.07293	+	3.90283i	−0.790628	+	0.508106i	0.0819173	+	0.996639i	$0.473896\pi$
$60$	−5.81210	+	6.70752i	−0.750338	+	0.865936i
$61$	3.08639	−	6.75826i	0.395172	−	0.865306i	−0.602565	−	0.798070i	$-0.705855\pi$
$61$	3.08639	−	6.75826i	0.395172	−	0.865306i	0.997737	−	0.0672363i	$-0.0214181\pi$
$62$	3.30473	+	2.12382i	0.419701	+	0.269726i
$63$	7.55141	−	2.21729i	0.951388	−	0.279353i
$64$	8.35283	+	9.63968i	1.04410	+	1.20496i
$65$	0.233095	+	0.0684429i	0.0289119	+	0.00848929i
$66$	4.39867	+	9.63174i	0.541439	+	1.18559i
$67$	−1.03413	+	7.19254i	−0.126339	+	0.878708i	0.823800	+	0.566881i	$0.191850\pi$
$67$	−1.03413	+	7.19254i	−0.126339	+	0.878708i	−0.950139	+	0.311827i	$0.899059\pi$
$68$	−4.45497			−0.540244
$69$	2.35404	+	11.8214i	0.283394	+	1.42313i
$70$	6.46519			0.772738
$71$	0.103930	−	0.722850i	0.0123342	−	0.0857866i	−0.982725	−	0.185074i	$-0.940747\pi$
$71$	0.103930	−	0.722850i	0.0123342	−	0.0857866i	0.995059	+	0.0992879i	$0.0316565\pi$
$72$	2.59884	+	5.69067i	0.306276	+	0.670652i
$73$	6.18330	+	1.81558i	0.723700	+	0.212498i	0.622780	−	0.782397i	$-0.286003\pi$
$73$	6.18330	+	1.81558i	0.723700	+	0.212498i	0.100920	+	0.994895i	$0.467821\pi$
$74$	−5.60373	−	6.46705i	−0.651421	−	0.751780i
$75$	−8.37071	+	2.45786i	−0.966566	+	0.283809i
$76$	−19.1831	−	12.3282i	−2.20045	−	1.41414i
$77$	1.88449	−	4.12645i	0.214757	−	0.470253i
$78$	0.712591	−	0.822373i	0.0806850	−	0.0931154i
$79$	−4.77671	+	3.06980i	−0.537422	+	0.345380i	−0.781030	−	0.624494i	$-0.785305\pi$
$79$	−4.77671	+	3.06980i	−0.537422	+	0.345380i	0.243608	+	0.969874i	$0.421669\pi$
$80$	−0.273730	−	1.90383i	−0.0306039	−	0.212855i
$81$	1.13126	+	7.86810i	0.125696	+	0.874233i
$82$	0.790638	−	0.508112i	0.0873113	−	0.0561116i
$83$	8.44098	−	9.74141i	0.926518	−	1.06926i	−0.0709025	−	0.997483i	$-0.522588\pi$
$83$	8.44098	−	9.74141i	0.926518	−	1.06926i	0.997421	−	0.0717758i	$-0.0228666\pi$
$84$	7.07518	−	15.4925i	0.771966	−	1.69037i
$85$	1.62260	+	1.04278i	0.175996	+	0.113106i
$86$	−9.41558	+	2.76466i	−1.01531	+	0.298121i
$87$	8.19209	+	9.45418i	0.878284	+	1.01359i
$88$	3.45991	+	1.01592i	0.368827	+	0.108297i
$89$	−5.77436	−	12.6441i	−0.612081	−	1.34027i	−0.921141	−	0.389228i	$-0.872742\pi$
$89$	−5.77436	−	12.6441i	−0.612081	−	1.34027i	0.309060	−	0.951043i	$-0.399986\pi$
$90$	1.28618	−	8.94555i	0.135575	−	0.942944i
$91$	−0.466190			−0.0488700
$92$	11.9035	+	6.77503i	1.24103	+	0.706346i
$93$	−4.48047			−0.464603
$94$	0.811746	−	5.64582i	0.0837252	−	0.582322i
$95$	4.10123	+	8.98044i	0.420777	+	0.921374i
$96$	−17.3632	−	5.09830i	−1.77213	−	0.520343i
$97$	−2.83147	−	3.26769i	−0.287492	−	0.331783i	0.593572	−	0.804781i	$-0.297717\pi$
$97$	−2.83147	−	3.26769i	−0.287492	−	0.331783i	−0.881064	+	0.472998i	$0.843172\pi$
$98$	2.89643	−	0.850468i	0.292583	−	0.0859103i
$99$	−5.33466	−	3.42838i	−0.536154	−	0.344565i
$100$	−4.11811	+	9.01741i	−0.411811	+	0.901741i
$101$	1.19203	−	1.37567i	0.118611	−	0.136885i	−0.693338	−	0.720612i	$-0.743861\pi$
$101$	1.19203	−	1.37567i	0.118611	−	0.136885i	0.811950	+	0.583727i	$0.198406\pi$
$102$	7.26795	−	4.67083i	0.719634	−	0.462481i
$103$	2.17930	+	15.1574i	0.214733	+	1.49350i	0.757067	+	0.653337i	$0.226631\pi$
$103$	2.17930	+	15.1574i	0.214733	+	1.49350i	−0.542335	+	0.840163i	$0.682459\pi$
$104$	−0.0527381	−	0.366802i	−0.00517140	−	0.0359679i
$105$	−6.20330	+	3.98662i	−0.605380	+	0.389054i
$106$	−14.1700	+	16.3530i	−1.37631	+	1.58835i
$107$	0.825981	−	1.80865i	0.0798506	−	0.174848i	−0.865496	−	0.500916i	$-0.832996\pi$
$107$	0.825981	−	1.80865i	0.0798506	−	0.174848i	0.945346	+	0.326068i	$0.105724\pi$
$108$	−1.91336	−	1.22964i	−0.184113	−	0.118322i
$109$	−14.9631	+	4.39356i	−1.43320	+	0.420826i	−0.903950	−	0.427638i	$-0.859346\pi$
$109$	−14.9631	+	4.39356i	−1.43320	+	0.420826i	−0.529253	+	0.848464i	$0.677528\pi$
$110$	−3.41133	−	3.93689i	−0.325258	−	0.375367i
$111$	9.36451	+	2.74967i	0.888840	+	0.260987i
$112$	1.53330	+	3.35745i	0.144883	+	0.317249i
$113$	0.211799	−	1.47310i	0.0199244	−	0.138577i	−0.977431	−	0.211254i	$-0.932245\pi$
$113$	0.211799	−	1.47310i	0.0199244	−	0.138577i	0.997356	+	0.0726771i	$0.0231542\pi$
$114$	44.2213			4.14171
$115$	−2.74969	−	5.25390i	−0.256410	−	0.489929i
$116$	14.2148			1.31981
$117$	−0.0927432	+	0.645043i	−0.00857412	+	0.0596343i
$118$	−6.60829	−	14.4701i	−0.608343	−	1.33208i
$119$	−3.55139	−	1.04278i	−0.325556	−	0.0955917i
$120$	−3.83845	−	4.42981i	−0.350401	−	0.404385i
$121$	7.04733	−	2.06928i	0.640667	−	0.188117i
$122$	13.7731	+	8.85143i	1.24696	+	0.801371i
$123$	−0.445295	+	0.975060i	−0.0401509	+	0.0879182i
$124$	−3.33402	+	3.84767i	−0.299404	+	0.345531i
$125$	8.81159	−	5.66287i	0.788133	−	0.506502i
$126$	2.46815	+	17.1664i	0.219881	+	1.52930i
$127$	−0.853087	−	5.93335i	−0.0756993	−	0.526500i	−0.992023	−	0.126061i	$-0.959767\pi$
$127$	−0.853087	−	5.93335i	−0.0756993	−	0.526500i	0.916323	−	0.400439i	$-0.131142\pi$
$128$	−11.5312	+	7.41067i	−1.01923	+	0.655017i
$129$	7.32941	−	8.45859i	0.645319	−	0.744737i
$130$	−0.222387	+	0.486959i	−0.0195046	+	0.0427092i
$131$	−10.7418	−	6.90335i	−0.938517	−	0.603148i	−0.0205431	−	0.999789i	$-0.506540\pi$
$131$	−10.7418	−	6.90335i	−0.938517	−	0.603148i	−0.917974	+	0.396641i	$0.870176\pi$
$132$	−13.1671	+	3.86622i	−1.14605	+	0.336511i
$133$	−12.4066	−	14.3180i	−1.07579	−	1.24153i
$134$	−15.3640	−	4.51126i	−1.32724	−	0.389714i
$135$	0.409064	+	0.895726i	0.0352067	+	0.0770918i
$136$	0.418715	−	2.91223i	0.0359045	−	0.249721i
$137$	0.697560			0.0595966			0.0297983	−	0.999556i	$-0.490514\pi$
$137$	0.697560			0.0595966			0.0297983	+	0.999556i	$0.490514\pi$
$138$	−26.5230	+	1.42732i	−2.25779	+	0.121502i
$139$	13.9559			1.18372			0.591862	−	0.806039i	$-0.298393\pi$
$139$	13.9559			1.18372			0.591862	+	0.806039i	$0.298393\pi$
$140$	−1.19245	+	8.29370i	−0.100781	+	0.700946i
$141$	2.70251	+	5.91767i	0.227592	+	0.498358i
$142$	1.54408	+	0.453382i	0.129576	+	0.0380470i
$143$	0.245983	+	0.283880i	0.0205702	+	0.0237392i
$144$	4.95056	−	1.45362i	0.412547	−	0.121135i
$145$	−5.17736	−	3.32729i	−0.429957	−	0.276316i
$146$	−5.89924	+	12.9175i	−0.488225	+	1.06906i
$147$	−2.25468	+	2.60204i	−0.185963	+	0.214613i
$148$	9.32966	−	5.99581i	0.766893	−	0.492852i
$149$	2.36798	+	16.4697i	0.193993	+	1.34925i	0.821309	+	0.570483i	$0.193244\pi$
$149$	2.36798	+	16.4697i	0.193993	+	1.34925i	−0.627317	+	0.778764i	$0.715847\pi$
$150$	−2.73594	−	19.0289i	−0.223388	−	1.55370i
$151$	11.0961	−	7.13103i	0.902988	−	0.580315i	−0.00468679	−	0.999989i	$-0.501492\pi$
$151$	11.0961	−	7.13103i	0.902988	−	0.580315i	0.907675	+	0.419674i	$0.137855\pi$
$152$	9.86198	−	11.3813i	0.799913	−	0.923148i
$153$	−2.14935	+	4.70643i	−0.173765	+	0.380492i
$154$	8.40957	+	5.40450i	0.677662	+	0.435507i
$155$	2.11496	−	0.621008i	0.169877	−	0.0498805i
$156$	0.923529	+	1.06581i	0.0739415	+	0.0853330i
$157$	−3.96143	−	1.16318i	−0.316157	−	0.0928320i	0.119804	−	0.992798i	$-0.461773\pi$
$157$	−3.96143	−	1.16318i	−0.316157	−	0.0928320i	−0.435961	+	0.899965i	$0.643591\pi$
$158$	−5.19780	−	11.3816i	−0.413515	−	0.905471i
$159$	3.51225	−	24.4282i	0.278540	−	1.93729i
$160$	8.90276			0.703825
$161$	7.90335	+	8.18717i	0.622871	+	0.645239i
$162$	−17.5166			−1.37623
$163$	2.10474	−	14.6388i	0.164856	−	1.14660i	−0.724464	−	0.689312i	$-0.757913\pi$
$163$	2.10474	−	14.6388i	0.164856	−	1.14660i	0.889320	−	0.457285i	$-0.151178\pi$
$164$	0.505992	+	1.10797i	0.0395113	+	0.0865177i
$165$	5.70075	+	1.67389i	0.443802	+	0.130312i
$166$	18.6007	+	21.4663i	1.44369	+	1.66611i
$167$	−1.27588	+	0.374632i	−0.0987306	+	0.0289899i	−0.330725	−	0.943727i	$-0.607293\pi$
$167$	−1.27588	+	0.374632i	−0.0987306	+	0.0289899i	0.231994	+	0.972717i	$0.425475\pi$
$168$	9.46250	+	6.08118i	0.730048	+	0.469173i
$169$	−5.38436	+	11.7901i	−0.414181	+	0.906931i
$170$	−2.78336	+	3.21217i	−0.213474	+	0.246362i
$171$	−22.2792	+	14.3180i	−1.70373	+	1.09492i
$172$	−1.80995	−	12.5885i	−0.138007	−	0.959861i
$173$	2.41025	+	16.7637i	0.183248	+	1.27452i	0.849019	+	0.528362i	$0.177194\pi$
$173$	2.41025	+	16.7637i	0.183248	+	1.27452i	−0.665771	+	0.746156i	$0.731897\pi$
$174$	−23.1904	+	14.9036i	−1.75806	+	1.12984i
$175$	−5.39358	+	6.22452i	−0.407716	+	0.470530i
$176$	1.23543	−	2.70522i	0.0931244	−	0.203914i
$177$	15.2633	+	9.80914i	1.14726	+	0.737300i
$178$	29.3900	−	8.62968i	2.20287	−	0.646822i
$179$	0.937335	+	1.08174i	0.0700597	+	0.0808532i	0.789697	−	0.613497i	$-0.210238\pi$
$179$	0.937335	+	1.08174i	0.0700597	+	0.0808532i	−0.719638	+	0.694350i	$0.755692\pi$
$180$	11.2383	+	3.29988i	0.837657	+	0.245958i
$181$	−6.70121	−	14.6736i	−0.498097	−	1.09068i	−0.977083	−	0.212858i	$-0.931723\pi$
$181$	−6.70121	−	14.6736i	−0.498097	−	1.09068i	0.478986	−	0.877822i	$-0.341004\pi$
$182$	0.146201	−	1.01685i	0.0108371	−	0.0753737i
$183$	−18.6732			−1.38037
$184$	−5.54765	+	7.14459i	−0.408978	+	0.526706i
$185$	−4.80153			−0.353015
$186$	1.40511	−	9.77275i	0.103028	−	0.716573i
$187$	1.23889	+	2.71279i	0.0905967	+	0.198379i
$188$	7.09288	+	2.08266i	0.517301	+	0.151893i
$189$	−1.23746	−	1.42810i	−0.0900118	−	0.103879i
$190$	−20.8742	+	6.12922i	−1.51437	+	0.444660i
$191$	−17.4514	−	11.2153i	−1.26274	−	0.811512i	−0.274081	−	0.961707i	$-0.588374\pi$
$191$	−17.4514	−	11.2153i	−1.26274	−	0.811512i	−0.988656	+	0.150195i	$0.952010\pi$
$192$	13.3173	−	29.1609i	0.961096	−	2.10451i
$193$	−9.59519	+	11.0734i	−0.690677	+	0.797083i	−0.987461	−	0.157861i	$-0.949540\pi$
$193$	−9.59519	+	11.0734i	−0.690677	+	0.797083i	0.296785	+	0.954944i	$0.404086\pi$
$194$	8.01540	−	5.15119i	0.575472	−	0.369834i
$195$	−0.0868945	−	0.604364i	−0.00622264	−	0.0432794i
$196$	0.556778	+	3.87247i	0.0397698	+	0.276605i
$197$	9.82407	−	6.31355i	0.699936	−	0.449822i	−0.141669	−	0.989914i	$-0.545247\pi$
$197$	9.82407	−	6.31355i	0.699936	−	0.449822i	0.841606	+	0.540092i	$0.181611\pi$
$198$	9.15092	−	10.5607i	0.650328	−	0.750518i
$199$	−2.37759	+	5.20620i	−0.168543	+	0.369057i	−0.974990	−	0.222249i	$-0.928660\pi$
$199$	−2.37759	+	5.20620i	−0.168543	+	0.369057i	0.806447	+	0.591306i	$0.201388\pi$
$200$	−5.50765	−	3.53955i	−0.389450	−	0.250284i
$201$	17.5234	−	5.14533i	1.23600	−	0.362923i
$202$	2.62677	+	3.03146i	0.184819	+	0.213293i
$203$	11.3317	+	3.32729i	0.795330	+	0.233530i
$204$	4.65133	+	10.1850i	0.325659	+	0.713093i
$205$	0.0750502	−	0.521985i	0.00524173	−	0.0364570i
$206$	−33.7445			−2.35109
$207$	12.9004	−	9.30671i	0.896643	−	0.646861i
$208$	−0.305626			−0.0211913
$209$	−2.17244	+	15.1097i	−0.150271	+	1.04516i
$210$	−6.75016	−	14.7808i	−0.465805	−	1.01997i
$211$	13.4979	+	3.96334i	0.929234	+	0.272848i	0.711116	−	0.703075i	$-0.248190\pi$
$211$	13.4979	+	3.96334i	0.929234	+	0.272848i	0.218118	+	0.975922i	$0.430008\pi$
$212$	−18.3645	−	21.1938i	−1.26128	−	1.45560i
$213$	−1.76110	+	0.517106i	−0.120669	+	0.0354315i
$214$	3.68596	+	2.36882i	0.251967	+	0.161929i
$215$	−2.28738	+	5.00866i	−0.155998	+	0.341588i
$216$	0.983652	−	1.13520i	0.0669291	−	0.0772403i
$217$	−3.55843	+	2.28687i	−0.241562	+	0.155243i
$218$	−4.89064	−	34.0151i	−0.331236	−	2.30379i
$219$	−2.30504	−	16.0319i	−0.155760	−	1.08334i
$220$	5.67953	−	3.65001i	0.382914	−	0.246084i
$221$	0.200702	−	0.231623i	0.0135007	−	0.0155806i
$222$	−8.93432	+	19.5634i	−0.599632	+	1.31301i
$223$	−3.53628	−	2.27263i	−0.236807	−	0.152187i	0.416856	−	0.908973i	$-0.363132\pi$
$223$	−3.53628	−	2.27263i	−0.236807	−	0.152187i	−0.653663	+	0.756786i	$0.726768\pi$
$224$	−16.3922	+	4.81319i	−1.09525	+	0.321595i
$225$	7.53956	+	8.70112i	0.502638	+	0.580075i
$226$	3.14668	+	0.923948i	0.209314	+	0.0614601i
$227$	7.65642	+	16.7652i	0.508174	+	1.11275i	0.973725	+	0.227726i	$0.0731289\pi$
$227$	7.65642	+	16.7652i	0.508174	+	1.11275i	−0.465551	+	0.885021i	$0.654144\pi$
$228$	−8.15629	+	56.7282i	−0.540163	+	3.75692i
$229$	10.9247			0.721923			0.360961	−	0.932581i	$-0.382449\pi$
$229$	10.9247			0.721923			0.360961	+	0.932581i	$0.382449\pi$
$230$	12.3221	−	4.34992i	0.812492	−	0.286825i
$231$	−11.4015			−0.750163
$232$	−1.33603	+	9.29227i	−0.0877145	+	0.610068i
$233$	1.73013	+	3.78846i	0.113345	+	0.248190i	0.957800	−	0.287436i	$-0.0928029\pi$
$233$	1.73013	+	3.78846i	0.113345	+	0.248190i	−0.844455	+	0.535626i	$0.820076\pi$
$234$	−1.37787	−	0.404581i	−0.0900745	−	0.0264483i
$235$	−2.09590	−	2.41879i	−0.136721	−	0.157785i
$236$	19.7815	−	5.80837i	1.28767	−	0.378093i
$237$	12.0055	+	7.71545i	0.779839	+	0.501172i
$238$	3.38825	−	7.41922i	0.219627	−	0.480917i
$239$	14.7456	−	17.0173i	0.953813	−	1.10076i	−0.0410120	−	0.999159i	$-0.513058\pi$
$239$	14.7456	−	17.0173i	0.953813	−	1.10076i	0.994825	−	0.101601i	$-0.0323964\pi$
$240$	−4.06677	+	2.61355i	−0.262509	+	0.168704i
$241$	−0.843804	−	5.86878i	−0.0543542	−	0.378042i	−0.998783	−	0.0493250i	$-0.984293\pi$
$241$	−0.843804	−	5.86878i	−0.0543542	−	0.378042i	0.944429	−	0.328717i	$-0.106616\pi$
$242$	2.30340	+	16.0205i	0.148068	+	1.02984i
$243$	18.8169	−	12.0929i	1.20710	−	0.775759i
$244$	−13.8952	+	16.0359i	−0.889548	+	1.02659i
$245$	0.703646	−	1.54077i	0.0449543	−	0.0984361i
$246$	−1.98714	−	1.27706i	−0.126695	−	0.0814222i
$247$	1.50519	−	0.441964i	0.0957730	−	0.0281215i
$248$	−2.20187	−	2.54110i	−0.139819	−	0.161360i
$249$	−31.0840	−	9.12708i	−1.96987	−	0.578405i
$250$	9.58839	+	20.9956i	0.606423	+	1.32788i
$251$	0.220675	−	1.53483i	0.0139289	−	0.0968775i	−0.981671	−	0.190583i	$-0.938962\pi$
$251$	0.220675	−	1.53483i	0.0139289	−	0.0968775i	0.995600	+	0.0937056i	$0.0298712\pi$
$252$	−22.4767			−1.41590
$253$	0.815292	−	9.13256i	0.0512570	−	0.574159i
$254$	13.2093			0.828824
$255$	0.689900	−	4.79836i	0.0432032	−	0.300485i
$256$	−1.95044	−	4.27088i	−0.121903	−	0.266930i
$257$	−26.3456	−	7.73578i	−1.64340	−	0.482545i	−0.676230	−	0.736690i	$-0.736388\pi$
$257$	−26.3456	−	7.73578i	−1.64340	−	0.482545i	−0.967166	+	0.254145i	$0.918206\pi$
$258$	16.1512	+	18.6395i	1.00553	+	1.16044i
$259$	8.84083	−	2.59590i	0.549342	−	0.161301i
$260$	−0.583666	−	0.375099i	−0.0361974	−	0.0232627i
$261$	6.85812	−	15.0172i	0.424507	−	0.929540i
$262$	18.4262	−	21.2650i	1.13837	−	1.31375i
$263$	−10.8864	+	6.99627i	−0.671285	+	0.431408i	−0.831388	−	0.555692i	$-0.812453\pi$
$263$	−10.8864	+	6.99627i	−0.671285	+	0.431408i	0.160104	+	0.987100i	$0.448817\pi$
$264$	−1.28980	−	8.97078i	−0.0793819	−	0.552113i
$265$	1.72791	+	12.0179i	0.106145	+	0.738253i
$266$	35.1210	−	22.5709i	2.15341	−	1.38391i
$267$	−22.8782	+	26.4028i	−1.40012	+	1.61583i
$268$	8.62092	−	18.8772i	0.526607	−	1.15311i
$269$	−8.41057	−	5.40514i	−0.512801	−	0.329557i	0.258517	−	0.966007i	$-0.416766\pi$
$269$	−8.41057	−	5.40514i	−0.512801	−	0.329557i	−0.771319	+	0.636449i	$0.780402\pi$
$270$	−2.08203	+	0.611339i	−0.126708	+	0.0372049i
$271$	−2.88885	−	3.33391i	−0.175485	−	0.202520i	0.661193	−	0.750216i	$-0.270051\pi$
$271$	−2.88885	−	3.33391i	−0.175485	−	0.202520i	−0.836678	+	0.547696i	$0.815505\pi$
$272$	−2.32823	−	0.683629i	−0.141169	−	0.0414511i
$273$	0.486739	+	1.06581i	0.0294588	+	0.0645057i
$274$	−0.218760	+	1.52151i	−0.0132158	+	0.0919177i
$275$	6.63624			0.400180
$276$	3.06096	−	34.2876i	0.184248	−	2.06387i
$277$	−30.8042			−1.85085			−0.925423	−	0.378935i	$-0.876290\pi$
$277$	−30.8042			−1.85085			−0.925423	+	0.378935i	$0.876290\pi$
$278$	−4.37667	+	30.4404i	−0.262495	+	1.82570i
$279$	2.45631	+	5.37857i	0.147055	+	0.322006i
$280$	−5.30954	−	1.55902i	−0.317306	−	0.0931694i
$281$	2.34395	+	2.70506i	0.139828	+	0.161370i	0.821344	−	0.570433i	$-0.193225\pi$
$281$	2.34395	+	2.70506i	0.139828	+	0.161370i	−0.681516	+	0.731803i	$0.738679\pi$
$282$	−13.7551	+	4.03885i	−0.819102	+	0.240510i
$283$	12.4341	+	7.99089i	0.739129	+	0.475009i	0.855243	−	0.518227i	$-0.173408\pi$
$283$	12.4341	+	7.99089i	0.739129	+	0.475009i	−0.116115	+	0.993236i	$0.537044\pi$
$284$	−0.866403	+	1.89716i	−0.0514116	+	0.112576i
$285$	16.2492	−	18.7526i	0.962519	−	1.11081i
$286$	−0.696337	+	0.447509i	−0.0411753	+	0.0264618i
$287$	0.144020	+	1.00168i	0.00850125	+	0.0591275i
$288$	3.39872	+	23.6386i	0.200272	+	1.39292i
$289$	−12.2543	+	7.87535i	−0.720840	+	0.463256i
$290$	8.88110	−	10.2493i	0.521516	−	0.601862i
$291$	−4.51435	+	9.88506i	−0.264636	+	0.579472i
$292$	−15.4829	−	9.95024i	−0.906067	−	0.582294i
$293$	−20.6420	+	6.06104i	−1.20592	+	0.354090i	−0.822113	−	0.569324i	$-0.807205\pi$
$293$	−20.6420	+	6.06104i	−1.20592	+	0.354090i	−0.383806	+	0.923414i	$0.625387\pi$
$294$	−4.96845	−	5.73389i	−0.289766	−	0.334408i
$295$	−8.56445	−	2.51475i	−0.498642	−	0.146414i
$296$	3.04260	+	6.66236i	0.176847	+	0.387242i
$297$	−0.216683	+	1.50707i	−0.0125732	+	0.0874488i
$298$	−36.6660			−2.12401
$299$	−0.888516	+	0.313663i	−0.0513842	+	0.0181396i
$300$	24.9153			1.43849
$301$	1.50376	−	10.4589i	0.0866752	−	0.602839i
$302$	12.0743	+	26.4390i	0.694797	+	1.52139i
$303$	−4.38965	−	1.28892i	−0.252179	−	0.0740464i
$304$	−8.13354	−	9.38660i	−0.466490	−	0.538359i
$305$	8.81450	−	2.58817i	0.504717	−	0.148198i
$306$	−9.59155	−	6.16411i	−0.548312	−	0.352379i
$307$	5.87602	−	12.8667i	0.335362	−	0.734341i	−0.664555	−	0.747240i	$-0.731379\pi$
$307$	5.87602	−	12.8667i	0.335362	−	0.734341i	0.999917	+	0.0128989i	$0.00410596\pi$
$308$	−8.48411	+	9.79118i	−0.483427	+	0.557904i
$309$	32.3776	−	20.8078i	1.84190	−	1.18371i
$310$	0.691267	+	4.80787i	0.0392613	+	0.273069i
$311$	−0.0811393	−	0.564336i	−0.00460099	−	0.0320006i	0.987392	−	0.158297i	$-0.0506002\pi$
$311$	−0.0811393	−	0.564336i	−0.00460099	−	0.0320006i	−0.991993	+	0.126296i	$0.959691\pi$
$312$	−0.783524	+	0.503540i	−0.0443583	+	0.0285073i
$313$	13.8390	−	15.9711i	0.782227	−	0.902738i	−0.215041	−	0.976605i	$-0.568989\pi$
$313$	13.8390	−	15.9711i	0.782227	−	0.902738i	0.997268	+	0.0738672i	$0.0235341\pi$
$314$	3.77945	−	8.27584i	0.213287	−	0.467033i
$315$	8.18653	+	5.26116i	0.461259	+	0.296433i
$316$	15.5593	−	4.56862i	0.875279	−	0.257005i
$317$	5.77072	+	6.65977i	0.324116	+	0.374050i	0.894301	−	0.447467i	$-0.147674\pi$
$317$	5.77072	+	6.65977i	0.324116	+	0.374050i	−0.570185	+	0.821517i	$0.693128\pi$
$318$	52.1811	+	15.3217i	2.92617	+	0.859201i
$319$	−3.95303	−	8.65592i	−0.221327	−	0.484639i
$320$	−2.24451	+	15.6109i	−0.125472	+	0.872676i
$321$	−4.99734			−0.278924
$322$	−20.3363	+	14.6711i	−1.13330	+	0.817589i
$323$	12.4550			0.693015
$324$	3.23080	−	22.4707i	0.179489	−	1.24837i
$325$	−0.283306	−	0.620354i	−0.0157150	−	0.0344111i
$326$	31.2698	+	9.18165i	1.73188	+	0.508525i
$327$	25.6672	+	29.6216i	1.41940	+	1.63808i
$328$	−0.771839	+	0.226632i	−0.0426177	+	0.0125137i
$329$	5.16678	+	3.32049i	0.284854	+	0.183064i
$330$	−5.43886	+	11.9094i	−0.299399	+	0.655593i
$331$	−19.7686	+	22.8142i	−1.08658	+	1.25398i	−0.121342	+	0.992611i	$0.538720\pi$
$331$	−19.7686	+	22.8142i	−1.08658	+	1.25398i	−0.965239	+	0.261371i	$0.915826\pi$
$332$	−30.9683	+	19.9021i	−1.69961	+	1.09227i
$333$	−1.83303	−	12.7490i	−0.100450	−	0.698642i
$334$	−0.417017	−	2.90042i	−0.0228182	−	0.158704i
$335$	−7.55856	+	4.85759i	−0.412968	+	0.265398i
$336$	6.07496	−	7.01088i	0.331416	−	0.382475i
$337$	−2.05870	+	4.50792i	−0.112145	+	0.245562i	−0.957380	−	0.288832i	$-0.906733\pi$
$337$	−2.05870	+	4.50792i	−0.112145	+	0.245562i	0.845235	+	0.534394i	$0.179460\pi$
$338$	−24.0278	−	15.4418i	−1.30694	−	0.839920i
$339$	−3.58895	+	1.05381i	−0.194925	+	0.0572351i
$340$	−3.60728	−	4.16303i	−0.195632	−	0.225772i
$341$	3.27015	+	0.960202i	0.177088	+	0.0519979i
$342$	−24.2433	−	53.0853i	−1.31093	−	2.87053i
$343$	−2.82637	+	19.6578i	−0.152609	+	1.06142i
$344$	8.39923			0.452856
$345$	−9.14064	+	11.7719i	−0.492115	+	0.633775i
$346$	−37.3205			−2.00636
$347$	0.963038	−	6.69808i	0.0516986	−	0.359572i	−0.947508	−	0.319733i	$-0.896407\pi$
$347$	0.963038	−	6.69808i	0.0516986	−	0.359572i	0.999206	−	0.0398383i	$-0.0126843\pi$
$348$	−14.8414	−	32.4981i	−0.795582	−	1.74208i
$349$	−9.68306	−	2.84320i	−0.518322	−	0.152193i	0.0121000	−	0.999927i	$-0.496148\pi$
$349$	−9.68306	−	2.84320i	−0.518322	−	0.152193i	−0.530422	+	0.847734i	$0.677967\pi$
$350$	−11.8854	−	13.7165i	−0.635300	−	0.733175i
$351$	0.150131	−	0.0440823i	0.00801338	−	0.00235294i
$352$	11.5802	+	7.44216i	0.617228	+	0.396669i
$353$	10.1649	−	22.2580i	0.541023	−	1.18468i	−0.419827	−	0.907604i	$-0.637909\pi$
$353$	10.1649	−	22.2580i	0.541023	−	1.18468i	0.960850	−	0.277071i	$-0.0893636\pi$
$354$	−26.1822	+	30.2159i	−1.39157	+	1.60596i
$355$	0.759635	−	0.488188i	0.0403173	−	0.0259103i
$356$	5.64961	+	39.2939i	0.299429	+	2.08257i
$357$	1.32391	+	9.20798i	0.0700686	+	0.487338i
$358$	−2.65343	+	1.70526i	−0.140238	+	0.0901257i
$359$	−0.274264	+	0.316518i	−0.0144751	+	0.0167052i	−0.762941	−	0.646468i	$-0.776245\pi$
$359$	−0.274264	+	0.316518i	−0.0144751	+	0.0167052i	0.748466	+	0.663173i	$0.230791\pi$
$360$	−3.21341	+	7.03639i	−0.169362	+	0.370850i
$361$	37.6474	+	24.1945i	1.98144	+	1.27340i
$362$	34.1074	−	10.0148i	1.79265	−	0.526368i
$363$	−12.0888	−	13.9512i	−0.634497	−	0.732248i
$364$	1.27747	+	0.375099i	0.0669577	+	0.0196606i
$365$	3.31015	+	7.24821i	0.173261	+	0.379389i
$366$	5.85606	−	40.7298i	0.306101	−	2.12898i
$367$	28.5682			1.49125			0.745624	−	0.666367i	$-0.232151\pi$
$367$	28.5682			1.49125			0.745624	+	0.666367i	$0.232151\pi$
$368$	5.18129	+	5.36735i	0.270093	+	0.279793i
$369$	1.41463			0.0736426
$370$	1.50579	−	10.4730i	0.0782825	−	0.544466i
$371$	−9.67888	−	21.1938i	−0.502503	−	1.10033i
$372$	12.2776	+	3.60502i	0.636562	+	0.186911i
$373$	−9.43508	−	10.8887i	−0.488530	−	0.563794i	0.456942	−	0.889496i	$-0.348945\pi$
$373$	−9.43508	−	10.8887i	−0.488530	−	0.563794i	−0.945472	+	0.325703i	$0.894399\pi$
$374$	−6.30563	+	1.85150i	−0.326056	+	0.0957388i
$375$	−22.1465	−	14.2327i	−1.14364	−	0.734973i
$376$	−2.02809	+	4.44089i	−0.104591	+	0.229021i
$377$	−0.640396	+	0.739056i	−0.0329821	+	0.0380633i
$378$	3.50303	−	2.25126i	0.180176	−	0.115792i
$379$	0.800823	+	5.56985i	0.0411355	+	0.286104i	0.999998	+	0.00223119i	$0.000710211\pi$
$379$	0.800823	+	5.56985i	0.0411355	+	0.286104i	−0.958862	+	0.283873i	$0.908381\pi$
$380$	−4.01263	−	27.9084i	−0.205843	−	1.43167i
$381$	−12.6742	+	8.14522i	−0.649320	+	0.417292i
$382$	29.9356	−	34.5475i	1.53164	−	1.76760i
$383$	0.0962350	−	0.210725i	0.00491738	−	0.0107676i	−0.907157	−	0.420792i	$-0.861752\pi$
$383$	0.0962350	−	0.210725i	0.00491738	−	0.0107676i	0.912075	+	0.410024i	$0.134480\pi$
$384$	28.9819	+	18.6255i	1.47898	+	0.950480i
$385$	5.38195	−	1.58028i	0.274289	−	0.0805386i
$386$	−21.1441	−	24.4016i	−1.07621	−	1.24201i
$387$	−14.1722	−	4.16135i	−0.720416	−	0.211533i
$388$	5.12969	+	11.2325i	0.260421	+	0.570241i
$389$	4.29361	−	29.8627i	0.217695	−	1.51410i	−0.528821	−	0.848733i	$-0.677366\pi$
$389$	4.29361	−	29.8627i	0.217695	−	1.51410i	0.746516	−	0.665367i	$-0.231725\pi$
$390$	1.34548			0.0681311
$391$	−7.47023	+	0.402007i	−0.377786	+	0.0203304i
$392$	−2.58378			−0.130500
$393$	−4.56722	+	31.7657i	−0.230386	+	1.60237i
$394$	10.6901	+	23.4081i	0.538561	+	1.17928i
$395$	−6.73644	−	1.97800i	−0.338947	−	0.0995238i
$396$	11.8597	+	13.6869i	0.595975	+	0.687791i
$397$	12.5168	−	3.67528i	0.628202	−	0.184457i	0.0478924	−	0.998853i	$-0.484750\pi$
$397$	12.5168	−	3.67528i	0.628202	−	0.184457i	0.580310	+	0.814396i	$0.302931\pi$
$398$	−10.6101	−	6.81867i	−0.531834	−	0.341789i
$399$	−19.7805	+	43.3132i	−0.990263	+	2.16837i
$400$	−3.53593	+	4.08068i	−0.176797	+	0.204034i
$401$	−17.9404	+	11.5296i	−0.895899	+	0.575759i	−0.905571	−	0.424194i	$-0.860557\pi$
$401$	−17.9404	+	11.5296i	−0.895899	+	0.575759i	0.00967246	+	0.999953i	$0.496921\pi$
$402$	5.72746	+	39.8354i	0.285660	+	1.98681i
$403$	−0.0498457	−	0.346685i	−0.00248299	−	0.0172696i
$404$	−4.37332	+	2.81056i	−0.217581	+	0.139831i
$405$	−6.43648	+	7.42810i	−0.319831	+	0.369105i
$406$	−10.8111	+	23.6731i	−0.536548	+	1.17488i
$407$	−6.24557	−	4.01378i	−0.309581	−	0.198956i
$408$	−7.09514	+	2.08332i	−0.351262	+	0.103140i
$409$	5.99134	+	6.91437i	0.296253	+	0.341894i	0.884288	−	0.466941i	$-0.154644\pi$
$409$	5.99134	+	6.91437i	0.296253	+	0.341894i	−0.588036	+	0.808835i	$0.700099\pi$
$410$	1.11501	+	0.327397i	0.0550665	+	0.0161690i
$411$	−0.728307	−	1.59477i	−0.0359247	−	0.0786642i
$412$	6.22391	−	43.2882i	0.306630	−	2.13266i
$413$	17.1289			0.842859
$414$	16.2540	+	31.0569i	0.798840	+	1.52636i
$415$	15.9379			0.782360
$416$	0.201323	−	1.40023i	0.00987065	−	0.0686519i
$417$	−14.5711	−	31.9062i	−0.713548	−	1.56245i
$418$	−32.2757	−	9.47700i	−1.57866	−	0.463535i
$419$	5.87685	+	6.78225i	0.287103	+	0.331334i	0.880920	−	0.473266i	$-0.156925\pi$
$419$	5.87685	+	6.78225i	0.287103	+	0.331334i	−0.593817	+	0.804600i	$0.702380\pi$
$420$	20.2062	−	5.93307i	0.985960	−	0.289504i
$421$	26.4762	+	17.0152i	1.29037	+	0.829270i	0.992129	−	0.125221i	$-0.0399638\pi$
$421$	26.4762	+	17.0152i	1.29037	+	0.829270i	0.298241	+	0.954491i	$0.403600\pi$
$422$	−12.8778	+	28.1985i	−0.626882	+	1.37268i
$423$	5.62226	−	6.48843i	0.273364	−	0.315478i
$424$	15.5805	−	10.0130i	0.756656	−	0.486273i
$425$	−0.770581	−	5.35951i	−0.0373787	−	0.259974i
$426$	−0.575610	−	4.00346i	−0.0278884	−	0.193968i
$427$	−14.8305	+	9.53095i	−0.717696	+	0.461235i
$428$	−3.71863	+	4.29153i	−0.179747	+	0.207439i
$429$	0.392184	−	0.858763i	0.0189348	−	0.0414615i
$430$	−10.2075	−	6.55995i	−0.492249	−	0.316349i
$431$	21.2071	−	6.22697i	1.02151	−	0.299942i	0.272256	−	0.962225i	$-0.412230\pi$
$431$	21.2071	−	6.22697i	1.02151	−	0.299942i	0.749254	+	0.662283i	$0.230412\pi$
$432$	−0.811254	−	0.936237i	−0.0390315	−	0.0450447i
$433$	−12.1810	−	3.57666i	−0.585382	−	0.171884i	−0.0243864	−	0.999703i	$-0.507763\pi$
$433$	−12.1810	−	3.57666i	−0.585382	−	0.171884i	−0.560995	+	0.827819i	$0.689581\pi$
$434$	−3.87213	−	8.47878i	−0.185868	−	0.406994i
$435$	−2.20132	+	15.3105i	−0.105545	+	0.734082i
$436$	44.5375			2.13296
$437$	−33.2793	−	18.9413i	−1.59196	−	0.906086i
$438$	35.6915			1.70541
$439$	−2.62158	+	18.2335i	−0.125121	+	0.870238i	0.826494	+	0.562946i	$0.190332\pi$
$439$	−2.62158	+	18.2335i	−0.125121	+	0.870238i	−0.951615	+	0.307292i	$0.900577\pi$
$440$	1.85221	+	4.05578i	0.0883009	+	0.193352i
$441$	4.35968	+	1.28012i	0.207604	+	0.0609580i
$442$	0.442270	+	0.510407i	0.0210366	+	0.0242776i
$443$	13.3492	−	3.91968i	0.634240	−	0.186230i	0.0512201	−	0.998687i	$-0.483689\pi$
$443$	13.3492	−	3.91968i	0.634240	−	0.186230i	0.583020	+	0.812458i	$0.301871\pi$
$444$	−23.4486	−	15.0695i	−1.11282	−	0.715166i
$445$	7.13988	−	15.6342i	0.338463	−	0.741130i
$446$	6.06603	−	7.00057i	0.287235	−	0.331487i
$447$	35.1808	−	22.6093i	1.66399	−	1.06938i
$448$	−4.30718	−	29.9571i	−0.203495	−	1.41534i
$449$	−4.28260	−	29.7862i	−0.202109	−	1.40570i	−0.798013	−	0.602641i	$-0.794115\pi$
$449$	−4.28260	−	29.7862i	−0.202109	−	1.40570i	0.595904	−	0.803056i	$-0.296794\pi$
$450$	−21.3432	+	13.7165i	−1.00613	+	0.646600i
$451$	0.533969	−	0.616233i	0.0251436	−	0.0290173i
$452$	−1.76564	+	3.86622i	−0.0830489	+	0.181852i
$453$	−27.8883	−	17.9227i	−1.31030	−	0.842082i
$454$	−38.9692	+	11.4424i	−1.82891	+	0.537017i
$455$	−0.377484	−	0.435640i	−0.0176967	−	0.0204231i
$456$	−36.3168	−	10.6636i	−1.70069	−	0.499368i
$457$	15.8055	+	34.6093i	0.739351	+	1.61895i	0.784619	+	0.619978i	$0.212859\pi$
$457$	15.8055	+	34.6093i	0.739351	+	1.61895i	−0.0452680	+	0.998975i	$0.514414\pi$
$458$	−3.42606	+	23.8287i	−0.160089	+	1.11344i
$459$	1.24228			0.0579849
$460$	3.30748	+	16.6093i	0.154212	+	0.774415i
$461$	8.76016			0.408001			0.204001	−	0.978971i	$-0.434606\pi$
$461$	8.76016			0.408001			0.204001	+	0.978971i	$0.434606\pi$
$462$	3.57559	−	24.8688i	0.166352	−	1.15700i
$463$	−11.5638	−	25.3212i	−0.537415	−	1.17677i	−0.962416	−	0.271581i	$-0.912453\pi$
$463$	−11.5638	−	25.3212i	−0.537415	−	1.17677i	0.425001	−	0.905193i	$-0.360274\pi$
$464$	7.42886	+	2.18131i	0.344876	+	0.101265i
$465$	−3.62794	−	4.18686i	−0.168241	−	0.194161i
$466$	−8.80592	+	2.58565i	−0.407926	+	0.119778i
$467$	−14.6095	−	9.38895i	−0.676047	−	0.434469i	0.157054	−	0.987590i	$-0.449800\pi$
$467$	−14.6095	−	9.38895i	−0.676047	−	0.434469i	−0.833101	+	0.553121i	$0.813437\pi$
$468$	0.773144	−	1.69295i	0.0357386	−	0.0782566i
$469$	11.2910	−	13.0305i	0.521370	−	0.601693i
$470$	5.93313	−	3.81299i	0.273675	−	0.175880i
$471$	1.47677	+	10.2711i	0.0680458	+	0.473269i
$472$	1.93772	+	13.4771i	0.0891909	+	0.620336i
$473$	−7.16224	+	4.60289i	−0.329320	+	0.211641i
$474$	−20.5938	+	23.7666i	−0.945906	+	1.09163i
$475$	11.5132	−	25.2105i	0.528263	−	1.15674i
$476$	8.89263	+	5.71494i	0.407593	+	0.261944i
$477$	−31.2503	+	9.17591i	−1.43085	+	0.420136i
$478$	32.4936	+	37.4996i	1.48622	+	1.71519i
$479$	24.4458	+	7.17792i	1.11695	+	0.327968i	0.787568	−	0.616228i	$-0.211340\pi$
$479$	24.4458	+	7.17792i	1.11695	+	0.327968i	0.329387	+	0.944195i	$0.393158\pi$
$480$	−9.29517	−	20.3536i	−0.424265	−	0.929010i
$481$	−0.108579	+	0.755186i	−0.00495079	+	0.0344335i
$482$	13.0655			0.595119
$483$	10.4659	−	26.6168i	0.476214	−	1.21110i
$484$	−20.9763			−0.953469
$485$	0.760851	−	5.29183i	0.0345485	−	0.240290i
$486$	20.4757	+	44.8356i	0.928797	+	2.03378i
$487$	5.91151	+	1.73577i	0.267876	+	0.0786555i	0.412912	−	0.910771i	$-0.364512\pi$
$487$	5.91151	+	1.73577i	0.267876	+	0.0786555i	−0.145036	+	0.989426i	$0.546330\pi$
$488$	−9.17673	−	10.5905i	−0.415411	−	0.479410i
$489$	−35.6649	+	10.4721i	−1.61282	+	0.473567i
$490$	3.14004	+	2.01798i	0.141852	+	0.0911630i
$491$	−13.5623	+	29.6973i	−0.612058	+	1.34022i	0.309099	+	0.951030i	$0.399973\pi$
$491$	−13.5623	+	29.6973i	−0.612058	+	1.34022i	−0.921157	+	0.389191i	$0.872755\pi$
$492$	2.00475	−	2.31361i	0.0903812	−	0.104306i
$493$	−6.53161	+	4.19761i	−0.294169	+	0.189051i
$494$	0.491967	+	3.42171i	0.0221346	+	0.153950i
$495$	−1.11588	−	7.76111i	−0.0501550	−	0.348836i
$496$	−2.33284	+	1.49923i	−0.104748	+	0.0673172i
$497$	−1.13475	+	1.30957i	−0.0509004	+	0.0587421i
$498$	29.6560	−	64.9376i	1.32892	−	2.90992i
$499$	−7.21265	−	4.63529i	−0.322882	−	0.207504i	0.369151	−	0.929369i	$-0.379649\pi$
$499$	−7.21265	−	4.63529i	−0.322882	−	0.207504i	−0.692033	+	0.721866i	$0.743285\pi$
$500$	−28.7022	+	8.42774i	−1.28360	+	0.376900i
$501$	2.18861	+	2.52579i	0.0977797	+	0.112844i
$502$	3.27854	+	0.962667i	0.146329	+	0.0429659i
$503$	2.80635	+	6.14505i	0.125129	+	0.273994i	0.961821	−	0.273679i	$-0.0882408\pi$
$503$	2.80635	+	6.14505i	0.125129	+	0.273994i	−0.836692	+	0.547674i	$0.815513\pi$
$504$	2.11255	−	14.6931i	0.0941003	−	0.654482i
$505$	2.25073			0.100156
$506$	19.6641	+	4.64234i	0.874177	+	0.206377i
$507$	32.5764			1.44677
$508$	−2.43635	+	16.9452i	−0.108096	+	0.751821i
$509$	17.0206	+	37.2699i	0.754425	+	1.65196i	0.758246	+	0.651968i	$0.226057\pi$
$509$	17.0206	+	37.2699i	0.754425	+	1.65196i	−0.00382066	+	0.999993i	$0.501216\pi$
$510$	10.2498	+	3.00960i	0.453867	+	0.133267i
$511$	−10.0135	−	11.5562i	−0.442971	−	0.511216i
$512$	−16.3767	+	4.80863i	−0.723754	+	0.212513i
$513$	5.34928	+	3.43777i	0.236176	+	0.151781i
$514$	25.1354	−	55.0388i	1.10867	−	2.42766i
$515$	−12.3995	+	14.3097i	−0.546385	+	0.630562i
$516$	−26.8902	+	17.2813i	−1.18377	+	0.760765i
$517$	−0.704266	−	4.89828i	−0.0309736	−	0.215426i
$518$	2.88960	+	20.0976i	0.126962	+	0.883037i
$519$	35.8088	−	23.0129i	1.57183	−	1.01016i
$520$	0.300061	−	0.346289i	0.0131586	−	0.0151858i
$521$	−7.77941	+	17.0345i	−0.340822	+	0.746297i	−0.999984	−	0.00570487i	$-0.998184\pi$
$521$	−7.77941	+	17.0345i	−0.340822	+	0.746297i	0.659162	+	0.752001i	$0.270911\pi$
$522$	30.6045	+	19.6683i	1.33952	+	0.860859i
$523$	−22.6095	+	6.63875i	−0.988644	+	0.290292i	−0.735788	−	0.677212i	$-0.763188\pi$
$523$	−22.6095	+	6.63875i	−0.988644	+	0.290292i	−0.252856	+	0.967504i	$0.581370\pi$
$524$	23.8807	+	27.5597i	1.04323	+	1.20395i
$525$	19.8619	+	5.83198i	0.866844	+	0.254528i
$526$	−11.8461	−	25.9394i	−0.516515	−	1.13101i
$527$	0.395751	−	2.75251i	0.0172392	−	0.119901i
$528$	−7.47461			−0.325291
$529$	20.5716	+	10.2864i	0.894416	+	0.447237i
$530$	−26.7551			−1.16217
$531$	3.40760	−	23.7004i	0.147877	−	1.02851i
$532$	22.4767	+	49.2171i	0.974488	+	2.13383i
$533$	−0.0804009	−	0.0236078i	−0.00348255	−	0.00102257i
$534$	−50.4147	−	58.1817i	−2.18166	−	2.51777i
$535$	2.35894	−	0.692647i	0.101986	−	0.0299457i
$536$	11.5298	+	7.40976i	0.498012	+	0.320053i
$537$	1.49444	−	3.27237i	0.0644899	−	0.141213i
$538$	14.4272	−	16.6499i	0.622002	−	0.717829i
$539$	2.20325	−	1.41595i	0.0949009	−	0.0609891i
$540$	−0.400227	−	2.78364i	−0.0172230	−	0.119789i
$541$	−0.135667	−	0.943585i	−0.00583278	−	0.0405679i	0.986697	−	0.162569i	$-0.0519780\pi$
$541$	−0.135667	−	0.943585i	−0.00583278	−	0.0405679i	−0.992530	+	0.122001i	$0.961069\pi$
$542$	8.17784	−	5.25558i	0.351268	−	0.225746i
$543$	−26.5504	+	30.6408i	−1.13939	+	1.31492i
$544$	4.66572	−	10.2165i	0.200041	−	0.438029i
$545$	−16.2216	−	10.4250i	−0.694856	−	0.446557i
$546$	−2.47737	+	0.727422i	−0.106022	+	0.0311308i
$547$	−19.5057	−	22.5108i	−0.834003	−	0.962491i	0.165717	−	0.986173i	$-0.447006\pi$
$547$	−19.5057	−	22.5108i	−0.834003	−	0.962491i	−0.999720	+	0.0236827i	$0.992461\pi$
$548$	−1.91148	−	0.561261i	−0.0816544	−	0.0239759i
$549$	10.2371	+	22.4162i	0.436911	+	0.956701i
$550$	−2.08117	+	14.4749i	−0.0887415	+	0.617211i
$551$	−39.7412			−1.69303
$552$	22.1262	+	5.22359i	0.941754	+	0.222331i
$553$	13.4729			0.572925
$554$	9.66043	−	67.1897i	0.410432	−	2.85462i
$555$	5.01317	+	10.9773i	0.212797	+	0.465961i
$556$	−38.2425	−	11.2290i	−1.62184	−	0.476216i
$557$	3.93487	+	4.54108i	0.166726	+	0.192412i	0.832964	−	0.553327i	$-0.186642\pi$
$557$	3.93487	+	4.54108i	0.166726	+	0.192412i	−0.666238	+	0.745739i	$0.732097\pi$
$558$	−12.5020	+	3.67091i	−0.529251	+	0.155402i
$559$	0.736039	+	0.473023i	0.0311311	+	0.0200068i
$560$	−1.89589	+	4.15141i	−0.0801159	+	0.175429i
$561$	4.90852	−	5.66473i	0.207238	−	0.239165i
$562$	−6.63532	+	4.26426i	−0.279894	+	0.179877i
$563$	−0.0126931	−	0.0882822i	−0.000534949	−	0.00372065i	0.989552	−	0.144175i	$-0.0460528\pi$
$563$	−0.0126931	−	0.0882822i	−0.000534949	−	0.00372065i	−0.990087	+	0.140454i	$0.955144\pi$
$564$	−2.64412	−	18.3903i	−0.111338	−	0.774370i
$565$	1.54806	−	0.994879i	0.0651274	−	0.0418549i
$566$	−21.3290	+	24.6150i	−0.896526	+	1.03465i
$567$	7.83526	−	17.1568i	0.329050	−	0.720519i
$568$	−1.15875	−	0.744681i	−0.0486199	−	0.0312461i
$569$	39.6842	−	11.6523i	1.66365	−	0.488491i	0.691406	−	0.722466i	$-0.256991\pi$
$569$	39.6842	−	11.6523i	1.66365	−	0.488491i	0.972243	+	0.233975i	$0.0751733\pi$
$570$	35.8070	+	41.3235i	1.49979	+	1.73085i
$571$	−24.7458	−	7.26602i	−1.03558	−	0.304073i	−0.280602	−	0.959824i	$-0.590534\pi$
$571$	−24.7458	−	7.26602i	−1.03558	−	0.304073i	−0.754977	+	0.655751i	$0.772352\pi$
$572$	−0.445641	−	0.975819i	−0.0186332	−	0.0408010i
$573$	−7.42000	+	51.6072i	−0.309975	+	2.15592i
$574$	−2.23002			−0.0930793
$575$	−6.09167	+	15.4923i	−0.254040	+	0.646073i
$576$	−42.3070			−1.76279
$577$	−3.86302	+	26.8679i	−0.160820	+	1.11853i	0.736273	+	0.676684i	$0.236584\pi$
$577$	−3.86302	+	26.8679i	−0.160820	+	1.11853i	−0.897093	+	0.441842i	$0.854325\pi$
$578$	−13.3346	−	29.1986i	−0.554645	−	1.21450i
$579$	35.3343	+	10.3751i	1.46845	+	0.431174i
$580$	11.5100	+	13.2833i	0.477929	+	0.551559i
$581$	−29.3457	+	8.61667i	−1.21746	+	0.357480i
$582$	−20.1454	−	12.9467i	−0.835054	−	0.536657i
$583$	−7.79865	+	17.0767i	−0.322987	+	0.707243i
$584$	7.95971	−	9.18600i	0.329375	−	0.380119i
$585$	−0.677869	+	0.435640i	−0.0280264	+	0.0180115i
$586$	−6.74678	−	46.9249i	−0.278707	−	1.93845i
$587$	−4.50210	−	31.3128i	−0.185822	−	1.29242i	−0.842685	−	0.538407i	$-0.819026\pi$
$587$	−4.50210	−	31.3128i	−0.185822	−	1.29242i	0.656863	−	0.754010i	$-0.271883\pi$
$588$	8.27197	−	5.31608i	0.341130	−	0.219231i
$589$	9.32111	−	10.7571i	0.384070	−	0.443240i
$590$	8.17101	−	17.8920i	0.336395	−	0.736603i
$591$	−24.6912	−	15.8681i	−1.01566	−	0.652726i
$592$	5.79588	−	1.70182i	0.238209	−	0.0699446i
$593$	16.8600	+	19.4575i	0.692358	+	0.799024i	0.987699	−	0.156368i	$-0.0499786\pi$
$593$	16.8600	+	19.4575i	0.692358	+	0.799024i	−0.295341	+	0.955392i	$0.595433\pi$
$594$	−3.21924	−	0.945253i	−0.132087	−	0.0387842i
$595$	−1.90119	−	4.16303i	−0.0779412	−	0.170667i
$596$	6.76277	−	47.0361i	0.277014	−	1.92667i
$597$	14.3849			0.588733
$598$	−0.405513	−	2.03638i	−0.0165826	−	0.0832740i
$599$	16.9434			0.692289			0.346144	−	0.938181i	$-0.387491\pi$
$599$	16.9434			0.692289			0.346144	+	0.938181i	$0.387491\pi$
$600$	−2.34175	+	16.2872i	−0.0956015	+	0.664923i
$601$	−4.01081	−	8.78246i	−0.163605	−	0.358244i	0.810019	−	0.586403i	$-0.199457\pi$
$601$	−4.01081	−	8.78246i	−0.163605	−	0.358244i	−0.973624	+	0.228159i	$0.926729\pi$
$602$	22.3411	+	6.55995i	0.910557	+	0.267364i
$603$	−15.7834	−	18.2151i	−0.642752	−	0.741775i
$604$	−36.1436	+	10.6127i	−1.47066	+	0.431826i
$605$	7.64006	+	4.90997i	0.310613	+	0.199619i
$606$	4.18800	−	9.17043i	0.170126	−	0.372523i
$607$	−2.12520	+	2.45261i	−0.0862592	+	0.0995484i	−0.797238	−	0.603665i	$-0.793707\pi$
$607$	−2.12520	+	2.45261i	−0.0862592	+	0.0995484i	0.710979	+	0.703213i	$0.248252\pi$
$608$	48.3627	−	31.0808i	1.96136	−	1.26049i
$609$	−4.22430	−	29.3806i	−0.171177	−	1.19056i
$610$	2.88099	+	20.0377i	0.116648	+	0.811304i
$611$	−0.427825	+	0.274946i	−0.0173079	+	0.0111231i
$612$	9.67656	−	11.1673i	0.391152	−	0.451413i
$613$	−13.6731	+	29.9399i	−0.552251	+	1.20926i	0.403471	+	0.914992i	$0.367803\pi$
$613$	−13.6731	+	29.9399i	−0.552251	+	1.20926i	−0.955723	+	0.294269i	$0.904924\pi$
$614$	26.2219	+	16.8518i	1.05823	+	0.680083i
$615$	−1.27173	+	0.373413i	−0.0512810	+	0.0150575i
$616$	−5.60312	−	6.46634i	−0.225756	−	0.260536i
$617$	−2.90191	−	0.852079i	−0.116827	−	0.0343034i	0.222797	−	0.974865i	$-0.428481\pi$
$617$	−2.90191	−	0.852079i	−0.116827	−	0.0343034i	−0.339623	+	0.940562i	$0.610300\pi$
$618$	35.2319	+	77.1470i	1.41723	+	3.10331i
$619$	−1.48326	+	10.3163i	−0.0596172	+	0.414647i	0.938057	+	0.346482i	$0.112624\pi$
$619$	−1.48326	+	10.3163i	−0.0596172	+	0.414647i	−0.997674	+	0.0681655i	$0.978285\pi$
$620$	−6.29515			−0.252819
$621$	−3.31934	−	1.88924i	−0.133200	−	0.0758127i
$622$	1.25637			0.0503758
$623$	−4.69386	+	32.6465i	−0.188056	+	1.30796i
$624$	0.319097	+	0.698725i	0.0127741	+	0.0279714i
$625$	−4.22587	−	1.24083i	−0.169035	−	0.0496331i
$626$	30.4958	+	35.1941i	1.21886	+	1.40664i
$627$	36.8121	−	10.8090i	1.47013	−	0.431670i
$628$	9.91937	+	6.37479i	0.395826	+	0.254382i
$629$	−2.51636	+	5.51006i	−0.100334	+	0.219701i
$630$	−14.0429	+	16.2064i	−0.559484	+	0.645678i
$631$	28.6878	−	18.4366i	1.14205	−	0.733948i	0.174005	−	0.984745i	$-0.444329\pi$
$631$	28.6878	−	18.4366i	1.14205	−	0.733948i	0.968040	+	0.250797i	$0.0806926\pi$
$632$	1.52413	+	10.6006i	0.0606266	+	0.421667i
$633$	−5.03182	−	34.9971i	−0.199997	−	1.39101i
$634$	−16.3359	+	10.4985i	−0.648783	+	0.416947i
$635$	4.85377	−	5.60155i	0.192616	−	0.222291i
$636$	−29.2795	+	64.1132i	−1.16101	+	2.54225i
$637$	−0.226421	−	0.145512i	−0.00897113	−	0.00576539i
$638$	20.1199	−	5.90773i	0.796553	−	0.233889i
$639$	1.58624	+	1.83062i	0.0627506	+	0.0724180i
$640$	−16.2621	−	4.77499i	−0.642817	−	0.188748i
$641$	−3.74109	−	8.19184i	−0.147764	−	0.323558i	0.821248	−	0.570571i	$-0.193278\pi$
$641$	−3.74109	−	8.19184i	−0.147764	−	0.323558i	−0.969012	+	0.247013i	$0.920551\pi$
$642$	1.56720	−	10.9001i	0.0618525	−	0.430194i
$643$	−22.9522			−0.905146			−0.452573	−	0.891727i	$-0.649494\pi$
$643$	−22.9522			−0.905146			−0.452573	+	0.891727i	$0.649494\pi$
$644$	−15.0696	−	28.7939i	−0.593825	−	1.13464i
$645$	13.8391			0.544913
$646$	−3.90598	+	27.1667i	−0.153679	+	1.06886i
$647$	−18.6747	−	40.8919i	−0.734178	−	1.60763i	−0.792900	−	0.609352i	$-0.791430\pi$
$647$	−18.6747	−	40.8919i	−0.734178	−	1.60763i	0.0587216	−	0.998274i	$-0.481298\pi$
$648$	14.3855	+	4.22396i	0.565115	+	0.165933i
$649$	−9.03801	−	10.4304i	−0.354773	−	0.409430i
$650$	1.44196	−	0.423396i	0.0565581	−	0.0166070i
$651$	8.94354	+	5.74766i	0.350525	+	0.225269i
$652$	−17.5459	+	38.4202i	−0.687152	+	1.50465i
$653$	19.2289	−	22.1914i	0.752486	−	0.868415i	−0.242321	−	0.970196i	$-0.577909\pi$
$653$	19.2289	−	22.1914i	0.752486	−	0.868415i	0.994807	+	0.101781i	$0.0324542\pi$
$654$	−72.6596	+	46.6955i	−2.84121	+	1.82594i
$655$	−2.24692	−	15.6277i	−0.0877945	−	0.610624i
$656$	0.0944170	+	0.656685i	0.00368636	+	0.0256392i
$657$	−17.9818	+	11.5562i	−0.701536	+	0.450850i
$658$	−8.86294	+	10.2284i	−0.345513	+	0.398744i
$659$	−16.6805	+	36.5251i	−0.649778	+	1.42282i	0.241970	+	0.970284i	$0.422206\pi$
$659$	−16.6805	+	36.5251i	−0.649778	+	1.42282i	−0.891748	+	0.452532i	$0.850521\pi$
$660$	−14.2746	−	9.17371i	−0.555637	−	0.357086i
$661$	−9.56288	+	2.80792i	−0.371953	+	0.109215i	−0.462366	−	0.886689i	$-0.652999\pi$
$661$	−9.56288	+	2.80792i	−0.371953	+	0.109215i	0.0904132	+	0.995904i	$0.471181\pi$
$662$	−43.5624	−	50.2737i	−1.69310	−	1.95394i
$663$	−0.739087	−	0.217015i	−0.0287037	−	0.00842818i
$664$	−10.0994	−	22.1146i	−0.391933	−	0.858214i
$665$	3.33381	−	23.1872i	0.129280	−	0.899159i
$666$	28.3829			1.09981
$667$	23.8359	−	1.28272i	0.922929	−	0.0496669i
$668$	3.79764			0.146935
$669$	−1.50356	+	10.4575i	−0.0581310	+	0.404310i
$670$	−8.22489	−	18.0100i	−0.317755	−	0.695787i
$671$	13.6290	+	4.00183i	0.526141	+	0.154489i
$672$	28.1188	+	32.4508i	1.08470	+	1.25182i
$673$	32.6772	−	9.59489i	1.25961	−	0.369856i	0.417263	−	0.908786i	$-0.362989\pi$
$673$	32.6772	−	9.59489i	1.25961	−	0.369856i	0.842351	+	0.538930i	$0.181171\pi$
$674$	−9.18700	−	5.90412i	−0.353870	−	0.227418i
$675$	1.14835	−	2.51454i	0.0442000	−	0.0967846i
$676$	24.2408	−	27.9754i	0.932339	−	1.07598i
$677$	−21.0239	+	13.5112i	−0.808012	+	0.519278i	−0.878221	−	0.478254i	$-0.841270\pi$
$677$	−21.0239	+	13.5112i	−0.808012	+	0.519278i	0.0702091	+	0.997532i	$0.477633\pi$
$678$	−1.17304	−	8.15864i	−0.0450502	−	0.313331i
$679$	1.46006	+	10.1550i	0.0560320	+	0.389711i
$680$	3.06043	−	1.96682i	0.117362	−	0.0754240i
$681$	30.3349	−	35.0084i	1.16244	−	1.34152i
$682$	−3.11992	+	6.83168i	−0.119468	+	0.261598i
$683$	29.0032	+	18.6392i	1.10978	+	0.713210i	0.961244	−	0.275698i	$-0.0889088\pi$
$683$	29.0032	+	18.6392i	1.10978	+	0.713210i	0.148532	+	0.988908i	$0.452545\pi$
$684$	72.5707	−	21.3087i	2.77481	−	0.814757i
$685$	0.564829	+	0.651848i	0.0215810	+	0.0249058i
$686$	−41.9910	−	12.3297i	−1.60322	−	0.470749i
$687$	−11.4062	−	24.9761i	−0.435174	−	0.952898i
$688$	0.985836	−	6.85664i	0.0375846	−	0.261407i
$689$	1.92925			0.0734987
$690$	−22.8100	−	23.6292i	−0.868363	−	0.899547i
$691$	−21.2259			−0.807470			−0.403735	−	0.914876i	$-0.632288\pi$
$691$	−21.2259			−0.807470			−0.403735	+	0.914876i	$0.632288\pi$
$692$	6.88349	−	47.8757i	0.261671	−	1.81996i
$693$	6.25059	+	13.6869i	0.237440	+	0.519921i
$694$	14.3077	+	4.20113i	0.543114	+	0.159473i
$695$	11.3004	+	13.0414i	0.428649	+	0.494687i
$696$	22.6390	−	6.64742i	0.858130	−	0.251970i
$697$	−0.559680	−	0.359685i	−0.0211994	−	0.0136240i
$698$	9.23823	−	20.2289i	0.349672	−	0.765675i
$699$	6.85483	−	7.91090i	0.259274	−	0.299218i
$700$	19.7880	−	12.7170i	0.747915	−	0.480656i
$701$	3.43351	+	23.8806i	0.129682	+	0.901957i	0.945957	+	0.324293i	$0.105126\pi$
$701$	3.43351	+	23.8806i	0.129682	+	0.901957i	−0.816275	+	0.577664i	$0.803965\pi$
$702$	0.0490697	+	0.341287i	0.00185202	+	0.0128811i
$703$	−26.0834	+	16.7628i	−0.983756	+	0.632221i
$704$	−15.9693	+	18.4296i	−0.601866	+	0.694590i
$705$	−3.34160	+	7.31707i	−0.125852	+	0.275577i
$706$	45.3611	+	29.1518i	1.70719	+	1.09714i
$707$	−4.14417	+	1.21684i	−0.155858	+	0.0457639i
$708$	−33.9326	−	39.1603i	−1.27527	−	1.47173i
$709$	−6.75188	−	1.98253i	−0.253572	−	0.0744556i	0.152476	−	0.988307i	$-0.451275\pi$
$709$	−6.75188	−	1.98253i	−0.253572	−	0.0744556i	−0.406048	+	0.913852i	$0.633094\pi$
$710$	0.826602	+	1.81001i	0.0310218	+	0.0679283i
$711$	2.68028	−	18.6417i	0.100518	−	0.699119i
$712$	−26.2175			−0.982544
$713$	−5.24339	+	6.75275i	−0.196367	+	0.252892i
$714$	−20.4995			−0.767175
$715$	−0.0660988	+	0.459728i	−0.00247196	+	0.0171928i
$716$	−1.69814	−	3.71841i	−0.0634626	−	0.138964i
$717$	−54.3008	−	15.9441i	−2.02790	−	0.595445i
$718$	−0.604373	−	0.697483i	−0.0225550	−	0.0260298i
$719$	−25.4920	+	7.48514i	−0.950693	+	0.279149i	−0.720075	−	0.693896i	$-0.755893\pi$
$719$	−25.4920	+	7.48514i	−0.950693	+	0.279149i	−0.230618	+	0.973044i	$0.574075\pi$
$720$	5.36693	+	3.44912i	0.200014	+	0.128541i
$721$	15.0941	−	33.0515i	0.562134	−	1.23090i
$722$	−64.5792	+	74.5284i	−2.40339	+	2.77366i
$723$	−12.5363	+	8.05658i	−0.466230	+	0.299628i
$724$	6.55643	+	45.6010i	0.243668	+	1.69475i
$725$	2.45875	+	17.1010i	0.0913158	+	0.635115i
$726$	34.2213	−	21.9927i	1.27007	−	0.816226i
$727$	3.42332	−	3.95072i	0.126964	−	0.146524i	−0.688708	−	0.725039i	$-0.741822\pi$
$727$	3.42332	−	3.95072i	0.126964	−	0.146524i	0.815672	+	0.578514i	$0.196367\pi$
$728$	−0.365271	+	0.799832i	−0.0135378	+	0.0296437i
$729$	−27.2318	−	17.5008i	−1.00859	−	0.648179i
$730$	−16.8478	+	4.94696i	−0.623564	+	0.183095i
$731$	4.54901	+	5.24983i	0.168251	+	0.194172i
$732$	51.1691	+	15.0246i	1.89126	+	0.555325i
$733$	−11.0870	−	24.2771i	−0.409506	−	0.896694i	−0.996217	−	0.0868973i	$-0.972305\pi$
$733$	−11.0870	−	24.2771i	−0.409506	−	0.896694i	0.586711	−	0.809796i	$-0.300422\pi$
$734$	−8.95920	+	62.3126i	−0.330690	+	2.30000i
$735$	−4.25719			−0.157029
$736$	−28.0037	+	20.2026i	−1.03223	+	0.744677i
$737$	−13.8924			−0.511734
$738$	−0.443638	+	3.08557i	−0.0163305	+	0.113581i
$739$	−0.930342	−	2.03716i	−0.0342232	−	0.0749383i	0.891748	−	0.452532i	$-0.149479\pi$
$739$	−0.930342	−	2.03716i	−0.0342232	−	0.0749383i	−0.925972	+	0.377593i	$0.876752\pi$
$740$	13.1573	+	3.86334i	0.483673	+	0.142019i
$741$	−2.58196	−	2.97974i	−0.0948507	−	0.109464i
$742$	49.2630	−	14.4649i	1.80850	−	0.531024i
$743$	15.2605	+	9.80730i	0.559852	+	0.359795i	0.789759	−	0.613418i	$-0.210206\pi$
$743$	15.2605	+	9.80730i	0.559852	+	0.359795i	−0.229907	+	0.973213i	$0.573842\pi$
$744$	−3.51056	+	7.68705i	−0.128703	+	0.281821i
$745$	−13.4730	+	15.5486i	−0.493612	+	0.569658i
$746$	26.7091	−	17.1649i	0.977890	−	0.628452i
$747$	6.08446	+	42.3183i	0.222619	+	1.54835i
$748$	−1.21212	−	8.43051i	−0.0443197	−	0.308250i
$749$	−3.96893	+	2.55068i	−0.145022	+	0.0931997i
$750$	37.9895	−	43.8422i	1.38718	−	1.60089i
$751$	11.7258	−	25.6759i	0.427880	−	0.936927i	−0.565786	−	0.824552i	$-0.691427\pi$
$751$	11.7258	−	25.6759i	0.427880	−	0.936927i	0.993666	−	0.112375i	$-0.0358457\pi$
$752$	3.38724	+	2.17685i	0.123520	+	0.0793815i
$753$	−3.73935	+	1.09797i	−0.136269	+	0.0400123i
$754$	−1.41119	−	1.62860i	−0.0513924	−	0.0593100i
$755$	15.6485	+	4.59481i	0.569507	+	0.167222i
$756$	2.24187	+	4.90900i	0.0815359	+	0.178539i
$757$	−0.0173643	+	0.120772i	−0.000631118	+	0.00438952i	−0.990135	−	0.140120i	$-0.955251\pi$
$757$	−0.0173643	+	0.120772i	−0.000631118	+	0.00438952i	0.989503	+	0.144509i	$0.0461603\pi$
$758$	−12.4000			−0.450389
$759$	−21.7302	+	7.67118i	−0.788756	+	0.278446i
$760$	18.6210			0.675453
$761$	3.80057	−	26.4336i	0.137771	−	0.958216i	−0.797257	−	0.603640i	$-0.793716\pi$
$761$	3.80057	−	26.4336i	0.137771	−	0.958216i	0.935027	−	0.354576i	$-0.115375\pi$
$762$	−13.7915	−	30.1992i	−0.499614	−	1.09400i
$763$	35.5042	+	10.4250i	1.28534	+	0.377409i
$764$	38.7970	+	44.7741i	1.40363	+	1.61987i
$765$	−6.13839	+	1.80239i	−0.221934	+	0.0651657i
$766$	0.429451	+	0.275992i	0.0155167	+	0.00997198i
$767$	−0.589194	+	1.29015i	−0.0212745	+	0.0465848i
$768$	−7.72771	+	8.91825i	−0.278850	+	0.321810i
$769$	−6.60471	+	4.24459i	−0.238172	+	0.153064i	−0.654283	−	0.756250i	$-0.727029\pi$
$769$	−6.60471	+	4.24459i	−0.238172	+	0.153064i	0.416111	+	0.909314i	$0.363393\pi$
$770$	1.75907	+	12.2346i	0.0633926	+	0.440905i
$771$	9.82128	+	68.3085i	0.353705	+	2.46007i
$772$	35.2028	−	22.6235i	1.26698	−	0.814237i
$773$	22.4497	−	25.9084i	0.807460	−	0.931859i	−0.191305	−	0.981531i	$-0.561272\pi$
$773$	22.4497	−	25.9084i	0.807460	−	0.931859i	0.998766	+	0.0496716i	$0.0158175\pi$
$774$	13.5212	−	29.6073i	0.486009	−	1.06421i
$775$	−5.20559	−	3.34543i	−0.186990	−	0.120171i
$776$	−7.82482	+	2.29757i	−0.280895	+	0.0824781i
$777$	−15.1653	−	17.5017i	−0.544052	−	0.627869i
$778$	63.7897	+	18.7303i	2.28697	+	0.671515i
$779$	−1.41463	−	3.09760i	−0.0506843	−	0.110983i
$780$	−0.248164	+	1.72602i	−0.00888569	+	0.0618013i
$781$	1.39619			0.0499596
$782$	1.46587	−	16.4200i	0.0524193	−	0.587180i
$783$	−3.96386			−0.141657
$784$	−0.303264	+	2.10925i	−0.0108308	+	0.0753302i
$785$	−2.12070	−	4.64369i	−0.0756911	−	0.165740i
$786$	−67.8546	−	19.9239i	−2.42029	−	0.710662i
$787$	−10.4860	−	12.1015i	−0.373785	−	0.431370i	0.537426	−	0.843311i	$-0.319397\pi$
$787$	−10.4860	−	12.1015i	−0.373785	−	0.431370i	−0.911211	+	0.411940i	$0.864851\pi$
$788$	−32.0002	+	9.39611i	−1.13996	+	0.334723i
$789$	27.3612	+	17.5840i	0.974085	+	0.626006i
$790$	6.42697	−	14.0731i	0.228661	−	0.500699i
$791$	−2.31250	+	2.66877i	−0.0822231	+	0.0948905i
$792$	−10.0618	+	6.46634i	−0.357531	+	0.229772i
$793$	−0.207742	−	1.44488i	−0.00737712	−	0.0513090i
$794$	4.09109	+	28.4542i	0.145187	+	1.00980i
$795$	25.6714	−	16.4980i	0.910469	−	0.585123i
$796$	10.7041	−	12.3532i	0.379397	−	0.437847i
$797$	8.94128	−	19.5787i	0.316716	−	0.693512i	−0.682588	−	0.730803i	$-0.739146\pi$
$797$	8.94128	−	19.5787i	0.316716	−	0.693512i	0.999304	+	0.0372914i	$0.0118730\pi$
$798$	−88.2709	−	56.7282i	−3.12475	−	2.00816i
$799$	−3.87413	+	1.13755i	−0.137057	+	0.0402435i
$800$	−16.3665	−	18.8880i	−0.578644	−	0.667791i
$801$	44.2376	+	12.9893i	1.56306	+	0.458955i
$802$	−19.5219	−	42.7470i	−0.689343	−	1.50945i
$803$	−1.75340	+	12.1952i	−0.0618761	+	0.430358i
$804$	−52.1582			−1.83948
$805$	−1.25114	+	14.0148i	−0.0440969	+	0.493955i
$806$	0.771816			0.0271860
$807$	−3.57601	+	24.8717i	−0.125882	+	0.875526i
$808$	−1.42623	−	3.12301i	−0.0501746	−	0.109867i
$809$	−23.1479	−	6.79683i	−0.813836	−	0.238964i	−0.151776	−	0.988415i	$-0.548499\pi$
$809$	−23.1479	−	6.79683i	−0.813836	−	0.238964i	−0.662060	+	0.749451i	$0.730318\pi$
$810$	−14.1835	−	16.3687i	−0.498359	−	0.575136i
$811$	−13.7575	+	4.03956i	−0.483091	+	0.141848i	−0.514205	−	0.857668i	$-0.671913\pi$
$811$	−13.7575	+	4.03956i	−0.483091	+	0.141848i	0.0311137	+	0.999516i	$0.490095\pi$
$812$	−28.3744	−	18.2351i	−0.995747	−	0.639927i
$813$	−4.60584	+	10.0854i	−0.161534	+	0.353710i
$814$	10.7135	−	12.3640i	0.375507	−	0.433358i
$815$	15.3837	−	9.88652i	0.538868	−	0.346310i
$816$	0.867929	+	6.03658i	0.0303836	+	0.211323i
$817$	5.06017	+	35.1942i	0.177033	+	1.23129i
$818$	−16.9605	+	10.8998i	−0.593008	+	0.381103i
$819$	1.01260	−	1.16861i	0.0353832	−	0.0408344i
$820$	−0.625648	+	1.36998i	−0.0218486	+	0.0478417i
$821$	11.9529	+	7.68167i	0.417160	+	0.268092i	0.732339	−	0.680940i	$-0.238428\pi$
$821$	11.9529	+	7.68167i	0.417160	+	0.268092i	−0.315180	+	0.949032i	$0.602065\pi$
$822$	3.70689	−	1.08844i	0.129293	−	0.0379638i
$823$	−10.4929	−	12.1095i	−0.365760	−	0.422109i	0.542802	−	0.839861i	$-0.317364\pi$
$823$	−10.4929	−	12.1095i	−0.365760	−	0.422109i	−0.908561	+	0.417752i	$0.862818\pi$
$824$	27.7127	+	8.13718i	0.965417	+	0.283472i
$825$	−6.92875	−	15.1719i	−0.241228	−	0.528216i
$826$	−5.37175	+	37.3613i	−0.186907	+	1.29997i
$827$	35.1240			1.22138			0.610690	−	0.791870i	$-0.290892\pi$
$827$	35.1240			1.22138			0.610690	+	0.791870i	$0.290892\pi$
$828$	−42.8385	+	15.1228i	−1.48874	+	0.525554i
$829$	−2.29604			−0.0797447			−0.0398723	−	0.999205i	$-0.512695\pi$
$829$	−2.29604			−0.0797447			−0.0398723	+	0.999205i	$0.512695\pi$
$830$	−4.99824	+	34.7635i	−0.173491	+	1.20666i
$831$	32.1620	+	70.4250i	1.11569	+	2.44302i
$832$	2.40453	+	0.706035i	0.0833622	+	0.0244774i
$833$	−1.39937	−	1.61496i	−0.0484853	−	0.0559550i
$834$	74.1629	−	21.7762i	2.56805	−	0.754048i
$835$	−1.38319	−	0.888922i	−0.0478672	−	0.0307624i
$836$	18.1103	−	39.6561i	0.626359	−	1.37153i
$837$	0.929704	−	1.07294i	0.0321353	−	0.0370861i
$838$	−16.6364	+	10.6915i	−0.574694	+	0.369333i
$839$	−5.49501	−	38.2187i	−0.189709	−	1.31945i	−0.832761	−	0.553632i	$-0.813241\pi$
$839$	−5.49501	−	38.2187i	−0.189709	−	1.31945i	0.643052	−	0.765822i	$-0.277668\pi$
$840$	1.97932	+	13.7665i	0.0682930	+	0.474989i
$841$	−3.55542	+	2.28493i	−0.122601	+	0.0787906i
$842$	−45.4164	+	52.4134i	−1.56515	+	1.80628i
$843$	3.73708	−	8.18306i	0.128712	−	0.281839i
$844$	−33.7985	−	21.7210i	−1.16339	−	0.747667i
$845$	−15.3773	+	4.51519i	−0.528996	+	0.155327i
$846$	12.3893	+	14.2980i	0.425953	+	0.491576i
$847$	−16.7218	−	4.90997i	−0.574568	−	0.168708i
$848$	−6.34530	−	13.8943i	−0.217898	−	0.477131i
$849$	5.28673	−	36.7700i	0.181440	−	1.26194i
$850$	11.9317			0.409255
$851$	15.1032	−	10.8959i	0.517732	−	0.373505i
$852$	5.24190			0.179584
$853$	5.46907	−	38.0382i	0.187257	−	1.30240i	−0.651812	−	0.758380i	$-0.725991\pi$
$853$	5.46907	−	38.0382i	0.187257	−	1.30240i	0.839070	−	0.544024i	$-0.183100\pi$
$854$	−16.1378	−	35.3369i	−0.552226	−	1.20921i
$855$	−31.4197	−	9.22564i	−1.07453	−	0.315510i
$856$	−2.45588	−	2.83423i	−0.0839402	−	0.0968721i
$857$	48.8281	−	14.3372i	1.66794	−	0.489750i	0.694650	−	0.719348i	$-0.255559\pi$
$857$	48.8281	−	14.3372i	1.66794	−	0.489750i	0.973286	+	0.229598i	$0.0737411\pi$
$858$	1.75013	+	1.12474i	0.0597485	+	0.0383980i
$859$	3.79985	−	8.32050i	0.129649	−	0.283892i	−0.833664	−	0.552272i	$-0.813761\pi$
$859$	3.79985	−	8.32050i	0.129649	−	0.283892i	0.963313	+	0.268380i	$0.0864883\pi$
$860$	10.2980	−	11.8845i	0.351158	−	0.405257i
$861$	2.13969	−	1.37510i	0.0729205	−	0.0468631i
$862$	6.93147	+	48.2094i	0.236087	+	1.64202i
$863$	−1.75600	−	12.2133i	−0.0597750	−	0.415744i	−0.997635	−	0.0687310i	$-0.978105\pi$
$863$	−1.75600	−	12.2133i	−0.0597750	−	0.415744i	0.937860	−	0.347013i	$-0.112804\pi$
$864$	4.82378	−	3.10006i	0.164108	−	0.105466i
$865$	−13.7135	+	15.8262i	−0.466272	+	0.538107i
$866$	11.6214	−	25.4474i	0.394912	−	0.864737i
$867$	30.7991	+	19.7934i	1.04599	+	0.672219i
$868$	11.5910	−	3.40342i	0.393423	−	0.115519i
$869$	−7.10891	−	8.20412i	−0.241153	−	0.278306i
$870$	−32.7047	−	9.60297i	−1.10879	−	0.325571i
$871$	0.593078	+	1.29866i	0.0200957	+	0.0440034i
$872$	−4.18600	+	29.1143i	−0.141756	+	0.985934i
$873$	14.3414			0.485381
$874$	51.7512	−	66.6482i	1.75051	−	2.25441i
$875$	−24.8534			−0.840199
$876$	−6.58303	+	45.7860i	−0.222420	+	1.54696i
$877$	0.958445	+	2.09870i	0.0323644	+	0.0708681i	0.925124	−	0.379666i	$-0.123961\pi$
$877$	0.958445	+	2.09870i	0.0323644	+	0.0708681i	−0.892759	+	0.450534i	$0.851234\pi$
$878$	−38.9485	−	11.4363i	−1.31445	−	0.385957i
$879$	35.4087	+	40.8638i	1.19431	+	1.37830i
$880$	3.52831	−	1.03600i	0.118939	−	0.0349237i
$881$	−29.9489	−	19.2470i	−1.00901	−	0.648448i	−0.0718697	−	0.997414i	$-0.522897\pi$
$881$	−29.9489	−	19.2470i	−1.00901	−	0.648448i	−0.937135	+	0.348966i	$0.886533\pi$
$882$	−4.15940	+	9.10782i	−0.140054	+	0.306676i
$883$	−19.9566	+	23.0311i	−0.671592	+	0.775059i	−0.984625	−	0.174684i	$-0.944110\pi$
$883$	−19.9566	+	23.0311i	−0.671592	+	0.775059i	0.313032	+	0.949742i	$0.398655\pi$
$884$	−0.736336	+	0.473214i	−0.0247657	+	0.0159159i
$885$	3.19271	+	22.2058i	0.107322	+	0.746438i
$886$	4.36315	+	30.3464i	0.146583	+	1.01951i
$887$	17.4906	−	11.2405i	0.587278	−	0.377421i	−0.212998	−	0.977053i	$-0.568323\pi$
$887$	17.4906	−	11.2405i	0.587278	−	0.377421i	0.800276	+	0.599632i	$0.204686\pi$
$888$	12.0549	−	13.9121i	0.404535	−	0.466858i
$889$	−5.90859	+	12.9380i	−0.198168	+	0.433927i
$890$	31.8619	+	20.4764i	1.06801	+	0.686370i
$891$	−14.5817	+	4.28156i	−0.488504	+	0.143438i
$892$	7.86168	+	9.07286i	0.263228	+	0.303782i
$893$	−19.8299	−	5.82260i	−0.663584	−	0.194846i
$894$	38.2822	+	83.8263i	1.28035	+	2.80357i
$895$	−0.251874	+	1.75182i	−0.00841920	+	0.0585569i
$896$	32.5243			1.08656
$897$	1.64478	+	1.70385i	0.0549176	+	0.0568898i
$898$	66.3122			2.21287
$899$	−1.26275	+	8.78264i	−0.0421152	+	0.292918i
$900$	−13.6592	−	29.9095i	−0.455307	−	0.996984i
$901$	14.6969	+	4.31539i	0.489624	+	0.143766i
$902$	1.17666	+	1.35794i	0.0391786	+	0.0452145i
$903$	−25.4812	+	7.48196i	−0.847962	+	0.248984i
$904$	−2.36141	−	1.51759i	−0.0785393	−	0.0504742i
$905$	8.28590	−	18.1436i	0.275433	−	0.603114i
$906$	47.8387	−	55.2088i	1.58933	−	1.83419i
$907$	−19.1064	+	12.2789i	−0.634417	+	0.407715i	−0.817943	−	0.575300i	$-0.804885\pi$
$907$	−19.1064	+	12.2789i	−0.634417	+	0.407715i	0.183525	+	0.983015i	$0.441249\pi$
$908$	−7.49100	−	52.1011i	−0.248598	−	1.72903i
$909$	0.859242	+	5.97616i	0.0284992	+	0.198217i
$910$	1.06859	−	0.686743i	0.0354235	−	0.0227653i
$911$	−0.546182	+	0.630328i	−0.0180958	+	0.0208837i	−0.764725	−	0.644356i	$-0.777125\pi$
$911$	−0.546182	+	0.630328i	−0.0180958	+	0.0208837i	0.746630	+	0.665240i	$0.231671\pi$
$912$	−12.9677	+	28.3953i	−0.429404	+	0.940264i
$913$	20.7312	+	13.3231i	0.686101	+	0.440930i
$914$	−80.4460	+	23.6211i	−2.66092	+	0.781315i
$915$	−15.1201	−	17.4496i	−0.499856	−	0.576864i
$916$	−29.9362	−	8.79006i	−0.989120	−	0.290432i
$917$	12.5861	+	27.5597i	0.415630	+	0.910103i
$918$	−0.389589	+	2.70965i	−0.0128584	+	0.0894319i
$919$	−45.3320			−1.49537			−0.747683	−	0.664056i	$-0.768834\pi$
$919$	−45.3320			−1.49537			−0.747683	+	0.664056i	$0.768834\pi$
$920$	−11.1684	+	0.601024i	−0.368213	+	0.0198152i
$921$	−35.5510			−1.17145
$922$	−2.74725	+	19.1075i	−0.0904758	+	0.629273i
$923$	−0.0596044	−	0.130515i	−0.00196190	−	0.00429597i
$924$	31.2428	+	9.17371i	1.02781	+	0.301793i
$925$	8.82696	+	10.1869i	0.290229	+	0.334942i
$926$	58.8566	−	17.2819i	1.93415	−	0.567918i
$927$	−42.7289	−	27.4602i	−1.40340	−	0.901910i
$928$	−14.8873	+	32.5986i	−0.488699	+	1.07010i
$929$	11.5958	−	13.3822i	0.380445	−	0.439056i	−0.532941	−	0.846153i	$-0.678913\pi$
$929$	11.5958	−	13.3822i	0.380445	−	0.439056i	0.913385	+	0.407096i	$0.133459\pi$
$930$	10.2701	−	6.60017i	0.336769	−	0.216428i
$931$	−1.55661	−	10.8265i	−0.0510159	−	0.354824i
$932$	−1.69275	−	11.7734i	−0.0554480	−	0.385649i
$933$	−1.20548	+	0.774713i	−0.0394655	+	0.0253630i
$934$	25.0607	−	28.9216i	0.820011	−	0.946343i
$935$	−1.53186	+	3.35431i	−0.0500972	+	0.109698i
$936$	1.03402	+	0.664524i	0.0337980	+	0.0217207i
$937$	22.3812	−	6.57170i	0.731161	−	0.214688i	0.105099	−	0.994462i	$-0.466484\pi$
$937$	22.3812	−	6.57170i	0.731161	−	0.214688i	0.626062	+	0.779774i	$0.284666\pi$
$938$	24.8810	+	28.7143i	0.812395	+	0.937554i
$939$	−50.9622	−	14.9639i	−1.66309	−	0.488327i
$940$	3.79708	+	8.31444i	0.123847	+	0.271187i
$941$	−1.65295	+	11.4965i	−0.0538847	+	0.374776i	0.944980	+	0.327130i	$0.106081\pi$
$941$	−1.65295	+	11.4965i	−0.0538847	+	0.374776i	−0.998864	+	0.0476470i	$0.984828\pi$
$942$	−22.8664			−0.745027
$943$	0.948444	+	1.81222i	0.0308856	+	0.0590139i
$944$	11.2294			0.365486
$945$	0.332520	−	2.31273i	0.0108169	−	0.0752331i
$946$	−7.79363	−	17.0657i	−0.253393	−	0.554853i
$947$	−5.75498	−	1.68981i	−0.187012	−	0.0549116i	0.186886	−	0.982382i	$-0.440161\pi$
$947$	−5.75498	−	1.68981i	−0.187012	−	0.0549116i	−0.373897	+	0.927470i	$0.621979\pi$
$948$	−26.6899	−	30.8018i	−0.866849	−	1.00040i
$949$	1.21486	−	0.356714i	0.0394359	−	0.0115794i
$950$	51.3781	+	33.0187i	1.66692	+	1.07127i
$951$	9.20056	−	20.1464i	0.298348	−	0.653292i
$952$	−4.57168	+	5.27600i	−0.148169	+	0.170996i
$953$	−15.0640	+	9.68107i	−0.487972	+	0.313601i	−0.761389	−	0.648295i	$-0.775482\pi$
$953$	−15.0640	+	9.68107i	−0.487972	+	0.313601i	0.273417	+	0.961896i	$0.411846\pi$
$954$	−10.2141	−	71.0403i	−0.330692	−	2.30002i
$955$	−3.65039	−	25.3890i	−0.118124	−	0.821570i
$956$	−54.0987	+	34.7671i	−1.74968	+	1.12445i
$957$	−15.6620	+	18.0749i	−0.506281	+	0.584279i
$958$	−23.3227	+	51.0697i	−0.753524	+	1.64999i
$959$	−1.39241	−	0.894847i	−0.0449632	−	0.0288961i
$960$	38.0333	−	11.1676i	1.22752	−	0.360432i
$961$	18.2196	+	21.0265i	0.587728	+	0.678274i
$962$	−1.61315	−	0.473664i	−0.0520101	−	0.0152715i
$963$	2.73967	+	5.99903i	0.0882845	+	0.193316i
$964$	−2.40984	+	16.7608i	−0.0776156	+	0.539829i
$965$	−18.1172			−0.583213
$966$	54.7739	+	31.1753i	1.76232	+	1.00305i
$967$	33.5068			1.07751			0.538753	−	0.842464i	$-0.318896\pi$
$967$	33.5068			1.07751			0.538753	+	0.842464i	$0.318896\pi$
$968$	1.97153	−	13.7123i	0.0633673	−	0.440730i
$969$	−13.0040	−	28.4748i	−0.417748	−	0.914741i
$970$	11.3039	+	3.31911i	0.362945	+	0.106570i
$971$	−38.8241	−	44.8054i	−1.24592	−	1.43787i	−0.855960	−	0.517042i	$-0.827033\pi$
$971$	−38.8241	−	44.8054i	−1.24592	−	1.43787i	−0.389964	−	0.920830i	$-0.627513\pi$
$972$	−61.2928	+	17.9972i	−1.96597	+	0.577260i
$973$	−27.8576	−	17.9030i	−0.893073	−	0.573943i
$974$	−5.63994	+	12.3497i	−0.180715	+	0.395711i
$975$	−1.12247	+	1.29540i	−0.0359477	+	0.0414859i
$976$	−9.72257	+	6.24832i	−0.311212	+	0.200004i
$977$	1.79914	+	12.5133i	0.0575596	+	0.400336i	0.998150	+	0.0607934i	$0.0193631\pi$
$977$	1.79914	+	12.5133i	0.0575596	+	0.400336i	−0.940591	+	0.339542i	$0.889728\pi$
$978$	−11.6569	−	81.0758i	−0.372748	−	2.59252i
$979$	22.3564	−	14.3676i	0.714513	−	0.459189i
$980$	−3.16787	+	3.65592i	−0.101194	+	0.116784i
$981$	21.4877	−	47.0514i	0.686048	−	1.50224i
$982$	−60.5221	−	38.8952i	−1.93134	−	1.24120i
$983$	56.0008	−	16.4433i	1.78615	−	0.524461i	0.790077	−	0.613008i	$-0.210040\pi$
$983$	56.0008	−	16.4433i	1.78615	−	0.524461i	0.996072	+	0.0885469i	$0.0282223\pi$
$984$	1.32399	+	1.52797i	0.0422072	+	0.0487097i
$985$	13.8546	+	4.06807i	0.441444	+	0.129620i
$986$	−7.10741	−	15.5631i	−0.226346	−	0.495629i
$987$	2.19682	−	15.2792i	0.0699254	−	0.486342i
$988$	−4.48019			−0.142534
$989$	−4.17093	−	20.9454i	−0.132628	−	0.666025i
$990$	17.2784			0.549142
$991$	6.51675	−	45.3250i	0.207011	−	1.43980i	−0.575828	−	0.817571i	$-0.695320\pi$
$991$	6.51675	−	45.3250i	0.207011	−	1.43980i	0.782839	−	0.622224i	$-0.213771\pi$
$992$	−5.33204	−	11.6755i	−0.169292	−	0.370699i
$993$	72.7980	+	21.3754i	2.31018	+	0.678329i
$994$	−2.50055	−	2.88578i	−0.0793125	−	0.0915315i
$995$	−6.79021	+	1.99379i	−0.215264	+	0.0632073i
$996$	77.8338	+	50.0207i	2.46626	+	1.58497i
$997$	−16.3475	+	35.7959i	−0.517729	+	1.13367i	0.452563	+	0.891732i	$0.350510\pi$
$997$	−16.3475	+	35.7959i	−0.517729	+	1.13367i	−0.970292	+	0.241936i	$0.922218\pi$
$998$	12.3724	−	14.2785i	0.391640	−	0.451977i
$999$	−2.60161	+	1.67195i	−0.0823113	+	0.0528983i

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	23.2.c.a.8.1	yes	10
3.2	odd	2		207.2.i.c.100.1		10
4.3	odd	2		368.2.m.c.353.1		10
5.2	odd	4		575.2.p.b.399.1		20
5.3	odd	4		575.2.p.b.399.2		20
5.4	even	2		575.2.k.b.376.1		10
23.2	even	11		529.2.c.b.170.1		10
23.3	even	11	inner	23.2.c.a.3.1	✓	10
23.4	even	11		529.2.c.d.266.1		10
23.5	odd	22		529.2.c.e.177.1		10
23.6	even	11		529.2.c.i.334.1		10
23.7	odd	22		529.2.a.j.1.5		5
23.8	even	11		529.2.c.g.466.1		10
23.9	even	11		529.2.c.g.487.1		10
23.10	odd	22		529.2.c.c.501.1		10
23.11	odd	22		529.2.c.h.255.1		10
23.12	even	11		529.2.c.i.255.1		10
23.13	even	11		529.2.c.b.501.1		10
23.14	odd	22		529.2.c.f.487.1		10
23.15	odd	22		529.2.c.f.466.1		10
23.16	even	11		529.2.a.i.1.5		5
23.17	odd	22		529.2.c.h.334.1		10
23.18	even	11		529.2.c.d.177.1		10
23.19	odd	22		529.2.c.e.266.1		10
23.20	odd	22		529.2.c.a.118.1		10
23.21	odd	22		529.2.c.c.170.1		10
23.22	odd	2		529.2.c.a.399.1		10
69.26	odd	22		207.2.i.c.118.1		10
69.53	even	22		4761.2.a.bn.1.1		5
69.62	odd	22		4761.2.a.bo.1.1		5
92.3	odd	22		368.2.m.c.49.1		10
92.7	even	22		8464.2.a.bt.1.5		5
92.39	odd	22		8464.2.a.bs.1.5		5
115.3	odd	44		575.2.p.b.49.1		20
115.49	even	22		575.2.k.b.26.1		10
115.72	odd	44		575.2.p.b.49.2		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
23.2.c.a.3.1	✓	10	23.3	even	11	inner
23.2.c.a.8.1	yes	10	1.1	even	1	trivial
207.2.i.c.100.1		10	3.2	odd	2
207.2.i.c.118.1		10	69.26	odd	22
368.2.m.c.49.1		10	92.3	odd	22
368.2.m.c.353.1		10	4.3	odd	2
529.2.a.i.1.5		5	23.16	even	11
529.2.a.j.1.5		5	23.7	odd	22
529.2.c.a.118.1		10	23.20	odd	22
529.2.c.a.399.1		10	23.22	odd	2
529.2.c.b.170.1		10	23.2	even	11
529.2.c.b.501.1		10	23.13	even	11
529.2.c.c.170.1		10	23.21	odd	22
529.2.c.c.501.1		10	23.10	odd	22
529.2.c.d.177.1		10	23.18	even	11
529.2.c.d.266.1		10	23.4	even	11
529.2.c.e.177.1		10	23.5	odd	22
529.2.c.e.266.1		10	23.19	odd	22
529.2.c.f.466.1		10	23.15	odd	22
529.2.c.f.487.1		10	23.14	odd	22
529.2.c.g.466.1		10	23.8	even	11
529.2.c.g.487.1		10	23.9	even	11
529.2.c.h.255.1		10	23.11	odd	22
529.2.c.h.334.1		10	23.17	odd	22
529.2.c.i.255.1		10	23.12	even	11
529.2.c.i.334.1		10	23.6	even	11
575.2.k.b.26.1		10	115.49	even	22
575.2.k.b.376.1		10	5.4	even	2
575.2.p.b.49.1		20	115.3	odd	44
575.2.p.b.49.2		20	115.72	odd	44
575.2.p.b.399.1		20	5.2	odd	4
575.2.p.b.399.2		20	5.3	odd	4
4761.2.a.bn.1.1		5	69.53	even	22
4761.2.a.bo.1.1		5	69.62	odd	22
8464.2.a.bs.1.5		5	92.39	odd	22
8464.2.a.bt.1.5		5	92.7	even	22

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

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Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

Coefficient data

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	23.2.c.a.8.1

Level	$23$
Weight	$2$
Character	23.8
Analytic conductor	$0.184$
Analytic rank	$0$
Dimension	$10$
Inner twists	$2$