LMFDB - Embedded newform 29.2.d.a.24.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [29,2,Mod(7,29)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(29, base_ring=CyclotomicField(14))

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

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

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

chi := DirichletCharacter("29.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$N$	$=$	$29$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	29.d (of order $7$ , degree $6$ , minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$0.231566165862$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	$\Q(\zeta_{14})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$x^{6} - x^{5} + x^{4} - x^{3} + x^{2} - x + 1$ 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:	$\mathrm{SU}(2)[C_{7}]$

Embedding invariants

Embedding label			24.1
Root			$0.222521 - 0.974928i$ of defining polynomial
Character	$\chi$	$=$	29.24
Dual form			29.2.d.a.23.1

$q$ -expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.12349 - 1.40881i) q^{2} +(-0.0990311 - 0.433884i) q^{3} +(-0.277479 + 1.21572i) q^{4} +(0.222521 + 0.279032i) q^{5} +(-0.500000 + 0.626980i) q^{6} +(0.900969 + 3.94740i) q^{7} +(-1.22252 + 0.588735i) q^{8} +(2.52446 - 1.21572i) q^{9} +(0.143104 - 0.626980i) q^{10} +(-2.62349 - 1.26341i) q^{11} +0.554958 q^{12} +(-4.67241 - 2.25011i) q^{13} +(4.54892 - 5.70416i) q^{14} +(0.0990311 - 0.124181i) q^{15} +(4.44989 + 2.14295i) q^{16} +1.10992 q^{17} +(-4.54892 - 2.19064i) q^{18} +(-0.455927 + 1.99755i) q^{19} +(-0.400969 + 0.193096i) q^{20} +(1.62349 - 0.781831i) q^{21} +(1.16756 + 5.11543i) q^{22} +(-2.57942 + 3.23449i) q^{23} +(0.376510 + 0.472129i) q^{24} +(1.08426 - 4.75046i) q^{25} +(2.07942 + 9.11052i) q^{26} +(-1.60992 - 2.01877i) q^{27} -5.04892 q^{28} +(4.38404 + 3.12733i) q^{29} -0.286208 q^{30} +(-3.96346 - 4.97002i) q^{31} +(-1.37651 - 6.03089i) q^{32} +(-0.288364 + 1.26341i) q^{33} +(-1.24698 - 1.56366i) q^{34} +(-0.900969 + 1.12978i) q^{35} +(0.777479 + 3.40636i) q^{36} +(2.62349 - 1.26341i) q^{37} +(3.32640 - 1.60191i) q^{38} +(-0.513574 + 2.25011i) q^{39} +(-0.436313 - 0.210117i) q^{40} +0.396125 q^{41} +(-2.92543 - 1.40881i) q^{42} +(3.57942 - 4.48845i) q^{43} +(2.26391 - 2.83885i) q^{44} +(0.900969 + 0.433884i) q^{45} +7.45473 q^{46} +(7.02930 + 3.38513i) q^{47} +(0.489115 - 2.14295i) q^{48} +(-8.46346 + 4.07579i) q^{49} +(-7.91066 + 3.80957i) q^{50} +(-0.109916 - 0.481575i) q^{51} +(4.03199 - 5.05596i) q^{52} +(-2.71648 - 3.40636i) q^{53} +(-1.03534 + 4.53614i) q^{54} +(-0.231250 - 1.01317i) q^{55} +(-3.42543 - 4.29535i) q^{56} +0.911854 q^{57} +(-0.519614 - 9.68981i) q^{58} -9.10992 q^{59} +(0.123490 + 0.154851i) q^{60} +(1.34601 + 5.89726i) q^{61} +(-2.54892 + 11.1675i) q^{62} +(7.07338 + 8.86973i) q^{63} +(-0.791053 + 0.991949i) q^{64} +(-0.411854 - 1.80445i) q^{65} +(2.10388 - 1.01317i) q^{66} +(-0.337282 + 0.162426i) q^{67} +(-0.307979 + 1.34934i) q^{68} +(1.65883 + 0.798852i) q^{69} +2.60388 q^{70} +(10.2763 + 4.94880i) q^{71} +(-2.37047 + 2.97247i) q^{72} +(-5.57942 + 6.99637i) q^{73} +(-4.72737 - 2.27658i) q^{74} -2.16852 q^{75} +(-2.30194 - 1.10855i) q^{76} +(2.62349 - 11.4943i) q^{77} +(3.74698 - 1.80445i) q^{78} +(0.535344 - 0.257808i) q^{79} +(0.392240 + 1.71851i) q^{80} +(4.52446 - 5.67349i) q^{81} +(-0.445042 - 0.558065i) q^{82} +(2.09903 - 9.19646i) q^{83} +(0.500000 + 2.19064i) q^{84} +(0.246980 + 0.309703i) q^{85} -10.3448 q^{86} +(0.922739 - 2.21187i) q^{87} +3.95108 q^{88} +(0.887395 + 1.11276i) q^{89} +(-0.400969 - 1.75676i) q^{90} +(4.67241 - 20.4712i) q^{91} +(-3.21648 - 4.03334i) q^{92} +(-1.76391 + 2.21187i) q^{93} +(-3.12833 - 13.7061i) q^{94} +(-0.658834 + 0.317278i) q^{95} +(-2.48039 + 1.19449i) q^{96} +(-3.50484 + 15.3557i) q^{97} +(15.2506 + 7.34432i) q^{98} -8.15883 q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$6 q - 2 q^{2} - 5 q^{3} - 2 q^{4} + q^{5} - 3 q^{6} + q^{7} - 7 q^{8} + 6 q^{9} + 9 q^{10} - 11 q^{11} + 4 q^{12} - 5 q^{13} + 9 q^{14} + 5 q^{15} + 4 q^{16} + 8 q^{17} - 9 q^{18} + q^{19} + 2 q^{20}+ \cdots - 32 q^{99}+O(q^{100})$ 6 * q - 2 * q^2 - 5 * q^3 - 2 * q^4 + q^5 - 3 * q^6 + q^7 - 7 * q^8 + 6 * q^9 + 9 * q^10 - 11 * q^11 + 4 * q^12 - 5 * q^13 + 9 * q^14 + 5 * q^15 + 4 * q^16 + 8 * q^17 - 9 * q^18 + q^19 + 2 * q^20 + 5 * q^21 + 6 * q^22 - 7 * q^23 + 7 * q^24 - 24 * q^25 + 4 * q^26 - 11 * q^27 - 12 * q^28 + 6 * q^29 - 18 * q^30 + 5 * q^31 - 13 * q^32 + q^33 + 2 * q^34 - q^35 + 5 * q^36 + 11 * q^37 + 2 * q^38 + 3 * q^39 + 14 * q^40 + 20 * q^41 - 4 * q^42 + 13 * q^43 + 20 * q^44 + q^45 + 11 * q^47 + 6 * q^48 - 22 * q^49 + q^50 - 2 * q^51 - 10 * q^52 + 3 * q^53 + 6 * q^54 - 17 * q^55 - 7 * q^56 - 2 * q^57 - 16 * q^58 - 56 * q^59 - 4 * q^60 + 3 * q^61 + 3 * q^62 + 15 * q^63 + q^64 + 5 * q^65 - 5 * q^66 + 19 * q^67 - 12 * q^68 - 7 * q^69 - 2 * q^70 + 21 * q^71 - 25 * q^73 - 6 * q^74 + 48 * q^75 - 5 * q^76 + 11 * q^77 + 13 * q^78 - 9 * q^79 - 18 * q^80 + 18 * q^81 - 2 * q^82 + 17 * q^83 + 3 * q^84 - 8 * q^85 - 16 * q^86 - 5 * q^87 + 42 * q^88 + 7 * q^89 + 2 * q^90 + 5 * q^91 - 17 * q^93 + 8 * q^94 + 13 * q^95 - 2 * q^96 + q^97 + 19 * q^98 - 32 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/29\mathbb{Z}\right)^\times$ .

$n$	$2$
$\chi(n)$	$e\left(\frac{2}{7}\right)$

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

)

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

$2$	−1.12349	−	1.40881i	−0.794427	−	0.996180i	−0.999847	−	0.0175063i	$-0.994427\pi$
$2$	−1.12349	−	1.40881i	−0.794427	−	0.996180i	0.205419	−	0.978674i	$-0.434144\pi$
$3$	−0.0990311	−	0.433884i	−0.0571757	−	0.250503i	0.938261	−	0.345928i	$-0.112436\pi$
$3$	−0.0990311	−	0.433884i	−0.0571757	−	0.250503i	−0.995437	+	0.0954255i	$0.969579\pi$
$4$	−0.277479	+	1.21572i	−0.138740	+	0.607858i
$5$	0.222521	+	0.279032i	0.0995144	+	0.124787i	0.829095	−	0.559108i	$-0.188856\pi$
$5$	0.222521	+	0.279032i	0.0995144	+	0.124787i	−0.729581	+	0.683895i	$0.760285\pi$
$6$	−0.500000	+	0.626980i	−0.204124	+	0.255964i
$7$	0.900969	+	3.94740i	0.340534	+	1.49198i	0.797949	+	0.602725i	$0.205918\pi$
$7$	0.900969	+	3.94740i	0.340534	+	1.49198i	−0.457415	+	0.889253i	$0.651225\pi$
$8$	−1.22252	+	0.588735i	−0.432226	+	0.208149i
$9$	2.52446	−	1.21572i	0.841486	−	0.405238i
$10$	0.143104	−	0.626980i	0.0452535	−	0.198269i
$11$	−2.62349	−	1.26341i	−0.791012	−	0.380931i	−0.00566249	−	0.999984i	$-0.501802\pi$
$11$	−2.62349	−	1.26341i	−0.791012	−	0.380931i	−0.785349	+	0.619053i	$0.787517\pi$
$12$	0.554958			0.160203
$13$	−4.67241	−	2.25011i	−1.29589	−	0.624069i	−0.346467	−	0.938062i	$-0.612619\pi$
$13$	−4.67241	−	2.25011i	−1.29589	−	0.624069i	−0.949425	+	0.313993i	$0.898333\pi$
$14$	4.54892	−	5.70416i	1.21575	−	1.52450i
$15$	0.0990311	−	0.124181i	0.0255697	−	0.0320634i
$16$	4.44989	+	2.14295i	1.11247	+	0.535738i
$17$	1.10992			0.269194			0.134597	−	0.990900i	$-0.457026\pi$
$17$	1.10992			0.269194			0.134597	+	0.990900i	$0.457026\pi$
$18$	−4.54892	−	2.19064i	−1.07219	−	0.516340i
$19$	−0.455927	+	1.99755i	−0.104597	+	0.458269i	0.895321	+	0.445422i	$0.146946\pi$
$19$	−0.455927	+	1.99755i	−0.104597	+	0.458269i	−0.999917	+	0.0128465i	$0.995911\pi$
$20$	−0.400969	+	0.193096i	−0.0896594	+	0.0431777i
$21$	1.62349	−	0.781831i	0.354275	−	0.170610i
$22$	1.16756	+	5.11543i	0.248925	+	1.09061i
$23$	−2.57942	+	3.23449i	−0.537846	+	0.674437i	−0.974291	−	0.225294i	$-0.927666\pi$
$23$	−2.57942	+	3.23449i	−0.537846	+	0.674437i	0.436445	+	0.899731i	$0.356237\pi$
$24$	0.376510	+	0.472129i	0.0768548	+	0.0963729i
$25$	1.08426	−	4.75046i	0.216852	−	0.950092i
$26$	2.07942	+	9.11052i	0.407807	+	1.78672i
$27$	−1.60992	−	2.01877i	−0.309829	−	0.388513i
$28$	−5.04892			−0.954156
$29$	4.38404	+	3.12733i	0.814096	+	0.580730i
$29$	4.38404	+	3.12733i	0.814096	+	0.580730i
$30$	−0.286208			−0.0522542
$31$	−3.96346	−	4.97002i	−0.711858	−	0.892642i	0.285988	−	0.958233i	$-0.407678\pi$
$31$	−3.96346	−	4.97002i	−0.711858	−	0.892642i	−0.997847	+	0.0655910i	$0.979107\pi$
$32$	−1.37651	−	6.03089i	−0.243335	−	1.06612i
$33$	−0.288364	+	1.26341i	−0.0501978	+	0.219931i
$34$	−1.24698	−	1.56366i	−0.213855	−	0.268166i
$35$	−0.900969	+	1.12978i	−0.152292	+	0.190968i
$36$	0.777479	+	3.40636i	0.129580	+	0.567726i
$37$	2.62349	−	1.26341i	0.431299	−	0.207703i	−0.205622	−	0.978631i	$-0.565922\pi$
$37$	2.62349	−	1.26341i	0.431299	−	0.207703i	0.636921	+	0.770929i	$0.280208\pi$
$38$	3.32640	−	1.60191i	0.539613	−	0.259864i
$39$	−0.513574	+	2.25011i	−0.0822376	+	0.360306i
$40$	−0.436313	−	0.210117i	−0.0689871	−	0.0332224i
$41$	0.396125			0.0618643			0.0309321	−	0.999521i	$-0.490152\pi$
$41$	0.396125			0.0618643			0.0309321	+	0.999521i	$0.490152\pi$
$42$	−2.92543	−	1.40881i	−0.451403	−	0.217384i
$43$	3.57942	−	4.48845i	0.545856	−	0.684482i	−0.430017	−	0.902821i	$-0.641492\pi$
$43$	3.57942	−	4.48845i	0.545856	−	0.684482i	0.975873	+	0.218339i	$0.0700639\pi$
$44$	2.26391	−	2.83885i	0.341297	−	0.427972i
$45$	0.900969	+	0.433884i	0.134309	+	0.0646796i
$46$	7.45473			1.09914
$47$	7.02930	+	3.38513i	1.02533	+	0.493773i	0.869459	−	0.494005i	$-0.164468\pi$
$47$	7.02930	+	3.38513i	1.02533	+	0.493773i	0.155870	+	0.987778i	$0.450182\pi$
$48$	0.489115	−	2.14295i	0.0705977	−	0.309309i
$49$	−8.46346	+	4.07579i	−1.20907	+	0.582255i
$50$	−7.91066	+	3.80957i	−1.11874	+	0.538755i
$51$	−0.109916	−	0.481575i	−0.0153914	−	0.0674339i
$52$	4.03199	−	5.05596i	0.559137	−	0.701135i
$53$	−2.71648	−	3.40636i	−0.373137	−	0.467899i	0.559439	−	0.828871i	$-0.311016\pi$
$53$	−2.71648	−	3.40636i	−0.373137	−	0.467899i	−0.932577	+	0.360972i	$0.882445\pi$
$54$	−1.03534	+	4.53614i	−0.140892	+	0.617290i
$55$	−0.231250	−	1.01317i	−0.0311818	−	0.136616i
$56$	−3.42543	−	4.29535i	−0.457742	−	0.573990i
$57$	0.911854			0.120778
$58$	−0.519614	−	9.68981i	−0.0682287	−	1.27233i
$59$	−9.10992			−1.18601			−0.593005	−	0.805199i	$-0.702059\pi$
$59$	−9.10992			−1.18601			−0.593005	+	0.805199i	$0.702059\pi$
$60$	0.123490	+	0.154851i	0.0159425	+	0.0199912i
$61$	1.34601	+	5.89726i	0.172339	+	0.755067i	0.985032	+	0.172374i	$0.0551437\pi$
$61$	1.34601	+	5.89726i	0.172339	+	0.755067i	−0.812693	+	0.582693i	$0.801999\pi$
$62$	−2.54892	+	11.1675i	−0.323713	+	1.41828i
$63$	7.07338	+	8.86973i	0.891162	+	1.11748i
$64$	−0.791053	+	0.991949i	−0.0988816	+	0.123994i
$65$	−0.411854	−	1.80445i	−0.0510842	−	0.223815i
$66$	2.10388	−	1.01317i	0.258969	−	0.124713i
$67$	−0.337282	+	0.162426i	−0.0412055	+	0.0198435i	−0.454373	−	0.890812i	$-0.650137\pi$
$67$	−0.337282	+	0.162426i	−0.0412055	+	0.0198435i	0.413168	+	0.910655i	$0.364422\pi$
$68$	−0.307979	+	1.34934i	−0.0373479	+	0.163632i
$69$	1.65883	+	0.798852i	0.199700	+	0.0961705i
$70$	2.60388			0.311223
$71$	10.2763	+	4.94880i	1.21957	+	0.587314i	0.929192	−	0.369598i	$-0.120505\pi$
$71$	10.2763	+	4.94880i	1.21957	+	0.587314i	0.290379	+	0.956912i	$0.406219\pi$
$72$	−2.37047	+	2.97247i	−0.279362	+	0.350309i
$73$	−5.57942	+	6.99637i	−0.653021	+	0.818863i	−0.992563	−	0.121728i	$-0.961156\pi$
$73$	−5.57942	+	6.99637i	−0.653021	+	0.818863i	0.339542	+	0.940591i	$0.389728\pi$
$74$	−4.72737	−	2.27658i	−0.549545	−	0.264647i
$75$	−2.16852			−0.250399
$76$	−2.30194	−	1.10855i	−0.264050	−	0.127160i
$77$	2.62349	−	11.4943i	0.298974	−	1.30989i
$78$	3.74698	−	1.80445i	0.424262	−	0.204314i
$79$	0.535344	−	0.257808i	0.0602309	−	0.0290057i	−0.403526	−	0.914968i	$-0.632215\pi$
$79$	0.535344	−	0.257808i	0.0602309	−	0.0290057i	0.463757	+	0.885963i	$0.346501\pi$
$80$	0.392240	+	1.71851i	0.0438537	+	0.192136i
$81$	4.52446	−	5.67349i	0.502718	−	0.630388i
$82$	−0.445042	−	0.558065i	−0.0491467	−	0.0616280i
$83$	2.09903	−	9.19646i	0.230399	−	1.00944i	−0.718912	−	0.695101i	$-0.755359\pi$
$83$	2.09903	−	9.19646i	0.230399	−	1.00944i	0.949310	−	0.314341i	$-0.101783\pi$
$84$	0.500000	+	2.19064i	0.0545545	+	0.239019i
$85$	0.246980	+	0.309703i	0.0267887	+	0.0335920i
$86$	−10.3448			−1.11551
$87$	0.922739	−	2.21187i	0.0989280	−	0.237137i
$88$	3.95108			0.421187
$89$	0.887395	+	1.11276i	0.0940637	+	0.117952i	0.826636	−	0.562737i	$-0.190252\pi$
$89$	0.887395	+	1.11276i	0.0940637	+	0.117952i	−0.732572	+	0.680689i	$0.761680\pi$
$90$	−0.400969	−	1.75676i	−0.0422658	−	0.185179i
$91$	4.67241	−	20.4712i	0.489801	−	2.14596i
$92$	−3.21648	−	4.03334i	−0.335341	−	0.420505i
$93$	−1.76391	+	2.21187i	−0.182908	+	0.229360i
$94$	−3.12833	−	13.7061i	−0.322663	−	1.41368i
$95$	−0.658834	+	0.317278i	−0.0675949	+	0.0325520i
$96$	−2.48039	+	1.19449i	−0.253153	+	0.121912i
$97$	−3.50484	+	15.3557i	−0.355863	+	1.55914i	0.407523	+	0.913195i	$0.366393\pi$
$97$	−3.50484	+	15.3557i	−0.355863	+	1.55914i	−0.763386	+	0.645943i	$0.776464\pi$
$98$	15.2506	+	7.34432i	1.54055	+	0.741888i
$99$	−8.15883			−0.819994
$100$	5.47434	+	2.63631i	0.547434	+	0.263631i
$101$	−10.8753	+	13.6372i	−1.08213	+	1.35695i	−0.152570	+	0.988293i	$0.548755\pi$
$101$	−10.8753	+	13.6372i	−1.08213	+	1.35695i	−0.929564	+	0.368661i	$0.879816\pi$
$102$	−0.554958	+	0.695895i	−0.0549490	+	0.0689039i
$103$	2.53534	+	1.22096i	0.249815	+	0.120304i	0.554601	−	0.832116i	$-0.312871\pi$
$103$	2.53534	+	1.22096i	0.249815	+	0.120304i	−0.304786	+	0.952421i	$0.598585\pi$
$104$	7.03684			0.690019
$105$	0.579417	+	0.279032i	0.0565453	+	0.0272308i
$106$	−1.74698	+	7.65402i	−0.169682	+	0.743424i
$107$	6.72132	−	3.23682i	0.649775	−	0.312915i	−0.0798052	−	0.996810i	$-0.525430\pi$
$107$	6.72132	−	3.23682i	0.649775	−	0.312915i	0.729580	+	0.683895i	$0.239716\pi$
$108$	2.90097	−	1.39703i	0.279146	−	0.134430i
$109$	0.367781	+	1.61135i	0.0352270	+	0.154340i	0.989482	−	0.144653i	$-0.0462066\pi$
$109$	0.367781	+	1.61135i	0.0352270	+	0.154340i	−0.954255	+	0.298993i	$0.903349\pi$
$110$	−1.16756	+	1.46408i	−0.111323	+	0.139594i
$111$	−0.807979	−	1.01317i	−0.0766899	−	0.0961661i
$112$	−4.44989	+	19.4962i	−0.420475	+	1.84222i
$113$	−1.92274	−	8.42407i	−0.180876	−	0.792470i	−0.981214	−	0.192921i	$-0.938204\pi$
$113$	−1.92274	−	8.42407i	−0.180876	−	0.792470i	0.800338	−	0.599549i	$-0.204653\pi$
$114$	−1.02446	−	1.28463i	−0.0959493	−	0.120317i
$115$	−1.47650			−0.137684
$116$	−5.01842	+	4.46198i	−0.465948	+	0.414284i
$117$	−14.5308			−1.34337
$118$	10.2349	+	12.8342i	0.942199	+	1.18148i
$119$	1.00000	+	4.38129i	0.0916698	+	0.401632i
$120$	−0.0479579	+	0.210117i	−0.00437793	+	0.0191810i
$121$	−1.57188	−	1.97108i	−0.142899	−	0.179189i
$122$	6.79590	−	8.52179i	0.615272	−	0.771526i
$123$	−0.0392287	−	0.171872i	−0.00353713	−	0.0154972i
$124$	7.14191	−	3.43936i	0.641362	−	0.308864i
$125$	3.17456	−	1.52879i	0.283942	−	0.136739i
$126$	4.54892	−	19.9301i	0.405250	−	1.77552i
$127$	−9.43512	−	4.54371i	−0.837231	−	0.403189i	−0.0344090	−	0.999408i	$-0.510955\pi$
$127$	−9.43512	−	4.54371i	−0.837231	−	0.403189i	−0.802822	+	0.596219i	$0.796669\pi$
$128$	−10.0858			−0.891463
$129$	−2.30194	−	1.10855i	−0.202674	−	0.0976028i
$130$	−2.07942	+	2.60751i	−0.182377	+	0.228693i
$131$	−0.283520	+	0.355523i	−0.0247712	+	0.0310622i	−0.794063	−	0.607836i	$-0.792038\pi$
$131$	−0.283520	+	0.355523i	−0.0247712	+	0.0310622i	0.769292	+	0.638898i	$0.220609\pi$
$132$	−1.45593	−	0.701137i	−0.126722	−	0.0610262i
$133$	−8.29590			−0.719345
$134$	0.607760	+	0.292682i	0.0525025	+	0.0252839i
$135$	0.205063	−	0.898438i	0.0176490	−	0.0773252i
$136$	−1.35690	+	0.653447i	−0.116353	+	0.0560326i
$137$	11.9291	−	5.74474i	1.01917	−	0.490806i	0.151769	−	0.988416i	$-0.451503\pi$
$137$	11.9291	−	5.74474i	1.01917	−	0.490806i	0.867401	+	0.497610i	$0.165789\pi$
$138$	−0.738250	−	3.23449i	−0.0628440	−	0.275338i
$139$	−1.74363	+	2.18644i	−0.147893	+	0.185451i	−0.850260	−	0.526364i	$-0.823555\pi$
$139$	−1.74363	+	2.18644i	−0.147893	+	0.185451i	0.702367	+	0.711815i	$0.252127\pi$
$140$	−1.12349	−	1.40881i	−0.0949522	−	0.119066i
$141$	0.772635	−	3.38513i	0.0650676	−	0.285080i
$142$	−4.57338	−	20.0373i	−0.383789	−	1.68149i
$143$	9.41521	+	11.8063i	0.787339	+	0.987292i
$144$	13.8388			1.15323
$145$	0.102916	+	1.91919i	0.00854671	+	0.159380i
$146$	16.1250			1.33451
$147$	2.60656	+	3.26853i	0.214986	+	0.269584i
$148$	0.807979	+	3.53999i	0.0664154	+	0.290985i
$149$	−0.602679	+	2.64051i	−0.0493734	+	0.216319i	−0.993596	−	0.112988i	$-0.963958\pi$
$149$	−0.602679	+	2.64051i	−0.0493734	+	0.216319i	0.944223	+	0.329307i	$0.106815\pi$
$150$	2.43631	+	3.05504i	0.198924	+	0.249443i
$151$	−1.51842	+	1.90404i	−0.123567	+	0.154948i	−0.839767	−	0.542947i	$-0.817308\pi$
$151$	−1.51842	+	1.90404i	−0.123567	+	0.154948i	0.716200	+	0.697895i	$0.245880\pi$
$152$	−0.618645	−	2.71046i	−0.0501788	−	0.219848i
$153$	2.80194	−	1.34934i	0.226523	−	0.109088i
$154$	−19.1407	+	9.21768i	−1.54240	+	0.742782i
$155$	0.504844	−	2.21187i	0.0405501	−	0.177661i
$156$	−2.59299	−	1.24872i	−0.207605	−	0.0999775i
$157$	17.6775			1.41082			0.705411	−	0.708799i	$-0.250762\pi$
$157$	17.6775			1.41082			0.705411	+	0.708799i	$0.250762\pi$
$158$	−0.964656	−	0.464554i	−0.0767439	−	0.0369579i
$159$	−1.20895	+	1.51597i	−0.0958758	+	0.120224i
$160$	1.37651	−	1.72609i	0.108823	−	0.136459i
$161$	−15.0918	−	7.26782i	−1.18940	−	0.572785i
$162$	−13.0761			−1.02735
$163$	4.47434	+	2.15473i	0.350458	+	0.168772i	0.600827	−	0.799379i	$-0.294838\pi$
$163$	4.47434	+	2.15473i	0.350458	+	0.168772i	−0.250370	+	0.968150i	$0.580552\pi$
$164$	−0.109916	+	0.481575i	−0.00858302	+	0.0376047i
$165$	−0.416698	+	0.200671i	−0.0324399	+	0.0156222i
$166$	−15.3143	+	7.37499i	−1.18862	+	0.572410i
$167$	−3.21864	−	14.1018i	−0.249066	−	1.09123i	−0.932487	−	0.361203i	$-0.882366\pi$
$167$	−3.21864	−	14.1018i	−0.249066	−	1.09123i	0.683422	−	0.730024i	$-0.260491\pi$
$168$	−1.52446	+	1.91161i	−0.117615	+	0.147484i
$169$	8.66301	+	10.8631i	0.666386	+	0.835621i
$170$	0.158834	−	0.695895i	0.0121820	−	0.0533727i
$171$	1.27748	+	5.59700i	0.0976913	+	0.428013i
$172$	4.46346	+	5.59700i	0.340336	+	0.426767i
$173$	10.5133			0.799314			0.399657	−	0.916665i	$-0.369129\pi$
$173$	10.5133			0.799314			0.399657	+	0.916665i	$0.369129\pi$
$174$	−4.15279	+	1.18505i	−0.314822	+	0.0898380i
$175$	19.7289			1.49136
$176$	−8.96681	−	11.2440i	−0.675899	−	0.847550i
$177$	0.902165	+	3.95264i	0.0678109	+	0.297099i
$178$	0.570688	−	2.50035i	0.0427748	−	0.187409i
$179$	−3.57942	−	4.48845i	−0.267538	−	0.335482i	0.629856	−	0.776712i	$-0.283114\pi$
$179$	−3.57942	−	4.48845i	−0.267538	−	0.335482i	−0.897394	+	0.441230i	$0.854542\pi$
$180$	−0.777479	+	0.974928i	−0.0579499	+	0.0726668i
$181$	1.47770	+	6.47421i	0.109836	+	0.481225i	0.999688	+	0.0249747i	$0.00795053\pi$
$181$	1.47770	+	6.47421i	0.109836	+	0.481225i	−0.889852	+	0.456250i	$0.849192\pi$
$182$	−34.0894	+	16.4166i	−2.52687	+	1.21688i
$183$	2.42543	−	1.16802i	0.179293	−	0.0863428i
$184$	1.24914	−	5.47282i	0.0920875	−	0.403462i
$185$	0.936313	+	0.450904i	0.0688391	+	0.0331512i
$186$	5.09783			0.373791
$187$	−2.91185	−	1.40227i	−0.212936	−	0.102545i
$188$	−6.06584	+	7.60633i	−0.442397	+	0.554748i
$189$	6.51842	−	8.17384i	0.474145	−	0.594559i
$190$	1.18718	+	0.571714i	0.0861269	+	0.0414765i
$191$	−18.8116			−1.36116			−0.680581	−	0.732673i	$-0.738272\pi$
$191$	−18.8116			−1.36116			−0.680581	+	0.732673i	$0.738272\pi$
$192$	0.508729	+	0.244991i	0.0367144	+	0.0176807i
$193$	−2.42208	+	10.6118i	−0.174345	+	0.763854i	0.809832	+	0.586662i	$0.199558\pi$
$193$	−2.42208	+	10.6118i	−0.174345	+	0.763854i	−0.984176	+	0.177192i	$0.943299\pi$
$194$	25.5710	−	12.3143i	1.83589	−	0.884118i
$195$	−0.742135	+	0.357394i	−0.0531454	+	0.0255935i
$196$	−2.60656	−	11.4201i	−0.186183	−	0.815722i
$197$	−5.23759	+	6.56773i	−0.373163	+	0.467931i	−0.932584	−	0.360952i	$-0.882452\pi$
$197$	−5.23759	+	6.56773i	−0.373163	+	0.467931i	0.559422	+	0.828883i	$0.311023\pi$
$198$	9.16637	+	11.4943i	0.651425	+	0.816861i
$199$	1.47339	−	6.45532i	0.104446	−	0.457606i	−0.895476	−	0.445109i	$-0.853165\pi$
$199$	1.47339	−	6.45532i	0.104446	−	0.457606i	0.999922	−	0.0124967i	$-0.00397793\pi$
$200$	1.47123	+	6.44588i	0.104032	+	0.455792i
$201$	0.103875	+	0.130256i	0.00732681	+	0.00918753i
$202$	31.4306			2.21145
$203$	−8.39493	+	20.1232i	−0.589208	+	1.41237i
$204$	0.615957			0.0431256
$205$	0.0881460	+	0.110532i	0.00615638	+	0.00771986i
$206$	−1.12833	−	4.94355i	−0.0786148	−	0.344434i
$207$	−2.57942	+	11.3012i	−0.179282	+	0.785485i
$208$	−15.9698	−	20.0255i	−1.10731	−	1.38852i
$209$	3.71983	−	4.66452i	0.257306	−	0.322652i
$210$	−0.257865	−	1.12978i	−0.0177944	−	0.0779622i
$211$	7.29805	−	3.51456i	0.502419	−	0.241952i	−0.165468	−	0.986215i	$-0.552913\pi$
$211$	7.29805	−	3.51456i	0.502419	−	0.241952i	0.667887	+	0.744263i	$0.267199\pi$
$212$	4.89493	−	2.35727i	0.336185	−	0.161898i
$213$	1.12953	−	4.94880i	0.0773942	−	0.339086i
$214$	−12.1114	−	5.83255i	−0.827919	−	0.398705i
$215$	2.04892			0.139735
$216$	3.15668	+	1.52018i	0.214785	+	0.103435i
$217$	16.0477	−	20.1232i	1.08939	−	1.36605i
$218$	1.85690	−	2.32847i	0.125765	−	0.157704i
$219$	3.58815	+	1.72796i	0.242464	+	0.116765i
$220$	1.29590			0.0873694
$221$	−5.18598	−	2.49744i	−0.348847	−	0.167996i
$222$	−0.519614	+	2.27658i	−0.0348742	+	0.152794i
$223$	−19.7485	+	9.51036i	−1.32246	+	0.636861i	−0.955943	−	0.293552i	$-0.905163\pi$
$223$	−19.7485	+	9.51036i	−1.32246	+	0.636861i	−0.366512	+	0.930413i	$0.619448\pi$
$224$	22.5661	−	10.8673i	1.50776	−	0.726101i
$225$	−3.03803	−	13.3105i	−0.202535	−	0.887366i
$226$	−9.70775	+	12.1731i	−0.645750	+	0.809745i
$227$	−11.3964	−	14.2907i	−0.756407	−	0.948504i	0.243363	−	0.969935i	$-0.421749\pi$
$227$	−11.3964	−	14.2907i	−0.756407	−	0.948504i	−0.999770	+	0.0214309i	$0.993178\pi$
$228$	−0.253020	+	1.10855i	−0.0167567	+	0.0734158i
$229$	−3.56584	−	15.6230i	−0.235638	−	1.03240i	−0.944876	−	0.327427i	$-0.893818\pi$
$229$	−3.56584	−	15.6230i	−0.235638	−	1.03240i	0.709239	−	0.704968i	$-0.249039\pi$
$230$	1.65883	+	2.08011i	0.109380	+	0.137158i
$231$	−5.24698			−0.345226
$232$	−7.20075	−	1.24218i	−0.472752	−	0.0815532i
$233$	1.95646			0.128172			0.0640860	−	0.997944i	$-0.479587\pi$
$233$	1.95646			0.128172			0.0640860	+	0.997944i	$0.479587\pi$
$234$	16.3252	+	20.4712i	1.06721	+	1.33824i
$235$	0.619605	+	2.71467i	0.0404186	+	0.177085i
$236$	2.52781	−	11.0751i	0.164546	−	0.720925i
$237$	−0.164874	−	0.206746i	−0.0107097	−	0.0134296i
$238$	5.04892	−	6.33114i	0.327273	−	0.410387i
$239$	1.99449	+	8.73844i	0.129013	+	0.565243i	0.997571	+	0.0696554i	$0.0221900\pi$
$239$	1.99449	+	8.73844i	0.129013	+	0.565243i	−0.868558	+	0.495587i	$0.834953\pi$
$240$	0.706791	−	0.340373i	0.0456232	−	0.0219710i
$241$	−17.9291	+	8.63419i	−1.15491	+	0.556177i	−0.910506	−	0.413496i	$-0.864308\pi$
$241$	−17.9291	+	8.63419i	−1.15491	+	0.556177i	−0.244407	+	0.969673i	$0.578593\pi$
$242$	−1.01089	+	4.42898i	−0.0649822	+	0.284705i
$243$	−9.88889	−	4.76224i	−0.634372	−	0.305498i
$244$	−7.54288			−0.482883
$245$	−3.02057	−	1.45463i	−0.192977	−	0.0929330i
$246$	−0.198062	+	0.248362i	−0.0126280	+	0.0158350i
$247$	6.62498	−	8.30746i	0.421537	−	0.528591i
$248$	7.77144	+	3.74253i	0.493487	+	0.237651i
$249$	−4.19806			−0.266041
$250$	−5.72037	−	2.75478i	−0.361788	−	0.174228i
$251$	−5.74214	+	25.1579i	−0.362440	+	1.58795i	0.384540	+	0.923108i	$0.374360\pi$
$251$	−5.74214	+	25.1579i	−0.362440	+	1.58795i	−0.746980	+	0.664847i	$0.768497\pi$
$252$	−12.7458	+	6.13805i	−0.802909	+	0.386661i
$253$	10.8535	−	5.22679i	0.682356	−	0.328606i
$254$	4.19902	+	18.3971i	0.263470	+	1.15434i
$255$	0.109916	−	0.137831i	0.00688322	−	0.00863129i
$256$	12.9133	+	16.1928i	0.807084	+	1.01205i
$257$	−2.65937	+	11.6514i	−0.165887	+	0.726797i	0.821726	+	0.569883i	$0.193012\pi$
$257$	−2.65937	+	11.6514i	−0.165887	+	0.726797i	−0.987612	+	0.156914i	$0.949846\pi$
$258$	1.02446	+	4.48845i	0.0637800	+	0.279438i
$259$	7.35086	+	9.21768i	0.456760	+	0.572759i
$260$	2.30798			0.143135
$261$	14.8693	+	2.56506i	0.920385	+	0.158773i
$262$	0.819396			0.0506225
$263$	−0.207455	−	0.260141i	−0.0127923	−	0.0160410i	0.775394	−	0.631477i	$-0.217551\pi$
$263$	−0.207455	−	0.260141i	−0.0127923	−	0.0160410i	−0.788186	+	0.615437i	$0.788980\pi$
$264$	−0.391280	−	1.71431i	−0.0240816	−	0.105509i
$265$	0.346011	−	1.51597i	0.0212553	−	0.0931254i
$266$	9.32036	+	11.6874i	0.571468	+	0.716598i
$267$	0.394928	−	0.495224i	0.0241692	−	0.0303072i
$268$	−0.103875	−	0.455108i	−0.00634520	−	0.0278002i
$269$	0.958615	−	0.461645i	0.0584478	−	0.0281470i	−0.404432	−	0.914568i	$-0.632531\pi$
$269$	0.958615	−	0.461645i	0.0584478	−	0.0281470i	0.462879	+	0.886421i	$0.346816\pi$
$270$	−1.49612	+	0.720491i	−0.0910507	+	0.0438477i
$271$	3.66368	−	16.0516i	0.222553	−	0.975067i	−0.732996	−	0.680233i	$-0.761879\pi$
$271$	3.66368	−	16.0516i	0.222553	−	0.975067i	0.955549	−	0.294834i	$-0.0952642\pi$
$272$	4.93900	+	2.37850i	0.299471	+	0.144218i
$273$	−9.34481			−0.565574
$274$	−21.4955	−	10.3517i	−1.29859	−	0.625367i
$275$	−8.84631	+	11.0929i	−0.533452	+	0.668928i
$276$	−1.43147	+	1.79500i	−0.0861643	+	0.108047i
$277$	−5.94116	−	2.86111i	−0.356970	−	0.171907i	0.246800	−	0.969066i	$-0.420621\pi$
$277$	−5.94116	−	2.86111i	−0.356970	−	0.171907i	−0.603769	+	0.797159i	$0.706335\pi$
$278$	5.03923			0.302233
$279$	−16.0477	−	7.72818i	−0.960752	−	0.462674i
$280$	0.436313	−	1.91161i	0.0260747	−	0.114241i
$281$	27.5112	−	13.2487i	1.64118	−	0.790350i	0.641448	−	0.767166i	$-0.278334\pi$
$281$	27.5112	−	13.2487i	1.64118	−	0.790350i	0.999731	−	0.0231840i	$-0.00738037\pi$
$282$	−5.63706	+	2.71467i	−0.335682	+	0.161656i
$283$	0.791053	+	3.46583i	0.0470232	+	0.206022i	0.992982	−	0.118264i	$-0.0377330\pi$
$283$	0.791053	+	3.46583i	0.0470232	+	0.206022i	−0.945959	+	0.324286i	$0.894876\pi$
$284$	−8.86778	+	11.1198i	−0.526206	+	0.659841i
$285$	0.202907	+	0.254437i	0.0120191	+	0.0150715i
$286$	6.05496	−	26.5285i	0.358037	−	1.56866i
$287$	0.356896	+	1.56366i	0.0210669	+	0.0923001i
$288$	−10.8068	−	13.5513i	−0.636796	−	0.798517i
$289$	−15.7681			−0.927534
$290$	2.58815	−	2.30117i	0.151981	−	0.135130i
$291$	7.00969			0.410915
$292$	−6.95742	−	8.72433i	−0.407152	−	0.510553i
$293$	−7.31647	−	32.0556i	−0.427433	−	1.87271i	−0.485246	−	0.874378i	$-0.661270\pi$
$293$	−7.31647	−	32.0556i	−0.427433	−	1.87271i	0.0578127	−	0.998327i	$-0.481587\pi$
$294$	1.67629	−	7.34432i	0.0977633	−	0.428329i
$295$	−2.02715	−	2.54196i	−0.118025	−	0.147999i
$296$	−2.46346	+	3.08908i	−0.143186	+	0.179549i
$297$	1.67307	+	7.33020i	0.0970814	+	0.425342i
$298$	4.39708	−	2.11752i	0.254716	−	0.122665i
$299$	19.3300	−	9.30886i	1.11789	−	0.538345i
$300$	0.601720	−	2.63631i	0.0347403	−	0.152207i
$301$	20.9426	+	10.0854i	1.20711	+	0.581316i
$302$	4.38835			0.252521
$303$	6.99396	+	3.36811i	0.401792	+	0.193493i
$304$	−6.30947	+	7.91183i	−0.361873	+	0.453774i
$305$	−1.34601	+	1.68784i	−0.0770724	+	0.0966457i
$306$	−5.04892	−	2.43143i	−0.288627	−	0.138996i
$307$	14.6703			0.837275			0.418638	−	0.908153i	$-0.362508\pi$
$307$	14.6703			0.837275			0.418638	+	0.908153i	$0.362508\pi$
$308$	13.2458	+	6.37883i	0.754749	+	0.363468i
$309$	0.278676	−	1.22096i	0.0158533	−	0.0694578i
$310$	−3.68329	+	1.77378i	−0.209197	+	0.100744i
$311$	−16.6918	+	8.03834i	−0.946504	+	0.455812i	−0.842459	−	0.538760i	$-0.818893\pi$
$311$	−16.6918	+	8.03834i	−0.946504	+	0.455812i	−0.104045	+	0.994573i	$0.533179\pi$
$312$	−0.696866	−	3.05317i	−0.0394523	−	0.172852i
$313$	14.3354	−	17.9760i	0.810286	−	1.01607i	−0.189132	−	0.981952i	$-0.560567\pi$
$313$	14.3354	−	17.9760i	0.810286	−	1.01607i	0.999418	−	0.0341147i	$-0.0108612\pi$
$314$	−19.8605	−	24.9043i	−1.12080	−	1.40543i
$315$	−0.900969	+	3.94740i	−0.0507638	+	0.222411i
$316$	0.164874	+	0.722362i	0.00927491	+	0.0406360i
$317$	8.76540	+	10.9915i	0.492314	+	0.617342i	0.964476	−	0.264170i	$-0.0850979\pi$
$317$	8.76540	+	10.9915i	0.492314	+	0.617342i	−0.472162	+	0.881512i	$0.656526\pi$
$318$	3.49396			0.195932
$319$	−7.55041	−	13.7433i	−0.422742	−	0.769479i
$320$	−0.452812			−0.0253129
$321$	−2.07002	−	2.59573i	−0.115537	−	0.144879i
$322$	6.71648	+	29.4268i	0.374295	+	1.63989i
$323$	−0.506041	+	2.21711i	−0.0281569	+	0.123363i
$324$	5.64191	+	7.07473i	0.313439	+	0.393040i
$325$	−15.7552	+	19.7564i	−0.873940	+	1.09589i
$326$	−1.99127	−	8.72433i	−0.110286	−	0.483196i
$327$	0.662718	−	0.319148i	0.0366484	−	0.0176489i
$328$	−0.484271	+	0.233212i	−0.0267394	+	0.0128770i
$329$	−7.02930	+	30.7974i	−0.387538	+	1.69792i
$330$	0.750864	+	0.361597i	0.0413337	+	0.0199053i
$331$	13.9565			0.767116			0.383558	−	0.923517i	$-0.374699\pi$
$331$	13.9565			0.767116			0.383558	+	0.923517i	$0.374699\pi$
$332$	10.5978	+	5.10365i	0.581632	+	0.280099i
$333$	5.08695	−	6.37883i	0.278763	−	0.349558i
$334$	−16.2506	+	20.3776i	−0.889195	+	1.11501i
$335$	−0.120374	−	0.0579692i	−0.00657676	−	0.00316720i
$336$	8.89977			0.485522
$337$	12.6114	+	6.07333i	0.686987	+	0.330836i	0.744607	−	0.667503i	$-0.232637\pi$
$337$	12.6114	+	6.07333i	0.686987	+	0.330836i	−0.0576199	+	0.998339i	$0.518351\pi$
$338$	5.57122	−	24.4091i	0.303034	−	1.32768i
$339$	−3.46466	+	1.66849i	−0.188174	+	0.0906200i
$340$	−0.445042	+	0.214321i	−0.0241358	+	0.0116232i
$341$	4.11894	+	18.0463i	0.223053	+	0.977260i
$342$	6.44989	−	8.08790i	0.348770	−	0.437344i
$343$	−6.04288	−	7.57753i	−0.326285	−	0.409148i
$344$	−1.73341	+	7.59455i	−0.0934590	+	0.409471i
$345$	0.146220	+	0.640630i	0.00787220	+	0.0344903i
$346$	−11.8116	−	14.8113i	−0.634997	−	0.796261i
$347$	−19.8538			−1.06581			−0.532905	−	0.846175i	$-0.678900\pi$
$347$	−19.8538			−1.06581			−0.532905	+	0.846175i	$0.678900\pi$
$348$	2.43296	+	1.73553i	0.130420	+	0.0930344i
$349$	−26.9202			−1.44101			−0.720503	−	0.693452i	$-0.756089\pi$
$349$	−26.9202			−1.44101			−0.720503	+	0.693452i	$0.756089\pi$
$350$	−22.1652	−	27.7942i	−1.18478	−	1.48566i
$351$	2.97972	+	13.0550i	0.159046	+	0.696825i
$352$	−4.00820	+	17.5611i	−0.213638	+	0.936007i
$353$	−2.50335	−	3.13910i	−0.133240	−	0.167078i	0.710736	−	0.703459i	$-0.248362\pi$
$353$	−2.50335	−	3.13910i	−0.133240	−	0.167078i	−0.843976	+	0.536382i	$0.819791\pi$
$354$	4.55496	−	5.71174i	0.242093	−	0.303575i
$355$	0.905813	+	3.96863i	0.0480756	+	0.210633i
$356$	−1.59903	+	0.770053i	−0.0847485	+	0.0408127i
$357$	1.80194	−	0.867767i	0.0953687	−	0.0459271i
$358$	−2.30194	+	10.0854i	−0.121661	+	0.533032i
$359$	0.672407	+	0.323814i	0.0354883	+	0.0170903i	0.451544	−	0.892249i	$-0.350873\pi$
$359$	0.672407	+	0.323814i	0.0354883	+	0.0170903i	−0.416055	+	0.909339i	$0.636588\pi$
$360$	−1.35690			−0.0715147
$361$	13.3361	+	6.42232i	0.701899	+	0.338017i
$362$	7.46077	−	9.35551i	0.392129	−	0.491715i
$363$	−0.699554	+	0.877213i	−0.0367171	+	0.0460418i
$364$	23.5906	+	11.3606i	1.23648	+	0.595459i
$365$	−3.19375			−0.167169
$366$	−4.37047	−	2.10471i	−0.228448	−	0.110015i
$367$	7.57660	−	33.1952i	0.395495	−	1.73278i	−0.249304	−	0.968425i	$-0.580202\pi$
$367$	7.57660	−	33.1952i	0.395495	−	1.73278i	0.644799	−	0.764352i	$-0.276941\pi$
$368$	−18.4095	+	8.86553i	−0.959659	+	0.462148i
$369$	1.00000	−	0.481575i	0.0520579	−	0.0250698i
$370$	−0.416698	−	1.82567i	−0.0216631	−	0.0949123i
$371$	10.9988	−	13.7921i	0.571029	−	0.716048i
$372$	−2.19955	−	2.75815i	−0.114042	−	0.143004i
$373$	−6.23072	+	27.2986i	−0.322614	+	1.41347i	0.510268	+	0.860015i	$0.329546\pi$
$373$	−6.23072	+	27.2986i	−0.322614	+	1.41347i	−0.832882	+	0.553450i	$0.813311\pi$
$374$	1.29590	+	5.67770i	0.0670092	+	0.293587i
$375$	−0.977697	−	1.22599i	−0.0504881	−	0.0633100i
$376$	−10.5864			−0.545953
$377$	−13.4472	−	24.4767i	−0.692566	−	1.26062i
$378$	−18.8388			−0.968962
$379$	14.2661	+	17.8891i	0.732798	+	0.918900i	0.998986	−	0.0450211i	$-0.0143355\pi$
$379$	14.2661	+	17.8891i	0.732798	+	0.918900i	−0.266188	+	0.963921i	$0.585764\pi$
$380$	−0.202907	−	0.888992i	−0.0104089	−	0.0456043i
$381$	−1.03707	+	4.54371i	−0.0531308	+	0.232781i
$382$	21.1347	+	26.5020i	1.08134	+	1.35596i
$383$	7.39344	−	9.27108i	0.377787	−	0.473730i	−0.556194	−	0.831052i	$-0.687739\pi$
$383$	7.39344	−	9.27108i	0.377787	−	0.473730i	0.933981	+	0.357323i	$0.116310\pi$
$384$	0.998804	+	4.37604i	0.0509700	+	0.223314i
$385$	3.79105	−	1.82567i	0.193210	−	0.0930450i
$386$	17.6712	−	8.51001i	0.899441	−	0.433148i
$387$	3.57942	−	15.6824i	0.181952	−	0.797184i
$388$	−17.6957	−	8.52179i	−0.898362	−	0.432628i
$389$	−10.3913			−0.526862			−0.263431	−	0.964678i	$-0.584854\pi$
$389$	−10.3913			−0.526862			−0.263431	+	0.964678i	$0.584854\pi$
$390$	1.33728	+	0.644001i	0.0677159	+	0.0326103i
$391$	−2.86294	+	3.59001i	−0.144785	+	0.181555i
$392$	7.94720	−	9.96547i	0.401394	−	0.503332i
$393$	0.182333	+	0.0878068i	0.00919747	+	0.00442927i
$394$	15.1371			0.762594
$395$	0.191062	+	0.0920106i	0.00961337	+	0.00462956i
$396$	2.26391	−	9.91882i	0.113766	−	0.498439i
$397$	−7.40366	+	3.56541i	−0.371579	+	0.178943i	−0.610348	−	0.792133i	$-0.708970\pi$
$397$	−7.40366	+	3.56541i	−0.371579	+	0.178943i	0.238769	+	0.971076i	$0.423256\pi$
$398$	−10.7497	+	5.17677i	−0.538832	+	0.259488i
$399$	0.821552	+	3.59945i	0.0411290	+	0.180198i
$400$	15.0048	−	18.8155i	0.750242	−	0.940774i
$401$	15.5130	+	19.4527i	0.774684	+	0.971423i	0.999996	−	0.00286337i	$-0.000911439\pi$
$401$	15.5130	+	19.4527i	0.774684	+	0.971423i	−0.225312	+	0.974287i	$0.572340\pi$
$402$	0.0668027	−	0.292682i	0.00333182	−	0.0145976i
$403$	7.33579	+	32.1402i	0.365422	+	1.60102i
$404$	−13.5613	−	17.0053i	−0.674700	−	0.846047i
$405$	2.58987			0.128692
$406$	37.7814	−	10.7813i	1.87506	−	0.535069i
$407$	−8.47889			−0.420283
$408$	0.417895	+	0.524023i	0.0206889	+	0.0259430i
$409$	−4.20464	−	18.4217i	−0.207906	−	0.910895i	−0.965958	−	0.258701i	$-0.916706\pi$
$409$	−4.20464	−	18.4217i	−0.207906	−	0.910895i	0.758052	−	0.652194i	$-0.226151\pi$
$410$	0.0566871	−	0.248362i	0.00279957	−	0.0122657i
$411$	−3.67390	−	4.60692i	−0.181220	−	0.227243i
$412$	−2.18784	+	2.74347i	−0.107787	+	0.135161i
$413$	−8.20775	−	35.9605i	−0.403877	−	1.76950i
$414$	18.8192	−	9.06283i	0.924911	−	0.445414i
$415$	3.03319	−	1.46071i	0.148893	−	0.0717033i
$416$	−7.13856	+	31.2761i	−0.349996	+	1.53343i
$417$	1.12133	+	0.540006i	0.0549120	+	0.0264442i
$418$	−10.7506			−0.525830
$419$	9.81378	+	4.72607i	0.479435	+	0.230884i	0.657962	−	0.753051i	$-0.271419\pi$
$419$	9.81378	+	4.72607i	0.479435	+	0.230884i	−0.178527	+	0.983935i	$0.557133\pi$
$420$	−0.500000	+	0.626980i	−0.0243975	+	0.0305935i
$421$	−12.4453	+	15.6060i	−0.606549	+	0.760588i	−0.986383	−	0.164467i	$-0.947410\pi$
$421$	−12.4453	+	15.6060i	−0.606549	+	0.760588i	0.379834	+	0.925055i	$0.375981\pi$
$422$	−13.1506	−	6.33301i	−0.640163	−	0.308286i
$423$	21.8605			1.06290
$424$	5.32640	+	2.56506i	0.258673	+	0.124570i
$425$	1.20344	−	5.27261i	0.0583754	−	0.255759i
$426$	−8.24094	+	3.96863i	−0.399275	+	0.192281i
$427$	−22.0661	+	10.6265i	−1.06786	+	0.514252i
$428$	2.07002	+	9.06937i	0.100058	+	0.438384i
$429$	4.19016	−	5.25430i	0.202303	−	0.253680i
$430$	−2.30194	−	2.88654i	−0.111009	−	0.139201i
$431$	6.71797	−	29.4334i	0.323593	−	1.41776i	−0.507514	−	0.861643i	$-0.669436\pi$
$431$	6.71797	−	29.4334i	0.323593	−	1.41776i	0.831108	−	0.556112i	$-0.187707\pi$
$432$	−2.83781	−	12.4333i	−0.136534	−	0.598196i
$433$	−12.5891	−	15.7862i	−0.604994	−	0.758638i	0.381153	−	0.924512i	$-0.375527\pi$
$433$	−12.5891	−	15.7862i	−0.604994	−	0.758638i	−0.986147	+	0.165874i	$0.946956\pi$
$434$	−46.3793			−2.22628
$435$	0.822512	−	0.234713i	0.0394364	−	0.0112536i
$436$	−2.06100			−0.0987039
$437$	−5.28501	−	6.62720i	−0.252816	−	0.317022i
$438$	−1.59688	−	6.99637i	−0.0763016	−	0.334299i
$439$	2.37316	−	10.3975i	0.113265	−	0.496245i	−0.886193	−	0.463316i	$-0.846659\pi$
$439$	2.37316	−	10.3975i	0.113265	−	0.496245i	0.999458	−	0.0329287i	$-0.0104834\pi$
$440$	0.879199	+	1.10248i	0.0419141	+	0.0525587i
$441$	−16.4107	+	20.5783i	−0.781460	+	0.979920i
$442$	2.30798	+	10.1119i	0.109779	+	0.480975i
$443$	18.3349	−	8.82962i	0.871117	−	0.419508i	0.0557448	−	0.998445i	$-0.482247\pi$
$443$	18.3349	−	8.82962i	0.871117	−	0.419508i	0.815372	+	0.578937i	$0.196532\pi$
$444$	1.45593	−	0.701137i	0.0690952	−	0.0332745i
$445$	−0.113032	+	0.495224i	−0.00535822	+	0.0234759i
$446$	35.5855	+	17.1371i	1.68502	+	0.811464i
$447$	1.20536			0.0570115
$448$	−4.62833	−	2.22889i	−0.218668	−	0.105305i
$449$	12.1102	−	15.1857i	0.571516	−	0.716659i	−0.409124	−	0.912479i	$-0.634166\pi$
$449$	12.1102	−	15.1857i	0.571516	−	0.716659i	0.980640	+	0.195820i	$0.0627369\pi$
$450$	−15.3388	+	19.2342i	−0.723077	+	0.906710i
$451$	−1.03923	−	0.500466i	−0.0489354	−	0.0235660i
$452$	10.7748			0.506804
$453$	0.976501	+	0.470258i	0.0458800	+	0.0220946i
$454$	−7.32908	+	32.1108i	−0.343971	+	1.50704i
$455$	6.75182	−	3.25151i	0.316530	−	0.152433i
$456$	−1.11476	+	0.536840i	−0.0522034	+	0.0251399i
$457$	2.76391	+	12.1095i	0.129290	+	0.566457i	0.997526	+	0.0703045i	$0.0223971\pi$
$457$	2.76391	+	12.1095i	0.129290	+	0.566457i	−0.868236	+	0.496152i	$0.834746\pi$
$458$	−18.0036	+	22.5759i	−0.841255	+	1.05490i
$459$	−1.78687	−	2.24067i	−0.0834041	−	0.104585i
$460$	0.409698	−	1.79500i	0.0191023	−	0.0836925i
$461$	4.88351	+	21.3961i	0.227448	+	0.996514i	0.951712	+	0.306991i	$0.0993223\pi$
$461$	4.88351	+	21.3961i	0.227448	+	0.996514i	−0.724265	+	0.689522i	$0.757821\pi$
$462$	5.89493	+	7.39201i	0.274257	+	0.343907i
$463$	−33.0073			−1.53398			−0.766990	−	0.641660i	$-0.778246\pi$
$463$	−33.0073			−1.53398			−0.766990	+	0.641660i	$0.778246\pi$
$464$	12.8068	+	23.3110i	0.594540	+	1.08219i
$465$	−1.00969			−0.0468232
$466$	−2.19806	−	2.75628i	−0.101823	−	0.127682i
$467$	5.80851	+	25.4487i	0.268786	+	1.17763i	0.911427	+	0.411461i	$0.134981\pi$
$467$	5.80851	+	25.4487i	0.268786	+	1.17763i	−0.642642	+	0.766167i	$0.722162\pi$
$468$	4.03199	−	17.6653i	0.186379	−	0.816579i
$469$	−0.945042	−	1.18505i	−0.0436380	−	0.0547203i
$470$	3.12833	−	3.92281i	0.144299	−	0.180946i
$471$	−1.75063	−	7.67000i	−0.0806647	−	0.353415i
$472$	11.1371	−	5.36333i	0.512625	−	0.246867i
$473$	−15.0613	+	7.25314i	−0.692519	+	0.333500i
$474$	−0.106031	+	0.464554i	−0.00487018	+	0.0213377i
$475$	8.99492	+	4.33172i	0.412715	+	0.198753i
$476$	−5.60388			−0.256853
$477$	−10.9988	−	5.29674i	−0.503601	−	0.242521i
$478$	10.0700	−	12.6274i	0.460592	−	0.577564i
$479$	20.6163	−	25.8520i	0.941981	−	1.18121i	−0.0413068	−	0.999147i	$-0.513152\pi$
$479$	20.6163	−	25.8520i	0.941981	−	1.18121i	0.983287	−	0.182060i	$-0.0582765\pi$
$480$	−0.885239	−	0.426309i	−0.0404055	−	0.0194582i
$481$	−15.1008			−0.688538
$482$	32.3071	+	15.5583i	1.47155	+	0.708660i
$483$	−1.65883	+	7.26782i	−0.0754795	+	0.330697i
$484$	2.83244	−	1.36403i	0.128747	−	0.0620014i
$485$	−5.06465	+	2.43901i	−0.229974	+	0.110750i
$486$	4.40097	+	19.2819i	0.199632	+	0.874645i
$487$	−6.33244	+	7.94063i	−0.286950	+	0.359824i	−0.904325	−	0.426845i	$-0.859625\pi$
$487$	−6.33244	+	7.94063i	−0.286950	+	0.359824i	0.617375	+	0.786669i	$0.288196\pi$
$488$	−5.11745	−	6.41708i	−0.231656	−	0.290487i
$489$	0.491803	−	2.15473i	0.0222401	−	0.0974403i
$490$	1.34428	+	5.88968i	0.0607285	+	0.266069i
$491$	−12.2714	−	15.3879i	−0.553802	−	0.694446i	0.423596	−	0.905851i	$-0.360768\pi$
$491$	−12.2714	−	15.3879i	−0.553802	−	0.694446i	−0.977399	+	0.211405i	$0.932196\pi$
$492$	0.219833			0.00991082
$493$	4.86592	+	3.47107i	0.219150	+	0.156329i
$494$	−19.1468			−0.861453
$495$	−1.81551	−	2.27658i	−0.0816012	−	0.102325i
$496$	−6.98643	−	30.6095i	−0.313700	−	1.37441i
$497$	−10.2763	+	45.0233i	−0.460954	+	2.01957i
$498$	4.71648	+	5.91428i	0.211351	+	0.265025i
$499$	17.3639	−	21.7736i	0.777315	−	0.974722i	−0.222685	−	0.974890i	$-0.571482\pi$
$499$	17.3639	−	21.7736i	0.777315	−	0.974722i	1.00000		0.000168534i	$5.36461e-5\pi$
$500$	0.977697	+	4.28357i	0.0437240	+	0.191567i
$501$	−5.79978	+	2.79303i	−0.259115	+	0.124783i
$502$	41.8940	−	20.1751i	1.86982	−	0.900459i
$503$	0.0501138	−	0.219563i	0.00223446	−	0.00978982i	−0.973798	−	0.227413i	$-0.926973\pi$
$503$	0.0501138	−	0.219563i	0.00223446	−	0.00978982i	0.976033	+	0.217623i	$0.0698304\pi$
$504$	−13.8693	−	6.67909i	−0.617787	−	0.297510i
$505$	−6.22521			−0.277018
$506$	−19.5574	−	9.41835i	−0.869433	−	0.418697i
$507$	3.85540	−	4.83452i	0.171224	−	0.214709i
$508$	8.14191	−	10.2096i	0.361239	−	0.452979i
$509$	22.7974	+	10.9786i	1.01048	+	0.486620i	0.864481	−	0.502665i	$-0.167647\pi$
$509$	22.7974	+	10.9786i	1.01048	+	0.486620i	0.145995	+	0.989285i	$0.453362\pi$
$510$	−0.317667			−0.0140665
$511$	−32.6444	−	15.7207i	−1.44410	−	0.695443i
$512$	3.81604	−	16.7192i	0.168647	−	0.738890i
$513$	4.76659	−	2.29547i	0.210450	−	0.101348i
$514$	19.4025	−	9.34373i	0.855806	−	0.412134i
$515$	0.223480	+	0.979132i	0.00984772	+	0.0431457i
$516$	1.98643	−	2.49090i	0.0874475	−	0.109656i
$517$	−14.1645	−	17.7617i	−0.622954	−	0.781160i
$518$	4.72737	−	20.7119i	0.207709	−	0.910030i
$519$	−1.04115	−	4.56157i	−0.0457013	−	0.200231i
$520$	1.56584	+	1.96351i	0.0686668	+	0.0861054i
$521$	23.5797			1.03305			0.516523	−	0.856273i	$-0.327226\pi$
$521$	23.5797			1.03305			0.516523	+	0.856273i	$0.327226\pi$
$522$	−13.0918	−	23.8298i	−0.573012	−	1.04300i
$523$	3.96508			0.173381			0.0866905	−	0.996235i	$-0.472371\pi$
$523$	3.96508			0.173381			0.0866905	+	0.996235i	$0.472371\pi$
$524$	−0.353543	−	0.443330i	−0.0154446	−	0.0193669i
$525$	−1.95377	−	8.56003i	−0.0852696	−	0.373590i
$526$	−0.133415	+	0.584531i	−0.00581719	+	0.0254868i
$527$	−4.39911	−	5.51631i	−0.191628	−	0.240294i
$528$	−3.99061	+	5.00406i	−0.173669	+	0.217774i
$529$	1.30947	+	5.73717i	0.0569335	+	0.249442i
$530$	−2.52446	+	1.21572i	−0.109655	+	0.0528073i
$531$	−22.9976	+	11.0751i	−0.998011	+	0.480617i
$532$	2.30194	−	10.0854i	0.0998017	−	0.437260i
$533$	−1.85086	−	0.891325i	−0.0801694	−	0.0386076i
$534$	−1.14138			−0.0493921
$535$	2.39881	+	1.15521i	0.103710	+	0.0499440i
$536$	0.316708	−	0.397139i	0.0136797	−	0.0171538i
$537$	−1.59299	+	1.99755i	−0.0687426	+	0.0862005i
$538$	−1.72737	−	0.831855i	−0.0744720	−	0.0358638i
$539$	27.3532			1.17818
$540$	1.03534	+	0.498595i	0.0445541	+	0.0214561i
$541$	5.48739	−	24.0418i	0.235921	−	1.03364i	−0.708709	−	0.705501i	$-0.750722\pi$
$541$	5.48739	−	24.0418i	0.235921	−	1.03364i	0.944630	−	0.328137i	$-0.106421\pi$
$542$	−26.7298	+	12.8724i	−1.14814	+	0.552917i
$543$	2.66272	−	1.28230i	0.114268	−	0.0550287i
$544$	−1.52781	−	6.69378i	−0.0655044	−	0.286993i
$545$	−0.367781	+	0.461183i	−0.0157540	+	0.0197549i
$546$	10.4988	+	13.1651i	0.449307	+	0.563414i
$547$	−5.52768	+	24.2183i	−0.236347	+	1.03550i	0.707913	+	0.706300i	$0.249637\pi$
$547$	−5.52768	+	24.2183i	−0.236347	+	1.03550i	−0.944259	+	0.329202i	$0.893220\pi$
$548$	3.67390	+	16.0964i	0.156941	+	0.687604i
$549$	10.5673	+	13.2510i	0.451003	+	0.565540i
$550$	25.5666			1.09016
$551$	−8.24578	+	7.33150i	−0.351282	+	0.312332i
$552$	−2.49827			−0.106333
$553$	1.50000	+	1.88094i	0.0637865	+	0.0799857i
$554$	2.64406	+	11.5844i	0.112335	+	0.492174i
$555$	0.102916	−	0.450904i	0.00436854	−	0.0191398i
$556$	−2.17427	−	2.72645i	−0.0922095	−	0.115627i
$557$	4.84146	−	6.07100i	0.205139	−	0.257237i	−0.668610	−	0.743613i	$-0.733110\pi$
$557$	4.84146	−	6.07100i	0.205139	−	0.257237i	0.873749	+	0.486377i	$0.161682\pi$
$558$	7.14191	+	31.2907i	0.302341	+	1.32464i
$559$	−26.8240	+	12.9178i	−1.13453	+	0.546363i
$560$	−6.43027	+	3.09666i	−0.271729	+	0.130858i
$561$	−0.320060	+	1.40227i	−0.0135129	+	0.0592041i
$562$	−49.5734	−	23.8733i	−2.09113	−	1.00703i
$563$	20.8009			0.876652			0.438326	−	0.898816i	$-0.355571\pi$
$563$	20.8009			0.876652			0.438326	+	0.898816i	$0.355571\pi$
$564$	3.90097	+	1.87861i	0.164260	+	0.0791036i
$565$	1.92274	−	2.41104i	0.0808902	−	0.101433i
$566$	3.99396	−	5.00827i	0.167879	−	0.210513i
$567$	26.4720	+	12.7482i	1.11172	+	0.535375i
$568$	−15.4765			−0.649380
$569$	−2.53103	−	1.21888i	−0.106106	−	0.0510981i	0.380078	−	0.924955i	$-0.375897\pi$
$569$	−2.53103	−	1.21888i	−0.106106	−	0.0510981i	−0.486184	+	0.873856i	$0.661612\pi$
$570$	0.130490	−	0.571714i	0.00546563	−	0.0239465i
$571$	−2.60603	+	1.25500i	−0.109059	+	0.0525201i	−0.487618	−	0.873057i	$-0.662134\pi$
$571$	−2.60603	+	1.25500i	−0.109059	+	0.0525201i	0.378559	+	0.925577i	$0.376420\pi$
$572$	−16.9656	+	8.17021i	−0.709368	+	0.341614i
$573$	1.86294	+	8.16206i	0.0778253	+	0.340975i
$574$	1.80194	−	2.25956i	0.0752114	−	0.0943121i
$575$	12.5685	+	15.7604i	0.524144	+	0.657256i
$576$	−0.791053	+	3.46583i	−0.0329605	+	0.144409i
$577$	−1.59970	−	7.00872i	−0.0665962	−	0.291777i	0.930653	−	0.365904i	$-0.119240\pi$
$577$	−1.59970	−	7.00872i	−0.0665962	−	0.291777i	−0.997249	+	0.0741270i	$0.976383\pi$
$578$	17.7153	+	22.2143i	0.736859	+	0.923992i
$579$	4.84415			0.201316
$580$	−2.36174	−	0.407417i	−0.0980659	−	0.0169171i
$581$	38.1933			1.58452
$582$	−7.87531	−	9.87533i	−0.326442	−	0.409346i
$583$	2.82304	+	12.3686i	0.116919	+	0.512254i
$584$	2.70195	−	11.8380i	0.111807	−	0.489860i
$585$	−3.23341	−	4.05456i	−0.133685	−	0.167636i
$586$	−36.9403	+	46.3216i	−1.52599	+	1.91353i
$587$	6.90635	+	30.2587i	0.285055	+	1.24891i	0.891220	+	0.453570i	$0.149850\pi$
$587$	6.90635	+	30.2587i	0.285055	+	1.24891i	−0.606165	+	0.795339i	$0.707293\pi$
$588$	−4.69687	+	2.26189i	−0.193695	+	0.0932788i
$589$	11.7349	−	5.65123i	0.483528	−	0.232855i
$590$	−1.30367	+	5.71174i	−0.0536711	+	0.235148i
$591$	3.36831	+	1.62209i	0.138554	+	0.0667240i
$592$	14.3817			0.591082
$593$	−32.8560	−	15.8226i	−1.34923	−	0.649757i	−0.387025	−	0.922069i	$-0.626497\pi$
$593$	−32.8560	−	15.8226i	−1.34923	−	0.649757i	−0.962209	+	0.272312i	$0.912212\pi$
$594$	8.44720	−	10.5925i	0.346593	−	0.434614i
$595$	−1.00000	+	1.25396i	−0.0409960	+	0.0514074i
$596$	−3.04288	−	1.46537i	−0.124641	−	0.0600240i
$597$	−2.94677			−0.120603
$598$	−34.8315	−	16.7740i	−1.42437	−	0.685939i
$599$	−6.69083	+	29.3144i	−0.273380	+	1.19775i	0.632615	+	0.774466i	$0.281981\pi$
$599$	−6.69083	+	29.3144i	−0.273380	+	1.19775i	−0.905995	+	0.423288i	$0.860876\pi$
$600$	2.65106	−	1.27669i	0.108229	−	0.0521205i
$601$	29.8995	−	14.3989i	1.21963	−	0.587342i	0.290420	−	0.956899i	$-0.406205\pi$
$601$	29.8995	−	14.3989i	1.21963	−	0.587342i	0.929208	+	0.369558i	$0.120491\pi$
$602$	−9.32036	−	40.8351i	−0.379869	−	1.66432i
$603$	−0.653989	+	0.820077i	−0.0266325	+	0.0333961i
$604$	−1.89344	−	2.37429i	−0.0770428	−	0.0966086i
$605$	0.200218	−	0.877213i	0.00814003	−	0.0356638i
$606$	−3.11260	−	13.6372i	−0.126441	−	0.553974i
$607$	−9.42729	−	11.8214i	−0.382642	−	0.479818i	0.552792	−	0.833319i	$-0.313562\pi$
$607$	−9.42729	−	11.8214i	−0.382642	−	0.479818i	−0.935434	+	0.353502i	$0.884991\pi$
$608$	12.6746			0.514021
$609$	9.56249	+	1.64960i	0.387492	+	0.0668451i
$610$	3.89008			0.157505
$611$	−25.2268	−	31.6334i	−1.02057	−	1.27975i
$612$	0.862937	+	3.78077i	0.0348821	+	0.152829i
$613$	−0.835658	+	3.66126i	−0.0337519	+	0.147877i	−0.988996	−	0.147942i	$-0.952735\pi$
$613$	−0.835658	+	3.66126i	−0.0337519	+	0.147877i	0.955244	+	0.295818i	$0.0955923\pi$
$614$	−16.4819	−	20.6676i	−0.665154	−	0.834077i
$615$	0.0392287	−	0.0491912i	0.00158185	−	0.00198358i
$616$	3.55980	+	15.5965i	0.143429	+	0.628401i
$617$	−26.8995	+	12.9541i	−1.08293	+	0.521514i	−0.888254	−	0.459353i	$-0.848081\pi$
$617$	−26.8995	+	12.9541i	−1.08293	+	0.521514i	−0.194681	+	0.980867i	$0.562367\pi$
$618$	−2.03319	+	0.979132i	−0.0817868	+	0.0393865i
$619$	10.2622	−	44.9615i	0.412472	−	1.80716i	−0.159866	−	0.987139i	$-0.551106\pi$
$619$	10.2622	−	44.9615i	0.412472	−	1.80716i	0.572338	−	0.820018i	$-0.306037\pi$
$620$	2.54892	+	1.22749i	0.102367	+	0.0492973i
$621$	10.6823			0.428667
$622$	30.0776	+	14.4846i	1.20600	+	0.580779i
$623$	−3.59299	+	4.50547i	−0.143950	+	0.180508i
$624$	−7.10723	+	8.91218i	−0.284517	+	0.356773i
$625$	−20.8174	−	10.0251i	−0.832697	−	0.401006i
$626$	−41.4306			−1.65590
$627$	−2.39224	−	1.15204i	−0.0955368	−	0.0460081i
$628$	−4.90515	+	21.4909i	−0.195737	+	0.857579i
$629$	2.91185	−	1.40227i	0.116103	−	0.0559124i
$630$	6.57338	−	3.16557i	0.261890	−	0.126119i
$631$	−2.81043	−	12.3133i	−0.111881	−	0.490185i	−0.999558	−	0.0297178i	$-0.990539\pi$
$631$	−2.81043	−	12.3133i	−0.111881	−	0.490185i	0.887677	−	0.460467i	$-0.152318\pi$
$632$	−0.502688	+	0.630351i	−0.0199959	+	0.0250740i
$633$	−2.24764	−	2.81846i	−0.0893358	−	0.112024i
$634$	5.63706	−	24.6976i	0.223876	−	0.980867i
$635$	−0.831668	−	3.64377i	−0.0330037	−	0.144599i
$636$	−1.50753	−	1.89039i	−0.0597776	−	0.0749587i
$637$	48.7157			1.93019
$638$	−10.8790	+	26.0776i	−0.430702	+	1.03242i
$639$	31.9584			1.26425
$640$	−2.24429	−	2.81425i	−0.0887134	−	0.111243i
$641$	−8.67874	−	38.0241i	−0.342790	−	1.50186i	−0.793157	−	0.609017i	$-0.791564\pi$
$641$	−8.67874	−	38.0241i	−0.342790	−	1.50186i	0.450368	−	0.892843i	$-0.351293\pi$
$642$	−1.33124	+	5.83255i	−0.0525399	+	0.230192i
$643$	25.7479	+	32.2869i	1.01540	+	1.27327i	0.961523	+	0.274723i	$0.0885862\pi$
$643$	25.7479	+	32.2869i	1.01540	+	1.27327i	0.0538762	+	0.998548i	$0.482842\pi$
$644$	13.0233	−	16.3307i	0.513188	−	0.643518i
$645$	−0.202907	−	0.888992i	−0.00798944	−	0.0350040i
$646$	3.69202	−	1.77798i	0.145261	−	0.0699538i
$647$	16.1368	−	7.77109i	0.634404	−	0.305513i	−0.0889021	−	0.996040i	$-0.528336\pi$
$647$	16.1368	−	7.77109i	0.634404	−	0.305513i	0.723306	+	0.690527i	$0.242622\pi$
$648$	−2.19106	+	9.59967i	−0.0860730	+	0.377111i
$649$	23.8998	+	11.5095i	0.938148	+	0.451788i
$650$	45.5338			1.78598
$651$	−10.3204	−	4.97002i	−0.404487	−	0.194790i
$652$	−3.86108	+	4.84164i	−0.151211	+	0.189613i
$653$	−8.30529	+	10.4145i	−0.325011	+	0.407551i	−0.917314	−	0.398164i	$-0.869647\pi$
$653$	−8.30529	+	10.4145i	−0.325011	+	0.407551i	0.592303	+	0.805715i	$0.298219\pi$
$654$	−1.19418	−	0.575086i	−0.0466960	−	0.0224876i
$655$	−0.162291			−0.00634125
$656$	1.76271	+	0.848876i	0.0688222	+	0.0331430i
$657$	−5.57942	+	24.4450i	−0.217674	+	0.953691i
$658$	51.2851	−	24.6976i	1.99930	−	0.962812i
$659$	−16.9073	+	8.14213i	−0.658615	+	0.317172i	−0.733171	−	0.680045i	$-0.761960\pi$
$659$	−16.9073	+	8.14213i	−0.658615	+	0.317172i	0.0745557	+	0.997217i	$0.476246\pi$
$660$	−0.128334	−	0.562269i	−0.00499540	−	0.0218863i
$661$	−15.4182	+	19.3338i	−0.599698	+	0.751998i	−0.985331	−	0.170655i	$-0.945412\pi$
$661$	−15.4182	+	19.3338i	−0.599698	+	0.751998i	0.385633	+	0.922652i	$0.373983\pi$
$662$	−15.6799	−	19.6620i	−0.609418	−	0.764186i
$663$	−0.570024	+	2.49744i	−0.0221379	+	0.0969924i
$664$	2.84817	+	12.4786i	0.110530	+	0.484265i
$665$	−1.84601	−	2.31482i	−0.0715852	−	0.0897650i
$666$	−14.7017			−0.569680
$667$	−21.4236	+	6.11345i	−0.829524	+	0.236714i
$668$	18.0368			0.697866
$669$	6.08211	+	7.62672i	0.235148	+	0.294866i
$670$	0.0535716	+	0.234713i	0.00206965	+	0.00906774i
$671$	3.91939	−	17.1720i	0.151306	−	0.662916i
$672$	−6.94989	−	8.71488i	−0.268098	−	0.336184i
$673$	15.8632	−	19.8919i	0.611483	−	0.766775i	−0.375636	−	0.926767i	$-0.622576\pi$
$673$	15.8632	−	19.8919i	0.611483	−	0.766775i	0.987118	+	0.159992i	$0.0511470\pi$
$674$	−5.61260	−	24.5904i	−0.216189	−	0.947188i
$675$	−11.3357	+	5.45897i	−0.436310	+	0.210116i
$676$	−15.6102	+	7.51748i	−0.600393	+	0.289134i
$677$	−0.137195	+	0.601090i	−0.00527283	+	0.0231018i	−0.977496	−	0.210954i	$-0.932343\pi$
$677$	−0.137195	+	0.601090i	−0.00527283	+	0.0231018i	0.972223	+	0.234056i	$0.0752000\pi$
$678$	6.24309	+	3.00652i	0.239765	+	0.115465i
$679$	−63.7730			−2.44738
$680$	−0.484271	−	0.233212i	−0.0185709	−	0.00894329i
$681$	−5.07188	+	6.35994i	−0.194355	+	0.243713i
$682$	20.7962	−	26.0776i	0.796327	−	0.998563i
$683$	−16.2371	−	7.81935i	−0.621294	−	0.299199i	0.0966308	−	0.995320i	$-0.469193\pi$
$683$	−16.2371	−	7.81935i	−0.621294	−	0.299199i	−0.717924	+	0.696121i	$0.754908\pi$
$684$	−7.15883			−0.273725
$685$	4.25744	+	2.05027i	0.162668	+	0.0783369i
$686$	−3.88620	+	17.0265i	−0.148376	+	0.650077i
$687$	−6.42543	+	3.09432i	−0.245145	+	0.118056i
$688$	25.5465	−	12.3026i	0.973952	−	0.469031i
$689$	5.02781	+	22.0283i	0.191544	+	0.839211i
$690$	0.738250	−	0.925737i	0.0281047	−	0.0352422i
$691$	7.69769	+	9.65260i	0.292834	+	0.367202i	0.906385	−	0.422453i	$-0.138831\pi$
$691$	7.69769	+	9.65260i	0.292834	+	0.367202i	−0.613551	+	0.789655i	$0.710259\pi$
$692$	−2.91723	+	12.7812i	−0.110896	+	0.485869i
$693$	−7.35086	−	32.2062i	−0.279236	−	1.22341i
$694$	22.3056	+	27.9703i	0.846708	+	1.06174i
$695$	−0.998081			−0.0378594
$696$	0.174136	+	3.24730i	0.00660061	+	0.123089i
$697$	0.439665			0.0166535
$698$	30.2446	+	37.9255i	1.14477	+	1.43550i
$699$	−0.193750	−	0.848876i	−0.00732831	−	0.0321074i
$700$	−5.47434	+	23.9847i	−0.206911	+	0.906535i
$701$	−21.2594	−	26.6584i	−0.802955	−	1.00687i	−0.999651	−	0.0264091i	$-0.991593\pi$
$701$	−21.2594	−	26.6584i	−0.802955	−	1.00687i	0.196696	−	0.980464i	$-0.436979\pi$
$702$	15.0444	−	18.8650i	0.567813	−	0.712015i
$703$	1.32759	+	5.81656i	0.0500711	+	0.219376i
$704$	3.32855	−	1.60295i	0.125450	−	0.0604133i
$705$	1.11649	−	0.537673i	0.0420494	−	0.0202499i
$706$	−1.60992	+	7.05350i	−0.0605900	+	0.265462i
$707$	−63.6299	−	30.6425i	−2.39305	−	1.15243i
$708$	−5.05562			−0.190002
$709$	−37.9267	−	18.2645i	−1.42437	−	0.685939i	−0.446426	−	0.894821i	$-0.647303\pi$
$709$	−37.9267	−	18.2645i	−1.42437	−	0.685939i	−0.977941	+	0.208882i	$0.933018\pi$
$710$	4.57338	−	5.73483i	0.171636	−	0.215224i
$711$	1.03803	−	1.30165i	0.0389292	−	0.0488157i
$712$	−1.73998	−	0.837930i	−0.0652085	−	0.0314028i
$713$	26.2989			0.984901
$714$	−3.24698	−	1.56366i	−0.121515	−	0.0585186i
$715$	−1.19926	+	5.25430i	−0.0448497	+	0.196500i
$716$	6.44989	−	3.10610i	0.241044	−	0.116080i
$717$	3.59395	−	1.73076i	0.134219	−	0.0646362i
$718$	−0.299249	−	1.31110i	−0.0111679	−	0.0489297i
$719$	−32.5800	+	40.8540i	−1.21503	+	1.52360i	−0.431667	+	0.902033i	$0.642074\pi$
$719$	−32.5800	+	40.8540i	−1.21503	+	1.52360i	−0.783362	+	0.621566i	$0.786497\pi$
$720$	3.07942	+	3.86147i	0.114763	+	0.143908i
$721$	−2.53534	+	11.1081i	−0.0944211	+	0.413686i
$722$	−5.93512	−	26.0034i	−0.220882	−	0.967748i
$723$	5.52177	+	6.92408i	0.205357	+	0.257509i
$724$	−8.28083			−0.307755
$725$	19.6097	−	17.4354i	0.728285	−	0.647534i
$726$	2.02177			0.0750349
$727$	18.6953	+	23.4432i	0.693370	+	0.869459i	0.996509	−	0.0834876i	$-0.0266059\pi$
$727$	18.6953	+	23.4432i	0.693370	+	0.869459i	−0.303138	+	0.952947i	$0.598034\pi$
$728$	6.33997	+	27.7772i	0.234975	+	1.02949i
$729$	3.75733	−	16.4619i	0.139160	−	0.609702i
$730$	3.58815	+	4.49939i	0.132803	+	0.166530i
$731$	3.97285	−	4.98180i	0.146941	−	0.184259i
$732$	0.746980	+	3.27273i	0.0276092	+	0.120964i
$733$	−2.71595	+	1.30793i	−0.100316	+	0.0483096i	−0.483369	−	0.875417i	$-0.660587\pi$
$733$	−2.71595	+	1.30793i	−0.100316	+	0.0483096i	0.383053	+	0.923726i	$0.374873\pi$
$734$	−55.2781	+	26.6205i	−2.04035	+	0.982581i
$735$	−0.332010	+	1.45463i	−0.0122464	+	0.0536549i
$736$	23.0574	+	11.1039i	0.849907	+	0.409294i
$737$	1.09006			0.0401531
$738$	−1.80194	−	0.867767i	−0.0663302	−	0.0319430i
$739$	−12.9919	+	16.2914i	−0.477916	+	0.599288i	−0.961090	−	0.276237i	$-0.910913\pi$
$739$	−12.9919	+	16.2914i	−0.477916	+	0.599288i	0.483174	+	0.875525i	$0.339484\pi$
$740$	−0.807979	+	1.01317i	−0.0297019	+	0.0372450i
$741$	−4.26055	−	2.05177i	−0.156515	−	0.0753738i
$742$	−31.7875			−1.16695
$743$	27.7189	+	13.3487i	1.01691	+	0.489718i	0.866643	−	0.498928i	$-0.166273\pi$
$743$	27.7189	+	13.3487i	1.01691	+	0.489718i	0.150266	+	0.988646i	$0.451987\pi$
$744$	0.854207	−	3.74253i	0.0313168	−	0.137208i
$745$	−0.870896	+	0.419402i	−0.0319072	+	0.0153657i
$746$	45.4587	−	21.8917i	1.66436	−	0.801514i
$747$	−5.88135	−	25.7679i	−0.215188	−	0.942798i
$748$	2.51275	−	3.15088i	0.0918751	−	0.115208i
$749$	18.8327	+	23.6155i	0.688133	+	0.862892i
$750$	−0.628761	+	2.75478i	−0.0229591	+	0.100590i
$751$	0.994492	+	4.35715i	0.0362895	+	0.158995i	0.989826	−	0.142283i	$-0.0454442\pi$
$751$	0.994492	+	4.35715i	0.0362895	+	0.158995i	−0.953537	+	0.301277i	$0.902587\pi$
$752$	24.0254	+	30.1269i	0.876117	+	1.09862i
$753$	11.4843			0.418510
$754$	−19.3753	+	46.4439i	−0.705607	+	1.69139i
$755$	−0.869167			−0.0316322
$756$	8.12833	+	10.1926i	0.295625	+	0.370702i
$757$	1.88159	+	8.24379i	0.0683876	+	0.299626i	0.997542	−	0.0700652i	$-0.0223207\pi$
$757$	1.88159	+	8.24379i	0.0683876	+	0.299626i	−0.929155	+	0.369691i	$0.879464\pi$
$758$	9.17456	−	40.1964i	0.333235	−	1.46000i
$759$	−3.34266	−	4.19156i	−0.121331	−	0.152144i
$760$	0.618645	−	0.775757i	0.0224406	−	0.0281397i
$761$	−5.49516	−	24.0759i	−0.199199	−	0.872749i	−0.971415	−	0.237388i	$-0.923709\pi$
$761$	−5.49516	−	24.0759i	−0.199199	−	0.872749i	0.772216	−	0.635361i	$-0.219149\pi$
$762$	7.56638	−	3.64377i	0.274101	−	0.132000i
$763$	−6.02930	+	2.90356i	−0.218275	+	0.105116i
$764$	5.21983	−	22.8696i	0.188847	−	0.827392i
$765$	1.00000	+	0.481575i	0.0361551	+	0.0174114i
$766$	−21.3676			−0.772045
$767$	42.5652	+	20.4983i	1.53694	+	0.740152i
$768$	5.74698	−	7.20648i	0.207376	−	0.260042i
$769$	18.7939	−	23.5668i	0.677724	−	0.849839i	−0.317418	−	0.948286i	$-0.602816\pi$
$769$	18.7939	−	23.5668i	0.677724	−	0.849839i	0.995142	+	0.0984462i	$0.0313872\pi$
$770$	−6.83124	−	3.28975i	−0.246181	−	0.118554i
$771$	5.31873			0.191549
$772$	−12.2289	−	5.88911i	−0.440126	−	0.211954i
$773$	−1.26324	+	5.53462i	−0.0454356	+	0.199067i	−0.992552	−	0.121825i	$-0.961125\pi$
$773$	−1.26324	+	5.53462i	−0.0454356	+	0.199067i	0.947116	+	0.320892i	$0.103982\pi$
$774$	−26.1151	+	12.5763i	−0.938686	+	0.452048i
$775$	−27.9073	+	13.4394i	−1.00246	+	0.482759i
$776$	−4.75571	−	20.8361i	−0.170720	−	0.747973i
$777$	3.27144	−	4.10225i	0.117362	−	0.147168i
$778$	11.6746	+	14.6394i	0.418553	+	0.524849i
$779$	−0.180604	+	0.791277i	−0.00647081	+	0.0283504i
$780$	−0.228562	−	1.00139i	−0.00818382	−	0.0358557i
$781$	−20.7074	−	25.9662i	−0.740968	−	0.929145i
$782$	8.27413			0.295882
$783$	−0.744587	−	13.8851i	−0.0266094	−	0.496213i
$784$	−46.3957			−1.65699
$785$	3.93362	+	4.93261i	0.140397	+	0.176052i
$786$	−0.0811457	−	0.355523i	−0.00289437	−	0.0126811i
$787$	0.803134	−	3.51876i	0.0286286	−	0.125430i	−0.958594	−	0.284775i	$-0.908081\pi$
$787$	0.803134	−	3.51876i	0.0286286	−	0.125430i	0.987223	+	0.159345i	$0.0509382\pi$
$788$	−6.53116	−	8.18982i	−0.232663	−	0.291750i
$789$	−0.0923264	+	0.115774i	−0.00328691	+	0.00412165i
$790$	−0.0850306	−	0.372543i	−0.00302525	−	0.0132545i
$791$	31.5209	−	15.1797i	1.12075	−	0.539726i
$792$	9.97434	−	4.80339i	0.354423	−	0.170681i
$793$	6.98039	−	30.5831i	0.247881	−	1.08604i
$794$	13.3409	+	6.42465i	0.473452	+	0.228002i
$795$	−0.692021			−0.0245435
$796$	7.43900	+	3.58243i	0.263668	+	0.126976i
$797$	−19.1930	+	24.0672i	−0.679850	+	0.852505i	−0.995340	−	0.0964236i	$-0.969260\pi$
$797$	−19.1930	+	24.0672i	−0.679850	+	0.852505i	0.315490	+	0.948929i	$0.397831\pi$
$798$	4.14795	−	5.20136i	0.146836	−	0.184126i
$799$	7.80194	+	3.75722i	0.276013	+	0.132921i
$800$	−30.1420			−1.06568
$801$	3.59299	+	1.73029i	0.126952	+	0.0611369i
$802$	9.97650	−	43.7099i	0.352282	−	1.54345i
$803$	23.4768	−	11.3058i	0.828478	−	0.398974i
$804$	−0.187177	+	0.0901398i	−0.00660123	+	0.00317898i
$805$	−1.33028	−	5.82834i	−0.0468863	−	0.205422i
$806$	37.0378	−	46.4439i	1.30460	−	1.63592i
$807$	−0.295233	−	0.370210i	−0.0103927	−	0.0130320i
$808$	5.26659	−	23.0745i	0.185278	−	0.811757i
$809$	−1.16541	−	5.10598i	−0.0409735	−	0.179517i	0.950300	−	0.311334i	$-0.100776\pi$
$809$	−1.16541	−	5.10598i	−0.0409735	−	0.179517i	−0.991274	+	0.131817i	$0.957919\pi$
$810$	−2.90970	−	3.64865i	−0.102236	−	0.128200i
$811$	41.8646			1.47006			0.735032	−	0.678032i	$-0.237167\pi$
$811$	41.8646			1.47006			0.735032	+	0.678032i	$0.237167\pi$
$812$	−22.1347	−	15.7896i	−0.776775	−	0.554107i
$813$	−7.32736			−0.256982
$814$	9.52595	+	11.9452i	0.333884	+	0.418678i
$815$	0.394396	+	1.72796i	0.0138151	+	0.0605278i
$816$	0.542877	−	2.37850i	0.0190045	−	0.0832641i
$817$	7.33393	+	9.19646i	0.256582	+	0.321743i
$818$	−21.2289	+	26.6201i	−0.742250	+	0.930752i
$819$	−13.0918	−	57.3589i	−0.457464	−	2.00428i
$820$	−0.158834	+	0.0764902i	−0.00554671	+	0.00267115i
$821$	−13.8802	+	6.68433i	−0.484421	+	0.233285i	−0.660121	−	0.751159i	$-0.729495\pi$
$821$	−13.8802	+	6.68433i	−0.484421	+	0.233285i	0.175701	+	0.984444i	$0.443781\pi$
$822$	−2.36270	+	10.3517i	−0.0824086	+	0.361056i
$823$	32.1247	+	15.4705i	1.11980	+	0.539266i	0.899830	−	0.436241i	$-0.143690\pi$
$823$	32.1247	+	15.4705i	1.11980	+	0.539266i	0.219968	+	0.975507i	$0.429405\pi$
$824$	−3.81833			−0.133018
$825$	5.68910	+	2.73972i	0.198069	+	0.0953850i
$826$	−41.4403	+	51.9644i	−1.44189	+	1.80807i
$827$	−32.4550	+	40.6973i	−1.12857	+	1.41518i	−0.231760	+	0.972773i	$0.574448\pi$
$827$	−32.4550	+	40.6973i	−1.12857	+	1.41518i	−0.896812	+	0.442411i	$0.854123\pi$
$828$	−13.0233	−	6.27167i	−0.452590	−	0.217956i
$829$	−13.4168			−0.465986			−0.232993	−	0.972478i	$-0.574852\pi$
$829$	−13.4168			−0.465986			−0.232993	+	0.972478i	$0.574852\pi$
$830$	−5.46562	−	2.63210i	−0.189714	−	0.0913616i
$831$	−0.653030	+	2.86111i	−0.0226534	+	0.0992508i
$832$	5.92812	−	2.85483i	0.205520	−	0.0989734i
$833$	−9.39373	+	4.52378i	−0.325474	+	0.156740i
$834$	−0.499041	−	2.18644i	−0.0172804	−	0.0757102i
$835$	3.21864	−	4.03604i	0.111385	−	0.139673i
$836$	4.63856	+	5.81656i	0.160428	+	0.201170i
$837$	−3.65250	+	16.0026i	−0.126249	+	0.553132i
$838$	−4.36754	−	19.1355i	−0.150874	−	0.661024i
$839$	−19.3602	−	24.2769i	−0.668387	−	0.838131i	0.325840	−	0.945425i	$-0.394353\pi$
$839$	−19.3602	−	24.2769i	−0.668387	−	0.838131i	−0.994227	+	0.107294i	$0.965782\pi$
$840$	−0.872625			−0.0301084
$841$	9.43967	+	27.4207i	0.325506	+	0.945540i
$842$	35.9681			1.23954
$843$	−8.47285	−	10.6246i	−0.291821	−	0.365931i
$844$	2.24764	+	9.84757i	0.0773671	+	0.338967i
$845$	−1.10345	+	4.83452i	−0.0379598	+	0.166313i
$846$	−24.5601	−	30.7974i	−0.844394	−	1.05884i
$847$	6.36443	−	7.98074i	0.218684	−	0.274222i
$848$	−4.78836	−	20.9792i	−0.164433	−	0.720428i
$849$	1.42543	−	0.686450i	0.0489205	−	0.0235589i
$850$	−8.78017	+	4.22831i	−0.301157	+	0.145030i
$851$	−2.68060	+	11.7445i	−0.0918899	+	0.402596i
$852$	5.70291	+	2.74638i	0.195378	+	0.0940893i
$853$	21.3357			0.730521			0.365261	−	0.930905i	$-0.380980\pi$
$853$	21.3357			0.730521			0.365261	+	0.930905i	$0.380980\pi$
$854$	39.7618	+	19.1483i	1.36062	+	0.655241i
$855$	−1.27748	+	1.60191i	−0.0436889	+	0.0547841i
$856$	−6.31133	+	7.91416i	−0.215717	+	0.270500i
$857$	8.85839	+	4.26597i	0.302597	+	0.145723i	0.579021	−	0.815313i	$-0.303435\pi$
$857$	8.85839	+	4.26597i	0.302597	+	0.145723i	−0.276424	+	0.961036i	$0.589149\pi$
$858$	−12.1099			−0.413426
$859$	46.6555	+	22.4681i	1.59187	+	0.766602i	0.999244	−	0.0388778i	$-0.0123783\pi$
$859$	46.6555	+	22.4681i	1.59187	+	0.766602i	0.592623	+	0.805480i	$0.298093\pi$
$860$	−0.568532	+	2.49090i	−0.0193868	+	0.0849390i
$861$	0.643104	−	0.309703i	0.0219169	−	0.0105546i
$862$	−49.0136	+	23.6037i	−1.66941	+	0.803946i
$863$	3.62147	+	15.8667i	0.123276	+	0.540108i	0.998417	+	0.0562402i	$0.0179113\pi$
$863$	3.62147	+	15.8667i	0.123276	+	0.540108i	−0.875141	+	0.483868i	$0.839232\pi$
$864$	−9.95891	+	12.4881i	−0.338809	+	0.424853i
$865$	2.33944	+	2.93356i	0.0795433	+	0.0997441i
$866$	−8.09611	+	35.4714i	−0.275117	+	1.20537i
$867$	1.56153	+	6.84152i	0.0530324	+	0.232350i
$868$	20.0112	+	25.0932i	0.679224	+	0.851720i
$869$	−1.73019			−0.0586925
$870$	−1.25475	−	0.895067i	−0.0425400	−	0.0303456i
$871$	1.94139			0.0657816
$872$	−1.39828	−	1.75339i	−0.0473518	−	0.0593772i
$873$	9.82036	+	43.0258i	0.332369	+	1.45620i
$874$	−3.39881	+	14.8912i	−0.114967	+	0.503701i
$875$	8.89493	+	11.1539i	0.300703	+	0.377070i
$876$	−3.09634	+	3.88269i	−0.104616	+	0.131184i
$877$	−3.29470	−	14.4350i	−0.111254	−	0.487436i	−0.999601	−	0.0282623i	$-0.991003\pi$
$877$	−3.29470	−	14.4350i	−0.111254	−	0.487436i	0.888346	−	0.459174i	$-0.151855\pi$
$878$	−17.3143	+	8.33813i	−0.584330	+	0.281398i
$879$	−13.1838	+	6.34900i	−0.444679	+	0.214146i
$880$	1.14214	−	5.00406i	0.0385017	−	0.168687i
$881$	16.7920	+	8.08661i	0.565737	+	0.272445i	0.694813	−	0.719190i	$-0.255487\pi$
$881$	16.7920	+	8.08661i	0.565737	+	0.272445i	−0.129076	+	0.991635i	$0.541201\pi$
$882$	47.4282			1.59699
$883$	29.1857	+	14.0551i	0.982178	+	0.472992i	0.854854	−	0.518869i	$-0.173647\pi$
$883$	29.1857	+	14.0551i	0.982178	+	0.472992i	0.127325	+	0.991861i	$0.459361\pi$
$884$	4.47517	−	5.61169i	0.150516	−	0.188742i
$885$	−0.902165	+	1.13128i	−0.0303260	+	0.0380275i
$886$	−33.0383	−	15.9104i	−1.10994	−	0.534521i
$887$	−6.16288			−0.206929			−0.103465	−	0.994633i	$-0.532993\pi$
$887$	−6.16288			−0.206929			−0.103465	+	0.994633i	$0.532993\pi$
$888$	1.58426	+	0.762940i	0.0531643	+	0.0256026i
$889$	9.43512	−	41.3379i	0.316444	−	1.38643i
$890$	0.824667	−	0.397139i	0.0276429	−	0.0133121i
$891$	−19.0378	+	9.16812i	−0.637790	+	0.307144i
$892$	−6.08211	−	26.6474i	−0.203644	−	0.892222i
$893$	−9.96681	+	12.4980i	−0.333527	+	0.418229i
$894$	−1.35421	−	1.69812i	−0.0452915	−	0.0567937i
$895$	0.455927	−	1.99755i	0.0152400	−	0.0667706i
$896$	−9.08695	−	39.8125i	−0.303574	−	1.33004i
$897$	−5.95324	−	7.46513i	−0.198773	−	0.249253i
$898$	−34.9995			−1.16795
$899$	−1.83310	−	34.1838i	−0.0611373	−	1.14009i
$900$	17.0248			0.567492
$901$	−3.01507	−	3.78077i	−0.100446	−	0.125956i
$902$	0.462500	+	2.02635i	0.0153996	+	0.0674699i
$903$	2.30194	−	10.0854i	0.0766037	−	0.335623i
$904$	7.31013	+	9.16662i	0.243131	+	0.304877i
$905$	−1.47770	+	1.85297i	−0.0491203	+	0.0615949i
$906$	−0.434584	−	1.90404i	−0.0144381	−	0.0632574i
$907$	−39.6284	+	19.0840i	−1.31584	+	0.633675i	−0.954347	−	0.298700i	$-0.903447\pi$
$907$	−39.6284	+	19.0840i	−1.31584	+	0.633675i	−0.361492	+	0.932375i	$0.617733\pi$
$908$	20.5356	−	9.88944i	0.681499	−	0.328193i
$909$	−10.8753	+	47.6479i	−0.360711	+	1.58038i
$910$	−12.1664	−	5.85901i	−0.403311	−	0.194224i
$911$	−25.6233			−0.848936			−0.424468	−	0.905443i	$-0.639539\pi$
$911$	−25.6233			−0.848936			−0.424468	+	0.905443i	$0.639539\pi$
$912$	4.05765	+	1.95406i	0.134362	+	0.0647054i
$913$	−17.1256	+	21.4749i	−0.566776	+	0.710715i
$914$	13.9547	−	17.4987i	0.461581	−	0.578805i
$915$	0.865625	+	0.416863i	0.0286167	+	0.0137811i
$916$	19.9825			0.660242
$917$	−1.65883	−	0.798852i	−0.0547795	−	0.0263804i
$918$	−1.14914	+	5.03473i	−0.0379274	+	0.166171i
$919$	5.62349	−	2.70813i	0.185502	−	0.0893330i	−0.338828	−	0.940848i	$-0.610030\pi$
$919$	5.62349	−	2.70813i	0.185502	−	0.0893330i	0.524329	+	0.851516i	$0.324316\pi$
$920$	1.80505	−	0.869268i	0.0595108	−	0.0286589i
$921$	−1.45281	−	6.36518i	−0.0478718	−	0.209740i
$922$	24.6564	−	30.9182i	0.812017	−	1.01824i
$923$	−36.8796	−	46.2456i	−1.21391	−	1.52219i
$924$	1.45593	−	6.37883i	0.0478965	−	0.209848i
$925$	−3.15721	−	13.8326i	−0.103808	−	0.454814i
$926$	37.0834	+	46.5011i	1.21863	+	1.52812i
$927$	7.88471			0.258968
$928$	12.8259	−	30.7445i	0.421030	−	1.00924i
$929$	−24.5133			−0.804256			−0.402128	−	0.915583i	$-0.631729\pi$
$929$	−24.5133			−0.804256			−0.402128	+	0.915583i	$0.631729\pi$
$930$	1.13437	+	1.42246i	0.0371976	+	0.0466443i
$931$	−4.28286	−	18.7644i	−0.140365	−	0.614979i
$932$	−0.542877	+	2.37850i	−0.0177825	+	0.0779103i
$933$	5.14071	+	6.44625i	0.168299	+	0.211041i
$934$	29.3267	−	36.7745i	0.959599	−	1.20330i
$935$	−0.256668	−	1.12454i	−0.00839395	−	0.0367763i
$936$	17.7642	−	8.55479i	0.580641	−	0.279622i
$937$	3.68449	−	1.77436i	0.120367	−	0.0579657i	−0.372731	−	0.927939i	$-0.621579\pi$
$937$	3.68449	−	1.77436i	0.120367	−	0.0579657i	0.493098	+	0.869974i	$0.335864\pi$
$938$	−0.607760	+	2.66277i	−0.0198441	+	0.0869426i
$939$	−9.21917	−	4.43972i	−0.300856	−	0.144885i
$940$	−3.47219			−0.113250
$941$	−5.55280	−	2.67409i	−0.181016	−	0.0871728i	0.341181	−	0.939998i	$-0.389173\pi$
$941$	−5.55280	−	2.67409i	−0.181016	−	0.0871728i	−0.522197	+	0.852825i	$0.674887\pi$
$942$	−8.83877	+	11.0835i	−0.287983	+	0.361119i
$943$	−1.02177	+	1.28126i	−0.0332734	+	0.0417235i
$944$	−40.5381	−	19.5221i	−1.31940	−	0.635391i
$945$	3.73125			0.121378
$946$	27.1395	+	13.0697i	0.882382	+	0.424933i
$947$	11.0598	−	48.4562i	0.359395	−	1.57461i	−0.395309	−	0.918548i	$-0.629362\pi$
$947$	11.0598	−	48.4562i	0.359395	−	1.57461i	0.754704	−	0.656065i	$-0.227780\pi$
$948$	0.297093	−	0.143073i	0.00964914	−	0.00464678i
$949$	41.8119	−	20.1356i	1.35727	−	0.653628i
$950$	−4.00312	−	17.5388i	−0.129878	−	0.569034i
$951$	3.90097	−	4.89166i	0.126498	−	0.158623i
$952$	−3.80194	−	4.76748i	−0.123222	−	0.154515i
$953$	−3.93541	+	17.2422i	−0.127480	+	0.558529i	0.870335	+	0.492461i	$0.163902\pi$
$953$	−3.93541	+	17.2422i	−0.127480	+	0.558529i	−0.997815	+	0.0660678i	$0.978955\pi$
$954$	4.89493	+	21.4461i	0.158479	+	0.694343i
$955$	−4.18598	−	5.24905i	−0.135455	−	0.169855i
$956$	−11.1769			−0.361486
$957$	−5.21528	+	4.63702i	−0.168586	+	0.149893i
$958$	−59.5827			−1.92503
$959$	33.4245	+	41.9130i	1.07933	+	1.35344i
$960$	0.0448424	+	0.196468i	0.00144728	+	0.00634096i
$961$	−2.09395	+	9.17419i	−0.0675468	+	0.295942i
$962$	16.9656	+	21.2742i	0.546993	+	0.685908i
$963$	13.0327	−	16.3424i	0.419971	−	0.526628i
$964$	−5.52177	−	24.1925i	−0.177844	−	0.779187i
$965$	−3.50000	+	1.68551i	−0.112669	+	0.0542585i
$966$	12.1027	−	5.82834i	0.389397	−	0.187524i
$967$	2.86904	−	12.5701i	0.0922620	−	0.404226i	−0.907617	−	0.419800i	$-0.862100\pi$
$967$	2.86904	−	12.5701i	0.0922620	−	0.404226i	0.999879	+	0.0155736i	$0.00495744\pi$
$968$	3.08211	+	1.48426i	0.0990626	+	0.0477060i
$969$	1.01208			0.0325127
$970$	9.12618	+	4.39494i	0.293024	+	0.141113i
$971$	3.01610	−	3.78207i	0.0967912	−	0.121372i	−0.731077	−	0.682295i	$-0.760982\pi$
$971$	3.01610	−	3.78207i	0.0967912	−	0.121372i	0.827868	+	0.560923i	$0.189553\pi$
$972$	8.53348	−	10.7006i	0.273712	−	0.343223i
$973$	−10.2017	−	4.91288i	−0.327052	−	0.157500i
$974$	18.3013			0.586411
$975$	10.1322	+	4.87942i	0.324491	+	0.156266i
$976$	−6.64795	+	29.1266i	−0.212796	+	0.932319i
$977$	−14.8138	+	7.13394i	−0.473935	+	0.228235i	−0.655575	−	0.755130i	$-0.727574\pi$
$977$	−14.8138	+	7.13394i	−0.473935	+	0.228235i	0.181640	+	0.983365i	$0.441859\pi$
$978$	−3.58815	+	1.72796i	−0.114736	+	0.0552541i
$979$	−0.922207	−	4.04045i	−0.0294739	−	0.129133i
$980$	2.60656	−	3.26853i	0.0832636	−	0.104409i
$981$	2.88740	+	3.62068i	0.0921874	+	0.115599i
$982$	−7.89181	+	34.5763i	−0.251838	+	1.10337i
$983$	−5.89666	−	25.8349i	−0.188074	−	0.824007i	−0.977631	−	0.210329i	$-0.932547\pi$
$983$	−5.89666	−	25.8349i	−0.188074	−	0.824007i	0.789557	−	0.613678i	$-0.210311\pi$
$984$	0.149145	+	0.187022i	0.00475457	+	0.00596204i
$985$	−2.99808			−0.0955268
$986$	−0.576728	−	10.7549i	−0.0183668	−	0.342505i
$987$	14.0586			0.447490
$988$	8.26122	+	10.3592i	0.262824	+	0.329571i
$989$	5.28501	+	23.1551i	0.168054	+	0.736291i
$990$	−1.16756	+	5.11543i	−0.0371076	+	0.162579i
$991$	25.1930	+	31.5910i	0.800281	+	1.00352i	0.999721	+	0.0236111i	$0.00751634\pi$
$991$	25.1930	+	31.5910i	0.800281	+	1.00352i	−0.199440	+	0.979910i	$0.563912\pi$
$992$	−24.5179	+	30.7445i	−0.778444	+	0.976137i
$993$	−1.38212	−	6.05548i	−0.0438604	−	0.192165i
$994$	74.9747	−	36.1059i	2.37805	−	1.14521i
$995$	2.12910	−	1.02532i	0.0674971	−	0.0325049i
$996$	1.16487	−	5.10365i	0.0369105	−	0.161715i
$997$	21.1325	+	10.1769i	0.669273	+	0.322305i	0.737483	−	0.675366i	$-0.236014\pi$
$997$	21.1325	+	10.1769i	0.669273	+	0.322305i	−0.0682093	+	0.997671i	$0.521729\pi$
$998$	−50.1831			−1.58852
$999$	−6.77413	−	3.26225i	−0.214324	−	0.103213i

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	29.2.d.a.24.1	yes	6
3.2	odd	2		261.2.k.a.82.1		6
4.3	odd	2		464.2.u.f.401.1		6
5.2	odd	4		725.2.r.b.24.2		12
5.3	odd	4		725.2.r.b.24.1		12
5.4	even	2		725.2.l.b.401.1		6
29.2	odd	28		841.2.e.b.270.1		12
29.3	odd	28		841.2.e.b.651.2		12
29.4	even	14		841.2.d.c.645.1		6
29.5	even	14		841.2.d.a.571.1		6
29.6	even	14		841.2.d.d.574.1		6
29.7	even	7		841.2.d.e.190.1		6
29.8	odd	28		841.2.b.c.840.1		6
29.9	even	14		841.2.a.f.1.3		3
29.10	odd	28		841.2.e.c.196.1		12
29.11	odd	28		841.2.e.c.236.1		12
29.12	odd	4		841.2.e.d.63.2		12
29.13	even	14		841.2.d.c.605.1		6
29.14	odd	28		841.2.e.d.267.2		12
29.15	odd	28		841.2.e.d.267.1		12
29.16	even	7		841.2.d.b.605.1		6
29.17	odd	4		841.2.e.d.63.1		12
29.18	odd	28		841.2.e.c.236.2		12
29.19	odd	28		841.2.e.c.196.2		12
29.20	even	7		841.2.a.e.1.1		3
29.21	odd	28		841.2.b.c.840.6		6
29.22	even	14		841.2.d.a.190.1		6
29.23	even	7	inner	29.2.d.a.23.1	✓	6
29.24	even	7		841.2.d.e.571.1		6
29.25	even	7		841.2.d.b.645.1		6
29.26	odd	28		841.2.e.b.651.1		12
29.27	odd	28		841.2.e.b.270.2		12
29.28	even	2		841.2.d.d.778.1		6
87.20	odd	14		7569.2.a.r.1.3		3
87.23	odd	14		261.2.k.a.226.1		6
87.38	odd	14		7569.2.a.p.1.1		3
116.23	odd	14		464.2.u.f.81.1		6
145.23	odd	28		725.2.r.b.574.2		12
145.52	odd	28		725.2.r.b.574.1		12
145.139	even	14		725.2.l.b.226.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
29.2.d.a.23.1	✓	6	29.23	even	7	inner
29.2.d.a.24.1	yes	6	1.1	even	1	trivial
261.2.k.a.82.1		6	3.2	odd	2
261.2.k.a.226.1		6	87.23	odd	14
464.2.u.f.81.1		6	116.23	odd	14
464.2.u.f.401.1		6	4.3	odd	2
725.2.l.b.226.1		6	145.139	even	14
725.2.l.b.401.1		6	5.4	even	2
725.2.r.b.24.1		12	5.3	odd	4
725.2.r.b.24.2		12	5.2	odd	4
725.2.r.b.574.1		12	145.52	odd	28
725.2.r.b.574.2		12	145.23	odd	28
841.2.a.e.1.1		3	29.20	even	7
841.2.a.f.1.3		3	29.9	even	14
841.2.b.c.840.1		6	29.8	odd	28
841.2.b.c.840.6		6	29.21	odd	28
841.2.d.a.190.1		6	29.22	even	14
841.2.d.a.571.1		6	29.5	even	14
841.2.d.b.605.1		6	29.16	even	7
841.2.d.b.645.1		6	29.25	even	7
841.2.d.c.605.1		6	29.13	even	14
841.2.d.c.645.1		6	29.4	even	14
841.2.d.d.574.1		6	29.6	even	14
841.2.d.d.778.1		6	29.28	even	2
841.2.d.e.190.1		6	29.7	even	7
841.2.d.e.571.1		6	29.24	even	7
841.2.e.b.270.1		12	29.2	odd	28
841.2.e.b.270.2		12	29.27	odd	28
841.2.e.b.651.1		12	29.26	odd	28
841.2.e.b.651.2		12	29.3	odd	28
841.2.e.c.196.1		12	29.10	odd	28
841.2.e.c.196.2		12	29.19	odd	28
841.2.e.c.236.1		12	29.11	odd	28
841.2.e.c.236.2		12	29.18	odd	28
841.2.e.d.63.1		12	29.17	odd	4
841.2.e.d.63.2		12	29.12	odd	4
841.2.e.d.267.1		12	29.15	odd	28
841.2.e.d.267.2		12	29.14	odd	28
7569.2.a.p.1.1		3	87.38	odd	14
7569.2.a.r.1.3		3	87.20	odd	14

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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Learn more

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	29.2.d.a.24.1

Level	$29$
Weight	$2$
Character	29.24
Analytic conductor	$0.232$
Analytic rank	$0$
Dimension	$6$
Inner twists	$2$