LMFDB - Embedded newform 63.2.o.a.20.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [63,2,Mod(20,63)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(63, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([1, 3]))

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

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

chi := DirichletCharacter("63.20");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 63 = 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	63.o (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$0.503057532734$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 7x^{10} + 37x^{8} - 78x^{6} + 123x^{4} - 36x^{2} + 9 $ x^12 - 7x^10 + 37x^8 - 78x^6 + 123x^4 - 36*x^2 + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			20.4
Root			$0.474636 + 0.274031i$ of defining polynomial
Character	$\chi$	$=$	63.20
Dual form			63.2.o.a.41.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.555632 - 0.320794i) q^{2} +(1.58016 + 0.709292i) q^{3} +(-0.794182 - 1.37556i) q^{4} +(1.10552 + 1.91482i) q^{5} +(-0.650451 - 0.901012i) q^{6} +(-0.906161 - 2.48573i) q^{7} +2.30225i q^{8} +(1.99381 + 2.24159i) q^{9} +O(q^{10})$	\(q+(-0.555632 - 0.320794i) q^{2} +(1.58016 + 0.709292i) q^{3} +(-0.794182 - 1.37556i) q^{4} +(1.10552 + 1.91482i) q^{5} +(-0.650451 - 0.901012i) q^{6} +(-0.906161 - 2.48573i) q^{7} +2.30225i q^{8} +(1.99381 + 2.24159i) q^{9} -1.41858i q^{10} +(-2.93818 - 1.69636i) q^{11} +(-0.279258 - 2.73692i) q^{12} +(-1.56060 + 0.901012i) q^{13} +(-0.293917 + 1.67184i) q^{14} +(0.388736 + 3.80987i) q^{15} +(-0.849814 + 1.47192i) q^{16} -5.96901 q^{17} +(-0.388736 - 1.88510i) q^{18} +1.64419i q^{19} +(1.75597 - 3.04144i) q^{20} +(0.331232 - 4.57059i) q^{21} +(1.08836 + 1.88510i) q^{22} +(2.05563 - 1.18682i) q^{23} +(-1.63297 + 3.63793i) q^{24} +(0.0556321 - 0.0963576i) q^{25} +1.15616 q^{26} +(1.56060 + 4.95626i) q^{27} +(-2.69963 + 3.22061i) q^{28} +(2.44437 + 1.41126i) q^{29} +(1.00619 - 2.24159i) q^{30} +(9.28558 - 5.36103i) q^{31} +(4.93199 - 2.84748i) q^{32} +(-3.43958 - 4.76454i) q^{33} +(3.31657 + 1.91482i) q^{34} +(3.75796 - 4.48318i) q^{35} +(1.50000 - 4.52284i) q^{36} +1.69963 q^{37} +(0.527445 - 0.913562i) q^{38} +(-3.10507 + 0.316823i) q^{39} +(-4.40841 + 2.54520i) q^{40} +(-0.455074 - 0.788211i) q^{41} +(-1.65026 + 2.43331i) q^{42} +(-1.96108 + 3.39669i) q^{43} +5.38887i q^{44} +(-2.08804 + 6.29593i) q^{45} -1.52290 q^{46} +(0.123005 - 0.213051i) q^{47} +(-2.38686 + 1.72310i) q^{48} +(-5.35774 + 4.50495i) q^{49} +(-0.0618219 + 0.0356929i) q^{50} +(-9.43199 - 4.23377i) q^{51} +(2.47880 + 1.43113i) q^{52} +7.87589i q^{53} +(0.722823 - 3.25449i) q^{54} -7.50146i q^{55} +(5.72279 - 2.08621i) q^{56} +(-1.16621 + 2.59808i) q^{57} +(-0.905446 - 1.56828i) q^{58} +(-5.39093 - 9.33736i) q^{59} +(4.93199 - 3.56046i) q^{60} +(1.22853 + 0.709292i) q^{61} -6.87916 q^{62} +(3.76528 - 6.98732i) q^{63} -0.254572 q^{64} +(-3.45056 - 1.99218i) q^{65} +(0.382702 + 3.75073i) q^{66} +(3.99381 + 6.91748i) q^{67} +(4.74048 + 8.21075i) q^{68} +(4.09003 - 0.417322i) q^{69} +(-3.52622 + 1.28547i) q^{70} -12.1743i q^{71} +(-5.16071 + 4.59026i) q^{72} -0.426103i q^{73} +(-0.944368 - 0.545231i) q^{74} +(0.156253 - 0.112801i) q^{75} +(2.26168 - 1.30578i) q^{76} +(-1.55423 + 8.84070i) q^{77} +(1.82691 + 0.820053i) q^{78} +(2.49381 - 4.31941i) q^{79} -3.75796 q^{80} +(-1.04944 + 8.93861i) q^{81} +0.583940i q^{82} +(-4.28541 + 7.42254i) q^{83} +(-6.55019 + 3.17425i) q^{84} +(-6.59888 - 11.4296i) q^{85} +(2.17928 - 1.25821i) q^{86} +(2.86150 + 3.96378i) q^{87} +(3.90545 - 6.76443i) q^{88} +10.5358 q^{89} +(3.17988 - 2.82839i) q^{90} +(3.65383 + 3.06277i) q^{91} +(-3.26509 - 1.88510i) q^{92} +(18.4752 - 1.88510i) q^{93} +(-0.136691 + 0.0789188i) q^{94} +(-3.14833 + 1.81769i) q^{95} +(9.81303 - 1.00126i) q^{96} +(-6.30108 - 3.63793i) q^{97} +(4.42210 - 0.784360i) q^{98} +(-2.05563 - 9.96840i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 6 q^{2} + 2 q^{4} - 2 q^{7} - 12 q^{9}+O(q^{10}) $ 12 * q - 6 * q^2 + 2 * q^4 - 2 * q^7 - 12 * q^9	$ 12 q - 6 q^{2} + 2 q^{4} - 2 q^{7} - 12 q^{9} - 12 q^{14} + 6 q^{15} + 2 q^{16} - 6 q^{18} - 24 q^{21} - 10 q^{22} + 24 q^{23} - 8 q^{28} + 30 q^{29} + 48 q^{30} - 12 q^{32} + 18 q^{36} - 4 q^{37} + 36 q^{42} - 10 q^{43} - 40 q^{46} + 6 q^{49} - 36 q^{50} - 42 q^{51} + 42 q^{56} - 18 q^{57} + 2 q^{58} - 12 q^{60} + 24 q^{63} + 16 q^{64} - 78 q^{65} + 12 q^{67} + 18 q^{70} - 24 q^{72} - 12 q^{74} - 24 q^{77} - 12 q^{78} - 6 q^{79} + 24 q^{81} - 60 q^{84} - 6 q^{85} + 96 q^{86} + 34 q^{88} - 24 q^{91} + 30 q^{92} + 78 q^{93} + 72 q^{95} - 24 q^{99}+O(q^{100}) $ 12 * q - 6 * q^2 + 2 * q^4 - 2 * q^7 - 12 * q^9 - 12 * q^14 + 6 * q^15 + 2 * q^16 - 6 * q^18 - 24 * q^21 - 10 * q^22 + 24 * q^23 - 8 * q^28 + 30 * q^29 + 48 * q^30 - 12 * q^32 + 18 * q^36 - 4 * q^37 + 36 * q^42 - 10 * q^43 - 40 * q^46 + 6 * q^49 - 36 * q^50 - 42 * q^51 + 42 * q^56 - 18 * q^57 + 2 * q^58 - 12 * q^60 + 24 * q^63 + 16 * q^64 - 78 * q^65 + 12 * q^67 + 18 * q^70 - 24 * q^72 - 12 * q^74 - 24 * q^77 - 12 * q^78 - 6 * q^79 + 24 * q^81 - 60 * q^84 - 6 * q^85 + 96 * q^86 + 34 * q^88 - 24 * q^91 + 30 * q^92 + 78 * q^93 + 72 * q^95 - 24 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/63\mathbb{Z}\right)^\times$.

$n$	$10$	$29$
$\chi(n)$	$-1$	$e\left(\frac{1}{6}\right)$

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 $

$2$	−0.555632	−	0.320794i	−0.392891	−	0.226836i	0.290521	−	0.956869i	$-0.406171\pi$
$2$	−0.555632	−	0.320794i	−0.392891	−	0.226836i	−0.683412	+	0.730033i	$0.739505\pi$
$3$	1.58016	+	0.709292i	0.912306	+	0.409510i
$3$	1.58016	+	0.709292i	0.912306	+	0.409510i
$4$	−0.794182	−	1.37556i	−0.397091	−	0.687782i
$5$	1.10552	+	1.91482i	0.494405	+	0.856335i	0.999979	−	0.00644798i	$-0.00205247\pi$
$5$	1.10552	+	1.91482i	0.494405	+	0.856335i	−0.505574	+	0.862783i	$0.668719\pi$
$6$	−0.650451	−	0.901012i	−0.265545	−	0.367836i
$7$	−0.906161	−	2.48573i	−0.342497	−	0.939519i
$7$	−0.906161	−	2.48573i	−0.342497	−	0.939519i
$8$			2.30225i			0.813970i
$9$	1.99381	+	2.24159i	0.664603	+	0.747196i
$10$		−	1.41858i		−	0.448596i
$11$	−2.93818	−	1.69636i	−0.885894	−	0.511471i	−0.0132968	−	0.999912i	$-0.504233\pi$
$11$	−2.93818	−	1.69636i	−0.885894	−	0.511471i	−0.872597	+	0.488440i	$0.837566\pi$
$12$	−0.279258	−	2.73692i	−0.0806150	−	0.790080i
$13$	−1.56060	+	0.901012i	−0.432832	+	0.249896i	−0.700552	−	0.713601i	$-0.747063\pi$
$13$	−1.56060	+	0.901012i	−0.432832	+	0.249896i	0.267720	+	0.963497i	$0.413730\pi$
$14$	−0.293917	+	1.67184i	−0.0785527	+	0.446819i
$15$	0.388736	+	3.80987i	0.100371	+	0.983704i
$16$	−0.849814	+	1.47192i	−0.212454	+	0.367980i
$17$	−5.96901			−1.44770			−0.723849	−	0.689959i	$-0.757629\pi$
$17$	−5.96901			−1.44770			−0.723849	+	0.689959i	$0.757629\pi$
$18$	−0.388736	−	1.88510i	−0.0916259	−	0.444323i
$19$			1.64419i			0.377202i	0.982054	+	0.188601i	$0.0603953\pi$
$19$			1.64419i			0.377202i	−0.982054	+	0.188601i	$0.939605\pi$
$20$	1.75597	−	3.04144i	0.392648	−	0.680086i
$21$	0.331232	−	4.57059i	0.0722807	−	0.997384i
$22$	1.08836	+	1.88510i	0.232040	+	0.401905i
$23$	2.05563	−	1.18682i	0.428629	−	0.247469i	−0.270133	−	0.962823i	$-0.587068\pi$
$23$	2.05563	−	1.18682i	0.428629	−	0.247469i	0.698762	+	0.715354i	$0.253734\pi$
$24$	−1.63297	+	3.63793i	−0.333329	+	0.742589i
$25$	0.0556321	−	0.0963576i	0.0111264	−	0.0192715i
$26$	1.15616			0.226741
$27$	1.56060	+	4.95626i	0.300337	+	0.953833i
$28$	−2.69963	+	3.22061i	−0.510182	+	0.608638i
$29$	2.44437	+	1.41126i	0.453908	+	0.262064i	0.709479	−	0.704726i	$-0.248930\pi$
$29$	2.44437	+	1.41126i	0.453908	+	0.262064i	−0.255571	+	0.966790i	$0.582264\pi$
$30$	1.00619	−	2.24159i	0.183704	−	0.409256i
$31$	9.28558	−	5.36103i	1.66774	−	0.962870i	0.698887	−	0.715232i	$-0.253679\pi$
$31$	9.28558	−	5.36103i	1.66774	−	0.962870i	0.968853	−	0.247638i	$-0.0796544\pi$
$32$	4.93199	−	2.84748i	0.871861	−	0.503369i
$33$	−3.43958	−	4.76454i	−0.598754	−	0.829400i
$34$	3.31657	+	1.91482i	0.568788	+	0.328390i
$35$	3.75796	−	4.48318i	0.635211	−	0.757795i
$36$	1.50000	−	4.52284i	0.250000	−	0.753807i
$37$	1.69963			0.279417			0.139709	−	0.990193i	$-0.455383\pi$
$37$	1.69963			0.279417			0.139709	+	0.990193i	$0.455383\pi$
$38$	0.527445	−	0.913562i	0.0855630	−	0.148199i
$39$	−3.10507	+	0.316823i	−0.497210	+	0.0507323i
$40$	−4.40841	+	2.54520i	−0.697031	+	0.402431i
$41$	−0.455074	−	0.788211i	−0.0710706	−	0.123098i	0.828300	−	0.560285i	$-0.189308\pi$
$41$	−0.455074	−	0.788211i	−0.0710706	−	0.123098i	−0.899371	+	0.437187i	$0.855975\pi$
$42$	−1.65026	+	2.43331i	−0.254641	+	0.375468i
$43$	−1.96108	+	3.39669i	−0.299062	+	0.517990i	−0.975922	−	0.218122i	$-0.930007\pi$
$43$	−1.96108	+	3.39669i	−0.299062	+	0.517990i	0.676860	+	0.736112i	$0.263340\pi$
$44$			5.38887i			0.812402i
$45$	−2.08804	+	6.29593i	−0.311267	+	0.938541i
$46$	−1.52290			−0.224539
$47$	0.123005	−	0.213051i	0.0179422	−	0.0310767i	−0.856915	−	0.515458i	$-0.827622\pi$
$47$	0.123005	−	0.213051i	0.0179422	−	0.0310767i	0.874857	+	0.484381i	$0.160955\pi$
$48$	−2.38686	+	1.72310i	−0.344514	+	0.248709i
$49$	−5.35774	+	4.50495i	−0.765392	+	0.643564i
$50$	−0.0618219	+	0.0356929i	−0.00874294	+	0.00504774i
$51$	−9.43199	−	4.23377i	−1.32074	−	0.592846i
$52$	2.47880	+	1.43113i	0.343747	+	0.198463i
$53$			7.87589i			1.08184i	0.841075	+	0.540919i	$0.181923\pi$
$53$			7.87589i			1.08184i	−0.841075	+	0.540919i	$0.818077\pi$
$54$	0.722823	−	3.25449i	0.0983637	−	0.442880i
$55$		−	7.50146i		−	1.01150i
$56$	5.72279	−	2.08621i	0.764740	−	0.278782i
$57$	−1.16621	+	2.59808i	−0.154468	+	0.344124i
$58$	−0.905446	−	1.56828i	−0.118891	−	0.205925i
$59$	−5.39093	−	9.33736i	−0.701839	−	1.21562i	−0.967820	−	0.251643i	$-0.919029\pi$
$59$	−5.39093	−	9.33736i	−0.701839	−	1.21562i	0.265981	−	0.963978i	$-0.414304\pi$
$60$	4.93199	−	3.56046i	0.636717	−	0.459653i
$61$	1.22853	+	0.709292i	0.157297	+	0.0908155i	0.576582	−	0.817039i	$-0.304386\pi$
$61$	1.22853	+	0.709292i	0.157297	+	0.0908155i	−0.419285	+	0.907855i	$0.637719\pi$
$62$	−6.87916			−0.873654
$63$	3.76528	−	6.98732i	0.474381	−	0.880320i
$64$	−0.254572			−0.0318214
$65$	−3.45056	−	1.99218i	−0.427989	−	0.247100i
$66$	0.382702	+	3.75073i	0.0471073	+	0.461683i
$67$	3.99381	+	6.91748i	0.487922	+	0.845105i	0.999904	−	0.0138913i	$-0.00442187\pi$
$67$	3.99381	+	6.91748i	0.487922	+	0.845105i	−0.511982	+	0.858996i	$0.671089\pi$
$68$	4.74048	+	8.21075i	0.574868	+	0.995700i
$69$	4.09003	−	0.417322i	0.492382	−	0.0502396i
$70$	−3.52622	+	1.28547i	−0.421464	+	0.153642i
$71$		−	12.1743i		−	1.44482i	−0.691463	−	0.722412i	$-0.743034\pi$
$71$		−	12.1743i		−	1.44482i	0.691463	−	0.722412i	$-0.256966\pi$
$72$	−5.16071	+	4.59026i	−0.608195	+	0.540967i
$73$		−	0.426103i		−	0.0498715i	−0.999689	−	0.0249358i	$-0.992062\pi$
$73$		−	0.426103i		−	0.0498715i	0.999689	−	0.0249358i	$-0.00793812\pi$
$74$	−0.944368	−	0.545231i	−0.109781	−	0.0633818i
$75$	0.156253	−	0.112801i	0.0180426	−	0.0130251i
$76$	2.26168	−	1.30578i	0.259433	−	0.149784i
$77$	−1.55423	+	8.84070i	−0.177121	+	1.00749i
$78$	1.82691	+	0.820053i	0.206857	+	0.0928527i
$79$	2.49381	−	4.31941i	0.280576	−	0.485971i	−0.690951	−	0.722902i	$-0.742808\pi$
$79$	2.49381	−	4.31941i	0.280576	−	0.485971i	0.971527	+	0.236930i	$0.0761413\pi$
$80$	−3.75796			−0.420153
$81$	−1.04944	+	8.93861i	−0.116605	+	0.993178i
$82$			0.583940i			0.0644854i
$83$	−4.28541	+	7.42254i	−0.470384	+	0.814730i	−0.999426	−	0.0338660i	$-0.989218\pi$
$83$	−4.28541	+	7.42254i	−0.470384	+	0.814730i	0.529042	+	0.848596i	$0.322551\pi$
$84$	−6.55019	+	3.17425i	−0.714685	+	0.346339i
$85$	−6.59888	−	11.4296i	−0.715750	−	1.23971i
$86$	2.17928	−	1.25821i	0.234997	−	0.135676i
$87$	2.86150	+	3.96378i	0.306785	+	0.424962i
$88$	3.90545	−	6.76443i	0.416322	−	0.721091i
$89$	10.5358			1.11680			0.558399	−	0.829573i	$-0.311416\pi$
$89$	10.5358			1.11680			0.558399	+	0.829573i	$0.311416\pi$
$90$	3.17988	−	2.82839i	0.335189	−	0.298138i
$91$	3.65383	+	3.06277i	0.383025	+	0.321065i
$92$	−3.26509	−	1.88510i	−0.340409	−	0.196535i
$93$	18.4752	−	1.88510i	1.91579	−	0.195476i
$94$	−0.136691	+	0.0789188i	−0.0140986	+	0.00813985i
$95$	−3.14833	+	1.81769i	−0.323012	+	0.186491i
$96$	9.81303	−	1.00126i	1.00154	−	0.102191i
$97$	−6.30108	−	3.63793i	−0.639777	−	0.369376i	0.144751	−	0.989468i	$-0.453762\pi$
$97$	−6.30108	−	3.63793i	−0.639777	−	0.369376i	−0.784529	+	0.620092i	$0.787095\pi$
$98$	4.42210	−	0.784360i	0.446699	−	0.0792324i
$99$	−2.05563	−	9.96840i	−0.206599	−	1.00186i
$100$	−0.176728			−0.0176728
$101$	−2.33405	+	4.04270i	−0.232247	+	0.402264i	−0.958469	−	0.285197i	$-0.907941\pi$
$101$	−2.33405	+	4.04270i	−0.232247	+	0.402264i	0.726222	+	0.687460i	$0.241274\pi$
$102$	3.88255	+	5.37815i	0.384429	+	0.532516i
$103$	−5.40462	+	3.12036i	−0.532533	+	0.307458i	−0.742047	−	0.670348i	$-0.766145\pi$
$103$	−5.40462	+	3.12036i	−0.532533	+	0.307458i	0.209515	+	0.977806i	$0.432812\pi$
$104$	−2.07436	−	3.59289i	−0.203407	−	0.352312i
$105$	9.11806	−	4.41865i	0.889832	−	0.431216i
$106$	2.52654	−	4.37610i	0.245399	−	0.425044i
$107$			1.48939i			0.143985i	0.997405	+	0.0719925i	$0.0229358\pi$
$107$			1.48939i			0.143985i	−0.997405	+	0.0719925i	$0.977064\pi$
$108$	5.57825	−	6.08288i	0.536768	−	0.585325i
$109$	−4.38688			−0.420187			−0.210093	−	0.977681i	$-0.567377\pi$
$109$	−4.38688			−0.420187			−0.210093	+	0.977681i	$0.567377\pi$
$110$	−2.40643	+	4.16805i	−0.229444	+	0.397408i
$111$	2.68568	+	1.20553i	0.254914	+	0.114424i
$112$	4.42887	+	0.778614i	0.418489	+	0.0735721i
$113$	−14.8764	+	8.58887i	−1.39945	+	0.807973i	−0.994335	−	0.106293i	$-0.966102\pi$
$113$	−14.8764	+	8.58887i	−1.39945	+	0.807973i	−0.405115	+	0.914266i	$0.632769\pi$
$114$	1.48143	−	1.06946i	0.138749	−	0.100164i
$115$	4.54510	+	2.62412i	0.423833	+	0.244700i
$116$		−	4.48318i		−	0.416253i
$117$	−5.13123	−	1.70177i	−0.474383	−	0.157329i
$118$			6.91752i			0.636809i
$119$	5.40888	+	14.8374i	0.495831	+	1.36014i
$120$	−8.77128	+	0.894969i	−0.800705	+	0.0816991i
$121$	0.255260	+	0.442124i	0.0232055	+	0.0401931i
$122$	−0.455074	−	0.788211i	−0.0412004	−	0.0713612i
$123$	−0.160018	−	1.56828i	−0.0144283	−	0.141407i
$124$	−14.7489	−	8.51527i	−1.32449	−	0.764694i
$125$	11.3013			1.01081
$126$	−4.33360	+	2.67450i	−0.386068	+	0.238263i
$127$	6.32141			0.560935			0.280467	−	0.959864i	$-0.409511\pi$
$127$	6.32141			0.560935			0.280467	+	0.959864i	$0.409511\pi$
$128$	−9.72253	−	5.61330i	−0.859358	−	0.496151i
$129$	−5.50806	+	3.97633i	−0.484958	+	0.350096i
$130$	1.27816	+	2.21384i	0.112102	+	0.194167i
$131$	−8.51213	−	14.7434i	−0.743708	−	1.28814i	−0.950796	−	0.309818i	$-0.899732\pi$
$131$	−8.51213	−	14.7434i	−0.743708	−	1.28814i	0.207088	−	0.978322i	$-0.433601\pi$
$132$	−3.82228	+	8.51527i	−0.332687	+	0.741159i
$133$	4.08701	−	1.48990i	0.354389	−	0.129190i
$134$		−	5.12477i		−	0.442712i
$135$	−7.76509	+	8.46754i	−0.668313	+	0.728770i
$136$		−	13.7422i		−	1.17838i
$137$	5.42580	+	3.13259i	0.463557	+	0.267635i	0.713539	−	0.700616i	$-0.247091\pi$
$137$	5.42580	+	3.13259i	0.463557	+	0.267635i	−0.249982	+	0.968251i	$0.580425\pi$
$138$	−2.40643	−	1.08018i	−0.204849	−	0.0919511i
$139$	6.65488	−	3.84220i	0.564460	−	0.325891i	−0.190474	−	0.981692i	$-0.561002\pi$
$139$	6.65488	−	3.84220i	0.564460	−	0.325891i	0.754934	+	0.655801i	$0.227669\pi$
$140$	−9.15140	−	1.60885i	−0.773435	−	0.135973i
$141$	0.345483	−	0.249409i	0.0290950	−	0.0210040i
$142$	−3.90545	+	6.76443i	−0.327738	+	0.567658i
$143$	6.11375			0.511258
$144$	−4.99381	+	1.02980i	−0.416151	+	0.0858165i
$145$			6.24071i			0.518263i
$146$	−0.136691	+	0.236756i	−0.0113127	+	0.0195941i
$147$	−11.6614	+	3.31834i	−0.961817	+	0.273692i
$148$	−1.34981	−	2.33795i	−0.110954	−	0.192178i
$149$	13.3695	−	7.71887i	1.09527	−	0.632355i	0.160296	−	0.987069i	$-0.448755\pi$
$149$	13.3695	−	7.71887i	1.09527	−	0.632355i	0.934975	+	0.354714i	$0.115422\pi$
$150$	−0.123005	+	0.0125507i	−0.0100433	+	0.00102476i
$151$	−5.84362	+	10.1215i	−0.475547	+	0.823672i	−0.999608	−	0.0280089i	$-0.991083\pi$
$151$	−5.84362	+	10.1215i	−0.475547	+	0.823672i	0.524060	+	0.851681i	$0.324417\pi$
$152$	−3.78533			−0.307031
$153$	−11.9011	−	13.3801i	−0.962145	−	1.08171i
$154$	3.69963	−	4.41359i	0.298125	−	0.355657i
$155$	20.5309	+	11.8535i	1.64908	+	0.952096i
$156$	2.90180	+	4.01961i	0.232330	+	0.321827i
$157$	−4.93586	+	2.84972i	−0.393924	+	0.227432i	−0.683859	−	0.729614i	$-0.739700\pi$
$157$	−4.93586	+	2.84972i	−0.393924	+	0.227432i	0.289935	+	0.957046i	$0.406366\pi$
$158$	−2.77128	+	1.60000i	−0.220471	+	0.127289i
$159$	−5.58631	+	12.4452i	−0.443023	+	0.986966i
$160$	10.9049	+	6.29593i	0.862105	+	0.497737i
$161$	−4.81285	−	4.03430i	−0.379306	−	0.317948i
$162$	3.45056	−	4.62992i	0.271101	−	0.363761i
$163$	−10.2101			−0.799721			−0.399860	−	0.916576i	$-0.630941\pi$
$163$	−10.2101			−0.799721			−0.399860	+	0.916576i	$0.630941\pi$
$164$	−0.722823	+	1.25197i	−0.0564430	+	0.0977621i
$165$	5.32072	−	11.8535i	0.414218	−	0.922794i
$166$	4.76222	−	2.74947i	0.369620	−	0.213400i
$167$	1.80661	+	3.12914i	0.139800	+	0.242140i	0.927421	−	0.374020i	$-0.122021\pi$
$167$	1.80661	+	3.12914i	0.139800	+	0.242140i	−0.787621	+	0.616160i	$0.788688\pi$
$168$	10.5227	+	0.762579i	0.811841	+	0.0588343i
$169$	−4.87636	+	8.44610i	−0.375104	+	0.649700i
$170$			8.46754i			0.649431i
$171$	−3.68559	+	3.27819i	−0.281844	+	0.250690i
$172$	6.22981			0.475019
$173$	9.03957	−	15.6570i	0.687266	−	1.19038i	−0.285453	−	0.958393i	$-0.592144\pi$
$173$	9.03957	−	15.6570i	0.687266	−	1.19038i	0.972719	−	0.231987i	$-0.0745226\pi$
$174$	−0.318382	−	3.12036i	−0.0241365	−	0.236554i
$175$	−0.289931	−	0.0509711i	−0.0219167	−	0.00385305i
$176$	4.99381	−	2.88318i	0.376423	−	0.217328i
$177$	−1.89561	−	18.5783i	−0.142483	−	1.39643i
$178$	−5.85406	−	3.37984i	−0.438780	−	0.253330i
$179$		−	5.03194i		−	0.376105i	−0.982159	−	0.188052i	$-0.939783\pi$
$179$		−	5.03194i		−	0.376105i	0.982159	−	0.188052i	$-0.0602175\pi$
$180$	10.3187	−	2.12788i	0.769113	−	0.158602i
$181$			13.5592i			1.00785i	0.863747	+	0.503925i	$0.168111\pi$
$181$			13.5592i			1.00785i	−0.863747	+	0.503925i	$0.831889\pi$
$182$	−1.04766	−	2.87390i	−0.0776581	−	0.213028i
$183$	1.43818	+	1.99218i	0.106313	+	0.147266i
$184$	2.73236	+	4.73259i	0.201432	+	0.348891i
$185$	1.87898	+	3.25449i	0.138145	+	0.239275i
$186$	−10.8702	−	4.87933i	−0.797039	−	0.357770i
$187$	17.5380	+	10.1256i	1.28251	+	0.740455i
$188$	−0.390754			−0.0284987
$189$	10.9058	−	8.37040i	0.793280	−	0.608857i
$190$	2.33242			0.169211
$191$	−8.86948	−	5.12080i	−0.641773	−	0.370528i	0.143524	−	0.989647i	$-0.454156\pi$
$191$	−8.86948	−	5.12080i	−0.641773	−	0.370528i	−0.785297	+	0.619119i	$0.787490\pi$
$192$	−0.402264	−	0.180566i	−0.0290309	−	0.0130312i
$193$	−8.06615	−	13.9710i	−0.580614	−	1.00565i	−0.995407	−	0.0957374i	$-0.969479\pi$
$193$	−8.06615	−	13.9710i	−0.580614	−	1.00565i	0.414792	−	0.909916i	$-0.363854\pi$
$194$	2.33405	+	4.04270i	0.167575	+	0.290249i
$195$	−4.03940	−	5.59542i	−0.289267	−	0.400696i
$196$	10.4519	+	3.79217i	0.746562	+	0.270869i
$197$		−	3.86303i		−	0.275230i	−0.990486	−	0.137615i	$-0.956056\pi$
$197$		−	3.86303i		−	0.275230i	0.990486	−	0.137615i	$-0.0439436\pi$
$198$	−2.05563	+	6.19820i	−0.146087	+	0.440487i
$199$			15.2034i			1.07774i	0.842388	+	0.538871i	$0.181149\pi$
$199$			15.2034i			1.07774i	−0.842388	+	0.538871i	$0.818851\pi$
$200$	0.221840	+	0.128079i	0.0156864	+	0.00905656i
$201$	1.40434	+	13.7635i	0.0990548	+	0.970803i
$202$	2.59375	−	1.49750i	0.182496	−	0.105364i
$203$	1.29302	−	7.35487i	0.0907520	−	0.516211i
$204$	1.66690	+	16.3367i	0.116706	+	1.14380i
$205$	1.00619	−	1.74277i	0.0702753	−	0.121720i
$206$	4.00397			0.278970
$207$	6.75890	+	2.24159i	0.469776	+	0.155801i
$208$		−	3.06277i		−	0.212365i
$209$	2.78913	−	4.83091i	0.192928	−	0.334161i
$210$	−6.48376	−	0.469880i	−0.447422	−	0.0324248i
$211$	11.9523	+	20.7021i	0.822833	+	1.42519i	0.903564	+	0.428453i	$0.140941\pi$
$211$	11.9523	+	20.7021i	0.822833	+	1.42519i	−0.0807311	+	0.996736i	$0.525726\pi$
$212$	10.8338	−	6.25489i	0.744068	−	0.429588i
$213$	8.63513	−	19.2373i	0.591669	−	1.31812i
$214$	0.477789	−	0.827554i	0.0326610	−	0.0565704i
$215$	−8.67208			−0.591431
$216$	−11.4106	+	3.59289i	−0.776391	+	0.244465i
$217$	−21.7403	−	18.2235i	−1.47583	−	1.23709i
$218$	2.43749	+	1.40729i	0.165088	+	0.0953134i
$219$	0.302231	−	0.673310i	0.0204229	−	0.0454981i
$220$	−10.3187	+	5.95752i	−0.695689	+	0.401656i
$221$	9.31522	−	5.37815i	0.626610	−	0.361773i
$222$	−1.10552	−	1.53138i	−0.0741979	−	0.102780i
$223$	−16.6198	−	9.59545i	−1.11294	−	0.642559i	−0.173354	−	0.984860i	$-0.555461\pi$
$223$	−16.6198	−	9.59545i	−1.11294	−	0.642559i	−0.939591	+	0.342300i	$0.888794\pi$
$224$	−11.5473	−	9.67933i	−0.771534	−	0.646727i
$225$	0.326914	−	0.0674145i	0.0217943	−	0.00449430i
$226$	11.0210			0.733109
$227$	4.33604	−	7.51024i	0.287793	−	0.498472i	−0.685490	−	0.728082i	$-0.740412\pi$
$227$	4.33604	−	7.51024i	0.287793	−	0.498472i	0.973283	+	0.229610i	$0.0737451\pi$
$228$	4.50000	−	0.459153i	0.298020	−	0.0304081i
$229$	12.4437	−	7.18439i	0.822304	−	0.474758i	−0.0289060	−	0.999582i	$-0.509202\pi$
$229$	12.4437	−	7.18439i	0.822304	−	0.474758i	0.851211	+	0.524824i	$0.175869\pi$
$230$	−1.68360	−	2.91609i	−0.111014	−	0.192281i
$231$	−8.72657	+	12.8673i	−0.574166	+	0.846607i
$232$	−3.24907	+	5.62755i	−0.213312	+	0.369467i
$233$			29.7160i			1.94676i	0.229194	+	0.973381i	$0.426391\pi$
$233$			29.7160i			1.94676i	−0.229194	+	0.973381i	$0.573609\pi$
$234$	2.30516	+	2.59163i	0.150693	+	0.169420i
$235$	0.543941			0.0354828
$236$	−8.56276	+	14.8311i	−0.557388	+	0.965425i
$237$	7.00434	−	5.05651i	0.454981	−	0.328456i
$238$	1.75439	−	9.97926i	0.113721	−	0.646859i
$239$	−13.7101	+	7.91556i	−0.886836	+	0.512015i	−0.872906	−	0.487888i	$-0.837767\pi$
$239$	−13.7101	+	7.91556i	−0.886836	+	0.512015i	−0.0139296	+	0.999903i	$0.504434\pi$
$240$	−5.93818	−	2.66549i	−0.383308	−	0.172057i
$241$	−4.34973	−	2.51132i	−0.280190	−	0.161768i	0.353319	−	0.935503i	$-0.385053\pi$
$241$	−4.34973	−	2.51132i	−0.280190	−	0.161768i	−0.633510	+	0.773735i	$0.718386\pi$
$242$		−	0.327544i		−	0.0210553i
$243$	−7.99837	+	13.3801i	−0.513095	+	0.858332i
$244$		−	2.25323i		−	0.144248i
$245$	−14.5493	−	5.27881i	−0.929521	−	0.337251i
$246$	−0.414184	+	0.922719i	−0.0264074	+	0.0588304i
$247$	−1.48143	−	2.56591i	−0.0942612	−	0.163265i
$248$	12.3425	+	21.3778i	0.783747	+	1.35749i
$249$	−12.0364	+	8.68920i	−0.762774	+	0.550655i
$250$	−6.27934	−	3.62538i	−0.397140	−	0.229289i
$251$	−7.29728			−0.460600			−0.230300	−	0.973120i	$-0.573971\pi$
$251$	−7.29728			−0.460600			−0.230300	+	0.973120i	$0.573971\pi$
$252$	−12.6018	+	0.369822i	−0.793840	+	0.0232966i
$253$	−8.05308			−0.506293
$254$	−3.51238	−	2.02787i	−0.220386	−	0.127240i
$255$	−2.32037	−	22.7411i	−0.145307	−	1.42411i
$256$	3.85600	+	6.67879i	0.241000	+	0.417425i
$257$	−4.00397	−	6.93508i	−0.249761	−	0.432598i	0.713699	−	0.700453i	$-0.247019\pi$
$257$	−4.00397	−	6.93508i	−0.249761	−	0.432598i	−0.963459	+	0.267855i	$0.913685\pi$
$258$	4.33604	−	0.442423i	0.269950	−	0.0275441i
$259$	−1.54014	−	4.22482i	−0.0956994	−	0.262518i
$260$			6.32862i			0.392484i
$261$	1.71015	+	8.29305i	0.105856	+	0.513327i
$262$			10.9226i			0.674798i
$263$	−13.6051	−	7.85489i	−0.838925	−	0.484353i	0.0179738	−	0.999838i	$-0.494278\pi$
$263$	−13.6051	−	7.85489i	−0.838925	−	0.484353i	−0.856899	+	0.515485i	$0.827612\pi$
$264$	10.9692	−	7.91878i	0.675107	−	0.487367i
$265$	−15.0810	+	8.70699i	−0.926416	+	0.534866i
$266$	−2.74882	−	0.483255i	−0.168541	−	0.0296302i
$267$	16.6483	+	7.47299i	1.01886	+	0.457340i
$268$	6.34362	−	10.9875i	0.387499	−	0.671167i
$269$	10.4924			0.639731			0.319866	−	0.947463i	$-0.396362\pi$
$269$	10.4924			0.639731			0.319866	+	0.947463i	$0.396362\pi$
$270$	7.03087	−	2.21384i	0.427885	−	0.134730i
$271$		−	22.2537i		−	1.35181i	−0.736987	−	0.675907i	$-0.763752\pi$
$271$		−	22.2537i		−	1.35181i	0.736987	−	0.675907i	$-0.236248\pi$
$272$	5.07255	−	8.78591i	0.307568	−	0.532724i
$273$	3.60123	+	7.43130i	0.217957	+	0.449762i
$274$	−2.00983	−	3.48113i	−0.121418	−	0.210303i
$275$	−0.326914	+	0.188744i	−0.0197137	+	0.0113817i
$276$	−3.82228	−	5.29467i	−0.230074	−	0.318701i
$277$	11.4251	−	19.7889i	0.686468	−	1.18900i	−0.286505	−	0.958079i	$-0.592493\pi$
$277$	11.4251	−	19.7889i	0.686468	−	1.18900i	0.972973	−	0.230919i	$-0.0741733\pi$
$278$	−4.93022			−0.295695
$279$	30.5309	+	10.1256i	1.82784	+	0.606202i
$280$	10.3214	+	8.65178i	0.616822	+	0.517043i
$281$	0.796041	+	0.459595i	0.0474878	+	0.0274171i	0.523556	−	0.851991i	$-0.324605\pi$
$281$	0.796041	+	0.459595i	0.0474878	+	0.0274171i	−0.476068	+	0.879408i	$0.657938\pi$
$282$	−0.271971	+	0.0277502i	−0.0161956	+	0.00165250i
$283$	−19.1573	+	11.0605i	−1.13878	+	0.657477i	−0.946129	−	0.323790i	$-0.895043\pi$
$283$	−19.1573	+	11.0605i	−1.13878	+	0.657477i	−0.192654	+	0.981267i	$0.561710\pi$
$284$	−16.7465	+	9.66861i	−0.993723	+	0.573726i
$285$	−6.26413	+	0.639154i	−0.371055	+	0.0378602i
$286$	−3.39700	−	1.96126i	−0.200869	−	0.115972i
$287$	−1.54691	+	1.84544i	−0.0913113	+	0.108933i
$288$	16.2163	+	5.37815i	0.955557	+	0.316910i
$289$	18.6291			1.09583
$290$	2.00199	−	3.46754i	0.117561	−	0.203621i
$291$	−7.37636	−	10.2178i	−0.432410	−	0.598979i
$292$	−0.586131	+	0.338403i	−0.0343007	+	0.0198035i
$293$	14.6259	+	25.3328i	0.854453	+	1.47996i	0.877152	+	0.480214i	$0.159441\pi$
$293$	14.6259	+	25.3328i	0.854453	+	1.47996i	−0.0226986	+	0.999742i	$0.507226\pi$
$294$	7.54396	+	1.89714i	0.439973	+	0.110644i
$295$	11.9196	−	20.6454i	0.693986	−	1.20202i
$296$			3.91298i			0.227437i
$297$	3.82228	−	17.2097i	0.221791	−	0.998609i
$298$	−9.90468			−0.573763
$299$	−2.13868	+	3.70430i	−0.123683	+	0.214225i
$300$	−0.279258	−	0.125352i	−0.0161230	−	0.00723718i
$301$	10.2203	+	1.79677i	0.589089	+	0.103564i
$302$	6.49381	−	3.74920i	0.373677	−	0.215742i
$303$	−6.55563	+	4.73259i	−0.376611	+	0.271880i
$304$	−2.42011	−	1.39725i	−0.138803	−	0.0801379i
$305$			3.13656i			0.179599i
$306$	2.32037	+	11.2522i	0.132647	+	0.643245i
$307$		−	14.8451i		−	0.847254i	−0.905837	−	0.423627i	$-0.860757\pi$
$307$		−	14.8451i		−	0.847254i	0.905837	−	0.423627i	$-0.139243\pi$
$308$	13.3953	−	4.88318i	0.763267	−	0.278245i
$309$	−10.7534	+	1.09721i	−0.611740	+	0.0624182i
$310$	−7.60507	−	13.1724i	−0.431939	−	0.748141i
$311$	9.69002	+	16.7836i	0.549471	+	0.951711i	0.998311	+	0.0580991i	$0.0185040\pi$
$311$	9.69002	+	16.7836i	0.549471	+	0.951711i	−0.448840	+	0.893612i	$0.648163\pi$
$312$	−0.729407	−	7.14867i	−0.0412945	−	0.404714i
$313$	12.6608	+	7.30974i	0.715633	+	0.413171i	0.813143	−	0.582064i	$-0.197755\pi$
$313$	12.6608	+	7.30974i	0.715633	+	0.413171i	−0.0975102	+	0.995235i	$0.531088\pi$
$314$	3.65669			0.206359
$315$	17.5421	−	0.514803i	0.988385	−	0.0290059i
$316$	−7.92216			−0.445656
$317$	−14.7046	−	8.48973i	−0.825895	−	0.476831i	0.0265499	−	0.999647i	$-0.491548\pi$
$317$	−14.7046	−	8.48973i	−0.825895	−	0.476831i	−0.852445	+	0.522817i	$0.824881\pi$
$318$	7.09627	−	5.12288i	0.397939	−	0.287277i
$319$	−4.78799	−	8.29305i	−0.268076	−	0.464321i
$320$	−0.281435	−	0.487460i	−0.0157327	−	0.0272498i
$321$	−1.05641	+	2.35348i	−0.0589633	+	0.131358i
$322$	1.37999	+	3.78552i	0.0769040	+	0.210959i
$323$		−	9.81416i		−	0.546074i
$324$	13.1291	−	5.65531i	0.729393	−	0.314184i
$325$			0.200501i			0.0111218i
$326$	5.67309	+	3.27536i	0.314203	+	0.181405i
$327$	−6.93197	−	3.11158i	−0.383339	−	0.172071i
$328$	1.81466	−	1.04769i	0.100198	−	0.0578493i
$329$	−0.641051	−	0.112699i	−0.0353423	−	0.00621332i
$330$	−6.75890	+	4.87933i	−0.372065	+	0.268598i
$331$	−9.94801	+	17.2305i	−0.546792	+	0.947072i	0.451700	+	0.892170i	$0.350818\pi$
$331$	−9.94801	+	17.2305i	−0.546792	+	0.947072i	−0.998492	+	0.0549016i	$0.982515\pi$
$332$	13.6136			0.747142
$333$	3.38874	+	3.80987i	0.185702	+	0.208779i
$334$		−	2.31820i		−	0.126846i
$335$	−8.83051	+	15.2949i	−0.482462	+	0.835649i
$336$	6.44606	+	4.37170i	0.351661	+	0.238496i
$337$	0.490168	+	0.848996i	0.0267012	+	0.0462478i	0.879067	−	0.476698i	$-0.158166\pi$
$337$	0.490168	+	0.848996i	0.0267012	+	0.0462478i	−0.852366	+	0.522946i	$0.824833\pi$
$338$	5.41892	−	3.12861i	0.294750	−	0.170174i
$339$	−29.5990	+	3.02011i	−1.60760	+	0.164030i
$340$	−10.4814	+	18.1544i	−0.568435	+	0.984559i
$341$	−36.3769			−1.96992
$342$	3.09946	−	0.639154i	0.167599	−	0.0345615i
$343$	16.0531	+	9.23572i	0.866785	+	0.498682i
$344$	−7.82004	−	4.51490i	−0.421628	−	0.243427i
$345$	5.32072	+	7.37033i	0.286458	+	0.396805i
$346$	−10.0454	+	5.79969i	−0.540041	+	0.311793i
$347$	18.3702	−	10.6060i	0.986162	−	0.569361i	0.0820373	−	0.996629i	$-0.473857\pi$
$347$	18.3702	−	10.6060i	0.986162	−	0.569361i	0.904125	+	0.427268i	$0.140524\pi$
$348$	3.17988	−	7.08414i	0.170460	−	0.379750i
$349$	8.69945	+	5.02263i	0.465671	+	0.268855i	0.714426	−	0.699711i	$-0.246688\pi$
$349$	8.69945	+	5.02263i	0.465671	+	0.268855i	−0.248755	+	0.968566i	$0.580021\pi$
$350$	0.144744	+	0.121329i	0.00773688	+	0.00648533i
$351$	−6.90112	−	6.32862i	−0.368354	−	0.337797i
$352$	−19.3214			−1.02983
$353$	1.37327	−	2.37858i	0.0730920	−	0.126599i	−0.827163	−	0.561962i	$-0.810047\pi$
$353$	1.37327	−	2.37858i	0.0730920	−	0.126599i	0.900255	+	0.435363i	$0.143380\pi$
$354$	−4.90654	+	10.9308i	−0.260780	+	0.580965i
$355$	23.3116	−	13.4590i	1.23725	−	0.714329i
$356$	−8.36738	−	14.4927i	−0.443470	−	0.768113i
$357$	−1.97712	+	27.2819i	−0.104641	+	1.44391i
$358$	−1.61422	+	2.79591i	−0.0853140	+	0.147768i
$359$		−	10.0013i		−	0.527849i	−0.964543	−	0.263925i	$-0.914983\pi$
$359$		−	10.0013i		−	0.527849i	0.964543	−	0.263925i	$-0.0850170\pi$
$360$	−14.4948	−	4.80721i	−0.763944	−	0.253362i
$361$	16.2967			0.857719
$362$	4.34973	−	7.53395i	0.228616	−	0.395975i
$363$	0.0897572	+	0.879680i	0.00471103	+	0.0461712i
$364$	1.31123	−	7.45847i	0.0687271	−	0.390930i
$365$	0.815912	−	0.471067i	0.0427068	−	0.0246568i
$366$	−0.160018	−	1.56828i	−0.00836426	−	0.0819752i
$367$	−5.03560	−	2.90731i	−0.262856	−	0.151760i	0.362781	−	0.931875i	$-0.381827\pi$
$367$	−5.03560	−	2.90731i	−0.262856	−	0.151760i	−0.625637	+	0.780114i	$0.715161\pi$
$368$			4.03430i			0.210303i
$369$	0.859514	−	2.59163i	0.0447445	−	0.134915i
$370$		−	2.41106i		−	0.125345i
$371$	19.5774	−	7.13683i	1.01641	−	0.370526i
$372$	−17.2658	−	23.9168i	−0.895189	−	1.24003i
$373$	7.75959	+	13.4400i	0.401776	+	0.695897i	0.993940	−	0.109920i	$-0.0350596\pi$
$373$	7.75959	+	13.4400i	0.401776	+	0.695897i	−0.592164	+	0.805817i	$0.701726\pi$
$374$	−6.49645	−	11.2522i	−0.335924	−	0.581837i
$375$	17.8578	+	8.01589i	0.922172	+	0.413939i
$376$	0.490498	+	0.283189i	0.0252955	+	0.0146044i
$377$	−5.08623			−0.261954
$378$	−8.74479	+	1.15235i	−0.449783	+	0.0592703i
$379$	2.79714			0.143679			0.0718396	−	0.997416i	$-0.477113\pi$
$379$	2.79714			0.143679			0.0718396	+	0.997416i	$0.477113\pi$
$380$	5.00069	+	2.88715i	0.256530	+	0.148108i
$381$	9.98884	+	4.48373i	0.511744	+	0.229708i
$382$	3.28544	+	5.69056i	0.168098	+	0.291154i
$383$	−1.74229	−	3.01773i	−0.0890268	−	0.154199i	0.818073	−	0.575114i	$-0.195042\pi$
$383$	−1.74229	−	3.01773i	−0.0890268	−	0.154199i	−0.907100	+	0.420915i	$0.861709\pi$
$384$	−11.3817	−	15.7660i	−0.580819	−	0.804557i
$385$	−18.6466	+	6.79753i	−0.950320	+	0.346434i
$386$			10.3503i			0.526817i
$387$	−11.5240	+	2.37642i	−0.585798	+	0.120800i
$388$			11.5567i			0.586703i
$389$	−6.37017	−	3.67782i	−0.322980	−	0.186473i	0.329740	−	0.944072i	$-0.393039\pi$
$389$	−6.37017	−	3.67782i	−0.322980	−	0.186473i	−0.652720	+	0.757599i	$0.726372\pi$
$390$	0.449440	+	4.40481i	0.0227583	+	0.223046i
$391$	−12.2701	+	7.08414i	−0.620525	+	0.358260i
$392$	−10.3715	−	12.3349i	−0.523842	−	0.623006i
$393$	−2.99312	−	29.3346i	−0.150983	−	1.47973i
$394$	−1.23924	+	2.14642i	−0.0624319	+	0.108135i
$395$	11.0279			0.554872
$396$	−12.0796	+	10.7444i	−0.607024	+	0.539925i
$397$			19.2838i			0.967825i	0.875116	+	0.483912i	$0.160785\pi$
$397$			19.2838i			0.967825i	−0.875116	+	0.483912i	$0.839215\pi$
$398$	4.87717	−	8.44751i	0.244470	−	0.423435i
$399$	7.51490	+	0.544606i	0.376215	+	0.0272644i
$400$	0.0945538	+	0.163772i	0.00472769	+	0.00818860i
$401$	9.60576	−	5.54589i	0.479689	−	0.276949i	−0.240598	−	0.970625i	$-0.577344\pi$
$401$	9.60576	−	5.54589i	0.479689	−	0.276949i	0.720287	+	0.693676i	$0.244010\pi$
$402$	3.63496	−	8.09795i	0.181295	−	0.403889i
$403$	−9.66071	+	16.7328i	−0.481234	+	0.833522i
$404$	7.41465			0.368893
$405$	−18.2760	+	7.87235i	−0.908144	+	0.391180i
$406$	−3.07784	+	3.67181i	−0.152751	+	0.182229i
$407$	−4.99381	−	2.88318i	−0.247534	−	0.142914i
$408$	9.74721	−	21.7148i	0.482559	−	1.07504i
$409$	17.5597	−	10.1381i	0.868274	−	0.501298i	0.00149954	−	0.999999i	$-0.499523\pi$
$409$	17.5597	−	10.1381i	0.868274	−	0.501298i	0.866774	+	0.498701i	$0.166189\pi$
$410$	−1.11814	+	0.645560i	−0.0552211	+	0.0318819i
$411$	6.35171	+	8.79846i	0.313307	+	0.433996i
$412$	8.58450	+	4.95626i	0.422928	+	0.244178i
$413$	−18.3252	+	21.8616i	−0.901722	+	1.07574i
$414$	−3.03637	−	3.41372i	−0.149230	−	0.167775i
$415$	−18.9505			−0.930243
$416$	−5.13123	+	8.88756i	−0.251579	+	0.435748i
$417$	13.2410	−	1.35103i	0.648416	−	0.0661604i
$418$	−3.09946	+	1.78947i	−0.151599	+	0.0875260i
$419$	−5.54936	−	9.61177i	−0.271104	−	0.469566i	0.698041	−	0.716058i	$-0.254055\pi$
$419$	−5.54936	−	9.61177i	−0.271104	−	0.469566i	−0.969145	+	0.246492i	$0.920722\pi$
$420$	−13.3195	−	9.03326i	−0.649926	−	0.440778i
$421$	4.59269	−	7.95478i	0.223834	−	0.387692i	−0.732135	−	0.681160i	$-0.761476\pi$
$421$	4.59269	−	7.95478i	0.223834	−	0.387692i	0.955969	+	0.293467i	$0.0948092\pi$
$422$		−	15.3370i		−	0.746592i
$423$	0.722823	−	0.149057i	0.0351448	−	0.00724738i
$424$	−18.1323			−0.880583
$425$	−0.332068	+	0.575159i	−0.0161077	+	0.0278993i
$426$	−10.9692	+	7.91878i	−0.531459	+	0.383666i
$427$	0.649865	−	3.69653i	0.0314492	−	0.178888i
$428$	2.04875	−	1.18285i	0.0990302	−	0.0571751i
$429$	9.66071	+	4.33643i	0.466423	+	0.209365i
$430$	4.81849	+	2.78195i	0.232368	+	0.134158i
$431$			15.1102i			0.727833i	0.931432	+	0.363916i	$0.118561\pi$
$431$			15.1102i			0.727833i	−0.931432	+	0.363916i	$0.881439\pi$
$432$	−8.62145	−	1.91482i	−0.414799	−	0.0921270i
$433$		−	3.33578i		−	0.160307i	−0.996783	−	0.0801537i	$-0.974459\pi$
$433$		−	3.33578i		−	0.160307i	0.996783	−	0.0801537i	$-0.0255411\pi$
$434$	6.23362	+	17.0998i	0.299223	+	0.820814i
$435$	−4.42649	+	9.86132i	−0.212234	+	0.472814i
$436$	3.48398	+	6.03443i	0.166852	+	0.288997i
$437$	1.95135	+	3.37984i	0.0933458	+	0.161680i
$438$	−0.383923	+	0.277159i	−0.0183446	+	0.0132432i
$439$	5.91032	+	3.41233i	0.282084	+	0.162861i	0.634367	−	0.773032i	$-0.281261\pi$
$439$	5.91032	+	3.41233i	0.282084	+	0.162861i	−0.352282	+	0.935894i	$0.614594\pi$
$440$	17.2703			0.823327
$441$	−20.7806	−	3.02785i	−0.989551	−	0.144183i
$442$	−6.90112			−0.328253
$443$	9.77747	+	5.64503i	0.464542	+	0.268203i	0.713952	−	0.700195i	$-0.246903\pi$
$443$	9.77747	+	5.64503i	0.464542	+	0.268203i	−0.249410	+	0.968398i	$0.580237\pi$
$444$	−0.474636	−	4.65174i	−0.0225252	−	0.220762i
$445$	11.6476	+	20.1743i	0.552151	+	0.956354i
$446$	6.15633	+	10.6631i	0.291511	+	0.504912i
$447$	26.6008	−	2.71419i	1.25818	−	0.128377i
$448$	0.230683	+	0.632797i	0.0108987	+	0.0298968i
$449$		−	24.8554i		−	1.17300i	−0.809950	−	0.586498i	$-0.800506\pi$
$449$		−	24.8554i		−	1.17300i	0.809950	−	0.586498i	$-0.199494\pi$
$450$	−0.203270	−	0.0674145i	−0.00958224	−	0.00317795i
$451$			3.08787i			0.145402i
$452$	23.6291	+	13.6422i	1.11142	+	0.641677i
$453$	−16.4129	+	11.8487i	−0.771146	+	0.556700i
$454$	−4.81849	+	2.78195i	−0.226143	+	0.130564i
$455$	−1.82527	+	10.3824i	−0.0855700	+	0.486735i
$456$	−5.98143	−	2.68491i	−0.280106	−	0.125732i
$457$	6.30470	−	10.9201i	0.294922	−	0.510819i	−0.680045	−	0.733170i	$-0.738040\pi$
$457$	6.30470	−	10.9201i	0.294922	−	0.510819i	0.974967	+	0.222351i	$0.0713732\pi$
$458$	−9.21884			−0.430768
$459$	−9.31522	−	29.5840i	−0.434797	−	1.38086i
$460$		−	8.33610i		−	0.388673i
$461$	14.4031	−	24.9470i	0.670821	−	1.16190i	−0.306851	−	0.951758i	$-0.599275\pi$
$461$	14.4031	−	24.9470i	0.670821	−	1.16190i	0.977672	−	0.210138i	$-0.0673913\pi$
$462$	8.97653	−	4.35006i	0.417626	−	0.202383i
$463$	−12.5858	−	21.7993i	−0.584912	−	1.01310i	−0.994886	−	0.101001i	$-0.967796\pi$
$463$	−12.5858	−	21.7993i	−0.584912	−	1.01310i	0.409974	−	0.912097i	$-0.365538\pi$
$464$	−4.15452	+	2.39861i	−0.192869	+	0.111353i
$465$	24.0345	+	33.2928i	1.11457	+	1.54392i
$466$	9.53273	−	16.5112i	0.441595	−	0.764865i
$467$	25.5951			1.18440			0.592199	−	0.805792i	$-0.298260\pi$
$467$	25.5951			1.18440			0.592199	+	0.805792i	$0.298260\pi$
$468$	1.73424	+	8.40986i	0.0801651	+	0.388746i
$469$	13.5760	−	16.1959i	0.626881	−	0.747857i
$470$	−0.302231	−	0.174493i	−0.0139409	−	0.00804877i
$471$	−9.82072	+	1.00205i	−0.452515	+	0.0461719i
$472$	21.4970	−	12.4113i	0.989479	−	0.571276i
$473$	11.5240	−	6.65338i	0.529874	−	0.305923i
$474$	−5.51394	+	0.562609i	−0.253263	+	0.0258415i
$475$	0.158430	+	0.0914695i	0.00726926	+	0.00419691i
$476$	16.1141	−	19.2238i	0.738589	−	0.881123i
$477$	−17.6545	+	15.7030i	−0.808345	+	0.718993i
$478$	10.1571			0.464573
$479$	−0.267749	+	0.463755i	−0.0122338	+	0.0211895i	−0.872077	−	0.489368i	$-0.837228\pi$
$479$	−0.267749	+	0.463755i	−0.0122338	+	0.0211895i	0.859844	+	0.510557i	$0.170561\pi$
$480$	12.7658	+	17.6833i	0.582676	+	0.807129i
$481$	−2.65244	+	1.53138i	−0.120941	+	0.0698251i
$482$	1.61123	+	2.79073i	0.0733896	+	0.127114i
$483$	−4.74358	−	9.78856i	−0.215840	−	0.445395i
$484$	0.405446	−	0.702253i	0.0184294	−	0.0319206i
$485$		−	16.0873i		−	0.730485i
$486$	8.73640	−	4.86856i	0.396291	−	0.220842i
$487$	34.1323			1.54668			0.773341	−	0.633990i	$-0.218584\pi$
$487$	34.1323			1.54668			0.773341	+	0.633990i	$0.218584\pi$
$488$	−1.63297	+	2.82839i	−0.0739211	+	0.128035i
$489$	−16.1337	−	7.24198i	−0.729590	−	0.327493i
$490$	6.39065	+	7.60041i	0.288700	+	0.343352i
$491$	5.86948	−	3.38874i	0.264886	−	0.152932i	−0.361675	−	0.932304i	$-0.617795\pi$
$491$	5.86948	−	3.38874i	0.264886	−	0.152932i	0.626561	+	0.779372i	$0.284462\pi$
$492$	−2.03018	+	1.46561i	−0.0915278	+	0.0660749i
$493$	−14.5905	−	8.42380i	−0.657121	−	0.379389i
$494$			1.90094i			0.0855272i
$495$	16.8152	−	14.9565i	0.755787	−	0.672244i
$496$			18.2235i			0.818260i
$497$	−30.2621	+	11.0319i	−1.35744	+	0.494847i
$498$	9.47524	−	0.966796i	0.424596	−	0.0433232i
$499$	−4.30037	−	7.44846i	−0.192511	−	0.333439i	0.753571	−	0.657367i	$-0.228330\pi$
$499$	−4.30037	−	7.44846i	−0.192511	−	0.333439i	−0.946082	+	0.323928i	$0.894996\pi$
$500$	−8.97525	−	15.5456i	−0.401385	−	0.695220i
$501$	0.635258	+	6.22595i	0.0283812	+	0.278155i
$502$	4.05460	+	2.34093i	0.180966	+	0.104481i
$503$	−2.96518			−0.132211			−0.0661055	−	0.997813i	$-0.521057\pi$
$503$	−2.96518			−0.132211			−0.0661055	+	0.997813i	$0.521057\pi$
$504$	16.0866	+	8.66863i	0.716554	+	0.386132i
$505$	−10.3214			−0.459297
$506$	4.47455	+	2.58338i	0.198918	+	0.114845i
$507$	−13.6962	+	9.88742i	−0.608268	+	0.439116i
$508$	−5.02035	−	8.69551i	−0.222742	−	0.385801i
$509$	−3.04882	−	5.28072i	−0.135137	−	0.234064i	0.790513	−	0.612445i	$-0.209814\pi$
$509$	−3.04882	−	5.28072i	−0.135137	−	0.234064i	−0.925650	+	0.378382i	$0.876481\pi$
$510$	−6.00596	+	13.3801i	−0.265948	+	0.592479i
$511$	−1.05918	+	0.386118i	−0.0468553	+	0.0170808i
$512$			17.5053i			0.773631i
$513$	−8.14902	+	2.56591i	−0.359788	+	0.113288i
$514$			5.13780i			0.226619i
$515$	−11.9499	−	6.89926i	−0.526574	−	0.304018i
$516$	9.84410	+	4.41875i	0.433362	+	0.194525i
$517$	−0.722823	+	0.417322i	−0.0317897	+	0.0183538i
$518$	−0.499550	+	2.84151i	−0.0219490	+	0.124849i
$519$	25.3893	−	18.3289i	1.11447	−	0.804548i
$520$	4.58650	−	7.94406i	0.201132	−	0.348370i
$521$	−32.6929			−1.43230			−0.716150	−	0.697946i	$-0.754097\pi$
$521$	−32.6929			−1.43230			−0.716150	+	0.697946i	$0.754097\pi$
$522$	1.71015	−	5.15649i	0.0748512	−	0.225693i
$523$			2.00252i			0.0875643i	0.999041	+	0.0437821i	$0.0139407\pi$
$523$			2.00252i			0.0875643i	−0.999041	+	0.0437821i	$0.986059\pi$
$524$	−13.5204	+	23.4179i	−0.590639	+	1.02302i
$525$	−0.421984	−	0.286188i	−0.0184169	−	0.0124903i
$526$	5.03961	+	8.72886i	0.219737	+	0.380596i
$527$	−55.4257	+	32.0001i	−2.41438	+	1.39394i
$528$	9.93603	−	1.01381i	0.432410	−	0.0441205i
$529$	−8.68292	+	15.0393i	−0.377518	+	0.653881i
$530$	11.1726			0.485307
$531$	10.1820	−	30.7012i	0.441863	−	1.33232i
$532$	−5.29528	−	4.43869i	−0.229579	−	0.192442i
$533$	1.42037	+	0.820053i	0.0615232	+	0.0355204i
$534$	−6.85305	−	9.49292i	−0.296561	−	0.410799i
$535$	−2.85192	+	1.64656i	−0.123299	+	0.0711870i
$536$	−15.9258	+	9.19476i	−0.687890	+	0.397153i
$537$	3.56911	−	7.95127i	0.154019	−	0.343122i
$538$	−5.82990	−	3.36589i	−0.251345	−	0.145114i
$539$	23.3840	−	4.14769i	1.00722	−	0.178654i
$540$	17.8145	+	3.95661i	0.766615	+	0.170265i
$541$	−11.4451			−0.492061			−0.246031	−	0.969262i	$-0.579126\pi$
$541$	−11.4451			−0.492061			−0.246031	+	0.969262i	$0.579126\pi$
$542$	−7.13885	+	12.3649i	−0.306640	+	0.531116i
$543$	−9.61745	+	21.4258i	−0.412724	+	0.919467i
$544$	−29.4391	+	16.9967i	−1.26219	+	0.728726i
$545$	−4.84980	−	8.40010i	−0.207743	−	0.359821i
$546$	0.382956	−	5.28432i	0.0163890	−	0.226148i
$547$	−3.91961	+	6.78896i	−0.167590	+	0.290275i	−0.937572	−	0.347791i	$-0.886932\pi$
$547$	−3.91961	+	6.78896i	−0.167590	+	0.290275i	0.769982	+	0.638066i	$0.220265\pi$
$548$		−	9.95137i		−	0.425102i
$549$	0.859514	+	4.16805i	0.0366832	+	0.177888i
$550$	0.242192			0.0103271
$551$	−2.32037	+	4.01899i	−0.0988510	+	0.171215i
$552$	0.960781	+	9.41628i	0.0408935	+	0.400784i
$553$	−12.9967	−	2.28487i	−0.552675	−	0.0971626i
$554$	−12.6963	+	7.33022i	−0.539415	+	0.311431i
$555$	0.660706	+	6.47536i	0.0280454	+	0.274864i
$556$	−10.5704	−	6.10281i	−0.448284	−	0.258817i
$557$		−	0.0134996i		−	0.000571997i	−1.00000		0.000285998i	$-0.999909\pi$
$557$		−	0.0134996i		−	0.000571997i	1.00000		0.000285998i	$-9.10361e-5\pi$
$558$	−13.7157	−	15.4202i	−0.580633	−	0.652791i
$559$		−	7.06782i		−	0.298937i
$560$	3.40532	+	9.34129i	0.143901	+	0.394742i
$561$	20.5309	+	28.4396i	0.866814	+	1.20072i
$562$	−0.294871	−	0.510731i	−0.0124384	−	0.0215439i
$563$	−9.54528	−	16.5329i	−0.402286	−	0.696779i	0.591716	−	0.806147i	$-0.298451\pi$
$563$	−9.54528	−	16.5329i	−0.402286	−	0.696779i	−0.994001	+	0.109368i	$0.965117\pi$
$564$	−0.617454	−	0.277159i	−0.0259995	−	0.0116705i
$565$	−32.8923	−	18.9904i	−1.38379	−	0.798932i
$566$	14.1925			0.596557
$567$	23.1700	−	5.49118i	0.973047	−	0.230608i
$568$	28.0283			1.17604
$569$	32.3406	+	18.6719i	1.35579	+	0.782765i	0.989053	−	0.147561i	$-0.0471422\pi$
$569$	32.3406	+	18.6719i	1.35579	+	0.782765i	0.366735	+	0.930325i	$0.380475\pi$
$570$	3.68559	+	1.65436i	0.154372	+	0.0692936i
$571$	−22.6421	−	39.2173i	−0.947544	−	1.64119i	−0.750576	−	0.660784i	$-0.770224\pi$
$571$	−22.6421	−	39.2173i	−0.947544	−	1.64119i	−0.196968	−	0.980410i	$-0.563110\pi$
$572$	−4.85543	−	8.40986i	−0.203016	−	0.351634i
$573$	−10.3831	−	14.3827i	−0.433758	−	0.600847i
$574$	1.45152	−	0.529144i	0.0605853	−	0.0220860i
$575$		−	0.264101i		−	0.0110138i
$576$	−0.507567	−	0.570645i	−0.0211486	−	0.0237769i
$577$		−	37.0988i		−	1.54444i	−0.635354	−	0.772221i	$-0.719146\pi$
$577$		−	37.0988i		−	1.54444i	0.635354	−	0.772221i	$-0.280854\pi$
$578$	−10.3509	−	5.97610i	−0.430541	−	0.248573i
$579$	−2.83630	−	27.7976i	−0.117873	−	1.15523i
$580$	8.58450	−	4.95626i	0.356452	−	0.205798i
$581$	22.3337	+	3.92636i	0.926559	+	0.162893i
$582$	0.820724	+	8.04364i	0.0340201	+	0.333419i
$583$	13.3603	−	23.1408i	0.553329	−	0.958393i
$584$	0.980996			0.0405939
$585$	−2.41411	−	11.7068i	−0.0998111	−	0.484015i
$586$		−	18.7676i		−	0.775282i
$587$	−17.0612	+	29.5509i	−0.704191	+	1.21969i	0.262792	+	0.964853i	$0.415357\pi$
$587$	−17.0612	+	29.5509i	−0.704191	+	1.21969i	−0.966983	+	0.254842i	$0.917977\pi$
$588$	13.8259	+	13.4057i	0.570169	+	0.552840i
$589$	8.81453	+	15.2672i	0.363197	+	0.629075i
$590$	−13.2458	+	7.64749i	−0.545322	+	0.314842i
$591$	2.74002	−	6.10421i	0.112709	−	0.251094i
$592$	−1.44437	+	2.50172i	−0.0593632	+	0.102820i
$593$	19.6999			0.808980			0.404490	−	0.914542i	$-0.367449\pi$
$593$	19.6999			0.808980			0.404490	+	0.914542i	$0.367449\pi$
$594$	−7.64456	+	8.33610i	−0.313660	+	0.342034i
$595$	−22.4313	+	26.7601i	−0.919594	+	1.09706i
$596$	−21.2356	−	12.2604i	−0.869844	−	0.502205i
$597$	−10.7837	+	24.0238i	−0.441346	+	0.983230i
$598$	2.37663	−	1.37215i	0.0971878	−	0.0561114i
$599$	−9.74033	+	5.62358i	−0.397979	+	0.229773i	−0.685612	−	0.727967i	$-0.740465\pi$
$599$	−9.74033	+	5.62358i	−0.397979	+	0.229773i	0.287632	+	0.957741i	$0.407132\pi$
$600$	0.259697	+	0.359735i	0.0106021	+	0.0146861i
$601$	29.7646	+	17.1846i	1.21412	+	0.700975i	0.963655	−	0.267150i	$-0.0860818\pi$
$601$	29.7646	+	17.1846i	1.21412	+	0.700975i	0.250469	+	0.968125i	$0.419415\pi$
$602$	−5.10234	−	4.27696i	−0.207956	−	0.174316i
$603$	−7.54325	+	22.7446i	−0.307185	+	0.926233i
$604$	18.5636			0.755342
$605$	−0.564393	+	0.977557i	−0.0229458	+	0.0397433i
$606$	5.16071	−	0.526567i	0.209639	−	0.0213903i
$607$	−33.7888	+	19.5080i	−1.37145	+	0.791804i	−0.991110	−	0.133044i	$-0.957525\pi$
$607$	−33.7888	+	19.5080i	−1.37145	+	0.791804i	−0.380335	+	0.924849i	$0.624191\pi$
$608$	4.68179	+	8.10910i	0.189872	+	0.328868i
$609$	7.25993	−	10.7047i	0.294187	−	0.433778i
$610$	1.00619	−	1.74277i	0.0407394	−	0.0705628i
$611$			0.443317i			0.0179347i
$612$	−8.95351	+	26.9969i	−0.361924	+	1.09128i
$613$	−16.1099			−0.650672			−0.325336	−	0.945598i	$-0.605477\pi$
$613$	−16.1099			−0.650672			−0.325336	+	0.945598i	$0.605477\pi$
$614$	−4.76222	+	8.24840i	−0.192187	+	0.332878i
$615$	2.82607	−	2.04018i	0.113958	−	0.0822678i
$616$	−20.3535	−	3.57824i	−0.820067	−	0.144171i
$617$	7.03569	−	4.06205i	0.283246	−	0.163532i	−0.351646	−	0.936133i	$-0.614378\pi$
$617$	7.03569	−	4.06205i	0.283246	−	0.163532i	0.634892	+	0.772601i	$0.281045\pi$
$618$	6.32691	+	2.83998i	0.254506	+	0.114241i
$619$	32.4018	+	18.7072i	1.30234	+	0.751906i	0.980805	−	0.194991i	$-0.0624678\pi$
$619$	32.4018	+	18.7072i	1.30234	+	0.751906i	0.321535	+	0.946898i	$0.395801\pi$
$620$		−	37.6554i		−	1.51228i
$621$	9.09020	+	8.33610i	0.364777	+	0.334516i
$622$		−	12.4340i		−	0.498559i
$623$	−9.54718	−	26.1893i	−0.382499	−	1.04925i
$624$	2.17240	−	4.83967i	0.0869655	−	0.193742i
$625$	12.2156	+	21.1581i	0.488626	+	0.846325i
$626$	−4.68985	−	8.12305i	−0.187444	−	0.324662i
$627$	7.83379	−	5.65531i	0.312852	−	0.225851i
$628$	7.83994	+	4.52639i	0.312848	+	0.180623i
$629$	−10.1451			−0.404511
$630$	−9.91210	−	5.34137i	−0.394908	−	0.212805i
$631$	−19.8268			−0.789294			−0.394647	−	0.918833i	$-0.629133\pi$
$631$	−19.8268			−0.789294			−0.394647	+	0.918833i	$0.629133\pi$
$632$	9.94437	+	5.74138i	0.395566	+	0.228380i
$633$	4.20281	+	41.1903i	0.167047	+	1.63717i
$634$	5.44692	+	9.43434i	0.216325	+	0.374685i
$635$	6.98848	+	12.1044i	0.277329	+	0.480348i
$636$	21.5557	−	2.19941i	0.854738	−	0.0872123i
$637$	4.30227	−	11.8578i	0.170462	−	0.469823i
$638$			6.14384i			0.243237i
$639$	27.2898	−	24.2732i	1.07957	−	0.960235i
$640$		−	24.8226i		−	0.981199i
$641$	−8.01849	−	4.62948i	−0.316711	−	0.182853i	0.333214	−	0.942851i	$-0.391867\pi$
$641$	−8.01849	−	4.62948i	−0.316711	−	0.182853i	−0.649926	+	0.759998i	$0.725200\pi$
$642$	1.34196	−	0.968776i	0.0529629	−	0.0382345i
$643$	36.3456	−	20.9841i	1.43333	−	0.827534i	0.435958	−	0.899967i	$-0.356410\pi$
$643$	36.3456	−	20.9841i	1.43333	−	0.827534i	0.997373	+	0.0724332i	$0.0230764\pi$
$644$	−1.72716	+	9.82435i	−0.0680597	+	0.387134i
$645$	−13.7033	−	6.15103i	−0.539566	−	0.242197i
$646$	−3.14833	+	5.45306i	−0.123869	+	0.214548i
$647$	6.28587			0.247123			0.123561	−	0.992337i	$-0.460568\pi$
$647$	6.28587			0.247123			0.123561	+	0.992337i	$0.460568\pi$
$648$	−20.5789	−	2.41608i	−0.808417	−	0.0949127i
$649$			36.5798i			1.43588i
$650$	0.0643195	−	0.111405i	0.00252282	−	0.00436965i
$651$	−21.4274	−	44.2163i	−0.839806	−	1.73297i
$652$	8.10872	+	14.0447i	0.317562	+	0.550033i
$653$	20.1668	−	11.6433i	0.789189	−	0.455638i	−0.0504882	−	0.998725i	$-0.516078\pi$
$653$	20.1668	−	11.6433i	0.789189	−	0.455638i	0.839677	+	0.543086i	$0.182744\pi$
$654$	2.85345	+	3.95263i	0.111579	+	0.154560i
$655$	18.8207	−	32.5985i	0.735387	−	1.27373i
$656$	1.54691			0.0603968
$657$	0.955147	−	0.849568i	0.0372638	−	0.0331448i
$658$	0.320035	+	0.268265i	0.0124763	+	0.0104581i
$659$	25.8880	+	14.9464i	1.00845	+	0.582230i	0.910738	−	0.412984i	$-0.135514\pi$
$659$	25.8880	+	14.9464i	1.00845	+	0.582230i	0.0977141	+	0.995215i	$0.468847\pi$
$660$	−20.5309	+	2.09485i	−0.799163	+	0.0815418i
$661$	17.6184	−	10.1720i	0.685278	−	0.395645i	−0.116563	−	0.993183i	$-0.537188\pi$
$661$	17.6184	−	10.1720i	0.685278	−	0.395645i	0.801841	+	0.597538i	$0.203854\pi$
$662$	11.0549	−	6.38253i	0.429660	−	0.248064i
$663$	18.5342	−	1.89112i	0.719809	−	0.0734450i
$664$	−17.0886	−	9.86609i	−0.663165	−	0.382879i
$665$	7.37118	+	6.17878i	0.285842	+	0.239603i
$666$	−0.660706	−	3.20397i	−0.0256019	−	0.124151i
$667$	6.69963			0.259411
$668$	2.86955	−	4.97021i	0.111026	−	0.192303i
$669$	−19.4560	−	26.9506i	−0.752212	−	1.04197i
$670$	9.81303	−	5.66555i	0.379110	−	0.218879i
$671$	−2.40643	−	4.16805i	−0.0928990	−	0.160906i
$672$	−11.3811	−	23.4853i	−0.439034	−	0.905964i
$673$	−8.55996	+	14.8263i	−0.329962	+	0.571511i	−0.982504	−	0.186241i	$-0.940369\pi$
$673$	−8.55996	+	14.8263i	−0.329962	+	0.571511i	0.652542	+	0.757753i	$0.273703\pi$
$674$		−	0.628973i		−	0.0242271i
$675$	0.564393	+	0.125352i	0.0217235	+	0.00482479i
$676$	15.4909			0.595802
$677$	14.2078	−	24.6085i	0.546048	−	0.945783i	−0.452492	−	0.891769i	$-0.649465\pi$
$677$	14.2078	−	24.6085i	0.546048	−	0.945783i	0.998540	−	0.0540148i	$-0.0172018\pi$
$678$	17.4150	+	7.81713i	0.668819	+	0.300215i
$679$	−3.33313	+	18.9593i	−0.127914	+	0.727593i
$680$	26.3138	−	15.1923i	1.00909	−	0.582598i
$681$	12.1786	−	8.79186i	0.466684	−	0.336905i
$682$	20.2122	+	11.6695i	0.773965	+	0.446849i
$683$			20.9274i			0.800764i	0.916348	+	0.400382i	$0.131123\pi$
$683$			20.9274i			0.800764i	−0.916348	+	0.400382i	$0.868877\pi$
$684$	7.43639	+	2.46628i	0.284338	+	0.0943005i
$685$			13.8526i			0.529281i
$686$	−5.95684	−	10.2814i	−0.227433	−	0.392546i
$687$	24.7589	−	2.52625i	0.944611	−	0.0963824i
$688$	−3.33310	−	5.77311i	−0.127073	−	0.220098i
$689$	−7.09627	−	12.2911i	−0.270346	−	0.468254i
$690$	−0.592006	−	5.80205i	−0.0225373	−	0.220880i
$691$	−20.7918	−	12.0041i	−0.790957	−	0.456659i	0.0493424	−	0.998782i	$-0.484287\pi$
$691$	−20.7918	−	12.0041i	−0.790957	−	0.456659i	−0.840299	+	0.542123i	$0.817621\pi$
$692$	−28.7163			−1.09163
$693$	−22.9161	+	14.1427i	−0.870509	+	0.537238i
$694$	−13.6094			−0.516606
$695$	14.7143	+	8.49529i	0.558144	+	0.322245i
$696$	−9.12563	+	6.58790i	−0.345906	+	0.249714i
$697$	2.71634	+	4.70484i	0.102889	+	0.178208i
$698$	−3.22246	−	5.58147i	−0.121972	−	0.211262i
$699$	−21.0773	+	46.9561i	−0.797218	+	1.77604i
$700$	0.160144	+	0.439299i	0.00605287	+	0.0166039i
$701$			42.0117i			1.58676i	0.608728	+	0.793379i	$0.291680\pi$
$701$			42.0117i			1.58676i	−0.608728	+	0.793379i	$0.708320\pi$
$702$	1.80430	+	5.73022i	0.0680988	+	0.216273i
$703$			2.79450i			0.105397i
$704$	0.747976	+	0.431844i	0.0281904	+	0.0162757i
$705$	0.859514	+	0.385813i	0.0323712	+	0.0145306i
$706$	−1.52607	+	0.881077i	−0.0574344	+	0.0331598i
$707$	12.1641	+	2.13850i	0.457478	+	0.0804266i
$708$	−24.0501	+	17.3621i	−0.903859	+	0.652506i
$709$	−18.6094	+	32.2324i	−0.698891	+	1.21051i	0.269960	+	0.962871i	$0.412989\pi$
$709$	−18.6094	+	32.2324i	−0.698891	+	1.21051i	−0.968851	+	0.247643i	$0.920344\pi$
$710$	−17.2703			−0.648141
$711$	14.6545	−	3.02198i	0.549587	−	0.113333i
$712$			24.2562i			0.909039i
$713$	12.7252	−	22.0406i	0.476561	−	0.825428i
$714$	9.85043	−	14.5244i	0.368643	−	0.543564i
$715$	6.75890	+	11.7068i	0.252769	+	0.437808i
$716$	−6.92175	+	3.99627i	−0.258678	+	0.149348i
$717$	−27.2787	+	2.78335i	−1.01874	+	0.103946i
$718$	−3.20837	+	5.55705i	−0.119735	+	0.207387i
$719$	18.2978			0.682392			0.341196	−	0.939992i	$-0.389168\pi$
$719$	18.2978			0.682392			0.341196	+	0.939992i	$0.389168\pi$
$720$	−7.49266	−	8.42380i	−0.279235	−	0.313937i
$721$	12.6538	+	10.6069i	0.471253	+	0.395021i
$722$	−9.05494	−	5.22787i	−0.336990	−	0.194561i
$723$	−5.09201	−	7.05350i	−0.189374	−	0.262323i
$724$	18.6516	−	10.7685i	0.693181	−	0.400208i
$725$	0.271971	−	0.157022i	0.0101007	−	0.00583166i
$726$	0.232324	−	0.517572i	0.00862237	−	0.0192089i
$727$	−28.3214	−	16.3514i	−1.05038	−	0.606439i	−0.127626	−	0.991822i	$-0.540736\pi$
$727$	−28.3214	−	16.3514i	−1.05038	−	0.606439i	−0.922756	+	0.385384i	$0.874069\pi$
$728$	−7.05127	+	8.41204i	−0.261338	+	0.311771i
$729$	−22.1291	+	15.4695i	−0.819595	+	0.572943i
$730$	−0.604462			−0.0223722
$731$	11.7057	−	20.2749i	0.432951	−	0.749893i
$732$	1.59820	−	3.56046i	0.0590710	−	0.131598i
$733$	0.431812	−	0.249307i	0.0159494	−	0.00920836i	−0.492004	−	0.870593i	$-0.663736\pi$
$733$	0.431812	−	0.249307i	0.0159494	−	0.00920836i	0.507953	+	0.861385i	$0.330402\pi$
$734$	1.86529	+	3.23078i	0.0688493	+	0.119250i
$735$	−19.2460	−	18.6611i	−0.709900	−	0.688324i
$736$	6.75890	−	11.7068i	0.249136	−	0.431517i
$737$		−	27.0997i		−	0.998231i
$738$	−1.30895	+	1.16427i	−0.0481833	+	0.0428572i
$739$	−47.7046			−1.75484			−0.877421	−	0.479722i	$-0.840737\pi$
$739$	−47.7046			−1.75484			−0.877421	+	0.479722i	$0.840737\pi$
$740$	2.98450	−	5.16931i	0.109713	−	0.190028i
$741$	−0.520916	−	5.10532i	−0.0191363	−	0.187549i
$742$	−13.1673	−	2.31486i	−0.483386	−	0.0849812i
$743$	9.20534	−	5.31470i	0.337711	−	0.194978i	−0.321548	−	0.946893i	$-0.604203\pi$
$743$	9.20534	−	5.31470i	0.337711	−	0.194978i	0.659259	+	0.751916i	$0.270870\pi$
$744$	4.33998	+	42.5347i	0.159111	+	1.55940i
$745$	29.5606	+	17.0668i	1.08302	+	0.625279i
$746$		−	9.95693i		−	0.364549i
$747$	−25.1826	+	5.19302i	−0.921382	+	0.190003i
$748$		−	32.1662i		−	1.17611i
$749$	3.70223	−	1.34963i	0.135277	−	0.0493144i
$750$	−7.35091	−	10.1826i	−0.268417	−	0.371815i
$751$	−9.55927	−	16.5571i	−0.348823	−	0.604179i	0.637218	−	0.770684i	$-0.280085\pi$
$751$	−9.55927	−	16.5571i	−0.348823	−	0.604179i	−0.986041	+	0.166505i	$0.946752\pi$
$752$	0.209063	+	0.362108i	0.00762375	+	0.0132047i
$753$	−11.5309	−	5.17590i	−0.420208	−	0.188620i
$754$	2.82607	+	1.63164i	0.102920	+	0.0594206i
$755$	−25.8411			−0.940453
$756$	−20.1752	−	8.35399i	−0.733765	−	0.303832i
$757$	28.5388			1.03726			0.518631	−	0.854998i	$-0.326442\pi$
$757$	28.5388			1.03726			0.518631	+	0.854998i	$0.326442\pi$
$758$	−1.55418	−	0.897305i	−0.0564503	−	0.0325916i
$759$	−12.7252	−	5.71199i	−0.461894	−	0.207332i
$760$	−4.18478	−	7.24825i	−0.151798	−	0.262922i
$761$	21.6650	+	37.5249i	0.785355	+	1.36028i	0.928787	+	0.370615i	$0.120853\pi$
$761$	21.6650	+	37.5249i	0.785355	+	1.36028i	−0.143431	+	0.989660i	$0.545814\pi$
$762$	−4.11177	−	5.69567i	−0.148954	−	0.206332i
$763$	3.97522	+	10.9046i	0.143912	+	0.394773i
$764$			16.2674i			0.588533i
$765$	12.4635	−	37.5804i	0.450621	−	1.35872i
$766$			2.23567i			0.0807779i
$767$	16.8261	+	9.71458i	0.607557	+	0.350773i
$768$	1.35589	+	13.2886i	0.0489264	+	0.479511i
$769$	5.75189	−	3.32086i	0.207419	−	0.119753i	−0.392693	−	0.919670i	$-0.628456\pi$
$769$	5.75189	−	3.32086i	0.207419	−	0.119753i	0.600111	+	0.799917i	$0.295123\pi$
$770$	12.5413	+	2.20481i	0.451956	+	0.0794558i
$771$	−1.40792	−	13.7985i	−0.0507049	−	0.496942i
$772$	−12.8120	+	22.1910i	−0.461113	+	0.798672i
$773$	−44.4831			−1.59995			−0.799973	−	0.600036i	$-0.795153\pi$
$773$	−44.4831			−1.59995			−0.799973	+	0.600036i	$0.795153\pi$
$774$	7.16544	+	2.37642i	0.257557	+	0.0854186i
$775$		−	1.19298i		−	0.0428532i
$776$	8.37543	−	14.5067i	0.300661	−	0.520759i
$777$	0.562971	−	7.76830i	0.0201965	−	0.278686i
$778$	2.35965	+	4.08703i	0.0845974	+	0.146527i
$779$	1.29596	−	0.748226i	0.0464328	−	0.0268080i
$780$	−4.48884	+	10.0002i	−0.160726	+	0.358065i
$781$	−20.6520	+	35.7703i	−0.738986	+	1.27996i
$782$	9.09020			0.325065
$783$	−3.17988	+	14.3173i	−0.113640	+	0.511660i
$784$	−2.07784	−	11.7145i	−0.0742087	−	0.418377i
$785$	−10.9134	−	6.30087i	−0.389517	−	0.224888i
$786$	−7.74729	+	17.2594i	−0.276337	+	0.615622i
$787$	−19.0399	+	10.9927i	−0.678700	+	0.391848i	−0.799365	−	0.600846i	$-0.794831\pi$
$787$	−19.0399	+	10.9927i	−0.678700	+	0.391848i	0.120665	+	0.992693i	$0.461497\pi$
$788$	−5.31385	+	3.06795i	−0.189298	+	0.109291i
$789$	−15.9268	−	22.0620i	−0.567008	−	0.785426i
$790$	−6.12744	−	3.53768i	−0.218004	−	0.125865i
$791$	34.8300	+	29.1958i	1.23841	+	1.03808i
$792$	22.9498	−	4.73259i	0.815485	−	0.168165i
$793$	−2.55632			−0.0907776
$794$	6.18612	−	10.7147i	0.219537	−	0.380250i
$795$	−30.0061	+	3.06164i	−1.06421	+	0.108585i
$796$	20.9133	−	12.0743i	0.741251	−	0.427962i
$797$	−9.71892	−	16.8337i	−0.344262	−	0.596279i	0.640958	−	0.767576i	$-0.278537\pi$
$797$	−9.71892	−	16.8337i	−0.344262	−	0.596279i	−0.985219	+	0.171297i	$0.945204\pi$
$798$	−4.00081	−	2.71334i	−0.141627	−	0.0960511i
$799$	−0.734219	+	1.27171i	−0.0259748	+	0.0449897i
$800$		−	0.633646i		−	0.0224028i
$801$	21.0065	+	23.6170i	0.742228	+	0.834467i
$802$	−7.11636			−0.251287
$803$	−0.722823	+	1.25197i	−0.0255079	+	0.0441809i
$804$	17.8173	−	12.8625i	0.628367	−	0.453625i
$805$	2.40426	−	13.6758i	0.0847390	−	0.482008i
$806$	10.7356	−	6.19820i	0.378145	−	0.218322i
$807$	16.5796	+	7.44215i	0.583630	+	0.261976i
$808$	−9.30732	−	5.37358i	−0.327430	−	0.189042i
$809$		−	21.0058i		−	0.738526i	−0.929325	−	0.369263i	$-0.879610\pi$
$809$		−	21.0058i		−	0.738526i	0.929325	−	0.369263i	$-0.120390\pi$
$810$	12.6802	+	1.48872i	0.445535	+	0.0523083i
$811$			37.3291i			1.31080i	0.755281	+	0.655401i	$0.227500\pi$
$811$			37.3291i			1.31080i	−0.755281	+	0.655401i	$0.772500\pi$
$812$	−11.1440	+	4.06248i	−0.391077	+	0.142565i
$813$	15.7844	−	35.1644i	0.553581	−	1.23327i
$814$	1.84981	+	3.20397i	0.0648359	+	0.112299i
$815$	−11.2876	−	19.5506i	−0.395386	−	0.684829i
$816$	14.2472	−	10.2852i	0.498752	−	0.360055i
$817$	−5.58478	−	3.22438i	−0.195387	−	0.112807i
$818$	−13.0090			−0.454849
$819$	0.419569	+	14.2970i	0.0146609	+	0.499576i
$820$	−3.19639			−0.111623
$821$	−10.9017	−	6.29412i	−0.380473	−	0.219666i	0.297551	−	0.954706i	$-0.403830\pi$
$821$	−10.9017	−	6.29412i	−0.380473	−	0.219666i	−0.678024	+	0.735040i	$0.737163\pi$
$822$	−0.706718	−	6.92630i	−0.0246496	−	0.241582i
$823$	22.4189	+	38.8307i	0.781474	+	1.35355i	0.931083	+	0.364808i	$0.118865\pi$
$823$	22.4189	+	38.8307i	0.781474	+	1.35355i	−0.149608	+	0.988745i	$0.547801\pi$
$824$	−7.18385	−	12.4428i	−0.250261	−	0.433465i
$825$	−0.650451	+	0.0663681i	−0.0226458	+	0.00231064i
$826$	17.1951	−	6.26839i	0.598294	−	0.218105i
$827$			25.7293i			0.894695i	0.894360	+	0.447347i	$0.147631\pi$
$827$			25.7293i			0.894695i	−0.894360	+	0.447347i	$0.852369\pi$
$828$	−2.28435	−	11.0775i	−0.0793867	−	0.384971i
$829$		−	16.9628i		−	0.589142i	−0.955630	−	0.294571i	$-0.904823\pi$
$829$		−	16.9628i		−	0.589142i	0.955630	−	0.294571i	$-0.0951767\pi$
$830$	10.5295	+	6.07921i	0.365484	+	0.211012i
$831$	32.0896	−	23.1658i	1.11318	−	0.803614i
$832$	0.397284	−	0.229372i	0.0137733	−	0.00795204i
$833$	31.9804	−	26.8901i	1.10806	−	0.931686i
$834$	−7.79054	−	3.49697i	−0.269764	−	0.121090i
$835$	−3.99450	+	6.91867i	−0.138235	+	0.239431i
$836$	−8.86030			−0.306440
$837$	41.0617	+	37.6554i	1.41930	+	1.30156i
$838$			7.12081i			0.245984i
$839$	−13.3539	+	23.1296i	−0.461027	+	0.798522i	−0.999012	−	0.0444321i	$-0.985852\pi$
$839$	−13.3539	+	23.1296i	−0.461027	+	0.798522i	0.537986	+	0.842954i	$0.319185\pi$
$840$	10.1728	+	20.9921i	0.350997	+	0.724296i
$841$	−10.5167	−	18.2155i	−0.362645	−	0.628120i
$842$	−5.10370	+	2.94662i	−0.175885	+	0.101547i
$843$	0.931886	+	1.29086i	0.0320958	+	0.0444595i
$844$	18.9847	−	32.8824i	0.653479	−	1.13186i
$845$	−21.5637			−0.741815
$846$	−0.449440	−	0.149057i	−0.0154521	−	0.00512467i
$847$	0.867695	−	1.03514i	0.0298144	−	0.0355680i
$848$	−11.5927	−	6.69305i	−0.398095	−	0.229840i
$849$	−38.1167	+	3.88920i	−1.30816	+	0.133477i
$850$	0.369016	−	0.213051i	0.0126571	−	0.00730760i
$851$	3.49381	−	2.01715i	0.119766	−	0.0691471i
$852$	−33.3200	+	3.39978i	−1.14153	+	0.116474i
$853$	37.6287	+	21.7249i	1.28838	+	0.743848i	0.978366	−	0.206883i	$-0.0663319\pi$
$853$	37.6287	+	21.7249i	1.28838	+	0.743848i	0.310017	+	0.950731i	$0.399665\pi$
$854$	−1.54691	+	1.84544i	−0.0529342	+	0.0631496i
$855$	−10.3517	−	3.43313i	−0.354020	−	0.117411i
$856$	−3.42896			−0.117199
$857$	−7.83430	+	13.5694i	−0.267615	+	0.463522i	−0.968245	−	0.250002i	$-0.919569\pi$
$857$	−7.83430	+	13.5694i	−0.267615	+	0.463522i	0.700631	+	0.713524i	$0.252902\pi$
$858$	−3.97669	−	5.50856i	−0.135762	−	0.188059i
$859$	−17.3578	+	10.0216i	−0.592242	+	0.341931i	−0.765984	−	0.642860i	$-0.777748\pi$
$859$	−17.3578	+	10.0216i	−0.592242	+	0.341931i	0.173742	+	0.984791i	$0.444414\pi$
$860$	6.88721	+	11.9290i	0.234852	+	0.406775i
$861$	−3.75332	+	1.81887i	−0.127913	+	0.0619871i
$862$	4.84727	−	8.39571i	0.165099	−	0.285959i
$863$		−	40.0219i		−	1.36236i	−0.732115	−	0.681181i	$-0.761467\pi$
$863$		−	40.0219i		−	1.36236i	0.732115	−	0.681181i	$-0.238533\pi$
$864$	21.8097	+	20.0004i	0.741982	+	0.680429i
$865$	39.9739			1.35915
$866$	−1.07010	+	1.85347i	−0.0363635	+	0.0629834i
$867$	29.4369	+	13.2134i	0.999730	+	0.448752i
$868$	−7.80184	+	44.3780i	−0.264812	+	1.50629i
$869$	−14.6545	+	8.46079i	−0.497120	+	0.287013i
$870$	5.62296	−	4.05928i	0.190636	−	0.137622i
$871$	−12.4655	−	7.19694i	−0.422376	−	0.243859i
$872$		−	10.0997i		−	0.342019i
$873$	−4.40841	−	21.3778i	−0.149202	−	0.723528i
$874$		−	2.50393i		−	0.0846967i
$875$	−10.2408	−	28.0919i	−0.346201	−	0.949680i
$876$	−1.16621	+	0.118993i	−0.0394025	+	0.00402039i
$877$	−22.6353	−	39.2054i	−0.764338	−	1.32387i	−0.940596	−	0.339529i	$-0.889732\pi$
$877$	−22.6353	−	39.2054i	−0.764338	−	1.32387i	0.176257	−	0.984344i	$-0.443601\pi$
$878$	−2.18931	−	3.79200i	−0.0738856	−	0.127974i
$879$	5.14290	+	50.4038i	0.173466	+	1.70008i
$880$	11.0416	+	6.37485i	0.372211	+	0.214896i
$881$	45.3385			1.52749			0.763746	−	0.645517i	$-0.223358\pi$
$881$	45.3385			1.52749			0.763746	+	0.645517i	$0.223358\pi$
$882$	10.5750	+	8.34866i	0.356080	+	0.281114i
$883$	12.5650			0.422845			0.211423	−	0.977395i	$-0.432190\pi$
$883$	12.5650			0.422845			0.211423	+	0.977395i	$0.432190\pi$
$884$	−14.7960	−	8.54245i	−0.497642	−	0.287314i
$885$	33.4785	−	24.1685i	1.12537	−	0.812415i
$886$	−3.62178	−	6.27311i	−0.121676	−	0.210749i
$887$	17.8620	+	30.9379i	0.599748	+	1.03879i	0.992858	+	0.119303i	$0.0380659\pi$
$887$	17.8620	+	30.9379i	0.599748	+	1.03879i	−0.393110	+	0.919492i	$0.628601\pi$
$888$	−2.77544	+	6.18313i	−0.0931377	+	0.207492i
$889$	−5.72822	−	15.7133i	−0.192118	−	0.527009i
$890$		−	14.9460i		−	0.500991i
$891$	18.2465	−	24.4830i	0.611282	−	0.820211i
$892$			30.4821i			1.02062i
$893$	0.350296	+	0.202243i	0.0117222	+	0.00676782i
$894$	−15.6510	−	7.02531i	−0.523447	−	0.234961i
$895$	9.63528	−	5.56293i	0.322072	−	0.185948i
$896$	−5.14301	+	29.2542i	−0.171816	+	0.977313i
$897$	−6.00688	+	4.33643i	−0.200564	+	0.144789i
$898$	−7.97346	+	13.8104i	−0.266078	+	0.460860i
$899$	30.2632			1.00933
$900$	−0.352362	−	0.396151i	−0.0117454	−	0.0132050i
$901$		−	47.0113i		−	1.56617i
$902$	0.990571	−	1.71572i	0.0329824	−	0.0571272i
$903$	14.8753	+	10.0884i	0.495019	+	0.335720i
$904$	−19.7738	−	34.2491i	−0.657665	−	1.13911i
$905$	−25.9635	+	14.9901i	−0.863058	+	0.498287i
$906$	12.9205	−	1.31833i	0.429256	−	0.0437987i
$907$	4.52104	−	7.83067i	0.150119	−	0.260013i	−0.781152	−	0.624341i	$-0.785368\pi$
$907$	4.52104	−	7.83067i	0.150119	−	0.260013i	0.931271	+	0.364327i	$0.118701\pi$
$908$	−13.7744			−0.457120
$909$	−13.7157	+	2.82839i	−0.454922	+	0.0938117i
$910$	4.34479	−	5.18326i	0.144029	−	0.171823i
$911$	−35.5171	−	20.5058i	−1.17673	−	0.679388i	−0.221478	−	0.975165i	$-0.571088\pi$
$911$	−35.5171	−	20.5058i	−1.17673	−	0.679388i	−0.955257	+	0.295777i	$0.904421\pi$
$912$	−2.83310	−	3.92445i	−0.0938134	−	0.129951i
$913$	25.1826	−	14.5392i	0.833421	−	0.481176i
$914$	−7.00619	+	4.04503i	−0.231744	+	0.133798i
$915$	−2.22473	+	4.95626i	−0.0735475	+	0.163849i
$916$	−19.7652	−	11.4114i	−0.653059	−	0.377044i
$917$	−28.9349	+	34.5188i	−0.955515	+	1.13991i
$918$	−4.31453	+	19.4261i	−0.142401	+	0.641156i
$919$	10.2326			0.337541			0.168771	−	0.985655i	$-0.446020\pi$
$919$	10.2326			0.337541			0.168771	+	0.985655i	$0.446020\pi$
$920$	−6.04138	+	10.4640i	−0.199178	+	0.344987i
$921$	10.5295	−	23.4576i	0.346959	−	0.772954i
$922$	−16.0057	+	9.24088i	−0.527119	+	0.304332i
$923$	10.9692	+	18.9992i	0.361055	+	0.625366i
$924$	24.6303	+	1.78496i	0.810277	+	0.0587210i
$925$	0.0945538	−	0.163772i	0.00310891	−	0.00538479i
$926$			16.1498i			0.530716i
$927$	−17.7703	−	5.89353i	−0.583654	−	0.193569i
$928$	16.0741			0.527659
$929$	−12.8330	+	22.2273i	−0.421036	+	0.729255i	−0.996041	−	0.0888945i	$-0.971667\pi$
$929$	−12.8330	+	22.2273i	−0.421036	+	0.729255i	0.575005	+	0.818150i	$0.305000\pi$
$930$	−2.67417	−	26.2087i	−0.0876896	−	0.859416i
$931$	−7.40697	−	8.80913i	−0.242754	−	0.288707i
$932$	40.8763	−	23.5999i	1.33895	−	0.773041i
$933$	3.40731	+	33.3938i	0.111550	+	1.09327i
$934$	−14.2214	−	8.21075i	−0.465340	−	0.268664i
$935$			44.7763i			1.46434i
$936$	3.91791	−	11.8134i	0.128061	−	0.386133i
$937$			15.9276i			0.520333i	0.965564	+	0.260167i	$0.0837775\pi$
$937$			15.9276i			0.520333i	−0.965564	+	0.260167i	$0.916223\pi$
$938$	−12.7388	+	4.64386i	−0.415937	+	0.151628i
$939$	14.8214	+	20.5308i	0.483679	+	0.669997i
$940$	−0.431988	−	0.748226i	−0.0140899	−	0.0244044i
$941$	19.6767	+	34.0810i	0.641442	+	1.11101i	0.985111	+	0.171919i	$0.0549967\pi$
$941$	19.6767	+	34.0810i	0.641442	+	1.11101i	−0.343669	+	0.939091i	$0.611670\pi$
$942$	5.77816	+	2.59366i	0.188263	+	0.0845061i
$943$	−1.87093	−	1.08018i	−0.0609258	−	0.0351755i
$944$	18.3252			0.596433
$945$	28.0845	+	11.6290i	0.913588	+	0.378291i
$946$	−8.53747			−0.277577
$947$	28.9086	+	16.6904i	0.939403	+	0.542365i	0.889773	−	0.456403i	$-0.150862\pi$
$947$	28.9086	+	16.6904i	0.939403	+	0.542365i	0.0496302	+	0.998768i	$0.484196\pi$
$948$	−12.5183	−	5.61912i	−0.406575	−	0.182501i
$949$	0.383923	+	0.664975i	0.0124627	+	0.0215860i
$950$	−0.0586858	−	0.101647i	−0.00190402	−	0.00329786i
$951$	−17.2140	−	23.8450i	−0.558202	−	0.773228i
$952$	−34.1594	+	12.4526i	−1.10711	+	0.403592i
$953$		−	44.4622i		−	1.44027i	−0.693832	−	0.720137i	$-0.744079\pi$
$953$		−	44.4622i		−	1.44027i	0.693832	−	0.720137i	$-0.255921\pi$
$954$	14.8469	−	3.06164i	0.480685	−	0.0991243i
$955$		−	22.6447i		−	0.732764i
$956$	21.7767	+	12.5728i	0.704309	+	0.406633i
$957$	−1.68360	−	16.5004i	−0.0544232	−	0.533383i
$958$	0.297540	−	0.171785i	0.00961307	−	0.00555011i
$959$	2.87013	−	16.3257i	0.0926813	−	0.527185i
$960$	−0.0989611	−	0.969884i	−0.00319395	−	0.0313029i
$961$	41.9814	−	72.7138i	1.35424	−	2.34561i
$962$	1.96504			0.0633554
$963$	−3.33860	+	2.96957i	−0.107585	+	0.0956929i
$964$			7.97776i			0.256947i
$965$	17.8347	−	30.8905i	0.574118	−	0.994401i
$966$	−0.504433	+	6.96055i	−0.0162299	+	0.223952i
$967$	−20.0556	−	34.7372i	−0.644943	−	1.11707i	−0.984315	−	0.176422i	$-0.943548\pi$
$967$	−20.0556	−	34.7372i	−0.644943	−	1.11707i	0.339371	−	0.940652i	$-0.389786\pi$
$968$	−1.01788	+	0.587674i	−0.0327159	+	0.0188886i
$969$	6.96110	−	15.5079i	0.223623	−	0.498187i
$970$	−5.16071	+	8.93861i	−0.165700	+	0.287001i
$971$	−46.0026			−1.47629			−0.738147	−	0.674640i	$-0.764299\pi$
$971$	−46.0026			−1.47629			−0.738147	+	0.674640i	$0.764299\pi$
$972$	24.7573	+	0.376055i	0.794090	+	0.0120620i
$973$	−15.5811	−	13.0606i	−0.499506	−	0.418704i
$974$	−18.9650	−	10.9494i	−0.607678	−	0.350843i
$975$	−0.142213	+	0.316823i	−0.00455448	+	0.0101465i
$976$	−2.08804	+	1.20553i	−0.0668366	+	0.0385882i
$977$	−46.8323	+	27.0386i	−1.49830	+	0.865042i	−0.999998	−	0.00196335i	$-0.999375\pi$
$977$	−46.8323	+	27.0386i	−1.49830	+	0.865042i	−0.498299	+	0.867005i	$0.666042\pi$
$978$	6.64120	+	9.19946i	0.212362	+	0.294166i
$979$	−30.9562	−	17.8726i	−0.989365	−	0.571210i
$980$	4.29346	+	24.2058i	0.137149	+	0.773227i
$981$	−8.74660	−	9.83357i	−0.279257	−	0.313962i
$982$	−4.34836			−0.138762
$983$	−6.97890	+	12.0878i	−0.222592	+	0.385541i	−0.955594	−	0.294685i	$-0.904785\pi$
$983$	−6.97890	+	12.0878i	−0.222592	+	0.385541i	0.733002	+	0.680226i	$0.238119\pi$
$984$	3.61058	−	0.368401i	0.115101	−	0.0117442i
$985$	7.39703	−	4.27068i	0.235689	−	0.136075i
$986$	5.40462	+	9.36107i	0.172118	+	0.298117i
$987$	−0.933027	−	0.632776i	−0.0296986	−	0.0201415i
$988$	−2.35305	+	4.07560i	−0.0748605	+	0.129662i
$989$			9.30979i			0.296034i
$990$	−14.1410	+	2.91609i	−0.449431	+	0.0926793i
$991$	−37.0297			−1.17629			−0.588144	−	0.808756i	$-0.700141\pi$
$991$	−37.0297			−1.17629			−0.588144	+	0.808756i	$0.700141\pi$
$992$	30.5309	−	52.8811i	0.969358	−	1.67898i
$993$	−27.9409	+	20.1708i	−0.886677	+	0.640102i
$994$	20.3535	+	3.57824i	0.645575	+	0.113495i
$995$	−29.1119	+	16.8077i	−0.922909	+	0.532841i
$996$	21.5116	+	9.65599i	0.681622	+	0.305962i
$997$	−43.4282	−	25.0733i	−1.37538	−	0.794079i	−0.383785	−	0.923422i	$-0.625380\pi$
$997$	−43.4282	−	25.0733i	−1.37538	−	0.794079i	−0.991600	+	0.129344i	$0.958713\pi$
$998$			5.51814i			0.174674i
$999$	2.65244	+	8.42380i	0.0839194	+	0.266517i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	63.2.o.a.20.4	yes	12
3.2	odd	2		189.2.o.a.62.3		12
4.3	odd	2		1008.2.cc.a.209.1		12
7.2	even	3		441.2.i.c.227.3		12
7.3	odd	6		441.2.s.c.362.4		12
7.4	even	3		441.2.s.c.362.3		12
7.5	odd	6		441.2.i.c.227.4		12
7.6	odd	2	inner	63.2.o.a.20.3	✓	12
9.2	odd	6		567.2.c.c.566.6		12
9.4	even	3		189.2.o.a.125.4		12
9.5	odd	6	inner	63.2.o.a.41.3	yes	12
9.7	even	3		567.2.c.c.566.7		12
12.11	even	2		3024.2.cc.a.2897.2		12
21.2	odd	6		1323.2.i.c.521.3		12
21.5	even	6		1323.2.i.c.521.4		12
21.11	odd	6		1323.2.s.c.656.4		12
21.17	even	6		1323.2.s.c.656.3		12
21.20	even	2		189.2.o.a.62.4		12
28.27	even	2		1008.2.cc.a.209.6		12
36.23	even	6		1008.2.cc.a.545.6		12
36.31	odd	6		3024.2.cc.a.881.5		12
63.4	even	3		1323.2.i.c.1097.4		12
63.5	even	6		441.2.s.c.374.3		12
63.13	odd	6		189.2.o.a.125.3		12
63.20	even	6		567.2.c.c.566.5		12
63.23	odd	6		441.2.s.c.374.4		12
63.31	odd	6		1323.2.i.c.1097.3		12
63.32	odd	6		441.2.i.c.68.4		12
63.34	odd	6		567.2.c.c.566.8		12
63.40	odd	6		1323.2.s.c.962.4		12
63.41	even	6	inner	63.2.o.a.41.4	yes	12
63.58	even	3		1323.2.s.c.962.3		12
63.59	even	6		441.2.i.c.68.3		12
84.83	odd	2		3024.2.cc.a.2897.5		12
252.139	even	6		3024.2.cc.a.881.2		12
252.167	odd	6		1008.2.cc.a.545.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.2.o.a.20.3	✓	12	7.6	odd	2	inner
63.2.o.a.20.4	yes	12	1.1	even	1	trivial
63.2.o.a.41.3	yes	12	9.5	odd	6	inner
63.2.o.a.41.4	yes	12	63.41	even	6	inner
189.2.o.a.62.3		12	3.2	odd	2
189.2.o.a.62.4		12	21.20	even	2
189.2.o.a.125.3		12	63.13	odd	6
189.2.o.a.125.4		12	9.4	even	3
441.2.i.c.68.3		12	63.59	even	6
441.2.i.c.68.4		12	63.32	odd	6
441.2.i.c.227.3		12	7.2	even	3
441.2.i.c.227.4		12	7.5	odd	6
441.2.s.c.362.3		12	7.4	even	3
441.2.s.c.362.4		12	7.3	odd	6
441.2.s.c.374.3		12	63.5	even	6
441.2.s.c.374.4		12	63.23	odd	6
567.2.c.c.566.5		12	63.20	even	6
567.2.c.c.566.6		12	9.2	odd	6
567.2.c.c.566.7		12	9.7	even	3
567.2.c.c.566.8		12	63.34	odd	6
1008.2.cc.a.209.1		12	4.3	odd	2
1008.2.cc.a.209.6		12	28.27	even	2
1008.2.cc.a.545.1		12	252.167	odd	6
1008.2.cc.a.545.6		12	36.23	even	6
1323.2.i.c.521.3		12	21.2	odd	6
1323.2.i.c.521.4		12	21.5	even	6
1323.2.i.c.1097.3		12	63.31	odd	6
1323.2.i.c.1097.4		12	63.4	even	3
1323.2.s.c.656.3		12	21.17	even	6
1323.2.s.c.656.4		12	21.11	odd	6
1323.2.s.c.962.3		12	63.58	even	3
1323.2.s.c.962.4		12	63.40	odd	6
3024.2.cc.a.881.2		12	252.139	even	6
3024.2.cc.a.881.5		12	36.31	odd	6
3024.2.cc.a.2897.2		12	12.11	even	2
3024.2.cc.a.2897.5		12	84.83	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 63 = 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	63.o (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.555632 - 0.320794i) q^{2} +(1.58016 + 0.709292i) q^{3} +(-0.794182 - 1.37556i) q^{4} +(1.10552 + 1.91482i) q^{5} +(-0.650451 - 0.901012i) q^{6} +(-0.906161 - 2.48573i) q^{7} +2.30225i q^{8} +(1.99381 + 2.24159i) q^{9} +O(q^{10})\)	\(q+(-0.555632 - 0.320794i) q^{2} +(1.58016 + 0.709292i) q^{3} +(-0.794182 - 1.37556i) q^{4} +(1.10552 + 1.91482i) q^{5} +(-0.650451 - 0.901012i) q^{6} +(-0.906161 - 2.48573i) q^{7} +2.30225i q^{8} +(1.99381 + 2.24159i) q^{9} -1.41858i q^{10} +(-2.93818 - 1.69636i) q^{11} +(-0.279258 - 2.73692i) q^{12} +(-1.56060 + 0.901012i) q^{13} +(-0.293917 + 1.67184i) q^{14} +(0.388736 + 3.80987i) q^{15} +(-0.849814 + 1.47192i) q^{16} -5.96901 q^{17} +(-0.388736 - 1.88510i) q^{18} +1.64419i q^{19} +(1.75597 - 3.04144i) q^{20} +(0.331232 - 4.57059i) q^{21} +(1.08836 + 1.88510i) q^{22} +(2.05563 - 1.18682i) q^{23} +(-1.63297 + 3.63793i) q^{24} +(0.0556321 - 0.0963576i) q^{25} +1.15616 q^{26} +(1.56060 + 4.95626i) q^{27} +(-2.69963 + 3.22061i) q^{28} +(2.44437 + 1.41126i) q^{29} +(1.00619 - 2.24159i) q^{30} +(9.28558 - 5.36103i) q^{31} +(4.93199 - 2.84748i) q^{32} +(-3.43958 - 4.76454i) q^{33} +(3.31657 + 1.91482i) q^{34} +(3.75796 - 4.48318i) q^{35} +(1.50000 - 4.52284i) q^{36} +1.69963 q^{37} +(0.527445 - 0.913562i) q^{38} +(-3.10507 + 0.316823i) q^{39} +(-4.40841 + 2.54520i) q^{40} +(-0.455074 - 0.788211i) q^{41} +(-1.65026 + 2.43331i) q^{42} +(-1.96108 + 3.39669i) q^{43} +5.38887i q^{44} +(-2.08804 + 6.29593i) q^{45} -1.52290 q^{46} +(0.123005 - 0.213051i) q^{47} +(-2.38686 + 1.72310i) q^{48} +(-5.35774 + 4.50495i) q^{49} +(-0.0618219 + 0.0356929i) q^{50} +(-9.43199 - 4.23377i) q^{51} +(2.47880 + 1.43113i) q^{52} +7.87589i q^{53} +(0.722823 - 3.25449i) q^{54} -7.50146i q^{55} +(5.72279 - 2.08621i) q^{56} +(-1.16621 + 2.59808i) q^{57} +(-0.905446 - 1.56828i) q^{58} +(-5.39093 - 9.33736i) q^{59} +(4.93199 - 3.56046i) q^{60} +(1.22853 + 0.709292i) q^{61} -6.87916 q^{62} +(3.76528 - 6.98732i) q^{63} -0.254572 q^{64} +(-3.45056 - 1.99218i) q^{65} +(0.382702 + 3.75073i) q^{66} +(3.99381 + 6.91748i) q^{67} +(4.74048 + 8.21075i) q^{68} +(4.09003 - 0.417322i) q^{69} +(-3.52622 + 1.28547i) q^{70} -12.1743i q^{71} +(-5.16071 + 4.59026i) q^{72} -0.426103i q^{73} +(-0.944368 - 0.545231i) q^{74} +(0.156253 - 0.112801i) q^{75} +(2.26168 - 1.30578i) q^{76} +(-1.55423 + 8.84070i) q^{77} +(1.82691 + 0.820053i) q^{78} +(2.49381 - 4.31941i) q^{79} -3.75796 q^{80} +(-1.04944 + 8.93861i) q^{81} +0.583940i q^{82} +(-4.28541 + 7.42254i) q^{83} +(-6.55019 + 3.17425i) q^{84} +(-6.59888 - 11.4296i) q^{85} +(2.17928 - 1.25821i) q^{86} +(2.86150 + 3.96378i) q^{87} +(3.90545 - 6.76443i) q^{88} +10.5358 q^{89} +(3.17988 - 2.82839i) q^{90} +(3.65383 + 3.06277i) q^{91} +(-3.26509 - 1.88510i) q^{92} +(18.4752 - 1.88510i) q^{93} +(-0.136691 + 0.0789188i) q^{94} +(-3.14833 + 1.81769i) q^{95} +(9.81303 - 1.00126i) q^{96} +(-6.30108 - 3.63793i) q^{97} +(4.42210 - 0.784360i) q^{98} +(-2.05563 - 9.96840i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 6 q^{2} + 2 q^{4} - 2 q^{7} - 12 q^{9}+O(q^{10}) \) 12 * q - 6 * q^2 + 2 * q^4 - 2 * q^7 - 12 * q^9	\( 12 q - 6 q^{2} + 2 q^{4} - 2 q^{7} - 12 q^{9} - 12 q^{14} + 6 q^{15} + 2 q^{16} - 6 q^{18} - 24 q^{21} - 10 q^{22} + 24 q^{23} - 8 q^{28} + 30 q^{29} + 48 q^{30} - 12 q^{32} + 18 q^{36} - 4 q^{37} + 36 q^{42} - 10 q^{43} - 40 q^{46} + 6 q^{49} - 36 q^{50} - 42 q^{51} + 42 q^{56} - 18 q^{57} + 2 q^{58} - 12 q^{60} + 24 q^{63} + 16 q^{64} - 78 q^{65} + 12 q^{67} + 18 q^{70} - 24 q^{72} - 12 q^{74} - 24 q^{77} - 12 q^{78} - 6 q^{79} + 24 q^{81} - 60 q^{84} - 6 q^{85} + 96 q^{86} + 34 q^{88} - 24 q^{91} + 30 q^{92} + 78 q^{93} + 72 q^{95} - 24 q^{99}+O(q^{100}) \) 12 * q - 6 * q^2 + 2 * q^4 - 2 * q^7 - 12 * q^9 - 12 * q^14 + 6 * q^15 + 2 * q^16 - 6 * q^18 - 24 * q^21 - 10 * q^22 + 24 * q^23 - 8 * q^28 + 30 * q^29 + 48 * q^30 - 12 * q^32 + 18 * q^36 - 4 * q^37 + 36 * q^42 - 10 * q^43 - 40 * q^46 + 6 * q^49 - 36 * q^50 - 42 * q^51 + 42 * q^56 - 18 * q^57 + 2 * q^58 - 12 * q^60 + 24 * q^63 + 16 * q^64 - 78 * q^65 + 12 * q^67 + 18 * q^70 - 24 * q^72 - 12 * q^74 - 24 * q^77 - 12 * q^78 - 6 * q^79 + 24 * q^81 - 60 * q^84 - 6 * q^85 + 96 * q^86 + 34 * q^88 - 24 * q^91 + 30 * q^92 + 78 * q^93 + 72 * q^95 - 24 * q^99

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