LMFDB - Embedded newform 138.2.e.b.55.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [138,2,Mod(13,138)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("138.13"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(138, base_ring=CyclotomicField(22)) chi = DirichletCharacter(H, H._module([0, 14])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 138 = 2 \cdot 3 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	138.e (of order $11$, degree $10$, minimal)

Newform invariants

comment:select newform

sage:traces = [10,-1,1] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$1.10193554789$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	$\Q(\zeta_{22})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - x^{9} + x^{8} - x^{7} + x^{6} - x^{5} + x^{4} - x^{3} + x^{2} - x + 1 $ x^10 - x^9 + x^8 - x^7 + x^6 - x^5 + x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			55.1
Root			$0.959493 - 0.281733i$ of defining polynomial
Character	$\chi$	$=$	138.55
Dual form			138.2.e.b.133.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.959493 + 0.281733i) q^{2} +(0.654861 + 0.755750i) q^{3} +(0.841254 - 0.540641i) q^{4} +(-0.544078 - 3.78415i) q^{5} +(-0.841254 - 0.540641i) q^{6} +(1.20217 - 2.63238i) q^{7} +(-0.654861 + 0.755750i) q^{8} +(-0.142315 + 0.989821i) q^{9} +(1.58816 + 3.47758i) q^{10} +(1.51662 + 0.445319i) q^{11} +(0.959493 + 0.281733i) q^{12} +(1.95653 + 4.28419i) q^{13} +(-0.411844 + 2.86444i) q^{14} +(2.50357 - 2.88927i) q^{15} +(0.415415 - 0.909632i) q^{16} +(-3.98569 - 2.56145i) q^{17} +(-0.142315 - 0.989821i) q^{18} +(1.80728 - 1.16147i) q^{19} +(-2.50357 - 2.88927i) q^{20} +(2.77667 - 0.815304i) q^{21} -1.58065 q^{22} +(2.88909 + 3.82794i) q^{23} -1.00000 q^{24} +(-9.22627 + 2.70908i) q^{25} +(-3.08427 - 3.55944i) q^{26} +(-0.841254 + 0.540641i) q^{27} +(-0.411844 - 2.86444i) q^{28} +(-0.495008 - 0.318122i) q^{29} +(-1.58816 + 3.47758i) q^{30} +(-0.111819 + 0.129046i) q^{31} +(-0.142315 + 0.989821i) q^{32} +(0.656624 + 1.43781i) q^{33} +(4.54589 + 1.33479i) q^{34} +(-10.6154 - 3.11696i) q^{35} +(0.415415 + 0.909632i) q^{36} +(-0.685789 + 4.76977i) q^{37} +(-1.40685 + 1.62359i) q^{38} +(-1.95653 + 4.28419i) q^{39} +(3.21616 + 2.06690i) q^{40} +(1.47968 + 10.2914i) q^{41} +(-2.43450 + 1.56456i) q^{42} +(-8.03389 - 9.27160i) q^{43} +(1.51662 - 0.445319i) q^{44} +3.82306 q^{45} +(-3.85052 - 2.85894i) q^{46} +5.45520 q^{47} +(0.959493 - 0.281733i) q^{48} +(-0.900187 - 1.03887i) q^{49} +(8.08931 - 5.19868i) q^{50} +(-0.674259 - 4.68958i) q^{51} +(3.96215 + 2.54632i) q^{52} +(-4.28201 + 9.37628i) q^{53} +(0.654861 - 0.755750i) q^{54} +(0.859995 - 5.98139i) q^{55} +(1.20217 + 2.63238i) q^{56} +(2.06130 + 0.605253i) q^{57} +(0.564582 + 0.165776i) q^{58} +(-0.790420 - 1.73078i) q^{59} +(0.544078 - 3.78415i) q^{60} +(8.28691 - 9.56361i) q^{61} +(0.0709331 - 0.155322i) q^{62} +(2.43450 + 1.56456i) q^{63} +(-0.142315 - 0.989821i) q^{64} +(15.1475 - 9.73472i) q^{65} +(-1.03510 - 1.19457i) q^{66} +(-5.63806 + 1.65548i) q^{67} -4.73780 q^{68} +(-1.00102 + 4.69020i) q^{69} +11.0635 q^{70} +(11.3427 - 3.33053i) q^{71} +(-0.654861 - 0.755750i) q^{72} +(-11.1159 + 7.14378i) q^{73} +(-0.685789 - 4.76977i) q^{74} +(-8.08931 - 5.19868i) q^{75} +(0.892446 - 1.95418i) q^{76} +(2.99548 - 3.45697i) q^{77} +(0.670276 - 4.66187i) q^{78} +(4.85393 + 10.6286i) q^{79} +(-3.66820 - 1.07708i) q^{80} +(-0.959493 - 0.281733i) q^{81} +(-4.31917 - 9.45767i) q^{82} +(0.0161168 - 0.112095i) q^{83} +(1.89510 - 2.18706i) q^{84} +(-7.52436 + 16.4761i) q^{85} +(10.3206 + 6.63263i) q^{86} +(-0.0837405 - 0.582428i) q^{87} +(-1.32972 + 0.854562i) q^{88} +(8.01460 + 9.24934i) q^{89} +(-3.66820 + 1.07708i) q^{90} +13.6297 q^{91} +(4.50000 + 1.65831i) q^{92} -0.170752 q^{93} +(-5.23423 + 1.53691i) q^{94} +(-5.37848 - 6.20710i) q^{95} +(-0.841254 + 0.540641i) q^{96} +(-0.124317 - 0.864646i) q^{97} +(1.15641 + 0.743178i) q^{98} +(-0.656624 + 1.43781i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - q^{2} + q^{3} - q^{4} - 2 q^{5} + q^{6} - q^{8} - q^{9} + 9 q^{10} + 11 q^{11} + q^{12} + 13 q^{13} - 11 q^{14} + 13 q^{15} - q^{16} - 24 q^{17} - q^{18} - 14 q^{19} - 13 q^{20} + 11 q^{21}+ \cdots - 22 q^{99}+O(q^{100}) $ 10 * q - q^2 + q^3 - q^4 - 2 * q^5 + q^6 - q^8 - q^9 + 9 * q^10 + 11 * q^11 + q^12 + 13 * q^13 - 11 * q^14 + 13 * q^15 - q^16 - 24 * q^17 - q^18 - 14 * q^19 - 13 * q^20 + 11 * q^21 + 22 * q^22 - 10 * q^23 - 10 * q^24 - 43 * q^25 - 9 * q^26 + q^27 - 11 * q^28 + 13 * q^29 - 9 * q^30 + 8 * q^31 - q^32 + 22 * q^33 + 9 * q^34 - q^36 - 13 * q^37 - 3 * q^38 - 13 * q^39 + 9 * q^40 - 10 * q^41 - 8 * q^43 + 11 * q^44 - 2 * q^45 + q^46 - 8 * q^47 + q^48 + 29 * q^49 + 23 * q^50 - 9 * q^51 + 2 * q^52 - 35 * q^53 + q^54 - 11 * q^55 + 3 * q^57 + 13 * q^58 + 37 * q^59 + 2 * q^60 - 2 * q^61 + 8 * q^62 - q^64 + 37 * q^65 + 14 * q^67 - 2 * q^68 - q^69 - 22 * q^70 + 44 * q^71 - q^72 - 49 * q^73 - 13 * q^74 - 23 * q^75 + 8 * q^76 + 44 * q^77 + 20 * q^78 - 8 * q^79 - 2 * q^80 - q^81 + 12 * q^82 - 17 * q^83 - 11 * q^84 - 37 * q^85 + 14 * q^86 - 2 * q^87 + 59 * q^89 - 2 * q^90 + 66 * q^91 + 45 * q^92 + 36 * q^93 - 19 * q^94 - 28 * q^95 + q^96 - 21 * q^97 - 26 * q^98 - 22 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/138\mathbb{Z}\right)^\times$.

$n$	$47$	$97$
$\chi(n)$	$1$	$e\left(\frac{5}{11}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

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

$2$	−0.959493	+	0.281733i	−0.678464	+	0.199215i
$2$	−0.959493	+	0.281733i	−0.678464	+	0.199215i
$3$	0.654861	+	0.755750i	0.378084	+	0.436332i
$3$	0.654861	+	0.755750i	0.378084	+	0.436332i
$4$	0.841254	−	0.540641i	0.420627	−	0.270320i
$5$	−0.544078	−	3.78415i	−0.243319	−	1.69232i	−0.635234	−	0.772320i	$-0.719096\pi$
$5$	−0.544078	−	3.78415i	−0.243319	−	1.69232i	0.391915	−	0.920001i	$-0.371813\pi$
$6$	−0.841254	−	0.540641i	−0.343440	−	0.220716i
$7$	1.20217	−	2.63238i	0.454376	−	0.994946i	−0.534357	−	0.845259i	$-0.679446\pi$
$7$	1.20217	−	2.63238i	0.454376	−	0.994946i	0.988733	−	0.149687i	$-0.0478265\pi$
$8$	−0.654861	+	0.755750i	−0.231528	+	0.267198i
$9$	−0.142315	+	0.989821i	−0.0474383	+	0.329940i
$10$	1.58816	+	3.47758i	0.502219	+	1.09971i
$11$	1.51662	+	0.445319i	0.457278	+	0.134269i	0.502256	−	0.864719i	$-0.332504\pi$
$11$	1.51662	+	0.445319i	0.457278	+	0.134269i	−0.0449780	+	0.998988i	$0.514322\pi$
$12$	0.959493	+	0.281733i	0.276982	+	0.0813292i
$13$	1.95653	+	4.28419i	0.542643	+	1.18822i	0.960134	+	0.279541i	$0.0901822\pi$
$13$	1.95653	+	4.28419i	0.542643	+	1.18822i	−0.417491	+	0.908681i	$0.637091\pi$
$14$	−0.411844	+	2.86444i	−0.110070	+	0.765553i
$15$	2.50357	−	2.88927i	0.646419	−	0.746008i
$16$	0.415415	−	0.909632i	0.103854	−	0.227408i
$17$	−3.98569	−	2.56145i	−0.966672	−	0.621242i	−0.0408352	−	0.999166i	$-0.513002\pi$
$17$	−3.98569	−	2.56145i	−0.966672	−	0.621242i	−0.925837	+	0.377924i	$0.876638\pi$
$18$	−0.142315	−	0.989821i	−0.0335439	−	0.233303i
$19$	1.80728	−	1.16147i	0.414619	−	0.266460i	−0.316658	−	0.948540i	$-0.602561\pi$
$19$	1.80728	−	1.16147i	0.414619	−	0.266460i	0.731278	+	0.682080i	$0.238924\pi$
$20$	−2.50357	−	2.88927i	−0.559815	−	0.646062i
$21$	2.77667	−	0.815304i	0.605919	−	0.177914i
$22$	−1.58065			−0.336995
$23$	2.88909	+	3.82794i	0.602417	+	0.798182i
$23$	2.88909	+	3.82794i	0.602417	+	0.798182i
$24$	−1.00000			−0.204124
$25$	−9.22627	+	2.70908i	−1.84525	+	0.541815i
$26$	−3.08427	−	3.55944i	−0.604875	−	0.698063i
$27$	−0.841254	+	0.540641i	−0.161899	+	0.104046i
$28$	−0.411844	−	2.86444i	−0.0778312	−	0.541328i
$29$	−0.495008	−	0.318122i	−0.0919207	−	0.0590739i	0.493873	−	0.869534i	$-0.335581\pi$
$29$	−0.495008	−	0.318122i	−0.0919207	−	0.0590739i	−0.585794	+	0.810460i	$0.699217\pi$
$30$	−1.58816	+	3.47758i	−0.289956	+	0.634916i
$31$	−0.111819	+	0.129046i	−0.0200833	+	0.0231774i	−0.765702	−	0.643195i	$-0.777608\pi$
$31$	−0.111819	+	0.129046i	−0.0200833	+	0.0231774i	0.745619	+	0.666372i	$0.232154\pi$
$32$	−0.142315	+	0.989821i	−0.0251579	+	0.174977i
$33$	0.656624	+	1.43781i	0.114304	+	0.250290i
$34$	4.54589	+	1.33479i	0.779613	+	0.228915i
$35$	−10.6154	−	3.11696i	−1.79433	−	0.526862i
$36$	0.415415	+	0.909632i	0.0692358	+	0.151605i
$37$	−0.685789	+	4.76977i	−0.112743	+	0.784145i	0.852488	+	0.522747i	$0.175093\pi$
$37$	−0.685789	+	4.76977i	−0.112743	+	0.784145i	−0.965231	+	0.261398i	$0.915816\pi$
$38$	−1.40685	+	1.62359i	−0.228222	+	0.263382i
$39$	−1.95653	+	4.28419i	−0.313295	+	0.686020i
$40$	3.21616	+	2.06690i	0.508520	+	0.326806i
$41$	1.47968	+	10.2914i	0.231088	+	1.60725i	0.693414	+	0.720540i	$0.256106\pi$
$41$	1.47968	+	10.2914i	0.231088	+	1.60725i	−0.462326	+	0.886710i	$0.652985\pi$
$42$	−2.43450	+	1.56456i	−0.375651	+	0.241416i
$43$	−8.03389	−	9.27160i	−1.22516	−	1.41391i	−0.879739	−	0.475456i	$-0.842283\pi$
$43$	−8.03389	−	9.27160i	−1.22516	−	1.41391i	−0.345417	−	0.938449i	$-0.612262\pi$
$44$	1.51662	−	0.445319i	0.228639	−	0.0671344i
$45$	3.82306			0.569908
$46$	−3.85052	−	2.85894i	−0.567728	−	0.421527i
$47$	5.45520			0.795723			0.397862	−	0.917445i	$-0.369752\pi$
$47$	5.45520			0.795723			0.397862	+	0.917445i	$0.369752\pi$
$48$	0.959493	−	0.281733i	0.138491	−	0.0406646i
$49$	−0.900187	−	1.03887i	−0.128598	−	0.148410i
$50$	8.08931	−	5.19868i	1.14400	−	0.735205i
$51$	−0.674259	−	4.68958i	−0.0944152	−	0.656672i
$52$	3.96215	+	2.54632i	0.549451	+	0.353110i
$53$	−4.28201	+	9.37628i	−0.588179	+	1.28793i	0.348358	+	0.937362i	$0.386739\pi$
$53$	−4.28201	+	9.37628i	−0.588179	+	1.28793i	−0.936537	+	0.350570i	$0.885988\pi$
$54$	0.654861	−	0.755750i	0.0891153	−	0.102844i
$55$	0.859995	−	5.98139i	0.115962	−	0.806531i
$56$	1.20217	+	2.63238i	0.160646	+	0.351766i
$57$	2.06130	+	0.605253i	0.273026	+	0.0801677i
$58$	0.564582	+	0.165776i	0.0741333	+	0.0217675i
$59$	−0.790420	−	1.73078i	−0.102904	−	0.225328i	0.851176	−	0.524881i	$-0.175890\pi$
$59$	−0.790420	−	1.73078i	−0.102904	−	0.225328i	−0.954080	+	0.299552i	$0.903163\pi$
$60$	0.544078	−	3.78415i	0.0702402	−	0.488531i
$61$	8.28691	−	9.56361i	1.06103	−	1.22449i	0.0874457	−	0.996169i	$-0.472130\pi$
$61$	8.28691	−	9.56361i	1.06103	−	1.22449i	0.973585	−	0.228325i	$-0.0733250\pi$
$62$	0.0709331	−	0.155322i	0.00900851	−	0.0197259i
$63$	2.43450	+	1.56456i	0.306718	+	0.197116i
$64$	−0.142315	−	0.989821i	−0.0177894	−	0.123728i
$65$	15.1475	−	9.73472i	1.87882	−	1.20744i
$66$	−1.03510	−	1.19457i	−0.127412	−	0.147042i
$67$	−5.63806	+	1.65548i	−0.688799	+	0.202250i	−0.607358	−	0.794429i	$-0.707770\pi$
$67$	−5.63806	+	1.65548i	−0.688799	+	0.202250i	−0.0814412	+	0.996678i	$0.525952\pi$
$68$	−4.73780			−0.574543
$69$	−1.00102	+	4.69020i	−0.120508	+	0.564634i
$70$	11.0635			1.32234
$71$	11.3427	−	3.33053i	1.34614	−	0.395261i	0.472281	−	0.881448i	$-0.343431\pi$
$71$	11.3427	−	3.33053i	1.34614	−	0.395261i	0.873855	+	0.486187i	$0.161612\pi$
$72$	−0.654861	−	0.755750i	−0.0771761	−	0.0890659i
$73$	−11.1159	+	7.14378i	−1.30102	+	0.836116i	−0.993323	−	0.115368i	$-0.963195\pi$
$73$	−11.1159	+	7.14378i	−1.30102	+	0.836116i	−0.307699	+	0.951484i	$0.599559\pi$
$74$	−0.685789	−	4.76977i	−0.0797213	−	0.554474i
$75$	−8.08931	−	5.19868i	−0.934073	−	0.600292i
$76$	0.892446	−	1.95418i	0.102371	−	0.224160i
$77$	2.99548	−	3.45697i	0.341366	−	0.393958i
$78$	0.670276	−	4.66187i	0.0758938	−	0.527853i
$79$	4.85393	+	10.6286i	0.546110	+	1.19581i	0.958575	+	0.284841i	$0.0919408\pi$
$79$	4.85393	+	10.6286i	0.546110	+	1.19581i	−0.412465	+	0.910974i	$0.635332\pi$
$80$	−3.66820	−	1.07708i	−0.410117	−	0.120421i
$81$	−0.959493	−	0.281733i	−0.106610	−	0.0313036i
$82$	−4.31917	−	9.45767i	−0.476973	−	1.04442i
$83$	0.0161168	−	0.112095i	0.00176905	−	0.0123040i	−0.988918	−	0.148464i	$-0.952567\pi$
$83$	0.0161168	−	0.112095i	0.00176905	−	0.0123040i	0.990687	+	0.136160i	$0.0434761\pi$
$84$	1.89510	−	2.18706i	0.206772	−	0.238628i
$85$	−7.52436	+	16.4761i	−0.816132	+	1.78708i
$86$	10.3206	+	6.63263i	1.11290	+	0.715214i
$87$	−0.0837405	−	0.582428i	−0.00897793	−	0.0624429i
$88$	−1.32972	+	0.854562i	−0.141749	+	0.0910966i
$89$	8.01460	+	9.24934i	0.849546	+	0.980428i	0.999966	−	0.00819403i	$-0.00260827\pi$
$89$	8.01460	+	9.24934i	0.849546	+	0.980428i	−0.150421	+	0.988622i	$0.548063\pi$
$90$	−3.66820	+	1.07708i	−0.386662	+	0.113534i
$91$	13.6297			1.42878
$92$	4.50000	+	1.65831i	0.469157	+	0.172891i
$93$	−0.170752			−0.0177062
$94$	−5.23423	+	1.53691i	−0.539869	+	0.158520i
$95$	−5.37848	−	6.20710i	−0.551820	−	0.636835i
$96$	−0.841254	+	0.540641i	−0.0858601	+	0.0551789i
$97$	−0.124317	−	0.864646i	−0.0126225	−	0.0877915i	0.982536	−	0.186071i	$-0.0595753\pi$
$97$	−0.124317	−	0.864646i	−0.0126225	−	0.0877915i	−0.995159	+	0.0982791i	$0.968666\pi$
$98$	1.15641	+	0.743178i	0.116815	+	0.0750723i
$99$	−0.656624	+	1.43781i	−0.0659932	+	0.144505i
$100$	−6.29699	+	7.26712i	−0.629699	+	0.726712i
$101$	1.55270	−	10.7992i	0.154499	−	1.07456i	−0.754060	−	0.656806i	$-0.771907\pi$
$101$	1.55270	−	10.7992i	0.154499	−	1.07456i	0.908558	−	0.417758i	$-0.137184\pi$
$102$	1.96815	+	4.30965i	0.194876	+	0.426719i
$103$	−3.54321	−	1.04038i	−0.349123	−	0.102512i	0.102469	−	0.994736i	$-0.467326\pi$
$103$	−3.54321	−	1.04038i	−0.349123	−	0.102512i	−0.451592	+	0.892224i	$0.649144\pi$
$104$	−4.51903	−	1.32691i	−0.443127	−	0.130114i
$105$	−4.59596	−	10.0637i	−0.448519	−	0.982120i
$106$	1.46695	−	10.2029i	0.142483	−	0.990989i
$107$	−7.05053	+	8.13674i	−0.681600	+	0.786608i	−0.986144	−	0.165890i	$-0.946950\pi$
$107$	−7.05053	+	8.13674i	−0.681600	+	0.786608i	0.304544	+	0.952498i	$0.401496\pi$
$108$	−0.415415	+	0.909632i	−0.0399733	+	0.0875294i
$109$	−6.99382	−	4.49466i	−0.669887	−	0.430510i	0.160998	−	0.986955i	$-0.448529\pi$
$109$	−6.99382	−	4.49466i	−0.669887	−	0.430510i	−0.830885	+	0.556445i	$0.812165\pi$
$110$	0.859995	+	5.98139i	0.0819973	+	0.570304i
$111$	−4.05384	+	2.60525i	−0.384774	+	0.247279i
$112$	−1.89510	−	2.18706i	−0.179070	−	0.206658i
$113$	−7.20846	+	2.11660i	−0.678115	+	0.199113i	−0.602614	−	0.798033i	$-0.705874\pi$
$113$	−7.20846	+	2.11660i	−0.678115	+	0.199113i	−0.0755016	+	0.997146i	$0.524056\pi$
$114$	−2.14832			−0.201209
$115$	12.9136	−	13.0154i	1.20420	−	1.21370i
$116$	−0.588417			−0.0546332
$117$	−4.51903	+	1.32691i	−0.417785	+	0.122673i
$118$	1.24602	+	1.43798i	0.114705	+	0.132377i
$119$	−11.5342	+	7.41256i	−1.05734	+	0.679508i
$120$	0.544078	+	3.78415i	0.0496673	+	0.345444i
$121$	−7.15197	−	4.59629i	−0.650179	−	0.417844i
$122$	−5.25686	+	11.5109i	−0.475933	+	1.04215i
$123$	−6.80875	+	7.85772i	−0.613924	+	0.708506i
$124$	−0.0243006	+	0.169014i	−0.00218226	+	0.0151779i
$125$	7.33057	+	16.0517i	0.655666	+	1.43571i
$126$	−2.77667	−	0.815304i	−0.247366	−	0.0726331i
$127$	7.28023	+	2.13767i	0.646016	+	0.189687i	0.588296	−	0.808645i	$-0.299799\pi$
$127$	7.28023	+	2.13767i	0.646016	+	0.189687i	0.0577198	+	0.998333i	$0.481617\pi$
$128$	0.415415	+	0.909632i	0.0367178	+	0.0804009i
$129$	1.74593	−	12.1432i	0.153721	−	1.06915i
$130$	−11.7913	+	13.6079i	−1.03417	+	1.19350i
$131$	7.39794	−	16.1992i	0.646361	−	1.41533i	−0.248343	−	0.968672i	$-0.579886\pi$
$131$	7.39794	−	16.1992i	0.646361	−	1.41533i	0.894704	−	0.446660i	$-0.147387\pi$
$132$	1.32972	+	0.854562i	0.115738	+	0.0743801i
$133$	−0.884774	−	6.15374i	−0.0767196	−	0.533597i
$134$	4.94328	−	3.17685i	0.427034	−	0.274438i
$135$	2.50357	+	2.88927i	0.215473	+	0.248669i
$136$	4.54589	−	1.33479i	0.389806	−	0.114458i
$137$	−0.762968			−0.0651847			−0.0325924	−	0.999469i	$-0.510376\pi$
$137$	−0.762968			−0.0651847			−0.0325924	+	0.999469i	$0.510376\pi$
$138$	−0.360914	−	4.78223i	−0.0307230	−	0.407091i
$139$	9.22612			0.782549			0.391275	−	0.920274i	$-0.372034\pi$
$139$	9.22612			0.782549			0.391275	+	0.920274i	$0.372034\pi$
$140$	−10.6154	+	3.11696i	−0.897163	+	0.263431i
$141$	3.57240	+	4.12277i	0.300850	+	0.347200i
$142$	−9.94497	+	6.39124i	−0.834563	+	0.536341i
$143$	1.05947	+	7.36877i	0.0885973	+	0.616207i
$144$	0.841254	+	0.540641i	0.0701045	+	0.0450534i
$145$	−0.934499	+	2.04627i	−0.0776059	+	0.169933i
$146$	8.65303	−	9.98613i	0.716130	−	0.826458i
$147$	0.195629	−	1.36063i	0.0161352	−	0.112223i
$148$	2.00181	+	4.38335i	0.164548	+	0.360309i
$149$	−17.7421	−	5.20954i	−1.45349	−	0.426782i	−0.542794	−	0.839866i	$-0.682633\pi$
$149$	−17.7421	−	5.20954i	−1.45349	−	0.426782i	−0.910693	+	0.413084i	$0.864452\pi$
$150$	9.22627	+	2.70908i	0.753322	+	0.221195i
$151$	−0.412045	−	0.902252i	−0.0335317	−	0.0734243i	0.892125	−	0.451789i	$-0.149214\pi$
$151$	−0.412045	−	0.902252i	−0.0335317	−	0.0734243i	−0.925657	+	0.378364i	$0.876487\pi$
$152$	−0.305738	+	2.12646i	−0.0247986	+	0.172478i
$153$	3.10260	−	3.58059i	0.250830	−	0.289474i
$154$	−1.90020	+	4.16086i	−0.153123	+	0.335292i
$155$	0.549167	+	0.352928i	0.0441102	+	0.0283479i
$156$	0.670276	+	4.66187i	0.0536650	+	0.373248i
$157$	6.82233	−	4.38445i	0.544481	−	0.349917i	−0.239308	−	0.970944i	$-0.576921\pi$
$157$	6.82233	−	4.38445i	0.544481	−	0.349917i	0.783789	+	0.621027i	$0.213284\pi$
$158$	−7.65175	−	8.83059i	−0.608740	−	0.702524i
$159$	−9.89024	+	2.90404i	−0.784347	+	0.230305i
$160$	3.82306			0.302239
$161$	13.5498	−	3.00335i	1.06787	−	0.236697i
$162$	1.00000			0.0785674
$163$	22.1412	−	6.50124i	1.73423	−	0.509217i	0.746502	−	0.665383i	$-0.231732\pi$
$163$	22.1412	−	6.50124i	1.73423	−	0.509217i	0.987731	+	0.156166i	$0.0499135\pi$
$164$	6.80875	+	7.85772i	0.531674	+	0.613585i
$165$	5.08361	−	3.26704i	0.395759	−	0.254339i
$166$	0.0161168	+	0.112095i	0.00125091	+	0.00870026i
$167$	−4.44588	−	2.85719i	−0.344032	−	0.221096i	0.357202	−	0.934027i	$-0.383731\pi$
$167$	−4.44588	−	2.85719i	−0.344032	−	0.221096i	−0.701234	+	0.712931i	$0.747367\pi$
$168$	−1.20217	+	2.63238i	−0.0927492	+	0.203092i
$169$	−6.01314	+	6.93953i	−0.462549	+	0.533810i
$170$	2.57773	−	17.9285i	0.197703	−	1.37505i
$171$	0.892446	+	1.95418i	0.0682470	+	0.149440i
$172$	−11.7711	−	3.45632i	−0.897541	−	0.263542i
$173$	−13.8077	−	4.05430i	−1.04978	−	0.308243i	−0.289051	−	0.957314i	$-0.593340\pi$
$173$	−13.8077	−	4.05430i	−1.04978	−	0.308243i	−0.760728	+	0.649071i	$0.775158\pi$
$174$	0.244437	+	0.535243i	0.0185308	+	0.0405767i
$175$	−3.96020	+	27.5438i	−0.299363	+	2.08212i
$176$	1.03510	−	1.19457i	0.0780238	−	0.0900443i
$177$	0.790420	−	1.73078i	0.0594116	−	0.130093i
$178$	−10.2958	−	6.61670i	−0.771702	−	0.495943i
$179$	−1.59394	−	11.0861i	−0.119136	−	0.828612i	−0.958510	−	0.285057i	$-0.907987\pi$
$179$	−1.59394	−	11.0861i	−0.119136	−	0.828612i	0.839374	−	0.543554i	$-0.182922\pi$
$180$	3.21616	−	2.06690i	0.239719	−	0.154058i
$181$	−5.75929	−	6.64657i	−0.428084	−	0.494036i	0.500198	−	0.865911i	$-0.333260\pi$
$181$	−5.75929	−	6.64657i	−0.428084	−	0.494036i	−0.928283	+	0.371875i	$0.878715\pi$
$182$	−13.0776	+	3.83993i	−0.969376	+	0.284634i
$183$	12.6545			0.935445
$184$	−4.78492	−	0.323343i	−0.352749	−	0.0238371i
$185$	18.4226			1.35446
$186$	0.163836	−	0.0481065i	0.0120130	−	0.00352734i
$187$	−4.90411	−	5.65965i	−0.358624	−	0.413874i
$188$	4.58921	−	2.94931i	0.334702	−	0.215100i
$189$	0.411844	+	2.86444i	0.0299572	+	0.208357i
$190$	6.90935	+	4.44037i	0.501257	+	0.322138i
$191$	−2.63041	+	5.75979i	−0.190330	+	0.416764i	−0.980607	−	0.195986i	$-0.937209\pi$
$191$	−2.63041	+	5.75979i	−0.190330	+	0.416764i	0.790277	+	0.612750i	$0.209937\pi$
$192$	0.654861	−	0.755750i	0.0472605	−	0.0545415i
$193$	0.437455	−	3.04256i	0.0314887	−	0.219009i	−0.968001	−	0.250946i	$-0.919258\pi$
$193$	0.437455	−	3.04256i	0.0314887	−	0.219009i	0.999490	+	0.0319370i	$0.0101676\pi$
$194$	0.362880	+	0.794597i	0.0260533	+	0.0570488i
$195$	17.2765	+	5.07284i	1.23720	+	0.363274i
$196$	−1.31894	−	0.387276i	−0.0942101	−	0.0276626i
$197$	−0.400217	−	0.876353i	−0.0285143	−	0.0624376i	0.894839	−	0.446389i	$-0.147290\pi$
$197$	−0.400217	−	0.876353i	−0.0285143	−	0.0624376i	−0.923353	+	0.383951i	$0.874563\pi$
$198$	0.224949	−	1.56456i	0.0159865	−	0.111188i
$199$	−2.14354	+	2.47378i	−0.151952	+	0.175362i	−0.826622	−	0.562758i	$-0.809740\pi$
$199$	−2.14354	+	2.47378i	−0.151952	+	0.175362i	0.674670	+	0.738119i	$0.264286\pi$
$200$	3.99454	−	8.74682i	0.282456	−	0.618493i
$201$	−4.94328	−	3.17685i	−0.348672	−	0.224078i
$202$	1.55270	+	10.7992i	0.109247	+	0.759831i
$203$	−1.43250	+	0.920613i	−0.100542	+	0.0646144i
$204$	−3.10260	−	3.58059i	−0.217225	−	0.250691i
$205$	38.1392	−	11.1987i	2.66375	−	0.782149i
$206$	3.69279			0.257289
$207$	−4.20014	+	2.31491i	−0.291930	+	0.160897i
$208$	4.70981			0.326567
$209$	3.25819	−	0.956690i	0.225373	−	0.0661756i
$210$	7.24507	+	8.36126i	0.499957	+	0.576981i
$211$	−20.5413	+	13.2011i	−1.41412	+	0.908798i	−0.999999	−	0.00142429i	$-0.999547\pi$
$211$	−20.5413	+	13.2011i	−1.41412	+	0.908798i	−0.414119	+	0.910223i	$0.635910\pi$
$212$	1.46695	+	10.2029i	0.100751	+	0.700735i
$213$	9.94497	+	6.39124i	0.681418	+	0.437921i
$214$	4.47255	−	9.79351i	0.305737	−	0.669470i
$215$	−30.7140	+	35.4459i	−2.09468	+	2.41739i
$216$	0.142315	−	0.989821i	0.00968330	−	0.0673488i
$217$	0.205273	+	0.449485i	0.0139348	+	0.0305130i
$218$	7.97681	+	2.34220i	0.540258	+	0.158634i
$219$	−12.6783	−	3.72268i	−0.856720	−	0.251556i
$220$	−2.51031	−	5.49682i	−0.169245	−	0.370595i
$221$	3.17563	−	22.0870i	0.213616	−	1.48573i
$222$	3.15565	−	3.64182i	0.211793	−	0.244423i
$223$	6.31394	−	13.8256i	0.422813	−	0.925831i	−0.571626	−	0.820514i	$-0.693687\pi$
$223$	6.31394	−	13.8256i	0.422813	−	0.925831i	0.994439	−	0.105316i	$-0.0335856\pi$
$224$	2.43450	+	1.56456i	0.162662	+	0.104536i
$225$	−1.36847	−	9.51790i	−0.0912312	−	0.634527i
$226$	6.32016	−	4.06172i	0.420411	−	0.270181i
$227$	−8.46896	−	9.77370i	−0.562105	−	0.648703i	0.401555	−	0.915835i	$-0.368470\pi$
$227$	−8.46896	−	9.77370i	−0.562105	−	0.648703i	−0.963660	+	0.267131i	$0.913924\pi$
$228$	2.06130	−	0.605253i	0.136513	−	0.0400838i
$229$	−0.948502			−0.0626788			−0.0313394	−	0.999509i	$-0.509977\pi$
$229$	−0.948502			−0.0626788			−0.0313394	+	0.999509i	$0.509977\pi$
$230$	−8.72365	+	16.1264i	−0.575220	+	1.06334i
$231$	4.57422			0.300962
$232$	0.564582	−	0.165776i	0.0370667	−	0.0108838i
$233$	−9.13414	−	10.5414i	−0.598397	−	0.690587i	0.373058	−	0.927808i	$-0.378309\pi$
$233$	−9.13414	−	10.5414i	−0.598397	−	0.690587i	−0.971456	+	0.237220i	$0.923764\pi$
$234$	3.96215	−	2.54632i	0.259014	−	0.166458i
$235$	−2.96806	−	20.6433i	−0.193615	−	1.34662i
$236$	−1.60067	−	1.02869i	−0.104195	−	0.0669621i
$237$	−4.85393	+	10.6286i	−0.315297	+	0.690404i
$238$	8.97859	−	10.3618i	0.581996	−	0.671659i
$239$	0.347717	−	2.41842i	0.0224919	−	0.156435i	−0.975480	−	0.220087i	$-0.929366\pi$
$239$	0.347717	−	2.41842i	0.0224919	−	0.156435i	0.997972	+	0.0636524i	$0.0202749\pi$
$240$	−1.58816	−	3.47758i	−0.102515	−	0.224477i
$241$	−10.4235	−	3.06062i	−0.671438	−	0.197152i	−0.0717947	−	0.997419i	$-0.522873\pi$
$241$	−10.4235	−	3.06062i	−0.671438	−	0.197152i	−0.599643	+	0.800267i	$0.704691\pi$
$242$	8.15719	+	2.39517i	0.524364	+	0.153967i
$243$	−0.415415	−	0.909632i	−0.0266489	−	0.0583529i
$244$	1.80092	−	12.5257i	0.115292	−	0.801873i
$245$	−3.44147	+	3.97166i	−0.219867	+	0.253740i
$246$	4.31917	−	9.45767i	0.275380	−	0.602999i
$247$	8.51197	+	5.47031i	0.541603	+	0.348067i
$248$	−0.0243006	−	0.169014i	−0.00154309	−	0.0107324i
$249$	0.0952700	−	0.0612263i	0.00603749	−	0.00388006i
$250$	−11.5559	−	13.3362i	−0.730861	−	0.843458i
$251$	13.7410	−	4.03472i	0.867324	−	0.254669i	0.182347	−	0.983234i	$-0.441630\pi$
$251$	13.7410	−	4.03472i	0.867324	−	0.254669i	0.684977	+	0.728565i	$0.259812\pi$
$252$	2.89389			0.182298
$253$	2.67699	+	7.09210i	0.168301	+	0.445877i
$254$	−7.58758			−0.476087
$255$	−17.3792	+	5.10299i	−1.08833	+	0.319562i
$256$	−0.654861	−	0.755750i	−0.0409288	−	0.0472343i
$257$	−3.57053	+	2.29464i	−0.222724	+	0.143136i	−0.647245	−	0.762282i	$-0.724079\pi$
$257$	−3.57053	+	2.29464i	−0.222724	+	0.143136i	0.424521	+	0.905418i	$0.360442\pi$
$258$	1.74593	+	12.1432i	0.108697	+	0.756003i
$259$	11.7314	+	7.53931i	0.728953	+	0.468470i
$260$	7.47991	−	16.3787i	0.463885	−	1.01577i
$261$	0.385331	−	0.444696i	0.0238514	−	0.0275260i
$262$	−2.53442	+	17.6273i	−0.156577	+	1.08902i
$263$	−2.95101	−	6.46180i	−0.181967	−	0.398452i	0.796563	−	0.604555i	$-0.206649\pi$
$263$	−2.95101	−	6.46180i	−0.181967	−	0.398452i	−0.978530	+	0.206103i	$0.933922\pi$
$264$	−1.51662	−	0.445319i	−0.0933414	−	0.0274075i
$265$	37.8110	+	11.1023i	2.32271	+	0.682009i
$266$	2.58264	+	5.65520i	0.158352	+	0.346743i
$267$	−1.74174	+	12.1141i	−0.106593	+	0.741368i
$268$	−3.84802	+	4.44085i	−0.235055	+	0.271268i
$269$	−3.21213	+	7.03359i	−0.195847	+	0.428846i	−0.981922	−	0.189286i	$-0.939383\pi$
$269$	−3.21213	+	7.03359i	−0.195847	+	0.428846i	0.786075	+	0.618131i	$0.212110\pi$
$270$	−3.21616	−	2.06690i	−0.195729	−	0.125788i
$271$	0.723042	+	5.02887i	0.0439217	+	0.305482i	0.999926	+	0.0121307i	$0.00386142\pi$
$271$	0.723042	+	5.02887i	0.0439217	+	0.305482i	−0.956005	+	0.293351i	$0.905229\pi$
$272$	−3.98569	+	2.56145i	−0.241668	+	0.155311i
$273$	8.92555	+	10.3006i	0.540199	+	0.623423i
$274$	0.732062	−	0.214953i	0.0442255	−	0.0129858i
$275$	−15.1991			−0.916543
$276$	1.69360	+	4.48684i	0.101943	+	0.270076i
$277$	−15.3909			−0.924751			−0.462376	−	0.886684i	$-0.653003\pi$
$277$	−15.3909			−0.924751			−0.462376	+	0.886684i	$0.653003\pi$
$278$	−8.85240	+	2.59930i	−0.530932	+	0.155896i
$279$	−0.111819	−	0.129046i	−0.00669443	−	0.00772578i
$280$	9.30723	−	5.98139i	0.556213	−	0.357457i
$281$	0.469579	+	3.26599i	0.0280127	+	0.194833i	0.999022	−	0.0442076i	$-0.0140763\pi$
$281$	0.469579	+	3.26599i	0.0280127	+	0.194833i	−0.971010	+	0.239040i	$0.923167\pi$
$282$	−4.58921	−	2.94931i	−0.273283	−	0.175629i
$283$	−10.7520	+	23.5436i	−0.639141	+	1.39952i	0.261603	+	0.965175i	$0.415749\pi$
$283$	−10.7520	+	23.5436i	−0.639141	+	1.39952i	−0.900745	+	0.434349i	$0.856979\pi$
$284$	7.74150	−	8.93417i	0.459374	−	0.530146i
$285$	1.16886	−	8.12957i	0.0692370	−	0.481554i
$286$	−3.09258	−	6.77180i	−0.182868	−	0.400425i
$287$	28.8697	+	8.47692i	1.70413	+	0.500377i
$288$	−0.959493	−	0.281733i	−0.0565387	−	0.0166013i
$289$	2.26266	+	4.95453i	0.133098	+	0.291443i
$290$	0.320145	−	2.22666i	0.0187996	−	0.130754i
$291$	0.572045	−	0.660175i	0.0335339	−	0.0387002i
$292$	−5.48910	+	12.0195i	−0.321225	+	0.703386i
$293$	5.48975	+	3.52805i	0.320715	+	0.206111i	0.691085	−	0.722773i	$-0.257133\pi$
$293$	5.48975	+	3.52805i	0.320715	+	0.206111i	−0.370371	+	0.928884i	$0.620769\pi$
$294$	0.195629	+	1.36063i	0.0114093	+	0.0793537i
$295$	−6.11947	+	3.93275i	−0.356289	+	0.228973i
$296$	−3.15565	−	3.64182i	−0.183419	−	0.211676i
$297$	−1.51662	+	0.445319i	−0.0880031	+	0.0258401i
$298$	18.4911			1.07116
$299$	−10.7471	+	19.8669i	−0.621520	+	1.14893i
$300$	−9.61578			−0.555167
$301$	−34.0644	+	10.0022i	−1.96344	+	0.576518i
$302$	0.649548	+	0.749618i	0.0373773	+	0.0431357i
$303$	9.17831	−	5.89854i	0.527280	−	0.338863i
$304$	−0.305738	−	2.12646i	−0.0175353	−	0.121961i
$305$	−40.6988	−	26.1555i	−2.33041	−	1.49766i
$306$	−1.96815	+	4.30965i	−0.112512	+	0.246367i
$307$	−3.02366	+	3.48950i	−0.172570	+	0.199156i	−0.835445	−	0.549573i	$-0.814790\pi$
$307$	−3.02366	+	3.48950i	−0.172570	+	0.199156i	0.662876	+	0.748729i	$0.269336\pi$
$308$	0.650980	−	4.52766i	0.0370930	−	0.257988i
$309$	−1.53404	−	3.35908i	−0.0872686	−	0.191091i
$310$	−0.626353	−	0.183914i	−0.0355745	−	0.0104456i
$311$	10.3050	+	3.02582i	0.584342	+	0.171578i	0.560524	−	0.828138i	$-0.310600\pi$
$311$	10.3050	+	3.02582i	0.584342	+	0.171578i	0.0238177	+	0.999716i	$0.492418\pi$
$312$	−1.95653	−	4.28419i	−0.110766	−	0.242545i
$313$	−3.79837	+	26.4182i	−0.214696	+	1.49325i	0.542498	+	0.840057i	$0.317479\pi$
$313$	−3.79837	+	26.4182i	−0.214696	+	1.49325i	−0.757194	+	0.653190i	$0.773430\pi$
$314$	−5.31074	+	6.12892i	−0.299702	+	0.345875i
$315$	4.59596	−	10.0637i	0.258953	−	0.567027i
$316$	9.82966	+	6.31714i	0.552962	+	0.355367i
$317$	−2.72980	−	18.9862i	−0.153321	−	1.06637i	−0.910603	−	0.413282i	$-0.864382\pi$
$317$	−2.72980	−	18.9862i	−0.153321	−	1.06637i	0.757282	−	0.653087i	$-0.226527\pi$
$318$	8.67145	−	5.57281i	0.486271	−	0.312507i
$319$	−0.609073	−	0.702907i	−0.0341015	−	0.0393553i
$320$	−3.66820	+	1.07708i	−0.205058	+	0.0602106i
$321$	−10.7665			−0.600925
$322$	−12.1548	+	6.69910i	−0.677359	+	0.373326i
$323$	−10.1783			−0.566337
$324$	−0.959493	+	0.281733i	−0.0533052	+	0.0156518i
$325$	−29.6577	−	34.2268i	−1.64511	−	1.89856i
$326$	−19.4127	+	12.4758i	−1.07517	+	0.690970i
$327$	−1.18314	−	8.22895i	−0.0654280	−	0.455062i
$328$	−8.74672	−	5.62118i	−0.482957	−	0.310378i
$329$	6.55807	−	14.3602i	0.361558	−	0.791701i
$330$	−3.95726	+	4.56692i	−0.217840	+	0.251401i
$331$	−1.24393	+	8.65169i	−0.0683723	+	0.475540i	0.926653	+	0.375918i	$0.122672\pi$
$331$	−1.24393	+	8.65169i	−0.0683723	+	0.475540i	−0.995025	+	0.0996221i	$0.968237\pi$
$332$	−0.0470448	−	0.103014i	−0.00258192	−	0.00565361i
$333$	−4.62362	−	1.35762i	−0.253373	−	0.0743969i
$334$	5.07075	+	1.48891i	0.277459	+	0.0814694i
$335$	9.33214	+	20.4345i	0.509869	+	1.11646i
$336$	0.411844	−	2.86444i	0.0224679	−	0.156268i
$337$	2.13088	−	2.45916i	0.116076	−	0.133959i	−0.694738	−	0.719263i	$-0.744479\pi$
$337$	2.13088	−	2.45916i	0.116076	−	0.133959i	0.810814	+	0.585304i	$0.199025\pi$
$338$	3.81447	−	8.35253i	0.207480	−	0.454318i
$339$	−6.32016	−	4.06172i	−0.343264	−	0.220602i
$340$	2.57773	+	17.9285i	0.139797	+	0.972311i
$341$	−0.227054	+	0.145918i	−0.0122956	+	0.00790193i
$342$	−1.40685	−	1.62359i	−0.0760739	−	0.0877939i
$343$	15.6198	−	4.58639i	0.843391	−	0.247642i
$344$	12.2681			0.661451
$345$	18.2930	+	1.23616i	0.984863	+	0.0665525i
$346$	14.3906			0.773644
$347$	5.00067	−	1.46833i	0.268450	−	0.0788241i	−0.144737	−	0.989470i	$-0.546234\pi$
$347$	5.00067	−	1.46833i	0.268450	−	0.0788241i	0.413187	+	0.910646i	$0.364415\pi$
$348$	−0.385331	−	0.444696i	−0.0206559	−	0.0238382i
$349$	13.0168	−	8.36539i	0.696773	−	0.447789i	−0.143715	−	0.989619i	$-0.545905\pi$
$349$	13.0168	−	8.36539i	0.696773	−	0.447789i	0.840488	+	0.541830i	$0.182268\pi$
$350$	−3.96020	−	27.5438i	−0.211682	−	1.47228i
$351$	−3.96215	−	2.54632i	−0.211484	−	0.135912i
$352$	−0.656624	+	1.43781i	−0.0349982	+	0.0766353i
$353$	1.05867	−	1.22177i	0.0563473	−	0.0650283i	−0.726876	−	0.686769i	$-0.759029\pi$
$353$	1.05867	−	1.22177i	0.0563473	−	0.0650283i	0.783224	+	0.621740i	$0.213574\pi$
$354$	−0.270786	+	1.88336i	−0.0143921	+	0.100099i
$355$	−18.7746	−	41.1105i	−0.996450	−	2.18192i
$356$	11.7429	+	3.44802i	0.622371	+	0.182745i
$357$	−13.1553	−	3.86275i	−0.696253	−	0.204438i
$358$	4.65268	+	10.1879i	0.245902	+	0.538449i
$359$	−1.92950	+	13.4199i	−0.101835	+	0.708278i	0.873383	+	0.487033i	$0.161921\pi$
$359$	−1.92950	+	13.4199i	−0.101835	+	0.708278i	−0.975218	+	0.221244i	$0.928988\pi$
$360$	−2.50357	+	2.88927i	−0.131950	+	0.152278i
$361$	−5.97562	+	13.0848i	−0.314507	+	0.688673i
$362$	7.39855	+	4.75476i	0.388859	+	0.249905i
$363$	−1.20990	−	8.41502i	−0.0635032	−	0.441674i
$364$	11.4660	−	7.36877i	0.600983	−	0.386228i
$365$	33.0810	+	38.1775i	1.73154	+	1.99830i
$366$	−12.1419	+	3.56518i	−0.634666	+	0.186355i
$367$	16.2735			0.849467			0.424734	−	0.905318i	$-0.360368\pi$
$367$	16.2735			0.849467			0.424734	+	0.905318i	$0.360368\pi$
$368$	4.68219	−	1.03782i	0.244076	−	0.0541002i
$369$	−10.3972			−0.541259
$370$	−17.6764	+	5.19025i	−0.918950	+	0.269828i
$371$	19.5342	+	22.5437i	1.01417	+	1.17041i
$372$	−0.143646	+	0.0923157i	−0.00744770	+	0.00478635i
$373$	−0.992630	−	6.90390i	−0.0513965	−	0.357470i	−0.999249	−	0.0387597i	$-0.987659\pi$
$373$	−0.992630	−	6.90390i	−0.0513965	−	0.357470i	0.947852	−	0.318710i	$-0.103250\pi$
$374$	6.29997	+	4.04874i	0.325763	+	0.209355i
$375$	−7.33057	+	16.0517i	−0.378549	+	0.828907i
$376$	−3.57240	+	4.12277i	−0.184232	+	0.212615i
$377$	0.394402	−	2.74313i	0.0203127	−	0.141278i
$378$	−1.20217	−	2.63238i	−0.0618328	−	0.135395i
$379$	−15.8428	−	4.65185i	−0.813788	−	0.238950i	−0.151749	−	0.988419i	$-0.548490\pi$
$379$	−15.8428	−	4.65185i	−0.813788	−	0.238950i	−0.662039	+	0.749470i	$0.730309\pi$
$380$	−7.88047	−	2.31392i	−0.404260	−	0.118701i
$381$	3.15200	+	6.90191i	0.161482	+	0.353595i
$382$	0.901138	−	6.26755i	0.0461062	−	0.320676i
$383$	14.6610	−	16.9196i	0.749140	−	0.864553i	−0.245345	−	0.969436i	$-0.578901\pi$
$383$	14.6610	−	16.9196i	0.749140	−	0.864553i	0.994485	+	0.104883i	$0.0334467\pi$
$384$	−0.415415	+	0.909632i	−0.0211991	+	0.0464195i
$385$	−14.7114	−	9.45447i	−0.749764	−	0.481844i
$386$	0.437455	+	3.04256i	0.0222659	+	0.154862i
$387$	10.3206	−	6.63263i	0.524624	−	0.337155i
$388$	−0.572045	−	0.660175i	−0.0290412	−	0.0335153i
$389$	7.23675	−	2.12490i	0.366918	−	0.107737i	−0.0930757	−	0.995659i	$-0.529670\pi$
$389$	7.23675	−	2.12490i	0.366918	−	0.107737i	0.459994	+	0.887922i	$0.347852\pi$
$390$	−18.0059			−0.911763
$391$	−1.70994	−	22.6573i	−0.0864752	−	1.14583i
$392$	1.37462			0.0694290
$393$	17.0872	−	5.01725i	0.861934	−	0.253087i
$394$	0.630903	+	0.728101i	0.0317844	+	0.0366812i
$395$	37.5794	−	24.1508i	1.89082	−	1.21516i
$396$	0.224949	+	1.56456i	0.0113041	+	0.0786220i
$397$	24.1929	+	15.5478i	1.21421	+	0.780323i	0.981358	−	0.192190i	$-0.0615589\pi$
$397$	24.1929	+	15.5478i	1.21421	+	0.780323i	0.232849	+	0.972513i	$0.425195\pi$
$398$	1.35977	−	2.97748i	0.0681592	−	0.149248i
$399$	4.07128	−	4.69851i	0.203819	−	0.235220i
$400$	−1.36847	+	9.51790i	−0.0684234	+	0.475895i
$401$	2.83133	+	6.19974i	0.141390	+	0.309600i	0.967058	−	0.254555i	$-0.0819291\pi$
$401$	2.83133	+	6.19974i	0.141390	+	0.309600i	−0.825668	+	0.564156i	$0.809202\pi$
$402$	5.63806	+	1.65548i	0.281201	+	0.0825680i
$403$	−0.771635	−	0.226573i	−0.0384379	−	0.0112864i
$404$	−4.53230	−	9.92434i	−0.225490	−	0.493755i
$405$	−0.544078	+	3.78415i	−0.0270355	+	0.188036i
$406$	1.11511	−	1.28690i	0.0553419	−	0.0638680i
$407$	−3.16415	+	6.92852i	−0.156841	+	0.343434i
$408$	3.98569	+	2.56145i	0.197321	+	0.126811i
$409$	3.95559	+	27.5118i	0.195592	+	1.36037i	0.816889	+	0.576794i	$0.195697\pi$
$409$	3.95559	+	27.5118i	0.195592	+	1.36037i	−0.621298	+	0.783574i	$0.713394\pi$
$410$	−33.4392	+	21.4901i	−1.65145	+	1.06132i
$411$	−0.499638	−	0.576613i	−0.0246453	−	0.0284422i
$412$	−3.54321	+	1.04038i	−0.174561	+	0.0512558i
$413$	−5.50628			−0.270947
$414$	3.37782	−	3.40446i	0.166011	−	0.167320i
$415$	−0.432953			−0.0212528
$416$	−4.51903	+	1.32691i	−0.221564	+	0.0650570i
$417$	6.04182	+	6.97264i	0.295869	+	0.341452i
$418$	−2.85668	+	1.83587i	−0.139725	+	0.0897956i
$419$	2.15488	+	14.9875i	0.105273	+	0.732189i	0.972268	+	0.233871i	$0.0751395\pi$
$419$	2.15488	+	14.9875i	0.105273	+	0.732189i	−0.866995	+	0.498317i	$0.833951\pi$
$420$	−9.30723	−	5.98139i	−0.454146	−	0.291862i
$421$	15.8458	−	34.6974i	0.772276	−	1.69105i	0.0507004	−	0.998714i	$-0.483855\pi$
$421$	15.8458	−	34.6974i	0.772276	−	1.69105i	0.721576	−	0.692335i	$-0.243418\pi$
$422$	15.9900	−	18.4535i	0.778382	−	0.898301i
$423$	−0.776356	+	5.39968i	−0.0377477	+	0.262541i
$424$	−4.28201	−	9.37628i	−0.207953	−	0.455353i
$425$	43.7122	+	12.8351i	2.12035	+	0.622592i
$426$	−11.3427	−	3.33053i	−0.549558	−	0.161365i
$427$	−15.2128	−	33.3114i	−0.736198	−	1.61205i
$428$	−1.53223	+	10.6569i	−0.0740629	+	0.515119i
$429$	−4.87514	+	5.62621i	−0.235374	+	0.271636i
$430$	19.4836	−	42.6632i	0.939584	−	2.05740i
$431$	8.59239	+	5.52199i	0.413881	+	0.265985i	0.730969	−	0.682411i	$-0.239069\pi$
$431$	8.59239	+	5.52199i	0.413881	+	0.265985i	−0.317088	+	0.948396i	$0.602705\pi$
$432$	0.142315	+	0.989821i	0.00684713	+	0.0476228i
$433$	−8.26339	+	5.31056i	−0.397113	+	0.255209i	−0.723923	−	0.689881i	$-0.757663\pi$
$433$	−8.26339	+	5.31056i	−0.397113	+	0.255209i	0.326810	+	0.945090i	$0.394026\pi$
$434$	−0.323592	−	0.373446i	−0.0155329	−	0.0179260i
$435$	−2.15843	+	0.633773i	−0.103489	+	0.0303871i
$436$	−8.31357			−0.398148
$437$	9.66745	+	3.56259i	0.462457	+	0.170422i
$438$	13.2135			0.631367
$439$	7.48022	−	2.19639i	0.357011	−	0.104828i	−0.0983084	−	0.995156i	$-0.531343\pi$
$439$	7.48022	−	2.19639i	0.357011	−	0.104828i	0.455320	+	0.890328i	$0.349525\pi$
$440$	3.95726	+	4.56692i	0.188655	+	0.217719i
$441$	1.15641	−	0.743178i	0.0550670	−	0.0353894i
$442$	3.17563	+	22.0870i	0.151049	+	1.05057i
$443$	−23.7409	−	15.2573i	−1.12796	−	0.724898i	−0.162829	−	0.986654i	$-0.552062\pi$
$443$	−23.7409	−	15.2573i	−1.12796	−	0.724898i	−0.965134	+	0.261756i	$0.915698\pi$
$444$	−2.00181	+	4.38335i	−0.0950016	+	0.208024i
$445$	30.6403	−	35.3608i	1.45249	−	1.67626i
$446$	−2.16306	+	15.0444i	−0.102424	+	0.712373i
$447$	−7.68147	−	16.8201i	−0.363321	−	0.795562i
$448$	−2.77667	−	0.815304i	−0.131185	−	0.0385195i
$449$	12.2407	+	3.59418i	0.577673	+	0.169620i	0.557501	−	0.830176i	$-0.311760\pi$
$449$	12.2407	+	3.59418i	0.577673	+	0.169620i	0.0201722	+	0.999797i	$0.493579\pi$
$450$	3.99454	+	8.74682i	0.188304	+	0.412329i
$451$	−2.33885	+	16.2671i	−0.110132	+	0.765987i
$452$	−4.91983	+	5.67778i	−0.231409	+	0.267060i
$453$	0.412045	−	0.902252i	0.0193596	−	0.0423915i
$454$	10.8795	+	6.99182i	0.510599	+	0.328142i
$455$	−7.41562	−	51.5767i	−0.347649	−	2.41796i
$456$	−1.80728	+	1.16147i	−0.0846338	+	0.0543909i
$457$	−6.13629	−	7.08166i	−0.287044	−	0.331266i	0.593854	−	0.804573i	$-0.297606\pi$
$457$	−6.13629	−	7.08166i	−0.287044	−	0.331266i	−0.880898	+	0.473307i	$0.843060\pi$
$458$	0.910081	−	0.267224i	0.0425253	−	0.0124865i
$459$	4.73780			0.221142
$460$	3.82694	−	17.9309i	0.178432	−	0.836033i
$461$	−11.6569			−0.542916			−0.271458	−	0.962450i	$-0.587506\pi$
$461$	−11.6569			−0.542916			−0.271458	+	0.962450i	$0.587506\pi$
$462$	−4.38893	+	1.28871i	−0.204192	+	0.0599561i
$463$	−8.92436	−	10.2993i	−0.414750	−	0.478647i	0.509480	−	0.860482i	$-0.329838\pi$
$463$	−8.92436	−	10.2993i	−0.414750	−	0.478647i	−0.924230	+	0.381835i	$0.875292\pi$
$464$	−0.495008	+	0.318122i	−0.0229802	+	0.0147685i
$465$	0.0929026	+	0.646152i	0.00430825	+	0.0299646i
$466$	11.7340	+	7.54097i	0.543566	+	0.349329i
$467$	2.73218	−	5.98265i	0.126430	−	0.276844i	−0.835823	−	0.548999i	$-0.815009\pi$
$467$	2.73218	−	5.98265i	0.126430	−	0.276844i	0.962253	+	0.272155i	$0.0877364\pi$
$468$	−3.08427	+	3.55944i	−0.142570	+	0.164535i
$469$	−2.42003	+	16.8317i	−0.111747	+	0.777215i
$470$	8.66371	+	18.9709i	0.399627	+	0.875062i
$471$	7.78122	+	2.28477i	0.358540	+	0.105277i
$472$	1.82565	+	0.536060i	0.0840324	+	0.0246741i
$473$	−8.05552	−	17.6391i	−0.370393	−	0.811048i
$474$	1.66288	−	11.5656i	0.0763788	−	0.531226i
$475$	−13.5280	+	15.6121i	−0.620706	+	0.716333i
$476$	−5.69563	+	12.4717i	−0.261059	+	0.571639i
$477$	−8.67145	−	5.57281i	−0.397039	−	0.255161i
$478$	0.347717	+	2.41842i	0.0159042	+	0.110616i
$479$	7.77358	−	4.99577i	0.355184	−	0.228263i	−0.350865	−	0.936426i	$-0.614112\pi$
$479$	7.77358	−	4.99577i	0.355184	−	0.228263i	0.706049	+	0.708163i	$0.250476\pi$
$480$	2.50357	+	2.88927i	0.114272	+	0.131877i
$481$	−21.7764	+	6.39412i	−0.992917	+	0.291547i
$482$	10.8636			0.494822
$483$	11.1430	+	8.27346i	0.507024	+	0.376455i
$484$	−8.50156			−0.386434
$485$	−3.20431	+	0.940870i	−0.145500	+	0.0427227i
$486$	0.654861	+	0.755750i	0.0297051	+	0.0342815i
$487$	−31.9883	+	20.5576i	−1.44953	+	0.931556i	−0.450277	+	0.892889i	$0.648675\pi$
$487$	−31.9883	+	20.5576i	−1.44953	+	0.931556i	−0.999252	+	0.0386669i	$0.987689\pi$
$488$	1.80092	+	12.5257i	0.0815237	+	0.567010i
$489$	19.4127	+	12.4758i	0.877873	+	0.564175i
$490$	2.18312	−	4.78036i	0.0986231	−	0.215955i
$491$	2.80715	−	3.23963i	0.126685	−	0.146202i	−0.688863	−	0.724891i	$-0.741890\pi$
$491$	2.80715	−	3.23963i	0.126685	−	0.146202i	0.815548	+	0.578689i	$0.196435\pi$
$492$	−1.47968	+	10.2914i	−0.0667092	+	0.463973i
$493$	1.15810	+	2.53588i	0.0521580	+	0.114210i
$494$	−9.70834	−	2.85062i	−0.436799	−	0.128256i
$495$	5.79812	+	1.70248i	0.260606	+	0.0765209i
$496$	0.0709331	+	0.155322i	0.00318499	+	0.00697416i
$497$	4.86866	−	33.8623i	0.218389	−	1.51893i
$498$	−0.0741615	+	0.0855869i	−0.00332326	+	0.00383524i
$499$	−12.5785	+	27.5431i	−0.563091	+	1.23300i	0.387304	+	0.921952i	$0.373407\pi$
$499$	−12.5785	+	27.5431i	−0.563091	+	1.23300i	−0.950395	+	0.311046i	$0.899321\pi$
$500$	14.8451	+	9.54036i	0.663892	+	0.426658i
$501$	−0.752109	−	5.23103i	−0.0336018	−	0.233705i
$502$	−12.0477	+	7.74258i	−0.537714	+	0.345568i
$503$	−7.63837	−	8.81514i	−0.340578	−	0.393048i	0.559462	−	0.828856i	$-0.311008\pi$
$503$	−7.63837	−	8.81514i	−0.340578	−	0.393048i	−0.900039	+	0.435808i	$0.856463\pi$
$504$	−2.77667	+	0.815304i	−0.123683	+	0.0363165i
$505$	−41.7107			−1.85610
$506$	−4.56663	−	6.05063i	−0.203011	−	0.268983i
$507$	−9.18232			−0.407801
$508$	7.28023	−	2.13767i	0.323008	−	0.0948437i
$509$	10.0217	+	11.5656i	0.444203	+	0.512638i	0.933057	−	0.359728i	$-0.117130\pi$
$509$	10.0217	+	11.5656i	0.444203	+	0.512638i	−0.488854	+	0.872366i	$0.662585\pi$
$510$	15.2375	−	9.79257i	0.674729	−	0.433622i
$511$	5.44192	+	37.8494i	0.240736	+	1.67436i
$512$	0.841254	+	0.540641i	0.0371785	+	0.0238932i
$513$	−0.892446	+	1.95418i	−0.0394024	+	0.0862793i
$514$	2.77942	−	3.20763i	0.122595	−	0.141482i
$515$	−2.00917	+	13.9741i	−0.0885345	+	0.615771i
$516$	−5.09635	−	11.1594i	−0.224354	−	0.491267i
$517$	8.27346	+	2.42931i	0.363866	+	0.106841i
$518$	−13.3803	−	3.92880i	−0.587895	−	0.172622i
$519$	−5.97807	−	13.0902i	−0.262408	−	0.574594i
$520$	−2.56250	+	17.8226i	−0.112373	+	0.781573i
$521$	−1.26434	+	1.45913i	−0.0553918	+	0.0639256i	−0.782769	−	0.622312i	$-0.786194\pi$
$521$	−1.26434	+	1.45913i	−0.0553918	+	0.0639256i	0.727377	+	0.686238i	$0.240739\pi$
$522$	−0.244437	+	0.535243i	−0.0106987	+	0.0234270i
$523$	−15.3733	−	9.87985i	−0.672229	−	0.432016i	0.159499	−	0.987198i	$-0.449012\pi$
$523$	−15.3733	−	9.87985i	−0.672229	−	0.432016i	−0.831729	+	0.555183i	$0.812648\pi$
$524$	−2.53442	−	17.6273i	−0.110717	−	0.770051i
$525$	−23.4096	+	15.0444i	−1.02168	+	0.656593i
$526$	4.65197	+	5.36866i	0.202836	+	0.234085i
$527$	0.776221	−	0.227919i	0.0338127	−	0.00992831i
$528$	1.58065			0.0687888
$529$	−6.30632	+	22.1186i	−0.274188	+	0.961676i
$530$	−39.4072			−1.71174
$531$	1.82565	−	0.536060i	0.0792265	−	0.0232630i
$532$	−4.07128	−	4.69851i	−0.176512	−	0.203706i
$533$	−41.1954	+	26.4747i	−1.78437	+	1.14675i
$534$	−1.74174	−	12.1141i	−0.0753724	−	0.524227i
$535$	34.6266	+	22.2532i	1.49704	+	0.962089i
$536$	2.44101	−	5.34507i	0.105436	−	0.230872i
$537$	7.33448	−	8.46445i	0.316506	−	0.365268i
$538$	1.10043	−	7.65364i	0.0474428	−	0.329972i
$539$	−0.902611	−	1.97644i	−0.0388782	−	0.0851314i
$540$	3.66820	+	1.07708i	0.157854	+	0.0463501i
$541$	−42.6494	−	12.5230i	−1.83364	−	0.538405i	−0.833734	−	0.552167i	$-0.813801\pi$
$541$	−42.6494	−	12.5230i	−1.83364	−	0.538405i	−0.999905	+	0.0137620i	$0.995619\pi$
$542$	−2.11055	−	4.62146i	−0.0906558	−	0.198509i
$543$	1.25161	−	8.70516i	0.0537118	−	0.373574i
$544$	3.10260	−	3.58059i	0.133023	−	0.153517i
$545$	−13.2032	+	28.9111i	−0.565565	+	1.23841i
$546$	−11.4660	−	7.36877i	−0.490701	−	0.315354i
$547$	−2.71929	−	18.9131i	−0.116268	−	0.808665i	−0.961606	−	0.274433i	$-0.911510\pi$
$547$	−2.71929	−	18.9131i	−0.116268	−	0.808665i	0.845338	−	0.534232i	$-0.179399\pi$
$548$	−0.641849	+	0.412491i	−0.0274184	+	0.0176208i
$549$	8.28691	+	9.56361i	0.353677	+	0.408165i
$550$	14.5835	−	4.28209i	0.621841	−	0.182589i
$551$	−1.26411			−0.0538529
$552$	−2.88909	−	3.82794i	−0.122968	−	0.162928i
$553$	33.8138			1.43791
$554$	14.7675	−	4.33613i	0.627411	−	0.184224i
$555$	12.0642	+	13.9229i	0.512099	+	0.590993i
$556$	7.76151	−	4.98802i	0.329161	−	0.211539i
$557$	6.27333	+	43.6320i	0.265809	+	1.84875i	0.486856	+	0.873482i	$0.338144\pi$
$557$	6.27333	+	43.6320i	0.265809	+	1.84875i	−0.221047	+	0.975263i	$0.570947\pi$
$558$	0.143646	+	0.0923157i	0.00608102	+	0.00390804i
$559$	24.0028	−	52.5589i	1.01521	−	2.22300i
$560$	−7.24507	+	8.36126i	−0.306160	+	0.353328i
$561$	1.06577	−	7.41256i	0.0449966	−	0.312958i
$562$	−1.37069	−	3.00140i	−0.0578192	−	0.126606i
$563$	−37.8423	−	11.1115i	−1.59486	−	0.468294i	−0.640751	−	0.767749i	$-0.721377\pi$
$563$	−37.8423	−	11.1115i	−1.59486	−	0.468294i	−0.954110	+	0.299455i	$0.903195\pi$
$564$	5.23423	+	1.53691i	0.220401	+	0.0647155i
$565$	11.9315	+	26.1263i	0.501961	+	1.09914i
$566$	3.68348	−	25.6192i	0.154828	−	1.07685i
$567$	−1.89510	+	2.18706i	−0.0795866	+	0.0918479i
$568$	−4.91087	+	10.7533i	−0.206056	+	0.451199i
$569$	−32.2425	−	20.7210i	−1.35168	−	0.868669i	−0.353897	−	0.935284i	$-0.615144\pi$
$569$	−32.2425	−	20.7210i	−1.35168	−	0.868669i	−0.997779	+	0.0666150i	$0.978780\pi$
$570$	1.16886	+	8.12957i	0.0489580	+	0.340510i
$571$	−14.2767	+	9.17508i	−0.597462	+	0.383965i	−0.804137	−	0.594444i	$-0.797372\pi$
$571$	−14.2767	+	9.17508i	−0.597462	+	0.383965i	0.206675	+	0.978410i	$0.433736\pi$
$572$	4.87514	+	5.62621i	0.203840	+	0.235244i
$573$	−6.07551	+	1.78393i	−0.253808	+	0.0745248i
$574$	−30.0885			−1.25587
$575$	−37.0257	−	27.4909i	−1.54408	−	1.14645i
$576$	1.00000			0.0416667
$577$	27.9974	−	8.22079i	1.16555	−	0.342236i	0.358962	−	0.933352i	$-0.383131\pi$
$577$	27.9974	−	8.22079i	1.16555	−	0.342236i	0.806586	+	0.591116i	$0.201313\pi$
$578$	−3.56686	−	4.11638i	−0.148362	−	0.171219i
$579$	2.58589	−	1.66185i	0.107466	−	0.0690641i
$580$	0.320145	+	2.22666i	0.0132933	+	0.0924569i
$581$	−0.275701	−	0.177183i	−0.0114380	−	0.00735077i
$582$	−0.362880	+	0.794597i	−0.0150419	+	0.0329371i
$583$	−10.6696	+	12.3134i	−0.441890	+	0.509968i
$584$	1.88048	−	13.0790i	0.0778149	−	0.541215i
$585$	7.47991	+	16.3787i	0.309256	+	0.677177i
$586$	−6.26134	−	1.83850i	−0.258654	−	0.0759476i
$587$	14.5667	+	4.27716i	0.601231	+	0.176537i	0.568163	−	0.822916i	$-0.307654\pi$
$587$	14.5667	+	4.27716i	0.601231	+	0.176537i	0.0330675	+	0.999453i	$0.489472\pi$
$588$	−0.571039	−	1.25040i	−0.0235493	−	0.0515657i
$589$	−0.0522055	+	0.363097i	−0.00215109	+	0.0149612i
$590$	4.76361	−	5.49750i	0.196115	−	0.226328i
$591$	0.400217	−	0.876353i	0.0164627	−	0.0360484i
$592$	4.05384	+	2.60525i	0.166612	+	0.107075i
$593$	4.44889	+	30.9427i	0.182694	+	1.27066i	0.850359	+	0.526203i	$0.176385\pi$
$593$	4.44889	+	30.9427i	0.182694	+	1.27066i	−0.667665	+	0.744462i	$0.732706\pi$
$594$	1.32972	−	0.854562i	0.0545592	−	0.0350631i
$595$	34.3257	+	39.6140i	1.40722	+	1.62401i
$596$	−17.7421	+	5.20954i	−0.726743	+	0.213391i
$597$	−3.27328			−0.133967
$598$	4.71460	−	22.0899i	0.192794	−	0.903325i
$599$	−30.8576			−1.26081			−0.630405	−	0.776267i	$-0.717111\pi$
$599$	−30.8576			−1.26081			−0.630405	+	0.776267i	$0.717111\pi$
$600$	9.22627	−	2.70908i	0.376661	−	0.110598i
$601$	−4.34025	−	5.00891i	−0.177042	−	0.204318i	0.660292	−	0.751009i	$-0.270433\pi$
$601$	−4.34025	−	5.00891i	−0.177042	−	0.204318i	−0.837334	+	0.546691i	$0.815887\pi$
$602$	29.8666	−	19.1941i	1.21727	−	0.782294i
$603$	−0.836254	−	5.81627i	−0.0340549	−	0.236857i
$604$	−0.834429	−	0.536255i	−0.0339524	−	0.0218199i
$605$	−13.5018	+	29.5648i	−0.548926	+	1.20198i
$606$	−7.14472	+	8.24544i	−0.290234	+	0.334948i
$607$	3.35546	−	23.3377i	0.136194	−	0.947250i	−0.801055	−	0.598590i	$-0.795728\pi$
$607$	3.35546	−	23.3377i	0.136194	−	0.947250i	0.937249	−	0.348660i	$-0.113363\pi$
$608$	0.892446	+	1.95418i	0.0361934	+	0.0792526i
$609$	−1.63384	−	0.479739i	−0.0662066	−	0.0194400i
$610$	46.4191	+	13.6299i	1.87945	+	0.551857i
$611$	10.6732	+	23.3712i	0.431793	+	0.945496i
$612$	0.674259	−	4.68958i	0.0272553	−	0.189565i
$613$	21.3290	−	24.6150i	0.861469	−	0.994189i	−0.138523	−	0.990359i	$-0.544236\pi$
$613$	21.3290	−	24.6150i	0.861469	−	0.994189i	0.999993	−	0.00382949i	$-0.00121897\pi$
$614$	1.91808	−	4.20001i	0.0774074	−	0.169499i
$615$	33.4392	+	21.4901i	1.34840	+	0.866564i
$616$	0.650980	+	4.52766i	0.0262287	+	0.182425i
$617$	−5.04770	+	3.24396i	−0.203213	+	0.130597i	−0.638289	−	0.769797i	$-0.720358\pi$
$617$	−5.04770	+	3.24396i	−0.203213	+	0.130597i	0.435077	+	0.900393i	$0.356721\pi$
$618$	2.41826	+	2.79083i	0.0972769	+	0.112263i
$619$	12.3649	−	3.63066i	0.496986	−	0.145928i	−0.0236271	−	0.999721i	$-0.507521\pi$
$619$	12.3649	−	3.63066i	0.496986	−	0.145928i	0.520613	+	0.853792i	$0.325703\pi$
$620$	0.652796			0.0262169
$621$	−4.50000	−	1.65831i	−0.180579	−	0.0665458i
$622$	−10.7400			−0.430636
$623$	33.9827	−	9.97821i	1.36149	−	0.399768i
$624$	3.08427	+	3.55944i	0.123470	+	0.142492i
$625$	16.3071	−	10.4799i	0.652284	−	0.419197i
$626$	−3.79837	−	26.4182i	−0.151813	−	1.05588i
$627$	2.85668	+	1.83587i	0.114085	+	0.0733178i
$628$	3.36890	−	7.37686i	0.134434	−	0.294369i
$629$	14.9508	−	17.2542i	0.596129	−	0.687970i
$630$	−1.57450	+	10.9509i	−0.0627297	+	0.436295i
$631$	8.90725	+	19.5041i	0.354592	+	0.776448i	0.999921	+	0.0125435i	$0.00399282\pi$
$631$	8.90725	+	19.5041i	0.354592	+	0.776448i	−0.645329	+	0.763904i	$0.723280\pi$
$632$	−11.2112	−	3.29192i	−0.445959	−	0.130945i
$633$	−23.4284	−	6.87919i	−0.931193	−	0.273423i
$634$	7.96824	+	17.4480i	0.316459	+	0.692949i
$635$	4.12824	−	28.7125i	0.163824	−	1.13942i
$636$	−6.75016	+	7.79010i	−0.267661	+	0.308897i
$637$	2.68949	−	5.88915i	0.106561	−	0.233337i
$638$	0.782433	+	0.502839i	0.0309768	+	0.0199076i
$639$	1.68239	+	11.7013i	0.0665543	+	0.462895i
$640$	3.21616	−	2.06690i	0.127130	−	0.0817015i
$641$	−20.1426	−	23.2459i	−0.795587	−	0.918156i	0.202544	−	0.979273i	$-0.435079\pi$
$641$	−20.1426	−	23.2459i	−0.795587	−	0.918156i	−0.998131	+	0.0611172i	$0.980534\pi$
$642$	10.3303	−	3.03326i	0.407706	−	0.119713i
$643$	28.7980			1.13568			0.567842	−	0.823138i	$-0.307778\pi$
$643$	28.7980			1.13568			0.567842	+	0.823138i	$0.307778\pi$
$644$	9.77506	−	9.85214i	0.385191	−	0.388229i
$645$	−46.9016			−1.84675
$646$	9.76603	−	2.86757i	0.384239	−	0.112823i
$647$	13.6600	+	15.7645i	0.537031	+	0.619767i	0.957812	−	0.287395i	$-0.0927893\pi$
$647$	13.6600	+	15.7645i	0.537031	+	0.619767i	−0.420781	+	0.907162i	$0.638244\pi$
$648$	0.841254	−	0.540641i	0.0330476	−	0.0212384i
$649$	−0.428017	−	2.97692i	−0.0168011	−	0.116854i
$650$	38.0991	+	24.4848i	1.49437	+	0.960373i
$651$	−0.205273	+	0.449485i	−0.00804528	+	0.0176167i
$652$	15.1115	−	17.4396i	0.591813	−	0.682989i
$653$	−3.78327	+	26.3132i	−0.148051	+	1.02972i	0.771355	+	0.636406i	$0.219580\pi$
$653$	−3.78327	+	26.3132i	−0.148051	+	1.02972i	−0.919405	+	0.393311i	$0.871330\pi$
$654$	3.45358	+	7.56229i	0.135046	+	0.295709i
$655$	−65.3253	−	19.1812i	−2.55247	−	0.749473i
$656$	9.97609	+	2.92924i	0.389501	+	0.114368i
$657$	−5.48910	−	12.0195i	−0.214150	−	0.468924i
$658$	−2.24669	+	15.6261i	−0.0875852	+	0.609169i
$659$	17.9541	−	20.7202i	0.699394	−	0.807144i	−0.289276	−	0.957246i	$-0.593415\pi$
$659$	17.9541	−	20.7202i	0.699394	−	0.807144i	0.988671	+	0.150102i	$0.0479601\pi$
$660$	2.51031	−	5.49682i	0.0977138	−	0.213963i
$661$	6.84724	+	4.40046i	0.266327	+	0.171158i	0.666988	−	0.745068i	$-0.267583\pi$
$661$	6.84724	+	4.40046i	0.266327	+	0.171158i	−0.400661	+	0.916226i	$0.631220\pi$
$662$	−1.24393	−	8.65169i	−0.0483465	−	0.336257i
$663$	18.7718	−	12.0639i	0.729038	−	0.468524i
$664$	0.0741615	+	0.0855869i	0.00287802	+	0.00332142i
$665$	−22.8053	+	6.69623i	−0.884350	+	0.259669i
$666$	4.81881			0.186725
$667$	−0.212368	−	2.81395i	−0.00822292	−	0.108957i
$668$	−5.28482			−0.204476
$669$	14.5834	−	4.28209i	0.563829	−	0.165555i
$670$	−14.7112	−	16.9776i	−0.568343	−	0.655903i
$671$	16.8269	−	10.8140i	0.649597	−	0.417471i
$672$	0.411844	+	2.86444i	0.0158872	+	0.110498i
$673$	26.0896	+	16.7667i	1.00568	+	0.646310i	0.936271	−	0.351278i	$-0.114253\pi$
$673$	26.0896	+	16.7667i	1.00568	+	0.646310i	0.0694072	+	0.997588i	$0.477889\pi$
$674$	−1.35173	+	2.95989i	−0.0520669	+	0.114011i
$675$	6.29699	−	7.26712i	0.242371	−	0.279712i
$676$	−1.30678	+	9.08886i	−0.0502608	+	0.349571i
$677$	−8.47632	−	18.5606i	−0.325772	−	0.713340i	0.673904	−	0.738819i	$-0.264616\pi$
$677$	−8.47632	−	18.5606i	−0.325772	−	0.713340i	−0.999675	+	0.0254788i	$0.991889\pi$
$678$	7.20846	+	2.11660i	0.276839	+	0.0812874i
$679$	−2.42553	−	0.712199i	−0.0930831	−	0.0273317i
$680$	−7.52436	−	16.4761i	−0.288546	−	0.631828i
$681$	1.84048	−	12.8008i	0.0705274	−	0.490529i
$682$	0.176746	−	0.203976i	0.00676797	−	0.00781065i
$683$	8.63468	−	18.9073i	0.330397	−	0.723468i	−0.669414	−	0.742889i	$-0.733455\pi$
$683$	8.63468	−	18.9073i	0.330397	−	0.723468i	0.999811	+	0.0194207i	$0.00618219\pi$
$684$	1.80728	+	1.16147i	0.0691032	+	0.0444100i
$685$	0.415114	+	2.88718i	0.0158607	+	0.110314i
$686$	−13.6950	+	8.80122i	−0.522876	+	0.336032i
$687$	−0.621137	−	0.716830i	−0.0236978	−	0.0273488i
$688$	−11.7711	+	3.45632i	−0.448770	+	0.131771i
$689$	−48.5477			−1.84952
$690$	−17.9003	+	3.96766i	−0.681453	+	0.151046i
$691$	−13.6695			−0.520012			−0.260006	−	0.965607i	$-0.583725\pi$
$691$	−13.6695			−0.520012			−0.260006	+	0.965607i	$0.583725\pi$
$692$	−13.8077	+	4.05430i	−0.524890	+	0.154121i
$693$	2.99548	+	3.45697i	0.113789	+	0.131319i
$694$	−4.38443	+	2.81770i	−0.166431	+	0.106959i
$695$	−5.01973	−	34.9130i	−0.190409	−	1.32432i
$696$	0.495008	+	0.318122i	0.0187632	+	0.0120584i
$697$	20.4634	−	44.8085i	0.775106	−	1.69724i
$698$	−10.1327	+	11.6938i	−0.383529	+	0.442616i
$699$	1.98504	−	13.8062i	0.0750810	−	0.522200i
$700$	11.5598	+	25.3124i	0.436918	+	0.956718i
$701$	2.12031	+	0.622581i	0.0800832	+	0.0235145i	0.321529	−	0.946900i	$-0.395803\pi$
$701$	2.12031	+	0.622581i	0.0800832	+	0.0235145i	−0.241446	+	0.970414i	$0.577622\pi$
$702$	4.51903	+	1.32691i	0.170560	+	0.0500809i
$703$	4.30053	+	9.41685i	0.162198	+	0.355163i
$704$	0.224949	−	1.56456i	0.00847810	−	0.0589665i
$705$	13.6575	−	15.7616i	0.514371	−	0.593615i
$706$	−0.671574	+	1.47054i	−0.0252750	+	0.0553446i
$707$	−26.5611	−	17.0698i	−0.998932	−	0.641975i
$708$	−0.270786	−	1.88336i	−0.0101768	−	0.0707809i
$709$	−15.7884	+	10.1466i	−0.592946	+	0.381063i	−0.802428	−	0.596749i	$-0.796459\pi$
$709$	−15.7884	+	10.1466i	−0.592946	+	0.381063i	0.209482	+	0.977813i	$0.432822\pi$
$710$	29.5962	+	34.1559i	1.11073	+	1.28185i
$711$	−11.2112	+	3.29192i	−0.420454	+	0.123456i
$712$	−12.2386			−0.458662
$713$	−0.817036	−	0.0552115i	−0.0305982	−	0.00206769i
$714$	13.7107			0.513110
$715$	27.3081	−	8.01837i	1.02126	−	0.299870i
$716$	−7.33448	−	8.46445i	−0.274103	−	0.316331i
$717$	2.05543	−	1.32094i	0.0767614	−	0.0493316i
$718$	−1.92950	−	13.4199i	−0.0720082	−	0.500828i
$719$	17.3887	+	11.1751i	0.648490	+	0.416759i	0.823114	−	0.567876i	$-0.192235\pi$
$719$	17.3887	+	11.1751i	0.648490	+	0.416759i	−0.174624	+	0.984635i	$0.555871\pi$
$720$	1.58816	−	3.47758i	0.0591871	−	0.129602i
$721$	−6.99820	+	8.07636i	−0.260627	+	0.300779i
$722$	2.04716	−	14.2383i	0.0761873	−	0.529894i
$723$	−4.51289	−	9.88185i	−0.167836	−	0.367510i
$724$	−8.43843	−	2.47775i	−0.313612	−	0.0920847i
$725$	5.42890	+	1.59407i	0.201624	+	0.0592022i
$726$	3.53167	+	7.73329i	0.131073	+	0.287009i
$727$	4.48938	−	31.2244i	0.166502	−	1.15805i	−0.719543	−	0.694448i	$-0.755649\pi$
$727$	4.48938	−	31.2244i	0.166502	−	1.15805i	0.886045	−	0.463599i	$-0.153442\pi$
$728$	−8.92555	+	10.3006i	−0.330803	+	0.381767i
$729$	0.415415	−	0.909632i	0.0153857	−	0.0336901i
$730$	−42.4969	−	27.3111i	−1.57288	−	1.01083i
$731$	8.27187	+	57.5321i	0.305946	+	2.12790i
$732$	10.6456	−	6.84152i	0.393473	−	0.252870i
$733$	15.9963	+	18.4607i	0.590836	+	0.681861i	0.969898	−	0.243510i	$-0.0782988\pi$
$733$	15.9963	+	18.4607i	0.590836	+	0.681861i	−0.379062	+	0.925371i	$0.623753\pi$
$734$	−15.6143	+	4.58476i	−0.576333	+	0.169227i
$735$	−5.25527			−0.193843
$736$	−4.20014	+	2.31491i	−0.154819	+	0.0853287i
$737$	−9.28801			−0.342128
$738$	9.97609	−	2.92924i	0.367225	−	0.107827i
$739$	27.6042	+	31.8570i	1.01544	+	1.17188i	0.985038	+	0.172340i	$0.0551326\pi$
$739$	27.6042	+	31.8570i	1.01544	+	1.17188i	0.0304000	+	0.999538i	$0.490322\pi$
$740$	15.4981	−	9.96001i	0.569721	−	0.366137i
$741$	1.43997	+	10.0152i	0.0528986	+	0.367918i
$742$	−25.0943	−	16.1271i	−0.921240	−	0.592045i
$743$	1.24173	−	2.71901i	0.0455546	−	0.0997507i	−0.885486	−	0.464665i	$-0.846175\pi$
$743$	1.24173	−	2.71901i	0.0455546	−	0.0997507i	0.931041	+	0.364915i	$0.118902\pi$
$744$	0.111819	−	0.129046i	0.00409948	−	0.00473106i
$745$	−10.0606	+	69.9729i	−0.368592	+	2.56361i
$746$	2.89747	+	6.34458i	0.106084	+	0.232292i
$747$	0.108660	+	0.0319056i	0.00397568	+	0.00116736i
$748$	−7.18544	−	2.10983i	−0.262726	−	0.0771432i
$749$	12.9431	+	28.3414i	0.472930	+	1.03557i
$750$	2.51134	−	17.4668i	0.0917013	−	0.637796i
$751$	−25.6872	+	29.6446i	−0.937338	+	1.08175i	0.0591703	+	0.998248i	$0.481155\pi$
$751$	−25.6872	+	29.6446i	−0.937338	+	1.08175i	−0.996508	+	0.0834975i	$0.973391\pi$
$752$	2.26617	−	4.96223i	0.0826388	−	0.180954i
$753$	12.0477	+	7.74258i	0.439042	+	0.282155i
$754$	0.394402	+	2.74313i	0.0143633	+	0.0998988i
$755$	−3.19007	+	2.05013i	−0.116099	+	0.0746120i
$756$	1.89510	+	2.18706i	0.0689240	+	0.0795426i
$757$	45.5285	−	13.3684i	1.65476	−	0.485882i	0.684718	−	0.728808i	$-0.259926\pi$
$757$	45.5285	−	13.3684i	1.65476	−	0.485882i	0.970045	+	0.242926i	$0.0781074\pi$
$758$	16.5116			0.599728
$759$	−3.60680	+	6.66747i	−0.130918	+	0.242014i
$760$	8.21316			0.297923
$761$	29.5001	−	8.66200i	1.06938	−	0.313997i	0.300755	−	0.953701i	$-0.402761\pi$
$761$	29.5001	−	8.66200i	1.06938	−	0.313997i	0.768621	+	0.639704i	$0.220943\pi$
$762$	−4.96881	−	5.73431i	−0.180001	−	0.207732i
$763$	−20.2394	+	13.0071i	−0.732715	+	0.470887i
$764$	0.901138	+	6.26755i	0.0326020	+	0.226752i
$765$	−15.2375	−	9.79257i	−0.550914	−	0.354051i
$766$	−9.30027	+	20.3647i	−0.336032	+	0.735808i
$767$	5.86852	−	6.77263i	0.211900	−	0.244546i
$768$	0.142315	−	0.989821i	0.00513534	−	0.0357171i
$769$	−13.4905	−	29.5400i	−0.486479	−	1.06524i	−0.980631	−	0.195864i	$-0.937249\pi$
$769$	−13.4905	−	29.5400i	−0.486479	−	1.06524i	0.494153	−	0.869375i	$-0.335478\pi$
$770$	16.7792	+	4.92680i	0.604679	+	0.177550i
$771$	−4.07237	−	1.19576i	−0.146663	−	0.0430641i
$772$	−1.27692	−	2.79607i	−0.0459575	−	0.100633i
$773$	−1.76947	+	12.3070i	−0.0636435	+	0.442650i	0.932938	+	0.360037i	$0.117236\pi$
$773$	−1.76947	+	12.3070i	−0.0636435	+	0.442650i	−0.996582	+	0.0826137i	$0.973673\pi$
$774$	−8.03389	+	9.27160i	−0.288772	+	0.333261i
$775$	0.682077	−	1.49354i	0.0245009	−	0.0536495i
$776$	0.734866	+	0.472270i	0.0263802	+	0.0169535i
$777$	1.98460	+	13.8032i	0.0711971	+	0.495187i
$778$	−6.34496	+	4.07766i	−0.227478	+	0.146191i
$779$	14.6274	+	16.8809i	0.524081	+	0.604821i
$780$	17.2765	−	5.07284i	0.618599	−	0.181637i
$781$	18.6858			0.668629
$782$	8.02396	+	21.2577i	0.286936	+	0.760175i
$783$	0.588417			0.0210283
$784$	−1.31894	+	0.387276i	−0.0471051	+	0.0138313i
$785$	−20.3033	−	23.4312i	−0.724654	−	0.836296i
$786$	−14.9815	+	9.62803i	−0.534372	+	0.343420i
$787$	0.584258	+	4.06361i	0.0208266	+	0.144852i	0.997581	−	0.0695074i	$-0.0221428\pi$
$787$	0.584258	+	4.06361i	0.0208266	+	0.144852i	−0.976755	+	0.214359i	$0.931234\pi$
$788$	−0.810476	−	0.520862i	−0.0288720	−	0.0185549i
$789$	2.95101	−	6.46180i	0.105059	−	0.230046i
$790$	−29.2531	+	33.7598i	−1.04078	+	1.20112i
$791$	−3.09410	+	21.5199i	−0.110013	+	0.765160i
$792$	−0.656624	−	1.43781i	−0.0233321	−	0.0510902i
$793$	57.1859	+	16.7913i	2.03073	+	0.596277i
$794$	−27.5932	−	8.10211i	−0.979248	−	0.287533i
$795$	16.3704	+	35.8461i	0.580597	+	1.27133i
$796$	−0.465837	+	3.23997i	−0.0165111	+	0.114838i
$797$	25.2895	−	29.1857i	0.895801	−	1.03381i	−0.103432	−	0.994637i	$-0.532982\pi$
$797$	25.2895	−	29.1857i	0.895801	−	1.03381i	0.999232	−	0.0391727i	$-0.0124722\pi$
$798$	−2.58264	+	5.65520i	−0.0914246	+	0.200192i
$799$	−21.7428	−	13.9732i	−0.769203	−	0.494337i
$800$	−1.36847	−	9.51790i	−0.0483826	−	0.336509i
$801$	−10.2958	+	6.61670i	−0.363784	+	0.233790i
$802$	−4.46331	−	5.15093i	−0.157605	−	0.181886i
$803$	−20.0399	+	5.88425i	−0.707193	+	0.207651i
$804$	−5.87608			−0.207233
$805$	−18.7372	−	49.6402i	−0.660401	−	1.74959i
$806$	0.804211			0.0283271
$807$	−7.41913	+	2.17845i	−0.261166	+	0.0766852i
$808$	7.14472	+	8.24544i	0.251350	+	0.290074i
$809$	30.9861	−	19.9136i	1.08941	−	0.700123i	0.132700	−	0.991156i	$-0.457635\pi$
$809$	30.9861	−	19.9136i	1.08941	−	0.700123i	0.956713	+	0.291033i	$0.0939989\pi$
$810$	−0.544078	−	3.78415i	−0.0191170	−	0.132961i
$811$	−37.6052	−	24.1674i	−1.32050	−	0.848631i	−0.325212	−	0.945641i	$-0.605436\pi$
$811$	−37.6052	−	24.1674i	−1.32050	−	0.848631i	−0.995283	+	0.0970099i	$0.969072\pi$
$812$	−0.707376	+	1.54894i	−0.0248240	+	0.0543571i
$813$	−3.32707	+	3.83965i	−0.116686	+	0.134662i
$814$	1.08399	−	7.53931i	0.0379938	−	0.264253i
$815$	−36.6482	−	80.2484i	−1.28373	−	2.81098i
$816$	−4.54589	−	1.33479i	−0.159138	−	0.0467271i
$817$	−25.2882	−	7.42529i	−0.884722	−	0.259778i
$818$	−11.5463	−	25.2829i	−0.403708	−	0.883996i
$819$	−1.93971	+	13.4910i	−0.0677789	+	0.471412i
$820$	26.0302	−	30.0405i	0.909016	−	1.04906i
$821$	15.4538	−	33.8391i	0.539341	−	1.18099i	−0.422244	−	0.906482i	$-0.638757\pi$
$821$	15.4538	−	33.8391i	0.539341	−	1.18099i	0.961584	−	0.274509i	$-0.0885154\pi$
$822$	0.641849	+	0.412491i	0.0223871	+	0.0143873i
$823$	−5.84078	−	40.6235i	−0.203597	−	1.41605i	−0.793498	−	0.608572i	$-0.791743\pi$
$823$	−5.84078	−	40.6235i	−0.203597	−	1.41605i	0.589902	−	0.807475i	$-0.299167\pi$
$824$	3.10657	−	1.99647i	0.108223	−	0.0695505i
$825$	−9.95332	−	11.4867i	−0.346530	−	0.399917i
$826$	5.28324	−	1.55130i	0.183827	−	0.0539766i
$827$	6.42848			0.223540			0.111770	−	0.993734i	$-0.464348\pi$
$827$	6.42848			0.223540			0.111770	+	0.993734i	$0.464348\pi$
$828$	−2.28185	+	4.21819i	−0.0792998	+	0.146592i
$829$	15.8721			0.551262			0.275631	−	0.961264i	$-0.411113\pi$
$829$	15.8721			0.551262			0.275631	+	0.961264i	$0.411113\pi$
$830$	0.415415	−	0.121977i	0.0144193	−	0.00423388i
$831$	−10.0789	−	11.6317i	−0.349634	−	0.403499i
$832$	3.96215	−	2.54632i	0.137363	−	0.0882776i
$833$	0.926852	+	6.44640i	0.0321135	+	0.223355i
$834$	−7.76151	−	4.98802i	−0.268759	−	0.172721i
$835$	−8.39313	+	18.3784i	−0.290456	+	0.636010i
$836$	2.22374	−	2.56633i	0.0769095	−	0.0887583i
$837$	0.0243006	−	0.169014i	0.000839951	−	0.00584199i
$838$	−6.29007	−	13.7733i	−0.217287	−	0.475792i
$839$	−10.0042	−	2.93748i	−0.345382	−	0.101413i	0.104441	−	0.994531i	$-0.466695\pi$
$839$	−10.0042	−	2.93748i	−0.345382	−	0.101413i	−0.449823	+	0.893118i	$0.648513\pi$
$840$	10.6154	+	3.11696i	0.366265	+	0.107545i
$841$	−11.9032	−	26.0644i	−0.410455	−	0.898772i
$842$	−5.42852	+	37.7562i	−0.187079	+	1.30117i
$843$	−2.16076	+	2.49365i	−0.0744206	+	0.0858860i
$844$	−10.1434	+	22.2109i	−0.349149	+	0.764530i
$845$	29.5318	+	18.9789i	1.01593	+	0.652896i
$846$	−0.776356	−	5.39968i	−0.0266917	−	0.185645i
$847$	−20.6970	+	13.3012i	−0.711158	+	0.457034i
$848$	6.75016	+	7.79010i	0.231801	+	0.267513i
$849$	−24.8342	+	7.29197i	−0.852307	+	0.250260i
$850$	−45.5576			−1.56261
$851$	−20.2397	+	11.1551i	−0.693808	+	0.382392i
$852$	11.8216			0.405001
$853$	−25.2284	+	7.40772i	−0.863803	+	0.253636i	−0.683478	−	0.729971i	$-0.739533\pi$
$853$	−25.2284	+	7.40772i	−0.863803	+	0.253636i	−0.180326	+	0.983607i	$0.557715\pi$
$854$	23.9815	+	27.6761i	0.820628	+	0.947056i
$855$	6.90935	−	4.44037i	0.236295	−	0.151858i
$856$	−1.53223	−	10.6569i	−0.0523704	−	0.364244i
$857$	27.2849	+	17.5349i	0.932033	+	0.598981i	0.916125	−	0.400892i	$-0.131300\pi$
$857$	27.2849	+	17.5349i	0.932033	+	0.598981i	0.0159081	+	0.999873i	$0.494936\pi$
$858$	3.09258	−	6.77180i	0.105579	−	0.231185i
$859$	36.1249	−	41.6904i	1.23257	−	1.42246i	0.360724	−	0.932673i	$-0.382530\pi$
$859$	36.1249	−	41.6904i	1.23257	−	1.42246i	0.871843	−	0.489785i	$-0.162925\pi$
$860$	−6.67479	+	46.4242i	−0.227609	+	1.58305i
$861$	12.4992	+	27.3695i	0.425973	+	0.932750i
$862$	−9.80006	−	2.87756i	−0.333791	−	0.0980100i
$863$	−17.4765	−	5.13157i	−0.594908	−	0.174681i	−0.0296015	−	0.999562i	$-0.509424\pi$
$863$	−17.4765	−	5.13157i	−0.594908	−	0.174681i	−0.565306	+	0.824881i	$0.691242\pi$
$864$	−0.415415	−	0.909632i	−0.0141327	−	0.0309463i
$865$	−7.82961	+	54.4562i	−0.266215	+	1.85156i
$866$	6.43251	−	7.42351i	0.218585	−	0.252261i
$867$	−2.26266	+	4.95453i	−0.0768440	+	0.168265i
$868$	0.415696	+	0.267152i	0.0141097	+	0.00906773i
$869$	2.62843	+	18.2811i	0.0891634	+	0.620145i
$870$	1.89245	−	1.21620i	0.0641599	−	0.0412331i
$871$	−18.1234	−	20.9156i	−0.614089	−	0.708696i
$872$	7.97681	−	2.34220i	0.270129	−	0.0793170i
$873$	0.873537			0.0295648
$874$	−10.2796	−	0.694644i	−0.347711	−	0.0234967i
$875$	51.0668			1.72637
$876$	−12.6783	+	3.72268i	−0.428360	+	0.125778i
$877$	18.8581	+	21.7634i	0.636791	+	0.734896i	0.978804	−	0.204799i	$-0.0656541\pi$
$877$	18.8581	+	21.7634i	0.636791	+	0.734896i	−0.342013	+	0.939695i	$0.611109\pi$
$878$	−6.55842	+	4.21484i	−0.221336	+	0.142244i
$879$	0.928701	+	6.45925i	0.0313243	+	0.217865i
$880$	−5.08361	−	3.26704i	−0.171369	−	0.110132i
$881$	−8.74991	+	19.1596i	−0.294792	+	0.645505i	−0.997844	−	0.0656341i	$-0.979093\pi$
$881$	−8.74991	+	19.1596i	−0.294792	+	0.645505i	0.703052	+	0.711139i	$0.251820\pi$
$882$	−0.900187	+	1.03887i	−0.0303109	+	0.0349806i
$883$	2.01508	−	14.0152i	0.0678127	−	0.471648i	−0.927412	−	0.374041i	$-0.877972\pi$
$883$	2.01508	−	14.0152i	0.0678127	−	0.471648i	0.995225	−	0.0976071i	$-0.0311188\pi$
$884$	−9.26963	−	20.2977i	−0.311771	−	0.682684i
$885$	−6.97957	−	2.04939i	−0.234616	−	0.0688894i
$886$	27.0777	+	7.95073i	0.909693	+	0.267110i
$887$	23.8989	+	52.3313i	0.802446	+	1.75711i	0.636954	+	0.770901i	$0.280194\pi$
$887$	23.8989	+	52.3313i	0.802446	+	1.75711i	0.165492	+	0.986211i	$0.447079\pi$
$888$	0.685789	−	4.76977i	0.0230136	−	0.160063i
$889$	14.3792	−	16.5945i	0.482263	−	0.556561i
$890$	−19.4369	+	42.5608i	−0.651525	+	1.42664i
$891$	−1.32972	−	0.854562i	−0.0445474	−	0.0286289i
$892$	−2.16306	−	15.0444i	−0.0724246	−	0.503724i
$893$	9.85910	−	6.33606i	0.329922	−	0.212028i
$894$	12.1091	+	13.9746i	0.404988	+	0.467381i
$895$	−41.0841	+	12.0634i	−1.37329	+	0.403234i
$896$	2.89389			0.0966782
$897$	−22.0522	+	4.88795i	−0.736303	+	0.163204i
$898$	−12.7574			−0.425721
$899$	0.0964038	−	0.0283067i	0.00321525	−	0.000944081i
$900$	−6.29699	−	7.26712i	−0.209900	−	0.242237i
$901$	41.0836	−	26.4028i	1.36869	−	0.879606i
$902$	−2.33885	−	16.2671i	−0.0778753	−	0.541635i
$903$	−29.8666	−	19.1941i	−0.993899	−	0.638740i
$904$	3.12092	−	6.83387i	0.103800	−	0.227291i
$905$	−22.0181	+	25.4102i	−0.731906	+	0.844665i
$906$	−0.141160	+	0.981791i	−0.00468974	+	0.0326178i
$907$	18.7643	+	41.0880i	0.623057	+	1.36430i	0.913275	+	0.407344i	$0.133545\pi$
$907$	18.7643	+	41.0880i	0.623057	+	1.36430i	−0.290218	+	0.956961i	$0.593728\pi$
$908$	−12.4086	−	3.64350i	−0.411794	−	0.120914i
$909$	10.4683	+	3.07378i	0.347213	+	0.101951i
$910$	21.6461	+	47.3983i	0.717561	+	1.57124i
$911$	−3.47784	+	24.1889i	−0.115226	+	0.801414i	0.847473	+	0.530839i	$0.178123\pi$
$911$	−3.47784	+	24.1889i	−0.115226	+	0.801414i	−0.962699	+	0.270576i	$0.912786\pi$
$912$	1.40685	−	1.62359i	0.0465855	−	0.0537626i
$913$	0.0743612	−	0.162828i	0.00246100	−	0.00538883i
$914$	7.88287	+	5.06601i	0.260742	+	0.167569i
$915$	−6.88502	−	47.8863i	−0.227612	−	1.58307i
$916$	−0.797930	+	0.512799i	−0.0263644	+	0.0169433i
$917$	−33.7489	−	38.9483i	−1.11449	−	1.28619i
$918$	−4.54589	+	1.33479i	−0.150037	+	0.0440547i
$919$	−1.40194			−0.0462457			−0.0231229	−	0.999733i	$-0.507361\pi$
$919$	−1.40194			−0.0462457			−0.0231229	+	0.999733i	$0.507361\pi$
$920$	1.37979	+	18.2828i	0.0454904	+	0.602764i
$921$	−4.61726			−0.152144
$922$	11.1847	−	3.28413i	0.368349	−	0.108157i
$923$	36.4610	+	42.0783i	1.20013	+	1.38502i
$924$	3.84808	−	2.47301i	0.126593	−	0.0813561i
$925$	−6.59439	−	45.8650i	−0.216822	−	1.50803i
$926$	11.4645	+	7.36778i	0.376747	+	0.242120i
$927$	1.53404	−	3.35908i	0.0503845	−	0.110327i
$928$	0.385331	−	0.444696i	0.0126491	−	0.0145979i
$929$	1.24366	−	8.64984i	0.0408031	−	0.283792i	−0.959196	−	0.282741i	$-0.908756\pi$
$929$	1.24366	−	8.64984i	0.0408031	−	0.283792i	0.999999	−	0.00105110i	$-0.000334576\pi$
$930$	−0.271181	−	0.593804i	−0.00889239	−	0.0194716i
$931$	−2.83351	−	0.831994i	−0.0928646	−	0.0272675i
$932$	−13.3832	−	3.92967i	−0.438382	−	0.128721i
$933$	4.46157	+	9.76947i	0.146065	+	0.319838i
$934$	−0.936004	+	6.51005i	−0.0306270	+	0.213015i
$935$	−18.7487	+	21.6372i	−0.613148	+	0.707611i
$936$	1.95653	−	4.28419i	0.0639511	−	0.140033i
$937$	6.69009	+	4.29946i	0.218556	+	0.140457i	0.645338	−	0.763897i	$-0.276717\pi$
$937$	6.69009	+	4.29946i	0.218556	+	0.140457i	−0.426782	+	0.904354i	$0.640353\pi$
$938$	−2.42003	−	16.8317i	−0.0790168	−	0.549574i
$939$	−22.4530	+	14.4296i	−0.732725	+	0.470894i
$940$	−13.6575	−	15.7616i	−0.445458	−	0.514086i
$941$	−19.8857	+	5.83896i	−0.648255	+	0.190345i	−0.589298	−	0.807916i	$-0.700596\pi$
$941$	−19.8857	+	5.83896i	−0.648255	+	0.190345i	−0.0589567	+	0.998261i	$0.518777\pi$
$942$	−8.10972			−0.264229
$943$	−35.1200	+	35.3970i	−1.14367	+	1.15268i
$944$	−1.90272			−0.0619284
$945$	10.6154	−	3.11696i	0.345318	−	0.101395i
$946$	12.6987	+	14.6551i	0.412871	+	0.476479i
$947$	46.2003	−	29.6911i	1.50131	−	0.964832i	0.506590	−	0.862187i	$-0.330906\pi$
$947$	46.2003	−	29.6911i	1.50131	−	0.964832i	0.994718	−	0.102645i	$-0.0327306\pi$
$948$	1.66288	+	11.5656i	0.0540079	+	0.375633i
$949$	−52.3540	−	33.6458i	−1.69948	−	1.09219i
$950$	8.58156	−	18.7910i	0.278422	−	0.609660i
$951$	12.5611	−	14.4963i	0.407323	−	0.470076i
$952$	1.95123	−	13.5711i	0.0632399	−	0.439843i
$953$	3.60974	+	7.90422i	0.116931	+	0.256043i	0.959044	−	0.283259i	$-0.0914155\pi$
$953$	3.60974	+	7.90422i	0.116931	+	0.256043i	−0.842113	+	0.539302i	$0.818688\pi$
$954$	9.89024	+	2.90404i	0.320208	+	0.0940217i
$955$	23.2270	+	6.82007i	0.751609	+	0.220692i
$956$	−1.01498	−	2.22250i	−0.0328268	−	0.0718807i
$957$	0.132364	−	0.920613i	0.00427873	−	0.0297592i
$958$	−6.05122	+	6.98348i	−0.195506	+	0.225626i
$959$	−0.917215	+	2.00842i	−0.0296184	+	0.0648553i
$960$	−3.21616	−	2.06690i	−0.103801	−	0.0667090i
$961$	4.40761	+	30.6556i	0.142181	+	0.988890i
$962$	19.0928	−	12.2702i	0.615578	−	0.395608i
$963$	−7.05053	−	8.13674i	−0.227200	−	0.262203i
$964$	−10.4235	+	3.06062i	−0.335719	+	0.0985760i
$965$	−11.7515			−0.378295
$966$	−13.0225	−	4.79898i	−0.418993	−	0.154405i
$967$	39.3485			1.26536			0.632681	−	0.774412i	$-0.281954\pi$
$967$	39.3485			1.26536			0.632681	+	0.774412i	$0.281954\pi$
$968$	8.15719	−	2.39517i	0.262182	−	0.0769835i
$969$	−6.66538	−	7.69226i	−0.214123	−	0.247111i
$970$	2.80944	−	1.80552i	0.0902056	−	0.0579716i
$971$	2.29390	+	15.9545i	0.0736149	+	0.512003i	0.992951	+	0.118529i	$0.0378178\pi$
$971$	2.29390	+	15.9545i	0.0736149	+	0.512003i	−0.919336	+	0.393474i	$0.871273\pi$
$972$	−0.841254	−	0.540641i	−0.0269832	−	0.0173411i
$973$	11.0913	−	24.2866i	0.355572	−	0.778594i
$974$	24.9008	−	28.7371i	0.797873	−	0.920795i
$975$	6.44522	−	44.8275i	0.206412	−	1.43563i
$976$	−5.25686	−	11.5109i	−0.168268	−	0.368455i
$977$	34.1171	+	10.0177i	1.09150	+	0.320494i	0.777472	−	0.628918i	$-0.216502\pi$
$977$	34.1171	+	10.0177i	1.09150	+	0.320494i	0.314032	+	0.949412i	$0.398320\pi$
$978$	−22.1412	−	6.50124i	−0.707998	−	0.207887i
$979$	8.03618	+	17.5968i	0.256837	+	0.562395i
$980$	−0.747902	+	5.20177i	−0.0238909	+	0.166165i
$981$	5.44423	−	6.28298i	0.173821	−	0.200600i
$982$	−1.78074	+	3.89927i	−0.0568255	+	0.124431i
$983$	−45.9456	−	29.5274i	−1.46544	−	0.941779i	−0.998341	−	0.0575723i	$-0.981664\pi$
$983$	−45.9456	−	29.5274i	−1.46544	−	0.941779i	−0.467096	−	0.884207i	$-0.654700\pi$
$984$	−1.47968	−	10.2914i	−0.0471706	−	0.328078i
$985$	−3.09850	+	1.99128i	−0.0987264	+	0.0634476i
$986$	−1.82562	−	2.10688i	−0.0581397	−	0.0670968i
$987$	15.1473	−	4.44765i	0.482144	−	0.141570i
$988$	10.1182			0.321903
$989$	12.2806	−	57.5397i	0.390499	−	1.82966i
$990$	−6.04290			−0.192056
$991$	−25.7849	+	7.57113i	−0.819084	+	0.240505i	−0.664321	−	0.747447i	$-0.731279\pi$
$991$	−25.7849	+	7.57113i	−0.819084	+	0.240505i	−0.154762	+	0.987952i	$0.549461\pi$
$992$	−0.111819	−	0.129046i	−0.00355026	−	0.00409722i
$993$	−7.35311	+	4.72556i	−0.233344	+	0.149961i
$994$	4.86866	+	33.8623i	0.154424	+	1.07405i
$995$	10.5274	+	6.76555i	0.333741	+	0.214482i
$996$	0.0470448	−	0.103014i	0.00149067	−	0.00326412i
$997$	17.6635	−	20.3847i	0.559408	−	0.645591i	−0.403641	−	0.914917i	$-0.632256\pi$
$997$	17.6635	−	20.3847i	0.559408	−	0.645591i	0.963049	+	0.269327i	$0.0868011\pi$
$998$	4.30920	−	29.9712i	0.136405	−	0.948721i
$999$	−2.00181	−	4.38335i	−0.0633344	−	0.138683i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	138.2.e.b.55.1	✓	10
3.2	odd	2		414.2.i.e.55.1		10
23.8	even	11		3174.2.a.ba.1.5		5
23.15	odd	22		3174.2.a.bb.1.1		5
23.18	even	11	inner	138.2.e.b.133.1	yes	10
69.8	odd	22		9522.2.a.bs.1.1		5
69.38	even	22		9522.2.a.br.1.5		5
69.41	odd	22		414.2.i.e.271.1		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
138.2.e.b.55.1	✓	10	1.1	even	1	trivial
138.2.e.b.133.1	yes	10	23.18	even	11	inner
414.2.i.e.55.1		10	3.2	odd	2
414.2.i.e.271.1		10	69.41	odd	22
3174.2.a.ba.1.5		5	23.8	even	11
3174.2.a.bb.1.1		5	23.15	odd	22
9522.2.a.br.1.5		5	69.38	even	22
9522.2.a.bs.1.1		5	69.8	odd	22

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 138 = 2 \cdot 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	138.e (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.959493 + 0.281733i) q^{2} +(0.654861 + 0.755750i) q^{3} +(0.841254 - 0.540641i) q^{4} +(-0.544078 - 3.78415i) q^{5} +(-0.841254 - 0.540641i) q^{6} +(1.20217 - 2.63238i) q^{7} +(-0.654861 + 0.755750i) q^{8} +(-0.142315 + 0.989821i) q^{9} +(1.58816 + 3.47758i) q^{10} +(1.51662 + 0.445319i) q^{11} +(0.959493 + 0.281733i) q^{12} +(1.95653 + 4.28419i) q^{13} +(-0.411844 + 2.86444i) q^{14} +(2.50357 - 2.88927i) q^{15} +(0.415415 - 0.909632i) q^{16} +(-3.98569 - 2.56145i) q^{17} +(-0.142315 - 0.989821i) q^{18} +(1.80728 - 1.16147i) q^{19} +(-2.50357 - 2.88927i) q^{20} +(2.77667 - 0.815304i) q^{21} -1.58065 q^{22} +(2.88909 + 3.82794i) q^{23} -1.00000 q^{24} +(-9.22627 + 2.70908i) q^{25} +(-3.08427 - 3.55944i) q^{26} +(-0.841254 + 0.540641i) q^{27} +(-0.411844 - 2.86444i) q^{28} +(-0.495008 - 0.318122i) q^{29} +(-1.58816 + 3.47758i) q^{30} +(-0.111819 + 0.129046i) q^{31} +(-0.142315 + 0.989821i) q^{32} +(0.656624 + 1.43781i) q^{33} +(4.54589 + 1.33479i) q^{34} +(-10.6154 - 3.11696i) q^{35} +(0.415415 + 0.909632i) q^{36} +(-0.685789 + 4.76977i) q^{37} +(-1.40685 + 1.62359i) q^{38} +(-1.95653 + 4.28419i) q^{39} +(3.21616 + 2.06690i) q^{40} +(1.47968 + 10.2914i) q^{41} +(-2.43450 + 1.56456i) q^{42} +(-8.03389 - 9.27160i) q^{43} +(1.51662 - 0.445319i) q^{44} +3.82306 q^{45} +(-3.85052 - 2.85894i) q^{46} +5.45520 q^{47} +(0.959493 - 0.281733i) q^{48} +(-0.900187 - 1.03887i) q^{49} +(8.08931 - 5.19868i) q^{50} +(-0.674259 - 4.68958i) q^{51} +(3.96215 + 2.54632i) q^{52} +(-4.28201 + 9.37628i) q^{53} +(0.654861 - 0.755750i) q^{54} +(0.859995 - 5.98139i) q^{55} +(1.20217 + 2.63238i) q^{56} +(2.06130 + 0.605253i) q^{57} +(0.564582 + 0.165776i) q^{58} +(-0.790420 - 1.73078i) q^{59} +(0.544078 - 3.78415i) q^{60} +(8.28691 - 9.56361i) q^{61} +(0.0709331 - 0.155322i) q^{62} +(2.43450 + 1.56456i) q^{63} +(-0.142315 - 0.989821i) q^{64} +(15.1475 - 9.73472i) q^{65} +(-1.03510 - 1.19457i) q^{66} +(-5.63806 + 1.65548i) q^{67} -4.73780 q^{68} +(-1.00102 + 4.69020i) q^{69} +11.0635 q^{70} +(11.3427 - 3.33053i) q^{71} +(-0.654861 - 0.755750i) q^{72} +(-11.1159 + 7.14378i) q^{73} +(-0.685789 - 4.76977i) q^{74} +(-8.08931 - 5.19868i) q^{75} +(0.892446 - 1.95418i) q^{76} +(2.99548 - 3.45697i) q^{77} +(0.670276 - 4.66187i) q^{78} +(4.85393 + 10.6286i) q^{79} +(-3.66820 - 1.07708i) q^{80} +(-0.959493 - 0.281733i) q^{81} +(-4.31917 - 9.45767i) q^{82} +(0.0161168 - 0.112095i) q^{83} +(1.89510 - 2.18706i) q^{84} +(-7.52436 + 16.4761i) q^{85} +(10.3206 + 6.63263i) q^{86} +(-0.0837405 - 0.582428i) q^{87} +(-1.32972 + 0.854562i) q^{88} +(8.01460 + 9.24934i) q^{89} +(-3.66820 + 1.07708i) q^{90} +13.6297 q^{91} +(4.50000 + 1.65831i) q^{92} -0.170752 q^{93} +(-5.23423 + 1.53691i) q^{94} +(-5.37848 - 6.20710i) q^{95} +(-0.841254 + 0.540641i) q^{96} +(-0.124317 - 0.864646i) q^{97} +(1.15641 + 0.743178i) q^{98} +(-0.656624 + 1.43781i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - q^{2} + q^{3} - q^{4} - 2 q^{5} + q^{6} - q^{8} - q^{9} + 9 q^{10} + 11 q^{11} + q^{12} + 13 q^{13} - 11 q^{14} + 13 q^{15} - q^{16} - 24 q^{17} - q^{18} - 14 q^{19} - 13 q^{20} + 11 q^{21}+ \cdots - 22 q^{99}+O(q^{100}) \) 10 * q - q^2 + q^3 - q^4 - 2 * q^5 + q^6 - q^8 - q^9 + 9 * q^10 + 11 * q^11 + q^12 + 13 * q^13 - 11 * q^14 + 13 * q^15 - q^16 - 24 * q^17 - q^18 - 14 * q^19 - 13 * q^20 + 11 * q^21 + 22 * q^22 - 10 * q^23 - 10 * q^24 - 43 * q^25 - 9 * q^26 + q^27 - 11 * q^28 + 13 * q^29 - 9 * q^30 + 8 * q^31 - q^32 + 22 * q^33 + 9 * q^34 - q^36 - 13 * q^37 - 3 * q^38 - 13 * q^39 + 9 * q^40 - 10 * q^41 - 8 * q^43 + 11 * q^44 - 2 * q^45 + q^46 - 8 * q^47 + q^48 + 29 * q^49 + 23 * q^50 - 9 * q^51 + 2 * q^52 - 35 * q^53 + q^54 - 11 * q^55 + 3 * q^57 + 13 * q^58 + 37 * q^59 + 2 * q^60 - 2 * q^61 + 8 * q^62 - q^64 + 37 * q^65 + 14 * q^67 - 2 * q^68 - q^69 - 22 * q^70 + 44 * q^71 - q^72 - 49 * q^73 - 13 * q^74 - 23 * q^75 + 8 * q^76 + 44 * q^77 + 20 * q^78 - 8 * q^79 - 2 * q^80 - q^81 + 12 * q^82 - 17 * q^83 - 11 * q^84 - 37 * q^85 + 14 * q^86 - 2 * q^87 + 59 * q^89 - 2 * q^90 + 66 * q^91 + 45 * q^92 + 36 * q^93 - 19 * q^94 - 28 * q^95 + q^96 - 21 * q^97 - 26 * q^98 - 22 * q^99

Introduction

L-functions

Modular forms

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