LMFDB - Embedded newform 546.2.u.a.425.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(185,546)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(546, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 1, 2]))

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

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

chi := DirichletCharacter("546.185");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.u (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:	$4.35983195036$
Analytic rank:	$0$
Dimension:	$76$
Relative dimension:	$38$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			425.19
Character	$\chi$	$=$	546.425
Dual form			546.2.u.a.185.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 + 0.500000i) q^{2} +(1.72102 + 0.195177i) q^{3} +(0.500000 - 0.866025i) q^{4} +(0.349437 - 0.605242i) q^{5} +(-1.58803 + 0.691481i) q^{6} +(-1.78017 + 1.95729i) q^{7} +1.00000i q^{8} +(2.92381 + 0.671806i) q^{9} +O(q^{10})$	\(q+(-0.866025 + 0.500000i) q^{2} +(1.72102 + 0.195177i) q^{3} +(0.500000 - 0.866025i) q^{4} +(0.349437 - 0.605242i) q^{5} +(-1.58803 + 0.691481i) q^{6} +(-1.78017 + 1.95729i) q^{7} +1.00000i q^{8} +(2.92381 + 0.671806i) q^{9} +0.698873i q^{10} +1.47903i q^{11} +(1.02954 - 1.39286i) q^{12} +(-0.668235 + 3.54309i) q^{13} +(0.563029 - 2.58515i) q^{14} +(0.719516 - 0.973431i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(0.789186 - 1.36691i) q^{17} +(-2.86800 + 0.880105i) q^{18} +7.68450i q^{19} +(-0.349437 - 0.605242i) q^{20} +(-3.44573 + 3.02109i) q^{21} +(-0.739517 - 1.28088i) q^{22} +(6.95754 - 4.01694i) q^{23} +(-0.195177 + 1.72102i) q^{24} +(2.25579 + 3.90714i) q^{25} +(-1.19284 - 3.40252i) q^{26} +(4.90081 + 1.72685i) q^{27} +(0.804977 + 2.52032i) q^{28} +(-4.06467 - 2.34674i) q^{29} +(-0.136404 + 1.20277i) q^{30} +(5.83175 - 3.36696i) q^{31} +(0.866025 + 0.500000i) q^{32} +(-0.288673 + 2.54545i) q^{33} +1.57837i q^{34} +(0.562577 + 1.76138i) q^{35} +(2.04371 - 2.19619i) q^{36} +(-0.914289 - 1.58359i) q^{37} +(-3.84225 - 6.65498i) q^{38} +(-1.84157 + 5.96729i) q^{39} +(0.605242 + 0.349437i) q^{40} +(1.63806 - 2.83721i) q^{41} +(1.47354 - 4.33920i) q^{42} +(-1.35510 - 2.34709i) q^{43} +(1.28088 + 0.739517i) q^{44} +(1.42829 - 1.53486i) q^{45} +(-4.01694 + 6.95754i) q^{46} +(3.64146 - 6.30720i) q^{47} +(-0.691481 - 1.58803i) q^{48} +(-0.661973 - 6.96863i) q^{49} +(-3.90714 - 2.25579i) q^{50} +(1.62499 - 2.19845i) q^{51} +(2.73429 + 2.35025i) q^{52} +(-6.97573 + 4.02744i) q^{53} +(-5.10766 + 0.954911i) q^{54} +(0.895173 + 0.516829i) q^{55} +(-1.95729 - 1.78017i) q^{56} +(-1.49984 + 13.2252i) q^{57} +4.69348 q^{58} +(-6.89630 + 11.9447i) q^{59} +(-0.483258 - 1.10983i) q^{60} -3.69483i q^{61} +(-3.36696 + 5.83175i) q^{62} +(-6.51981 + 4.52682i) q^{63} -1.00000 q^{64} +(1.91092 + 1.64253i) q^{65} +(-1.02272 - 2.34876i) q^{66} -3.95565 q^{67} +(-0.789186 - 1.36691i) q^{68} +(12.7581 - 5.55527i) q^{69} +(-1.36790 - 1.24411i) q^{70} +(11.6622 - 6.73317i) q^{71} +(-0.671806 + 2.92381i) q^{72} +(-12.7319 + 7.35079i) q^{73} +(1.58359 + 0.914289i) q^{74} +(3.11967 + 7.16454i) q^{75} +(6.65498 + 3.84225i) q^{76} +(-2.89490 - 2.63294i) q^{77} +(-1.38880 - 6.08862i) q^{78} +(-2.64220 + 4.57643i) q^{79} -0.698873 q^{80} +(8.09735 + 3.92847i) q^{81} +3.27613i q^{82} -0.659952 q^{83} +(0.893473 + 4.49463i) q^{84} +(-0.551541 - 0.955297i) q^{85} +(2.34709 + 1.35510i) q^{86} +(-6.53735 - 4.83211i) q^{87} -1.47903 q^{88} +(-3.02094 - 5.23242i) q^{89} +(-0.469507 + 2.04337i) q^{90} +(-5.74528 - 7.61523i) q^{91} -8.03387i q^{92} +(10.6937 - 4.65639i) q^{93} +7.28293i q^{94} +(4.65098 + 2.68525i) q^{95} +(1.39286 + 1.02954i) q^{96} +(10.8368 - 6.25663i) q^{97} +(4.05760 + 5.70402i) q^{98} +(-0.993624 + 4.32442i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 76 q + 38 q^{4} + 10 q^{7} - 8 q^{9}+O(q^{10}) $ 76 * q + 38 * q^4 + 10 * q^7 - 8 * q^9	$ 76 q + 38 q^{4} + 10 q^{7} - 8 q^{9} + 2 q^{13} + 12 q^{15} - 38 q^{16} - 8 q^{21} - 42 q^{25} + 20 q^{28} + 20 q^{30} + 12 q^{31} - 4 q^{36} - 6 q^{37} + 12 q^{39} + 8 q^{42} - 2 q^{43} - 4 q^{46} + 2 q^{49} + 10 q^{51} - 14 q^{52} + 18 q^{54} + 24 q^{55} + 8 q^{57} + 16 q^{58} - 12 q^{60} + 32 q^{63} - 76 q^{64} - 24 q^{66} + 96 q^{67} - 30 q^{69} - 54 q^{73} - 12 q^{75} + 18 q^{76} - 12 q^{78} - 60 q^{79} + 8 q^{81} + 8 q^{84} + 8 q^{85} - 24 q^{87} + 48 q^{91} + 16 q^{93} - 66 q^{97}+O(q^{100}) $ 76 * q + 38 * q^4 + 10 * q^7 - 8 * q^9 + 2 * q^13 + 12 * q^15 - 38 * q^16 - 8 * q^21 - 42 * q^25 + 20 * q^28 + 20 * q^30 + 12 * q^31 - 4 * q^36 - 6 * q^37 + 12 * q^39 + 8 * q^42 - 2 * q^43 - 4 * q^46 + 2 * q^49 + 10 * q^51 - 14 * q^52 + 18 * q^54 + 24 * q^55 + 8 * q^57 + 16 * q^58 - 12 * q^60 + 32 * q^63 - 76 * q^64 - 24 * q^66 + 96 * q^67 - 30 * q^69 - 54 * q^73 - 12 * q^75 + 18 * q^76 - 12 * q^78 - 60 * q^79 + 8 * q^81 + 8 * q^84 + 8 * q^85 - 24 * q^87 + 48 * q^91 + 16 * q^93 - 66 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/546\mathbb{Z}\right)^\times$.

$n$	$157$	$365$	$379$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$3$	1.72102	+	0.195177i	0.993631	+	0.112685i
$3$	1.72102	+	0.195177i	0.993631	+	0.112685i
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$	0.349437	−	0.605242i	0.156273	−	0.270672i	−0.777249	−	0.629193i	$-0.783385\pi$
$5$	0.349437	−	0.605242i	0.156273	−	0.270672i	0.933522	+	0.358521i	$0.116719\pi$
$6$	−1.58803	+	0.691481i	−0.648312	+	0.282296i
$7$	−1.78017	+	1.95729i	−0.672842	+	0.739786i
$7$	−1.78017	+	1.95729i	−0.672842	+	0.739786i
$8$			1.00000i			0.353553i
$9$	2.92381	+	0.671806i	0.974604	+	0.223935i
$10$			0.698873i			0.221003i
$11$			1.47903i			0.445946i	0.974825	+	0.222973i	$0.0715761\pi$
$11$			1.47903i			0.445946i	−0.974825	+	0.222973i	$0.928424\pi$
$12$	1.02954	−	1.39286i	0.297202	−	0.402083i
$13$	−0.668235	+	3.54309i	−0.185335	+	0.982675i
$13$	−0.668235	+	3.54309i	−0.185335	+	0.982675i
$14$	0.563029	−	2.58515i	0.150476	−	0.690910i
$15$	0.719516	−	0.973431i	0.185778	−	0.251339i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	0.789186	−	1.36691i	0.191406	−	0.331524i	−0.754311	−	0.656518i	$-0.772029\pi$
$17$	0.789186	−	1.36691i	0.191406	−	0.331524i	0.945716	+	0.324993i	$0.105362\pi$
$18$	−2.86800	+	0.880105i	−0.675994	+	0.207443i
$19$			7.68450i			1.76295i	0.472234	+	0.881473i	$0.343448\pi$
$19$			7.68450i			1.76295i	−0.472234	+	0.881473i	$0.656552\pi$
$20$	−0.349437	−	0.605242i	−0.0781364	−	0.135336i
$21$	−3.44573	+	3.02109i	−0.751919	+	0.659255i
$22$	−0.739517	−	1.28088i	−0.157666	−	0.273085i
$23$	6.95754	−	4.01694i	1.45075	−	0.837589i	0.452223	−	0.891905i	$-0.350631\pi$
$23$	6.95754	−	4.01694i	1.45075	−	0.837589i	0.998524	+	0.0543159i	$0.0172978\pi$
$24$	−0.195177	+	1.72102i	−0.0398403	+	0.351302i
$25$	2.25579	+	3.90714i	0.451158	+	0.781428i
$26$	−1.19284	−	3.40252i	−0.233934	−	0.667289i
$27$	4.90081	+	1.72685i	0.943162	+	0.332333i
$28$	0.804977	+	2.52032i	0.152126	+	0.476296i
$29$	−4.06467	−	2.34674i	−0.754790	−	0.435778i	0.0726317	−	0.997359i	$-0.476860\pi$
$29$	−4.06467	−	2.34674i	−0.754790	−	0.435778i	−0.827422	+	0.561580i	$0.810194\pi$
$30$	−0.136404	+	1.20277i	−0.0249038	+	0.219595i
$31$	5.83175	−	3.36696i	1.04741	−	0.604725i	0.125490	−	0.992095i	$-0.459950\pi$
$31$	5.83175	−	3.36696i	1.04741	−	0.604725i	0.921924	+	0.387370i	$0.126616\pi$
$32$	0.866025	+	0.500000i	0.153093	+	0.0883883i
$33$	−0.288673	+	2.54545i	−0.0502515	+	0.443105i
$34$			1.57837i			0.270688i
$35$	0.562577	+	1.76138i	0.0950929	+	0.297728i
$36$	2.04371	−	2.19619i	0.340618	−	0.366032i
$37$	−0.914289	−	1.58359i	−0.150308	−	0.260341i	0.781033	−	0.624490i	$-0.214693\pi$
$37$	−0.914289	−	1.58359i	−0.150308	−	0.260341i	−0.931341	+	0.364149i	$0.881360\pi$
$38$	−3.84225	−	6.65498i	−0.623296	−	1.07958i
$39$	−1.84157	+	5.96729i	−0.294888	+	0.955532i
$40$	0.605242	+	0.349437i	0.0956972	+	0.0552508i
$41$	1.63806	−	2.83721i	0.255823	−	0.443098i	−0.709296	−	0.704911i	$-0.750987\pi$
$41$	1.63806	−	2.83721i	0.255823	−	0.443098i	0.965119	+	0.261813i	$0.0843204\pi$
$42$	1.47354	−	4.33920i	0.227373	−	0.669553i
$43$	−1.35510	−	2.34709i	−0.206650	−	0.357929i	0.744007	−	0.668172i	$-0.232923\pi$
$43$	−1.35510	−	2.34709i	−0.206650	−	0.357929i	−0.950657	+	0.310243i	$0.899590\pi$
$44$	1.28088	+	0.739517i	0.193100	+	0.111486i
$45$	1.42829	−	1.53486i	0.212917	−	0.228803i
$46$	−4.01694	+	6.95754i	−0.592265	+	1.02583i
$47$	3.64146	−	6.30720i	0.531162	−	0.919999i	−0.468177	−	0.883635i	$-0.655089\pi$
$47$	3.64146	−	6.30720i	0.531162	−	0.919999i	0.999339	−	0.0363646i	$-0.0115778\pi$
$48$	−0.691481	−	1.58803i	−0.0998067	−	0.229213i
$49$	−0.661973	−	6.96863i	−0.0945676	−	0.995518i
$50$	−3.90714	−	2.25579i	−0.552553	−	0.319017i
$51$	1.62499	−	2.19845i	0.227544	−	0.307844i
$52$	2.73429	+	2.35025i	0.379177	+	0.325921i
$53$	−6.97573	+	4.02744i	−0.958190	+	0.553212i	−0.895616	−	0.444829i	$-0.853265\pi$
$53$	−6.97573	+	4.02744i	−0.958190	+	0.553212i	−0.0625748	+	0.998040i	$0.519931\pi$
$54$	−5.10766	+	0.954911i	−0.695064	+	0.129947i
$55$	0.895173	+	0.516829i	0.120705	+	0.0696892i
$56$	−1.95729	−	1.78017i	−0.261554	−	0.237886i
$57$	−1.49984	+	13.2252i	−0.198658	+	1.75172i
$58$	4.69348			0.616284
$59$	−6.89630	+	11.9447i	−0.897822	+	1.55507i	−0.0675492	+	0.997716i	$0.521518\pi$
$59$	−6.89630	+	11.9447i	−0.897822	+	1.55507i	−0.830273	+	0.557357i	$0.811815\pi$
$60$	−0.483258	−	1.10983i	−0.0623883	−	0.143279i
$61$		−	3.69483i		−	0.473074i	−0.971622	−	0.236537i	$-0.923988\pi$
$61$		−	3.69483i		−	0.473074i	0.971622	−	0.236537i	$-0.0760125\pi$
$62$	−3.36696	+	5.83175i	−0.427605	+	0.740633i
$63$	−6.51981	+	4.52682i	−0.821419	+	0.570326i
$64$	−1.00000			−0.125000
$65$	1.91092	+	1.64253i	0.237020	+	0.203731i
$66$	−1.02272	−	2.34876i	−0.125889	−	0.289112i
$67$	−3.95565			−0.483260			−0.241630	−	0.970368i	$-0.577682\pi$
$67$	−3.95565			−0.483260			−0.241630	+	0.970368i	$0.577682\pi$
$68$	−0.789186	−	1.36691i	−0.0957028	−	0.165762i
$69$	12.7581	−	5.55527i	1.53589	−	0.668776i
$70$	−1.36790	−	1.24411i	−0.163495	−	0.148700i
$71$	11.6622	−	6.73317i	1.38405	−	0.799081i	0.391412	−	0.920215i	$-0.371987\pi$
$71$	11.6622	−	6.73317i	1.38405	−	0.799081i	0.992636	+	0.121135i	$0.0386533\pi$
$72$	−0.671806	+	2.92381i	−0.0791731	+	0.344575i
$73$	−12.7319	+	7.35079i	−1.49016	+	0.860345i	−0.999937	−	0.0112512i	$-0.996419\pi$
$73$	−12.7319	+	7.35079i	−1.49016	+	0.860345i	−0.490225	+	0.871596i	$0.663085\pi$
$74$	1.58359	+	0.914289i	0.184089	+	0.106284i
$75$	3.11967	+	7.16454i	0.360229	+	0.827290i
$76$	6.65498	+	3.84225i	0.763378	+	0.440737i
$77$	−2.89490	−	2.63294i	−0.329904	−	0.300051i
$78$	−1.38880	−	6.08862i	−0.157250	−	0.689400i
$79$	−2.64220	+	4.57643i	−0.297271	+	0.514888i	−0.975511	−	0.219952i	$-0.929410\pi$
$79$	−2.64220	+	4.57643i	−0.297271	+	0.514888i	0.678240	+	0.734841i	$0.262743\pi$
$80$	−0.698873			−0.0781364
$81$	8.09735	+	3.92847i	0.899706	+	0.436496i
$82$			3.27613i			0.361788i
$83$	−0.659952			−0.0724392			−0.0362196	−	0.999344i	$-0.511532\pi$
$83$	−0.659952			−0.0724392			−0.0362196	+	0.999344i	$0.511532\pi$
$84$	0.893473	+	4.49463i	0.0974859	+	0.490404i
$85$	−0.551541	−	0.955297i	−0.0598230	−	0.103616i
$86$	2.34709	+	1.35510i	0.253094	+	0.146124i
$87$	−6.53735	−	4.83211i	−0.700877	−	0.518057i
$88$	−1.47903			−0.157666
$89$	−3.02094	−	5.23242i	−0.320219	−	0.554635i	0.660314	−	0.750989i	$-0.270423\pi$
$89$	−3.02094	−	5.23242i	−0.320219	−	0.554635i	−0.980533	+	0.196354i	$0.937090\pi$
$90$	−0.469507	+	2.04337i	−0.0494904	+	0.215391i
$91$	−5.74528	−	7.61523i	−0.602269	−	0.798293i
$92$		−	8.03387i		−	0.837589i
$93$	10.6937	−	4.65639i	1.10889	−	0.482845i
$94$			7.28293i			0.751176i
$95$	4.65098	+	2.68525i	0.477181	+	0.275501i
$96$	1.39286	+	1.02954i	0.142158	+	0.105077i
$97$	10.8368	−	6.25663i	1.10031	−	0.635265i	0.164008	−	0.986459i	$-0.447558\pi$
$97$	10.8368	−	6.25663i	1.10031	−	0.635265i	0.936303	+	0.351194i	$0.114224\pi$
$98$	4.05760	+	5.70402i	0.409880	+	0.576193i
$99$	−0.993624	+	4.32442i	−0.0998630	+	0.434620i
$100$	4.51158			0.451158
$101$	1.11527			0.110974			0.0554869	−	0.998459i	$-0.482329\pi$
$101$	1.11527			0.110974			0.0554869	+	0.998459i	$0.482329\pi$
$102$	−0.308061	+	2.71641i	−0.0305026	+	0.268964i
$103$	−13.1642	−	7.60037i	−1.29711	−	0.748887i	−0.317206	−	0.948357i	$-0.602745\pi$
$103$	−13.1642	−	7.60037i	−1.29711	−	0.748887i	−0.979904	+	0.199470i	$0.936078\pi$
$104$	−3.54309	−	0.668235i	−0.347428	−	0.0655258i
$105$	0.624425	+	3.14118i	0.0609376	+	0.306548i
$106$	4.02744	−	6.97573i	0.391180	−	0.677543i
$107$	−9.24982	+	5.34039i	−0.894214	+	0.516275i	−0.875319	−	0.483547i	$-0.839348\pi$
$107$	−9.24982	+	5.34039i	−0.894214	+	0.516275i	−0.0188956	+	0.999821i	$0.506015\pi$
$108$	3.94590	−	3.38080i	0.379695	−	0.325318i
$109$	−4.58784	−	7.94637i	−0.439435	−	0.761124i	0.558211	−	0.829699i	$-0.311488\pi$
$109$	−4.58784	−	7.94637i	−0.439435	−	0.761124i	−0.997646	+	0.0685753i	$0.978155\pi$
$110$	−1.03366			−0.0985554
$111$	−1.26443	−	2.90384i	−0.120014	−	0.275621i
$112$	2.58515	+	0.563029i	0.244274	+	0.0532012i
$113$	−8.76754	+	5.06194i	−0.824781	+	0.476187i	−0.852062	−	0.523440i	$-0.824648\pi$
$113$	−8.76754	+	5.06194i	−0.824781	+	0.476187i	0.0272816	+	0.999628i	$0.491315\pi$
$114$	−5.31369	−	12.2033i	−0.497673	−	1.14294i
$115$		−	5.61466i		−	0.523570i
$116$	−4.06467	+	2.34674i	−0.377395	+	0.217889i
$117$	−4.33406	+	9.91040i	−0.400684	+	0.916216i
$118$		−	13.7926i		−	1.26971i
$119$	1.27055	+	3.97800i	0.116471	+	0.364663i
$120$	0.973431	+	0.719516i	0.0888617	+	0.0656825i
$121$	8.81246			0.801133
$122$	1.84741	+	3.19981i	0.167257	+	0.289698i
$123$	3.37290	−	4.56318i	0.304124	−	0.411448i
$124$		−	6.73393i		−	0.604725i
$125$	6.64739			0.594560
$126$	3.38291	−	7.18025i	0.301374	−	0.639667i
$127$	6.67458	−	11.5607i	0.592273	−	1.02585i	−0.401652	−	0.915792i	$-0.631564\pi$
$127$	6.67458	−	11.5607i	0.592273	−	1.02585i	0.993925	−	0.110055i	$-0.0351027\pi$
$128$	0.866025	−	0.500000i	0.0765466	−	0.0441942i
$129$	−1.87405	−	4.30388i	−0.165001	−	0.378935i
$130$	−2.47617	−	0.467011i	−0.217174	−	0.0409596i
$131$	9.16140	−	15.8680i	0.800435	−	1.38639i	−0.118895	−	0.992907i	$-0.537935\pi$
$131$	9.16140	−	15.8680i	0.800435	−	1.38639i	0.919330	−	0.393487i	$-0.128731\pi$
$132$	2.06008	+	1.52272i	0.179307	+	0.132536i
$133$	−15.0408	−	13.6797i	−1.30420	−	1.18618i
$134$	3.42570	−	1.97783i	0.295935	−	0.170858i
$135$	2.75769	−	2.36275i	0.237344	−	0.203353i
$136$	1.36691	+	0.789186i	0.117212	+	0.0676721i
$137$	−17.2602	−	9.96519i	−1.47464	−	0.851384i	−0.475048	−	0.879960i	$-0.657569\pi$
$137$	−17.2602	−	9.96519i	−1.47464	−	0.851384i	−0.999592	+	0.0285764i	$0.990903\pi$
$138$	−8.27117	+	11.1900i	−0.704089	+	0.952559i
$139$	10.8758	−	6.27916i	0.922475	−	0.532591i	0.0380515	−	0.999276i	$-0.487885\pi$
$139$	10.8758	−	6.27916i	0.922475	−	0.532591i	0.884424	+	0.466684i	$0.154552\pi$
$140$	1.80669	+	0.393486i	0.152693	+	0.0332556i
$141$	7.49804	−	10.1441i	0.631449	−	0.854286i
$142$	−6.73317	+	11.6622i	−0.565035	+	0.978670i
$143$	−5.24035	−	0.988342i	−0.438220	−	0.0826493i
$144$	−0.880105	−	2.86800i	−0.0733421	−	0.239000i
$145$	−2.84069	+	1.64007i	−0.235906	+	0.136201i
$146$	7.35079	−	12.7319i	0.608356	−	1.05370i
$147$	0.220846	−	12.1223i	0.0182151	−	0.999834i
$148$	−1.82858			−0.150308
$149$		−	6.75118i		−	0.553078i	−0.961003	−	0.276539i	$-0.910812\pi$
$149$		−	6.75118i		−	0.553078i	0.961003	−	0.276539i	$-0.0891876\pi$
$150$	−6.28398	−	4.64484i	−0.513085	−	0.379249i
$151$	3.81143	+	6.60158i	0.310169	+	0.537229i	0.978399	−	0.206726i	$-0.0662809\pi$
$151$	3.81143	+	6.60158i	0.310169	+	0.537229i	−0.668229	+	0.743955i	$0.732948\pi$
$152$	−7.68450			−0.623296
$153$	3.22573	−	3.46641i	0.260785	−	0.280242i
$154$	3.82352	+	0.832739i	0.308108	+	0.0671040i
$155$		−	4.70616i		−	0.378008i
$156$	4.24704	+	4.57850i	0.340036	+	0.366573i
$157$	5.16669	−	2.98299i	0.412347	−	0.238069i	−0.279451	−	0.960160i	$-0.590152\pi$
$157$	5.16669	−	2.98299i	0.412347	−	0.238069i	0.691798	+	0.722091i	$0.256819\pi$
$158$		−	5.28440i		−	0.420404i
$159$	−12.7914	+	5.56980i	−1.01443	+	0.441714i
$160$	0.605242	−	0.349437i	0.0478486	−	0.0276254i
$161$	−4.52330	+	20.7688i	−0.356486	+	1.63681i
$162$	−8.97675	+	0.646523i	−0.705280	+	0.0507957i
$163$	7.57988			0.593702			0.296851	−	0.954924i	$-0.404063\pi$
$163$	7.57988			0.593702			0.296851	+	0.954924i	$0.404063\pi$
$164$	−1.63806	−	2.83721i	−0.127911	−	0.221549i
$165$	1.43974	+	1.06419i	0.112083	+	0.0828470i
$166$	0.571535	−	0.329976i	0.0443597	−	0.0256111i
$167$	0.895737	−	1.55146i	0.0693142	−	0.120056i	−0.829285	−	0.558825i	$-0.811252\pi$
$167$	0.895737	−	1.55146i	0.0693142	−	0.120056i	0.898600	+	0.438770i	$0.144586\pi$
$168$	−3.02109	−	3.44573i	−0.233082	−	0.265844i
$169$	−12.1069	−	4.73523i	−0.931302	−	0.364248i
$170$	0.955297	+	0.551541i	0.0732679	+	0.0423012i
$171$	−5.16250	+	22.4680i	−0.394786	+	1.71817i
$172$	−2.71019			−0.206650
$173$	16.1435			1.22737			0.613685	−	0.789551i	$-0.289687\pi$
$173$	16.1435			1.22737			0.613685	+	0.789551i	$0.289687\pi$
$174$	8.07756	+	0.916058i	0.612359	+	0.0694462i
$175$	−11.6631	−	2.54015i	−0.881647	−	0.192017i
$176$	1.28088	−	0.739517i	0.0965500	−	0.0557432i
$177$	−14.2000	+	19.2111i	−1.06734	+	1.44400i
$178$	5.23242	+	3.02094i	0.392186	+	0.226429i
$179$			0.980251i			0.0732674i	0.999329	+	0.0366337i	$0.0116635\pi$
$179$			0.980251i			0.0732674i	−0.999329	+	0.0366337i	$0.988337\pi$
$180$	−0.615082	−	2.00437i	−0.0458455	−	0.149397i
$181$			7.63392i			0.567425i	0.958909	+	0.283712i	$0.0915661\pi$
$181$			7.63392i			0.567425i	−0.958909	+	0.283712i	$0.908434\pi$
$182$	8.78317	+	3.72235i	0.651052	+	0.275919i
$183$	0.721145	−	6.35887i	0.0533085	−	0.470061i
$184$	4.01694	+	6.95754i	0.296132	+	0.512916i
$185$	−1.27794			−0.0939563
$186$	−6.93283	+	9.37940i	−0.508340	+	0.687731i
$187$	2.02171	+	1.16723i	0.147842	+	0.0853565i
$188$	−3.64146	−	6.30720i	−0.265581	−	0.460000i
$189$	−12.1042	+	6.51823i	−0.880454	+	0.474131i
$190$	−5.37049			−0.389617
$191$		−	22.2493i		−	1.60991i	−0.593338	−	0.804953i	$-0.702190\pi$
$191$		−	22.2493i		−	1.60991i	0.593338	−	0.804953i	$-0.297810\pi$
$192$	−1.72102	−	0.195177i	−0.124204	−	0.0140857i
$193$	−7.96297			−0.573187			−0.286593	−	0.958052i	$-0.592523\pi$
$193$	−7.96297			−0.573187			−0.286593	+	0.958052i	$0.592523\pi$
$194$	−6.25663	+	10.8368i	−0.449200	+	0.778037i
$195$	2.96814	+	3.19979i	0.212553	+	0.229142i
$196$	−6.36600	−	2.91103i	−0.454714	−	0.207931i
$197$	−7.75682	−	4.47840i	−0.552651	−	0.319073i	0.197540	−	0.980295i	$-0.436705\pi$
$197$	−7.75682	−	4.47840i	−0.552651	−	0.319073i	−0.750190	+	0.661222i	$0.770038\pi$
$198$	−1.30171	−	4.24187i	−0.0925082	−	0.301456i
$199$	18.8892	+	10.9057i	1.33902	+	0.773082i	0.986662	−	0.162784i	$-0.0520473\pi$
$199$	18.8892	+	10.9057i	1.33902	+	0.773082i	0.352356	+	0.935866i	$0.385381\pi$
$200$	−3.90714	+	2.25579i	−0.276276	+	0.159508i
$201$	−6.80776	−	0.772052i	−0.480182	−	0.0544564i
$202$	−0.965855	+	0.557637i	−0.0679573	+	0.0392352i
$203$	11.8291	−	3.77814i	0.830238	−	0.265174i
$204$	−1.09141	−	2.50651i	−0.0764143	−	0.175491i
$205$	−1.14480	−	1.98285i	−0.0799562	−	0.138488i
$206$	15.2007			1.05909
$207$	23.0411	−	7.07065i	1.60147	−	0.491444i
$208$	3.40252	−	1.19284i	0.235922	−	0.0827082i
$209$	−11.3656			−0.786178
$210$	−2.11136	−	2.40813i	−0.145697	−	0.166177i
$211$	6.15759	−	10.6653i	0.423906	−	0.734227i	−0.572412	−	0.819966i	$-0.693992\pi$
$211$	6.15759	−	10.6653i	0.423906	−	0.734227i	0.996318	+	0.0857397i	$0.0273253\pi$
$212$			8.05488i			0.553212i
$213$	21.3850	−	9.31173i	1.46528	−	0.638029i
$214$	5.34039	−	9.24982i	0.365061	−	0.632305i
$215$	−1.89408			−0.129175
$216$	−1.72685	+	4.90081i	−0.117497	+	0.333458i
$217$	−3.79140	+	17.4082i	−0.257377	+	1.18175i
$218$	7.94637	+	4.58784i	0.538196	+	0.310727i
$219$	−23.3466	+	10.1659i	−1.57762	+	0.686946i
$220$	0.895173	−	0.516829i	0.0603526	−	0.0348446i
$221$	4.31572	+	3.70957i	0.290307	+	0.249533i
$222$	2.54695	+	1.88259i	0.170940	+	0.126351i
$223$	10.0515	+	5.80325i	0.673100	+	0.388615i	0.797250	−	0.603649i	$-0.206287\pi$
$223$	10.0515	+	5.80325i	0.673100	+	0.388615i	−0.124150	+	0.992263i	$0.539620\pi$
$224$	−2.52032	+	0.804977i	−0.168396	+	0.0537848i
$225$	3.97066	+	12.9392i	0.264711	+	0.862613i
$226$	5.06194	−	8.76754i	0.336715	−	0.583208i
$227$	0.594606	−	1.02989i	0.0394654	−	0.0683560i	−0.845618	−	0.533788i	$-0.820768\pi$
$227$	0.594606	−	1.02989i	0.0394654	−	0.0683560i	0.885083	+	0.465432i	$0.154101\pi$
$228$	10.7034	+	7.91149i	0.708851	+	0.523951i
$229$	5.77423	+	3.33375i	0.381572	+	0.220301i	0.678502	−	0.734599i	$-0.262630\pi$
$229$	5.77423	+	3.33375i	0.381572	+	0.220301i	−0.296930	+	0.954899i	$0.595963\pi$
$230$	2.80733	+	4.86244i	0.185110	+	0.320620i
$231$	−4.46829	−	5.09635i	−0.293992	−	0.335315i
$232$	2.34674	−	4.06467i	0.154071	−	0.266859i
$233$	−6.24464	−	3.60534i	−0.409100	−	0.236194i	0.281303	−	0.959619i	$-0.409233\pi$
$233$	−6.24464	−	3.60534i	−0.409100	−	0.236194i	−0.690403	+	0.723425i	$0.742567\pi$
$234$	−1.20179	−	10.7497i	−0.0785636	−	0.702729i
$235$	−2.54492	−	4.40793i	−0.166012	−	0.287542i
$236$	6.89630	+	11.9447i	0.448911	+	0.777537i
$237$	−5.44049	+	7.36042i	−0.353398	+	0.478111i
$238$	−3.08933	−	2.80977i	−0.200252	−	0.182131i
$239$		−	6.59526i		−	0.426612i	−0.976985	−	0.213306i	$-0.931577\pi$
$239$		−	6.59526i		−	0.426612i	0.976985	−	0.213306i	$-0.0684231\pi$
$240$	−1.20277	−	0.136404i	−0.0776387	−	0.00880483i
$241$	−3.82445	−	2.20804i	−0.246354	−	0.142233i	0.371740	−	0.928337i	$-0.378761\pi$
$241$	−3.82445	−	2.20804i	−0.246354	−	0.142233i	−0.618094	+	0.786104i	$0.712095\pi$
$242$	−7.63181	+	4.40623i	−0.490592	+	0.283243i
$243$	13.1690	+	8.34138i	0.844789	+	0.535100i
$244$	−3.19981	−	1.84741i	−0.204847	−	0.118269i
$245$	−4.44902	−	2.03444i	−0.284238	−	0.129976i
$246$	−0.639424	+	5.63828i	−0.0407682	+	0.359484i
$247$	−27.2269	−	5.13505i	−1.73240	−	0.326736i
$248$	3.36696	+	5.83175i	0.213802	+	0.370317i
$249$	−1.13579	−	0.128807i	−0.0719778	−	0.00816283i
$250$	−5.75681	+	3.32369i	−0.364092	+	0.210209i
$251$	7.62856	+	13.2131i	0.481511	+	0.834001i	0.999775	−	0.0212197i	$-0.00675495\pi$
$251$	7.62856	+	13.2131i	0.481511	+	0.834001i	−0.518264	+	0.855221i	$0.673422\pi$
$252$	0.660437	+	7.90973i	0.0416036	+	0.498266i
$253$	5.94119	+	10.2904i	0.373519	+	0.646954i
$254$			13.3492i			0.837601i
$255$	−0.762760	−	1.75173i	−0.0477659	−	0.109698i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	7.35225	+	12.7345i	0.458621	+	0.794355i	0.998888	−	0.0471387i	$-0.0150103\pi$
$257$	7.35225	+	12.7345i	0.458621	+	0.794355i	−0.540267	+	0.841493i	$0.681677\pi$
$258$	3.77491	+	2.79024i	0.235016	+	0.173713i
$259$	4.72715	+	1.02954i	0.293731	+	0.0639727i
$260$	2.37793	−	0.833640i	0.147473	−	0.0517002i
$261$	−10.3078	−	9.59209i	−0.638036	−	0.593736i
$262$			18.3228i			1.13199i
$263$		−	13.3459i		−	0.822944i	−0.911422	−	0.411472i	$-0.865015\pi$
$263$		−	13.3459i		−	0.822944i	0.911422	−	0.411472i	$-0.134985\pi$
$264$	−2.54545	−	0.288673i	−0.156661	−	0.0177666i
$265$			5.62934i			0.345808i
$266$	19.8656	+	4.32660i	1.21804	+	0.265281i
$267$	−4.17785	−	9.59471i	−0.255680	−	0.587187i
$268$	−1.97783	+	3.42570i	−0.120815	+	0.209258i
$269$	−9.42280	+	16.3208i	−0.574518	+	0.995095i	0.421576	+	0.906793i	$0.361477\pi$
$269$	−9.42280	+	16.3208i	−0.574518	+	0.995095i	−0.996094	+	0.0883015i	$0.971856\pi$
$270$	−1.20685	+	3.42505i	−0.0734465	+	0.208442i
$271$	−8.32026	+	4.80370i	−0.505420	+	0.291804i	−0.730949	−	0.682432i	$-0.760922\pi$
$271$	−8.32026	+	4.80370i	−0.505420	+	0.291804i	0.225529	+	0.974236i	$0.427589\pi$
$272$	−1.57837			−0.0957028
$273$	−8.40141	−	14.2273i	−0.508477	−	0.861076i
$274$	19.9304			1.20404
$275$	−5.77879	+	3.33639i	−0.348474	+	0.201192i
$276$	1.56803	−	13.8264i	0.0943840	−	0.832254i
$277$	−2.92622	+	5.06836i	−0.175819	+	0.304528i	−0.940445	−	0.339947i	$-0.889591\pi$
$277$	−2.92622	+	5.06836i	−0.175819	+	0.304528i	0.764625	+	0.644475i	$0.222924\pi$
$278$	−6.27916	+	10.8758i	−0.376599	+	0.652289i
$279$	19.3129	−	5.92656i	1.15623	−	0.354814i
$280$	−1.76138	+	0.562577i	−0.105263	+	0.0336204i
$281$		−	5.61993i		−	0.335257i	−0.985850	−	0.167628i	$-0.946389\pi$
$281$		−	5.61993i		−	0.335257i	0.985850	−	0.167628i	$-0.0536109\pi$
$282$	−1.42146	+	12.5341i	−0.0846466	+	0.746392i
$283$		−	15.7084i		−	0.933770i	−0.884318	−	0.466885i	$-0.845376\pi$
$283$		−	15.7084i		−	0.933770i	0.884318	−	0.466885i	$-0.154624\pi$
$284$		−	13.4663i		−	0.799081i
$285$	7.48033	+	5.52913i	0.443097	+	0.327517i
$286$	5.03244	−	1.76424i	0.297575	−	0.104322i
$287$	2.63721	+	8.25689i	0.155670	+	0.487389i
$288$	2.19619	+	2.04371i	0.129412	+	0.120427i
$289$	7.25437	+	12.5649i	0.426728	+	0.739114i
$290$	1.64007	−	2.84069i	0.0963084	−	0.166811i
$291$	19.8715	−	8.65269i	1.16489	−	0.507230i
$292$			14.7016i			0.860345i
$293$	−1.93283	−	3.34776i	−0.112917	−	0.195578i	0.804028	−	0.594591i	$-0.202686\pi$
$293$	−1.93283	−	3.34776i	−0.112917	−	0.195578i	−0.916945	+	0.399013i	$0.869353\pi$
$294$	5.86991	+	10.6087i	0.342340	+	0.618711i
$295$	4.81964	+	8.34786i	0.280610	+	0.486031i
$296$	1.58359	−	0.914289i	0.0920446	−	0.0531420i
$297$	−2.55407	+	7.24847i	−0.148202	+	0.420599i
$298$	3.37559	+	5.84670i	0.195543	+	0.338690i
$299$	9.58308	+	27.3354i	0.554204	+	1.58085i
$300$	7.76451	+	0.880555i	0.448284	+	0.0508389i
$301$	7.00625	+	1.52592i	0.403833	+	0.0879524i
$302$	−6.60158	−	3.81143i	−0.379878	−	0.219323i
$303$	1.91941	+	0.217675i	0.110267	+	0.0125051i
$304$	6.65498	−	3.84225i	0.381689	−	0.220368i
$305$	−2.23626	−	1.29111i	−0.128048	−	0.0739286i
$306$	−1.06036	+	4.61486i	−0.0606167	+	0.263814i
$307$			23.4663i			1.33929i	0.742681	+	0.669645i	$0.233554\pi$
$307$			23.4663i			1.33929i	−0.742681	+	0.669645i	$0.766446\pi$
$308$	−3.72764	+	1.19059i	−0.212402	+	0.0678401i
$309$	−21.1725	−	15.6497i	−1.20446	−	0.890282i
$310$	2.35308	+	4.07566i	0.133646	+	0.231482i
$311$	8.46088	+	14.6547i	0.479773	+	0.830991i	0.999731	−	0.0232012i	$-0.00738583\pi$
$311$	8.46088	+	14.6547i	0.479773	+	0.830991i	−0.519958	+	0.854192i	$0.674052\pi$
$312$	−5.96729	−	1.84157i	−0.337832	−	0.104259i
$313$	14.8585	+	8.57858i	0.839854	+	0.484890i	0.857214	−	0.514960i	$-0.172193\pi$
$313$	14.8585	+	8.57858i	0.839854	+	0.484890i	−0.0173608	+	0.999849i	$0.505526\pi$
$314$	−2.98299	+	5.16669i	−0.168340	+	0.291573i
$315$	0.461561	+	5.52790i	0.0260060	+	0.311462i
$316$	2.64220	+	4.57643i	0.148635	+	0.257444i
$317$	−21.3869	−	12.3478i	−1.20121	−	0.693519i	−0.240386	−	0.970677i	$-0.577274\pi$
$317$	−21.3869	−	12.3478i	−1.20121	−	0.693519i	−0.960824	+	0.277158i	$0.910607\pi$
$318$	8.29280	−	11.2193i	0.465037	−	0.629147i
$319$	3.47091	−	6.01179i	0.194333	−	0.336595i
$320$	−0.349437	+	0.605242i	−0.0195341	+	0.0338341i
$321$	−16.9614	+	7.38556i	−0.946695	+	0.412222i
$322$	−6.46708	−	20.2479i	−0.360397	−	1.12837i
$323$	10.5040	+	6.06450i	0.584459	+	0.337438i
$324$	7.45083	−	5.04828i	0.413935	−	0.280460i
$325$	−15.3507	+	5.38157i	−0.851505	+	0.298516i
$326$	−6.56437	+	3.78994i	−0.363567	+	0.209905i
$327$	−6.34481	−	14.5713i	−0.350869	−	0.805794i
$328$	2.83721	+	1.63806i	0.156659	+	0.0904470i
$329$	5.86259	+	18.3553i	0.323215	+	1.01196i
$330$	−1.77894	−	0.201746i	−0.0979276	−	0.0111057i
$331$	32.0333			1.76071			0.880354	−	0.474318i	$-0.157305\pi$
$331$	32.0333			1.76071			0.880354	+	0.474318i	$0.157305\pi$
$332$	−0.329976	+	0.571535i	−0.0181098	+	0.0313671i
$333$	−1.60934	−	5.24436i	−0.0881913	−	0.287389i
$334$			1.79147i			0.0980251i
$335$	−1.38225	+	2.39413i	−0.0755204	+	0.130805i
$336$	4.33920	+	1.47354i	0.236723	+	0.0803885i
$337$	−22.5440			−1.22805			−0.614024	−	0.789287i	$-0.710450\pi$
$337$	−22.5440			−1.22805			−0.614024	+	0.789287i	$0.710450\pi$
$338$	12.8525	−	1.95264i	0.699085	−	0.106209i
$339$	−16.0771	+	7.00048i	−0.873187	+	0.380214i
$340$	−1.10308			−0.0598230
$341$	4.97985	+	8.62536i	0.269674	+	0.467090i
$342$	−6.76317	−	22.0391i	−0.365710	−	1.19174i
$343$	14.8181	+	11.1097i	0.800100	+	0.599867i
$344$	2.34709	−	1.35510i	0.126547	−	0.0730619i
$345$	1.09585	−	9.66293i	0.0589986	−	0.520235i
$346$	−13.9807	+	8.07176i	−0.751607	+	0.433941i
$347$	13.7226	+	7.92275i	0.736668	+	0.425316i	0.820857	−	0.571134i	$-0.193496\pi$
$347$	13.7226	+	7.92275i	0.736668	+	0.425316i	−0.0841884	+	0.996450i	$0.526830\pi$
$348$	−7.45340	+	3.24545i	−0.399544	+	0.173975i
$349$	−19.3134	−	11.1506i	−1.03382	−	0.596878i	−0.115746	−	0.993279i	$-0.536926\pi$
$349$	−19.3134	−	11.1506i	−1.03382	−	0.596878i	−0.918078	+	0.396401i	$0.870259\pi$
$350$	11.3706	−	3.63172i	0.607785	−	0.194123i
$351$	−9.39328	+	16.2101i	−0.501376	+	0.865229i
$352$	−0.739517	+	1.28088i	−0.0394164	+	0.0682712i
$353$	−9.10955			−0.484852			−0.242426	−	0.970170i	$-0.577943\pi$
$353$	−9.10955			−0.484852			−0.242426	+	0.970170i	$0.577943\pi$
$354$	2.69200	−	23.7373i	0.143078	−	1.26162i
$355$		−	9.41127i		−	0.499498i
$356$	−6.04188			−0.320219
$357$	1.41023	+	7.09420i	0.0746374	+	0.375465i
$358$	−0.490125	−	0.848922i	−0.0259039	−	0.0448669i
$359$	2.65584	+	1.53335i	0.140170	+	0.0809271i	0.568445	−	0.822721i	$-0.307545\pi$
$359$	2.65584	+	1.53335i	0.140170	+	0.0809271i	−0.428275	+	0.903648i	$0.640879\pi$
$360$	1.53486	+	1.42829i	0.0808942	+	0.0752776i
$361$	−40.0516			−2.10798
$362$	−3.81696	−	6.61117i	−0.200615	−	0.347475i
$363$	15.1664	+	1.71999i	0.796030	+	0.0902759i
$364$	−9.46762	+	1.16794i	−0.496238	+	0.0612166i
$365$			10.2745i			0.537794i
$366$	2.55490	+	5.86751i	0.133547	+	0.306700i
$367$		−	2.64140i		−	0.137880i	−0.997621	−	0.0689399i	$-0.978038\pi$
$367$		−	2.64140i		−	0.137880i	0.997621	−	0.0689399i	$-0.0219617\pi$
$368$	−6.95754	−	4.01694i	−0.362687	−	0.209397i
$369$	6.69545	−	7.19501i	0.348551	−	0.374557i
$370$	1.10673	−	0.638972i	0.0575363	−	0.0332186i
$371$	4.53513	−	20.8231i	0.235452	−	1.08108i
$372$	1.31431	−	11.5892i	0.0681436	−	0.600873i
$373$	−5.38330			−0.278737			−0.139368	−	0.990241i	$-0.544507\pi$
$373$	−5.38330			−0.278737			−0.139368	+	0.990241i	$0.544507\pi$
$374$	−2.33446			−0.120712
$375$	11.4403	+	1.29742i	0.590773	+	0.0669982i
$376$	6.30720	+	3.64146i	0.325269	+	0.187794i
$377$	11.0309	−	12.8333i	0.568118	−	0.660949i
$378$	7.22347	−	11.6971i	0.371535	−	0.601632i
$379$	6.88920	−	11.9324i	0.353874	−	0.612929i	−0.633050	−	0.774111i	$-0.718197\pi$
$379$	6.88920	−	11.9324i	0.353874	−	0.612929i	0.986925	+	0.161182i	$0.0515307\pi$
$380$	4.65098	−	2.68525i	0.238590	−	0.137750i
$381$	13.7435	−	18.5935i	0.704099	−	0.952573i
$382$	11.1247	+	19.2685i	0.569188	+	0.985862i
$383$	−28.7083			−1.46692			−0.733462	−	0.679730i	$-0.762097\pi$
$383$	−28.7083			−1.46692			−0.733462	+	0.679730i	$0.762097\pi$
$384$	1.58803	−	0.691481i	0.0810390	−	0.0352870i
$385$	−2.60515	+	0.832071i	−0.132771	+	0.0424062i
$386$	6.89613	−	3.98148i	0.351004	−	0.202652i
$387$	−2.38525	−	7.77282i	−0.121249	−	0.395115i
$388$		−	12.5133i		−	0.635265i
$389$	−19.7202	+	11.3855i	−0.999855	+	0.577267i	−0.908205	−	0.418525i	$-0.862547\pi$
$389$	−19.7202	+	11.3855i	−0.999855	+	0.577267i	−0.0916497	+	0.995791i	$0.529214\pi$
$390$	−4.17038	−	1.28703i	−0.211176	−	0.0651711i
$391$		−	12.6804i		−	0.641277i
$392$	6.96863	−	0.661973i	0.351969	−	0.0334347i
$393$	18.8640	−	25.5210i	0.951563	−	1.28737i
$394$	8.95681			0.451237
$395$	1.84656	+	3.19834i	0.0929107	+	0.160926i
$396$	3.24824	+	3.02271i	0.163230	+	0.151897i
$397$		−	10.7013i		−	0.537084i	−0.963268	−	0.268542i	$-0.913458\pi$
$397$		−	10.7013i		−	0.537084i	0.963268	−	0.268542i	$-0.0865418\pi$
$398$	−21.8113			−1.09330
$399$	−23.2155	−	26.4787i	−1.16223	−	1.32559i
$400$	2.25579	−	3.90714i	0.112789	−	0.195357i
$401$	10.7399	−	6.20069i	0.536326	−	0.309648i	−0.207263	−	0.978285i	$-0.566456\pi$
$401$	10.7399	−	6.20069i	0.536326	−	0.309648i	0.743588	+	0.668638i	$0.233122\pi$
$402$	6.28172	−	2.73526i	0.313304	−	0.136422i
$403$	8.03247	+	22.9123i	0.400126	+	1.14134i
$404$	0.557637	−	0.965855i	0.0277435	−	0.0480531i
$405$	5.20719	−	3.52811i	0.258747	−	0.175313i
$406$	−8.35520	+	9.18650i	−0.414662	+	0.455918i
$407$	2.34219	−	1.35226i	0.116098	−	0.0670293i
$408$	2.19845	+	1.62499i	0.108839	+	0.0804491i
$409$	10.2314	+	5.90709i	0.505909	+	0.292087i	0.731151	−	0.682216i	$-0.238984\pi$
$409$	10.2314	+	5.90709i	0.505909	+	0.292087i	−0.225241	+	0.974303i	$0.572317\pi$
$410$	1.98285	+	1.14480i	0.0979260	+	0.0565376i
$411$	−27.7602	−	20.5191i	−1.36931	−	1.01213i
$412$	−13.1642	+	7.60037i	−0.648555	+	0.374443i
$413$	−11.1027	−	34.7618i	−0.546330	−	1.71051i
$414$	−16.4189	+	17.6439i	−0.806944	+	0.867152i
$415$	−0.230611	+	0.399431i	−0.0113203	+	0.0196073i
$416$	−2.35025	+	2.73429i	−0.115231	+	0.134059i
$417$	19.9430	−	8.68385i	0.976615	−	0.425250i
$418$	9.84294	−	5.68282i	0.481434	−	0.277956i
$419$	−7.76922	+	13.4567i	−0.379551	+	0.657402i	−0.990997	−	0.133884i	$-0.957255\pi$
$419$	−7.76922	+	13.4567i	−0.379551	+	0.657402i	0.611446	+	0.791286i	$0.290588\pi$
$420$	3.03255	+	1.02982i	0.147973	+	0.0502501i
$421$	−26.1683			−1.27537			−0.637683	−	0.770299i	$-0.720107\pi$
$421$	−26.1683			−1.27537			−0.637683	+	0.770299i	$0.720107\pi$
$422$			12.3152i			0.599494i
$423$	14.8842	−	15.9947i	0.723693	−	0.777689i
$424$	−4.02744	−	6.97573i	−0.195590	−	0.338771i
$425$	7.12094			0.345416
$426$	−13.8641	+	18.7567i	−0.671718	+	0.908765i
$427$	7.23185	+	6.57743i	0.349974	+	0.318304i
$428$			10.6808i			0.516275i
$429$	−8.82583	−	2.72375i	−0.426115	−	0.131504i
$430$	1.64032	−	0.947040i	0.0791033	−	0.0456703i
$431$		−	22.4841i		−	1.08302i	−0.840694	−	0.541510i	$-0.817853\pi$
$431$		−	22.4841i		−	1.08302i	0.840694	−	0.541510i	$-0.182147\pi$
$432$	−0.954911	−	5.10766i	−0.0459432	−	0.245742i
$433$	18.0042	−	10.3947i	0.865226	−	0.499538i	−0.000532949	−	1.00000i	$-0.500170\pi$
$433$	18.0042	−	10.3947i	0.865226	−	0.499538i	0.865759	+	0.500461i	$0.166836\pi$
$434$	−5.42066	−	16.9717i	−0.260200	−	0.814665i
$435$	−5.20899	+	2.26816i	−0.249752	+	0.108750i
$436$	−9.17567			−0.439435
$437$	30.8682	+	53.4652i	1.47662	+	2.55759i
$438$	15.1358	−	20.4772i	0.723218	−	0.978439i
$439$	9.11578	−	5.26300i	0.435072	−	0.251189i	−0.266433	−	0.963853i	$-0.585845\pi$
$439$	9.11578	−	5.26300i	0.435072	−	0.251189i	0.701505	+	0.712664i	$0.252512\pi$
$440$	−0.516829	+	0.895173i	−0.0246388	+	0.0426757i
$441$	2.74608	−	20.8197i	0.130766	−	0.991413i
$442$	−5.59231	−	1.05472i	−0.265999	−	0.0501680i
$443$	−22.9533	−	13.2521i	−1.09054	−	0.629625i	−0.156822	−	0.987627i	$-0.550125\pi$
$443$	−22.9533	−	13.2521i	−1.09054	−	0.629625i	−0.933721	+	0.358002i	$0.883458\pi$
$444$	−3.14702	−	0.356896i	−0.149351	−	0.0169375i
$445$	−4.22251			−0.200166
$446$	−11.6065			−0.549584
$447$	1.31767	−	11.6189i	0.0623238	−	0.549556i
$448$	1.78017	−	1.95729i	0.0841052	−	0.0924733i
$449$	17.4966	−	10.1017i	0.825716	−	0.476728i	−0.0266674	−	0.999644i	$-0.508490\pi$
$449$	17.4966	−	10.1017i	0.825716	−	0.476728i	0.852384	+	0.522917i	$0.175156\pi$
$450$	−9.90829	−	9.22034i	−0.467081	−	0.434651i
$451$	4.19633	+	2.42275i	0.197597	+	0.114083i
$452$			10.1239i			0.476187i
$453$	5.27106	+	12.1054i	0.247656	+	0.568759i
$454$			1.18921i			0.0558124i
$455$	−6.61667	+	0.816241i	−0.310194	+	0.0382660i
$456$	−13.2252	−	1.49984i	−0.619326	−	0.0702363i
$457$	6.76192	+	11.7120i	0.316309	+	0.547864i	0.979715	−	0.200396i	$-0.0642229\pi$
$457$	6.76192	+	11.7120i	0.316309	+	0.547864i	−0.663406	+	0.748260i	$0.730890\pi$
$458$	−6.66750			−0.311552
$459$	6.22810	−	5.33616i	0.290703	−	0.249071i
$460$	−4.86244	−	2.80733i	−0.226712	−	0.130892i
$461$	−15.2621	−	26.4348i	−0.710828	−	1.23119i	−0.964547	−	0.263913i	$-0.914987\pi$
$461$	−15.2621	−	26.4348i	−0.710828	−	1.23119i	0.253718	−	0.967278i	$-0.418346\pi$
$462$	6.41783	+	2.17942i	0.298584	+	0.101396i
$463$	−18.9355			−0.880007			−0.440004	−	0.897996i	$-0.645023\pi$
$463$	−18.9355			−0.880007			−0.440004	+	0.897996i	$0.645023\pi$
$464$			4.69348i			0.217889i
$465$	0.918534	−	8.09939i	0.0425960	−	0.375600i
$466$	7.21069			0.334029
$467$	0.784961	−	1.35959i	0.0363237	−	0.0629144i	−0.847292	−	0.531127i	$-0.821769\pi$
$467$	0.784961	−	1.35959i	0.0363237	−	0.0629144i	0.883616	+	0.468213i	$0.155102\pi$
$468$	6.41562	+	8.70860i	0.296562	+	0.402555i
$469$	7.04175	−	7.74237i	0.325158	−	0.357509i
$470$	4.40793	+	2.54492i	0.203323	+	0.117388i
$471$	9.47418	−	4.12536i	0.436547	−	0.190087i
$472$	−11.9447	−	6.89630i	−0.549801	−	0.317428i
$473$	3.47143	−	2.00423i	0.159617	−	0.0921547i
$474$	1.03139	−	9.09456i	0.0473734	−	0.417727i
$475$	−30.0244	+	17.3346i	−1.37762	+	0.795367i
$476$	4.08033	+	0.888669i	0.187021	+	0.0407321i
$477$	−23.1014	+	7.08914i	−1.05774	+	0.324589i
$478$	3.29763	+	5.71166i	0.150830	+	0.261245i
$479$	29.7134			1.35764			0.678819	−	0.734305i	$-0.262492\pi$
$479$	29.7134			1.35764			0.678819	+	0.734305i	$0.262492\pi$
$480$	1.10983	−	0.483258i	0.0506568	−	0.0220576i
$481$	6.22177	−	2.18119i	0.283688	−	0.0994538i
$482$	4.41609			0.201147
$483$	−11.8383	+	34.8606i	−0.538660	+	1.58621i
$484$	4.40623	−	7.63181i	0.200283	−	0.346901i
$485$		−	8.74519i		−	0.397098i
$486$	−15.5753	−	0.639374i	−0.706512	−	0.0290026i
$487$	−10.3865	+	17.9899i	−0.470657	+	0.815202i	−0.999437	−	0.0335574i	$-0.989316\pi$
$487$	−10.3865	+	17.9899i	−0.470657	+	0.815202i	0.528780	+	0.848759i	$0.322650\pi$
$488$	3.69483			0.167257
$489$	13.0451	+	1.47942i	0.589921	+	0.0669016i
$490$	4.87019	−	0.462636i	0.220013	−	0.0208997i
$491$	−11.1439	−	6.43392i	−0.502916	−	0.290359i	0.227001	−	0.973895i	$-0.427108\pi$
$491$	−11.1439	−	6.43392i	−0.502916	−	0.290359i	−0.729917	+	0.683536i	$0.760441\pi$
$492$	−2.26538	−	5.20260i	−0.102131	−	0.234552i
$493$	−6.41556	+	3.70403i	−0.288942	+	0.166821i
$494$	26.1467	−	9.16635i	1.17639	−	0.412413i
$495$	2.27011	+	2.11249i	0.102034	+	0.0949495i
$496$	−5.83175	−	3.36696i	−0.261853	−	0.151181i
$497$	−7.58195	+	34.8125i	−0.340097	+	1.56156i
$498$	1.04803	−	0.456345i	0.0469632	−	0.0204493i
$499$	20.6074	−	35.6931i	0.922516	−	1.59784i	0.127007	−	0.991902i	$-0.459463\pi$
$499$	20.6074	−	35.6931i	0.922516	−	1.59784i	0.795509	−	0.605942i	$-0.207204\pi$
$500$	3.32369	−	5.75681i	0.148640	−	0.257452i
$501$	1.84439	−	2.49527i	0.0824013	−	0.111480i
$502$	−13.2131	−	7.62856i	−0.589728	−	0.340479i
$503$	10.4430	+	18.0877i	0.465629	+	0.806492i	0.999230	−	0.0392439i	$-0.0124949\pi$
$503$	10.4430	+	18.0877i	0.465629	+	0.806492i	−0.533601	+	0.845736i	$0.679162\pi$
$504$	−4.52682	−	6.51981i	−0.201641	−	0.290415i
$505$	0.389717	−	0.675010i	0.0173422	−	0.0300376i
$506$	−10.2904	−	5.94119i	−0.457466	−	0.264118i
$507$	−19.9120	−	10.5124i	−0.884325	−	0.466872i
$508$	−6.67458	−	11.5607i	−0.296137	−	0.512924i
$509$	10.1690	+	17.6131i	0.450731	+	0.780689i	0.998432	−	0.0559855i	$-0.0178301\pi$
$509$	10.1690	+	17.6131i	0.450731	+	0.780689i	−0.547701	+	0.836674i	$0.684497\pi$
$510$	1.53644	+	1.13566i	0.0680345	+	0.0502880i
$511$	8.27742	−	38.0058i	0.366171	−	1.68128i
$512$		−	1.00000i		−	0.0441942i
$513$	−13.2700	+	37.6603i	−0.585885	+	1.66274i
$514$	−12.7345	−	7.35225i	−0.561694	−	0.324294i
$515$	−9.20013	+	5.31170i	−0.405406	+	0.234061i
$516$	−4.66429	−	0.528966i	−0.205334	−	0.0232864i
$517$	9.32856	+	5.38585i	0.410270	+	0.236869i
$518$	−4.60860	+	1.47196i	−0.202490	+	0.0646744i
$519$	27.7833	+	3.15084i	1.21955	+	0.138307i
$520$	−1.64253	+	1.91092i	−0.0720296	+	0.0837993i
$521$	21.7920	+	37.7449i	0.954725	+	1.65363i	0.734997	+	0.678071i	$0.237184\pi$
$521$	21.7920	+	37.7449i	0.954725	+	1.65363i	0.219728	+	0.975561i	$0.429483\pi$
$522$	13.7228	+	3.15311i	0.600633	+	0.138008i
$523$	10.3687	−	5.98635i	0.453390	−	0.261765i	−0.255871	−	0.966711i	$-0.582362\pi$
$523$	10.3687	−	5.98635i	0.453390	−	0.261765i	0.709261	+	0.704946i	$0.249029\pi$
$524$	−9.16140	−	15.8680i	−0.400217	−	0.693197i
$525$	−19.5766	−	6.64801i	−0.854394	−	0.290143i
$526$	6.67295	+	11.5579i	0.290955	+	0.503948i
$527$		−	10.6286i		−	0.462991i
$528$	2.34876	−	1.02272i	0.102217	−	0.0445084i
$529$	20.7715	−	35.9774i	0.903111	−	1.56423i
$530$	−2.81467	−	4.87515i	−0.122261	−	0.211763i
$531$	−28.1880	+	30.2912i	−1.22326	+	1.31453i
$532$	−19.3674	+	6.18585i	−0.839684	+	0.268191i
$533$	8.95787	+	7.69973i	0.388008	+	0.333512i
$534$	8.41548	+	6.22034i	0.364173	+	0.269180i
$535$			7.46451i			0.322719i
$536$		−	3.95565i		−	0.170858i
$537$	−0.191322	+	1.68703i	−0.00825616	+	0.0728007i
$538$		−	18.8456i		−	0.812491i
$539$	10.3068	−	0.979081i	0.443947	−	0.0421720i
$540$	−0.667361	−	3.56960i	−0.0287187	−	0.153611i
$541$	3.75077	−	6.49652i	0.161258	−	0.279307i	−0.774062	−	0.633110i	$-0.781778\pi$
$541$	3.75077	−	6.49652i	0.161258	−	0.279307i	0.935320	+	0.353802i	$0.115111\pi$
$542$	4.80370	−	8.32026i	0.206337	−	0.357386i
$543$	−1.48996	+	13.1381i	−0.0639405	+	0.563811i
$544$	1.36691	−	0.789186i	0.0586058	−	0.0338361i
$545$	−6.41263			−0.274687
$546$	14.3895	+	8.12050i	0.615813	+	0.347525i
$547$	0.731374			0.0312713			0.0156357	−	0.999878i	$-0.495023\pi$
$547$	0.731374			0.0312713			0.0156357	+	0.999878i	$0.495023\pi$
$548$	−17.2602	+	9.96519i	−0.737320	+	0.425692i
$549$	2.48221	−	10.8030i	0.105938	−	0.461060i
$550$	3.33639	−	5.77879i	0.142264	−	0.246409i
$551$	18.0335	−	31.2350i	0.768254	−	1.33066i
$552$	5.55527	+	12.7581i	0.236448	+	0.543019i
$553$	−4.25382	−	13.3184i	−0.180891	−	0.566355i
$554$		−	5.85244i		−	0.248646i
$555$	−2.19937	−	0.249425i	−0.0933579	−	0.0105875i
$556$		−	12.5583i		−	0.532591i
$557$			7.05913i			0.299105i	0.988754	+	0.149552i	$0.0477833\pi$
$557$			7.05913i			0.299105i	−0.988754	+	0.149552i	$0.952217\pi$
$558$	−13.7622	+	14.7890i	−0.582599	+	0.626068i
$559$	9.22148	−	3.23281i	0.390027	−	0.136733i
$560$	1.24411	−	1.36790i	0.0525734	−	0.0578042i
$561$	3.25158	+	2.40342i	0.137282	+	0.101472i
$562$	2.80997	+	4.86700i	0.118531	+	0.205302i
$563$	−14.3073	+	24.7810i	−0.602981	+	1.04439i	0.389386	+	0.921075i	$0.372687\pi$
$563$	−14.3073	+	24.7810i	−0.602981	+	1.04439i	−0.992367	+	0.123319i	$0.960646\pi$
$564$	−5.03601	−	11.5655i	−0.212054	−	0.486997i
$565$			7.07531i			0.297661i
$566$	7.85422	+	13.6039i	0.330138	+	0.571815i
$567$	−22.1038	+	8.85552i	−0.928274	+	0.371897i
$568$	6.73317	+	11.6622i	0.282518	+	0.489335i
$569$	9.19011	−	5.30591i	0.385269	−	0.222435i	−0.294839	−	0.955547i	$-0.595266\pi$
$569$	9.19011	−	5.30591i	0.385269	−	0.222435i	0.680108	+	0.733112i	$0.261933\pi$
$570$	−9.24272	−	1.04820i	−0.387135	−	0.0439041i
$571$	−5.54867	−	9.61058i	−0.232205	−	0.402190i	0.726252	−	0.687429i	$-0.241261\pi$
$571$	−5.54867	−	9.61058i	−0.232205	−	0.402190i	−0.958457	+	0.285238i	$0.907927\pi$
$572$	−3.47610	+	4.04410i	−0.145343	+	0.169092i
$573$	4.34256	−	38.2916i	0.181413	−	1.59965i
$574$	−6.41234	−	5.83207i	−0.267646	−	0.243426i
$575$	31.3895	+	18.1227i	1.30903	+	0.755769i
$576$	−2.92381	−	0.671806i	−0.121826	−	0.0279919i
$577$	−6.35102	+	3.66676i	−0.264396	+	0.152649i	−0.626338	−	0.779551i	$-0.715447\pi$
$577$	−6.35102	+	3.66676i	−0.264396	+	0.152649i	0.361942	+	0.932201i	$0.382114\pi$
$578$	−12.5649	−	7.25437i	−0.522633	−	0.301742i
$579$	−13.7044	−	1.55419i	−0.569536	−	0.0645898i
$580$			3.28015i			0.136201i
$581$	1.17483	−	1.29172i	0.0487401	−	0.0535895i
$582$	−12.8829	+	17.4292i	−0.534012	+	0.722464i
$583$	−5.95672	−	10.3173i	−0.246702	−	0.427301i
$584$	−7.35079	−	12.7319i	−0.304178	−	0.526852i
$585$	4.48371	+	6.08621i	0.185379	+	0.251634i
$586$	3.34776	+	1.93283i	0.138295	+	0.0798444i
$587$	−14.0104	+	24.2667i	−0.578271	+	1.00159i	0.417407	+	0.908720i	$0.362939\pi$
$587$	−14.0104	+	24.2667i	−0.578271	+	1.00159i	−0.995678	+	0.0928746i	$0.970394\pi$
$588$	−10.3878	−	6.25243i	−0.428387	−	0.257846i
$589$	25.8735	+	44.8141i	1.06610	+	1.84653i
$590$	−8.34786	−	4.81964i	−0.343676	−	0.198421i
$591$	−12.4756	−	9.22137i	−0.513176	−	0.379316i
$592$	−0.914289	+	1.58359i	−0.0375770	+	0.0650853i
$593$	20.0207	−	34.6769i	0.822152	−	1.42401i	−0.0819254	−	0.996638i	$-0.526107\pi$
$593$	20.0207	−	34.6769i	0.822152	−	1.42401i	0.904077	−	0.427370i	$-0.140560\pi$
$594$	−1.41235	−	7.55440i	−0.0579492	−	0.309961i
$595$	2.85163	+	0.621067i	0.116905	+	0.0254613i
$596$	−5.84670	−	3.37559i	−0.239490	−	0.138270i
$597$	30.3801	+	22.4556i	1.24337	+	0.919046i
$598$	−21.9669	−	18.8816i	−0.898293	−	0.772127i
$599$	−36.5373	+	21.0948i	−1.49287	+	0.861911i	−0.999967	−	0.00817029i	$-0.997399\pi$
$599$	−36.5373	+	21.0948i	−1.49287	+	0.861911i	−0.492908	+	0.870082i	$0.664066\pi$
$600$	−7.16454	+	3.11967i	−0.292491	+	0.127360i
$601$	12.5623	+	7.25284i	0.512426	+	0.295850i	0.733831	−	0.679333i	$-0.237731\pi$
$601$	12.5623	+	7.25284i	0.512426	+	0.295850i	−0.221404	+	0.975182i	$0.571064\pi$
$602$	−6.83055	+	2.18164i	−0.278392	+	0.0889171i
$603$	−11.5656	−	2.65743i	−0.470987	−	0.108219i
$604$	7.62285			0.310169
$605$	3.07940	−	5.33367i	0.125195	−	0.216845i
$606$	−1.77109	+	0.771191i	−0.0719457	+	0.0313275i
$607$		−	0.360914i		−	0.0146490i	−0.999973	−	0.00732452i	$-0.997669\pi$
$607$		−	0.360914i		−	0.0146490i	0.999973	−	0.00732452i	$-0.00233149\pi$
$608$	−3.84225	+	6.65498i	−0.155824	+	0.269895i
$609$	21.0954	−	4.19350i	0.854831	−	0.169929i
$610$	2.58222			0.104551
$611$	19.9136	+	17.1167i	0.805618	+	0.692468i
$612$	−1.38913	−	4.52677i	−0.0561524	−	0.182984i
$613$	11.8236			0.477552			0.238776	−	0.971075i	$-0.423254\pi$
$613$	11.8236			0.477552			0.238776	+	0.971075i	$0.423254\pi$
$614$	−11.7331	−	20.3224i	−0.473511	−	0.820144i
$615$	−1.58321	−	3.63596i	−0.0638414	−	0.146616i
$616$	2.63294	−	2.89490i	0.106084	−	0.116639i
$617$	−9.75168	+	5.63013i	−0.392588	+	0.226661i	−0.683281	−	0.730156i	$-0.739447\pi$
$617$	−9.75168	+	5.63013i	−0.392588	+	0.226661i	0.290693	+	0.956816i	$0.406114\pi$
$618$	26.1608	+	2.96683i	1.05234	+	0.119344i
$619$	13.8755	−	8.01105i	0.557705	−	0.321991i	−0.194519	−	0.980899i	$-0.562315\pi$
$619$	13.8755	−	8.01105i	0.557705	−	0.321991i	0.752224	+	0.658908i	$0.228981\pi$
$620$	−4.07566	−	2.35308i	−0.163682	−	0.0945020i
$621$	41.0343	−	7.67163i	1.64665	−	0.307852i
$622$	−14.6547	−	8.46088i	−0.587599	−	0.339250i
$623$	15.6192	+	3.40175i	0.625768	+	0.136288i
$624$	6.08862	−	1.38880i	0.243740	−	0.0555964i
$625$	−8.95610	+	15.5124i	−0.358244	+	0.620497i
$626$	−17.1572			−0.685738
$627$	−19.5605	−	2.21831i	−0.781171	−	0.0885908i
$628$		−	5.96598i		−	0.238069i
$629$	−2.88617			−0.115079
$630$	−3.16367	−	4.55652i	−0.126044	−	0.181536i
$631$	12.2109	+	21.1499i	0.486107	+	0.841963i	0.999872	−	0.0159683i	$-0.00508308\pi$
$631$	12.2109	+	21.1499i	0.486107	+	0.841963i	−0.513765	+	0.857931i	$0.671750\pi$
$632$	−4.57643	−	2.64220i	−0.182040	−	0.105101i
$633$	12.6789	−	17.1533i	0.503943	−	0.681782i
$634$	24.6955			0.980784
$635$	−4.66469	−	8.07947i	−0.185112	−	0.320624i
$636$	−1.57213	+	13.8626i	−0.0623388	+	0.549688i
$637$	25.1328	+	2.31125i	0.995798	+	0.0915751i
$638$			6.94181i			0.274829i
$639$	38.6215	−	11.8518i	1.52784	−	0.468850i
$640$		−	0.698873i		−	0.0276254i
$641$	14.5095	+	8.37708i	0.573092	+	0.330875i	0.758383	−	0.651809i	$-0.225990\pi$
$641$	14.5095	+	8.37708i	0.573092	+	0.330875i	−0.185291	+	0.982684i	$0.559323\pi$
$642$	10.9963	−	14.8768i	0.433988	−	0.587141i
$643$	−10.0110	+	5.77985i	−0.394795	+	0.227935i	−0.684236	−	0.729261i	$-0.739864\pi$
$643$	−10.0110	+	5.77985i	−0.394795	+	0.227935i	0.289441	+	0.957196i	$0.406531\pi$
$644$	15.7246	+	14.3017i	0.619637	+	0.563565i
$645$	−3.25975	−	0.369680i	−0.128352	−	0.0145562i
$646$	−12.1290			−0.477209
$647$	−29.9969			−1.17930			−0.589649	−	0.807659i	$-0.700734\pi$
$647$	−29.9969			−1.17930			−0.589649	+	0.807659i	$0.700734\pi$
$648$	−3.92847	+	8.09735i	−0.154325	+	0.318094i
$649$	−17.6667	−	10.1999i	−0.693478	−	0.400380i
$650$	10.6033	−	12.3359i	0.415897	−	0.483855i
$651$	−9.92275	+	29.2199i	−0.388903	+	1.14522i
$652$	3.78994	−	6.56437i	0.148426	−	0.257081i
$653$	−22.1413	+	12.7833i	−0.866457	+	0.500249i	−0.866169	−	0.499751i	$-0.833425\pi$
$653$	−22.1413	+	12.7833i	−0.866457	+	0.500249i	−0.000287486		1.00000i	$0.500092\pi$
$654$	12.7804	+	9.44670i	0.499753	+	0.369395i
$655$	−6.40266	−	11.0897i	−0.250172	−	0.433311i
$656$	−3.27613			−0.127911
$657$	−42.1641	+	12.9389i	−1.64498	+	0.504796i
$658$	−14.2548	−	12.9649i	−0.555710	−	0.505423i
$659$	−6.23900	+	3.60209i	−0.243037	+	0.140317i	−0.616572	−	0.787299i	$-0.711479\pi$
$659$	−6.23900	+	3.60209i	−0.243037	+	0.140317i	0.373535	+	0.927616i	$0.378146\pi$
$660$	1.64148	−	0.714755i	0.0638947	−	0.0278218i
$661$			18.0796i			0.703215i	0.936148	+	0.351607i	$0.114365\pi$
$661$			18.0796i			0.703215i	−0.936148	+	0.351607i	$0.885635\pi$
$662$	−27.7416	+	16.0166i	−1.07821	+	0.622504i
$663$	6.70341	+	7.22657i	0.260339	+	0.280657i
$664$		−	0.659952i		−	0.0256111i
$665$	−13.5354	+	4.32313i	−0.524879	+	0.167644i
$666$	4.01591	+	3.73708i	0.155613	+	0.144809i
$667$	−37.7068			−1.46001
$668$	−0.895737	−	1.55146i	−0.0346571	−	0.0600279i
$669$	16.1662	+	11.9493i	0.625022	+	0.461988i
$670$		−	2.76450i		−	0.106802i
$671$	5.46478			0.210965
$672$	−4.49463	+	0.893473i	−0.173384	+	0.0344665i
$673$	−16.0613	+	27.8191i	−0.619119	+	1.07235i	0.370528	+	0.928821i	$0.379177\pi$
$673$	−16.0613	+	27.8191i	−0.619119	+	1.07235i	−0.989647	+	0.143524i	$0.954157\pi$
$674$	19.5236	−	11.2720i	0.752023	−	0.434181i
$675$	4.30815	+	23.0436i	0.165821	+	0.886948i
$676$	−10.1543	+	8.11729i	−0.390550	+	0.312203i
$677$	9.18179	−	15.9033i	0.352885	−	0.611214i	−0.633869	−	0.773441i	$-0.718534\pi$
$677$	9.18179	−	15.9033i	0.352885	−	0.611214i	0.986754	+	0.162226i	$0.0518674\pi$
$678$	10.4229	−	14.1011i	0.400290	−	0.541550i
$679$	−7.04533	+	32.3487i	−0.270375	+	1.24143i
$680$	0.955297	−	0.551541i	0.0366339	−	0.0211506i
$681$	1.22434	−	1.65640i	0.0469167	−	0.0634735i
$682$	−8.62536	−	4.97985i	−0.330282	−	0.190689i
$683$	−18.4956	−	10.6785i	−0.707715	−	0.408600i	0.102499	−	0.994733i	$-0.467316\pi$
$683$	−18.4956	−	10.6785i	−0.707715	−	0.408600i	−0.810214	+	0.586134i	$0.800649\pi$
$684$	16.8767	+	15.7049i	0.645295	+	0.600491i
$685$	−12.0627	+	6.96440i	−0.460892	+	0.266096i
$686$	−18.3877	−	2.21224i	−0.702044	−	0.0844637i
$687$	9.28688	+	6.86444i	0.354317	+	0.261895i
$688$	−1.35510	+	2.34709i	−0.0516625	+	0.0894821i
$689$	−9.60814	−	27.4069i	−0.366041	−	1.04412i
$690$	3.88243	+	8.91627i	0.147802	+	0.339437i
$691$	−3.04686	+	1.75911i	−0.115908	+	0.0669196i	−0.556833	−	0.830624i	$-0.687984\pi$
$691$	−3.04686	+	1.75911i	−0.115908	+	0.0669196i	0.440925	+	0.897544i	$0.354650\pi$
$692$	8.07176	−	13.9807i	0.306842	−	0.531467i
$693$	−6.69532	−	9.64302i	−0.254334	−	0.366308i
$694$	−15.8455			−0.601487
$695$		−	8.77668i		−	0.332918i
$696$	4.83211	−	6.53735i	0.183161	−	0.247797i
$697$	−2.58547	−	4.47817i	−0.0979318	−	0.169623i
$698$	22.3012			0.844113
$699$	−10.0435	−	7.42367i	−0.379879	−	0.280789i
$700$	−8.03138	+	8.83047i	−0.303558	+	0.333760i
$701$		−	21.8719i		−	0.826089i	−0.910711	−	0.413044i	$-0.864465\pi$
$701$		−	21.8719i		−	0.826089i	0.910711	−	0.413044i	$-0.135535\pi$
$702$	0.0297819	−	18.7350i	0.00112404	−	0.707106i
$703$	12.1691	−	7.02586i	0.458968	−	0.264985i
$704$		−	1.47903i		−	0.0557432i
$705$	−3.51953	−	8.08284i	−0.132553	−	0.304418i
$706$	7.88910	−	4.55477i	0.296910	−	0.171421i
$707$	−1.98538	+	2.18291i	−0.0746678	+	0.0820969i
$708$	9.53733	+	21.9031i	0.358435	+	0.823170i
$709$	−11.3165			−0.425002			−0.212501	−	0.977161i	$-0.568161\pi$
$709$	−11.3165			−0.425002			−0.212501	+	0.977161i	$0.568161\pi$
$710$	4.70564	+	8.15040i	0.176599	+	0.305879i
$711$	−10.7998	+	11.6056i	−0.405023	+	0.435243i
$712$	5.23242	−	3.02094i	0.196093	−	0.113214i
$713$	27.0498	−	46.8516i	1.01302	−	1.75460i
$714$	−4.76840	−	5.43864i	−0.178453	−	0.203536i
$715$	−2.42935	+	2.82631i	−0.0908527	+	0.105698i
$716$	0.848922	+	0.490125i	0.0317257	+	0.0183168i
$717$	1.28724	−	11.3506i	0.0480729	−	0.423894i
$718$	−3.06670			−0.114448
$719$	−13.9466			−0.520119			−0.260060	−	0.965593i	$-0.583742\pi$
$719$	−13.9466			−0.520119			−0.260060	+	0.965593i	$0.583742\pi$
$720$	−2.04337	−	0.469507i	−0.0761521	−	0.0174975i
$721$	38.3107	−	12.2363i	1.42677	−	0.455702i
$722$	34.6857	−	20.0258i	1.29087	−	0.745283i
$723$	−6.15098	−	4.54653i	−0.228758	−	0.169087i
$724$	6.61117	+	3.81696i	0.245702	+	0.141856i
$725$		−	21.1750i		−	0.786419i
$726$	−13.9945	+	6.09365i	−0.519384	+	0.226157i
$727$		−	5.92782i		−	0.219850i	−0.993940	−	0.109925i	$-0.964939\pi$
$727$		−	5.92782i		−	0.219850i	0.993940	−	0.109925i	$-0.0350611\pi$
$728$	7.61523	−	5.74528i	0.282239	−	0.212934i
$729$	21.0360	+	16.9260i	0.779110	+	0.626887i
$730$	−5.13727	−	8.89801i	−0.190139	−	0.329330i
$731$	−4.27769			−0.158216
$732$	−5.14637	−	3.80396i	−0.190215	−	0.140599i
$733$	−24.5262	−	14.1602i	−0.905896	−	0.523019i	−0.0267874	−	0.999641i	$-0.508528\pi$
$733$	−24.5262	−	14.1602i	−0.905896	−	0.523019i	−0.879108	+	0.476622i	$0.841861\pi$
$734$	1.32070	+	2.28752i	0.0487479	+	0.0844338i
$735$	−7.25978	−	4.36966i	−0.267781	−	0.161177i
$736$	8.03387			0.296132
$737$		−	5.85055i		−	0.215508i
$738$	−2.20092	+	9.57878i	−0.0810171	+	0.352600i
$739$	47.0720			1.73157			0.865785	−	0.500416i	$-0.166820\pi$
$739$	47.0720			1.73157			0.865785	+	0.500416i	$0.166820\pi$
$740$	−0.638972	+	1.10673i	−0.0234891	+	0.0406843i
$741$	−45.8557	−	14.1516i	−1.68455	−	0.519871i
$742$	6.48400	+	20.3009i	0.238035	+	0.745269i
$743$	17.7056	+	10.2223i	0.649554	+	0.375020i	0.788285	−	0.615310i	$-0.210969\pi$
$743$	17.7056	+	10.2223i	0.649554	+	0.375020i	−0.138732	+	0.990330i	$0.544303\pi$
$744$	4.65639	+	10.6937i	0.170711	+	0.392050i
$745$	−4.08610	−	2.35911i	−0.149703	−	0.0864311i
$746$	4.66207	−	2.69165i	0.170691	−	0.0985483i
$747$	−1.92958	−	0.443360i	−0.0705995	−	0.0162217i
$748$	2.02171	−	1.16723i	0.0739209	−	0.0426782i
$749$	6.01359	−	27.6114i	0.219732	−	1.00890i
$750$	−10.5563	+	4.59654i	−0.385461	+	0.167842i
$751$	−21.7069	−	37.5975i	−0.792097	−	1.37195i	−0.924666	−	0.380779i	$-0.875656\pi$
$751$	−21.7069	−	37.5975i	−0.792097	−	1.37195i	0.132569	−	0.991174i	$-0.457677\pi$
$752$	−7.28293			−0.265581
$753$	10.5500	+	24.2288i	0.384464	+	0.882948i
$754$	−3.13634	+	16.6294i	−0.114219	+	0.605607i
$755$	5.32741			0.193884
$756$	−0.407172	+	13.7417i	−0.0148087	+	0.499781i
$757$	−6.03356	+	10.4504i	−0.219293	+	0.379827i	−0.954592	−	0.297916i	$-0.903709\pi$
$757$	−6.03356	+	10.4504i	−0.219293	+	0.379827i	0.735299	+	0.677743i	$0.237042\pi$
$758$			13.7784i			0.500454i
$759$	8.21644	+	18.8696i	0.298238	+	0.684924i
$760$	−2.68525	+	4.65098i	−0.0974042	+	0.168709i
$761$	0.990826			0.0359174			0.0179587	−	0.999839i	$-0.494283\pi$
$761$	0.990826			0.0359174			0.0179587	+	0.999839i	$0.494283\pi$
$762$	−2.60545	+	22.9742i	−0.0943854	+	0.832266i
$763$	23.7205	+	5.16617i	0.858739	+	0.187028i
$764$	−19.2685	−	11.1247i	−0.697110	−	0.402477i
$765$	−0.970828	−	3.16364i	−0.0351003	−	0.114381i
$766$	24.8621	−	14.3541i	0.898304	−	0.518636i
$767$	−37.7129	−	32.4161i	−1.36173	−	1.17048i
$768$	−1.02954	+	1.39286i	−0.0371502	+	0.0502604i
$769$	−41.7420	−	24.0998i	−1.50526	−	0.869060i	−0.999981	−	0.00610115i	$-0.998058\pi$
$769$	−41.7420	−	24.0998i	−1.50526	−	0.869060i	−0.505274	−	0.862959i	$-0.668609\pi$
$770$	1.84009	−	2.02317i	0.0663122	−	0.0729099i
$771$	10.1679	+	23.3513i	0.366188	+	0.840975i
$772$	−3.98148	+	6.89613i	−0.143297	+	0.248197i
$773$	−5.46527	+	9.46613i	−0.196572	+	0.340473i	−0.947415	−	0.320008i	$-0.896314\pi$
$773$	−5.46527	+	9.46613i	−0.196572	+	0.340473i	0.750843	+	0.660481i	$0.229648\pi$
$774$	5.95210	+	5.53884i	0.213944	+	0.199089i
$775$	26.3104	+	15.1903i	0.945097	+	0.545652i
$776$	6.25663	+	10.8368i	0.224600	+	0.389019i
$777$	7.93457	+	2.69449i	0.284651	+	0.0966643i
$778$	11.3855	−	19.7202i	0.408189	−	0.707004i
$779$	21.8026	+	12.5877i	0.781158	+	0.451002i
$780$	4.25517	−	0.970594i	0.152360	−	0.0347528i
$781$	9.95859	+	17.2488i	0.356346	+	0.617210i
$782$	6.34022	+	10.9816i	0.226726	+	0.392700i
$783$	−15.8677	−	18.5200i	−0.567066	−	0.661851i
$784$	−5.70402	+	4.05760i	−0.203715	+	0.144914i
$785$		−	4.16946i		−	0.148815i
$786$	−3.57618	+	31.5339i	−0.127558	+	1.12478i
$787$	23.2360	+	13.4153i	0.828274	+	0.478204i	0.853261	−	0.521484i	$-0.174621\pi$
$787$	23.2360	+	13.4153i	0.828274	+	0.478204i	−0.0249873	+	0.999688i	$0.507955\pi$
$788$	−7.75682	+	4.47840i	−0.276325	+	0.159537i
$789$	2.60481	−	22.9686i	0.0927338	−	0.817702i
$790$	−3.19834	−	1.84656i	−0.113792	−	0.0656978i
$791$	5.70004	−	26.1717i	0.202670	−	0.930560i
$792$	−4.32442	−	0.993624i	−0.153661	−	0.0353069i
$793$	13.0911	+	2.46901i	0.464878	+	0.0876772i
$794$	5.35066	+	9.26762i	0.189888	+	0.328895i
$795$	−1.09872	+	9.68820i	−0.0389675	+	0.343605i
$796$	18.8892	−	10.9057i	0.669509	−	0.386541i
$797$	20.5234	+	35.5476i	0.726977	+	1.25916i	0.958155	+	0.286250i	$0.0924088\pi$
$797$	20.5234	+	35.5476i	0.726977	+	1.25916i	−0.231178	+	0.972912i	$0.574258\pi$
$798$	33.3446	+	11.3235i	1.18039	+	0.400846i
$799$	−5.74758	−	9.95510i	−0.203335	−	0.352186i
$800$			4.51158i			0.159508i
$801$	−5.31749	−	17.3281i	−0.187884	−	0.612258i
$802$	−6.20069	+	10.7399i	−0.218954	+	0.379239i
$803$	−10.8721	−	18.8310i	−0.383667	−	0.664531i
$804$	−4.07249	+	5.50966i	−0.143626	+	0.194311i
$805$	10.9895	+	9.99506i	0.387330	+	0.352280i
$806$	−18.4125	−	15.8264i	−0.648552	−	0.557462i
$807$	−19.4023	+	26.2492i	−0.682992	+	0.924017i
$808$			1.11527i			0.0392352i
$809$			39.4944i			1.38855i	0.719710	+	0.694275i	$0.244275\pi$
$809$			39.4944i			1.38855i	−0.719710	+	0.694275i	$0.755725\pi$
$810$	−2.74550	+	5.65902i	−0.0964671	+	0.198838i
$811$			51.6567i			1.81391i	0.421226	+	0.906956i	$0.361600\pi$
$811$			51.6567i			1.81391i	−0.421226	+	0.906956i	$0.638400\pi$
$812$	2.64256	−	12.1333i	0.0927358	−	0.425797i
$813$	−15.2569	+	6.64334i	−0.535083	+	0.232992i
$814$	−1.35226	+	2.34219i	−0.0473968	+	0.0820937i
$815$	2.64869	−	4.58766i	0.0927795	−	0.160699i
$816$	−2.71641	−	0.308061i	−0.0950933	−	0.0107843i
$817$	18.0363	−	10.4132i	0.631009	−	0.364313i
$818$	−11.8142			−0.413073
$819$	−11.6822	−	26.1252i	−0.408207	−	0.912889i
$820$	−2.28960			−0.0799562
$821$	41.1557	−	23.7613i	1.43634	−	0.829273i	0.438750	−	0.898609i	$-0.355421\pi$
$821$	41.1557	−	23.7613i	1.43634	−	0.829273i	0.997593	+	0.0693355i	$0.0220879\pi$
$822$	34.3006	+	3.88995i	1.19637	+	0.135677i
$823$	−19.8401	+	34.3641i	−0.691583	+	1.19786i	0.279736	+	0.960077i	$0.409753\pi$
$823$	−19.8401	+	34.3641i	−0.691583	+	1.19786i	−0.971319	+	0.237780i	$0.923580\pi$
$824$	7.60037	−	13.1642i	0.264772	−	0.458598i
$825$	−10.5966	+	4.61410i	−0.368926	+	0.160642i
$826$	26.9961	+	24.5532i	0.939316	+	0.854315i
$827$			1.16764i			0.0406030i	0.999794	+	0.0203015i	$0.00646261\pi$
$827$			1.16764i			0.0406030i	−0.999794	+	0.0203015i	$0.993537\pi$
$828$	5.39720	−	23.4895i	0.187566	−	0.816318i
$829$		−	1.68864i		−	0.0586491i	−0.999570	−	0.0293245i	$-0.990664\pi$
$829$		−	1.68864i		−	0.0586491i	0.999570	−	0.0293245i	$-0.00933563\pi$
$830$		−	0.461223i		−	0.0160093i
$831$	−6.02531	+	8.15161i	−0.209016	+	0.282776i
$832$	0.668235	−	3.54309i	0.0231669	−	0.122834i
$833$	−10.0479	−	4.59468i	−0.348139	−	0.159196i
$834$	−12.9293	+	17.4920i	−0.447704	+	0.605697i
$835$	−0.626007	−	1.08428i	−0.0216639	−	0.0375229i
$836$	−5.68282	+	9.84294i	−0.196545	+	0.340425i
$837$	34.3946	−	6.43030i	1.18885	−	0.222264i
$838$		−	15.5384i		−	0.536767i
$839$	−9.54818	−	16.5379i	−0.329640	−	0.570953i	0.652801	−	0.757530i	$-0.273594\pi$
$839$	−9.54818	−	16.5379i	−0.329640	−	0.570953i	−0.982440	+	0.186577i	$0.940261\pi$
$840$	−3.14118	+	0.624425i	−0.108381	+	0.0215447i
$841$	−3.48563	−	6.03729i	−0.120194	−	0.208183i
$842$	22.6624	−	13.0842i	0.780999	−	0.450910i
$843$	1.09688	−	9.67201i	0.0377786	−	0.333122i
$844$	−6.15759	−	10.6653i	−0.211953	−	0.367113i
$845$	−7.09656	+	5.67296i	−0.244129	+	0.195156i
$846$	−4.89271	+	21.2939i	−0.168215	+	0.732100i
$847$	−15.6877	+	17.2485i	−0.539036	+	0.592667i
$848$	6.97573	+	4.02744i	0.239548	+	0.138303i
$849$	3.06592	−	27.0345i	0.105222	−	0.927823i
$850$	−6.16692	+	3.56047i	−0.211523	+	0.122123i
$851$	−12.7224	−	7.34528i	−0.436118	−	0.251793i
$852$	2.62832	−	23.1758i	0.0900447	−	0.793991i
$853$			24.3423i			0.833465i	0.909029	+	0.416733i	$0.136825\pi$
$853$			24.3423i			0.833465i	−0.909029	+	0.416733i	$0.863175\pi$
$854$	−9.55168	−	2.08030i	−0.326852	−	0.0711862i
$855$	11.7946	+	10.9757i	0.403368	+	0.375362i
$856$	−5.34039	−	9.24982i	−0.182531	−	0.316152i
$857$	−24.2077	−	41.9290i	−0.826920	−	1.43227i	−0.900443	−	0.434975i	$-0.856757\pi$
$857$	−24.2077	−	41.9290i	−0.826920	−	1.43227i	0.0735222	−	0.997294i	$-0.476576\pi$
$858$	9.00527	−	2.05408i	0.307435	−	0.0701251i
$859$	−16.3050	−	9.41372i	−0.556321	−	0.321192i	0.195347	−	0.980734i	$-0.437417\pi$
$859$	−16.3050	−	9.41372i	−0.556321	−	0.321192i	−0.751667	+	0.659542i	$0.770750\pi$
$860$	−0.947040	+	1.64032i	−0.0322938	+	0.0559345i
$861$	2.92713	+	14.7250i	0.0997564	+	0.501826i
$862$	11.2420	+	19.4718i	0.382905	+	0.663212i
$863$	−36.4727	−	21.0575i	−1.24154	−	0.716806i	−0.272136	−	0.962259i	$-0.587730\pi$
$863$	−36.4727	−	21.0575i	−1.24154	−	0.716806i	−0.969409	+	0.245453i	$0.921063\pi$
$864$	3.38080	+	3.94590i	0.115017	+	0.134242i
$865$	5.64114	−	9.77074i	0.191804	−	0.332215i
$866$	−10.3947	+	18.0042i	−0.353227	+	0.611807i
$867$	10.0325	+	23.0404i	0.340722	+	0.782493i
$868$	13.1803	+	11.9876i	0.447367	+	0.406884i
$869$	−6.76869	−	3.90791i	−0.229612	−	0.132567i
$870$	3.37703	−	4.56878i	0.114492	−	0.154896i
$871$	2.64331	−	14.0152i	0.0895650	−	0.474888i
$872$	7.94637	−	4.58784i	0.269098	−	0.155364i
$873$	35.8880	−	11.0130i	1.21463	−	0.372733i
$874$	−53.4652	−	30.8682i	−1.80849	−	1.04413i
$875$	−11.8335	+	13.0109i	−0.400045	+	0.439848i
$876$	−2.86941	+	25.3017i	−0.0969483	+	0.854865i
$877$	8.36751			0.282551			0.141275	−	0.989970i	$-0.454880\pi$
$877$	8.36751			0.282551			0.141275	+	0.989970i	$0.454880\pi$
$878$	−5.26300	+	9.11578i	−0.177618	+	0.307643i
$879$	−2.67303	−	6.13880i	−0.0901591	−	0.207057i
$880$		−	1.03366i		−	0.0348446i
$881$	0.557391	−	0.965430i	0.0187790	−	0.0325262i	−0.856483	−	0.516175i	$-0.827355\pi$
$881$	0.557391	−	0.965430i	0.0187790	−	0.0325262i	0.875262	+	0.483649i	$0.160689\pi$
$882$	8.03166	+	19.4034i	0.270440	+	0.653347i
$883$	−1.05349			−0.0354528			−0.0177264	−	0.999843i	$-0.505643\pi$
$883$	−1.05349			−0.0354528			−0.0177264	+	0.999843i	$0.505643\pi$
$884$	5.37044	−	1.88274i	0.180627	−	0.0633233i
$885$	6.66538	+	15.3075i	0.224054	+	0.514556i
$886$	26.5042			0.890424
$887$	7.65471	+	13.2583i	0.257020	+	0.445172i	0.965442	−	0.260617i	$-0.0839260\pi$
$887$	7.65471	+	13.2583i	0.257020	+	0.445172i	−0.708422	+	0.705789i	$0.750593\pi$
$888$	2.90384	−	1.26443i	0.0974466	−	0.0424314i
$889$	10.7458	+	33.6442i	0.360402	+	1.12839i
$890$	3.65680	−	2.11125i	0.122576	−	0.0707694i
$891$	−5.81034	+	11.9763i	−0.194654	+	0.401220i
$892$	10.0515	−	5.80325i	0.336550	−	0.194307i
$893$	48.4677	+	27.9828i	1.62191	+	0.936410i
$894$	4.66832	+	10.7211i	0.156132	+	0.358568i
$895$	0.593289	+	0.342536i	0.0198315	+	0.0114497i
$896$	−0.563029	+	2.58515i	−0.0188095	+	0.0863638i
$897$	11.1574	+	48.9152i	0.372536	+	1.63323i
$898$	−10.1017	+	17.4966i	−0.337097	+	0.583870i
$899$	−31.6055			−1.05410
$900$	13.1910	+	3.03090i	0.439700	+	0.101030i
$901$			12.7136i			0.423551i
$902$	−4.84551			−0.161338
$903$	11.7601	+	3.99359i	0.391350	+	0.132898i
$904$	−5.06194	−	8.76754i	−0.168358	−	0.291604i
$905$	4.62037	+	2.66757i	0.153586	+	0.0886730i
$906$	−10.6175	−	7.84801i	−0.352744	−	0.260733i
$907$	−3.67637			−0.122072			−0.0610359	−	0.998136i	$-0.519440\pi$
$907$	−3.67637			−0.122072			−0.0610359	+	0.998136i	$0.519440\pi$
$908$	−0.594606	−	1.02989i	−0.0197327	−	0.0341780i
$909$	3.26085	+	0.749247i	0.108156	+	0.0248510i
$910$	5.32208	−	4.01522i	0.176425	−	0.133103i
$911$		−	48.3126i		−	1.60067i	−0.599556	−	0.800333i	$-0.704656\pi$
$911$		−	48.3126i		−	1.60067i	0.599556	−	0.800333i	$-0.295344\pi$
$912$	12.2033	−	5.31369i	0.404090	−	0.175954i
$913$		−	0.976092i		−	0.0323039i
$914$	−11.7120	−	6.76192i	−0.387398	−	0.223664i
$915$	−3.59666	−	2.65849i	−0.118902	−	0.0878869i
$916$	5.77423	−	3.33375i	0.190786	−	0.110150i
$917$	14.7494	+	46.1793i	0.487069	+	1.52497i
$918$	−2.72561	+	7.73531i	−0.0899586	+	0.255303i
$919$	28.2525			0.931963			0.465982	−	0.884794i	$-0.345701\pi$
$919$	28.2525			0.931963			0.465982	+	0.884794i	$0.345701\pi$
$920$	5.61466			0.185110
$921$	−4.58007	+	40.3859i	−0.150918	+	1.33076i
$922$	26.4348	+	15.2621i	0.870583	+	0.502632i
$923$	16.0631	+	45.8195i	0.528724	+	1.50817i
$924$	−6.64771	+	1.32148i	−0.218694	+	0.0434734i
$925$	4.12488	−	7.14451i	0.135625	−	0.234910i
$926$	16.3986	−	9.46775i	0.538892	−	0.311130i
$927$	−33.3838	−	31.0659i	−1.09647	−	1.02034i
$928$	−2.34674	−	4.06467i	−0.0770355	−	0.133429i
$929$	−16.2097			−0.531823			−0.265911	−	0.963997i	$-0.585673\pi$
$929$	−16.2097			−0.531823			−0.265911	+	0.963997i	$0.585673\pi$
$930$	3.25422	+	7.47355i	0.106710	+	0.245067i
$931$	53.5505	−	5.08694i	1.75505	−	0.166718i
$932$	−6.24464	+	3.60534i	−0.204550	+	0.118097i
$933$	11.7011	+	26.8723i	0.383076	+	0.879761i
$934$			1.56992i			0.0513694i
$935$	1.41292	−	0.815747i	0.0462073	−	0.0266778i
$936$	−9.91040	−	4.33406i	−0.323931	−	0.141663i
$937$		−	40.9010i		−	1.33618i	−0.744082	−	0.668088i	$-0.767113\pi$
$937$		−	40.9010i		−	1.33618i	0.744082	−	0.668088i	$-0.232887\pi$
$938$	−2.22715	+	10.2260i	−0.0727190	+	0.333889i
$939$	23.8975	+	17.6639i	0.779864	+	0.576441i
$940$	−5.08984			−0.166012
$941$	−21.0594	−	36.4760i	−0.686517	−	1.18908i	−0.972957	−	0.230984i	$-0.925805\pi$
$941$	−21.0594	−	36.4760i	−0.686517	−	1.18908i	0.286441	−	0.958098i	$-0.407528\pi$
$942$	−6.14220	+	8.30976i	−0.200124	+	0.270747i
$943$		−	26.3200i		−	0.857097i
$944$	13.7926			0.448911
$945$	−0.284561	+	9.60370i	−0.00925679	+	0.312409i
$946$	−2.00423	+	3.47143i	−0.0651632	+	0.112866i
$947$	−44.5633	+	25.7286i	−1.44811	+	0.836068i	−0.998369	−	0.0570898i	$-0.981818\pi$
$947$	−44.5633	+	25.7286i	−1.44811	+	0.836068i	−0.449743	+	0.893158i	$0.648485\pi$
$948$	3.65407	+	8.39181i	0.118679	+	0.272553i
$949$	−17.5366	−	50.0224i	−0.569261	−	1.62380i
$950$	17.3346	−	30.0244i	0.562409	−	0.974121i
$951$	−34.3973	−	25.4250i	−1.11541	−	0.824461i
$952$	−3.97800	+	1.27055i	−0.128928	+	0.0411789i
$953$	−9.84866	+	5.68613i	−0.319029	+	0.184192i	−0.650960	−	0.759112i	$-0.725633\pi$
$953$	−9.84866	+	5.68613i	−0.319029	+	0.184192i	0.331931	+	0.943304i	$0.392300\pi$
$954$	16.4618	−	17.6901i	0.532971	−	0.572737i
$955$	−13.4662	−	7.77474i	−0.435757	−	0.251585i
$956$	−5.71166	−	3.29763i	−0.184728	−	0.106653i
$957$	7.14686	−	9.66896i	0.231025	−	0.312553i
$958$	−25.7325	+	14.8567i	−0.831381	+	0.479998i
$959$	50.2309	−	16.0435i	1.62204	−	0.518072i
$960$	−0.719516	+	0.973431i	−0.0232223	+	0.0314173i
$961$	7.17290	−	12.4238i	0.231384	−	0.400769i
$962$	−4.29762	+	4.99985i	−0.138561	+	0.161202i
$963$	−30.6324	+	9.40021i	−0.987117	+	0.302917i
$964$	−3.82445	+	2.20804i	−0.123177	+	0.0711163i
$965$	−2.78255	+	4.81952i	−0.0895735	+	0.155146i
$966$	−7.17805	−	36.1093i	−0.230950	−	1.16180i
$967$	12.5442			0.403396			0.201698	−	0.979448i	$-0.435354\pi$
$967$	12.5442			0.403396			0.201698	+	0.979448i	$0.435354\pi$
$968$			8.81246i			0.283243i
$969$	16.8940	+	12.4873i	0.542713	+	0.401149i
$970$	4.37259	+	7.57355i	0.140396	+	0.243172i
$971$	−9.33395			−0.299541			−0.149770	−	0.988721i	$-0.547853\pi$
$971$	−9.33395			−0.299541			−0.149770	+	0.988721i	$0.547853\pi$
$972$	13.8083	−	7.23396i	0.442902	−	0.232029i
$973$	−7.07070	+	32.4651i	−0.226676	+	1.04078i
$974$		−	20.7730i		−	0.665609i
$975$	−27.4693	+	6.26567i	−0.879720	+	0.200662i
$976$	−3.19981	+	1.84741i	−0.102424	+	0.0591343i
$977$		−	16.1067i		−	0.515299i	−0.966238	−	0.257650i	$-0.917052\pi$
$977$		−	16.1067i		−	0.515299i	0.966238	−	0.257650i	$-0.0829480\pi$
$978$	−12.0371	+	5.24135i	−0.384905	+	0.167600i
$979$	7.73893	−	4.46807i	0.247337	−	0.142800i
$980$	−3.98639	+	2.83575i	−0.127341	+	0.0905847i
$981$	−8.07556	−	26.3158i	−0.257833	−	0.840199i
$982$	12.8678			0.410629
$983$	−11.9633	−	20.7211i	−0.381570	−	0.660899i	0.609717	−	0.792619i	$-0.291283\pi$
$983$	−11.9633	−	20.7211i	−0.381570	−	0.660899i	−0.991287	+	0.131720i	$0.957950\pi$
$984$	4.56318	+	3.37290i	0.145469	+	0.107524i
$985$	−5.42104	+	3.12984i	−0.172729	+	0.0997249i
$986$	3.70403	−	6.41556i	0.117960	−	0.204313i
$987$	6.50710	+	32.7341i	0.207123	+	1.04194i
$988$	−18.0605	+	21.0116i	−0.574582	+	0.668469i
$989$	−18.8563	−	10.8867i	−0.599594	−	0.346176i
$990$	−3.02222	−	0.694417i	−0.0960524	−	0.0220700i
$991$	16.9341			0.537929			0.268965	−	0.963150i	$-0.413319\pi$
$991$	16.9341			0.537929			0.268965	+	0.963150i	$0.413319\pi$
$992$	6.73393			0.213802
$993$	55.1299	+	6.25215i	1.74949	+	0.198406i
$994$	−10.8401	−	33.9395i	−0.343827	−	1.07650i
$995$	13.2011	−	7.62168i	0.418504	−	0.241623i
$996$	−0.679445	+	0.919219i	−0.0215291	+	0.0291266i
$997$	−8.17448	−	4.71954i	−0.258888	−	0.149469i	0.364939	−	0.931031i	$-0.381090\pi$
$997$	−8.17448	−	4.71954i	−0.258888	−	0.149469i	−0.623827	+	0.781562i	$0.714423\pi$
$998$			41.2149i			1.30463i
$999$	−1.74613	−	9.33975i	−0.0552451	−	0.295496i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.u.a.425.19	yes	76
3.2	odd	2	inner	546.2.u.a.425.20	yes	76
7.3	odd	6		546.2.bb.a.269.12	yes	76
13.3	even	3		546.2.bb.a.341.6	yes	76
21.17	even	6		546.2.bb.a.269.25	yes	76
39.29	odd	6		546.2.bb.a.341.31	yes	76
91.3	odd	6	inner	546.2.u.a.185.20	yes	76
273.185	even	6	inner	546.2.u.a.185.19	✓	76

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.u.a.185.19	✓	76	273.185	even	6	inner
546.2.u.a.185.20	yes	76	91.3	odd	6	inner
546.2.u.a.425.19	yes	76	1.1	even	1	trivial
546.2.u.a.425.20	yes	76	3.2	odd	2	inner
546.2.bb.a.269.12	yes	76	7.3	odd	6
546.2.bb.a.269.25	yes	76	21.17	even	6
546.2.bb.a.341.6	yes	76	13.3	even	3
546.2.bb.a.341.31	yes	76	39.29	odd	6

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:	\( N \)	\(=\)	\( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	546.u (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 + 0.500000i) q^{2} +(1.72102 + 0.195177i) q^{3} +(0.500000 - 0.866025i) q^{4} +(0.349437 - 0.605242i) q^{5} +(-1.58803 + 0.691481i) q^{6} +(-1.78017 + 1.95729i) q^{7} +1.00000i q^{8} +(2.92381 + 0.671806i) q^{9} +O(q^{10})\)	\(q+(-0.866025 + 0.500000i) q^{2} +(1.72102 + 0.195177i) q^{3} +(0.500000 - 0.866025i) q^{4} +(0.349437 - 0.605242i) q^{5} +(-1.58803 + 0.691481i) q^{6} +(-1.78017 + 1.95729i) q^{7} +1.00000i q^{8} +(2.92381 + 0.671806i) q^{9} +0.698873i q^{10} +1.47903i q^{11} +(1.02954 - 1.39286i) q^{12} +(-0.668235 + 3.54309i) q^{13} +(0.563029 - 2.58515i) q^{14} +(0.719516 - 0.973431i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(0.789186 - 1.36691i) q^{17} +(-2.86800 + 0.880105i) q^{18} +7.68450i q^{19} +(-0.349437 - 0.605242i) q^{20} +(-3.44573 + 3.02109i) q^{21} +(-0.739517 - 1.28088i) q^{22} +(6.95754 - 4.01694i) q^{23} +(-0.195177 + 1.72102i) q^{24} +(2.25579 + 3.90714i) q^{25} +(-1.19284 - 3.40252i) q^{26} +(4.90081 + 1.72685i) q^{27} +(0.804977 + 2.52032i) q^{28} +(-4.06467 - 2.34674i) q^{29} +(-0.136404 + 1.20277i) q^{30} +(5.83175 - 3.36696i) q^{31} +(0.866025 + 0.500000i) q^{32} +(-0.288673 + 2.54545i) q^{33} +1.57837i q^{34} +(0.562577 + 1.76138i) q^{35} +(2.04371 - 2.19619i) q^{36} +(-0.914289 - 1.58359i) q^{37} +(-3.84225 - 6.65498i) q^{38} +(-1.84157 + 5.96729i) q^{39} +(0.605242 + 0.349437i) q^{40} +(1.63806 - 2.83721i) q^{41} +(1.47354 - 4.33920i) q^{42} +(-1.35510 - 2.34709i) q^{43} +(1.28088 + 0.739517i) q^{44} +(1.42829 - 1.53486i) q^{45} +(-4.01694 + 6.95754i) q^{46} +(3.64146 - 6.30720i) q^{47} +(-0.691481 - 1.58803i) q^{48} +(-0.661973 - 6.96863i) q^{49} +(-3.90714 - 2.25579i) q^{50} +(1.62499 - 2.19845i) q^{51} +(2.73429 + 2.35025i) q^{52} +(-6.97573 + 4.02744i) q^{53} +(-5.10766 + 0.954911i) q^{54} +(0.895173 + 0.516829i) q^{55} +(-1.95729 - 1.78017i) q^{56} +(-1.49984 + 13.2252i) q^{57} +4.69348 q^{58} +(-6.89630 + 11.9447i) q^{59} +(-0.483258 - 1.10983i) q^{60} -3.69483i q^{61} +(-3.36696 + 5.83175i) q^{62} +(-6.51981 + 4.52682i) q^{63} -1.00000 q^{64} +(1.91092 + 1.64253i) q^{65} +(-1.02272 - 2.34876i) q^{66} -3.95565 q^{67} +(-0.789186 - 1.36691i) q^{68} +(12.7581 - 5.55527i) q^{69} +(-1.36790 - 1.24411i) q^{70} +(11.6622 - 6.73317i) q^{71} +(-0.671806 + 2.92381i) q^{72} +(-12.7319 + 7.35079i) q^{73} +(1.58359 + 0.914289i) q^{74} +(3.11967 + 7.16454i) q^{75} +(6.65498 + 3.84225i) q^{76} +(-2.89490 - 2.63294i) q^{77} +(-1.38880 - 6.08862i) q^{78} +(-2.64220 + 4.57643i) q^{79} -0.698873 q^{80} +(8.09735 + 3.92847i) q^{81} +3.27613i q^{82} -0.659952 q^{83} +(0.893473 + 4.49463i) q^{84} +(-0.551541 - 0.955297i) q^{85} +(2.34709 + 1.35510i) q^{86} +(-6.53735 - 4.83211i) q^{87} -1.47903 q^{88} +(-3.02094 - 5.23242i) q^{89} +(-0.469507 + 2.04337i) q^{90} +(-5.74528 - 7.61523i) q^{91} -8.03387i q^{92} +(10.6937 - 4.65639i) q^{93} +7.28293i q^{94} +(4.65098 + 2.68525i) q^{95} +(1.39286 + 1.02954i) q^{96} +(10.8368 - 6.25663i) q^{97} +(4.05760 + 5.70402i) q^{98} +(-0.993624 + 4.32442i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 76 q + 38 q^{4} + 10 q^{7} - 8 q^{9}+O(q^{10}) \) 76 * q + 38 * q^4 + 10 * q^7 - 8 * q^9	\( 76 q + 38 q^{4} + 10 q^{7} - 8 q^{9} + 2 q^{13} + 12 q^{15} - 38 q^{16} - 8 q^{21} - 42 q^{25} + 20 q^{28} + 20 q^{30} + 12 q^{31} - 4 q^{36} - 6 q^{37} + 12 q^{39} + 8 q^{42} - 2 q^{43} - 4 q^{46} + 2 q^{49} + 10 q^{51} - 14 q^{52} + 18 q^{54} + 24 q^{55} + 8 q^{57} + 16 q^{58} - 12 q^{60} + 32 q^{63} - 76 q^{64} - 24 q^{66} + 96 q^{67} - 30 q^{69} - 54 q^{73} - 12 q^{75} + 18 q^{76} - 12 q^{78} - 60 q^{79} + 8 q^{81} + 8 q^{84} + 8 q^{85} - 24 q^{87} + 48 q^{91} + 16 q^{93} - 66 q^{97}+O(q^{100}) \) 76 * q + 38 * q^4 + 10 * q^7 - 8 * q^9 + 2 * q^13 + 12 * q^15 - 38 * q^16 - 8 * q^21 - 42 * q^25 + 20 * q^28 + 20 * q^30 + 12 * q^31 - 4 * q^36 - 6 * q^37 + 12 * q^39 + 8 * q^42 - 2 * q^43 - 4 * q^46 + 2 * q^49 + 10 * q^51 - 14 * q^52 + 18 * q^54 + 24 * q^55 + 8 * q^57 + 16 * q^58 - 12 * q^60 + 32 * q^63 - 76 * q^64 - 24 * q^66 + 96 * q^67 - 30 * q^69 - 54 * q^73 - 12 * q^75 + 18 * q^76 - 12 * q^78 - 60 * q^79 + 8 * q^81 + 8 * q^84 + 8 * q^85 - 24 * q^87 + 48 * q^91 + 16 * q^93 - 66 * q^97

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