LMFDB - Embedded newform 546.2.u.a.185.19

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			185.19
Character	$\chi$	$=$	546.185
Dual form			546.2.u.a.425.19

$q$-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 $\left(\mathbb{Z}/546\mathbb{Z}\right)^\times$.

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

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	0.933522	−	0.358521i	$-0.116719\pi$
$5$	0.349437	+	0.605242i	0.156273	+	0.270672i	−0.777249	+	0.629193i	$0.783385\pi$
$6$	−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	$-0.928424\pi$
$11$		−	1.47903i		−	0.445946i	0.974825	−	0.222973i	$-0.0715761\pi$
$12$	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	0.945716	−	0.324993i	$-0.105362\pi$
$17$	0.789186	+	1.36691i	0.191406	+	0.331524i	−0.754311	+	0.656518i	$0.772029\pi$
$18$	−2.86800	−	0.880105i	−0.675994	−	0.207443i
$19$		−	7.68450i		−	1.76295i	−0.472234	−	0.881473i	$-0.656552\pi$
$19$		−	7.68450i		−	1.76295i	0.472234	−	0.881473i	$-0.343448\pi$
$20$	−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	0.998524	−	0.0543159i	$-0.0172978\pi$
$23$	6.95754	+	4.01694i	1.45075	+	0.837589i	0.452223	+	0.891905i	$0.350631\pi$
$24$	−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	−0.827422	−	0.561580i	$-0.810194\pi$
$29$	−4.06467	+	2.34674i	−0.754790	+	0.435778i	0.0726317	+	0.997359i	$0.476860\pi$
$30$	−0.136404	−	1.20277i	−0.0249038	−	0.219595i
$31$	5.83175	+	3.36696i	1.04741	+	0.604725i	0.921924	−	0.387370i	$-0.126616\pi$
$31$	5.83175	+	3.36696i	1.04741	+	0.604725i	0.125490	+	0.992095i	$0.459950\pi$
$32$	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	−0.931341	−	0.364149i	$-0.881360\pi$
$37$	−0.914289	+	1.58359i	−0.150308	+	0.260341i	0.781033	+	0.624490i	$0.214693\pi$
$38$	−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	0.965119	−	0.261813i	$-0.0843204\pi$
$41$	1.63806	+	2.83721i	0.255823	+	0.443098i	−0.709296	+	0.704911i	$0.750987\pi$
$42$	1.47354	+	4.33920i	0.227373	+	0.669553i
$43$	−1.35510	+	2.34709i	−0.206650	+	0.357929i	−0.950657	−	0.310243i	$-0.899590\pi$
$43$	−1.35510	+	2.34709i	−0.206650	+	0.357929i	0.744007	+	0.668172i	$0.232923\pi$
$44$	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	0.999339	+	0.0363646i	$0.0115778\pi$
$47$	3.64146	+	6.30720i	0.531162	+	0.919999i	−0.468177	+	0.883635i	$0.655089\pi$
$48$	−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	−0.0625748	−	0.998040i	$-0.519931\pi$
$53$	−6.97573	−	4.02744i	−0.958190	−	0.553212i	−0.895616	+	0.444829i	$0.853265\pi$
$54$	−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	−0.830273	−	0.557357i	$-0.811815\pi$
$59$	−6.89630	−	11.9447i	−0.897822	−	1.55507i	−0.0675492	−	0.997716i	$-0.521518\pi$
$60$	−0.483258	+	1.10983i	−0.0623883	+	0.143279i
$61$			3.69483i			0.473074i	0.971622	+	0.236537i	$0.0760125\pi$
$61$			3.69483i			0.473074i	−0.971622	+	0.236537i	$0.923988\pi$
$62$	−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	0.992636	−	0.121135i	$-0.0386533\pi$
$71$	11.6622	+	6.73317i	1.38405	+	0.799081i	0.391412	+	0.920215i	$0.371987\pi$
$72$	−0.671806	−	2.92381i	−0.0791731	−	0.344575i
$73$	−12.7319	−	7.35079i	−1.49016	−	0.860345i	−0.490225	−	0.871596i	$-0.663085\pi$
$73$	−12.7319	−	7.35079i	−1.49016	−	0.860345i	−0.999937	+	0.0112512i	$0.996419\pi$
$74$	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	0.678240	−	0.734841i	$-0.262743\pi$
$79$	−2.64220	−	4.57643i	−0.297271	−	0.514888i	−0.975511	+	0.219952i	$0.929410\pi$
$80$	−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	−0.980533	−	0.196354i	$-0.937090\pi$
$89$	−3.02094	+	5.23242i	−0.320219	+	0.554635i	0.660314	+	0.750989i	$0.270423\pi$
$90$	−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	0.936303	−	0.351194i	$-0.114224\pi$
$97$	10.8368	+	6.25663i	1.10031	+	0.635265i	0.164008	+	0.986459i	$0.447558\pi$
$98$	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	−0.979904	−	0.199470i	$-0.936078\pi$
$103$	−13.1642	+	7.60037i	−1.29711	+	0.748887i	−0.317206	+	0.948357i	$0.602745\pi$
$104$	−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	−0.0188956	−	0.999821i	$-0.506015\pi$
$107$	−9.24982	−	5.34039i	−0.894214	−	0.516275i	−0.875319	+	0.483547i	$0.839348\pi$
$108$	3.94590	+	3.38080i	0.379695	+	0.325318i
$109$	−4.58784	+	7.94637i	−0.439435	+	0.761124i	−0.997646	−	0.0685753i	$-0.978155\pi$
$109$	−4.58784	+	7.94637i	−0.439435	+	0.761124i	0.558211	+	0.829699i	$0.311488\pi$
$110$	−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	0.0272816	−	0.999628i	$-0.491315\pi$
$113$	−8.76754	−	5.06194i	−0.824781	−	0.476187i	−0.852062	+	0.523440i	$0.824648\pi$
$114$	−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	0.993925	+	0.110055i	$0.0351027\pi$
$127$	6.67458	+	11.5607i	0.592273	+	1.02585i	−0.401652	+	0.915792i	$0.631564\pi$
$128$	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	0.919330	+	0.393487i	$0.128731\pi$
$131$	9.16140	+	15.8680i	0.800435	+	1.38639i	−0.118895	+	0.992907i	$0.537935\pi$
$132$	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	−0.999592	−	0.0285764i	$-0.990903\pi$
$137$	−17.2602	+	9.96519i	−1.47464	+	0.851384i	−0.475048	+	0.879960i	$0.657569\pi$
$138$	−8.27117	−	11.1900i	−0.704089	−	0.952559i
$139$	10.8758	+	6.27916i	0.922475	+	0.532591i	0.884424	−	0.466684i	$-0.154552\pi$
$139$	10.8758	+	6.27916i	0.922475	+	0.532591i	0.0380515	+	0.999276i	$0.487885\pi$
$140$	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	$0.0891876\pi$
$149$			6.75118i			0.553078i	−0.961003	+	0.276539i	$0.910812\pi$
$150$	−6.28398	+	4.64484i	−0.513085	+	0.379249i
$151$	3.81143	−	6.60158i	0.310169	−	0.537229i	−0.668229	−	0.743955i	$-0.732948\pi$
$151$	3.81143	−	6.60158i	0.310169	−	0.537229i	0.978399	+	0.206726i	$0.0662809\pi$
$152$	−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	0.691798	−	0.722091i	$-0.256819\pi$
$157$	5.16669	+	2.98299i	0.412347	+	0.238069i	−0.279451	+	0.960160i	$0.590152\pi$
$158$			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	0.898600	−	0.438770i	$-0.144586\pi$
$167$	0.895737	+	1.55146i	0.0693142	+	0.120056i	−0.829285	+	0.558825i	$0.811252\pi$
$168$	−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	$-0.988337\pi$
$179$		−	0.980251i		−	0.0732674i	0.999329	−	0.0366337i	$-0.0116635\pi$
$180$	−0.615082	+	2.00437i	−0.0458455	+	0.149397i
$181$		−	7.63392i		−	0.567425i	−0.958909	−	0.283712i	$-0.908434\pi$
$181$		−	7.63392i		−	0.567425i	0.958909	−	0.283712i	$-0.0915661\pi$
$182$	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	$0.297810\pi$
$191$			22.2493i			1.60991i	−0.593338	+	0.804953i	$0.702190\pi$
$192$	−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	−0.750190	−	0.661222i	$-0.770038\pi$
$197$	−7.75682	+	4.47840i	−0.552651	+	0.319073i	0.197540	+	0.980295i	$0.436705\pi$
$198$	−1.30171	+	4.24187i	−0.0925082	+	0.301456i
$199$	18.8892	−	10.9057i	1.33902	−	0.773082i	0.352356	−	0.935866i	$-0.385381\pi$
$199$	18.8892	−	10.9057i	1.33902	−	0.773082i	0.986662	+	0.162784i	$0.0520473\pi$
$200$	−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	0.996318	−	0.0857397i	$-0.0273253\pi$
$211$	6.15759	+	10.6653i	0.423906	+	0.734227i	−0.572412	+	0.819966i	$0.693992\pi$
$212$		−	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	−0.124150	−	0.992263i	$-0.539620\pi$
$223$	10.0515	−	5.80325i	0.673100	−	0.388615i	0.797250	+	0.603649i	$0.206287\pi$
$224$	−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	0.885083	−	0.465432i	$-0.154101\pi$
$227$	0.594606	+	1.02989i	0.0394654	+	0.0683560i	−0.845618	+	0.533788i	$0.820768\pi$
$228$	10.7034	−	7.91149i	0.708851	−	0.523951i
$229$	5.77423	−	3.33375i	0.381572	−	0.220301i	−0.296930	−	0.954899i	$-0.595963\pi$
$229$	5.77423	−	3.33375i	0.381572	−	0.220301i	0.678502	+	0.734599i	$0.262630\pi$
$230$	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	−0.690403	−	0.723425i	$-0.742567\pi$
$233$	−6.24464	+	3.60534i	−0.409100	+	0.236194i	0.281303	+	0.959619i	$0.409233\pi$
$234$	−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	$0.0684231\pi$
$239$			6.59526i			0.426612i	−0.976985	+	0.213306i	$0.931577\pi$
$240$	−1.20277	+	0.136404i	−0.0776387	+	0.00880483i
$241$	−3.82445	+	2.20804i	−0.246354	+	0.142233i	−0.618094	−	0.786104i	$-0.712095\pi$
$241$	−3.82445	+	2.20804i	−0.246354	+	0.142233i	0.371740	+	0.928337i	$0.378761\pi$
$242$	−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	−0.518264	−	0.855221i	$-0.673422\pi$
$251$	7.62856	−	13.2131i	0.481511	−	0.834001i	0.999775	+	0.0212197i	$0.00675495\pi$
$252$	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	−0.540267	−	0.841493i	$-0.681677\pi$
$257$	7.35225	−	12.7345i	0.458621	−	0.794355i	0.998888	+	0.0471387i	$0.0150103\pi$
$258$	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	$0.134985\pi$
$263$			13.3459i			0.822944i	−0.911422	+	0.411472i	$0.865015\pi$
$264$	−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	−0.996094	−	0.0883015i	$-0.971856\pi$
$269$	−9.42280	−	16.3208i	−0.574518	−	0.995095i	0.421576	−	0.906793i	$-0.361477\pi$
$270$	−1.20685	−	3.42505i	−0.0734465	−	0.208442i
$271$	−8.32026	−	4.80370i	−0.505420	−	0.291804i	0.225529	−	0.974236i	$-0.427589\pi$
$271$	−8.32026	−	4.80370i	−0.505420	−	0.291804i	−0.730949	+	0.682432i	$0.760922\pi$
$272$	−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	0.764625	−	0.644475i	$-0.222924\pi$
$277$	−2.92622	−	5.06836i	−0.175819	−	0.304528i	−0.940445	+	0.339947i	$0.889591\pi$
$278$	−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	$0.0536109\pi$
$281$			5.61993i			0.335257i	−0.985850	+	0.167628i	$0.946389\pi$
$282$	−1.42146	−	12.5341i	−0.0846466	−	0.746392i
$283$			15.7084i			0.933770i	0.884318	+	0.466885i	$0.154624\pi$
$283$			15.7084i			0.933770i	−0.884318	+	0.466885i	$0.845376\pi$
$284$			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	−0.916945	−	0.399013i	$-0.869353\pi$
$293$	−1.93283	+	3.34776i	−0.112917	+	0.195578i	0.804028	+	0.594591i	$0.202686\pi$
$294$	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	$-0.766446\pi$
$307$		−	23.4663i		−	1.33929i	0.742681	−	0.669645i	$-0.233554\pi$
$308$	−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	−0.519958	−	0.854192i	$-0.674052\pi$
$311$	8.46088	−	14.6547i	0.479773	−	0.830991i	0.999731	+	0.0232012i	$0.00738583\pi$
$312$	−5.96729	+	1.84157i	−0.337832	+	0.104259i
$313$	14.8585	−	8.57858i	0.839854	−	0.484890i	−0.0173608	−	0.999849i	$-0.505526\pi$
$313$	14.8585	−	8.57858i	0.839854	−	0.484890i	0.857214	+	0.514960i	$0.172193\pi$
$314$	−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	−0.960824	−	0.277158i	$-0.910607\pi$
$317$	−21.3869	+	12.3478i	−1.20121	+	0.693519i	−0.240386	+	0.970677i	$0.577274\pi$
$318$	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	−0.0841884	−	0.996450i	$-0.526830\pi$
$347$	13.7226	−	7.92275i	0.736668	−	0.425316i	0.820857	+	0.571134i	$0.193496\pi$
$348$	−7.45340	−	3.24545i	−0.399544	−	0.173975i
$349$	−19.3134	+	11.1506i	−1.03382	+	0.596878i	−0.918078	−	0.396401i	$-0.870259\pi$
$349$	−19.3134	+	11.1506i	−1.03382	+	0.596878i	−0.115746	+	0.993279i	$0.536926\pi$
$350$	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	−0.428275	−	0.903648i	$-0.640879\pi$
$359$	2.65584	−	1.53335i	0.140170	−	0.0809271i	0.568445	+	0.822721i	$0.307545\pi$
$360$	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	$0.0219617\pi$
$367$			2.64140i			0.137880i	−0.997621	+	0.0689399i	$0.978038\pi$
$368$	−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	0.986925	−	0.161182i	$-0.0515307\pi$
$379$	6.88920	+	11.9324i	0.353874	+	0.612929i	−0.633050	+	0.774111i	$0.718197\pi$
$380$	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	−0.0916497	−	0.995791i	$-0.529214\pi$
$389$	−19.7202	−	11.3855i	−0.999855	−	0.577267i	−0.908205	+	0.418525i	$0.862547\pi$
$390$	−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	$0.0865418\pi$
$397$			10.7013i			0.537084i	−0.963268	+	0.268542i	$0.913458\pi$
$398$	−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	0.743588	−	0.668638i	$-0.233122\pi$
$401$	10.7399	+	6.20069i	0.536326	+	0.309648i	−0.207263	+	0.978285i	$0.566456\pi$
$402$	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	−0.225241	−	0.974303i	$-0.572317\pi$
$409$	10.2314	−	5.90709i	0.505909	−	0.292087i	0.731151	+	0.682216i	$0.238984\pi$
$410$	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	0.611446	−	0.791286i	$-0.290588\pi$
$419$	−7.76922	−	13.4567i	−0.379551	−	0.657402i	−0.990997	+	0.133884i	$0.957255\pi$
$420$	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	$0.182147\pi$
$431$			22.4841i			1.08302i	−0.840694	+	0.541510i	$0.817853\pi$
$432$	−0.954911	+	5.10766i	−0.0459432	+	0.245742i
$433$	18.0042	+	10.3947i	0.865226	+	0.499538i	0.865759	−	0.500461i	$-0.166836\pi$
$433$	18.0042	+	10.3947i	0.865226	+	0.499538i	−0.000532949		1.00000i	$0.500170\pi$
$434$	−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	0.701505	−	0.712664i	$-0.252512\pi$
$439$	9.11578	+	5.26300i	0.435072	+	0.251189i	−0.266433	+	0.963853i	$0.585845\pi$
$440$	−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	−0.933721	−	0.358002i	$-0.883458\pi$
$443$	−22.9533	+	13.2521i	−1.09054	+	0.629625i	−0.156822	+	0.987627i	$0.550125\pi$
$444$	−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	0.852384	−	0.522917i	$-0.175156\pi$
$449$	17.4966	+	10.1017i	0.825716	+	0.476728i	−0.0266674	+	0.999644i	$0.508490\pi$
$450$	−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	−0.663406	−	0.748260i	$-0.730890\pi$
$457$	6.76192	−	11.7120i	0.316309	−	0.547864i	0.979715	+	0.200396i	$0.0642229\pi$
$458$	−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	0.253718	+	0.967278i	$0.418346\pi$
$461$	−15.2621	+	26.4348i	−0.710828	+	1.23119i	−0.964547	+	0.263913i	$0.914987\pi$
$462$	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	0.883616	−	0.468213i	$-0.155102\pi$
$467$	0.784961	+	1.35959i	0.0363237	+	0.0629144i	−0.847292	+	0.531127i	$0.821769\pi$
$468$	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	0.528780	−	0.848759i	$-0.322650\pi$
$487$	−10.3865	−	17.9899i	−0.470657	−	0.815202i	−0.999437	+	0.0335574i	$0.989316\pi$
$488$	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	−0.729917	−	0.683536i	$-0.760441\pi$
$491$	−11.1439	+	6.43392i	−0.502916	+	0.290359i	0.227001	+	0.973895i	$0.427108\pi$
$492$	−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	0.795509	+	0.605942i	$0.207204\pi$
$499$	20.6074	+	35.6931i	0.922516	+	1.59784i	0.127007	+	0.991902i	$0.459463\pi$
$500$	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	−0.533601	−	0.845736i	$-0.679162\pi$
$503$	10.4430	−	18.0877i	0.465629	−	0.806492i	0.999230	+	0.0392439i	$0.0124949\pi$
$504$	−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	−0.547701	−	0.836674i	$-0.684497\pi$
$509$	10.1690	−	17.6131i	0.450731	−	0.780689i	0.998432	+	0.0559855i	$0.0178301\pi$
$510$	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	0.219728	−	0.975561i	$-0.429483\pi$
$521$	21.7920	−	37.7449i	0.954725	−	1.65363i	0.734997	−	0.678071i	$-0.237184\pi$
$522$	13.7228	−	3.15311i	0.600633	−	0.138008i
$523$	10.3687	+	5.98635i	0.453390	+	0.261765i	0.709261	−	0.704946i	$-0.249029\pi$
$523$	10.3687	+	5.98635i	0.453390	+	0.261765i	−0.255871	+	0.966711i	$0.582362\pi$
$524$	−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	0.935320	−	0.353802i	$-0.115111\pi$
$541$	3.75077	+	6.49652i	0.161258	+	0.279307i	−0.774062	+	0.633110i	$0.781778\pi$
$542$	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	$-0.952217\pi$
$557$		−	7.05913i		−	0.299105i	0.988754	−	0.149552i	$-0.0477833\pi$
$558$	−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	−0.992367	−	0.123319i	$-0.960646\pi$
$563$	−14.3073	−	24.7810i	−0.602981	−	1.04439i	0.389386	−	0.921075i	$-0.372687\pi$
$564$	−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	0.680108	−	0.733112i	$-0.261933\pi$
$569$	9.19011	+	5.30591i	0.385269	+	0.222435i	−0.294839	+	0.955547i	$0.595266\pi$
$570$	−9.24272	+	1.04820i	−0.387135	+	0.0439041i
$571$	−5.54867	+	9.61058i	−0.232205	+	0.402190i	−0.958457	−	0.285238i	$-0.907927\pi$
$571$	−5.54867	+	9.61058i	−0.232205	+	0.402190i	0.726252	+	0.687429i	$0.241261\pi$
$572$	−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	0.361942	−	0.932201i	$-0.382114\pi$
$577$	−6.35102	−	3.66676i	−0.264396	−	0.152649i	−0.626338	+	0.779551i	$0.715447\pi$
$578$	−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	−0.995678	−	0.0928746i	$-0.970394\pi$
$587$	−14.0104	−	24.2667i	−0.578271	−	1.00159i	0.417407	−	0.908720i	$-0.362939\pi$
$588$	−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	0.904077	+	0.427370i	$0.140560\pi$
$593$	20.0207	+	34.6769i	0.822152	+	1.42401i	−0.0819254	+	0.996638i	$0.526107\pi$
$594$	−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	−0.492908	−	0.870082i	$-0.664066\pi$
$599$	−36.5373	−	21.0948i	−1.49287	−	0.861911i	−0.999967	+	0.00817029i	$0.997399\pi$
$600$	−7.16454	−	3.11967i	−0.292491	−	0.127360i
$601$	12.5623	−	7.25284i	0.512426	−	0.295850i	−0.221404	−	0.975182i	$-0.571064\pi$
$601$	12.5623	−	7.25284i	0.512426	−	0.295850i	0.733831	+	0.679333i	$0.237731\pi$
$602$	−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	$0.00233149\pi$
$607$			0.360914i			0.0146490i	−0.999973	+	0.00732452i	$0.997669\pi$
$608$	−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	0.290693	−	0.956816i	$-0.406114\pi$
$617$	−9.75168	−	5.63013i	−0.392588	−	0.226661i	−0.683281	+	0.730156i	$0.739447\pi$
$618$	26.1608	−	2.96683i	1.05234	−	0.119344i
$619$	13.8755	+	8.01105i	0.557705	+	0.321991i	0.752224	−	0.658908i	$-0.228981\pi$
$619$	13.8755	+	8.01105i	0.557705	+	0.321991i	−0.194519	+	0.980899i	$0.562315\pi$
$620$	−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	−0.513765	−	0.857931i	$-0.671750\pi$
$631$	12.2109	−	21.1499i	0.486107	−	0.841963i	0.999872	+	0.0159683i	$0.00508308\pi$
$632$	−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	−0.185291	−	0.982684i	$-0.559323\pi$
$641$	14.5095	−	8.37708i	0.573092	−	0.330875i	0.758383	+	0.651809i	$0.225990\pi$
$642$	10.9963	+	14.8768i	0.433988	+	0.587141i
$643$	−10.0110	−	5.77985i	−0.394795	−	0.227935i	0.289441	−	0.957196i	$-0.406531\pi$
$643$	−10.0110	−	5.77985i	−0.394795	−	0.227935i	−0.684236	+	0.729261i	$0.739864\pi$
$644$	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	−0.000287486	−	1.00000i	$-0.500092\pi$
$653$	−22.1413	−	12.7833i	−0.866457	−	0.500249i	−0.866169	+	0.499751i	$0.833425\pi$
$654$	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	0.373535	−	0.927616i	$-0.378146\pi$
$659$	−6.23900	−	3.60209i	−0.243037	−	0.140317i	−0.616572	+	0.787299i	$0.711479\pi$
$660$	1.64148	+	0.714755i	0.0638947	+	0.0278218i
$661$		−	18.0796i		−	0.703215i	−0.936148	−	0.351607i	$-0.885635\pi$
$661$		−	18.0796i		−	0.703215i	0.936148	−	0.351607i	$-0.114365\pi$
$662$	−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	−0.989647	−	0.143524i	$-0.954157\pi$
$673$	−16.0613	−	27.8191i	−0.619119	−	1.07235i	0.370528	−	0.928821i	$-0.379177\pi$
$674$	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	0.986754	−	0.162226i	$-0.0518674\pi$
$677$	9.18179	+	15.9033i	0.352885	+	0.611214i	−0.633869	+	0.773441i	$0.718534\pi$
$678$	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	−0.810214	−	0.586134i	$-0.800649\pi$
$683$	−18.4956	+	10.6785i	−0.707715	+	0.408600i	0.102499	+	0.994733i	$0.467316\pi$
$684$	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	0.440925	−	0.897544i	$-0.354650\pi$
$691$	−3.04686	−	1.75911i	−0.115908	−	0.0669196i	−0.556833	+	0.830624i	$0.687984\pi$
$692$	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	$0.135535\pi$
$701$			21.8719i			0.826089i	−0.910711	+	0.413044i	$0.864465\pi$
$702$	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	$0.0350611\pi$
$727$			5.92782i			0.219850i	−0.993940	+	0.109925i	$0.964939\pi$
$728$	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	−0.879108	−	0.476622i	$-0.841861\pi$
$733$	−24.5262	+	14.1602i	−0.905896	+	0.523019i	−0.0267874	+	0.999641i	$0.508528\pi$
$734$	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	−0.138732	−	0.990330i	$-0.544303\pi$
$743$	17.7056	−	10.2223i	0.649554	−	0.375020i	0.788285	+	0.615310i	$0.210969\pi$
$744$	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	0.132569	+	0.991174i	$0.457677\pi$
$751$	−21.7069	+	37.5975i	−0.792097	+	1.37195i	−0.924666	+	0.380779i	$0.875656\pi$
$752$	−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	0.735299	−	0.677743i	$-0.237042\pi$
$757$	−6.03356	−	10.4504i	−0.219293	−	0.379827i	−0.954592	+	0.297916i	$0.903709\pi$
$758$		−	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	−0.505274	+	0.862959i	$0.668609\pi$
$769$	−41.7420	+	24.0998i	−1.50526	+	0.869060i	−0.999981	+	0.00610115i	$0.998058\pi$
$770$	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	0.750843	−	0.660481i	$-0.229648\pi$
$773$	−5.46527	−	9.46613i	−0.196572	−	0.340473i	−0.947415	+	0.320008i	$0.896314\pi$
$774$	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	−0.0249873	−	0.999688i	$-0.507955\pi$
$787$	23.2360	−	13.4153i	0.828274	−	0.478204i	0.853261	+	0.521484i	$0.174621\pi$
$788$	−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	−0.231178	−	0.972912i	$-0.574258\pi$
$797$	20.5234	−	35.5476i	0.726977	−	1.25916i	0.958155	−	0.286250i	$-0.0924088\pi$
$798$	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	$-0.755725\pi$
$809$		−	39.4944i		−	1.38855i	0.719710	−	0.694275i	$-0.244275\pi$
$810$	−2.74550	−	5.65902i	−0.0964671	−	0.198838i
$811$		−	51.6567i		−	1.81391i	−0.421226	−	0.906956i	$-0.638400\pi$
$811$		−	51.6567i		−	1.81391i	0.421226	−	0.906956i	$-0.361600\pi$
$812$	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	0.997593	−	0.0693355i	$-0.0220879\pi$
$821$	41.1557	+	23.7613i	1.43634	+	0.829273i	0.438750	+	0.898609i	$0.355421\pi$
$822$	34.3006	−	3.88995i	1.19637	−	0.135677i
$823$	−19.8401	−	34.3641i	−0.691583	−	1.19786i	−0.971319	−	0.237780i	$-0.923580\pi$
$823$	−19.8401	−	34.3641i	−0.691583	−	1.19786i	0.279736	−	0.960077i	$-0.409753\pi$
$824$	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	$-0.993537\pi$
$827$		−	1.16764i		−	0.0406030i	0.999794	−	0.0203015i	$-0.00646261\pi$
$828$	5.39720	+	23.4895i	0.187566	+	0.816318i
$829$			1.68864i			0.0586491i	0.999570	+	0.0293245i	$0.00933563\pi$
$829$			1.68864i			0.0586491i	−0.999570	+	0.0293245i	$0.990664\pi$
$830$			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	−0.982440	−	0.186577i	$-0.940261\pi$
$839$	−9.54818	+	16.5379i	−0.329640	+	0.570953i	0.652801	+	0.757530i	$0.273594\pi$
$840$	−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	$-0.863175\pi$
$853$		−	24.3423i		−	0.833465i	0.909029	−	0.416733i	$-0.136825\pi$
$854$	−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	0.0735222	+	0.997294i	$0.476576\pi$
$857$	−24.2077	+	41.9290i	−0.826920	+	1.43227i	−0.900443	+	0.434975i	$0.856757\pi$
$858$	9.00527	+	2.05408i	0.307435	+	0.0701251i
$859$	−16.3050	+	9.41372i	−0.556321	+	0.321192i	−0.751667	−	0.659542i	$-0.770750\pi$
$859$	−16.3050	+	9.41372i	−0.556321	+	0.321192i	0.195347	+	0.980734i	$0.437417\pi$
$860$	−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	−0.969409	−	0.245453i	$-0.921063\pi$
$863$	−36.4727	+	21.0575i	−1.24154	+	0.716806i	−0.272136	+	0.962259i	$0.587730\pi$
$864$	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	0.875262	−	0.483649i	$-0.160689\pi$
$881$	0.557391	+	0.965430i	0.0187790	+	0.0325262i	−0.856483	+	0.516175i	$0.827355\pi$
$882$	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	−0.708422	−	0.705789i	$-0.750593\pi$
$887$	7.65471	−	13.2583i	0.257020	−	0.445172i	0.965442	+	0.260617i	$0.0839260\pi$
$888$	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	$0.295344\pi$
$911$			48.3126i			1.60067i	−0.599556	+	0.800333i	$0.704656\pi$
$912$	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	$0.232887\pi$
$937$			40.9010i			1.33618i	−0.744082	+	0.668088i	$0.767113\pi$
$938$	−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	0.286441	+	0.958098i	$0.407528\pi$
$941$	−21.0594	+	36.4760i	−0.686517	+	1.18908i	−0.972957	+	0.230984i	$0.925805\pi$
$942$	−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	−0.449743	−	0.893158i	$-0.648485\pi$
$947$	−44.5633	−	25.7286i	−1.44811	−	0.836068i	−0.998369	+	0.0570898i	$0.981818\pi$
$948$	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	0.331931	−	0.943304i	$-0.392300\pi$
$953$	−9.84866	−	5.68613i	−0.319029	−	0.184192i	−0.650960	+	0.759112i	$0.725633\pi$
$954$	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	$0.0829480\pi$
$977$			16.1067i			0.515299i	−0.966238	+	0.257650i	$0.917052\pi$
$978$	−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	−0.991287	−	0.131720i	$-0.957950\pi$
$983$	−11.9633	+	20.7211i	−0.381570	+	0.660899i	0.609717	+	0.792619i	$0.291283\pi$
$984$	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	−0.623827	−	0.781562i	$-0.714423\pi$
$997$	−8.17448	+	4.71954i	−0.258888	+	0.149469i	0.364939	+	0.931031i	$0.381090\pi$
$998$		−	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.185.19	✓	76
3.2	odd	2	inner	546.2.u.a.185.20	yes	76
7.5	odd	6		546.2.bb.a.341.31	yes	76
13.9	even	3		546.2.bb.a.269.25	yes	76
21.5	even	6		546.2.bb.a.341.6	yes	76
39.35	odd	6		546.2.bb.a.269.12	yes	76
91.61	odd	6	inner	546.2.u.a.425.20	yes	76
273.152	even	6	inner	546.2.u.a.425.19	yes	76

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.u.a.185.19	✓	76	1.1	even	1	trivial
546.2.u.a.185.20	yes	76	3.2	odd	2	inner
546.2.u.a.425.19	yes	76	273.152	even	6	inner
546.2.u.a.425.20	yes	76	91.61	odd	6	inner
546.2.bb.a.269.12	yes	76	39.35	odd	6
546.2.bb.a.269.25	yes	76	13.9	even	3
546.2.bb.a.341.6	yes	76	21.5	even	6
546.2.bb.a.341.31	yes	76	7.5	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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