LMFDB - Embedded newform 546.2.u.a.185.20

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			185.20
Character	$\chi$	$=$	546.185
Dual form			546.2.u.a.425.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 + 0.500000i) q^{2} +(-1.72102 - 0.195177i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-0.349437 - 0.605242i) q^{5} +(-1.39286 - 1.02954i) q^{6} +(-1.78017 - 1.95729i) q^{7} +1.00000i q^{8} +(2.92381 + 0.671806i) q^{9} +O(q^{10})$	\(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} +(-1.39286 - 1.02954i) 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} +(-0.691481 - 1.58803i) q^{12} +(-0.668235 - 3.54309i) q^{13} +(-0.563029 - 2.58515i) q^{14} +(0.483258 + 1.10983i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-0.789186 - 1.36691i) q^{17} +(2.19619 + 2.04371i) q^{18} -7.68450i q^{19} +(0.349437 - 0.605242i) q^{20} +(2.68169 + 3.71598i) 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} +(0.880105 + 2.86800i) q^{36} +(-0.914289 + 1.58359i) q^{37} +(3.84225 - 6.65498i) q^{38} +(0.458516 + 6.22814i) q^{39} +(0.605242 - 0.349437i) q^{40} +(-1.63806 - 2.83721i) q^{41} +(0.464422 + 4.55898i) q^{42} +(-1.35510 + 2.34709i) q^{43} +(-1.28088 + 0.739517i) q^{44} +(-0.615082 - 2.00437i) q^{45} +(-4.01694 - 6.95754i) q^{46} +(-3.64146 - 6.30720i) q^{47} +(1.02954 - 1.39286i) q^{48} +(-0.661973 + 6.96863i) q^{49} +(3.90714 - 2.25579i) q^{50} +(1.09141 + 2.50651i) q^{51} +(2.73429 - 2.35025i) q^{52} +(6.97573 + 4.02744i) q^{53} +(-3.38080 - 3.94590i) 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} +(-0.719516 + 0.973431i) q^{60} +3.69483i q^{61} +(3.36696 + 5.83175i) q^{62} +(-3.88997 - 6.91868i) q^{63} -1.00000 q^{64} +(-1.91092 + 1.64253i) q^{65} +(1.52272 - 2.06008i) q^{66} -3.95565 q^{67} +(0.789186 - 1.36691i) q^{68} +(11.1900 + 8.27117i) 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} +(-4.64484 + 6.28398i) q^{75} +(6.65498 - 3.84225i) q^{76} +(2.89490 - 2.63294i) q^{77} +(-2.71698 + 5.62299i) 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} +(-1.87729 + 4.18040i) q^{84} +(-0.551541 + 0.955297i) q^{85} +(-2.34709 + 1.35510i) q^{86} +(-7.45340 + 3.24545i) 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} +(-9.37940 - 6.93283i) q^{93} -7.28293i q^{94} +(-4.65098 + 2.68525i) q^{95} +(1.58803 - 0.691481i) 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	0.777249	−	0.629193i	$-0.216615\pi$
$5$	−0.349437	−	0.605242i	−0.156273	−	0.270672i	−0.933522	+	0.358521i	$0.883281\pi$
$6$	−1.39286	−	1.02954i	−0.568632	−	0.420307i
$7$	−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	$0.928424\pi$
$12$	−0.691481	−	1.58803i	−0.199613	−	0.458426i
$13$	−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
$15$	0.483258	+	1.10983i	0.124777	+	0.286558i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−0.789186	−	1.36691i	−0.191406	−	0.331524i	0.754311	−	0.656518i	$-0.227971\pi$
$17$	−0.789186	−	1.36691i	−0.191406	−	0.331524i	−0.945716	+	0.324993i	$0.894638\pi$
$18$	2.19619	+	2.04371i	0.517648	+	0.481706i
$19$		−	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
$21$	2.68169	+	3.71598i	0.585193	+	0.810894i
$22$	−0.739517	+	1.28088i	−0.157666	+	0.273085i
$23$	−6.95754	−	4.01694i	−1.45075	−	0.837589i	−0.452223	−	0.891905i	$-0.649369\pi$
$23$	−6.95754	−	4.01694i	−1.45075	−	0.837589i	−0.998524	+	0.0543159i	$0.982702\pi$
$24$	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	$-0.523140\pi$
$29$	4.06467	−	2.34674i	0.754790	−	0.435778i	0.827422	+	0.561580i	$0.189806\pi$
$30$	−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
$36$	0.880105	+	2.86800i	0.146684	+	0.478000i
$37$	−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
$39$	0.458516	+	6.22814i	0.0734214	+	0.997301i
$40$	0.605242	−	0.349437i	0.0956972	−	0.0552508i
$41$	−1.63806	−	2.83721i	−0.255823	−	0.443098i	0.709296	−	0.704911i	$-0.249013\pi$
$41$	−1.63806	−	2.83721i	−0.255823	−	0.443098i	−0.965119	+	0.261813i	$0.915680\pi$
$42$	0.464422	+	4.55898i	0.0716619	+	0.703466i
$43$	−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
$45$	−0.615082	−	2.00437i	−0.0916910	−	0.298793i
$46$	−4.01694	−	6.95754i	−0.592265	−	1.02583i
$47$	−3.64146	−	6.30720i	−0.531162	−	0.919999i	−0.999339	−	0.0363646i	$-0.988422\pi$
$47$	−3.64146	−	6.30720i	−0.531162	−	0.919999i	0.468177	−	0.883635i	$-0.344911\pi$
$48$	1.02954	−	1.39286i	0.148601	−	0.201042i
$49$	−0.661973	+	6.96863i	−0.0945676	+	0.995518i
$50$	3.90714	−	2.25579i	0.552553	−	0.319017i
$51$	1.09141	+	2.50651i	0.152829	+	0.350981i
$52$	2.73429	−	2.35025i	0.379177	−	0.325921i
$53$	6.97573	+	4.02744i	0.958190	+	0.553212i	0.895616	−	0.444829i	$-0.146735\pi$
$53$	6.97573	+	4.02744i	0.958190	+	0.553212i	0.0625748	+	0.998040i	$0.480069\pi$
$54$	−3.38080	−	3.94590i	−0.460069	−	0.536970i
$55$	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	$0.188185\pi$
$59$	6.89630	+	11.9447i	0.897822	+	1.55507i	0.0675492	+	0.997716i	$0.478482\pi$
$60$	−0.719516	+	0.973431i	−0.0928891	+	0.125669i
$61$			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
$63$	−3.88997	−	6.91868i	−0.490090	−	0.871672i
$64$	−1.00000			−0.125000
$65$	−1.91092	+	1.64253i	−0.237020	+	0.203731i
$66$	1.52272	−	2.06008i	0.187434	−	0.253579i
$67$	−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
$69$	11.1900	+	8.27117i	1.34712	+	0.995732i
$70$	−1.36790	+	1.24411i	−0.163495	+	0.148700i
$71$	−11.6622	−	6.73317i	−1.38405	−	0.799081i	−0.391412	−	0.920215i	$-0.628013\pi$
$71$	−11.6622	−	6.73317i	−1.38405	−	0.799081i	−0.992636	+	0.121135i	$0.961347\pi$
$72$	−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
$75$	−4.64484	+	6.28398i	−0.536340	+	0.725612i
$76$	6.65498	−	3.84225i	0.763378	−	0.440737i
$77$	2.89490	−	2.63294i	0.329904	−	0.300051i
$78$	−2.71698	+	5.62299i	−0.307638	+	0.636678i
$79$	−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	$-0.488468\pi$
$83$	0.659952			0.0724392			0.0362196	+	0.999344i	$0.488468\pi$
$84$	−1.87729	+	4.18040i	−0.204829	+	0.456120i
$85$	−0.551541	+	0.955297i	−0.0598230	+	0.103616i
$86$	−2.34709	+	1.35510i	−0.253094	+	0.146124i
$87$	−7.45340	+	3.24545i	−0.799089	+	0.347949i
$88$	−1.47903			−0.157666
$89$	3.02094	−	5.23242i	0.320219	−	0.554635i	−0.660314	−	0.750989i	$-0.729577\pi$
$89$	3.02094	−	5.23242i	0.320219	−	0.554635i	0.980533	+	0.196354i	$0.0629102\pi$
$90$	0.469507	−	2.04337i	0.0494904	−	0.215391i
$91$	−5.74528	+	7.61523i	−0.602269	+	0.798293i
$92$		−	8.03387i		−	0.837589i
$93$	−9.37940	−	6.93283i	−0.972599	−	0.718901i
$94$		−	7.28293i		−	0.751176i
$95$	−4.65098	+	2.68525i	−0.477181	+	0.275501i
$96$	1.58803	−	0.691481i	0.162078	−	0.0705740i
$97$	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	$-0.517671\pi$
$101$	−1.11527			−0.110974			−0.0554869	+	0.998459i	$0.517671\pi$
$102$	−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
$105$	1.31199	−	2.92157i	0.128037	−	0.285116i
$106$	4.02744	+	6.97573i	0.391180	+	0.677543i
$107$	9.24982	+	5.34039i	0.894214	+	0.516275i	0.875319	−	0.483547i	$-0.160652\pi$
$107$	9.24982	+	5.34039i	0.894214	+	0.516275i	0.0188956	+	0.999821i	$0.493985\pi$
$108$	−0.954911	−	5.10766i	−0.0918863	−	0.491484i
$109$	−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
$111$	1.88259	−	2.54695i	0.178687	−	0.241746i
$112$	2.58515	−	0.563029i	0.244274	−	0.0532012i
$113$	8.76754	+	5.06194i	0.824781	+	0.476187i	0.852062	−	0.523440i	$-0.175352\pi$
$113$	8.76754	+	5.06194i	0.824781	+	0.476187i	−0.0272816	+	0.999628i	$0.508685\pi$
$114$	−7.91149	+	10.7034i	−0.740979	+	1.00247i
$115$			5.61466i			0.523570i
$116$	4.06467	+	2.34674i	0.377395	+	0.217889i
$117$	0.426474	−	10.8082i	0.0394275	−	0.999222i
$118$			13.7926i			1.26971i
$119$	−1.27055	+	3.97800i	−0.116471	+	0.364663i
$120$	−1.10983	+	0.483258i	−0.101314	+	0.0441152i
$121$	8.81246			0.801133
$122$	−1.84741	+	3.19981i	−0.167257	+	0.289698i
$123$	2.26538	+	5.20260i	0.204263	+	0.469103i
$124$			6.73393i			0.604725i
$125$	−6.64739			−0.594560
$126$	0.0905275	−	7.93674i	0.00806484	−	0.707061i
$127$	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
$129$	2.79024	−	3.77491i	0.245667	−	0.332362i
$130$	−2.47617	+	0.467011i	−0.217174	+	0.0409596i
$131$	−9.16140	−	15.8680i	−0.800435	−	1.38639i	−0.919330	−	0.393487i	$-0.871269\pi$
$131$	−9.16140	−	15.8680i	−0.800435	−	1.38639i	0.118895	−	0.992907i	$-0.462065\pi$
$132$	2.34876	−	1.02272i	0.204433	−	0.0890167i
$133$	−15.0408	+	13.6797i	−1.30420	+	1.18618i
$134$	−3.42570	−	1.97783i	−0.295935	−	0.170858i
$135$	0.667361	+	3.56960i	0.0574373	+	0.307223i
$136$	1.36691	−	0.789186i	0.117212	−	0.0676721i
$137$	17.2602	−	9.96519i	1.47464	−	0.851384i	0.475048	−	0.879960i	$-0.342431\pi$
$137$	17.2602	−	9.96519i	1.47464	−	0.851384i	0.999592	+	0.0285764i	$0.00909740\pi$
$138$	5.55527	+	12.7581i	0.472896	+	1.08604i
$139$	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
$141$	5.03601	+	11.5655i	0.424108	+	0.973994i
$142$	−6.73317	−	11.6622i	−0.565035	−	0.978670i
$143$	5.24035	−	0.988342i	0.438220	−	0.0826493i
$144$	−2.04371	+	2.19619i	−0.170309	+	0.183016i
$145$	−2.84069	−	1.64007i	−0.235906	−	0.136201i
$146$	−7.35079	−	12.7319i	−0.608356	−	1.05370i
$147$	2.49938	−	11.8639i	0.206146	−	0.978521i
$148$	−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	$-0.0891876\pi$
$150$	−7.16454	+	3.11967i	−0.584982	+	0.254720i
$151$	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
$153$	−1.38913	−	4.52677i	−0.112305	−	0.365967i
$154$	3.82352	−	0.832739i	0.308108	−	0.0671040i
$155$		−	4.70616i		−	0.378008i
$156$	−5.16447	+	3.51116i	−0.413489	+	0.281118i
$157$	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
$159$	−11.2193	−	8.29280i	−0.889749	−	0.657662i
$160$	0.605242	+	0.349437i	0.0478486	+	0.0276254i
$161$	4.52330	+	20.7688i	0.356486	+	1.63681i
$162$	5.04828	+	7.45083i	0.396630	+	0.585393i
$163$	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
$165$	−1.64148	+	0.714755i	−0.127789	+	0.0556436i
$166$	0.571535	+	0.329976i	0.0443597	+	0.0256111i
$167$	−0.895737	−	1.55146i	−0.0693142	−	0.120056i	0.829285	−	0.558825i	$-0.188748\pi$
$167$	−0.895737	−	1.55146i	−0.0693142	−	0.120056i	−0.898600	+	0.438770i	$0.855414\pi$
$168$	−3.71598	+	2.68169i	−0.286694	+	0.206897i
$169$	−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	$-0.710313\pi$
$173$	−16.1435			−1.22737			−0.613685	+	0.789551i	$0.710313\pi$
$174$	−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
$177$	−9.53733	−	21.9031i	−0.716869	−	1.64634i
$178$	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	$0.988337\pi$
$180$	1.42829	−	1.53486i	0.106459	−	0.114402i
$181$		−	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
$186$	−4.65639	−	10.6937i	−0.341423	−	0.784101i
$187$	2.02171	−	1.16723i	0.147842	−	0.0853565i
$188$	3.64146	−	6.30720i	0.265581	−	0.460000i
$189$	5.34435	+	12.6664i	0.388744	+	0.921346i
$190$	−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
$195$	3.60931	−	2.45385i	0.258468	−	0.175724i
$196$	−6.36600	+	2.91103i	−0.454714	+	0.207931i
$197$	7.75682	−	4.47840i	0.552651	−	0.319073i	−0.197540	−	0.980295i	$-0.563295\pi$
$197$	7.75682	−	4.47840i	0.552651	−	0.319073i	0.750190	+	0.661222i	$0.229962\pi$
$198$	−3.02271	+	3.24824i	−0.214815	+	0.230843i
$199$	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
$204$	−1.62499	+	2.19845i	−0.113772	+	0.153922i
$205$	−1.14480	+	1.98285i	−0.0799562	+	0.138488i
$206$	−15.2007			−1.05909
$207$	−17.6439	−	16.4189i	−1.22634	−	1.14119i
$208$	3.40252	+	1.19284i	0.235922	+	0.0827082i
$209$	11.3656			0.786178
$210$	2.59700	−	1.87416i	0.179210	−	0.129330i
$211$	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
$213$	18.7567	+	13.8641i	1.28519	+	0.949953i
$214$	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
$219$	20.4772	+	15.1358i	1.38372	+	1.02278i
$220$	0.895173	+	0.516829i	0.0603526	+	0.0348446i
$221$	−4.31572	+	3.70957i	−0.290307	+	0.249533i
$222$	2.90384	−	1.26443i	0.194893	−	0.0848628i
$223$	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
$225$	9.22034	−	9.90829i	0.614689	−	0.660553i
$226$	5.06194	+	8.76754i	0.336715	+	0.583208i
$227$	−0.594606	−	1.02989i	−0.0394654	−	0.0683560i	0.845618	−	0.533788i	$-0.179232\pi$
$227$	−0.594606	−	1.02989i	−0.0394654	−	0.0683560i	−0.885083	+	0.465432i	$0.845899\pi$
$228$	−12.2033	+	5.31369i	−0.808181	+	0.351908i
$229$	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
$231$	−5.49606	+	3.96631i	−0.361615	+	0.260964i
$232$	2.34674	+	4.06467i	0.154071	+	0.266859i
$233$	6.24464	−	3.60534i	0.409100	−	0.236194i	−0.281303	−	0.959619i	$-0.590767\pi$
$233$	6.24464	−	3.60534i	0.409100	−	0.236194i	0.690403	+	0.723425i	$0.257433\pi$
$234$	5.77346	−	9.14698i	0.377423	−	0.597957i
$235$	−2.54492	+	4.40793i	−0.166012	+	0.287542i
$236$	−6.89630	+	11.9447i	−0.448911	+	0.777537i
$237$	3.65407	+	8.39181i	0.237357	+	0.545107i
$238$	−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	−0.618094	−	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	−0.999775	−	0.0212197i	$-0.993245\pi$
$251$	−7.62856	+	13.2131i	−0.481511	+	0.834001i	0.518264	+	0.855221i	$0.326578\pi$
$252$	4.04677	−	6.82815i	0.254922	−	0.430133i
$253$	5.94119	−	10.2904i	0.373519	−	0.646954i
$254$			13.3492i			0.837601i
$255$	1.13566	−	1.53644i	0.0711180	−	0.0962153i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−7.35225	+	12.7345i	−0.458621	+	0.794355i	−0.998888	−	0.0471387i	$-0.984990\pi$
$257$	−7.35225	+	12.7345i	−0.458621	+	0.794355i	0.540267	+	0.841493i	$0.318323\pi$
$258$	4.30388	−	1.87405i	0.267948	−	0.116673i
$259$	4.72715	−	1.02954i	0.293731	−	0.0639727i
$260$	−2.37793	−	0.833640i	−0.147473	−	0.0517002i
$261$	13.4609	−	4.13075i	0.833208	−	0.255687i
$262$		−	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
$267$	−6.22034	+	8.41548i	−0.380679	+	0.515019i
$268$	−1.97783	−	3.42570i	−0.120815	−	0.209258i
$269$	9.42280	+	16.3208i	0.574518	+	0.995095i	0.996094	+	0.0883015i	$0.0281439\pi$
$269$	9.42280	+	16.3208i	0.574518	+	0.995095i	−0.421576	+	0.906793i	$0.638523\pi$
$270$	−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
$273$	11.3740	−	11.9846i	0.688389	−	0.725342i
$274$	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
$279$	14.7890	+	13.7622i	0.885395	+	0.823920i
$280$	−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	$0.154624\pi$
$283$			15.7084i			0.933770i	−0.884318	+	0.466885i	$0.845376\pi$
$284$		−	13.4663i		−	0.799081i
$285$	8.52853	−	3.71360i	0.505187	−	0.219975i
$286$	5.03244	+	1.76424i	0.297575	+	0.104322i
$287$	−2.63721	+	8.25689i	−0.155670	+	0.487389i
$288$	−2.86800	+	0.880105i	−0.168998	+	0.0518607i
$289$	7.25437	−	12.5649i	0.426728	−	0.739114i
$290$	−1.64007	−	2.84069i	−0.0963084	−	0.166811i
$291$	−17.4292	−	12.8829i	−1.02172	−	0.755208i
$292$		−	14.7016i		−	0.860345i
$293$	1.93283	−	3.34776i	0.112917	−	0.195578i	−0.804028	−	0.594591i	$-0.797314\pi$
$293$	1.93283	−	3.34776i	0.112917	−	0.195578i	0.916945	+	0.399013i	$0.130647\pi$
$294$	8.09650	−	9.02478i	0.472197	−	0.526336i
$295$	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
$309$	24.1393	−	10.5110i	1.37324	−	0.597952i
$310$	2.35308	−	4.07566i	0.133646	−	0.231482i
$311$	−8.46088	+	14.6547i	−0.479773	+	0.830991i	−0.999731	−	0.0232012i	$-0.992614\pi$
$311$	−8.46088	+	14.6547i	−0.479773	+	0.830991i	0.519958	+	0.854192i	$0.325948\pi$
$312$	−6.22814	+	0.458516i	−0.352599	+	0.0259584i
$313$	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
$315$	−2.82818	+	4.77201i	−0.159350	+	0.268872i
$316$	2.64220	−	4.57643i	0.148635	−	0.257444i
$317$	21.3869	−	12.3478i	1.20121	−	0.693519i	0.240386	−	0.970677i	$-0.422726\pi$
$317$	21.3869	−	12.3478i	1.20121	−	0.693519i	0.960824	+	0.277158i	$0.0893927\pi$
$318$	−5.56980	−	12.7914i	−0.312339	−	0.717308i
$319$	3.47091	+	6.01179i	0.194333	+	0.336595i
$320$	0.349437	+	0.605242i	0.0195341	+	0.0338341i
$321$	−14.8768	−	10.9963i	−0.830342	−	0.613751i
$322$	−6.46708	+	20.2479i	−0.360397	+	1.12837i
$323$	−10.5040	+	6.06450i	−0.584459	+	0.337438i
$324$	0.646523	+	8.97675i	0.0359180	+	0.498708i
$325$	−15.3507	−	5.38157i	−0.851505	−	0.298516i
$326$	6.56437	+	3.78994i	0.363567	+	0.209905i
$327$	9.44670	−	12.7804i	0.522404	−	0.706758i
$328$	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
$333$	−3.73708	+	4.01591i	−0.204791	+	0.220070i
$334$		−	1.79147i		−	0.0980251i
$335$	1.38225	+	2.39413i	0.0755204	+	0.130805i
$336$	−4.55898	+	0.464422i	−0.248713	+	0.0253363i
$337$	−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
$339$	−14.1011	−	10.4229i	−0.765868	−	0.566095i
$340$	−1.10308			−0.0598230
$341$	−4.97985	+	8.62536i	−0.269674	+	0.467090i
$342$	15.7049	−	16.8767i	0.849222	−	0.912585i
$343$	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	$-0.806504\pi$
$347$	−13.7226	+	7.92275i	−0.736668	+	0.425316i	0.0841884	+	0.996450i	$0.473170\pi$
$348$	−6.53735	−	4.83211i	−0.350439	−	0.259028i
$349$	−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
$351$	−2.84349	+	18.5180i	−0.151774	+	0.988415i
$352$	−0.739517	−	1.28088i	−0.0394164	−	0.0682712i
$353$	9.10955			0.484852			0.242426	−	0.970170i	$-0.422057\pi$
$353$	9.10955			0.484852			0.242426	+	0.970170i	$0.422057\pi$
$354$	2.69200	−	23.7373i	0.143078	−	1.26162i
$355$			9.41127i			0.499498i
$356$	6.04188			0.320219
$357$	2.96306	−	6.59823i	0.156822	−	0.349215i
$358$	−0.490125	+	0.848922i	−0.0259039	+	0.0448669i
$359$	−2.65584	+	1.53335i	−0.140170	+	0.0809271i	−0.568445	−	0.822721i	$-0.692455\pi$
$359$	−2.65584	+	1.53335i	−0.140170	+	0.0809271i	0.428275	+	0.903648i	$0.359121\pi$
$360$	2.00437	−	0.615082i	0.105639	−	0.0324177i
$361$	−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
$366$	3.80396	−	5.14637i	0.198836	−	0.269005i
$367$			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
$369$	−2.88334	−	9.39593i	−0.150101	−	0.489133i
$370$	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
$378$	−1.70487	+	13.6416i	−0.0876889	+	0.701649i
$379$	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
$381$	−9.23070	−	21.1989i	−0.472903	−	1.08605i
$382$	11.1247	−	19.2685i	0.569188	−	0.985862i
$383$	28.7083			1.46692			0.733462	−	0.679730i	$-0.237903\pi$
$383$	28.7083			1.46692			0.733462	+	0.679730i	$0.237903\pi$
$384$	1.39286	+	1.02954i	0.0710790	+	0.0525384i
$385$	−2.60515	−	0.832071i	−0.132771	−	0.0424062i
$386$	−6.89613	−	3.98148i	−0.351004	−	0.202652i
$387$	−5.53884	+	5.95210i	−0.281555	+	0.302562i
$388$			12.5133i			0.635265i
$389$	19.7202	+	11.3855i	0.999855	+	0.577267i	0.908205	−	0.418525i	$-0.137453\pi$
$389$	19.7202	+	11.3855i	0.999855	+	0.577267i	0.0916497	+	0.995791i	$0.470786\pi$
$390$	4.35268	−	0.320445i	0.220407	−	0.0162264i
$391$			12.6804i			0.641277i
$392$	−6.96863	−	0.661973i	−0.351969	−	0.0334347i
$393$	12.6699	+	29.0972i	0.639110	+	1.46776i
$394$	8.95681			0.451237
$395$	−1.84656	+	3.19834i	−0.0929107	+	0.160926i
$396$	−4.24187	+	1.30171i	−0.213162	+	0.0654132i
$397$			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
$399$	28.5555	−	20.6075i	1.42956	−	1.03166i
$400$	2.25579	+	3.90714i	0.112789	+	0.195357i
$401$	−10.7399	−	6.20069i	−0.536326	−	0.309648i	0.207263	−	0.978285i	$-0.433544\pi$
$401$	−10.7399	−	6.20069i	−0.536326	−	0.309648i	−0.743588	+	0.668638i	$0.766878\pi$
$402$	5.50966	+	4.07249i	0.274797	+	0.203118i
$403$	8.03247	−	22.9123i	0.400126	−	1.14134i
$404$	−0.557637	−	0.965855i	−0.0277435	−	0.0480531i
$405$	−0.451838	−	6.27361i	−0.0224520	−	0.311738i
$406$	−8.35520	−	9.18650i	−0.414662	−	0.455918i
$407$	−2.34219	−	1.35226i	−0.116098	−	0.0670293i
$408$	−2.50651	+	1.09141i	−0.124091	+	0.0540331i
$409$	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
$411$	−31.6501	+	13.7815i	−1.56119	+	0.679790i
$412$	−13.1642	−	7.60037i	−0.648555	−	0.374443i
$413$	11.1027	−	34.7618i	0.546330	−	1.71051i
$414$	−7.07065	−	23.0411i	−0.347504	−	1.13241i
$415$	−0.230611	−	0.399431i	−0.0113203	−	0.0196073i
$416$	2.35025	+	2.73429i	0.115231	+	0.134059i
$417$	−17.4920	−	12.9293i	−0.856585	−	0.633149i
$418$	9.84294	+	5.68282i	0.481434	+	0.277956i
$419$	7.76922	+	13.4567i	0.379551	+	0.657402i	0.990997	−	0.133884i	$-0.0427450\pi$
$419$	7.76922	+	13.4567i	0.379551	+	0.657402i	−0.611446	+	0.791286i	$0.709412\pi$
$420$	3.18615	−	0.324572i	0.155468	−	0.0158375i
$421$	−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
$423$	−6.40974	−	20.8874i	−0.311652	−	1.01558i
$424$	−4.02744	+	6.97573i	−0.195590	+	0.338771i
$425$	−7.12094			−0.345416
$426$	9.31173	+	21.3850i	0.451155	+	1.03611i
$427$	7.23185	−	6.57743i	0.349974	−	0.318304i
$428$			10.6808i			0.516275i
$429$	−9.21164	+	0.678161i	−0.444742	+	0.0327419i
$430$	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	$-0.182147\pi$
$432$	3.94590	−	3.38080i	0.189847	−	0.162659i
$433$	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
$435$	4.56878	+	3.37703i	0.219056	+	0.161916i
$436$	−9.17567			−0.439435
$437$	−30.8682	+	53.4652i	−1.47662	+	2.55759i
$438$	10.1659	+	23.3466i	0.485744	+	1.11554i
$439$	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
$441$	−6.61705	+	19.9302i	−0.315098	+	0.949059i
$442$	−5.59231	+	1.05472i	−0.265999	+	0.0501680i
$443$	22.9533	−	13.2521i	1.09054	−	0.629625i	0.156822	−	0.987627i	$-0.449875\pi$
$443$	22.9533	−	13.2521i	1.09054	−	0.629625i	0.933721	+	0.358002i	$0.116542\pi$
$444$	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	$-0.491510\pi$
$449$	−17.4966	−	10.1017i	−0.825716	−	0.476728i	−0.852384	+	0.522917i	$0.824844\pi$
$450$	12.9392	−	3.97066i	0.609959	−	0.187179i
$451$	4.19633	−	2.42275i	0.197597	−	0.114083i
$452$			10.1239i			0.476187i
$453$	−7.84801	+	10.6175i	−0.368732	+	0.498856i
$454$		−	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
$459$	1.50720	+	8.06178i	0.0703502	+	0.376292i
$460$	−4.86244	+	2.80733i	−0.226712	+	0.130892i
$461$	15.2621	−	26.4348i	0.710828	−	1.23119i	−0.253718	−	0.967278i	$-0.581654\pi$
$461$	15.2621	−	26.4348i	0.710828	−	1.23119i	0.964547	−	0.263913i	$-0.0850131\pi$
$462$	−6.74289	+	0.686897i	−0.313708	+	0.0319573i
$463$	−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	$-0.178231\pi$
$467$	−0.784961	−	1.35959i	−0.0363237	−	0.0629144i	−0.883616	+	0.468213i	$0.844898\pi$
$468$	9.57345	−	5.03478i	0.442533	−	0.232733i
$469$	7.04175	+	7.74237i	0.325158	+	0.357509i
$470$	−4.40793	+	2.54492i	−0.203323	+	0.117388i
$471$	−8.30976	−	6.14220i	−0.382894	−	0.283018i
$472$	−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
$477$	17.6901	+	16.4618i	0.809973	+	0.753735i
$478$	3.29763	−	5.71166i	0.150830	−	0.261245i
$479$	−29.7134			−1.35764			−0.678819	−	0.734305i	$-0.737508\pi$
$479$	−29.7134			−1.35764			−0.678819	+	0.734305i	$0.737508\pi$
$480$	−0.973431	−	0.719516i	−0.0444308	−	0.0328413i
$481$	6.22177	+	2.18119i	0.283688	+	0.0994538i
$482$	−4.41609			−0.201147
$483$	−3.73111	−	36.6263i	−0.169771	−	1.66655i
$484$	4.40623	+	7.63181i	0.200283	+	0.346901i
$485$		−	8.74519i		−	0.397098i
$486$	−7.23396	−	13.8083i	−0.328139	−	0.626358i
$487$	−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	−0.227001	−	0.973895i	$-0.572892\pi$
$491$	11.1439	−	6.43392i	0.502916	−	0.290359i	0.729917	+	0.683536i	$0.239559\pi$
$492$	−3.37290	+	4.56318i	−0.152062	+	0.205724i
$493$	−6.41556	−	3.70403i	−0.288942	−	0.166821i
$494$	−26.1467	−	9.16635i	−1.17639	−	0.412413i
$495$	2.96453	−	0.909727i	0.133246	−	0.0408892i
$496$	−5.83175	+	3.36696i	−0.261853	+	0.151181i
$497$	7.58195	+	34.8125i	0.340097	+	1.56156i
$498$	−0.919219	−	0.679445i	−0.0411912	−	0.0304467i
$499$	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
$501$	1.23877	+	2.84492i	0.0553442	+	0.127102i
$502$	−13.2131	+	7.62856i	−0.589728	+	0.340479i
$503$	−10.4430	+	18.0877i	−0.465629	+	0.806492i	−0.999230	−	0.0392439i	$-0.987505\pi$
$503$	−10.4430	+	18.0877i	−0.465629	+	0.806492i	0.533601	+	0.845736i	$0.320838\pi$
$504$	6.91868	−	3.88997i	0.308183	−	0.173273i
$505$	0.389717	+	0.675010i	0.0173422	+	0.0300376i
$506$	10.2904	−	5.94119i	0.457466	−	0.264118i
$507$	21.7605	−	5.78642i	0.966416	−	0.256984i
$508$	−6.67458	+	11.5607i	−0.296137	+	0.512924i
$509$	−10.1690	+	17.6131i	−0.450731	+	0.780689i	−0.998432	−	0.0559855i	$-0.982170\pi$
$509$	−10.1690	+	17.6131i	−0.450731	+	0.780689i	0.547701	+	0.836674i	$0.315503\pi$
$510$	1.75173	−	0.762760i	0.0775680	−	0.0337756i
$511$	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	$0.570517\pi$
$521$	−21.7920	+	37.7449i	−0.954725	+	1.65363i	−0.734997	+	0.678071i	$0.762816\pi$
$522$	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
$525$	20.5682	−	2.09528i	0.897669	−	0.0914454i
$526$	6.67295	−	11.5579i	0.290955	−	0.503948i
$527$		−	10.6286i		−	0.462991i
$528$	2.06008	+	1.52272i	0.0896536	+	0.0662679i
$529$	20.7715	+	35.9774i	0.903111	+	1.56423i
$530$	2.81467	−	4.87515i	0.122261	−	0.211763i
$531$	12.1389	+	39.5572i	0.526785	+	1.71663i
$532$	−19.3674	−	6.18585i	−0.839684	−	0.268191i
$533$	−8.95787	+	7.69973i	−0.388008	+	0.333512i
$534$	−9.59471	+	4.17785i	−0.415204	+	0.180793i
$535$		−	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
$540$	−2.75769	+	2.36275i	−0.118672	+	0.101677i
$541$	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
$546$	15.8425	−	4.69196i	0.677997	−	0.200797i
$547$	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
$552$	−8.27117	+	11.1900i	−0.352044	+	0.476280i
$553$	−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	$0.952217\pi$
$558$	5.92656	+	19.3129i	0.250891	+	0.817580i
$559$	9.22148	+	3.23281i	0.390027	+	0.136733i
$560$	−1.24411	−	1.36790i	−0.0525734	−	0.0578042i
$561$	−3.70721	+	1.61424i	−0.156519	+	0.0681532i
$562$	2.80997	−	4.86700i	0.118531	−	0.205302i
$563$	14.3073	+	24.7810i	0.602981	+	1.04439i	0.992367	+	0.123319i	$0.0393540\pi$
$563$	14.3073	+	24.7810i	0.602981	+	1.04439i	−0.389386	+	0.921075i	$0.627313\pi$
$564$	−7.49804	+	10.1441i	−0.315725	+	0.427143i
$565$		−	7.07531i		−	0.297661i
$566$	−7.85422	+	13.6039i	−0.330138	+	0.571815i
$567$	−6.72553	−	22.8422i	−0.282446	−	0.959283i
$568$	6.73317	−	11.6622i	0.282518	−	0.489335i
$569$	−9.19011	−	5.30591i	−0.385269	−	0.222435i	0.294839	−	0.955547i	$-0.404734\pi$
$569$	−9.19011	−	5.30591i	−0.385269	−	0.222435i	−0.680108	+	0.733112i	$0.738067\pi$
$570$	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
$582$	−8.65269	−	19.8715i	−0.358666	−	0.823700i
$583$	−5.95672	+	10.3173i	−0.246702	+	0.427301i
$584$	7.35079	−	12.7319i	0.304178	−	0.526852i
$585$	−6.69063	+	3.51868i	−0.276623	+	0.145479i
$586$	3.34776	−	1.93283i	0.138295	−	0.0798444i
$587$	14.0104	+	24.2667i	0.578271	+	1.00159i	0.995678	+	0.0928746i	$0.0296056\pi$
$587$	14.0104	+	24.2667i	0.578271	+	1.00159i	−0.417407	+	0.908720i	$0.637061\pi$
$588$	11.5242	−	3.76744i	0.475249	−	0.155367i
$589$	25.8735	−	44.8141i	1.06610	−	1.84653i
$590$	8.34786	−	4.81964i	0.343676	−	0.198421i
$591$	−14.2237	+	6.19347i	−0.585086	+	0.254765i
$592$	−0.914289	−	1.58359i	−0.0375770	−	0.0650853i
$593$	−20.0207	−	34.6769i	−0.822152	−	1.42401i	−0.904077	−	0.427370i	$-0.859440\pi$
$593$	−20.0207	−	34.6769i	−0.822152	−	1.42401i	0.0819254	−	0.996638i	$-0.473893\pi$
$594$	5.83613	−	5.00033i	0.239459	−	0.205166i
$595$	2.85163	−	0.621067i	0.116905	−	0.0254613i
$596$	5.84670	−	3.37559i	0.239490	−	0.138270i
$597$	−34.6371	+	15.0821i	−1.41760	+	0.617271i
$598$	−21.9669	+	18.8816i	−0.898293	+	0.772127i
$599$	36.5373	+	21.0948i	1.49287	+	0.861911i	0.999967	−	0.00817029i	$-0.00260071\pi$
$599$	36.5373	+	21.0948i	1.49287	+	0.861911i	0.492908	+	0.870082i	$0.335934\pi$
$600$	−6.28398	−	4.64484i	−0.256543	−	0.189625i
$601$	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
$606$	1.55342	+	1.14822i	0.0631033	+	0.0466431i
$607$			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
$609$	19.6206	+	8.81101i	0.795068	+	0.357040i
$610$	2.58222			0.104551
$611$	−19.9136	+	17.1167i	−0.805618	+	0.692468i
$612$	3.22573	−	3.46641i	0.130392	−	0.140121i
$613$	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
$615$	2.35723	−	3.18908i	0.0950526	−	0.128596i
$616$	2.63294	+	2.89490i	0.106084	+	0.116639i
$617$	9.75168	+	5.63013i	0.392588	+	0.226661i	0.683281	−	0.730156i	$-0.260553\pi$
$617$	9.75168	+	5.63013i	0.392588	+	0.226661i	−0.290693	+	0.956816i	$0.593886\pi$
$618$	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
$621$	27.1610	+	31.7009i	1.08993	+	1.27211i
$622$	−14.6547	+	8.46088i	−0.587599	+	0.339250i
$623$	−15.6192	+	3.40175i	−0.625768	+	0.136288i
$624$	−5.62299	−	2.71698i	−0.225100	−	0.108766i
$625$	−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
$630$	−4.83528	+	2.71860i	−0.192642	+	0.108311i
$631$	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
$633$	−8.51572	−	19.5569i	−0.338469	−	0.777318i
$634$	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
$639$	−29.5747	−	27.5213i	−1.16996	−	1.08872i
$640$			0.698873i			0.0276254i
$641$	−14.5095	+	8.37708i	−0.573092	+	0.330875i	−0.758383	−	0.651809i	$-0.774010\pi$
$641$	−14.5095	+	8.37708i	−0.573092	+	0.330875i	0.185291	+	0.982684i	$0.440677\pi$
$642$	−7.38556	−	16.9614i	−0.291485	−	0.669415i
$643$	−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	$-0.299266\pi$
$647$	29.9969			1.17930			0.589649	+	0.807659i	$0.299266\pi$
$648$	−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
$651$	3.12739	+	30.6999i	0.122572	+	1.20322i
$652$	3.78994	+	6.56437i	0.148426	+	0.257081i
$653$	22.1413	+	12.7833i	0.866457	+	0.500249i	0.866169	−	0.499751i	$-0.166575\pi$
$653$	22.1413	+	12.7833i	0.866457	+	0.500249i	0.000287486		1.00000i	$0.499908\pi$
$654$	14.5713	−	6.34481i	0.569782	−	0.248102i
$655$	−6.40266	+	11.0897i	−0.250172	+	0.433311i
$656$	3.27613			0.127911
$657$	−32.2875	−	30.0457i	−1.25966	−	1.17220i
$658$	−14.2548	+	12.9649i	−0.555710	+	0.505423i
$659$	6.23900	+	3.60209i	0.243037	+	0.140317i	0.616572	−	0.787299i	$-0.288521\pi$
$659$	6.23900	+	3.60209i	0.243037	+	0.140317i	−0.373535	+	0.927616i	$0.621854\pi$
$660$	−1.43974	−	1.06419i	−0.0560417	−	0.0414235i
$661$		−	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
$663$	8.15145	−	5.54191i	0.316576	−	0.215230i
$664$			0.659952i			0.0256111i
$665$	13.5354	+	4.32313i	0.524879	+	0.167644i
$666$	−5.24436	+	1.60934i	−0.203215	+	0.0623607i
$667$	−37.7068			−1.46001
$668$	0.895737	−	1.55146i	0.0346571	−	0.0600279i
$669$	−18.4315	+	8.02569i	−0.712604	+	0.310291i
$670$			2.76450i			0.106802i
$671$	−5.46478			−0.210965
$672$	−4.18040	−	1.87729i	−0.161263	−	0.0724180i
$673$	−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
$675$	−17.8022	+	15.2528i	−0.685209	+	0.587079i
$676$	−10.1543	−	8.11729i	−0.390550	−	0.312203i
$677$	−9.18179	−	15.9033i	−0.352885	−	0.611214i	0.633869	−	0.773441i	$-0.281466\pi$
$677$	−9.18179	−	15.9033i	−0.352885	−	0.611214i	−0.986754	+	0.162226i	$0.948133\pi$
$678$	−7.00048	−	16.0771i	−0.268852	−	0.617436i
$679$	−7.04533	−	32.3487i	−0.270375	−	1.24143i
$680$	−0.955297	−	0.551541i	−0.0366339	−	0.0211506i
$681$	0.822317	+	1.88851i	0.0315113	+	0.0723678i
$682$	−8.62536	+	4.97985i	−0.330282	+	0.190689i
$683$	18.4956	−	10.6785i	0.707715	−	0.408600i	−0.102499	−	0.994733i	$-0.532684\pi$
$683$	18.4956	−	10.6785i	0.707715	−	0.408600i	0.810214	+	0.586134i	$0.199351\pi$
$684$	22.0391	−	6.76317i	0.842688	−	0.258596i
$685$	−12.0627	−	6.96440i	−0.460892	−	0.266096i
$686$	18.3877	−	2.21224i	0.702044	−	0.0844637i
$687$	−10.5882	+	4.61045i	−0.403966	+	0.175900i
$688$	−1.35510	−	2.34709i	−0.0516625	−	0.0894821i
$689$	9.60814	−	27.4069i	0.366041	−	1.04412i
$690$	5.78050	−	7.82042i	0.220060	−	0.297718i
$691$	−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
$693$	10.2330	−	5.75340i	0.388718	−	0.218554i
$694$	−15.8455			−0.601487
$695$		−	8.77668i		−	0.332918i
$696$	−3.24545	−	7.45340i	−0.123019	−	0.282521i
$697$	−2.58547	+	4.47817i	−0.0979318	+	0.169623i
$698$	−22.3012			−0.844113
$699$	−11.4508	+	4.98606i	−0.433110	+	0.188590i
$700$	−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	$-0.135535\pi$
$702$	−11.7215	+	14.6153i	−0.442400	+	0.551618i
$703$	12.1691	+	7.02586i	0.458968	+	0.264985i
$704$		−	1.47903i		−	0.0557432i
$705$	5.24018	−	7.08943i	0.197357	−	0.267003i
$706$	7.88910	+	4.55477i	0.296910	+	0.171421i
$707$	1.98538	+	2.18291i	0.0746678	+	0.0820969i
$708$	14.2000	−	19.2111i	0.533669	−	0.721999i
$709$	−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
$711$	−4.65083	−	15.1557i	−0.174420	−	0.568382i
$712$	5.23242	+	3.02094i	0.196093	+	0.113214i
$713$	−27.0498	−	46.8516i	−1.01302	−	1.75460i
$714$	5.86520	−	4.23271i	0.219500	−	0.158405i
$715$	−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	$-0.416258\pi$
$719$	13.9466			0.520119			0.260060	+	0.965593i	$0.416258\pi$
$720$	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
$723$	7.01290	−	3.05364i	0.260813	−	0.113566i
$724$	6.61117	−	3.81696i	0.245702	−	0.141856i
$725$		−	21.1750i		−	0.786419i
$726$	−12.2745	−	9.07276i	−0.455549	−	0.336722i
$727$			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
$732$	5.86751	−	2.55490i	0.216870	−	0.0944320i
$733$	−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
$735$	−8.05393	+	2.63296i	−0.297074	+	0.0971183i
$736$	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
$741$	47.8602	−	3.52347i	1.75819	−	0.129438i
$742$	6.48400	−	20.3009i	0.238035	−	0.745269i
$743$	−17.7056	+	10.2223i	−0.649554	+	0.375020i	−0.788285	−	0.615310i	$-0.789031\pi$
$743$	−17.7056	+	10.2223i	−0.649554	+	0.375020i	0.138732	+	0.990330i	$0.455697\pi$
$744$	6.93283	−	9.37940i	0.254170	−	0.343866i
$745$	−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
$750$	9.25886	+	6.84373i	0.338086	+	0.249898i
$751$	−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
$753$	15.7078	−	21.2510i	0.572423	−	0.774430i
$754$	−3.13634	−	16.6294i	−0.114219	−	0.605607i
$755$	−5.32741			−0.193884
$756$	−8.29726	+	10.9615i	−0.301768	+	0.398668i
$757$	−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
$759$	−12.2333	+	16.5505i	−0.444042	+	0.600743i
$760$	−2.68525	−	4.65098i	−0.0974042	−	0.168709i
$761$	−0.990826			−0.0359174			−0.0179587	−	0.999839i	$-0.505717\pi$
$761$	−0.990826			−0.0359174			−0.0179587	+	0.999839i	$0.505717\pi$
$762$	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
$765$	−2.25438	+	2.42258i	−0.0815071	+	0.0875885i
$766$	24.8621	+	14.3541i	0.898304	+	0.518636i
$767$	37.7129	−	32.4161i	1.36173	−	1.17048i
$768$	0.691481	+	1.58803i	0.0249517	+	0.0573033i
$769$	−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
$771$	15.1388	−	20.4813i	0.545212	−	0.737615i

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)

\(f(q)\)	\(=\)	\(q+(0.866025 + 0.500000i) q^{2} +(-1.72102 - 0.195177i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-0.349437 - 0.605242i) q^{5} +(-1.39286 - 1.02954i) q^{6} +(-1.78017 - 1.95729i) q^{7} +1.00000i q^{8} +(2.92381 + 0.671806i) q^{9} +O(q^{10})\)	\(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} +(-1.39286 - 1.02954i) 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} +(-0.691481 - 1.58803i) q^{12} +(-0.668235 - 3.54309i) q^{13} +(-0.563029 - 2.58515i) q^{14} +(0.483258 + 1.10983i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-0.789186 - 1.36691i) q^{17} +(2.19619 + 2.04371i) q^{18} -7.68450i q^{19} +(0.349437 - 0.605242i) q^{20} +(2.68169 + 3.71598i) 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} +(0.880105 + 2.86800i) q^{36} +(-0.914289 + 1.58359i) q^{37} +(3.84225 - 6.65498i) q^{38} +(0.458516 + 6.22814i) q^{39} +(0.605242 - 0.349437i) q^{40} +(-1.63806 - 2.83721i) q^{41} +(0.464422 + 4.55898i) q^{42} +(-1.35510 + 2.34709i) q^{43} +(-1.28088 + 0.739517i) q^{44} +(-0.615082 - 2.00437i) q^{45} +(-4.01694 - 6.95754i) q^{46} +(-3.64146 - 6.30720i) q^{47} +(1.02954 - 1.39286i) q^{48} +(-0.661973 + 6.96863i) q^{49} +(3.90714 - 2.25579i) q^{50} +(1.09141 + 2.50651i) q^{51} +(2.73429 - 2.35025i) q^{52} +(6.97573 + 4.02744i) q^{53} +(-3.38080 - 3.94590i) 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} +(-0.719516 + 0.973431i) q^{60} +3.69483i q^{61} +(3.36696 + 5.83175i) q^{62} +(-3.88997 - 6.91868i) q^{63} -1.00000 q^{64} +(-1.91092 + 1.64253i) q^{65} +(1.52272 - 2.06008i) q^{66} -3.95565 q^{67} +(0.789186 - 1.36691i) q^{68} +(11.1900 + 8.27117i) 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} +(-4.64484 + 6.28398i) q^{75} +(6.65498 - 3.84225i) q^{76} +(2.89490 - 2.63294i) q^{77} +(-2.71698 + 5.62299i) 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} +(-1.87729 + 4.18040i) q^{84} +(-0.551541 + 0.955297i) q^{85} +(-2.34709 + 1.35510i) q^{86} +(-7.45340 + 3.24545i) 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} +(-9.37940 - 6.93283i) q^{93} -7.28293i q^{94} +(-4.65098 + 2.68525i) q^{95} +(1.58803 - 0.691481i) 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

Introduction

L-functions

Modular forms

Varieties

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