LMFDB - Embedded newform 546.2.bb.a.269.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(269,546)]

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, 4]))

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

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

chi := DirichletCharacter("546.269");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.bb (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			269.12
Character	$\chi$	$=$	546.269
Dual form			546.2.bb.a.341.31

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} +(0.691481 + 1.58803i) q^{3} -1.00000 q^{4} +(-0.349437 - 0.605242i) q^{5} +(1.58803 - 0.691481i) q^{6} +(2.58515 - 0.563029i) q^{7} +1.00000i q^{8} +(-2.04371 + 2.19619i) q^{9} +O(q^{10})$	\(q-1.00000i q^{2} +(0.691481 + 1.58803i) q^{3} -1.00000 q^{4} +(-0.349437 - 0.605242i) q^{5} +(1.58803 - 0.691481i) q^{6} +(2.58515 - 0.563029i) q^{7} +1.00000i q^{8} +(-2.04371 + 2.19619i) q^{9} +(-0.605242 + 0.349437i) q^{10} +(1.28088 - 0.739517i) q^{11} +(-0.691481 - 1.58803i) q^{12} +(0.668235 - 3.54309i) q^{13} +(-0.563029 - 2.58515i) q^{14} +(0.719516 - 0.973431i) q^{15} +1.00000 q^{16} +1.57837 q^{17} +(2.19619 + 2.04371i) q^{18} +(6.65498 + 3.84225i) q^{19} +(0.349437 + 0.605242i) q^{20} +(2.68169 + 3.71598i) q^{21} +(-0.739517 - 1.28088i) q^{22} +8.03387i q^{23} +(-1.58803 + 0.691481i) q^{24} +(2.25579 - 3.90714i) q^{25} +(-3.54309 - 0.668235i) q^{26} +(-4.90081 - 1.72685i) q^{27} +(-2.58515 + 0.563029i) q^{28} +(-4.06467 - 2.34674i) q^{29} +(-0.973431 - 0.719516i) q^{30} +(5.83175 + 3.36696i) q^{31} -1.00000i q^{32} +(2.06008 + 1.52272i) q^{33} -1.57837i q^{34} +(-1.24411 - 1.36790i) q^{35} +(2.04371 - 2.19619i) q^{36} +1.82858 q^{37} +(3.84225 - 6.65498i) q^{38} +(6.08862 - 1.38880i) q^{39} +(0.605242 - 0.349437i) q^{40} +(-1.63806 + 2.83721i) q^{41} +(3.71598 - 2.68169i) q^{42} +(-1.35510 - 2.34709i) q^{43} +(-1.28088 + 0.739517i) q^{44} +(2.04337 + 0.469507i) q^{45} +8.03387 q^{46} +(-3.64146 - 6.30720i) q^{47} +(0.691481 + 1.58803i) q^{48} +(6.36600 - 2.91103i) q^{49} +(-3.90714 - 2.25579i) q^{50} +(1.09141 + 2.50651i) q^{51} +(-0.668235 + 3.54309i) q^{52} +(6.97573 + 4.02744i) q^{53} +(-1.72685 + 4.90081i) q^{54} +(-0.895173 - 0.516829i) q^{55} +(0.563029 + 2.58515i) q^{56} +(-1.49984 + 13.2252i) q^{57} +(-2.34674 + 4.06467i) q^{58} -13.7926 q^{59} +(-0.719516 + 0.973431i) q^{60} +(-3.19981 - 1.84741i) q^{61} +(3.36696 - 5.83175i) q^{62} +(-4.04677 + 6.82815i) q^{63} -1.00000 q^{64} +(-2.37793 + 0.833640i) q^{65} +(1.52272 - 2.06008i) q^{66} +(1.97783 + 3.42570i) q^{67} -1.57837 q^{68} +(-12.7581 + 5.55527i) q^{69} +(-1.36790 + 1.24411i) q^{70} +(11.6622 - 6.73317i) q^{71} +(-2.19619 - 2.04371i) q^{72} +(-12.7319 - 7.35079i) q^{73} -1.82858i q^{74} +(7.76451 + 0.880555i) 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} +(-0.349437 - 0.605242i) q^{80} +(-0.646523 - 8.97675i) q^{81} +(2.83721 + 1.63806i) q^{82} +0.659952 q^{83} +(-2.68169 - 3.71598i) q^{84} +(-0.551541 - 0.955297i) q^{85} +(-2.34709 + 1.35510i) q^{86} +(0.916058 - 8.07756i) q^{87} +(0.739517 + 1.28088i) q^{88} -6.04188 q^{89} +(0.469507 - 2.04337i) q^{90} +(-0.267374 - 9.53564i) q^{91} -8.03387i q^{92} +(-1.31431 + 11.5892i) q^{93} +(-6.30720 + 3.64146i) q^{94} -5.37049i q^{95} +(1.58803 - 0.691481i) q^{96} +(-10.8368 + 6.25663i) q^{97} +(-2.91103 - 6.36600i) q^{98} +(-0.993624 + 4.32442i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 76 q - 76 q^{4} + 10 q^{7} + 4 q^{9}+O(q^{10}) $ 76 * q - 76 * q^4 + 10 * q^7 + 4 * q^9	$ 76 q - 76 q^{4} + 10 q^{7} + 4 q^{9} - 2 q^{13} + 12 q^{15} + 76 q^{16} + 18 q^{19} - 8 q^{21} - 42 q^{25} - 10 q^{28} - 10 q^{30} + 12 q^{31} + 72 q^{33} - 4 q^{36} + 12 q^{37} - 42 q^{39} + 2 q^{42} - 2 q^{43} + 8 q^{46} - 10 q^{49} + 10 q^{51} + 2 q^{52} - 24 q^{55} + 8 q^{57} - 8 q^{58} - 12 q^{60} + 78 q^{61} + 2 q^{63} - 76 q^{64} - 24 q^{66} - 48 q^{67} + 30 q^{69} - 54 q^{73} - 18 q^{76} - 12 q^{78} - 60 q^{79} - 4 q^{81} - 24 q^{82} + 8 q^{84} + 8 q^{85} - 8 q^{91} - 32 q^{93} - 24 q^{94} + 66 q^{97}+O(q^{100}) $ 76 * q - 76 * q^4 + 10 * q^7 + 4 * q^9 - 2 * q^13 + 12 * q^15 + 76 * q^16 + 18 * q^19 - 8 * q^21 - 42 * q^25 - 10 * q^28 - 10 * q^30 + 12 * q^31 + 72 * q^33 - 4 * q^36 + 12 * q^37 - 42 * q^39 + 2 * q^42 - 2 * q^43 + 8 * q^46 - 10 * q^49 + 10 * q^51 + 2 * q^52 - 24 * q^55 + 8 * q^57 - 8 * q^58 - 12 * q^60 + 78 * q^61 + 2 * q^63 - 76 * q^64 - 24 * q^66 - 48 * q^67 + 30 * q^69 - 54 * q^73 - 18 * q^76 - 12 * q^78 - 60 * q^79 - 4 * q^81 - 24 * q^82 + 8 * q^84 + 8 * q^85 - 8 * q^91 - 32 * q^93 - 24 * q^94 + 66 * q^97

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$		−	1.00000i		−	0.707107i
$2$		−	1.00000i		−	0.707107i
$3$	0.691481	+	1.58803i	0.399227	+	0.916852i
$3$	0.691481	+	1.58803i	0.399227	+	0.916852i
$4$	−1.00000			−0.500000
$5$	−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	$0.883281\pi$
$6$	1.58803	−	0.691481i	0.648312	−	0.282296i
$7$	2.58515	−	0.563029i	0.977095	−	0.212805i
$7$	2.58515	−	0.563029i	0.977095	−	0.212805i
$8$			1.00000i			0.353553i
$9$	−2.04371	+	2.19619i	−0.681236	+	0.732064i
$10$	−0.605242	+	0.349437i	−0.191394	+	0.110502i
$11$	1.28088	−	0.739517i	0.386200	−	0.222973i	−0.294312	−	0.955709i	$-0.595091\pi$
$11$	1.28088	−	0.739517i	0.386200	−	0.222973i	0.680512	+	0.732737i	$0.261757\pi$
$12$	−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
$15$	0.719516	−	0.973431i	0.185778	−	0.251339i
$16$	1.00000			0.250000
$17$	1.57837			0.382811			0.191406	−	0.981511i	$-0.438695\pi$
$17$	1.57837			0.382811			0.191406	+	0.981511i	$0.438695\pi$
$18$	2.19619	+	2.04371i	0.517648	+	0.481706i
$19$	6.65498	+	3.84225i	1.52676	+	0.881473i	0.999495	+	0.0317697i	$0.0101143\pi$
$19$	6.65498	+	3.84225i	1.52676	+	0.881473i	0.527261	+	0.849703i	$0.323219\pi$
$20$	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
$23$			8.03387i			1.67518i	0.546301	+	0.837589i	$0.316036\pi$
$23$			8.03387i			1.67518i	−0.546301	+	0.837589i	$0.683964\pi$
$24$	−1.58803	+	0.691481i	−0.324156	+	0.141148i
$25$	2.25579	−	3.90714i	0.451158	−	0.781428i
$26$	−3.54309	−	0.668235i	−0.694856	−	0.131052i
$27$	−4.90081	−	1.72685i	−0.943162	−	0.332333i
$28$	−2.58515	+	0.563029i	−0.488547	+	0.106402i
$29$	−4.06467	−	2.34674i	−0.754790	−	0.435778i	0.0726317	−	0.997359i	$-0.476860\pi$
$29$	−4.06467	−	2.34674i	−0.754790	−	0.435778i	−0.827422	+	0.561580i	$0.810194\pi$
$30$	−0.973431	−	0.719516i	−0.177723	−	0.131365i
$31$	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	$0.459950\pi$
$32$		−	1.00000i		−	0.176777i
$33$	2.06008	+	1.52272i	0.358615	+	0.265072i
$34$		−	1.57837i		−	0.270688i
$35$	−1.24411	−	1.36790i	−0.210294	−	0.231217i
$36$	2.04371	−	2.19619i	0.340618	−	0.366032i
$37$	1.82858			0.300616			0.150308	−	0.988639i	$-0.451973\pi$
$37$	1.82858			0.300616			0.150308	+	0.988639i	$0.451973\pi$
$38$	3.84225	−	6.65498i	0.623296	−	1.07958i
$39$	6.08862	−	1.38880i	0.974959	−	0.222386i
$40$	0.605242	−	0.349437i	0.0956972	−	0.0552508i
$41$	−1.63806	+	2.83721i	−0.255823	+	0.443098i	−0.965119	−	0.261813i	$-0.915680\pi$
$41$	−1.63806	+	2.83721i	−0.255823	+	0.443098i	0.709296	+	0.704911i	$0.249013\pi$
$42$	3.71598	−	2.68169i	0.573389	−	0.413794i
$43$	−1.35510	−	2.34709i	−0.206650	−	0.357929i	0.744007	−	0.668172i	$-0.232923\pi$
$43$	−1.35510	−	2.34709i	−0.206650	−	0.357929i	−0.950657	+	0.310243i	$0.899590\pi$
$44$	−1.28088	+	0.739517i	−0.193100	+	0.111486i
$45$	2.04337	+	0.469507i	0.304608	+	0.0699900i
$46$	8.03387			1.18453
$47$	−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	$-0.344911\pi$
$48$	0.691481	+	1.58803i	0.0998067	+	0.229213i
$49$	6.36600	−	2.91103i	0.909428	−	0.415861i
$50$	−3.90714	−	2.25579i	−0.552553	−	0.319017i
$51$	1.09141	+	2.50651i	0.152829	+	0.350981i
$52$	−0.668235	+	3.54309i	−0.0926675	+	0.491338i
$53$	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	$0.480069\pi$
$54$	−1.72685	+	4.90081i	−0.234995	+	0.666916i
$55$	−0.895173	−	0.516829i	−0.120705	−	0.0696892i
$56$	0.563029	+	2.58515i	0.0752379	+	0.345455i
$57$	−1.49984	+	13.2252i	−0.198658	+	1.75172i
$58$	−2.34674	+	4.06467i	−0.308142	+	0.533717i
$59$	−13.7926			−1.79564			−0.897822	−	0.440359i	$-0.854851\pi$
$59$	−13.7926			−1.79564			−0.897822	+	0.440359i	$0.854851\pi$
$60$	−0.719516	+	0.973431i	−0.0928891	+	0.125669i
$61$	−3.19981	−	1.84741i	−0.409694	−	0.236537i	0.280964	−	0.959718i	$-0.409346\pi$
$61$	−3.19981	−	1.84741i	−0.409694	−	0.236537i	−0.690658	+	0.723181i	$0.742679\pi$
$62$	3.36696	−	5.83175i	0.427605	−	0.740633i
$63$	−4.04677	+	6.82815i	−0.509845	+	0.860266i
$64$	−1.00000			−0.125000
$65$	−2.37793	+	0.833640i	−0.294946	+	0.103400i
$66$	1.52272	−	2.06008i	0.187434	−	0.253579i
$67$	1.97783	+	3.42570i	0.241630	+	0.418516i	0.961179	−	0.275926i	$-0.0889846\pi$
$67$	1.97783	+	3.42570i	0.241630	+	0.418516i	−0.719549	+	0.694442i	$0.755651\pi$
$68$	−1.57837			−0.191406
$69$	−12.7581	+	5.55527i	−1.53589	+	0.668776i
$70$	−1.36790	+	1.24411i	−0.163495	+	0.148700i
$71$	11.6622	−	6.73317i	1.38405	−	0.799081i	0.391412	−	0.920215i	$-0.371987\pi$
$71$	11.6622	−	6.73317i	1.38405	−	0.799081i	0.992636	+	0.121135i	$0.0386533\pi$
$72$	−2.19619	−	2.04371i	−0.258824	−	0.240853i
$73$	−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	$0.996419\pi$
$74$		−	1.82858i		−	0.212568i
$75$	7.76451	+	0.880555i	0.896568	+	0.101678i
$76$	−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	$0.929410\pi$
$80$	−0.349437	−	0.605242i	−0.0390682	−	0.0676681i
$81$	−0.646523	−	8.97675i	−0.0718359	−	0.997416i
$82$	2.83721	+	1.63806i	0.313317	+	0.180894i
$83$	0.659952			0.0724392			0.0362196	−	0.999344i	$-0.488468\pi$
$83$	0.659952			0.0724392			0.0362196	+	0.999344i	$0.488468\pi$
$84$	−2.68169	−	3.71598i	−0.292597	−	0.405447i
$85$	−0.551541	−	0.955297i	−0.0598230	−	0.103616i
$86$	−2.34709	+	1.35510i	−0.253094	+	0.146124i
$87$	0.916058	−	8.07756i	0.0982117	−	0.866006i
$88$	0.739517	+	1.28088i	0.0788328	+	0.136542i
$89$	−6.04188			−0.640438			−0.320219	−	0.947344i	$-0.603756\pi$
$89$	−6.04188			−0.640438			−0.320219	+	0.947344i	$0.603756\pi$
$90$	0.469507	−	2.04337i	0.0494904	−	0.215391i
$91$	−0.267374	−	9.53564i	−0.0280284	−	0.999607i
$92$		−	8.03387i		−	0.837589i
$93$	−1.31431	+	11.5892i	−0.136287	+	1.20175i
$94$	−6.30720	+	3.64146i	−0.650538	+	0.375588i
$95$		−	5.37049i		−	0.551001i
$96$	1.58803	−	0.691481i	0.162078	−	0.0705740i
$97$	−10.8368	+	6.25663i	−1.10031	+	0.635265i	−0.936303	−	0.351194i	$-0.885776\pi$
$97$	−10.8368	+	6.25663i	−1.10031	+	0.635265i	−0.164008	+	0.986459i	$0.552442\pi$
$98$	−2.91103	−	6.36600i	−0.294058	−	0.643063i
$99$	−0.993624	+	4.32442i	−0.0998630	+	0.434620i
$100$	−2.25579	+	3.90714i	−0.225579	+	0.390714i
$101$	0.557637	+	0.965855i	0.0554869	+	0.0961062i	0.892435	−	0.451177i	$-0.148996\pi$
$101$	0.557637	+	0.965855i	0.0554869	+	0.0961062i	−0.836948	+	0.547283i	$0.815662\pi$
$102$	2.50651	−	1.09141i	0.248181	−	0.108066i
$103$	−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
$107$		−	10.6808i		−	1.03255i	−0.856423	−	0.516275i	$-0.827318\pi$
$107$		−	10.6808i		−	1.03255i	0.856423	−	0.516275i	$-0.172682\pi$
$108$	4.90081	+	1.72685i	0.471581	+	0.166166i
$109$	−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	$0.311488\pi$
$110$	−0.516829	+	0.895173i	−0.0492777	+	0.0853514i
$111$	1.26443	+	2.90384i	0.120014	+	0.275621i
$112$	2.58515	−	0.563029i	0.244274	−	0.0532012i
$113$	−8.76754	+	5.06194i	−0.824781	+	0.476187i	−0.852062	−	0.523440i	$-0.824648\pi$
$113$	−8.76754	+	5.06194i	−0.824781	+	0.476187i	0.0272816	+	0.999628i	$0.491315\pi$
$114$	13.2252	+	1.49984i	1.23865	+	0.140473i
$115$	4.86244	−	2.80733i	0.453425	−	0.261785i
$116$	4.06467	+	2.34674i	0.377395	+	0.217889i
$117$	6.41562	+	8.70860i	0.593125	+	0.805111i
$118$			13.7926i			1.26971i
$119$	4.08033	−	0.888669i	0.374043	−	0.0814641i
$120$	0.973431	+	0.719516i	0.0888617	+	0.0656825i
$121$	−4.40623	+	7.63181i	−0.400566	+	0.693801i
$122$	−1.84741	+	3.19981i	−0.167257	+	0.289698i
$123$	−5.63828	−	0.639424i	−0.508386	−	0.0576549i
$124$	−5.83175	−	3.36696i	−0.523707	−	0.302362i
$125$	−6.64739			−0.594560
$126$	6.82815	+	4.04677i	0.608300	+	0.360515i
$127$	6.67458	−	11.5607i	0.592273	−	1.02585i	−0.401652	−	0.915792i	$-0.631564\pi$
$127$	6.67458	−	11.5607i	0.592273	−	1.02585i	0.993925	−	0.110055i	$-0.0351027\pi$
$128$			1.00000i			0.0883883i
$129$	2.79024	−	3.77491i	0.245667	−	0.332362i
$130$	0.833640	+	2.37793i	0.0731151	+	0.208558i
$131$	−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	$-0.462065\pi$
$132$	−2.06008	−	1.52272i	−0.179307	−	0.132536i
$133$	19.3674	+	6.18585i	1.67937	+	0.536381i
$134$	3.42570	−	1.97783i	0.295935	−	0.170858i
$135$	0.667361	+	3.56960i	0.0574373	+	0.307223i
$136$			1.57837i			0.135344i
$137$			19.9304i			1.70277i	0.524544	+	0.851384i	$0.324236\pi$
$137$			19.9304i			1.70277i	−0.524544	+	0.851384i	$0.675764\pi$
$138$	5.55527	+	12.7581i	0.472896	+	1.08604i
$139$	−10.8758	+	6.27916i	−0.922475	+	0.532591i	−0.884424	−	0.466684i	$-0.845448\pi$
$139$	−10.8758	+	6.27916i	−0.922475	+	0.532591i	−0.0380515	+	0.999276i	$0.512115\pi$
$140$	1.24411	+	1.36790i	0.105147	+	0.115608i
$141$	7.49804	−	10.1441i	0.631449	−	0.854286i
$142$	−6.73317	−	11.6622i	−0.565035	−	0.978670i
$143$	−1.76424	−	5.03244i	−0.147533	−	0.420834i
$144$	−2.04371	+	2.19619i	−0.170309	+	0.183016i
$145$			3.28015i			0.272401i
$146$	−7.35079	+	12.7319i	−0.608356	+	1.05370i
$147$	9.02478	+	8.09650i	0.744351	+	0.667788i
$148$	−1.82858			−0.150308
$149$	5.84670	+	3.37559i	0.478980	+	0.276539i	0.719991	−	0.693983i	$-0.244146\pi$
$149$	5.84670	+	3.37559i	0.478980	+	0.276539i	−0.241011	+	0.970522i	$0.577479\pi$
$150$	0.880555	−	7.76451i	0.0718970	−	0.633969i
$151$	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	$0.0662809\pi$
$152$	−3.84225	+	6.65498i	−0.311648	+	0.539790i
$153$	−3.22573	+	3.46641i	−0.260785	+	0.280242i
$154$	−2.63294	−	2.89490i	−0.212168	−	0.233278i
$155$		−	4.70616i		−	0.378008i
$156$	−6.08862	+	1.38880i	−0.487479	+	0.111193i
$157$	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	$0.590152\pi$
$158$	−4.57643	+	2.64220i	−0.364081	+	0.210202i
$159$	−1.57213	+	13.8626i	−0.124678	+	1.09938i
$160$	−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
$163$	−3.78994	+	6.56437i	−0.296851	+	0.514161i	−0.975414	−	0.220381i	$-0.929270\pi$
$163$	−3.78994	+	6.56437i	−0.296851	+	0.514161i	0.678563	+	0.734543i	$0.262603\pi$
$164$	1.63806	−	2.83721i	0.127911	−	0.221549i
$165$	0.201746	−	1.77894i	0.0157059	−	0.138491i
$166$		−	0.659952i		−	0.0512222i
$167$	−0.895737	+	1.55146i	−0.0693142	+	0.120056i	−0.898600	−	0.438770i	$-0.855414\pi$
$167$	−0.895737	+	1.55146i	−0.0693142	+	0.120056i	0.829285	+	0.558825i	$0.188748\pi$
$168$	−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
$171$	−22.0391	+	6.76317i	−1.68538	+	0.517193i
$172$	1.35510	+	2.34709i	0.103325	+	0.178964i
$173$	8.07176	−	13.9807i	0.613685	−	1.06293i	−0.376929	−	0.926242i	$-0.623020\pi$
$173$	8.07176	−	13.9807i	0.613685	−	1.06293i	0.990614	−	0.136691i	$-0.0436468\pi$
$174$	−8.07756	−	0.916058i	−0.612359	−	0.0694462i
$175$	3.63172	−	11.3706i	0.274532	−	0.859538i
$176$	1.28088	−	0.739517i	0.0965500	−	0.0557432i
$177$	−9.53733	−	21.9031i	−0.716869	−	1.64634i
$178$			6.04188i			0.452858i
$179$	0.848922	−	0.490125i	0.0634514	−	0.0366337i	−0.467939	−	0.883761i	$-0.655003\pi$
$179$	0.848922	−	0.490125i	0.0634514	−	0.0366337i	0.531390	+	0.847127i	$0.321670\pi$
$180$	−2.04337	−	0.469507i	−0.152304	−	0.0349950i
$181$		−	7.63392i		−	0.567425i	−0.958909	−	0.283712i	$-0.908434\pi$
$181$		−	7.63392i		−	0.567425i	0.958909	−	0.283712i	$-0.0915661\pi$
$182$	−9.53564	+	0.267374i	−0.706829	+	0.0198191i
$183$	0.721145	−	6.35887i	0.0533085	−	0.470061i
$184$	−8.03387			−0.592265
$185$	−0.638972	−	1.10673i	−0.0469782	−	0.0813686i
$186$	11.5892	+	1.31431i	0.849763	+	0.0963696i
$187$	2.02171	−	1.16723i	0.147842	−	0.0853565i
$188$	3.64146	+	6.30720i	0.265581	+	0.460000i
$189$	−13.6416	−	1.70487i	−0.992281	−	0.124011i
$190$	−5.37049			−0.389617
$191$	19.2685	+	11.1247i	1.39422	+	0.804953i	0.993779	−	0.111369i	$-0.0355237\pi$
$191$	19.2685	+	11.1247i	1.39422	+	0.804953i	0.400441	+	0.916323i	$0.368857\pi$
$192$	−0.691481	−	1.58803i	−0.0499034	−	0.114607i
$193$	3.98148	+	6.89613i	0.286593	+	0.496394i	0.972994	−	0.230829i	$-0.0741438\pi$
$193$	3.98148	+	6.89613i	0.286593	+	0.496394i	−0.686401	+	0.727223i	$0.740810\pi$
$194$	6.25663	+	10.8368i	0.449200	+	0.778037i
$195$	−2.96814	−	3.19979i	−0.212553	−	0.229142i
$196$	−6.36600	+	2.91103i	−0.454714	+	0.207931i
$197$	−7.75682	−	4.47840i	−0.552651	−	0.319073i	0.197540	−	0.980295i	$-0.436705\pi$
$197$	−7.75682	−	4.47840i	−0.552651	−	0.319073i	−0.750190	+	0.661222i	$0.770038\pi$
$198$	4.32442	+	0.993624i	0.307323	+	0.0706138i
$199$			21.8113i			1.54616i	0.634306	+	0.773082i	$0.281286\pi$
$199$			21.8113i			1.54616i	−0.634306	+	0.773082i	$0.718714\pi$
$200$	3.90714	+	2.25579i	0.276276	+	0.159508i
$201$	−4.07249	+	5.50966i	−0.287252	+	0.388622i
$202$	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
$205$	2.28960			0.159912
$206$	7.60037	+	13.1642i	0.529543	+	0.917195i
$207$	−17.6439	−	16.4189i	−1.22634	−	1.14119i
$208$	0.668235	−	3.54309i	0.0463337	−	0.245669i
$209$	11.3656			0.786178
$210$	−2.92157	−	1.31199i	−0.201608	−	0.0905357i
$211$	6.15759	−	10.6653i	0.423906	−	0.734227i	−0.572412	−	0.819966i	$-0.693992\pi$
$211$	6.15759	−	10.6653i	0.423906	−	0.734227i	0.996318	+	0.0857397i	$0.0273253\pi$
$212$	−6.97573	−	4.02744i	−0.479095	−	0.276606i
$213$	18.7567	+	13.8641i	1.28519	+	0.949953i
$214$	−10.6808			−0.730123
$215$	−0.947040	+	1.64032i	−0.0645876	+	0.111869i
$216$	1.72685	−	4.90081i	0.117497	−	0.333458i
$217$	16.9717	+	5.42066i	1.15211	+	0.367978i
$218$	7.94637	+	4.58784i	0.538196	+	0.310727i
$219$	2.86941	−	25.3017i	0.193897	−	1.70973i
$220$	0.895173	+	0.516829i	0.0603526	+	0.0348446i
$221$	1.05472	−	5.59231i	0.0709483	−	0.376179i
$222$	2.90384	−	1.26443i	0.194893	−	0.0848628i
$223$	−10.0515	−	5.80325i	−0.673100	−	0.388615i	0.124150	−	0.992263i	$-0.460380\pi$
$223$	−10.0515	−	5.80325i	−0.673100	−	0.388615i	−0.797250	+	0.603649i	$0.793713\pi$
$224$	−0.563029	−	2.58515i	−0.0376190	−	0.172728i
$225$	3.97066	+	12.9392i	0.264711	+	0.862613i
$226$	5.06194	+	8.76754i	0.336715	+	0.583208i
$227$	1.18921			0.0789307			0.0394654	−	0.999221i	$-0.487435\pi$
$227$	1.18921			0.0789307			0.0394654	+	0.999221i	$0.487435\pi$
$228$	1.49984	−	13.2252i	0.0993291	−	0.875859i
$229$	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
$231$	6.18296	+	2.77657i	0.406809	+	0.182685i
$232$	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	$0.257433\pi$
$234$	8.70860	−	6.41562i	0.569299	−	0.419402i
$235$	−2.54492	+	4.40793i	−0.166012	+	0.287542i
$236$	13.7926			0.897822
$237$	5.44049	−	7.36042i	0.353398	−	0.478111i
$238$	−0.888669	−	4.08033i	−0.0576038	−	0.264488i
$239$		−	6.59526i		−	0.426612i	−0.976985	−	0.213306i	$-0.931577\pi$
$239$		−	6.59526i		−	0.426612i	0.976985	−	0.213306i	$-0.0684231\pi$
$240$	0.719516	−	0.973431i	0.0464446	−	0.0628347i
$241$		−	4.41609i		−	0.284465i	−0.989833	−	0.142233i	$-0.954572\pi$
$241$		−	4.41609i		−	0.284465i	0.989833	−	0.142233i	$-0.0454281\pi$
$242$	7.63181	+	4.40623i	0.490592	+	0.283243i
$243$	13.8083	−	7.23396i	0.885805	−	0.464058i
$244$	3.19981	+	1.84741i	0.204847	+	0.118269i
$245$	−3.98639	−	2.83575i	−0.254681	−	0.181169i
$246$	−0.639424	+	5.63828i	−0.0407682	+	0.359484i
$247$	18.0605	−	21.0116i	1.14916	−	1.33694i
$248$	−3.36696	+	5.83175i	−0.213802	+	0.370317i
$249$	0.456345	+	1.04803i	0.0289197	+	0.0664160i
$250$			6.64739i			0.420418i
$251$	−7.62856	−	13.2131i	−0.481511	−	0.834001i	0.518264	−	0.855221i	$-0.326578\pi$
$251$	−7.62856	−	13.2131i	−0.481511	−	0.834001i	−0.999775	+	0.0212197i	$0.993245\pi$
$252$	4.04677	−	6.82815i	0.254922	−	0.430133i
$253$	5.94119	+	10.2904i	0.373519	+	0.646954i
$254$	−11.5607	−	6.67458i	−0.725384	−	0.418800i
$255$	1.13566	−	1.53644i	0.0711180	−	0.0962153i
$256$	1.00000			0.0625000
$257$	14.7045			0.917242			0.458621	−	0.888632i	$-0.348344\pi$
$257$	14.7045			0.917242			0.458621	+	0.888632i	$0.348344\pi$
$258$	−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
$261$	13.4609	−	4.13075i	0.833208	−	0.255687i
$262$	−15.8680	+	9.16140i	−0.980329	+	0.565993i
$263$	−11.5579	+	6.67295i	−0.712690	+	0.411472i	−0.812056	−	0.583579i	$-0.801652\pi$
$263$	−11.5579	+	6.67295i	−0.712690	+	0.411472i	0.0993660	+	0.995051i	$0.468319\pi$
$264$	−1.52272	+	2.06008i	−0.0937170	+	0.126789i
$265$		−	5.62934i		−	0.345808i
$266$	6.18585	−	19.3674i	0.379279	−	1.18749i
$267$	−4.17785	−	9.59471i	−0.255680	−	0.587187i
$268$	−1.97783	−	3.42570i	−0.120815	−	0.209258i
$269$	−18.8456			−1.14904			−0.574518	−	0.818492i	$-0.694811\pi$
$269$	−18.8456			−1.14904			−0.574518	+	0.818492i	$0.694811\pi$
$270$	3.56960	−	0.667361i	0.217239	−	0.0406143i
$271$			9.60741i			0.583608i	0.956478	+	0.291804i	$0.0942555\pi$
$271$			9.60741i			0.583608i	−0.956478	+	0.291804i	$0.905744\pi$
$272$	1.57837			0.0957028
$273$	14.9580	−	7.01832i	0.905302	−	0.424768i
$274$	19.9304			1.20404
$275$		−	6.67277i		−	0.402383i
$276$	12.7581	−	5.55527i	0.767945	−	0.334388i
$277$	5.85244			0.351639			0.175819	−	0.984422i	$-0.443742\pi$
$277$	5.85244			0.351639			0.175819	+	0.984422i	$0.443742\pi$
$278$	6.27916	+	10.8758i	0.376599	+	0.652289i
$279$	−19.3129	+	5.92656i	−1.15623	+	0.354814i
$280$	1.36790	−	1.24411i	0.0817475	−	0.0743501i
$281$		−	5.61993i		−	0.335257i	−0.985850	−	0.167628i	$-0.946389\pi$
$281$		−	5.61993i		−	0.335257i	0.985850	−	0.167628i	$-0.0536109\pi$
$282$	−10.1441	−	7.49804i	−0.604071	−	0.446502i
$283$	13.6039	−	7.85422i	0.808669	−	0.466885i	−0.0378246	−	0.999284i	$-0.512043\pi$
$283$	13.6039	−	7.85422i	0.808669	−	0.466885i	0.846493	+	0.532399i	$0.178709\pi$
$284$	−11.6622	+	6.73317i	−0.692024	+	0.399540i
$285$	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
$288$	2.19619	+	2.04371i	0.129412	+	0.120427i
$289$	−14.5087			−0.853456
$290$	3.28015			0.192617
$291$	−17.4292	−	12.8829i	−1.02172	−	0.755208i
$292$	12.7319	+	7.35079i	0.745081	+	0.430173i
$293$	1.93283	+	3.34776i	0.112917	+	0.195578i	0.916945	−	0.399013i	$-0.130647\pi$
$293$	1.93283	+	3.34776i	0.112917	+	0.195578i	−0.804028	+	0.594591i	$0.797314\pi$
$294$	8.09650	−	9.02478i	0.472197	−	0.526336i
$295$	4.81964	+	8.34786i	0.280610	+	0.486031i
$296$			1.82858i			0.106284i
$297$	−7.55440	+	1.41235i	−0.438351	+	0.0819526i
$298$	3.37559	−	5.84670i	0.195543	−	0.338690i
$299$	28.4647	+	5.36851i	1.64616	+	0.310469i
$300$	−7.76451	−	0.880555i	−0.448284	−	0.0508389i
$301$	−4.82461	−	5.30463i	−0.278086	−	0.305754i
$302$	−6.60158	−	3.81143i	−0.379878	−	0.219323i
$303$	−1.14822	+	1.55342i	−0.0659633	+	0.0892415i
$304$	6.65498	+	3.84225i	0.381689	+	0.220368i
$305$			2.58222i			0.147857i
$306$	3.46641	+	3.22573i	0.198161	+	0.184403i
$307$		−	23.4663i		−	1.33929i	−0.742681	−	0.669645i	$-0.766446\pi$
$307$		−	23.4663i		−	1.33929i	0.742681	−	0.669645i	$-0.233554\pi$
$308$	−2.89490	+	2.63294i	−0.164952	+	0.150025i
$309$	−21.1725	−	15.6497i	−1.20446	−	0.890282i
$310$	−4.70616			−0.267292
$311$	−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	$0.325948\pi$
$312$	1.38880	+	6.08862i	0.0786252	+	0.344700i
$313$	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
$315$	5.54677	+	0.0632673i	0.312525	+	0.00356471i
$316$	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	$0.0893927\pi$
$318$	13.8626	+	1.57213i	0.777376	+	0.0881604i
$319$	−6.94181			−0.388667
$320$	0.349437	+	0.605242i	0.0195341	+	0.0338341i
$321$	16.9614	−	7.38556i	0.946695	−	0.412222i
$322$	20.7688	−	4.52330i	1.15740	−	0.252074i
$323$	10.5040	+	6.06450i	0.584459	+	0.337438i
$324$	0.646523	+	8.97675i	0.0359180	+	0.498708i
$325$	−12.3359	−	10.6033i	−0.684275	−	0.588167i
$326$	6.56437	+	3.78994i	0.363567	+	0.209905i
$327$	−15.7915	−	1.79088i	−0.873272	−	0.0990358i
$328$	−2.83721	−	1.63806i	−0.156659	−	0.0904470i
$329$	−12.9649	−	14.2548i	−0.714776	−	0.785893i
$330$	−1.77894	−	0.201746i	−0.0979276	−	0.0111057i
$331$	−16.0166	+	27.7416i	−0.880354	+	1.52482i	−0.0294057	+	0.999568i	$0.509361\pi$
$331$	−16.0166	+	27.7416i	−0.880354	+	1.52482i	−0.850948	+	0.525250i	$0.823972\pi$
$332$	−0.659952			−0.0362196
$333$	−3.73708	+	4.01591i	−0.204791	+	0.220070i
$334$	1.55146	+	0.895737i	0.0848923	+	0.0490126i
$335$	1.38225	−	2.39413i	0.0755204	−	0.130805i
$336$	2.68169	+	3.71598i	0.146298	+	0.202723i
$337$	−22.5440			−1.22805			−0.614024	−	0.789287i	$-0.710450\pi$
$337$	−22.5440			−1.22805			−0.614024	+	0.789287i	$0.710450\pi$
$338$	−4.73523	+	12.1069i	−0.257562	+	0.658530i
$339$	−14.1011	−	10.4229i	−0.765868	−	0.566095i
$340$	0.551541	+	0.955297i	0.0299115	+	0.0518082i
$341$	9.95971			0.539349
$342$	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
$345$	7.82042	+	5.78050i	0.421037	+	0.311212i
$346$	−13.9807	−	8.07176i	−0.751607	−	0.433941i
$347$		−	15.8455i		−	0.850631i	−0.905045	−	0.425316i	$-0.860163\pi$
$347$		−	15.8455i		−	0.850631i	0.905045	−	0.425316i	$-0.139837\pi$
$348$	−0.916058	+	8.07756i	−0.0491059	+	0.433003i
$349$	19.3134	+	11.1506i	1.03382	+	0.596878i	0.918078	−	0.396401i	$-0.129741\pi$
$349$	19.3134	+	11.1506i	1.03382	+	0.596878i	0.115746	+	0.993279i	$0.463074\pi$
$350$	−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
$353$	−4.55477	−	7.88910i	−0.242426	−	0.419895i	0.718979	−	0.695032i	$-0.244610\pi$
$353$	−4.55477	−	7.88910i	−0.242426	−	0.419895i	−0.961405	+	0.275138i	$0.911277\pi$
$354$	−21.9031	+	9.53733i	−1.16414	+	0.506903i
$355$	−8.15040	−	4.70564i	−0.432578	−	0.249749i
$356$	6.04188			0.320219
$357$	4.23271	+	5.86520i	0.224019	+	0.310419i
$358$	−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	$0.359121\pi$
$360$	−0.469507	+	2.04337i	−0.0247452	+	0.107695i
$361$	20.0258	+	34.6857i	1.05399	+	1.82556i
$362$	−7.63392			−0.401230
$363$	−15.1664	−	1.71999i	−0.796030	−	0.0902759i
$364$	0.267374	+	9.53564i	0.0140142	+	0.499804i
$365$			10.2745i			0.537794i
$366$	−6.35887	−	0.721145i	−0.332383	−	0.0376948i
$367$	2.28752	−	1.32070i	0.119407	−	0.0689399i	−0.439107	−	0.898435i	$-0.644705\pi$
$367$	2.28752	−	1.32070i	0.119407	−	0.0689399i	0.558514	+	0.829495i	$0.311372\pi$
$368$			8.03387i			0.418795i
$369$	−2.88334	−	9.39593i	−0.150101	−	0.489133i
$370$	−1.10673	+	0.638972i	−0.0575363	+	0.0332186i
$371$	20.3009	+	6.48400i	1.05397	+	0.336632i
$372$	1.31431	−	11.5892i	0.0681436	−	0.600873i
$373$	2.69165	−	4.66207i	0.139368	−	0.241393i	−0.787889	−	0.615817i	$-0.788826\pi$
$373$	2.69165	−	4.66207i	0.139368	−	0.241393i	0.927258	+	0.374424i	$0.122159\pi$
$374$	−1.16723	−	2.02171i	−0.0603562	−	0.104540i
$375$	−4.59654	−	10.5563i	−0.237364	−	0.545124i
$376$	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	−0.633050	−	0.774111i	$-0.718197\pi$
$379$	6.88920	−	11.9324i	0.353874	−	0.612929i	0.986925	+	0.161182i	$0.0515307\pi$
$380$			5.37049i			0.275501i
$381$	22.9742	+	2.60545i	1.17700	+	0.133481i
$382$	11.1247	−	19.2685i	0.569188	−	0.985862i
$383$	−14.3541	+	24.8621i	−0.733462	+	1.27039i	0.221933	+	0.975062i	$0.428763\pi$
$383$	−14.3541	+	24.8621i	−0.733462	+	1.27039i	−0.955395	+	0.295332i	$0.904570\pi$
$384$	−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
$387$	7.92409	+	1.82072i	0.402804	+	0.0925525i
$388$	10.8368	−	6.25663i	0.550156	−	0.317632i
$389$	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	$0.470786\pi$
$390$	−3.19979	+	2.96814i	−0.162028	+	0.150298i
$391$			12.6804i			0.641277i
$392$	2.91103	+	6.36600i	0.147029	+	0.321531i
$393$	18.8640	−	25.5210i	0.951563	−	1.28737i
$394$	−4.47840	+	7.75682i	−0.225619	+	0.390783i
$395$	−1.84656	+	3.19834i	−0.0929107	+	0.160926i
$396$	0.993624	−	4.32442i	0.0499315	−	0.217310i
$397$	−9.26762	−	5.35066i	−0.465128	−	0.268542i	0.249070	−	0.968486i	$-0.419875\pi$
$397$	−9.26762	−	5.35066i	−0.465128	−	0.268542i	−0.714198	+	0.699944i	$0.753208\pi$
$398$	21.8113			1.09330
$399$	3.56886	+	35.0335i	0.178666	+	1.75387i
$400$	2.25579	−	3.90714i	0.112789	−	0.195357i
$401$			12.4014i			0.619295i	0.950851	+	0.309648i	$0.100211\pi$
$401$			12.4014i			0.619295i	−0.950851	+	0.309648i	$0.899789\pi$
$402$	5.50966	+	4.07249i	0.274797	+	0.203118i
$403$	15.8264	−	18.4125i	0.788370	−	0.917191i
$404$	−0.557637	−	0.965855i	−0.0277435	−	0.0480531i
$405$	−5.20719	+	3.52811i	−0.258747	+	0.175313i
$406$	−3.77814	+	11.8291i	−0.187506	+	0.587067i
$407$	2.34219	−	1.35226i	0.116098	−	0.0670293i
$408$	−2.50651	+	1.09141i	−0.124091	+	0.0540331i
$409$			11.8142i			0.584174i	0.956392	+	0.292087i	$0.0943496\pi$
$409$			11.8142i			0.584174i	−0.956392	+	0.292087i	$0.905650\pi$
$410$		−	2.28960i		−	0.113075i
$411$	−31.6501	+	13.7815i	−1.56119	+	0.679790i
$412$	13.1642	−	7.60037i	0.648555	−	0.374443i
$413$	−35.6559	+	7.76564i	−1.75451	+	0.382122i
$414$	−16.4189	+	17.6439i	−0.806944	+	0.867152i
$415$	−0.230611	−	0.399431i	−0.0113203	−	0.0196073i
$416$	−3.54309	−	0.668235i	−0.173714	−	0.0327629i
$417$	−17.4920	−	12.9293i	−0.856585	−	0.633149i
$418$		−	11.3656i		−	0.555912i
$419$	7.76922	−	13.4567i	0.379551	−	0.657402i	−0.611446	−	0.791286i	$-0.709412\pi$
$419$	7.76922	−	13.4567i	0.379551	−	0.657402i	0.990997	+	0.133884i	$0.0427450\pi$
$420$	−1.31199	+	2.92157i	−0.0640184	+	0.142558i
$421$	−26.1683			−1.27537			−0.637683	−	0.770299i	$-0.720107\pi$
$421$	−26.1683			−1.27537			−0.637683	+	0.770299i	$0.720107\pi$
$422$	−10.6653	−	6.15759i	−0.519177	−	0.299747i
$423$	21.2939	+	4.89271i	1.03535	+	0.237892i
$424$	−4.02744	+	6.97573i	−0.195590	+	0.338771i
$425$	3.56047	−	6.16692i	0.172708	−	0.299139i
$426$	13.8641	−	18.7567i	0.671718	−	0.908765i
$427$	−9.31215	−	2.97425i	−0.450646	−	0.143934i
$428$			10.6808i			0.516275i
$429$	6.77175	−	6.28152i	0.326943	−	0.303275i
$430$	1.64032	+	0.947040i	0.0791033	+	0.0456703i
$431$	−19.4718	+	11.2420i	−0.937923	+	0.541510i	−0.889309	−	0.457308i	$-0.848814\pi$
$431$	−19.4718	+	11.2420i	−0.937923	+	0.541510i	−0.0486143	+	0.998818i	$0.515481\pi$
$432$	−4.90081	−	1.72685i	−0.235791	−	0.0830832i
$433$	−18.0042	+	10.3947i	−0.865226	+	0.499538i	−0.865759	−	0.500461i	$-0.833164\pi$
$433$	−18.0042	+	10.3947i	−0.865226	+	0.499538i	0.000532949		1.00000i	$0.499830\pi$
$434$	5.42066	−	16.9717i	0.260200	−	0.814665i
$435$	−5.20899	+	2.26816i	−0.249752	+	0.108750i
$436$	4.58784	−	7.94637i	0.219718	−	0.380562i
$437$	−30.8682	+	53.4652i	−1.47662	+	2.55759i
$438$	−25.3017	−	2.86941i	−1.20896	−	0.137106i
$439$		−	10.5260i		−	0.502378i	−0.967938	−	0.251189i	$-0.919178\pi$
$439$		−	10.5260i		−	0.502378i	0.967938	−	0.251189i	$-0.0808216\pi$
$440$	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	$0.116542\pi$
$444$	−1.26443	−	2.90384i	−0.0600071	−	0.137810i
$445$	2.11125	+	3.65680i	0.100083	+	0.173349i
$446$	−5.80325	+	10.0515i	−0.274792	+	0.475954i
$447$	−1.31767	+	11.6189i	−0.0623238	+	0.549556i
$448$	−2.58515	+	0.563029i	−0.122137	+	0.0266006i
$449$	17.4966	−	10.1017i	0.825716	−	0.476728i	−0.0266674	−	0.999644i	$-0.508490\pi$
$449$	17.4966	−	10.1017i	0.825716	−	0.476728i	0.852384	+	0.522917i	$0.175156\pi$
$450$	12.9392	−	3.97066i	0.609959	−	0.187179i
$451$			4.84551i			0.228166i
$452$	8.76754	−	5.06194i	0.412390	−	0.238094i
$453$	13.1191	+	1.48780i	0.616388	+	0.0699031i
$454$		−	1.18921i		−	0.0558124i
$455$	−5.67794	+	3.49393i	−0.266186	+	0.163798i
$456$	−13.2252	−	1.49984i	−0.619326	−	0.0702363i
$457$	−13.5238			−0.632619			−0.316309	−	0.948656i	$-0.602444\pi$
$457$	−13.5238			−0.632619			−0.316309	+	0.948656i	$0.602444\pi$
$458$	−3.33375	−	5.77423i	−0.155776	−	0.269812i
$459$	−7.73531	−	2.72561i	−0.361053	−	0.127221i
$460$	−4.86244	+	2.80733i	−0.226712	+	0.130892i
$461$	15.2621	+	26.4348i	0.710828	+	1.23119i	0.964547	+	0.263913i	$0.0850131\pi$
$461$	15.2621	+	26.4348i	0.710828	+	1.23119i	−0.253718	+	0.967278i	$0.581654\pi$
$462$	2.77657	−	6.18296i	0.129178	−	0.287657i
$463$	−18.9355			−0.880007			−0.440004	−	0.897996i	$-0.645023\pi$
$463$	−18.9355			−0.880007			−0.440004	+	0.897996i	$0.645023\pi$
$464$	−4.06467	−	2.34674i	−0.188698	−	0.108945i
$465$	7.47355	−	3.25422i	0.346578	−	0.150911i
$466$	−3.60534	−	6.24464i	−0.167014	−	0.289277i
$467$	−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	$0.844898\pi$
$468$	−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
$471$	−1.16442	+	10.2676i	−0.0536537	+	0.473104i
$472$		−	13.7926i		−	0.634856i
$473$	−3.47143	−	2.00423i	−0.159617	−	0.0921547i
$474$	−7.36042	−	5.44049i	−0.338075	−	0.249890i
$475$	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
$478$	−6.59526			−0.301660
$479$	14.8567	+	25.7325i	0.678819	+	1.17575i	0.975337	+	0.220722i	$0.0708414\pi$
$479$	14.8567	+	25.7325i	0.678819	+	1.17575i	−0.296517	+	0.955027i	$0.595825\pi$
$480$	−0.973431	−	0.719516i	−0.0444308	−	0.0328413i
$481$	1.22192	−	6.47881i	0.0557147	−	0.295408i
$482$	−4.41609			−0.201147
$483$	−29.8537	+	21.5444i	−1.35839	+	0.980303i
$484$	4.40623	−	7.63181i	0.200283	−	0.346901i
$485$	7.57355	+	4.37259i	0.343897	+	0.198549i
$486$	−7.23396	−	13.8083i	−0.328139	−	0.626358i
$487$	20.7730			0.941314			0.470657	−	0.882316i	$-0.344017\pi$
$487$	20.7730			0.941314			0.470657	+	0.882316i	$0.344017\pi$
$488$	1.84741	−	3.19981i	0.0836285	−	0.144849i
$489$	−13.0451	−	1.47942i	−0.589921	−	0.0669016i
$490$	−2.83575	+	3.98639i	−0.128106	+	0.180087i
$491$	−11.1439	−	6.43392i	−0.502916	−	0.290359i	0.227001	−	0.973895i	$-0.427108\pi$
$491$	−11.1439	−	6.43392i	−0.502916	−	0.290359i	−0.729917	+	0.683536i	$0.760441\pi$
$492$	5.63828	+	0.639424i	0.254193	+	0.0288275i
$493$	−6.41556	−	3.70403i	−0.288942	−	0.166821i
$494$	−21.0116	−	18.0605i	−0.945358	−	0.812581i
$495$	2.96453	−	0.909727i	0.133246	−	0.0408892i
$496$	5.83175	+	3.36696i	0.261853	+	0.151181i
$497$	26.3576	−	23.9724i	1.18230	−	1.07531i
$498$	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	$0.459463\pi$
$500$	6.64739			0.297280
$501$	−3.08316	−	0.349654i	−0.137746	−	0.0156214i
$502$	−13.2131	+	7.62856i	−0.589728	+	0.340479i
$503$	−10.4430	−	18.0877i	−0.465629	−	0.806492i	0.533601	−	0.845736i	$-0.320838\pi$
$503$	−10.4430	−	18.0877i	−0.465629	−	0.806492i	−0.999230	+	0.0392439i	$0.987505\pi$
$504$	−6.82815	−	4.04677i	−0.304150	−	0.180257i
$505$	0.389717	−	0.675010i	0.0173422	−	0.0300376i
$506$	10.2904	−	5.94119i	0.457466	−	0.264118i
$507$	−0.852009	−	22.5005i	−0.0378391	−	0.999284i
$508$	−6.67458	+	11.5607i	−0.296137	+	0.512924i
$509$	20.3379			0.901462			0.450731	−	0.892660i	$-0.351163\pi$
$509$	20.3379			0.901462			0.450731	+	0.892660i	$0.351163\pi$
$510$	−1.53644	−	1.13566i	−0.0680345	−	0.0502880i
$511$	−37.0527	−	11.8344i	−1.63911	−	0.523525i
$512$		−	1.00000i		−	0.0441942i
$513$	−25.9798	−	30.3223i	−1.14704	−	1.33876i
$514$		−	14.7045i		−	0.648588i
$515$	9.20013	+	5.31170i	0.405406	+	0.234061i
$516$	−2.79024	+	3.77491i	−0.122834	+	0.166181i
$517$	−9.32856	−	5.38585i	−0.410270	−	0.236869i
$518$	−1.02954	−	4.72715i	−0.0452355	−	0.207699i
$519$	27.7833	+	3.15084i	1.21955	+	0.138307i
$520$	−0.833640	−	2.37793i	−0.0365576	−	0.104279i
$521$	−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	$0.762816\pi$
$522$	−4.13075	−	13.4609i	−0.180798	−	0.589167i
$523$		−	11.9727i		−	0.523530i	−0.965132	−	0.261765i	$-0.915696\pi$
$523$		−	11.9727i		−	0.523530i	0.965132	−	0.261765i	$-0.0843045\pi$
$524$	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
$527$	9.20467	+	5.31432i	0.400962	+	0.231495i
$528$	2.06008	+	1.52272i	0.0896536	+	0.0662679i
$529$	−41.5431			−1.80622
$530$	−5.62934			−0.244523
$531$	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
$534$	−9.59471	+	4.17785i	−0.415204	+	0.180793i
$535$	−6.46445	+	3.73225i	−0.279483	+	0.161359i
$536$	−3.42570	+	1.97783i	−0.147968	+	0.0854291i
$537$	1.36535	+	1.00921i	0.0589192	+	0.0435504i
$538$			18.8456i			0.812491i
$539$	6.00133	−	8.43644i	0.258496	−	0.363383i
$540$	−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	$0.781778\pi$
$542$	9.60741			0.412673
$543$	12.1229	−	5.27871i	0.520244	−	0.226531i
$544$		−	1.57837i		−	0.0676721i
$545$	6.41263			0.274687
$546$	−7.01832	−	14.9580i	−0.300356	−	0.640145i
$547$	0.731374			0.0312713			0.0156357	−	0.999878i	$-0.495023\pi$
$547$	0.731374			0.0312713			0.0156357	+	0.999878i	$0.495023\pi$
$548$		−	19.9304i		−	0.851384i
$549$	10.5968	−	3.25184i	0.452259	−	0.138785i
$550$	−6.67277			−0.284528
$551$	−18.0335	−	31.2350i	−0.768254	−	1.33066i
$552$	−5.55527	−	12.7581i	−0.236448	−	0.543019i
$553$	−9.40715	−	10.3431i	−0.400033	−	0.439834i
$554$		−	5.85244i		−	0.248646i
$555$	1.31569	−	1.77999i	0.0558480	−	0.0755565i
$556$	10.8758	−	6.27916i	0.461238	−	0.266296i
$557$	6.11339	−	3.52957i	0.259033	−	0.149552i	−0.364861	−	0.931062i	$-0.618883\pi$
$557$	6.11339	−	3.52957i	0.259033	−	0.149552i	0.623893	+	0.781510i	$0.285550\pi$
$558$	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
$561$	3.25158	+	2.40342i	0.137282	+	0.101472i
$562$	−5.61993			−0.237062
$563$	−28.6146			−1.20596			−0.602981	−	0.797755i	$-0.706021\pi$
$563$	−28.6146			−1.20596			−0.602981	+	0.797755i	$0.706021\pi$
$564$	−7.49804	+	10.1441i	−0.315725	+	0.427143i
$565$	6.12740	+	3.53765i	0.257782	+	0.148830i
$566$	−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
$569$			10.6118i			0.444871i	0.974947	+	0.222435i	$0.0714006\pi$
$569$			10.6118i			0.444871i	−0.974947	+	0.222435i	$0.928599\pi$
$570$	−3.71360	−	8.52853i	−0.155545	−	0.357221i
$571$	−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	$0.241261\pi$
$572$	1.76424	+	5.03244i	0.0737667	+	0.210417i
$573$	−4.34256	+	38.2916i	−0.181413	+	1.59965i
$574$	8.25689	+	2.63721i	0.344636	+	0.110075i
$575$	31.3895	+	18.1227i	1.30903	+	0.755769i
$576$	2.04371	−	2.19619i	0.0851545	−	0.0915080i
$577$	−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	$0.715447\pi$
$578$			14.5087i			0.603484i
$579$	−8.19817	+	11.0913i	−0.340704	+	0.460938i
$580$		−	3.28015i		−	0.136201i
$581$	1.70607	−	0.371572i	0.0707799	−	0.0154154i
$582$	−12.8829	+	17.4292i	−0.534012	+	0.722464i
$583$	11.9134			0.493404
$584$	7.35079	−	12.7319i	0.304178	−	0.526852i
$585$	3.02896	−	6.92611i	0.125232	−	0.286359i
$586$	3.34776	−	1.93283i	0.138295	−	0.0798444i
$587$	14.0104	−	24.2667i	0.578271	−	1.00159i	−0.417407	−	0.908720i	$-0.637061\pi$
$587$	14.0104	−	24.2667i	0.578271	−	1.00159i	0.995678	−	0.0928746i	$-0.0296056\pi$
$588$	−9.02478	−	8.09650i	−0.372176	−	0.333894i
$589$	25.8735	+	44.8141i	1.06610	+	1.84653i
$590$	8.34786	−	4.81964i	0.343676	−	0.198421i
$591$	1.74816	−	15.4148i	0.0719097	−	0.634082i
$592$	1.82858			0.0751541
$593$	−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	$-0.473893\pi$
$594$	1.41235	+	7.55440i	0.0579492	+	0.309961i
$595$	−1.96367	−	2.15905i	−0.0805028	−	0.0885125i
$596$	−5.84670	−	3.37559i	−0.239490	−	0.138270i
$597$	−34.6371	+	15.0821i	−1.41760	+	0.617271i
$598$	5.36851	−	28.4647i	0.219535	−	1.16401i
$599$	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	$0.335934\pi$
$600$	−0.880555	+	7.76451i	−0.0359485	+	0.316985i
$601$	−12.5623	−	7.25284i	−0.512426	−	0.295850i	0.221404	−	0.975182i	$-0.428936\pi$
$601$	−12.5623	−	7.25284i	−0.512426	−	0.295850i	−0.733831	+	0.679333i	$0.762269\pi$
$602$	−5.30463	+	4.82461i	−0.216201	+	0.196636i
$603$	−11.5656	−	2.65743i	−0.470987	−	0.108219i
$604$	−3.81143	+	6.60158i	−0.155085	+	0.268615i
$605$	6.15879			0.250390
$606$	1.55342	+	1.14822i	0.0631033	+	0.0466431i
$607$	−0.312560	−	0.180457i	−0.0126864	−	0.00732452i	0.493643	−	0.869664i	$-0.335665\pi$
$607$	−0.312560	−	0.180457i	−0.0126864	−	0.00732452i	−0.506330	+	0.862340i	$0.668998\pi$
$608$	3.84225	−	6.65498i	0.155824	−	0.269895i
$609$	−2.17976	−	21.3975i	−0.0883282	−	0.867070i
$610$	2.58222			0.104551
$611$	−24.7803	+	8.68733i	−1.00250	+	0.351452i
$612$	3.22573	−	3.46641i	0.130392	−	0.140121i
$613$	−5.91182	−	10.2396i	−0.238776	−	0.413572i	0.721587	−	0.692323i	$-0.243413\pi$
$613$	−5.91182	−	10.2396i	−0.238776	−	0.413572i	−0.960363	+	0.278751i	$0.910079\pi$
$614$	−23.4663			−0.947021
$615$	1.58321	+	3.63596i	0.0638414	+	0.146616i
$616$	2.63294	+	2.89490i	0.106084	+	0.116639i
$617$	−9.75168	+	5.63013i	−0.392588	+	0.226661i	−0.683281	−	0.730156i	$-0.739447\pi$
$617$	−9.75168	+	5.63013i	−0.392588	+	0.226661i	0.290693	+	0.956816i	$0.406114\pi$
$618$	−15.6497	+	21.1725i	−0.629525	+	0.851682i
$619$	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	$0.562315\pi$
$620$			4.70616i			0.189004i
$621$	13.8733	−	39.3725i	0.556716	−	1.57996i
$622$	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
$626$	−8.57858	−	14.8585i	−0.342869	−	0.593866i
$627$	7.85913	+	18.0490i	0.313863	+	0.720809i
$628$	−5.16669	−	2.98299i	−0.206173	−	0.119034i
$629$	2.88617			0.115079
$630$	0.0632673	−	5.54677i	0.00252063	−	0.220989i
$631$	12.2109	+	21.1499i	0.486107	+	0.841963i	0.999872	−	0.0159683i	$-0.00508308\pi$
$631$	12.2109	+	21.1499i	0.486107	+	0.841963i	−0.513765	+	0.857931i	$0.671750\pi$
$632$	4.57643	−	2.64220i	0.182040	−	0.105101i
$633$	21.1947	+	2.40364i	0.842412	+	0.0955360i
$634$	−12.3478	−	21.3869i	−0.490392	−	0.849384i
$635$	−9.32937			−0.370225
$636$	1.57213	−	13.8626i	0.0623388	−	0.549688i
$637$	−6.06005	−	24.5005i	−0.240108	−	0.970746i
$638$			6.94181i			0.274829i
$639$	−9.04677	+	39.3731i	−0.357885	+	1.55757i
$640$	0.605242	−	0.349437i	0.0239243	−	0.0138127i
$641$		−	16.7542i		−	0.661750i	−0.943675	−	0.330875i	$-0.892656\pi$
$641$		−	16.7542i		−	0.661750i	0.943675	−	0.330875i	$-0.107344\pi$
$642$	−7.38556	−	16.9614i	−0.291485	−	0.669415i
$643$	10.0110	−	5.77985i	0.394795	−	0.227935i	−0.289441	−	0.957196i	$-0.593469\pi$
$643$	10.0110	−	5.77985i	0.394795	−	0.227935i	0.684236	+	0.729261i	$0.260136\pi$
$644$	−4.52330	−	20.7688i	−0.178243	−	0.818404i
$645$	−3.25975	−	0.369680i	−0.128352	−	0.0145562i
$646$	6.06450	−	10.5040i	0.238605	−	0.413275i
$647$	−14.9984	−	25.9780i	−0.589649	−	1.02130i	−0.994278	−	0.106822i	$-0.965933\pi$
$647$	−14.9984	−	25.9780i	−0.589649	−	1.02130i	0.404629	−	0.914481i	$-0.367401\pi$
$648$	8.97675	−	0.646523i	0.352640	−	0.0253978i
$649$	−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
$653$		−	25.5666i		−	1.00050i	−0.865882	−	0.500249i	$-0.833242\pi$
$653$		−	25.5666i		−	1.00050i	0.865882	−	0.500249i	$-0.166758\pi$
$654$	−1.79088	+	15.7915i	−0.0700289	+	0.617497i
$655$	−6.40266	+	11.0897i	−0.250172	+	0.433311i
$656$	−1.63806	+	2.83721i	−0.0639557	+	0.110774i
$657$	42.1641	−	12.9389i	1.64498	−	0.504796i
$658$	−14.2548	+	12.9649i	−0.555710	+	0.505423i
$659$	−6.23900	+	3.60209i	−0.243037	+	0.140317i	−0.616572	−	0.787299i	$-0.711479\pi$
$659$	−6.23900	+	3.60209i	−0.243037	+	0.140317i	0.373535	+	0.927616i	$0.378146\pi$
$660$	−0.201746	+	1.77894i	−0.00785295	+	0.0692453i
$661$	−15.6574	+	9.03980i	−0.609002	+	0.351607i	−0.772575	−	0.634924i	$-0.781031\pi$
$661$	−15.6574	+	9.03980i	−0.609002	+	0.351607i	0.163573	+	0.986531i	$0.447698\pi$
$662$	27.7416	+	16.0166i	1.07821	+	0.622504i
$663$	9.61010	−	2.19204i	0.373225	−	0.0851318i
$664$			0.659952i			0.0256111i
$665$	−3.02374	−	13.8835i	−0.117256	−	0.538380i
$666$	4.01591	+	3.73708i	0.155613	+	0.144809i
$667$	18.8534	−	32.6550i	0.730007	−	1.26441i
$668$	0.895737	−	1.55146i	0.0346571	−	0.0600279i
$669$	2.26532	−	19.9750i	0.0875824	−	0.772279i
$670$	−2.39413	−	1.38225i	−0.0924932	−	0.0534010i
$671$	−5.46478			−0.210965
$672$	3.71598	−	2.68169i	0.143347	−	0.103449i
$673$	−16.0613	+	27.8191i	−0.619119	+	1.07235i	0.370528	+	0.928821i	$0.379177\pi$
$673$	−16.0613	+	27.8191i	−0.619119	+	1.07235i	−0.989647	+	0.143524i	$0.954157\pi$
$674$			22.5440i			0.868361i
$675$	−17.8022	+	15.2528i	−0.685209	+	0.587079i
$676$	12.1069	+	4.73523i	0.465651	+	0.182124i
$677$	−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	$0.948133\pi$
$678$	−10.4229	+	14.1011i	−0.400290	+	0.541550i
$679$	−24.4921	+	22.2758i	−0.939921	+	0.854866i
$680$	0.955297	−	0.551541i	0.0366339	−	0.0211506i
$681$	0.822317	+	1.88851i	0.0315113	+	0.0723678i
$682$		−	9.95971i		−	0.381377i
$683$			21.3569i			0.817199i	0.912714	+	0.408600i	$0.133983\pi$
$683$			21.3569i			0.817199i	−0.912714	+	0.408600i	$0.866017\pi$
$684$	22.0391	−	6.76317i	0.842688	−	0.258596i
$685$	12.0627	−	6.96440i	0.460892	−	0.266096i
$686$	−11.1097	−	14.8181i	−0.424170	−	0.565756i
$687$	9.28688	+	6.86444i	0.354317	+	0.261895i
$688$	−1.35510	−	2.34709i	−0.0516625	−	0.0894821i
$689$	18.9310	−	22.0243i	0.721214	−	0.839061i
$690$	5.78050	−	7.82042i	0.220060	−	0.297718i
$691$			3.51821i			0.133839i	0.997758	+	0.0669196i	$0.0213171\pi$
$691$			3.51821i			0.133839i	−0.997758	+	0.0669196i	$0.978683\pi$
$692$	−8.07176	+	13.9807i	−0.306842	+	0.531467i
$693$	−0.133893	+	11.7387i	−0.00508619	+	0.445917i
$694$	−15.8455			−0.601487
$695$	7.60082	+	4.38834i	0.288316	+	0.166459i
$696$	8.07756	+	0.916058i	0.306179	+	0.0347231i
$697$	−2.58547	+	4.47817i	−0.0979318	+	0.169623i
$698$	11.1506	−	19.3134i	0.422057	−	0.731024i
$699$	10.0435	+	7.42367i	0.379879	+	0.280789i
$700$	−3.63172	+	11.3706i	−0.137266	+	0.429769i
$701$		−	21.8719i		−	0.826089i	−0.910711	−	0.413044i	$-0.864465\pi$
$701$		−	21.8719i		−	0.826089i	0.910711	−	0.413044i	$-0.135535\pi$
$702$	16.2101	+	9.39328i	0.611810	+	0.354526i
$703$	12.1691	+	7.02586i	0.458968	+	0.264985i
$704$	−1.28088	+	0.739517i	−0.0482750	+	0.0278716i
$705$	−8.75971	−	0.993419i	−0.329910	−	0.0374143i
$706$	−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
$709$	5.65827	−	9.80041i	0.212501	−	0.368062i	−0.739996	−	0.672612i	$-0.765173\pi$
$709$	5.65827	−	9.80041i	0.212501	−	0.368062i	0.952497	+	0.304549i	$0.0985059\pi$
$710$	−4.70564	+	8.15040i	−0.176599	+	0.305879i
$711$	15.4506	+	3.55009i	0.579443	+	0.133139i
$712$		−	6.04188i		−	0.226429i
$713$	−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
$717$	10.4735	−	4.56050i	0.391140	−	0.170315i
$718$	1.53335	+	2.65584i	0.0572241	+	0.0991151i
$719$	−6.97329	+	12.0781i	−0.260060	+	0.450437i	−0.966258	−	0.257578i	$-0.917076\pi$
$719$	−6.97329	+	12.0781i	−0.260060	+	0.450437i	0.706198	+	0.708015i	$0.250409\pi$
$720$	2.04337	+	0.469507i	0.0761521	+	0.0174975i
$721$	−29.7523	+	27.0599i	−1.10803	+	1.00776i
$722$	34.6857	−	20.0258i	1.29087	−	0.745283i
$723$	7.01290	−	3.05364i	0.260813	−	0.113566i
$724$			7.63392i			0.283712i
$725$	−18.3381	+	10.5875i	−0.681059	+	0.393210i
$726$	−1.71999	+	15.1664i	−0.0638347	+	0.562878i
$727$			5.92782i			0.219850i	0.993940	+	0.109925i	$0.0350611\pi$
$727$			5.92782i			0.219850i	−0.993940	+	0.109925i	$0.964939\pi$
$728$	9.53564	−	0.267374i	0.353414	−	0.00990954i
$729$	21.0360	+	16.9260i	0.779110	+	0.626887i
$730$	10.2745			0.380278
$731$	−2.13884	−	3.70459i	−0.0791080	−	0.137019i
$732$	−0.721145	+	6.35887i	−0.0266543	+	0.235031i
$733$	−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
$735$	1.74675	−	8.29139i	0.0644299	−	0.305833i
$736$	8.03387			0.296132
$737$	5.06672	+	2.92527i	0.186635	+	0.107754i
$738$	−9.39593	+	2.88334i	−0.345869	+	0.106137i
$739$	−23.5360	−	40.7655i	−0.865785	−	1.49958i	−0.866266	−	0.499584i	$-0.833486\pi$
$739$	−23.5360	−	40.7655i	−0.865785	−	1.49958i	0.000480469	−	1.00000i	$-0.499847\pi$
$740$	0.638972	+	1.10673i	0.0234891	+	0.0406843i
$741$	45.8557	+	14.1516i	1.68455	+	0.519871i
$742$	6.48400	−	20.3009i	0.238035	−	0.745269i
$743$	17.7056	+	10.2223i	0.649554	+	0.375020i	0.788285	−	0.615310i	$-0.210969\pi$
$743$	17.7056	+	10.2223i	0.649554	+	0.375020i	−0.138732	+	0.990330i	$0.544303\pi$
$744$	−11.5892	−	1.31431i	−0.424881	−	0.0481848i
$745$		−	4.71822i		−	0.172862i
$746$	−4.66207	−	2.69165i	−0.170691	−	0.0985483i
$747$	−1.34875	+	1.44938i	−0.0493481	+	0.0530301i
$748$	−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
$751$	43.4139			1.58419			0.792097	−	0.610395i	$-0.208989\pi$
$751$	43.4139			1.58419			0.792097	+	0.610395i	$0.208989\pi$
$752$	−3.64146	−	6.30720i	−0.132790	−	0.230000i
$753$	15.7078	−	21.2510i	0.572423	−	0.774430i
$754$	12.8333	+	11.0309i	0.467362	+	0.401720i
$755$	−5.32741			−0.193884
$756$	13.6416	+	1.70487i	0.496140	+	0.0620054i
$757$	−6.03356	+	10.4504i	−0.219293	+	0.379827i	−0.954592	−	0.297916i	$-0.903709\pi$
$757$	−6.03356	+	10.4504i	−0.219293	+	0.379827i	0.735299	+	0.677743i	$0.237042\pi$
$758$	−11.9324	−	6.88920i	−0.433406	−	0.250227i
$759$	−12.2333	+	16.5505i	−0.444042	+	0.600743i
$760$	5.37049			0.194808
$761$	0.495413	−	0.858081i	0.0179587	−	0.0311054i	−0.856906	−	0.515472i	$-0.827617\pi$
$761$	0.495413	−	0.858081i	0.0179587	−	0.0311054i	0.874865	+	0.484367i	$0.160950\pi$
$762$	2.60545	−	22.9742i	0.0943854	−	0.832266i
$763$	−7.38621	+	23.1256i	−0.267399	+	0.837204i
$764$	−19.2685	−	11.1247i	−0.697110	−	0.402477i
$765$	3.22520	+	0.741057i	0.116607	+	0.0267930i
$766$	24.8621	+	14.3541i	0.898304	+	0.518636i
$767$	−9.21670	+	48.8684i	−0.332796	+	1.76454i
$768$	0.691481	+	1.58803i	0.0249517	+	0.0573033i
$769$	41.7420	+	24.0998i	1.50526	+	0.869060i	0.999981	+	0.00610115i	$0.00194207\pi$
$769$	41.7420	+	24.0998i	1.50526	+	0.869060i	0.505274	+	0.862959i	$0.331391\pi$
$770$	−0.832071	+	2.60515i	−0.0299857	+	0.0938830i
$771$	10.1679	+	23.3513i	0.366188	+	0.840975i
$772$	−3.98148	−	6.89613i	−0.143297	−	0.248197i
$773$	−10.9305			−0.393144			−0.196572	−	0.980489i	$-0.562981\pi$
$773$	−10.9305			−0.393144			−0.196572	+	0.980489i	$0.562981\pi$
$774$	1.82072	−	7.92409i	0.0654445	−	0.284826i
$775$	26.3104	−	15.1903i	0.945097	−	0.545652i
$776$	−6.25663	−	10.8368i	−0.224600	−	0.389019i
$777$	4.90368	+	6.79496i	0.175919	+	0.243768i
$778$	11.3855	−	19.7202i	0.408189	−	0.707004i
$779$	−21.8026	+	12.5877i	−0.781158	+	0.451002i
$780$	2.96814	+	3.19979i	0.106277	+	0.114571i
$781$	9.95859	−	17.2488i	0.356346	−	0.617210i
$782$	12.6804			0.453451
$783$	15.8677	+	18.5200i	0.567066	+	0.661851i
$784$	6.36600	−	2.91103i	0.227357	−	0.103965i
$785$		−	4.16946i		−	0.148815i
$786$	−25.5210	−	18.8640i	−0.910305	−	0.672857i
$787$			26.8306i			0.956409i	0.878249	+	0.478204i	$0.158712\pi$
$787$			26.8306i			0.956409i	−0.878249	+	0.478204i	$0.841288\pi$
$788$	7.75682	+	4.47840i	0.276325	+	0.159537i
$789$	−18.5890	−	13.7401i	−0.661784	−	0.489161i
$790$	3.19834	+	1.84656i	0.113792	+	0.0656978i
$791$	−19.8154	+	18.0223i	−0.704554	+	0.640798i
$792$	−4.32442	−	0.993624i	−0.153661	−	0.0353069i
$793$	−8.68377	+	10.1027i	−0.308370	+	0.358758i
$794$	−5.35066	+	9.26762i	−0.189888	+	0.328895i
$795$	8.93959	−	3.89258i	0.317054	−	0.138056i
$796$		−	21.8113i		−	0.773082i
$797$	−20.5234	−	35.5476i	−0.726977	−	1.25916i	−0.958155	−	0.286250i	$-0.907591\pi$
$797$	−20.5234	−	35.5476i	−0.726977	−	1.25916i	0.231178	−	0.972912i	$-0.425742\pi$
$798$	35.0335	−	3.56886i	1.24017	−	0.126336i
$799$	−5.74758	−	9.95510i	−0.203335	−	0.352186i
$800$	−3.90714	−	2.25579i	−0.138138	−	0.0797542i
$801$	12.3478	−	13.2691i	0.436289	−	0.468842i
$802$	12.4014			0.437908
$803$	−21.7441			−0.767334
$804$	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
$807$	−13.0314	−	29.9275i	−0.458726	−	1.05350i
$808$	−0.965855	+	0.557637i	−0.0339787	+	0.0196176i
$809$	34.2032	−	19.7472i	1.20252	−	0.694275i	0.241405	−	0.970424i	$-0.422392\pi$
$809$	34.2032	−	19.7472i	1.20252	−	0.694275i	0.961115	+	0.276149i	$0.0890584\pi$
$810$	3.52811	+	5.20719i	0.123965	+	0.182962i
$811$		−	51.6567i		−	1.81391i	−0.421226	−	0.906956i	$-0.638400\pi$
$811$		−	51.6567i		−	1.81391i	0.421226	−	0.906956i	$-0.361600\pi$
$812$	11.8291	+	3.77814i	0.415119	+	0.132587i
$813$	−15.2569	+	6.64334i	−0.535083	+	0.232992i
$814$	−1.35226	−	2.34219i	−0.0473968	−	0.0820937i
$815$	5.29738			0.185559
$816$	1.09141	+	2.50651i	0.0382071	+	0.0877453i
$817$		−	20.8265i		−	0.728626i
$818$	11.8142			0.413073
$819$	21.4885	+	18.9009i	0.750871	+	0.660449i
$820$	−2.28960			−0.0799562
$821$			47.5225i			1.65855i	0.558843	+	0.829273i	$0.311245\pi$
$821$			47.5225i			1.65855i	−0.558843	+	0.829273i	$0.688755\pi$
$822$	13.7815	+	31.6501i	0.480684	+	1.10392i
$823$	39.6803			1.38317			0.691583	−	0.722297i	$-0.256913\pi$
$823$	39.6803			1.38317			0.691583	+	0.722297i	$0.256913\pi$
$824$	−7.60037	−	13.1642i	−0.264772	−	0.458598i
$825$	10.5966	−	4.61410i	0.368926	−	0.160642i
$826$	7.76564	+	35.6559i	0.270201	+	1.24063i
$827$			1.16764i			0.0406030i	0.999794	+	0.0203015i	$0.00646261\pi$
$827$			1.16764i			0.0406030i	−0.999794	+	0.0203015i	$0.993537\pi$
$828$	17.6439	+	16.4189i	0.613169	+	0.570596i
$829$	1.46241	−	0.844322i	0.0507916	−	0.0293245i	−0.474389	−	0.880315i	$-0.657331\pi$
$829$	1.46241	−	0.844322i	0.0507916	−	0.0293245i	0.525181	+	0.850991i	$0.323998\pi$
$830$	−0.399431	+	0.230611i	−0.0138644	+	0.00800464i
$831$	4.04685	+	9.29388i	0.140384	+	0.322401i
$832$	−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
$835$	1.25201			0.0433277
$836$	−11.3656			−0.393089
$837$	−22.7661	−	26.5714i	−0.786911	−	0.918443i
$838$	−13.4567	−	7.76922i	−0.464854	−	0.268383i
$839$	9.54818	+	16.5379i	0.329640	+	0.570953i	0.982440	−	0.186577i	$-0.0597394\pi$
$839$	9.54818	+	16.5379i	0.329640	+	0.570953i	−0.652801	+	0.757530i	$0.726406\pi$
$840$	2.92157	+	1.31199i	0.100804	+	0.0452679i
$841$	−3.48563	−	6.03729i	−0.120194	−	0.208183i
$842$			26.1683i			0.901820i
$843$	8.92464	−	3.88608i	0.307381	−	0.133844i
$844$	−6.15759	+	10.6653i	−0.211953	+	0.367113i
$845$	1.36464	+	8.98228i	0.0469452	+	0.309000i
$846$	4.89271	−	21.2939i	0.168215	−	0.732100i
$847$	−7.09383	+	22.2102i	−0.243747	+	0.763152i
$848$	6.97573	+	4.02744i	0.239548	+	0.138303i
$849$	21.8796	+	16.1724i	0.750907	+	0.555037i
$850$	−6.16692	−	3.56047i	−0.211523	−	0.122123i
$851$			14.6906i			0.503586i
$852$	−18.7567	−	13.8641i	−0.642594	−	0.474977i
$853$		−	24.3423i		−	0.833465i	−0.909029	−	0.416733i	$-0.863175\pi$
$853$		−	24.3423i		−	0.833465i	0.909029	−	0.416733i	$-0.136825\pi$
$854$	−2.97425	+	9.31215i	−0.101777	+	0.318655i
$855$	11.7946	+	10.9757i	0.403368	+	0.375362i
$856$	10.6808			0.365061
$857$	24.2077	−	41.9290i	0.826920	−	1.43227i	−0.0735222	−	0.997294i	$-0.523424\pi$
$857$	24.2077	−	41.9290i	0.826920	−	1.43227i	0.900443	−	0.434975i	$-0.143243\pi$
$858$	−6.28152	−	6.77175i	−0.214448	−	0.231184i
$859$	−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
$861$	−14.9358	+	1.52151i	−0.509011	+	0.0518528i
$862$	11.2420	+	19.4718i	0.382905	+	0.663212i
$863$	36.4727	−	21.0575i	1.24154	−	0.716806i	0.272136	−	0.962259i	$-0.412270\pi$
$863$	36.4727	−	21.0575i	1.24154	−	0.716806i	0.969409	+	0.245453i	$0.0789367\pi$
$864$	−1.72685	+	4.90081i	−0.0587487	+	0.166729i
$865$	−11.2823			−0.383609
$866$	10.3947	+	18.0042i	0.353227	+	0.611807i
$867$	−10.0325	−	23.0404i	−0.340722	−	0.782493i
$868$	−16.9717	−	5.42066i	−0.576055	−	0.183989i
$869$	−6.76869	−	3.90791i	−0.229612	−	0.132567i
$870$	2.26816	+	5.20899i	0.0768978	+	0.176601i
$871$	13.4592	−	4.71844i	0.456047	−	0.159878i
$872$	−7.94637	−	4.58784i	−0.269098	−	0.155364i
$873$	8.40649	−	36.5864i	0.284516	−	1.23826i
$874$	53.4652	+	30.8682i	1.80849	+	1.04413i
$875$	−17.1845	+	3.74267i	−0.580942	+	0.126525i
$876$	−2.86941	+	25.3017i	−0.0969483	+	0.854865i
$877$	−4.18376	+	7.24648i	−0.141275	+	0.244696i	−0.927977	−	0.372637i	$-0.878454\pi$
$877$	−4.18376	+	7.24648i	−0.141275	+	0.244696i	0.786702	+	0.617333i	$0.211787\pi$
$878$	−10.5260			−0.355235
$879$	−3.97984	+	5.38431i	−0.134237	+	0.181608i
$880$	−0.895173	−	0.516829i	−0.0301763	−	0.0174223i
$881$	−0.557391	+	0.965430i	−0.0187790	+	0.0325262i	−0.875262	−	0.483649i	$-0.839311\pi$
$881$	−0.557391	+	0.965430i	−0.0187790	+	0.0325262i	0.856483	+	0.516175i	$0.172645\pi$
$882$	19.9302	+	6.61705i	0.671086	+	0.222808i
$883$	−1.05349			−0.0354528			−0.0177264	−	0.999843i	$-0.505643\pi$
$883$	−1.05349			−0.0354528			−0.0177264	+	0.999843i	$0.505643\pi$
$884$	−1.05472	+	5.59231i	−0.0354742	+	0.188090i
$885$	−9.92400	+	13.4261i	−0.333592	+	0.451315i
$886$	−13.2521	−	22.9533i	−0.445212	−	0.771130i
$887$	15.3094			0.514040			0.257020	−	0.966406i	$-0.417259\pi$
$887$	15.3094			0.514040			0.257020	+	0.966406i	$0.417259\pi$
$888$	−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
$891$	−7.46658	−	11.0200i	−0.250140	−	0.369185i
$892$	10.0515	+	5.80325i	0.336550	+	0.194307i
$893$		−	55.9657i		−	1.87282i
$894$	11.6189	+	1.31767i	0.388595	+	0.0440696i
$895$	−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
$899$	−15.8028	−	27.3712i	−0.527052	−	0.912881i
$900$	−3.97066	−	12.9392i	−0.132355	−	0.431306i
$901$	11.0103	+	6.35680i	0.366806	+	0.211776i
$902$	4.84551			0.161338
$903$	5.08781	−	11.3297i	0.169312	−	0.377029i
$904$	−5.06194	−	8.76754i	−0.168358	−	0.291604i
$905$	−4.62037	+	2.66757i	−0.153586	+	0.0886730i
$906$	1.48780	−	13.1191i	0.0494290	−	0.435852i
$907$	1.83818	+	3.18383i	0.0610359	+	0.105717i	0.894929	−	0.446209i	$-0.147226\pi$
$907$	1.83818	+	3.18383i	0.0610359	+	0.105717i	−0.833893	+	0.551926i	$0.813893\pi$
$908$	−1.18921			−0.0394654
$909$	−3.26085	−	0.749247i	−0.108156	−	0.0248510i
$910$	3.49393	+	5.67794i	0.115823	+	0.188222i
$911$		−	48.3126i		−	1.60067i	−0.599556	−	0.800333i	$-0.704656\pi$
$911$		−	48.3126i		−	1.60067i	0.599556	−	0.800333i	$-0.295344\pi$
$912$	−1.49984	+	13.2252i	−0.0496646	+	0.437929i
$913$	0.845320	−	0.488046i	0.0279760	−	0.0161520i
$914$			13.5238i			0.447329i
$915$	−4.10065	+	1.78555i	−0.135563	+	0.0590286i
$916$	−5.77423	+	3.33375i	−0.190786	+	0.110150i
$917$	−32.6177	−	35.8630i	−1.07713	−	1.18430i
$918$	−2.72561	+	7.73531i	−0.0899586	+	0.255303i
$919$	−14.1262	+	24.4674i	−0.465982	+	0.807104i	−0.999245	−	0.0388453i	$-0.987632\pi$
$919$	−14.1262	+	24.4674i	−0.465982	+	0.807104i	0.533264	+	0.845949i	$0.320965\pi$
$920$	2.80733	+	4.86244i	0.0925549	+	0.160310i
$921$	37.2652	−	16.2265i	1.22793	−	0.534681i
$922$	26.4348	−	15.2621i	0.870583	−	0.502632i
$923$	−16.0631	−	45.8195i	−0.528724	−	1.50817i
$924$	−6.18296	−	2.77657i	−0.203404	−	0.0913426i
$925$	4.12488	−	7.14451i	0.135625	−	0.234910i
$926$			18.9355i			0.622259i
$927$	10.2120	−	44.4441i	0.335404	−	1.45974i
$928$	−2.34674	+	4.06467i	−0.0770355	+	0.133429i
$929$	−8.10485	+	14.0380i	−0.265911	+	0.460572i	−0.967802	−	0.251713i	$-0.919006\pi$
$929$	−8.10485	+	14.0380i	−0.265911	+	0.460572i	0.701891	+	0.712285i	$0.252340\pi$
$930$	−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
$933$	−29.1227	−	3.30274i	−0.953434	−	0.108127i
$934$	−1.35959	+	0.784961i	−0.0444872	+	0.0256847i
$935$	−1.41292	−	0.815747i	−0.0462073	−	0.0266778i
$936$	−8.70860	+	6.41562i	−0.284650	+	0.209701i
$937$			40.9010i			1.33618i	0.744082	+	0.668088i	$0.232887\pi$
$937$			40.9010i			1.33618i	−0.744082	+	0.668088i	$0.767113\pi$
$938$	7.74237	−	7.04175i	0.252797	−	0.229921i
$939$	23.8975	+	17.6639i	0.779864	+	0.576441i
$940$	2.54492	−	4.40793i	0.0830062	−	0.143771i
$941$	21.0594	−	36.4760i	0.686517	−	1.18908i	−0.286441	−	0.958098i	$-0.592472\pi$
$941$	21.0594	−	36.4760i	0.686517	−	1.18908i	0.972957	−	0.230984i	$-0.0741946\pi$
$942$	10.2676	+	1.16442i	0.334535	+	0.0379389i
$943$	−22.7938	−	13.1600i	−0.742268	−	0.428548i
$944$	−13.7926			−0.448911
$945$	3.73502	+	8.85222i	0.121500	+	0.287963i
$946$	−2.00423	+	3.47143i	−0.0651632	+	0.112866i
$947$		−	51.4573i		−	1.67214i	−0.548626	−	0.836068i	$-0.684849\pi$
$947$		−	51.4573i		−	1.67214i	0.548626	−	0.836068i	$-0.315151\pi$
$948$	−5.44049	+	7.36042i	−0.176699	+	0.239055i
$949$	−34.5524	+	40.1983i	−1.12162	+	1.30489i
$950$	−17.3346	−	30.0244i	−0.562409	−	0.974121i
$951$	34.3973	+	25.4250i	1.11541	+	0.824461i
$952$	0.888669	+	4.08033i	0.0288019	+	0.132244i
$953$	−9.84866	+	5.68613i	−0.319029	+	0.184192i	−0.650960	−	0.759112i	$-0.725633\pi$
$953$	−9.84866	+	5.68613i	−0.319029	+	0.184192i	0.331931	+	0.943304i	$0.392300\pi$
$954$	7.08914	+	23.1014i	0.229519	+	0.747935i
$955$		−	15.5495i		−	0.503169i
$956$			6.59526i			0.213306i
$957$	−4.80013	−	11.0238i	−0.155166	−	0.356350i
$958$	25.7325	−	14.8567i	0.831381	−	0.479998i
$959$	11.2214	+	51.5230i	0.362357	+	1.66376i
$960$	−0.719516	+	0.973431i	−0.0232223	+	0.0314173i
$961$	7.17290	+	12.4238i	0.231384	+	0.400769i
$962$	−6.47881	−	1.22192i	−0.208885	−	0.0393963i
$963$	23.4570	+	21.8284i	0.755893	+	0.703410i
$964$			4.41609i			0.142233i
$965$	2.78255	−	4.81952i	0.0895735	−	0.155146i
$966$	21.5444	+	29.8537i	0.693179	+	0.960528i
$967$	12.5442			0.403396			0.201698	−	0.979448i	$-0.435354\pi$
$967$	12.5442			0.403396			0.201698	+	0.979448i	$0.435354\pi$
$968$	−7.63181	−	4.40623i	−0.245296	−	0.141622i
$969$	−2.36730	+	20.8742i	−0.0760486	+	0.670577i
$970$	4.37259	−	7.57355i	0.140396	−	0.243172i
$971$	−4.66697	+	8.08344i	−0.149770	+	0.259410i	−0.931143	−	0.364655i	$-0.881187\pi$
$971$	−4.66697	+	8.08344i	−0.149770	+	0.259410i	0.781372	+	0.624065i	$0.214520\pi$
$972$	−13.8083	+	7.23396i	−0.442902	+	0.232029i
$973$	−24.5803	+	22.3560i	−0.788008	+	0.716700i
$974$		−	20.7730i		−	0.665609i
$975$	8.30840	−	26.9219i	0.266082	−	0.862191i
$976$	−3.19981	−	1.84741i	−0.102424	−	0.0591343i
$977$	−13.9488	+	8.05336i	−0.446262	+	0.257650i	−0.706250	−	0.707962i	$-0.749615\pi$
$977$	−13.9488	+	8.05336i	−0.446262	+	0.257650i	0.259988	+	0.965612i	$0.416281\pi$
$978$	−1.47942	+	13.0451i	−0.0473066	+	0.417137i
$979$	−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
$982$	−6.43392	+	11.1439i	−0.205315	+	0.355615i
$983$	11.9633	−	20.7211i	0.381570	−	0.660899i	−0.609717	−	0.792619i	$-0.708717\pi$
$983$	11.9633	−	20.7211i	0.381570	−	0.660899i	0.991287	+	0.131720i	$0.0420501\pi$
$984$	0.639424	−	5.63828i	0.0203841	−	0.179742i
$985$			6.25967i			0.199450i
$986$	−3.70403	+	6.41556i	−0.117960	+	0.204313i
$987$	13.6722	−	30.4456i	0.435190	−	0.969093i
$988$	−18.0605	+	21.0116i	−0.574582	+	0.668469i
$989$	18.8563	−	10.8867i	0.599594	−	0.346176i
$990$	−0.909727	−	2.96453i	−0.0289130	−	0.0942189i
$991$	−8.46705	−	14.6654i	−0.268965	−	0.465861i	0.699630	−	0.714505i	$-0.253348\pi$
$991$	−8.46705	−	14.6654i	−0.268965	−	0.465861i	−0.968595	+	0.248645i	$0.920015\pi$
$992$	3.36696	−	5.83175i	0.106901	−	0.185158i
$993$	−55.1299	−	6.25215i	−1.74949	−	0.198406i
$994$	−23.9724	−	26.3576i	−0.760359	−	0.836011i
$995$	13.2011	−	7.62168i	0.418504	−	0.241623i
$996$	−0.456345	−	1.04803i	−0.0144598	−	0.0332080i
$997$		−	9.43908i		−	0.298939i	−0.988766	−	0.149469i	$-0.952243\pi$
$997$		−	9.43908i		−	0.298939i	0.988766	−	0.149469i	$-0.0477565\pi$
$998$	35.6931	−	20.6074i	1.12985	−	0.652317i
$999$	−8.96152	−	3.15768i	−0.283530	−	0.0999046i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.u.a.185.19	✓	76	39.29	odd	6
546.2.u.a.185.20	yes	76	13.3	even	3
546.2.u.a.425.19	yes	76	7.5	odd	6
546.2.u.a.425.20	yes	76	21.5	even	6
546.2.bb.a.269.12	yes	76	1.1	even	1	trivial
546.2.bb.a.269.25	yes	76	3.2	odd	2	inner
546.2.bb.a.341.6	yes	76	91.68	odd	6	inner
546.2.bb.a.341.31	yes	76	273.68	even	6	inner

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.bb (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} +(0.691481 + 1.58803i) q^{3} -1.00000 q^{4} +(-0.349437 - 0.605242i) q^{5} +(1.58803 - 0.691481i) q^{6} +(2.58515 - 0.563029i) q^{7} +1.00000i q^{8} +(-2.04371 + 2.19619i) q^{9} +O(q^{10})\)	\(q-1.00000i q^{2} +(0.691481 + 1.58803i) q^{3} -1.00000 q^{4} +(-0.349437 - 0.605242i) q^{5} +(1.58803 - 0.691481i) q^{6} +(2.58515 - 0.563029i) q^{7} +1.00000i q^{8} +(-2.04371 + 2.19619i) q^{9} +(-0.605242 + 0.349437i) q^{10} +(1.28088 - 0.739517i) q^{11} +(-0.691481 - 1.58803i) q^{12} +(0.668235 - 3.54309i) q^{13} +(-0.563029 - 2.58515i) q^{14} +(0.719516 - 0.973431i) q^{15} +1.00000 q^{16} +1.57837 q^{17} +(2.19619 + 2.04371i) q^{18} +(6.65498 + 3.84225i) q^{19} +(0.349437 + 0.605242i) q^{20} +(2.68169 + 3.71598i) q^{21} +(-0.739517 - 1.28088i) q^{22} +8.03387i q^{23} +(-1.58803 + 0.691481i) q^{24} +(2.25579 - 3.90714i) q^{25} +(-3.54309 - 0.668235i) q^{26} +(-4.90081 - 1.72685i) q^{27} +(-2.58515 + 0.563029i) q^{28} +(-4.06467 - 2.34674i) q^{29} +(-0.973431 - 0.719516i) q^{30} +(5.83175 + 3.36696i) q^{31} -1.00000i q^{32} +(2.06008 + 1.52272i) q^{33} -1.57837i q^{34} +(-1.24411 - 1.36790i) q^{35} +(2.04371 - 2.19619i) q^{36} +1.82858 q^{37} +(3.84225 - 6.65498i) q^{38} +(6.08862 - 1.38880i) q^{39} +(0.605242 - 0.349437i) q^{40} +(-1.63806 + 2.83721i) q^{41} +(3.71598 - 2.68169i) q^{42} +(-1.35510 - 2.34709i) q^{43} +(-1.28088 + 0.739517i) q^{44} +(2.04337 + 0.469507i) q^{45} +8.03387 q^{46} +(-3.64146 - 6.30720i) q^{47} +(0.691481 + 1.58803i) q^{48} +(6.36600 - 2.91103i) q^{49} +(-3.90714 - 2.25579i) q^{50} +(1.09141 + 2.50651i) q^{51} +(-0.668235 + 3.54309i) q^{52} +(6.97573 + 4.02744i) q^{53} +(-1.72685 + 4.90081i) q^{54} +(-0.895173 - 0.516829i) q^{55} +(0.563029 + 2.58515i) q^{56} +(-1.49984 + 13.2252i) q^{57} +(-2.34674 + 4.06467i) q^{58} -13.7926 q^{59} +(-0.719516 + 0.973431i) q^{60} +(-3.19981 - 1.84741i) q^{61} +(3.36696 - 5.83175i) q^{62} +(-4.04677 + 6.82815i) q^{63} -1.00000 q^{64} +(-2.37793 + 0.833640i) q^{65} +(1.52272 - 2.06008i) q^{66} +(1.97783 + 3.42570i) q^{67} -1.57837 q^{68} +(-12.7581 + 5.55527i) q^{69} +(-1.36790 + 1.24411i) q^{70} +(11.6622 - 6.73317i) q^{71} +(-2.19619 - 2.04371i) q^{72} +(-12.7319 - 7.35079i) q^{73} -1.82858i q^{74} +(7.76451 + 0.880555i) 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} +(-0.349437 - 0.605242i) q^{80} +(-0.646523 - 8.97675i) q^{81} +(2.83721 + 1.63806i) q^{82} +0.659952 q^{83} +(-2.68169 - 3.71598i) q^{84} +(-0.551541 - 0.955297i) q^{85} +(-2.34709 + 1.35510i) q^{86} +(0.916058 - 8.07756i) q^{87} +(0.739517 + 1.28088i) q^{88} -6.04188 q^{89} +(0.469507 - 2.04337i) q^{90} +(-0.267374 - 9.53564i) q^{91} -8.03387i q^{92} +(-1.31431 + 11.5892i) q^{93} +(-6.30720 + 3.64146i) q^{94} -5.37049i q^{95} +(1.58803 - 0.691481i) q^{96} +(-10.8368 + 6.25663i) q^{97} +(-2.91103 - 6.36600i) q^{98} +(-0.993624 + 4.32442i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 76 q - 76 q^{4} + 10 q^{7} + 4 q^{9}+O(q^{10}) \) 76 * q - 76 * q^4 + 10 * q^7 + 4 * q^9	\( 76 q - 76 q^{4} + 10 q^{7} + 4 q^{9} - 2 q^{13} + 12 q^{15} + 76 q^{16} + 18 q^{19} - 8 q^{21} - 42 q^{25} - 10 q^{28} - 10 q^{30} + 12 q^{31} + 72 q^{33} - 4 q^{36} + 12 q^{37} - 42 q^{39} + 2 q^{42} - 2 q^{43} + 8 q^{46} - 10 q^{49} + 10 q^{51} + 2 q^{52} - 24 q^{55} + 8 q^{57} - 8 q^{58} - 12 q^{60} + 78 q^{61} + 2 q^{63} - 76 q^{64} - 24 q^{66} - 48 q^{67} + 30 q^{69} - 54 q^{73} - 18 q^{76} - 12 q^{78} - 60 q^{79} - 4 q^{81} - 24 q^{82} + 8 q^{84} + 8 q^{85} - 8 q^{91} - 32 q^{93} - 24 q^{94} + 66 q^{97}+O(q^{100}) \) 76 * q - 76 * q^4 + 10 * q^7 + 4 * q^9 - 2 * q^13 + 12 * q^15 + 76 * q^16 + 18 * q^19 - 8 * q^21 - 42 * q^25 - 10 * q^28 - 10 * q^30 + 12 * q^31 + 72 * q^33 - 4 * q^36 + 12 * q^37 - 42 * q^39 + 2 * q^42 - 2 * q^43 + 8 * q^46 - 10 * q^49 + 10 * q^51 + 2 * q^52 - 24 * q^55 + 8 * q^57 - 8 * q^58 - 12 * q^60 + 78 * q^61 + 2 * q^63 - 76 * q^64 - 24 * q^66 - 48 * q^67 + 30 * q^69 - 54 * q^73 - 18 * q^76 - 12 * q^78 - 60 * q^79 - 4 * q^81 - 24 * q^82 + 8 * q^84 + 8 * q^85 - 8 * q^91 - 32 * q^93 - 24 * q^94 + 66 * q^97

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