LMFDB - Embedded newform 570.2.v.c.83.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [570,2,Mod(83,570)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(570, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 9, 4]))

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

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

chi := DirichletCharacter("570.83");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 570 = 2 \cdot 3 \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	570.v (of order $12$, degree $4$, 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:	$4.55147291521$
Analytic rank:	$0$
Dimension:	$144$
Relative dimension:	$36$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			83.10
Character	$\chi$	$=$	570.83
Dual form			570.2.v.c.467.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.258819 + 0.965926i) q^{2} +(-0.366145 + 1.69291i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(-0.619415 + 2.14856i) q^{5} +(-1.54046 - 0.791825i) q^{6} +(-1.07462 + 1.07462i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-2.73188 - 1.23970i) q^{9} +O(q^{10})$	\(q+(-0.258819 + 0.965926i) q^{2} +(-0.366145 + 1.69291i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(-0.619415 + 2.14856i) q^{5} +(-1.54046 - 0.791825i) q^{6} +(-1.07462 + 1.07462i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-2.73188 - 1.23970i) q^{9} +(-1.91504 - 1.15440i) q^{10} +5.54910i q^{11} +(1.16354 - 1.28303i) q^{12} +(0.316753 - 0.0848738i) q^{13} +(-0.759868 - 1.31613i) q^{14} +(-3.41053 - 1.83530i) q^{15} +(0.500000 + 0.866025i) q^{16} +(1.64252 - 6.12997i) q^{17} +(1.90452 - 2.31793i) q^{18} +(-1.73771 - 3.99755i) q^{19} +(1.61071 - 1.55100i) q^{20} +(-1.42576 - 2.21269i) q^{21} +(-5.36001 - 1.43621i) q^{22} +(2.01431 + 7.51752i) q^{23} +(0.938163 + 1.45597i) q^{24} +(-4.23265 - 2.66171i) q^{25} +0.327927i q^{26} +(3.09896 - 4.17091i) q^{27} +(1.46795 - 0.393337i) q^{28} +(-2.43524 + 4.21797i) q^{29} +(2.65547 - 2.81930i) q^{30} -4.22261 q^{31} +(-0.965926 + 0.258819i) q^{32} +(-9.39411 - 2.03177i) q^{33} +(5.49598 + 3.17311i) q^{34} +(-1.64325 - 2.97451i) q^{35} +(1.74602 + 2.43955i) q^{36} +(3.78717 - 3.78717i) q^{37} +(4.31108 - 0.643857i) q^{38} +(0.0277060 + 0.567310i) q^{39} +(1.08127 + 1.95726i) q^{40} +(-1.04419 + 0.602864i) q^{41} +(2.50631 - 0.804493i) q^{42} +(2.35615 - 8.79326i) q^{43} +(2.77455 - 4.80566i) q^{44} +(4.35574 - 5.10172i) q^{45} -7.78271 q^{46} +(2.38585 - 0.639288i) q^{47} +(-1.64917 + 0.529363i) q^{48} +4.69040i q^{49} +(3.66650 - 3.39953i) q^{50} +(9.77608 + 5.02509i) q^{51} +(-0.316753 - 0.0848738i) q^{52} +(-1.50577 - 5.61960i) q^{53} +(3.22672 + 4.07287i) q^{54} +(-11.9226 - 3.43719i) q^{55} +1.51974i q^{56} +(7.40373 - 1.47810i) q^{57} +(-3.44396 - 3.44396i) q^{58} +(2.29536 + 3.97569i) q^{59} +(2.03595 + 3.29468i) q^{60} +(-4.12362 + 7.14232i) q^{61} +(1.09289 - 4.07873i) q^{62} +(4.26792 - 1.60352i) q^{63} -1.00000i q^{64} +(-0.0138450 + 0.733136i) q^{65} +(4.39392 - 8.54815i) q^{66} +(0.216807 + 0.809136i) q^{67} +(-4.48745 + 4.48745i) q^{68} +(-13.4640 + 0.657548i) q^{69} +(3.29846 - 0.817394i) q^{70} +(-7.44126 + 4.29621i) q^{71} +(-2.80833 + 1.05513i) q^{72} +(-2.65264 + 9.89978i) q^{73} +(2.67793 + 4.63831i) q^{74} +(6.05578 - 6.19092i) q^{75} +(-0.493872 + 4.33083i) q^{76} +(-5.96314 - 5.96314i) q^{77} +(-0.555150 - 0.120069i) q^{78} +(-4.24944 + 2.45342i) q^{79} +(-2.17042 + 0.537853i) q^{80} +(5.92629 + 6.77341i) q^{81} +(-0.312065 - 1.16464i) q^{82} +(-2.14772 + 2.14772i) q^{83} +(0.128400 + 2.62913i) q^{84} +(12.1532 + 7.32606i) q^{85} +(7.88383 + 4.55173i) q^{86} +(-6.24898 - 5.66703i) q^{87} +(3.92380 + 3.92380i) q^{88} +(1.34160 - 2.32371i) q^{89} +(3.80054 + 5.52774i) q^{90} +(-0.249181 + 0.431594i) q^{91} +(2.01431 - 7.51752i) q^{92} +(1.54609 - 7.14850i) q^{93} +2.47002i q^{94} +(9.66534 - 1.25744i) q^{95} +(-0.0844883 - 1.72999i) q^{96} +(-8.94113 - 2.39577i) q^{97} +(-4.53058 - 1.21397i) q^{98} +(6.87921 - 15.1594i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q - 4 q^{3} + 8 q^{6}+O(q^{10}) $ 144 * q - 4 * q^3 + 8 * q^6	$ 144 q - 4 q^{3} + 8 q^{6} - 16 q^{10} - 8 q^{12} - 32 q^{13} + 4 q^{15} + 72 q^{16} + 32 q^{18} - 24 q^{21} + 8 q^{22} + 40 q^{25} - 16 q^{27} - 8 q^{30} - 16 q^{33} - 16 q^{37} + 8 q^{40} - 44 q^{42} - 16 q^{43} - 56 q^{45} - 48 q^{46} + 4 q^{48} + 32 q^{51} + 32 q^{52} + 8 q^{55} - 64 q^{57} + 32 q^{58} - 24 q^{60} + 76 q^{63} + 16 q^{66} - 56 q^{67} - 8 q^{70} + 16 q^{72} + 88 q^{73} + 32 q^{75} + 48 q^{76} - 56 q^{81} - 152 q^{87} - 16 q^{88} - 4 q^{90} + 80 q^{91} - 52 q^{93} + 16 q^{96} + 32 q^{97}+O(q^{100}) $ 144 * q - 4 * q^3 + 8 * q^6 - 16 * q^10 - 8 * q^12 - 32 * q^13 + 4 * q^15 + 72 * q^16 + 32 * q^18 - 24 * q^21 + 8 * q^22 + 40 * q^25 - 16 * q^27 - 8 * q^30 - 16 * q^33 - 16 * q^37 + 8 * q^40 - 44 * q^42 - 16 * q^43 - 56 * q^45 - 48 * q^46 + 4 * q^48 + 32 * q^51 + 32 * q^52 + 8 * q^55 - 64 * q^57 + 32 * q^58 - 24 * q^60 + 76 * q^63 + 16 * q^66 - 56 * q^67 - 8 * q^70 + 16 * q^72 + 88 * q^73 + 32 * q^75 + 48 * q^76 - 56 * q^81 - 152 * q^87 - 16 * q^88 - 4 * q^90 + 80 * q^91 - 52 * q^93 + 16 * q^96 + 32 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/570\mathbb{Z}\right)^\times$.

$n$	$191$	$211$	$457$
$\chi(n)$	$-1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−0.258819	+	0.965926i	−0.183013	+	0.683013i
$2$	−0.258819	+	0.965926i	−0.183013	+	0.683013i
$3$	−0.366145	+	1.69291i	−0.211394	+	0.977401i
$3$	−0.366145	+	1.69291i	−0.211394	+	0.977401i
$4$	−0.866025	−	0.500000i	−0.433013	−	0.250000i
$5$	−0.619415	+	2.14856i	−0.277011	+	0.960867i
$5$	−0.619415	+	2.14856i	−0.277011	+	0.960867i
$6$	−1.54046	−	0.791825i	−0.628890	−	0.323261i
$7$	−1.07462	+	1.07462i	−0.406166	+	0.406166i	−0.880399	−	0.474233i	$-0.842725\pi$
$7$	−1.07462	+	1.07462i	−0.406166	+	0.406166i	0.474233	+	0.880399i	$0.342725\pi$
$8$	0.707107	−	0.707107i	0.250000	−	0.250000i
$9$	−2.73188	−	1.23970i	−0.910625	−	0.413233i
$10$	−1.91504	−	1.15440i	−0.605588	−	0.365053i
$11$			5.54910i			1.67312i	0.547879	+	0.836558i	$0.315435\pi$
$11$			5.54910i			1.67312i	−0.547879	+	0.836558i	$0.684565\pi$
$12$	1.16354	−	1.28303i	0.335886	−	0.370379i
$13$	0.316753	−	0.0848738i	0.0878515	−	0.0235397i	−0.214626	−	0.976696i	$-0.568853\pi$
$13$	0.316753	−	0.0848738i	0.0878515	−	0.0235397i	0.302477	+	0.953157i	$0.402186\pi$
$14$	−0.759868	−	1.31613i	−0.203083	−	0.351750i
$15$	−3.41053	−	1.83530i	−0.880594	−	0.473872i
$16$	0.500000	+	0.866025i	0.125000	+	0.216506i
$17$	1.64252	−	6.12997i	0.398370	−	1.48674i	−0.417594	−	0.908634i	$-0.637127\pi$
$17$	1.64252	−	6.12997i	0.398370	−	1.48674i	0.815964	−	0.578103i	$-0.196207\pi$
$18$	1.90452	−	2.31793i	0.448899	−	0.546342i
$19$	−1.73771	−	3.99755i	−0.398658	−	0.917100i
$19$	−1.73771	−	3.99755i	−0.398658	−	0.917100i
$20$	1.61071	−	1.55100i	0.360166	−	0.346815i
$21$	−1.42576	−	2.21269i	−0.311126	−	0.482849i
$22$	−5.36001	−	1.43621i	−1.14276	−	0.306201i
$23$	2.01431	+	7.51752i	0.420014	+	1.56751i	0.774577	+	0.632480i	$0.217963\pi$
$23$	2.01431	+	7.51752i	0.420014	+	1.56751i	−0.354563	+	0.935032i	$0.615370\pi$
$24$	0.938163	+	1.45597i	0.191502	+	0.297199i
$25$	−4.23265	−	2.66171i	−0.846530	−	0.532341i
$26$			0.327927i			0.0643118i
$27$	3.09896	−	4.17091i	0.596395	−	0.802691i
$28$	1.46795	−	0.393337i	0.277417	−	0.0743336i
$29$	−2.43524	+	4.21797i	−0.452214	+	0.783257i	−0.998523	−	0.0543264i	$-0.982699\pi$
$29$	−2.43524	+	4.21797i	−0.452214	+	0.783257i	0.546310	+	0.837583i	$0.316032\pi$
$30$	2.65547	−	2.81930i	0.484820	−	0.514732i
$31$	−4.22261			−0.758404			−0.379202	−	0.925314i	$-0.623801\pi$
$31$	−4.22261			−0.758404			−0.379202	+	0.925314i	$0.623801\pi$
$32$	−0.965926	+	0.258819i	−0.170753	+	0.0457532i
$33$	−9.39411	−	2.03177i	−1.63530	−	0.353686i
$34$	5.49598	+	3.17311i	0.942553	+	0.544183i
$35$	−1.64325	−	2.97451i	−0.277759	−	0.502784i
$36$	1.74602	+	2.43955i	0.291004	+	0.406591i
$37$	3.78717	−	3.78717i	0.622606	−	0.622606i	−0.323591	−	0.946197i	$-0.604890\pi$
$37$	3.78717	−	3.78717i	0.622606	−	0.622606i	0.946197	+	0.323591i	$0.104890\pi$
$38$	4.31108	−	0.643857i	0.699350	−	0.104447i
$39$	0.0277060	+	0.567310i	0.00443651	+	0.0908423i
$40$	1.08127	+	1.95726i	0.170964	+	0.309469i
$41$	−1.04419	+	0.602864i	−0.163075	+	0.0941515i	−0.579317	−	0.815103i	$-0.696680\pi$
$41$	−1.04419	+	0.602864i	−0.163075	+	0.0941515i	0.416241	+	0.909254i	$0.363347\pi$
$42$	2.50631	−	0.804493i	0.386732	−	0.124136i
$43$	2.35615	−	8.79326i	0.359309	−	1.34096i	−0.515665	−	0.856790i	$-0.672455\pi$
$43$	2.35615	−	8.79326i	0.359309	−	1.34096i	0.874974	−	0.484170i	$-0.160878\pi$
$44$	2.77455	−	4.80566i	0.418279	−	0.724480i
$45$	4.35574	−	5.10172i	0.649315	−	0.760520i
$46$	−7.78271			−1.14750
$47$	2.38585	−	0.639288i	0.348013	−	0.0932497i	−0.0805785	−	0.996748i	$-0.525677\pi$
$47$	2.38585	−	0.639288i	0.348013	−	0.0932497i	0.428591	+	0.903499i	$0.359010\pi$
$48$	−1.64917	+	0.529363i	−0.238038	+	0.0764070i
$49$			4.69040i			0.670058i
$50$	3.66650	−	3.39953i	0.518521	−	0.480766i
$51$	9.77608	+	5.02509i	1.36892	+	0.703654i
$52$	−0.316753	−	0.0848738i	−0.0439258	−	0.0117699i
$53$	−1.50577	−	5.61960i	−0.206833	−	0.771911i	−0.988883	−	0.148696i	$-0.952493\pi$
$53$	−1.50577	−	5.61960i	−0.206833	−	0.771911i	0.782050	−	0.623216i	$-0.214174\pi$
$54$	3.22672	+	4.07287i	0.439101	+	0.554248i
$55$	−11.9226	−	3.43719i	−1.60764	−	0.463471i
$56$			1.51974i			0.203083i
$57$	7.40373	−	1.47810i	0.980648	−	0.195779i
$58$	−3.44396	−	3.44396i	−0.452214	−	0.452214i
$59$	2.29536	+	3.97569i	0.298831	+	0.517590i	0.975869	−	0.218358i	$-0.0700700\pi$
$59$	2.29536	+	3.97569i	0.298831	+	0.517590i	−0.677038	+	0.735948i	$0.736737\pi$
$60$	2.03595	+	3.29468i	0.262840	+	0.425341i
$61$	−4.12362	+	7.14232i	−0.527975	+	0.914480i	0.471493	+	0.881870i	$0.343715\pi$
$61$	−4.12362	+	7.14232i	−0.527975	+	0.914480i	−0.999468	+	0.0326100i	$0.989618\pi$
$62$	1.09289	−	4.07873i	0.138798	−	0.518000i
$63$	4.26792	−	1.60352i	0.537707	−	0.202024i
$64$		−	1.00000i		−	0.125000i
$65$	−0.0138450	+	0.733136i	−0.00171727	+	0.0909344i
$66$	4.39392	−	8.54815i	0.540854	−	1.05220i
$67$	0.216807	+	0.809136i	0.0264872	+	0.0988517i	0.977904	−	0.209054i	$-0.0670385\pi$
$67$	0.216807	+	0.809136i	0.0264872	+	0.0988517i	−0.951417	+	0.307906i	$0.900372\pi$
$68$	−4.48745	+	4.48745i	−0.544183	+	0.544183i
$69$	−13.4640	+	0.657548i	−1.62088	+	0.0791595i
$70$	3.29846	−	0.817394i	0.394242	−	0.0976972i
$71$	−7.44126	+	4.29621i	−0.883115	+	0.509866i	−0.871684	−	0.490068i	$-0.836972\pi$
$71$	−7.44126	+	4.29621i	−0.883115	+	0.509866i	−0.0114305	+	0.999935i	$0.503639\pi$
$72$	−2.80833	+	1.05513i	−0.330965	+	0.124348i
$73$	−2.65264	+	9.89978i	−0.310468	+	1.15868i	0.617668	+	0.786439i	$0.288078\pi$
$73$	−2.65264	+	9.89978i	−0.310468	+	1.15868i	−0.928135	+	0.372243i	$0.878589\pi$
$74$	2.67793	+	4.63831i	0.311303	+	0.539193i
$75$	6.05578	−	6.19092i	0.699262	−	0.714866i
$76$	−0.493872	+	4.33083i	−0.0566510	+	0.496780i
$77$	−5.96314	−	5.96314i	−0.679563	−	0.679563i
$78$	−0.555150	−	0.120069i	−0.0628584	−	0.0135951i
$79$	−4.24944	+	2.45342i	−0.478100	+	0.276031i	−0.719624	−	0.694364i	$-0.755686\pi$
$79$	−4.24944	+	2.45342i	−0.478100	+	0.276031i	0.241524	+	0.970395i	$0.422353\pi$
$80$	−2.17042	+	0.537853i	−0.242660	+	0.0601337i
$81$	5.92629	+	6.77341i	0.658477	+	0.752601i
$82$	−0.312065	−	1.16464i	−0.0344618	−	0.128613i
$83$	−2.14772	+	2.14772i	−0.235743	+	0.235743i	−0.815085	−	0.579342i	$-0.803310\pi$
$83$	−2.14772	+	2.14772i	−0.235743	+	0.235743i	0.579342	+	0.815085i	$0.303310\pi$
$84$	0.128400	+	2.62913i	0.0140096	+	0.286861i
$85$	12.1532	+	7.32606i	1.31820	+	0.794623i
$86$	7.88383	+	4.55173i	0.850135	+	0.490826i
$87$	−6.24898	−	5.66703i	−0.669961	−	0.607570i
$88$	3.92380	+	3.92380i	0.418279	+	0.418279i
$89$	1.34160	−	2.32371i	0.142209	−	0.246313i	−0.786119	−	0.618075i	$-0.787913\pi$
$89$	1.34160	−	2.32371i	0.142209	−	0.246313i	0.928328	+	0.371762i	$0.121246\pi$
$90$	3.80054	+	5.52774i	0.400612	+	0.582675i
$91$	−0.249181	+	0.431594i	−0.0261213	+	0.0452434i
$92$	2.01431	−	7.51752i	0.210007	−	0.783756i
$93$	1.54609	−	7.14850i	0.160322	−	0.741265i
$94$			2.47002i			0.254763i
$95$	9.66534	−	1.25744i	0.991643	−	0.129010i
$96$	−0.0844883	−	1.72999i	−0.00862305	−	0.176566i
$97$	−8.94113	−	2.39577i	−0.907834	−	0.243253i	−0.225457	−	0.974253i	$-0.572387\pi$
$97$	−8.94113	−	2.39577i	−0.907834	−	0.243253i	−0.682378	+	0.731000i	$0.739054\pi$
$98$	−4.53058	−	1.21397i	−0.457658	−	0.122629i
$99$	6.87921	−	15.1594i	0.691386	−	1.52358i
$100$	2.33473	+	4.42143i	0.233473	+	0.442143i
$101$	−4.87192	−	2.81280i	−0.484774	−	0.279884i	0.237630	−	0.971356i	$-0.423629\pi$
$101$	−4.87192	−	2.81280i	−0.484774	−	0.279884i	−0.722404	+	0.691471i	$0.756963\pi$
$102$	−7.38410	+	8.14238i	−0.731135	+	0.806216i
$103$	12.1547	+	12.1547i	1.19764	+	1.19764i	0.974871	+	0.222770i	$0.0715098\pi$
$103$	12.1547	+	12.1547i	1.19764	+	1.19764i	0.222770	+	0.974871i	$0.428490\pi$
$104$	0.163964	−	0.283993i	0.0160779	−	0.0278478i
$105$	5.63724	−	1.69276i	0.550138	−	0.165197i
$106$	5.81784			0.565078
$107$	3.09394	+	3.09394i	0.299102	+	0.299102i	0.840662	−	0.541560i	$-0.182166\pi$
$107$	3.09394	+	3.09394i	0.299102	+	0.299102i	−0.541560	+	0.840662i	$0.682166\pi$
$108$	−4.76923	+	2.06263i	−0.458919	+	0.198477i
$109$	6.31208	−	3.64428i	0.604588	−	0.349059i	−0.166256	−	0.986083i	$-0.553168\pi$
$109$	6.31208	−	3.64428i	0.604588	−	0.349059i	0.770844	+	0.637024i	$0.219835\pi$
$110$	6.40587	−	10.6267i	0.610775	−	1.01322i
$111$	5.02468	+	7.79798i	0.476921	+	0.740151i
$112$	−1.46795	−	0.393337i	−0.138708	−	0.0371668i
$113$	−11.1820	+	11.1820i	−1.05192	+	1.05192i	−0.0533396	+	0.998576i	$0.516987\pi$
$113$	−11.1820	+	11.1820i	−1.05192	+	1.05192i	−0.998576	+	0.0533396i	$0.983013\pi$
$114$	−0.488489	+	7.53401i	−0.0457512	+	0.705625i
$115$	−17.3996	−	0.328585i	−1.62252	−	0.0306407i
$116$	4.21797	−	2.43524i	0.391628	−	0.226107i
$117$	−0.970548	−	0.160814i	−0.0897272	−	0.0148672i
$118$	−4.43430	+	1.18817i	−0.408211	+	0.109380i
$119$	4.82228	+	8.35244i	0.442058	+	0.765667i
$120$	−3.70936	+	1.11385i	−0.338616	+	0.101680i
$121$	−19.7925			−1.79931
$122$	−5.83168	−	5.83168i	−0.527975	−	0.527975i
$123$	−0.638268	−	1.98845i	−0.0575507	−	0.179293i
$124$	3.65689	+	2.11131i	0.328399	+	0.189601i
$125$	8.34061	−	7.44542i	0.746007	−	0.665938i
$126$	0.444261	+	4.53751i	0.0395779	+	0.404234i
$127$	5.24881	+	19.5888i	0.465757	+	1.73823i	0.654369	+	0.756176i	$0.272934\pi$
$127$	5.24881	+	19.5888i	0.465757	+	1.73823i	−0.188612	+	0.982052i	$0.560399\pi$
$128$	0.965926	+	0.258819i	0.0853766	+	0.0228766i
$129$	14.0235	+	7.20835i	1.23470	+	0.634660i
$130$	−0.704572	−	0.203123i	−0.0617950	−	0.0178151i
$131$	−8.41111	+	4.85616i	−0.734882	+	0.424284i	−0.820205	−	0.572069i	$-0.806141\pi$
$131$	−8.41111	+	4.85616i	−0.734882	+	0.424284i	0.0853235	+	0.996353i	$0.472808\pi$
$132$	7.11965	+	6.45662i	0.619686	+	0.561977i
$133$	6.16319	+	2.42845i	0.534417	+	0.210574i
$134$	−0.837680			−0.0723645
$135$	7.04192	+	9.24183i	0.606072	+	0.795410i
$136$	−3.17311	−	5.49598i	−0.272092	−	0.471277i
$137$	−19.6780	+	5.27271i	−1.68121	+	0.450478i	−0.968098	−	0.250574i	$-0.919381\pi$
$137$	−19.6780	+	5.27271i	−1.68121	+	0.450478i	−0.713110	+	0.701052i	$0.752714\pi$
$138$	2.84960	−	13.1754i	0.242574	−	1.12157i
$139$	9.46841	+	5.46659i	0.803100	+	0.463670i	0.844554	−	0.535471i	$-0.179866\pi$
$139$	9.46841	+	5.46659i	0.803100	+	0.463670i	−0.0414541	+	0.999140i	$0.513199\pi$
$140$	−0.0641631	+	3.39763i	−0.00542277	+	0.287152i
$141$	0.208687	+	4.27310i	0.0175747	+	0.359860i
$142$	−2.22388	−	8.29964i	−0.186624	−	0.696491i
$143$	0.470973	+	1.75769i	0.0393847	+	0.146986i
$144$	−0.292328	−	2.98572i	−0.0243606	−	0.248810i
$145$	−7.55414	−	7.84495i	−0.627338	−	0.651488i
$146$	−8.87590	−	5.12450i	−0.734575	−	0.424107i
$147$	−7.94042	−	1.71737i	−0.654915	−	0.141646i
$148$	−5.17337	+	1.38620i	−0.425248	+	0.113945i
$149$	1.46783	+	2.54235i	0.120249	+	0.208278i	0.919866	−	0.392233i	$-0.128297\pi$
$149$	1.46783	+	2.54235i	0.120249	+	0.208278i	−0.799617	+	0.600511i	$0.794964\pi$
$150$	4.41262	+	7.45177i	0.360289	+	0.608434i
$151$	14.3038			1.16403			0.582015	−	0.813178i	$-0.302265\pi$
$151$	14.3038			1.16403			0.582015	+	0.813178i	$0.302265\pi$
$152$	−4.05544	−	1.59795i	−0.328939	−	0.129610i
$153$	−12.0865	+	14.7101i	−0.977134	+	1.18924i
$154$	7.30333	−	4.21658i	0.588519	−	0.339782i
$155$	2.61555	−	9.07256i	0.210086	−	0.728725i
$156$	0.259661	−	0.505158i	0.0207895	−	0.0404450i
$157$	−5.58125	−	1.49549i	−0.445432	−	0.119353i	0.0291291	−	0.999576i	$-0.490727\pi$
$157$	−5.58125	−	1.49549i	−0.445432	−	0.119353i	−0.474561	+	0.880222i	$0.657393\pi$
$158$	−1.26998	−	4.73964i	−0.101034	−	0.377066i
$159$	10.0648	−	0.491539i	0.798190	−	0.0389816i
$160$	0.0422199	−	2.23567i	0.00333778	−	0.176745i
$161$	−10.2431	−	5.91383i	−0.807266	−	0.466075i
$162$	−8.07645	+	3.97127i	−0.634546	+	0.312013i
$163$	8.02418	+	8.02418i	0.628502	+	0.628502i	0.947691	−	0.319189i	$-0.103410\pi$
$163$	8.02418	+	8.02418i	0.628502	+	0.628502i	−0.319189	+	0.947691i	$0.603410\pi$
$164$	1.20573			0.0941515
$165$	10.1842	−	18.9253i	0.792842	−	1.47333i
$166$	−1.51867	−	2.63041i	−0.117872	−	0.204160i
$167$	7.93409	−	2.12593i	0.613958	−	0.164510i	0.0615785	−	0.998102i	$-0.480387\pi$
$167$	7.93409	−	2.12593i	0.613958	−	0.164510i	0.552380	+	0.833593i	$0.313720\pi$
$168$	−2.57277	−	0.556443i	−0.198494	−	0.0429305i
$169$	−11.1652	+	6.44623i	−0.858862	+	0.495864i
$170$	−10.2219	+	9.84300i	−0.783985	+	0.754923i
$171$	−0.208545	+	13.0750i	−0.0159479	+	0.999873i
$172$	−6.43712	+	6.43712i	−0.490826	+	0.490826i
$173$	18.6499	+	4.99724i	1.41793	+	0.379933i	0.884749	−	0.466068i	$-0.154330\pi$
$173$	18.6499	+	4.99724i	1.41793	+	0.379933i	0.533181	+	0.846001i	$0.320997\pi$
$174$	7.09129	−	4.56932i	0.537589	−	0.346399i
$175$	7.40878	−	1.68816i	0.560051	−	0.127613i
$176$	−4.80566	+	2.77455i	−0.362240	+	0.209139i
$177$	−7.57091	+	2.43016i	−0.569064	+	0.182662i
$178$	1.89730	+	1.89730i	0.142209	+	0.142209i
$179$	5.87259			0.438938			0.219469	−	0.975619i	$-0.429568\pi$
$179$	5.87259			0.438938			0.219469	+	0.975619i	$0.429568\pi$
$180$	−6.32304	+	2.24035i	−0.471292	+	0.166986i
$181$	2.02582	−	3.50883i	0.150578	−	0.260809i	−0.780862	−	0.624704i	$-0.785220\pi$
$181$	2.02582	−	3.50883i	0.150578	−	0.260809i	0.931440	+	0.363894i	$0.118553\pi$
$182$	−0.352395	−	0.352395i	−0.0261213	−	0.0261213i
$183$	−10.5814	−	9.59603i	−0.782203	−	0.709359i
$184$	6.74003	+	3.89136i	0.496881	+	0.286875i
$185$	5.79114	+	10.4828i	0.425773	+	0.770711i
$186$	6.50476	+	3.34357i	0.476952	+	0.245163i
$187$	34.0158	+	9.11451i	2.48748	+	0.666519i
$188$	−2.38585	−	0.639288i	−0.174006	−	0.0466248i
$189$	1.15193	+	7.81231i	0.0837907	+	0.568262i
$190$	−1.28698	+	9.66145i	−0.0933675	+	0.700915i
$191$			22.4627i			1.62535i	0.582720	+	0.812673i	$0.301988\pi$
$191$			22.4627i			1.62535i	−0.582720	+	0.812673i	$0.698012\pi$
$192$	1.69291	+	0.366145i	0.122175	+	0.0264242i
$193$	5.12794	−	19.1377i	0.369118	−	1.37757i	−0.492635	−	0.870236i	$-0.663966\pi$
$193$	5.12794	−	19.1377i	0.369118	−	1.37757i	0.861752	−	0.507329i	$-0.169367\pi$
$194$	4.62827	−	8.01640i	0.332290	−	0.575544i
$195$	−1.23606	−	0.291872i	−0.0885163	−	0.0209014i
$196$	2.34520	−	4.06201i	0.167514	−	0.290143i
$197$	−9.54319	−	9.54319i	−0.679924	−	0.679924i	0.280059	−	0.959983i	$-0.409646\pi$
$197$	−9.54319	−	9.54319i	−0.679924	−	0.679924i	−0.959983	+	0.280059i	$0.909646\pi$
$198$	12.8624	+	10.5684i	0.914093	+	0.751060i
$199$	−23.6010	−	13.6261i	−1.67303	−	0.965926i	−0.965926	−	0.258819i	$-0.916667\pi$
$199$	−23.6010	−	13.6261i	−1.67303	−	0.965926i	−0.707107	−	0.707107i	$-0.750000\pi$
$200$	−4.87505	+	1.11083i	−0.344718	+	0.0785472i
$201$	−1.44918	+	0.0707741i	−0.102217	+	0.00499202i
$202$	3.97790	−	3.97790i	0.279884	−	0.279884i
$203$	−1.91574	−	7.14964i	−0.134459	−	0.501807i
$204$	−5.95379	−	9.23990i	−0.416848	−	0.646922i
$205$	−0.648503	−	2.61693i	−0.0452934	−	0.182774i
$206$	−14.8864	+	8.59469i	−1.03719	+	0.598820i
$207$	3.81661	−	23.0341i	0.265272	−	1.60098i
$208$	0.231879	+	0.231879i	0.0160779	+	0.0160779i
$209$	22.1828	−	9.64271i	1.53441	−	0.667000i
$210$	0.176058	+	5.88328i	0.0121492	+	0.405985i
$211$	−5.64036	−	9.76939i	−0.388299	−	0.672553i	0.603922	−	0.797043i	$-0.293604\pi$
$211$	−5.64036	−	9.76939i	−0.388299	−	0.672553i	−0.992221	+	0.124490i	$0.960270\pi$
$212$	−1.50577	+	5.61960i	−0.103416	+	0.385956i
$213$	−4.54851	−	14.1704i	−0.311659	−	0.970940i
$214$	−3.78928	+	2.18774i	−0.259030	+	0.149551i
$215$	17.4335	+	10.5090i	1.18895	+	0.716709i
$216$	−0.757982	−	5.14057i	−0.0515741	−	0.349772i
$217$	4.53769	−	4.53769i	0.308038	−	0.308038i
$218$	1.88642	+	7.04021i	0.127764	+	0.476823i
$219$	−15.7882	−	8.11543i	−1.06687	−	0.548390i
$220$	8.60666	+	8.93799i	0.580261	+	0.602599i
$221$		−	2.08109i		−	0.139990i
$222$	−8.83275	+	2.83520i	−0.592815	+	0.190286i
$223$	4.06984	−	15.1888i	0.272537	−	1.01712i	−0.684938	−	0.728602i	$-0.740171\pi$
$223$	4.06984	−	15.1888i	0.272537	−	1.01712i	0.957474	−	0.288519i	$-0.0931627\pi$
$224$	0.759868	−	1.31613i	0.0507708	−	0.0879376i
$225$	8.26336	+	12.5187i	0.550891	+	0.834577i
$226$	−7.90688	−	13.6951i	−0.525958	−	0.910986i
$227$	−6.77684	−	6.77684i	−0.449795	−	0.449795i	0.445491	−	0.895286i	$-0.353029\pi$
$227$	−6.77684	−	6.77684i	−0.449795	−	0.449795i	−0.895286	+	0.445491i	$0.853029\pi$
$228$	−7.15087	−	2.42179i	−0.473578	−	0.160387i
$229$		−	6.62816i		−	0.438001i	−0.975725	−	0.219001i	$-0.929720\pi$
$229$		−	6.62816i		−	0.438001i	0.975725	−	0.219001i	$-0.0702797\pi$
$230$	4.82073	−	16.7217i	0.317870	−	1.10259i
$231$	12.2784	−	7.91168i	0.807861	−	0.520550i
$232$	1.26058	+	4.70453i	0.0827608	+	0.308868i
$233$	18.5333	+	4.96598i	1.21416	+	0.325332i	0.808391	−	0.588646i	$-0.200339\pi$
$233$	18.5333	+	4.96598i	1.21416	+	0.325332i	0.405764	+	0.913978i	$0.367005\pi$
$234$	0.406531	−	0.895856i	0.0265757	−	0.0585639i
$235$	−0.104284	+	5.52214i	−0.00680273	+	0.360225i
$236$		−	4.59073i		−	0.298831i
$237$	−2.59750	−	8.09223i	−0.168726	−	0.525647i
$238$	−9.31594	+	2.49620i	−0.603862	+	0.161804i
$239$	1.12257			0.0726132			0.0363066	−	0.999341i	$-0.488441\pi$
$239$	1.12257			0.0726132			0.0363066	+	0.999341i	$0.488441\pi$
$240$	−0.115848	−	3.87125i	−0.00747795	−	0.249888i
$241$	9.42945	−	16.3323i	0.607404	−	1.05205i	−0.384262	−	0.923224i	$-0.625544\pi$
$241$	9.42945	−	16.3323i	0.607404	−	1.05205i	0.991667	−	0.128831i	$-0.0411224\pi$
$242$	5.12267	−	19.1180i	0.329297	−	1.22895i
$243$	−13.6366	+	7.55263i	−0.874791	+	0.484501i
$244$	7.14232	−	4.12362i	0.457240	−	0.263988i
$245$	−10.0776	−	2.90531i	−0.643836	−	0.185613i
$246$	2.08589	−	0.101870i	0.132992	−	0.00649498i
$247$	−0.889712	−	1.11875i	−0.0566110	−	0.0711843i
$248$	−2.98584	+	2.98584i	−0.189601	+	0.189601i
$249$	−2.84952	−	4.42228i	−0.180581	−	0.280250i
$250$	5.03301	+	9.98343i	0.318316	+	0.631407i
$251$	8.57297	+	4.94961i	0.541121	+	0.312417i	0.745533	−	0.666468i	$-0.232195\pi$
$251$	8.57297	+	4.94961i	0.541121	+	0.312417i	−0.204412	+	0.978885i	$0.565528\pi$
$252$	−4.49788	−	0.745271i	−0.283340	−	0.0469477i
$253$	−41.7155	+	11.1776i	−2.62263	+	0.702731i
$254$	−20.2798			−1.27247
$255$	−16.8522	+	17.8919i	−1.05532	+	1.12043i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−12.8168	+	3.43424i	−0.799488	+	0.214222i	−0.635359	−	0.772217i	$-0.719148\pi$
$257$	−12.8168	+	3.43424i	−0.799488	+	0.214222i	−0.164129	+	0.986439i	$0.552481\pi$
$258$	−10.5923	+	11.6800i	−0.659446	+	0.727165i
$259$			8.13950i			0.505764i
$260$	0.378558	−	0.627992i	0.0234772	−	0.0389464i
$261$	11.8818	−	8.50400i	0.735465	−	0.526384i
$262$	−2.51373	−	9.38137i	−0.155299	−	0.579583i
$263$	−8.14708	−	2.18300i	−0.502370	−	0.134610i	−0.00127044	−	0.999999i	$-0.500404\pi$
$263$	−8.14708	−	2.18300i	−0.502370	−	0.134610i	−0.501100	+	0.865389i	$0.667071\pi$
$264$	−8.07932	+	5.20596i	−0.497248	+	0.320405i
$265$	13.0068	+	0.245628i	0.798999	+	0.0150888i
$266$	−3.94086	+	5.32466i	−0.241630	+	0.326476i
$267$	3.44262	+	3.12202i	0.210685	+	0.191064i
$268$	0.216807	−	0.809136i	0.0132436	−	0.0494259i
$269$	10.0671	+	17.4367i	0.613800	+	1.06313i	0.990594	+	0.136835i	$0.0436930\pi$
$269$	10.0671	+	17.4367i	0.613800	+	1.06313i	−0.376794	+	0.926297i	$0.622974\pi$
$270$	−10.7495	+	4.41001i	−0.654194	+	0.268384i
$271$	3.11454	+	5.39453i	0.189195	+	0.327695i	0.944982	−	0.327122i	$-0.106079\pi$
$271$	3.11454	+	5.39453i	0.189195	+	0.327695i	−0.755787	+	0.654817i	$0.772746\pi$
$272$	6.12997	−	1.64252i	0.371684	−	0.0995925i
$273$	−0.639413	−	0.579867i	−0.0386991	−	0.0350951i
$274$		−	20.3722i		−	1.23073i
$275$	14.7701	−	23.4874i	0.890668	−	1.41634i
$276$	11.9889	+	6.16255i	0.721650	+	0.370942i
$277$	9.19367	−	9.19367i	0.552394	−	0.552394i	−0.374737	−	0.927131i	$-0.622267\pi$
$277$	9.19367	−	9.19367i	0.552394	−	0.552394i	0.927131	+	0.374737i	$0.122267\pi$
$278$	−7.73092	+	7.73092i	−0.463670	+	0.463670i
$279$	11.5357	+	5.23477i	0.690622	+	0.313397i
$280$	−3.26525	−	0.941347i	−0.195136	−	0.0562563i
$281$	−10.1136	−	5.83910i	−0.603328	−	0.348332i	0.167022	−	0.985953i	$-0.446585\pi$
$281$	−10.1136	−	5.83910i	−0.603328	−	0.348332i	−0.770350	+	0.637622i	$0.779918\pi$
$282$	−4.18151	−	0.904384i	−0.249005	−	0.0538553i
$283$	−2.95096	+	11.0131i	−0.175416	+	0.654662i	0.821064	+	0.570836i	$0.193381\pi$
$283$	−2.95096	+	11.0131i	−0.175416	+	0.654662i	−0.996480	+	0.0838264i	$0.973286\pi$
$284$	8.59242			0.509866
$285$	−1.41019	+	16.8229i	−0.0835322	+	0.996505i
$286$	−1.81970			−0.107601
$287$	0.474256	−	1.76995i	0.0279945	−	0.104477i
$288$	2.95965	+	0.490395i	0.174399	+	0.0288968i
$289$	−20.1562	−	11.6372i	−1.18566	−	0.684542i
$290$	9.53280	−	5.26632i	0.559785	−	0.309249i
$291$	7.32956	−	14.2593i	0.429667	−	0.835896i
$292$	7.24714	−	7.24714i	0.424107	−	0.424107i
$293$	19.9884	−	19.9884i	1.16774	−	1.16774i	0.184996	−	0.982739i	$-0.440773\pi$
$293$	19.9884	−	19.9884i	1.16774	−	1.16774i	0.982739	−	0.184996i	$-0.0592272\pi$
$294$	3.71398	−	7.22537i	0.216604	−	0.421392i
$295$	−9.96380	+	2.46913i	−0.580115	+	0.143759i
$296$		−	5.35586i		−	0.311303i
$297$	23.1448	+	17.1964i	1.34300	+	0.997837i
$298$	−2.83563	+	0.759803i	−0.164263	+	0.0440142i
$299$	1.27608	+	2.21024i	0.0737977	+	0.127821i
$300$	−8.33992	+	2.33360i	−0.481506	+	0.134730i
$301$	6.91742	+	11.9813i	0.398714	+	0.690592i
$302$	−3.70210	+	13.8164i	−0.213032	+	0.795047i
$303$	6.54564	−	7.21782i	0.376037	−	0.414653i
$304$	2.59312	−	3.50367i	0.148726	−	0.200949i
$305$	−12.7915	−	13.2839i	−0.732438	−	0.760635i
$306$	−11.0806	−	15.4819i	−0.633438	−	0.885041i
$307$	−13.4389	−	3.60093i	−0.766996	−	0.205516i	−0.145952	−	0.989292i	$-0.546625\pi$
$307$	−13.4389	−	3.60093i	−0.766996	−	0.205516i	−0.621044	+	0.783776i	$0.713291\pi$
$308$	2.18266	+	8.14581i	0.124369	+	0.464150i
$309$	−25.0272	+	16.1264i	−1.42375	+	0.917402i
$310$	8.08646	+	4.87458i	0.459280	+	0.276857i
$311$		−	15.6542i		−	0.887668i	−0.896109	−	0.443834i	$-0.853618\pi$
$311$		−	15.6542i		−	0.887668i	0.896109	−	0.443834i	$-0.146382\pi$
$312$	0.420740	+	0.381558i	0.0238197	+	0.0216015i
$313$	27.2696	−	7.30687i	1.54137	−	0.413009i	0.614662	−	0.788791i	$-0.289293\pi$
$313$	27.2696	−	7.30687i	1.54137	−	0.413009i	0.926708	+	0.375782i	$0.122626\pi$
$314$	2.88907	−	5.00401i	0.163039	−	0.282393i
$315$	0.801646	+	10.1631i	0.0451677	+	0.572627i
$316$	4.90684			0.276031
$317$	11.5074	−	3.08341i	0.646322	−	0.173182i	0.0792567	−	0.996854i	$-0.474745\pi$
$317$	11.5074	−	3.08341i	0.646322	−	0.173182i	0.567065	+	0.823673i	$0.308079\pi$
$318$	−2.13017	+	9.84906i	−0.119454	+	0.552308i
$319$	−23.4059	−	13.5134i	−1.31048	−	0.756605i
$320$	2.14856	+	0.619415i	0.120108	+	0.0346264i
$321$	−6.37058	+	4.10492i	−0.355571	+	0.229114i
$322$	8.36342	−	8.36342i	0.466075	−	0.466075i
$323$	−27.3591	+	4.08606i	−1.52230	+	0.227354i
$324$	−1.74562	−	8.82909i	−0.0969788	−	0.490505i
$325$	−1.56661	−	0.483863i	−0.0869001	−	0.0268399i
$326$	−9.82757	+	5.67395i	−0.544299	+	0.314251i
$327$	3.85830	+	12.0201i	0.213364	+	0.664714i
$328$	−0.312065	+	1.16464i	−0.0172309	+	0.0643066i
$329$	−1.87689	+	3.25086i	−0.103476	+	0.179226i
$330$	15.6446	+	14.7355i	0.861206	+	0.811160i
$331$	32.3937			1.78052			0.890261	−	0.455452i	$-0.150522\pi$
$331$	32.3937			1.78052			0.890261	+	0.455452i	$0.150522\pi$
$332$	2.93384	−	0.786121i	0.161016	−	0.0431440i
$333$	−15.0410	+	5.65113i	−0.824243	+	0.309680i
$334$			8.21397i			0.449449i
$335$	−1.87277	−	0.0353668i	−0.102321	−	0.00193229i
$336$	1.20337	−	2.34109i	0.0656490	−	0.127717i
$337$	−0.810601	−	0.217200i	−0.0441562	−	0.0118316i	0.236673	−	0.971589i	$-0.423943\pi$
$337$	−0.810601	−	0.217200i	−0.0441562	−	0.0118316i	−0.280830	+	0.959758i	$0.590610\pi$
$338$	−3.33682	−	12.4532i	−0.181499	−	0.677363i
$339$	−14.8359	−	23.0244i	−0.805775	−	1.25051i
$340$	−6.86198	−	12.4212i	−0.372143	−	0.673632i
$341$		−	23.4317i		−	1.26890i
$342$	−12.5755	−	3.58551i	−0.680007	−	0.193882i
$343$	−12.5627	−	12.5627i	−0.678321	−	0.678321i
$344$	−4.55173	−	7.88383i	−0.245413	−	0.425067i
$345$	6.92703	−	29.3356i	0.372939	−	1.57937i
$346$	−9.65392	+	16.7211i	−0.518998	+	0.898931i
$347$	−1.36128	+	5.08036i	−0.0730773	+	0.272728i	−0.992790	−	0.119863i	$-0.961755\pi$
$347$	−1.36128	+	5.08036i	−0.0730773	+	0.272728i	0.919713	+	0.392591i	$0.128421\pi$
$348$	2.57826	+	8.03228i	0.138209	+	0.430576i
$349$			6.06639i			0.324726i	0.986731	+	0.162363i	$0.0519116\pi$
$349$			6.06639i			0.324726i	−0.986731	+	0.162363i	$0.948088\pi$
$350$	−0.286895	+	7.59326i	−0.0153352	+	0.405877i
$351$	0.627604	−	1.58417i	0.0334990	−	0.0845566i
$352$	−1.43621	−	5.36001i	−0.0765503	−	0.285690i
$353$	−11.4496	+	11.4496i	−0.609401	+	0.609401i	−0.942790	−	0.333388i	$-0.891808\pi$
$353$	−11.4496	+	11.4496i	−0.609401	+	0.609401i	0.333388	+	0.942790i	$0.391808\pi$
$354$	−0.387863	−	7.94191i	−0.0206147	−	0.422108i
$355$	−4.62146	−	18.6491i	−0.245281	−	0.989794i
$356$	−2.32371	+	1.34160i	−0.123157	+	0.0711045i
$357$	−15.9056	+	5.10548i	−0.841812	+	0.270211i
$358$	−1.51994	+	5.67248i	−0.0803312	+	0.299800i
$359$	−1.60117	−	2.77331i	−0.0845064	−	0.146369i	0.820674	−	0.571396i	$-0.193598\pi$
$359$	−1.60117	−	2.77331i	−0.0845064	−	0.146369i	−0.905181	+	0.425027i	$0.860265\pi$
$360$	−0.527491	−	6.68743i	−0.0278012	−	0.352459i
$361$	−12.9607	+	13.8931i	−0.682144	+	0.731218i
$362$	2.86495	+	2.86495i	0.150578	+	0.150578i
$363$	7.24690	−	33.5068i	0.380364	−	1.75865i
$364$	0.431594	−	0.249181i	0.0226217	−	0.0130606i
$365$	−19.6272	−	11.8314i	−1.02734	−	0.619286i
$366$	12.0077	−	7.73726i	0.627654	−	0.404433i
$367$	3.05860	+	11.4149i	0.159658	+	0.595851i	0.998661	+	0.0517249i	$0.0164719\pi$
$367$	3.05860	+	11.4149i	0.159658	+	0.595851i	−0.839004	+	0.544126i	$0.816861\pi$
$368$	−5.50321	+	5.50321i	−0.286875	+	0.286875i
$369$	3.59997	−	0.352467i	0.187407	−	0.0183487i
$370$	−11.6245	+	2.88066i	−0.604327	+	0.149759i
$371$	7.65703	+	4.42079i	0.397533	+	0.229516i
$372$	−4.91320	+	5.41774i	−0.254738	+	0.280897i
$373$	3.81587	+	3.81587i	0.197578	+	0.197578i	0.798961	−	0.601383i	$-0.205383\pi$
$373$	3.81587	+	3.81587i	0.197578	+	0.197578i	−0.601383	+	0.798961i	$0.705383\pi$
$374$	−17.6079	+	30.4977i	−0.910481	+	1.57700i
$375$	9.55054	+	16.8460i	0.493188	+	0.869923i
$376$	1.23501	−	2.13910i	0.0636907	−	0.110316i
$377$	−0.413377	+	1.54274i	−0.0212900	+	0.0794553i
$378$	−7.84425	−	0.909293i	−0.403465	−	0.0467690i
$379$		−	16.9464i		−	0.870479i	−0.900315	−	0.435240i	$-0.856664\pi$
$379$		−	16.9464i		−	0.870479i	0.900315	−	0.435240i	$-0.143336\pi$
$380$	−8.99915	−	3.74370i	−0.461647	−	0.192048i
$381$	−35.0839	+	1.71341i	−1.79740	+	0.0877806i
$382$	−21.6973	−	5.81378i	−1.11013	−	0.297459i
$383$	35.6166	+	9.54345i	1.81992	+	0.487647i	0.996780	−	0.0801848i	$-0.0255510\pi$
$383$	35.6166	+	9.54345i	1.81992	+	0.487647i	0.823144	+	0.567832i	$0.192218\pi$
$384$	−0.791825	+	1.54046i	−0.0404077	+	0.0786112i
$385$	16.5059	−	9.11853i	0.841216	−	0.464723i
$386$	17.1584	+	9.90643i	0.873341	+	0.504224i
$387$	−17.3377	+	21.1012i	−0.881325	+	1.07263i
$388$	6.54536	+	6.54536i	0.332290	+	0.332290i
$389$	−11.4391	+	19.8130i	−0.579983	+	1.00456i	0.415497	+	0.909594i	$0.363608\pi$
$389$	−11.4391	+	19.8130i	−0.579983	+	1.00456i	−0.995481	+	0.0949662i	$0.969726\pi$
$390$	0.601844	−	1.11840i	0.0304755	−	0.0566326i
$391$	49.3908			2.49780
$392$	3.31662	+	3.31662i	0.167514	+	0.167514i
$393$	−5.14134	−	16.0173i	−0.259346	−	0.807965i
$394$	11.6880	−	6.74805i	0.588832	−	0.339962i
$395$	−2.63915	−	10.6499i	−0.132790	−	0.535854i
$396$	−13.5373	+	9.68886i	−0.680274	+	0.486883i
$397$	21.3930	+	5.73223i	1.07368	+	0.287692i	0.752005	−	0.659157i	$-0.229087\pi$
$397$	21.3930	+	5.73223i	1.07368	+	0.287692i	0.321677	+	0.946849i	$0.395753\pi$
$398$	19.2702	−	19.2702i	0.965926	−	0.965926i
$399$	−6.36777	+	9.54455i	−0.318787	+	0.477825i
$400$	0.188779	−	4.99643i	0.00943897	−	0.249822i
$401$	−24.2430	+	13.9967i	−1.21064	+	0.698962i	−0.962898	−	0.269865i	$-0.913021\pi$
$401$	−24.2430	+	13.9967i	−1.21064	+	0.698962i	−0.247740	+	0.968827i	$0.579688\pi$
$402$	0.306712	−	1.41811i	0.0152974	−	0.0707291i
$403$	−1.33753	+	0.358389i	−0.0666269	+	0.0178526i
$404$	2.81280	+	4.87192i	0.139942	+	0.242387i
$405$	−18.2239	+	8.53747i	−0.905554	+	0.424230i
$406$	7.40186			0.367348
$407$	21.0154	+	21.0154i	1.04169	+	1.04169i
$408$	10.4660	−	3.35945i	0.518145	−	0.166318i
$409$	28.0050	+	16.1687i	1.38476	+	0.799489i	0.992718	−	0.120460i	$-0.0384369\pi$
$409$	28.0050	+	16.1687i	1.38476	+	0.799489i	0.392038	+	0.919949i	$0.371770\pi$
$410$	2.69561	+	0.0509057i	0.133127	+	0.00251405i
$411$	−1.72121	−	35.2437i	−0.0849011	−	1.73844i
$412$	−4.44894	−	16.6037i	−0.219183	−	0.818004i
$413$	−6.73897	−	1.80570i	−0.331603	−	0.0888527i
$414$	21.2614	+	9.64822i	1.04494	+	0.474184i
$415$	−3.28419	−	5.94485i	−0.161214	−	0.291821i
$416$	−0.283993	+	0.163964i	−0.0139239	+	0.00803897i
$417$	−12.7212	+	14.0276i	−0.622962	+	0.686934i
$418$	3.57283	+	23.9226i	0.174753	+	1.17009i
$419$	−11.9046			−0.581579			−0.290789	−	0.956787i	$-0.593918\pi$
$419$	−11.9046			−0.581579			−0.290789	+	0.956787i	$0.593918\pi$
$420$	−5.72838	−	1.35265i	−0.279516	−	0.0660023i
$421$	0.988395	+	1.71195i	0.0481714	+	0.0834354i	0.889106	−	0.457702i	$-0.151327\pi$
$421$	0.988395	+	1.71195i	0.0481714	+	0.0834354i	−0.840934	+	0.541137i	$0.817994\pi$
$422$	10.8963	−	2.91967i	0.530426	−	0.142127i
$423$	−7.31038	−	1.21129i	−0.355443	−	0.0588947i
$424$	−5.03839	−	2.90892i	−0.244686	−	0.141270i
$425$	−23.2684	+	21.5741i	−1.12868	+	1.04650i
$426$	14.8648	−	0.725959i	0.720202	−	0.0351728i
$427$	−3.24394	−	12.1065i	−0.156985	−	0.585877i
$428$	−1.13246	−	4.22640i	−0.0547395	−	0.204291i
$429$	−3.14806	+	0.153743i	−0.151990	+	0.00742279i
$430$	−14.6630	+	14.1195i	−0.707114	+	0.680902i
$431$	21.9831	+	12.6919i	1.05889	+	0.611350i	0.925125	−	0.379664i	$-0.123960\pi$
$431$	21.9831	+	12.6919i	1.05889	+	0.611350i	0.133764	+	0.991013i	$0.457294\pi$
$432$	5.16159	+	0.598323i	0.248337	+	0.0287868i
$433$	7.33652	−	1.96581i	0.352570	−	0.0944710i	−0.0781870	−	0.996939i	$-0.524913\pi$
$433$	7.33652	−	1.96581i	0.352570	−	0.0944710i	0.430757	+	0.902468i	$0.358246\pi$
$434$	3.20863	+	5.55751i	0.154019	+	0.266769i
$435$	16.0467	−	9.91608i	0.769380	−	0.475440i
$436$	−7.28857			−0.349059
$437$	26.5513	−	21.1156i	1.27012	−	1.01010i
$438$	11.9252	−	13.1498i	0.569807	−	0.628321i
$439$	20.3162	−	11.7296i	0.969642	−	0.559823i	0.0705146	−	0.997511i	$-0.477536\pi$
$439$	20.3162	−	11.7296i	0.969642	−	0.559823i	0.899127	+	0.437688i	$0.144203\pi$
$440$	−10.8610	+	6.00008i	−0.517778	+	0.286042i
$441$	5.81469	−	12.8136i	0.276890	−	0.610172i
$442$	2.01018	+	0.538627i	0.0956147	+	0.0256199i
$443$	−0.908258	−	3.38967i	−0.0431526	−	0.161048i	0.940987	−	0.338442i	$-0.109900\pi$
$443$	−0.908258	−	3.38967i	−0.0431526	−	0.161048i	−0.984140	+	0.177394i	$0.943233\pi$
$444$	−0.452508	−	9.26558i	−0.0214751	−	0.439725i
$445$	4.16164	+	4.32185i	0.197281	+	0.204875i
$446$	13.6179	+	7.86232i	0.644828	+	0.372292i
$447$	−4.84141	+	1.55403i	−0.228991	+	0.0735030i
$448$	1.07462	+	1.07462i	0.0507708	+	0.0507708i
$449$	−11.3256			−0.534489			−0.267245	−	0.963629i	$-0.586113\pi$
$449$	−11.3256			−0.534489			−0.267245	+	0.963629i	$0.586113\pi$
$450$	−14.2308	+	4.74173i	−0.670847	+	0.223527i
$451$	−3.34535	−	5.79431i	−0.157526	−	0.272843i
$452$	15.2749	−	4.09290i	0.718472	−	0.192514i
$453$	−5.23727	+	24.2151i	−0.246068	+	1.13772i
$454$	8.29990	−	4.79195i	0.389534	−	0.224897i
$455$	−0.772961	−	0.802718i	−0.0362370	−	0.0376320i
$456$	4.19005	−	6.28040i	0.196217	−	0.294107i
$457$	0.535268	−	0.535268i	0.0250388	−	0.0250388i	−0.694477	−	0.719515i	$-0.744364\pi$
$457$	0.535268	−	0.535268i	0.0250388	−	0.0250388i	0.719515	+	0.694477i	$0.244364\pi$
$458$	6.40232	+	1.71550i	0.299161	+	0.0801598i
$459$	−20.4774	−	25.8473i	−0.955805	−	1.20645i
$460$	14.9042	+	8.98435i	0.694911	+	0.418897i
$461$	−9.95183	+	5.74569i	−0.463503	+	0.267603i	−0.713516	−	0.700639i	$-0.752898\pi$
$461$	−9.95183	+	5.74569i	−0.463503	+	0.267603i	0.250013	+	0.968242i	$0.419565\pi$
$462$	4.46421	+	13.9077i	0.207694	+	0.647047i
$463$	−13.2370	−	13.2370i	−0.615175	−	0.615175i	0.329115	−	0.944290i	$-0.393250\pi$
$463$	−13.2370	−	13.2370i	−0.615175	−	0.615175i	−0.944290	+	0.329115i	$0.893250\pi$
$464$	−4.87049			−0.226107
$465$	14.4013	+	7.74976i	0.667846	+	0.359386i
$466$	−9.59353	+	16.6165i	−0.444412	+	0.769744i
$467$	8.10528	+	8.10528i	0.375068	+	0.375068i	0.869319	−	0.494251i	$-0.164558\pi$
$467$	8.10528	+	8.10528i	0.375068	+	0.375068i	−0.494251	+	0.869319i	$0.664558\pi$
$468$	0.760113	+	0.624543i	0.0351362	+	0.0288695i
$469$	−1.10250	−	0.636526i	−0.0509085	−	0.0293920i
$470$	−5.30699	−	1.52997i	−0.244793	−	0.0705721i
$471$	4.57527	−	8.90098i	0.210817	−	0.410135i
$472$	4.43430	+	1.18817i	0.204105	+	0.0546899i
$473$	48.7947	+	13.0745i	2.24358	+	0.601166i
$474$	8.48877	−	0.414570i	0.389902	−	0.0190418i
$475$	−3.28517	+	21.5455i	−0.150734	+	0.988574i
$476$		−	9.64457i		−	0.442058i
$477$	−2.85304	+	17.2187i	−0.130632	+	0.788392i
$478$	−0.290543	+	1.08432i	−0.0132891	+	0.0495958i
$479$	4.37640	−	7.58015i	0.199963	−	0.346346i	−0.748553	−	0.663075i	$-0.769251\pi$
$479$	4.37640	−	7.58015i	0.199963	−	0.346346i	0.948516	+	0.316729i	$0.102584\pi$
$480$	3.76932	+	0.890053i	0.172045	+	0.0406252i
$481$	0.878166	−	1.52103i	0.0400409	−	0.0693529i
$482$	13.3353	+	13.3353i	0.607404	+	0.607404i
$483$	13.7620	−	15.1752i	0.626194	−	0.690497i
$484$	17.1408	+	9.89623i	0.779126	+	0.449829i
$485$	10.6857	−	17.7266i	0.485214	−	0.804924i
$486$	−3.76585	−	15.1267i	−0.170823	−	0.686163i
$487$	−11.2313	+	11.2313i	−0.508938	+	0.508938i	−0.914200	−	0.405263i	$-0.867180\pi$
$487$	−11.2313	+	11.2313i	−0.508938	+	0.508938i	0.405263	+	0.914200i	$0.367180\pi$
$488$	2.13454	+	7.96622i	0.0966262	+	0.360614i
$489$	−16.5222	+	10.6462i	−0.747160	+	0.481437i
$490$	5.41459	−	8.98229i	0.244606	−	0.405779i
$491$	−23.4053	+	13.5131i	−1.05627	+	0.609837i	−0.924398	−	0.381430i	$-0.875432\pi$
$491$	−23.4053	+	13.5131i	−1.05627	+	0.609837i	−0.131870	+	0.991267i	$0.542098\pi$
$492$	−0.441471	+	2.04119i	−0.0199030	+	0.0920237i
$493$	21.8561	+	21.8561i	0.984348	+	0.984348i
$494$	1.31090	−	0.569842i	0.0589803	−	0.0256384i
$495$	28.3099	+	24.1704i	1.27244	+	1.08638i
$496$	−2.11131	−	3.65689i	−0.0948005	−	0.164199i
$497$	3.37971	−	12.6133i	0.151601	−	0.565782i
$498$	5.00910	−	1.60786i	0.224463	−	0.0720498i
$499$	13.8947	−	8.02211i	0.622012	−	0.359119i	−0.155640	−	0.987814i	$-0.549744\pi$
$499$	13.8947	−	8.02211i	0.622012	−	0.359119i	0.777652	+	0.628695i	$0.216411\pi$
$500$	−10.9459	+	2.27761i	−0.489515	+	0.101858i
$501$	0.693984	+	14.2101i	0.0310049	+	0.634860i
$502$	−6.99980	+	6.99980i	−0.312417	+	0.312417i
$503$	0.802896	+	2.99645i	0.0357994	+	0.133605i	0.981513	−	0.191397i	$-0.0613017\pi$
$503$	0.802896	+	2.99645i	0.0357994	+	0.133605i	−0.945713	+	0.325002i	$0.894635\pi$
$504$	1.88401	−	4.15173i	0.0839207	−	0.184933i
$505$	9.06122	−	8.72533i	0.403219	−	0.388272i
$506$		−	43.1870i		−	1.91990i
$507$	−6.82480	−	21.2619i	−0.303100	−	0.944275i
$508$	5.24881	−	19.5888i	0.232878	−	0.869114i
$509$	−3.84072	+	6.65232i	−0.170237	+	0.294859i	−0.938503	−	0.345272i	$-0.887787\pi$
$509$	−3.84072	+	6.65232i	−0.170237	+	0.294859i	0.768266	+	0.640131i	$0.221120\pi$
$510$	−12.9206	−	20.9087i	−0.572133	−	0.925854i
$511$	−7.78789	−	13.4890i	−0.344516	−	0.596719i
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$	−22.0585	−	5.14040i	−0.973905	−	0.226954i
$514$		−	13.2689i		−	0.585266i
$515$	−33.6440	+	18.5864i	−1.48253	+	0.819014i
$516$	−8.54053	−	13.2544i	−0.375976	−	0.583491i
$517$	3.54747	+	13.2393i	0.156017	+	0.582265i
$518$	−7.86215	−	2.10666i	−0.345443	−	0.0925612i
$519$	−15.2884	+	29.7429i	−0.671088	+	1.30557i
$520$	0.508616	+	0.528196i	0.0223043	+	0.0231629i
$521$			26.4763i			1.15995i	0.814635	+	0.579974i	$0.196937\pi$
$521$			26.4763i			1.15995i	−0.814635	+	0.579974i	$0.803063\pi$
$522$	5.13899	+	13.6779i	0.224928	+	0.598667i
$523$	0.0174603	−	0.00467848i	0.000763486	−	0.000204576i	−0.258437	−	0.966028i	$-0.583208\pi$
$523$	0.0174603	−	0.00467848i	0.000763486	−	0.000204576i	0.259201	+	0.965823i	$0.416541\pi$
$524$	9.71231			0.424284
$525$	0.145216	+	13.1605i	0.00633776	+	0.574371i
$526$	4.21724	−	7.30447i	0.183880	−	0.318490i
$527$	−6.93573	+	25.8845i	−0.302125	+	1.12755i
$528$	−2.93749	−	9.15142i	−0.127838	−	0.398265i
$529$	−32.5371	+	18.7853i	−1.41466	+	0.816753i
$530$	−3.60366	+	12.5000i	−0.156533	+	0.542965i
$531$	−1.34200	−	13.7066i	−0.0582377	−	0.594818i
$532$	−4.12325	−	5.18470i	−0.178766	−	0.224785i
$533$	−0.279583	+	0.279583i	−0.0121101	+	0.0121101i
$534$	−3.90665	+	2.51727i	−0.169057	+	0.108933i
$535$	−8.56395	+	4.73109i	−0.370252	+	0.204543i
$536$	0.725452	+	0.418840i	0.0313347	+	0.0180911i
$537$	−2.15022	+	9.94175i	−0.0927887	+	0.429018i
$538$	−19.4481	+	5.21109i	−0.838466	+	0.224666i
$539$	−26.0275			−1.12108
$540$	−1.47756	−	11.5246i	−0.0635842	−	0.495941i
$541$	−9.18693	+	15.9122i	−0.394977	+	0.684120i	−0.993098	−	0.117285i	$-0.962581\pi$
$541$	−9.18693	+	15.9122i	−0.394977	+	0.684120i	0.598121	+	0.801406i	$0.295914\pi$
$542$	−6.01682	+	1.61220i	−0.258445	+	0.0692500i
$543$	5.19838	+	4.71428i	0.223084	+	0.202309i
$544$			6.34621i			0.272092i
$545$	3.92017	+	15.8192i	0.167922	+	0.677622i
$546$	0.725601	−	0.467545i	0.0310528	−	0.0200091i
$547$	11.5513	+	43.1101i	0.493899	+	1.84325i	0.536113	+	0.844146i	$0.319892\pi$
$547$	11.5513	+	43.1101i	0.493899	+	1.84325i	−0.0422142	+	0.999109i	$0.513441\pi$
$548$	19.6780	+	5.27271i	0.840604	+	0.225239i
$549$	20.1195	−	14.3999i	0.858681	−	0.614572i
$550$	18.8643	+	20.3458i	0.804376	+	0.867546i
$551$	21.0933	+	2.40540i	0.898603	+	0.102473i
$552$	−9.05553	+	9.98545i	−0.385429	+	0.425009i
$553$	1.93004	−	7.20300i	0.0820736	−	0.306303i
$554$	6.50091	+	11.2599i	0.276197	+	0.478387i
$555$	−19.8668	+	5.96565i	−0.843299	+	0.253228i
$556$	−5.46659	−	9.46841i	−0.231835	−	0.401550i
$557$	6.04346	−	1.61934i	0.256070	−	0.0686137i	−0.128500	−	0.991709i	$-0.541016\pi$
$557$	6.04346	−	1.61934i	0.256070	−	0.0686137i	0.384570	+	0.923096i	$0.374350\pi$
$558$	−8.04205	+	9.78773i	−0.340447	+	0.414348i
$559$		−	2.98527i		−	0.126263i
$560$	1.75438	−	2.91035i	0.0741361	−	0.122985i
$561$	−27.8847	+	54.2484i	−1.17729	+	2.29037i
$562$	8.25774	−	8.25774i	0.348332	−	0.348332i
$563$	−15.5095	+	15.5095i	−0.653649	+	0.653649i	−0.953870	−	0.300221i	$-0.902940\pi$
$563$	−15.5095	+	15.5095i	−0.653649	+	0.653649i	0.300221	+	0.953870i	$0.402940\pi$
$564$	1.95582	−	3.80496i	0.0823550	−	0.160218i
$565$	−17.0990	−	30.9516i	−0.719359	−	1.30214i
$566$	−9.87410	−	5.70081i	−0.415039	−	0.239623i
$567$	−13.6473	−	0.910320i	−0.573132	−	0.0382298i
$568$	−2.22388	+	8.29964i	−0.0933120	+	0.348245i
$569$	−18.4866			−0.774998			−0.387499	−	0.921870i	$-0.626661\pi$
$569$	−18.4866			−0.774998			−0.387499	+	0.921870i	$0.626661\pi$
$570$	−15.8847	−	5.71623i	−0.665338	−	0.239427i
$571$	−26.7844			−1.12089			−0.560446	−	0.828191i	$-0.689370\pi$
$571$	−26.7844			−1.12089			−0.560446	+	0.828191i	$0.689370\pi$
$572$	0.470973	−	1.75769i	0.0196924	−	0.0734929i
$573$	−38.0273	−	8.22461i	−1.58861	−	0.343588i
$574$	1.58689	+	0.916193i	0.0662356	+	0.0382412i
$575$	11.4835	−	37.1806i	0.478897	−	1.55054i
$576$	−1.23970	+	2.73188i	−0.0516541	+	0.113828i
$577$	16.5592	−	16.5592i	0.689367	−	0.689367i	−0.272725	−	0.962092i	$-0.587925\pi$
$577$	16.5592	−	16.5592i	0.689367	−	0.689367i	0.962092	+	0.272725i	$0.0879249\pi$
$578$	16.4575	−	16.4575i	0.684542	−	0.684542i
$579$	30.5209	+	15.6883i	1.26840	+	0.651985i
$580$	2.61961	+	10.5710i	0.108773	+	0.438937i
$581$		−	4.61595i		−	0.191502i
$582$	11.8764	+	10.7704i	0.492293	+	0.446447i
$583$	31.1837	−	8.35564i	1.29150	−	0.346055i
$584$	5.12450	+	8.87590i	0.212053	+	0.367287i
$585$	0.946691	−	1.98567i	0.0391409	−	0.0820975i
$586$	14.1339	+	24.4807i	0.583868	+	1.01129i
$587$	8.38105	−	31.2785i	0.345923	−	1.29100i	−0.545608	−	0.838041i	$-0.683701\pi$
$587$	8.38105	−	31.2785i	0.345923	−	1.29100i	0.891530	−	0.452961i	$-0.149632\pi$
$588$	6.01792	+	5.45749i	0.248175	+	0.225063i
$589$	7.33768	+	16.8801i	0.302344	+	0.695532i
$590$	0.193820	−	10.2633i	0.00797945	−	0.422535i
$591$	19.6499	−	12.6616i	0.808290	−	0.520827i
$592$	5.17337	+	1.38620i	0.212624	+	0.0569724i
$593$	−7.02193	−	26.2062i	−0.288356	−	1.07616i	−0.946352	−	0.323138i	$-0.895262\pi$
$593$	−7.02193	−	26.2062i	−0.288356	−	1.07616i	0.657996	−	0.753022i	$-0.271405\pi$
$594$	−22.6008	+	17.9054i	−0.927321	+	0.734666i
$595$	−20.9327	+	5.18735i	−0.858159	+	0.212661i
$596$		−	2.93566i		−	0.120249i
$597$	31.7091	−	34.9653i	1.29777	−	1.43103i
$598$	−2.46520	+	0.660548i	−0.100809	+	0.0270118i
$599$	−18.8225	+	32.6016i	−0.769068	+	1.33206i	0.169001	+	0.985616i	$0.445946\pi$
$599$	−18.8225	+	32.6016i	−0.769068	+	1.33206i	−0.938069	+	0.346449i	$0.887388\pi$
$600$	−0.0955537	−	8.65973i	−0.00390096	−	0.353532i
$601$	8.80796			0.359284			0.179642	−	0.983732i	$-0.442506\pi$
$601$	8.80796			0.359284			0.179642	+	0.983732i	$0.442506\pi$
$602$	−13.3634	+	3.58072i	−0.544653	+	0.145939i
$603$	0.410794	−	2.47924i	0.0167288	−	0.100962i
$604$	−12.3875	−	7.15191i	−0.504039	−	0.291007i
$605$	12.2597	−	42.5254i	0.498430	−	1.72890i
$606$	5.27774	+	8.19071i	0.214393	+	0.332725i
$607$	−19.7817	+	19.7817i	−0.802914	+	0.802914i	−0.983550	−	0.180636i	$-0.942184\pi$
$607$	−19.7817	+	19.7817i	−0.802914	+	0.802914i	0.180636	+	0.983550i	$0.442184\pi$
$608$	2.71314	+	3.41158i	0.110032	+	0.138358i
$609$	12.8051	−	0.625370i	0.518890	−	0.0253413i
$610$	16.1420	−	8.91750i	0.653569	−	0.361059i
$611$	0.701468	−	0.404993i	0.0283784	−	0.0163843i
$612$	17.8222	−	6.69607i	0.720422	−	0.270673i
$613$	4.06784	−	15.1814i	0.164299	−	0.613171i	−0.833830	−	0.552021i	$-0.813857\pi$
$613$	4.06784	−	15.1814i	0.164299	−	0.613171i	0.998129	−	0.0611496i	$-0.0194767\pi$
$614$	6.95647	−	12.0490i	0.280740	−	0.486256i
$615$	4.66767	−	0.139681i	0.188219	−	0.00563248i
$616$	−8.43316			−0.339782
$617$	13.5593	−	3.63321i	0.545878	−	0.146268i	0.0246676	−	0.999696i	$-0.492147\pi$
$617$	13.5593	−	3.63321i	0.545878	−	0.146268i	0.521211	+	0.853428i	$0.325481\pi$
$618$	−9.09943	−	28.3483i	−0.366033	−	1.14033i
$619$			37.7827i			1.51861i	0.650732	+	0.759307i	$0.274462\pi$
$619$			37.7827i			1.51861i	−0.650732	+	0.759307i	$0.725538\pi$
$620$	−6.80141	+	6.54929i	−0.273151	+	0.263026i
$621$	37.5972	+	14.8950i	1.50872	+	0.597715i
$622$	15.1208	+	4.05161i	0.606289	+	0.162455i
$623$	1.05540	+	3.93880i	0.0422836	+	0.157805i
$624$	−0.477452	+	0.307649i	−0.0191134	+	0.0123158i
$625$	10.8306	+	22.5321i	0.433226	+	0.901285i
$626$			28.2316i			1.12836i
$627$	8.20213	+	41.0840i	0.327562	+	1.64074i
$628$	4.08576	+	4.08576i	0.163039	+	0.163039i
$629$	−16.9947	−	29.4357i	−0.677624	−	1.17368i
$630$	−10.0243	−	1.85608i	−0.399378	−	0.0739480i
$631$	−23.5081	+	40.7172i	−0.935843	+	1.62093i	−0.162719	+	0.986673i	$0.552026\pi$
$631$	−23.5081	+	40.7172i	−0.935843	+	1.62093i	−0.773124	+	0.634255i	$0.781307\pi$
$632$	−1.26998	+	4.73964i	−0.0505172	+	0.188533i
$633$	18.6039	−	5.97160i	0.739438	−	0.237350i
$634$			11.9134i			0.473141i
$635$	−45.3390	−	0.856213i	−1.79922	−	0.0339778i
$636$	−8.96213	−	4.60671i	−0.355372	−	0.182668i
$637$	0.398092	+	1.48570i	0.0157730	+	0.0588656i
$638$	19.1108	−	19.1108i	0.756605	−	0.756605i
$639$	25.6546	−	2.51180i	1.01488	−	0.0993653i
$640$	−1.15440	+	1.91504i	−0.0456316	+	0.0756985i
$641$	36.9801	−	21.3505i	1.46063	−	0.843293i	0.461587	−	0.887095i	$-0.347280\pi$
$641$	36.9801	−	21.3505i	1.46063	−	0.843293i	0.999040	+	0.0438018i	$0.0139470\pi$
$642$	−2.31622	−	7.21594i	−0.0914140	−	0.284790i
$643$	5.38182	−	20.0852i	0.212238	−	0.792084i	−0.774882	−	0.632106i	$-0.782191\pi$
$643$	5.38182	−	20.0852i	0.212238	−	0.792084i	0.987121	−	0.159978i	$-0.0511424\pi$
$644$	5.91383	+	10.2431i	0.233038	+	0.403633i
$645$	−24.1740	+	25.6654i	−0.951849	+	1.01057i
$646$	3.13422	−	27.4844i	0.123314	−	1.08136i
$647$	8.55101	+	8.55101i	0.336175	+	0.336175i	0.854926	−	0.518751i	$-0.173603\pi$
$647$	8.55101	+	8.55101i	0.336175	+	0.336175i	−0.518751	+	0.854926i	$0.673603\pi$
$648$	8.98004	+	0.598999i	0.352769	+	0.0235309i
$649$	−22.0615	+	12.7372i	−0.865988	+	0.499979i
$650$	0.872845	−	1.38800i	0.0342358	−	0.0544418i
$651$	6.02044	+	9.34334i	0.235960	+	0.366194i
$652$	−2.93705	−	10.9612i	−0.115024	−	0.429275i
$653$	3.37460	−	3.37460i	0.132058	−	0.132058i	−0.637988	−	0.770046i	$-0.720233\pi$
$653$	3.37460	−	3.37460i	0.132058	−	0.132058i	0.770046	+	0.637988i	$0.220233\pi$
$654$	−12.6091	+	0.615798i	−0.493056	+	0.0240796i
$655$	−5.22379	−	21.0798i	−0.204110	−	0.823655i
$656$	−1.04419	−	0.602864i	−0.0407688	−	0.0235379i
$657$	19.5194	−	23.7565i	0.761525	−	0.926830i
$658$	−2.65432	−	2.65432i	−0.103476	−	0.103476i
$659$	14.0786	−	24.3848i	0.548424	−	0.949898i	−0.449959	−	0.893049i	$-0.648561\pi$
$659$	14.0786	−	24.3848i	0.548424	−	0.949898i	0.998383	−	0.0568487i	$-0.0181053\pi$
$660$	−18.2825	+	11.2977i	−0.711645	+	0.439762i
$661$	8.42839	−	14.5984i	0.327827	−	0.567812i	−0.654254	−	0.756275i	$-0.727017\pi$
$661$	8.42839	−	14.5984i	0.327827	−	0.567812i	0.982080	+	0.188463i	$0.0603505\pi$
$662$	−8.38412	+	31.2900i	−0.325858	+	1.21612i
$663$	3.52310	+	0.761982i	0.136826	+	0.0295929i
$664$			3.03734i			0.117872i
$665$	−9.03526	+	11.7378i	−0.350372	+	0.455172i
$666$	−1.56567	−	15.9911i	−0.0606683	−	0.619644i
$667$	−36.6140	−	9.81070i	−1.41770	−	0.379872i
$668$	−7.93409	−	2.12593i	−0.306979	−	0.0822548i
$669$	24.2232	+	12.4512i	0.936522	+	0.481390i
$670$	0.518871	−	1.79981i	0.0200458	−	0.0695326i
$671$	−39.6334	−	22.8823i	−1.53003	−	0.883363i
$672$	1.94987	+	1.76828i	0.0752177	+	0.0682129i
$673$	−1.30451	−	1.30451i	−0.0502852	−	0.0502852i	0.681517	−	0.731802i	$-0.261321\pi$
$673$	−1.30451	−	1.30451i	−0.0502852	−	0.0502852i	−0.731802	+	0.681517i	$0.761321\pi$
$674$	0.419598	−	0.726765i	0.0161623	−	0.0279939i
$675$	−24.2185	+	9.40547i	−0.932172	+	0.362017i
$676$	12.8925			0.495864
$677$	19.7011	+	19.7011i	0.757177	+	0.757177i	0.975808	−	0.218631i	$-0.0701591\pi$
$677$	19.7011	+	19.7011i	0.757177	+	0.757177i	−0.218631	+	0.975808i	$0.570159\pi$
$678$	26.0796	−	8.37123i	1.00158	−	0.321495i
$679$	12.1828	−	7.03375i	0.467533	−	0.269930i
$680$	13.7739	−	3.41333i	0.528206	−	0.130895i
$681$	13.9539	−	8.99126i	0.534714	−	0.344546i
$682$	22.6333	+	6.06457i	0.866673	+	0.232224i
$683$	8.63638	−	8.63638i	0.330462	−	0.330462i	−0.522300	−	0.852762i	$-0.674926\pi$
$683$	8.63638	−	8.63638i	0.330462	−	0.330462i	0.852762	+	0.522300i	$0.174926\pi$
$684$	6.71812	−	11.2190i	0.256874	−	0.428971i
$685$	0.860112	−	45.5455i	0.0328632	−	1.74020i
$686$	15.3861	−	8.88316i	0.587444	−	0.339161i
$687$	11.2209	+	2.42687i	0.428103	+	0.0925908i
$688$	8.79326	−	2.35615i	0.335240	−	0.0898273i
$689$	−0.953913	−	1.65223i	−0.0363412	−	0.0629448i
$690$	26.5431	+	14.2836i	1.01048	+	0.543767i
$691$	22.1493			0.842597			0.421299	−	0.906922i	$-0.361574\pi$
$691$	22.1493			0.842597			0.421299	+	0.906922i	$0.361574\pi$
$692$	−13.6527	−	13.6527i	−0.518998	−	0.518998i
$693$	8.89807	+	23.6831i	0.338010	+	0.899645i
$694$	−4.55493	−	2.62979i	−0.172903	−	0.0998254i
$695$	−17.6102	+	16.9574i	−0.667992	+	0.643230i
$696$	−8.42589	+	0.411499i	−0.319383	+	0.0155978i
$697$	1.98043	+	7.39107i	0.0750142	+	0.279957i
$698$	−5.85968	−	1.57010i	−0.221792	−	0.0594290i
$699$	−15.1928	+	29.5569i	−0.574645	+	1.11794i
$700$	−7.26027	−	2.24240i	−0.274412	−	0.0847547i
$701$	8.04403	−	4.64422i	0.303819	−	0.175410i	−0.340338	−	0.940303i	$-0.610542\pi$
$701$	8.04403	−	4.64422i	0.303819	−	0.175410i	0.644157	+	0.764893i	$0.277208\pi$
$702$	1.36775	+	1.01623i	0.0516225	+	0.0383552i
$703$	−21.7204	−	8.55838i	−0.819199	−	0.322785i
$704$	5.54910			0.209139
$705$	−9.31030	−	2.19845i	−0.350646	−	0.0827983i
$706$	−8.09610	−	14.0229i	−0.304701	−	0.527757i
$707$	8.25812	−	2.21276i	0.310578	−	0.0832193i
$708$	7.77168	+	1.68087i	0.292078	+	0.0631710i
$709$	15.4954	+	8.94626i	0.581941	+	0.335984i	0.761904	−	0.647689i	$-0.224265\pi$
$709$	15.4954	+	8.94626i	0.581941	+	0.335984i	−0.179963	+	0.983673i	$0.557598\pi$
$710$	19.2098	+	0.362771i	0.720932	+	0.0136146i
$711$	14.6505	−	1.43440i	0.549435	−	0.0537943i
$712$	−0.694462	−	2.59177i	−0.0260260	−	0.0971305i
$713$	−8.50567	−	31.7436i	−0.318540	−	1.18881i
$714$	−0.814853	−	16.6850i	−0.0304951	−	0.624420i
$715$	−4.06824	−	0.0768275i	−0.152144	−	0.00287318i
$716$	−5.08581	−	2.93629i	−0.190066	−	0.109734i
$717$	−0.411024	+	1.90041i	−0.0153500	+	0.0709722i
$718$	3.09322	−	0.828826i	0.115438	−	0.0309315i
$719$	7.88538	+	13.6579i	0.294075	+	0.509353i	0.974769	−	0.223215i	$-0.0716551\pi$
$719$	7.88538	+	13.6579i	0.294075	+	0.509353i	−0.680694	+	0.732568i	$0.738322\pi$
$720$	6.59609	+	1.22132i	0.245822	+	0.0455158i
$721$	−26.1233			−0.972883
$722$	−10.0653	−	16.1149i	−0.374590	−	0.599735i
$723$	24.1965	+	21.9432i	0.899878	+	0.816075i
$724$	−3.50883	+	2.02582i	−0.130405	+	0.0752892i
$725$	21.5345	−	11.3713i	0.799772	−	0.422319i
$726$	30.4895	+	15.6722i	1.13157	+	0.581649i
$727$	−7.96089	−	2.13311i	−0.295253	−	0.0791128i	0.108152	−	0.994134i	$-0.465507\pi$
$727$	−7.96089	−	2.13311i	−0.295253	−	0.0791128i	−0.403405	+	0.915022i	$0.632173\pi$
$728$	0.128986	+	0.481381i	0.00478053	+	0.0178412i
$729$	−7.79292	−	25.8509i	−0.288627	−	0.957442i
$730$	16.5082	−	15.8962i	0.610996	−	0.588346i
$731$	−50.0324	−	28.8862i	−1.85052	−	1.06840i
$732$	4.36579	+	13.6011i	0.161364	+	0.502712i
$733$	36.6964	+	36.6964i	1.35541	+	1.35541i	0.879485	+	0.475927i	$0.157887\pi$
$733$	36.6964	+	36.6964i	1.35541	+	1.35541i	0.475927	+	0.879485i	$0.342113\pi$
$734$	−11.8175			−0.436193
$735$	8.60829	−	15.9967i	0.317522	−	0.590049i
$736$	−3.89136	−	6.74003i	−0.143437	−	0.248441i
$737$	−4.48998	+	1.20309i	−0.165390	+	0.0443162i
$738$	−0.591283	+	3.56853i	−0.0217654	+	0.131359i
$739$	10.8990	−	6.29255i	0.400927	−	0.231475i	−0.285957	−	0.958242i	$-0.592311\pi$
$739$	10.8990	−	6.29255i	0.400927	−	0.231475i	0.686884	+	0.726767i	$0.258978\pi$
$740$	0.226124	−	11.9739i	0.00831248	−	0.440171i
$741$	2.21970	−	1.09658i	0.0815428	−	0.0402837i
$742$	−6.25194	+	6.25194i	−0.229516	+	0.229516i
$743$	17.3284	+	4.64313i	0.635717	+	0.170340i	0.562263	−	0.826959i	$-0.309931\pi$
$743$	17.3284	+	4.64313i	0.635717	+	0.170340i	0.0734545	+	0.997299i	$0.476598\pi$
$744$	−3.96150	−	6.14800i	−0.145236	−	0.225397i
$745$	−6.37160	+	1.57895i	−0.233437	+	0.0578482i
$746$	−4.67347	+	2.69823i	−0.171108	+	0.0987891i
$747$	8.52984	−	3.20478i	0.312091	−	0.117257i
$748$	−24.9013	−	24.9013i	−0.910481	−	0.910481i
$749$	−6.64958			−0.242971
$750$	−18.7438	+	4.86505i	−0.684428	+	0.177646i
$751$	−0.654469	+	1.13357i	−0.0238819	+	0.0413647i	−0.877719	−	0.479175i	$-0.840936\pi$
$751$	−0.654469	+	1.13357i	−0.0238819	+	0.0413647i	0.853837	+	0.520540i	$0.174269\pi$
$752$	1.74657	+	1.74657i	0.0636907	+	0.0636907i
$753$	−11.5182	+	12.7010i	−0.419746	+	0.462850i
$754$	−1.38319	−	0.798583i	−0.0503726	−	0.0290827i
$755$	−8.86001	+	30.7327i	−0.322449	+	1.11848i
$756$	2.90855	−	7.34162i	0.105783	−	0.267012i
$757$	−23.3587	−	6.25895i	−0.848987	−	0.227485i	−0.192007	−	0.981394i	$-0.561500\pi$
$757$	−23.3587	−	6.25895i	−0.848987	−	0.227485i	−0.656980	+	0.753908i	$0.728166\pi$
$758$	16.3690	+	4.38606i	0.594548	+	0.159309i
$759$	−3.64880	−	74.7131i	−0.132443	−	2.71191i
$760$	5.94529	−	7.72357i	0.215658	−	0.280163i
$761$			3.83472i			0.139009i	0.997582	+	0.0695043i	$0.0221418\pi$
$761$			3.83472i			0.139009i	−0.997582	+	0.0695043i	$0.977858\pi$
$762$	7.42536	−	34.3319i	0.268992	−	1.24371i
$763$	−2.86686	+	10.6993i	−0.103787	+	0.387339i
$764$	11.2314	−	19.4533i	0.406337	−	0.703795i
$765$	−24.1190	−	35.0802i	−0.872025	−	1.26833i
$766$	−18.4365	+	31.9330i	−0.666139	+	1.15379i
$767$	1.06450	+	1.06450i	0.0384367	+	0.0384367i
$768$	−1.28303	−	1.16354i	−0.0462973	−	0.0419858i
$769$	10.7161	+	6.18694i	0.386432	+	0.223107i	0.680613	−	0.732643i	$-0.261713\pi$
$769$	10.7161	+	6.18694i	0.386432	+	0.223107i	−0.294181	+	0.955750i	$0.595047\pi$
$770$	4.53580	+	18.3035i	0.163459	+	0.659612i
$771$	−1.12107	−	22.9550i	−0.0403742	−	0.826706i
$772$	−14.0098	+	14.0098i	−0.504224	+	0.504224i
$773$	−0.943960	−	3.52291i	−0.0339519	−	0.126710i	0.946870	−	0.321617i	$-0.104226\pi$
$773$	−0.943960	−	3.52291i	−0.0339519	−	0.126710i	−0.980822	+	0.194907i	$0.937560\pi$
$774$	−15.8949	−	22.2083i	−0.571329	−	0.798262i
$775$	17.8728	+	11.2394i	0.642012	+	0.403730i
$776$	−8.01640	+	4.62827i	−0.287772	+	0.166145i
$777$	−13.7794	−	2.98023i	−0.494334	−	0.106915i
$778$	−16.1773	−	16.1773i	−0.579983	−	0.579983i
$779$	4.22447	+	3.12660i	0.151357	+	0.112022i
$780$	0.924526	+	0.870800i	0.0331033	+	0.0311797i
$781$	−23.8401	−	41.2922i	−0.853065	−	1.47755i
$782$	−12.7833	+	47.7078i	−0.457129	+	1.70603i
$783$	10.0460	+	23.2285i	0.359016	+	0.830118i
$784$	−4.06201	+	2.34520i	−0.145072	+	0.0837572i
$785$	6.67027	−	11.0653i	0.238072	−	0.394939i
$786$	16.8022	−	0.820576i	0.599314	−	0.0292690i
$787$	8.45948	−	8.45948i	0.301548	−	0.301548i	−0.540071	−	0.841619i	$-0.681603\pi$
$787$	8.45948	−	8.45948i	0.301548	−	0.301548i	0.841619	+	0.540071i	$0.181603\pi$
$788$	3.49305	+	13.0362i	0.124435	+	0.464397i
$789$	6.67863	−	12.9930i	0.237766	−	0.462562i
$790$	10.9701	+	0.207166i	0.390297	+	0.00737064i
$791$		−	24.0327i		−	0.854506i
$792$	−5.85501	−	15.5837i	−0.208049	−	0.553742i
$793$	−0.699974	+	2.61234i	−0.0248568	+	0.0927668i
$794$	−11.0738	+	19.1804i	−0.392995	+	0.680687i
$795$	−5.17818	+	21.9293i	−0.183651	+	0.777752i
$796$	13.6261	+	23.6010i	0.482963	+	0.836516i
$797$	25.9354	+	25.9354i	0.918680	+	0.918680i	0.996933	−	0.0782539i	$-0.0249345\pi$
$797$	25.9354	+	25.9354i	0.918680	+	0.918680i	−0.0782539	+	0.996933i	$0.524934\pi$
$798$	−7.57123	−	8.62111i	−0.268019	−	0.305184i
$799$		−	15.6753i		−	0.554551i
$800$	4.77733	+	1.47552i	0.168904	+	0.0521675i
$801$	−6.54578	+	4.68492i	−0.231284	+	0.165534i
$802$	−7.24523	−	27.0396i	−0.255838	−	0.954800i
$803$	−54.9348	−	14.7197i	−1.93861	−	0.519449i
$804$	1.29041	+	0.663296i	0.0455093	+	0.0233926i
$805$	19.0510	−	18.3447i	0.671458	−	0.646567i
$806$		−	1.38471i		−	0.0487743i
$807$	−33.2047	+	10.6583i	−1.16886	+	0.375189i
$808$	−5.43392	+	1.45601i	−0.191165	+	0.0512224i
$809$	15.0218			0.528139			0.264069	−	0.964504i	$-0.414935\pi$
$809$	15.0218			0.528139			0.264069	+	0.964504i	$0.414935\pi$
$810$	−3.52986	−	19.8126i	−0.124027	−	0.696145i
$811$	22.8510	−	39.5790i	0.802406	−	1.38981i	−0.115623	−	0.993293i	$-0.536886\pi$
$811$	22.8510	−	39.5790i	0.802406	−	1.38981i	0.918029	−	0.396514i	$-0.129780\pi$
$812$	−1.91574	+	7.14964i	−0.0672293	+	0.250903i
$813$	−10.2728	+	3.29744i	−0.360284	+	0.115646i
$814$	−25.7384	+	14.8601i	−0.902132	+	0.520846i
$815$	−22.2108	+	12.2702i	−0.778009	+	0.429805i
$816$	0.536181	+	10.9789i	0.0187701	+	0.384338i
$817$	−39.2458	+	5.86133i	−1.37304	+	0.205062i
$818$	−22.8660	+	22.8660i	−0.799489	+	0.799489i
$819$	1.21578	−	0.870153i	0.0424828	−	0.0304056i
$820$	−0.746846	+	2.59058i	−0.0260810	+	0.0904670i
$821$	−27.0755	−	15.6321i	−0.944942	−	0.545563i	−0.0534361	−	0.998571i	$-0.517017\pi$
$821$	−27.0755	−	15.6321i	−0.944942	−	0.545563i	−0.891506	+	0.453009i	$0.850351\pi$
$822$	34.4883	+	7.45917i	1.20292	+	0.260169i
$823$	−29.5736	+	7.92423i	−1.03087	+	0.276221i	−0.734326	−	0.678797i	$-0.762502\pi$
$823$	−29.5736	+	7.92423i	−1.03087	+	0.276221i	−0.296546	+	0.955019i	$0.595835\pi$
$824$	17.1894			0.598820
$825$	34.3540	+	33.6041i	1.19605	+	1.16995i
$826$	3.48835	−	6.04199i	0.121375	−	0.210228i
$827$	−34.1873	+	9.16046i	−1.18881	+	0.318540i	−0.798415	−	0.602108i	$-0.794328\pi$
$827$	−34.1873	+	9.16046i	−1.18881	+	0.318540i	−0.390394	+	0.920648i	$0.627661\pi$
$828$	−14.8223	+	18.0398i	−0.515111	+	0.626926i
$829$			2.88415i			0.100171i	0.998745	+	0.0500854i	$0.0159493\pi$
$829$			2.88415i			0.100171i	−0.998745	+	0.0500854i	$0.984051\pi$
$830$	6.59230	−	1.63364i	0.228822	−	0.0567045i
$831$	12.1978	+	18.9303i	0.423138	+	0.656683i
$832$	−0.0848738	−	0.316753i	−0.00294247	−	0.0109814i
$833$	28.7520	+	7.70409i	0.996199	+	0.266931i
$834$	−10.2571	−	15.9184i	−0.355174	−	0.551208i
$835$	−0.346793	+	18.3637i	−0.0120013	+	0.635503i
$836$	−24.0322	−	2.74054i	−0.831171	−	0.0947837i
$837$	−13.0857	+	17.6121i	−0.452308	+	0.608764i
$838$	3.08114	−	11.4990i	0.106436	−	0.397226i
$839$	4.21356	+	7.29810i	0.145468	+	0.251958i	0.929548	−	0.368702i	$-0.120198\pi$
$839$	4.21356	+	7.29810i	0.145468	+	0.251958i	−0.784079	+	0.620661i	$0.786865\pi$
$840$	2.78917	−	5.18310i	0.0962354	−	0.178834i
$841$	2.63917	+	4.57117i	0.0910057	+	0.157627i
$842$	−1.90943	+	0.511631i	−0.0658034	+	0.0176320i
$843$	13.5881	−	14.9835i	0.468000	−	0.516058i
$844$			11.2807i			0.388299i
$845$	−6.93424	−	27.9820i	−0.238545	−	0.962611i
$846$	3.06208	−	6.74778i	0.105276	−	0.231994i
$847$	21.2693	−	21.2693i	0.730821	−	0.730821i
$848$	4.11383	−	4.11383i	0.141270	−	0.141270i
$849$	−17.5637	−	9.02810i	−0.602786	−	0.309844i
$850$	−14.8167	−	28.0593i	−0.508208	−	0.962427i
$851$	36.0987	+	20.8416i	1.23745	+	0.714440i
$852$	−3.14607	+	14.5462i	−0.107783	+	0.498344i
$853$	4.25126	−	15.8659i	0.145560	−	0.543239i	−0.854169	−	0.519995i	$-0.825934\pi$
$853$	4.25126	−	15.8659i	0.145560	−	0.543239i	0.999730	−	0.0232441i	$-0.00739948\pi$
$854$	12.5336			0.428892
$855$	−27.9634	−	8.54695i	−0.956327	−	0.292299i
$856$	4.37549			0.149551
$857$	−4.66530	+	17.4111i	−0.159364	+	0.594753i	0.839329	+	0.543624i	$0.182948\pi$
$857$	−4.66530	+	17.4111i	−0.159364	+	0.594753i	−0.998692	+	0.0511283i	$0.983718\pi$
$858$	0.666273	−	3.08058i	0.0227462	−	0.105169i
$859$	−37.3902	−	21.5872i	−1.27574	−	0.736546i	−0.299675	−	0.954041i	$-0.596878\pi$
$859$	−37.3902	−	21.5872i	−1.27574	−	0.736546i	−0.976061	+	0.217495i	$0.930211\pi$
$860$	−9.84331	−	17.8178i	−0.335654	−	0.607582i
$861$	2.82272	+	1.45093i	0.0961979	+	0.0494476i
$862$	−17.9491	+	17.9491i	−0.611350	+	0.611350i
$863$	7.38719	−	7.38719i	0.251463	−	0.251463i	−0.570107	−	0.821570i	$-0.693098\pi$
$863$	7.38719	−	7.38719i	0.251463	−	0.251463i	0.821570	+	0.570107i	$0.193098\pi$
$864$	−1.91385	+	4.83086i	−0.0651106	+	0.164349i
$865$	−22.2889	+	36.9752i	−0.757847	+	1.25720i
$866$			7.59532i			0.258100i
$867$	27.0808	−	29.8618i	0.919714	−	1.01416i
$868$	−6.19859	+	1.66091i	−0.210394	+	0.0563749i
$869$	−13.6143	−	23.5806i	−0.461832	−	0.799916i
$870$	5.42501	+	18.0664i	0.183925	+	0.612508i
$871$	0.137349	+	0.237895i	0.00465389	+	0.00806077i
$872$	1.88642	−	7.04021i	0.0638822	−	0.238412i
$873$	21.4560	+	17.6293i	0.726177	+	0.596660i
$874$	13.5241	+	31.1117i	0.457459	+	1.05237i
$875$	−0.961989	+	16.9639i	−0.0325212	+	0.573485i
$876$	9.61525	+	14.9223i	0.324869	+	0.504176i
$877$	19.1257	+	5.12473i	0.645830	+	0.173050i	0.566843	−	0.823826i	$-0.308165\pi$
$877$	19.1257	+	5.12473i	0.645830	+	0.173050i	0.0789874	+	0.996876i	$0.474831\pi$
$878$	6.07168	+	22.6598i	0.204909	+	0.764732i
$879$	26.5199	+	41.1572i	0.894494	+	1.38820i
$880$	−2.98460	−	12.0439i	−0.100611	−	0.405998i
$881$		−	48.8801i		−	1.64681i	−0.567451	−	0.823407i	$-0.692071\pi$
$881$		−	48.8801i		−	1.64681i	0.567451	−	0.823407i	$-0.307929\pi$
$882$	10.8720	+	8.93296i	0.366081	+	0.300788i
$883$	−51.5136	+	13.8030i	−1.73357	+	0.464509i	−0.981001	−	0.194003i	$-0.937853\pi$
$883$	−51.5136	+	13.8030i	−1.73357	+	0.464509i	−0.752570	+	0.658512i	$0.771186\pi$
$884$	−1.04055	+	1.80228i	−0.0349974	+	0.0606173i
$885$	−0.531826	−	17.7719i	−0.0178771	−	0.597394i
$886$	3.50924			0.117895
$887$	−22.6677	+	6.07378i	−0.761106	+	0.203938i	−0.618439	−	0.785833i	$-0.712234\pi$
$887$	−22.6677	+	6.07378i	−0.761106	+	0.203938i	−0.142667	+	0.989771i	$0.545568\pi$
$888$	9.06698	+	1.96102i	0.304268	+	0.0658076i
$889$	−26.6909	−	15.4100i	−0.895184	−	0.516835i
$890$	−5.25170	+	2.90126i	−0.176037	+	0.0972505i
$891$	−37.5863	+	32.8856i	−1.25919	+	1.10171i
$892$	−11.1190	+	11.1190i	−0.372292	+	0.372292i
$893$	−6.70150	−	8.42666i	−0.224257	−	0.281987i
$894$	−0.248028	−	5.07865i	−0.00829531	−	0.169856i
$895$	−3.63757	+	12.6176i	−0.121591	+	0.421761i
$896$	−1.31613	+	0.759868i	−0.0439688	+	0.0253854i
$897$	−4.20896	+	1.35102i	−0.140533	+	0.0451093i
$898$	2.93129	−	10.9397i	0.0978184	−	0.365063i
$899$	10.2831	−	17.8109i	0.342961	−	0.594025i
$900$	−0.896952	−	14.9732i	−0.0298984	−	0.499105i
$901$	−36.9212			−1.23002
$902$	6.46271	−	1.73168i	0.215185	−	0.0576586i
$903$	−22.8161	+	7.32366i	−0.759271	+	0.243716i
$904$			15.8138i			0.525958i
$905$	6.28412	+	6.52604i	0.208891	+	0.216933i
$906$	−22.0345	−	11.3261i	−0.732046	−	0.376286i
$907$	−9.34088	−	2.50288i	−0.310159	−	0.0831068i	0.100382	−	0.994949i	$-0.467993\pi$
$907$	−9.34088	−	2.50288i	−0.310159	−	0.0831068i	−0.410541	+	0.911842i	$0.634660\pi$
$908$	2.48050	+	9.25734i	0.0823181	+	0.307216i
$909$	9.82245	+	13.7239i	0.325790	+	0.455194i
$910$	0.975423	−	0.538865i	0.0323350	−	0.0178632i
$911$			4.05796i			0.134446i	0.997738	+	0.0672232i	$0.0214140\pi$
$911$			4.05796i			0.134446i	−0.997738	+	0.0672232i	$0.978586\pi$
$912$	4.98194	+	5.67277i	0.164968	+	0.187844i
$913$	−11.9179	−	11.9179i	−0.394426	−	0.394426i
$914$	0.378492	+	0.655567i	0.0125194	+	0.0216842i
$915$	27.1720	−	16.7910i	0.898278	−	0.555093i
$916$	−3.31408	+	5.74016i	−0.109500	+	0.189660i
$917$	3.82021	−	14.2572i	0.126154	−	0.470814i
$918$	30.2666	−	13.0899i	0.998945	−	0.432031i
$919$		−	5.35052i		−	0.176497i	−0.996098	−	0.0882487i	$-0.971873\pi$
$919$		−	5.35052i		−	0.176497i	0.996098	−	0.0882487i	$-0.0281270\pi$
$920$	−12.5357	+	12.0710i	−0.413290	+	0.397969i
$921$	11.0166	−	21.4323i	0.363010	−	0.706218i
$922$	−2.97419	−	11.0998i	−0.0979497	−	0.365553i
$923$	−1.99241	+	1.99241i	−0.0655808	+	0.0655808i
$924$	−14.5893	+	0.712503i	−0.479952	+	0.0234396i
$925$	−26.1101	+	5.94943i	−0.858494	+	0.195616i
$926$	16.2119	−	9.35997i	0.532757	−	0.307588i
$927$	−18.1370	−	48.2734i	−0.595698	−	1.58551i
$928$	1.26058	−	4.70453i	0.0413804	−	0.154434i
$929$	−16.4259	−	28.4504i	−0.538915	−	0.933428i	−0.998963	−	0.0455340i	$-0.985501\pi$
$929$	−16.4259	−	28.4504i	−0.538915	−	0.933428i	0.460048	−	0.887894i	$-0.347832\pi$
$930$	−11.2130	+	11.9048i	−0.367690	+	0.390375i
$931$	18.7501	−	8.15056i	0.614510	−	0.267124i
$932$	−13.5673	−	13.5673i	−0.444412	−	0.444412i
$933$	26.5011	+	5.73170i	0.867608	+	0.187648i
$934$	−9.92690	+	5.73130i	−0.324818	+	0.187534i
$935$	−40.6530	+	67.4394i	−1.32950	+	2.20551i
$936$	−0.799994	+	0.572569i	−0.0261486	+	0.0187150i
$937$	−6.87291	−	25.6500i	−0.224528	−	0.837950i	−0.982593	−	0.185771i	$-0.940522\pi$
$937$	−6.87291	−	25.6500i	−0.224528	−	0.837950i	0.758065	−	0.652179i	$-0.226145\pi$
$938$	0.900183	−	0.900183i	0.0293920	−	0.0293920i
$939$	2.38524	+	48.8403i	0.0778393	+	1.59384i
$940$	2.85138	−	4.73017i	0.0930019	−	0.154281i
$941$	16.0727	+	9.27957i	0.523954	+	0.302505i	0.738551	−	0.674198i	$-0.235510\pi$
$941$	16.0727	+	9.27957i	0.523954	+	0.302505i	−0.214597	+	0.976703i	$0.568844\pi$
$942$	7.41351	+	6.72312i	0.241545	+	0.219051i
$943$	−6.63537	−	6.63537i	−0.216077	−	0.216077i
$944$	−2.29536	+	3.97569i	−0.0747077	+	0.129398i
$945$	−17.4988	−	2.36406i	−0.569235	−	0.0769029i
$946$	−25.2580	+	43.7481i	−0.821208	+	1.42237i
$947$	11.1307	−	41.5402i	0.361698	−	1.34988i	−0.510144	−	0.860089i	$-0.670408\pi$
$947$	11.1307	−	41.5402i	0.361698	−	1.34988i	0.871842	−	0.489787i	$-0.162926\pi$
$948$	−1.79661	+	8.30682i	−0.0583512	+	0.269793i
$949$			3.36093i			0.109100i
$950$	−19.9611	−	8.74961i	−0.647623	−	0.283875i
$951$	1.00654	+	20.6100i	0.0326393	+	0.668325i
$952$	9.31594	+	2.49620i	0.301931	+	0.0809022i
$953$	−0.502197	−	0.134563i	−0.0162678	−	0.00435894i	0.250676	−	0.968071i	$-0.419347\pi$
$953$	−0.502197	−	0.134563i	−0.0162678	−	0.00435894i	−0.266944	+	0.963712i	$0.586014\pi$
$954$	−15.8936	−	7.21236i	−0.514575	−	0.233509i
$955$	−48.2626	−	13.9138i	−1.56174	−	0.450239i
$956$	−0.972177	−	0.561287i	−0.0314425	−	0.0181533i
$957$	31.4469	−	34.6762i	1.01653	−	1.12092i
$958$	6.18917	+	6.18917i	0.199963	+	0.199963i
$959$	15.4802	−	26.8125i	0.499881	−	0.865819i
$960$	−1.83530	+	3.41053i	−0.0592340	+	0.110074i
$961$	−13.1695			−0.424823
$962$	1.24191	+	1.24191i	0.0400409	+	0.0400409i
$963$	−4.61670	−	12.2878i	−0.148771	−	0.395969i
$964$	−16.3323	+	9.42945i	−0.526027	+	0.303702i
$965$	37.9423	+	22.8719i	1.22141	+	0.736273i
$966$	11.0963	+	17.2207i	0.357017	+	0.554068i
$967$	−16.1729	−	4.33353i	−0.520087	−	0.139357i	−0.0107801	−	0.999942i	$-0.503431\pi$
$967$	−16.1729	−	4.33353i	−0.520087	−	0.139357i	−0.509307	+	0.860585i	$0.670098\pi$
$968$	−13.9954	+	13.9954i	−0.449829	+	0.449829i
$969$	3.10006	−	47.8125i	0.0995882	−	1.53596i
$970$	14.3569	+	14.9096i	0.460973	+	0.478719i
$971$	−18.2443	+	10.5334i	−0.585487	+	0.338031i	−0.763311	−	0.646031i	$-0.776428\pi$
$971$	−18.2443	+	10.5334i	−0.585487	+	0.338031i	0.177824	+	0.984062i	$0.443094\pi$
$972$	15.5860	+	0.277553i	0.499921	+	0.00890251i
$973$	−16.0494	+	4.30042i	−0.514519	+	0.137865i
$974$	−7.94171	−	13.7554i	−0.254469	−	0.440753i
$975$	1.39274	−	2.47497i	0.0446035	−	0.0792625i
$976$	−8.24724			−0.263988
$977$	−39.3563	−	39.3563i	−1.25912	−	1.25912i	−0.951514	−	0.307605i	$-0.900473\pi$
$977$	−39.3563	−	39.3563i	−1.25912	−	1.25912i	−0.307605	−	0.951514i	$-0.599527\pi$
$978$	−6.00717	−	18.7147i	−0.192088	−	0.598429i
$979$	12.8945	+	7.44465i	0.412110	+	0.237932i
$980$	7.27483	+	7.55488i	0.232386	+	0.241332i
$981$	−21.7616	+	2.13065i	−0.694796	+	0.0680264i
$982$	−6.99488	−	26.1053i	−0.223216	−	0.833052i
$983$	17.9643	+	4.81352i	0.572973	+	0.153528i	0.533660	−	0.845699i	$-0.320816\pi$
$983$	17.9643	+	4.81352i	0.572973	+	0.153528i	0.0393131	+	0.999227i	$0.487483\pi$
$984$	−1.85737	−	0.954725i	−0.0592109	−	0.0304355i
$985$	26.4153	−	14.5930i	0.841663	−	0.464970i
$986$	−26.7681	+	15.4546i	−0.852471	+	0.492174i
$987$	−4.81620	−	4.36768i	−0.153301	−	0.139025i
$988$	0.211138	+	1.41372i	0.00671720	+	0.0449765i
$989$	70.8496			2.25289
$990$	−30.6740	+	21.0895i	−0.974883	+	0.670270i
$991$	5.33927	+	9.24789i	0.169608	+	0.293769i	0.938282	−	0.345871i	$-0.112417\pi$
$991$	5.33927	+	9.24789i	0.169608	+	0.293769i	−0.768674	+	0.639640i	$0.779083\pi$
$992$	4.07873	−	1.09289i	0.129500	−	0.0346994i
$993$	−11.8608	+	54.8396i	−0.376391	+	1.74028i
$994$	11.3087	+	6.52911i	0.358692	+	0.207091i
$995$	43.8953	−	42.2681i	1.39157	−	1.33999i
$996$	0.256619	+	5.25456i	0.00813130	+	0.166497i
$997$	7.41494	+	27.6729i	0.234834	+	0.876411i	0.978224	+	0.207553i	$0.0665499\pi$
$997$	7.41494	+	27.6729i	0.234834	+	0.876411i	−0.743390	+	0.668858i	$0.766783\pi$
$998$	4.15255	+	15.4975i	0.131447	+	0.490566i
$999$	−4.05965	−	27.5322i	−0.128442	−	0.871080i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	570.2.v.c.83.10	✓	144
3.2	odd	2	inner	570.2.v.c.83.24	yes	144
5.2	odd	4	inner	570.2.v.c.197.18	yes	144
15.2	even	4	inner	570.2.v.c.197.34	yes	144
19.11	even	3	inner	570.2.v.c.353.34	yes	144
57.11	odd	6	inner	570.2.v.c.353.18	yes	144
95.87	odd	12	inner	570.2.v.c.467.24	yes	144
285.182	even	12	inner	570.2.v.c.467.10	yes	144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.2.v.c.83.10	✓	144	1.1	even	1	trivial
570.2.v.c.83.24	yes	144	3.2	odd	2	inner
570.2.v.c.197.18	yes	144	5.2	odd	4	inner
570.2.v.c.197.34	yes	144	15.2	even	4	inner
570.2.v.c.353.18	yes	144	57.11	odd	6	inner
570.2.v.c.353.34	yes	144	19.11	even	3	inner
570.2.v.c.467.10	yes	144	285.182	even	12	inner
570.2.v.c.467.24	yes	144	95.87	odd	12	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:	\( N \)	\(=\)	\( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	570.v (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.258819 + 0.965926i) q^{2} +(-0.366145 + 1.69291i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(-0.619415 + 2.14856i) q^{5} +(-1.54046 - 0.791825i) q^{6} +(-1.07462 + 1.07462i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-2.73188 - 1.23970i) q^{9} +O(q^{10})\)	\(q+(-0.258819 + 0.965926i) q^{2} +(-0.366145 + 1.69291i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(-0.619415 + 2.14856i) q^{5} +(-1.54046 - 0.791825i) q^{6} +(-1.07462 + 1.07462i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-2.73188 - 1.23970i) q^{9} +(-1.91504 - 1.15440i) q^{10} +5.54910i q^{11} +(1.16354 - 1.28303i) q^{12} +(0.316753 - 0.0848738i) q^{13} +(-0.759868 - 1.31613i) q^{14} +(-3.41053 - 1.83530i) q^{15} +(0.500000 + 0.866025i) q^{16} +(1.64252 - 6.12997i) q^{17} +(1.90452 - 2.31793i) q^{18} +(-1.73771 - 3.99755i) q^{19} +(1.61071 - 1.55100i) q^{20} +(-1.42576 - 2.21269i) q^{21} +(-5.36001 - 1.43621i) q^{22} +(2.01431 + 7.51752i) q^{23} +(0.938163 + 1.45597i) q^{24} +(-4.23265 - 2.66171i) q^{25} +0.327927i q^{26} +(3.09896 - 4.17091i) q^{27} +(1.46795 - 0.393337i) q^{28} +(-2.43524 + 4.21797i) q^{29} +(2.65547 - 2.81930i) q^{30} -4.22261 q^{31} +(-0.965926 + 0.258819i) q^{32} +(-9.39411 - 2.03177i) q^{33} +(5.49598 + 3.17311i) q^{34} +(-1.64325 - 2.97451i) q^{35} +(1.74602 + 2.43955i) q^{36} +(3.78717 - 3.78717i) q^{37} +(4.31108 - 0.643857i) q^{38} +(0.0277060 + 0.567310i) q^{39} +(1.08127 + 1.95726i) q^{40} +(-1.04419 + 0.602864i) q^{41} +(2.50631 - 0.804493i) q^{42} +(2.35615 - 8.79326i) q^{43} +(2.77455 - 4.80566i) q^{44} +(4.35574 - 5.10172i) q^{45} -7.78271 q^{46} +(2.38585 - 0.639288i) q^{47} +(-1.64917 + 0.529363i) q^{48} +4.69040i q^{49} +(3.66650 - 3.39953i) q^{50} +(9.77608 + 5.02509i) q^{51} +(-0.316753 - 0.0848738i) q^{52} +(-1.50577 - 5.61960i) q^{53} +(3.22672 + 4.07287i) q^{54} +(-11.9226 - 3.43719i) q^{55} +1.51974i q^{56} +(7.40373 - 1.47810i) q^{57} +(-3.44396 - 3.44396i) q^{58} +(2.29536 + 3.97569i) q^{59} +(2.03595 + 3.29468i) q^{60} +(-4.12362 + 7.14232i) q^{61} +(1.09289 - 4.07873i) q^{62} +(4.26792 - 1.60352i) q^{63} -1.00000i q^{64} +(-0.0138450 + 0.733136i) q^{65} +(4.39392 - 8.54815i) q^{66} +(0.216807 + 0.809136i) q^{67} +(-4.48745 + 4.48745i) q^{68} +(-13.4640 + 0.657548i) q^{69} +(3.29846 - 0.817394i) q^{70} +(-7.44126 + 4.29621i) q^{71} +(-2.80833 + 1.05513i) q^{72} +(-2.65264 + 9.89978i) q^{73} +(2.67793 + 4.63831i) q^{74} +(6.05578 - 6.19092i) q^{75} +(-0.493872 + 4.33083i) q^{76} +(-5.96314 - 5.96314i) q^{77} +(-0.555150 - 0.120069i) q^{78} +(-4.24944 + 2.45342i) q^{79} +(-2.17042 + 0.537853i) q^{80} +(5.92629 + 6.77341i) q^{81} +(-0.312065 - 1.16464i) q^{82} +(-2.14772 + 2.14772i) q^{83} +(0.128400 + 2.62913i) q^{84} +(12.1532 + 7.32606i) q^{85} +(7.88383 + 4.55173i) q^{86} +(-6.24898 - 5.66703i) q^{87} +(3.92380 + 3.92380i) q^{88} +(1.34160 - 2.32371i) q^{89} +(3.80054 + 5.52774i) q^{90} +(-0.249181 + 0.431594i) q^{91} +(2.01431 - 7.51752i) q^{92} +(1.54609 - 7.14850i) q^{93} +2.47002i q^{94} +(9.66534 - 1.25744i) q^{95} +(-0.0844883 - 1.72999i) q^{96} +(-8.94113 - 2.39577i) q^{97} +(-4.53058 - 1.21397i) q^{98} +(6.87921 - 15.1594i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q - 4 q^{3} + 8 q^{6}+O(q^{10}) \) 144 * q - 4 * q^3 + 8 * q^6	\( 144 q - 4 q^{3} + 8 q^{6} - 16 q^{10} - 8 q^{12} - 32 q^{13} + 4 q^{15} + 72 q^{16} + 32 q^{18} - 24 q^{21} + 8 q^{22} + 40 q^{25} - 16 q^{27} - 8 q^{30} - 16 q^{33} - 16 q^{37} + 8 q^{40} - 44 q^{42} - 16 q^{43} - 56 q^{45} - 48 q^{46} + 4 q^{48} + 32 q^{51} + 32 q^{52} + 8 q^{55} - 64 q^{57} + 32 q^{58} - 24 q^{60} + 76 q^{63} + 16 q^{66} - 56 q^{67} - 8 q^{70} + 16 q^{72} + 88 q^{73} + 32 q^{75} + 48 q^{76} - 56 q^{81} - 152 q^{87} - 16 q^{88} - 4 q^{90} + 80 q^{91} - 52 q^{93} + 16 q^{96} + 32 q^{97}+O(q^{100}) \) 144 * q - 4 * q^3 + 8 * q^6 - 16 * q^10 - 8 * q^12 - 32 * q^13 + 4 * q^15 + 72 * q^16 + 32 * q^18 - 24 * q^21 + 8 * q^22 + 40 * q^25 - 16 * q^27 - 8 * q^30 - 16 * q^33 - 16 * q^37 + 8 * q^40 - 44 * q^42 - 16 * q^43 - 56 * q^45 - 48 * q^46 + 4 * q^48 + 32 * q^51 + 32 * q^52 + 8 * q^55 - 64 * q^57 + 32 * q^58 - 24 * q^60 + 76 * q^63 + 16 * q^66 - 56 * q^67 - 8 * q^70 + 16 * q^72 + 88 * q^73 + 32 * q^75 + 48 * q^76 - 56 * q^81 - 152 * q^87 - 16 * q^88 - 4 * q^90 + 80 * q^91 - 52 * q^93 + 16 * q^96 + 32 * q^97

Introduction

L-functions

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