LMFDB - Embedded newform 570.2.bc.b.169.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [570,2,Mod(139,570)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(570, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 9, 14]))

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

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

chi := DirichletCharacter("570.139");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 570 = 2 \cdot 3 \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	570.bc (of order $18$, degree $6$, 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:	$60$
Relative dimension:	$10$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			169.7
Character	$\chi$	$=$	570.169
Dual form			570.2.bc.b.199.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.984808 + 0.173648i) q^{2} +(0.642788 - 0.766044i) q^{3} +(0.939693 + 0.342020i) q^{4} +(-0.103744 - 2.23366i) q^{5} +(0.766044 - 0.642788i) q^{6} +(2.04388 - 1.18003i) q^{7} +(0.866025 + 0.500000i) q^{8} +(-0.173648 - 0.984808i) q^{9} +O(q^{10})$	\(q+(0.984808 + 0.173648i) q^{2} +(0.642788 - 0.766044i) q^{3} +(0.939693 + 0.342020i) q^{4} +(-0.103744 - 2.23366i) q^{5} +(0.766044 - 0.642788i) q^{6} +(2.04388 - 1.18003i) q^{7} +(0.866025 + 0.500000i) q^{8} +(-0.173648 - 0.984808i) q^{9} +(0.285703 - 2.21774i) q^{10} +(-1.70083 + 2.94592i) q^{11} +(0.866025 - 0.500000i) q^{12} +(-1.41172 - 1.68242i) q^{13} +(2.21774 - 0.807191i) q^{14} +(-1.77777 - 1.35630i) q^{15} +(0.766044 + 0.642788i) q^{16} +(4.22938 + 0.745754i) q^{17} -1.00000i q^{18} +(-0.451815 - 4.33542i) q^{19} +(0.666469 - 2.13444i) q^{20} +(0.409822 - 2.32421i) q^{21} +(-2.18654 + 2.60582i) q^{22} +(-0.246861 + 0.678245i) q^{23} +(0.939693 - 0.342020i) q^{24} +(-4.97847 + 0.463458i) q^{25} +(-1.09812 - 1.90200i) q^{26} +(-0.866025 - 0.500000i) q^{27} +(2.32421 - 0.409822i) q^{28} +(1.15254 + 6.53637i) q^{29} +(-1.51524 - 1.64440i) q^{30} +(-3.93768 - 6.82025i) q^{31} +(0.642788 + 0.766044i) q^{32} +(1.16343 + 3.19651i) q^{33} +(4.03563 + 1.46885i) q^{34} +(-2.84784 - 4.44291i) q^{35} +(0.173648 - 0.984808i) q^{36} +3.19346i q^{37} +(0.307887 - 4.34801i) q^{38} -2.19624 q^{39} +(1.02699 - 1.98628i) q^{40} +(3.54350 + 2.97335i) q^{41} +(0.807191 - 2.21774i) q^{42} +(2.11201 + 5.80269i) q^{43} +(-2.60582 + 2.18654i) q^{44} +(-2.18171 + 0.490039i) q^{45} +(-0.360886 + 0.625074i) q^{46} +(13.2070 - 2.32875i) q^{47} +(0.984808 - 0.173648i) q^{48} +(-0.715037 + 1.23848i) q^{49} +(-4.98332 - 0.408086i) q^{50} +(3.28987 - 2.76053i) q^{51} +(-0.751158 - 2.06379i) q^{52} +(1.78896 - 4.91514i) q^{53} +(-0.766044 - 0.642788i) q^{54} +(6.75663 + 3.49345i) q^{55} +2.36007 q^{56} +(-3.61155 - 2.44064i) q^{57} +6.63720i q^{58} +(-2.61090 + 14.8071i) q^{59} +(-1.20668 - 1.88253i) q^{60} +(-2.43783 - 0.887297i) q^{61} +(-2.69353 - 7.40041i) q^{62} +(-1.51702 - 1.80792i) q^{63} +(0.500000 + 0.866025i) q^{64} +(-3.61149 + 3.32783i) q^{65} +(0.590691 + 3.34997i) q^{66} +(-1.22562 + 0.216110i) q^{67} +(3.71925 + 2.14731i) q^{68} +(0.360886 + 0.625074i) q^{69} +(-2.03307 - 4.86993i) q^{70} +(-15.7074 + 5.71704i) q^{71} +(0.342020 - 0.939693i) q^{72} +(1.17960 - 1.40579i) q^{73} +(-0.554538 + 3.14494i) q^{74} +(-2.84507 + 4.11164i) q^{75} +(1.05823 - 4.22849i) q^{76} +8.02814i q^{77} +(-2.16287 - 0.381373i) q^{78} +(7.57288 + 6.35440i) q^{79} +(1.35630 - 1.77777i) q^{80} +(-0.939693 + 0.342020i) q^{81} +(2.97335 + 3.54350i) q^{82} +(-10.7928 + 6.23121i) q^{83} +(1.18003 - 2.04388i) q^{84} +(1.22699 - 9.52436i) q^{85} +(1.07229 + 6.08128i) q^{86} +(5.74799 + 3.31860i) q^{87} +(-2.94592 + 1.70083i) q^{88} +(9.59204 - 8.04868i) q^{89} +(-2.23366 + 0.103744i) q^{90} +(-4.87069 - 1.77279i) q^{91} +(-0.463947 + 0.552910i) q^{92} +(-7.75571 - 1.36754i) q^{93} +13.4108 q^{94} +(-9.63698 + 1.45897i) q^{95} +1.00000 q^{96} +(-1.54012 - 0.271565i) q^{97} +(-0.919234 + 1.09550i) q^{98} +(3.19651 + 1.16343i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 60 q + 6 q^{5}+O(q^{10}) $ 60 * q + 6 * q^5	$ 60 q + 6 q^{5} + 6 q^{10} - 12 q^{11} + 12 q^{15} + 24 q^{19} + 12 q^{20} - 18 q^{21} - 6 q^{25} - 6 q^{26} + 12 q^{29} + 6 q^{30} - 36 q^{31} - 6 q^{35} - 12 q^{39} - 6 q^{40} - 30 q^{41} - 6 q^{44} - 6 q^{45} - 36 q^{46} + 18 q^{49} - 90 q^{55} + 24 q^{56} + 60 q^{59} + 6 q^{60} + 36 q^{61} + 30 q^{64} + 24 q^{65} - 12 q^{66} + 36 q^{69} - 72 q^{70} - 72 q^{71} + 6 q^{74} + 6 q^{76} + 6 q^{80} + 12 q^{84} + 18 q^{85} - 12 q^{86} + 60 q^{89} + 12 q^{90} - 48 q^{91} - 156 q^{94} - 84 q^{95} + 60 q^{96} - 6 q^{99}+O(q^{100}) $ 60 * q + 6 * q^5 + 6 * q^10 - 12 * q^11 + 12 * q^15 + 24 * q^19 + 12 * q^20 - 18 * q^21 - 6 * q^25 - 6 * q^26 + 12 * q^29 + 6 * q^30 - 36 * q^31 - 6 * q^35 - 12 * q^39 - 6 * q^40 - 30 * q^41 - 6 * q^44 - 6 * q^45 - 36 * q^46 + 18 * q^49 - 90 * q^55 + 24 * q^56 + 60 * q^59 + 6 * q^60 + 36 * q^61 + 30 * q^64 + 24 * q^65 - 12 * q^66 + 36 * q^69 - 72 * q^70 - 72 * q^71 + 6 * q^74 + 6 * q^76 + 6 * q^80 + 12 * q^84 + 18 * q^85 - 12 * q^86 + 60 * q^89 + 12 * q^90 - 48 * q^91 - 156 * q^94 - 84 * q^95 + 60 * q^96 - 6 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$191$	$211$	$457$
$\chi(n)$	$1$	$e\left(\frac{5}{9}\right)$	$-1$

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 $

$2$	0.984808	+	0.173648i	0.696364	+	0.122788i
$2$	0.984808	+	0.173648i	0.696364	+	0.122788i
$3$	0.642788	−	0.766044i	0.371114	−	0.442276i
$3$	0.642788	−	0.766044i	0.371114	−	0.442276i
$4$	0.939693	+	0.342020i	0.469846	+	0.171010i
$5$	−0.103744	−	2.23366i	−0.0463958	−	0.998923i
$5$	−0.103744	−	2.23366i	−0.0463958	−	0.998923i
$6$	0.766044	−	0.642788i	0.312736	−	0.262417i
$7$	2.04388	−	1.18003i	0.772514	−	0.446011i	−0.0612567	−	0.998122i	$-0.519511\pi$
$7$	2.04388	−	1.18003i	0.772514	−	0.446011i	0.833771	+	0.552111i	$0.186178\pi$
$8$	0.866025	+	0.500000i	0.306186	+	0.176777i
$9$	−0.173648	−	0.984808i	−0.0578827	−	0.328269i
$10$	0.285703	−	2.21774i	0.0903472	−	0.701311i
$11$	−1.70083	+	2.94592i	−0.512818	+	0.888228i	0.487071	+	0.873362i	$0.338065\pi$
$11$	−1.70083	+	2.94592i	−0.512818	+	0.888228i	−0.999890	+	0.0148653i	$0.995268\pi$
$12$	0.866025	−	0.500000i	0.250000	−	0.144338i
$13$	−1.41172	−	1.68242i	−0.391539	−	0.466619i	0.533881	−	0.845559i	$-0.320733\pi$
$13$	−1.41172	−	1.68242i	−0.391539	−	0.466619i	−0.925421	+	0.378941i	$0.876288\pi$
$14$	2.21774	−	0.807191i	0.592716	−	0.215731i
$15$	−1.77777	−	1.35630i	−0.459018	−	0.350194i
$16$	0.766044	+	0.642788i	0.191511	+	0.160697i
$17$	4.22938	+	0.745754i	1.02578	+	0.180872i	0.661127	−	0.750274i	$-0.270078\pi$
$17$	4.22938	+	0.745754i	1.02578	+	0.180872i	0.364648	+	0.931145i	$0.381189\pi$
$18$		−	1.00000i		−	0.235702i
$19$	−0.451815	−	4.33542i	−0.103653	−	0.994613i
$19$	−0.451815	−	4.33542i	−0.103653	−	0.994613i
$20$	0.666469	−	2.13444i	0.149027	−	0.477274i
$21$	0.409822	−	2.32421i	0.0894304	−	0.507185i
$22$	−2.18654	+	2.60582i	−0.466172	+	0.555562i
$23$	−0.246861	+	0.678245i	−0.0514740	+	0.141424i	−0.962765	−	0.270339i	$-0.912864\pi$
$23$	−0.246861	+	0.678245i	−0.0514740	+	0.141424i	0.911291	+	0.411762i	$0.135087\pi$
$24$	0.939693	−	0.342020i	0.191814	−	0.0698146i
$25$	−4.97847	+	0.463458i	−0.995695	+	0.0926916i
$26$	−1.09812	−	1.90200i	−0.215359	−	0.373013i
$27$	−0.866025	−	0.500000i	−0.166667	−	0.0962250i
$28$	2.32421	−	0.409822i	0.439235	−	0.0774490i
$29$	1.15254	+	6.53637i	0.214021	+	1.21377i	0.882597	+	0.470130i	$0.155793\pi$
$29$	1.15254	+	6.53637i	0.214021	+	1.21377i	−0.668576	+	0.743644i	$0.733096\pi$
$30$	−1.51524	−	1.64440i	−0.276644	−	0.300225i
$31$	−3.93768	−	6.82025i	−0.707227	−	1.22495i	−0.965882	−	0.258984i	$-0.916612\pi$
$31$	−3.93768	−	6.82025i	−0.707227	−	1.22495i	0.258654	−	0.965970i	$-0.416721\pi$
$32$	0.642788	+	0.766044i	0.113630	+	0.135419i
$33$	1.16343	+	3.19651i	0.202528	+	0.556441i
$34$	4.03563	+	1.46885i	0.692104	+	0.251905i
$35$	−2.84784	−	4.44291i	−0.481372	−	0.750989i
$36$	0.173648	−	0.984808i	0.0289414	−	0.164135i
$37$			3.19346i			0.525001i	0.964932	+	0.262501i	$0.0845472\pi$
$37$			3.19346i			0.525001i	−0.964932	+	0.262501i	$0.915453\pi$
$38$	0.307887	−	4.34801i	0.0499459	−	0.705341i
$39$	−2.19624			−0.351680
$40$	1.02699	−	1.98628i	0.162381	−	0.314058i
$41$	3.54350	+	2.97335i	0.553402	+	0.464359i	0.876091	−	0.482146i	$-0.160142\pi$
$41$	3.54350	+	2.97335i	0.553402	+	0.464359i	−0.322689	+	0.946505i	$0.604587\pi$
$42$	0.807191	−	2.21774i	0.124552	−	0.342205i
$43$	2.11201	+	5.80269i	0.322078	+	0.884903i	0.990050	+	0.140716i	$0.0449404\pi$
$43$	2.11201	+	5.80269i	0.322078	+	0.884903i	−0.667972	+	0.744187i	$0.732837\pi$
$44$	−2.60582	+	2.18654i	−0.392842	+	0.329633i
$45$	−2.18171	+	0.490039i	−0.325230	+	0.0730507i
$46$	−0.360886	+	0.625074i	−0.0532098	+	0.0921621i
$47$	13.2070	−	2.32875i	1.92644	−	0.339684i	0.927063	−	0.374906i	$-0.122325\pi$
$47$	13.2070	−	2.32875i	1.92644	−	0.339684i	0.999380	+	0.0352218i	$0.0112138\pi$
$48$	0.984808	−	0.173648i	0.142145	−	0.0250640i
$49$	−0.715037	+	1.23848i	−0.102148	+	0.176926i
$50$	−4.98332	−	0.408086i	−0.704748	−	0.0577121i
$51$	3.28987	−	2.76053i	0.460674	−	0.386552i
$52$	−0.751158	−	2.06379i	−0.104167	−	0.286196i
$53$	1.78896	−	4.91514i	0.245733	−	0.675147i	−0.754098	−	0.656762i	$-0.771926\pi$
$53$	1.78896	−	4.91514i	0.245733	−	0.675147i	0.999831	−	0.0183843i	$-0.00585224\pi$
$54$	−0.766044	−	0.642788i	−0.104245	−	0.0874723i
$55$	6.75663	+	3.49345i	0.911064	+	0.471056i
$56$	2.36007			0.315377
$57$	−3.61155	−	2.44064i	−0.478361	−	0.323271i
$58$			6.63720i			0.871508i
$59$	−2.61090	+	14.8071i	−0.339910	+	1.92773i	0.0320719	+	0.999486i	$0.489789\pi$
$59$	−2.61090	+	14.8071i	−0.339910	+	1.92773i	−0.371982	+	0.928240i	$0.621322\pi$
$60$	−1.20668	−	1.88253i	−0.155781	−	0.243034i
$61$	−2.43783	−	0.887297i	−0.312132	−	0.113607i	0.181204	−	0.983446i	$-0.442001\pi$
$61$	−2.43783	−	0.887297i	−0.312132	−	0.113607i	−0.493336	+	0.869839i	$0.664223\pi$
$62$	−2.69353	−	7.40041i	−0.342078	−	0.939853i
$63$	−1.51702	−	1.80792i	−0.191127	−	0.227776i
$64$	0.500000	+	0.866025i	0.0625000	+	0.108253i
$65$	−3.61149	+	3.32783i	−0.447950	+	0.412767i
$66$	0.590691	+	3.34997i	0.0727090	+	0.412353i
$67$	−1.22562	+	0.216110i	−0.149734	+	0.0264021i	−0.248012	−	0.968757i	$-0.579777\pi$
$67$	−1.22562	+	0.216110i	−0.149734	+	0.0264021i	0.0982789	+	0.995159i	$0.468666\pi$
$68$	3.71925	+	2.14731i	0.451026	+	0.260400i
$69$	0.360886	+	0.625074i	0.0434456	+	0.0752500i
$70$	−2.03307	−	4.86993i	−0.242998	−	0.582069i
$71$	−15.7074	+	5.71704i	−1.86413	+	0.678488i	−0.888578	+	0.458726i	$0.848306\pi$
$71$	−15.7074	+	5.71704i	−1.86413	+	0.678488i	−0.975553	+	0.219762i	$0.929472\pi$
$72$	0.342020	−	0.939693i	0.0403075	−	0.110744i
$73$	1.17960	−	1.40579i	0.138062	−	0.164536i	−0.692583	−	0.721338i	$-0.743527\pi$
$73$	1.17960	−	1.40579i	0.138062	−	0.164536i	0.830645	+	0.556802i	$0.187972\pi$
$74$	−0.554538	+	3.14494i	−0.0644638	+	0.365592i
$75$	−2.84507	+	4.11164i	−0.328521	+	0.474771i
$76$	1.05823	−	4.22849i	0.121388	−	0.485041i
$77$			8.02814i			0.914891i
$78$	−2.16287	−	0.381373i	−0.244897	−	0.0431820i
$79$	7.57288	+	6.35440i	0.852015	+	0.714926i	0.960233	−	0.279202i	$-0.0900698\pi$
$79$	7.57288	+	6.35440i	0.852015	+	0.714926i	−0.108217	+	0.994127i	$0.534514\pi$
$80$	1.35630	−	1.77777i	0.151639	−	0.198761i
$81$	−0.939693	+	0.342020i	−0.104410	+	0.0380022i
$82$	2.97335	+	3.54350i	0.328352	+	0.391314i
$83$	−10.7928	+	6.23121i	−1.18466	+	0.683964i	−0.957088	−	0.289797i	$-0.906412\pi$
$83$	−10.7928	+	6.23121i	−1.18466	+	0.683964i	−0.227572	+	0.973761i	$0.573079\pi$
$84$	1.18003	−	2.04388i	0.128752	−	0.223006i
$85$	1.22699	−	9.52436i	0.133085	−	1.03306i
$86$	1.07229	+	6.08128i	0.115628	+	0.655762i
$87$	5.74799	+	3.31860i	0.616249	+	0.355792i
$88$	−2.94592	+	1.70083i	−0.314036	+	0.181309i
$89$	9.59204	−	8.04868i	1.01675	−	0.853158i	0.0275381	−	0.999621i	$-0.491233\pi$
$89$	9.59204	−	8.04868i	1.01675	−	0.853158i	0.989216	+	0.146463i	$0.0467888\pi$
$90$	−2.23366	+	0.103744i	−0.235448	+	0.0109356i
$91$	−4.87069	−	1.77279i	−0.510587	−	0.185838i
$92$	−0.463947	+	0.552910i	−0.0483698	+	0.0576449i
$93$	−7.75571	−	1.36754i	−0.804229	−	0.141807i
$94$	13.4108			1.38321
$95$	−9.63698	+	1.45897i	−0.988733	+	0.149688i
$96$	1.00000			0.102062
$97$	−1.54012	−	0.271565i	−0.156376	−	0.0275732i	0.0949122	−	0.995486i	$-0.469743\pi$
$97$	−1.54012	−	0.271565i	−0.156376	−	0.0275732i	−0.251288	+	0.967912i	$0.580854\pi$
$98$	−0.919234	+	1.09550i	−0.0928566	+	0.110662i
$99$	3.19651	+	1.16343i	0.321261	+	0.116929i
$100$	−4.83675	−	1.26723i	−0.483675	−	0.126723i
$101$	0.832290	−	0.698374i	0.0828159	−	0.0694908i	−0.600440	−	0.799670i	$-0.705008\pi$
$101$	0.832290	−	0.698374i	0.0828159	−	0.0694908i	0.683256	+	0.730179i	$0.260563\pi$
$102$	3.71925	−	2.14731i	0.368261	−	0.212616i
$103$	−7.74552	−	4.47188i	−0.763189	−	0.440627i	0.0672506	−	0.997736i	$-0.478577\pi$
$103$	−7.74552	−	4.47188i	−0.763189	−	0.440627i	−0.830440	+	0.557109i	$0.811911\pi$
$104$	−0.381373	−	2.16287i	−0.0373967	−	0.212087i
$105$	−5.23402	−	0.674279i	−0.510788	−	0.0658029i
$106$	2.61529	−	4.52982i	0.254020	−	0.439975i
$107$	−5.73709	+	3.31231i	−0.554625	+	0.320213i	−0.750985	−	0.660319i	$-0.770421\pi$
$107$	−5.73709	+	3.31231i	−0.554625	+	0.320213i	0.196360	+	0.980532i	$0.437088\pi$
$108$	−0.642788	−	0.766044i	−0.0618523	−	0.0737127i
$109$	3.50573	−	1.27598i	0.335788	−	0.122217i	−0.168623	−	0.985681i	$-0.553932\pi$
$109$	3.50573	−	1.27598i	0.335788	−	0.122217i	0.504411	+	0.863464i	$0.331710\pi$
$110$	6.04735	+	4.61365i	0.576592	+	0.439894i
$111$	2.44633	+	2.05272i	0.232196	+	0.194835i
$112$	2.32421	+	0.409822i	0.219618	+	0.0387245i
$113$		−	1.59593i		−	0.150133i	−0.997179	−	0.0750664i	$-0.976083\pi$
$113$		−	1.59593i		−	0.150133i	0.997179	−	0.0750664i	$-0.0239169\pi$
$114$	−3.13286	−	3.03070i	−0.293420	−	0.283851i
$115$	1.54058	+	0.481039i	0.143660	+	0.0448571i
$116$	−1.15254	+	6.53637i	−0.107011	+	0.606887i
$117$	−1.41172	+	1.68242i	−0.130513	+	0.155540i
$118$	−5.14247	+	14.1288i	−0.473402	+	1.30066i
$119$	9.52436	−	3.46658i	0.873097	−	0.317781i
$120$	−0.861444	−	2.06347i	−0.0786387	−	0.188368i
$121$	−0.285621	−	0.494710i	−0.0259655	−	0.0449736i
$122$	−2.24672	−	1.29714i	−0.203408	−	0.117438i
$123$	4.55544	−	0.803246i	0.410750	−	0.0724263i
$124$	−1.36754	−	7.75571i	−0.122809	−	0.696483i
$125$	1.55169	+	11.0721i	0.138788	+	0.990322i
$126$	−1.18003	−	2.04388i	−0.105126	−	0.182083i
$127$	−6.30417	−	7.51302i	−0.559405	−	0.666672i	0.410016	−	0.912078i	$-0.365523\pi$
$127$	−6.30417	−	7.51302i	−0.559405	−	0.666672i	−0.969420	+	0.245406i	$0.921079\pi$
$128$	0.342020	+	0.939693i	0.0302306	+	0.0830579i
$129$	5.80269	+	2.11201i	0.510899	+	0.185952i
$130$	−4.13450	+	2.65015i	−0.362619	+	0.232433i
$131$	0.961542	−	5.45317i	0.0840103	−	0.476446i	−0.913555	−	0.406714i	$-0.866675\pi$
$131$	0.961542	−	5.45317i	0.0840103	−	0.476446i	0.997566	−	0.0697319i	$-0.0222144\pi$
$132$			3.40165i			0.296076i
$133$	−6.03940	−	8.32792i	−0.523682	−	0.722122i
$134$	−1.24453			−0.107511
$135$	−1.02699	+	1.98628i	−0.0883888	+	0.170952i
$136$	3.28987	+	2.76053i	0.282104	+	0.236714i
$137$	−4.26346	+	11.7138i	−0.364252	+	1.00077i	0.613257	+	0.789883i	$0.289859\pi$
$137$	−4.26346	+	11.7138i	−0.364252	+	1.00077i	−0.977510	+	0.210891i	$0.932363\pi$
$138$	0.246861	+	0.678245i	0.0210142	+	0.0577360i
$139$	−11.5839	+	9.72009i	−0.982538	+	0.824447i	−0.984470	−	0.175551i	$-0.943829\pi$
$139$	−11.5839	+	9.72009i	−0.982538	+	0.824447i	0.00193275	+	0.999998i	$0.499385\pi$
$140$	−1.15653	−	5.14899i	−0.0977443	−	0.435169i
$141$	6.70538	−	11.6141i	0.564695	−	0.978081i
$142$	−16.4616	+	2.90262i	−1.38142	+	0.243582i
$143$	7.35735	−	1.29730i	0.615252	−	0.108486i
$144$	0.500000	−	0.866025i	0.0416667	−	0.0721688i
$145$	14.4805	−	3.25249i	1.20254	−	0.270105i
$146$	1.40579	−	1.17960i	0.116344	−	0.0976244i
$147$	0.489114	+	1.34383i	0.0403415	+	0.110837i
$148$	−1.09223	+	3.00087i	−0.0897805	+	0.246670i
$149$	15.9713	+	13.4015i	1.30842	+	1.09789i	0.988624	+	0.150408i	$0.0480587\pi$
$149$	15.9713	+	13.4015i	1.30842	+	1.09789i	0.319795	+	0.947487i	$0.396386\pi$
$150$	−3.51583	+	3.55513i	−0.287066	+	0.290275i
$151$	6.35887			0.517477			0.258739	−	0.965947i	$-0.416693\pi$
$151$	6.35887			0.517477			0.258739	+	0.965947i	$0.416693\pi$
$152$	1.77643	−	3.98049i	0.144087	−	0.322860i
$153$		−	4.29462i		−	0.347200i
$154$	−1.39407	+	7.90617i	−0.112337	+	0.637097i
$155$	−14.8256	+	9.50299i	−1.19082	+	0.763298i
$156$	−2.06379	−	0.751158i	−0.165235	−	0.0601408i
$157$	−1.85014	−	5.08322i	−0.147657	−	0.405685i	0.843710	−	0.536799i	$-0.180367\pi$
$157$	−1.85014	−	5.08322i	−0.147657	−	0.405685i	−0.991367	+	0.131114i	$0.958145\pi$
$158$	6.35440	+	7.57288i	0.505529	+	0.602466i
$159$	−2.61529	−	4.52982i	−0.207406	−	0.359238i
$160$	1.64440	−	1.51524i	0.130001	−	0.119790i
$161$	0.295798	+	1.67755i	0.0233122	+	0.132210i
$162$	−0.984808	+	0.173648i	−0.0773738	+	0.0136431i
$163$	−4.69279	−	2.70938i	−0.367568	−	0.212215i	0.304828	−	0.952408i	$-0.401401\pi$
$163$	−4.69279	−	2.70938i	−0.367568	−	0.212215i	−0.672395	+	0.740192i	$0.734734\pi$
$164$	2.31286	+	4.00598i	0.180604	+	0.312815i
$165$	7.01921	−	2.93033i	0.546445	−	0.228126i
$166$	−11.7108	+	4.26240i	−0.908937	+	0.330826i
$167$	−0.0449046	+	0.123374i	−0.00347483	+	0.00954700i	−0.941418	−	0.337242i	$-0.890506\pi$
$167$	−0.0449046	+	0.123374i	−0.00347483	+	0.00954700i	0.937943	+	0.346789i	$0.112728\pi$
$168$	1.51702	−	1.80792i	0.117041	−	0.139484i
$169$	1.41984	−	8.05231i	0.109218	−	0.619409i
$170$	2.86224	−	9.16660i	0.219523	−	0.703046i
$171$	−4.19110	+	1.19779i	−0.320501	+	0.0915972i
$172$			6.17510i			0.470847i
$173$	−22.8030	−	4.02078i	−1.73368	−	0.305695i	−0.784430	−	0.620217i	$-0.787044\pi$
$173$	−22.8030	−	4.02078i	−1.73368	−	0.305695i	−0.949250	+	0.314523i	$0.898155\pi$
$174$	5.08439	+	4.26631i	0.385447	+	0.323428i
$175$	−9.62851	+	6.82202i	−0.727847	+	0.515697i
$176$	−3.19651	+	1.16343i	−0.240946	+	0.0876971i
$177$	9.66467	+	11.5179i	0.726441	+	0.865739i
$178$	10.8440	−	6.26076i	0.812789	−	0.469264i
$179$	3.45944	−	5.99192i	0.258571	−	0.447857i	−0.707289	−	0.706925i	$-0.750082\pi$
$179$	3.45944	−	5.99192i	0.258571	−	0.447857i	0.965859	+	0.259068i	$0.0834152\pi$
$180$	−2.21774	−	0.285703i	−0.165301	−	0.0212950i
$181$	−1.36591	−	7.74647i	−0.101527	−	0.575790i	−0.992551	−	0.121833i	$-0.961123\pi$
$181$	−1.36591	−	7.74647i	−0.101527	−	0.575790i	0.891023	−	0.453958i	$-0.149988\pi$
$182$	−4.48885	−	2.59164i	−0.332736	−	0.192105i
$183$	−2.24672	+	1.29714i	−0.166082	+	0.0958875i
$184$	−0.552910	+	0.463947i	−0.0407611	+	0.0342026i
$185$	7.13310	−	0.331302i	0.524436	−	0.0243578i
$186$	−7.40041	−	2.69353i	−0.542624	−	0.197499i
$187$	−9.39037	+	11.1910i	−0.686692	+	0.818368i
$188$	13.2070	+	2.32875i	0.963221	+	0.169842i
$189$	−2.36007			−0.171670
$190$	−9.74392	−	0.236635i	−0.706898	−	0.0171673i
$191$	−18.2443			−1.32011			−0.660056	−	0.751216i	$-0.729468\pi$
$191$	−18.2443			−1.32011			−0.660056	+	0.751216i	$0.729468\pi$
$192$	0.984808	+	0.173648i	0.0710724	+	0.0125320i
$193$	13.2330	−	15.7704i	0.952529	−	1.13518i	−0.0381926	−	0.999270i	$-0.512160\pi$
$193$	13.2330	−	15.7704i	0.952529	−	1.13518i	0.990721	−	0.135909i	$-0.0433955\pi$
$194$	−1.46957	−	0.534878i	−0.105509	−	0.0384020i
$195$	0.227847	+	4.90565i	0.0163165	+	0.351301i
$196$	−1.09550	+	0.919234i	−0.0782500	+	0.0656596i
$197$	17.1447	−	9.89848i	1.22151	−	0.705237i	0.256268	−	0.966606i	$-0.417507\pi$
$197$	17.1447	−	9.89848i	1.22151	−	0.705237i	0.965239	+	0.261368i	$0.0841737\pi$
$198$	2.94592	+	1.70083i	0.209357	+	0.120872i
$199$	2.42542	+	13.7552i	0.171933	+	0.975083i	0.941624	+	0.336666i	$0.109299\pi$
$199$	2.42542	+	13.7552i	0.171933	+	0.975083i	−0.769691	+	0.638417i	$0.779590\pi$
$200$	−4.54321	−	2.08787i	−0.321254	−	0.147635i
$201$	−0.622265	+	1.07779i	−0.0438912	+	0.0760217i
$202$	0.940917	−	0.543239i	0.0662027	−	0.0382221i
$203$	10.0688	+	11.9995i	0.706691	+	0.842201i
$204$	4.03563	−	1.46885i	0.282550	−	0.102840i
$205$	6.27383	−	8.22344i	0.438184	−	0.574350i
$206$	−6.85132	−	5.74894i	−0.477354	−	0.400547i
$207$	0.710807	+	0.125335i	0.0494045	+	0.00871135i
$208$		−	2.19624i		−	0.152282i
$209$	13.5402	+	6.04279i	0.936599	+	0.417988i
$210$	−5.03742	−	1.57291i	−0.347615	−	0.108541i
$211$	−1.53569	+	8.70931i	−0.105721	+	0.599573i	0.885209	+	0.465194i	$0.154015\pi$
$211$	−1.53569	+	8.70931i	−0.105721	+	0.599573i	−0.990930	+	0.134380i	$0.957096\pi$
$212$	3.36215	−	4.00686i	0.230914	−	0.275192i
$213$	−5.71704	+	15.7074i	−0.391725	+	1.07626i
$214$	−6.22511	+	2.26575i	−0.425540	+	0.154884i
$215$	12.7421	−	5.31950i	0.869007	−	0.362787i
$216$	−0.500000	−	0.866025i	−0.0340207	−	0.0589256i
$217$	−16.0963	−	9.29319i	−1.09269	−	0.630863i
$218$	3.67404	−	0.647833i	0.248838	−	0.0438768i
$219$	−0.318667	−	1.80725i	−0.0215335	−	0.122123i
$220$	5.15433	+	5.59367i	0.347505	+	0.377125i
$221$	−4.71601	−	8.16837i	−0.317233	−	0.549464i
$222$	2.05272	+	2.44633i	0.137769	+	0.164187i
$223$	−9.49050	−	26.0749i	−0.635531	−	1.74611i	−0.665329	−	0.746550i	$-0.731709\pi$
$223$	−9.49050	−	26.0749i	−0.635531	−	1.74611i	0.0297987	−	0.999556i	$-0.490513\pi$
$224$	2.21774	+	0.807191i	0.148179	+	0.0539327i
$225$	1.32092	+	4.82236i	0.0880613	+	0.321491i
$226$	0.277131	−	1.57169i	0.0184345	−	0.104547i
$227$		−	7.75259i		−	0.514557i	−0.966337	−	0.257279i	$-0.917174\pi$
$227$		−	7.75259i		−	0.514557i	0.966337	−	0.257279i	$-0.0828259\pi$
$228$	−2.55899	−	3.52868i	−0.169473	−	0.233692i
$229$	7.75602			0.512532			0.256266	−	0.966606i	$-0.417508\pi$
$229$	7.75602			0.512532			0.256266	+	0.966606i	$0.417508\pi$
$230$	1.43364	+	0.741250i	0.0945315	+	0.0488766i
$231$	6.14991	+	5.16039i	0.404634	+	0.339528i
$232$	−2.27006	+	6.23693i	−0.149037	+	0.409475i
$233$	−3.92662	−	10.7883i	−0.257241	−	0.706765i	−0.999335	−	0.0364682i	$-0.988389\pi$
$233$	−3.92662	−	10.7883i	−0.257241	−	0.706765i	0.742094	−	0.670296i	$-0.233833\pi$
$234$	−1.68242	+	1.41172i	−0.109983	+	0.0922867i
$235$	−6.57180	−	29.2584i	−0.428697	−	1.90861i
$236$	−7.51778	+	13.0212i	−0.489366	+	0.847607i
$237$	9.73550	−	1.71663i	0.632389	−	0.111507i
$238$	9.98163	−	1.76003i	0.647013	−	0.114086i
$239$	0.708992	−	1.22801i	0.0458609	−	0.0794334i	−0.842184	−	0.539191i	$-0.818730\pi$
$239$	0.708992	−	1.22801i	0.0458609	−	0.0794334i	0.888045	+	0.459757i	$0.152064\pi$
$240$	−0.490039	−	2.18171i	−0.0316319	−	0.140829i
$241$	11.3459	−	9.52032i	0.730852	−	0.613258i	−0.199511	−	0.979895i	$-0.563936\pi$
$241$	11.3459	−	9.52032i	0.730852	−	0.613258i	0.930364	+	0.366638i	$0.119491\pi$
$242$	−0.195376	−	0.536792i	−0.0125593	−	0.0345063i
$243$	−0.342020	+	0.939693i	−0.0219406	+	0.0602813i
$244$	−1.98734	−	1.66757i	−0.127226	−	0.106755i
$245$	2.84053	+	1.46866i	0.181475	+	0.0938295i
$246$	4.62571			0.294925
$247$	−6.65615	+	6.88052i	−0.423521	+	0.437797i
$248$		−	7.87535i		−	0.500085i
$249$	−2.16408	+	12.2731i	−0.137143	+	0.777775i
$250$	−0.394536	+	11.1734i	−0.0249526	+	0.706666i
$251$	−8.36692	−	3.04531i	−0.528115	−	0.192218i	0.0641814	−	0.997938i	$-0.479556\pi$
$251$	−8.36692	−	3.04531i	−0.528115	−	0.192218i	−0.592297	+	0.805720i	$0.701779\pi$
$252$	−0.807191	−	2.21774i	−0.0508483	−	0.139704i
$253$	−1.57819	−	1.88081i	−0.0992197	−	0.118245i
$254$	−4.90377	−	8.49358i	−0.307690	−	0.532935i
$255$	−6.50739	−	7.06207i	−0.407509	−	0.442244i
$256$	0.173648	+	0.984808i	0.0108530	+	0.0615505i
$257$	−5.90599	+	1.04139i	−0.368406	+	0.0649599i	−0.354786	−	0.934947i	$-0.615446\pi$
$257$	−5.90599	+	1.04139i	−0.368406	+	0.0649599i	−0.0136193	+	0.999907i	$0.504335\pi$
$258$	5.34779	+	3.08755i	0.332939	+	0.192222i
$259$	3.76839	+	6.52705i	0.234156	+	0.405571i
$260$	−4.53188	+	1.89194i	−0.281055	+	0.117333i
$261$	6.23693	−	2.27006i	0.386056	−	0.140513i
$262$	1.89387	−	5.20336i	0.117004	−	0.321465i
$263$	5.34248	−	6.36692i	0.329431	−	0.392601i	−0.575750	−	0.817625i	$-0.695290\pi$
$263$	5.34248	−	6.36692i	0.329431	−	0.392601i	0.905182	+	0.425024i	$0.139734\pi$
$264$	−0.590691	+	3.34997i	−0.0363545	+	0.206177i
$265$	−11.1643	−	3.48602i	−0.685820	−	0.214145i
$266$	−4.50152	−	9.25013i	−0.276006	−	0.567162i
$267$		−	12.5215i		−	0.766305i
$268$	−1.22562	−	0.216110i	−0.0748668	−	0.0132010i
$269$	1.60256	+	1.34471i	0.0977100	+	0.0819885i	0.690334	−	0.723491i	$-0.257464\pi$
$269$	1.60256	+	1.34471i	0.0977100	+	0.0819885i	−0.592624	+	0.805479i	$0.701908\pi$
$270$	−1.35630	+	1.77777i	−0.0825416	+	0.108192i
$271$	24.1210	−	8.77934i	1.46525	−	0.533307i	0.518442	−	0.855113i	$-0.326512\pi$
$271$	24.1210	−	8.77934i	1.46525	−	0.533307i	0.946806	+	0.321806i	$0.104290\pi$
$272$	2.76053	+	3.28987i	0.167382	+	0.199478i
$273$	−4.48885	+	2.59164i	−0.271678	+	0.156853i
$274$	−6.23276	+	10.7955i	−0.376535	+	0.652178i
$275$	7.10221	−	15.4544i	0.428279	−	0.931938i
$276$	0.125335	+	0.710807i	0.00754425	+	0.0427856i
$277$	10.6885	+	6.17102i	0.642211	+	0.370781i	0.785466	−	0.618905i	$-0.212424\pi$
$277$	10.6885	+	6.17102i	0.642211	+	0.370781i	−0.143255	+	0.989686i	$0.545757\pi$
$278$	−13.0958	+	7.56088i	−0.785436	+	0.453472i
$279$	−6.03287	+	5.06218i	−0.361178	+	0.303065i
$280$	−0.244843	−	5.27159i	−0.0146322	−	0.315038i
$281$	−14.3240	−	5.21352i	−0.854499	−	0.311012i	−0.122626	−	0.992453i	$-0.539132\pi$
$281$	−14.3240	−	5.21352i	−0.854499	−	0.311012i	−0.731873	+	0.681441i	$0.761354\pi$
$282$	8.62027	−	10.2732i	0.513330	−	0.611763i
$283$	14.3932	+	2.53790i	0.855585	+	0.150863i	0.584202	−	0.811608i	$-0.301408\pi$
$283$	14.3932	+	2.53790i	0.855585	+	0.150863i	0.271384	+	0.962471i	$0.412519\pi$
$284$	−16.7155			−0.991884
$285$	−5.07689	+	8.32017i	−0.300729	+	0.492844i
$286$	7.47084			0.441760
$287$	10.7511	+	1.89572i	0.634620	+	0.111901i
$288$	0.642788	−	0.766044i	0.0378766	−	0.0451396i
$289$	1.35673	+	0.493810i	0.0798077	+	0.0290476i
$290$	14.8253	−	0.688571i	0.870569	−	0.0404343i
$291$	−1.19800	+	1.00524i	−0.0702281	+	0.0589284i
$292$	1.58927	−	0.917566i	0.0930050	−	0.0536965i
$293$	−2.14417	−	1.23794i	−0.125264	−	0.0723212i	0.436059	−	0.899918i	$-0.356374\pi$
$293$	−2.14417	−	1.23794i	−0.125264	−	0.0723212i	−0.561323	+	0.827597i	$0.689707\pi$
$294$	0.248330	+	1.40835i	0.0144829	+	0.0821365i
$295$	33.3450	+	4.29571i	1.94142	+	0.250106i
$296$	−1.59673	+	2.76562i	−0.0928080	+	0.160748i
$297$	2.94592	−	1.70083i	0.170939	−	0.0986920i
$298$	13.4015	+	15.9713i	0.776329	+	0.925192i
$299$	1.48959	−	0.542166i	0.0861451	−	0.0313542i
$300$	−4.07976	+	2.89060i	−0.235545	+	0.166889i
$301$	11.1641	+	9.36777i	0.643486	+	0.539949i
$302$	6.26226	+	1.10421i	0.360353	+	0.0635399i
$303$		−	1.08648i		−	0.0624165i
$304$	2.44064	−	3.61155i	0.139981	−	0.207136i
$305$	−1.72901	+	5.53733i	−0.0990028	+	0.317067i
$306$	0.745754	−	4.22938i	0.0426319	−	0.241778i
$307$	−14.3947	+	17.1550i	−0.821551	+	0.979087i	−0.999988	−	0.00486479i	$-0.998451\pi$
$307$	−14.3947	+	17.1550i	−0.821551	+	0.979087i	0.178437	+	0.983951i	$0.442896\pi$
$308$	−2.74578	+	7.54398i	−0.156456	+	0.429858i
$309$	−8.40438	+	3.05895i	−0.478109	+	0.174017i
$310$	−16.2506	+	6.78418i	−0.922970	+	0.385315i
$311$	6.71903	+	11.6377i	0.381001	+	0.659914i	0.991206	−	0.132330i	$-0.0422460\pi$
$311$	6.71903	+	11.6377i	0.381001	+	0.659914i	−0.610204	+	0.792244i	$0.708913\pi$
$312$	−1.90200	−	1.09812i	−0.107680	−	0.0621688i
$313$	32.7312	−	5.77139i	1.85007	−	0.326218i	0.865463	−	0.500973i	$-0.167025\pi$
$313$	32.7312	−	5.77139i	1.85007	−	0.326218i	0.984612	+	0.174755i	$0.0559134\pi$
$314$	−0.939341	−	5.32727i	−0.0530101	−	0.300635i
$315$	−3.88089	+	3.57607i	−0.218663	+	0.201489i
$316$	4.94284	+	8.56126i	0.278057	+	0.481608i
$317$	12.7108	+	15.1481i	0.713909	+	0.850803i	0.994024	−	0.109163i	$-0.0348171\pi$
$317$	12.7108	+	15.1481i	0.713909	+	0.850803i	−0.280115	+	0.959966i	$0.590373\pi$
$318$	−1.78896	−	4.91514i	−0.100320	−	0.275627i
$319$	−21.2159	−	7.72195i	−1.18786	−	0.432346i
$320$	1.88253	−	1.20668i	0.105237	−	0.0674552i
$321$	−1.15035	+	6.52398i	−0.0642065	+	0.364133i
$322$			1.70343i			0.0949286i
$323$	1.32226	−	18.6731i	0.0735725	−	1.03900i
$324$	−1.00000			−0.0555556
$325$	7.80792	+	7.72160i	0.433105	+	0.428317i
$326$	−4.15102	−	3.48312i	−0.229904	−	0.192912i
$327$	1.27598	−	3.50573i	0.0705620	−	0.193867i
$328$	1.58209	+	4.34675i	0.0873561	+	0.240009i
$329$	24.2456	−	20.3444i	1.33670	−	1.12163i
$330$	7.42142	−	1.66694i	0.408536	−	0.0917622i
$331$	−2.71112	+	4.69579i	−0.149016	+	0.258104i	−0.930864	−	0.365365i	$-0.880944\pi$
$331$	−2.71112	+	4.69579i	−0.149016	+	0.258104i	0.781848	+	0.623469i	$0.214277\pi$
$332$	−12.2731	+	2.16408i	−0.673573	+	0.118769i
$333$	3.14494	−	0.554538i	0.172342	−	0.0303885i
$334$	−0.0656462	+	0.113703i	−0.00359200	+	0.00622153i
$335$	0.609868	+	2.71520i	0.0333206	+	0.148347i
$336$	1.80792	−	1.51702i	0.0986300	−	0.0827604i
$337$	−6.18025	−	16.9801i	−0.336660	−	0.924965i	−0.986335	−	0.164753i	$-0.947317\pi$
$337$	−6.18025	−	16.9801i	−0.336660	−	0.924965i	0.649675	−	0.760212i	$-0.274905\pi$
$338$	2.79654	−	7.68343i	0.152112	−	0.417923i
$339$	−1.22256	−	1.02585i	−0.0664001	−	0.0557163i
$340$	4.41052	−	8.53032i	0.239194	−	0.462622i
$341$	26.7892			1.45072
$342$	−4.33542	+	0.451815i	−0.234433	+	0.0244313i
$343$			19.8956i			1.07426i
$344$	−1.07229	+	6.08128i	−0.0578142	+	0.327881i
$345$	1.35876	−	0.870945i	0.0731533	−	0.0468901i
$346$	−21.7584	−	7.91940i	−1.16974	−	0.425749i
$347$	−9.84824	−	27.0578i	−0.528681	−	1.45254i	−0.860624	−	0.509240i	$-0.829927\pi$
$347$	−9.84824	−	27.0578i	−0.528681	−	1.45254i	0.331943	−	0.943299i	$-0.392296\pi$
$348$	4.26631	+	5.08439i	0.228698	+	0.272552i
$349$	−2.03263	−	3.52062i	−0.108804	−	0.188455i	0.806482	−	0.591259i	$-0.201369\pi$
$349$	−2.03263	−	3.52062i	−0.108804	−	0.188455i	−0.915286	+	0.402804i	$0.868036\pi$
$350$	−10.6669	+	5.04641i	−0.570168	+	0.269742i
$351$	0.381373	+	2.16287i	0.0203562	+	0.115446i
$352$	−3.34997	+	0.590691i	−0.178554	+	0.0314839i
$353$	−29.7905	−	17.1995i	−1.58559	−	0.915439i	−0.994022	−	0.109182i	$-0.965177\pi$
$353$	−29.7905	−	17.1995i	−1.58559	−	0.915439i	−0.591565	−	0.806257i	$-0.701490\pi$
$354$	7.51778	+	13.0212i	0.399566	+	0.692068i
$355$	14.3995	+	34.4920i	0.764245	+	1.83064i
$356$	11.7664	−	4.28261i	0.623617	−	0.226978i
$357$	3.46658	−	9.52436i	0.183471	−	0.504083i
$358$	4.44737	−	5.30017i	0.235051	−	0.280123i
$359$	3.20114	−	18.1545i	0.168949	−	0.958160i	−0.775949	−	0.630796i	$-0.782728\pi$
$359$	3.20114	−	18.1545i	0.168949	−	0.958160i	0.944898	−	0.327364i	$-0.106160\pi$
$360$	−2.13444	−	0.666469i	−0.112495	−	0.0351260i
$361$	−18.5917	+	3.91761i	−0.978512	+	0.206190i
$362$		−	7.86597i		−	0.413426i
$363$	−0.562563	−	0.0991951i	−0.0295269	−	0.00520639i
$364$	−3.97062	−	3.33175i	−0.208117	−	0.174631i
$365$	−3.26244	−	2.48898i	−0.170764	−	0.130279i
$366$	−2.43783	+	0.887297i	−0.127427	+	0.0463798i
$367$	−19.9819	−	23.8135i	−1.04305	−	1.24305i	−0.969327	−	0.245774i	$-0.920958\pi$
$367$	−19.9819	−	23.8135i	−1.04305	−	1.24305i	−0.0737184	−	0.997279i	$-0.523487\pi$
$368$	−0.625074	+	0.360886i	−0.0325842	+	0.0188125i
$369$	2.31286	−	4.00598i	0.120402	−	0.208543i
$370$	7.08226	+	0.912381i	0.368189	+	0.0474324i
$371$	−2.14361	−	12.1570i	−0.111291	−	0.631160i
$372$	−6.82025	−	3.93768i	−0.353614	−	0.204159i
$373$	−0.609390	+	0.351832i	−0.0315530	+	0.0182172i	−0.515694	−	0.856773i	$-0.672466\pi$
$373$	−0.609390	+	0.351832i	−0.0315530	+	0.0182172i	0.484141	+	0.874990i	$0.339132\pi$
$374$	−11.1910	+	9.39037i	−0.578673	+	0.485564i
$375$	9.47916	+	5.92837i	0.489502	+	0.306140i
$376$	12.6020	+	4.58675i	0.649898	+	0.236544i
$377$	9.36985	−	11.1665i	0.482572	−	0.575106i
$378$	−2.32421	−	0.409822i	−0.119545	−	0.0210790i
$379$	−5.85859			−0.300936			−0.150468	−	0.988615i	$-0.548078\pi$
$379$	−5.85859			−0.300936			−0.150468	+	0.988615i	$0.548078\pi$
$380$	−9.55480	−	1.92505i	−0.490151	−	0.0987532i
$381$	−9.80755			−0.502456
$382$	−17.9671	−	3.16809i	−0.919279	−	0.162094i
$383$	−9.06045	+	10.7978i	−0.462967	+	0.551743i	−0.946130	−	0.323788i	$-0.895044\pi$
$383$	−9.06045	+	10.7978i	−0.462967	+	0.551743i	0.483162	+	0.875531i	$0.339488\pi$
$384$	0.939693	+	0.342020i	0.0479535	+	0.0174536i
$385$	17.9321	−	0.832871i	0.913906	−	0.0424471i
$386$	15.7704	−	13.2330i	0.802693	−	0.673540i
$387$	5.34779	−	3.08755i	0.271844	−	0.156949i
$388$	−1.35436	−	0.781940i	−0.0687572	−	0.0396970i
$389$	−4.74904	−	26.9331i	−0.240786	−	1.36556i	−0.830079	−	0.557645i	$-0.811705\pi$
$389$	−4.74904	−	26.9331i	−0.240786	−	1.36556i	0.589294	−	0.807919i	$-0.299406\pi$
$390$	−0.627472	+	4.87069i	−0.0317733	+	0.246637i
$391$	−1.54987	+	2.68446i	−0.0783804	+	0.135759i
$392$	−1.23848	+	0.715037i	−0.0625527	+	0.0361148i
$393$	−3.55931	−	4.24182i	−0.179543	−	0.213971i
$394$	18.6031	−	6.77096i	0.937208	−	0.341116i
$395$	13.4079	−	17.5745i	0.674626	−	0.884267i
$396$	2.60582	+	2.18654i	0.130947	+	0.109878i
$397$	8.37742	+	1.47717i	0.420451	+	0.0741368i	0.379871	−	0.925040i	$-0.375968\pi$
$397$	8.37742	+	1.47717i	0.420451	+	0.0741368i	0.0405798	+	0.999176i	$0.487080\pi$
$398$			13.9674i			0.700124i
$399$	−10.2616	−	0.726635i	−0.513723	−	0.0363772i
$400$	−4.11164	−	2.84507i	−0.205582	−	0.142254i
$401$	−0.357851	+	2.02947i	−0.0178702	+	0.101347i	−0.992438	−	0.122745i	$-0.960830\pi$
$401$	−0.357851	+	2.02947i	−0.0178702	+	0.101347i	0.974568	+	0.224092i	$0.0719415\pi$
$402$	−0.799968	+	0.953365i	−0.0398988	+	0.0475495i
$403$	−5.91563	+	16.2531i	−0.294679	+	0.809623i
$404$	1.02095	−	0.371597i	0.0507944	−	0.0184876i
$405$	0.861444	+	2.06347i	0.0428055	+	0.102535i
$406$	7.83213	+	13.5656i	0.388702	+	0.673252i
$407$	−9.40767	−	5.43152i	−0.466321	−	0.269230i
$408$	4.22938	−	0.745754i	0.209386	−	0.0369203i
$409$	−1.45770	−	8.26701i	−0.0720785	−	0.408777i	−0.999404	−	0.0345214i	$-0.989009\pi$
$409$	−1.45770	−	8.26701i	−0.0720785	−	0.408777i	0.927326	−	0.374256i	$-0.122102\pi$
$410$	7.60651	−	7.00907i	0.375659	−	0.346153i
$411$	6.23276	+	10.7955i	0.307440	+	0.532501i
$412$	−5.74894	−	6.85132i	−0.283230	−	0.337540i
$413$	12.1366	+	33.3450i	0.597202	+	1.64080i
$414$	0.678245	+	0.246861i	0.0333339	+	0.0121325i
$415$	15.0381	+	23.4609i	0.738191	+	1.15165i
$416$	0.381373	−	2.16287i	0.0186983	−	0.106044i
$417$			15.1218i			0.740516i
$418$	12.2852	+	8.30222i	0.600890	+	0.406075i
$419$	−32.6721			−1.59614			−0.798068	−	0.602568i	$-0.794144\pi$
$419$	−32.6721			−1.59614			−0.798068	+	0.602568i	$0.794144\pi$
$420$	−4.68775	−	2.42376i	−0.228739	−	0.118267i
$421$	13.9741	+	11.7257i	0.681057	+	0.571474i	0.916315	−	0.400458i	$-0.131149\pi$
$421$	13.9741	+	11.7257i	0.681057	+	0.571474i	−0.235258	+	0.971933i	$0.575594\pi$
$422$	−3.02471	+	8.31032i	−0.147241	+	0.404540i
$423$	−4.58675	−	12.6020i	−0.223015	−	0.612730i
$424$	4.00686	−	3.36215i	0.194590	−	0.163281i
$425$	−21.4015	−	1.75258i	−1.03812	−	0.0850124i
$426$	−8.35776	+	14.4761i	−0.404935	+	0.701368i
$427$	−6.02967	+	1.06319i	−0.291796	+	0.0514516i
$428$	−6.52398	+	1.15035i	−0.315348	+	0.0556044i
$429$	3.73542	−	6.46994i	0.180348	−	0.312372i
$430$	13.4723	−	3.02604i	0.649691	−	0.145929i
$431$	−4.38687	+	3.68102i	−0.211308	+	0.177309i	−0.742299	−	0.670069i	$-0.766264\pi$
$431$	−4.38687	+	3.68102i	−0.211308	+	0.177309i	0.530990	+	0.847378i	$0.321820\pi$
$432$	−0.342020	−	0.939693i	−0.0164555	−	0.0452110i
$433$	6.32153	−	17.3683i	0.303793	−	0.834665i	−0.690039	−	0.723772i	$-0.742407\pi$
$433$	6.32153	−	17.3683i	0.303793	−	0.834665i	0.993832	−	0.110893i	$-0.0353711\pi$
$434$	−14.2380	−	11.9471i	−0.683445	−	0.573479i
$435$	6.81631	−	13.1833i	0.326817	−	0.632093i
$436$	3.73072			0.178669
$437$	3.05201	+	0.763804i	0.145997	+	0.0365377i
$438$		−	1.83513i		−	0.0876860i
$439$	2.02842	−	11.5038i	0.0968113	−	0.549044i	−0.897366	−	0.441287i	$-0.854522\pi$
$439$	2.02842	−	11.5038i	0.0968113	−	0.549044i	0.994177	−	0.107757i	$-0.0343668\pi$
$440$	4.10469	+	6.40373i	0.195683	+	0.305286i
$441$	1.34383	+	0.489114i	0.0639919	+	0.0232912i
$442$	−3.22594	−	8.86320i	−0.153442	−	0.421580i
$443$	−1.45549	−	1.73459i	−0.0691526	−	0.0824128i	0.730359	−	0.683063i	$-0.239353\pi$
$443$	−1.45549	−	1.73459i	−0.0691526	−	0.0824128i	−0.799512	+	0.600651i	$0.794908\pi$
$444$	1.59673	+	2.76562i	0.0757774	+	0.131250i
$445$	−18.9731	−	20.5904i	−0.899412	−	0.976076i
$446$	−4.81845	−	27.3268i	−0.228160	−	1.29396i
$447$	20.5323	−	3.62040i	0.971145	−	0.171239i
$448$	2.04388	+	1.18003i	0.0965642	+	0.0557514i
$449$	−19.5230	−	33.8148i	−0.921346	−	1.59582i	−0.797334	−	0.603538i	$-0.793757\pi$
$449$	−19.5230	−	33.8148i	−0.921346	−	1.59582i	−0.124012	−	0.992281i	$-0.539576\pi$
$450$	0.463458	+	4.97847i	0.0218476	+	0.234688i
$451$	−14.7861	+	5.38171i	−0.696251	+	0.253415i
$452$	0.545842	−	1.49969i	0.0256742	−	0.0705394i
$453$	4.08740	−	4.87118i	0.192043	−	0.228868i
$454$	1.34622	−	7.63481i	0.0631814	−	0.358319i
$455$	−3.45449	+	11.0634i	−0.161949	+	0.518659i
$456$	−1.90737	−	3.91943i	−0.0893207	−	0.183544i
$457$			13.3920i			0.626451i	0.949679	+	0.313225i	$0.101410\pi$
$457$			13.3920i			0.626451i	−0.949679	+	0.313225i	$0.898590\pi$
$458$	7.63819	+	1.34682i	0.356909	+	0.0629327i
$459$	−3.28987	−	2.76053i	−0.153558	−	0.128851i
$460$	1.28314	+	0.978938i	0.0598269	+	0.0456432i
$461$	7.26036	−	2.64256i	0.338149	−	0.123076i	−0.167364	−	0.985895i	$-0.553526\pi$
$461$	7.26036	−	2.64256i	0.338149	−	0.123076i	0.505513	+	0.862819i	$0.331303\pi$
$462$	5.16039	+	6.14991i	0.240083	+	0.286120i
$463$	−4.12534	+	2.38177i	−0.191721	+	0.110690i	−0.592788	−	0.805359i	$-0.701973\pi$
$463$	−4.12534	+	2.38177i	−0.191721	+	0.110690i	0.401067	+	0.916049i	$0.368639\pi$
$464$	−3.31860	+	5.74799i	−0.154062	+	0.266844i
$465$	−2.25001	+	17.4655i	−0.104342	+	0.809942i
$466$	−1.99360	−	11.3062i	−0.0923515	−	0.523752i
$467$	12.9615	+	7.48335i	0.599788	+	0.346288i	0.768958	−	0.639299i	$-0.220775\pi$
$467$	12.9615	+	7.48335i	0.599788	+	0.346288i	−0.169170	+	0.985587i	$0.554109\pi$
$468$	−1.90200	+	1.09812i	−0.0879199	+	0.0507606i
$469$	−2.25001	+	1.88798i	−0.103896	+	0.0871788i
$470$	−1.39129	−	29.9551i	−0.0641753	−	1.38173i
$471$	−5.08322	−	1.85014i	−0.234222	−	0.0852500i
$472$	−9.66467	+	11.5179i	−0.444853	+	0.530155i
$473$	−20.6864	−	3.64757i	−0.951162	−	0.167716i
$474$	9.88569			0.454065
$475$	4.25863	+	21.3744i	0.195399	+	0.980724i
$476$	10.1356			0.464565
$477$	−5.15112	−	0.908281i	−0.235854	−	0.0415873i
$478$	0.911462	−	1.08624i	0.0416893	−	0.0496834i
$479$	28.2334	+	10.2761i	1.29002	+	0.469528i	0.893733	−	0.448599i	$-0.148077\pi$
$479$	28.2334	+	10.2761i	1.29002	+	0.469528i	0.396285	+	0.918127i	$0.370299\pi$
$480$	−0.103744	−	2.23366i	−0.00473525	−	0.101952i
$481$	5.37273	−	4.50826i	0.244975	−	0.205559i
$482$	12.8267	−	7.40550i	0.584240	−	0.337311i
$483$	1.47522	+	0.851717i	0.0671247	+	0.0387545i
$484$	−0.0991951	−	0.562563i	−0.00450887	−	0.0255711i
$485$	−0.446805	+	3.46828i	−0.0202884	+	0.157486i
$486$	−0.500000	+	0.866025i	−0.0226805	+	0.0392837i
$487$	−16.0349	+	9.25773i	−0.726609	+	0.419508i	−0.817180	−	0.576382i	$-0.804464\pi$
$487$	−16.0349	+	9.25773i	−0.726609	+	0.419508i	0.0905715	+	0.995890i	$0.471131\pi$
$488$	−1.66757	−	1.98734i	−0.0754875	−	0.0899625i
$489$	−5.09197	+	1.85333i	−0.230267	+	0.0838104i
$490$	2.54234	+	1.93960i	0.114851	+	0.0876224i
$491$	1.95883	+	1.64366i	0.0884009	+	0.0741771i	0.685917	−	0.727680i	$-0.259401\pi$
$491$	1.95883	+	1.64366i	0.0884009	+	0.0741771i	−0.597516	+	0.801857i	$0.703846\pi$
$492$	4.55544	+	0.803246i	0.205375	+	0.0362131i
$493$			28.5043i			1.28377i
$494$	−7.74982	+	5.62016i	−0.348681	+	0.252863i
$495$	2.26710	−	7.26061i	0.101898	−	0.326340i
$496$	1.36754	−	7.75571i	0.0614044	−	0.348241i
$497$	−25.3578	+	30.2203i	−1.13745	+	1.35556i
$498$	−4.26240	+	11.7108i	−0.191003	+	0.524775i
$499$	−36.7788	+	13.3864i	−1.64644	+	0.599257i	−0.988148	−	0.153502i	$-0.950945\pi$
$499$	−36.7788	+	13.3864i	−1.64644	+	0.599257i	−0.658297	+	0.752759i	$0.728723\pi$
$500$	−2.32878	+	10.9351i	−0.104146	+	0.489033i
$501$	0.0656462	+	0.113703i	0.00293286	+	0.00507986i
$502$	−7.71099	−	4.45194i	−0.344158	−	0.198700i
$503$	18.3464	−	3.23496i	0.818025	−	0.144240i	0.251049	−	0.967974i	$-0.419224\pi$
$503$	18.3464	−	3.23496i	0.818025	−	0.144240i	0.566976	+	0.823734i	$0.308113\pi$
$504$	−0.409822	−	2.32421i	−0.0182549	−	0.103529i
$505$	−1.64628	−	1.78660i	−0.0732583	−	0.0795027i
$506$	−1.22761	−	2.12628i	−0.0545739	−	0.0945248i
$507$	−5.25577	−	6.26359i	−0.233417	−	0.278176i
$508$	−3.35438	−	9.21608i	−0.148826	−	0.408897i
$509$	8.45637	+	3.07787i	0.374822	+	0.136424i	0.522560	−	0.852602i	$-0.324977\pi$
$509$	8.45637	+	3.07787i	0.374822	+	0.136424i	−0.147738	+	0.989027i	$0.547199\pi$
$510$	−5.18222	−	8.08478i	−0.229472	−	0.358000i
$511$	0.752077	−	4.26524i	0.0332699	−	0.188683i
$512$			1.00000i			0.0441942i
$513$	−1.77643	+	3.98049i	−0.0784312	+	0.175743i
$514$	−5.99710			−0.264521
$515$	−9.18510	+	17.7648i	−0.404744	+	0.782810i
$516$	4.73040	+	3.96928i	0.208244	+	0.174738i
$517$	−15.6025	+	42.8676i	−0.686199	+	1.88532i
$518$	2.57773	+	7.08226i	0.113259	+	0.311177i
$519$	−17.7376	+	14.8836i	−0.778594	+	0.653318i
$520$	−4.79156	+	1.07624i	−0.210124	+	0.0471964i
$521$	−11.6877	+	20.2436i	−0.512046	+	0.886890i	0.487856	+	0.872924i	$0.337779\pi$
$521$	−11.6877	+	20.2436i	−0.512046	+	0.886890i	−0.999902	+	0.0139663i	$0.995554\pi$
$522$	6.53637	−	1.15254i	0.286089	−	0.0504452i
$523$	−21.5925	+	3.80733i	−0.944173	+	0.166483i	−0.624482	−	0.781039i	$-0.714690\pi$
$523$	−21.5925	+	3.80733i	−0.944173	+	0.166483i	−0.319690	+	0.947522i	$0.603579\pi$
$524$	2.76865	−	4.79544i	0.120949	−	0.209490i
$525$	−0.963111	+	11.7610i	−0.0420336	+	0.513291i
$526$	6.36692	−	5.34248i	0.277611	−	0.232943i
$527$	−11.5677	−	31.7820i	−0.503897	−	1.38444i
$528$	−1.16343	+	3.19651i	−0.0506320	+	0.139110i
$529$	17.2199	+	14.4493i	0.748693	+	0.628228i
$530$	−10.3894	−	5.37173i	−0.451286	−	0.233333i
$531$	15.0356			0.652488
$532$	−2.82686	−	9.89128i	−0.122560	−	0.428841i
$533$		−	10.1592i		−	0.440042i
$534$	2.17434	−	12.3313i	0.0940929	−	0.533627i
$535$	7.99377	+	12.4711i	0.345601	+	0.539172i
$536$	−1.16947	−	0.425654i	−0.0505136	−	0.0183855i
$537$	−2.36639	−	6.50162i	−0.102117	−	0.280565i
$538$	1.34471	+	1.60256i	0.0579746	+	0.0690914i
$539$	−2.43231	−	4.21288i	−0.104767	−	0.181462i
$540$	−1.64440	+	1.51524i	−0.0707636	+	0.0652056i
$541$	5.42104	+	30.7443i	0.233069	+	1.32180i	0.846643	+	0.532162i	$0.178620\pi$
$541$	5.42104	+	30.7443i	0.233069	+	1.32180i	−0.613574	+	0.789637i	$0.710269\pi$
$542$	25.2791	−	4.45739i	1.08583	−	0.191461i
$543$	−6.81213	−	3.93299i	−0.292336	−	0.168781i
$544$	2.14731	+	3.71925i	0.0920653	+	0.159462i
$545$	−3.21381	−	7.69824i	−0.137664	−	0.329756i
$546$	−4.87069	+	1.77279i	−0.208446	+	0.0758682i
$547$	−1.53285	+	4.21147i	−0.0655400	+	0.180070i	−0.968139	−	0.250412i	$-0.919434\pi$
$547$	−1.53285	+	4.21147i	−0.0655400	+	0.180070i	0.902599	+	0.430481i	$0.141656\pi$
$548$	−8.01269	+	9.54915i	−0.342285	+	0.407919i
$549$	−0.450493	+	2.55487i	−0.0192266	+	0.109039i
$550$	9.67795	−	13.9864i	0.412669	−	0.596381i
$551$	27.8172	−	7.94997i	1.18505	−	0.338680i
$552$			0.721773i			0.0307207i
$553$	22.9765	+	4.05137i	0.977058	+	0.172282i
$554$	9.45455	+	7.93331i	0.401685	+	0.337054i
$555$	4.33128	−	5.67723i	0.183852	−	0.240985i
$556$	−14.2098	+	5.17195i	−0.602630	+	0.219340i
$557$	8.09188	+	9.64353i	0.342864	+	0.408609i	0.909730	−	0.415201i	$-0.136289\pi$
$557$	8.09188	+	9.64353i	0.342864	+	0.408609i	−0.566866	+	0.823810i	$0.691844\pi$
$558$	−6.82025	+	3.93768i	−0.288724	+	0.166695i
$559$	6.78100	−	11.7450i	0.286806	−	0.496762i
$560$	0.674279	−	5.23402i	0.0284935	−	0.221178i
$561$	2.53680	+	14.3869i	0.107104	+	0.607415i
$562$	−13.2011	−	7.62165i	−0.556854	−	0.321500i
$563$	−14.1441	+	8.16610i	−0.596102	+	0.344160i	−0.767507	−	0.641041i	$-0.778503\pi$
$563$	−14.1441	+	8.16610i	−0.596102	+	0.344160i	0.171404	+	0.985201i	$0.445170\pi$
$564$	10.2732	−	8.62027i	0.432581	−	0.362979i
$565$	−3.56477	+	0.165569i	−0.149971	+	0.00696553i
$566$	13.7338	+	4.99870i	0.577275	+	0.210111i
$567$	−1.51702	+	1.80792i	−0.0637090	+	0.0759254i
$568$	−16.4616	−	2.90262i	−0.690712	−	0.121791i
$569$	−26.3518			−1.10473			−0.552363	−	0.833603i	$-0.686274\pi$
$569$	−26.3518			−1.10473			−0.552363	+	0.833603i	$0.686274\pi$
$570$	−6.44454	+	7.31217i	−0.269932	+	0.306273i
$571$	−29.5610			−1.23709			−0.618546	−	0.785749i	$-0.712278\pi$
$571$	−29.5610			−1.23709			−0.618546	+	0.785749i	$0.712278\pi$
$572$	7.35735	+	1.29730i	0.307626	+	0.0542428i
$573$	−11.7272	+	13.9760i	−0.489912	+	0.583854i
$574$	10.2586	+	3.73383i	0.428187	+	0.155847i
$575$	0.914652	−	3.49103i	0.0381436	−	0.145586i
$576$	0.766044	−	0.642788i	0.0319185	−	0.0267828i
$577$	2.74833	−	1.58675i	0.114414	−	0.0660572i	−0.441701	−	0.897162i	$-0.645625\pi$
$577$	2.74833	−	1.58675i	0.114414	−	0.0660572i	0.556115	+	0.831105i	$0.312291\pi$
$578$	1.25037	+	0.721902i	0.0520086	+	0.0300272i
$579$	−3.57486	−	20.2741i	−0.148566	−	0.842561i
$580$	14.7196	+	1.89627i	0.611198	+	0.0787383i
$581$	−14.7061	+	25.4717i	−0.610111	+	1.05674i
$582$	−1.35436	+	0.781940i	−0.0561400	+	0.0324125i
$583$	11.4369	+	13.6299i	0.473667	+	0.564495i
$584$	1.72446	−	0.627652i	0.0713587	−	0.0259724i
$585$	3.90440	+	2.97875i	0.161427	+	0.123156i
$586$	−1.89663	−	1.59146i	−0.0783492	−	0.0657428i
$587$	1.31575	+	0.232003i	0.0543069	+	0.00957577i	0.200736	−	0.979645i	$-0.435667\pi$
$587$	1.31575	+	0.232003i	0.0543069	+	0.00957577i	−0.146429	+	0.989221i	$0.546778\pi$
$588$			1.43007i			0.0589753i
$589$	−27.7896	+	20.1530i	−1.14505	+	0.830388i
$590$	32.0925	+	10.0207i	1.32123	+	0.412547i
$591$	3.43771	−	19.4962i	0.141408	−	0.801966i
$592$	−2.05272	+	2.44633i	−0.0843661	+	0.100544i
$593$	−9.96925	+	27.3903i	−0.409388	+	1.12478i	0.548125	+	0.836396i	$0.315342\pi$
$593$	−9.96925	+	27.3903i	−0.409388	+	1.12478i	−0.957513	+	0.288389i	$0.906881\pi$
$594$	3.19651	−	1.16343i	0.131154	−	0.0477363i
$595$	−8.73126	−	20.9145i	−0.357947	−	0.857413i
$596$	10.4245	+	18.0558i	0.427005	+	0.739595i
$597$	12.0961	+	6.98371i	0.495062	+	0.285824i
$598$	1.56110	−	0.275265i	0.0638383	−	0.0112564i
$599$	0.365078	+	2.07046i	0.0149167	+	0.0845966i	0.991357	−	0.131190i	$-0.0418797\pi$
$599$	0.365078	+	2.07046i	0.0149167	+	0.0845966i	−0.976441	+	0.215786i	$0.930769\pi$
$600$	−4.51972	+	2.13825i	−0.184517	+	0.0872936i
$601$	16.2457	+	28.1384i	0.662676	+	1.14779i	0.979910	+	0.199441i	$0.0639127\pi$
$601$	16.2457	+	28.1384i	0.662676	+	1.14779i	−0.317234	+	0.948347i	$0.602754\pi$
$602$	9.36777	+	11.1641i	0.381802	+	0.455013i
$603$	0.425654	+	1.16947i	0.0173340	+	0.0476247i
$604$	5.97538	+	2.17486i	0.243135	+	0.0884938i
$605$	−1.07538	+	0.689303i	−0.0437205	+	0.0280242i
$606$	0.188665	−	1.06997i	0.00766398	−	0.0434646i
$607$			34.2262i			1.38920i	0.719397	+	0.694599i	$0.244418\pi$
$607$			34.2262i			1.38920i	−0.719397	+	0.694599i	$0.755582\pi$
$608$	3.03070	−	3.13286i	0.122911	−	0.127054i
$609$	15.6643			0.634748
$610$	−2.66429	+	5.15297i	−0.107874	+	0.208638i
$611$	−22.5625	−	18.9322i	−0.912781	−	0.765914i
$612$	1.46885	−	4.03563i	0.0593747	−	0.163131i
$613$	−11.6361	−	31.9699i	−0.469977	−	1.29125i	−0.917769	−	0.397114i	$-0.870012\pi$
$613$	−11.6361	−	31.9699i	−0.469977	−	1.29125i	0.447792	−	0.894138i	$-0.352210\pi$
$614$	−17.1550	+	14.3947i	−0.692319	+	0.580924i
$615$	−2.26678	−	10.0920i	−0.0914053	−	0.406947i
$616$	−4.01407	+	6.95257i	−0.161731	+	0.280127i
$617$	14.4637	−	2.55034i	0.582287	−	0.102673i	0.125257	−	0.992124i	$-0.460024\pi$
$617$	14.4637	−	2.55034i	0.582287	−	0.102673i	0.457030	+	0.889451i	$0.348913\pi$
$618$	−8.80788	+	1.55307i	−0.354305	+	0.0624735i
$619$	0.262033	−	0.453855i	0.0105320	−	0.0182420i	−0.860711	−	0.509093i	$-0.829981\pi$
$619$	0.262033	−	0.453855i	0.0105320	−	0.0182420i	0.871243	+	0.490851i	$0.163314\pi$
$620$	−17.1817	+	3.85923i	−0.690035	+	0.154990i
$621$	0.552910	−	0.463947i	0.0221875	−	0.0186175i
$622$	4.59609	+	12.6277i	0.184286	+	0.506323i
$623$	10.1073	−	27.7695i	0.404939	−	1.11256i
$624$	−1.68242	−	1.41172i	−0.0673506	−	0.0565139i
$625$	24.5704	−	4.61463i	0.982817	−	0.184585i
$626$	33.2361			1.32838
$627$	13.3325	−	6.48820i	0.532451	−	0.259114i
$628$		−	5.40945i		−	0.215860i
$629$	−2.38153	+	13.5064i	−0.0949580	+	0.538534i
$630$	−4.44291	+	2.84784i	−0.177010	+	0.113461i
$631$	43.9457	+	15.9949i	1.74945	+	0.636748i	0.999688	−	0.0249586i	$-0.00794541\pi$
$631$	43.9457	+	15.9949i	1.74945	+	0.636748i	0.749763	+	0.661707i	$0.230168\pi$
$632$	3.38110	+	9.28951i	0.134493	+	0.369517i
$633$	5.68460	+	6.77464i	0.225942	+	0.269268i
$634$	9.88723	+	17.1252i	0.392672	+	0.680128i
$635$	−16.1275	+	14.8608i	−0.640001	+	0.589733i
$636$	−0.908281	−	5.15112i	−0.0360157	−	0.204255i
$637$	3.09307	−	0.545392i	0.122552	−	0.0216092i
$638$	−19.5527	−	11.2887i	−0.774097	−	0.446925i
$639$	8.35776	+	14.4761i	0.330628	+	0.572664i
$640$	2.06347	−	0.861444i	0.0815659	−	0.0340516i
$641$	15.7203	−	5.72171i	0.620913	−	0.225994i	−0.0123584	−	0.999924i	$-0.503934\pi$
$641$	15.7203	−	5.72171i	0.620913	−	0.225994i	0.633271	+	0.773930i	$0.281712\pi$
$642$	−2.26575	+	6.22511i	−0.0894222	+	0.245685i
$643$	−11.6423	+	13.8748i	−0.459128	+	0.547168i	−0.945089	−	0.326813i	$-0.894025\pi$
$643$	−11.6423	+	13.8748i	−0.459128	+	0.547168i	0.485961	+	0.873981i	$0.338470\pi$
$644$	−0.295798	+	1.67755i	−0.0116561	+	0.0661049i
$645$	4.11551	−	13.1804i	0.162048	−	0.518976i
$646$	4.54472	−	18.1598i	0.178810	−	0.714487i
$647$		−	4.88290i		−	0.191967i	−0.995383	−	0.0959833i	$-0.969400\pi$
$647$		−	4.88290i		−	0.191967i	0.995383	−	0.0959833i	$-0.0305995\pi$
$648$	−0.984808	−	0.173648i	−0.0386869	−	0.00682154i
$649$	−39.1799	−	32.8759i	−1.53795	−	1.29049i
$650$	6.34846	+	8.96012i	0.249007	+	0.351445i
$651$	−17.4655	+	6.35691i	−0.684526	+	0.249147i
$652$	−3.48312	−	4.15102i	−0.136409	−	0.162566i
$653$	31.5857	−	18.2360i	1.23604	−	0.713630i	0.267760	−	0.963486i	$-0.413716\pi$
$653$	31.5857	−	18.2360i	1.23604	−	0.713630i	0.968283	+	0.249855i	$0.0803831\pi$
$654$	1.86536	−	3.23090i	0.0729414	−	0.126338i
$655$	−12.2803	−	1.58202i	−0.479831	−	0.0618147i
$656$	0.803246	+	4.55544i	0.0313615	+	0.177860i
$657$	−1.58927	−	0.917566i	−0.0620034	−	0.0357977i
$658$	27.4100	−	15.8252i	1.06855	−	0.616929i
$659$	−24.2507	+	20.3488i	−0.944675	+	0.792676i	−0.978393	−	0.206755i	$-0.933710\pi$
$659$	−24.2507	+	20.3488i	−0.944675	+	0.792676i	0.0337179	+	0.999431i	$0.489265\pi$
$660$	7.59814	−	0.352901i	0.295757	−	0.0137367i
$661$	−46.4561	−	16.9086i	−1.80693	−	0.657670i	−0.997516	−	0.0704344i	$-0.977561\pi$
$661$	−46.4561	−	16.9086i	−1.80693	−	0.657670i	−0.809416	−	0.587235i	$-0.800216\pi$
$662$	−3.48535	+	4.15367i	−0.135462	+	0.161437i
$663$	−9.28873	−	1.63785i	−0.360744	−	0.0636090i
$664$	−12.4624			−0.483635
$665$	−17.9752	+	14.3539i	−0.697048	+	0.556622i
$666$	3.19346			0.123744
$667$	−4.71777	−	0.831871i	−0.182673	−	0.0322102i
$668$	−0.0843931	+	0.100576i	−0.00326527	+	0.00389139i
$669$	−26.0749	−	9.49050i	−1.00811	−	0.366924i
$670$	0.129113	+	2.77985i	0.00498805	+	0.107395i
$671$	6.76023	−	5.67251i	0.260976	−	0.218985i
$672$	2.04388	−	1.18003i	0.0788444	−	0.0455208i
$673$	−33.8475	−	19.5418i	−1.30472	−	0.753283i	−0.323514	−	0.946223i	$-0.604864\pi$
$673$	−33.8475	−	19.5418i	−1.30472	−	0.753283i	−0.981210	+	0.192941i	$0.938198\pi$
$674$	−3.13780	−	17.7953i	−0.120863	−	0.685451i
$675$	4.54321	+	2.08787i	0.174868	+	0.0803622i
$676$	4.08827	−	7.08108i	0.157241	−	0.272349i
$677$	−16.6661	+	9.62217i	−0.640529	+	0.369810i	−0.784818	−	0.619726i	$-0.787244\pi$
$677$	−16.6661	+	9.62217i	−0.640529	+	0.369810i	0.144289	+	0.989536i	$0.453911\pi$
$678$	−1.02585	−	1.22256i	−0.0393974	−	0.0469520i
$679$	−3.46828	+	1.26235i	−0.133100	+	0.0484445i
$680$	5.82478	−	7.63485i	0.223370	−	0.292783i
$681$	−5.93883	−	4.98327i	−0.227576	−	0.190959i
$682$	26.3822	+	4.65190i	1.01023	+	0.178130i
$683$			39.2458i			1.50170i	0.660474	+	0.750849i	$0.270356\pi$
$683$			39.2458i			1.50170i	−0.660474	+	0.750849i	$0.729644\pi$
$684$	−4.34801	−	0.307887i	−0.166250	−	0.0117724i
$685$	26.6069	+	8.30789i	1.01660	+	0.317428i
$686$	−3.45483	+	19.5933i	−0.131906	+	0.748076i
$687$	4.98548	−	5.94146i	0.190208	−	0.226681i
$688$	−2.11201	+	5.80269i	−0.0805195	+	0.221226i
$689$	−10.7948	+	3.92900i	−0.411250	+	0.149683i
$690$	1.48936	−	0.621767i	0.0566989	−	0.0236703i
$691$	−16.8942	−	29.2616i	−0.642685	−	1.11316i	−0.984831	−	0.173516i	$-0.944487\pi$
$691$	−16.8942	−	29.2616i	−0.642685	−	1.11316i	0.342146	−	0.939647i	$-0.388846\pi$
$692$	−20.0526	−	11.5774i	−0.762286	−	0.440106i
$693$	7.90617	−	1.39407i	0.300331	−	0.0529564i
$694$	−5.00008	−	28.3569i	−0.189800	−	1.07641i
$695$	22.9131	+	24.8662i	0.869145	+	0.943229i
$696$	3.31860	+	5.74799i	0.125791	+	0.217877i
$697$	12.7694	+	15.2180i	0.483676	+	0.576423i
$698$	−1.39040	−	3.82010i	−0.0526275	−	0.144593i
$699$	−10.7883	−	3.92662i	−0.408051	−	0.148518i
$700$	−11.3811	+	3.11746i	−0.430165	+	0.117829i
$701$	2.03073	−	11.5169i	0.0766997	−	0.434986i	−0.922141	−	0.386853i	$-0.873562\pi$
$701$	2.03073	−	11.5169i	0.0766997	−	0.434986i	0.998841	−	0.0481324i	$-0.0153269\pi$
$702$			2.19624i			0.0828917i
$703$	13.8450	−	1.44285i	0.522174	−	0.0544182i
$704$	−3.40165			−0.128205
$705$	−26.6375	−	13.7727i	−1.00323	−	0.518708i
$706$	−26.3512	−	22.1113i	−0.991741	−	0.832170i
$707$	0.876995	−	2.40952i	0.0329828	−	0.0906195i
$708$	5.14247	+	14.1288i	0.193266	+	0.530993i
$709$	1.40702	−	1.18063i	0.0528418	−	0.0443395i	−0.615984	−	0.787758i	$-0.711242\pi$
$709$	1.40702	−	1.18063i	0.0528418	−	0.0443395i	0.668826	+	0.743419i	$0.266797\pi$
$710$	8.19126	+	36.4684i	0.307412	+	1.36864i
$711$	4.94284	−	8.56126i	0.185371	−	0.321072i
$712$	12.3313	−	2.17434i	0.462135	−	0.0814868i
$713$	5.59786	−	0.987053i	0.209641	−	0.0369654i
$714$	5.06781	−	8.77770i	0.189658	−	0.328497i
$715$	−3.66100	−	16.2992i	−0.136914	−	0.609556i
$716$	5.30017	−	4.44737i	0.198077	−	0.166206i
$717$	−0.484979	−	1.33247i	−0.0181119	−	0.0497620i
$718$	6.30501	−	17.3229i	0.235301	−	0.646484i
$719$	13.4118	+	11.2539i	0.500178	+	0.419699i	0.857657	−	0.514222i	$-0.171919\pi$
$719$	13.4118	+	11.2539i	0.500178	+	0.419699i	−0.357479	+	0.933921i	$0.616364\pi$
$720$	−1.98628	−	1.02699i	−0.0740242	−	0.0382735i
$721$	−21.1079			−0.786099
$722$	−18.9896	+	0.629676i	−0.706718	+	0.0234341i
$723$		−	14.8110i		−	0.550827i
$724$	1.36591	−	7.74647i	0.0507637	−	0.287895i
$725$	−8.76722	−	32.0070i	−0.325606	−	1.18871i
$726$	−0.536792	−	0.195376i	−0.0199222	−	0.00725109i
$727$	4.32282	+	11.8768i	0.160324	+	0.440488i	0.993680	−	0.112249i	$-0.0358056\pi$
$727$	4.32282	+	11.8768i	0.160324	+	0.440488i	−0.833356	+	0.552737i	$0.813583\pi$
$728$	−3.33175	−	3.97062i	−0.123483	−	0.147161i
$729$	0.500000	+	0.866025i	0.0185185	+	0.0320750i
$730$	−2.78067	−	3.01769i	−0.102917	−	0.111690i
$731$	4.60510	+	26.1168i	0.170326	+	0.965966i
$732$	−2.55487	+	0.450493i	−0.0944308	+	0.0166507i
$733$	−0.902146	−	0.520854i	−0.0333215	−	0.0192382i	0.483247	−	0.875484i	$-0.339457\pi$
$733$	−0.902146	−	0.520854i	−0.0333215	−	0.0192382i	−0.516568	+	0.856246i	$0.672791\pi$
$734$	−15.5431	−	26.9215i	−0.573708	−	0.993691i
$735$	2.95092	−	1.23193i	0.108846	−	0.0454404i
$736$	−0.678245	+	0.246861i	−0.0250004	+	0.00909941i
$737$	1.44793	−	3.97815i	0.0533351	−	0.146537i
$738$	2.97335	−	3.54350i	0.109451	−	0.130438i
$739$	4.15204	−	23.5474i	0.152735	−	0.866204i	−0.808092	−	0.589056i	$-0.799500\pi$
$739$	4.15204	−	23.5474i	0.152735	−	0.866204i	0.960827	−	0.277148i	$-0.0893892\pi$
$740$	6.81624	+	2.12834i	0.250570	+	0.0782394i
$741$	0.992293	+	9.52162i	0.0364528	+	0.349785i
$742$		−	12.3445i		−	0.453182i
$743$	−32.8918	−	5.79972i	−1.20668	−	0.212771i	−0.466099	−	0.884733i	$-0.654341\pi$
$743$	−32.8918	−	5.79972i	−1.20668	−	0.212771i	−0.740586	+	0.671962i	$0.765452\pi$
$744$	−6.03287	−	5.06218i	−0.221176	−	0.185588i
$745$	28.2775	−	37.0648i	1.03601	−	1.35795i
$746$	−0.661227	+	0.240667i	−0.0242092	+	0.00881145i
$747$	8.01069	+	9.54676i	0.293096	+	0.349298i
$748$	−12.6516	+	7.30441i	−0.462589	+	0.267076i
$749$	−7.81728	+	13.5399i	−0.285637	+	0.494738i
$750$	8.30570	+	7.48434i	0.303281	+	0.273289i
$751$	3.22635	+	18.2975i	0.117731	+	0.667686i	0.985362	+	0.170477i	$0.0545308\pi$
$751$	3.22635	+	18.2975i	0.117731	+	0.667686i	−0.867631	+	0.497209i	$0.834358\pi$
$752$	11.6141	+	6.70538i	0.423521	+	0.244520i
$753$	−7.71099	+	4.45194i	−0.281004	+	0.162238i
$754$	11.1665	−	9.36985i	0.406662	−	0.341230i
$755$	−0.659695	−	14.2035i	−0.0240088	−	0.516920i
$756$	−2.21774	−	0.807191i	−0.0806584	−	0.0293573i
$757$	25.9142	−	30.8833i	0.941868	−	1.12247i	−0.0504461	−	0.998727i	$-0.516064\pi$
$757$	25.9142	−	30.8833i	0.941868	−	1.12247i	0.992314	−	0.123747i	$-0.0394913\pi$
$758$	−5.76959	−	1.01733i	−0.209561	−	0.0369512i
$759$	−2.45522			−0.0891189
$760$	−9.07536	−	3.55498i	−0.329198	−	0.128953i
$761$	−45.9451			−1.66551			−0.832755	−	0.553642i	$-0.813238\pi$
$761$	−45.9451			−1.66551			−0.832755	+	0.553642i	$0.813238\pi$
$762$	−9.65855	−	1.70306i	−0.349892	−	0.0616954i
$763$	5.65959	−	6.74484i	0.204891	−	0.244180i
$764$	−17.1441	−	6.23992i	−0.620250	−	0.225753i
$765$	−9.59273	+	0.445542i	−0.346826	+	0.0161086i
$766$	−10.7978	+	9.06045i	−0.390141	+	0.327367i
$767$	28.5976	−	16.5109i	1.03260	−	0.596172i
$768$	0.866025	+	0.500000i	0.0312500	+	0.0180422i
$769$	1.95845	+	11.1069i	0.0706235	+	0.400526i	0.999543	+	0.0302429i	$0.00962807\pi$
$769$	1.95845	+	11.1069i	0.0706235	+	0.400526i	−0.928919	+	0.370283i	$0.879261\pi$
$770$	17.8043	+	2.29366i	0.641623	+	0.0826579i
$771$	−2.99855	+	5.19364i	−0.107990	+	0.187045i
$772$	17.8287	−	10.2934i	0.641669	−	0.370468i
$773$	15.1406	+	18.0438i	0.544568	+	0.648991i	0.966205	−	0.257774i	$-0.0829889\pi$
$773$	15.1406	+	18.0438i	0.544568	+	0.648991i	−0.421637	+	0.906765i	$0.638544\pi$
$774$	5.80269	−	2.11201i	0.208574	−	0.0759146i
$775$	22.7645	+	32.1295i	0.817726	+	1.15413i
$776$	−1.19800	−	1.00524i	−0.0430057	−	0.0360861i
$777$	7.42228	+	1.30875i	0.266273	+	0.0469511i
$778$		−	27.3486i		−	0.980495i
$779$	11.2897	−	16.7060i	0.404496	−	0.598553i
$780$	−1.46373	+	4.68773i	−0.0524098	+	0.167848i
$781$	9.87370	−	55.9966i	0.353309	−	2.00371i
$782$	−1.99248	+	2.37454i	−0.0712508	+	0.0849134i
$783$	2.27006	−	6.23693i	0.0811252	−	0.222890i
$784$	−1.34383	+	0.489114i	−0.0479939	+	0.0174684i
$785$	−11.1622	+	4.65994i	−0.398397	+	0.166320i
$786$	−2.76865	−	4.79544i	−0.0987544	−	0.171048i
$787$	−22.9088	−	13.2264i	−0.816609	−	0.471469i	0.0326367	−	0.999467i	$-0.489610\pi$
$787$	−22.9088	−	13.2264i	−0.816609	−	0.471469i	−0.849246	+	0.527998i	$0.822943\pi$
$788$	19.4962	−	3.43771i	0.694523	−	0.122463i
$789$	−1.44326	−	8.18515i	−0.0513815	−	0.291399i
$790$	16.2560	−	14.9792i	0.578363	−	0.532936i
$791$	−1.88326	−	3.26190i	−0.0669609	−	0.115980i
$792$	2.18654	+	2.60582i	0.0776953	+	0.0925937i
$793$	1.94872	+	5.35406i	0.0692010	+	0.190128i
$794$	7.99364	+	2.90945i	0.283684	+	0.103252i
$795$	−9.84675	+	6.31161i	−0.349228	+	0.223850i
$796$	−2.42542	+	13.7552i	−0.0859667	+	0.487541i
$797$			15.1862i			0.537923i	0.963151	+	0.268962i	$0.0866805\pi$
$797$			15.1862i			0.537923i	−0.963151	+	0.268962i	$0.913319\pi$
$798$	−9.97953	−	2.49751i	−0.353272	−	0.0884107i
$799$	57.5942			2.03754
$800$	−3.55513	−	3.51583i	−0.125693	−	0.124303i
$801$	−9.59204	−	8.04868i	−0.338918	−	0.284386i
$802$	−0.704829	+	1.93650i	−0.0248884	+	0.0683803i
$803$	2.13505	+	5.86601i	0.0753444	+	0.207007i
$804$	−0.953365	+	0.799968i	−0.0336226	+	0.0282127i
$805$	3.71640	−	0.834749i	0.130986	−	0.0294210i
$806$	−8.64808	+	14.9789i	−0.304616	+	0.527610i
$807$	2.06022	−	0.363272i	0.0725231	−	0.0127878i
$808$	1.06997	−	0.188665i	0.0376415	−	0.00663720i
$809$	−0.546413	+	0.946415i	−0.0192108	+	0.0332742i	−0.875471	−	0.483271i	$-0.839449\pi$
$809$	−0.546413	+	0.946415i	−0.0192108	+	0.0332742i	0.856260	+	0.516545i	$0.172782\pi$
$810$	0.490039	+	2.18171i	0.0172182	+	0.0766575i
$811$	37.7214	−	31.6520i	1.32458	−	1.11145i	0.339266	−	0.940691i	$-0.389821\pi$
$811$	37.7214	−	31.6520i	1.32458	−	1.11145i	0.985312	−	0.170763i	$-0.0546231\pi$
$812$	5.35749	+	14.7196i	0.188011	+	0.516556i
$813$	8.77934	−	24.1210i	0.307905	−	0.845961i
$814$	−8.32157	−	6.98263i	−0.291671	−	0.244741i
$815$	−5.56499	+	10.7632i	−0.194933	+	0.377018i
$816$	4.29462			0.150342
$817$	24.2029	−	11.7782i	0.846751	−	0.412066i
$818$		−	8.39454i		−	0.293508i
$819$	−0.900067	+	5.10453i	−0.0314509	+	0.178367i
$820$	8.70806	−	5.58173i	0.304099	−	0.194922i
$821$	43.6931	+	15.9030i	1.52490	+	0.555018i	0.962366	−	0.271758i	$-0.0876049\pi$
$821$	43.6931	+	15.9030i	1.52490	+	0.555018i	0.562533	+	0.826775i	$0.309827\pi$
$822$	4.26346	+	11.7138i	0.148705	+	0.408564i
$823$	14.4729	+	17.2482i	0.504495	+	0.601233i	0.956842	−	0.290609i	$-0.0938577\pi$
$823$	14.4729	+	17.2482i	0.504495	+	0.601233i	−0.452347	+	0.891842i	$0.649413\pi$
$824$	−4.47188	−	7.74552i	−0.155785	−	0.269828i
$825$	−7.27357	−	15.3745i	−0.253233	−	0.535272i
$826$	6.16190	+	34.9459i	0.214400	+	1.21592i
$827$	47.9925	−	8.46237i	1.66886	−	0.294265i	0.742205	−	0.670173i	$-0.233780\pi$
$827$	47.9925	−	8.46237i	1.66886	−	0.294265i	0.926657	+	0.375908i	$0.122669\pi$
$828$	0.625074	+	0.360886i	0.0217228	+	0.0125417i
$829$	−23.7189	−	41.0824i	−0.823792	−	1.42685i	−0.902839	−	0.429979i	$-0.858521\pi$
$829$	−23.7189	−	41.0824i	−0.823792	−	1.42685i	0.0790463	−	0.996871i	$-0.474813\pi$
$830$	10.7357	+	25.7158i	0.372641	+	0.892610i
$831$	11.5977	−	4.22123i	0.402321	−	0.146433i
$832$	0.751158	−	2.06379i	0.0260417	−	0.0715490i
$833$	−3.94776	+	4.70476i	−0.136782	+	0.163010i
$834$	−2.62587	+	14.8920i	−0.0909264	+	0.515669i
$835$	0.280235	+	0.0875023i	0.00969794	+	0.00302814i
$836$	10.6569	+	10.3094i	0.368577	+	0.356558i
$837$			7.87535i			0.272212i
$838$	−32.1757	−	5.67345i	−1.11149	−	0.195986i
$839$	34.4894	+	28.9400i	1.19071	+	0.999121i	0.999847	+	0.0175033i	$0.00557175\pi$
$839$	34.4894	+	28.9400i	1.19071	+	0.999121i	0.190859	+	0.981617i	$0.438873\pi$
$840$	−4.19566	−	3.20095i	−0.144764	−	0.110443i
$841$	−14.1447	+	5.14825i	−0.487749	+	0.177526i
$842$	11.7257	+	13.9741i	0.404093	+	0.481580i
$843$	−13.2011	+	7.62165i	−0.454670	+	0.262504i
$844$	−4.42183	+	7.65884i	−0.152206	+	0.263628i
$845$	−18.1334	−	2.33606i	−0.623809	−	0.0803629i
$846$	−2.32875	−	13.2070i	−0.0800642	−	0.454067i
$847$	−1.16755	−	0.674085i	−0.0401175	−	0.0231618i
$848$	4.52982	−	2.61529i	0.155555	−	0.0898095i
$849$	11.1959	−	9.39448i	0.384242	−	0.322418i
$850$	−20.7720	−	5.44228i	−0.712474	−	0.186669i
$851$	−2.16595	−	0.788340i	−0.0742477	−	0.0270239i
$852$	−10.7445	+	12.8048i	−0.368101	+	0.438686i
$853$	11.9837	+	2.11305i	0.410315	+	0.0723495i	0.374996	−	0.927027i	$-0.377644\pi$
$853$	11.9837	+	2.11305i	0.410315	+	0.0723495i	0.0353189	+	0.999376i	$0.488755\pi$
$854$	−6.12269			−0.209514
$855$	3.11025	+	9.23722i	0.106368	+	0.315906i
$856$	−6.62462			−0.226425
$857$	39.7180	+	7.00335i	1.35674	+	0.239230i	0.804251	−	0.594290i	$-0.202567\pi$
$857$	39.7180	+	7.00335i	1.35674	+	0.239230i	0.552489	+	0.833520i	$0.313678\pi$
$858$	4.80217	−	5.72300i	0.163943	−	0.195380i
$859$	−7.59679	−	2.76500i	−0.259199	−	0.0943407i	0.209152	−	0.977883i	$-0.432930\pi$
$859$	−7.59679	−	2.76500i	−0.259199	−	0.0943407i	−0.468351	+	0.883542i	$0.655152\pi$
$860$	13.7931	−	0.640630i	0.470340	−	0.0218453i
$861$	8.36290	−	7.01731i	0.285007	−	0.239149i
$862$	−4.95943	+	2.86333i	−0.168919	+	0.0975253i
$863$	22.7173	+	13.1159i	0.773307	+	0.446469i	0.834053	−	0.551684i	$-0.186015\pi$
$863$	22.7173	+	13.1159i	0.773307	+	0.446469i	−0.0607458	+	0.998153i	$0.519348\pi$
$864$	−0.173648	−	0.984808i	−0.00590763	−	0.0335038i
$865$	−6.61539	+	51.3513i	−0.224930	+	1.74600i
$866$	9.24146	−	16.0067i	0.314038	−	0.543929i
$867$	1.25037	−	0.721902i	0.0424648	−	0.0245171i
$868$	−11.9471	−	14.2380i	−0.405511	−	0.483269i
$869$	−31.5997	+	11.5013i	−1.07195	+	0.390156i
$870$	9.00202	−	11.7994i	0.305197	−	0.400038i
$871$	2.09382	+	1.75692i	0.0709463	+	0.0595310i
$872$	3.67404	+	0.647833i	0.124419	+	0.0219384i
$873$			1.56388i			0.0529293i
$874$	2.87301	+	1.28218i	0.0971810	+	0.0433703i
$875$	16.2370	+	20.7991i	0.548910	+	0.703137i
$876$	0.318667	−	1.80725i	0.0107668	−	0.0610614i
$877$	−19.0731	+	22.7305i	−0.644054	+	0.767554i	−0.985005	−	0.172527i	$-0.944807\pi$
$877$	−19.0731	+	22.7305i	−0.644054	+	0.767554i	0.340951	+	0.940081i	$0.389251\pi$
$878$	3.99521	−	10.9768i	0.134832	−	0.370447i
$879$	−2.32657	+	0.846801i	−0.0784731	+	0.0285619i
$880$	2.93033	+	7.01921i	0.0987815	+	0.236618i
$881$	24.4327	+	42.3186i	0.823158	+	1.42575i	0.903319	+	0.428969i	$0.141123\pi$
$881$	24.4327	+	42.3186i	0.823158	+	1.42575i	−0.0801617	+	0.996782i	$0.525544\pi$
$882$	1.23848	+	0.715037i	0.0417018	+	0.0240766i
$883$	43.6607	−	7.69856i	1.46930	−	0.259077i	0.619006	−	0.785386i	$-0.287536\pi$
$883$	43.6607	−	7.69856i	1.46930	−	0.259077i	0.850293	+	0.526309i	$0.176424\pi$
$884$	−1.63785	−	9.28873i	−0.0550870	−	0.312414i
$885$	24.7244	−	22.7825i	0.831103	−	0.765826i
$886$	−1.13217	−	1.96098i	−0.0380361	−	0.0658804i
$887$	−35.8985	−	42.7822i	−1.20535	−	1.43648i	−0.869045	−	0.494733i	$-0.835266\pi$
$887$	−35.8985	−	42.7822i	−1.20535	−	1.43648i	−0.336309	−	0.941752i	$-0.609179\pi$
$888$	1.09223	+	3.00087i	0.0366527	+	0.100703i
$889$	−21.7506	−	7.91656i	−0.729491	−	0.265513i
$890$	−15.1094	−	23.5722i	−0.506468	−	0.790142i
$891$	0.590691	−	3.34997i	0.0197889	−	0.112228i
$892$		−	27.7484i		−	0.929084i
$893$	−16.0633	−	56.2058i	−0.537536	−	1.88086i
$894$	20.8490			0.697296
$895$	−13.7428	−	7.10558i	−0.459372	−	0.237513i
$896$	1.80792	+	1.51702i	0.0603983	+	0.0506802i
$897$	0.542166	−	1.48959i	0.0181024	−	0.0497359i
$898$	−13.3545	−	36.6912i	−0.445646	−	1.22440i
$899$	40.0414	−	33.5987i	1.33545	−	1.12058i
$900$	−0.408086	+	4.98332i	−0.0136029	+	0.166111i
$901$	11.2317	−	19.4539i	0.374182	−	0.648102i
$902$	−15.4960	+	2.73236i	−0.515961	+	0.0909778i
$903$	14.3523	−	2.53069i	0.477613	−	0.0842161i
$904$	0.797967	−	1.38212i	0.0265400	−	0.0459686i
$905$	−17.1613	+	3.85463i	−0.570460	+	0.128132i
$906$	4.87118	−	4.08740i	0.161834	−	0.135795i
$907$	−19.4623	−	53.4721i	−0.646234	−	1.77551i	−0.631194	−	0.775625i	$-0.717435\pi$
$907$	−19.4623	−	53.4721i	−0.646234	−	1.77551i	−0.0150398	−	0.999887i	$-0.504787\pi$
$908$	2.65154	−	7.28505i	0.0879945	−	0.241763i
$909$	−0.832290	−	0.698374i	−0.0276053	−	0.0231636i
$910$	−5.32315	+	10.2954i	−0.176461	+	0.341290i
$911$	−28.0424			−0.929086			−0.464543	−	0.885550i	$-0.653781\pi$
$911$	−28.0424			−0.929086			−0.464543	+	0.885550i	$0.653781\pi$
$912$	−1.19779	−	4.19110i	−0.0396627	−	0.138781i
$913$		−	42.3928i		−	1.40300i
$914$	−2.32549	+	13.1885i	−0.0769205	+	0.436238i
$915$	3.13046	+	4.88383i	0.103490	+	0.161454i
$916$	7.28828	+	2.65272i	0.240811	+	0.0876482i
$917$	−4.46966	−	12.2803i	−0.147601	−	0.405531i
$918$	−2.76053	−	3.28987i	−0.0911111	−	0.108582i
$919$	−11.3350	−	19.6328i	−0.373908	−	0.647628i	0.616255	−	0.787547i	$-0.288649\pi$
$919$	−11.3350	−	19.6328i	−0.373908	−	0.647628i	−0.990163	+	0.139919i	$0.955316\pi$
$920$	1.09366	+	1.18688i	0.0360569	+	0.0391303i
$921$	3.88872	+	22.0540i	0.128138	+	0.726705i
$922$	7.60894	−	1.34166i	0.250587	−	0.0441852i
$923$	31.7929	+	18.3556i	1.04648	+	0.604183i
$924$	4.01407	+	6.95257i	0.132053	+	0.228723i
$925$	−1.48003	−	15.8986i	−0.0486632	−	0.522741i
$926$	−4.47625	+	1.62922i	−0.147099	+	0.0535396i
$927$	−3.05895	+	8.40438i	−0.100469	+	0.276036i
$928$	−4.26631	+	5.08439i	−0.140049	+	0.166903i
$929$	−1.13560	+	6.44030i	−0.0372578	+	0.211300i	−0.997753	−	0.0669963i	$-0.978658\pi$
$929$	−1.13560	+	6.44030i	−0.0372578	+	0.211300i	0.960495	+	0.278296i	$0.0897695\pi$
$930$	−5.24868	+	16.8094i	−0.172111	+	0.551203i
$931$	5.69240	+	2.54042i	0.186561	+	0.0832590i
$932$		−	11.4807i		−	0.376062i
$933$	13.2339	+	2.33350i	0.433259	+	0.0763952i
$934$	11.4652	+	9.62040i	0.375151	+	0.314789i
$935$	25.9711	+	19.8139i	0.849346	+	0.647984i
$936$	−2.06379	+	0.751158i	−0.0674571	+	0.0245524i
$937$	15.1352	+	18.0375i	0.494446	+	0.589258i	0.954343	−	0.298714i	$-0.0965578\pi$
$937$	15.1352	+	18.0375i	0.494446	+	0.589258i	−0.459896	+	0.887973i	$0.652113\pi$
$938$	−2.54367	+	1.46859i	−0.0830537	+	0.0479511i
$939$	16.6180	−	28.7833i	0.542309	−	0.939308i
$940$	3.83150	−	29.7416i	0.124970	−	0.970064i
$941$	−6.13760	−	34.8080i	−0.200080	−	1.13471i	−0.904996	−	0.425419i	$-0.860127\pi$
$941$	−6.13760	−	34.8080i	−0.200080	−	1.13471i	0.704916	−	0.709290i	$-0.250984\pi$
$942$	−4.68472	−	2.70472i	−0.152636	−	0.0881247i
$943$	−2.89141	+	1.66936i	−0.0941572	+	0.0543617i
$944$	−11.5179	+	9.66467i	−0.374876	+	0.314558i
$945$	0.244843	+	5.27159i	0.00796475	+	0.171485i
$946$	−19.7387	−	7.18432i	−0.641762	−	0.233582i
$947$	−2.04624	+	2.43861i	−0.0664938	+	0.0792443i	−0.798266	−	0.602305i	$-0.794249\pi$
$947$	−2.04624	+	2.43861i	−0.0664938	+	0.0792443i	0.731772	+	0.681549i	$0.238694\pi$
$948$	9.73550	+	1.71663i	0.316194	+	0.0557536i
$949$	−4.03039			−0.130832
$950$	0.482313	+	21.7892i	0.0156483	+	0.706934i
$951$	19.7745			0.641231
$952$	9.98163	+	1.76003i	0.323506	+	0.0570429i
$953$	5.62282	−	6.70102i	0.182141	−	0.217067i	−0.667246	−	0.744837i	$-0.732527\pi$
$953$	5.62282	−	6.70102i	0.182141	−	0.217067i	0.849387	+	0.527770i	$0.176972\pi$
$954$	−4.91514	−	1.78896i	−0.159134	−	0.0579199i
$955$	1.89274	+	40.7516i	0.0612476	+	1.31869i
$956$	1.08624	−	0.911462i	0.0351315	−	0.0294788i
$957$	−19.5527	+	11.2887i	−0.632048	+	0.364913i
$958$	26.0201	+	15.0227i	0.840670	+	0.485361i
$959$	5.10864	+	28.9726i	0.164967	+	0.935573i
$960$	0.285703	−	2.21774i	0.00922103	−	0.0715773i
$961$	−15.5106	+	26.8651i	−0.500341	+	0.866616i
$962$	6.07396	−	3.50680i	0.195832	−	0.113064i
$963$	4.25822	+	5.07475i	0.137219	+	0.163532i
$964$	13.9178	−	5.06566i	0.448262	−	0.163154i
$965$	−36.5986	−	27.9218i	−1.17815	−	0.898835i
$966$	1.30491	+	1.09495i	0.0419847	+	0.0352293i
$967$	21.9286	+	3.86661i	0.705177	+	0.124342i	0.514726	−	0.857355i	$-0.327894\pi$
$967$	21.9286	+	3.86661i	0.705177	+	0.124342i	0.190451	+	0.981697i	$0.439005\pi$
$968$		−	0.571242i		−	0.0183604i
$969$	−13.4545	−	13.0157i	−0.432220	−	0.418126i
$970$	−1.04228	+	3.33800i	−0.0334655	+	0.107177i
$971$	10.1550	−	57.5920i	0.325890	−	1.84821i	−0.177454	−	0.984129i	$-0.556786\pi$
$971$	10.1550	−	57.5920i	0.325890	−	1.84821i	0.503345	−	0.864086i	$-0.332103\pi$
$972$	−0.642788	+	0.766044i	−0.0206174	+	0.0245709i
$973$	−12.2062	+	33.5361i	−0.391311	+	1.07512i
$974$	−17.3988	+	6.33266i	−0.557495	+	0.202912i
$975$	10.9339	−	1.01786i	0.350166	−	0.0325978i
$976$	−1.29714	−	2.24672i	−0.0415205	−	0.0719156i
$977$	16.9450	+	9.78318i	0.542117	+	0.312992i	0.745937	−	0.666017i	$-0.232002\pi$
$977$	16.9450	+	9.78318i	0.542117	+	0.312992i	−0.203819	+	0.979009i	$0.565335\pi$
$978$	−5.33644	+	0.940959i	−0.170641	+	0.0300885i
$979$	7.39635	+	41.9468i	0.236388	+	1.34062i
$980$	2.16691	+	2.35161i	0.0692193	+	0.0751194i
$981$	−1.86536	−	3.23090i	−0.0595564	−	0.103155i
$982$	1.64366	+	1.95883i	0.0524512	+	0.0625089i
$983$	−7.74914	−	21.2906i	−0.247159	−	0.679064i	−0.999787	−	0.0206184i	$-0.993437\pi$
$983$	−7.74914	−	21.2906i	−0.247159	−	0.679064i	0.752628	−	0.658446i	$-0.228786\pi$
$984$	4.34675	+	1.58209i	0.138569	+	0.0504351i
$985$	−23.8885	−	37.2685i	−0.761151	−	1.18747i
$986$	−4.94972	+	28.0713i	−0.157631	+	0.893971i
$987$		−	31.6503i		−	1.00744i
$988$	−8.60801	+	4.18904i	−0.273857	+	0.133271i
$989$	−4.45702			−0.141725
$990$	3.49345	−	6.75663i	0.111029	−	0.214740i
$991$	28.6317	+	24.0249i	0.909517	+	0.763175i	0.972027	−	0.234869i	$-0.0754661\pi$
$991$	28.6317	+	24.0249i	0.909517	+	0.763175i	−0.0625100	+	0.998044i	$0.519911\pi$
$992$	2.69353	−	7.40041i	0.0855196	−	0.234963i
$993$	1.85451	+	5.09523i	0.0588512	+	0.161692i
$994$	−30.2203	+	25.3578i	−0.958529	+	0.804301i
$995$	30.4729	−	6.84458i	0.966056	−	0.216988i
$996$	−6.23121	+	10.7928i	−0.197443	+	0.341982i
$997$	−51.2189	+	9.03128i	−1.62212	+	0.286024i	−0.909555	−	0.415583i	$-0.863578\pi$
$997$	−51.2189	+	9.03128i	−1.62212	+	0.286024i	−0.712565	+	0.701606i	$0.752467\pi$
$998$	−38.5446	+	6.79645i	−1.22011	+	0.215138i
$999$	1.59673	−	2.76562i	0.0505183	−	0.0875002i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	570.2.bc.b.169.7	yes	60
5.4	even	2	inner	570.2.bc.b.169.4	✓	60
19.9	even	9	inner	570.2.bc.b.199.4	yes	60
95.9	even	18	inner	570.2.bc.b.199.7	yes	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.2.bc.b.169.4	✓	60	5.4	even	2	inner
570.2.bc.b.169.7	yes	60	1.1	even	1	trivial
570.2.bc.b.199.4	yes	60	19.9	even	9	inner
570.2.bc.b.199.7	yes	60	95.9	even	18	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.bc (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.984808 + 0.173648i) q^{2} +(0.642788 - 0.766044i) q^{3} +(0.939693 + 0.342020i) q^{4} +(-0.103744 - 2.23366i) q^{5} +(0.766044 - 0.642788i) q^{6} +(2.04388 - 1.18003i) q^{7} +(0.866025 + 0.500000i) q^{8} +(-0.173648 - 0.984808i) q^{9} +O(q^{10})\)	\(q+(0.984808 + 0.173648i) q^{2} +(0.642788 - 0.766044i) q^{3} +(0.939693 + 0.342020i) q^{4} +(-0.103744 - 2.23366i) q^{5} +(0.766044 - 0.642788i) q^{6} +(2.04388 - 1.18003i) q^{7} +(0.866025 + 0.500000i) q^{8} +(-0.173648 - 0.984808i) q^{9} +(0.285703 - 2.21774i) q^{10} +(-1.70083 + 2.94592i) q^{11} +(0.866025 - 0.500000i) q^{12} +(-1.41172 - 1.68242i) q^{13} +(2.21774 - 0.807191i) q^{14} +(-1.77777 - 1.35630i) q^{15} +(0.766044 + 0.642788i) q^{16} +(4.22938 + 0.745754i) q^{17} -1.00000i q^{18} +(-0.451815 - 4.33542i) q^{19} +(0.666469 - 2.13444i) q^{20} +(0.409822 - 2.32421i) q^{21} +(-2.18654 + 2.60582i) q^{22} +(-0.246861 + 0.678245i) q^{23} +(0.939693 - 0.342020i) q^{24} +(-4.97847 + 0.463458i) q^{25} +(-1.09812 - 1.90200i) q^{26} +(-0.866025 - 0.500000i) q^{27} +(2.32421 - 0.409822i) q^{28} +(1.15254 + 6.53637i) q^{29} +(-1.51524 - 1.64440i) q^{30} +(-3.93768 - 6.82025i) q^{31} +(0.642788 + 0.766044i) q^{32} +(1.16343 + 3.19651i) q^{33} +(4.03563 + 1.46885i) q^{34} +(-2.84784 - 4.44291i) q^{35} +(0.173648 - 0.984808i) q^{36} +3.19346i q^{37} +(0.307887 - 4.34801i) q^{38} -2.19624 q^{39} +(1.02699 - 1.98628i) q^{40} +(3.54350 + 2.97335i) q^{41} +(0.807191 - 2.21774i) q^{42} +(2.11201 + 5.80269i) q^{43} +(-2.60582 + 2.18654i) q^{44} +(-2.18171 + 0.490039i) q^{45} +(-0.360886 + 0.625074i) q^{46} +(13.2070 - 2.32875i) q^{47} +(0.984808 - 0.173648i) q^{48} +(-0.715037 + 1.23848i) q^{49} +(-4.98332 - 0.408086i) q^{50} +(3.28987 - 2.76053i) q^{51} +(-0.751158 - 2.06379i) q^{52} +(1.78896 - 4.91514i) q^{53} +(-0.766044 - 0.642788i) q^{54} +(6.75663 + 3.49345i) q^{55} +2.36007 q^{56} +(-3.61155 - 2.44064i) q^{57} +6.63720i q^{58} +(-2.61090 + 14.8071i) q^{59} +(-1.20668 - 1.88253i) q^{60} +(-2.43783 - 0.887297i) q^{61} +(-2.69353 - 7.40041i) q^{62} +(-1.51702 - 1.80792i) q^{63} +(0.500000 + 0.866025i) q^{64} +(-3.61149 + 3.32783i) q^{65} +(0.590691 + 3.34997i) q^{66} +(-1.22562 + 0.216110i) q^{67} +(3.71925 + 2.14731i) q^{68} +(0.360886 + 0.625074i) q^{69} +(-2.03307 - 4.86993i) q^{70} +(-15.7074 + 5.71704i) q^{71} +(0.342020 - 0.939693i) q^{72} +(1.17960 - 1.40579i) q^{73} +(-0.554538 + 3.14494i) q^{74} +(-2.84507 + 4.11164i) q^{75} +(1.05823 - 4.22849i) q^{76} +8.02814i q^{77} +(-2.16287 - 0.381373i) q^{78} +(7.57288 + 6.35440i) q^{79} +(1.35630 - 1.77777i) q^{80} +(-0.939693 + 0.342020i) q^{81} +(2.97335 + 3.54350i) q^{82} +(-10.7928 + 6.23121i) q^{83} +(1.18003 - 2.04388i) q^{84} +(1.22699 - 9.52436i) q^{85} +(1.07229 + 6.08128i) q^{86} +(5.74799 + 3.31860i) q^{87} +(-2.94592 + 1.70083i) q^{88} +(9.59204 - 8.04868i) q^{89} +(-2.23366 + 0.103744i) q^{90} +(-4.87069 - 1.77279i) q^{91} +(-0.463947 + 0.552910i) q^{92} +(-7.75571 - 1.36754i) q^{93} +13.4108 q^{94} +(-9.63698 + 1.45897i) q^{95} +1.00000 q^{96} +(-1.54012 - 0.271565i) q^{97} +(-0.919234 + 1.09550i) q^{98} +(3.19651 + 1.16343i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q + 6 q^{5}+O(q^{10}) \) 60 * q + 6 * q^5	\( 60 q + 6 q^{5} + 6 q^{10} - 12 q^{11} + 12 q^{15} + 24 q^{19} + 12 q^{20} - 18 q^{21} - 6 q^{25} - 6 q^{26} + 12 q^{29} + 6 q^{30} - 36 q^{31} - 6 q^{35} - 12 q^{39} - 6 q^{40} - 30 q^{41} - 6 q^{44} - 6 q^{45} - 36 q^{46} + 18 q^{49} - 90 q^{55} + 24 q^{56} + 60 q^{59} + 6 q^{60} + 36 q^{61} + 30 q^{64} + 24 q^{65} - 12 q^{66} + 36 q^{69} - 72 q^{70} - 72 q^{71} + 6 q^{74} + 6 q^{76} + 6 q^{80} + 12 q^{84} + 18 q^{85} - 12 q^{86} + 60 q^{89} + 12 q^{90} - 48 q^{91} - 156 q^{94} - 84 q^{95} + 60 q^{96} - 6 q^{99}+O(q^{100}) \) 60 * q + 6 * q^5 + 6 * q^10 - 12 * q^11 + 12 * q^15 + 24 * q^19 + 12 * q^20 - 18 * q^21 - 6 * q^25 - 6 * q^26 + 12 * q^29 + 6 * q^30 - 36 * q^31 - 6 * q^35 - 12 * q^39 - 6 * q^40 - 30 * q^41 - 6 * q^44 - 6 * q^45 - 36 * q^46 + 18 * q^49 - 90 * q^55 + 24 * q^56 + 60 * q^59 + 6 * q^60 + 36 * q^61 + 30 * q^64 + 24 * q^65 - 12 * q^66 + 36 * q^69 - 72 * q^70 - 72 * q^71 + 6 * q^74 + 6 * q^76 + 6 * q^80 + 12 * q^84 + 18 * q^85 - 12 * q^86 + 60 * q^89 + 12 * q^90 - 48 * q^91 - 156 * q^94 - 84 * q^95 + 60 * q^96 - 6 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more