LMFDB - Embedded newform 570.2.k.a.533.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [570,2,Mod(77,570)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(570, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1, 0]))

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

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

chi := DirichletCharacter("570.77");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 570 = 2 \cdot 3 \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	570.k (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$4.55147291521$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$18$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			533.15
Character	$\chi$	$=$	570.533
Dual form			570.2.k.a.77.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 + 0.707107i) q^{2} +(0.867616 - 1.49908i) q^{3} +1.00000i q^{4} +(0.850241 - 2.06811i) q^{5} +(1.67351 - 0.446512i) q^{6} +(0.811234 - 0.811234i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-1.49448 - 2.60125i) q^{9} +O(q^{10})$	\(q+(0.707107 + 0.707107i) q^{2} +(0.867616 - 1.49908i) q^{3} +1.00000i q^{4} +(0.850241 - 2.06811i) q^{5} +(1.67351 - 0.446512i) q^{6} +(0.811234 - 0.811234i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-1.49448 - 2.60125i) q^{9} +(2.06359 - 0.861165i) q^{10} +1.25204i q^{11} +(1.49908 + 0.867616i) q^{12} +(3.40609 + 3.40609i) q^{13} +1.14726 q^{14} +(-2.36258 - 3.06891i) q^{15} -1.00000 q^{16} +(-3.04078 - 3.04078i) q^{17} +(0.782605 - 2.89612i) q^{18} -1.00000i q^{19} +(2.06811 + 0.850241i) q^{20} +(-0.512265 - 1.91995i) q^{21} +(-0.885325 + 0.885325i) q^{22} +(5.51574 - 5.51574i) q^{23} +(0.446512 + 1.67351i) q^{24} +(-3.55418 - 3.51679i) q^{25} +4.81693i q^{26} +(-5.19613 - 0.0165399i) q^{27} +(0.811234 + 0.811234i) q^{28} +5.49893 q^{29} +(0.499447 - 3.84064i) q^{30} -5.80986 q^{31} +(-0.707107 - 0.707107i) q^{32} +(1.87691 + 1.08629i) q^{33} -4.30032i q^{34} +(-0.987979 - 2.36747i) q^{35} +(2.60125 - 1.49448i) q^{36} +(-7.08962 + 7.08962i) q^{37} +(0.707107 - 0.707107i) q^{38} +(8.06117 - 2.15082i) q^{39} +(0.861165 + 2.06359i) q^{40} -0.259187i q^{41} +(0.995380 - 1.71983i) q^{42} +(5.60388 + 5.60388i) q^{43} -1.25204 q^{44} +(-6.65036 + 0.879067i) q^{45} +7.80043 q^{46} +(6.12099 + 6.12099i) q^{47} +(-0.867616 + 1.49908i) q^{48} +5.68380i q^{49} +(-0.0264390 - 4.99993i) q^{50} +(-7.19661 + 1.92015i) q^{51} +(-3.40609 + 3.40609i) q^{52} +(-0.465266 + 0.465266i) q^{53} +(-3.66252 - 3.68591i) q^{54} +(2.58936 + 1.06454i) q^{55} +1.14726i q^{56} +(-1.49908 - 0.867616i) q^{57} +(3.88833 + 3.88833i) q^{58} -9.08034 q^{59} +(3.06891 - 2.36258i) q^{60} +6.32624 q^{61} +(-4.10819 - 4.10819i) q^{62} +(-3.32260 - 0.897850i) q^{63} -1.00000i q^{64} +(9.94016 - 4.14817i) q^{65} +(0.559051 + 2.09530i) q^{66} +(-2.40925 + 2.40925i) q^{67} +(3.04078 - 3.04078i) q^{68} +(-3.48299 - 13.0541i) q^{69} +(0.975447 - 2.37266i) q^{70} -0.747767i q^{71} +(2.89612 + 0.782605i) q^{72} +(5.45994 + 5.45994i) q^{73} -10.0262 q^{74} +(-8.35561 + 2.27678i) q^{75} +1.00000 q^{76} +(1.01570 + 1.01570i) q^{77} +(7.22097 + 4.17925i) q^{78} -4.84381i q^{79} +(-0.850241 + 2.06811i) q^{80} +(-4.53304 + 7.77506i) q^{81} +(0.183273 - 0.183273i) q^{82} +(-4.22891 + 4.22891i) q^{83} +(1.91995 - 0.512265i) q^{84} +(-8.87408 + 3.70328i) q^{85} +7.92509i q^{86} +(4.77097 - 8.24334i) q^{87} +(-0.885325 - 0.885325i) q^{88} +12.7982 q^{89} +(-5.32411 - 4.08092i) q^{90} +5.52627 q^{91} +(5.51574 + 5.51574i) q^{92} +(-5.04073 + 8.70945i) q^{93} +8.65639i q^{94} +(-2.06811 - 0.850241i) q^{95} +(-1.67351 + 0.446512i) q^{96} +(-12.5537 + 12.5537i) q^{97} +(-4.01905 + 4.01905i) q^{98} +(3.25687 - 1.87115i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q + 4 q^{3} + 4 q^{6} - 12 q^{7}+O(q^{10}) $ 36 * q + 4 * q^3 + 4 * q^6 - 12 * q^7	$ 36 q + 4 q^{3} + 4 q^{6} - 12 q^{7} - 4 q^{10} - 4 q^{12} + 8 q^{13} + 4 q^{15} - 36 q^{16} - 32 q^{21} - 4 q^{22} + 32 q^{25} + 28 q^{27} - 12 q^{28} - 8 q^{30} + 8 q^{31} + 36 q^{33} + 4 q^{36} - 32 q^{37} - 8 q^{40} + 12 q^{42} - 24 q^{43} - 28 q^{45} - 16 q^{46} - 4 q^{48} - 40 q^{51} - 8 q^{52} - 4 q^{55} + 4 q^{57} - 4 q^{58} - 24 q^{60} + 200 q^{61} + 28 q^{63} + 12 q^{70} - 68 q^{73} - 36 q^{75} + 36 q^{76} + 24 q^{78} - 92 q^{81} + 24 q^{82} + 24 q^{85} + 28 q^{87} - 4 q^{88} - 68 q^{90} + 64 q^{91} + 16 q^{93} - 4 q^{96} - 148 q^{97}+O(q^{100}) $ 36 * q + 4 * q^3 + 4 * q^6 - 12 * q^7 - 4 * q^10 - 4 * q^12 + 8 * q^13 + 4 * q^15 - 36 * q^16 - 32 * q^21 - 4 * q^22 + 32 * q^25 + 28 * q^27 - 12 * q^28 - 8 * q^30 + 8 * q^31 + 36 * q^33 + 4 * q^36 - 32 * q^37 - 8 * q^40 + 12 * q^42 - 24 * q^43 - 28 * q^45 - 16 * q^46 - 4 * q^48 - 40 * q^51 - 8 * q^52 - 4 * q^55 + 4 * q^57 - 4 * q^58 - 24 * q^60 + 200 * q^61 + 28 * q^63 + 12 * q^70 - 68 * q^73 - 36 * q^75 + 36 * q^76 + 24 * q^78 - 92 * q^81 + 24 * q^82 + 24 * q^85 + 28 * q^87 - 4 * q^88 - 68 * q^90 + 64 * q^91 + 16 * q^93 - 4 * q^96 - 148 * q^97

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	0.707107	+	0.707107i	0.500000	+	0.500000i
$2$	0.707107	+	0.707107i	0.500000	+	0.500000i
$3$	0.867616	−	1.49908i	0.500919	−	0.865494i
$3$	0.867616	−	1.49908i	0.500919	−	0.865494i
$4$			1.00000i			0.500000i
$5$	0.850241	−	2.06811i	0.380239	−	0.924888i
$5$	0.850241	−	2.06811i	0.380239	−	0.924888i
$6$	1.67351	−	0.446512i	0.683207	−	0.182288i
$7$	0.811234	−	0.811234i	0.306618	−	0.306618i	−0.536978	−	0.843596i	$-0.680434\pi$
$7$	0.811234	−	0.811234i	0.306618	−	0.306618i	0.843596	+	0.536978i	$0.180434\pi$
$8$	−0.707107	+	0.707107i	−0.250000	+	0.250000i
$9$	−1.49448	−	2.60125i	−0.498161	−	0.867084i
$10$	2.06359	−	0.861165i	0.652564	−	0.272324i
$11$			1.25204i			0.377504i	0.982025	+	0.188752i	$0.0604442\pi$
$11$			1.25204i			0.377504i	−0.982025	+	0.188752i	$0.939556\pi$
$12$	1.49908	+	0.867616i	0.432747	+	0.250459i
$13$	3.40609	+	3.40609i	0.944678	+	0.944678i	0.998548	−	0.0538698i	$-0.0171556\pi$
$13$	3.40609	+	3.40609i	0.944678	+	0.944678i	−0.0538698	+	0.998548i	$0.517156\pi$
$14$	1.14726			0.306618
$15$	−2.36258	−	3.06891i	−0.610016	−	0.792389i
$16$	−1.00000			−0.250000
$17$	−3.04078	−	3.04078i	−0.737498	−	0.737498i	0.234595	−	0.972093i	$-0.424624\pi$
$17$	−3.04078	−	3.04078i	−0.737498	−	0.737498i	−0.972093	+	0.234595i	$0.924624\pi$
$18$	0.782605	−	2.89612i	0.184462	−	0.682623i
$19$		−	1.00000i		−	0.229416i
$19$		−	1.00000i		−	0.229416i
$20$	2.06811	+	0.850241i	0.462444	+	0.190120i
$21$	−0.512265	−	1.91995i	−0.111785	−	0.418966i
$22$	−0.885325	+	0.885325i	−0.188752	+	0.188752i
$23$	5.51574	−	5.51574i	1.15011	−	1.15011i	0.163581	−	0.986530i	$-0.447696\pi$
$23$	5.51574	−	5.51574i	1.15011	−	1.15011i	0.986530	−	0.163581i	$-0.0523045\pi$
$24$	0.446512	+	1.67351i	0.0911439	+	0.341603i
$25$	−3.55418	−	3.51679i	−0.710836	−	0.703358i
$26$			4.81693i			0.944678i
$27$	−5.19613	−	0.0165399i	−0.999995	−	0.00318310i
$28$	0.811234	+	0.811234i	0.153309	+	0.153309i
$29$	5.49893			1.02113			0.510563	−	0.859840i	$-0.329437\pi$
$29$	5.49893			1.02113			0.510563	+	0.859840i	$0.329437\pi$
$30$	0.499447	−	3.84064i	0.0911862	−	0.701203i
$31$	−5.80986			−1.04348			−0.521741	−	0.853104i	$-0.674717\pi$
$31$	−5.80986			−1.04348			−0.521741	+	0.853104i	$0.674717\pi$
$32$	−0.707107	−	0.707107i	−0.125000	−	0.125000i
$33$	1.87691	+	1.08629i	0.326728	+	0.189099i
$34$		−	4.30032i		−	0.737498i
$35$	−0.987979	−	2.36747i	−0.166999	−	0.400175i
$36$	2.60125	−	1.49448i	0.433542	−	0.249081i
$37$	−7.08962	+	7.08962i	−1.16553	+	1.16553i	−0.182280	+	0.983247i	$0.558348\pi$
$37$	−7.08962	+	7.08962i	−1.16553	+	1.16553i	−0.983247	+	0.182280i	$0.941652\pi$
$38$	0.707107	−	0.707107i	0.114708	−	0.114708i
$39$	8.06117	−	2.15082i	1.29082	−	0.344407i
$40$	0.861165	+	2.06359i	0.136162	+	0.326282i
$41$		−	0.259187i		−	0.0404782i	−0.999795	−	0.0202391i	$-0.993557\pi$
$41$		−	0.259187i		−	0.0404782i	0.999795	−	0.0202391i	$-0.00644274\pi$
$42$	0.995380	−	1.71983i	0.153591	−	0.265376i
$43$	5.60388	+	5.60388i	0.854584	+	0.854584i	0.990694	−	0.136109i	$-0.0434599\pi$
$43$	5.60388	+	5.60388i	0.854584	+	0.854584i	−0.136109	+	0.990694i	$0.543460\pi$
$44$	−1.25204			−0.188752
$45$	−6.65036	+	0.879067i	−0.991377	+	0.131044i
$46$	7.80043			1.15011
$47$	6.12099	+	6.12099i	0.892838	+	0.892838i	0.994789	−	0.101951i	$-0.0325086\pi$
$47$	6.12099	+	6.12099i	0.892838	+	0.892838i	−0.101951	+	0.994789i	$0.532509\pi$
$48$	−0.867616	+	1.49908i	−0.125230	+	0.216374i
$49$			5.68380i			0.811971i
$50$	−0.0264390	−	4.99993i	−0.00373904	−	0.707097i
$51$	−7.19661	+	1.92015i	−1.00773	+	0.268874i
$52$	−3.40609	+	3.40609i	−0.472339	+	0.472339i
$53$	−0.465266	+	0.465266i	−0.0639091	+	0.0639091i	−0.738339	−	0.674430i	$-0.764390\pi$
$53$	−0.465266	+	0.465266i	−0.0639091	+	0.0639091i	0.674430	+	0.738339i	$0.264390\pi$
$54$	−3.66252	−	3.68591i	−0.498406	−	0.501589i
$55$	2.58936	+	1.06454i	0.349149	+	0.143542i
$56$			1.14726i			0.153309i
$57$	−1.49908	−	0.867616i	−0.198558	−	0.114919i
$58$	3.88833	+	3.88833i	0.510563	+	0.510563i
$59$	−9.08034			−1.18216			−0.591080	−	0.806613i	$-0.701298\pi$
$59$	−9.08034			−1.18216			−0.591080	+	0.806613i	$0.701298\pi$
$60$	3.06891	−	2.36258i	0.396194	−	0.305008i
$61$	6.32624			0.809992			0.404996	−	0.914318i	$-0.367273\pi$
$61$	6.32624			0.809992			0.404996	+	0.914318i	$0.367273\pi$
$62$	−4.10819	−	4.10819i	−0.521741	−	0.521741i
$63$	−3.32260	−	0.897850i	−0.418609	−	0.113118i
$64$		−	1.00000i		−	0.125000i
$65$	9.94016	−	4.14817i	1.23293	−	0.514518i
$66$	0.559051	+	2.09530i	0.0688144	+	0.257913i
$67$	−2.40925	+	2.40925i	−0.294336	+	0.294336i	−0.838791	−	0.544454i	$-0.816737\pi$
$67$	−2.40925	+	2.40925i	−0.294336	+	0.294336i	0.544454	+	0.838791i	$0.316737\pi$
$68$	3.04078	−	3.04078i	0.368749	−	0.368749i
$69$	−3.48299	−	13.0541i	−0.419303	−	1.57153i
$70$	0.975447	−	2.37266i	0.116588	−	0.283587i
$71$		−	0.747767i		−	0.0887437i	−0.999015	−	0.0443718i	$-0.985871\pi$
$71$		−	0.747767i		−	0.0887437i	0.999015	−	0.0443718i	$-0.0141286\pi$
$72$	2.89612	+	0.782605i	0.341311	+	0.0922308i
$73$	5.45994	+	5.45994i	0.639038	+	0.639038i	0.950318	−	0.311280i	$-0.100758\pi$
$73$	5.45994	+	5.45994i	0.639038	+	0.639038i	−0.311280	+	0.950318i	$0.600758\pi$
$74$	−10.0262			−1.16553
$75$	−8.35561	+	2.27678i	−0.964823	+	0.262899i
$76$	1.00000			0.114708
$77$	1.01570	+	1.01570i	0.115749	+	0.115749i
$78$	7.22097	+	4.17925i	0.817614	+	0.473207i
$79$		−	4.84381i		−	0.544971i	−0.962160	−	0.272485i	$-0.912154\pi$
$79$		−	4.84381i		−	0.544971i	0.962160	−	0.272485i	$-0.0878457\pi$
$80$	−0.850241	+	2.06811i	−0.0950599	+	0.231222i
$81$	−4.53304	+	7.77506i	−0.503671	+	0.863896i
$82$	0.183273	−	0.183273i	0.0202391	−	0.0202391i
$83$	−4.22891	+	4.22891i	−0.464183	+	0.464183i	−0.900024	−	0.435841i	$-0.856451\pi$
$83$	−4.22891	+	4.22891i	−0.464183	+	0.464183i	0.435841	+	0.900024i	$0.356451\pi$
$84$	1.91995	−	0.512265i	0.209483	−	0.0558927i
$85$	−8.87408	+	3.70328i	−0.962530	+	0.401678i
$86$			7.92509i			0.854584i
$87$	4.77097	−	8.24334i	0.511501	−	0.883779i
$88$	−0.885325	−	0.885325i	−0.0943760	−	0.0943760i
$89$	12.7982			1.35660			0.678302	−	0.734784i	$-0.262716\pi$
$89$	12.7982			1.35660			0.678302	+	0.734784i	$0.262716\pi$
$90$	−5.32411	−	4.08092i	−0.561210	−	0.430167i
$91$	5.52627			0.579310
$92$	5.51574	+	5.51574i	0.575055	+	0.575055i
$93$	−5.04073	+	8.70945i	−0.522699	+	0.903128i
$94$			8.65639i			0.892838i
$95$	−2.06811	−	0.850241i	−0.212184	−	0.0872329i
$96$	−1.67351	+	0.446512i	−0.170802	+	0.0455720i
$97$	−12.5537	+	12.5537i	−1.27463	+	1.27463i	−0.331005	+	0.943629i	$0.607388\pi$
$97$	−12.5537	+	12.5537i	−1.27463	+	1.27463i	−0.943629	+	0.331005i	$0.892612\pi$
$98$	−4.01905	+	4.01905i	−0.405986	+	0.405986i
$99$	3.25687	−	1.87115i	0.327328	−	0.188058i
$100$	3.51679	−	3.55418i	0.351679	−	0.355418i
$101$			3.55522i			0.353758i	0.984233	+	0.176879i	$0.0566001\pi$
$101$			3.55522i			0.353758i	−0.984233	+	0.176879i	$0.943400\pi$
$102$	−6.44652	−	3.73103i	−0.638301	−	0.369427i
$103$	−8.68610	−	8.68610i	−0.855867	−	0.855867i	0.134981	−	0.990848i	$-0.456903\pi$
$103$	−8.68610	−	8.68610i	−0.855867	−	0.855867i	−0.990848	+	0.134981i	$0.956903\pi$
$104$	−4.81693			−0.472339
$105$	−4.40621	−	0.572995i	−0.430002	−	0.0559186i
$106$	−0.657985			−0.0639091
$107$	5.27680	+	5.27680i	0.510128	+	0.510128i	0.914566	−	0.404438i	$-0.132533\pi$
$107$	5.27680	+	5.27680i	0.510128	+	0.510128i	−0.404438	+	0.914566i	$0.632533\pi$
$108$	0.0165399	−	5.19613i	0.00159155	−	0.499997i
$109$			19.4996i			1.86773i	0.357632	+	0.933863i	$0.383584\pi$
$109$			19.4996i			1.86773i	−0.357632	+	0.933863i	$0.616416\pi$
$110$	1.07821	+	2.58369i	0.102804	+	0.246345i
$111$	4.47684	+	16.7790i	0.424923	+	1.59259i
$112$	−0.811234	+	0.811234i	−0.0766544	+	0.0766544i
$113$	−3.30686	+	3.30686i	−0.311083	+	0.311083i	−0.845329	−	0.534246i	$-0.820596\pi$
$113$	−3.30686	+	3.30686i	−0.311083	+	0.311083i	0.534246	+	0.845329i	$0.320596\pi$
$114$	−0.446512	−	1.67351i	−0.0418197	−	0.156738i
$115$	−6.71746	−	16.0969i	−0.626406	−	1.50104i
$116$			5.49893i			0.510563i
$117$	3.76975	−	13.9504i	0.348514	−	1.28972i
$118$	−6.42077	−	6.42077i	−0.591080	−	0.591080i
$119$	−4.93358			−0.452260
$120$	3.84064	+	0.499447i	0.350601	+	0.0455931i
$121$	9.43240			0.857491
$122$	4.47333	+	4.47333i	0.404996	+	0.404996i
$123$	−0.388542	−	0.224875i	−0.0350336	−	0.0202763i
$124$		−	5.80986i		−	0.521741i
$125$	−10.2950	+	4.36032i	−0.920815	+	0.389999i
$126$	−1.71456	−	2.98431i	−0.152745	−	0.265864i
$127$	−5.40945	+	5.40945i	−0.480011	+	0.480011i	−0.905135	−	0.425124i	$-0.860231\pi$
$127$	−5.40945	+	5.40945i	−0.480011	+	0.480011i	0.425124	+	0.905135i	$0.360231\pi$
$128$	0.707107	−	0.707107i	0.0625000	−	0.0625000i
$129$	13.2627	−	3.53865i	1.16772	−	0.311561i
$130$	9.96196	+	4.09555i	0.873722	+	0.359204i
$131$		−	21.4587i		−	1.87485i	−0.348185	−	0.937426i	$-0.613202\pi$
$131$		−	21.4587i		−	1.87485i	0.348185	−	0.937426i	$-0.386798\pi$
$132$	−1.08629	+	1.87691i	−0.0945494	+	0.163364i
$133$	−0.811234	−	0.811234i	−0.0703429	−	0.0703429i
$134$	−3.40719			−0.294336
$135$	−4.45217	+	10.7321i	−0.383182	+	0.923673i
$136$	4.30032			0.368749
$137$	−13.6290	−	13.6290i	−1.16440	−	1.16440i	−0.983501	−	0.180902i	$-0.942098\pi$
$137$	−13.6290	−	13.6290i	−1.16440	−	1.16440i	−0.180902	−	0.983501i	$-0.557902\pi$
$138$	6.76778	−	11.6935i	0.576112	−	0.995414i
$139$		−	10.5758i		−	0.897030i	−0.893775	−	0.448515i	$-0.851953\pi$
$139$		−	10.5758i		−	0.897030i	0.893775	−	0.448515i	$-0.148047\pi$
$140$	2.36747	−	0.987979i	0.200088	−	0.0834995i
$141$	14.4865	−	3.86518i	1.21999	−	0.325507i
$142$	0.528751	−	0.528751i	0.0443718	−	0.0443718i
$143$	−4.26455	+	4.26455i	−0.356620	+	0.356620i
$144$	1.49448	+	2.60125i	0.124540	+	0.216771i
$145$	4.67542	−	11.3724i	0.388273	−	0.944428i
$146$			7.72152i			0.639038i
$147$	8.52047	+	4.93136i	0.702756	+	0.406731i
$148$	−7.08962	−	7.08962i	−0.582763	−	0.582763i
$149$	−0.688172			−0.0563772			−0.0281886	−	0.999603i	$-0.508974\pi$
$149$	−0.688172			−0.0563772			−0.0281886	+	0.999603i	$0.508974\pi$
$150$	−7.51824	−	4.29839i	−0.613861	−	0.350962i
$151$	−7.78234			−0.633318			−0.316659	−	0.948539i	$-0.602561\pi$
$151$	−7.78234			−0.633318			−0.316659	+	0.948539i	$0.602561\pi$
$152$	0.707107	+	0.707107i	0.0573539	+	0.0573539i
$153$	−3.36545	+	12.4543i	−0.272080	+	1.00687i
$154$			1.43641i			0.115749i
$155$	−4.93978	+	12.0154i	−0.396773	+	0.965104i
$156$	2.15082	+	8.06117i	0.172203	+	0.645410i
$157$	4.92864	−	4.92864i	0.393348	−	0.393348i	−0.482531	−	0.875879i	$-0.660282\pi$
$157$	4.92864	−	4.92864i	0.393348	−	0.393348i	0.875879	+	0.482531i	$0.160282\pi$
$158$	3.42509	−	3.42509i	0.272485	−	0.272485i
$159$	0.293798	+	1.10114i	0.0232997	+	0.0873263i
$160$	−2.06359	+	0.861165i	−0.163141	+	0.0680811i
$161$		−	8.94911i		−	0.705289i
$162$	−8.70314	+	2.29245i	−0.683783	+	0.180112i
$163$	−0.293352	−	0.293352i	−0.0229771	−	0.0229771i	0.695525	−	0.718502i	$-0.255172\pi$
$163$	−0.293352	−	0.293352i	−0.0229771	−	0.0229771i	−0.718502	+	0.695525i	$0.755172\pi$
$164$	0.259187			0.0202391
$165$	3.84239	−	2.95805i	0.299130	−	0.230284i
$166$	−5.98058			−0.464183
$167$	−4.29057	−	4.29057i	−0.332015	−	0.332015i	0.521337	−	0.853351i	$-0.325434\pi$
$167$	−4.29057	−	4.29057i	−0.332015	−	0.332015i	−0.853351	+	0.521337i	$0.825434\pi$
$168$	1.71983	+	0.995380i	0.132688	+	0.0767953i
$169$			10.2028i			0.784834i
$170$	−8.89354	−	3.65631i	−0.682104	−	0.280426i
$171$	−2.60125	+	1.49448i	−0.198923	+	0.114286i
$172$	−5.60388	+	5.60388i	−0.427292	+	0.427292i
$173$	−3.16382	+	3.16382i	−0.240541	+	0.240541i	−0.817074	−	0.576533i	$-0.804405\pi$
$173$	−3.16382	+	3.16382i	−0.240541	+	0.240541i	0.576533	+	0.817074i	$0.304405\pi$
$174$	9.20251	−	2.45534i	0.697640	−	0.186139i
$175$	−5.73621	+	0.0303324i	−0.433617	+	0.00229291i
$176$		−	1.25204i		−	0.0943760i
$177$	−7.87825	+	13.6122i	−0.592166	+	1.02315i
$178$	9.04967	+	9.04967i	0.678302	+	0.678302i
$179$	3.82605			0.285973			0.142986	−	0.989725i	$-0.454330\pi$
$179$	3.82605			0.285973			0.142986	+	0.989725i	$0.454330\pi$
$180$	−0.879067	−	6.65036i	−0.0655218	−	0.495688i
$181$	11.7262			0.871603			0.435801	−	0.900043i	$-0.356465\pi$
$181$	11.7262			0.871603			0.435801	+	0.900043i	$0.356465\pi$
$182$	3.90766	+	3.90766i	0.289655	+	0.289655i
$183$	5.48875	−	9.48354i	0.405740	−	0.701044i
$184$			7.80043i			0.575055i
$185$	8.63425	+	20.6900i	0.634803	+	1.52116i
$186$	−9.72284	+	2.59417i	−0.712913	+	0.190214i
$187$	3.80718	−	3.80718i	0.278409	−	0.278409i
$188$	−6.12099	+	6.12099i	−0.446419	+	0.446419i
$189$	−4.22869	+	4.20186i	−0.307592	+	0.305640i
$190$	−0.861165	−	2.06359i	−0.0624755	−	0.149708i
$191$			11.0228i			0.797579i	0.917042	+	0.398790i	$0.130570\pi$
$191$			11.0228i			0.797579i	−0.917042	+	0.398790i	$0.869430\pi$
$192$	−1.49908	−	0.867616i	−0.108187	−	0.0626148i
$193$	6.75179	+	6.75179i	0.486004	+	0.486004i	0.907043	−	0.421039i	$-0.138334\pi$
$193$	6.75179	+	6.75179i	0.486004	+	0.486004i	−0.421039	+	0.907043i	$0.638334\pi$
$194$	−17.7536			−1.27463
$195$	2.40580	−	18.5001i	0.172283	−	1.32482i
$196$	−5.68380			−0.405986
$197$	−7.05740	−	7.05740i	−0.502819	−	0.502819i	0.409494	−	0.912313i	$-0.365705\pi$
$197$	−7.05740	−	7.05740i	−0.502819	−	0.502819i	−0.912313	+	0.409494i	$0.865705\pi$
$198$	3.62606	+	0.979852i	0.257693	+	0.0696350i
$199$		−	23.7718i		−	1.68514i	−0.538588	−	0.842569i	$-0.681042\pi$
$199$		−	23.7718i		−	1.68514i	0.538588	−	0.842569i	$-0.318958\pi$
$200$	4.99993	−	0.0264390i	0.353548	−	0.00186952i
$201$	1.52135	+	5.70196i	0.107308	+	0.402185i
$202$	−2.51392	+	2.51392i	−0.176879	+	0.176879i
$203$	4.46092	−	4.46092i	0.313096	−	0.313096i
$204$	−1.92015	−	7.19661i	−0.134437	−	0.503864i
$205$	−0.536027	−	0.220371i	−0.0374378	−	0.0153914i
$206$		−	12.2840i		−	0.855867i
$207$	−22.5910	−	6.10465i	−1.57018	−	0.424303i
$208$	−3.40609	−	3.40609i	−0.236170	−	0.236170i
$209$	1.25204			0.0866054
$210$	−2.71049	−	3.52083i	−0.187042	−	0.242960i
$211$	16.9279			1.16536			0.582682	−	0.812700i	$-0.302003\pi$
$211$	16.9279			1.16536			0.582682	+	0.812700i	$0.302003\pi$
$212$	−0.465266	−	0.465266i	−0.0319546	−	0.0319546i
$213$	−1.12096	−	0.648775i	−0.0768071	−	0.0444534i
$214$			7.46253i			0.510128i
$215$	16.3541	−	6.82481i	1.11534	−	0.465448i
$216$	3.68591	−	3.66252i	0.250795	−	0.249203i
$217$	−4.71316	+	4.71316i	−0.319950	+	0.319950i
$218$	−13.7883	+	13.7883i	−0.933863	+	0.933863i
$219$	12.9220	−	3.44776i	0.873190	−	0.232978i
$220$	−1.06454	+	2.58936i	−0.0717710	+	0.174574i
$221$		−	20.7143i		−	1.39340i
$222$	−8.69893	+	15.0301i	−0.583834	+	1.00876i
$223$	−13.0760	−	13.0760i	−0.875634	−	0.875634i	0.117446	−	0.993079i	$-0.462529\pi$
$223$	−13.0760	−	13.0760i	−0.875634	−	0.875634i	−0.993079	+	0.117446i	$0.962529\pi$
$224$	−1.14726			−0.0766544
$225$	−3.83640	+	14.5011i	−0.255760	+	0.966740i
$226$	−4.67660			−0.311083
$227$	−18.5524	−	18.5524i	−1.23136	−	1.23136i	−0.963440	−	0.267923i	$-0.913663\pi$
$227$	−18.5524	−	18.5524i	−1.23136	−	1.23136i	−0.267923	−	0.963440i	$-0.586337\pi$
$228$	0.867616	−	1.49908i	0.0574593	−	0.0992790i
$229$		−	2.63822i		−	0.174338i	−0.996194	−	0.0871692i	$-0.972218\pi$
$229$		−	2.63822i		−	0.174338i	0.996194	−	0.0871692i	$-0.0277821\pi$
$230$	6.63225	−	16.1322i	0.437317	−	1.06372i
$231$	2.40385	−	0.641376i	0.158162	−	0.0421994i
$232$	−3.88833	+	3.88833i	−0.255282	+	0.255282i
$233$	−13.3570	+	13.3570i	−0.875046	+	0.875046i	−0.993017	−	0.117971i	$-0.962361\pi$
$233$	−13.3570	+	13.3570i	−0.875046	+	0.875046i	0.117971	+	0.993017i	$0.462361\pi$
$234$	12.5301	−	7.19883i	0.819116	−	0.470602i
$235$	17.8632	−	7.45458i	1.16527	−	0.486283i
$236$		−	9.08034i		−	0.591080i
$237$	−7.26126	−	4.20257i	−0.471669	−	0.272986i
$238$	−3.48857	−	3.48857i	−0.226130	−	0.226130i
$239$	0.359134			0.0232304			0.0116152	−	0.999933i	$-0.496303\pi$
$239$	0.359134			0.0232304			0.0116152	+	0.999933i	$0.496303\pi$
$240$	2.36258	+	3.06891i	0.152504	+	0.198097i
$241$	5.42354			0.349361			0.174681	−	0.984625i	$-0.444111\pi$
$241$	5.42354			0.349361			0.174681	+	0.984625i	$0.444111\pi$
$242$	6.66971	+	6.66971i	0.428745	+	0.428745i
$243$	7.72250	+	13.5412i	0.495399	+	0.868666i
$244$			6.32624i			0.404996i
$245$	11.7547	+	4.83260i	0.750982	+	0.308743i
$246$	−0.115730	−	0.433751i	−0.00737868	−	0.0276549i
$247$	3.40609	−	3.40609i	0.216724	−	0.216724i
$248$	4.10819	−	4.10819i	0.260870	−	0.260870i
$249$	2.67040	+	10.0085i	0.169230	+	0.634265i
$250$	−10.3629	−	4.19647i	−0.655407	−	0.265408i
$251$		−	13.3902i		−	0.845179i	−0.906321	−	0.422590i	$-0.861121\pi$
$251$		−	13.3902i		−	0.845179i	0.906321	−	0.422590i	$-0.138879\pi$
$252$	0.897850	−	3.32260i	0.0565592	−	0.209304i
$253$	6.90592	+	6.90592i	0.434171	+	0.434171i
$254$	−7.65012			−0.480011
$255$	−2.14778	+	16.5160i	−0.134499	+	1.03427i
$256$	1.00000			0.0625000
$257$	16.2263	+	16.2263i	1.01217	+	1.01217i	0.999925	+	0.0122435i	$0.00389731\pi$
$257$	16.2263	+	16.2263i	1.01217	+	1.01217i	0.0122435	+	0.999925i	$0.496103\pi$
$258$	11.8803	+	6.87594i	0.739638	+	0.428077i
$259$			11.5027i			0.714742i
$260$	4.14817	+	9.94016i	0.257259	+	0.616463i
$261$	−8.21807	−	14.3041i	−0.508686	−	0.885403i
$262$	15.1736	−	15.1736i	0.937426	−	0.937426i
$263$	−3.46688	+	3.46688i	−0.213777	+	0.213777i	−0.805870	−	0.592093i	$-0.798302\pi$
$263$	−3.46688	+	3.46688i	−0.213777	+	0.213777i	0.592093	+	0.805870i	$0.298302\pi$
$264$	−2.09530	+	0.559051i	−0.128957	+	0.0344072i
$265$	0.566634	+	1.35781i	0.0348080	+	0.0834096i
$266$		−	1.14726i		−	0.0703429i
$267$	11.1039	−	19.1855i	0.679548	−	1.17413i
$268$	−2.40925	−	2.40925i	−0.147168	−	0.147168i
$269$	4.91421			0.299625			0.149812	−	0.988714i	$-0.452133\pi$
$269$	4.91421			0.299625			0.149812	+	0.988714i	$0.452133\pi$
$270$	−10.7369	+	4.44059i	−0.653427	+	0.270246i
$271$	6.09935			0.370509			0.185255	−	0.982691i	$-0.440689\pi$
$271$	6.09935			0.370509			0.185255	+	0.982691i	$0.440689\pi$
$272$	3.04078	+	3.04078i	0.184375	+	0.184375i
$273$	4.79468	−	8.28432i	0.290187	−	0.501390i
$274$		−	19.2743i		−	1.16440i
$275$	4.40316	−	4.44997i	0.265520	−	0.268343i
$276$	13.0541	−	3.48299i	0.785763	−	0.209651i
$277$	−11.4817	+	11.4817i	−0.689866	+	0.689866i	−0.962202	−	0.272336i	$-0.912204\pi$
$277$	−11.4817	+	11.4817i	−0.689866	+	0.689866i	0.272336	+	0.962202i	$0.412204\pi$
$278$	7.47824	−	7.47824i	0.448515	−	0.448515i
$279$	8.68274	+	15.1129i	0.519822	+	0.904787i
$280$	2.37266	+	0.975447i	0.141794	+	0.0582941i
$281$		−	19.8457i		−	1.18389i	−0.805977	−	0.591947i	$-0.798359\pi$
$281$		−	19.8457i		−	1.18389i	0.805977	−	0.591947i	$-0.201641\pi$
$282$	12.9766	+	7.51042i	0.772746	+	0.447239i
$283$	13.5529	+	13.5529i	0.805635	+	0.805635i	0.983970	−	0.178335i	$-0.0570711\pi$
$283$	13.5529	+	13.5529i	0.805635	+	0.805635i	−0.178335	+	0.983970i	$0.557071\pi$
$284$	0.747767			0.0443718
$285$	−3.06891	+	2.36258i	−0.181786	+	0.139947i
$286$	−6.03099			−0.356620
$287$	−0.210261	−	0.210261i	−0.0124113	−	0.0124113i
$288$	−0.782605	+	2.89612i	−0.0461154	+	0.170656i
$289$			1.49273i			0.0878079i
$290$	11.3475	−	4.73549i	0.666350	−	0.278078i
$291$	7.92720	+	29.7108i	0.464701	+	1.74168i
$292$	−5.45994	+	5.45994i	−0.319519	+	0.319519i
$293$	−4.72321	+	4.72321i	−0.275933	+	0.275933i	−0.831483	−	0.555550i	$-0.812508\pi$
$293$	−4.72321	+	4.72321i	−0.275933	+	0.275933i	0.555550	+	0.831483i	$0.312508\pi$
$294$	2.53789	+	9.51188i	0.148013	+	0.554744i
$295$	−7.72048	+	18.7792i	−0.449504	+	1.09336i
$296$		−	10.0262i		−	0.582763i
$297$	0.0207086	−	6.50575i	0.00120163	−	0.377502i
$298$	−0.486611	−	0.486611i	−0.0281886	−	0.0281886i
$299$	37.5741			2.17297
$300$	−2.27678	−	8.35561i	−0.131450	−	0.482412i
$301$	9.09213			0.524062
$302$	−5.50294	−	5.50294i	−0.316659	−	0.316659i
$303$	5.32956	+	3.08457i	0.306175	+	0.177204i
$304$			1.00000i			0.0573539i
$305$	5.37883	−	13.0834i	0.307991	−	0.749152i
$306$	−11.1862	+	6.42675i	−0.639473	+	0.367393i
$307$	10.8953	−	10.8953i	0.621830	−	0.621830i	−0.324169	−	0.945999i	$-0.605085\pi$
$307$	10.8953	−	10.8953i	0.621830	−	0.621830i	0.945999	+	0.324169i	$0.105085\pi$
$308$	−1.01570	+	1.01570i	−0.0578747	+	0.0578747i
$309$	−20.5574	+	5.48496i	−1.16947	+	0.312028i
$310$	−11.9892	+	5.00325i	−0.680938	+	0.284165i
$311$		−	18.6727i		−	1.05883i	−0.848363	−	0.529415i	$-0.822412\pi$
$311$		−	18.6727i		−	1.05883i	0.848363	−	0.529415i	$-0.177588\pi$
$312$	−4.17925	+	7.22097i	−0.236603	+	0.408807i
$313$	−5.71317	−	5.71317i	−0.322928	−	0.322928i	0.526961	−	0.849889i	$-0.323331\pi$
$313$	−5.71317	−	5.71317i	−0.322928	−	0.322928i	−0.849889	+	0.526961i	$0.823331\pi$
$314$	6.97014			0.393348
$315$	−4.68187	+	6.10813i	−0.263793	+	0.344154i
$316$	4.84381			0.272485
$317$	11.0822	+	11.0822i	0.622438	+	0.622438i	0.946154	−	0.323716i	$-0.104932\pi$
$317$	11.0822	+	11.0822i	0.622438	+	0.622438i	−0.323716	+	0.946154i	$0.604932\pi$
$318$	−0.570878	+	0.986372i	−0.0320133	+	0.0553130i
$319$			6.88488i			0.385479i
$320$	−2.06811	−	0.850241i	−0.115611	−	0.0475299i
$321$	12.4886	−	3.33211i	0.697045	−	0.185980i
$322$	6.32798	−	6.32798i	0.352644	−	0.352644i
$323$	−3.04078	+	3.04078i	−0.169194	+	0.169194i
$324$	−7.77506	−	4.53304i	−0.431948	−	0.251836i
$325$	−0.127355	−	24.0843i	−0.00706438	−	1.33596i
$326$		−	0.414863i		−	0.0229771i
$327$	29.2315	+	16.9182i	1.61651	+	0.935578i
$328$	0.183273	+	0.183273i	0.0101195	+	0.0101195i
$329$	9.93112			0.547520
$330$	4.80864	+	0.625327i	0.264707	+	0.0344231i
$331$	20.0068			1.09967			0.549837	−	0.835272i	$-0.314690\pi$
$331$	20.0068			1.09967			0.549837	+	0.835272i	$0.314690\pi$
$332$	−4.22891	−	4.22891i	−0.232091	−	0.232091i
$333$	29.0372	+	7.84658i	1.59123	+	0.429990i
$334$		−	6.06779i		−	0.332015i
$335$	2.93415	+	7.03103i	0.160310	+	0.384146i
$336$	0.512265	+	1.91995i	0.0279464	+	0.104742i
$337$	8.69484	−	8.69484i	0.473638	−	0.473638i	−0.429452	−	0.903090i	$-0.641293\pi$
$337$	8.69484	−	8.69484i	0.473638	−	0.473638i	0.903090	+	0.429452i	$0.141293\pi$
$338$	−7.21450	+	7.21450i	−0.392417	+	0.392417i
$339$	2.08816	+	7.82632i	0.113413	+	0.425068i
$340$	−3.70328	−	8.87408i	−0.200839	−	0.481265i
$341$		−	7.27417i		−	0.393919i
$342$	−2.89612	−	0.782605i	−0.156604	−	0.0423184i
$343$	10.2895	+	10.2895i	0.555583	+	0.555583i
$344$	−7.92509			−0.427292
$345$	−29.9587	−	3.89590i	−1.61292	−	0.209748i
$346$	−4.47431			−0.240541
$347$	−5.08826	−	5.08826i	−0.273152	−	0.273152i	0.557216	−	0.830368i	$-0.311870\pi$
$347$	−5.08826	−	5.08826i	−0.273152	−	0.273152i	−0.830368	+	0.557216i	$0.811870\pi$
$348$	8.24334	+	4.77097i	0.441890	+	0.255751i
$349$		−	21.6797i		−	1.16049i	−0.814442	−	0.580244i	$-0.802957\pi$
$349$		−	21.6797i		−	1.16049i	0.814442	−	0.580244i	$-0.197043\pi$
$350$	−4.07756	−	4.03467i	−0.217955	−	0.215662i
$351$	−17.6421	−	17.7548i	−0.941666	−	0.947680i
$352$	0.885325	−	0.885325i	0.0471880	−	0.0471880i
$353$	−7.11922	+	7.11922i	−0.378918	+	0.378918i	−0.870712	−	0.491794i	$-0.836341\pi$
$353$	−7.11922	+	7.11922i	−0.378918	+	0.378918i	0.491794	+	0.870712i	$0.336341\pi$
$354$	−15.1960	+	4.05448i	−0.807659	+	0.215493i
$355$	−1.54647	−	0.635783i	−0.0820780	−	0.0337438i
$356$			12.7982i			0.678302i
$357$	−4.28045	+	7.39583i	−0.226546	+	0.391429i
$358$	2.70543	+	2.70543i	0.142986	+	0.142986i
$359$	−24.6824			−1.30269			−0.651343	−	0.758783i	$-0.725794\pi$
$359$	−24.6824			−1.30269			−0.651343	+	0.758783i	$0.725794\pi$
$360$	4.08092	−	5.32411i	0.215083	−	0.280605i
$361$	−1.00000			−0.0526316
$362$	8.29169	+	8.29169i	0.435801	+	0.435801i
$363$	8.18370	−	14.1399i	0.429533	−	0.742153i
$364$			5.52627i			0.289655i
$365$	15.9340	−	6.64951i	0.834026	−	0.348051i
$366$	10.5870	−	2.82474i	0.553392	−	0.147652i
$367$	−1.59834	+	1.59834i	−0.0834327	+	0.0834327i	−0.747591	−	0.664159i	$-0.768790\pi$
$367$	−1.59834	+	1.59834i	−0.0834327	+	0.0834327i	0.664159	+	0.747591i	$0.268790\pi$
$368$	−5.51574	+	5.51574i	−0.287528	+	0.287528i
$369$	−0.674210	+	0.387350i	−0.0350980	+	0.0201647i
$370$	−8.52472	+	20.7354i	−0.443179	+	1.07798i
$371$			0.754879i			0.0391914i
$372$	−8.70945	−	5.04073i	−0.451564	−	0.261350i
$373$	−20.6849	−	20.6849i	−1.07102	−	1.07102i	−0.997277	−	0.0737477i	$-0.976504\pi$
$373$	−20.6849	−	20.6849i	−1.07102	−	1.07102i	−0.0737477	−	0.997277i	$-0.523496\pi$
$374$	5.38417			0.278409
$375$	−2.39566	+	19.2162i	−0.123711	+	0.992318i
$376$	−8.65639			−0.446419
$377$	18.7298	+	18.7298i	0.964636	+	0.964636i
$378$	−5.96130	−	0.0189755i	−0.306616	−	0.000975995i
$379$		−	19.2862i		−	0.990668i	−0.868703	−	0.495334i	$-0.835046\pi$
$379$		−	19.2862i		−	0.990668i	0.868703	−	0.495334i	$-0.164954\pi$
$380$	0.850241	−	2.06811i	0.0436165	−	0.106092i
$381$	3.41587	+	12.8025i	0.175001	+	0.655894i
$382$	−7.79427	+	7.79427i	−0.398790	+	0.398790i
$383$	22.7437	−	22.7437i	1.16215	−	1.16215i	0.178146	−	0.984004i	$-0.442990\pi$
$383$	22.7437	−	22.7437i	1.16215	−	1.16215i	0.984004	−	0.178146i	$-0.0570100\pi$
$384$	−0.446512	−	1.67351i	−0.0227860	−	0.0854008i
$385$	2.96416	−	1.23699i	0.151068	−	0.0630428i
$386$			9.54847i			0.486004i
$387$	6.20221	−	22.9520i	0.315276	−	1.16672i
$388$	−12.5537	−	12.5537i	−0.637317	−	0.637317i
$389$	−20.2169			−1.02504			−0.512519	−	0.858676i	$-0.671287\pi$
$389$	−20.2169			−1.02504			−0.512519	+	0.858676i	$0.671287\pi$
$390$	14.7827	−	11.3804i	0.748552	−	0.576269i
$391$	−33.5443			−1.69641
$392$	−4.01905	−	4.01905i	−0.202993	−	0.202993i
$393$	−32.1683	−	18.6179i	−1.62267	−	0.939148i
$394$		−	9.98068i		−	0.502819i
$395$	−10.0175	−	4.11841i	−0.504037	−	0.207219i
$396$	1.87115	+	3.25687i	0.0940289	+	0.163664i
$397$	0.250592	−	0.250592i	0.0125768	−	0.0125768i	−0.700790	−	0.713367i	$-0.747169\pi$
$397$	0.250592	−	0.250592i	0.0125768	−	0.0125768i	0.713367	+	0.700790i	$0.247169\pi$
$398$	16.8092	−	16.8092i	0.842569	−	0.842569i
$399$	−1.91995	+	0.512265i	−0.0961175	+	0.0256453i
$400$	3.55418	+	3.51679i	0.177709	+	0.175839i
$401$			21.6861i			1.08295i	0.840716	+	0.541476i	$0.182134\pi$
$401$			21.6861i			1.08295i	−0.840716	+	0.541476i	$0.817866\pi$
$402$	−2.95613	+	5.10765i	−0.147439	+	0.254746i
$403$	−19.7889	−	19.7889i	−0.985754	−	0.985754i
$404$	−3.55522			−0.176879
$405$	12.2255	+	15.9855i	0.607491	+	0.794326i
$406$	6.30870			0.313096
$407$	−8.87649	−	8.87649i	−0.439991	−	0.439991i
$408$	3.73103	−	6.44652i	0.184713	−	0.319150i
$409$			5.94808i			0.294114i	0.989128	+	0.147057i	$0.0469800\pi$
$409$			5.94808i			0.294114i	−0.989128	+	0.147057i	$0.953020\pi$
$410$	−0.223203	−	0.534855i	−0.0110232	−	0.0264146i
$411$	−32.2557	+	8.60622i	−1.59106	+	0.424513i
$412$	8.68610	−	8.68610i	0.427933	−	0.427933i
$413$	−7.36628	+	7.36628i	−0.362471	+	0.362471i
$414$	−11.6576	−	20.2909i	−0.572940	−	0.997243i
$415$	5.15026	+	12.3414i	0.252817	+	0.605818i
$416$		−	4.81693i		−	0.236170i
$417$	−15.8540	−	9.17576i	−0.776375	−	0.449339i
$418$	0.885325	+	0.885325i	0.0433027	+	0.0433027i
$419$	35.8879			1.75324			0.876620	−	0.481184i	$-0.159793\pi$
$419$	35.8879			1.75324			0.876620	+	0.481184i	$0.159793\pi$
$420$	0.572995	−	4.40621i	0.0279593	−	0.215001i
$421$	−13.5450			−0.660145			−0.330073	−	0.943956i	$-0.607073\pi$
$421$	−13.5450			−0.660145			−0.330073	+	0.943956i	$0.607073\pi$
$422$	11.9698	+	11.9698i	0.582682	+	0.582682i
$423$	6.77453	−	25.0700i	0.329389	−	1.21894i
$424$		−	0.657985i		−	0.0319546i
$425$	0.113696	+	21.5013i	0.00551507	+	1.04297i
$426$	−0.333887	−	1.25139i	−0.0161769	−	0.0606302i
$427$	5.13206	−	5.13206i	0.248358	−	0.248358i
$428$	−5.27680	+	5.27680i	−0.255064	+	0.255064i
$429$	2.69291	+	10.0929i	0.130015	+	0.487290i
$430$	16.3900	+	6.73824i	0.790395	+	0.324947i
$431$			0.445342i			0.0214514i	0.999942	+	0.0107257i	$0.00341416\pi$
$431$			0.445342i			0.0214514i	−0.999942	+	0.0107257i	$0.996586\pi$
$432$	5.19613	+	0.0165399i	0.249999	+	0.000795775i
$433$	20.9273	+	20.9273i	1.00570	+	1.00570i	0.999984	+	0.00571854i	$0.00182028\pi$
$433$	20.9273	+	20.9273i	1.00570	+	1.00570i	0.00571854	+	0.999984i	$0.498180\pi$
$434$	−6.66541			−0.319950
$435$	−12.9917	−	16.8757i	−0.622904	−	0.809129i
$436$	−19.4996			−0.933863
$437$	−5.51574	−	5.51574i	−0.263854	−	0.263854i
$438$	11.5752	+	6.69932i	0.553084	+	0.320106i
$439$			0.487999i			0.0232909i	0.999932	+	0.0116455i	$0.00370695\pi$
$439$			0.487999i			0.0232909i	−0.999932	+	0.0116455i	$0.996293\pi$
$440$	−2.58369	+	1.07821i	−0.123173	+	0.0514018i
$441$	14.7850	−	8.49434i	0.704048	−	0.404492i
$442$	14.6473	−	14.6473i	0.696699	−	0.696699i
$443$	5.91639	−	5.91639i	0.281096	−	0.281096i	−0.552450	−	0.833546i	$-0.686307\pi$
$443$	5.91639	−	5.91639i	0.281096	−	0.281096i	0.833546	+	0.552450i	$0.186307\pi$
$444$	−16.7790	+	4.47684i	−0.796295	+	0.212461i
$445$	10.8815	−	26.4681i	0.515834	−	1.25471i
$446$		−	18.4923i		−	0.875634i
$447$	−0.597069	+	1.03162i	−0.0282404	+	0.0487942i
$448$	−0.811234	−	0.811234i	−0.0383272	−	0.0383272i
$449$	−16.3599			−0.772074			−0.386037	−	0.922483i	$-0.626156\pi$
$449$	−16.3599			−0.772074			−0.386037	+	0.922483i	$0.626156\pi$
$450$	−12.9666	+	7.54109i	−0.611250	+	0.355490i
$451$	0.324512			0.0152807
$452$	−3.30686	−	3.30686i	−0.155541	−	0.155541i
$453$	−6.75209	+	11.6664i	−0.317241	+	0.548133i
$454$		−	26.2370i		−	1.23136i
$455$	4.69866	−	11.4289i	0.220277	−	0.535797i
$456$	1.67351	−	0.446512i	0.0783692	−	0.0209099i
$457$	−22.9810	+	22.9810i	−1.07501	+	1.07501i	−0.0780586	+	0.996949i	$0.524872\pi$
$457$	−22.9810	+	22.9810i	−1.07501	+	1.07501i	−0.996949	+	0.0780586i	$0.975128\pi$
$458$	1.86550	−	1.86550i	0.0871692	−	0.0871692i
$459$	15.7500	+	15.8506i	0.735147	+	0.739842i
$460$	16.0969	−	6.71746i	0.750521	−	0.313203i
$461$		−	16.8678i		−	0.785612i	−0.919621	−	0.392806i	$-0.871504\pi$
$461$		−	16.8678i		−	0.785612i	0.919621	−	0.392806i	$-0.128496\pi$
$462$	2.15330	+	1.24626i	0.100180	+	0.0579811i
$463$	−17.7793	−	17.7793i	−0.826272	−	0.826272i	0.160727	−	0.986999i	$-0.448616\pi$
$463$	−17.7793	−	17.7793i	−0.826272	−	0.826272i	−0.986999	+	0.160727i	$0.948616\pi$
$464$	−5.49893			−0.255282
$465$	13.7263	+	17.8299i	0.636541	+	0.826843i
$466$	−18.8897			−0.875046
$467$	12.4366	+	12.4366i	0.575497	+	0.575497i	0.933659	−	0.358162i	$-0.116596\pi$
$467$	12.4366	+	12.4366i	0.575497	+	0.575497i	−0.358162	+	0.933659i	$0.616596\pi$
$468$	13.9504	+	3.76975i	0.644859	+	0.174257i
$469$			3.90893i			0.180497i
$470$	17.9024	+	7.36002i	0.825775	+	0.339492i
$471$	−3.11225	−	11.6646i	−0.143405	−	0.537476i
$472$	6.42077	−	6.42077i	0.295540	−	0.295540i
$473$	−7.01628	+	7.01628i	−0.322609	+	0.322609i
$474$	−2.16282	−	8.10615i	−0.0993416	−	0.372328i
$475$	−3.51679	+	3.55418i	−0.161361	+	0.163077i
$476$		−	4.93358i		−	0.226130i
$477$	1.90561	+	0.514942i	0.0872517	+	0.0235776i
$478$	0.253946	+	0.253946i	0.0116152	+	0.0116152i
$479$	−37.6990			−1.72251			−0.861256	−	0.508172i	$-0.830321\pi$
$479$	−37.6990			−1.72251			−0.861256	+	0.508172i	$0.830321\pi$
$480$	−0.499447	+	3.84064i	−0.0227965	+	0.175301i
$481$	−48.2957			−2.20210
$482$	3.83502	+	3.83502i	0.174681	+	0.174681i
$483$	−13.4154	−	7.76440i	−0.610423	−	0.353292i
$484$			9.43240i			0.428745i
$485$	15.2888	+	36.6361i	0.694228	+	1.66356i
$486$	−4.11441	+	15.0357i	−0.186634	+	0.682032i
$487$	1.14616	−	1.14616i	0.0519376	−	0.0519376i	−0.680661	−	0.732599i	$-0.738307\pi$
$487$	1.14616	−	1.14616i	0.0519376	−	0.0519376i	0.732599	+	0.680661i	$0.238307\pi$
$488$	−4.47333	+	4.47333i	−0.202498	+	0.202498i
$489$	−0.694276	+	0.185241i	−0.0313963	+	0.00837691i
$490$	4.89469	+	11.7290i	0.221119	+	0.529863i
$491$		−	11.1351i		−	0.502519i	−0.967920	−	0.251260i	$-0.919155\pi$
$491$		−	11.1351i		−	0.502519i	0.967920	−	0.251260i	$-0.0808448\pi$
$492$	0.224875	−	0.388542i	0.0101381	−	0.0175168i
$493$	−16.7211	−	16.7211i	−0.753079	−	0.753079i
$494$	4.81693			0.216724
$495$	−1.10063	−	8.32651i	−0.0494695	−	0.374249i
$496$	5.80986			0.260870
$497$	−0.606615	−	0.606615i	−0.0272104	−	0.0272104i
$498$	−5.18885	+	8.96537i	−0.232518	+	0.401748i
$499$		−	2.14480i		−	0.0960142i	−0.998847	−	0.0480071i	$-0.984713\pi$
$499$		−	2.14480i		−	0.0960142i	0.998847	−	0.0480071i	$-0.0152870\pi$
$500$	−4.36032	−	10.2950i	−0.195000	−	0.460408i
$501$	−10.1545	+	2.70934i	−0.453669	+	0.121044i
$502$	9.46827	−	9.46827i	0.422590	−	0.422590i
$503$	−22.0328	+	22.0328i	−0.982393	+	0.982393i	−0.999848	−	0.0174544i	$-0.994444\pi$
$503$	−22.0328	+	22.0328i	−0.982393	+	0.982393i	0.0174544	+	0.999848i	$0.494444\pi$
$504$	2.98431	−	1.71456i	0.132932	−	0.0763725i
$505$	7.35260	+	3.02280i	0.327186	+	0.134513i
$506$			9.76645i			0.434171i
$507$	15.2949	+	8.85215i	0.679269	+	0.393138i
$508$	−5.40945	−	5.40945i	−0.240006	−	0.240006i
$509$	−44.4681			−1.97101			−0.985507	−	0.169634i	$-0.945741\pi$
$509$	−44.4681			−1.97101			−0.985507	+	0.169634i	$0.945741\pi$
$510$	−13.1973	+	10.1599i	−0.584385	+	0.449886i
$511$	8.85858			0.391881
$512$	0.707107	+	0.707107i	0.0312500	+	0.0312500i
$513$	−0.0165399	+	5.19613i	−0.000730253	+	0.229415i
$514$			22.9474i			1.01217i
$515$	−25.3491	+	10.5785i	−1.11702	+	0.466147i
$516$	3.53865	+	13.2627i	0.155780	+	0.583858i
$517$	−7.66372	+	7.66372i	−0.337050	+	0.337050i
$518$	−8.13363	+	8.13363i	−0.357371	+	0.357371i
$519$	1.99784	+	7.48780i	0.0876953	+	0.328678i
$520$	−4.09555	+	9.96196i	−0.179602	+	0.436861i
$521$			24.7771i			1.08551i	0.839892	+	0.542753i	$0.182618\pi$
$521$			24.7771i			1.08551i	−0.839892	+	0.542753i	$0.817382\pi$
$522$	4.30349	−	15.9256i	0.188359	−	0.697044i
$523$	−15.2015	−	15.2015i	−0.664717	−	0.664717i	0.291771	−	0.956488i	$-0.405755\pi$
$523$	−15.2015	−	15.2015i	−0.664717	−	0.664717i	−0.956488	+	0.291771i	$0.905755\pi$
$524$	21.4587			0.937426
$525$	−4.93136	+	8.62536i	−0.215222	+	0.376442i
$526$	−4.90290			−0.213777
$527$	17.6665	+	17.6665i	0.769566	+	0.769566i
$528$	−1.87691	−	1.08629i	−0.0816819	−	0.0472747i
$529$		−	37.8467i		−	1.64551i
$530$	−0.559446	+	1.36079i	−0.0243008	+	0.0591088i
$531$	13.5704	+	23.6203i	0.588906	+	1.02503i
$532$	0.811234	−	0.811234i	0.0351715	−	0.0351715i
$533$	0.882812	−	0.882812i	0.0382388	−	0.0382388i
$534$	21.4178	−	5.71454i	0.926840	−	0.247292i
$535$	15.3996	−	6.42647i	0.665782	−	0.277840i
$536$		−	3.40719i		−	0.147168i
$537$	3.31955	−	5.73556i	0.143249	−	0.247508i
$538$	3.47487	+	3.47487i	0.149812	+	0.149812i
$539$	−7.11634			−0.306522
$540$	−10.7321	−	4.45217i	−0.461837	−	0.191591i
$541$	30.5234			1.31231			0.656153	−	0.754628i	$-0.272183\pi$
$541$	30.5234			1.31231			0.656153	+	0.754628i	$0.272183\pi$
$542$	4.31289	+	4.31289i	0.185255	+	0.185255i
$543$	10.1739	−	17.5785i	0.436602	−	0.754367i
$544$			4.30032i			0.184375i
$545$	40.3274	+	16.5794i	1.72744	+	0.710183i
$546$	9.24825	−	2.46755i	0.395788	−	0.105601i
$547$	2.58026	−	2.58026i	0.110324	−	0.110324i	−0.649790	−	0.760114i	$-0.725143\pi$
$547$	2.58026	−	2.58026i	0.110324	−	0.110324i	0.760114	+	0.649790i	$0.225143\pi$
$548$	13.6290	−	13.6290i	0.582202	−	0.582202i
$549$	−9.45446	−	16.4562i	−0.403507	−	0.702332i
$550$	6.26011	−	0.0331027i	0.266932	−	0.00141150i
$551$		−	5.49893i		−	0.234263i
$552$	11.6935	+	6.76778i	0.497707	+	0.288056i
$553$	−3.92946	−	3.92946i	−0.167098	−	0.167098i
$554$	−16.2375			−0.689866
$555$	38.5072	+	5.00758i	1.63454	+	0.212560i
$556$	10.5758			0.448515
$557$	23.0216	+	23.0216i	0.975455	+	0.975455i	0.999706	−	0.0242514i	$-0.00772021\pi$
$557$	23.0216	+	23.0216i	0.975455	+	0.975455i	−0.0242514	+	0.999706i	$0.507720\pi$
$558$	−4.54682	+	16.8261i	−0.192482	+	0.712304i
$559$			38.1746i			1.61461i
$560$	0.987979	+	2.36747i	0.0417497	+	0.100044i
$561$	−2.40410	−	9.01044i	−0.101501	−	0.380421i
$562$	14.0330	−	14.0330i	0.591947	−	0.591947i
$563$	−29.0925	+	29.0925i	−1.22610	+	1.22610i	−0.260676	+	0.965426i	$0.583945\pi$
$563$	−29.0925	+	29.0925i	−1.22610	+	1.22610i	−0.965426	+	0.260676i	$0.916055\pi$
$564$	3.86518	+	14.4865i	0.162754	+	0.609993i
$565$	4.02732	+	9.65057i	0.169431	+	0.406003i
$566$			19.1667i			0.805635i
$567$	2.63004	+	9.98475i	0.110451	+	0.419320i
$568$	0.528751	+	0.528751i	0.0221859	+	0.0221859i
$569$	−31.9886			−1.34103			−0.670515	−	0.741896i	$-0.733927\pi$
$569$	−31.9886			−1.34103			−0.670515	+	0.741896i	$0.733927\pi$
$570$	−3.84064	−	0.499447i	−0.160867	−	0.0209195i
$571$	−19.7915			−0.828248			−0.414124	−	0.910220i	$-0.635912\pi$
$571$	−19.7915			−0.828248			−0.414124	+	0.910220i	$0.635912\pi$
$572$	−4.26455	−	4.26455i	−0.178310	−	0.178310i
$573$	16.5240	+	9.56353i	0.690300	+	0.399522i
$574$		−	0.297354i		−	0.0124113i
$575$	−39.0016	+	0.206236i	−1.62648	+	0.00860062i
$576$	−2.60125	+	1.49448i	−0.108386	+	0.0622701i
$577$	21.8776	−	21.8776i	0.910777	−	0.910777i	−0.0855565	−	0.996333i	$-0.527267\pi$
$577$	21.8776	−	21.8776i	0.910777	−	0.910777i	0.996333	+	0.0855565i	$0.0272668\pi$
$578$	−1.05552	+	1.05552i	−0.0439040	+	0.0439040i
$579$	15.9794	−	4.26351i	0.664082	−	0.177185i
$580$	11.3724	+	4.67542i	0.472214	+	0.194136i
$581$			6.86127i			0.284653i
$582$	−15.4033	+	26.6141i	−0.638488	+	1.10319i
$583$	−0.582531	−	0.582531i	−0.0241260	−	0.0241260i
$584$	−7.72152			−0.319519
$585$	−25.6459	−	19.6575i	−1.06033	−	0.812738i
$586$	−6.67963			−0.275933
$587$	−19.3270	−	19.3270i	−0.797710	−	0.797710i	0.185024	−	0.982734i	$-0.440764\pi$
$587$	−19.3270	−	19.3270i	−0.797710	−	0.797710i	−0.982734	+	0.185024i	$0.940764\pi$
$588$	−4.93136	+	8.52047i	−0.203366	+	0.351378i
$589$			5.80986i			0.239391i
$590$	−18.7381	+	7.81967i	−0.771434	+	0.321931i
$591$	−16.7027	+	4.45649i	−0.687059	+	0.183316i
$592$	7.08962	−	7.08962i	0.291382	−	0.291382i
$593$	4.82260	−	4.82260i	0.198040	−	0.198040i	−0.601119	−	0.799159i	$-0.705278\pi$
$593$	4.82260	−	4.82260i	0.198040	−	0.198040i	0.799159	+	0.601119i	$0.205278\pi$
$594$	4.61491	−	4.58562i	0.189352	−	0.188150i
$595$	−4.19473	+	10.2032i	−0.171967	+	0.418290i
$596$		−	0.688172i		−	0.0281886i
$597$	−35.6358	−	20.6248i	−1.45848	−	0.844117i
$598$	26.5689	+	26.5689i	1.08648	+	1.08648i
$599$	−12.4755			−0.509735			−0.254868	−	0.966976i	$-0.582032\pi$
$599$	−12.4755			−0.509735			−0.254868	+	0.966976i	$0.582032\pi$
$600$	4.29839	−	7.51824i	0.175481	−	0.306931i
$601$	33.9363			1.38429			0.692145	−	0.721758i	$-0.256666\pi$
$601$	33.9363			1.38429			0.692145	+	0.721758i	$0.256666\pi$
$602$	6.42911	+	6.42911i	0.262031	+	0.262031i
$603$	9.86764	+	2.66648i	0.401841	+	0.108588i
$604$		−	7.78234i		−	0.316659i
$605$	8.01981	−	19.5073i	0.326052	−	0.793083i
$606$	1.58745	+	5.94969i	0.0644858	+	0.241690i
$607$	9.17452	−	9.17452i	0.372382	−	0.372382i	−0.495962	−	0.868344i	$-0.665185\pi$
$607$	9.17452	−	9.17452i	0.372382	−	0.372382i	0.868344	+	0.495962i	$0.165185\pi$
$608$	−0.707107	+	0.707107i	−0.0286770	+	0.0286770i
$609$	−2.81691	−	10.5577i	−0.114147	−	0.427818i
$610$	13.0548	−	5.44794i	0.528571	−	0.220581i
$611$			41.6972i			1.68689i
$612$	−12.4543	−	3.36545i	−0.503433	−	0.136040i
$613$	−9.18173	−	9.18173i	−0.370847	−	0.370847i	0.496939	−	0.867786i	$-0.334457\pi$
$613$	−9.18173	−	9.18173i	−0.370847	−	0.370847i	−0.867786	+	0.496939i	$0.834457\pi$
$614$	15.4083			0.621830
$615$	−0.795420	+	0.612350i	−0.0320744	+	0.0246924i
$616$	−1.43641			−0.0578747
$617$	22.1031	+	22.1031i	0.889839	+	0.889839i	0.994507	−	0.104668i	$-0.0333780\pi$
$617$	22.1031	+	22.1031i	0.889839	+	0.889839i	−0.104668	+	0.994507i	$0.533378\pi$
$618$	−18.4147	−	10.6578i	−0.740748	−	0.428720i
$619$			45.0921i			1.81240i	0.422844	+	0.906202i	$0.361032\pi$
$619$			45.0921i			1.81240i	−0.422844	+	0.906202i	$0.638968\pi$
$620$	−12.0154	−	4.93978i	−0.482552	−	0.198386i
$621$	−28.7517	+	28.5692i	−1.15377	+	1.14644i
$622$	13.2036	−	13.2036i	0.529415	−	0.529415i
$623$	10.3823	−	10.3823i	0.415959	−	0.415959i
$624$	−8.06117	+	2.15082i	−0.322705	+	0.0861017i
$625$	0.264386	+	24.9986i	0.0105755	+	0.999944i
$626$		−	8.07965i		−	0.322928i
$627$	1.08629	−	1.87691i	0.0433822	−	0.0749565i
$628$	4.92864	+	4.92864i	0.196674	+	0.196674i
$629$	43.1160			1.71915
$630$	−7.62968	+	1.00852i	−0.303974	+	0.0401803i
$631$	−10.9260			−0.434958			−0.217479	−	0.976065i	$-0.569783\pi$
$631$	−10.9260			−0.434958			−0.217479	+	0.976065i	$0.569783\pi$
$632$	3.42509	+	3.42509i	0.136243	+	0.136243i
$633$	14.6869	−	25.3763i	0.583752	−	1.00862i
$634$			15.6726i			0.622438i
$635$	6.58802	+	15.7867i	0.261438	+	0.626476i
$636$	−1.10114	+	0.293798i	−0.0436631	+	0.0116499i
$637$	−19.3595	+	19.3595i	−0.767051	+	0.767051i
$638$	−4.86835	+	4.86835i	−0.192740	+	0.192740i
$639$	−1.94513	+	1.11753i	−0.0769483	+	0.0442086i
$640$	−0.861165	−	2.06359i	−0.0340405	−	0.0815705i
$641$		−	26.0023i		−	1.02703i	−0.858081	−	0.513515i	$-0.828343\pi$
$641$		−	26.0023i		−	1.02703i	0.858081	−	0.513515i	$-0.171657\pi$
$642$	11.1869	+	6.47461i	0.441513	+	0.255533i
$643$	9.72854	+	9.72854i	0.383656	+	0.383656i	0.872418	−	0.488761i	$-0.162551\pi$
$643$	9.72854	+	9.72854i	0.383656	+	0.383656i	−0.488761	+	0.872418i	$0.662551\pi$
$644$	8.94911			0.352644
$645$	3.95816	−	30.4375i	0.155853	−	1.19847i
$646$	−4.30032			−0.169194
$647$	−27.1481	−	27.1481i	−1.06730	−	1.06730i	−0.997565	−	0.0697360i	$-0.977784\pi$
$647$	−27.1481	−	27.1481i	−1.06730	−	1.06730i	−0.0697360	−	0.997565i	$-0.522216\pi$
$648$	−2.29245	−	8.70314i	−0.0900561	−	0.341892i
$649$		−	11.3689i		−	0.446270i
$650$	16.9401	−	17.1202i	0.664447	−	0.671511i
$651$	2.97619	+	11.1546i	0.116646	+	0.437184i
$652$	0.293352	−	0.293352i	0.0114886	−	0.0114886i
$653$	14.8598	−	14.8598i	0.581507	−	0.581507i	−0.353810	−	0.935317i	$-0.615114\pi$
$653$	14.8598	−	14.8598i	0.581507	−	0.581507i	0.935317	+	0.353810i	$0.115114\pi$
$654$	8.70682	+	32.6328i	0.340464	+	1.27604i
$655$	−44.3789	−	18.2450i	−1.73403	−	0.712893i
$656$			0.259187i			0.0101195i
$657$	6.04290	−	22.3625i	0.235756	−	0.872444i
$658$	7.02236	+	7.02236i	0.273760	+	0.273760i
$659$	−3.67408			−0.143122			−0.0715609	−	0.997436i	$-0.522798\pi$
$659$	−3.67408			−0.143122			−0.0715609	+	0.997436i	$0.522798\pi$
$660$	2.95805	+	3.84239i	0.115142	+	0.149565i
$661$	5.30895			0.206494			0.103247	−	0.994656i	$-0.467077\pi$
$661$	5.30895			0.206494			0.103247	+	0.994656i	$0.467077\pi$
$662$	14.1470	+	14.1470i	0.549837	+	0.549837i
$663$	−31.0525	−	17.9721i	−1.20598	−	0.697979i
$664$		−	5.98058i		−	0.232091i
$665$	−2.36747	+	0.987979i	−0.0918065	+	0.0383122i
$666$	14.9840	+	26.0808i	0.580620	+	1.01061i
$667$	30.3307	−	30.3307i	1.17441	−	1.17441i
$668$	4.29057	−	4.29057i	0.166007	−	0.166007i
$669$	−30.9469	+	8.25702i	−1.19648	+	0.319235i
$670$	−2.89693	+	7.04645i	−0.111918	+	0.272228i
$671$			7.92070i			0.305775i
$672$	−0.995380	+	1.71983i	−0.0383976	+	0.0663440i
$673$	25.8750	+	25.8750i	0.997409	+	0.997409i	0.999997	−	0.00258791i	$-0.000823758\pi$
$673$	25.8750	+	25.8750i	0.997409	+	0.997409i	−0.00258791	+	0.999997i	$0.500824\pi$
$674$	12.2964			0.473638
$675$	18.4098	+	18.3325i	0.708593	+	0.705617i
$676$	−10.2028			−0.392417
$677$	−19.1276	−	19.1276i	−0.735134	−	0.735134i	0.236498	−	0.971632i	$-0.424000\pi$
$677$	−19.1276	−	19.1276i	−0.735134	−	0.735134i	−0.971632	+	0.236498i	$0.924000\pi$
$678$	−4.05749	+	7.01060i	−0.155827	+	0.269240i
$679$			20.3680i			0.781651i
$680$	3.65631	−	8.89354i	0.140213	−	0.341052i
$681$	−43.9078	+	11.7151i	−1.68255	+	0.448925i
$682$	5.14362	−	5.14362i	0.196959	−	0.196959i
$683$	3.97993	−	3.97993i	0.152288	−	0.152288i	−0.626851	−	0.779139i	$-0.715657\pi$
$683$	3.97993	−	3.97993i	0.152288	−	0.152288i	0.779139	+	0.626851i	$0.215657\pi$
$684$	−1.49448	−	2.60125i	−0.0571430	−	0.0994614i
$685$	−39.7742	+	16.5984i	−1.51970	+	0.634191i
$686$			14.5516i			0.555583i
$687$	−3.95490	−	2.28896i	−0.150889	−	0.0873293i
$688$	−5.60388	−	5.60388i	−0.213646	−	0.213646i
$689$	−3.16947			−0.120747
$690$	−18.4292	−	23.9388i	−0.701586	−	0.911335i
$691$	−15.6719			−0.596186			−0.298093	−	0.954537i	$-0.596351\pi$
$691$	−15.6719			−0.596186			−0.298093	+	0.954537i	$0.596351\pi$
$692$	−3.16382	−	3.16382i	−0.120270	−	0.120270i
$693$	1.12414	−	4.16003i	0.0427027	−	0.158026i
$694$		−	7.19589i		−	0.273152i
$695$	−21.8720	−	8.99201i	−0.829653	−	0.341086i
$696$	2.45534	+	9.20251i	0.0930695	+	0.348820i
$697$	−0.788131	+	0.788131i	−0.0298526	+	0.0298526i
$698$	15.3299	−	15.3299i	0.580244	−	0.580244i
$699$	8.43446	+	31.6120i	0.319021	+	1.19567i
$700$	−0.0303324	−	5.73621i	−0.00114646	−	0.216808i
$701$		−	43.9609i		−	1.66038i	−0.557480	−	0.830191i	$-0.688232\pi$
$701$		−	43.9609i		−	1.66038i	0.557480	−	0.830191i	$-0.311768\pi$
$702$	0.0796715	−	25.0294i	0.00300701	−	0.944673i
$703$	7.08962	+	7.08962i	0.267390	+	0.267390i
$704$	1.25204			0.0471880
$705$	4.32341	−	33.2461i	0.162829	−	1.25212i
$706$	−10.0681			−0.378918
$707$	2.88412	+	2.88412i	0.108468	+	0.108468i
$708$	−13.6122	−	7.87825i	−0.511576	−	0.296083i
$709$			25.0308i			0.940050i	0.882653	+	0.470025i	$0.155755\pi$
$709$			25.0308i			0.940050i	−0.882653	+	0.470025i	$0.844245\pi$
$710$	−0.643951	−	1.54308i	−0.0241671	−	0.0579109i
$711$	−12.6000	+	7.23899i	−0.472536	+	0.271483i
$712$	−9.04967	+	9.04967i	−0.339151	+	0.339151i
$713$	−32.0457	+	32.0457i	−1.20012	+	1.20012i
$714$	−8.25638	+	2.20290i	−0.308987	+	0.0824416i
$715$	5.19368	+	12.4455i	0.194233	+	0.465434i
$716$			3.82605i			0.142986i
$717$	0.311590	−	0.538370i	0.0116366	−	0.0201058i
$718$	−17.4531	−	17.4531i	−0.651343	−	0.651343i
$719$	22.3343			0.832930			0.416465	−	0.909152i	$-0.363269\pi$
$719$	22.3343			0.832930			0.416465	+	0.909152i	$0.363269\pi$
$720$	6.65036	−	0.879067i	0.247844	−	0.0327609i
$721$	−14.0929			−0.524848
$722$	−0.707107	−	0.707107i	−0.0263158	−	0.0263158i
$723$	4.70555	−	8.13033i	0.175001	−	0.302370i
$724$			11.7262i			0.435801i
$725$	−19.5442	−	19.3386i	−0.725853	−	0.718217i
$726$	15.7852	−	4.21168i	0.585843	−	0.156310i
$727$	−27.5404	+	27.5404i	−1.02142	+	1.02142i	−0.0216511	+	0.999766i	$0.506892\pi$
$727$	−27.5404	+	27.5404i	−1.02142	+	1.02142i	−0.999766	+	0.0216511i	$0.993108\pi$
$728$	−3.90766	+	3.90766i	−0.144828	+	0.144828i
$729$	26.9995	+	0.171887i	0.999980	+	0.00636617i
$730$	15.9690	+	6.56516i	0.591038	+	0.242987i
$731$		−	34.0804i		−	1.26051i
$732$	9.48354	+	5.48875i	0.350522	+	0.202870i
$733$	−28.9159	−	28.9159i	−1.06803	−	1.06803i	−0.997510	−	0.0705243i	$-0.977533\pi$
$733$	−28.9159	−	28.9159i	−1.06803	−	1.06803i	−0.0705243	−	0.997510i	$-0.522467\pi$
$734$	−2.26039			−0.0834327
$735$	17.4431	−	13.4284i	0.643397	−	0.495316i
$736$	−7.80043			−0.287528
$737$	−3.01647	−	3.01647i	−0.111113	−	0.111113i
$738$	−0.750637	−	0.202841i	−0.0276313	−	0.00746667i
$739$		−	20.1578i		−	0.741515i	−0.928730	−	0.370758i	$-0.879098\pi$
$739$		−	20.1578i		−	0.741515i	0.928730	−	0.370758i	$-0.120902\pi$
$740$	−20.6900	+	8.63425i	−0.760581	+	0.317401i
$741$	−2.15082	−	8.06117i	−0.0790123	−	0.296135i
$742$	−0.533780	+	0.533780i	−0.0195957	+	0.0195957i
$743$	26.7472	−	26.7472i	0.981260	−	0.981260i	−0.0185673	−	0.999828i	$-0.505910\pi$
$743$	26.7472	−	26.7472i	0.981260	−	0.981260i	0.999828	+	0.0185673i	$0.00591049\pi$
$744$	−2.59417	−	9.72284i	−0.0951070	−	0.356457i
$745$	−0.585112	+	1.42322i	−0.0214369	+	0.0521426i
$746$		−	29.2529i		−	1.07102i
$747$	17.3205	+	4.68043i	0.633724	+	0.171248i
$748$	3.80718	+	3.80718i	0.139204	+	0.139204i
$749$	8.56145			0.312828
$750$	−15.2819	+	11.8939i	−0.558015	+	0.434304i
$751$	−30.8503			−1.12574			−0.562871	−	0.826545i	$-0.690303\pi$
$751$	−30.8503			−1.12574			−0.562871	+	0.826545i	$0.690303\pi$
$752$	−6.12099	−	6.12099i	−0.223210	−	0.223210i
$753$	−20.0729	−	11.6175i	−0.731498	−	0.423366i
$754$			26.4880i			0.964636i
$755$	−6.61687	+	16.0948i	−0.240812	+	0.585748i
$756$	−4.20186	−	4.22869i	−0.152820	−	0.153796i
$757$	25.2568	−	25.2568i	0.917975	−	0.917975i	−0.0789067	−	0.996882i	$-0.525143\pi$
$757$	25.2568	−	25.2568i	0.917975	−	0.917975i	0.996882	+	0.0789067i	$0.0251429\pi$
$758$	13.6374	−	13.6374i	0.495334	−	0.495334i
$759$	16.3442	−	4.36084i	0.593258	−	0.158288i
$760$	2.06359	−	0.861165i	0.0748542	−	0.0312377i
$761$		−	7.51765i		−	0.272514i	−0.990673	−	0.136257i	$-0.956493\pi$
$761$		−	7.51765i		−	0.272514i	0.990673	−	0.136257i	$-0.0435074\pi$
$762$	−6.63737	+	11.4681i	−0.240447	+	0.415447i
$763$	15.8188	+	15.8188i	0.572678	+	0.572678i
$764$	−11.0228			−0.398790
$765$	22.8954	+	17.5492i	0.827783	+	0.634494i
$766$	32.1645			1.16215
$767$	−30.9284	−	30.9284i	−1.11676	−	1.11676i
$768$	0.867616	−	1.49908i	0.0313074	−	0.0540934i
$769$		−	45.1162i		−	1.62693i	−0.581611	−	0.813467i	$-0.697578\pi$
$769$		−	45.1162i		−	1.62693i	0.581611	−	0.813467i	$-0.302422\pi$
$770$	2.97066	+	1.22130i	0.107055	+	0.0440125i
$771$	38.4027	−	10.2463i	1.38304	−	0.369012i
$772$	−6.75179	+	6.75179i	−0.243002	+	0.243002i
$773$	25.7371	−	25.7371i	0.925698	−	0.925698i	−0.0717268	−	0.997424i	$-0.522851\pi$
$773$	25.7371	−	25.7371i	0.925698	−	0.925698i	0.997424	+	0.0717268i	$0.0228510\pi$
$774$	20.6152	−	11.8439i	0.740997	−	0.425721i
$775$	20.6493	+	20.4321i	0.741744	+	0.733941i
$776$		−	17.7536i		−	0.637317i
$777$	17.2435	+	9.97992i	0.618606	+	0.358028i
$778$	−14.2955	−	14.2955i	−0.512519	−	0.512519i
$779$	−0.259187			−0.00928633
$780$	18.5001	+	2.40580i	0.662411	+	0.0861416i
$781$	0.936234			0.0335011
$782$	−23.7194	−	23.7194i	−0.848205	−	0.848205i
$783$	−28.5732	−	0.0909517i	−1.02112	−	0.00325035i
$784$		−	5.68380i		−	0.202993i
$785$	−6.00244	−	14.3835i	−0.214236	−	0.513369i
$786$	−9.58156	−	35.9112i	−0.341763	−	1.28091i
$787$	−23.2941	+	23.2941i	−0.830343	+	0.830343i	−0.987564	−	0.157220i	$-0.949747\pi$
$787$	−23.2941	+	23.2941i	−0.830343	+	0.830343i	0.157220	+	0.987564i	$0.449747\pi$
$788$	7.05740	−	7.05740i	0.251410	−	0.251410i
$789$	2.18921	+	8.20505i	0.0779378	+	0.292107i
$790$	−4.17132	−	9.99562i	−0.148409	−	0.355628i
$791$			5.36527i			0.190767i
$792$	−0.979852	+	3.62606i	−0.0348175	+	0.128846i
$793$	21.5477	+	21.5477i	0.765182	+	0.765182i
$794$	0.354390			0.0125768
$795$	2.52709	+	0.328629i	0.0896265	+	0.0116553i
$796$	23.7718			0.842569
$797$	16.2849	+	16.2849i	0.576840	+	0.576840i	0.934031	−	0.357192i	$-0.116266\pi$
$797$	16.2849	+	16.2849i	0.576840	+	0.576840i	−0.357192	+	0.934031i	$0.616266\pi$
$798$	−1.71983	−	0.995380i	−0.0608814	−	0.0352361i
$799$		−	37.2252i		−	1.31693i
$800$	0.0264390	+	4.99993i	0.000934760	+	0.176774i
$801$	−19.1267	−	33.2913i	−0.675807	−	1.17629i
$802$	−15.3344	+	15.3344i	−0.541476	+	0.541476i
$803$	−6.83606	+	6.83606i	−0.241239	+	0.241239i
$804$	−5.70196	+	1.52135i	−0.201092	+	0.0536539i
$805$	−18.5078	−	7.60890i	−0.652313	−	0.268179i
$806$		−	27.9857i		−	0.985754i
$807$	4.26365	−	7.36680i	0.150088	−	0.259323i
$808$	−2.51392	−	2.51392i	−0.0884394	−	0.0884394i
$809$	20.3523			0.715549			0.357775	−	0.933808i	$-0.383536\pi$
$809$	20.3523			0.715549			0.357775	+	0.933808i	$0.383536\pi$
$810$	−2.65871	+	19.9482i	−0.0934177	+	0.700909i
$811$	32.7529			1.15011			0.575056	−	0.818114i	$-0.304980\pi$
$811$	32.7529			1.15011			0.575056	+	0.818114i	$0.304980\pi$
$812$	4.46092	+	4.46092i	0.156548	+	0.156548i
$813$	5.29190	−	9.14342i	0.185595	−	0.320674i
$814$		−	12.5532i		−	0.439991i
$815$	−0.856106	+	0.357266i	−0.0299881	+	0.0125145i
$816$	7.19661	−	1.92015i	0.251932	−	0.0672185i
$817$	5.60388	−	5.60388i	0.196055	−	0.196055i
$818$	−4.20593	+	4.20593i	−0.147057	+	0.147057i
$819$	−8.25891	−	14.3752i	−0.288590	−	0.502311i
$820$	0.220371	−	0.536027i	0.00769570	−	0.0187189i
$821$			15.1106i			0.527363i	0.964610	+	0.263681i	$0.0849367\pi$
$821$			15.1106i			0.527363i	−0.964610	+	0.263681i	$0.915063\pi$
$822$	−28.8937	−	16.7227i	−1.00778	−	0.583271i
$823$	38.5308	+	38.5308i	1.34310	+	1.34310i	0.892958	+	0.450139i	$0.148626\pi$
$823$	38.5308	+	38.5308i	1.34310	+	1.34310i	0.450139	+	0.892958i	$0.351374\pi$
$824$	12.2840			0.427933
$825$	−2.85061	−	10.4616i	−0.0992456	−	0.364225i
$826$	−10.4175			−0.362471
$827$	7.31829	+	7.31829i	0.254482	+	0.254482i	0.822805	−	0.568323i	$-0.192408\pi$
$827$	7.31829	+	7.31829i	0.254482	+	0.254482i	−0.568323	+	0.822805i	$0.692408\pi$
$828$	6.10465	−	22.5910i	0.212151	−	0.785092i
$829$			0.579874i			0.0201399i	0.999949	+	0.0100699i	$0.00320541\pi$
$829$			0.579874i			0.0201399i	−0.999949	+	0.0100699i	$0.996795\pi$
$830$	−5.08493	+	12.3685i	−0.176501	+	0.429317i
$831$	7.25025	+	27.1736i	0.251509	+	0.942642i
$832$	3.40609	−	3.40609i	0.118085	−	0.118085i
$833$	17.2832	−	17.2832i	0.598827	−	0.598827i
$834$	−4.72224	−	17.6987i	−0.163518	−	0.612857i
$835$	−12.5214	+	5.22537i	−0.433321	+	0.180831i
$836$			1.25204i			0.0433027i
$837$	30.1888	+	0.0960944i	1.04348	+	0.00332151i
$838$	25.3766	+	25.3766i	0.876620	+	0.876620i
$839$	14.3633			0.495878			0.247939	−	0.968776i	$-0.420247\pi$
$839$	14.3633			0.495878			0.247939	+	0.968776i	$0.420247\pi$
$840$	3.52083	−	2.71049i	0.121480	−	0.0935209i
$841$	1.23828			0.0426995
$842$	−9.57779	−	9.57779i	−0.330073	−	0.330073i
$843$	−29.7503	−	17.2184i	−1.02465	−	0.593035i
$844$			16.9279i			0.582682i
$845$	21.1006	+	8.67487i	0.725883	+	0.298425i
$846$	22.5175	−	12.9368i	0.774166	−	0.444777i
$847$	7.65188	−	7.65188i	0.262922	−	0.262922i
$848$	0.465266	−	0.465266i	0.0159773	−	0.0159773i
$849$	32.0755	−	8.55815i	1.10083	−	0.293715i
$850$	−15.1233	+	15.2841i	−0.518725	+	0.524240i
$851$			78.2090i			2.68097i
$852$	0.648775	−	1.12096i	0.0222267	−	0.0384036i
$853$	−28.0005	−	28.0005i	−0.958719	−	0.958719i	0.0404617	−	0.999181i	$-0.487117\pi$
$853$	−28.0005	−	28.0005i	−0.958719	−	0.958719i	−0.999181	+	0.0404617i	$0.987117\pi$
$854$	7.25783			0.248358
$855$	0.879067	+	6.65036i	0.0300635	+	0.227437i
$856$	−7.46253			−0.255064
$857$	32.1199	+	32.1199i	1.09720	+	1.09720i	0.994737	+	0.102459i	$0.0326711\pi$
$857$	32.1199	+	32.1199i	1.09720	+	1.09720i	0.102459	+	0.994737i	$0.467329\pi$
$858$	−5.23259	+	9.04094i	−0.178638	+	0.308652i
$859$			18.3812i			0.627159i	0.949562	+	0.313579i	$0.101528\pi$
$859$			18.3812i			0.627159i	−0.949562	+	0.313579i	$0.898472\pi$
$860$	6.82481	+	16.3541i	0.232724	+	0.557671i
$861$	−0.497624	+	0.132772i	−0.0169590	+	0.00452487i
$862$	−0.314904	+	0.314904i	−0.0107257	+	0.0107257i
$863$	11.6814	−	11.6814i	0.397638	−	0.397638i	−0.479761	−	0.877399i	$-0.659277\pi$
$863$	11.6814	−	11.6814i	0.397638	−	0.397638i	0.877399	+	0.479761i	$0.159277\pi$
$864$	3.66252	+	3.68591i	0.124601	+	0.125397i
$865$	3.85312	+	9.23314i	0.131010	+	0.313936i
$866$			29.5957i			1.00570i
$867$	2.23773	+	1.29512i	0.0759973	+	0.0439846i
$868$	−4.71316	−	4.71316i	−0.159975	−	0.159975i
$869$	6.06464			0.205729
$870$	2.74643	−	21.1195i	0.0931126	−	0.716017i
$871$	−16.4122			−0.556106
$872$	−13.7883	−	13.7883i	−0.466931	−	0.466931i
$873$	51.4166	+	13.8940i	1.74019	+	0.470242i
$874$		−	7.80043i		−	0.263854i
$875$	−4.81443	+	11.8889i	−0.162758	+	0.401919i
$876$	3.44776	+	12.9220i	0.116489	+	0.436595i
$877$	−14.5905	+	14.5905i	−0.492685	+	0.492685i	−0.909151	−	0.416466i	$-0.863268\pi$
$877$	−14.5905	+	14.5905i	−0.492685	+	0.492685i	0.416466	+	0.909151i	$0.363268\pi$
$878$	−0.345068	+	0.345068i	−0.0116455	+	0.0116455i
$879$	2.98254	+	11.1784i	0.100598	+	0.377038i
$880$	−2.58936	−	1.06454i	−0.0872872	−	0.0358855i
$881$		−	4.06288i		−	0.136882i	−0.997655	−	0.0684409i	$-0.978198\pi$
$881$		−	4.06288i		−	0.136882i	0.997655	−	0.0684409i	$-0.0218025\pi$
$882$	16.4610	+	4.44817i	0.554270	+	0.149778i
$883$	39.1005	+	39.1005i	1.31584	+	1.31584i	0.917039	+	0.398798i	$0.130572\pi$
$883$	39.1005	+	39.1005i	1.31584	+	1.31584i	0.398798	+	0.917039i	$0.369428\pi$
$884$	20.7143			0.696699
$885$	21.4531	+	27.8667i	0.721137	+	0.936730i
$886$	8.36703			0.281096
$887$	7.54810	+	7.54810i	0.253440	+	0.253440i	0.822380	−	0.568939i	$-0.192646\pi$
$887$	7.54810	+	7.54810i	0.253440	+	0.253440i	−0.568939	+	0.822380i	$0.692646\pi$
$888$	−15.0301	−	8.69893i	−0.504378	−	0.291917i
$889$			8.77667i			0.294360i
$890$	26.4101	−	11.0213i	0.885270	−	0.369436i
$891$	−9.73468	−	5.67554i	−0.326124	−	0.190138i
$892$	13.0760	−	13.0760i	0.437817	−	0.437817i
$893$	6.12099	−	6.12099i	0.204831	−	0.204831i
$894$	−1.15166	+	0.307277i	−0.0385173	+	0.0102769i
$895$	3.25307	−	7.91271i	0.108738	−	0.264493i
$896$		−	1.14726i		−	0.0383272i
$897$	32.5999	−	56.3267i	1.08848	−	1.88069i
$898$	−11.5682	−	11.5682i	−0.386037	−	0.386037i
$899$	−31.9480			−1.06553
$900$	−14.5011	−	3.83640i	−0.483370	−	0.127880i
$901$	2.82954			0.0942658
$902$	0.229465	+	0.229465i	0.00764034	+	0.00764034i
$903$	7.88848	−	13.6298i	0.262512	−	0.453572i
$904$		−	4.67660i		−	0.155541i
$905$	9.97011	−	24.2511i	0.331418	−	0.806135i
$906$	−13.0238	+	3.47491i	−0.432687	+	0.115446i
$907$	−36.9489	+	36.9489i	−1.22687	+	1.22687i	−0.261724	+	0.965143i	$0.584291\pi$
$907$	−36.9489	+	36.9489i	−1.22687	+	1.22687i	−0.965143	+	0.261724i	$0.915709\pi$
$908$	18.5524	−	18.5524i	0.615682	−	0.615682i
$909$	9.24803	−	5.31322i	0.306738	−	0.176228i
$910$	11.4039	−	4.75903i	0.378037	−	0.157760i
$911$		−	17.9950i		−	0.596200i	−0.954535	−	0.298100i	$-0.903647\pi$
$911$		−	17.9950i		−	0.596200i	0.954535	−	0.298100i	$-0.0963529\pi$
$912$	1.49908	+	0.867616i	0.0496395	+	0.0287297i
$913$	−5.29476	−	5.29476i	−0.175231	−	0.175231i
$914$	−32.5001			−1.07501
$915$	−14.9463	−	19.4147i	−0.494109	−	0.641829i
$916$	2.63822			0.0871692
$917$	−17.4080	−	17.4080i	−0.574863	−	0.574863i
$918$	−0.0711267	+	22.3450i	−0.00234753	+	0.737495i
$919$			7.22194i			0.238230i	0.992880	+	0.119115i	$0.0380057\pi$
$919$			7.22194i			0.238230i	−0.992880	+	0.119115i	$0.961994\pi$
$920$	16.1322	+	6.63225i	0.531862	+	0.218659i
$921$	−6.88001	−	25.7860i	−0.226704	−	0.849676i
$922$	11.9273	−	11.9273i	0.392806	−	0.392806i
$923$	2.54696	−	2.54696i	0.0838342	−	0.0838342i
$924$	0.641376	+	2.40385i	0.0210997	+	0.0790808i
$925$	50.1305	−	0.265084i	1.64828	−	0.00871590i
$926$		−	25.1437i		−	0.826272i
$927$	−9.61351	+	35.5760i	−0.315749	+	1.16847i
$928$	−3.88833	−	3.88833i	−0.127641	−	0.127641i
$929$	−10.0132			−0.328523			−0.164262	−	0.986417i	$-0.552524\pi$
$929$	−10.0132			−0.328523			−0.164262	+	0.986417i	$0.552524\pi$
$930$	−2.90172	+	22.3136i	−0.0951511	+	0.731692i
$931$	5.68380			0.186279
$932$	−13.3570	−	13.3570i	−0.437523	−	0.437523i
$933$	−27.9918	−	16.2007i	−0.916411	−	0.530387i
$934$			17.5880i			0.575497i
$935$	−4.63666	−	11.1107i	−0.151635	−	0.363359i
$936$	7.19883	+	12.5301i	0.235301	+	0.409558i
$937$	32.1574	−	32.1574i	1.05054	−	1.05054i	0.0518829	−	0.998653i	$-0.483478\pi$
$937$	32.1574	−	32.1574i	1.05054	−	1.05054i	0.998653	−	0.0518829i	$-0.0165223\pi$
$938$	−2.76403	+	2.76403i	−0.0902487	+	0.0902487i
$939$	−13.5213	+	3.60766i	−0.441253	+	0.117732i
$940$	7.45458	+	17.8632i	0.243142	+	0.582634i
$941$		−	10.3250i		−	0.336585i	−0.985737	−	0.168292i	$-0.946175\pi$
$941$		−	10.3250i		−	0.336585i	0.985737	−	0.168292i	$-0.0538252\pi$
$942$	6.04741	−	10.4488i	0.197035	−	0.340440i
$943$	−1.42961	−	1.42961i	−0.0465544	−	0.0465544i
$944$	9.08034			0.295540
$945$	5.09451	+	12.3180i	0.165724	+	0.400705i
$946$	−9.92252			−0.322609
$947$	7.92954	+	7.92954i	0.257676	+	0.257676i	0.824108	−	0.566433i	$-0.191677\pi$
$947$	7.92954	+	7.92954i	0.257676	+	0.257676i	−0.566433	+	0.824108i	$0.691677\pi$
$948$	4.20257	−	7.26126i	0.136493	−	0.235835i
$949$			37.1941i			1.20737i
$950$	−4.99993	+	0.0264390i	−0.162219	+	0.000857795i
$951$	26.2282	−	6.99801i	0.850508	−	0.226926i
$952$	3.48857	−	3.48857i	0.113065	−	0.113065i
$953$	−18.1770	+	18.1770i	−0.588812	+	0.588812i	−0.937310	−	0.348498i	$-0.886692\pi$
$953$	−18.1770	+	18.1770i	−0.588812	+	0.588812i	0.348498	+	0.937310i	$0.386692\pi$
$954$	0.983347	+	1.71159i	0.0318370	+	0.0554146i
$955$	22.7963	+	9.37201i	0.737671	+	0.303271i
$956$			0.359134i			0.0116152i
$957$	10.3210	+	5.97344i	0.333630	+	0.193094i
$958$	−26.6572	−	26.6572i	−0.861256	−	0.861256i
$959$	−22.1126			−0.714054
$960$	−3.06891	+	2.36258i	−0.0990486	+	0.0762521i
$961$	2.75447			0.0888539
$962$	−34.1502	−	34.1502i	−1.10105	−	1.10105i
$963$	5.84021	−	21.6124i	0.188198	−	0.696450i
$964$			5.42354i			0.174681i
$965$	19.7041	−	8.22281i	0.634297	−	0.264701i
$966$	−3.99589	−	14.9764i	−0.128566	−	0.481858i
$967$	9.81253	−	9.81253i	0.315550	−	0.315550i	−0.531505	−	0.847055i	$-0.678373\pi$
$967$	9.81253	−	9.81253i	0.315550	−	0.315550i	0.847055	+	0.531505i	$0.178373\pi$
$968$	−6.66971	+	6.66971i	−0.214373	+	0.214373i
$969$	1.92015	+	7.19661i	0.0616839	+	0.231189i
$970$	−15.0948	+	36.7164i	−0.484666	+	1.17889i
$971$			13.6046i			0.436594i	0.975882	+	0.218297i	$0.0700501\pi$
$971$			13.6046i			0.436594i	−0.975882	+	0.218297i	$0.929950\pi$
$972$	−13.5412	+	7.72250i	−0.434333	+	0.247699i
$973$	−8.57948	−	8.57948i	−0.275045	−	0.275045i
$974$	1.62092			0.0519376
$975$	−36.2148	−	20.7050i	−1.15980	−	0.663092i
$976$	−6.32624			−0.202498
$977$	−1.36368	−	1.36368i	−0.0436279	−	0.0436279i	0.684956	−	0.728584i	$-0.259821\pi$
$977$	−1.36368	−	1.36368i	−0.0436279	−	0.0436279i	−0.728584	+	0.684956i	$0.759821\pi$
$978$	−0.621913	−	0.359942i	−0.0198866	−	0.0115097i
$979$			16.0238i			0.512123i
$980$	−4.83260	+	11.7547i	−0.154372	+	0.375491i
$981$	50.7235	−	29.1419i	1.61948	−	0.930428i
$982$	7.87369	−	7.87369i	0.251260	−	0.251260i
$983$	−22.8849	+	22.8849i	−0.729917	+	0.729917i	−0.970603	−	0.240686i	$-0.922627\pi$
$983$	−22.8849	+	22.8849i	−0.729917	+	0.729917i	0.240686	+	0.970603i	$0.422627\pi$
$984$	0.433751	−	0.115730i	0.0138275	−	0.00368934i
$985$	−20.5960	+	8.59501i	−0.656243	+	0.273860i
$986$		−	23.6472i		−	0.753079i
$987$	8.61640	−	14.8875i	0.274263	−	0.473876i
$988$	3.40609	+	3.40609i	0.108362	+	0.108362i
$989$	61.8191			1.96573
$990$	5.10947	−	6.66599i	0.162390	−	0.211859i
$991$	−26.5275			−0.842673			−0.421336	−	0.906904i	$-0.638439\pi$
$991$	−26.5275			−0.842673			−0.421336	+	0.906904i	$0.638439\pi$
$992$	4.10819	+	4.10819i	0.130435	+	0.130435i
$993$	17.3582	−	29.9918i	0.550847	−	0.951761i
$994$		−	0.857883i		−	0.0272104i
$995$	−49.1628	−	20.2118i	−1.55856	−	0.640756i
$996$	−10.0085	+	2.67040i	−0.317133	+	0.0846149i
$997$	38.6488	−	38.6488i	1.22402	−	1.22402i	0.257830	−	0.966190i	$-0.416993\pi$
$997$	38.6488	−	38.6488i	1.22402	−	1.22402i	0.966190	−	0.257830i	$-0.0830074\pi$
$998$	1.51660	−	1.51660i	0.0480071	−	0.0480071i
$999$	36.9558	−	36.7213i	1.16923	−	1.16181i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	570.2.k.a.533.15	yes	36
3.2	odd	2	inner	570.2.k.a.533.1	yes	36
5.2	odd	4	inner	570.2.k.a.77.1	✓	36
15.2	even	4	inner	570.2.k.a.77.15	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.2.k.a.77.1	✓	36	5.2	odd	4	inner
570.2.k.a.77.15	yes	36	15.2	even	4	inner
570.2.k.a.533.1	yes	36	3.2	odd	2	inner
570.2.k.a.533.15	yes	36	1.1	even	1	trivial

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.k (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 + 0.707107i) q^{2} +(0.867616 - 1.49908i) q^{3} +1.00000i q^{4} +(0.850241 - 2.06811i) q^{5} +(1.67351 - 0.446512i) q^{6} +(0.811234 - 0.811234i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-1.49448 - 2.60125i) q^{9} +O(q^{10})\)	\(q+(0.707107 + 0.707107i) q^{2} +(0.867616 - 1.49908i) q^{3} +1.00000i q^{4} +(0.850241 - 2.06811i) q^{5} +(1.67351 - 0.446512i) q^{6} +(0.811234 - 0.811234i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-1.49448 - 2.60125i) q^{9} +(2.06359 - 0.861165i) q^{10} +1.25204i q^{11} +(1.49908 + 0.867616i) q^{12} +(3.40609 + 3.40609i) q^{13} +1.14726 q^{14} +(-2.36258 - 3.06891i) q^{15} -1.00000 q^{16} +(-3.04078 - 3.04078i) q^{17} +(0.782605 - 2.89612i) q^{18} -1.00000i q^{19} +(2.06811 + 0.850241i) q^{20} +(-0.512265 - 1.91995i) q^{21} +(-0.885325 + 0.885325i) q^{22} +(5.51574 - 5.51574i) q^{23} +(0.446512 + 1.67351i) q^{24} +(-3.55418 - 3.51679i) q^{25} +4.81693i q^{26} +(-5.19613 - 0.0165399i) q^{27} +(0.811234 + 0.811234i) q^{28} +5.49893 q^{29} +(0.499447 - 3.84064i) q^{30} -5.80986 q^{31} +(-0.707107 - 0.707107i) q^{32} +(1.87691 + 1.08629i) q^{33} -4.30032i q^{34} +(-0.987979 - 2.36747i) q^{35} +(2.60125 - 1.49448i) q^{36} +(-7.08962 + 7.08962i) q^{37} +(0.707107 - 0.707107i) q^{38} +(8.06117 - 2.15082i) q^{39} +(0.861165 + 2.06359i) q^{40} -0.259187i q^{41} +(0.995380 - 1.71983i) q^{42} +(5.60388 + 5.60388i) q^{43} -1.25204 q^{44} +(-6.65036 + 0.879067i) q^{45} +7.80043 q^{46} +(6.12099 + 6.12099i) q^{47} +(-0.867616 + 1.49908i) q^{48} +5.68380i q^{49} +(-0.0264390 - 4.99993i) q^{50} +(-7.19661 + 1.92015i) q^{51} +(-3.40609 + 3.40609i) q^{52} +(-0.465266 + 0.465266i) q^{53} +(-3.66252 - 3.68591i) q^{54} +(2.58936 + 1.06454i) q^{55} +1.14726i q^{56} +(-1.49908 - 0.867616i) q^{57} +(3.88833 + 3.88833i) q^{58} -9.08034 q^{59} +(3.06891 - 2.36258i) q^{60} +6.32624 q^{61} +(-4.10819 - 4.10819i) q^{62} +(-3.32260 - 0.897850i) q^{63} -1.00000i q^{64} +(9.94016 - 4.14817i) q^{65} +(0.559051 + 2.09530i) q^{66} +(-2.40925 + 2.40925i) q^{67} +(3.04078 - 3.04078i) q^{68} +(-3.48299 - 13.0541i) q^{69} +(0.975447 - 2.37266i) q^{70} -0.747767i q^{71} +(2.89612 + 0.782605i) q^{72} +(5.45994 + 5.45994i) q^{73} -10.0262 q^{74} +(-8.35561 + 2.27678i) q^{75} +1.00000 q^{76} +(1.01570 + 1.01570i) q^{77} +(7.22097 + 4.17925i) q^{78} -4.84381i q^{79} +(-0.850241 + 2.06811i) q^{80} +(-4.53304 + 7.77506i) q^{81} +(0.183273 - 0.183273i) q^{82} +(-4.22891 + 4.22891i) q^{83} +(1.91995 - 0.512265i) q^{84} +(-8.87408 + 3.70328i) q^{85} +7.92509i q^{86} +(4.77097 - 8.24334i) q^{87} +(-0.885325 - 0.885325i) q^{88} +12.7982 q^{89} +(-5.32411 - 4.08092i) q^{90} +5.52627 q^{91} +(5.51574 + 5.51574i) q^{92} +(-5.04073 + 8.70945i) q^{93} +8.65639i q^{94} +(-2.06811 - 0.850241i) q^{95} +(-1.67351 + 0.446512i) q^{96} +(-12.5537 + 12.5537i) q^{97} +(-4.01905 + 4.01905i) q^{98} +(3.25687 - 1.87115i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 4 q^{3} + 4 q^{6} - 12 q^{7}+O(q^{10}) \) 36 * q + 4 * q^3 + 4 * q^6 - 12 * q^7	\( 36 q + 4 q^{3} + 4 q^{6} - 12 q^{7} - 4 q^{10} - 4 q^{12} + 8 q^{13} + 4 q^{15} - 36 q^{16} - 32 q^{21} - 4 q^{22} + 32 q^{25} + 28 q^{27} - 12 q^{28} - 8 q^{30} + 8 q^{31} + 36 q^{33} + 4 q^{36} - 32 q^{37} - 8 q^{40} + 12 q^{42} - 24 q^{43} - 28 q^{45} - 16 q^{46} - 4 q^{48} - 40 q^{51} - 8 q^{52} - 4 q^{55} + 4 q^{57} - 4 q^{58} - 24 q^{60} + 200 q^{61} + 28 q^{63} + 12 q^{70} - 68 q^{73} - 36 q^{75} + 36 q^{76} + 24 q^{78} - 92 q^{81} + 24 q^{82} + 24 q^{85} + 28 q^{87} - 4 q^{88} - 68 q^{90} + 64 q^{91} + 16 q^{93} - 4 q^{96} - 148 q^{97}+O(q^{100}) \) 36 * q + 4 * q^3 + 4 * q^6 - 12 * q^7 - 4 * q^10 - 4 * q^12 + 8 * q^13 + 4 * q^15 - 36 * q^16 - 32 * q^21 - 4 * q^22 + 32 * q^25 + 28 * q^27 - 12 * q^28 - 8 * q^30 + 8 * q^31 + 36 * q^33 + 4 * q^36 - 32 * q^37 - 8 * q^40 + 12 * q^42 - 24 * q^43 - 28 * q^45 - 16 * q^46 - 4 * q^48 - 40 * q^51 - 8 * q^52 - 4 * q^55 + 4 * q^57 - 4 * q^58 - 24 * q^60 + 200 * q^61 + 28 * q^63 + 12 * q^70 - 68 * q^73 - 36 * q^75 + 36 * q^76 + 24 * q^78 - 92 * q^81 + 24 * q^82 + 24 * q^85 + 28 * q^87 - 4 * q^88 - 68 * q^90 + 64 * q^91 + 16 * q^93 - 4 * q^96 - 148 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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