LMFDB - Embedded newform 570.2.k.a.533.1

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			533.1
Character	$\chi$	$=$	570.533
Dual form			570.2.k.a.77.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 - 0.707107i) q^{2} +(-1.49908 + 0.867616i) q^{3} +1.00000i q^{4} +(-0.850241 + 2.06811i) q^{5} +(1.67351 + 0.446512i) q^{6} +(0.811234 - 0.811234i) q^{7} +(0.707107 - 0.707107i) q^{8} +(1.49448 - 2.60125i) q^{9} +O(q^{10})$	\(q+(-0.707107 - 0.707107i) q^{2} +(-1.49908 + 0.867616i) 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} +(-0.867616 - 1.49908i) q^{12} +(3.40609 + 3.40609i) q^{13} -1.14726 q^{14} +(-0.519749 - 3.83795i) q^{15} -1.00000 q^{16} +(3.04078 + 3.04078i) q^{17} +(-2.89612 + 0.782605i) 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} +(0.0165399 + 5.19613i) q^{27} +(0.811234 + 0.811234i) q^{28} -5.49893 q^{29} +(-2.34632 + 3.08136i) q^{30} -5.80986 q^{31} +(0.707107 + 0.707107i) q^{32} +(1.08629 + 1.87691i) 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} +(1.71983 - 0.995380i) q^{42} +(5.60388 + 5.60388i) q^{43} +1.25204 q^{44} +(4.10901 + 5.30245i) q^{45} +7.80043 q^{46} +(-6.12099 - 6.12099i) q^{47} +(1.49908 - 0.867616i) 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} +(0.867616 + 1.49908i) q^{57} +(3.88833 + 3.88833i) q^{58} +9.08034 q^{59} +(3.83795 - 0.519749i) q^{60} +6.32624 q^{61} +(4.10819 + 4.10819i) q^{62} +(-0.897850 - 3.32260i) 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} +(-0.782605 - 2.89612i) q^{72} +(5.45994 + 5.45994i) q^{73} +10.0262 q^{74} +(8.37922 + 2.18828i) q^{75} +1.00000 q^{76} +(-1.01570 - 1.01570i) q^{77} +(4.17925 + 7.22097i) 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} +(8.24334 - 4.77097i) q^{87} +(-0.885325 - 0.885325i) q^{88} -12.7982 q^{89} +(0.843889 - 6.65491i) q^{90} +5.52627 q^{91} +(-5.51574 - 5.51574i) q^{92} +(8.70945 - 5.04073i) 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
$3$	−1.49908	+	0.867616i	−0.865494	+	0.500919i
$3$	−1.49908	+	0.867616i	−0.865494	+	0.500919i
$4$			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	$-0.939556\pi$
$11$		−	1.25204i		−	0.377504i	0.982025	−	0.188752i	$-0.0604442\pi$
$12$	−0.867616	−	1.49908i	−0.250459	−	0.432747i
$13$	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
$15$	−0.519749	−	3.83795i	−0.134199	−	0.990954i
$16$	−1.00000			−0.250000
$17$	3.04078	+	3.04078i	0.737498	+	0.737498i	0.972093	−	0.234595i	$-0.0753763\pi$
$17$	3.04078	+	3.04078i	0.737498	+	0.737498i	−0.234595	+	0.972093i	$0.575376\pi$
$18$	−2.89612	+	0.782605i	−0.682623	+	0.184462i
$19$		−	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	$0.552304\pi$
$23$	−5.51574	+	5.51574i	−1.15011	+	1.15011i	−0.986530	+	0.163581i	$0.947696\pi$
$24$	−0.446512	+	1.67351i	−0.0911439	+	0.341603i
$25$	−3.55418	−	3.51679i	−0.710836	−	0.703358i
$26$		−	4.81693i		−	0.944678i
$27$	0.0165399	+	5.19613i	0.00318310	+	0.999995i
$28$	0.811234	+	0.811234i	0.153309	+	0.153309i
$29$	−5.49893			−1.02113			−0.510563	−	0.859840i	$-0.670563\pi$
$29$	−5.49893			−1.02113			−0.510563	+	0.859840i	$0.670563\pi$
$30$	−2.34632	+	3.08136i	−0.428378	+	0.562577i
$31$	−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
$33$	1.08629	+	1.87691i	0.189099	+	0.326728i
$34$		−	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	$0.00644274\pi$
$41$			0.259187i			0.0404782i	−0.999795	+	0.0202391i	$0.993557\pi$
$42$	1.71983	−	0.995380i	0.265376	−	0.153591i
$43$	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
$45$	4.10901	+	5.30245i	0.612536	+	0.790443i
$46$	7.80043			1.15011
$47$	−6.12099	−	6.12099i	−0.892838	−	0.892838i	0.101951	−	0.994789i	$-0.467491\pi$
$47$	−6.12099	−	6.12099i	−0.892838	−	0.892838i	−0.994789	+	0.101951i	$0.967491\pi$
$48$	1.49908	−	0.867616i	0.216374	−	0.125230i
$49$			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	−0.674430	−	0.738339i	$-0.735610\pi$
$53$	0.465266	−	0.465266i	0.0639091	−	0.0639091i	0.738339	+	0.674430i	$0.235610\pi$
$54$	3.66252	−	3.68591i	0.498406	−	0.501589i
$55$	2.58936	+	1.06454i	0.349149	+	0.143542i
$56$		−	1.14726i		−	0.153309i
$57$	0.867616	+	1.49908i	0.114919	+	0.198558i
$58$	3.88833	+	3.88833i	0.510563	+	0.510563i
$59$	9.08034			1.18216			0.591080	−	0.806613i	$-0.298702\pi$
$59$	9.08034			1.18216			0.591080	+	0.806613i	$0.298702\pi$
$60$	3.83795	−	0.519749i	0.495477	−	0.0670993i
$61$	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
$63$	−0.897850	−	3.32260i	−0.113118	−	0.418609i
$64$		−	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	$0.0141286\pi$
$71$			0.747767i			0.0887437i	−0.999015	+	0.0443718i	$0.985871\pi$
$72$	−0.782605	−	2.89612i	−0.0922308	−	0.341311i
$73$	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
$75$	8.37922	+	2.18828i	0.967550	+	0.252681i
$76$	1.00000			0.114708
$77$	−1.01570	−	1.01570i	−0.115749	−	0.115749i
$78$	4.17925	+	7.22097i	0.473207	+	0.817614i
$79$		−	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	−0.435841	−	0.900024i	$-0.643549\pi$
$83$	4.22891	−	4.22891i	0.464183	−	0.464183i	0.900024	+	0.435841i	$0.143549\pi$
$84$	−1.91995	−	0.512265i	−0.209483	−	0.0558927i
$85$	−8.87408	+	3.70328i	−0.962530	+	0.401678i
$86$		−	7.92509i		−	0.854584i
$87$	8.24334	−	4.77097i	0.883779	−	0.511501i
$88$	−0.885325	−	0.885325i	−0.0943760	−	0.0943760i
$89$	−12.7982			−1.35660			−0.678302	−	0.734784i	$-0.737284\pi$
$89$	−12.7982			−1.35660			−0.678302	+	0.734784i	$0.737284\pi$
$90$	0.843889	−	6.65491i	0.0889537	−	0.701489i
$91$	5.52627			0.579310
$92$	−5.51574	−	5.51574i	−0.575055	−	0.575055i
$93$	8.70945	−	5.04073i	0.903128	−	0.522699i
$94$			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	$-0.943400\pi$
$101$		−	3.55522i		−	0.353758i	0.984233	−	0.176879i	$-0.0566001\pi$
$102$	3.73103	+	6.44652i	0.369427	+	0.638301i
$103$	−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
$105$	−3.53511	−	2.69184i	−0.344992	−	0.262697i
$106$	−0.657985			−0.0639091
$107$	−5.27680	−	5.27680i	−0.510128	−	0.510128i	0.404438	−	0.914566i	$-0.367467\pi$
$107$	−5.27680	−	5.27680i	−0.510128	−	0.510128i	−0.914566	+	0.404438i	$0.867467\pi$
$108$	−5.19613	+	0.0165399i	−0.499997	+	0.00159155i
$109$			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	−0.534246	−	0.845329i	$-0.679404\pi$
$113$	3.30686	−	3.30686i	0.311083	−	0.311083i	0.845329	+	0.534246i	$0.179404\pi$
$114$	0.446512	−	1.67351i	0.0418197	−	0.156738i
$115$	−6.71746	−	16.0969i	−0.626406	−	1.50104i
$116$		−	5.49893i		−	0.510563i
$117$	13.9504	−	3.76975i	1.28972	−	0.348514i
$118$	−6.42077	−	6.42077i	−0.591080	−	0.591080i
$119$	4.93358			0.452260
$120$	−3.08136	−	2.34632i	−0.281288	−	0.214189i
$121$	9.43240			0.857491
$122$	−4.47333	−	4.47333i	−0.404996	−	0.404996i
$123$	−0.224875	−	0.388542i	−0.0202763	−	0.0350336i
$124$		−	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	$0.386798\pi$
$131$			21.4587i			1.87485i	−0.348185	+	0.937426i	$0.613202\pi$
$132$	−1.87691	+	1.08629i	−0.163364	+	0.0945494i
$133$	−0.811234	−	0.811234i	−0.0703429	−	0.0703429i
$134$	3.40719			0.294336
$135$	−10.7602	−	4.38375i	−0.926094	−	0.377294i
$136$	4.30032			0.368749
$137$	13.6290	+	13.6290i	1.16440	+	1.16440i	0.983501	+	0.180902i	$0.0579018\pi$
$137$	13.6290	+	13.6290i	1.16440	+	1.16440i	0.180902	+	0.983501i	$0.442098\pi$
$138$	−11.6935	+	6.76778i	−0.995414	+	0.576112i
$139$		−	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
$147$	−4.93136	−	8.52047i	−0.406731	−	0.702756i
$148$	−7.08962	−	7.08962i	−0.582763	−	0.582763i
$149$	0.688172			0.0563772			0.0281886	−	0.999603i	$-0.491026\pi$
$149$	0.688172			0.0563772			0.0281886	+	0.999603i	$0.491026\pi$
$150$	−4.37766	−	7.47236i	−0.357434	−	0.610115i
$151$	−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
$153$	12.4543	−	3.36545i	1.00687	−	0.272080i
$154$			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
$162$	−2.29245	+	8.70314i	−0.180112	+	0.683783i
$163$	−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
$165$	−4.80526	+	0.650746i	−0.374089	+	0.0506605i
$166$	−5.98058			−0.464183
$167$	4.29057	+	4.29057i	0.332015	+	0.332015i	0.853351	−	0.521337i	$-0.174566\pi$
$167$	4.29057	+	4.29057i	0.332015	+	0.332015i	−0.521337	+	0.853351i	$0.674566\pi$
$168$	0.995380	+	1.71983i	0.0767953	+	0.132688i
$169$			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	−0.576533	−	0.817074i	$-0.695595\pi$
$173$	3.16382	−	3.16382i	0.240541	−	0.240541i	0.817074	+	0.576533i	$0.195595\pi$
$174$	−9.20251	−	2.45534i	−0.697640	−	0.186139i
$175$	−5.73621	+	0.0303324i	−0.433617	+	0.00229291i
$176$			1.25204i			0.0943760i
$177$	−13.6122	+	7.87825i	−1.02315	+	0.592166i
$178$	9.04967	+	9.04967i	0.678302	+	0.678302i
$179$	−3.82605			−0.285973			−0.142986	−	0.989725i	$-0.545670\pi$
$179$	−3.82605			−0.285973			−0.142986	+	0.989725i	$0.545670\pi$
$180$	−5.30245	+	4.10901i	−0.395221	+	0.306268i
$181$	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
$183$	−9.48354	+	5.48875i	−0.701044	+	0.405740i
$184$			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	$-0.869430\pi$
$191$		−	11.0228i		−	0.797579i	0.917042	−	0.398790i	$-0.130570\pi$
$192$	0.867616	+	1.49908i	0.0626148	+	0.108187i
$193$	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
$195$	11.3021	−	14.8427i	0.809359	−	1.06291i
$196$	−5.68380			−0.405986
$197$	7.05740	+	7.05740i	0.502819	+	0.502819i	0.912313	−	0.409494i	$-0.134295\pi$
$197$	7.05740	+	7.05740i	0.502819	+	0.502819i	−0.409494	+	0.912313i	$0.634295\pi$
$198$	0.979852	+	3.62606i	0.0696350	+	0.257693i
$199$		−	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
$207$	6.10465	+	22.5910i	0.424303	+	1.57018i
$208$	−3.40609	−	3.40609i	−0.236170	−	0.236170i
$209$	−1.25204			−0.0866054
$210$	0.596286	+	4.40312i	0.0411477	+	0.303844i
$211$	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
$213$	−0.648775	−	1.12096i	−0.0444534	−	0.0768071i
$214$			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
$222$	−15.0301	+	8.69893i	−1.00876	+	0.583834i
$223$	−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
$225$	−14.4597	+	3.98954i	−0.963982	+	0.265969i
$226$	−4.67660			−0.311083
$227$	18.5524	+	18.5524i	1.23136	+	1.23136i	0.963440	+	0.267923i	$0.0863373\pi$
$227$	18.5524	+	18.5524i	1.23136	+	1.23136i	0.267923	+	0.963440i	$0.413663\pi$
$228$	−1.49908	+	0.867616i	−0.0992790	+	0.0574593i
$229$		−	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	−0.117971	−	0.993017i	$-0.537639\pi$
$233$	13.3570	−	13.3570i	0.875046	−	0.875046i	0.993017	+	0.117971i	$0.0376389\pi$
$234$	−12.5301	−	7.19883i	−0.819116	−	0.470602i
$235$	17.8632	−	7.45458i	1.16527	−	0.486283i
$236$			9.08034i			0.591080i
$237$	4.20257	+	7.26126i	0.272986	+	0.471669i
$238$	−3.48857	−	3.48857i	−0.226130	−	0.226130i
$239$	−0.359134			−0.0232304			−0.0116152	−	0.999933i	$-0.503697\pi$
$239$	−0.359134			−0.0232304			−0.0116152	+	0.999933i	$0.503697\pi$
$240$	0.519749	+	3.83795i	0.0335496	+	0.247739i
$241$	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
$243$	13.5412	+	7.72250i	0.868666	+	0.495399i
$244$			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	$0.138879\pi$
$251$			13.3902i			0.845179i	−0.906321	+	0.422590i	$0.861121\pi$
$252$	3.32260	−	0.897850i	0.209304	−	0.0565592i
$253$	6.90592	+	6.90592i	0.434171	+	0.434171i
$254$	7.65012			0.480011
$255$	10.0899	−	13.2508i	0.631856	−	0.829799i
$256$	1.00000			0.0625000
$257$	−16.2263	−	16.2263i	−1.01217	−	1.01217i	−0.999925	−	0.0122435i	$-0.996103\pi$
$257$	−16.2263	−	16.2263i	−1.01217	−	1.01217i	−0.0122435	−	0.999925i	$-0.503897\pi$
$258$	6.87594	+	11.8803i	0.428077	+	0.739638i
$259$			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	−0.592093	−	0.805870i	$-0.701698\pi$
$263$	3.46688	−	3.46688i	0.213777	−	0.213777i	0.805870	+	0.592093i	$0.201698\pi$
$264$	2.09530	+	0.559051i	0.128957	+	0.0344072i
$265$	0.566634	+	1.35781i	0.0348080	+	0.0834096i
$266$			1.14726i			0.0703429i
$267$	19.1855	−	11.1039i	1.17413	−	0.679548i
$268$	−2.40925	−	2.40925i	−0.147168	−	0.147168i
$269$	−4.91421			−0.299625			−0.149812	−	0.988714i	$-0.547867\pi$
$269$	−4.91421			−0.299625			−0.149812	+	0.988714i	$0.547867\pi$
$270$	4.50885	+	10.7084i	0.274400	+	0.651694i
$271$	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
$273$	−8.28432	+	4.79468i	−0.501390	+	0.290187i
$274$		−	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	$0.201641\pi$
$281$			19.8457i			1.18389i	−0.805977	+	0.591947i	$0.798359\pi$
$282$	−7.51042	−	12.9766i	−0.447239	−	0.772746i
$283$	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
$285$	−3.83795	+	0.519749i	−0.227341	+	0.0307873i
$286$	−6.03099			−0.356620
$287$	0.210261	+	0.210261i	0.0124113	+	0.0124113i
$288$	2.89612	−	0.782605i	0.170656	−	0.0461154i
$289$			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	−0.555550	−	0.831483i	$-0.687492\pi$
$293$	4.72321	−	4.72321i	0.275933	−	0.275933i	0.831483	+	0.555550i	$0.187492\pi$
$294$	−2.53789	+	9.51188i	−0.148013	+	0.554744i
$295$	−7.72048	+	18.7792i	−0.449504	+	1.09336i
$296$			10.0262i			0.582763i
$297$	6.50575	−	0.0207086i	0.377502	−	0.00120163i
$298$	−0.486611	−	0.486611i	−0.0281886	−	0.0281886i
$299$	−37.5741			−2.17297
$300$	−2.18828	+	8.37922i	−0.126341	+	0.483775i
$301$	9.09213			0.524062
$302$	5.50294	+	5.50294i	0.316659	+	0.316659i
$303$	3.08457	+	5.32956i	0.177204	+	0.306175i
$304$			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	$0.177588\pi$
$311$			18.6727i			1.05883i	−0.848363	+	0.529415i	$0.822412\pi$
$312$	−7.22097	+	4.17925i	−0.408807	+	0.236603i
$313$	−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
$315$	7.63490	+	0.968159i	0.430178	+	0.0545496i
$316$	4.84381			0.272485
$317$	−11.0822	−	11.0822i	−0.622438	−	0.622438i	0.323716	−	0.946154i	$-0.395068\pi$
$317$	−11.0822	−	11.0822i	−0.622438	−	0.622438i	−0.946154	+	0.323716i	$0.895068\pi$
$318$	0.986372	−	0.570878i	0.0553130	−	0.0320133i
$319$			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
$327$	−16.9182	−	29.2315i	−0.935578	−	1.61651i
$328$	0.183273	+	0.183273i	0.0101195	+	0.0101195i
$329$	−9.93112			−0.547520
$330$	3.85798	+	2.93769i	0.212375	+	0.161714i
$331$	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
$333$	7.84658	+	29.0372i	0.429990	+	1.59123i
$334$		−	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
$342$	0.782605	+	2.89612i	0.0423184	+	0.156604i
$343$	10.2895	+	10.2895i	0.555583	+	0.555583i
$344$	7.92509			0.427292
$345$	24.0359	+	18.3023i	1.29405	+	0.985364i
$346$	−4.47431			−0.240541
$347$	5.08826	+	5.08826i	0.273152	+	0.273152i	0.830368	−	0.557216i	$-0.188130\pi$
$347$	5.08826	+	5.08826i	0.273152	+	0.273152i	−0.557216	+	0.830368i	$0.688130\pi$
$348$	4.77097	+	8.24334i	0.255751	+	0.441890i
$349$		−	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	−0.491794	−	0.870712i	$-0.663659\pi$
$353$	7.11922	−	7.11922i	0.378918	−	0.378918i	0.870712	+	0.491794i	$0.163659\pi$
$354$	15.1960	+	4.05448i	0.807659	+	0.215493i
$355$	−1.54647	−	0.635783i	−0.0820780	−	0.0337438i
$356$		−	12.7982i		−	0.678302i
$357$	−7.39583	+	4.28045i	−0.391429	+	0.226546i
$358$	2.70543	+	2.70543i	0.142986	+	0.142986i
$359$	24.6824			1.30269			0.651343	−	0.758783i	$-0.274206\pi$
$359$	24.6824			1.30269			0.651343	+	0.758783i	$0.274206\pi$
$360$	6.65491	+	0.843889i	0.350745	+	0.0444768i
$361$	−1.00000			−0.0526316
$362$	−8.29169	−	8.29169i	−0.435801	−	0.435801i
$363$	−14.1399	+	8.18370i	−0.742153	+	0.429533i
$364$			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
$372$	5.04073	+	8.70945i	0.261350	+	0.451564i
$373$	−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
$375$	−11.6500	+	15.4686i	−0.601602	+	0.798796i
$376$	−8.65639			−0.446419
$377$	−18.7298	−	18.7298i	−0.964636	−	0.964636i
$378$	−0.0189755	−	5.96130i	−0.000975995	−	0.306616i
$379$		−	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	$0.557010\pi$
$383$	−22.7437	+	22.7437i	−1.16215	+	1.16215i	−0.984004	+	0.178146i	$0.942990\pi$
$384$	0.446512	−	1.67351i	0.0227860	−	0.0854008i
$385$	2.96416	−	1.23699i	0.151068	−	0.0630428i
$386$		−	9.54847i		−	0.486004i
$387$	22.9520	−	6.20221i	1.16672	−	0.315276i
$388$	−12.5537	−	12.5537i	−0.637317	−	0.637317i
$389$	20.2169			1.02504			0.512519	−	0.858676i	$-0.328713\pi$
$389$	20.2169			1.02504			0.512519	+	0.858676i	$0.328713\pi$
$390$	−18.4871	+	2.50359i	−0.936133	+	0.126774i
$391$	−33.5443			−1.69641
$392$	4.01905	+	4.01905i	0.202993	+	0.202993i
$393$	−18.6179	−	32.1683i	−0.939148	−	1.62267i
$394$		−	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	$-0.817866\pi$
$401$		−	21.6861i		−	1.08295i	0.840716	−	0.541476i	$-0.182134\pi$
$402$	−5.10765	+	2.95613i	−0.254746	+	0.147439i
$403$	−19.7889	−	19.7889i	−0.985754	−	0.985754i
$404$	3.55522			0.176879
$405$	19.9339	−	2.76416i	0.990522	−	0.137352i
$406$	6.30870			0.313096
$407$	8.87649	+	8.87649i	0.439991	+	0.439991i
$408$	−6.44652	+	3.73103i	−0.319150	+	0.184713i
$409$			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
$417$	9.17576	+	15.8540i	0.449339	+	0.776375i
$418$	0.885325	+	0.885325i	0.0433027	+	0.0433027i
$419$	−35.8879			−1.75324			−0.876620	−	0.481184i	$-0.840207\pi$
$419$	−35.8879			−1.75324			−0.876620	+	0.481184i	$0.840207\pi$
$420$	2.69184	−	3.53511i	0.131348	−	0.172496i
$421$	−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
$423$	−25.0700	+	6.77453i	−1.21894	+	0.329389i
$424$		−	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	$-0.996586\pi$
$431$		−	0.445342i		−	0.0214514i	0.999942	−	0.0107257i	$-0.00341416\pi$
$432$	−0.0165399	−	5.19613i	−0.000795775	−	0.249999i
$433$	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
$435$	2.85806	+	21.1046i	0.137034	+	1.01189i
$436$	−19.4996			−0.933863
$437$	5.51574	+	5.51574i	0.263854	+	0.263854i
$438$	6.69932	+	11.5752i	0.320106	+	0.553084i
$439$			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	−0.833546	−	0.552450i	$-0.813693\pi$
$443$	−5.91639	+	5.91639i	−0.281096	+	0.281096i	0.552450	+	0.833546i	$0.313693\pi$
$444$	16.7790	+	4.47684i	0.796295	+	0.212461i
$445$	10.8815	−	26.4681i	0.515834	−	1.25471i
$446$			18.4923i			0.875634i
$447$	−1.03162	+	0.597069i	−0.0487942	+	0.0282404i
$448$	−0.811234	−	0.811234i	−0.0383272	−	0.0383272i
$449$	16.3599			0.772074			0.386037	−	0.922483i	$-0.373844\pi$
$449$	16.3599			0.772074			0.386037	+	0.922483i	$0.373844\pi$
$450$	13.0456	+	7.40354i	0.614975	+	0.349006i
$451$	0.324512			0.0152807
$452$	3.30686	+	3.30686i	0.155541	+	0.155541i
$453$	11.6664	−	6.75209i	0.548133	−	0.317241i
$454$		−	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	$0.128496\pi$
$461$			16.8678i			0.785612i	−0.919621	+	0.392806i	$0.871504\pi$
$462$	−1.24626	−	2.15330i	−0.0579811	−	0.100180i
$463$	−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
$465$	3.01967	+	22.2980i	0.140034	+	1.03404i
$466$	−18.8897			−0.875046
$467$	−12.4366	−	12.4366i	−0.575497	−	0.575497i	0.358162	−	0.933659i	$-0.383404\pi$
$467$	−12.4366	−	12.4366i	−0.575497	−	0.575497i	−0.933659	+	0.358162i	$0.883404\pi$
$468$	3.76975	+	13.9504i	0.174257	+	0.644859i
$469$			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
$477$	−0.514942	−	1.90561i	−0.0235776	−	0.0872517i
$478$	0.253946	+	0.253946i	0.0116152	+	0.0116152i
$479$	37.6990			1.72251			0.861256	−	0.508172i	$-0.169679\pi$
$479$	37.6990			1.72251			0.861256	+	0.508172i	$0.169679\pi$
$480$	2.34632	−	3.08136i	0.107094	−	0.140644i
$481$	−48.2957			−2.20210
$482$	−3.83502	−	3.83502i	−0.174681	−	0.174681i
$483$	−7.76440	−	13.4154i	−0.353292	−	0.610423i
$484$			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	$0.0808448\pi$
$491$			11.1351i			0.502519i	−0.967920	+	0.251260i	$0.919155\pi$
$492$	0.388542	−	0.224875i	0.0175168	−	0.0101381i
$493$	−16.7211	−	16.7211i	−0.753079	−	0.753079i
$494$	−4.81693			−0.216724
$495$	6.63888	−	5.14465i	0.298395	−	0.231235i
$496$	5.80986			0.260870
$497$	0.606615	+	0.606615i	0.0272104	+	0.0272104i
$498$	8.96537	−	5.18885i	0.401748	−	0.232518i
$499$		−	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	−0.0174544	−	0.999848i	$-0.505556\pi$
$503$	22.0328	−	22.0328i	0.982393	−	0.982393i	0.999848	+	0.0174544i	$0.00555619\pi$
$504$	−2.98431	−	1.71456i	−0.132932	−	0.0763725i
$505$	7.35260	+	3.02280i	0.327186	+	0.134513i
$506$		−	9.76645i		−	0.434171i
$507$	−8.85215	−	15.2949i	−0.393138	−	0.679269i
$508$	−5.40945	−	5.40945i	−0.240006	−	0.240006i
$509$	44.4681			1.97101			0.985507	−	0.169634i	$-0.0542586\pi$
$509$	44.4681			1.97101			0.985507	+	0.169634i	$0.0542586\pi$
$510$	−16.5044	+	2.23508i	−0.730827	+	0.0989712i
$511$	8.85858			0.391881
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$	5.19613	−	0.0165399i	0.229415	−	0.000730253i
$514$			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	$-0.817382\pi$
$521$		−	24.7771i		−	1.08551i	0.839892	−	0.542753i	$-0.182618\pi$
$522$	15.9256	−	4.30349i	0.697044	−	0.188359i
$523$	−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
$525$	8.57273	−	5.02230i	0.374144	−	0.219191i
$526$	−4.90290			−0.213777
$527$	−17.6665	−	17.6665i	−0.769566	−	0.769566i
$528$	−1.08629	−	1.87691i	−0.0472747	−	0.0816819i
$529$		−	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
$537$	5.73556	−	3.31955i	0.247508	−	0.143249i
$538$	3.47487	+	3.47487i	0.149812	+	0.149812i
$539$	7.11634			0.306522
$540$	4.38375	−	10.7602i	0.188647	−	0.463047i
$541$	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
$543$	−17.5785	+	10.1739i	−0.754367	+	0.436602i
$544$			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
$552$	−6.76778	−	11.6935i	−0.288056	−	0.497707i
$553$	−3.92946	−	3.92946i	−0.167098	−	0.167098i
$554$	16.2375			0.689866
$555$	30.8944	+	23.5248i	1.31140	+	0.998572i
$556$	10.5758			0.448515
$557$	−23.0216	−	23.0216i	−0.975455	−	0.975455i	0.0242514	−	0.999706i	$-0.492280\pi$
$557$	−23.0216	−	23.0216i	−0.975455	−	0.975455i	−0.999706	+	0.0242514i	$0.992280\pi$
$558$	16.8261	−	4.54682i	0.712304	−	0.192482i
$559$			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	$-0.416055\pi$
$563$	29.0925	−	29.0925i	1.22610	−	1.22610i	0.965426	−	0.260676i	$-0.0839453\pi$
$564$	−3.86518	+	14.4865i	−0.162754	+	0.609993i
$565$	4.02732	+	9.65057i	0.169431	+	0.406003i
$566$		−	19.1667i		−	0.805635i
$567$	−9.98475	−	2.63004i	−0.419320	−	0.110451i
$568$	0.528751	+	0.528751i	0.0221859	+	0.0221859i
$569$	31.9886			1.34103			0.670515	−	0.741896i	$-0.266073\pi$
$569$	31.9886			1.34103			0.670515	+	0.741896i	$0.266073\pi$
$570$	3.08136	+	2.34632i	0.129064	+	0.0982766i
$571$	−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
$573$	9.56353	+	16.5240i	0.399522	+	0.690300i
$574$		−	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
$582$	−26.6141	+	15.4033i	−1.10319	+	0.638488i
$583$	−0.582531	−	0.582531i	−0.0241260	−	0.0241260i
$584$	7.72152			0.319519
$585$	−4.06496	+	32.0563i	−0.168065	+	1.32536i
$586$	−6.67963			−0.275933
$587$	19.3270	+	19.3270i	0.797710	+	0.797710i	0.982734	−	0.185024i	$-0.0592363\pi$
$587$	19.3270	+	19.3270i	0.797710	+	0.797710i	−0.185024	+	0.982734i	$0.559236\pi$
$588$	8.52047	−	4.93136i	0.351378	−	0.203366i
$589$			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	−0.799159	−	0.601119i	$-0.794722\pi$
$593$	−4.82260	+	4.82260i	−0.198040	+	0.198040i	0.601119	+	0.799159i	$0.294722\pi$
$594$	−4.61491	−	4.58562i	−0.189352	−	0.188150i
$595$	−4.19473	+	10.2032i	−0.171967	+	0.418290i
$596$			0.688172i			0.0281886i
$597$	20.6248	+	35.6358i	0.844117	+	1.45848i
$598$	26.5689	+	26.5689i	1.08648	+	1.08648i
$599$	12.4755			0.509735			0.254868	−	0.966976i	$-0.417968\pi$
$599$	12.4755			0.509735			0.254868	+	0.966976i	$0.417968\pi$
$600$	7.47236	−	4.37766i	0.305058	−	0.178717i
$601$	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
$603$	2.66648	+	9.86764i	0.108588	+	0.401841i
$604$		−	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
$612$	3.36545	+	12.4543i	0.136040	+	0.503433i
$613$	−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
$615$	0.994746	−	0.134712i	0.0401120	−	0.00543211i
$616$	−1.43641			−0.0578747
$617$	−22.1031	−	22.1031i	−0.889839	−	0.889839i	0.104668	−	0.994507i	$-0.466622\pi$
$617$	−22.1031	−	22.1031i	−0.889839	−	0.889839i	−0.994507	+	0.104668i	$0.966622\pi$
$618$	−10.6578	−	18.4147i	−0.428720	−	0.740748i
$619$			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
$627$	1.87691	−	1.08629i	0.0749565	−	0.0433822i
$628$	4.92864	+	4.92864i	0.196674	+	0.196674i
$629$	−43.1160			−1.71915
$630$	−4.71410	−	6.08328i	−0.187814	−	0.242364i
$631$	−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
$633$	−25.3763	+	14.6869i	−1.00862	+	0.583752i
$634$			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	$0.171657\pi$
$641$			26.0023i			1.02703i	−0.858081	+	0.513515i	$0.828343\pi$
$642$	−6.47461	−	11.1869i	−0.255533	−	0.441513i
$643$	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
$645$	18.5948	−	24.4200i	0.732170	−	0.961538i
$646$	−4.30032			−0.169194
$647$	27.1481	+	27.1481i	1.06730	+	1.06730i	0.997565	+	0.0697360i	$0.0222157\pi$
$647$	27.1481	+	27.1481i	1.06730	+	1.06730i	0.0697360	+	0.997565i	$0.477784\pi$
$648$	−8.70314	−	2.29245i	−0.341892	−	0.0900561i
$649$		−	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	−0.935317	−	0.353810i	$-0.884886\pi$
$653$	−14.8598	+	14.8598i	−0.581507	+	0.581507i	0.353810	+	0.935317i	$0.384886\pi$
$654$	−8.70682	+	32.6328i	−0.340464	+	1.27604i
$655$	−44.3789	−	18.2450i	−1.73403	−	0.712893i
$656$		−	0.259187i		−	0.0101195i
$657$	22.3625	−	6.04290i	0.872444	−	0.235756i
$658$	7.02236	+	7.02236i	0.273760	+	0.273760i
$659$	3.67408			0.143122			0.0715609	−	0.997436i	$-0.477202\pi$
$659$	3.67408			0.143122			0.0715609	+	0.997436i	$0.477202\pi$
$660$	−0.650746	−	4.80526i	−0.0253302	−	0.187045i
$661$	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
$663$	−17.9721	−	31.0525i	−0.697979	−	1.20598i
$664$		−	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
$672$	−1.71983	+	0.995380i	−0.0663440	+	0.0383976i
$673$	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
$675$	18.2149	−	18.5261i	0.701092	−	0.713071i
$676$	−10.2028			−0.392417
$677$	19.1276	+	19.1276i	0.735134	+	0.735134i	0.971632	−	0.236498i	$-0.0759996\pi$
$677$	19.1276	+	19.1276i	0.735134	+	0.735134i	−0.236498	+	0.971632i	$0.576000\pi$
$678$	7.01060	−	4.05749i	0.269240	−	0.155827i
$679$			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	−0.779139	−	0.626851i	$-0.784343\pi$
$683$	−3.97993	+	3.97993i	−0.152288	+	0.152288i	0.626851	+	0.779139i	$0.284343\pi$
$684$	1.49448	−	2.60125i	0.0571430	−	0.0994614i
$685$	−39.7742	+	16.5984i	−1.51970	+	0.634191i
$686$		−	14.5516i		−	0.555583i
$687$	2.28896	+	3.95490i	0.0873293	+	0.150889i
$688$	−5.60388	−	5.60388i	−0.213646	−	0.213646i
$689$	3.16947			0.120747
$690$	−4.05426	−	29.9377i	−0.154343	−	1.13971i
$691$	−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
$693$	−4.16003	+	1.12414i	−0.158026	+	0.0427027i
$694$		−	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	$0.311768\pi$
$701$			43.9609i			1.66038i	−0.557480	+	0.830191i	$0.688232\pi$
$702$	25.0294	−	0.0796715i	0.944673	−	0.00300701i
$703$	7.08962	+	7.08962i	0.267390	+	0.267390i
$704$	−1.25204			−0.0471880
$705$	−20.3107	+	26.6734i	−0.764944	+	1.00458i
$706$	−10.0681			−0.378918
$707$	−2.88412	−	2.88412i	−0.108468	−	0.108468i
$708$	−7.87825	−	13.6122i	−0.296083	−	0.511576i
$709$			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
$717$	0.538370	−	0.311590i	0.0201058	−	0.0116366i
$718$	−17.4531	−	17.4531i	−0.651343	−	0.651343i
$719$	−22.3343			−0.832930			−0.416465	−	0.909152i	$-0.636731\pi$
$719$	−22.3343			−0.832930			−0.416465	+	0.909152i	$0.636731\pi$
$720$	−4.10901	−	5.30245i	−0.153134	−	0.197611i
$721$	−14.0929			−0.524848
$722$	0.707107	+	0.707107i	0.0263158	+	0.0263158i
$723$	−8.13033	+	4.70555i	−0.302370	+	0.175001i
$724$			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
$732$	−5.48875	−	9.48354i	−0.202870	−	0.350522i
$733$	−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
$735$	21.8141	−	2.95415i	0.804626	−	0.108965i
$736$	−7.80043			−0.287528
$737$	3.01647	+	3.01647i	0.111113	+	0.111113i
$738$	−0.202841	−	0.750637i	−0.00746667	−	0.0276313i
$739$		−	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	−0.999828	−	0.0185673i	$-0.994090\pi$
$743$	−26.7472	+	26.7472i	−0.981260	+	0.981260i	0.0185673	+	0.999828i	$0.494090\pi$
$744$	2.59417	−	9.72284i	0.0951070	−	0.356457i
$745$	−0.585112	+	1.42322i	−0.0214369	+	0.0521426i
$746$			29.2529i			1.07102i
$747$	−4.68043	−	17.3205i	−0.171248	−	0.633724i
$748$	3.80718	+	3.80718i	0.139204	+	0.139204i
$749$	−8.56145			−0.312828
$750$	19.1757	−	2.70018i	0.700199	−	0.0985966i
$751$	−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
$753$	−11.6175	−	20.0729i	−0.423366	−	0.731498i
$754$			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	$0.0435074\pi$
$761$			7.51765i			0.272514i	−0.990673	+	0.136257i	$0.956493\pi$
$762$	−11.4681	+	6.63737i	−0.415447	+	0.240447i
$763$	15.8188	+	15.8188i	0.572678	+	0.572678i
$764$	11.0228			0.398790
$765$	−3.62899	+	28.6182i	−0.131206	+	1.03469i
$766$	32.1645			1.16215
$767$	30.9284	+	30.9284i	1.11676	+	1.11676i
$768$	−1.49908	+	0.867616i	−0.0540934	+	0.0313074i
$769$		−	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	−0.997424	−	0.0717268i	$-0.977149\pi$
$773$	−25.7371	+	25.7371i	−0.925698	+	0.925698i	0.0717268	+	0.997424i	$0.477149\pi$
$774$	−20.6152	−	11.8439i	−0.740997	−	0.425721i
$775$	20.6493	+	20.4321i	0.741744	+	0.733941i
$776$			17.7536i			0.637317i
$777$	−9.97992	−	17.2435i	−0.358028	−	0.618606i
$778$	−14.2955	−	14.2955i	−0.512519	−	0.512519i
$779$	0.259187			0.00928633
$780$	14.8427	+	11.3021i	0.531454	+	0.404679i
$781$	0.936234			0.0335011
$782$	23.7194	+	23.7194i	0.848205	+	0.848205i
$783$	−0.0909517	−	28.5732i	−0.00325035	−	1.02112i
$784$		−	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
$792$	−3.62606	+	0.979852i	−0.128846	+	0.0348175i
$793$	21.5477	+	21.5477i	0.765182	+	0.765182i
$794$	−0.354390			−0.0125768
$795$	−2.02749	−	1.54384i	−0.0719076	−	0.0547545i
$796$	23.7718			0.842569
$797$	−16.2849	−	16.2849i	−0.576840	−	0.576840i	0.357192	−	0.934031i	$-0.383734\pi$
$797$	−16.2849	−	16.2849i	−0.576840	−	0.576840i	−0.934031	+	0.357192i	$0.883734\pi$
$798$	−0.995380	−	1.71983i	−0.0352361	−	0.0608814i
$799$		−	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
$807$	7.36680	−	4.26365i	0.259323	−	0.150088i
$808$	−2.51392	−	2.51392i	−0.0884394	−	0.0884394i
$809$	−20.3523			−0.715549			−0.357775	−	0.933808i	$-0.616464\pi$
$809$	−20.3523			−0.715549			−0.357775	+	0.933808i	$0.616464\pi$
$810$	−16.0499	−	12.1408i	−0.563937	−	0.426585i
$811$	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
$813$	−9.14342	+	5.29190i	−0.320674	+	0.185595i
$814$		−	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	$-0.915063\pi$
$821$		−	15.1106i		−	0.527363i	0.964610	−	0.263681i	$-0.0849367\pi$
$822$	16.7227	+	28.8937i	0.583271	+	1.00778i
$823$	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
$825$	2.73982	−	10.4911i	0.0953882	−	0.365254i
$826$	−10.4175			−0.362471
$827$	−7.31829	−	7.31829i	−0.254482	−	0.254482i	0.568323	−	0.822805i	$-0.307592\pi$
$827$	−7.31829	−	7.31829i	−0.254482	−	0.254482i	−0.822805	+	0.568323i	$0.807592\pi$
$828$	−22.5910	+	6.10465i	−0.785092	+	0.212151i
$829$			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
$837$	−0.0960944	−	30.1888i	−0.00332151	−	1.04348i
$838$	25.3766	+	25.3766i	0.876620	+	0.876620i
$839$	−14.3633			−0.495878			−0.247939	−	0.968776i	$-0.579753\pi$
$839$	−14.3633			−0.495878			−0.247939	+	0.968776i	$0.579753\pi$
$840$	−4.40312	+	0.596286i	−0.151922	+	0.0205738i
$841$	1.23828			0.0426995
$842$	9.57779	+	9.57779i	0.330073	+	0.330073i
$843$	−17.2184	−	29.7503i	−0.593035	−	1.02465i
$844$			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
$852$	1.12096	−	0.648775i	0.0384036	−	0.0222267i
$853$	−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
$855$	5.30245	−	4.10901i	0.181340	−	0.140525i
$856$	−7.46253			−0.255064
$857$	−32.1199	−	32.1199i	−1.09720	−	1.09720i	−0.994737	−	0.102459i	$-0.967329\pi$
$857$	−32.1199	−	32.1199i	−1.09720	−	1.09720i	−0.102459	−	0.994737i	$-0.532671\pi$
$858$	9.04094	−	5.23259i	0.308652	−	0.178638i
$859$			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	−0.877399	−	0.479761i	$-0.840723\pi$
$863$	−11.6814	+	11.6814i	−0.397638	+	0.397638i	0.479761	+	0.877399i	$0.340723\pi$
$864$	−3.66252	+	3.68591i	−0.124601	+	0.125397i
$865$	3.85312	+	9.23314i	0.131010	+	0.313936i
$866$		−	29.5957i		−	1.00570i
$867$	−1.29512	−	2.23773i	−0.0439846	−	0.0759973i
$868$	−4.71316	−	4.71316i	−0.159975	−	0.159975i
$869$	−6.06464			−0.205729
$870$	12.9023	−	16.9442i	0.437428	−	0.574462i
$871$	−16.4122			−0.556106
$872$	13.7883	+	13.7883i	0.466931	+	0.466931i
$873$	13.8940	+	51.4166i	0.470242	+	1.74019i
$874$		−	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	$0.0218025\pi$
$881$			4.06288i			0.136882i	−0.997655	+	0.0684409i	$0.978198\pi$
$882$	−4.44817	−	16.4610i	−0.149778	−	0.554270i
$883$	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
$885$	−4.71949	−	34.8499i	−0.158644	−	1.17147i
$886$	8.36703			0.281096
$887$	−7.54810	−	7.54810i	−0.253440	−	0.253440i	0.568939	−	0.822380i	$-0.307354\pi$
$887$	−7.54810	−	7.54810i	−0.253440	−	0.253440i	−0.822380	+	0.568939i	$0.807354\pi$
$888$	−8.69893	−	15.0301i	−0.291917	−	0.504378i
$889$			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
$897$	56.3267	−	32.5999i	1.88069	−	1.08848i
$898$	−11.5682	−	11.5682i	−0.386037	−	0.386037i
$899$	31.9480			1.06553
$900$	−3.98954	−	14.4597i	−0.132985	−	0.481991i
$901$	2.82954			0.0942658
$902$	−0.229465	−	0.229465i	−0.00764034	−	0.00764034i
$903$	−13.6298	+	7.88848i	−0.453572	+	0.262512i
$904$		−	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	$0.0963529\pi$
$911$			17.9950i			0.596200i	−0.954535	+	0.298100i	$0.903647\pi$
$912$	−0.867616	−	1.49908i	−0.0287297	−	0.0496395i
$913$	−5.29476	−	5.29476i	−0.175231	−	0.175231i
$914$	32.5001			1.07501
$915$	−3.28806	−	24.2798i	−0.108700	−	0.802665i
$916$	2.63822			0.0871692
$917$	17.4080	+	17.4080i	0.574863	+	0.574863i
$918$	22.3450	−	0.0711267i	0.737495	−	0.00234753i
$919$			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
$927$	−35.5760	+	9.61351i	−1.16847	+	0.315749i
$928$	−3.88833	−	3.88833i	−0.127641	−	0.127641i
$929$	10.0132			0.328523			0.164262	−	0.986417i	$-0.447476\pi$
$929$	10.0132			0.328523			0.164262	+	0.986417i	$0.447476\pi$
$930$	13.6318	−	17.9023i	0.447005	−	0.587038i
$931$	5.68380			0.186279
$932$	13.3570	+	13.3570i	0.437523	+	0.437523i
$933$	−16.2007	−	27.9918i	−0.530387	−	0.916411i
$934$			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	$0.0538252\pi$
$941$			10.3250i			0.336585i	−0.985737	+	0.168292i	$0.946175\pi$
$942$	10.4488	−	6.04741i	0.340440	−	0.197035i
$943$	−1.42961	−	1.42961i	−0.0465544	−	0.0465544i
$944$	−9.08034			−0.295540
$945$	−12.2853	+	5.17282i	−0.399642	+	0.168272i
$946$	−9.92252			−0.322609
$947$	−7.92954	−	7.92954i	−0.257676	−	0.257676i	0.566433	−	0.824108i	$-0.308323\pi$
$947$	−7.92954	−	7.92954i	−0.257676	−	0.257676i	−0.824108	+	0.566433i	$0.808323\pi$
$948$	−7.26126	+	4.20257i	−0.235835	+	0.136493i
$949$			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	−0.348498	−	0.937310i	$-0.613308\pi$
$953$	18.1770	−	18.1770i	0.588812	−	0.588812i	0.937310	+	0.348498i	$0.113308\pi$
$954$	−0.983347	+	1.71159i	−0.0318370	+	0.0554146i
$955$	22.7963	+	9.37201i	0.737671	+	0.303271i
$956$		−	0.359134i		−	0.0116152i
$957$	−5.97344	−	10.3210i	−0.193094	−	0.333630i
$958$	−26.6572	−	26.6572i	−0.861256	−	0.861256i
$959$	22.1126			0.714054
$960$	−3.83795	+	0.519749i	−0.123869	+	0.0167748i
$961$	2.75447			0.0888539
$962$	34.1502	+	34.1502i	1.10105	+	1.10105i
$963$	−21.6124	+	5.84021i	−0.696450	+	0.188198i
$964$			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	$-0.929950\pi$
$971$		−	13.6046i		−	0.436594i	0.975882	−	0.218297i	$-0.0700501\pi$
$972$	−7.72250	+	13.5412i	−0.247699	+	0.434333i
$973$	−8.57948	−	8.57948i	−0.275045	−	0.275045i
$974$	−1.62092			−0.0519376
$975$	21.0869	+	35.9938i	0.675320	+	1.15273i
$976$	−6.32624			−0.202498
$977$	1.36368	+	1.36368i	0.0436279	+	0.0436279i	0.728584	−	0.684956i	$-0.240179\pi$
$977$	1.36368	+	1.36368i	0.0436279	+	0.0436279i	−0.684956	+	0.728584i	$0.740179\pi$
$978$	−0.359942	−	0.621913i	−0.0115097	−	0.0198866i
$979$			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	−0.240686	−	0.970603i	$-0.577373\pi$
$983$	22.8849	−	22.8849i	0.729917	−	0.729917i	0.970603	+	0.240686i	$0.0773725\pi$
$984$	−0.433751	−	0.115730i	−0.0138275	−	0.00368934i
$985$	−20.5960	+	8.59501i	−0.656243	+	0.273860i
$986$			23.6472i			0.753079i
$987$	14.8875	−	8.61640i	0.473876	−	0.274263i
$988$	3.40609	+	3.40609i	0.108362	+	0.108362i
$989$	−61.8191			−1.96573
$990$	−8.33221	−	1.05658i	−0.264815	−	0.0335804i
$991$	−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
$993$	−29.9918	+	17.3582i	−0.951761	+	0.550847i
$994$		−	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.533.1	yes	36
3.2	odd	2	inner	570.2.k.a.533.15	yes	36
5.2	odd	4	inner	570.2.k.a.77.15	yes	36
15.2	even	4	inner	570.2.k.a.77.1	✓	36

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

\(f(q)\)	\(=\)	\(q+(-0.707107 - 0.707107i) q^{2} +(-1.49908 + 0.867616i) q^{3} +1.00000i q^{4} +(-0.850241 + 2.06811i) q^{5} +(1.67351 + 0.446512i) q^{6} +(0.811234 - 0.811234i) q^{7} +(0.707107 - 0.707107i) q^{8} +(1.49448 - 2.60125i) q^{9} +O(q^{10})\)	\(q+(-0.707107 - 0.707107i) q^{2} +(-1.49908 + 0.867616i) 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} +(-0.867616 - 1.49908i) q^{12} +(3.40609 + 3.40609i) q^{13} -1.14726 q^{14} +(-0.519749 - 3.83795i) q^{15} -1.00000 q^{16} +(3.04078 + 3.04078i) q^{17} +(-2.89612 + 0.782605i) 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} +(0.0165399 + 5.19613i) q^{27} +(0.811234 + 0.811234i) q^{28} -5.49893 q^{29} +(-2.34632 + 3.08136i) q^{30} -5.80986 q^{31} +(0.707107 + 0.707107i) q^{32} +(1.08629 + 1.87691i) 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} +(1.71983 - 0.995380i) q^{42} +(5.60388 + 5.60388i) q^{43} +1.25204 q^{44} +(4.10901 + 5.30245i) q^{45} +7.80043 q^{46} +(-6.12099 - 6.12099i) q^{47} +(1.49908 - 0.867616i) 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} +(0.867616 + 1.49908i) q^{57} +(3.88833 + 3.88833i) q^{58} +9.08034 q^{59} +(3.83795 - 0.519749i) q^{60} +6.32624 q^{61} +(4.10819 + 4.10819i) q^{62} +(-0.897850 - 3.32260i) 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} +(-0.782605 - 2.89612i) q^{72} +(5.45994 + 5.45994i) q^{73} +10.0262 q^{74} +(8.37922 + 2.18828i) q^{75} +1.00000 q^{76} +(-1.01570 - 1.01570i) q^{77} +(4.17925 + 7.22097i) 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} +(8.24334 - 4.77097i) q^{87} +(-0.885325 - 0.885325i) q^{88} -12.7982 q^{89} +(0.843889 - 6.65491i) q^{90} +5.52627 q^{91} +(-5.51574 - 5.51574i) q^{92} +(8.70945 - 5.04073i) 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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