LMFDB - Embedded newform 506.2.e.h.47.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [506,2,Mod(47,506)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(506, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([8, 0]))

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

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

chi := DirichletCharacter("506.47");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 506 = 2 \cdot 11 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	506.e (of order $5$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.04043034228$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$5$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 2 x^{19} + 13 x^{18} - 32 x^{17} + 171 x^{16} + 76 x^{15} + 1273 x^{14} + 1050 x^{13} + \cdots + 16 $ x^20 - 2x^19 + 13x^18 - 32x^17 + 171x^16 + 76x^15 + 1273x^14 + 1050x^13 + 6271x^12 + 2624x^11 + 18490x^10 - 2604x^9 + 35980x^8 + 23896x^7 + 30384x^6 + 55208x^5 + 62008x^4 + 27768x^3 + 5744x^2 + 256*x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			47.2
Root			$-0.658008 + 2.02514i$ of defining polynomial
Character	$\chi$	$=$	506.47
Dual form			506.2.e.h.323.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.809017 + 0.587785i) q^{2} +(-0.348991 - 1.07408i) q^{3} +(0.309017 - 0.951057i) q^{4} +(2.43018 + 1.76563i) q^{5} +(0.913669 + 0.663820i) q^{6} +(0.436107 - 1.34220i) q^{7} +(0.309017 + 0.951057i) q^{8} +(1.39519 - 1.01367i) q^{9} +O(q^{10})$	\(q+(-0.809017 + 0.587785i) q^{2} +(-0.348991 - 1.07408i) q^{3} +(0.309017 - 0.951057i) q^{4} +(2.43018 + 1.76563i) q^{5} +(0.913669 + 0.663820i) q^{6} +(0.436107 - 1.34220i) q^{7} +(0.309017 + 0.951057i) q^{8} +(1.39519 - 1.01367i) q^{9} -3.00387 q^{10} +(-0.516825 + 3.27611i) q^{11} -1.12936 q^{12} +(0.705636 - 0.512675i) q^{13} +(0.436107 + 1.34220i) q^{14} +(1.04832 - 3.22640i) q^{15} +(-0.809017 - 0.587785i) q^{16} +(1.93934 + 1.40901i) q^{17} +(-0.532916 + 1.64015i) q^{18} +(-0.237518 - 0.731004i) q^{19} +(2.43018 - 1.76563i) q^{20} -1.59383 q^{21} +(-1.50753 - 2.95421i) q^{22} -1.00000 q^{23} +(0.913669 - 0.663820i) q^{24} +(1.24324 + 3.82631i) q^{25} +(-0.269529 + 0.829525i) q^{26} +(-4.31668 - 3.13625i) q^{27} +(-1.14174 - 0.829525i) q^{28} +(-0.719336 + 2.21389i) q^{29} +(1.04832 + 3.22640i) q^{30} +(7.52285 - 5.46567i) q^{31} +1.00000 q^{32} +(3.69918 - 0.588218i) q^{33} -2.39716 q^{34} +(3.42965 - 2.49178i) q^{35} +(-0.532916 - 1.64015i) q^{36} +(0.873579 - 2.68860i) q^{37} +(0.621829 + 0.451785i) q^{38} +(-0.796915 - 0.578993i) q^{39} +(-0.928246 + 2.85685i) q^{40} +(3.09048 + 9.51152i) q^{41} +(1.28944 - 0.936830i) q^{42} +6.13188 q^{43} +(2.95606 + 1.50390i) q^{44} +5.18033 q^{45} +(0.809017 - 0.587785i) q^{46} +(0.788149 + 2.42567i) q^{47} +(-0.348991 + 1.07408i) q^{48} +(4.05181 + 2.94381i) q^{49} +(-3.25485 - 2.36479i) q^{50} +(0.836585 - 2.57474i) q^{51} +(-0.269529 - 0.829525i) q^{52} +(9.60192 - 6.97621i) q^{53} +5.33571 q^{54} +(-7.04037 + 7.04901i) q^{55} +1.41127 q^{56} +(-0.702267 + 0.510227i) q^{57} +(-0.719336 - 2.21389i) q^{58} +(1.83699 - 5.65368i) q^{59} +(-2.74454 - 1.99403i) q^{60} +(-6.29515 - 4.57370i) q^{61} +(-2.87347 + 8.84364i) q^{62} +(-0.752090 - 2.31469i) q^{63} +(-0.809017 + 0.587785i) q^{64} +2.62002 q^{65} +(-2.64695 + 2.65020i) q^{66} -13.4543 q^{67} +(1.93934 - 1.40901i) q^{68} +(0.348991 + 1.07408i) q^{69} +(-1.31001 + 4.03179i) q^{70} +(0.244235 + 0.177447i) q^{71} +(1.39519 + 1.01367i) q^{72} +(-1.53573 + 4.72648i) q^{73} +(0.873579 + 2.68860i) q^{74} +(3.67589 - 2.67069i) q^{75} -0.768623 q^{76} +(4.17180 + 2.12242i) q^{77} +0.985042 q^{78} +(-10.1724 + 7.39067i) q^{79} +(-0.928246 - 2.85685i) q^{80} +(-0.263364 + 0.810550i) q^{81} +(-8.09098 - 5.87844i) q^{82} +(-9.60819 - 6.98076i) q^{83} +(-0.492521 + 1.51582i) q^{84} +(2.22515 + 6.84831i) q^{85} +(-4.96080 + 3.60423i) q^{86} +2.62894 q^{87} +(-3.27547 + 0.520843i) q^{88} +7.28452 q^{89} +(-4.19097 + 3.04492i) q^{90} +(-0.380379 - 1.17069i) q^{91} +(-0.309017 + 0.951057i) q^{92} +(-8.49598 - 6.17269i) q^{93} +(-2.06340 - 1.49915i) q^{94} +(0.713471 - 2.19584i) q^{95} +(-0.348991 - 1.07408i) q^{96} +(2.90613 - 2.11143i) q^{97} -5.00831 q^{98} +(2.59981 + 5.09469i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 5 q^{2} - 3 q^{3} - 5 q^{4} - q^{5} - 3 q^{6} + 3 q^{7} - 5 q^{8} - 8 q^{9}+O(q^{10}) $ 20 * q - 5 * q^2 - 3 * q^3 - 5 * q^4 - q^5 - 3 * q^6 + 3 * q^7 - 5 * q^8 - 8 * q^9	\( 20 q - 5 q^{2} - 3 q^{3} - 5 q^{4} - q^{5} - 3 q^{6} + 3 q^{7} - 5 q^{8} - 8 q^{9} + 24 q^{10} + 8 q^{11} + 12 q^{12} + 4 q^{13} + 3 q^{14} - 3 q^{15} - 5 q^{16} + 7 q^{17} - 8 q^{18} - 9 q^{19} - q^{20} + 16 q^{21} - 7 q^{22} - 20 q^{23} - 3 q^{24} - 22 q^{25} - q^{26} - 21 q^{27} - 7 q^{28} - 20 q^{29} - 3 q^{30} + 10 q^{31} + 20 q^{32} - 23 q^{33} - 8 q^{34} - 39 q^{35} - 8 q^{36} + q^{37} + q^{38} + 8 q^{39} - 11 q^{40} + 31 q^{41} + 21 q^{42} + 8 q^{43} + 3 q^{44} + 144 q^{45} + 5 q^{46} - 36 q^{47} - 3 q^{48} - 36 q^{49} - 12 q^{50} - 19 q^{51} - q^{52} - 8 q^{53} + 24 q^{54} - 7 q^{55} + 8 q^{56} - 43 q^{57} - 20 q^{58} - 37 q^{59} - 3 q^{60} - 3 q^{61} - 10 q^{62} + 40 q^{63} - 5 q^{64} - 62 q^{65} - 33 q^{66} + 48 q^{67} + 7 q^{68} + 3 q^{69} + 31 q^{70} - 56 q^{71} - 8 q^{72} + 51 q^{73} + q^{74} + 86 q^{75} + 16 q^{76} + 19 q^{77} + 58 q^{78} - q^{79} - 11 q^{80} - 25 q^{81} - 34 q^{82} + 12 q^{83} - 29 q^{84} + 35 q^{85} - 42 q^{86} + 30 q^{87} + 3 q^{88} + 126 q^{89} - 46 q^{90} - 93 q^{91} + 5 q^{92} - 74 q^{93} - 6 q^{94} + 5 q^{95} - 3 q^{96} + 29 q^{97} + 24 q^{98} + 76 q^{99}+O(q^{100}) \) 20 * q - 5 * q^2 - 3 * q^3 - 5 * q^4 - q^5 - 3 * q^6 + 3 * q^7 - 5 * q^8 - 8 * q^9 + 24 * q^10 + 8 * q^11 + 12 * q^12 + 4 * q^13 + 3 * q^14 - 3 * q^15 - 5 * q^16 + 7 * q^17 - 8 * q^18 - 9 * q^19 - q^20 + 16 * q^21 - 7 * q^22 - 20 * q^23 - 3 * q^24 - 22 * q^25 - q^26 - 21 * q^27 - 7 * q^28 - 20 * q^29 - 3 * q^30 + 10 * q^31 + 20 * q^32 - 23 * q^33 - 8 * q^34 - 39 * q^35 - 8 * q^36 + q^37 + q^38 + 8 * q^39 - 11 * q^40 + 31 * q^41 + 21 * q^42 + 8 * q^43 + 3 * q^44 + 144 * q^45 + 5 * q^46 - 36 * q^47 - 3 * q^48 - 36 * q^49 - 12 * q^50 - 19 * q^51 - q^52 - 8 * q^53 + 24 * q^54 - 7 * q^55 + 8 * q^56 - 43 * q^57 - 20 * q^58 - 37 * q^59 - 3 * q^60 - 3 * q^61 - 10 * q^62 + 40 * q^63 - 5 * q^64 - 62 * q^65 - 33 * q^66 + 48 * q^67 + 7 * q^68 + 3 * q^69 + 31 * q^70 - 56 * q^71 - 8 * q^72 + 51 * q^73 + q^74 + 86 * q^75 + 16 * q^76 + 19 * q^77 + 58 * q^78 - q^79 - 11 * q^80 - 25 * q^81 - 34 * q^82 + 12 * q^83 - 29 * q^84 + 35 * q^85 - 42 * q^86 + 30 * q^87 + 3 * q^88 + 126 * q^89 - 46 * q^90 - 93 * q^91 + 5 * q^92 - 74 * q^93 - 6 * q^94 + 5 * q^95 - 3 * q^96 + 29 * q^97 + 24 * q^98 + 76 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/506\mathbb{Z}\right)^\times$.

$n$	$277$	$419$
$\chi(n)$	$e\left(\frac{4}{5}\right)$	$1$

Coefficient data

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

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

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

$2$	−0.809017	+	0.587785i	−0.572061	+	0.415627i
$2$	−0.809017	+	0.587785i	−0.572061	+	0.415627i
$3$	−0.348991	−	1.07408i	−0.201490	−	0.620122i	−0.999839	−	0.0179275i	$-0.994293\pi$
$3$	−0.348991	−	1.07408i	−0.201490	−	0.620122i	0.798349	−	0.602194i	$-0.205707\pi$
$4$	0.309017	−	0.951057i	0.154508	−	0.475528i
$5$	2.43018	+	1.76563i	1.08681	+	0.789613i	0.978858	−	0.204543i	$-0.0655708\pi$
$5$	2.43018	+	1.76563i	1.08681	+	0.789613i	0.107952	+	0.994156i	$0.465571\pi$
$6$	0.913669	+	0.663820i	0.373004	+	0.271003i
$7$	0.436107	−	1.34220i	0.164833	−	0.507304i	−0.834191	−	0.551476i	$-0.814065\pi$
$7$	0.436107	−	1.34220i	0.164833	−	0.507304i	0.999024	+	0.0441719i	$0.0140649\pi$
$8$	0.309017	+	0.951057i	0.109254	+	0.336249i
$9$	1.39519	−	1.01367i	0.465064	−	0.337889i
$10$	−3.00387			−0.949906
$11$	−0.516825	+	3.27611i	−0.155829	+	0.987784i
$11$	−0.516825	+	3.27611i	−0.155829	+	0.987784i
$12$	−1.12936			−0.326017
$13$	0.705636	−	0.512675i	0.195708	−	0.142190i	−0.485616	−	0.874172i	$-0.661405\pi$
$13$	0.705636	−	0.512675i	0.195708	−	0.142190i	0.681324	+	0.731982i	$0.261405\pi$
$14$	0.436107	+	1.34220i	0.116555	+	0.358718i
$15$	1.04832	−	3.22640i	0.270675	−	0.833053i
$16$	−0.809017	−	0.587785i	−0.202254	−	0.146946i
$17$	1.93934	+	1.40901i	0.470359	+	0.341736i	0.797581	−	0.603211i	$-0.206113\pi$
$17$	1.93934	+	1.40901i	0.470359	+	0.341736i	−0.327222	+	0.944947i	$0.606113\pi$
$18$	−0.532916	+	1.64015i	−0.125609	+	0.386586i
$19$	−0.237518	−	0.731004i	−0.0544903	−	0.167704i	0.920108	−	0.391665i	$-0.128101\pi$
$19$	−0.237518	−	0.731004i	−0.0544903	−	0.167704i	−0.974598	+	0.223962i	$0.928101\pi$
$20$	2.43018	−	1.76563i	0.543405	−	0.394807i
$21$	−1.59383			−0.347802
$22$	−1.50753	−	2.95421i	−0.321406	−	0.629840i
$23$	−1.00000			−0.208514
$23$	−1.00000			−0.208514
$24$	0.913669	−	0.663820i	0.186502	−	0.135502i
$25$	1.24324	+	3.82631i	0.248648	+	0.765261i
$26$	−0.269529	+	0.829525i	−0.0528590	+	0.162683i
$27$	−4.31668	−	3.13625i	−0.830745	−	0.603572i
$28$	−1.14174	−	0.829525i	−0.215769	−	0.156766i
$29$	−0.719336	+	2.21389i	−0.133577	+	0.411109i	−0.995366	−	0.0961587i	$-0.969344\pi$
$29$	−0.719336	+	2.21389i	−0.133577	+	0.411109i	0.861789	+	0.507267i	$0.169344\pi$
$30$	1.04832	+	3.22640i	0.191396	+	0.589058i
$31$	7.52285	−	5.46567i	1.35114	−	0.981663i	0.352189	−	0.935929i	$-0.385437\pi$
$31$	7.52285	−	5.46567i	1.35114	−	0.981663i	0.998954	−	0.0457342i	$-0.0145627\pi$
$32$	1.00000			0.176777
$33$	3.69918	−	0.588218i	0.643944	−	0.102396i
$34$	−2.39716			−0.411109
$35$	3.42965	−	2.49178i	0.579716	−	0.421188i
$36$	−0.532916	−	1.64015i	−0.0888193	−	0.273358i
$37$	0.873579	−	2.68860i	0.143616	−	0.442003i	−0.853215	−	0.521560i	$-0.825350\pi$
$37$	0.873579	−	2.68860i	0.143616	−	0.442003i	0.996830	+	0.0795565i	$0.0253504\pi$
$38$	0.621829	+	0.451785i	0.100874	+	0.0732892i
$39$	−0.796915	−	0.578993i	−0.127609	−	0.0927131i
$40$	−0.928246	+	2.85685i	−0.146769	+	0.451707i
$41$	3.09048	+	9.51152i	0.482652	+	1.48545i	0.835353	+	0.549714i	$0.185263\pi$
$41$	3.09048	+	9.51152i	0.482652	+	1.48545i	−0.352701	+	0.935736i	$0.614737\pi$
$42$	1.28944	−	0.936830i	0.198964	−	0.144556i
$43$	6.13188			0.935103			0.467552	−	0.883966i	$-0.345136\pi$
$43$	6.13188			0.935103			0.467552	+	0.883966i	$0.345136\pi$
$44$	2.95606	+	1.50390i	0.445642	+	0.226722i
$45$	5.18033			0.772237
$46$	0.809017	−	0.587785i	0.119283	−	0.0866642i
$47$	0.788149	+	2.42567i	0.114963	+	0.353821i	0.991939	−	0.126713i	$-0.0404428\pi$
$47$	0.788149	+	2.42567i	0.114963	+	0.353821i	−0.876976	+	0.480534i	$0.840443\pi$
$48$	−0.348991	+	1.07408i	−0.0503725	+	0.155030i
$49$	4.05181	+	2.94381i	0.578830	+	0.420544i
$50$	−3.25485	−	2.36479i	−0.460305	−	0.334431i
$51$	0.836585	−	2.57474i	0.117145	−	0.360536i
$52$	−0.269529	−	0.829525i	−0.0373770	−	0.115034i
$53$	9.60192	−	6.97621i	1.31893	−	0.958256i	0.318981	−	0.947761i	$-0.396659\pi$
$53$	9.60192	−	6.97621i	1.31893	−	0.958256i	0.999945	−	0.0104945i	$-0.00334056\pi$
$54$	5.33571			0.726098
$55$	−7.04037	+	7.04901i	−0.949323	+	0.950488i
$56$	1.41127			0.188589
$57$	−0.702267	+	0.510227i	−0.0930175	+	0.0675812i
$58$	−0.719336	−	2.21389i	−0.0944534	−	0.290698i
$59$	1.83699	−	5.65368i	0.239156	−	0.736047i	−0.757387	−	0.652966i	$-0.773524\pi$
$59$	1.83699	−	5.65368i	0.239156	−	0.736047i	0.996543	−	0.0830802i	$-0.0264758\pi$
$60$	−2.74454	−	1.99403i	−0.354319	−	0.257428i
$61$	−6.29515	−	4.57370i	−0.806012	−	0.585602i	0.106660	−	0.994296i	$-0.465984\pi$
$61$	−6.29515	−	4.57370i	−0.806012	−	0.585602i	−0.912672	+	0.408694i	$0.865984\pi$
$62$	−2.87347	+	8.84364i	−0.364931	+	1.12314i
$63$	−0.752090	−	2.31469i	−0.0947544	−	0.291624i
$64$	−0.809017	+	0.587785i	−0.101127	+	0.0734732i
$65$	2.62002			0.324973
$66$	−2.64695	+	2.65020i	−0.325817	+	0.326217i
$67$	−13.4543			−1.64370			−0.821851	−	0.569703i	$-0.807058\pi$
$67$	−13.4543			−1.64370			−0.821851	+	0.569703i	$0.807058\pi$
$68$	1.93934	−	1.40901i	0.235180	−	0.170868i
$69$	0.348991	+	1.07408i	0.0420135	+	0.129304i
$70$	−1.31001	+	4.03179i	−0.156576	+	0.481891i
$71$	0.244235	+	0.177447i	0.0289853	+	0.0210591i	0.602184	−	0.798358i	$-0.294298\pi$
$71$	0.244235	+	0.177447i	0.0289853	+	0.0210591i	−0.573198	+	0.819417i	$0.694298\pi$
$72$	1.39519	+	1.01367i	0.164425	+	0.119462i
$73$	−1.53573	+	4.72648i	−0.179743	+	0.553192i	−0.999818	−	0.0190634i	$-0.993932\pi$
$73$	−1.53573	+	4.72648i	−0.179743	+	0.553192i	0.820075	+	0.572256i	$0.193932\pi$
$74$	0.873579	+	2.68860i	0.101552	+	0.312543i
$75$	3.67589	−	2.67069i	0.424455	−	0.308385i
$76$	−0.768623			−0.0881671
$77$	4.17180	+	2.12242i	0.475421	+	0.241872i
$78$	0.985042			0.111534
$79$	−10.1724	+	7.39067i	−1.14448	+	0.831515i	−0.987737	−	0.156124i	$-0.950100\pi$
$79$	−10.1724	+	7.39067i	−1.14448	+	0.831515i	−0.156745	+	0.987639i	$0.550100\pi$
$80$	−0.928246	−	2.85685i	−0.103781	−	0.319405i
$81$	−0.263364	+	0.810550i	−0.0292626	+	0.0900611i
$82$	−8.09098	−	5.87844i	−0.893500	−	0.649166i
$83$	−9.60819	−	6.98076i	−1.05464	−	0.766238i	−0.0815475	−	0.996669i	$-0.525986\pi$
$83$	−9.60819	−	6.98076i	−1.05464	−	0.766238i	−0.973089	+	0.230432i	$0.925986\pi$
$84$	−0.492521	+	1.51582i	−0.0537384	+	0.165390i
$85$	2.22515	+	6.84831i	0.241352	+	0.742804i
$86$	−4.96080	+	3.60423i	−0.534936	+	0.388654i
$87$	2.62894			0.281852
$88$	−3.27547	+	0.520843i	−0.349167	+	0.0555221i
$89$	7.28452			0.772158			0.386079	−	0.922466i	$-0.373829\pi$
$89$	7.28452			0.772158			0.386079	+	0.922466i	$0.373829\pi$
$90$	−4.19097	+	3.04492i	−0.441767	+	0.320963i
$91$	−0.380379	−	1.17069i	−0.0398745	−	0.122721i
$92$	−0.309017	+	0.951057i	−0.0322172	+	0.0991545i
$93$	−8.49598	−	6.17269i	−0.880992	−	0.640078i
$94$	−2.06340	−	1.49915i	−0.212824	−	0.154625i
$95$	0.713471	−	2.19584i	0.0732006	−	0.225288i
$96$	−0.348991	−	1.07408i	−0.0356187	−	0.109623i
$97$	2.90613	−	2.11143i	0.295073	−	0.214383i	−0.430392	−	0.902642i	$-0.641625\pi$
$97$	2.90613	−	2.11143i	0.295073	−	0.214383i	0.725465	+	0.688259i	$0.241625\pi$
$98$	−5.00831			−0.505916
$99$	2.59981	+	5.09469i	0.261291	+	0.512036i
$100$	4.02322			0.402322
$101$	−15.2215	+	11.0591i	−1.51459	+	1.10042i	−0.550508	+	0.834830i	$0.685566\pi$
$101$	−15.2215	+	11.0591i	−1.51459	+	1.10042i	−0.964087	+	0.265587i	$0.914434\pi$
$102$	0.836585	+	2.57474i	0.0828343	+	0.254938i
$103$	−2.09133	+	6.43644i	−0.206065	+	0.634201i	0.793603	+	0.608435i	$0.208202\pi$
$103$	−2.09133	+	6.43644i	−0.206065	+	0.634201i	−0.999668	+	0.0257661i	$0.991798\pi$
$104$	0.705636	+	0.512675i	0.0691933	+	0.0502719i
$105$	−3.87329	−	2.81411i	−0.377995	−	0.274629i
$106$	−3.66761	+	11.2877i	−0.356230	+	1.09636i
$107$	−5.11821	−	15.7522i	−0.494796	−	1.52282i	−0.817275	−	0.576248i	$-0.804516\pi$
$107$	−5.11821	−	15.7522i	−0.494796	−	1.52282i	0.322479	−	0.946577i	$-0.395484\pi$
$108$	−4.31668	+	3.13625i	−0.415373	+	0.301786i
$109$	−0.214079			−0.0205050			−0.0102525	−	0.999947i	$-0.503264\pi$
$109$	−0.214079			−0.0205050			−0.0102525	+	0.999947i	$0.503264\pi$
$110$	1.55247	−	9.84100i	0.148023	−	0.938302i
$111$	−3.19265			−0.303033
$112$	−1.14174	+	0.829525i	−0.107885	+	0.0783828i
$113$	2.27533	+	7.00274i	0.214045	+	0.658762i	0.999220	+	0.0394886i	$0.0125729\pi$
$113$	2.27533	+	7.00274i	0.214045	+	0.658762i	−0.785175	+	0.619274i	$0.787427\pi$
$114$	0.268242	−	0.825564i	0.0251232	−	0.0773212i
$115$	−2.43018	−	1.76563i	−0.226615	−	0.164646i
$116$	1.88325	+	1.36826i	0.174855	+	0.127040i
$117$	0.464817	−	1.43056i	0.0429723	−	0.132255i
$118$	1.83699	+	5.65368i	0.169109	+	0.520464i
$119$	2.73694	−	1.98850i	0.250895	−	0.182286i
$120$	3.39244			0.309686
$121$	−10.4658	−	3.38635i	−0.951435	−	0.307850i
$122$	7.78124			0.704480
$123$	9.13761	−	6.63886i	0.823911	−	0.598606i
$124$	−2.87347	−	8.84364i	−0.258045	−	0.794182i
$125$	0.906696	−	2.79052i	0.0810974	−	0.249592i
$126$	1.96900	+	1.43056i	0.175412	+	0.127444i
$127$	−6.16987	−	4.48267i	−0.547487	−	0.397773i	0.279371	−	0.960183i	$-0.409874\pi$
$127$	−6.16987	−	4.48267i	−0.547487	−	0.397773i	−0.826858	+	0.562410i	$0.809874\pi$
$128$	0.309017	−	0.951057i	0.0273135	−	0.0840623i
$129$	−2.13997	−	6.58615i	−0.188414	−	0.579878i
$130$	−2.11964	+	1.54001i	−0.185904	+	0.135068i
$131$	−10.9427			−0.956067			−0.478033	−	0.878342i	$-0.658650\pi$
$131$	−10.9427			−0.956067			−0.478033	+	0.878342i	$0.658650\pi$
$132$	0.583680	−	3.69990i	0.0508029	−	0.322035i
$133$	−1.08474			−0.0940586
$134$	10.8847	−	7.90823i	0.940298	−	0.683167i
$135$	−4.95285	−	15.2433i	−0.426273	−	1.31193i
$136$	−0.740762	+	2.27983i	−0.0635198	+	0.195494i
$137$	−16.7529	−	12.1717i	−1.43130	−	1.03990i	−0.989773	−	0.142651i	$-0.954437\pi$
$137$	−16.7529	−	12.1717i	−1.43130	−	1.03990i	−0.441526	−	0.897248i	$-0.645563\pi$
$138$	−0.913669	−	0.663820i	−0.0777767	−	0.0565081i
$139$	−1.07643	+	3.31293i	−0.0913020	+	0.280999i	−0.986272	−	0.165127i	$-0.947197\pi$
$139$	−1.07643	+	3.31293i	−0.0913020	+	0.280999i	0.894970	+	0.446126i	$0.147197\pi$
$140$	−1.31001	−	4.03179i	−0.110716	−	0.340748i
$141$	2.33032	−	1.69307i	0.196248	−	0.142583i
$142$	−0.301890			−0.0253341
$143$	1.31489	+	2.57670i	0.109956	+	0.215475i
$144$	−1.72455			−0.143713
$145$	−5.65702	+	4.11007i	−0.469790	+	0.341322i
$146$	−1.53573	−	4.72648i	−0.127098	−	0.391166i
$147$	1.74785	−	5.37934i	0.144160	−	0.443680i
$148$	−2.28706	−	1.66165i	−0.187995	−	0.136586i
$149$	−0.189431	−	0.137630i	−0.0155188	−	0.0112751i	0.579999	−	0.814617i	$-0.303053\pi$
$149$	−0.189431	−	0.137630i	−0.0155188	−	0.0112751i	−0.595518	+	0.803342i	$0.703053\pi$
$150$	−1.40406	+	4.32127i	−0.114641	+	0.352830i
$151$	0.721536	+	2.22066i	0.0587178	+	0.180715i	0.976113	−	0.217262i	$-0.0697125\pi$
$151$	0.721536	+	2.22066i	0.0587178	+	0.180715i	−0.917396	+	0.397977i	$0.869713\pi$
$152$	0.621829	−	0.451785i	0.0504370	−	0.0366446i
$153$	4.13402			0.334216
$154$	−4.62258	+	0.735052i	−0.372498	+	0.0592322i
$155$	27.9322			2.24357
$156$	−0.796915	+	0.578993i	−0.0638043	+	0.0463565i
$157$	0.577593	+	1.77765i	0.0460970	+	0.141872i	0.971456	−	0.237220i	$-0.0762363\pi$
$157$	0.577593	+	1.77765i	0.0460970	+	0.141872i	−0.925359	+	0.379092i	$0.876236\pi$
$158$	3.88551	−	11.9584i	0.309114	−	0.951356i
$159$	−10.8440	−	7.87863i	−0.859985	−	0.624816i
$160$	2.43018	+	1.76563i	0.192123	+	0.139585i
$161$	−0.436107	+	1.34220i	−0.0343701	+	0.105780i
$162$	−0.263364	−	0.810550i	−0.0206918	−	0.0636828i
$163$	−0.166490	+	0.120962i	−0.0130405	+	0.00947450i	−0.594286	−	0.804253i	$-0.702565\pi$
$163$	−0.166490	+	0.120962i	−0.0130405	+	0.00947450i	0.581246	+	0.813728i	$0.302565\pi$
$164$	10.0010			0.780947
$165$	10.0282	+	5.10190i	0.780698	+	0.397182i
$166$	11.8764			0.921786
$167$	−3.58189	+	2.60240i	−0.277175	+	0.201379i	−0.717684	−	0.696369i	$-0.754798\pi$
$167$	−3.58189	+	2.60240i	−0.277175	+	0.201379i	0.440509	+	0.897748i	$0.354798\pi$
$168$	−0.492521	−	1.51582i	−0.0379988	−	0.116948i
$169$	−3.78213	+	11.6402i	−0.290933	+	0.895401i
$170$	−5.82552	−	4.23249i	−0.446797	−	0.324617i
$171$	−1.07238	−	0.779127i	−0.0820067	−	0.0595813i
$172$	1.89486	−	5.83177i	0.144481	−	0.444668i
$173$	3.57710	+	11.0092i	0.271962	+	0.837013i	0.990007	+	0.141017i	$0.0450371\pi$
$173$	3.57710	+	11.0092i	0.271962	+	0.837013i	−0.718045	+	0.695996i	$0.754963\pi$
$174$	−2.12686	+	1.54525i	−0.161237	+	0.117145i
$175$	5.67785			0.429205
$176$	2.34377	−	2.34665i	0.176668	−	0.176885i
$177$	−6.71361			−0.504626
$178$	−5.89330	+	4.28173i	−0.441722	+	0.320929i
$179$	7.46462	+	22.9737i	0.557932	+	1.71714i	0.688072	+	0.725642i	$0.258457\pi$
$179$	7.46462	+	22.9737i	0.557932	+	1.71714i	−0.130140	+	0.991496i	$0.541543\pi$
$180$	1.60081	−	4.92678i	0.119317	−	0.367221i
$181$	−8.97707	−	6.52222i	−0.667260	−	0.484793i	0.201847	−	0.979417i	$-0.435306\pi$
$181$	−8.97707	−	6.52222i	−0.667260	−	0.484793i	−0.869107	+	0.494624i	$0.835306\pi$
$182$	0.995845	+	0.723524i	0.0738169	+	0.0536311i
$183$	−2.71558	+	8.35769i	−0.200741	+	0.617818i
$184$	−0.309017	−	0.951057i	−0.0227810	−	0.0701128i
$185$	6.87002	−	4.99136i	0.505094	−	0.366972i
$186$	10.5016			0.770015
$187$	−5.61838	+	5.62528i	−0.410857	+	0.411361i
$188$	2.55050			0.186015
$189$	−6.09201	+	4.42610i	−0.443128	+	0.321952i
$190$	0.713471	+	2.19584i	0.0517606	+	0.159303i
$191$	−1.46123	+	4.49722i	−0.105731	+	0.325407i	−0.989901	−	0.141758i	$-0.954725\pi$
$191$	−1.46123	+	4.49722i	−0.105731	+	0.325407i	0.884170	+	0.467165i	$0.154725\pi$
$192$	0.913669	+	0.663820i	0.0659384	+	0.0479070i
$193$	−7.10387	−	5.16127i	−0.511348	−	0.371516i	0.301987	−	0.953312i	$-0.402350\pi$
$193$	−7.10387	−	5.16127i	−0.511348	−	0.371516i	−0.813335	+	0.581796i	$0.802350\pi$
$194$	−1.11004	+	3.41636i	−0.0796965	+	0.245281i
$195$	−0.914361	−	2.81411i	−0.0654787	−	0.201523i
$196$	4.05181	−	2.94381i	0.289415	−	0.210272i
$197$	0.205305			0.0146274			0.00731369	−	0.999973i	$-0.497672\pi$
$197$	0.205305			0.0146274			0.00731369	+	0.999973i	$0.497672\pi$
$198$	−5.09788	−	2.59356i	−0.362290	−	0.184316i
$199$	16.3140			1.15647			0.578235	−	0.815871i	$-0.303742\pi$
$199$	16.3140			1.15647			0.578235	+	0.815871i	$0.303742\pi$
$200$	−3.25485	+	2.36479i	−0.230153	+	0.167216i
$201$	4.69542	+	14.4510i	0.331189	+	1.01930i
$202$	5.81409	−	17.8939i	0.409078	−	1.25901i
$203$	2.65777	+	1.93099i	0.186539	+	0.135529i
$204$	−2.19021	−	1.59128i	−0.153345	−	0.111412i
$205$	−9.28339	+	28.5713i	−0.648380	+	1.99551i
$206$	−2.09133	−	6.43644i	−0.145710	−	0.448448i
$207$	−1.39519	+	1.01367i	−0.0969726	+	0.0704547i
$208$	−0.872214			−0.0604772
$209$	2.51760	−	0.400332i	0.174146	−	0.0276916i
$210$	4.78766			0.330380
$211$	−1.75748	+	1.27688i	−0.120990	+	0.0879043i	−0.646635	−	0.762800i	$-0.723824\pi$
$211$	−1.75748	+	1.27688i	−0.120990	+	0.0879043i	0.525645	+	0.850704i	$0.323824\pi$
$212$	−3.66761	−	11.2877i	−0.251892	−	0.775245i
$213$	0.105357	−	0.324255i	0.00721894	−	0.0222176i
$214$	13.3996	+	9.73541i	0.915981	+	0.665499i
$215$	14.9016	+	10.8266i	1.01628	+	0.738370i
$216$	1.64882	−	5.07456i	0.112188	−	0.345280i
$217$	−4.05525	−	12.4808i	−0.275288	−	0.847251i
$218$	0.173193	−	0.125832i	0.0117301	−	0.00852244i
$219$	5.61258			0.379263
$220$	4.52841	+	8.87405i	0.305306	+	0.598289i
$221$	2.09083			0.140645
$222$	2.58291	−	1.87659i	0.173353	−	0.125949i
$223$	1.35482	+	4.16970i	0.0907252	+	0.279224i	0.986116	−	0.166058i	$-0.0531037\pi$
$223$	1.35482	+	4.16970i	0.0907252	+	0.279224i	−0.895391	+	0.445281i	$0.853104\pi$
$224$	0.436107	−	1.34220i	0.0291386	−	0.0896795i
$225$	5.61316	+	4.07820i	0.374211	+	0.271880i
$226$	−5.95689	−	4.32793i	−0.396246	−	0.287890i
$227$	8.57530	−	26.3921i	0.569163	−	1.75170i	−0.0860840	−	0.996288i	$-0.527435\pi$
$227$	8.57530	−	26.3921i	0.569163	−	1.75170i	0.655247	−	0.755415i	$-0.272565\pi$
$228$	0.268242	+	0.825564i	0.0177648	+	0.0546743i
$229$	−17.7182	+	12.8730i	−1.17085	+	0.850671i	−0.991110	−	0.133043i	$-0.957525\pi$
$229$	−17.7182	+	12.8730i	−1.17085	+	0.850671i	−0.179738	+	0.983714i	$0.557525\pi$
$230$	3.00387			0.198069
$231$	0.823732	−	5.22156i	0.0541976	−	0.343554i
$232$	−2.32782			−0.152829
$233$	−10.0523	+	7.30344i	−0.658550	+	0.478464i	−0.866173	−	0.499745i	$-0.833427\pi$
$233$	−10.0523	+	7.30344i	−0.658550	+	0.478464i	0.207623	+	0.978209i	$0.433427\pi$
$234$	0.464817	+	1.43056i	0.0303860	+	0.0935186i
$235$	−2.36749	+	7.28640i	−0.154438	+	0.475312i
$236$	−4.80931	−	3.49417i	−0.313059	−	0.227451i
$237$	11.4883	+	8.34671i	0.746242	+	0.542177i
$238$	−1.04542	+	3.21746i	−0.0677644	+	0.208557i
$239$	1.69777	+	5.22519i	0.109819	+	0.337990i	0.990831	−	0.135105i	$-0.0431370\pi$
$239$	1.69777	+	5.22519i	0.109819	+	0.337990i	−0.881012	+	0.473094i	$0.843137\pi$
$240$	−2.74454	+	1.99403i	−0.177159	+	0.128714i
$241$	−10.0588			−0.647946			−0.323973	−	0.946066i	$-0.605019\pi$
$241$	−10.0588			−0.647946			−0.323973	+	0.946066i	$0.605019\pi$
$242$	10.4574	−	3.41202i	0.672230	−	0.219333i
$243$	−15.0446			−0.965112
$244$	−6.29515	+	4.57370i	−0.403006	+	0.292801i
$245$	4.64894	+	14.3080i	0.297010	+	0.914103i
$246$	−3.49026	+	10.7419i	−0.222531	+	0.684879i
$247$	−0.542368	−	0.394054i	−0.0345101	−	0.0250730i
$248$	7.52285	+	5.46567i	0.477701	+	0.347070i
$249$	−4.14474	+	12.7562i	−0.262662	+	0.808392i
$250$	0.906696	+	2.79052i	0.0573445	+	0.176488i
$251$	1.46478	−	1.06422i	0.0924561	−	0.0671733i	−0.540597	−	0.841282i	$-0.681802\pi$
$251$	1.46478	−	1.06422i	0.0924561	−	0.0671733i	0.633053	+	0.774109i	$0.281802\pi$
$252$	−2.43381			−0.153316
$253$	0.516825	−	3.27611i	0.0324925	−	0.205967i
$254$	7.62638			0.478521
$255$	6.57910	−	4.77999i	0.411999	−	0.299335i
$256$	0.309017	+	0.951057i	0.0193136	+	0.0594410i
$257$	4.34144	−	13.3616i	0.270812	−	0.833472i	−0.719486	−	0.694507i	$-0.755622\pi$
$257$	4.34144	−	13.3616i	0.270812	−	0.833472i	0.990297	−	0.138965i	$-0.0443776\pi$
$258$	5.60251	+	4.07046i	0.348797	+	0.253416i
$259$	−3.22766	−	2.34504i	−0.200557	−	0.145713i
$260$	0.809629	−	2.49178i	0.0502111	−	0.154534i
$261$	1.24053	+	3.81797i	0.0767870	+	0.236326i
$262$	8.85282	−	6.43195i	0.546929	−	0.397367i
$263$	3.63063			0.223874			0.111937	−	0.993715i	$-0.464294\pi$
$263$	3.63063			0.223874			0.111937	+	0.993715i	$0.464294\pi$
$264$	1.70254	+	3.33636i	0.104784	+	0.205339i
$265$	35.6518			2.19007
$266$	0.877570	−	0.637592i	0.0538073	−	0.0390933i
$267$	−2.54223	−	7.82418i	−0.155582	−	0.478832i
$268$	−4.15760	+	12.7958i	−0.253966	+	0.781627i
$269$	−10.0205	−	7.28035i	−0.610963	−	0.443891i	0.238790	−	0.971071i	$-0.423249\pi$
$269$	−10.0205	−	7.28035i	−0.610963	−	0.443891i	−0.849753	+	0.527181i	$0.823249\pi$
$270$	12.9667	+	9.42088i	0.789130	+	0.573336i
$271$	−2.63957	+	8.12375i	−0.160342	+	0.493483i	−0.998663	−	0.0516948i	$-0.983538\pi$
$271$	−2.63957	+	8.12375i	−0.160342	+	0.493483i	0.838321	+	0.545177i	$0.183538\pi$
$272$	−0.740762	−	2.27983i	−0.0449153	−	0.138235i
$273$	−1.12466	+	0.817117i	−0.0680678	+	0.0494542i
$274$	20.7078			1.25100
$275$	−13.1779	+	2.09547i	−0.794659	+	0.126361i
$276$	1.12936			0.0679793
$277$	−6.82700	+	4.96010i	−0.410194	+	0.298024i	−0.773681	−	0.633576i	$-0.781586\pi$
$277$	−6.82700	+	4.96010i	−0.410194	+	0.298024i	0.363486	+	0.931600i	$0.381586\pi$
$278$	−1.07643	−	3.31293i	−0.0645603	−	0.198696i
$279$	4.95545	−	15.2513i	0.296675	−	0.913072i
$280$	3.42965	+	2.49178i	0.204961	+	0.148913i
$281$	18.9199	+	13.7461i	1.12867	+	0.820025i	0.985500	−	0.169673i	$-0.0542712\pi$
$281$	18.9199	+	13.7461i	1.12867	+	0.820025i	0.143168	+	0.989698i	$0.454271\pi$
$282$	−0.890102	+	2.73945i	−0.0530048	+	0.163132i
$283$	−3.47848	−	10.7057i	−0.206774	−	0.636385i	−0.999636	−	0.0269836i	$-0.991410\pi$
$283$	−3.47848	−	10.7057i	−0.206774	−	0.636385i	0.792862	−	0.609401i	$-0.208590\pi$
$284$	0.244235	−	0.177447i	0.0144927	−	0.0105295i
$285$	−2.60751			−0.154455
$286$	−2.57832	−	1.31173i	−0.152459	−	0.0775640i
$287$	14.1141			0.833132
$288$	1.39519	−	1.01367i	0.0822125	−	0.0597309i
$289$	−3.47757	−	10.7028i	−0.204563	−	0.629579i
$290$	2.16079	−	6.65023i	0.126886	−	0.390515i
$291$	−3.28206	−	2.38456i	−0.192398	−	0.139785i
$292$	4.02058	+	2.92112i	0.235287	+	0.170946i
$293$	5.51320	−	16.9679i	0.322085	−	0.991275i	−0.650654	−	0.759374i	$-0.725505\pi$
$293$	5.51320	−	16.9679i	0.322085	−	0.991275i	0.972739	−	0.231901i	$-0.0744946\pi$
$294$	1.74785	+	5.37934i	0.101937	+	0.313729i
$295$	14.4465	−	10.4960i	0.841109	−	0.611102i
$296$	2.82696			0.164314
$297$	12.5057	−	12.5210i	0.725652	−	0.726543i
$298$	0.234149			0.0135639
$299$	−0.705636	+	0.512675i	−0.0408080	+	0.0296487i
$300$	−1.40406	−	4.32127i	−0.0810637	−	0.249488i
$301$	2.67416	−	8.23021i	0.154136	−	0.474381i
$302$	−1.88901	−	1.37244i	−0.108700	−	0.0789752i
$303$	17.1905	+	12.4896i	0.987568	+	0.717510i
$304$	−0.237518	+	0.731004i	−0.0136226	+	0.0419259i
$305$	−7.22290	−	22.2298i	−0.413582	−	1.27287i
$306$	−3.34449	+	2.42992i	−0.191192	+	0.138909i
$307$	19.7390			1.12657			0.563283	−	0.826264i	$-0.309538\pi$
$307$	19.7390			1.12657			0.563283	+	0.826264i	$0.309538\pi$
$308$	3.30770	−	3.31176i	0.188474	−	0.188705i
$309$	7.64312			0.434802
$310$	−22.5976	+	16.4181i	−1.28346	+	0.932488i
$311$	3.01540	+	9.28044i	0.170987	+	0.526245i	0.999428	−	0.0338324i	$-0.0107713\pi$
$311$	3.01540	+	9.28044i	0.170987	+	0.526245i	−0.828440	+	0.560078i	$0.810771\pi$
$312$	0.304395	−	0.936830i	0.0172330	−	0.0530376i
$313$	3.10134	+	2.25325i	0.175298	+	0.127361i	0.671974	−	0.740574i	$-0.265446\pi$
$313$	3.10134	+	2.25325i	0.175298	+	0.127361i	−0.496677	+	0.867936i	$0.665446\pi$
$314$	−1.51216	−	1.09865i	−0.0853361	−	0.0620003i
$315$	2.25918	−	6.95303i	0.127290	−	0.391759i
$316$	3.88551	+	11.9584i	0.218577	+	0.672710i
$317$	−3.51695	+	2.55522i	−0.197532	+	0.143515i	−0.682155	−	0.731208i	$-0.738957\pi$
$317$	−3.51695	+	2.55522i	−0.197532	+	0.143515i	0.484623	+	0.874723i	$0.338957\pi$
$318$	13.4039			0.751655
$319$	−6.88117	−	3.50082i	−0.385272	−	0.196008i
$320$	−3.00387			−0.167921
$321$	−15.1330	+	10.9948i	−0.844641	+	0.613667i
$322$	−0.436107	−	1.34220i	−0.0243033	−	0.0747979i
$323$	0.569367	−	1.75233i	0.0316804	−	0.0975023i
$324$	0.689495	+	0.500948i	0.0383053	+	0.0278304i
$325$	2.83893	+	2.06260i	0.157475	+	0.114413i
$326$	0.0635937	−	0.195721i	0.00352213	−	0.0108400i
$327$	0.0747115	+	0.229938i	0.00413155	+	0.0127156i
$328$	−8.09098	+	5.87844i	−0.446750	+	0.324583i
$329$	3.59946			0.198444
$330$	−11.1118	+	1.76693i	−0.611687	+	0.0972662i
$331$	−30.0198			−1.65004			−0.825019	−	0.565104i	$-0.808836\pi$
$331$	−30.0198			−1.65004			−0.825019	+	0.565104i	$0.808836\pi$
$332$	−9.60819	+	6.98076i	−0.527318	+	0.383119i
$333$	−1.50653	−	4.63663i	−0.0825575	−	0.254086i
$334$	1.36816	−	4.21076i	0.0748624	−	0.230403i
$335$	−32.6963	−	23.7553i	−1.78639	−	1.29789i
$336$	1.28944	+	0.936830i	0.0703445	+	0.0511083i
$337$	9.63992	−	29.6686i	0.525120	−	1.61615i	−0.238959	−	0.971030i	$-0.576806\pi$
$337$	9.63992	−	29.6686i	0.525120	−	1.61615i	0.764079	−	0.645123i	$-0.223194\pi$
$338$	−3.78213	−	11.6402i	−0.205721	−	0.633144i
$339$	6.72745	−	4.88778i	0.365385	−	0.265468i
$340$	7.20074			0.390515
$341$	14.0181	+	27.4705i	0.759124	+	1.48761i
$342$	1.32553			0.0716765
$343$	13.7104	−	9.96120i	0.740293	−	0.537854i
$344$	1.89486	+	5.83177i	0.102164	+	0.314428i
$345$	−1.04832	+	3.22640i	−0.0564397	+	0.173704i
$346$	−9.36497	−	6.80405i	−0.503464	−	0.365788i
$347$	10.2279	+	7.43101i	0.549063	+	0.398918i	0.827440	−	0.561554i	$-0.189796\pi$
$347$	10.2279	+	7.43101i	0.549063	+	0.398918i	−0.278377	+	0.960472i	$0.589796\pi$
$348$	0.812387	−	2.50027i	0.0435485	−	0.134029i
$349$	−1.28116	−	3.94302i	−0.0685792	−	0.211065i	0.910894	−	0.412641i	$-0.135394\pi$
$349$	−1.28116	−	3.94302i	−0.0685792	−	0.211065i	−0.979473	+	0.201576i	$0.935394\pi$
$350$	−4.59348	+	3.33736i	−0.245532	+	0.178389i
$351$	−4.65388			−0.248406
$352$	−0.516825	+	3.27611i	−0.0275469	+	0.174617i
$353$	−10.9557			−0.583114			−0.291557	−	0.956554i	$-0.594173\pi$
$353$	−10.9557			−0.583114			−0.291557	+	0.956554i	$0.594173\pi$
$354$	5.43143	−	3.94616i	0.288677	−	0.209736i
$355$	0.280229	+	0.862455i	0.0148730	+	0.0457744i
$356$	2.25104	−	6.92799i	0.119305	−	0.367183i
$357$	−3.09098	−	2.24573i	−0.163592	−	0.118857i
$358$	−19.5426	−	14.1986i	−1.03286	−	0.750417i
$359$	−6.29437	+	19.3721i	−0.332204	+	1.02242i	0.635879	+	0.771789i	$0.280638\pi$
$359$	−6.29437	+	19.3721i	−0.332204	+	1.02242i	−0.968083	+	0.250630i	$0.919362\pi$
$360$	1.60081	+	4.92678i	0.0843700	+	0.259664i
$361$	14.8934	−	10.8207i	0.783862	−	0.569509i
$362$	11.0963			0.583207
$363$	0.0152379	+	12.4229i	0.000799781	+	0.652034i
$364$	−1.23093			−0.0645184
$365$	−12.0773	+	8.77467i	−0.632154	+	0.459287i
$366$	−2.71558	−	8.35769i	−0.141946	−	0.436864i
$367$	−2.06048	+	6.34150i	−0.107556	+	0.331024i	−0.990322	−	0.138790i	$-0.955679\pi$
$367$	−2.06048	+	6.34150i	−0.107556	+	0.331024i	0.882766	+	0.469813i	$0.155679\pi$
$368$	0.809017	+	0.587785i	0.0421729	+	0.0306404i
$369$	13.9533	+	10.1377i	0.726381	+	0.527747i
$370$	−2.62412	+	8.07620i	−0.136421	+	0.419862i
$371$	−5.17600	−	15.9301i	−0.268724	−	0.827048i
$372$	−8.49598	+	6.17269i	−0.440496	+	0.320039i
$373$	−1.72565			−0.0893508			−0.0446754	−	0.999002i	$-0.514225\pi$
$373$	−1.72565			−0.0893508			−0.0446754	+	0.999002i	$0.514225\pi$
$374$	1.23891	−	7.85335i	0.0640626	−	0.406087i
$375$	−3.31368			−0.171118
$376$	−2.06340	+	1.49915i	−0.106412	+	0.0773127i
$377$	0.627415	+	1.93099i	0.0323135	+	0.0994508i
$378$	2.32694	−	7.16159i	0.119685	−	0.368352i
$379$	−8.95379	−	6.50531i	−0.459925	−	0.334155i	0.333577	−	0.942723i	$-0.391744\pi$
$379$	−8.95379	−	6.50531i	−0.459925	−	0.334155i	−0.793502	+	0.608568i	$0.791744\pi$
$380$	−1.86789	−	1.35710i	−0.0958208	−	0.0696179i
$381$	−2.66153	+	8.19136i	−0.136355	+	0.419656i
$382$	−1.46123	−	4.49722i	−0.0747633	−	0.230098i
$383$	−12.2053	+	8.86770i	−0.623664	+	0.453118i	−0.854199	−	0.519946i	$-0.825952\pi$
$383$	−12.2053	+	8.86770i	−0.623664	+	0.453118i	0.230536	+	0.973064i	$0.425952\pi$
$384$	−1.12936			−0.0576323
$385$	6.39083	+	12.5237i	0.325707	+	0.638267i
$386$	8.78087			0.446935
$387$	8.55515	−	6.21568i	0.434883	−	0.315961i
$388$	−1.11004	−	3.41636i	−0.0563539	−	0.173440i
$389$	0.883432	−	2.71892i	0.0447918	−	0.137855i	−0.926160	−	0.377132i	$-0.876910\pi$
$389$	0.883432	−	2.71892i	0.0447918	−	0.137855i	0.970951	+	0.239277i	$0.0769104\pi$
$390$	2.39383	+	1.73922i	0.121216	+	0.0880687i
$391$	−1.93934	−	1.40901i	−0.0980767	−	0.0712569i
$392$	−1.54765	+	4.76319i	−0.0781683	+	0.240577i
$393$	3.81889	+	11.7533i	0.192638	+	0.592878i
$394$	−0.166095	+	0.120675i	−0.00836776	+	0.00607954i
$395$	−37.7699			−1.90041
$396$	5.64872	−	0.898222i	0.283859	−	0.0451373i
$397$	−15.7519			−0.790563			−0.395281	−	0.918560i	$-0.629353\pi$
$397$	−15.7519			−0.790563			−0.395281	+	0.918560i	$0.629353\pi$
$398$	−13.1983	+	9.58913i	−0.661571	+	0.480660i
$399$	0.378563	+	1.16510i	0.0189518	+	0.0583278i
$400$	1.24324	−	3.82631i	0.0621621	−	0.191315i
$401$	−28.6408	−	20.8088i	−1.43025	−	1.03914i	−0.989969	−	0.141283i	$-0.954877\pi$
$401$	−28.6408	−	20.8088i	−1.43025	−	1.03914i	−0.440285	−	0.897858i	$-0.645123\pi$
$402$	−12.2928	−	8.93121i	−0.613107	−	0.445448i
$403$	2.50628	−	7.71355i	0.124847	−	0.384239i
$404$	5.81409	+	17.8939i	0.289262	+	0.890256i
$405$	−2.07115	+	1.50478i	−0.102916	+	0.0747731i
$406$	−3.28519			−0.163041
$407$	8.35666	+	4.25148i	0.414224	+	0.210738i
$408$	2.70725			0.134029
$409$	14.4812	−	10.5212i	0.716048	−	0.520239i	−0.169071	−	0.985604i	$-0.554077\pi$
$409$	14.4812	−	10.5212i	0.716048	−	0.520239i	0.885119	+	0.465365i	$0.154077\pi$
$410$	−9.28339	−	28.5713i	−0.458474	−	1.41104i
$411$	−7.22681	+	22.2418i	−0.356472	+	1.09711i
$412$	5.47516	+	3.97794i	0.269742	+	0.195979i
$413$	−6.78725	−	4.93122i	−0.333979	−	0.242650i
$414$	0.532916	−	1.64015i	0.0261914	−	0.0806088i
$415$	−11.0242	−	33.9290i	−0.541157	−	1.66551i
$416$	0.705636	−	0.512675i	0.0345967	−	0.0251359i
$417$	3.93402			0.192650
$418$	−1.80147	+	1.80369i	−0.0881130	+	0.0882212i
$419$	−32.7237			−1.59866			−0.799329	−	0.600893i	$-0.794812\pi$
$419$	−32.7237			−1.59866			−0.799329	+	0.600893i	$0.794812\pi$
$420$	−3.87329	+	2.81411i	−0.188997	+	0.137315i
$421$	3.94668	+	12.1466i	0.192349	+	0.591991i	0.999997	+	0.00232562i	$0.000740269\pi$
$421$	3.94668	+	12.1466i	0.192349	+	0.591991i	−0.807648	+	0.589665i	$0.799260\pi$
$422$	0.671298	−	2.06604i	0.0326783	−	0.100573i
$423$	3.55844	+	2.58536i	0.173017	+	0.125704i
$424$	9.60192	+	6.97621i	0.466311	+	0.338795i
$425$	−2.98025	+	9.17226i	−0.144563	+	0.444920i
$426$	0.105357	+	0.324255i	0.00510456	+	0.0157102i
$427$	−8.88418	+	6.45473i	−0.429935	+	0.312366i
$428$	−16.5629			−0.800596
$429$	2.30871	−	2.31154i	0.111466	−	0.111602i
$430$	−18.4194			−0.888260
$431$	21.0798	−	15.3154i	1.01538	−	0.737715i	0.0500469	−	0.998747i	$-0.484063\pi$
$431$	21.0798	−	15.3154i	1.01538	−	0.737715i	0.965330	+	0.261032i	$0.0840629\pi$
$432$	1.64882	+	5.07456i	0.0793291	+	0.244150i
$433$	0.632113	−	1.94544i	0.0303774	−	0.0934920i	−0.934718	−	0.355389i	$-0.884348\pi$
$433$	0.632113	−	1.94544i	0.0303774	−	0.0934920i	0.965096	+	0.261897i	$0.0843482\pi$
$434$	10.6168	+	7.71355i	0.509622	+	0.370262i
$435$	6.38880	+	4.64173i	0.306319	+	0.222554i
$436$	−0.0661540	+	0.203601i	−0.00316820	+	0.00975072i
$437$	0.237518	+	0.731004i	0.0113620	+	0.0349687i
$438$	−4.54067	+	3.29899i	−0.216962	+	0.157632i
$439$	20.0406			0.956485			0.478243	−	0.878228i	$-0.341274\pi$
$439$	20.0406			0.956485			0.478243	+	0.878228i	$0.341274\pi$
$440$	−8.87960	−	4.51753i	−0.423318	−	0.215365i
$441$	8.63709			0.411290
$442$	−1.69152	+	1.22896i	−0.0804575	+	0.0584558i
$443$	8.80211	+	27.0901i	0.418201	+	1.28709i	0.909357	+	0.416018i	$0.136575\pi$
$443$	8.80211	+	27.0901i	0.418201	+	1.28709i	−0.491156	+	0.871072i	$0.663425\pi$
$444$	−0.986583	+	3.03639i	−0.0468212	+	0.144101i
$445$	17.7027	+	12.8618i	0.839188	+	0.609706i
$446$	−3.54696	−	2.57701i	−0.167953	−	0.122025i
$447$	−0.0817159	+	0.251496i	−0.00386503	+	0.0118953i
$448$	0.436107	+	1.34220i	0.0206041	+	0.0634130i
$449$	14.2179	−	10.3299i	0.670984	−	0.487498i	−0.199370	−	0.979924i	$-0.563890\pi$
$449$	14.2179	−	10.3299i	0.670984	−	0.487498i	0.870354	+	0.492426i	$0.163890\pi$
$450$	−6.93825			−0.327072
$451$	−32.7580	+	5.20896i	−1.54252	+	0.245280i
$452$	7.36312			0.346332
$453$	2.13336	−	1.54998i	0.100234	−	0.0728243i
$454$	8.57530	+	26.3921i	0.402459	+	1.23864i
$455$	1.14261	−	3.51658i	0.0535663	−	0.164860i
$456$	−0.702267	−	0.510227i	−0.0328867	−	0.0238936i
$457$	−17.3242	−	12.5868i	−0.810391	−	0.588784i	0.103553	−	0.994624i	$-0.466979\pi$
$457$	−17.3242	−	12.5868i	−0.810391	−	0.588784i	−0.913944	+	0.405840i	$0.866979\pi$
$458$	6.76773	−	20.8289i	0.316235	−	0.973272i
$459$	−3.95249	−	12.1645i	−0.184486	−	0.567791i
$460$	−2.43018	+	1.76563i	−0.113308	+	0.0823229i
$461$	17.8109			0.829538			0.414769	−	0.909927i	$-0.363862\pi$
$461$	17.8109			0.829538			0.414769	+	0.909927i	$0.363862\pi$
$462$	2.40274	+	4.70851i	0.111786	+	0.219060i
$463$	10.6864			0.496639			0.248320	−	0.968678i	$-0.420122\pi$
$463$	10.6864			0.496639			0.248320	+	0.968678i	$0.420122\pi$
$464$	1.88325	−	1.36826i	0.0874275	−	0.0635198i
$465$	−9.74808	−	30.0015i	−0.452056	−	1.39129i
$466$	3.83965	−	11.8172i	0.177868	−	0.547422i
$467$	−18.0177	−	13.0906i	−0.833759	−	0.605761i	0.0868614	−	0.996220i	$-0.472316\pi$
$467$	−18.0177	−	13.0906i	−0.833759	−	0.605761i	−0.920620	+	0.390459i	$0.872316\pi$
$468$	−1.21691	−	0.884134i	−0.0562515	−	0.0408691i
$469$	−5.86751	+	18.0583i	−0.270936	+	0.833856i
$470$	−2.36749	−	7.28640i	−0.109204	−	0.336096i
$471$	1.70777	−	1.24077i	0.0786898	−	0.0571715i
$472$	5.94463			0.273624
$473$	−3.16911	+	20.0887i	−0.145716	+	0.923680i
$474$	−14.2003			−0.652240
$475$	2.50175	−	1.81763i	0.114788	−	0.0833986i
$476$	−1.04542	−	3.21746i	−0.0479166	−	0.147472i
$477$	6.32498	−	19.4663i	0.289601	−	0.891300i
$478$	−4.44481	−	3.22935i	−0.203301	−	0.147707i
$479$	−15.5731	−	11.3145i	−0.711555	−	0.516975i	0.172120	−	0.985076i	$-0.444938\pi$
$479$	−15.5731	−	11.3145i	−0.711555	−	0.516975i	−0.883675	+	0.468101i	$0.844938\pi$
$480$	1.04832	−	3.22640i	0.0478491	−	0.147264i
$481$	−0.761948	−	2.34504i	−0.0347419	−	0.106924i
$482$	8.13777	−	5.91243i	0.370665	−	0.269304i
$483$	1.59383			0.0725218
$484$	−6.45472	+	8.90711i	−0.293396	+	0.404869i
$485$	10.7904			0.489968
$486$	12.1713	−	8.84300i	0.552104	−	0.401127i
$487$	−7.14423	−	21.9877i	−0.323736	−	0.996357i	−0.972008	−	0.234948i	$-0.924508\pi$
$487$	−7.14423	−	21.9877i	−0.323736	−	0.996357i	0.648272	−	0.761409i	$-0.275492\pi$
$488$	2.40453	−	7.40040i	0.108848	−	0.335000i
$489$	0.188027	+	0.136610i	0.00850288	+	0.00617770i
$490$	−12.1711	−	8.84282i	−0.549834	−	0.399478i
$491$	−6.23241	+	19.1814i	−0.281265	+	0.865643i	0.706229	+	0.707984i	$0.250395\pi$
$491$	−6.23241	+	19.1814i	−0.281265	+	0.865643i	−0.987493	+	0.157660i	$0.949605\pi$
$492$	−3.49026	−	10.7419i	−0.157353	−	0.484283i
$493$	−4.51444	+	3.27993i	−0.203320	+	0.147721i
$494$	0.670404			0.0301629
$495$	−2.67732	+	16.9713i	−0.120337	+	0.762804i
$496$	−9.29875			−0.417526
$497$	0.344681	−	0.250426i	0.0154611	−	0.0112331i
$498$	−4.14474	−	12.7562i	−0.185730	−	0.571619i
$499$	10.2945	−	31.6834i	0.460847	−	1.41834i	−0.403284	−	0.915075i	$-0.632131\pi$
$499$	10.2945	−	31.6834i	0.460847	−	1.41834i	0.864131	−	0.503267i	$-0.167869\pi$
$500$	−2.37376	−	1.72464i	−0.106158	−	0.0771282i
$501$	4.04523	+	2.93903i	0.180728	+	0.131306i
$502$	−0.559496	+	1.72195i	−0.0249715	+	0.0768545i
$503$	10.5846	+	32.5759i	0.471942	+	1.45249i	0.850037	+	0.526722i	$0.176579\pi$
$503$	10.5846	+	32.5759i	0.471942	+	1.45249i	−0.378095	+	0.925767i	$0.623421\pi$
$504$	1.96900	−	1.43056i	0.0877061	−	0.0637222i
$505$	−56.5171			−2.51498
$506$	1.50753	+	2.95421i	0.0670178	+	0.131331i
$507$	13.8225			0.613878
$508$	−6.16987	+	4.48267i	−0.273744	+	0.198886i
$509$	3.96884	+	12.2148i	0.175916	+	0.541413i	0.999674	−	0.0255283i	$-0.00812679\pi$
$509$	3.96884	+	12.2148i	0.175916	+	0.541413i	−0.823758	+	0.566941i	$0.808127\pi$
$510$	−2.51299	+	7.73419i	−0.111277	+	0.342476i
$511$	5.67414	+	4.12250i	0.251009	+	0.182369i
$512$	−0.809017	−	0.587785i	−0.0357538	−	0.0259767i
$513$	−1.26732	+	3.90042i	−0.0559537	+	0.172208i
$514$	4.34144	+	13.3616i	0.191493	+	0.589354i
$515$	−16.4467	+	11.9492i	−0.724727	+	0.526545i
$516$	−6.92509			−0.304860
$517$	−8.35410	+	1.32841i	−0.367413	+	0.0584235i
$518$	3.98961			0.175294
$519$	10.5764	−	7.68421i	0.464253	−	0.337299i
$520$	0.809629	+	2.49178i	0.0355046	+	0.109272i
$521$	−12.2612	+	37.7360i	−0.537171	+	1.65324i	0.201739	+	0.979439i	$0.435341\pi$
$521$	−12.2612	+	37.7360i	−0.537171	+	1.65324i	−0.738911	+	0.673803i	$0.764659\pi$
$522$	−3.24776	−	2.35963i	−0.142150	−	0.103278i
$523$	11.4201	+	8.29716i	0.499364	+	0.362809i	0.808774	−	0.588119i	$-0.200132\pi$
$523$	11.4201	+	8.29716i	0.499364	+	0.362809i	−0.309410	+	0.950929i	$0.600132\pi$
$524$	−3.38148	+	10.4071i	−0.147720	+	0.454637i
$525$	−1.98152	−	6.09848i	−0.0864805	−	0.266160i
$526$	−2.93724	+	2.13403i	−0.128070	+	0.0930482i
$527$	22.2906			0.970992
$528$	−3.33844	−	1.69844i	−0.145287	−	0.0739153i
$529$	1.00000			0.0434783
$530$	−28.8429	+	20.9556i	−1.25286	+	0.910253i
$531$	−3.16799	−	9.75007i	−0.137479	−	0.423117i
$532$	−0.335202	+	1.03165i	−0.0145328	+	0.0447275i
$533$	7.05707	+	5.12726i	0.305676	+	0.222086i
$534$	6.65564	+	4.83561i	0.288018	+	0.209257i
$535$	15.3744	−	47.3176i	0.664694	−	2.04572i
$536$	−4.15760	−	12.7958i	−0.179581	−	0.552694i
$537$	22.0706	−	16.0352i	0.952417	−	0.691971i
$538$	12.3861			0.534001
$539$	−11.7383	+	11.7527i	−0.505605	+	0.506226i
$540$	−16.0278			−0.689725
$541$	36.8141	−	26.7470i	1.58276	−	1.14994i	0.669316	−	0.742978i	$-0.266587\pi$
$541$	36.8141	−	26.7470i	1.58276	−	1.14994i	0.913444	−	0.406964i	$-0.133413\pi$
$542$	−2.63957	−	8.12375i	−0.113379	−	0.348945i
$543$	−3.87249	+	11.9183i	−0.166185	+	0.511464i
$544$	1.93934	+	1.40901i	0.0831486	+	0.0604110i
$545$	−0.520250	−	0.377984i	−0.0222851	−	0.0161910i
$546$	0.429584	−	1.32212i	0.0183845	−	0.0565816i
$547$	11.0719	+	34.0757i	0.473399	+	1.45697i	0.848105	+	0.529829i	$0.177744\pi$
$547$	11.0719	+	34.0757i	0.473399	+	1.45697i	−0.374705	+	0.927144i	$0.622256\pi$
$548$	−16.7529	+	12.1717i	−0.715650	+	0.519950i
$549$	−13.4192			−0.572715
$550$	9.42949	−	9.44106i	0.402075	−	0.402568i
$551$	1.78922			0.0762232
$552$	−0.913669	+	0.663820i	−0.0388883	+	0.0282540i
$553$	5.48351	+	16.8765i	0.233182	+	0.717662i
$554$	2.60768	−	8.02562i	0.110790	−	0.340976i
$555$	−7.75871	−	5.63703i	−0.329339	−	0.239279i
$556$	2.81814	+	2.04750i	0.119516	+	0.0868334i
$557$	−3.65806	+	11.2583i	−0.154997	+	0.477031i	−0.998161	−	0.0606257i	$-0.980690\pi$
$557$	−3.65806	+	11.2583i	−0.154997	+	0.477031i	0.843164	+	0.537657i	$0.180690\pi$
$558$	4.95545	+	15.2513i	0.209781	+	0.645640i
$559$	4.32688	−	3.14366i	0.183007	−	0.132963i
$560$	−4.23927			−0.179142
$561$	8.00278	+	4.07144i	0.337877	+	0.171896i
$562$	−23.3863			−0.986492
$563$	20.1974	−	14.6742i	0.851217	−	0.618445i	−0.0742644	−	0.997239i	$-0.523661\pi$
$563$	20.1974	−	14.6742i	0.851217	−	0.618445i	0.925481	+	0.378793i	$0.123661\pi$
$564$	−0.890102	−	2.73945i	−0.0374800	−	0.115352i
$565$	−6.83478	+	21.0353i	−0.287541	+	0.884962i
$566$	9.10677	+	6.61646i	0.382786	+	0.278110i
$567$	0.973066	+	0.706974i	0.0408649	+	0.0296901i
$568$	−0.0932893	+	0.287115i	−0.00391433	+	0.0120471i
$569$	−4.86692	−	14.9788i	−0.204032	−	0.627945i	−0.999752	−	0.0222807i	$-0.992907\pi$
$569$	−4.86692	−	14.9788i	−0.204032	−	0.627945i	0.795720	−	0.605665i	$-0.207093\pi$
$570$	2.10952	−	1.53265i	0.0883579	−	0.0641958i
$571$	8.20461			0.343352			0.171676	−	0.985153i	$-0.445082\pi$
$571$	8.20461			0.343352			0.171676	+	0.985153i	$0.445082\pi$
$572$	2.85691	−	0.454287i	0.119454	−	0.0189947i
$573$	5.34034			0.223096
$574$	−11.4186	+	8.29609i	−0.476602	+	0.346272i
$575$	−1.24324	−	3.82631i	−0.0518468	−	0.159568i
$576$	−0.532916	+	1.64015i	−0.0222048	+	0.0683394i
$577$	−15.4685	−	11.2385i	−0.643963	−	0.467867i	0.217246	−	0.976117i	$-0.430293\pi$
$577$	−15.4685	−	11.2385i	−0.643963	−	0.467867i	−0.861210	+	0.508250i	$0.830293\pi$
$578$	9.10438	+	6.61472i	0.378692	+	0.275136i
$579$	−3.06444	+	9.43138i	−0.127354	+	0.391955i
$580$	2.16079	+	6.65023i	0.0897219	+	0.276136i
$581$	−13.5598	+	9.85175i	−0.562554	+	0.408720i
$582$	4.05685			0.168162
$583$	17.8923	+	35.0624i	0.741023	+	1.45214i
$584$	−4.96971			−0.205648
$585$	3.65543	−	2.65582i	0.151133	−	0.109805i
$586$	5.51320	+	16.9679i	0.227748	+	0.700937i
$587$	−0.131011	+	0.403211i	−0.00540740	+	0.0166423i	−0.953724	−	0.300684i	$-0.902785\pi$
$587$	−0.131011	+	0.403211i	−0.00540740	+	0.0166423i	0.948316	+	0.317326i	$0.102785\pi$
$588$	−4.57594	−	3.32461i	−0.188709	−	0.137105i
$589$	−5.78223	−	4.20104i	−0.238253	−	0.173101i
$590$	−5.51808	+	16.9829i	−0.227176	+	0.699175i
$591$	−0.0716496	−	0.220515i	−0.00294727	−	0.00907076i
$592$	−2.28706	+	1.66165i	−0.0939976	+	0.0682932i
$593$	−24.2623			−0.996334			−0.498167	−	0.867081i	$-0.665993\pi$
$593$	−24.2623			−0.996334			−0.498167	+	0.867081i	$0.665993\pi$
$594$	−2.75763	+	17.4804i	−0.113147	+	0.717228i
$595$	10.1622			0.416610
$596$	−0.189431	+	0.137630i	−0.00775939	+	0.00563753i
$597$	−5.69343	−	17.5226i	−0.233017	−	0.717152i
$598$	0.269529	−	0.829525i	0.0110219	−	0.0339218i
$599$	26.4281	+	19.2012i	1.07982	+	0.784538i	0.977652	−	0.210228i	$-0.0674208\pi$
$599$	26.4281	+	19.2012i	1.07982	+	0.784538i	0.102172	+	0.994767i	$0.467421\pi$
$600$	3.67589	+	2.67069i	0.150068	+	0.109030i
$601$	−5.73676	+	17.6559i	−0.234007	+	0.720200i	0.763244	+	0.646110i	$0.223605\pi$
$601$	−5.73676	+	17.6559i	−0.234007	+	0.720200i	−0.997252	+	0.0740902i	$0.976395\pi$
$602$	2.67416	+	8.23021i	0.108991	+	0.335438i
$603$	−18.7713	+	13.6382i	−0.764427	+	0.555388i
$604$	2.33494			0.0950073
$605$	−19.4547	−	26.7081i	−0.790946	−	1.08584i
$606$	−21.2486			−0.863166
$607$	34.6864	−	25.2012i	1.40788	−	1.02288i	0.414252	−	0.910162i	$-0.364043\pi$
$607$	34.6864	−	25.2012i	1.40788	−	1.02288i	0.993627	−	0.112722i	$-0.0359568\pi$
$608$	−0.237518	−	0.731004i	−0.00963261	−	0.0296461i
$609$	1.14650	−	3.52856i	0.0464585	−	0.142985i
$610$	18.9098	+	13.7388i	0.765636	+	0.556267i
$611$	1.79973	+	1.30758i	0.0728092	+	0.0528990i
$612$	1.27748	−	3.93169i	0.0516392	−	0.158929i
$613$	−5.78813	−	17.8140i	−0.233780	−	0.719502i	−0.997281	−	0.0736945i	$-0.976521\pi$
$613$	−5.78813	−	17.8140i	−0.233780	−	0.719502i	0.763501	−	0.645807i	$-0.223479\pi$
$614$	−15.9692	+	11.6023i	−0.644465	+	0.468231i
$615$	33.9278			1.36810
$616$	−0.729381	+	4.62348i	−0.0293876	+	0.186285i
$617$	−4.45081			−0.179183			−0.0895914	−	0.995979i	$-0.528556\pi$
$617$	−4.45081			−0.179183			−0.0895914	+	0.995979i	$0.528556\pi$
$618$	−6.18342	+	4.49251i	−0.248733	+	0.180715i
$619$	2.95779	+	9.10313i	0.118884	+	0.365886i	0.992737	−	0.120303i	$-0.0383867\pi$
$619$	2.95779	+	9.10313i	0.118884	+	0.365886i	−0.873854	+	0.486189i	$0.838387\pi$
$620$	8.63153	−	26.5651i	0.346650	−	1.06688i
$621$	4.31668	+	3.13625i	0.173222	+	0.125853i
$622$	−7.89441	−	5.73563i	−0.316537	−	0.229978i
$623$	3.17683	−	9.77728i	0.127277	−	0.391719i
$624$	0.304395	+	0.936830i	0.0121855	+	0.0375032i
$625$	23.4047	−	17.0045i	0.936188	−	0.680181i
$626$	−3.83346			−0.153216
$627$	−1.30861	−	2.56440i	−0.0522608	−	0.102412i
$628$	1.86913			0.0745864
$629$	5.48244	−	3.98323i	0.218599	−	0.158822i
$630$	2.25918	+	6.95303i	0.0900078	+	0.277015i
$631$	0.199052	−	0.612620i	0.00792415	−	0.0243880i	−0.947016	−	0.321186i	$-0.895919\pi$
$631$	0.199052	−	0.612620i	0.00792415	−	0.0243880i	0.954940	+	0.296798i	$0.0959187\pi$
$632$	−10.1724	−	7.39067i	−0.404636	−	0.293985i
$633$	1.98482	+	1.44206i	0.0788896	+	0.0573167i
$634$	1.34336	−	4.13443i	0.0533515	−	0.164199i
$635$	−7.07915	−	21.7874i	−0.280928	−	0.864606i
$636$	−10.8440	+	7.87863i	−0.429993	+	0.312408i
$637$	4.36832			0.173079
$638$	7.62471	−	1.21243i	0.301865	−	0.0480006i
$639$	0.520626			0.0205956
$640$	2.43018	−	1.76563i	0.0960613	−	0.0697926i
$641$	7.19878	+	22.1556i	0.284335	+	0.875092i	0.986597	+	0.163174i	$0.0521732\pi$
$641$	7.19878	+	22.1556i	0.284335	+	0.875092i	−0.702263	+	0.711918i	$0.747827\pi$
$642$	5.78028	−	17.7899i	0.228130	−	0.702111i
$643$	−9.51391	−	6.91226i	−0.375192	−	0.272593i	0.384169	−	0.923263i	$-0.374488\pi$
$643$	−9.51391	−	6.91226i	−0.375192	−	0.272593i	−0.759361	+	0.650670i	$0.774488\pi$
$644$	1.14174	+	0.829525i	0.0449910	+	0.0326879i
$645$	6.42818	−	19.7839i	0.253109	−	0.778991i
$646$	0.569367	+	1.75233i	0.0224014	+	0.0689445i
$647$	−30.1832	+	21.9294i	−1.18662	+	0.862132i	−0.992903	−	0.118925i	$-0.962055\pi$
$647$	−30.1832	+	21.9294i	−1.18662	+	0.862132i	−0.193720	+	0.981057i	$0.562055\pi$
$648$	−0.852263			−0.0334801
$649$	17.5727	+	8.94015i	0.689788	+	0.350932i
$650$	−3.50911			−0.137638
$651$	−11.9901	+	8.71135i	−0.469931	+	0.341425i
$652$	0.0635937	+	0.195721i	0.00249052	+	0.00766503i
$653$	9.94077	−	30.5946i	0.389013	−	1.19726i	−0.544515	−	0.838751i	$-0.683286\pi$
$653$	9.94077	−	30.5946i	0.389013	−	1.19726i	0.933527	−	0.358506i	$-0.116714\pi$
$654$	−0.195597	−	0.142110i	−0.00764846	−	0.00555693i
$655$	−26.5927	−	19.3207i	−1.03906	−	0.754923i
$656$	3.09048	−	9.51152i	0.120663	−	0.371363i
$657$	2.64844	+	8.15106i	0.103325	+	0.318003i
$658$	−2.91202	+	2.11571i	−0.113522	+	0.0824788i
$659$	−1.34581			−0.0524251			−0.0262126	−	0.999656i	$-0.508345\pi$
$659$	−1.34581			−0.0524251			−0.0262126	+	0.999656i	$0.508345\pi$
$660$	7.95109	−	7.96085i	0.309496	−	0.309876i
$661$	43.9478			1.70937			0.854685	−	0.519147i	$-0.173750\pi$
$661$	43.9478			1.70937			0.854685	+	0.519147i	$0.173750\pi$
$662$	24.2866	−	17.6452i	0.943924	−	0.685801i
$663$	−0.729682	−	2.24573i	−0.0283385	−	0.0872169i
$664$	3.67000	−	11.2951i	0.142424	−	0.438335i
$665$	−2.63610	−	1.91524i	−0.102224	−	0.0742699i
$666$	3.94415	+	2.86560i	0.152833	+	0.111040i
$667$	0.719336	−	2.21389i	0.0278528	−	0.0857221i
$668$	1.36816	+	4.21076i	0.0529357	+	0.162919i
$669$	4.00578	−	2.91037i	0.154872	−	0.112521i
$670$	40.4149			1.56136
$671$	18.2374	−	18.2598i	0.704048	−	0.704912i
$672$	−1.59383			−0.0614834
$673$	38.1853	−	27.7432i	1.47193	−	1.06942i	0.491887	−	0.870659i	$-0.336307\pi$
$673$	38.1853	−	27.7432i	1.47193	−	1.06942i	0.980047	−	0.198764i	$-0.0636927\pi$
$674$	9.63992	+	29.6686i	0.371316	+	1.14279i
$675$	6.63358	−	20.4160i	0.255326	−	0.785814i
$676$	9.90175	+	7.19405i	0.380837	+	0.276694i
$677$	−34.4754	−	25.0478i	−1.32500	−	0.962666i	−0.999855	−	0.0170010i	$-0.994588\pi$
$677$	−34.4754	−	25.0478i	−1.32500	−	0.962666i	−0.325141	−	0.945665i	$-0.605412\pi$
$678$	−2.56966	+	7.90860i	−0.0986871	+	0.303728i
$679$	−1.56657	−	4.82142i	−0.0601196	−	0.185029i
$680$	−5.82552	+	4.23249i	−0.223399	+	0.162309i
$681$	−31.3400			−1.20095
$682$	−27.4876	−	13.9844i	−1.05256	−	0.535491i
$683$	−33.8626			−1.29571			−0.647857	−	0.761762i	$-0.724335\pi$
$683$	−33.8626			−1.29571			−0.647857	+	0.761762i	$0.724335\pi$
$684$	−1.07238	+	0.779127i	−0.0410033	+	0.0297907i
$685$	−19.2219	−	59.1589i	−0.734431	−	2.26034i
$686$	−5.23691	+	16.1176i	−0.199946	+	0.615371i
$687$	20.0101	+	14.5382i	0.763434	+	0.554667i
$688$	−4.96080	−	3.60423i	−0.189129	−	0.137410i
$689$	3.19894	−	9.84533i	0.121870	−	0.375077i
$690$	−1.04832	−	3.22640i	−0.0399089	−	0.122827i
$691$	−2.92103	+	2.12226i	−0.111121	+	0.0807344i	−0.641958	−	0.766740i	$-0.721878\pi$
$691$	−2.92103	+	2.12226i	−0.111121	+	0.0807344i	0.530837	+	0.847474i	$0.321878\pi$
$692$	11.5757			0.440044
$693$	7.97189	−	1.26764i	0.302827	−	0.0481535i
$694$	−12.6424			−0.479899
$695$	−8.46532	+	6.15042i	−0.321108	+	0.233299i
$696$	0.812387	+	2.50027i	0.0307935	+	0.0947725i
$697$	−7.40837	+	22.8006i	−0.280612	+	0.863635i
$698$	3.35413	+	2.43692i	0.126956	+	0.0922388i
$699$	11.3527	+	8.24819i	0.429397	+	0.311975i
$700$	1.75455	−	5.39996i	0.0663159	−	0.204099i
$701$	2.32272	+	7.14859i	0.0877279	+	0.269999i	0.985290	−	0.170889i	$-0.0546639\pi$
$701$	2.32272	+	7.14859i	0.0877279	+	0.269999i	−0.897562	+	0.440887i	$0.854664\pi$
$702$	3.76507	−	2.73548i	0.142103	−	0.103244i
$703$	−2.17287			−0.0819513
$704$	−1.50753	−	2.95421i	−0.0568171	−	0.111341i
$705$	8.65243			0.325869
$706$	8.86336	−	6.43961i	0.333577	−	0.242358i
$707$	8.20527	+	25.2532i	0.308591	+	0.949745i
$708$	−2.07462	+	6.38503i	−0.0779690	+	0.239964i
$709$	18.6950	+	13.5827i	0.702107	+	0.510111i	0.880618	−	0.473827i	$-0.157128\pi$
$709$	18.6950	+	13.5827i	0.702107	+	0.510111i	−0.178511	+	0.983938i	$0.557128\pi$
$710$	−0.733648	−	0.533026i	−0.0275333	−	0.0200041i
$711$	−6.70076	+	20.6228i	−0.251298	+	0.773416i
$712$	2.25104	+	6.92799i	0.0843613	+	0.259637i
$713$	−7.52285	+	5.46567i	−0.281733	+	0.204691i
$714$	3.82066			0.142985
$715$	−1.35409	+	8.58346i	−0.0506401	+	0.321003i
$716$	24.1560			0.902753
$717$	5.01978	−	3.64709i	0.187467	−	0.136203i
$718$	−6.29437	−	19.3721i	−0.234904	−	0.722959i
$719$	−1.16462	+	3.58434i	−0.0434331	+	0.133673i	−0.970422	−	0.241416i	$-0.922388\pi$
$719$	−1.16462	+	3.58434i	−0.0434331	+	0.133673i	0.926989	+	0.375090i	$0.122388\pi$
$720$	−4.19097	−	3.04492i	−0.156188	−	0.113477i
$721$	7.72695	+	5.61396i	0.287767	+	0.209075i
$722$	−5.68876	+	17.5082i	−0.211714	+	0.651588i
$723$	3.51044	+	10.8040i	0.130555	+	0.401806i
$724$	−8.97707	+	6.52222i	−0.333630	+	0.242397i
$725$	−9.36532			−0.347819
$726$	−7.31434	−	10.0414i	−0.271461	−	0.372671i
$727$	0.902406			0.0334684			0.0167342	−	0.999860i	$-0.494673\pi$
$727$	0.902406			0.0334684			0.0167342	+	0.999860i	$0.494673\pi$
$728$	0.995845	−	0.723524i	0.0369085	−	0.0268156i
$729$	6.04052	+	18.5908i	0.223723	+	0.688548i
$730$	4.61312	−	14.1977i	0.170739	−	0.525481i
$731$	11.8918	+	8.63991i	0.439834	+	0.319558i
$732$	7.10948	+	5.16534i	0.262774	+	0.190916i
$733$	−11.5170	+	35.4457i	−0.425390	+	1.30922i	0.477231	+	0.878778i	$0.341641\pi$
$733$	−11.5170	+	35.4457i	−0.425390	+	1.30922i	−0.902621	+	0.430437i	$0.858359\pi$
$734$	−2.06048	−	6.34150i	−0.0760536	−	0.234069i
$735$	13.7455	−	9.98670i	0.507011	−	0.368365i
$736$	−1.00000			−0.0368605
$737$	6.95351	−	44.0777i	0.256136	−	1.62362i
$738$	−17.2473			−0.634880
$739$	−31.1727	+	22.6483i	−1.14671	+	0.833131i	−0.988039	−	0.154202i	$-0.950719\pi$
$739$	−31.1727	+	22.6483i	−1.14671	+	0.833131i	−0.158666	+	0.987332i	$0.550719\pi$
$740$	−2.62412	−	8.07620i	−0.0964644	−	0.296887i
$741$	−0.233965	+	0.720069i	−0.00859491	+	0.0264524i
$742$	13.5509	+	9.84533i	0.497470	+	0.361433i
$743$	39.7928	+	28.9112i	1.45986	+	1.06065i	0.983400	+	0.181452i	$0.0580796\pi$
$743$	39.7928	+	28.9112i	1.45986	+	1.06065i	0.476458	+	0.879197i	$0.341920\pi$
$744$	3.24518	−	9.98762i	0.118974	−	0.366164i
$745$	−0.217348	−	0.668929i	−0.00796302	−	0.0245077i
$746$	1.39608	−	1.01431i	0.0511141	−	0.0371366i
$747$	−20.4814			−0.749376
$748$	3.61378	+	7.08171i	0.132133	+	0.258933i
$749$	−23.3747			−0.854094
$750$	2.68082	−	1.94773i	0.0978899	−	0.0711211i
$751$	3.45334	+	10.6283i	0.126014	+	0.387832i	0.994085	−	0.108609i	$-0.0346398\pi$
$751$	3.45334	+	10.6283i	0.126014	+	0.387832i	−0.868070	+	0.496441i	$0.834640\pi$
$752$	0.788149	−	2.42567i	0.0287408	−	0.0884552i
$753$	−1.65426	−	1.20189i	−0.0602846	−	0.0437993i
$754$	−1.64259	−	1.19341i	−0.0598198	−	0.0434616i
$755$	−2.16740	+	6.67056i	−0.0788797	+	0.242767i
$756$	2.32694	+	7.16159i	0.0846300	+	0.260464i
$757$	35.4824	−	25.7795i	1.28963	−	0.936971i	0.289832	−	0.957077i	$-0.406400\pi$
$757$	35.4824	−	25.7795i	1.28963	−	0.936971i	0.999798	+	0.0201061i	$0.00640042\pi$
$758$	11.0675			0.401989
$759$	−3.69918	+	0.588218i	−0.134272	+	0.0213510i
$760$	2.30884			0.0837505
$761$	41.5568	−	30.1928i	1.50643	−	1.09449i	0.538706	−	0.842494i	$-0.318913\pi$
$761$	41.5568	−	30.1928i	1.50643	−	1.09449i	0.967729	−	0.251995i	$-0.0810866\pi$
$762$	−2.66153	−	8.19136i	−0.0964172	−	0.296742i
$763$	−0.0933613	+	0.287337i	−0.00337991	+	0.0104023i
$764$	3.82556	+	2.77943i	0.138404	+	0.100556i
$765$	10.0464	+	7.29915i	0.363229	+	0.263901i
$766$	4.66202	−	14.3482i	0.168446	−	0.518423i
$767$	−1.60225	−	4.93122i	−0.0578539	−	0.178056i
$768$	0.913669	−	0.663820i	0.0329692	−	0.0239535i
$769$	−23.3690			−0.842707			−0.421353	−	0.906897i	$-0.638445\pi$
$769$	−23.3690			−0.842707			−0.421353	+	0.906897i	$0.638445\pi$
$770$	−12.5315	−	6.37546i	−0.451605	−	0.229756i
$771$	−15.8666			−0.571420
$772$	−7.10387	+	5.16127i	−0.255674	+	0.185758i
$773$	−5.26289	−	16.1975i	−0.189293	−	0.582584i	0.810703	−	0.585458i	$-0.199085\pi$
$773$	−5.26289	−	16.1975i	−0.189293	−	0.582584i	−0.999996	+	0.00287391i	$0.999085\pi$
$774$	−3.26778	+	10.0572i	−0.117458	+	0.361498i
$775$	30.2660	+	21.9896i	1.08719	+	0.789888i
$776$	2.90613	+	2.11143i	0.104324	+	0.0757959i
$777$	−1.39234	+	4.28517i	−0.0499498	+	0.153730i
$778$	0.883432	+	2.71892i	0.0316726	+	0.0974782i
$779$	6.21892	−	4.51831i	0.222816	−	0.161885i
$780$	−2.95893			−0.105947
$781$	−0.707562	+	0.708430i	−0.0253185	+	0.0253496i
$782$	2.39716			0.0857222
$783$	10.0485	−	7.30063i	0.359102	−	0.260903i
$784$	−1.54765	−	4.76319i	−0.0552733	−	0.170114i
$785$	−1.73501	+	5.33982i	−0.0619253	+	0.190586i
$786$	−9.99799	−	7.26397i	−0.356617	−	0.259097i
$787$	−30.7396	−	22.3336i	−1.09575	−	0.796108i	−0.115388	−	0.993321i	$-0.536811\pi$
$787$	−30.7396	−	22.3336i	−1.09575	−	0.796108i	−0.980361	+	0.197213i	$0.936811\pi$
$788$	0.0634428	−	0.195257i	0.00226006	−	0.00695574i
$789$	−1.26706	−	3.89960i	−0.0451084	−	0.138829i
$790$	30.5565	−	22.2006i	1.08715	−	0.789861i
$791$	10.3914			0.369474
$792$	−4.04195	+	4.04691i	−0.143625	+	0.143801i
$793$	−6.78691			−0.241010
$794$	12.7435	−	9.25871i	0.452251	−	0.328579i
$795$	−12.4421	−	38.2930i	−0.441277	−	1.35811i
$796$	5.04130	−	15.5155i	0.178684	−	0.549934i
$797$	16.4585	+	11.9578i	0.582990	+	0.423567i	0.839801	−	0.542895i	$-0.182672\pi$
$797$	16.4585	+	11.9578i	0.582990	+	0.423567i	−0.256811	+	0.966462i	$0.582672\pi$
$798$	−0.991090	−	0.720069i	−0.0350842	−	0.0254902i
$799$	−1.88932	+	5.81472i	−0.0668392	+	0.205710i
$800$	1.24324	+	3.82631i	0.0439552	+	0.135280i
$801$	10.1633	−	7.38407i	0.359103	−	0.260903i
$802$	35.4020			1.25009
$803$	−14.6908	−	7.47397i	−0.518426	−	0.263751i
$804$	15.1947			0.535875
$805$	−3.42965	+	2.49178i	−0.120879	+	0.0878238i
$806$	2.50628	+	7.71355i	0.0882801	+	0.271698i
$807$	−4.32262	+	13.3037i	−0.152163	+	0.468311i
$808$	−15.2215	−	11.0591i	−0.535490	−	0.389056i
$809$	34.0565	+	24.7435i	1.19736	+	0.869936i	0.994023	−	0.109172i	$-0.0348198\pi$
$809$	34.0565	+	24.7435i	1.19736	+	0.869936i	0.203342	+	0.979108i	$0.434820\pi$
$810$	0.791110	−	2.43478i	0.0277968	−	0.0855496i
$811$	4.25441	+	13.0937i	0.149393	+	0.459783i	0.997550	−	0.0699615i	$-0.0222876\pi$
$811$	4.25441	+	13.0937i	0.149393	+	0.459783i	−0.848157	+	0.529745i	$0.822288\pi$
$812$	2.65777	−	1.93099i	0.0932696	−	0.0677643i
$813$	9.64676			0.338327
$814$	−9.25964	+	1.47240i	−0.324550	+	0.0516077i
$815$	−0.618176			−0.0216538
$816$	−2.19021	+	1.59128i	−0.0766726	+	0.0557059i
$817$	−1.45643	−	4.48243i	−0.0509540	−	0.156820i
$818$	−5.53132	+	17.0236i	−0.193398	+	0.595218i
$819$	−1.71739	−	1.24775i	−0.0600104	−	0.0436001i
$820$	24.3042	+	17.6581i	0.848741	+	0.616646i
$821$	8.06946	−	24.8353i	0.281626	−	0.866756i	−0.705763	−	0.708448i	$-0.749396\pi$
$821$	8.06946	−	24.8353i	0.281626	−	0.866756i	0.987390	−	0.158309i	$-0.0506041\pi$
$822$	−7.22681	−	22.2418i	−0.252064	−	0.775773i
$823$	36.9759	−	26.8646i	1.28890	−	0.936440i	0.289117	−	0.957294i	$-0.406638\pi$
$823$	36.9759	−	26.8646i	1.28890	−	0.936440i	0.999783	+	0.0208535i	$0.00663836\pi$
$824$	−6.76767			−0.235763
$825$	6.84968	+	13.4229i	0.238475	+	0.467325i
$826$	8.38950			0.291908
$827$	−35.6353	+	25.8906i	−1.23916	+	0.900304i	−0.997542	−	0.0700675i	$-0.977679\pi$
$827$	−35.6353	+	25.8906i	−1.23916	+	0.900304i	−0.241619	+	0.970371i	$0.577679\pi$
$828$	0.532916	+	1.64015i	0.0185201	+	0.0569990i
$829$	4.35190	−	13.3938i	0.151148	−	0.465185i	−0.846602	−	0.532226i	$-0.821356\pi$
$829$	4.35190	−	13.3938i	0.151148	−	0.465185i	0.997750	+	0.0670406i	$0.0213557\pi$
$830$	28.8617	+	20.9693i	1.00181	+	0.727854i
$831$	7.71012	+	5.60173i	0.267461	+	0.194322i
$832$	−0.269529	+	0.829525i	−0.00934424	+	0.0287586i
$833$	3.70997	+	11.4181i	0.128543	+	0.395614i
$834$	−3.18269	+	2.31236i	−0.110208	+	0.0800705i
$835$	−13.2995			−0.460248
$836$	0.397244	−	2.51809i	0.0137390	−	0.0870901i
$837$	−49.6154			−1.71496
$838$	26.4741	−	19.2345i	0.914531	−	0.664446i
$839$	3.34094	+	10.2823i	0.115342	+	0.354986i	0.992018	−	0.126095i	$-0.0402444\pi$
$839$	3.34094	+	10.2823i	0.115342	+	0.354986i	−0.876676	+	0.481081i	$0.840244\pi$
$840$	1.47947	−	4.55333i	0.0510465	−	0.157105i
$841$	19.0776	+	13.8607i	0.657849	+	0.477956i
$842$	−10.3325	−	7.50703i	−0.356083	−	0.258709i
$843$	8.16160	−	25.1188i	0.281101	−	0.865139i
$844$	0.671298	+	2.06604i	0.0231070	+	0.0711161i
$845$	−29.7436	+	21.6100i	−1.02321	+	0.743405i
$846$	−4.39848			−0.151223
$847$	−9.10936	+	12.5704i	−0.313001	+	0.431923i
$848$	−11.8686			−0.407570
$849$	−10.2848	+	7.47234i	−0.352973	+	0.256450i
$850$	−2.98025	−	9.17226i	−0.102222	−	0.314606i
$851$	−0.873579	+	2.68860i	−0.0299459	+	0.0921640i
$852$	−0.275828	−	0.200401i	−0.00944971	−	0.00686562i
$853$	25.5500	+	18.5631i	0.874815	+	0.635590i	0.931875	−	0.362781i	$-0.118173\pi$
$853$	25.5500	+	18.5631i	0.874815	+	0.635590i	−0.0570599	+	0.998371i	$0.518173\pi$
$854$	3.39345	−	10.4440i	0.116122	−	0.357386i
$855$	−1.23042	−	3.78684i	−0.0420794	−	0.129507i
$856$	13.3996	−	9.73541i	0.457990	−	0.332749i
$857$	−44.5969			−1.52340			−0.761701	−	0.647929i	$-0.775635\pi$
$857$	−44.5969			−1.52340			−0.761701	+	0.647929i	$0.775635\pi$
$858$	−0.509094	+	3.22710i	−0.0173802	+	0.110172i
$859$	−22.3644			−0.763064			−0.381532	−	0.924356i	$-0.624603\pi$
$859$	−22.3644			−0.763064			−0.381532	+	0.924356i	$0.624603\pi$
$860$	14.9016	−	10.8266i	0.508139	−	0.369185i
$861$	−4.92570	−	15.1598i	−0.167868	−	0.516643i
$862$	−8.05176	+	24.7808i	−0.274244	+	0.844036i
$863$	45.9232	+	33.3652i	1.56325	+	1.13576i	0.933285	+	0.359136i	$0.116929\pi$
$863$	45.9232	+	33.3652i	1.56325	+	1.13576i	0.629960	+	0.776628i	$0.283071\pi$
$864$	−4.31668	−	3.13625i	−0.146856	−	0.106697i
$865$	−10.7451	+	33.0701i	−0.365346	+	1.12442i
$866$	0.632113	+	1.94544i	0.0214801	+	0.0661088i
$867$	−10.2821	+	7.47038i	−0.349198	+	0.253708i
$868$	−13.1231			−0.445426
$869$	−18.9553	−	37.1455i	−0.643014	−	1.26008i
$870$	−7.89699			−0.267733
$871$	−9.49383	+	6.89767i	−0.321686	+	0.233719i
$872$	−0.0661540	−	0.203601i	−0.00224026	−	0.00689480i
$873$	1.91433	−	5.89170i	0.0647902	−	0.199404i
$874$	−0.621829	−	0.451785i	−0.0210337	−	0.0152819i
$875$	−3.35002	−	2.43393i	−0.113251	−	0.0822820i
$876$	1.73438	−	5.33788i	0.0585994	−	0.180350i
$877$	−14.0889	−	43.3613i	−0.475749	−	1.46421i	−0.844945	−	0.534854i	$-0.820367\pi$
$877$	−14.0889	−	43.3613i	−0.475749	−	1.46421i	0.369196	−	0.929352i	$-0.379633\pi$
$878$	−16.2132	+	11.7796i	−0.547168	+	0.397541i
$879$	−20.1490			−0.679608
$880$	9.83908	−	1.56454i	0.331675	−	0.0527408i
$881$	39.8248			1.34173			0.670866	−	0.741579i	$-0.265923\pi$
$881$	39.8248			1.34173			0.670866	+	0.741579i	$0.265923\pi$
$882$	−6.98755	+	5.07676i	−0.235283	+	0.170943i
$883$	10.4878	+	32.2781i	0.352943	+	1.08625i	0.957193	+	0.289451i	$0.0934728\pi$
$883$	10.4878	+	32.2781i	0.352943	+	1.08625i	−0.604250	+	0.796795i	$0.706527\pi$
$884$	0.646104	−	1.98850i	0.0217308	−	0.0668806i
$885$	−16.3153	−	11.8537i	−0.548432	−	0.398459i
$886$	−23.0442	−	16.7426i	−0.774185	−	0.562479i
$887$	5.59307	−	17.2137i	0.187797	−	0.577979i	−0.812189	−	0.583395i	$-0.801724\pi$
$887$	5.59307	−	17.2137i	0.187797	−	0.577979i	0.999985	+	0.00541602i	$0.00172398\pi$
$888$	−0.986583	−	3.03639i	−0.0331076	−	0.101895i
$889$	−8.70737	+	6.32627i	−0.292036	+	0.212176i
$890$	−21.8817			−0.733477
$891$	−2.51934	−	1.28172i	−0.0844010	−	0.0429393i
$892$	4.38428			0.146797
$893$	1.58598	−	1.15228i	0.0530727	−	0.0385596i
$894$	−0.0817159	−	0.251496i	−0.00273299	−	0.00841128i
$895$	−22.4227	+	69.0100i	−0.749509	+	2.30675i
$896$	−1.14174	−	0.829525i	−0.0381430	−	0.0277125i
$897$	0.796915	+	0.578993i	0.0266082	+	0.0193320i
$898$	−5.43075	+	16.7141i	−0.181227	+	0.557758i
$899$	6.68893	+	20.5864i	0.223088	+	0.686595i
$900$	5.61316	−	4.07820i	0.187105	−	0.135940i
$901$	28.4510			0.947839
$902$	23.4401	−	23.4688i	0.780468	−	0.781426i
$903$	−9.77318			−0.325231
$904$	−5.95689	+	4.32793i	−0.198123	+	0.143945i
$905$	−10.3001	−	31.7003i	−0.342386	−	1.05376i
$906$	−0.814872	+	2.50792i	−0.0270723	+	0.0833200i
$907$	29.3444	+	21.3200i	0.974366	+	0.707918i	0.956442	−	0.291921i	$-0.0942945\pi$
$907$	29.3444	+	21.3200i	0.974366	+	0.707918i	0.0179234	+	0.999839i	$0.494294\pi$
$908$	−22.4504	−	16.3112i	−0.745044	−	0.541306i
$909$	−10.0267	+	30.8590i	−0.332565	+	1.02353i
$910$	1.14261	+	3.51658i	0.0378771	+	0.116574i
$911$	−11.2078	+	8.14294i	−0.371331	+	0.269788i	−0.757763	−	0.652530i	$-0.773707\pi$
$911$	−11.2078	+	8.14294i	−0.371331	+	0.269788i	0.386432	+	0.922318i	$0.373707\pi$
$912$	0.868050			0.0287440
$913$	27.8355	−	27.8697i	0.921220	−	0.922351i
$914$	21.4139			0.708308
$915$	−21.3559	+	15.5160i	−0.706005	+	0.512943i
$916$	6.76773	+	20.8289i	0.223612	+	0.688208i
$917$	−4.77218	+	14.6873i	−0.157591	+	0.485016i
$918$	10.3478	+	7.51808i	0.341527	+	0.248134i
$919$	2.68224	+	1.94876i	0.0884790	+	0.0642838i	0.631145	−	0.775665i	$-0.282585\pi$
$919$	2.68224	+	1.94876i	0.0884790	+	0.0642838i	−0.542666	+	0.839948i	$0.682585\pi$
$920$	0.928246	−	2.85685i	0.0306034	−	0.0941875i
$921$	−6.88874	−	21.2014i	−0.226992	−	0.698608i
$922$	−14.4093	+	10.4690i	−0.474547	+	0.344778i
$923$	0.263313			0.00866706
$924$	−4.71146	−	2.39697i	−0.154995	−	0.0788544i
$925$	11.3735			0.373958
$926$	−8.64548	+	6.28131i	−0.284108	+	0.206417i
$927$	3.60660	+	11.1000i	0.118456	+	0.364571i
$928$	−0.719336	+	2.21389i	−0.0236134	+	0.0726745i
$929$	−38.8077	−	28.1954i	−1.27324	−	0.925062i	−0.273912	−	0.961755i	$-0.588318\pi$
$929$	−38.8077	−	28.1954i	−1.27324	−	0.925062i	−0.999327	+	0.0366933i	$0.988318\pi$
$930$	25.5208	+	18.5419i	0.836860	+	0.608014i
$931$	1.18956	−	3.66109i	0.0389863	−	0.119988i
$932$	3.83965	+	11.8172i	0.125772	+	0.387086i
$933$	8.91561	−	6.47757i	0.291884	−	0.212066i
$934$	22.2711			0.728732
$935$	−23.5858	+	3.75046i	−0.771339	+	0.122653i
$936$	1.50418			0.0491656
$937$	−48.5808	+	35.2960i	−1.58707	+	1.15307i	−0.679086	+	0.734059i	$0.737624\pi$
$937$	−48.5808	+	35.2960i	−1.58707	+	1.15307i	−0.907981	+	0.419012i	$0.862376\pi$
$938$	−5.86751	−	18.0583i	−0.191581	−	0.589626i
$939$	1.33784	−	4.11746i	0.0436588	−	0.134368i
$940$	6.19818	+	4.50324i	0.202162	+	0.146880i
$941$	−30.3475	−	22.0488i	−0.989301	−	0.718769i	−0.0295327	−	0.999564i	$-0.509402\pi$
$941$	−30.3475	−	22.0488i	−0.989301	−	0.718769i	−0.959768	+	0.280795i	$0.909402\pi$
$942$	−0.652309	+	2.00760i	−0.0212534	+	0.0654112i
$943$	−3.09048	−	9.51152i	−0.100640	−	0.309738i
$944$	−4.80931	+	3.49417i	−0.156530	+	0.113725i
$945$	−22.6195			−0.735813
$946$	−9.24399	−	18.1149i	−0.300548	−	0.588965i
$947$	28.6387			0.930634			0.465317	−	0.885144i	$-0.345940\pi$
$947$	28.6387			0.930634			0.465317	+	0.885144i	$0.345940\pi$
$948$	11.4883	−	8.34671i	0.373121	−	0.271088i
$949$	1.33948	+	4.12250i	0.0434814	+	0.133822i
$950$	−0.955584	+	2.94099i	−0.0310032	+	0.0954182i
$951$	3.97190	+	2.88575i	0.128798	+	0.0935769i
$952$	2.73694	+	1.98850i	0.0887047	+	0.0644477i
$953$	−4.57146	+	14.0695i	−0.148084	+	0.455757i	−0.997395	−	0.0721372i	$-0.977018\pi$
$953$	−4.57146	+	14.0695i	−0.148084	+	0.455757i	0.849310	+	0.527894i	$0.177018\pi$
$954$	6.32498	+	19.4663i	0.204779	+	0.630245i
$955$	−11.4915	+	8.34905i	−0.371855	+	0.270169i
$956$	5.49409			0.177692
$957$	−1.35870	+	8.61270i	−0.0439206	+	0.278409i
$958$	19.2495			0.621922
$959$	−23.6429	+	17.1776i	−0.763470	+	0.554694i
$960$	1.04832	+	3.22640i	0.0338344	+	0.104132i
$961$	17.1402	−	52.7520i	0.552909	−	1.70168i
$962$	1.99481	+	1.44931i	0.0643151	+	0.0467277i
$963$	−23.1084	−	16.7892i	−0.744657	−	0.541025i
$964$	−3.10835	+	9.56652i	−0.100113	+	0.308117i
$965$	−8.15081	−	25.0856i	−0.262384	−	0.807534i
$966$	−1.28944	+	0.936830i	−0.0414869	+	0.0301420i
$967$	31.4447			1.01119			0.505596	−	0.862770i	$-0.331272\pi$
$967$	31.4447			1.01119			0.505596	+	0.862770i	$0.331272\pi$
$968$	−0.0134925	−	11.0000i	−0.000433666	−	0.353553i
$969$	−2.08085			−0.0668466
$970$	−8.72963	+	6.34245i	−0.280292	+	0.203644i
$971$	15.8637	+	48.8236i	0.509091	+	1.56682i	0.793782	+	0.608203i	$0.208109\pi$
$971$	15.8637	+	48.8236i	0.509091	+	1.56682i	−0.284690	+	0.958620i	$0.591891\pi$
$972$	−4.64904	+	14.3083i	−0.149118	+	0.458938i
$973$	3.97717	+	2.88958i	0.127502	+	0.0926357i
$974$	18.7038	+	13.5891i	0.599309	+	0.435424i
$975$	1.22465	−	3.76907i	0.0392200	−	0.120707i
$976$	2.40453	+	7.40040i	0.0769673	+	0.236881i
$977$	21.1206	−	15.3450i	0.675708	−	0.490931i	−0.196223	−	0.980559i	$-0.562868\pi$
$977$	21.1206	−	15.3450i	0.675708	−	0.490931i	0.871931	+	0.489629i	$0.162868\pi$
$978$	−0.232414			−0.00743179
$979$	−3.76482	+	23.8649i	−0.120324	+	0.762725i
$980$	15.0443			0.480572
$981$	−0.298681	+	0.217004i	−0.00953615	+	0.00692842i
$982$	−6.23241	−	19.1814i	−0.198884	−	0.612102i
$983$	−0.715813	+	2.20305i	−0.0228309	+	0.0702663i	−0.961823	−	0.273673i	$-0.911761\pi$
$983$	−0.715813	+	2.20305i	−0.0228309	+	0.0702663i	0.938992	+	0.343939i	$0.111761\pi$
$984$	9.13761	+	6.63886i	0.291296	+	0.211639i
$985$	0.498928	+	0.362493i	0.0158972	+	0.0115500i
$986$	1.72436	−	5.30704i	0.0549149	−	0.169011i
$987$	−1.25618	−	3.86611i	−0.0399845	−	0.123060i
$988$	−0.542368	+	0.394054i	−0.0172550	+	0.0125365i
$989$	−6.13188			−0.194983
$990$	−7.80949	−	15.3038i	−0.248202	−	0.486386i
$991$	24.4932			0.778053			0.389026	−	0.921227i	$-0.372812\pi$
$991$	24.4932			0.778053			0.389026	+	0.921227i	$0.372812\pi$
$992$	7.52285	−	5.46567i	0.238851	−	0.173535i
$993$	10.4766	+	32.2438i	0.332466	+	1.02323i
$994$	−0.131657	+	0.405197i	−0.00417589	+	0.0128521i
$995$	39.6460	+	28.8045i	1.25686	+	0.913163i
$996$	10.8511	+	7.88377i	0.343830	+	0.249807i
$997$	2.51361	−	7.73610i	0.0796069	−	0.245005i	−0.903331	−	0.428945i	$-0.858885\pi$
$997$	2.51361	−	7.73610i	0.0796069	−	0.245005i	0.982937	+	0.183940i	$0.0588853\pi$
$998$	10.2945	+	31.6834i	0.325868	+	1.00292i
$999$	−12.2031	+	8.86606i	−0.386088	+	0.280510i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	506.2.e.h.47.2	✓	20
11.2	odd	10		5566.2.a.bt.1.3		10
11.4	even	5	inner	506.2.e.h.323.2	yes	20
11.9	even	5		5566.2.a.bu.1.3		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
506.2.e.h.47.2	✓	20	1.1	even	1	trivial
506.2.e.h.323.2	yes	20	11.4	even	5	inner
5566.2.a.bt.1.3		10	11.2	odd	10
5566.2.a.bu.1.3		10	11.9	even	5

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:	\( N \)	\(=\)	\( 506 = 2 \cdot 11 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	506.e (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.809017 + 0.587785i) q^{2} +(-0.348991 - 1.07408i) q^{3} +(0.309017 - 0.951057i) q^{4} +(2.43018 + 1.76563i) q^{5} +(0.913669 + 0.663820i) q^{6} +(0.436107 - 1.34220i) q^{7} +(0.309017 + 0.951057i) q^{8} +(1.39519 - 1.01367i) q^{9} +O(q^{10})\)	\(q+(-0.809017 + 0.587785i) q^{2} +(-0.348991 - 1.07408i) q^{3} +(0.309017 - 0.951057i) q^{4} +(2.43018 + 1.76563i) q^{5} +(0.913669 + 0.663820i) q^{6} +(0.436107 - 1.34220i) q^{7} +(0.309017 + 0.951057i) q^{8} +(1.39519 - 1.01367i) q^{9} -3.00387 q^{10} +(-0.516825 + 3.27611i) q^{11} -1.12936 q^{12} +(0.705636 - 0.512675i) q^{13} +(0.436107 + 1.34220i) q^{14} +(1.04832 - 3.22640i) q^{15} +(-0.809017 - 0.587785i) q^{16} +(1.93934 + 1.40901i) q^{17} +(-0.532916 + 1.64015i) q^{18} +(-0.237518 - 0.731004i) q^{19} +(2.43018 - 1.76563i) q^{20} -1.59383 q^{21} +(-1.50753 - 2.95421i) q^{22} -1.00000 q^{23} +(0.913669 - 0.663820i) q^{24} +(1.24324 + 3.82631i) q^{25} +(-0.269529 + 0.829525i) q^{26} +(-4.31668 - 3.13625i) q^{27} +(-1.14174 - 0.829525i) q^{28} +(-0.719336 + 2.21389i) q^{29} +(1.04832 + 3.22640i) q^{30} +(7.52285 - 5.46567i) q^{31} +1.00000 q^{32} +(3.69918 - 0.588218i) q^{33} -2.39716 q^{34} +(3.42965 - 2.49178i) q^{35} +(-0.532916 - 1.64015i) q^{36} +(0.873579 - 2.68860i) q^{37} +(0.621829 + 0.451785i) q^{38} +(-0.796915 - 0.578993i) q^{39} +(-0.928246 + 2.85685i) q^{40} +(3.09048 + 9.51152i) q^{41} +(1.28944 - 0.936830i) q^{42} +6.13188 q^{43} +(2.95606 + 1.50390i) q^{44} +5.18033 q^{45} +(0.809017 - 0.587785i) q^{46} +(0.788149 + 2.42567i) q^{47} +(-0.348991 + 1.07408i) q^{48} +(4.05181 + 2.94381i) q^{49} +(-3.25485 - 2.36479i) q^{50} +(0.836585 - 2.57474i) q^{51} +(-0.269529 - 0.829525i) q^{52} +(9.60192 - 6.97621i) q^{53} +5.33571 q^{54} +(-7.04037 + 7.04901i) q^{55} +1.41127 q^{56} +(-0.702267 + 0.510227i) q^{57} +(-0.719336 - 2.21389i) q^{58} +(1.83699 - 5.65368i) q^{59} +(-2.74454 - 1.99403i) q^{60} +(-6.29515 - 4.57370i) q^{61} +(-2.87347 + 8.84364i) q^{62} +(-0.752090 - 2.31469i) q^{63} +(-0.809017 + 0.587785i) q^{64} +2.62002 q^{65} +(-2.64695 + 2.65020i) q^{66} -13.4543 q^{67} +(1.93934 - 1.40901i) q^{68} +(0.348991 + 1.07408i) q^{69} +(-1.31001 + 4.03179i) q^{70} +(0.244235 + 0.177447i) q^{71} +(1.39519 + 1.01367i) q^{72} +(-1.53573 + 4.72648i) q^{73} +(0.873579 + 2.68860i) q^{74} +(3.67589 - 2.67069i) q^{75} -0.768623 q^{76} +(4.17180 + 2.12242i) q^{77} +0.985042 q^{78} +(-10.1724 + 7.39067i) q^{79} +(-0.928246 - 2.85685i) q^{80} +(-0.263364 + 0.810550i) q^{81} +(-8.09098 - 5.87844i) q^{82} +(-9.60819 - 6.98076i) q^{83} +(-0.492521 + 1.51582i) q^{84} +(2.22515 + 6.84831i) q^{85} +(-4.96080 + 3.60423i) q^{86} +2.62894 q^{87} +(-3.27547 + 0.520843i) q^{88} +7.28452 q^{89} +(-4.19097 + 3.04492i) q^{90} +(-0.380379 - 1.17069i) q^{91} +(-0.309017 + 0.951057i) q^{92} +(-8.49598 - 6.17269i) q^{93} +(-2.06340 - 1.49915i) q^{94} +(0.713471 - 2.19584i) q^{95} +(-0.348991 - 1.07408i) q^{96} +(2.90613 - 2.11143i) q^{97} -5.00831 q^{98} +(2.59981 + 5.09469i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 5 q^{2} - 3 q^{3} - 5 q^{4} - q^{5} - 3 q^{6} + 3 q^{7} - 5 q^{8} - 8 q^{9}+O(q^{10}) \) 20 * q - 5 * q^2 - 3 * q^3 - 5 * q^4 - q^5 - 3 * q^6 + 3 * q^7 - 5 * q^8 - 8 * q^9	\( 20 q - 5 q^{2} - 3 q^{3} - 5 q^{4} - q^{5} - 3 q^{6} + 3 q^{7} - 5 q^{8} - 8 q^{9} + 24 q^{10} + 8 q^{11} + 12 q^{12} + 4 q^{13} + 3 q^{14} - 3 q^{15} - 5 q^{16} + 7 q^{17} - 8 q^{18} - 9 q^{19} - q^{20} + 16 q^{21} - 7 q^{22} - 20 q^{23} - 3 q^{24} - 22 q^{25} - q^{26} - 21 q^{27} - 7 q^{28} - 20 q^{29} - 3 q^{30} + 10 q^{31} + 20 q^{32} - 23 q^{33} - 8 q^{34} - 39 q^{35} - 8 q^{36} + q^{37} + q^{38} + 8 q^{39} - 11 q^{40} + 31 q^{41} + 21 q^{42} + 8 q^{43} + 3 q^{44} + 144 q^{45} + 5 q^{46} - 36 q^{47} - 3 q^{48} - 36 q^{49} - 12 q^{50} - 19 q^{51} - q^{52} - 8 q^{53} + 24 q^{54} - 7 q^{55} + 8 q^{56} - 43 q^{57} - 20 q^{58} - 37 q^{59} - 3 q^{60} - 3 q^{61} - 10 q^{62} + 40 q^{63} - 5 q^{64} - 62 q^{65} - 33 q^{66} + 48 q^{67} + 7 q^{68} + 3 q^{69} + 31 q^{70} - 56 q^{71} - 8 q^{72} + 51 q^{73} + q^{74} + 86 q^{75} + 16 q^{76} + 19 q^{77} + 58 q^{78} - q^{79} - 11 q^{80} - 25 q^{81} - 34 q^{82} + 12 q^{83} - 29 q^{84} + 35 q^{85} - 42 q^{86} + 30 q^{87} + 3 q^{88} + 126 q^{89} - 46 q^{90} - 93 q^{91} + 5 q^{92} - 74 q^{93} - 6 q^{94} + 5 q^{95} - 3 q^{96} + 29 q^{97} + 24 q^{98} + 76 q^{99}+O(q^{100}) \) 20 * q - 5 * q^2 - 3 * q^3 - 5 * q^4 - q^5 - 3 * q^6 + 3 * q^7 - 5 * q^8 - 8 * q^9 + 24 * q^10 + 8 * q^11 + 12 * q^12 + 4 * q^13 + 3 * q^14 - 3 * q^15 - 5 * q^16 + 7 * q^17 - 8 * q^18 - 9 * q^19 - q^20 + 16 * q^21 - 7 * q^22 - 20 * q^23 - 3 * q^24 - 22 * q^25 - q^26 - 21 * q^27 - 7 * q^28 - 20 * q^29 - 3 * q^30 + 10 * q^31 + 20 * q^32 - 23 * q^33 - 8 * q^34 - 39 * q^35 - 8 * q^36 + q^37 + q^38 + 8 * q^39 - 11 * q^40 + 31 * q^41 + 21 * q^42 + 8 * q^43 + 3 * q^44 + 144 * q^45 + 5 * q^46 - 36 * q^47 - 3 * q^48 - 36 * q^49 - 12 * q^50 - 19 * q^51 - q^52 - 8 * q^53 + 24 * q^54 - 7 * q^55 + 8 * q^56 - 43 * q^57 - 20 * q^58 - 37 * q^59 - 3 * q^60 - 3 * q^61 - 10 * q^62 + 40 * q^63 - 5 * q^64 - 62 * q^65 - 33 * q^66 + 48 * q^67 + 7 * q^68 + 3 * q^69 + 31 * q^70 - 56 * q^71 - 8 * q^72 + 51 * q^73 + q^74 + 86 * q^75 + 16 * q^76 + 19 * q^77 + 58 * q^78 - q^79 - 11 * q^80 - 25 * q^81 - 34 * q^82 + 12 * q^83 - 29 * q^84 + 35 * q^85 - 42 * q^86 + 30 * q^87 + 3 * q^88 + 126 * q^89 - 46 * q^90 - 93 * q^91 + 5 * q^92 - 74 * q^93 - 6 * q^94 + 5 * q^95 - 3 * q^96 + 29 * q^97 + 24 * q^98 + 76 * q^99

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