LMFDB - Embedded newform 506.2.e.g.47.1

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:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 2 x^{15} + 4 x^{14} - x^{13} + 31 x^{12} - 108 x^{11} + 386 x^{10} - 568 x^{9} + 968 x^{8} + \cdots + 16 $ x^16 - 2x^15 + 4x^14 - x^13 + 31x^12 - 108x^11 + 386x^10 - 568x^9 + 968x^8 - 968x^7 + 1128x^6 - 624x^5 + 536x^4 + 120x^3 + 256x^2 + 96x + 16
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			47.1
Root			$-0.375603 - 1.15599i$ of defining polynomial
Character	$\chi$	$=$	506.47
Dual form			506.2.e.g.323.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.809017 + 0.587785i) q^{2} +(-0.916756 - 2.82148i) q^{3} +(0.309017 - 0.951057i) q^{4} +(-0.174325 - 0.126655i) q^{5} +(2.40010 + 1.74377i) q^{6} +(-0.406350 + 1.25062i) q^{7} +(0.309017 + 0.951057i) q^{8} +(-4.69328 + 3.40987i) q^{9} +O(q^{10})$	\(q+(-0.809017 + 0.587785i) q^{2} +(-0.916756 - 2.82148i) q^{3} +(0.309017 - 0.951057i) q^{4} +(-0.174325 - 0.126655i) q^{5} +(2.40010 + 1.74377i) q^{6} +(-0.406350 + 1.25062i) q^{7} +(0.309017 + 0.951057i) q^{8} +(-4.69328 + 3.40987i) q^{9} +0.215478 q^{10} +(-3.29057 - 0.414881i) q^{11} -2.96668 q^{12} +(-3.47606 + 2.52550i) q^{13} +(-0.406350 - 1.25062i) q^{14} +(-0.197540 + 0.607967i) q^{15} +(-0.809017 - 0.587785i) q^{16} +(4.03559 + 2.93203i) q^{17} +(1.79267 - 5.51728i) q^{18} +(0.117595 + 0.361919i) q^{19} +(-0.174325 + 0.126655i) q^{20} +3.90111 q^{21} +(2.90599 - 1.59850i) q^{22} +1.00000 q^{23} +(2.40010 - 1.74377i) q^{24} +(-1.53074 - 4.71112i) q^{25} +(1.32774 - 4.08635i) q^{26} +(6.72319 + 4.88468i) q^{27} +(1.06384 + 0.772923i) q^{28} +(-2.19069 + 6.74226i) q^{29} +(-0.197540 - 0.607967i) q^{30} +(-0.203954 + 0.148181i) q^{31} +1.00000 q^{32} +(1.84607 + 9.66465i) q^{33} -4.98826 q^{34} +(0.229233 - 0.166548i) q^{35} +(1.79267 + 5.51728i) q^{36} +(0.330413 - 1.01691i) q^{37} +(-0.307867 - 0.223678i) q^{38} +(10.3124 + 7.49237i) q^{39} +(0.0665862 - 0.204931i) q^{40} +(3.62075 + 11.1435i) q^{41} +(-3.15607 + 2.29302i) q^{42} -4.37961 q^{43} +(-1.41142 + 3.00132i) q^{44} +1.25003 q^{45} +(-0.809017 + 0.587785i) q^{46} +(-1.98296 - 6.10292i) q^{47} +(-0.916756 + 2.82148i) q^{48} +(4.26420 + 3.09812i) q^{49} +(4.00752 + 2.91164i) q^{50} +(4.57302 - 14.0743i) q^{51} +(1.32774 + 4.08635i) q^{52} +(-9.20894 + 6.69069i) q^{53} -8.31032 q^{54} +(0.521083 + 0.489090i) q^{55} -1.31497 q^{56} +(0.913344 - 0.663583i) q^{57} +(-2.19069 - 6.74226i) q^{58} +(-2.80178 + 8.62299i) q^{59} +(0.517167 + 0.375744i) q^{60} +(-9.13608 - 6.63775i) q^{61} +(0.0779036 - 0.239763i) q^{62} +(-2.35732 - 7.25509i) q^{63} +(-0.809017 + 0.587785i) q^{64} +0.925830 q^{65} +(-7.17424 - 6.73377i) q^{66} +7.04885 q^{67} +(4.03559 - 2.93203i) q^{68} +(-0.916756 - 2.82148i) q^{69} +(-0.0875592 + 0.269480i) q^{70} +(-4.78473 - 3.47631i) q^{71} +(-4.69328 - 3.40987i) q^{72} +(2.80376 - 8.62909i) q^{73} +(0.330413 + 1.01691i) q^{74} +(-11.8891 + 8.63790i) q^{75} +0.380544 q^{76} +(1.85598 - 3.94665i) q^{77} -12.7468 q^{78} +(4.70225 - 3.41638i) q^{79} +(0.0665862 + 0.204931i) q^{80} +(2.24051 - 6.89558i) q^{81} +(-9.47925 - 6.88708i) q^{82} +(5.63287 + 4.09252i) q^{83} +(1.20551 - 3.71018i) q^{84} +(-0.332150 - 1.02225i) q^{85} +(3.54317 - 2.57427i) q^{86} +21.0315 q^{87} +(-0.622268 - 3.25773i) q^{88} -15.8794 q^{89} +(-1.01130 + 0.734750i) q^{90} +(-1.74594 - 5.37344i) q^{91} +(0.309017 - 0.951057i) q^{92} +(0.605068 + 0.439608i) q^{93} +(5.19146 + 3.77181i) q^{94} +(0.0253390 - 0.0779855i) q^{95} +(-0.916756 - 2.82148i) q^{96} +(-2.30810 + 1.67693i) q^{97} -5.27084 q^{98} +(16.8583 - 9.27327i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 4 q^{2} + 5 q^{3} - 4 q^{4} + 7 q^{5} + 8 q^{7} - 4 q^{8} - 15 q^{9}+O(q^{10}) $ 16 * q - 4 * q^2 + 5 * q^3 - 4 * q^4 + 7 * q^5 + 8 * q^7 - 4 * q^8 - 15 * q^9	\( 16 q - 4 q^{2} + 5 q^{3} - 4 q^{4} + 7 q^{5} + 8 q^{7} - 4 q^{8} - 15 q^{9} - 18 q^{10} - 7 q^{11} - 10 q^{12} + 9 q^{13} + 8 q^{14} - 26 q^{15} - 4 q^{16} + 2 q^{17} + 10 q^{18} + 2 q^{19} + 7 q^{20} + 30 q^{21} + 8 q^{22} + 16 q^{23} + q^{25} - q^{26} + 14 q^{27} - 2 q^{28} + 6 q^{29} - 26 q^{30} - 15 q^{31} + 16 q^{32} - 35 q^{33} + 2 q^{34} + 11 q^{35} + 10 q^{36} - 19 q^{37} + 2 q^{38} + 40 q^{39} + 2 q^{40} - 4 q^{43} - 2 q^{44} - 48 q^{45} - 4 q^{46} + 23 q^{47} + 5 q^{48} + 28 q^{49} + 6 q^{50} + 32 q^{51} - q^{52} - 40 q^{53} - 16 q^{54} - 9 q^{55} - 12 q^{56} + 8 q^{57} + 6 q^{58} - 20 q^{59} + 24 q^{60} + 3 q^{61} + 25 q^{62} + 10 q^{63} - 4 q^{64} + 38 q^{65} + 10 q^{66} + 12 q^{67} + 2 q^{68} + 5 q^{69} - 24 q^{70} + 25 q^{71} - 15 q^{72} + 5 q^{73} - 19 q^{74} - 73 q^{75} - 8 q^{76} - 48 q^{77} - 60 q^{78} + 34 q^{79} + 2 q^{80} - 25 q^{81} - 5 q^{82} + 19 q^{83} - 15 q^{84} + 10 q^{85} + 21 q^{86} + 22 q^{87} + 3 q^{88} - 74 q^{89} - 3 q^{90} + 15 q^{91} - 4 q^{92} + 63 q^{93} + 23 q^{94} - 22 q^{95} + 5 q^{96} - 48 q^{97} + 8 q^{98} - 6 q^{99}+O(q^{100}) \) 16 * q - 4 * q^2 + 5 * q^3 - 4 * q^4 + 7 * q^5 + 8 * q^7 - 4 * q^8 - 15 * q^9 - 18 * q^10 - 7 * q^11 - 10 * q^12 + 9 * q^13 + 8 * q^14 - 26 * q^15 - 4 * q^16 + 2 * q^17 + 10 * q^18 + 2 * q^19 + 7 * q^20 + 30 * q^21 + 8 * q^22 + 16 * q^23 + q^25 - q^26 + 14 * q^27 - 2 * q^28 + 6 * q^29 - 26 * q^30 - 15 * q^31 + 16 * q^32 - 35 * q^33 + 2 * q^34 + 11 * q^35 + 10 * q^36 - 19 * q^37 + 2 * q^38 + 40 * q^39 + 2 * q^40 - 4 * q^43 - 2 * q^44 - 48 * q^45 - 4 * q^46 + 23 * q^47 + 5 * q^48 + 28 * q^49 + 6 * q^50 + 32 * q^51 - q^52 - 40 * q^53 - 16 * q^54 - 9 * q^55 - 12 * q^56 + 8 * q^57 + 6 * q^58 - 20 * q^59 + 24 * q^60 + 3 * q^61 + 25 * q^62 + 10 * q^63 - 4 * q^64 + 38 * q^65 + 10 * q^66 + 12 * q^67 + 2 * q^68 + 5 * q^69 - 24 * q^70 + 25 * q^71 - 15 * q^72 + 5 * q^73 - 19 * q^74 - 73 * q^75 - 8 * q^76 - 48 * q^77 - 60 * q^78 + 34 * q^79 + 2 * q^80 - 25 * q^81 - 5 * q^82 + 19 * q^83 - 15 * q^84 + 10 * q^85 + 21 * q^86 + 22 * q^87 + 3 * q^88 - 74 * q^89 - 3 * q^90 + 15 * q^91 - 4 * q^92 + 63 * q^93 + 23 * q^94 - 22 * q^95 + 5 * q^96 - 48 * q^97 + 8 * q^98 - 6 * 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
$3$	−0.916756	−	2.82148i	−0.529289	−	1.62898i	−0.755675	−	0.654947i	$-0.772691\pi$
$3$	−0.916756	−	2.82148i	−0.529289	−	1.62898i	0.226386	−	0.974038i	$-0.427309\pi$
$4$	0.309017	−	0.951057i	0.154508	−	0.475528i
$5$	−0.174325	−	0.126655i	−0.0779605	−	0.0566416i	0.548122	−	0.836398i	$-0.315343\pi$
$5$	−0.174325	−	0.126655i	−0.0779605	−	0.0566416i	−0.626083	+	0.779757i	$0.715343\pi$
$6$	2.40010	+	1.74377i	0.979836	+	0.711892i
$7$	−0.406350	+	1.25062i	−0.153586	+	0.472688i	−0.998015	−	0.0629791i	$-0.979940\pi$
$7$	−0.406350	+	1.25062i	−0.153586	+	0.472688i	0.844429	+	0.535667i	$0.179940\pi$
$8$	0.309017	+	0.951057i	0.109254	+	0.336249i
$9$	−4.69328	+	3.40987i	−1.56443	+	1.13662i
$10$	0.215478			0.0681400
$11$	−3.29057	−	0.414881i	−0.992145	−	0.125091i
$11$	−3.29057	−	0.414881i	−0.992145	−	0.125091i
$12$	−2.96668			−0.856408
$13$	−3.47606	+	2.52550i	−0.964084	+	0.700448i	−0.954096	−	0.299502i	$-0.903180\pi$
$13$	−3.47606	+	2.52550i	−0.964084	+	0.700448i	−0.00998860	+	0.999950i	$0.503180\pi$
$14$	−0.406350	−	1.25062i	−0.108601	−	0.334241i
$15$	−0.197540	+	0.607967i	−0.0510047	+	0.156976i
$16$	−0.809017	−	0.587785i	−0.202254	−	0.146946i
$17$	4.03559	+	2.93203i	0.978774	+	0.711121i	0.957434	−	0.288651i	$-0.0932068\pi$
$17$	4.03559	+	2.93203i	0.978774	+	0.711121i	0.0213400	+	0.999772i	$0.493207\pi$
$18$	1.79267	−	5.51728i	0.422537	−	1.30044i
$19$	0.117595	+	0.361919i	0.0269781	+	0.0830300i	0.963639	−	0.267207i	$-0.0861009\pi$
$19$	0.117595	+	0.361919i	0.0269781	+	0.0830300i	−0.936661	+	0.350237i	$0.886101\pi$
$20$	−0.174325	+	0.126655i	−0.0389803	+	0.0283208i
$21$	3.90111			0.851293
$22$	2.90599	−	1.59850i	0.619559	−	0.340802i
$23$	1.00000			0.208514
$23$	1.00000			0.208514
$24$	2.40010	−	1.74377i	0.489918	−	0.355946i
$25$	−1.53074	−	4.71112i	−0.306147	−	0.942225i
$26$	1.32774	−	4.08635i	0.260390	−	0.801399i
$27$	6.72319	+	4.88468i	1.29388	+	0.940057i
$28$	1.06384	+	0.772923i	0.201046	+	0.146069i
$29$	−2.19069	+	6.74226i	−0.406801	+	1.25201i	0.512580	+	0.858639i	$0.328690\pi$
$29$	−2.19069	+	6.74226i	−0.406801	+	1.25201i	−0.919382	+	0.393367i	$0.871310\pi$
$30$	−0.197540	−	0.607967i	−0.0360658	−	0.110999i
$31$	−0.203954	+	0.148181i	−0.0366313	+	0.0266142i	−0.605950	−	0.795503i	$-0.707207\pi$
$31$	−0.203954	+	0.148181i	−0.0366313	+	0.0266142i	0.569319	+	0.822117i	$0.307207\pi$
$32$	1.00000			0.176777
$33$	1.84607	+	9.66465i	0.321360	+	1.68240i
$34$	−4.98826			−0.855480
$35$	0.229233	−	0.166548i	0.0387474	−	0.0281517i
$36$	1.79267	+	5.51728i	0.298779	+	0.919547i
$37$	0.330413	−	1.01691i	0.0543196	−	0.167179i	−0.920216	−	0.391410i	$-0.871987\pi$
$37$	0.330413	−	1.01691i	0.0543196	−	0.167179i	0.974536	+	0.224232i	$0.0719873\pi$
$38$	−0.307867	−	0.223678i	−0.0499426	−	0.0362854i
$39$	10.3124	+	7.49237i	1.65130	+	1.19974i
$40$	0.0665862	−	0.204931i	0.0105282	−	0.0324025i
$41$	3.62075	+	11.1435i	0.565466	+	1.74033i	0.666562	+	0.745449i	$0.267765\pi$
$41$	3.62075	+	11.1435i	0.565466	+	1.74033i	−0.101096	+	0.994877i	$0.532235\pi$
$42$	−3.15607	+	2.29302i	−0.486992	+	0.353820i
$43$	−4.37961			−0.667884			−0.333942	−	0.942594i	$-0.608379\pi$
$43$	−4.37961			−0.667884			−0.333942	+	0.942594i	$0.608379\pi$
$44$	−1.41142	+	3.00132i	−0.212779	+	0.452465i
$45$	1.25003			0.186344
$46$	−0.809017	+	0.587785i	−0.119283	+	0.0866642i
$47$	−1.98296	−	6.10292i	−0.289244	−	0.890203i	−0.985094	−	0.172015i	$-0.944972\pi$
$47$	−1.98296	−	6.10292i	−0.289244	−	0.890203i	0.695850	−	0.718187i	$-0.255028\pi$
$48$	−0.916756	+	2.82148i	−0.132322	+	0.407246i
$49$	4.26420	+	3.09812i	0.609172	+	0.442589i
$50$	4.00752	+	2.91164i	0.566749	+	0.411767i
$51$	4.57302	−	14.0743i	0.640351	−	1.97080i
$52$	1.32774	+	4.08635i	0.184124	+	0.566675i
$53$	−9.20894	+	6.69069i	−1.26494	+	0.919036i	−0.998989	−	0.0449490i	$-0.985687\pi$
$53$	−9.20894	+	6.69069i	−1.26494	+	0.919036i	−0.265956	+	0.963985i	$0.585687\pi$
$54$	−8.31032			−1.13089
$55$	0.521083	+	0.489090i	0.0702628	+	0.0659489i
$56$	−1.31497			−0.175721
$57$	0.913344	−	0.663583i	0.120975	−	0.0878937i
$58$	−2.19069	−	6.74226i	−0.287652	−	0.885302i
$59$	−2.80178	+	8.62299i	−0.364761	+	1.12262i	0.585370	+	0.810766i	$0.300949\pi$
$59$	−2.80178	+	8.62299i	−0.364761	+	1.12262i	−0.950131	+	0.311852i	$0.899051\pi$
$60$	0.517167	+	0.375744i	0.0667660	+	0.0485083i
$61$	−9.13608	−	6.63775i	−1.16976	−	0.849877i	−0.178776	−	0.983890i	$-0.557214\pi$
$61$	−9.13608	−	6.63775i	−1.16976	−	0.849877i	−0.990980	+	0.134013i	$0.957214\pi$
$62$	0.0779036	−	0.239763i	0.00989377	−	0.0304499i
$63$	−2.35732	−	7.25509i	−0.296994	−	0.914055i
$64$	−0.809017	+	0.587785i	−0.101127	+	0.0734732i
$65$	0.925830			0.114835
$66$	−7.17424	−	6.73377i	−0.883088	−	0.828870i
$67$	7.04885			0.861154			0.430577	−	0.902554i	$-0.358310\pi$
$67$	7.04885			0.861154			0.430577	+	0.902554i	$0.358310\pi$
$68$	4.03559	−	2.93203i	0.489387	−	0.355561i
$69$	−0.916756	−	2.82148i	−0.110364	−	0.339667i
$70$	−0.0875592	+	0.269480i	−0.0104653	+	0.0322090i
$71$	−4.78473	−	3.47631i	−0.567842	−	0.412562i	0.266478	−	0.963841i	$-0.414140\pi$
$71$	−4.78473	−	3.47631i	−0.567842	−	0.412562i	−0.834321	+	0.551279i	$0.814140\pi$
$72$	−4.69328	−	3.40987i	−0.553108	−	0.401857i
$73$	2.80376	−	8.62909i	0.328155	−	1.00996i	−0.641841	−	0.766838i	$-0.721829\pi$
$73$	2.80376	−	8.62909i	0.328155	−	1.00996i	0.969996	−	0.243120i	$-0.0781710\pi$
$74$	0.330413	+	1.01691i	0.0384098	+	0.118213i
$75$	−11.8891	+	8.63790i	−1.37283	+	0.997419i
$76$	0.380544			0.0436514
$77$	1.85598	−	3.94665i	0.211508	−	0.449763i
$78$	−12.7468			−1.44329
$79$	4.70225	−	3.41638i	0.529044	−	0.384373i	−0.290956	−	0.956736i	$-0.593973\pi$
$79$	4.70225	−	3.41638i	0.529044	−	0.384373i	0.820000	+	0.572363i	$0.193973\pi$
$80$	0.0665862	+	0.204931i	0.00744457	+	0.0229120i
$81$	2.24051	−	6.89558i	0.248946	−	0.766176i
$82$	−9.47925	−	6.88708i	−1.04681	−	0.760550i
$83$	5.63287	+	4.09252i	0.618287	+	0.449212i	0.852323	−	0.523016i	$-0.175193\pi$
$83$	5.63287	+	4.09252i	0.618287	+	0.449212i	−0.234035	+	0.972228i	$0.575193\pi$
$84$	1.20551	−	3.71018i	0.131532	−	0.404814i
$85$	−0.332150	−	1.02225i	−0.0360267	−	0.110879i
$86$	3.54317	−	2.57427i	0.382070	−	0.277590i
$87$	21.0315			2.25481
$88$	−0.622268	−	3.25773i	−0.0663340	−	0.347275i
$89$	−15.8794			−1.68321			−0.841606	−	0.540093i	$-0.818389\pi$
$89$	−15.8794			−1.68321			−0.841606	+	0.540093i	$0.818389\pi$
$90$	−1.01130	+	0.734750i	−0.106600	+	0.0774495i
$91$	−1.74594	−	5.37344i	−0.183024	−	0.563290i
$92$	0.309017	−	0.951057i	0.0322172	−	0.0991545i
$93$	0.605068	+	0.439608i	0.0627426	+	0.0455852i
$94$	5.19146	+	3.77181i	0.535458	+	0.389033i
$95$	0.0253390	−	0.0779855i	0.00259973	−	0.00800114i
$96$	−0.916756	−	2.82148i	−0.0935660	−	0.287967i
$97$	−2.30810	+	1.67693i	−0.234352	+	0.170267i	−0.698763	−	0.715353i	$-0.746266\pi$
$97$	−2.30810	+	1.67693i	−0.234352	+	0.170267i	0.464411	+	0.885620i	$0.346266\pi$
$98$	−5.27084			−0.532435
$99$	16.8583	−	9.27327i	1.69432	−	0.931998i
$100$	−4.95357			−0.495357
$101$	−6.51484	+	4.73331i	−0.648251	+	0.470982i	−0.862675	−	0.505759i	$-0.831212\pi$
$101$	−6.51484	+	4.73331i	−0.648251	+	0.470982i	0.214424	+	0.976741i	$0.431212\pi$
$102$	4.57302	+	14.0743i	0.452796	+	1.39356i
$103$	0.969849	−	2.98489i	0.0955621	−	0.294110i	−0.891838	−	0.452356i	$-0.850584\pi$
$103$	0.969849	−	2.98489i	0.0955621	−	0.294110i	0.987400	+	0.158246i	$0.0505838\pi$
$104$	−3.47606	−	2.52550i	−0.340855	−	0.247646i
$105$	−0.680062	−	0.494094i	−0.0663672	−	0.0482186i
$106$	3.51750	−	10.8258i	0.341650	−	1.05149i
$107$	−0.261275	−	0.804123i	−0.0252584	−	0.0777375i	0.937633	−	0.347628i	$-0.113013\pi$
$107$	−0.261275	−	0.804123i	−0.0252584	−	0.0777375i	−0.962891	+	0.269890i	$0.913013\pi$
$108$	6.72319	−	4.88468i	0.646939	−	0.470029i
$109$	−15.3211			−1.46750			−0.733750	−	0.679420i	$-0.762232\pi$
$109$	−15.3211			−1.46750			−0.733750	+	0.679420i	$0.762232\pi$
$110$	−0.709045	−	0.0893976i	−0.0676048	−	0.00852373i
$111$	−3.17210			−0.301082
$112$	1.06384	−	0.772923i	0.100523	−	0.0730343i
$113$	2.21553	+	6.81870i	0.208420	+	0.641450i	0.999556	+	0.0298093i	$0.00949000\pi$
$113$	2.21553	+	6.81870i	0.208420	+	0.641450i	−0.791136	+	0.611640i	$0.790510\pi$
$114$	−0.348866	+	1.07370i	−0.0326743	+	0.100561i
$115$	−0.174325	−	0.126655i	−0.0162559	−	0.0118106i
$116$	5.73531	+	4.16695i	0.532510	+	0.386891i
$117$	7.70248	−	23.7058i	0.712094	−	2.19160i
$118$	−2.80178	−	8.62299i	−0.257925	−	0.793811i
$119$	−5.30670	+	3.85554i	−0.486464	+	0.353437i
$120$	−0.639254			−0.0583556
$121$	10.6557	+	2.73039i	0.968704	+	0.248218i
$122$	11.2928			1.02240
$123$	28.1219	−	20.4318i	2.53567	−	1.84227i
$124$	0.0779036	+	0.239763i	0.00699595	+	0.0215313i
$125$	−0.662771	+	2.03980i	−0.0592800	+	0.182445i
$126$	6.17155	+	4.48389i	0.549805	+	0.399457i
$127$	−6.43628	−	4.67623i	−0.571127	−	0.414948i	0.264387	−	0.964417i	$-0.414830\pi$
$127$	−6.43628	−	4.67623i	−0.571127	−	0.414948i	−0.835515	+	0.549468i	$0.814830\pi$
$128$	0.309017	−	0.951057i	0.0273135	−	0.0840623i
$129$	4.01503	+	12.3570i	0.353504	+	1.08797i
$130$	−0.749012	+	0.544189i	−0.0656927	+	0.0477285i
$131$	−17.6432			−1.54149			−0.770746	−	0.637143i	$-0.780116\pi$
$131$	−17.6432			−1.54149			−0.770746	+	0.637143i	$0.780116\pi$
$132$	9.76209	+	1.23082i	0.849681	+	0.107129i
$133$	−0.500406			−0.0433907
$134$	−5.70264	+	4.14321i	−0.492633	+	0.357919i
$135$	−0.553353	−	1.70304i	−0.0476250	−	0.146575i
$136$	−1.54146	+	4.74412i	−0.132179	+	0.406805i
$137$	7.14419	+	5.19056i	0.610370	+	0.443459i	0.849544	−	0.527517i	$-0.176877\pi$
$137$	7.14419	+	5.19056i	0.610370	+	0.443459i	−0.239175	+	0.970977i	$0.576877\pi$
$138$	2.40010	+	1.74377i	0.204310	+	0.148440i
$139$	−3.55548	+	10.9426i	−0.301572	+	0.928142i	0.679363	+	0.733802i	$0.262256\pi$
$139$	−3.55548	+	10.9426i	−0.301572	+	0.928142i	−0.980934	+	0.194339i	$0.937744\pi$
$140$	−0.0875592	−	0.269480i	−0.00740010	−	0.0227752i
$141$	−15.4014	+	11.1898i	−1.29703	+	0.942349i
$142$	5.91425			0.496313
$143$	12.4860	−	6.86820i	1.04413	−	0.574348i
$144$	5.80121			0.483435
$145$	1.23583	−	0.897883i	0.102630	−	0.0745652i
$146$	2.80376	+	8.62909i	0.232041	+	0.714148i
$147$	4.83207	−	14.8716i	0.398543	−	1.22659i
$148$	−0.865033	−	0.628483i	−0.0711053	−	0.0516610i
$149$	−5.98766	−	4.35029i	−0.490528	−	0.356390i	0.314859	−	0.949138i	$-0.398043\pi$
$149$	−5.98766	−	4.35029i	−0.490528	−	0.356390i	−0.805387	+	0.592749i	$0.798043\pi$
$150$	4.54121	−	13.9764i	0.370789	−	1.14117i
$151$	−3.88474	−	11.9560i	−0.316136	−	0.972966i	−0.975284	−	0.220953i	$-0.929083\pi$
$151$	−3.88474	−	11.9560i	−0.316136	−	0.972966i	0.659149	−	0.752013i	$-0.270917\pi$
$152$	−0.307867	+	0.223678i	−0.0249713	+	0.0181427i
$153$	−28.9380			−2.33950
$154$	0.818266	+	4.28383i	0.0659378	+	0.345201i
$155$	0.0543222			0.00436326
$156$	10.3124	−	7.49237i	0.825649	−	0.599869i
$157$	−2.60906	−	8.02988i	−0.208226	−	0.640854i	−0.999565	−	0.0294768i	$-0.990616\pi$
$157$	−2.60906	−	8.02988i	−0.208226	−	0.640854i	0.791339	−	0.611377i	$-0.209384\pi$
$158$	−1.79610	+	5.52782i	−0.142890	+	0.439770i
$159$	27.3200	+	19.8491i	2.16662	+	1.57414i
$160$	−0.174325	−	0.126655i	−0.0137816	−	0.0100129i
$161$	−0.406350	+	1.25062i	−0.0320248	+	0.0985623i
$162$	2.24051	+	6.89558i	0.176031	+	0.541768i
$163$	−3.61202	+	2.62429i	−0.282915	+	0.205550i	−0.720188	−	0.693779i	$-0.755944\pi$
$163$	−3.61202	+	2.62429i	−0.282915	+	0.205550i	0.437273	+	0.899329i	$0.355944\pi$
$164$	11.7170			0.914944
$165$	0.902255	−	1.91860i	0.0702404	−	0.149363i
$166$	−6.96261			−0.540403
$167$	13.0236	−	9.46220i	1.00780	−	0.732207i	0.0440511	−	0.999029i	$-0.485974\pi$
$167$	13.0236	−	9.46220i	1.00780	−	0.732207i	0.963746	+	0.266822i	$0.0859736\pi$
$168$	1.20551	+	3.71018i	0.0930072	+	0.286247i
$169$	1.68758	−	5.19384i	0.129814	−	0.399526i
$170$	0.869579	+	0.631786i	0.0666937	+	0.0484558i
$171$	−1.78600	−	1.29761i	−0.136579	−	0.0992304i
$172$	−1.35337	+	4.16525i	−0.103194	+	0.317597i
$173$	−4.14780	−	12.7656i	−0.315351	−	0.970552i	−0.975610	−	0.219513i	$-0.929553\pi$
$173$	−4.14780	−	12.7656i	−0.315351	−	0.970552i	0.660258	−	0.751039i	$-0.270447\pi$
$174$	−17.0148	+	12.3620i	−1.28989	+	0.937162i
$175$	6.51382			0.492398
$176$	2.41827	+	2.26980i	0.182284	+	0.171092i
$177$	26.8982			2.02179
$178$	12.8467	−	9.33367i	0.962900	−	0.699588i
$179$	−2.48506	−	7.64821i	−0.185742	−	0.571654i	0.814219	−	0.580558i	$-0.197166\pi$
$179$	−2.48506	−	7.64821i	−0.185742	−	0.571654i	−0.999960	+	0.00890408i	$0.997166\pi$
$180$	0.386281	−	1.18885i	0.0287917	−	0.0886117i
$181$	−0.756655	−	0.549742i	−0.0562417	−	0.0408620i	0.559309	−	0.828959i	$-0.311066\pi$
$181$	−0.756655	−	0.549742i	−0.0562417	−	0.0408620i	−0.615551	+	0.788097i	$0.711066\pi$
$182$	4.57092	+	3.32097i	0.338819	+	0.246167i
$183$	−10.3528	+	31.8625i	−0.765298	+	2.35534i
$184$	0.309017	+	0.951057i	0.0227810	+	0.0701128i
$185$	−0.186395	+	0.135424i	−0.0137041	+	0.00995658i
$186$	−0.747905			−0.0548391
$187$	−12.0630	−	11.3223i	−0.882131	−	0.827972i
$188$	−6.41699			−0.468007
$189$	−8.84082	+	6.42323i	−0.643075	+	0.467221i
$190$	0.0253390	+	0.0779855i	0.00183829	+	0.00565766i
$191$	−0.0692001	+	0.212976i	−0.00500715	+	0.0154104i	−0.953529	−	0.301302i	$-0.902579\pi$
$191$	−0.0692001	+	0.212976i	−0.00500715	+	0.0154104i	0.948522	+	0.316712i	$0.102579\pi$
$192$	2.40010	+	1.74377i	0.173212	+	0.125846i
$193$	15.7941	+	11.4751i	1.13688	+	0.825994i	0.986682	−	0.162662i	$-0.0520079\pi$
$193$	15.7941	+	11.4751i	1.13688	+	0.825994i	0.150201	+	0.988655i	$0.452008\pi$
$194$	0.881615	−	2.71333i	0.0632963	−	0.194806i
$195$	−0.848760	−	2.61221i	−0.0607810	−	0.187065i
$196$	4.26420	−	3.09812i	0.304586	−	0.221295i
$197$	3.56218			0.253795			0.126897	−	0.991916i	$-0.459498\pi$
$197$	3.56218			0.253795			0.126897	+	0.991916i	$0.459498\pi$
$198$	−8.18794	+	17.4113i	−0.581892	+	1.23737i
$199$	−24.6931			−1.75045			−0.875225	−	0.483716i	$-0.839287\pi$
$199$	−24.6931			−1.75045			−0.875225	+	0.483716i	$0.839287\pi$
$200$	4.00752	−	2.91164i	0.283375	−	0.205884i
$201$	−6.46207	−	19.8882i	−0.455799	−	1.40281i
$202$	2.48845	−	7.65865i	0.175086	−	0.538861i
$203$	−7.54179	−	5.47943i	−0.529330	−	0.384580i
$204$	−11.9723	−	8.69840i	−0.838230	−	0.609010i
$205$	0.780190	−	2.40118i	0.0544909	−	0.167706i
$206$	0.969849	+	2.98489i	0.0675726	+	0.207967i
$207$	−4.69328	+	3.40987i	−0.326206	+	0.237002i
$208$	4.29664			0.297918
$209$	−0.236801	−	1.23971i	−0.0163798	−	0.0857525i
$210$	0.840603			0.0580071
$211$	−3.21897	+	2.33872i	−0.221603	+	0.161004i	−0.693048	−	0.720892i	$-0.743733\pi$
$211$	−3.21897	+	2.33872i	−0.221603	+	0.161004i	0.471445	+	0.881895i	$0.343733\pi$
$212$	3.51750	+	10.8258i	0.241583	+	0.743516i
$213$	−5.42192	+	16.6870i	−0.371504	+	1.14337i
$214$	0.684028	+	0.496975i	0.0467592	+	0.0339725i
$215$	0.763475	+	0.554697i	0.0520685	+	0.0378300i
$216$	−2.56803	+	7.90358i	−0.174732	+	0.537771i
$217$	−0.102441	−	0.315282i	−0.00695417	−	0.0214027i
$218$	12.3951	−	9.00554i	0.839500	−	0.609932i
$219$	−26.9172			−1.81890
$220$	0.626176	−	0.344442i	0.0422168	−	0.0232223i
$221$	−21.4328			−1.44172
$222$	2.56628	−	1.86451i	0.172237	−	0.125138i
$223$	−1.52755	−	4.70133i	−0.102293	−	0.314824i	0.886793	−	0.462167i	$-0.152928\pi$
$223$	−1.52755	−	4.70133i	−0.102293	−	0.314824i	−0.989085	+	0.147343i	$0.952928\pi$
$224$	−0.406350	+	1.25062i	−0.0271504	+	0.0835602i
$225$	23.2485	+	16.8910i	1.54990	+	1.12607i
$226$	−5.80033	−	4.21419i	−0.385833	−	0.280324i
$227$	−6.88289	+	21.1833i	−0.456833	+	1.40599i	0.412136	+	0.911122i	$0.364783\pi$
$227$	−6.88289	+	21.1833i	−0.456833	+	1.40599i	−0.868969	+	0.494866i	$0.835217\pi$
$228$	−0.348866	−	1.07370i	−0.0231042	−	0.0711075i
$229$	−13.3489	+	9.69856i	−0.882122	+	0.640899i	−0.933812	−	0.357764i	$-0.883539\pi$
$229$	−13.3489	+	9.69856i	−0.882122	+	0.640899i	0.0516903	+	0.998663i	$0.483539\pi$
$230$	0.215478			0.0142082
$231$	−12.8369	−	1.61850i	−0.844606	−	0.106489i
$232$	−7.08923			−0.465431
$233$	0.901843	−	0.655227i	0.0590817	−	0.0429253i	−0.557852	−	0.829940i	$-0.688374\pi$
$233$	0.901843	−	0.655227i	0.0590817	−	0.0429253i	0.616934	+	0.787015i	$0.288374\pi$
$234$	7.70248	+	23.7058i	0.503527	+	1.54970i
$235$	−0.427283	+	1.31504i	−0.0278729	+	0.0857839i
$236$	7.33515	+	5.32930i	0.477478	+	0.346908i
$237$	−13.9501	−	10.1353i	−0.906155	−	0.658360i
$238$	2.02698	−	6.23840i	0.131389	−	0.404375i
$239$	9.31755	+	28.6765i	0.602702	+	1.85493i	0.511875	+	0.859060i	$0.328951\pi$
$239$	9.31755	+	28.6765i	0.602702	+	1.85493i	0.0908277	+	0.995867i	$0.471049\pi$
$240$	0.517167	−	0.375744i	0.0333830	−	0.0242542i
$241$	−5.97112			−0.384634			−0.192317	−	0.981333i	$-0.561600\pi$
$241$	−5.97112			−0.384634			−0.192317	+	0.981333i	$0.561600\pi$
$242$	−10.2256	+	4.05436i	−0.657324	+	0.260624i
$243$	3.42118			0.219469
$244$	−9.13608	+	6.63775i	−0.584878	+	0.424939i
$245$	−0.350966	−	1.08016i	−0.0224224	−	0.0690089i
$246$	−10.7416	+	33.0593i	−0.684861	+	2.10778i
$247$	−1.32279	−	0.961066i	−0.0841673	−	0.0611512i
$248$	−0.203954	−	0.148181i	−0.0129511	−	0.00940953i
$249$	6.38301	−	19.6449i	0.404507	−	1.24494i
$250$	−0.662771	−	2.03980i	−0.0419173	−	0.129008i
$251$	21.8410	−	15.8684i	1.37859	−	1.00161i	0.381581	−	0.924335i	$-0.375380\pi$
$251$	21.8410	−	15.8684i	1.37859	−	1.00161i	0.997010	−	0.0772699i	$-0.0246203\pi$
$252$	−7.62845			−0.480547
$253$	−3.29057	−	0.414881i	−0.206877	−	0.0260834i
$254$	7.95568			0.499184
$255$	−2.57977	+	1.87431i	−0.161551	+	0.117374i
$256$	0.309017	+	0.951057i	0.0193136	+	0.0594410i
$257$	−3.49286	+	10.7499i	−0.217878	+	0.670561i	0.781058	+	0.624458i	$0.214680\pi$
$257$	−3.49286	+	10.7499i	−0.217878	+	0.670561i	−0.998937	+	0.0461028i	$0.985320\pi$
$258$	−10.5115	−	7.63704i	−0.654416	−	0.475461i
$259$	1.13750	+	0.826440i	0.0706806	+	0.0513525i
$260$	0.286097	−	0.880516i	0.0177430	−	0.0546073i
$261$	−12.7087	−	39.1133i	−0.786648	−	2.42105i
$262$	14.2736	−	10.3704i	0.881828	−	0.640685i
$263$	1.02905			0.0634537			0.0317269	−	0.999497i	$-0.489899\pi$
$263$	1.02905			0.0634537			0.0317269	+	0.999497i	$0.489899\pi$
$264$	−8.62116	+	4.74226i	−0.530596	+	0.291866i
$265$	2.45275			0.150671
$266$	0.404837	−	0.294131i	0.0248222	−	0.0180344i
$267$	14.5575	+	44.8034i	0.890905	+	2.74193i
$268$	2.17821	−	6.70385i	0.133056	−	0.409503i
$269$	16.4722	+	11.9678i	1.00433	+	0.729687i	0.963012	−	0.269459i	$-0.0868449\pi$
$269$	16.4722	+	11.9678i	1.00433	+	0.729687i	0.0413163	+	0.999146i	$0.486845\pi$
$270$	1.44870	+	1.05254i	0.0881648	+	0.0640555i
$271$	0.468139	−	1.44078i	0.0284374	−	0.0875214i	−0.935830	−	0.352450i	$-0.885349\pi$
$271$	0.468139	−	1.44078i	0.0284374	−	0.0875214i	0.964268	+	0.264929i	$0.0853485\pi$
$272$	−1.54146	−	4.74412i	−0.0934646	−	0.287655i
$273$	−13.5605	+	9.85227i	−0.820718	+	0.596287i
$274$	−8.83071			−0.533483
$275$	3.08245	+	16.1374i	0.185879	+	0.973120i
$276$	−2.96668			−0.178573
$277$	−3.43889	+	2.49850i	−0.206623	+	0.150120i	−0.686284	−	0.727333i	$-0.740759\pi$
$277$	−3.43889	+	2.49850i	−0.206623	+	0.150120i	0.479662	+	0.877454i	$0.340759\pi$
$278$	−3.55548	−	10.9426i	−0.213243	−	0.656295i
$279$	0.451935	−	1.39091i	0.0270567	−	0.0832719i
$280$	0.229233	+	0.166548i	0.0136993	+	0.00995312i
$281$	−2.47557	−	1.79861i	−0.147680	−	0.107296i	0.511492	−	0.859288i	$-0.329093\pi$
$281$	−2.47557	−	1.79861i	−0.147680	−	0.107296i	−0.659172	+	0.751992i	$0.729093\pi$
$282$	5.88281	−	18.1054i	0.350316	−	1.07816i
$283$	−4.73968	−	14.5872i	−0.281745	−	0.867122i	−0.987355	−	0.158522i	$-0.949327\pi$
$283$	−4.73968	−	14.5872i	−0.281745	−	0.867122i	0.705611	−	0.708600i	$-0.250673\pi$
$284$	−4.78473	+	3.47631i	−0.283921	+	0.206281i
$285$	−0.243265			−0.0144097
$286$	−6.06436	+	12.8956i	−0.358593	+	0.762531i
$287$	−15.4075			−0.909479
$288$	−4.69328	+	3.40987i	−0.276554	+	0.200928i
$289$	2.43591	+	7.49696i	0.143289	+	0.440998i
$290$	−0.472045	+	1.45281i	−0.0277195	+	0.0853117i
$291$	6.84740	+	4.97493i	0.401402	+	0.291635i
$292$	−7.34034	−	5.33307i	−0.429561	−	0.312094i
$293$	6.17311	−	18.9989i	0.360637	−	1.10993i	−0.592032	−	0.805915i	$-0.701674\pi$
$293$	6.17311	−	18.9989i	0.360637	−	1.10993i	0.952668	−	0.304011i	$-0.0983261\pi$
$294$	4.83207	+	14.8716i	0.281812	+	0.867329i
$295$	1.58056	−	1.14835i	0.0920238	−	0.0668592i
$296$	1.06924			0.0621483
$297$	−20.0966	−	18.8627i	−1.16612	−	1.09453i
$298$	7.40115			0.428737
$299$	−3.47606	+	2.52550i	−0.201025	+	0.146054i
$300$	4.54121	+	13.9764i	0.262187	+	0.806929i
$301$	1.77965	−	5.47720i	0.102577	−	0.315701i
$302$	10.1704	+	7.38922i	0.585240	+	0.425202i
$303$	19.3275	+	14.0422i	1.11033	+	0.806705i
$304$	0.117595	−	0.361919i	0.00674452	−	0.0207575i
$305$	0.751946	+	2.31425i	0.0430563	+	0.132514i
$306$	23.4113	−	17.0093i	1.33834	−	0.972358i
$307$	12.8781			0.734993			0.367496	−	0.930025i	$-0.380215\pi$
$307$	12.8781			0.734993			0.367496	+	0.930025i	$0.380215\pi$
$308$	−3.17996	−	2.98472i	−0.181195	−	0.170070i
$309$	−9.31093			−0.529681
$310$	−0.0439476	+	0.0319298i	−0.00249605	+	0.00181349i
$311$	−7.96710	−	24.5202i	−0.451773	−	1.39041i	−0.874883	−	0.484335i	$-0.839062\pi$
$311$	−7.96710	−	24.5202i	−0.451773	−	1.39041i	0.423110	−	0.906078i	$-0.360938\pi$
$312$	−3.93897	+	12.1229i	−0.223000	+	0.686324i
$313$	−11.0599	−	8.03546i	−0.625141	−	0.454191i	0.229573	−	0.973292i	$-0.426267\pi$
$313$	−11.0599	−	8.03546i	−0.625141	−	0.454191i	−0.854713	+	0.519100i	$0.826267\pi$
$314$	6.83062	+	4.96274i	0.385474	+	0.280063i
$315$	−0.507950	+	1.56331i	−0.0286197	+	0.0880825i
$316$	−1.79610	−	5.52782i	−0.101038	−	0.310964i
$317$	12.6954	−	9.22375i	0.713045	−	0.518057i	−0.171110	−	0.985252i	$-0.554735\pi$
$317$	12.6954	−	9.22375i	0.713045	−	0.518057i	0.884155	+	0.467195i	$0.154735\pi$
$318$	−33.7694			−1.89369
$319$	10.0059	−	21.2770i	0.560221	−	1.19128i
$320$	0.215478			0.0120456
$321$	−2.02929	+	1.47437i	−0.113264	+	0.0822912i
$322$	−0.406350	−	1.25062i	−0.0226450	−	0.0696941i
$323$	−0.586593	+	1.80535i	−0.0326389	+	0.100452i
$324$	−5.86573	−	4.26170i	−0.325874	−	0.236761i
$325$	17.2189	+	12.5102i	0.955132	+	0.693944i
$326$	1.37967	−	4.24618i	0.0764128	−	0.235174i
$327$	14.0457	+	43.2284i	0.776732	+	2.39053i
$328$	−9.47925	+	6.88708i	−0.523404	+	0.380275i
$329$	8.43818			0.465212
$330$	0.397787	+	2.08251i	0.0218975	+	0.114639i
$331$	26.7979			1.47294			0.736472	−	0.676468i	$-0.236490\pi$
$331$	26.7979			1.47294			0.736472	+	0.676468i	$0.236490\pi$
$332$	5.63287	−	4.09252i	0.309144	−	0.224606i
$333$	1.91680	+	5.89930i	0.105040	+	0.323280i
$334$	−4.97457	+	15.3102i	−0.272197	+	0.837735i
$335$	−1.22879	−	0.892769i	−0.0671360	−	0.0487772i
$336$	−3.15607	−	2.29302i	−0.172178	−	0.125094i
$337$	1.53423	−	4.72189i	0.0835751	−	0.257218i	−0.900533	−	0.434787i	$-0.856824\pi$
$337$	1.53423	−	4.72189i	0.0835751	−	0.257218i	0.984108	+	0.177570i	$0.0568235\pi$
$338$	1.68758	+	5.19384i	0.0917922	+	0.282507i
$339$	17.2078	−	12.5022i	0.934597	−	0.679025i
$340$	−1.07486			−0.0582924
$341$	0.732604	−	0.402985i	0.0396727	−	0.0218229i
$342$	2.20762			0.119374
$343$	−13.0542	+	9.48441i	−0.704859	+	0.512110i
$344$	−1.35337	−	4.16525i	−0.0729689	−	0.224575i
$345$	−0.197540	+	0.607967i	−0.0106352	+	0.0327318i
$346$	10.8591	+	7.88959i	0.583788	+	0.424147i
$347$	7.83770	+	5.69442i	0.420750	+	0.305692i	0.777939	−	0.628339i	$-0.216265\pi$
$347$	7.83770	+	5.69442i	0.420750	+	0.305692i	−0.357190	+	0.934032i	$0.616265\pi$
$348$	6.49909	−	20.0022i	0.348388	−	1.07223i
$349$	−3.68390	−	11.3379i	−0.197194	−	0.606902i	−0.999944	−	0.0105858i	$-0.996630\pi$
$349$	−3.68390	−	11.3379i	−0.197194	−	0.606902i	0.802749	−	0.596316i	$-0.203370\pi$
$350$	−5.26979	+	3.82873i	−0.281682	+	0.204654i
$351$	−35.7064			−1.90587
$352$	−3.29057	−	0.414881i	−0.175388	−	0.0221132i
$353$	28.0838			1.49475			0.747374	−	0.664403i	$-0.231314\pi$
$353$	28.0838			1.49475			0.747374	+	0.664403i	$0.231314\pi$
$354$	−21.7611	+	15.8104i	−1.15659	+	0.840311i
$355$	0.393807	+	1.21201i	0.0209011	+	0.0643271i
$356$	−4.90700	+	15.1022i	−0.260070	+	0.800414i
$357$	15.7433	+	11.4382i	0.833224	+	0.605372i
$358$	6.50596	+	4.72686i	0.343851	+	0.249822i
$359$	−7.79162	+	23.9801i	−0.411226	+	1.26562i	0.504357	+	0.863495i	$0.331730\pi$
$359$	−7.79162	+	23.9801i	−0.411226	+	1.26562i	−0.915583	+	0.402129i	$0.868270\pi$
$360$	0.386281	+	1.18885i	0.0203588	+	0.0626579i
$361$	15.2542	−	11.0828i	0.802851	−	0.583305i
$362$	0.935277			0.0491571
$363$	−2.06496	−	32.5681i	−0.108382	−	1.70938i
$364$	−5.64997			−0.296139
$365$	−1.58168	+	1.14916i	−0.0827888	+	0.0601496i
$366$	−10.3528	−	31.8625i	−0.541147	−	1.66548i
$367$	−6.94340	+	21.3696i	−0.362442	+	1.11548i	0.589125	+	0.808042i	$0.299473\pi$
$367$	−6.94340	+	21.3696i	−0.362442	+	1.11548i	−0.951567	+	0.307441i	$0.900527\pi$
$368$	−0.809017	−	0.587785i	−0.0421729	−	0.0306404i
$369$	−54.9911	−	39.9534i	−2.86272	−	2.07989i
$370$	0.0711967	−	0.219121i	0.00370134	−	0.0113915i
$371$	−4.62542	−	14.2356i	−0.240140	−	0.739075i
$372$	0.605068	−	0.439608i	0.0313713	−	0.0227926i
$373$	32.5209			1.68387			0.841934	−	0.539581i	$-0.181417\pi$
$373$	32.5209			1.68387			0.841934	+	0.539581i	$0.181417\pi$
$374$	16.4142	+	2.06954i	0.848761	+	0.107013i
$375$	6.36286			0.328577
$376$	5.19146	−	3.77181i	0.267729	−	0.194516i
$377$	−9.41262	−	28.9691i	−0.484775	−	1.49198i
$378$	3.37689	−	10.3930i	0.173689	−	0.534559i
$379$	27.6543	+	20.0920i	1.42051	+	1.03206i	0.991688	+	0.128667i	$0.0410698\pi$
$379$	27.6543	+	20.0920i	1.42051	+	1.03206i	0.428818	+	0.903391i	$0.358930\pi$
$380$	−0.0663384	−	0.0481977i	−0.00340309	−	0.00247249i
$381$	−7.29341	+	22.4468i	−0.373653	+	1.14999i
$382$	−0.0692001	−	0.212976i	−0.00354059	−	0.0108968i
$383$	23.0520	−	16.7482i	1.17790	−	0.855794i	0.185967	−	0.982556i	$-0.440458\pi$
$383$	23.0520	−	16.7482i	1.17790	−	0.855794i	0.991933	+	0.126762i	$0.0404583\pi$
$384$	−2.96668			−0.151393
$385$	−0.823405	+	0.452932i	−0.0419646	+	0.0230836i
$386$	−19.5226			−0.993672
$387$	20.5547	−	14.9339i	1.04485	−	0.759132i
$388$	0.881615	+	2.71333i	0.0447572	+	0.137749i
$389$	−6.07048	+	18.6830i	−0.307786	+	0.947267i	0.670837	+	0.741604i	$0.265935\pi$
$389$	−6.07048	+	18.6830i	−0.307786	+	0.947267i	−0.978623	+	0.205662i	$0.934065\pi$
$390$	2.22208	+	1.61444i	0.112519	+	0.0817502i
$391$	4.03559	+	2.93203i	0.204089	+	0.148279i
$392$	−1.62878	+	5.01287i	−0.0822658	+	0.253188i
$393$	16.1745	+	49.7799i	0.815895	+	2.51107i
$394$	−2.88187	+	2.09380i	−0.145186	+	0.105484i
$395$	−1.25242			−0.0630161
$396$	−3.60991	−	18.8988i	−0.181405	−	0.949699i
$397$	−6.66705			−0.334610			−0.167305	−	0.985905i	$-0.553506\pi$
$397$	−6.66705			−0.334610			−0.167305	+	0.985905i	$0.553506\pi$
$398$	19.9772	−	14.5143i	1.00137	−	0.727534i
$399$	0.458750	+	1.41189i	0.0229662	+	0.0706828i
$400$	−1.53074	+	4.71112i	−0.0765369	+	0.235556i
$401$	7.37929	+	5.36137i	0.368504	+	0.267734i	0.756590	−	0.653889i	$-0.226864\pi$
$401$	7.37929	+	5.36137i	0.368504	+	0.267734i	−0.388086	+	0.921623i	$0.626864\pi$
$402$	16.9179	+	12.2916i	0.843789	+	0.613049i
$403$	0.334724	−	1.03017i	0.0166738	−	0.0513166i
$404$	2.48845	+	7.65865i	0.123805	+	0.381032i
$405$	−1.26393	+	0.918302i	−0.0628054	+	0.0456308i
$406$	9.32216			0.462651
$407$	−1.50914	+	3.20913i	−0.0748055	+	0.159070i
$408$	14.7986			0.732640
$409$	14.7590	−	10.7231i	0.729787	−	0.530222i	−0.159709	−	0.987164i	$-0.551056\pi$
$409$	14.7590	−	10.7231i	0.729787	−	0.530222i	0.889496	+	0.456943i	$0.151056\pi$
$410$	0.780190	+	2.40118i	0.0385309	+	0.118586i
$411$	8.09560	−	24.9157i	0.399327	−	1.22900i
$412$	−2.53910	−	1.84476i	−0.125092	−	0.0908850i
$413$	−9.64554	−	7.00790i	−0.474626	−	0.344836i
$414$	1.79267	−	5.51728i	0.0881051	−	0.271160i
$415$	−0.463614	−	1.42686i	−0.0227579	−	0.0700416i
$416$	−3.47606	+	2.52550i	−0.170428	+	0.123823i
$417$	34.1340			1.67155
$418$	0.920259	+	0.863758i	0.0450113	+	0.0422478i
$419$	−9.27139			−0.452937			−0.226469	−	0.974018i	$-0.572718\pi$
$419$	−9.27139			−0.452937			−0.226469	+	0.974018i	$0.572718\pi$
$420$	−0.680062	+	0.494094i	−0.0331836	+	0.0241093i
$421$	12.3555	+	38.0264i	0.602172	+	1.85329i	0.515173	+	0.857086i	$0.327728\pi$
$421$	12.3555	+	38.0264i	0.602172	+	1.85329i	0.0869991	+	0.996208i	$0.472272\pi$
$422$	1.22954	−	3.78412i	0.0598528	−	0.184208i
$423$	30.1167	+	21.8811i	1.46433	+	1.06390i
$424$	−9.20894	−	6.69069i	−0.447226	−	0.324928i
$425$	7.63572	−	23.5003i	0.370387	−	1.13993i
$426$	−5.42192	−	16.6870i	−0.262693	−	0.808485i
$427$	12.0137	−	8.72848i	0.581385	−	0.422401i
$428$	−0.845505			−0.0408690
$429$	−30.8251	−	28.9326i	−1.48825	−	1.39688i
$430$	−0.943707			−0.0455096
$431$	−16.9337	+	12.3030i	−0.815666	+	0.592616i	−0.915468	−	0.402391i	$-0.868179\pi$
$431$	−16.9337	+	12.3030i	−0.815666	+	0.592616i	0.0998015	+	0.995007i	$0.468179\pi$
$432$	−2.56803	−	7.90358i	−0.123554	−	0.380261i
$433$	−4.95205	+	15.2408i	−0.237980	+	0.732428i	0.758732	+	0.651403i	$0.225819\pi$
$433$	−4.95205	+	15.2408i	−0.237980	+	0.732428i	−0.996712	+	0.0810249i	$0.974181\pi$
$434$	0.268195	+	0.194855i	0.0128738	+	0.00935333i
$435$	−3.66632	−	2.66374i	−0.175787	−	0.127716i
$436$	−4.73449	+	14.5713i	−0.226741	+	0.697838i
$437$	0.117595	+	0.361919i	0.00562532	+	0.0173129i
$438$	21.7765	−	15.8215i	1.04052	−	0.755982i
$439$	−2.98766			−0.142593			−0.0712965	−	0.997455i	$-0.522714\pi$
$439$	−2.98766			−0.142593			−0.0712965	+	0.997455i	$0.522714\pi$
$440$	−0.304129	+	0.646716i	−0.0144988	+	0.0308310i
$441$	−30.5773			−1.45606
$442$	17.3395	−	12.5979i	0.824755	−	0.599220i
$443$	−8.62123	−	26.5334i	−0.409607	−	1.26064i	−0.916987	−	0.398918i	$-0.869386\pi$
$443$	−8.62123	−	26.5334i	−0.409607	−	1.26064i	0.507380	−	0.861723i	$-0.330614\pi$
$444$	−0.980232	+	3.01684i	−0.0465197	+	0.143173i
$445$	2.76817	+	2.01120i	0.131224	+	0.0953398i
$446$	3.99919	+	2.90558i	0.189367	+	0.137583i
$447$	−6.78505	+	20.8822i	−0.320922	+	0.987696i
$448$	−0.406350	−	1.25062i	−0.0191982	−	0.0590860i
$449$	33.9904	−	24.6955i	1.60411	−	1.16545i	0.725093	−	0.688651i	$-0.241797\pi$
$449$	33.9904	−	24.6955i	1.60411	−	1.16545i	0.879012	−	0.476800i	$-0.158203\pi$
$450$	−28.7367			−1.35466
$451$	−7.29111	−	38.1708i	−0.343325	−	1.79739i
$452$	7.16961			0.337230
$453$	−30.1723	+	21.9215i	−1.41762	+	1.02996i
$454$	−6.88289	−	21.1833i	−0.323030	−	0.994184i
$455$	−0.376210	+	1.15786i	−0.0176370	+	0.0542812i
$456$	0.913344	+	0.663583i	0.0427712	+	0.0310751i
$457$	−29.9223	−	21.7398i	−1.39970	−	1.01695i	−0.994720	−	0.102621i	$-0.967277\pi$
$457$	−29.9223	−	21.7398i	−1.39970	−	1.01695i	−0.404984	−	0.914324i	$-0.632723\pi$
$458$	5.09883	−	15.6926i	0.238253	−	0.733267i
$459$	12.8100	+	39.4251i	0.597920	+	1.84021i
$460$	−0.174325	+	0.126655i	−0.00812795	+	0.00590530i
$461$	29.7761			1.38681			0.693405	−	0.720548i	$-0.256110\pi$
$461$	29.7761			1.38681			0.693405	+	0.720548i	$0.256110\pi$
$462$	11.3366	−	6.23595i	0.527426	−	0.290123i
$463$	−15.3480			−0.713282			−0.356641	−	0.934241i	$-0.616078\pi$
$463$	−15.3480			−0.713282			−0.356641	+	0.934241i	$0.616078\pi$
$464$	5.73531	−	4.16695i	0.266255	−	0.193446i
$465$	−0.0498002	−	0.153269i	−0.00230943	−	0.00710769i
$466$	−0.344473	+	1.06018i	−0.0159574	+	0.0491119i
$467$	−31.5583	−	22.9284i	−1.46034	−	1.06100i	−0.983274	−	0.182134i	$-0.941699\pi$
$467$	−31.5583	−	22.9284i	−1.46034	−	1.06100i	−0.477068	−	0.878866i	$-0.658301\pi$
$468$	−20.1653	−	14.6510i	−0.932143	−	0.677242i
$469$	−2.86430	+	8.81540i	−0.132261	+	0.407057i
$470$	−0.427283	−	1.31504i	−0.0197091	−	0.0606584i
$471$	−20.2643	+	14.7229i	−0.933729	+	0.678394i
$472$	−9.06675			−0.417331
$473$	14.4114	+	1.81702i	0.662637	+	0.0835465i
$474$	17.2432			0.792009
$475$	1.52504	−	1.10801i	0.0699736	−	0.0508388i
$476$	2.02698	+	6.23840i	0.0929064	+	0.285936i
$477$	20.4058	−	62.8025i	0.934316	−	2.87553i
$478$	−24.3937	−	17.7230i	−1.11574	−	0.810633i
$479$	−23.7675	−	17.2681i	−1.08597	−	0.789001i	−0.107253	−	0.994232i	$-0.534206\pi$
$479$	−23.7675	−	17.2681i	−1.08597	−	0.789001i	−0.978714	+	0.205231i	$0.934206\pi$
$480$	−0.197540	+	0.607967i	−0.00901644	+	0.0277498i
$481$	1.41967	+	4.36929i	0.0647313	+	0.199222i
$482$	4.83074	−	3.50974i	0.220034	−	0.159864i
$483$	3.90111			0.177507
$484$	5.88957	−	9.29048i	0.267708	−	0.422295i
$485$	0.614750			0.0279144
$486$	−2.76779	+	2.01092i	−0.125550	+	0.0912171i
$487$	1.21712	+	3.74591i	0.0551530	+	0.169743i	0.974838	−	0.222912i	$-0.0715564\pi$
$487$	1.21712	+	3.74591i	0.0551530	+	0.169743i	−0.919686	+	0.392656i	$0.871556\pi$
$488$	3.48967	−	10.7401i	0.157970	−	0.486182i
$489$	10.7157	+	7.78543i	0.484582	+	0.352069i
$490$	0.918840	+	0.667576i	0.0415089	+	0.0301580i
$491$	−12.0398	+	37.0547i	−0.543349	+	1.67226i	0.181533	+	0.983385i	$0.441894\pi$
$491$	−12.0398	+	37.0547i	−0.543349	+	1.67226i	−0.724883	+	0.688872i	$0.758106\pi$
$492$	−10.7416	−	33.0593i	−0.484270	−	1.49043i
$493$	−28.6092	+	20.7858i	−1.28849	+	0.936146i
$494$	1.63506			0.0735650
$495$	−4.11332	−	0.518615i	−0.184880	−	0.0233100i
$496$	0.252101			0.0113197
$497$	6.29179	−	4.57126i	0.282225	−	0.205049i
$498$	6.38301	+	19.6449i	0.286030	+	0.880308i
$499$	−1.60379	+	4.93597i	−0.0717956	+	0.220964i	−0.980515	−	0.196443i	$-0.937061\pi$
$499$	−1.60379	+	4.93597i	−0.0717956	+	0.220964i	0.908720	+	0.417407i	$0.137061\pi$
$500$	1.73516	+	1.26066i	0.0775985	+	0.0563786i
$501$	−38.6369	−	28.0714i	−1.72617	−	1.25414i
$502$	−8.34252	+	25.6756i	−0.372345	+	1.14596i
$503$	2.73966	+	8.43180i	0.122155	+	0.375955i	0.993372	−	0.114943i	$-0.0366686\pi$
$503$	2.73966	+	8.43180i	0.122155	+	0.375955i	−0.871217	+	0.490898i	$0.836669\pi$
$504$	6.17155	−	4.48389i	0.274902	−	0.199728i
$505$	1.73519			0.0772151
$506$	2.90599	−	1.59850i	0.129187	−	0.0710622i
$507$	−16.2014			−0.719531
$508$	−6.43628	+	4.67623i	−0.285564	+	0.207474i
$509$	−7.69585	−	23.6854i	−0.341113	−	1.04984i	−0.963632	−	0.267232i	$-0.913891\pi$
$509$	−7.69585	−	23.6854i	−0.341113	−	1.04984i	0.622520	−	0.782604i	$-0.286109\pi$
$510$	0.985383	−	3.03270i	0.0436335	−	0.134290i
$511$	9.65236	+	7.01285i	0.426995	+	0.310230i
$512$	−0.809017	−	0.587785i	−0.0357538	−	0.0259767i
$513$	−0.977249	+	3.00766i	−0.0431466	+	0.132792i
$514$	−3.49286	−	10.7499i	−0.154063	−	0.474158i
$515$	−0.547119	+	0.397505i	−0.0241089	+	0.0175162i
$516$	12.9929			0.571981
$517$	3.99309	+	20.9048i	0.175616	+	0.919392i
$518$	−1.40602			−0.0617771
$519$	−32.2155	+	23.4059i	−1.41410	+	1.02741i
$520$	0.286097	+	0.880516i	0.0125462	+	0.0386132i
$521$	−13.0229	+	40.0803i	−0.570542	+	1.75595i	0.0803375	+	0.996768i	$0.474400\pi$
$521$	−13.0229	+	40.0803i	−0.570542	+	1.75595i	−0.650880	+	0.759181i	$0.725600\pi$
$522$	33.2718	+	24.1733i	1.45627	+	1.05804i
$523$	21.9302	+	15.9332i	0.958941	+	0.696711i	0.952905	−	0.303270i	$-0.0980785\pi$
$523$	21.9302	+	15.9332i	0.958941	+	0.696711i	0.00603643	+	0.999982i	$0.498079\pi$
$524$	−5.45204	+	16.7797i	−0.238174	+	0.733023i
$525$	−5.97158	−	18.3786i	−0.260621	−	0.802109i
$526$	−0.832516	+	0.604859i	−0.0362994	+	0.0263731i
$527$	−1.25755			−0.0547796
$528$	4.18723	−	8.90396i	0.182226	−	0.387495i
$529$	1.00000			0.0434783
$530$	−1.98432	+	1.44169i	−0.0861933	+	0.0626231i
$531$	−16.2537	−	50.0238i	−0.705352	−	2.17085i
$532$	−0.154634	+	0.475915i	−0.00670424	+	0.0206335i
$533$	−40.7289	−	29.5913i	−1.76417	−	1.28174i
$534$	−38.1121	−	27.6900i	−1.64927	−	1.19827i
$535$	−0.0562990	+	0.173270i	−0.00243402	+	0.00749114i
$536$	2.17821	+	6.70385i	0.0940845	+	0.289562i
$537$	−19.3011	+	14.0231i	−0.832905	+	0.605141i
$538$	−20.3608			−0.877815
$539$	−12.7463	−	11.9637i	−0.549023	−	0.515315i
$540$	−1.79069			−0.0770589
$541$	18.3180	−	13.3088i	0.787553	−	0.572191i	−0.119683	−	0.992812i	$-0.538188\pi$
$541$	18.3180	−	13.3088i	0.787553	−	0.572191i	0.907236	+	0.420621i	$0.138188\pi$
$542$	0.468139	+	1.44078i	0.0201083	+	0.0618870i
$543$	−0.857421	+	2.63887i	−0.0367955	+	0.113245i
$544$	4.03559	+	2.93203i	0.173024	+	0.125710i
$545$	2.67086	+	1.94049i	0.114407	+	0.0831216i
$546$	5.17965	−	15.9413i	0.221668	−	0.682225i
$547$	−6.56637	−	20.2092i	−0.280758	−	0.864083i	−0.987638	−	0.156750i	$-0.949898\pi$
$547$	−6.56637	−	20.2092i	−0.280758	−	0.864083i	0.706881	−	0.707333i	$-0.250102\pi$
$548$	7.14419	−	5.19056i	0.305185	−	0.221730i
$549$	65.5121			2.79599
$550$	−11.9791	−	11.2436i	−0.510789	−	0.479428i
$551$	−2.69777			−0.114929
$552$	2.40010	−	1.74377i	0.102155	−	0.0742199i
$553$	2.36182	+	7.26895i	0.100435	+	0.309107i
$554$	1.31354	−	4.04265i	0.0558069	−	0.171756i
$555$	0.552976	+	0.401760i	0.0234725	+	0.0170538i
$556$	9.30836	+	6.76292i	0.394762	+	0.286812i
$557$	10.3138	−	31.7427i	0.437011	−	1.34498i	−0.454000	−	0.891002i	$-0.650004\pi$
$557$	10.3138	−	31.7427i	0.437011	−	1.34498i	0.891012	−	0.453981i	$-0.149996\pi$
$558$	0.451935	+	1.39091i	0.0191320	+	0.0588821i
$559$	15.2237	−	11.0607i	0.643896	−	0.467818i
$560$	−0.283348			−0.0119736
$561$	−20.8870	+	44.4153i	−0.881851	+	1.87521i
$562$	3.05998			0.129077
$563$	4.57828	−	3.32632i	0.192952	−	0.140188i	−0.487115	−	0.873338i	$-0.661951\pi$
$563$	4.57828	−	3.32632i	0.192952	−	0.140188i	0.680067	+	0.733150i	$0.261951\pi$
$564$	5.88281	+	18.1054i	0.247711	+	0.762377i
$565$	0.477397	−	1.46928i	0.0200843	−	0.0618130i
$566$	12.4086	+	9.01541i	0.521574	+	0.378946i
$567$	7.71329	+	5.60403i	0.323928	+	0.235347i
$568$	1.82760	−	5.62478i	0.0766845	−	0.236011i
$569$	4.09642	+	12.6075i	0.171731	+	0.528533i	0.999469	−	0.0325812i	$-0.0103727\pi$
$569$	4.09642	+	12.6075i	0.171731	+	0.528533i	−0.827738	+	0.561114i	$0.810373\pi$
$570$	0.196805	−	0.142987i	0.00824326	−	0.00598908i
$571$	18.1974			0.761537			0.380769	−	0.924670i	$-0.375659\pi$
$571$	18.1974			0.761537			0.380769	+	0.924670i	$0.375659\pi$
$572$	−2.67366	−	13.9973i	−0.111791	−	0.585256i
$573$	0.664348			0.0277535
$574$	12.4650	−	9.05633i	0.520278	−	0.378004i
$575$	−1.53074	−	4.71112i	−0.0638362	−	0.196467i
$576$	1.79267	−	5.51728i	0.0746947	−	0.229887i
$577$	−2.26907	−	1.64858i	−0.0944627	−	0.0686312i	0.539551	−	0.841953i	$-0.318594\pi$
$577$	−2.26907	−	1.64858i	−0.0944627	−	0.0686312i	−0.634014	+	0.773322i	$0.718594\pi$
$578$	−6.37730	−	4.63338i	−0.265261	−	0.192723i
$579$	17.8974	−	55.0826i	0.743791	−	2.28915i
$580$	−0.472045	−	1.45281i	−0.0196006	−	0.0603245i
$581$	−7.40708	+	5.38156i	−0.307297	+	0.223265i
$582$	−8.46385			−0.350838
$583$	33.0785	−	18.1956i	1.36997	−	0.753584i
$584$	9.07316			0.375450
$585$	−4.34518	+	3.15696i	−0.179651	+	0.130524i
$586$	6.17311	+	18.9989i	0.255009	+	0.784836i
$587$	−0.370959	+	1.14169i	−0.0153111	+	0.0471227i	−0.958420	−	0.285361i	$-0.907887\pi$
$587$	−0.370959	+	1.14169i	−0.0153111	+	0.0471227i	0.943109	+	0.332484i	$0.107887\pi$
$588$	−12.6505	−	9.19115i	−0.521699	−	0.379037i
$589$	−0.0776137	−	0.0563896i	−0.00319802	−	0.00232349i
$590$	−0.603721	+	1.85806i	−0.0248548	+	0.0764952i
$591$	−3.26565	−	10.0506i	−0.134331	−	0.413428i
$592$	−0.865033	+	0.628483i	−0.0355526	+	0.0258305i
$593$	2.40666			0.0988297			0.0494148	−	0.998778i	$-0.484264\pi$
$593$	2.40666			0.0988297			0.0494148	+	0.998778i	$0.484264\pi$
$594$	27.3457	+	3.44779i	1.12201	+	0.141465i
$595$	1.41341			0.0579443
$596$	−5.98766	+	4.35029i	−0.245264	+	0.178195i
$597$	22.6376	+	69.6713i	0.926495	+	2.85146i
$598$	1.32774	−	4.08635i	0.0542951	−	0.167103i
$599$	−18.5655	−	13.4886i	−0.758566	−	0.551130i	0.139904	−	0.990165i	$-0.455320\pi$
$599$	−18.5655	−	13.4886i	−0.758566	−	0.551130i	−0.898470	+	0.439035i	$0.855320\pi$
$600$	−11.8891	−	8.63790i	−0.485368	−	0.352641i
$601$	−4.50607	+	13.8683i	−0.183806	+	0.565698i	−0.999926	−	0.0121854i	$-0.996121\pi$
$601$	−4.50607	+	13.8683i	−0.183806	+	0.565698i	0.816119	+	0.577883i	$0.196121\pi$
$602$	1.77965	+	5.47720i	0.0725331	+	0.223234i
$603$	−33.0822	+	24.0356i	−1.34721	+	0.978807i
$604$	−12.5713			−0.511518
$605$	−1.51175	−	1.82557i	−0.0614612	−	0.0742202i
$606$	−23.8901			−0.970467
$607$	−3.80645	+	2.76555i	−0.154499	+	0.112250i	−0.662349	−	0.749195i	$-0.730440\pi$
$607$	−3.80645	+	2.76555i	−0.154499	+	0.112250i	0.507850	+	0.861445i	$0.330440\pi$
$608$	0.117595	+	0.361919i	0.00476910	+	0.0146778i
$609$	−8.54614	+	26.3023i	−0.346307	+	1.06582i
$610$	−1.96862	−	1.43029i	−0.0797071	−	0.0579106i
$611$	22.3058	+	16.2061i	0.902397	+	0.655630i
$612$	−8.94233	+	27.5217i	−0.361472	+	1.11250i
$613$	10.1617	+	31.2745i	0.410427	+	1.26317i	0.916278	+	0.400544i	$0.131179\pi$
$613$	10.1617	+	31.2745i	0.410427	+	1.26317i	−0.505850	+	0.862621i	$0.668821\pi$
$614$	−10.4186	+	7.56956i	−0.420461	+	0.305483i
$615$	−7.49013			−0.302031
$616$	4.32702	+	0.545558i	0.174341	+	0.0219812i
$617$	29.1850			1.17494			0.587472	−	0.809244i	$-0.300123\pi$
$617$	29.1850			1.17494			0.587472	+	0.809244i	$0.300123\pi$
$618$	7.53270	−	5.47283i	0.303010	−	0.220149i
$619$	−7.35923	−	22.6494i	−0.295792	−	0.910355i	−0.982954	−	0.183851i	$-0.941144\pi$
$619$	−7.35923	−	22.6494i	−0.295792	−	0.910355i	0.687162	−	0.726504i	$-0.258856\pi$
$620$	0.0167865	−	0.0516635i	0.000674161	−	0.00207485i
$621$	6.72319	+	4.88468i	0.269792	+	0.196016i
$622$	20.8581	+	15.1543i	0.836335	+	0.607633i
$623$	6.45258	−	19.8590i	0.258517	−	0.795634i
$624$	−3.93897	−	12.1229i	−0.157685	−	0.485305i
$625$	−19.6637	+	14.2865i	−0.786549	+	0.571461i
$626$	13.6707			0.546393
$627$	−3.28073	+	1.80464i	−0.131020	+	0.0720704i
$628$	−8.44311			−0.336917
$629$	4.31501	−	3.13504i	0.172051	−	0.125002i
$630$	−0.507950	−	1.56331i	−0.0202372	−	0.0622837i
$631$	1.27167	−	3.91380i	0.0506244	−	0.155806i	−0.922548	−	0.385882i	$-0.873897\pi$
$631$	1.27167	−	3.91380i	0.0506244	−	0.155806i	0.973173	+	0.230076i	$0.0738973\pi$
$632$	4.70225	+	3.41638i	0.187045	+	0.135896i
$633$	9.54965	+	6.93823i	0.379565	+	0.275770i
$634$	−4.84921	+	14.9243i	−0.192587	+	0.592721i
$635$	0.529739	+	1.63037i	0.0210220	+	0.0646992i
$636$	27.3200	−	19.8491i	1.08331	−	0.787070i
$637$	−22.6469			−0.897303
$638$	4.41140	+	23.0948i	0.174649	+	0.914331i
$639$	34.3098			1.35728
$640$	−0.174325	+	0.126655i	−0.00689080	+	0.00500646i
$641$	6.49013	+	19.9746i	0.256345	+	0.788948i	0.993562	+	0.113292i	$0.0361395\pi$
$641$	6.49013	+	19.9746i	0.256345	+	0.788948i	−0.737217	+	0.675656i	$0.763860\pi$
$642$	0.775122	−	2.38558i	0.0305916	−	0.0941513i
$643$	−35.6384	−	25.8928i	−1.40544	−	1.02111i	−0.993965	−	0.109694i	$-0.965013\pi$
$643$	−35.6384	−	25.8928i	−1.40544	−	1.02111i	−0.411477	−	0.911420i	$-0.634987\pi$
$644$	1.06384	+	0.772923i	0.0419210	+	0.0304574i
$645$	0.865149	−	2.66265i	0.0340652	−	0.104842i
$646$	−0.586593	−	1.80535i	−0.0230792	−	0.0710305i
$647$	−29.4100	+	21.3676i	−1.15623	+	0.840048i	−0.989296	−	0.145921i	$-0.953385\pi$
$647$	−29.4100	+	21.3676i	−1.15623	+	0.840048i	−0.166930	+	0.985969i	$0.553385\pi$
$648$	7.25044			0.284824
$649$	12.7970	−	27.2122i	0.502325	−	1.06817i
$650$	−21.2837			−0.834816
$651$	−0.795649	+	0.578073i	−0.0311839	+	0.0226565i
$652$	1.37967	+	4.24618i	0.0540320	+	0.166293i
$653$	−12.6384	+	38.8971i	−0.494580	+	1.52216i	0.323029	+	0.946389i	$0.395299\pi$
$653$	−12.6384	+	38.8971i	−0.494580	+	1.52216i	−0.817610	+	0.575773i	$0.804701\pi$
$654$	−36.7722	−	26.7166i	−1.43791	−	1.04470i
$655$	3.07565	+	2.23459i	0.120175	+	0.0873126i
$656$	3.62075	−	11.1435i	0.141367	−	0.435081i
$657$	16.2652	+	50.0592i	0.634566	+	1.95299i
$658$	−6.82663	+	4.95984i	−0.266130	+	0.193355i
$659$	9.26565			0.360939			0.180469	−	0.983581i	$-0.442238\pi$
$659$	9.26565			0.360939			0.180469	+	0.983581i	$0.442238\pi$
$660$	−1.54589	−	1.45098i	−0.0601736	−	0.0564792i
$661$	3.72948			0.145060			0.0725299	−	0.997366i	$-0.476893\pi$
$661$	3.72948			0.145060			0.0725299	+	0.997366i	$0.476893\pi$
$662$	−21.6799	+	15.7514i	−0.842614	+	0.612195i
$663$	19.6486	+	60.4722i	0.763089	+	2.34855i
$664$	−2.15156	+	6.62183i	−0.0834969	+	0.256977i
$665$	0.0872333	+	0.0633787i	0.00338276	+	0.00245772i
$666$	−5.01824	−	3.64597i	−0.194453	−	0.141278i
$667$	−2.19069	+	6.74226i	−0.0848240	+	0.261061i
$668$	−4.97457	−	15.3102i	−0.192472	−	0.592368i
$669$	−11.8643	+	8.61993i	−0.458701	+	0.333266i
$670$	1.51887			0.0586790
$671$	27.3091	+	25.6324i	1.05426	+	0.989528i
$672$	3.90111			0.150489
$673$	−17.7180	+	12.8729i	−0.682978	+	0.496212i	−0.874344	−	0.485306i	$-0.838708\pi$
$673$	−17.7180	+	12.8729i	−0.682978	+	0.496212i	0.191367	+	0.981519i	$0.438708\pi$
$674$	1.53423	+	4.72189i	0.0590965	+	0.181880i
$675$	12.7209	−	39.1509i	0.489628	−	1.50692i
$676$	−4.41814	−	3.20997i	−0.169928	−	0.123460i
$677$	25.7915	+	18.7387i	0.991250	+	0.720185i	0.960194	−	0.279333i	$-0.0901132\pi$
$677$	25.7915	+	18.7387i	0.991250	+	0.720185i	0.0310553	+	0.999518i	$0.490113\pi$
$678$	−6.57278	+	20.2289i	−0.252426	+	0.776888i
$679$	−1.15930	−	3.56796i	−0.0444899	−	0.136926i
$680$	0.869579	−	0.631786i	0.0333468	−	0.0242279i
$681$	66.0784			2.53213
$682$	−0.355821	+	0.756636i	−0.0136251	+	0.0289731i
$683$	−43.2032			−1.65312			−0.826562	−	0.562846i	$-0.809706\pi$
$683$	−43.2032			−1.65312			−0.826562	+	0.562846i	$0.809706\pi$
$684$	−1.78600	+	1.29761i	−0.0682895	+	0.0496152i
$685$	−0.588004	−	1.80969i	−0.0224665	−	0.0691447i
$686$	4.98625	−	15.3461i	0.190376	−	0.585917i
$687$	39.6020	+	28.7726i	1.51091	+	1.09774i
$688$	3.54317	+	2.57427i	0.135082	+	0.0981430i
$689$	15.1134	−	46.5144i	0.575776	−	1.77206i
$690$	−0.197540	−	0.607967i	−0.00752023	−	0.0231449i
$691$	31.8361	−	23.1303i	1.21110	−	0.879918i	0.215773	−	0.976444i	$-0.430773\pi$
$691$	31.8361	−	23.1303i	1.21110	−	0.879918i	0.995330	+	0.0965258i	$0.0307730\pi$
$692$	−13.4226			−0.510249
$693$	4.74694	+	24.8514i	0.180321	+	0.944027i
$694$	−9.68792			−0.367749
$695$	2.00574	−	1.45726i	0.0760821	−	0.0552769i
$696$	6.49909	+	20.0022i	0.246348	+	0.758180i
$697$	−18.0613	+	55.5868i	−0.684119	+	2.10550i
$698$	9.64457	+	7.00719i	0.365052	+	0.265226i
$699$	−2.67548	−	1.94385i	−0.101196	−	0.0735232i
$700$	2.01288	−	6.19501i	0.0760797	−	0.234149i
$701$	3.61937	+	11.1393i	0.136702	+	0.420725i	0.995851	−	0.0910008i	$-0.0290066\pi$
$701$	3.61937	+	11.1393i	0.136702	+	0.420725i	−0.859149	+	0.511725i	$0.829007\pi$
$702$	28.8871	−	20.9877i	1.09027	−	0.792131i
$703$	0.406893			0.0153463
$704$	2.90599	−	1.59850i	0.109524	−	0.0602459i
$705$	4.10209			0.154494
$706$	−22.7202	+	16.5072i	−0.855088	+	0.621258i
$707$	−3.27224	−	10.0709i	−0.123065	−	0.378756i
$708$	8.31200	−	25.5817i	0.312384	−	0.961419i
$709$	−14.7778	−	10.7367i	−0.554993	−	0.403226i	0.274630	−	0.961550i	$-0.411445\pi$
$709$	−14.7778	−	10.7367i	−0.554993	−	0.403226i	−0.829623	+	0.558324i	$0.811445\pi$
$710$	−1.03100	−	0.749066i	−0.0386928	−	0.0281120i
$711$	−10.4196	+	32.0681i	−0.390764	+	1.20265i
$712$	−4.90700	−	15.1022i	−0.183898	−	0.565978i
$713$	−0.203954	+	0.148181i	−0.00763815	+	0.00554944i
$714$	−19.4598			−0.728264
$715$	−3.04651	−	0.384109i	−0.113933	−	0.0143649i
$716$	−8.04181			−0.300536
$717$	72.3683	−	52.5786i	2.70264	−	1.96359i
$718$	−7.79162	−	23.9801i	−0.290781	−	0.894931i
$719$	7.43379	−	22.8789i	0.277234	−	0.853238i	−0.711386	−	0.702801i	$-0.751932\pi$
$719$	7.43379	−	22.8789i	0.277234	−	0.853238i	0.988620	−	0.150436i	$-0.0480678\pi$
$720$	−1.01130	−	0.734750i	−0.0376888	−	0.0273825i
$721$	3.33885	+	2.42582i	0.124345	+	0.0903421i
$722$	−5.82657	+	17.9323i	−0.216843	+	0.667373i
$723$	5.47406	+	16.8474i	0.203583	+	0.626563i
$724$	−0.756655	+	0.549742i	−0.0281209	+	0.0204310i
$725$	35.1170			1.30421
$726$	20.8136	+	25.1344i	0.772467	+	0.932826i
$727$	−5.65718			−0.209813			−0.104907	−	0.994482i	$-0.533454\pi$
$727$	−5.65718			−0.209813			−0.104907	+	0.994482i	$0.533454\pi$
$728$	4.57092	−	3.32097i	0.169410	−	0.123083i
$729$	−9.85792	−	30.3395i	−0.365108	−	1.12369i
$730$	0.604148	−	1.85937i	0.0223605	−	0.0688186i
$731$	−17.6743	−	12.8411i	−0.653707	−	0.474946i
$732$	27.1039	+	19.6921i	1.00179	+	0.727842i
$733$	−8.10799	+	24.9538i	−0.299476	+	0.921691i	0.682206	+	0.731160i	$0.261021\pi$
$733$	−8.10799	+	24.9538i	−0.299476	+	0.921691i	−0.981681	+	0.190531i	$0.938979\pi$
$734$	−6.94340	−	21.3696i	−0.256285	−	0.788766i
$735$	−2.72591	+	1.98049i	−0.100547	+	0.0730514i
$736$	1.00000			0.0368605
$737$	−23.1947	−	2.92443i	−0.854390	−	0.107723i
$738$	67.9728			2.50211
$739$	−3.85160	+	2.79835i	−0.141683	+	0.102939i	−0.656369	−	0.754440i	$-0.727909\pi$
$739$	−3.85160	+	2.79835i	−0.141683	+	0.102939i	0.514686	+	0.857379i	$0.327909\pi$
$740$	0.0711967	+	0.219121i	0.00261724	+	0.00805504i
$741$	−1.49895	+	4.61330i	−0.0550654	+	0.169474i
$742$	12.1095	+	8.79808i	0.444554	+	0.322988i
$743$	−41.3554	−	30.0465i	−1.51718	−	1.10230i	−0.962862	−	0.269994i	$-0.912978\pi$
$743$	−41.3554	−	30.0465i	−1.51718	−	1.10230i	−0.554320	−	0.832303i	$-0.687022\pi$
$744$	−0.231115	+	0.711300i	−0.00847310	+	0.0260775i
$745$	0.492815	+	1.51673i	0.0180553	+	0.0555686i
$746$	−26.3099	+	19.1153i	−0.963276	+	0.699861i
$747$	−40.3916			−1.47785
$748$	−14.4958	+	7.97376i	−0.530021	+	0.291550i
$749$	1.11182			0.0406249
$750$	−5.14766	+	3.73999i	−0.187966	+	0.136565i
$751$	4.21920	+	12.9853i	0.153961	+	0.473842i	0.998054	−	0.0623540i	$-0.0198608\pi$
$751$	4.21920	+	12.9853i	0.153961	+	0.473842i	−0.844093	+	0.536196i	$0.819861\pi$
$752$	−1.98296	+	6.10292i	−0.0723111	+	0.222551i
$753$	−64.7953	−	47.0766i	−2.36127	−	1.71557i
$754$	24.6426	+	17.9039i	0.897429	+	0.652020i
$755$	−0.837074	+	2.57625i	−0.0304643	+	0.0937594i
$756$	3.37689	+	10.3930i	0.122816	+	0.377990i
$757$	39.3029	−	28.5552i	1.42849	−	1.03786i	0.438192	−	0.898881i	$-0.355619\pi$
$757$	39.3029	−	28.5552i	1.42849	−	1.03786i	0.990296	−	0.138976i	$-0.0443809\pi$
$758$	−34.1826			−1.24157
$759$	1.84607	+	9.66465i	0.0670082	+	0.350804i
$760$	0.0819988			0.00297441
$761$	−21.4731	+	15.6011i	−0.778401	+	0.565541i	−0.904499	−	0.426477i	$-0.859755\pi$
$761$	−21.4731	+	15.6011i	−0.778401	+	0.565541i	0.126098	+	0.992018i	$0.459755\pi$
$762$	−7.29341	−	22.4468i	−0.264213	−	0.813163i
$763$	6.22574	−	19.1609i	0.225387	−	0.693670i
$764$	0.181168	+	0.131626i	0.00655444	+	0.00476208i
$765$	5.04461	+	3.66513i	0.182388	+	0.132513i
$766$	−8.80506	+	27.0992i	−0.318140	+	0.979134i
$767$	−12.0382	−	37.0499i	−0.434676	−	1.33779i
$768$	2.40010	−	1.74377i	0.0866061	−	0.0629230i
$769$	−2.11401			−0.0762333			−0.0381167	−	0.999273i	$-0.512136\pi$
$769$	−2.11401			−0.0762333			−0.0381167	+	0.999273i	$0.512136\pi$
$770$	0.399922	−	0.850416i	0.0144122	−	0.0306468i
$771$	33.5328			1.20765
$772$	15.7941	−	11.4751i	0.568441	−	0.412997i
$773$	−15.5723	−	47.9267i	−0.560098	−	1.72380i	−0.682087	−	0.731271i	$-0.738927\pi$
$773$	−15.5723	−	47.9267i	−0.560098	−	1.72380i	0.121989	−	0.992531i	$-0.461073\pi$
$774$	−7.85120	+	24.1635i	−0.282206	+	0.868540i
$775$	1.01030	+	0.734027i	0.0362911	+	0.0263670i
$776$	−2.30810	−	1.67693i	−0.0828559	−	0.0601983i
$777$	1.28898	−	3.96707i	0.0462419	−	0.142318i
$778$	−6.07048	−	18.6830i	−0.217637	−	0.669819i
$779$	−3.60727	+	2.62084i	−0.129244	+	0.0939013i
$780$	−2.74664			−0.0983456
$781$	14.3022	+	13.4241i	0.511774	+	0.480353i
$782$	−4.98826			−0.178380
$783$	−47.6622	+	34.6286i	−1.70331	+	1.23753i
$784$	−1.62878	−	5.01287i	−0.0581707	−	0.179031i
$785$	−0.562195	+	1.73026i	−0.0200656	+	0.0617556i
$786$	−42.3453	−	30.7657i	−1.51041	−	1.09738i
$787$	24.7578	+	17.9876i	0.882519	+	0.641187i	0.933917	−	0.357491i	$-0.116368\pi$
$787$	24.7578	+	17.9876i	0.882519	+	0.641187i	−0.0513979	+	0.998678i	$0.516368\pi$
$788$	1.10077	−	3.38784i	0.0392135	−	0.120687i
$789$	−0.943385	−	2.90344i	−0.0335854	−	0.103365i
$790$	1.01323	−	0.736154i	0.0360491	−	0.0261912i
$791$	−9.42785			−0.335216
$792$	14.0289	+	13.1676i	0.498495	+	0.467889i
$793$	48.5212			1.72304
$794$	5.39376	−	3.91880i	0.191417	−	0.139073i
$795$	−2.24858	−	6.92041i	−0.0797488	−	0.245442i
$796$	−7.63060	+	23.4846i	−0.270459	+	0.832389i
$797$	33.7624	+	24.5298i	1.19592	+	0.868890i	0.993878	−	0.110486i	$-0.0352406\pi$
$797$	33.7624	+	24.5298i	1.19592	+	0.868890i	0.202047	+	0.979376i	$0.435241\pi$
$798$	−1.20102	−	0.872595i	−0.0425158	−	0.0308895i
$799$	9.89152	−	30.4430i	0.349937	−	1.07700i
$800$	−1.53074	−	4.71112i	−0.0541197	−	0.166563i
$801$	74.5264	−	54.1466i	2.63326	−	1.91318i
$802$	−9.12130			−0.322084
$803$	−12.8060	+	27.2314i	−0.451915	+	0.960976i
$804$	−20.9117			−0.737499
$805$	0.229233	−	0.166548i	0.00807940	−	0.00587003i
$806$	0.334724	+	1.03017i	0.0117901	+	0.0362863i
$807$	18.6659	−	57.4476i	0.657069	−	2.02225i
$808$	−6.51484	−	4.73331i	−0.229191	−	0.166517i
$809$	−29.1877	−	21.2061i	−1.02619	−	0.745567i	−0.0586435	−	0.998279i	$-0.518678\pi$
$809$	−29.1877	−	21.2061i	−1.02619	−	0.745567i	−0.967542	+	0.252712i	$0.918678\pi$
$810$	0.482780	−	1.48584i	0.0169631	−	0.0522072i
$811$	−6.19557	−	19.0680i	−0.217556	−	0.669568i	−0.998962	−	0.0455458i	$-0.985497\pi$
$811$	−6.19557	−	19.0680i	−0.217556	−	0.669568i	0.781406	−	0.624023i	$-0.214503\pi$
$812$	−7.54179	+	5.47943i	−0.264665	+	0.192290i
$813$	−4.49432			−0.157623
$814$	−0.665353	−	3.48329i	−0.0233206	−	0.122089i
$815$	0.962043			0.0336989
$816$	−11.9723	+	8.69840i	−0.419115	+	0.304505i
$817$	−0.515018	−	1.58506i	−0.0180182	−	0.0554544i
$818$	−5.63745	+	17.3503i	−0.197109	+	0.606639i
$819$	26.5169	+	19.2657i	0.926576	+	0.673197i
$820$	−2.04257	−	1.48401i	−0.0713295	−	0.0518239i
$821$	−3.93894	+	12.1228i	−0.137470	+	0.423089i	−0.995966	−	0.0897310i	$-0.971399\pi$
$821$	−3.93894	+	12.1228i	−0.137470	+	0.423089i	0.858496	+	0.512820i	$0.171399\pi$
$822$	8.09560	+	24.9157i	0.282367	+	0.869035i
$823$	−43.6265	+	31.6965i	−1.52073	+	1.10487i	−0.559599	+	0.828764i	$0.689045\pi$
$823$	−43.6265	+	31.6965i	−1.52073	+	1.10487i	−0.961127	+	0.276108i	$0.910955\pi$
$824$	3.13850			0.109335
$825$	42.7055	−	23.4911i	1.48681	−	0.817855i
$826$	11.9225			0.414838
$827$	−10.5975	+	7.69950i	−0.368509	+	0.267738i	−0.756593	−	0.653887i	$-0.773137\pi$
$827$	−10.5975	+	7.69950i	−0.368509	+	0.267738i	0.388083	+	0.921624i	$0.373137\pi$
$828$	1.79267	+	5.51728i	0.0622997	+	0.191739i
$829$	1.95548	−	6.01836i	0.0679167	−	0.209026i	−0.911338	−	0.411659i	$-0.864950\pi$
$829$	1.95548	−	6.01836i	0.0679167	−	0.209026i	0.979255	+	0.202632i	$0.0649496\pi$
$830$	1.21376	+	0.881846i	0.0421301	+	0.0306093i
$831$	10.2021	+	7.41225i	0.353907	+	0.257128i
$832$	1.32774	−	4.08635i	0.0460309	−	0.141669i
$833$	8.12478	+	25.0055i	0.281507	+	0.866390i
$834$	−27.6150	+	20.0634i	−0.956228	+	0.694740i
$835$	−3.46877			−0.120042
$836$	−1.25221	−	0.157881i	−0.0433086	−	0.00546042i
$837$	−2.09504			−0.0724153
$838$	7.50071	−	5.44959i	0.259108	−	0.188253i
$839$	−8.82847	−	27.1712i	−0.304793	−	0.938055i	−0.979755	−	0.200203i	$-0.935840\pi$
$839$	−8.82847	−	27.1712i	−0.304793	−	0.938055i	0.674962	−	0.737852i	$-0.264160\pi$
$840$	0.259761	−	0.799461i	0.00896259	−	0.0275840i
$841$	−17.1974	−	12.4947i	−0.593015	−	0.430851i
$842$	−32.3472	−	23.5016i	−1.11476	−	0.809919i
$843$	−2.80525	+	8.63368i	−0.0966180	+	0.297360i
$844$	1.22954	+	3.78412i	0.0423224	+	0.130255i
$845$	−0.952010	+	0.691676i	−0.0327501	+	0.0237944i
$846$	−37.2263			−1.27987
$847$	−7.74463	+	12.2167i	−0.266109	+	0.419772i
$848$	11.3829			0.390889
$849$	−36.8125	+	26.7459i	−1.26340	+	0.917916i
$850$	7.63572	+	23.5003i	0.261903	+	0.806055i
$851$	0.330413	−	1.01691i	0.0113264	−	0.0348591i
$852$	14.1948	+	10.3131i	0.486305	+	0.353321i
$853$	40.8407	+	29.6725i	1.39836	+	1.01597i	0.994889	+	0.100972i	$0.0321954\pi$
$853$	40.8407	+	29.6725i	1.39836	+	1.01597i	0.403468	+	0.914994i	$0.367805\pi$
$854$	−4.58883	+	14.1230i	−0.157027	+	0.483278i
$855$	0.146997	+	0.452411i	0.00502719	+	0.0154721i
$856$	0.684028	−	0.496975i	0.0233796	−	0.0169863i
$857$	−20.9431			−0.715404			−0.357702	−	0.933836i	$-0.616440\pi$
$857$	−20.9431			−0.715404			−0.357702	+	0.933836i	$0.616440\pi$
$858$	41.9442	+	5.28840i	1.43195	+	0.180543i
$859$	−27.6888			−0.944728			−0.472364	−	0.881404i	$-0.656599\pi$
$859$	−27.6888			−0.944728			−0.472364	+	0.881404i	$0.656599\pi$
$860$	0.763475	−	0.554697i	0.0260343	−	0.0189150i
$861$	14.1250	+	43.4722i	0.481377	+	1.48153i
$862$	6.46809	−	19.9067i	0.220304	−	0.678026i
$863$	−8.49401	−	6.17126i	−0.289139	−	0.210072i	0.433755	−	0.901031i	$-0.357188\pi$
$863$	−8.49401	−	6.17126i	−0.289139	−	0.210072i	−0.722894	+	0.690959i	$0.757188\pi$
$864$	6.72319	+	4.88468i	0.228727	+	0.166180i
$865$	−0.893758	+	2.75070i	−0.0303887	+	0.0935268i
$866$	−4.95205	−	15.2408i	−0.168278	−	0.517905i
$867$	18.9194	−	13.7458i	0.642537	−	0.466831i
$868$	−0.331507			−0.0112521
$869$	−16.8905	+	9.29098i	−0.572970	+	0.315175i
$870$	4.53182			0.153643
$871$	−24.5022	+	17.8019i	−0.830225	+	0.603194i
$872$	−4.73449	−	14.5713i	−0.160330	−	0.493446i
$873$	5.11444	−	15.7406i	0.173097	−	0.532739i
$874$	−0.307867	−	0.223678i	−0.0104138	−	0.00756604i
$875$	−2.28169	−	1.65774i	−0.0771351	−	0.0560419i
$876$	−8.31787	+	25.5998i	−0.281035	+	0.864936i
$877$	6.74512	+	20.7593i	0.227767	+	0.700993i	0.997999	+	0.0632301i	$0.0201402\pi$
$877$	6.74512	+	20.7593i	0.227767	+	0.700993i	−0.770232	+	0.637763i	$0.779860\pi$
$878$	2.41706	−	1.75610i	0.0815720	−	0.0592655i
$879$	−59.2643			−1.99893
$880$	−0.134085	−	0.701967i	−0.00452000	−	0.0236633i
$881$	−54.8603			−1.84829			−0.924145	−	0.382041i	$-0.875221\pi$
$881$	−54.8603			−1.84829			−0.924145	+	0.382041i	$0.875221\pi$
$882$	24.7375	−	17.9729i	0.832956	−	0.605178i
$883$	−7.12576	−	21.9308i	−0.239801	−	0.738032i	−0.996448	−	0.0842083i	$-0.973164\pi$
$883$	−7.12576	−	21.9308i	−0.239801	−	0.738032i	0.756647	−	0.653823i	$-0.226836\pi$
$884$	−6.62309	+	20.3838i	−0.222759	+	0.685581i
$885$	−4.68903	−	3.40678i	−0.157620	−	0.114518i
$886$	22.5707	+	16.3986i	0.758276	+	0.550920i
$887$	6.63192	−	20.4109i	0.222678	−	0.685332i	−0.775841	−	0.630928i	$-0.782674\pi$
$887$	6.63192	−	20.4109i	0.222678	−	0.685332i	0.998519	−	0.0544039i	$-0.0173259\pi$
$888$	−0.980232	−	3.01684i	−0.0328944	−	0.101239i
$889$	8.46354	−	6.14912i	0.283858	−	0.206235i
$890$	−3.42165			−0.114694
$891$	−10.2334	+	21.7609i	−0.342832	+	0.729017i
$892$	−4.94327			−0.165513
$893$	1.97558	−	1.43534i	0.0661102	−	0.0480319i
$894$	−6.78505	−	20.8822i	−0.226926	−	0.698407i
$895$	−0.535474	+	1.64802i	−0.0178989	+	0.0550872i
$896$	1.06384	+	0.772923i	0.0355403	+	0.0258215i
$897$	10.3124	+	7.49237i	0.344320	+	0.250163i
$898$	−12.9832	+	39.9581i	−0.433254	+	1.33342i
$899$	−0.552277	−	1.69973i	−0.0184195	−	0.0566893i
$900$	23.2485	−	16.8910i	0.774950	−	0.563034i
$901$	−56.7808			−1.89164
$902$	28.3348	+	26.5952i	0.943447	+	0.885523i
$903$	−17.0853			−0.568564
$904$	−5.80033	+	4.21419i	−0.192916	+	0.140162i
$905$	0.0622766	+	0.191668i	0.00207014	+	0.00637125i
$906$	11.5248	−	35.4697i	0.382886	−	1.17840i
$907$	−19.9083	−	14.4642i	−0.661044	−	0.480277i	0.205971	−	0.978558i	$-0.433965\pi$
$907$	−19.9083	−	14.4642i	−0.661044	−	0.480277i	−0.867015	+	0.498281i	$0.833965\pi$
$908$	18.0196	+	13.0920i	0.598002	+	0.434474i
$909$	14.4360	−	44.4295i	0.478812	−	1.47363i
$910$	−0.376210	−	1.15786i	−0.0124713	−	0.0383826i
$911$	−10.4309	+	7.57847i	−0.345590	+	0.251086i	−0.747017	−	0.664805i	$-0.768515\pi$
$911$	−10.4309	+	7.57847i	−0.345590	+	0.251086i	0.401426	+	0.915891i	$0.368515\pi$
$912$	−1.12896			−0.0373834
$913$	−16.8375	−	15.8037i	−0.557238	−	0.523026i
$914$	36.9860			1.22339
$915$	5.84028	−	4.24321i	0.193074	−	0.140276i
$916$	5.09883	+	15.6926i	0.168470	+	0.518498i
$917$	7.16930	−	22.0648i	0.236751	−	0.728645i
$918$	−33.5370	−	24.3661i	−1.10689	−	0.804200i
$919$	26.0290	+	18.9112i	0.858617	+	0.623822i	0.927508	−	0.373803i	$-0.121946\pi$
$919$	26.0290	+	18.9112i	0.858617	+	0.623822i	−0.0688916	+	0.997624i	$0.521946\pi$
$920$	0.0665862	−	0.204931i	0.00219528	−	0.00675639i
$921$	−11.8061	−	36.3354i	−0.389024	−	1.19729i
$922$	−24.0893	+	17.5019i	−0.793340	+	0.576395i
$923$	25.4114			0.836426
$924$	−5.50610	+	11.7085i	−0.181138	+	0.385181i
$925$	−5.29655			−0.174150
$926$	12.4168	−	9.02133i	0.408041	−	0.296459i
$927$	5.62630	+	17.3160i	0.184792	+	0.568732i
$928$	−2.19069	+	6.74226i	−0.0719130	+	0.221326i
$929$	−11.0987	−	8.06370i	−0.364137	−	0.264561i	0.390638	−	0.920544i	$-0.372254\pi$
$929$	−11.0987	−	8.06370i	−0.364137	−	0.264561i	−0.754776	+	0.655983i	$0.772254\pi$
$930$	0.130379	+	0.0947256i	0.00427528	+	0.00310617i
$931$	−0.619823	+	1.90762i	−0.0203139	+	0.0625197i
$932$	−0.344473	−	1.06018i	−0.0112836	−	0.0347273i
$933$	−61.8795	+	44.9581i	−2.02584	+	1.47186i
$934$	39.0082			1.27639
$935$	0.668850	+	3.50160i	0.0218737	+	0.114514i
$936$	24.9257			0.814723
$937$	−43.7891	+	31.8147i	−1.43053	+	1.03934i	−0.440611	+	0.897698i	$0.645238\pi$
$937$	−43.7891	+	31.8147i	−1.43053	+	1.03934i	−0.989918	+	0.141642i	$0.954762\pi$
$938$	−2.86430	−	8.81540i	−0.0935226	−	0.287833i
$939$	−12.5327	+	38.5718i	−0.408990	+	1.25874i
$940$	1.11864	+	0.812741i	0.0364861	+	0.0265087i
$941$	−4.10287	−	2.98091i	−0.133750	−	0.0971748i	0.518899	−	0.854836i	$-0.326342\pi$
$941$	−4.10287	−	2.98091i	−0.133750	−	0.0971748i	−0.652648	+	0.757661i	$0.726342\pi$
$942$	7.74027	−	23.8221i	0.252192	−	0.776166i
$943$	3.62075	+	11.1435i	0.117908	+	0.362883i
$944$	7.33515	−	5.32930i	0.238739	−	0.173454i
$945$	2.35471			0.0765987
$946$	−12.7271	+	7.00082i	−0.413793	+	0.227616i
$947$	−2.32430			−0.0755295			−0.0377648	−	0.999287i	$-0.512024\pi$
$947$	−2.32430			−0.0755295			−0.0377648	+	0.999287i	$0.512024\pi$
$948$	−13.9501	+	10.1353i	−0.453077	+	0.329180i
$949$	12.0468	+	37.0761i	0.391054	+	1.20354i
$950$	−0.582514	+	1.79279i	−0.0188992	+	0.0581659i
$951$	−37.6633	−	27.3640i	−1.22131	−	0.887337i
$952$	−5.30670	−	3.85554i	−0.171991	−	0.124959i
$953$	−5.16538	+	15.8974i	−0.167323	+	0.514968i	−0.999200	−	0.0399927i	$-0.987267\pi$
$953$	−5.16538	+	15.8974i	−0.167323	+	0.514968i	0.831877	+	0.554960i	$0.187267\pi$
$954$	20.4058	+	62.8025i	0.660661	+	2.03331i
$955$	0.0390377	−	0.0283626i	0.00126323	−	0.000917791i
$956$	30.1522			0.975193
$957$	−69.2057	−	8.72558i	−2.23710	−	0.282058i
$958$	29.3783			0.949170
$959$	−9.39443	+	6.82545i	−0.303362	+	0.220405i
$960$	−0.197540	−	0.607967i	−0.00637559	−	0.0196220i
$961$	−9.55989	+	29.4223i	−0.308383	+	0.949107i
$962$	−3.71674	−	2.70037i	−0.119832	−	0.0870633i
$963$	3.96819	+	2.88306i	0.127873	+	0.0929053i
$964$	−1.84518	+	5.67887i	−0.0594292	+	0.182904i
$965$	−1.29993	−	4.00078i	−0.0418463	−	0.128790i
$966$	−3.15607	+	2.29302i	−0.101545	+	0.0737766i
$967$	48.4286			1.55736			0.778680	−	0.627422i	$-0.215890\pi$
$967$	48.4286			1.55736			0.778680	+	0.627422i	$0.215890\pi$
$968$	0.696048	+	10.9780i	0.0223718	+	0.352845i
$969$	5.63153			0.180911
$970$	−0.497343	+	0.361341i	−0.0159687	+	0.0116020i
$971$	17.0533	+	52.4847i	0.547267	+	1.68432i	0.715537	+	0.698575i	$0.246182\pi$
$971$	17.0533	+	52.4847i	0.547267	+	1.68432i	−0.168270	+	0.985741i	$0.553818\pi$
$972$	1.05720	−	3.25373i	0.0339098	−	0.104364i
$973$	−12.2403	−	8.89306i	−0.392404	−	0.285099i
$974$	−3.18646	−	2.31510i	−0.102101	−	0.0741806i
$975$	19.5120	−	60.0516i	0.624883	−	1.92319i
$976$	3.48967	+	10.7401i	0.111702	+	0.343783i
$977$	15.7546	−	11.4464i	0.504036	−	0.366203i	−0.306521	−	0.951864i	$-0.599165\pi$
$977$	15.7546	−	11.4464i	0.504036	−	0.366203i	0.810556	+	0.585661i	$0.199165\pi$
$978$	−13.2454			−0.423540
$979$	52.2523	+	6.58806i	1.66999	+	0.210555i
$980$	−1.13575			−0.0362801
$981$	71.9064	−	52.2431i	2.29580	−	1.66799i
$982$	−12.0398	−	37.0547i	−0.384206	−	1.18246i
$983$	11.7525	−	36.1705i	0.374847	−	1.15366i	−0.568736	−	0.822520i	$-0.692567\pi$
$983$	11.7525	−	36.1705i	0.374847	−	1.15366i	0.943582	−	0.331139i	$-0.107433\pi$
$984$	28.1219	+	20.4318i	0.896494	+	0.651341i
$985$	−0.620978	−	0.451167i	−0.0197860	−	0.0143754i
$986$	10.9278	−	33.6322i	0.348011	−	1.07107i
$987$	−7.73575	−	23.8082i	−0.246232	−	0.757823i
$988$	−1.32279	+	0.961066i	−0.0420837	+	0.0305756i
$989$	−4.37961			−0.139263
$990$	3.63258	−	1.99818i	0.115451	−	0.0635064i
$991$	9.73602			0.309275			0.154637	−	0.987971i	$-0.450579\pi$
$991$	9.73602			0.309275			0.154637	+	0.987971i	$0.450579\pi$
$992$	−0.203954	+	0.148181i	−0.00647555	+	0.00470477i
$993$	−24.5671	−	75.6097i	−0.779613	−	2.39940i
$994$	−2.40325	+	7.39645i	−0.0762265	+	0.234601i
$995$	4.30463	+	3.12750i	0.136466	+	0.0991484i
$996$	−16.7109	−	12.1412i	−0.529506	−	0.384709i
$997$	11.9461	−	36.7663i	0.378336	−	1.16440i	−0.562864	−	0.826550i	$-0.690300\pi$
$997$	11.9461	−	36.7663i	0.378336	−	1.16440i	0.941200	−	0.337850i	$-0.109700\pi$
$998$	−1.60379	−	4.93597i	−0.0507672	−	0.156245i
$999$	7.18870	−	5.22290i	0.227440	−	0.165245i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	506.2.e.g.47.1	✓	16
11.2	odd	10		5566.2.a.bn.1.1		8
11.4	even	5	inner	506.2.e.g.323.1	yes	16
11.9	even	5		5566.2.a.bq.1.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
506.2.e.g.47.1	✓	16	1.1	even	1	trivial
506.2.e.g.323.1	yes	16	11.4	even	5	inner
5566.2.a.bn.1.1		8	11.2	odd	10
5566.2.a.bq.1.1		8	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)

\(f(q)\)	\(=\)	\(q+(-0.809017 + 0.587785i) q^{2} +(-0.916756 - 2.82148i) q^{3} +(0.309017 - 0.951057i) q^{4} +(-0.174325 - 0.126655i) q^{5} +(2.40010 + 1.74377i) q^{6} +(-0.406350 + 1.25062i) q^{7} +(0.309017 + 0.951057i) q^{8} +(-4.69328 + 3.40987i) q^{9} +O(q^{10})\)	\(q+(-0.809017 + 0.587785i) q^{2} +(-0.916756 - 2.82148i) q^{3} +(0.309017 - 0.951057i) q^{4} +(-0.174325 - 0.126655i) q^{5} +(2.40010 + 1.74377i) q^{6} +(-0.406350 + 1.25062i) q^{7} +(0.309017 + 0.951057i) q^{8} +(-4.69328 + 3.40987i) q^{9} +0.215478 q^{10} +(-3.29057 - 0.414881i) q^{11} -2.96668 q^{12} +(-3.47606 + 2.52550i) q^{13} +(-0.406350 - 1.25062i) q^{14} +(-0.197540 + 0.607967i) q^{15} +(-0.809017 - 0.587785i) q^{16} +(4.03559 + 2.93203i) q^{17} +(1.79267 - 5.51728i) q^{18} +(0.117595 + 0.361919i) q^{19} +(-0.174325 + 0.126655i) q^{20} +3.90111 q^{21} +(2.90599 - 1.59850i) q^{22} +1.00000 q^{23} +(2.40010 - 1.74377i) q^{24} +(-1.53074 - 4.71112i) q^{25} +(1.32774 - 4.08635i) q^{26} +(6.72319 + 4.88468i) q^{27} +(1.06384 + 0.772923i) q^{28} +(-2.19069 + 6.74226i) q^{29} +(-0.197540 - 0.607967i) q^{30} +(-0.203954 + 0.148181i) q^{31} +1.00000 q^{32} +(1.84607 + 9.66465i) q^{33} -4.98826 q^{34} +(0.229233 - 0.166548i) q^{35} +(1.79267 + 5.51728i) q^{36} +(0.330413 - 1.01691i) q^{37} +(-0.307867 - 0.223678i) q^{38} +(10.3124 + 7.49237i) q^{39} +(0.0665862 - 0.204931i) q^{40} +(3.62075 + 11.1435i) q^{41} +(-3.15607 + 2.29302i) q^{42} -4.37961 q^{43} +(-1.41142 + 3.00132i) q^{44} +1.25003 q^{45} +(-0.809017 + 0.587785i) q^{46} +(-1.98296 - 6.10292i) q^{47} +(-0.916756 + 2.82148i) q^{48} +(4.26420 + 3.09812i) q^{49} +(4.00752 + 2.91164i) q^{50} +(4.57302 - 14.0743i) q^{51} +(1.32774 + 4.08635i) q^{52} +(-9.20894 + 6.69069i) q^{53} -8.31032 q^{54} +(0.521083 + 0.489090i) q^{55} -1.31497 q^{56} +(0.913344 - 0.663583i) q^{57} +(-2.19069 - 6.74226i) q^{58} +(-2.80178 + 8.62299i) q^{59} +(0.517167 + 0.375744i) q^{60} +(-9.13608 - 6.63775i) q^{61} +(0.0779036 - 0.239763i) q^{62} +(-2.35732 - 7.25509i) q^{63} +(-0.809017 + 0.587785i) q^{64} +0.925830 q^{65} +(-7.17424 - 6.73377i) q^{66} +7.04885 q^{67} +(4.03559 - 2.93203i) q^{68} +(-0.916756 - 2.82148i) q^{69} +(-0.0875592 + 0.269480i) q^{70} +(-4.78473 - 3.47631i) q^{71} +(-4.69328 - 3.40987i) q^{72} +(2.80376 - 8.62909i) q^{73} +(0.330413 + 1.01691i) q^{74} +(-11.8891 + 8.63790i) q^{75} +0.380544 q^{76} +(1.85598 - 3.94665i) q^{77} -12.7468 q^{78} +(4.70225 - 3.41638i) q^{79} +(0.0665862 + 0.204931i) q^{80} +(2.24051 - 6.89558i) q^{81} +(-9.47925 - 6.88708i) q^{82} +(5.63287 + 4.09252i) q^{83} +(1.20551 - 3.71018i) q^{84} +(-0.332150 - 1.02225i) q^{85} +(3.54317 - 2.57427i) q^{86} +21.0315 q^{87} +(-0.622268 - 3.25773i) q^{88} -15.8794 q^{89} +(-1.01130 + 0.734750i) q^{90} +(-1.74594 - 5.37344i) q^{91} +(0.309017 - 0.951057i) q^{92} +(0.605068 + 0.439608i) q^{93} +(5.19146 + 3.77181i) q^{94} +(0.0253390 - 0.0779855i) q^{95} +(-0.916756 - 2.82148i) q^{96} +(-2.30810 + 1.67693i) q^{97} -5.27084 q^{98} +(16.8583 - 9.27327i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 4 q^{2} + 5 q^{3} - 4 q^{4} + 7 q^{5} + 8 q^{7} - 4 q^{8} - 15 q^{9}+O(q^{10}) \) 16 * q - 4 * q^2 + 5 * q^3 - 4 * q^4 + 7 * q^5 + 8 * q^7 - 4 * q^8 - 15 * q^9	\( 16 q - 4 q^{2} + 5 q^{3} - 4 q^{4} + 7 q^{5} + 8 q^{7} - 4 q^{8} - 15 q^{9} - 18 q^{10} - 7 q^{11} - 10 q^{12} + 9 q^{13} + 8 q^{14} - 26 q^{15} - 4 q^{16} + 2 q^{17} + 10 q^{18} + 2 q^{19} + 7 q^{20} + 30 q^{21} + 8 q^{22} + 16 q^{23} + q^{25} - q^{26} + 14 q^{27} - 2 q^{28} + 6 q^{29} - 26 q^{30} - 15 q^{31} + 16 q^{32} - 35 q^{33} + 2 q^{34} + 11 q^{35} + 10 q^{36} - 19 q^{37} + 2 q^{38} + 40 q^{39} + 2 q^{40} - 4 q^{43} - 2 q^{44} - 48 q^{45} - 4 q^{46} + 23 q^{47} + 5 q^{48} + 28 q^{49} + 6 q^{50} + 32 q^{51} - q^{52} - 40 q^{53} - 16 q^{54} - 9 q^{55} - 12 q^{56} + 8 q^{57} + 6 q^{58} - 20 q^{59} + 24 q^{60} + 3 q^{61} + 25 q^{62} + 10 q^{63} - 4 q^{64} + 38 q^{65} + 10 q^{66} + 12 q^{67} + 2 q^{68} + 5 q^{69} - 24 q^{70} + 25 q^{71} - 15 q^{72} + 5 q^{73} - 19 q^{74} - 73 q^{75} - 8 q^{76} - 48 q^{77} - 60 q^{78} + 34 q^{79} + 2 q^{80} - 25 q^{81} - 5 q^{82} + 19 q^{83} - 15 q^{84} + 10 q^{85} + 21 q^{86} + 22 q^{87} + 3 q^{88} - 74 q^{89} - 3 q^{90} + 15 q^{91} - 4 q^{92} + 63 q^{93} + 23 q^{94} - 22 q^{95} + 5 q^{96} - 48 q^{97} + 8 q^{98} - 6 q^{99}+O(q^{100}) \) 16 * q - 4 * q^2 + 5 * q^3 - 4 * q^4 + 7 * q^5 + 8 * q^7 - 4 * q^8 - 15 * q^9 - 18 * q^10 - 7 * q^11 - 10 * q^12 + 9 * q^13 + 8 * q^14 - 26 * q^15 - 4 * q^16 + 2 * q^17 + 10 * q^18 + 2 * q^19 + 7 * q^20 + 30 * q^21 + 8 * q^22 + 16 * q^23 + q^25 - q^26 + 14 * q^27 - 2 * q^28 + 6 * q^29 - 26 * q^30 - 15 * q^31 + 16 * q^32 - 35 * q^33 + 2 * q^34 + 11 * q^35 + 10 * q^36 - 19 * q^37 + 2 * q^38 + 40 * q^39 + 2 * q^40 - 4 * q^43 - 2 * q^44 - 48 * q^45 - 4 * q^46 + 23 * q^47 + 5 * q^48 + 28 * q^49 + 6 * q^50 + 32 * q^51 - q^52 - 40 * q^53 - 16 * q^54 - 9 * q^55 - 12 * q^56 + 8 * q^57 + 6 * q^58 - 20 * q^59 + 24 * q^60 + 3 * q^61 + 25 * q^62 + 10 * q^63 - 4 * q^64 + 38 * q^65 + 10 * q^66 + 12 * q^67 + 2 * q^68 + 5 * q^69 - 24 * q^70 + 25 * q^71 - 15 * q^72 + 5 * q^73 - 19 * q^74 - 73 * q^75 - 8 * q^76 - 48 * q^77 - 60 * q^78 + 34 * q^79 + 2 * q^80 - 25 * q^81 - 5 * q^82 + 19 * q^83 - 15 * q^84 + 10 * q^85 + 21 * q^86 + 22 * q^87 + 3 * q^88 - 74 * q^89 - 3 * q^90 + 15 * q^91 - 4 * q^92 + 63 * q^93 + 23 * q^94 - 22 * q^95 + 5 * q^96 - 48 * q^97 + 8 * q^98 - 6 * q^99

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