LMFDB - Embedded newform 420.2.l.f.239.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [420,2,Mod(239,420)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(420, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("420.239");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 420 = 2^{2} \cdot 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	420.l (of order $2$, degree $1$, 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:	$3.35371688489$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	8.0.386672896.3
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{6} - 2x^{5} + 2x^{4} - 4x^{3} - 4x^{2} + 16 $ x^8 - x^6 - 2x^5 + 2x^4 - 4x^3 - 4x^2 + 16
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			239.3
Root			$0.621372 - 1.27039i$ of defining polynomial
Character	$\chi$	$=$	420.239
Dual form			420.2.l.f.239.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.621372 - 1.27039i) q^{2} +(1.72779 + 0.121372i) q^{3} +(-1.22779 + 1.57877i) q^{4} +(1.00000 - 2.00000i) q^{5} +(-0.919412 - 2.27039i) q^{6} +1.00000 q^{7} +(2.76858 + 0.578773i) q^{8} +(2.97054 + 0.419412i) q^{9} +O(q^{10})$	\(q+(-0.621372 - 1.27039i) q^{2} +(1.72779 + 0.121372i) q^{3} +(-1.22779 + 1.57877i) q^{4} +(1.00000 - 2.00000i) q^{5} +(-0.919412 - 2.27039i) q^{6} +1.00000 q^{7} +(2.76858 + 0.578773i) q^{8} +(2.97054 + 0.419412i) q^{9} +(-3.16216 - 0.0276478i) q^{10} +3.45559 q^{11} +(-2.31299 + 2.57877i) q^{12} +4.83882i q^{13} +(-0.621372 - 1.27039i) q^{14} +(1.97054 - 3.33421i) q^{15} +(-0.985049 - 3.87681i) q^{16} -5.94108 q^{17} +(-1.31299 - 4.03436i) q^{18} -1.08157i q^{19} +(1.92975 + 4.03436i) q^{20} +(1.72779 + 0.121372i) q^{21} +(-2.14721 - 4.38995i) q^{22} +0.596080i q^{23} +(4.71328 + 1.33603i) q^{24} +(-3.00000 - 4.00000i) q^{25} +(6.14721 - 3.00671i) q^{26} +(5.08157 + 1.08520i) q^{27} +(-1.22779 + 1.57877i) q^{28} -4.83882i q^{29} +(-5.46020 - 0.431568i) q^{30} -9.56706i q^{31} +(-4.31299 + 3.66034i) q^{32} +(5.97054 + 0.419412i) q^{33} +(3.69162 + 7.54750i) q^{34} +(1.00000 - 2.00000i) q^{35} +(-4.30936 + 4.17485i) q^{36} +2.91117i q^{37} +(-1.37402 + 0.672057i) q^{38} +(-0.587299 + 8.36049i) q^{39} +(3.92612 - 4.95838i) q^{40} +6.91117i q^{41} +(-0.919412 - 2.27039i) q^{42} +7.39666 q^{43} +(-4.24274 + 5.45559i) q^{44} +(3.80936 - 5.52166i) q^{45} +(0.757255 - 0.370388i) q^{46} -0.242745i q^{47} +(-1.23142 - 6.81789i) q^{48} +1.00000 q^{49} +(-3.21745 + 6.29667i) q^{50} +(-10.2649 - 0.721082i) q^{51} +(-7.63941 - 5.94108i) q^{52} -11.8223 q^{53} +(-1.77892 - 7.12990i) q^{54} +(3.45559 - 6.91117i) q^{55} +(2.76858 + 0.578773i) q^{56} +(0.131272 - 1.86873i) q^{57} +(-6.14721 + 3.00671i) q^{58} +3.25197 q^{59} +(2.84455 + 7.20476i) q^{60} -12.6486 q^{61} +(-12.1539 + 5.94470i) q^{62} +(2.97054 + 0.419412i) q^{63} +(7.33004 + 3.20476i) q^{64} +(9.67765 + 4.83882i) q^{65} +(-3.17711 - 7.84554i) q^{66} -5.71901 q^{67} +(7.29441 - 9.37961i) q^{68} +(-0.0723476 + 1.02990i) q^{69} +(-3.16216 - 0.0276478i) q^{70} -8.00000 q^{71} +(7.98142 + 2.88044i) q^{72} +8.00000i q^{73} +(3.69833 - 1.80892i) q^{74} +(-4.69789 - 7.27529i) q^{75} +(1.70755 + 1.32794i) q^{76} +3.45559 q^{77} +(10.9860 - 4.44887i) q^{78} +0.949416i q^{79} +(-8.73867 - 1.90672i) q^{80} +(8.64819 + 2.49176i) q^{81} +(8.77990 - 4.29441i) q^{82} +16.9637i q^{83} +(-2.31299 + 2.57877i) q^{84} +(-5.94108 + 11.8822i) q^{85} +(-4.59608 - 9.39666i) q^{86} +(0.587299 - 8.36049i) q^{87} +(9.56706 + 2.00000i) q^{88} +5.23352i q^{89} +(-9.38171 - 1.40838i) q^{90} +4.83882i q^{91} +(-0.941075 - 0.731863i) q^{92} +(1.16118 - 16.5299i) q^{93} +(-0.308381 + 0.150835i) q^{94} +(-2.16314 - 1.08157i) q^{95} +(-7.89622 + 5.80084i) q^{96} -3.30587i q^{97} +(-0.621372 - 1.27039i) q^{98} +(10.2649 + 1.44932i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 2 q^{3} + 2 q^{4} + 8 q^{5} + 4 q^{6} + 8 q^{7} - 6 q^{8} + 2 q^{9}+O(q^{10}) $ 8 * q + 2 * q^3 + 2 * q^4 + 8 * q^5 + 4 * q^6 + 8 * q^7 - 6 * q^8 + 2 * q^9	$ 8 q + 2 q^{3} + 2 q^{4} + 8 q^{5} + 4 q^{6} + 8 q^{7} - 6 q^{8} + 2 q^{9} - 4 q^{10} + 4 q^{11} - 14 q^{12} - 6 q^{15} - 6 q^{16} - 4 q^{17} - 6 q^{18} + 10 q^{20} + 2 q^{21} + 6 q^{22} + 6 q^{24} - 24 q^{25} + 26 q^{26} + 8 q^{27} + 2 q^{28} - 16 q^{30} - 30 q^{32} + 26 q^{33} + 30 q^{34} + 8 q^{35} + 10 q^{36} - 20 q^{38} + 18 q^{39} - 14 q^{40} + 4 q^{42} - 8 q^{43} - 24 q^{44} - 14 q^{45} + 16 q^{46} - 38 q^{48} + 8 q^{49} - 8 q^{50} - 14 q^{51} + 16 q^{52} + 8 q^{54} + 4 q^{55} - 6 q^{56} + 20 q^{57} - 26 q^{58} + 8 q^{59} + 10 q^{60} - 16 q^{61} - 40 q^{62} + 2 q^{63} + 26 q^{64} + 32 q^{65} - 6 q^{66} - 24 q^{67} + 12 q^{68} + 24 q^{69} - 4 q^{70} - 64 q^{71} + 22 q^{72} - 4 q^{74} - 22 q^{75} - 28 q^{76} + 4 q^{77} + 42 q^{78} - 38 q^{80} + 2 q^{81} + 4 q^{82} - 14 q^{84} - 4 q^{85} - 24 q^{86} - 18 q^{87} + 24 q^{88} - 6 q^{90} + 36 q^{92} + 32 q^{93} - 2 q^{94} + 48 q^{95} - 14 q^{96} + 14 q^{99}+O(q^{100}) $ 8 * q + 2 * q^3 + 2 * q^4 + 8 * q^5 + 4 * q^6 + 8 * q^7 - 6 * q^8 + 2 * q^9 - 4 * q^10 + 4 * q^11 - 14 * q^12 - 6 * q^15 - 6 * q^16 - 4 * q^17 - 6 * q^18 + 10 * q^20 + 2 * q^21 + 6 * q^22 + 6 * q^24 - 24 * q^25 + 26 * q^26 + 8 * q^27 + 2 * q^28 - 16 * q^30 - 30 * q^32 + 26 * q^33 + 30 * q^34 + 8 * q^35 + 10 * q^36 - 20 * q^38 + 18 * q^39 - 14 * q^40 + 4 * q^42 - 8 * q^43 - 24 * q^44 - 14 * q^45 + 16 * q^46 - 38 * q^48 + 8 * q^49 - 8 * q^50 - 14 * q^51 + 16 * q^52 + 8 * q^54 + 4 * q^55 - 6 * q^56 + 20 * q^57 - 26 * q^58 + 8 * q^59 + 10 * q^60 - 16 * q^61 - 40 * q^62 + 2 * q^63 + 26 * q^64 + 32 * q^65 - 6 * q^66 - 24 * q^67 + 12 * q^68 + 24 * q^69 - 4 * q^70 - 64 * q^71 + 22 * q^72 - 4 * q^74 - 22 * q^75 - 28 * q^76 + 4 * q^77 + 42 * q^78 - 38 * q^80 + 2 * q^81 + 4 * q^82 - 14 * q^84 - 4 * q^85 - 24 * q^86 - 18 * q^87 + 24 * q^88 - 6 * q^90 + 36 * q^92 + 32 * q^93 - 2 * q^94 + 48 * q^95 - 14 * q^96 + 14 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/420\mathbb{Z}\right)^\times$.

$n$	$211$	$241$	$281$	$337$
$\chi(n)$	$-1$	$1$	$-1$	$-1$

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 $

$2$	−0.621372	−	1.27039i	−0.439377	−	0.898303i
$2$	−0.621372	−	1.27039i	−0.439377	−	0.898303i
$3$	1.72779	+	0.121372i	0.997542	+	0.0700743i
$3$	1.72779	+	0.121372i	0.997542	+	0.0700743i
$4$	−1.22779	+	1.57877i	−0.613897	+	0.789387i
$5$	1.00000	−	2.00000i	0.447214	−	0.894427i
$5$	1.00000	−	2.00000i	0.447214	−	0.894427i
$6$	−0.919412	−	2.27039i	−0.375348	−	0.926884i
$7$	1.00000			0.377964
$7$	1.00000			0.377964
$8$	2.76858	+	0.578773i	0.978840	+	0.204627i
$9$	2.97054	+	0.419412i	0.990179	+	0.139804i
$10$	−3.16216	−	0.0276478i	−0.999962	−	0.00874299i
$11$	3.45559			1.04190			0.520949	−	0.853588i	$-0.325578\pi$
$11$	3.45559			1.04190			0.520949	+	0.853588i	$0.325578\pi$
$12$	−2.31299	+	2.57877i	−0.667703	+	0.744428i
$13$			4.83882i			1.34205i	0.741435	+	0.671024i	$0.234145\pi$
$13$			4.83882i			1.34205i	−0.741435	+	0.671024i	$0.765855\pi$
$14$	−0.621372	−	1.27039i	−0.166069	−	0.339527i
$15$	1.97054	−	3.33421i	0.508791	−	0.860890i
$16$	−0.985049	−	3.87681i	−0.246262	−	0.969203i
$17$	−5.94108			−1.44092			−0.720461	−	0.693495i	$-0.756070\pi$
$17$	−5.94108			−1.44092			−0.720461	+	0.693495i	$0.756070\pi$
$18$	−1.31299	−	4.03436i	−0.309475	−	0.950908i
$19$		−	1.08157i		−	0.248129i	−0.992274	−	0.124064i	$-0.960407\pi$
$19$		−	1.08157i		−	0.248129i	0.992274	−	0.124064i	$-0.0395930\pi$
$20$	1.92975	+	4.03436i	0.431506	+	0.902110i
$21$	1.72779	+	0.121372i	0.377035	+	0.0264856i
$22$	−2.14721	−	4.38995i	−0.457786	−	0.935940i
$23$			0.596080i			0.124291i	0.998067	+	0.0621456i	$0.0197943\pi$
$23$			0.596080i			0.124291i	−0.998067	+	0.0621456i	$0.980206\pi$
$24$	4.71328	+	1.33603i	0.962095	+	0.272716i
$25$	−3.00000	−	4.00000i	−0.600000	−	0.800000i
$26$	6.14721	−	3.00671i	1.20557	−	0.589665i
$27$	5.08157	+	1.08520i	0.977948	+	0.208847i
$28$	−1.22779	+	1.57877i	−0.232031	+	0.298360i
$29$		−	4.83882i		−	0.898547i	−0.893394	−	0.449274i	$-0.851683\pi$
$29$		−	4.83882i		−	0.898547i	0.893394	−	0.449274i	$-0.148317\pi$
$30$	−5.46020	−	0.431568i	−0.996891	−	0.0787931i
$31$		−	9.56706i		−	1.71829i	−0.511729	−	0.859147i	$-0.670995\pi$
$31$		−	9.56706i		−	1.71829i	0.511729	−	0.859147i	$-0.329005\pi$
$32$	−4.31299	+	3.66034i	−0.762436	+	0.647063i
$33$	5.97054	+	0.419412i	1.03934	+	0.0730103i
$34$	3.69162	+	7.54750i	0.633107	+	1.29438i
$35$	1.00000	−	2.00000i	0.169031	−	0.338062i
$36$	−4.30936	+	4.17485i	−0.718227	+	0.695809i
$37$			2.91117i			0.478594i	0.970946	+	0.239297i	$0.0769169\pi$
$37$			2.91117i			0.478594i	−0.970946	+	0.239297i	$0.923083\pi$
$38$	−1.37402	+	0.672057i	−0.222895	+	0.109022i
$39$	−0.587299	+	8.36049i	−0.0940431	+	1.33875i
$40$	3.92612	−	4.95838i	0.620775	−	0.783989i
$41$			6.91117i			1.07934i	0.841875	+	0.539672i	$0.181452\pi$
$41$			6.91117i			1.07934i	−0.841875	+	0.539672i	$0.818548\pi$
$42$	−0.919412	−	2.27039i	−0.141868	−	0.350329i
$43$	7.39666			1.12798			0.563990	−	0.825782i	$-0.309266\pi$
$43$	7.39666			1.12798			0.563990	+	0.825782i	$0.309266\pi$
$44$	−4.24274	+	5.45559i	−0.639618	+	0.822461i
$45$	3.80936	−	5.52166i	0.567866	−	0.823121i
$46$	0.757255	−	0.370388i	0.111651	−	0.0546107i
$47$		−	0.242745i		−	0.0354079i	−0.999843	−	0.0177040i	$-0.994364\pi$
$47$		−	0.242745i		−	0.0354079i	0.999843	−	0.0177040i	$-0.00563564\pi$
$48$	−1.23142	−	6.81789i	−0.177741	−	0.984077i
$49$	1.00000			0.142857
$50$	−3.21745	+	6.29667i	−0.455016	+	0.890483i
$51$	−10.2649	−	0.721082i	−1.43738	−	0.100972i
$52$	−7.63941	−	5.94108i	−1.05939	−	0.823879i
$53$	−11.8223			−1.62392			−0.811962	−	0.583710i	$-0.801600\pi$
$53$	−11.8223			−1.62392			−0.811962	+	0.583710i	$0.801600\pi$
$54$	−1.77892	−	7.12990i	−0.242080	−	0.970256i
$55$	3.45559	−	6.91117i	0.465951	−	0.931902i
$56$	2.76858	+	0.578773i	0.369967	+	0.0773418i
$57$	0.131272	−	1.86873i	0.0173875	−	0.247519i
$58$	−6.14721	+	3.00671i	−0.807168	+	0.394801i
$59$	3.25197			0.423370			0.211685	−	0.977338i	$-0.432105\pi$
$59$	3.25197			0.423370			0.211685	+	0.977338i	$0.432105\pi$
$60$	2.84455	+	7.20476i	0.367230	+	0.930130i
$61$	−12.6486			−1.61949			−0.809745	−	0.586781i	$-0.800395\pi$
$61$	−12.6486			−1.61949			−0.809745	+	0.586781i	$0.800395\pi$
$62$	−12.1539	+	5.94470i	−1.54355	+	0.754978i
$63$	2.97054	+	0.419412i	0.374253	+	0.0528410i
$64$	7.33004	+	3.20476i	0.916255	+	0.400595i
$65$	9.67765	+	4.83882i	1.20036	+	0.600182i
$66$	−3.17711	−	7.84554i	−0.391075	−	0.965719i
$67$	−5.71901			−0.698689			−0.349344	−	0.936994i	$-0.613596\pi$
$67$	−5.71901			−0.698689			−0.349344	+	0.936994i	$0.613596\pi$
$68$	7.29441	−	9.37961i	0.884577	−	1.13744i
$69$	−0.0723476	+	1.02990i	−0.00870963	+	0.123986i
$70$	−3.16216	−	0.0276478i	−0.377950	−	0.00330454i
$71$	−8.00000			−0.949425			−0.474713	−	0.880141i	$-0.657448\pi$
$71$	−8.00000			−0.949425			−0.474713	+	0.880141i	$0.657448\pi$
$72$	7.98142	+	2.88044i	0.940619	+	0.339463i
$73$			8.00000i			0.936329i	0.883641	+	0.468165i	$0.155085\pi$
$73$			8.00000i			0.936329i	−0.883641	+	0.468165i	$0.844915\pi$
$74$	3.69833	−	1.80892i	0.429922	−	0.210283i
$75$	−4.69789	−	7.27529i	−0.542466	−	0.840078i
$76$	1.70755	+	1.32794i	0.195870	+	0.152326i
$77$	3.45559			0.393801
$78$	10.9860	−	4.44887i	1.24392	−	0.503736i
$79$			0.949416i			0.106818i	0.998573	+	0.0534088i	$0.0170086\pi$
$79$			0.949416i			0.106818i	−0.998573	+	0.0534088i	$0.982991\pi$
$80$	−8.73867	−	1.90672i	−0.977014	−	0.213177i
$81$	8.64819	+	2.49176i	0.960910	+	0.276862i
$82$	8.77990	−	4.29441i	0.969578	−	0.474238i
$83$			16.9637i			1.86201i	0.365006	+	0.931005i	$0.381067\pi$
$83$			16.9637i			1.86201i	−0.365006	+	0.931005i	$0.618933\pi$
$84$	−2.31299	+	2.57877i	−0.252368	+	0.281367i
$85$	−5.94108	+	11.8822i	−0.644400	+	1.28880i
$86$	−4.59608	−	9.39666i	−0.495608	−	1.01327i
$87$	0.587299	−	8.36049i	0.0629651	−	0.896338i
$88$	9.56706	+	2.00000i	1.01985	+	0.213201i
$89$			5.23352i			0.554752i	0.960761	+	0.277376i	$0.0894648\pi$
$89$			5.23352i			0.554752i	−0.960761	+	0.277376i	$0.910535\pi$
$90$	−9.38171	−	1.40838i	−0.988919	−	0.148456i
$91$			4.83882i			0.507247i
$92$	−0.941075	−	0.731863i	−0.0981139	−	0.0763020i
$93$	1.16118	−	16.5299i	0.120408	−	1.71407i
$94$	−0.308381	+	0.150835i	−0.0318070	+	0.0155574i
$95$	−2.16314	−	1.08157i	−0.221933	−	0.110967i
$96$	−7.89622	+	5.80084i	−0.805905	+	0.592045i
$97$		−	3.30587i		−	0.335660i	−0.985816	−	0.167830i	$-0.946324\pi$
$97$		−	3.30587i		−	0.335660i	0.985816	−	0.167830i	$-0.0536760\pi$
$98$	−0.621372	−	1.27039i	−0.0627681	−	0.128329i
$99$	10.2649	+	1.44932i	1.03167	+	0.145662i
$100$	9.99847	+	0.174853i	0.999847	+	0.0174853i
$101$			7.73746i			0.769906i	0.922936	+	0.384953i	$0.125782\pi$
$101$			7.73746i			0.769906i	−0.922936	+	0.384953i	$0.874218\pi$
$102$	5.46230	+	13.4886i	0.540848	+	1.33557i
$103$	−5.61872			−0.553629			−0.276815	−	0.960923i	$-0.589279\pi$
$103$	−5.61872			−0.553629			−0.276815	+	0.960923i	$0.589279\pi$
$104$	−2.80058	+	13.3967i	−0.274620	+	1.31365i
$105$	1.97054	−	3.33421i	0.192305	−	0.325386i
$106$	7.34608	+	15.0190i	0.713514	+	1.45878i
$107$		−	1.68491i		−	0.162886i	−0.996678	−	0.0814431i	$-0.974047\pi$
$107$		−	1.68491i		−	0.162886i	0.996678	−	0.0814431i	$-0.0259529\pi$
$108$	−7.95240	+	6.69025i	−0.765220	+	0.643769i
$109$	9.94108			0.952182			0.476091	−	0.879396i	$-0.342053\pi$
$109$	9.94108			0.952182			0.476091	+	0.879396i	$0.342053\pi$
$110$	−10.9271	−	0.0955392i	−1.04186	−	0.00910931i
$111$	−0.353336	+	5.02990i	−0.0335371	+	0.477417i
$112$	−0.985049	−	3.87681i	−0.0930783	−	0.366324i
$113$	3.23352			0.304184			0.152092	−	0.988366i	$-0.451399\pi$
$113$	3.23352			0.304184			0.152092	+	0.988366i	$0.451399\pi$
$114$	−2.45559	+	0.994408i	−0.229987	+	0.0931348i
$115$	1.19216	+	0.596080i	0.111170	+	0.0555848i
$116$	7.63941	+	5.94108i	0.709301	+	0.551615i
$117$	−2.02946	+	14.3739i	−0.187624	+	1.32887i
$118$	−2.02068	−	4.13127i	−0.186019	−	0.380314i
$119$	−5.94108			−0.544617
$120$	7.38534	−	8.09054i	0.674186	−	0.738561i
$121$	0.941075			0.0855523
$122$	7.85951	+	16.0687i	0.711566	+	1.45479i
$123$	−0.838825	+	11.9411i	−0.0756343	+	1.07669i
$124$	15.1042	+	11.7464i	1.35640	+	1.05485i
$125$	−11.0000	+	2.00000i	−0.983870	+	0.178885i
$126$	−1.31299	−	4.03436i	−0.116971	−	0.359409i
$127$	1.08883			0.0966178			0.0483089	−	0.998832i	$-0.484617\pi$
$127$	1.08883			0.0966178			0.0483089	+	0.998832i	$0.484617\pi$
$128$	−0.483388	−	11.3034i	−0.0427259	−	0.999087i
$129$	12.7799	+	0.897749i	1.12521	+	0.0790424i
$130$	0.133783	−	15.3011i	0.0117335	−	1.34200i
$131$	6.30783			0.551118			0.275559	−	0.961284i	$-0.411137\pi$
$131$	6.30783			0.551118			0.275559	+	0.961284i	$0.411137\pi$
$132$	−7.99274	+	8.91117i	−0.695679	+	0.775618i
$133$		−	1.08157i		−	0.0937839i
$134$	3.55364	+	7.26539i	0.306987	+	0.627634i
$135$	7.25197	−	9.07794i	0.624150	−	0.781305i
$136$	−16.4483	−	3.43853i	−1.41043	−	0.294852i
$137$	8.64863			0.738902			0.369451	−	0.929250i	$-0.379546\pi$
$137$	8.64863			0.738902			0.369451	+	0.929250i	$0.379546\pi$
$138$	1.35334	−	0.548043i	0.115204	−	0.0466525i
$139$			5.82960i			0.494460i	0.968957	+	0.247230i	$0.0795204\pi$
$139$			5.82960i			0.494460i	−0.968957	+	0.247230i	$0.920480\pi$
$140$	1.92975	+	4.03436i	0.163094	+	0.340966i
$141$	0.0294624	−	0.419412i	0.00248119	−	0.0353209i
$142$	4.97098	+	10.1631i	0.417155	+	0.852872i
$143$			16.7210i			1.39828i
$144$	−1.30014	−	11.9294i	−0.108345	−	0.994113i
$145$	−9.67765	−	4.83882i	−0.803685	−	0.401843i
$146$	10.1631	−	4.97098i	0.841107	−	0.411401i
$147$	1.72779	+	0.121372i	0.142506	+	0.0100106i
$148$	−4.59608	−	3.57432i	−0.377795	−	0.293807i
$149$		−	17.8223i		−	1.46006i	−0.683413	−	0.730032i	$-0.739505\pi$
$149$		−	17.8223i		−	1.46006i	0.683413	−	0.730032i	$-0.260495\pi$
$150$	−6.32333	+	10.4888i	−0.516298	+	0.856409i
$151$			15.7427i			1.28113i	0.767906	+	0.640563i	$0.221299\pi$
$151$			15.7427i			1.28113i	−0.767906	+	0.640563i	$0.778701\pi$
$152$	0.625983	−	2.99441i	0.0507739	−	0.242879i
$153$	−17.6482	−	2.49176i	−1.42677	−	0.201447i
$154$	−2.14721	−	4.38995i	−0.173027	−	0.353752i
$155$	−19.1341	−	9.56706i	−1.53689	−	0.768445i
$156$	−12.4782	−	11.1922i	−0.999058	−	0.896090i
$157$		−	17.8223i		−	1.42238i	−0.703001	−	0.711189i	$-0.748157\pi$
$157$		−	17.8223i		−	1.42238i	0.703001	−	0.711189i	$-0.251843\pi$
$158$	1.20613	−	0.589941i	0.0959546	−	0.0469331i
$159$	−20.4266	−	1.43490i	−1.61993	−	0.113795i
$160$	3.00769	+	12.2863i	0.237779	+	0.971319i
$161$			0.596080i			0.0469777i
$162$	−2.20823	−	12.5349i	−0.173495	−	0.984835i
$163$	−11.2520			−0.881322			−0.440661	−	0.897674i	$-0.645256\pi$
$163$	−11.2520			−0.881322			−0.440661	+	0.897674i	$0.645256\pi$
$164$	−10.9112	−	8.48549i	−0.852019	−	0.662605i
$165$	6.80936	−	11.5217i	0.530108	−	0.896960i
$166$	21.5506	−	10.5408i	1.67265	−	0.818124i
$167$		−	16.7137i		−	1.29335i	−0.762767	−	0.646673i	$-0.776160\pi$
$167$		−	16.7137i		−	1.29335i	0.762767	−	0.646673i	$-0.223840\pi$
$168$	4.71328	+	1.33603i	0.363638	+	0.103077i
$169$	−10.4142			−0.801094
$170$	18.7866	+	0.164257i	1.44087	+	0.0125980i
$171$	0.453623	−	3.21284i	0.0346894	−	0.245692i
$172$	−9.08157	+	11.6776i	−0.692463	+	0.890412i
$173$	−1.94108			−0.147577			−0.0737886	−	0.997274i	$-0.523509\pi$
$173$	−1.94108			−0.147577			−0.0737886	+	0.997274i	$0.523509\pi$
$174$	−10.9860	+	4.44887i	−0.832849	+	0.337268i
$175$	−3.00000	−	4.00000i	−0.226779	−	0.302372i
$176$	−3.40392	−	13.3967i	−0.256580	−	1.00981i
$177$	5.61872	+	0.394698i	0.422329	+	0.0296674i
$178$	6.64863	−	3.25197i	0.498336	−	0.243745i
$179$	6.80784			0.508842			0.254421	−	0.967094i	$-0.418115\pi$
$179$	6.80784			0.508842			0.254421	+	0.967094i	$0.418115\pi$
$180$	4.04034	+	12.7936i	0.301149	+	0.953577i
$181$	−2.97098			−0.220831			−0.110416	−	0.993886i	$-0.535218\pi$
$181$	−2.97098			−0.220831			−0.110416	+	0.993886i	$0.535218\pi$
$182$	6.14721	−	3.00671i	0.455661	−	0.222872i
$183$	−21.8542	−	1.53519i	−1.61551	−	0.113485i
$184$	−0.344995	+	1.65029i	−0.0254334	+	0.121661i
$185$	5.82234	+	2.91117i	0.428067	+	0.214034i
$186$	−21.7210	+	8.79607i	−1.59266	+	0.644959i
$187$	−20.5299			−1.50129
$188$	0.383238	+	0.298040i	0.0279505	+	0.0217368i
$189$	5.08157	+	1.08520i	0.369630	+	0.0789366i
$190$	−0.0299030	+	3.42009i	−0.00216939	+	0.248119i
$191$	20.6477			1.49402			0.747009	−	0.664814i	$-0.231489\pi$
$191$	20.6477			1.49402			0.747009	+	0.664814i	$0.231489\pi$
$192$	12.2758	+	6.42682i	0.885932	+	0.463816i
$193$		−	9.55980i		−	0.688129i	−0.938946	−	0.344065i	$-0.888196\pi$
$193$		−	9.55980i		−	0.688129i	0.938946	−	0.344065i	$-0.111804\pi$
$194$	−4.19975	+	2.05418i	−0.301525	+	0.147481i
$195$	16.1337	+	9.53509i	1.15536	+	0.682822i
$196$	−1.22779	+	1.57877i	−0.0876995	+	0.112770i
$197$	11.5598			0.823602			0.411801	−	0.911274i	$-0.364900\pi$
$197$	11.5598			0.823602			0.411801	+	0.911274i	$0.364900\pi$
$198$	−4.53716	−	13.9411i	−0.322442	−	0.990749i
$199$			16.9637i			1.20253i	0.799051	+	0.601263i	$0.205336\pi$
$199$			16.9637i			1.20253i	−0.799051	+	0.601263i	$0.794664\pi$
$200$	−5.99064	−	12.8106i	−0.423602	−	0.905848i
$201$	−9.88127	−	0.694129i	−0.696971	−	0.0489601i
$202$	9.82960	−	4.80784i	0.691608	−	0.338278i
$203$		−	4.83882i		−	0.339619i
$204$	13.7417	−	15.3207i	0.962108	−	1.07266i
$205$	13.8223	+	6.91117i	0.965394	+	0.482697i
$206$	3.49132	+	7.13798i	0.243252	+	0.497327i
$207$	−0.250003	+	1.77068i	−0.0173764	+	0.123071i
$208$	18.7592	−	4.76648i	1.30072	−	0.330496i
$209$		−	3.73746i		−	0.258525i
$210$	−5.46020	−	0.431568i	−0.376789	−	0.0297810i
$211$		−	16.7137i		−	1.15062i	−0.817936	−	0.575310i	$-0.804881\pi$
$211$		−	16.7137i		−	1.15062i	0.817936	−	0.575310i	$-0.195119\pi$
$212$	14.5154	−	18.6648i	0.996921	−	1.28190i
$213$	−13.8223	−	0.970978i	−0.947091	−	0.0665303i
$214$	−2.14049	+	1.04696i	−0.146321	+	0.0715684i
$215$	7.39666	−	14.7933i	0.504448	−	1.00890i
$216$	13.4406	+	5.94553i	0.914519	+	0.404542i
$217$		−	9.56706i		−	0.649454i
$218$	−6.17711	−	12.6291i	−0.418367	−	0.855348i
$219$	−0.970978	+	13.8223i	−0.0656126	+	0.934027i
$220$	6.66843	+	13.9411i	0.449585	+	0.939907i
$221$		−	28.7478i		−	1.93379i
$222$	6.60950	−	2.67657i	0.443601	−	0.179639i
$223$	−8.76736			−0.587106			−0.293553	−	0.955943i	$-0.594838\pi$
$223$	−8.76736			−0.587106			−0.293553	+	0.955943i	$0.594838\pi$
$224$	−4.31299	+	3.66034i	−0.288174	+	0.244567i
$225$	−7.23396	−	13.1404i	−0.482264	−	0.876026i
$226$	−2.00922	−	4.10784i	−0.133651	−	0.273250i
$227$			0.242745i			0.0161115i	0.999968	+	0.00805576i	$0.00256426\pi$
$227$			0.242745i			0.0161115i	−0.999968	+	0.00805576i	$0.997436\pi$
$228$	2.78912	+	2.50166i	0.184714	+	0.165676i
$229$	−26.3531			−1.74146			−0.870732	−	0.491758i	$-0.836354\pi$
$229$	−26.3531			−1.74146			−0.870732	+	0.491758i	$0.836354\pi$
$230$	0.0164803	−	1.88490i	0.00108668	−	0.124287i
$231$	5.97054	+	0.419412i	0.392833	+	0.0275953i
$232$	2.80058	−	13.3967i	0.183867	−	0.879534i
$233$	−6.44413			−0.422169			−0.211084	−	0.977468i	$-0.567699\pi$
$233$	−6.44413			−0.422169			−0.211084	+	0.977468i	$0.567699\pi$
$234$	19.5216	−	6.35334i	1.27616	−	0.415331i
$235$	−0.485489	−	0.242745i	−0.0316698	−	0.0158349i
$236$	−3.99274	+	5.13412i	−0.259905	+	0.334202i
$237$	−0.115233	+	1.64039i	−0.00748517	+	0.106555i
$238$	3.69162	+	7.54750i	0.239292	+	0.489231i
$239$	16.6495			1.07697			0.538484	−	0.842636i	$-0.318997\pi$
$239$	16.6495			1.07697			0.538484	+	0.842636i	$0.318997\pi$
$240$	−14.8672	−	4.35504i	−0.959674	−	0.281117i
$241$	−5.61784			−0.361877			−0.180939	−	0.983494i	$-0.557914\pi$
$241$	−5.61784			−0.361877			−0.180939	+	0.983494i	$0.557914\pi$
$242$	−0.584758	−	1.19553i	−0.0375897	−	0.0768519i
$243$	14.6398	+	5.35490i	0.939147	+	0.343517i
$244$	15.5299	−	19.9693i	0.994200	−	1.27840i
$245$	1.00000	−	2.00000i	0.0638877	−	0.127775i
$246$	15.6911	−	6.35422i	1.00043	−	0.405130i
$247$	5.23352			0.333001
$248$	5.53716	−	26.4871i	0.351610	−	1.68194i
$249$	−2.05892	+	29.3098i	−0.130479	+	1.85743i
$250$	9.37588	+	12.7316i	0.592983	+	0.805215i
$251$	3.25197			0.205262			0.102631	−	0.994719i	$-0.467274\pi$
$251$	3.25197			0.205262			0.102631	+	0.994719i	$0.467274\pi$
$252$	−4.30936	+	4.17485i	−0.271464	+	0.262991i
$253$			2.05981i			0.129499i
$254$	−0.676567	−	1.38324i	−0.0424516	−	0.0867921i
$255$	−11.7071	+	19.8088i	−0.733128	+	1.24048i
$256$	−14.0594	+	7.63770i	−0.878710	+	0.477356i
$257$	0.467046			0.0291335			0.0145668	−	0.999894i	$-0.495363\pi$
$257$	0.467046			0.0291335			0.0145668	+	0.999894i	$0.495363\pi$
$258$	−6.80058	−	16.7933i	−0.423386	−	1.04551i
$259$			2.91117i			0.180891i
$260$	−19.5216	+	9.33774i	−1.21068	+	0.579102i
$261$	2.02946	−	14.3739i	0.125621	−	0.889723i
$262$	−3.91951	−	8.01342i	−0.242148	−	0.495071i
$263$			8.47823i			0.522790i	0.965232	+	0.261395i	$0.0841825\pi$
$263$			8.47823i			0.522790i	−0.965232	+	0.261395i	$0.915817\pi$
$264$	16.2872	+	4.61676i	1.00240	+	0.284142i
$265$	−11.8223	+	23.6447i	−0.726241	+	1.45248i
$266$	−1.37402	+	0.672057i	−0.0842464	+	0.0412065i
$267$	−0.635205	+	9.04244i	−0.0388739	+	0.553389i
$268$	7.02176	−	9.02902i	0.428922	−	0.551535i
$269$			0.144695i			0.00882222i	0.999990	+	0.00441111i	$0.00140410\pi$
$269$			0.144695i			0.00882222i	−0.999990	+	0.00441111i	$0.998596\pi$
$270$	−16.0387	−	3.57206i	−0.976085	−	0.217389i
$271$		−	23.1251i		−	1.40475i	−0.711807	−	0.702375i	$-0.752123\pi$
$271$		−	23.1251i		−	1.40475i	0.711807	−	0.702375i	$-0.247877\pi$
$272$	5.85225	+	23.0324i	0.354845	+	1.39655i
$273$	−0.587299	+	8.36049i	−0.0355450	+	0.506000i
$274$	−5.37402	−	10.9871i	−0.324656	−	0.663758i
$275$	−10.3668	−	13.8223i	−0.625139	−	0.833519i
$276$	−1.53716	−	1.37873i	−0.0925259	−	0.0829897i
$277$			0.826283i			0.0496465i	0.999692	+	0.0248233i	$0.00790230\pi$
$277$			0.826283i			0.0496465i	−0.999692	+	0.0248233i	$0.992098\pi$
$278$	7.40588	−	3.62235i	0.444175	−	0.217254i
$279$	4.01254	−	28.4193i	0.240225	−	1.70142i
$280$	3.92612	−	4.95838i	0.234631	−	0.296320i
$281$			14.6612i			0.874612i	0.899313	+	0.437306i	$0.144067\pi$
$281$			14.6612i			0.874612i	−0.899313	+	0.437306i	$0.855933\pi$
$282$	−0.551125	+	0.223182i	−0.0328190	+	0.0132903i
$283$	20.4266			1.21423			0.607117	−	0.794613i	$-0.292326\pi$
$283$	20.4266			1.21423			0.607117	+	0.794613i	$0.292326\pi$
$284$	9.82234	−	12.6302i	0.582849	−	0.749464i
$285$	−3.60618	−	2.13127i	−0.213612	−	0.126246i
$286$	21.2422	−	10.3899i	1.25608	−	0.614371i
$287$			6.91117i			0.407954i
$288$	−14.3471	+	9.06426i	−0.845411	+	0.534117i
$289$	18.2964			1.07626
$290$	−0.133783	+	15.3011i	−0.00785599	+	0.898513i
$291$	0.401241	−	5.71186i	0.0235212	−	0.334835i
$292$	−12.6302	−	9.82234i	−0.739126	−	0.574809i
$293$	−5.41422			−0.316302			−0.158151	−	0.987415i	$-0.550553\pi$
$293$	−5.41422			−0.316302			−0.158151	+	0.987415i	$0.550553\pi$
$294$	−0.919412	−	2.27039i	−0.0536212	−	0.132412i
$295$	3.25197	−	6.50393i	0.189337	−	0.378674i
$296$	−1.68491	+	8.05981i	−0.0979333	+	0.468467i
$297$	17.5598	+	3.75000i	1.01892	+	0.217597i
$298$	−22.6414	+	11.0743i	−1.31158	+	0.641518i
$299$	−2.88433			−0.166805
$300$	17.2541	+	1.51565i	0.996164	+	0.0875059i
$301$	7.39666			0.426336
$302$	19.9995	−	9.78210i	1.15084	−	0.562897i
$303$	−0.939112	+	13.3687i	−0.0539506	+	0.768013i
$304$	−4.19304	+	1.06540i	−0.240487	+	0.0611048i
$305$	−12.6486	+	25.2973i	−0.724258	+	1.44852i
$306$	7.80058	+	23.9684i	0.445930	+	1.37018i
$307$	−16.3070			−0.930687			−0.465343	−	0.885130i	$-0.654069\pi$
$307$	−16.3070			−0.930687			−0.465343	+	0.885130i	$0.654069\pi$
$308$	−4.24274	+	5.45559i	−0.241753	+	0.310861i
$309$	−9.70799	−	0.681957i	−0.552268	−	0.0387952i
$310$	−0.264508	+	30.2525i	−0.0150230	+	1.71823i
$311$	−24.3531			−1.38094			−0.690469	−	0.723362i	$-0.742596\pi$
$311$	−24.3531			−1.38094			−0.690469	+	0.723362i	$0.742596\pi$
$312$	−6.46481	+	22.8067i	−0.365998	+	1.29118i
$313$			30.6612i			1.73307i	0.499115	+	0.866536i	$0.333659\pi$
$313$			30.6612i			1.73307i	−0.499115	+	0.866536i	$0.666341\pi$
$314$	−22.6414	+	11.0743i	−1.27773	+	0.624959i
$315$	3.80936	−	5.52166i	0.214633	−	0.311110i
$316$	−1.49891	−	1.16569i	−0.0843204	−	0.0655750i
$317$	−13.8822			−0.779699			−0.389850	−	0.920879i	$-0.627473\pi$
$317$	−13.8822			−0.779699			−0.389850	+	0.920879i	$0.627473\pi$
$318$	10.8696	+	26.8414i	0.609537	+	1.50519i
$319$		−	16.7210i		−	0.936195i
$320$	13.7396	−	11.4553i	0.768065	−	0.640372i
$321$	0.204501	−	2.91117i	0.0114141	−	0.162486i
$322$	0.757255	−	0.370388i	0.0422002	−	0.0206409i
$323$			6.42568i			0.357535i
$324$	−14.5521	+	10.5942i	−0.808450	+	0.588564i
$325$	19.3553	−	14.5165i	1.07364	−	0.805229i
$326$	6.99166	+	14.2944i	0.387232	+	0.791694i
$327$	17.1761	+	1.20657i	0.949842	+	0.0667235i
$328$	−4.00000	+	19.1341i	−0.220863	+	1.05650i
$329$		−	0.242745i		−	0.0133829i
$330$	−18.8682	−	1.49132i	−1.03866	−	0.0820944i
$331$			18.1559i			0.997937i	0.866620	+	0.498969i	$0.166288\pi$
$331$			18.1559i			0.997937i	−0.866620	+	0.498969i	$0.833712\pi$
$332$	−26.7819	−	20.8279i	−1.46985	−	1.14308i
$333$	−1.22098	+	8.64775i	−0.0669094	+	0.473894i
$334$	−21.2330	+	10.3854i	−1.16182	+	0.568266i
$335$	−5.71901	+	11.4380i	−0.312463	+	0.624926i
$336$	−1.23142	−	6.81789i	−0.0671796	−	0.371946i
$337$			17.4419i			0.950124i	0.879952	+	0.475062i	$0.157574\pi$
$337$			17.4419i			0.950124i	−0.879952	+	0.475062i	$0.842426\pi$
$338$	6.47111	+	13.2301i	0.351982	+	0.719625i
$339$	5.58686	+	0.392460i	0.303437	+	0.0213155i
$340$	−11.4648	−	23.9684i	−0.621766	−	1.29987i
$341$		−	33.0598i		−	1.79029i
$342$	−4.36344	+	1.42009i	−0.235948	+	0.0767897i
$343$	1.00000			0.0539949
$344$	20.4782	+	4.28099i	1.10411	+	0.230815i
$345$	1.98746	+	1.17460i	0.107001	+	0.0632382i
$346$	1.20613	+	2.46593i	0.0648420	+	0.132569i
$347$		−	33.8564i		−	1.81751i	−0.417331	−	0.908755i	$-0.637034\pi$
$347$		−	33.8564i		−	1.81751i	0.417331	−	0.908755i	$-0.362966\pi$
$348$	12.4782	+	11.1922i	0.668903	+	0.599963i
$349$	−9.29333			−0.497460			−0.248730	−	0.968573i	$-0.580013\pi$
$349$	−9.29333			−0.497460			−0.248730	+	0.968573i	$0.580013\pi$
$350$	−3.21745	+	6.29667i	−0.171980	+	0.336571i
$351$	−5.25108	+	24.5888i	−0.280282	+	1.31245i
$352$	−14.9039	+	12.6486i	−0.794381	+	0.674174i
$353$	7.47403			0.397802			0.198901	−	0.980020i	$-0.436263\pi$
$353$	7.47403			0.397802			0.198901	+	0.980020i	$0.436263\pi$
$354$	−2.98990	−	7.38324i	−0.158911	−	0.392415i
$355$	−8.00000	+	16.0000i	−0.424596	+	0.849192i
$356$	−8.26254	−	6.42568i	−0.437914	−	0.340561i
$357$	−10.2649	−	0.721082i	−0.543279	−	0.0381637i
$358$	−4.23020	−	8.64863i	−0.223573	−	0.457094i
$359$	−11.3553			−0.599310			−0.299655	−	0.954048i	$-0.596872\pi$
$359$	−11.3553			−0.599310			−0.299655	+	0.954048i	$0.596872\pi$
$360$	13.7423	−	13.0824i	0.724283	−	0.689503i
$361$	17.8302			0.938432
$362$	1.84608	+	3.77431i	0.0970280	+	0.198373i
$363$	1.62598	+	0.114220i	0.0853420	+	0.00599502i
$364$	−7.63941	−	5.94108i	−0.400414	−	0.311397i
$365$	16.0000	+	8.00000i	0.837478	+	0.418739i
$366$	11.6293	+	28.7173i	0.607873	+	1.50108i
$367$	4.24051			0.221353			0.110676	−	0.993857i	$-0.464698\pi$
$367$	4.24051			0.221353			0.110676	+	0.993857i	$0.464698\pi$
$368$	2.31089	−	0.587168i	0.120464	−	0.0306082i
$369$	−2.89863	+	20.5299i	−0.150897	+	1.06874i
$370$	0.0804874	−	9.20558i	0.00418434	−	0.478575i
$371$	−11.8223			−0.613786
$372$	24.6713	+	22.1285i	1.27915	+	1.14731i
$373$		−	23.0559i		−	1.19379i	−0.802320	−	0.596894i	$-0.796401\pi$
$373$		−	23.0559i		−	1.19379i	0.802320	−	0.596894i	$-0.203599\pi$
$374$	12.7567	+	26.0810i	0.659634	+	1.34862i
$375$	−19.2485	+	2.12049i	−0.993987	+	0.109502i
$376$	0.140494	−	0.672057i	0.00724542	−	0.0346587i
$377$	23.4142			1.20589
$378$	−1.77892	−	7.12990i	−0.0914977	−	0.366722i
$379$		−	28.8441i		−	1.48162i	−0.671713	−	0.740811i	$-0.734441\pi$
$379$		−	28.8441i		−	1.48162i	0.671713	−	0.740811i	$-0.265559\pi$
$380$	4.36344	−	2.08716i	0.223840	−	0.107069i
$381$	1.88127	+	0.132153i	0.0963803	+	0.00677043i
$382$	−12.8299	−	26.2307i	−0.656437	−	1.34208i
$383$			6.51119i			0.332706i	0.986066	+	0.166353i	$0.0531992\pi$
$383$			6.51119i			0.332706i	−0.986066	+	0.166353i	$0.946801\pi$
$384$	0.536721	−	19.5886i	0.0273894	−	0.999625i
$385$	3.45559	−	6.91117i	0.176113	−	0.352226i
$386$	−12.1447	+	5.94019i	−0.618149	+	0.302348i
$387$	21.9721	+	3.10225i	1.11690	+	0.157696i
$388$	5.21922	+	4.05892i	0.264966	+	0.206061i
$389$		−	22.8059i		−	1.15630i	−0.815929	−	0.578152i	$-0.803774\pi$
$389$		−	22.8059i		−	1.15630i	0.815929	−	0.578152i	$-0.196226\pi$
$390$	2.08828	−	26.4209i	0.105744	−	1.33788i
$391$		−	3.54136i		−	0.179094i
$392$	2.76858	+	0.578773i	0.139834	+	0.0292325i
$393$	10.8986	+	0.765596i	0.549763	+	0.0386192i
$394$	−7.18294	−	14.6855i	−0.361871	−	0.739844i
$395$	1.89883	+	0.949416i	0.0955406	+	0.0477703i
$396$	−14.8914	+	14.4266i	−0.748320	+	0.724962i
$397$		−	13.1031i		−	0.657627i	−0.944395	−	0.328814i	$-0.893351\pi$
$397$		−	13.1031i		−	0.657627i	0.944395	−	0.328814i	$-0.106649\pi$
$398$	21.5506	−	10.5408i	1.08023	−	0.528362i
$399$	0.131272	−	1.86873i	0.00657184	−	0.0935534i
$400$	−12.5521	+	15.5706i	−0.627605	+	0.778532i
$401$			10.7808i			0.538366i	0.963089	+	0.269183i	$0.0867537\pi$
$401$			10.7808i			0.538366i	−0.963089	+	0.269183i	$0.913246\pi$
$402$	5.25813	+	12.9844i	0.262252	+	0.647603i
$403$	46.2933			2.30603
$404$	−12.2157	−	9.49999i	−0.607753	−	0.472642i
$405$	13.6317	−	14.8046i	0.677365	−	0.735647i
$406$	−6.14721	+	3.00671i	−0.305081	+	0.149221i
$407$			10.0598i			0.498646i
$408$	−28.0020	−	7.93745i	−1.38630	−	0.392962i
$409$	15.7045			0.776537			0.388269	−	0.921546i	$-0.373073\pi$
$409$	15.7045			0.776537			0.388269	+	0.921546i	$0.373073\pi$
$410$	0.191078	−	21.8542i	0.00943669	−	1.07930i
$411$	14.9430	+	1.04970i	0.737086	+	0.0517781i
$412$	6.89863	−	8.87069i	0.339871	−	0.437028i
$413$	3.25197			0.160019
$414$	2.40480	−	0.782648i	0.118190	−	0.0384651i
$415$	33.9274	+	16.9637i	1.66543	+	0.832716i
$416$	−17.7118	−	20.8698i	−0.868390	−	1.02323i
$417$	−0.707552	+	10.0723i	−0.0346490	+	0.493245i
$418$	−4.74803	+	2.32235i	−0.232234	+	0.113590i
$419$	−33.0743			−1.61579			−0.807893	−	0.589329i	$-0.799392\pi$
$419$	−33.0743			−1.61579			−0.807893	+	0.589329i	$0.799392\pi$
$420$	2.84455	+	7.20476i	0.138800	+	0.351556i
$421$	7.88127			0.384110			0.192055	−	0.981384i	$-0.438485\pi$
$421$	7.88127			0.384110			0.192055	+	0.981384i	$0.438485\pi$
$422$	−21.2330	+	10.3854i	−1.03361	+	0.505555i
$423$	0.101810	−	0.721082i	0.00495017	−	0.0350602i
$424$	−32.7311	−	6.84245i	−1.58956	−	0.332299i
$425$	17.8232	+	23.7643i	0.864553	+	1.15274i
$426$	7.35530	+	18.1631i	0.356365	+	0.880007i
$427$	−12.6486			−0.612110
$428$	2.66009	+	2.06872i	0.128580	+	0.0999953i
$429$	−2.02946	+	28.8904i	−0.0979834	+	1.39484i
$430$	−23.3894	−	0.204501i	−1.12794	−	0.00986192i
$431$	26.3522			1.26934			0.634671	−	0.772782i	$-0.281135\pi$
$431$	26.3522			1.26934			0.634671	+	0.772782i	$0.281135\pi$
$432$	−0.798481	−	20.7693i	−0.0384169	−	0.999262i
$433$		−	37.2973i		−	1.79239i	−0.443659	−	0.896196i	$-0.646320\pi$
$433$		−	37.2973i		−	1.79239i	0.443659	−	0.896196i	$-0.353680\pi$
$434$	−12.1539	+	5.94470i	−0.583407	+	0.285355i
$435$	−16.1337	−	9.53509i	−0.773551	−	0.457172i
$436$	−12.2056	+	15.6947i	−0.584541	+	0.751640i
$437$	0.644702			0.0308403
$438$	18.1631	−	7.35530i	0.867868	−	0.351450i
$439$		−	12.6229i		−	0.602459i	−0.953552	−	0.301230i	$-0.902603\pi$
$439$		−	12.6229i		−	0.602459i	0.953552	−	0.301230i	$-0.0973971\pi$
$440$	13.5671	−	17.1341i	0.646784	−	0.816837i
$441$	2.97054	+	0.419412i	0.141454	+	0.0199720i
$442$	−36.5210	+	17.8631i	−1.73713	+	0.849661i
$443$		−	21.7118i		−	1.03156i	−0.856722	−	0.515778i	$-0.827503\pi$
$443$		−	21.7118i		−	1.03156i	0.856722	−	0.515778i	$-0.172497\pi$
$444$	−7.50725	−	6.73352i	−0.356278	−	0.319559i
$445$	10.4670	+	5.23352i	0.496186	+	0.248093i
$446$	5.44779	+	11.1380i	0.257960	+	0.527399i
$447$	2.16314	−	30.7933i	0.102313	−	1.45647i
$448$	7.33004	+	3.20476i	0.346312	+	0.151410i
$449$		−	14.6361i		−	0.690720i	−0.938470	−	0.345360i	$-0.887757\pi$
$449$		−	14.6361i		−	0.690720i	0.938470	−	0.345360i	$-0.112243\pi$
$450$	−12.1985	+	17.3550i	−0.575041	+	0.818125i
$451$			23.8822i			1.12457i
$452$	−3.97010	+	5.10500i	−0.186738	+	0.240119i
$453$	−1.91073	+	27.2002i	−0.0897740	+	1.27798i
$454$	0.308381	−	0.150835i	0.0144730	−	0.00707902i
$455$	9.67765	+	4.83882i	0.453695	+	0.226848i
$456$	1.44501	−	5.09774i	0.0676687	−	0.238724i
$457$		−	4.00176i		−	0.187195i	−0.995610	−	0.0935973i	$-0.970163\pi$
$457$		−	4.00176i		−	0.187195i	0.995610	−	0.0935973i	$-0.0298366\pi$
$458$	16.3751	+	33.4788i	0.765158	+	1.56436i
$459$	−30.1900	−	6.44725i	−1.40915	−	0.300932i
$460$	−2.40480	+	1.15029i	−0.112124	+	0.0536324i
$461$			36.9419i			1.72056i	0.509824	+	0.860279i	$0.329711\pi$
$461$			36.9419i			1.72056i	−0.509824	+	0.860279i	$0.670289\pi$
$462$	−3.17711	−	7.84554i	−0.147812	−	0.365007i
$463$	6.12178			0.284503			0.142252	−	0.989831i	$-0.454566\pi$
$463$	6.12178			0.284503			0.142252	+	0.989831i	$0.454566\pi$
$464$	−18.7592	+	4.76648i	−0.870875	+	0.221278i
$465$	−31.8986	−	18.8522i	−1.47926	−	0.874252i
$466$	4.00420	+	8.18657i	0.185491	+	0.379235i
$467$			14.0651i			0.650855i	0.945567	+	0.325427i	$0.105508\pi$
$467$			14.0651i			0.650855i	−0.945567	+	0.325427i	$0.894492\pi$
$468$	−20.2014	−	20.8522i	−0.933809	−	0.963895i
$469$	−5.71901			−0.264079
$470$	−0.00671134	+	0.767596i	−0.000309571	+	0.0354066i
$471$	2.16314	−	30.7933i	0.0996721	−	1.41888i
$472$	9.00332	+	1.88215i	0.414411	+	0.0866330i
$473$	25.5598			1.17524
$474$	2.15555	−	0.872904i	0.0990075	−	0.0400938i
$475$	−4.32628	+	3.24471i	−0.198503	+	0.148877i
$476$	7.29441	−	9.37961i	0.334339	−	0.429914i
$477$	−35.1187	−	4.95844i	−1.60798	−	0.227031i
$478$	−10.3455	−	21.1514i	−0.473194	−	0.967443i
$479$	33.4419			1.52800			0.764001	−	0.645215i	$-0.223232\pi$
$479$	33.4419			1.52800			0.764001	+	0.645215i	$0.223232\pi$
$480$	3.70545	+	21.5933i	0.169130	+	0.985594i
$481$	−14.0867			−0.642296
$482$	3.49077	+	7.13686i	0.159000	+	0.325075i
$483$	−0.0723476	+	1.02990i	−0.00329193	+	0.0468622i
$484$	−1.15545	+	1.48574i	−0.0525202	+	0.0675338i
$485$	−6.61174	−	3.30587i	−0.300224	−	0.150112i
$486$	−2.29398	−	21.9257i	−0.104057	−	0.994571i
$487$	17.8241			0.807687			0.403844	−	0.914828i	$-0.367674\pi$
$487$	17.8241			0.807687			0.403844	+	0.914828i	$0.367674\pi$
$488$	−35.0187	−	7.32068i	−1.58522	−	0.331392i
$489$	−19.4411	−	1.36568i	−0.879156	−	0.0617580i
$490$	−3.16216	−	0.0276478i	−0.142852	−	0.00124900i
$491$	−12.3087			−0.555485			−0.277742	−	0.960656i	$-0.589586\pi$
$491$	−12.3087			−0.555485			−0.277742	+	0.960656i	$0.589586\pi$
$492$	−17.8223	−	15.9855i	−0.803493	−	0.720681i
$493$			28.7478i			1.29474i
$494$	−3.25197	−	6.64863i	−0.146313	−	0.299136i
$495$	13.1636	−	19.0806i	0.591659	−	0.857608i
$496$	−37.0897	+	9.42402i	−1.66538	+	0.423151i
$497$	−8.00000			−0.358849
$498$	38.5143	−	15.5967i	1.72587	−	0.698903i
$499$		−	13.0941i		−	0.586173i	−0.956086	−	0.293086i	$-0.905318\pi$
$499$		−	13.0941i		−	0.586173i	0.956086	−	0.293086i	$-0.0946824\pi$
$500$	10.3482	−	19.8221i	0.462785	−	0.886471i
$501$	2.02858	−	28.8778i	0.0906303	−	1.29017i
$502$	−2.02068	−	4.13127i	−0.0901874	−	0.184388i
$503$			15.9639i			0.711796i	0.934525	+	0.355898i	$0.115825\pi$
$503$			15.9639i			0.711796i	−0.934525	+	0.355898i	$0.884175\pi$
$504$	7.98142	+	2.88044i	0.355521	+	0.128305i
$505$	15.4749	+	7.73746i	0.688624	+	0.344312i
$506$	2.61676	−	1.27991i	0.116329	−	0.0568988i
$507$	−17.9936	−	1.26400i	−0.799125	−	0.0561361i
$508$	−1.33686	+	1.71901i	−0.0593134	+	0.0762688i
$509$		−	13.6776i		−	0.606251i	−0.952951	−	0.303126i	$-0.901970\pi$
$509$		−	13.6776i		−	0.606251i	0.952951	−	0.303126i	$-0.0980302\pi$
$510$	32.4394	+	2.56398i	1.43644	+	0.113535i
$511$			8.00000i			0.353899i
$512$	18.4390	+	13.1150i	0.814895	+	0.579609i
$513$	1.17372	−	5.49607i	0.0518209	−	0.242657i
$514$	−0.290209	−	0.593332i	−0.0128006	−	0.0261707i
$515$	−5.61872	+	11.2374i	−0.247591	+	0.495181i
$516$	−17.1084	+	19.0743i	−0.753156	+	0.839700i
$517$		−	0.838825i		−	0.0368915i
$518$	3.69833	−	1.80892i	0.162495	−	0.0794795i
$519$	−3.35378	−	0.235593i	−0.147214	−	0.0103414i
$520$	23.9927	+	18.9978i	1.05215	+	0.833110i
$521$			22.4112i			0.981851i	0.871202	+	0.490925i	$0.163341\pi$
$521$			22.4112i			0.981851i	−0.871202	+	0.490925i	$0.836659\pi$
$522$	−19.5216	+	6.35334i	−0.854435	+	0.278078i
$523$	8.74980			0.382602			0.191301	−	0.981531i	$-0.438729\pi$
$523$	8.74980			0.382602			0.191301	+	0.981531i	$0.438729\pi$
$524$	−7.74471	+	9.95864i	−0.338329	+	0.435045i
$525$	−4.69789	−	7.27529i	−0.205033	−	0.317520i
$526$	10.7707	−	5.26814i	0.469624	−	0.229702i
$527$			56.8386i			2.47593i
$528$	−4.25529	−	23.5598i	−0.185188	−	1.02531i
$529$	22.6447			0.984552
$530$	37.3841	+	0.326861i	1.62386	+	0.0141979i
$531$	9.66009	+	1.36391i	0.419212	+	0.0591888i
$532$	1.70755	+	1.32794i	0.0740318	+	0.0575736i
$533$	−33.4419			−1.44853
$534$	11.8822	−	4.81177i	0.514191	−	0.208225i
$535$	−3.36982	−	1.68491i	−0.145690	−	0.0728449i
$536$	−15.8335	−	3.31001i	−0.683904	−	0.142971i
$537$	11.7625	+	0.826283i	0.507591	+	0.0356567i
$538$	0.183820	−	0.0899096i	0.00792503	−	0.00387628i
$539$	3.45559			0.148843
$540$	5.42809	+	22.5950i	0.233588	+	0.972336i
$541$	23.3562			1.00416			0.502080	−	0.864821i	$-0.332568\pi$
$541$	23.3562			1.00416			0.502080	+	0.864821i	$0.332568\pi$
$542$	−29.3779	+	14.3693i	−1.26189	+	0.617214i
$543$	−5.13324	−	0.360594i	−0.220288	−	0.0154746i
$544$	25.6238	−	21.7464i	1.09861	−	0.932368i
$545$	9.94108	−	19.8822i	0.425829	−	0.851658i
$546$	10.9860	−	4.44887i	0.470159	−	0.190394i
$547$	27.7229			1.18535			0.592674	−	0.805443i	$-0.298072\pi$
$547$	27.7229			1.18535			0.592674	+	0.805443i	$0.298072\pi$
$548$	−10.6187	+	13.6542i	−0.453609	+	0.583279i
$549$	−37.5732	−	5.30499i	−1.60359	−	0.226411i
$550$	−11.1182	+	21.7587i	−0.474081	+	0.927793i
$551$	−5.23352			−0.222956
$552$	−0.796380	+	2.80949i	−0.0338962	+	0.119580i
$553$			0.949416i			0.0403733i
$554$	1.04970	−	0.513429i	0.0445976	−	0.0218135i
$555$	9.70647	+	5.73657i	0.412017	+	0.243504i
$556$	−9.20362	−	7.15755i	−0.390320	−	0.303548i
$557$	−15.8241			−0.670489			−0.335244	−	0.942131i	$-0.608819\pi$
$557$	−15.8241			−0.670489			−0.335244	+	0.942131i	$0.608819\pi$
$558$	−38.5969	+	12.5615i	−1.63394	+	0.531769i
$559$			35.7911i			1.51380i
$560$	−8.73867	−	1.90672i	−0.369276	−	0.0805735i
$561$	−35.4714	−	2.49176i	−1.49760	−	0.105202i
$562$	18.6254	−	9.11004i	0.785667	−	0.384284i
$563$		−	37.5112i		−	1.58091i	−0.612522	−	0.790454i	$-0.709845\pi$
$563$		−	37.5112i		−	1.58091i	0.612522	−	0.790454i	$-0.290155\pi$
$564$	0.625983	+	0.561466i	0.0263586	+	0.0236420i
$565$	3.23352	−	6.46705i	0.136035	−	0.272071i
$566$	−12.6925	−	25.9497i	−0.533506	−	1.09075i
$567$	8.64819	+	2.49176i	0.363190	+	0.104644i
$568$	−22.1486	−	4.63018i	−0.929335	−	0.194278i
$569$			19.8804i			0.833429i	0.909037	+	0.416715i	$0.136819\pi$
$569$			19.8804i			0.833429i	−0.909037	+	0.416715i	$0.863181\pi$
$570$	−0.466770	+	5.90558i	−0.0195509	+	0.247358i
$571$		−	3.37707i		−	0.141326i	−0.997500	−	0.0706631i	$-0.977488\pi$
$571$		−	3.37707i		−	0.141326i	0.997500	−	0.0706631i	$-0.0225115\pi$
$572$	−26.3986	−	20.5299i	−1.10378	−	0.858398i
$573$	35.6750	+	2.50606i	1.49035	+	0.104692i
$574$	8.77990	−	4.29441i	0.366466	−	0.179245i
$575$	2.38432	−	1.78824i	0.0994330	−	0.0745748i
$576$	20.4301	+	12.5942i	0.851252	+	0.524757i
$577$		−	6.66117i		−	0.277308i	−0.990341	−	0.138654i	$-0.955722\pi$
$577$		−	6.66117i		−	0.277308i	0.990341	−	0.138654i	$-0.0442776\pi$
$578$	−11.3689	−	23.2436i	−0.472882	−	0.966805i
$579$	1.16029	−	16.5174i	0.0482202	−	0.686438i
$580$	19.5216	−	9.33774i	0.810588	−	0.387728i
$581$			16.9637i			0.703774i
$582$	−7.50562	+	3.03946i	−0.311118	+	0.125990i
$583$	−40.8531			−1.69196
$584$	−4.63018	+	22.1486i	−0.191598	+	0.916516i
$585$	26.7184	+	18.4328i	1.10467	+	0.762104i
$586$	3.36425	+	6.87819i	0.138976	+	0.284135i
$587$		−	31.7716i		−	1.31135i	−0.755042	−	0.655676i	$-0.772384\pi$
$587$		−	31.7716i		−	1.31135i	0.755042	−	0.655676i	$-0.227616\pi$
$588$	−2.31299	+	2.57877i	−0.0953862	+	0.106347i
$589$	−10.3474			−0.426359
$590$	−10.2832	−	0.0899096i	−0.423354	−	0.00370152i
$591$	19.9729	+	1.40304i	0.821577	+	0.0577133i
$592$	11.2861	−	2.86765i	0.463855	−	0.117860i
$593$	−24.2903			−0.997482			−0.498741	−	0.866751i	$-0.666204\pi$
$593$	−24.2903			−0.997482			−0.498741	+	0.866751i	$0.666204\pi$
$594$	−6.14721	−	24.6380i	−0.252223	−	1.01091i
$595$	−5.94108	+	11.8822i	−0.243560	+	0.487121i
$596$	28.1374	+	21.8822i	1.15255	+	0.896328i
$597$	−2.05892	+	29.3098i	−0.0842662	+	1.19957i
$598$	1.79224	+	3.66423i	0.0732902	+	0.149841i
$599$	34.0277			1.39034			0.695168	−	0.718848i	$-0.255330\pi$
$599$	34.0277			1.39034			0.695168	+	0.718848i	$0.255330\pi$
$600$	−8.79573	−	22.8612i	−0.359084	−	0.933305i
$601$	8.99390			0.366869			0.183434	−	0.983032i	$-0.441279\pi$
$601$	8.99390			0.366869			0.183434	+	0.983032i	$0.441279\pi$
$602$	−4.59608	−	9.39666i	−0.187322	−	0.382979i
$603$	−16.9885	−	2.39862i	−0.691827	−	0.0976795i
$604$	−24.8542	−	19.3288i	−1.01130	−	0.786479i
$605$	0.941075	−	1.88215i	0.0382601	−	0.0765203i
$606$	17.5671	−	7.11391i	0.713613	−	0.288983i
$607$	−0.649508			−0.0263627			−0.0131814	−	0.999913i	$-0.504196\pi$
$607$	−0.649508			−0.0263627			−0.0131814	+	0.999913i	$0.504196\pi$
$608$	3.95891	+	4.66480i	0.160555	+	0.189183i
$609$	0.587299	−	8.36049i	0.0237986	−	0.338784i
$610$	39.9969	+	0.349706i	1.61943	+	0.0141592i
$611$	1.17460			0.0475192
$612$	25.6022	−	24.8031i	1.03491	−	1.00261i
$613$			24.6157i			0.994217i	0.867688	+	0.497109i	$0.165605\pi$
$613$			24.6157i			0.994217i	−0.867688	+	0.497109i	$0.834395\pi$
$614$	10.1327	+	20.7162i	0.408922	+	0.836039i
$615$	23.0433	+	13.6187i	0.929197	+	0.549160i
$616$	9.56706	+	2.00000i	0.385468	+	0.0805823i
$617$	−26.9710			−1.08581			−0.542905	−	0.839794i	$-0.682676\pi$
$617$	−26.9710			−1.08581			−0.542905	+	0.839794i	$0.682676\pi$
$618$	5.16592	+	12.7567i	0.207804	+	0.513150i
$619$		−	35.7302i		−	1.43612i	−0.695982	−	0.718059i	$-0.745031\pi$
$619$		−	35.7302i		−	1.43612i	0.695982	−	0.718059i	$-0.254969\pi$
$620$	38.5969	−	18.4621i	1.55009	−	0.741454i
$621$	−0.646865	+	3.02902i	−0.0259578	+	0.121550i
$622$	15.1324	+	30.9380i	0.606752	+	1.24050i
$623$			5.23352i			0.209677i
$624$	32.9906	−	5.95864i	1.32068	−	0.238536i
$625$	−7.00000	+	24.0000i	−0.280000	+	0.960000i
$626$	38.9517	−	19.0520i	1.55682	−	0.761471i
$627$	0.453623	−	6.45755i	0.0181160	−	0.257890i
$628$	28.1374	+	21.8822i	1.12281	+	0.873193i
$629$		−	17.2955i		−	0.689616i
$630$	−9.38171	−	1.40838i	−0.373776	−	0.0561110i
$631$			28.1517i			1.12070i	0.828255	+	0.560352i	$0.189334\pi$
$631$			28.1517i			1.12070i	−0.828255	+	0.560352i	$0.810666\pi$
$632$	−0.549496	+	2.62853i	−0.0218578	+	0.104557i
$633$	2.02858	−	28.8778i	0.0806289	−	1.14779i
$634$	8.62598	+	17.6358i	0.342582	+	0.700406i
$635$	1.08883	−	2.17766i	0.0432088	−	0.0864176i
$636$	27.3450	−	30.4871i	1.08430	−	1.20889i
$637$			4.83882i			0.191721i
$638$	−21.2422	+	10.3899i	−0.840987	+	0.411342i
$639$	−23.7643	−	3.35530i	−0.940101	−	0.132734i
$640$	−23.0901	−	10.3366i	−0.912718	−	0.408590i
$641$		−	36.5329i		−	1.44296i	−0.692433	−	0.721482i	$-0.743461\pi$
$641$		−	36.5329i		−	1.44296i	0.692433	−	0.721482i	$-0.256539\pi$
$642$	−3.82540	+	1.54913i	−0.150977	+	0.0611391i
$643$	−29.7221			−1.17212			−0.586062	−	0.810266i	$-0.699322\pi$
$643$	−29.7221			−1.17212			−0.586062	+	0.810266i	$0.699322\pi$
$644$	−0.941075	−	0.731863i	−0.0370836	−	0.0288394i
$645$	14.5754	−	24.6620i	0.573906	−	0.971067i
$646$	8.16314	−	3.99274i	0.321174	−	0.157092i
$647$			6.11899i			0.240562i	0.992740	+	0.120281i	$0.0383796\pi$
$647$			6.11899i			0.240562i	−0.992740	+	0.120281i	$0.961620\pi$
$648$	22.5010	+	11.9040i	0.883923	+	0.467632i
$649$	11.2374			0.441108
$650$	−30.4685	−	15.5687i	−1.19507	−	0.610654i
$651$	1.16118	−	16.5299i	0.0455101	−	0.647858i
$652$	13.8151	−	17.7643i	0.541041	−	0.695704i
$653$	21.9090			0.857365			0.428683	−	0.903455i	$-0.358978\pi$
$653$	21.9090			0.857365			0.428683	+	0.903455i	$0.358978\pi$
$654$	−9.13995	−	22.5701i	−0.357400	−	0.882562i
$655$	6.30783	−	12.6157i	0.246467	−	0.492935i
$656$	26.7933	−	6.80784i	1.04610	−	0.265801i
$657$	−3.35530	+	23.7643i	−0.130903	+	0.927134i
$658$	−0.308381	+	0.150835i	−0.0120219	+	0.00588015i
$659$	45.4864			1.77190			0.885948	−	0.463784i	$-0.153509\pi$
$659$	45.4864			1.77190			0.885948	+	0.463784i	$0.153509\pi$
$660$	9.82960	+	24.8967i	0.382617	+	0.969101i
$661$	18.7335			0.728649			0.364325	−	0.931272i	$-0.381300\pi$
$661$	18.7335			0.728649			0.364325	+	0.931272i	$0.381300\pi$
$662$	23.0651	−	11.2816i	0.896450	−	0.438470i
$663$	3.48919	−	49.6703i	0.135509	−	1.92903i
$664$	−9.81814	+	46.9654i	−0.381018	+	1.82261i
$665$	−2.16314	−	1.08157i	−0.0838829	−	0.0419414i
$666$	11.7447	−	3.82234i	0.455098	−	0.148113i
$667$	2.88433			0.111682
$668$	26.3872	+	20.5210i	1.02095	+	0.793981i
$669$	−15.1482	−	1.06411i	−0.585662	−	0.0411410i
$670$	18.0844	+	0.158118i	0.698662	+	0.00610863i
$671$	−43.7084			−1.68734
$672$	−7.89622	+	5.80084i	−0.304603	+	0.223772i
$673$		−	5.67589i		−	0.218789i	−0.993998	−	0.109395i	$-0.965109\pi$
$673$		−	5.67589i		−	0.218789i	0.993998	−	0.109395i	$-0.0348912\pi$
$674$	22.1581	−	10.8379i	0.853499	−	0.417462i
$675$	−10.9039	−	23.5819i	−0.419692	−	0.907667i
$676$	12.7865	−	16.4417i	0.491789	−	0.632373i
$677$	−29.7036			−1.14160			−0.570801	−	0.821088i	$-0.693367\pi$
$677$	−29.7036			−1.14160			−0.570801	+	0.821088i	$0.693367\pi$
$678$	−2.97294	−	7.34137i	−0.114175	−	0.281943i
$679$		−	3.30587i		−	0.126868i
$680$	−23.3254	+	29.4581i	−0.894488	+	1.12967i
$681$	−0.0294624	+	0.419412i	−0.00112900	+	0.0160719i
$682$	−41.9989	+	20.5424i	−1.60822	+	0.786611i
$683$		−	44.4223i		−	1.69977i	−0.526965	−	0.849887i	$-0.676670\pi$
$683$		−	44.4223i		−	1.69977i	0.526965	−	0.849887i	$-0.323330\pi$
$684$	4.51539	+	4.66087i	0.172650	+	0.178213i
$685$	8.64863	−	17.2973i	0.330447	−	0.660894i
$686$	−0.621372	−	1.27039i	−0.0237241	−	0.0485038i
$687$	−45.5327	−	3.19854i	−1.73718	−	0.122032i
$688$	−7.28607	−	28.6755i	−0.277779	−	1.09324i
$689$		−	57.2062i		−	2.17938i
$690$	0.257249	−	3.25471i	0.00979330	−	0.123905i
$691$			6.30057i			0.239685i	0.992793	+	0.119843i	$0.0382390\pi$
$691$			6.30057i			0.239685i	−0.992793	+	0.119843i	$0.961761\pi$
$692$	2.38324	−	3.06452i	0.0905971	−	0.116495i
$693$	10.2649	+	1.44932i	0.389933	+	0.0550549i
$694$	−43.0110	+	21.0375i	−1.63267	+	0.798571i
$695$	11.6592	+	5.82960i	0.442259	+	0.221129i
$696$	6.46481	−	22.8067i	0.245048	−	0.864487i
$697$		−	41.0598i		−	1.55525i
$698$	5.77462	+	11.8062i	0.218572	+	0.446870i
$699$	−11.1341	−	0.782138i	−0.421131	−	0.0295832i
$700$	9.99847	+	0.174853i	0.377907	+	0.00660882i
$701$			40.7478i			1.53902i	0.638632	+	0.769512i	$0.279500\pi$
$701$			40.7478i			1.53902i	−0.638632	+	0.769512i	$0.720500\pi$
$702$	34.5003	−	8.60787i	1.30213	−	0.324883i
$703$	3.14863			0.118753
$704$	25.3296	+	11.0743i	0.954645	+	0.417379i
$705$	−0.809362	−	0.478337i	−0.0304823	−	0.0180152i
$706$	−4.64415	−	9.49495i	−0.174785	−	0.357347i
$707$			7.73746i			0.290997i
$708$	−7.52177	+	8.38608i	−0.282685	+	0.315168i
$709$	−38.8830			−1.46028			−0.730141	−	0.683296i	$-0.760546\pi$
$709$	−38.8830			−1.46028			−0.730141	+	0.683296i	$0.760546\pi$
$710$	25.2973	+	0.221182i	0.949389	+	0.00830081i
$711$	−0.398197	+	2.82027i	−0.0149335	+	0.105769i
$712$	−3.02902	+	14.4894i	−0.113517	+	0.543014i
$713$	5.70273			0.213569
$714$	5.46230	+	13.4886i	0.204421	+	0.504797i
$715$	33.4419	+	16.7210i	1.25066	+	0.625329i
$716$	−8.35862	+	10.7480i	−0.312376	+	0.401673i
$717$	28.7669	+	2.02079i	1.07432	+	0.0754677i
$718$	7.05587	+	14.4257i	0.263323	+	0.538362i
$719$	−5.03295			−0.187697			−0.0938486	−	0.995586i	$-0.529917\pi$
$719$	−5.03295			−0.187697			−0.0938486	+	0.995586i	$0.529917\pi$
$720$	−25.1589	−	9.32908i	−0.937615	−	0.347674i
$721$	−5.61872			−0.209252
$722$	−11.0792	−	22.6514i	−0.412325	−	0.842996i
$723$	−9.70647	−	0.681850i	−0.360988	−	0.0253583i
$724$	3.64775	−	4.69050i	0.135567	−	0.174321i
$725$	−19.3553	+	14.5165i	−0.718838	+	0.539128i
$726$	−0.865236	−	2.13661i	−0.0321119	−	0.0792970i
$727$	−11.3553			−0.421145			−0.210572	−	0.977578i	$-0.567533\pi$
$727$	−11.3553			−0.421145			−0.210572	+	0.977578i	$0.567533\pi$
$728$	−2.80058	+	13.3967i	−0.103796	+	0.496513i
$729$	24.6447	+	11.0290i	0.912766	+	0.408482i
$730$	0.221182	−	25.2973i	0.00818631	−	0.936293i
$731$	−43.9441			−1.62533
$732$	29.2562	−	32.6179i	1.08134	−	1.20559i
$733$		−	14.7808i		−	0.545941i	−0.962022	−	0.272970i	$-0.911994\pi$
$733$		−	14.7808i		−	0.545941i	0.962022	−	0.272970i	$-0.0880061\pi$
$734$	−2.63493	−	5.38711i	−0.0972571	−	0.198842i
$735$	1.97054	−	3.33421i	0.0726844	−	0.122984i
$736$	−2.18186	−	2.57089i	−0.0804243	−	0.0947642i
$737$	−19.7625			−0.727962
$738$	27.8822	−	9.07431i	1.02636	−	0.334030i
$739$			36.3478i			1.33708i	0.743678	+	0.668538i	$0.233080\pi$
$739$			36.3478i			1.33708i	−0.743678	+	0.668538i	$0.766920\pi$
$740$	−11.7447	+	5.61784i	−0.431744	+	0.206516i
$741$	9.04244	+	0.635205i	0.332183	+	0.0233348i
$742$	7.34608	+	15.0190i	0.269683	+	0.551365i
$743$		−	1.48881i		−	0.0546191i	−0.999627	−	0.0273096i	$-0.991306\pi$
$743$		−	1.48881i		−	0.0546191i	0.999627	−	0.0273096i	$-0.00869398\pi$
$744$	12.7819	−	45.0922i	0.468606	−	1.65316i
$745$	−35.6447	−	17.8223i	−1.30592	−	0.652960i
$746$	−29.2900	+	14.3263i	−1.07238	+	0.524522i
$747$	−7.11479	+	50.3914i	−0.260317	+	1.84372i
$748$	25.2065	−	32.4120i	0.921640	−	1.18510i
$749$		−	1.68491i		−	0.0615652i
$750$	14.6543	+	23.1355i	0.535100	+	0.844789i
$751$			7.56116i			0.275911i	0.990438	+	0.137955i	$0.0440530\pi$
$751$			7.56116i			0.275911i	−0.990438	+	0.137955i	$0.955947\pi$
$752$	−0.941075	+	0.239115i	−0.0343175	+	0.00871963i
$753$	5.61872	+	0.394698i	0.204758	+	0.0143836i
$754$	−14.5489	−	29.7452i	−0.529841	−	1.08326i
$755$	31.4855	+	15.7427i	1.14587	+	0.572937i
$756$	−7.95240	+	6.69025i	−0.289226	+	0.243322i
$757$			9.61568i			0.349488i	0.984614	+	0.174744i	$0.0559098\pi$
$757$			9.61568i			0.349488i	−0.984614	+	0.174744i	$0.944090\pi$
$758$	−36.6433	+	17.9229i	−1.33095	+	0.650990i
$759$	−0.250003	+	3.55892i	−0.00907454	+	0.129181i
$760$	−5.36283	−	4.24637i	−0.194530	−	0.154032i
$761$			26.2665i			0.952159i	0.879402	+	0.476079i	$0.157943\pi$
$761$			26.2665i			0.952159i	−0.879402	+	0.476079i	$0.842057\pi$
$762$	−1.00108	−	2.47207i	−0.0362654	−	0.0895535i
$763$	9.94108			0.359891
$764$	−25.3512	+	32.5981i	−0.917173	+	1.17936i
$765$	−22.6317	+	32.8046i	−0.818251	+	1.18605i
$766$	8.27177	−	4.04587i	0.298871	−	0.146183i
$767$			15.7357i			0.568183i
$768$	−25.2187	+	11.4899i	−0.910000	+	0.414608i
$769$	35.5849			1.28322			0.641612	−	0.767029i	$-0.278266\pi$
$769$	35.5849			1.28322			0.641612	+	0.767029i	$0.278266\pi$
$770$	−10.9271	−	0.0955392i	−0.393786	−	0.00344299i
$771$	0.806959	+	0.0566864i	0.0290619	+	0.00204151i
$772$	15.0928	+	11.7375i	0.543200	+	0.422440i
$773$	28.5338			1.02629			0.513145	−	0.858302i	$-0.328480\pi$
$773$	28.5338			1.02629			0.513145	+	0.858302i	$0.328480\pi$
$774$	−9.71175	−	29.8408i	−0.349082	−	1.07260i
$775$	−38.2682	+	28.7012i	−1.37464	+	1.03098i
$776$	1.91335	−	9.15256i	0.0686852	−	0.328558i
$777$	−0.353336	+	5.02990i	−0.0126758	+	0.180447i
$778$	−28.9724	+	14.1709i	−1.03871	+	0.508052i
$779$	7.47491			0.267816
$780$	−34.8626	+	13.7643i	−1.24828	+	0.492841i
$781$	−27.6447			−0.989205
$782$	−4.49891	+	2.20050i	−0.160881	+	0.0786897i
$783$	5.25108	−	24.5888i	0.187658	−	0.878733i
$784$	−0.985049	−	3.87681i	−0.0351803	−	0.138458i
$785$	−35.6447	−	17.8223i	−1.27221	−	0.636107i
$786$	−5.79950	−	14.3213i	−0.206861	−	0.510822i
$787$	−12.1372			−0.432644			−0.216322	−	0.976322i	$-0.569406\pi$
$787$	−12.1372			−0.432644			−0.216322	+	0.976322i	$0.569406\pi$
$788$	−14.1930	+	18.2503i	−0.505606	+	0.650140i
$789$	−1.02902	+	14.6486i	−0.0366342	+	0.521505i
$790$	0.0262492	−	3.00220i	0.000933905	−	0.106814i
$791$	3.23352			0.114971
$792$	27.5805	+	9.95362i	0.980030	+	0.353686i
$793$		−	61.2045i		−	2.17344i
$794$	−16.6461	+	8.14192i	−0.590749	+	0.288946i
$795$	−23.2964	+	39.4182i	−0.826237	+	1.39802i
$796$	−26.7819	−	20.8279i	−0.949258	−	0.738227i
$797$	48.9428			1.73364			0.866822	−	0.498618i	$-0.166159\pi$
$797$	48.9428			1.73364			0.866822	+	0.498618i	$0.166159\pi$
$798$	−2.45559	+	0.994408i	−0.0869268	+	0.0352017i
$799$			1.44216i			0.0510201i
$800$	27.5803	+	6.27094i	0.975112	+	0.221711i
$801$	−2.19500	+	15.5464i	−0.0775566	+	0.549304i
$802$	13.6958	−	6.69888i	0.483616	−	0.236546i
$803$			27.6447i			0.975560i
$804$	13.2280	−	14.7480i	0.466517	−	0.520123i
$805$	1.19216	+	0.596080i	0.0420181	+	0.0210091i
$806$	−28.7654	−	58.8107i	−1.01322	−	2.07152i
$807$	−0.0175620	+	0.250003i	−0.000618211	+	0.00880053i
$808$	−4.47823	+	21.4217i	−0.157544	+	0.753614i
$809$			28.7478i			1.01072i	0.862909	+	0.505360i	$0.168640\pi$
$809$			28.7478i			1.01072i	−0.862909	+	0.505360i	$0.831360\pi$
$810$	−27.2780	−	8.11844i	−0.958452	−	0.285253i
$811$		−	16.2821i		−	0.571743i	−0.958268	−	0.285871i	$-0.907717\pi$
$811$		−	16.2821i		−	0.571743i	0.958268	−	0.285871i	$-0.0922830\pi$
$812$	7.63941	+	5.94108i	0.268091	+	0.208491i
$813$	2.80675	−	39.9554i	0.0984368	−	1.40130i
$814$	12.7799	−	6.25088i	0.447935	−	0.219093i
$815$	−11.2520	+	22.5039i	−0.394139	+	0.788278i
$816$	7.31597	+	40.5056i	0.256110	+	1.41798i
$817$		−	8.00000i		−	0.279885i
$818$	−9.75834	−	19.9509i	−0.341192	−	0.697566i
$819$	−2.02946	+	14.3739i	−0.0709152	+	0.502265i
$820$	−27.8822	+	13.3369i	−0.973687	+	0.465743i
$821$		−	36.0780i		−	1.25913i	−0.776947	−	0.629566i	$-0.783233\pi$
$821$		−	36.0780i		−	1.25913i	0.776947	−	0.629566i	$-0.216767\pi$
$822$	−7.95165	−	19.6358i	−0.277346	−	0.684876i
$823$	−45.6117			−1.58992			−0.794962	−	0.606659i	$-0.792509\pi$
$823$	−45.6117			−1.58992			−0.794962	+	0.606659i	$0.792509\pi$
$824$	−15.5559	−	3.25197i	−0.541915	−	0.113288i
$825$	−16.2340	−	25.1404i	−0.565194	−	0.875276i
$826$	−2.02068	−	4.13127i	−0.0703085	−	0.143745i
$827$			27.6374i			0.961048i	0.876982	+	0.480524i	$0.159553\pi$
$827$			27.6374i			0.961048i	−0.876982	+	0.480524i	$0.840447\pi$
$828$	−2.48855	−	2.56872i	−0.0864830	−	0.0892694i
$829$	4.88609			0.169701			0.0848504	−	0.996394i	$-0.472959\pi$
$829$	4.88609			0.169701			0.0848504	+	0.996394i	$0.472959\pi$
$830$	0.469009	−	53.6419i	0.0162795	−	1.86194i
$831$	−0.100288	+	1.42765i	−0.00347895	+	0.0495245i
$832$	−15.5073	+	35.4688i	−0.537617	+	1.22966i
$833$	−5.94108			−0.205846
$834$	13.2355	−	5.35981i	0.458307	−	0.185595i
$835$	−33.4274	−	16.7137i	−1.15680	−	0.578402i
$836$	5.90059	+	4.58882i	0.204076	+	0.158708i
$837$	10.3822	−	48.6157i	0.358860	−	1.68040i
$838$	20.5515	+	42.0173i	0.709938	+	1.45147i
$839$	41.3592			1.42788			0.713939	−	0.700207i	$-0.246909\pi$
$839$	41.3592			1.42788			0.713939	+	0.700207i	$0.246909\pi$
$840$	7.38534	−	8.09054i	0.254818	−	0.279150i
$841$	5.58578			0.192613
$842$	−4.89720	−	10.0123i	−0.168769	−	0.345047i
$843$	−1.77946	+	25.3315i	−0.0612878	+	0.872462i
$844$	26.3872	+	20.5210i	0.908284	+	0.706361i
$845$	−10.4142	+	20.8284i	−0.358260	+	0.716520i
$846$	−0.979319	+	0.318721i	−0.0336697	+	0.0109579i
$847$	0.941075			0.0323357
$848$	11.6456	+	45.8330i	0.399911	+	1.57391i
$849$	35.2929	+	2.47922i	1.21125	+	0.0850865i
$850$	19.1151	−	37.4090i	0.655643	−	1.28312i
$851$	−1.73529			−0.0594850
$852$	18.5039	−	20.6302i	0.633934	−	0.706778i
$853$		−	17.2973i		−	0.592247i	−0.955150	−	0.296123i	$-0.904306\pi$
$853$		−	17.2973i		−	0.592247i	0.955150	−	0.296123i	$-0.0956939\pi$
$854$	7.85951	+	16.0687i	0.268947	+	0.549860i
$855$	−5.97206	−	4.12009i	−0.204240	−	0.140904i
$856$	0.975179	−	4.66480i	0.0333309	−	0.159440i
$857$	−40.4749			−1.38260			−0.691298	−	0.722570i	$-0.742961\pi$
$857$	−40.4749			−1.38260			−0.691298	+	0.722570i	$0.742961\pi$
$858$	37.9632	−	15.3735i	1.29604	−	0.524842i
$859$			40.6849i			1.38815i	0.719902	+	0.694075i	$0.244187\pi$
$859$			40.6849i			1.38815i	−0.719902	+	0.694075i	$0.755813\pi$
$860$	14.2737	+	29.8408i	0.486730	+	1.01756i
$861$	−0.838825	+	11.9411i	−0.0285871	+	0.406951i
$862$	−16.3746	−	33.4777i	−0.557719	−	1.14025i
$863$		−	7.84981i		−	0.267211i	−0.991035	−	0.133605i	$-0.957345\pi$
$863$		−	7.84981i		−	0.267211i	0.991035	−	0.133605i	$-0.0426554\pi$
$864$	−25.8890	+	13.9198i	−0.880760	+	0.473562i
$865$	−1.94108	+	3.88215i	−0.0659985	+	0.131997i
$866$	−47.3821	+	23.1755i	−1.61011	+	0.787535i
$867$	31.6123	+	2.22067i	1.07361	+	0.0754180i
$868$	15.1042	+	11.7464i	0.512670	+	0.398698i
$869$			3.28079i			0.111293i
$870$	−2.08828	+	26.4209i	−0.0707993	+	0.895754i
$871$		−	27.6733i		−	0.937674i
$872$	27.5226	+	5.75363i	0.932034	+	0.194842i
$873$	1.38652	−	9.82021i	0.0469267	−	0.332364i
$874$	−0.400600	−	0.819024i	−0.0135505	−	0.0277039i
$875$	−11.0000	+	2.00000i	−0.371868	+	0.0676123i
$876$	−20.6302	−	18.5039i	−0.697029	−	0.625190i
$877$		−	4.58882i		−	0.154953i	−0.996994	−	0.0774767i	$-0.975314\pi$
$877$		−	4.58882i		−	0.154953i	0.996994	−	0.0774767i	$-0.0246864\pi$
$878$	−16.0361	+	7.84354i	−0.541191	+	0.264707i
$879$	−9.35466	−	0.657136i	−0.315525	−	0.0221647i
$880$	−30.1972	−	6.58882i	−1.01795	−	0.222109i
$881$			13.0906i			0.441033i	0.975383	+	0.220517i	$0.0707743\pi$
$881$			13.0906i			0.441033i	−0.975383	+	0.220517i	$0.929226\pi$
$882$	−1.31299	−	4.03436i	−0.0442107	−	0.135844i
$883$	19.4335			0.653991			0.326995	−	0.945026i	$-0.393964\pi$
$883$	19.4335			0.653991			0.326995	+	0.945026i	$0.393964\pi$
$884$	45.3863	+	35.2964i	1.52651	+	1.18715i
$885$	6.40812	−	10.8427i	0.215407	−	0.364475i
$886$	−27.5824	+	13.4911i	−0.926650	+	0.453242i
$887$		−	33.1704i		−	1.11375i	−0.830595	−	0.556876i	$-0.812000\pi$
$887$		−	33.1704i		−	1.11375i	0.830595	−	0.556876i	$-0.188000\pi$
$888$	−3.88941	+	13.7212i	−0.130520	+	0.460452i
$889$	1.08883			0.0365181
$890$	0.144695	−	16.5492i	0.00485019	−	0.554731i
$891$	29.8846	+	8.61049i	1.00117	+	0.288462i
$892$	10.7645	−	13.8417i	0.360422	−	0.463453i
$893$	−0.262545			−0.00878573
$894$	−40.4637	+	16.3861i	−1.35331	+	0.548033i
$895$	6.80784	−	13.6157i	0.227561	−	0.455122i
$896$	−0.483388	−	11.3034i	−0.0161489	−	0.377619i
$897$	−4.98352	−	0.350077i	−0.166395	−	0.0116887i
$898$	−18.5936	+	9.09446i	−0.620475	+	0.303486i
$899$	−46.2933			−1.54397
$900$	29.6275	+	4.71289i	0.987583	+	0.157096i
$901$	70.2374			2.33995
$902$	30.3397	−	14.8397i	1.01020	−	0.494108i
$903$	12.7799	+	0.897749i	0.425288	+	0.0298752i
$904$	8.95226	+	1.87148i	0.297748	+	0.0622444i
$905$	−2.97098	+	5.94196i	−0.0987587	+	0.197517i
$906$	35.7422	−	14.4741i	1.18745	−	0.480869i
$907$	−35.6051			−1.18225			−0.591124	−	0.806581i	$-0.701316\pi$
$907$	−35.6051			−1.18225			−0.591124	+	0.806581i	$0.701316\pi$
$908$	−0.383238	−	0.298040i	−0.0127182	−	0.00989081i
$909$	−3.24518	+	22.9844i	−0.107636	+	0.762344i
$910$	0.133783	−	15.3011i	0.00443485	−	0.507227i
$911$	2.26038			0.0748898			0.0374449	−	0.999299i	$-0.488078\pi$
$911$	2.26038			0.0748898			0.0374449	+	0.999299i	$0.488078\pi$
$912$	−7.37402	+	1.33187i	−0.244178	+	0.0441026i
$913$			58.6196i			1.94003i
$914$	−5.08381	+	2.48658i	−0.168157	+	0.0822489i
$915$	−24.9246	+	42.1732i	−0.823982	+	1.39420i
$916$	32.3562	−	41.6056i	1.06908	−	1.37469i
$917$	6.30783			0.208303
$918$	10.5687	+	42.3593i	0.348819	+	1.39806i
$919$			2.42040i			0.0798416i	0.999203	+	0.0399208i	$0.0127106\pi$
$919$			2.42040i			0.0798416i	−0.999203	+	0.0399208i	$0.987289\pi$
$920$	2.95559	+	2.34028i	0.0974430	+	0.0771569i
$921$	−28.1750	−	1.97921i	−0.928399	−	0.0652172i
$922$	46.9308	−	22.9547i	1.54558	−	0.755973i
$923$		−	38.7106i		−	1.27417i
$924$	−7.99274	+	8.91117i	−0.262942	+	0.293156i
$925$	11.6447	−	8.73352i	0.382875	−	0.287156i
$926$	−3.80390	−	7.77706i	−0.125004	−	0.255570i
$927$	−16.6906	−	2.35656i	−0.548192	−	0.0773996i
$928$	17.7118	+	20.8698i	0.581417	+	0.685085i
$929$		−	18.9380i		−	0.621336i	−0.950518	−	0.310668i	$-0.899447\pi$
$929$		−	18.9380i		−	0.621336i	0.950518	−	0.310668i	$-0.100553\pi$
$930$	−4.12883	+	52.2380i	−0.135390	+	1.71295i
$931$		−	1.08157i		−	0.0354470i
$932$	7.91205	−	10.1738i	0.259168	−	0.333254i
$933$	−42.0772	−	2.95579i	−1.37754	−	0.0967683i
$934$	17.8682	−	8.73966i	0.584665	−	0.285970i
$935$	−20.5299	+	41.0598i	−0.671399	+	1.34280i
$936$	−13.9380	+	38.6207i	−0.455576	+	1.26236i
$937$			13.4835i			0.440488i	0.975445	+	0.220244i	$0.0706853\pi$
$937$			13.4835i			0.440488i	−0.975445	+	0.220244i	$0.929315\pi$
$938$	3.55364	+	7.26539i	0.116030	+	0.237223i
$939$	−3.72142	+	52.9762i	−0.121444	+	1.72881i
$940$	0.979319	−	0.468437i	0.0319418	−	0.0152787i
$941$			60.5598i			1.97419i	0.160128	+	0.987096i	$0.448809\pi$
$941$			60.5598i			1.97419i	−0.160128	+	0.987096i	$0.551191\pi$
$942$	−40.4637	+	16.3861i	−1.31838	+	0.533887i
$943$	−4.11961			−0.134153
$944$	−3.20334	−	12.6073i	−0.104260	−	0.410332i
$945$	7.25197	−	9.07794i	0.235906	−	0.295305i
$946$	−15.8822	−	32.4710i	−0.516373	−	1.05572i
$947$		−	27.9514i		−	0.908298i	−0.890926	−	0.454149i	$-0.849943\pi$
$947$		−	27.9514i		−	0.908298i	0.890926	−	0.454149i	$-0.150057\pi$
$948$	−2.44833	−	2.19599i	−0.0795180	−	0.0713224i
$949$	−38.7106			−1.25660
$950$	6.81028	+	3.47990i	0.220955	+	0.112903i
$951$	−23.9855	−	1.68491i	−0.777783	−	0.0546369i
$952$	−16.4483	−	3.43853i	−0.533093	−	0.111444i
$953$	28.4112			0.920328			0.460164	−	0.887834i	$-0.347791\pi$
$953$	28.4112			0.920328			0.460164	+	0.887834i	$0.347791\pi$
$954$	15.5226	+	47.6956i	0.502564	+	1.54420i
$955$	20.6477	−	41.2955i	0.668145	−	1.33629i
$956$	−20.4422	+	26.2858i	−0.661146	+	0.850143i
$957$	2.02946	−	28.8904i	0.0656032	−	0.933893i
$958$	−20.7799	−	42.4844i	−0.671368	−	1.37261i
$959$	8.64863			0.279279
$960$	25.1295	−	18.1248i	0.811050	−	0.584977i
$961$	−60.5286			−1.95254
$962$	8.75305	+	17.8956i	0.282210	+	0.576976i
$963$	0.706671	−	5.00508i	0.0227722	−	0.161287i
$964$	6.89755	−	8.86930i	0.222155	−	0.285661i
$965$	−19.1196	−	9.55980i	−0.615482	−	0.307741i
$966$	1.35334	−	0.548043i	0.0435429	−	0.0176330i
$967$	41.1776			1.32418			0.662092	−	0.749423i	$-0.269669\pi$
$967$	41.1776			1.32418			0.662092	+	0.749423i	$0.269669\pi$
$968$	2.60544	+	0.544669i	0.0837420	+	0.0175063i
$969$	−0.779900	+	11.1023i	−0.0250540	+	0.356656i
$970$	−0.0913999	+	10.4537i	−0.00293467	+	0.335647i
$971$	35.1592			1.12831			0.564156	−	0.825668i	$-0.309202\pi$
$971$	35.1592			1.12831			0.564156	+	0.825668i	$0.309202\pi$
$972$	−26.4289	+	16.5383i	−0.847706	+	0.530466i
$973$			5.82960i			0.186888i
$974$	−11.0754	−	22.6436i	−0.354879	−	0.725548i
$975$	35.2038	−	22.7323i	1.12743	−	0.728015i
$976$	12.4595	+	49.0364i	0.398819	+	1.56962i
$977$	48.4129			1.54887			0.774433	−	0.632655i	$-0.218035\pi$
$977$	48.4129			1.54887			0.774433	+	0.632655i	$0.218035\pi$
$978$	10.3452	+	25.5464i	0.330803	+	0.816883i
$979$			18.0849i			0.577996i
$980$	1.92975	+	4.03436i	0.0616437	+	0.128873i
$981$	29.5303	+	4.16941i	0.942831	+	0.133119i
$982$	7.64829	+	15.6369i	0.244067	+	0.498993i
$983$		−	18.6557i		−	0.595024i	−0.954718	−	0.297512i	$-0.903843\pi$
$983$		−	18.6557i		−	0.595024i	0.954718	−	0.297512i	$-0.0961568\pi$
$984$	−9.23352	+	32.5743i	−0.294354	+	1.03843i
$985$	11.5598	−	23.1196i	0.368326	−	0.736652i
$986$	36.5210	−	17.8631i	1.16307	−	0.568877i
$987$	0.0294624	−	0.419412i	0.000937800	−	0.0133500i
$988$	−6.42568	+	8.26254i	−0.204428	+	0.262867i
$989$			4.40900i			0.140198i
$990$	−32.4193	−	4.86676i	−1.03035	−	0.154676i
$991$		−	11.8876i		−	0.377624i	−0.982013	−	0.188812i	$-0.939536\pi$
$991$		−	11.8876i		−	0.377624i	0.982013	−	0.188812i	$-0.0604636\pi$
$992$	35.0187	+	41.2626i	1.11185	+	1.31009i
$993$	−2.20362	+	31.3696i	−0.0699298	+	0.995484i
$994$	4.97098	+	10.1631i	0.157670	+	0.322355i
$995$	33.9274	+	16.9637i	1.07557	+	0.537786i
$996$	−43.7456	−	39.2369i	−1.38613	−	1.24327i
$997$			46.0451i			1.45826i	0.684374	+	0.729131i	$0.260076\pi$
$997$			46.0451i			1.45826i	−0.684374	+	0.729131i	$0.739924\pi$
$998$	−16.6347	+	8.13632i	−0.526561	+	0.257551i
$999$	−3.15920	+	14.7933i	−0.0999527	+	0.468040i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	420.2.l.f.239.3	yes	8
3.2	odd	2		420.2.l.e.239.6	yes	8
4.3	odd	2		420.2.l.d.239.4	yes	8
5.4	even	2		420.2.l.c.239.6	yes	8
12.11	even	2		420.2.l.c.239.5	✓	8
15.14	odd	2		420.2.l.d.239.3	yes	8
20.19	odd	2		420.2.l.e.239.5	yes	8
60.59	even	2	inner	420.2.l.f.239.4	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
420.2.l.c.239.5	✓	8	12.11	even	2
420.2.l.c.239.6	yes	8	5.4	even	2
420.2.l.d.239.3	yes	8	15.14	odd	2
420.2.l.d.239.4	yes	8	4.3	odd	2
420.2.l.e.239.5	yes	8	20.19	odd	2
420.2.l.e.239.6	yes	8	3.2	odd	2
420.2.l.f.239.3	yes	8	1.1	even	1	trivial
420.2.l.f.239.4	yes	8	60.59	even	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 420 = 2^{2} \cdot 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	420.l (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.621372 - 1.27039i) q^{2} +(1.72779 + 0.121372i) q^{3} +(-1.22779 + 1.57877i) q^{4} +(1.00000 - 2.00000i) q^{5} +(-0.919412 - 2.27039i) q^{6} +1.00000 q^{7} +(2.76858 + 0.578773i) q^{8} +(2.97054 + 0.419412i) q^{9} +O(q^{10})\)	\(q+(-0.621372 - 1.27039i) q^{2} +(1.72779 + 0.121372i) q^{3} +(-1.22779 + 1.57877i) q^{4} +(1.00000 - 2.00000i) q^{5} +(-0.919412 - 2.27039i) q^{6} +1.00000 q^{7} +(2.76858 + 0.578773i) q^{8} +(2.97054 + 0.419412i) q^{9} +(-3.16216 - 0.0276478i) q^{10} +3.45559 q^{11} +(-2.31299 + 2.57877i) q^{12} +4.83882i q^{13} +(-0.621372 - 1.27039i) q^{14} +(1.97054 - 3.33421i) q^{15} +(-0.985049 - 3.87681i) q^{16} -5.94108 q^{17} +(-1.31299 - 4.03436i) q^{18} -1.08157i q^{19} +(1.92975 + 4.03436i) q^{20} +(1.72779 + 0.121372i) q^{21} +(-2.14721 - 4.38995i) q^{22} +0.596080i q^{23} +(4.71328 + 1.33603i) q^{24} +(-3.00000 - 4.00000i) q^{25} +(6.14721 - 3.00671i) q^{26} +(5.08157 + 1.08520i) q^{27} +(-1.22779 + 1.57877i) q^{28} -4.83882i q^{29} +(-5.46020 - 0.431568i) q^{30} -9.56706i q^{31} +(-4.31299 + 3.66034i) q^{32} +(5.97054 + 0.419412i) q^{33} +(3.69162 + 7.54750i) q^{34} +(1.00000 - 2.00000i) q^{35} +(-4.30936 + 4.17485i) q^{36} +2.91117i q^{37} +(-1.37402 + 0.672057i) q^{38} +(-0.587299 + 8.36049i) q^{39} +(3.92612 - 4.95838i) q^{40} +6.91117i q^{41} +(-0.919412 - 2.27039i) q^{42} +7.39666 q^{43} +(-4.24274 + 5.45559i) q^{44} +(3.80936 - 5.52166i) q^{45} +(0.757255 - 0.370388i) q^{46} -0.242745i q^{47} +(-1.23142 - 6.81789i) q^{48} +1.00000 q^{49} +(-3.21745 + 6.29667i) q^{50} +(-10.2649 - 0.721082i) q^{51} +(-7.63941 - 5.94108i) q^{52} -11.8223 q^{53} +(-1.77892 - 7.12990i) q^{54} +(3.45559 - 6.91117i) q^{55} +(2.76858 + 0.578773i) q^{56} +(0.131272 - 1.86873i) q^{57} +(-6.14721 + 3.00671i) q^{58} +3.25197 q^{59} +(2.84455 + 7.20476i) q^{60} -12.6486 q^{61} +(-12.1539 + 5.94470i) q^{62} +(2.97054 + 0.419412i) q^{63} +(7.33004 + 3.20476i) q^{64} +(9.67765 + 4.83882i) q^{65} +(-3.17711 - 7.84554i) q^{66} -5.71901 q^{67} +(7.29441 - 9.37961i) q^{68} +(-0.0723476 + 1.02990i) q^{69} +(-3.16216 - 0.0276478i) q^{70} -8.00000 q^{71} +(7.98142 + 2.88044i) q^{72} +8.00000i q^{73} +(3.69833 - 1.80892i) q^{74} +(-4.69789 - 7.27529i) q^{75} +(1.70755 + 1.32794i) q^{76} +3.45559 q^{77} +(10.9860 - 4.44887i) q^{78} +0.949416i q^{79} +(-8.73867 - 1.90672i) q^{80} +(8.64819 + 2.49176i) q^{81} +(8.77990 - 4.29441i) q^{82} +16.9637i q^{83} +(-2.31299 + 2.57877i) q^{84} +(-5.94108 + 11.8822i) q^{85} +(-4.59608 - 9.39666i) q^{86} +(0.587299 - 8.36049i) q^{87} +(9.56706 + 2.00000i) q^{88} +5.23352i q^{89} +(-9.38171 - 1.40838i) q^{90} +4.83882i q^{91} +(-0.941075 - 0.731863i) q^{92} +(1.16118 - 16.5299i) q^{93} +(-0.308381 + 0.150835i) q^{94} +(-2.16314 - 1.08157i) q^{95} +(-7.89622 + 5.80084i) q^{96} -3.30587i q^{97} +(-0.621372 - 1.27039i) q^{98} +(10.2649 + 1.44932i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 2 q^{3} + 2 q^{4} + 8 q^{5} + 4 q^{6} + 8 q^{7} - 6 q^{8} + 2 q^{9}+O(q^{10}) \) 8 * q + 2 * q^3 + 2 * q^4 + 8 * q^5 + 4 * q^6 + 8 * q^7 - 6 * q^8 + 2 * q^9	\( 8 q + 2 q^{3} + 2 q^{4} + 8 q^{5} + 4 q^{6} + 8 q^{7} - 6 q^{8} + 2 q^{9} - 4 q^{10} + 4 q^{11} - 14 q^{12} - 6 q^{15} - 6 q^{16} - 4 q^{17} - 6 q^{18} + 10 q^{20} + 2 q^{21} + 6 q^{22} + 6 q^{24} - 24 q^{25} + 26 q^{26} + 8 q^{27} + 2 q^{28} - 16 q^{30} - 30 q^{32} + 26 q^{33} + 30 q^{34} + 8 q^{35} + 10 q^{36} - 20 q^{38} + 18 q^{39} - 14 q^{40} + 4 q^{42} - 8 q^{43} - 24 q^{44} - 14 q^{45} + 16 q^{46} - 38 q^{48} + 8 q^{49} - 8 q^{50} - 14 q^{51} + 16 q^{52} + 8 q^{54} + 4 q^{55} - 6 q^{56} + 20 q^{57} - 26 q^{58} + 8 q^{59} + 10 q^{60} - 16 q^{61} - 40 q^{62} + 2 q^{63} + 26 q^{64} + 32 q^{65} - 6 q^{66} - 24 q^{67} + 12 q^{68} + 24 q^{69} - 4 q^{70} - 64 q^{71} + 22 q^{72} - 4 q^{74} - 22 q^{75} - 28 q^{76} + 4 q^{77} + 42 q^{78} - 38 q^{80} + 2 q^{81} + 4 q^{82} - 14 q^{84} - 4 q^{85} - 24 q^{86} - 18 q^{87} + 24 q^{88} - 6 q^{90} + 36 q^{92} + 32 q^{93} - 2 q^{94} + 48 q^{95} - 14 q^{96} + 14 q^{99}+O(q^{100}) \) 8 * q + 2 * q^3 + 2 * q^4 + 8 * q^5 + 4 * q^6 + 8 * q^7 - 6 * q^8 + 2 * q^9 - 4 * q^10 + 4 * q^11 - 14 * q^12 - 6 * q^15 - 6 * q^16 - 4 * q^17 - 6 * q^18 + 10 * q^20 + 2 * q^21 + 6 * q^22 + 6 * q^24 - 24 * q^25 + 26 * q^26 + 8 * q^27 + 2 * q^28 - 16 * q^30 - 30 * q^32 + 26 * q^33 + 30 * q^34 + 8 * q^35 + 10 * q^36 - 20 * q^38 + 18 * q^39 - 14 * q^40 + 4 * q^42 - 8 * q^43 - 24 * q^44 - 14 * q^45 + 16 * q^46 - 38 * q^48 + 8 * q^49 - 8 * q^50 - 14 * q^51 + 16 * q^52 + 8 * q^54 + 4 * q^55 - 6 * q^56 + 20 * q^57 - 26 * q^58 + 8 * q^59 + 10 * q^60 - 16 * q^61 - 40 * q^62 + 2 * q^63 + 26 * q^64 + 32 * q^65 - 6 * q^66 - 24 * q^67 + 12 * q^68 + 24 * q^69 - 4 * q^70 - 64 * q^71 + 22 * q^72 - 4 * q^74 - 22 * q^75 - 28 * q^76 + 4 * q^77 + 42 * q^78 - 38 * q^80 + 2 * q^81 + 4 * q^82 - 14 * q^84 - 4 * q^85 - 24 * q^86 - 18 * q^87 + 24 * q^88 - 6 * q^90 + 36 * q^92 + 32 * q^93 - 2 * q^94 + 48 * q^95 - 14 * q^96 + 14 * q^99

Introduction

L-functions

Modular forms

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Database

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