Properties

Label 539.2.e.j.67.1
Level $539$
Weight $2$
Character 539.67
Analytic conductor $4.304$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [539,2,Mod(67,539)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(539, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([4, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("539.67");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 539 = 7^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 539.e (of order \(3\), degree \(2\), not 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: \(4.30393666895\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\Q(\sqrt{-3}, \sqrt{5})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} - x^{3} + 2x^{2} + x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: no (minimal twist has level 77)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 67.1
Root \(0.809017 + 1.40126i\) of defining polynomial
Character \(\chi\) \(=\) 539.67
Dual form 539.2.e.j.177.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.11803 - 1.93649i) q^{2} +(-0.618034 + 1.07047i) q^{3} +(-1.50000 + 2.59808i) q^{4} +(-1.00000 - 1.73205i) q^{5} +2.76393 q^{6} +2.23607 q^{8} +(0.736068 + 1.27491i) q^{9} +O(q^{10})\) \(q+(-1.11803 - 1.93649i) q^{2} +(-0.618034 + 1.07047i) q^{3} +(-1.50000 + 2.59808i) q^{4} +(-1.00000 - 1.73205i) q^{5} +2.76393 q^{6} +2.23607 q^{8} +(0.736068 + 1.27491i) q^{9} +(-2.23607 + 3.87298i) q^{10} +(0.500000 - 0.866025i) q^{11} +(-1.85410 - 3.21140i) q^{12} -3.23607 q^{13} +2.47214 q^{15} +(0.500000 + 0.866025i) q^{16} +(-1.61803 + 2.80252i) q^{17} +(1.64590 - 2.85078i) q^{18} +(3.23607 + 5.60503i) q^{19} +6.00000 q^{20} -2.23607 q^{22} +(-1.23607 - 2.14093i) q^{23} +(-1.38197 + 2.39364i) q^{24} +(0.500000 - 0.866025i) q^{25} +(3.61803 + 6.26662i) q^{26} -5.52786 q^{27} +8.47214 q^{29} +(-2.76393 - 4.78727i) q^{30} +(-1.38197 + 2.39364i) q^{31} +(3.35410 - 5.80948i) q^{32} +(0.618034 + 1.07047i) q^{33} +7.23607 q^{34} -4.41641 q^{36} +(4.23607 + 7.33708i) q^{37} +(7.23607 - 12.5332i) q^{38} +(2.00000 - 3.46410i) q^{39} +(-2.23607 - 3.87298i) q^{40} +11.2361 q^{41} +8.00000 q^{43} +(1.50000 + 2.59808i) q^{44} +(1.47214 - 2.54981i) q^{45} +(-2.76393 + 4.78727i) q^{46} +(1.38197 + 2.39364i) q^{47} -1.23607 q^{48} -2.23607 q^{50} +(-2.00000 - 3.46410i) q^{51} +(4.85410 - 8.40755i) q^{52} +(0.236068 - 0.408882i) q^{53} +(6.18034 + 10.7047i) q^{54} -2.00000 q^{55} -8.00000 q^{57} +(-9.47214 - 16.4062i) q^{58} +(-0.618034 + 1.07047i) q^{59} +(-3.70820 + 6.42280i) q^{60} +(-3.61803 - 6.26662i) q^{61} +6.18034 q^{62} -13.0000 q^{64} +(3.23607 + 5.60503i) q^{65} +(1.38197 - 2.39364i) q^{66} +(-7.23607 + 12.5332i) q^{67} +(-4.85410 - 8.40755i) q^{68} +3.05573 q^{69} -10.4721 q^{71} +(1.64590 + 2.85078i) q^{72} +(-0.381966 + 0.661585i) q^{73} +(9.47214 - 16.4062i) q^{74} +(0.618034 + 1.07047i) q^{75} -19.4164 q^{76} -8.94427 q^{78} +(4.47214 + 7.74597i) q^{79} +(1.00000 - 1.73205i) q^{80} +(1.20820 - 2.09267i) q^{81} +(-12.5623 - 21.7586i) q^{82} +11.4164 q^{83} +6.47214 q^{85} +(-8.94427 - 15.4919i) q^{86} +(-5.23607 + 9.06914i) q^{87} +(1.11803 - 1.93649i) q^{88} +(1.00000 + 1.73205i) q^{89} -6.58359 q^{90} +7.41641 q^{92} +(-1.70820 - 2.95870i) q^{93} +(3.09017 - 5.35233i) q^{94} +(6.47214 - 11.2101i) q^{95} +(4.14590 + 7.18091i) q^{96} -17.4164 q^{97} +1.47214 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 2 q^{3} - 6 q^{4} - 4 q^{5} + 20 q^{6} - 6 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q + 2 q^{3} - 6 q^{4} - 4 q^{5} + 20 q^{6} - 6 q^{9} + 2 q^{11} + 6 q^{12} - 4 q^{13} - 8 q^{15} + 2 q^{16} - 2 q^{17} + 20 q^{18} + 4 q^{19} + 24 q^{20} + 4 q^{23} - 10 q^{24} + 2 q^{25} + 10 q^{26} - 40 q^{27} + 16 q^{29} - 20 q^{30} - 10 q^{31} - 2 q^{33} + 20 q^{34} + 36 q^{36} + 8 q^{37} + 20 q^{38} + 8 q^{39} + 36 q^{41} + 32 q^{43} + 6 q^{44} - 12 q^{45} - 20 q^{46} + 10 q^{47} + 4 q^{48} - 8 q^{51} + 6 q^{52} - 8 q^{53} - 20 q^{54} - 8 q^{55} - 32 q^{57} - 20 q^{58} + 2 q^{59} + 12 q^{60} - 10 q^{61} - 20 q^{62} - 52 q^{64} + 4 q^{65} + 10 q^{66} - 20 q^{67} - 6 q^{68} + 48 q^{69} - 24 q^{71} + 20 q^{72} - 6 q^{73} + 20 q^{74} - 2 q^{75} - 24 q^{76} + 4 q^{80} - 22 q^{81} - 10 q^{82} - 8 q^{83} + 8 q^{85} - 12 q^{87} + 4 q^{89} - 80 q^{90} - 24 q^{92} + 20 q^{93} - 10 q^{94} + 8 q^{95} + 30 q^{96} - 16 q^{97} - 12 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/539\mathbb{Z}\right)^\times\).

\(n\) \(199\) \(442\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(1\)

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 \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.11803 1.93649i −0.790569 1.36931i −0.925615 0.378467i \(-0.876451\pi\)
0.135045 0.990839i \(-0.456882\pi\)
\(3\) −0.618034 + 1.07047i −0.356822 + 0.618034i −0.987428 0.158069i \(-0.949473\pi\)
0.630606 + 0.776103i \(0.282806\pi\)
\(4\) −1.50000 + 2.59808i −0.750000 + 1.29904i
\(5\) −1.00000 1.73205i −0.447214 0.774597i 0.550990 0.834512i \(-0.314250\pi\)
−0.998203 + 0.0599153i \(0.980917\pi\)
\(6\) 2.76393 1.12837
\(7\) 0 0
\(8\) 2.23607 0.790569
\(9\) 0.736068 + 1.27491i 0.245356 + 0.424969i
\(10\) −2.23607 + 3.87298i −0.707107 + 1.22474i
\(11\) 0.500000 0.866025i 0.150756 0.261116i
\(12\) −1.85410 3.21140i −0.535233 0.927051i
\(13\) −3.23607 −0.897524 −0.448762 0.893651i \(-0.648135\pi\)
−0.448762 + 0.893651i \(0.648135\pi\)
\(14\) 0 0
\(15\) 2.47214 0.638303
\(16\) 0.500000 + 0.866025i 0.125000 + 0.216506i
\(17\) −1.61803 + 2.80252i −0.392431 + 0.679710i −0.992770 0.120036i \(-0.961699\pi\)
0.600339 + 0.799746i \(0.295032\pi\)
\(18\) 1.64590 2.85078i 0.387942 0.671935i
\(19\) 3.23607 + 5.60503i 0.742405 + 1.28588i 0.951397 + 0.307966i \(0.0996482\pi\)
−0.208993 + 0.977917i \(0.567018\pi\)
\(20\) 6.00000 1.34164
\(21\) 0 0
\(22\) −2.23607 −0.476731
\(23\) −1.23607 2.14093i −0.257738 0.446415i 0.707898 0.706315i \(-0.249644\pi\)
−0.965636 + 0.259900i \(0.916310\pi\)
\(24\) −1.38197 + 2.39364i −0.282093 + 0.488599i
\(25\) 0.500000 0.866025i 0.100000 0.173205i
\(26\) 3.61803 + 6.26662i 0.709555 + 1.22899i
\(27\) −5.52786 −1.06384
\(28\) 0 0
\(29\) 8.47214 1.57324 0.786618 0.617440i \(-0.211830\pi\)
0.786618 + 0.617440i \(0.211830\pi\)
\(30\) −2.76393 4.78727i −0.504623 0.874032i
\(31\) −1.38197 + 2.39364i −0.248208 + 0.429910i −0.963029 0.269399i \(-0.913175\pi\)
0.714820 + 0.699308i \(0.246508\pi\)
\(32\) 3.35410 5.80948i 0.592927 1.02698i
\(33\) 0.618034 + 1.07047i 0.107586 + 0.186344i
\(34\) 7.23607 1.24098
\(35\) 0 0
\(36\) −4.41641 −0.736068
\(37\) 4.23607 + 7.33708i 0.696405 + 1.20621i 0.969705 + 0.244280i \(0.0785517\pi\)
−0.273299 + 0.961929i \(0.588115\pi\)
\(38\) 7.23607 12.5332i 1.17385 2.03316i
\(39\) 2.00000 3.46410i 0.320256 0.554700i
\(40\) −2.23607 3.87298i −0.353553 0.612372i
\(41\) 11.2361 1.75478 0.877390 0.479779i \(-0.159283\pi\)
0.877390 + 0.479779i \(0.159283\pi\)
\(42\) 0 0
\(43\) 8.00000 1.21999 0.609994 0.792406i \(-0.291172\pi\)
0.609994 + 0.792406i \(0.291172\pi\)
\(44\) 1.50000 + 2.59808i 0.226134 + 0.391675i
\(45\) 1.47214 2.54981i 0.219453 0.380104i
\(46\) −2.76393 + 4.78727i −0.407520 + 0.705845i
\(47\) 1.38197 + 2.39364i 0.201580 + 0.349148i 0.949038 0.315162i \(-0.102059\pi\)
−0.747457 + 0.664310i \(0.768726\pi\)
\(48\) −1.23607 −0.178411
\(49\) 0 0
\(50\) −2.23607 −0.316228
\(51\) −2.00000 3.46410i −0.280056 0.485071i
\(52\) 4.85410 8.40755i 0.673143 1.16592i
\(53\) 0.236068 0.408882i 0.0324264 0.0561642i −0.849357 0.527819i \(-0.823010\pi\)
0.881783 + 0.471655i \(0.156343\pi\)
\(54\) 6.18034 + 10.7047i 0.841038 + 1.45672i
\(55\) −2.00000 −0.269680
\(56\) 0 0
\(57\) −8.00000 −1.05963
\(58\) −9.47214 16.4062i −1.24375 2.15424i
\(59\) −0.618034 + 1.07047i −0.0804612 + 0.139363i −0.903448 0.428697i \(-0.858973\pi\)
0.822987 + 0.568060i \(0.192306\pi\)
\(60\) −3.70820 + 6.42280i −0.478727 + 0.829180i
\(61\) −3.61803 6.26662i −0.463242 0.802358i 0.535878 0.844295i \(-0.319981\pi\)
−0.999120 + 0.0419368i \(0.986647\pi\)
\(62\) 6.18034 0.784904
\(63\) 0 0
\(64\) −13.0000 −1.62500
\(65\) 3.23607 + 5.60503i 0.401385 + 0.695219i
\(66\) 1.38197 2.39364i 0.170108 0.294636i
\(67\) −7.23607 + 12.5332i −0.884026 + 1.53118i −0.0372009 + 0.999308i \(0.511844\pi\)
−0.846825 + 0.531871i \(0.821489\pi\)
\(68\) −4.85410 8.40755i −0.588646 1.01957i
\(69\) 3.05573 0.367866
\(70\) 0 0
\(71\) −10.4721 −1.24281 −0.621407 0.783488i \(-0.713439\pi\)
−0.621407 + 0.783488i \(0.713439\pi\)
\(72\) 1.64590 + 2.85078i 0.193971 + 0.335968i
\(73\) −0.381966 + 0.661585i −0.0447057 + 0.0774326i −0.887512 0.460784i \(-0.847568\pi\)
0.842807 + 0.538216i \(0.180902\pi\)
\(74\) 9.47214 16.4062i 1.10111 1.90718i
\(75\) 0.618034 + 1.07047i 0.0713644 + 0.123607i
\(76\) −19.4164 −2.22721
\(77\) 0 0
\(78\) −8.94427 −1.01274
\(79\) 4.47214 + 7.74597i 0.503155 + 0.871489i 0.999993 + 0.00364646i \(0.00116071\pi\)
−0.496839 + 0.867843i \(0.665506\pi\)
\(80\) 1.00000 1.73205i 0.111803 0.193649i
\(81\) 1.20820 2.09267i 0.134245 0.232519i
\(82\) −12.5623 21.7586i −1.38727 2.40283i
\(83\) 11.4164 1.25311 0.626557 0.779376i \(-0.284464\pi\)
0.626557 + 0.779376i \(0.284464\pi\)
\(84\) 0 0
\(85\) 6.47214 0.702002
\(86\) −8.94427 15.4919i −0.964486 1.67054i
\(87\) −5.23607 + 9.06914i −0.561365 + 0.972313i
\(88\) 1.11803 1.93649i 0.119183 0.206431i
\(89\) 1.00000 + 1.73205i 0.106000 + 0.183597i 0.914146 0.405385i \(-0.132862\pi\)
−0.808146 + 0.588982i \(0.799529\pi\)
\(90\) −6.58359 −0.693972
\(91\) 0 0
\(92\) 7.41641 0.773214
\(93\) −1.70820 2.95870i −0.177132 0.306802i
\(94\) 3.09017 5.35233i 0.318727 0.552051i
\(95\) 6.47214 11.2101i 0.664027 1.15013i
\(96\) 4.14590 + 7.18091i 0.423139 + 0.732898i
\(97\) −17.4164 −1.76837 −0.884184 0.467139i \(-0.845285\pi\)
−0.884184 + 0.467139i \(0.845285\pi\)
\(98\) 0 0
\(99\) 1.47214 0.147955
\(100\) 1.50000 + 2.59808i 0.150000 + 0.259808i
\(101\) −2.38197 + 4.12569i −0.237014 + 0.410521i −0.959856 0.280493i \(-0.909502\pi\)
0.722842 + 0.691014i \(0.242836\pi\)
\(102\) −4.47214 + 7.74597i −0.442807 + 0.766965i
\(103\) 3.85410 + 6.67550i 0.379756 + 0.657757i 0.991027 0.133665i \(-0.0426746\pi\)
−0.611271 + 0.791422i \(0.709341\pi\)
\(104\) −7.23607 −0.709555
\(105\) 0 0
\(106\) −1.05573 −0.102541
\(107\) 2.00000 + 3.46410i 0.193347 + 0.334887i 0.946357 0.323122i \(-0.104732\pi\)
−0.753010 + 0.658009i \(0.771399\pi\)
\(108\) 8.29180 14.3618i 0.797878 1.38197i
\(109\) 2.23607 3.87298i 0.214176 0.370965i −0.738841 0.673880i \(-0.764627\pi\)
0.953018 + 0.302915i \(0.0979599\pi\)
\(110\) 2.23607 + 3.87298i 0.213201 + 0.369274i
\(111\) −10.4721 −0.993971
\(112\) 0 0
\(113\) 2.00000 0.188144 0.0940721 0.995565i \(-0.470012\pi\)
0.0940721 + 0.995565i \(0.470012\pi\)
\(114\) 8.94427 + 15.4919i 0.837708 + 1.45095i
\(115\) −2.47214 + 4.28187i −0.230528 + 0.399286i
\(116\) −12.7082 + 22.0113i −1.17993 + 2.04369i
\(117\) −2.38197 4.12569i −0.220213 0.381420i
\(118\) 2.76393 0.254441
\(119\) 0 0
\(120\) 5.52786 0.504623
\(121\) −0.500000 0.866025i −0.0454545 0.0787296i
\(122\) −8.09017 + 14.0126i −0.732450 + 1.26864i
\(123\) −6.94427 + 12.0278i −0.626144 + 1.08451i
\(124\) −4.14590 7.18091i −0.372313 0.644864i
\(125\) −12.0000 −1.07331
\(126\) 0 0
\(127\) 3.05573 0.271152 0.135576 0.990767i \(-0.456712\pi\)
0.135576 + 0.990767i \(0.456712\pi\)
\(128\) 7.82624 + 13.5554i 0.691748 + 1.19814i
\(129\) −4.94427 + 8.56373i −0.435319 + 0.753994i
\(130\) 7.23607 12.5332i 0.634645 1.09924i
\(131\) 10.9443 + 18.9560i 0.956205 + 1.65620i 0.731585 + 0.681750i \(0.238781\pi\)
0.224620 + 0.974446i \(0.427886\pi\)
\(132\) −3.70820 −0.322758
\(133\) 0 0
\(134\) 32.3607 2.79554
\(135\) 5.52786 + 9.57454i 0.475763 + 0.824045i
\(136\) −3.61803 + 6.26662i −0.310244 + 0.537358i
\(137\) −8.23607 + 14.2653i −0.703655 + 1.21877i 0.263520 + 0.964654i \(0.415116\pi\)
−0.967175 + 0.254112i \(0.918217\pi\)
\(138\) −3.41641 5.91739i −0.290824 0.503722i
\(139\) 1.52786 0.129592 0.0647959 0.997899i \(-0.479360\pi\)
0.0647959 + 0.997899i \(0.479360\pi\)
\(140\) 0 0
\(141\) −3.41641 −0.287713
\(142\) 11.7082 + 20.2792i 0.982531 + 1.70179i
\(143\) −1.61803 + 2.80252i −0.135307 + 0.234358i
\(144\) −0.736068 + 1.27491i −0.0613390 + 0.106242i
\(145\) −8.47214 14.6742i −0.703573 1.21862i
\(146\) 1.70820 0.141372
\(147\) 0 0
\(148\) −25.4164 −2.08922
\(149\) −7.00000 12.1244i −0.573462 0.993266i −0.996207 0.0870170i \(-0.972267\pi\)
0.422744 0.906249i \(-0.361067\pi\)
\(150\) 1.38197 2.39364i 0.112837 0.195440i
\(151\) −4.47214 + 7.74597i −0.363937 + 0.630358i −0.988605 0.150533i \(-0.951901\pi\)
0.624668 + 0.780891i \(0.285234\pi\)
\(152\) 7.23607 + 12.5332i 0.586923 + 1.01658i
\(153\) −4.76393 −0.385141
\(154\) 0 0
\(155\) 5.52786 0.444009
\(156\) 6.00000 + 10.3923i 0.480384 + 0.832050i
\(157\) 5.47214 9.47802i 0.436724 0.756428i −0.560711 0.828012i \(-0.689472\pi\)
0.997435 + 0.0715837i \(0.0228053\pi\)
\(158\) 10.0000 17.3205i 0.795557 1.37795i
\(159\) 0.291796 + 0.505406i 0.0231409 + 0.0400813i
\(160\) −13.4164 −1.06066
\(161\) 0 0
\(162\) −5.40325 −0.424520
\(163\) 1.70820 + 2.95870i 0.133797 + 0.231743i 0.925137 0.379633i \(-0.123950\pi\)
−0.791340 + 0.611376i \(0.790616\pi\)
\(164\) −16.8541 + 29.1922i −1.31608 + 2.27952i
\(165\) 1.23607 2.14093i 0.0962278 0.166671i
\(166\) −12.7639 22.1078i −0.990673 1.71590i
\(167\) −4.94427 −0.382599 −0.191300 0.981532i \(-0.561270\pi\)
−0.191300 + 0.981532i \(0.561270\pi\)
\(168\) 0 0
\(169\) −2.52786 −0.194451
\(170\) −7.23607 12.5332i −0.554981 0.961255i
\(171\) −4.76393 + 8.25137i −0.364307 + 0.630998i
\(172\) −12.0000 + 20.7846i −0.914991 + 1.58481i
\(173\) −6.38197 11.0539i −0.485212 0.840412i 0.514644 0.857404i \(-0.327924\pi\)
−0.999856 + 0.0169925i \(0.994591\pi\)
\(174\) 23.4164 1.77519
\(175\) 0 0
\(176\) 1.00000 0.0753778
\(177\) −0.763932 1.32317i −0.0574206 0.0994555i
\(178\) 2.23607 3.87298i 0.167600 0.290292i
\(179\) 4.47214 7.74597i 0.334263 0.578961i −0.649080 0.760720i \(-0.724846\pi\)
0.983343 + 0.181760i \(0.0581792\pi\)
\(180\) 4.41641 + 7.64944i 0.329180 + 0.570156i
\(181\) 25.4164 1.88919 0.944593 0.328243i \(-0.106456\pi\)
0.944593 + 0.328243i \(0.106456\pi\)
\(182\) 0 0
\(183\) 8.94427 0.661180
\(184\) −2.76393 4.78727i −0.203760 0.352922i
\(185\) 8.47214 14.6742i 0.622884 1.07887i
\(186\) −3.81966 + 6.61585i −0.280071 + 0.485097i
\(187\) 1.61803 + 2.80252i 0.118322 + 0.204940i
\(188\) −8.29180 −0.604741
\(189\) 0 0
\(190\) −28.9443 −2.09984
\(191\) 1.52786 + 2.64634i 0.110552 + 0.191482i 0.915993 0.401194i \(-0.131405\pi\)
−0.805441 + 0.592676i \(0.798071\pi\)
\(192\) 8.03444 13.9161i 0.579836 1.00431i
\(193\) −5.94427 + 10.2958i −0.427878 + 0.741107i −0.996684 0.0813650i \(-0.974072\pi\)
0.568806 + 0.822472i \(0.307405\pi\)
\(194\) 19.4721 + 33.7267i 1.39802 + 2.42144i
\(195\) −8.00000 −0.572892
\(196\) 0 0
\(197\) −2.00000 −0.142494 −0.0712470 0.997459i \(-0.522698\pi\)
−0.0712470 + 0.997459i \(0.522698\pi\)
\(198\) −1.64590 2.85078i −0.116969 0.202596i
\(199\) −1.09017 + 1.88823i −0.0772801 + 0.133853i −0.902076 0.431578i \(-0.857957\pi\)
0.824795 + 0.565431i \(0.191290\pi\)
\(200\) 1.11803 1.93649i 0.0790569 0.136931i
\(201\) −8.94427 15.4919i −0.630880 1.09272i
\(202\) 10.6525 0.749506
\(203\) 0 0
\(204\) 12.0000 0.840168
\(205\) −11.2361 19.4614i −0.784761 1.35925i
\(206\) 8.61803 14.9269i 0.600447 1.04000i
\(207\) 1.81966 3.15174i 0.126475 0.219061i
\(208\) −1.61803 2.80252i −0.112190 0.194320i
\(209\) 6.47214 0.447687
\(210\) 0 0
\(211\) −13.8885 −0.956127 −0.478063 0.878325i \(-0.658661\pi\)
−0.478063 + 0.878325i \(0.658661\pi\)
\(212\) 0.708204 + 1.22665i 0.0486396 + 0.0842463i
\(213\) 6.47214 11.2101i 0.443463 0.768101i
\(214\) 4.47214 7.74597i 0.305709 0.529503i
\(215\) −8.00000 13.8564i −0.545595 0.944999i
\(216\) −12.3607 −0.841038
\(217\) 0 0
\(218\) −10.0000 −0.677285
\(219\) −0.472136 0.817763i −0.0319040 0.0552593i
\(220\) 3.00000 5.19615i 0.202260 0.350325i
\(221\) 5.23607 9.06914i 0.352216 0.610056i
\(222\) 11.7082 + 20.2792i 0.785803 + 1.36105i
\(223\) 10.1803 0.681726 0.340863 0.940113i \(-0.389281\pi\)
0.340863 + 0.940113i \(0.389281\pi\)
\(224\) 0 0
\(225\) 1.47214 0.0981424
\(226\) −2.23607 3.87298i −0.148741 0.257627i
\(227\) 2.94427 5.09963i 0.195418 0.338474i −0.751619 0.659597i \(-0.770727\pi\)
0.947038 + 0.321123i \(0.104060\pi\)
\(228\) 12.0000 20.7846i 0.794719 1.37649i
\(229\) −2.23607 3.87298i −0.147764 0.255934i 0.782637 0.622478i \(-0.213874\pi\)
−0.930401 + 0.366544i \(0.880541\pi\)
\(230\) 11.0557 0.728993
\(231\) 0 0
\(232\) 18.9443 1.24375
\(233\) −4.70820 8.15485i −0.308445 0.534242i 0.669578 0.742742i \(-0.266475\pi\)
−0.978022 + 0.208500i \(0.933142\pi\)
\(234\) −5.32624 + 9.22531i −0.348187 + 0.603078i
\(235\) 2.76393 4.78727i 0.180299 0.312287i
\(236\) −1.85410 3.21140i −0.120692 0.209044i
\(237\) −11.0557 −0.718147
\(238\) 0 0
\(239\) −9.88854 −0.639637 −0.319818 0.947479i \(-0.603622\pi\)
−0.319818 + 0.947479i \(0.603622\pi\)
\(240\) 1.23607 + 2.14093i 0.0797878 + 0.138197i
\(241\) −6.56231 + 11.3662i −0.422715 + 0.732164i −0.996204 0.0870491i \(-0.972256\pi\)
0.573489 + 0.819213i \(0.305590\pi\)
\(242\) −1.11803 + 1.93649i −0.0718699 + 0.124482i
\(243\) −6.79837 11.7751i −0.436116 0.755375i
\(244\) 21.7082 1.38973
\(245\) 0 0
\(246\) 31.0557 1.98004
\(247\) −10.4721 18.1383i −0.666326 1.15411i
\(248\) −3.09017 + 5.35233i −0.196226 + 0.339873i
\(249\) −7.05573 + 12.2209i −0.447139 + 0.774467i
\(250\) 13.4164 + 23.2379i 0.848528 + 1.46969i
\(251\) −4.29180 −0.270896 −0.135448 0.990784i \(-0.543247\pi\)
−0.135448 + 0.990784i \(0.543247\pi\)
\(252\) 0 0
\(253\) −2.47214 −0.155422
\(254\) −3.41641 5.91739i −0.214364 0.371290i
\(255\) −4.00000 + 6.92820i −0.250490 + 0.433861i
\(256\) 4.50000 7.79423i 0.281250 0.487139i
\(257\) −3.00000 5.19615i −0.187135 0.324127i 0.757159 0.653231i \(-0.226587\pi\)
−0.944294 + 0.329104i \(0.893253\pi\)
\(258\) 22.1115 1.37660
\(259\) 0 0
\(260\) −19.4164 −1.20415
\(261\) 6.23607 + 10.8012i 0.386003 + 0.668577i
\(262\) 24.4721 42.3870i 1.51189 2.61868i
\(263\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(264\) 1.38197 + 2.39364i 0.0850541 + 0.147318i
\(265\) −0.944272 −0.0580062
\(266\) 0 0
\(267\) −2.47214 −0.151292
\(268\) −21.7082 37.5997i −1.32604 2.29677i
\(269\) 6.70820 11.6190i 0.409006 0.708420i −0.585772 0.810476i \(-0.699209\pi\)
0.994779 + 0.102056i \(0.0325420\pi\)
\(270\) 12.3607 21.4093i 0.752247 1.30293i
\(271\) −5.23607 9.06914i −0.318068 0.550911i 0.662017 0.749489i \(-0.269701\pi\)
−0.980085 + 0.198578i \(0.936368\pi\)
\(272\) −3.23607 −0.196215
\(273\) 0 0
\(274\) 36.8328 2.22515
\(275\) −0.500000 0.866025i −0.0301511 0.0522233i
\(276\) −4.58359 + 7.93901i −0.275900 + 0.477873i
\(277\) 9.94427 17.2240i 0.597493 1.03489i −0.395696 0.918381i \(-0.629497\pi\)
0.993190 0.116508i \(-0.0371699\pi\)
\(278\) −1.70820 2.95870i −0.102451 0.177451i
\(279\) −4.06888 −0.243598
\(280\) 0 0
\(281\) −3.52786 −0.210455 −0.105227 0.994448i \(-0.533557\pi\)
−0.105227 + 0.994448i \(0.533557\pi\)
\(282\) 3.81966 + 6.61585i 0.227457 + 0.393968i
\(283\) 14.9443 25.8842i 0.888345 1.53866i 0.0465134 0.998918i \(-0.485189\pi\)
0.841831 0.539741i \(-0.181478\pi\)
\(284\) 15.7082 27.2074i 0.932110 1.61446i
\(285\) 8.00000 + 13.8564i 0.473879 + 0.820783i
\(286\) 7.23607 0.427878
\(287\) 0 0
\(288\) 9.87539 0.581913
\(289\) 3.26393 + 5.65330i 0.191996 + 0.332547i
\(290\) −18.9443 + 32.8124i −1.11245 + 1.92681i
\(291\) 10.7639 18.6437i 0.630993 1.09291i
\(292\) −1.14590 1.98475i −0.0670586 0.116149i
\(293\) 25.1246 1.46780 0.733898 0.679260i \(-0.237699\pi\)
0.733898 + 0.679260i \(0.237699\pi\)
\(294\) 0 0
\(295\) 2.47214 0.143933
\(296\) 9.47214 + 16.4062i 0.550557 + 0.953592i
\(297\) −2.76393 + 4.78727i −0.160380 + 0.277786i
\(298\) −15.6525 + 27.1109i −0.906724 + 1.57049i
\(299\) 4.00000 + 6.92820i 0.231326 + 0.400668i
\(300\) −3.70820 −0.214093
\(301\) 0 0
\(302\) 20.0000 1.15087
\(303\) −2.94427 5.09963i −0.169144 0.292966i
\(304\) −3.23607 + 5.60503i −0.185601 + 0.321471i
\(305\) −7.23607 + 12.5332i −0.414336 + 0.717651i
\(306\) 5.32624 + 9.22531i 0.304481 + 0.527376i
\(307\) 8.94427 0.510477 0.255238 0.966878i \(-0.417846\pi\)
0.255238 + 0.966878i \(0.417846\pi\)
\(308\) 0 0
\(309\) −9.52786 −0.542021
\(310\) −6.18034 10.7047i −0.351020 0.607984i
\(311\) −4.14590 + 7.18091i −0.235092 + 0.407192i −0.959300 0.282391i \(-0.908873\pi\)
0.724207 + 0.689582i \(0.242206\pi\)
\(312\) 4.47214 7.74597i 0.253185 0.438529i
\(313\) 7.47214 + 12.9421i 0.422350 + 0.731532i 0.996169 0.0874505i \(-0.0278720\pi\)
−0.573819 + 0.818982i \(0.694539\pi\)
\(314\) −24.4721 −1.38104
\(315\) 0 0
\(316\) −26.8328 −1.50946
\(317\) −7.00000 12.1244i −0.393159 0.680972i 0.599705 0.800221i \(-0.295285\pi\)
−0.992864 + 0.119249i \(0.961951\pi\)
\(318\) 0.652476 1.13012i 0.0365890 0.0633741i
\(319\) 4.23607 7.33708i 0.237174 0.410798i
\(320\) 13.0000 + 22.5167i 0.726722 + 1.25872i
\(321\) −4.94427 −0.275962
\(322\) 0 0
\(323\) −20.9443 −1.16537
\(324\) 3.62461 + 6.27801i 0.201367 + 0.348778i
\(325\) −1.61803 + 2.80252i −0.0897524 + 0.155456i
\(326\) 3.81966 6.61585i 0.211551 0.366418i
\(327\) 2.76393 + 4.78727i 0.152846 + 0.264737i
\(328\) 25.1246 1.38727
\(329\) 0 0
\(330\) −5.52786 −0.304299
\(331\) 6.94427 + 12.0278i 0.381692 + 0.661109i 0.991304 0.131590i \(-0.0420083\pi\)
−0.609613 + 0.792700i \(0.708675\pi\)
\(332\) −17.1246 + 29.6607i −0.939835 + 1.62784i
\(333\) −6.23607 + 10.8012i −0.341734 + 0.591901i
\(334\) 5.52786 + 9.57454i 0.302471 + 0.523896i
\(335\) 28.9443 1.58139
\(336\) 0 0
\(337\) −11.5279 −0.627963 −0.313981 0.949429i \(-0.601663\pi\)
−0.313981 + 0.949429i \(0.601663\pi\)
\(338\) 2.82624 + 4.89519i 0.153727 + 0.266263i
\(339\) −1.23607 + 2.14093i −0.0671340 + 0.116279i
\(340\) −9.70820 + 16.8151i −0.526501 + 0.911927i
\(341\) 1.38197 + 2.39364i 0.0748377 + 0.129623i
\(342\) 21.3050 1.15204
\(343\) 0 0
\(344\) 17.8885 0.964486
\(345\) −3.05573 5.29268i −0.164515 0.284948i
\(346\) −14.2705 + 24.7172i −0.767187 + 1.32881i
\(347\) −10.4721 + 18.1383i −0.562174 + 0.973713i 0.435133 + 0.900366i \(0.356701\pi\)
−0.997306 + 0.0733471i \(0.976632\pi\)
\(348\) −15.7082 27.2074i −0.842048 1.45847i
\(349\) 7.23607 0.387338 0.193669 0.981067i \(-0.437961\pi\)
0.193669 + 0.981067i \(0.437961\pi\)
\(350\) 0 0
\(351\) 17.8885 0.954820
\(352\) −3.35410 5.80948i −0.178774 0.309646i
\(353\) 9.94427 17.2240i 0.529280 0.916740i −0.470137 0.882594i \(-0.655795\pi\)
0.999417 0.0341465i \(-0.0108713\pi\)
\(354\) −1.70820 + 2.95870i −0.0907900 + 0.157253i
\(355\) 10.4721 + 18.1383i 0.555803 + 0.962679i
\(356\) −6.00000 −0.317999
\(357\) 0 0
\(358\) −20.0000 −1.05703
\(359\) 12.4721 + 21.6024i 0.658254 + 1.14013i 0.981067 + 0.193667i \(0.0620381\pi\)
−0.322813 + 0.946463i \(0.604629\pi\)
\(360\) 3.29180 5.70156i 0.173493 0.300498i
\(361\) −11.4443 + 19.8221i −0.602330 + 1.04327i
\(362\) −28.4164 49.2187i −1.49353 2.58688i
\(363\) 1.23607 0.0648767
\(364\) 0 0
\(365\) 1.52786 0.0799721
\(366\) −10.0000 17.3205i −0.522708 0.905357i
\(367\) −11.5623 + 20.0265i −0.603547 + 1.04537i 0.388732 + 0.921351i \(0.372913\pi\)
−0.992279 + 0.124024i \(0.960420\pi\)
\(368\) 1.23607 2.14093i 0.0644345 0.111604i
\(369\) 8.27051 + 14.3249i 0.430546 + 0.745727i
\(370\) −37.8885 −1.96973
\(371\) 0 0
\(372\) 10.2492 0.531397
\(373\) −3.00000 5.19615i −0.155334 0.269047i 0.777847 0.628454i \(-0.216312\pi\)
−0.933181 + 0.359408i \(0.882979\pi\)
\(374\) 3.61803 6.26662i 0.187084 0.324039i
\(375\) 7.41641 12.8456i 0.382982 0.663344i
\(376\) 3.09017 + 5.35233i 0.159363 + 0.276025i
\(377\) −27.4164 −1.41202
\(378\) 0 0
\(379\) 37.3050 1.91623 0.958113 0.286389i \(-0.0924551\pi\)
0.958113 + 0.286389i \(0.0924551\pi\)
\(380\) 19.4164 + 33.6302i 0.996041 + 1.72519i
\(381\) −1.88854 + 3.27105i −0.0967530 + 0.167581i
\(382\) 3.41641 5.91739i 0.174799 0.302760i
\(383\) −2.32624 4.02916i −0.118865 0.205881i 0.800453 0.599395i \(-0.204592\pi\)
−0.919318 + 0.393515i \(0.871259\pi\)
\(384\) −19.3475 −0.987324
\(385\) 0 0
\(386\) 26.5836 1.35307
\(387\) 5.88854 + 10.1993i 0.299332 + 0.518457i
\(388\) 26.1246 45.2492i 1.32628 2.29718i
\(389\) −7.94427 + 13.7599i −0.402791 + 0.697654i −0.994062 0.108819i \(-0.965293\pi\)
0.591271 + 0.806473i \(0.298626\pi\)
\(390\) 8.94427 + 15.4919i 0.452911 + 0.784465i
\(391\) 8.00000 0.404577
\(392\) 0 0
\(393\) −27.0557 −1.36478
\(394\) 2.23607 + 3.87298i 0.112651 + 0.195118i
\(395\) 8.94427 15.4919i 0.450035 0.779484i
\(396\) −2.20820 + 3.82472i −0.110966 + 0.192199i
\(397\) −17.9443 31.0804i −0.900597 1.55988i −0.826721 0.562613i \(-0.809796\pi\)
−0.0738766 0.997267i \(-0.523537\pi\)
\(398\) 4.87539 0.244381
\(399\) 0 0
\(400\) 1.00000 0.0500000
\(401\) −11.4721 19.8703i −0.572891 0.992277i −0.996267 0.0863225i \(-0.972488\pi\)
0.423376 0.905954i \(-0.360845\pi\)
\(402\) −20.0000 + 34.6410i −0.997509 + 1.72774i
\(403\) 4.47214 7.74597i 0.222773 0.385854i
\(404\) −7.14590 12.3771i −0.355522 0.615782i
\(405\) −4.83282 −0.240145
\(406\) 0 0
\(407\) 8.47214 0.419948
\(408\) −4.47214 7.74597i −0.221404 0.383482i
\(409\) 4.56231 7.90215i 0.225592 0.390736i −0.730905 0.682479i \(-0.760902\pi\)
0.956497 + 0.291743i \(0.0942352\pi\)
\(410\) −25.1246 + 43.5171i −1.24082 + 2.14916i
\(411\) −10.1803 17.6329i −0.502159 0.869765i
\(412\) −23.1246 −1.13927
\(413\) 0 0
\(414\) −8.13777 −0.399949
\(415\) −11.4164 19.7738i −0.560409 0.970658i
\(416\) −10.8541 + 18.7999i −0.532166 + 0.921739i
\(417\) −0.944272 + 1.63553i −0.0462412 + 0.0800921i
\(418\) −7.23607 12.5332i −0.353928 0.613021i
\(419\) −24.6525 −1.20435 −0.602176 0.798363i \(-0.705700\pi\)
−0.602176 + 0.798363i \(0.705700\pi\)
\(420\) 0 0
\(421\) 22.3607 1.08979 0.544896 0.838503i \(-0.316569\pi\)
0.544896 + 0.838503i \(0.316569\pi\)
\(422\) 15.5279 + 26.8950i 0.755885 + 1.30923i
\(423\) −2.03444 + 3.52376i −0.0989179 + 0.171331i
\(424\) 0.527864 0.914287i 0.0256353 0.0444017i
\(425\) 1.61803 + 2.80252i 0.0784862 + 0.135942i
\(426\) −28.9443 −1.40235
\(427\) 0 0
\(428\) −12.0000 −0.580042
\(429\) −2.00000 3.46410i −0.0965609 0.167248i
\(430\) −17.8885 + 30.9839i −0.862662 + 1.49417i
\(431\) −6.00000 + 10.3923i −0.289010 + 0.500580i −0.973574 0.228373i \(-0.926659\pi\)
0.684564 + 0.728953i \(0.259993\pi\)
\(432\) −2.76393 4.78727i −0.132980 0.230328i
\(433\) 8.47214 0.407145 0.203572 0.979060i \(-0.434745\pi\)
0.203572 + 0.979060i \(0.434745\pi\)
\(434\) 0 0
\(435\) 20.9443 1.00420
\(436\) 6.70820 + 11.6190i 0.321265 + 0.556447i
\(437\) 8.00000 13.8564i 0.382692 0.662842i
\(438\) −1.05573 + 1.82857i −0.0504446 + 0.0873727i
\(439\) 5.23607 + 9.06914i 0.249904 + 0.432846i 0.963499 0.267712i \(-0.0862676\pi\)
−0.713595 + 0.700558i \(0.752934\pi\)
\(440\) −4.47214 −0.213201
\(441\) 0 0
\(442\) −23.4164 −1.11380
\(443\) 12.4721 + 21.6024i 0.592569 + 1.02636i 0.993885 + 0.110420i \(0.0352196\pi\)
−0.401316 + 0.915940i \(0.631447\pi\)
\(444\) 15.7082 27.2074i 0.745478 1.29121i
\(445\) 2.00000 3.46410i 0.0948091 0.164214i
\(446\) −11.3820 19.7141i −0.538952 0.933492i
\(447\) 17.3050 0.818496
\(448\) 0 0
\(449\) −28.4721 −1.34368 −0.671842 0.740695i \(-0.734496\pi\)
−0.671842 + 0.740695i \(0.734496\pi\)
\(450\) −1.64590 2.85078i −0.0775884 0.134387i
\(451\) 5.61803 9.73072i 0.264543 0.458202i
\(452\) −3.00000 + 5.19615i −0.141108 + 0.244406i
\(453\) −5.52786 9.57454i −0.259722 0.449851i
\(454\) −13.1672 −0.617967
\(455\) 0 0
\(456\) −17.8885 −0.837708
\(457\) 14.4164 + 24.9700i 0.674371 + 1.16805i 0.976652 + 0.214826i \(0.0689185\pi\)
−0.302281 + 0.953219i \(0.597748\pi\)
\(458\) −5.00000 + 8.66025i −0.233635 + 0.404667i
\(459\) 8.94427 15.4919i 0.417483 0.723102i
\(460\) −7.41641 12.8456i −0.345792 0.598929i
\(461\) 12.1803 0.567295 0.283647 0.958929i \(-0.408455\pi\)
0.283647 + 0.958929i \(0.408455\pi\)
\(462\) 0 0
\(463\) −5.52786 −0.256902 −0.128451 0.991716i \(-0.541000\pi\)
−0.128451 + 0.991716i \(0.541000\pi\)
\(464\) 4.23607 + 7.33708i 0.196655 + 0.340616i
\(465\) −3.41641 + 5.91739i −0.158432 + 0.274412i
\(466\) −10.5279 + 18.2348i −0.487694 + 0.844711i
\(467\) 12.0344 + 20.8443i 0.556888 + 0.964558i 0.997754 + 0.0669848i \(0.0213379\pi\)
−0.440866 + 0.897573i \(0.645329\pi\)
\(468\) 14.2918 0.660639
\(469\) 0 0
\(470\) −12.3607 −0.570156
\(471\) 6.76393 + 11.7155i 0.311666 + 0.539821i
\(472\) −1.38197 + 2.39364i −0.0636101 + 0.110176i
\(473\) 4.00000 6.92820i 0.183920 0.318559i
\(474\) 12.3607 + 21.4093i 0.567745 + 0.983363i
\(475\) 6.47214 0.296962
\(476\) 0 0
\(477\) 0.695048 0.0318241
\(478\) 11.0557 + 19.1491i 0.505677 + 0.875859i
\(479\) 6.76393 11.7155i 0.309052 0.535294i −0.669103 0.743169i \(-0.733322\pi\)
0.978155 + 0.207876i \(0.0666550\pi\)
\(480\) 8.29180 14.3618i 0.378467 0.655524i
\(481\) −13.7082 23.7433i −0.625040 1.08260i
\(482\) 29.3475 1.33674
\(483\) 0 0
\(484\) 3.00000 0.136364
\(485\) 17.4164 + 30.1661i 0.790838 + 1.36977i
\(486\) −15.2016 + 26.3300i −0.689560 + 1.19435i
\(487\) 18.1803 31.4893i 0.823830 1.42692i −0.0789805 0.996876i \(-0.525166\pi\)
0.902810 0.430039i \(-0.141500\pi\)
\(488\) −8.09017 14.0126i −0.366225 0.634320i
\(489\) −4.22291 −0.190967
\(490\) 0 0
\(491\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(492\) −20.8328 36.0835i −0.939216 1.62677i
\(493\) −13.7082 + 23.7433i −0.617386 + 1.06934i
\(494\) −23.4164 + 40.5584i −1.05355 + 1.82481i
\(495\) −1.47214 2.54981i −0.0661676 0.114606i
\(496\) −2.76393 −0.124104
\(497\) 0 0
\(498\) 31.5542 1.41398
\(499\) −0.763932 1.32317i −0.0341983 0.0592332i 0.848420 0.529324i \(-0.177554\pi\)
−0.882618 + 0.470091i \(0.844221\pi\)
\(500\) 18.0000 31.1769i 0.804984 1.39427i
\(501\) 3.05573 5.29268i 0.136520 0.236459i
\(502\) 4.79837 + 8.31103i 0.214162 + 0.370939i
\(503\) −23.4164 −1.04409 −0.522043 0.852919i \(-0.674830\pi\)
−0.522043 + 0.852919i \(0.674830\pi\)
\(504\) 0 0
\(505\) 9.52786 0.423984
\(506\) 2.76393 + 4.78727i 0.122872 + 0.212820i
\(507\) 1.56231 2.70599i 0.0693844 0.120177i
\(508\) −4.58359 + 7.93901i −0.203364 + 0.352237i
\(509\) 20.2361 + 35.0499i 0.896948 + 1.55356i 0.831375 + 0.555712i \(0.187554\pi\)
0.0655728 + 0.997848i \(0.479113\pi\)
\(510\) 17.8885 0.792118
\(511\) 0 0
\(512\) 11.1803 0.494106
\(513\) −17.8885 30.9839i −0.789799 1.36797i
\(514\) −6.70820 + 11.6190i −0.295886 + 0.512490i
\(515\) 7.70820 13.3510i 0.339664 0.588315i
\(516\) −14.8328 25.6912i −0.652978 1.13099i
\(517\) 2.76393 0.121558
\(518\) 0 0
\(519\) 15.7771 0.692537
\(520\) 7.23607 + 12.5332i 0.317323 + 0.549619i
\(521\) 15.1803 26.2931i 0.665063 1.15192i −0.314206 0.949355i \(-0.601738\pi\)
0.979268 0.202568i \(-0.0649286\pi\)
\(522\) 13.9443 24.1522i 0.610324 1.05711i
\(523\) 22.0000 + 38.1051i 0.961993 + 1.66622i 0.717486 + 0.696573i \(0.245293\pi\)
0.244507 + 0.969648i \(0.421374\pi\)
\(524\) −65.6656 −2.86862
\(525\) 0 0
\(526\) 0 0
\(527\) −4.47214 7.74597i −0.194809 0.337420i
\(528\) −0.618034 + 1.07047i −0.0268965 + 0.0465861i
\(529\) 8.44427 14.6259i 0.367142 0.635909i
\(530\) 1.05573 + 1.82857i 0.0458579 + 0.0794282i
\(531\) −1.81966 −0.0789665
\(532\) 0 0
\(533\) −36.3607 −1.57496
\(534\) 2.76393 + 4.78727i 0.119607 + 0.207165i
\(535\) 4.00000 6.92820i 0.172935 0.299532i
\(536\) −16.1803 + 28.0252i −0.698884 + 1.21050i
\(537\) 5.52786 + 9.57454i 0.238545 + 0.413172i
\(538\) −30.0000 −1.29339
\(539\) 0 0
\(540\) −33.1672 −1.42729
\(541\) −10.4164 18.0417i −0.447836 0.775675i 0.550409 0.834895i \(-0.314472\pi\)
−0.998245 + 0.0592201i \(0.981139\pi\)
\(542\) −11.7082 + 20.2792i −0.502910 + 0.871066i
\(543\) −15.7082 + 27.2074i −0.674104 + 1.16758i
\(544\) 10.8541 + 18.7999i 0.465366 + 0.806037i
\(545\) −8.94427 −0.383131
\(546\) 0 0
\(547\) 28.0000 1.19719 0.598597 0.801050i \(-0.295725\pi\)
0.598597 + 0.801050i \(0.295725\pi\)
\(548\) −24.7082 42.7959i −1.05548 1.82815i
\(549\) 5.32624 9.22531i 0.227318 0.393727i
\(550\) −1.11803 + 1.93649i −0.0476731 + 0.0825723i
\(551\) 27.4164 + 47.4866i 1.16798 + 2.02300i
\(552\) 6.83282 0.290824
\(553\) 0 0
\(554\) −44.4721 −1.88944
\(555\) 10.4721 + 18.1383i 0.444517 + 0.769927i
\(556\) −2.29180 + 3.96951i −0.0971938 + 0.168345i
\(557\) 19.4721 33.7267i 0.825061 1.42905i −0.0768119 0.997046i \(-0.524474\pi\)
0.901873 0.432002i \(-0.142193\pi\)
\(558\) 4.54915 + 7.87936i 0.192581 + 0.333560i
\(559\) −25.8885 −1.09497
\(560\) 0 0
\(561\) −4.00000 −0.168880
\(562\) 3.94427 + 6.83168i 0.166379 + 0.288177i
\(563\) 6.29180 10.8977i 0.265168 0.459284i −0.702440 0.711743i \(-0.747906\pi\)
0.967608 + 0.252459i \(0.0812394\pi\)
\(564\) 5.12461 8.87609i 0.215785 0.373751i
\(565\) −2.00000 3.46410i −0.0841406 0.145736i
\(566\) −66.8328 −2.80919
\(567\) 0 0
\(568\) −23.4164 −0.982531
\(569\) −3.76393 6.51932i −0.157792 0.273304i 0.776280 0.630388i \(-0.217104\pi\)
−0.934072 + 0.357084i \(0.883771\pi\)
\(570\) 17.8885 30.9839i 0.749269 1.29777i
\(571\) 7.52786 13.0386i 0.315031 0.545650i −0.664413 0.747366i \(-0.731318\pi\)
0.979444 + 0.201716i \(0.0646516\pi\)
\(572\) −4.85410 8.40755i −0.202960 0.351537i
\(573\) −3.77709 −0.157790
\(574\) 0 0
\(575\) −2.47214 −0.103095
\(576\) −9.56888 16.5738i −0.398703 0.690575i
\(577\) −9.76393 + 16.9116i −0.406478 + 0.704040i −0.994492 0.104810i \(-0.966576\pi\)
0.588014 + 0.808850i \(0.299910\pi\)
\(578\) 7.29837 12.6412i 0.303572 0.525803i
\(579\) −7.34752 12.7263i −0.305353 0.528886i
\(580\) 50.8328 2.11072
\(581\) 0 0
\(582\) −48.1378 −1.99537
\(583\) −0.236068 0.408882i −0.00977694 0.0169342i
\(584\) −0.854102 + 1.47935i −0.0353430 + 0.0612159i
\(585\) −4.76393 + 8.25137i −0.196964 + 0.341152i
\(586\) −28.0902 48.6536i −1.16039 2.00986i
\(587\) −27.1246 −1.11955 −0.559776 0.828644i \(-0.689113\pi\)
−0.559776 + 0.828644i \(0.689113\pi\)
\(588\) 0 0
\(589\) −17.8885 −0.737085
\(590\) −2.76393 4.78727i −0.113789 0.197089i
\(591\) 1.23607 2.14093i 0.0508450 0.0880662i
\(592\) −4.23607 + 7.33708i −0.174101 + 0.301552i
\(593\) −22.8541 39.5845i −0.938505 1.62554i −0.768260 0.640137i \(-0.778877\pi\)
−0.170245 0.985402i \(-0.554456\pi\)
\(594\) 12.3607 0.507165
\(595\) 0 0
\(596\) 42.0000 1.72039
\(597\) −1.34752 2.33398i −0.0551505 0.0955235i
\(598\) 8.94427 15.4919i 0.365758 0.633512i
\(599\) 11.7082 20.2792i 0.478384 0.828586i −0.521309 0.853368i \(-0.674556\pi\)
0.999693 + 0.0247824i \(0.00788929\pi\)
\(600\) 1.38197 + 2.39364i 0.0564185 + 0.0977198i
\(601\) 37.1246 1.51434 0.757172 0.653215i \(-0.226580\pi\)
0.757172 + 0.653215i \(0.226580\pi\)
\(602\) 0 0
\(603\) −21.3050 −0.867605
\(604\) −13.4164 23.2379i −0.545906 0.945537i
\(605\) −1.00000 + 1.73205i −0.0406558 + 0.0704179i
\(606\) −6.58359 + 11.4031i −0.267440 + 0.463220i
\(607\) 6.47214 + 11.2101i 0.262696 + 0.455003i 0.966957 0.254938i \(-0.0820551\pi\)
−0.704262 + 0.709941i \(0.748722\pi\)
\(608\) 43.4164 1.76077
\(609\) 0 0
\(610\) 32.3607 1.31025
\(611\) −4.47214 7.74597i −0.180923 0.313368i
\(612\) 7.14590 12.3771i 0.288856 0.500313i
\(613\) −7.65248 + 13.2545i −0.309081 + 0.535343i −0.978162 0.207846i \(-0.933355\pi\)
0.669081 + 0.743190i \(0.266688\pi\)
\(614\) −10.0000 17.3205i −0.403567 0.698999i
\(615\) 27.7771 1.12008
\(616\) 0 0
\(617\) 6.58359 0.265045 0.132523 0.991180i \(-0.457692\pi\)
0.132523 + 0.991180i \(0.457692\pi\)
\(618\) 10.6525 + 18.4506i 0.428505 + 0.742193i
\(619\) 5.56231 9.63420i 0.223568 0.387231i −0.732321 0.680960i \(-0.761563\pi\)
0.955889 + 0.293729i \(0.0948962\pi\)
\(620\) −8.29180 + 14.3618i −0.333007 + 0.576784i
\(621\) 6.83282 + 11.8348i 0.274191 + 0.474914i
\(622\) 18.5410 0.743427
\(623\) 0 0
\(624\) 4.00000 0.160128
\(625\) 9.50000 + 16.4545i 0.380000 + 0.658179i
\(626\) 16.7082 28.9395i 0.667794 1.15665i
\(627\) −4.00000 + 6.92820i −0.159745 + 0.276686i
\(628\) 16.4164 + 28.4341i 0.655086 + 1.13464i
\(629\) −27.4164 −1.09316
\(630\) 0 0
\(631\) −24.0000 −0.955425 −0.477712 0.878516i \(-0.658534\pi\)
−0.477712 + 0.878516i \(0.658534\pi\)
\(632\) 10.0000 + 17.3205i 0.397779 + 0.688973i
\(633\) 8.58359 14.8672i 0.341167 0.590919i
\(634\) −15.6525 + 27.1109i −0.621639 + 1.07671i
\(635\) −3.05573 5.29268i −0.121263 0.210033i
\(636\) −1.75078 −0.0694228
\(637\) 0 0
\(638\) −18.9443 −0.750011
\(639\) −7.70820 13.3510i −0.304932 0.528157i
\(640\) 15.6525 27.1109i 0.618718 1.07165i
\(641\) 7.76393 13.4475i 0.306657 0.531145i −0.670972 0.741483i \(-0.734123\pi\)
0.977629 + 0.210337i \(0.0674563\pi\)
\(642\) 5.52786 + 9.57454i 0.218167 + 0.377877i
\(643\) −11.1246 −0.438712 −0.219356 0.975645i \(-0.570396\pi\)
−0.219356 + 0.975645i \(0.570396\pi\)
\(644\) 0 0
\(645\) 19.7771 0.778722
\(646\) 23.4164 + 40.5584i 0.921306 + 1.59575i
\(647\) 18.0344 31.2366i 0.709007 1.22804i −0.256219 0.966619i \(-0.582477\pi\)
0.965226 0.261417i \(-0.0841899\pi\)
\(648\) 2.70163 4.67935i 0.106130 0.183822i
\(649\) 0.618034 + 1.07047i 0.0242600 + 0.0420195i
\(650\) 7.23607 0.283822
\(651\) 0 0
\(652\) −10.2492 −0.401391
\(653\) −12.5279 21.6989i −0.490253 0.849143i 0.509684 0.860362i \(-0.329762\pi\)
−0.999937 + 0.0112183i \(0.996429\pi\)
\(654\) 6.18034 10.7047i 0.241670 0.418585i
\(655\) 21.8885 37.9121i 0.855256 1.48135i
\(656\) 5.61803 + 9.73072i 0.219347 + 0.379921i
\(657\) −1.12461 −0.0438753
\(658\) 0 0
\(659\) −17.8885 −0.696839 −0.348419 0.937339i \(-0.613281\pi\)
−0.348419 + 0.937339i \(0.613281\pi\)
\(660\) 3.70820 + 6.42280i 0.144342 + 0.250007i
\(661\) −20.4164 + 35.3623i −0.794106 + 1.37543i 0.129299 + 0.991606i \(0.458727\pi\)
−0.923405 + 0.383827i \(0.874606\pi\)
\(662\) 15.5279 26.8950i 0.603508 1.04531i
\(663\) 6.47214 + 11.2101i 0.251357 + 0.435363i
\(664\) 25.5279 0.990673
\(665\) 0 0
\(666\) 27.8885 1.08066
\(667\) −10.4721 18.1383i −0.405483 0.702317i
\(668\) 7.41641 12.8456i 0.286949 0.497011i
\(669\) −6.29180 + 10.8977i −0.243255 + 0.421330i
\(670\) −32.3607 56.0503i −1.25020 2.16541i
\(671\) −7.23607 −0.279345
\(672\) 0 0
\(673\) −21.4164 −0.825542 −0.412771 0.910835i \(-0.635439\pi\)
−0.412771 + 0.910835i \(0.635439\pi\)
\(674\) 12.8885 + 22.3236i 0.496448 + 0.859873i
\(675\) −2.76393 + 4.78727i −0.106384 + 0.184262i
\(676\) 3.79180 6.56758i 0.145838 0.252599i
\(677\) −4.85410 8.40755i −0.186558 0.323128i 0.757542 0.652786i \(-0.226400\pi\)
−0.944101 + 0.329658i \(0.893067\pi\)
\(678\) 5.52786 0.212296
\(679\) 0 0
\(680\) 14.4721 0.554981
\(681\) 3.63932 + 6.30349i 0.139459 + 0.241550i
\(682\) 3.09017 5.35233i 0.118329 0.204951i
\(683\) 2.94427 5.09963i 0.112659 0.195132i −0.804182 0.594383i \(-0.797396\pi\)
0.916842 + 0.399251i \(0.130730\pi\)
\(684\) −14.2918 24.7541i −0.546460 0.946497i
\(685\) 32.9443 1.25874
\(686\) 0 0
\(687\) 5.52786 0.210901
\(688\) 4.00000 + 6.92820i 0.152499 + 0.264135i
\(689\) −0.763932 + 1.32317i −0.0291035 + 0.0504087i
\(690\) −6.83282 + 11.8348i −0.260121 + 0.450543i
\(691\) 9.27051 + 16.0570i 0.352667 + 0.610837i 0.986716 0.162456i \(-0.0519416\pi\)
−0.634049 + 0.773293i \(0.718608\pi\)
\(692\) 38.2918 1.45564
\(693\) 0 0
\(694\) 46.8328 1.77775
\(695\) −1.52786 2.64634i −0.0579552 0.100381i
\(696\) −11.7082 + 20.2792i −0.443798 + 0.768681i
\(697\) −18.1803 + 31.4893i −0.688629 + 1.19274i
\(698\) −8.09017 14.0126i −0.306217 0.530384i
\(699\) 11.6393 0.440240
\(700\) 0 0
\(701\) −15.5279 −0.586479 −0.293240 0.956039i \(-0.594733\pi\)
−0.293240 + 0.956039i \(0.594733\pi\)
\(702\) −20.0000 34.6410i −0.754851 1.30744i
\(703\) −27.4164 + 47.4866i −1.03403 + 1.79099i
\(704\) −6.50000 + 11.2583i −0.244978 + 0.424314i
\(705\) 3.41641 + 5.91739i 0.128669 + 0.222862i
\(706\) −44.4721 −1.67373
\(707\) 0 0
\(708\) 4.58359 0.172262
\(709\) 7.47214 + 12.9421i 0.280622 + 0.486051i 0.971538 0.236883i \(-0.0761260\pi\)
−0.690916 + 0.722935i \(0.742793\pi\)
\(710\) 23.4164 40.5584i 0.878802 1.52213i
\(711\) −6.58359 + 11.4031i −0.246904 + 0.427650i
\(712\) 2.23607 + 3.87298i 0.0838002 + 0.145146i
\(713\) 6.83282 0.255891
\(714\) 0 0
\(715\) 6.47214 0.242044
\(716\) 13.4164 + 23.2379i 0.501395 + 0.868441i
\(717\) 6.11146 10.5854i 0.228237 0.395317i
\(718\) 27.8885 48.3044i 1.04079 1.80270i
\(719\) −25.7426 44.5876i −0.960039 1.66284i −0.722392 0.691484i \(-0.756957\pi\)
−0.237647 0.971352i \(-0.576376\pi\)
\(720\) 2.94427 0.109727
\(721\) 0 0
\(722\) 51.1803 1.90474
\(723\) −8.11146 14.0495i −0.301668 0.522505i
\(724\) −38.1246 + 66.0338i −1.41689 + 2.45413i
\(725\) 4.23607 7.33708i 0.157324 0.272492i
\(726\) −1.38197 2.39364i −0.0512896 0.0888361i
\(727\) −25.0132 −0.927687 −0.463843 0.885917i \(-0.653530\pi\)
−0.463843 + 0.885917i \(0.653530\pi\)
\(728\) 0 0
\(729\) 24.0557 0.890953
\(730\) −1.70820 2.95870i −0.0632235 0.109506i
\(731\) −12.9443 + 22.4201i −0.478761 + 0.829239i
\(732\) −13.4164 + 23.2379i −0.495885 + 0.858898i
\(733\) 4.38197 + 7.58979i 0.161852 + 0.280335i 0.935533 0.353240i \(-0.114920\pi\)
−0.773681 + 0.633575i \(0.781587\pi\)
\(734\) 51.7082 1.90858
\(735\) 0 0
\(736\) −16.5836 −0.611279
\(737\) 7.23607 + 12.5332i 0.266544 + 0.461668i
\(738\) 18.4934 32.0315i 0.680752 1.17910i
\(739\) −12.4721 + 21.6024i −0.458795 + 0.794656i −0.998898 0.0469430i \(-0.985052\pi\)
0.540103 + 0.841599i \(0.318385\pi\)
\(740\) 25.4164 + 44.0225i 0.934326 + 1.61830i
\(741\) 25.8885 0.951039
\(742\) 0 0
\(743\) 1.88854 0.0692840 0.0346420 0.999400i \(-0.488971\pi\)
0.0346420 + 0.999400i \(0.488971\pi\)
\(744\) −3.81966 6.61585i −0.140036 0.242549i
\(745\) −14.0000 + 24.2487i −0.512920 + 0.888404i
\(746\) −6.70820 + 11.6190i −0.245605 + 0.425400i
\(747\) 8.40325 + 14.5549i 0.307459 + 0.532534i
\(748\) −9.70820 −0.354967
\(749\) 0 0
\(750\) −33.1672 −1.21109
\(751\) −14.7639 25.5719i −0.538744 0.933131i −0.998972 0.0453307i \(-0.985566\pi\)
0.460229 0.887800i \(-0.347767\pi\)
\(752\) −1.38197 + 2.39364i −0.0503951 + 0.0872869i
\(753\) 2.65248 4.59422i 0.0966616 0.167423i
\(754\) 30.6525 + 53.0916i 1.11630 + 1.93348i
\(755\) 17.8885 0.651031
\(756\) 0 0
\(757\) 15.8885 0.577479 0.288739 0.957408i \(-0.406764\pi\)
0.288739 + 0.957408i \(0.406764\pi\)
\(758\) −41.7082 72.2407i −1.51491 2.62390i
\(759\) 1.52786 2.64634i 0.0554580 0.0960560i
\(760\) 14.4721 25.0665i 0.524960 0.909257i
\(761\) −15.7984 27.3636i −0.572691 0.991929i −0.996288 0.0860788i \(-0.972566\pi\)
0.423598 0.905850i \(-0.360767\pi\)
\(762\) 8.44582 0.305960
\(763\) 0 0
\(764\) −9.16718 −0.331657
\(765\) 4.76393 + 8.25137i 0.172240 + 0.298329i
\(766\) −5.20163 + 9.00948i −0.187942 + 0.325526i
\(767\) 2.00000 3.46410i 0.0722158 0.125081i
\(768\) 5.56231 + 9.63420i 0.200712 + 0.347644i
\(769\) −18.2918 −0.659619 −0.329810 0.944047i \(-0.606985\pi\)
−0.329810 + 0.944047i \(0.606985\pi\)
\(770\) 0 0
\(771\) 7.41641 0.267095
\(772\) −17.8328 30.8873i −0.641817 1.11166i
\(773\) −19.1803 + 33.2213i −0.689869 + 1.19489i 0.282011 + 0.959411i \(0.408999\pi\)
−0.971880 + 0.235477i \(0.924335\pi\)
\(774\) 13.1672 22.8062i 0.473285 0.819753i
\(775\) 1.38197 + 2.39364i 0.0496417 + 0.0859819i
\(776\) −38.9443 −1.39802