Properties

Label 273.2.bd.a.43.1
Level $273$
Weight $2$
Character 273.43
Analytic conductor $2.180$
Analytic rank $0$
Dimension $16$
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [273,2,Mod(43,273)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(273, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 0, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("273.43");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 273 = 3 \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 273.bd (of order \(6\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(2.17991597518\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(8\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} + \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{16} + 22x^{14} + 187x^{12} + 774x^{10} + 1619x^{8} + 1618x^{6} + 690x^{4} + 96x^{2} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 43.1
Root \(-2.60802i\) of defining polynomial
Character \(\chi\) \(=\) 273.43
Dual form 273.2.bd.a.127.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-2.25861 - 1.30401i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(2.40088 + 4.15844i) q^{4} -1.50528i q^{5} +(2.25861 - 1.30401i) q^{6} +(-0.866025 + 0.500000i) q^{7} -7.30704i q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\) \(q+(-2.25861 - 1.30401i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(2.40088 + 4.15844i) q^{4} -1.50528i q^{5} +(2.25861 - 1.30401i) q^{6} +(-0.866025 + 0.500000i) q^{7} -7.30704i q^{8} +(-0.500000 - 0.866025i) q^{9} +(-1.96290 + 3.39983i) q^{10} +(0.0753030 + 0.0434762i) q^{11} -4.80176 q^{12} +(-1.30332 + 3.36175i) q^{13} +2.60802 q^{14} +(1.30361 + 0.752639i) q^{15} +(-4.72668 + 8.18685i) q^{16} +(3.24732 + 5.62452i) q^{17} +2.60802i q^{18} +(4.58318 - 2.64610i) q^{19} +(6.25961 - 3.61399i) q^{20} -1.00000i q^{21} +(-0.113387 - 0.196391i) q^{22} +(-2.60110 + 4.50524i) q^{23} +(6.32808 + 3.65352i) q^{24} +2.73414 q^{25} +(7.32743 - 5.89335i) q^{26} +1.00000 q^{27} +(-4.15844 - 2.40088i) q^{28} +(2.98801 - 5.17538i) q^{29} +(-1.96290 - 3.39983i) q^{30} +2.00289i q^{31} +(8.69531 - 5.02024i) q^{32} +(-0.0753030 + 0.0434762i) q^{33} -16.9381i q^{34} +(0.752639 + 1.30361i) q^{35} +(2.40088 - 4.15844i) q^{36} +(8.24566 + 4.76063i) q^{37} -13.8022 q^{38} +(-2.25970 - 2.80958i) q^{39} -10.9991 q^{40} +(5.57631 + 3.21948i) q^{41} +(-1.30401 + 2.25861i) q^{42} +(3.40536 + 5.89825i) q^{43} +0.417524i q^{44} +(-1.30361 + 0.752639i) q^{45} +(11.7498 - 6.78372i) q^{46} +1.83051i q^{47} +(-4.72668 - 8.18685i) q^{48} +(0.500000 - 0.866025i) q^{49} +(-6.17535 - 3.56534i) q^{50} -6.49464 q^{51} +(-17.1088 + 2.65139i) q^{52} -3.28476 q^{53} +(-2.25861 - 1.30401i) q^{54} +(0.0654437 - 0.113352i) q^{55} +(3.65352 + 6.32808i) q^{56} +5.29220i q^{57} +(-13.4975 + 7.79278i) q^{58} +(-2.31669 + 1.33754i) q^{59} +7.22798i q^{60} +(3.27278 + 5.66863i) q^{61} +(2.61179 - 4.52375i) q^{62} +(0.866025 + 0.500000i) q^{63} -7.27901 q^{64} +(5.06037 + 1.96185i) q^{65} +0.226773 q^{66} +(-7.18333 - 4.14730i) q^{67} +(-15.5928 + 27.0076i) q^{68} +(-2.60110 - 4.50524i) q^{69} -3.92579i q^{70} +(-11.1872 + 6.45892i) q^{71} +(-6.32808 + 3.65352i) q^{72} -14.5507i q^{73} +(-12.4158 - 21.5048i) q^{74} +(-1.36707 + 2.36783i) q^{75} +(22.0073 + 12.7059i) q^{76} -0.0869524 q^{77} +(1.44007 + 9.29242i) q^{78} -11.6780 q^{79} +(12.3235 + 7.11497i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-8.39647 - 14.5431i) q^{82} +1.29310i q^{83} +(4.15844 - 2.40088i) q^{84} +(8.46647 - 4.88812i) q^{85} -17.7625i q^{86} +(2.98801 + 5.17538i) q^{87} +(0.317682 - 0.550241i) q^{88} +(13.7225 + 7.92270i) q^{89} +3.92579 q^{90} +(-0.552171 - 3.56302i) q^{91} -24.9797 q^{92} +(-1.73455 - 1.00144i) q^{93} +(2.38701 - 4.13442i) q^{94} +(-3.98312 - 6.89896i) q^{95} +10.0405i q^{96} +(-5.08340 + 2.93490i) q^{97} +(-2.25861 + 1.30401i) q^{98} -0.0869524i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q - 8 q^{3} + 6 q^{4} - 8 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 16 q - 8 q^{3} + 6 q^{4} - 8 q^{9} - 4 q^{10} - 12 q^{11} - 12 q^{12} + 4 q^{13} + 4 q^{14} - 10 q^{16} + 10 q^{17} + 6 q^{20} - 2 q^{22} - 2 q^{23} + 12 q^{25} + 20 q^{26} + 16 q^{27} + 12 q^{29} - 4 q^{30} + 30 q^{32} + 12 q^{33} - 2 q^{35} + 6 q^{36} + 18 q^{37} - 32 q^{38} - 8 q^{39} - 60 q^{40} + 18 q^{41} - 2 q^{42} - 10 q^{43} + 30 q^{46} - 10 q^{48} + 8 q^{49} - 24 q^{50} - 20 q^{51} - 26 q^{52} + 12 q^{53} + 10 q^{55} + 12 q^{56} - 54 q^{58} - 60 q^{59} - 6 q^{61} + 16 q^{62} + 16 q^{64} - 20 q^{65} + 4 q^{66} - 18 q^{67} - 20 q^{68} - 2 q^{69} + 6 q^{71} + 18 q^{74} - 6 q^{75} + 72 q^{76} - 16 q^{77} + 14 q^{78} - 4 q^{79} + 30 q^{80} - 8 q^{81} - 18 q^{82} - 24 q^{85} + 12 q^{87} - 2 q^{88} + 78 q^{89} + 8 q^{90} - 8 q^{91} - 20 q^{92} + 6 q^{93} + 16 q^{94} - 4 q^{95} - 54 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/273\mathbb{Z}\right)^\times\).

\(n\) \(92\) \(106\) \(157\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{6}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.25861 1.30401i −1.59708 0.922074i −0.992046 0.125872i \(-0.959827\pi\)
−0.605032 0.796201i \(-0.706840\pi\)
\(3\) −0.500000 + 0.866025i −0.288675 + 0.500000i
\(4\) 2.40088 + 4.15844i 1.20044 + 2.07922i
\(5\) 1.50528i 0.673181i −0.941651 0.336590i \(-0.890726\pi\)
0.941651 0.336590i \(-0.109274\pi\)
\(6\) 2.25861 1.30401i 0.922074 0.532359i
\(7\) −0.866025 + 0.500000i −0.327327 + 0.188982i
\(8\) 7.30704i 2.58343i
\(9\) −0.500000 0.866025i −0.166667 0.288675i
\(10\) −1.96290 + 3.39983i −0.620722 + 1.07512i
\(11\) 0.0753030 + 0.0434762i 0.0227047 + 0.0131086i 0.511309 0.859397i \(-0.329161\pi\)
−0.488605 + 0.872505i \(0.662494\pi\)
\(12\) −4.80176 −1.38615
\(13\) −1.30332 + 3.36175i −0.361475 + 0.932382i
\(14\) 2.60802 0.697022
\(15\) 1.30361 + 0.752639i 0.336590 + 0.194330i
\(16\) −4.72668 + 8.18685i −1.18167 + 2.04671i
\(17\) 3.24732 + 5.62452i 0.787591 + 1.36415i 0.927439 + 0.373974i \(0.122005\pi\)
−0.139848 + 0.990173i \(0.544662\pi\)
\(18\) 2.60802i 0.614716i
\(19\) 4.58318 2.64610i 1.05145 0.607057i 0.128398 0.991723i \(-0.459016\pi\)
0.923056 + 0.384665i \(0.125683\pi\)
\(20\) 6.25961 3.61399i 1.39969 0.808113i
\(21\) 1.00000i 0.218218i
\(22\) −0.113387 0.196391i −0.0241741 0.0418708i
\(23\) −2.60110 + 4.50524i −0.542367 + 0.939408i 0.456400 + 0.889775i \(0.349139\pi\)
−0.998768 + 0.0496333i \(0.984195\pi\)
\(24\) 6.32808 + 3.65352i 1.29171 + 0.745771i
\(25\) 2.73414 0.546828
\(26\) 7.32743 5.89335i 1.43703 1.15578i
\(27\) 1.00000 0.192450
\(28\) −4.15844 2.40088i −0.785872 0.453723i
\(29\) 2.98801 5.17538i 0.554859 0.961045i −0.443055 0.896494i \(-0.646105\pi\)
0.997914 0.0645503i \(-0.0205613\pi\)
\(30\) −1.96290 3.39983i −0.358374 0.620722i
\(31\) 2.00289i 0.359730i 0.983691 + 0.179865i \(0.0575660\pi\)
−0.983691 + 0.179865i \(0.942434\pi\)
\(32\) 8.69531 5.02024i 1.53713 0.887461i
\(33\) −0.0753030 + 0.0434762i −0.0131086 + 0.00756823i
\(34\) 16.9381i 2.90487i
\(35\) 0.752639 + 1.30361i 0.127219 + 0.220350i
\(36\) 2.40088 4.15844i 0.400147 0.693074i
\(37\) 8.24566 + 4.76063i 1.35558 + 0.782643i 0.989024 0.147754i \(-0.0472042\pi\)
0.366554 + 0.930397i \(0.380538\pi\)
\(38\) −13.8022 −2.23901
\(39\) −2.25970 2.80958i −0.361842 0.449893i
\(40\) −10.9991 −1.73911
\(41\) 5.57631 + 3.21948i 0.870873 + 0.502799i 0.867638 0.497196i \(-0.165637\pi\)
0.00323453 + 0.999995i \(0.498970\pi\)
\(42\) −1.30401 + 2.25861i −0.201213 + 0.348511i
\(43\) 3.40536 + 5.89825i 0.519312 + 0.899475i 0.999748 + 0.0224449i \(0.00714502\pi\)
−0.480436 + 0.877030i \(0.659522\pi\)
\(44\) 0.417524i 0.0629441i
\(45\) −1.30361 + 0.752639i −0.194330 + 0.112197i
\(46\) 11.7498 6.78372i 1.73241 1.00021i
\(47\) 1.83051i 0.267008i 0.991048 + 0.133504i \(0.0426229\pi\)
−0.991048 + 0.133504i \(0.957377\pi\)
\(48\) −4.72668 8.18685i −0.682238 1.18167i
\(49\) 0.500000 0.866025i 0.0714286 0.123718i
\(50\) −6.17535 3.56534i −0.873327 0.504216i
\(51\) −6.49464 −0.909431
\(52\) −17.1088 + 2.65139i −2.37256 + 0.367682i
\(53\) −3.28476 −0.451197 −0.225598 0.974220i \(-0.572434\pi\)
−0.225598 + 0.974220i \(0.572434\pi\)
\(54\) −2.25861 1.30401i −0.307358 0.177453i
\(55\) 0.0654437 0.113352i 0.00882443 0.0152844i
\(56\) 3.65352 + 6.32808i 0.488222 + 0.845625i
\(57\) 5.29220i 0.700969i
\(58\) −13.4975 + 7.79278i −1.77231 + 1.02324i
\(59\) −2.31669 + 1.33754i −0.301608 + 0.174133i −0.643165 0.765728i \(-0.722379\pi\)
0.341557 + 0.939861i \(0.389046\pi\)
\(60\) 7.22798i 0.933128i
\(61\) 3.27278 + 5.66863i 0.419037 + 0.725794i 0.995843 0.0910877i \(-0.0290344\pi\)
−0.576806 + 0.816881i \(0.695701\pi\)
\(62\) 2.61179 4.52375i 0.331697 0.574516i
\(63\) 0.866025 + 0.500000i 0.109109 + 0.0629941i
\(64\) −7.27901 −0.909876
\(65\) 5.06037 + 1.96185i 0.627661 + 0.243338i
\(66\) 0.226773 0.0279139
\(67\) −7.18333 4.14730i −0.877583 0.506673i −0.00772242 0.999970i \(-0.502458\pi\)
−0.869861 + 0.493297i \(0.835791\pi\)
\(68\) −15.5928 + 27.0076i −1.89091 + 3.27515i
\(69\) −2.60110 4.50524i −0.313136 0.542367i
\(70\) 3.92579i 0.469222i
\(71\) −11.1872 + 6.45892i −1.32767 + 0.766533i −0.984940 0.172899i \(-0.944687\pi\)
−0.342735 + 0.939432i \(0.611353\pi\)
\(72\) −6.32808 + 3.65352i −0.745771 + 0.430571i
\(73\) 14.5507i 1.70303i −0.524334 0.851513i \(-0.675686\pi\)
0.524334 0.851513i \(-0.324314\pi\)
\(74\) −12.4158 21.5048i −1.44331 2.49989i
\(75\) −1.36707 + 2.36783i −0.157856 + 0.273414i
\(76\) 22.0073 + 12.7059i 2.52441 + 1.45747i
\(77\) −0.0869524 −0.00990914
\(78\) 1.44007 + 9.29242i 0.163056 + 1.05216i
\(79\) −11.6780 −1.31387 −0.656936 0.753946i \(-0.728148\pi\)
−0.656936 + 0.753946i \(0.728148\pi\)
\(80\) 12.3235 + 7.11497i 1.37781 + 0.795478i
\(81\) −0.500000 + 0.866025i −0.0555556 + 0.0962250i
\(82\) −8.39647 14.5431i −0.927235 1.60602i
\(83\) 1.29310i 0.141937i 0.997479 + 0.0709683i \(0.0226089\pi\)
−0.997479 + 0.0709683i \(0.977391\pi\)
\(84\) 4.15844 2.40088i 0.453723 0.261957i
\(85\) 8.46647 4.88812i 0.918317 0.530191i
\(86\) 17.7625i 1.91538i
\(87\) 2.98801 + 5.17538i 0.320348 + 0.554859i
\(88\) 0.317682 0.550241i 0.0338650 0.0586559i
\(89\) 13.7225 + 7.92270i 1.45458 + 0.839805i 0.998737 0.0502531i \(-0.0160028\pi\)
0.455848 + 0.890058i \(0.349336\pi\)
\(90\) 3.92579 0.413815
\(91\) −0.552171 3.56302i −0.0578833 0.373506i
\(92\) −24.9797 −2.60432
\(93\) −1.73455 1.00144i −0.179865 0.103845i
\(94\) 2.38701 4.13442i 0.246201 0.426433i
\(95\) −3.98312 6.89896i −0.408659 0.707819i
\(96\) 10.0405i 1.02475i
\(97\) −5.08340 + 2.93490i −0.516141 + 0.297994i −0.735354 0.677683i \(-0.762984\pi\)
0.219213 + 0.975677i \(0.429651\pi\)
\(98\) −2.25861 + 1.30401i −0.228154 + 0.131725i
\(99\) 0.0869524i 0.00873904i
\(100\) 6.56434 + 11.3698i 0.656434 + 1.13698i
\(101\) −3.34086 + 5.78654i −0.332428 + 0.575782i −0.982987 0.183673i \(-0.941201\pi\)
0.650559 + 0.759455i \(0.274534\pi\)
\(102\) 14.6689 + 8.46907i 1.45243 + 0.838563i
\(103\) 4.52273 0.445637 0.222819 0.974860i \(-0.428474\pi\)
0.222819 + 0.974860i \(0.428474\pi\)
\(104\) 24.5644 + 9.52337i 2.40874 + 0.933843i
\(105\) −1.50528 −0.146900
\(106\) 7.41900 + 4.28336i 0.720597 + 0.416037i
\(107\) 5.12241 8.87227i 0.495202 0.857715i −0.504783 0.863246i \(-0.668427\pi\)
0.999985 + 0.00553163i \(0.00176078\pi\)
\(108\) 2.40088 + 4.15844i 0.231025 + 0.400147i
\(109\) 13.5552i 1.29835i −0.760637 0.649177i \(-0.775113\pi\)
0.760637 0.649177i \(-0.224887\pi\)
\(110\) −0.295624 + 0.170678i −0.0281866 + 0.0162735i
\(111\) −8.24566 + 4.76063i −0.782643 + 0.451859i
\(112\) 9.45336i 0.893259i
\(113\) −6.69370 11.5938i −0.629691 1.09066i −0.987614 0.156905i \(-0.949848\pi\)
0.357923 0.933751i \(-0.383485\pi\)
\(114\) 6.90108 11.9530i 0.646345 1.11950i
\(115\) 6.78164 + 3.91538i 0.632391 + 0.365111i
\(116\) 28.6954 2.66430
\(117\) 3.56302 0.552171i 0.329401 0.0510482i
\(118\) 6.97667 0.642255
\(119\) −5.62452 3.24732i −0.515599 0.297681i
\(120\) 5.49956 9.52551i 0.502039 0.869556i
\(121\) −5.49622 9.51973i −0.499656 0.865430i
\(122\) 17.0710i 1.54553i
\(123\) −5.57631 + 3.21948i −0.502799 + 0.290291i
\(124\) −8.32891 + 4.80870i −0.747958 + 0.431834i
\(125\) 11.6420i 1.04129i
\(126\) −1.30401 2.25861i −0.116170 0.201213i
\(127\) 6.47234 11.2104i 0.574328 0.994765i −0.421787 0.906695i \(-0.638597\pi\)
0.996114 0.0880695i \(-0.0280698\pi\)
\(128\) −0.950172 0.548582i −0.0839841 0.0484883i
\(129\) −6.81071 −0.599650
\(130\) −8.87113 11.0298i −0.778049 0.967379i
\(131\) 5.84887 0.511018 0.255509 0.966807i \(-0.417757\pi\)
0.255509 + 0.966807i \(0.417757\pi\)
\(132\) −0.361587 0.208762i −0.0314721 0.0181704i
\(133\) −2.64610 + 4.58318i −0.229446 + 0.397412i
\(134\) 10.8162 + 18.7342i 0.934379 + 1.61839i
\(135\) 1.50528i 0.129554i
\(136\) 41.0986 23.7283i 3.52417 2.03468i
\(137\) −4.42616 + 2.55545i −0.378153 + 0.218327i −0.677014 0.735970i \(-0.736726\pi\)
0.298862 + 0.954296i \(0.403393\pi\)
\(138\) 13.5674i 1.15494i
\(139\) 9.66376 + 16.7381i 0.819669 + 1.41971i 0.905926 + 0.423436i \(0.139176\pi\)
−0.0862564 + 0.996273i \(0.527490\pi\)
\(140\) −3.61399 + 6.25961i −0.305438 + 0.529034i
\(141\) −1.58527 0.915257i −0.133504 0.0770786i
\(142\) 33.6900 2.82720
\(143\) −0.244300 + 0.196487i −0.0204294 + 0.0164310i
\(144\) 9.45336 0.787780
\(145\) −7.79039 4.49778i −0.646957 0.373521i
\(146\) −18.9742 + 32.8643i −1.57031 + 2.71987i
\(147\) 0.500000 + 0.866025i 0.0412393 + 0.0714286i
\(148\) 45.7188i 3.75806i
\(149\) −8.23614 + 4.75514i −0.674731 + 0.389556i −0.797867 0.602834i \(-0.794038\pi\)
0.123136 + 0.992390i \(0.460705\pi\)
\(150\) 6.17535 3.56534i 0.504216 0.291109i
\(151\) 12.7770i 1.03977i 0.854235 + 0.519887i \(0.174026\pi\)
−0.854235 + 0.519887i \(0.825974\pi\)
\(152\) −19.3352 33.4895i −1.56829 2.71636i
\(153\) 3.24732 5.62452i 0.262530 0.454716i
\(154\) 0.196391 + 0.113387i 0.0158257 + 0.00913696i
\(155\) 3.01490 0.242163
\(156\) 6.25821 16.1423i 0.501057 1.29242i
\(157\) −2.57466 −0.205480 −0.102740 0.994708i \(-0.532761\pi\)
−0.102740 + 0.994708i \(0.532761\pi\)
\(158\) 26.3759 + 15.2282i 2.09836 + 1.21149i
\(159\) 1.64238 2.84469i 0.130249 0.225598i
\(160\) −7.55685 13.0888i −0.597421 1.03476i
\(161\) 5.20221i 0.409991i
\(162\) 2.25861 1.30401i 0.177453 0.102453i
\(163\) −16.9135 + 9.76499i −1.32476 + 0.764853i −0.984485 0.175471i \(-0.943855\pi\)
−0.340280 + 0.940324i \(0.610522\pi\)
\(164\) 30.9183i 2.41432i
\(165\) 0.0654437 + 0.113352i 0.00509479 + 0.00882443i
\(166\) 1.68622 2.92062i 0.130876 0.226684i
\(167\) −1.20942 0.698261i −0.0935881 0.0540331i 0.452476 0.891777i \(-0.350541\pi\)
−0.546064 + 0.837744i \(0.683874\pi\)
\(168\) −7.30704 −0.563750
\(169\) −9.60274 8.76284i −0.738672 0.674065i
\(170\) −25.4966 −1.95550
\(171\) −4.58318 2.64610i −0.350485 0.202352i
\(172\) −16.3517 + 28.3220i −1.24680 + 2.15953i
\(173\) 8.59070 + 14.8795i 0.653138 + 1.13127i 0.982357 + 0.187015i \(0.0598814\pi\)
−0.329219 + 0.944254i \(0.606785\pi\)
\(174\) 15.5856i 1.18154i
\(175\) −2.36783 + 1.36707i −0.178991 + 0.103341i
\(176\) −0.711866 + 0.410996i −0.0536589 + 0.0309800i
\(177\) 2.67509i 0.201072i
\(178\) −20.6625 35.7886i −1.54872 2.68247i
\(179\) −0.718538 + 1.24454i −0.0537061 + 0.0930216i −0.891629 0.452768i \(-0.850437\pi\)
0.837923 + 0.545789i \(0.183770\pi\)
\(180\) −6.25961 3.61399i −0.466564 0.269371i
\(181\) 4.31882 0.321015 0.160508 0.987035i \(-0.448687\pi\)
0.160508 + 0.987035i \(0.448687\pi\)
\(182\) −3.39907 + 8.76751i −0.251956 + 0.649891i
\(183\) −6.54557 −0.483862
\(184\) 32.9200 + 19.0064i 2.42689 + 1.40117i
\(185\) 7.16607 12.4120i 0.526860 0.912549i
\(186\) 2.61179 + 4.52375i 0.191505 + 0.331697i
\(187\) 0.564724i 0.0412967i
\(188\) −7.61209 + 4.39484i −0.555169 + 0.320527i
\(189\) −0.866025 + 0.500000i −0.0629941 + 0.0363696i
\(190\) 20.7761i 1.50726i
\(191\) 3.39359 + 5.87788i 0.245552 + 0.425308i 0.962287 0.272038i \(-0.0876975\pi\)
−0.716735 + 0.697346i \(0.754364\pi\)
\(192\) 3.63950 6.30381i 0.262659 0.454938i
\(193\) −18.5112 10.6875i −1.33247 0.769300i −0.346790 0.937943i \(-0.612728\pi\)
−0.985677 + 0.168642i \(0.946062\pi\)
\(194\) 15.3085 1.09909
\(195\) −4.22920 + 3.40148i −0.302859 + 0.243585i
\(196\) 4.80176 0.342983
\(197\) 19.7438 + 11.3991i 1.40669 + 0.812153i 0.995067 0.0992006i \(-0.0316286\pi\)
0.411623 + 0.911354i \(0.364962\pi\)
\(198\) −0.113387 + 0.196391i −0.00805804 + 0.0139569i
\(199\) 1.33183 + 2.30679i 0.0944107 + 0.163524i 0.909363 0.416005i \(-0.136570\pi\)
−0.814952 + 0.579529i \(0.803237\pi\)
\(200\) 19.9785i 1.41269i
\(201\) 7.18333 4.14730i 0.506673 0.292528i
\(202\) 15.0914 8.71302i 1.06183 0.613046i
\(203\) 5.97602i 0.419434i
\(204\) −15.5928 27.0076i −1.09172 1.89091i
\(205\) 4.84621 8.39389i 0.338474 0.586255i
\(206\) −10.2151 5.89767i −0.711718 0.410910i
\(207\) 5.20221 0.361578
\(208\) −21.3618 26.5600i −1.48117 1.84160i
\(209\) 0.460170 0.0318306
\(210\) 3.39983 + 1.96290i 0.234611 + 0.135453i
\(211\) 12.0916 20.9432i 0.832419 1.44179i −0.0636958 0.997969i \(-0.520289\pi\)
0.896115 0.443823i \(-0.146378\pi\)
\(212\) −7.88632 13.6595i −0.541635 0.938138i
\(213\) 12.9178i 0.885116i
\(214\) −23.1390 + 13.3593i −1.58175 + 0.913225i
\(215\) 8.87850 5.12601i 0.605509 0.349591i
\(216\) 7.30704i 0.497181i
\(217\) −1.00144 1.73455i −0.0679825 0.117749i
\(218\) −17.6761 + 30.6160i −1.19718 + 2.07357i
\(219\) 12.6012 + 7.27533i 0.851513 + 0.491621i
\(220\) 0.628490 0.0423728
\(221\) −23.1405 + 3.58615i −1.55660 + 0.241231i
\(222\) 24.8316 1.66659
\(223\) −14.6428 8.45400i −0.980551 0.566122i −0.0781148 0.996944i \(-0.524890\pi\)
−0.902437 + 0.430823i \(0.858223\pi\)
\(224\) −5.02024 + 8.69531i −0.335429 + 0.580980i
\(225\) −1.36707 2.36783i −0.0911380 0.157856i
\(226\) 34.9146i 2.32248i
\(227\) 10.0833 5.82157i 0.669249 0.386391i −0.126543 0.991961i \(-0.540388\pi\)
0.795792 + 0.605570i \(0.207055\pi\)
\(228\) −22.0073 + 12.7059i −1.45747 + 0.841471i
\(229\) 7.90801i 0.522576i 0.965261 + 0.261288i \(0.0841473\pi\)
−0.965261 + 0.261288i \(0.915853\pi\)
\(230\) −10.2114 17.6866i −0.673319 1.16622i
\(231\) 0.0434762 0.0753030i 0.00286052 0.00495457i
\(232\) −37.8167 21.8335i −2.48279 1.43344i
\(233\) 24.0854 1.57789 0.788945 0.614464i \(-0.210628\pi\)
0.788945 + 0.614464i \(0.210628\pi\)
\(234\) −8.76751 3.39907i −0.573150 0.222204i
\(235\) 2.75543 0.179745
\(236\) −11.1242 6.42256i −0.724124 0.418073i
\(237\) 5.83898 10.1134i 0.379282 0.656936i
\(238\) 8.46907 + 14.6689i 0.548968 + 0.950841i
\(239\) 10.9354i 0.707352i −0.935368 0.353676i \(-0.884932\pi\)
0.935368 0.353676i \(-0.115068\pi\)
\(240\) −12.3235 + 7.11497i −0.795478 + 0.459269i
\(241\) 17.2385 9.95268i 1.11043 0.641108i 0.171491 0.985186i \(-0.445142\pi\)
0.938941 + 0.344077i \(0.111808\pi\)
\(242\) 28.6685i 1.84288i
\(243\) −0.500000 0.866025i −0.0320750 0.0555556i
\(244\) −15.7151 + 27.2194i −1.00606 + 1.74254i
\(245\) −1.30361 0.752639i −0.0832845 0.0480843i
\(246\) 16.7929 1.07068
\(247\) 2.92220 + 18.8562i 0.185935 + 1.19979i
\(248\) 14.6352 0.929335
\(249\) −1.11986 0.646552i −0.0709683 0.0409736i
\(250\) −15.1813 + 26.2948i −0.960150 + 1.66303i
\(251\) −11.6942 20.2549i −0.738129 1.27848i −0.953337 0.301909i \(-0.902376\pi\)
0.215208 0.976568i \(-0.430957\pi\)
\(252\) 4.80176i 0.302482i
\(253\) −0.391741 + 0.226172i −0.0246286 + 0.0142193i
\(254\) −29.2370 + 16.8800i −1.83449 + 1.05914i
\(255\) 9.77623i 0.612212i
\(256\) 8.70972 + 15.0857i 0.544357 + 0.942855i
\(257\) 6.02975 10.4438i 0.376125 0.651468i −0.614369 0.789019i \(-0.710590\pi\)
0.990495 + 0.137550i \(0.0439229\pi\)
\(258\) 15.3827 + 8.88123i 0.957688 + 0.552921i
\(259\) −9.52127 −0.591623
\(260\) 3.99108 + 25.7534i 0.247516 + 1.59716i
\(261\) −5.97602 −0.369906
\(262\) −13.2103 7.62698i −0.816136 0.471196i
\(263\) −2.26613 + 3.92505i −0.139736 + 0.242029i −0.927396 0.374080i \(-0.877959\pi\)
0.787661 + 0.616109i \(0.211292\pi\)
\(264\) 0.317682 + 0.550241i 0.0195520 + 0.0338650i
\(265\) 4.94448i 0.303737i
\(266\) 11.9530 6.90108i 0.732887 0.423132i
\(267\) −13.7225 + 7.92270i −0.839805 + 0.484861i
\(268\) 39.8286i 2.43292i
\(269\) 13.9800 + 24.2140i 0.852375 + 1.47636i 0.879059 + 0.476713i \(0.158172\pi\)
−0.0266843 + 0.999644i \(0.508495\pi\)
\(270\) −1.96290 + 3.39983i −0.119458 + 0.206907i
\(271\) 3.62825 + 2.09477i 0.220400 + 0.127248i 0.606136 0.795361i \(-0.292719\pi\)
−0.385735 + 0.922609i \(0.626052\pi\)
\(272\) −61.3962 −3.72269
\(273\) 3.36175 + 1.30332i 0.203462 + 0.0788802i
\(274\) 13.3293 0.805252
\(275\) 0.205889 + 0.118870i 0.0124156 + 0.00716813i
\(276\) 12.4899 21.6331i 0.751802 1.30216i
\(277\) 4.93402 + 8.54598i 0.296457 + 0.513478i 0.975323 0.220784i \(-0.0708616\pi\)
−0.678866 + 0.734262i \(0.737528\pi\)
\(278\) 50.4065i 3.02318i
\(279\) 1.73455 1.00144i 0.103845 0.0599549i
\(280\) 9.52551 5.49956i 0.569258 0.328661i
\(281\) 2.76496i 0.164944i 0.996593 + 0.0824719i \(0.0262815\pi\)
−0.996593 + 0.0824719i \(0.973719\pi\)
\(282\) 2.38701 + 4.13442i 0.142144 + 0.246201i
\(283\) −2.87040 + 4.97167i −0.170627 + 0.295535i −0.938639 0.344900i \(-0.887913\pi\)
0.768012 + 0.640435i \(0.221246\pi\)
\(284\) −53.7181 31.0142i −3.18759 1.84035i
\(285\) 7.96623 0.471879
\(286\) 0.807998 0.125218i 0.0477779 0.00740428i
\(287\) −6.43896 −0.380080
\(288\) −8.69531 5.02024i −0.512376 0.295820i
\(289\) −12.5902 + 21.8068i −0.740598 + 1.28275i
\(290\) 11.7303 + 20.3175i 0.688827 + 1.19308i
\(291\) 5.86980i 0.344094i
\(292\) 60.5081 34.9344i 3.54097 2.04438i
\(293\) 13.6845 7.90072i 0.799454 0.461565i −0.0438259 0.999039i \(-0.513955\pi\)
0.843280 + 0.537474i \(0.180621\pi\)
\(294\) 2.60802i 0.152103i
\(295\) 2.01337 + 3.48727i 0.117223 + 0.203036i
\(296\) 34.7861 60.2513i 2.02190 3.50204i
\(297\) 0.0753030 + 0.0434762i 0.00436952 + 0.00252274i
\(298\) 24.8030 1.43680
\(299\) −11.7554 14.6160i −0.679835 0.845266i
\(300\) −13.1287 −0.757985
\(301\) −5.89825 3.40536i −0.339969 0.196281i
\(302\) 16.6613 28.8582i 0.958749 1.66060i
\(303\) −3.34086 5.78654i −0.191927 0.332428i
\(304\) 50.0291i 2.86937i
\(305\) 8.53286 4.92645i 0.488590 0.282088i
\(306\) −14.6689 + 8.46907i −0.838563 + 0.484144i
\(307\) 10.1195i 0.577549i 0.957397 + 0.288774i \(0.0932478\pi\)
−0.957397 + 0.288774i \(0.906752\pi\)
\(308\) −0.208762 0.361587i −0.0118953 0.0206033i
\(309\) −2.26136 + 3.91680i −0.128644 + 0.222819i
\(310\) −6.80949 3.93146i −0.386753 0.223292i
\(311\) −14.4989 −0.822155 −0.411077 0.911600i \(-0.634847\pi\)
−0.411077 + 0.911600i \(0.634847\pi\)
\(312\) −20.5297 + 16.5117i −1.16227 + 0.934793i
\(313\) 13.2670 0.749897 0.374948 0.927046i \(-0.377660\pi\)
0.374948 + 0.927046i \(0.377660\pi\)
\(314\) 5.81516 + 3.35738i 0.328168 + 0.189468i
\(315\) 0.752639 1.30361i 0.0424064 0.0734500i
\(316\) −28.0374 48.5621i −1.57722 2.73183i
\(317\) 30.4190i 1.70850i −0.519860 0.854252i \(-0.674016\pi\)
0.519860 0.854252i \(-0.325984\pi\)
\(318\) −7.41900 + 4.28336i −0.416037 + 0.240199i
\(319\) 0.450012 0.259814i 0.0251958 0.0145468i
\(320\) 10.9569i 0.612511i
\(321\) 5.12241 + 8.87227i 0.285905 + 0.495202i
\(322\) −6.78372 + 11.7498i −0.378042 + 0.654788i
\(323\) 29.7661 + 17.1855i 1.65623 + 0.956226i
\(324\) −4.80176 −0.266764
\(325\) −3.56345 + 9.19150i −0.197664 + 0.509852i
\(326\) 50.9345 2.82100
\(327\) 11.7392 + 6.77761i 0.649177 + 0.374803i
\(328\) 23.5249 40.7463i 1.29894 2.24984i
\(329\) −0.915257 1.58527i −0.0504598 0.0873989i
\(330\) 0.341357i 0.0187911i
\(331\) 8.05659 4.65147i 0.442830 0.255668i −0.261967 0.965077i \(-0.584371\pi\)
0.704797 + 0.709409i \(0.251038\pi\)
\(332\) −5.37730 + 3.10459i −0.295118 + 0.170386i
\(333\) 9.52127i 0.521762i
\(334\) 1.82108 + 3.15420i 0.0996450 + 0.172590i
\(335\) −6.24283 + 10.8129i −0.341082 + 0.590772i
\(336\) 8.18685 + 4.72668i 0.446629 + 0.257862i
\(337\) −13.3054 −0.724789 −0.362395 0.932025i \(-0.618041\pi\)
−0.362395 + 0.932025i \(0.618041\pi\)
\(338\) 10.2620 + 32.3139i 0.558180 + 1.75764i
\(339\) 13.3874 0.727104
\(340\) 40.6539 + 23.4716i 2.20477 + 1.27292i
\(341\) −0.0870780 + 0.150824i −0.00471554 + 0.00816755i
\(342\) 6.90108 + 11.9530i 0.373168 + 0.646345i
\(343\) 1.00000i 0.0539949i
\(344\) 43.0987 24.8831i 2.32373 1.34160i
\(345\) −6.78164 + 3.91538i −0.365111 + 0.210797i
\(346\) 44.8094i 2.40897i
\(347\) 8.43801 + 14.6151i 0.452976 + 0.784578i 0.998569 0.0534723i \(-0.0170289\pi\)
−0.545593 + 0.838050i \(0.683696\pi\)
\(348\) −14.3477 + 24.8509i −0.769117 + 1.33215i
\(349\) −2.08469 1.20360i −0.111591 0.0644271i 0.443166 0.896440i \(-0.353855\pi\)
−0.554757 + 0.832013i \(0.687189\pi\)
\(350\) 7.13069 0.381151
\(351\) −1.30332 + 3.36175i −0.0695658 + 0.179437i
\(352\) 0.873043 0.0465333
\(353\) −26.5988 15.3568i −1.41571 0.817361i −0.419793 0.907620i \(-0.637897\pi\)
−0.995918 + 0.0902583i \(0.971231\pi\)
\(354\) −3.48834 + 6.04198i −0.185403 + 0.321127i
\(355\) 9.72247 + 16.8398i 0.516015 + 0.893765i
\(356\) 76.0858i 4.03254i
\(357\) 5.62452 3.24732i 0.297681 0.171866i
\(358\) 3.24579 1.87396i 0.171546 0.0990419i
\(359\) 10.6322i 0.561145i −0.959833 0.280572i \(-0.909476\pi\)
0.959833 0.280572i \(-0.0905243\pi\)
\(360\) 5.49956 + 9.52551i 0.289852 + 0.502039i
\(361\) 4.50371 7.80065i 0.237037 0.410561i
\(362\) −9.75453 5.63178i −0.512687 0.296000i
\(363\) 10.9924 0.576953
\(364\) 13.4909 10.8506i 0.707116 0.568723i
\(365\) −21.9028 −1.14644
\(366\) 14.7839 + 8.53548i 0.772766 + 0.446157i
\(367\) −13.1031 + 22.6953i −0.683977 + 1.18468i 0.289780 + 0.957093i \(0.406418\pi\)
−0.973757 + 0.227590i \(0.926915\pi\)
\(368\) −24.5892 42.5897i −1.28180 2.22014i
\(369\) 6.43896i 0.335199i
\(370\) −32.3707 + 18.6893i −1.68287 + 0.971608i
\(371\) 2.84469 1.64238i 0.147689 0.0852682i
\(372\) 9.61739i 0.498639i
\(373\) −9.10509 15.7705i −0.471444 0.816565i 0.528022 0.849230i \(-0.322934\pi\)
−0.999466 + 0.0326656i \(0.989600\pi\)
\(374\) 0.736405 1.27549i 0.0380786 0.0659541i
\(375\) 10.0823 + 5.82101i 0.520647 + 0.300596i
\(376\) 13.3756 0.689796
\(377\) 13.5040 + 16.7901i 0.695493 + 0.864734i
\(378\) 2.60802 0.134142
\(379\) −25.0235 14.4473i −1.28537 0.742110i −0.307547 0.951533i \(-0.599508\pi\)
−0.977825 + 0.209423i \(0.932842\pi\)
\(380\) 19.1260 33.1271i 0.981141 1.69939i
\(381\) 6.47234 + 11.2104i 0.331588 + 0.574328i
\(382\) 17.7011i 0.905668i
\(383\) −15.0050 + 8.66312i −0.766718 + 0.442665i −0.831702 0.555222i \(-0.812633\pi\)
0.0649848 + 0.997886i \(0.479300\pi\)
\(384\) 0.950172 0.548582i 0.0484883 0.0279947i
\(385\) 0.130887i 0.00667064i
\(386\) 27.8731 + 48.2776i 1.41870 + 2.45727i
\(387\) 3.40536 5.89825i 0.173104 0.299825i
\(388\) −24.4092 14.0927i −1.23919 0.715448i
\(389\) −13.6737 −0.693282 −0.346641 0.937998i \(-0.612678\pi\)
−0.346641 + 0.937998i \(0.612678\pi\)
\(390\) 13.9877 2.16771i 0.708293 0.109766i
\(391\) −33.7865 −1.70865
\(392\) −6.32808 3.65352i −0.319616 0.184531i
\(393\) −2.92444 + 5.06527i −0.147518 + 0.255509i
\(394\) −29.7291 51.4923i −1.49773 2.59415i
\(395\) 17.5786i 0.884473i
\(396\) 0.361587 0.208762i 0.0181704 0.0104907i
\(397\) −13.3743 + 7.72167i −0.671238 + 0.387540i −0.796546 0.604578i \(-0.793342\pi\)
0.125307 + 0.992118i \(0.460008\pi\)
\(398\) 6.94686i 0.348215i
\(399\) −2.64610 4.58318i −0.132471 0.229446i
\(400\) −12.9234 + 22.3840i −0.646170 + 1.11920i
\(401\) 12.3265 + 7.11671i 0.615556 + 0.355391i 0.775137 0.631794i \(-0.217681\pi\)
−0.159581 + 0.987185i \(0.551014\pi\)
\(402\) −21.6324 −1.07893
\(403\) −6.73322 2.61040i −0.335405 0.130033i
\(404\) −32.0840 −1.59624
\(405\) 1.30361 + 0.752639i 0.0647768 + 0.0373989i
\(406\) 7.79278 13.4975i 0.386749 0.669869i
\(407\) 0.413948 + 0.716979i 0.0205187 + 0.0355394i
\(408\) 47.4566i 2.34945i
\(409\) 12.1987 7.04291i 0.603185 0.348249i −0.167108 0.985939i \(-0.553443\pi\)
0.770294 + 0.637689i \(0.220110\pi\)
\(410\) −21.8914 + 12.6390i −1.08114 + 0.624196i
\(411\) 5.11089i 0.252102i
\(412\) 10.8585 + 18.8075i 0.534961 + 0.926579i
\(413\) 1.33754 2.31669i 0.0658162 0.113997i
\(414\) −11.7498 6.78372i −0.577469 0.333402i
\(415\) 1.94648 0.0955489
\(416\) 5.54406 + 35.7744i 0.271820 + 1.75398i
\(417\) −19.3275 −0.946473
\(418\) −1.03934 0.600065i −0.0508360 0.0293502i
\(419\) 18.8362 32.6252i 0.920207 1.59385i 0.121114 0.992639i \(-0.461353\pi\)
0.799093 0.601207i \(-0.205313\pi\)
\(420\) −3.61399 6.25961i −0.176345 0.305438i
\(421\) 2.28615i 0.111420i 0.998447 + 0.0557101i \(0.0177423\pi\)
−0.998447 + 0.0557101i \(0.982258\pi\)
\(422\) −54.6203 + 31.5351i −2.65888 + 1.53510i
\(423\) 1.58527 0.915257i 0.0770786 0.0445013i
\(424\) 24.0019i 1.16563i
\(425\) 8.87863 + 15.3782i 0.430677 + 0.745954i
\(426\) −16.8450 + 29.1764i −0.816142 + 1.41360i
\(427\) −5.66863 3.27278i −0.274324 0.158381i
\(428\) 49.1931 2.37784
\(429\) −0.0480126 0.309813i −0.00231807 0.0149579i
\(430\) −26.7374 −1.28939
\(431\) 1.71575 + 0.990590i 0.0826449 + 0.0477150i 0.540753 0.841181i \(-0.318139\pi\)
−0.458108 + 0.888897i \(0.651473\pi\)
\(432\) −4.72668 + 8.18685i −0.227413 + 0.393890i
\(433\) −2.94544 5.10165i −0.141549 0.245170i 0.786531 0.617550i \(-0.211875\pi\)
−0.928080 + 0.372381i \(0.878542\pi\)
\(434\) 5.22357i 0.250740i
\(435\) 7.79039 4.49778i 0.373521 0.215652i
\(436\) 56.3686 32.5444i 2.69957 1.55860i
\(437\) 27.5311i 1.31699i
\(438\) −18.9742 32.8643i −0.906622 1.57031i
\(439\) −4.03281 + 6.98504i −0.192476 + 0.333378i −0.946070 0.323962i \(-0.894985\pi\)
0.753594 + 0.657340i \(0.228318\pi\)
\(440\) −0.828266 0.478200i −0.0394860 0.0227973i
\(441\) −1.00000 −0.0476190
\(442\) 56.9418 + 22.0757i 2.70845 + 1.05004i
\(443\) 6.65984 0.316419 0.158209 0.987406i \(-0.449428\pi\)
0.158209 + 0.987406i \(0.449428\pi\)
\(444\) −39.5937 22.8594i −1.87903 1.08486i
\(445\) 11.9259 20.6562i 0.565340 0.979198i
\(446\) 22.0482 + 38.1886i 1.04401 + 1.80828i
\(447\) 9.51027i 0.449821i
\(448\) 6.30381 3.63950i 0.297827 0.171950i
\(449\) −17.1899 + 9.92456i −0.811239 + 0.468369i −0.847386 0.530977i \(-0.821825\pi\)
0.0361468 + 0.999346i \(0.488492\pi\)
\(450\) 7.13069i 0.336144i
\(451\) 0.279942 + 0.484873i 0.0131819 + 0.0228318i
\(452\) 32.1415 55.6708i 1.51181 2.61853i
\(453\) −11.0652 6.38848i −0.519887 0.300157i
\(454\) −30.3655 −1.42512
\(455\) −5.36333 + 0.831171i −0.251437 + 0.0389659i
\(456\) 38.6703 1.81090
\(457\) 2.24200 + 1.29442i 0.104876 + 0.0605505i 0.551521 0.834161i \(-0.314048\pi\)
−0.446644 + 0.894712i \(0.647381\pi\)
\(458\) 10.3121 17.8611i 0.481854 0.834595i
\(459\) 3.24732 + 5.62452i 0.151572 + 0.262530i
\(460\) 37.6014i 1.75318i
\(461\) 22.8342 13.1834i 1.06350 0.614010i 0.137099 0.990557i \(-0.456222\pi\)
0.926397 + 0.376547i \(0.122889\pi\)
\(462\) −0.196391 + 0.113387i −0.00913696 + 0.00527522i
\(463\) 29.3082i 1.36207i −0.732252 0.681034i \(-0.761531\pi\)
0.732252 0.681034i \(-0.238469\pi\)
\(464\) 28.2467 + 48.9248i 1.31132 + 2.27128i
\(465\) −1.50745 + 2.61098i −0.0699064 + 0.121081i
\(466\) −54.3996 31.4076i −2.52001 1.45493i
\(467\) −3.23005 −0.149469 −0.0747345 0.997203i \(-0.523811\pi\)
−0.0747345 + 0.997203i \(0.523811\pi\)
\(468\) 10.8506 + 13.4909i 0.501567 + 0.623618i
\(469\) 8.29459 0.383009
\(470\) −6.22345 3.59311i −0.287066 0.165738i
\(471\) 1.28733 2.22972i 0.0593171 0.102740i
\(472\) 9.77348 + 16.9282i 0.449861 + 0.779182i
\(473\) 0.592207i 0.0272297i
\(474\) −26.3759 + 15.2282i −1.21149 + 0.699452i
\(475\) 12.5311 7.23481i 0.574965 0.331956i
\(476\) 31.1857i 1.42939i
\(477\) 1.64238 + 2.84469i 0.0751995 + 0.130249i
\(478\) −14.2599 + 24.6988i −0.652230 + 1.12970i
\(479\) 6.85282 + 3.95648i 0.313114 + 0.180776i 0.648319 0.761369i \(-0.275472\pi\)
−0.335205 + 0.942145i \(0.608806\pi\)
\(480\) 15.1137 0.689843
\(481\) −26.7508 + 21.5152i −1.21973 + 0.981011i
\(482\) −51.9135 −2.36460
\(483\) 4.50524 + 2.60110i 0.204996 + 0.118354i
\(484\) 26.3915 45.7114i 1.19961 2.07779i
\(485\) 4.41784 + 7.65192i 0.200604 + 0.347456i
\(486\) 2.60802i 0.118302i
\(487\) −13.3758 + 7.72253i −0.606116 + 0.349941i −0.771444 0.636297i \(-0.780465\pi\)
0.165328 + 0.986239i \(0.447132\pi\)
\(488\) 41.4209 23.9144i 1.87503 1.08255i
\(489\) 19.5300i 0.883176i
\(490\) 1.96290 + 3.39983i 0.0886746 + 0.153589i
\(491\) −7.45311 + 12.9092i −0.336354 + 0.582582i −0.983744 0.179577i \(-0.942527\pi\)
0.647390 + 0.762159i \(0.275861\pi\)
\(492\) −26.7761 15.4592i −1.20716 0.696953i
\(493\) 38.8121 1.74801
\(494\) 17.9886 46.3994i 0.809344 2.08761i
\(495\) −0.130887 −0.00588295
\(496\) −16.3974 9.46702i −0.736263 0.425082i
\(497\) 6.45892 11.1872i 0.289722 0.501814i
\(498\) 1.68622 + 2.92062i 0.0755613 + 0.130876i
\(499\) 25.4306i 1.13843i 0.822189 + 0.569214i \(0.192752\pi\)
−0.822189 + 0.569214i \(0.807248\pi\)
\(500\) 48.4127 27.9511i 2.16508 1.25001i
\(501\) 1.20942 0.698261i 0.0540331 0.0311960i
\(502\) 60.9972i 2.72244i
\(503\) −14.3956 24.9339i −0.641867 1.11175i −0.985016 0.172465i \(-0.944827\pi\)
0.343149 0.939281i \(-0.388507\pi\)
\(504\) 3.65352 6.32808i 0.162741 0.281875i
\(505\) 8.71034 + 5.02892i 0.387605 + 0.223784i
\(506\) 1.17972 0.0524450
\(507\) 12.3902 3.93479i 0.550269 0.174750i
\(508\) 62.1573 2.75778
\(509\) −13.5662 7.83245i −0.601311 0.347167i 0.168246 0.985745i \(-0.446190\pi\)
−0.769557 + 0.638578i \(0.779523\pi\)
\(510\) 12.7483 22.0807i 0.564504 0.977750i
\(511\) 7.27533 + 12.6012i 0.321842 + 0.557446i
\(512\) 43.2359i 1.91077i
\(513\) 4.58318 2.64610i 0.202352 0.116828i
\(514\) −27.2377 + 15.7257i −1.20140 + 0.693631i
\(515\) 6.80796i 0.299994i
\(516\) −16.3517 28.3220i −0.719843 1.24680i
\(517\) −0.0795838 + 0.137843i −0.00350009 + 0.00606233i
\(518\) 21.5048 + 12.4158i 0.944868 + 0.545520i
\(519\) −17.1814 −0.754179
\(520\) 14.3353 36.9763i 0.628645 1.62152i
\(521\) 4.38082 0.191927 0.0959636 0.995385i \(-0.469407\pi\)
0.0959636 + 0.995385i \(0.469407\pi\)
\(522\) 13.4975 + 7.79278i 0.590769 + 0.341081i
\(523\) 10.6603 18.4643i 0.466144 0.807386i −0.533108 0.846047i \(-0.678976\pi\)
0.999252 + 0.0386616i \(0.0123094\pi\)
\(524\) 14.0424 + 24.3222i 0.613447 + 1.06252i
\(525\) 2.73414i 0.119328i
\(526\) 10.2366 5.91011i 0.446337 0.257693i
\(527\) −11.2653 + 6.50402i −0.490724 + 0.283320i
\(528\) 0.821992i 0.0357726i
\(529\) −2.03147 3.51862i −0.0883250 0.152983i
\(530\) 6.44765 11.1676i 0.280068 0.485092i
\(531\) 2.31669 + 1.33754i 0.100536 + 0.0580444i
\(532\) −25.4119 −1.10174
\(533\) −18.0908 + 14.5502i −0.783599 + 0.630237i
\(534\) 41.3251 1.78831
\(535\) −13.3552 7.71064i −0.577397 0.333360i
\(536\) −30.3044 + 52.4888i −1.30895 + 2.26717i
\(537\) −0.718538 1.24454i −0.0310072 0.0537061i
\(538\) 72.9201i 3.14381i
\(539\) 0.0753030 0.0434762i 0.00324353 0.00187265i
\(540\) 6.25961 3.61399i 0.269371 0.155521i
\(541\) 18.7093i 0.804374i −0.915557 0.402187i \(-0.868250\pi\)
0.915557 0.402187i \(-0.131750\pi\)
\(542\) −5.46320 9.46253i −0.234664 0.406451i
\(543\) −2.15941 + 3.74021i −0.0926691 + 0.160508i
\(544\) 56.4729 + 32.6046i 2.42125 + 1.39791i
\(545\) −20.4044 −0.874027
\(546\) −5.89335 7.32743i −0.252212 0.313585i
\(547\) 26.4218 1.12972 0.564858 0.825188i \(-0.308931\pi\)
0.564858 + 0.825188i \(0.308931\pi\)
\(548\) −21.2534 12.2706i −0.907899 0.524176i
\(549\) 3.27278 5.66863i 0.139679 0.241931i
\(550\) −0.310015 0.536962i −0.0132191 0.0228961i
\(551\) 31.6263i 1.34733i
\(552\) −32.9200 + 19.0064i −1.40117 + 0.808964i
\(553\) 10.1134 5.83898i 0.430066 0.248299i
\(554\) 25.7360i 1.09342i
\(555\) 7.16607 + 12.4120i 0.304183 + 0.526860i
\(556\) −46.4030 + 80.3724i −1.96793 + 3.40855i
\(557\) 15.6452 + 9.03278i 0.662910 + 0.382731i 0.793385 0.608721i \(-0.208317\pi\)
−0.130475 + 0.991452i \(0.541650\pi\)
\(558\) −5.22357 −0.221131
\(559\) −24.2667 + 3.76068i −1.02637 + 0.159060i
\(560\) −14.2299 −0.601325
\(561\) −0.489066 0.282362i −0.0206484 0.0119213i
\(562\) 3.60554 6.24497i 0.152090 0.263428i
\(563\) −16.4758 28.5369i −0.694371 1.20269i −0.970392 0.241534i \(-0.922349\pi\)
0.276021 0.961151i \(-0.410984\pi\)
\(564\) 8.78969i 0.370113i
\(565\) −17.4519 + 10.0759i −0.734209 + 0.423895i
\(566\) 12.9662 7.48605i 0.545011 0.314662i
\(567\) 1.00000i 0.0419961i
\(568\) 47.1956 + 81.7451i 1.98028 + 3.42995i
\(569\) 3.33237 5.77184i 0.139700 0.241968i −0.787683 0.616081i \(-0.788719\pi\)
0.927383 + 0.374113i \(0.122053\pi\)
\(570\) −17.9926 10.3880i −0.753628 0.435107i
\(571\) 40.5063 1.69513 0.847567 0.530688i \(-0.178066\pi\)
0.847567 + 0.530688i \(0.178066\pi\)
\(572\) −1.40361 0.544166i −0.0586880 0.0227527i
\(573\) −6.78719 −0.283539
\(574\) 14.5431 + 8.39647i 0.607018 + 0.350462i
\(575\) −7.11178 + 12.3180i −0.296582 + 0.513695i
\(576\) 3.63950 + 6.30381i 0.151646 + 0.262659i
\(577\) 16.2052i 0.674632i −0.941391 0.337316i \(-0.890481\pi\)
0.941391 0.337316i \(-0.109519\pi\)
\(578\) 56.8726 32.8354i 2.36559 1.36577i
\(579\) 18.5112 10.6875i 0.769300 0.444156i
\(580\) 43.1945i 1.79356i
\(581\) −0.646552 1.11986i −0.0268235 0.0464597i
\(582\) −7.65427 + 13.2576i −0.317280 + 0.549545i
\(583\) −0.247352 0.142809i −0.0102443 0.00591454i
\(584\) −106.322 −4.39964
\(585\) −0.831171 5.36333i −0.0343647 0.221747i
\(586\) −41.2105 −1.70239
\(587\) 15.5385 + 8.97113i 0.641341 + 0.370278i 0.785131 0.619330i \(-0.212596\pi\)
−0.143790 + 0.989608i \(0.545929\pi\)
\(588\) −2.40088 + 4.15844i −0.0990106 + 0.171491i
\(589\) 5.29985 + 9.17961i 0.218377 + 0.378239i
\(590\) 10.5018i 0.432354i
\(591\) −19.7438 + 11.3991i −0.812153 + 0.468897i
\(592\) −77.9492 + 45.0040i −3.20369 + 1.84965i
\(593\) 34.1889i 1.40397i 0.712193 + 0.701984i \(0.247702\pi\)
−0.712193 + 0.701984i \(0.752298\pi\)
\(594\) −0.113387 0.196391i −0.00465231 0.00805804i
\(595\) −4.88812 + 8.46647i −0.200393 + 0.347091i
\(596\) −39.5479 22.8330i −1.61995 0.935277i
\(597\) −2.66365 −0.109016
\(598\) 7.49155 + 48.3411i 0.306352 + 1.97681i
\(599\) −9.68405 −0.395680 −0.197840 0.980234i \(-0.563393\pi\)
−0.197840 + 0.980234i \(0.563393\pi\)
\(600\) 17.3019 + 9.98923i 0.706345 + 0.407809i
\(601\) −6.44431 + 11.1619i −0.262869 + 0.455302i −0.967003 0.254765i \(-0.918002\pi\)
0.704134 + 0.710067i \(0.251335\pi\)
\(602\) 8.88123 + 15.3827i 0.361972 + 0.626954i
\(603\) 8.29459i 0.337782i
\(604\) −53.1323 + 30.6760i −2.16192 + 1.24819i
\(605\) −14.3298 + 8.27334i −0.582591 + 0.336359i
\(606\) 17.4260i 0.707884i
\(607\) −7.90895 13.6987i −0.321014 0.556013i 0.659683 0.751544i \(-0.270690\pi\)
−0.980698 + 0.195531i \(0.937357\pi\)
\(608\) 26.5681 46.0173i 1.07748 1.86625i
\(609\) −5.17538 2.98801i −0.209717 0.121080i
\(610\) −25.6965 −1.04042
\(611\) −6.15373 2.38574i −0.248953 0.0965166i
\(612\) 31.1857 1.26061
\(613\) −22.6303 13.0656i −0.914031 0.527716i −0.0323051 0.999478i \(-0.510285\pi\)
−0.881726 + 0.471762i \(0.843618\pi\)
\(614\) 13.1959 22.8559i 0.532543 0.922391i
\(615\) 4.84621 + 8.39389i 0.195418 + 0.338474i
\(616\) 0.635364i 0.0255995i
\(617\) 19.7693 11.4138i 0.795880 0.459502i −0.0461483 0.998935i \(-0.514695\pi\)
0.842029 + 0.539433i \(0.181361\pi\)
\(618\) 10.2151 5.89767i 0.410910 0.237239i
\(619\) 25.4700i 1.02373i 0.859067 + 0.511863i \(0.171044\pi\)
−0.859067 + 0.511863i \(0.828956\pi\)
\(620\) 7.23842 + 12.5373i 0.290702 + 0.503511i
\(621\) −2.60110 + 4.50524i −0.104379 + 0.180789i
\(622\) 32.7473 + 18.9066i 1.31305 + 0.758087i
\(623\) −15.8454 −0.634833
\(624\) 33.6825 5.21988i 1.34838 0.208962i
\(625\) −3.85378 −0.154151
\(626\) −29.9650 17.3003i −1.19764 0.691460i
\(627\) −0.230085 + 0.398519i −0.00918870 + 0.0159153i
\(628\) −6.18145 10.7066i −0.246667 0.427239i
\(629\) 61.8372i 2.46561i
\(630\) −3.39983 + 1.96290i −0.135453 + 0.0782036i
\(631\) 13.3886 7.72994i 0.532993 0.307724i −0.209241 0.977864i \(-0.567099\pi\)
0.742235 + 0.670140i \(0.233766\pi\)
\(632\) 85.3312i 3.39429i
\(633\) 12.0916 + 20.9432i 0.480597 + 0.832419i
\(634\) −39.6667 + 68.7047i −1.57537 + 2.72861i
\(635\) −16.8748 9.74267i −0.669656 0.386626i
\(636\) 15.7726 0.625426
\(637\) 2.25970 + 2.80958i 0.0895327 + 0.111320i
\(638\) −1.35520 −0.0536529
\(639\) 11.1872 + 6.45892i 0.442558 + 0.255511i
\(640\) −0.825768 + 1.43027i −0.0326414 + 0.0565365i
\(641\) −11.6918 20.2509i −0.461800 0.799861i 0.537251 0.843422i \(-0.319463\pi\)
−0.999051 + 0.0435617i \(0.986129\pi\)
\(642\) 26.7187i 1.05450i
\(643\) −1.05918 + 0.611515i −0.0417698 + 0.0241158i −0.520739 0.853716i \(-0.674344\pi\)
0.478970 + 0.877831i \(0.341010\pi\)
\(644\) 21.6331 12.4899i 0.852463 0.492170i
\(645\) 10.2520i 0.403673i
\(646\) −44.8200 77.6306i −1.76342 3.05433i
\(647\) 6.18090 10.7056i 0.242996 0.420882i −0.718570 0.695455i \(-0.755203\pi\)
0.961566 + 0.274573i \(0.0885363\pi\)
\(648\) 6.32808 + 3.65352i 0.248590 + 0.143524i
\(649\) −0.232605 −0.00913055
\(650\) 20.0342 16.1132i 0.785807 0.632013i
\(651\) 2.00289 0.0784994
\(652\) −81.2143 46.8891i −3.18060 1.83632i
\(653\) −4.93154 + 8.54168i −0.192986 + 0.334262i −0.946238 0.323470i \(-0.895151\pi\)
0.753252 + 0.657732i \(0.228484\pi\)
\(654\) −17.6761 30.6160i −0.691191 1.19718i
\(655\) 8.80417i 0.344008i
\(656\) −52.7149 + 30.4349i −2.05817 + 1.18828i
\(657\) −12.6012 + 7.27533i −0.491621 + 0.283838i
\(658\) 4.77401i 0.186110i
\(659\) −7.27455 12.5999i −0.283376 0.490822i 0.688838 0.724916i \(-0.258121\pi\)
−0.972214 + 0.234093i \(0.924788\pi\)
\(660\) −0.314245 + 0.544288i −0.0122320 + 0.0211864i
\(661\) 16.8095 + 9.70496i 0.653813 + 0.377479i 0.789916 0.613216i \(-0.210124\pi\)
−0.136102 + 0.990695i \(0.543458\pi\)
\(662\) −24.2622 −0.942979
\(663\) 8.46456 21.8334i 0.328736 0.847937i
\(664\) 9.44876 0.366683
\(665\) 6.89896 + 3.98312i 0.267530 + 0.154459i
\(666\) −12.4158 + 21.5048i −0.481103 + 0.833295i
\(667\) 15.5442 + 26.9234i 0.601875 + 1.04248i
\(668\) 6.70577i 0.259454i
\(669\) 14.6428 8.45400i 0.566122 0.326850i
\(670\) 28.2002 16.2814i 1.08947 0.629006i
\(671\) 0.569153i 0.0219719i
\(672\) −5.02024 8.69531i −0.193660 0.335429i
\(673\) 17.6889 30.6381i 0.681859 1.18101i −0.292554 0.956249i \(-0.594505\pi\)
0.974413 0.224765i \(-0.0721614\pi\)
\(674\) 30.0516 + 17.3503i 1.15755 + 0.668309i
\(675\) 2.73414 0.105237
\(676\) 13.3848 60.9710i 0.514799 2.34504i
\(677\) 10.9841 0.422154 0.211077 0.977469i \(-0.432303\pi\)
0.211077 + 0.977469i \(0.432303\pi\)
\(678\) −30.2369 17.4573i −1.16124 0.670444i
\(679\) 2.93490 5.08340i 0.112631 0.195083i
\(680\) −35.7176 61.8648i −1.36971 2.37241i
\(681\) 11.6431i 0.446166i
\(682\) 0.393350 0.227101i 0.0150622 0.00869615i
\(683\) 5.55922 3.20962i 0.212718 0.122813i −0.389856 0.920876i \(-0.627475\pi\)
0.602574 + 0.798063i \(0.294142\pi\)
\(684\) 25.4119i 0.971648i
\(685\) 3.84666 + 6.66260i 0.146973 + 0.254565i
\(686\) 1.30401 2.25861i 0.0497873 0.0862341i
\(687\) −6.84854 3.95401i −0.261288 0.150855i
\(688\) −64.3841 −2.45462
\(689\) 4.28108 11.0426i 0.163096 0.420688i
\(690\) 20.4228 0.777482
\(691\) −23.9076 13.8031i −0.909490 0.525094i −0.0292227 0.999573i \(-0.509303\pi\)
−0.880267 + 0.474479i \(0.842637\pi\)
\(692\) −41.2504 + 71.4479i −1.56811 + 2.71604i
\(693\) 0.0434762 + 0.0753030i 0.00165152 + 0.00286052i
\(694\) 44.0130i 1.67071i
\(695\) 25.1955 14.5466i 0.955721 0.551786i
\(696\) 37.8167 21.8335i 1.43344 0.827596i
\(697\) 41.8187i 1.58400i
\(698\) 3.13900 + 5.43691i 0.118813 + 0.205790i
\(699\) −12.0427 + 20.8586i −0.455497 + 0.788945i
\(700\) −11.3698 6.56434i −0.429737 0.248109i
\(701\) −15.9426 −0.602144 −0.301072 0.953601i \(-0.597344\pi\)
−0.301072 + 0.953601i \(0.597344\pi\)
\(702\) 7.32743 5.89335i 0.276556 0.222430i
\(703\) 50.3885 1.90044
\(704\) −0.548131 0.316463i −0.0206585 0.0119272i
\(705\) −1.37772 + 2.38627i −0.0518878 + 0.0898723i
\(706\) 40.0509 + 69.3702i 1.50733 + 2.61078i
\(707\) 6.68172i 0.251292i
\(708\) 11.1242 6.42256i 0.418073 0.241375i
\(709\) −10.8489 + 6.26364i −0.407440 + 0.235236i −0.689689 0.724105i \(-0.742253\pi\)
0.282249 + 0.959341i \(0.408920\pi\)
\(710\) 50.7128i 1.90322i
\(711\) 5.83898 + 10.1134i 0.218979 + 0.379282i
\(712\) 57.8915 100.271i 2.16957 3.75781i
\(713\) −9.02350 5.20972i −0.337933 0.195106i
\(714\) −16.9381 −0.633894
\(715\) 0.295767 + 0.367739i 0.0110611 + 0.0137526i
\(716\) −6.90049 −0.257883
\(717\) 9.47033 + 5.46770i 0.353676 + 0.204195i
\(718\) −13.8645 + 24.0139i −0.517417 + 0.896192i
\(719\) −21.2816 36.8608i −0.793670 1.37468i −0.923680 0.383164i \(-0.874834\pi\)
0.130010 0.991513i \(-0.458499\pi\)
\(720\) 14.2299i 0.530318i
\(721\) −3.91680 + 2.26136i −0.145869 + 0.0842175i
\(722\) −20.3442 + 11.7458i −0.757134 + 0.437132i
\(723\) 19.9054i 0.740288i
\(724\) 10.3690 + 17.9596i 0.385360 + 0.667462i
\(725\) 8.16964 14.1502i 0.303413 0.525526i
\(726\) −24.8276 14.3342i −0.921440 0.531994i
\(727\) 25.1186 0.931596 0.465798 0.884891i \(-0.345767\pi\)
0.465798 + 0.884891i \(0.345767\pi\)
\(728\) −26.0351 + 4.03473i −0.964925 + 0.149537i
\(729\) 1.00000 0.0370370
\(730\) 49.4698 + 28.5614i 1.83096 + 1.05711i
\(731\) −22.1166 + 38.3070i −0.818010 + 1.41684i
\(732\) −15.7151 27.2194i −0.580848 1.00606i
\(733\) 2.32992i 0.0860574i 0.999074 + 0.0430287i \(0.0137007\pi\)
−0.999074 + 0.0430287i \(0.986299\pi\)
\(734\) 59.1897 34.1732i 2.18473 1.26135i
\(735\) 1.30361 0.752639i 0.0480843 0.0277615i
\(736\) 52.2326i 1.92532i
\(737\) −0.360617 0.624607i −0.0132835 0.0230077i
\(738\) −8.39647 + 14.5431i −0.309078 + 0.535339i
\(739\) 23.2242 + 13.4085i 0.854315 + 0.493239i 0.862105 0.506731i \(-0.169146\pi\)
−0.00778923 + 0.999970i \(0.502479\pi\)
\(740\) 68.8195 2.52986
\(741\) −17.7911 6.89741i −0.653571 0.253383i
\(742\) −8.56672 −0.314494
\(743\) −43.1876 24.9344i −1.58440 0.914753i −0.994206 0.107490i \(-0.965719\pi\)
−0.590192 0.807263i \(-0.700948\pi\)
\(744\) −7.31759 + 12.6744i −0.268276 + 0.464668i
\(745\) 7.15780 + 12.3977i 0.262242 + 0.454216i
\(746\) 47.4925i 1.73882i
\(747\) 1.11986 0.646552i 0.0409736 0.0236561i
\(748\) −2.34837 + 1.35583i −0.0858651 + 0.0495742i
\(749\) 10.2448i 0.374337i
\(750\) −15.1813 26.2948i −0.554343 0.960150i
\(751\) 1.39391 2.41432i 0.0508645 0.0881000i −0.839472 0.543403i \(-0.817136\pi\)
0.890337 + 0.455303i \(0.150469\pi\)
\(752\) −14.9862 8.65226i −0.546489 0.315515i
\(753\) 23.3883 0.852318
\(754\) −8.60590 55.5317i −0.313408 2.02234i
\(755\) 19.2329 0.699956
\(756\) −4.15844 2.40088i −0.151241 0.0873191i
\(757\) −6.92483 + 11.9941i −0.251687 + 0.435935i −0.963990 0.265937i \(-0.914319\pi\)
0.712303 + 0.701872i \(0.247652\pi\)
\(758\) 37.6789 + 65.2618i 1.36856 + 2.37042i
\(759\) 0.452344i 0.0164191i
\(760\) −50.4110 + 29.1048i −1.82860 + 1.05574i
\(761\) −38.7289 + 22.3601i −1.40392 + 0.810555i −0.994792 0.101922i \(-0.967501\pi\)
−0.409130 + 0.912476i \(0.634168\pi\)
\(762\) 33.7600i 1.22299i
\(763\) 6.77761 + 11.7392i 0.245366 + 0.424986i
\(764\) −16.2952 + 28.2241i −0.589540 + 1.02111i
\(765\) −8.46647 4.88812i −0.306106 0.176730i
\(766\) 45.1871 1.63268
\(767\) −1.47711 9.53139i −0.0533352 0.344158i
\(768\) −17.4194 −0.628570
\(769\) −11.1497 6.43728i −0.402068 0.232134i 0.285308