Properties

Label 189.2.f.a.127.3
Level $189$
Weight $2$
Character 189.127
Analytic conductor $1.509$
Analytic rank $0$
Dimension $6$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [189,2,Mod(64,189)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(189, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([2, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("189.64");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 189 = 3^{3} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 189.f (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: \(1.50917259820\)
Analytic rank: \(0\)
Dimension: \(6\)
Relative dimension: \(3\) over \(\Q(\zeta_{3})\)
Coefficient field: 6.0.309123.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{6} - 3x^{5} + 10x^{4} - 15x^{3} + 19x^{2} - 12x + 3 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{4}]\)
Coefficient ring index: \( 3 \)
Twist minimal: no (minimal twist has level 63)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 127.3
Root \(0.500000 + 0.224437i\) of defining polynomial
Character \(\chi\) \(=\) 189.127
Dual form 189.2.f.a.64.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.849814 - 1.47192i) q^{2} +(-0.444368 - 0.769668i) q^{4} +(-1.79418 - 3.10761i) q^{5} +(0.500000 - 0.866025i) q^{7} +1.88874 q^{8} +O(q^{10})\) \(q+(0.849814 - 1.47192i) q^{2} +(-0.444368 - 0.769668i) q^{4} +(-1.79418 - 3.10761i) q^{5} +(0.500000 - 0.866025i) q^{7} +1.88874 q^{8} -6.09888 q^{10} +(-1.40545 + 2.43430i) q^{11} +(-0.500000 - 0.866025i) q^{13} +(-0.849814 - 1.47192i) q^{14} +(2.49381 - 4.31941i) q^{16} +4.11126 q^{17} -0.888736 q^{19} +(-1.59455 + 2.76185i) q^{20} +(2.38874 + 4.13741i) q^{22} +(2.93818 + 5.08907i) q^{23} +(-3.93818 + 6.82112i) q^{25} -1.69963 q^{26} -0.888736 q^{28} +(-0.849814 + 1.47192i) q^{29} +(3.49381 + 6.05146i) q^{31} +(-2.34981 - 4.07000i) q^{32} +(3.49381 - 6.05146i) q^{34} -3.58836 q^{35} +4.76509 q^{37} +(-0.755260 + 1.30815i) q^{38} +(-3.38874 - 5.86946i) q^{40} +(-2.70582 - 4.68661i) q^{41} +(-2.60507 + 4.51212i) q^{43} +2.49814 q^{44} +9.98762 q^{46} +(-1.33310 + 2.30900i) q^{47} +(-0.500000 - 0.866025i) q^{49} +(6.69344 + 11.5934i) q^{50} +(-0.444368 + 0.769668i) q^{52} +0.123644 q^{53} +10.0865 q^{55} +(0.944368 - 1.63569i) q^{56} +(1.44437 + 2.50172i) q^{58} +(-4.43818 - 7.68715i) q^{59} +(-1.93818 + 3.35702i) q^{61} +11.8764 q^{62} +1.98762 q^{64} +(-1.79418 + 3.10761i) q^{65} +(-6.15452 - 10.6599i) q^{67} +(-1.82691 - 3.16431i) q^{68} +(-3.04944 + 5.28179i) q^{70} +2.87636 q^{71} -10.6414 q^{73} +(4.04944 - 7.01384i) q^{74} +(0.394926 + 0.684031i) q^{76} +(1.40545 + 2.43430i) q^{77} +(3.54325 - 6.13709i) q^{79} -17.8974 q^{80} -9.19777 q^{82} +(-2.05563 + 3.56046i) q^{83} +(-7.37636 - 12.7762i) q^{85} +(4.42766 + 7.66893i) q^{86} +(-2.65452 + 4.59776i) q^{88} -9.60940 q^{89} -1.00000 q^{91} +(2.61126 - 4.52284i) q^{92} +(2.26578 + 3.92445i) q^{94} +(1.59455 + 2.76185i) q^{95} +(-3.66071 + 6.34053i) q^{97} -1.69963 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q - q^{2} - 3 q^{4} - 5 q^{5} + 3 q^{7} + 12 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 6 q - q^{2} - 3 q^{4} - 5 q^{5} + 3 q^{7} + 12 q^{8} - 2 q^{11} - 3 q^{13} + q^{14} - 3 q^{16} + 24 q^{17} - 6 q^{19} - 16 q^{20} + 15 q^{22} - 6 q^{25} + 2 q^{26} - 6 q^{28} + q^{29} + 3 q^{31} - 8 q^{32} + 3 q^{34} - 10 q^{35} - 6 q^{37} + 8 q^{38} - 21 q^{40} - 22 q^{41} + 3 q^{43} - 46 q^{44} + 24 q^{46} - 9 q^{47} - 3 q^{49} + 10 q^{50} - 3 q^{52} + 36 q^{53} - 12 q^{55} + 6 q^{56} + 9 q^{58} - 9 q^{59} + 6 q^{61} + 36 q^{62} - 24 q^{64} - 5 q^{65} + 6 q^{68} - 18 q^{71} + 6 q^{73} + 6 q^{74} + 21 q^{76} + 2 q^{77} - 15 q^{79} - 22 q^{80} + 18 q^{82} - 12 q^{83} - 9 q^{85} + 34 q^{86} + 21 q^{88} + 4 q^{89} - 6 q^{91} + 15 q^{92} - 24 q^{94} + 16 q^{95} - 3 q^{97} + 2 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/189\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(136\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.849814 1.47192i 0.600909 1.04081i −0.391774 0.920061i \(-0.628139\pi\)
0.992684 0.120744i \(-0.0385280\pi\)
\(3\) 0 0
\(4\) −0.444368 0.769668i −0.222184 0.384834i
\(5\) −1.79418 3.10761i −0.802383 1.38977i −0.918044 0.396479i \(-0.870232\pi\)
0.115661 0.993289i \(-0.463101\pi\)
\(6\) 0 0
\(7\) 0.500000 0.866025i 0.188982 0.327327i
\(8\) 1.88874 0.667769
\(9\) 0 0
\(10\) −6.09888 −1.92864
\(11\) −1.40545 + 2.43430i −0.423758 + 0.733970i −0.996304 0.0859026i \(-0.972623\pi\)
0.572546 + 0.819873i \(0.305956\pi\)
\(12\) 0 0
\(13\) −0.500000 0.866025i −0.138675 0.240192i 0.788320 0.615265i \(-0.210951\pi\)
−0.926995 + 0.375073i \(0.877618\pi\)
\(14\) −0.849814 1.47192i −0.227122 0.393387i
\(15\) 0 0
\(16\) 2.49381 4.31941i 0.623453 1.07985i
\(17\) 4.11126 0.997128 0.498564 0.866853i \(-0.333861\pi\)
0.498564 + 0.866853i \(0.333861\pi\)
\(18\) 0 0
\(19\) −0.888736 −0.203890 −0.101945 0.994790i \(-0.532507\pi\)
−0.101945 + 0.994790i \(0.532507\pi\)
\(20\) −1.59455 + 2.76185i −0.356553 + 0.617568i
\(21\) 0 0
\(22\) 2.38874 + 4.13741i 0.509280 + 0.882099i
\(23\) 2.93818 + 5.08907i 0.612652 + 1.06115i 0.990792 + 0.135396i \(0.0432308\pi\)
−0.378139 + 0.925749i \(0.623436\pi\)
\(24\) 0 0
\(25\) −3.93818 + 6.82112i −0.787636 + 1.36422i
\(26\) −1.69963 −0.333325
\(27\) 0 0
\(28\) −0.888736 −0.167955
\(29\) −0.849814 + 1.47192i −0.157807 + 0.273329i −0.934077 0.357071i \(-0.883776\pi\)
0.776271 + 0.630399i \(0.217109\pi\)
\(30\) 0 0
\(31\) 3.49381 + 6.05146i 0.627507 + 1.08687i 0.988050 + 0.154131i \(0.0492579\pi\)
−0.360544 + 0.932742i \(0.617409\pi\)
\(32\) −2.34981 4.07000i −0.415392 0.719481i
\(33\) 0 0
\(34\) 3.49381 6.05146i 0.599183 1.03782i
\(35\) −3.58836 −0.606544
\(36\) 0 0
\(37\) 4.76509 0.783376 0.391688 0.920098i \(-0.371891\pi\)
0.391688 + 0.920098i \(0.371891\pi\)
\(38\) −0.755260 + 1.30815i −0.122519 + 0.212210i
\(39\) 0 0
\(40\) −3.38874 5.86946i −0.535806 0.928044i
\(41\) −2.70582 4.68661i −0.422578 0.731926i 0.573613 0.819126i \(-0.305541\pi\)
−0.996191 + 0.0872002i \(0.972208\pi\)
\(42\) 0 0
\(43\) −2.60507 + 4.51212i −0.397270 + 0.688092i −0.993388 0.114805i \(-0.963376\pi\)
0.596118 + 0.802897i \(0.296709\pi\)
\(44\) 2.49814 0.376609
\(45\) 0 0
\(46\) 9.98762 1.47259
\(47\) −1.33310 + 2.30900i −0.194453 + 0.336803i −0.946721 0.322055i \(-0.895627\pi\)
0.752268 + 0.658857i \(0.228960\pi\)
\(48\) 0 0
\(49\) −0.500000 0.866025i −0.0714286 0.123718i
\(50\) 6.69344 + 11.5934i 0.946595 + 1.63955i
\(51\) 0 0
\(52\) −0.444368 + 0.769668i −0.0616227 + 0.106734i
\(53\) 0.123644 0.0169838 0.00849190 0.999964i \(-0.497297\pi\)
0.00849190 + 0.999964i \(0.497297\pi\)
\(54\) 0 0
\(55\) 10.0865 1.36006
\(56\) 0.944368 1.63569i 0.126196 0.218579i
\(57\) 0 0
\(58\) 1.44437 + 2.50172i 0.189655 + 0.328492i
\(59\) −4.43818 7.68715i −0.577802 1.00078i −0.995731 0.0923022i \(-0.970577\pi\)
0.417929 0.908479i \(-0.362756\pi\)
\(60\) 0 0
\(61\) −1.93818 + 3.35702i −0.248158 + 0.429823i −0.963015 0.269448i \(-0.913159\pi\)
0.714857 + 0.699271i \(0.246492\pi\)
\(62\) 11.8764 1.50830
\(63\) 0 0
\(64\) 1.98762 0.248453
\(65\) −1.79418 + 3.10761i −0.222541 + 0.385452i
\(66\) 0 0
\(67\) −6.15452 10.6599i −0.751894 1.30232i −0.946904 0.321517i \(-0.895807\pi\)
0.195010 0.980801i \(-0.437526\pi\)
\(68\) −1.82691 3.16431i −0.221546 0.383729i
\(69\) 0 0
\(70\) −3.04944 + 5.28179i −0.364478 + 0.631295i
\(71\) 2.87636 0.341361 0.170680 0.985326i \(-0.445403\pi\)
0.170680 + 0.985326i \(0.445403\pi\)
\(72\) 0 0
\(73\) −10.6414 −1.24549 −0.622744 0.782426i \(-0.713982\pi\)
−0.622744 + 0.782426i \(0.713982\pi\)
\(74\) 4.04944 7.01384i 0.470738 0.815342i
\(75\) 0 0
\(76\) 0.394926 + 0.684031i 0.0453011 + 0.0784638i
\(77\) 1.40545 + 2.43430i 0.160165 + 0.277415i
\(78\) 0 0
\(79\) 3.54325 6.13709i 0.398647 0.690477i −0.594912 0.803791i \(-0.702813\pi\)
0.993559 + 0.113314i \(0.0361465\pi\)
\(80\) −17.8974 −2.00099
\(81\) 0 0
\(82\) −9.19777 −1.01572
\(83\) −2.05563 + 3.56046i −0.225635 + 0.390811i −0.956510 0.291700i \(-0.905779\pi\)
0.730875 + 0.682512i \(0.239112\pi\)
\(84\) 0 0
\(85\) −7.37636 12.7762i −0.800078 1.38578i
\(86\) 4.42766 + 7.66893i 0.477447 + 0.826962i
\(87\) 0 0
\(88\) −2.65452 + 4.59776i −0.282972 + 0.490123i
\(89\) −9.60940 −1.01859 −0.509297 0.860591i \(-0.670095\pi\)
−0.509297 + 0.860591i \(0.670095\pi\)
\(90\) 0 0
\(91\) −1.00000 −0.104828
\(92\) 2.61126 4.52284i 0.272243 0.471539i
\(93\) 0 0
\(94\) 2.26578 + 3.92445i 0.233697 + 0.404776i
\(95\) 1.59455 + 2.76185i 0.163598 + 0.283360i
\(96\) 0 0
\(97\) −3.66071 + 6.34053i −0.371688 + 0.643783i −0.989825 0.142287i \(-0.954554\pi\)
0.618137 + 0.786070i \(0.287888\pi\)
\(98\) −1.69963 −0.171688
\(99\) 0 0
\(100\) 7.00000 0.700000
\(101\) 1.73236 3.00054i 0.172376 0.298564i −0.766874 0.641798i \(-0.778189\pi\)
0.939250 + 0.343233i \(0.111522\pi\)
\(102\) 0 0
\(103\) 7.93818 + 13.7493i 0.782172 + 1.35476i 0.930674 + 0.365849i \(0.119221\pi\)
−0.148502 + 0.988912i \(0.547445\pi\)
\(104\) −0.944368 1.63569i −0.0926029 0.160393i
\(105\) 0 0
\(106\) 0.105074 0.181994i 0.0102057 0.0176768i
\(107\) 5.35346 0.517538 0.258769 0.965939i \(-0.416683\pi\)
0.258769 + 0.965939i \(0.416683\pi\)
\(108\) 0 0
\(109\) −18.8640 −1.80684 −0.903421 0.428755i \(-0.858952\pi\)
−0.903421 + 0.428755i \(0.858952\pi\)
\(110\) 8.57165 14.8465i 0.817275 1.41556i
\(111\) 0 0
\(112\) −2.49381 4.31941i −0.235643 0.408145i
\(113\) −9.27561 16.0658i −0.872576 1.51135i −0.859322 0.511434i \(-0.829114\pi\)
−0.0132538 0.999912i \(-0.504219\pi\)
\(114\) 0 0
\(115\) 10.5433 18.2614i 0.983163 1.70289i
\(116\) 1.51052 0.140248
\(117\) 0 0
\(118\) −15.0865 −1.38883
\(119\) 2.05563 3.56046i 0.188439 0.326387i
\(120\) 0 0
\(121\) 1.54944 + 2.68371i 0.140858 + 0.243974i
\(122\) 3.29418 + 5.70569i 0.298241 + 0.516569i
\(123\) 0 0
\(124\) 3.10507 5.37815i 0.278844 0.482972i
\(125\) 10.3214 0.923175
\(126\) 0 0
\(127\) 9.98762 0.886258 0.443129 0.896458i \(-0.353868\pi\)
0.443129 + 0.896458i \(0.353868\pi\)
\(128\) 6.38874 11.0656i 0.564690 0.978071i
\(129\) 0 0
\(130\) 3.04944 + 5.28179i 0.267454 + 0.463244i
\(131\) 8.02654 + 13.9024i 0.701282 + 1.21466i 0.968017 + 0.250886i \(0.0807220\pi\)
−0.266734 + 0.963770i \(0.585945\pi\)
\(132\) 0 0
\(133\) −0.444368 + 0.769668i −0.0385316 + 0.0667387i
\(134\) −20.9208 −1.80728
\(135\) 0 0
\(136\) 7.76509 0.665851
\(137\) −6.49381 + 11.2476i −0.554804 + 0.960948i 0.443115 + 0.896465i \(0.353873\pi\)
−0.997919 + 0.0644834i \(0.979460\pi\)
\(138\) 0 0
\(139\) −0.555632 0.962383i −0.0471281 0.0816283i 0.841499 0.540259i \(-0.181674\pi\)
−0.888627 + 0.458630i \(0.848340\pi\)
\(140\) 1.59455 + 2.76185i 0.134764 + 0.233419i
\(141\) 0 0
\(142\) 2.44437 4.23377i 0.205127 0.355290i
\(143\) 2.81089 0.235059
\(144\) 0 0
\(145\) 6.09888 0.506485
\(146\) −9.04325 + 15.6634i −0.748425 + 1.29631i
\(147\) 0 0
\(148\) −2.11745 3.66754i −0.174054 0.301470i
\(149\) 4.21634 + 7.30291i 0.345416 + 0.598278i 0.985429 0.170086i \(-0.0544045\pi\)
−0.640013 + 0.768364i \(0.721071\pi\)
\(150\) 0 0
\(151\) 7.42580 12.8619i 0.604303 1.04668i −0.387858 0.921719i \(-0.626785\pi\)
0.992161 0.124964i \(-0.0398816\pi\)
\(152\) −1.67859 −0.136151
\(153\) 0 0
\(154\) 4.77747 0.384980
\(155\) 12.5371 21.7148i 1.00700 1.74418i
\(156\) 0 0
\(157\) −1.44437 2.50172i −0.115273 0.199659i 0.802616 0.596496i \(-0.203441\pi\)
−0.917889 + 0.396837i \(0.870108\pi\)
\(158\) −6.02221 10.4308i −0.479101 0.829828i
\(159\) 0 0
\(160\) −8.43199 + 14.6046i −0.666607 + 1.15460i
\(161\) 5.87636 0.463122
\(162\) 0 0
\(163\) −10.3090 −0.807466 −0.403733 0.914877i \(-0.632287\pi\)
−0.403733 + 0.914877i \(0.632287\pi\)
\(164\) −2.40476 + 4.16516i −0.187780 + 0.325245i
\(165\) 0 0
\(166\) 3.49381 + 6.05146i 0.271172 + 0.469684i
\(167\) 6.07598 + 10.5239i 0.470174 + 0.814365i 0.999418 0.0341045i \(-0.0108579\pi\)
−0.529244 + 0.848469i \(0.677525\pi\)
\(168\) 0 0
\(169\) 6.00000 10.3923i 0.461538 0.799408i
\(170\) −25.0741 −1.92310
\(171\) 0 0
\(172\) 4.63045 0.353068
\(173\) −3.30470 + 5.72391i −0.251252 + 0.435181i −0.963871 0.266370i \(-0.914176\pi\)
0.712619 + 0.701551i \(0.247509\pi\)
\(174\) 0 0
\(175\) 3.93818 + 6.82112i 0.297698 + 0.515629i
\(176\) 7.00983 + 12.1414i 0.528386 + 0.915191i
\(177\) 0 0
\(178\) −8.16621 + 14.1443i −0.612083 + 1.06016i
\(179\) 3.84294 0.287234 0.143617 0.989633i \(-0.454127\pi\)
0.143617 + 0.989633i \(0.454127\pi\)
\(180\) 0 0
\(181\) 18.5426 1.37826 0.689129 0.724639i \(-0.257993\pi\)
0.689129 + 0.724639i \(0.257993\pi\)
\(182\) −0.849814 + 1.47192i −0.0629924 + 0.109106i
\(183\) 0 0
\(184\) 5.54944 + 9.61192i 0.409110 + 0.708600i
\(185\) −8.54944 14.8081i −0.628567 1.08871i
\(186\) 0 0
\(187\) −5.77816 + 10.0081i −0.422541 + 0.731862i
\(188\) 2.36955 0.172818
\(189\) 0 0
\(190\) 5.42030 0.393230
\(191\) 2.31708 4.01330i 0.167658 0.290392i −0.769938 0.638119i \(-0.779713\pi\)
0.937596 + 0.347726i \(0.113046\pi\)
\(192\) 0 0
\(193\) 12.6483 + 21.9075i 0.910446 + 1.57694i 0.813435 + 0.581656i \(0.197595\pi\)
0.0970118 + 0.995283i \(0.469072\pi\)
\(194\) 6.22184 + 10.7765i 0.446702 + 0.773711i
\(195\) 0 0
\(196\) −0.444368 + 0.769668i −0.0317406 + 0.0549763i
\(197\) −10.7207 −0.763816 −0.381908 0.924200i \(-0.624733\pi\)
−0.381908 + 0.924200i \(0.624733\pi\)
\(198\) 0 0
\(199\) −8.76647 −0.621439 −0.310719 0.950502i \(-0.600570\pi\)
−0.310719 + 0.950502i \(0.600570\pi\)
\(200\) −7.43818 + 12.8833i −0.525959 + 0.910987i
\(201\) 0 0
\(202\) −2.94437 5.09979i −0.207165 0.358820i
\(203\) 0.849814 + 1.47192i 0.0596453 + 0.103309i
\(204\) 0 0
\(205\) −9.70946 + 16.8173i −0.678138 + 1.17457i
\(206\) 26.9839 1.88006
\(207\) 0 0
\(208\) −4.98762 −0.345829
\(209\) 1.24907 2.16345i 0.0864000 0.149649i
\(210\) 0 0
\(211\) −5.26509 9.11941i −0.362464 0.627806i 0.625902 0.779902i \(-0.284731\pi\)
−0.988366 + 0.152096i \(0.951398\pi\)
\(212\) −0.0549434 0.0951647i −0.00377353 0.00653594i
\(213\) 0 0
\(214\) 4.54944 7.87987i 0.310993 0.538656i
\(215\) 18.6959 1.27505
\(216\) 0 0
\(217\) 6.98762 0.474351
\(218\) −16.0309 + 27.7663i −1.08575 + 1.88057i
\(219\) 0 0
\(220\) −4.48212 7.76326i −0.302184 0.523399i
\(221\) −2.05563 3.56046i −0.138277 0.239502i
\(222\) 0 0
\(223\) 2.83379 4.90827i 0.189765 0.328682i −0.755407 0.655256i \(-0.772561\pi\)
0.945172 + 0.326574i \(0.105894\pi\)
\(224\) −4.69963 −0.314007
\(225\) 0 0
\(226\) −31.5302 −2.09736
\(227\) −5.54944 + 9.61192i −0.368329 + 0.637965i −0.989304 0.145865i \(-0.953403\pi\)
0.620975 + 0.783830i \(0.286737\pi\)
\(228\) 0 0
\(229\) −9.82141 17.0112i −0.649017 1.12413i −0.983358 0.181679i \(-0.941847\pi\)
0.334341 0.942452i \(-0.391486\pi\)
\(230\) −17.9196 31.0377i −1.18158 2.04656i
\(231\) 0 0
\(232\) −1.60507 + 2.78007i −0.105378 + 0.182521i
\(233\) −8.96286 −0.587177 −0.293588 0.955932i \(-0.594849\pi\)
−0.293588 + 0.955932i \(0.594849\pi\)
\(234\) 0 0
\(235\) 9.56732 0.624103
\(236\) −3.94437 + 6.83185i −0.256756 + 0.444715i
\(237\) 0 0
\(238\) −3.49381 6.05146i −0.226470 0.392258i
\(239\) 5.61126 + 9.71899i 0.362963 + 0.628670i 0.988447 0.151567i \(-0.0484320\pi\)
−0.625484 + 0.780237i \(0.715099\pi\)
\(240\) 0 0
\(241\) 3.49312 6.05026i 0.225012 0.389732i −0.731311 0.682044i \(-0.761091\pi\)
0.956323 + 0.292312i \(0.0944246\pi\)
\(242\) 5.26695 0.338572
\(243\) 0 0
\(244\) 3.44506 0.220547
\(245\) −1.79418 + 3.10761i −0.114626 + 0.198538i
\(246\) 0 0
\(247\) 0.444368 + 0.769668i 0.0282745 + 0.0489728i
\(248\) 6.59888 + 11.4296i 0.419030 + 0.725781i
\(249\) 0 0
\(250\) 8.77128 15.1923i 0.554745 0.960846i
\(251\) −4.62041 −0.291638 −0.145819 0.989311i \(-0.546582\pi\)
−0.145819 + 0.989311i \(0.546582\pi\)
\(252\) 0 0
\(253\) −16.5178 −1.03847
\(254\) 8.48762 14.7010i 0.532561 0.922422i
\(255\) 0 0
\(256\) −8.87085 15.3648i −0.554428 0.960298i
\(257\) −0.712008 1.23323i −0.0444138 0.0769270i 0.842964 0.537970i \(-0.180809\pi\)
−0.887378 + 0.461043i \(0.847475\pi\)
\(258\) 0 0
\(259\) 2.38255 4.12669i 0.148044 0.256420i
\(260\) 3.18911 0.197780
\(261\) 0 0
\(262\) 27.2843 1.68563
\(263\) 8.13162 14.0844i 0.501417 0.868480i −0.498582 0.866843i \(-0.666146\pi\)
0.999999 0.00163692i \(-0.000521048\pi\)
\(264\) 0 0
\(265\) −0.221840 0.384237i −0.0136275 0.0236035i
\(266\) 0.755260 + 1.30815i 0.0463080 + 0.0802078i
\(267\) 0 0
\(268\) −5.46974 + 9.47387i −0.334118 + 0.578709i
\(269\) 18.6538 1.13734 0.568672 0.822564i \(-0.307457\pi\)
0.568672 + 0.822564i \(0.307457\pi\)
\(270\) 0 0
\(271\) 3.96286 0.240727 0.120363 0.992730i \(-0.461594\pi\)
0.120363 + 0.992730i \(0.461594\pi\)
\(272\) 10.2527 17.7582i 0.621662 1.07675i
\(273\) 0 0
\(274\) 11.0371 + 19.1168i 0.666773 + 1.15489i
\(275\) −11.0698 19.1734i −0.667534 1.15620i
\(276\) 0 0
\(277\) 1.16690 2.02112i 0.0701120 0.121438i −0.828838 0.559488i \(-0.810998\pi\)
0.898950 + 0.438051i \(0.144331\pi\)
\(278\) −1.88874 −0.113279
\(279\) 0 0
\(280\) −6.77747 −0.405031
\(281\) 13.9975 24.2443i 0.835018 1.44629i −0.0589978 0.998258i \(-0.518790\pi\)
0.894016 0.448035i \(-0.147876\pi\)
\(282\) 0 0
\(283\) −5.16002 8.93741i −0.306731 0.531274i 0.670914 0.741535i \(-0.265902\pi\)
−0.977645 + 0.210261i \(0.932569\pi\)
\(284\) −1.27816 2.21384i −0.0758449 0.131367i
\(285\) 0 0
\(286\) 2.38874 4.13741i 0.141249 0.244650i
\(287\) −5.41164 −0.319439
\(288\) 0 0
\(289\) −0.0975070 −0.00573571
\(290\) 5.18292 8.97708i 0.304351 0.527152i
\(291\) 0 0
\(292\) 4.72872 + 8.19038i 0.276727 + 0.479306i
\(293\) −15.3480 26.5834i −0.896637 1.55302i −0.831765 0.555127i \(-0.812670\pi\)
−0.0648718 0.997894i \(-0.520664\pi\)
\(294\) 0 0
\(295\) −15.9258 + 27.5843i −0.927236 + 1.60602i
\(296\) 9.00000 0.523114
\(297\) 0 0
\(298\) 14.3324 0.830255
\(299\) 2.93818 5.08907i 0.169919 0.294309i
\(300\) 0 0
\(301\) 2.60507 + 4.51212i 0.150154 + 0.260074i
\(302\) −12.6211 21.8604i −0.726262 1.25792i
\(303\) 0 0
\(304\) −2.21634 + 3.83881i −0.127116 + 0.220171i
\(305\) 13.9098 0.796471
\(306\) 0 0
\(307\) −11.4437 −0.653125 −0.326563 0.945176i \(-0.605890\pi\)
−0.326563 + 0.945176i \(0.605890\pi\)
\(308\) 1.24907 2.16345i 0.0711724 0.123274i
\(309\) 0 0
\(310\) −21.3083 36.9071i −1.21023 2.09618i
\(311\) 5.98143 + 10.3601i 0.339176 + 0.587470i 0.984278 0.176627i \(-0.0565185\pi\)
−0.645102 + 0.764096i \(0.723185\pi\)
\(312\) 0 0
\(313\) 6.77197 11.7294i 0.382774 0.662985i −0.608683 0.793413i \(-0.708302\pi\)
0.991458 + 0.130429i \(0.0416353\pi\)
\(314\) −4.90978 −0.277075
\(315\) 0 0
\(316\) −6.29803 −0.354292
\(317\) −14.9814 + 25.9486i −0.841441 + 1.45742i 0.0472355 + 0.998884i \(0.484959\pi\)
−0.888676 + 0.458535i \(0.848374\pi\)
\(318\) 0 0
\(319\) −2.38874 4.13741i −0.133744 0.231651i
\(320\) −3.56615 6.17676i −0.199354 0.345291i
\(321\) 0 0
\(322\) 4.99381 8.64953i 0.278294 0.482020i
\(323\) −3.65383 −0.203304
\(324\) 0 0
\(325\) 7.87636 0.436902
\(326\) −8.76076 + 15.1741i −0.485214 + 0.840415i
\(327\) 0 0
\(328\) −5.11058 8.85178i −0.282184 0.488758i
\(329\) 1.33310 + 2.30900i 0.0734964 + 0.127299i
\(330\) 0 0
\(331\) −1.04325 + 1.80697i −0.0573423 + 0.0993198i −0.893272 0.449517i \(-0.851596\pi\)
0.835929 + 0.548837i \(0.184929\pi\)
\(332\) 3.65383 0.200530
\(333\) 0 0
\(334\) 20.6538 1.13013
\(335\) −22.0846 + 38.2517i −1.20661 + 2.08992i
\(336\) 0 0
\(337\) 8.10439 + 14.0372i 0.441474 + 0.764655i 0.997799 0.0663093i \(-0.0211224\pi\)
−0.556325 + 0.830965i \(0.687789\pi\)
\(338\) −10.1978 17.6631i −0.554686 0.960743i
\(339\) 0 0
\(340\) −6.55563 + 11.3547i −0.355529 + 0.615794i
\(341\) −19.6414 −1.06364
\(342\) 0 0
\(343\) −1.00000 −0.0539949
\(344\) −4.92030 + 8.52220i −0.265285 + 0.459486i
\(345\) 0 0
\(346\) 5.61677 + 9.72852i 0.301959 + 0.523009i
\(347\) 5.63348 + 9.75747i 0.302421 + 0.523808i 0.976684 0.214683i \(-0.0688719\pi\)
−0.674263 + 0.738491i \(0.735539\pi\)
\(348\) 0 0
\(349\) 0.0988844 0.171273i 0.00529316 0.00916803i −0.863367 0.504577i \(-0.831648\pi\)
0.868660 + 0.495409i \(0.164982\pi\)
\(350\) 13.3869 0.715559
\(351\) 0 0
\(352\) 13.2101 0.704103
\(353\) −6.25093 + 10.8269i −0.332703 + 0.576259i −0.983041 0.183386i \(-0.941294\pi\)
0.650338 + 0.759645i \(0.274627\pi\)
\(354\) 0 0
\(355\) −5.16071 8.93861i −0.273902 0.474412i
\(356\) 4.27011 + 7.39605i 0.226315 + 0.391990i
\(357\) 0 0
\(358\) 3.26578 5.65650i 0.172602 0.298955i
\(359\) −20.0197 −1.05660 −0.528299 0.849059i \(-0.677170\pi\)
−0.528299 + 0.849059i \(0.677170\pi\)
\(360\) 0 0
\(361\) −18.2101 −0.958429
\(362\) 15.7577 27.2932i 0.828208 1.43450i
\(363\) 0 0
\(364\) 0.444368 + 0.769668i 0.0232912 + 0.0403416i
\(365\) 19.0927 + 33.0695i 0.999357 + 1.73094i
\(366\) 0 0
\(367\) −15.0364 + 26.0438i −0.784892 + 1.35947i 0.144171 + 0.989553i \(0.453948\pi\)
−0.929063 + 0.369921i \(0.879385\pi\)
\(368\) 29.3090 1.52784
\(369\) 0 0
\(370\) −29.0617 −1.51085
\(371\) 0.0618219 0.107079i 0.00320963 0.00555925i
\(372\) 0 0
\(373\) −3.50619 6.07290i −0.181544 0.314443i 0.760863 0.648913i \(-0.224776\pi\)
−0.942406 + 0.334470i \(0.891443\pi\)
\(374\) 9.82072 + 17.0100i 0.507818 + 0.879566i
\(375\) 0 0
\(376\) −2.51788 + 4.36110i −0.129850 + 0.224906i
\(377\) 1.69963 0.0875353
\(378\) 0 0
\(379\) −19.0741 −0.979772 −0.489886 0.871787i \(-0.662962\pi\)
−0.489886 + 0.871787i \(0.662962\pi\)
\(380\) 1.41714 2.45455i 0.0726976 0.125916i
\(381\) 0 0
\(382\) −3.93818 6.82112i −0.201495 0.348999i
\(383\) 1.60507 + 2.78007i 0.0820155 + 0.142055i 0.904116 0.427288i \(-0.140531\pi\)
−0.822100 + 0.569343i \(0.807198\pi\)
\(384\) 0 0
\(385\) 5.04325 8.73517i 0.257028 0.445185i
\(386\) 42.9949 2.18838
\(387\) 0 0
\(388\) 6.50680 0.330333
\(389\) 2.56801 4.44793i 0.130203 0.225519i −0.793552 0.608503i \(-0.791770\pi\)
0.923755 + 0.382984i \(0.125104\pi\)
\(390\) 0 0
\(391\) 12.0796 + 20.9225i 0.610893 + 1.05810i
\(392\) −0.944368 1.63569i −0.0476978 0.0826150i
\(393\) 0 0
\(394\) −9.11058 + 15.7800i −0.458984 + 0.794984i
\(395\) −25.4290 −1.27947
\(396\) 0 0
\(397\) 22.9381 1.15123 0.575615 0.817721i \(-0.304763\pi\)
0.575615 + 0.817721i \(0.304763\pi\)
\(398\) −7.44987 + 12.9036i −0.373428 + 0.646797i
\(399\) 0 0
\(400\) 19.6421 + 34.0212i 0.982107 + 1.70106i
\(401\) −9.10507 15.7705i −0.454686 0.787539i 0.543984 0.839095i \(-0.316915\pi\)
−0.998670 + 0.0515566i \(0.983582\pi\)
\(402\) 0 0
\(403\) 3.49381 6.05146i 0.174039 0.301445i
\(404\) −3.07922 −0.153197
\(405\) 0 0
\(406\) 2.88874 0.143366
\(407\) −6.69708 + 11.5997i −0.331962 + 0.574975i
\(408\) 0 0
\(409\) 7.66621 + 13.2783i 0.379070 + 0.656568i 0.990927 0.134400i \(-0.0429108\pi\)
−0.611858 + 0.790968i \(0.709577\pi\)
\(410\) 16.5025 + 28.5831i 0.814999 + 1.41162i
\(411\) 0 0
\(412\) 7.05494 12.2195i 0.347572 0.602013i
\(413\) −8.87636 −0.436777
\(414\) 0 0
\(415\) 14.7527 0.724182
\(416\) −2.34981 + 4.07000i −0.115209 + 0.199548i
\(417\) 0 0
\(418\) −2.12296 3.67707i −0.103837 0.179851i
\(419\) 5.28435 + 9.15276i 0.258157 + 0.447142i 0.965748 0.259481i \(-0.0835513\pi\)
−0.707591 + 0.706622i \(0.750218\pi\)
\(420\) 0 0
\(421\) 18.0858 31.3256i 0.881449 1.52671i 0.0317181 0.999497i \(-0.489902\pi\)
0.849731 0.527217i \(-0.176765\pi\)
\(422\) −17.8974 −0.871232
\(423\) 0 0
\(424\) 0.233531 0.0113412
\(425\) −16.1909 + 28.0434i −0.785374 + 1.36031i
\(426\) 0 0
\(427\) 1.93818 + 3.35702i 0.0937950 + 0.162458i
\(428\) −2.37890 4.12038i −0.114989 0.199166i
\(429\) 0 0
\(430\) 15.8880 27.5189i 0.766190 1.32708i
\(431\) −35.0989 −1.69065 −0.845327 0.534249i \(-0.820594\pi\)
−0.845327 + 0.534249i \(0.820594\pi\)
\(432\) 0 0
\(433\) −41.1730 −1.97865 −0.989324 0.145731i \(-0.953447\pi\)
−0.989324 + 0.145731i \(0.953447\pi\)
\(434\) 5.93818 10.2852i 0.285042 0.493707i
\(435\) 0 0
\(436\) 8.38255 + 14.5190i 0.401451 + 0.695334i
\(437\) −2.61126 4.52284i −0.124914 0.216357i
\(438\) 0 0
\(439\) 2.33929 4.05178i 0.111648 0.193381i −0.804787 0.593564i \(-0.797720\pi\)
0.916435 + 0.400184i \(0.131054\pi\)
\(440\) 19.0507 0.908209
\(441\) 0 0
\(442\) −6.98762 −0.332367
\(443\) 15.0865 26.1306i 0.716781 1.24150i −0.245487 0.969400i \(-0.578948\pi\)
0.962268 0.272102i \(-0.0877188\pi\)
\(444\) 0 0
\(445\) 17.2410 + 29.8623i 0.817303 + 1.41561i
\(446\) −4.81639 8.34224i −0.228063 0.395016i
\(447\) 0 0
\(448\) 0.993810 1.72133i 0.0469531 0.0813252i
\(449\) −0.333792 −0.0157526 −0.00787632 0.999969i \(-0.502507\pi\)
−0.00787632 + 0.999969i \(0.502507\pi\)
\(450\) 0 0
\(451\) 15.2115 0.716283
\(452\) −8.24357 + 14.2783i −0.387745 + 0.671594i
\(453\) 0 0
\(454\) 9.43199 + 16.3367i 0.442665 + 0.766719i
\(455\) 1.79418 + 3.10761i 0.0841125 + 0.145687i
\(456\) 0 0
\(457\) 9.65452 16.7221i 0.451619 0.782227i −0.546868 0.837219i \(-0.684180\pi\)
0.998487 + 0.0549917i \(0.0175132\pi\)
\(458\) −33.3855 −1.56000
\(459\) 0 0
\(460\) −18.7403 −0.873773
\(461\) 19.5538 33.8681i 0.910710 1.57740i 0.0976463 0.995221i \(-0.468869\pi\)
0.813064 0.582175i \(-0.197798\pi\)
\(462\) 0 0
\(463\) −10.9382 18.9455i −0.508340 0.880471i −0.999953 0.00965741i \(-0.996926\pi\)
0.491613 0.870814i \(-0.336407\pi\)
\(464\) 4.23855 + 7.34138i 0.196770 + 0.340815i
\(465\) 0 0
\(466\) −7.61677 + 13.1926i −0.352840 + 0.611137i
\(467\) 12.3200 0.570103 0.285052 0.958512i \(-0.407989\pi\)
0.285052 + 0.958512i \(0.407989\pi\)
\(468\) 0 0
\(469\) −12.3090 −0.568378
\(470\) 8.13045 14.0823i 0.375029 0.649570i
\(471\) 0 0
\(472\) −8.38255 14.5190i −0.385838 0.668291i
\(473\) −7.32258 12.6831i −0.336693 0.583169i
\(474\) 0 0
\(475\) 3.50000 6.06218i 0.160591 0.278152i
\(476\) −3.65383 −0.167473
\(477\) 0 0
\(478\) 19.0741 0.872430
\(479\) 6.74474 11.6822i 0.308175 0.533775i −0.669788 0.742552i \(-0.733615\pi\)
0.977963 + 0.208777i \(0.0669484\pi\)
\(480\) 0 0
\(481\) −2.38255 4.12669i −0.108635 0.188161i
\(482\) −5.93701 10.2832i −0.270423 0.468387i
\(483\) 0 0
\(484\) 1.37704 2.38511i 0.0625929 0.108414i
\(485\) 26.2719 1.19295
\(486\) 0 0
\(487\) 7.54394 0.341849 0.170924 0.985284i \(-0.445325\pi\)
0.170924 + 0.985284i \(0.445325\pi\)
\(488\) −3.66071 + 6.34053i −0.165712 + 0.287022i
\(489\) 0 0
\(490\) 3.04944 + 5.28179i 0.137760 + 0.238607i
\(491\) −8.06979 13.9773i −0.364185 0.630786i 0.624460 0.781057i \(-0.285319\pi\)
−0.988645 + 0.150270i \(0.951986\pi\)
\(492\) 0 0
\(493\) −3.49381 + 6.05146i −0.157353 + 0.272544i
\(494\) 1.51052 0.0679615
\(495\) 0 0
\(496\) 34.8516 1.56488
\(497\) 1.43818 2.49100i 0.0645111 0.111737i
\(498\) 0 0
\(499\) 15.4327 + 26.7302i 0.690862 + 1.19661i 0.971556 + 0.236810i \(0.0761019\pi\)
−0.280694 + 0.959797i \(0.590565\pi\)
\(500\) −4.58650 7.94406i −0.205115 0.355269i
\(501\) 0 0
\(502\) −3.92649 + 6.80088i −0.175248 + 0.303538i
\(503\) −24.6304 −1.09822 −0.549109 0.835751i \(-0.685033\pi\)
−0.549109 + 0.835751i \(0.685033\pi\)
\(504\) 0 0
\(505\) −12.4327 −0.553247
\(506\) −14.0371 + 24.3129i −0.624024 + 1.08084i
\(507\) 0 0
\(508\) −4.43818 7.68715i −0.196912 0.341062i
\(509\) 6.79487 + 11.7691i 0.301177 + 0.521654i 0.976403 0.215957i \(-0.0692870\pi\)
−0.675226 + 0.737611i \(0.735954\pi\)
\(510\) 0 0
\(511\) −5.32072 + 9.21576i −0.235375 + 0.407681i
\(512\) −4.59937 −0.203265
\(513\) 0 0
\(514\) −2.42030 −0.106755
\(515\) 28.4851 49.3376i 1.25520 2.17407i
\(516\) 0 0
\(517\) −3.74721 6.49036i −0.164802 0.285446i
\(518\) −4.04944 7.01384i −0.177922 0.308170i
\(519\) 0 0
\(520\) −3.38874 + 5.86946i −0.148606 + 0.257393i
\(521\) 39.1730 1.71620 0.858100 0.513482i \(-0.171645\pi\)
0.858100 + 0.513482i \(0.171645\pi\)
\(522\) 0 0
\(523\) 19.1236 0.836219 0.418109 0.908397i \(-0.362693\pi\)
0.418109 + 0.908397i \(0.362693\pi\)
\(524\) 7.13348 12.3555i 0.311627 0.539754i
\(525\) 0 0
\(526\) −13.8207 23.9382i −0.602612 1.04375i
\(527\) 14.3640 + 24.8791i 0.625705 + 1.08375i
\(528\) 0 0
\(529\) −5.76578 + 9.98663i −0.250686 + 0.434201i
\(530\) −0.754090 −0.0327556
\(531\) 0 0
\(532\) 0.789851 0.0342444
\(533\) −2.70582 + 4.68661i −0.117202 + 0.203000i
\(534\) 0 0
\(535\) −9.60507 16.6365i −0.415264 0.719258i
\(536\) −11.6243 20.1338i −0.502091 0.869648i
\(537\) 0 0
\(538\) 15.8523 27.4570i 0.683441 1.18375i
\(539\) 2.81089 0.121074
\(540\) 0 0
\(541\) 2.53018 0.108781 0.0543906 0.998520i \(-0.482678\pi\)
0.0543906 + 0.998520i \(0.482678\pi\)
\(542\) 3.36769 5.83302i 0.144655 0.250550i
\(543\) 0 0
\(544\) −9.66071 16.7328i −0.414199 0.717414i
\(545\) 33.8454 + 58.6220i 1.44978 + 2.51109i
\(546\) 0 0
\(547\) −8.92580 + 15.4599i −0.381640 + 0.661019i −0.991297 0.131646i \(-0.957974\pi\)
0.609657 + 0.792665i \(0.291307\pi\)
\(548\) 11.5426 0.493074
\(549\) 0 0
\(550\) −37.6291 −1.60451
\(551\) 0.755260 1.30815i 0.0321752 0.0557290i
\(552\) 0 0
\(553\) −3.54325 6.13709i −0.150674 0.260976i
\(554\) −1.98329 3.43516i −0.0842619 0.145946i
\(555\) 0 0
\(556\) −0.493810 + 0.855304i −0.0209422 + 0.0362730i
\(557\) −41.3607 −1.75251 −0.876255 0.481847i \(-0.839966\pi\)
−0.876255 + 0.481847i \(0.839966\pi\)
\(558\) 0 0
\(559\) 5.21015 0.220366
\(560\) −8.94870 + 15.4996i −0.378152 + 0.654978i
\(561\) 0 0
\(562\) −23.7905 41.2063i −1.00354 1.73818i
\(563\) −10.3683 17.9584i −0.436972 0.756858i 0.560482 0.828166i \(-0.310616\pi\)
−0.997454 + 0.0713087i \(0.977282\pi\)
\(564\) 0 0
\(565\) −33.2843 + 57.6501i −1.40028 + 2.42536i
\(566\) −17.5402 −0.737271
\(567\) 0 0
\(568\) 5.43268 0.227950
\(569\) −0.134164 + 0.232379i −0.00562446 + 0.00974185i −0.868824 0.495121i \(-0.835124\pi\)
0.863199 + 0.504863i \(0.168457\pi\)
\(570\) 0 0
\(571\) −17.9684 31.1221i −0.751953 1.30242i −0.946875 0.321601i \(-0.895779\pi\)
0.194923 0.980819i \(-0.437554\pi\)
\(572\) −1.24907 2.16345i −0.0522263 0.0904585i
\(573\) 0 0
\(574\) −4.59888 + 7.96550i −0.191954 + 0.332474i
\(575\) −46.2843 −1.93019
\(576\) 0 0
\(577\) 5.43130 0.226108 0.113054 0.993589i \(-0.463937\pi\)
0.113054 + 0.993589i \(0.463937\pi\)
\(578\) −0.0828628 + 0.143523i −0.00344664 + 0.00596976i
\(579\) 0 0
\(580\) −2.71015 4.69412i −0.112533 0.194913i
\(581\) 2.05563 + 3.56046i 0.0852820 + 0.147713i
\(582\) 0 0
\(583\) −0.173775 + 0.300987i −0.00719702 + 0.0124656i
\(584\) −20.0989 −0.831698
\(585\) 0 0
\(586\) −52.1716 −2.15519
\(587\) 17.5822 30.4532i 0.725694 1.25694i −0.232994 0.972478i \(-0.574852\pi\)
0.958688 0.284461i \(-0.0918145\pi\)
\(588\) 0 0
\(589\) −3.10507 5.37815i −0.127942 0.221603i
\(590\) 27.0679 + 46.8830i 1.11437 + 1.93014i
\(591\) 0 0
\(592\) 11.8832 20.5824i 0.488398 0.845930i
\(593\) 33.5068 1.37596 0.687980 0.725730i \(-0.258498\pi\)
0.687980 + 0.725730i \(0.258498\pi\)
\(594\) 0 0
\(595\) −14.7527 −0.604802
\(596\) 3.74721 6.49036i 0.153492 0.265856i
\(597\) 0 0
\(598\) −4.99381 8.64953i −0.204212 0.353706i
\(599\) 3.12364 + 5.41031i 0.127629 + 0.221059i 0.922757 0.385381i \(-0.125930\pi\)
−0.795129 + 0.606441i \(0.792597\pi\)
\(600\) 0 0
\(601\) −11.2040 + 19.4058i −0.457019 + 0.791580i −0.998802 0.0489384i \(-0.984416\pi\)
0.541783 + 0.840519i \(0.317750\pi\)
\(602\) 8.85532 0.360916
\(603\) 0 0
\(604\) −13.1991 −0.537066
\(605\) 5.55996 9.63014i 0.226045 0.391521i
\(606\) 0 0
\(607\) −7.47524 12.9475i −0.303411 0.525523i 0.673496 0.739191i \(-0.264792\pi\)
−0.976906 + 0.213669i \(0.931459\pi\)
\(608\) 2.08836 + 3.61715i 0.0846943 + 0.146695i
\(609\) 0 0
\(610\) 11.8207 20.4741i 0.478607 0.828972i
\(611\) 2.66621 0.107863
\(612\) 0 0
\(613\) 35.1978 1.42162 0.710812 0.703382i \(-0.248328\pi\)
0.710812 + 0.703382i \(0.248328\pi\)
\(614\) −9.72500 + 16.8442i −0.392469 + 0.679776i
\(615\) 0 0
\(616\) 2.65452 + 4.59776i 0.106954 + 0.185249i
\(617\) −1.00619 1.74277i −0.0405077 0.0701614i 0.845061 0.534670i \(-0.179564\pi\)
−0.885568 + 0.464509i \(0.846231\pi\)
\(618\) 0 0
\(619\) −19.6909 + 34.1056i −0.791444 + 1.37082i 0.133629 + 0.991031i \(0.457337\pi\)
−0.925073 + 0.379789i \(0.875996\pi\)
\(620\) −22.2843 −0.894958
\(621\) 0 0
\(622\) 20.3324 0.815256
\(623\) −4.80470 + 8.32199i −0.192496 + 0.333413i
\(624\) 0 0
\(625\) 1.17240 + 2.03065i 0.0468959 + 0.0812261i
\(626\) −11.5098 19.9356i −0.460025 0.796787i
\(627\) 0 0
\(628\) −1.28366 + 2.22337i −0.0512237 + 0.0887220i
\(629\) 19.5906 0.781126
\(630\) 0 0
\(631\) 44.3832 1.76687 0.883433 0.468558i \(-0.155226\pi\)
0.883433 + 0.468558i \(0.155226\pi\)
\(632\) 6.69227 11.5913i 0.266204 0.461079i
\(633\) 0 0
\(634\) 25.4629 + 44.1030i 1.01126 + 1.75155i
\(635\) −17.9196 31.0377i −0.711118 1.23169i
\(636\) 0 0
\(637\) −0.500000 + 0.866025i −0.0198107 + 0.0343132i
\(638\) −8.11993 −0.321471
\(639\) 0 0
\(640\) −45.8502 −1.81239
\(641\) −7.49312 + 12.9785i −0.295961 + 0.512619i −0.975208 0.221291i \(-0.928973\pi\)
0.679247 + 0.733909i \(0.262306\pi\)
\(642\) 0 0
\(643\) 5.32691 + 9.22649i 0.210073 + 0.363857i 0.951737 0.306914i \(-0.0992965\pi\)
−0.741664 + 0.670771i \(0.765963\pi\)
\(644\) −2.61126 4.52284i −0.102898 0.178225i
\(645\) 0 0
\(646\) −3.10507 + 5.37815i −0.122168 + 0.211600i
\(647\) −2.12955 −0.0837213 −0.0418606 0.999123i \(-0.513329\pi\)
−0.0418606 + 0.999123i \(0.513329\pi\)
\(648\) 0 0
\(649\) 24.9505 0.979392
\(650\) 6.69344 11.5934i 0.262538 0.454730i
\(651\) 0 0
\(652\) 4.58100 + 7.93453i 0.179406 + 0.310740i
\(653\) 5.58582 + 9.67492i 0.218590 + 0.378609i 0.954377 0.298604i \(-0.0965210\pi\)
−0.735787 + 0.677213i \(0.763188\pi\)
\(654\) 0 0
\(655\) 28.8022 49.8868i 1.12539 1.94924i
\(656\) −26.9912 −1.05383
\(657\) 0 0
\(658\) 4.53156 0.176659
\(659\) −5.65452 + 9.79391i −0.220269 + 0.381517i −0.954890 0.296961i \(-0.904027\pi\)
0.734621 + 0.678478i \(0.237360\pi\)
\(660\) 0 0
\(661\) −16.1785 28.0220i −0.629271 1.08993i −0.987698 0.156372i \(-0.950020\pi\)
0.358427 0.933558i \(-0.383313\pi\)
\(662\) 1.77314 + 3.07117i 0.0689151 + 0.119364i
\(663\) 0 0
\(664\) −3.88255 + 6.72477i −0.150672 + 0.260972i
\(665\) 3.18911 0.123668
\(666\) 0 0
\(667\) −9.98762 −0.386722
\(668\) 5.39995 9.35298i 0.208930 0.361878i
\(669\) 0 0
\(670\) 37.5357 + 65.0137i 1.45013 + 2.51170i
\(671\) −5.44801 9.43623i −0.210318 0.364282i
\(672\) 0 0
\(673\) 12.0803 20.9237i 0.465662 0.806550i −0.533569 0.845756i \(-0.679150\pi\)
0.999231 + 0.0392063i \(0.0124830\pi\)
\(674\) 27.5489 1.06114
\(675\) 0 0
\(676\) −10.6648 −0.410186
\(677\) 12.5371 21.7148i 0.481838 0.834569i −0.517944 0.855414i \(-0.673303\pi\)
0.999783 + 0.0208457i \(0.00663587\pi\)
\(678\) 0 0
\(679\) 3.66071 + 6.34053i 0.140485 + 0.243327i
\(680\) −13.9320 24.1309i −0.534267 0.925378i
\(681\) 0 0
\(682\) −16.6916 + 28.9107i −0.639154 + 1.10705i
\(683\) 47.6784 1.82436 0.912182 0.409785i \(-0.134396\pi\)
0.912182 + 0.409785i \(0.134396\pi\)
\(684\) 0 0
\(685\) 46.6043 1.78066
\(686\) −0.849814 + 1.47192i −0.0324461 + 0.0561982i
\(687\) 0 0
\(688\) 12.9931 + 22.5047i 0.495358 + 0.857985i
\(689\) −0.0618219 0.107079i −0.00235523 0.00407937i
\(690\) 0 0
\(691\) 12.3400 21.3735i 0.469435 0.813085i −0.529954 0.848026i \(-0.677791\pi\)
0.999389 + 0.0349408i \(0.0111243\pi\)
\(692\) 5.87402 0.223297
\(693\) 0 0
\(694\) 19.1496 0.726910
\(695\) −1.99381 + 3.45338i −0.0756295 + 0.130994i
\(696\) 0 0
\(697\) −11.1243 19.2679i −0.421364 0.729824i
\(698\) −0.168067 0.291100i −0.00636142 0.0110183i
\(699\) 0 0
\(700\) 3.50000 6.06218i 0.132288 0.229129i
\(701\) 29.6784 1.12094 0.560469 0.828175i \(-0.310621\pi\)
0.560469 + 0.828175i \(0.310621\pi\)
\(702\) 0 0
\(703\) −4.23491 −0.159723
\(704\) −2.79349 + 4.83847i −0.105284 + 0.182357i
\(705\) 0 0
\(706\) 10.6243 + 18.4018i 0.399849 + 0.692559i
\(707\) −1.73236 3.00054i −0.0651521 0.112847i
\(708\) 0 0
\(709\) 14.6291 25.3383i 0.549406 0.951599i −0.448909 0.893577i \(-0.648187\pi\)
0.998315 0.0580220i \(-0.0184794\pi\)
\(710\) −17.5426 −0.658361
\(711\) 0 0
\(712\) −18.1496 −0.680186
\(713\) −20.5309 + 35.5605i −0.768887 + 1.33175i
\(714\) 0 0
\(715\) −5.04325 8.73517i −0.188607 0.326677i
\(716\) −1.70768 2.95778i −0.0638189 0.110538i
\(717\) 0 0
\(718\) −17.0130 + 29.4674i −0.634919 + 1.09971i
\(719\) −1.07413 −0.0400581 −0.0200291 0.999799i \(-0.506376\pi\)
−0.0200291 + 0.999799i \(0.506376\pi\)
\(720\) 0 0
\(721\) 15.8764 0.591266
\(722\) −15.4752 + 26.8039i −0.575929 + 0.997538i
\(723\) 0 0
\(724\) −8.23972 14.2716i −0.306227 0.530400i
\(725\) −6.69344 11.5934i −0.248588 0.430567i
\(726\) 0 0
\(727\) −12.7163 + 22.0253i −0.471623 + 0.816875i −0.999473 0.0324628i \(-0.989665\pi\)
0.527850 + 0.849338i \(0.322998\pi\)
\(728\) −1.88874 −0.0700012
\(729\) 0 0
\(730\) 64.9010 2.40209
\(731\) −10.7101 + 18.5505i −0.396129 + 0.686116i
\(732\) 0 0
\(733\) 5.69777 + 9.86883i 0.210452 + 0.364513i 0.951856 0.306545i \(-0.0991731\pi\)
−0.741404 + 0.671059i \(0.765840\pi\)
\(734\) 25.5562 + 44.2647i 0.943298 + 1.63384i
\(735\) 0 0
\(736\) 13.8083 23.9168i 0.508982 0.881583i
\(737\) 34.5994 1.27448
\(738\) 0 0
\(739\) −29.9395 −1.10134 −0.550671 0.834723i \(-0.685628\pi\)
−0.550671 + 0.834723i \(0.685628\pi\)
\(740\) −7.59820 + 13.1605i −0.279315 + 0.483788i
\(741\) 0 0
\(742\) −0.105074 0.181994i −0.00385740 0.00668121i
\(743\) −9.50069 16.4557i −0.348546 0.603700i 0.637445 0.770496i \(-0.279991\pi\)
−0.985991 + 0.166796i \(0.946658\pi\)
\(744\) 0 0
\(745\) 15.1298 26.2055i 0.554311 0.960096i
\(746\) −11.9184 −0.436365
\(747\) 0 0
\(748\) 10.2705 0.375527
\(749\) 2.67673 4.63623i 0.0978055 0.169404i
\(750\) 0 0
\(751\) −0.0130684 0.0226352i −0.000476873 0.000825969i 0.865787 0.500413i \(-0.166818\pi\)
−0.866264 + 0.499587i \(0.833485\pi\)
\(752\) 6.64902 + 11.5164i 0.242465 + 0.419961i
\(753\) 0 0
\(754\) 1.44437 2.50172i 0.0526008 0.0911072i
\(755\) −53.2929 −1.93953
\(756\) 0 0
\(757\) −13.6910 −0.497607 −0.248803 0.968554i \(-0.580037\pi\)
−0.248803 + 0.968554i \(0.580037\pi\)
\(758\) −16.2095 + 28.0756i −0.588754 + 1.01975i
\(759\) 0 0
\(760\) 3.01169 + 5.21640i 0.109246 + 0.189219i
\(761\) −7.32141 12.6811i −0.265401 0.459688i 0.702268 0.711913i \(-0.252171\pi\)
−0.967669 + 0.252225i \(0.918838\pi\)
\(762\) 0 0
\(763\) −9.43199 + 16.3367i −0.341461 + 0.591428i
\(764\) −4.11855 −0.149004
\(765\) 0 0
\(766\) 5.45606 0.197135
\(767\) −4.43818 + 7.68715i −0.160253 + 0.277567i
\(768\) 0 0
\(769\) −24.5672 42.5517i −0.885918 1.53445i −0.844658 0.535306i \(-0.820196\pi\)
−0.0412592 0.999148i \(-0.513137\pi\)
\(770\) −8.57165 14.8465i −0.308901 0.535032i
\(771\) 0 0
\(772\) 11.2410 19.4700i 0.404573 0.700741i
\(773\) −12.4413 −0.447484 −0.223742 0.974648i \(-0.571827\pi\)
−0.223742 + 0.974648i \(0.571827\pi\)
\(774\) 0 0
\(775\) −55.0370 −1.97699
\(776\) −6.91411 + 11.9756i −0.248202 + 0.429898i
\(777\) 0 0
\(778\) −4.36467 7.55982i −0.156481 0.271033i
\(779\) 2.40476 + 4.16516i 0.0861594 + 0.149232i
\(780\) 0 0
\(781\) −4.04256 + 7.00193i −0.144654 + 0.250549i
\(782\) 41.0617 1.46837
\(783\) 0 0