Properties

Label 729.2.e.a.568.1
Level $729$
Weight $2$
Character 729.568
Analytic conductor $5.821$
Analytic rank $1$
Dimension $6$
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] = [729,2,Mod(82,729)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(729, base_ring=CyclotomicField(18))
 
chi = DirichletCharacter(H, H._module([8]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("729.82");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 729 = 3^{6} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 729.e (of order \(9\), degree \(6\), 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: \(5.82109430735\)
Analytic rank: \(1\)
Dimension: \(6\)
Coefficient field: \(\Q(\zeta_{18})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{6} - x^{3} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{4}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 243)
Sato-Tate group: $\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label 568.1
Root \(-0.173648 - 0.984808i\) of defining polynomial
Character \(\chi\) \(=\) 729.568
Dual form 729.2.e.a.163.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.826352 - 0.300767i) q^{2} +(-0.939693 - 0.788496i) q^{4} +(-0.673648 + 3.82045i) q^{5} +(-1.67365 + 1.40436i) q^{7} +(1.41875 + 2.45734i) q^{8} +O(q^{10})\) \(q+(-0.826352 - 0.300767i) q^{2} +(-0.939693 - 0.788496i) q^{4} +(-0.673648 + 3.82045i) q^{5} +(-1.67365 + 1.40436i) q^{7} +(1.41875 + 2.45734i) q^{8} +(1.70574 - 2.95442i) q^{10} +(-0.0282185 - 0.160035i) q^{11} +(-2.26604 + 0.824773i) q^{13} +(1.80541 - 0.657115i) q^{14} +(-0.00727396 - 0.0412527i) q^{16} +(1.50000 - 2.59808i) q^{17} +(-1.79813 - 3.11446i) q^{19} +(3.64543 - 3.05888i) q^{20} +(-0.0248149 + 0.140732i) q^{22} +(-2.17365 - 1.82391i) q^{23} +(-9.44356 - 3.43718i) q^{25} +2.12061 q^{26} +2.68004 q^{28} +(6.31180 + 2.29731i) q^{29} +(-3.97178 - 3.33272i) q^{31} +(0.979055 - 5.55250i) q^{32} +(-2.02094 + 1.69577i) q^{34} +(-4.23783 - 7.34013i) q^{35} +(3.31908 - 5.74881i) q^{37} +(0.549163 + 3.11446i) q^{38} +(-10.3439 + 3.76487i) q^{40} +(-5.45084 + 1.98394i) q^{41} +(-1.08125 - 6.13208i) q^{43} +(-0.0996702 + 0.172634i) q^{44} +(1.24763 + 2.16095i) q^{46} +(-5.66637 + 4.75465i) q^{47} +(-0.386659 + 2.19285i) q^{49} +(6.76991 + 5.68063i) q^{50} +(2.77972 + 1.01173i) q^{52} -1.40373 q^{53} +0.630415 q^{55} +(-5.82547 - 2.12030i) q^{56} +(-4.52481 - 3.79677i) q^{58} +(0.889185 - 5.04282i) q^{59} +(-2.89646 + 2.43042i) q^{61} +(2.27972 + 3.94858i) q^{62} +(-2.52094 + 4.36640i) q^{64} +(-1.62449 - 9.21291i) q^{65} +(5.51114 - 2.00589i) q^{67} +(-3.45811 + 1.25865i) q^{68} +(1.29426 + 7.34013i) q^{70} +(-7.65910 + 13.2660i) q^{71} +(-4.34002 - 7.51714i) q^{73} +(-4.47178 + 3.75227i) q^{74} +(-0.766044 + 4.34445i) q^{76} +(0.271974 + 0.228213i) q^{77} +(1.19207 + 0.433877i) q^{79} +0.162504 q^{80} +5.10101 q^{82} +(-7.96451 - 2.89884i) q^{83} +(8.91534 + 7.48086i) q^{85} +(-0.950837 + 5.39246i) q^{86} +(0.353226 - 0.296392i) q^{88} +(3.86097 + 6.68739i) q^{89} +(2.63429 - 4.56272i) q^{91} +(0.604418 + 3.42782i) q^{92} +(6.11246 - 2.22475i) q^{94} +(13.1099 - 4.77163i) q^{95} +(-0.678396 - 3.84737i) q^{97} +(0.979055 - 1.69577i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q - 6 q^{2} - 3 q^{5} - 9 q^{7} + 6 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 6 q - 6 q^{2} - 3 q^{5} - 9 q^{7} + 6 q^{8} - 15 q^{11} - 9 q^{13} + 15 q^{14} - 18 q^{16} + 9 q^{17} + 3 q^{19} + 6 q^{20} + 27 q^{22} - 12 q^{23} - 27 q^{25} + 24 q^{26} - 24 q^{28} + 3 q^{29} - 9 q^{31} + 9 q^{32} - 9 q^{34} - 6 q^{35} + 3 q^{37} + 15 q^{38} - 18 q^{40} - 21 q^{41} - 9 q^{43} - 15 q^{44} - 9 q^{46} - 15 q^{47} - 9 q^{49} + 12 q^{50} - 9 q^{52} - 36 q^{53} + 18 q^{55} + 21 q^{56} - 3 q^{59} - 27 q^{61} - 12 q^{62} - 12 q^{64} + 3 q^{65} + 27 q^{67} - 27 q^{68} + 18 q^{70} - 9 q^{71} - 6 q^{73} - 12 q^{74} + 24 q^{77} + 18 q^{79} + 6 q^{80} + 36 q^{82} - 15 q^{83} + 9 q^{85} + 6 q^{86} + 27 q^{88} + 6 q^{91} + 51 q^{92} - 27 q^{94} + 30 q^{95} - 36 q^{97} + 9 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/729\mathbb{Z}\right)^\times\).

\(n\) \(2\)
\(\chi(n)\) \(e\left(\frac{1}{9}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.826352 0.300767i −0.584319 0.212675i 0.0329100 0.999458i \(-0.489523\pi\)
−0.617229 + 0.786784i \(0.711745\pi\)
\(3\) 0 0
\(4\) −0.939693 0.788496i −0.469846 0.394248i
\(5\) −0.673648 + 3.82045i −0.301265 + 1.70856i 0.339322 + 0.940670i \(0.389802\pi\)
−0.640586 + 0.767886i \(0.721309\pi\)
\(6\) 0 0
\(7\) −1.67365 + 1.40436i −0.632580 + 0.530797i −0.901729 0.432301i \(-0.857702\pi\)
0.269150 + 0.963098i \(0.413257\pi\)
\(8\) 1.41875 + 2.45734i 0.501603 + 0.868802i
\(9\) 0 0
\(10\) 1.70574 2.95442i 0.539401 0.934271i
\(11\) −0.0282185 0.160035i −0.00850820 0.0482524i 0.980258 0.197722i \(-0.0633544\pi\)
−0.988766 + 0.149470i \(0.952243\pi\)
\(12\) 0 0
\(13\) −2.26604 + 0.824773i −0.628488 + 0.228751i −0.636573 0.771217i \(-0.719649\pi\)
0.00808527 + 0.999967i \(0.497426\pi\)
\(14\) 1.80541 0.657115i 0.482515 0.175621i
\(15\) 0 0
\(16\) −0.00727396 0.0412527i −0.00181849 0.0103132i
\(17\) 1.50000 2.59808i 0.363803 0.630126i −0.624780 0.780801i \(-0.714811\pi\)
0.988583 + 0.150675i \(0.0481447\pi\)
\(18\) 0 0
\(19\) −1.79813 3.11446i −0.412520 0.714506i 0.582645 0.812727i \(-0.302018\pi\)
−0.995165 + 0.0982214i \(0.968685\pi\)
\(20\) 3.64543 3.05888i 0.815143 0.683986i
\(21\) 0 0
\(22\) −0.0248149 + 0.140732i −0.00529056 + 0.0300043i
\(23\) −2.17365 1.82391i −0.453237 0.380311i 0.387398 0.921912i \(-0.373374\pi\)
−0.840635 + 0.541601i \(0.817818\pi\)
\(24\) 0 0
\(25\) −9.44356 3.43718i −1.88871 0.687435i
\(26\) 2.12061 0.415887
\(27\) 0 0
\(28\) 2.68004 0.506481
\(29\) 6.31180 + 2.29731i 1.17207 + 0.426600i 0.853396 0.521264i \(-0.174539\pi\)
0.318677 + 0.947863i \(0.396761\pi\)
\(30\) 0 0
\(31\) −3.97178 3.33272i −0.713353 0.598574i 0.212185 0.977230i \(-0.431942\pi\)
−0.925538 + 0.378655i \(0.876387\pi\)
\(32\) 0.979055 5.55250i 0.173074 0.981553i
\(33\) 0 0
\(34\) −2.02094 + 1.69577i −0.346589 + 0.290823i
\(35\) −4.23783 7.34013i −0.716323 1.24071i
\(36\) 0 0
\(37\) 3.31908 5.74881i 0.545653 0.945099i −0.452912 0.891555i \(-0.649615\pi\)
0.998566 0.0535438i \(-0.0170517\pi\)
\(38\) 0.549163 + 3.11446i 0.0890860 + 0.505232i
\(39\) 0 0
\(40\) −10.3439 + 3.76487i −1.63551 + 0.595278i
\(41\) −5.45084 + 1.98394i −0.851278 + 0.309840i −0.730561 0.682847i \(-0.760741\pi\)
−0.120717 + 0.992687i \(0.538519\pi\)
\(42\) 0 0
\(43\) −1.08125 6.13208i −0.164889 0.935134i −0.949178 0.314739i \(-0.898083\pi\)
0.784289 0.620396i \(-0.213028\pi\)
\(44\) −0.0996702 + 0.172634i −0.0150259 + 0.0260255i
\(45\) 0 0
\(46\) 1.24763 + 2.16095i 0.183952 + 0.318615i
\(47\) −5.66637 + 4.75465i −0.826526 + 0.693537i −0.954490 0.298241i \(-0.903600\pi\)
0.127965 + 0.991779i \(0.459156\pi\)
\(48\) 0 0
\(49\) −0.386659 + 2.19285i −0.0552370 + 0.313265i
\(50\) 6.76991 + 5.68063i 0.957411 + 0.803363i
\(51\) 0 0
\(52\) 2.77972 + 1.01173i 0.385477 + 0.140302i
\(53\) −1.40373 −0.192818 −0.0964088 0.995342i \(-0.530736\pi\)
−0.0964088 + 0.995342i \(0.530736\pi\)
\(54\) 0 0
\(55\) 0.630415 0.0850051
\(56\) −5.82547 2.12030i −0.778462 0.283337i
\(57\) 0 0
\(58\) −4.52481 3.79677i −0.594137 0.498540i
\(59\) 0.889185 5.04282i 0.115762 0.656519i −0.870608 0.491977i \(-0.836274\pi\)
0.986370 0.164542i \(-0.0526146\pi\)
\(60\) 0 0
\(61\) −2.89646 + 2.43042i −0.370854 + 0.311183i −0.809099 0.587672i \(-0.800044\pi\)
0.438246 + 0.898855i \(0.355600\pi\)
\(62\) 2.27972 + 3.94858i 0.289524 + 0.501470i
\(63\) 0 0
\(64\) −2.52094 + 4.36640i −0.315118 + 0.545801i
\(65\) −1.62449 9.21291i −0.201493 1.14272i
\(66\) 0 0
\(67\) 5.51114 2.00589i 0.673293 0.245059i 0.0173282 0.999850i \(-0.494484\pi\)
0.655965 + 0.754791i \(0.272262\pi\)
\(68\) −3.45811 + 1.25865i −0.419358 + 0.152634i
\(69\) 0 0
\(70\) 1.29426 + 7.34013i 0.154694 + 0.877313i
\(71\) −7.65910 + 13.2660i −0.908968 + 1.57438i −0.0934675 + 0.995622i \(0.529795\pi\)
−0.815500 + 0.578756i \(0.803538\pi\)
\(72\) 0 0
\(73\) −4.34002 7.51714i −0.507961 0.879815i −0.999958 0.00921733i \(-0.997066\pi\)
0.491996 0.870597i \(-0.336267\pi\)
\(74\) −4.47178 + 3.75227i −0.519834 + 0.436193i
\(75\) 0 0
\(76\) −0.766044 + 4.34445i −0.0878713 + 0.498343i
\(77\) 0.271974 + 0.228213i 0.0309943 + 0.0260073i
\(78\) 0 0
\(79\) 1.19207 + 0.433877i 0.134118 + 0.0488149i 0.408207 0.912889i \(-0.366154\pi\)
−0.274089 + 0.961704i \(0.588376\pi\)
\(80\) 0.162504 0.0181685
\(81\) 0 0
\(82\) 5.10101 0.563313
\(83\) −7.96451 2.89884i −0.874218 0.318189i −0.134344 0.990935i \(-0.542893\pi\)
−0.739874 + 0.672745i \(0.765115\pi\)
\(84\) 0 0
\(85\) 8.91534 + 7.48086i 0.967005 + 0.811413i
\(86\) −0.950837 + 5.39246i −0.102531 + 0.581484i
\(87\) 0 0
\(88\) 0.353226 0.296392i 0.0376540 0.0315955i
\(89\) 3.86097 + 6.68739i 0.409262 + 0.708862i 0.994807 0.101778i \(-0.0324530\pi\)
−0.585546 + 0.810640i \(0.699120\pi\)
\(90\) 0 0
\(91\) 2.63429 4.56272i 0.276148 0.478303i
\(92\) 0.604418 + 3.42782i 0.0630149 + 0.357375i
\(93\) 0 0
\(94\) 6.11246 2.22475i 0.630452 0.229466i
\(95\) 13.1099 4.77163i 1.34505 0.489559i
\(96\) 0 0
\(97\) −0.678396 3.84737i −0.0688807 0.390642i −0.999684 0.0251223i \(-0.992002\pi\)
0.930804 0.365519i \(-0.119109\pi\)
\(98\) 0.979055 1.69577i 0.0988995 0.171299i
\(99\) 0 0
\(100\) 6.16385 + 10.6761i 0.616385 + 1.06761i
\(101\) 6.21554 5.21546i 0.618469 0.518957i −0.278853 0.960334i \(-0.589954\pi\)
0.897322 + 0.441377i \(0.145510\pi\)
\(102\) 0 0
\(103\) 3.23783 18.3626i 0.319032 1.80932i −0.229629 0.973278i \(-0.573751\pi\)
0.548661 0.836045i \(-0.315138\pi\)
\(104\) −5.24170 4.39831i −0.513991 0.431289i
\(105\) 0 0
\(106\) 1.15998 + 0.422197i 0.112667 + 0.0410074i
\(107\) −7.59627 −0.734359 −0.367179 0.930150i \(-0.619676\pi\)
−0.367179 + 0.930150i \(0.619676\pi\)
\(108\) 0 0
\(109\) −15.6382 −1.49786 −0.748932 0.662647i \(-0.769433\pi\)
−0.748932 + 0.662647i \(0.769433\pi\)
\(110\) −0.520945 0.189608i −0.0496701 0.0180784i
\(111\) 0 0
\(112\) 0.0701076 + 0.0588272i 0.00662454 + 0.00555865i
\(113\) 0.401674 2.27801i 0.0377863 0.214297i −0.960068 0.279766i \(-0.909743\pi\)
0.997855 + 0.0654689i \(0.0208543\pi\)
\(114\) 0 0
\(115\) 8.43242 7.07564i 0.786327 0.659807i
\(116\) −4.11974 7.13559i −0.382508 0.662523i
\(117\) 0 0
\(118\) −2.25150 + 3.89971i −0.207267 + 0.358997i
\(119\) 1.13816 + 6.45480i 0.104335 + 0.591711i
\(120\) 0 0
\(121\) 10.3118 3.75319i 0.937437 0.341199i
\(122\) 3.12449 1.13722i 0.282878 0.102959i
\(123\) 0 0
\(124\) 1.10442 + 6.26347i 0.0991797 + 0.562476i
\(125\) 9.79473 16.9650i 0.876067 1.51739i
\(126\) 0 0
\(127\) −0.0209445 0.0362770i −0.00185853 0.00321906i 0.865095 0.501609i \(-0.167258\pi\)
−0.866953 + 0.498390i \(0.833925\pi\)
\(128\) −5.24170 + 4.39831i −0.463305 + 0.388759i
\(129\) 0 0
\(130\) −1.42855 + 8.10170i −0.125292 + 0.710566i
\(131\) −14.0556 11.7940i −1.22804 1.03045i −0.998364 0.0571807i \(-0.981789\pi\)
−0.229676 0.973267i \(-0.573767\pi\)
\(132\) 0 0
\(133\) 7.38326 + 2.68729i 0.640209 + 0.233017i
\(134\) −5.15745 −0.445536
\(135\) 0 0
\(136\) 8.51249 0.729940
\(137\) 13.4500 + 4.89538i 1.14911 + 0.418241i 0.845195 0.534459i \(-0.179485\pi\)
0.303913 + 0.952700i \(0.401707\pi\)
\(138\) 0 0
\(139\) 8.03983 + 6.74622i 0.681929 + 0.572207i 0.916569 0.399876i \(-0.130947\pi\)
−0.234640 + 0.972082i \(0.575391\pi\)
\(140\) −1.80541 + 10.2390i −0.152585 + 0.865351i
\(141\) 0 0
\(142\) 10.3191 8.65873i 0.865958 0.726625i
\(143\) 0.195937 + 0.339373i 0.0163851 + 0.0283798i
\(144\) 0 0
\(145\) −13.0287 + 22.5663i −1.08197 + 1.87403i
\(146\) 1.32547 + 7.51714i 0.109697 + 0.622123i
\(147\) 0 0
\(148\) −7.65183 + 2.78504i −0.628976 + 0.228929i
\(149\) −1.19459 + 0.434796i −0.0978648 + 0.0356199i −0.390489 0.920608i \(-0.627694\pi\)
0.292624 + 0.956228i \(0.405472\pi\)
\(150\) 0 0
\(151\) 1.36437 + 7.73773i 0.111031 + 0.629688i 0.988639 + 0.150309i \(0.0480268\pi\)
−0.877608 + 0.479379i \(0.840862\pi\)
\(152\) 5.10220 8.83726i 0.413843 0.716797i
\(153\) 0 0
\(154\) −0.156107 0.270386i −0.0125795 0.0217883i
\(155\) 15.4081 12.9289i 1.23761 1.03847i
\(156\) 0 0
\(157\) −2.14496 + 12.1647i −0.171187 + 0.970848i 0.771267 + 0.636512i \(0.219623\pi\)
−0.942454 + 0.334336i \(0.891488\pi\)
\(158\) −0.854570 0.717070i −0.0679860 0.0570470i
\(159\) 0 0
\(160\) 20.5535 + 7.48086i 1.62490 + 0.591414i
\(161\) 6.19934 0.488576
\(162\) 0 0
\(163\) −13.7469 −1.07674 −0.538371 0.842708i \(-0.680960\pi\)
−0.538371 + 0.842708i \(0.680960\pi\)
\(164\) 6.68644 + 2.43367i 0.522123 + 0.190037i
\(165\) 0 0
\(166\) 5.70961 + 4.79093i 0.443151 + 0.371848i
\(167\) 0.645430 3.66041i 0.0499448 0.283251i −0.949598 0.313469i \(-0.898509\pi\)
0.999543 + 0.0302175i \(0.00961999\pi\)
\(168\) 0 0
\(169\) −5.50387 + 4.61830i −0.423375 + 0.355254i
\(170\) −5.11721 8.86327i −0.392472 0.679782i
\(171\) 0 0
\(172\) −3.81908 + 6.61484i −0.291202 + 0.504377i
\(173\) 0.270792 + 1.53574i 0.0205879 + 0.116760i 0.993370 0.114963i \(-0.0366749\pi\)
−0.972782 + 0.231723i \(0.925564\pi\)
\(174\) 0 0
\(175\) 20.6322 7.50952i 1.55965 0.567666i
\(176\) −0.00639661 + 0.00232818i −0.000482163 + 0.000175493i
\(177\) 0 0
\(178\) −1.17917 6.68739i −0.0883823 0.501241i
\(179\) −6.09627 + 10.5590i −0.455656 + 0.789220i −0.998726 0.0504679i \(-0.983929\pi\)
0.543069 + 0.839688i \(0.317262\pi\)
\(180\) 0 0
\(181\) 8.43629 + 14.6121i 0.627064 + 1.08611i 0.988138 + 0.153570i \(0.0490771\pi\)
−0.361073 + 0.932537i \(0.617590\pi\)
\(182\) −3.54916 + 2.97810i −0.263081 + 0.220752i
\(183\) 0 0
\(184\) 1.39811 7.92907i 0.103070 0.584538i
\(185\) 19.7271 + 16.5530i 1.45037 + 1.21700i
\(186\) 0 0
\(187\) −0.458111 0.166739i −0.0335004 0.0121931i
\(188\) 9.07367 0.661766
\(189\) 0 0
\(190\) −12.2686 −0.890056
\(191\) −16.4217 5.97702i −1.18824 0.432482i −0.329132 0.944284i \(-0.606756\pi\)
−0.859104 + 0.511802i \(0.828978\pi\)
\(192\) 0 0
\(193\) −1.52616 1.28060i −0.109855 0.0921796i 0.586205 0.810162i \(-0.300621\pi\)
−0.696061 + 0.717983i \(0.745066\pi\)
\(194\) −0.596571 + 3.38332i −0.0428313 + 0.242909i
\(195\) 0 0
\(196\) 2.09240 1.75573i 0.149457 0.125409i
\(197\) 10.5963 + 18.3533i 0.754953 + 1.30762i 0.945398 + 0.325919i \(0.105674\pi\)
−0.190445 + 0.981698i \(0.560993\pi\)
\(198\) 0 0
\(199\) 1.54189 2.67063i 0.109302 0.189316i −0.806186 0.591662i \(-0.798472\pi\)
0.915488 + 0.402346i \(0.131805\pi\)
\(200\) −4.95171 28.0826i −0.350139 1.98574i
\(201\) 0 0
\(202\) −6.70486 + 2.44037i −0.471752 + 0.171704i
\(203\) −13.7900 + 5.01914i −0.967867 + 0.352275i
\(204\) 0 0
\(205\) −3.90760 22.1611i −0.272919 1.54780i
\(206\) −8.19846 + 14.2002i −0.571214 + 0.989372i
\(207\) 0 0
\(208\) 0.0505072 + 0.0874810i 0.00350204 + 0.00606572i
\(209\) −0.447682 + 0.375650i −0.0309668 + 0.0259842i
\(210\) 0 0
\(211\) 0.174992 0.992431i 0.0120470 0.0683218i −0.978192 0.207705i \(-0.933401\pi\)
0.990239 + 0.139383i \(0.0445118\pi\)
\(212\) 1.31908 + 1.10684i 0.0905946 + 0.0760179i
\(213\) 0 0
\(214\) 6.27719 + 2.28471i 0.429100 + 0.156180i
\(215\) 24.1557 1.64740
\(216\) 0 0
\(217\) 11.3277 0.768974
\(218\) 12.9226 + 4.70345i 0.875230 + 0.318558i
\(219\) 0 0
\(220\) −0.592396 0.497079i −0.0399393 0.0335131i
\(221\) −1.25624 + 7.12452i −0.0845041 + 0.479247i
\(222\) 0 0
\(223\) 14.0064 11.7528i 0.937938 0.787023i −0.0392875 0.999228i \(-0.512509\pi\)
0.977225 + 0.212205i \(0.0680644\pi\)
\(224\) 6.15910 + 10.6679i 0.411522 + 0.712777i
\(225\) 0 0
\(226\) −1.01707 + 1.76162i −0.0676548 + 0.117181i
\(227\) 0.459293 + 2.60478i 0.0304843 + 0.172885i 0.996249 0.0865353i \(-0.0275795\pi\)
−0.965764 + 0.259421i \(0.916468\pi\)
\(228\) 0 0
\(229\) 3.25402 1.18437i 0.215032 0.0782652i −0.232258 0.972654i \(-0.574611\pi\)
0.447290 + 0.894389i \(0.352389\pi\)
\(230\) −9.09627 + 3.31077i −0.599790 + 0.218306i
\(231\) 0 0
\(232\) 3.30958 + 18.7696i 0.217285 + 1.23228i
\(233\) 3.06283 5.30498i 0.200653 0.347541i −0.748086 0.663602i \(-0.769027\pi\)
0.948739 + 0.316061i \(0.102360\pi\)
\(234\) 0 0
\(235\) −14.3478 24.8511i −0.935945 1.62110i
\(236\) −4.81180 + 4.03758i −0.313222 + 0.262824i
\(237\) 0 0
\(238\) 1.00088 5.67626i 0.0648772 0.367937i
\(239\) 22.1780 + 18.6095i 1.43457 + 1.20375i 0.942946 + 0.332946i \(0.108043\pi\)
0.491629 + 0.870805i \(0.336402\pi\)
\(240\) 0 0
\(241\) −20.9795 7.63592i −1.35141 0.491873i −0.438022 0.898964i \(-0.644321\pi\)
−0.913388 + 0.407091i \(0.866543\pi\)
\(242\) −9.65002 −0.620326
\(243\) 0 0
\(244\) 4.63816 0.296927
\(245\) −8.11721 2.95442i −0.518590 0.188751i
\(246\) 0 0
\(247\) 6.64337 + 5.57445i 0.422708 + 0.354694i
\(248\) 2.55468 14.4883i 0.162222 0.920009i
\(249\) 0 0
\(250\) −13.1964 + 11.0731i −0.834614 + 0.700324i
\(251\) −11.3610 19.6778i −0.717098 1.24205i −0.962145 0.272539i \(-0.912137\pi\)
0.245047 0.969511i \(-0.421197\pi\)
\(252\) 0 0
\(253\) −0.230552 + 0.399328i −0.0144947 + 0.0251055i
\(254\) 0.00639661 + 0.0362770i 0.000401359 + 0.00227622i
\(255\) 0 0
\(256\) 15.1300 5.50687i 0.945625 0.344179i
\(257\) −18.4081 + 6.69999i −1.14826 + 0.417934i −0.844891 0.534938i \(-0.820335\pi\)
−0.303373 + 0.952872i \(0.598113\pi\)
\(258\) 0 0
\(259\) 2.51842 + 14.2827i 0.156487 + 0.887481i
\(260\) −5.73783 + 9.93821i −0.355845 + 0.616341i
\(261\) 0 0
\(262\) 8.06758 + 13.9735i 0.498417 + 0.863283i
\(263\) −13.6361 + 11.4420i −0.840838 + 0.705547i −0.957752 0.287595i \(-0.907144\pi\)
0.116914 + 0.993142i \(0.462700\pi\)
\(264\) 0 0
\(265\) 0.945622 5.36289i 0.0580891 0.329440i
\(266\) −5.29292 4.44129i −0.324530 0.272313i
\(267\) 0 0
\(268\) −6.76042 2.46059i −0.412958 0.150305i
\(269\) −22.7888 −1.38946 −0.694729 0.719272i \(-0.744476\pi\)
−0.694729 + 0.719272i \(0.744476\pi\)
\(270\) 0 0
\(271\) −3.44562 −0.209307 −0.104653 0.994509i \(-0.533373\pi\)
−0.104653 + 0.994509i \(0.533373\pi\)
\(272\) −0.118089 0.0429807i −0.00716017 0.00260609i
\(273\) 0 0
\(274\) −9.64203 8.09062i −0.582496 0.488772i
\(275\) −0.283585 + 1.60829i −0.0171008 + 0.0969837i
\(276\) 0 0
\(277\) −2.00206 + 1.67993i −0.120292 + 0.100937i −0.700949 0.713211i \(-0.747240\pi\)
0.580657 + 0.814148i \(0.302796\pi\)
\(278\) −4.61468 7.99287i −0.276770 0.479380i
\(279\) 0 0
\(280\) 12.0248 20.8276i 0.718620 1.24469i
\(281\) 2.37639 + 13.4772i 0.141764 + 0.803982i 0.969909 + 0.243468i \(0.0782851\pi\)
−0.828145 + 0.560514i \(0.810604\pi\)
\(282\) 0 0
\(283\) −21.5005 + 7.82553i −1.27807 + 0.465179i −0.889793 0.456363i \(-0.849152\pi\)
−0.388277 + 0.921543i \(0.626929\pi\)
\(284\) 17.6573 6.42675i 1.04777 0.381357i
\(285\) 0 0
\(286\) −0.0598406 0.339373i −0.00353845 0.0200675i
\(287\) 6.33662 10.9753i 0.374039 0.647854i
\(288\) 0 0
\(289\) 4.00000 + 6.92820i 0.235294 + 0.407541i
\(290\) 17.5535 14.7291i 1.03078 0.864925i
\(291\) 0 0
\(292\) −1.84895 + 10.4859i −0.108201 + 0.613640i
\(293\) −18.6006 15.6078i −1.08666 0.911815i −0.0902023 0.995923i \(-0.528751\pi\)
−0.996457 + 0.0841084i \(0.973196\pi\)
\(294\) 0 0
\(295\) 18.6668 + 6.79417i 1.08683 + 0.395572i
\(296\) 18.8357 1.09481
\(297\) 0 0
\(298\) 1.11793 0.0647597
\(299\) 6.42989 + 2.34029i 0.371850 + 0.135342i
\(300\) 0 0
\(301\) 10.4213 + 8.74449i 0.600672 + 0.504024i
\(302\) 1.19981 6.80445i 0.0690412 0.391552i
\(303\) 0 0
\(304\) −0.115400 + 0.0968323i −0.00661865 + 0.00555371i
\(305\) −7.33409 12.7030i −0.419949 0.727373i
\(306\) 0 0
\(307\) 8.07444 13.9853i 0.460833 0.798186i −0.538170 0.842836i \(-0.680884\pi\)
0.999003 + 0.0446505i \(0.0142174\pi\)
\(308\) −0.0756268 0.428901i −0.00430924 0.0244389i
\(309\) 0 0
\(310\) −16.6211 + 6.04958i −0.944014 + 0.343593i
\(311\) 17.5817 6.39922i 0.996968 0.362867i 0.208553 0.978011i \(-0.433125\pi\)
0.788414 + 0.615144i \(0.210902\pi\)
\(312\) 0 0
\(313\) 0.481582 + 2.73119i 0.0272206 + 0.154376i 0.995388 0.0959261i \(-0.0305813\pi\)
−0.968168 + 0.250302i \(0.919470\pi\)
\(314\) 5.43124 9.40718i 0.306502 0.530878i
\(315\) 0 0
\(316\) −0.778066 1.34765i −0.0437696 0.0758112i
\(317\) −13.3923 + 11.2375i −0.752189 + 0.631161i −0.936081 0.351785i \(-0.885575\pi\)
0.183892 + 0.982946i \(0.441130\pi\)
\(318\) 0 0
\(319\) 0.189540 1.07494i 0.0106122 0.0601849i
\(320\) −14.9834 12.5726i −0.837597 0.702827i
\(321\) 0 0
\(322\) −5.12284 1.86456i −0.285485 0.103908i
\(323\) −10.7888 −0.600305
\(324\) 0 0
\(325\) 24.2344 1.34428
\(326\) 11.3598 + 4.13462i 0.629160 + 0.228996i
\(327\) 0 0
\(328\) −12.6086 10.5799i −0.696193 0.584175i
\(329\) 2.80628 15.9152i 0.154715 0.877435i
\(330\) 0 0
\(331\) −24.8653 + 20.8645i −1.36672 + 1.14681i −0.392878 + 0.919590i \(0.628521\pi\)
−0.973842 + 0.227224i \(0.927035\pi\)
\(332\) 5.19846 + 9.00400i 0.285303 + 0.494159i
\(333\) 0 0
\(334\) −1.63429 + 2.83067i −0.0894241 + 0.154887i
\(335\) 3.95084 + 22.4063i 0.215857 + 1.22419i
\(336\) 0 0
\(337\) −7.78611 + 2.83391i −0.424137 + 0.154373i −0.545265 0.838264i \(-0.683571\pi\)
0.121128 + 0.992637i \(0.461349\pi\)
\(338\) 5.93717 2.16095i 0.322939 0.117540i
\(339\) 0 0
\(340\) −2.47906 14.0594i −0.134446 0.762479i
\(341\) −0.421274 + 0.729669i −0.0228133 + 0.0395138i
\(342\) 0 0
\(343\) −10.0792 17.4577i −0.544225 0.942626i
\(344\) 13.5346 11.3569i 0.729738 0.612323i
\(345\) 0 0
\(346\) 0.238131 1.35051i 0.0128020 0.0726037i
\(347\) −11.4624 9.61814i −0.615336 0.516329i 0.280997 0.959709i \(-0.409335\pi\)
−0.896334 + 0.443380i \(0.853779\pi\)
\(348\) 0 0
\(349\) −31.6168 11.5076i −1.69241 0.615986i −0.697483 0.716601i \(-0.745697\pi\)
−0.994925 + 0.100615i \(0.967919\pi\)
\(350\) −19.3081 −1.03206
\(351\) 0 0
\(352\) −0.916222 −0.0488348
\(353\) −14.8037 5.38809i −0.787919 0.286779i −0.0834482 0.996512i \(-0.526593\pi\)
−0.704471 + 0.709733i \(0.748816\pi\)
\(354\) 0 0
\(355\) −45.5223 38.1978i −2.41608 2.02733i
\(356\) 1.64486 9.32845i 0.0871772 0.494407i
\(357\) 0 0
\(358\) 8.21348 6.89193i 0.434096 0.364250i
\(359\) 9.06283 + 15.6973i 0.478318 + 0.828471i 0.999691 0.0248577i \(-0.00791328\pi\)
−0.521373 + 0.853329i \(0.674580\pi\)
\(360\) 0 0
\(361\) 3.03343 5.25406i 0.159654 0.276529i
\(362\) −2.57650 14.6121i −0.135418 0.767994i
\(363\) 0 0
\(364\) −6.07310 + 2.21043i −0.318317 + 0.115858i
\(365\) 31.6425 11.5169i 1.65624 0.602823i
\(366\) 0 0
\(367\) −3.32413 18.8521i −0.173518 0.984071i −0.939840 0.341614i \(-0.889026\pi\)
0.766322 0.642457i \(-0.222085\pi\)
\(368\) −0.0594300 + 0.102936i −0.00309800 + 0.00536590i
\(369\) 0 0
\(370\) −11.3229 19.6119i −0.588652 1.01958i
\(371\) 2.34936 1.97134i 0.121972 0.102347i
\(372\) 0 0
\(373\) −2.64812 + 15.0182i −0.137114 + 0.777614i 0.836250 + 0.548349i \(0.184743\pi\)
−0.973364 + 0.229265i \(0.926368\pi\)
\(374\) 0.328411 + 0.275570i 0.0169817 + 0.0142494i
\(375\) 0 0
\(376\) −19.7230 7.17858i −1.01713 0.370207i
\(377\) −16.1976 −0.834218
\(378\) 0 0
\(379\) 9.84760 0.505837 0.252919 0.967488i \(-0.418610\pi\)
0.252919 + 0.967488i \(0.418610\pi\)
\(380\) −16.0817 5.85327i −0.824975 0.300266i
\(381\) 0 0
\(382\) 11.7724 + 9.87825i 0.602330 + 0.505415i
\(383\) −4.92989 + 27.9588i −0.251906 + 1.42863i 0.551986 + 0.833853i \(0.313870\pi\)
−0.803892 + 0.594775i \(0.797241\pi\)
\(384\) 0 0
\(385\) −1.05509 + 0.885328i −0.0537725 + 0.0451205i
\(386\) 0.875982 + 1.51724i 0.0445863 + 0.0772257i
\(387\) 0 0
\(388\) −2.39615 + 4.15026i −0.121646 + 0.210698i
\(389\) −1.89006 10.7191i −0.0958300 0.543479i −0.994490 0.104833i \(-0.966569\pi\)
0.898660 0.438646i \(-0.144542\pi\)
\(390\) 0 0
\(391\) −7.99912 + 2.91144i −0.404533 + 0.147238i
\(392\) −5.93717 + 2.16095i −0.299872 + 0.109145i
\(393\) 0 0
\(394\) −3.23618 18.3533i −0.163036 0.924624i
\(395\) −2.46064 + 4.26195i −0.123808 + 0.214442i
\(396\) 0 0
\(397\) 9.05350 + 15.6811i 0.454382 + 0.787013i 0.998652 0.0518969i \(-0.0165267\pi\)
−0.544270 + 0.838910i \(0.683193\pi\)
\(398\) −2.07738 + 1.74313i −0.104130 + 0.0873752i
\(399\) 0 0
\(400\) −0.0731006 + 0.414574i −0.00365503 + 0.0207287i
\(401\) −1.09833 0.921605i −0.0548478 0.0460228i 0.614952 0.788565i \(-0.289176\pi\)
−0.669799 + 0.742542i \(0.733620\pi\)
\(402\) 0 0
\(403\) 11.7490 + 4.27628i 0.585258 + 0.213016i
\(404\) −9.95306 −0.495183
\(405\) 0 0
\(406\) 12.9050 0.640463
\(407\) −1.01367 0.368946i −0.0502458 0.0182880i
\(408\) 0 0
\(409\) 6.59105 + 5.53055i 0.325907 + 0.273468i 0.791029 0.611778i \(-0.209545\pi\)
−0.465123 + 0.885246i \(0.653990\pi\)
\(410\) −3.43629 + 19.4882i −0.169706 + 0.962452i
\(411\) 0 0
\(412\) −17.5214 + 14.7022i −0.863218 + 0.724326i
\(413\) 5.59374 + 9.68864i 0.275250 + 0.476747i
\(414\) 0 0
\(415\) 16.4402 28.4752i 0.807016 1.39779i
\(416\) 2.36097 + 13.3897i 0.115756 + 0.656484i
\(417\) 0 0
\(418\) 0.482926 0.175771i 0.0236207 0.00859722i
\(419\) −11.5689 + 4.21074i −0.565179 + 0.205708i −0.608778 0.793341i \(-0.708340\pi\)
0.0435988 + 0.999049i \(0.486118\pi\)
\(420\) 0 0
\(421\) 1.93036 + 10.9476i 0.0940800 + 0.533554i 0.995025 + 0.0996216i \(0.0317632\pi\)
−0.900945 + 0.433932i \(0.857126\pi\)
\(422\) −0.443096 + 0.767465i −0.0215696 + 0.0373596i
\(423\) 0 0
\(424\) −1.99154 3.44946i −0.0967179 0.167520i
\(425\) −23.0954 + 19.3793i −1.12029 + 0.940036i
\(426\) 0 0
\(427\) 1.43448 8.13533i 0.0694193 0.393696i
\(428\) 7.13816 + 5.98962i 0.345036 + 0.289519i
\(429\) 0 0
\(430\) −19.9611 7.26525i −0.962610 0.350361i
\(431\) 36.8958 1.77721 0.888604 0.458675i \(-0.151676\pi\)
0.888604 + 0.458675i \(0.151676\pi\)
\(432\) 0 0
\(433\) −37.9982 −1.82608 −0.913040 0.407871i \(-0.866271\pi\)
−0.913040 + 0.407871i \(0.866271\pi\)
\(434\) −9.36066 3.40700i −0.449326 0.163541i
\(435\) 0 0
\(436\) 14.6951 + 12.3306i 0.703766 + 0.590530i
\(437\) −1.77197 + 10.0494i −0.0847650 + 0.480726i
\(438\) 0 0
\(439\) 0.154763 0.129862i 0.00738644 0.00619796i −0.639087 0.769135i \(-0.720688\pi\)
0.646473 + 0.762937i \(0.276243\pi\)
\(440\) 0.894400 + 1.54915i 0.0426388 + 0.0738526i
\(441\) 0 0
\(442\) 3.18092 5.50952i 0.151301 0.262061i
\(443\) −3.68644 20.9068i −0.175148 0.993314i −0.937973 0.346709i \(-0.887299\pi\)
0.762825 0.646605i \(-0.223812\pi\)
\(444\) 0 0
\(445\) −28.1498 + 10.2457i −1.33443 + 0.485692i
\(446\) −15.1091 + 5.49925i −0.715435 + 0.260397i
\(447\) 0 0
\(448\) −1.91282 10.8481i −0.0903722 0.512526i
\(449\) −16.6297 + 28.8035i −0.784804 + 1.35932i 0.144312 + 0.989532i \(0.453903\pi\)
−0.929116 + 0.369788i \(0.879430\pi\)
\(450\) 0 0
\(451\) 0.471315 + 0.816341i 0.0221933 + 0.0384400i
\(452\) −2.17365 + 1.82391i −0.102240 + 0.0857894i
\(453\) 0 0
\(454\) 0.403895 2.29061i 0.0189558 0.107503i
\(455\) 15.6570 + 13.1378i 0.734013 + 0.615910i
\(456\) 0 0
\(457\) 0.0320889 + 0.0116794i 0.00150105 + 0.000546339i 0.342771 0.939419i \(-0.388635\pi\)
−0.341270 + 0.939965i \(0.610857\pi\)
\(458\) −3.04519 −0.142292
\(459\) 0 0
\(460\) −13.5030 −0.629580
\(461\) −14.0826 5.12565i −0.655892 0.238725i −0.00743018 0.999972i \(-0.502365\pi\)
−0.648462 + 0.761247i \(0.724587\pi\)
\(462\) 0 0
\(463\) −23.3203 19.5680i −1.08378 0.909403i −0.0875549 0.996160i \(-0.527905\pi\)
−0.996230 + 0.0867566i \(0.972350\pi\)
\(464\) 0.0488583 0.277089i 0.00226819 0.0128635i
\(465\) 0 0
\(466\) −4.12654 + 3.46258i −0.191158 + 0.160401i
\(467\) −0.255367 0.442308i −0.0118170 0.0204676i 0.860056 0.510199i \(-0.170428\pi\)
−0.871873 + 0.489731i \(0.837095\pi\)
\(468\) 0 0
\(469\) −6.40673 + 11.0968i −0.295835 + 0.512401i
\(470\) 4.38191 + 24.8511i 0.202123 + 1.14629i
\(471\) 0 0
\(472\) 13.6535 4.96946i 0.628452 0.228738i
\(473\) −0.950837 + 0.346076i −0.0437195 + 0.0159126i
\(474\) 0 0
\(475\) 6.27584 + 35.5921i 0.287955 + 1.63308i
\(476\) 4.02007 6.96296i 0.184259 0.319147i
\(477\) 0 0
\(478\) −12.7297 22.0484i −0.582242 1.00847i
\(479\) 11.8359 9.93150i 0.540796 0.453782i −0.331014 0.943626i \(-0.607391\pi\)
0.871810 + 0.489844i \(0.162946\pi\)
\(480\) 0 0
\(481\) −2.77972 + 15.7645i −0.126744 + 0.718801i
\(482\) 15.0398 + 12.6199i 0.685045 + 0.574821i
\(483\) 0 0
\(484\) −12.6493 4.60397i −0.574968 0.209271i
\(485\) 15.1557 0.688185
\(486\) 0 0
\(487\) 29.5107 1.33726 0.668629 0.743596i \(-0.266881\pi\)
0.668629 + 0.743596i \(0.266881\pi\)
\(488\) −10.0817 3.66945i −0.456378 0.166108i
\(489\) 0 0
\(490\) 5.81908 + 4.88279i 0.262879 + 0.220582i
\(491\) −0.374638 + 2.12467i −0.0169072 + 0.0958852i −0.992094 0.125500i \(-0.959947\pi\)
0.975187 + 0.221385i \(0.0710577\pi\)
\(492\) 0 0
\(493\) 15.4363 12.9526i 0.695215 0.583355i
\(494\) −3.81315 6.60457i −0.171562 0.297153i
\(495\) 0 0
\(496\) −0.108593 + 0.188089i −0.00487597 + 0.00844543i
\(497\) −5.81150 32.9586i −0.260681 1.47840i
\(498\) 0 0
\(499\) −7.04323 + 2.56353i −0.315298 + 0.114759i −0.494822 0.868994i \(-0.664767\pi\)
0.179523 + 0.983754i \(0.442544\pi\)
\(500\) −22.5808 + 8.21875i −1.00985 + 0.367554i
\(501\) 0 0
\(502\) 3.46972 + 19.6778i 0.154861 + 0.878262i
\(503\) 14.2981 24.7651i 0.637522 1.10422i −0.348453 0.937326i \(-0.613293\pi\)
0.985975 0.166894i \(-0.0533739\pi\)
\(504\) 0 0
\(505\) 15.7383 + 27.2595i 0.700345 + 1.21303i
\(506\) 0.310622 0.260643i 0.0138088 0.0115870i
\(507\) 0 0
\(508\) −0.00892283 + 0.0506039i −0.000395887 + 0.00224518i
\(509\) 1.29607 + 1.08754i 0.0574475 + 0.0482041i 0.671059 0.741404i \(-0.265840\pi\)
−0.613612 + 0.789608i \(0.710284\pi\)
\(510\) 0 0
\(511\) 17.8204 + 6.48610i 0.788329 + 0.286928i
\(512\) −0.473897 −0.0209435
\(513\) 0 0
\(514\) 17.2267 0.759836
\(515\) 67.9723 + 24.7399i 2.99522 + 1.09017i
\(516\) 0 0
\(517\) 0.920807 + 0.772649i 0.0404971 + 0.0339811i
\(518\) 2.21466 12.5600i 0.0973066 0.551853i
\(519\) 0 0
\(520\) 20.3346 17.0627i 0.891729 0.748250i
\(521\) −11.2019 19.4022i −0.490763 0.850026i 0.509181 0.860660i \(-0.329948\pi\)
−0.999943 + 0.0106337i \(0.996615\pi\)
\(522\) 0 0
\(523\) −1.21436 + 2.10332i −0.0531000 + 0.0919720i −0.891354 0.453309i \(-0.850244\pi\)
0.838254 + 0.545281i \(0.183577\pi\)
\(524\) 3.90838 + 22.1655i 0.170738 + 0.968304i
\(525\) 0 0
\(526\) 14.7096 5.35386i 0.641369 0.233439i
\(527\) −14.6163 + 5.31991i −0.636698 + 0.231739i
\(528\) 0 0
\(529\) −2.59580 14.7215i −0.112861 0.640066i
\(530\) −2.39440 + 4.14722i −0.104006 + 0.180144i
\(531\) 0 0
\(532\) −4.81908 8.34689i −0.208934 0.361883i
\(533\) 10.7155 8.99140i 0.464141 0.389461i
\(534\) 0 0
\(535\) 5.11721 29.0211i 0.221236 1.25469i
\(536\) 12.7481 + 10.6969i 0.550634 + 0.462037i
\(537\) 0 0
\(538\) 18.8316 + 6.85413i 0.811886 + 0.295503i
\(539\) 0.361844 0.0155857
\(540\) 0 0
\(541\) 38.9394 1.67414 0.837069 0.547098i \(-0.184267\pi\)
0.837069 + 0.547098i \(0.184267\pi\)
\(542\) 2.84730 + 1.03633i 0.122302 + 0.0445142i
\(543\) 0 0
\(544\) −12.9572 10.8724i −0.555537 0.466151i
\(545\) 10.5346 59.7448i 0.451253 2.55918i
\(546\) 0 0
\(547\) −11.2396 + 9.43118i −0.480572 + 0.403248i −0.850633 0.525759i \(-0.823781\pi\)
0.370061 + 0.929007i \(0.379337\pi\)
\(548\) −8.77884 15.2054i −0.375013 0.649542i
\(549\) 0 0
\(550\) 0.718063 1.24372i 0.0306183 0.0530325i
\(551\) −4.19459 23.7887i −0.178696 1.01343i
\(552\) 0 0
\(553\) −2.60442 + 0.947931i −0.110751 + 0.0403101i
\(554\) 2.15967 0.786057i 0.0917557 0.0333963i
\(555\) 0 0
\(556\) −2.23560 12.6787i −0.0948107 0.537698i
\(557\) −5.55350 + 9.61894i −0.235309 + 0.407568i −0.959363 0.282176i \(-0.908944\pi\)
0.724053 + 0.689744i \(0.242277\pi\)
\(558\) 0 0
\(559\) 7.50774 + 13.0038i 0.317544 + 0.550002i
\(560\) −0.271974 + 0.228213i −0.0114930 + 0.00964378i
\(561\) 0 0
\(562\) 2.08976 11.8516i 0.0881514 0.499931i
\(563\) −12.4927 10.4826i −0.526506 0.441791i 0.340387 0.940285i \(-0.389442\pi\)
−0.866893 + 0.498495i \(0.833886\pi\)
\(564\) 0 0
\(565\) 8.43242 + 3.06915i 0.354755 + 0.129120i
\(566\) 20.1206 0.845733
\(567\) 0 0
\(568\) −43.4653 −1.82376
\(569\) 33.8444 + 12.3183i 1.41883 + 0.516412i 0.933708 0.358035i \(-0.116553\pi\)
0.485121 + 0.874447i \(0.338775\pi\)
\(570\) 0 0
\(571\) 29.9971 + 25.1705i 1.25534 + 1.05335i 0.996162 + 0.0875234i \(0.0278953\pi\)
0.259176 + 0.965830i \(0.416549\pi\)
\(572\) 0.0834734 0.473401i 0.00349020 0.0197939i
\(573\) 0 0
\(574\) −8.53730 + 7.16365i −0.356340 + 0.299005i
\(575\) 14.2579 + 24.6954i 0.594595 + 1.02987i
\(576\) 0 0
\(577\) −5.90286 + 10.2240i −0.245739 + 0.425633i −0.962339 0.271852i \(-0.912364\pi\)
0.716600 + 0.697484i \(0.245697\pi\)
\(578\) −1.22163 6.92820i −0.0508131 0.288175i
\(579\) 0 0
\(580\) 30.0364 10.9324i 1.24719 0.453942i
\(581\) 17.4008 6.33337i 0.721907 0.262753i
\(582\) 0 0
\(583\) 0.0396112 + 0.224647i 0.00164053 + 0.00930391i
\(584\) 12.3148 21.3299i 0.509590 0.882636i
\(585\) 0 0
\(586\) 10.6763 + 18.4920i 0.441035 + 0.763896i
\(587\) 30.6122 25.6867i 1.26350 1.06020i 0.268201 0.963363i \(-0.413571\pi\)
0.995300 0.0968406i \(-0.0308737\pi\)
\(588\) 0 0
\(589\) −3.23783 + 18.3626i −0.133412 + 0.756619i
\(590\) −13.3819 11.2288i −0.550925 0.462281i
\(591\) 0 0
\(592\) −0.261297 0.0951042i −0.0107392 0.00390876i
\(593\) 29.2995 1.20319 0.601594 0.798802i \(-0.294533\pi\)
0.601594 + 0.798802i \(0.294533\pi\)
\(594\) 0 0
\(595\) −25.4270 −1.04240
\(596\) 1.46538 + 0.533356i 0.0600245 + 0.0218471i
\(597\) 0 0
\(598\) −4.60947 3.86780i −0.188495 0.158166i
\(599\) −1.74897 + 9.91890i −0.0714610 + 0.405275i 0.928004 + 0.372570i \(0.121523\pi\)
−0.999465 + 0.0327053i \(0.989588\pi\)
\(600\) 0 0
\(601\) −23.3025 + 19.5531i −0.950528 + 0.797587i −0.979386 0.201996i \(-0.935257\pi\)
0.0288587 + 0.999584i \(0.490813\pi\)
\(602\) −5.98158 10.3604i −0.243791 0.422259i
\(603\) 0 0
\(604\) 4.81908 8.34689i 0.196085 0.339630i
\(605\) 7.39234 + 41.9240i 0.300541 + 1.70445i
\(606\) 0 0
\(607\) 21.6827 7.89187i 0.880075 0.320321i 0.137835 0.990455i \(-0.455986\pi\)
0.742240 + 0.670134i \(0.233763\pi\)
\(608\) −19.0535 + 6.93491i −0.772721 + 0.281248i
\(609\) 0 0
\(610\) 2.23989 + 12.7030i 0.0906903 + 0.514330i
\(611\) 8.91875 15.4477i 0.360814 0.624948i
\(612\) 0 0
\(613\) −0.382789 0.663010i −0.0154607 0.0267787i 0.858192 0.513330i \(-0.171588\pi\)
−0.873652 + 0.486551i \(0.838255\pi\)
\(614\) −10.8787 + 9.12829i −0.439027 + 0.368388i
\(615\) 0 0
\(616\) −0.174936 + 0.992112i −0.00704837 + 0.0399733i
\(617\) 7.11515 + 5.97032i 0.286445 + 0.240356i 0.774676 0.632359i \(-0.217913\pi\)
−0.488231 + 0.872715i \(0.662357\pi\)
\(618\) 0 0
\(619\) 32.9666 + 11.9989i 1.32504 + 0.482275i 0.905070 0.425263i \(-0.139818\pi\)
0.419970 + 0.907538i \(0.362040\pi\)
\(620\) −24.6732 −0.990901
\(621\) 0 0
\(622\) −16.4534 −0.659720
\(623\) −15.8534 5.77016i −0.635153 0.231177i
\(624\) 0 0
\(625\) 19.7233 + 16.5498i 0.788931 + 0.661992i
\(626\) 0.423496 2.40176i 0.0169263 0.0959938i
\(627\) 0 0
\(628\) 11.6074 9.73977i 0.463186 0.388659i
\(629\) −9.95723 17.2464i −0.397021 0.687660i
\(630\) 0 0
\(631\) −17.8810 + 30.9709i −0.711833 + 1.23293i 0.252336 + 0.967640i \(0.418801\pi\)
−0.964168 + 0.265291i \(0.914532\pi\)
\(632\) 0.625058 + 3.54488i 0.0248635 + 0.141008i
\(633\) 0 0
\(634\) 14.4467 5.25815i 0.573750 0.208828i
\(635\) 0.152704 0.0555796i 0.00605986 0.00220561i
\(636\) 0 0
\(637\) −0.932419 5.28801i −0.0369438 0.209519i
\(638\) −0.479933 + 0.831268i −0.0190007 + 0.0329102i
\(639\) 0 0
\(640\) −13.2724 22.9885i −0.524639 0.908702i
\(641\) −2.24170 + 1.88101i −0.0885417 + 0.0742953i −0.685984 0.727616i \(-0.740628\pi\)
0.597442 + 0.801912i \(0.296184\pi\)
\(642\) 0 0
\(643\) −3.51666 + 19.9440i −0.138684 + 0.786514i 0.833540 + 0.552459i \(0.186311\pi\)
−0.972223 + 0.234055i \(0.924801\pi\)
\(644\) −5.82547 4.88815i −0.229556 0.192620i
\(645\) 0 0
\(646\) 8.91534 + 3.24492i 0.350770 + 0.127670i
\(647\) −10.7219 −0.421523 −0.210761 0.977538i \(-0.567594\pi\)
−0.210761 + 0.977538i \(0.567594\pi\)
\(648\) 0 0
\(649\) −0.832119 −0.0326635
\(650\) −20.0262 7.28893i −0.785491 0.285895i
\(651\) 0 0
\(652\) 12.9179 + 10.8394i 0.505903 + 0.424503i
\(653\) −6.20393 + 35.1842i −0.242778 + 1.37686i 0.582818 + 0.812603i \(0.301950\pi\)
−0.825596 + 0.564262i \(0.809161\pi\)
\(654\) 0 0
\(655\) 54.5269 45.7535i 2.13054 1.78774i
\(656\) 0.121492 + 0.210430i 0.00474347 + 0.00821593i
\(657\) 0 0
\(658\) −7.10576 + 12.3075i −0.277011 + 0.479798i
\(659\) −5.35978 30.3969i −0.208788 1.18409i −0.891367 0.453282i \(-0.850253\pi\)
0.682580 0.730811i \(-0.260858\pi\)
\(660\) 0 0
\(661\) 9.25402 3.36819i 0.359940 0.131007i −0.155719 0.987801i \(-0.549769\pi\)
0.515659 + 0.856794i \(0.327547\pi\)
\(662\) 26.8228 9.76272i 1.04250 0.379439i
\(663\) 0 0
\(664\) −4.17617 23.6843i −0.162067 0.919128i
\(665\) −15.2404 + 26.3971i −0.590996 + 1.02363i
\(666\) 0 0
\(667\) −9.52956 16.5057i −0.368986 0.639103i
\(668\) −3.49273 + 2.93075i −0.135138 + 0.113394i
\(669\) 0 0
\(670\) 3.47431 19.7038i 0.134224 0.761223i
\(671\) 0.470686 + 0.394952i 0.0181706 + 0.0152470i
\(672\) 0 0
\(673\) 18.5094 + 6.73687i 0.713485 + 0.259687i 0.673157 0.739499i \(-0.264938\pi\)
0.0403273 + 0.999187i \(0.487160\pi\)
\(674\) 7.28642 0.280662
\(675\) 0 0
\(676\) 8.81345 0.338979
\(677\) −26.7408 9.73286i −1.02773 0.374064i −0.227516 0.973774i \(-0.573060\pi\)
−0.800217 + 0.599710i \(0.795283\pi\)
\(678\) 0 0
\(679\) 6.53849 + 5.48644i 0.250924 + 0.210550i
\(680\) −5.73442 + 32.5215i −0.219905 + 1.24714i
\(681\) 0 0
\(682\) 0.567581 0.476257i 0.0217338 0.0182368i
\(683\) 6.25537 + 10.8346i 0.239355 + 0.414575i 0.960529 0.278179i \(-0.0897307\pi\)
−0.721174 + 0.692754i \(0.756397\pi\)
\(684\) 0 0
\(685\) −27.7631 + 48.0871i −1.06077 + 1.83731i
\(686\) 3.07826 + 17.4577i 0.117528 + 0.666537i
\(687\) 0 0
\(688\) −0.245100 + 0.0892091i −0.00934435 + 0.00340106i
\(689\) 3.18092 1.15776i 0.121183 0.0441072i
\(690\) 0 0
\(691\) 7.40184 + 41.9779i 0.281579 + 1.59691i 0.717255 + 0.696811i \(0.245398\pi\)
−0.435676 + 0.900104i \(0.643491\pi\)
\(692\) 0.956462 1.65664i 0.0363592 0.0629760i
\(693\) 0 0
\(694\) 6.57919 + 11.3955i 0.249743 + 0.432567i
\(695\) −31.1896 + 26.1712i −1.18309 + 0.992729i
\(696\) 0 0
\(697\) −3.02182 + 17.1376i −0.114460 + 0.649133i
\(698\) 22.6655 + 19.0186i 0.857902 + 0.719865i
\(699\) 0 0
\(700\) −25.3092 9.21179i −0.956597 0.348173i
\(701\) −51.7701 −1.95533 −0.977665 0.210167i \(-0.932599\pi\)
−0.977665 + 0.210167i \(0.932599\pi\)
\(702\) 0 0
\(703\) −23.8726 −0.900371
\(704\) 0.769915 + 0.280226i 0.0290173 + 0.0105614i
\(705\) 0 0
\(706\) 10.6125 + 8.90491i 0.399405 + 0.335141i
\(707\) −3.07826 + 17.4577i −0.115770 + 0.656563i
\(708\) 0 0
\(709\) 11.6120 9.74362i 0.436098 0.365929i −0.398149 0.917321i \(-0.630347\pi\)
0.834247 + 0.551391i \(0.185903\pi\)
\(710\) 26.1288 + 45.2564i 0.980597 + 1.69844i
\(711\) 0 0
\(712\) −10.9555 + 18.9754i −0.410574 + 0.711135i
\(713\) 2.55468 + 14.4883i 0.0956736 + 0.542592i
\(714\) 0 0
\(715\) −1.42855 + 0.519949i −0.0534247 + 0.0194450i
\(716\) 14.0544 5.11538i 0.525237 0.191171i
\(717\) 0 0
\(718\) −2.76786 15.6973i −0.103295 0.585818i
\(719\) −1.30747 + 2.26460i −0.0487603 + 0.0844553i −0.889375 0.457178i \(-0.848860\pi\)
0.840615 + 0.541633i \(0.182194\pi\)
\(720\) 0 0
\(721\) 20.3687 + 35.2796i 0.758570 + 1.31388i
\(722\) −4.08693 + 3.42934i −0.152100 + 0.127627i
\(723\) 0 0
\(724\) 3.59405 20.3828i 0.133572 0.757522i
\(725\) −51.7097 43.3896i −1.92045 1.61145i
\(726\) 0 0
\(727\) 3.85204 + 1.40203i 0.142864 + 0.0519984i 0.412463 0.910974i \(-0.364669\pi\)
−0.269598 + 0.962973i \(0.586891\pi\)
\(728\) 14.9495 0.554067
\(729\) 0 0
\(730\) −29.6117 −1.09598
\(731\) −17.5535 6.38895i −0.649240 0.236304i
\(732\) 0 0
\(733\) −29.2690 24.5596i −1.08108 0.907131i −0.0850668 0.996375i \(-0.527110\pi\)
−0.996010 + 0.0892443i \(0.971555\pi\)
\(734\) −2.92319 + 16.5782i −0.107897 + 0.611914i
\(735\) 0 0
\(736\) −12.2554 + 10.2835i −0.451739 + 0.379054i
\(737\) −0.476529 0.825373i −0.0175532 0.0304030i
\(738\) 0 0
\(739\) 12.1047 20.9660i 0.445279 0.771247i −0.552792 0.833319i \(-0.686438\pi\)
0.998072 + 0.0620725i \(0.0197710\pi\)
\(740\) −5.48545 31.1095i −0.201649 1.14361i
\(741\) 0 0
\(742\) −2.53431 + 0.922414i −0.0930375 + 0.0338629i
\(743\) −3.11169 + 1.13256i −0.114157 + 0.0415497i −0.398467 0.917183i \(-0.630458\pi\)
0.284310 + 0.958732i \(0.408235\pi\)
\(744\) 0 0
\(745\) −0.856381 4.85678i −0.0313754 0.177939i
\(746\) 6.70527 11.6139i 0.245497 0.425214i
\(747\) 0 0
\(748\) 0.299011 + 0.517902i 0.0109329 + 0.0189364i
\(749\) 12.7135 10.6679i 0.464540 0.389796i
\(750\) 0 0
\(751\) 2.38089 13.5027i 0.0868800 0.492721i −0.910055 0.414487i \(-0.863961\pi\)
0.996935 0.0782335i \(-0.0249280\pi\)
\(752\) 0.237359 + 0.199168i 0.00865560 + 0.00726291i
\(753\) 0 0
\(754\) 13.3849 + 4.87171i 0.487449 + 0.177417i
\(755\) −30.4807 −1.10931
\(756\) 0 0
\(757\) 12.3833 0.450079 0.225040 0.974350i \(-0.427749\pi\)
0.225040 + 0.974350i \(0.427749\pi\)
\(758\) −8.13758 2.96184i −0.295570 0.107579i
\(759\) 0 0
\(760\) 30.3252 + 25.4459i 1.10001 + 0.923019i
\(761\) −1.31671 + 7.46745i −0.0477308 + 0.270695i −0.999328 0.0366529i \(-0.988330\pi\)
0.951597 + 0.307348i \(0.0994415\pi\)
\(762\) 0 0
\(763\) 26.1728 21.9616i 0.947518 0.795062i
\(764\) 10.7185 + 18.5650i 0.387783 + 0.671660i
\(765\) 0 0
\(766\) 12.4829 21.6211i 0.451026 0.781201i
\(767\) 2.14425 + 12.1606i 0.0774243 + 0.439095i
\(768\) 0 0
\(769\) −3.02317 + 1.10034i −0.109018 + 0.0396794i −0.395953 0.918271i \(-0.629586\pi\)
0.286935 + 0.957950i \(0.407364\pi\)
\(770\) 1.13816 0.414255i 0.0410163 0.0149287i
\(771\) 0 0
\(772\) 0.424373 + 2.40674i 0.0152735 + 0.0866205i
\(773\) −0.0922341 + 0.159754i −0.00331743 + 0.00574596i −0.867679 0.497124i \(-0.834389\pi\)
0.864362 + 0.502870i \(0.167723\pi\)
\(774\) 0 0
\(775\) 26.0526 + 45.1245i 0.935838 + 1.62092i
\(776\) 8.49185 7.12551i 0.304840 0.255791i
\(777\) 0 0
\(778\) −1.66209 + 9.42620i −0.0595889 + 0.337946i