Properties

Label 729.2.e.i.163.1
Level $729$
Weight $2$
Character 729.163
Analytic conductor $5.821$
Analytic rank $0$
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: \(0\)
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 163.1
Root \(-0.173648 + 0.984808i\) of defining polynomial
Character \(\chi\) \(=\) 729.163
Dual form 729.2.e.i.568.1

$q$-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 \(\left(\mathbb{Z}/729\mathbb{Z}\right)^\times\).

\(n\) \(2\)
\(\chi(n)\) \(e\left(\frac{8}{9}\right)\)

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 \(-0.510477\pi\)
0.617229 + 0.786784i \(0.288255\pi\)
\(3\) 0 0
\(4\) −0.939693 + 0.788496i −0.469846 + 0.394248i
\(5\) 0.673648 + 3.82045i 0.301265 + 1.70856i 0.640586 + 0.767886i \(0.278691\pi\)
−0.339322 + 0.940670i \(0.610198\pi\)
\(6\) 0 0
\(7\) −1.67365 1.40436i −0.632580 0.530797i 0.269150 0.963098i \(-0.413257\pi\)
−0.901729 + 0.432301i \(0.857702\pi\)
\(8\) −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 \(-0.936646\pi\)
0.988766 + 0.149470i \(0.0477567\pi\)
\(12\) 0 0
\(13\) −2.26604 0.824773i −0.628488 0.228751i 0.00808527 0.999967i \(-0.497426\pi\)
−0.636573 + 0.771217i \(0.719649\pi\)
\(14\) −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 \(-0.285189\pi\)
−0.988583 + 0.150675i \(0.951855\pi\)
\(18\) 0 0
\(19\) −1.79813 + 3.11446i −0.412520 + 0.714506i −0.995165 0.0982214i \(-0.968685\pi\)
0.582645 + 0.812727i \(0.302018\pi\)
\(20\) −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 \(-0.626626\pi\)
0.840635 + 0.541601i \(0.182182\pi\)
\(24\) 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 \(-0.825461\pi\)
−0.318677 + 0.947863i \(0.603239\pi\)
\(30\) 0 0
\(31\) −3.97178 + 3.33272i −0.713353 + 0.598574i −0.925538 0.378655i \(-0.876387\pi\)
0.212185 + 0.977230i \(0.431942\pi\)
\(32\) −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 0.998566 + 0.0535438i \(0.0170517\pi\)
−0.452912 + 0.891555i \(0.649615\pi\)
\(38\) −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 \(-0.239259\pi\)
0.120717 + 0.992687i \(0.461481\pi\)
\(42\) 0 0
\(43\) −1.08125 + 6.13208i −0.164889 + 0.935134i 0.784289 + 0.620396i \(0.213028\pi\)
−0.949178 + 0.314739i \(0.898083\pi\)
\(44\) 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 \(-0.0964000\pi\)
−0.127965 + 0.991779i \(0.540844\pi\)
\(48\) 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 \(-0.469264\pi\)
0.0964088 + 0.995342i \(0.469264\pi\)
\(54\) 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 −0.986370 0.164542i \(-0.947385\pi\)
0.870608 0.491977i \(-0.163726\pi\)
\(60\) 0 0
\(61\) −2.89646 2.43042i −0.370854 0.311183i 0.438246 0.898855i \(-0.355600\pi\)
−0.809099 + 0.587672i \(0.800044\pi\)
\(62\) −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 0.655965 0.754791i \(-0.272262\pi\)
0.0173282 + 0.999850i \(0.494484\pi\)
\(68\) 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 0.815500 + 0.578756i \(0.196462\pi\)
0.0934675 + 0.995622i \(0.470205\pi\)
\(72\) 0 0
\(73\) −4.34002 + 7.51714i −0.507961 + 0.879815i 0.491996 + 0.870597i \(0.336267\pi\)
−0.999958 + 0.00921733i \(0.997066\pi\)
\(74\) 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 −0.274089 0.961704i \(-0.588376\pi\)
0.408207 + 0.912889i \(0.366154\pi\)
\(80\) −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 \(-0.457107\pi\)
0.739874 + 0.672745i \(0.234885\pi\)
\(84\) 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 \(-0.967547\pi\)
0.585546 + 0.810640i \(0.300880\pi\)
\(90\) 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 0.930804 + 0.365519i \(0.119109\pi\)
−0.999684 + 0.0251223i \(0.992002\pi\)
\(98\) −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 \(-0.410046\pi\)
−0.897322 + 0.441377i \(0.854490\pi\)
\(102\) 0 0
\(103\) 3.23783 + 18.3626i 0.319032 + 1.80932i 0.548661 + 0.836045i \(0.315138\pi\)
−0.229629 + 0.973278i \(0.573751\pi\)
\(104\) 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 \(-0.380324\pi\)
0.367179 + 0.930150i \(0.380324\pi\)
\(108\) 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 \(-0.0902568\pi\)
−0.997855 + 0.0654689i \(0.979146\pi\)
\(114\) 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 −0.866953 0.498390i \(-0.833925\pi\)
0.865095 + 0.501609i \(0.167258\pi\)
\(128\) 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 0.229676 0.973267i \(-0.426233\pi\)
0.998364 0.0571807i \(-0.0182111\pi\)
\(132\) 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 \(-0.820515\pi\)
−0.303913 + 0.952700i \(0.598293\pi\)
\(138\) 0 0
\(139\) 8.03983 6.74622i 0.681929 0.572207i −0.234640 0.972082i \(-0.575391\pi\)
0.916569 + 0.399876i \(0.130947\pi\)
\(140\) 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 \(-0.372306\pi\)
−0.292624 + 0.956228i \(0.594528\pi\)
\(150\) 0 0
\(151\) 1.36437 7.73773i 0.111031 0.629688i −0.877608 0.479379i \(-0.840862\pi\)
0.988639 0.150309i \(-0.0480268\pi\)
\(152\) −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 −0.942454 0.334336i \(-0.891488\pi\)
0.771267 0.636512i \(-0.219623\pi\)
\(158\) 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 \(-0.101491\pi\)
−0.999543 + 0.0302175i \(0.990380\pi\)
\(168\) 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 \(-0.963325\pi\)
0.972782 + 0.231723i \(0.0744362\pi\)
\(174\) 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 \(-0.0160713\pi\)
−0.543069 + 0.839688i \(0.682738\pi\)
\(180\) 0 0
\(181\) 8.43629 14.6121i 0.627064 1.08611i −0.361073 0.932537i \(-0.617590\pi\)
0.988138 0.153570i \(-0.0490771\pi\)
\(182\) 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 \(-0.393244\pi\)
0.859104 + 0.511802i \(0.171022\pi\)
\(192\) 0 0
\(193\) −1.52616 + 1.28060i −0.109855 + 0.0921796i −0.696061 0.717983i \(-0.745066\pi\)
0.586205 + 0.810162i \(0.300621\pi\)
\(194\) 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 0.190445 + 0.981698i \(0.439007\pi\)
−0.945398 + 0.325919i \(0.894326\pi\)
\(198\) 0 0
\(199\) 1.54189 + 2.67063i 0.109302 + 0.189316i 0.915488 0.402346i \(-0.131805\pi\)
−0.806186 + 0.591662i \(0.798472\pi\)
\(200\) 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 0.990239 0.139383i \(-0.0445118\pi\)
−0.978192 + 0.207705i \(0.933401\pi\)
\(212\) −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 0.977225 0.212205i \(-0.0680644\pi\)
−0.0392875 + 0.999228i \(0.512509\pi\)
\(224\) −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 \(-0.972420\pi\)
0.965764 + 0.259421i \(0.0835316\pi\)
\(228\) 0 0
\(229\) 3.25402 + 1.18437i 0.215032 + 0.0782652i 0.447290 0.894389i \(-0.352389\pi\)
−0.232258 + 0.972654i \(0.574611\pi\)
\(230\) 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 \(-0.230973\pi\)
−0.948739 + 0.316061i \(0.897640\pi\)
\(234\) 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 −0.491629 + 0.870805i \(0.663598\pi\)
−0.942946 + 0.332946i \(0.891957\pi\)
\(240\) 0 0
\(241\) −20.9795 + 7.63592i −1.35141 + 0.491873i −0.913388 0.407091i \(-0.866543\pi\)
−0.438022 + 0.898964i \(0.644321\pi\)
\(242\) 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 −0.245047 0.969511i \(-0.578803\pi\)
0.962145 0.272539i \(-0.0878633\pi\)
\(252\) 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 \(-0.179665\pi\)
0.303373 + 0.952872i \(0.401887\pi\)
\(258\) 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 \(-0.0928558\pi\)
−0.116914 + 0.993142i \(0.537300\pi\)
\(264\) 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 \(-0.255524\pi\)
0.694729 + 0.719272i \(0.255524\pi\)
\(270\) 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 0.580657 0.814148i \(-0.302796\pi\)
−0.700949 + 0.713211i \(0.747240\pi\)
\(278\) 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 0.828145 + 0.560514i \(0.189396\pi\)
−0.969909 + 0.243468i \(0.921715\pi\)
\(282\) 0 0
\(283\) −21.5005 7.82553i −1.27807 0.465179i −0.388277 0.921543i \(-0.626929\pi\)
−0.889793 + 0.456363i \(0.849152\pi\)
\(284\) −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 \(-0.471249\pi\)
0.996457 + 0.0841084i \(0.0268042\pi\)
\(294\) 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 0.999003 0.0446505i \(-0.0142174\pi\)
−0.538170 + 0.842836i \(0.680884\pi\)
\(308\) 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 \(-0.566875\pi\)
−0.788414 + 0.615144i \(0.789098\pi\)
\(312\) 0 0
\(313\) 0.481582 2.73119i 0.0272206 0.154376i −0.968168 0.250302i \(-0.919470\pi\)
0.995388 + 0.0959261i \(0.0305813\pi\)
\(314\) −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 \(-0.114425\pi\)
−0.183892 + 0.982946i \(0.558870\pi\)
\(318\) 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 −0.973842 0.227224i \(-0.927035\pi\)
−0.392878 0.919590i \(-0.628521\pi\)
\(332\) −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 0.121128 0.992637i \(-0.461349\pi\)
−0.545265 + 0.838264i \(0.683571\pi\)
\(338\) −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 \(-0.590665\pi\)
0.896334 + 0.443380i \(0.146221\pi\)
\(348\) 0 0
\(349\) −31.6168 + 11.5076i −1.69241 + 0.615986i −0.994925 0.100615i \(-0.967919\pi\)
−0.697483 + 0.716601i \(0.745697\pi\)
\(350\) 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 \(-0.473407\pi\)
0.704471 + 0.709733i \(0.251184\pi\)
\(354\) 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 \(-0.992087\pi\)
0.521373 + 0.853329i \(0.325420\pi\)
\(360\) 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 0.766322 + 0.642457i \(0.222085\pi\)
−0.939840 + 0.341614i \(0.889026\pi\)
\(368\) 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 −0.973364 0.229265i \(-0.926368\pi\)
0.836250 0.548349i \(-0.184743\pi\)
\(374\) −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 0.803892 + 0.594775i \(0.202759\pi\)
−0.551986 + 0.833853i \(0.686130\pi\)
\(384\) 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 −0.898660 0.438646i \(-0.855458\pi\)
0.994490 0.104833i \(-0.0334307\pi\)
\(390\) 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 −0.544270 0.838910i \(-0.683193\pi\)
0.998652 + 0.0518969i \(0.0165267\pi\)
\(398\) 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 \(-0.710824\pi\)
0.669799 + 0.742542i \(0.266380\pi\)
\(402\) 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 −0.465123 0.885246i \(-0.653990\pi\)
0.791029 + 0.611778i \(0.209545\pi\)
\(410\) 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 \(-0.291660\pi\)
−0.0435988 + 0.999049i \(0.513882\pi\)
\(420\) 0 0
\(421\) 1.93036 10.9476i 0.0940800 0.533554i −0.900945 0.433932i \(-0.857126\pi\)
0.995025 0.0996216i \(-0.0317632\pi\)
\(422\) 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 \(-0.848324\pi\)
−0.888604 + 0.458675i \(0.848324\pi\)
\(432\) 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 0.646473 0.762937i \(-0.276243\pi\)
−0.639087 + 0.769135i \(0.720688\pi\)
\(440\) −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 −0.762825 0.646605i \(-0.776188\pi\)
0.937973 0.346709i \(-0.112701\pi\)
\(444\) 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 0.929116 + 0.369788i \(0.120570\pi\)
−0.144312 + 0.989532i \(0.546097\pi\)
\(450\) 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 −0.341270 0.939965i \(-0.610857\pi\)
0.342771 + 0.939419i \(0.388635\pi\)
\(458\) 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 \(-0.497635\pi\)
0.648462 + 0.761247i \(0.275413\pi\)
\(462\) 0 0
\(463\) −23.3203 + 19.5680i −1.08378 + 0.909403i −0.996230 0.0867566i \(-0.972350\pi\)
−0.0875549 + 0.996160i \(0.527905\pi\)
\(464\) −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 \(-0.829572\pi\)
0.871873 + 0.489731i \(0.162905\pi\)
\(468\) 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 \(-0.392609\pi\)
−0.871810 + 0.489844i \(0.837054\pi\)
\(480\) 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 \(-0.0400534\pi\)
−0.975187 + 0.221385i \(0.928942\pi\)
\(492\) 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 0.179523 0.983754i \(-0.442544\pi\)
−0.494822 + 0.868994i \(0.664767\pi\)
\(500\) 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 −0.985975 0.166894i \(-0.946626\pi\)
0.348453 0.937326i \(-0.386707\pi\)
\(504\) 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 \(-0.734160\pi\)
0.613612 + 0.789608i \(0.289716\pi\)
\(510\) 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 \(-0.670052\pi\)
0.999943 + 0.0106337i \(0.00338487\pi\)
\(522\) 0 0
\(523\) −1.21436 2.10332i −0.0531000 0.0919720i 0.838254 0.545281i \(-0.183577\pi\)
−0.891354 + 0.453309i \(0.850244\pi\)
\(524\) −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 0.370061 0.929007i \(-0.379337\pi\)
−0.850633 + 0.525759i \(0.823781\pi\)
\(548\) 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 \(-0.0910563\pi\)
−0.724053 + 0.689744i \(0.757723\pi\)
\(558\) 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 \(-0.610558\pi\)
0.866893 + 0.498495i \(0.166114\pi\)
\(564\) 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 \(-0.883447\pi\)
−0.485121 + 0.874447i \(0.661225\pi\)
\(570\) 0 0
\(571\) 29.9971 25.1705i 1.25534 1.05335i 0.259176 0.965830i \(-0.416549\pi\)
0.996162 0.0875234i \(-0.0278953\pi\)
\(572\) −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 0.716600 0.697484i \(-0.245697\pi\)
−0.962339 + 0.271852i \(0.912364\pi\)
\(578\) 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 −0.995300 0.0968406i \(-0.969126\pi\)
−0.268201 0.963363i \(-0.586429\pi\)
\(588\) 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 \(-0.705467\pi\)
−0.601594 + 0.798802i \(0.705467\pi\)
\(594\) 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 0.999465 + 0.0327053i \(0.0104123\pi\)
−0.928004 + 0.372570i \(0.878477\pi\)
\(600\) 0 0
\(601\) −23.3025 19.5531i −0.950528 0.797587i 0.0288587 0.999584i \(-0.490813\pi\)
−0.979386 + 0.201996i \(0.935257\pi\)
\(602\) 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 0.742240 0.670134i \(-0.233763\pi\)
0.137835 + 0.990455i \(0.455986\pi\)
\(608\) 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 −0.873652 0.486551i \(-0.838255\pi\)
0.858192 + 0.513330i \(0.171588\pi\)
\(614\) 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 \(-0.782087\pi\)
0.488231 + 0.872715i \(0.337643\pi\)
\(618\) 0 0
\(619\) 32.9666 11.9989i 1.32504 0.482275i 0.419970 0.907538i \(-0.362040\pi\)
0.905070 + 0.425263i \(0.139818\pi\)
\(620\) 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 −0.964168 0.265291i \(-0.914532\pi\)
0.252336 0.967640i \(-0.418801\pi\)
\(632\) −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 \(-0.259372\pi\)
−0.597442 + 0.801912i \(0.703816\pi\)
\(642\) 0 0
\(643\) −3.51666 19.9440i −0.138684 0.786514i −0.972223 0.234055i \(-0.924801\pi\)
0.833540 0.552459i \(-0.186311\pi\)
\(644\) 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 \(-0.432406\pi\)
0.210761 + 0.977538i \(0.432406\pi\)
\(648\) 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 0.825596 + 0.564262i \(0.190839\pi\)
−0.582818 + 0.812603i \(0.698050\pi\)
\(654\) 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 −0.682580 0.730811i \(-0.739142\pi\)
0.891367 0.453282i \(-0.149747\pi\)
\(660\) 0 0
\(661\) 9.25402 + 3.36819i 0.359940 + 0.131007i 0.515659 0.856794i \(-0.327547\pi\)
−0.155719 + 0.987801i \(0.549769\pi\)
\(662\) −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 0.0403273 0.999187i \(-0.487160\pi\)
0.673157 + 0.739499i \(0.264938\pi\)
\(674\) −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 \(-0.426940\pi\)
0.800217 + 0.599710i \(0.204717\pi\)
\(678\) 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 \(-0.910269\pi\)
0.721174 + 0.692754i \(0.243603\pi\)
\(684\) 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 −0.435676 0.900104i \(-0.643491\pi\)
0.717255 0.696811i \(-0.245398\pi\)
\(692\) −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 \(-0.0674008\pi\)
0.977665 + 0.210167i \(0.0674008\pi\)
\(702\) 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 0.834247 0.551391i \(-0.185903\pi\)
−0.398149 + 0.917321i \(0.630347\pi\)
\(710\) −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 \(-0.151140\pi\)
−0.840615 + 0.541633i \(0.817806\pi\)
\(720\) 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 −0.269598 0.962973i \(-0.586891\pi\)
0.412463 + 0.910974i \(0.364669\pi\)
\(728\) −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 −0.996010 0.0892443i \(-0.971555\pi\)
−0.0850668 + 0.996375i \(0.527110\pi\)
\(734\) 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 0.998072 0.0620725i \(-0.0197710\pi\)
−0.552792 + 0.833319i \(0.686438\pi\)
\(740\) 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 \(-0.369542\pi\)
−0.284310 + 0.958732i \(0.591765\pi\)
\(744\) 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 0.996935 + 0.0782335i \(0.0249280\pi\)
−0.910055 + 0.414487i \(0.863961\pi\)
\(752\) −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 \(-0.0116696\pi\)
−0.951597 + 0.307348i \(0.900558\pi\)
\(762\) 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 0.286935 0.957950i \(-0.407364\pi\)
−0.395953 + 0.918271i \(0.629586\pi\)
\(770\) −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 \(-0.165611\pi\)
−0.864362 + 0.502870i \(0.832277\pi\)
\(774\) 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