Properties

Label 729.2.i.a.685.11
Level $729$
Weight $2$
Character 729.685
Analytic conductor $5.821$
Analytic rank $0$
Dimension $1404$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 729 = 3^{6} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 729.i (of order \(81\), degree \(54\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(5.82109430735\)
Analytic rank: \(0\)
Dimension: \(1404\)
Relative dimension: \(26\) over \(\Q(\zeta_{81})\)
Twist minimal: no (minimal twist has level 243)
Sato-Tate group: $\mathrm{SU}(2)[C_{81}]$

Embedding invariants

Embedding label 685.11
Character \(\chi\) \(=\) 729.685
Dual form 729.2.i.a.613.11

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.450088 - 0.125291i) q^{2} +(-1.52545 - 0.920615i) q^{4} +(1.87359 - 0.0727037i) q^{5} +(-1.75996 - 0.275253i) q^{7} +(1.21247 + 1.28514i) q^{8} +O(q^{10})\) \(q+(-0.450088 - 0.125291i) q^{2} +(-1.52545 - 0.920615i) q^{4} +(1.87359 - 0.0727037i) q^{5} +(-1.75996 - 0.275253i) q^{7} +(1.21247 + 1.28514i) q^{8} +(-0.852388 - 0.202020i) q^{10} +(-0.122185 - 0.894554i) q^{11} +(1.98767 - 2.89810i) q^{13} +(0.757651 + 0.344395i) q^{14} +(1.27602 + 2.42246i) q^{16} +(-1.35064 + 0.678319i) q^{17} +(-0.248678 - 4.26964i) q^{19} +(-2.92500 - 1.61395i) q^{20} +(-0.0570851 + 0.417937i) q^{22} +(-0.323131 + 0.836929i) q^{23} +(-1.47992 + 0.115029i) q^{25} +(-1.25773 + 1.05536i) q^{26} +(2.43133 + 2.04013i) q^{28} +(-5.35430 - 3.82702i) q^{29} +(6.83714 - 7.83449i) q^{31} +(-1.01890 - 4.70375i) q^{32} +(0.692896 - 0.136080i) q^{34} +(-3.31745 - 0.387754i) q^{35} +(-4.40805 - 5.92103i) q^{37} +(-0.423019 + 1.95287i) q^{38} +(2.36510 + 2.31968i) q^{40} +(-1.34270 + 5.21270i) q^{41} +(2.48398 + 2.25409i) q^{43} +(-0.637152 + 1.47708i) q^{44} +(0.250297 - 0.336207i) q^{46} +(-5.78474 - 6.62858i) q^{47} +(-3.64404 - 1.16841i) q^{49} +(0.680508 + 0.133647i) q^{50} +(-5.70013 + 2.59103i) q^{52} +(-0.445346 + 2.52568i) q^{53} +(-0.293962 - 1.66714i) q^{55} +(-1.78016 - 2.59554i) q^{56} +(1.93042 + 2.39334i) q^{58} +(7.15832 - 2.92449i) q^{59} +(-4.04975 + 2.44404i) q^{61} +(-4.05890 + 2.66958i) q^{62} +(0.187657 - 3.22194i) q^{64} +(3.51337 - 5.57435i) q^{65} +(4.78295 - 3.41865i) q^{67} +(2.68481 + 0.208680i) q^{68} +(1.44456 + 0.590169i) q^{70} +(-4.36841 - 14.5915i) q^{71} +(-4.63749 + 1.09911i) q^{73} +(1.24216 + 3.21727i) q^{74} +(-3.55135 + 6.74207i) q^{76} +(-0.0311873 + 1.60801i) q^{77} +(5.00473 - 4.90860i) q^{79} +(2.56685 + 4.44592i) q^{80} +(1.25744 - 2.17794i) q^{82} +(-1.78039 - 6.91191i) q^{83} +(-2.48123 + 1.36909i) q^{85} +(-0.835593 - 1.32576i) q^{86} +(1.00148 - 1.24164i) q^{88} +(-1.01568 + 3.39260i) q^{89} +(-4.29593 + 4.55342i) q^{91} +(1.26341 - 0.979216i) q^{92} +(1.77315 + 3.70822i) q^{94} +(-0.776339 - 7.98146i) q^{95} +(-4.63384 - 0.179814i) q^{97} +(1.49375 + 0.982453i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 1404 q + 54 q^{2} - 54 q^{4} + 54 q^{5} - 54 q^{7} + 54 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 1404 q + 54 q^{2} - 54 q^{4} + 54 q^{5} - 54 q^{7} + 54 q^{8} - 54 q^{10} + 54 q^{11} - 54 q^{13} + 54 q^{14} - 54 q^{16} + 54 q^{17} - 54 q^{19} + 54 q^{20} - 54 q^{22} + 54 q^{23} - 54 q^{25} + 54 q^{26} - 54 q^{28} + 54 q^{29} - 54 q^{31} + 54 q^{32} - 54 q^{34} + 54 q^{35} - 54 q^{37} + 54 q^{38} - 54 q^{40} + 54 q^{41} - 54 q^{43} + 54 q^{44} - 54 q^{46} + 54 q^{47} - 54 q^{49} + 54 q^{50} - 54 q^{52} + 54 q^{53} - 54 q^{55} + 54 q^{56} - 54 q^{58} + 54 q^{59} - 54 q^{61} + 54 q^{62} - 54 q^{64} - 54 q^{67} - 135 q^{68} - 54 q^{70} - 54 q^{71} - 54 q^{73} - 162 q^{74} - 54 q^{76} - 162 q^{77} - 54 q^{79} - 351 q^{80} - 27 q^{82} - 54 q^{83} - 54 q^{85} - 162 q^{86} - 54 q^{88} - 81 q^{89} - 54 q^{91} - 270 q^{92} - 54 q^{94} - 54 q^{95} - 54 q^{97} - 54 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(2\)
\(\chi(n)\) \(e\left(\frac{7}{81}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.450088 0.125291i −0.318260 0.0885938i 0.105359 0.994434i \(-0.466401\pi\)
−0.423619 + 0.905840i \(0.639240\pi\)
\(3\) 0 0
\(4\) −1.52545 0.920615i −0.762726 0.460308i
\(5\) 1.87359 0.0727037i 0.837893 0.0325141i 0.383744 0.923440i \(-0.374635\pi\)
0.454150 + 0.890925i \(0.349943\pi\)
\(6\) 0 0
\(7\) −1.75996 0.275253i −0.665203 0.104036i −0.187101 0.982341i \(-0.559909\pi\)
−0.478101 + 0.878305i \(0.658675\pi\)
\(8\) 1.21247 + 1.28514i 0.428673 + 0.454367i
\(9\) 0 0
\(10\) −0.852388 0.202020i −0.269549 0.0638843i
\(11\) −0.122185 0.894554i −0.0368402 0.269718i −1.00000 0.000787206i \(-0.999749\pi\)
0.963159 0.268931i \(-0.0866703\pi\)
\(12\) 0 0
\(13\) 1.98767 2.89810i 0.551281 0.803788i −0.444478 0.895790i \(-0.646611\pi\)
0.995759 + 0.0920024i \(0.0293267\pi\)
\(14\) 0.757651 + 0.344395i 0.202491 + 0.0920433i
\(15\) 0 0
\(16\) 1.27602 + 2.42246i 0.319005 + 0.605616i
\(17\) −1.35064 + 0.678319i −0.327579 + 0.164517i −0.604986 0.796236i \(-0.706821\pi\)
0.277407 + 0.960753i \(0.410525\pi\)
\(18\) 0 0
\(19\) −0.248678 4.26964i −0.0570507 0.979523i −0.898441 0.439095i \(-0.855299\pi\)
0.841390 0.540428i \(-0.181738\pi\)
\(20\) −2.92500 1.61395i −0.654050 0.360889i
\(21\) 0 0
\(22\) −0.0570851 + 0.417937i −0.0121706 + 0.0891044i
\(23\) −0.323131 + 0.836929i −0.0673774 + 0.174512i −0.962483 0.271343i \(-0.912532\pi\)
0.895105 + 0.445855i \(0.147100\pi\)
\(24\) 0 0
\(25\) −1.47992 + 0.115029i −0.295985 + 0.0230057i
\(26\) −1.25773 + 1.05536i −0.246662 + 0.206974i
\(27\) 0 0
\(28\) 2.43133 + 2.04013i 0.459479 + 0.385549i
\(29\) −5.35430 3.82702i −0.994268 0.710660i −0.0368369 0.999321i \(-0.511728\pi\)
−0.957431 + 0.288661i \(0.906790\pi\)
\(30\) 0 0
\(31\) 6.83714 7.83449i 1.22799 1.40712i 0.344416 0.938817i \(-0.388077\pi\)
0.883570 0.468299i \(-0.155133\pi\)
\(32\) −1.01890 4.70375i −0.180117 0.831514i
\(33\) 0 0
\(34\) 0.692896 0.136080i 0.118831 0.0233376i
\(35\) −3.31745 0.387754i −0.560752 0.0655425i
\(36\) 0 0
\(37\) −4.40805 5.92103i −0.724678 0.973412i −0.999928 0.0120389i \(-0.996168\pi\)
0.275249 0.961373i \(-0.411240\pi\)
\(38\) −0.423019 + 1.95287i −0.0686227 + 0.316798i
\(39\) 0 0
\(40\) 2.36510 + 2.31968i 0.373955 + 0.366773i
\(41\) −1.34270 + 5.21270i −0.209695 + 0.814086i 0.773842 + 0.633379i \(0.218333\pi\)
−0.983537 + 0.180707i \(0.942161\pi\)
\(42\) 0 0
\(43\) 2.48398 + 2.25409i 0.378803 + 0.343746i 0.839059 0.544041i \(-0.183106\pi\)
−0.460255 + 0.887787i \(0.652242\pi\)
\(44\) −0.637152 + 1.47708i −0.0960543 + 0.222679i
\(45\) 0 0
\(46\) 0.250297 0.336207i 0.0369042 0.0495710i
\(47\) −5.78474 6.62858i −0.843792 0.966878i 0.155990 0.987759i \(-0.450143\pi\)
−0.999782 + 0.0208806i \(0.993353\pi\)
\(48\) 0 0
\(49\) −3.64404 1.16841i −0.520577 0.166916i
\(50\) 0.680508 + 0.133647i 0.0962384 + 0.0189006i
\(51\) 0 0
\(52\) −5.70013 + 2.59103i −0.790466 + 0.359311i
\(53\) −0.445346 + 2.52568i −0.0611730 + 0.346929i 0.938824 + 0.344398i \(0.111917\pi\)
−0.999997 + 0.00253147i \(0.999194\pi\)
\(54\) 0 0
\(55\) −0.293962 1.66714i −0.0396378 0.224797i
\(56\) −1.78016 2.59554i −0.237884 0.346843i
\(57\) 0 0
\(58\) 1.93042 + 2.39334i 0.253476 + 0.314261i
\(59\) 7.15832 2.92449i 0.931934 0.380737i 0.139172 0.990268i \(-0.455556\pi\)
0.792762 + 0.609532i \(0.208642\pi\)
\(60\) 0 0
\(61\) −4.04975 + 2.44404i −0.518517 + 0.312927i −0.751699 0.659506i \(-0.770765\pi\)
0.233182 + 0.972433i \(0.425086\pi\)
\(62\) −4.05890 + 2.66958i −0.515481 + 0.339037i
\(63\) 0 0
\(64\) 0.187657 3.22194i 0.0234571 0.402742i
\(65\) 3.51337 5.57435i 0.435780 0.691413i
\(66\) 0 0
\(67\) 4.78295 3.41865i 0.584330 0.417654i −0.250536 0.968107i \(-0.580607\pi\)
0.834866 + 0.550453i \(0.185545\pi\)
\(68\) 2.68481 + 0.208680i 0.325582 + 0.0253062i
\(69\) 0 0
\(70\) 1.44456 + 0.590169i 0.172658 + 0.0705387i
\(71\) −4.36841 14.5915i −0.518435 1.73169i −0.669161 0.743117i \(-0.733346\pi\)
0.150727 0.988576i \(-0.451839\pi\)
\(72\) 0 0
\(73\) −4.63749 + 1.09911i −0.542777 + 0.128641i −0.492853 0.870112i \(-0.664046\pi\)
−0.0499241 + 0.998753i \(0.515898\pi\)
\(74\) 1.24216 + 3.21727i 0.144398 + 0.374000i
\(75\) 0 0
\(76\) −3.55135 + 6.74207i −0.407368 + 0.773368i
\(77\) −0.0311873 + 1.60801i −0.00355413 + 0.183250i
\(78\) 0 0
\(79\) 5.00473 4.90860i 0.563076 0.552261i −0.361934 0.932204i \(-0.617883\pi\)
0.925010 + 0.379943i \(0.124056\pi\)
\(80\) 2.56685 + 4.44592i 0.286983 + 0.497069i
\(81\) 0 0
\(82\) 1.25744 2.17794i 0.138861 0.240514i
\(83\) −1.78039 6.91191i −0.195424 0.758681i −0.988711 0.149834i \(-0.952126\pi\)
0.793288 0.608847i \(-0.208368\pi\)
\(84\) 0 0
\(85\) −2.48123 + 1.36909i −0.269128 + 0.148498i
\(86\) −0.835593 1.32576i −0.0901043 0.142960i
\(87\) 0 0
\(88\) 1.00148 1.24164i 0.106758 0.132360i
\(89\) −1.01568 + 3.39260i −0.107662 + 0.359615i −0.994795 0.101899i \(-0.967508\pi\)
0.887133 + 0.461513i \(0.152693\pi\)
\(90\) 0 0
\(91\) −4.29593 + 4.55342i −0.450336 + 0.477329i
\(92\) 1.26341 0.979216i 0.131720 0.102090i
\(93\) 0 0
\(94\) 1.77315 + 3.70822i 0.182886 + 0.382474i
\(95\) −0.776339 7.98146i −0.0796507 0.818881i
\(96\) 0 0
\(97\) −4.63384 0.179814i −0.470495 0.0182574i −0.197562 0.980290i \(-0.563302\pi\)
−0.272933 + 0.962033i \(0.587994\pi\)
\(98\) 1.49375 + 0.982453i 0.150891 + 0.0992427i
\(99\) 0 0
\(100\) 2.36345 + 1.18697i 0.236345 + 0.118697i
\(101\) 0.314091 + 16.1945i 0.0312532 + 1.61141i 0.607627 + 0.794222i \(0.292121\pi\)
−0.576374 + 0.817186i \(0.695533\pi\)
\(102\) 0 0
\(103\) 6.79852 + 5.26925i 0.669878 + 0.519195i 0.889816 0.456319i \(-0.150832\pi\)
−0.219938 + 0.975514i \(0.570586\pi\)
\(104\) 6.13446 0.959412i 0.601533 0.0940781i
\(105\) 0 0
\(106\) 0.516890 1.08098i 0.0502047 0.104994i
\(107\) 17.5878 + 6.40142i 1.70027 + 0.618848i 0.995856 0.0909392i \(-0.0289869\pi\)
0.704416 + 0.709788i \(0.251209\pi\)
\(108\) 0 0
\(109\) 7.26826 2.64543i 0.696173 0.253386i 0.0303968 0.999538i \(-0.490323\pi\)
0.665776 + 0.746152i \(0.268101\pi\)
\(110\) −0.0765683 + 0.787191i −0.00730050 + 0.0750557i
\(111\) 0 0
\(112\) −1.57895 4.61467i −0.149197 0.436045i
\(113\) 7.44187 6.75314i 0.700072 0.635282i −0.242162 0.970236i \(-0.577857\pi\)
0.942235 + 0.334954i \(0.108721\pi\)
\(114\) 0 0
\(115\) −0.544565 + 1.59155i −0.0507810 + 0.148413i
\(116\) 4.64451 + 10.7672i 0.431232 + 0.999708i
\(117\) 0 0
\(118\) −3.58829 + 0.419410i −0.330328 + 0.0386099i
\(119\) 2.56379 0.822046i 0.235022 0.0753569i
\(120\) 0 0
\(121\) 9.81178 2.73130i 0.891980 0.248300i
\(122\) 2.12896 0.592636i 0.192747 0.0536548i
\(123\) 0 0
\(124\) −17.6423 + 5.65677i −1.58432 + 0.507993i
\(125\) −12.0760 + 1.41148i −1.08011 + 0.126247i
\(126\) 0 0
\(127\) −2.08101 4.82432i −0.184660 0.428089i 0.800590 0.599213i \(-0.204520\pi\)
−0.985250 + 0.171123i \(0.945260\pi\)
\(128\) −3.60430 + 10.5340i −0.318578 + 0.931080i
\(129\) 0 0
\(130\) −2.27974 + 2.06876i −0.199947 + 0.181442i
\(131\) 2.05417 + 6.00354i 0.179474 + 0.524532i 0.998809 0.0487823i \(-0.0155340\pi\)
−0.819336 + 0.573314i \(0.805658\pi\)
\(132\) 0 0
\(133\) −0.737567 + 7.58285i −0.0639551 + 0.657516i
\(134\) −2.58107 + 0.939434i −0.222971 + 0.0811547i
\(135\) 0 0
\(136\) −2.50935 0.913330i −0.215175 0.0783174i
\(137\) −8.16172 + 17.0688i −0.697303 + 1.45829i 0.182627 + 0.983182i \(0.441540\pi\)
−0.879930 + 0.475103i \(0.842411\pi\)
\(138\) 0 0
\(139\) 3.51242 0.549332i 0.297919 0.0465938i −0.00379271 0.999993i \(-0.501207\pi\)
0.301712 + 0.953399i \(0.402442\pi\)
\(140\) 4.70364 + 3.64560i 0.397530 + 0.308109i
\(141\) 0 0
\(142\) 0.137991 + 7.11478i 0.0115800 + 0.597059i
\(143\) −2.83537 1.42398i −0.237105 0.119079i
\(144\) 0 0
\(145\) −10.3100 6.78098i −0.856197 0.563130i
\(146\) 2.22499 + 0.0863397i 0.184141 + 0.00714552i
\(147\) 0 0
\(148\) 1.27327 + 13.0904i 0.104662 + 1.07602i
\(149\) 2.74004 + 5.73030i 0.224473 + 0.469445i 0.983334 0.181807i \(-0.0581947\pi\)
−0.758862 + 0.651252i \(0.774244\pi\)
\(150\) 0 0
\(151\) −6.43072 + 4.98419i −0.523325 + 0.405607i −0.839720 0.543020i \(-0.817281\pi\)
0.316395 + 0.948628i \(0.397528\pi\)
\(152\) 5.18558 5.49640i 0.420606 0.445817i
\(153\) 0 0
\(154\) 0.215506 0.719839i 0.0173659 0.0580063i
\(155\) 12.2404 15.1757i 0.983171 1.21894i
\(156\) 0 0
\(157\) 6.85527 + 10.8766i 0.547110 + 0.868050i 0.999720 0.0236589i \(-0.00753156\pi\)
−0.452610 + 0.891709i \(0.649507\pi\)
\(158\) −2.86757 + 1.58226i −0.228132 + 0.125878i
\(159\) 0 0
\(160\) −2.25097 8.73881i −0.177955 0.690864i
\(161\) 0.799064 1.38402i 0.0629751 0.109076i
\(162\) 0 0
\(163\) 5.11716 + 8.86319i 0.400807 + 0.694218i 0.993824 0.110972i \(-0.0353964\pi\)
−0.593016 + 0.805190i \(0.702063\pi\)
\(164\) 6.84712 6.71560i 0.534670 0.524401i
\(165\) 0 0
\(166\) −0.0646636 + 3.33404i −0.00501887 + 0.258772i
\(167\) −3.23761 + 6.14644i −0.250533 + 0.475626i −0.977469 0.211080i \(-0.932302\pi\)
0.726935 + 0.686706i \(0.240944\pi\)
\(168\) 0 0
\(169\) 0.234184 + 0.606551i 0.0180141 + 0.0466578i
\(170\) 1.28831 0.305334i 0.0988087 0.0234181i
\(171\) 0 0
\(172\) −1.71404 5.72530i −0.130694 0.436550i
\(173\) −1.27457 0.520719i −0.0969038 0.0395896i 0.329230 0.944250i \(-0.393211\pi\)
−0.426133 + 0.904660i \(0.640125\pi\)
\(174\) 0 0
\(175\) 2.63627 + 0.204907i 0.199283 + 0.0154895i
\(176\) 2.01111 1.43746i 0.151593 0.108352i
\(177\) 0 0
\(178\) 0.882205 1.39971i 0.0661240 0.104913i
\(179\) −0.276549 + 4.74816i −0.0206702 + 0.354894i 0.972076 + 0.234666i \(0.0753997\pi\)
−0.992746 + 0.120228i \(0.961637\pi\)
\(180\) 0 0
\(181\) 21.6513 14.2403i 1.60933 1.05847i 0.656785 0.754078i \(-0.271916\pi\)
0.952546 0.304395i \(-0.0984544\pi\)
\(182\) 2.50405 1.51120i 0.185613 0.112018i
\(183\) 0 0
\(184\) −1.46736 + 0.599482i −0.108175 + 0.0441944i
\(185\) −8.68934 10.7731i −0.638853 0.792053i
\(186\) 0 0
\(187\) 0.771822 + 1.12534i 0.0564412 + 0.0822933i
\(188\) 2.72198 + 15.4371i 0.198521 + 1.12587i
\(189\) 0 0
\(190\) −0.650581 + 3.68963i −0.0471981 + 0.267674i
\(191\) 3.07826 1.39924i 0.222735 0.101246i −0.299335 0.954148i \(-0.596765\pi\)
0.522070 + 0.852903i \(0.325160\pi\)
\(192\) 0 0
\(193\) −3.96882 0.779450i −0.285682 0.0561061i 0.0478186 0.998856i \(-0.484773\pi\)
−0.333500 + 0.942750i \(0.608230\pi\)
\(194\) 2.06311 + 0.661509i 0.148123 + 0.0474936i
\(195\) 0 0
\(196\) 4.48315 + 5.13712i 0.320225 + 0.366937i
\(197\) −1.82371 + 2.44966i −0.129934 + 0.174531i −0.862329 0.506348i \(-0.830995\pi\)
0.732395 + 0.680880i \(0.238402\pi\)
\(198\) 0 0
\(199\) −5.56982 + 12.9123i −0.394834 + 0.915328i 0.598614 + 0.801038i \(0.295719\pi\)
−0.993447 + 0.114290i \(0.963541\pi\)
\(200\) −1.94219 1.76244i −0.137334 0.124624i
\(201\) 0 0
\(202\) 1.88764 7.32828i 0.132814 0.515616i
\(203\) 8.36996 + 8.20919i 0.587456 + 0.576173i
\(204\) 0 0
\(205\) −2.13669 + 9.86406i −0.149233 + 0.688936i
\(206\) −2.39975 3.22342i −0.167198 0.224586i
\(207\) 0 0
\(208\) 9.55684 + 1.11703i 0.662648 + 0.0774524i
\(209\) −3.78904 + 0.744143i −0.262093 + 0.0514734i
\(210\) 0 0
\(211\) −1.37379 6.34212i −0.0945755 0.436609i −0.999929 0.0119496i \(-0.996196\pi\)
0.905353 0.424660i \(-0.139606\pi\)
\(212\) 3.00454 3.44282i 0.206352 0.236454i
\(213\) 0 0
\(214\) −7.11400 5.08478i −0.486303 0.347589i
\(215\) 4.81783 + 4.04264i 0.328573 + 0.275706i
\(216\) 0 0
\(217\) −14.1896 + 11.9065i −0.963250 + 0.808263i
\(218\) −3.60280 + 0.280032i −0.244013 + 0.0189662i
\(219\) 0 0
\(220\) −1.08637 + 2.81377i −0.0732431 + 0.189704i
\(221\) −0.718804 + 5.26258i −0.0483520 + 0.353999i
\(222\) 0 0
\(223\) 11.1459 + 6.15004i 0.746384 + 0.411837i 0.810222 0.586123i \(-0.199347\pi\)
−0.0638382 + 0.997960i \(0.520334\pi\)
\(224\) 0.498498 + 8.55887i 0.0333073 + 0.571864i
\(225\) 0 0
\(226\) −4.19560 + 2.10711i −0.279087 + 0.140163i
\(227\) −9.68874 18.3936i −0.643064 1.22083i −0.962000 0.273051i \(-0.911967\pi\)
0.318935 0.947777i \(-0.396675\pi\)
\(228\) 0 0
\(229\) −6.45622 2.93471i −0.426639 0.193931i 0.188970 0.981983i \(-0.439485\pi\)
−0.615609 + 0.788052i \(0.711090\pi\)
\(230\) 0.444509 0.648110i 0.0293100 0.0427351i
\(231\) 0 0
\(232\) −1.57365 11.5212i −0.103315 0.756403i
\(233\) 21.5817 + 5.11496i 1.41386 + 0.335092i 0.865400 0.501082i \(-0.167064\pi\)
0.548464 + 0.836174i \(0.315213\pi\)
\(234\) 0 0
\(235\) −11.3201 11.9987i −0.738445 0.782706i
\(236\) −13.6120 2.12888i −0.886066 0.138578i
\(237\) 0 0
\(238\) −1.25693 + 0.0487745i −0.0814744 + 0.00316158i
\(239\) −25.2311 15.2271i −1.63207 0.984957i −0.972376 0.233419i \(-0.925009\pi\)
−0.659690 0.751538i \(-0.729312\pi\)
\(240\) 0 0
\(241\) 25.4744 + 7.09129i 1.64095 + 0.456790i 0.961019 0.276483i \(-0.0891690\pi\)
0.679934 + 0.733273i \(0.262008\pi\)
\(242\) −4.75837 −0.305880
\(243\) 0 0
\(244\) 8.42772 0.539529
\(245\) −6.91237 1.92419i −0.441615 0.122932i
\(246\) 0 0
\(247\) −12.8681 7.76595i −0.818779 0.494136i
\(248\) 18.3583 0.712384i 1.16575 0.0452364i
\(249\) 0 0
\(250\) 5.61211 + 0.877718i 0.354941 + 0.0555117i
\(251\) −13.3165 14.1147i −0.840532 0.890912i 0.154748 0.987954i \(-0.450543\pi\)
−0.995280 + 0.0970418i \(0.969062\pi\)
\(252\) 0 0
\(253\) 0.788160 + 0.186797i 0.0495512 + 0.0117438i
\(254\) 0.332195 + 2.43210i 0.0208438 + 0.152604i
\(255\) 0 0
\(256\) −0.708817 + 1.03348i −0.0443011 + 0.0645925i
\(257\) −4.37509 1.98872i −0.272911 0.124053i 0.272680 0.962105i \(-0.412090\pi\)
−0.545591 + 0.838052i \(0.683695\pi\)
\(258\) 0 0
\(259\) 6.12821 + 11.6341i 0.380788 + 0.722909i
\(260\) −10.4913 + 5.26894i −0.650644 + 0.326766i
\(261\) 0 0
\(262\) −0.172371 2.95949i −0.0106491 0.182838i
\(263\) 22.9343 + 12.6546i 1.41419 + 0.780315i 0.992005 0.126196i \(-0.0402769\pi\)
0.422181 + 0.906511i \(0.361265\pi\)
\(264\) 0 0
\(265\) −0.650768 + 4.76447i −0.0399764 + 0.292679i
\(266\) 1.28203 3.32054i 0.0786063 0.203595i
\(267\) 0 0
\(268\) −10.4434 + 0.811726i −0.637933 + 0.0495841i
\(269\) 8.13168 6.82329i 0.495798 0.416024i −0.360301 0.932836i \(-0.617326\pi\)
0.856099 + 0.516813i \(0.172882\pi\)
\(270\) 0 0
\(271\) 11.4212 + 9.58355i 0.693791 + 0.582159i 0.920000 0.391919i \(-0.128189\pi\)
−0.226209 + 0.974079i \(0.572633\pi\)
\(272\) −3.36665 2.40634i −0.204133 0.145906i
\(273\) 0 0
\(274\) 5.81205 6.65988i 0.351119 0.402338i
\(275\) 0.283724 + 1.30982i 0.0171092 + 0.0789849i
\(276\) 0 0
\(277\) 12.3172 2.41902i 0.740068 0.145345i 0.191549 0.981483i \(-0.438649\pi\)
0.548519 + 0.836138i \(0.315192\pi\)
\(278\) −1.64972 0.192825i −0.0989439 0.0115649i
\(279\) 0 0
\(280\) −3.52399 4.73354i −0.210599 0.282883i
\(281\) 6.58217 30.3867i 0.392659 1.81272i −0.169316 0.985562i \(-0.554156\pi\)
0.561975 0.827154i \(-0.310042\pi\)
\(282\) 0 0
\(283\) 6.81157 + 6.68074i 0.404906 + 0.397129i 0.873926 0.486058i \(-0.161566\pi\)
−0.469020 + 0.883187i \(0.655393\pi\)
\(284\) −6.76936 + 26.2803i −0.401688 + 1.55945i
\(285\) 0 0
\(286\) 1.09775 + 0.996159i 0.0649116 + 0.0589041i
\(287\) 3.79791 8.80456i 0.224184 0.519716i
\(288\) 0 0
\(289\) −8.78757 + 11.8038i −0.516916 + 0.694339i
\(290\) 3.79081 + 4.34378i 0.222604 + 0.255076i
\(291\) 0 0
\(292\) 8.08613 + 2.59271i 0.473205 + 0.151727i
\(293\) −5.48264 1.07676i −0.320299 0.0629048i 0.0299786 0.999551i \(-0.490456\pi\)
−0.350278 + 0.936646i \(0.613913\pi\)
\(294\) 0 0
\(295\) 13.1991 5.99973i 0.768482 0.349318i
\(296\) 2.26475 12.8440i 0.131636 0.746545i
\(297\) 0 0
\(298\) −0.515306 2.92244i −0.0298509 0.169293i
\(299\) 1.78322 + 2.60000i 0.103127 + 0.150362i
\(300\) 0 0
\(301\) −3.75126 4.65083i −0.216219 0.268070i
\(302\) 3.51886 1.43761i 0.202488 0.0827254i
\(303\) 0 0
\(304\) 10.0257 6.05056i 0.575015 0.347023i
\(305\) −7.40987 + 4.87355i −0.424288 + 0.279058i
\(306\) 0 0
\(307\) 0.118695 2.03792i 0.00677429 0.116310i −0.993226 0.116201i \(-0.962928\pi\)
1.00000 0.000108965i \(-3.46846e-5\pi\)
\(308\) 1.52793 2.42423i 0.0870621 0.138133i
\(309\) 0 0
\(310\) −7.41062 + 5.29679i −0.420895 + 0.300838i
\(311\) −22.0644 1.71498i −1.25116 0.0972478i −0.565241 0.824926i \(-0.691217\pi\)
−0.685919 + 0.727678i \(0.740599\pi\)
\(312\) 0 0
\(313\) −26.0445 10.6404i −1.47212 0.601429i −0.506702 0.862121i \(-0.669136\pi\)
−0.965422 + 0.260692i \(0.916049\pi\)
\(314\) −1.72274 5.75435i −0.0972197 0.324737i
\(315\) 0 0
\(316\) −12.1534 + 2.88041i −0.683683 + 0.162036i
\(317\) 7.90513 + 20.4748i 0.443996 + 1.14998i 0.956613 + 0.291362i \(0.0941083\pi\)
−0.512617 + 0.858618i \(0.671324\pi\)
\(318\) 0 0
\(319\) −2.76926 + 5.25731i −0.155049 + 0.294353i
\(320\) 0.117344 6.05022i 0.00655973 0.338218i
\(321\) 0 0
\(322\) −0.533054 + 0.522816i −0.0297059 + 0.0291354i
\(323\) 3.23205 + 5.59808i 0.179836 + 0.311486i
\(324\) 0 0
\(325\) −2.60824 + 4.51760i −0.144679 + 0.250591i
\(326\) −1.19270 4.63035i −0.0660576 0.256451i
\(327\) 0 0
\(328\) −8.32705 + 4.59467i −0.459784 + 0.253698i
\(329\) 8.35639 + 13.2583i 0.460702 + 0.730954i
\(330\) 0 0
\(331\) 10.0036 12.4026i 0.549849 0.681706i −0.424840 0.905268i \(-0.639670\pi\)
0.974690 + 0.223562i \(0.0717686\pi\)
\(332\) −3.64731 + 12.1829i −0.200172 + 0.668621i
\(333\) 0 0
\(334\) 2.22730 2.36080i 0.121872 0.129177i
\(335\) 8.71272 6.75287i 0.476027 0.368949i
\(336\) 0 0
\(337\) −15.3002 31.9976i −0.833453 1.74302i −0.649916 0.760006i \(-0.725196\pi\)
−0.183537 0.983013i \(-0.558755\pi\)
\(338\) −0.0294082 0.302343i −0.00159959 0.0164453i
\(339\) 0 0
\(340\) 5.04540 + 0.195785i 0.273625 + 0.0106179i
\(341\) −7.84377 5.15893i −0.424764 0.279372i
\(342\) 0 0
\(343\) 17.2349 + 8.65569i 0.930597 + 0.467363i
\(344\) 0.114921 + 5.92529i 0.00619611 + 0.319470i
\(345\) 0 0
\(346\) 0.508428 + 0.394061i 0.0273332 + 0.0211849i
\(347\) 14.7901 2.31313i 0.793974 0.124175i 0.255491 0.966812i \(-0.417763\pi\)
0.538483 + 0.842636i \(0.318998\pi\)
\(348\) 0 0
\(349\) 4.48271 9.37480i 0.239954 0.501821i −0.746597 0.665277i \(-0.768313\pi\)
0.986551 + 0.163456i \(0.0522641\pi\)
\(350\) −1.16088 0.422526i −0.0620517 0.0225850i
\(351\) 0 0
\(352\) −4.08327 + 1.48619i −0.217639 + 0.0792140i
\(353\) −1.65039 + 16.9675i −0.0878414 + 0.903088i 0.843060 + 0.537819i \(0.180752\pi\)
−0.930902 + 0.365269i \(0.880977\pi\)
\(354\) 0 0
\(355\) −9.24545 27.0208i −0.490698 1.43412i
\(356\) 4.67264 4.24020i 0.247650 0.224730i
\(357\) 0 0
\(358\) 0.719372 2.10244i 0.0380200 0.111118i
\(359\) −11.4556 26.5571i −0.604604 1.40163i −0.895580 0.444900i \(-0.853239\pi\)
0.290976 0.956730i \(-0.406020\pi\)
\(360\) 0 0
\(361\) 0.703538 0.0822318i 0.0370283 0.00432799i
\(362\) −11.5292 + 3.69668i −0.605960 + 0.194293i
\(363\) 0 0
\(364\) 10.7452 2.99113i 0.563201 0.156778i
\(365\) −8.60884 + 2.39643i −0.450607 + 0.125435i
\(366\) 0 0
\(367\) −27.0455 + 8.67178i −1.41176 + 0.452663i −0.910815 0.412815i \(-0.864546\pi\)
−0.500947 + 0.865478i \(0.667015\pi\)
\(368\) −2.43975 + 0.285166i −0.127181 + 0.0148653i
\(369\) 0 0
\(370\) 2.56120 + 5.93753i 0.133151 + 0.308678i
\(371\) 1.47899 4.32252i 0.0767855 0.224414i
\(372\) 0 0
\(373\) −6.29249 + 5.71013i −0.325813 + 0.295659i −0.818453 0.574574i \(-0.805168\pi\)
0.492640 + 0.870233i \(0.336032\pi\)
\(374\) −0.206393 0.603206i −0.0106723 0.0311910i
\(375\) 0 0
\(376\) 1.50485 15.4712i 0.0776065 0.797865i
\(377\) −21.7337 + 7.91041i −1.11934 + 0.407407i
\(378\) 0 0
\(379\) −20.9992 7.64310i −1.07866 0.392599i −0.259250 0.965810i \(-0.583475\pi\)
−0.819408 + 0.573211i \(0.805698\pi\)
\(380\) −6.16359 + 12.8900i −0.316185 + 0.661246i
\(381\) 0 0
\(382\) −1.56080 + 0.244105i −0.0798575 + 0.0124895i
\(383\) −8.03476 6.22741i −0.410557 0.318206i 0.386300 0.922373i \(-0.373753\pi\)
−0.796858 + 0.604167i \(0.793506\pi\)
\(384\) 0 0
\(385\) 0.0584762 + 3.01502i 0.00298022 + 0.153659i
\(386\) 1.68866 + 0.848077i 0.0859505 + 0.0431660i
\(387\) 0 0
\(388\) 6.90316 + 4.54028i 0.350455 + 0.230498i
\(389\) 25.7940 + 1.00092i 1.30781 + 0.0507488i 0.683223 0.730210i \(-0.260578\pi\)
0.624582 + 0.780959i \(0.285269\pi\)
\(390\) 0 0
\(391\) −0.131271 1.34958i −0.00663864 0.0682511i
\(392\) −2.91671 6.09978i −0.147316 0.308085i
\(393\) 0 0
\(394\) 1.12775 0.874071i 0.0568151 0.0440351i
\(395\) 9.01992 9.56056i 0.453842 0.481044i
\(396\) 0 0
\(397\) 9.70298 32.4102i 0.486978 1.62662i −0.262742 0.964866i \(-0.584627\pi\)
0.749720 0.661755i \(-0.230188\pi\)
\(398\) 4.12470 5.11382i 0.206752 0.256333i
\(399\) 0 0
\(400\) −2.16706 3.43828i −0.108353 0.171914i
\(401\) −15.8842 + 8.76455i −0.793221 + 0.437681i −0.827315 0.561738i \(-0.810133\pi\)
0.0340946 + 0.999419i \(0.489145\pi\)
\(402\) 0 0
\(403\) −9.11513 35.3871i −0.454057 1.76276i
\(404\) 14.4297 24.9930i 0.717906 1.24345i
\(405\) 0 0
\(406\) −2.73868 4.74354i −0.135919 0.235418i
\(407\) −4.75808 + 4.66670i −0.235849 + 0.231320i
\(408\) 0 0
\(409\) 0.113529 5.85353i 0.00561365 0.289438i −0.986476 0.163906i \(-0.947591\pi\)
0.992090 0.125532i \(-0.0400638\pi\)
\(410\) 2.19757 4.17199i 0.108530 0.206040i
\(411\) 0 0
\(412\) −5.51987 14.2968i −0.271944 0.704353i
\(413\) −13.4033 + 3.17665i −0.659535 + 0.156313i
\(414\) 0 0
\(415\) −3.83824 12.8206i −0.188412 0.629340i
\(416\) −15.6572 6.39666i −0.767656 0.313622i
\(417\) 0 0
\(418\) 1.79864 + 0.139801i 0.0879741 + 0.00683789i
\(419\) −8.90668 + 6.36611i −0.435120 + 0.311005i −0.777874 0.628420i \(-0.783702\pi\)
0.342754 + 0.939425i \(0.388640\pi\)
\(420\) 0 0
\(421\) 20.6049 32.6920i 1.00422 1.59331i 0.217446 0.976072i \(-0.430228\pi\)
0.786778 0.617236i \(-0.211748\pi\)
\(422\) −0.176281 + 3.02663i −0.00858124 + 0.147334i
\(423\) 0 0
\(424\) −3.78583 + 2.48998i −0.183856 + 0.120924i
\(425\) 1.92082 1.15922i 0.0931736 0.0562306i
\(426\) 0 0
\(427\) 7.80013 3.18670i 0.377475 0.154215i
\(428\) −20.9360 25.9566i −1.01198 1.25466i
\(429\) 0 0
\(430\) −1.66194 2.42317i −0.0801461 0.116856i
\(431\) −2.53731 14.3898i −0.122218 0.693134i −0.982921 0.184026i \(-0.941087\pi\)
0.860703 0.509107i \(-0.170024\pi\)
\(432\) 0 0
\(433\) −3.94200 + 22.3562i −0.189440 + 1.07437i 0.730676 + 0.682724i \(0.239205\pi\)
−0.920116 + 0.391645i \(0.871906\pi\)
\(434\) 7.87832 3.58114i 0.378171 0.171900i
\(435\) 0 0
\(436\) −13.5228 2.65579i −0.647625 0.127189i
\(437\) 3.65374 + 1.17153i 0.174782 + 0.0560416i
\(438\) 0 0
\(439\) 18.1855 + 20.8382i 0.867945 + 0.994554i 0.999995 + 0.00331127i \(0.00105401\pi\)
−0.132050 + 0.991243i \(0.542156\pi\)
\(440\) 1.78609 2.39914i 0.0851487 0.114375i
\(441\) 0 0
\(442\) 0.982876 2.27856i 0.0467507 0.108380i
\(443\) 15.5564 + 14.1167i 0.739106 + 0.670703i 0.951905 0.306393i \(-0.0991221\pi\)
−0.212799 + 0.977096i \(0.568258\pi\)
\(444\) 0 0
\(445\) −1.65630 + 6.43017i −0.0785163 + 0.304819i
\(446\) −4.24609 4.16454i −0.201058 0.197196i
\(447\) 0 0
\(448\) −1.21712 + 5.61883i −0.0575033 + 0.265465i
\(449\) −6.52791 8.76850i −0.308071 0.413811i 0.620943 0.783856i \(-0.286750\pi\)
−0.929014 + 0.370045i \(0.879342\pi\)
\(450\) 0 0
\(451\) 4.82709 + 0.564206i 0.227299 + 0.0265674i
\(452\) −17.5693 + 3.45049i −0.826389 + 0.162297i
\(453\) 0 0
\(454\) 2.05624 + 9.49266i 0.0965041 + 0.445513i
\(455\) −7.71776 + 8.84357i −0.361814 + 0.414593i
\(456\) 0 0
\(457\) −14.4425 10.3229i −0.675593 0.482885i 0.191201 0.981551i \(-0.438762\pi\)
−0.866794 + 0.498666i \(0.833823\pi\)
\(458\) 2.53818 + 2.12978i 0.118601 + 0.0995182i
\(459\) 0 0
\(460\) 2.29591 1.92650i 0.107048 0.0898236i
\(461\) −19.6842 + 1.52998i −0.916785 + 0.0712581i −0.527208 0.849736i \(-0.676761\pi\)
−0.389576 + 0.920994i \(0.627379\pi\)
\(462\) 0 0
\(463\) −6.01266 + 15.5732i −0.279432 + 0.723747i 0.720121 + 0.693848i \(0.244086\pi\)
−0.999553 + 0.0298982i \(0.990482\pi\)
\(464\) 2.43863 17.8539i 0.113211 0.828848i
\(465\) 0 0
\(466\) −9.07281 5.00617i −0.420290 0.231906i
\(467\) 0.258949 + 4.44599i 0.0119827 + 0.205736i 0.998986 + 0.0450326i \(0.0143392\pi\)
−0.987003 + 0.160703i \(0.948624\pi\)
\(468\) 0 0
\(469\) −9.35879 + 4.70016i −0.432149 + 0.217033i
\(470\) 3.59174 + 6.81876i 0.165675 + 0.314526i
\(471\) 0 0
\(472\) 12.4376 + 5.65360i 0.572489 + 0.260228i
\(473\) 1.71290 2.49747i 0.0787592 0.114834i
\(474\) 0 0
\(475\) 0.859156 + 6.29014i 0.0394208 + 0.288611i
\(476\) −4.66773 1.10627i −0.213945 0.0507059i
\(477\) 0 0
\(478\) 9.44842 + 10.0147i 0.432161 + 0.458064i
\(479\) 3.03252 + 0.474278i 0.138560 + 0.0216703i 0.223418 0.974723i \(-0.428278\pi\)
−0.0848586 + 0.996393i \(0.527044\pi\)
\(480\) 0 0
\(481\) −25.9215 + 1.00587i −1.18192 + 0.0458638i
\(482\) −10.5773 6.38342i −0.481781 0.290757i
\(483\) 0 0
\(484\) −17.4819 4.86641i −0.794631 0.221201i
\(485\) −8.69498 −0.394819
\(486\) 0 0
\(487\) 9.63920 0.436794 0.218397 0.975860i \(-0.429917\pi\)
0.218397 + 0.975860i \(0.429917\pi\)
\(488\) −8.05113 2.24119i −0.364458 0.101454i
\(489\) 0 0
\(490\) 2.87009 + 1.73211i 0.129658 + 0.0782488i
\(491\) −33.0502 + 1.28250i −1.49154 + 0.0578784i −0.771576 0.636137i \(-0.780531\pi\)
−0.719960 + 0.694015i \(0.755840\pi\)
\(492\) 0 0
\(493\) 9.82770 + 1.53702i 0.442617 + 0.0692241i
\(494\) 4.81879 + 5.10762i 0.216808 + 0.229803i
\(495\) 0 0
\(496\) 27.7031 + 6.56575i 1.24390 + 0.294811i
\(497\) 3.67188 + 26.8829i 0.164706 + 1.20586i
\(498\) 0 0
\(499\) 5.86546 8.55205i 0.262574 0.382842i −0.670864 0.741580i \(-0.734077\pi\)
0.933438 + 0.358738i \(0.116793\pi\)
\(500\) 19.7208 + 8.96420i 0.881940 + 0.400891i
\(501\) 0 0
\(502\) 4.22518 + 8.02130i 0.188579 + 0.358008i
\(503\) 34.8610 17.5079i 1.55438 0.780638i 0.555667 0.831405i \(-0.312463\pi\)
0.998710 + 0.0507675i \(0.0161668\pi\)
\(504\) 0 0
\(505\) 1.76587 + 30.3189i 0.0785803 + 1.34917i
\(506\) −0.331337 0.182824i −0.0147297 0.00812753i
\(507\) 0 0
\(508\) −1.26686 + 9.27508i −0.0562080 + 0.411515i
\(509\) 6.86979 17.7932i 0.304498 0.788670i −0.693193 0.720752i \(-0.743797\pi\)
0.997691 0.0679178i \(-0.0216356\pi\)
\(510\) 0 0
\(511\) 8.46434 0.657900i 0.374440 0.0291038i
\(512\) 17.5061 14.6893i 0.773666 0.649183i
\(513\) 0 0
\(514\) 1.72001 + 1.44326i 0.0758663 + 0.0636594i
\(515\) 13.1207 + 9.37812i 0.578168 + 0.413249i
\(516\) 0 0
\(517\) −5.22281 + 5.98468i −0.229699 + 0.263206i
\(518\) −1.30059 6.00418i −0.0571446 0.263809i
\(519\) 0 0
\(520\) 11.4237 2.24354i 0.500962 0.0983857i
\(521\) 15.9939 + 1.86942i 0.700706 + 0.0819008i 0.458984 0.888445i \(-0.348214\pi\)
0.241722 + 0.970345i \(0.422288\pi\)
\(522\) 0 0
\(523\) 12.2469 + 16.4504i 0.535519 + 0.719327i 0.984728 0.174100i \(-0.0557016\pi\)
−0.449209 + 0.893427i \(0.648294\pi\)
\(524\) 2.39341 11.0492i 0.104557 0.482687i
\(525\) 0 0
\(526\) −8.73694 8.56913i −0.380949 0.373632i
\(527\) −3.92026 + 15.2194i −0.170769 + 0.662966i
\(528\) 0 0
\(529\) 16.4365 + 14.9153i 0.714629 + 0.648492i
\(530\) 0.889846 2.06289i 0.0386524 0.0896064i
\(531\) 0 0
\(532\) 8.10601 10.8883i 0.351440 0.472066i
\(533\) 12.4380 + 14.2524i 0.538751 + 0.617341i
\(534\) 0 0
\(535\) 33.4176 + 10.7149i 1.44477 + 0.463246i
\(536\) 10.1926 + 2.00177i 0.440254 + 0.0864631i
\(537\) 0 0
\(538\) −4.51487 + 2.05226i −0.194650 + 0.0884792i
\(539\) −0.599961 + 3.40255i −0.0258422 + 0.146558i
\(540\) 0 0
\(541\) 6.69020 + 37.9420i 0.287634 + 1.63125i 0.695722 + 0.718311i \(0.255085\pi\)
−0.408088 + 0.912943i \(0.633804\pi\)
\(542\) −3.93983 5.74442i −0.169230 0.246744i
\(543\) 0 0
\(544\) 4.56681 + 5.66196i 0.195801 + 0.242755i
\(545\) 13.4254 5.48487i 0.575080 0.234946i
\(546\) 0 0
\(547\) −14.1747 + 8.55450i −0.606068 + 0.365764i −0.786286 0.617863i \(-0.787999\pi\)
0.180218 + 0.983627i \(0.442320\pi\)
\(548\) 28.1641 18.5238i 1.20311 0.791298i
\(549\) 0 0
\(550\) 0.0364068 0.625081i 0.00155239 0.0266535i
\(551\) −15.0085 + 23.8126i −0.639384 + 1.01445i
\(552\) 0 0
\(553\) −10.1592 + 7.26139i −0.432015 + 0.308786i
\(554\) −5.84690 0.454457i −0.248411 0.0193080i
\(555\) 0 0
\(556\) −5.86375 2.39561i −0.248678 0.101596i
\(557\) 0.0385061 + 0.128619i 0.00163155 + 0.00544977i 0.958801 0.284077i \(-0.0916872\pi\)
−0.957170 + 0.289527i \(0.906502\pi\)
\(558\) 0 0
\(559\) 11.4699 2.71842i 0.485126 0.114977i
\(560\) −3.29381 8.53118i −0.139189 0.360508i
\(561\) 0 0
\(562\) −6.76972 + 12.8520i −0.285563 + 0.542129i
\(563\) −0.779847 + 40.2087i −0.0328666 + 1.69459i 0.514332 + 0.857591i \(0.328040\pi\)
−0.547199 + 0.837003i \(0.684306\pi\)
\(564\) 0 0
\(565\) 13.4520 13.1936i 0.565931 0.555061i
\(566\) −2.22877 3.86035i −0.0936823 0.162263i
\(567\) 0 0
\(568\) 13.4556 23.3058i 0.564584 0.977889i
\(569\) −0.314826 1.22223i −0.0131982 0.0512385i 0.961452 0.274973i \(-0.0886689\pi\)
−0.974650 + 0.223735i \(0.928175\pi\)
\(570\) 0 0
\(571\) −17.4379 + 9.62182i −0.729753 + 0.402661i −0.804039 0.594576i \(-0.797320\pi\)
0.0742863 + 0.997237i \(0.476332\pi\)
\(572\) 3.01429 + 4.78249i 0.126034 + 0.199966i
\(573\) 0 0
\(574\) −2.81252 + 3.48698i −0.117393 + 0.145544i
\(575\) 0.381937 1.27576i 0.0159279 0.0532029i
\(576\) 0 0
\(577\) −0.0495128 + 0.0524805i −0.00206125 + 0.00218479i −0.728403 0.685148i \(-0.759737\pi\)
0.726342 + 0.687333i \(0.241219\pi\)
\(578\) 5.43408 4.21173i 0.226028 0.175185i
\(579\) 0 0
\(580\) 9.48471 + 19.8356i 0.393831 + 0.823628i
\(581\) 1.23090 + 12.6548i 0.0510663 + 0.525008i
\(582\) 0 0
\(583\) 2.31377 + 0.0897850i 0.0958267 + 0.00371851i
\(584\) −7.03533 4.62721i −0.291124 0.191475i
\(585\) 0 0
\(586\) 2.33277 + 1.17156i 0.0963657 + 0.0483967i
\(587\) 0.856182 + 44.1445i 0.0353384 + 1.82204i 0.429576 + 0.903031i \(0.358663\pi\)
−0.394238 + 0.919009i \(0.628991\pi\)
\(588\) 0 0
\(589\) −35.1507 27.2439i −1.44836 1.12256i
\(590\) −6.69247 + 1.04668i −0.275525 + 0.0430913i
\(591\) 0 0
\(592\) 8.71873 18.2337i 0.358338 0.749399i
\(593\) 24.7882 + 9.02215i 1.01793 + 0.370495i 0.796472 0.604675i \(-0.206697\pi\)
0.221455 + 0.975170i \(0.428919\pi\)
\(594\) 0 0
\(595\) 4.74372 1.72657i 0.194473 0.0707826i
\(596\) 1.09561 11.2638i 0.0448778 0.461384i
\(597\) 0 0
\(598\) −0.476852 1.39365i −0.0194999 0.0569907i
\(599\) −11.8840 + 10.7842i −0.485567 + 0.440628i −0.877651 0.479301i \(-0.840890\pi\)
0.392084 + 0.919930i \(0.371754\pi\)
\(600\) 0 0
\(601\) −10.4057 + 30.4118i −0.424457 + 1.24052i 0.502244 + 0.864726i \(0.332508\pi\)
−0.926702 + 0.375798i \(0.877369\pi\)
\(602\) 1.10569 + 2.56328i 0.0450647 + 0.104472i
\(603\) 0 0
\(604\) 14.3983 1.68292i 0.585857 0.0684769i
\(605\) 18.1847 5.83067i 0.739311 0.237051i
\(606\) 0 0
\(607\) 37.9002 10.5502i 1.53832 0.428221i 0.607688 0.794176i \(-0.292097\pi\)
0.930632 + 0.365956i \(0.119258\pi\)
\(608\) −19.8300 + 5.52005i −0.804211 + 0.223867i
\(609\) 0 0
\(610\) 3.94570 1.26514i 0.159757 0.0512240i
\(611\) −30.7085 + 3.58930i −1.24233 + 0.145208i
\(612\) 0 0
\(613\) −1.34534 3.11885i −0.0543378 0.125969i 0.888884 0.458131i \(-0.151481\pi\)
−0.943222 + 0.332162i \(0.892222\pi\)
\(614\) −0.308755 + 0.902371i −0.0124603 + 0.0364167i
\(615\) 0 0
\(616\) −2.10434 + 1.90958i −0.0847862 + 0.0769394i
\(617\) 3.18158 + 9.29851i 0.128085 + 0.374344i 0.991492 0.130164i \(-0.0415504\pi\)
−0.863407 + 0.504508i \(0.831674\pi\)
\(618\) 0 0
\(619\) −3.28266 + 33.7487i −0.131941 + 1.35648i 0.662467 + 0.749091i \(0.269509\pi\)
−0.794408 + 0.607384i \(0.792219\pi\)
\(620\) −32.6431 + 11.8811i −1.31098 + 0.477157i
\(621\) 0 0
\(622\) 9.71607 + 3.53636i 0.389579 + 0.141795i
\(623\) 2.72137 5.69127i 0.109029 0.228016i
\(624\) 0 0
\(625\) −15.1900 + 2.37567i −0.607600 + 0.0950270i
\(626\) 10.3892 + 8.05224i 0.415236 + 0.321832i
\(627\) 0 0
\(628\) −0.444200 22.9029i −0.0177255 0.913923i
\(629\) 9.97005 + 5.00715i 0.397532 + 0.199648i
\(630\) 0 0
\(631\) −21.6011 14.2073i −0.859928 0.565584i 0.0411931 0.999151i \(-0.486884\pi\)
−0.901121 + 0.433568i \(0.857255\pi\)
\(632\) 12.3763 + 0.480258i 0.492304 + 0.0191037i
\(633\) 0 0
\(634\) −0.992705 10.2059i −0.0394254 0.405328i
\(635\) −4.24970 8.88749i −0.168644 0.352689i
\(636\) 0 0
\(637\) −10.6293 + 8.23835i −0.421149 + 0.326415i
\(638\) 1.90510 2.01929i 0.0754238 0.0799445i
\(639\) 0 0
\(640\) −5.98711 + 19.9983i −0.236661 + 0.790504i
\(641\) 27.3014 33.8484i 1.07834 1.33693i 0.140417 0.990092i \(-0.455156\pi\)
0.937924 0.346841i \(-0.112746\pi\)
\(642\) 0 0
\(643\) 4.54621 + 7.21305i 0.179285 + 0.284455i 0.923588 0.383388i \(-0.125243\pi\)
−0.744303 + 0.667842i \(0.767218\pi\)
\(644\) −2.49308 + 1.37563i −0.0982412 + 0.0542072i
\(645\) 0 0
\(646\) −0.753322 2.92458i −0.0296391 0.115066i
\(647\) 22.6475 39.2266i 0.890365 1.54216i 0.0509259 0.998702i \(-0.483783\pi\)
0.839439 0.543454i \(-0.182884\pi\)
\(648\) 0 0
\(649\) −3.49076 6.04617i −0.137024 0.237333i
\(650\) 1.73995 1.70653i 0.0682465 0.0669357i
\(651\) 0 0
\(652\) 0.353596 18.2313i 0.0138479 0.713993i
\(653\) −15.5349 + 29.4923i −0.607928 + 1.15412i 0.366710 + 0.930335i \(0.380484\pi\)
−0.974638 + 0.223788i \(0.928158\pi\)
\(654\) 0 0
\(655\) 4.28515 + 11.0988i 0.167435 + 0.433666i
\(656\) −14.3409 + 3.39885i −0.559917 + 0.132703i
\(657\) 0 0
\(658\) −2.09997 7.01439i −0.0818653 0.273449i
\(659\) −7.08244 2.89350i −0.275893 0.112715i 0.236031 0.971746i \(-0.424153\pi\)
−0.511924 + 0.859031i \(0.671067\pi\)
\(660\) 0 0
\(661\) −36.0710 2.80366i −1.40300 0.109050i −0.646434 0.762970i \(-0.723741\pi\)
−0.756564 + 0.653920i \(0.773123\pi\)
\(662\) −6.05644 + 4.32888i −0.235390 + 0.168247i
\(663\) 0 0
\(664\) 6.72412 10.6685i 0.260947 0.414020i
\(665\) −0.830594 + 14.2607i −0.0322091 + 0.553008i
\(666\) 0 0
\(667\) 4.93308 3.24454i 0.191010 0.125629i
\(668\) 10.5973 6.39552i 0.410023 0.247450i
\(669\) 0 0
\(670\) −4.76756 + 1.94776i −0.184187 + 0.0752487i
\(671\) 2.68114 + 3.32409i 0.103504 + 0.128325i
\(672\) 0 0
\(673\) 23.3868 + 34.0988i 0.901495 + 1.31441i 0.948913 + 0.315536i \(0.102184\pi\)
−0.0474187 + 0.998875i \(0.515099\pi\)
\(674\) 2.87743 + 16.3187i 0.110834 + 0.628573i
\(675\) 0 0
\(676\) 0.201164 1.14086i 0.00773708 0.0438792i
\(677\) 2.22569 1.01170i 0.0855401 0.0388828i −0.370584 0.928799i \(-0.620842\pi\)
0.456124 + 0.889916i \(0.349237\pi\)
\(678\) 0 0
\(679\) 8.10588 + 1.59194i 0.311075 + 0.0610932i
\(680\) −4.76789 1.52876i −0.182840 0.0586254i
\(681\) 0 0
\(682\) 2.88402 + 3.30472i 0.110435 + 0.126544i
\(683\) 13.4172 18.0225i 0.513396 0.689611i −0.467533 0.883976i \(-0.654857\pi\)
0.980929 + 0.194365i \(0.0622646\pi\)
\(684\) 0 0
\(685\) −14.0507 + 32.5733i −0.536851 + 1.24456i
\(686\) −6.67275 6.05519i −0.254767 0.231188i
\(687\) 0 0
\(688\) −2.29085 + 8.89361i −0.0873377 + 0.339066i
\(689\) 6.43447 + 6.31089i 0.245134 + 0.240426i
\(690\) 0 0
\(691\) 7.04469 32.5219i 0.267993 1.23719i −0.622654 0.782497i \(-0.713946\pi\)
0.890647 0.454695i \(-0.150252\pi\)
\(692\) 1.46491 + 1.96772i 0.0556877 + 0.0748015i
\(693\) 0 0
\(694\) −6.94666 0.811948i −0.263692 0.0308211i
\(695\) 6.54088 1.28459i 0.248110 0.0487272i
\(696\) 0 0
\(697\) −1.72236 7.95128i −0.0652389 0.301176i
\(698\) −3.19219 + 3.65784i −0.120826 + 0.138451i
\(699\) 0 0
\(700\) −3.83286 2.73956i −0.144869 0.103546i
\(701\) 15.2208 + 12.7717i 0.574880 + 0.482381i 0.883261 0.468881i \(-0.155343\pi\)
−0.308381 + 0.951263i \(0.599787\pi\)
\(702\) 0 0
\(703\) −24.1845 + 20.2932i −0.912136 + 0.765373i
\(704\) −2.90513 + 0.225804i −0.109491 + 0.00851032i
\(705\) 0 0
\(706\) 2.86869 7.43009i 0.107964 0.279635i
\(707\) 3.90478 28.5881i 0.146854 1.07516i
\(708\) 0 0
\(709\) −35.6004 19.6435i −1.33700 0.737726i −0.356510 0.934291i \(-0.616034\pi\)
−0.980491 + 0.196565i \(0.937021\pi\)
\(710\) 0.775809 + 13.3201i 0.0291156 + 0.499896i
\(711\) 0 0
\(712\) −5.59145 + 2.80813i −0.209548 + 0.105239i
\(713\) 4.34762 + 8.25376i 0.162820 + 0.309106i
\(714\) 0 0
\(715\) −5.41584 2.46180i −0.202541 0.0920661i
\(716\) 4.79309 6.98850i 0.179126 0.261173i
\(717\) 0 0
\(718\) 1.82868 + 13.3883i 0.0682458 + 0.499648i
\(719\) 17.2835 + 4.09626i 0.644566 + 0.152765i 0.539882 0.841741i \(-0.318469\pi\)
0.104684 + 0.994506i \(0.466617\pi\)
\(720\) 0 0
\(721\) −10.5148 11.1450i −0.391590 0.415061i
\(722\) −0.326957 0.0511352i −0.0121681 0.00190305i
\(723\) 0 0
\(724\) −46.1379 + 1.79036i −1.71470 + 0.0665382i
\(725\) 8.36417 + 5.04780i 0.310637 + 0.187471i
\(726\) 0 0
\(727\) −14.0616 3.91432i −0.521517 0.145174i −0.00259617 0.999997i \(-0.500826\pi\)
−0.518920 + 0.854823i \(0.673666\pi\)
\(728\) −11.0605 −0.409929
\(729\) 0 0
\(730\) 4.17499 0.154523
\(731\) −4.88397 1.35954i −0.180640 0.0502846i
\(732\) 0 0
\(733\) −3.74272 2.25874i −0.138241 0.0834286i 0.445892 0.895087i \(-0.352886\pi\)
−0.584133 + 0.811658i \(0.698565\pi\)
\(734\) 13.2593 0.514523i 0.489411 0.0189914i
\(735\) 0 0
\(736\) 4.26594 + 0.667181i 0.157245 + 0.0245926i
\(737\) −3.64257 3.86090i −0.134176 0.142218i
\(738\) 0 0
\(739\) −27.4866 6.51443i −1.01111 0.239637i −0.308509 0.951222i \(-0.599830\pi\)
−0.702601 + 0.711584i \(0.747978\pi\)
\(740\) 3.33730 + 24.4334i 0.122682 + 0.898188i
\(741\) 0 0
\(742\) −1.20725 + 1.76021i −0.0443195 + 0.0646194i
\(743\) 37.8764 + 17.2169i 1.38955 + 0.631628i 0.962171 0.272445i \(-0.0878322\pi\)
0.427379 + 0.904073i \(0.359437\pi\)
\(744\) 0 0
\(745\) 5.55031 + 10.5370i 0.203348 + 0.386046i
\(746\) 3.54760 1.78167i 0.129887 0.0652316i
\(747\) 0 0
\(748\) −0.141369 2.42721i −0.00516895 0.0887475i
\(749\) −29.1917 16.1073i −1.06664 0.588549i
\(750\) 0 0
\(751\) 5.38496 39.4249i 0.196500 1.43863i −0.583123 0.812384i \(-0.698169\pi\)
0.779623 0.626249i \(-0.215411\pi\)
\(752\) 8.67604 22.4715i 0.316383 0.819452i
\(753\) 0 0
\(754\) 10.7732 0.837357i 0.392336 0.0304947i
\(755\) −11.6861 + 9.80584i −0.425302 + 0.356871i
\(756\) 0 0
\(757\) 24.3567 + 20.4377i 0.885258 + 0.742820i 0.967253 0.253813i \(-0.0816848\pi\)
−0.0819953 + 0.996633i \(0.526129\pi\)
\(758\) 8.49390 + 6.07107i 0.308512 + 0.220511i
\(759\) 0 0
\(760\) 9.31603 10.6750i 0.337928 0.387222i
\(761\) −3.92626 18.1256i −0.142327 0.657054i −0.991626 0.129142i \(-0.958778\pi\)
0.849299 0.527912i \(-0.177025\pi\)
\(762\) 0 0
\(763\) −13.5200 + 2.65524i −0.489457 + 0.0961262i
\(764\) −5.98390 0.699418i −0.216490 0.0253040i
\(765\) 0 0
\(766\) 2.83612 + 3.80956i 0.102473 + 0.137645i
\(767\) 5.75292 26.5584i 0.207726 0.958970i
\(768\) 0 0
\(769\) 9.03368 + 8.86017i 0.325763 + 0.319506i 0.844632 0.535348i \(-0.179820\pi\)
−0.518869 + 0.854854i \(0.673647\pi\)
\(770\) 0.351434 1.36435i 0.0126648 0.0491677i
\(771\) 0 0
\(772\) 5.33667 + 4.84277i 0.192071 + 0.174295i
\(773\) 13.9231 32.2775i 0.500780 1.16094i −0.461070 0.887364i \(-0.652534\pi\)
0.961850 0.273576i \(-0.0882064\pi\)
\(774\) 0 0
\(775\) −9.21725 + 12.3809i −0.331093 + 0.444735i
\(776\) −5.38730 6.17317i −0.193393 0.221604i
\(777\) 0 0
\(778\) −11.4841 3.68224i −0.411727 0.132015i
\(779\) 22.5902 + 4.43658i 0.809379 + 0.158957i
\(780\) 0 0
\(781\) −12.5191 + 5.69064i −0.447970 + 0.203627i
\(782\) −0.110006 + 0.623877i −0.00393382 + 0.0223098i
\(783\) 0 0
\(784\) −1.81942 10.3185i −0.0649794 0.368516i
\(785\) 13.6347 + 19.8799i 0.486644 + 0.709545i
\(786\) 0 0