Properties

Label 729.2.i.a.613.1
Level $729$
Weight $2$
Character 729.613
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 613.1
Character \(\chi\) \(=\) 729.613
Dual form 729.2.i.a.685.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-2.57987 + 0.718157i) q^{2} +(4.42767 - 2.67211i) q^{4} +(3.51654 + 0.136458i) q^{5} +(-3.43073 + 0.536556i) q^{7} +(-5.82837 + 6.17771i) q^{8} +O(q^{10})\) \(q+(-2.57987 + 0.718157i) q^{2} +(4.42767 - 2.67211i) q^{4} +(3.51654 + 0.136458i) q^{5} +(-3.43073 + 0.536556i) q^{7} +(-5.82837 + 6.17771i) q^{8} +(-9.17022 + 2.17338i) q^{10} +(0.305175 - 2.23427i) q^{11} +(-1.63172 - 2.37910i) q^{13} +(8.46551 - 3.84805i) q^{14} +(5.77961 - 10.9723i) q^{16} +(-1.77656 - 0.892221i) q^{17} +(0.153093 - 2.62850i) q^{19} +(15.9347 - 8.79239i) q^{20} +(0.817247 + 5.98331i) q^{22} +(-1.99084 - 5.15640i) q^{23} +(7.36244 + 0.572254i) q^{25} +(5.91820 + 4.96596i) q^{26} +(-13.7564 + 11.5430i) q^{28} +(-3.05917 + 2.18657i) q^{29} +(-5.26689 - 6.03518i) q^{31} +(-3.43474 + 15.8565i) q^{32} +(5.22405 + 1.02597i) q^{34} +(-12.1375 + 1.41867i) q^{35} +(0.347087 - 0.466219i) q^{37} +(1.49272 + 6.89116i) q^{38} +(-21.3387 + 20.9288i) q^{40} +(-0.455952 - 1.77012i) q^{41} +(0.802684 - 0.728397i) q^{43} +(-4.61902 - 10.7081i) q^{44} +(8.83921 + 11.8731i) q^{46} +(-7.33012 + 8.39939i) q^{47} +(4.81625 - 1.54427i) q^{49} +(-19.4052 + 3.81105i) q^{50} +(-13.5819 - 6.17375i) q^{52} +(-0.570971 - 3.23814i) q^{53} +(1.37804 - 7.81526i) q^{55} +(16.6809 - 24.3213i) q^{56} +(6.32199 - 7.83804i) q^{58} +(10.5222 + 4.29880i) q^{59} +(2.86548 + 1.72933i) q^{61} +(17.9221 + 11.7876i) q^{62} +(-1.08412 - 18.6136i) q^{64} +(-5.41335 - 8.58886i) q^{65} +(-5.67055 - 4.05307i) q^{67} +(-10.2501 + 0.796703i) q^{68} +(30.2944 - 12.3766i) q^{70} +(3.36638 - 11.2445i) q^{71} +(5.59498 + 1.32604i) q^{73} +(-0.560623 + 1.45205i) q^{74} +(-6.34581 - 12.0472i) q^{76} +(0.151842 + 7.82892i) q^{77} +(-1.57898 - 1.54866i) q^{79} +(21.8215 - 37.7959i) q^{80} +(2.44752 + 4.23923i) q^{82} +(3.97987 - 15.4508i) q^{83} +(-6.12558 - 3.37995i) q^{85} +(-1.54772 + 2.45562i) q^{86} +(12.0240 + 14.9074i) q^{88} +(-2.46600 - 8.23703i) q^{89} +(6.87450 + 7.28654i) q^{91} +(-22.5932 - 17.5111i) q^{92} +(12.8787 - 26.9335i) q^{94} +(0.897036 - 9.22234i) q^{95} +(4.01124 - 0.155654i) q^{97} +(-11.3163 + 7.44284i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 1404 q + 54 q^{2} - 54 q^{4} + 54 q^{5} - 54 q^{7} + 54 q^{8}+O(q^{10}) \) 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 \(\left(\mathbb{Z}/729\mathbb{Z}\right)^\times\).

\(n\) \(2\)
\(\chi(n)\) \(e\left(\frac{74}{81}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.57987 + 0.718157i −1.82425 + 0.507814i −0.998424 0.0561163i \(-0.982128\pi\)
−0.825823 + 0.563930i \(0.809289\pi\)
\(3\) 0 0
\(4\) 4.42767 2.67211i 2.21383 1.33606i
\(5\) 3.51654 + 0.136458i 1.57264 + 0.0610257i 0.810248 0.586087i \(-0.199332\pi\)
0.762395 + 0.647112i \(0.224024\pi\)
\(6\) 0 0
\(7\) −3.43073 + 0.536556i −1.29669 + 0.202799i −0.764940 0.644101i \(-0.777232\pi\)
−0.531752 + 0.846900i \(0.678466\pi\)
\(8\) −5.82837 + 6.17771i −2.06064 + 2.18415i
\(9\) 0 0
\(10\) −9.17022 + 2.17338i −2.89988 + 0.687284i
\(11\) 0.305175 2.23427i 0.0920136 0.673659i −0.885783 0.464100i \(-0.846378\pi\)
0.977796 0.209558i \(-0.0672026\pi\)
\(12\) 0 0
\(13\) −1.63172 2.37910i −0.452557 0.659844i 0.529526 0.848294i \(-0.322370\pi\)
−0.982083 + 0.188449i \(0.939654\pi\)
\(14\) 8.46551 3.84805i 2.26250 1.02843i
\(15\) 0 0
\(16\) 5.77961 10.9723i 1.44490 2.74308i
\(17\) −1.77656 0.892221i −0.430879 0.216395i 0.220122 0.975472i \(-0.429354\pi\)
−0.651001 + 0.759077i \(0.725651\pi\)
\(18\) 0 0
\(19\) 0.153093 2.62850i 0.0351219 0.603020i −0.934127 0.356940i \(-0.883820\pi\)
0.969249 0.246081i \(-0.0791428\pi\)
\(20\) 15.9347 8.79239i 3.56310 1.96604i
\(21\) 0 0
\(22\) 0.817247 + 5.98331i 0.174238 + 1.27565i
\(23\) −1.99084 5.15640i −0.415118 1.07518i −0.969968 0.243232i \(-0.921792\pi\)
0.554850 0.831950i \(-0.312776\pi\)
\(24\) 0 0
\(25\) 7.36244 + 0.572254i 1.47249 + 0.114451i
\(26\) 5.91820 + 4.96596i 1.16065 + 0.973904i
\(27\) 0 0
\(28\) −13.7564 + 11.5430i −2.59971 + 2.18142i
\(29\) −3.05917 + 2.18657i −0.568074 + 0.406035i −0.828938 0.559340i \(-0.811054\pi\)
0.260864 + 0.965376i \(0.415993\pi\)
\(30\) 0 0
\(31\) −5.26689 6.03518i −0.945961 1.08395i −0.996362 0.0852220i \(-0.972840\pi\)
0.0504009 0.998729i \(-0.483950\pi\)
\(32\) −3.43474 + 15.8565i −0.607182 + 2.80306i
\(33\) 0 0
\(34\) 5.22405 + 1.02597i 0.895918 + 0.175953i
\(35\) −12.1375 + 1.41867i −2.05161 + 0.239799i
\(36\) 0 0
\(37\) 0.347087 0.466219i 0.0570608 0.0766459i −0.772677 0.634800i \(-0.781083\pi\)
0.829738 + 0.558154i \(0.188490\pi\)
\(38\) 1.49272 + 6.89116i 0.242151 + 1.11789i
\(39\) 0 0
\(40\) −21.3387 + 20.9288i −3.37394 + 3.30914i
\(41\) −0.455952 1.77012i −0.0712078 0.276446i 0.922871 0.385110i \(-0.125836\pi\)
−0.994078 + 0.108664i \(0.965343\pi\)
\(42\) 0 0
\(43\) 0.802684 0.728397i 0.122408 0.111079i −0.608505 0.793550i \(-0.708230\pi\)
0.730913 + 0.682471i \(0.239095\pi\)
\(44\) −4.61902 10.7081i −0.696343 1.61430i
\(45\) 0 0
\(46\) 8.83921 + 11.8731i 1.30327 + 1.75060i
\(47\) −7.33012 + 8.39939i −1.06921 + 1.22518i −0.0959682 + 0.995384i \(0.530595\pi\)
−0.973240 + 0.229792i \(0.926195\pi\)
\(48\) 0 0
\(49\) 4.81625 1.54427i 0.688036 0.220610i
\(50\) −19.4052 + 3.81105i −2.74430 + 0.538964i
\(51\) 0 0
\(52\) −13.5819 6.17375i −1.88348 0.856145i
\(53\) −0.570971 3.23814i −0.0784290 0.444793i −0.998582 0.0532340i \(-0.983047\pi\)
0.920153 0.391559i \(-0.128064\pi\)
\(54\) 0 0
\(55\) 1.37804 7.81526i 0.185815 1.05381i
\(56\) 16.6809 24.3213i 2.22907 3.25007i
\(57\) 0 0
\(58\) 6.32199 7.83804i 0.830118 1.02918i
\(59\) 10.5222 + 4.29880i 1.36988 + 0.559656i 0.939362 0.342928i \(-0.111419\pi\)
0.430515 + 0.902584i \(0.358332\pi\)
\(60\) 0 0
\(61\) 2.86548 + 1.72933i 0.366887 + 0.221418i 0.688143 0.725575i \(-0.258426\pi\)
−0.321256 + 0.946992i \(0.604105\pi\)
\(62\) 17.9221 + 11.7876i 2.27611 + 1.49702i
\(63\) 0 0
\(64\) −1.08412 18.6136i −0.135515 2.32670i
\(65\) −5.41335 8.58886i −0.671443 1.06532i
\(66\) 0 0
\(67\) −5.67055 4.05307i −0.692768 0.495161i 0.179769 0.983709i \(-0.442465\pi\)
−0.872537 + 0.488548i \(0.837527\pi\)
\(68\) −10.2501 + 0.796703i −1.24301 + 0.0966144i
\(69\) 0 0
\(70\) 30.2944 12.3766i 3.62087 1.47929i
\(71\) 3.36638 11.2445i 0.399515 1.33447i −0.487657 0.873035i \(-0.662148\pi\)
0.887172 0.461439i \(-0.152667\pi\)
\(72\) 0 0
\(73\) 5.59498 + 1.32604i 0.654843 + 0.155201i 0.544589 0.838703i \(-0.316685\pi\)
0.110254 + 0.993903i \(0.464834\pi\)
\(74\) −0.560623 + 1.45205i −0.0651711 + 0.168797i
\(75\) 0 0
\(76\) −6.34581 12.0472i −0.727915 1.38191i
\(77\) 0.151842 + 7.82892i 0.0173040 + 0.892188i
\(78\) 0 0
\(79\) −1.57898 1.54866i −0.177650 0.174238i 0.605952 0.795501i \(-0.292792\pi\)
−0.783602 + 0.621264i \(0.786620\pi\)
\(80\) 21.8215 37.7959i 2.43971 4.22571i
\(81\) 0 0
\(82\) 2.44752 + 4.23923i 0.270283 + 0.468145i
\(83\) 3.97987 15.4508i 0.436848 1.69595i −0.249252 0.968439i \(-0.580185\pi\)
0.686100 0.727508i \(-0.259321\pi\)
\(84\) 0 0
\(85\) −6.12558 3.37995i −0.664413 0.366608i
\(86\) −1.54772 + 2.45562i −0.166895 + 0.264797i
\(87\) 0 0
\(88\) 12.0240 + 14.9074i 1.28177 + 1.58914i
\(89\) −2.46600 8.23703i −0.261396 0.873123i −0.983433 0.181269i \(-0.941979\pi\)
0.722038 0.691854i \(-0.243206\pi\)
\(90\) 0 0
\(91\) 6.87450 + 7.28654i 0.720643 + 0.763837i
\(92\) −22.5932 17.5111i −2.35551 1.82566i
\(93\) 0 0
\(94\) 12.8787 26.9335i 1.32834 2.77798i
\(95\) 0.897036 9.22234i 0.0920340 0.946192i
\(96\) 0 0
\(97\) 4.01124 0.155654i 0.407279 0.0158043i 0.165678 0.986180i \(-0.447019\pi\)
0.241601 + 0.970376i \(0.422327\pi\)
\(98\) −11.3163 + 7.44284i −1.14312 + 0.751841i
\(99\) 0 0
\(100\) 34.1276 17.1395i 3.41276 1.71395i
\(101\) −0.0135561 + 0.698949i −0.00134888 + 0.0695480i 0.998533 + 0.0541536i \(0.0172461\pi\)
−0.999881 + 0.0153944i \(0.995100\pi\)
\(102\) 0 0
\(103\) −4.73288 + 3.66826i −0.466344 + 0.361444i −0.818509 0.574494i \(-0.805199\pi\)
0.352165 + 0.935938i \(0.385446\pi\)
\(104\) 24.2077 + 3.78601i 2.37376 + 0.371249i
\(105\) 0 0
\(106\) 3.79853 + 7.94395i 0.368946 + 0.771584i
\(107\) −14.7855 + 5.38148i −1.42937 + 0.520247i −0.936750 0.349999i \(-0.886182\pi\)
−0.492617 + 0.870246i \(0.663960\pi\)
\(108\) 0 0
\(109\) −7.14750 2.60148i −0.684606 0.249176i −0.0237821 0.999717i \(-0.507571\pi\)
−0.660824 + 0.750541i \(0.729793\pi\)
\(110\) 2.05741 + 21.1520i 0.196166 + 2.01677i
\(111\) 0 0
\(112\) −13.9410 + 40.7441i −1.31730 + 3.84995i
\(113\) 13.2652 + 12.0375i 1.24788 + 1.13239i 0.985903 + 0.167319i \(0.0535110\pi\)
0.261979 + 0.965074i \(0.415625\pi\)
\(114\) 0 0
\(115\) −6.29722 18.4043i −0.587219 1.71621i
\(116\) −7.70226 + 17.8558i −0.715137 + 1.65787i
\(117\) 0 0
\(118\) −30.2332 3.53376i −2.78319 0.325309i
\(119\) 6.57361 + 2.10774i 0.602602 + 0.193217i
\(120\) 0 0
\(121\) 5.69824 + 1.58621i 0.518021 + 0.144201i
\(122\) −8.63451 2.40358i −0.781732 0.217610i
\(123\) 0 0
\(124\) −39.4467 12.6481i −3.54242 1.13583i
\(125\) 8.33528 + 0.974254i 0.745530 + 0.0871400i
\(126\) 0 0
\(127\) −0.563057 + 1.30531i −0.0499632 + 0.115828i −0.941370 0.337377i \(-0.890460\pi\)
0.891406 + 0.453205i \(0.149719\pi\)
\(128\) 5.65970 + 16.5411i 0.500252 + 1.46204i
\(129\) 0 0
\(130\) 20.1339 + 18.2706i 1.76586 + 1.60243i
\(131\) 2.22093 6.49092i 0.194044 0.567114i −0.805636 0.592411i \(-0.798176\pi\)
0.999680 + 0.0252962i \(0.00805289\pi\)
\(132\) 0 0
\(133\) 0.885119 + 9.09982i 0.0767496 + 0.789054i
\(134\) 17.5400 + 6.38406i 1.51523 + 0.551498i
\(135\) 0 0
\(136\) 15.8663 5.77487i 1.36053 0.495191i
\(137\) 4.48316 + 9.37572i 0.383022 + 0.801022i 0.999902 + 0.0139655i \(0.00444550\pi\)
−0.616881 + 0.787057i \(0.711604\pi\)
\(138\) 0 0
\(139\) −12.4487 1.94695i −1.05589 0.165138i −0.397336 0.917673i \(-0.630065\pi\)
−0.658552 + 0.752535i \(0.728831\pi\)
\(140\) −49.9499 + 38.7141i −4.22154 + 3.27194i
\(141\) 0 0
\(142\) −0.609525 + 31.4269i −0.0511502 + 2.63729i
\(143\) −5.81352 + 2.91966i −0.486151 + 0.244154i
\(144\) 0 0
\(145\) −11.0561 + 7.27169i −0.918157 + 0.603881i
\(146\) −15.3867 + 0.597072i −1.27341 + 0.0494141i
\(147\) 0 0
\(148\) 0.290998 2.99172i 0.0239199 0.245918i
\(149\) 0.0524588 0.109708i 0.00429759 0.00898765i −0.900007 0.435875i \(-0.856439\pi\)
0.904305 + 0.426887i \(0.140390\pi\)
\(150\) 0 0
\(151\) 2.39813 + 1.85869i 0.195157 + 0.151258i 0.705493 0.708717i \(-0.250726\pi\)
−0.510336 + 0.859975i \(0.670479\pi\)
\(152\) 15.3459 + 16.2657i 1.24471 + 1.31932i
\(153\) 0 0
\(154\) −6.01413 20.0886i −0.484632 1.61878i
\(155\) −17.6977 21.9417i −1.42151 1.76240i
\(156\) 0 0
\(157\) 10.3424 16.4094i 0.825417 1.30961i −0.122941 0.992414i \(-0.539233\pi\)
0.948359 0.317200i \(-0.102743\pi\)
\(158\) 5.18576 + 2.86138i 0.412557 + 0.227639i
\(159\) 0 0
\(160\) −14.2421 + 55.2913i −1.12594 + 4.37116i
\(161\) 9.59671 + 16.6220i 0.756326 + 1.31000i
\(162\) 0 0
\(163\) 11.6564 20.1895i 0.913001 1.58136i 0.103199 0.994661i \(-0.467092\pi\)
0.809802 0.586703i \(-0.199575\pi\)
\(164\) −6.74875 6.61913i −0.526989 0.516867i
\(165\) 0 0
\(166\) 0.828540 + 42.7193i 0.0643072 + 3.31566i
\(167\) −9.40517 17.8553i −0.727794 1.38168i −0.916655 0.399679i \(-0.869122\pi\)
0.188861 0.982004i \(-0.439520\pi\)
\(168\) 0 0
\(169\) 1.68468 4.36344i 0.129591 0.335649i
\(170\) 18.2306 + 4.32073i 1.39822 + 0.331385i
\(171\) 0 0
\(172\) 1.60766 5.36996i 0.122583 0.409456i
\(173\) 6.03559 2.46581i 0.458877 0.187472i −0.136961 0.990576i \(-0.543734\pi\)
0.595838 + 0.803105i \(0.296820\pi\)
\(174\) 0 0
\(175\) −25.5656 + 1.98711i −1.93258 + 0.150212i
\(176\) −22.7513 16.2617i −1.71495 1.22577i
\(177\) 0 0
\(178\) 12.2775 + 19.4795i 0.920235 + 1.46005i
\(179\) −0.101316 1.73952i −0.00757268 0.130018i −0.999976 0.00698754i \(-0.997776\pi\)
0.992403 0.123030i \(-0.0392613\pi\)
\(180\) 0 0
\(181\) −9.71472 6.38947i −0.722090 0.474926i 0.134507 0.990913i \(-0.457055\pi\)
−0.856597 + 0.515987i \(0.827425\pi\)
\(182\) −22.9682 13.8614i −1.70252 1.02747i
\(183\) 0 0
\(184\) 43.4581 + 17.7546i 3.20377 + 1.30888i
\(185\) 1.28416 1.59211i 0.0944136 0.117054i
\(186\) 0 0
\(187\) −2.53563 + 3.69703i −0.185423 + 0.270354i
\(188\) −10.0112 + 56.7766i −0.730145 + 4.14086i
\(189\) 0 0
\(190\) 4.30885 + 24.4367i 0.312597 + 1.77282i
\(191\) 2.81476 + 1.27946i 0.203669 + 0.0925787i 0.513048 0.858360i \(-0.328516\pi\)
−0.309379 + 0.950939i \(0.600121\pi\)
\(192\) 0 0
\(193\) 9.00633 1.76879i 0.648290 0.127320i 0.142251 0.989831i \(-0.454566\pi\)
0.506039 + 0.862511i \(0.331109\pi\)
\(194\) −10.2367 + 3.28227i −0.734952 + 0.235653i
\(195\) 0 0
\(196\) 17.1983 19.7071i 1.22845 1.40765i
\(197\) 2.39351 + 3.21504i 0.170530 + 0.229062i 0.879170 0.476509i \(-0.158098\pi\)
−0.708639 + 0.705571i \(0.750691\pi\)
\(198\) 0 0
\(199\) 6.53734 + 15.1553i 0.463420 + 1.07433i 0.976408 + 0.215932i \(0.0692791\pi\)
−0.512989 + 0.858395i \(0.671462\pi\)
\(200\) −46.4463 + 42.1477i −3.28425 + 2.98030i
\(201\) 0 0
\(202\) −0.466982 1.81294i −0.0328567 0.127558i
\(203\) 9.32197 9.14293i 0.654274 0.641708i
\(204\) 0 0
\(205\) −1.36183 6.28689i −0.0951141 0.439096i
\(206\) 9.57584 12.8626i 0.667181 0.896179i
\(207\) 0 0
\(208\) −35.5349 + 4.15344i −2.46391 + 0.287989i
\(209\) −5.82608 1.14420i −0.402998 0.0791462i
\(210\) 0 0
\(211\) −5.29295 + 24.4350i −0.364382 + 1.68217i 0.315559 + 0.948906i \(0.397808\pi\)
−0.679941 + 0.733267i \(0.737994\pi\)
\(212\) −11.1807 12.8117i −0.767897 0.879912i
\(213\) 0 0
\(214\) 34.2799 24.5018i 2.34333 1.67491i
\(215\) 2.92206 2.45190i 0.199283 0.167218i
\(216\) 0 0
\(217\) 21.3075 + 17.8791i 1.44644 + 1.21371i
\(218\) 20.3079 + 1.57846i 1.37543 + 0.106907i
\(219\) 0 0
\(220\) −14.7817 38.2857i −0.996584 2.58122i
\(221\) 0.776156 + 5.68247i 0.0522099 + 0.382244i
\(222\) 0 0
\(223\) −8.91346 + 4.91824i −0.596889 + 0.329350i −0.752625 0.658449i \(-0.771213\pi\)
0.155736 + 0.987799i \(0.450225\pi\)
\(224\) 3.27574 56.2423i 0.218870 3.75785i
\(225\) 0 0
\(226\) −42.8673 21.5288i −2.85149 1.43207i
\(227\) −3.74958 + 7.11840i −0.248868 + 0.472465i −0.977076 0.212892i \(-0.931712\pi\)
0.728208 + 0.685357i \(0.240354\pi\)
\(228\) 0 0
\(229\) 11.9353 5.42525i 0.788706 0.358511i 0.0213826 0.999771i \(-0.493193\pi\)
0.767323 + 0.641261i \(0.221588\pi\)
\(230\) 29.4632 + 42.9584i 1.94275 + 2.83260i
\(231\) 0 0
\(232\) 4.32202 31.6428i 0.283755 2.07745i
\(233\) 12.6130 2.98934i 0.826306 0.195838i 0.204358 0.978896i \(-0.434489\pi\)
0.621948 + 0.783058i \(0.286341\pi\)
\(234\) 0 0
\(235\) −26.9228 + 28.5365i −1.75625 + 1.86152i
\(236\) 58.0758 9.08289i 3.78041 0.591246i
\(237\) 0 0
\(238\) −18.4728 0.716828i −1.19741 0.0464651i
\(239\) 12.2967 7.42110i 0.795408 0.480031i −0.0598666 0.998206i \(-0.519068\pi\)
0.855274 + 0.518175i \(0.173389\pi\)
\(240\) 0 0
\(241\) −0.547763 + 0.152480i −0.0352845 + 0.00982212i −0.285770 0.958298i \(-0.592249\pi\)
0.250485 + 0.968120i \(0.419410\pi\)
\(242\) −15.8399 −1.01823
\(243\) 0 0
\(244\) 17.3084 1.10805
\(245\) 17.1472 4.77326i 1.09550 0.304953i
\(246\) 0 0
\(247\) −6.50329 + 3.92475i −0.413794 + 0.249726i
\(248\) 67.9810 + 2.63797i 4.31680 + 0.167511i
\(249\) 0 0
\(250\) −22.2036 + 3.47259i −1.40428 + 0.219626i
\(251\) −10.3643 + 10.9855i −0.654189 + 0.693399i −0.966525 0.256572i \(-0.917407\pi\)
0.312337 + 0.949972i \(0.398888\pi\)
\(252\) 0 0
\(253\) −12.1283 + 2.87447i −0.762503 + 0.180716i
\(254\) 0.515196 3.77190i 0.0323263 0.236670i
\(255\) 0 0
\(256\) −5.38877 7.85702i −0.336798 0.491064i
\(257\) −17.8094 + 8.09537i −1.11092 + 0.504975i −0.883316 0.468778i \(-0.844694\pi\)
−0.227605 + 0.973754i \(0.573089\pi\)
\(258\) 0 0
\(259\) −0.940608 + 1.78570i −0.0584465 + 0.110958i
\(260\) −46.9189 23.5636i −2.90979 1.46135i
\(261\) 0 0
\(262\) −1.06823 + 18.3407i −0.0659952 + 1.13309i
\(263\) 8.12111 4.48104i 0.500769 0.276313i −0.212552 0.977150i \(-0.568178\pi\)
0.713321 + 0.700837i \(0.247190\pi\)
\(264\) 0 0
\(265\) −1.56597 11.4650i −0.0961970 0.704286i
\(266\) −8.81860 22.8407i −0.540703 1.40046i
\(267\) 0 0
\(268\) −35.9376 2.79329i −2.19524 0.170627i
\(269\) 4.50400 + 3.77930i 0.274614 + 0.230428i 0.769685 0.638424i \(-0.220413\pi\)
−0.495071 + 0.868853i \(0.664858\pi\)
\(270\) 0 0
\(271\) −13.8736 + 11.6414i −0.842764 + 0.707163i −0.958184 0.286154i \(-0.907623\pi\)
0.115420 + 0.993317i \(0.463179\pi\)
\(272\) −20.0575 + 14.3363i −1.21617 + 0.869264i
\(273\) 0 0
\(274\) −18.2992 20.9686i −1.10550 1.26676i
\(275\) 3.52540 16.2751i 0.212590 0.981424i
\(276\) 0 0
\(277\) −6.91358 1.35778i −0.415397 0.0815813i −0.0193527 0.999813i \(-0.506161\pi\)
−0.396044 + 0.918231i \(0.629617\pi\)
\(278\) 33.5144 3.91727i 2.01006 0.234942i
\(279\) 0 0
\(280\) 61.9777 83.2504i 3.70387 4.97516i
\(281\) 5.69383 + 26.2856i 0.339665 + 1.56807i 0.753331 + 0.657641i \(0.228446\pi\)
−0.413666 + 0.910429i \(0.635752\pi\)
\(282\) 0 0
\(283\) 8.50564 8.34227i 0.505608 0.495897i −0.402044 0.915620i \(-0.631700\pi\)
0.907652 + 0.419724i \(0.137873\pi\)
\(284\) −15.1413 58.7822i −0.898471 3.48808i
\(285\) 0 0
\(286\) 12.9014 11.7074i 0.762875 0.692272i
\(287\) 2.51401 + 5.82814i 0.148397 + 0.344024i
\(288\) 0 0
\(289\) −7.79159 10.4659i −0.458329 0.615643i
\(290\) 23.3011 26.7001i 1.36829 1.56788i
\(291\) 0 0
\(292\) 28.3160 9.07917i 1.65707 0.531318i
\(293\) −13.9083 + 2.73150i −0.812530 + 0.159576i −0.581684 0.813415i \(-0.697606\pi\)
−0.230846 + 0.972990i \(0.574149\pi\)
\(294\) 0 0
\(295\) 36.4152 + 16.5527i 2.12017 + 0.963737i
\(296\) 0.857214 + 4.86150i 0.0498245 + 0.282569i
\(297\) 0 0
\(298\) −0.0565493 + 0.320707i −0.00327581 + 0.0185781i
\(299\) −9.01911 + 13.1502i −0.521589 + 0.760495i
\(300\) 0 0
\(301\) −2.36296 + 2.92961i −0.136199 + 0.168860i
\(302\) −7.52172 3.07296i −0.432826 0.176829i
\(303\) 0 0
\(304\) −27.9560 16.8715i −1.60338 0.967647i
\(305\) 9.84059 + 6.47226i 0.563471 + 0.370600i
\(306\) 0 0
\(307\) 0.808201 + 13.8763i 0.0461264 + 0.791960i 0.939480 + 0.342605i \(0.111309\pi\)
−0.893353 + 0.449355i \(0.851654\pi\)
\(308\) 21.5921 + 34.2581i 1.23032 + 1.95204i
\(309\) 0 0
\(310\) 61.4153 + 43.8970i 3.48815 + 2.49318i
\(311\) 2.68794 0.208923i 0.152419 0.0118470i −0.00105605 0.999999i \(-0.500336\pi\)
0.153475 + 0.988152i \(0.450953\pi\)
\(312\) 0 0
\(313\) −11.9006 + 4.86193i −0.672661 + 0.274812i −0.688686 0.725059i \(-0.741812\pi\)
0.0160253 + 0.999872i \(0.494899\pi\)
\(314\) −14.8977 + 49.7617i −0.840725 + 2.80822i
\(315\) 0 0
\(316\) −11.1294 2.63772i −0.626078 0.148383i
\(317\) −8.91302 + 23.0853i −0.500605 + 1.29660i 0.420502 + 0.907292i \(0.361854\pi\)
−0.921107 + 0.389309i \(0.872714\pi\)
\(318\) 0 0
\(319\) 3.95180 + 7.50232i 0.221259 + 0.420049i
\(320\) −1.27238 65.6034i −0.0711280 3.66734i
\(321\) 0 0
\(322\) −36.6955 35.9907i −2.04496 2.00568i
\(323\) −2.61719 + 4.53310i −0.145624 + 0.252228i
\(324\) 0 0
\(325\) −10.6520 18.4498i −0.590866 1.02341i
\(326\) −15.5729 + 60.4575i −0.862501 + 3.34843i
\(327\) 0 0
\(328\) 13.5927 + 7.50014i 0.750532 + 0.414126i
\(329\) 20.6409 32.7490i 1.13797 1.80551i
\(330\) 0 0
\(331\) −2.68057 3.32339i −0.147338 0.182670i 0.699319 0.714810i \(-0.253487\pi\)
−0.846656 + 0.532140i \(0.821388\pi\)
\(332\) −23.6647 79.0457i −1.29877 4.33820i
\(333\) 0 0
\(334\) 37.0871 + 39.3100i 2.02931 + 2.15095i
\(335\) −19.3876 15.0265i −1.05926 0.820988i
\(336\) 0 0
\(337\) −4.76025 + 9.95522i −0.259307 + 0.542295i −0.990110 0.140294i \(-0.955195\pi\)
0.730803 + 0.682589i \(0.239146\pi\)
\(338\) −1.21264 + 12.4670i −0.0659587 + 0.678115i
\(339\) 0 0
\(340\) −36.1537 + 1.40293i −1.96071 + 0.0760844i
\(341\) −15.0916 + 9.92588i −0.817254 + 0.537517i
\(342\) 0 0
\(343\) 6.02689 3.02682i 0.325422 0.163433i
\(344\) −0.178514 + 9.20411i −0.00962481 + 0.496253i
\(345\) 0 0
\(346\) −13.8002 + 10.6960i −0.741904 + 0.575019i
\(347\) 20.3801 + 3.18739i 1.09406 + 0.171108i 0.675703 0.737174i \(-0.263840\pi\)
0.418358 + 0.908282i \(0.362606\pi\)
\(348\) 0 0
\(349\) 13.2299 + 27.6680i 0.708182 + 1.48104i 0.869396 + 0.494117i \(0.164508\pi\)
−0.161214 + 0.986919i \(0.551541\pi\)
\(350\) 64.5289 23.4866i 3.44922 1.25541i
\(351\) 0 0
\(352\) 34.3796 + 12.5131i 1.83244 + 0.666953i
\(353\) −1.56304 16.0694i −0.0831921 0.855289i −0.940344 0.340225i \(-0.889497\pi\)
0.857152 0.515064i \(-0.172232\pi\)
\(354\) 0 0
\(355\) 13.3724 39.0823i 0.709732 2.07427i
\(356\) −32.9289 29.8814i −1.74523 1.58371i
\(357\) 0 0
\(358\) 1.51063 + 4.41499i 0.0798393 + 0.233339i
\(359\) 5.07277 11.7600i 0.267730 0.620669i −0.730318 0.683107i \(-0.760628\pi\)
0.998049 + 0.0624379i \(0.0198875\pi\)
\(360\) 0 0
\(361\) 11.9859 + 1.40095i 0.630838 + 0.0737344i
\(362\) 29.6514 + 9.50734i 1.55844 + 0.499695i
\(363\) 0 0
\(364\) 49.9085 + 13.8930i 2.61591 + 0.728189i
\(365\) 19.4940 + 5.42653i 1.02036 + 0.284038i
\(366\) 0 0
\(367\) 30.2454 + 9.69781i 1.57880 + 0.506221i 0.960159 0.279454i \(-0.0901533\pi\)
0.618640 + 0.785675i \(0.287684\pi\)
\(368\) −68.0838 7.95786i −3.54911 0.414832i
\(369\) 0 0
\(370\) −2.16959 + 5.02968i −0.112792 + 0.261481i
\(371\) 3.69629 + 10.8028i 0.191902 + 0.560854i
\(372\) 0 0
\(373\) −19.7351 17.9087i −1.02185 0.927277i −0.0244731 0.999700i \(-0.507791\pi\)
−0.997374 + 0.0724237i \(0.976927\pi\)
\(374\) 3.88655 11.3589i 0.200969 0.587353i
\(375\) 0 0
\(376\) −9.16633 94.2381i −0.472717 4.85996i
\(377\) 10.1938 + 3.71023i 0.525006 + 0.191087i
\(378\) 0 0
\(379\) −16.8995 + 6.15091i −0.868068 + 0.315951i −0.737385 0.675473i \(-0.763939\pi\)
−0.130684 + 0.991424i \(0.541717\pi\)
\(380\) −20.6713 43.2305i −1.06042 2.21768i
\(381\) 0 0
\(382\) −8.18057 1.27942i −0.418555 0.0654607i
\(383\) 12.3584 9.57846i 0.631483 0.489436i −0.245856 0.969306i \(-0.579069\pi\)
0.877340 + 0.479870i \(0.159316\pi\)
\(384\) 0 0
\(385\) −0.534359 + 27.5514i −0.0272335 + 1.40415i
\(386\) −21.9649 + 11.0312i −1.11799 + 0.561474i
\(387\) 0 0
\(388\) 17.3445 11.4077i 0.880534 0.579136i
\(389\) −29.9502 + 1.16220i −1.51854 + 0.0589261i −0.784476 0.620159i \(-0.787068\pi\)
−0.734060 + 0.679085i \(0.762377\pi\)
\(390\) 0 0
\(391\) −1.06381 + 10.9369i −0.0537991 + 0.553103i
\(392\) −18.5308 + 38.7540i −0.935949 + 1.95737i
\(393\) 0 0
\(394\) −8.48385 6.57548i −0.427410 0.331268i
\(395\) −5.34123 5.66138i −0.268747 0.284855i
\(396\) 0 0
\(397\) −5.23059 17.4714i −0.262516 0.876864i −0.983033 0.183427i \(-0.941281\pi\)
0.720518 0.693437i \(-0.243904\pi\)
\(398\) −27.7494 34.4038i −1.39095 1.72451i
\(399\) 0 0
\(400\) 48.8310 77.4756i 2.44155 3.87378i
\(401\) −2.07598 1.14548i −0.103670 0.0572024i 0.430430 0.902624i \(-0.358362\pi\)
−0.534100 + 0.845421i \(0.679349\pi\)
\(402\) 0 0
\(403\) −5.76425 + 22.3782i −0.287138 + 1.11474i
\(404\) 1.80765 + 3.13094i 0.0899338 + 0.155770i
\(405\) 0 0
\(406\) −17.4835 + 30.2822i −0.867690 + 1.50288i
\(407\) −0.935738 0.917765i −0.0463828 0.0454919i
\(408\) 0 0
\(409\) −0.117638 6.06536i −0.00581680 0.299913i −0.991411 0.130784i \(-0.958250\pi\)
0.985594 0.169128i \(-0.0540952\pi\)
\(410\) 8.02832 + 15.2414i 0.396490 + 0.752719i
\(411\) 0 0
\(412\) −11.1536 + 28.8886i −0.549499 + 1.42324i
\(413\) −38.4054 9.10225i −1.88981 0.447892i
\(414\) 0 0
\(415\) 16.1037 53.7902i 0.790501 2.64046i
\(416\) 43.3288 17.7018i 2.12437 0.867900i
\(417\) 0 0
\(418\) 15.8523 1.23214i 0.775360 0.0602657i
\(419\) 24.5351 + 17.5366i 1.19862 + 0.856720i 0.992552 0.121819i \(-0.0388727\pi\)
0.206064 + 0.978538i \(0.433934\pi\)
\(420\) 0 0
\(421\) −8.52740 13.5296i −0.415600 0.659395i 0.571297 0.820743i \(-0.306440\pi\)
−0.986897 + 0.161349i \(0.948416\pi\)
\(422\) −3.89301 66.8403i −0.189509 3.25374i
\(423\) 0 0
\(424\) 23.3321 + 15.3458i 1.13311 + 0.745257i
\(425\) −12.5692 7.58557i −0.609698 0.367954i
\(426\) 0 0
\(427\) −10.7586 4.39536i −0.520643 0.212706i
\(428\) −51.0853 + 63.3359i −2.46930 + 3.06145i
\(429\) 0 0
\(430\) −5.77770 + 8.42410i −0.278626 + 0.406246i
\(431\) −1.91990 + 10.8883i −0.0924782 + 0.524470i 0.903013 + 0.429614i \(0.141350\pi\)
−0.995491 + 0.0948563i \(0.969761\pi\)
\(432\) 0 0
\(433\) 5.97542 + 33.8883i 0.287160 + 1.62857i 0.697466 + 0.716618i \(0.254311\pi\)
−0.410306 + 0.911948i \(0.634578\pi\)
\(434\) −67.8106 30.8237i −3.25501 1.47958i
\(435\) 0 0
\(436\) −38.5982 + 7.58044i −1.84852 + 0.363037i
\(437\) −13.8584 + 4.44351i −0.662937 + 0.212562i
\(438\) 0 0
\(439\) −13.2555 + 15.1891i −0.632650 + 0.724937i −0.976842 0.213963i \(-0.931363\pi\)
0.344192 + 0.938899i \(0.388153\pi\)
\(440\) 40.2487 + 54.0634i 1.91878 + 2.57737i
\(441\) 0 0
\(442\) −6.08329 14.1027i −0.289353 0.670795i
\(443\) −11.7676 + 10.6785i −0.559094 + 0.507351i −0.901836 0.432079i \(-0.857780\pi\)
0.342742 + 0.939430i \(0.388644\pi\)
\(444\) 0 0
\(445\) −7.54779 29.3023i −0.357799 1.38906i
\(446\) 19.4635 19.0897i 0.921625 0.903924i
\(447\) 0 0
\(448\) 13.7066 + 63.2765i 0.647574 + 2.98953i
\(449\) −9.07259 + 12.1866i −0.428162 + 0.575122i −0.962887 0.269905i \(-0.913008\pi\)
0.534725 + 0.845026i \(0.320415\pi\)
\(450\) 0 0
\(451\) −4.09407 + 0.478528i −0.192782 + 0.0225330i
\(452\) 90.8993 + 17.8520i 4.27554 + 0.839689i
\(453\) 0 0
\(454\) 4.56131 21.0574i 0.214073 0.988271i
\(455\) 23.1801 + 26.5615i 1.08670 + 1.24522i
\(456\) 0 0
\(457\) 23.9805 17.1402i 1.12176 0.801786i 0.139670 0.990198i \(-0.455396\pi\)
0.982090 + 0.188412i \(0.0603341\pi\)
\(458\) −26.8953 + 22.5679i −1.25674 + 1.05453i
\(459\) 0 0
\(460\) −77.0604 64.6614i −3.59296 3.01485i
\(461\) 28.8210 + 2.24014i 1.34233 + 0.104334i 0.728467 0.685081i \(-0.240233\pi\)
0.613860 + 0.789415i \(0.289616\pi\)
\(462\) 0 0
\(463\) 3.84725 + 9.96462i 0.178797 + 0.463095i 0.993090 0.117359i \(-0.0374429\pi\)
−0.814293 + 0.580454i \(0.802875\pi\)
\(464\) 6.31087 + 46.2037i 0.292975 + 2.14495i
\(465\) 0 0
\(466\) −30.3932 + 16.7702i −1.40794 + 0.776867i
\(467\) −0.270504 + 4.64438i −0.0125174 + 0.214916i 0.986249 + 0.165265i \(0.0528480\pi\)
−0.998767 + 0.0496511i \(0.984189\pi\)
\(468\) 0 0
\(469\) 21.6288 + 10.8624i 0.998725 + 0.501579i
\(470\) 48.9637 92.9554i 2.25853 4.28771i
\(471\) 0 0
\(472\) −87.8841 + 39.9482i −4.04520 + 1.83877i
\(473\) −1.38248 2.01570i −0.0635664 0.0926821i
\(474\) 0 0
\(475\) 2.63131 19.2646i 0.120733 0.883921i
\(476\) 34.7379 8.23304i 1.59221 0.377361i
\(477\) 0 0
\(478\) −26.3944 + 27.9765i −1.20725 + 1.27961i
\(479\) 9.57753 1.49790i 0.437609 0.0684407i 0.0681224 0.997677i \(-0.478299\pi\)
0.369486 + 0.929236i \(0.379534\pi\)
\(480\) 0 0
\(481\) −1.67553 0.0650182i −0.0763976 0.00296458i
\(482\) 1.30366 0.786760i 0.0593799 0.0358359i
\(483\) 0 0
\(484\) 29.4684 8.20310i 1.33947 0.372868i
\(485\) 14.1269 0.641469
\(486\) 0 0
\(487\) 30.6732 1.38994 0.694969 0.719040i \(-0.255418\pi\)
0.694969 + 0.719040i \(0.255418\pi\)
\(488\) −27.3844 + 7.62296i −1.23963 + 0.345075i
\(489\) 0 0
\(490\) −40.8098 + 24.6288i −1.84360 + 1.11262i
\(491\) −35.0800 1.36126i −1.58314 0.0614330i −0.767905 0.640564i \(-0.778701\pi\)
−0.815235 + 0.579131i \(0.803392\pi\)
\(492\) 0 0
\(493\) 7.38571 1.15510i 0.332635 0.0520232i
\(494\) 13.9591 14.7958i 0.628048 0.665692i
\(495\) 0 0
\(496\) −96.6605 + 22.9089i −4.34018 + 1.02864i
\(497\) −5.51582 + 40.3830i −0.247418 + 1.81142i
\(498\) 0 0
\(499\) −15.2857 22.2871i −0.684283 0.997709i −0.998825 0.0484651i \(-0.984567\pi\)
0.314542 0.949244i \(-0.398149\pi\)
\(500\) 39.5092 17.9591i 1.76690 0.803156i
\(501\) 0 0
\(502\) 18.8493 35.7844i 0.841284 1.59714i
\(503\) 15.9307 + 8.00071i 0.710316 + 0.356734i 0.766990 0.641659i \(-0.221753\pi\)
−0.0566747 + 0.998393i \(0.518050\pi\)
\(504\) 0 0
\(505\) −0.143047 + 2.45603i −0.00636553 + 0.109292i
\(506\) 29.2253 16.1258i 1.29922 0.716881i
\(507\) 0 0
\(508\) 0.994911 + 7.28404i 0.0441421 + 0.323177i
\(509\) −12.4098 32.1422i −0.550055 1.42468i −0.877394 0.479771i \(-0.840720\pi\)
0.327339 0.944907i \(-0.393848\pi\)
\(510\) 0 0
\(511\) −19.9063 1.54724i −0.880605 0.0684460i
\(512\) −7.23991 6.07501i −0.319962 0.268480i
\(513\) 0 0
\(514\) 40.1323 33.6750i 1.77016 1.48534i
\(515\) −17.1439 + 12.2537i −0.755450 + 0.539963i
\(516\) 0 0
\(517\) 16.5296 + 18.9408i 0.726969 + 0.833014i
\(518\) 1.14424 5.28239i 0.0502749 0.232095i
\(519\) 0 0
\(520\) 84.6105 + 16.6170i 3.71042 + 0.728702i
\(521\) −1.59725 + 0.186692i −0.0699768 + 0.00817912i −0.151009 0.988532i \(-0.548252\pi\)
0.0810325 + 0.996711i \(0.474178\pi\)
\(522\) 0 0
\(523\) 25.3488 34.0494i 1.10843 1.48888i 0.255527 0.966802i \(-0.417751\pi\)
0.852900 0.522074i \(-0.174842\pi\)
\(524\) −7.51091 34.6742i −0.328116 1.51475i
\(525\) 0 0
\(526\) −17.7334 + 17.3927i −0.773211 + 0.758360i
\(527\) 3.97222 + 15.4211i 0.173032 + 0.671753i
\(528\) 0 0
\(529\) −5.59247 + 5.07490i −0.243151 + 0.220648i
\(530\) 12.2737 + 28.4535i 0.533133 + 1.23594i
\(531\) 0 0
\(532\) 28.2348 + 37.9259i 1.22413 + 1.64429i
\(533\) −3.46730 + 3.97309i −0.150185 + 0.172093i
\(534\) 0 0
\(535\) −52.7280 + 16.9066i −2.27963 + 0.730935i
\(536\) 58.0887 11.4083i 2.50905 0.492762i
\(537\) 0 0
\(538\) −14.3339 6.51555i −0.617978 0.280905i
\(539\) −1.98052 11.2321i −0.0853070 0.483800i
\(540\) 0 0
\(541\) 2.24013 12.7044i 0.0963107 0.546205i −0.898027 0.439940i \(-0.855000\pi\)
0.994338 0.106265i \(-0.0338892\pi\)
\(542\) 27.4319 39.9967i 1.17830 1.71801i
\(543\) 0 0
\(544\) 20.2495 25.1055i 0.868192 1.07639i
\(545\) −24.7794 10.1235i −1.06143 0.433644i
\(546\) 0 0
\(547\) 5.98649 + 3.61286i 0.255964 + 0.154475i 0.638876 0.769310i \(-0.279400\pi\)
−0.382912 + 0.923785i \(0.625079\pi\)
\(548\) 44.9029 + 29.5331i 1.91816 + 1.26159i
\(549\) 0 0
\(550\) 2.59296 + 44.5194i 0.110564 + 1.89832i
\(551\) 5.27906 + 8.37580i 0.224896 + 0.356821i
\(552\) 0 0
\(553\) 6.24800 + 4.46581i 0.265692 + 0.189905i
\(554\) 18.8113 1.46213i 0.799215 0.0621199i
\(555\) 0 0
\(556\) −60.3214 + 24.6440i −2.55820 + 1.04514i
\(557\) 9.55467 31.9148i 0.404844 1.35227i −0.476240 0.879315i \(-0.658001\pi\)
0.881084 0.472959i \(-0.156814\pi\)
\(558\) 0 0
\(559\) −3.04268 0.721129i −0.128692 0.0305005i
\(560\) −54.5838 + 141.376i −2.30659 + 5.97421i
\(561\) 0 0
\(562\) −33.5666 63.7246i −1.41592 2.68806i
\(563\) 0.796122 + 41.0478i 0.0335525 + 1.72996i 0.518208 + 0.855255i \(0.326599\pi\)
−0.484656 + 0.874705i \(0.661055\pi\)
\(564\) 0 0
\(565\) 45.0048 + 44.1404i 1.89337 + 1.85700i
\(566\) −15.9524 + 27.6304i −0.670530 + 1.16139i
\(567\) 0 0
\(568\) 49.8447 + 86.3335i 2.09144 + 3.62247i
\(569\) 7.25036 28.1476i 0.303951 1.18001i −0.615927 0.787803i \(-0.711218\pi\)
0.919877 0.392206i \(-0.128288\pi\)
\(570\) 0 0
\(571\) 17.1842 + 9.48182i 0.719135 + 0.396802i 0.800061 0.599918i \(-0.204800\pi\)
−0.0809266 + 0.996720i \(0.525788\pi\)
\(572\) −17.9387 + 28.4617i −0.750055 + 1.19004i
\(573\) 0 0
\(574\) −10.6714 13.2304i −0.445414 0.552226i
\(575\) −11.7067 39.1029i −0.488201 1.63071i
\(576\) 0 0
\(577\) −1.52241 1.61366i −0.0633786 0.0671774i 0.694908 0.719098i \(-0.255445\pi\)
−0.758287 + 0.651921i \(0.773963\pi\)
\(578\) 27.6175 + 21.4052i 1.14874 + 0.890338i
\(579\) 0 0
\(580\) −29.5219 + 61.7397i −1.22583 + 2.56360i
\(581\) −5.36363 + 55.1429i −0.222521 + 2.28771i
\(582\) 0 0
\(583\) −7.40913 + 0.287508i −0.306855 + 0.0119074i
\(584\) −40.8015 + 26.8356i −1.68838 + 1.11046i
\(585\) 0 0
\(586\) 33.9200 17.0352i 1.40122 0.703719i
\(587\) −0.00727026 + 0.374853i −0.000300076 + 0.0154718i −0.999932 0.0116548i \(-0.996290\pi\)
0.999632 + 0.0271267i \(0.00863574\pi\)
\(588\) 0 0
\(589\) −16.6698 + 12.9201i −0.686868 + 0.532363i
\(590\) −105.834 16.5521i −4.35712 0.681441i
\(591\) 0 0
\(592\) −3.10947 6.50291i −0.127798 0.267268i
\(593\) 2.72790 0.992874i 0.112021 0.0407724i −0.285401 0.958408i \(-0.592127\pi\)
0.397423 + 0.917636i \(0.369905\pi\)
\(594\) 0 0
\(595\) 22.8287 + 8.30898i 0.935887 + 0.340635i
\(596\) −0.0608826 0.625927i −0.00249385 0.0256390i
\(597\) 0 0
\(598\) 13.8243 40.4030i 0.565317 1.65220i
\(599\) 5.40057 + 4.90076i 0.220661 + 0.200240i 0.774838 0.632159i \(-0.217831\pi\)
−0.554177 + 0.832399i \(0.686967\pi\)
\(600\) 0 0
\(601\) −5.11858 14.9596i −0.208791 0.610215i 0.791208 0.611547i \(-0.209452\pi\)
−0.999999 + 0.00133218i \(0.999576\pi\)
\(602\) 3.99222 9.25501i 0.162711 0.377206i
\(603\) 0 0
\(604\) 15.5848 + 1.82160i 0.634136 + 0.0741198i
\(605\) 19.8216 + 6.35554i 0.805863 + 0.258390i
\(606\) 0 0
\(607\) 42.1352 + 11.7291i 1.71021 + 0.476071i 0.978621 0.205670i \(-0.0659375\pi\)
0.731593 + 0.681741i \(0.238777\pi\)
\(608\) 41.1531 + 11.4557i 1.66898 + 0.464592i
\(609\) 0 0
\(610\) −30.0356 9.63052i −1.21611 0.389928i
\(611\) 31.9437 + 3.73368i 1.29230 + 0.151049i
\(612\) 0 0
\(613\) −6.48640 + 15.0372i −0.261983 + 0.607346i −0.997539 0.0701190i \(-0.977662\pi\)
0.735555 + 0.677465i \(0.236921\pi\)
\(614\) −12.0504 35.2186i −0.486314 1.42131i
\(615\) 0 0
\(616\) −49.2498 44.6918i −1.98433 1.80068i
\(617\) −2.28849 + 6.68838i −0.0921313 + 0.269264i −0.982586 0.185808i \(-0.940510\pi\)
0.890455 + 0.455072i \(0.150386\pi\)
\(618\) 0 0
\(619\) 0.587886 + 6.04400i 0.0236291 + 0.242929i 0.999678 + 0.0253771i \(0.00807866\pi\)
−0.976049 + 0.217552i \(0.930193\pi\)
\(620\) −136.990 49.8603i −5.50165 2.00244i
\(621\) 0 0
\(622\) −6.78452 + 2.46936i −0.272034 + 0.0990124i
\(623\) 12.8798 + 26.9358i 0.516019 + 1.07916i
\(624\) 0 0
\(625\) −7.30143 1.14192i −0.292057 0.0456769i
\(626\) 27.2104 21.0897i 1.08755 0.842912i
\(627\) 0 0
\(628\) 1.94515 100.292i 0.0776201 4.00207i
\(629\) −1.03259 + 0.518587i −0.0411721 + 0.0206774i
\(630\) 0 0
\(631\) −22.1240 + 14.5512i −0.880743 + 0.579274i −0.907352 0.420372i \(-0.861899\pi\)
0.0266090 + 0.999646i \(0.491529\pi\)
\(632\) 18.7701 0.728364i 0.746633 0.0289728i
\(633\) 0 0
\(634\) 6.41560 65.9582i 0.254796 2.61953i
\(635\) −2.15813 + 4.51334i −0.0856427 + 0.179107i
\(636\) 0 0
\(637\) −11.5327 8.93854i −0.456944 0.354158i
\(638\) −15.5830 16.5170i −0.616937 0.653915i
\(639\) 0 0
\(640\) 17.6454 + 58.9397i 0.697495 + 2.32980i
\(641\) 18.0665 + 22.3989i 0.713584 + 0.884705i 0.997242 0.0742202i \(-0.0236468\pi\)
−0.283658 + 0.958926i \(0.591548\pi\)
\(642\) 0 0
\(643\) −18.0533 + 28.6435i −0.711952 + 1.12959i 0.273865 + 0.961768i \(0.411698\pi\)
−0.985818 + 0.167821i \(0.946327\pi\)
\(644\) 86.9068 + 47.9532i 3.42461 + 1.88962i
\(645\) 0 0
\(646\) 3.49653 13.5744i 0.137569 0.534077i
\(647\) −7.77654 13.4694i −0.305727 0.529535i 0.671696 0.740827i \(-0.265566\pi\)
−0.977423 + 0.211292i \(0.932233\pi\)
\(648\) 0 0
\(649\) 12.8158 22.1976i 0.503064 0.871333i
\(650\) 40.7306 + 39.9483i 1.59759 + 1.56690i
\(651\) 0 0
\(652\) −2.33786 120.540i −0.0915578 4.72070i
\(653\) 4.79220 + 9.09776i 0.187533 + 0.356023i 0.960436 0.278502i \(-0.0898378\pi\)
−0.772903 + 0.634525i \(0.781196\pi\)
\(654\) 0 0
\(655\) 8.69573 22.5225i 0.339770 0.880027i
\(656\) −22.0575 5.22772i −0.861200 0.204108i
\(657\) 0 0
\(658\) −29.7320 + 99.3117i −1.15907 + 3.87157i
\(659\) 12.4153 5.07221i 0.483631 0.197585i −0.123253 0.992375i \(-0.539333\pi\)
0.606884 + 0.794790i \(0.292419\pi\)
\(660\) 0 0
\(661\) 15.2379 1.18438i 0.592685 0.0460671i 0.222352 0.974966i \(-0.428626\pi\)
0.370333 + 0.928899i \(0.379244\pi\)
\(662\) 9.30225 + 6.64885i 0.361542 + 0.258415i
\(663\) 0 0
\(664\) 72.2545 + 114.639i 2.80402 + 4.44888i
\(665\) 1.87081 + 32.1206i 0.0725470 + 1.24558i
\(666\) 0 0
\(667\) 17.3651 + 11.4212i 0.672380 + 0.442231i
\(668\) −89.3543 53.9256i −3.45722 2.08644i
\(669\) 0 0
\(670\) 60.8091 + 24.8432i 2.34926 + 0.959778i
\(671\) 4.73826 5.87452i 0.182918 0.226783i
\(672\) 0 0
\(673\) 11.5361 16.8201i 0.444685 0.648366i −0.535941 0.844255i \(-0.680043\pi\)
0.980626 + 0.195889i \(0.0627593\pi\)
\(674\) 5.13144 29.1018i 0.197656 1.12096i
\(675\) 0 0
\(676\) −4.20038 23.8215i −0.161553 0.916212i
\(677\) −13.4120 6.09652i −0.515466 0.234308i 0.139147 0.990272i \(-0.455564\pi\)
−0.654614 + 0.755963i \(0.727169\pi\)
\(678\) 0 0
\(679\) −13.6779 + 2.68626i −0.524911 + 0.103089i
\(680\) 56.5826 18.1425i 2.16984 0.695732i
\(681\) 0 0
\(682\) 31.8060 36.4456i 1.21792 1.39558i
\(683\) −23.8037 31.9739i −0.910822 1.22345i −0.974253 0.225459i \(-0.927612\pi\)
0.0634310 0.997986i \(-0.479796\pi\)
\(684\) 0 0
\(685\) 14.4858 + 33.5818i 0.553474 + 1.28310i
\(686\) −13.3749 + 12.1371i −0.510656 + 0.463395i
\(687\) 0 0
\(688\) −3.35300 13.0171i −0.127832 0.496274i
\(689\) −6.77220 + 6.64213i −0.258000 + 0.253045i
\(690\) 0 0
\(691\) −0.264884 1.22284i −0.0100766 0.0465190i 0.972019 0.234903i \(-0.0754774\pi\)
−0.982095 + 0.188384i \(0.939675\pi\)
\(692\) 20.1347 27.0455i 0.765405 1.02812i
\(693\) 0 0
\(694\) −54.8671 + 6.41305i −2.08273 + 0.243436i
\(695\) −43.5108 8.54524i −1.65046 0.324139i
\(696\) 0 0
\(697\) −0.769309 + 3.55152i −0.0291396 + 0.134524i
\(698\) −54.0015 61.8789i −2.04399 2.34215i
\(699\) 0 0
\(700\) −107.886 + 77.1124i −4.07771 + 2.91457i
\(701\) 2.95564 2.48008i 0.111633 0.0936713i −0.585262 0.810844i \(-0.699009\pi\)
0.696896 + 0.717173i \(0.254564\pi\)
\(702\) 0 0
\(703\) −1.17232 0.983695i −0.0442149 0.0371007i
\(704\) −41.9187 3.25818i −1.57987 0.122797i
\(705\) 0 0
\(706\) 15.5728 + 40.3346i 0.586091 + 1.51801i
\(707\) −0.328518 2.40518i −0.0123552 0.0904559i
\(708\) 0 0
\(709\) 7.26991 4.01136i 0.273027 0.150650i −0.340691 0.940175i \(-0.610661\pi\)
0.613718 + 0.789525i \(0.289673\pi\)
\(710\) −6.43186 + 110.431i −0.241383 + 4.14439i
\(711\) 0 0
\(712\) 65.2588 + 32.7742i 2.44568 + 1.22826i
\(713\) −20.6343 + 39.1732i −0.772760 + 1.46705i
\(714\) 0 0
\(715\) −20.8419 + 9.47380i −0.779442 + 0.354300i
\(716\) −5.09679 7.43130i −0.190476 0.277721i
\(717\) 0 0
\(718\) −4.64158 + 33.9824i −0.173222 + 1.26821i
\(719\) −16.2321 + 3.84707i −0.605354 + 0.143472i −0.521852 0.853036i \(-0.674759\pi\)
−0.0835020 + 0.996508i \(0.526610\pi\)
\(720\) 0 0
\(721\) 14.2690 15.1242i 0.531404 0.563256i
\(722\) −31.9283 + 4.99350i −1.18825 + 0.185839i
\(723\) 0 0
\(724\) −60.0870 2.33165i −2.23311 0.0866550i
\(725\) −23.7743 + 14.3478i −0.882954 + 0.532866i
\(726\) 0 0
\(727\) −51.5142 + 14.3400i −1.91056 + 0.531840i −0.920592 + 0.390525i \(0.872294\pi\)
−0.989965 + 0.141315i \(0.954867\pi\)
\(728\) −85.0813 −3.15332
\(729\) 0 0
\(730\) −54.1892 −2.00563
\(731\) −2.07591 + 0.577868i −0.0767802 + 0.0213732i
\(732\) 0 0
\(733\) 20.3675 12.2919i 0.752292 0.454010i −0.0880168 0.996119i \(-0.528053\pi\)
0.840308 + 0.542109i \(0.182374\pi\)
\(734\) −84.9940 3.29815i −3.13718 0.121737i
\(735\) 0 0
\(736\) 88.6005 13.8569i 3.26586 0.510771i
\(737\) −10.7862 + 11.4327i −0.397313 + 0.421128i
\(738\) 0 0
\(739\) −12.6011 + 2.98652i −0.463540 + 0.109861i −0.455748 0.890109i \(-0.650628\pi\)
−0.00779154 + 0.999970i \(0.502480\pi\)
\(740\) 1.43155 10.4808i 0.0526247 0.385281i
\(741\) 0 0
\(742\) −17.2941 25.2154i −0.634886 0.925686i
\(743\) −2.51318 + 1.14238i −0.0921997 + 0.0419099i −0.459380 0.888240i \(-0.651928\pi\)
0.367180 + 0.930150i \(0.380323\pi\)
\(744\) 0 0
\(745\) 0.199444 0.378635i 0.00730705 0.0138721i
\(746\) 63.7754 + 32.0292i 2.33499 + 1.17267i
\(747\) 0 0
\(748\) −1.34803 + 23.1447i −0.0492887 + 0.846255i
\(749\) 47.8375 26.3956i 1.74794 0.964474i
\(750\) 0 0
\(751\) 2.87073 + 21.0175i 0.104755 + 0.766939i 0.965962 + 0.258685i \(0.0832891\pi\)
−0.861207 + 0.508254i \(0.830291\pi\)
\(752\) 49.7955 + 128.974i 1.81585 + 4.70318i
\(753\) 0 0
\(754\) −28.9632 2.25120i −1.05478 0.0819838i
\(755\) 8.17949 + 6.86341i 0.297682 + 0.249785i
\(756\) 0 0
\(757\) 33.2104 27.8669i 1.20705 1.01284i 0.207653 0.978202i \(-0.433417\pi\)
0.999400 0.0346355i \(-0.0110270\pi\)
\(758\) 39.1812 28.0051i 1.42313 1.01719i
\(759\) 0 0
\(760\) 51.7447 + 59.2929i 1.87698 + 2.15078i
\(761\) 7.89806 36.4615i 0.286304 1.32173i −0.576876 0.816832i \(-0.695728\pi\)
0.863180 0.504896i \(-0.168469\pi\)
\(762\) 0 0
\(763\) 25.9169 + 5.08992i 0.938256 + 0.184268i
\(764\) 15.8817 1.85630i 0.574579 0.0671586i
\(765\) 0 0
\(766\) −25.0042 + 33.5865i −0.903439 + 1.21353i
\(767\) −6.94201 32.0479i −0.250661 1.15718i
\(768\) 0 0
\(769\) 32.7917 32.1619i 1.18250 1.15979i 0.198787 0.980043i \(-0.436300\pi\)
0.983713 0.179745i \(-0.0575273\pi\)
\(770\) −18.4077 71.4629i −0.663366 2.57534i
\(771\) 0 0
\(772\) 35.1507 31.8975i 1.26510 1.14802i
\(773\) −7.22941 16.7596i −0.260024 0.602803i 0.737328 0.675535i \(-0.236087\pi\)
−0.997351 + 0.0727325i \(0.976828\pi\)
\(774\) 0 0
\(775\) −35.3235 47.4477i −1.26886 1.70437i
\(776\) −22.4174 + 25.6875i −0.804737 + 0.922126i
\(777\) 0 0
\(778\) 76.4332 24.5073i 2.74026 0.878629i
\(779\) −4.72256 + 0.927480i −0.169203 + 0.0332304i
\(780\) 0 0
\(781\) −24.0959 10.9529i −0.862219 0.391927i
\(782\) −5.10993 28.9798i −0.182731 1.03632i
\(783\) 0 0
\(784\) 10.8918 61.7707i 0.388994 2.20609i
\(785\) 38.6088 56.2930i 1.37801 2.00918i
\(786\) 0 0
\(787\) 16