Properties

Label 729.2.i.a.685.1
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 685.1
Character \(\chi\) \(=\) 729.685
Dual form 729.2.i.a.613.1

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

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

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.57987 0.718157i −1.82425 0.507814i −0.825823 0.563930i \(-0.809289\pi\)
−0.998424 + 0.0561163i \(0.982128\pi\)
\(3\) 0 0
\(4\) 4.42767 + 2.67211i 2.21383 + 1.33606i
\(5\) 3.51654 0.136458i 1.57264 0.0610257i 0.762395 0.647112i \(-0.224024\pi\)
0.810248 + 0.586087i \(0.199332\pi\)
\(6\) 0 0
\(7\) −3.43073 0.536556i −1.29669 0.202799i −0.531752 0.846900i \(-0.678466\pi\)
−0.764940 + 0.644101i \(0.777232\pi\)
\(8\) −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 0.977796 + 0.209558i \(0.0672026\pi\)
−0.885783 + 0.464100i \(0.846378\pi\)
\(12\) 0 0
\(13\) −1.63172 + 2.37910i −0.452557 + 0.659844i −0.982083 0.188449i \(-0.939654\pi\)
0.529526 + 0.848294i \(0.322370\pi\)
\(14\) 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 −0.651001 0.759077i \(-0.725651\pi\)
0.220122 + 0.975472i \(0.429354\pi\)
\(18\) 0 0
\(19\) 0.153093 + 2.62850i 0.0351219 + 0.603020i 0.969249 + 0.246081i \(0.0791428\pi\)
−0.934127 + 0.356940i \(0.883820\pi\)
\(20\) 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 0.554850 + 0.831950i \(0.312776\pi\)
−0.969968 + 0.243232i \(0.921792\pi\)
\(24\) 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 0.260864 0.965376i \(-0.415993\pi\)
−0.828938 + 0.559340i \(0.811054\pi\)
\(30\) 0 0
\(31\) −5.26689 + 6.03518i −0.945961 + 1.08395i 0.0504009 + 0.998729i \(0.483950\pi\)
−0.996362 + 0.0852220i \(0.972840\pi\)
\(32\) −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 0.829738 0.558154i \(-0.188490\pi\)
−0.772677 + 0.634800i \(0.781083\pi\)
\(38\) 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 −0.994078 0.108664i \(-0.965343\pi\)
0.922871 + 0.385110i \(0.125836\pi\)
\(42\) 0 0
\(43\) 0.802684 + 0.728397i 0.122408 + 0.111079i 0.730913 0.682471i \(-0.239095\pi\)
−0.608505 + 0.793550i \(0.708230\pi\)
\(44\) −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 −0.973240 0.229792i \(-0.926195\pi\)
−0.0959682 0.995384i \(-0.530595\pi\)
\(48\) 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 0.920153 + 0.391559i \(0.128064\pi\)
−0.998582 + 0.0532340i \(0.983047\pi\)
\(54\) 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 0.430515 0.902584i \(-0.358332\pi\)
0.939362 + 0.342928i \(0.111419\pi\)
\(60\) 0 0
\(61\) 2.86548 1.72933i 0.366887 0.221418i −0.321256 0.946992i \(-0.604105\pi\)
0.688143 + 0.725575i \(0.258426\pi\)
\(62\) 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 −0.872537 0.488548i \(-0.837527\pi\)
0.179769 + 0.983709i \(0.442465\pi\)
\(68\) −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 0.887172 + 0.461439i \(0.152667\pi\)
−0.487657 + 0.873035i \(0.662148\pi\)
\(72\) 0 0
\(73\) 5.59498 1.32604i 0.654843 0.155201i 0.110254 0.993903i \(-0.464834\pi\)
0.544589 + 0.838703i \(0.316685\pi\)
\(74\) −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 −0.783602 0.621264i \(-0.786620\pi\)
0.605952 + 0.795501i \(0.292792\pi\)
\(80\) 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 0.686100 + 0.727508i \(0.259321\pi\)
−0.249252 + 0.968439i \(0.580185\pi\)
\(84\) 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 0.722038 + 0.691854i \(0.243206\pi\)
−0.983433 + 0.181269i \(0.941979\pi\)
\(90\) 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 0.241601 0.970376i \(-0.422327\pi\)
0.165678 + 0.986180i \(0.447019\pi\)
\(98\) −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 −0.999881 0.0153944i \(-0.995100\pi\)
0.998533 0.0541536i \(-0.0172461\pi\)
\(102\) 0 0
\(103\) −4.73288 3.66826i −0.466344 0.361444i 0.352165 0.935938i \(-0.385446\pi\)
−0.818509 + 0.574494i \(0.805199\pi\)
\(104\) 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 −0.492617 0.870246i \(-0.663960\pi\)
−0.936750 + 0.349999i \(0.886182\pi\)
\(108\) 0 0
\(109\) −7.14750 + 2.60148i −0.684606 + 0.249176i −0.660824 0.750541i \(-0.729793\pi\)
−0.0237821 + 0.999717i \(0.507571\pi\)
\(110\) 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 0.261979 0.965074i \(-0.415625\pi\)
0.985903 0.167319i \(-0.0535110\pi\)
\(114\) 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 0.891406 0.453205i \(-0.149719\pi\)
−0.941370 + 0.337377i \(0.890460\pi\)
\(128\) 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 0.999680 0.0252962i \(-0.00805289\pi\)
−0.805636 + 0.592411i \(0.798176\pi\)
\(132\) 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 −0.616881 0.787057i \(-0.711604\pi\)
0.999902 0.0139655i \(-0.00444550\pi\)
\(138\) 0 0
\(139\) −12.4487 + 1.94695i −1.05589 + 0.165138i −0.658552 0.752535i \(-0.728831\pi\)
−0.397336 + 0.917673i \(0.630065\pi\)
\(140\) −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 0.904305 0.426887i \(-0.140390\pi\)
−0.900007 + 0.435875i \(0.856439\pi\)
\(150\) 0 0
\(151\) 2.39813 1.85869i 0.195157 0.151258i −0.510336 0.859975i \(-0.670479\pi\)
0.705493 + 0.708717i \(0.250726\pi\)
\(152\) 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 0.948359 + 0.317200i \(0.102743\pi\)
−0.122941 + 0.992414i \(0.539233\pi\)
\(158\) 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 0.809802 + 0.586703i \(0.199575\pi\)
0.103199 + 0.994661i \(0.467092\pi\)
\(164\) −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 0.188861 + 0.982004i \(0.439520\pi\)
−0.916655 + 0.399679i \(0.869122\pi\)
\(168\) 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 0.595838 0.803105i \(-0.296820\pi\)
−0.136961 + 0.990576i \(0.543734\pi\)
\(174\) 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 0.992403 + 0.123030i \(0.0392613\pi\)
−0.999976 + 0.00698754i \(0.997776\pi\)
\(180\) 0 0
\(181\) −9.71472 + 6.38947i −0.722090 + 0.474926i −0.856597 0.515987i \(-0.827425\pi\)
0.134507 + 0.990913i \(0.457055\pi\)
\(182\) −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 −0.309379 0.950939i \(-0.600121\pi\)
0.513048 + 0.858360i \(0.328516\pi\)
\(192\) 0 0
\(193\) 9.00633 + 1.76879i 0.648290 + 0.127320i 0.506039 0.862511i \(-0.331109\pi\)
0.142251 + 0.989831i \(0.454566\pi\)
\(194\) −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 −0.708639 0.705571i \(-0.750691\pi\)
0.879170 + 0.476509i \(0.158098\pi\)
\(198\) 0 0
\(199\) 6.53734 15.1553i 0.463420 1.07433i −0.512989 0.858395i \(-0.671462\pi\)
0.976408 0.215932i \(-0.0692791\pi\)
\(200\) −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 −0.679941 0.733267i \(-0.737994\pi\)
0.315559 0.948906i \(-0.397808\pi\)
\(212\) −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 0.155736 0.987799i \(-0.450225\pi\)
−0.752625 + 0.658449i \(0.771213\pi\)
\(224\) 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 0.728208 0.685357i \(-0.240354\pi\)
−0.977076 + 0.212892i \(0.931712\pi\)
\(228\) 0 0
\(229\) 11.9353 + 5.42525i 0.788706 + 0.358511i 0.767323 0.641261i \(-0.221588\pi\)
0.0213826 + 0.999771i \(0.493193\pi\)
\(230\) 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 0.621948 0.783058i \(-0.286341\pi\)
0.204358 + 0.978896i \(0.434489\pi\)
\(234\) 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 0.855274 0.518175i \(-0.173389\pi\)
−0.0598666 + 0.998206i \(0.519068\pi\)
\(240\) 0 0
\(241\) −0.547763 0.152480i −0.0352845 0.00982212i 0.250485 0.968120i \(-0.419410\pi\)
−0.285770 + 0.958298i \(0.592249\pi\)
\(242\) −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 0.312337 0.949972i \(-0.398888\pi\)
−0.966525 + 0.256572i \(0.917407\pi\)
\(252\) 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 −0.227605 0.973754i \(-0.573089\pi\)
−0.883316 + 0.468778i \(0.844694\pi\)
\(258\) 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 0.713321 0.700837i \(-0.247190\pi\)
−0.212552 + 0.977150i \(0.568178\pi\)
\(264\) 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 −0.495071 0.868853i \(-0.664858\pi\)
0.769685 + 0.638424i \(0.220413\pi\)
\(270\) 0 0
\(271\) −13.8736 11.6414i −0.842764 0.707163i 0.115420 0.993317i \(-0.463179\pi\)
−0.958184 + 0.286154i \(0.907623\pi\)
\(272\) −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 −0.396044 0.918231i \(-0.629617\pi\)
−0.0193527 + 0.999813i \(0.506161\pi\)
\(278\) 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 −0.413666 0.910429i \(-0.635752\pi\)
0.753331 0.657641i \(-0.228446\pi\)
\(282\) 0 0
\(283\) 8.50564 + 8.34227i 0.505608 + 0.495897i 0.907652 0.419724i \(-0.137873\pi\)
−0.402044 + 0.915620i \(0.631700\pi\)
\(284\) −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 −0.230846 0.972990i \(-0.574149\pi\)
−0.581684 + 0.813415i \(0.697606\pi\)
\(294\) 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 −0.893353 0.449355i \(-0.851654\pi\)
0.939480 0.342605i \(-0.111309\pi\)
\(308\) 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 0.153475 0.988152i \(-0.450953\pi\)
−0.00105605 + 0.999999i \(0.500336\pi\)
\(312\) 0 0
\(313\) −11.9006 4.86193i −0.672661 0.274812i 0.0160253 0.999872i \(-0.494899\pi\)
−0.688686 + 0.725059i \(0.741812\pi\)
\(314\) −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 −0.921107 0.389309i \(-0.872714\pi\)
0.420502 0.907292i \(-0.361854\pi\)
\(318\) 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 −0.846656 0.532140i \(-0.821388\pi\)
0.699319 + 0.714810i \(0.253487\pi\)
\(332\) −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 0.730803 0.682589i \(-0.239146\pi\)
−0.990110 + 0.140294i \(0.955195\pi\)
\(338\) −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 0.418358 0.908282i \(-0.362606\pi\)
0.675703 + 0.737174i \(0.263840\pi\)
\(348\) 0 0
\(349\) 13.2299 27.6680i 0.708182 1.48104i −0.161214 0.986919i \(-0.551541\pi\)
0.869396 0.494117i \(-0.164508\pi\)
\(350\) 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 0.857152 + 0.515064i \(0.172232\pi\)
−0.940344 + 0.340225i \(0.889497\pi\)
\(354\) 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 0.998049 0.0624379i \(-0.0198875\pi\)
−0.730318 + 0.683107i \(0.760628\pi\)
\(360\) 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 0.618640 0.785675i \(-0.287684\pi\)
0.960159 + 0.279454i \(0.0901533\pi\)
\(368\) −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 −0.997374 0.0724237i \(-0.976927\pi\)
−0.0244731 + 0.999700i \(0.507791\pi\)
\(374\) 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 −0.130684 0.991424i \(-0.541717\pi\)
−0.737385 + 0.675473i \(0.763939\pi\)
\(380\) −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 0.877340 0.479870i \(-0.159316\pi\)
−0.245856 + 0.969306i \(0.579069\pi\)
\(384\) 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 −0.734060 0.679085i \(-0.762377\pi\)
−0.784476 + 0.620159i \(0.787068\pi\)
\(390\) 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 0.720518 + 0.693437i \(0.243904\pi\)
−0.983033 + 0.183427i \(0.941281\pi\)
\(398\) −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 −0.534100 0.845421i \(-0.679349\pi\)
0.430430 + 0.902624i \(0.358362\pi\)
\(402\) 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 0.985594 + 0.169128i \(0.0540952\pi\)
−0.991411 + 0.130784i \(0.958250\pi\)
\(410\) 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 0.206064 0.978538i \(-0.433934\pi\)
0.992552 + 0.121819i \(0.0388727\pi\)
\(420\) 0 0
\(421\) −8.52740 + 13.5296i −0.415600 + 0.659395i −0.986897 0.161349i \(-0.948416\pi\)
0.571297 + 0.820743i \(0.306440\pi\)
\(422\) −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 −0.995491 0.0948563i \(-0.969761\pi\)
0.903013 0.429614i \(-0.141350\pi\)
\(432\) 0 0
\(433\) 5.97542 33.8883i 0.287160 1.62857i −0.410306 0.911948i \(-0.634578\pi\)
0.697466 0.716618i \(-0.254311\pi\)
\(434\) −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 0.344192 0.938899i \(-0.388153\pi\)
−0.976842 + 0.213963i \(0.931363\pi\)
\(440\) 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 0.342742 0.939430i \(-0.388644\pi\)
−0.901836 + 0.432079i \(0.857780\pi\)
\(444\) 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 0.534725 0.845026i \(-0.320415\pi\)
−0.962887 + 0.269905i \(0.913008\pi\)
\(450\) 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 0.982090 0.188412i \(-0.0603341\pi\)
0.139670 + 0.990198i \(0.455396\pi\)
\(458\) −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 0.613860 0.789415i \(-0.289616\pi\)
0.728467 + 0.685081i \(0.240233\pi\)
\(462\) 0 0
\(463\) 3.84725 9.96462i 0.178797 0.463095i −0.814293 0.580454i \(-0.802875\pi\)
0.993090 + 0.117359i \(0.0374429\pi\)
\(464\) 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 −0.998767 0.0496511i \(-0.984189\pi\)
0.986249 0.165265i \(-0.0528480\pi\)
\(468\) 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 0.369486 0.929236i \(-0.379534\pi\)
0.0681224 + 0.997677i \(0.478299\pi\)
\(480\) 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 −0.815235 0.579131i \(-0.803392\pi\)
−0.767905 + 0.640564i \(0.778701\pi\)
\(492\) 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 0.314542 + 0.949244i \(0.398149\pi\)
−0.998825 + 0.0484651i \(0.984567\pi\)
\(500\) 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 −0.0566747 0.998393i \(-0.518050\pi\)
0.766990 + 0.641659i \(0.221753\pi\)
\(504\) 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 0.327339 + 0.944907i \(0.393848\pi\)
−0.877394 + 0.479771i \(0.840720\pi\)
\(510\) 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 0.0810325 0.996711i \(-0.474178\pi\)
−0.151009 + 0.988532i \(0.548252\pi\)
\(522\) 0 0
\(523\) 25.3488 + 34.0494i 1.10843 + 1.48888i 0.852900 + 0.522074i \(0.174842\pi\)
0.255527 + 0.966802i \(0.417751\pi\)
\(524\) −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 0.994338 + 0.106265i \(0.0338892\pi\)
−0.898027 + 0.439940i \(0.855000\pi\)
\(542\) 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 −0.382912 0.923785i \(-0.625079\pi\)
0.638876 + 0.769310i \(0.279400\pi\)
\(548\) 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 0.881084 + 0.472959i \(0.156814\pi\)
−0.476240 + 0.879315i \(0.658001\pi\)
\(558\) 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 −0.484656 0.874705i \(-0.661055\pi\)
0.518208 0.855255i \(-0.326599\pi\)
\(564\) 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 0.919877 + 0.392206i \(0.128288\pi\)
−0.615927 + 0.787803i \(0.711218\pi\)
\(570\) 0 0
\(571\) 17.1842 9.48182i 0.719135 0.396802i −0.0809266 0.996720i \(-0.525788\pi\)
0.800061 + 0.599918i \(0.204800\pi\)
\(572\) −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 −0.758287 0.651921i \(-0.773963\pi\)
0.694908 + 0.719098i \(0.255445\pi\)
\(578\) 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 0.999632 0.0271267i \(-0.00863574\pi\)
−0.999932 + 0.0116548i \(0.996290\pi\)
\(588\) 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 0.397423 0.917636i \(-0.369905\pi\)
−0.285401 + 0.958408i \(0.592127\pi\)
\(594\) 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 −0.554177 0.832399i \(-0.686967\pi\)
0.774838 + 0.632159i \(0.217831\pi\)
\(600\) 0 0
\(601\) −5.11858 + 14.9596i −0.208791 + 0.610215i −0.999999 0.00133218i \(-0.999576\pi\)
0.791208 + 0.611547i \(0.209452\pi\)
\(602\) 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 0.731593 0.681741i \(-0.238777\pi\)
0.978621 + 0.205670i \(0.0659375\pi\)
\(608\) 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 0.735555 0.677465i \(-0.236921\pi\)
−0.997539 + 0.0701190i \(0.977662\pi\)
\(614\) −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 0.890455 0.455072i \(-0.150386\pi\)
−0.982586 + 0.185808i \(0.940510\pi\)
\(618\) 0 0
\(619\) 0.587886 6.04400i 0.0236291 0.242929i −0.976049 0.217552i \(-0.930193\pi\)
0.999678 0.0253771i \(-0.00807866\pi\)
\(620\) −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 0.0266090 0.999646i \(-0.491529\pi\)
−0.907352 + 0.420372i \(0.861899\pi\)
\(632\) 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 −0.283658 0.958926i \(-0.591548\pi\)
0.997242 + 0.0742202i \(0.0236468\pi\)
\(642\) 0 0
\(643\) −18.0533 28.6435i −0.711952 1.12959i −0.985818 0.167821i \(-0.946327\pi\)
0.273865 0.961768i \(-0.411698\pi\)
\(644\) 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 −0.977423 0.211292i \(-0.932233\pi\)
0.671696 + 0.740827i \(0.265566\pi\)
\(648\) 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 −0.772903 0.634525i \(-0.781196\pi\)
0.960436 + 0.278502i \(0.0898378\pi\)
\(654\) 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 0.606884 0.794790i \(-0.292419\pi\)
−0.123253 + 0.992375i \(0.539333\pi\)
\(660\) 0 0
\(661\) 15.2379 + 1.18438i 0.592685 + 0.0460671i 0.370333 0.928899i \(-0.379244\pi\)
0.222352 + 0.974966i \(0.428626\pi\)
\(662\) 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 0.980626 0.195889i \(-0.0627593\pi\)
−0.535941 + 0.844255i \(0.680043\pi\)
\(674\) 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 −0.654614 0.755963i \(-0.727169\pi\)
0.139147 + 0.990272i \(0.455564\pi\)
\(678\) 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 0.0634310 + 0.997986i \(0.479796\pi\)
−0.974253 + 0.225459i \(0.927612\pi\)
\(684\) 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 −0.982095 0.188384i \(-0.939675\pi\)
0.972019 + 0.234903i \(0.0754774\pi\)
\(692\) 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 0.696896 0.717173i \(-0.254564\pi\)
−0.585262 + 0.810844i \(0.699009\pi\)
\(702\) 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 0.613718 0.789525i \(-0.289673\pi\)
−0.340691 + 0.940175i \(0.610661\pi\)
\(710\) −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 −0.0835020 0.996508i \(-0.526610\pi\)
−0.521852 + 0.853036i \(0.674759\pi\)
\(720\) 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 −0.989965 0.141315i \(-0.954867\pi\)
−0.920592 0.390525i \(-0.872294\pi\)
\(728\) −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 0.840308 0.542109i \(-0.182374\pi\)
−0.0880168 + 0.996119i \(0.528053\pi\)
\(734\) −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 −0.00779154 0.999970i \(-0.502480\pi\)
−0.455748 + 0.890109i \(0.650628\pi\)
\(740\) 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 0.367180 0.930150i \(-0.380323\pi\)
−0.459380 + 0.888240i \(0.651928\pi\)
\(744\) 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 −0.861207 0.508254i \(-0.830291\pi\)
0.965962 0.258685i \(-0.0832891\pi\)
\(752\) 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 0.999400 + 0.0346355i \(0.0110270\pi\)
0.207653 + 0.978202i \(0.433417\pi\)
\(758\) 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 0.863180 + 0.504896i \(0.168469\pi\)
−0.576876 + 0.816832i \(0.695728\pi\)
\(762\) 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 0.983713 + 0.179745i \(0.0575273\pi\)
0.198787 + 0.980043i \(0.436300\pi\)
\(770\) −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 −0.997351 0.0727325i \(-0.976828\pi\)
0.737328 + 0.675535i \(0.236087\pi\)
\(774\) 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
\(787\) 16.6408