Properties

Label 729.2.i.a.685.6
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 685.6
Character \(\chi\) \(=\) 729.685
Dual form 729.2.i.a.613.6

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.75661 - 0.488987i) q^{2} +(1.13425 + 0.684522i) q^{4} +(-0.390492 + 0.0151529i) q^{5} +(-1.38312 - 0.216316i) q^{7} +(0.844877 + 0.895518i) q^{8} +O(q^{10})\) \(q+(-1.75661 - 0.488987i) q^{2} +(1.13425 + 0.684522i) q^{4} +(-0.390492 + 0.0151529i) q^{5} +(-1.38312 - 0.216316i) q^{7} +(0.844877 + 0.895518i) q^{8} +(0.693352 + 0.164328i) q^{10} +(0.144396 + 1.05716i) q^{11} +(0.399665 - 0.582725i) q^{13} +(2.32383 + 1.05631i) q^{14} +(-2.28105 - 4.33047i) q^{16} +(1.16568 - 0.585429i) q^{17} +(-0.116551 - 2.00110i) q^{19} +(-0.453287 - 0.250113i) q^{20} +(0.263292 - 1.92764i) q^{22} +(-0.395794 + 1.02513i) q^{23} +(-4.83271 + 0.375628i) q^{25} +(-0.987001 + 0.828192i) q^{26} +(-1.42073 - 1.19213i) q^{28} +(-3.81175 - 2.72447i) q^{29} +(1.34481 - 1.54098i) q^{31} +(1.36810 + 6.31585i) q^{32} +(-2.33392 + 0.458368i) q^{34} +(0.543374 + 0.0635113i) q^{35} +(2.79926 + 3.76005i) q^{37} +(-0.773776 + 3.57215i) q^{38} +(-0.343487 - 0.336890i) q^{40} +(-0.191462 + 0.743302i) q^{41} +(-3.68245 - 3.34164i) q^{43} +(-0.559871 + 1.29793i) q^{44} +(1.19653 - 1.60722i) q^{46} +(-4.92054 - 5.63831i) q^{47} +(-4.79951 - 1.53890i) q^{49} +(8.67288 + 1.70330i) q^{50} +(0.852207 - 0.387376i) q^{52} +(0.355618 - 2.01681i) q^{53} +(-0.0724044 - 0.410626i) q^{55} +(-0.974851 - 1.42137i) q^{56} +(5.36353 + 6.64974i) q^{58} +(-13.4421 + 5.49170i) q^{59} +(-9.43154 + 5.69196i) q^{61} +(-3.11583 + 2.04932i) q^{62} +(0.115964 - 1.99103i) q^{64} +(-0.147236 + 0.233605i) q^{65} +(6.23219 - 4.45450i) q^{67} +(1.72291 + 0.133915i) q^{68} +(-0.923442 - 0.377267i) q^{70} +(-1.57545 - 5.26238i) q^{71} +(-4.21048 + 0.997901i) q^{73} +(-3.07859 - 7.97376i) q^{74} +(1.23760 - 2.34952i) q^{76} +(0.0289648 - 1.49342i) q^{77} +(-10.2004 + 10.0045i) q^{79} +(0.956351 + 1.65645i) q^{80} +(0.699789 - 1.21207i) q^{82} +(-1.59815 - 6.20441i) q^{83} +(-0.446319 + 0.246268i) q^{85} +(4.83462 + 7.67065i) q^{86} +(-0.824712 + 1.02248i) q^{88} +(-3.45371 + 11.5362i) q^{89} +(-0.678836 + 0.719524i) q^{91} +(-1.15065 + 0.891823i) q^{92} +(5.88642 + 12.3104i) q^{94} +(0.0758344 + 0.779646i) q^{95} +(2.31768 + 0.0899365i) q^{97} +(7.67838 + 5.05015i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 1404 q + 54 q^{2} - 54 q^{4} + 54 q^{5} - 54 q^{7} + 54 q^{8}+O(q^{10}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.75661 0.488987i −1.24211 0.345766i −0.416049 0.909342i \(-0.636586\pi\)
−0.826064 + 0.563576i \(0.809425\pi\)
\(3\) 0 0
\(4\) 1.13425 + 0.684522i 0.567124 + 0.342261i
\(5\) −0.390492 + 0.0151529i −0.174633 + 0.00677656i −0.125944 0.992037i \(-0.540196\pi\)
−0.0486895 + 0.998814i \(0.515504\pi\)
\(6\) 0 0
\(7\) −1.38312 0.216316i −0.522770 0.0817597i −0.112372 0.993666i \(-0.535845\pi\)
−0.410398 + 0.911907i \(0.634610\pi\)
\(8\) 0.844877 + 0.895518i 0.298709 + 0.316613i
\(9\) 0 0
\(10\) 0.693352 + 0.164328i 0.219257 + 0.0519649i
\(11\) 0.144396 + 1.05716i 0.0435370 + 0.318747i 0.999667 + 0.0258044i \(0.00821471\pi\)
−0.956130 + 0.292943i \(0.905366\pi\)
\(12\) 0 0
\(13\) 0.399665 0.582725i 0.110847 0.161619i −0.765283 0.643694i \(-0.777401\pi\)
0.876130 + 0.482075i \(0.160117\pi\)
\(14\) 2.32383 + 1.05631i 0.621069 + 0.282311i
\(15\) 0 0
\(16\) −2.28105 4.33047i −0.570263 1.08262i
\(17\) 1.16568 0.585429i 0.282720 0.141987i −0.301789 0.953375i \(-0.597584\pi\)
0.584509 + 0.811388i \(0.301287\pi\)
\(18\) 0 0
\(19\) −0.116551 2.00110i −0.0267386 0.459083i −0.984930 0.172955i \(-0.944669\pi\)
0.958191 0.286129i \(-0.0923685\pi\)
\(20\) −0.453287 0.250113i −0.101358 0.0559270i
\(21\) 0 0
\(22\) 0.263292 1.92764i 0.0561340 0.410973i
\(23\) −0.395794 + 1.02513i −0.0825287 + 0.213755i −0.968006 0.250929i \(-0.919264\pi\)
0.885477 + 0.464683i \(0.153832\pi\)
\(24\) 0 0
\(25\) −4.83271 + 0.375628i −0.966542 + 0.0751256i
\(26\) −0.987001 + 0.828192i −0.193567 + 0.162422i
\(27\) 0 0
\(28\) −1.42073 1.19213i −0.268492 0.225291i
\(29\) −3.81175 2.72447i −0.707824 0.505922i 0.169676 0.985500i \(-0.445728\pi\)
−0.877499 + 0.479578i \(0.840790\pi\)
\(30\) 0 0
\(31\) 1.34481 1.54098i 0.241535 0.276769i −0.619851 0.784720i \(-0.712807\pi\)
0.861386 + 0.507951i \(0.169597\pi\)
\(32\) 1.36810 + 6.31585i 0.241848 + 1.11649i
\(33\) 0 0
\(34\) −2.33392 + 0.458368i −0.400265 + 0.0786094i
\(35\) 0.543374 + 0.0635113i 0.0918470 + 0.0107354i
\(36\) 0 0
\(37\) 2.79926 + 3.76005i 0.460195 + 0.618149i 0.970283 0.241973i \(-0.0777946\pi\)
−0.510088 + 0.860122i \(0.670387\pi\)
\(38\) −0.773776 + 3.57215i −0.125523 + 0.579479i
\(39\) 0 0
\(40\) −0.343487 0.336890i −0.0543101 0.0532670i
\(41\) −0.191462 + 0.743302i −0.0299014 + 0.116084i −0.981600 0.190951i \(-0.938843\pi\)
0.951698 + 0.307035i \(0.0993368\pi\)
\(42\) 0 0
\(43\) −3.68245 3.34164i −0.561568 0.509596i 0.341046 0.940047i \(-0.389219\pi\)
−0.902614 + 0.430451i \(0.858355\pi\)
\(44\) −0.559871 + 1.29793i −0.0844038 + 0.195670i
\(45\) 0 0
\(46\) 1.19653 1.60722i 0.176419 0.236972i
\(47\) −4.92054 5.63831i −0.717734 0.822432i 0.272455 0.962169i \(-0.412164\pi\)
−0.990189 + 0.139737i \(0.955374\pi\)
\(48\) 0 0
\(49\) −4.79951 1.53890i −0.685645 0.219843i
\(50\) 8.67288 + 1.70330i 1.22653 + 0.240883i
\(51\) 0 0
\(52\) 0.852207 0.387376i 0.118180 0.0537193i
\(53\) 0.355618 2.01681i 0.0488479 0.277030i −0.950594 0.310437i \(-0.899525\pi\)
0.999442 + 0.0334067i \(0.0106357\pi\)
\(54\) 0 0
\(55\) −0.0724044 0.410626i −0.00976301 0.0553688i
\(56\) −0.974851 1.42137i −0.130270 0.189938i
\(57\) 0 0
\(58\) 5.36353 + 6.64974i 0.704267 + 0.873153i
\(59\) −13.4421 + 5.49170i −1.75001 + 0.714958i −0.751539 + 0.659688i \(0.770688\pi\)
−0.998471 + 0.0552697i \(0.982398\pi\)
\(60\) 0 0
\(61\) −9.43154 + 5.69196i −1.20758 + 0.728781i −0.970122 0.242616i \(-0.921995\pi\)
−0.237462 + 0.971397i \(0.576316\pi\)
\(62\) −3.11583 + 2.04932i −0.395711 + 0.260263i
\(63\) 0 0
\(64\) 0.115964 1.99103i 0.0144956 0.248879i
\(65\) −0.147236 + 0.233605i −0.0182623 + 0.0289752i
\(66\) 0 0
\(67\) 6.23219 4.45450i 0.761384 0.544204i −0.133208 0.991088i \(-0.542528\pi\)
0.894592 + 0.446884i \(0.147466\pi\)
\(68\) 1.72291 + 0.133915i 0.208934 + 0.0162396i
\(69\) 0 0
\(70\) −0.923442 0.377267i −0.110372 0.0450921i
\(71\) −1.57545 5.26238i −0.186972 0.624529i −0.999154 0.0411254i \(-0.986906\pi\)
0.812182 0.583404i \(-0.198279\pi\)
\(72\) 0 0
\(73\) −4.21048 + 0.997901i −0.492799 + 0.116796i −0.469499 0.882933i \(-0.655565\pi\)
−0.0233001 + 0.999729i \(0.507417\pi\)
\(74\) −3.07859 7.97376i −0.357879 0.926931i
\(75\) 0 0
\(76\) 1.23760 2.34952i 0.141962 0.269509i
\(77\) 0.0289648 1.49342i 0.00330085 0.170191i
\(78\) 0 0
\(79\) −10.2004 + 10.0045i −1.14764 + 1.12559i −0.157209 + 0.987565i \(0.550250\pi\)
−0.990428 + 0.138029i \(0.955923\pi\)
\(80\) 0.956351 + 1.65645i 0.106923 + 0.185197i
\(81\) 0 0
\(82\) 0.699789 1.21207i 0.0772788 0.133851i
\(83\) −1.59815 6.20441i −0.175420 0.681022i −0.994259 0.106999i \(-0.965876\pi\)
0.818839 0.574023i \(-0.194618\pi\)
\(84\) 0 0
\(85\) −0.446319 + 0.246268i −0.0484101 + 0.0267116i
\(86\) 4.83462 + 7.67065i 0.521330 + 0.827147i
\(87\) 0 0
\(88\) −0.824712 + 1.02248i −0.0879146 + 0.108997i
\(89\) −3.45371 + 11.5362i −0.366092 + 1.22283i 0.554459 + 0.832211i \(0.312925\pi\)
−0.920551 + 0.390622i \(0.872260\pi\)
\(90\) 0 0
\(91\) −0.678836 + 0.719524i −0.0711614 + 0.0754266i
\(92\) −1.15065 + 0.891823i −0.119964 + 0.0929790i
\(93\) 0 0
\(94\) 5.88642 + 12.3104i 0.607138 + 1.26972i
\(95\) 0.0758344 + 0.779646i 0.00778045 + 0.0799900i
\(96\) 0 0
\(97\) 2.31768 + 0.0899365i 0.235325 + 0.00913166i 0.156168 0.987731i \(-0.450086\pi\)
0.0791567 + 0.996862i \(0.474777\pi\)
\(98\) 7.67838 + 5.05015i 0.775634 + 0.510142i
\(99\) 0 0
\(100\) −5.73862 2.88204i −0.573862 0.288204i
\(101\) −0.0914416 4.71471i −0.00909878 0.469131i −0.976456 0.215715i \(-0.930792\pi\)
0.967358 0.253415i \(-0.0815540\pi\)
\(102\) 0 0
\(103\) −9.07098 7.03054i −0.893791 0.692740i 0.0583840 0.998294i \(-0.481405\pi\)
−0.952175 + 0.305554i \(0.901158\pi\)
\(104\) 0.859508 0.134425i 0.0842817 0.0131814i
\(105\) 0 0
\(106\) −1.61088 + 3.36887i −0.156462 + 0.327213i
\(107\) −15.8624 5.77346i −1.53348 0.558141i −0.569009 0.822331i \(-0.692673\pi\)
−0.964471 + 0.264190i \(0.914895\pi\)
\(108\) 0 0
\(109\) −11.1308 + 4.05127i −1.06613 + 0.388041i −0.814730 0.579841i \(-0.803115\pi\)
−0.251404 + 0.967882i \(0.580892\pi\)
\(110\) −0.0736040 + 0.756715i −0.00701787 + 0.0721500i
\(111\) 0 0
\(112\) 2.21822 + 6.48298i 0.209602 + 0.612584i
\(113\) −3.84986 + 3.49356i −0.362165 + 0.328647i −0.832690 0.553740i \(-0.813200\pi\)
0.470525 + 0.882387i \(0.344064\pi\)
\(114\) 0 0
\(115\) 0.139020 0.406303i 0.0129637 0.0378879i
\(116\) −2.45850 5.69945i −0.228266 0.529181i
\(117\) 0 0
\(118\) 26.2979 3.07379i 2.42092 0.282965i
\(119\) −1.73892 + 0.557561i −0.159406 + 0.0511116i
\(120\) 0 0
\(121\) 9.50033 2.64460i 0.863667 0.240418i
\(122\) 19.3509 5.38668i 1.75194 0.487687i
\(123\) 0 0
\(124\) 2.58019 0.827303i 0.231707 0.0742940i
\(125\) 3.82216 0.446746i 0.341864 0.0399582i
\(126\) 0 0
\(127\) −0.814139 1.88739i −0.0722432 0.167478i 0.878268 0.478168i \(-0.158699\pi\)
−0.950511 + 0.310690i \(0.899440\pi\)
\(128\) 3.00685 8.78786i 0.265771 0.776745i
\(129\) 0 0
\(130\) 0.372866 0.338358i 0.0327025 0.0296760i
\(131\) 0.942657 + 2.75502i 0.0823603 + 0.240707i 0.979642 0.200751i \(-0.0643381\pi\)
−0.897282 + 0.441458i \(0.854462\pi\)
\(132\) 0 0
\(133\) −0.271666 + 2.79297i −0.0235564 + 0.242181i
\(134\) −13.1257 + 4.77738i −1.13389 + 0.412703i
\(135\) 0 0
\(136\) 1.50912 + 0.549276i 0.129406 + 0.0471000i
\(137\) 6.49394 13.5809i 0.554815 1.16030i −0.413486 0.910511i \(-0.635689\pi\)
0.968301 0.249787i \(-0.0803605\pi\)
\(138\) 0 0
\(139\) 12.3619 1.93336i 1.04852 0.163986i 0.393290 0.919414i \(-0.371337\pi\)
0.655231 + 0.755429i \(0.272571\pi\)
\(140\) 0.572846 + 0.443989i 0.0484143 + 0.0375239i
\(141\) 0 0
\(142\) 0.194228 + 10.0143i 0.0162992 + 0.840384i
\(143\) 0.673746 + 0.338368i 0.0563415 + 0.0282958i
\(144\) 0 0
\(145\) 1.52974 + 1.00613i 0.127038 + 0.0835542i
\(146\) 7.88414 + 0.305941i 0.652496 + 0.0253198i
\(147\) 0 0
\(148\) 0.601211 + 6.18099i 0.0494192 + 0.508074i
\(149\) −3.60667 7.54271i −0.295470 0.617923i 0.699879 0.714262i \(-0.253237\pi\)
−0.995349 + 0.0963386i \(0.969287\pi\)
\(150\) 0 0
\(151\) 11.7774 9.12817i 0.958430 0.742840i −0.00794677 0.999968i \(-0.502530\pi\)
0.966377 + 0.257129i \(0.0827765\pi\)
\(152\) 1.69355 1.79506i 0.137365 0.145598i
\(153\) 0 0
\(154\) −0.781141 + 2.60919i −0.0629462 + 0.210255i
\(155\) −0.501787 + 0.622119i −0.0403045 + 0.0499698i
\(156\) 0 0
\(157\) 4.22014 + 6.69571i 0.336804 + 0.534376i 0.971087 0.238725i \(-0.0767293\pi\)
−0.634283 + 0.773101i \(0.718705\pi\)
\(158\) 22.8103 12.5862i 1.81469 1.00130i
\(159\) 0 0
\(160\) −0.629934 2.44556i −0.0498007 0.193338i
\(161\) 0.769181 1.33226i 0.0606200 0.104997i
\(162\) 0 0
\(163\) −4.54889 7.87892i −0.356297 0.617124i 0.631042 0.775749i \(-0.282628\pi\)
−0.987339 + 0.158624i \(0.949294\pi\)
\(164\) −0.725972 + 0.712028i −0.0566889 + 0.0556001i
\(165\) 0 0
\(166\) −0.226538 + 11.6802i −0.0175827 + 0.906561i
\(167\) 2.37891 4.51624i 0.184085 0.349477i −0.775292 0.631603i \(-0.782397\pi\)
0.959378 + 0.282125i \(0.0910394\pi\)
\(168\) 0 0
\(169\) 4.50247 + 11.6617i 0.346344 + 0.897054i
\(170\) 0.904432 0.214354i 0.0693668 0.0164402i
\(171\) 0 0
\(172\) −1.88938 6.31097i −0.144064 0.481207i
\(173\) 20.3734 + 8.32347i 1.54896 + 0.632822i 0.981652 0.190681i \(-0.0610697\pi\)
0.567312 + 0.823503i \(0.307983\pi\)
\(174\) 0 0
\(175\) 6.76546 + 0.525853i 0.511421 + 0.0397508i
\(176\) 4.24865 3.03675i 0.320254 0.228904i
\(177\) 0 0
\(178\) 11.7079 18.5758i 0.877542 1.39232i
\(179\) −0.581976 + 9.99214i −0.0434989 + 0.746848i 0.904087 + 0.427348i \(0.140552\pi\)
−0.947586 + 0.319500i \(0.896485\pi\)
\(180\) 0 0
\(181\) 15.2029 9.99911i 1.13002 0.743228i 0.160211 0.987083i \(-0.448783\pi\)
0.969812 + 0.243855i \(0.0784121\pi\)
\(182\) 1.54429 0.931984i 0.114470 0.0690832i
\(183\) 0 0
\(184\) −1.25242 + 0.511670i −0.0923296 + 0.0377208i
\(185\) −1.15006 1.42585i −0.0845542 0.104831i
\(186\) 0 0
\(187\) 0.787214 + 1.14779i 0.0575668 + 0.0839344i
\(188\) −1.72156 9.76345i −0.125558 0.712073i
\(189\) 0 0
\(190\) 0.248025 1.40662i 0.0179936 0.102047i
\(191\) −8.71387 + 3.96094i −0.630513 + 0.286603i −0.703463 0.710732i \(-0.748364\pi\)
0.0729494 + 0.997336i \(0.476759\pi\)
\(192\) 0 0
\(193\) 7.25388 + 1.42462i 0.522146 + 0.102546i 0.446839 0.894614i \(-0.352550\pi\)
0.0753065 + 0.997160i \(0.476006\pi\)
\(194\) −4.02729 1.29130i −0.289142 0.0927097i
\(195\) 0 0
\(196\) −4.39042 5.03087i −0.313602 0.359348i
\(197\) 5.64352 7.58056i 0.402084 0.540092i −0.554257 0.832345i \(-0.686998\pi\)
0.956341 + 0.292253i \(0.0944050\pi\)
\(198\) 0 0
\(199\) 6.94883 16.1092i 0.492590 1.14195i −0.472807 0.881166i \(-0.656759\pi\)
0.965397 0.260785i \(-0.0839815\pi\)
\(200\) −4.41943 4.01042i −0.312501 0.283579i
\(201\) 0 0
\(202\) −2.14480 + 8.32663i −0.150908 + 0.585859i
\(203\) 4.68275 + 4.59281i 0.328665 + 0.322352i
\(204\) 0 0
\(205\) 0.0635012 0.293154i 0.00443512 0.0204748i
\(206\) 12.4964 + 16.7855i 0.870663 + 1.16950i
\(207\) 0 0
\(208\) −3.43513 0.401509i −0.238184 0.0278397i
\(209\) 2.09866 0.412163i 0.145167 0.0285099i
\(210\) 0 0
\(211\) −2.99118 13.8088i −0.205921 0.950637i −0.956924 0.290338i \(-0.906232\pi\)
0.751003 0.660299i \(-0.229570\pi\)
\(212\) 1.78391 2.04414i 0.122520 0.140392i
\(213\) 0 0
\(214\) 25.0410 + 17.8982i 1.71177 + 1.22350i
\(215\) 1.48860 + 1.24908i 0.101522 + 0.0851869i
\(216\) 0 0
\(217\) −2.19337 + 1.84046i −0.148896 + 0.124938i
\(218\) 21.5335 1.67371i 1.45843 0.113358i
\(219\) 0 0
\(220\) 0.198958 0.515314i 0.0134137 0.0347424i
\(221\) 0.124739 0.913249i 0.00839083 0.0614318i
\(222\) 0 0
\(223\) −2.45224 1.35309i −0.164214 0.0906097i 0.398876 0.917005i \(-0.369400\pi\)
−0.563091 + 0.826395i \(0.690388\pi\)
\(224\) −0.526025 9.03151i −0.0351465 0.603443i
\(225\) 0 0
\(226\) 8.47103 4.25431i 0.563484 0.282992i
\(227\) 11.6167 + 22.0537i 0.771026 + 1.46376i 0.882662 + 0.470007i \(0.155749\pi\)
−0.111637 + 0.993749i \(0.535609\pi\)
\(228\) 0 0
\(229\) −24.4020 11.0921i −1.61253 0.732985i −0.614113 0.789218i \(-0.710486\pi\)
−0.998418 + 0.0562336i \(0.982091\pi\)
\(230\) −0.442882 + 0.645737i −0.0292028 + 0.0425787i
\(231\) 0 0
\(232\) −0.780645 5.71533i −0.0512519 0.375230i
\(233\) 9.74148 + 2.30877i 0.638186 + 0.151253i 0.536956 0.843610i \(-0.319574\pi\)
0.101230 + 0.994863i \(0.467722\pi\)
\(234\) 0 0
\(235\) 2.00686 + 2.12715i 0.130913 + 0.138760i
\(236\) −19.0058 2.97246i −1.23718 0.193491i
\(237\) 0 0
\(238\) 3.32724 0.129112i 0.215673 0.00836910i
\(239\) −13.2283 7.98330i −0.855666 0.516397i 0.0197293 0.999805i \(-0.493720\pi\)
−0.875395 + 0.483409i \(0.839399\pi\)
\(240\) 0 0
\(241\) −19.1228 5.32320i −1.23181 0.342897i −0.409696 0.912222i \(-0.634365\pi\)
−0.822113 + 0.569325i \(0.807205\pi\)
\(242\) −17.9816 −1.15590
\(243\) 0 0
\(244\) −14.5940 −0.934283
\(245\) 1.89749 + 0.528202i 0.121226 + 0.0337456i
\(246\) 0 0
\(247\) −1.21267 0.731851i −0.0771605 0.0465666i
\(248\) 2.51618 0.0976391i 0.159777 0.00620009i
\(249\) 0 0
\(250\) −6.93250 1.08422i −0.438450 0.0685723i
\(251\) 20.4981 + 21.7268i 1.29383 + 1.37138i 0.889611 + 0.456719i \(0.150975\pi\)
0.404220 + 0.914662i \(0.367543\pi\)
\(252\) 0 0
\(253\) −1.14088 0.270394i −0.0717267 0.0169995i
\(254\) 0.507221 + 3.71351i 0.0318259 + 0.233006i
\(255\) 0 0
\(256\) −11.8351 + 17.2560i −0.739696 + 1.07850i
\(257\) −4.82876 2.19494i −0.301210 0.136917i 0.257504 0.966277i \(-0.417100\pi\)
−0.558714 + 0.829361i \(0.688705\pi\)
\(258\) 0 0
\(259\) −3.05834 5.80612i −0.190036 0.360775i
\(260\) −0.326910 + 0.164180i −0.0202741 + 0.0101820i
\(261\) 0 0
\(262\) −0.308716 5.30045i −0.0190725 0.327463i
\(263\) 23.7223 + 13.0894i 1.46278 + 0.807127i 0.996972 0.0777603i \(-0.0247769\pi\)
0.465806 + 0.884887i \(0.345765\pi\)
\(264\) 0 0
\(265\) −0.108306 + 0.792937i −0.00665316 + 0.0487097i
\(266\) 1.84294 4.77332i 0.112998 0.292671i
\(267\) 0 0
\(268\) 10.1181 0.786438i 0.618059 0.0480393i
\(269\) −13.6424 + 11.4474i −0.831794 + 0.697958i −0.955702 0.294336i \(-0.904902\pi\)
0.123908 + 0.992294i \(0.460457\pi\)
\(270\) 0 0
\(271\) −18.0036 15.1069i −1.09364 0.917676i −0.0966624 0.995317i \(-0.530817\pi\)
−0.996981 + 0.0776412i \(0.975261\pi\)
\(272\) −5.19417 3.71257i −0.314943 0.225108i
\(273\) 0 0
\(274\) −18.0482 + 20.6810i −1.09033 + 1.24938i
\(275\) −1.09492 5.05473i −0.0660264 0.304812i
\(276\) 0 0
\(277\) 27.0188 5.30632i 1.62340 0.318826i 0.703417 0.710777i \(-0.251657\pi\)
0.919986 + 0.391952i \(0.128200\pi\)
\(278\) −22.6604 2.64862i −1.35908 0.158854i
\(279\) 0 0
\(280\) 0.402209 + 0.540260i 0.0240366 + 0.0322867i
\(281\) −3.97998 + 18.3736i −0.237426 + 1.09608i 0.690505 + 0.723328i \(0.257388\pi\)
−0.927931 + 0.372752i \(0.878414\pi\)
\(282\) 0 0
\(283\) −13.2527 12.9981i −0.787789 0.772658i 0.190104 0.981764i \(-0.439118\pi\)
−0.977893 + 0.209106i \(0.932945\pi\)
\(284\) 1.81526 7.04727i 0.107716 0.418179i
\(285\) 0 0
\(286\) −1.01805 0.923834i −0.0601988 0.0546275i
\(287\) 0.425603 0.986658i 0.0251225 0.0582406i
\(288\) 0 0
\(289\) −9.13560 + 12.2712i −0.537388 + 0.721838i
\(290\) −2.19518 2.51539i −0.128905 0.147709i
\(291\) 0 0
\(292\) −5.45881 1.75030i −0.319453 0.102428i
\(293\) 5.31186 + 1.04322i 0.310322 + 0.0609453i 0.345449 0.938438i \(-0.387727\pi\)
−0.0351266 + 0.999383i \(0.511183\pi\)
\(294\) 0 0
\(295\) 5.16581 2.34815i 0.300765 0.136714i
\(296\) −1.00217 + 5.68357i −0.0582497 + 0.330351i
\(297\) 0 0
\(298\) 2.64724 + 15.0132i 0.153351 + 0.869694i
\(299\) 0.439185 + 0.640348i 0.0253987 + 0.0370323i
\(300\) 0 0
\(301\) 4.37041 + 5.41846i 0.251906 + 0.312315i
\(302\) −25.1519 + 10.2757i −1.44733 + 0.591298i
\(303\) 0 0
\(304\) −8.39984 + 5.06933i −0.481764 + 0.290746i
\(305\) 3.59669 2.36558i 0.205946 0.135453i
\(306\) 0 0
\(307\) 0.0257695 0.442444i 0.00147074 0.0252516i −0.997493 0.0707660i \(-0.977456\pi\)
0.998964 + 0.0455144i \(0.0144927\pi\)
\(308\) 1.05513 1.67408i 0.0601217 0.0953895i
\(309\) 0 0
\(310\) 1.18565 0.847454i 0.0673406 0.0481322i
\(311\) −28.3459 2.20322i −1.60735 0.124933i −0.757817 0.652467i \(-0.773734\pi\)
−0.849534 + 0.527534i \(0.823117\pi\)
\(312\) 0 0
\(313\) 15.5192 + 6.34028i 0.877196 + 0.358374i 0.771655 0.636041i \(-0.219429\pi\)
0.105540 + 0.994415i \(0.466343\pi\)
\(314\) −4.13904 13.8254i −0.233580 0.780211i
\(315\) 0 0
\(316\) −18.4181 + 4.36517i −1.03610 + 0.245560i
\(317\) −7.18856 18.6188i −0.403750 1.04574i −0.974455 0.224583i \(-0.927898\pi\)
0.570705 0.821155i \(-0.306670\pi\)
\(318\) 0 0
\(319\) 2.32981 4.42304i 0.130445 0.247643i
\(320\) −0.0151133 + 0.779239i −0.000844860 + 0.0435608i
\(321\) 0 0
\(322\) −2.00261 + 1.96415i −0.111601 + 0.109458i
\(323\) −1.30736 2.26442i −0.0727436 0.125996i
\(324\) 0 0
\(325\) −1.71258 + 2.96627i −0.0949966 + 0.164539i
\(326\) 4.13796 + 16.0646i 0.229181 + 0.889733i
\(327\) 0 0
\(328\) −0.827402 + 0.456541i −0.0456856 + 0.0252083i
\(329\) 5.58603 + 8.86284i 0.307968 + 0.488624i
\(330\) 0 0
\(331\) −6.05106 + 7.50214i −0.332596 + 0.412355i −0.916860 0.399209i \(-0.869285\pi\)
0.584263 + 0.811564i \(0.301383\pi\)
\(332\) 2.43435 8.13130i 0.133602 0.446263i
\(333\) 0 0
\(334\) −6.38720 + 6.77004i −0.349492 + 0.370440i
\(335\) −2.36612 + 1.83388i −0.129275 + 0.100196i
\(336\) 0 0
\(337\) 5.72348 + 11.9696i 0.311778 + 0.652028i 0.997091 0.0762205i \(-0.0242853\pi\)
−0.685313 + 0.728248i \(0.740335\pi\)
\(338\) −2.20669 22.6867i −0.120028 1.23400i
\(339\) 0 0
\(340\) −0.674813 0.0261858i −0.0365969 0.00142012i
\(341\) 1.82326 + 1.19917i 0.0987349 + 0.0649389i
\(342\) 0 0
\(343\) 15.0626 + 7.56471i 0.813303 + 0.408456i
\(344\) −0.118716 6.12098i −0.00640075 0.330021i
\(345\) 0 0
\(346\) −31.7182 24.5835i −1.70518 1.32161i
\(347\) −14.4473 + 2.25952i −0.775573 + 0.121297i −0.529905 0.848057i \(-0.677773\pi\)
−0.245668 + 0.969354i \(0.579007\pi\)
\(348\) 0 0
\(349\) −4.82908 + 10.0992i −0.258495 + 0.540596i −0.989971 0.141271i \(-0.954881\pi\)
0.731476 + 0.681867i \(0.238832\pi\)
\(350\) −11.6272 4.23194i −0.621498 0.226207i
\(351\) 0 0
\(352\) −6.47934 + 2.35829i −0.345350 + 0.125697i
\(353\) −0.605119 + 6.22117i −0.0322072 + 0.331119i 0.965333 + 0.261022i \(0.0840595\pi\)
−0.997540 + 0.0700976i \(0.977669\pi\)
\(354\) 0 0
\(355\) 0.694941 + 2.03104i 0.0368836 + 0.107796i
\(356\) −11.8141 + 10.7208i −0.626148 + 0.568199i
\(357\) 0 0
\(358\) 5.90833 17.2677i 0.312265 0.912629i
\(359\) −8.39468 19.4611i −0.443054 1.02712i −0.982697 0.185221i \(-0.940700\pi\)
0.539643 0.841894i \(-0.318559\pi\)
\(360\) 0 0
\(361\) 14.8807 1.73931i 0.783196 0.0915424i
\(362\) −31.5950 + 10.1305i −1.66060 + 0.532450i
\(363\) 0 0
\(364\) −1.26250 + 0.351440i −0.0661729 + 0.0184205i
\(365\) 1.62904 0.453473i 0.0852676 0.0237359i
\(366\) 0 0
\(367\) 0.193167 0.0619366i 0.0100833 0.00323307i −0.300280 0.953851i \(-0.597080\pi\)
0.310363 + 0.950618i \(0.399549\pi\)
\(368\) 5.34213 0.624405i 0.278478 0.0325494i
\(369\) 0 0
\(370\) 1.32299 + 3.06704i 0.0687790 + 0.159448i
\(371\) −0.928130 + 2.71256i −0.0481861 + 0.140829i
\(372\) 0 0
\(373\) −8.86637 + 8.04580i −0.459083 + 0.416596i −0.868452 0.495773i \(-0.834885\pi\)
0.409369 + 0.912369i \(0.365749\pi\)
\(374\) −0.821578 2.40115i −0.0424828 0.124161i
\(375\) 0 0
\(376\) 0.891956 9.17011i 0.0459991 0.472912i
\(377\) −3.11104 + 1.13233i −0.160227 + 0.0583178i
\(378\) 0 0
\(379\) −0.403266 0.146777i −0.0207144 0.00753941i 0.331642 0.943405i \(-0.392397\pi\)
−0.352357 + 0.935866i \(0.614620\pi\)
\(380\) −0.447670 + 0.936222i −0.0229650 + 0.0480272i
\(381\) 0 0
\(382\) 17.2437 2.69687i 0.882266 0.137984i
\(383\) −12.8780 9.98119i −0.658034 0.510015i 0.227985 0.973665i \(-0.426786\pi\)
−0.886018 + 0.463650i \(0.846540\pi\)
\(384\) 0 0
\(385\) 0.0113190 + 0.583606i 0.000576871 + 0.0297433i
\(386\) −12.0456 6.04955i −0.613107 0.307914i
\(387\) 0 0
\(388\) 2.56726 + 1.68851i 0.130333 + 0.0857212i
\(389\) −2.29930 0.0892232i −0.116579 0.00452380i −0.0195801 0.999808i \(-0.506233\pi\)
−0.0969988 + 0.995284i \(0.530924\pi\)
\(390\) 0 0
\(391\) 0.138771 + 1.42669i 0.00701794 + 0.0721507i
\(392\) −2.67689 5.59823i −0.135203 0.282753i
\(393\) 0 0
\(394\) −13.6203 + 10.5565i −0.686179 + 0.531829i
\(395\) 3.83158 4.06124i 0.192788 0.204343i
\(396\) 0 0
\(397\) −11.0071 + 36.7663i −0.552432 + 1.84525i −0.0183259 + 0.999832i \(0.505834\pi\)
−0.534106 + 0.845418i \(0.679352\pi\)
\(398\) −20.0836 + 24.8998i −1.00670 + 1.24811i
\(399\) 0 0
\(400\) 12.6503 + 20.0711i 0.632516 + 1.00355i
\(401\) 5.37452 2.96553i 0.268391 0.148092i −0.343209 0.939259i \(-0.611514\pi\)
0.611600 + 0.791167i \(0.290526\pi\)
\(402\) 0 0
\(403\) −0.360496 1.39953i −0.0179576 0.0697156i
\(404\) 3.12360 5.41024i 0.155405 0.269169i
\(405\) 0 0
\(406\) −5.97996 10.3576i −0.296780 0.514039i
\(407\) −3.57079 + 3.50221i −0.176998 + 0.173598i
\(408\) 0 0
\(409\) 0.213277 10.9965i 0.0105459 0.543743i −0.956865 0.290532i \(-0.906168\pi\)
0.967411 0.253211i \(-0.0814866\pi\)
\(410\) −0.254896 + 0.483907i −0.0125884 + 0.0238985i
\(411\) 0 0
\(412\) −5.47618 14.1837i −0.269792 0.698779i
\(413\) 19.7799 4.68793i 0.973307 0.230678i
\(414\) 0 0
\(415\) 0.718079 + 2.39855i 0.0352491 + 0.117740i
\(416\) 4.22719 + 1.72700i 0.207255 + 0.0846729i
\(417\) 0 0
\(418\) −3.88808 0.302205i −0.190172 0.0147813i
\(419\) −21.6493 + 15.4740i −1.05764 + 0.755954i −0.970708 0.240261i \(-0.922767\pi\)
−0.0869289 + 0.996215i \(0.527705\pi\)
\(420\) 0 0
\(421\) −2.21382 + 3.51247i −0.107895 + 0.171187i −0.895593 0.444875i \(-0.853248\pi\)
0.787698 + 0.616062i \(0.211273\pi\)
\(422\) −1.49798 + 25.7194i −0.0729206 + 1.25200i
\(423\) 0 0
\(424\) 2.10654 1.38550i 0.102303 0.0672856i
\(425\) −5.41351 + 3.26707i −0.262594 + 0.158476i
\(426\) 0 0
\(427\) 14.2762 5.83247i 0.690873 0.282253i
\(428\) −14.0399 17.4067i −0.678643 0.841385i
\(429\) 0 0
\(430\) −2.00411 2.92206i −0.0966468 0.140914i
\(431\) −2.27022 12.8750i −0.109352 0.620169i −0.989392 0.145269i \(-0.953595\pi\)
0.880040 0.474900i \(-0.157516\pi\)
\(432\) 0 0
\(433\) 1.66547 9.44535i 0.0800374 0.453915i −0.918280 0.395931i \(-0.870422\pi\)
0.998318 0.0579834i \(-0.0184670\pi\)
\(434\) 4.75286 2.16044i 0.228145 0.103705i
\(435\) 0 0
\(436\) −15.3982 3.02411i −0.737441 0.144829i
\(437\) 2.09752 + 0.672542i 0.100338 + 0.0321721i
\(438\) 0 0
\(439\) 3.86429 + 4.42799i 0.184433 + 0.211336i 0.838206 0.545355i \(-0.183605\pi\)
−0.653773 + 0.756691i \(0.726815\pi\)
\(440\) 0.306550 0.411768i 0.0146142 0.0196303i
\(441\) 0 0
\(442\) −0.665684 + 1.54323i −0.0316634 + 0.0734039i
\(443\) −18.7127 16.9809i −0.889068 0.806786i 0.0929311 0.995673i \(-0.470376\pi\)
−0.981999 + 0.188886i \(0.939512\pi\)
\(444\) 0 0
\(445\) 1.17384 4.55712i 0.0556453 0.216028i
\(446\) 3.64600 + 3.57597i 0.172643 + 0.169327i
\(447\) 0 0
\(448\) −0.591084 + 2.72875i −0.0279261 + 0.128921i
\(449\) 9.67207 + 12.9918i 0.456453 + 0.613123i 0.969456 0.245264i \(-0.0788745\pi\)
−0.513003 + 0.858387i \(0.671467\pi\)
\(450\) 0 0
\(451\) −0.813438 0.0950773i −0.0383033 0.00447701i
\(452\) −6.75812 + 1.32725i −0.317875 + 0.0624287i
\(453\) 0 0
\(454\) −9.62203 44.4202i −0.451584 2.08475i
\(455\) 0.254177 0.291255i 0.0119160 0.0136542i
\(456\) 0 0
\(457\) 8.49821 + 6.07415i 0.397529 + 0.284137i 0.762635 0.646829i \(-0.223905\pi\)
−0.365105 + 0.930966i \(0.618967\pi\)
\(458\) 37.4410 + 31.4167i 1.74950 + 1.46801i
\(459\) 0 0
\(460\) 0.435807 0.365685i 0.0203196 0.0170502i
\(461\) 30.4960 2.37034i 1.42034 0.110398i 0.655781 0.754951i \(-0.272339\pi\)
0.764559 + 0.644554i \(0.222957\pi\)
\(462\) 0 0
\(463\) 13.3009 34.4503i 0.618146 1.60104i −0.169926 0.985457i \(-0.554353\pi\)
0.788073 0.615582i \(-0.211079\pi\)
\(464\) −3.10346 + 22.7213i −0.144074 + 1.05481i
\(465\) 0 0
\(466\) −15.9831 8.81908i −0.740401 0.408536i
\(467\) −1.54014 26.4431i −0.0712690 1.22364i −0.824491 0.565875i \(-0.808538\pi\)
0.753222 0.657767i \(-0.228499\pi\)
\(468\) 0 0
\(469\) −9.58344 + 4.81298i −0.442522 + 0.222243i
\(470\) −2.48514 4.71791i −0.114631 0.217621i
\(471\) 0 0
\(472\) −16.2748 7.39782i −0.749110 0.340512i
\(473\) 3.00094 4.37547i 0.137983 0.201184i
\(474\) 0 0
\(475\) 1.31492 + 9.62695i 0.0603329 + 0.441715i
\(476\) −2.35403 0.557914i −0.107897 0.0255720i
\(477\) 0 0
\(478\) 19.3332 + 20.4920i 0.884281 + 0.937283i
\(479\) 11.3088 + 1.76867i 0.516714 + 0.0808126i 0.407499 0.913206i \(-0.366401\pi\)
0.109215 + 0.994018i \(0.465166\pi\)
\(480\) 0 0
\(481\) 3.30984 0.128437i 0.150916 0.00585622i
\(482\) 30.9884 + 18.7016i 1.41148 + 0.851835i
\(483\) 0 0
\(484\) 12.5860 + 3.50356i 0.572092 + 0.159253i
\(485\) −0.906397 −0.0411574
\(486\) 0 0
\(487\) −5.02714 −0.227801 −0.113901 0.993492i \(-0.536335\pi\)
−0.113901 + 0.993492i \(0.536335\pi\)
\(488\) −13.0657 3.63710i −0.591458 0.164644i
\(489\) 0 0
\(490\) −3.07487 1.85569i −0.138908 0.0838317i
\(491\) 31.9329 1.23914i 1.44111 0.0559217i 0.693692 0.720272i \(-0.255983\pi\)
0.747421 + 0.664350i \(0.231292\pi\)
\(492\) 0 0
\(493\) −6.03828 0.944370i −0.271950 0.0425323i
\(494\) 1.77233 + 1.87856i 0.0797409 + 0.0845204i
\(495\) 0 0
\(496\) −9.74077 2.30860i −0.437373 0.103659i
\(497\) 1.04070 + 7.61928i 0.0466818 + 0.341772i
\(498\) 0 0
\(499\) −16.0712 + 23.4324i −0.719447 + 1.04898i 0.276672 + 0.960964i \(0.410768\pi\)
−0.996119 + 0.0880152i \(0.971948\pi\)
\(500\) 4.64108 + 2.10963i 0.207555 + 0.0943455i
\(501\) 0 0
\(502\) −25.3832 48.1888i −1.13291 2.15077i
\(503\) 13.8015 6.93138i 0.615379 0.309055i −0.113668 0.993519i \(-0.536260\pi\)
0.729047 + 0.684464i \(0.239964\pi\)
\(504\) 0 0
\(505\) 0.107148 + 1.83967i 0.00476804 + 0.0818641i
\(506\) 1.87187 + 1.03285i 0.0832148 + 0.0459160i
\(507\) 0 0
\(508\) 0.368522 2.69806i 0.0163505 0.119707i
\(509\) −9.34854 + 24.2133i −0.414367 + 1.07324i 0.555911 + 0.831242i \(0.312370\pi\)
−0.970277 + 0.241995i \(0.922198\pi\)
\(510\) 0 0
\(511\) 6.03945 0.469423i 0.267170 0.0207661i
\(512\) 14.9976 12.5845i 0.662807 0.556161i
\(513\) 0 0
\(514\) 7.40897 + 6.21686i 0.326796 + 0.274214i
\(515\) 3.64868 + 2.60792i 0.160780 + 0.114919i
\(516\) 0 0
\(517\) 5.25011 6.01596i 0.230900 0.264582i
\(518\) 2.53321 + 11.6946i 0.111303 + 0.513831i
\(519\) 0 0
\(520\) −0.333594 + 0.0655157i −0.0146291 + 0.00287305i
\(521\) 19.5777 + 2.28830i 0.857713 + 0.100252i 0.533570 0.845756i \(-0.320850\pi\)
0.324143 + 0.946008i \(0.394924\pi\)
\(522\) 0 0
\(523\) 0.335414 + 0.450539i 0.0146666 + 0.0197007i 0.809396 0.587263i \(-0.199795\pi\)
−0.794729 + 0.606964i \(0.792387\pi\)
\(524\) −0.816665 + 3.77014i −0.0356762 + 0.164700i
\(525\) 0 0
\(526\) −35.2703 34.5929i −1.53786 1.50832i
\(527\) 0.665490 2.58359i 0.0289892 0.112543i
\(528\) 0 0
\(529\) 16.1383 + 14.6447i 0.701664 + 0.636726i
\(530\) 0.577987 1.33992i 0.0251061 0.0582026i
\(531\) 0 0
\(532\) −2.21998 + 2.98196i −0.0962485 + 0.129284i
\(533\) 0.356620 + 0.408641i 0.0154469 + 0.0177002i
\(534\) 0 0
\(535\) 6.28163 + 2.01413i 0.271579 + 0.0870782i
\(536\) 9.25453 + 1.81753i 0.399735 + 0.0785053i
\(537\) 0 0
\(538\) 29.5621 13.4376i 1.27451 0.579337i
\(539\) 0.933842 5.29608i 0.0402234 0.228118i
\(540\) 0 0
\(541\) 1.60787 + 9.11870i 0.0691278 + 0.392043i 0.999666 + 0.0258482i \(0.00822864\pi\)
−0.930538 + 0.366195i \(0.880660\pi\)
\(542\) 24.2384 + 35.3404i 1.04113 + 1.51800i
\(543\) 0 0
\(544\) 5.29225 + 6.56136i 0.226903 + 0.281316i
\(545\) 4.28508 1.75065i 0.183553 0.0749896i
\(546\) 0 0
\(547\) −22.0383 + 13.3002i −0.942291 + 0.568676i −0.902574 0.430535i \(-0.858325\pi\)
−0.0397173 + 0.999211i \(0.512646\pi\)
\(548\) 16.6622 10.9589i 0.711773 0.468141i
\(549\) 0 0
\(550\) −0.548338 + 9.41461i −0.0233812 + 0.401440i
\(551\) −5.00768 + 7.94522i −0.213334 + 0.338478i
\(552\) 0 0
\(553\) 16.2725 11.6309i 0.691978 0.494596i
\(554\) −50.0563 3.89068i −2.12669 0.165299i
\(555\) 0 0
\(556\) 15.3449 + 6.26907i 0.650767 + 0.265868i
\(557\) −7.85382 26.2336i −0.332777 1.11155i −0.946681 0.322172i \(-0.895587\pi\)
0.613904 0.789380i \(-0.289598\pi\)
\(558\) 0 0
\(559\) −3.41901 + 0.810319i −0.144609 + 0.0342728i
\(560\) −0.964431 2.49794i −0.0407546 0.105557i
\(561\) 0 0
\(562\) 15.9758 30.3292i 0.673897 1.27936i
\(563\) −0.361870 + 18.6579i −0.0152510 + 0.786337i 0.911636 + 0.410998i \(0.134820\pi\)
−0.926887 + 0.375340i \(0.877526\pi\)
\(564\) 0 0
\(565\) 1.45040 1.42254i 0.0610189 0.0598469i
\(566\) 16.9239 + 29.3131i 0.711365 + 1.23212i
\(567\) 0 0
\(568\) 3.38149 5.85691i 0.141884 0.245750i
\(569\) −6.37380 24.7446i −0.267204 1.03735i −0.951377 0.308029i \(-0.900331\pi\)
0.684173 0.729320i \(-0.260163\pi\)
\(570\) 0 0
\(571\) 3.25553 1.79633i 0.136240 0.0751739i −0.413528 0.910491i \(-0.635704\pi\)
0.549768 + 0.835317i \(0.314716\pi\)
\(572\) 0.532575 + 0.844987i 0.0222681 + 0.0353307i
\(573\) 0 0
\(574\) −1.23008 + 1.52506i −0.0513426 + 0.0636548i
\(575\) 1.52769 5.10283i 0.0637090 0.212803i
\(576\) 0 0
\(577\) −20.4742 + 21.7014i −0.852354 + 0.903442i −0.996283 0.0861458i \(-0.972545\pi\)
0.143929 + 0.989588i \(0.454026\pi\)
\(578\) 22.0482 17.0886i 0.917084 0.710794i
\(579\) 0 0
\(580\) 1.04639 + 2.18834i 0.0434489 + 0.0908657i
\(581\) 0.868322 + 8.92713i 0.0360241 + 0.370360i
\(582\) 0 0
\(583\) 2.18345 + 0.0847278i 0.0904293 + 0.00350907i
\(584\) −4.45098 2.92745i −0.184183 0.121139i
\(585\) 0 0
\(586\) −8.82077 4.42996i −0.364383 0.183000i
\(587\) −0.253953 13.0937i −0.0104818 0.540437i −0.967845 0.251549i \(-0.919060\pi\)
0.957363 0.288888i \(-0.0932855\pi\)
\(588\) 0 0
\(589\) −3.24040 2.51150i −0.133518 0.103484i
\(590\) −10.2225 + 1.59878i −0.420855 + 0.0658206i
\(591\) 0 0
\(592\) 9.89756 20.6990i 0.406787 0.850723i
\(593\) −1.48149 0.539218i −0.0608375 0.0221430i 0.311422 0.950272i \(-0.399195\pi\)
−0.372260 + 0.928129i \(0.621417\pi\)
\(594\) 0 0
\(595\) 0.670584 0.244073i 0.0274913 0.0100060i
\(596\) 1.07229 11.0242i 0.0439229 0.451567i
\(597\) 0 0
\(598\) −0.458357 1.33960i −0.0187436 0.0547803i
\(599\) 11.8851 10.7851i 0.485610 0.440668i −0.392055 0.919942i \(-0.628236\pi\)
0.877665 + 0.479274i \(0.159100\pi\)
\(600\) 0 0
\(601\) 7.45525 21.7888i 0.304106 0.888784i −0.683239 0.730195i \(-0.739429\pi\)
0.987345 0.158588i \(-0.0506943\pi\)
\(602\) −5.02757 11.6552i −0.204908 0.475031i
\(603\) 0 0
\(604\) 19.6069 2.29172i 0.797794 0.0932487i
\(605\) −3.66973 + 1.17665i −0.149196 + 0.0478377i
\(606\) 0 0
\(607\) 37.8811 10.5449i 1.53755 0.428005i 0.607158 0.794581i \(-0.292309\pi\)
0.930388 + 0.366576i \(0.119470\pi\)
\(608\) 12.4792 3.47382i 0.506098 0.140882i
\(609\) 0 0
\(610\) −7.47472 + 2.39667i −0.302643 + 0.0970385i
\(611\) −5.25215 + 0.613888i −0.212479 + 0.0248353i
\(612\) 0 0
\(613\) 8.12572 + 18.8375i 0.328195 + 0.760841i 0.999801 + 0.0199332i \(0.00634535\pi\)
−0.671606 + 0.740908i \(0.734395\pi\)
\(614\) −0.261616 + 0.764603i −0.0105580 + 0.0308569i
\(615\) 0 0
\(616\) 1.36185 1.23582i 0.0548707 0.0497925i
\(617\) 7.02045 + 20.5180i 0.282633 + 0.826025i 0.992561 + 0.121751i \(0.0388510\pi\)
−0.709928 + 0.704274i \(0.751272\pi\)
\(618\) 0 0
\(619\) −0.773315 + 7.95038i −0.0310822 + 0.319553i 0.966854 + 0.255332i \(0.0821847\pi\)
−0.997936 + 0.0642210i \(0.979544\pi\)
\(620\) −0.995005 + 0.362152i −0.0399604 + 0.0145444i
\(621\) 0 0
\(622\) 48.7155 + 17.7310i 1.95331 + 0.710948i
\(623\) 7.27235 15.2088i 0.291360 0.609329i
\(624\) 0 0
\(625\) 22.4596 3.51262i 0.898384 0.140505i
\(626\) −24.1609 18.7261i −0.965663 0.748445i
\(627\) 0 0
\(628\) 0.203325 + 10.4834i 0.00811355 + 0.418332i
\(629\) 5.46429 + 2.74427i 0.217876 + 0.109421i
\(630\) 0 0
\(631\) −10.5366 6.93003i −0.419455 0.275880i 0.322187 0.946676i \(-0.395582\pi\)
−0.741642 + 0.670796i \(0.765953\pi\)
\(632\) −17.5773 0.682080i −0.699188 0.0271317i
\(633\) 0 0
\(634\) 3.52316 + 36.2212i 0.139922 + 1.43853i
\(635\) 0.346514 + 0.724672i 0.0137510 + 0.0287577i
\(636\) 0 0
\(637\) −2.81495 + 2.18175i −0.111532 + 0.0864442i
\(638\) −6.25539 + 6.63033i −0.247653 + 0.262497i
\(639\) 0 0
\(640\) −1.04099 + 3.47715i −0.0411488 + 0.137446i
\(641\) −28.2756 + 35.0562i −1.11682 + 1.38464i −0.202676 + 0.979246i \(0.564964\pi\)
−0.914143 + 0.405392i \(0.867135\pi\)
\(642\) 0 0
\(643\) 21.9387 + 34.8082i 0.865179 + 1.37270i 0.927177 + 0.374624i \(0.122228\pi\)
−0.0619979 + 0.998076i \(0.519747\pi\)
\(644\) 1.78440 0.984593i 0.0703154 0.0387984i
\(645\) 0 0
\(646\) 1.18926 + 4.61699i 0.0467908 + 0.181653i
\(647\) 14.2572 24.6943i 0.560510 0.970831i −0.436942 0.899490i \(-0.643939\pi\)
0.997452 0.0713418i \(-0.0227281\pi\)
\(648\) 0 0
\(649\) −7.74660 13.4175i −0.304081 0.526683i
\(650\) 4.45880 4.37316i 0.174888 0.171529i
\(651\) 0 0
\(652\) 0.233718 12.0505i 0.00915312 0.471933i
\(653\) 11.2697 21.3950i 0.441018 0.837252i −0.558950 0.829201i \(-0.688796\pi\)
0.999968 0.00805008i \(-0.00256245\pi\)
\(654\) 0 0
\(655\) −0.409846 1.06153i −0.0160140 0.0414773i
\(656\) 3.65558 0.866389i 0.142726 0.0338268i
\(657\) 0 0
\(658\) −5.47868 18.3001i −0.213581 0.713411i
\(659\) 26.5871 + 10.8620i 1.03568 + 0.423124i 0.831334 0.555774i \(-0.187578\pi\)
0.204351 + 0.978898i \(0.434492\pi\)
\(660\) 0 0
\(661\) −25.9412 2.01631i −1.00900 0.0784254i −0.437659 0.899141i \(-0.644192\pi\)
−0.571337 + 0.820715i \(0.693575\pi\)
\(662\) 14.2978 10.2195i 0.555701 0.397191i
\(663\) 0 0
\(664\) 4.20591 6.67314i 0.163221 0.258968i
\(665\) 0.0637618 1.09475i 0.00247257 0.0424525i
\(666\) 0 0
\(667\) 4.30161 2.82921i 0.166559 0.109548i
\(668\) 5.78974 3.49413i 0.224012 0.135192i
\(669\) 0 0
\(670\) 5.05310 2.06442i 0.195218 0.0797555i
\(671\) −7.37921 9.14879i −0.284871 0.353185i
\(672\) 0 0
\(673\) 14.6469 + 21.3557i 0.564598 + 0.823204i 0.996913 0.0785191i \(-0.0250191\pi\)
−0.432315 + 0.901723i \(0.642303\pi\)
\(674\) −4.20094 23.8247i −0.161814 0.917694i
\(675\) 0 0
\(676\) −2.87577 + 16.3093i −0.110607 + 0.627281i
\(677\) −1.64001 + 0.745476i −0.0630307 + 0.0286510i −0.445078 0.895492i \(-0.646824\pi\)
0.382047 + 0.924143i \(0.375219\pi\)
\(678\) 0 0
\(679\) −3.18617 0.625743i −0.122274 0.0240138i
\(680\) −0.597623 0.191620i −0.0229178 0.00734829i
\(681\) 0 0
\(682\) −2.61638 2.99803i −0.100186 0.114801i
\(683\) 24.6081 33.0545i 0.941604 1.26479i −0.0226308 0.999744i \(-0.507204\pi\)
0.964235 0.265050i \(-0.0853884\pi\)
\(684\) 0 0
\(685\) −2.33004 + 5.40164i −0.0890263 + 0.206386i
\(686\) −22.7601 20.6537i −0.868984 0.788561i
\(687\) 0 0
\(688\) −6.07104 + 23.5692i −0.231456 + 0.898568i
\(689\) −1.03312 1.01328i −0.0393587 0.0386027i
\(690\) 0 0
\(691\) −0.127205 + 0.587242i −0.00483909 + 0.0223397i −0.979690 0.200520i \(-0.935737\pi\)
0.974850 + 0.222860i \(0.0715392\pi\)
\(692\) 17.4109 + 23.3869i 0.661865 + 0.889038i
\(693\) 0 0
\(694\) 26.4832 + 3.09545i 1.00529 + 0.117502i
\(695\) −4.79791 + 0.942280i −0.181995 + 0.0357427i
\(696\) 0 0
\(697\) 0.211966 + 0.978542i 0.00802877 + 0.0370649i
\(698\) 13.4212 15.3790i 0.507999 0.582103i
\(699\) 0 0
\(700\) 7.31375 + 5.22756i 0.276434 + 0.197583i
\(701\) 21.6232 + 18.1441i 0.816699 + 0.685292i 0.952197 0.305486i \(-0.0988189\pi\)
−0.135498 + 0.990778i \(0.543263\pi\)
\(702\) 0 0
\(703\) 7.19798 6.03983i 0.271477 0.227796i
\(704\) 2.12159 0.164903i 0.0799605 0.00621503i
\(705\) 0 0
\(706\) 4.10503 10.6323i 0.154495 0.400152i
\(707\) −0.893390 + 6.54077i −0.0335994 + 0.245991i
\(708\) 0 0
\(709\) 4.73589 + 2.61315i 0.177860 + 0.0981391i 0.569544 0.821961i \(-0.307120\pi\)
−0.391684 + 0.920100i \(0.628107\pi\)
\(710\) −0.227590 3.90757i −0.00854130 0.146649i
\(711\) 0 0
\(712\) −13.2488 + 6.65381i −0.496521 + 0.249362i
\(713\) 1.04744 + 1.98852i 0.0392270 + 0.0744706i
\(714\) 0 0
\(715\) −0.268219 0.121921i −0.0100308 0.00455958i
\(716\) −7.49995 + 10.9352i −0.280286 + 0.408667i
\(717\) 0 0
\(718\) 5.23001 + 38.2904i 0.195182 + 1.42899i
\(719\) −35.5693 8.43007i −1.32651 0.314389i −0.494514 0.869170i \(-0.664654\pi\)
−0.831996 + 0.554781i \(0.812802\pi\)
\(720\) 0 0
\(721\) 11.0254 + 11.6863i 0.410608 + 0.435219i
\(722\) −26.9902 4.22118i −1.00447 0.157096i
\(723\) 0 0
\(724\) 24.0885 0.934742i 0.895241 0.0347394i
\(725\) 19.4445 + 11.7348i 0.722149 + 0.435819i
\(726\) 0 0
\(727\) −36.6368 10.1985i −1.35878 0.378243i −0.489261 0.872138i \(-0.662733\pi\)
−0.869522 + 0.493895i \(0.835573\pi\)
\(728\) −1.21788 −0.0451376
\(729\) 0 0
\(730\) −3.08333 −0.114119
\(731\) −6.24887 1.73949i −0.231123 0.0643374i
\(732\) 0 0
\(733\) −13.3974 8.08540i −0.494846 0.298641i 0.247230 0.968957i \(-0.420480\pi\)
−0.742076 + 0.670316i \(0.766159\pi\)
\(734\) −0.369607 + 0.0143424i −0.0136424 + 0.000529388i
\(735\) 0 0
\(736\) −7.01606 1.09729i −0.258615 0.0404467i
\(737\) 5.60904 + 5.94524i 0.206612 + 0.218996i
\(738\) 0 0
\(739\) −10.3965 2.46402i −0.382442 0.0906405i 0.0348978 0.999391i \(-0.488889\pi\)
−0.417340 + 0.908750i \(0.637038\pi\)
\(740\) −0.328427 2.40451i −0.0120732 0.0883917i
\(741\) 0 0
\(742\) 2.95677 4.31108i 0.108547 0.158265i
\(743\) −32.4169 14.7353i −1.18926 0.540586i −0.281292 0.959622i \(-0.590763\pi\)
−0.907969 + 0.419036i \(0.862368\pi\)
\(744\) 0 0
\(745\) 1.52267 + 2.89072i 0.0557863 + 0.105908i
\(746\) 19.5091 9.79783i 0.714278 0.358724i
\(747\) 0 0
\(748\) 0.107211 + 1.84074i 0.00392002 + 0.0673041i
\(749\) 20.6907 + 11.4167i 0.756023 + 0.417156i
\(750\) 0 0
\(751\) −7.27761 + 53.2815i −0.265564 + 1.94427i 0.0586281 + 0.998280i \(0.481327\pi\)
−0.324192 + 0.945991i \(0.605092\pi\)
\(752\) −13.1925 + 34.1695i −0.481082 + 1.24603i
\(753\) 0 0
\(754\) 6.01859 0.467801i 0.219184 0.0170363i
\(755\) −4.46065 + 3.74293i −0.162340 + 0.136219i
\(756\) 0 0
\(757\) −11.5258 9.67128i −0.418912 0.351509i 0.408837 0.912607i \(-0.365934\pi\)
−0.827749 + 0.561099i \(0.810379\pi\)
\(758\) 0.636610 + 0.455021i 0.0231227 + 0.0165271i
\(759\) 0 0
\(760\) −0.634116 + 0.726617i −0.0230018 + 0.0263572i
\(761\) −8.25302 38.1002i −0.299172 1.38113i −0.841179 0.540757i \(-0.818138\pi\)
0.542007 0.840374i \(-0.317665\pi\)
\(762\) 0 0
\(763\) 16.2715 3.19562i 0.589068 0.115689i
\(764\) −12.5950 1.47215i −0.455672 0.0532605i
\(765\) 0 0
\(766\) 17.7410 + 23.8302i 0.641007 + 0.861022i
\(767\) −2.17218 + 10.0279i −0.0784327 + 0.362086i
\(768\) 0 0
\(769\) −30.8524 30.2598i −1.11257 1.09120i −0.995175 0.0981110i \(-0.968720\pi\)
−0.117390 0.993086i \(-0.537453\pi\)
\(770\) 0.265492 1.03071i 0.00956768 0.0371440i
\(771\) 0 0
\(772\) 7.25251 + 6.58131i 0.261024 + 0.236866i
\(773\) −2.08796 + 4.84044i −0.0750988 + 0.174099i −0.951630 0.307247i \(-0.900592\pi\)
0.876531 + 0.481345i \(0.159852\pi\)
\(774\) 0 0
\(775\) −5.92025 + 7.95227i −0.212662 + 0.285654i
\(776\) 1.87761 + 2.15151i 0.0674024 + 0.0772346i
\(777\) 0 0
\(778\) 3.99535 + 1.28106i 0.143240 + 0.0459281i
\(779\) 1.50973 + 0.296502i 0.0540919 + 0.0106233i
\(780\) 0 0
\(781\) 5.33571 2.42538i 0.190927 0.0867868i
\(782\) 0.453865 2.57400i 0.0162302 0.0920459i
\(783\) 0 0
\(784\) 4.28377 + 24.2945i 0.152992 + 0.867660i
\(785\) −1.74939 2.55067i −0.0624384 0.0910374i
\(786\) 0