Properties

Label 729.2.i.a.685.22
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 685.22
Character \(\chi\) \(=\) 729.685
Dual form 729.2.i.a.613.22

$q$-expansion

\(f(q)\) \(=\) \(q+(1.83535 + 0.510904i) q^{2} +(1.39514 + 0.841972i) q^{4} +(-2.94702 + 0.114358i) q^{5} +(-2.67089 - 0.417720i) q^{7} +(-0.484358 - 0.513389i) q^{8} +O(q^{10})\) \(q+(1.83535 + 0.510904i) q^{2} +(1.39514 + 0.841972i) q^{4} +(-2.94702 + 0.114358i) q^{5} +(-2.67089 - 0.417720i) q^{7} +(-0.484358 - 0.513389i) q^{8} +(-5.46724 - 1.29576i) q^{10} +(-0.589047 - 4.31259i) q^{11} +(1.84548 - 2.69078i) q^{13} +(-4.68860 - 2.13123i) q^{14} +(-2.14553 - 4.07318i) q^{16} +(-4.70279 + 2.36183i) q^{17} +(0.0335399 + 0.575858i) q^{19} +(-4.20780 - 2.32177i) q^{20} +(1.12221 - 8.21604i) q^{22} +(-2.84305 + 7.36370i) q^{23} +(3.68691 - 0.286569i) q^{25} +(4.76183 - 3.99565i) q^{26} +(-3.37456 - 2.83159i) q^{28} +(0.495027 + 0.353824i) q^{29} +(5.02592 - 5.75907i) q^{31} +(-1.55794 - 7.19223i) q^{32} +(-9.83791 + 1.93210i) q^{34} +(7.91895 + 0.925592i) q^{35} +(1.86718 + 2.50805i) q^{37} +(-0.232651 + 1.07404i) q^{38} +(1.48612 + 1.45758i) q^{40} +(2.17856 - 8.45769i) q^{41} +(0.623280 + 0.565596i) q^{43} +(2.80928 - 6.51263i) q^{44} +(-8.98013 + 12.0624i) q^{46} +(-5.83765 - 6.68920i) q^{47} +(0.293432 + 0.0940850i) q^{49} +(6.91316 + 1.35770i) q^{50} +(4.84027 - 2.20017i) q^{52} +(-2.35120 + 13.3343i) q^{53} +(2.22912 + 12.6419i) q^{55} +(1.07921 + 1.57353i) q^{56} +(0.727777 + 0.902301i) q^{58} +(-6.01839 + 2.45878i) q^{59} +(4.92623 - 2.97299i) q^{61} +(12.1666 - 8.00212i) q^{62} +(0.279822 - 4.80436i) q^{64} +(-5.13097 + 8.14083i) q^{65} +(-7.89248 + 5.64120i) q^{67} +(-8.54964 - 0.664531i) q^{68} +(14.0611 + 5.74460i) q^{70} +(-0.635585 - 2.12300i) q^{71} +(-5.07940 + 1.20384i) q^{73} +(2.14554 + 5.55709i) q^{74} +(-0.438064 + 0.831643i) q^{76} +(-0.228172 + 11.7645i) q^{77} +(8.20313 - 8.04557i) q^{79} +(6.78872 + 11.7584i) q^{80} +(8.31948 - 14.4098i) q^{82} +(-3.22782 - 12.5312i) q^{83} +(13.5891 - 7.49816i) q^{85} +(0.854969 + 1.35650i) q^{86} +(-1.92873 + 2.39125i) q^{88} +(-1.18058 + 3.94341i) q^{89} +(-6.05307 + 6.41588i) q^{91} +(-10.1665 + 7.87962i) q^{92} +(-7.29657 - 15.2595i) q^{94} +(-0.164697 - 1.69323i) q^{95} +(-4.78397 - 0.185640i) q^{97} +(0.490480 + 0.322594i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 1404 q + 54 q^{2} - 54 q^{4} + 54 q^{5} - 54 q^{7} + 54 q^{8}+O(q^{10}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.83535 + 0.510904i 1.29779 + 0.361263i 0.847107 0.531423i \(-0.178342\pi\)
0.450679 + 0.892686i \(0.351182\pi\)
\(3\) 0 0
\(4\) 1.39514 + 0.841972i 0.697571 + 0.420986i
\(5\) −2.94702 + 0.114358i −1.31795 + 0.0511424i −0.688123 0.725594i \(-0.741565\pi\)
−0.629826 + 0.776736i \(0.716874\pi\)
\(6\) 0 0
\(7\) −2.67089 0.417720i −1.00950 0.157883i −0.371919 0.928265i \(-0.621300\pi\)
−0.637583 + 0.770382i \(0.720066\pi\)
\(8\) −0.484358 0.513389i −0.171246 0.181510i
\(9\) 0 0
\(10\) −5.46724 1.29576i −1.72889 0.409755i
\(11\) −0.589047 4.31259i −0.177604 1.30029i −0.836461 0.548026i \(-0.815379\pi\)
0.658857 0.752268i \(-0.271040\pi\)
\(12\) 0 0
\(13\) 1.84548 2.69078i 0.511845 0.746288i −0.479505 0.877539i \(-0.659184\pi\)
0.991349 + 0.131252i \(0.0418996\pi\)
\(14\) −4.68860 2.13123i −1.25308 0.569595i
\(15\) 0 0
\(16\) −2.14553 4.07318i −0.536382 1.01830i
\(17\) −4.70279 + 2.36183i −1.14059 + 0.572827i −0.915822 0.401584i \(-0.868460\pi\)
−0.224771 + 0.974412i \(0.572163\pi\)
\(18\) 0 0
\(19\) 0.0335399 + 0.575858i 0.00769459 + 0.132111i 0.999968 + 0.00803807i \(0.00255862\pi\)
−0.992273 + 0.124073i \(0.960404\pi\)
\(20\) −4.20780 2.32177i −0.940893 0.519163i
\(21\) 0 0
\(22\) 1.12221 8.21604i 0.239256 1.75167i
\(23\) −2.84305 + 7.36370i −0.592818 + 1.53544i 0.233573 + 0.972339i \(0.424958\pi\)
−0.826390 + 0.563098i \(0.809610\pi\)
\(24\) 0 0
\(25\) 3.68691 0.286569i 0.737382 0.0573138i
\(26\) 4.76183 3.99565i 0.933871 0.783611i
\(27\) 0 0
\(28\) −3.37456 2.83159i −0.637732 0.535121i
\(29\) 0.495027 + 0.353824i 0.0919242 + 0.0657035i 0.626525 0.779401i \(-0.284476\pi\)
−0.534601 + 0.845104i \(0.679538\pi\)
\(30\) 0 0
\(31\) 5.02592 5.75907i 0.902682 1.03436i −0.0965560 0.995328i \(-0.530783\pi\)
0.999238 0.0390313i \(-0.0124272\pi\)
\(32\) −1.55794 7.19223i −0.275407 1.27142i
\(33\) 0 0
\(34\) −9.83791 + 1.93210i −1.68719 + 0.331353i
\(35\) 7.91895 + 0.925592i 1.33855 + 0.156454i
\(36\) 0 0
\(37\) 1.86718 + 2.50805i 0.306962 + 0.412321i 0.928658 0.370937i \(-0.120964\pi\)
−0.621696 + 0.783259i \(0.713556\pi\)
\(38\) −0.232651 + 1.07404i −0.0377409 + 0.174232i
\(39\) 0 0
\(40\) 1.48612 + 1.45758i 0.234977 + 0.230464i
\(41\) 2.17856 8.45769i 0.340234 1.32087i −0.538124 0.842866i \(-0.680867\pi\)
0.878358 0.478003i \(-0.158639\pi\)
\(42\) 0 0
\(43\) 0.623280 + 0.565596i 0.0950492 + 0.0862526i 0.718147 0.695891i \(-0.244990\pi\)
−0.623098 + 0.782144i \(0.714126\pi\)
\(44\) 2.80928 6.51263i 0.423514 0.981816i
\(45\) 0 0
\(46\) −8.98013 + 12.0624i −1.32405 + 1.77851i
\(47\) −5.83765 6.68920i −0.851508 0.975720i 0.148405 0.988927i \(-0.452586\pi\)
−0.999913 + 0.0132066i \(0.995796\pi\)
\(48\) 0 0
\(49\) 0.293432 + 0.0940850i 0.0419188 + 0.0134407i
\(50\) 6.91316 + 1.35770i 0.977669 + 0.192008i
\(51\) 0 0
\(52\) 4.84027 2.20017i 0.671224 0.305109i
\(53\) −2.35120 + 13.3343i −0.322963 + 1.83161i 0.200660 + 0.979661i \(0.435691\pi\)
−0.523622 + 0.851950i \(0.675420\pi\)
\(54\) 0 0
\(55\) 2.22912 + 12.6419i 0.300574 + 1.70464i
\(56\) 1.07921 + 1.57353i 0.144216 + 0.210272i
\(57\) 0 0
\(58\) 0.727777 + 0.902301i 0.0955617 + 0.118478i
\(59\) −6.01839 + 2.45878i −0.783528 + 0.320107i −0.734427 0.678687i \(-0.762549\pi\)
−0.0491009 + 0.998794i \(0.515636\pi\)
\(60\) 0 0
\(61\) 4.92623 2.97299i 0.630739 0.380653i −0.164999 0.986294i \(-0.552762\pi\)
0.795738 + 0.605641i \(0.207083\pi\)
\(62\) 12.1666 8.00212i 1.54516 1.01627i
\(63\) 0 0
\(64\) 0.279822 4.80436i 0.0349778 0.600545i
\(65\) −5.13097 + 8.14083i −0.636418 + 1.00975i
\(66\) 0 0
\(67\) −7.89248 + 5.64120i −0.964220 + 0.689183i −0.950500 0.310723i \(-0.899429\pi\)
−0.0137191 + 0.999906i \(0.504367\pi\)
\(68\) −8.54964 0.664531i −1.03680 0.0805862i
\(69\) 0 0
\(70\) 14.0611 + 5.74460i 1.68063 + 0.686611i
\(71\) −0.635585 2.12300i −0.0754300 0.251954i 0.911955 0.410290i \(-0.134572\pi\)
−0.987385 + 0.158336i \(0.949387\pi\)
\(72\) 0 0
\(73\) −5.07940 + 1.20384i −0.594499 + 0.140899i −0.516841 0.856081i \(-0.672892\pi\)
−0.0776577 + 0.996980i \(0.524744\pi\)
\(74\) 2.14554 + 5.55709i 0.249414 + 0.645999i
\(75\) 0 0
\(76\) −0.438064 + 0.831643i −0.0502493 + 0.0953960i
\(77\) −0.228172 + 11.7645i −0.0260027 + 1.34069i
\(78\) 0 0
\(79\) 8.20313 8.04557i 0.922924 0.905198i −0.0728211 0.997345i \(-0.523200\pi\)
0.995745 + 0.0921472i \(0.0293730\pi\)
\(80\) 6.78872 + 11.7584i 0.759002 + 1.31463i
\(81\) 0 0
\(82\) 8.31948 14.4098i 0.918732 1.59129i
\(83\) −3.22782 12.5312i −0.354300 1.37548i −0.858909 0.512128i \(-0.828857\pi\)
0.504609 0.863348i \(-0.331637\pi\)
\(84\) 0 0
\(85\) 13.5891 7.49816i 1.47395 0.813290i
\(86\) 0.854969 + 1.35650i 0.0921937 + 0.146275i
\(87\) 0 0
\(88\) −1.92873 + 2.39125i −0.205603 + 0.254908i
\(89\) −1.18058 + 3.94341i −0.125141 + 0.418001i −0.997484 0.0708941i \(-0.977415\pi\)
0.872343 + 0.488895i \(0.162600\pi\)
\(90\) 0 0
\(91\) −6.05307 + 6.41588i −0.634534 + 0.672567i
\(92\) −10.1665 + 7.87962i −1.05993 + 0.821508i
\(93\) 0 0
\(94\) −7.29657 15.2595i −0.752583 1.57389i
\(95\) −0.164697 1.69323i −0.0168975 0.173722i
\(96\) 0 0
\(97\) −4.78397 0.185640i −0.485738 0.0188489i −0.205257 0.978708i \(-0.565803\pi\)
−0.280482 + 0.959859i \(0.590494\pi\)
\(98\) 0.490480 + 0.322594i 0.0495460 + 0.0325869i
\(99\) 0 0
\(100\) 5.38504 + 2.70447i 0.538504 + 0.270447i
\(101\) −0.178798 9.21880i −0.0177911 0.917305i −0.897300 0.441422i \(-0.854474\pi\)
0.879509 0.475883i \(-0.157871\pi\)
\(102\) 0 0
\(103\) 4.98182 + 3.86120i 0.490874 + 0.380456i 0.827754 0.561092i \(-0.189619\pi\)
−0.336880 + 0.941548i \(0.609372\pi\)
\(104\) −2.27529 + 0.355849i −0.223110 + 0.0348938i
\(105\) 0 0
\(106\) −11.1278 + 23.2719i −1.08083 + 2.26037i
\(107\) 8.46716 + 3.08179i 0.818551 + 0.297928i 0.717151 0.696918i \(-0.245446\pi\)
0.101400 + 0.994846i \(0.467668\pi\)
\(108\) 0 0
\(109\) 9.81756 3.57330i 0.940352 0.342260i 0.174047 0.984737i \(-0.444315\pi\)
0.766305 + 0.642477i \(0.222093\pi\)
\(110\) −2.36761 + 24.3412i −0.225743 + 2.32084i
\(111\) 0 0
\(112\) 4.02902 + 11.7753i 0.380706 + 1.11266i
\(113\) 6.12995 5.56264i 0.576658 0.523289i −0.330652 0.943753i \(-0.607269\pi\)
0.907309 + 0.420464i \(0.138133\pi\)
\(114\) 0 0
\(115\) 7.53645 22.0261i 0.702778 2.05395i
\(116\) 0.392723 + 0.910434i 0.0364634 + 0.0845317i
\(117\) 0 0
\(118\) −12.3020 + 1.43790i −1.13249 + 0.132370i
\(119\) 13.5472 4.34374i 1.24187 0.398190i
\(120\) 0 0
\(121\) −7.65436 + 2.13074i −0.695851 + 0.193703i
\(122\) 10.5603 2.93965i 0.956080 0.266143i
\(123\) 0 0
\(124\) 11.8608 3.80303i 1.06514 0.341522i
\(125\) 3.81386 0.445777i 0.341122 0.0398715i
\(126\) 0 0
\(127\) −3.31800 7.69199i −0.294425 0.682553i 0.705226 0.708983i \(-0.250846\pi\)
−0.999651 + 0.0264293i \(0.991586\pi\)
\(128\) −1.79660 + 5.25076i −0.158799 + 0.464106i
\(129\) 0 0
\(130\) −13.5763 + 12.3198i −1.19072 + 1.08052i
\(131\) −1.47113 4.29953i −0.128533 0.375652i 0.863051 0.505117i \(-0.168551\pi\)
−0.991584 + 0.129465i \(0.958674\pi\)
\(132\) 0 0
\(133\) 0.150966 1.55206i 0.0130904 0.134581i
\(134\) −17.3675 + 6.32127i −1.50033 + 0.546075i
\(135\) 0 0
\(136\) 3.49037 + 1.27039i 0.299296 + 0.108935i
\(137\) −2.02186 + 4.22836i −0.172739 + 0.361253i −0.970270 0.242025i \(-0.922188\pi\)
0.797531 + 0.603278i \(0.206139\pi\)
\(138\) 0 0
\(139\) 2.85495 0.446507i 0.242154 0.0378722i −0.0322771 0.999479i \(-0.510276\pi\)
0.274431 + 0.961607i \(0.411510\pi\)
\(140\) 10.2687 + 7.95887i 0.867866 + 0.672647i
\(141\) 0 0
\(142\) −0.0818694 4.22116i −0.00687033 0.354232i
\(143\) −12.6913 6.37381i −1.06130 0.533005i
\(144\) 0 0
\(145\) −1.49932 0.986118i −0.124512 0.0818927i
\(146\) −9.93751 0.385621i −0.822434 0.0319142i
\(147\) 0 0
\(148\) 0.493264 + 5.07120i 0.0405461 + 0.416850i
\(149\) −7.64332 15.9846i −0.626165 1.30951i −0.933727 0.357985i \(-0.883464\pi\)
0.307562 0.951528i \(-0.400487\pi\)
\(150\) 0 0
\(151\) −0.737056 + 0.571262i −0.0599808 + 0.0464886i −0.642150 0.766579i \(-0.721957\pi\)
0.582169 + 0.813068i \(0.302204\pi\)
\(152\) 0.279394 0.296140i 0.0226618 0.0240202i
\(153\) 0 0
\(154\) −6.42931 + 21.4754i −0.518088 + 1.73054i
\(155\) −14.1529 + 17.5469i −1.13679 + 1.40940i
\(156\) 0 0
\(157\) −0.553431 0.878077i −0.0441686 0.0700782i 0.823176 0.567786i \(-0.192200\pi\)
−0.867345 + 0.497708i \(0.834175\pi\)
\(158\) 19.1661 10.5754i 1.52477 0.841334i
\(159\) 0 0
\(160\) 5.41376 + 21.0175i 0.427995 + 1.66158i
\(161\) 10.6694 18.4800i 0.840870 1.45643i
\(162\) 0 0
\(163\) −3.52004 6.09689i −0.275711 0.477545i 0.694603 0.719393i \(-0.255580\pi\)
−0.970314 + 0.241848i \(0.922247\pi\)
\(164\) 10.1605 9.96538i 0.793404 0.778166i
\(165\) 0 0
\(166\) 0.478051 24.6482i 0.0371039 1.91307i
\(167\) 7.51784 14.2723i 0.581748 1.10442i −0.400405 0.916338i \(-0.631131\pi\)
0.982153 0.188083i \(-0.0602275\pi\)
\(168\) 0 0
\(169\) 0.847826 + 2.19592i 0.0652174 + 0.168917i
\(170\) 28.7716 6.81899i 2.20668 0.522993i
\(171\) 0 0
\(172\) 0.393347 + 1.31387i 0.0299924 + 0.100182i
\(173\) 16.1339 + 6.59141i 1.22663 + 0.501135i 0.896603 0.442835i \(-0.146027\pi\)
0.330031 + 0.943970i \(0.392941\pi\)
\(174\) 0 0
\(175\) −9.96703 0.774699i −0.753437 0.0585618i
\(176\) −16.3021 + 11.6521i −1.22882 + 0.878308i
\(177\) 0 0
\(178\) −4.18148 + 6.63437i −0.313415 + 0.497267i
\(179\) −1.21144 + 20.7996i −0.0905472 + 1.55464i 0.581141 + 0.813803i \(0.302606\pi\)
−0.671689 + 0.740834i \(0.734431\pi\)
\(180\) 0 0
\(181\) −12.3454 + 8.11973i −0.917630 + 0.603534i −0.918050 0.396465i \(-0.870237\pi\)
0.000420068 1.00000i \(0.499866\pi\)
\(182\) −14.3874 + 8.68283i −1.06646 + 0.643614i
\(183\) 0 0
\(184\) 5.15750 2.10707i 0.380216 0.155335i
\(185\) −5.78943 7.17777i −0.425647 0.527720i
\(186\) 0 0
\(187\) 12.9558 + 18.8899i 0.947418 + 1.38137i
\(188\) −2.51222 14.2475i −0.183223 1.03911i
\(189\) 0 0
\(190\) 0.562803 3.19181i 0.0408300 0.231558i
\(191\) 19.2046 8.72954i 1.38959 0.631647i 0.427411 0.904057i \(-0.359426\pi\)
0.962181 + 0.272410i \(0.0878207\pi\)
\(192\) 0 0
\(193\) −14.3546 2.81916i −1.03327 0.202927i −0.352796 0.935700i \(-0.614769\pi\)
−0.680473 + 0.732773i \(0.738226\pi\)
\(194\) −8.68539 2.78486i −0.623575 0.199941i
\(195\) 0 0
\(196\) 0.330161 + 0.378323i 0.0235830 + 0.0270231i
\(197\) 12.6636 17.0101i 0.902242 1.21192i −0.0744395 0.997226i \(-0.523717\pi\)
0.976681 0.214695i \(-0.0688758\pi\)
\(198\) 0 0
\(199\) 3.50981 8.13666i 0.248804 0.576793i −0.747348 0.664433i \(-0.768673\pi\)
0.996152 + 0.0876400i \(0.0279325\pi\)
\(200\) −1.93290 1.75402i −0.136677 0.124028i
\(201\) 0 0
\(202\) 4.38176 17.0110i 0.308300 1.19689i
\(203\) −1.17436 1.15181i −0.0824242 0.0808411i
\(204\) 0 0
\(205\) −5.45306 + 25.1741i −0.380858 + 1.75824i
\(206\) 7.17067 + 9.63188i 0.499604 + 0.671085i
\(207\) 0 0
\(208\) −14.9196 1.74385i −1.03449 0.120914i
\(209\) 2.46368 0.483852i 0.170417 0.0334687i
\(210\) 0 0
\(211\) 0.809358 + 3.73641i 0.0557185 + 0.257225i 0.996694 0.0812502i \(-0.0258913\pi\)
−0.940975 + 0.338475i \(0.890089\pi\)
\(212\) −14.5074 + 16.6236i −0.996372 + 1.14172i
\(213\) 0 0
\(214\) 13.9657 + 9.98206i 0.954674 + 0.682360i
\(215\) −1.90150 1.59555i −0.129681 0.108815i
\(216\) 0 0
\(217\) −15.8294 + 13.2824i −1.07457 + 0.901669i
\(218\) 19.8442 1.54242i 1.34402 0.104466i
\(219\) 0 0
\(220\) −7.53423 + 19.5141i −0.507958 + 1.31564i
\(221\) −2.32375 + 17.0129i −0.156312 + 1.14441i
\(222\) 0 0
\(223\) −21.8674 12.0659i −1.46435 0.807992i −0.467249 0.884126i \(-0.654755\pi\)
−0.997098 + 0.0761338i \(0.975742\pi\)
\(224\) 1.15674 + 19.8604i 0.0772879 + 1.32698i
\(225\) 0 0
\(226\) 14.0926 7.07755i 0.937423 0.470792i
\(227\) −0.567868 1.07807i −0.0376907 0.0715541i 0.865193 0.501439i \(-0.167196\pi\)
−0.902884 + 0.429885i \(0.858554\pi\)
\(228\) 0 0
\(229\) −14.2095 6.45902i −0.938991 0.426824i −0.114961 0.993370i \(-0.536674\pi\)
−0.824030 + 0.566546i \(0.808279\pi\)
\(230\) 25.0852 36.5752i 1.65407 2.41169i
\(231\) 0 0
\(232\) −0.0581207 0.425519i −0.00381581 0.0279367i
\(233\) −11.3621 2.69288i −0.744359 0.176416i −0.159099 0.987263i \(-0.550859\pi\)
−0.585259 + 0.810846i \(0.699007\pi\)
\(234\) 0 0
\(235\) 17.9686 + 19.0457i 1.17215 + 1.24240i
\(236\) −10.4667 1.63697i −0.681327 0.106558i
\(237\) 0 0
\(238\) 27.0831 1.05095i 1.75553 0.0681227i
\(239\) 0.622167 + 0.375480i 0.0402447 + 0.0242878i 0.536679 0.843787i \(-0.319679\pi\)
−0.496434 + 0.868074i \(0.665358\pi\)
\(240\) 0 0
\(241\) −16.6418 4.63256i −1.07199 0.298410i −0.313164 0.949699i \(-0.601389\pi\)
−0.758829 + 0.651289i \(0.774228\pi\)
\(242\) −15.1370 −0.973044
\(243\) 0 0
\(244\) 9.37596 0.600235
\(245\) −0.875509 0.243715i −0.0559342 0.0155704i
\(246\) 0 0
\(247\) 1.61140 + 0.972487i 0.102531 + 0.0618779i
\(248\) −5.39098 + 0.209195i −0.342328 + 0.0132839i
\(249\) 0 0
\(250\) 7.22751 + 1.13036i 0.457108 + 0.0714904i
\(251\) −21.0933 22.3575i −1.33139 1.41120i −0.842344 0.538940i \(-0.818825\pi\)
−0.489050 0.872256i \(-0.662657\pi\)
\(252\) 0 0
\(253\) 33.4313 + 7.92336i 2.10181 + 0.498137i
\(254\) −2.15981 15.8126i −0.135519 0.992173i
\(255\) 0 0
\(256\) −11.4240 + 16.6566i −0.713999 + 1.04104i
\(257\) 8.91225 + 4.05111i 0.555931 + 0.252702i 0.672015 0.740538i \(-0.265429\pi\)
−0.116084 + 0.993239i \(0.537034\pi\)
\(258\) 0 0
\(259\) −3.93936 7.47869i −0.244780 0.464703i
\(260\) −14.0128 + 7.03748i −0.869036 + 0.436446i
\(261\) 0 0
\(262\) −0.503382 8.64273i −0.0310990 0.533950i
\(263\) 7.05204 + 3.89115i 0.434847 + 0.239939i 0.685403 0.728163i \(-0.259626\pi\)
−0.250556 + 0.968102i \(0.580614\pi\)
\(264\) 0 0
\(265\) 5.40416 39.5655i 0.331975 2.43049i
\(266\) 1.07003 2.77145i 0.0656078 0.169928i
\(267\) 0 0
\(268\) −15.7609 + 1.22503i −0.962748 + 0.0748307i
\(269\) −21.6606 + 18.1754i −1.32067 + 1.10818i −0.334510 + 0.942392i \(0.608571\pi\)
−0.986162 + 0.165784i \(0.946985\pi\)
\(270\) 0 0
\(271\) −20.5231 17.2209i −1.24669 1.04610i −0.996971 0.0777801i \(-0.975217\pi\)
−0.249721 0.968318i \(-0.580339\pi\)
\(272\) 19.7101 + 14.0879i 1.19510 + 0.854206i
\(273\) 0 0
\(274\) −5.87109 + 6.72753i −0.354686 + 0.406425i
\(275\) −3.40762 15.7313i −0.205487 0.948634i
\(276\) 0 0
\(277\) 2.98501 0.586237i 0.179352 0.0352236i −0.102230 0.994761i \(-0.532598\pi\)
0.281582 + 0.959537i \(0.409141\pi\)
\(278\) 5.46795 + 0.639112i 0.327946 + 0.0383314i
\(279\) 0 0
\(280\) −3.36041 4.51382i −0.200823 0.269752i
\(281\) −0.347356 + 1.60358i −0.0207215 + 0.0956613i −0.986524 0.163620i \(-0.947683\pi\)
0.965802 + 0.259281i \(0.0834855\pi\)
\(282\) 0 0
\(283\) 16.1852 + 15.8743i 0.962108 + 0.943629i 0.998447 0.0557106i \(-0.0177424\pi\)
−0.0363389 + 0.999340i \(0.511570\pi\)
\(284\) 0.900777 3.49703i 0.0534513 0.207511i
\(285\) 0 0
\(286\) −20.0365 18.1822i −1.18478 1.07513i
\(287\) −9.35164 + 21.6795i −0.552010 + 1.27970i
\(288\) 0 0
\(289\) 6.38626 8.57824i 0.375663 0.504602i
\(290\) −2.24796 2.57588i −0.132005 0.151261i
\(291\) 0 0
\(292\) −8.10008 2.59719i −0.474021 0.151989i
\(293\) −9.76298 1.91739i −0.570359 0.112015i −0.100785 0.994908i \(-0.532136\pi\)
−0.469574 + 0.882893i \(0.655592\pi\)
\(294\) 0 0
\(295\) 17.4552 7.93435i 1.01628 0.461956i
\(296\) 0.383226 2.17338i 0.0222746 0.126325i
\(297\) 0 0
\(298\) −5.86153 33.2424i −0.339549 1.92568i
\(299\) 14.5673 + 21.2396i 0.842447 + 1.22832i
\(300\) 0 0
\(301\) −1.42845 1.77100i −0.0823345 0.102079i
\(302\) −1.64461 + 0.671899i −0.0946369 + 0.0386634i
\(303\) 0 0
\(304\) 2.27361 1.37213i 0.130401 0.0786972i
\(305\) −14.1777 + 9.32484i −0.811814 + 0.533939i
\(306\) 0 0
\(307\) 0.854376 14.6691i 0.0487618 0.837208i −0.881925 0.471390i \(-0.843752\pi\)
0.930686 0.365818i \(-0.119211\pi\)
\(308\) −10.2237 + 16.2210i −0.582551 + 0.924279i
\(309\) 0 0
\(310\) −34.9403 + 24.9738i −1.98447 + 1.41842i
\(311\) 6.07999 + 0.472574i 0.344764 + 0.0267972i 0.248708 0.968579i \(-0.419994\pi\)
0.0960569 + 0.995376i \(0.469377\pi\)
\(312\) 0 0
\(313\) −12.2888 5.02051i −0.694602 0.283776i 0.00327429 0.999995i \(-0.498958\pi\)
−0.697876 + 0.716219i \(0.745871\pi\)
\(314\) −0.567124 1.89433i −0.0320047 0.106903i
\(315\) 0 0
\(316\) 18.2187 4.31791i 1.02488 0.242901i
\(317\) −6.55288 16.9724i −0.368046 0.953264i −0.985955 0.167014i \(-0.946588\pi\)
0.617908 0.786250i \(-0.287980\pi\)
\(318\) 0 0
\(319\) 1.23430 2.34327i 0.0691077 0.131198i
\(320\) −0.275226 + 14.1906i −0.0153856 + 0.793277i
\(321\) 0 0
\(322\) 29.0237 28.4662i 1.61742 1.58636i
\(323\) −1.51781 2.62892i −0.0844531 0.146277i
\(324\) 0 0
\(325\) 6.03303 10.4495i 0.334652 0.579635i
\(326\) −3.34557 12.9883i −0.185294 0.719355i
\(327\) 0 0
\(328\) −5.39729 + 2.97810i −0.298015 + 0.164438i
\(329\) 12.7975 + 20.3046i 0.705549 + 1.11943i
\(330\) 0 0
\(331\) −2.43120 + 3.01422i −0.133631 + 0.165676i −0.840760 0.541408i \(-0.817891\pi\)
0.707129 + 0.707085i \(0.249990\pi\)
\(332\) 6.04764 20.2005i 0.331907 1.10865i
\(333\) 0 0
\(334\) 21.0896 22.3537i 1.15397 1.22314i
\(335\) 22.6142 17.5273i 1.23555 0.957620i
\(336\) 0 0
\(337\) 11.7344 + 24.5405i 0.639215 + 1.33680i 0.925532 + 0.378669i \(0.123618\pi\)
−0.286318 + 0.958135i \(0.592431\pi\)
\(338\) 0.434149 + 4.46344i 0.0236146 + 0.242779i
\(339\) 0 0
\(340\) 25.2720 + 0.980669i 1.37057 + 0.0531842i
\(341\) −27.7970 18.2824i −1.50529 0.990046i
\(342\) 0 0
\(343\) 16.1662 + 8.11899i 0.872895 + 0.438384i
\(344\) −0.0115194 0.593936i −0.000621083 0.0320229i
\(345\) 0 0
\(346\) 26.2436 + 20.3404i 1.41087 + 1.09350i
\(347\) 16.8812 2.64017i 0.906231 0.141732i 0.315806 0.948824i \(-0.397725\pi\)
0.590426 + 0.807092i \(0.298960\pi\)
\(348\) 0 0
\(349\) −14.5995 + 30.5323i −0.781493 + 1.63435i −0.00848026 + 0.999964i \(0.502699\pi\)
−0.773013 + 0.634390i \(0.781251\pi\)
\(350\) −17.8972 6.51404i −0.956644 0.348190i
\(351\) 0 0
\(352\) −30.0994 + 10.9553i −1.60431 + 0.583919i
\(353\) −1.57672 + 16.2101i −0.0839205 + 0.862779i 0.854996 + 0.518634i \(0.173559\pi\)
−0.938917 + 0.344144i \(0.888169\pi\)
\(354\) 0 0
\(355\) 2.11586 + 6.18385i 0.112298 + 0.328205i
\(356\) −4.96732 + 4.50760i −0.263268 + 0.238903i
\(357\) 0 0
\(358\) −12.8500 + 37.5556i −0.679144 + 1.98487i
\(359\) 2.97661 + 6.90056i 0.157099 + 0.364198i 0.978528 0.206114i \(-0.0660818\pi\)
−0.821429 + 0.570311i \(0.806823\pi\)
\(360\) 0 0
\(361\) 18.5410 2.16714i 0.975844 0.114060i
\(362\) −26.8066 + 8.59518i −1.40892 + 0.451753i
\(363\) 0 0
\(364\) −13.8469 + 3.85454i −0.725774 + 0.202033i
\(365\) 14.8314 4.12862i 0.776313 0.216102i
\(366\) 0 0
\(367\) 4.11329 1.31887i 0.214712 0.0688446i −0.196023 0.980599i \(-0.562803\pi\)
0.410735 + 0.911755i \(0.365272\pi\)
\(368\) 36.0935 4.21873i 1.88150 0.219916i
\(369\) 0 0
\(370\) −6.95846 16.1315i −0.361753 0.838638i
\(371\) 11.8498 34.6324i 0.615212 1.79802i
\(372\) 0 0
\(373\) −8.37068 + 7.59598i −0.433417 + 0.393305i −0.859299 0.511474i \(-0.829100\pi\)
0.425882 + 0.904779i \(0.359964\pi\)
\(374\) 14.1274 + 41.2887i 0.730508 + 2.13499i
\(375\) 0 0
\(376\) −0.606654 + 6.23695i −0.0312858 + 0.321646i
\(377\) 1.86563 0.679032i 0.0960846 0.0349719i
\(378\) 0 0
\(379\) −4.04003 1.47045i −0.207522 0.0755319i 0.236168 0.971712i \(-0.424109\pi\)
−0.443690 + 0.896180i \(0.646331\pi\)
\(380\) 1.19588 2.50097i 0.0613473 0.128297i
\(381\) 0 0
\(382\) 39.7070 6.21006i 2.03158 0.317734i
\(383\) 12.1682 + 9.43104i 0.621765 + 0.481904i 0.874107 0.485734i \(-0.161448\pi\)
−0.252342 + 0.967638i \(0.581201\pi\)
\(384\) 0 0
\(385\) −0.672936 34.6964i −0.0342960 1.76829i
\(386\) −24.9054 12.5080i −1.26765 0.636639i
\(387\) 0 0
\(388\) −6.51801 4.28696i −0.330902 0.217637i
\(389\) −18.5472 0.719717i −0.940381 0.0364911i −0.435976 0.899958i \(-0.643597\pi\)
−0.504405 + 0.863467i \(0.668288\pi\)
\(390\) 0 0
\(391\) −4.02151 41.3447i −0.203376 2.09089i
\(392\) −0.0938236 0.196215i −0.00473881 0.00991037i
\(393\) 0 0
\(394\) 31.9326 24.7496i 1.60874 1.24687i
\(395\) −23.2547 + 24.6486i −1.17007 + 1.24021i
\(396\) 0 0
\(397\) −0.00656058 + 0.0219139i −0.000329266 + 0.00109983i −0.958154 0.286253i \(-0.907590\pi\)
0.957825 + 0.287353i \(0.0927753\pi\)
\(398\) 10.5988 13.1404i 0.531269 0.658670i
\(399\) 0 0
\(400\) −9.07761 14.4026i −0.453880 0.720130i
\(401\) −1.61439 + 0.890782i −0.0806187 + 0.0444835i −0.522910 0.852388i \(-0.675154\pi\)
0.442291 + 0.896872i \(0.354166\pi\)
\(402\) 0 0
\(403\) −6.22112 24.1519i −0.309896 1.20309i
\(404\) 7.51252 13.0121i 0.373762 0.647375i
\(405\) 0 0
\(406\) −1.56690 2.71395i −0.0777641 0.134691i
\(407\) 9.71634 9.52972i 0.481621 0.472371i
\(408\) 0 0
\(409\) −0.235192 + 12.1265i −0.0116295 + 0.599615i 0.947988 + 0.318306i \(0.103114\pi\)
−0.959617 + 0.281308i \(0.909232\pi\)
\(410\) −22.8698 + 43.4173i −1.12946 + 2.14423i
\(411\) 0 0
\(412\) 3.69932 + 9.58148i 0.182252 + 0.472046i
\(413\) 17.1016 4.05314i 0.841513 0.199442i
\(414\) 0 0
\(415\) 10.9455 + 36.5606i 0.537294 + 1.79469i
\(416\) −22.2278 9.08107i −1.08981 0.445236i
\(417\) 0 0
\(418\) 4.76891 + 0.370669i 0.233255 + 0.0181300i
\(419\) −19.7120 + 14.0893i −0.962996 + 0.688308i −0.950210 0.311610i \(-0.899132\pi\)
−0.0127860 + 0.999918i \(0.504070\pi\)
\(420\) 0 0
\(421\) −3.18020 + 5.04574i −0.154994 + 0.245914i −0.914500 0.404586i \(-0.867416\pi\)
0.759506 + 0.650500i \(0.225440\pi\)
\(422\) −0.423494 + 7.27111i −0.0206154 + 0.353952i
\(423\) 0 0
\(424\) 7.98452 5.25150i 0.387763 0.255036i
\(425\) −16.6619 + 10.0555i −0.808221 + 0.487764i
\(426\) 0 0
\(427\) −14.3993 + 5.88276i −0.696831 + 0.284687i
\(428\) 9.21810 + 11.4286i 0.445574 + 0.552424i
\(429\) 0 0
\(430\) −2.67474 3.89987i −0.128987 0.188068i
\(431\) −5.12465 29.0633i −0.246846 1.39993i −0.816167 0.577817i \(-0.803905\pi\)
0.569321 0.822116i \(-0.307206\pi\)
\(432\) 0 0
\(433\) −1.65067 + 9.36143i −0.0793262 + 0.449881i 0.919111 + 0.393999i \(0.128908\pi\)
−0.998437 + 0.0558830i \(0.982203\pi\)
\(434\) −35.8384 + 16.2905i −1.72030 + 0.781971i
\(435\) 0 0
\(436\) 16.7055 + 3.28085i 0.800049 + 0.157124i
\(437\) −4.33580 1.39022i −0.207410 0.0665032i
\(438\) 0 0
\(439\) −0.0529657 0.0606920i −0.00252791 0.00289667i 0.752171 0.658968i \(-0.229007\pi\)
−0.754698 + 0.656072i \(0.772217\pi\)
\(440\) 5.41054 7.26762i 0.257938 0.346470i
\(441\) 0 0
\(442\) −12.9568 + 30.0373i −0.616293 + 1.42873i
\(443\) −25.2756 22.9364i −1.20088 1.08974i −0.993773 0.111422i \(-0.964459\pi\)
−0.207107 0.978318i \(-0.566405\pi\)
\(444\) 0 0
\(445\) 3.02824 11.7563i 0.143552 0.557304i
\(446\) −33.9697 33.3172i −1.60851 1.57762i
\(447\) 0 0
\(448\) −2.75425 + 12.7150i −0.130126 + 0.600729i
\(449\) 20.9958 + 28.2023i 0.990854 + 1.33095i 0.943251 + 0.332081i \(0.107751\pi\)
0.0476032 + 0.998866i \(0.484842\pi\)
\(450\) 0 0
\(451\) −37.7578 4.41325i −1.77795 0.207812i
\(452\) 13.2357 2.59941i 0.622557 0.122266i
\(453\) 0 0
\(454\) −0.491445 2.26876i −0.0230646 0.106478i
\(455\) 17.1048 19.6000i 0.801887 0.918861i
\(456\) 0 0
\(457\) −8.24919 5.89617i −0.385881 0.275811i 0.371962 0.928248i \(-0.378685\pi\)
−0.757843 + 0.652437i \(0.773747\pi\)
\(458\) −22.7795 19.1142i −1.06441 0.893149i
\(459\) 0 0
\(460\) 29.0598 24.3841i 1.35492 1.13691i
\(461\) 17.2190 1.33836i 0.801968 0.0623339i 0.330035 0.943969i \(-0.392939\pi\)
0.471932 + 0.881635i \(0.343557\pi\)
\(462\) 0 0
\(463\) 8.94970 23.1803i 0.415928 1.07728i −0.553705 0.832713i \(-0.686786\pi\)
0.969632 0.244567i \(-0.0786457\pi\)
\(464\) 0.379096 2.77547i 0.0175991 0.128848i
\(465\) 0 0
\(466\) −19.4777 10.7473i −0.902286 0.497860i
\(467\) 0.391271 + 6.71786i 0.0181059 + 0.310866i 0.995187 + 0.0979970i \(0.0312436\pi\)
−0.977081 + 0.212869i \(0.931719\pi\)
\(468\) 0 0
\(469\) 23.4364 11.7702i 1.08219 0.543497i
\(470\) 23.2482 + 44.1356i 1.07236 + 2.03582i
\(471\) 0 0
\(472\) 4.17737 + 1.89885i 0.192279 + 0.0874015i
\(473\) 2.07204 3.02111i 0.0952726 0.138911i
\(474\) 0 0
\(475\) 0.288682 + 2.11353i 0.0132456 + 0.0969752i
\(476\) 22.5576 + 5.34624i 1.03392 + 0.245045i
\(477\) 0 0
\(478\) 0.950059 + 1.00700i 0.0434547 + 0.0460593i
\(479\) 11.5631 + 1.80843i 0.528330 + 0.0826293i 0.413058 0.910705i \(-0.364461\pi\)
0.115272 + 0.993334i \(0.463226\pi\)
\(480\) 0 0
\(481\) 10.1945 0.395591i 0.464827 0.0180374i
\(482\) −28.1767 17.0047i −1.28341 0.774544i
\(483\) 0 0
\(484\) −12.4729 3.47208i −0.566952 0.157822i
\(485\) 14.1197 0.641142
\(486\) 0 0
\(487\) 12.2482 0.555018 0.277509 0.960723i \(-0.410491\pi\)
0.277509 + 0.960723i \(0.410491\pi\)
\(488\) −3.91236 1.08908i −0.177104 0.0493003i
\(489\) 0 0
\(490\) −1.48235 0.894602i −0.0669657 0.0404140i
\(491\) −10.6518 + 0.413338i −0.480709 + 0.0186537i −0.277991 0.960584i \(-0.589669\pi\)
−0.202717 + 0.979237i \(0.564977\pi\)
\(492\) 0 0
\(493\) −3.16368 0.494790i −0.142485 0.0222842i
\(494\) 2.46064 + 2.60812i 0.110709 + 0.117345i
\(495\) 0 0
\(496\) −34.2410 8.11526i −1.53746 0.364386i
\(497\) 0.810758 + 5.93580i 0.0363675 + 0.266257i
\(498\) 0 0
\(499\) −1.94472 + 2.83548i −0.0870578 + 0.126933i −0.865758 0.500463i \(-0.833163\pi\)
0.778700 + 0.627396i \(0.215879\pi\)
\(500\) 5.69621 + 2.58925i 0.254742 + 0.115795i
\(501\) 0 0
\(502\) −27.2909 51.8105i −1.21805 2.31241i
\(503\) 12.8559 6.45647i 0.573216 0.287880i −0.138483 0.990365i \(-0.544223\pi\)
0.711698 + 0.702485i \(0.247926\pi\)
\(504\) 0 0
\(505\) 1.58117 + 27.1476i 0.0703610 + 1.20805i
\(506\) 57.3099 + 31.6223i 2.54774 + 1.40578i
\(507\) 0 0
\(508\) 1.84736 13.5251i 0.0819634 0.600078i
\(509\) 4.00720 10.3789i 0.177616 0.460037i −0.815274 0.579076i \(-0.803413\pi\)
0.992890 + 0.119039i \(0.0379814\pi\)
\(510\) 0 0
\(511\) 14.0694 1.09356i 0.622393 0.0483762i
\(512\) −20.9744 + 17.5996i −0.926945 + 0.777799i
\(513\) 0 0
\(514\) 14.2873 + 11.9885i 0.630187 + 0.528790i
\(515\) −15.1231 10.8094i −0.666404 0.476317i
\(516\) 0 0
\(517\) −25.4091 + 29.1156i −1.11749 + 1.28050i
\(518\) −3.40920 15.7386i −0.149792 0.691515i
\(519\) 0 0
\(520\) 6.66464 1.30889i 0.292264 0.0573987i
\(521\) 17.5572 + 2.05214i 0.769193 + 0.0899058i 0.491633 0.870802i \(-0.336400\pi\)
0.277560 + 0.960708i \(0.410474\pi\)
\(522\) 0 0
\(523\) 5.66315 + 7.60693i 0.247632 + 0.332628i 0.908508 0.417867i \(-0.137222\pi\)
−0.660876 + 0.750495i \(0.729815\pi\)
\(524\) 1.56765 7.23710i 0.0684833 0.316154i
\(525\) 0 0
\(526\) 10.9549 + 10.7445i 0.477658 + 0.468483i
\(527\) −10.0339 + 38.9540i −0.437084 + 1.69686i
\(528\) 0 0
\(529\) −29.1086 26.4146i −1.26559 1.14846i
\(530\) 30.1327 69.8554i 1.30888 3.03432i
\(531\) 0 0
\(532\) 1.51741 2.03824i 0.0657882 0.0883689i
\(533\) −18.7373 21.4705i −0.811601 0.929992i
\(534\) 0 0
\(535\) −25.3053 8.11383i −1.09405 0.350792i
\(536\) 6.71891 + 1.31955i 0.290213 + 0.0569959i
\(537\) 0 0
\(538\) −49.0407 + 22.2917i −2.11429 + 0.961065i
\(539\) 0.232905 1.32087i 0.0100319 0.0568939i
\(540\) 0 0
\(541\) 2.32999 + 13.2140i 0.100174 + 0.568114i 0.993039 + 0.117789i \(0.0375808\pi\)
−0.892865 + 0.450325i \(0.851308\pi\)
\(542\) −28.8688 42.0918i −1.24002 1.80800i
\(543\) 0 0
\(544\) 24.3134 + 30.1439i 1.04243 + 1.29241i
\(545\) −28.5240 + 11.6533i −1.22183 + 0.499173i
\(546\) 0 0
\(547\) 3.42671 2.06803i 0.146515 0.0884225i −0.441547 0.897238i \(-0.645570\pi\)
0.588062 + 0.808816i \(0.299891\pi\)
\(548\) −6.38093 + 4.19681i −0.272580 + 0.179279i
\(549\) 0 0
\(550\) 1.78303 30.6134i 0.0760285 1.30536i
\(551\) −0.187149 + 0.296933i −0.00797283 + 0.0126498i
\(552\) 0 0
\(553\) −25.2705 + 18.0622i −1.07461 + 0.768085i
\(554\) 5.77804 + 0.449105i 0.245485 + 0.0190806i
\(555\) 0 0
\(556\) 4.35901 + 1.78085i 0.184863 + 0.0755250i
\(557\) −0.834823 2.78850i −0.0353726 0.118153i 0.938480 0.345334i \(-0.112234\pi\)
−0.973853 + 0.227181i \(0.927049\pi\)
\(558\) 0 0
\(559\) 2.67214 0.633310i 0.113020 0.0267862i
\(560\) −13.2202 34.2412i −0.558656 1.44695i
\(561\) 0 0
\(562\) −1.45679 + 2.76565i −0.0614511 + 0.116662i
\(563\) 0.609188 31.4096i 0.0256742 1.32375i −0.736524 0.676411i \(-0.763534\pi\)
0.762198 0.647344i \(-0.224120\pi\)
\(564\) 0 0
\(565\) −17.4290 + 17.0942i −0.733243 + 0.719160i
\(566\) 21.5951 + 37.4039i 0.907712 + 1.57220i
\(567\) 0 0
\(568\) −0.782075 + 1.35459i −0.0328151 + 0.0568375i
\(569\) 0.922457 + 3.58120i 0.0386714 + 0.150132i 0.984812 0.173625i \(-0.0555480\pi\)
−0.946140 + 0.323756i \(0.895054\pi\)
\(570\) 0 0
\(571\) −28.9327 + 15.9644i −1.21080 + 0.668089i −0.954414 0.298487i \(-0.903518\pi\)
−0.256382 + 0.966576i \(0.582531\pi\)
\(572\) −12.3396 19.5781i −0.515944 0.818601i
\(573\) 0 0
\(574\) −28.2396 + 35.0117i −1.17870 + 1.46136i
\(575\) −8.37187 + 27.9640i −0.349131 + 1.16618i
\(576\) 0 0
\(577\) −24.2426 + 25.6956i −1.00923 + 1.06972i −0.0116702 + 0.999932i \(0.503715\pi\)
−0.997562 + 0.0697914i \(0.977767\pi\)
\(578\) 16.1037 12.4813i 0.669824 0.519153i
\(579\) 0 0
\(580\) −1.26148 2.63816i −0.0523801 0.109544i
\(581\) 3.38664 + 34.8178i 0.140502 + 1.44448i
\(582\) 0 0
\(583\) 58.8905 + 2.28522i 2.43899 + 0.0946441i
\(584\) 3.07828 + 2.02462i 0.127380 + 0.0837794i
\(585\) 0 0
\(586\) −16.9388 8.50701i −0.699737 0.351421i
\(587\) −0.719307 37.0873i −0.0296890 1.53076i −0.658134 0.752901i \(-0.728654\pi\)
0.628445 0.777854i \(-0.283692\pi\)
\(588\) 0 0
\(589\) 3.48497 + 2.70106i 0.143596 + 0.111295i
\(590\) 36.0900 5.64437i 1.48580 0.232375i
\(591\) 0 0
\(592\) 6.20968 12.9864i 0.255216 0.533739i
\(593\) −14.2684 5.19326i −0.585932 0.213262i 0.0320074 0.999488i \(-0.489810\pi\)
−0.617939 + 0.786226i \(0.712032\pi\)
\(594\) 0 0
\(595\) −39.4272 + 14.3503i −1.61636 + 0.588306i
\(596\) 2.79512 28.7363i 0.114492 1.17708i
\(597\) 0 0
\(598\) 15.8846 + 46.4245i 0.649570 + 1.89844i
\(599\) 28.9497 26.2705i 1.18285 1.07338i 0.187005 0.982359i \(-0.440122\pi\)
0.995849 0.0910237i \(-0.0290139\pi\)
\(600\) 0 0
\(601\) 6.72378 19.6510i 0.274269 0.801581i −0.719932 0.694044i \(-0.755827\pi\)
0.994201 0.107537i \(-0.0342963\pi\)
\(602\) −1.71689 3.98020i −0.0699753 0.162221i
\(603\) 0 0
\(604\) −1.50928 + 0.176410i −0.0614119 + 0.00717802i
\(605\) 22.3139 7.15467i 0.907190 0.290879i
\(606\) 0 0
\(607\) 13.9219 3.87544i 0.565074 0.157299i 0.0261568 0.999658i \(-0.491673\pi\)
0.538917 + 0.842359i \(0.318834\pi\)
\(608\) 4.08945 1.13838i 0.165849 0.0461673i
\(609\) 0 0
\(610\) −30.7851 + 9.87086i −1.24645 + 0.399659i
\(611\) −28.7724 + 3.36301i −1.16401 + 0.136053i
\(612\) 0 0
\(613\) −2.13026 4.93849i −0.0860403 0.199464i 0.869764 0.493468i \(-0.164271\pi\)
−0.955804 + 0.294005i \(0.905012\pi\)
\(614\) 9.06256 26.4863i 0.365735 1.06890i
\(615\) 0 0
\(616\) 6.15029 5.58109i 0.247802 0.224868i
\(617\) 7.87738 + 23.0225i 0.317131 + 0.926851i 0.983449 + 0.181183i \(0.0579928\pi\)
−0.666318 + 0.745668i \(0.732131\pi\)
\(618\) 0 0
\(619\) 3.30867 34.0161i 0.132987 1.36722i −0.656903 0.753975i \(-0.728134\pi\)
0.789890 0.613249i \(-0.210138\pi\)
\(620\) −34.5193 + 12.5640i −1.38633 + 0.504582i
\(621\) 0 0
\(622\) 10.9174 + 3.97362i 0.437750 + 0.159328i
\(623\) 4.80044 10.0393i 0.192326 0.402215i
\(624\) 0 0
\(625\) −29.4566 + 4.60694i −1.17827 + 0.184277i
\(626\) −19.9891 15.4927i −0.798927 0.619215i
\(627\) 0 0
\(628\) −0.0327972 1.69102i −0.00130875 0.0674788i
\(629\) −14.7045 7.38489i −0.586307 0.294455i
\(630\) 0 0
\(631\) 5.94167 + 3.90790i 0.236534 + 0.155571i 0.662243 0.749289i \(-0.269605\pi\)
−0.425709 + 0.904860i \(0.639975\pi\)
\(632\) −8.10376 0.314463i −0.322350 0.0125087i
\(633\) 0 0
\(634\) −3.35555 34.4981i −0.133266 1.37009i
\(635\) 10.6579 + 22.2890i 0.422944 + 0.884513i
\(636\) 0 0
\(637\) 0.794684 0.615927i 0.0314865 0.0244039i
\(638\) 3.46256 3.67010i 0.137084 0.145301i
\(639\) 0 0
\(640\) 4.69416 15.6796i 0.185553 0.619790i
\(641\) −18.5297 + 22.9732i −0.731878 + 0.907386i −0.998406 0.0564412i \(-0.982025\pi\)
0.266528 + 0.963827i \(0.414123\pi\)
\(642\) 0 0
\(643\) −4.62450 7.33727i −0.182373 0.289354i 0.742337 0.670026i \(-0.233717\pi\)
−0.924710 + 0.380673i \(0.875693\pi\)
\(644\) 30.4451 16.7989i 1.19970 0.661968i
\(645\) 0 0
\(646\) −1.44258 5.60044i −0.0567575 0.220346i
\(647\) 22.2567 38.5498i 0.875002 1.51555i 0.0182408 0.999834i \(-0.494193\pi\)
0.856761 0.515714i \(-0.172473\pi\)
\(648\) 0 0
\(649\) 14.1488 + 24.5065i 0.555391 + 0.961965i
\(650\) 16.4114 16.0962i 0.643708 0.631344i
\(651\) 0 0
\(652\) 0.222456 11.4698i 0.00871206 0.449192i
\(653\) −16.6696 + 31.6464i −0.652330 + 1.23842i 0.305803 + 0.952095i \(0.401075\pi\)
−0.958133 + 0.286323i \(0.907567\pi\)
\(654\) 0 0
\(655\) 4.82713 + 12.5026i 0.188612 + 0.488516i
\(656\) −39.1239 + 9.27252i −1.52753 + 0.362031i
\(657\) 0 0
\(658\) 13.1141 + 43.8043i 0.511243 + 1.70767i
\(659\) 26.7663 + 10.9352i 1.04267 + 0.425977i 0.833858 0.551979i \(-0.186127\pi\)
0.208810 + 0.977956i \(0.433041\pi\)
\(660\) 0 0
\(661\) 37.7591 + 2.93487i 1.46866 + 0.114153i 0.786744 0.617279i \(-0.211765\pi\)
0.681914 + 0.731432i \(0.261148\pi\)
\(662\) −6.00208 + 4.29003i −0.233277 + 0.166737i
\(663\) 0 0
\(664\) −4.86995 + 7.72670i −0.188991 + 0.299854i
\(665\) −0.267409 + 4.59124i −0.0103697 + 0.178041i
\(666\) 0 0
\(667\) −4.01284 + 2.63929i −0.155378 + 0.102194i
\(668\) 22.5053 13.5820i 0.870757 0.525504i
\(669\) 0 0
\(670\) 50.4597 20.6151i 1.94943 0.796429i
\(671\) −15.7231 19.4936i −0.606983 0.752541i
\(672\) 0 0
\(673\) −17.8691 26.0538i −0.688803 1.00430i −0.998569 0.0534860i \(-0.982967\pi\)
0.309766 0.950813i \(-0.399749\pi\)
\(674\) 8.99892 + 51.0354i 0.346625 + 1.96581i
\(675\) 0 0
\(676\) −0.666070 + 3.77747i −0.0256181 + 0.145287i
\(677\) −13.4713 + 6.12347i −0.517745 + 0.235344i −0.655600 0.755108i \(-0.727584\pi\)
0.137855 + 0.990452i \(0.455979\pi\)
\(678\) 0 0
\(679\) 12.6999 + 2.49418i 0.487378 + 0.0957179i
\(680\) −10.4315 3.34472i −0.400029 0.128264i
\(681\) 0 0
\(682\) −41.6766 47.7561i −1.59588 1.82867i
\(683\) −6.33715 + 8.51226i −0.242484 + 0.325713i −0.906659 0.421865i \(-0.861376\pi\)
0.664175 + 0.747577i \(0.268783\pi\)
\(684\) 0 0
\(685\) 5.47492 12.6923i 0.209186 0.484947i
\(686\) 25.5226 + 23.1606i 0.974459 + 0.884274i
\(687\) 0 0
\(688\) 0.966513 3.75223i 0.0368479 0.143053i
\(689\) 31.5406 + 30.9348i 1.20160 + 1.17852i
\(690\) 0 0
\(691\) −0.0718770 + 0.331821i −0.00273433 + 0.0126231i −0.978681 0.205388i \(-0.934154\pi\)
0.975946 + 0.218011i \(0.0699569\pi\)
\(692\) 16.9592 + 22.7802i 0.644693 + 0.865973i
\(693\) 0 0
\(694\) 32.3318 + 3.77904i 1.22730 + 0.143450i
\(695\) −8.36256 + 1.64235i −0.317210 + 0.0622980i
\(696\) 0 0
\(697\) 9.73030 + 44.9201i 0.368561 + 1.70147i
\(698\) −42.3942 + 48.5783i −1.60464 + 1.83872i
\(699\) 0 0
\(700\) −13.2531 9.47278i −0.500922 0.358037i
\(701\) 28.5457 + 23.9527i 1.07816 + 0.904681i 0.995767 0.0919188i \(-0.0293000\pi\)
0.0823907 + 0.996600i \(0.473744\pi\)
\(702\) 0 0
\(703\) −1.38166 + 1.15935i −0.0521102 + 0.0437257i
\(704\) −20.8841 + 1.62324i −0.787098 + 0.0611781i
\(705\) 0 0
\(706\) −11.1757 + 28.9457i −0.420601 + 1.08938i
\(707\) −3.37332 + 24.6971i −0.126867 + 0.928830i
\(708\) 0 0
\(709\) 23.5431 + 12.9905i 0.884181 + 0.487870i 0.859096 0.511815i \(-0.171027\pi\)
0.0250850 + 0.999685i \(0.492014\pi\)
\(710\) 0.723995 + 12.4305i 0.0271710 + 0.466509i
\(711\) 0 0
\(712\) 2.59633 1.30393i 0.0973015 0.0488667i
\(713\) 28.1190 + 53.3827i 1.05307 + 1.99920i
\(714\) 0 0
\(715\) 38.1304 + 17.3324i 1.42600 + 0.648196i
\(716\) −19.2028 + 27.9984i −0.717643 + 1.04635i
\(717\) 0 0
\(718\) 1.93759 + 14.1857i 0.0723103 + 0.529405i
\(719\) 37.6978 + 8.93455i 1.40589 + 0.333203i 0.862407 0.506216i \(-0.168956\pi\)
0.543486 + 0.839418i \(0.317104\pi\)
\(720\) 0 0
\(721\) −11.6930 12.3939i −0.435470 0.461572i
\(722\) 35.1364 + 5.49524i 1.30764 + 0.204512i
\(723\) 0 0
\(724\) −24.0602 + 0.933646i −0.894191 + 0.0346987i
\(725\) 1.92652 + 1.16266i 0.0715490 + 0.0431800i
\(726\) 0 0
\(727\) 14.1793 + 3.94709i 0.525883 + 0.146390i 0.520932 0.853598i \(-0.325585\pi\)
0.00495097 + 0.999988i \(0.498424\pi\)
\(728\) 6.22569 0.230740
\(729\) 0 0
\(730\) 29.3302 1.08556
\(731\) −4.26699 1.18780i −0.157820 0.0439323i
\(732\) 0 0
\(733\) −7.82473 4.72225i −0.289013 0.174420i 0.364780 0.931094i \(-0.381144\pi\)
−0.653793 + 0.756674i \(0.726823\pi\)
\(734\) 8.22313 0.319095i 0.303521 0.0117780i
\(735\) 0 0
\(736\) 57.3907 + 8.97574i 2.11545 + 0.330850i
\(737\) 28.9772 + 30.7141i 1.06739 + 1.13137i
\(738\) 0 0
\(739\) 27.9445 + 6.62296i 1.02795 + 0.243630i 0.709795 0.704408i \(-0.248787\pi\)
0.318159 + 0.948037i \(0.396936\pi\)
\(740\) −2.03359 14.8885i −0.0747564 0.547313i
\(741\) 0 0
\(742\) 39.4423 57.5083i 1.44797 2.11120i
\(743\) 28.0396 + 12.7456i 1.02867 + 0.467590i 0.855774 0.517349i \(-0.173081\pi\)
0.172900 + 0.984939i \(0.444686\pi\)
\(744\) 0 0
\(745\) 24.3530 + 46.2331i 0.892226 + 1.69385i
\(746\) −19.2439 + 9.66466i −0.704570 + 0.353848i
\(747\) 0 0
\(748\) 2.17030 + 37.2625i 0.0793539 + 1.36245i
\(749\) −21.3275 11.7680i −0.779291 0.429994i
\(750\) 0 0
\(751\) 5.24462 38.3974i 0.191379 1.40114i −0.604943 0.796269i \(-0.706804\pi\)
0.796322 0.604873i \(-0.206776\pi\)
\(752\) −14.7215 + 38.1296i −0.536838 + 1.39045i
\(753\) 0 0
\(754\) 3.77099 0.293105i 0.137331 0.0106742i
\(755\) 2.10679 1.76781i 0.0766741 0.0643372i
\(756\) 0 0
\(757\) 6.10708 + 5.12445i 0.221966 + 0.186251i 0.746989 0.664837i \(-0.231499\pi\)
−0.525023 + 0.851088i \(0.675943\pi\)
\(758\) −6.66359 4.76285i −0.242033 0.172995i
\(759\) 0 0
\(760\) −0.789515 + 0.904684i −0.0286387 + 0.0328163i
\(761\) 3.81026 + 17.5901i 0.138122 + 0.637641i 0.992930 + 0.118698i \(0.0378720\pi\)
−0.854809 + 0.518943i \(0.826326\pi\)
\(762\) 0 0
\(763\) −27.7143 + 5.44291i −1.00332 + 0.197046i
\(764\) 34.1431 + 3.99075i 1.23525 + 0.144380i
\(765\) 0 0
\(766\) 17.5145 + 23.5260i 0.632823 + 0.850029i
\(767\) −4.49079 + 20.7318i −0.162153 + 0.748582i
\(768\) 0 0
\(769\) 34.9971 + 34.3249i 1.26203 + 1.23779i 0.958541 + 0.284953i \(0.0919781\pi\)
0.303487 + 0.952836i \(0.401849\pi\)
\(770\) 16.4914 64.0237i 0.594310 2.30725i
\(771\) 0 0
\(772\) −17.6531 16.0193i −0.635349 0.576548i
\(773\) −4.60233 + 10.6694i −0.165534 + 0.383752i −0.980712 0.195460i \(-0.937380\pi\)
0.815177 + 0.579211i \(0.196639\pi\)
\(774\) 0 0
\(775\) 16.8797 22.6734i 0.606338 0.814453i
\(776\) 2.22185 + 2.54595i 0.0797596 + 0.0913944i
\(777\) 0 0
\(778\) −33.6729 10.7968i −1.20723 0.387083i
\(779\) 4.94350 + 0.970871i 0.177119 + 0.0347851i
\(780\) 0 0
\(781\) −8.78124 + 3.99156i −0.314217 + 0.142829i
\(782\) 13.7423 77.9364i 0.491424 2.78700i
\(783\) 0 0
\(784\) −0.246340 1.39706i −0.00879785 0.0498951i
\(785\) 1.73139 + 2.52443i 0.0617959 + 0.0901006i
\(786\) 0 0