Properties

Label 729.2.i.a.685.10
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 685.10
Character \(\chi\) \(=\) 729.685
Dual form 729.2.i.a.613.10

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.984101 - 0.273943i) q^{2} +(-0.818925 - 0.494224i) q^{4} +(-2.73706 + 0.106211i) q^{5} +(0.877096 + 0.137175i) q^{7} +(2.07253 + 2.19675i) q^{8} +O(q^{10})\) \(q+(-0.984101 - 0.273943i) q^{2} +(-0.818925 - 0.494224i) q^{4} +(-2.73706 + 0.106211i) q^{5} +(0.877096 + 0.137175i) q^{7} +(2.07253 + 2.19675i) q^{8} +(2.72264 + 0.645278i) q^{10} +(0.602874 + 4.41382i) q^{11} +(3.10343 - 4.52491i) q^{13} +(-0.825572 - 0.375269i) q^{14} +(-0.546251 - 1.03703i) q^{16} +(-1.67001 + 0.838712i) q^{17} +(0.0797307 + 1.36892i) q^{19} +(2.29394 + 1.26574i) q^{20} +(0.615847 - 4.50880i) q^{22} +(3.01412 - 7.80676i) q^{23} +(2.49528 - 0.193948i) q^{25} +(-4.29366 + 3.60281i) q^{26} +(-0.650480 - 0.545818i) q^{28} +(-6.07359 - 4.34114i) q^{29} +(-3.66393 + 4.19840i) q^{31} +(-1.02526 - 4.73314i) q^{32} +(1.87322 - 0.367888i) q^{34} +(-2.41524 - 0.282301i) q^{35} +(-5.28091 - 7.09349i) q^{37} +(0.296544 - 1.36900i) q^{38} +(-5.90597 - 5.79254i) q^{40} +(0.508525 - 1.97421i) q^{41} +(3.65414 + 3.31596i) q^{43} +(1.68771 - 3.91254i) q^{44} +(-5.10480 + 6.85694i) q^{46} +(-3.30800 - 3.79054i) q^{47} +(-5.91526 - 1.89665i) q^{49} +(-2.50874 - 0.492700i) q^{50} +(-4.77780 + 2.17178i) q^{52} +(1.25461 - 7.11526i) q^{53} +(-2.11890 - 12.0169i) q^{55} +(1.51647 + 2.21106i) q^{56} +(4.78780 + 5.93594i) q^{58} +(0.734578 - 0.300108i) q^{59} +(5.51875 - 3.33058i) q^{61} +(4.75579 - 3.12794i) q^{62} +(-0.423953 + 7.27899i) q^{64} +(-8.01370 + 12.7146i) q^{65} +(4.19634 - 2.99937i) q^{67} +(1.78213 + 0.138518i) q^{68} +(2.29950 + 0.939450i) q^{70} +(1.74374 + 5.82449i) q^{71} +(0.740362 - 0.175469i) q^{73} +(3.25373 + 8.42737i) q^{74} +(0.611261 - 1.16045i) q^{76} +(-0.0766886 + 3.95404i) q^{77} +(4.92388 - 4.82930i) q^{79} +(1.60527 + 2.78040i) q^{80} +(-1.04126 + 1.80352i) q^{82} +(0.337095 + 1.30868i) q^{83} +(4.48185 - 2.47298i) q^{85} +(-2.68766 - 4.26426i) q^{86} +(-8.44660 + 10.4721i) q^{88} +(5.30103 - 17.7067i) q^{89} +(3.34271 - 3.54307i) q^{91} +(-6.32662 + 4.90350i) q^{92} +(2.21701 + 4.63648i) q^{94} +(-0.363622 - 3.73836i) q^{95} +(16.1419 + 0.626379i) q^{97} +(5.30163 + 3.48694i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 1404 q + 54 q^{2} - 54 q^{4} + 54 q^{5} - 54 q^{7} + 54 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 1404 q + 54 q^{2} - 54 q^{4} + 54 q^{5} - 54 q^{7} + 54 q^{8} - 54 q^{10} + 54 q^{11} - 54 q^{13} + 54 q^{14} - 54 q^{16} + 54 q^{17} - 54 q^{19} + 54 q^{20} - 54 q^{22} + 54 q^{23} - 54 q^{25} + 54 q^{26} - 54 q^{28} + 54 q^{29} - 54 q^{31} + 54 q^{32} - 54 q^{34} + 54 q^{35} - 54 q^{37} + 54 q^{38} - 54 q^{40} + 54 q^{41} - 54 q^{43} + 54 q^{44} - 54 q^{46} + 54 q^{47} - 54 q^{49} + 54 q^{50} - 54 q^{52} + 54 q^{53} - 54 q^{55} + 54 q^{56} - 54 q^{58} + 54 q^{59} - 54 q^{61} + 54 q^{62} - 54 q^{64} - 54 q^{67} - 135 q^{68} - 54 q^{70} - 54 q^{71} - 54 q^{73} - 162 q^{74} - 54 q^{76} - 162 q^{77} - 54 q^{79} - 351 q^{80} - 27 q^{82} - 54 q^{83} - 54 q^{85} - 162 q^{86} - 54 q^{88} - 81 q^{89} - 54 q^{91} - 270 q^{92} - 54 q^{94} - 54 q^{95} - 54 q^{97} - 54 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

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

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.984101 0.273943i −0.695864 0.193707i −0.0978602 0.995200i \(-0.531200\pi\)
−0.598004 + 0.801493i \(0.704039\pi\)
\(3\) 0 0
\(4\) −0.818925 0.494224i −0.409462 0.247112i
\(5\) −2.73706 + 0.106211i −1.22405 + 0.0474988i −0.642677 0.766137i \(-0.722176\pi\)
−0.581375 + 0.813636i \(0.697485\pi\)
\(6\) 0 0
\(7\) 0.877096 + 0.137175i 0.331511 + 0.0518474i 0.318084 0.948062i \(-0.396961\pi\)
0.0134269 + 0.999910i \(0.495726\pi\)
\(8\) 2.07253 + 2.19675i 0.732750 + 0.776670i
\(9\) 0 0
\(10\) 2.72264 + 0.645278i 0.860975 + 0.204055i
\(11\) 0.602874 + 4.41382i 0.181773 + 1.33082i 0.824997 + 0.565138i \(0.191177\pi\)
−0.643223 + 0.765679i \(0.722403\pi\)
\(12\) 0 0
\(13\) 3.10343 4.52491i 0.860737 1.25499i −0.104741 0.994500i \(-0.533401\pi\)
0.965478 0.260486i \(-0.0838827\pi\)
\(14\) −0.825572 0.375269i −0.220643 0.100295i
\(15\) 0 0
\(16\) −0.546251 1.03703i −0.136563 0.259258i
\(17\) −1.67001 + 0.838712i −0.405037 + 0.203417i −0.639641 0.768674i \(-0.720917\pi\)
0.234604 + 0.972091i \(0.424621\pi\)
\(18\) 0 0
\(19\) 0.0797307 + 1.36892i 0.0182915 + 0.314053i 0.995027 + 0.0996053i \(0.0317580\pi\)
−0.976736 + 0.214447i \(0.931205\pi\)
\(20\) 2.29394 + 1.26574i 0.512941 + 0.283029i
\(21\) 0 0
\(22\) 0.615847 4.50880i 0.131299 0.961278i
\(23\) 3.01412 7.80676i 0.628487 1.62782i −0.141630 0.989920i \(-0.545234\pi\)
0.770117 0.637903i \(-0.220198\pi\)
\(24\) 0 0
\(25\) 2.49528 0.193948i 0.499056 0.0387897i
\(26\) −4.29366 + 3.60281i −0.842056 + 0.706569i
\(27\) 0 0
\(28\) −0.650480 0.545818i −0.122929 0.103150i
\(29\) −6.07359 4.34114i −1.12784 0.806130i −0.144787 0.989463i \(-0.546250\pi\)
−0.983051 + 0.183333i \(0.941311\pi\)
\(30\) 0 0
\(31\) −3.66393 + 4.19840i −0.658061 + 0.754054i −0.981346 0.192247i \(-0.938422\pi\)
0.323286 + 0.946301i \(0.395213\pi\)
\(32\) −1.02526 4.73314i −0.181243 0.836710i
\(33\) 0 0
\(34\) 1.87322 0.367888i 0.321254 0.0630923i
\(35\) −2.41524 0.282301i −0.408250 0.0477175i
\(36\) 0 0
\(37\) −5.28091 7.09349i −0.868175 1.16616i −0.984922 0.173000i \(-0.944654\pi\)
0.116746 0.993162i \(-0.462754\pi\)
\(38\) 0.296544 1.36900i 0.0481058 0.222081i
\(39\) 0 0
\(40\) −5.90597 5.79254i −0.933816 0.915880i
\(41\) 0.508525 1.97421i 0.0794182 0.308320i −0.916332 0.400420i \(-0.868864\pi\)
0.995750 + 0.0920999i \(0.0293579\pi\)
\(42\) 0 0
\(43\) 3.65414 + 3.31596i 0.557252 + 0.505679i 0.901255 0.433290i \(-0.142647\pi\)
−0.344003 + 0.938969i \(0.611783\pi\)
\(44\) 1.68771 3.91254i 0.254431 0.589838i
\(45\) 0 0
\(46\) −5.10480 + 6.85694i −0.752662 + 1.01100i
\(47\) −3.30800 3.79054i −0.482521 0.552908i 0.459624 0.888114i \(-0.347984\pi\)
−0.942145 + 0.335206i \(0.891194\pi\)
\(48\) 0 0
\(49\) −5.91526 1.89665i −0.845036 0.270950i
\(50\) −2.50874 0.492700i −0.354789 0.0696782i
\(51\) 0 0
\(52\) −4.77780 + 2.17178i −0.662561 + 0.301171i
\(53\) 1.25461 7.11526i 0.172334 0.977356i −0.768842 0.639439i \(-0.779167\pi\)
0.941176 0.337917i \(-0.109722\pi\)
\(54\) 0 0
\(55\) −2.11890 12.0169i −0.285712 1.62036i
\(56\) 1.51647 + 2.21106i 0.202647 + 0.295466i
\(57\) 0 0
\(58\) 4.78780 + 5.93594i 0.628669 + 0.779427i
\(59\) 0.734578 0.300108i 0.0956340 0.0390708i −0.329878 0.944024i \(-0.607008\pi\)
0.425512 + 0.904953i \(0.360094\pi\)
\(60\) 0 0
\(61\) 5.51875 3.33058i 0.706603 0.426437i −0.117353 0.993090i \(-0.537441\pi\)
0.823957 + 0.566653i \(0.191762\pi\)
\(62\) 4.75579 3.12794i 0.603986 0.397248i
\(63\) 0 0
\(64\) −0.423953 + 7.27899i −0.0529941 + 0.909874i
\(65\) −8.01370 + 12.7146i −0.993977 + 1.57705i
\(66\) 0 0
\(67\) 4.19634 2.99937i 0.512665 0.366431i −0.295542 0.955330i \(-0.595500\pi\)
0.808207 + 0.588899i \(0.200438\pi\)
\(68\) 1.78213 + 0.138518i 0.216114 + 0.0167977i
\(69\) 0 0
\(70\) 2.29950 + 0.939450i 0.274843 + 0.112286i
\(71\) 1.74374 + 5.82449i 0.206944 + 0.691240i 0.996943 + 0.0781325i \(0.0248957\pi\)
−0.789999 + 0.613108i \(0.789919\pi\)
\(72\) 0 0
\(73\) 0.740362 0.175469i 0.0866529 0.0205371i −0.187061 0.982348i \(-0.559896\pi\)
0.273714 + 0.961811i \(0.411748\pi\)
\(74\) 3.25373 + 8.42737i 0.378238 + 0.979662i
\(75\) 0 0
\(76\) 0.611261 1.16045i 0.0701164 0.133113i
\(77\) −0.0766886 + 3.95404i −0.00873947 + 0.450605i
\(78\) 0 0
\(79\) 4.92388 4.82930i 0.553979 0.543339i −0.368378 0.929676i \(-0.620087\pi\)
0.922358 + 0.386337i \(0.126260\pi\)
\(80\) 1.60527 + 2.78040i 0.179474 + 0.310859i
\(81\) 0 0
\(82\) −1.04126 + 1.80352i −0.114988 + 0.199165i
\(83\) 0.337095 + 1.30868i 0.0370010 + 0.143647i 0.984223 0.176931i \(-0.0566169\pi\)
−0.947222 + 0.320577i \(0.896123\pi\)
\(84\) 0 0
\(85\) 4.48185 2.47298i 0.486125 0.268232i
\(86\) −2.68766 4.26426i −0.289818 0.459827i
\(87\) 0 0
\(88\) −8.44660 + 10.4721i −0.900411 + 1.11633i
\(89\) 5.30103 17.7067i 0.561908 1.87690i 0.0884671 0.996079i \(-0.471803\pi\)
0.473441 0.880825i \(-0.343012\pi\)
\(90\) 0 0
\(91\) 3.34271 3.54307i 0.350412 0.371415i
\(92\) −6.32662 + 4.90350i −0.659596 + 0.511225i
\(93\) 0 0
\(94\) 2.21701 + 4.63648i 0.228667 + 0.478216i
\(95\) −0.363622 3.73836i −0.0373069 0.383548i
\(96\) 0 0
\(97\) 16.1419 + 0.626379i 1.63896 + 0.0635992i 0.841669 0.539994i \(-0.181574\pi\)
0.797292 + 0.603593i \(0.206265\pi\)
\(98\) 5.30163 + 3.48694i 0.535546 + 0.352234i
\(99\) 0 0
\(100\) −2.13930 1.07440i −0.213930 0.107440i
\(101\) −0.297597 15.3440i −0.0296121 1.52679i −0.660447 0.750873i \(-0.729633\pi\)
0.630835 0.775917i \(-0.282712\pi\)
\(102\) 0 0
\(103\) −10.2106 7.91381i −1.00608 0.779771i −0.0305271 0.999534i \(-0.509719\pi\)
−0.975553 + 0.219763i \(0.929472\pi\)
\(104\) 16.3721 2.56055i 1.60542 0.251082i
\(105\) 0 0
\(106\) −3.18384 + 6.65844i −0.309242 + 0.646725i
\(107\) −8.67791 3.15850i −0.838925 0.305344i −0.113409 0.993548i \(-0.536177\pi\)
−0.725517 + 0.688205i \(0.758399\pi\)
\(108\) 0 0
\(109\) −14.6358 + 5.32701i −1.40186 + 0.510235i −0.928730 0.370758i \(-0.879098\pi\)
−0.473129 + 0.880993i \(0.656876\pi\)
\(110\) −1.20673 + 12.4063i −0.115057 + 1.18289i
\(111\) 0 0
\(112\) −0.336859 0.984508i −0.0318302 0.0930273i
\(113\) −4.01096 + 3.63975i −0.377319 + 0.342399i −0.838494 0.544910i \(-0.816564\pi\)
0.461175 + 0.887309i \(0.347428\pi\)
\(114\) 0 0
\(115\) −7.42068 + 21.6877i −0.691982 + 2.02239i
\(116\) 2.82832 + 6.55678i 0.262603 + 0.608782i
\(117\) 0 0
\(118\) −0.805112 + 0.0941040i −0.0741165 + 0.00866298i
\(119\) −1.57981 + 0.506546i −0.144821 + 0.0464350i
\(120\) 0 0
\(121\) −8.52126 + 2.37206i −0.774660 + 0.215641i
\(122\) −6.34339 + 1.76580i −0.574304 + 0.159868i
\(123\) 0 0
\(124\) 5.07543 1.62737i 0.455787 0.146142i
\(125\) 6.79388 0.794091i 0.607663 0.0710256i
\(126\) 0 0
\(127\) −1.42268 3.29814i −0.126242 0.292663i 0.843360 0.537349i \(-0.180574\pi\)
−0.969602 + 0.244686i \(0.921315\pi\)
\(128\) −0.724389 + 2.11711i −0.0640276 + 0.187128i
\(129\) 0 0
\(130\) 11.3694 10.3171i 0.997159 0.904874i
\(131\) −2.11285 6.17504i −0.184601 0.539516i 0.814577 0.580055i \(-0.196969\pi\)
−0.999178 + 0.0405392i \(0.987092\pi\)
\(132\) 0 0
\(133\) −0.117851 + 1.21161i −0.0102190 + 0.105060i
\(134\) −4.95128 + 1.80212i −0.427725 + 0.155679i
\(135\) 0 0
\(136\) −5.30360 1.93035i −0.454780 0.165526i
\(137\) −1.93773 + 4.05243i −0.165552 + 0.346222i −0.968179 0.250259i \(-0.919484\pi\)
0.802627 + 0.596481i \(0.203435\pi\)
\(138\) 0 0
\(139\) −9.45164 + 1.47821i −0.801678 + 0.125380i −0.542069 0.840334i \(-0.682359\pi\)
−0.259609 + 0.965714i \(0.583594\pi\)
\(140\) 1.83838 + 1.42485i 0.155371 + 0.120422i
\(141\) 0 0
\(142\) −0.120435 6.20957i −0.0101066 0.521096i
\(143\) 21.8431 + 10.9700i 1.82661 + 0.917360i
\(144\) 0 0
\(145\) 17.0849 + 11.2369i 1.41882 + 0.933175i
\(146\) −0.776659 0.0301379i −0.0642768 0.00249423i
\(147\) 0 0
\(148\) 0.818895 + 8.41898i 0.0673128 + 0.692036i
\(149\) −0.334935 0.700458i −0.0274390 0.0573837i 0.887992 0.459860i \(-0.152100\pi\)
−0.915431 + 0.402476i \(0.868150\pi\)
\(150\) 0 0
\(151\) 18.0411 13.9829i 1.46816 1.13791i 0.506993 0.861950i \(-0.330757\pi\)
0.961169 0.275961i \(-0.0889961\pi\)
\(152\) −2.84195 + 3.01229i −0.230512 + 0.244329i
\(153\) 0 0
\(154\) 1.15865 3.87017i 0.0933668 0.311867i
\(155\) 9.58249 11.8804i 0.769684 0.954259i
\(156\) 0 0
\(157\) −4.81328 7.63679i −0.384141 0.609482i 0.597123 0.802150i \(-0.296311\pi\)
−0.981264 + 0.192668i \(0.938286\pi\)
\(158\) −6.16854 + 3.40366i −0.490743 + 0.270780i
\(159\) 0 0
\(160\) 3.30892 + 12.8460i 0.261593 + 1.01557i
\(161\) 3.71456 6.43382i 0.292749 0.507056i
\(162\) 0 0
\(163\) 2.19502 + 3.80188i 0.171927 + 0.297787i 0.939094 0.343662i \(-0.111667\pi\)
−0.767166 + 0.641448i \(0.778334\pi\)
\(164\) −1.39215 + 1.36541i −0.108708 + 0.106620i
\(165\) 0 0
\(166\) 0.0267694 1.38022i 0.00207770 0.107126i
\(167\) 0.728491 1.38301i 0.0563723 0.107020i −0.854956 0.518700i \(-0.826416\pi\)
0.911328 + 0.411680i \(0.135058\pi\)
\(168\) 0 0
\(169\) −6.16125 15.9580i −0.473942 1.22754i
\(170\) −5.08805 + 1.20589i −0.390236 + 0.0924875i
\(171\) 0 0
\(172\) −1.35364 4.52149i −0.103214 0.344760i
\(173\) 2.36083 + 0.964505i 0.179491 + 0.0733300i 0.466164 0.884698i \(-0.345636\pi\)
−0.286673 + 0.958028i \(0.592549\pi\)
\(174\) 0 0
\(175\) 2.21520 + 0.172179i 0.167454 + 0.0130155i
\(176\) 4.24795 3.03625i 0.320201 0.228866i
\(177\) 0 0
\(178\) −10.0674 + 15.9730i −0.754581 + 1.19722i
\(179\) −1.18057 + 20.2696i −0.0882400 + 1.51502i 0.606107 + 0.795383i \(0.292730\pi\)
−0.694347 + 0.719640i \(0.744307\pi\)
\(180\) 0 0
\(181\) −8.40142 + 5.52570i −0.624473 + 0.410722i −0.821929 0.569589i \(-0.807102\pi\)
0.197456 + 0.980312i \(0.436732\pi\)
\(182\) −4.26017 + 2.57102i −0.315784 + 0.190577i
\(183\) 0 0
\(184\) 23.3964 9.55848i 1.72481 0.704660i
\(185\) 15.2076 + 18.8544i 1.11808 + 1.38621i
\(186\) 0 0
\(187\) −4.70873 6.86549i −0.344336 0.502055i
\(188\) 0.835624 + 4.73906i 0.0609442 + 0.345632i
\(189\) 0 0
\(190\) −0.666258 + 3.77854i −0.0483355 + 0.274124i
\(191\) 14.2941 6.49747i 1.03429 0.470141i 0.176583 0.984286i \(-0.443496\pi\)
0.857703 + 0.514145i \(0.171891\pi\)
\(192\) 0 0
\(193\) 19.1167 + 3.75440i 1.37605 + 0.270248i 0.825428 0.564507i \(-0.190934\pi\)
0.550622 + 0.834755i \(0.314390\pi\)
\(194\) −15.7137 5.03838i −1.12817 0.361735i
\(195\) 0 0
\(196\) 3.90678 + 4.47667i 0.279056 + 0.319762i
\(197\) −10.9788 + 14.7471i −0.782208 + 1.05069i 0.215044 + 0.976604i \(0.431011\pi\)
−0.997252 + 0.0740839i \(0.976397\pi\)
\(198\) 0 0
\(199\) −9.41644 + 21.8298i −0.667514 + 1.54747i 0.160667 + 0.987009i \(0.448636\pi\)
−0.828180 + 0.560462i \(0.810624\pi\)
\(200\) 5.59760 + 5.07955i 0.395810 + 0.359178i
\(201\) 0 0
\(202\) −3.91053 + 15.1816i −0.275144 + 1.06817i
\(203\) −4.73163 4.64075i −0.332095 0.325717i
\(204\) 0 0
\(205\) −1.18218 + 5.45756i −0.0825672 + 0.381173i
\(206\) 7.88032 + 10.5851i 0.549048 + 0.737500i
\(207\) 0 0
\(208\) −6.38773 0.746619i −0.442909 0.0517687i
\(209\) −5.99411 + 1.17721i −0.414622 + 0.0814290i
\(210\) 0 0
\(211\) 1.54557 + 7.13514i 0.106401 + 0.491203i 0.999172 + 0.0406915i \(0.0129561\pi\)
−0.892770 + 0.450512i \(0.851241\pi\)
\(212\) −4.54396 + 5.20680i −0.312081 + 0.357605i
\(213\) 0 0
\(214\) 7.67469 + 5.48554i 0.524631 + 0.374983i
\(215\) −10.3538 8.68789i −0.706125 0.592509i
\(216\) 0 0
\(217\) −3.78953 + 3.17979i −0.257250 + 0.215859i
\(218\) 15.8624 1.23293i 1.07434 0.0835043i
\(219\) 0 0
\(220\) −4.20381 + 10.8881i −0.283421 + 0.734078i
\(221\) −1.38767 + 10.1595i −0.0933448 + 0.683405i
\(222\) 0 0
\(223\) −0.168498 0.0929734i −0.0112835 0.00622596i 0.477461 0.878653i \(-0.341557\pi\)
−0.488744 + 0.872427i \(0.662545\pi\)
\(224\) −0.249984 4.29206i −0.0167028 0.286775i
\(225\) 0 0
\(226\) 4.94427 2.48311i 0.328888 0.165174i
\(227\) −1.92124 3.64739i −0.127517 0.242085i 0.812684 0.582704i \(-0.198005\pi\)
−0.940201 + 0.340619i \(0.889363\pi\)
\(228\) 0 0
\(229\) −10.8316 4.92358i −0.715774 0.325359i 0.0226056 0.999744i \(-0.492804\pi\)
−0.738380 + 0.674385i \(0.764409\pi\)
\(230\) 13.2439 19.3101i 0.873277 1.27327i
\(231\) 0 0
\(232\) −3.05128 22.3394i −0.200327 1.46665i
\(233\) 17.7434 + 4.20527i 1.16241 + 0.275496i 0.766163 0.642647i \(-0.222164\pi\)
0.396248 + 0.918143i \(0.370312\pi\)
\(234\) 0 0
\(235\) 9.45680 + 10.0236i 0.616893 + 0.653869i
\(236\) −0.749885 0.117280i −0.0488134 0.00763427i
\(237\) 0 0
\(238\) 1.69346 0.0657139i 0.109771 0.00425960i
\(239\) 1.47571 + 0.890596i 0.0954558 + 0.0576078i 0.563624 0.826032i \(-0.309407\pi\)
−0.468168 + 0.883639i \(0.655086\pi\)
\(240\) 0 0
\(241\) −5.30942 1.47798i −0.342010 0.0952049i 0.0929091 0.995675i \(-0.470383\pi\)
−0.434919 + 0.900470i \(0.643223\pi\)
\(242\) 9.03559 0.580830
\(243\) 0 0
\(244\) −6.16549 −0.394705
\(245\) 16.3919 + 4.56299i 1.04724 + 0.291519i
\(246\) 0 0
\(247\) 6.44170 + 3.88759i 0.409876 + 0.247361i
\(248\) −16.8164 + 0.652555i −1.06785 + 0.0414373i
\(249\) 0 0
\(250\) −6.90340 1.07967i −0.436609 0.0682844i
\(251\) −11.5955 12.2905i −0.731902 0.775771i 0.249368 0.968409i \(-0.419777\pi\)
−0.981270 + 0.192638i \(0.938296\pi\)
\(252\) 0 0
\(253\) 36.2748 + 8.59728i 2.28058 + 0.540506i
\(254\) 0.496556 + 3.63544i 0.0311567 + 0.228107i
\(255\) 0 0
\(256\) 9.54089 13.9110i 0.596306 0.869435i
\(257\) 5.82991 + 2.65002i 0.363660 + 0.165304i 0.587302 0.809368i \(-0.300190\pi\)
−0.223643 + 0.974671i \(0.571795\pi\)
\(258\) 0 0
\(259\) −3.65881 6.94608i −0.227347 0.431608i
\(260\) 12.8465 6.45174i 0.796704 0.400120i
\(261\) 0 0
\(262\) 0.387648 + 6.65566i 0.0239490 + 0.411188i
\(263\) −19.7700 10.9087i −1.21907 0.672656i −0.262721 0.964872i \(-0.584620\pi\)
−0.956352 + 0.292216i \(0.905607\pi\)
\(264\) 0 0
\(265\) −2.67824 + 19.6082i −0.164523 + 1.20452i
\(266\) 0.447891 1.16007i 0.0274619 0.0711282i
\(267\) 0 0
\(268\) −4.91885 + 0.382323i −0.300466 + 0.0233541i
\(269\) 12.2734 10.2986i 0.748321 0.627916i −0.186737 0.982410i \(-0.559791\pi\)
0.935058 + 0.354494i \(0.115347\pi\)
\(270\) 0 0
\(271\) −11.5105 9.65850i −0.699216 0.586712i 0.222334 0.974970i \(-0.428632\pi\)
−0.921550 + 0.388259i \(0.873077\pi\)
\(272\) 1.78202 + 1.27371i 0.108051 + 0.0772299i
\(273\) 0 0
\(274\) 3.01706 3.45717i 0.182267 0.208855i
\(275\) 2.36039 + 10.8968i 0.142337 + 0.657101i
\(276\) 0 0
\(277\) −16.6503 + 3.27000i −1.00042 + 0.196475i −0.666002 0.745950i \(-0.731996\pi\)
−0.334415 + 0.942426i \(0.608539\pi\)
\(278\) 9.70631 + 1.13451i 0.582146 + 0.0680431i
\(279\) 0 0
\(280\) −4.38551 5.89076i −0.262084 0.352040i
\(281\) −0.402812 + 1.85959i −0.0240297 + 0.110934i −0.987773 0.155896i \(-0.950174\pi\)
0.963744 + 0.266829i \(0.0859760\pi\)
\(282\) 0 0
\(283\) −1.39461 1.36782i −0.0829007 0.0813085i 0.657586 0.753380i \(-0.271578\pi\)
−0.740487 + 0.672071i \(0.765405\pi\)
\(284\) 1.45061 5.63162i 0.0860780 0.334175i
\(285\) 0 0
\(286\) −18.4907 16.7794i −1.09338 0.992186i
\(287\) 0.716838 1.66182i 0.0423136 0.0980940i
\(288\) 0 0
\(289\) −8.06619 + 10.8348i −0.474482 + 0.637340i
\(290\) −13.7350 15.7385i −0.806546 0.924199i
\(291\) 0 0
\(292\) −0.693022 0.222209i −0.0405560 0.0130038i
\(293\) −9.70882 1.90675i −0.567196 0.111394i −0.0991096 0.995077i \(-0.531599\pi\)
−0.468086 + 0.883683i \(0.655056\pi\)
\(294\) 0 0
\(295\) −1.97871 + 0.899436i −0.115205 + 0.0523672i
\(296\) 4.63781 26.3023i 0.269567 1.52879i
\(297\) 0 0
\(298\) 0.137724 + 0.781074i 0.00797816 + 0.0452464i
\(299\) −25.9708 37.8664i −1.50193 2.18987i
\(300\) 0 0
\(301\) 2.75017 + 3.40967i 0.158517 + 0.196530i
\(302\) −21.5847 + 8.81834i −1.24206 + 0.507438i
\(303\) 0 0
\(304\) 1.37606 0.830459i 0.0789227 0.0476301i
\(305\) −14.7514 + 9.70217i −0.844664 + 0.555545i
\(306\) 0 0
\(307\) −0.0274664 + 0.471580i −0.00156759 + 0.0269145i −0.999001 0.0446823i \(-0.985772\pi\)
0.997434 + 0.0715968i \(0.0228095\pi\)
\(308\) 2.01698 3.20016i 0.114928 0.182346i
\(309\) 0 0
\(310\) −12.6847 + 9.06648i −0.720442 + 0.514941i
\(311\) 14.1884 + 1.10281i 0.804549 + 0.0625345i 0.473179 0.880966i \(-0.343106\pi\)
0.331370 + 0.943501i \(0.392489\pi\)
\(312\) 0 0
\(313\) −4.48719 1.83322i −0.253631 0.103620i 0.247819 0.968806i \(-0.420286\pi\)
−0.501450 + 0.865187i \(0.667200\pi\)
\(314\) 2.64471 + 8.83393i 0.149249 + 0.498528i
\(315\) 0 0
\(316\) −6.41904 + 1.52134i −0.361099 + 0.0855821i
\(317\) 5.61316 + 14.5384i 0.315266 + 0.816560i 0.996430 + 0.0844286i \(0.0269065\pi\)
−0.681163 + 0.732132i \(0.738526\pi\)
\(318\) 0 0
\(319\) 15.4994 29.4249i 0.867801 1.64748i
\(320\) 0.387281 19.9681i 0.0216497 1.11625i
\(321\) 0 0
\(322\) −5.41800 + 5.31394i −0.301934 + 0.296134i
\(323\) −1.28128 2.21925i −0.0712925 0.123482i
\(324\) 0 0
\(325\) 6.86633 11.8928i 0.380875 0.659695i
\(326\) −1.11862 4.34275i −0.0619546 0.240523i
\(327\) 0 0
\(328\) 5.39080 2.97452i 0.297657 0.164240i
\(329\) −2.38146 3.77845i −0.131294 0.208312i
\(330\) 0 0
\(331\) 20.7687 25.7491i 1.14155 1.41530i 0.246607 0.969115i \(-0.420684\pi\)
0.894942 0.446183i \(-0.147217\pi\)
\(332\) 0.370727 1.23831i 0.0203463 0.0679613i
\(333\) 0 0
\(334\) −1.09577 + 1.16145i −0.0599580 + 0.0635518i
\(335\) −11.1671 + 8.65515i −0.610124 + 0.472881i
\(336\) 0 0
\(337\) −12.6722 26.5017i −0.690301 1.44364i −0.886335 0.463044i \(-0.846757\pi\)
0.196035 0.980597i \(-0.437193\pi\)
\(338\) 1.69169 + 17.3921i 0.0920161 + 0.946008i
\(339\) 0 0
\(340\) −4.89251 0.189851i −0.265333 0.0102961i
\(341\) −20.7398 13.6408i −1.12313 0.738691i
\(342\) 0 0
\(343\) −10.4814 5.26395i −0.565941 0.284226i
\(344\) 0.288979 + 14.8997i 0.0155807 + 0.803337i
\(345\) 0 0
\(346\) −2.05907 1.59590i −0.110697 0.0857963i
\(347\) 3.11755 0.487576i 0.167359 0.0261745i −0.0702841 0.997527i \(-0.522391\pi\)
0.237643 + 0.971353i \(0.423625\pi\)
\(348\) 0 0
\(349\) −9.35966 + 19.5741i −0.501011 + 1.04778i 0.483965 + 0.875087i \(0.339196\pi\)
−0.984976 + 0.172689i \(0.944754\pi\)
\(350\) −2.13281 0.776281i −0.114004 0.0414940i
\(351\) 0 0
\(352\) 20.2731 7.37882i 1.08056 0.393292i
\(353\) −1.06172 + 10.9154i −0.0565097 + 0.580971i 0.923715 + 0.383081i \(0.125137\pi\)
−0.980224 + 0.197889i \(0.936591\pi\)
\(354\) 0 0
\(355\) −5.39135 15.7568i −0.286143 0.836285i
\(356\) −13.0922 + 11.8805i −0.693886 + 0.629668i
\(357\) 0 0
\(358\) 6.71453 19.6239i 0.354874 1.03716i
\(359\) −0.245387 0.568871i −0.0129510 0.0300239i 0.911618 0.411039i \(-0.134834\pi\)
−0.924569 + 0.381015i \(0.875575\pi\)
\(360\) 0 0
\(361\) 17.0039 1.98747i 0.894944 0.104604i
\(362\) 9.78158 3.13634i 0.514108 0.164842i
\(363\) 0 0
\(364\) −4.48850 + 1.24946i −0.235261 + 0.0654895i
\(365\) −2.00778 + 0.558905i −0.105092 + 0.0292544i
\(366\) 0 0
\(367\) 34.7752 11.1502i 1.81525 0.582037i 0.815257 0.579099i \(-0.196596\pi\)
0.999996 0.00293835i \(-0.000935308\pi\)
\(368\) −9.74232 + 1.13871i −0.507854 + 0.0593596i
\(369\) 0 0
\(370\) −9.80074 22.7207i −0.509516 1.18119i
\(371\) 2.07645 6.06866i 0.107804 0.315069i
\(372\) 0 0
\(373\) −8.58167 + 7.78745i −0.444342 + 0.403219i −0.863224 0.504822i \(-0.831558\pi\)
0.418881 + 0.908041i \(0.362422\pi\)
\(374\) 2.75311 + 8.04626i 0.142360 + 0.416062i
\(375\) 0 0
\(376\) 1.47097 15.1229i 0.0758594 0.779903i
\(377\) −38.4923 + 14.0100i −1.98245 + 0.721554i
\(378\) 0 0
\(379\) −14.3131 5.20955i −0.735215 0.267596i −0.0528444 0.998603i \(-0.516829\pi\)
−0.682371 + 0.731006i \(0.739051\pi\)
\(380\) −1.54981 + 3.24115i −0.0795035 + 0.166267i
\(381\) 0 0
\(382\) −15.8468 + 2.47839i −0.810792 + 0.126806i
\(383\) 11.2959 + 8.75500i 0.577195 + 0.447360i 0.858901 0.512141i \(-0.171147\pi\)
−0.281707 + 0.959501i \(0.590900\pi\)
\(384\) 0 0
\(385\) −0.210060 10.8306i −0.0107056 0.551979i
\(386\) −17.7843 8.93159i −0.905195 0.454606i
\(387\) 0 0
\(388\) −12.9094 8.49066i −0.655377 0.431048i
\(389\) −17.0236 0.660592i −0.863130 0.0334934i −0.396592 0.917995i \(-0.629807\pi\)
−0.466537 + 0.884501i \(0.654499\pi\)
\(390\) 0 0
\(391\) 1.51401 + 15.5654i 0.0765667 + 0.787174i
\(392\) −8.09308 16.9252i −0.408762 0.854853i
\(393\) 0 0
\(394\) 14.8441 11.5051i 0.747837 0.579617i
\(395\) −12.9640 + 13.7411i −0.652292 + 0.691389i
\(396\) 0 0
\(397\) 7.51986 25.1181i 0.377411 1.26064i −0.532710 0.846298i \(-0.678826\pi\)
0.910121 0.414343i \(-0.135989\pi\)
\(398\) 15.2468 18.9031i 0.764255 0.947527i
\(399\) 0 0
\(400\) −1.56418 2.48174i −0.0782089 0.124087i
\(401\) 4.11300 2.26946i 0.205394 0.113331i −0.377081 0.926180i \(-0.623072\pi\)
0.582475 + 0.812849i \(0.302085\pi\)
\(402\) 0 0
\(403\) 7.62663 + 29.6084i 0.379909 + 1.47490i
\(404\) −7.33968 + 12.7127i −0.365163 + 0.632480i
\(405\) 0 0
\(406\) 3.38510 + 5.86316i 0.167999 + 0.290984i
\(407\) 28.1256 27.5854i 1.39414 1.36736i
\(408\) 0 0
\(409\) −0.419979 + 21.6540i −0.0207666 + 1.07072i 0.834017 + 0.551738i \(0.186035\pi\)
−0.854784 + 0.518984i \(0.826310\pi\)
\(410\) 2.65845 5.04694i 0.131291 0.249251i
\(411\) 0 0
\(412\) 4.45052 + 11.5271i 0.219261 + 0.567901i
\(413\) 0.685463 0.162458i 0.0337294 0.00799402i
\(414\) 0 0
\(415\) −1.06165 3.54615i −0.0521142 0.174074i
\(416\) −24.5989 10.0498i −1.20606 0.492730i
\(417\) 0 0
\(418\) 6.22130 + 0.483558i 0.304294 + 0.0236516i
\(419\) 10.0218 7.16316i 0.489597 0.349943i −0.309744 0.950820i \(-0.600243\pi\)
0.799342 + 0.600877i \(0.205182\pi\)
\(420\) 0 0
\(421\) −15.6312 + 24.8006i −0.761818 + 1.20871i 0.211079 + 0.977469i \(0.432302\pi\)
−0.972897 + 0.231238i \(0.925722\pi\)
\(422\) 0.433627 7.44510i 0.0211087 0.362422i
\(423\) 0 0
\(424\) 18.2307 11.9905i 0.885361 0.582311i
\(425\) −4.00448 + 2.41671i −0.194246 + 0.117228i
\(426\) 0 0
\(427\) 5.29735 2.16420i 0.256357 0.104733i
\(428\) 5.54555 + 6.87540i 0.268054 + 0.332335i
\(429\) 0 0
\(430\) 7.80921 + 11.3861i 0.376594 + 0.549087i
\(431\) 1.43533 + 8.14018i 0.0691376 + 0.392099i 0.999665 + 0.0258768i \(0.00823777\pi\)
−0.930528 + 0.366222i \(0.880651\pi\)
\(432\) 0 0
\(433\) 2.78198 15.7774i 0.133694 0.758214i −0.842067 0.539373i \(-0.818661\pi\)
0.975761 0.218841i \(-0.0702275\pi\)
\(434\) 4.60036 2.09112i 0.220824 0.100377i
\(435\) 0 0
\(436\) 14.6184 + 2.87096i 0.700094 + 0.137494i
\(437\) 10.9272 + 3.50366i 0.522718 + 0.167603i
\(438\) 0 0
\(439\) −22.9254 26.2696i −1.09417 1.25378i −0.965026 0.262155i \(-0.915567\pi\)
−0.129145 0.991626i \(-0.541223\pi\)
\(440\) 22.0066 29.5601i 1.04913 1.40922i
\(441\) 0 0
\(442\) 4.14875 9.61787i 0.197336 0.457476i
\(443\) 23.7838 + 21.5827i 1.13000 + 1.02542i 0.999422 + 0.0339855i \(0.0108200\pi\)
0.130581 + 0.991438i \(0.458316\pi\)
\(444\) 0 0
\(445\) −12.6286 + 49.0274i −0.598655 + 2.32412i
\(446\) 0.140350 + 0.137654i 0.00664575 + 0.00651811i
\(447\) 0 0
\(448\) −1.37035 + 6.32622i −0.0647427 + 0.298886i
\(449\) −13.3958 17.9937i −0.632187 0.849174i 0.364441 0.931226i \(-0.381260\pi\)
−0.996628 + 0.0820520i \(0.973853\pi\)
\(450\) 0 0
\(451\) 9.02040 + 1.05433i 0.424754 + 0.0496466i
\(452\) 5.08352 0.998372i 0.239109 0.0469595i
\(453\) 0 0
\(454\) 0.891518 + 4.11570i 0.0418410 + 0.193160i
\(455\) −8.77291 + 10.0526i −0.411280 + 0.471275i
\(456\) 0 0
\(457\) −9.89787 7.07457i −0.463003 0.330934i 0.325951 0.945387i \(-0.394315\pi\)
−0.788954 + 0.614452i \(0.789377\pi\)
\(458\) 9.31063 + 7.81255i 0.435057 + 0.365056i
\(459\) 0 0
\(460\) 16.7956 14.0932i 0.783098 0.657097i
\(461\) −14.3194 + 1.11299i −0.666921 + 0.0518372i −0.406490 0.913655i \(-0.633247\pi\)
−0.260431 + 0.965492i \(0.583865\pi\)
\(462\) 0 0
\(463\) −6.32862 + 16.3915i −0.294116 + 0.761779i 0.704526 + 0.709678i \(0.251160\pi\)
−0.998642 + 0.0521007i \(0.983408\pi\)
\(464\) −1.18420 + 8.66986i −0.0549750 + 0.402488i
\(465\) 0 0
\(466\) −16.3093 8.99910i −0.755515 0.416875i
\(467\) −0.619940 10.6440i −0.0286874 0.492543i −0.981799 0.189924i \(-0.939176\pi\)
0.953111 0.302620i \(-0.0978611\pi\)
\(468\) 0 0
\(469\) 4.09203 2.05510i 0.188953 0.0948955i
\(470\) −6.56054 12.4549i −0.302615 0.574501i
\(471\) 0 0
\(472\) 2.18170 + 0.991705i 0.100421 + 0.0456469i
\(473\) −12.4331 + 18.1278i −0.571672 + 0.833519i
\(474\) 0 0
\(475\) 0.464451 + 3.40038i 0.0213105 + 0.156020i
\(476\) 1.54409 + 0.365957i 0.0707734 + 0.0167736i
\(477\) 0 0
\(478\) −1.20827 1.28070i −0.0552652 0.0585777i
\(479\) 28.4548 + 4.45025i 1.30013 + 0.203337i 0.766426 0.642332i \(-0.222033\pi\)
0.533707 + 0.845670i \(0.320799\pi\)
\(480\) 0 0
\(481\) −48.4863 + 1.88149i −2.21079 + 0.0857886i
\(482\) 4.82012 + 2.90896i 0.219550 + 0.132499i
\(483\) 0 0
\(484\) 8.15060 + 2.26887i 0.370482 + 0.103131i
\(485\) −44.2479 −2.00920
\(486\) 0 0
\(487\) 33.0583 1.49801 0.749006 0.662563i \(-0.230531\pi\)
0.749006 + 0.662563i \(0.230531\pi\)
\(488\) 18.7543 + 5.22060i 0.848965 + 0.236326i
\(489\) 0 0
\(490\) −14.8813 8.98089i −0.672267 0.405715i
\(491\) −0.230994 + 0.00896363i −0.0104246 + 0.000404523i −0.0439872 0.999032i \(-0.514006\pi\)
0.0335625 + 0.999437i \(0.489315\pi\)
\(492\) 0 0
\(493\) 13.7839 + 2.15577i 0.620798 + 0.0970910i
\(494\) −5.27430 5.59044i −0.237302 0.251526i
\(495\) 0 0
\(496\) 6.35529 + 1.50623i 0.285361 + 0.0676318i
\(497\) 0.730450 + 5.34784i 0.0327651 + 0.239883i
\(498\) 0 0
\(499\) −7.57199 + 11.0402i −0.338969 + 0.494229i −0.956265 0.292502i \(-0.905512\pi\)
0.617296 + 0.786731i \(0.288228\pi\)
\(500\) −5.95614 2.70740i −0.266366 0.121078i
\(501\) 0 0
\(502\) 8.04424 + 15.2716i 0.359032 + 0.681605i
\(503\) −27.1474 + 13.6339i −1.21044 + 0.607907i −0.935423 0.353532i \(-0.884981\pi\)
−0.275020 + 0.961439i \(0.588684\pi\)
\(504\) 0 0
\(505\) 2.44424 + 41.9660i 0.108767 + 1.86746i
\(506\) −33.3429 18.3978i −1.48227 0.817882i
\(507\) 0 0
\(508\) −0.464952 + 3.40405i −0.0206289 + 0.151030i
\(509\) −9.06128 + 23.4693i −0.401634 + 1.04026i 0.573610 + 0.819128i \(0.305542\pi\)
−0.975244 + 0.221130i \(0.929025\pi\)
\(510\) 0 0
\(511\) 0.673439 0.0523438i 0.0297912 0.00231555i
\(512\) −9.77179 + 8.19951i −0.431856 + 0.362370i
\(513\) 0 0
\(514\) −5.01126 4.20495i −0.221037 0.185472i
\(515\) 28.7876 + 20.5761i 1.26853 + 0.906693i
\(516\) 0 0
\(517\) 14.7365 16.8861i 0.648109 0.742651i
\(518\) 1.69781 + 7.83794i 0.0745973 + 0.344379i
\(519\) 0 0
\(520\) −44.5395 + 8.74727i −1.95319 + 0.383593i
\(521\) 24.3092 + 2.84134i 1.06500 + 0.124481i 0.630501 0.776189i \(-0.282850\pi\)
0.434504 + 0.900670i \(0.356924\pi\)
\(522\) 0 0
\(523\) −0.991286 1.33153i −0.0433459 0.0582236i 0.779922 0.625877i \(-0.215259\pi\)
−0.823268 + 0.567653i \(0.807851\pi\)
\(524\) −1.32158 + 6.10112i −0.0577337 + 0.266528i
\(525\) 0 0
\(526\) 16.4674 + 16.1511i 0.718011 + 0.704220i
\(527\) 2.59756 10.0844i 0.113152 0.439281i
\(528\) 0 0
\(529\) −34.8281 31.6048i −1.51427 1.37412i
\(530\) 8.00718 18.5627i 0.347810 0.806314i
\(531\) 0 0
\(532\) 0.695320 0.933976i 0.0301459 0.0404930i
\(533\) −7.35498 8.42787i −0.318579 0.365052i
\(534\) 0 0
\(535\) 24.0875 + 7.72334i 1.04139 + 0.333909i
\(536\) 15.2859 + 3.00206i 0.660251 + 0.129669i
\(537\) 0 0
\(538\) −14.8995 + 6.77264i −0.642362 + 0.291989i
\(539\) 4.80532 27.2523i 0.206980 1.17384i
\(540\) 0 0
\(541\) −5.48009 31.0791i −0.235607 1.33620i −0.841331 0.540520i \(-0.818227\pi\)
0.605724 0.795675i \(-0.292884\pi\)
\(542\) 8.68166 + 12.6582i 0.372909 + 0.543715i
\(543\) 0 0
\(544\) 5.68195 + 7.04451i 0.243611 + 0.302031i
\(545\) 39.4934 16.1348i 1.69171 0.691141i
\(546\) 0 0
\(547\) −4.68567 + 2.82781i −0.200345 + 0.120909i −0.613323 0.789832i \(-0.710168\pi\)
0.412978 + 0.910741i \(0.364489\pi\)
\(548\) 3.58967 2.36096i 0.153343 0.100855i
\(549\) 0 0
\(550\) 0.662235 11.3701i 0.0282378 0.484824i
\(551\) 5.45844 8.66041i 0.232537 0.368946i
\(552\) 0 0
\(553\) 4.98117 3.56033i 0.211821 0.151401i
\(554\) 17.2813 + 1.34321i 0.734213 + 0.0570675i
\(555\) 0 0
\(556\) 8.47075 + 3.46068i 0.359240 + 0.146766i
\(557\) 4.62603 + 15.4520i 0.196011 + 0.654723i 0.998327 + 0.0578228i \(0.0184158\pi\)
−0.802316 + 0.596900i \(0.796399\pi\)
\(558\) 0 0
\(559\) 26.3448 6.24384i 1.11427 0.264086i
\(560\) 1.02657 + 2.65888i 0.0433805 + 0.112358i
\(561\) 0 0
\(562\) 0.905828 1.71967i 0.0382100 0.0725400i
\(563\) −0.361837 + 18.6562i −0.0152496 + 0.786265i 0.911652 + 0.410962i \(0.134807\pi\)
−0.926902 + 0.375303i \(0.877539\pi\)
\(564\) 0 0
\(565\) 10.5917 10.3882i 0.445595 0.437037i
\(566\) 0.997728 + 1.72812i 0.0419376 + 0.0726381i
\(567\) 0 0
\(568\) −9.18103 + 15.9020i −0.385228 + 0.667234i
\(569\) 3.73219 + 14.4892i 0.156461 + 0.607420i 0.997763 + 0.0668540i \(0.0212962\pi\)
−0.841301 + 0.540566i \(0.818210\pi\)
\(570\) 0 0
\(571\) 21.2431 11.7215i 0.888996 0.490527i 0.0282729 0.999600i \(-0.490999\pi\)
0.860723 + 0.509073i \(0.170012\pi\)
\(572\) −12.4662 19.7790i −0.521239 0.827003i
\(573\) 0 0
\(574\) −1.16068 + 1.43902i −0.0484460 + 0.0600637i
\(575\) 6.00695 20.0646i 0.250507 0.836753i
\(576\) 0 0
\(577\) −15.8788 + 16.8305i −0.661043 + 0.700665i −0.967969 0.251068i \(-0.919218\pi\)
0.306926 + 0.951733i \(0.400700\pi\)
\(578\) 10.9061 8.45283i 0.453632 0.351591i
\(579\) 0 0
\(580\) −8.43770 17.6459i −0.350356 0.732708i
\(581\) 0.116146 + 1.19408i 0.00481853 + 0.0495389i
\(582\) 0 0
\(583\) 32.1618 + 1.24803i 1.33201 + 0.0516879i
\(584\) 1.91989 + 1.26273i 0.0794455 + 0.0522521i
\(585\) 0 0
\(586\) 9.03212 + 4.53610i 0.373113 + 0.187385i
\(587\) 0.0869337 + 4.48228i 0.00358814 + 0.185003i 0.997318 + 0.0731935i \(0.0233191\pi\)
−0.993730 + 0.111810i \(0.964335\pi\)
\(588\) 0 0
\(589\) −6.03941 4.68090i −0.248850 0.192873i
\(590\) 2.19365 0.343080i 0.0903110 0.0141244i
\(591\) 0 0
\(592\) −4.47147 + 9.35129i −0.183776 + 0.384336i
\(593\) 22.8131 + 8.30328i 0.936820 + 0.340975i 0.764909 0.644138i \(-0.222784\pi\)
0.171911 + 0.985113i \(0.445006\pi\)
\(594\) 0 0
\(595\) 4.27025 1.55424i 0.175063 0.0637177i
\(596\) −0.0718960 + 0.739155i −0.00294497 + 0.0302770i
\(597\) 0 0
\(598\) 15.1847 + 44.3788i 0.620947 + 1.81479i
\(599\) 25.2859 22.9458i 1.03315 0.937538i 0.0350692 0.999385i \(-0.488835\pi\)
0.998086 + 0.0618468i \(0.0196990\pi\)
\(600\) 0 0
\(601\) −2.60915 + 7.62553i −0.106430 + 0.311052i −0.986493 0.163804i \(-0.947623\pi\)
0.880063 + 0.474856i \(0.157500\pi\)
\(602\) −1.77238 4.10885i −0.0722370 0.167464i
\(603\) 0 0
\(604\) −21.6850 + 2.53461i −0.882348 + 0.103132i
\(605\) 23.0713 7.39752i 0.937982 0.300752i
\(606\) 0 0
\(607\) 25.7893 7.17895i 1.04676 0.291385i 0.298233 0.954493i \(-0.403603\pi\)
0.748523 + 0.663109i \(0.230763\pi\)
\(608\) 6.39757 1.78088i 0.259456 0.0722244i
\(609\) 0 0
\(610\) 17.1747 5.50686i 0.695385 0.222966i
\(611\) −27.4180 + 3.20471i −1.10921 + 0.129649i
\(612\) 0 0
\(613\) 18.8407 + 43.6777i 0.760969 + 1.76412i 0.635606 + 0.772014i \(0.280750\pi\)
0.125363 + 0.992111i \(0.459990\pi\)
\(614\) 0.156216 0.456558i 0.00630435 0.0184252i
\(615\) 0 0
\(616\) −8.84500 + 8.02641i −0.356375 + 0.323393i
\(617\) 5.52097 + 16.1356i 0.222266 + 0.649596i 0.999785 + 0.0207372i \(0.00660132\pi\)
−0.777519 + 0.628859i \(0.783522\pi\)
\(618\) 0 0
\(619\) 2.37339 24.4005i 0.0953944 0.980741i −0.818423 0.574616i \(-0.805151\pi\)
0.913818 0.406125i \(-0.133120\pi\)
\(620\) −13.7189 + 4.99328i −0.550965 + 0.200535i
\(621\) 0 0
\(622\) −13.6607 4.97208i −0.547743 0.199362i
\(623\) 7.07843 14.8033i 0.283591 0.593081i
\(624\) 0 0
\(625\) −30.8747 + 4.82871i −1.23499 + 0.193148i
\(626\) 3.91365 + 3.03331i 0.156421 + 0.121235i
\(627\) 0 0
\(628\) 0.167433 + 8.63279i 0.00668129 + 0.344486i
\(629\) 14.7686 + 7.41705i 0.588861 + 0.295737i
\(630\) 0 0
\(631\) −2.29673 1.51058i −0.0914314 0.0601354i 0.502970 0.864304i \(-0.332241\pi\)
−0.594401 + 0.804168i \(0.702611\pi\)
\(632\) 20.8137 + 0.807666i 0.827924 + 0.0321272i
\(633\) 0 0
\(634\) −1.54120 15.8450i −0.0612091 0.629284i
\(635\) 4.24426 + 8.87612i 0.168428 + 0.352238i
\(636\) 0 0
\(637\) −26.9398 + 20.8799i −1.06739 + 0.827292i
\(638\) −23.3137 + 24.7111i −0.923000 + 0.978322i
\(639\) 0 0
\(640\) 1.75784 5.87160i 0.0694848 0.232095i
\(641\) −9.15349 + 11.3486i −0.361541 + 0.448241i −0.926171 0.377103i \(-0.876920\pi\)
0.564630 + 0.825344i \(0.309019\pi\)
\(642\) 0 0
\(643\) 1.22908 + 1.95007i 0.0484703 + 0.0769034i 0.869347 0.494202i \(-0.164540\pi\)
−0.820877 + 0.571105i \(0.806515\pi\)
\(644\) −6.22169 + 3.43298i −0.245169 + 0.135279i
\(645\) 0 0
\(646\) 0.652964 + 2.53496i 0.0256905 + 0.0997367i
\(647\) 14.6670 25.4040i 0.576618 0.998732i −0.419245 0.907873i \(-0.637705\pi\)
0.995864 0.0908594i \(-0.0289614\pi\)
\(648\) 0 0
\(649\) 1.76748 + 3.06137i 0.0693797 + 0.120169i
\(650\) −10.0151 + 9.82275i −0.392825 + 0.385280i
\(651\) 0 0
\(652\) 0.0814257 4.19829i 0.00318888 0.164418i
\(653\) −21.8381 + 41.4586i −0.854592 + 1.62240i −0.0740872 + 0.997252i \(0.523604\pi\)
−0.780504 + 0.625150i \(0.785038\pi\)
\(654\) 0 0
\(655\) 6.43887 + 16.6771i 0.251587 + 0.651627i
\(656\) −2.32510 + 0.551060i −0.0907801 + 0.0215153i
\(657\) 0 0
\(658\) 1.30852 + 4.37076i 0.0510114 + 0.170390i
\(659\) −40.2567 16.4467i −1.56818 0.640672i −0.583042 0.812442i \(-0.698138\pi\)
−0.985137 + 0.171771i \(0.945051\pi\)
\(660\) 0 0
\(661\) −10.5438 0.819526i −0.410105 0.0318759i −0.129217 0.991616i \(-0.541246\pi\)
−0.280888 + 0.959741i \(0.590629\pi\)
\(662\) −27.4922 + 19.6503i −1.06852 + 0.763730i
\(663\) 0 0
\(664\) −2.17622 + 3.45280i −0.0844536 + 0.133995i
\(665\) 0.193880 3.32878i 0.00751833 0.129085i
\(666\) 0 0
\(667\) −52.1968 + 34.3304i −2.02107 + 1.32928i
\(668\) −1.28009 + 0.772540i −0.0495283 + 0.0298905i
\(669\) 0 0
\(670\) 13.3606 5.45839i 0.516164 0.210876i
\(671\) 18.0277 + 22.3508i 0.695952 + 0.862845i
\(672\) 0 0
\(673\) −17.2692 25.1791i −0.665677 0.970582i −0.999608 0.0279840i \(-0.991091\pi\)
0.333931 0.942598i \(-0.391625\pi\)
\(674\) 5.21079 + 29.5518i 0.200712 + 1.13829i
\(675\) 0 0
\(676\) −2.84124 + 16.1135i −0.109278 + 0.619749i
\(677\) 9.41592 4.28006i 0.361883 0.164496i −0.224613 0.974448i \(-0.572112\pi\)
0.586496 + 0.809952i \(0.300507\pi\)
\(678\) 0 0
\(679\) 14.0721 + 2.76366i 0.540036 + 0.106060i
\(680\) 14.7213 + 4.72020i 0.564537 + 0.181011i
\(681\) 0 0
\(682\) 16.6733 + 19.1055i 0.638453 + 0.731586i
\(683\) −11.6548 + 15.6552i −0.445960 + 0.599029i −0.967086 0.254452i \(-0.918105\pi\)
0.521125 + 0.853480i \(0.325512\pi\)
\(684\) 0 0
\(685\) 4.87329 11.2976i 0.186199 0.431658i
\(686\) 8.87271 + 8.05155i 0.338762 + 0.307410i
\(687\) 0 0
\(688\) 1.44267 5.60081i 0.0550015 0.213529i
\(689\) −28.3023 27.7587i −1.07823 1.05752i
\(690\) 0 0
\(691\) −4.30928 + 19.8939i −0.163933 + 0.756799i 0.819141 + 0.573592i \(0.194450\pi\)
−0.983074 + 0.183207i \(0.941352\pi\)
\(692\) −1.45666 1.95664i −0.0553739 0.0743801i
\(693\) 0 0
\(694\) −3.20155 0.374208i −0.121529 0.0142047i
\(695\) 25.7128 5.04982i 0.975341 0.191551i
\(696\) 0 0
\(697\) 0.806554 + 3.72347i 0.0305504 + 0.141036i
\(698\) 14.5730 16.6988i 0.551597 0.632060i
\(699\) 0 0
\(700\) −1.72899 1.23581i −0.0653497 0.0467091i
\(701\) 0.925503 + 0.776590i 0.0349558 + 0.0293314i 0.660098 0.751179i \(-0.270515\pi\)
−0.625142 + 0.780511i \(0.714959\pi\)
\(702\) 0 0
\(703\) 9.28939 7.79472i 0.350356 0.293984i
\(704\) −32.3837 + 2.51706i −1.22051 + 0.0948654i
\(705\) 0 0
\(706\) 4.03505 10.4510i 0.151861 0.393330i
\(707\) 1.84380 13.4990i 0.0693433 0.507683i
\(708\) 0 0
\(709\) 22.0574 + 12.1708i 0.828383 + 0.457082i 0.839828 0.542852i \(-0.182656\pi\)
−0.0114455 + 0.999934i \(0.503643\pi\)
\(710\) 0.989159 + 16.9832i 0.0371225 + 0.637369i
\(711\) 0 0
\(712\) 49.8838 25.0526i 1.86947 0.938885i
\(713\) 21.7324 + 41.2579i 0.813883 + 1.54512i
\(714\) 0 0
\(715\) −60.9512 27.7057i −2.27945 1.03614i
\(716\) 10.9845 16.0158i 0.410511 0.598540i
\(717\) 0 0
\(718\) 0.0856472 + 0.627049i 0.00319633 + 0.0234013i
\(719\) 16.3701 + 3.87979i 0.610502 + 0.144692i 0.524225 0.851580i \(-0.324355\pi\)
0.0862768 + 0.996271i \(0.472503\pi\)
\(720\) 0 0
\(721\) −7.87010 8.34181i −0.293098 0.310665i
\(722\) −17.2780 2.70224i −0.643022 0.100567i
\(723\) 0 0
\(724\) 9.61107 0.372953i 0.357193 0.0138607i
\(725\) −15.9973 9.65440i −0.594123 0.358555i
\(726\) 0 0
\(727\) 15.5314 + 4.32345i 0.576026 + 0.160348i 0.543921 0.839137i \(-0.316939\pi\)
0.0321055 + 0.999484i \(0.489779\pi\)
\(728\) 14.7111 0.545231
\(729\) 0 0
\(730\) 2.12897 0.0787966
\(731\) −8.88360 2.47292i −0.328572 0.0914642i
\(732\) 0 0
\(733\) 18.1838 + 10.9740i 0.671632 + 0.405332i 0.811110 0.584893i \(-0.198864\pi\)
−0.139478 + 0.990225i \(0.544543\pi\)
\(734\) −37.2769 + 1.44651i −1.37591 + 0.0533917i
\(735\) 0 0
\(736\) −40.0408 6.26227i −1.47592 0.230830i
\(737\) 15.7685 + 16.7137i 0.580841 + 0.615655i
\(738\) 0 0
\(739\) −4.47861 1.06145i −0.164748 0.0390461i 0.147414 0.989075i \(-0.452905\pi\)
−0.312162 + 0.950029i \(0.601053\pi\)
\(740\) −3.13555 22.9563i −0.115265 0.843891i
\(741\) 0 0
\(742\) −3.70591 + 5.40334i −0.136048 + 0.198363i
\(743\) 9.03661 + 4.10764i 0.331521 + 0.150695i 0.572654 0.819797i \(-0.305914\pi\)
−0.241133 + 0.970492i \(0.577519\pi\)
\(744\) 0 0
\(745\) 0.991136 + 1.88162i 0.0363124 + 0.0689374i
\(746\) 10.5785 5.31275i 0.387308 0.194514i
\(747\) 0 0
\(748\) 0.463005 + 7.94949i 0.0169291 + 0.290662i
\(749\) −7.17809 3.96070i −0.262282 0.144721i
\(750\) 0 0
\(751\) −2.19869 + 16.0972i −0.0802313 + 0.587397i 0.906154 + 0.422947i \(0.139005\pi\)
−0.986386 + 0.164450i \(0.947415\pi\)
\(752\) −2.12392 + 5.50109i −0.0774513 + 0.200604i
\(753\) 0 0
\(754\) 41.7182 3.24260i 1.51929 0.118088i
\(755\) −47.8945 + 40.1882i −1.74306 + 1.46260i
\(756\) 0 0
\(757\) 40.0675 + 33.6207i 1.45628 + 1.22196i 0.927833 + 0.372997i \(0.121670\pi\)
0.528447 + 0.848967i \(0.322775\pi\)
\(758\) 12.6584 + 9.04769i 0.459774 + 0.328627i
\(759\) 0 0
\(760\) 7.45865 8.54667i 0.270554 0.310020i
\(761\) −8.78357 40.5495i −0.318404 1.46992i −0.803420 0.595413i \(-0.796989\pi\)
0.485016 0.874505i \(-0.338814\pi\)
\(762\) 0 0
\(763\) −13.5678 + 2.66462i −0.491186 + 0.0964658i
\(764\) −14.9170 1.74355i −0.539678 0.0630794i
\(765\) 0 0
\(766\) −8.71795 11.7102i −0.314992 0.423108i
\(767\) 0.921750 4.25527i 0.0332824 0.153649i
\(768\) 0 0
\(769\) −15.5633 15.2643i −0.561225 0.550446i 0.363248 0.931692i \(-0.381668\pi\)
−0.924473 + 0.381247i \(0.875495\pi\)
\(770\) −2.76025 + 10.7160i −0.0994726 + 0.386176i
\(771\) 0 0
\(772\) −13.7996 12.5225i −0.496660 0.450695i
\(773\) 15.5539 36.0580i 0.559435 1.29692i −0.370377 0.928881i \(-0.620772\pi\)
0.929812 0.368034i \(-0.119969\pi\)
\(774\) 0 0
\(775\) −8.32825 + 11.1868i −0.299159 + 0.401841i
\(776\) 32.0786 + 36.7580i 1.15155 + 1.31953i
\(777\) 0 0
\(778\) 16.5719 + 5.31358i 0.594133 + 0.190501i
\(779\) 2.74309 + 0.538726i 0.0982815 + 0.0193019i
\(780\) 0 0
\(781\) −24.6570 + 11.2080i −0.882297 + 0.401053i
\(782\) 2.77409 15.7326i 0.0992012 0.562598i
\(783\) 0 0
\(784\) 1.26433 + 7.17035i 0.0451545 + 0.256084i
\(785\) 13.9854 + 20.3912i 0.499159 + 0.727792i
\(786\) 0 0
\(787\) −28