Properties

Label 441.2.w.a.188.17
Level $441$
Weight $2$
Character 441.188
Analytic conductor $3.521$
Analytic rank $0$
Dimension $120$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 441 = 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 441.w (of order \(14\), degree \(6\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.52140272914\)
Analytic rank: \(0\)
Dimension: \(120\)
Relative dimension: \(20\) over \(\Q(\zeta_{14})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{14}]$

Embedding invariants

Embedding label 188.17
Character \(\chi\) \(=\) 441.188
Dual form 441.2.w.a.251.17

$q$-expansion

\(f(q)\) \(=\) \(q+(1.61627 - 1.28893i) q^{2} +(0.505936 - 2.21665i) q^{4} +(3.93097 - 1.89305i) q^{5} +(-2.02319 - 1.70491i) q^{7} +(-0.245458 - 0.509698i) q^{8} +O(q^{10})\) \(q+(1.61627 - 1.28893i) q^{2} +(0.505936 - 2.21665i) q^{4} +(3.93097 - 1.89305i) q^{5} +(-2.02319 - 1.70491i) q^{7} +(-0.245458 - 0.509698i) q^{8} +(3.91348 - 8.12642i) q^{10} +(-3.17960 + 2.53564i) q^{11} +(-1.07613 + 0.858184i) q^{13} +(-5.46752 - 0.147843i) q^{14} +(3.04329 + 1.46557i) q^{16} +(-0.000551178 - 0.00241487i) q^{17} +4.84659i q^{19} +(-2.20742 - 9.67134i) q^{20} +(-1.87081 + 8.19655i) q^{22} +(-1.08174 - 0.246900i) q^{23} +(8.75139 - 10.9739i) q^{25} +(-0.633172 + 2.77411i) q^{26} +(-4.80279 + 3.62212i) q^{28} +(-1.58525 + 0.361823i) q^{29} +3.23885i q^{31} +(7.91087 - 1.80561i) q^{32} +(-0.00400344 - 0.00319264i) q^{34} +(-11.1806 - 2.87194i) q^{35} +(-2.10701 - 9.23141i) q^{37} +(6.24691 + 7.83338i) q^{38} +(-1.92977 - 1.53894i) q^{40} +(-7.61140 + 3.66546i) q^{41} +(-0.421609 - 0.203036i) q^{43} +(4.01196 + 8.33093i) q^{44} +(-2.06662 + 0.995232i) q^{46} +(1.51205 + 1.89605i) q^{47} +(1.18657 + 6.89870i) q^{49} -29.0167i q^{50} +(1.35784 + 2.81959i) q^{52} +(-6.81397 - 1.55524i) q^{53} +(-7.69878 + 15.9867i) q^{55} +(-0.372382 + 1.44970i) q^{56} +(-2.09582 + 2.62808i) q^{58} +(7.40362 + 3.56539i) q^{59} +(14.5677 - 3.32497i) q^{61} +(4.17465 + 5.23485i) q^{62} +(6.24673 - 7.83315i) q^{64} +(-2.60564 + 5.41066i) q^{65} +11.7825 q^{67} -0.00563178 q^{68} +(-21.7725 + 9.76913i) q^{70} +(4.38641 + 1.00117i) q^{71} +(-4.34434 - 3.46449i) q^{73} +(-15.3041 - 12.2046i) q^{74} +(10.7432 + 2.45206i) q^{76} +(10.7560 + 0.290843i) q^{77} -10.0580 q^{79} +14.7375 q^{80} +(-7.57754 + 15.7349i) q^{82} +(-10.4803 + 13.1419i) q^{83} +(-0.00673813 - 0.00844935i) q^{85} +(-0.943132 + 0.215264i) q^{86} +(2.07287 + 0.998241i) q^{88} +(-3.92695 + 4.92424i) q^{89} +(3.64033 + 0.0984354i) q^{91} +(-1.09458 + 2.27293i) q^{92} +(4.88775 + 1.11560i) q^{94} +(9.17485 + 19.0518i) q^{95} -2.91734i q^{97} +(10.8097 + 9.62073i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 120 q + 24 q^{4} + O(q^{10}) \) \( 120 q + 24 q^{4} - 32 q^{16} - 44 q^{22} - 4 q^{25} - 56 q^{28} + 112 q^{34} - 76 q^{37} + 28 q^{40} + 8 q^{43} - 40 q^{46} - 84 q^{49} - 140 q^{52} + 12 q^{58} - 84 q^{61} + 24 q^{64} + 16 q^{67} + 112 q^{70} - 84 q^{76} - 24 q^{79} + 140 q^{82} - 96 q^{85} - 24 q^{88} - 112 q^{91} - 112 q^{94} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/441\mathbb{Z}\right)^\times\).

\(n\) \(199\) \(344\)
\(\chi(n)\) \(e\left(\frac{5}{14}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.61627 1.28893i 1.14287 0.911411i 0.145911 0.989298i \(-0.453389\pi\)
0.996962 + 0.0778871i \(0.0248174\pi\)
\(3\) 0 0
\(4\) 0.505936 2.21665i 0.252968 1.10832i
\(5\) 3.93097 1.89305i 1.75798 0.846599i 0.783741 0.621088i \(-0.213309\pi\)
0.974241 0.225511i \(-0.0724052\pi\)
\(6\) 0 0
\(7\) −2.02319 1.70491i −0.764693 0.644395i
\(8\) −0.245458 0.509698i −0.0867824 0.180206i
\(9\) 0 0
\(10\) 3.91348 8.12642i 1.23755 2.56980i
\(11\) −3.17960 + 2.53564i −0.958684 + 0.764525i −0.971902 0.235387i \(-0.924364\pi\)
0.0132172 + 0.999913i \(0.495793\pi\)
\(12\) 0 0
\(13\) −1.07613 + 0.858184i −0.298464 + 0.238017i −0.761259 0.648448i \(-0.775418\pi\)
0.462794 + 0.886466i \(0.346847\pi\)
\(14\) −5.46752 0.147843i −1.46126 0.0395126i
\(15\) 0 0
\(16\) 3.04329 + 1.46557i 0.760824 + 0.366393i
\(17\) −0.000551178 0.00241487i −0.000133680 0.000585691i 0.974861 0.222814i \(-0.0715242\pi\)
−0.974995 + 0.222228i \(0.928667\pi\)
\(18\) 0 0
\(19\) 4.84659i 1.11188i 0.831221 + 0.555942i \(0.187642\pi\)
−0.831221 + 0.555942i \(0.812358\pi\)
\(20\) −2.20742 9.67134i −0.493594 2.16258i
\(21\) 0 0
\(22\) −1.87081 + 8.19655i −0.398858 + 1.74751i
\(23\) −1.08174 0.246900i −0.225559 0.0514823i 0.108248 0.994124i \(-0.465476\pi\)
−0.333806 + 0.942642i \(0.608333\pi\)
\(24\) 0 0
\(25\) 8.75139 10.9739i 1.75028 2.19478i
\(26\) −0.633172 + 2.77411i −0.124175 + 0.544047i
\(27\) 0 0
\(28\) −4.80279 + 3.62212i −0.907642 + 0.684517i
\(29\) −1.58525 + 0.361823i −0.294374 + 0.0671889i −0.367157 0.930159i \(-0.619669\pi\)
0.0727835 + 0.997348i \(0.476812\pi\)
\(30\) 0 0
\(31\) 3.23885i 0.581715i 0.956766 + 0.290857i \(0.0939405\pi\)
−0.956766 + 0.290857i \(0.906059\pi\)
\(32\) 7.91087 1.80561i 1.39846 0.319189i
\(33\) 0 0
\(34\) −0.00400344 0.00319264i −0.000686585 0.000547533i
\(35\) −11.1806 2.87194i −1.88986 0.485446i
\(36\) 0 0
\(37\) −2.10701 9.23141i −0.346390 1.51764i −0.785306 0.619107i \(-0.787495\pi\)
0.438916 0.898528i \(-0.355363\pi\)
\(38\) 6.24691 + 7.83338i 1.01338 + 1.27074i
\(39\) 0 0
\(40\) −1.92977 1.53894i −0.305124 0.243328i
\(41\) −7.61140 + 3.66546i −1.18870 + 0.572449i −0.920435 0.390896i \(-0.872165\pi\)
−0.268267 + 0.963345i \(0.586451\pi\)
\(42\) 0 0
\(43\) −0.421609 0.203036i −0.0642948 0.0309627i 0.401460 0.915877i \(-0.368503\pi\)
−0.465755 + 0.884914i \(0.654217\pi\)
\(44\) 4.01196 + 8.33093i 0.604826 + 1.25593i
\(45\) 0 0
\(46\) −2.06662 + 0.995232i −0.304706 + 0.146739i
\(47\) 1.51205 + 1.89605i 0.220555 + 0.276568i 0.879783 0.475376i \(-0.157688\pi\)
−0.659227 + 0.751944i \(0.729117\pi\)
\(48\) 0 0
\(49\) 1.18657 + 6.89870i 0.169510 + 0.985529i
\(50\) 29.0167i 4.10358i
\(51\) 0 0
\(52\) 1.35784 + 2.81959i 0.188299 + 0.391006i
\(53\) −6.81397 1.55524i −0.935970 0.213629i −0.272777 0.962077i \(-0.587942\pi\)
−0.663193 + 0.748448i \(0.730799\pi\)
\(54\) 0 0
\(55\) −7.69878 + 15.9867i −1.03810 + 2.15564i
\(56\) −0.372382 + 1.44970i −0.0497617 + 0.193724i
\(57\) 0 0
\(58\) −2.09582 + 2.62808i −0.275195 + 0.345084i
\(59\) 7.40362 + 3.56539i 0.963869 + 0.464175i 0.848528 0.529151i \(-0.177490\pi\)
0.115341 + 0.993326i \(0.463204\pi\)
\(60\) 0 0
\(61\) 14.5677 3.32497i 1.86520 0.425719i 0.867742 0.497015i \(-0.165571\pi\)
0.997455 + 0.0712956i \(0.0227134\pi\)
\(62\) 4.17465 + 5.23485i 0.530181 + 0.664826i
\(63\) 0 0
\(64\) 6.24673 7.83315i 0.780841 0.979144i
\(65\) −2.60564 + 5.41066i −0.323189 + 0.671110i
\(66\) 0 0
\(67\) 11.7825 1.43946 0.719731 0.694253i \(-0.244265\pi\)
0.719731 + 0.694253i \(0.244265\pi\)
\(68\) −0.00563178 −0.000682953
\(69\) 0 0
\(70\) −21.7725 + 9.76913i −2.60231 + 1.16763i
\(71\) 4.38641 + 1.00117i 0.520571 + 0.118817i 0.474729 0.880132i \(-0.342546\pi\)
0.0458416 + 0.998949i \(0.485403\pi\)
\(72\) 0 0
\(73\) −4.34434 3.46449i −0.508466 0.405488i 0.335372 0.942086i \(-0.391138\pi\)
−0.843838 + 0.536597i \(0.819709\pi\)
\(74\) −15.3041 12.2046i −1.77907 1.41876i
\(75\) 0 0
\(76\) 10.7432 + 2.45206i 1.23233 + 0.281271i
\(77\) 10.7560 + 0.290843i 1.22576 + 0.0331447i
\(78\) 0 0
\(79\) −10.0580 −1.13162 −0.565809 0.824536i \(-0.691436\pi\)
−0.565809 + 0.824536i \(0.691436\pi\)
\(80\) 14.7375 1.64770
\(81\) 0 0
\(82\) −7.57754 + 15.7349i −0.836799 + 1.73763i
\(83\) −10.4803 + 13.1419i −1.15036 + 1.44251i −0.273433 + 0.961891i \(0.588159\pi\)
−0.876930 + 0.480618i \(0.840412\pi\)
\(84\) 0 0
\(85\) −0.00673813 0.00844935i −0.000730853 0.000916461i
\(86\) −0.943132 + 0.215264i −0.101701 + 0.0232125i
\(87\) 0 0
\(88\) 2.07287 + 0.998241i 0.220969 + 0.106413i
\(89\) −3.92695 + 4.92424i −0.416256 + 0.521968i −0.945113 0.326742i \(-0.894049\pi\)
0.528858 + 0.848710i \(0.322620\pi\)
\(90\) 0 0
\(91\) 3.64033 + 0.0984354i 0.381611 + 0.0103188i
\(92\) −1.09458 + 2.27293i −0.114118 + 0.236969i
\(93\) 0 0
\(94\) 4.88775 + 1.11560i 0.504133 + 0.115065i
\(95\) 9.17485 + 19.0518i 0.941320 + 1.95467i
\(96\) 0 0
\(97\) 2.91734i 0.296211i −0.988972 0.148106i \(-0.952682\pi\)
0.988972 0.148106i \(-0.0473176\pi\)
\(98\) 10.8097 + 9.62073i 1.09195 + 0.971841i
\(99\) 0 0
\(100\) −19.8976 24.9509i −1.98976 2.49509i
\(101\) −8.25227 + 3.97408i −0.821131 + 0.395436i −0.796781 0.604268i \(-0.793466\pi\)
−0.0243497 + 0.999704i \(0.507752\pi\)
\(102\) 0 0
\(103\) −1.26385 2.62441i −0.124531 0.258590i 0.829378 0.558688i \(-0.188695\pi\)
−0.953909 + 0.300098i \(0.902981\pi\)
\(104\) 0.701559 + 0.337853i 0.0687935 + 0.0331292i
\(105\) 0 0
\(106\) −13.0178 + 6.26903i −1.26440 + 0.608902i
\(107\) −11.1132 8.86244i −1.07435 0.856765i −0.0841534 0.996453i \(-0.526819\pi\)
−0.990196 + 0.139688i \(0.955390\pi\)
\(108\) 0 0
\(109\) −4.95739 6.21637i −0.474831 0.595420i 0.485515 0.874228i \(-0.338632\pi\)
−0.960347 + 0.278808i \(0.910061\pi\)
\(110\) 8.16242 + 35.7619i 0.778256 + 3.40976i
\(111\) 0 0
\(112\) −3.65848 8.15367i −0.345694 0.770449i
\(113\) 11.6381 + 9.28105i 1.09482 + 0.873088i 0.992570 0.121671i \(-0.0388254\pi\)
0.102247 + 0.994759i \(0.467397\pi\)
\(114\) 0 0
\(115\) −4.71969 + 1.07724i −0.440113 + 0.100453i
\(116\) 3.69701i 0.343259i
\(117\) 0 0
\(118\) 16.5618 3.78011i 1.52463 0.347988i
\(119\) −0.00300199 + 0.00582544i −0.000275192 + 0.000534017i
\(120\) 0 0
\(121\) 1.23262 5.40044i 0.112056 0.490949i
\(122\) 19.2596 24.1507i 1.74368 2.18650i
\(123\) 0 0
\(124\) 7.17940 + 1.63865i 0.644729 + 0.147155i
\(125\) 8.77291 38.4366i 0.784673 3.43788i
\(126\) 0 0
\(127\) −3.67465 16.0997i −0.326073 1.42862i −0.826547 0.562867i \(-0.809698\pi\)
0.500474 0.865751i \(-0.333159\pi\)
\(128\) 4.48341i 0.396282i
\(129\) 0 0
\(130\) 2.76256 + 12.1035i 0.242292 + 1.06155i
\(131\) −3.65928 1.76222i −0.319713 0.153966i 0.267143 0.963657i \(-0.413920\pi\)
−0.586856 + 0.809691i \(0.699635\pi\)
\(132\) 0 0
\(133\) 8.26300 9.80556i 0.716493 0.850250i
\(134\) 19.0437 15.1868i 1.64512 1.31194i
\(135\) 0 0
\(136\) −0.00109556 0.000873682i −9.39437e−5 7.49176e-5i
\(137\) 2.27979 4.73403i 0.194775 0.404455i −0.780592 0.625041i \(-0.785082\pi\)
0.975368 + 0.220585i \(0.0707967\pi\)
\(138\) 0 0
\(139\) −2.09638 4.35318i −0.177813 0.369232i 0.792945 0.609293i \(-0.208547\pi\)
−0.970758 + 0.240061i \(0.922832\pi\)
\(140\) −12.0227 + 23.3304i −1.01611 + 1.97178i
\(141\) 0 0
\(142\) 8.38004 4.03562i 0.703238 0.338661i
\(143\) 1.24561 5.45736i 0.104163 0.456367i
\(144\) 0 0
\(145\) −5.54662 + 4.42328i −0.460622 + 0.367334i
\(146\) −11.4871 −0.950679
\(147\) 0 0
\(148\) −21.5288 −1.76966
\(149\) 8.30896 6.62617i 0.680696 0.542837i −0.220964 0.975282i \(-0.570920\pi\)
0.901660 + 0.432445i \(0.142349\pi\)
\(150\) 0 0
\(151\) 1.62392 7.11488i 0.132153 0.579001i −0.864877 0.501984i \(-0.832604\pi\)
0.997030 0.0770162i \(-0.0245393\pi\)
\(152\) 2.47030 1.18963i 0.200368 0.0964920i
\(153\) 0 0
\(154\) 17.7594 13.3936i 1.43109 1.07929i
\(155\) 6.13132 + 12.7318i 0.492479 + 1.02264i
\(156\) 0 0
\(157\) −5.67493 + 11.7841i −0.452909 + 0.940475i 0.542065 + 0.840337i \(0.317643\pi\)
−0.994974 + 0.100138i \(0.968071\pi\)
\(158\) −16.2565 + 12.9641i −1.29330 + 1.03137i
\(159\) 0 0
\(160\) 27.6793 22.0735i 2.18824 1.74506i
\(161\) 1.76762 + 2.34380i 0.139308 + 0.184717i
\(162\) 0 0
\(163\) −0.348080 0.167627i −0.0272638 0.0131295i 0.420202 0.907431i \(-0.361959\pi\)
−0.447466 + 0.894301i \(0.647673\pi\)
\(164\) 4.27416 + 18.7263i 0.333756 + 1.46228i
\(165\) 0 0
\(166\) 34.7492i 2.69706i
\(167\) −1.61253 7.06498i −0.124782 0.546704i −0.998213 0.0597569i \(-0.980967\pi\)
0.873431 0.486947i \(-0.161890\pi\)
\(168\) 0 0
\(169\) −2.47120 + 10.8270i −0.190092 + 0.832849i
\(170\) −0.0217812 0.00497143i −0.00167054 0.000381291i
\(171\) 0 0
\(172\) −0.663368 + 0.831837i −0.0505813 + 0.0634269i
\(173\) 0.637002 2.79089i 0.0484304 0.212187i −0.944923 0.327293i \(-0.893864\pi\)
0.993353 + 0.115106i \(0.0367207\pi\)
\(174\) 0 0
\(175\) −36.4152 + 7.28192i −2.75273 + 0.550461i
\(176\) −13.3926 + 3.05678i −1.00951 + 0.230413i
\(177\) 0 0
\(178\) 13.0204i 0.975923i
\(179\) −10.4981 + 2.39612i −0.784665 + 0.179095i −0.596040 0.802954i \(-0.703260\pi\)
−0.188625 + 0.982049i \(0.560403\pi\)
\(180\) 0 0
\(181\) 11.6008 + 9.25131i 0.862279 + 0.687645i 0.951260 0.308389i \(-0.0997897\pi\)
−0.0889812 + 0.996033i \(0.528361\pi\)
\(182\) 6.01062 4.53304i 0.445537 0.336011i
\(183\) 0 0
\(184\) 0.139677 + 0.611965i 0.0102971 + 0.0451147i
\(185\) −25.7581 32.2997i −1.89378 2.37472i
\(186\) 0 0
\(187\) 0.00787577 + 0.00628071i 0.000575933 + 0.000459291i
\(188\) 4.96788 2.39241i 0.362320 0.174484i
\(189\) 0 0
\(190\) 39.3854 + 18.9670i 2.85732 + 1.37601i
\(191\) −5.09937 10.5890i −0.368978 0.766190i 0.630976 0.775802i \(-0.282655\pi\)
−0.999954 + 0.00961204i \(0.996940\pi\)
\(192\) 0 0
\(193\) −5.53509 + 2.66556i −0.398424 + 0.191871i −0.622357 0.782734i \(-0.713825\pi\)
0.223933 + 0.974605i \(0.428110\pi\)
\(194\) −3.76025 4.71520i −0.269970 0.338532i
\(195\) 0 0
\(196\) 15.8923 + 0.860093i 1.13517 + 0.0614352i
\(197\) 3.01370i 0.214717i −0.994220 0.107359i \(-0.965761\pi\)
0.994220 0.107359i \(-0.0342393\pi\)
\(198\) 0 0
\(199\) −9.17541 19.0529i −0.650428 1.35063i −0.921617 0.388101i \(-0.873131\pi\)
0.271189 0.962526i \(-0.412583\pi\)
\(200\) −7.74147 1.76694i −0.547405 0.124942i
\(201\) 0 0
\(202\) −8.21555 + 17.0598i −0.578044 + 1.20032i
\(203\) 3.82414 + 1.97067i 0.268402 + 0.138314i
\(204\) 0 0
\(205\) −22.9813 + 28.8176i −1.60508 + 2.01271i
\(206\) −5.42539 2.61273i −0.378005 0.182038i
\(207\) 0 0
\(208\) −4.53271 + 1.03456i −0.314287 + 0.0717339i
\(209\) −12.2892 15.4102i −0.850064 1.06595i
\(210\) 0 0
\(211\) 9.60477 12.0440i 0.661220 0.829144i −0.332256 0.943189i \(-0.607810\pi\)
0.993475 + 0.114046i \(0.0363811\pi\)
\(212\) −6.89486 + 14.3173i −0.473541 + 0.983318i
\(213\) 0 0
\(214\) −29.3849 −2.00871
\(215\) −2.04169 −0.139242
\(216\) 0 0
\(217\) 5.52195 6.55280i 0.374854 0.444833i
\(218\) −16.0249 3.65758i −1.08534 0.247723i
\(219\) 0 0
\(220\) 31.5418 + 25.1537i 2.12655 + 1.69586i
\(221\) 0.00266554 + 0.00212570i 0.000179303 + 0.000142990i
\(222\) 0 0
\(223\) 4.82462 + 1.10119i 0.323080 + 0.0737410i 0.380985 0.924581i \(-0.375585\pi\)
−0.0579050 + 0.998322i \(0.518442\pi\)
\(224\) −19.0836 9.83424i −1.27507 0.657078i
\(225\) 0 0
\(226\) 30.7728 2.04698
\(227\) 19.8226 1.31567 0.657835 0.753162i \(-0.271472\pi\)
0.657835 + 0.753162i \(0.271472\pi\)
\(228\) 0 0
\(229\) 5.43984 11.2959i 0.359475 0.746457i −0.640290 0.768133i \(-0.721186\pi\)
0.999765 + 0.0216759i \(0.00690019\pi\)
\(230\) −6.23979 + 7.82444i −0.411439 + 0.515929i
\(231\) 0 0
\(232\) 0.573533 + 0.719188i 0.0376543 + 0.0472170i
\(233\) −20.9996 + 4.79302i −1.37573 + 0.314001i −0.845556 0.533888i \(-0.820731\pi\)
−0.530174 + 0.847889i \(0.677873\pi\)
\(234\) 0 0
\(235\) 9.53315 + 4.59092i 0.621874 + 0.299479i
\(236\) 11.6490 14.6074i 0.758284 0.950858i
\(237\) 0 0
\(238\) 0.00265655 + 0.0132848i 0.000172199 + 0.000861127i
\(239\) 4.22999 8.78367i 0.273615 0.568168i −0.718202 0.695835i \(-0.755034\pi\)
0.991817 + 0.127667i \(0.0407488\pi\)
\(240\) 0 0
\(241\) 9.34327 + 2.13254i 0.601853 + 0.137369i 0.512582 0.858638i \(-0.328689\pi\)
0.0892712 + 0.996007i \(0.471546\pi\)
\(242\) −4.96855 10.3173i −0.319391 0.663221i
\(243\) 0 0
\(244\) 33.9736i 2.17494i
\(245\) 17.7240 + 24.8723i 1.13234 + 1.58903i
\(246\) 0 0
\(247\) −4.15927 5.21555i −0.264648 0.331858i
\(248\) 1.65084 0.795001i 0.104828 0.0504826i
\(249\) 0 0
\(250\) −35.3627 73.4315i −2.23654 4.64421i
\(251\) 3.12043 + 1.50272i 0.196960 + 0.0948508i 0.529764 0.848145i \(-0.322281\pi\)
−0.332804 + 0.942996i \(0.607995\pi\)
\(252\) 0 0
\(253\) 4.06555 1.95787i 0.255599 0.123090i
\(254\) −26.6906 21.2851i −1.67472 1.33554i
\(255\) 0 0
\(256\) 6.71465 + 8.41991i 0.419666 + 0.526244i
\(257\) 4.15911 + 18.2222i 0.259438 + 1.13667i 0.921854 + 0.387537i \(0.126674\pi\)
−0.662416 + 0.749136i \(0.730469\pi\)
\(258\) 0 0
\(259\) −11.4758 + 22.2691i −0.713075 + 1.38374i
\(260\) 10.6753 + 8.51323i 0.662051 + 0.527968i
\(261\) 0 0
\(262\) −8.18575 + 1.86834i −0.505717 + 0.115427i
\(263\) 20.9882i 1.29419i −0.762410 0.647095i \(-0.775984\pi\)
0.762410 0.647095i \(-0.224016\pi\)
\(264\) 0 0
\(265\) −29.7296 + 6.78559i −1.82628 + 0.416836i
\(266\) 0.716533 26.4988i 0.0439335 1.62475i
\(267\) 0 0
\(268\) 5.96119 26.1177i 0.364138 1.59539i
\(269\) −7.08941 + 8.88983i −0.432249 + 0.542023i −0.949482 0.313822i \(-0.898391\pi\)
0.517233 + 0.855844i \(0.326962\pi\)
\(270\) 0 0
\(271\) −4.25141 0.970356i −0.258255 0.0589449i 0.0914332 0.995811i \(-0.470855\pi\)
−0.349688 + 0.936866i \(0.613712\pi\)
\(272\) 0.00186177 0.00815695i 0.000112886 0.000494587i
\(273\) 0 0
\(274\) −2.41708 10.5899i −0.146021 0.639761i
\(275\) 57.0830i 3.44223i
\(276\) 0 0
\(277\) −3.49711 15.3218i −0.210121 0.920599i −0.964484 0.264142i \(-0.914911\pi\)
0.754363 0.656457i \(-0.227946\pi\)
\(278\) −8.99926 4.33381i −0.539739 0.259925i
\(279\) 0 0
\(280\) 1.28053 + 6.40365i 0.0765265 + 0.382691i
\(281\) −12.2719 + 9.78649i −0.732079 + 0.583813i −0.916975 0.398945i \(-0.869377\pi\)
0.184896 + 0.982758i \(0.440805\pi\)
\(282\) 0 0
\(283\) −0.591566 + 0.471759i −0.0351650 + 0.0280431i −0.640915 0.767612i \(-0.721445\pi\)
0.605750 + 0.795655i \(0.292873\pi\)
\(284\) 4.43848 9.21661i 0.263376 0.546905i
\(285\) 0 0
\(286\) −5.02092 10.4260i −0.296893 0.616505i
\(287\) 21.6486 + 5.56085i 1.27787 + 0.328246i
\(288\) 0 0
\(289\) 15.3165 7.37602i 0.900969 0.433884i
\(290\) −3.26352 + 14.2984i −0.191640 + 0.839631i
\(291\) 0 0
\(292\) −9.87753 + 7.87707i −0.578039 + 0.460970i
\(293\) 15.5966 0.911164 0.455582 0.890194i \(-0.349431\pi\)
0.455582 + 0.890194i \(0.349431\pi\)
\(294\) 0 0
\(295\) 35.8528 2.08743
\(296\) −4.18805 + 3.33986i −0.243426 + 0.194125i
\(297\) 0 0
\(298\) 4.88882 21.4193i 0.283202 1.24079i
\(299\) 1.37598 0.662637i 0.0795749 0.0383213i
\(300\) 0 0
\(301\) 0.506836 + 1.12959i 0.0292135 + 0.0651082i
\(302\) −6.54588 13.5927i −0.376673 0.782170i
\(303\) 0 0
\(304\) −7.10304 + 14.7496i −0.407387 + 0.845948i
\(305\) 50.9706 40.6477i 2.91857 2.32748i
\(306\) 0 0
\(307\) 1.03488 0.825290i 0.0590638 0.0471018i −0.593513 0.804824i \(-0.702259\pi\)
0.652577 + 0.757723i \(0.273688\pi\)
\(308\) 6.08652 23.6950i 0.346812 1.35015i
\(309\) 0 0
\(310\) 26.3203 + 12.6752i 1.49489 + 0.719901i
\(311\) −1.16016 5.08300i −0.0657867 0.288230i 0.931324 0.364192i \(-0.118655\pi\)
−0.997111 + 0.0759611i \(0.975798\pi\)
\(312\) 0 0
\(313\) 8.11203i 0.458519i 0.973365 + 0.229259i \(0.0736304\pi\)
−0.973365 + 0.229259i \(0.926370\pi\)
\(314\) 6.01669 + 26.3609i 0.339542 + 1.48763i
\(315\) 0 0
\(316\) −5.08872 + 22.2952i −0.286263 + 1.25420i
\(317\) −8.11359 1.85187i −0.455705 0.104012i −0.0114939 0.999934i \(-0.503659\pi\)
−0.444211 + 0.895922i \(0.646516\pi\)
\(318\) 0 0
\(319\) 4.12301 5.17009i 0.230844 0.289469i
\(320\) 9.72710 42.6172i 0.543762 2.38238i
\(321\) 0 0
\(322\) 5.87794 + 1.50986i 0.327565 + 0.0841412i
\(323\) 0.0117039 0.00267133i 0.000651221 0.000148637i
\(324\) 0 0
\(325\) 19.3196i 1.07166i
\(326\) −0.778649 + 0.177722i −0.0431254 + 0.00984309i
\(327\) 0 0
\(328\) 3.73656 + 2.97980i 0.206317 + 0.164532i
\(329\) 0.173435 6.41398i 0.00956179 0.353614i
\(330\) 0 0
\(331\) 4.34040 + 19.0165i 0.238570 + 1.04524i 0.942299 + 0.334774i \(0.108660\pi\)
−0.703729 + 0.710469i \(0.748483\pi\)
\(332\) 23.8286 + 29.8801i 1.30776 + 1.63988i
\(333\) 0 0
\(334\) −11.7125 9.34044i −0.640882 0.511086i
\(335\) 46.3166 22.3049i 2.53055 1.21865i
\(336\) 0 0
\(337\) 20.7554 + 9.99525i 1.13062 + 0.544476i 0.903157 0.429311i \(-0.141244\pi\)
0.227460 + 0.973787i \(0.426958\pi\)
\(338\) 9.96116 + 20.6846i 0.541816 + 1.12509i
\(339\) 0 0
\(340\) −0.0221383 + 0.0106613i −0.00120062 + 0.000578188i
\(341\) −8.21257 10.2982i −0.444736 0.557681i
\(342\) 0 0
\(343\) 9.36101 15.9803i 0.505447 0.862858i
\(344\) 0.264730i 0.0142733i
\(345\) 0 0
\(346\) −2.56769 5.33187i −0.138040 0.286643i
\(347\) −21.6884 4.95023i −1.16429 0.265742i −0.403650 0.914913i \(-0.632259\pi\)
−0.760642 + 0.649171i \(0.775116\pi\)
\(348\) 0 0
\(349\) 1.84031 3.82143i 0.0985093 0.204557i −0.845890 0.533357i \(-0.820930\pi\)
0.944399 + 0.328801i \(0.106644\pi\)
\(350\) −49.4708 + 58.7061i −2.64432 + 3.13798i
\(351\) 0 0
\(352\) −20.5750 + 25.8002i −1.09665 + 1.37516i
\(353\) −4.11202 1.98025i −0.218861 0.105398i 0.321241 0.946997i \(-0.395900\pi\)
−0.540102 + 0.841600i \(0.681614\pi\)
\(354\) 0 0
\(355\) 19.1381 4.36815i 1.01574 0.231837i
\(356\) 8.92852 + 11.1960i 0.473211 + 0.593388i
\(357\) 0 0
\(358\) −13.8793 + 17.4041i −0.733544 + 0.919835i
\(359\) −7.99103 + 16.5935i −0.421750 + 0.875774i 0.576525 + 0.817079i \(0.304408\pi\)
−0.998276 + 0.0586947i \(0.981306\pi\)
\(360\) 0 0
\(361\) −4.48944 −0.236286
\(362\) 30.6742 1.61220
\(363\) 0 0
\(364\) 2.05997 8.01954i 0.107972 0.420338i
\(365\) −23.6359 5.39474i −1.23716 0.282374i
\(366\) 0 0
\(367\) −26.5459 21.1697i −1.38569 1.10505i −0.981732 0.190269i \(-0.939064\pi\)
−0.403955 0.914779i \(-0.632365\pi\)
\(368\) −2.93021 2.33676i −0.152748 0.121812i
\(369\) 0 0
\(370\) −83.2640 19.0045i −4.32869 0.987996i
\(371\) 11.1344 + 14.7637i 0.578068 + 0.766495i
\(372\) 0 0
\(373\) 26.8836 1.39198 0.695990 0.718051i \(-0.254966\pi\)
0.695990 + 0.718051i \(0.254966\pi\)
\(374\) 0.0208247 0.00107682
\(375\) 0 0
\(376\) 0.595270 1.23609i 0.0306987 0.0637465i
\(377\) 1.39542 1.74981i 0.0718680 0.0901196i
\(378\) 0 0
\(379\) −12.2638 15.3783i −0.629948 0.789929i 0.359758 0.933046i \(-0.382859\pi\)
−0.989706 + 0.143116i \(0.954288\pi\)
\(380\) 46.8730 10.6985i 2.40454 0.548819i
\(381\) 0 0
\(382\) −21.8904 10.5418i −1.12001 0.539368i
\(383\) 14.9439 18.7390i 0.763597 0.957520i −0.236303 0.971679i \(-0.575936\pi\)
0.999900 + 0.0141595i \(0.00450726\pi\)
\(384\) 0 0
\(385\) 42.8319 19.2183i 2.18292 0.979456i
\(386\) −5.51046 + 11.4426i −0.280475 + 0.582412i
\(387\) 0 0
\(388\) −6.46673 1.47599i −0.328298 0.0749320i
\(389\) −9.56032 19.8522i −0.484728 1.00655i −0.989666 0.143392i \(-0.954199\pi\)
0.504938 0.863155i \(-0.331515\pi\)
\(390\) 0 0
\(391\) 0.00274835i 0.000138990i
\(392\) 3.22500 2.29813i 0.162887 0.116073i
\(393\) 0 0
\(394\) −3.88445 4.87094i −0.195696 0.245394i
\(395\) −39.5378 + 19.0404i −1.98936 + 0.958027i
\(396\) 0 0
\(397\) 10.8708 + 22.5735i 0.545592 + 1.13293i 0.973410 + 0.229069i \(0.0735680\pi\)
−0.427818 + 0.903865i \(0.640718\pi\)
\(398\) −39.3878 18.9682i −1.97433 0.950788i
\(399\) 0 0
\(400\) 42.7161 20.5710i 2.13581 1.02855i
\(401\) 11.8949 + 9.48584i 0.594002 + 0.473700i 0.873752 0.486372i \(-0.161680\pi\)
−0.279750 + 0.960073i \(0.590252\pi\)
\(402\) 0 0
\(403\) −2.77953 3.48542i −0.138458 0.173621i
\(404\) 4.63403 + 20.3030i 0.230552 + 1.01011i
\(405\) 0 0
\(406\) 8.72088 1.74391i 0.432810 0.0865486i
\(407\) 30.1070 + 24.0095i 1.49235 + 1.19011i
\(408\) 0 0
\(409\) 12.1656 2.77673i 0.601552 0.137300i 0.0891093 0.996022i \(-0.471598\pi\)
0.512442 + 0.858722i \(0.328741\pi\)
\(410\) 76.1981i 3.76316i
\(411\) 0 0
\(412\) −6.45682 + 1.47373i −0.318105 + 0.0726053i
\(413\) −8.90022 19.8360i −0.437951 0.976063i
\(414\) 0 0
\(415\) −16.3194 + 71.5001i −0.801089 + 3.50980i
\(416\) −6.96357 + 8.73204i −0.341417 + 0.428124i
\(417\) 0 0
\(418\) −39.7253 9.06705i −1.94303 0.443484i
\(419\) −4.14796 + 18.1734i −0.202641 + 0.887830i 0.766679 + 0.642030i \(0.221908\pi\)
−0.969321 + 0.245799i \(0.920950\pi\)
\(420\) 0 0
\(421\) 2.49894 + 10.9486i 0.121791 + 0.533600i 0.998606 + 0.0527737i \(0.0168062\pi\)
−0.876816 + 0.480827i \(0.840337\pi\)
\(422\) 31.8462i 1.55025i
\(423\) 0 0
\(424\) 0.879836 + 3.85481i 0.0427286 + 0.187206i
\(425\) −0.0313241 0.0150849i −0.00151944 0.000731724i
\(426\) 0 0
\(427\) −35.1419 18.1095i −1.70063 0.876380i
\(428\) −25.2675 + 20.1501i −1.22135 + 0.973994i
\(429\) 0 0
\(430\) −3.29991 + 2.63159i −0.159136 + 0.126907i
\(431\) −17.6980 + 36.7503i −0.852482 + 1.77020i −0.257881 + 0.966177i \(0.583024\pi\)
−0.594601 + 0.804021i \(0.702690\pi\)
\(432\) 0 0
\(433\) −5.73036 11.8992i −0.275383 0.571840i 0.716706 0.697376i \(-0.245649\pi\)
−0.992089 + 0.125536i \(0.959935\pi\)
\(434\) 0.478841 17.7085i 0.0229851 0.850034i
\(435\) 0 0
\(436\) −16.2876 + 7.84371i −0.780036 + 0.375645i
\(437\) 1.19663 5.24276i 0.0572424 0.250795i
\(438\) 0 0
\(439\) −14.0789 + 11.2275i −0.671949 + 0.535861i −0.898960 0.438031i \(-0.855676\pi\)
0.227011 + 0.973892i \(0.427105\pi\)
\(440\) 10.0381 0.478548
\(441\) 0 0
\(442\) 0.00704809 0.000335243
\(443\) 17.2953 13.7925i 0.821723 0.655302i −0.119595 0.992823i \(-0.538160\pi\)
0.941318 + 0.337520i \(0.109588\pi\)
\(444\) 0 0
\(445\) −6.11485 + 26.7909i −0.289872 + 1.27001i
\(446\) 9.21722 4.43878i 0.436448 0.210182i
\(447\) 0 0
\(448\) −25.9931 + 5.19782i −1.22806 + 0.245574i
\(449\) 3.37716 + 7.01274i 0.159378 + 0.330952i 0.965331 0.261027i \(-0.0840612\pi\)
−0.805953 + 0.591979i \(0.798347\pi\)
\(450\) 0 0
\(451\) 14.9069 30.9545i 0.701938 1.45759i
\(452\) 26.4609 21.1019i 1.24462 0.992550i
\(453\) 0 0
\(454\) 32.0386 25.5499i 1.50364 1.19912i
\(455\) 14.4964 6.50440i 0.679600 0.304931i
\(456\) 0 0
\(457\) 16.4925 + 7.94239i 0.771488 + 0.371529i 0.777850 0.628451i \(-0.216311\pi\)
−0.00636122 + 0.999980i \(0.502025\pi\)
\(458\) −5.76745 25.2688i −0.269495 1.18073i
\(459\) 0 0
\(460\) 11.0069i 0.513200i
\(461\) 6.73601 + 29.5124i 0.313727 + 1.37453i 0.848349 + 0.529437i \(0.177597\pi\)
−0.534622 + 0.845091i \(0.679546\pi\)
\(462\) 0 0
\(463\) −5.33895 + 23.3915i −0.248122 + 1.08709i 0.685285 + 0.728275i \(0.259678\pi\)
−0.933407 + 0.358819i \(0.883180\pi\)
\(464\) −5.35467 1.22217i −0.248584 0.0567377i
\(465\) 0 0
\(466\) −27.7631 + 34.8138i −1.28610 + 1.61272i
\(467\) 3.08333 13.5090i 0.142679 0.625120i −0.852127 0.523335i \(-0.824688\pi\)
0.994806 0.101785i \(-0.0324552\pi\)
\(468\) 0 0
\(469\) −23.8382 20.0881i −1.10075 0.927583i
\(470\) 21.3255 4.86740i 0.983671 0.224516i
\(471\) 0 0
\(472\) 4.64876i 0.213977i
\(473\) 1.85537 0.423477i 0.0853102 0.0194715i
\(474\) 0 0
\(475\) 53.1860 + 42.4144i 2.44034 + 1.94611i
\(476\) 0.0113941 + 0.00960167i 0.000522249 + 0.000440092i
\(477\) 0 0
\(478\) −4.48474 19.6489i −0.205127 0.898720i
\(479\) 6.76546 + 8.48362i 0.309122 + 0.387626i 0.911989 0.410215i \(-0.134546\pi\)
−0.602867 + 0.797842i \(0.705975\pi\)
\(480\) 0 0
\(481\) 10.1897 + 8.12599i 0.464609 + 0.370513i
\(482\) 17.8499 8.59607i 0.813041 0.391540i
\(483\) 0 0
\(484\) −11.3473 5.46455i −0.515785 0.248389i
\(485\) −5.52269 11.4680i −0.250772 0.520734i
\(486\) 0 0
\(487\) 12.1205 5.83690i 0.549230 0.264495i −0.138623 0.990345i \(-0.544268\pi\)
0.687853 + 0.725850i \(0.258553\pi\)
\(488\) −5.27048 6.60897i −0.238583 0.299174i
\(489\) 0 0
\(490\) 60.7053 + 17.3553i 2.74239 + 0.784034i
\(491\) 32.1316i 1.45008i 0.688708 + 0.725039i \(0.258178\pi\)
−0.688708 + 0.725039i \(0.741822\pi\)
\(492\) 0 0
\(493\) 0.00174751 + 0.00362874i 7.87039e−5 + 0.000163430i
\(494\) −13.4450 3.06872i −0.604917 0.138068i
\(495\) 0 0
\(496\) −4.74678 + 9.85678i −0.213137 + 0.442583i
\(497\) −7.16762 9.50398i −0.321512 0.426312i
\(498\) 0 0
\(499\) 2.66616 3.34326i 0.119354 0.149665i −0.718565 0.695460i \(-0.755201\pi\)
0.837919 + 0.545795i \(0.183772\pi\)
\(500\) −80.7620 38.8929i −3.61179 1.73934i
\(501\) 0 0
\(502\) 6.98034 1.59322i 0.311548 0.0711088i
\(503\) 15.4247 + 19.3419i 0.687752 + 0.862414i 0.996042 0.0888785i \(-0.0283283\pi\)
−0.308290 + 0.951292i \(0.599757\pi\)
\(504\) 0 0
\(505\) −24.9162 + 31.2440i −1.10876 + 1.39034i
\(506\) 4.04746 8.40465i 0.179932 0.373632i
\(507\) 0 0
\(508\) −37.5466 −1.66586
\(509\) −9.79261 −0.434050 −0.217025 0.976166i \(-0.569635\pi\)
−0.217025 + 0.976166i \(0.569635\pi\)
\(510\) 0 0
\(511\) 2.88276 + 14.4160i 0.127526 + 0.637727i
\(512\) 30.4473 + 6.94941i 1.34560 + 0.307123i
\(513\) 0 0
\(514\) 30.2094 + 24.0912i 1.33248 + 1.06262i
\(515\) −9.93628 7.92392i −0.437845 0.349170i
\(516\) 0 0
\(517\) −9.61542 2.19466i −0.422886 0.0965209i
\(518\) 10.1553 + 50.7844i 0.446199 + 2.23134i
\(519\) 0 0
\(520\) 3.39738 0.148985
\(521\) 12.2091 0.534892 0.267446 0.963573i \(-0.413820\pi\)
0.267446 + 0.963573i \(0.413820\pi\)
\(522\) 0 0
\(523\) 7.65067 15.8868i 0.334541 0.694681i −0.664054 0.747685i \(-0.731165\pi\)
0.998594 + 0.0530043i \(0.0168797\pi\)
\(524\) −5.75758 + 7.21978i −0.251521 + 0.315397i
\(525\) 0 0
\(526\) −27.0523 33.9226i −1.17954 1.47909i
\(527\) 0.00782140 0.00178518i 0.000340705 7.77638e-5i
\(528\) 0 0
\(529\) −19.6131 9.44516i −0.852743 0.410659i
\(530\) −39.3049 + 49.2867i −1.70729 + 2.14088i
\(531\) 0 0
\(532\) −17.5549 23.2772i −0.761103 1.00919i
\(533\) 5.04521 10.4765i 0.218532 0.453787i
\(534\) 0 0
\(535\) −60.4625 13.8002i −2.61402 0.596633i
\(536\) −2.89211 6.00552i −0.124920 0.259399i
\(537\) 0 0
\(538\) 23.5061i 1.01342i
\(539\) −21.2655 18.9264i −0.915968 0.815216i
\(540\) 0 0
\(541\) −6.97220 8.74286i −0.299758 0.375885i 0.609027 0.793150i \(-0.291560\pi\)
−0.908785 + 0.417265i \(0.862989\pi\)
\(542\) −8.12213 + 3.91141i −0.348875 + 0.168009i
\(543\) 0 0
\(544\) −0.00872059 0.0181085i −0.000373892 0.000776396i
\(545\) −31.2552 15.0517i −1.33883 0.644745i
\(546\) 0 0
\(547\) −13.9058 + 6.69667i −0.594568 + 0.286329i −0.706868 0.707346i \(-0.749893\pi\)
0.112300 + 0.993674i \(0.464178\pi\)
\(548\) −9.34025 7.44860i −0.398996 0.318189i
\(549\) 0 0
\(550\) 73.5759 + 92.2613i 3.13729 + 3.93404i
\(551\) −1.75361 7.68307i −0.0747063 0.327310i
\(552\) 0 0
\(553\) 20.3493 + 17.1480i 0.865340 + 0.729209i
\(554\) −25.4010 20.2566i −1.07919 0.860622i
\(555\) 0 0
\(556\) −10.7101 + 2.44451i −0.454210 + 0.103670i
\(557\) 18.1025i 0.767028i 0.923535 + 0.383514i \(0.125286\pi\)
−0.923535 + 0.383514i \(0.874714\pi\)
\(558\) 0 0
\(559\) 0.627948 0.143325i 0.0265594 0.00606200i
\(560\) −29.8167 25.1261i −1.25999 1.06177i
\(561\) 0 0
\(562\) −7.22052 + 31.6352i −0.304579 + 1.33445i
\(563\) −5.44395 + 6.82650i −0.229435 + 0.287703i −0.883201 0.468994i \(-0.844617\pi\)
0.653766 + 0.756697i \(0.273188\pi\)
\(564\) 0 0
\(565\) 63.3184 + 14.4520i 2.66382 + 0.608000i
\(566\) −0.348066 + 1.52497i −0.0146303 + 0.0640995i
\(567\) 0 0
\(568\) −0.566384 2.48149i −0.0237649 0.104121i
\(569\) 0.531762i 0.0222926i 0.999938 + 0.0111463i \(0.00354806\pi\)
−0.999938 + 0.0111463i \(0.996452\pi\)
\(570\) 0 0
\(571\) −1.82542 7.99770i −0.0763916 0.334693i 0.922262 0.386565i \(-0.126338\pi\)
−0.998654 + 0.0518716i \(0.983481\pi\)
\(572\) −11.4669 5.52214i −0.479453 0.230892i
\(573\) 0 0
\(574\) 42.1574 18.9157i 1.75962 0.789525i
\(575\) −12.1762 + 9.71020i −0.507783 + 0.404943i
\(576\) 0 0
\(577\) −7.32438 + 5.84100i −0.304918 + 0.243164i −0.763979 0.645241i \(-0.776757\pi\)
0.459062 + 0.888404i \(0.348186\pi\)
\(578\) 15.2483 31.6635i 0.634246 1.31703i
\(579\) 0 0
\(580\) 6.99863 + 14.5328i 0.290602 + 0.603442i
\(581\) 43.6093 8.72052i 1.80922 0.361788i
\(582\) 0 0
\(583\) 25.6092 12.3327i 1.06063 0.510770i
\(584\) −0.699495 + 3.06469i −0.0289453 + 0.126818i
\(585\) 0 0
\(586\) 25.2083 20.1029i 1.04134 0.830445i
\(587\) 22.2926 0.920113 0.460057 0.887890i \(-0.347829\pi\)
0.460057 + 0.887890i \(0.347829\pi\)
\(588\) 0 0
\(589\) −15.6974 −0.646800
\(590\) 57.9477 46.2118i 2.38567 1.90251i
\(591\) 0 0
\(592\) 7.11706 31.1819i 0.292510 1.28157i
\(593\) 2.68385 1.29248i 0.110213 0.0530756i −0.377965 0.925820i \(-0.623376\pi\)
0.488178 + 0.872744i \(0.337662\pi\)
\(594\) 0 0
\(595\) −0.000772877 0.0285825i −3.16849e−5 0.00117177i
\(596\) −10.4841 21.7705i −0.429446 0.891753i
\(597\) 0 0
\(598\) 1.36986 2.84454i 0.0560176 0.116322i
\(599\) 6.09092 4.85734i 0.248868 0.198466i −0.491108 0.871099i \(-0.663408\pi\)
0.739976 + 0.672633i \(0.234837\pi\)
\(600\) 0 0
\(601\) −7.47364 + 5.96003i −0.304856 + 0.243115i −0.763953 0.645271i \(-0.776744\pi\)
0.459097 + 0.888386i \(0.348173\pi\)
\(602\) 2.27514 + 1.17244i 0.0927277 + 0.0477849i
\(603\) 0 0
\(604\) −14.9496 7.19934i −0.608290 0.292937i
\(605\) −5.37795 23.5624i −0.218645 0.957946i
\(606\) 0 0
\(607\) 40.3837i 1.63912i 0.572990 + 0.819562i \(0.305783\pi\)
−0.572990 + 0.819562i \(0.694217\pi\)
\(608\) 8.75103 + 38.3408i 0.354901 + 1.55492i
\(609\) 0 0
\(610\) 29.9901 131.395i 1.21426 5.32003i
\(611\) −3.25432 0.742778i −0.131656 0.0300496i
\(612\) 0 0
\(613\) 28.5198 35.7627i 1.15190 1.44444i 0.276523 0.961007i \(-0.410818\pi\)
0.875381 0.483434i \(-0.160611\pi\)
\(614\) 0.608903 2.66778i 0.0245733 0.107663i
\(615\) 0 0
\(616\) −2.49189 5.55368i −0.100401 0.223764i
\(617\) 16.4516 3.75497i 0.662316 0.151169i 0.121867 0.992546i \(-0.461112\pi\)
0.540448 + 0.841377i \(0.318255\pi\)
\(618\) 0 0
\(619\) 27.2418i 1.09494i 0.836825 + 0.547470i \(0.184409\pi\)
−0.836825 + 0.547470i \(0.815591\pi\)
\(620\) 31.3240 7.14951i 1.25800 0.287131i
\(621\) 0 0
\(622\) −8.42676 6.72011i −0.337882 0.269452i
\(623\) 16.3403 3.26756i 0.654661 0.130912i
\(624\) 0 0
\(625\) −22.6599 99.2795i −0.906396 3.97118i
\(626\) 10.4558 + 13.1112i 0.417899 + 0.524029i
\(627\) 0 0
\(628\) 23.2501 + 18.5413i 0.927781 + 0.739880i
\(629\) −0.0211313 + 0.0101763i −0.000842560 + 0.000405756i
\(630\) 0 0
\(631\) −24.7711 11.9292i −0.986124 0.474892i −0.129917 0.991525i \(-0.541471\pi\)
−0.856207 + 0.516633i \(0.827185\pi\)
\(632\) 2.46882 + 5.12657i 0.0982045 + 0.203924i
\(633\) 0 0
\(634\) −15.5007 + 7.46472i −0.615610 + 0.296462i
\(635\) −44.9226 56.3311i −1.78270 2.23543i
\(636\) 0 0
\(637\) −7.19725 6.40559i −0.285165 0.253799i
\(638\) 13.6705i 0.541220i
\(639\) 0 0
\(640\) −8.48734 17.6241i −0.335492 0.696656i
\(641\) 14.5469 + 3.32024i 0.574569 + 0.131142i 0.499925 0.866069i \(-0.333361\pi\)
0.0746437 + 0.997210i \(0.476218\pi\)
\(642\) 0 0
\(643\) 9.62506 19.9866i 0.379575 0.788196i −0.620417 0.784272i \(-0.713037\pi\)
0.999992 0.00392394i \(-0.00124903\pi\)
\(644\) 6.08968 2.73239i 0.239967 0.107671i
\(645\) 0 0
\(646\) 0.0154734 0.0194031i 0.000608793 0.000763403i
\(647\) 31.9879 + 15.4046i 1.25757 + 0.605616i 0.939532 0.342461i \(-0.111260\pi\)
0.318042 + 0.948077i \(0.396975\pi\)
\(648\) 0 0
\(649\) −32.5811 + 7.43642i −1.27892 + 0.291905i
\(650\) 24.9016 + 31.2257i 0.976722 + 1.22477i
\(651\) 0 0
\(652\) −0.547676 + 0.686764i −0.0214486 + 0.0268958i
\(653\) −9.55151 + 19.8339i −0.373780 + 0.776161i −0.999994 0.00348962i \(-0.998889\pi\)
0.626214 + 0.779651i \(0.284604\pi\)
\(654\) 0 0
\(655\) −17.7205 −0.692397
\(656\) −28.5357 −1.11413
\(657\) 0 0
\(658\) −7.98684 10.5902i −0.311360 0.412850i
\(659\) −22.7399 5.19024i −0.885822 0.202183i −0.244679 0.969604i \(-0.578683\pi\)
−0.641143 + 0.767421i \(0.721540\pi\)
\(660\) 0 0
\(661\) 4.64300 + 3.70267i 0.180592 + 0.144017i 0.709614 0.704591i \(-0.248870\pi\)
−0.529022 + 0.848608i \(0.677441\pi\)
\(662\) 31.5262 + 25.1413i 1.22530 + 0.977144i
\(663\) 0 0
\(664\) 9.27087 + 2.11602i 0.359779 + 0.0821173i
\(665\) 13.9191 54.1876i 0.539760 2.10131i
\(666\) 0 0
\(667\) 1.80417 0.0698576
\(668\) −16.4764 −0.637492
\(669\) 0 0
\(670\) 46.1106 95.7496i 1.78141 3.69913i
\(671\) −37.8883 + 47.5105i −1.46266 + 1.83412i
\(672\) 0 0
\(673\) −4.78696 6.00266i −0.184524 0.231386i 0.680962 0.732319i \(-0.261562\pi\)
−0.865486 + 0.500933i \(0.832990\pi\)
\(674\) 46.4294 10.5972i 1.78839 0.408189i
\(675\) 0 0
\(676\) 22.7495 + 10.9556i 0.874980 + 0.421368i
\(677\) −27.0462 + 33.9149i −1.03947 + 1.30346i −0.0878656 + 0.996132i \(0.528005\pi\)
−0.951605 + 0.307323i \(0.900567\pi\)
\(678\) 0 0
\(679\) −4.97381 + 5.90233i −0.190877 + 0.226511i
\(680\) −0.00265269 + 0.00550837i −0.000101726 + 0.000211237i
\(681\) 0 0
\(682\) −26.5474 6.05927i −1.01655 0.232022i
\(683\) −9.51245 19.7528i −0.363984 0.755820i 0.635889 0.771781i \(-0.280634\pi\)
−0.999873 + 0.0159608i \(0.994919\pi\)
\(684\) 0 0
\(685\) 22.9251i 0.875921i
\(686\) −5.46766 37.8942i −0.208756 1.44681i
\(687\) 0 0
\(688\) −0.985517 1.23580i −0.0375725 0.0471144i
\(689\) 8.66739 4.17399i 0.330201 0.159017i
\(690\) 0 0
\(691\) −15.6054 32.4051i −0.593659 1.23275i −0.953967 0.299913i \(-0.903042\pi\)
0.360307 0.932834i \(-0.382672\pi\)
\(692\) −5.86414 2.82402i −0.222921 0.107353i
\(693\) 0 0
\(694\) −41.4347 + 19.9539i −1.57284 + 0.757439i
\(695\) −16.4816 13.1436i −0.625183 0.498567i
\(696\) 0 0
\(697\) 0.0130468 + 0.0163602i 0.000494184 + 0.000619687i
\(698\) −1.95113 8.54848i −0.0738515 0.323565i
\(699\) 0 0
\(700\) −2.28230 + 84.4039i −0.0862628 + 3.19017i
\(701\) −7.18722 5.73162i −0.271458 0.216480i 0.478294 0.878200i \(-0.341255\pi\)
−0.749751 + 0.661720i \(0.769827\pi\)
\(702\) 0 0
\(703\) 44.7409 10.2118i 1.68743 0.385146i
\(704\) 40.7457i 1.53566i
\(705\) 0 0
\(706\) −9.19852 + 2.09950i −0.346191 + 0.0790158i
\(707\) 23.4713 + 6.02906i 0.882730 + 0.226746i
\(708\) 0 0
\(709\) 7.15245 31.3369i 0.268616 1.17688i −0.643009 0.765859i \(-0.722314\pi\)
0.911625 0.411024i \(-0.134829\pi\)
\(710\) 25.3020 31.7277i 0.949568 1.19072i
\(711\) 0 0
\(712\) 3.47377 + 0.792866i 0.130185 + 0.0297139i
\(713\) 0.799674 3.50360i 0.0299480 0.131211i
\(714\) 0 0
\(715\) −5.43463 23.8107i −0.203244 0.890469i
\(716\) 24.4829i 0.914969i
\(717\) 0 0
\(718\) 8.47228 + 37.1195i 0.316182 + 1.38529i
\(719\) 31.2682 + 15.0580i 1.16611 + 0.561568i 0.913834 0.406087i \(-0.133107\pi\)
0.252274 + 0.967656i \(0.418821\pi\)
\(720\) 0 0
\(721\) −1.91738 + 7.46441i −0.0714068 + 0.277989i
\(722\) −7.25613 + 5.78657i −0.270045 + 0.215354i
\(723\) 0 0
\(724\) 26.3762 21.0343i 0.980263 0.781734i
\(725\) −9.90255 + 20.5629i −0.367771 + 0.763685i
\(726\) 0 0
\(727\) 6.04878 + 12.5604i 0.224337 + 0.465840i 0.982509 0.186214i \(-0.0596217\pi\)
−0.758172 + 0.652054i \(0.773907\pi\)
\(728\) −0.843376 1.87963i −0.0312576 0.0696638i
\(729\) 0 0
\(730\) −45.1554 + 21.7457i −1.67128 + 0.804844i
\(731\) −0.000257924 0.00113004i −9.53967e−6 4.17960e-5i
\(732\) 0 0
\(733\) 29.0186 23.1416i 1.07183 0.854753i 0.0819430 0.996637i \(-0.473887\pi\)
0.989883 + 0.141884i \(0.0453160\pi\)
\(734\) −70.1915 −2.59082
\(735\) 0 0
\(736\) −9.00333 −0.331867
\(737\) −37.4636 + 29.8762i −1.37999 + 1.10051i
\(738\) 0 0
\(739\) −5.18637 + 22.7230i −0.190784 + 0.835878i 0.785410 + 0.618976i \(0.212452\pi\)
−0.976193 + 0.216902i \(0.930405\pi\)
\(740\) −84.6291 + 40.7552i −3.11103 + 1.49819i
\(741\) 0 0
\(742\) 37.0255 + 9.51072i 1.35925 + 0.349149i
\(743\) 2.69045 + 5.58678i 0.0987032 + 0.204959i 0.944473 0.328588i \(-0.106573\pi\)
−0.845770 + 0.533548i \(0.820859\pi\)
\(744\) 0 0
\(745\) 20.1185 41.7766i 0.737086 1.53058i
\(746\) 43.4511 34.6511i 1.59086 1.26867i
\(747\) 0 0
\(748\) 0.0179068 0.0142802i 0.000654737 0.000522135i
\(749\) 7.37432 + 36.8773i 0.269452 + 1.34747i
\(750\) 0 0
\(751\) 6.48350 + 3.12229i 0.236586 + 0.113934i 0.548421 0.836202i \(-0.315229\pi\)
−0.311835 + 0.950136i \(0.600943\pi\)
\(752\) 1.82281 + 7.98627i 0.0664712 + 0.291229i
\(753\) 0 0
\(754\) 4.62675i 0.168496i
\(755\) −7.08525 31.0425i −0.257859 1.12975i
\(756\) 0 0
\(757\) −7.52407 + 32.9651i −0.273467 + 1.19814i 0.632423 + 0.774624i \(0.282061\pi\)
−0.905890 + 0.423514i \(0.860796\pi\)
\(758\) −39.6430 9.04827i −1.43990 0.328648i
\(759\) 0 0
\(760\) 7.45862 9.35281i 0.270553 0.339262i
\(761\) 7.11305 31.1643i 0.257848 1.12971i −0.665699 0.746220i \(-0.731867\pi\)
0.923547 0.383485i \(-0.125276\pi\)
\(762\) 0 0
\(763\) −0.568622 + 21.0288i −0.0205855 + 0.761292i
\(764\) −26.0520 + 5.94619i −0.942527 + 0.215126i
\(765\) 0 0
\(766\) 49.5489i 1.79027i
\(767\) −11.0270 + 2.51684i −0.398162 + 0.0908779i
\(768\) 0 0
\(769\) 24.2017 + 19.3002i 0.872735 + 0.695983i 0.953708 0.300734i \(-0.0972315\pi\)
−0.0809736 + 0.996716i \(0.525803\pi\)
\(770\) 44.4567 86.2692i 1.60211 3.10893i
\(771\) 0 0
\(772\) 3.10821 + 13.6179i 0.111867 + 0.490121i
\(773\) −5.89943 7.39765i −0.212188 0.266075i 0.664336 0.747434i \(-0.268715\pi\)
−0.876523 + 0.481359i \(0.840143\pi\)
\(774\) 0 0
\(775\) 35.5428 + 28.3445i 1.27674 + 1.01816i
\(776\) −1.48696 + 0.716084i −0.0533789 + 0.0257059i
\(777\) 0 0
\(778\) −41.0401 19.7639i −1.47136 0.708570i
\(779\) −17.7650 36.8894i −0.636496 1.32170i
\(780\) 0 0
\(781\) −16.4856 + 7.93906i −0.589902 + 0.284082i
\(782\) 0.00354243 + 0.00444206i 0.000126677 + 0.000158848i
\(783\) 0 0
\(784\) −6.49947 + 22.7338i −0.232124 + 0.811921i
\(785\) 57.0659i 2.03677i
\(786\) 0 0
\(787\) −1.28538 2.66912i −0.0458189 0.0951439i 0.876803 0.480850i \(-0.159672\pi\)
−0.922622 + 0.385707i \(0.873958\pi\)
\(788\) −6.68032 1.52474i −0.237976 0.0543166i
\(789\)