Properties

Label 441.2.w.a.251.17
Level $441$
Weight $2$
Character 441.251
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 251.17
Character \(\chi\) \(=\) 441.251
Dual form 441.2.w.a.188.17

$q$-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 \(\left(\mathbb{Z}/441\mathbb{Z}\right)^\times\).

\(n\) \(199\) \(344\)
\(\chi(n)\) \(e\left(\frac{9}{14}\right)\) \(-1\)

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 0.996962 0.0778871i \(-0.0248174\pi\)
0.145911 + 0.989298i \(0.453389\pi\)
\(3\) 0 0
\(4\) 0.505936 + 2.21665i 0.252968 + 1.10832i
\(5\) 3.93097 + 1.89305i 1.75798 + 0.846599i 0.974241 + 0.225511i \(0.0724052\pi\)
0.783741 + 0.621088i \(0.213309\pi\)
\(6\) 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 0.0132172 0.999913i \(-0.495793\pi\)
−0.971902 + 0.235387i \(0.924364\pi\)
\(12\) 0 0
\(13\) −1.07613 0.858184i −0.298464 0.238017i 0.462794 0.886466i \(-0.346847\pi\)
−0.761259 + 0.648448i \(0.775418\pi\)
\(14\) −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 −0.974995 0.222228i \(-0.928667\pi\)
0.974861 + 0.222814i \(0.0715242\pi\)
\(18\) 0 0
\(19\) 4.84659i 1.11188i −0.831221 0.555942i \(-0.812358\pi\)
0.831221 0.555942i \(-0.187642\pi\)
\(20\) −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 −0.333806 0.942642i \(-0.608333\pi\)
0.108248 + 0.994124i \(0.465476\pi\)
\(24\) 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 0.0727835 0.997348i \(-0.476812\pi\)
−0.367157 + 0.930159i \(0.619669\pi\)
\(30\) 0 0
\(31\) 3.23885i 0.581715i −0.956766 0.290857i \(-0.906059\pi\)
0.956766 0.290857i \(-0.0939405\pi\)
\(32\) 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 0.438916 + 0.898528i \(0.355363\pi\)
−0.785306 + 0.619107i \(0.787495\pi\)
\(38\) 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 −0.268267 0.963345i \(-0.586451\pi\)
−0.920435 + 0.390896i \(0.872165\pi\)
\(42\) 0 0
\(43\) −0.421609 + 0.203036i −0.0642948 + 0.0309627i −0.465755 0.884914i \(-0.654217\pi\)
0.401460 + 0.915877i \(0.368503\pi\)
\(44\) 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 −0.659227 0.751944i \(-0.729117\pi\)
0.879783 + 0.475376i \(0.157688\pi\)
\(48\) 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 −0.663193 0.748448i \(-0.730799\pi\)
−0.272777 + 0.962077i \(0.587942\pi\)
\(54\) 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 0.115341 0.993326i \(-0.463204\pi\)
0.848528 + 0.529151i \(0.177490\pi\)
\(60\) 0 0
\(61\) 14.5677 + 3.32497i 1.86520 + 0.425719i 0.997455 0.0712956i \(-0.0227134\pi\)
0.867742 + 0.497015i \(0.165571\pi\)
\(62\) 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 0.0458416 0.998949i \(-0.485403\pi\)
0.474729 + 0.880132i \(0.342546\pi\)
\(72\) 0 0
\(73\) −4.34434 + 3.46449i −0.508466 + 0.405488i −0.843838 0.536597i \(-0.819709\pi\)
0.335372 + 0.942086i \(0.391138\pi\)
\(74\) −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 −0.876930 0.480618i \(-0.840412\pi\)
−0.273433 0.961891i \(-0.588159\pi\)
\(84\) 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 0.528858 0.848710i \(-0.322620\pi\)
−0.945113 + 0.326742i \(0.894049\pi\)
\(90\) 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 \(0.0473176\pi\)
−0.988972 + 0.148106i \(0.952682\pi\)
\(98\) 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 −0.0243497 0.999704i \(-0.507752\pi\)
−0.796781 + 0.604268i \(0.793466\pi\)
\(102\) 0 0
\(103\) −1.26385 + 2.62441i −0.124531 + 0.258590i −0.953909 0.300098i \(-0.902981\pi\)
0.829378 + 0.558688i \(0.188695\pi\)
\(104\) 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 −0.990196 0.139688i \(-0.955390\pi\)
−0.0841534 + 0.996453i \(0.526819\pi\)
\(108\) 0 0
\(109\) −4.95739 + 6.21637i −0.474831 + 0.595420i −0.960347 0.278808i \(-0.910061\pi\)
0.485515 + 0.874228i \(0.338632\pi\)
\(110\) 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 0.102247 0.994759i \(-0.467397\pi\)
0.992570 + 0.121671i \(0.0388254\pi\)
\(114\) 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 0.500474 + 0.865751i \(0.333159\pi\)
−0.826547 + 0.562867i \(0.809698\pi\)
\(128\) 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 −0.586856 0.809691i \(-0.699635\pi\)
0.267143 + 0.963657i \(0.413920\pi\)
\(132\) 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 0.975368 0.220585i \(-0.0707967\pi\)
−0.780592 + 0.625041i \(0.785082\pi\)
\(138\) 0 0
\(139\) −2.09638 + 4.35318i −0.177813 + 0.369232i −0.970758 0.240061i \(-0.922832\pi\)
0.792945 + 0.609293i \(0.208547\pi\)
\(140\) −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 0.901660 0.432445i \(-0.142349\pi\)
−0.220964 + 0.975282i \(0.570920\pi\)
\(150\) 0 0
\(151\) 1.62392 + 7.11488i 0.132153 + 0.579001i 0.997030 + 0.0770162i \(0.0245393\pi\)
−0.864877 + 0.501984i \(0.832604\pi\)
\(152\) 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 −0.994974 0.100138i \(-0.968071\pi\)
0.542065 0.840337i \(-0.317643\pi\)
\(158\) −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 −0.447466 0.894301i \(-0.647673\pi\)
0.420202 + 0.907431i \(0.361959\pi\)
\(164\) 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 0.873431 + 0.486947i \(0.161890\pi\)
−0.998213 + 0.0597569i \(0.980967\pi\)
\(168\) 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 0.993353 0.115106i \(-0.0367207\pi\)
−0.944923 + 0.327293i \(0.893864\pi\)
\(174\) 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 −0.188625 0.982049i \(-0.560403\pi\)
−0.596040 + 0.802954i \(0.703260\pi\)
\(180\) 0 0
\(181\) 11.6008 9.25131i 0.862279 0.687645i −0.0889812 0.996033i \(-0.528361\pi\)
0.951260 + 0.308389i \(0.0997897\pi\)
\(182\) 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 −0.999954 0.00961204i \(-0.996940\pi\)
0.630976 + 0.775802i \(0.282655\pi\)
\(192\) 0 0
\(193\) −5.53509 2.66556i −0.398424 0.191871i 0.223933 0.974605i \(-0.428110\pi\)
−0.622357 + 0.782734i \(0.713825\pi\)
\(194\) −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 \(0.0342393\pi\)
−0.994220 + 0.107359i \(0.965761\pi\)
\(198\) 0 0
\(199\) −9.17541 + 19.0529i −0.650428 + 1.35063i 0.271189 + 0.962526i \(0.412583\pi\)
−0.921617 + 0.388101i \(0.873131\pi\)
\(200\) −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 0.993475 0.114046i \(-0.0363811\pi\)
−0.332256 + 0.943189i \(0.607810\pi\)
\(212\) −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 −0.0579050 0.998322i \(-0.518442\pi\)
0.380985 + 0.924581i \(0.375585\pi\)
\(224\) −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 0.999765 0.0216759i \(-0.00690019\pi\)
−0.640290 + 0.768133i \(0.721186\pi\)
\(230\) −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 −0.530174 0.847889i \(-0.677873\pi\)
−0.845556 + 0.533888i \(0.820731\pi\)
\(234\) 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 0.991817 0.127667i \(-0.0407488\pi\)
−0.718202 + 0.695835i \(0.755034\pi\)
\(240\) 0 0
\(241\) 9.34327 2.13254i 0.601853 0.137369i 0.0892712 0.996007i \(-0.471546\pi\)
0.512582 + 0.858638i \(0.328689\pi\)
\(242\) −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 −0.332804 0.942996i \(-0.607995\pi\)
0.529764 + 0.848145i \(0.322281\pi\)
\(252\) 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 −0.662416 0.749136i \(-0.730469\pi\)
0.921854 0.387537i \(-0.126674\pi\)
\(258\) 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 \(0.224016\pi\)
−0.762410 + 0.647095i \(0.775984\pi\)
\(264\) 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 0.517233 0.855844i \(-0.326962\pi\)
−0.949482 + 0.313822i \(0.898391\pi\)
\(270\) 0 0
\(271\) −4.25141 + 0.970356i −0.258255 + 0.0589449i −0.349688 0.936866i \(-0.613712\pi\)
0.0914332 + 0.995811i \(0.470855\pi\)
\(272\) 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 0.754363 + 0.656457i \(0.227946\pi\)
−0.964484 + 0.264142i \(0.914911\pi\)
\(278\) −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 0.184896 0.982758i \(-0.440805\pi\)
−0.916975 + 0.398945i \(0.869377\pi\)
\(282\) 0 0
\(283\) −0.591566 0.471759i −0.0351650 0.0280431i 0.605750 0.795655i \(-0.292873\pi\)
−0.640915 + 0.767612i \(0.721445\pi\)
\(284\) 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 0.652577 0.757723i \(-0.273688\pi\)
−0.593513 + 0.804824i \(0.702259\pi\)
\(308\) 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 −0.997111 0.0759611i \(-0.975798\pi\)
0.931324 + 0.364192i \(0.118655\pi\)
\(312\) 0 0
\(313\) 8.11203i 0.458519i −0.973365 0.229259i \(-0.926370\pi\)
0.973365 0.229259i \(-0.0736304\pi\)
\(314\) 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 −0.444211 0.895922i \(-0.646516\pi\)
−0.0114939 + 0.999934i \(0.503659\pi\)
\(318\) 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 −0.703729 0.710469i \(-0.748483\pi\)
0.942299 0.334774i \(-0.108660\pi\)
\(332\) 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 0.227460 0.973787i \(-0.426958\pi\)
0.903157 + 0.429311i \(0.141244\pi\)
\(338\) 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 −0.760642 0.649171i \(-0.775116\pi\)
−0.403650 + 0.914913i \(0.632259\pi\)
\(348\) 0 0
\(349\) 1.84031 + 3.82143i 0.0985093 + 0.204557i 0.944399 0.328801i \(-0.106644\pi\)
−0.845890 + 0.533357i \(0.820930\pi\)
\(350\) −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 −0.540102 0.841600i \(-0.681614\pi\)
0.321241 + 0.946997i \(0.395900\pi\)
\(354\) 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 −0.998276 0.0586947i \(-0.981306\pi\)
0.576525 0.817079i \(-0.304408\pi\)
\(360\) 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 −0.403955 + 0.914779i \(0.632365\pi\)
−0.981732 + 0.190269i \(0.939064\pi\)
\(368\) −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 −0.989706 0.143116i \(-0.954288\pi\)
0.359758 + 0.933046i \(0.382859\pi\)
\(380\) 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 0.999900 0.0141595i \(-0.00450726\pi\)
−0.236303 + 0.971679i \(0.575936\pi\)
\(384\) 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 0.504938 + 0.863155i \(0.331515\pi\)
−0.989666 + 0.143392i \(0.954199\pi\)
\(390\) 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 −0.427818 0.903865i \(-0.640718\pi\)
0.973410 0.229069i \(-0.0735680\pi\)
\(398\) −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 −0.279750 0.960073i \(-0.590252\pi\)
0.873752 + 0.486372i \(0.161680\pi\)
\(402\) 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 0.512442 0.858722i \(-0.328741\pi\)
0.0891093 + 0.996022i \(0.471598\pi\)
\(410\) 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 −0.969321 0.245799i \(-0.920950\pi\)
0.766679 0.642030i \(-0.221908\pi\)
\(420\) 0 0
\(421\) 2.49894 10.9486i 0.121791 0.533600i −0.876816 0.480827i \(-0.840337\pi\)
0.998606 0.0527737i \(-0.0168062\pi\)
\(422\) 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 −0.594601 0.804021i \(-0.702690\pi\)
−0.257881 0.966177i \(-0.583024\pi\)
\(432\) 0 0
\(433\) −5.73036 + 11.8992i −0.275383 + 0.571840i −0.992089 0.125536i \(-0.959935\pi\)
0.716706 + 0.697376i \(0.245649\pi\)
\(434\) 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 0.227011 0.973892i \(-0.427105\pi\)
−0.898960 + 0.438031i \(0.855676\pi\)
\(440\) 10.0381 0.478548
\(441\) 0 0
\(442\) 0.00704809 0.000335243
\(443\) 17.2953 + 13.7925i 0.821723 + 0.655302i 0.941318 0.337520i \(-0.109588\pi\)
−0.119595 + 0.992823i \(0.538160\pi\)
\(444\) 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 −0.805953 0.591979i \(-0.798347\pi\)
0.965331 + 0.261027i \(0.0840612\pi\)
\(450\) 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 −0.00636122 0.999980i \(-0.502025\pi\)
0.777850 + 0.628451i \(0.216311\pi\)
\(458\) −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 −0.534622 0.845091i \(-0.679546\pi\)
0.848349 0.529437i \(-0.177597\pi\)
\(462\) 0 0
\(463\) −5.33895 23.3915i −0.248122 1.08709i −0.933407 0.358819i \(-0.883180\pi\)
0.685285 0.728275i \(-0.259678\pi\)
\(464\) −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 0.994806 + 0.101785i \(0.0324552\pi\)
−0.852127 + 0.523335i \(0.824688\pi\)
\(468\) 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 −0.602867 0.797842i \(-0.705975\pi\)
0.911989 + 0.410215i \(0.134546\pi\)
\(480\) 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 0.687853 0.725850i \(-0.258553\pi\)
−0.138623 + 0.990345i \(0.544268\pi\)
\(488\) −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 \(-0.741822\pi\)
0.688708 0.725039i \(-0.258178\pi\)
\(492\) 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 0.837919 0.545795i \(-0.183772\pi\)
−0.718565 + 0.695460i \(0.755201\pi\)
\(500\) −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 −0.308290 0.951292i \(-0.599757\pi\)
0.996042 + 0.0888785i \(0.0283283\pi\)
\(504\) 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 0.998594 0.0530043i \(-0.0168797\pi\)
−0.664054 + 0.747685i \(0.731165\pi\)
\(524\) −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 −0.908785 0.417265i \(-0.862989\pi\)
0.609027 + 0.793150i \(0.291560\pi\)
\(542\) −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 0.112300 0.993674i \(-0.464178\pi\)
−0.706868 + 0.707346i \(0.749893\pi\)
\(548\) −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 \(-0.874714\pi\)
0.923535 0.383514i \(-0.125286\pi\)
\(558\) 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 0.653766 0.756697i \(-0.273188\pi\)
−0.883201 + 0.468994i \(0.844617\pi\)
\(564\) 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 \(-0.996452\pi\)
0.999938 0.0111463i \(-0.00354806\pi\)
\(570\) 0 0
\(571\) −1.82542 + 7.99770i −0.0763916 + 0.334693i −0.998654 0.0518716i \(-0.983481\pi\)
0.922262 + 0.386565i \(0.126338\pi\)
\(572\) −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 0.459062 0.888404i \(-0.348186\pi\)
−0.763979 + 0.645241i \(0.776757\pi\)
\(578\) 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 0.488178 0.872744i \(-0.337662\pi\)
−0.377965 + 0.925820i \(0.623376\pi\)
\(594\) 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 0.739976 0.672633i \(-0.234837\pi\)
−0.491108 + 0.871099i \(0.663408\pi\)
\(600\) 0 0
\(601\) −7.47364 5.96003i −0.304856 0.243115i 0.459097 0.888386i \(-0.348173\pi\)
−0.763953 + 0.645271i \(0.776744\pi\)
\(602\) 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 \(-0.694217\pi\)
0.572990 0.819562i \(-0.305783\pi\)
\(608\) 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 0.875381 + 0.483434i \(0.160611\pi\)
0.276523 + 0.961007i \(0.410818\pi\)
\(614\) 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 0.540448 0.841377i \(-0.318255\pi\)
0.121867 + 0.992546i \(0.461112\pi\)
\(618\) 0 0
\(619\) 27.2418i 1.09494i −0.836825 0.547470i \(-0.815591\pi\)
0.836825 0.547470i \(-0.184409\pi\)
\(620\) 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 −0.856207 0.516633i \(-0.827185\pi\)
−0.129917 + 0.991525i \(0.541471\pi\)
\(632\) 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 0.0746437 0.997210i \(-0.476218\pi\)
0.499925 + 0.866069i \(0.333361\pi\)
\(642\) 0 0
\(643\) 9.62506 + 19.9866i 0.379575 + 0.788196i 0.999992 + 0.00392394i \(0.00124903\pi\)
−0.620417 + 0.784272i \(0.713037\pi\)
\(644\) 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 0.318042 0.948077i \(-0.396975\pi\)
0.939532 + 0.342461i \(0.111260\pi\)
\(648\) 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 0.626214 0.779651i \(-0.284604\pi\)
−0.999994 + 0.00348962i \(0.998889\pi\)
\(654\) 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 −0.641143 0.767421i \(-0.721540\pi\)
−0.244679 + 0.969604i \(0.578683\pi\)
\(660\) 0 0
\(661\) 4.64300 3.70267i 0.180592 0.144017i −0.529022 0.848608i \(-0.677441\pi\)
0.709614 + 0.704591i \(0.248870\pi\)
\(662\) 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 −0.865486 0.500933i \(-0.832990\pi\)
0.680962 + 0.732319i \(0.261562\pi\)
\(674\) 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 −0.951605 0.307323i \(-0.900567\pi\)
−0.0878656 0.996132i \(-0.528005\pi\)
\(678\) 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 −0.999873 0.0159608i \(-0.994919\pi\)
0.635889 + 0.771781i \(0.280634\pi\)
\(684\) 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 0.360307 + 0.932834i \(0.382672\pi\)
−0.953967 + 0.299913i \(0.903042\pi\)
\(692\) −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 −0.749751 0.661720i \(-0.769827\pi\)
0.478294 + 0.878200i \(0.341255\pi\)
\(702\) 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 0.911625 + 0.411024i \(0.134829\pi\)
−0.643009 + 0.765859i \(0.722314\pi\)
\(710\) 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 0.252274 0.967656i \(-0.418821\pi\)
0.913834 + 0.406087i \(0.133107\pi\)
\(720\) 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 −0.758172 0.652054i \(-0.773907\pi\)
0.982509 + 0.186214i \(0.0596217\pi\)
\(728\) −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 0.989883 0.141884i \(-0.0453160\pi\)
0.0819430 + 0.996637i \(0.473887\pi\)
\(734\) −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 −0.976193 0.216902i \(-0.930405\pi\)
0.785410 0.618976i \(-0.212452\pi\)
\(740\) −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 −0.845770 0.533548i \(-0.820859\pi\)
0.944473 + 0.328588i \(0.106573\pi\)
\(744\) 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 −0.311835 0.950136i \(-0.600943\pi\)
0.548421 + 0.836202i \(0.315229\pi\)
\(752\) 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 −0.905890 0.423514i \(-0.860796\pi\)
0.632423 0.774624i \(-0.282061\pi\)
\(758\) −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 0.923547 + 0.383485i \(0.125276\pi\)
−0.665699 + 0.746220i \(0.731867\pi\)
\(762\) 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 −0.0809736 0.996716i \(-0.525803\pi\)
0.953708 + 0.300734i \(0.0972315\pi\)
\(770\) 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 −0.876523 0.481359i \(-0.840143\pi\)
0.664336 + 0.747434i \(0.268715\pi\)
\(774\) 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 −0.922622 0.385707i \(-0.873958\pi\)
0.876803 + 0.480850i \(0.159672\pi\)
\(788\) −6.68032 + 1.52474i −0.237976 + 0.0543166i
\(789\) 0