Properties

Label 3024.2.q.k.2305.3
Level $3024$
Weight $2$
Character 3024.2305
Analytic conductor $24.147$
Analytic rank $0$
Dimension $22$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 3024 = 2^{4} \cdot 3^{3} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3024.q (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(24.1467615712\)
Analytic rank: \(0\)
Dimension: \(22\)
Relative dimension: \(11\) over \(\Q(\zeta_{3})\)
Twist minimal: no (minimal twist has level 504)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 2305.3
Character \(\chi\) \(=\) 3024.2305
Dual form 3024.2.q.k.2881.3

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.26145 - 2.18490i) q^{5} +(-2.63136 - 0.275550i) q^{7} +O(q^{10})\) \(q+(-1.26145 - 2.18490i) q^{5} +(-2.63136 - 0.275550i) q^{7} +(2.85648 - 4.94757i) q^{11} +(-2.45245 + 4.24777i) q^{13} +(-2.49483 - 4.32118i) q^{17} +(0.00383929 - 0.00664984i) q^{19} +(-0.333877 - 0.578292i) q^{23} +(-0.682524 + 1.18217i) q^{25} +(-3.85082 - 6.66981i) q^{29} +7.76605 q^{31} +(2.71729 + 6.09686i) q^{35} +(-3.19562 + 5.53498i) q^{37} +(-5.21159 + 9.02673i) q^{41} +(-4.42935 - 7.67185i) q^{43} +2.16104 q^{47} +(6.84814 + 1.45015i) q^{49} +(3.69858 + 6.40613i) q^{53} -14.4133 q^{55} -0.523594 q^{59} -8.99082 q^{61} +12.3746 q^{65} +5.09582 q^{67} -5.68471 q^{71} +(-1.52062 - 2.63379i) q^{73} +(-8.87975 + 12.2318i) q^{77} -6.16230 q^{79} +(-0.258726 - 0.448126i) q^{83} +(-6.29422 + 10.9019i) q^{85} +(-1.19093 + 2.06274i) q^{89} +(7.62377 - 10.5017i) q^{91} -0.0193723 q^{95} +(4.32994 + 7.49968i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 22q - 3q^{5} + 5q^{7} + O(q^{10}) \) \( 22q - 3q^{5} + 5q^{7} - 3q^{11} - 3q^{13} - 7q^{17} + q^{19} + 2q^{23} - 10q^{25} - 9q^{29} - 8q^{31} + 14q^{35} + 2q^{37} - 16q^{41} - 10q^{47} + 15q^{49} - 11q^{53} - 22q^{55} + 38q^{59} + 26q^{61} + 26q^{65} + 52q^{67} - 48q^{71} - 35q^{73} - 17q^{77} + 20q^{79} - 28q^{83} - 20q^{85} - 6q^{89} + 37q^{91} - 24q^{95} - 29q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/3024\mathbb{Z}\right)^\times\).

\(n\) \(757\) \(785\) \(1135\) \(2593\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{3}\right)\) \(1\) \(e\left(\frac{1}{3}\right)\)

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 0
\(3\) 0 0
\(4\) 0 0
\(5\) −1.26145 2.18490i −0.564139 0.977117i −0.997129 0.0757184i \(-0.975875\pi\)
0.432991 0.901398i \(-0.357458\pi\)
\(6\) 0 0
\(7\) −2.63136 0.275550i −0.994562 0.104148i
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 2.85648 4.94757i 0.861262 1.49175i −0.00944971 0.999955i \(-0.503008\pi\)
0.870712 0.491794i \(-0.163659\pi\)
\(12\) 0 0
\(13\) −2.45245 + 4.24777i −0.680188 + 1.17812i 0.294735 + 0.955579i \(0.404769\pi\)
−0.974923 + 0.222541i \(0.928565\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −2.49483 4.32118i −0.605086 1.04804i −0.992038 0.125939i \(-0.959806\pi\)
0.386952 0.922100i \(-0.373528\pi\)
\(18\) 0 0
\(19\) 0.00383929 0.00664984i 0.000880793 0.00152558i −0.865585 0.500763i \(-0.833053\pi\)
0.866465 + 0.499237i \(0.166386\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −0.333877 0.578292i −0.0696181 0.120582i 0.829115 0.559078i \(-0.188845\pi\)
−0.898733 + 0.438496i \(0.855511\pi\)
\(24\) 0 0
\(25\) −0.682524 + 1.18217i −0.136505 + 0.236433i
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) −3.85082 6.66981i −0.715079 1.23855i −0.962929 0.269754i \(-0.913058\pi\)
0.247851 0.968798i \(-0.420276\pi\)
\(30\) 0 0
\(31\) 7.76605 1.39482 0.697412 0.716671i \(-0.254335\pi\)
0.697412 + 0.716671i \(0.254335\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 2.71729 + 6.09686i 0.459306 + 1.03056i
\(36\) 0 0
\(37\) −3.19562 + 5.53498i −0.525357 + 0.909946i 0.474207 + 0.880414i \(0.342735\pi\)
−0.999564 + 0.0295319i \(0.990598\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −5.21159 + 9.02673i −0.813913 + 1.40974i 0.0961931 + 0.995363i \(0.469333\pi\)
−0.910106 + 0.414376i \(0.864000\pi\)
\(42\) 0 0
\(43\) −4.42935 7.67185i −0.675469 1.16995i −0.976332 0.216279i \(-0.930608\pi\)
0.300863 0.953668i \(-0.402725\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 2.16104 0.315220 0.157610 0.987501i \(-0.449621\pi\)
0.157610 + 0.987501i \(0.449621\pi\)
\(48\) 0 0
\(49\) 6.84814 + 1.45015i 0.978306 + 0.207164i
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 3.69858 + 6.40613i 0.508039 + 0.879950i 0.999957 + 0.00930815i \(0.00296292\pi\)
−0.491917 + 0.870642i \(0.663704\pi\)
\(54\) 0 0
\(55\) −14.4133 −1.94348
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −0.523594 −0.0681661 −0.0340831 0.999419i \(-0.510851\pi\)
−0.0340831 + 0.999419i \(0.510851\pi\)
\(60\) 0 0
\(61\) −8.99082 −1.15116 −0.575578 0.817747i \(-0.695223\pi\)
−0.575578 + 0.817747i \(0.695223\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 12.3746 1.53488
\(66\) 0 0
\(67\) 5.09582 0.622554 0.311277 0.950319i \(-0.399243\pi\)
0.311277 + 0.950319i \(0.399243\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −5.68471 −0.674651 −0.337325 0.941388i \(-0.609522\pi\)
−0.337325 + 0.941388i \(0.609522\pi\)
\(72\) 0 0
\(73\) −1.52062 2.63379i −0.177975 0.308262i 0.763212 0.646148i \(-0.223621\pi\)
−0.941187 + 0.337887i \(0.890288\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −8.87975 + 12.2318i −1.01194 + 1.39394i
\(78\) 0 0
\(79\) −6.16230 −0.693313 −0.346657 0.937992i \(-0.612683\pi\)
−0.346657 + 0.937992i \(0.612683\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) −0.258726 0.448126i −0.0283988 0.0491882i 0.851477 0.524392i \(-0.175708\pi\)
−0.879876 + 0.475204i \(0.842374\pi\)
\(84\) 0 0
\(85\) −6.29422 + 10.9019i −0.682704 + 1.18248i
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −1.19093 + 2.06274i −0.126238 + 0.218650i −0.922216 0.386675i \(-0.873624\pi\)
0.795978 + 0.605325i \(0.206957\pi\)
\(90\) 0 0
\(91\) 7.62377 10.5017i 0.799188 1.10087i
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −0.0193723 −0.00198756
\(96\) 0 0
\(97\) 4.32994 + 7.49968i 0.439639 + 0.761477i 0.997662 0.0683485i \(-0.0217730\pi\)
−0.558022 + 0.829826i \(0.688440\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −4.66783 + 8.08492i −0.464466 + 0.804479i −0.999177 0.0405558i \(-0.987087\pi\)
0.534711 + 0.845035i \(0.320420\pi\)
\(102\) 0 0
\(103\) 8.10926 + 14.0456i 0.799029 + 1.38396i 0.920249 + 0.391333i \(0.127986\pi\)
−0.121220 + 0.992626i \(0.538681\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 4.50171 7.79718i 0.435196 0.753782i −0.562115 0.827059i \(-0.690012\pi\)
0.997312 + 0.0732767i \(0.0233456\pi\)
\(108\) 0 0
\(109\) 3.71563 + 6.43566i 0.355893 + 0.616424i 0.987270 0.159051i \(-0.0508435\pi\)
−0.631378 + 0.775476i \(0.717510\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −7.14642 + 12.3780i −0.672278 + 1.16442i 0.304978 + 0.952359i \(0.401351\pi\)
−0.977256 + 0.212061i \(0.931982\pi\)
\(114\) 0 0
\(115\) −0.842339 + 1.45897i −0.0785486 + 0.136050i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 5.37411 + 12.0580i 0.492644 + 1.10536i
\(120\) 0 0
\(121\) −10.8190 18.7390i −0.983544 1.70355i
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −9.17064 −0.820247
\(126\) 0 0
\(127\) 1.96011 0.173932 0.0869660 0.996211i \(-0.472283\pi\)
0.0869660 + 0.996211i \(0.472283\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 1.99412 + 3.45392i 0.174227 + 0.301771i 0.939894 0.341467i \(-0.110924\pi\)
−0.765666 + 0.643238i \(0.777591\pi\)
\(132\) 0 0
\(133\) −0.0119349 + 0.0164402i −0.00103489 + 0.00142555i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −3.70422 + 6.41589i −0.316473 + 0.548147i −0.979749 0.200227i \(-0.935832\pi\)
0.663277 + 0.748374i \(0.269165\pi\)
\(138\) 0 0
\(139\) −6.92660 + 11.9972i −0.587507 + 1.01759i 0.407051 + 0.913405i \(0.366557\pi\)
−0.994558 + 0.104186i \(0.966776\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 14.0108 + 24.2674i 1.17164 + 2.02934i
\(144\) 0 0
\(145\) −9.71524 + 16.8273i −0.806807 + 1.39743i
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −7.05202 12.2144i −0.577724 1.00065i −0.995740 0.0922071i \(-0.970608\pi\)
0.418016 0.908440i \(-0.362726\pi\)
\(150\) 0 0
\(151\) −5.30027 + 9.18034i −0.431330 + 0.747086i −0.996988 0.0775543i \(-0.975289\pi\)
0.565658 + 0.824640i \(0.308622\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −9.79650 16.9680i −0.786874 1.36291i
\(156\) 0 0
\(157\) −0.259558 −0.0207150 −0.0103575 0.999946i \(-0.503297\pi\)
−0.0103575 + 0.999946i \(0.503297\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 0.719203 + 1.61370i 0.0566811 + 0.127177i
\(162\) 0 0
\(163\) −6.31882 + 10.9445i −0.494928 + 0.857241i −0.999983 0.00584647i \(-0.998139\pi\)
0.505055 + 0.863087i \(0.331472\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −5.74959 + 9.95859i −0.444917 + 0.770619i −0.998046 0.0624765i \(-0.980100\pi\)
0.553129 + 0.833095i \(0.313433\pi\)
\(168\) 0 0
\(169\) −5.52905 9.57659i −0.425311 0.736661i
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 15.8094 1.20197 0.600984 0.799261i \(-0.294775\pi\)
0.600984 + 0.799261i \(0.294775\pi\)
\(174\) 0 0
\(175\) 2.12171 2.92264i 0.160387 0.220931i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −8.49849 14.7198i −0.635207 1.10021i −0.986471 0.163934i \(-0.947582\pi\)
0.351265 0.936276i \(-0.385752\pi\)
\(180\) 0 0
\(181\) 6.35841 0.472617 0.236308 0.971678i \(-0.424062\pi\)
0.236308 + 0.971678i \(0.424062\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 16.1245 1.18550
\(186\) 0 0
\(187\) −28.5058 −2.08455
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −4.14094 −0.299628 −0.149814 0.988714i \(-0.547867\pi\)
−0.149814 + 0.988714i \(0.547867\pi\)
\(192\) 0 0
\(193\) −7.69586 −0.553960 −0.276980 0.960876i \(-0.589334\pi\)
−0.276980 + 0.960876i \(0.589334\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −3.29508 −0.234765 −0.117383 0.993087i \(-0.537450\pi\)
−0.117383 + 0.993087i \(0.537450\pi\)
\(198\) 0 0
\(199\) −8.08840 14.0095i −0.573371 0.993108i −0.996216 0.0869063i \(-0.972302\pi\)
0.422845 0.906202i \(-0.361031\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 8.29503 + 18.6118i 0.582197 + 1.30629i
\(204\) 0 0
\(205\) 26.2967 1.83664
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −0.0219337 0.0379903i −0.00151719 0.00262784i
\(210\) 0 0
\(211\) 13.9633 24.1851i 0.961273 1.66497i 0.241961 0.970286i \(-0.422209\pi\)
0.719312 0.694687i \(-0.244457\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) −11.1748 + 19.3554i −0.762116 + 1.32002i
\(216\) 0 0
\(217\) −20.4353 2.13994i −1.38724 0.145268i
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 24.4738 1.64629
\(222\) 0 0
\(223\) 10.1652 + 17.6066i 0.680711 + 1.17903i 0.974764 + 0.223237i \(0.0716623\pi\)
−0.294054 + 0.955789i \(0.595004\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 2.84470 4.92716i 0.188809 0.327027i −0.756044 0.654520i \(-0.772871\pi\)
0.944853 + 0.327493i \(0.106204\pi\)
\(228\) 0 0
\(229\) −7.42708 12.8641i −0.490795 0.850082i 0.509149 0.860679i \(-0.329960\pi\)
−0.999944 + 0.0105964i \(0.996627\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −6.70652 + 11.6160i −0.439358 + 0.760991i −0.997640 0.0686603i \(-0.978128\pi\)
0.558282 + 0.829652i \(0.311461\pi\)
\(234\) 0 0
\(235\) −2.72605 4.72166i −0.177828 0.308007i
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −9.33123 + 16.1622i −0.603587 + 1.04544i 0.388686 + 0.921370i \(0.372929\pi\)
−0.992273 + 0.124073i \(0.960404\pi\)
\(240\) 0 0
\(241\) 10.7080 18.5468i 0.689762 1.19470i −0.282153 0.959369i \(-0.591049\pi\)
0.971915 0.235333i \(-0.0756181\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) −5.47018 16.7918i −0.349477 1.07279i
\(246\) 0 0
\(247\) 0.0188313 + 0.0326168i 0.00119821 + 0.00207536i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) −0.462898 −0.0292179 −0.0146089 0.999893i \(-0.504650\pi\)
−0.0146089 + 0.999893i \(0.504650\pi\)
\(252\) 0 0
\(253\) −3.81485 −0.239838
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 0.401256 + 0.694996i 0.0250297 + 0.0433527i 0.878269 0.478167i \(-0.158699\pi\)
−0.853239 + 0.521520i \(0.825365\pi\)
\(258\) 0 0
\(259\) 9.93401 13.6840i 0.617270 0.850282i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −0.100693 + 0.174406i −0.00620902 + 0.0107543i −0.869113 0.494613i \(-0.835310\pi\)
0.862904 + 0.505368i \(0.168643\pi\)
\(264\) 0 0
\(265\) 9.33117 16.1621i 0.573209 0.992828i
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 11.1773 + 19.3596i 0.681490 + 1.18038i 0.974526 + 0.224274i \(0.0720011\pi\)
−0.293036 + 0.956101i \(0.594666\pi\)
\(270\) 0 0
\(271\) 1.78925 3.09907i 0.108689 0.188255i −0.806550 0.591166i \(-0.798668\pi\)
0.915240 + 0.402910i \(0.132001\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 3.89924 + 6.75367i 0.235133 + 0.407262i
\(276\) 0 0
\(277\) 5.05336 8.75267i 0.303627 0.525897i −0.673328 0.739344i \(-0.735136\pi\)
0.976955 + 0.213447i \(0.0684690\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −12.7114 22.0167i −0.758296 1.31341i −0.943719 0.330749i \(-0.892699\pi\)
0.185422 0.982659i \(-0.440635\pi\)
\(282\) 0 0
\(283\) −3.87666 −0.230443 −0.115222 0.993340i \(-0.536758\pi\)
−0.115222 + 0.993340i \(0.536758\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 16.2009 22.3166i 0.956308 1.31730i
\(288\) 0 0
\(289\) −3.94838 + 6.83879i −0.232257 + 0.402282i
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −0.428834 + 0.742762i −0.0250527 + 0.0433926i −0.878280 0.478147i \(-0.841309\pi\)
0.853227 + 0.521539i \(0.174642\pi\)
\(294\) 0 0
\(295\) 0.660489 + 1.14400i 0.0384551 + 0.0666063i
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 3.27527 0.189414
\(300\) 0 0
\(301\) 9.54124 + 21.4079i 0.549948 + 1.23393i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 11.3415 + 19.6440i 0.649412 + 1.12481i
\(306\) 0 0
\(307\) 0.717950 0.0409756 0.0204878 0.999790i \(-0.493478\pi\)
0.0204878 + 0.999790i \(0.493478\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −9.45213 −0.535981 −0.267990 0.963422i \(-0.586360\pi\)
−0.267990 + 0.963422i \(0.586360\pi\)
\(312\) 0 0
\(313\) −23.2635 −1.31493 −0.657464 0.753486i \(-0.728371\pi\)
−0.657464 + 0.753486i \(0.728371\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −13.2354 −0.743375 −0.371687 0.928358i \(-0.621221\pi\)
−0.371687 + 0.928358i \(0.621221\pi\)
\(318\) 0 0
\(319\) −43.9992 −2.46348
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) −0.0383135 −0.00213182
\(324\) 0 0
\(325\) −3.34772 5.79841i −0.185698 0.321638i
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) −5.68649 0.595476i −0.313506 0.0328297i
\(330\) 0 0
\(331\) 30.4330 1.67275 0.836375 0.548158i \(-0.184671\pi\)
0.836375 + 0.548158i \(0.184671\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) −6.42813 11.1339i −0.351206 0.608307i
\(336\) 0 0
\(337\) −0.767420 + 1.32921i −0.0418041 + 0.0724067i −0.886170 0.463360i \(-0.846644\pi\)
0.844366 + 0.535766i \(0.179977\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 22.1836 38.4231i 1.20131 2.08073i
\(342\) 0 0
\(343\) −17.6204 5.70287i −0.951410 0.307926i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −28.6072 −1.53571 −0.767856 0.640622i \(-0.778677\pi\)
−0.767856 + 0.640622i \(0.778677\pi\)
\(348\) 0 0
\(349\) −9.05123 15.6772i −0.484501 0.839181i 0.515340 0.856986i \(-0.327666\pi\)
−0.999841 + 0.0178047i \(0.994332\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 7.29541 12.6360i 0.388295 0.672547i −0.603925 0.797041i \(-0.706397\pi\)
0.992220 + 0.124494i \(0.0397307\pi\)
\(354\) 0 0
\(355\) 7.17099 + 12.4205i 0.380596 + 0.659212i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −1.05831 + 1.83304i −0.0558554 + 0.0967443i −0.892601 0.450847i \(-0.851122\pi\)
0.836746 + 0.547592i \(0.184455\pi\)
\(360\) 0 0
\(361\) 9.49997 + 16.4544i 0.499998 + 0.866023i
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) −3.83638 + 6.64480i −0.200805 + 0.347805i
\(366\) 0 0
\(367\) 3.33104 5.76954i 0.173879 0.301167i −0.765894 0.642967i \(-0.777703\pi\)
0.939773 + 0.341800i \(0.111036\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) −7.96710 17.8760i −0.413631 0.928076i
\(372\) 0 0
\(373\) 6.24916 + 10.8239i 0.323569 + 0.560438i 0.981222 0.192883i \(-0.0617838\pi\)
−0.657653 + 0.753321i \(0.728451\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 37.7758 1.94555
\(378\) 0 0
\(379\) 19.5504 1.00423 0.502117 0.864800i \(-0.332555\pi\)
0.502117 + 0.864800i \(0.332555\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 1.33740 + 2.31644i 0.0683379 + 0.118365i 0.898170 0.439649i \(-0.144897\pi\)
−0.829832 + 0.558013i \(0.811564\pi\)
\(384\) 0 0
\(385\) 37.9265 + 3.97158i 1.93292 + 0.202411i
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −1.98155 + 3.43214i −0.100469 + 0.174017i −0.911878 0.410462i \(-0.865368\pi\)
0.811409 + 0.584478i \(0.198701\pi\)
\(390\) 0 0
\(391\) −1.66593 + 2.88548i −0.0842499 + 0.145925i
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 7.77345 + 13.4640i 0.391125 + 0.677448i
\(396\) 0 0
\(397\) 10.2978 17.8362i 0.516829 0.895175i −0.482980 0.875632i \(-0.660446\pi\)
0.999809 0.0195431i \(-0.00622114\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −1.91979 3.32517i −0.0958696 0.166051i 0.814102 0.580722i \(-0.197230\pi\)
−0.909971 + 0.414671i \(0.863897\pi\)
\(402\) 0 0
\(403\) −19.0459 + 32.9884i −0.948742 + 1.64327i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 18.2565 + 31.6212i 0.904940 + 1.56740i
\(408\) 0 0
\(409\) −29.4227 −1.45486 −0.727428 0.686184i \(-0.759285\pi\)
−0.727428 + 0.686184i \(0.759285\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 1.37777 + 0.144276i 0.0677954 + 0.00709938i
\(414\) 0 0
\(415\) −0.652741 + 1.13058i −0.0320418 + 0.0554980i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 4.40821 7.63525i 0.215355 0.373006i −0.738027 0.674771i \(-0.764242\pi\)
0.953382 + 0.301765i \(0.0975757\pi\)
\(420\) 0 0
\(421\) −17.6437 30.5597i −0.859899 1.48939i −0.872024 0.489462i \(-0.837193\pi\)
0.0121255 0.999926i \(-0.496140\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 6.81113 0.330388
\(426\) 0 0
\(427\) 23.6581 + 2.47742i 1.14490 + 0.119891i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −12.8099 22.1873i −0.617030 1.06873i −0.990025 0.140893i \(-0.955003\pi\)
0.372995 0.927833i \(-0.378331\pi\)
\(432\) 0 0
\(433\) 16.8556 0.810030 0.405015 0.914310i \(-0.367266\pi\)
0.405015 + 0.914310i \(0.367266\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −0.00512739 −0.000245277
\(438\) 0 0
\(439\) −30.9192 −1.47569 −0.737846 0.674969i \(-0.764157\pi\)
−0.737846 + 0.674969i \(0.764157\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −9.31087 −0.442373 −0.221186 0.975232i \(-0.570993\pi\)
−0.221186 + 0.975232i \(0.570993\pi\)
\(444\) 0 0
\(445\) 6.00918 0.284862
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −23.8055 −1.12345 −0.561724 0.827324i \(-0.689862\pi\)
−0.561724 + 0.827324i \(0.689862\pi\)
\(450\) 0 0
\(451\) 29.7736 + 51.5694i 1.40198 + 2.42831i
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) −32.5621 3.40983i −1.52653 0.159855i
\(456\) 0 0
\(457\) −13.8110 −0.646053 −0.323027 0.946390i \(-0.604700\pi\)
−0.323027 + 0.946390i \(0.604700\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 0.00256407 + 0.00444110i 0.000119421 + 0.000206843i 0.866085 0.499897i \(-0.166629\pi\)
−0.865966 + 0.500103i \(0.833295\pi\)
\(462\) 0 0
\(463\) −12.9682 + 22.4616i −0.602685 + 1.04388i 0.389728 + 0.920930i \(0.372569\pi\)
−0.992413 + 0.122951i \(0.960764\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −12.0484 + 20.8684i −0.557532 + 0.965673i 0.440170 + 0.897914i \(0.354918\pi\)
−0.997702 + 0.0677588i \(0.978415\pi\)
\(468\) 0 0
\(469\) −13.4090 1.40416i −0.619168 0.0648379i
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −50.6094 −2.32702
\(474\) 0 0
\(475\) 0.00524081 + 0.00907735i 0.000240465 + 0.000416497i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −7.39114 + 12.8018i −0.337710 + 0.584931i −0.984002 0.178160i \(-0.942986\pi\)
0.646292 + 0.763091i \(0.276319\pi\)
\(480\) 0 0
\(481\) −15.6742 27.1486i −0.714683 1.23787i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 10.9240 18.9210i 0.496035 0.859158i
\(486\) 0 0
\(487\) −9.38360 16.2529i −0.425211 0.736488i 0.571229 0.820791i \(-0.306467\pi\)
−0.996440 + 0.0843033i \(0.973134\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 18.2871 31.6741i 0.825284 1.42943i −0.0764182 0.997076i \(-0.524348\pi\)
0.901702 0.432358i \(-0.142318\pi\)
\(492\) 0 0
\(493\) −19.2143 + 33.2801i −0.865368 + 1.49886i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 14.9585 + 1.56642i 0.670982 + 0.0702637i
\(498\) 0 0
\(499\) 2.31591 + 4.01127i 0.103674 + 0.179569i 0.913196 0.407521i \(-0.133607\pi\)
−0.809521 + 0.587090i \(0.800273\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 16.4143 0.731879 0.365940 0.930639i \(-0.380748\pi\)
0.365940 + 0.930639i \(0.380748\pi\)
\(504\) 0 0
\(505\) 23.5530 1.04809
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 5.24169 + 9.07888i 0.232334 + 0.402414i 0.958495 0.285111i \(-0.0920305\pi\)
−0.726161 + 0.687525i \(0.758697\pi\)
\(510\) 0 0
\(511\) 3.27556 + 7.34947i 0.144902 + 0.325121i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 20.4589 35.4358i 0.901526 1.56149i
\(516\) 0 0
\(517\) 6.17298 10.6919i 0.271487 0.470230i
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 11.0087 + 19.0675i 0.482298 + 0.835364i 0.999793 0.0203215i \(-0.00646899\pi\)
−0.517496 + 0.855686i \(0.673136\pi\)
\(522\) 0 0
\(523\) 1.18541 2.05320i 0.0518346 0.0897801i −0.838944 0.544218i \(-0.816826\pi\)
0.890778 + 0.454438i \(0.150160\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −19.3750 33.5585i −0.843988 1.46183i
\(528\) 0 0
\(529\) 11.2771 19.5324i 0.490307 0.849236i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) −25.5623 44.2753i −1.10723 1.91777i
\(534\) 0 0
\(535\) −22.7147 −0.982044
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 26.7363 29.7394i 1.15161 1.28097i
\(540\) 0 0
\(541\) 6.65209 11.5218i 0.285996 0.495359i −0.686854 0.726795i \(-0.741009\pi\)
0.972850 + 0.231436i \(0.0743423\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 9.37418 16.2366i 0.401546 0.695498i
\(546\) 0 0
\(547\) 2.43685 + 4.22074i 0.104192 + 0.180466i 0.913408 0.407046i \(-0.133441\pi\)
−0.809216 + 0.587512i \(0.800108\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −0.0591375 −0.00251934
\(552\) 0 0
\(553\) 16.2153 + 1.69802i 0.689543 + 0.0722074i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −7.09601 12.2907i −0.300668 0.520772i 0.675620 0.737250i \(-0.263876\pi\)
−0.976287 + 0.216479i \(0.930543\pi\)
\(558\) 0 0
\(559\) 43.4511 1.83778
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 7.03971 0.296688 0.148344 0.988936i \(-0.452606\pi\)
0.148344 + 0.988936i \(0.452606\pi\)
\(564\) 0 0
\(565\) 36.0595 1.51703
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 18.3016 0.767244 0.383622 0.923490i \(-0.374677\pi\)
0.383622 + 0.923490i \(0.374677\pi\)
\(570\) 0 0
\(571\) 30.4383 1.27380 0.636902 0.770944i \(-0.280215\pi\)
0.636902 + 0.770944i \(0.280215\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 0.911516 0.0380128
\(576\) 0 0
\(577\) 5.65385 + 9.79275i 0.235373 + 0.407678i 0.959381 0.282114i \(-0.0910356\pi\)
−0.724008 + 0.689791i \(0.757702\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 0.557320 + 1.25047i 0.0231215 + 0.0518784i
\(582\) 0 0
\(583\) 42.2597 1.75022
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −9.89755 17.1431i −0.408516 0.707570i 0.586208 0.810161i \(-0.300620\pi\)
−0.994724 + 0.102591i \(0.967287\pi\)
\(588\) 0 0
\(589\) 0.0298161 0.0516430i 0.00122855 0.00212791i
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −2.69067 + 4.66038i −0.110493 + 0.191379i −0.915969 0.401249i \(-0.868576\pi\)
0.805476 + 0.592628i \(0.201910\pi\)
\(594\) 0 0
\(595\) 19.5664 26.9525i 0.802145 1.10495i
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 2.25959 0.0923243 0.0461622 0.998934i \(-0.485301\pi\)
0.0461622 + 0.998934i \(0.485301\pi\)
\(600\) 0 0
\(601\) 18.1873 + 31.5013i 0.741875 + 1.28496i 0.951641 + 0.307213i \(0.0993964\pi\)
−0.209766 + 0.977752i \(0.567270\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −27.2953 + 47.2768i −1.10971 + 1.92207i
\(606\) 0 0
\(607\) 8.10803 + 14.0435i 0.329095 + 0.570009i 0.982333 0.187144i \(-0.0599231\pi\)
−0.653238 + 0.757153i \(0.726590\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −5.29985 + 9.17961i −0.214409 + 0.371367i
\(612\) 0 0
\(613\) 21.6357 + 37.4741i 0.873857 + 1.51357i 0.857975 + 0.513691i \(0.171722\pi\)
0.0158822 + 0.999874i \(0.494944\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 5.92248 10.2580i 0.238430 0.412973i −0.721834 0.692066i \(-0.756701\pi\)
0.960264 + 0.279093i \(0.0900339\pi\)
\(618\) 0 0
\(619\) 20.1644 34.9257i 0.810475 1.40378i −0.102057 0.994779i \(-0.532542\pi\)
0.912532 0.409006i \(-0.134124\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 3.70215 5.09967i 0.148323 0.204314i
\(624\) 0 0
\(625\) 14.9809 + 25.9478i 0.599238 + 1.03791i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 31.8902 1.27154
\(630\) 0 0
\(631\) −13.9489 −0.555298 −0.277649 0.960683i \(-0.589555\pi\)
−0.277649 + 0.960683i \(0.589555\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −2.47259 4.28265i −0.0981217 0.169952i
\(636\) 0 0
\(637\) −22.9546 + 25.5329i −0.909496 + 1.01165i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 8.76975 15.1896i 0.346384 0.599955i −0.639220 0.769024i \(-0.720743\pi\)
0.985604 + 0.169069i \(0.0540761\pi\)
\(642\) 0 0
\(643\) 13.5329 23.4397i 0.533686 0.924371i −0.465540 0.885027i \(-0.654140\pi\)
0.999226 0.0393443i \(-0.0125269\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 11.3252 + 19.6159i 0.445240 + 0.771179i 0.998069 0.0621160i \(-0.0197849\pi\)
−0.552828 + 0.833295i \(0.686452\pi\)
\(648\) 0 0
\(649\) −1.49564 + 2.59052i −0.0587089 + 0.101687i
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −0.392054 0.679058i −0.0153423 0.0265736i 0.858252 0.513228i \(-0.171550\pi\)
−0.873595 + 0.486654i \(0.838217\pi\)
\(654\) 0 0
\(655\) 5.03098 8.71392i 0.196577 0.340481i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) −16.7219 28.9632i −0.651392 1.12824i −0.982785 0.184752i \(-0.940852\pi\)
0.331393 0.943493i \(-0.392481\pi\)
\(660\) 0 0
\(661\) 3.06516 0.119221 0.0596104 0.998222i \(-0.481014\pi\)
0.0596104 + 0.998222i \(0.481014\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 0.0509756 + 0.00533805i 0.00197675 + 0.000207001i
\(666\) 0 0
\(667\) −2.57140 + 4.45379i −0.0995649 + 0.172451i
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −25.6821 + 44.4827i −0.991447 + 1.71724i
\(672\) 0 0
\(673\) 14.4618 + 25.0487i 0.557463 + 0.965555i 0.997707 + 0.0676766i \(0.0215586\pi\)
−0.440244 + 0.897878i \(0.645108\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 11.7164 0.450296 0.225148 0.974325i \(-0.427713\pi\)
0.225148 + 0.974325i \(0.427713\pi\)
\(678\) 0 0
\(679\) −9.32711 20.9275i −0.357942 0.803124i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 20.7190 + 35.8864i 0.792791 + 1.37315i 0.924232 + 0.381831i \(0.124706\pi\)
−0.131441 + 0.991324i \(0.541960\pi\)
\(684\) 0 0
\(685\) 18.6908 0.714138
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) −36.2824 −1.38225
\(690\) 0 0
\(691\) 6.91350 0.263002 0.131501 0.991316i \(-0.458020\pi\)
0.131501 + 0.991316i \(0.458020\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 34.9503 1.32574
\(696\) 0 0
\(697\) 52.0081 1.96995
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) −39.1954 −1.48039 −0.740195 0.672392i \(-0.765267\pi\)
−0.740195 + 0.672392i \(0.765267\pi\)
\(702\) 0 0
\(703\) 0.0245378 + 0.0425008i 0.000925462 + 0.00160295i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 14.5106 19.9881i 0.545726 0.751731i
\(708\) 0 0
\(709\) 20.4871 0.769409 0.384705 0.923040i \(-0.374303\pi\)
0.384705 + 0.923040i \(0.374303\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −2.59290 4.49104i −0.0971050 0.168191i
\(714\) 0 0
\(715\) 35.3479 61.2243i 1.32193 2.28966i
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 17.1300 29.6700i 0.638840 1.10650i −0.346848 0.937921i \(-0.612748\pi\)
0.985688 0.168582i \(-0.0539187\pi\)
\(720\) 0 0
\(721\) −17.4681 39.1937i −0.650547 1.45965i
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 10.5131 0.390447
\(726\) 0 0
\(727\) −7.18914 12.4520i −0.266631 0.461818i 0.701359 0.712808i \(-0.252577\pi\)
−0.967990 + 0.250991i \(0.919244\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −22.1010 + 38.2800i −0.817433 + 1.41584i
\(732\) 0 0
\(733\) −19.7887 34.2750i −0.730911 1.26597i −0.956494 0.291751i \(-0.905762\pi\)
0.225584 0.974224i \(-0.427571\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 14.5561 25.2119i 0.536182 0.928694i
\(738\) 0 0
\(739\) −10.8407 18.7767i −0.398783 0.690712i 0.594793 0.803879i \(-0.297234\pi\)
−0.993576 + 0.113167i \(0.963901\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 16.5692 28.6987i 0.607864 1.05285i −0.383727 0.923446i \(-0.625360\pi\)
0.991592 0.129406i \(-0.0413069\pi\)
\(744\) 0 0
\(745\) −17.7916 + 30.8159i −0.651832 + 1.12901i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −13.9941 + 19.2768i −0.511335 + 0.704358i
\(750\) 0 0
\(751\) −12.9662 22.4581i −0.473144 0.819509i 0.526384 0.850247i \(-0.323548\pi\)
−0.999527 + 0.0307381i \(0.990214\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 26.7442 0.973320
\(756\) 0 0
\(757\) −30.5846 −1.11162 −0.555808 0.831311i \(-0.687591\pi\)
−0.555808 + 0.831311i \(0.687591\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −18.2648 31.6355i −0.662097 1.14679i −0.980064 0.198684i \(-0.936333\pi\)
0.317967 0.948102i \(-0.397000\pi\)
\(762\) 0 0
\(763\) −8.00382 17.9584i −0.289758 0.650138i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 1.28409 2.22411i 0.0463658 0.0803079i
\(768\) 0 0
\(769\) −21.3107 + 36.9113i −0.768485 + 1.33105i 0.169900 + 0.985461i \(0.445656\pi\)
−0.938384 + 0.345593i \(0.887678\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −16.1309 27.9395i −0.580187 1.00491i −0.995457 0.0952148i \(-0.969646\pi\)
0.415270 0.909698i \(-0.363687\pi\)
\(774\) 0 0
\(775\) −5.30051 + 9.18076i −0.190400 + 0.329783i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 0.0400175 + 0.0693124i 0.00143378 + 0.00248337i
\(780\) 0 0
\(781\) −16.2383 + 28.1255i −0.581051 + 1.00641i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 0.327420 + 0.567107i 0.0116861 + 0.0202409i
\(786\) 0 0
\(787\) −30.7676 −1.09675 −0.548373 0.836234i \(-0.684753\pi\)
−0.548373 + 0.836234i \(0.684753\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 22.2156 30.6017i 0.789895 1.08807i
\(792\) 0 0
\(793\) 22.0496 38.1910i 0.783003 1.35620i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 3.59378 6.22460i 0.127298 0.220487i −0.795331 0.606176i \(-0.792703\pi\)
0.922629 + 0.385689i \(0.126036\pi\)