Properties

Label 3024.2.q.l.2305.5
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 2305.5
Character \(\chi\) \(=\) 3024.2305
Dual form 3024.2.q.l.2881.5

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.234085 - 0.405446i) q^{5} +(-0.212345 + 2.63722i) q^{7} +O(q^{10})\) \(q+(-0.234085 - 0.405446i) q^{5} +(-0.212345 + 2.63722i) q^{7} +(0.674293 - 1.16791i) q^{11} +(-3.16486 + 5.48171i) q^{13} +(2.47120 + 4.28024i) q^{17} +(-2.38910 + 4.13804i) q^{19} +(-3.81399 - 6.60603i) q^{23} +(2.39041 - 4.14031i) q^{25} +(1.80565 + 3.12747i) q^{29} -6.49878 q^{31} +(1.11896 - 0.531237i) q^{35} +(5.24214 - 9.07966i) q^{37} +(0.0251630 - 0.0435837i) q^{41} +(0.431869 + 0.748019i) q^{43} -10.9883 q^{47} +(-6.90982 - 1.12000i) q^{49} +(-5.84976 - 10.1321i) q^{53} -0.631366 q^{55} -3.87784 q^{59} +3.74462 q^{61} +2.96338 q^{65} +2.64871 q^{67} -7.04562 q^{71} +(-3.30117 - 5.71779i) q^{73} +(2.93685 + 2.02626i) q^{77} -3.17902 q^{79} +(4.90272 + 8.49176i) q^{83} +(1.15694 - 2.00388i) q^{85} +(-5.30709 + 9.19214i) q^{89} +(-13.7844 - 9.51045i) q^{91} +2.23701 q^{95} +(6.97792 + 12.0861i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 22q - q^{5} - 5q^{7} + O(q^{10}) \) \( 22q - q^{5} - 5q^{7} + 3q^{11} + 7q^{13} + q^{17} - 13q^{19} - 22q^{25} + 7q^{29} + 12q^{31} + 2q^{35} + 6q^{37} - 4q^{41} - 2q^{43} - 34q^{47} - 25q^{49} - q^{53} - 2q^{55} + 42q^{59} - 62q^{61} - 6q^{65} - 52q^{67} - 32q^{71} + 17q^{73} + q^{77} - 32q^{79} - 36q^{83} + 28q^{85} + 2q^{89} - 15q^{91} + 48q^{95} + 19q^{97} + O(q^{100}) \)

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
\(5\) −0.234085 0.405446i −0.104686 0.181321i 0.808924 0.587913i \(-0.200050\pi\)
−0.913610 + 0.406592i \(0.866717\pi\)
\(6\) 0 0
\(7\) −0.212345 + 2.63722i −0.0802590 + 0.996774i
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 0.674293 1.16791i 0.203307 0.352138i −0.746285 0.665626i \(-0.768164\pi\)
0.949592 + 0.313489i \(0.101498\pi\)
\(12\) 0 0
\(13\) −3.16486 + 5.48171i −0.877775 + 1.52035i −0.0239988 + 0.999712i \(0.507640\pi\)
−0.853777 + 0.520640i \(0.825694\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 2.47120 + 4.28024i 0.599353 + 1.03811i 0.992917 + 0.118813i \(0.0379089\pi\)
−0.393563 + 0.919298i \(0.628758\pi\)
\(18\) 0 0
\(19\) −2.38910 + 4.13804i −0.548097 + 0.949332i 0.450308 + 0.892873i \(0.351314\pi\)
−0.998405 + 0.0564585i \(0.982019\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −3.81399 6.60603i −0.795273 1.37745i −0.922666 0.385600i \(-0.873994\pi\)
0.127393 0.991852i \(-0.459339\pi\)
\(24\) 0 0
\(25\) 2.39041 4.14031i 0.478082 0.828062i
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 1.80565 + 3.12747i 0.335300 + 0.580757i 0.983542 0.180677i \(-0.0578290\pi\)
−0.648242 + 0.761434i \(0.724496\pi\)
\(30\) 0 0
\(31\) −6.49878 −1.16721 −0.583607 0.812036i \(-0.698359\pi\)
−0.583607 + 0.812036i \(0.698359\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 1.11896 0.531237i 0.189138 0.0897954i
\(36\) 0 0
\(37\) 5.24214 9.07966i 0.861803 1.49269i −0.00838383 0.999965i \(-0.502669\pi\)
0.870187 0.492722i \(-0.163998\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 0.0251630 0.0435837i 0.00392981 0.00680662i −0.864054 0.503399i \(-0.832082\pi\)
0.867984 + 0.496593i \(0.165416\pi\)
\(42\) 0 0
\(43\) 0.431869 + 0.748019i 0.0658594 + 0.114072i 0.897075 0.441879i \(-0.145688\pi\)
−0.831215 + 0.555950i \(0.812354\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −10.9883 −1.60282 −0.801408 0.598118i \(-0.795915\pi\)
−0.801408 + 0.598118i \(0.795915\pi\)
\(48\) 0 0
\(49\) −6.90982 1.12000i −0.987117 0.160000i
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −5.84976 10.1321i −0.803526 1.39175i −0.917282 0.398239i \(-0.869622\pi\)
0.113756 0.993509i \(-0.463712\pi\)
\(54\) 0 0
\(55\) −0.631366 −0.0851334
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −3.87784 −0.504852 −0.252426 0.967616i \(-0.581228\pi\)
−0.252426 + 0.967616i \(0.581228\pi\)
\(60\) 0 0
\(61\) 3.74462 0.479450 0.239725 0.970841i \(-0.422943\pi\)
0.239725 + 0.970841i \(0.422943\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 2.96338 0.367562
\(66\) 0 0
\(67\) 2.64871 0.323592 0.161796 0.986824i \(-0.448271\pi\)
0.161796 + 0.986824i \(0.448271\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −7.04562 −0.836161 −0.418081 0.908410i \(-0.637297\pi\)
−0.418081 + 0.908410i \(0.637297\pi\)
\(72\) 0 0
\(73\) −3.30117 5.71779i −0.386373 0.669217i 0.605586 0.795780i \(-0.292939\pi\)
−0.991959 + 0.126563i \(0.959605\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 2.93685 + 2.02626i 0.334685 + 0.230913i
\(78\) 0 0
\(79\) −3.17902 −0.357667 −0.178834 0.983879i \(-0.557232\pi\)
−0.178834 + 0.983879i \(0.557232\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 4.90272 + 8.49176i 0.538143 + 0.932092i 0.999004 + 0.0446192i \(0.0142074\pi\)
−0.460861 + 0.887472i \(0.652459\pi\)
\(84\) 0 0
\(85\) 1.15694 2.00388i 0.125488 0.217351i
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −5.30709 + 9.19214i −0.562550 + 0.974365i 0.434723 + 0.900564i \(0.356846\pi\)
−0.997273 + 0.0738011i \(0.976487\pi\)
\(90\) 0 0
\(91\) −13.7844 9.51045i −1.44500 0.996966i
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 2.23701 0.229512
\(96\) 0 0
\(97\) 6.97792 + 12.0861i 0.708500 + 1.22716i 0.965413 + 0.260724i \(0.0839611\pi\)
−0.256913 + 0.966434i \(0.582706\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 2.12472 3.68013i 0.211418 0.366187i −0.740741 0.671791i \(-0.765525\pi\)
0.952159 + 0.305604i \(0.0988585\pi\)
\(102\) 0 0
\(103\) −4.47820 7.75647i −0.441250 0.764268i 0.556532 0.830826i \(-0.312132\pi\)
−0.997783 + 0.0665580i \(0.978798\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −0.810731 + 1.40423i −0.0783763 + 0.135752i −0.902550 0.430586i \(-0.858307\pi\)
0.824173 + 0.566338i \(0.191640\pi\)
\(108\) 0 0
\(109\) 2.97644 + 5.15534i 0.285091 + 0.493792i 0.972631 0.232354i \(-0.0746428\pi\)
−0.687540 + 0.726146i \(0.741309\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −4.14346 + 7.17669i −0.389784 + 0.675126i −0.992420 0.122890i \(-0.960784\pi\)
0.602636 + 0.798016i \(0.294117\pi\)
\(114\) 0 0
\(115\) −1.78559 + 3.09274i −0.166508 + 0.288399i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −11.8127 + 5.60819i −1.08287 + 0.514102i
\(120\) 0 0
\(121\) 4.59066 + 7.95125i 0.417333 + 0.722841i
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −4.57908 −0.409565
\(126\) 0 0
\(127\) −8.12368 −0.720860 −0.360430 0.932786i \(-0.617370\pi\)
−0.360430 + 0.932786i \(0.617370\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −9.74823 16.8844i −0.851707 1.47520i −0.879667 0.475591i \(-0.842234\pi\)
0.0279597 0.999609i \(-0.491099\pi\)
\(132\) 0 0
\(133\) −10.4056 7.17927i −0.902280 0.622521i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −7.55175 + 13.0800i −0.645189 + 1.11750i 0.339069 + 0.940762i \(0.389888\pi\)
−0.984258 + 0.176739i \(0.943445\pi\)
\(138\) 0 0
\(139\) 2.18826 3.79017i 0.185605 0.321478i −0.758175 0.652051i \(-0.773909\pi\)
0.943780 + 0.330573i \(0.107242\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 4.26809 + 7.39255i 0.356916 + 0.618196i
\(144\) 0 0
\(145\) 0.845348 1.46419i 0.0702023 0.121594i
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −5.87820 10.1813i −0.481561 0.834087i 0.518215 0.855250i \(-0.326597\pi\)
−0.999776 + 0.0211627i \(0.993263\pi\)
\(150\) 0 0
\(151\) −2.57153 + 4.45401i −0.209268 + 0.362462i −0.951484 0.307698i \(-0.900441\pi\)
0.742216 + 0.670160i \(0.233775\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 1.52126 + 2.63490i 0.122191 + 0.211641i
\(156\) 0 0
\(157\) −12.0889 −0.964803 −0.482401 0.875950i \(-0.660235\pi\)
−0.482401 + 0.875950i \(0.660235\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 18.2314 8.65557i 1.43684 0.682154i
\(162\) 0 0
\(163\) 2.74663 4.75730i 0.215133 0.372621i −0.738181 0.674603i \(-0.764315\pi\)
0.953314 + 0.301982i \(0.0976482\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −3.59378 + 6.22461i −0.278095 + 0.481675i −0.970911 0.239440i \(-0.923036\pi\)
0.692816 + 0.721114i \(0.256370\pi\)
\(168\) 0 0
\(169\) −13.5327 23.4394i −1.04098 1.80303i
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 7.95902 0.605113 0.302557 0.953131i \(-0.402160\pi\)
0.302557 + 0.953131i \(0.402160\pi\)
\(174\) 0 0
\(175\) 10.4113 + 7.18320i 0.787020 + 0.542999i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 0.168821 + 0.292406i 0.0126182 + 0.0218554i 0.872266 0.489032i \(-0.162650\pi\)
−0.859647 + 0.510888i \(0.829317\pi\)
\(180\) 0 0
\(181\) 7.05801 0.524618 0.262309 0.964984i \(-0.415516\pi\)
0.262309 + 0.964984i \(0.415516\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −4.90842 −0.360874
\(186\) 0 0
\(187\) 6.66524 0.487411
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 17.7187 1.28208 0.641039 0.767508i \(-0.278504\pi\)
0.641039 + 0.767508i \(0.278504\pi\)
\(192\) 0 0
\(193\) −16.8024 −1.20946 −0.604732 0.796429i \(-0.706720\pi\)
−0.604732 + 0.796429i \(0.706720\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −5.97545 −0.425733 −0.212867 0.977081i \(-0.568280\pi\)
−0.212867 + 0.977081i \(0.568280\pi\)
\(198\) 0 0
\(199\) −6.26093 10.8443i −0.443826 0.768729i 0.554144 0.832421i \(-0.313046\pi\)
−0.997970 + 0.0636923i \(0.979712\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −8.63124 + 4.09778i −0.605794 + 0.287607i
\(204\) 0 0
\(205\) −0.0235611 −0.00164558
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 3.22190 + 5.58050i 0.222864 + 0.386011i
\(210\) 0 0
\(211\) −1.17688 + 2.03842i −0.0810198 + 0.140330i −0.903688 0.428191i \(-0.859151\pi\)
0.822668 + 0.568521i \(0.192484\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 0.202188 0.350199i 0.0137891 0.0238834i
\(216\) 0 0
\(217\) 1.37999 17.1387i 0.0936795 1.16345i
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −31.2840 −2.10439
\(222\) 0 0
\(223\) −5.30709 9.19215i −0.355389 0.615552i 0.631795 0.775135i \(-0.282318\pi\)
−0.987184 + 0.159583i \(0.948985\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −0.637749 + 1.10461i −0.0423289 + 0.0733158i −0.886414 0.462894i \(-0.846811\pi\)
0.844085 + 0.536210i \(0.180144\pi\)
\(228\) 0 0
\(229\) 6.73313 + 11.6621i 0.444938 + 0.770655i 0.998048 0.0624532i \(-0.0198924\pi\)
−0.553110 + 0.833108i \(0.686559\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −9.98509 + 17.2947i −0.654145 + 1.13301i 0.327963 + 0.944691i \(0.393638\pi\)
−0.982107 + 0.188321i \(0.939695\pi\)
\(234\) 0 0
\(235\) 2.57220 + 4.45519i 0.167792 + 0.290624i
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −14.1092 + 24.4379i −0.912650 + 1.58076i −0.102345 + 0.994749i \(0.532635\pi\)
−0.810305 + 0.586008i \(0.800699\pi\)
\(240\) 0 0
\(241\) 8.67622 15.0277i 0.558884 0.968016i −0.438706 0.898631i \(-0.644563\pi\)
0.997590 0.0693852i \(-0.0221038\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 1.16338 + 3.06374i 0.0743257 + 0.195735i
\(246\) 0 0
\(247\) −15.1223 26.1927i −0.962212 1.66660i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 6.29051 0.397054 0.198527 0.980095i \(-0.436384\pi\)
0.198527 + 0.980095i \(0.436384\pi\)
\(252\) 0 0
\(253\) −10.2870 −0.646738
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −3.06819 5.31426i −0.191388 0.331494i 0.754322 0.656504i \(-0.227966\pi\)
−0.945711 + 0.325010i \(0.894632\pi\)
\(258\) 0 0
\(259\) 22.8319 + 15.7527i 1.41870 + 0.978825i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −2.93957 + 5.09148i −0.181262 + 0.313954i −0.942310 0.334740i \(-0.891351\pi\)
0.761049 + 0.648695i \(0.224685\pi\)
\(264\) 0 0
\(265\) −2.73868 + 4.74352i −0.168235 + 0.291392i
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 15.4633 + 26.7832i 0.942812 + 1.63300i 0.760074 + 0.649837i \(0.225163\pi\)
0.182738 + 0.983162i \(0.441504\pi\)
\(270\) 0 0
\(271\) −5.44528 + 9.43150i −0.330777 + 0.572923i −0.982664 0.185393i \(-0.940644\pi\)
0.651887 + 0.758316i \(0.273978\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −3.22367 5.58356i −0.194395 0.336701i
\(276\) 0 0
\(277\) −9.79498 + 16.9654i −0.588524 + 1.01935i 0.405903 + 0.913916i \(0.366957\pi\)
−0.994426 + 0.105436i \(0.966376\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 0.142477 + 0.246777i 0.00849944 + 0.0147215i 0.870244 0.492621i \(-0.163961\pi\)
−0.861744 + 0.507343i \(0.830628\pi\)
\(282\) 0 0
\(283\) −2.84269 −0.168981 −0.0844903 0.996424i \(-0.526926\pi\)
−0.0844903 + 0.996424i \(0.526926\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 0.109596 + 0.0756152i 0.00646926 + 0.00446342i
\(288\) 0 0
\(289\) −3.71364 + 6.43221i −0.218449 + 0.378365i
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 1.45979 2.52842i 0.0852816 0.147712i −0.820230 0.572034i \(-0.806154\pi\)
0.905511 + 0.424322i \(0.139488\pi\)
\(294\) 0 0
\(295\) 0.907743 + 1.57226i 0.0528509 + 0.0915404i
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 48.2831 2.79228
\(300\) 0 0
\(301\) −2.06439 + 0.980094i −0.118990 + 0.0564917i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −0.876558 1.51824i −0.0501916 0.0869344i
\(306\) 0 0
\(307\) 4.12553 0.235457 0.117728 0.993046i \(-0.462439\pi\)
0.117728 + 0.993046i \(0.462439\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 15.3917 0.872781 0.436390 0.899757i \(-0.356257\pi\)
0.436390 + 0.899757i \(0.356257\pi\)
\(312\) 0 0
\(313\) −20.7240 −1.17139 −0.585694 0.810533i \(-0.699178\pi\)
−0.585694 + 0.810533i \(0.699178\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 0.488292 0.0274252 0.0137126 0.999906i \(-0.495635\pi\)
0.0137126 + 0.999906i \(0.495635\pi\)
\(318\) 0 0
\(319\) 4.87014 0.272675
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) −23.6157 −1.31402
\(324\) 0 0
\(325\) 15.1306 + 26.2070i 0.839297 + 1.45370i
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 2.33333 28.9787i 0.128640 1.59764i
\(330\) 0 0
\(331\) 18.9573 1.04199 0.520993 0.853561i \(-0.325562\pi\)
0.520993 + 0.853561i \(0.325562\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) −0.620023 1.07391i −0.0338755 0.0586740i
\(336\) 0 0
\(337\) 11.6202 20.1268i 0.632993 1.09638i −0.353944 0.935267i \(-0.615160\pi\)
0.986937 0.161109i \(-0.0515071\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −4.38208 + 7.58998i −0.237303 + 0.411020i
\(342\) 0 0
\(343\) 4.42096 17.9849i 0.238709 0.971091i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 18.1888 0.976425 0.488212 0.872725i \(-0.337649\pi\)
0.488212 + 0.872725i \(0.337649\pi\)
\(348\) 0 0
\(349\) −9.40155 16.2840i −0.503253 0.871661i −0.999993 0.00376081i \(-0.998803\pi\)
0.496740 0.867900i \(-0.334530\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −5.95997 + 10.3230i −0.317217 + 0.549436i −0.979906 0.199458i \(-0.936082\pi\)
0.662689 + 0.748895i \(0.269415\pi\)
\(354\) 0 0
\(355\) 1.64927 + 2.85662i 0.0875342 + 0.151614i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −17.3849 + 30.1115i −0.917540 + 1.58923i −0.114400 + 0.993435i \(0.536495\pi\)
−0.803140 + 0.595791i \(0.796839\pi\)
\(360\) 0 0
\(361\) −1.91559 3.31790i −0.100821 0.174626i
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) −1.54551 + 2.67689i −0.0808954 + 0.140115i
\(366\) 0 0
\(367\) −14.4431 + 25.0161i −0.753922 + 1.30583i 0.191987 + 0.981398i \(0.438507\pi\)
−0.945909 + 0.324433i \(0.894826\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 27.9626 13.2756i 1.45175 0.689233i
\(372\) 0 0
\(373\) −7.15472 12.3923i −0.370457 0.641651i 0.619179 0.785250i \(-0.287466\pi\)
−0.989636 + 0.143599i \(0.954132\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −22.8585 −1.17727
\(378\) 0 0
\(379\) −1.15511 −0.0593340 −0.0296670 0.999560i \(-0.509445\pi\)
−0.0296670 + 0.999560i \(0.509445\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −16.9131 29.2944i −0.864219 1.49687i −0.867820 0.496878i \(-0.834479\pi\)
0.00360069 0.999994i \(-0.498854\pi\)
\(384\) 0 0
\(385\) 0.134068 1.66505i 0.00683272 0.0848587i
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 9.66080 16.7330i 0.489822 0.848397i −0.510109 0.860110i \(-0.670395\pi\)
0.999931 + 0.0117128i \(0.00372838\pi\)
\(390\) 0 0
\(391\) 18.8503 32.6496i 0.953299 1.65116i
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 0.744159 + 1.28892i 0.0374427 + 0.0648526i
\(396\) 0 0
\(397\) −6.18190 + 10.7074i −0.310261 + 0.537387i −0.978419 0.206632i \(-0.933750\pi\)
0.668158 + 0.744019i \(0.267083\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −15.2568 26.4256i −0.761889 1.31963i −0.941876 0.335961i \(-0.890939\pi\)
0.179987 0.983669i \(-0.442394\pi\)
\(402\) 0 0
\(403\) 20.5677 35.6244i 1.02455 1.77458i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −7.06948 12.2447i −0.350421 0.606947i
\(408\) 0 0
\(409\) −5.25446 −0.259816 −0.129908 0.991526i \(-0.541468\pi\)
−0.129908 + 0.991526i \(0.541468\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 0.823443 10.2267i 0.0405190 0.503224i
\(414\) 0 0
\(415\) 2.29530 3.97558i 0.112672 0.195154i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 15.2824 26.4699i 0.746594 1.29314i −0.202852 0.979209i \(-0.565021\pi\)
0.949446 0.313930i \(-0.101646\pi\)
\(420\) 0 0
\(421\) 3.11608 + 5.39721i 0.151869 + 0.263044i 0.931914 0.362678i \(-0.118138\pi\)
−0.780046 + 0.625722i \(0.784804\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 23.6287 1.14616
\(426\) 0 0
\(427\) −0.795154 + 9.87538i −0.0384802 + 0.477903i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 14.8142 + 25.6590i 0.713576 + 1.23595i 0.963506 + 0.267686i \(0.0862590\pi\)
−0.249930 + 0.968264i \(0.580408\pi\)
\(432\) 0 0
\(433\) 7.36815 0.354091 0.177045 0.984203i \(-0.443346\pi\)
0.177045 + 0.984203i \(0.443346\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 36.4480 1.74355
\(438\) 0 0
\(439\) −10.4427 −0.498403 −0.249201 0.968452i \(-0.580168\pi\)
−0.249201 + 0.968452i \(0.580168\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 5.66664 0.269230 0.134615 0.990898i \(-0.457020\pi\)
0.134615 + 0.990898i \(0.457020\pi\)
\(444\) 0 0
\(445\) 4.96923 0.235564
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −11.4794 −0.541748 −0.270874 0.962615i \(-0.587313\pi\)
−0.270874 + 0.962615i \(0.587313\pi\)
\(450\) 0 0
\(451\) −0.0339345 0.0587763i −0.00159791 0.00276767i
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) −0.629261 + 7.81508i −0.0295002 + 0.366377i
\(456\) 0 0
\(457\) 19.5872 0.916251 0.458126 0.888887i \(-0.348521\pi\)
0.458126 + 0.888887i \(0.348521\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −17.3028 29.9693i −0.805871 1.39581i −0.915701 0.401859i \(-0.868364\pi\)
0.109830 0.993950i \(-0.464969\pi\)
\(462\) 0 0
\(463\) −6.91882 + 11.9837i −0.321545 + 0.556932i −0.980807 0.194981i \(-0.937535\pi\)
0.659262 + 0.751913i \(0.270869\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 3.71088 6.42743i 0.171719 0.297426i −0.767302 0.641286i \(-0.778401\pi\)
0.939021 + 0.343860i \(0.111735\pi\)
\(468\) 0 0
\(469\) −0.562442 + 6.98523i −0.0259712 + 0.322548i
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 1.16482 0.0535587
\(474\) 0 0
\(475\) 11.4218 + 19.7832i 0.524070 + 0.907716i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 3.89577 6.74767i 0.178002 0.308309i −0.763194 0.646170i \(-0.776370\pi\)
0.941196 + 0.337860i \(0.109703\pi\)
\(480\) 0 0
\(481\) 33.1813 + 57.4718i 1.51294 + 2.62049i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 3.26684 5.65834i 0.148340 0.256932i
\(486\) 0 0
\(487\) 1.04434 + 1.80886i 0.0473238 + 0.0819672i 0.888717 0.458456i \(-0.151597\pi\)
−0.841393 + 0.540423i \(0.818264\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −16.8767 + 29.2312i −0.761633 + 1.31919i 0.180375 + 0.983598i \(0.442269\pi\)
−0.942008 + 0.335590i \(0.891064\pi\)
\(492\) 0 0
\(493\) −8.92422 + 15.4572i −0.401927 + 0.696157i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 1.49611 18.5808i 0.0671095 0.833464i
\(498\) 0 0
\(499\) 20.9098 + 36.2169i 0.936052 + 1.62129i 0.772747 + 0.634714i \(0.218882\pi\)
0.163304 + 0.986576i \(0.447785\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 6.54978 0.292040 0.146020 0.989282i \(-0.453354\pi\)
0.146020 + 0.989282i \(0.453354\pi\)
\(504\) 0 0
\(505\) −1.98946 −0.0885299
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −6.30653 10.9232i −0.279532 0.484164i 0.691736 0.722150i \(-0.256846\pi\)
−0.971269 + 0.237986i \(0.923513\pi\)
\(510\) 0 0
\(511\) 15.7800 7.49175i 0.698068 0.331415i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −2.09656 + 3.63134i −0.0923853 + 0.160016i
\(516\) 0 0
\(517\) −7.40936 + 12.8334i −0.325863 + 0.564412i
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −10.2688 17.7861i −0.449883 0.779221i 0.548495 0.836154i \(-0.315201\pi\)
−0.998378 + 0.0569331i \(0.981868\pi\)
\(522\) 0 0
\(523\) −14.4579 + 25.0419i −0.632202 + 1.09501i 0.354899 + 0.934905i \(0.384515\pi\)
−0.987101 + 0.160101i \(0.948818\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −16.0598 27.8163i −0.699574 1.21170i
\(528\) 0 0
\(529\) −17.5931 + 30.4721i −0.764917 + 1.32488i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 0.159275 + 0.275873i 0.00689897 + 0.0119494i
\(534\) 0 0
\(535\) 0.759119 0.0328196
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −5.96730 + 7.31483i −0.257030 + 0.315072i
\(540\) 0 0
\(541\) 3.29262 5.70299i 0.141561 0.245191i −0.786524 0.617560i \(-0.788121\pi\)
0.928085 + 0.372369i \(0.121455\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 1.39348 2.41357i 0.0596900 0.103386i
\(546\) 0 0
\(547\) −4.46777 7.73840i −0.191028 0.330870i 0.754563 0.656227i \(-0.227849\pi\)
−0.945591 + 0.325357i \(0.894515\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −17.2555 −0.735108
\(552\) 0 0
\(553\) 0.675050 8.38376i 0.0287060 0.356514i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 2.93523 + 5.08396i 0.124370 + 0.215414i 0.921486 0.388411i \(-0.126976\pi\)
−0.797117 + 0.603825i \(0.793642\pi\)
\(558\) 0 0
\(559\) −5.46723 −0.231239
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 27.5972 1.16308 0.581541 0.813517i \(-0.302450\pi\)
0.581541 + 0.813517i \(0.302450\pi\)
\(564\) 0 0
\(565\) 3.87968 0.163220
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 27.9202 1.17048 0.585238 0.810862i \(-0.301001\pi\)
0.585238 + 0.810862i \(0.301001\pi\)
\(570\) 0 0
\(571\) 31.7974 1.33068 0.665339 0.746541i \(-0.268287\pi\)
0.665339 + 0.746541i \(0.268287\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −36.4680 −1.52082
\(576\) 0 0
\(577\) 13.7476 + 23.8115i 0.572320 + 0.991287i 0.996327 + 0.0856281i \(0.0272897\pi\)
−0.424007 + 0.905659i \(0.639377\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) −23.4357 + 11.1263i −0.972276 + 0.461599i
\(582\) 0 0
\(583\) −15.7778 −0.653449
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −7.12422 12.3395i −0.294048 0.509306i 0.680715 0.732548i \(-0.261669\pi\)
−0.974763 + 0.223242i \(0.928336\pi\)
\(588\) 0 0
\(589\) 15.5262 26.8922i 0.639747 1.10807i
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −15.4636 + 26.7838i −0.635015 + 1.09988i 0.351498 + 0.936189i \(0.385673\pi\)
−0.986512 + 0.163689i \(0.947661\pi\)
\(594\) 0 0
\(595\) 5.03898 + 3.47661i 0.206578 + 0.142527i
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 36.5315 1.49264 0.746318 0.665589i \(-0.231820\pi\)
0.746318 + 0.665589i \(0.231820\pi\)
\(600\) 0 0
\(601\) 7.11575 + 12.3248i 0.290257 + 0.502741i 0.973871 0.227104i \(-0.0729257\pi\)
−0.683613 + 0.729845i \(0.739592\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 2.14920 3.72253i 0.0873776 0.151342i
\(606\) 0 0
\(607\) −14.6729 25.4141i −0.595553 1.03153i −0.993469 0.114106i \(-0.963600\pi\)
0.397916 0.917422i \(-0.369734\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 34.7766 60.2349i 1.40691 2.43684i
\(612\) 0 0
\(613\) −3.79264 6.56905i −0.153183 0.265321i 0.779213 0.626760i \(-0.215619\pi\)
−0.932396 + 0.361438i \(0.882286\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 10.4367 18.0769i 0.420165 0.727748i −0.575790 0.817598i \(-0.695305\pi\)
0.995955 + 0.0898500i \(0.0286388\pi\)
\(618\) 0 0
\(619\) −12.6300 + 21.8758i −0.507642 + 0.879262i 0.492319 + 0.870415i \(0.336149\pi\)
−0.999961 + 0.00884679i \(0.997184\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −23.1147 15.9478i −0.926072 0.638937i
\(624\) 0 0
\(625\) −10.8802 18.8450i −0.435206 0.753799i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 51.8175 2.06610
\(630\) 0 0
\(631\) 34.0114 1.35397 0.676986 0.735996i \(-0.263286\pi\)
0.676986 + 0.735996i \(0.263286\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 1.90163 + 3.29372i 0.0754638 + 0.130707i
\(636\) 0 0
\(637\) 28.0082 34.3329i 1.10972 1.36032i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 2.64947 4.58902i 0.104648 0.181255i −0.808946 0.587882i \(-0.799962\pi\)
0.913594 + 0.406627i \(0.133295\pi\)
\(642\) 0 0
\(643\) −19.4304 + 33.6544i −0.766260 + 1.32720i 0.173318 + 0.984866i \(0.444551\pi\)
−0.939578 + 0.342335i \(0.888782\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 4.11420 + 7.12601i 0.161746 + 0.280152i 0.935495 0.353340i \(-0.114954\pi\)
−0.773749 + 0.633492i \(0.781621\pi\)
\(648\) 0 0
\(649\) −2.61480 + 4.52897i −0.102640 + 0.177778i
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 21.0164 + 36.4015i 0.822436 + 1.42450i 0.903863 + 0.427821i \(0.140719\pi\)
−0.0814277 + 0.996679i \(0.525948\pi\)
\(654\) 0 0
\(655\) −4.56382 + 7.90477i −0.178323 + 0.308865i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 7.33484 + 12.7043i 0.285725 + 0.494890i 0.972785 0.231711i \(-0.0744323\pi\)
−0.687060 + 0.726601i \(0.741099\pi\)
\(660\) 0 0
\(661\) 5.86605 0.228163 0.114081 0.993471i \(-0.463608\pi\)
0.114081 + 0.993471i \(0.463608\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −0.475018 + 5.89947i −0.0184204 + 0.228771i
\(666\) 0 0
\(667\) 13.7734 23.8563i 0.533310 0.923720i
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 2.52497 4.37338i 0.0974754 0.168832i
\(672\) 0 0
\(673\) 9.42591 + 16.3261i 0.363342 + 0.629327i 0.988509 0.151165i \(-0.0483023\pi\)
−0.625167 + 0.780491i \(0.714969\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −29.9144 −1.14970 −0.574852 0.818257i \(-0.694941\pi\)
−0.574852 + 0.818257i \(0.694941\pi\)
\(678\) 0 0
\(679\) −33.3554 + 15.8358i −1.28006 + 0.607724i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 12.8525 + 22.2612i 0.491788 + 0.851802i 0.999955 0.00945677i \(-0.00301023\pi\)
−0.508167 + 0.861258i \(0.669677\pi\)
\(684\) 0 0
\(685\) 7.07099 0.270169
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 74.0547 2.82126
\(690\) 0 0
\(691\) −38.4020 −1.46088 −0.730440 0.682976i \(-0.760685\pi\)
−0.730440 + 0.682976i \(0.760685\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −2.04895 −0.0777210
\(696\) 0 0
\(697\) 0.248731 0.00942137
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) −11.5694 −0.436972 −0.218486 0.975840i \(-0.570112\pi\)
−0.218486 + 0.975840i \(0.570112\pi\)
\(702\) 0 0
\(703\) 25.0480 + 43.3844i 0.944703 + 1.63627i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 9.25413 + 6.38482i 0.348037 + 0.240126i
\(708\) 0 0
\(709\) 52.0550 1.95497 0.977483 0.211013i \(-0.0676763\pi\)
0.977483 + 0.211013i \(0.0676763\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 24.7863 + 42.9311i 0.928254 + 1.60778i
\(714\) 0 0
\(715\) 1.99819 3.46096i 0.0747280 0.129433i
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 0.416175 0.720836i 0.0155207 0.0268827i −0.858161 0.513381i \(-0.828393\pi\)
0.873681 + 0.486498i \(0.161726\pi\)
\(720\) 0 0
\(721\) 21.4064 10.1629i 0.797217 0.378488i
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 17.2649 0.641203
\(726\) 0 0
\(727\) −10.7029 18.5379i −0.396948 0.687534i 0.596400 0.802687i \(-0.296597\pi\)
−0.993348 + 0.115154i \(0.963264\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −2.13447 + 3.69701i −0.0789461 + 0.136739i
\(732\) 0 0
\(733\) 3.72620 + 6.45396i 0.137630 + 0.238383i 0.926599 0.376051i \(-0.122718\pi\)
−0.788969 + 0.614433i \(0.789385\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 1.78601 3.09346i 0.0657885 0.113949i
\(738\) 0 0
\(739\) 17.9473 + 31.0857i 0.660203 + 1.14351i 0.980562 + 0.196210i \(0.0628633\pi\)
−0.320358 + 0.947296i \(0.603803\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 16.8379 29.1641i 0.617723 1.06993i −0.372177 0.928162i \(-0.621389\pi\)
0.989900 0.141766i \(-0.0452781\pi\)
\(744\) 0 0
\(745\) −2.75199 + 4.76659i −0.100825 + 0.174634i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −3.53110 2.43625i −0.129023 0.0890188i
\(750\) 0 0
\(751\) 7.51689 + 13.0196i 0.274295 + 0.475093i 0.969957 0.243276i \(-0.0782222\pi\)
−0.695662 + 0.718369i \(0.744889\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 2.40782 0.0876295
\(756\) 0 0
\(757\) −34.2548 −1.24501 −0.622507 0.782615i \(-0.713886\pi\)
−0.622507 + 0.782615i \(0.713886\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 21.1043 + 36.5538i 0.765031 + 1.32507i 0.940230 + 0.340540i \(0.110610\pi\)
−0.175199 + 0.984533i \(0.556057\pi\)
\(762\) 0 0
\(763\) −14.2278 + 6.75480i −0.515081 + 0.244540i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 12.2728 21.2572i 0.443147 0.767553i
\(768\) 0 0
\(769\) 22.2741 38.5799i 0.803226 1.39123i −0.114256 0.993451i \(-0.536448\pi\)
0.917482 0.397777i \(-0.130218\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 9.61003 + 16.6451i 0.345649 + 0.598681i 0.985471 0.169841i \(-0.0543256\pi\)
−0.639823 + 0.768523i \(0.720992\pi\)
\(774\) 0 0
\(775\) −15.5347 + 26.9069i −0.558024 + 0.966526i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 0.120234 + 0.208251i 0.00430783 + 0.00746138i
\(780\) 0 0
\(781\) −4.75081 + 8.22864i −0.169997 + 0.294444i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 2.82984 + 4.90142i 0.101001 + 0.174939i
\(786\) 0 0
\(787\) 40.3502 1.43833 0.719165 0.694839i \(-0.244524\pi\)
0.719165 + 0.694839i \(0.244524\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) −18.0466 12.4512i −0.641665 0.442712i
\(792\) 0 0
\(793\) −11.8512 + 20.5269i −0.420849 + 0.728932i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −22.4965 + 38.9651i −0.796867 + 1.38021i 0.124780 + 0.992184i \(0.460177\pi\)
−0.921647 + 0.388029i \(0.873156\pi\)
\(798\)