Properties

Label 2736.2.bm.n.559.3
Level $2736$
Weight $2$
Character 2736.559
Analytic conductor $21.847$
Analytic rank $0$
Dimension $6$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 2736 = 2^{4} \cdot 3^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2736.bm (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(21.8470699930\)
Analytic rank: \(0\)
Dimension: \(6\)
Relative dimension: \(3\) over \(\Q(\zeta_{6})\)
Coefficient field: 6.0.954288.1
Defining polynomial: \(x^{6} - x^{5} - 2 x^{4} + 3 x^{3} - 6 x^{2} - 9 x + 27\)
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: no (minimal twist has level 912)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 559.3
Root \(0.403374 - 1.68443i\) of defining polynomial
Character \(\chi\) \(=\) 2736.559
Dual form 2736.2.bm.n.1855.3

$q$-expansion

\(f(q)\) \(=\) \(q+(1.66044 - 2.87597i) q^{5} +2.71781i q^{7} +O(q^{10})\) \(q+(1.66044 - 2.87597i) q^{5} +2.71781i q^{7} -0.985762i q^{11} +(4.33502 - 2.50283i) q^{13} +(2.51414 - 4.35461i) q^{17} +(-0.193252 + 4.35461i) q^{19} +(3.68872 - 2.12968i) q^{23} +(-3.01414 - 5.22064i) q^{25} +(-5.83502 + 3.36885i) q^{29} -2.32088 q^{31} +(7.81635 + 4.51277i) q^{35} -8.27925i q^{37} +(9.96265 + 5.75194i) q^{41} +(-9.48133 - 5.47405i) q^{43} +(6.41478 - 3.70357i) q^{47} -0.386505 q^{49} +(-5.14631 + 2.97122i) q^{53} +(-2.83502 - 1.63680i) q^{55} +(-1.66044 + 2.87597i) q^{59} +(3.62763 + 6.28324i) q^{61} -16.6232i q^{65} +(6.67458 + 11.5607i) q^{67} +(2.19325 - 3.79882i) q^{71} +(-2.52827 + 4.37910i) q^{73} +2.67912 q^{77} +(5.48133 - 9.49394i) q^{79} -8.70923i q^{83} +(-8.34916 - 14.4612i) q^{85} +(6.10896 - 3.52701i) q^{89} +(6.80221 + 11.7818i) q^{91} +(12.2029 + 7.78637i) q^{95} +(-7.12763 - 4.11514i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6q + 2q^{5} + O(q^{10}) \) \( 6q + 2q^{5} - 3q^{13} + 2q^{17} - 4q^{19} - 12q^{23} - 5q^{25} - 6q^{29} + 2q^{31} - 6q^{35} + 12q^{41} - 33q^{43} + 18q^{47} - 8q^{49} - 36q^{53} + 12q^{55} - 2q^{59} + 3q^{61} + 19q^{67} + 16q^{71} + 11q^{73} + 32q^{77} + 9q^{79} - 8q^{85} - 6q^{89} + q^{91} + 26q^{95} - 24q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2736\mathbb{Z}\right)^\times\).

\(n\) \(1009\) \(1217\) \(1711\) \(2053\)
\(\chi(n)\) \(e\left(\frac{1}{6}\right)\) \(1\) \(-1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 0 0
\(4\) 0 0
\(5\) 1.66044 2.87597i 0.742572 1.28617i −0.208748 0.977969i \(-0.566939\pi\)
0.951320 0.308204i \(-0.0997278\pi\)
\(6\) 0 0
\(7\) 2.71781i 1.02724i 0.858019 + 0.513618i \(0.171695\pi\)
−0.858019 + 0.513618i \(0.828305\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 0.985762i 0.297218i −0.988896 0.148609i \(-0.952520\pi\)
0.988896 0.148609i \(-0.0474796\pi\)
\(12\) 0 0
\(13\) 4.33502 2.50283i 1.20232 0.694159i 0.241248 0.970463i \(-0.422443\pi\)
0.961070 + 0.276304i \(0.0891098\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 2.51414 4.35461i 0.609768 1.05615i −0.381511 0.924364i \(-0.624596\pi\)
0.991278 0.131784i \(-0.0420706\pi\)
\(18\) 0 0
\(19\) −0.193252 + 4.35461i −0.0443351 + 0.999017i
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 3.68872 2.12968i 0.769150 0.444069i −0.0634210 0.997987i \(-0.520201\pi\)
0.832571 + 0.553918i \(0.186868\pi\)
\(24\) 0 0
\(25\) −3.01414 5.22064i −0.602827 1.04413i
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) −5.83502 + 3.36885i −1.08354 + 0.625580i −0.931848 0.362848i \(-0.881804\pi\)
−0.151688 + 0.988428i \(0.548471\pi\)
\(30\) 0 0
\(31\) −2.32088 −0.416843 −0.208422 0.978039i \(-0.566833\pi\)
−0.208422 + 0.978039i \(0.566833\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 7.81635 + 4.51277i 1.32120 + 0.762797i
\(36\) 0 0
\(37\) 8.27925i 1.36110i −0.732701 0.680550i \(-0.761741\pi\)
0.732701 0.680550i \(-0.238259\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 9.96265 + 5.75194i 1.55591 + 0.898302i 0.997642 + 0.0686385i \(0.0218655\pi\)
0.558263 + 0.829664i \(0.311468\pi\)
\(42\) 0 0
\(43\) −9.48133 5.47405i −1.44589 0.834784i −0.447656 0.894206i \(-0.647741\pi\)
−0.998233 + 0.0594217i \(0.981074\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 6.41478 3.70357i 0.935692 0.540222i 0.0470845 0.998891i \(-0.485007\pi\)
0.888607 + 0.458669i \(0.151674\pi\)
\(48\) 0 0
\(49\) −0.386505 −0.0552150
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −5.14631 + 2.97122i −0.706899 + 0.408129i −0.809912 0.586551i \(-0.800485\pi\)
0.103013 + 0.994680i \(0.467152\pi\)
\(54\) 0 0
\(55\) −2.83502 1.63680i −0.382274 0.220706i
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −1.66044 + 2.87597i −0.216171 + 0.374419i −0.953634 0.300968i \(-0.902690\pi\)
0.737463 + 0.675387i \(0.236024\pi\)
\(60\) 0 0
\(61\) 3.62763 + 6.28324i 0.464471 + 0.804487i 0.999177 0.0405508i \(-0.0129113\pi\)
−0.534707 + 0.845038i \(0.679578\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 16.6232i 2.06185i
\(66\) 0 0
\(67\) 6.67458 + 11.5607i 0.815430 + 1.41237i 0.909019 + 0.416755i \(0.136833\pi\)
−0.0935894 + 0.995611i \(0.529834\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 2.19325 3.79882i 0.260291 0.450838i −0.706028 0.708184i \(-0.749515\pi\)
0.966319 + 0.257346i \(0.0828481\pi\)
\(72\) 0 0
\(73\) −2.52827 + 4.37910i −0.295912 + 0.512535i −0.975197 0.221340i \(-0.928957\pi\)
0.679285 + 0.733875i \(0.262290\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 2.67912 0.305314
\(78\) 0 0
\(79\) 5.48133 9.49394i 0.616697 1.06815i −0.373387 0.927676i \(-0.621804\pi\)
0.990084 0.140476i \(-0.0448631\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 8.70923i 0.955962i −0.878370 0.477981i \(-0.841369\pi\)
0.878370 0.477981i \(-0.158631\pi\)
\(84\) 0 0
\(85\) −8.34916 14.4612i −0.905593 1.56853i
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 6.10896 3.52701i 0.647548 0.373862i −0.139968 0.990156i \(-0.544700\pi\)
0.787516 + 0.616294i \(0.211367\pi\)
\(90\) 0 0
\(91\) 6.80221 + 11.7818i 0.713065 + 1.23507i
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 12.2029 + 7.78637i 1.25199 + 0.798865i
\(96\) 0 0
\(97\) −7.12763 4.11514i −0.723701 0.417829i 0.0924121 0.995721i \(-0.470542\pi\)
−0.816113 + 0.577892i \(0.803876\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −2.83502 4.91040i −0.282095 0.488603i 0.689805 0.723995i \(-0.257696\pi\)
−0.971901 + 0.235392i \(0.924363\pi\)
\(102\) 0 0
\(103\) 10.1222 0.997367 0.498683 0.866784i \(-0.333817\pi\)
0.498683 + 0.866784i \(0.333817\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 0.971726 0.0939403 0.0469702 0.998896i \(-0.485043\pi\)
0.0469702 + 0.998896i \(0.485043\pi\)
\(108\) 0 0
\(109\) −0.579757 0.334723i −0.0555307 0.0320607i 0.471978 0.881611i \(-0.343540\pi\)
−0.527508 + 0.849550i \(0.676874\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 8.39291i 0.789539i −0.918780 0.394769i \(-0.870825\pi\)
0.918780 0.394769i \(-0.129175\pi\)
\(114\) 0 0
\(115\) 14.1449i 1.31901i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 11.8350 + 6.83295i 1.08491 + 0.626376i
\(120\) 0 0
\(121\) 10.0283 0.911661
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −3.41478 −0.305427
\(126\) 0 0
\(127\) −3.70739 6.42139i −0.328978 0.569806i 0.653332 0.757072i \(-0.273371\pi\)
−0.982309 + 0.187266i \(0.940037\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −16.5424 9.55077i −1.44532 0.834454i −0.447120 0.894474i \(-0.647550\pi\)
−0.998197 + 0.0600198i \(0.980884\pi\)
\(132\) 0 0
\(133\) −11.8350 0.525224i −1.02623 0.0455427i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −10.5424 18.2600i −0.900699 1.56006i −0.826589 0.562806i \(-0.809722\pi\)
−0.0741101 0.997250i \(-0.523612\pi\)
\(138\) 0 0
\(139\) −10.8588 + 6.26931i −0.921028 + 0.531756i −0.883963 0.467557i \(-0.845134\pi\)
−0.0370651 + 0.999313i \(0.511801\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −2.46719 4.27330i −0.206317 0.357351i
\(144\) 0 0
\(145\) 22.3751i 1.85815i
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −3.04695 + 5.27747i −0.249616 + 0.432347i −0.963419 0.267999i \(-0.913638\pi\)
0.713804 + 0.700346i \(0.246971\pi\)
\(150\) 0 0
\(151\) 12.6983 1.03337 0.516687 0.856174i \(-0.327165\pi\)
0.516687 + 0.856174i \(0.327165\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −3.85369 + 6.67479i −0.309536 + 0.536132i
\(156\) 0 0
\(157\) −8.43438 + 14.6088i −0.673137 + 1.16591i 0.303873 + 0.952713i \(0.401720\pi\)
−0.977010 + 0.213195i \(0.931613\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 5.78807 + 10.0252i 0.456164 + 0.790100i
\(162\) 0 0
\(163\) 16.1932i 1.26835i −0.773189 0.634175i \(-0.781340\pi\)
0.773189 0.634175i \(-0.218660\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 6.68872 + 11.5852i 0.517588 + 0.896489i 0.999791 + 0.0204298i \(0.00650347\pi\)
−0.482203 + 0.876060i \(0.660163\pi\)
\(168\) 0 0
\(169\) 6.02827 10.4413i 0.463713 0.803175i
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −10.9572 6.32614i −0.833060 0.480967i 0.0218394 0.999761i \(-0.493048\pi\)
−0.854899 + 0.518794i \(0.826381\pi\)
\(174\) 0 0
\(175\) 14.1887 8.19186i 1.07257 0.619246i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 0.735663 0.0549861 0.0274930 0.999622i \(-0.491248\pi\)
0.0274930 + 0.999622i \(0.491248\pi\)
\(180\) 0 0
\(181\) 5.42024 3.12938i 0.402883 0.232605i −0.284844 0.958574i \(-0.591942\pi\)
0.687727 + 0.725969i \(0.258608\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −23.8109 13.7472i −1.75061 1.01072i
\(186\) 0 0
\(187\) −4.29261 2.47834i −0.313907 0.181234i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 1.84571i 0.133551i 0.997768 + 0.0667754i \(0.0212711\pi\)
−0.997768 + 0.0667754i \(0.978729\pi\)
\(192\) 0 0
\(193\) −3.92024 2.26335i −0.282185 0.162920i 0.352227 0.935915i \(-0.385424\pi\)
−0.634412 + 0.772995i \(0.718758\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 13.6892 0.975318 0.487659 0.873034i \(-0.337851\pi\)
0.487659 + 0.873034i \(0.337851\pi\)
\(198\) 0 0
\(199\) −2.10389 + 1.21468i −0.149141 + 0.0861067i −0.572714 0.819756i \(-0.694109\pi\)
0.423572 + 0.905862i \(0.360776\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −9.15591 15.8585i −0.642619 1.11305i
\(204\) 0 0
\(205\) 33.0848 19.1015i 2.31074 1.33411i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 4.29261 + 0.190501i 0.296926 + 0.0131772i
\(210\) 0 0
\(211\) −6.77394 + 11.7328i −0.466337 + 0.807720i −0.999261 0.0384438i \(-0.987760\pi\)
0.532924 + 0.846163i \(0.321093\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) −31.4864 + 18.1787i −2.14735 + 1.23978i
\(216\) 0 0
\(217\) 6.30773i 0.428197i
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 25.1698i 1.69310i
\(222\) 0 0
\(223\) −7.80221 + 13.5138i −0.522475 + 0.904953i 0.477183 + 0.878804i \(0.341658\pi\)
−0.999658 + 0.0261490i \(0.991676\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 16.2926 1.08138 0.540689 0.841222i \(-0.318163\pi\)
0.540689 + 0.841222i \(0.318163\pi\)
\(228\) 0 0
\(229\) 11.3118 0.747506 0.373753 0.927528i \(-0.378071\pi\)
0.373753 + 0.927528i \(0.378071\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 12.7977 22.1662i 0.838404 1.45216i −0.0528253 0.998604i \(-0.516823\pi\)
0.891229 0.453554i \(-0.149844\pi\)
\(234\) 0 0
\(235\) 24.5983i 1.60462i
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 2.47834i 0.160310i 0.996782 + 0.0801552i \(0.0255416\pi\)
−0.996782 + 0.0801552i \(0.974458\pi\)
\(240\) 0 0
\(241\) −13.9148 + 8.03370i −0.896330 + 0.517496i −0.876008 0.482297i \(-0.839803\pi\)
−0.0203221 + 0.999793i \(0.506469\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) −0.641769 + 1.11158i −0.0410011 + 0.0710160i
\(246\) 0 0
\(247\) 10.0611 + 19.3610i 0.640171 + 1.23191i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) −2.45213 + 1.41574i −0.154777 + 0.0893604i −0.575388 0.817881i \(-0.695149\pi\)
0.420611 + 0.907241i \(0.361816\pi\)
\(252\) 0 0
\(253\) −2.09936 3.63620i −0.131986 0.228606i
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 2.23113 1.28814i 0.139174 0.0803521i −0.428796 0.903401i \(-0.641062\pi\)
0.567970 + 0.823049i \(0.307729\pi\)
\(258\) 0 0
\(259\) 22.5015 1.39817
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −24.7977 14.3169i −1.52909 0.882821i −0.999400 0.0346292i \(-0.988975\pi\)
−0.529690 0.848191i \(-0.677692\pi\)
\(264\) 0 0
\(265\) 19.7342i 1.21226i
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 19.2685 + 11.1247i 1.17482 + 0.678282i 0.954810 0.297215i \(-0.0960580\pi\)
0.220009 + 0.975498i \(0.429391\pi\)
\(270\) 0 0
\(271\) 2.67004 + 1.54155i 0.162194 + 0.0936425i 0.578900 0.815399i \(-0.303482\pi\)
−0.416706 + 0.909041i \(0.636816\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −5.14631 + 2.97122i −0.310334 + 0.179171i
\(276\) 0 0
\(277\) 4.25526 0.255674 0.127837 0.991795i \(-0.459197\pi\)
0.127837 + 0.991795i \(0.459197\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −13.2366 + 7.64215i −0.789629 + 0.455892i −0.839832 0.542847i \(-0.817346\pi\)
0.0502030 + 0.998739i \(0.484013\pi\)
\(282\) 0 0
\(283\) 24.3027 + 14.0312i 1.44465 + 0.834068i 0.998155 0.0607193i \(-0.0193394\pi\)
0.446493 + 0.894787i \(0.352673\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −15.6327 + 27.0766i −0.922769 + 1.59828i
\(288\) 0 0
\(289\) −4.14177 7.17375i −0.243633 0.421986i
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 1.11158i 0.0649390i 0.999473 + 0.0324695i \(0.0103372\pi\)
−0.999473 + 0.0324695i \(0.989663\pi\)
\(294\) 0 0
\(295\) 5.51414 + 9.55077i 0.321045 + 0.556067i
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 10.6604 18.4644i 0.616509 1.06783i
\(300\) 0 0
\(301\) 14.8774 25.7685i 0.857521 1.48527i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 24.0939 1.37961
\(306\) 0 0
\(307\) 12.4485 21.5615i 0.710474 1.23058i −0.254205 0.967150i \(-0.581814\pi\)
0.964679 0.263427i \(-0.0848529\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 9.06236i 0.513879i 0.966427 + 0.256940i \(0.0827141\pi\)
−0.966427 + 0.256940i \(0.917286\pi\)
\(312\) 0 0
\(313\) 3.19325 + 5.53088i 0.180493 + 0.312624i 0.942049 0.335476i \(-0.108897\pi\)
−0.761555 + 0.648100i \(0.775564\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −2.39611 + 1.38339i −0.134579 + 0.0776990i −0.565778 0.824558i \(-0.691424\pi\)
0.431199 + 0.902257i \(0.358091\pi\)
\(318\) 0 0
\(319\) 3.32088 + 5.75194i 0.185934 + 0.322047i
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 18.4768 + 11.7896i 1.02808 + 0.655993i
\(324\) 0 0
\(325\) −26.1327 15.0877i −1.44958 0.836916i
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 10.0656 + 17.4342i 0.554936 + 0.961177i
\(330\) 0 0
\(331\) −27.6610 −1.52038 −0.760192 0.649698i \(-0.774895\pi\)
−0.760192 + 0.649698i \(0.774895\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 44.3310 2.42206
\(336\) 0 0
\(337\) 15.9202 + 9.19156i 0.867231 + 0.500696i 0.866427 0.499304i \(-0.166411\pi\)
0.000803838 1.00000i \(0.499744\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 2.28784i 0.123893i
\(342\) 0 0
\(343\) 17.9742i 0.970518i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 4.73153 + 2.73175i 0.254002 + 0.146648i 0.621595 0.783339i \(-0.286485\pi\)
−0.367594 + 0.929987i \(0.619818\pi\)
\(348\) 0 0
\(349\) 22.6700 1.21350 0.606750 0.794893i \(-0.292473\pi\)
0.606750 + 0.794893i \(0.292473\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −2.03735 −0.108437 −0.0542185 0.998529i \(-0.517267\pi\)
−0.0542185 + 0.998529i \(0.517267\pi\)
\(354\) 0 0
\(355\) −7.28354 12.6155i −0.386570 0.669559i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 30.7175 + 17.7348i 1.62121 + 0.936005i 0.986597 + 0.163174i \(0.0521731\pi\)
0.634611 + 0.772832i \(0.281160\pi\)
\(360\) 0 0
\(361\) −18.9253 1.68308i −0.996069 0.0885831i
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 8.39611 + 14.5425i 0.439472 + 0.761188i
\(366\) 0 0
\(367\) −1.44398 + 0.833682i −0.0753752 + 0.0435179i −0.537214 0.843446i \(-0.680523\pi\)
0.461839 + 0.886964i \(0.347190\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) −8.07522 13.9867i −0.419245 0.726153i
\(372\) 0 0
\(373\) 17.5110i 0.906686i 0.891336 + 0.453343i \(0.149769\pi\)
−0.891336 + 0.453343i \(0.850231\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −16.8633 + 29.2081i −0.868504 + 1.50429i
\(378\) 0 0
\(379\) −22.4905 −1.15526 −0.577630 0.816298i \(-0.696022\pi\)
−0.577630 + 0.816298i \(0.696022\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 10.1746 17.6229i 0.519897 0.900488i −0.479836 0.877358i \(-0.659304\pi\)
0.999732 0.0231292i \(-0.00736291\pi\)
\(384\) 0 0
\(385\) 4.44852 7.70506i 0.226717 0.392686i
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −11.7881 20.4175i −0.597679 1.03521i −0.993163 0.116738i \(-0.962756\pi\)
0.395484 0.918473i \(-0.370577\pi\)
\(390\) 0 0
\(391\) 21.4172i 1.08312i
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) −18.2029 31.5283i −0.915885 1.58636i
\(396\) 0 0
\(397\) −16.3633 + 28.3421i −0.821250 + 1.42245i 0.0835014 + 0.996508i \(0.473390\pi\)
−0.904752 + 0.425939i \(0.859944\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 16.3533 + 9.44158i 0.816645 + 0.471490i 0.849258 0.527978i \(-0.177050\pi\)
−0.0326134 + 0.999468i \(0.510383\pi\)
\(402\) 0 0
\(403\) −10.0611 + 5.80877i −0.501178 + 0.289355i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −8.16137 −0.404544
\(408\) 0 0
\(409\) 15.6646 9.04395i 0.774564 0.447194i −0.0599366 0.998202i \(-0.519090\pi\)
0.834500 + 0.551008i \(0.185757\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) −7.81635 4.51277i −0.384617 0.222059i
\(414\) 0 0
\(415\) −25.0475 14.4612i −1.22953 0.709871i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 0.353130i 0.0172515i −0.999963 0.00862577i \(-0.997254\pi\)
0.999963 0.00862577i \(-0.00274570\pi\)
\(420\) 0 0
\(421\) 24.7977 + 14.3169i 1.20856 + 0.697765i 0.962446 0.271474i \(-0.0875112\pi\)
0.246119 + 0.969240i \(0.420845\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) −30.3118 −1.47034
\(426\) 0 0
\(427\) −17.0767 + 9.85922i −0.826398 + 0.477121i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −6.41478 11.1107i −0.308989 0.535185i 0.669152 0.743125i \(-0.266657\pi\)
−0.978141 + 0.207940i \(0.933324\pi\)
\(432\) 0 0
\(433\) −20.0525 + 11.5773i −0.963664 + 0.556371i −0.897299 0.441424i \(-0.854473\pi\)
−0.0663649 + 0.997795i \(0.521140\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 8.56108 + 16.4745i 0.409532 + 0.788082i
\(438\) 0 0
\(439\) −13.0894 + 22.6714i −0.624721 + 1.08205i 0.363874 + 0.931448i \(0.381454\pi\)
−0.988595 + 0.150600i \(0.951879\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −17.2871 + 9.98074i −0.821337 + 0.474199i −0.850877 0.525364i \(-0.823929\pi\)
0.0295402 + 0.999564i \(0.490596\pi\)
\(444\) 0 0
\(445\) 23.4256i 1.11048i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 30.3224i 1.43100i 0.698613 + 0.715500i \(0.253801\pi\)
−0.698613 + 0.715500i \(0.746199\pi\)
\(450\) 0 0
\(451\) 5.67004 9.82080i 0.266992 0.462444i
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 45.1787 2.11801
\(456\) 0 0
\(457\) −14.5569 −0.680945 −0.340473 0.940254i \(-0.610587\pi\)
−0.340473 + 0.940254i \(0.610587\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −18.5147 + 32.0683i −0.862314 + 1.49357i 0.00737587 + 0.999973i \(0.497652\pi\)
−0.869690 + 0.493599i \(0.835681\pi\)
\(462\) 0 0
\(463\) 39.4283i 1.83239i 0.400735 + 0.916194i \(0.368755\pi\)
−0.400735 + 0.916194i \(0.631245\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 6.16620i 0.285338i −0.989770 0.142669i \(-0.954432\pi\)
0.989770 0.142669i \(-0.0455684\pi\)
\(468\) 0 0
\(469\) −31.4198 + 18.1403i −1.45083 + 0.837639i
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −5.39611 + 9.34633i −0.248113 + 0.429745i
\(474\) 0 0
\(475\) 23.3163 12.1165i 1.06983 0.555943i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −29.6382 + 17.1116i −1.35420 + 0.781849i −0.988835 0.149015i \(-0.952390\pi\)
−0.365367 + 0.930864i \(0.619057\pi\)
\(480\) 0 0
\(481\) −20.7215 35.8907i −0.944820 1.63648i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −23.6700 + 13.6659i −1.07480 + 0.620537i
\(486\) 0 0
\(487\) −18.0565 −0.818220 −0.409110 0.912485i \(-0.634161\pi\)
−0.409110 + 0.912485i \(0.634161\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −14.2871 8.24869i −0.644770 0.372258i 0.141680 0.989913i \(-0.454750\pi\)
−0.786450 + 0.617654i \(0.788083\pi\)
\(492\) 0 0
\(493\) 33.8790i 1.52583i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 10.3245 + 5.96085i 0.463117 + 0.267381i
\(498\) 0 0
\(499\) −29.0237 16.7569i −1.29928 0.750140i −0.319001 0.947754i \(-0.603347\pi\)
−0.980280 + 0.197614i \(0.936681\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −4.62723 + 2.67153i −0.206318 + 0.119118i −0.599599 0.800301i \(-0.704673\pi\)
0.393281 + 0.919418i \(0.371340\pi\)
\(504\) 0 0
\(505\) −18.8296 −0.837904
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −22.7074 + 13.1101i −1.00649 + 0.581096i −0.910161 0.414254i \(-0.864042\pi\)
−0.0963261 + 0.995350i \(0.530709\pi\)
\(510\) 0 0
\(511\) −11.9016 6.87137i −0.526494 0.303972i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 16.8073 29.1111i 0.740617 1.28279i
\(516\) 0 0
\(517\) −3.65084 6.32344i −0.160564 0.278105i
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 29.6197i 1.29766i −0.760933 0.648830i \(-0.775259\pi\)
0.760933 0.648830i \(-0.224741\pi\)
\(522\) 0 0
\(523\) −3.70285 6.41353i −0.161914 0.280444i 0.773641 0.633624i \(-0.218434\pi\)
−0.935555 + 0.353180i \(0.885100\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −5.83502 + 10.1066i −0.254178 + 0.440248i
\(528\) 0 0
\(529\) −2.42892 + 4.20701i −0.105605 + 0.182913i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 57.5844 2.49426
\(534\) 0 0
\(535\) 1.61350 2.79466i 0.0697575 0.120823i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 0.381002i 0.0164109i
\(540\) 0 0
\(541\) 7.30128 + 12.6462i 0.313907 + 0.543702i 0.979204 0.202876i \(-0.0650288\pi\)
−0.665298 + 0.746578i \(0.731695\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) −1.92531 + 1.11158i −0.0824711 + 0.0476147i
\(546\) 0 0
\(547\) 20.8022 + 36.0305i 0.889438 + 1.54055i 0.840541 + 0.541749i \(0.182238\pi\)
0.0488977 + 0.998804i \(0.484429\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −13.5424 26.0603i −0.576926 1.11021i
\(552\) 0 0
\(553\) 25.8027 + 14.8972i 1.09724 + 0.633494i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 22.2125 + 38.4731i 0.941172 + 1.63016i 0.763240 + 0.646115i \(0.223607\pi\)
0.177931 + 0.984043i \(0.443059\pi\)
\(558\) 0 0
\(559\) −54.8023 −2.31789
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −39.2545 −1.65438 −0.827189 0.561923i \(-0.810062\pi\)
−0.827189 + 0.561923i \(0.810062\pi\)
\(564\) 0 0
\(565\) −24.1378 13.9359i −1.01548 0.586290i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 27.2761i 1.14347i 0.820438 + 0.571736i \(0.193730\pi\)
−0.820438 + 0.571736i \(0.806270\pi\)
\(570\) 0 0
\(571\) 1.07155i 0.0448429i 0.999749 + 0.0224214i \(0.00713757\pi\)
−0.999749 + 0.0224214i \(0.992862\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −22.2366 12.8383i −0.927330 0.535394i
\(576\) 0 0
\(577\) 17.6135 0.733259 0.366630 0.930367i \(-0.380512\pi\)
0.366630 + 0.930367i \(0.380512\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 23.6700 0.981999
\(582\) 0 0
\(583\) 2.92892 + 5.07303i 0.121303 + 0.210103i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −19.2366 11.1063i −0.793979 0.458404i 0.0473824 0.998877i \(-0.484912\pi\)
−0.841361 + 0.540473i \(0.818245\pi\)
\(588\) 0 0
\(589\) 0.448517 10.1066i 0.0184808 0.416433i
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 6.10896 + 10.5810i 0.250865 + 0.434511i 0.963764 0.266756i \(-0.0859517\pi\)
−0.712899 + 0.701266i \(0.752618\pi\)
\(594\) 0 0
\(595\) 39.3027 22.6914i 1.61126 0.930259i
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 13.4955 + 23.3748i 0.551410 + 0.955070i 0.998173 + 0.0604175i \(0.0192432\pi\)
−0.446763 + 0.894652i \(0.647423\pi\)
\(600\) 0 0
\(601\) 24.4514i 0.997392i 0.866777 + 0.498696i \(0.166188\pi\)
−0.866777 + 0.498696i \(0.833812\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 16.6514 28.8410i 0.676974 1.17255i
\(606\) 0 0
\(607\) 13.7175 0.556777 0.278388 0.960469i \(-0.410200\pi\)
0.278388 + 0.960469i \(0.410200\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 18.5388 32.1101i 0.750000 1.29904i
\(612\) 0 0
\(613\) −20.6646 + 35.7921i −0.834634 + 1.44563i 0.0596932 + 0.998217i \(0.480988\pi\)
−0.894328 + 0.447413i \(0.852346\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −12.9157 22.3707i −0.519967 0.900609i −0.999731 0.0232112i \(-0.992611\pi\)
0.479764 0.877398i \(-0.340722\pi\)
\(618\) 0 0
\(619\) 38.1873i 1.53488i −0.641121 0.767440i \(-0.721530\pi\)
0.641121 0.767440i \(-0.278470\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 9.58575 + 16.6030i 0.384045 + 0.665185i
\(624\) 0 0
\(625\) 9.40064 16.2824i 0.376026 0.651296i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −36.0529 20.8152i −1.43752 0.829955i
\(630\) 0 0
\(631\) 22.6090 13.0533i 0.900048 0.519643i 0.0228325 0.999739i \(-0.492732\pi\)
0.877216 + 0.480096i \(0.159398\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −24.6236 −0.977159
\(636\) 0 0
\(637\) −1.67551 + 0.967354i −0.0663860 + 0.0383280i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 11.4249 + 6.59617i 0.451257 + 0.260533i 0.708361 0.705851i \(-0.249435\pi\)
−0.257104 + 0.966384i \(0.582768\pi\)
\(642\) 0 0
\(643\) −28.2790 16.3269i −1.11521 0.643870i −0.175040 0.984561i \(-0.556005\pi\)
−0.940175 + 0.340692i \(0.889339\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 23.5235i 0.924805i 0.886670 + 0.462403i \(0.153012\pi\)
−0.886670 + 0.462403i \(0.846988\pi\)
\(648\) 0 0
\(649\) 2.83502 + 1.63680i 0.111284 + 0.0642500i
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −49.5953 −1.94082 −0.970408 0.241471i \(-0.922370\pi\)
−0.970408 + 0.241471i \(0.922370\pi\)
\(654\) 0 0
\(655\) −54.9354 + 31.7170i −2.14651 + 1.23929i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 7.49546 + 12.9825i 0.291982 + 0.505727i 0.974278 0.225348i \(-0.0723520\pi\)
−0.682296 + 0.731076i \(0.739019\pi\)
\(660\) 0 0
\(661\) −19.5953 + 11.3134i −0.762171 + 0.440040i −0.830075 0.557652i \(-0.811702\pi\)
0.0679038 + 0.997692i \(0.478369\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −21.1619 + 33.1651i −0.820623 + 1.28609i
\(666\) 0 0
\(667\) −14.3492 + 24.8535i −0.555602 + 0.962330i
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 6.19378 3.57598i 0.239108 0.138049i
\(672\) 0 0
\(673\) 26.1398i 1.00762i −0.863815 0.503808i \(-0.831932\pi\)
0.863815 0.503808i \(-0.168068\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 4.42199i 0.169951i −0.996383 0.0849755i \(-0.972919\pi\)
0.996383 0.0849755i \(-0.0270812\pi\)
\(678\) 0 0
\(679\) 11.1842 19.3716i 0.429209 0.743413i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 18.2361 0.697784 0.348892 0.937163i \(-0.386558\pi\)
0.348892 + 0.937163i \(0.386558\pi\)
\(684\) 0 0
\(685\) −70.0203 −2.67534
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) −14.8729 + 25.7606i −0.566612 + 0.981401i
\(690\) 0 0
\(691\) 9.05341i 0.344408i 0.985061 + 0.172204i \(0.0550888\pi\)
−0.985061 + 0.172204i \(0.944911\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 41.6393i 1.57947i
\(696\) 0 0
\(697\) 50.0950 28.9223i 1.89748 1.09551i
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 10.6514 18.4487i 0.402297 0.696798i −0.591706 0.806154i \(-0.701545\pi\)
0.994003 + 0.109356i \(0.0348787\pi\)
\(702\) 0 0
\(703\) 36.0529 + 1.59999i 1.35976 + 0.0603446i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 13.3455 7.70506i 0.501911 0.289778i
\(708\) 0 0
\(709\) −2.50546 4.33959i −0.0940947 0.162977i 0.815136 0.579270i \(-0.196662\pi\)
−0.909230 + 0.416293i \(0.863329\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −8.56108 + 4.94274i −0.320615 + 0.185107i
\(714\) 0 0
\(715\) −16.3865 −0.612821
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −28.2366 16.3024i −1.05305 0.607977i −0.129546 0.991573i \(-0.541352\pi\)
−0.923501 + 0.383596i \(0.874685\pi\)
\(720\) 0 0
\(721\) 27.5102i 1.02453i
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 35.1751 + 20.3084i 1.30637 + 0.754233i
\(726\) 0 0
\(727\) 15.8113 + 9.12865i 0.586408 + 0.338563i 0.763676 0.645600i \(-0.223393\pi\)
−0.177268 + 0.984163i \(0.556726\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −47.6747 + 27.5250i −1.76331 + 1.01805i
\(732\) 0 0
\(733\) 46.0275 1.70006 0.850032 0.526731i \(-0.176583\pi\)
0.850032 + 0.526731i \(0.176583\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 11.3961 6.57954i 0.419781 0.242361i
\(738\) 0 0
\(739\) −25.5607 14.7575i −0.940265 0.542862i −0.0502216 0.998738i \(-0.515993\pi\)
−0.890043 + 0.455876i \(0.849326\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −7.18365 + 12.4424i −0.263543 + 0.456469i −0.967181 0.254089i \(-0.918224\pi\)
0.703638 + 0.710558i \(0.251558\pi\)
\(744\) 0 0
\(745\) 10.1186 + 17.5259i 0.370715 + 0.642098i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 2.64097i 0.0964989i
\(750\) 0 0
\(751\) 4.90157 + 8.48977i 0.178861 + 0.309796i 0.941491 0.337039i \(-0.109425\pi\)
−0.762630 + 0.646835i \(0.776092\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 21.0848 36.5200i 0.767355 1.32910i
\(756\) 0 0
\(757\) 12.5620 21.7580i 0.456574 0.790810i −0.542203 0.840247i \(-0.682410\pi\)
0.998777 + 0.0494379i \(0.0157430\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 24.8778 0.901821 0.450910 0.892569i \(-0.351099\pi\)
0.450910 + 0.892569i \(0.351099\pi\)
\(762\) 0 0
\(763\) 0.909714 1.57567i 0.0329339 0.0570431i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 16.6232i 0.600229i
\(768\) 0 0
\(769\) 9.36876 + 16.2272i 0.337846 + 0.585167i 0.984027 0.178017i \(-0.0569683\pi\)
−0.646181 + 0.763184i \(0.723635\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 18.9627 10.9481i 0.682039 0.393776i −0.118584 0.992944i \(-0.537835\pi\)
0.800623 + 0.599169i \(0.204502\pi\)
\(774\) 0 0
\(775\) 6.99546 + 12.1165i 0.251284 + 0.435237i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −26.9728 + 42.2719i −0.966400 + 1.51455i
\(780\) 0 0
\(781\) −3.74474 2.16202i −0.133997 0.0773633i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 28.0096 + 48.5141i 0.999706 + 1.73154i
\(786\) 0 0
\(787\) 42.9336 1.53042 0.765208 0.643783i \(-0.222636\pi\)
0.765208 + 0.643783i \(0.222636\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 22.8104 0.811043
\(792\) 0 0
\(793\) 31.4517 + 18.1587i 1.11688 + 0.644833i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 1.30208i 0.0461219i 0.999734 + 0.0230610i \(0.00734119\pi\)
−0.999734 + 0.0230610i \(0.992659\pi\)
\(798\) 0 0
\(799\) 37.2452i 1.31764i
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 4.31675 + 2.49228i 0.152335 + 0.0879505i
\(804\) 0 0