Properties

Label 2736.2.bm.o.1855.3
Level $2736$
Weight $2$
Character 2736.1855
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 1855.3
Root \(0.403374 + 1.68443i\) of defining polynomial
Character \(\chi\) \(=\) 2736.1855
Dual form 2736.2.bm.o.559.3

$q$-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 \(\left(\mathbb{Z}/2736\mathbb{Z}\right)^\times\).

\(n\) \(1009\) \(1217\) \(1711\) \(2053\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\) \(1\) \(-1\) \(1\)

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 0.951320 + 0.308204i \(0.0997278\pi\)
−0.208748 + 0.977969i \(0.566939\pi\)
\(6\) 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 0.961070 0.276304i \(-0.0891098\pi\)
0.241248 + 0.970463i \(0.422443\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 2.51414 + 4.35461i 0.609768 + 1.05615i 0.991278 + 0.131784i \(0.0420706\pi\)
−0.381511 + 0.924364i \(0.624596\pi\)
\(18\) 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 \(-0.479799\pi\)
−0.832571 + 0.553918i \(0.813132\pi\)
\(24\) 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 −0.151688 0.988428i \(-0.548471\pi\)
−0.931848 + 0.362848i \(0.881804\pi\)
\(30\) 0 0
\(31\) 2.32088 0.416843 0.208422 0.978039i \(-0.433167\pi\)
0.208422 + 0.978039i \(0.433167\pi\)
\(32\) 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 \(0.238259\pi\)
−0.732701 + 0.680550i \(0.761741\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 9.96265 5.75194i 1.55591 0.898302i 0.558263 0.829664i \(-0.311468\pi\)
0.997642 0.0686385i \(-0.0218655\pi\)
\(42\) 0 0
\(43\) 9.48133 5.47405i 1.44589 0.834784i 0.447656 0.894206i \(-0.352259\pi\)
0.998233 + 0.0594217i \(0.0189257\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −6.41478 3.70357i −0.935692 0.540222i −0.0470845 0.998891i \(-0.514993\pi\)
−0.888607 + 0.458669i \(0.848326\pi\)
\(48\) 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 0.103013 0.994680i \(-0.467152\pi\)
−0.809912 + 0.586551i \(0.800485\pi\)
\(54\) 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 \(-0.0973097\pi\)
−0.737463 + 0.675387i \(0.763976\pi\)
\(60\) 0 0
\(61\) 3.62763 6.28324i 0.464471 0.804487i −0.534707 0.845038i \(-0.679578\pi\)
0.999177 + 0.0405508i \(0.0129113\pi\)
\(62\) 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 0.0935894 + 0.995611i \(0.470166\pi\)
−0.909019 + 0.416755i \(0.863167\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −2.19325 3.79882i −0.260291 0.450838i 0.706028 0.708184i \(-0.250485\pi\)
−0.966319 + 0.257346i \(0.917152\pi\)
\(72\) 0 0
\(73\) −2.52827 4.37910i −0.295912 0.512535i 0.679285 0.733875i \(-0.262290\pi\)
−0.975197 + 0.221340i \(0.928957\pi\)
\(74\) 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 −0.990084 0.140476i \(-0.955137\pi\)
0.373387 0.927676i \(-0.378196\pi\)
\(80\) 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 0.787516 0.616294i \(-0.211367\pi\)
−0.139968 + 0.990156i \(0.544700\pi\)
\(90\) 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 −0.816113 0.577892i \(-0.803876\pi\)
0.0924121 + 0.995721i \(0.470542\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −2.83502 + 4.91040i −0.282095 + 0.488603i −0.971901 0.235392i \(-0.924363\pi\)
0.689805 + 0.723995i \(0.257696\pi\)
\(102\) 0 0
\(103\) −10.1222 −0.997367 −0.498683 0.866784i \(-0.666183\pi\)
−0.498683 + 0.866784i \(0.666183\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −0.971726 −0.0939403 −0.0469702 0.998896i \(-0.514957\pi\)
−0.0469702 + 0.998896i \(0.514957\pi\)
\(108\) 0 0
\(109\) −0.579757 + 0.334723i −0.0555307 + 0.0320607i −0.527508 0.849550i \(-0.676874\pi\)
0.471978 + 0.881611i \(0.343540\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 8.39291i 0.789539i 0.918780 + 0.394769i \(0.129175\pi\)
−0.918780 + 0.394769i \(0.870825\pi\)
\(114\) 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 \(-0.726629\pi\)
0.982309 + 0.187266i \(0.0599626\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 16.5424 9.55077i 1.44532 0.834454i 0.447120 0.894474i \(-0.352450\pi\)
0.998197 + 0.0600198i \(0.0191164\pi\)
\(132\) 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 −0.0741101 + 0.997250i \(0.523612\pi\)
−0.826589 + 0.562806i \(0.809722\pi\)
\(138\) 0 0
\(139\) 10.8588 + 6.26931i 0.921028 + 0.531756i 0.883963 0.467557i \(-0.154866\pi\)
0.0370651 + 0.999313i \(0.488199\pi\)
\(140\) 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 0.713804 0.700346i \(-0.246971\pi\)
−0.963419 + 0.267999i \(0.913638\pi\)
\(150\) 0 0
\(151\) −12.6983 −1.03337 −0.516687 0.856174i \(-0.672835\pi\)
−0.516687 + 0.856174i \(0.672835\pi\)
\(152\) 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 −0.977010 0.213195i \(-0.931613\pi\)
0.303873 0.952713i \(-0.401720\pi\)
\(158\) 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 0.482203 + 0.876060i \(0.339837\pi\)
−0.999791 + 0.0204298i \(0.993497\pi\)
\(168\) 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 −0.854899 0.518794i \(-0.826381\pi\)
0.0218394 + 0.999761i \(0.493048\pi\)
\(174\) 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 \(-0.508752\pi\)
−0.0274930 + 0.999622i \(0.508752\pi\)
\(180\) 0 0
\(181\) 5.42024 + 3.12938i 0.402883 + 0.232605i 0.687727 0.725969i \(-0.258608\pi\)
−0.284844 + 0.958574i \(0.591942\pi\)
\(182\) 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 −0.634412 0.772995i \(-0.718758\pi\)
0.352227 + 0.935915i \(0.385424\pi\)
\(194\) 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 \(-0.305891\pi\)
−0.423572 + 0.905862i \(0.639224\pi\)
\(200\) 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 \(-0.0122401\pi\)
−0.532924 + 0.846163i \(0.678907\pi\)
\(212\) 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 0.999658 + 0.0261490i \(0.00832443\pi\)
−0.477183 + 0.878804i \(0.658342\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −16.2926 −1.08138 −0.540689 0.841222i \(-0.681837\pi\)
−0.540689 + 0.841222i \(0.681837\pi\)
\(228\) 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 0.891229 + 0.453554i \(0.149844\pi\)
−0.0528253 + 0.998604i \(0.516823\pi\)
\(234\) 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 −0.0203221 0.999793i \(-0.506469\pi\)
−0.876008 + 0.482297i \(0.839803\pi\)
\(242\) 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 \(-0.304851\pi\)
−0.420611 + 0.907241i \(0.638184\pi\)
\(252\) 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 0.567970 0.823049i \(-0.307729\pi\)
−0.428796 + 0.903401i \(0.641062\pi\)
\(258\) 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 0.529690 0.848191i \(-0.322308\pi\)
0.999400 0.0346292i \(-0.0110250\pi\)
\(264\) 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 0.220009 0.975498i \(-0.429391\pi\)
0.954810 + 0.297215i \(0.0960580\pi\)
\(270\) 0 0
\(271\) −2.67004 + 1.54155i −0.162194 + 0.0936425i −0.578900 0.815399i \(-0.696518\pi\)
0.416706 + 0.909041i \(0.363184\pi\)
\(272\) 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 0.0502030 0.998739i \(-0.484013\pi\)
−0.839832 + 0.542847i \(0.817346\pi\)
\(282\) 0 0
\(283\) −24.3027 + 14.0312i −1.44465 + 0.834068i −0.998155 0.0607193i \(-0.980661\pi\)
−0.446493 + 0.894787i \(0.647327\pi\)
\(284\) 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 \(-0.989663\pi\)
0.999473 0.0324695i \(-0.0103372\pi\)
\(294\) 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 −0.964679 0.263427i \(-0.915147\pi\)
0.254205 0.967150i \(-0.418186\pi\)
\(308\) 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 −0.761555 0.648100i \(-0.775564\pi\)
0.942049 + 0.335476i \(0.108897\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −2.39611 1.38339i −0.134579 0.0776990i 0.431199 0.902257i \(-0.358091\pi\)
−0.565778 + 0.824558i \(0.691424\pi\)
\(318\) 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 \(-0.225105\pi\)
0.760192 + 0.649698i \(0.225105\pi\)
\(332\) 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 0.000803838 1.00000i \(-0.499744\pi\)
0.866427 + 0.499304i \(0.166411\pi\)
\(338\) 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 \(-0.713515\pi\)
0.367594 + 0.929987i \(0.380182\pi\)
\(348\) 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 −0.634611 + 0.772832i \(0.718840\pi\)
−0.986597 + 0.163174i \(0.947827\pi\)
\(360\) 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 \(-0.319477\pi\)
−0.461839 + 0.886964i \(0.652810\pi\)
\(368\) 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 \(-0.850231\pi\)
0.891336 0.453343i \(-0.149769\pi\)
\(374\) 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 \(-0.303978\pi\)
0.577630 + 0.816298i \(0.303978\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −10.1746 17.6229i −0.519897 0.900488i −0.999732 0.0231292i \(-0.992637\pi\)
0.479836 0.877358i \(-0.340696\pi\)
\(384\) 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 0.395484 + 0.918473i \(0.370577\pi\)
−0.993163 + 0.116738i \(0.962756\pi\)
\(390\) 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 −0.904752 0.425939i \(-0.859944\pi\)
0.0835014 0.996508i \(-0.473390\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 16.3533 9.44158i 0.816645 0.471490i −0.0326134 0.999468i \(-0.510383\pi\)
0.849258 + 0.527978i \(0.177050\pi\)
\(402\) 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 0.834500 0.551008i \(-0.185757\pi\)
−0.0599366 + 0.998202i \(0.519090\pi\)
\(410\) 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 0.246119 0.969240i \(-0.420845\pi\)
0.962446 + 0.271474i \(0.0875112\pi\)
\(422\) 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 \(-0.733343\pi\)
0.978141 + 0.207940i \(0.0666760\pi\)
\(432\) 0 0
\(433\) −20.0525 11.5773i −0.963664 0.556371i −0.0663649 0.997795i \(-0.521140\pi\)
−0.897299 + 0.441424i \(0.854473\pi\)
\(434\) 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 0.988595 + 0.150600i \(0.0481206\pi\)
−0.363874 + 0.931448i \(0.618546\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 17.2871 + 9.98074i 0.821337 + 0.474199i 0.850877 0.525364i \(-0.176071\pi\)
−0.0295402 + 0.999564i \(0.509404\pi\)
\(444\) 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 \(-0.746199\pi\)
0.698613 0.715500i \(-0.253801\pi\)
\(450\) 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 −0.869690 0.493599i \(-0.835681\pi\)
0.00737587 0.999973i \(-0.497652\pi\)
\(462\) 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 \(-0.0476101\pi\)
0.365367 + 0.930864i \(0.380943\pi\)
\(480\) 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 \(-0.365839\pi\)
0.409110 + 0.912485i \(0.365839\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 14.2871 8.24869i 0.644770 0.372258i −0.141680 0.989913i \(-0.545250\pi\)
0.786450 + 0.617654i \(0.211917\pi\)
\(492\) 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 \(-0.396653\pi\)
0.980280 + 0.197614i \(0.0633193\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 4.62723 + 2.67153i 0.206318 + 0.119118i 0.599599 0.800301i \(-0.295327\pi\)
−0.393281 + 0.919418i \(0.628660\pi\)
\(504\) 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 −0.0963261 0.995350i \(-0.530709\pi\)
−0.910161 + 0.414254i \(0.864042\pi\)
\(510\) 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 \(0.224741\pi\)
−0.760933 + 0.648830i \(0.775259\pi\)
\(522\) 0 0
\(523\) 3.70285 6.41353i 0.161914 0.280444i −0.773641 0.633624i \(-0.781566\pi\)
0.935555 + 0.353180i \(0.114900\pi\)
\(524\) 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 −0.665298 0.746578i \(-0.731695\pi\)
0.979204 + 0.202876i \(0.0650288\pi\)
\(542\) 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 −0.0488977 + 0.998804i \(0.515571\pi\)
−0.840541 + 0.541749i \(0.817762\pi\)
\(548\) 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 0.177931 0.984043i \(-0.443059\pi\)
0.763240 0.646115i \(-0.223607\pi\)
\(558\) 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 \(-0.189938\pi\)
0.827189 + 0.561923i \(0.189938\pi\)
\(564\) 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 \(-0.806270\pi\)
0.820438 0.571736i \(-0.193730\pi\)
\(570\) 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 \(-0.515088\pi\)
0.841361 + 0.540473i \(0.181755\pi\)
\(588\) 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 −0.712899 0.701266i \(-0.752618\pi\)
0.963764 + 0.266756i \(0.0859517\pi\)
\(594\) 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 0.446763 + 0.894652i \(0.352577\pi\)
−0.998173 + 0.0604175i \(0.980757\pi\)
\(600\) 0 0
\(601\) 24.4514i 0.997392i −0.866777 0.498696i \(-0.833812\pi\)
0.866777 0.498696i \(-0.166188\pi\)
\(602\) 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 \(-0.589800\pi\)
−0.278388 + 0.960469i \(0.589800\pi\)
\(608\) 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 −0.894328 0.447413i \(-0.852346\pi\)
0.0596932 0.998217i \(-0.480988\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −12.9157 + 22.3707i −0.519967 + 0.900609i 0.479764 + 0.877398i \(0.340722\pi\)
−0.999731 + 0.0232112i \(0.992611\pi\)
\(618\) 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 \(-0.507268\pi\)
−0.877216 + 0.480096i \(0.840602\pi\)
\(632\) 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 −0.257104 0.966384i \(-0.582768\pi\)
0.708361 + 0.705851i \(0.249435\pi\)
\(642\) 0 0
\(643\) 28.2790 16.3269i 1.11521 0.643870i 0.175040 0.984561i \(-0.443995\pi\)
0.940175 + 0.340692i \(0.110661\pi\)
\(644\) 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 \(-0.927648\pi\)
0.682296 + 0.731076i \(0.260981\pi\)
\(660\) 0 0
\(661\) −19.5953 11.3134i −0.762171 0.440040i 0.0679038 0.997692i \(-0.478369\pi\)
−0.830075 + 0.557652i \(0.811702\pi\)
\(662\) 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 \(0.168068\pi\)
−0.863815 + 0.503808i \(0.831932\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 4.42199i 0.169951i 0.996383 + 0.0849755i \(0.0270812\pi\)
−0.996383 + 0.0849755i \(0.972919\pi\)
\(678\) 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 \(-0.613442\pi\)
−0.348892 + 0.937163i \(0.613442\pi\)
\(684\) 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 0.994003 0.109356i \(-0.0348787\pi\)
−0.591706 + 0.806154i \(0.701545\pi\)
\(702\) 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 −0.909230 0.416293i \(-0.863329\pi\)
0.815136 + 0.579270i \(0.196662\pi\)
\(710\) 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 \(-0.458648\pi\)
0.923501 + 0.383596i \(0.125315\pi\)
\(720\) 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 \(-0.776607\pi\)
0.177268 + 0.984163i \(0.443274\pi\)
\(728\) 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 \(-0.484007\pi\)
0.890043 + 0.455876i \(0.150674\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 7.18365 + 12.4424i 0.263543 + 0.456469i 0.967181 0.254089i \(-0.0817757\pi\)
−0.703638 + 0.710558i \(0.748442\pi\)
\(744\) 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 \(-0.890575\pi\)
0.762630 + 0.646835i \(0.223908\pi\)
\(752\) 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 0.998777 0.0494379i \(-0.0157430\pi\)
−0.542203 + 0.840247i \(0.682410\pi\)
\(758\) 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 −0.646181 0.763184i \(-0.723635\pi\)
0.984027 + 0.178017i \(0.0569683\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 18.9627 + 10.9481i 0.682039 + 0.393776i 0.800623 0.599169i \(-0.204502\pi\)
−0.118584 + 0.992944i \(0.537835\pi\)
\(774\) 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 \(-0.777364\pi\)
−0.765208 + 0.643783i \(0.777364\pi\)
\(788\) 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 \(-0.992659\pi\)
0.999734 0.0230610i \(-0.00734119\pi\)
\(798\) 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