Properties

Label 2736.2.bm.n.559.1
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 559.1
Root \(-1.62241 + 0.606458i\) of defining polynomial
Character \(\chi\) \(=\) 2736.559
Dual form 2736.2.bm.n.1855.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.33641 + 2.31473i) q^{5} +3.93569i q^{7} +O(q^{10})\) \(q+(-1.33641 + 2.31473i) q^{5} +3.93569i q^{7} -2.20364i q^{11} +(-3.60083 + 2.07894i) q^{13} +(0.571993 - 0.990721i) q^{17} +(-4.24482 + 0.990721i) q^{19} +(-3.19243 + 1.84315i) q^{23} +(-1.07199 - 1.85675i) q^{25} +(2.10083 - 1.21292i) q^{29} +3.67282 q^{31} +(-9.11007 - 5.25970i) q^{35} +10.0478i q^{37} +(-8.01847 - 4.62947i) q^{41} +(-0.490764 - 0.283343i) q^{43} +(10.6336 - 6.13932i) q^{47} -8.48963 q^{49} +(-4.09159 + 2.36228i) q^{53} +(5.10083 + 2.94497i) q^{55} +(1.33641 - 2.31473i) q^{59} +(-6.41764 - 11.1157i) q^{61} -11.1133i q^{65} +(1.73558 + 3.00612i) q^{67} +(6.24482 - 10.8163i) q^{71} +(1.35601 - 2.34868i) q^{73} +8.67282 q^{77} +(-3.50924 + 6.07817i) q^{79} -1.98144i q^{83} +(1.52884 + 2.64802i) q^{85} +(-12.9269 + 7.46334i) q^{89} +(-8.18206 - 14.1717i) q^{91} +(3.37957 - 11.1496i) q^{95} +(2.91764 + 1.68450i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6q + 2q^{5} + O(q^{10}) \) \( 6q + 2q^{5} - 3q^{13} + 2q^{17} - 4q^{19} - 12q^{23} - 5q^{25} - 6q^{29} + 2q^{31} - 6q^{35} + 12q^{41} - 33q^{43} + 18q^{47} - 8q^{49} - 36q^{53} + 12q^{55} - 2q^{59} + 3q^{61} + 19q^{67} + 16q^{71} + 11q^{73} + 32q^{77} + 9q^{79} - 8q^{85} - 6q^{89} + q^{91} + 26q^{95} - 24q^{97} + O(q^{100}) \)

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
\(5\) −1.33641 + 2.31473i −0.597662 + 1.03518i 0.395504 + 0.918464i \(0.370570\pi\)
−0.993165 + 0.116716i \(0.962763\pi\)
\(6\) 0 0
\(7\) 3.93569i 1.48755i 0.668430 + 0.743775i \(0.266967\pi\)
−0.668430 + 0.743775i \(0.733033\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 2.20364i 0.664421i −0.943205 0.332211i \(-0.892205\pi\)
0.943205 0.332211i \(-0.107795\pi\)
\(12\) 0 0
\(13\) −3.60083 + 2.07894i −0.998691 + 0.576594i −0.907861 0.419272i \(-0.862285\pi\)
−0.0908300 + 0.995866i \(0.528952\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 0.571993 0.990721i 0.138729 0.240285i −0.788287 0.615308i \(-0.789032\pi\)
0.927016 + 0.375023i \(0.122365\pi\)
\(18\) 0 0
\(19\) −4.24482 + 0.990721i −0.973828 + 0.227287i
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −3.19243 + 1.84315i −0.665667 + 0.384323i −0.794433 0.607352i \(-0.792232\pi\)
0.128766 + 0.991675i \(0.458898\pi\)
\(24\) 0 0
\(25\) −1.07199 1.85675i −0.214399 0.371349i
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 2.10083 1.21292i 0.390114 0.225233i −0.292095 0.956389i \(-0.594352\pi\)
0.682210 + 0.731157i \(0.261019\pi\)
\(30\) 0 0
\(31\) 3.67282 0.659659 0.329829 0.944041i \(-0.393009\pi\)
0.329829 + 0.944041i \(0.393009\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) −9.11007 5.25970i −1.53988 0.889051i
\(36\) 0 0
\(37\) 10.0478i 1.65185i 0.563780 + 0.825925i \(0.309347\pi\)
−0.563780 + 0.825925i \(0.690653\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −8.01847 4.62947i −1.25227 0.723001i −0.280714 0.959791i \(-0.590571\pi\)
−0.971561 + 0.236790i \(0.923905\pi\)
\(42\) 0 0
\(43\) −0.490764 0.283343i −0.0748409 0.0432094i 0.462113 0.886821i \(-0.347092\pi\)
−0.536953 + 0.843612i \(0.680425\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 10.6336 6.13932i 1.55107 0.895512i 0.553018 0.833169i \(-0.313476\pi\)
0.998055 0.0623432i \(-0.0198573\pi\)
\(48\) 0 0
\(49\) −8.48963 −1.21280
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −4.09159 + 2.36228i −0.562024 + 0.324485i −0.753957 0.656923i \(-0.771858\pi\)
0.191934 + 0.981408i \(0.438524\pi\)
\(54\) 0 0
\(55\) 5.10083 + 2.94497i 0.687796 + 0.397099i
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 1.33641 2.31473i 0.173986 0.301353i −0.765824 0.643050i \(-0.777669\pi\)
0.939810 + 0.341698i \(0.111002\pi\)
\(60\) 0 0
\(61\) −6.41764 11.1157i −0.821695 1.42322i −0.904419 0.426645i \(-0.859696\pi\)
0.0827247 0.996572i \(-0.473638\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 11.1133i 1.37843i
\(66\) 0 0
\(67\) 1.73558 + 3.00612i 0.212035 + 0.367255i 0.952351 0.305003i \(-0.0986576\pi\)
−0.740316 + 0.672259i \(0.765324\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 6.24482 10.8163i 0.741123 1.28366i −0.210861 0.977516i \(-0.567627\pi\)
0.951984 0.306147i \(-0.0990400\pi\)
\(72\) 0 0
\(73\) 1.35601 2.34868i 0.158709 0.274893i −0.775694 0.631109i \(-0.782600\pi\)
0.934404 + 0.356216i \(0.115933\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 8.67282 0.988360
\(78\) 0 0
\(79\) −3.50924 + 6.07817i −0.394820 + 0.683848i −0.993078 0.117455i \(-0.962526\pi\)
0.598258 + 0.801303i \(0.295860\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 1.98144i 0.217492i −0.994070 0.108746i \(-0.965317\pi\)
0.994070 0.108746i \(-0.0346835\pi\)
\(84\) 0 0
\(85\) 1.52884 + 2.64802i 0.165826 + 0.287218i
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −12.9269 + 7.46334i −1.37025 + 0.791112i −0.990959 0.134167i \(-0.957164\pi\)
−0.379287 + 0.925279i \(0.623831\pi\)
\(90\) 0 0
\(91\) −8.18206 14.1717i −0.857713 1.48560i
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 3.37957 11.1496i 0.346736 1.14393i
\(96\) 0 0
\(97\) 2.91764 + 1.68450i 0.296242 + 0.171035i 0.640753 0.767747i \(-0.278622\pi\)
−0.344512 + 0.938782i \(0.611956\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 5.10083 + 8.83490i 0.507552 + 0.879105i 0.999962 + 0.00874190i \(0.00278267\pi\)
−0.492410 + 0.870363i \(0.663884\pi\)
\(102\) 0 0
\(103\) 16.4504 1.62091 0.810455 0.585802i \(-0.199220\pi\)
0.810455 + 0.585802i \(0.199220\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 4.85601 0.469449 0.234724 0.972062i \(-0.424581\pi\)
0.234724 + 0.972062i \(0.424581\pi\)
\(108\) 0 0
\(109\) −12.7345 7.35224i −1.21974 0.704217i −0.254877 0.966973i \(-0.582035\pi\)
−0.964862 + 0.262757i \(0.915368\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 14.4823i 1.36238i −0.732107 0.681189i \(-0.761463\pi\)
0.732107 0.681189i \(-0.238537\pi\)
\(114\) 0 0
\(115\) 9.85282i 0.918780i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 3.89917 + 2.25119i 0.357436 + 0.206366i
\(120\) 0 0
\(121\) 6.14399 0.558544
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −7.63362 −0.682772
\(126\) 0 0
\(127\) −5.81681 10.0750i −0.516158 0.894013i −0.999824 0.0187598i \(-0.994028\pi\)
0.483666 0.875253i \(-0.339305\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −10.7160 6.18687i −0.936260 0.540550i −0.0474737 0.998872i \(-0.515117\pi\)
−0.888786 + 0.458323i \(0.848450\pi\)
\(132\) 0 0
\(133\) −3.89917 16.7063i −0.338101 1.44862i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −4.71598 8.16832i −0.402913 0.697866i 0.591163 0.806552i \(-0.298669\pi\)
−0.994076 + 0.108686i \(0.965336\pi\)
\(138\) 0 0
\(139\) 11.8941 6.86705i 1.00884 0.582456i 0.0979905 0.995187i \(-0.468759\pi\)
0.910853 + 0.412731i \(0.135425\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 4.58123 + 7.93492i 0.383102 + 0.663551i
\(144\) 0 0
\(145\) 6.48382i 0.538452i
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −8.15322 + 14.1218i −0.667938 + 1.15690i 0.310542 + 0.950560i \(0.399490\pi\)
−0.978480 + 0.206343i \(0.933844\pi\)
\(150\) 0 0
\(151\) −7.05767 −0.574345 −0.287173 0.957879i \(-0.592715\pi\)
−0.287173 + 0.957879i \(0.592715\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −4.90841 + 8.50161i −0.394253 + 0.682866i
\(156\) 0 0
\(157\) 5.66246 9.80766i 0.451913 0.782737i −0.546592 0.837399i \(-0.684075\pi\)
0.998505 + 0.0546625i \(0.0174083\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) −7.25405 12.5644i −0.571699 0.990212i
\(162\) 0 0
\(163\) 0.915973i 0.0717445i 0.999356 + 0.0358723i \(0.0114209\pi\)
−0.999356 + 0.0358723i \(0.988579\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −0.192425 0.333290i −0.0148903 0.0257908i 0.858484 0.512840i \(-0.171407\pi\)
−0.873375 + 0.487049i \(0.838073\pi\)
\(168\) 0 0
\(169\) 2.14399 3.71349i 0.164922 0.285653i
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −9.34960 5.39799i −0.710837 0.410402i 0.100534 0.994934i \(-0.467945\pi\)
−0.811371 + 0.584532i \(0.801278\pi\)
\(174\) 0 0
\(175\) 7.30757 4.21903i 0.552401 0.318929i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −1.03920 −0.0776737 −0.0388368 0.999246i \(-0.512365\pi\)
−0.0388368 + 0.999246i \(0.512365\pi\)
\(180\) 0 0
\(181\) −6.73445 + 3.88814i −0.500568 + 0.289003i −0.728948 0.684569i \(-0.759990\pi\)
0.228380 + 0.973572i \(0.426657\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −23.2580 13.4280i −1.70996 0.987247i
\(186\) 0 0
\(187\) −2.18319 1.26047i −0.159651 0.0921743i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 26.2621i 1.90026i 0.311851 + 0.950131i \(0.399051\pi\)
−0.311851 + 0.950131i \(0.600949\pi\)
\(192\) 0 0
\(193\) 8.23445 + 4.75416i 0.592729 + 0.342212i 0.766176 0.642631i \(-0.222157\pi\)
−0.173447 + 0.984843i \(0.555491\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −27.9322 −1.99008 −0.995042 0.0994560i \(-0.968290\pi\)
−0.995042 + 0.0994560i \(0.968290\pi\)
\(198\) 0 0
\(199\) −6.87562 + 3.96964i −0.487399 + 0.281400i −0.723495 0.690330i \(-0.757466\pi\)
0.236096 + 0.971730i \(0.424132\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 4.77365 + 8.26821i 0.335045 + 0.580315i
\(204\) 0 0
\(205\) 21.4320 12.3737i 1.49687 0.864220i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 2.18319 + 9.35403i 0.151014 + 0.647032i
\(210\) 0 0
\(211\) 4.32605 7.49293i 0.297817 0.515835i −0.677819 0.735229i \(-0.737075\pi\)
0.975636 + 0.219394i \(0.0704081\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 1.31173 0.757326i 0.0894590 0.0516492i
\(216\) 0 0
\(217\) 14.4551i 0.981275i
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 4.75656i 0.319961i
\(222\) 0 0
\(223\) 7.18206 12.4397i 0.480946 0.833023i −0.518815 0.854887i \(-0.673627\pi\)
0.999761 + 0.0218634i \(0.00695988\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 14.1832 0.941371 0.470686 0.882301i \(-0.344007\pi\)
0.470686 + 0.882301i \(0.344007\pi\)
\(228\) 0 0
\(229\) −16.5473 −1.09348 −0.546738 0.837303i \(-0.684131\pi\)
−0.546738 + 0.837303i \(0.684131\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −13.1193 + 22.7233i −0.859474 + 1.48865i 0.0129574 + 0.999916i \(0.495875\pi\)
−0.872431 + 0.488737i \(0.837458\pi\)
\(234\) 0 0
\(235\) 32.8187i 2.14085i
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 1.26047i 0.0815327i 0.999169 + 0.0407664i \(0.0129799\pi\)
−0.999169 + 0.0407664i \(0.987020\pi\)
\(240\) 0 0
\(241\) −18.1336 + 10.4695i −1.16809 + 0.674397i −0.953229 0.302248i \(-0.902263\pi\)
−0.214860 + 0.976645i \(0.568930\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 11.3456 19.6512i 0.724847 1.25547i
\(246\) 0 0
\(247\) 13.2252 12.3921i 0.841500 0.788493i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) −24.6521 + 14.2329i −1.55603 + 0.898372i −0.558396 + 0.829575i \(0.688583\pi\)
−0.997631 + 0.0687973i \(0.978084\pi\)
\(252\) 0 0
\(253\) 4.06163 + 7.03494i 0.255352 + 0.442283i
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −10.4764 + 6.04858i −0.653503 + 0.377300i −0.789797 0.613368i \(-0.789814\pi\)
0.136294 + 0.990668i \(0.456481\pi\)
\(258\) 0 0
\(259\) −39.5450 −2.45721
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 1.11930 + 0.646229i 0.0690191 + 0.0398482i 0.534112 0.845413i \(-0.320646\pi\)
−0.465093 + 0.885262i \(0.653979\pi\)
\(264\) 0 0
\(265\) 12.6279i 0.775728i
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 24.5420 + 14.1693i 1.49635 + 0.863920i 0.999991 0.00419513i \(-0.00133536\pi\)
0.496363 + 0.868115i \(0.334669\pi\)
\(270\) 0 0
\(271\) −13.2017 7.62198i −0.801944 0.463002i 0.0422066 0.999109i \(-0.486561\pi\)
−0.844150 + 0.536106i \(0.819895\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −4.09159 + 2.36228i −0.246732 + 0.142451i
\(276\) 0 0
\(277\) −15.8353 −0.951450 −0.475725 0.879594i \(-0.657814\pi\)
−0.475725 + 0.879594i \(0.657814\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 15.8445 9.14784i 0.945205 0.545714i 0.0536166 0.998562i \(-0.482925\pi\)
0.891588 + 0.452847i \(0.149592\pi\)
\(282\) 0 0
\(283\) −25.4218 14.6773i −1.51117 0.872474i −0.999915 0.0130439i \(-0.995848\pi\)
−0.511254 0.859430i \(-0.670819\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 18.2201 31.5582i 1.07550 1.86282i
\(288\) 0 0
\(289\) 7.84565 + 13.5891i 0.461509 + 0.799356i
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 19.6512i 1.14804i −0.818842 0.574019i \(-0.805384\pi\)
0.818842 0.574019i \(-0.194616\pi\)
\(294\) 0 0
\(295\) 3.57199 + 6.18687i 0.207969 + 0.360214i
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 7.66359 13.2737i 0.443197 0.767639i
\(300\) 0 0
\(301\) 1.11515 1.93150i 0.0642761 0.111330i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 34.3064 1.96438
\(306\) 0 0
\(307\) −3.59046 + 6.21887i −0.204919 + 0.354929i −0.950107 0.311925i \(-0.899026\pi\)
0.745188 + 0.666854i \(0.232360\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 29.1868i 1.65503i 0.561444 + 0.827515i \(0.310246\pi\)
−0.561444 + 0.827515i \(0.689754\pi\)
\(312\) 0 0
\(313\) 7.24482 + 12.5484i 0.409501 + 0.709277i 0.994834 0.101516i \(-0.0323694\pi\)
−0.585333 + 0.810793i \(0.699036\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 2.37562 1.37156i 0.133428 0.0770346i −0.431800 0.901969i \(-0.642121\pi\)
0.565228 + 0.824935i \(0.308788\pi\)
\(318\) 0 0
\(319\) −2.67282 4.62947i −0.149649 0.259200i
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) −1.44648 + 4.77212i −0.0804842 + 0.265528i
\(324\) 0 0
\(325\) 7.72013 + 4.45722i 0.428236 + 0.247242i
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 24.1625 + 41.8506i 1.33212 + 2.30730i
\(330\) 0 0
\(331\) 10.0761 0.553835 0.276918 0.960894i \(-0.410687\pi\)
0.276918 + 0.960894i \(0.410687\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) −9.27781 −0.506901
\(336\) 0 0
\(337\) 3.76555 + 2.17404i 0.205123 + 0.118428i 0.599043 0.800717i \(-0.295548\pi\)
−0.393920 + 0.919145i \(0.628881\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 8.09357i 0.438291i
\(342\) 0 0
\(343\) 5.86273i 0.316558i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −0.542026 0.312939i −0.0290975 0.0167994i 0.485381 0.874303i \(-0.338681\pi\)
−0.514478 + 0.857503i \(0.672014\pi\)
\(348\) 0 0
\(349\) 6.79834 0.363907 0.181953 0.983307i \(-0.441758\pi\)
0.181953 + 0.983307i \(0.441758\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −20.0185 −1.06548 −0.532738 0.846280i \(-0.678837\pi\)
−0.532738 + 0.846280i \(0.678837\pi\)
\(354\) 0 0
\(355\) 16.6913 + 28.9102i 0.885882 + 1.53439i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −14.7882 8.53796i −0.780490 0.450616i 0.0561140 0.998424i \(-0.482129\pi\)
−0.836604 + 0.547808i \(0.815462\pi\)
\(360\) 0 0
\(361\) 17.0369 8.41086i 0.896681 0.442677i
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 3.62438 + 6.27762i 0.189709 + 0.328586i
\(366\) 0 0
\(367\) 25.5277 14.7384i 1.33254 0.769340i 0.346848 0.937921i \(-0.387252\pi\)
0.985688 + 0.168582i \(0.0539187\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) −9.29721 16.1032i −0.482687 0.836038i
\(372\) 0 0
\(373\) 26.6745i 1.38116i 0.723258 + 0.690578i \(0.242644\pi\)
−0.723258 + 0.690578i \(0.757356\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −5.04316 + 8.73500i −0.259736 + 0.449876i
\(378\) 0 0
\(379\) 6.80890 0.349750 0.174875 0.984591i \(-0.444048\pi\)
0.174875 + 0.984591i \(0.444048\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 5.23558 9.06829i 0.267526 0.463368i −0.700697 0.713459i \(-0.747127\pi\)
0.968222 + 0.250091i \(0.0804606\pi\)
\(384\) 0 0
\(385\) −11.5905 + 20.0753i −0.590705 + 1.02313i
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 1.25405 + 2.17208i 0.0635830 + 0.110129i 0.896065 0.443924i \(-0.146414\pi\)
−0.832482 + 0.554053i \(0.813081\pi\)
\(390\) 0 0
\(391\) 4.21707i 0.213267i
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) −9.37957 16.2459i −0.471937 0.817419i
\(396\) 0 0
\(397\) −4.54316 + 7.86898i −0.228014 + 0.394933i −0.957220 0.289363i \(-0.906557\pi\)
0.729205 + 0.684295i \(0.239890\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 9.97399 + 5.75848i 0.498077 + 0.287565i 0.727919 0.685663i \(-0.240488\pi\)
−0.229842 + 0.973228i \(0.573821\pi\)
\(402\) 0 0
\(403\) −13.2252 + 7.63558i −0.658795 + 0.380355i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 22.1417 1.09752
\(408\) 0 0
\(409\) 16.1664 9.33368i 0.799378 0.461521i −0.0438759 0.999037i \(-0.513971\pi\)
0.843253 + 0.537516i \(0.180637\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 9.11007 + 5.25970i 0.448277 + 0.258813i
\(414\) 0 0
\(415\) 4.58651 + 2.64802i 0.225143 + 0.129986i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 27.2053i 1.32907i −0.747259 0.664533i \(-0.768630\pi\)
0.747259 0.664533i \(-0.231370\pi\)
\(420\) 0 0
\(421\) −1.11930 0.646229i −0.0545514 0.0314953i 0.472476 0.881343i \(-0.343360\pi\)
−0.527028 + 0.849848i \(0.676694\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) −2.45269 −0.118973
\(426\) 0 0
\(427\) 43.7478 25.2578i 2.11711 1.22231i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −10.6336 18.4180i −0.512203 0.887162i −0.999900 0.0141492i \(-0.995496\pi\)
0.487696 0.873013i \(-0.337837\pi\)
\(432\) 0 0
\(433\) 33.3890 19.2771i 1.60457 0.926401i 0.614017 0.789293i \(-0.289553\pi\)
0.990556 0.137108i \(-0.0437807\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 11.7252 10.9866i 0.560893 0.525562i
\(438\) 0 0
\(439\) −12.3692 + 21.4241i −0.590350 + 1.02252i 0.403835 + 0.914832i \(0.367677\pi\)
−0.994185 + 0.107684i \(0.965656\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −31.5513 + 18.2161i −1.49905 + 0.865474i −0.999999 0.00110093i \(-0.999650\pi\)
−0.499046 + 0.866575i \(0.666316\pi\)
\(444\) 0 0
\(445\) 39.8964i 1.89127i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 28.9509i 1.36628i −0.730289 0.683138i \(-0.760615\pi\)
0.730289 0.683138i \(-0.239385\pi\)
\(450\) 0 0
\(451\) −10.2017 + 17.6698i −0.480377 + 0.832038i
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 43.7384 2.05049
\(456\) 0 0
\(457\) −14.2224 −0.665295 −0.332648 0.943051i \(-0.607942\pi\)
−0.332648 + 0.943051i \(0.607942\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 18.1677 31.4674i 0.846156 1.46559i −0.0384575 0.999260i \(-0.512244\pi\)
0.884613 0.466325i \(-0.154422\pi\)
\(462\) 0 0
\(463\) 29.6264i 1.37685i 0.725306 + 0.688427i \(0.241698\pi\)
−0.725306 + 0.688427i \(0.758302\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 30.4879i 1.41081i 0.708803 + 0.705407i \(0.249236\pi\)
−0.708803 + 0.705407i \(0.750764\pi\)
\(468\) 0 0
\(469\) −11.8311 + 6.83071i −0.546311 + 0.315413i
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −0.624385 + 1.08147i −0.0287092 + 0.0497259i
\(474\) 0 0
\(475\) 6.38993 + 6.81950i 0.293190 + 0.312900i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 20.5882 11.8866i 0.940699 0.543113i 0.0505196 0.998723i \(-0.483912\pi\)
0.890179 + 0.455610i \(0.150579\pi\)
\(480\) 0 0
\(481\) −20.8888 36.1805i −0.952447 1.64969i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −7.79834 + 4.50237i −0.354104 + 0.204442i
\(486\) 0 0
\(487\) −10.2880 −0.466193 −0.233096 0.972454i \(-0.574886\pi\)
−0.233096 + 0.972454i \(0.574886\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −28.5513 16.4841i −1.28850 0.743916i −0.310114 0.950699i \(-0.600367\pi\)
−0.978387 + 0.206783i \(0.933700\pi\)
\(492\) 0 0
\(493\) 2.77512i 0.124985i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 42.5697 + 24.5776i 1.90951 + 1.10246i
\(498\) 0 0
\(499\) −14.2067 8.20227i −0.635981 0.367184i 0.147084 0.989124i \(-0.453011\pi\)
−0.783065 + 0.621940i \(0.786345\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 12.8521 7.42014i 0.573045 0.330848i −0.185320 0.982678i \(-0.559332\pi\)
0.758365 + 0.651831i \(0.225999\pi\)
\(504\) 0 0
\(505\) −27.2672 −1.21338
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −24.8168 + 14.3280i −1.09999 + 0.635077i −0.936217 0.351422i \(-0.885698\pi\)
−0.163769 + 0.986499i \(0.552365\pi\)
\(510\) 0 0
\(511\) 9.24369 + 5.33684i 0.408917 + 0.236088i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −21.9846 + 38.0784i −0.968755 + 1.67793i
\(516\) 0 0
\(517\) −13.5288 23.4326i −0.594998 1.03057i
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 0.911178i 0.0399194i −0.999801 0.0199597i \(-0.993646\pi\)
0.999801 0.0199597i \(-0.00635380\pi\)
\(522\) 0 0
\(523\) 5.12043 + 8.86885i 0.223901 + 0.387808i 0.955989 0.293402i \(-0.0947875\pi\)
−0.732088 + 0.681210i \(0.761454\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 2.10083 3.63875i 0.0915136 0.158506i
\(528\) 0 0
\(529\) −4.70561 + 8.15036i −0.204592 + 0.354364i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 38.4975 1.66751
\(534\) 0 0
\(535\) −6.48963 + 11.2404i −0.280571 + 0.485964i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 18.7081i 0.805813i
\(540\) 0 0
\(541\) 19.6233 + 33.9885i 0.843670 + 1.46128i 0.886772 + 0.462208i \(0.152943\pi\)
−0.0431020 + 0.999071i \(0.513724\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 34.0369 19.6512i 1.45798 0.841767i
\(546\) 0 0
\(547\) 5.81794 + 10.0770i 0.248757 + 0.430860i 0.963181 0.268853i \(-0.0866446\pi\)
−0.714424 + 0.699713i \(0.753311\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −7.71598 + 7.22994i −0.328712 + 0.308006i
\(552\) 0 0
\(553\) −23.9218 13.8113i −1.01726 0.587314i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 0.514319 + 0.890827i 0.0217924 + 0.0377455i 0.876716 0.481008i \(-0.159729\pi\)
−0.854924 + 0.518754i \(0.826396\pi\)
\(558\) 0 0
\(559\) 2.35621 0.0996572
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −4.29588 −0.181050 −0.0905249 0.995894i \(-0.528854\pi\)
−0.0905249 + 0.995894i \(0.528854\pi\)
\(564\) 0 0
\(565\) 33.5226 + 19.3543i 1.41031 + 0.814241i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 25.9992i 1.08995i 0.838454 + 0.544973i \(0.183460\pi\)
−0.838454 + 0.544973i \(0.816540\pi\)
\(570\) 0 0
\(571\) 35.2310i 1.47437i 0.675691 + 0.737185i \(0.263846\pi\)
−0.675691 + 0.737185i \(0.736154\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 6.84452 + 3.95168i 0.285436 + 0.164797i
\(576\) 0 0
\(577\) 9.51037 0.395922 0.197961 0.980210i \(-0.436568\pi\)
0.197961 + 0.980210i \(0.436568\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 7.79834 0.323530
\(582\) 0 0
\(583\) 5.20561 + 9.01639i 0.215594 + 0.373421i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 9.84452 + 5.68373i 0.406327 + 0.234593i 0.689210 0.724561i \(-0.257958\pi\)
−0.282884 + 0.959154i \(0.591291\pi\)
\(588\) 0 0
\(589\) −15.5905 + 3.63875i −0.642394 + 0.149932i
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −12.9269 22.3900i −0.530843 0.919447i −0.999352 0.0359886i \(-0.988542\pi\)
0.468509 0.883459i \(-0.344791\pi\)
\(594\) 0 0
\(595\) −10.4218 + 6.01702i −0.427252 + 0.246674i
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 2.56276 + 4.43883i 0.104711 + 0.181366i 0.913620 0.406569i \(-0.133275\pi\)
−0.808909 + 0.587934i \(0.799941\pi\)
\(600\) 0 0
\(601\) 12.7822i 0.521398i −0.965420 0.260699i \(-0.916047\pi\)
0.965420 0.260699i \(-0.0839530\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −8.21090 + 14.2217i −0.333820 + 0.578194i
\(606\) 0 0
\(607\) −31.7882 −1.29024 −0.645121 0.764080i \(-0.723193\pi\)
−0.645121 + 0.764080i \(0.723193\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −25.5266 + 44.2133i −1.03269 + 1.78868i
\(612\) 0 0
\(613\) −21.1664 + 36.6613i −0.854903 + 1.48074i 0.0218315 + 0.999762i \(0.493050\pi\)
−0.876735 + 0.480974i \(0.840283\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 10.1717 + 17.6179i 0.409497 + 0.709270i 0.994833 0.101521i \(-0.0323709\pi\)
−0.585336 + 0.810791i \(0.699038\pi\)
\(618\) 0 0
\(619\) 13.1402i 0.528150i 0.964502 + 0.264075i \(0.0850667\pi\)
−0.964502 + 0.264075i \(0.914933\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −29.3734 50.8761i −1.17682 2.03831i
\(624\) 0 0
\(625\) 15.5616 26.9535i 0.622465 1.07814i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 9.95458 + 5.74728i 0.396915 + 0.229159i
\(630\) 0 0
\(631\) 3.57312 2.06294i 0.142244 0.0821245i −0.427189 0.904162i \(-0.640496\pi\)
0.569433 + 0.822038i \(0.307163\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 31.0946 1.23395
\(636\) 0 0
\(637\) 30.5697 17.6494i 1.21122 0.699296i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −31.9714 18.4587i −1.26279 0.729074i −0.289179 0.957275i \(-0.593382\pi\)
−0.973614 + 0.228201i \(0.926716\pi\)
\(642\) 0 0
\(643\) 6.62854 + 3.82699i 0.261404 + 0.150922i 0.624975 0.780645i \(-0.285109\pi\)
−0.363571 + 0.931567i \(0.618443\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 26.5387i 1.04335i 0.853146 + 0.521673i \(0.174692\pi\)
−0.853146 + 0.521673i \(0.825308\pi\)
\(648\) 0 0
\(649\) −5.10083 2.94497i −0.200225 0.115600i
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 2.23860 0.0876033 0.0438017 0.999040i \(-0.486053\pi\)
0.0438017 + 0.999040i \(0.486053\pi\)
\(654\) 0 0
\(655\) 28.6419 16.5364i 1.11913 0.646132i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) −3.43724 5.95348i −0.133896 0.231915i 0.791279 0.611455i \(-0.209415\pi\)
−0.925175 + 0.379540i \(0.876082\pi\)
\(660\) 0 0
\(661\) 32.2386 18.6130i 1.25394 0.723960i 0.282047 0.959400i \(-0.408986\pi\)
0.971889 + 0.235440i \(0.0756531\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 43.8815 + 13.3009i 1.70165 + 0.515788i
\(666\) 0 0
\(667\) −4.47116 + 7.74428i −0.173124 + 0.299860i
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −24.4949 + 14.1421i −0.945616 + 0.545952i
\(672\) 0 0
\(673\) 40.4406i 1.55887i 0.626482 + 0.779436i \(0.284494\pi\)
−0.626482 + 0.779436i \(0.715506\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 14.1650i 0.544405i −0.962240 0.272202i \(-0.912248\pi\)
0.962240 0.272202i \(-0.0877520\pi\)
\(678\) 0 0
\(679\) −6.62967 + 11.4829i −0.254423 + 0.440674i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 23.8952 0.914325 0.457163 0.889383i \(-0.348866\pi\)
0.457163 + 0.889383i \(0.348866\pi\)
\(684\) 0 0
\(685\) 25.2100 0.963223
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 9.82209 17.0124i 0.374192 0.648119i
\(690\) 0 0
\(691\) 19.0166i 0.723427i −0.932289 0.361714i \(-0.882192\pi\)
0.932289 0.361714i \(-0.117808\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 36.7088i 1.39245i
\(696\) 0 0
\(697\) −9.17302 + 5.29605i −0.347453 + 0.200602i
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) −14.2109 + 24.6140i −0.536738 + 0.929658i 0.462339 + 0.886703i \(0.347010\pi\)
−0.999077 + 0.0429544i \(0.986323\pi\)
\(702\) 0 0
\(703\) −9.95458 42.6511i −0.375444 1.60862i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −34.7714 + 20.0753i −1.30771 + 0.755008i
\(708\) 0 0
\(709\) 13.8681 + 24.0202i 0.520826 + 0.902098i 0.999707 + 0.0242175i \(0.00770943\pi\)
−0.478880 + 0.877880i \(0.658957\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −11.7252 + 6.76956i −0.439113 + 0.253522i
\(714\) 0 0
\(715\) −24.4896 −0.915860
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 0.844517 + 0.487582i 0.0314952 + 0.0181837i 0.515665 0.856790i \(-0.327545\pi\)
−0.484170 + 0.874974i \(0.660878\pi\)
\(720\) 0 0
\(721\) 64.7438i 2.41118i
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −4.50415 2.60047i −0.167280 0.0965792i
\(726\) 0 0
\(727\) 22.6924 + 13.1015i 0.841615 + 0.485907i 0.857813 0.513962i \(-0.171823\pi\)
−0.0161975 + 0.999869i \(0.505156\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −0.561428 + 0.324141i −0.0207652 + 0.0119888i
\(732\) 0 0
\(733\) 27.2751 1.00743 0.503715 0.863870i \(-0.331966\pi\)
0.503715 + 0.863870i \(0.331966\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 6.62438 3.82459i 0.244012 0.140881i
\(738\) 0 0
\(739\) −21.2908 12.2922i −0.783195 0.452178i 0.0543667 0.998521i \(-0.482686\pi\)
−0.837561 + 0.546343i \(0.816019\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −24.1101 + 41.7599i −0.884513 + 1.53202i −0.0382412 + 0.999269i \(0.512176\pi\)
−0.846271 + 0.532752i \(0.821158\pi\)
\(744\) 0 0
\(745\) −21.7921 37.7451i −0.798402 1.38287i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 19.1118i 0.698328i
\(750\) 0 0
\(751\) −16.2437 28.1349i −0.592741 1.02666i −0.993861 0.110632i \(-0.964713\pi\)
0.401121 0.916025i \(-0.368621\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 9.43196 16.3366i 0.343264 0.594551i
\(756\) 0 0
\(757\) −11.5801 + 20.0573i −0.420886 + 0.728996i −0.996026 0.0890590i \(-0.971614\pi\)
0.575141 + 0.818055i \(0.304947\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 18.5496 0.672421 0.336211 0.941787i \(-0.390855\pi\)
0.336211 + 0.941787i \(0.390855\pi\)
\(762\) 0 0
\(763\) 28.9361 50.1188i 1.04756 1.81442i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 11.1133i 0.401277i
\(768\) 0 0
\(769\) −18.8249 32.6057i −0.678844 1.17579i −0.975329 0.220755i \(-0.929148\pi\)
0.296486 0.955037i \(-0.404185\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 0.981529 0.566686i 0.0353031 0.0203823i −0.482245 0.876037i \(-0.660178\pi\)
0.517548 + 0.855654i \(0.326845\pi\)
\(774\) 0 0
\(775\) −3.93724 6.81950i −0.141430 0.244964i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 38.6235 + 11.7072i 1.38383 + 0.419453i
\(780\) 0 0
\(781\) −23.8353 13.7613i −0.852893 0.492418i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 15.1348 + 26.2142i 0.540182 + 0.935623i
\(786\) 0 0
\(787\) 13.9687 0.497930 0.248965 0.968512i \(-0.419910\pi\)
0.248965 + 0.968512i \(0.419910\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 56.9977 2.02661
\(792\) 0 0
\(793\) 46.2177 + 26.6838i 1.64124 + 0.947569i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 10.2972i 0.364746i −0.983229 0.182373i \(-0.941622\pi\)
0.983229 0.182373i \(-0.0583778\pi\)
\(798\) 0 0
\(799\) 14.0466i 0.496933i
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) −5.17565 2.98816i −0.182645 0.105450i
\(804\) 0 0