Properties

Label 1620.4.i.b.1081.1
Level $1620$
Weight $4$
Character 1620.1081
Analytic conductor $95.583$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1620 = 2^{2} \cdot 3^{4} \cdot 5 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1620.i (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(95.5830942093\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
Defining polynomial: \( x^{2} - x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 540)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 1081.1
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 1620.1081
Dual form 1620.4.i.b.541.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-2.50000 + 4.33013i) q^{5} +(-8.50000 - 14.7224i) q^{7} +O(q^{10})\) \(q+(-2.50000 + 4.33013i) q^{5} +(-8.50000 - 14.7224i) q^{7} +(15.0000 + 25.9808i) q^{11} +(30.5000 - 52.8275i) q^{13} -120.000 q^{17} -43.0000 q^{19} +(-45.0000 + 77.9423i) q^{23} +(-12.5000 - 21.6506i) q^{25} +(45.0000 + 77.9423i) q^{29} +(-4.00000 + 6.92820i) q^{31} +85.0000 q^{35} +317.000 q^{37} +(15.0000 - 25.9808i) q^{41} +(110.000 + 190.526i) q^{43} +(90.0000 + 155.885i) q^{47} +(27.0000 - 46.7654i) q^{49} -630.000 q^{53} -150.000 q^{55} +(420.000 - 727.461i) q^{59} +(-299.500 - 518.749i) q^{61} +(152.500 + 264.138i) q^{65} +(-53.5000 + 92.6647i) q^{67} -210.000 q^{71} -421.000 q^{73} +(255.000 - 441.673i) q^{77} +(-176.500 - 305.707i) q^{79} +(675.000 + 1169.13i) q^{83} +(300.000 - 519.615i) q^{85} +1020.00 q^{89} -1037.00 q^{91} +(107.500 - 186.195i) q^{95} +(498.500 + 863.427i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q - 5 q^{5} - 17 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 2 q - 5 q^{5} - 17 q^{7} + 30 q^{11} + 61 q^{13} - 240 q^{17} - 86 q^{19} - 90 q^{23} - 25 q^{25} + 90 q^{29} - 8 q^{31} + 170 q^{35} + 634 q^{37} + 30 q^{41} + 220 q^{43} + 180 q^{47} + 54 q^{49} - 1260 q^{53} - 300 q^{55} + 840 q^{59} - 599 q^{61} + 305 q^{65} - 107 q^{67} - 420 q^{71} - 842 q^{73} + 510 q^{77} - 353 q^{79} + 1350 q^{83} + 600 q^{85} + 2040 q^{89} - 2074 q^{91} + 215 q^{95} + 997 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1620\mathbb{Z}\right)^\times\).

\(n\) \(811\) \(1297\) \(1541\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{1}{3}\right)\)

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
\(5\) −2.50000 + 4.33013i −0.223607 + 0.387298i
\(6\) 0 0
\(7\) −8.50000 14.7224i −0.458957 0.794937i 0.539949 0.841698i \(-0.318443\pi\)
−0.998906 + 0.0467610i \(0.985110\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 15.0000 + 25.9808i 0.411152 + 0.712136i 0.995016 0.0997155i \(-0.0317933\pi\)
−0.583864 + 0.811851i \(0.698460\pi\)
\(12\) 0 0
\(13\) 30.5000 52.8275i 0.650706 1.12706i −0.332246 0.943193i \(-0.607806\pi\)
0.982952 0.183863i \(-0.0588603\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −120.000 −1.71202 −0.856008 0.516962i \(-0.827063\pi\)
−0.856008 + 0.516962i \(0.827063\pi\)
\(18\) 0 0
\(19\) −43.0000 −0.519204 −0.259602 0.965716i \(-0.583591\pi\)
−0.259602 + 0.965716i \(0.583591\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −45.0000 + 77.9423i −0.407963 + 0.706613i −0.994661 0.103193i \(-0.967094\pi\)
0.586698 + 0.809806i \(0.300427\pi\)
\(24\) 0 0
\(25\) −12.5000 21.6506i −0.100000 0.173205i
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 45.0000 + 77.9423i 0.288148 + 0.499087i 0.973368 0.229250i \(-0.0736272\pi\)
−0.685220 + 0.728336i \(0.740294\pi\)
\(30\) 0 0
\(31\) −4.00000 + 6.92820i −0.0231749 + 0.0401401i −0.877380 0.479796i \(-0.840711\pi\)
0.854205 + 0.519936i \(0.174044\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 85.0000 0.410503
\(36\) 0 0
\(37\) 317.000 1.40850 0.704250 0.709952i \(-0.251284\pi\)
0.704250 + 0.709952i \(0.251284\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 15.0000 25.9808i 0.0571367 0.0989637i −0.836042 0.548665i \(-0.815136\pi\)
0.893179 + 0.449701i \(0.148470\pi\)
\(42\) 0 0
\(43\) 110.000 + 190.526i 0.390113 + 0.675695i 0.992464 0.122536i \(-0.0391027\pi\)
−0.602351 + 0.798231i \(0.705769\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 90.0000 + 155.885i 0.279316 + 0.483789i 0.971215 0.238205i \(-0.0765590\pi\)
−0.691899 + 0.721994i \(0.743226\pi\)
\(48\) 0 0
\(49\) 27.0000 46.7654i 0.0787172 0.136342i
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −630.000 −1.63278 −0.816388 0.577503i \(-0.804027\pi\)
−0.816388 + 0.577503i \(0.804027\pi\)
\(54\) 0 0
\(55\) −150.000 −0.367745
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 420.000 727.461i 0.926769 1.60521i 0.138077 0.990422i \(-0.455908\pi\)
0.788692 0.614789i \(-0.210759\pi\)
\(60\) 0 0
\(61\) −299.500 518.749i −0.628640 1.08884i −0.987825 0.155570i \(-0.950279\pi\)
0.359185 0.933266i \(-0.383055\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 152.500 + 264.138i 0.291005 + 0.504035i
\(66\) 0 0
\(67\) −53.5000 + 92.6647i −0.0975532 + 0.168967i −0.910671 0.413132i \(-0.864435\pi\)
0.813118 + 0.582099i \(0.197768\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −210.000 −0.351020 −0.175510 0.984478i \(-0.556157\pi\)
−0.175510 + 0.984478i \(0.556157\pi\)
\(72\) 0 0
\(73\) −421.000 −0.674991 −0.337495 0.941327i \(-0.609580\pi\)
−0.337495 + 0.941327i \(0.609580\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 255.000 441.673i 0.377402 0.653679i
\(78\) 0 0
\(79\) −176.500 305.707i −0.251365 0.435376i 0.712537 0.701634i \(-0.247546\pi\)
−0.963902 + 0.266258i \(0.914213\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 675.000 + 1169.13i 0.892661 + 1.54613i 0.836673 + 0.547703i \(0.184498\pi\)
0.0559884 + 0.998431i \(0.482169\pi\)
\(84\) 0 0
\(85\) 300.000 519.615i 0.382818 0.663061i
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 1020.00 1.21483 0.607415 0.794385i \(-0.292207\pi\)
0.607415 + 0.794385i \(0.292207\pi\)
\(90\) 0 0
\(91\) −1037.00 −1.19458
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 107.500 186.195i 0.116098 0.201087i
\(96\) 0 0
\(97\) 498.500 + 863.427i 0.521804 + 0.903791i 0.999678 + 0.0253630i \(0.00807417\pi\)
−0.477874 + 0.878428i \(0.658592\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 480.000 + 831.384i 0.472889 + 0.819068i 0.999519 0.0310272i \(-0.00987784\pi\)
−0.526630 + 0.850095i \(0.676545\pi\)
\(102\) 0 0
\(103\) −590.500 + 1022.78i −0.564890 + 0.978419i 0.432170 + 0.901792i \(0.357748\pi\)
−0.997060 + 0.0766263i \(0.975585\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 330.000 0.298152 0.149076 0.988826i \(-0.452370\pi\)
0.149076 + 0.988826i \(0.452370\pi\)
\(108\) 0 0
\(109\) 1454.00 1.27769 0.638844 0.769336i \(-0.279413\pi\)
0.638844 + 0.769336i \(0.279413\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −615.000 + 1065.21i −0.511985 + 0.886784i 0.487918 + 0.872889i \(0.337756\pi\)
−0.999903 + 0.0138951i \(0.995577\pi\)
\(114\) 0 0
\(115\) −225.000 389.711i −0.182447 0.316007i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 1020.00 + 1766.69i 0.785742 + 1.36094i
\(120\) 0 0
\(121\) 215.500 373.257i 0.161908 0.280433i
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 125.000 0.0894427
\(126\) 0 0
\(127\) 1280.00 0.894344 0.447172 0.894448i \(-0.352431\pi\)
0.447172 + 0.894448i \(0.352431\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 1110.00 1922.58i 0.740314 1.28226i −0.212038 0.977261i \(-0.568010\pi\)
0.952352 0.305000i \(-0.0986566\pi\)
\(132\) 0 0
\(133\) 365.500 + 633.065i 0.238292 + 0.412734i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 585.000 + 1013.25i 0.364817 + 0.631882i 0.988747 0.149599i \(-0.0477982\pi\)
−0.623930 + 0.781480i \(0.714465\pi\)
\(138\) 0 0
\(139\) 696.500 1206.37i 0.425010 0.736139i −0.571412 0.820664i \(-0.693604\pi\)
0.996421 + 0.0845251i \(0.0269373\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 1830.00 1.07016
\(144\) 0 0
\(145\) −450.000 −0.257727
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −690.000 + 1195.12i −0.379376 + 0.657098i −0.990972 0.134072i \(-0.957195\pi\)
0.611596 + 0.791170i \(0.290528\pi\)
\(150\) 0 0
\(151\) 1329.50 + 2302.76i 0.716511 + 1.24103i 0.962374 + 0.271729i \(0.0875954\pi\)
−0.245863 + 0.969305i \(0.579071\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −20.0000 34.6410i −0.0103641 0.0179512i
\(156\) 0 0
\(157\) −925.000 + 1602.15i −0.470210 + 0.814428i −0.999420 0.0340630i \(-0.989155\pi\)
0.529209 + 0.848491i \(0.322489\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 1530.00 0.748950
\(162\) 0 0
\(163\) 1121.00 0.538672 0.269336 0.963046i \(-0.413196\pi\)
0.269336 + 0.963046i \(0.413196\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −150.000 + 259.808i −0.0695051 + 0.120386i −0.898684 0.438598i \(-0.855475\pi\)
0.829178 + 0.558984i \(0.188809\pi\)
\(168\) 0 0
\(169\) −762.000 1319.82i −0.346837 0.600739i
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 810.000 + 1402.96i 0.355972 + 0.616562i 0.987284 0.158967i \(-0.0508165\pi\)
−0.631312 + 0.775529i \(0.717483\pi\)
\(174\) 0 0
\(175\) −212.500 + 368.061i −0.0917914 + 0.158987i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −630.000 −0.263064 −0.131532 0.991312i \(-0.541990\pi\)
−0.131532 + 0.991312i \(0.541990\pi\)
\(180\) 0 0
\(181\) −2299.00 −0.944107 −0.472053 0.881570i \(-0.656487\pi\)
−0.472053 + 0.881570i \(0.656487\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −792.500 + 1372.65i −0.314950 + 0.545509i
\(186\) 0 0
\(187\) −1800.00 3117.69i −0.703899 1.21919i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −450.000 779.423i −0.170476 0.295273i 0.768111 0.640317i \(-0.221197\pi\)
−0.938586 + 0.345045i \(0.887864\pi\)
\(192\) 0 0
\(193\) −1730.50 + 2997.31i −0.645410 + 1.11788i 0.338797 + 0.940860i \(0.389980\pi\)
−0.984207 + 0.177023i \(0.943353\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 4560.00 1.64917 0.824585 0.565738i \(-0.191409\pi\)
0.824585 + 0.565738i \(0.191409\pi\)
\(198\) 0 0
\(199\) −2077.00 −0.739872 −0.369936 0.929057i \(-0.620620\pi\)
−0.369936 + 0.929057i \(0.620620\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 765.000 1325.02i 0.264495 0.458119i
\(204\) 0 0
\(205\) 75.0000 + 129.904i 0.0255523 + 0.0442579i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −645.000 1117.17i −0.213472 0.369744i
\(210\) 0 0
\(211\) 2010.50 3482.29i 0.655965 1.13616i −0.325686 0.945478i \(-0.605595\pi\)
0.981651 0.190686i \(-0.0610713\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) −1100.00 −0.348927
\(216\) 0 0
\(217\) 136.000 0.0425451
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −3660.00 + 6339.31i −1.11402 + 1.92954i
\(222\) 0 0
\(223\) −40.0000 69.2820i −0.0120117 0.0208048i 0.859957 0.510366i \(-0.170490\pi\)
−0.871969 + 0.489562i \(0.837157\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 1875.00 + 3247.60i 0.548230 + 0.949562i 0.998396 + 0.0566168i \(0.0180313\pi\)
−0.450166 + 0.892945i \(0.648635\pi\)
\(228\) 0 0
\(229\) 617.000 1068.68i 0.178046 0.308385i −0.763165 0.646203i \(-0.776356\pi\)
0.941211 + 0.337819i \(0.109689\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 5880.00 1.65327 0.826634 0.562739i \(-0.190253\pi\)
0.826634 + 0.562739i \(0.190253\pi\)
\(234\) 0 0
\(235\) −900.000 −0.249828
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −2565.00 + 4442.71i −0.694209 + 1.20241i 0.276237 + 0.961090i \(0.410913\pi\)
−0.970446 + 0.241316i \(0.922421\pi\)
\(240\) 0 0
\(241\) 3615.50 + 6262.23i 0.966369 + 1.67380i 0.705892 + 0.708319i \(0.250546\pi\)
0.260476 + 0.965480i \(0.416120\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 135.000 + 233.827i 0.0352034 + 0.0609741i
\(246\) 0 0
\(247\) −1311.50 + 2271.58i −0.337849 + 0.585172i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 7530.00 1.89358 0.946792 0.321847i \(-0.104304\pi\)
0.946792 + 0.321847i \(0.104304\pi\)
\(252\) 0 0
\(253\) −2700.00 −0.670939
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −2280.00 + 3949.08i −0.553395 + 0.958508i 0.444632 + 0.895714i \(0.353335\pi\)
−0.998026 + 0.0627945i \(0.979999\pi\)
\(258\) 0 0
\(259\) −2694.50 4667.01i −0.646440 1.11967i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 1050.00 + 1818.65i 0.246182 + 0.426399i 0.962463 0.271412i \(-0.0874907\pi\)
−0.716282 + 0.697811i \(0.754157\pi\)
\(264\) 0 0
\(265\) 1575.00 2727.98i 0.365100 0.632372i
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 3120.00 0.707174 0.353587 0.935402i \(-0.384962\pi\)
0.353587 + 0.935402i \(0.384962\pi\)
\(270\) 0 0
\(271\) 3449.00 0.773106 0.386553 0.922267i \(-0.373666\pi\)
0.386553 + 0.922267i \(0.373666\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 375.000 649.519i 0.0822304 0.142427i
\(276\) 0 0
\(277\) −1885.00 3264.92i −0.408876 0.708194i 0.585888 0.810392i \(-0.300746\pi\)
−0.994764 + 0.102198i \(0.967413\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 3360.00 + 5819.69i 0.713312 + 1.23549i 0.963607 + 0.267324i \(0.0861393\pi\)
−0.250294 + 0.968170i \(0.580527\pi\)
\(282\) 0 0
\(283\) 50.0000 86.6025i 0.0105024 0.0181908i −0.860726 0.509068i \(-0.829990\pi\)
0.871229 + 0.490877i \(0.163324\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −510.000 −0.104893
\(288\) 0 0
\(289\) 9487.00 1.93100
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −435.000 + 753.442i −0.0867337 + 0.150227i −0.906129 0.423002i \(-0.860976\pi\)
0.819395 + 0.573229i \(0.194310\pi\)
\(294\) 0 0
\(295\) 2100.00 + 3637.31i 0.414463 + 0.717872i
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 2745.00 + 4754.48i 0.530928 + 0.919594i
\(300\) 0 0
\(301\) 1870.00 3238.94i 0.358090 0.620230i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 2995.00 0.562273
\(306\) 0 0
\(307\) 3440.00 0.639515 0.319758 0.947499i \(-0.396399\pi\)
0.319758 + 0.947499i \(0.396399\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 2940.00 5092.23i 0.536052 0.928469i −0.463060 0.886327i \(-0.653249\pi\)
0.999112 0.0421419i \(-0.0134182\pi\)
\(312\) 0 0
\(313\) −920.500 1594.35i −0.166229 0.287917i 0.770862 0.637002i \(-0.219826\pi\)
−0.937091 + 0.349085i \(0.886492\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −1710.00 2961.81i −0.302975 0.524769i 0.673833 0.738884i \(-0.264647\pi\)
−0.976808 + 0.214115i \(0.931313\pi\)
\(318\) 0 0
\(319\) −1350.00 + 2338.27i −0.236945 + 0.410401i
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 5160.00 0.888886
\(324\) 0 0
\(325\) −1525.00 −0.260282
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 1530.00 2650.04i 0.256388 0.444077i
\(330\) 0 0
\(331\) 2820.50 + 4885.25i 0.468365 + 0.811231i 0.999346 0.0361519i \(-0.0115100\pi\)
−0.530982 + 0.847383i \(0.678177\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) −267.500 463.324i −0.0436271 0.0755644i
\(336\) 0 0
\(337\) 528.500 915.389i 0.0854280 0.147966i −0.820146 0.572155i \(-0.806108\pi\)
0.905574 + 0.424189i \(0.139441\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −240.000 −0.0381136
\(342\) 0 0
\(343\) −6749.00 −1.06242
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 645.000 1117.17i 0.0997851 0.172833i −0.811811 0.583921i \(-0.801518\pi\)
0.911596 + 0.411088i \(0.134851\pi\)
\(348\) 0 0
\(349\) −1733.50 3002.51i −0.265880 0.460518i 0.701914 0.712262i \(-0.252329\pi\)
−0.967794 + 0.251744i \(0.918996\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −3870.00 6703.04i −0.583511 1.01067i −0.995059 0.0992825i \(-0.968345\pi\)
0.411548 0.911388i \(-0.364988\pi\)
\(354\) 0 0
\(355\) 525.000 909.327i 0.0784904 0.135949i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 8130.00 1.19522 0.597611 0.801786i \(-0.296117\pi\)
0.597611 + 0.801786i \(0.296117\pi\)
\(360\) 0 0
\(361\) −5010.00 −0.730427
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 1052.50 1822.98i 0.150933 0.261423i
\(366\) 0 0
\(367\) −6056.50 10490.2i −0.861435 1.49205i −0.870544 0.492091i \(-0.836233\pi\)
0.00910851 0.999959i \(-0.497101\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 5355.00 + 9275.13i 0.749374 + 1.29795i
\(372\) 0 0
\(373\) −2174.50 + 3766.34i −0.301853 + 0.522826i −0.976556 0.215264i \(-0.930939\pi\)
0.674702 + 0.738090i \(0.264272\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 5490.00 0.749998
\(378\) 0 0
\(379\) −7663.00 −1.03858 −0.519290 0.854598i \(-0.673804\pi\)
−0.519290 + 0.854598i \(0.673804\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 1980.00 3429.46i 0.264160 0.457539i −0.703183 0.711009i \(-0.748239\pi\)
0.967343 + 0.253470i \(0.0815720\pi\)
\(384\) 0 0
\(385\) 1275.00 + 2208.36i 0.168779 + 0.292334i
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −660.000 1143.15i −0.0860240 0.148998i 0.819803 0.572645i \(-0.194083\pi\)
−0.905827 + 0.423648i \(0.860750\pi\)
\(390\) 0 0
\(391\) 5400.00 9353.07i 0.698439 1.20973i
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 1765.00 0.224827
\(396\) 0 0
\(397\) 14390.0 1.81918 0.909589 0.415510i \(-0.136397\pi\)
0.909589 + 0.415510i \(0.136397\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −4305.00 + 7456.48i −0.536113 + 0.928576i 0.462995 + 0.886361i \(0.346775\pi\)
−0.999109 + 0.0422147i \(0.986559\pi\)
\(402\) 0 0
\(403\) 244.000 + 422.620i 0.0301601 + 0.0522388i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 4755.00 + 8235.90i 0.579107 + 1.00304i
\(408\) 0 0
\(409\) −3548.50 + 6146.18i −0.429003 + 0.743054i −0.996785 0.0801246i \(-0.974468\pi\)
0.567782 + 0.823179i \(0.307802\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) −14280.0 −1.70139
\(414\) 0 0
\(415\) −6750.00 −0.798420
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 4440.00 7690.31i 0.517681 0.896649i −0.482108 0.876112i \(-0.660129\pi\)
0.999789 0.0205376i \(-0.00653779\pi\)
\(420\) 0 0
\(421\) 2739.50 + 4744.95i 0.317138 + 0.549299i 0.979890 0.199540i \(-0.0639449\pi\)
−0.662752 + 0.748839i \(0.730612\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 1500.00 + 2598.08i 0.171202 + 0.296530i
\(426\) 0 0
\(427\) −5091.50 + 8818.74i −0.577037 + 0.999458i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −12510.0 −1.39811 −0.699055 0.715068i \(-0.746396\pi\)
−0.699055 + 0.715068i \(0.746396\pi\)
\(432\) 0 0
\(433\) −6790.00 −0.753595 −0.376797 0.926296i \(-0.622975\pi\)
−0.376797 + 0.926296i \(0.622975\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 1935.00 3351.52i 0.211816 0.366876i
\(438\) 0 0
\(439\) 5588.00 + 9678.70i 0.607519 + 1.05225i 0.991648 + 0.128974i \(0.0411683\pi\)
−0.384129 + 0.923279i \(0.625498\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 6930.00 + 12003.1i 0.743238 + 1.28733i 0.951014 + 0.309149i \(0.100044\pi\)
−0.207776 + 0.978176i \(0.566623\pi\)
\(444\) 0 0
\(445\) −2550.00 + 4416.73i −0.271644 + 0.470501i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −4740.00 −0.498206 −0.249103 0.968477i \(-0.580136\pi\)
−0.249103 + 0.968477i \(0.580136\pi\)
\(450\) 0 0
\(451\) 900.000 0.0939675
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 2592.50 4490.34i 0.267117 0.462660i
\(456\) 0 0
\(457\) 845.000 + 1463.58i 0.0864933 + 0.149811i 0.906027 0.423221i \(-0.139101\pi\)
−0.819533 + 0.573032i \(0.805767\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −7350.00 12730.6i −0.742568 1.28616i −0.951323 0.308197i \(-0.900274\pi\)
0.208755 0.977968i \(-0.433059\pi\)
\(462\) 0 0
\(463\) 165.500 286.654i 0.0166122 0.0287731i −0.857600 0.514318i \(-0.828045\pi\)
0.874212 + 0.485544i \(0.161379\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −8580.00 −0.850182 −0.425091 0.905151i \(-0.639758\pi\)
−0.425091 + 0.905151i \(0.639758\pi\)
\(468\) 0 0
\(469\) 1819.00 0.179091
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −3300.00 + 5715.77i −0.320791 + 0.555626i
\(474\) 0 0
\(475\) 537.500 + 930.977i 0.0519204 + 0.0899288i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 7395.00 + 12808.5i 0.705399 + 1.22179i 0.966547 + 0.256488i \(0.0825655\pi\)
−0.261148 + 0.965299i \(0.584101\pi\)
\(480\) 0 0
\(481\) 9668.50 16746.3i 0.916519 1.58746i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −4985.00 −0.466716
\(486\) 0 0
\(487\) 13097.0 1.21865 0.609324 0.792921i \(-0.291441\pi\)
0.609324 + 0.792921i \(0.291441\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −795.000 + 1376.98i −0.0730710 + 0.126563i −0.900246 0.435382i \(-0.856613\pi\)
0.827175 + 0.561945i \(0.189947\pi\)
\(492\) 0 0
\(493\) −5400.00 9353.07i −0.493314 0.854445i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 1785.00 + 3091.71i 0.161103 + 0.279039i
\(498\) 0 0
\(499\) −8632.00 + 14951.1i −0.774392 + 1.34129i 0.160744 + 0.986996i \(0.448611\pi\)
−0.935136 + 0.354289i \(0.884723\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −14730.0 −1.30572 −0.652861 0.757478i \(-0.726431\pi\)
−0.652861 + 0.757478i \(0.726431\pi\)
\(504\) 0 0
\(505\) −4800.00 −0.422965
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −435.000 + 753.442i −0.0378802 + 0.0656105i −0.884344 0.466836i \(-0.845394\pi\)
0.846464 + 0.532446i \(0.178727\pi\)
\(510\) 0 0
\(511\) 3578.50 + 6198.14i 0.309792 + 0.536575i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −2952.50 5113.88i −0.252627 0.437562i
\(516\) 0 0
\(517\) −2700.00 + 4676.54i −0.229683 + 0.397822i
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −6990.00 −0.587788 −0.293894 0.955838i \(-0.594951\pi\)
−0.293894 + 0.955838i \(0.594951\pi\)
\(522\) 0 0
\(523\) 12119.0 1.01324 0.506622 0.862168i \(-0.330894\pi\)
0.506622 + 0.862168i \(0.330894\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 480.000 831.384i 0.0396758 0.0687204i
\(528\) 0 0
\(529\) 2033.50 + 3522.13i 0.167132 + 0.289482i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) −915.000 1584.83i −0.0743584 0.128793i
\(534\) 0 0
\(535\) −825.000 + 1428.94i −0.0666689 + 0.115474i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 1620.00 0.129459
\(540\) 0 0
\(541\) −21511.0 −1.70948 −0.854741 0.519054i \(-0.826284\pi\)
−0.854741 + 0.519054i \(0.826284\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) −3635.00 + 6296.00i −0.285700 + 0.494846i
\(546\) 0 0
\(547\) 5403.50 + 9359.14i 0.422371 + 0.731568i 0.996171 0.0874274i \(-0.0278646\pi\)
−0.573800 + 0.818996i \(0.694531\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −1935.00 3351.52i −0.149608 0.259128i
\(552\) 0 0
\(553\) −3000.50 + 5197.02i −0.230731 + 0.399638i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −20460.0 −1.55641 −0.778203 0.628013i \(-0.783868\pi\)
−0.778203 + 0.628013i \(0.783868\pi\)
\(558\) 0 0
\(559\) 13420.0 1.01539
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 2490.00 4312.81i 0.186396 0.322847i −0.757650 0.652661i \(-0.773653\pi\)
0.944046 + 0.329814i \(0.106986\pi\)
\(564\) 0 0
\(565\) −3075.00 5326.06i −0.228967 0.396582i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −7920.00 13717.8i −0.583521 1.01069i −0.995058 0.0992955i \(-0.968341\pi\)
0.411537 0.911393i \(-0.364992\pi\)
\(570\) 0 0
\(571\) 12195.5 21123.2i 0.893810 1.54813i 0.0585406 0.998285i \(-0.481355\pi\)
0.835270 0.549840i \(-0.185311\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 2250.00 0.163185
\(576\) 0 0
\(577\) 7673.00 0.553607 0.276803 0.960927i \(-0.410725\pi\)
0.276803 + 0.960927i \(0.410725\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 11475.0 19875.3i 0.819386 1.41922i
\(582\) 0 0
\(583\) −9450.00 16367.9i −0.671319 1.16276i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −9465.00 16393.9i −0.665524 1.15272i −0.979143 0.203172i \(-0.934875\pi\)
0.313619 0.949549i \(-0.398458\pi\)
\(588\) 0 0
\(589\) 172.000 297.913i 0.0120325 0.0208409i
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 14190.0 0.982653 0.491327 0.870975i \(-0.336512\pi\)
0.491327 + 0.870975i \(0.336512\pi\)
\(594\) 0 0
\(595\) −10200.0 −0.702789
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 6435.00 11145.7i 0.438943 0.760272i −0.558665 0.829393i \(-0.688686\pi\)
0.997608 + 0.0691215i \(0.0220196\pi\)
\(600\) 0 0
\(601\) −9799.00 16972.4i −0.665074 1.15194i −0.979265 0.202582i \(-0.935067\pi\)
0.314191 0.949360i \(-0.398267\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 1077.50 + 1866.28i 0.0724076 + 0.125414i
\(606\) 0 0
\(607\) 7581.50 13131.5i 0.506958 0.878077i −0.493009 0.870024i \(-0.664103\pi\)
0.999968 0.00805329i \(-0.00256347\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 10980.0 0.727010
\(612\) 0 0
\(613\) −29599.0 −1.95023 −0.975116 0.221695i \(-0.928841\pi\)
−0.975116 + 0.221695i \(0.928841\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 1245.00 2156.40i 0.0812347 0.140703i −0.822546 0.568699i \(-0.807447\pi\)
0.903781 + 0.427996i \(0.140780\pi\)
\(618\) 0 0
\(619\) −1856.50 3215.55i −0.120548 0.208795i 0.799436 0.600751i \(-0.205132\pi\)
−0.919984 + 0.391956i \(0.871798\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −8670.00 15016.9i −0.557554 0.965712i
\(624\) 0 0
\(625\) −312.500 + 541.266i −0.0200000 + 0.0346410i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −38040.0 −2.41137
\(630\) 0 0
\(631\) 19409.0 1.22450 0.612250 0.790664i \(-0.290264\pi\)
0.612250 + 0.790664i \(0.290264\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −3200.00 + 5542.56i −0.199981 + 0.346378i
\(636\) 0 0
\(637\) −1647.00 2852.69i −0.102444 0.177437i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −3240.00 5611.84i −0.199645 0.345795i 0.748768 0.662832i \(-0.230645\pi\)
−0.948413 + 0.317037i \(0.897312\pi\)
\(642\) 0 0
\(643\) −15130.0 + 26205.9i −0.927945 + 1.60725i −0.141191 + 0.989982i \(0.545093\pi\)
−0.786754 + 0.617266i \(0.788240\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 21510.0 1.30703 0.653513 0.756916i \(-0.273295\pi\)
0.653513 + 0.756916i \(0.273295\pi\)
\(648\) 0 0
\(649\) 25200.0 1.52417
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 270.000 467.654i 0.0161806 0.0280256i −0.857822 0.513947i \(-0.828183\pi\)
0.874002 + 0.485922i \(0.161516\pi\)
\(654\) 0 0
\(655\) 5550.00 + 9612.88i 0.331079 + 0.573445i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) −14640.0 25357.2i −0.865392 1.49890i −0.866657 0.498904i \(-0.833736\pi\)
0.00126511 0.999999i \(-0.499597\pi\)
\(660\) 0 0
\(661\) 10884.5 18852.5i 0.640481 1.10935i −0.344844 0.938660i \(-0.612068\pi\)
0.985325 0.170686i \(-0.0545983\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −3655.00 −0.213135
\(666\) 0 0
\(667\) −8100.00 −0.470215
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 8985.00 15562.5i 0.516933 0.895354i
\(672\) 0 0
\(673\) 7275.50 + 12601.5i 0.416716 + 0.721773i 0.995607 0.0936316i \(-0.0298476\pi\)
−0.578891 + 0.815405i \(0.696514\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 750.000 + 1299.04i 0.0425773 + 0.0737461i 0.886529 0.462674i \(-0.153110\pi\)
−0.843951 + 0.536420i \(0.819776\pi\)
\(678\) 0 0
\(679\) 8474.50 14678.3i 0.478971 0.829602i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 16530.0 0.926066 0.463033 0.886341i \(-0.346761\pi\)
0.463033 + 0.886341i \(0.346761\pi\)
\(684\) 0 0
\(685\) −5850.00 −0.326302
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) −19215.0 + 33281.4i −1.06246 + 1.84023i
\(690\) 0 0
\(691\) 12986.0 + 22492.4i 0.714921 + 1.23828i 0.962990 + 0.269538i \(0.0868709\pi\)
−0.248068 + 0.968743i \(0.579796\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 3482.50 + 6031.87i 0.190070 + 0.329211i
\(696\) 0 0
\(697\) −1800.00 + 3117.69i −0.0978190 + 0.169428i
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) −10230.0 −0.551187 −0.275593 0.961274i \(-0.588874\pi\)
−0.275593 + 0.961274i \(0.588874\pi\)
\(702\) 0 0
\(703\) −13631.0 −0.731299
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 8160.00 14133.5i 0.434071 0.751833i
\(708\) 0 0
\(709\) 7311.50 + 12663.9i 0.387291 + 0.670807i 0.992084 0.125575i \(-0.0400776\pi\)
−0.604793 + 0.796382i \(0.706744\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −360.000 623.538i −0.0189090 0.0327513i
\(714\) 0 0
\(715\) −4575.00 + 7924.13i −0.239294 + 0.414470i
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 6690.00 0.347003 0.173501 0.984834i \(-0.444492\pi\)
0.173501 + 0.984834i \(0.444492\pi\)
\(720\) 0 0
\(721\) 20077.0 1.03704
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 1125.00 1948.56i 0.0576296 0.0998174i
\(726\) 0 0
\(727\) −5860.00 10149.8i −0.298948 0.517794i 0.676947 0.736031i \(-0.263302\pi\)
−0.975896 + 0.218238i \(0.929969\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −13200.0 22863.1i −0.667879 1.15680i
\(732\) 0 0
\(733\) 2375.00 4113.62i 0.119676 0.207285i −0.799963 0.600049i \(-0.795148\pi\)
0.919639 + 0.392764i \(0.128481\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −3210.00 −0.160437
\(738\) 0 0
\(739\) −30724.0 −1.52936 −0.764682 0.644407i \(-0.777104\pi\)
−0.764682 + 0.644407i \(0.777104\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −480.000 + 831.384i −0.0237005 + 0.0410505i −0.877632 0.479334i \(-0.840878\pi\)
0.853932 + 0.520385i \(0.174211\pi\)
\(744\) 0 0
\(745\) −3450.00 5975.58i −0.169662 0.293863i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −2805.00 4858.40i −0.136839 0.237012i
\(750\) 0 0
\(751\) −11390.5 + 19728.9i −0.553456 + 0.958613i 0.444566 + 0.895746i \(0.353358\pi\)
−0.998022 + 0.0628674i \(0.979975\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) −13295.0 −0.640867
\(756\) 0 0
\(757\) 32387.0 1.55499 0.777494 0.628891i \(-0.216491\pi\)
0.777494 + 0.628891i \(0.216491\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −12645.0 + 21901.8i −0.602340 + 1.04328i 0.390126 + 0.920762i \(0.372432\pi\)
−0.992466 + 0.122522i \(0.960902\pi\)
\(762\) 0 0
\(763\) −12359.0 21406.4i −0.586403 1.01568i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −25620.0 44375.1i −1.20611 2.08904i
\(768\) 0 0
\(769\) −8141.50 + 14101.5i −0.381782 + 0.661265i −0.991317 0.131494i \(-0.958023\pi\)
0.609535 + 0.792759i \(0.291356\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −31050.0 −1.44475 −0.722374 0.691502i \(-0.756949\pi\)
−0.722374 + 0.691502i \(0.756949\pi\)
\(774\) 0 0
\(775\) 200.000 0.00926995
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −645.000 + 1117.17i −0.0296656 + 0.0513824i
\(780\) 0 0
\(781\) −3150.00 5455.96i −0.144322 0.249974i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) −4625.00 8010.73i −0.210284 0.364223i
\(786\) 0 0
\(787\) 2526.50 4376.03i 0.114435 0.198206i −0.803119 0.595819i \(-0.796828\pi\)
0.917554 + 0.397612i \(0.130161\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 20910.0 0.939917
\(792\) 0 0
\(793\) −36539.0 −1.63624
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −21840.0 + 37828.0i −0.970656 + 1.68122i −0.277071 + 0.960849i \(0.589364\pi\)
−0.693584 + 0.720375i \(0.743970\pi\)