Properties

Label 1620.4.i.b.541.1
Level $1620$
Weight $4$
Character 1620.541
Analytic conductor $95.583$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

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 541.1
Root \(0.500000 + 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 1620.541
Dual form 1620.4.i.b.1081.1

$q$-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 \(\left(\mathbb{Z}/1620\mathbb{Z}\right)^\times\).

\(n\) \(811\) \(1297\) \(1541\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{2}{3}\right)\)

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 −0.998906 0.0467610i \(-0.985110\pi\)
0.539949 + 0.841698i \(0.318443\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 15.0000 25.9808i 0.411152 0.712136i −0.583864 0.811851i \(-0.698460\pi\)
0.995016 + 0.0997155i \(0.0317933\pi\)
\(12\) 0 0
\(13\) 30.5000 + 52.8275i 0.650706 + 1.12706i 0.982952 + 0.183863i \(0.0588603\pi\)
−0.332246 + 0.943193i \(0.607806\pi\)
\(14\) 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 0.586698 0.809806i \(-0.300427\pi\)
−0.994661 + 0.103193i \(0.967094\pi\)
\(24\) 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 −0.685220 0.728336i \(-0.740294\pi\)
0.973368 + 0.229250i \(0.0736272\pi\)
\(30\) 0 0
\(31\) −4.00000 6.92820i −0.0231749 0.0401401i 0.854205 0.519936i \(-0.174044\pi\)
−0.877380 + 0.479796i \(0.840711\pi\)
\(32\) 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 0.893179 0.449701i \(-0.148470\pi\)
−0.836042 + 0.548665i \(0.815136\pi\)
\(42\) 0 0
\(43\) 110.000 190.526i 0.390113 0.675695i −0.602351 0.798231i \(-0.705769\pi\)
0.992464 + 0.122536i \(0.0391027\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 90.0000 155.885i 0.279316 0.483789i −0.691899 0.721994i \(-0.743226\pi\)
0.971215 + 0.238205i \(0.0765590\pi\)
\(48\) 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 0.788692 + 0.614789i \(0.210759\pi\)
0.138077 + 0.990422i \(0.455908\pi\)
\(60\) 0 0
\(61\) −299.500 + 518.749i −0.628640 + 1.08884i 0.359185 + 0.933266i \(0.383055\pi\)
−0.987825 + 0.155570i \(0.950279\pi\)
\(62\) 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 0.813118 0.582099i \(-0.197768\pi\)
−0.910671 + 0.413132i \(0.864435\pi\)
\(68\) 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 −0.963902 0.266258i \(-0.914213\pi\)
0.712537 + 0.701634i \(0.247546\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 675.000 1169.13i 0.892661 1.54613i 0.0559884 0.998431i \(-0.482169\pi\)
0.836673 0.547703i \(-0.184498\pi\)
\(84\) 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 −0.477874 0.878428i \(-0.658592\pi\)
0.999678 0.0253630i \(-0.00807417\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 480.000 831.384i 0.472889 0.819068i −0.526630 0.850095i \(-0.676545\pi\)
0.999519 + 0.0310272i \(0.00987784\pi\)
\(102\) 0 0
\(103\) −590.500 1022.78i −0.564890 0.978419i −0.997060 0.0766263i \(-0.975585\pi\)
0.432170 0.901792i \(-0.357748\pi\)
\(104\) 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 −0.999903 0.0138951i \(-0.995577\pi\)
0.487918 0.872889i \(-0.337756\pi\)
\(114\) 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 0.952352 + 0.305000i \(0.0986566\pi\)
−0.212038 + 0.977261i \(0.568010\pi\)
\(132\) 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 −0.623930 0.781480i \(-0.714465\pi\)
0.988747 + 0.149599i \(0.0477982\pi\)
\(138\) 0 0
\(139\) 696.500 + 1206.37i 0.425010 + 0.736139i 0.996421 0.0845251i \(-0.0269373\pi\)
−0.571412 + 0.820664i \(0.693604\pi\)
\(140\) 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 0.611596 0.791170i \(-0.290528\pi\)
−0.990972 + 0.134072i \(0.957195\pi\)
\(150\) 0 0
\(151\) 1329.50 2302.76i 0.716511 1.24103i −0.245863 0.969305i \(-0.579071\pi\)
0.962374 0.271729i \(-0.0875954\pi\)
\(152\) 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 0.529209 0.848491i \(-0.322489\pi\)
−0.999420 + 0.0340630i \(0.989155\pi\)
\(158\) 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 0.829178 0.558984i \(-0.188809\pi\)
−0.898684 + 0.438598i \(0.855475\pi\)
\(168\) 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 −0.631312 0.775529i \(-0.717483\pi\)
0.987284 + 0.158967i \(0.0508165\pi\)
\(174\) 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 −0.938586 0.345045i \(-0.887864\pi\)
0.768111 + 0.640317i \(0.221197\pi\)
\(192\) 0 0
\(193\) −1730.50 2997.31i −0.645410 1.11788i −0.984207 0.177023i \(-0.943353\pi\)
0.338797 0.940860i \(-0.389980\pi\)
\(194\) 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 0.981651 + 0.190686i \(0.0610713\pi\)
−0.325686 + 0.945478i \(0.605595\pi\)
\(212\) 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 −0.871969 0.489562i \(-0.837157\pi\)
0.859957 + 0.510366i \(0.170490\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 1875.00 3247.60i 0.548230 0.949562i −0.450166 0.892945i \(-0.648635\pi\)
0.998396 0.0566168i \(-0.0180313\pi\)
\(228\) 0 0
\(229\) 617.000 + 1068.68i 0.178046 + 0.308385i 0.941211 0.337819i \(-0.109689\pi\)
−0.763165 + 0.646203i \(0.776356\pi\)
\(230\) 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 −0.970446 0.241316i \(-0.922421\pi\)
0.276237 0.961090i \(-0.410913\pi\)
\(240\) 0 0
\(241\) 3615.50 6262.23i 0.966369 1.67380i 0.260476 0.965480i \(-0.416120\pi\)
0.705892 0.708319i \(-0.250546\pi\)
\(242\) 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 −0.998026 0.0627945i \(-0.979999\pi\)
0.444632 0.895714i \(-0.353335\pi\)
\(258\) 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 −0.716282 0.697811i \(-0.754157\pi\)
0.962463 + 0.271412i \(0.0874907\pi\)
\(264\) 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 −0.994764 0.102198i \(-0.967413\pi\)
0.585888 + 0.810392i \(0.300746\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 3360.00 5819.69i 0.713312 1.23549i −0.250294 0.968170i \(-0.580527\pi\)
0.963607 0.267324i \(-0.0861393\pi\)
\(282\) 0 0
\(283\) 50.0000 + 86.6025i 0.0105024 + 0.0181908i 0.871229 0.490877i \(-0.163324\pi\)
−0.860726 + 0.509068i \(0.829990\pi\)
\(284\) 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 0.819395 0.573229i \(-0.194310\pi\)
−0.906129 + 0.423002i \(0.860976\pi\)
\(294\) 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 0.999112 + 0.0421419i \(0.0134182\pi\)
−0.463060 + 0.886327i \(0.653249\pi\)
\(312\) 0 0
\(313\) −920.500 + 1594.35i −0.166229 + 0.287917i −0.937091 0.349085i \(-0.886492\pi\)
0.770862 + 0.637002i \(0.219826\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −1710.00 + 2961.81i −0.302975 + 0.524769i −0.976808 0.214115i \(-0.931313\pi\)
0.673833 + 0.738884i \(0.264647\pi\)
\(318\) 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 −0.530982 0.847383i \(-0.678177\pi\)
0.999346 + 0.0361519i \(0.0115100\pi\)
\(332\) 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 0.905574 0.424189i \(-0.139441\pi\)
−0.820146 + 0.572155i \(0.806108\pi\)
\(338\) 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 0.911596 0.411088i \(-0.134851\pi\)
−0.811811 + 0.583921i \(0.801518\pi\)
\(348\) 0 0
\(349\) −1733.50 + 3002.51i −0.265880 + 0.460518i −0.967794 0.251744i \(-0.918996\pi\)
0.701914 + 0.712262i \(0.252329\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −3870.00 + 6703.04i −0.583511 + 1.01067i 0.411548 + 0.911388i \(0.364988\pi\)
−0.995059 + 0.0992825i \(0.968345\pi\)
\(354\) 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 0.00910851 + 0.999959i \(0.497101\pi\)
−0.870544 + 0.492091i \(0.836233\pi\)
\(368\) 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 0.674702 0.738090i \(-0.264272\pi\)
−0.976556 + 0.215264i \(0.930939\pi\)
\(374\) 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 0.967343 0.253470i \(-0.0815720\pi\)
−0.703183 + 0.711009i \(0.748239\pi\)
\(384\) 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 −0.905827 0.423648i \(-0.860750\pi\)
0.819803 + 0.572645i \(0.194083\pi\)
\(390\) 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 −0.999109 0.0422147i \(-0.986559\pi\)
0.462995 0.886361i \(-0.346775\pi\)
\(402\) 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 0.567782 0.823179i \(-0.307802\pi\)
−0.996785 + 0.0801246i \(0.974468\pi\)
\(410\) 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 0.999789 + 0.0205376i \(0.00653779\pi\)
−0.482108 + 0.876112i \(0.660129\pi\)
\(420\) 0 0
\(421\) 2739.50 4744.95i 0.317138 0.549299i −0.662752 0.748839i \(-0.730612\pi\)
0.979890 + 0.199540i \(0.0639449\pi\)
\(422\) 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 −0.384129 0.923279i \(-0.625498\pi\)
0.991648 0.128974i \(-0.0411683\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 6930.00 12003.1i 0.743238 1.28733i −0.207776 0.978176i \(-0.566623\pi\)
0.951014 0.309149i \(-0.100044\pi\)
\(444\) 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 −0.819533 0.573032i \(-0.805767\pi\)
0.906027 + 0.423221i \(0.139101\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −7350.00 + 12730.6i −0.742568 + 1.28616i 0.208755 + 0.977968i \(0.433059\pi\)
−0.951323 + 0.308197i \(0.900274\pi\)
\(462\) 0 0
\(463\) 165.500 + 286.654i 0.0166122 + 0.0287731i 0.874212 0.485544i \(-0.161379\pi\)
−0.857600 + 0.514318i \(0.828045\pi\)
\(464\) 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 −0.261148 0.965299i \(-0.584101\pi\)
0.966547 0.256488i \(-0.0825655\pi\)
\(480\) 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 0.827175 0.561945i \(-0.189947\pi\)
−0.900246 + 0.435382i \(0.856613\pi\)
\(492\) 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 −0.935136 0.354289i \(-0.884723\pi\)
0.160744 0.986996i \(-0.448611\pi\)
\(500\) 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 0.846464 0.532446i \(-0.178727\pi\)
−0.884344 + 0.466836i \(0.845394\pi\)
\(510\) 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 −0.573800 0.818996i \(-0.694531\pi\)
0.996171 + 0.0874274i \(0.0278646\pi\)
\(548\) 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 0.944046 0.329814i \(-0.106986\pi\)
−0.757650 + 0.652661i \(0.773653\pi\)
\(564\) 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 0.411537 + 0.911393i \(0.364992\pi\)
−0.995058 + 0.0992955i \(0.968341\pi\)
\(570\) 0 0
\(571\) 12195.5 + 21123.2i 0.893810 + 1.54813i 0.835270 + 0.549840i \(0.185311\pi\)
0.0585406 + 0.998285i \(0.481355\pi\)
\(572\) 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 0.313619 + 0.949549i \(0.398458\pi\)
−0.979143 + 0.203172i \(0.934875\pi\)
\(588\) 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 0.997608 0.0691215i \(-0.0220196\pi\)
−0.558665 + 0.829393i \(0.688686\pi\)
\(600\) 0 0
\(601\) −9799.00 + 16972.4i −0.665074 + 1.15194i 0.314191 + 0.949360i \(0.398267\pi\)
−0.979265 + 0.202582i \(0.935067\pi\)
\(602\) 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 0.999968 + 0.00805329i \(0.00256347\pi\)
−0.493009 + 0.870024i \(0.664103\pi\)
\(608\) 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 0.903781 0.427996i \(-0.140780\pi\)
−0.822546 + 0.568699i \(0.807447\pi\)
\(618\) 0 0
\(619\) −1856.50 + 3215.55i −0.120548 + 0.208795i −0.919984 0.391956i \(-0.871798\pi\)
0.799436 + 0.600751i \(0.205132\pi\)
\(620\) 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 −0.948413 0.317037i \(-0.897312\pi\)
0.748768 + 0.662832i \(0.230645\pi\)
\(642\) 0 0
\(643\) −15130.0 26205.9i −0.927945 1.60725i −0.786754 0.617266i \(-0.788240\pi\)
−0.141191 0.989982i \(-0.545093\pi\)
\(644\) 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 0.874002 0.485922i \(-0.161516\pi\)
−0.857822 + 0.513947i \(0.828183\pi\)
\(654\) 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 0.00126511 + 0.999999i \(0.499597\pi\)
−0.866657 + 0.498904i \(0.833736\pi\)
\(660\) 0 0
\(661\) 10884.5 + 18852.5i 0.640481 + 1.10935i 0.985325 + 0.170686i \(0.0545983\pi\)
−0.344844 + 0.938660i \(0.612068\pi\)
\(662\) 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 −0.578891 0.815405i \(-0.696514\pi\)
0.995607 + 0.0936316i \(0.0298476\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 750.000 1299.04i 0.0425773 0.0737461i −0.843951 0.536420i \(-0.819776\pi\)
0.886529 + 0.462674i \(0.153110\pi\)
\(678\) 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 −0.248068 0.968743i \(-0.579796\pi\)
0.962990 0.269538i \(-0.0868709\pi\)
\(692\) 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 −0.604793 0.796382i \(-0.706744\pi\)
0.992084 + 0.125575i \(0.0400776\pi\)
\(710\) 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 −0.975896 0.218238i \(-0.929969\pi\)
0.676947 + 0.736031i \(0.263302\pi\)
\(728\) 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 0.919639 0.392764i \(-0.128481\pi\)
−0.799963 + 0.600049i \(0.795148\pi\)
\(734\) 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 0.853932 0.520385i \(-0.174211\pi\)
−0.877632 + 0.479334i \(0.840878\pi\)
\(744\) 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 −0.998022 0.0628674i \(-0.979975\pi\)
0.444566 0.895746i \(-0.353358\pi\)
\(752\) 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 −0.992466 0.122522i \(-0.960902\pi\)
0.390126 0.920762i \(-0.372432\pi\)
\(762\) 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 0.609535 0.792759i \(-0.291356\pi\)
−0.991317 + 0.131494i \(0.958023\pi\)
\(770\) 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 0.917554 0.397612i \(-0.130161\pi\)
−0.803119 + 0.595819i \(0.796828\pi\)
\(788\) 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 −0.693584 0.720375i \(-0.743970\pi\)
−0.277071 0.960849i \(-0.589364\pi\)