Newspace parameters
Level: | \( N \) | \(=\) | \( 1152 = 2^{7} \cdot 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1152.w (of order \(8\), degree \(4\), not minimal) |
Newform invariants
Self dual: | no |
Analytic conductor: | \(9.19876631285\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{8})\) |
Twist minimal: | no (minimal twist has level 288) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{8}]$ |
Embedding invariants
Embedding label | 143.2 | ||
Character | \(\chi\) | \(=\) | 1152.143 |
Dual form | 1152.2.w.b.1007.2 |
$q$-expansion
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1152\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(641\) | \(901\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(e\left(\frac{1}{8}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.12344 | + | 2.71222i | −0.502418 | + | 1.21294i | 0.445745 | + | 0.895160i | \(0.352939\pi\) |
−0.948163 | + | 0.317784i | \(0.897061\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −3.03150 | + | 3.03150i | −1.14580 | + | 1.14580i | −0.158430 | + | 0.987370i | \(0.550643\pi\) |
−0.987370 | + | 0.158430i | \(0.949357\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.616847 | + | 1.48920i | −0.185986 | + | 0.449011i | −0.989180 | − | 0.146707i | \(-0.953132\pi\) |
0.803194 | + | 0.595718i | \(0.203132\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.35133 | − | 1.38816i | 0.929490 | − | 0.385008i | 0.134005 | − | 0.990981i | \(-0.457216\pi\) |
0.795485 | + | 0.605973i | \(0.207216\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 4.76709 | 1.15619 | 0.578094 | − | 0.815970i | \(-0.303797\pi\) | ||||
0.578094 | + | 0.815970i | \(0.303797\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.13264 | − | 2.73444i | −0.259846 | − | 0.627323i | 0.739082 | − | 0.673615i | \(-0.235259\pi\) |
−0.998928 | + | 0.0462921i | \(0.985259\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −4.11192 | + | 4.11192i | −0.857395 | + | 0.857395i | −0.991031 | − | 0.133636i | \(-0.957335\pi\) |
0.133636 | + | 0.991031i | \(0.457335\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.55851 | − | 2.55851i | −0.511702 | − | 0.511702i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −8.16664 | + | 3.38273i | −1.51651 | + | 0.628158i | −0.976888 | − | 0.213751i | \(-0.931432\pi\) |
−0.539620 | + | 0.841909i | \(0.681432\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 6.16305i | − | 1.10692i | −0.832877 | − | 0.553458i | \(-0.813308\pi\) | ||
0.832877 | − | 0.553458i | \(-0.186692\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −4.81640 | − | 11.6278i | −0.814121 | − | 1.96546i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −9.38963 | − | 3.88931i | −1.54365 | − | 0.639399i | −0.561493 | − | 0.827482i | \(-0.689773\pi\) |
−0.982153 | + | 0.188083i | \(0.939773\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −0.169917 | − | 0.169917i | −0.0265365 | − | 0.0265365i | 0.693714 | − | 0.720251i | \(-0.255973\pi\) |
−0.720251 | + | 0.693714i | \(0.755973\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −7.57687 | − | 3.13844i | −1.15546 | − | 0.478608i | −0.279100 | − | 0.960262i | \(-0.590036\pi\) |
−0.876361 | + | 0.481654i | \(0.840036\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 2.44049i | 0.355981i | 0.984032 | + | 0.177991i | \(0.0569597\pi\) | ||||
−0.984032 | + | 0.177991i | \(0.943040\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | − | 11.3800i | − | 1.62572i | ||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 1.99073 | + | 0.824586i | 0.273447 | + | 0.113266i | 0.515193 | − | 0.857074i | \(-0.327720\pi\) |
−0.241746 | + | 0.970340i | \(0.577720\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −3.34605 | − | 3.34605i | −0.451182 | − | 0.451182i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −1.21488 | − | 0.503218i | −0.158163 | − | 0.0655134i | 0.302197 | − | 0.953245i | \(-0.402280\pi\) |
−0.460361 | + | 0.887732i | \(0.652280\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.04489 | + | 2.52258i | 0.133784 | + | 0.322983i | 0.976548 | − | 0.215300i | \(-0.0690731\pi\) |
−0.842764 | + | 0.538283i | \(0.819073\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 10.6491i | 1.32085i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −3.91551 | + | 1.62186i | −0.478355 | + | 0.198141i | −0.608815 | − | 0.793312i | \(-0.708355\pi\) |
0.130459 | + | 0.991454i | \(0.458355\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 5.28919 | + | 5.28919i | 0.627711 | + | 0.627711i | 0.947492 | − | 0.319781i | \(-0.103609\pi\) |
−0.319781 | + | 0.947492i | \(0.603609\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −1.57482 | + | 1.57482i | −0.184319 | + | 0.184319i | −0.793235 | − | 0.608916i | \(-0.791605\pi\) |
0.608916 | + | 0.793235i | \(0.291605\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −2.64454 | − | 6.38449i | −0.301373 | − | 0.727580i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 13.7711 | 1.54937 | 0.774684 | − | 0.632348i | \(-0.217909\pi\) | ||||
0.774684 | + | 0.632348i | \(0.217909\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −3.31934 | + | 1.37492i | −0.364345 | + | 0.150917i | −0.557343 | − | 0.830282i | \(-0.688179\pi\) |
0.192997 | + | 0.981199i | \(0.438179\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −5.35554 | + | 12.9294i | −0.580890 | + | 1.40239i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 6.99010 | − | 6.99010i | 0.740949 | − | 0.740949i | −0.231811 | − | 0.972761i | \(-0.574465\pi\) |
0.972761 | + | 0.231811i | \(0.0744652\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −5.95133 | + | 14.3678i | −0.623869 | + | 1.50615i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 8.68886 | 0.891459 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −13.5584 | −1.37665 | −0.688323 | − | 0.725404i | \(-0.741653\pi\) | ||||
−0.688323 | + | 0.725404i | \(0.741653\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1.10479 | + | 2.66720i | −0.109931 | + | 0.265396i | −0.969265 | − | 0.246018i | \(-0.920878\pi\) |
0.859335 | + | 0.511413i | \(0.170878\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 12.8009 | − | 12.8009i | 1.26131 | − | 1.26131i | 0.310851 | − | 0.950459i | \(-0.399386\pi\) |
0.950459 | − | 0.310851i | \(-0.100614\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 0.720677 | − | 1.73987i | 0.0696704 | − | 0.168199i | −0.885209 | − | 0.465194i | \(-0.845984\pi\) |
0.954879 | + | 0.296995i | \(0.0959845\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 4.45017 | − | 1.84332i | 0.426249 | − | 0.176558i | −0.159238 | − | 0.987240i | \(-0.550904\pi\) |
0.585486 | + | 0.810682i | \(0.300904\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −13.6612 | −1.28514 | −0.642568 | − | 0.766229i | \(-0.722131\pi\) | ||||
−0.642568 | + | 0.766229i | \(0.722131\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −6.53296 | − | 15.7720i | −0.609201 | − | 1.47074i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −14.4514 | + | 14.4514i | −1.32476 | + | 1.32476i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5.94096 | + | 5.94096i | 0.540087 | + | 0.540087i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −3.74754 | + | 1.55228i | −0.335190 | + | 0.138840i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 13.2014i | 1.17143i | 0.810515 | + | 0.585717i | \(0.199187\pi\) | ||||
−0.810515 | + | 0.585717i | \(0.800813\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2.56553 | + | 6.19375i | 0.224152 | + | 0.541150i | 0.995446 | − | 0.0953287i | \(-0.0303902\pi\) |
−0.771294 | + | 0.636479i | \(0.780390\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 11.7231 | + | 4.85585i | 1.01652 | + | 0.421056i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 9.77333 | + | 9.77333i | 0.834992 | + | 0.834992i | 0.988195 | − | 0.153203i | \(-0.0489587\pi\) |
−0.153203 | + | 0.988195i | \(0.548959\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 8.26616 | + | 3.42396i | 0.701127 | + | 0.290416i | 0.704627 | − | 0.709578i | \(-0.251114\pi\) |
−0.00350050 | + | 0.999994i | \(0.501114\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 5.84708i | 0.488957i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 25.9501i | − | 2.15504i | ||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −18.9803 | − | 7.86190i | −1.55493 | − | 0.644072i | −0.570729 | − | 0.821139i | \(-0.693339\pi\) |
−0.984199 | + | 0.177066i | \(0.943339\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −7.83326 | − | 7.83326i | −0.637462 | − | 0.637462i | 0.312467 | − | 0.949929i | \(-0.398845\pi\) |
−0.949929 | + | 0.312467i | \(0.898845\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 16.7156 | + | 6.92381i | 1.34263 | + | 0.556134i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 3.58014 | + | 8.64323i | 0.285727 | + | 0.689805i | 0.999949 | − | 0.0101140i | \(-0.00321944\pi\) |
−0.714222 | + | 0.699919i | \(0.753219\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 24.9306i | − | 1.96481i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 4.73693 | − | 1.96210i | 0.371025 | − | 0.153684i | −0.189377 | − | 0.981904i | \(-0.560647\pi\) |
0.560402 | + | 0.828221i | \(0.310647\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 4.55199 | + | 4.55199i | 0.352244 | + | 0.352244i | 0.860944 | − | 0.508700i | \(-0.169874\pi\) |
−0.508700 | + | 0.860944i | \(0.669874\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0.111994 | − | 0.111994i | 0.00861490 | − | 0.00861490i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −4.28444 | − | 10.3436i | −0.325740 | − | 0.786406i | −0.998899 | − | 0.0469083i | \(-0.985063\pi\) |
0.673159 | − | 0.739498i | \(-0.264937\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 15.5123 | 1.17262 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −10.2246 | + | 4.23519i | −0.764226 | + | 0.316553i | −0.730531 | − | 0.682880i | \(-0.760727\pi\) |
−0.0336946 | + | 0.999432i | \(0.510727\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1.33358 | + | 3.21956i | −0.0991246 | + | 0.239308i | −0.965661 | − | 0.259806i | \(-0.916341\pi\) |
0.866536 | + | 0.499114i | \(0.166341\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 21.0974 | − | 21.0974i | 1.55111 | − | 1.55111i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −2.94056 | + | 7.09915i | −0.215035 | + | 0.519141i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −4.82446 | −0.349085 | −0.174543 | − | 0.984650i | \(-0.555845\pi\) | ||||
−0.174543 | + | 0.984650i | \(0.555845\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 0.222878 | 0.0160431 | 0.00802155 | − | 0.999968i | \(-0.497447\pi\) | ||||
0.00802155 | + | 0.999968i | \(0.497447\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −9.44160 | + | 22.7940i | −0.672686 | + | 1.62401i | 0.104341 | + | 0.994542i | \(0.466727\pi\) |
−0.777028 | + | 0.629467i | \(0.783273\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −14.8710 | + | 14.8710i | −1.05418 | + | 1.05418i | −0.0557310 | + | 0.998446i | \(0.517749\pi\) |
−0.998446 | + | 0.0557310i | \(0.982251\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 14.5024 | − | 35.0120i | 1.01787 | − | 2.45736i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0.651743 | − | 0.269961i | 0.0455197 | − | 0.0188549i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 4.77079 | 0.330003 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 0.644000 | + | 1.55475i | 0.0443348 | + | 0.107034i | 0.944496 | − | 0.328524i | \(-0.106551\pi\) |
−0.900161 | + | 0.435558i | \(0.856551\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 17.0243 | − | 17.0243i | 1.16105 | − | 1.16105i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 18.6833 | + | 18.6833i | 1.26830 | + | 1.26830i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 15.9761 | − | 6.61750i | 1.07467 | − | 0.445141i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 23.4280i | 1.56885i | 0.620221 | + | 0.784427i | \(0.287043\pi\) | ||||
−0.620221 | + | 0.784427i | \(0.712957\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −5.10690 | − | 12.3292i | −0.338957 | − | 0.818315i | −0.997816 | − | 0.0660486i | \(-0.978961\pi\) |
0.658859 | − | 0.752266i | \(-0.271039\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −7.82666 | − | 3.24191i | −0.517200 | − | 0.214231i | 0.108786 | − | 0.994065i | \(-0.465304\pi\) |
−0.625987 | + | 0.779834i | \(0.715304\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 9.66805 | + | 9.66805i | 0.633375 | + | 0.633375i | 0.948913 | − | 0.315538i | \(-0.102185\pi\) |
−0.315538 | + | 0.948913i | \(0.602185\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −6.61915 | − | 2.74174i | −0.431785 | − | 0.178851i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 25.8579i | − | 1.67261i | −0.548268 | − | 0.836303i | \(-0.684713\pi\) | ||
0.548268 | − | 0.836303i | \(-0.315287\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 24.9358i | 1.60626i | 0.595805 | + | 0.803129i | \(0.296833\pi\) | ||||
−0.595805 | + | 0.803129i | \(0.703167\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 30.8652 | + | 12.7848i | 1.97190 | + | 0.816789i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −7.59170 | − | 7.59170i | −0.483048 | − | 0.483048i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −11.5486 | − | 4.78358i | −0.728939 | − | 0.301937i | −0.0128233 | − | 0.999918i | \(-0.504082\pi\) |
−0.716116 | + | 0.697981i | \(0.754082\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −3.58705 | − | 8.65990i | −0.225516 | − | 0.544443i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 17.0780i | 1.06530i | 0.846337 | + | 0.532648i | \(0.178803\pi\) | ||||
−0.846337 | + | 0.532648i | \(0.821197\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 40.2552 | − | 16.6742i | 2.50133 | − | 1.03609i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 10.4595 | + | 10.4595i | 0.644963 | + | 0.644963i | 0.951771 | − | 0.306809i | \(-0.0992612\pi\) |
−0.306809 | + | 0.951771i | \(0.599261\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −4.47292 | + | 4.47292i | −0.274770 | + | 0.274770i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −3.47587 | − | 8.39150i | −0.211928 | − | 0.511639i | 0.781792 | − | 0.623540i | \(-0.214306\pi\) |
−0.993719 | + | 0.111901i | \(0.964306\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 5.66173 | 0.343925 | 0.171963 | − | 0.985103i | \(-0.444989\pi\) | ||||
0.171963 | + | 0.985103i | \(0.444989\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 5.38834 | − | 2.23192i | 0.324929 | − | 0.134590i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −5.27625 | + | 12.7380i | −0.317019 | + | 0.765352i | 0.682390 | + | 0.730988i | \(0.260940\pi\) |
−0.999409 | + | 0.0343637i | \(0.989060\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −5.75892 | + | 5.75892i | −0.343548 | + | 0.343548i | −0.857700 | − | 0.514151i | \(-0.828107\pi\) |
0.514151 | + | 0.857700i | \(0.328107\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −10.4136 | + | 25.1407i | −0.619025 | + | 1.49446i | 0.233812 | + | 0.972282i | \(0.424880\pi\) |
−0.852837 | + | 0.522177i | \(0.825120\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 1.03021 | 0.0608111 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 5.72512 | 0.336772 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 5.21345 | − | 12.5864i | 0.304573 | − | 0.735304i | −0.695290 | − | 0.718729i | \(-0.744724\pi\) |
0.999863 | − | 0.0165743i | \(-0.00527600\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2.72968 | − | 2.72968i | 0.158928 | − | 0.158928i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −8.07236 | + | 19.4884i | −0.466837 | + | 1.12704i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 32.4835 | − | 13.4551i | 1.87232 | − | 0.775539i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −8.01566 | −0.458975 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 8.98052 | + | 21.6809i | 0.512545 | + | 1.23739i | 0.942398 | + | 0.334495i | \(0.108566\pi\) |
−0.429852 | + | 0.902899i | \(0.641434\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −12.7177 | + | 12.7177i | −0.721157 | + | 0.721157i | −0.968841 | − | 0.247684i | \(-0.920330\pi\) |
0.247684 | + | 0.968841i | \(0.420330\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 10.1388 | + | 10.1388i | 0.573081 | + | 0.573081i | 0.932988 | − | 0.359907i | \(-0.117192\pi\) |
−0.359907 | + | 0.932988i | \(0.617192\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 2.52668 | − | 1.04659i | 0.141913 | − | 0.0587822i | −0.310597 | − | 0.950542i | \(-0.600529\pi\) |
0.452509 | + | 0.891760i | \(0.350529\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 14.2484i | − | 0.797757i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −5.39940 | − | 13.0353i | −0.300431 | − | 0.725304i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −12.1260 | − | 5.02277i | −0.672631 | − | 0.278613i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −7.39834 | − | 7.39834i | −0.407884 | − | 0.407884i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 5.49794 | + | 2.27732i | 0.302194 | + | 0.125173i | 0.528628 | − | 0.848854i | \(-0.322707\pi\) |
−0.226434 | + | 0.974027i | \(0.572707\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − | 12.4418i | − | 0.679768i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 5.85273i | − | 0.318818i | −0.987213 | − | 0.159409i | \(-0.949041\pi\) | ||
0.987213 | − | 0.159409i | \(-0.0509589\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 9.17801 | + | 3.80166i | 0.497017 | + | 0.205871i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 13.2780 | + | 13.2780i | 0.716946 | + | 0.716946i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 7.23994 | + | 2.99888i | 0.388660 | + | 0.160988i | 0.568452 | − | 0.822716i | \(-0.307542\pi\) |
−0.179792 | + | 0.983705i | \(0.557542\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −4.01973 | − | 9.70449i | −0.215171 | − | 0.519469i | 0.779032 | − | 0.626984i | \(-0.215711\pi\) |
−0.994204 | + | 0.107515i | \(0.965711\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 16.6657i | 0.887026i | 0.896268 | + | 0.443513i | \(0.146268\pi\) | ||||
−0.896268 | + | 0.443513i | \(0.853732\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −20.2875 | + | 8.40338i | −1.07675 | + | 0.446005i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −9.54649 | − | 9.54649i | −0.503845 | − | 0.503845i | 0.408786 | − | 0.912630i | \(-0.365952\pi\) |
−0.912630 | + | 0.408786i | \(0.865952\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 7.24075 | − | 7.24075i | 0.381092 | − | 0.381092i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −2.50205 | − | 6.04049i | −0.130963 | − | 0.316173i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 6.31072 | 0.329417 | 0.164708 | − | 0.986342i | \(-0.447332\pi\) | ||||
0.164708 | + | 0.986342i | \(0.447332\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −8.53463 | + | 3.53516i | −0.443096 | + | 0.183536i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −3.06259 | + | 7.39375i | −0.158575 | + | 0.382834i | −0.983120 | − | 0.182963i | \(-0.941431\pi\) |
0.824545 | + | 0.565797i | \(0.191431\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −22.6733 | + | 22.6733i | −1.16773 | + | 1.16773i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 8.31838 | − | 20.0823i | 0.427286 | − | 1.03156i | −0.552858 | − | 0.833275i | \(-0.686463\pi\) |
0.980144 | − | 0.198285i | \(-0.0635372\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 7.95308 | 0.406383 | 0.203192 | − | 0.979139i | \(-0.434869\pi\) | ||||
0.203192 | + | 0.979139i | \(0.434869\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 20.2871 | 1.03393 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −2.38215 | + | 5.75102i | −0.120780 | + | 0.291588i | −0.972693 | − | 0.232094i | \(-0.925442\pi\) |
0.851913 | + | 0.523683i | \(0.175442\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −19.6019 | + | 19.6019i | −0.991310 | + | 0.991310i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −15.4710 | + | 37.3503i | −0.778430 | + | 1.87930i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 25.3118 | − | 10.4845i | 1.27036 | − | 0.526202i | 0.357288 | − | 0.933994i | \(-0.383701\pi\) |
0.913075 | + | 0.407792i | \(0.133701\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −1.81017 | −0.0903954 | −0.0451977 | − | 0.998978i | \(-0.514392\pi\) | ||||
−0.0451977 | + | 0.998978i | \(0.514392\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −8.55532 | − | 20.6544i | −0.426171 | − | 1.02887i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 11.5839 | − | 11.5839i | 0.574194 | − | 0.574194i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −14.4331 | − | 14.4331i | −0.713672 | − | 0.713672i | 0.253630 | − | 0.967301i | \(-0.418376\pi\) |
−0.967301 | + | 0.253630i | \(0.918376\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 5.20841 | − | 2.15739i | 0.256289 | − | 0.106158i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 10.5474i | − | 0.517754i | ||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 1.33902 | + | 3.23269i | 0.0654155 | + | 0.157927i | 0.953207 | − | 0.302320i | \(-0.0977610\pi\) |
−0.887791 | + | 0.460247i | \(0.847761\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −10.5557 | − | 4.37232i | −0.514454 | − | 0.213094i | 0.110325 | − | 0.993896i | \(-0.464811\pi\) |
−0.624779 | + | 0.780802i | \(0.714811\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −12.1966 | − | 12.1966i | −0.591624 | − | 0.591624i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −10.8148 | − | 4.47963i | −0.523364 | − | 0.216784i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 3.31967i | − | 0.159903i | −0.996799 | − | 0.0799513i | \(-0.974524\pi\) | ||
0.996799 | − | 0.0799513i | \(-0.0254765\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 4.53298i | 0.217841i | 0.994050 | + | 0.108921i | \(0.0347394\pi\) | ||||
−0.994050 | + | 0.108921i | \(0.965261\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 15.9011 | + | 6.58646i | 0.760654 | + | 0.315073i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −20.9703 | − | 20.9703i | −1.00086 | − | 1.00086i | −1.00000 | 0.000858061i | \(-0.999727\pi\) | |
−0.000858061 | − | 1.00000i | \(-0.500273\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 31.9708 | + | 13.2427i | 1.51898 | + | 0.629181i | 0.977386 | − | 0.211462i | \(-0.0678225\pi\) |
0.541590 | + | 0.840643i | \(0.317822\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 11.1058 | + | 26.8117i | 0.526464 | + | 1.27100i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 21.0485i | − | 0.993340i | −0.867940 | − | 0.496670i | \(-0.834556\pi\) | ||
0.867940 | − | 0.496670i | \(-0.165444\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0.357852 | − | 0.148227i | 0.0168506 | − | 0.00697975i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −32.2827 | − | 32.2827i | −1.51344 | − | 1.51344i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −4.62656 | + | 4.62656i | −0.216421 | + | 0.216421i | −0.806988 | − | 0.590567i | \(-0.798904\pi\) |
0.590567 | + | 0.806988i | \(0.298904\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 4.84388 | + | 11.6942i | 0.225602 | + | 0.544652i | 0.995633 | − | 0.0933550i | \(-0.0297592\pi\) |
−0.770031 | + | 0.638007i | \(0.779759\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −14.2219 | −0.660950 | −0.330475 | − | 0.943815i | \(-0.607209\pi\) | ||||
−0.330475 | + | 0.943815i | \(0.607209\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 34.5241 | − | 14.3003i | 1.59758 | − | 0.661741i | 0.606512 | − | 0.795074i | \(-0.292568\pi\) |
0.991071 | + | 0.133333i | \(0.0425681\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 6.95321 | − | 16.7865i | 0.321069 | − | 0.775130i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 9.34754 | − | 9.34754i | 0.429800 | − | 0.429800i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −4.09821 | + | 9.89396i | −0.188039 | + | 0.453966i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −13.4016 | −0.612333 | −0.306167 | − | 0.951978i | \(-0.599046\pi\) | ||||
−0.306167 | + | 0.951978i | \(0.599046\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −36.8667 | −1.68098 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 15.2320 | − | 36.7734i | 0.691652 | − | 1.66979i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −1.26750 | + | 1.26750i | −0.0574358 | + | 0.0574358i | −0.735241 | − | 0.677805i | \(-0.762931\pi\) |
0.677805 | + | 0.735241i | \(0.262931\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −8.81902 | + | 21.2910i | −0.397997 | + | 0.960849i | 0.590144 | + | 0.807298i | \(0.299071\pi\) |
−0.988141 | + | 0.153551i | \(0.950929\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −38.9311 | + | 16.1258i | −1.75337 | + | 0.726269i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −32.0684 | −1.43846 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 2.76574 | + | 6.67709i | 0.123812 | + | 0.298908i | 0.973617 | − | 0.228189i | \(-0.0732805\pi\) |
−0.849805 | + | 0.527097i | \(0.823281\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −17.1789 | + | 17.1789i | −0.765968 | + | 0.765968i | −0.977394 | − | 0.211426i | \(-0.932189\pi\) |
0.211426 | + | 0.977394i | \(0.432189\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −5.99287 | − | 5.99287i | −0.266679 | − | 0.266679i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 0.432418 | − | 0.179113i | 0.0191666 | − | 0.00793905i | −0.373080 | − | 0.927799i | \(-0.621698\pi\) |
0.392246 | + | 0.919860i | \(0.371698\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 9.54815i | − | 0.422385i | ||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 20.3379 | + | 49.0999i | 0.896193 | + | 2.16360i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −3.63437 | − | 1.50541i | −0.159839 | − | 0.0662077i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −20.6495 | − | 20.6495i | −0.904670 | − | 0.904670i | 0.0911655 | − | 0.995836i | \(-0.470941\pi\) |
−0.995836 | + | 0.0911655i | \(0.970941\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 40.6453 | + | 16.8358i | 1.77729 | + | 0.736180i | 0.993321 | + | 0.115386i | \(0.0368104\pi\) |
0.783974 | + | 0.620794i | \(0.213190\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 29.3798i | − | 1.27980i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | − | 10.8158i | − | 0.470252i | ||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −0.805318 | − | 0.333574i | −0.0348822 | − | 0.0144487i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 3.90927 | + | 3.90927i | 0.169013 | + | 0.169013i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 16.9471 | + | 7.01973i | 0.729964 | + | 0.302361i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −7.26862 | − | 17.5480i | −0.312502 | − | 0.754447i | −0.999611 | − | 0.0278925i | \(-0.991120\pi\) |
0.687109 | − | 0.726555i | \(-0.258880\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 14.1407i | 0.605721i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 5.22407 | − | 2.16388i | 0.223365 | − | 0.0925208i | −0.268195 | − | 0.963365i | \(-0.586427\pi\) |
0.491560 | + | 0.870844i | \(0.336427\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 18.4998 | + | 18.4998i | 0.788116 | + | 0.788116i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −41.7471 | + | 41.7471i | −1.77527 | + | 1.77527i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 7.20051 | + | 17.3836i | 0.305095 | + | 0.736565i | 0.999850 | + | 0.0173184i | \(0.00551288\pi\) |
−0.694755 | + | 0.719247i | \(0.744487\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −29.7492 | −1.25826 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −43.4445 | + | 17.9953i | −1.83097 | + | 0.758411i | −0.864007 | + | 0.503479i | \(0.832053\pi\) |
−0.966959 | + | 0.254932i | \(0.917947\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 15.3475 | − | 37.0522i | 0.645675 | − | 1.55880i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −5.66061 | + | 5.66061i | −0.237305 | + | 0.237305i | −0.815733 | − | 0.578428i | \(-0.803666\pi\) |
0.578428 | + | 0.815733i | \(0.303666\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 13.7365 | − | 33.1629i | 0.574856 | − | 1.38783i | −0.322522 | − | 0.946562i | \(-0.604531\pi\) |
0.897378 | − | 0.441263i | \(-0.145469\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 21.0408 | 0.877461 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 4.38583 | 0.182584 | 0.0912922 | − | 0.995824i | \(-0.470900\pi\) | ||||
0.0912922 | + | 0.995824i | \(0.470900\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 5.89454 | − | 14.2307i | 0.244547 | − | 0.590388i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −2.45595 | + | 2.45595i | −0.101715 | + | 0.101715i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 4.24918 | − | 10.2584i | 0.175382 | − | 0.423411i | −0.811605 | − | 0.584206i | \(-0.801406\pi\) |
0.986988 | + | 0.160795i | \(0.0514060\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −16.8525 | + | 6.98052i | −0.694394 | + | 0.287627i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 5.76763 | 0.236848 | 0.118424 | − | 0.992963i | \(-0.462216\pi\) | ||||
0.118424 | + | 0.992963i | \(0.462216\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −22.9602 | − | 55.4309i | −0.941277 | − | 2.27244i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 13.4401 | − | 13.4401i | 0.549149 | − | 0.549149i | −0.377045 | − | 0.926195i | \(-0.623060\pi\) |
0.926195 | + | 0.377045i | \(0.123060\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 8.58677 | + | 8.58677i | 0.350262 | + | 0.350262i | 0.860207 | − | 0.509945i | \(-0.170334\pi\) |
−0.509945 | + | 0.860207i | \(0.670334\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −22.7875 | + | 9.43890i | −0.926444 | + | 0.383746i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 13.3743i | − | 0.542847i | −0.962460 | − | 0.271424i | \(-0.912506\pi\) | ||
0.962460 | − | 0.271424i | \(-0.0874944\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 3.38780 | + | 8.17886i | 0.137056 | + | 0.330881i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −10.6749 | − | 4.42168i | −0.431154 | − | 0.178590i | 0.156542 | − | 0.987671i | \(-0.449965\pi\) |
−0.587697 | + | 0.809081i | \(0.699965\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −14.8713 | − | 14.8713i | −0.598695 | − | 0.598695i | 0.341270 | − | 0.939965i | \(-0.389143\pi\) |
−0.939965 | + | 0.341270i | \(0.889143\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 6.25062 | + | 2.58909i | 0.251234 | + | 0.104064i | 0.504746 | − | 0.863268i | \(-0.331586\pi\) |
−0.253513 | + | 0.967332i | \(0.581586\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 42.3810i | 1.69796i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | − | 29.9995i | − | 1.19998i | ||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −44.7612 | − | 18.5407i | −1.78475 | − | 0.739266i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 5.78346 | + | 5.78346i | 0.230236 | + | 0.230236i | 0.812791 | − | 0.582555i | \(-0.197947\pi\) |
−0.582555 | + | 0.812791i | \(0.697947\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −35.8052 | − | 14.8310i | −1.42088 | − | 0.588550i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −15.7973 | − | 38.1381i | −0.625913 | − | 1.51109i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 29.5203i | 1.16598i | 0.812479 | + | 0.582990i | \(0.198117\pi\) | ||||
−0.812479 | + | 0.582990i | \(0.801883\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −10.0660 | + | 4.16947i | −0.396964 | + | 0.164428i | −0.572230 | − | 0.820093i | \(-0.693921\pi\) |
0.175266 | + | 0.984521i | \(0.443921\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −31.9256 | − | 31.9256i | −1.25512 | − | 1.25512i | −0.953393 | − | 0.301730i | \(-0.902436\pi\) |
−0.301730 | − | 0.953393i | \(-0.597564\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1.49878 | − | 1.49878i | 0.0588324 | − | 0.0588324i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 6.05626 | + | 14.6211i | 0.237000 | + | 0.572168i | 0.996970 | − | 0.0777900i | \(-0.0247864\pi\) |
−0.759970 | + | 0.649958i | \(0.774786\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −19.6811 | −0.769002 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −28.2612 | + | 11.7062i | −1.10090 | + | 0.456008i | −0.857795 | − | 0.513992i | \(-0.828166\pi\) |
−0.243106 | + | 0.970000i | \(0.578166\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 6.64573 | − | 16.0442i | 0.258489 | − | 0.624047i | −0.740350 | − | 0.672221i | \(-0.765340\pi\) |
0.998839 | + | 0.0481743i | \(0.0153403\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −26.3403 | + | 26.3403i | −1.02143 | + | 1.02143i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 19.6711 | − | 47.4901i | 0.761666 | − | 1.83883i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −4.40116 | −0.169905 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 34.2884 | 1.32172 | 0.660860 | − | 0.750509i | \(-0.270192\pi\) | ||||
0.660860 | + | 0.750509i | \(0.270192\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −16.6560 | + | 40.2112i | −0.640142 | + | 1.54544i | 0.186345 | + | 0.982484i | \(0.440336\pi\) |
−0.826487 | + | 0.562956i | \(0.809664\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 41.1023 | − | 41.1023i | 1.57736 | − | 1.57736i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 5.35596 | − | 12.9304i | 0.204940 | − | 0.494769i | −0.787673 | − | 0.616094i | \(-0.788714\pi\) |
0.992613 | + | 0.121325i | \(0.0387142\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −37.4872 | + | 15.5277i | −1.43231 | + | 0.593284i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 7.81623 | 0.297775 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 19.9998 | + | 48.2837i | 0.760826 | + | 1.83680i | 0.480898 | + | 0.876777i | \(0.340311\pi\) |
0.279929 | + | 0.960021i | \(0.409689\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −18.5731 | + | 18.5731i | −0.704517 | + | 0.704517i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −0.810008 | − | 0.810008i | −0.0306812 | − | 0.0306812i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 22.6661 | − | 9.38859i | 0.856085 | − | 0.354602i | 0.0889098 | − | 0.996040i | \(-0.471662\pi\) |
0.767175 | + | 0.641438i | \(0.221662\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 30.0806i | 1.13451i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −4.73644 | − | 11.4348i | −0.178132 | − | 0.430049i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −6.91323 | − | 2.86355i | −0.259632 | − | 0.107543i | 0.249071 | − | 0.968485i | \(-0.419875\pi\) |
−0.508703 | + | 0.860942i | \(0.669875\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 25.3420 | + | 25.3420i | 0.949064 | + | 0.949064i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −15.8586 | − | 6.56884i | −0.593078 | − | 0.245661i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 32.1395i | 1.19860i | 0.800525 | + | 0.599300i | \(0.204554\pi\) | ||||
−0.800525 | + | 0.599300i | \(0.795446\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 77.6119i | 2.89042i | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 29.5492 | + | 12.2397i | 1.09743 | + | 0.454570i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −24.0313 | − | 24.0313i | −0.891271 | − | 0.891271i | 0.103372 | − | 0.994643i | \(-0.467037\pi\) |
−0.994643 | + | 0.103372i | \(0.967037\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −36.1196 | − | 14.9612i | −1.33593 | − | 0.553361i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −3.28110 | − | 7.92127i | −0.121190 | − | 0.292579i | 0.851629 | − | 0.524145i | \(-0.175615\pi\) |
−0.972819 | + | 0.231566i | \(0.925615\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 6.83141i | − | 0.251638i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −4.01435 | + | 1.66280i | −0.147670 | + | 0.0611671i | −0.455295 | − | 0.890341i | \(-0.650466\pi\) |
0.307624 | + | 0.951508i | \(0.400466\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 20.6253 | + | 20.6253i | 0.756669 | + | 0.756669i | 0.975715 | − | 0.219046i | \(-0.0702944\pi\) |
−0.219046 | + | 0.975715i | \(0.570294\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 42.6465 | − | 42.6465i | 1.56245 | − | 1.56245i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 3.08968 | + | 7.45915i | 0.112894 | + | 0.272551i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −13.6475 | −0.498004 | −0.249002 | − | 0.968503i | \(-0.580103\pi\) | ||||
−0.249002 | + | 0.968503i | \(0.580103\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 30.0458 | − | 12.4454i | 1.09348 | − | 0.452933i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1.50145 | − | 3.62481i | 0.0545710 | − | 0.131746i | −0.894243 | − | 0.447582i | \(-0.852285\pi\) |
0.948814 | + | 0.315836i | \(0.102285\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −10.5824 | + | 10.5824i | −0.383612 | + | 0.383612i | −0.872402 | − | 0.488790i | \(-0.837438\pi\) |
0.488790 | + | 0.872402i | \(0.337438\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −7.90266 | + | 19.0787i | −0.286096 | + | 0.690696i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −4.76999 | −0.172234 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −42.6343 | −1.53743 | −0.768715 | − | 0.639591i | \(-0.779104\pi\) | ||||
−0.768715 | + | 0.639591i | \(0.779104\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 13.5374 | − | 32.6822i | 0.486906 | − | 1.17550i | −0.469362 | − | 0.883006i | \(-0.655516\pi\) |
0.956268 | − | 0.292490i | \(-0.0944839\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −15.7682 | + | 15.7682i | −0.566411 | + | 0.566411i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −0.272172 | + | 0.657081i | −0.00975157 | + | 0.0235424i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −11.1393 | + | 4.61404i | −0.398595 | + | 0.165103i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −27.4645 | −0.980249 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 11.1547 | + | 26.9298i | 0.397622 | + | 0.959945i | 0.988228 | + | 0.152985i | \(0.0488887\pi\) |
−0.590606 | + | 0.806960i | \(0.701111\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 41.4139 | − | 41.4139i | 1.47251 | − | 1.47251i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 7.00350 | + | 7.00350i | 0.248702 | + | 0.248702i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 3.44606 | − | 1.42740i | 0.122066 | − | 0.0505612i | −0.320815 | − | 0.947142i | \(-0.603957\pi\) |
0.442880 | + | 0.896581i | \(0.353957\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 11.6340i | 0.411582i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −1.37380 | − | 3.31665i | −0.0484804 | − | 0.117042i | ||||
\(804\) | 0 | 0 |