Newspace parameters
Level: | \( N \) | \(=\) | \( 1216 = 2^{6} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1216.h (of order \(2\), degree \(1\), not minimal) |
Newform invariants
Self dual: | no |
Analytic conductor: | \(9.70980888579\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.14453810176.1 |
Defining polynomial: | \(x^{8} + 3 x^{6} + 6 x^{4} + 12 x^{2} + 16\) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{6} \) |
Twist minimal: | no (minimal twist has level 76) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1215.3 | ||
Root | \(1.06789 + 0.927153i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1216.1215 |
Dual form | 1216.2.h.d.1215.4 |
$q$-expansion
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1216\mathbb{Z}\right)^\times\).
\(n\) | \(191\) | \(705\) | \(837\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(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 | ||||||||
\(3\) | −1.19935 | −0.692447 | −0.346223 | − | 0.938152i | \(-0.612536\pi\) | ||||
−0.346223 | + | 0.938152i | \(0.612536\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.56155 | −0.698348 | −0.349174 | − | 0.937058i | \(-0.613538\pi\) | ||||
−0.349174 | + | 0.937058i | \(0.613538\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 0.868210i | − | 0.328153i | −0.986448 | − | 0.164076i | \(-0.947536\pi\) | ||
0.986448 | − | 0.164076i | \(-0.0524643\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.56155 | −0.520518 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.09218i | 0.932326i | 0.884699 | + | 0.466163i | \(0.154364\pi\) | ||||
−0.884699 | + | 0.466163i | \(0.845636\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 4.74990i | − | 1.31739i | −0.752412 | − | 0.658693i | \(-0.771110\pi\) | ||
0.752412 | − | 0.658693i | \(-0.228890\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.87285 | 0.483569 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1.00000 | −0.242536 | −0.121268 | − | 0.992620i | \(-0.538696\pi\) | ||||
−0.121268 | + | 0.992620i | \(0.538696\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.07221 | − | 3.09218i | 0.704812 | − | 0.709394i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.04129i | 0.227228i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 3.96039i | 0.825798i | 0.910777 | + | 0.412899i | \(0.135484\pi\) | ||||
−0.910777 | + | 0.412899i | \(0.864516\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.56155 | −0.512311 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.47091 | 1.05288 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 8.45851i | 1.57071i | 0.619048 | + | 0.785353i | \(0.287519\pi\) | ||||
−0.619048 | + | 0.785353i | \(0.712481\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.27156 | 0.767195 | 0.383597 | − | 0.923500i | \(-0.374685\pi\) | ||||
0.383597 | + | 0.923500i | \(0.374685\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − | 3.70861i | − | 0.645586i | ||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.35576i | 0.229165i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 3.70861i | − | 0.609692i | −0.952402 | − | 0.304846i | \(-0.901395\pi\) | ||
0.952402 | − | 0.304846i | \(-0.0986050\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 5.69681i | 0.912219i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 3.70861i | − | 0.579188i | −0.957150 | − | 0.289594i | \(-0.906480\pi\) | ||
0.957150 | − | 0.289594i | \(-0.0935202\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 11.0129i | 1.67946i | 0.543005 | + | 0.839729i | \(0.317286\pi\) | ||||
−0.543005 | + | 0.839729i | \(0.682714\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 2.43845 | 0.363502 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 9.27653i | 1.35312i | 0.736387 | + | 0.676560i | \(0.236530\pi\) | ||||
−0.736387 | + | 0.676560i | \(0.763470\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.24621 | 0.892316 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.19935 | 0.167943 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 1.04129i | − | 0.143032i | −0.997439 | − | 0.0715161i | \(-0.977216\pi\) | ||
0.997439 | − | 0.0715161i | \(-0.0227837\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 4.82860i | − | 0.651088i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −3.68466 | + | 3.70861i | −0.488045 | + | 0.491217i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 11.6153 | 1.51219 | 0.756093 | − | 0.654464i | \(-0.227106\pi\) | ||||
0.756093 | + | 0.654464i | \(0.227106\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.684658 | 0.0876615 | 0.0438308 | − | 0.999039i | \(-0.486044\pi\) | ||||
0.0438308 | + | 0.999039i | \(0.486044\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 1.35576i | 0.170809i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 7.41722i | 0.919993i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −9.74247 | −1.19023 | −0.595116 | − | 0.803640i | \(-0.702894\pi\) | ||||
−0.595116 | + | 0.803640i | \(0.702894\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − | 4.74990i | − | 0.571821i | ||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 10.9418 | 1.29856 | 0.649278 | − | 0.760551i | \(-0.275071\pi\) | ||||
0.649278 | + | 0.760551i | \(0.275071\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 8.12311 | 0.950738 | 0.475369 | − | 0.879787i | \(-0.342315\pi\) | ||||
0.475369 | + | 0.879787i | \(0.342315\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 3.07221 | 0.354748 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 2.68466 | 0.305945 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 8.01726 | 0.902013 | 0.451006 | − | 0.892521i | \(-0.351065\pi\) | ||||
0.451006 | + | 0.892521i | \(0.351065\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −1.87689 | −0.208544 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 9.65719i | 1.06001i | 0.847993 | + | 0.530007i | \(0.177811\pi\) | ||||
−0.847993 | + | 0.530007i | \(0.822189\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.56155 | 0.169374 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − | 10.1447i | − | 1.08763i | ||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 5.79119i | − | 0.613865i | −0.951731 | − | 0.306932i | \(-0.900697\pi\) | ||
0.951731 | − | 0.306932i | \(-0.0993026\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −4.12391 | −0.432303 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −5.12311 | −0.531241 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −4.79741 | + | 4.82860i | −0.492204 | + | 0.495404i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 16.9170i | 1.71766i | 0.512258 | + | 0.858832i | \(0.328809\pi\) | ||||
−0.512258 | + | 0.858832i | \(0.671191\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − | 4.82860i | − | 0.485292i | ||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −8.24621 | −0.820529 | −0.410264 | − | 0.911967i | \(-0.634564\pi\) | ||||
−0.410264 | + | 0.911967i | \(0.634564\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −3.74571 | −0.369075 | −0.184538 | − | 0.982825i | \(-0.559079\pi\) | ||||
−0.184538 | + | 0.982825i | \(0.559079\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | − | 1.62603i | − | 0.158684i | ||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 7.86962 | 0.760785 | 0.380392 | − | 0.924825i | \(-0.375789\pi\) | ||||
0.380392 | + | 0.924825i | \(0.375789\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 15.8757i | 1.52062i | 0.649561 | + | 0.760310i | \(0.274953\pi\) | ||||
−0.649561 | + | 0.760310i | \(0.725047\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 4.44793i | 0.422179i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 3.70861i | 0.348877i | 0.984668 | + | 0.174438i | \(0.0558110\pi\) | ||||
−0.984668 | + | 0.174438i | \(0.944189\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − | 6.18435i | − | 0.576694i | ||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 7.41722i | 0.685722i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0.868210i | 0.0795887i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.43845 | 0.130768 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 4.44793i | 0.401057i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 11.8078 | 1.05612 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.87285 | −0.166189 | −0.0830944 | − | 0.996542i | \(-0.526480\pi\) | ||||
−0.0830944 | + | 0.996542i | \(0.526480\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | − | 13.2084i | − | 1.16294i | ||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 4.82860i | − | 0.421876i | −0.977499 | − | 0.210938i | \(-0.932348\pi\) | ||
0.977499 | − | 0.210938i | \(-0.0676519\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2.68466 | − | 2.66732i | −0.232789 | − | 0.231286i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −8.54312 | −0.735274 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −3.87689 | −0.331225 | −0.165613 | − | 0.986191i | \(-0.552960\pi\) | ||||
−0.165613 | + | 0.986191i | \(0.552960\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 0.380664i | − | 0.0322875i | −0.999870 | − | 0.0161438i | \(-0.994861\pi\) | ||
0.999870 | − | 0.0161438i | \(-0.00513894\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | − | 11.1258i | − | 0.936964i | ||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 14.6875 | 1.22823 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 13.2084i | − | 1.09690i | ||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −7.49141 | −0.617881 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 17.8078 | 1.45887 | 0.729434 | − | 0.684051i | \(-0.239783\pi\) | ||||
0.729434 | + | 0.684051i | \(0.239783\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −24.2824 | −1.97607 | −0.988035 | − | 0.154231i | \(-0.950710\pi\) | ||||
−0.988035 | + | 0.154231i | \(0.950710\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 1.56155 | 0.126244 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −6.67026 | −0.535769 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −6.00000 | −0.478852 | −0.239426 | − | 0.970915i | \(-0.576959\pi\) | ||||
−0.239426 | + | 0.970915i | \(0.576959\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 1.24887i | 0.0990422i | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 3.43845 | 0.270988 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 10.6323i | − | 0.832785i | −0.909185 | − | 0.416392i | \(-0.863294\pi\) | ||
0.909185 | − | 0.416392i | \(-0.136706\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 5.79119i | 0.450844i | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −0.525853 | −0.0406917 | −0.0203459 | − | 0.999793i | \(-0.506477\pi\) | ||||
−0.0203459 | + | 0.999793i | \(0.506477\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −9.56155 | −0.735504 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −4.79741 | + | 4.82860i | −0.366867 | + | 0.369252i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − | 16.9170i | − | 1.28618i | −0.765792 | − | 0.643089i | \(-0.777653\pi\) | ||
0.765792 | − | 0.643089i | \(-0.222347\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2.22397i | 0.168116i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −13.9309 | −1.04711 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 9.06897 | 0.677847 | 0.338923 | − | 0.940814i | \(-0.389937\pi\) | ||||
0.338923 | + | 0.940814i | \(0.389937\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 2.08258i | − | 0.154797i | −0.997000 | − | 0.0773985i | \(-0.975339\pi\) | ||
0.997000 | − | 0.0773985i | \(-0.0246614\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −0.821147 | −0.0607009 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 5.79119i | 0.425777i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 3.09218i | − | 0.226122i | ||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | − | 4.74990i | − | 0.345504i | ||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 8.78898i | − | 0.635948i | −0.948099 | − | 0.317974i | \(-0.896997\pi\) | ||
0.948099 | − | 0.317974i | \(-0.103003\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 3.70861i | − | 0.266952i | −0.991052 | − | 0.133476i | \(-0.957386\pi\) | ||
0.991052 | − | 0.133476i | \(-0.0426138\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | − | 8.89586i | − | 0.637046i | ||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −10.4924 | −0.747554 | −0.373777 | − | 0.927519i | \(-0.621937\pi\) | ||||
−0.373777 | + | 0.927519i | \(0.621937\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 13.2369i | − | 0.938340i | −0.883108 | − | 0.469170i | \(-0.844553\pi\) | ||
0.883108 | − | 0.469170i | \(-0.155447\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 11.6847 | 0.824172 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 7.34376 | 0.515431 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 5.79119i | 0.404474i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − | 6.18435i | − | 0.429842i | ||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 9.56155 | + | 9.49980i | 0.661386 | + | 0.657115i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2.02050 | −0.139097 | −0.0695485 | − | 0.997579i | \(-0.522156\pi\) | ||||
−0.0695485 | + | 0.997579i | \(0.522156\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −13.1231 | −0.899180 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − | 17.1973i | − | 1.17285i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 3.70861i | − | 0.251757i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −9.74247 | −0.658335 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 4.74990i | 0.319513i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 16.2651 | 1.08919 | 0.544595 | − | 0.838699i | \(-0.316683\pi\) | ||||
0.544595 | + | 0.838699i | \(0.316683\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 4.00000 | 0.266667 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −17.4644 | −1.15916 | −0.579578 | − | 0.814917i | \(-0.696783\pi\) | ||||
−0.579578 | + | 0.814917i | \(0.696783\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2.43845 | 0.161137 | 0.0805686 | − | 0.996749i | \(-0.474326\pi\) | ||||
0.0805686 | + | 0.996749i | \(0.474326\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −3.21985 | −0.211851 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −9.80776 | −0.642528 | −0.321264 | − | 0.946990i | \(-0.604108\pi\) | ||||
−0.321264 | + | 0.946990i | \(0.604108\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − | 14.4858i | − | 0.944949i | ||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −9.61553 | −0.624596 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 19.4213i | 1.25626i | 0.778110 | + | 0.628129i | \(0.216179\pi\) | ||||
−0.778110 | + | 0.628129i | \(0.783821\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 15.2910i | 0.984979i | 0.870318 | + | 0.492490i | \(0.163913\pi\) | ||||
−0.870318 | + | 0.492490i | \(0.836087\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −14.1617 | −0.908472 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −9.75379 | −0.623147 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −14.6875 | − | 14.5927i | −0.934545 | − | 0.928509i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | − | 11.5824i | − | 0.734004i | ||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 22.4066i | 1.41429i | 0.707069 | + | 0.707145i | \(0.250017\pi\) | ||||
−0.707069 | + | 0.707145i | \(0.749983\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −12.2462 | −0.769913 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −1.87285 | −0.117283 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 18.9996i | − | 1.18516i | −0.805511 | − | 0.592581i | \(-0.798109\pi\) | ||
0.805511 | − | 0.592581i | \(-0.201891\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −3.21985 | −0.200072 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | − | 13.2084i | − | 0.817580i | ||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 6.56502i | − | 0.404816i | −0.979301 | − | 0.202408i | \(-0.935123\pi\) | ||
0.979301 | − | 0.202408i | \(-0.0648768\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1.62603i | 0.0998862i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 6.94568i | 0.425069i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 3.70861i | 0.226118i | 0.993588 | + | 0.113059i | \(0.0360649\pi\) | ||||
−0.993588 | + | 0.113059i | \(0.963935\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 15.3540i | 0.932689i | 0.884603 | + | 0.466345i | \(0.154429\pi\) | ||||
−0.884603 | + | 0.466345i | \(0.845571\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 4.94602 | 0.299347 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − | 7.92077i | − | 0.477641i | ||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 24.0540 | 1.44526 | 0.722632 | − | 0.691233i | \(-0.242932\pi\) | ||||
0.722632 | + | 0.691233i | \(0.242932\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −6.67026 | −0.399338 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 11.5824i | 0.690947i | 0.938429 | + | 0.345473i | \(0.112282\pi\) | ||||
−0.938429 | + | 0.345473i | \(0.887718\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 4.82860i | − | 0.287030i | −0.989648 | − | 0.143515i | \(-0.954159\pi\) | ||
0.989648 | − | 0.143515i | \(-0.0458406\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 5.75379 | − | 5.79119i | 0.340825 | − | 0.343041i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −3.21985 | −0.190062 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.0000 | −0.941176 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | − | 20.2895i | − | 1.18939i | ||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 4.74990i | 0.277492i | 0.990328 | + | 0.138746i | \(0.0443072\pi\) | ||||
−0.990328 | + | 0.138746i | \(0.955693\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −18.1379 | −1.05603 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 16.9170i | 0.981625i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 18.8114 | 1.08789 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 9.56155 | 0.551119 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 9.89012 | 0.568172 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −1.06913 | −0.0612182 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −8.01726 | −0.457569 | −0.228785 | − | 0.973477i | \(-0.573475\pi\) | ||||
−0.228785 | + | 0.973477i | \(0.573475\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 4.49242 | 0.255565 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 0.868210i | − | 0.0492317i | −0.999697 | − | 0.0246158i | \(-0.992164\pi\) | ||
0.999697 | − | 0.0246158i | \(-0.00783626\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −4.56155 | −0.257834 | −0.128917 | − | 0.991655i | \(-0.541150\pi\) | ||||
−0.128917 | + | 0.991655i | \(0.541150\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | − | 2.11708i | − | 0.119284i | ||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 4.74990i | − | 0.266781i | −0.991064 | − | 0.133390i | \(-0.957414\pi\) | ||
0.991064 | − | 0.133390i | \(-0.0425864\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −26.1552 | −1.46441 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −9.43845 | −0.526803 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −3.07221 | + | 3.09218i | −0.170942 | + | 0.172053i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 12.1671i | 0.674910i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − | 19.0406i | − | 1.05295i | ||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 8.05398 | 0.444030 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2.25106 | 0.123729 | 0.0618647 | − | 0.998085i | \(-0.480295\pi\) | ||||
0.0618647 | + | 0.998085i | \(0.480295\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 5.79119i | 0.317355i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 15.2134 | 0.831196 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 26.4168i | − | 1.43902i | −0.694484 | − | 0.719508i | \(-0.744367\pi\) | ||
0.694484 | − | 0.719508i | \(-0.255633\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | − | 4.44793i | − | 0.241579i | ||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 13.2084i | 0.715276i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 11.5005i | − | 0.620968i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 7.41722i | 0.399330i | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − | 24.1430i | − | 1.29606i | −0.761613 | − | 0.648032i | \(-0.775592\pi\) | ||
0.761613 | − | 0.648032i | \(-0.224408\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 28.0540 | 1.50169 | 0.750847 | − | 0.660476i | \(-0.229645\pi\) | ||||
0.750847 | + | 0.660476i | \(0.229645\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − | 25.9863i | − | 1.38705i | ||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 6.31534 | 0.336132 | 0.168066 | − | 0.985776i | \(-0.446248\pi\) | ||||
0.168066 | + | 0.985776i | \(0.446248\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −17.0862 | −0.906843 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | − | 1.04129i | − | 0.0551109i | ||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 27.3420i | 1.44306i | 0.692384 | + | 0.721529i | \(0.256560\pi\) | ||||
−0.692384 | + | 0.721529i | \(0.743440\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −0.123106 | − | 18.9996i | −0.00647924 | − | 0.999979i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −1.72521 | −0.0905498 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −12.6847 | −0.663945 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 14.1051i | 0.736282i | 0.929770 | + | 0.368141i | \(0.120006\pi\) | ||||
−0.929770 | + | 0.368141i | \(0.879994\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 5.79119i | 0.301477i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −0.904059 | −0.0469364 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 12.1671i | 0.629990i | 0.949093 | + | 0.314995i | \(0.102003\pi\) | ||||
−0.949093 | + | 0.314995i | \(0.897997\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −14.1617 | −0.731306 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 40.1771 | 2.06922 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 6.81791 | 0.350213 | 0.175106 | − | 0.984550i | \(-0.443973\pi\) | ||||
0.175106 | + | 0.984550i | \(0.443973\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 2.24621 | 0.115077 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −16.2651 | −0.831107 | −0.415554 | − | 0.909569i | \(-0.636412\pi\) | ||||
−0.415554 | + | 0.909569i | \(0.636412\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −4.19224 | −0.213656 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − | 17.1973i | − | 0.874188i | ||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 5.80776 | 0.294465 | 0.147233 | − | 0.989102i | \(-0.452963\pi\) | ||||
0.147233 | + | 0.989102i | \(0.452963\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 3.96039i | − | 0.200285i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 5.79119i | 0.292127i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −12.5194 | −0.629918 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −24.9309 | −1.25124 | −0.625622 | − | 0.780126i | \(-0.715155\pi\) | ||||
−0.625622 | + | 0.780126i | \(0.715155\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 3.21985 | + | 3.19906i | 0.161194 | + | 0.160153i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 20.6256i | − | 1.02999i | −0.857192 | − | 0.514997i | \(-0.827793\pi\) | ||
0.857192 | − | 0.514997i | \(-0.172207\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 20.2895i | − | 1.01069i | ||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 2.93087 | 0.145636 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 11.4677 | 0.568432 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 18.5431i | 0.916895i | 0.888722 | + | 0.458447i | \(0.151594\pi\) | ||||
−0.888722 | + | 0.458447i | \(0.848406\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 4.64976 | 0.229356 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − | 10.0845i | − | 0.496228i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 15.0802i | − | 0.740259i | ||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0.456551i | 0.0223574i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 27.4489i | 1.34097i | 0.741924 | + | 0.670484i | \(0.233913\pi\) | ||||
−0.741924 | + | 0.670484i | \(0.766087\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 23.2930i | − | 1.13523i | −0.823294 | − | 0.567614i | \(-0.807866\pi\) | ||
0.823294 | − | 0.567614i | \(-0.192134\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | − | 14.4858i | − | 0.704323i | ||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 2.56155 | 0.124254 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 0.594427i | − | 0.0287664i | ||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −17.6155 | −0.850486 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 17.0862 | 0.823015 | 0.411507 | − | 0.911406i | \(-0.365002\pi\) | ||||
0.411507 | + | 0.911406i | \(0.365002\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 28.0429i | 1.34765i | 0.738889 | + | 0.673827i | \(0.235351\pi\) | ||||
−0.738889 | + | 0.673827i | \(0.764649\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 15.8415i | 0.759544i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 12.2462 | + | 12.1671i | 0.585816 | + | 0.582032i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 24.8082 | 1.18403 | 0.592015 | − | 0.805927i | \(-0.298332\pi\) | ||||
0.592015 | + | 0.805927i | \(0.298332\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −9.75379 | −0.464466 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 34.7753i | 1.65222i | 0.563507 | + | 0.826111i | \(0.309452\pi\) | ||||
−0.563507 | + | 0.826111i | \(0.690548\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 9.04325i | 0.428691i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −21.3578 | −1.01019 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 35.9166i | 1.69501i | 0.530787 | + | 0.847505i | \(0.321896\pi\) | ||||
−0.530787 | + | 0.847505i | \(0.678104\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 11.4677 | 0.539992 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 29.1231 | 1.36832 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 6.43971 | 0.301898 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 12.1231 | 0.567095 | 0.283547 | − | 0.958958i | \(-0.408489\pi\) | ||||
0.283547 | + | 0.958958i | \(0.408489\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −5.47091 | −0.255360 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −19.3153 | −0.899605 | −0.449803 | − | 0.893128i | \(-0.648506\pi\) | ||||
−0.449803 | + | 0.893128i | \(0.648506\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 21.6452i | 1.00594i | 0.864304 | + | 0.502970i | \(0.167759\pi\) | ||||
−0.864304 | + | 0.502970i | \(0.832241\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 8.00000 | 0.370991 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 3.09218i | 0.143089i | 0.997437 | + | 0.0715444i | \(0.0227928\pi\) | ||||
−0.997437 | + | 0.0715444i | \(0.977207\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 8.45851i | 0.390578i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 7.19612 | 0.331580 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −34.0540 | −1.56580 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −7.86962 | + | 7.92077i | −0.361083 | + | 0.363430i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 1.62603i | 0.0744508i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − | 8.68210i | − | 0.396695i | −0.980132 | − | 0.198348i | \(-0.936442\pi\) | ||
0.980132 | − | 0.198348i | \(-0.0635575\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −17.6155 | −0.803199 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −4.12391 | −0.187644 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − | 26.4168i | − | 1.19953i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 9.59482 | 0.434783 | 0.217391 | − | 0.976085i | \(-0.430245\pi\) | ||||
0.217391 | + | 0.976085i | \(0.430245\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 12.7519i | 0.576659i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 2.71151i | 0.122369i | 0.998126 | + | 0.0611844i | \(0.0194878\pi\) | ||||
−0.998126 | + | 0.0611844i | \(0.980512\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 8.45851i | − | 0.380952i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 7.54011i | 0.338903i | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 9.49980i | − | 0.426124i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 11.0129i | 0.493007i | 0.969142 | + | 0.246504i | \(0.0792817\pi\) | ||||
−0.969142 | + | 0.246504i | \(0.920718\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0.630683 | 0.0281768 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 35.6435i | 1.58926i | 0.607091 | + | 0.794632i | \(0.292336\pi\) | ||||
−0.607091 | + | 0.794632i | \(0.707664\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 12.8769 | 0.573014 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 11.4677 | 0.509297 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 9.49980i | 0.421071i | 0.977586 | + | 0.210536i | \(0.0675208\pi\) | ||||
−0.977586 | + | 0.210536i | \(0.932479\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 7.05256i | − | 0.311987i | ||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 16.8078 | − | 16.9170i | 0.742081 | − | 0.746905i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 5.84912 | 0.257743 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −28.6847 | −1.26155 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 20.2895i | 0.890609i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 15.2910i | − | 0.669910i | −0.942234 | − | 0.334955i | \(-0.891279\pi\) | ||
0.942234 | − | 0.334955i | \(-0.108721\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 33.4990 | 1.46481 | 0.732404 | − | 0.680871i | \(-0.238398\pi\) | ||||
0.732404 | + | 0.680871i | \(0.238398\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | − | 2.66732i | − | 0.116411i | ||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −4.27156 | −0.186072 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 7.31534 | 0.318058 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −18.1379 | −0.787120 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −17.6155 | −0.763013 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −12.2888 | −0.531292 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −10.8769 | −0.469373 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 19.3144i | 0.831929i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 12.1922 | 0.524185 | 0.262093 | − | 0.965043i | \(-0.415587\pi\) | ||||
0.262093 | + | 0.965043i | \(0.415587\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 2.49775i | 0.107189i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 24.7908i | − | 1.06192i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 19.4849 | 0.833116 | 0.416558 | − | 0.909109i | \(-0.363236\pi\) | ||||
0.416558 | + | 0.909109i | \(0.363236\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −1.06913 | −0.0456294 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 26.1552 | + | 25.9863i | 1.11425 | + | 1.10705i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 6.96067i | − | 0.295998i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | − | 6.94568i | − | 0.294828i | ||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 18.9309 | 0.802127 | 0.401063 | − | 0.916050i | \(-0.368641\pi\) | ||||
0.401063 | + | 0.916050i | \(0.368641\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 52.3104 | 2.21249 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 3.70861i | 0.156578i | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 33.6466 | 1.41804 | 0.709018 | − | 0.705191i | \(-0.249139\pi\) | ||||
0.709018 | + | 0.705191i | \(0.249139\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − | 5.79119i | − | 0.243637i | ||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 1.62954i | 0.0684342i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 12.7519i | − | 0.534586i | −0.963615 | − | 0.267293i | \(-0.913871\pi\) | ||
0.963615 | − | 0.267293i | \(-0.0861291\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 17.5780i | − | 0.735615i | −0.929902 | − | 0.367807i | \(-0.880109\pi\) | ||
0.929902 | − | 0.367807i | \(-0.119891\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 10.5411i | 0.440360i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 10.1447i | − | 0.423065i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 27.0000 | 1.12402 | 0.562012 | − | 0.827129i | \(-0.310027\pi\) | ||||
0.562012 | + | 0.827129i | \(0.310027\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 4.44793i | 0.184850i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 8.38447 | 0.347847 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 3.21985 | 0.133353 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | − | 11.5824i | − | 0.478873i | ||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 4.82860i | − | 0.199297i | −0.995023 | − | 0.0996487i | \(-0.968228\pi\) | ||
0.995023 | − | 0.0996487i | \(-0.0317719\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 13.1231 | − | 13.2084i | 0.540728 | − | 0.544243i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 12.5841 | 0.517641 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −36.7386 | −1.50867 | −0.754337 | − | 0.656487i | \(-0.772042\pi\) | ||||
−0.754337 | + | 0.656487i | \(0.772042\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − | 1.35576i | − | 0.0555806i | ||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 15.8757i | 0.649750i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −7.72197 | −0.315511 | −0.157756 | − | 0.987478i | \(-0.550426\pi\) | ||||
−0.157756 | + | 0.987478i | \(0.550426\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 39.1687i | − | 1.59772i | −0.601514 | − | 0.798862i | \(-0.705436\pi\) | ||
0.601514 | − | 0.798862i | \(-0.294564\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 15.2134 | 0.619537 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −2.24621 | −0.0913215 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −13.6358 | −0.553461 | −0.276730 | − | 0.960948i | \(-0.589251\pi\) | ||||
−0.276730 | + | 0.960948i | \(0.589251\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −8.80776 | −0.356909 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 44.0626 | 1.78258 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −24.3002 | −0.981475 | −0.490738 | − | 0.871307i | \(-0.663273\pi\) | ||||
−0.490738 | + | 0.871307i | \(0.663273\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | − | 6.94568i | − | 0.280077i | ||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −28.5464 | −1.14923 | −0.574617 | − | 0.818422i | \(-0.694849\pi\) | ||||
−0.574617 | + | 0.818422i | \(0.694849\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 34.3946i | 1.38244i | 0.722646 | + | 0.691218i | \(0.242926\pi\) | ||||
−0.722646 | + | 0.691218i | \(0.757074\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 21.6669i | 0.869464i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −5.02797 | −0.201441 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −5.63068 | −0.225227 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −11.4677 | − | 11.3936i | −0.457975 | − | 0.455017i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 3.70861i | 0.147872i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 12.7494i | 0.507544i | 0.967264 | + | 0.253772i | \(0.0816713\pi\) | ||||
−0.967264 | + | 0.253772i | \(0.918329\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 2.42329 | 0.0963172 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 2.92456 | 0.116058 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − | 29.6689i | − | 1.17552i | ||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −17.0862 | −0.675921 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 48.6685i | 1.92229i | 0.276045 | + | 0.961145i | \(0.410976\pi\) | ||||
−0.276045 | + | 0.961145i | \(0.589024\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 6.56502i | 0.258899i | 0.991586 | + | 0.129449i | \(0.0413210\pi\) | ||||
−0.991586 | + | 0.129449i | \(0.958679\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 20.6256i | 0.812133i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 36.2379i | 1.42466i | 0.701845 | + | 0.712329i | \(0.252360\pi\) | ||||
−0.701845 | + | 0.712329i | \(0.747640\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 35.9166i | 1.40985i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 4.44793i | 0.174328i | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 45.8078 | 1.79260 | 0.896298 | − | 0.443452i | \(-0.146246\pi\) | ||||
0.896298 | + | 0.443452i | \(0.146246\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 7.54011i | 0.294616i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −12.6847 | −0.494876 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 3.36750 | 0.131179 | 0.0655896 | − | 0.997847i | \(-0.479107\pi\) | ||||
0.0655896 | + | 0.997847i | \(0.479107\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 17.5018i | − | 0.680740i | −0.940292 | − | 0.340370i | \(-0.889448\pi\) | ||
0.940292 | − | 0.340370i | \(-0.110552\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | − | 5.69681i | − | 0.221246i | ||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 4.19224 | + | 4.16516i | 0.162568 | + | 0.161518i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −33.4990 | −1.29709 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −19.5076 | −0.754207 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 2.11708i | 0.0817291i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 31.7515i | − | 1.22393i | −0.790885 | − | 0.611964i | \(-0.790380\pi\) | ||
0.790885 | − | 0.611964i | \(-0.209620\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −14.0140 | −0.539400 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 4.29335i | − | 0.165007i | −0.996591 | − | 0.0825034i | \(-0.973708\pi\) | ||
0.996591 | − | 0.0825034i | \(-0.0262915\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 14.6875 | 0.563656 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 20.9460 | 0.802653 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −13.6358 | −0.521760 | −0.260880 | − | 0.965371i | \(-0.584013\pi\) | ||||
−0.260880 | + | 0.965371i | \(0.584013\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 6.05398 | 0.231311 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −2.92456 | −0.111579 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −4.94602 | −0.188429 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 23.3817i | 0.889480i | 0.895660 | + | 0.444740i | \(0.146704\pi\) | ||||
−0.895660 | + | 0.444740i | \(0.853296\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −4.19224 | −0.159250 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0.594427i | 0.0225479i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 3.70861i | 0.140474i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 11.7630 | 0.444916 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −29.3693 | −1.10926 | −0.554632 | − | 0.832096i | \(-0.687141\pi\) | ||||
−0.554632 | + | 0.832096i | \(0.687141\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −11.4677 | − | 11.3936i | −0.432512 | − | 0.429718i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 17.3736i | 0.654327i | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 7.15944i | 0.269259i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −37.3693 | −1.40343 | −0.701717 | − | 0.712456i | \(-0.747583\pi\) | ||||
−0.701717 | + | 0.712456i | \(0.747583\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −12.5194 | −0.469513 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 16.9170i | 0.633547i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −22.9354 | −0.857733 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − | 23.2930i | − | 0.869891i | ||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 15.9484i | 0.594776i | 0.954757 | + | 0.297388i | \(0.0961155\pi\) | ||||
−0.954757 | + | 0.297388i | \(0.903885\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 3.25206i | 0.121113i | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − | 18.3393i | − | 0.682046i | ||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − | 21.6669i | − | 0.804689i | ||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 23.6554i | − | 0.877332i | −0.898650 | − | 0.438666i | \(-0.855451\pi\) | ||
0.898650 | − | 0.438666i | \(-0.144549\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 22.6155 | 0.837612 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 11.0129i | − | 0.407329i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −3.12311 | −0.115355 | −0.0576773 | − | 0.998335i | \(-0.518369\pi\) | ||||
−0.0576773 | + | 0.998335i | \(0.518369\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 11.6982 | 0.431496 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 30.1254i | − | 1.10968i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 30.3273i | 1.11561i | 0.829972 | + | 0.557804i | \(0.188356\pi\) | ||||
−0.829972 | + | 0.557804i | \(0.811644\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 17.6155 | + | 17.5018i | 0.647123 | + | 0.642943i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 38.4440 | 1.41037 | 0.705187 | − | 0.709021i | \(-0.250863\pi\) | ||||
0.705187 | + | 0.709021i | \(0.250863\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −27.8078 | −1.01880 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − | 15.0802i | − | 0.551756i | ||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − | 6.83248i | − | 0.249653i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 8.24782 | 0.300967 | 0.150484 | − | 0.988612i | \(-0.451917\pi\) | ||||
0.150484 | + | 0.988612i | \(0.451917\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | − | 26.8734i | − | 0.979320i | ||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 37.9182 | 1.37998 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 24.1922 | 0.879282 | 0.439641 | − | 0.898174i | \(-0.355106\pi\) | ||||
0.439641 | + | 0.898174i | \(0.355106\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 14.6875 | 0.533123 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −10.6155 | −0.384813 | −0.192406 | − | 0.981315i | \(-0.561629\pi\) | ||||
−0.192406 | + | 0.981315i | \(0.561629\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 13.7835 | 0.498995 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −2.43845 | −0.0881622 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 55.1716i | − | 1.99213i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 54.2311 | 1.95562 | 0.977811 | − | 0.209489i | \(-0.0671801\pi\) | ||||
0.977811 | + | 0.209489i | \(0.0671801\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 22.7872i | 0.820662i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 25.8321i | − | 0.929115i | −0.885543 | − | 0.464558i | \(-0.846213\pi\) | ||
0.885543 | − | 0.464558i | \(-0.153787\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −10.9418 | −0.393042 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 3.86174 | 0.138539 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −11.4677 | − | 11.3936i | −0.410872 | − | 0.408219i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 33.8340i | 1.21068i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 46.2758i | 1.65376i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 9.36932 | 0.334405 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −40.9904 | −1.46115 | −0.730575 | − | 0.682833i | \(-0.760748\pi\) | ||||
−0.730575 | + | 0.682833i | \(0.760748\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 7.87377i | 0.280314i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 3.21985 | 0.114485 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 3.25206i | − | 0.115484i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | − | 1.95018i | − | 0.0691659i | ||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 23.2930i | 0.825079i | 0.910940 | + | 0.412539i | \(0.135358\pi\) | ||||
−0.910940 | + | 0.412539i | \(0.864642\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 9.27653i | − | 0.328180i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 9.04325i | 0.319528i | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 25.1181i | 0.886398i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −5.36932 | −0.189244 | ||||||||
\(806\) | 0 | 0 |