Newspace parameters
Level: | \( N \) | \(=\) | \( 756 = 2^{2} \cdot 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 756.f (of order \(2\), degree \(1\), minimal) |
Newform invariants
Self dual: | no |
Analytic conductor: | \(44.6054439643\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
|
|
Defining polynomial: |
\( x^{16} - 4 x^{15} - 36 x^{14} - 780 x^{13} + 17052 x^{12} - 100012 x^{11} + 336938 x^{10} + \cdots + 1976222698452 \)
|
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 2^{8}\cdot 3^{26} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 377.3 | ||
Root | \(5.48402 - 5.91781i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 756.377 |
Dual form | 756.4.f.e.377.4 |
$q$-expansion
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/756\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(325\) | \(379\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(1\) |
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 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −13.6625 | −1.22201 | −0.611004 | − | 0.791627i | \(-0.709234\pi\) | ||||
−0.611004 | + | 0.791627i | \(0.709234\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −3.07615 | − | 18.2630i | −0.166096 | − | 0.986110i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 10.2320i | − | 0.280461i | −0.990119 | − | 0.140230i | \(-0.955216\pi\) | ||
0.990119 | − | 0.140230i | \(-0.0447843\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 15.7462i | − | 0.335940i | −0.985792 | − | 0.167970i | \(-0.946279\pi\) | ||
0.985792 | − | 0.167970i | \(-0.0537212\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −52.8157 | −0.753511 | −0.376756 | − | 0.926313i | \(-0.622960\pi\) | ||||
−0.376756 | + | 0.926313i | \(0.622960\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 61.7090i | − | 0.745106i | −0.928011 | − | 0.372553i | \(-0.878482\pi\) | ||
0.928011 | − | 0.372553i | \(-0.121518\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 46.2236i | 0.419056i | 0.977803 | + | 0.209528i | \(0.0671928\pi\) | ||||
−0.977803 | + | 0.209528i | \(0.932807\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 61.6631 | 0.493305 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 26.5770i | − | 0.170180i | −0.996373 | − | 0.0850900i | \(-0.972882\pi\) | ||
0.996373 | − | 0.0850900i | \(-0.0271178\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 172.182i | − | 0.997573i | −0.866725 | − | 0.498787i | \(-0.833779\pi\) | ||
0.866725 | − | 0.498787i | \(-0.166221\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 42.0277 | + | 249.518i | 0.202971 | + | 1.20503i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −66.8154 | −0.296875 | −0.148438 | − | 0.988922i | \(-0.547424\pi\) | ||||
−0.148438 | + | 0.988922i | \(0.547424\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −7.91347 | −0.0301433 | −0.0150717 | − | 0.999886i | \(-0.504798\pi\) | ||||
−0.0150717 | + | 0.999886i | \(0.504798\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 264.488 | 0.938000 | 0.469000 | − | 0.883198i | \(-0.344614\pi\) | ||||
0.469000 | + | 0.883198i | \(0.344614\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 136.842 | 0.424691 | 0.212346 | − | 0.977195i | \(-0.431890\pi\) | ||||
0.212346 | + | 0.977195i | \(0.431890\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −324.075 | + | 112.359i | −0.944824 | + | 0.327578i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 596.778i | 1.54668i | 0.633994 | + | 0.773338i | \(0.281414\pi\) | ||||
−0.633994 | + | 0.773338i | \(0.718586\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 139.795i | 0.342725i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 103.438 | 0.228245 | 0.114123 | − | 0.993467i | \(-0.463594\pi\) | ||||
0.114123 | + | 0.993467i | \(0.463594\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 588.967i | 1.23622i | 0.786091 | + | 0.618111i | \(0.212102\pi\) | ||||
−0.786091 | + | 0.618111i | \(0.787898\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 215.132i | 0.410521i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −309.072 | −0.563570 | −0.281785 | − | 0.959478i | \(-0.590926\pi\) | ||||
−0.281785 | + | 0.959478i | \(0.590926\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1030.43i | 1.72239i | 0.508271 | + | 0.861197i | \(0.330285\pi\) | ||||
−0.508271 | + | 0.861197i | \(0.669715\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 478.042i | 0.766447i | 0.923656 | + | 0.383223i | \(0.125186\pi\) | ||||
−0.923656 | + | 0.383223i | \(0.874814\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −186.867 | + | 31.4752i | −0.276565 | + | 0.0465835i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 54.8892 | 0.0781710 | 0.0390855 | − | 0.999236i | \(-0.487556\pi\) | ||||
0.0390855 | + | 0.999236i | \(0.487556\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −287.874 | −0.380702 | −0.190351 | − | 0.981716i | \(-0.560963\pi\) | ||||
−0.190351 | + | 0.981716i | \(0.560963\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 721.593 | 0.920797 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −1006.71 | −1.19900 | −0.599498 | − | 0.800376i | \(-0.704633\pi\) | ||||
−0.599498 | + | 0.800376i | \(0.704633\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −287.573 | + | 48.4377i | −0.331274 | + | 0.0557984i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 843.097i | 0.910526i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 59.9202i | − | 0.0627214i | −0.999508 | − | 0.0313607i | \(-0.990016\pi\) | ||
0.999508 | − | 0.0313607i | \(-0.00998405\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −536.646 | −0.528696 | −0.264348 | − | 0.964427i | \(-0.585157\pi\) | ||||
−0.264348 | + | 0.964427i | \(0.585157\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 982.064i | − | 0.939472i | −0.882807 | − | 0.469736i | \(-0.844349\pi\) | ||
0.882807 | − | 0.469736i | \(-0.155651\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1433.16i | 1.29485i | 0.762128 | + | 0.647426i | \(0.224154\pi\) | ||||
−0.762128 | + | 0.647426i | \(0.775846\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1184.49 | −1.04085 | −0.520427 | − | 0.853906i | \(-0.674227\pi\) | ||||
−0.520427 | + | 0.853906i | \(0.674227\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1072.31i | 0.892693i | 0.894860 | + | 0.446346i | \(0.147275\pi\) | ||||
−0.894860 | + | 0.446346i | \(0.852725\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − | 631.529i | − | 0.512090i | ||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 162.469 | + | 964.574i | 0.125155 | + | 0.743045i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1226.31 | 0.921342 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 865.338 | 0.619186 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2115.79 | 1.47831 | 0.739157 | − | 0.673533i | \(-0.235224\pi\) | ||||
0.739157 | + | 0.673533i | \(0.235224\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −592.183 | −0.394956 | −0.197478 | − | 0.980307i | \(-0.563275\pi\) | ||||
−0.197478 | + | 0.980307i | \(0.563275\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1126.99 | + | 189.826i | −0.734756 | + | 0.123759i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 562.803i | 0.350975i | 0.984482 | + | 0.175487i | \(0.0561501\pi\) | ||||
−0.984482 | + | 0.175487i | \(0.943850\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 1848.50i | − | 1.12797i | −0.825785 | − | 0.563986i | \(-0.809267\pi\) | ||
0.825785 | − | 0.563986i | \(-0.190733\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −161.116 | −0.0942179 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 363.107i | 0.207961i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 1875.82i | 1.03136i | 0.856780 | + | 0.515682i | \(0.172462\pi\) | ||||
−0.856780 | + | 0.515682i | \(0.827538\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −3006.73 | −1.62042 | −0.810212 | − | 0.586137i | \(-0.800648\pi\) | ||||
−0.810212 | + | 0.586137i | \(0.800648\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 2352.43i | 1.21904i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 1685.97i | − | 0.857038i | −0.903533 | − | 0.428519i | \(-0.859036\pi\) | ||
0.903533 | − | 0.428519i | \(-0.140964\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 844.183 | − | 142.191i | 0.413235 | − | 0.0696037i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 794.673 | 0.381862 | 0.190931 | − | 0.981603i | \(-0.438849\pi\) | ||||
0.190931 | + | 0.981603i | \(0.438849\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 35.6499 | 0.0165190 | 0.00825950 | − | 0.999966i | \(-0.497371\pi\) | ||||
0.00825950 | + | 0.999966i | \(0.497371\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1949.06 | 0.887144 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 1297.51 | 0.570218 | 0.285109 | − | 0.958495i | \(-0.407970\pi\) | ||||
0.285109 | + | 0.958495i | \(0.407970\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −189.685 | − | 1126.15i | −0.0819361 | − | 0.486453i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 65.8037i | 0.0274771i | 0.999906 | + | 0.0137386i | \(0.00437325\pi\) | ||||
−0.999906 | + | 0.0137386i | \(0.995627\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2308.22i | 0.947892i | 0.880554 | + | 0.473946i | \(0.157171\pi\) | ||||
−0.880554 | + | 0.473946i | \(0.842829\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 912.864 | 0.362784 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 540.411i | 0.211330i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 2207.89i | 0.836424i | 0.908349 | + | 0.418212i | \(0.137343\pi\) | ||||
−0.908349 | + | 0.418212i | \(0.862657\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −403.746 | −0.150582 | −0.0752908 | − | 0.997162i | \(-0.523989\pi\) | ||||
−0.0752908 | + | 0.997162i | \(0.523989\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 2469.69i | − | 0.893189i | −0.894737 | − | 0.446594i | \(-0.852637\pi\) | ||
0.894737 | − | 0.446594i | \(-0.147363\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 4468.48i | 1.59177i | 0.605448 | + | 0.795885i | \(0.292994\pi\) | ||||
−0.605448 | + | 0.795885i | \(0.707006\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −485.375 | + | 81.7546i | −0.167816 | + | 0.0282662i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 108.117 | 0.0368354 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −631.407 | −0.208973 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2489.38 | 0.812210 | 0.406105 | − | 0.913826i | \(-0.366887\pi\) | ||||
0.406105 | + | 0.913826i | \(0.366887\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −3613.56 | −1.14624 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −3144.56 | + | 529.657i | −0.983717 | + | 0.165693i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 831.649i | 0.253135i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 5052.46i | 1.51721i | 0.651551 | + | 0.758605i | \(0.274119\pi\) | ||||
−0.651551 | + | 0.758605i | \(0.725881\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −5275.48 | −1.54249 | −0.771246 | − | 0.636537i | \(-0.780366\pi\) | ||||
−0.771246 | + | 0.636537i | \(0.780366\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 2477.33i | − | 0.714875i | −0.933937 | − | 0.357438i | \(-0.883650\pi\) | ||
0.933937 | − | 0.357438i | \(-0.116350\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 6566.31i | − | 1.84624i | −0.384516 | − | 0.923118i | \(-0.625632\pi\) | ||
0.384516 | − | 0.923118i | \(-0.374368\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1869.60 | −0.518977 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 2805.72i | − | 0.759360i | −0.925118 | − | 0.379680i | \(-0.876034\pi\) | ||
0.925118 | − | 0.379680i | \(-0.123966\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1815.82i | 0.485342i | 0.970109 | + | 0.242671i | \(0.0780236\pi\) | ||||
−0.970109 | + | 0.242671i | \(0.921976\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 4427.66 | − | 1535.11i | 1.15458 | − | 0.400303i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −971.684 | −0.250311 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 3410.13 | 0.857551 | 0.428776 | − | 0.903411i | \(-0.358945\pi\) | ||||
0.428776 | + | 0.903411i | \(0.358945\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 472.961 | 0.117529 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −5607.99 | −1.36116 | −0.680578 | − | 0.732676i | \(-0.738271\pi\) | ||||
−0.680578 | + | 0.732676i | \(0.738271\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 205.534 | + | 1220.25i | 0.0493099 | + | 0.292752i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 1909.45i | 0.447686i | 0.974625 | + | 0.223843i | \(0.0718603\pi\) | ||||
−0.974625 | + | 0.223843i | \(0.928140\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 8153.47i | − | 1.89005i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 3112.24 | 0.705415 | 0.352708 | − | 0.935734i | \(-0.385261\pi\) | ||||
0.352708 | + | 0.935734i | \(0.385261\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 5037.27i | 1.12912i | 0.825391 | + | 0.564562i | \(0.190955\pi\) | ||||
−0.825391 | + | 0.564562i | \(0.809045\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − | 630.938i | − | 0.138353i | ||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 5634.96 | 1.22228 | 0.611141 | − | 0.791522i | \(-0.290711\pi\) | ||||
0.611141 | + | 0.791522i | \(0.290711\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 5695.98i | − | 1.20923i | −0.796518 | − | 0.604615i | \(-0.793327\pi\) | ||
0.796518 | − | 0.604615i | \(-0.206673\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 6805.18i | − | 1.42942i | −0.699421 | − | 0.714710i | \(-0.746559\pi\) | ||
0.699421 | − | 0.714710i | \(-0.253441\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 24.3430 | + | 144.524i | 0.00500669 | + | 0.0297246i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −2123.50 | −0.432221 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 6428.15 | 1.28169 | 0.640847 | − | 0.767669i | \(-0.278583\pi\) | ||||
0.640847 | + | 0.767669i | \(0.278583\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1413.22 | −0.278918 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 727.848 | 0.140778 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −813.603 | − | 4830.34i | −0.155798 | − | 0.924971i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − | 8046.75i | − | 1.51067i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 471.068i | 0.0875742i | 0.999041 | + | 0.0437871i | \(0.0139423\pi\) | ||||
−0.999041 | + | 0.0437871i | \(0.986058\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 6842.66 | 1.24763 | 0.623813 | − | 0.781573i | \(-0.285583\pi\) | ||||
0.623813 | + | 0.781573i | \(0.285583\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 1020.33i | − | 0.184258i | −0.995747 | − | 0.0921290i | \(-0.970633\pi\) | ||
0.995747 | − | 0.0921290i | \(-0.0293672\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 8891.25i | − | 1.57534i | −0.616099 | − | 0.787669i | \(-0.711288\pi\) | ||
0.616099 | − | 0.787669i | \(-0.288712\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −271.936 | −0.0477288 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 3259.21i | 0.561446i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − | 970.962i | − | 0.165721i | ||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −420.947 | − | 2499.15i | −0.0705396 | − | 0.418792i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1881.87 | 0.312498 | 0.156249 | − | 0.987718i | \(-0.450060\pi\) | ||||
0.156249 | + | 0.987718i | \(0.450060\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 4222.69 | 0.688687 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1039.79 | 0.168074 | 0.0840372 | − | 0.996463i | \(-0.473219\pi\) | ||||
0.0840372 | + | 0.996463i | \(0.473219\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1761.77 | −0.279780 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 3048.92 | + | 5572.94i | 0.479960 | + | 0.877291i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − | 8064.45i | − | 1.24761i | −0.781578 | − | 0.623807i | \(-0.785585\pi\) | ||
0.781578 | − | 0.623807i | \(-0.214415\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 408.871i | − | 0.0627116i | −0.999508 | − | 0.0313558i | \(-0.990018\pi\) | ||
0.999508 | − | 0.0313558i | \(-0.00998249\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −9445.34 | −1.42415 | −0.712075 | − | 0.702104i | \(-0.752244\pi\) | ||||
−0.712075 | + | 0.702104i | \(0.752244\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − | 14078.3i | − | 2.10478i | ||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 5770.25i | 0.848306i | 0.905590 | + | 0.424153i | \(0.139428\pi\) | ||||
−0.905590 | + | 0.424153i | \(0.860572\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 3051.00 | 0.444817 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − | 6531.24i | − | 0.936605i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 6065.00i | 0.862645i | 0.902198 | + | 0.431322i | \(0.141953\pi\) | ||||
−0.902198 | + | 0.431322i | \(0.858047\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 10899.0 | − | 1835.78i | 1.52519 | − | 0.256897i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −2155.94 | −0.299278 | −0.149639 | − | 0.988741i | \(-0.547811\pi\) | ||||
−0.149639 | + | 0.988741i | \(0.547811\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −418.487 | −0.0571702 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −7647.70 | −1.03651 | −0.518254 | − | 0.855227i | \(-0.673418\pi\) | ||||
−0.518254 | + | 0.855227i | \(0.673418\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −12433.2 | −1.65877 | −0.829383 | − | 0.558681i | \(-0.811308\pi\) | ||||
−0.829383 | + | 0.558681i | \(0.811308\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 2553.07 | − | 430.028i | 0.337965 | − | 0.0569254i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − | 14320.5i | − | 1.86653i | −0.359190 | − | 0.933264i | \(-0.616947\pi\) | ||
0.359190 | − | 0.933264i | \(-0.383053\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 2441.33i | − | 0.315764i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −749.921 | −0.0955257 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 9846.85i | 1.24483i | 0.782686 | + | 0.622417i | \(0.213849\pi\) | ||||
−0.782686 | + | 0.622417i | \(0.786151\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 9728.28i | − | 1.21149i | −0.795659 | − | 0.605744i | \(-0.792875\pi\) | ||
0.795659 | − | 0.605744i | \(-0.207125\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −2711.22 | −0.335125 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 683.656i | 0.0832619i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 1606.02i | − | 0.194163i | −0.995276 | − | 0.0970817i | \(-0.969049\pi\) | ||
0.995276 | − | 0.0970817i | \(-0.0309508\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −318.190 | − | 1889.09i | −0.0379107 | − | 0.225075i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 3933.07 | 0.465221 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 5853.73 | 0.682514 | 0.341257 | − | 0.939970i | \(-0.389147\pi\) | ||||
0.341257 | + | 0.939970i | \(0.389147\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −13183.4 | −1.52617 | −0.763086 | − | 0.646297i | \(-0.776317\pi\) | ||||
−0.763086 | + | 0.646297i | \(0.776317\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −3256.78 | −0.371711 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 10756.3 | − | 1811.75i | 1.21905 | − | 0.205332i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 12848.9i | 1.43599i | 0.696050 | + | 0.717993i | \(0.254939\pi\) | ||||
−0.696050 | + | 0.717993i | \(0.745061\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 12853.3i | 1.42654i | 0.700891 | + | 0.713268i | \(0.252786\pi\) | ||||
−0.700891 | + | 0.713268i | \(0.747214\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 2852.41 | 0.312241 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 13399.9i | 1.45682i | 0.685143 | + | 0.728408i | \(0.259740\pi\) | ||||
−0.685143 | + | 0.728408i | \(0.740260\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − | 4808.14i | − | 0.515670i | −0.966189 | − | 0.257835i | \(-0.916991\pi\) | ||
0.966189 | − | 0.257835i | \(-0.0830090\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 13754.1 | 1.46518 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 6631.03i | − | 0.696966i | −0.937315 | − | 0.348483i | \(-0.886697\pi\) | ||
0.937315 | − | 0.348483i | \(-0.113303\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 80.9707i | 0.00845401i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 3928.96 | − | 661.779i | 0.404819 | − | 0.0681861i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −12402.4 | −1.26949 | −0.634746 | − | 0.772721i | \(-0.718895\pi\) | ||||
−0.634746 | + | 0.772721i | \(0.718895\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 6950.99 | 0.702255 | 0.351128 | − | 0.936328i | \(-0.385798\pi\) | ||||
0.351128 | + | 0.936328i | \(0.385798\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −14388.5 | −1.44426 | −0.722128 | − | 0.691759i | \(-0.756836\pi\) | ||||
−0.722128 | + | 0.691759i | \(0.756836\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −13922.6 | −1.37957 | −0.689786 | − | 0.724013i | \(-0.742295\pi\) | ||||
−0.689786 | + | 0.724013i | \(0.742295\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 950.751 | + | 5644.59i | 0.0936068 | + | 0.555742i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 2706.24i | − | 0.263072i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 3805.17i | − | 0.367565i | ||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −19333.3 | −1.84418 | −0.922090 | − | 0.386976i | \(-0.873520\pi\) | ||||
−0.922090 | + | 0.386976i | \(0.873520\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1052.09i | 0.0997323i | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 818.658i | 0.0766460i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −7812.00 | −0.726890 | −0.363445 | − | 0.931616i | \(-0.618400\pi\) | ||||
−0.363445 | + | 0.931616i | \(0.618400\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 13829.4i | 1.27110i | 0.772058 | + | 0.635552i | \(0.219227\pi\) | ||||
−0.772058 | + | 0.635552i | \(0.780773\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1403.68i | 0.128232i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 18818.8 | − | 3169.77i | 1.69847 | − | 0.286083i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 12602.3 | 1.13057 | 0.565287 | − | 0.824894i | \(-0.308766\pi\) | ||||
0.565287 | + | 0.824894i | \(0.308766\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 13166.7 | 1.16715 | 0.583574 | − | 0.812060i | \(-0.301654\pi\) | ||||
0.583574 | + | 0.812060i | \(0.301654\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 7331.92 | 0.646071 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −17280.3 | −1.50479 | −0.752395 | − | 0.658712i | \(-0.771101\pi\) | ||||
−0.752395 | + | 0.658712i | \(0.771101\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 8730.49 | − | 1470.53i | 0.755801 | − | 0.127304i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 13417.4i | 1.14804i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 1400.17i | − | 0.119109i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 11014.5 | 0.926210 | 0.463105 | − | 0.886303i | \(-0.346735\pi\) | ||||
0.463105 | + | 0.886303i | \(0.346735\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 5231.77i | − | 0.437418i | −0.975790 | − | 0.218709i | \(-0.929816\pi\) | ||
0.975790 | − | 0.218709i | \(-0.0701845\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 9093.91i | 0.751683i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 10030.4 | 0.824392 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 124.607i | 0.0101263i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 19580.6i | − | 1.58232i | ||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1149.66 | + | 3315.94i | 0.0918728 | + | 0.264986i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −8203.85 | −0.651961 | −0.325981 | − | 0.945376i | \(-0.605694\pi\) | ||||
−0.325981 | + | 0.945376i | \(0.605694\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 16183.0 | 1.27193 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −10187.8 | −0.796342 | −0.398171 | − | 0.917311i | \(-0.630355\pi\) | ||||
−0.398171 | + | 0.917311i | \(0.630355\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1640.04 | −0.126802 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −168.847 | − | 1002.44i | −0.0129839 | − | 0.0770852i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 3644.61i | − | 0.277248i | −0.990345 | − | 0.138624i | \(-0.955732\pi\) | ||
0.990345 | − | 0.138624i | \(-0.0442679\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 4164.68i | − | 0.315112i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 3529.23 | 0.264190 | 0.132095 | − | 0.991237i | \(-0.457830\pi\) | ||||
0.132095 | + | 0.991237i | \(0.457830\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − | 14650.4i | − | 1.09088i | ||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 20979.7i | 1.54572i | 0.634575 | + | 0.772861i | \(0.281175\pi\) | ||||
−0.634575 | + | 0.772861i | \(0.718825\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 3866.54 | 0.283379 | 0.141690 | − | 0.989911i | \(-0.454747\pi\) | ||||
0.141690 | + | 0.989911i | \(0.454747\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 2850.29i | 0.206723i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 8556.67i | 0.617364i | 0.951165 | + | 0.308682i | \(0.0998878\pi\) | ||||
−0.951165 | + | 0.308682i | \(0.900112\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 885.542 | + | 5257.44i | 0.0632332 | + | 0.375414i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 6106.24 | 0.433782 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 689.300 | 0.0484676 | 0.0242338 | − | 0.999706i | \(-0.492285\pi\) | ||||
0.0242338 | + | 0.999706i | \(0.492285\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −10625.2 | −0.743298 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −16487.3 | −1.14174 | −0.570869 | − | 0.821041i | \(-0.693394\pi\) | ||||
−0.570869 | + | 0.821041i | \(0.693394\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −2219.73 | − | 13178.5i | −0.152941 | − | 0.908007i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 25662.6i | 1.75050i | 0.483675 | + | 0.875248i | \(0.339302\pi\) | ||||
−0.483675 | + | 0.875248i | \(0.660698\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 2857.59i | − | 0.193949i | −0.995287 | − | 0.0969745i | \(-0.969083\pi\) | ||
0.995287 | − | 0.0969745i | \(-0.0309165\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −16754.4 | −1.12589 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 3907.10i | − | 0.261259i | −0.991431 | − | 0.130629i | \(-0.958300\pi\) | ||
0.991431 | − | 0.130629i | \(-0.0416998\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 2154.75i | − | 0.142671i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 12098.4 | 0.797145 | 0.398572 | − | 0.917137i | \(-0.369506\pi\) | ||||
0.398572 | + | 0.917137i | \(0.369506\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 8194.00i | − | 0.534648i | −0.963607 | − | 0.267324i | \(-0.913861\pi\) | ||
0.963607 | − | 0.267324i | \(-0.0861394\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 6486.57i | 0.421191i | 0.977573 | + | 0.210596i | \(0.0675403\pi\) | ||||
−0.977573 | + | 0.210596i | \(0.932460\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 3096.77 | + | 18385.5i | 0.199149 | + | 1.18234i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −19530.5 | −1.24996 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 3528.90 | 0.223699 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 4594.51 | 0.289865 | 0.144932 | − | 0.989442i | \(-0.453704\pi\) | ||||
0.144932 | + | 0.989442i | \(0.453704\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −28906.9 | −1.80651 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1769.24 | + | 5102.95i | 0.110047 | + | 0.317404i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 12005.3i | 0.739751i | 0.929081 | + | 0.369875i | \(0.120600\pi\) | ||||
−0.929081 | + | 0.369875i | \(0.879400\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 3617.96i | − | 0.221895i | −0.993826 | − | 0.110948i | \(-0.964611\pi\) | ||
0.993826 | − | 0.110948i | \(-0.0353886\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −11293.2 | −0.686217 | −0.343109 | − | 0.939296i | \(-0.611480\pi\) | ||||
−0.343109 | + | 0.939296i | \(0.611480\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 1058.38i | − | 0.0640139i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 8362.09i | 0.501124i | 0.968101 | + | 0.250562i | \(0.0806154\pi\) | ||||
−0.968101 | + | 0.250562i | \(0.919385\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 8090.68 | 0.482640 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 5804.98i | 0.343141i | 0.985172 | + | 0.171570i | \(0.0548841\pi\) | ||||
−0.985172 | + | 0.171570i | \(0.945116\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 15522.3i | 0.913383i | 0.889625 | + | 0.456691i | \(0.150966\pi\) | ||||
−0.889625 | + | 0.456691i | \(0.849034\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 15397.5 | − | 2593.49i | 0.897878 | − | 0.151235i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1228.48 | 0.0713150 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 6026.32 | 0.346712 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 7294.62 | 0.417811 | 0.208906 | − | 0.977936i | \(-0.433010\pi\) | ||||
0.208906 | + | 0.977936i | \(0.433010\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −20845.4 | −1.18339 | −0.591693 | − | 0.806164i | \(-0.701540\pi\) | ||||
−0.591693 | + | 0.806164i | \(0.701540\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −1094.32 | + | 184.323i | −0.0618501 | + | 0.0104178i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 7625.94i | − | 0.427231i | −0.976918 | − | 0.213615i | \(-0.931476\pi\) | ||
0.976918 | − | 0.213615i | \(-0.0685239\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 7689.28i | − | 0.428894i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 9397.01 | 0.519590 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 7613.20i | 0.419131i | 0.977795 | + | 0.209566i | \(0.0672050\pi\) | ||||
−0.977795 | + | 0.209566i | \(0.932795\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 25255.1i | 1.37839i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 417.955 | 0.0227133 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 13841.2i | 0.745756i | 0.927880 | + | 0.372878i | \(0.121629\pi\) | ||||
−0.927880 | + | 0.372878i | \(0.878371\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 4123.11i | 0.221204i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 1650.80 | + | 9800.78i | 0.0878144 | + | 0.521352i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1122.62 | 0.0594651 | 0.0297326 | − | 0.999558i | \(-0.490534\pi\) | ||||
0.0297326 | + | 0.999558i | \(0.490534\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 7958.87 | 0.418039 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 2201.24 | 0.115135 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −32986.5 | −1.71097 | −0.855485 | − | 0.517827i | \(-0.826741\pi\) | ||||
−0.855485 | + | 0.517827i | \(0.826741\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −17935.4 | + | 3020.97i | −0.926422 | + | 0.156043i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − | 1638.82i | − | 0.0839506i | ||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 16174.0i | 0.825116i | 0.910931 | + | 0.412558i | \(0.135365\pi\) | ||||
−0.910931 | + | 0.412558i | \(0.864635\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −13969.1 | −0.706794 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 23202.0i | 1.16915i | 0.811340 | + | 0.584574i | \(0.198738\pi\) | ||||
−0.811340 | + | 0.584574i | \(0.801262\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 3162.43i | 0.158059i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −28250.5 | −1.40624 | −0.703120 | − | 0.711071i | \(-0.748210\pi\) | ||||
−0.703120 | + | 0.711071i | \(0.748210\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 30939.7i | 1.52768i | 0.645404 | + | 0.763841i | \(0.276689\pi\) | ||||
−0.645404 | + | 0.763841i | \(0.723311\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − | 25628.4i | − | 1.26034i | ||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 26173.9 | − | 4408.62i | 1.27687 | − | 0.215070i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 6241.46 | 0.303268 | 0.151634 | − | 0.988437i | \(-0.451546\pi\) | ||||
0.151634 | + | 0.988437i | \(0.451546\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 41079.3 | 1.98017 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 20696.0 | 0.993672 | 0.496836 | − | 0.867844i | \(-0.334495\pi\) | ||||
0.496836 | + | 0.867844i | \(0.334495\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −21392.7 | −1.01903 | −0.509516 | − | 0.860461i | \(-0.670176\pi\) | ||||
−0.509516 | + | 0.860461i | \(0.670176\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 3643.65 | + | 21632.3i | 0.172882 | + | 1.02640i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 1628.76i | − | 0.0766768i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 25114.3i | 1.17769i | 0.808246 | + | 0.588845i | \(0.200417\pi\) | ||||
−0.808246 | + | 0.588845i | \(0.799583\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −7411.13 | −0.344838 | −0.172419 | − | 0.985024i | \(-0.555158\pi\) | ||||
−0.172419 | + | 0.985024i | \(0.555158\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 10617.3i | − | 0.492108i | ||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 488.332i | 0.0224600i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 10543.4 | 0.483064 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 23034.5i | 1.04731i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 28731.4i | 1.30135i | 0.759355 | + | 0.650676i | \(0.225515\pi\) | ||||
−0.759355 | + | 0.650676i | \(0.774485\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 19583.6 | − | 3298.58i | 0.880293 | − | 0.148273i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 9274.02 | 0.415296 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 12556.5 | 0.558062 | 0.279031 | − | 0.960282i | \(-0.409987\pi\) | ||||
0.279031 | + | 0.960282i | \(0.409987\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −7227.42 | −0.320010 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 4891.33 | 0.214958 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −11533.6 | + | 1942.68i | −0.504977 | + | 0.0850563i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 24449.2i | 1.06253i | 0.847205 | + | 0.531266i | \(0.178284\pi\) | ||||
−0.847205 | + | 0.531266i | \(0.821716\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 2328.38i | 0.100815i | 0.998729 | + | 0.0504073i | \(0.0160519\pi\) | ||||
−0.998729 | + | 0.0504073i | \(0.983948\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −10857.2 | −0.466639 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 16321.3i | − | 0.698909i | ||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 24291.6i | − | 1.03262i | −0.856401 | − | 0.516311i | \(-0.827305\pi\) | ||
0.856401 | − | 0.516311i | \(-0.172695\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −30865.5 | −1.30730 | −0.653648 | − | 0.756799i | \(-0.726762\pi\) | ||||
−0.653648 | + | 0.756799i | \(0.726762\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 14505.4i | − | 0.609920i | −0.952365 | − | 0.304960i | \(-0.901357\pi\) | ||
0.952365 | − | 0.304960i | \(-0.0986430\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 13689.4i | − | 0.573527i | −0.958001 | − | 0.286764i | \(-0.907421\pi\) | ||
0.958001 | − | 0.286764i | \(-0.0925794\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 17116.2 | − | 5934.34i | 0.711936 | − | 0.246834i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −487.066 | −0.0201864 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 17721.3 | 0.729210 | 0.364605 | − | 0.931162i | \(-0.381204\pi\) | ||||
0.364605 | + | 0.931162i | \(0.381204\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 23682.7 | 0.971039 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −26628.9 | −1.08410 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −3772.30 | − | 22396.0i | −0.153031 | − | 0.908544i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 3088.45i | − | 0.124407i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 32915.4i | − | 1.32122i | −0.750728 | − | 0.660611i | \(-0.770297\pi\) | ||
0.750728 | − | 0.660611i | \(-0.229703\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −198.537 | −0.00791353 | −0.00395676 | − | 0.999992i | \(-0.501259\pi\) | ||||
−0.00395676 | + | 0.999992i | \(0.501259\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 17797.3i | 0.706909i | 0.935452 | + | 0.353455i | \(0.114993\pi\) | ||||
−0.935452 | + | 0.353455i | \(0.885007\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 19544.9i | 0.770934i | 0.922722 | + | 0.385467i | \(0.125960\pi\) | ||||
−0.922722 | + | 0.385467i | \(0.874040\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −17727.2 | −0.696812 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 561.626i | − | 0.0219239i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 4866.72i | 0.189326i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −2661.91 | − | 15803.7i | −0.102844 | − | 0.610585i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 977.650 | 0.0376430 | 0.0188215 | − | 0.999823i | \(-0.494009\pi\) | ||||
0.0188215 | + | 0.999823i | \(0.494009\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −6419.94 | −0.245509 | −0.122754 | − | 0.992437i | \(-0.539173\pi\) | ||||
−0.122754 | + | 0.992437i | \(0.539173\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 44260.8 | 1.68686 | 0.843429 | − | 0.537241i | \(-0.180533\pi\) | ||||
0.843429 | + | 0.537241i | \(0.180533\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 2960.18 | 0.112055 | 0.0560277 | − | 0.998429i | \(-0.482156\pi\) | ||||
0.0560277 | + | 0.998429i | \(0.482156\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −6508.48 | − | 38640.7i | −0.245542 | − | 1.45778i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − | 8444.40i | − | 0.316440i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 899.041i | − | 0.0335773i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −4576.07 | −0.169767 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 31519.3i | − | 1.16544i | ||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 31536.0i | − | 1.15833i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −28177.0 | −1.03154 | −0.515768 | − | 0.856728i | \(-0.672493\pi\) | ||||
−0.515768 | + | 0.856728i | \(0.672493\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 18518.8i | − | 0.673495i | −0.941595 | − | 0.336747i | \(-0.890673\pi\) | ||
0.941595 | − | 0.336747i | \(-0.109327\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 2945.53i | 0.106772i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 1821.64 | + | 10815.0i | 0.0656007 | + | 0.389470i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 39516.9 | 1.41843 | 0.709217 | − | 0.704990i | \(-0.249049\pi\) | ||||
0.709217 | + | 0.704990i | \(0.249049\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 16225.5 | 0.578621 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −4120.05 | −0.146450 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −35210.4 | −1.24351 | −0.621753 | − | 0.783213i | \(-0.713579\pi\) | ||||
−0.621753 | + | 0.783213i | \(0.713579\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 6933.58 | + | 19998.3i | 0.244080 | + | 0.703994i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − | 7383.35i | − | 0.258247i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 25099.1i | − | 0.875081i | −0.899199 | − | 0.437541i | \(-0.855850\pi\) | ||
0.899199 | − | 0.437541i | \(-0.144150\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −21420.0 | −0.742055 | −0.371027 | − | 0.928622i | \(-0.620994\pi\) | ||||
−0.371027 | + | 0.928622i | \(0.620994\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 365.789i | − | 0.0126317i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 45264.3i | − | 1.55321i | −0.629986 | − | 0.776607i | \(-0.716939\pi\) | ||
0.629986 | − | 0.776607i | \(-0.283061\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 7527.37 | 0.257480 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 5430.75i | 0.184595i | 0.995731 | + | 0.0922977i | \(0.0294211\pi\) | ||||
−0.995731 | + | 0.0922977i | \(0.970579\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 30165.2i | − | 1.02212i | ||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 10278.5 | − | 1731.26i | 0.346099 | − | 0.0582956i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 144.401 | 0.00484715 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 5516.17 | 0.184012 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 11336.0 | 0.376982 | 0.188491 | − | 0.982075i | \(-0.439640\pi\) | ||||
0.188491 | + | 0.982075i | \(0.439640\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −43570.7 | −1.44001 | −0.720006 | − | 0.693968i | \(-0.755861\pi\) | ||||
−0.720006 | + | 0.693968i | \(0.755861\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −33759.2 | + | 5686.26i | −1.11230 | + | 0.187352i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 44248.7i | − | 1.44897i | −0.689291 | − | 0.724484i | \(-0.742078\pi\) | ||
0.689291 | − | 0.724484i | \(-0.257922\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 10300.6i | 0.336271i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 16774.5 | 0.544275 | 0.272137 | − | 0.962258i | \(-0.412269\pi\) | ||||
0.272137 | + | 0.962258i | \(0.412269\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 33742.1i | 1.09148i | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 12225.6i | 0.393075i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −37053.5 | −1.18773 | −0.593866 | − | 0.804564i | \(-0.702399\pi\) | ||||
−0.593866 | + | 0.804564i | \(0.702399\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − | 61050.5i | − | 1.94516i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 36680.2i | − | 1.16517i | −0.812770 | − | 0.582585i | \(-0.802041\pi\) | ||
0.812770 | − | 0.582585i | \(-0.197959\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 756.4.f.e.377.3 | ✓ | 16 | |
3.2 | odd | 2 | inner | 756.4.f.e.377.13 | yes | 16 | |
7.6 | odd | 2 | inner | 756.4.f.e.377.14 | yes | 16 | |
21.20 | even | 2 | inner | 756.4.f.e.377.4 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
756.4.f.e.377.3 | ✓ | 16 | 1.1 | even | 1 | trivial | |
756.4.f.e.377.4 | yes | 16 | 21.20 | even | 2 | inner | |
756.4.f.e.377.13 | yes | 16 | 3.2 | odd | 2 | inner | |
756.4.f.e.377.14 | yes | 16 | 7.6 | odd | 2 | inner |