Newspace parameters
Level: | \( N \) | \(=\) | \( 2070 = 2 \cdot 3^{2} \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 2070.a (trivial) |
Newform invariants
Self dual: | yes |
Analytic conductor: | \(122.133953712\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{4} - \cdots)\) |
|
|
Defining polynomial: |
\( x^{4} - 2x^{3} - 60x^{2} - 45x + 108 \)
|
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | no (minimal twist has level 230) |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(9.04090\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2070.1 |
$q$-expansion
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.00000 | −0.707107 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 4.00000 | 0.500000 | ||||||||
\(5\) | −5.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 5.03071 | 0.271633 | 0.135816 | − | 0.990734i | \(-0.456634\pi\) | ||||
0.135816 | + | 0.990734i | \(0.456634\pi\) | |||||||
\(8\) | −8.00000 | −0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 10.0000 | 0.316228 | ||||||||
\(11\) | 5.58219 | 0.153008 | 0.0765042 | − | 0.997069i | \(-0.475624\pi\) | ||||
0.0765042 | + | 0.997069i | \(0.475624\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 62.7277 | 1.33827 | 0.669136 | − | 0.743140i | \(-0.266664\pi\) | ||||
0.669136 | + | 0.743140i | \(0.266664\pi\) | |||||||
\(14\) | −10.0614 | −0.192073 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 16.0000 | 0.250000 | ||||||||
\(17\) | 19.7435 | 0.281677 | 0.140838 | − | 0.990033i | \(-0.455020\pi\) | ||||
0.140838 | + | 0.990033i | \(0.455020\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 158.545 | 1.91435 | 0.957177 | − | 0.289505i | \(-0.0934907\pi\) | ||||
0.957177 | + | 0.289505i | \(0.0934907\pi\) | |||||||
\(20\) | −20.0000 | −0.223607 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −11.1644 | −0.108193 | ||||||||
\(23\) | 23.0000 | 0.208514 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 25.0000 | 0.200000 | ||||||||
\(26\) | −125.455 | −0.946301 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 20.1228 | 0.135816 | ||||||||
\(29\) | 35.5033 | 0.227338 | 0.113669 | − | 0.993519i | \(-0.463740\pi\) | ||||
0.113669 | + | 0.993519i | \(0.463740\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 282.041 | 1.63406 | 0.817032 | − | 0.576592i | \(-0.195618\pi\) | ||||
0.817032 | + | 0.576592i | \(0.195618\pi\) | |||||||
\(32\) | −32.0000 | −0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −39.4870 | −0.199175 | ||||||||
\(35\) | −25.1536 | −0.121478 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −139.981 | −0.621967 | −0.310984 | − | 0.950415i | \(-0.600658\pi\) | ||||
−0.310984 | + | 0.950415i | \(0.600658\pi\) | |||||||
\(38\) | −317.090 | −1.35365 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 40.0000 | 0.158114 | ||||||||
\(41\) | −227.680 | −0.867260 | −0.433630 | − | 0.901091i | \(-0.642768\pi\) | ||||
−0.433630 | + | 0.901091i | \(0.642768\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 436.962 | 1.54968 | 0.774838 | − | 0.632159i | \(-0.217831\pi\) | ||||
0.774838 | + | 0.632159i | \(0.217831\pi\) | |||||||
\(44\) | 22.3288 | 0.0765042 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −46.0000 | −0.147442 | ||||||||
\(47\) | −90.2701 | −0.280154 | −0.140077 | − | 0.990141i | \(-0.544735\pi\) | ||||
−0.140077 | + | 0.990141i | \(0.544735\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −317.692 | −0.926216 | ||||||||
\(50\) | −50.0000 | −0.141421 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 250.911 | 0.669136 | ||||||||
\(53\) | −330.183 | −0.855737 | −0.427869 | − | 0.903841i | \(-0.640735\pi\) | ||||
−0.427869 | + | 0.903841i | \(0.640735\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −27.9109 | −0.0684275 | ||||||||
\(56\) | −40.2457 | −0.0960367 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −71.0066 | −0.160752 | ||||||||
\(59\) | 796.203 | 1.75689 | 0.878447 | − | 0.477839i | \(-0.158580\pi\) | ||||
0.878447 | + | 0.477839i | \(0.158580\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −568.580 | −1.19343 | −0.596715 | − | 0.802453i | \(-0.703528\pi\) | ||||
−0.596715 | + | 0.802453i | \(0.703528\pi\) | |||||||
\(62\) | −564.081 | −1.15546 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 64.0000 | 0.125000 | ||||||||
\(65\) | −313.638 | −0.598493 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 85.1419 | 0.155250 | 0.0776250 | − | 0.996983i | \(-0.475266\pi\) | ||||
0.0776250 | + | 0.996983i | \(0.475266\pi\) | |||||||
\(68\) | 78.9740 | 0.140838 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 50.3071 | 0.0858978 | ||||||||
\(71\) | 369.578 | 0.617758 | 0.308879 | − | 0.951101i | \(-0.400046\pi\) | ||||
0.308879 | + | 0.951101i | \(0.400046\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −310.188 | −0.497325 | −0.248662 | − | 0.968590i | \(-0.579991\pi\) | ||||
−0.248662 | + | 0.968590i | \(0.579991\pi\) | |||||||
\(74\) | 279.963 | 0.439797 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 634.180 | 0.957177 | ||||||||
\(77\) | 28.0824 | 0.0415621 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1325.46 | −1.88766 | −0.943832 | − | 0.330427i | \(-0.892807\pi\) | ||||
−0.943832 | + | 0.330427i | \(0.892807\pi\) | |||||||
\(80\) | −80.0000 | −0.111803 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 455.360 | 0.613246 | ||||||||
\(83\) | 158.806 | 0.210014 | 0.105007 | − | 0.994471i | \(-0.466513\pi\) | ||||
0.105007 | + | 0.994471i | \(0.466513\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −98.7175 | −0.125970 | ||||||||
\(86\) | −873.924 | −1.09579 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −44.6575 | −0.0540967 | ||||||||
\(89\) | 1233.89 | 1.46957 | 0.734787 | − | 0.678298i | \(-0.237282\pi\) | ||||
0.734787 | + | 0.678298i | \(0.237282\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 315.565 | 0.363519 | ||||||||
\(92\) | 92.0000 | 0.104257 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 180.540 | 0.198099 | ||||||||
\(95\) | −792.725 | −0.856125 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −106.389 | −0.111363 | −0.0556814 | − | 0.998449i | \(-0.517733\pi\) | ||||
−0.0556814 | + | 0.998449i | \(0.517733\pi\) | |||||||
\(98\) | 635.384 | 0.654933 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 100.000 | 0.100000 | ||||||||
\(101\) | −642.676 | −0.633155 | −0.316578 | − | 0.948567i | \(-0.602534\pi\) | ||||
−0.316578 | + | 0.948567i | \(0.602534\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1621.99 | 1.55165 | 0.775823 | − | 0.630951i | \(-0.217335\pi\) | ||||
0.775823 | + | 0.630951i | \(0.217335\pi\) | |||||||
\(104\) | −501.822 | −0.473150 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 660.365 | 0.605098 | ||||||||
\(107\) | −1490.86 | −1.34698 | −0.673490 | − | 0.739196i | \(-0.735205\pi\) | ||||
−0.673490 | + | 0.739196i | \(0.735205\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1204.00 | 1.05800 | 0.529001 | − | 0.848621i | \(-0.322567\pi\) | ||||
0.529001 | + | 0.848621i | \(0.322567\pi\) | |||||||
\(110\) | 55.8219 | 0.0483855 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 80.4914 | 0.0679082 | ||||||||
\(113\) | −276.771 | −0.230411 | −0.115206 | − | 0.993342i | \(-0.536753\pi\) | ||||
−0.115206 | + | 0.993342i | \(0.536753\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −115.000 | −0.0932505 | ||||||||
\(116\) | 142.013 | 0.113669 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −1592.41 | −1.24231 | ||||||||
\(119\) | 99.3239 | 0.0765126 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1299.84 | −0.976588 | ||||||||
\(122\) | 1137.16 | 0.843883 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 1128.16 | 0.817032 | ||||||||
\(125\) | −125.000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1552.79 | 1.08494 | 0.542471 | − | 0.840075i | \(-0.317489\pi\) | ||||
0.542471 | + | 0.840075i | \(0.317489\pi\) | |||||||
\(128\) | −128.000 | −0.0883883 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 627.277 | 0.423199 | ||||||||
\(131\) | 313.873 | 0.209337 | 0.104669 | − | 0.994507i | \(-0.466622\pi\) | ||||
0.104669 | + | 0.994507i | \(0.466622\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 797.594 | 0.520001 | ||||||||
\(134\) | −170.284 | −0.109778 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −157.948 | −0.0995877 | ||||||||
\(137\) | 1066.09 | 0.664835 | 0.332417 | − | 0.943132i | \(-0.392136\pi\) | ||||
0.332417 | + | 0.943132i | \(0.392136\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1594.79 | −0.973152 | −0.486576 | − | 0.873638i | \(-0.661754\pi\) | ||||
−0.486576 | + | 0.873638i | \(0.661754\pi\) | |||||||
\(140\) | −100.614 | −0.0607389 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −739.155 | −0.436821 | ||||||||
\(143\) | 350.158 | 0.204767 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −177.517 | −0.101669 | ||||||||
\(146\) | 620.375 | 0.351662 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −559.925 | −0.310984 | ||||||||
\(149\) | 1096.91 | 0.603102 | 0.301551 | − | 0.953450i | \(-0.402496\pi\) | ||||
0.301551 | + | 0.953450i | \(0.402496\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2734.41 | 1.47366 | 0.736832 | − | 0.676076i | \(-0.236321\pi\) | ||||
0.736832 | + | 0.676076i | \(0.236321\pi\) | |||||||
\(152\) | −1268.36 | −0.676826 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −56.1647 | −0.0293889 | ||||||||
\(155\) | −1410.20 | −0.730776 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1439.63 | −0.731813 | −0.365907 | − | 0.930652i | \(-0.619241\pi\) | ||||
−0.365907 | + | 0.930652i | \(0.619241\pi\) | |||||||
\(158\) | 2650.91 | 1.33478 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 160.000 | 0.0790569 | ||||||||
\(161\) | 115.706 | 0.0566394 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −2995.82 | −1.43957 | −0.719787 | − | 0.694195i | \(-0.755760\pi\) | ||||
−0.719787 | + | 0.694195i | \(0.755760\pi\) | |||||||
\(164\) | −910.721 | −0.433630 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −317.611 | −0.148503 | ||||||||
\(167\) | 351.532 | 0.162888 | 0.0814442 | − | 0.996678i | \(-0.474047\pi\) | ||||
0.0814442 | + | 0.996678i | \(0.474047\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1737.76 | 0.790971 | ||||||||
\(170\) | 197.435 | 0.0890740 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 1747.85 | 0.774838 | ||||||||
\(173\) | 3701.77 | 1.62682 | 0.813411 | − | 0.581690i | \(-0.197608\pi\) | ||||
0.813411 | + | 0.581690i | \(0.197608\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 125.768 | 0.0543266 | ||||||||
\(176\) | 89.3150 | 0.0382521 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −2467.78 | −1.03915 | ||||||||
\(179\) | −3584.09 | −1.49658 | −0.748290 | − | 0.663372i | \(-0.769125\pi\) | ||||
−0.748290 | + | 0.663372i | \(0.769125\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 783.672 | 0.321822 | 0.160911 | − | 0.986969i | \(-0.448557\pi\) | ||||
0.160911 | + | 0.986969i | \(0.448557\pi\) | |||||||
\(182\) | −631.130 | −0.257046 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −184.000 | −0.0737210 | ||||||||
\(185\) | 699.907 | 0.278152 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 110.212 | 0.0430989 | ||||||||
\(188\) | −361.080 | −0.140077 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 1585.45 | 0.605372 | ||||||||
\(191\) | −1491.95 | −0.565201 | −0.282601 | − | 0.959238i | \(-0.591197\pi\) | ||||
−0.282601 | + | 0.959238i | \(0.591197\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 3091.09 | 1.15286 | 0.576430 | − | 0.817147i | \(-0.304446\pi\) | ||||
0.576430 | + | 0.817147i | \(0.304446\pi\) | |||||||
\(194\) | 212.778 | 0.0787454 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1270.77 | −0.463108 | ||||||||
\(197\) | −2820.30 | −1.01999 | −0.509995 | − | 0.860178i | \(-0.670353\pi\) | ||||
−0.509995 | + | 0.860178i | \(0.670353\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1316.11 | 0.468825 | 0.234413 | − | 0.972137i | \(-0.424683\pi\) | ||||
0.234413 | + | 0.972137i | \(0.424683\pi\) | |||||||
\(200\) | −200.000 | −0.0707107 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 1285.35 | 0.447708 | ||||||||
\(203\) | 178.607 | 0.0617524 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1138.40 | 0.387851 | ||||||||
\(206\) | −3243.98 | −1.09718 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 1003.64 | 0.334568 | ||||||||
\(209\) | 885.028 | 0.292912 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −3399.19 | −1.10905 | −0.554525 | − | 0.832167i | \(-0.687100\pi\) | ||||
−0.554525 | + | 0.832167i | \(0.687100\pi\) | |||||||
\(212\) | −1320.73 | −0.427869 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 2981.72 | 0.952458 | ||||||||
\(215\) | −2184.81 | −0.693037 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1418.86 | 0.443865 | ||||||||
\(218\) | −2408.00 | −0.748121 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −111.644 | −0.0342137 | ||||||||
\(221\) | 1238.46 | 0.376960 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 864.660 | 0.259650 | 0.129825 | − | 0.991537i | \(-0.458558\pi\) | ||||
0.129825 | + | 0.991537i | \(0.458558\pi\) | |||||||
\(224\) | −160.983 | −0.0480184 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 553.543 | 0.162925 | ||||||||
\(227\) | 1979.40 | 0.578754 | 0.289377 | − | 0.957215i | \(-0.406552\pi\) | ||||
0.289377 | + | 0.957215i | \(0.406552\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −3113.53 | −0.898462 | −0.449231 | − | 0.893416i | \(-0.648302\pi\) | ||||
−0.449231 | + | 0.893416i | \(0.648302\pi\) | |||||||
\(230\) | 230.000 | 0.0659380 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −284.026 | −0.0803761 | ||||||||
\(233\) | −6018.65 | −1.69225 | −0.846126 | − | 0.532983i | \(-0.821071\pi\) | ||||
−0.846126 | + | 0.532983i | \(0.821071\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 451.350 | 0.125289 | ||||||||
\(236\) | 3184.81 | 0.878447 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −198.648 | −0.0541026 | ||||||||
\(239\) | 4224.88 | 1.14345 | 0.571725 | − | 0.820445i | \(-0.306274\pi\) | ||||
0.571725 | + | 0.820445i | \(0.306274\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1394.24 | 0.372658 | 0.186329 | − | 0.982487i | \(-0.440341\pi\) | ||||
0.186329 | + | 0.982487i | \(0.440341\pi\) | |||||||
\(242\) | 2599.68 | 0.690552 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −2274.32 | −0.596715 | ||||||||
\(245\) | 1588.46 | 0.414216 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 9945.16 | 2.56192 | ||||||||
\(248\) | −2256.32 | −0.577729 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 250.000 | 0.0632456 | ||||||||
\(251\) | 5968.83 | 1.50099 | 0.750497 | − | 0.660874i | \(-0.229814\pi\) | ||||
0.750497 | + | 0.660874i | \(0.229814\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 128.390 | 0.0319045 | ||||||||
\(254\) | −3105.57 | −0.767169 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 256.000 | 0.0625000 | ||||||||
\(257\) | 1636.06 | 0.397100 | 0.198550 | − | 0.980091i | \(-0.436377\pi\) | ||||
0.198550 | + | 0.980091i | \(0.436377\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −704.206 | −0.168947 | ||||||||
\(260\) | −1254.55 | −0.299247 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −627.745 | −0.148024 | ||||||||
\(263\) | −2995.55 | −0.702333 | −0.351166 | − | 0.936313i | \(-0.614215\pi\) | ||||
−0.351166 | + | 0.936313i | \(0.614215\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1650.91 | 0.382697 | ||||||||
\(266\) | −1595.19 | −0.367696 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 340.568 | 0.0776250 | ||||||||
\(269\) | 5190.17 | 1.17640 | 0.588198 | − | 0.808717i | \(-0.299838\pi\) | ||||
0.588198 | + | 0.808717i | \(0.299838\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 6720.43 | 1.50641 | 0.753205 | − | 0.657786i | \(-0.228507\pi\) | ||||
0.753205 | + | 0.657786i | \(0.228507\pi\) | |||||||
\(272\) | 315.896 | 0.0704192 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −2132.18 | −0.470109 | ||||||||
\(275\) | 139.555 | 0.0306017 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −6114.74 | −1.32635 | −0.663176 | − | 0.748464i | \(-0.730792\pi\) | ||||
−0.663176 | + | 0.748464i | \(0.730792\pi\) | |||||||
\(278\) | 3189.58 | 0.688123 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 201.228 | 0.0429489 | ||||||||
\(281\) | 3549.07 | 0.753450 | 0.376725 | − | 0.926325i | \(-0.377050\pi\) | ||||
0.376725 | + | 0.926325i | \(0.377050\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 3103.11 | 0.651806 | 0.325903 | − | 0.945403i | \(-0.394332\pi\) | ||||
0.325903 | + | 0.945403i | \(0.394332\pi\) | |||||||
\(284\) | 1478.31 | 0.308879 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −700.316 | −0.144792 | ||||||||
\(287\) | −1145.39 | −0.235576 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −4523.19 | −0.920658 | ||||||||
\(290\) | 355.033 | 0.0718905 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −1240.75 | −0.248662 | ||||||||
\(293\) | −1218.51 | −0.242957 | −0.121478 | − | 0.992594i | \(-0.538763\pi\) | ||||
−0.121478 | + | 0.992594i | \(0.538763\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −3981.01 | −0.785707 | ||||||||
\(296\) | 1119.85 | 0.219899 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −2193.82 | −0.426458 | ||||||||
\(299\) | 1442.74 | 0.279049 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2198.23 | 0.420943 | ||||||||
\(302\) | −5468.82 | −1.04204 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 2536.72 | 0.478588 | ||||||||
\(305\) | 2842.90 | 0.533718 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 2564.45 | 0.476745 | 0.238373 | − | 0.971174i | \(-0.423386\pi\) | ||||
0.238373 | + | 0.971174i | \(0.423386\pi\) | |||||||
\(308\) | 112.329 | 0.0207811 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 2820.41 | 0.516736 | ||||||||
\(311\) | 92.6253 | 0.0168884 | 0.00844421 | − | 0.999964i | \(-0.497312\pi\) | ||||
0.00844421 | + | 0.999964i | \(0.497312\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −4276.44 | −0.772263 | −0.386132 | − | 0.922444i | \(-0.626189\pi\) | ||||
−0.386132 | + | 0.922444i | \(0.626189\pi\) | |||||||
\(314\) | 2879.25 | 0.517470 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −5301.82 | −0.943832 | ||||||||
\(317\) | 2964.24 | 0.525199 | 0.262600 | − | 0.964905i | \(-0.415420\pi\) | ||||
0.262600 | + | 0.964905i | \(0.415420\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 198.186 | 0.0347846 | ||||||||
\(320\) | −320.000 | −0.0559017 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −231.413 | −0.0400501 | ||||||||
\(323\) | 3130.23 | 0.539229 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1568.19 | 0.267654 | ||||||||
\(326\) | 5991.63 | 1.01793 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 1821.44 | 0.306623 | ||||||||
\(329\) | −454.123 | −0.0760991 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1348.81 | −0.223979 | −0.111989 | − | 0.993709i | \(-0.535722\pi\) | ||||
−0.111989 | + | 0.993709i | \(0.535722\pi\) | |||||||
\(332\) | 635.223 | 0.105007 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −703.064 | −0.115180 | ||||||||
\(335\) | −425.710 | −0.0694299 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −5764.30 | −0.931755 | −0.465878 | − | 0.884849i | \(-0.654261\pi\) | ||||
−0.465878 | + | 0.884849i | \(0.654261\pi\) | |||||||
\(338\) | −3475.53 | −0.559301 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −394.870 | −0.0629848 | ||||||||
\(341\) | 1574.40 | 0.250026 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −3323.75 | −0.523223 | ||||||||
\(344\) | −3495.70 | −0.547894 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −7403.53 | −1.15034 | ||||||||
\(347\) | −4066.16 | −0.629057 | −0.314528 | − | 0.949248i | \(-0.601846\pi\) | ||||
−0.314528 | + | 0.949248i | \(0.601846\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 8407.82 | 1.28957 | 0.644786 | − | 0.764363i | \(-0.276947\pi\) | ||||
0.644786 | + | 0.764363i | \(0.276947\pi\) | |||||||
\(350\) | −251.536 | −0.0384147 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −178.630 | −0.0270483 | ||||||||
\(353\) | −256.068 | −0.0386095 | −0.0193047 | − | 0.999814i | \(-0.506145\pi\) | ||||
−0.0193047 | + | 0.999814i | \(0.506145\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −1847.89 | −0.276270 | ||||||||
\(356\) | 4935.56 | 0.734787 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 7168.19 | 1.05824 | ||||||||
\(359\) | 12052.5 | 1.77189 | 0.885943 | − | 0.463794i | \(-0.153512\pi\) | ||||
0.885943 | + | 0.463794i | \(0.153512\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 18277.5 | 2.66475 | ||||||||
\(362\) | −1567.34 | −0.227563 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 1262.26 | 0.181759 | ||||||||
\(365\) | 1550.94 | 0.222410 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −9245.40 | −1.31500 | −0.657502 | − | 0.753453i | \(-0.728387\pi\) | ||||
−0.657502 | + | 0.753453i | \(0.728387\pi\) | |||||||
\(368\) | 368.000 | 0.0521286 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −1399.81 | −0.196683 | ||||||||
\(371\) | −1661.05 | −0.232446 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −869.265 | −0.120667 | −0.0603335 | − | 0.998178i | \(-0.519216\pi\) | ||||
−0.0603335 | + | 0.998178i | \(0.519216\pi\) | |||||||
\(374\) | −220.424 | −0.0304755 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 722.161 | 0.0990495 | ||||||||
\(377\) | 2227.04 | 0.304240 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1278.76 | 0.173313 | 0.0866566 | − | 0.996238i | \(-0.472382\pi\) | ||||
0.0866566 | + | 0.996238i | \(0.472382\pi\) | |||||||
\(380\) | −3170.90 | −0.428062 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 2983.89 | 0.399658 | ||||||||
\(383\) | 5343.75 | 0.712932 | 0.356466 | − | 0.934308i | \(-0.383982\pi\) | ||||
0.356466 | + | 0.934308i | \(0.383982\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −140.412 | −0.0185871 | ||||||||
\(386\) | −6182.19 | −0.815194 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −425.557 | −0.0556814 | ||||||||
\(389\) | 708.346 | 0.0923254 | 0.0461627 | − | 0.998934i | \(-0.485301\pi\) | ||||
0.0461627 | + | 0.998934i | \(0.485301\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 454.101 | 0.0587336 | ||||||||
\(392\) | 2541.54 | 0.327467 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 5640.60 | 0.721241 | ||||||||
\(395\) | 6627.28 | 0.844189 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −5924.01 | −0.748911 | −0.374455 | − | 0.927245i | \(-0.622170\pi\) | ||||
−0.374455 | + | 0.927245i | \(0.622170\pi\) | |||||||
\(398\) | −2632.21 | −0.331510 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 400.000 | 0.0500000 | ||||||||
\(401\) | 11393.6 | 1.41888 | 0.709441 | − | 0.704765i | \(-0.248948\pi\) | ||||
0.709441 | + | 0.704765i | \(0.248948\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 17691.8 | 2.18682 | ||||||||
\(404\) | −2570.71 | −0.316578 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −357.214 | −0.0436656 | ||||||||
\(407\) | −781.402 | −0.0951663 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 13804.4 | 1.66891 | 0.834457 | − | 0.551073i | \(-0.185782\pi\) | ||||
0.834457 | + | 0.551073i | \(0.185782\pi\) | |||||||
\(410\) | −2276.80 | −0.274252 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 6487.96 | 0.775823 | ||||||||
\(413\) | 4005.47 | 0.477230 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −794.028 | −0.0939212 | ||||||||
\(416\) | −2007.29 | −0.236575 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −1770.06 | −0.207120 | ||||||||
\(419\) | 14795.8 | 1.72512 | 0.862558 | − | 0.505958i | \(-0.168861\pi\) | ||||
0.862558 | + | 0.505958i | \(0.168861\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 5804.66 | 0.671976 | 0.335988 | − | 0.941866i | \(-0.390930\pi\) | ||||
0.335988 | + | 0.941866i | \(0.390930\pi\) | |||||||
\(422\) | 6798.37 | 0.784217 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 2641.46 | 0.302549 | ||||||||
\(425\) | 493.588 | 0.0563353 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −2860.36 | −0.324175 | ||||||||
\(428\) | −5963.44 | −0.673490 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 4369.62 | 0.490051 | ||||||||
\(431\) | −15268.2 | −1.70636 | −0.853181 | − | 0.521615i | \(-0.825330\pi\) | ||||
−0.853181 | + | 0.521615i | \(0.825330\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 2250.62 | 0.249788 | 0.124894 | − | 0.992170i | \(-0.460141\pi\) | ||||
0.124894 | + | 0.992170i | \(0.460141\pi\) | |||||||
\(434\) | −2837.73 | −0.313860 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 4816.00 | 0.529001 | ||||||||
\(437\) | 3646.53 | 0.399170 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 10366.2 | 1.12700 | 0.563499 | − | 0.826117i | \(-0.309455\pi\) | ||||
0.563499 | + | 0.826117i | \(0.309455\pi\) | |||||||
\(440\) | 223.288 | 0.0241928 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −2476.93 | −0.266551 | ||||||||
\(443\) | 3881.11 | 0.416246 | 0.208123 | − | 0.978103i | \(-0.433264\pi\) | ||||
0.208123 | + | 0.978103i | \(0.433264\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −6169.45 | −0.657214 | ||||||||
\(446\) | −1729.32 | −0.183600 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 321.965 | 0.0339541 | ||||||||
\(449\) | 10146.5 | 1.06647 | 0.533233 | − | 0.845968i | \(-0.320977\pi\) | ||||
0.533233 | + | 0.845968i | \(0.320977\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1270.95 | −0.132698 | ||||||||
\(452\) | −1107.09 | −0.115206 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −3958.79 | −0.409241 | ||||||||
\(455\) | −1577.82 | −0.162570 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −4728.87 | −0.484042 | −0.242021 | − | 0.970271i | \(-0.577810\pi\) | ||||
−0.242021 | + | 0.970271i | \(0.577810\pi\) | |||||||
\(458\) | 6227.06 | 0.635308 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −460.000 | −0.0466252 | ||||||||
\(461\) | −8380.69 | −0.846698 | −0.423349 | − | 0.905967i | \(-0.639146\pi\) | ||||
−0.423349 | + | 0.905967i | \(0.639146\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 6845.17 | 0.687089 | 0.343545 | − | 0.939136i | \(-0.388372\pi\) | ||||
0.343545 | + | 0.939136i | \(0.388372\pi\) | |||||||
\(464\) | 568.053 | 0.0568345 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 12037.3 | 1.19660 | ||||||||
\(467\) | 14884.0 | 1.47484 | 0.737418 | − | 0.675436i | \(-0.236045\pi\) | ||||
0.737418 | + | 0.675436i | \(0.236045\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 428.324 | 0.0421710 | ||||||||
\(470\) | −902.701 | −0.0885925 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −6369.62 | −0.621156 | ||||||||
\(473\) | 2439.20 | 0.237114 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 3963.62 | 0.382871 | ||||||||
\(476\) | 397.295 | 0.0382563 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −8449.76 | −0.808542 | ||||||||
\(479\) | −6048.69 | −0.576976 | −0.288488 | − | 0.957483i | \(-0.593153\pi\) | ||||
−0.288488 | + | 0.957483i | \(0.593153\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −8780.71 | −0.832361 | ||||||||
\(482\) | −2788.47 | −0.263509 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −5199.36 | −0.488294 | ||||||||
\(485\) | 531.946 | 0.0498029 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 3199.35 | 0.297693 | 0.148846 | − | 0.988860i | \(-0.452444\pi\) | ||||
0.148846 | + | 0.988860i | \(0.452444\pi\) | |||||||
\(488\) | 4548.64 | 0.421941 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −3176.92 | −0.292895 | ||||||||
\(491\) | 1614.41 | 0.148385 | 0.0741926 | − | 0.997244i | \(-0.476362\pi\) | ||||
0.0741926 | + | 0.997244i | \(0.476362\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 700.960 | 0.0640358 | ||||||||
\(494\) | −19890.3 | −1.81155 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 4512.65 | 0.408516 | ||||||||
\(497\) | 1859.24 | 0.167803 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −5392.04 | −0.483729 | −0.241864 | − | 0.970310i | \(-0.577759\pi\) | ||||
−0.241864 | + | 0.970310i | \(0.577759\pi\) | |||||||
\(500\) | −500.000 | −0.0447214 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −11937.7 | −1.06136 | ||||||||
\(503\) | −12625.4 | −1.11917 | −0.559583 | − | 0.828775i | \(-0.689039\pi\) | ||||
−0.559583 | + | 0.828775i | \(0.689039\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 3213.38 | 0.283156 | ||||||||
\(506\) | −256.781 | −0.0225599 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 6211.15 | 0.542471 | ||||||||
\(509\) | −7065.76 | −0.615294 | −0.307647 | − | 0.951501i | \(-0.599541\pi\) | ||||
−0.307647 | + | 0.951501i | \(0.599541\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1560.46 | −0.135090 | ||||||||
\(512\) | −512.000 | −0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −3272.12 | −0.280792 | ||||||||
\(515\) | −8109.96 | −0.693917 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −503.905 | −0.0428660 | ||||||||
\(518\) | 1408.41 | 0.119463 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 2509.11 | 0.211599 | ||||||||
\(521\) | 8399.20 | 0.706287 | 0.353144 | − | 0.935569i | \(-0.385113\pi\) | ||||
0.353144 | + | 0.935569i | \(0.385113\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −7002.06 | −0.585428 | −0.292714 | − | 0.956200i | \(-0.594558\pi\) | ||||
−0.292714 | + | 0.956200i | \(0.594558\pi\) | |||||||
\(524\) | 1255.49 | 0.104669 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 5991.10 | 0.496624 | ||||||||
\(527\) | 5568.47 | 0.460278 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 529.000 | 0.0434783 | ||||||||
\(530\) | −3301.83 | −0.270608 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 3190.37 | 0.260001 | ||||||||
\(533\) | −14281.9 | −1.16063 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 7454.30 | 0.602388 | ||||||||
\(536\) | −681.136 | −0.0548891 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −10380.3 | −0.831838 | ||||||||
\(539\) | −1773.42 | −0.141719 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 3338.13 | 0.265282 | 0.132641 | − | 0.991164i | \(-0.457654\pi\) | ||||
0.132641 | + | 0.991164i | \(0.457654\pi\) | |||||||
\(542\) | −13440.9 | −1.06519 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −631.792 | −0.0497939 | ||||||||
\(545\) | −6020.00 | −0.473153 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 9609.09 | 0.751106 | 0.375553 | − | 0.926801i | \(-0.377453\pi\) | ||||
0.375553 | + | 0.926801i | \(0.377453\pi\) | |||||||
\(548\) | 4264.37 | 0.332417 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −279.109 | −0.0216387 | ||||||||
\(551\) | 5628.87 | 0.435205 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −6667.98 | −0.512751 | ||||||||
\(554\) | 12229.5 | 0.937872 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −6379.15 | −0.486576 | ||||||||
\(557\) | 11931.1 | 0.907608 | 0.453804 | − | 0.891102i | \(-0.350067\pi\) | ||||
0.453804 | + | 0.891102i | \(0.350067\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 27409.6 | 2.07389 | ||||||||
\(560\) | −402.457 | −0.0303695 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −7098.13 | −0.532770 | ||||||||
\(563\) | 10082.4 | 0.754746 | 0.377373 | − | 0.926061i | \(-0.376827\pi\) | ||||
0.377373 | + | 0.926061i | \(0.376827\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1383.86 | 0.103043 | ||||||||
\(566\) | −6206.23 | −0.460896 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −2956.62 | −0.218410 | ||||||||
\(569\) | 18710.5 | 1.37853 | 0.689267 | − | 0.724507i | \(-0.257933\pi\) | ||||
0.689267 | + | 0.724507i | \(0.257933\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 13510.1 | 0.990159 | 0.495079 | − | 0.868848i | \(-0.335139\pi\) | ||||
0.495079 | + | 0.868848i | \(0.335139\pi\) | |||||||
\(572\) | 1400.63 | 0.102383 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 2290.79 | 0.166578 | ||||||||
\(575\) | 575.000 | 0.0417029 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 11582.3 | 0.835662 | 0.417831 | − | 0.908525i | \(-0.362790\pi\) | ||||
0.417831 | + | 0.908525i | \(0.362790\pi\) | |||||||
\(578\) | 9046.39 | 0.651004 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −710.066 | −0.0508343 | ||||||||
\(581\) | 798.905 | 0.0570468 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1843.14 | −0.130935 | ||||||||
\(584\) | 2481.50 | 0.175831 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 2437.03 | 0.171796 | ||||||||
\(587\) | 6019.34 | 0.423245 | 0.211623 | − | 0.977351i | \(-0.432125\pi\) | ||||
0.211623 | + | 0.977351i | \(0.432125\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 44716.1 | 3.12818 | ||||||||
\(590\) | 7962.03 | 0.555579 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −2239.70 | −0.155492 | ||||||||
\(593\) | −26299.3 | −1.82122 | −0.910608 | − | 0.413270i | \(-0.864387\pi\) | ||||
−0.910608 | + | 0.413270i | \(0.864387\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −496.619 | −0.0342175 | ||||||||
\(596\) | 4387.63 | 0.301551 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −2885.47 | −0.197317 | ||||||||
\(599\) | 27368.0 | 1.86682 | 0.933409 | − | 0.358813i | \(-0.116819\pi\) | ||||
0.933409 | + | 0.358813i | \(0.116819\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −3472.33 | −0.235673 | −0.117836 | − | 0.993033i | \(-0.537596\pi\) | ||||
−0.117836 | + | 0.993033i | \(0.537596\pi\) | |||||||
\(602\) | −4396.46 | −0.297652 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 10937.6 | 0.736832 | ||||||||
\(605\) | 6499.20 | 0.436744 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 5061.10 | 0.338425 | 0.169212 | − | 0.985580i | \(-0.445878\pi\) | ||||
0.169212 | + | 0.985580i | \(0.445878\pi\) | |||||||
\(608\) | −5073.44 | −0.338413 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −5685.80 | −0.377396 | ||||||||
\(611\) | −5662.44 | −0.374922 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −28272.6 | −1.86283 | −0.931417 | − | 0.363953i | \(-0.881427\pi\) | ||||
−0.931417 | + | 0.363953i | \(0.881427\pi\) | |||||||
\(614\) | −5128.90 | −0.337110 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −224.659 | −0.0146944 | ||||||||
\(617\) | 2222.47 | 0.145013 | 0.0725066 | − | 0.997368i | \(-0.476900\pi\) | ||||
0.0725066 | + | 0.997368i | \(0.476900\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −10498.2 | −0.681679 | −0.340840 | − | 0.940121i | \(-0.610711\pi\) | ||||
−0.340840 | + | 0.940121i | \(0.610711\pi\) | |||||||
\(620\) | −5640.81 | −0.365388 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −185.251 | −0.0119419 | ||||||||
\(623\) | 6207.34 | 0.399185 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 625.000 | 0.0400000 | ||||||||
\(626\) | 8552.87 | 0.546073 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −5758.51 | −0.365907 | ||||||||
\(629\) | −2763.72 | −0.175194 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −11402.2 | −0.719355 | −0.359678 | − | 0.933077i | \(-0.617113\pi\) | ||||
−0.359678 | + | 0.933077i | \(0.617113\pi\) | |||||||
\(632\) | 10603.6 | 0.667390 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −5928.47 | −0.371372 | ||||||||
\(635\) | −7763.93 | −0.485200 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −19928.1 | −1.23953 | ||||||||
\(638\) | −396.372 | −0.0245964 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 640.000 | 0.0395285 | ||||||||
\(641\) | −26128.3 | −1.60999 | −0.804996 | − | 0.593280i | \(-0.797833\pi\) | ||||
−0.804996 | + | 0.593280i | \(0.797833\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 863.502 | 0.0529599 | 0.0264799 | − | 0.999649i | \(-0.491570\pi\) | ||||
0.0264799 | + | 0.999649i | \(0.491570\pi\) | |||||||
\(644\) | 462.825 | 0.0283197 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −6260.47 | −0.381292 | ||||||||
\(647\) | 5477.43 | 0.332828 | 0.166414 | − | 0.986056i | \(-0.446781\pi\) | ||||
0.166414 | + | 0.986056i | \(0.446781\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 4444.55 | 0.268820 | ||||||||
\(650\) | −3136.38 | −0.189260 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −11983.3 | −0.719787 | ||||||||
\(653\) | −19233.2 | −1.15261 | −0.576305 | − | 0.817235i | \(-0.695506\pi\) | ||||
−0.576305 | + | 0.817235i | \(0.695506\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −1569.36 | −0.0936185 | ||||||||
\(656\) | −3642.88 | −0.216815 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 908.245 | 0.0538102 | ||||||||
\(659\) | −9952.51 | −0.588307 | −0.294154 | − | 0.955758i | \(-0.595038\pi\) | ||||
−0.294154 | + | 0.955758i | \(0.595038\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 3047.96 | 0.179352 | 0.0896762 | − | 0.995971i | \(-0.471417\pi\) | ||||
0.0896762 | + | 0.995971i | \(0.471417\pi\) | |||||||
\(662\) | 2697.61 | 0.158377 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −1270.45 | −0.0742513 | ||||||||
\(665\) | −3987.97 | −0.232552 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 816.576 | 0.0474032 | ||||||||
\(668\) | 1406.13 | 0.0814442 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 851.419 | 0.0490943 | ||||||||
\(671\) | −3173.92 | −0.182605 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 16245.9 | 0.930508 | 0.465254 | − | 0.885177i | \(-0.345963\pi\) | ||||
0.465254 | + | 0.885177i | \(0.345963\pi\) | |||||||
\(674\) | 11528.6 | 0.658850 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 6951.05 | 0.395486 | ||||||||
\(677\) | 30056.6 | 1.70631 | 0.853154 | − | 0.521659i | \(-0.174687\pi\) | ||||
0.853154 | + | 0.521659i | \(0.174687\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −535.213 | −0.0302498 | ||||||||
\(680\) | 789.740 | 0.0445370 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −3148.81 | −0.176795 | ||||||||
\(683\) | −10064.8 | −0.563866 | −0.281933 | − | 0.959434i | \(-0.590976\pi\) | ||||
−0.281933 | + | 0.959434i | \(0.590976\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −5330.46 | −0.297323 | ||||||||
\(686\) | 6647.50 | 0.369975 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 6991.39 | 0.387419 | ||||||||
\(689\) | −20711.6 | −1.14521 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 10260.7 | 0.564886 | 0.282443 | − | 0.959284i | \(-0.408855\pi\) | ||||
0.282443 | + | 0.959284i | \(0.408855\pi\) | |||||||
\(692\) | 14807.1 | 0.813411 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 8132.31 | 0.444810 | ||||||||
\(695\) | 7973.94 | 0.435207 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −4495.21 | −0.244287 | ||||||||
\(698\) | −16815.6 | −0.911865 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 503.071 | 0.0271633 | ||||||||
\(701\) | 19815.6 | 1.06766 | 0.533828 | − | 0.845593i | \(-0.320753\pi\) | ||||
0.533828 | + | 0.845593i | \(0.320753\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −22193.3 | −1.19067 | ||||||||
\(704\) | 357.260 | 0.0191261 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 512.136 | 0.0273010 | ||||||||
\(707\) | −3233.12 | −0.171986 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −30533.5 | −1.61736 | −0.808681 | − | 0.588247i | \(-0.799818\pi\) | ||||
−0.808681 | + | 0.588247i | \(0.799818\pi\) | |||||||
\(710\) | 3695.78 | 0.195352 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −9871.12 | −0.519573 | ||||||||
\(713\) | 6486.93 | 0.340726 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1750.79 | −0.0915745 | ||||||||
\(716\) | −14336.4 | −0.748290 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −24105.0 | −1.25291 | ||||||||
\(719\) | −9125.45 | −0.473327 | −0.236663 | − | 0.971592i | \(-0.576054\pi\) | ||||
−0.236663 | + | 0.971592i | \(0.576054\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 8159.77 | 0.421478 | ||||||||
\(722\) | −36555.0 | −1.88426 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 3134.69 | 0.160911 | ||||||||
\(725\) | 887.583 | 0.0454676 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 2635.53 | 0.134452 | 0.0672259 | − | 0.997738i | \(-0.478585\pi\) | ||||
0.0672259 | + | 0.997738i | \(0.478585\pi\) | |||||||
\(728\) | −2524.52 | −0.128523 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −3101.88 | −0.157268 | ||||||||
\(731\) | 8627.17 | 0.436508 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 10778.0 | 0.543102 | 0.271551 | − | 0.962424i | \(-0.412463\pi\) | ||||
0.271551 | + | 0.962424i | \(0.412463\pi\) | |||||||
\(734\) | 18490.8 | 0.929848 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −736.000 | −0.0368605 | ||||||||
\(737\) | 475.278 | 0.0237545 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −1758.72 | −0.0875449 | −0.0437725 | − | 0.999042i | \(-0.513938\pi\) | ||||
−0.0437725 | + | 0.999042i | \(0.513938\pi\) | |||||||
\(740\) | 2799.63 | 0.139076 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 3322.11 | 0.164364 | ||||||||
\(743\) | −9737.97 | −0.480823 | −0.240412 | − | 0.970671i | \(-0.577282\pi\) | ||||
−0.240412 | + | 0.970671i | \(0.577282\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −5484.54 | −0.269716 | ||||||||
\(746\) | 1738.53 | 0.0853245 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 440.848 | 0.0215495 | ||||||||
\(749\) | −7500.08 | −0.365884 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −23795.7 | −1.15621 | −0.578107 | − | 0.815961i | \(-0.696208\pi\) | ||||
−0.578107 | + | 0.815961i | \(0.696208\pi\) | |||||||
\(752\) | −1444.32 | −0.0700385 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −4454.08 | −0.215130 | ||||||||
\(755\) | −13672.1 | −0.659043 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 23647.6 | 1.13538 | 0.567692 | − | 0.823241i | \(-0.307837\pi\) | ||||
0.567692 | + | 0.823241i | \(0.307837\pi\) | |||||||
\(758\) | −2557.53 | −0.122551 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 6341.80 | 0.302686 | ||||||||
\(761\) | 4606.09 | 0.219410 | 0.109705 | − | 0.993964i | \(-0.465009\pi\) | ||||
0.109705 | + | 0.993964i | \(0.465009\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 6056.98 | 0.287388 | ||||||||
\(764\) | −5967.79 | −0.282601 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −10687.5 | −0.504119 | ||||||||
\(767\) | 49944.0 | 2.35120 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 17760.9 | 0.832867 | 0.416433 | − | 0.909166i | \(-0.363280\pi\) | ||||
0.416433 | + | 0.909166i | \(0.363280\pi\) | |||||||
\(770\) | 280.824 | 0.0131431 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 12364.4 | 0.576430 | ||||||||
\(773\) | −7147.47 | −0.332570 | −0.166285 | − | 0.986078i | \(-0.553177\pi\) | ||||
−0.166285 | + | 0.986078i | \(0.553177\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 7051.02 | 0.326813 | ||||||||
\(776\) | 851.114 | 0.0393727 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −1416.69 | −0.0652839 | ||||||||
\(779\) | −36097.6 | −1.66024 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 2063.05 | 0.0945222 | ||||||||
\(782\) | −908.201 | −0.0415310 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −5083.07 | −0.231554 | ||||||||
\(785\) | 7198.13 | 0.327277 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −31719.1 | −1.43668 | −0.718338 | − | 0.695694i | \(-0.755097\pi\) | ||||
−0.718338 | + | 0.695694i | \(0.755097\pi\) | |||||||
\(788\) | −11281.2 | −0.509995 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −13254.6 | −0.596932 | ||||||||
\(791\) | −1392.36 | −0.0625872 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −35665.7 | −1.59713 | ||||||||
\(794\) | 11848.0 | 0.529560 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 5264.42 | 0.234413 | ||||||||
\(797\) | −30828.3 | −1.37013 | −0.685066 | − | 0.728481i | \(-0.740227\pi\) | ||||
−0.685066 | + | 0.728481i | \(0.740227\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1782.25 | −0.0789129 | ||||||||
\(800\) | −800.000 | −0.0353553 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −22787.3 | −1.00330 | ||||||||
\(803\) | −1731.53 | −0.0760949 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −578.532 | −0.0253299 | ||||||||
\(806\) | −35383.5 | −1.54632 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 5141.41 | 0.223854 | ||||||||
\(809\) | −36679.2 | −1.59403 | −0.797015 | − | 0.603959i | \(-0.793589\pi\) | ||||
−0.797015 | + | 0.603959i | \(0.793589\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −12210.0 | −0.528672 | −0.264336 | − | 0.964431i | \(-0.585153\pi\) | ||||
−0.264336 | + | 0.964431i | \(0.585153\pi\) | |||||||
\(812\) | 714.427 | 0.0308762 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 1562.80 | 0.0672927 | ||||||||
\(815\) | 14979.1 | 0.643797 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 69278.2 | 2.96663 | ||||||||
\(818\) | −27608.9 | −1.18010 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 4553.60 | 0.193925 | ||||||||
\(821\) | 9996.47 | 0.424944 | 0.212472 | − | 0.977167i | \(-0.431849\pi\) | ||||
0.212472 | + | 0.977167i | \(0.431849\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −42868.8 | −1.81569 | −0.907845 | − | 0.419306i | \(-0.862273\pi\) | ||||
−0.907845 | + | 0.419306i | \(0.862273\pi\) | |||||||
\(824\) | −12975.9 | −0.548590 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −8010.93 | −0.337453 | ||||||||
\(827\) | 15833.4 | 0.665759 | 0.332880 | − | 0.942969i | \(-0.391980\pi\) | ||||
0.332880 | + | 0.942969i | \(0.391980\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −17722.3 | −0.742484 | −0.371242 | − | 0.928536i | \(-0.621068\pi\) | ||||
−0.371242 | + | 0.928536i | \(0.621068\pi\) | |||||||
\(830\) | 1588.06 | 0.0664123 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 4014.57 | 0.167284 | ||||||||
\(833\) | −6272.35 | −0.260893 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −1757.66 | −0.0728459 | ||||||||
\(836\) | 3540.11 | 0.146456 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −29591.7 | −1.21984 | ||||||||
\(839\) | 40528.4 | 1.66769 | 0.833847 | − | 0.551996i | \(-0.186134\pi\) | ||||
0.833847 | + | 0.551996i | \(0.186134\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −23128.5 | −0.948317 | ||||||||
\(842\) | −11609.3 | −0.475159 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −13596.7 | −0.554525 | ||||||||
\(845\) | −8688.82 | −0.353733 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −6539.11 | −0.265273 | ||||||||
\(848\) | −5282.92 | −0.213934 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −987.175 | −0.0398351 | ||||||||
\(851\) | −3219.57 | −0.129689 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 8116.97 | 0.325814 | 0.162907 | − | 0.986641i | \(-0.447913\pi\) | ||||
0.162907 | + | 0.986641i | \(0.447913\pi\) | |||||||
\(854\) | 5720.73 | 0.229226 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 11926.9 | 0.476229 | ||||||||
\(857\) | −16285.5 | −0.649126 | −0.324563 | − | 0.945864i | \(-0.605217\pi\) | ||||
−0.324563 | + | 0.945864i | \(0.605217\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −26487.5 | −1.05209 | −0.526043 | − | 0.850458i | \(-0.676325\pi\) | ||||
−0.526043 | + | 0.850458i | \(0.676325\pi\) | |||||||
\(860\) | −8739.24 | −0.346518 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 30536.3 | 1.20658 | ||||||||
\(863\) | −40396.2 | −1.59340 | −0.796699 | − | 0.604376i | \(-0.793422\pi\) | ||||
−0.796699 | + | 0.604376i | \(0.793422\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −18508.8 | −0.727537 | ||||||||
\(866\) | −4501.25 | −0.176627 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 5675.46 | 0.221933 | ||||||||
\(869\) | −7398.94 | −0.288828 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 5340.76 | 0.207767 | ||||||||
\(872\) | −9632.00 | −0.374060 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −7293.07 | −0.282256 | ||||||||
\(875\) | −628.839 | −0.0242956 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 10962.9 | 0.422109 | 0.211054 | − | 0.977474i | \(-0.432310\pi\) | ||||
0.211054 | + | 0.977474i | \(0.432310\pi\) | |||||||
\(878\) | −20732.4 | −0.796908 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −446.575 | −0.0171069 | ||||||||
\(881\) | −23906.5 | −0.914222 | −0.457111 | − | 0.889410i | \(-0.651116\pi\) | ||||
−0.457111 | + | 0.889410i | \(0.651116\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −30509.1 | −1.16275 | −0.581377 | − | 0.813634i | \(-0.697486\pi\) | ||||
−0.581377 | + | 0.813634i | \(0.697486\pi\) | |||||||
\(884\) | 4953.86 | 0.188480 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −7762.22 | −0.294331 | ||||||||
\(887\) | 40034.3 | 1.51547 | 0.757733 | − | 0.652565i | \(-0.226307\pi\) | ||||
0.757733 | + | 0.652565i | \(0.226307\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 7811.62 | 0.294706 | ||||||||
\(890\) | 12338.9 | 0.464720 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 3458.64 | 0.129825 | ||||||||
\(893\) | −14311.9 | −0.536314 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 17920.5 | 0.669291 | ||||||||
\(896\) | −643.931 | −0.0240092 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −20293.0 | −0.754106 | ||||||||
\(899\) | 10013.4 | 0.371485 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −6518.96 | −0.241041 | ||||||||
\(902\) | 2541.91 | 0.0938318 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 2214.17 | 0.0814626 | ||||||||
\(905\) | −3918.36 | −0.143923 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −2843.48 | −0.104097 | −0.0520486 | − | 0.998645i | \(-0.516575\pi\) | ||||
−0.0520486 | + | 0.998645i | \(0.516575\pi\) | |||||||
\(908\) | 7917.58 | 0.289377 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 3155.65 | 0.114955 | ||||||||
\(911\) | −42268.6 | −1.53723 | −0.768617 | − | 0.639710i | \(-0.779055\pi\) | ||||
−0.768617 | + | 0.639710i | \(0.779055\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 886.483 | 0.0321340 | ||||||||
\(914\) | 9457.74 | 0.342269 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −12454.1 | −0.449231 | ||||||||
\(917\) | 1579.00 | 0.0568629 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −12699.6 | −0.455844 | −0.227922 | − | 0.973679i | \(-0.573193\pi\) | ||||
−0.227922 | + | 0.973679i | \(0.573193\pi\) | |||||||
\(920\) | 920.000 | 0.0329690 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 16761.4 | 0.598706 | ||||||||
\(923\) | 23182.8 | 0.826728 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −3499.53 | −0.124393 | ||||||||
\(926\) | −13690.3 | −0.485845 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −1136.11 | −0.0401880 | ||||||||
\(929\) | 24889.6 | 0.879011 | 0.439505 | − | 0.898240i | \(-0.355154\pi\) | ||||
0.439505 | + | 0.898240i | \(0.355154\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −50368.5 | −1.77310 | ||||||||
\(932\) | −24074.6 | −0.846126 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −29768.0 | −1.04287 | ||||||||
\(935\) | −551.060 | −0.0192744 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 9585.48 | 0.334199 | 0.167099 | − | 0.985940i | \(-0.446560\pi\) | ||||
0.167099 | + | 0.985940i | \(0.446560\pi\) | |||||||
\(938\) | −856.649 | −0.0298194 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 1805.40 | 0.0626444 | ||||||||
\(941\) | 21146.9 | 0.732592 | 0.366296 | − | 0.930498i | \(-0.380626\pi\) | ||||
0.366296 | + | 0.930498i | \(0.380626\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −5236.65 | −0.180836 | ||||||||
\(944\) | 12739.2 | 0.439224 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −4878.41 | −0.167665 | ||||||||
\(947\) | −48747.2 | −1.67272 | −0.836362 | − | 0.548177i | \(-0.815322\pi\) | ||||
−0.836362 | + | 0.548177i | \(0.815322\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −19457.3 | −0.665556 | ||||||||
\(950\) | −7927.25 | −0.270730 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −794.591 | −0.0270513 | ||||||||
\(953\) | −24925.9 | −0.847249 | −0.423625 | − | 0.905838i | \(-0.639242\pi\) | ||||
−0.423625 | + | 0.905838i | \(0.639242\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 7459.73 | 0.252766 | ||||||||
\(956\) | 16899.5 | 0.571725 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 12097.4 | 0.407984 | ||||||||
\(959\) | 5363.20 | 0.180591 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 49755.9 | 1.67017 | ||||||||
\(962\) | 17561.4 | 0.588568 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 5576.95 | 0.186329 | ||||||||
\(965\) | −15455.5 | −0.515574 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1881.92 | −0.0625838 | −0.0312919 | − | 0.999510i | \(-0.509962\pi\) | ||||
−0.0312919 | + | 0.999510i | \(0.509962\pi\) | |||||||
\(968\) | 10398.7 | 0.345276 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −1063.89 | −0.0352160 | ||||||||
\(971\) | 14637.3 | 0.483763 | 0.241881 | − | 0.970306i | \(-0.422236\pi\) | ||||
0.241881 | + | 0.970306i | \(0.422236\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −8022.92 | −0.264340 | ||||||||
\(974\) | −6398.70 | −0.210501 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −9097.28 | −0.298358 | ||||||||
\(977\) | −42591.4 | −1.39470 | −0.697348 | − | 0.716733i | \(-0.745637\pi\) | ||||
−0.697348 | + | 0.716733i | \(0.745637\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 6887.81 | 0.224857 | ||||||||
\(980\) | 6353.84 | 0.207108 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −3228.81 | −0.104924 | ||||||||
\(983\) | 48858.3 | 1.58529 | 0.792644 | − | 0.609684i | \(-0.208704\pi\) | ||||
0.792644 | + | 0.609684i | \(0.208704\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 14101.5 | 0.456153 | ||||||||
\(986\) | −1401.92 | −0.0452801 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 39780.6 | 1.28096 | ||||||||
\(989\) | 10050.1 | 0.323130 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −56522.1 | −1.81179 | −0.905895 | − | 0.423502i | \(-0.860801\pi\) | ||||
−0.905895 | + | 0.423502i | \(0.860801\pi\) | |||||||
\(992\) | −9025.30 | −0.288864 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −3718.48 | −0.118655 | ||||||||
\(995\) | −6580.53 | −0.209665 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −20767.9 | −0.659706 | −0.329853 | − | 0.944032i | \(-0.606999\pi\) | ||||
−0.329853 | + | 0.944032i | \(0.606999\pi\) | |||||||
\(998\) | 10784.1 | 0.342048 | ||||||||
\(999\) | 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 | 2070.4.a.bg.1.3 | 4 | ||
3.2 | odd | 2 | 230.4.a.j.1.1 | ✓ | 4 | ||
12.11 | even | 2 | 1840.4.a.k.1.4 | 4 | |||
15.2 | even | 4 | 1150.4.b.o.599.8 | 8 | |||
15.8 | even | 4 | 1150.4.b.o.599.1 | 8 | |||
15.14 | odd | 2 | 1150.4.a.n.1.4 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
230.4.a.j.1.1 | ✓ | 4 | 3.2 | odd | 2 | ||
1150.4.a.n.1.4 | 4 | 15.14 | odd | 2 | |||
1150.4.b.o.599.1 | 8 | 15.8 | even | 4 | |||
1150.4.b.o.599.8 | 8 | 15.2 | even | 4 | |||
1840.4.a.k.1.4 | 4 | 12.11 | even | 2 | |||
2070.4.a.bg.1.3 | 4 | 1.1 | even | 1 | trivial |