Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2450,4,Mod(1,2450)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2450, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2450.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2450 = 2 \cdot 5^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 2450.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(144.554679514\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 146x^{6} + 4997x^{4} - 4646x^{2} + 676 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 2\cdot 7^{2}\cdot 11^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(-0.424582\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2450.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
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 | ||||||||
\(3\) | −1.83880 | −0.353876 | −0.176938 | − | 0.984222i | \(-0.556619\pi\) | ||||
−0.176938 | + | 0.984222i | \(0.556619\pi\) | |||||||
\(4\) | 4.00000 | 0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 3.67759 | 0.250228 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −8.00000 | −0.353553 | ||||||||
\(9\) | −23.6188 | −0.874771 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −69.0013 | −1.89133 | −0.945667 | − | 0.325138i | \(-0.894589\pi\) | ||||
−0.945667 | + | 0.325138i | \(0.894589\pi\) | |||||||
\(12\) | −7.35518 | −0.176938 | ||||||||
\(13\) | −8.88477 | −0.189553 | −0.0947766 | − | 0.995499i | \(-0.530214\pi\) | ||||
−0.0947766 | + | 0.995499i | \(0.530214\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 16.0000 | 0.250000 | ||||||||
\(17\) | 87.9891 | 1.25532 | 0.627661 | − | 0.778487i | \(-0.284012\pi\) | ||||
0.627661 | + | 0.778487i | \(0.284012\pi\) | |||||||
\(18\) | 47.2377 | 0.618557 | ||||||||
\(19\) | 150.474 | 1.81690 | 0.908452 | − | 0.417988i | \(-0.137265\pi\) | ||||
0.908452 | + | 0.417988i | \(0.137265\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 138.003 | 1.33737 | ||||||||
\(23\) | −56.9429 | −0.516236 | −0.258118 | − | 0.966113i | \(-0.583102\pi\) | ||||
−0.258118 | + | 0.966113i | \(0.583102\pi\) | |||||||
\(24\) | 14.7104 | 0.125114 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 17.7695 | 0.134034 | ||||||||
\(27\) | 93.0777 | 0.663437 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −160.791 | −1.02959 | −0.514796 | − | 0.857312i | \(-0.672132\pi\) | ||||
−0.514796 | + | 0.857312i | \(0.672132\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 121.614 | 0.704598 | 0.352299 | − | 0.935887i | \(-0.385400\pi\) | ||||
0.352299 | + | 0.935887i | \(0.385400\pi\) | |||||||
\(32\) | −32.0000 | −0.176777 | ||||||||
\(33\) | 126.879 | 0.669298 | ||||||||
\(34\) | −175.978 | −0.887647 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −94.4753 | −0.437386 | ||||||||
\(37\) | −96.0929 | −0.426961 | −0.213481 | − | 0.976947i | \(-0.568480\pi\) | ||||
−0.213481 | + | 0.976947i | \(0.568480\pi\) | |||||||
\(38\) | −300.949 | −1.28475 | ||||||||
\(39\) | 16.3373 | 0.0670784 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −165.669 | −0.631051 | −0.315525 | − | 0.948917i | \(-0.602181\pi\) | ||||
−0.315525 | + | 0.948917i | \(0.602181\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −311.670 | −1.10533 | −0.552666 | − | 0.833403i | \(-0.686390\pi\) | ||||
−0.552666 | + | 0.833403i | \(0.686390\pi\) | |||||||
\(44\) | −276.005 | −0.945667 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 113.886 | 0.365034 | ||||||||
\(47\) | −641.297 | −1.99027 | −0.995136 | − | 0.0985153i | \(-0.968591\pi\) | ||||
−0.995136 | + | 0.0985153i | \(0.968591\pi\) | |||||||
\(48\) | −29.4207 | −0.0884691 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −161.794 | −0.444229 | ||||||||
\(52\) | −35.5391 | −0.0947766 | ||||||||
\(53\) | −385.445 | −0.998960 | −0.499480 | − | 0.866325i | \(-0.666476\pi\) | ||||
−0.499480 | + | 0.866325i | \(0.666476\pi\) | |||||||
\(54\) | −186.155 | −0.469121 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −276.692 | −0.642960 | ||||||||
\(58\) | 321.583 | 0.728032 | ||||||||
\(59\) | 249.674 | 0.550928 | 0.275464 | − | 0.961311i | \(-0.411169\pi\) | ||||
0.275464 | + | 0.961311i | \(0.411169\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −453.791 | −0.952491 | −0.476245 | − | 0.879312i | \(-0.658003\pi\) | ||||
−0.476245 | + | 0.879312i | \(0.658003\pi\) | |||||||
\(62\) | −243.228 | −0.498226 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 64.0000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −253.759 | −0.473265 | ||||||||
\(67\) | −570.001 | −1.03935 | −0.519677 | − | 0.854363i | \(-0.673948\pi\) | ||||
−0.519677 | + | 0.854363i | \(0.673948\pi\) | |||||||
\(68\) | 351.956 | 0.627661 | ||||||||
\(69\) | 104.706 | 0.182684 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 274.128 | 0.458211 | 0.229106 | − | 0.973402i | \(-0.426420\pi\) | ||||
0.229106 | + | 0.973402i | \(0.426420\pi\) | |||||||
\(72\) | 188.951 | 0.309278 | ||||||||
\(73\) | 750.031 | 1.20253 | 0.601263 | − | 0.799051i | \(-0.294664\pi\) | ||||
0.601263 | + | 0.799051i | \(0.294664\pi\) | |||||||
\(74\) | 192.186 | 0.301907 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 601.898 | 0.908452 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −32.6746 | −0.0474316 | ||||||||
\(79\) | 427.803 | 0.609261 | 0.304631 | − | 0.952471i | \(-0.401467\pi\) | ||||
0.304631 | + | 0.952471i | \(0.401467\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 466.558 | 0.639997 | ||||||||
\(82\) | 331.337 | 0.446220 | ||||||||
\(83\) | −676.015 | −0.894003 | −0.447002 | − | 0.894533i | \(-0.647508\pi\) | ||||
−0.447002 | + | 0.894533i | \(0.647508\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 623.341 | 0.781588 | ||||||||
\(87\) | 295.662 | 0.364349 | ||||||||
\(88\) | 552.010 | 0.668687 | ||||||||
\(89\) | −658.636 | −0.784442 | −0.392221 | − | 0.919871i | \(-0.628293\pi\) | ||||
−0.392221 | + | 0.919871i | \(0.628293\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −227.772 | −0.258118 | ||||||||
\(93\) | −223.624 | −0.249341 | ||||||||
\(94\) | 1282.59 | 1.40733 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 58.8415 | 0.0625571 | ||||||||
\(97\) | −169.978 | −0.177924 | −0.0889619 | − | 0.996035i | \(-0.528355\pi\) | ||||
−0.0889619 | + | 0.996035i | \(0.528355\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1629.73 | 1.65448 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 386.870 | 0.381139 | 0.190570 | − | 0.981674i | \(-0.438967\pi\) | ||||
0.190570 | + | 0.981674i | \(0.438967\pi\) | |||||||
\(102\) | 323.588 | 0.314117 | ||||||||
\(103\) | −1690.37 | −1.61706 | −0.808531 | − | 0.588453i | \(-0.799737\pi\) | ||||
−0.808531 | + | 0.588453i | \(0.799737\pi\) | |||||||
\(104\) | 71.0782 | 0.0670172 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 770.889 | 0.706372 | ||||||||
\(107\) | −984.275 | −0.889285 | −0.444642 | − | 0.895708i | \(-0.646669\pi\) | ||||
−0.444642 | + | 0.895708i | \(0.646669\pi\) | |||||||
\(108\) | 372.311 | 0.331719 | ||||||||
\(109\) | 887.811 | 0.780155 | 0.390077 | − | 0.920782i | \(-0.372448\pi\) | ||||
0.390077 | + | 0.920782i | \(0.372448\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 176.695 | 0.151092 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 631.384 | 0.525625 | 0.262812 | − | 0.964847i | \(-0.415350\pi\) | ||||
0.262812 | + | 0.964847i | \(0.415350\pi\) | |||||||
\(114\) | 553.383 | 0.454641 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −643.165 | −0.514796 | ||||||||
\(117\) | 209.848 | 0.165816 | ||||||||
\(118\) | −499.347 | −0.389565 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 3430.18 | 2.57714 | ||||||||
\(122\) | 907.581 | 0.673512 | ||||||||
\(123\) | 304.631 | 0.223314 | ||||||||
\(124\) | 486.457 | 0.352299 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 520.877 | 0.363940 | 0.181970 | − | 0.983304i | \(-0.441753\pi\) | ||||
0.181970 | + | 0.983304i | \(0.441753\pi\) | |||||||
\(128\) | −128.000 | −0.0883883 | ||||||||
\(129\) | 573.098 | 0.391151 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 174.337 | 0.116274 | 0.0581370 | − | 0.998309i | \(-0.481484\pi\) | ||||
0.0581370 | + | 0.998309i | \(0.481484\pi\) | |||||||
\(132\) | 507.517 | 0.334649 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 1140.00 | 0.734934 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −703.913 | −0.443824 | ||||||||
\(137\) | −2185.52 | −1.36293 | −0.681465 | − | 0.731850i | \(-0.738657\pi\) | ||||
−0.681465 | + | 0.731850i | \(0.738657\pi\) | |||||||
\(138\) | −209.413 | −0.129177 | ||||||||
\(139\) | −761.596 | −0.464732 | −0.232366 | − | 0.972628i | \(-0.574647\pi\) | ||||
−0.232366 | + | 0.972628i | \(0.574647\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1179.21 | 0.704310 | ||||||||
\(142\) | −548.256 | −0.324004 | ||||||||
\(143\) | 613.060 | 0.358508 | ||||||||
\(144\) | −377.901 | −0.218693 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −1500.06 | −0.850315 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −384.372 | −0.213481 | ||||||||
\(149\) | −3228.60 | −1.77515 | −0.887574 | − | 0.460665i | \(-0.847611\pi\) | ||||
−0.887574 | + | 0.460665i | \(0.847611\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 3205.47 | 1.72753 | 0.863767 | − | 0.503891i | \(-0.168099\pi\) | ||||
0.863767 | + | 0.503891i | \(0.168099\pi\) | |||||||
\(152\) | −1203.80 | −0.642373 | ||||||||
\(153\) | −2078.20 | −1.09812 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 65.3491 | 0.0335392 | ||||||||
\(157\) | −237.052 | −0.120502 | −0.0602510 | − | 0.998183i | \(-0.519190\pi\) | ||||
−0.0602510 | + | 0.998183i | \(0.519190\pi\) | |||||||
\(158\) | −855.606 | −0.430813 | ||||||||
\(159\) | 708.754 | 0.353508 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −933.115 | −0.452546 | ||||||||
\(163\) | 741.303 | 0.356217 | 0.178108 | − | 0.984011i | \(-0.443002\pi\) | ||||
0.178108 | + | 0.984011i | \(0.443002\pi\) | |||||||
\(164\) | −662.674 | −0.315525 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 1352.03 | 0.632156 | ||||||||
\(167\) | 1723.47 | 0.798601 | 0.399300 | − | 0.916820i | \(-0.369253\pi\) | ||||
0.399300 | + | 0.916820i | \(0.369253\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2118.06 | −0.964070 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −3554.03 | −1.58938 | ||||||||
\(172\) | −1246.68 | −0.552666 | ||||||||
\(173\) | 4172.45 | 1.83367 | 0.916837 | − | 0.399261i | \(-0.130733\pi\) | ||||
0.916837 | + | 0.399261i | \(0.130733\pi\) | |||||||
\(174\) | −591.325 | −0.257633 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −1104.02 | −0.472833 | ||||||||
\(177\) | −459.099 | −0.194960 | ||||||||
\(178\) | 1317.27 | 0.554684 | ||||||||
\(179\) | 1387.62 | 0.579417 | 0.289709 | − | 0.957115i | \(-0.406442\pi\) | ||||
0.289709 | + | 0.957115i | \(0.406442\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −401.725 | −0.164972 | −0.0824862 | − | 0.996592i | \(-0.526286\pi\) | ||||
−0.0824862 | + | 0.996592i | \(0.526286\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 834.428 | 0.337064 | ||||||||
\(184\) | 455.543 | 0.182517 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 447.247 | 0.176311 | ||||||||
\(187\) | −6071.36 | −2.37423 | ||||||||
\(188\) | −2565.19 | −0.995136 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −3284.66 | −1.24434 | −0.622172 | − | 0.782880i | \(-0.713750\pi\) | ||||
−0.622172 | + | 0.782880i | \(0.713750\pi\) | |||||||
\(192\) | −117.683 | −0.0442346 | ||||||||
\(193\) | 1553.77 | 0.579496 | 0.289748 | − | 0.957103i | \(-0.406428\pi\) | ||||
0.289748 | + | 0.957103i | \(0.406428\pi\) | |||||||
\(194\) | 339.955 | 0.125811 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −3956.43 | −1.43088 | −0.715441 | − | 0.698673i | \(-0.753774\pi\) | ||||
−0.715441 | + | 0.698673i | \(0.753774\pi\) | |||||||
\(198\) | −3259.46 | −1.16990 | ||||||||
\(199\) | 3902.76 | 1.39025 | 0.695124 | − | 0.718890i | \(-0.255349\pi\) | ||||
0.695124 | + | 0.718890i | \(0.255349\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1048.12 | 0.367803 | ||||||||
\(202\) | −773.741 | −0.269506 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −647.176 | −0.222115 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 3380.75 | 1.14344 | ||||||||
\(207\) | 1344.92 | 0.451588 | ||||||||
\(208\) | −142.156 | −0.0473883 | ||||||||
\(209\) | −10382.9 | −3.43637 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1140.04 | −0.371961 | −0.185980 | − | 0.982553i | \(-0.559546\pi\) | ||||
−0.185980 | + | 0.982553i | \(0.559546\pi\) | |||||||
\(212\) | −1541.78 | −0.499480 | ||||||||
\(213\) | −504.065 | −0.162150 | ||||||||
\(214\) | 1968.55 | 0.628819 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −744.622 | −0.234561 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −1775.62 | −0.551653 | ||||||||
\(219\) | −1379.15 | −0.425546 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −781.763 | −0.237950 | ||||||||
\(222\) | −353.390 | −0.106838 | ||||||||
\(223\) | −2267.03 | −0.680768 | −0.340384 | − | 0.940287i | \(-0.610557\pi\) | ||||
−0.340384 | + | 0.940287i | \(0.610557\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −1262.77 | −0.371673 | ||||||||
\(227\) | 5404.26 | 1.58015 | 0.790074 | − | 0.613012i | \(-0.210042\pi\) | ||||
0.790074 | + | 0.613012i | \(0.210042\pi\) | |||||||
\(228\) | −1106.77 | −0.321480 | ||||||||
\(229\) | 4865.51 | 1.40402 | 0.702012 | − | 0.712165i | \(-0.252285\pi\) | ||||
0.702012 | + | 0.712165i | \(0.252285\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 1286.33 | 0.364016 | ||||||||
\(233\) | 4980.44 | 1.40034 | 0.700170 | − | 0.713976i | \(-0.253108\pi\) | ||||
0.700170 | + | 0.713976i | \(0.253108\pi\) | |||||||
\(234\) | −419.696 | −0.117249 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 998.695 | 0.275464 | ||||||||
\(237\) | −786.643 | −0.215603 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 3528.95 | 0.955098 | 0.477549 | − | 0.878605i | \(-0.341525\pi\) | ||||
0.477549 | + | 0.878605i | \(0.341525\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −860.934 | −0.230115 | −0.115057 | − | 0.993359i | \(-0.536705\pi\) | ||||
−0.115057 | + | 0.993359i | \(0.536705\pi\) | |||||||
\(242\) | −6860.35 | −1.82231 | ||||||||
\(243\) | −3371.00 | −0.889917 | ||||||||
\(244\) | −1815.16 | −0.476245 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −609.261 | −0.157907 | ||||||||
\(247\) | −1336.93 | −0.344400 | ||||||||
\(248\) | −972.913 | −0.249113 | ||||||||
\(249\) | 1243.05 | 0.316367 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −2359.10 | −0.593246 | −0.296623 | − | 0.954995i | \(-0.595861\pi\) | ||||
−0.296623 | + | 0.954995i | \(0.595861\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3929.13 | 0.976373 | ||||||||
\(254\) | −1041.75 | −0.257344 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 256.000 | 0.0625000 | ||||||||
\(257\) | 2388.61 | 0.579757 | 0.289878 | − | 0.957064i | \(-0.406385\pi\) | ||||
0.289878 | + | 0.957064i | \(0.406385\pi\) | |||||||
\(258\) | −1146.20 | −0.276586 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 3797.70 | 0.900658 | ||||||||
\(262\) | −348.674 | −0.0822181 | ||||||||
\(263\) | 4813.17 | 1.12849 | 0.564244 | − | 0.825608i | \(-0.309168\pi\) | ||||
0.564244 | + | 0.825608i | \(0.309168\pi\) | |||||||
\(264\) | −1015.03 | −0.236633 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 1211.10 | 0.277595 | ||||||||
\(268\) | −2280.00 | −0.519677 | ||||||||
\(269\) | 7915.05 | 1.79401 | 0.897006 | − | 0.442018i | \(-0.145737\pi\) | ||||
0.897006 | + | 0.442018i | \(0.145737\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 3063.01 | 0.686586 | 0.343293 | − | 0.939228i | \(-0.388458\pi\) | ||||
0.343293 | + | 0.939228i | \(0.388458\pi\) | |||||||
\(272\) | 1407.83 | 0.313831 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 4371.04 | 0.963738 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 418.826 | 0.0913418 | ||||||||
\(277\) | −5054.99 | −1.09648 | −0.548240 | − | 0.836321i | \(-0.684702\pi\) | ||||
−0.548240 | + | 0.836321i | \(0.684702\pi\) | |||||||
\(278\) | 1523.19 | 0.328615 | ||||||||
\(279\) | −2872.38 | −0.616362 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 3634.47 | 0.771581 | 0.385790 | − | 0.922586i | \(-0.373929\pi\) | ||||
0.385790 | + | 0.922586i | \(0.373929\pi\) | |||||||
\(282\) | −2358.43 | −0.498022 | ||||||||
\(283\) | 8273.74 | 1.73789 | 0.868945 | − | 0.494908i | \(-0.164798\pi\) | ||||
0.868945 | + | 0.494908i | \(0.164798\pi\) | |||||||
\(284\) | 1096.51 | 0.229106 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −1226.12 | −0.253504 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 755.803 | 0.154639 | ||||||||
\(289\) | 2829.08 | 0.575835 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 312.554 | 0.0629631 | ||||||||
\(292\) | 3000.12 | 0.601263 | ||||||||
\(293\) | 5476.76 | 1.09200 | 0.545999 | − | 0.837786i | \(-0.316150\pi\) | ||||
0.545999 | + | 0.837786i | \(0.316150\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 768.743 | 0.150954 | ||||||||
\(297\) | −6422.48 | −1.25478 | ||||||||
\(298\) | 6457.20 | 1.25522 | ||||||||
\(299\) | 505.925 | 0.0978541 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −6410.95 | −1.22155 | ||||||||
\(303\) | −711.376 | −0.134876 | ||||||||
\(304\) | 2407.59 | 0.454226 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 4156.40 | 0.776488 | ||||||||
\(307\) | 6893.24 | 1.28149 | 0.640746 | − | 0.767753i | \(-0.278625\pi\) | ||||
0.640746 | + | 0.767753i | \(0.278625\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 3108.25 | 0.572240 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 7000.66 | 1.27643 | 0.638217 | − | 0.769856i | \(-0.279672\pi\) | ||||
0.638217 | + | 0.769856i | \(0.279672\pi\) | |||||||
\(312\) | −130.698 | −0.0237158 | ||||||||
\(313\) | −1537.68 | −0.277684 | −0.138842 | − | 0.990315i | \(-0.544338\pi\) | ||||
−0.138842 | + | 0.990315i | \(0.544338\pi\) | |||||||
\(314\) | 474.104 | 0.0852078 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 1711.21 | 0.304631 | ||||||||
\(317\) | −9820.96 | −1.74006 | −0.870032 | − | 0.492995i | \(-0.835902\pi\) | ||||
−0.870032 | + | 0.492995i | \(0.835902\pi\) | |||||||
\(318\) | −1417.51 | −0.249968 | ||||||||
\(319\) | 11094.8 | 1.94730 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 1809.88 | 0.314697 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 13240.1 | 2.28080 | ||||||||
\(324\) | 1866.23 | 0.319998 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −1482.61 | −0.251883 | ||||||||
\(327\) | −1632.50 | −0.276078 | ||||||||
\(328\) | 1325.35 | 0.223110 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1173.01 | 0.194787 | 0.0973933 | − | 0.995246i | \(-0.468950\pi\) | ||||
0.0973933 | + | 0.995246i | \(0.468950\pi\) | |||||||
\(332\) | −2704.06 | −0.447002 | ||||||||
\(333\) | 2269.60 | 0.373494 | ||||||||
\(334\) | −3446.95 | −0.564696 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −7801.45 | −1.26104 | −0.630522 | − | 0.776171i | \(-0.717159\pi\) | ||||
−0.630522 | + | 0.776171i | \(0.717159\pi\) | |||||||
\(338\) | 4236.12 | 0.681700 | ||||||||
\(339\) | −1160.99 | −0.186006 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −8391.53 | −1.33263 | ||||||||
\(342\) | 7108.06 | 1.12386 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 2493.36 | 0.390794 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −8344.91 | −1.29660 | ||||||||
\(347\) | −6388.29 | −0.988303 | −0.494152 | − | 0.869376i | \(-0.664521\pi\) | ||||
−0.494152 | + | 0.869376i | \(0.664521\pi\) | |||||||
\(348\) | 1182.65 | 0.182174 | ||||||||
\(349\) | −6800.96 | −1.04312 | −0.521558 | − | 0.853216i | \(-0.674649\pi\) | ||||
−0.521558 | + | 0.853216i | \(0.674649\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −826.974 | −0.125757 | ||||||||
\(352\) | 2208.04 | 0.334344 | ||||||||
\(353\) | 5435.58 | 0.819567 | 0.409783 | − | 0.912183i | \(-0.365604\pi\) | ||||
0.409783 | + | 0.912183i | \(0.365604\pi\) | |||||||
\(354\) | 918.198 | 0.137858 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −2634.55 | −0.392221 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −2775.24 | −0.409710 | ||||||||
\(359\) | 5914.56 | 0.869522 | 0.434761 | − | 0.900546i | \(-0.356833\pi\) | ||||
0.434761 | + | 0.900546i | \(0.356833\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 15783.5 | 2.30114 | ||||||||
\(362\) | 803.450 | 0.116653 | ||||||||
\(363\) | −6307.39 | −0.911990 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −1668.86 | −0.238340 | ||||||||
\(367\) | −6135.60 | −0.872686 | −0.436343 | − | 0.899780i | \(-0.643727\pi\) | ||||
−0.436343 | + | 0.899780i | \(0.643727\pi\) | |||||||
\(368\) | −911.087 | −0.129059 | ||||||||
\(369\) | 3912.90 | 0.552025 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −894.494 | −0.124670 | ||||||||
\(373\) | −2819.17 | −0.391343 | −0.195671 | − | 0.980670i | \(-0.562689\pi\) | ||||
−0.195671 | + | 0.980670i | \(0.562689\pi\) | |||||||
\(374\) | 12142.7 | 1.67884 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 5130.37 | 0.703667 | ||||||||
\(377\) | 1428.59 | 0.195163 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 5166.94 | 0.700285 | 0.350142 | − | 0.936697i | \(-0.386133\pi\) | ||||
0.350142 | + | 0.936697i | \(0.386133\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −957.786 | −0.128790 | ||||||||
\(382\) | 6569.33 | 0.879885 | ||||||||
\(383\) | −1066.26 | −0.142254 | −0.0711270 | − | 0.997467i | \(-0.522660\pi\) | ||||
−0.0711270 | + | 0.997467i | \(0.522660\pi\) | |||||||
\(384\) | 235.366 | 0.0312786 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −3107.54 | −0.409766 | ||||||||
\(387\) | 7361.29 | 0.966913 | ||||||||
\(388\) | −679.911 | −0.0889619 | ||||||||
\(389\) | 9097.26 | 1.18573 | 0.592865 | − | 0.805302i | \(-0.297997\pi\) | ||||
0.592865 | + | 0.805302i | \(0.297997\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −5010.35 | −0.648042 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −320.570 | −0.0411466 | ||||||||
\(394\) | 7912.86 | 1.01179 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 6518.92 | 0.827242 | ||||||||
\(397\) | −4137.44 | −0.523053 | −0.261527 | − | 0.965196i | \(-0.584226\pi\) | ||||
−0.261527 | + | 0.965196i | \(0.584226\pi\) | |||||||
\(398\) | −7805.52 | −0.983054 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −7172.02 | −0.893151 | −0.446575 | − | 0.894746i | \(-0.647357\pi\) | ||||
−0.446575 | + | 0.894746i | \(0.647357\pi\) | |||||||
\(402\) | −2096.23 | −0.260076 | ||||||||
\(403\) | −1080.51 | −0.133559 | ||||||||
\(404\) | 1547.48 | 0.190570 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 6630.53 | 0.807526 | ||||||||
\(408\) | 1294.35 | 0.157059 | ||||||||
\(409\) | −11416.2 | −1.38018 | −0.690092 | − | 0.723721i | \(-0.742430\pi\) | ||||
−0.690092 | + | 0.723721i | \(0.742430\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 4018.72 | 0.482309 | ||||||||
\(412\) | −6761.50 | −0.808531 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −2689.85 | −0.319321 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 284.313 | 0.0335086 | ||||||||
\(417\) | 1400.42 | 0.164458 | ||||||||
\(418\) | 20765.8 | 2.42988 | ||||||||
\(419\) | −16264.2 | −1.89632 | −0.948161 | − | 0.317790i | \(-0.897059\pi\) | ||||
−0.948161 | + | 0.317790i | \(0.897059\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 7877.69 | 0.911960 | 0.455980 | − | 0.889990i | \(-0.349289\pi\) | ||||
0.455980 | + | 0.889990i | \(0.349289\pi\) | |||||||
\(422\) | 2280.08 | 0.263016 | ||||||||
\(423\) | 15146.7 | 1.74103 | ||||||||
\(424\) | 3083.56 | 0.353186 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 1008.13 | 0.114657 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −3937.10 | −0.444642 | ||||||||
\(429\) | −1127.29 | −0.126868 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −4770.51 | −0.533150 | −0.266575 | − | 0.963814i | \(-0.585892\pi\) | ||||
−0.266575 | + | 0.963814i | \(0.585892\pi\) | |||||||
\(432\) | 1489.24 | 0.165859 | ||||||||
\(433\) | −13725.8 | −1.52337 | −0.761686 | − | 0.647947i | \(-0.775628\pi\) | ||||
−0.761686 | + | 0.647947i | \(0.775628\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 3551.24 | 0.390077 | ||||||||
\(437\) | −8568.45 | −0.937951 | ||||||||
\(438\) | 2758.31 | 0.300906 | ||||||||
\(439\) | 11509.6 | 1.25131 | 0.625655 | − | 0.780100i | \(-0.284832\pi\) | ||||
0.625655 | + | 0.780100i | \(0.284832\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 1563.53 | 0.168256 | ||||||||
\(443\) | −6746.38 | −0.723544 | −0.361772 | − | 0.932267i | \(-0.617828\pi\) | ||||
−0.361772 | + | 0.932267i | \(0.617828\pi\) | |||||||
\(444\) | 706.781 | 0.0755458 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 4534.05 | 0.481376 | ||||||||
\(447\) | 5936.73 | 0.628183 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −9537.33 | −1.00244 | −0.501219 | − | 0.865320i | \(-0.667115\pi\) | ||||
−0.501219 | + | 0.865320i | \(0.667115\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 11431.3 | 1.19353 | ||||||||
\(452\) | 2525.54 | 0.262812 | ||||||||
\(453\) | −5894.21 | −0.611334 | ||||||||
\(454\) | −10808.5 | −1.11733 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 2213.53 | 0.227321 | ||||||||
\(457\) | 10645.8 | 1.08969 | 0.544846 | − | 0.838536i | \(-0.316588\pi\) | ||||
0.544846 | + | 0.838536i | \(0.316588\pi\) | |||||||
\(458\) | −9731.01 | −0.992796 | ||||||||
\(459\) | 8189.82 | 0.832828 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −767.927 | −0.0775834 | −0.0387917 | − | 0.999247i | \(-0.512351\pi\) | ||||
−0.0387917 | + | 0.999247i | \(0.512351\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 5752.63 | 0.577424 | 0.288712 | − | 0.957416i | \(-0.406773\pi\) | ||||
0.288712 | + | 0.957416i | \(0.406773\pi\) | |||||||
\(464\) | −2572.66 | −0.257398 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −9960.87 | −0.990190 | ||||||||
\(467\) | −10233.1 | −1.01399 | −0.506993 | − | 0.861950i | \(-0.669243\pi\) | ||||
−0.506993 | + | 0.861950i | \(0.669243\pi\) | |||||||
\(468\) | 839.392 | 0.0829079 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 435.890 | 0.0426428 | ||||||||
\(472\) | −1997.39 | −0.194782 | ||||||||
\(473\) | 21505.7 | 2.09055 | ||||||||
\(474\) | 1573.29 | 0.152454 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 9103.75 | 0.873862 | ||||||||
\(478\) | −7057.89 | −0.675357 | ||||||||
\(479\) | 561.498 | 0.0535606 | 0.0267803 | − | 0.999641i | \(-0.491475\pi\) | ||||
0.0267803 | + | 0.999641i | \(0.491475\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 853.763 | 0.0809319 | ||||||||
\(482\) | 1721.87 | 0.162716 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 13720.7 | 1.28857 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 6742.00 | 0.629266 | ||||||||
\(487\) | −10026.4 | −0.932933 | −0.466466 | − | 0.884539i | \(-0.654473\pi\) | ||||
−0.466466 | + | 0.884539i | \(0.654473\pi\) | |||||||
\(488\) | 3630.32 | 0.336756 | ||||||||
\(489\) | −1363.11 | −0.126057 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 7092.54 | 0.651897 | 0.325949 | − | 0.945387i | \(-0.394316\pi\) | ||||
0.325949 | + | 0.945387i | \(0.394316\pi\) | |||||||
\(492\) | 1218.52 | 0.111657 | ||||||||
\(493\) | −14147.9 | −1.29247 | ||||||||
\(494\) | 2673.86 | 0.243528 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 1945.83 | 0.176150 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −2486.11 | −0.223705 | ||||||||
\(499\) | 17.0592 | 0.00153041 | 0.000765207 | − | 1.00000i | \(-0.499756\pi\) | ||||
0.000765207 | 1.00000i | \(0.499756\pi\) | ||||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −3169.12 | −0.282606 | ||||||||
\(502\) | 4718.19 | 0.419488 | ||||||||
\(503\) | 10954.5 | 0.971044 | 0.485522 | − | 0.874224i | \(-0.338629\pi\) | ||||
0.485522 | + | 0.874224i | \(0.338629\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −7858.27 | −0.690400 | ||||||||
\(507\) | 3894.68 | 0.341161 | ||||||||
\(508\) | 2083.51 | 0.181970 | ||||||||
\(509\) | 20554.0 | 1.78986 | 0.894930 | − | 0.446207i | \(-0.147226\pi\) | ||||
0.894930 | + | 0.446207i | \(0.147226\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −512.000 | −0.0441942 | ||||||||
\(513\) | 14005.8 | 1.20540 | ||||||||
\(514\) | −4777.22 | −0.409950 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 2292.39 | 0.195575 | ||||||||
\(517\) | 44250.3 | 3.76427 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −7672.29 | −0.648894 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 12869.6 | 1.08220 | 0.541102 | − | 0.840957i | \(-0.318007\pi\) | ||||
0.541102 | + | 0.840957i | \(0.318007\pi\) | |||||||
\(522\) | −7595.40 | −0.636862 | ||||||||
\(523\) | 11156.7 | 0.932786 | 0.466393 | − | 0.884578i | \(-0.345553\pi\) | ||||
0.466393 | + | 0.884578i | \(0.345553\pi\) | |||||||
\(524\) | 697.348 | 0.0581370 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −9626.33 | −0.797962 | ||||||||
\(527\) | 10700.7 | 0.884498 | ||||||||
\(528\) | 2030.07 | 0.167325 | ||||||||
\(529\) | −8924.51 | −0.733501 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −5897.00 | −0.481936 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1471.93 | 0.119618 | ||||||||
\(534\) | −2422.20 | −0.196290 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 4560.01 | 0.367467 | ||||||||
\(537\) | −2551.55 | −0.205042 | ||||||||
\(538\) | −15830.1 | −1.26856 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 8229.32 | 0.653985 | 0.326993 | − | 0.945027i | \(-0.393965\pi\) | ||||
0.326993 | + | 0.945027i | \(0.393965\pi\) | |||||||
\(542\) | −6126.03 | −0.485490 | ||||||||
\(543\) | 738.691 | 0.0583798 | ||||||||
\(544\) | −2815.65 | −0.221912 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −11756.3 | −0.918946 | −0.459473 | − | 0.888192i | \(-0.651962\pi\) | ||||
−0.459473 | + | 0.888192i | \(0.651962\pi\) | |||||||
\(548\) | −8742.08 | −0.681465 | ||||||||
\(549\) | 10718.0 | 0.833212 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −24195.0 | −1.87067 | ||||||||
\(552\) | −837.651 | −0.0645884 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 10110.0 | 0.775328 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −3046.38 | −0.232366 | ||||||||
\(557\) | 8931.05 | 0.679391 | 0.339695 | − | 0.940536i | \(-0.389676\pi\) | ||||
0.339695 | + | 0.940536i | \(0.389676\pi\) | |||||||
\(558\) | 5744.77 | 0.435834 | ||||||||
\(559\) | 2769.12 | 0.209519 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 11164.0 | 0.840185 | ||||||||
\(562\) | −7268.94 | −0.545590 | ||||||||
\(563\) | −3444.77 | −0.257868 | −0.128934 | − | 0.991653i | \(-0.541156\pi\) | ||||
−0.128934 | + | 0.991653i | \(0.541156\pi\) | |||||||
\(564\) | 4716.85 | 0.352155 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −16547.5 | −1.22887 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −2193.02 | −0.162002 | ||||||||
\(569\) | 3753.62 | 0.276555 | 0.138278 | − | 0.990393i | \(-0.455843\pi\) | ||||
0.138278 | + | 0.990393i | \(0.455843\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −2168.51 | −0.158931 | −0.0794653 | − | 0.996838i | \(-0.525321\pi\) | ||||
−0.0794653 | + | 0.996838i | \(0.525321\pi\) | |||||||
\(572\) | 2452.24 | 0.179254 | ||||||||
\(573\) | 6039.82 | 0.440344 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −1511.61 | −0.109346 | ||||||||
\(577\) | 5135.98 | 0.370561 | 0.185280 | − | 0.982686i | \(-0.440681\pi\) | ||||
0.185280 | + | 0.982686i | \(0.440681\pi\) | |||||||
\(578\) | −5658.15 | −0.407177 | ||||||||
\(579\) | −2857.06 | −0.205070 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −625.108 | −0.0445216 | ||||||||
\(583\) | 26596.2 | 1.88937 | ||||||||
\(584\) | −6000.24 | −0.425157 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −10953.5 | −0.772160 | ||||||||
\(587\) | −5619.63 | −0.395139 | −0.197570 | − | 0.980289i | \(-0.563305\pi\) | ||||
−0.197570 | + | 0.980289i | \(0.563305\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 18299.8 | 1.28019 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 7275.06 | 0.506356 | ||||||||
\(592\) | −1537.49 | −0.106740 | ||||||||
\(593\) | −13827.3 | −0.957536 | −0.478768 | − | 0.877941i | \(-0.658917\pi\) | ||||
−0.478768 | + | 0.877941i | \(0.658917\pi\) | |||||||
\(594\) | 12845.0 | 0.887264 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −12914.4 | −0.887574 | ||||||||
\(597\) | −7176.38 | −0.491976 | ||||||||
\(598\) | −1011.85 | −0.0691933 | ||||||||
\(599\) | 10933.2 | 0.745771 | 0.372885 | − | 0.927877i | \(-0.378368\pi\) | ||||
0.372885 | + | 0.927877i | \(0.378368\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −7308.53 | −0.496042 | −0.248021 | − | 0.968755i | \(-0.579780\pi\) | ||||
−0.248021 | + | 0.968755i | \(0.579780\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 13462.8 | 0.909197 | ||||||||
\(604\) | 12821.9 | 0.863767 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 1422.75 | 0.0953718 | ||||||||
\(607\) | 7584.43 | 0.507154 | 0.253577 | − | 0.967315i | \(-0.418393\pi\) | ||||
0.253577 | + | 0.967315i | \(0.418393\pi\) | |||||||
\(608\) | −4815.18 | −0.321186 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 5697.77 | 0.377262 | ||||||||
\(612\) | −8312.80 | −0.549060 | ||||||||
\(613\) | −3199.18 | −0.210789 | −0.105395 | − | 0.994430i | \(-0.533611\pi\) | ||||
−0.105395 | + | 0.994430i | \(0.533611\pi\) | |||||||
\(614\) | −13786.5 | −0.906152 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 740.073 | 0.0482888 | 0.0241444 | − | 0.999708i | \(-0.492314\pi\) | ||||
0.0241444 | + | 0.999708i | \(0.492314\pi\) | |||||||
\(618\) | −6216.50 | −0.404635 | ||||||||
\(619\) | −2574.39 | −0.167162 | −0.0835811 | − | 0.996501i | \(-0.526636\pi\) | ||||
−0.0835811 | + | 0.996501i | \(0.526636\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −5300.11 | −0.342490 | ||||||||
\(622\) | −14001.3 | −0.902575 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 261.396 | 0.0167696 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 3075.37 | 0.196352 | ||||||||
\(627\) | 19092.1 | 1.21605 | ||||||||
\(628\) | −948.208 | −0.0602510 | ||||||||
\(629\) | −8455.12 | −0.535974 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 19747.1 | 1.24583 | 0.622916 | − | 0.782289i | \(-0.285948\pi\) | ||||
0.622916 | + | 0.782289i | \(0.285948\pi\) | |||||||
\(632\) | −3422.43 | −0.215406 | ||||||||
\(633\) | 2096.30 | 0.131628 | ||||||||
\(634\) | 19641.9 | 1.23041 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 2835.02 | 0.176754 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −22189.6 | −1.37695 | ||||||||
\(639\) | −6474.58 | −0.400830 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 7302.18 | 0.449951 | 0.224976 | − | 0.974364i | \(-0.427770\pi\) | ||||
0.224976 | + | 0.974364i | \(0.427770\pi\) | |||||||
\(642\) | −3619.76 | −0.222524 | ||||||||
\(643\) | 18721.9 | 1.14824 | 0.574121 | − | 0.818771i | \(-0.305344\pi\) | ||||
0.574121 | + | 0.818771i | \(0.305344\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −26480.2 | −1.61277 | ||||||||
\(647\) | −28433.5 | −1.72772 | −0.863861 | − | 0.503730i | \(-0.831961\pi\) | ||||
−0.863861 | + | 0.503730i | \(0.831961\pi\) | |||||||
\(648\) | −3732.46 | −0.226273 | ||||||||
\(649\) | −17227.8 | −1.04199 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 2965.21 | 0.178108 | ||||||||
\(653\) | 16152.5 | 0.967986 | 0.483993 | − | 0.875072i | \(-0.339186\pi\) | ||||
0.483993 | + | 0.875072i | \(0.339186\pi\) | |||||||
\(654\) | 3265.01 | 0.195217 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −2650.70 | −0.157763 | ||||||||
\(657\) | −17714.8 | −1.05194 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 15915.4 | 0.940785 | 0.470392 | − | 0.882457i | \(-0.344112\pi\) | ||||
0.470392 | + | 0.882457i | \(0.344112\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 7589.60 | 0.446598 | 0.223299 | − | 0.974750i | \(-0.428317\pi\) | ||||
0.223299 | + | 0.974750i | \(0.428317\pi\) | |||||||
\(662\) | −2346.02 | −0.137735 | ||||||||
\(663\) | 1437.50 | 0.0842050 | ||||||||
\(664\) | 5408.12 | 0.316078 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −4539.20 | −0.264100 | ||||||||
\(667\) | 9155.92 | 0.531512 | ||||||||
\(668\) | 6893.89 | 0.399300 | ||||||||
\(669\) | 4168.60 | 0.240908 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 31312.1 | 1.80148 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 30271.8 | 1.73387 | 0.866933 | − | 0.498425i | \(-0.166088\pi\) | ||||
0.866933 | + | 0.498425i | \(0.166088\pi\) | |||||||
\(674\) | 15602.9 | 0.891693 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −8472.24 | −0.482035 | ||||||||
\(677\) | 5637.68 | 0.320050 | 0.160025 | − | 0.987113i | \(-0.448843\pi\) | ||||
0.160025 | + | 0.987113i | \(0.448843\pi\) | |||||||
\(678\) | 2321.97 | 0.131526 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −9937.33 | −0.559177 | ||||||||
\(682\) | 16783.1 | 0.942312 | ||||||||
\(683\) | −956.383 | −0.0535798 | −0.0267899 | − | 0.999641i | \(-0.508529\pi\) | ||||
−0.0267899 | + | 0.999641i | \(0.508529\pi\) | |||||||
\(684\) | −14216.1 | −0.794688 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −8946.67 | −0.496851 | ||||||||
\(688\) | −4986.73 | −0.276333 | ||||||||
\(689\) | 3424.59 | 0.189356 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −17744.6 | −0.976898 | −0.488449 | − | 0.872592i | \(-0.662437\pi\) | ||||
−0.488449 | + | 0.872592i | \(0.662437\pi\) | |||||||
\(692\) | 16689.8 | 0.916837 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 12776.6 | 0.698836 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −2365.30 | −0.128817 | ||||||||
\(697\) | −14577.0 | −0.792172 | ||||||||
\(698\) | 13601.9 | 0.737594 | ||||||||
\(699\) | −9158.01 | −0.495547 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −16656.8 | −0.897459 | −0.448729 | − | 0.893668i | \(-0.648123\pi\) | ||||
−0.448729 | + | 0.893668i | \(0.648123\pi\) | |||||||
\(702\) | 1653.95 | 0.0889234 | ||||||||
\(703\) | −14459.5 | −0.775748 | ||||||||
\(704\) | −4416.08 | −0.236417 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −10871.2 | −0.579521 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −1836.40 | −0.0974802 | ||||||||
\(709\) | 7293.75 | 0.386350 | 0.193175 | − | 0.981164i | \(-0.438121\pi\) | ||||
0.193175 | + | 0.981164i | \(0.438121\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −10104.2 | −0.532964 | ||||||||
\(712\) | 5269.09 | 0.277342 | ||||||||
\(713\) | −6925.06 | −0.363739 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 5550.48 | 0.289709 | ||||||||
\(717\) | −6489.01 | −0.337987 | ||||||||
\(718\) | −11829.1 | −0.614845 | ||||||||
\(719\) | 35830.5 | 1.85849 | 0.929244 | − | 0.369467i | \(-0.120460\pi\) | ||||
0.929244 | + | 0.369467i | \(0.120460\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −31567.1 | −1.62715 | ||||||||
\(723\) | 1583.08 | 0.0814322 | ||||||||
\(724\) | −1606.90 | −0.0824862 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 12614.8 | 0.644874 | ||||||||
\(727\) | −31303.6 | −1.59696 | −0.798478 | − | 0.602024i | \(-0.794361\pi\) | ||||
−0.798478 | + | 0.602024i | \(0.794361\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −6398.47 | −0.325076 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −27423.6 | −1.38755 | ||||||||
\(732\) | 3337.71 | 0.168532 | ||||||||
\(733\) | −30654.4 | −1.54467 | −0.772337 | − | 0.635213i | \(-0.780912\pi\) | ||||
−0.772337 | + | 0.635213i | \(0.780912\pi\) | |||||||
\(734\) | 12271.2 | 0.617082 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1822.17 | 0.0912584 | ||||||||
\(737\) | 39330.8 | 1.96576 | ||||||||
\(738\) | −7825.80 | −0.390341 | ||||||||
\(739\) | −16502.7 | −0.821461 | −0.410731 | − | 0.911757i | \(-0.634726\pi\) | ||||
−0.410731 | + | 0.911757i | \(0.634726\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 2458.34 | 0.121875 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −17047.5 | −0.841738 | −0.420869 | − | 0.907121i | \(-0.638275\pi\) | ||||
−0.420869 | + | 0.907121i | \(0.638275\pi\) | |||||||
\(744\) | 1788.99 | 0.0881553 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 5638.33 | 0.276721 | ||||||||
\(747\) | 15966.7 | 0.782049 | ||||||||
\(748\) | −24285.4 | −1.18712 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 32522.8 | 1.58026 | 0.790129 | − | 0.612941i | \(-0.210014\pi\) | ||||
0.790129 | + | 0.612941i | \(0.210014\pi\) | |||||||
\(752\) | −10260.7 | −0.497568 | ||||||||
\(753\) | 4337.90 | 0.209936 | ||||||||
\(754\) | −2857.19 | −0.138001 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 39925.5 | 1.91693 | 0.958465 | − | 0.285211i | \(-0.0920637\pi\) | ||||
0.958465 | + | 0.285211i | \(0.0920637\pi\) | |||||||
\(758\) | −10333.9 | −0.495176 | ||||||||
\(759\) | −7224.87 | −0.345516 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 27457.5 | 1.30793 | 0.653963 | − | 0.756526i | \(-0.273105\pi\) | ||||
0.653963 | + | 0.756526i | \(0.273105\pi\) | |||||||
\(762\) | 1915.57 | 0.0910680 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −13138.7 | −0.622172 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 2132.52 | 0.100589 | ||||||||
\(767\) | −2218.29 | −0.104430 | ||||||||
\(768\) | −470.732 | −0.0221173 | ||||||||
\(769\) | 27170.3 | 1.27411 | 0.637053 | − | 0.770820i | \(-0.280153\pi\) | ||||
0.637053 | + | 0.770820i | \(0.280153\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −4392.17 | −0.205162 | ||||||||
\(772\) | 6215.08 | 0.289748 | ||||||||
\(773\) | 17904.3 | 0.833083 | 0.416542 | − | 0.909117i | \(-0.363242\pi\) | ||||
0.416542 | + | 0.909117i | \(0.363242\pi\) | |||||||
\(774\) | −14722.6 | −0.683711 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 1359.82 | 0.0629056 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −18194.5 | −0.838438 | ||||||||
\(779\) | −24928.9 | −1.14656 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −18915.2 | −0.866630 | ||||||||
\(782\) | 10020.7 | 0.458235 | ||||||||
\(783\) | −14966.1 | −0.683070 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 641.140 | 0.0290951 | ||||||||
\(787\) | 14190.9 | 0.642760 | 0.321380 | − | 0.946950i | \(-0.395853\pi\) | ||||
0.321380 | + | 0.946950i | \(0.395853\pi\) | |||||||
\(788\) | −15825.7 | −0.715441 | ||||||||
\(789\) | −8850.43 | −0.399346 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −13037.8 | −0.584949 | ||||||||
\(793\) | 4031.82 | 0.180548 | ||||||||
\(794\) | 8274.88 | 0.369854 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 15611.0 | 0.695124 | ||||||||
\(797\) | 29777.3 | 1.32342 | 0.661711 | − | 0.749759i | \(-0.269831\pi\) | ||||
0.661711 | + | 0.749759i | \(0.269831\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −56427.1 | −2.49843 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 15556.2 | 0.686207 | ||||||||
\(802\) | 14344.0 | 0.631553 | ||||||||
\(803\) | −51753.1 | −2.27438 | ||||||||
\(804\) | 4192.46 | 0.183901 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 2161.03 | 0.0944404 | ||||||||
\(807\) | −14554.2 | −0.634859 | ||||||||
\(808\) | −3094.96 | −0.134753 | ||||||||
\(809\) | −15905.3 | −0.691225 | −0.345612 | − | 0.938377i | \(-0.612329\pi\) | ||||
−0.345612 | + | 0.938377i | \(0.612329\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 10201.6 | 0.441712 | 0.220856 | − | 0.975306i | \(-0.429115\pi\) | ||||
0.220856 | + | 0.975306i | \(0.429115\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −5632.26 | −0.242967 | ||||||||
\(814\) | −13261.1 | −0.571007 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −2588.70 | −0.111057 | ||||||||
\(817\) | −46898.4 | −2.00828 | ||||||||
\(818\) | 22832.4 | 0.975938 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 21684.6 | 0.921800 | 0.460900 | − | 0.887452i | \(-0.347527\pi\) | ||||
0.460900 | + | 0.887452i | \(0.347527\pi\) | |||||||
\(822\) | −8037.45 | −0.341044 | ||||||||
\(823\) | 40608.3 | 1.71995 | 0.859974 | − | 0.510337i | \(-0.170479\pi\) | ||||
0.859974 | + | 0.510337i | \(0.170479\pi\) | |||||||
\(824\) | 13523.0 | 0.571718 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 30936.3 | 1.30080 | 0.650400 | − | 0.759592i | \(-0.274601\pi\) | ||||
0.650400 | + | 0.759592i | \(0.274601\pi\) | |||||||
\(828\) | 5379.70 | 0.225794 | ||||||||
\(829\) | −38463.5 | −1.61145 | −0.805726 | − | 0.592288i | \(-0.798225\pi\) | ||||
−0.805726 | + | 0.592288i | \(0.798225\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 9295.09 | 0.388018 | ||||||||
\(832\) | −568.625 | −0.0236942 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −2800.84 | −0.116289 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −41531.7 | −1.71819 | ||||||||
\(837\) | 11319.6 | 0.467457 | ||||||||
\(838\) | 32528.4 | 1.34090 | ||||||||
\(839\) | 1623.27 | 0.0667955 | 0.0333977 | − | 0.999442i | \(-0.489367\pi\) | ||||
0.0333977 | + | 0.999442i | \(0.489367\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1464.84 | 0.0600614 | ||||||||
\(842\) | −15755.4 | −0.644853 | ||||||||
\(843\) | −6683.05 | −0.273044 | ||||||||
\(844\) | −4560.17 | −0.185980 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −30293.4 | −1.23110 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −6167.11 | −0.249740 | ||||||||
\(849\) | −15213.7 | −0.614998 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 5471.81 | 0.220413 | ||||||||
\(852\) | −2016.26 | −0.0810751 | ||||||||
\(853\) | 46305.1 | 1.85868 | 0.929341 | − | 0.369222i | \(-0.120376\pi\) | ||||
0.929341 | + | 0.369222i | \(0.120376\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 7874.20 | 0.314410 | ||||||||
\(857\) | 30937.1 | 1.23313 | 0.616564 | − | 0.787305i | \(-0.288524\pi\) | ||||
0.616564 | + | 0.787305i | \(0.288524\pi\) | |||||||
\(858\) | 2254.59 | 0.0897090 | ||||||||
\(859\) | 36721.9 | 1.45860 | 0.729299 | − | 0.684195i | \(-0.239846\pi\) | ||||
0.729299 | + | 0.684195i | \(0.239846\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 9541.03 | 0.376994 | ||||||||
\(863\) | −27945.5 | −1.10229 | −0.551145 | − | 0.834409i | \(-0.685809\pi\) | ||||
−0.551145 | + | 0.834409i | \(0.685809\pi\) | |||||||
\(864\) | −2978.49 | −0.117280 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 27451.6 | 1.07719 | ||||||||
\(867\) | −5202.09 | −0.203774 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −29519.0 | −1.15232 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 5064.33 | 0.197013 | ||||||||
\(872\) | −7102.49 | −0.275826 | ||||||||
\(873\) | 4014.67 | 0.155643 | ||||||||
\(874\) | 17136.9 | 0.663231 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −5516.61 | −0.212773 | ||||||||
\(877\) | −18326.9 | −0.705650 | −0.352825 | − | 0.935689i | \(-0.614779\pi\) | ||||
−0.352825 | + | 0.935689i | \(0.614779\pi\) | |||||||
\(878\) | −23019.3 | −0.884810 | ||||||||
\(879\) | −10070.6 | −0.386433 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −19774.4 | −0.756205 | −0.378102 | − | 0.925764i | \(-0.623423\pi\) | ||||
−0.378102 | + | 0.925764i | \(0.623423\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 2629.82 | 0.100227 | 0.0501136 | − | 0.998744i | \(-0.484042\pi\) | ||||
0.0501136 | + | 0.998744i | \(0.484042\pi\) | |||||||
\(884\) | −3127.05 | −0.118975 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 13492.8 | 0.511623 | ||||||||
\(887\) | 41599.9 | 1.57473 | 0.787366 | − | 0.616485i | \(-0.211444\pi\) | ||||
0.787366 | + | 0.616485i | \(0.211444\pi\) | |||||||
\(888\) | −1413.56 | −0.0534189 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −32193.1 | −1.21045 | ||||||||
\(892\) | −9068.10 | −0.340384 | ||||||||
\(893\) | −96498.7 | −3.61613 | ||||||||
\(894\) | −11873.5 | −0.444192 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −930.292 | −0.0346283 | ||||||||
\(898\) | 19074.7 | 0.708831 | ||||||||
\(899\) | −19554.5 | −0.725449 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −33914.9 | −1.25402 | ||||||||
\(902\) | −22862.7 | −0.843951 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −5051.07 | −0.185836 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 11788.4 | 0.432278 | ||||||||
\(907\) | 21394.7 | 0.783240 | 0.391620 | − | 0.920127i | \(-0.371915\pi\) | ||||
0.391620 | + | 0.920127i | \(0.371915\pi\) | |||||||
\(908\) | 21617.0 | 0.790074 | ||||||||
\(909\) | −9137.43 | −0.333410 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −18422.5 | −0.669995 | −0.334998 | − | 0.942219i | \(-0.608735\pi\) | ||||
−0.334998 | + | 0.942219i | \(0.608735\pi\) | |||||||
\(912\) | −4427.07 | −0.160740 | ||||||||
\(913\) | 46645.9 | 1.69086 | ||||||||
\(914\) | −21291.6 | −0.770528 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 19462.0 | 0.702012 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −16379.6 | −0.588898 | ||||||||
\(919\) | −21452.5 | −0.770026 | −0.385013 | − | 0.922911i | \(-0.625803\pi\) | ||||
−0.385013 | + | 0.922911i | \(0.625803\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −12675.3 | −0.453490 | ||||||||
\(922\) | 1535.85 | 0.0548597 | ||||||||
\(923\) | −2435.56 | −0.0868554 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −11505.3 | −0.408300 | ||||||||
\(927\) | 39924.7 | 1.41456 | ||||||||
\(928\) | 5145.32 | 0.182008 | ||||||||
\(929\) | −19985.4 | −0.705812 | −0.352906 | − | 0.935659i | \(-0.614807\pi\) | ||||
−0.352906 | + | 0.935659i | \(0.614807\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 19921.7 | 0.700170 | ||||||||
\(933\) | −12872.8 | −0.451700 | ||||||||
\(934\) | 20466.2 | 0.716996 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −1678.78 | −0.0586247 | ||||||||
\(937\) | −32111.1 | −1.11956 | −0.559778 | − | 0.828643i | \(-0.689113\pi\) | ||||
−0.559778 | + | 0.828643i | \(0.689113\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 2827.49 | 0.0982658 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −47875.3 | −1.65855 | −0.829273 | − | 0.558844i | \(-0.811245\pi\) | ||||
−0.829273 | + | 0.558844i | \(0.811245\pi\) | |||||||
\(942\) | −871.780 | −0.0301530 | ||||||||
\(943\) | 9433.65 | 0.325771 | ||||||||
\(944\) | 3994.78 | 0.137732 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −43011.3 | −1.47824 | ||||||||
\(947\) | −6035.60 | −0.207107 | −0.103554 | − | 0.994624i | \(-0.533021\pi\) | ||||
−0.103554 | + | 0.994624i | \(0.533021\pi\) | |||||||
\(948\) | −3146.57 | −0.107802 | ||||||||
\(949\) | −6663.85 | −0.227943 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 18058.7 | 0.615768 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 14260.3 | 0.484719 | 0.242360 | − | 0.970186i | \(-0.422079\pi\) | ||||
0.242360 | + | 0.970186i | \(0.422079\pi\) | |||||||
\(954\) | −18207.5 | −0.617914 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 14115.8 | 0.477549 | ||||||||
\(957\) | −20401.1 | −0.689105 | ||||||||
\(958\) | −1123.00 | −0.0378730 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −15001.0 | −0.503541 | ||||||||
\(962\) | −1707.53 | −0.0572275 | ||||||||
\(963\) | 23247.4 | 0.777921 | ||||||||
\(964\) | −3443.74 | −0.115057 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −9534.48 | −0.317072 | −0.158536 | − | 0.987353i | \(-0.550677\pi\) | ||||
−0.158536 | + | 0.987353i | \(0.550677\pi\) | |||||||
\(968\) | −27441.4 | −0.911157 | ||||||||
\(969\) | −24345.8 | −0.807122 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −10365.4 | −0.342576 | −0.171288 | − | 0.985221i | \(-0.554793\pi\) | ||||
−0.171288 | + | 0.985221i | \(0.554793\pi\) | |||||||
\(972\) | −13484.0 | −0.444959 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 20052.7 | 0.659683 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −7260.65 | −0.238123 | ||||||||
\(977\) | 1885.14 | 0.0617309 | 0.0308655 | − | 0.999524i | \(-0.490174\pi\) | ||||
0.0308655 | + | 0.999524i | \(0.490174\pi\) | |||||||
\(978\) | 2726.21 | 0.0891356 | ||||||||
\(979\) | 45446.7 | 1.48364 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −20969.1 | −0.682457 | ||||||||
\(982\) | −14185.1 | −0.460961 | ||||||||
\(983\) | 9556.93 | 0.310090 | 0.155045 | − | 0.987907i | \(-0.450448\pi\) | ||||
0.155045 | + | 0.987907i | \(0.450448\pi\) | |||||||
\(984\) | −2437.05 | −0.0789534 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 28295.8 | 0.913915 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −5347.72 | −0.172200 | ||||||||
\(989\) | 17747.4 | 0.570612 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 30384.8 | 0.973970 | 0.486985 | − | 0.873410i | \(-0.338097\pi\) | ||||
0.486985 | + | 0.873410i | \(0.338097\pi\) | |||||||
\(992\) | −3891.65 | −0.124557 | ||||||||
\(993\) | −2156.92 | −0.0689304 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 4972.21 | 0.158183 | ||||||||
\(997\) | 43843.4 | 1.39271 | 0.696357 | − | 0.717696i | \(-0.254803\pi\) | ||||
0.696357 | + | 0.717696i | \(0.254803\pi\) | |||||||
\(998\) | −34.1185 | −0.00108217 | ||||||||
\(999\) | −8944.10 | −0.283262 |
(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 | 2450.4.a.cz.1.3 | ✓ | 8 | |
5.4 | even | 2 | 2450.4.a.da.1.6 | yes | 8 | ||
7.6 | odd | 2 | inner | 2450.4.a.cz.1.6 | yes | 8 | |
35.34 | odd | 2 | 2450.4.a.da.1.3 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2450.4.a.cz.1.3 | ✓ | 8 | 1.1 | even | 1 | trivial | |
2450.4.a.cz.1.6 | yes | 8 | 7.6 | odd | 2 | inner | |
2450.4.a.da.1.3 | yes | 8 | 35.34 | odd | 2 | ||
2450.4.a.da.1.6 | yes | 8 | 5.4 | even | 2 |