Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [608,4,Mod(1,608)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(608, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("608.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 608 = 2^{5} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 608.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: | \(35.8731612835\) |
Analytic rank: | \(1\) |
Dimension: | \(5\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{5} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{5} - 2x^{4} - 28x^{3} - 8x^{2} + 73x - 12 \)
|
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(6.33779\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 608.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −5.31962 | −1.02376 | −0.511880 | − | 0.859057i | \(-0.671051\pi\) | ||||
−0.511880 | + | 0.859057i | \(0.671051\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 9.41363 | 0.841981 | 0.420990 | − | 0.907065i | \(-0.361683\pi\) | ||||
0.420990 | + | 0.907065i | \(0.361683\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 16.2508 | 0.877461 | 0.438730 | − | 0.898619i | \(-0.355428\pi\) | ||||
0.438730 | + | 0.898619i | \(0.355428\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.29831 | 0.0480854 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 8.71440 | 0.238863 | 0.119431 | − | 0.992842i | \(-0.461893\pi\) | ||||
0.119431 | + | 0.992842i | \(0.461893\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −43.4140 | −0.926221 | −0.463110 | − | 0.886301i | \(-0.653267\pi\) | ||||
−0.463110 | + | 0.886301i | \(0.653267\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −50.0769 | −0.861987 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −124.442 | −1.77539 | −0.887697 | − | 0.460428i | \(-0.847696\pi\) | ||||
−0.887697 | + | 0.460428i | \(0.847696\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −19.0000 | −0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −86.4480 | −0.898309 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 71.6374 | 0.649454 | 0.324727 | − | 0.945808i | \(-0.394728\pi\) | ||||
0.324727 | + | 0.945808i | \(0.394728\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −36.3835 | −0.291068 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 136.723 | 0.974532 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 279.955 | 1.79263 | 0.896315 | − | 0.443418i | \(-0.146234\pi\) | ||||
0.896315 | + | 0.443418i | \(0.146234\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 252.949 | 1.46551 | 0.732757 | − | 0.680490i | \(-0.238233\pi\) | ||||
0.732757 | + | 0.680490i | \(0.238233\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −46.3573 | −0.244538 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 152.979 | 0.738805 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 17.9550 | 0.0797778 | 0.0398889 | − | 0.999204i | \(-0.487300\pi\) | ||||
0.0398889 | + | 0.999204i | \(0.487300\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 230.946 | 0.948228 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −466.221 | −1.77589 | −0.887944 | − | 0.459951i | \(-0.847867\pi\) | ||||
−0.887944 | + | 0.459951i | \(0.847867\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −340.723 | −1.20837 | −0.604184 | − | 0.796845i | \(-0.706501\pi\) | ||||
−0.604184 | + | 0.796845i | \(0.706501\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 12.2218 | 0.0404870 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −305.434 | −0.947916 | −0.473958 | − | 0.880547i | \(-0.657175\pi\) | ||||
−0.473958 | + | 0.880547i | \(0.657175\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −78.9116 | −0.230063 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 661.985 | 1.81758 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −293.326 | −0.760216 | −0.380108 | − | 0.924942i | \(-0.624113\pi\) | ||||
−0.380108 | + | 0.924942i | \(0.624113\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 82.0342 | 0.201118 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 101.073 | 0.234867 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −408.311 | −0.900976 | −0.450488 | − | 0.892782i | \(-0.648750\pi\) | ||||
−0.450488 | + | 0.892782i | \(0.648750\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 334.310 | 0.701704 | 0.350852 | − | 0.936431i | \(-0.385892\pi\) | ||||
0.350852 | + | 0.936431i | \(0.385892\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 21.0985 | 0.0421930 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −408.683 | −0.779860 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −754.117 | −1.37507 | −0.687537 | − | 0.726149i | \(-0.741308\pi\) | ||||
−0.687537 | + | 0.726149i | \(0.741308\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −381.084 | −0.664885 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −758.951 | −1.26861 | −0.634303 | − | 0.773085i | \(-0.718713\pi\) | ||||
−0.634303 | + | 0.773085i | \(0.718713\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −393.936 | −0.631599 | −0.315800 | − | 0.948826i | \(-0.602273\pi\) | ||||
−0.315800 | + | 0.948826i | \(0.602273\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 193.546 | 0.297984 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 141.616 | 0.209593 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 91.7062 | 0.130605 | 0.0653023 | − | 0.997866i | \(-0.479199\pi\) | ||||
0.0653023 | + | 0.997866i | \(0.479199\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −762.369 | −1.04577 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 1396.71 | 1.84710 | 0.923550 | − | 0.383478i | \(-0.125274\pi\) | ||||
0.923550 | + | 0.383478i | \(0.125274\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1171.45 | −1.49485 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −1489.25 | −1.83522 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 931.233 | 1.10911 | 0.554553 | − | 0.832148i | \(-0.312889\pi\) | ||||
0.554553 | + | 0.832148i | \(0.312889\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −705.512 | −0.812722 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −1345.59 | −1.50034 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −178.859 | −0.193164 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −282.166 | −0.295357 | −0.147679 | − | 0.989035i | \(-0.547180\pi\) | ||||
−0.147679 | + | 0.989035i | \(0.547180\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 11.3140 | 0.0114858 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 57.3942 | 0.0565440 | 0.0282720 | − | 0.999600i | \(-0.491000\pi\) | ||||
0.0282720 | + | 0.999600i | \(0.491000\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1320.03 | −1.26278 | −0.631390 | − | 0.775466i | \(-0.717515\pi\) | ||||
−0.631390 | + | 0.775466i | \(0.717515\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −813.789 | −0.756359 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 749.733 | 0.677377 | 0.338689 | − | 0.940898i | \(-0.390017\pi\) | ||||
0.338689 | + | 0.940898i | \(0.390017\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 645.208 | 0.566970 | 0.283485 | − | 0.958977i | \(-0.408509\pi\) | ||||
0.283485 | + | 0.958977i | \(0.408509\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −95.5136 | −0.0816734 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −2308.79 | −1.92206 | −0.961029 | − | 0.276448i | \(-0.910843\pi\) | ||||
−0.961029 | + | 0.276448i | \(0.910843\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 674.369 | 0.546828 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −56.3646 | −0.0445377 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −2022.29 | −1.55784 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1255.06 | −0.942945 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 2480.11 | 1.81808 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1519.21 | −1.08705 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 311.645 | 0.217749 | 0.108874 | − | 0.994056i | \(-0.465275\pi\) | ||||
0.108874 | + | 0.994056i | \(0.465275\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 1812.52 | 1.23708 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −514.521 | −0.343160 | −0.171580 | − | 0.985170i | \(-0.554887\pi\) | ||||
−0.171580 | + | 0.985170i | \(0.554887\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −308.765 | −0.201303 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1287.06 | 0.820538 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −2201.49 | −1.37289 | −0.686446 | − | 0.727181i | \(-0.740830\pi\) | ||||
−0.686446 | + | 0.727181i | \(0.740830\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −188.406 | −0.114967 | −0.0574835 | − | 0.998346i | \(-0.518308\pi\) | ||||
−0.0574835 | + | 0.998346i | \(0.518308\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1624.79 | 0.970439 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −378.327 | −0.221240 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2635.39 | 1.50936 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 419.779 | 0.235529 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −2002.07 | −1.10078 | −0.550390 | − | 0.834908i | \(-0.685521\pi\) | ||||
−0.550390 | + | 0.834908i | \(0.685521\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1324.14 | −0.713621 | −0.356810 | − | 0.934177i | \(-0.616136\pi\) | ||||
−0.356810 | + | 0.934177i | \(0.616136\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −161.564 | −0.0853705 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 2381.17 | 1.23394 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 360.790 | 0.183403 | 0.0917013 | − | 0.995787i | \(-0.470770\pi\) | ||||
0.0917013 | + | 0.995787i | \(0.470770\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 1560.38 | 0.778279 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1164.17 | 0.569870 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −634.639 | −0.304962 | −0.152481 | − | 0.988306i | \(-0.548726\pi\) | ||||
−0.152481 | + | 0.988306i | \(0.548726\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −436.390 | −0.205897 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 3740.13 | 1.73305 | 0.866526 | − | 0.499131i | \(-0.166348\pi\) | ||||
0.866526 | + | 0.499131i | \(0.166348\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −312.227 | −0.142115 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −24.6678 | −0.0110315 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 978.817 | 0.430162 | 0.215081 | − | 0.976596i | \(-0.430998\pi\) | ||||
0.215081 | + | 0.976596i | \(0.430998\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −591.262 | −0.255401 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 2172.06 | 0.922384 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −259.331 | −0.108287 | −0.0541434 | − | 0.998533i | \(-0.517243\pi\) | ||||
−0.0541434 | + | 0.998533i | \(0.517243\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 892.412 | 0.366478 | 0.183239 | − | 0.983068i | \(-0.441342\pi\) | ||||
0.183239 | + | 0.983068i | \(0.441342\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −1778.40 | −0.718377 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 169.022 | 0.0671714 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1084.44 | −0.424076 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 2221.86 | 0.855114 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −4020.76 | −1.52320 | −0.761601 | − | 0.648046i | \(-0.775587\pi\) | ||||
−0.761601 | + | 0.648046i | \(0.775587\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 407.021 | 0.151803 | 0.0759015 | − | 0.997115i | \(-0.475817\pi\) | ||||
0.0759015 | + | 0.997115i | \(0.475817\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 2174.04 | 0.798390 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −3699.86 | −1.33809 | −0.669046 | − | 0.743221i | \(-0.733297\pi\) | ||||
−0.669046 | + | 0.743221i | \(0.733297\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1802.62 | −0.642131 | −0.321066 | − | 0.947057i | \(-0.604041\pi\) | ||||
−0.321066 | + | 0.947057i | \(0.604041\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 4011.61 | 1.40775 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 4549.49 | 1.57296 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −4388.83 | −1.49526 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 93.0073 | 0.0312292 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −165.574 | −0.0547989 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 5032.87 | 1.64207 | 0.821035 | − | 0.570878i | \(-0.193397\pi\) | ||||
0.821035 | + | 0.570878i | \(0.193397\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 4037.33 | 1.29875 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −3207.45 | −1.01742 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 4110.62 | 1.28593 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 2095.59 | 0.646606 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 5402.54 | 1.64441 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 417.179 | 0.125275 | 0.0626376 | − | 0.998036i | \(-0.480049\pi\) | ||||
0.0626376 | + | 0.998036i | \(0.480049\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −47.2370 | −0.0139961 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −3166.92 | −0.925974 | −0.462987 | − | 0.886365i | \(-0.653222\pi\) | ||||
−0.462987 | + | 0.886365i | \(0.653222\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −2198.00 | −0.634271 | −0.317135 | − | 0.948380i | \(-0.602721\pi\) | ||||
−0.317135 | + | 0.948380i | \(0.602721\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −753.343 | −0.214573 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 1956.70 | 0.550161 | 0.275081 | − | 0.961421i | \(-0.411295\pi\) | ||||
0.275081 | + | 0.961421i | \(0.411295\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −2875.24 | −0.798127 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −487.842 | −0.133708 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 358.707 | 0.0970829 | 0.0485415 | − | 0.998821i | \(-0.484543\pi\) | ||||
0.0485415 | + | 0.998821i | \(0.484543\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 51.0894 | 0.0136554 | 0.00682771 | − | 0.999977i | \(-0.497827\pi\) | ||||
0.00682771 | + | 0.999977i | \(0.497827\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 363.984 | 0.0960887 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −742.845 | −0.193709 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 824.865 | 0.212490 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −7429.98 | −1.89099 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −460.611 | −0.115831 | −0.0579153 | − | 0.998322i | \(-0.518445\pi\) | ||||
−0.0579153 | + | 0.998322i | \(0.518445\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 624.278 | 0.155130 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 6231.69 | 1.53037 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 1349.26 | 0.327489 | 0.163744 | − | 0.986503i | \(-0.447643\pi\) | ||||
0.163744 | + | 0.986503i | \(0.447643\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 291.783 | 0.0700019 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 363.467 | 0.0861993 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 312.198 | 0.0731977 | 0.0365988 | − | 0.999330i | \(-0.488348\pi\) | ||||
0.0365988 | + | 0.999330i | \(0.488348\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −2761.26 | −0.640087 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −4953.80 | −1.13546 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 4178.51 | 0.947093 | 0.473546 | − | 0.880769i | \(-0.342974\pi\) | ||||
0.473546 | + | 0.880769i | \(0.342974\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2140.56 | 0.479815 | 0.239907 | − | 0.970796i | \(-0.422883\pi\) | ||||
0.239907 | + | 0.970796i | \(0.422883\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 3753.05 | 0.832033 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −317.061 | −0.0695254 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −6290.18 | −1.36440 | −0.682202 | − | 0.731164i | \(-0.738978\pi\) | ||||
−0.682202 | + | 0.731164i | \(0.738978\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 328.405 | 0.0704698 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 5960.18 | 1.26532 | 0.632659 | − | 0.774430i | \(-0.281963\pi\) | ||||
0.632659 | + | 0.774430i | \(0.281963\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 2151.83 | 0.451990 | 0.225995 | − | 0.974128i | \(-0.427437\pi\) | ||||
0.225995 | + | 0.974128i | \(0.427437\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 951.461 | 0.197753 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −7576.46 | −1.55827 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 10572.9 | 2.15203 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1501.02 | 0.302375 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 6159.82 | 1.22819 | 0.614096 | − | 0.789231i | \(-0.289521\pi\) | ||||
0.614096 | + | 0.789231i | \(0.289521\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −3843.69 | −0.758605 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 1191.46 | 0.232780 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −3110.07 | −0.601538 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −5537.03 | −1.06030 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −305.315 | −0.0578875 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 3147.07 | 0.590821 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −9672.80 | −1.79823 | −0.899114 | − | 0.437714i | \(-0.855788\pi\) | ||||
−0.899114 | + | 0.437714i | \(0.855788\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 7022.04 | 1.29278 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −6369.85 | −1.16142 | −0.580709 | − | 0.814111i | \(-0.697224\pi\) | ||||
−0.580709 | + | 0.814111i | \(0.697224\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −3346.98 | −0.604417 | −0.302209 | − | 0.953242i | \(-0.597724\pi\) | ||||
−0.302209 | + | 0.953242i | \(0.597724\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 198.614 | 0.0355257 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 10720.3 | 1.89941 | 0.949706 | − | 0.313142i | \(-0.101382\pi\) | ||||
0.949706 | + | 0.313142i | \(0.101382\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2439.64 | 0.428193 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −3988.29 | −0.693472 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 2364.40 | 0.407303 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1579.55 | 0.269594 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −3432.26 | −0.580442 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −4963.54 | −0.831759 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 6992.48 | 1.16115 | 0.580576 | − | 0.814206i | \(-0.302827\pi\) | ||||
0.580576 | + | 0.814206i | \(0.302827\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 23.3110 | 0.00383615 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −7098.98 | −1.15779 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −7780.91 | −1.25772 | −0.628862 | − | 0.777517i | \(-0.716479\pi\) | ||||
−0.628862 | + | 0.777517i | \(0.716479\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 12281.9 | 1.96773 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 2204.30 | 0.350057 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −6856.40 | −1.07933 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −3587.38 | −0.559821 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −2574.64 | −0.398311 | −0.199156 | − | 0.979968i | \(-0.563820\pi\) | ||||
−0.199156 | + | 0.979968i | \(0.563820\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 4736.45 | 0.726465 | 0.363232 | − | 0.931699i | \(-0.381673\pi\) | ||||
0.363232 | + | 0.931699i | \(0.381673\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −5935.69 | −0.902632 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 8513.83 | 1.28370 | 0.641849 | − | 0.766831i | \(-0.278167\pi\) | ||||
0.641849 | + | 0.766831i | \(0.278167\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −7144.49 | −1.06814 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 10757.8 | 1.59485 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 7961.99 | 1.17052 | 0.585261 | − | 0.810845i | \(-0.300992\pi\) | ||||
0.585261 | + | 0.810845i | \(0.300992\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 361.000 | 0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 6676.43 | 0.965349 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −3708.37 | −0.531794 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 2283.26 | 0.324755 | 0.162377 | − | 0.986729i | \(-0.448084\pi\) | ||||
0.162377 | + | 0.986729i | \(0.448084\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −605.297 | −0.0853943 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −4766.78 | −0.667060 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 7740.69 | 1.07452 | 0.537262 | − | 0.843415i | \(-0.319458\pi\) | ||||
0.537262 | + | 0.843415i | \(0.319458\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 8081.59 | 1.11288 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −12153.9 | −1.66037 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 8461.28 | 1.14677 | 0.573386 | − | 0.819285i | \(-0.305629\pi\) | ||||
0.573386 | + | 0.819285i | \(0.305629\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −1657.83 | −0.222922 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 11065.4 | 1.47628 | 0.738139 | − | 0.674649i | \(-0.235705\pi\) | ||||
0.738139 | + | 0.674649i | \(0.235705\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1333.12 | 0.176473 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −442.363 | −0.0581049 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −9051.42 | −1.17976 | −0.589878 | − | 0.807492i | \(-0.700824\pi\) | ||||
−0.589878 | + | 0.807492i | \(0.700824\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −8914.73 | −1.15304 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 2737.06 | 0.351313 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 863.289 | 0.109966 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 10777.0 | 1.36243 | 0.681213 | − | 0.732085i | \(-0.261453\pi\) | ||||
0.681213 | + | 0.732085i | \(0.261453\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 1642.51 | 0.206086 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 610.869 | 0.0760732 | 0.0380366 | − | 0.999276i | \(-0.487890\pi\) | ||||
0.0380366 | + | 0.999276i | \(0.487890\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −10981.5 | −1.35739 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −7176.66 | −0.880521 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 156.467 | 0.0190560 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −218.808 | −0.0264532 | −0.0132266 | − | 0.999913i | \(-0.504210\pi\) | ||||
−0.0132266 | + | 0.999913i | \(0.504210\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 11711.1 | 1.40551 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −6635.38 | −0.790571 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 13148.2 | 1.55522 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 1002.25 | 0.117699 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −4826.13 | −0.562702 | −0.281351 | − | 0.959605i | \(-0.590782\pi\) | ||||
−0.281351 | + | 0.959605i | \(0.590782\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −9386.61 | −1.08664 | −0.543320 | − | 0.839526i | \(-0.682833\pi\) | ||||
−0.543320 | + | 0.839526i | \(0.682833\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −396.546 | −0.0455809 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 4527.65 | 0.516761 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 5432.80 | 0.615718 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 2012.55 | 0.226496 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 8452.72 | 0.944671 | 0.472336 | − | 0.881419i | \(-0.343411\pi\) | ||||
0.472336 | + | 0.881419i | \(0.343411\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −10404.1 | −1.15471 | −0.577355 | − | 0.816494i | \(-0.695915\pi\) | ||||
−0.577355 | + | 0.816494i | \(0.695915\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −14019.3 | −1.54522 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −1361.11 | −0.148995 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 9961.31 | 1.08298 | 0.541489 | − | 0.840708i | \(-0.317861\pi\) | ||||
0.541489 | + | 0.840708i | \(0.317861\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −102.451 | −0.0110627 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 8962.09 | 0.961178 | 0.480589 | − | 0.876946i | \(-0.340423\pi\) | ||||
0.480589 | + | 0.876946i | \(0.340423\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 8766.28 | 0.933846 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 10650.3 | 1.12694 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 8431.24 | 0.886180 | 0.443090 | − | 0.896477i | \(-0.353882\pi\) | ||||
0.443090 | + | 0.896477i | \(0.353882\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −4062.83 | −0.424194 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 7043.90 | 0.730577 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −6641.43 | −0.684296 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −13669.0 | −1.39915 | −0.699574 | − | 0.714560i | \(-0.746627\pi\) | ||||
−0.699574 | + | 0.714560i | \(0.746627\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −17014.1 | −1.73018 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 270.681 | 0.0273468 | 0.0136734 | − | 0.999907i | \(-0.495647\pi\) | ||||
0.0136734 | + | 0.999907i | \(0.495647\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 17732.8 | 1.77995 | 0.889973 | − | 0.456013i | \(-0.150723\pi\) | ||||
0.889973 | + | 0.456013i | \(0.150723\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −12666.9 | −1.26325 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 55.8896 | 0.00553803 | 0.00276902 | − | 0.999996i | \(-0.499119\pi\) | ||||
0.00276902 | + | 0.999996i | \(0.499119\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −12255.0 | −1.20657 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −1919.27 | −0.187760 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −2969.20 | −0.288634 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 691.287 | 0.0667757 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −380.827 | −0.0365553 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 2012.67 | 0.191986 | 0.0959929 | − | 0.995382i | \(-0.469397\pi\) | ||||
0.0959929 | + | 0.995382i | \(0.469397\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −779.497 | −0.0738919 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −6192.91 | −0.583411 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −2656.21 | −0.248685 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 4313.69 | 0.401380 | 0.200690 | − | 0.979655i | \(-0.435682\pi\) | ||||
0.200690 | + | 0.979655i | \(0.435682\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 3376.03 | 0.312208 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −3762.75 | −0.345846 | −0.172923 | − | 0.984935i | \(-0.555321\pi\) | ||||
−0.172923 | + | 0.984935i | \(0.555321\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −34838.2 | −3.18263 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 106.505 | 0.00967083 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −12333.6 | −1.11315 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −4203.71 | −0.377122 | −0.188561 | − | 0.982061i | \(-0.560382\pi\) | ||||
−0.188561 | + | 0.982061i | \(0.560382\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −19896.0 | −1.77423 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 19614.2 | 1.73868 | 0.869340 | − | 0.494215i | \(-0.164545\pi\) | ||||
0.869340 | + | 0.494215i | \(0.164545\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 540.288 | 0.0476089 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 1660.93 | 0.145492 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −18720.4 | −1.63019 | −0.815093 | − | 0.579330i | \(-0.803314\pi\) | ||||
−0.815093 | + | 0.579330i | \(0.803314\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −6401.78 | −0.554203 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −2597.74 | −0.223573 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −12426.3 | −1.06324 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −2661.67 | −0.226422 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −5206.93 | −0.440383 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 20279.4 | 1.70529 | 0.852646 | − | 0.522489i | \(-0.174996\pi\) | ||||
0.852646 | + | 0.522489i | \(0.174996\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 12501.4 | 1.04522 | 0.522608 | − | 0.852573i | \(-0.324959\pi\) | ||||
0.522608 | + | 0.852573i | \(0.324959\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 3145.28 | 0.261469 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −31477.5 | −2.60187 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −7035.08 | −0.578210 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −530.113 | −0.0433238 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 20240.5 | 1.64486 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 7057.71 | 0.570339 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 1379.54 | 0.110860 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −687.667 | −0.0549535 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −11028.5 | −0.876437 | −0.438219 | − | 0.898868i | \(-0.644390\pi\) | ||||
−0.438219 | + | 0.898868i | \(0.644390\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −4747.29 | −0.375185 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 6073.75 | 0.477378 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −20679.4 | −1.61643 | −0.808215 | − | 0.588887i | \(-0.799566\pi\) | ||||
−0.808215 | + | 0.588887i | \(0.799566\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 434.036 | 0.0337417 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −5319.14 | −0.411258 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1490.30 | 0.114600 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −899.129 | −0.0687674 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −6393.51 | −0.486359 | −0.243179 | − | 0.969981i | \(-0.578190\pi\) | ||||
−0.243179 | + | 0.969981i | \(0.578190\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 14792.2 | 1.11922 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 5768.81 | 0.434152 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 2530.58 | 0.189434 | 0.0947170 | − | 0.995504i | \(-0.469805\pi\) | ||||
0.0947170 | + | 0.995504i | \(0.469805\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −21734.1 | −1.61834 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −12389.1 | −0.917625 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 18965.6 | 1.39733 | 0.698664 | − | 0.715450i | \(-0.253778\pi\) | ||||
0.698664 | + | 0.715450i | \(0.253778\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −19660.1 | −1.44089 | −0.720445 | − | 0.693512i | \(-0.756062\pi\) | ||||
−0.720445 | + | 0.693512i | \(0.756062\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 21388.9 | 1.55939 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −2606.42 | −0.189035 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −5446.15 | −0.392940 | −0.196470 | − | 0.980510i | \(-0.562948\pi\) | ||||
−0.196470 | + | 0.980510i | \(0.562948\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −2165.19 | −0.155410 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 22697.7 | 1.62076 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −2556.16 | −0.181587 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −530.596 | −0.0374999 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −3622.30 | −0.254699 | −0.127349 | − | 0.991858i | \(-0.540647\pi\) | ||||
−0.127349 | + | 0.991858i | \(0.540647\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −4806.03 | −0.336212 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 19681.8 | 1.36989 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 19137.7 | 1.32528 | 0.662641 | − | 0.748938i | \(-0.269436\pi\) | ||||
0.662641 | + | 0.748938i | \(0.269436\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −19037.1 | −1.31167 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 9589.23 | 0.657388 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −4350.42 | −0.296750 | −0.148375 | − | 0.988931i | \(-0.547404\pi\) | ||||
−0.148375 | + | 0.988931i | \(0.547404\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −10657.8 | −0.723362 | −0.361681 | − | 0.932302i | \(-0.617797\pi\) | ||||
−0.361681 | + | 0.932302i | \(0.617797\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −979.074 | −0.0661210 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −11814.7 | −0.793941 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −5515.67 | −0.368821 | −0.184410 | − | 0.982849i | \(-0.559038\pi\) | ||||
−0.184410 | + | 0.982849i | \(0.559038\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −24201.5 | −1.61034 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 13260.1 | 0.877980 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −26144.0 | −1.72259 | −0.861293 | − | 0.508109i | \(-0.830345\pi\) | ||||
−0.861293 | + | 0.508109i | \(0.830345\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 23346.9 | 1.53079 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −4104.01 | −0.267781 | −0.133891 | − | 0.990996i | \(-0.542747\pi\) | ||||
−0.133891 | + | 0.990996i | \(0.542747\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 265.000 | 0.0172072 | 0.00860360 | − | 0.999963i | \(-0.497261\pi\) | ||||
0.00860360 | + | 0.999963i | \(0.497261\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 9794.50 | 0.632914 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 15133.3 | 0.973197 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −9753.29 | −0.624211 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 880.788 | 0.0561009 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −2234.36 | −0.141637 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 23088.2 | 1.45662 | 0.728309 | − | 0.685249i | \(-0.240307\pi\) | ||||
0.728309 | + | 0.685249i | \(0.240307\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −26772.9 | −1.68109 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 2933.72 | 0.183340 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 3425.87 | 0.213089 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −985.351 | −0.0610014 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 3574.05 | 0.220229 | 0.110114 | − | 0.993919i | \(-0.464878\pi\) | ||||
0.110114 | + | 0.993919i | \(0.464878\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −25705.2 | −1.57654 | −0.788270 | − | 0.615329i | \(-0.789023\pi\) | ||||
−0.788270 | + | 0.615329i | \(0.789023\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 17062.4 | 1.04160 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 1822.68 | 0.110752 | 0.0553762 | − | 0.998466i | \(-0.482364\pi\) | ||||
0.0553762 | + | 0.998466i | \(0.482364\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −3558.19 | −0.215210 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −21866.9 | −1.31649 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −15678.9 | −0.939609 | −0.469804 | − | 0.882771i | \(-0.655676\pi\) | ||||
−0.469804 | + | 0.882771i | \(0.655676\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −4843.51 | −0.288934 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −511.450 | −0.0303707 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 18817.0 | 1.11230 | 0.556151 | − | 0.831081i | \(-0.312277\pi\) | ||||
0.556151 | + | 0.831081i | \(0.312277\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −2463.08 | −0.144936 | −0.0724680 | − | 0.997371i | \(-0.523088\pi\) | ||||
−0.0724680 | + | 0.997371i | \(0.523088\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −28739.4 | −1.68348 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −2906.60 | −0.169493 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 20055.2 | 1.16423 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −2219.23 | −0.128252 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 2913.31 | 0.167611 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −27177.3 | −1.55662 | −0.778312 | − | 0.627877i | \(-0.783924\pi\) | ||||
−0.778312 | + | 0.627877i | \(0.783924\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −4974.47 | −0.283656 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −3111.27 | −0.176626 | −0.0883131 | − | 0.996093i | \(-0.528148\pi\) | ||||
−0.0883131 | + | 0.996093i | \(0.528148\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −4585.43 | −0.259164 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 16846.8 | 0.947976 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 16068.7 | 0.900221 | 0.450110 | − | 0.892973i | \(-0.351385\pi\) | ||||
0.450110 | + | 0.892973i | \(0.351385\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −20724.0 | −1.15595 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 11692.5 | 0.649341 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 12734.5 | 0.704128 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −11854.9 | −0.652653 | −0.326327 | − | 0.945257i | \(-0.605811\pi\) | ||||
−0.326327 | + | 0.945257i | \(0.605811\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 183.861 | 0.0100783 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −1773.59 | −0.0968000 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 58017.6 | 3.15290 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −10408.9 | −0.563233 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 19270.9 | 1.03830 | 0.519151 | − | 0.854682i | \(-0.326248\pi\) | ||||
0.519151 | + | 0.854682i | \(0.326248\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −341.145 | −0.0183023 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 15295.2 | 0.817091 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 932.702 | 0.0496151 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −952.832 | −0.0504716 | −0.0252358 | − | 0.999682i | \(-0.508034\pi\) | ||||
−0.0252358 | + | 0.999682i | \(0.508034\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 119.063 | 0.00628017 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 18120.6 | 0.951784 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −3561.43 | −0.186280 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −1908.18 | −0.0993897 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 26859.5 | 1.39317 | 0.696585 | − | 0.717474i | \(-0.254702\pi\) | ||||
0.696585 | + | 0.717474i | \(0.254702\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −21451.5 | −1.10804 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −271.776 | −0.0139799 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −10185.7 | −0.521778 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −26684.9 | −1.36133 | −0.680667 | − | 0.732593i | \(-0.738310\pi\) | ||||
−0.680667 | + | 0.732593i | \(0.738310\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 18647.7 | 0.947401 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 42400.4 | 2.14533 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 30013.3 | 1.51237 | 0.756183 | − | 0.654360i | \(-0.227062\pi\) | ||||
0.756183 | + | 0.654360i | \(0.227062\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 3951.65 | 0.198311 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −6571.68 | −0.328454 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 12404.1 | 0.617444 | 0.308722 | − | 0.951152i | \(-0.400099\pi\) | ||||
0.308722 | + | 0.951152i | \(0.400099\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −4387.97 | −0.217538 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −35368.0 | −1.74634 | −0.873168 | − | 0.487420i | \(-0.837938\pi\) | ||||
−0.873168 | + | 0.487420i | \(0.837938\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −18846.8 | −0.926836 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 1813.36 | 0.0888185 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 12183.8 | 0.594372 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1974.41 | −0.0959348 | −0.0479674 | − | 0.998849i | \(-0.515274\pi\) | ||||
−0.0479674 | + | 0.998849i | \(0.515274\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 2450.27 | 0.118583 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −12464.9 | −0.600855 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 5328.85 | 0.255852 | 0.127926 | − | 0.991784i | \(-0.459168\pi\) | ||||
0.127926 | + | 0.991784i | \(0.459168\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −3320.92 | −0.158816 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −13374.6 | −0.637092 | −0.318546 | − | 0.947907i | \(-0.603195\pi\) | ||||
−0.318546 | + | 0.947907i | \(0.603195\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 10485.2 | 0.497494 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −1520.91 | −0.0718804 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 17726.4 | 0.834503 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −41658.8 | −1.95352 | −0.976760 | − | 0.214337i | \(-0.931241\pi\) | ||||
−0.976760 | + | 0.214337i | \(0.931241\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −7177.55 | −0.335270 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 24505.2 | 1.14022 | 0.570110 | − | 0.821569i | \(-0.306901\pi\) | ||||
0.570110 | + | 0.821569i | \(0.306901\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −9203.17 | −0.426565 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −1552.17 | −0.0716652 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 8858.19 | 0.407417 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −6613.81 | −0.303023 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 38276.3 | 1.74698 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 3396.35 | 0.154421 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 24681.7 | 1.11793 | 0.558963 | − | 0.829192i | \(-0.311199\pi\) | ||||
0.558963 | + | 0.829192i | \(0.311199\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −1660.78 | −0.0749369 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −37519.7 | −1.68653 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −14513.7 | −0.649933 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 14688.9 | 0.655296 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 7727.34 | 0.343434 | 0.171717 | − | 0.985146i | \(-0.445069\pi\) | ||||
0.171717 | + | 0.985146i | \(0.445069\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 38008.9 | 1.68293 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 1209.02 | 0.0533318 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −3432.92 | −0.150866 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 10959.0 | 0.479820 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −22228.0 | −0.969596 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 4220.96 | 0.183438 | 0.0917188 | − | 0.995785i | \(-0.470764\pi\) | ||||
0.0917188 | + | 0.995785i | \(0.470764\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −26026.3 | −1.12689 | −0.563445 | − | 0.826154i | \(-0.690524\pi\) | ||||
−0.563445 | + | 0.826154i | \(0.690524\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −11387.0 | −0.491215 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −5974.25 | −0.256772 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 6473.75 | 0.277219 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −915.970 | −0.0390801 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 13319.5 | 0.566204 | 0.283102 | − | 0.959090i | \(-0.408636\pi\) | ||||
0.283102 | + | 0.959090i | \(0.408636\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −10436.6 | −0.442038 | −0.221019 | − | 0.975270i | \(-0.570938\pi\) | ||||
−0.221019 | + | 0.975270i | \(0.570938\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 1686.64 | 0.0711774 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 8612.06 | 0.362117 | 0.181058 | − | 0.983472i | \(-0.442048\pi\) | ||||
0.181058 | + | 0.983472i | \(0.442048\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 10298.1 | 0.431444 | 0.215722 | − | 0.976455i | \(-0.430789\pi\) | ||||
0.215722 | + | 0.976455i | \(0.430789\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 33461.3 | 1.39682 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 9819.94 | 0.408452 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 35208.2 | 1.45920 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 34584.0 | 1.42819 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 14169.2 | 0.583045 | 0.291522 | − | 0.956564i | \(-0.405838\pi\) | ||||
0.291522 | + | 0.956564i | \(0.405838\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 53985.6 | 2.21352 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −31705.9 | −1.29538 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −2939.19 | −0.119658 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −20395.7 | −0.827397 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −11446.9 | −0.462730 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1286.25 | 0.0518120 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 9822.77 | 0.394285 | 0.197143 | − | 0.980375i | \(-0.436834\pi\) | ||||
0.197143 | + | 0.980375i | \(0.436834\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −232.214 | −0.00928835 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −11841.3 | −0.471983 | −0.235992 | − | 0.971755i | \(-0.575834\pi\) | ||||
−0.235992 | + | 0.971755i | \(0.575834\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 44204.6 | 1.75581 | 0.877905 | − | 0.478835i | \(-0.158941\pi\) | ||||
0.877905 | + | 0.478835i | \(0.158941\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 40303.8 | 1.59530 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 16756.6 | 0.660952 | 0.330476 | − | 0.943814i | \(-0.392791\pi\) | ||||
0.330476 | + | 0.943814i | \(0.392791\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 9214.22 | 0.362188 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −56243.8 | −2.20316 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 799.165 | 0.0311966 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 32739.2 | 1.27362 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −366.338 | −0.0142024 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −24688.3 | −0.953848 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −40606.0 | −1.56347 | −0.781737 | − | 0.623609i | \(-0.785666\pi\) | ||||
−0.781737 | + | 0.623609i | \(0.785666\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −32767.9 | −1.25737 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 18464.8 | 0.706124 | 0.353062 | − | 0.935600i | \(-0.385140\pi\) | ||||
0.353062 | + | 0.935600i | \(0.385140\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −20592.3 | −0.784809 | −0.392404 | − | 0.919793i | \(-0.628357\pi\) | ||||
−0.392404 | + | 0.919793i | \(0.628357\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 20447.0 | 0.776630 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −17682.8 | −0.669370 | −0.334685 | − | 0.942330i | \(-0.608630\pi\) | ||||
−0.334685 | + | 0.942330i | \(0.608630\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 5064.49 | 0.191066 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −6643.59 | −0.249796 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 5803.24 | 0.217467 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −2441.25 | −0.0911753 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 16544.4 | 0.615830 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 70814.2 | 2.62713 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 36502.2 | 1.34968 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 29454.9 | 1.08549 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 8400.84 | 0.308567 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 19256.9 | 0.704978 | 0.352489 | − | 0.935816i | \(-0.385335\pi\) | ||||
0.352489 | + | 0.935816i | \(0.385335\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 74.5153 | 0.00271894 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 24122.8 | 0.877306 | 0.438653 | − | 0.898657i | \(-0.355456\pi\) | ||||
0.438653 | + | 0.898657i | \(0.355456\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 12171.5 | 0.441204 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −16741.2 | −0.604860 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −8361.38 | −0.301109 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −16780.0 | −0.602309 | −0.301154 | − | 0.953575i | \(-0.597372\pi\) | ||||
−0.301154 | + | 0.953575i | \(0.597372\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 51455.6 | 1.84095 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 32949.1 | 1.17501 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −653.266 | −0.0232208 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −1713.80 | −0.0607212 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 32219.1 | 1.13786 | 0.568931 | − | 0.822386i | \(-0.307357\pi\) | ||||
0.568931 | + | 0.822386i | \(0.307357\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1499.32 | 0.0527801 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 33885.1 | 1.18901 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −10208.5 | −0.357064 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −36861.2 | −1.28517 | −0.642584 | − | 0.766215i | \(-0.722138\pi\) | ||||
−0.642584 | + | 0.766215i | \(0.722138\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 17804.7 | 0.618779 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 1000.08 | 0.0346460 | 0.0173230 | − | 0.999850i | \(-0.494486\pi\) | ||||
0.0173230 | + | 0.999850i | \(0.494486\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −33398.8 | −1.15336 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 20915.8 | 0.719989 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −50954.9 | −1.74848 | −0.874240 | − | 0.485494i | \(-0.838640\pi\) | ||||
−0.874240 | + | 0.485494i | \(0.838640\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 17102.3 | 0.585000 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −57028.0 | −1.94454 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −34671.8 | −1.17852 | −0.589260 | − | 0.807943i | \(-0.700581\pi\) | ||||
−0.589260 | + | 0.807943i | \(0.700581\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −37849.9 | −1.28251 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −12977.9 | −0.438367 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −35776.0 | −1.20466 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 34192.1 | 1.14773 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 973.382 | 0.0325720 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 3831.54 | 0.127815 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1487.32 | −0.0494610 | −0.0247305 | − | 0.999694i | \(-0.507873\pi\) | ||||
−0.0247305 | + | 0.999694i | \(0.507873\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −12577.7 | −0.416981 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −19161.1 | −0.633273 | −0.316636 | − | 0.948547i | \(-0.602553\pi\) | ||||
−0.316636 | + | 0.948547i | \(0.602553\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −3061.75 | −0.100879 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −8402.62 | −0.275999 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −29747.5 | −0.974110 | −0.487055 | − | 0.873371i | \(-0.661929\pi\) | ||||
−0.487055 | + | 0.873371i | \(0.661929\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 8115.14 | 0.264924 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 837.678 | 0.0272630 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −58843.1 | −1.90926 | −0.954631 | − | 0.297791i | \(-0.903750\pi\) | ||||
−0.954631 | + | 0.297791i | \(0.903750\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −34829.1 | −1.12665 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 26404.1 | 0.851522 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −24408.6 | −0.784780 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 48869.6 | 1.56649 | 0.783247 | − | 0.621711i | \(-0.213562\pi\) | ||||
0.783247 | + | 0.621711i | \(0.213562\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −37197.3 | −1.18874 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −16969.2 | −0.540662 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −2207.55 | −0.0701243 | −0.0350621 | − | 0.999385i | \(-0.511163\pi\) | ||||
−0.0350621 | + | 0.999385i | \(0.511163\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 2454.86 | 0.0777461 |
(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 | 608.4.a.h.1.1 | yes | 5 | |
4.3 | odd | 2 | 608.4.a.e.1.5 | ✓ | 5 | ||
8.3 | odd | 2 | 1216.4.a.bd.1.1 | 5 | |||
8.5 | even | 2 | 1216.4.a.y.1.5 | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
608.4.a.e.1.5 | ✓ | 5 | 4.3 | odd | 2 | ||
608.4.a.h.1.1 | yes | 5 | 1.1 | even | 1 | trivial | |
1216.4.a.y.1.5 | 5 | 8.5 | even | 2 | |||
1216.4.a.bd.1.1 | 5 | 8.3 | odd | 2 |