Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4140,2,Mod(1,4140)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4140, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4140.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4140 = 2^{2} \cdot 3^{2} \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4140.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: | \(33.0580664368\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{6}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 6 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-2.44949\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4140.1 |
$q$-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 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −3.44949 | −1.30378 | −0.651892 | − | 0.758312i | \(-0.726025\pi\) | ||||
−0.651892 | + | 0.758312i | \(0.726025\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.44949 | −0.738549 | −0.369274 | − | 0.929320i | \(-0.620394\pi\) | ||||
−0.369274 | + | 0.929320i | \(0.620394\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.44949 | 1.23407 | 0.617033 | − | 0.786937i | \(-0.288334\pi\) | ||||
0.617033 | + | 0.786937i | \(0.288334\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 5.44949 | 1.32170 | 0.660848 | − | 0.750520i | \(-0.270197\pi\) | ||||
0.660848 | + | 0.750520i | \(0.270197\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.55051 | −0.355711 | −0.177856 | − | 0.984057i | \(-0.556916\pi\) | ||||
−0.177856 | + | 0.984057i | \(0.556916\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.00000 | 0.208514 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.89898 | 0.352632 | 0.176316 | − | 0.984334i | \(-0.443582\pi\) | ||||
0.176316 | + | 0.984334i | \(0.443582\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −7.00000 | −1.25724 | −0.628619 | − | 0.777714i | \(-0.716379\pi\) | ||||
−0.628619 | + | 0.777714i | \(0.716379\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 3.44949 | 0.583070 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 6.34847 | 1.04368 | 0.521841 | − | 0.853043i | \(-0.325245\pi\) | ||||
0.521841 | + | 0.853043i | \(0.325245\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 7.89898 | 1.23361 | 0.616807 | − | 0.787115i | \(-0.288426\pi\) | ||||
0.616807 | + | 0.787115i | \(0.288426\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −8.89898 | −1.35708 | −0.678541 | − | 0.734563i | \(-0.737387\pi\) | ||||
−0.678541 | + | 0.734563i | \(0.737387\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −2.44949 | −0.357295 | −0.178647 | − | 0.983913i | \(-0.557172\pi\) | ||||
−0.178647 | + | 0.983913i | \(0.557172\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 4.89898 | 0.699854 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −4.34847 | −0.597308 | −0.298654 | − | 0.954361i | \(-0.596538\pi\) | ||||
−0.298654 | + | 0.954361i | \(0.596538\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.44949 | 0.330289 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −1.89898 | −0.247226 | −0.123613 | − | 0.992330i | \(-0.539448\pi\) | ||||
−0.123613 | + | 0.992330i | \(0.539448\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −5.34847 | −0.684801 | −0.342401 | − | 0.939554i | \(-0.611240\pi\) | ||||
−0.342401 | + | 0.939554i | \(0.611240\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −4.44949 | −0.551891 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.44949 | 0.177083 | 0.0885417 | − | 0.996072i | \(-0.471779\pi\) | ||||
0.0885417 | + | 0.996072i | \(0.471779\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 3.00000 | 0.356034 | 0.178017 | − | 0.984027i | \(-0.443032\pi\) | ||||
0.178017 | + | 0.984027i | \(0.443032\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 9.34847 | 1.09416 | 0.547078 | − | 0.837082i | \(-0.315740\pi\) | ||||
0.547078 | + | 0.837082i | \(0.315740\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 8.44949 | 0.962909 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −4.00000 | −0.450035 | −0.225018 | − | 0.974355i | \(-0.572244\pi\) | ||||
−0.225018 | + | 0.974355i | \(0.572244\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −10.3485 | −1.13589 | −0.567946 | − | 0.823066i | \(-0.692262\pi\) | ||||
−0.567946 | + | 0.823066i | \(0.692262\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −5.44949 | −0.591080 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −16.8990 | −1.79129 | −0.895644 | − | 0.444771i | \(-0.853285\pi\) | ||||
−0.895644 | + | 0.444771i | \(0.853285\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −15.3485 | −1.60896 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1.55051 | 0.159079 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −14.8990 | −1.51276 | −0.756381 | − | 0.654131i | \(-0.773034\pi\) | ||||
−0.756381 | + | 0.654131i | \(0.773034\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 18.7980 | 1.87047 | 0.935233 | − | 0.354032i | \(-0.115190\pi\) | ||||
0.935233 | + | 0.354032i | \(0.115190\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −4.00000 | −0.394132 | −0.197066 | − | 0.980390i | \(-0.563141\pi\) | ||||
−0.197066 | + | 0.980390i | \(0.563141\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 14.1464 | 1.36759 | 0.683793 | − | 0.729676i | \(-0.260329\pi\) | ||||
0.683793 | + | 0.729676i | \(0.260329\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −11.3485 | −1.08699 | −0.543493 | − | 0.839414i | \(-0.682899\pi\) | ||||
−0.543493 | + | 0.839414i | \(0.682899\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −16.3485 | −1.53793 | −0.768967 | − | 0.639288i | \(-0.779229\pi\) | ||||
−0.768967 | + | 0.639288i | \(0.779229\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.00000 | −0.0932505 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −18.7980 | −1.72321 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −5.00000 | −0.454545 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 3.34847 | 0.297129 | 0.148564 | − | 0.988903i | \(-0.452535\pi\) | ||||
0.148564 | + | 0.988903i | \(0.452535\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 10.8990 | 0.952248 | 0.476124 | − | 0.879378i | \(-0.342041\pi\) | ||||
0.476124 | + | 0.879378i | \(0.342041\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 5.34847 | 0.463771 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −16.8990 | −1.44378 | −0.721889 | − | 0.692009i | \(-0.756726\pi\) | ||||
−0.721889 | + | 0.692009i | \(0.756726\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −21.6969 | −1.84031 | −0.920155 | − | 0.391554i | \(-0.871938\pi\) | ||||
−0.920155 | + | 0.391554i | \(0.871938\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −10.8990 | −0.911418 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1.89898 | −0.157702 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 18.2474 | 1.49489 | 0.747445 | − | 0.664324i | \(-0.231281\pi\) | ||||
0.747445 | + | 0.664324i | \(0.231281\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −19.7980 | −1.61114 | −0.805568 | − | 0.592504i | \(-0.798139\pi\) | ||||
−0.805568 | + | 0.592504i | \(0.798139\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 7.00000 | 0.562254 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −14.3485 | −1.14513 | −0.572566 | − | 0.819858i | \(-0.694052\pi\) | ||||
−0.572566 | + | 0.819858i | \(0.694052\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −3.44949 | −0.271858 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −24.6969 | −1.93441 | −0.967207 | − | 0.253990i | \(-0.918257\pi\) | ||||
−0.967207 | + | 0.253990i | \(0.918257\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 0.247449 | 0.0191482 | 0.00957408 | − | 0.999954i | \(-0.496952\pi\) | ||||
0.00957408 | + | 0.999954i | \(0.496952\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 6.79796 | 0.522920 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −9.79796 | −0.744925 | −0.372463 | − | 0.928047i | \(-0.621486\pi\) | ||||
−0.372463 | + | 0.928047i | \(0.621486\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −3.44949 | −0.260757 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 0.898979 | 0.0668206 | 0.0334103 | − | 0.999442i | \(-0.489363\pi\) | ||||
0.0334103 | + | 0.999442i | \(0.489363\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −6.34847 | −0.466749 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −13.3485 | −0.976137 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 15.5505 | 1.12520 | 0.562598 | − | 0.826731i | \(-0.309802\pi\) | ||||
0.562598 | + | 0.826731i | \(0.309802\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −16.0000 | −1.15171 | −0.575853 | − | 0.817554i | \(-0.695330\pi\) | ||||
−0.575853 | + | 0.817554i | \(0.695330\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −15.7980 | −1.12556 | −0.562779 | − | 0.826607i | \(-0.690268\pi\) | ||||
−0.562779 | + | 0.826607i | \(0.690268\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 11.7980 | 0.836335 | 0.418168 | − | 0.908370i | \(-0.362672\pi\) | ||||
0.418168 | + | 0.908370i | \(0.362672\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −6.55051 | −0.459756 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −7.89898 | −0.551689 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 3.79796 | 0.262710 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 13.6969 | 0.942936 | 0.471468 | − | 0.881883i | \(-0.343724\pi\) | ||||
0.471468 | + | 0.881883i | \(0.343724\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 8.89898 | 0.606905 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 24.1464 | 1.63917 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 24.2474 | 1.63106 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −17.1010 | −1.14517 | −0.572585 | − | 0.819846i | \(-0.694059\pi\) | ||||
−0.572585 | + | 0.819846i | \(0.694059\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1.79796 | −0.118812 | −0.0594062 | − | 0.998234i | \(-0.518921\pi\) | ||||
−0.0594062 | + | 0.998234i | \(0.518921\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 24.4949 | 1.60471 | 0.802357 | − | 0.596844i | \(-0.203579\pi\) | ||||
0.802357 | + | 0.596844i | \(0.203579\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2.44949 | 0.159787 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 19.8990 | 1.28716 | 0.643579 | − | 0.765380i | \(-0.277449\pi\) | ||||
0.643579 | + | 0.765380i | \(0.277449\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 3.34847 | 0.215694 | 0.107847 | − | 0.994168i | \(-0.465604\pi\) | ||||
0.107847 | + | 0.994168i | \(0.465604\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −4.89898 | −0.312984 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −6.89898 | −0.438972 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −1.10102 | −0.0694958 | −0.0347479 | − | 0.999396i | \(-0.511063\pi\) | ||||
−0.0347479 | + | 0.999396i | \(0.511063\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2.44949 | −0.153998 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −19.3485 | −1.20692 | −0.603462 | − | 0.797392i | \(-0.706213\pi\) | ||||
−0.603462 | + | 0.797392i | \(0.706213\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −21.8990 | −1.36074 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 21.2474 | 1.31017 | 0.655087 | − | 0.755554i | \(-0.272632\pi\) | ||||
0.655087 | + | 0.755554i | \(0.272632\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 4.34847 | 0.267124 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −5.69694 | −0.347348 | −0.173674 | − | 0.984803i | \(-0.555564\pi\) | ||||
−0.173674 | + | 0.984803i | \(0.555564\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 25.6969 | 1.56098 | 0.780489 | − | 0.625170i | \(-0.214970\pi\) | ||||
0.780489 | + | 0.625170i | \(0.214970\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −2.44949 | −0.147710 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −14.8990 | −0.895193 | −0.447596 | − | 0.894236i | \(-0.647720\pi\) | ||||
−0.447596 | + | 0.894236i | \(0.647720\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −7.34847 | −0.438373 | −0.219186 | − | 0.975683i | \(-0.570340\pi\) | ||||
−0.219186 | + | 0.975683i | \(0.570340\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 8.55051 | 0.508275 | 0.254138 | − | 0.967168i | \(-0.418208\pi\) | ||||
0.254138 | + | 0.967168i | \(0.418208\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −27.2474 | −1.60837 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 12.6969 | 0.746879 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −22.3485 | −1.30561 | −0.652806 | − | 0.757525i | \(-0.726408\pi\) | ||||
−0.652806 | + | 0.757525i | \(0.726408\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1.89898 | 0.110563 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 4.44949 | 0.257321 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 30.6969 | 1.76934 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 5.34847 | 0.306252 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −12.4495 | −0.710530 | −0.355265 | − | 0.934766i | \(-0.615609\pi\) | ||||
−0.355265 | + | 0.934766i | \(0.615609\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −8.69694 | −0.493158 | −0.246579 | − | 0.969123i | \(-0.579307\pi\) | ||||
−0.246579 | + | 0.969123i | \(0.579307\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 3.65153 | 0.206397 | 0.103198 | − | 0.994661i | \(-0.467092\pi\) | ||||
0.103198 | + | 0.994661i | \(0.467092\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −24.2474 | −1.36187 | −0.680936 | − | 0.732343i | \(-0.738427\pi\) | ||||
−0.680936 | + | 0.732343i | \(0.738427\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −4.65153 | −0.260436 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −8.44949 | −0.470142 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 4.44949 | 0.246813 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 8.44949 | 0.465835 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1.00000 | −0.0549650 | −0.0274825 | − | 0.999622i | \(-0.508749\pi\) | ||||
−0.0274825 | + | 0.999622i | \(0.508749\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −1.44949 | −0.0791941 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 15.1010 | 0.822605 | 0.411303 | − | 0.911499i | \(-0.365074\pi\) | ||||
0.411303 | + | 0.911499i | \(0.365074\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 17.1464 | 0.928531 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 7.24745 | 0.391325 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 2.20204 | 0.118212 | 0.0591059 | − | 0.998252i | \(-0.481175\pi\) | ||||
0.0591059 | + | 0.998252i | \(0.481175\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −3.69694 | −0.197893 | −0.0989463 | − | 0.995093i | \(-0.531547\pi\) | ||||
−0.0989463 | + | 0.995093i | \(0.531547\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 14.4495 | 0.769069 | 0.384534 | − | 0.923111i | \(-0.374362\pi\) | ||||
0.384534 | + | 0.923111i | \(0.374362\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −3.00000 | −0.159223 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 11.1464 | 0.588286 | 0.294143 | − | 0.955761i | \(-0.404966\pi\) | ||||
0.294143 | + | 0.955761i | \(0.404966\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −16.5959 | −0.873469 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −9.34847 | −0.489321 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 5.24745 | 0.273915 | 0.136957 | − | 0.990577i | \(-0.456268\pi\) | ||||
0.136957 | + | 0.990577i | \(0.456268\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 15.0000 | 0.778761 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 14.0000 | 0.724893 | 0.362446 | − | 0.932005i | \(-0.381942\pi\) | ||||
0.362446 | + | 0.932005i | \(0.381942\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 8.44949 | 0.435171 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 25.3939 | 1.30440 | 0.652198 | − | 0.758049i | \(-0.273847\pi\) | ||||
0.652198 | + | 0.758049i | \(0.273847\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −10.3485 | −0.528782 | −0.264391 | − | 0.964416i | \(-0.585171\pi\) | ||||
−0.264391 | + | 0.964416i | \(0.585171\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −8.44949 | −0.430626 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −22.8990 | −1.16102 | −0.580512 | − | 0.814252i | \(-0.697148\pi\) | ||||
−0.580512 | + | 0.814252i | \(0.697148\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 5.44949 | 0.275593 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 4.00000 | 0.201262 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −1.79796 | −0.0902370 | −0.0451185 | − | 0.998982i | \(-0.514367\pi\) | ||||
−0.0451185 | + | 0.998982i | \(0.514367\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −8.69694 | −0.434304 | −0.217152 | − | 0.976138i | \(-0.569677\pi\) | ||||
−0.217152 | + | 0.976138i | \(0.569677\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −31.1464 | −1.55151 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −15.5505 | −0.770810 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −20.5959 | −1.01840 | −0.509201 | − | 0.860647i | \(-0.670059\pi\) | ||||
−0.509201 | + | 0.860647i | \(0.670059\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 6.55051 | 0.322330 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 10.3485 | 0.507986 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −17.1464 | −0.837658 | −0.418829 | − | 0.908065i | \(-0.637559\pi\) | ||||
−0.418829 | + | 0.908065i | \(0.637559\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −20.6515 | −1.00649 | −0.503247 | − | 0.864143i | \(-0.667861\pi\) | ||||
−0.503247 | + | 0.864143i | \(0.667861\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 5.44949 | 0.264339 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 18.4495 | 0.892833 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −19.5959 | −0.943902 | −0.471951 | − | 0.881625i | \(-0.656450\pi\) | ||||
−0.471951 | + | 0.881625i | \(0.656450\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −26.8434 | −1.29001 | −0.645005 | − | 0.764178i | \(-0.723145\pi\) | ||||
−0.645005 | + | 0.764178i | \(0.723145\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −1.55051 | −0.0741710 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 6.89898 | 0.329270 | 0.164635 | − | 0.986355i | \(-0.447355\pi\) | ||||
0.164635 | + | 0.986355i | \(0.447355\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 38.9444 | 1.85030 | 0.925152 | − | 0.379597i | \(-0.123937\pi\) | ||||
0.925152 | + | 0.379597i | \(0.123937\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 16.8990 | 0.801088 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −26.3939 | −1.24560 | −0.622802 | − | 0.782379i | \(-0.714006\pi\) | ||||
−0.622802 | + | 0.782379i | \(0.714006\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −19.3485 | −0.911084 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 15.3485 | 0.719547 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −26.3485 | −1.23253 | −0.616265 | − | 0.787539i | \(-0.711355\pi\) | ||||
−0.616265 | + | 0.787539i | \(0.711355\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 9.30306 | 0.433287 | 0.216643 | − | 0.976251i | \(-0.430489\pi\) | ||||
0.216643 | + | 0.976251i | \(0.430489\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 24.0454 | 1.11748 | 0.558742 | − | 0.829341i | \(-0.311284\pi\) | ||||
0.558742 | + | 0.829341i | \(0.311284\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 17.9444 | 0.830367 | 0.415184 | − | 0.909738i | \(-0.363717\pi\) | ||||
0.415184 | + | 0.909738i | \(0.363717\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −5.00000 | −0.230879 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 21.7980 | 1.00227 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1.55051 | −0.0711423 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −10.6515 | −0.486681 | −0.243340 | − | 0.969941i | \(-0.578243\pi\) | ||||
−0.243340 | + | 0.969941i | \(0.578243\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 28.2474 | 1.28797 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 14.8990 | 0.676528 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 1.14643 | 0.0519496 | 0.0259748 | − | 0.999663i | \(-0.491731\pi\) | ||||
0.0259748 | + | 0.999663i | \(0.491731\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 38.3939 | 1.73269 | 0.866346 | − | 0.499445i | \(-0.166463\pi\) | ||||
0.866346 | + | 0.499445i | \(0.166463\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 10.3485 | 0.466072 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −10.3485 | −0.464192 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −4.79796 | −0.214786 | −0.107393 | − | 0.994217i | \(-0.534250\pi\) | ||||
−0.107393 | + | 0.994217i | \(0.534250\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −14.1464 | −0.630758 | −0.315379 | − | 0.948966i | \(-0.602132\pi\) | ||||
−0.315379 | + | 0.948966i | \(0.602132\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −18.7980 | −0.836498 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 23.3939 | 1.03692 | 0.518458 | − | 0.855103i | \(-0.326506\pi\) | ||||
0.518458 | + | 0.855103i | \(0.326506\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −32.2474 | −1.42654 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 4.00000 | 0.176261 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 6.00000 | 0.263880 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 31.3485 | 1.37340 | 0.686701 | − | 0.726940i | \(-0.259058\pi\) | ||||
0.686701 | + | 0.726940i | \(0.259058\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −12.2020 | −0.533558 | −0.266779 | − | 0.963758i | \(-0.585959\pi\) | ||||
−0.266779 | + | 0.963758i | \(0.585959\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −38.1464 | −1.66168 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 35.1464 | 1.52236 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −14.1464 | −0.611603 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −12.0000 | −0.516877 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 15.1010 | 0.649244 | 0.324622 | − | 0.945844i | \(-0.394763\pi\) | ||||
0.324622 | + | 0.945844i | \(0.394763\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 11.3485 | 0.486115 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −33.3939 | −1.42782 | −0.713910 | − | 0.700238i | \(-0.753077\pi\) | ||||
−0.713910 | + | 0.700238i | \(0.753077\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −2.94439 | −0.125435 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 13.7980 | 0.586749 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −24.5505 | −1.04024 | −0.520119 | − | 0.854094i | \(-0.674113\pi\) | ||||
−0.520119 | + | 0.854094i | \(0.674113\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −39.5959 | −1.67473 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −38.1464 | −1.60768 | −0.803840 | − | 0.594845i | \(-0.797213\pi\) | ||||
−0.803840 | + | 0.594845i | \(0.797213\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 16.3485 | 0.687785 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 11.3939 | 0.477656 | 0.238828 | − | 0.971062i | \(-0.423237\pi\) | ||||
0.238828 | + | 0.971062i | \(0.423237\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −32.0454 | −1.34106 | −0.670529 | − | 0.741883i | \(-0.733933\pi\) | ||||
−0.670529 | + | 0.741883i | \(0.733933\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1.00000 | 0.0417029 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −26.2929 | −1.09459 | −0.547293 | − | 0.836941i | \(-0.684342\pi\) | ||||
−0.547293 | + | 0.836941i | \(0.684342\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 35.6969 | 1.48096 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 10.6515 | 0.441141 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 1.59592 | 0.0658706 | 0.0329353 | − | 0.999457i | \(-0.489514\pi\) | ||||
0.0329353 | + | 0.999457i | \(0.489514\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 10.8536 | 0.447214 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −41.1464 | −1.68968 | −0.844841 | − | 0.535018i | \(-0.820305\pi\) | ||||
−0.844841 | + | 0.535018i | \(0.820305\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 18.7980 | 0.770641 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −30.0000 | −1.22577 | −0.612883 | − | 0.790173i | \(-0.709990\pi\) | ||||
−0.612883 | + | 0.790173i | \(0.709990\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 14.7980 | 0.603621 | 0.301811 | − | 0.953368i | \(-0.402409\pi\) | ||||
0.301811 | + | 0.953368i | \(0.402409\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 5.00000 | 0.203279 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 24.6515 | 1.00057 | 0.500287 | − | 0.865859i | \(-0.333228\pi\) | ||||
0.500287 | + | 0.865859i | \(0.333228\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −10.8990 | −0.440926 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 22.6969 | 0.916721 | 0.458360 | − | 0.888766i | \(-0.348437\pi\) | ||||
0.458360 | + | 0.888766i | \(0.348437\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −16.3485 | −0.658165 | −0.329082 | − | 0.944301i | \(-0.606739\pi\) | ||||
−0.329082 | + | 0.944301i | \(0.606739\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −1.79796 | −0.0722661 | −0.0361330 | − | 0.999347i | \(-0.511504\pi\) | ||||
−0.0361330 | + | 0.999347i | \(0.511504\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 58.2929 | 2.33545 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 34.5959 | 1.37943 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −22.2474 | −0.885657 | −0.442828 | − | 0.896606i | \(-0.646025\pi\) | ||||
−0.442828 | + | 0.896606i | \(0.646025\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −3.34847 | −0.132880 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 21.7980 | 0.863667 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 26.4495 | 1.04469 | 0.522346 | − | 0.852734i | \(-0.325057\pi\) | ||||
0.522346 | + | 0.852734i | \(0.325057\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 24.3485 | 0.960210 | 0.480105 | − | 0.877211i | \(-0.340599\pi\) | ||||
0.480105 | + | 0.877211i | \(0.340599\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 20.4495 | 0.803952 | 0.401976 | − | 0.915650i | \(-0.368323\pi\) | ||||
0.401976 | + | 0.915650i | \(0.368323\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 4.65153 | 0.182589 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 27.5505 | 1.07813 | 0.539067 | − | 0.842263i | \(-0.318777\pi\) | ||||
0.539067 | + | 0.842263i | \(0.318777\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −10.8990 | −0.425858 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 14.4495 | 0.562872 | 0.281436 | − | 0.959580i | \(-0.409189\pi\) | ||||
0.281436 | + | 0.959580i | \(0.409189\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 26.0000 | 1.01128 | 0.505641 | − | 0.862744i | \(-0.331256\pi\) | ||||
0.505641 | + | 0.862744i | \(0.331256\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −5.34847 | −0.207405 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.89898 | 0.0735288 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 13.1010 | 0.505759 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 18.0454 | 0.695599 | 0.347800 | − | 0.937569i | \(-0.386929\pi\) | ||||
0.347800 | + | 0.937569i | \(0.386929\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −39.2474 | −1.50840 | −0.754201 | − | 0.656644i | \(-0.771976\pi\) | ||||
−0.754201 | + | 0.656644i | \(0.771976\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 51.3939 | 1.97232 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −19.3485 | −0.740349 | −0.370174 | − | 0.928962i | \(-0.620702\pi\) | ||||
−0.370174 | + | 0.928962i | \(0.620702\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 16.8990 | 0.645677 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −19.3485 | −0.737118 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 43.3939 | 1.65078 | 0.825390 | − | 0.564562i | \(-0.190955\pi\) | ||||
0.825390 | + | 0.564562i | \(0.190955\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 21.6969 | 0.823012 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 43.0454 | 1.63046 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −16.0454 | −0.606027 | −0.303013 | − | 0.952986i | \(-0.597993\pi\) | ||||
−0.303013 | + | 0.952986i | \(0.597993\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −9.84337 | −0.371250 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −64.8434 | −2.43869 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 52.9444 | 1.98837 | 0.994184 | − | 0.107694i | \(-0.0343466\pi\) | ||||
0.994184 | + | 0.107694i | \(0.0343466\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −7.00000 | −0.262152 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 10.8990 | 0.407599 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −49.2929 | −1.83831 | −0.919157 | − | 0.393892i | \(-0.871128\pi\) | ||||
−0.919157 | + | 0.393892i | \(0.871128\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 13.7980 | 0.513863 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 1.89898 | 0.0705263 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −17.6515 | −0.654659 | −0.327330 | − | 0.944910i | \(-0.606149\pi\) | ||||
−0.327330 | + | 0.944910i | \(0.606149\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −48.4949 | −1.79365 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 21.6515 | 0.799718 | 0.399859 | − | 0.916577i | \(-0.369059\pi\) | ||||
0.399859 | + | 0.916577i | \(0.369059\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −3.55051 | −0.130785 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −45.6969 | −1.68099 | −0.840495 | − | 0.541820i | \(-0.817735\pi\) | ||||
−0.840495 | + | 0.541820i | \(0.817735\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −14.2020 | −0.521022 | −0.260511 | − | 0.965471i | \(-0.583891\pi\) | ||||
−0.260511 | + | 0.965471i | \(0.583891\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −18.2474 | −0.668535 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −48.7980 | −1.78304 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 27.3485 | 0.997960 | 0.498980 | − | 0.866614i | \(-0.333708\pi\) | ||||
0.498980 | + | 0.866614i | \(0.333708\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 19.7980 | 0.720521 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 10.7526 | 0.390808 | 0.195404 | − | 0.980723i | \(-0.437398\pi\) | ||||
0.195404 | + | 0.980723i | \(0.437398\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −3.49490 | −0.126690 | −0.0633450 | − | 0.997992i | \(-0.520177\pi\) | ||||
−0.0633450 | + | 0.997992i | \(0.520177\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 39.1464 | 1.41720 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −8.44949 | −0.305093 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 31.1464 | 1.12317 | 0.561584 | − | 0.827419i | \(-0.310192\pi\) | ||||
0.561584 | + | 0.827419i | \(0.310192\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 20.6969 | 0.744417 | 0.372209 | − | 0.928149i | \(-0.378601\pi\) | ||||
0.372209 | + | 0.928149i | \(0.378601\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −7.00000 | −0.251447 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −12.2474 | −0.438810 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −7.34847 | −0.262949 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 14.3485 | 0.512119 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −13.8536 | −0.493827 | −0.246913 | − | 0.969038i | \(-0.579416\pi\) | ||||
−0.246913 | + | 0.969038i | \(0.579416\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 56.3939 | 2.00514 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −23.7980 | −0.845090 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −3.85357 | −0.136501 | −0.0682503 | − | 0.997668i | \(-0.521742\pi\) | ||||
−0.0682503 | + | 0.997668i | \(0.521742\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −13.3485 | −0.472235 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −22.8990 | −0.808087 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 3.44949 | 0.121579 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −18.7980 | −0.660901 | −0.330451 | − | 0.943823i | \(-0.607201\pi\) | ||||
−0.330451 | + | 0.943823i | \(0.607201\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 2.79796 | 0.0982496 | 0.0491248 | − | 0.998793i | \(-0.484357\pi\) | ||||
0.0491248 | + | 0.998793i | \(0.484357\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 24.6969 | 0.865096 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 13.7980 | 0.482729 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −13.5959 | −0.474501 | −0.237250 | − | 0.971449i | \(-0.576246\pi\) | ||||
−0.237250 | + | 0.971449i | \(0.576246\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 12.8990 | 0.449630 | 0.224815 | − | 0.974401i | \(-0.427822\pi\) | ||||
0.224815 | + | 0.974401i | \(0.427822\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 20.7526 | 0.721637 | 0.360818 | − | 0.932636i | \(-0.382497\pi\) | ||||
0.360818 | + | 0.932636i | \(0.382497\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −24.3939 | −0.847234 | −0.423617 | − | 0.905841i | \(-0.639240\pi\) | ||||
−0.423617 | + | 0.905841i | \(0.639240\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 26.6969 | 0.924994 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −0.247449 | −0.00856332 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −25.5959 | −0.883669 | −0.441835 | − | 0.897097i | \(-0.645672\pi\) | ||||
−0.441835 | + | 0.897097i | \(0.645672\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −25.3939 | −0.875651 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −6.79796 | −0.233857 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 17.2474 | 0.592629 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 6.34847 | 0.217623 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 23.7980 | 0.814827 | 0.407413 | − | 0.913244i | \(-0.366431\pi\) | ||||
0.407413 | + | 0.913244i | \(0.366431\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 16.2929 | 0.556553 | 0.278277 | − | 0.960501i | \(-0.410237\pi\) | ||||
0.278277 | + | 0.960501i | \(0.410237\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 17.0000 | 0.580033 | 0.290016 | − | 0.957022i | \(-0.406339\pi\) | ||||
0.290016 | + | 0.957022i | \(0.406339\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 25.5959 | 0.871295 | 0.435648 | − | 0.900117i | \(-0.356519\pi\) | ||||
0.435648 | + | 0.900117i | \(0.356519\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 9.79796 | 0.333141 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 9.79796 | 0.332373 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 6.44949 | 0.218533 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 3.44949 | 0.116614 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 23.7980 | 0.803600 | 0.401800 | − | 0.915727i | \(-0.368385\pi\) | ||||
0.401800 | + | 0.915727i | \(0.368385\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −35.1464 | −1.18411 | −0.592057 | − | 0.805896i | \(-0.701684\pi\) | ||||
−0.592057 | + | 0.805896i | \(0.701684\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −37.5505 | −1.26368 | −0.631838 | − | 0.775101i | \(-0.717699\pi\) | ||||
−0.631838 | + | 0.775101i | \(0.717699\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −37.5959 | −1.26235 | −0.631174 | − | 0.775642i | \(-0.717426\pi\) | ||||
−0.631174 | + | 0.775642i | \(0.717426\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −11.5505 | −0.387392 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 3.79796 | 0.127094 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −13.2929 | −0.443342 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −23.6969 | −0.789459 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −0.898979 | −0.0298831 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −2.34847 | −0.0779796 | −0.0389898 | − | 0.999240i | \(-0.512414\pi\) | ||||
−0.0389898 | + | 0.999240i | \(0.512414\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 24.4949 | 0.811552 | 0.405776 | − | 0.913973i | \(-0.367001\pi\) | ||||
0.405776 | + | 0.913973i | \(0.367001\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 25.3485 | 0.838912 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −37.5959 | −1.24153 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 36.8990 | 1.21719 | 0.608593 | − | 0.793483i | \(-0.291734\pi\) | ||||
0.608593 | + | 0.793483i | \(0.291734\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 13.3485 | 0.439370 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 6.34847 | 0.208736 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −27.0000 | −0.885841 | −0.442921 | − | 0.896561i | \(-0.646058\pi\) | ||||
−0.442921 | + | 0.896561i | \(0.646058\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −7.59592 | −0.248946 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 13.3485 | 0.436542 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 28.6969 | 0.937488 | 0.468744 | − | 0.883334i | \(-0.344707\pi\) | ||||
0.468744 | + | 0.883334i | \(0.344707\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 32.4495 | 1.05782 | 0.528912 | − | 0.848677i | \(-0.322600\pi\) | ||||
0.528912 | + | 0.848677i | \(0.322600\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 7.89898 | 0.257226 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 36.4949 | 1.18592 | 0.592962 | − | 0.805230i | \(-0.297958\pi\) | ||||
0.592962 | + | 0.805230i | \(0.297958\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 41.5959 | 1.35026 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −32.2020 | −1.04313 | −0.521563 | − | 0.853213i | \(-0.674651\pi\) | ||||
−0.521563 | + | 0.853213i | \(0.674651\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −15.5505 | −0.503203 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 58.2929 | 1.88237 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 18.0000 | 0.580645 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 16.0000 | 0.515058 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −8.65153 | −0.278214 | −0.139107 | − | 0.990277i | \(-0.544423\pi\) | ||||
−0.139107 | + | 0.990277i | \(0.544423\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −12.4949 | −0.400980 | −0.200490 | − | 0.979696i | \(-0.564253\pi\) | ||||
−0.200490 | + | 0.979696i | \(0.564253\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 74.8434 | 2.39937 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 40.3485 | 1.29086 | 0.645431 | − | 0.763819i | \(-0.276678\pi\) | ||||
0.645431 | + | 0.763819i | \(0.276678\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 41.3939 | 1.32295 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −16.3485 | −0.521435 | −0.260718 | − | 0.965415i | \(-0.583959\pi\) | ||||
−0.260718 | + | 0.965415i | \(0.583959\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 15.7980 | 0.503365 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −8.89898 | −0.282971 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 30.1010 | 0.956190 | 0.478095 | − | 0.878308i | \(-0.341327\pi\) | ||||
0.478095 | + | 0.878308i | \(0.341327\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −11.7980 | −0.374020 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 32.0000 | 1.01345 | 0.506725 | − | 0.862108i | \(-0.330856\pi\) | ||||
0.506725 | + | 0.862108i | \(0.330856\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 4140.2.a.l.1.1 | ✓ | 2 | |
3.2 | odd | 2 | 4140.2.a.q.1.1 | yes | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4140.2.a.l.1.1 | ✓ | 2 | 1.1 | even | 1 | trivial | |
4140.2.a.q.1.1 | yes | 2 | 3.2 | odd | 2 |