Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1250,2,Mod(1249,1250)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1250, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1250.1249");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1250 = 2 \cdot 5^{4} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1250.b (of order \(2\), degree \(1\), not minimal) |
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: | no |
Analytic conductor: | \(9.98130025266\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(i, \sqrt{5})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 3x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 50) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1249.4 | ||
Root | \(0.618034i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1250.1249 |
Dual form | 1250.2.b.b.1249.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1250\mathbb{Z}\right)^\times\).
\(n\) | \(627\) |
\(\chi(n)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000i | 0.707107i | ||||||||
\(3\) | − 0.381966i | − 0.220528i | −0.993902 | − | 0.110264i | \(-0.964830\pi\) | ||||
0.993902 | − | 0.110264i | \(-0.0351697\pi\) | |||||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0.381966 | 0.155937 | ||||||||
\(7\) | 3.00000i | 1.13389i | 0.823754 | + | 0.566947i | \(0.191875\pi\) | ||||
−0.823754 | + | 0.566947i | \(0.808125\pi\) | |||||||
\(8\) | − 1.00000i | − 0.353553i | ||||||||
\(9\) | 2.85410 | 0.951367 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.23607 | 1.27722 | 0.638611 | − | 0.769529i | \(-0.279509\pi\) | ||||
0.638611 | + | 0.769529i | \(0.279509\pi\) | |||||||
\(12\) | 0.381966i | 0.110264i | ||||||||
\(13\) | 1.00000i | 0.277350i | 0.990338 | + | 0.138675i | \(0.0442844\pi\) | ||||
−0.990338 | + | 0.138675i | \(0.955716\pi\) | |||||||
\(14\) | −3.00000 | −0.801784 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | − 1.14590i | − 0.277921i | −0.990298 | − | 0.138961i | \(-0.955624\pi\) | ||||
0.990298 | − | 0.138961i | \(-0.0443761\pi\) | |||||||
\(18\) | 2.85410i | 0.672718i | ||||||||
\(19\) | −5.85410 | −1.34302 | −0.671512 | − | 0.740994i | \(-0.734355\pi\) | ||||
−0.671512 | + | 0.740994i | \(0.734355\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.14590 | 0.250055 | ||||||||
\(22\) | 4.23607i | 0.903133i | ||||||||
\(23\) | − 1.76393i | − 0.367805i | −0.982944 | − | 0.183903i | \(-0.941127\pi\) | ||||
0.982944 | − | 0.183903i | \(-0.0588731\pi\) | |||||||
\(24\) | −0.381966 | −0.0779685 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −1.00000 | −0.196116 | ||||||||
\(27\) | − 2.23607i | − 0.430331i | ||||||||
\(28\) | − 3.00000i | − 0.566947i | ||||||||
\(29\) | 9.47214 | 1.75893 | 0.879466 | − | 0.475962i | \(-0.157900\pi\) | ||||
0.879466 | + | 0.475962i | \(0.157900\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.236068 | −0.0423991 | −0.0211995 | − | 0.999775i | \(-0.506749\pi\) | ||||
−0.0211995 | + | 0.999775i | \(0.506749\pi\) | |||||||
\(32\) | 1.00000i | 0.176777i | ||||||||
\(33\) | − 1.61803i | − 0.281664i | ||||||||
\(34\) | 1.14590 | 0.196520 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −2.85410 | −0.475684 | ||||||||
\(37\) | 8.32624i | 1.36883i | 0.729095 | + | 0.684413i | \(0.239941\pi\) | ||||
−0.729095 | + | 0.684413i | \(0.760059\pi\) | |||||||
\(38\) | − 5.85410i | − 0.949661i | ||||||||
\(39\) | 0.381966 | 0.0611635 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.47214 | 0.229909 | 0.114955 | − | 0.993371i | \(-0.463328\pi\) | ||||
0.114955 | + | 0.993371i | \(0.463328\pi\) | |||||||
\(42\) | 1.14590i | 0.176816i | ||||||||
\(43\) | − 6.23607i | − 0.950991i | −0.879718 | − | 0.475496i | \(-0.842269\pi\) | ||||
0.879718 | − | 0.475496i | \(-0.157731\pi\) | |||||||
\(44\) | −4.23607 | −0.638611 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1.76393 | 0.260078 | ||||||||
\(47\) | 11.9443i | 1.74225i | 0.491060 | + | 0.871126i | \(0.336609\pi\) | ||||
−0.491060 | + | 0.871126i | \(0.663391\pi\) | |||||||
\(48\) | − 0.381966i | − 0.0551320i | ||||||||
\(49\) | −2.00000 | −0.285714 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.437694 | −0.0612894 | ||||||||
\(52\) | − 1.00000i | − 0.138675i | ||||||||
\(53\) | 10.4721i | 1.43846i | 0.694773 | + | 0.719229i | \(0.255505\pi\) | ||||
−0.694773 | + | 0.719229i | \(0.744495\pi\) | |||||||
\(54\) | 2.23607 | 0.304290 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 3.00000 | 0.400892 | ||||||||
\(57\) | 2.23607i | 0.296174i | ||||||||
\(58\) | 9.47214i | 1.24375i | ||||||||
\(59\) | 4.47214 | 0.582223 | 0.291111 | − | 0.956689i | \(-0.405975\pi\) | ||||
0.291111 | + | 0.956689i | \(0.405975\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −8.85410 | −1.13365 | −0.566826 | − | 0.823838i | \(-0.691829\pi\) | ||||
−0.566826 | + | 0.823838i | \(0.691829\pi\) | |||||||
\(62\) | − 0.236068i | − 0.0299807i | ||||||||
\(63\) | 8.56231i | 1.07875i | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 1.61803 | 0.199166 | ||||||||
\(67\) | 10.2361i | 1.25053i | 0.780411 | + | 0.625267i | \(0.215010\pi\) | ||||
−0.780411 | + | 0.625267i | \(0.784990\pi\) | |||||||
\(68\) | 1.14590i | 0.138961i | ||||||||
\(69\) | −0.673762 | −0.0811114 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −3.00000 | −0.356034 | −0.178017 | − | 0.984027i | \(-0.556968\pi\) | ||||
−0.178017 | + | 0.984027i | \(0.556968\pi\) | |||||||
\(72\) | − 2.85410i | − 0.336359i | ||||||||
\(73\) | 7.70820i | 0.902177i | 0.892479 | + | 0.451089i | \(0.148964\pi\) | ||||
−0.892479 | + | 0.451089i | \(0.851036\pi\) | |||||||
\(74\) | −8.32624 | −0.967905 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 5.85410 | 0.671512 | ||||||||
\(77\) | 12.7082i | 1.44823i | ||||||||
\(78\) | 0.381966i | 0.0432491i | ||||||||
\(79\) | 7.23607 | 0.814121 | 0.407061 | − | 0.913401i | \(-0.366554\pi\) | ||||
0.407061 | + | 0.913401i | \(0.366554\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 7.70820 | 0.856467 | ||||||||
\(82\) | 1.47214i | 0.162570i | ||||||||
\(83\) | − 4.52786i | − 0.496998i | −0.968632 | − | 0.248499i | \(-0.920063\pi\) | ||||
0.968632 | − | 0.248499i | \(-0.0799372\pi\) | |||||||
\(84\) | −1.14590 | −0.125028 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 6.23607 | 0.672453 | ||||||||
\(87\) | − 3.61803i | − 0.387894i | ||||||||
\(88\) | − 4.23607i | − 0.451566i | ||||||||
\(89\) | −4.47214 | −0.474045 | −0.237023 | − | 0.971504i | \(-0.576172\pi\) | ||||
−0.237023 | + | 0.971504i | \(0.576172\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −3.00000 | −0.314485 | ||||||||
\(92\) | 1.76393i | 0.183903i | ||||||||
\(93\) | 0.0901699i | 0.00935019i | ||||||||
\(94\) | −11.9443 | −1.23196 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0.381966 | 0.0389842 | ||||||||
\(97\) | − 9.56231i | − 0.970905i | −0.874263 | − | 0.485453i | \(-0.838655\pi\) | ||||
0.874263 | − | 0.485453i | \(-0.161345\pi\) | |||||||
\(98\) | − 2.00000i | − 0.202031i | ||||||||
\(99\) | 12.0902 | 1.21511 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 0.618034 | 0.0614967 | 0.0307483 | − | 0.999527i | \(-0.490211\pi\) | ||||
0.0307483 | + | 0.999527i | \(0.490211\pi\) | |||||||
\(102\) | − 0.437694i | − 0.0433382i | ||||||||
\(103\) | − 13.1459i | − 1.29530i | −0.761936 | − | 0.647652i | \(-0.775751\pi\) | ||||
0.761936 | − | 0.647652i | \(-0.224249\pi\) | |||||||
\(104\) | 1.00000 | 0.0980581 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −10.4721 | −1.01714 | ||||||||
\(107\) | 1.09017i | 0.105391i | 0.998611 | + | 0.0526954i | \(0.0167812\pi\) | ||||
−0.998611 | + | 0.0526954i | \(0.983219\pi\) | |||||||
\(108\) | 2.23607i | 0.215166i | ||||||||
\(109\) | 15.0000 | 1.43674 | 0.718370 | − | 0.695662i | \(-0.244889\pi\) | ||||
0.718370 | + | 0.695662i | \(0.244889\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 3.18034 | 0.301865 | ||||||||
\(112\) | 3.00000i | 0.283473i | ||||||||
\(113\) | 3.76393i | 0.354081i | 0.984204 | + | 0.177040i | \(0.0566523\pi\) | ||||
−0.984204 | + | 0.177040i | \(0.943348\pi\) | |||||||
\(114\) | −2.23607 | −0.209427 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −9.47214 | −0.879466 | ||||||||
\(117\) | 2.85410i | 0.263862i | ||||||||
\(118\) | 4.47214i | 0.411693i | ||||||||
\(119\) | 3.43769 | 0.315133 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 6.94427 | 0.631297 | ||||||||
\(122\) | − 8.85410i | − 0.801613i | ||||||||
\(123\) | − 0.562306i | − 0.0507014i | ||||||||
\(124\) | 0.236068 | 0.0211995 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −8.56231 | −0.762791 | ||||||||
\(127\) | 3.52786i | 0.313047i | 0.987674 | + | 0.156524i | \(0.0500287\pi\) | ||||
−0.987674 | + | 0.156524i | \(0.949971\pi\) | |||||||
\(128\) | − 1.00000i | − 0.0883883i | ||||||||
\(129\) | −2.38197 | −0.209720 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −16.4164 | −1.43431 | −0.717154 | − | 0.696915i | \(-0.754556\pi\) | ||||
−0.717154 | + | 0.696915i | \(0.754556\pi\) | |||||||
\(132\) | 1.61803i | 0.140832i | ||||||||
\(133\) | − 17.5623i | − 1.52285i | ||||||||
\(134\) | −10.2361 | −0.884262 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −1.14590 | −0.0982599 | ||||||||
\(137\) | − 5.09017i | − 0.434883i | −0.976073 | − | 0.217441i | \(-0.930229\pi\) | ||||
0.976073 | − | 0.217441i | \(-0.0697711\pi\) | |||||||
\(138\) | − 0.673762i | − 0.0573544i | ||||||||
\(139\) | 5.32624 | 0.451766 | 0.225883 | − | 0.974154i | \(-0.427473\pi\) | ||||
0.225883 | + | 0.974154i | \(0.427473\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 4.56231 | 0.384215 | ||||||||
\(142\) | − 3.00000i | − 0.251754i | ||||||||
\(143\) | 4.23607i | 0.354238i | ||||||||
\(144\) | 2.85410 | 0.237842 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −7.70820 | −0.637935 | ||||||||
\(147\) | 0.763932i | 0.0630081i | ||||||||
\(148\) | − 8.32624i | − 0.684413i | ||||||||
\(149\) | −2.23607 | −0.183186 | −0.0915929 | − | 0.995797i | \(-0.529196\pi\) | ||||
−0.0915929 | + | 0.995797i | \(0.529196\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −9.70820 | −0.790042 | −0.395021 | − | 0.918672i | \(-0.629263\pi\) | ||||
−0.395021 | + | 0.918672i | \(0.629263\pi\) | |||||||
\(152\) | 5.85410i | 0.474830i | ||||||||
\(153\) | − 3.27051i | − 0.264405i | ||||||||
\(154\) | −12.7082 | −1.02406 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −0.381966 | −0.0305818 | ||||||||
\(157\) | − 4.56231i | − 0.364112i | −0.983288 | − | 0.182056i | \(-0.941725\pi\) | ||||
0.983288 | − | 0.182056i | \(-0.0582752\pi\) | |||||||
\(158\) | 7.23607i | 0.575671i | ||||||||
\(159\) | 4.00000 | 0.317221 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 5.29180 | 0.417052 | ||||||||
\(162\) | 7.70820i | 0.605614i | ||||||||
\(163\) | 1.85410i | 0.145224i | 0.997360 | + | 0.0726122i | \(0.0231336\pi\) | ||||
−0.997360 | + | 0.0726122i | \(0.976866\pi\) | |||||||
\(164\) | −1.47214 | −0.114955 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 4.52786 | 0.351430 | ||||||||
\(167\) | − 13.3820i | − 1.03553i | −0.855524 | − | 0.517764i | \(-0.826765\pi\) | ||||
0.855524 | − | 0.517764i | \(-0.173235\pi\) | |||||||
\(168\) | − 1.14590i | − 0.0884080i | ||||||||
\(169\) | 12.0000 | 0.923077 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −16.7082 | −1.27771 | ||||||||
\(172\) | 6.23607i | 0.475496i | ||||||||
\(173\) | − 1.23607i | − 0.0939765i | −0.998895 | − | 0.0469883i | \(-0.985038\pi\) | ||||
0.998895 | − | 0.0469883i | \(-0.0149623\pi\) | |||||||
\(174\) | 3.61803 | 0.274282 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 4.23607 | 0.319306 | ||||||||
\(177\) | − 1.70820i | − 0.128396i | ||||||||
\(178\) | − 4.47214i | − 0.335201i | ||||||||
\(179\) | −11.1803 | −0.835658 | −0.417829 | − | 0.908526i | \(-0.637209\pi\) | ||||
−0.417829 | + | 0.908526i | \(0.637209\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 5.41641 | 0.402598 | 0.201299 | − | 0.979530i | \(-0.435484\pi\) | ||||
0.201299 | + | 0.979530i | \(0.435484\pi\) | |||||||
\(182\) | − 3.00000i | − 0.222375i | ||||||||
\(183\) | 3.38197i | 0.250002i | ||||||||
\(184\) | −1.76393 | −0.130039 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −0.0901699 | −0.00661158 | ||||||||
\(187\) | − 4.85410i | − 0.354967i | ||||||||
\(188\) | − 11.9443i | − 0.871126i | ||||||||
\(189\) | 6.70820 | 0.487950 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −13.6525 | −0.987858 | −0.493929 | − | 0.869502i | \(-0.664440\pi\) | ||||
−0.493929 | + | 0.869502i | \(0.664440\pi\) | |||||||
\(192\) | 0.381966i | 0.0275660i | ||||||||
\(193\) | − 14.6525i | − 1.05471i | −0.849646 | − | 0.527354i | \(-0.823184\pi\) | ||||
0.849646 | − | 0.527354i | \(-0.176816\pi\) | |||||||
\(194\) | 9.56231 | 0.686534 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 2.00000 | 0.142857 | ||||||||
\(197\) | − 12.0000i | − 0.854965i | −0.904024 | − | 0.427482i | \(-0.859401\pi\) | ||||
0.904024 | − | 0.427482i | \(-0.140599\pi\) | |||||||
\(198\) | 12.0902i | 0.859211i | ||||||||
\(199\) | −2.56231 | −0.181637 | −0.0908185 | − | 0.995867i | \(-0.528948\pi\) | ||||
−0.0908185 | + | 0.995867i | \(0.528948\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 3.90983 | 0.275778 | ||||||||
\(202\) | 0.618034i | 0.0434847i | ||||||||
\(203\) | 28.4164i | 1.99444i | ||||||||
\(204\) | 0.437694 | 0.0306447 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 13.1459 | 0.915918 | ||||||||
\(207\) | − 5.03444i | − 0.349918i | ||||||||
\(208\) | 1.00000i | 0.0693375i | ||||||||
\(209\) | −24.7984 | −1.71534 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −22.2705 | −1.53317 | −0.766583 | − | 0.642146i | \(-0.778044\pi\) | ||||
−0.766583 | + | 0.642146i | \(0.778044\pi\) | |||||||
\(212\) | − 10.4721i | − 0.719229i | ||||||||
\(213\) | 1.14590i | 0.0785156i | ||||||||
\(214\) | −1.09017 | −0.0745225 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −2.23607 | −0.152145 | ||||||||
\(217\) | − 0.708204i | − 0.0480760i | ||||||||
\(218\) | 15.0000i | 1.01593i | ||||||||
\(219\) | 2.94427 | 0.198955 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.14590 | 0.0770814 | ||||||||
\(222\) | 3.18034i | 0.213450i | ||||||||
\(223\) | − 9.00000i | − 0.602685i | −0.953516 | − | 0.301342i | \(-0.902565\pi\) | ||||
0.953516 | − | 0.301342i | \(-0.0974347\pi\) | |||||||
\(224\) | −3.00000 | −0.200446 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −3.76393 | −0.250373 | ||||||||
\(227\) | − 29.3607i | − 1.94874i | −0.224958 | − | 0.974368i | \(-0.572225\pi\) | ||||
0.224958 | − | 0.974368i | \(-0.427775\pi\) | |||||||
\(228\) | − 2.23607i | − 0.148087i | ||||||||
\(229\) | 2.56231 | 0.169322 | 0.0846610 | − | 0.996410i | \(-0.473019\pi\) | ||||
0.0846610 | + | 0.996410i | \(0.473019\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 4.85410 | 0.319376 | ||||||||
\(232\) | − 9.47214i | − 0.621876i | ||||||||
\(233\) | 14.2918i | 0.936287i | 0.883653 | + | 0.468143i | \(0.155077\pi\) | ||||
−0.883653 | + | 0.468143i | \(0.844923\pi\) | |||||||
\(234\) | −2.85410 | −0.186578 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −4.47214 | −0.291111 | ||||||||
\(237\) | − 2.76393i | − 0.179537i | ||||||||
\(238\) | 3.43769i | 0.222833i | ||||||||
\(239\) | 6.90983 | 0.446960 | 0.223480 | − | 0.974709i | \(-0.428258\pi\) | ||||
0.223480 | + | 0.974709i | \(0.428258\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 15.6180 | 1.00605 | 0.503023 | − | 0.864273i | \(-0.332221\pi\) | ||||
0.503023 | + | 0.864273i | \(0.332221\pi\) | |||||||
\(242\) | 6.94427i | 0.446395i | ||||||||
\(243\) | − 9.65248i | − 0.619207i | ||||||||
\(244\) | 8.85410 | 0.566826 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0.562306 | 0.0358513 | ||||||||
\(247\) | − 5.85410i | − 0.372488i | ||||||||
\(248\) | 0.236068i | 0.0149903i | ||||||||
\(249\) | −1.72949 | −0.109602 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 0.819660 | 0.0517365 | 0.0258682 | − | 0.999665i | \(-0.491765\pi\) | ||||
0.0258682 | + | 0.999665i | \(0.491765\pi\) | |||||||
\(252\) | − 8.56231i | − 0.539375i | ||||||||
\(253\) | − 7.47214i | − 0.469769i | ||||||||
\(254\) | −3.52786 | −0.221358 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | − 25.7426i | − 1.60578i | −0.596126 | − | 0.802891i | \(-0.703294\pi\) | ||||
0.596126 | − | 0.802891i | \(-0.296706\pi\) | |||||||
\(258\) | − 2.38197i | − 0.148295i | ||||||||
\(259\) | −24.9787 | −1.55210 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 27.0344 | 1.67339 | ||||||||
\(262\) | − 16.4164i | − 1.01421i | ||||||||
\(263\) | 4.61803i | 0.284760i | 0.989812 | + | 0.142380i | \(0.0454755\pi\) | ||||
−0.989812 | + | 0.142380i | \(0.954524\pi\) | |||||||
\(264\) | −1.61803 | −0.0995831 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 17.5623 | 1.07681 | ||||||||
\(267\) | 1.70820i | 0.104540i | ||||||||
\(268\) | − 10.2361i | − 0.625267i | ||||||||
\(269\) | −1.90983 | −0.116444 | −0.0582222 | − | 0.998304i | \(-0.518543\pi\) | ||||
−0.0582222 | + | 0.998304i | \(0.518543\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 28.5066 | 1.73165 | 0.865826 | − | 0.500346i | \(-0.166794\pi\) | ||||
0.865826 | + | 0.500346i | \(0.166794\pi\) | |||||||
\(272\) | − 1.14590i | − 0.0694803i | ||||||||
\(273\) | 1.14590i | 0.0693529i | ||||||||
\(274\) | 5.09017 | 0.307508 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0.673762 | 0.0405557 | ||||||||
\(277\) | − 0.291796i | − 0.0175323i | −0.999962 | − | 0.00876616i | \(-0.997210\pi\) | ||||
0.999962 | − | 0.00876616i | \(-0.00279039\pi\) | |||||||
\(278\) | 5.32624i | 0.319447i | ||||||||
\(279\) | −0.673762 | −0.0403371 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 3.18034 | 0.189723 | 0.0948616 | − | 0.995490i | \(-0.469759\pi\) | ||||
0.0948616 | + | 0.995490i | \(0.469759\pi\) | |||||||
\(282\) | 4.56231i | 0.271681i | ||||||||
\(283\) | − 12.2918i | − 0.730671i | −0.930876 | − | 0.365336i | \(-0.880954\pi\) | ||||
0.930876 | − | 0.365336i | \(-0.119046\pi\) | |||||||
\(284\) | 3.00000 | 0.178017 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −4.23607 | −0.250484 | ||||||||
\(287\) | 4.41641i | 0.260692i | ||||||||
\(288\) | 2.85410i | 0.168180i | ||||||||
\(289\) | 15.6869 | 0.922760 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −3.65248 | −0.214112 | ||||||||
\(292\) | − 7.70820i | − 0.451089i | ||||||||
\(293\) | 8.56231i | 0.500215i | 0.968218 | + | 0.250108i | \(0.0804660\pi\) | ||||
−0.968218 | + | 0.250108i | \(0.919534\pi\) | |||||||
\(294\) | −0.763932 | −0.0445534 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 8.32624 | 0.483953 | ||||||||
\(297\) | − 9.47214i | − 0.549629i | ||||||||
\(298\) | − 2.23607i | − 0.129532i | ||||||||
\(299\) | 1.76393 | 0.102011 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 18.7082 | 1.07832 | ||||||||
\(302\) | − 9.70820i | − 0.558644i | ||||||||
\(303\) | − 0.236068i | − 0.0135618i | ||||||||
\(304\) | −5.85410 | −0.335756 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 3.27051 | 0.186963 | ||||||||
\(307\) | 23.1246i | 1.31979i | 0.751357 | + | 0.659896i | \(0.229400\pi\) | ||||
−0.751357 | + | 0.659896i | \(0.770600\pi\) | |||||||
\(308\) | − 12.7082i | − 0.724117i | ||||||||
\(309\) | −5.02129 | −0.285651 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −9.90983 | −0.561935 | −0.280967 | − | 0.959717i | \(-0.590655\pi\) | ||||
−0.280967 | + | 0.959717i | \(0.590655\pi\) | |||||||
\(312\) | − 0.381966i | − 0.0216246i | ||||||||
\(313\) | − 16.5623i | − 0.936157i | −0.883687 | − | 0.468078i | \(-0.844946\pi\) | ||||
0.883687 | − | 0.468078i | \(-0.155054\pi\) | |||||||
\(314\) | 4.56231 | 0.257466 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −7.23607 | −0.407061 | ||||||||
\(317\) | − 8.38197i | − 0.470778i | −0.971901 | − | 0.235389i | \(-0.924364\pi\) | ||||
0.971901 | − | 0.235389i | \(-0.0756364\pi\) | |||||||
\(318\) | 4.00000i | 0.224309i | ||||||||
\(319\) | 40.1246 | 2.24655 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0.416408 | 0.0232416 | ||||||||
\(322\) | 5.29180i | 0.294900i | ||||||||
\(323\) | 6.70820i | 0.373254i | ||||||||
\(324\) | −7.70820 | −0.428234 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −1.85410 | −0.102689 | ||||||||
\(327\) | − 5.72949i | − 0.316842i | ||||||||
\(328\) | − 1.47214i | − 0.0812851i | ||||||||
\(329\) | −35.8328 | −1.97553 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −15.5623 | −0.855382 | −0.427691 | − | 0.903925i | \(-0.640673\pi\) | ||||
−0.427691 | + | 0.903925i | \(0.640673\pi\) | |||||||
\(332\) | 4.52786i | 0.248499i | ||||||||
\(333\) | 23.7639i | 1.30226i | ||||||||
\(334\) | 13.3820 | 0.732229 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 1.14590 | 0.0625139 | ||||||||
\(337\) | 4.58359i | 0.249684i | 0.992177 | + | 0.124842i | \(0.0398424\pi\) | ||||
−0.992177 | + | 0.124842i | \(0.960158\pi\) | |||||||
\(338\) | 12.0000i | 0.652714i | ||||||||
\(339\) | 1.43769 | 0.0780848 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1.00000 | −0.0541530 | ||||||||
\(342\) | − 16.7082i | − 0.903476i | ||||||||
\(343\) | 15.0000i | 0.809924i | ||||||||
\(344\) | −6.23607 | −0.336226 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 1.23607 | 0.0664514 | ||||||||
\(347\) | 21.0902i | 1.13218i | 0.824344 | + | 0.566090i | \(0.191544\pi\) | ||||
−0.824344 | + | 0.566090i | \(0.808456\pi\) | |||||||
\(348\) | 3.61803i | 0.193947i | ||||||||
\(349\) | 17.7639 | 0.950881 | 0.475441 | − | 0.879748i | \(-0.342289\pi\) | ||||
0.475441 | + | 0.879748i | \(0.342289\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 2.23607 | 0.119352 | ||||||||
\(352\) | 4.23607i | 0.225783i | ||||||||
\(353\) | − 21.2361i | − 1.13028i | −0.824994 | − | 0.565141i | \(-0.808822\pi\) | ||||
0.824994 | − | 0.565141i | \(-0.191178\pi\) | |||||||
\(354\) | 1.70820 | 0.0907900 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 4.47214 | 0.237023 | ||||||||
\(357\) | − 1.31308i | − 0.0694957i | ||||||||
\(358\) | − 11.1803i | − 0.590899i | ||||||||
\(359\) | 8.09017 | 0.426983 | 0.213491 | − | 0.976945i | \(-0.431516\pi\) | ||||
0.213491 | + | 0.976945i | \(0.431516\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 15.2705 | 0.803711 | ||||||||
\(362\) | 5.41641i | 0.284680i | ||||||||
\(363\) | − 2.65248i | − 0.139219i | ||||||||
\(364\) | 3.00000 | 0.157243 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −3.38197 | −0.176778 | ||||||||
\(367\) | − 35.5410i | − 1.85523i | −0.373543 | − | 0.927613i | \(-0.621857\pi\) | ||||
0.373543 | − | 0.927613i | \(-0.378143\pi\) | |||||||
\(368\) | − 1.76393i | − 0.0919513i | ||||||||
\(369\) | 4.20163 | 0.218728 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −31.4164 | −1.63106 | ||||||||
\(372\) | − 0.0901699i | − 0.00467509i | ||||||||
\(373\) | − 11.7639i | − 0.609113i | −0.952494 | − | 0.304557i | \(-0.901492\pi\) | ||||
0.952494 | − | 0.304557i | \(-0.0985083\pi\) | |||||||
\(374\) | 4.85410 | 0.251000 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 11.9443 | 0.615979 | ||||||||
\(377\) | 9.47214i | 0.487840i | ||||||||
\(378\) | 6.70820i | 0.345033i | ||||||||
\(379\) | −9.47214 | −0.486551 | −0.243275 | − | 0.969957i | \(-0.578222\pi\) | ||||
−0.243275 | + | 0.969957i | \(0.578222\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1.34752 | 0.0690358 | ||||||||
\(382\) | − 13.6525i | − 0.698521i | ||||||||
\(383\) | 11.3262i | 0.578744i | 0.957217 | + | 0.289372i | \(0.0934464\pi\) | ||||
−0.957217 | + | 0.289372i | \(0.906554\pi\) | |||||||
\(384\) | −0.381966 | −0.0194921 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 14.6525 | 0.745791 | ||||||||
\(387\) | − 17.7984i | − 0.904742i | ||||||||
\(388\) | 9.56231i | 0.485453i | ||||||||
\(389\) | −18.2148 | −0.923526 | −0.461763 | − | 0.887003i | \(-0.652783\pi\) | ||||
−0.461763 | + | 0.887003i | \(0.652783\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2.02129 | −0.102221 | ||||||||
\(392\) | 2.00000i | 0.101015i | ||||||||
\(393\) | 6.27051i | 0.316305i | ||||||||
\(394\) | 12.0000 | 0.604551 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −12.0902 | −0.607554 | ||||||||
\(397\) | 10.2361i | 0.513734i | 0.966447 | + | 0.256867i | \(0.0826902\pi\) | ||||
−0.966447 | + | 0.256867i | \(0.917310\pi\) | |||||||
\(398\) | − 2.56231i | − 0.128437i | ||||||||
\(399\) | −6.70820 | −0.335830 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −14.1803 | −0.708132 | −0.354066 | − | 0.935220i | \(-0.615201\pi\) | ||||
−0.354066 | + | 0.935220i | \(0.615201\pi\) | |||||||
\(402\) | 3.90983i | 0.195005i | ||||||||
\(403\) | − 0.236068i | − 0.0117594i | ||||||||
\(404\) | −0.618034 | −0.0307483 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −28.4164 | −1.41028 | ||||||||
\(407\) | 35.2705i | 1.74829i | ||||||||
\(408\) | 0.437694i | 0.0216691i | ||||||||
\(409\) | 6.70820 | 0.331699 | 0.165850 | − | 0.986151i | \(-0.446963\pi\) | ||||
0.165850 | + | 0.986151i | \(0.446963\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −1.94427 | −0.0959039 | ||||||||
\(412\) | 13.1459i | 0.647652i | ||||||||
\(413\) | 13.4164i | 0.660178i | ||||||||
\(414\) | 5.03444 | 0.247429 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −1.00000 | −0.0490290 | ||||||||
\(417\) | − 2.03444i | − 0.0996270i | ||||||||
\(418\) | − 24.7984i | − 1.21293i | ||||||||
\(419\) | −22.7639 | −1.11209 | −0.556045 | − | 0.831152i | \(-0.687682\pi\) | ||||
−0.556045 | + | 0.831152i | \(0.687682\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 21.2705 | 1.03666 | 0.518331 | − | 0.855180i | \(-0.326554\pi\) | ||||
0.518331 | + | 0.855180i | \(0.326554\pi\) | |||||||
\(422\) | − 22.2705i | − 1.08411i | ||||||||
\(423\) | 34.0902i | 1.65752i | ||||||||
\(424\) | 10.4721 | 0.508572 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −1.14590 | −0.0555189 | ||||||||
\(427\) | − 26.5623i | − 1.28544i | ||||||||
\(428\) | − 1.09017i | − 0.0526954i | ||||||||
\(429\) | 1.61803 | 0.0781194 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 26.0689 | 1.25569 | 0.627847 | − | 0.778337i | \(-0.283936\pi\) | ||||
0.627847 | + | 0.778337i | \(0.283936\pi\) | |||||||
\(432\) | − 2.23607i | − 0.107583i | ||||||||
\(433\) | − 21.3607i | − 1.02653i | −0.858231 | − | 0.513264i | \(-0.828436\pi\) | ||||
0.858231 | − | 0.513264i | \(-0.171564\pi\) | |||||||
\(434\) | 0.708204 | 0.0339949 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −15.0000 | −0.718370 | ||||||||
\(437\) | 10.3262i | 0.493971i | ||||||||
\(438\) | 2.94427i | 0.140683i | ||||||||
\(439\) | −25.6525 | −1.22433 | −0.612163 | − | 0.790732i | \(-0.709700\pi\) | ||||
−0.612163 | + | 0.790732i | \(0.709700\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −5.70820 | −0.271819 | ||||||||
\(442\) | 1.14590i | 0.0545048i | ||||||||
\(443\) | 19.4164i | 0.922501i | 0.887270 | + | 0.461251i | \(0.152599\pi\) | ||||
−0.887270 | + | 0.461251i | \(0.847401\pi\) | |||||||
\(444\) | −3.18034 | −0.150932 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 9.00000 | 0.426162 | ||||||||
\(447\) | 0.854102i | 0.0403976i | ||||||||
\(448\) | − 3.00000i | − 0.141737i | ||||||||
\(449\) | 3.94427 | 0.186142 | 0.0930709 | − | 0.995659i | \(-0.470332\pi\) | ||||
0.0930709 | + | 0.995659i | \(0.470332\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 6.23607 | 0.293645 | ||||||||
\(452\) | − 3.76393i | − 0.177040i | ||||||||
\(453\) | 3.70820i | 0.174227i | ||||||||
\(454\) | 29.3607 | 1.37796 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 2.23607 | 0.104713 | ||||||||
\(457\) | − 40.2148i | − 1.88117i | −0.339561 | − | 0.940584i | \(-0.610278\pi\) | ||||
0.339561 | − | 0.940584i | \(-0.389722\pi\) | |||||||
\(458\) | 2.56231i | 0.119729i | ||||||||
\(459\) | −2.56231 | −0.119598 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 5.81966 | 0.271049 | 0.135524 | − | 0.990774i | \(-0.456728\pi\) | ||||
0.135524 | + | 0.990774i | \(0.456728\pi\) | |||||||
\(462\) | 4.85410i | 0.225833i | ||||||||
\(463\) | − 34.9787i | − 1.62560i | −0.582544 | − | 0.812799i | \(-0.697943\pi\) | ||||
0.582544 | − | 0.812799i | \(-0.302057\pi\) | |||||||
\(464\) | 9.47214 | 0.439733 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −14.2918 | −0.662055 | ||||||||
\(467\) | 19.1803i | 0.887560i | 0.896136 | + | 0.443780i | \(0.146363\pi\) | ||||
−0.896136 | + | 0.443780i | \(0.853637\pi\) | |||||||
\(468\) | − 2.85410i | − 0.131931i | ||||||||
\(469\) | −30.7082 | −1.41797 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −1.74265 | −0.0802969 | ||||||||
\(472\) | − 4.47214i | − 0.205847i | ||||||||
\(473\) | − 26.4164i | − 1.21463i | ||||||||
\(474\) | 2.76393 | 0.126952 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −3.43769 | −0.157566 | ||||||||
\(477\) | 29.8885i | 1.36850i | ||||||||
\(478\) | 6.90983i | 0.316048i | ||||||||
\(479\) | 15.2016 | 0.694580 | 0.347290 | − | 0.937758i | \(-0.387102\pi\) | ||||
0.347290 | + | 0.937758i | \(0.387102\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −8.32624 | −0.379644 | ||||||||
\(482\) | 15.6180i | 0.711382i | ||||||||
\(483\) | − 2.02129i | − 0.0919717i | ||||||||
\(484\) | −6.94427 | −0.315649 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 9.65248 | 0.437845 | ||||||||
\(487\) | − 22.1246i | − 1.00256i | −0.865285 | − | 0.501281i | \(-0.832862\pi\) | ||||
0.865285 | − | 0.501281i | \(-0.167138\pi\) | |||||||
\(488\) | 8.85410i | 0.400806i | ||||||||
\(489\) | 0.708204 | 0.0320261 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 19.2361 | 0.868112 | 0.434056 | − | 0.900886i | \(-0.357082\pi\) | ||||
0.434056 | + | 0.900886i | \(0.357082\pi\) | |||||||
\(492\) | 0.562306i | 0.0253507i | ||||||||
\(493\) | − 10.8541i | − 0.488844i | ||||||||
\(494\) | 5.85410 | 0.263388 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −0.236068 | −0.0105998 | ||||||||
\(497\) | − 9.00000i | − 0.403705i | ||||||||
\(498\) | − 1.72949i | − 0.0775003i | ||||||||
\(499\) | −34.1459 | −1.52858 | −0.764290 | − | 0.644873i | \(-0.776910\pi\) | ||||
−0.764290 | + | 0.644873i | \(0.776910\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −5.11146 | −0.228363 | ||||||||
\(502\) | 0.819660i | 0.0365832i | ||||||||
\(503\) | − 30.5066i | − 1.36022i | −0.733110 | − | 0.680111i | \(-0.761932\pi\) | ||||
0.733110 | − | 0.680111i | \(-0.238068\pi\) | |||||||
\(504\) | 8.56231 | 0.381395 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 7.47214 | 0.332177 | ||||||||
\(507\) | − 4.58359i | − 0.203564i | ||||||||
\(508\) | − 3.52786i | − 0.156524i | ||||||||
\(509\) | 1.90983 | 0.0846517 | 0.0423259 | − | 0.999104i | \(-0.486523\pi\) | ||||
0.0423259 | + | 0.999104i | \(0.486523\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −23.1246 | −1.02297 | ||||||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | 13.0902i | 0.577945i | ||||||||
\(514\) | 25.7426 | 1.13546 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 2.38197 | 0.104860 | ||||||||
\(517\) | 50.5967i | 2.22524i | ||||||||
\(518\) | − 24.9787i | − 1.09750i | ||||||||
\(519\) | −0.472136 | −0.0207245 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −23.4508 | −1.02740 | −0.513700 | − | 0.857970i | \(-0.671726\pi\) | ||||
−0.513700 | + | 0.857970i | \(0.671726\pi\) | |||||||
\(522\) | 27.0344i | 1.18327i | ||||||||
\(523\) | − 4.65248i | − 0.203439i | −0.994813 | − | 0.101719i | \(-0.967566\pi\) | ||||
0.994813 | − | 0.101719i | \(-0.0324343\pi\) | |||||||
\(524\) | 16.4164 | 0.717154 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −4.61803 | −0.201356 | ||||||||
\(527\) | 0.270510i | 0.0117836i | ||||||||
\(528\) | − 1.61803i | − 0.0704159i | ||||||||
\(529\) | 19.8885 | 0.864719 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 12.7639 | 0.553907 | ||||||||
\(532\) | 17.5623i | 0.761423i | ||||||||
\(533\) | 1.47214i | 0.0637653i | ||||||||
\(534\) | −1.70820 | −0.0739212 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 10.2361 | 0.442131 | ||||||||
\(537\) | 4.27051i | 0.184286i | ||||||||
\(538\) | − 1.90983i | − 0.0823386i | ||||||||
\(539\) | −8.47214 | −0.364921 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 15.2918 | 0.657446 | 0.328723 | − | 0.944426i | \(-0.393382\pi\) | ||||
0.328723 | + | 0.944426i | \(0.393382\pi\) | |||||||
\(542\) | 28.5066i | 1.22446i | ||||||||
\(543\) | − 2.06888i | − 0.0887843i | ||||||||
\(544\) | 1.14590 | 0.0491300 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −1.14590 | −0.0490399 | ||||||||
\(547\) | − 8.38197i | − 0.358387i | −0.983814 | − | 0.179193i | \(-0.942651\pi\) | ||||
0.983814 | − | 0.179193i | \(-0.0573488\pi\) | |||||||
\(548\) | 5.09017i | 0.217441i | ||||||||
\(549\) | −25.2705 | −1.07852 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −55.4508 | −2.36229 | ||||||||
\(552\) | 0.673762i | 0.0286772i | ||||||||
\(553\) | 21.7082i | 0.923127i | ||||||||
\(554\) | 0.291796 | 0.0123972 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −5.32624 | −0.225883 | ||||||||
\(557\) | − 24.8885i | − 1.05456i | −0.849691 | − | 0.527281i | \(-0.823212\pi\) | ||||
0.849691 | − | 0.527281i | \(-0.176788\pi\) | |||||||
\(558\) | − 0.673762i | − 0.0285226i | ||||||||
\(559\) | 6.23607 | 0.263758 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1.85410 | −0.0782802 | ||||||||
\(562\) | 3.18034i | 0.134155i | ||||||||
\(563\) | − 28.1459i | − 1.18621i | −0.805126 | − | 0.593104i | \(-0.797902\pi\) | ||||
0.805126 | − | 0.593104i | \(-0.202098\pi\) | |||||||
\(564\) | −4.56231 | −0.192108 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 12.2918 | 0.516663 | ||||||||
\(567\) | 23.1246i | 0.971142i | ||||||||
\(568\) | 3.00000i | 0.125877i | ||||||||
\(569\) | −17.7639 | −0.744703 | −0.372351 | − | 0.928092i | \(-0.621448\pi\) | ||||
−0.372351 | + | 0.928092i | \(0.621448\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 17.3262 | 0.725080 | 0.362540 | − | 0.931968i | \(-0.381910\pi\) | ||||
0.362540 | + | 0.931968i | \(0.381910\pi\) | |||||||
\(572\) | − 4.23607i | − 0.177119i | ||||||||
\(573\) | 5.21478i | 0.217851i | ||||||||
\(574\) | −4.41641 | −0.184337 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −2.85410 | −0.118921 | ||||||||
\(577\) | 43.0000i | 1.79011i | 0.445952 | + | 0.895057i | \(0.352865\pi\) | ||||
−0.445952 | + | 0.895057i | \(0.647135\pi\) | |||||||
\(578\) | 15.6869i | 0.652490i | ||||||||
\(579\) | −5.59675 | −0.232593 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 13.5836 | 0.563542 | ||||||||
\(582\) | − 3.65248i | − 0.151400i | ||||||||
\(583\) | 44.3607i | 1.83723i | ||||||||
\(584\) | 7.70820 | 0.318968 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −8.56231 | −0.353706 | ||||||||
\(587\) | 34.1803i | 1.41077i | 0.708823 | + | 0.705387i | \(0.249227\pi\) | ||||
−0.708823 | + | 0.705387i | \(0.750773\pi\) | |||||||
\(588\) | − 0.763932i | − 0.0315040i | ||||||||
\(589\) | 1.38197 | 0.0569429 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −4.58359 | −0.188544 | ||||||||
\(592\) | 8.32624i | 0.342206i | ||||||||
\(593\) | 29.0132i | 1.19143i | 0.803197 | + | 0.595714i | \(0.203131\pi\) | ||||
−0.803197 | + | 0.595714i | \(0.796869\pi\) | |||||||
\(594\) | 9.47214 | 0.388646 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 2.23607 | 0.0915929 | ||||||||
\(597\) | 0.978714i | 0.0400561i | ||||||||
\(598\) | 1.76393i | 0.0721325i | ||||||||
\(599\) | −8.94427 | −0.365453 | −0.182727 | − | 0.983164i | \(-0.558492\pi\) | ||||
−0.182727 | + | 0.983164i | \(0.558492\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 38.8328 | 1.58402 | 0.792012 | − | 0.610506i | \(-0.209034\pi\) | ||||
0.792012 | + | 0.610506i | \(0.209034\pi\) | |||||||
\(602\) | 18.7082i | 0.762489i | ||||||||
\(603\) | 29.2148i | 1.18972i | ||||||||
\(604\) | 9.70820 | 0.395021 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0.236068 | 0.00958961 | ||||||||
\(607\) | 33.8541i | 1.37410i | 0.726612 | + | 0.687048i | \(0.241094\pi\) | ||||
−0.726612 | + | 0.687048i | \(0.758906\pi\) | |||||||
\(608\) | − 5.85410i | − 0.237415i | ||||||||
\(609\) | 10.8541 | 0.439830 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −11.9443 | −0.483214 | ||||||||
\(612\) | 3.27051i | 0.132203i | ||||||||
\(613\) | − 21.4377i | − 0.865860i | −0.901427 | − | 0.432930i | \(-0.857480\pi\) | ||||
0.901427 | − | 0.432930i | \(-0.142520\pi\) | |||||||
\(614\) | −23.1246 | −0.933233 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 12.7082 | 0.512028 | ||||||||
\(617\) | − 14.3607i | − 0.578139i | −0.957308 | − | 0.289070i | \(-0.906654\pi\) | ||||
0.957308 | − | 0.289070i | \(-0.0933459\pi\) | |||||||
\(618\) | − 5.02129i | − 0.201986i | ||||||||
\(619\) | −46.9574 | −1.88738 | −0.943689 | − | 0.330833i | \(-0.892670\pi\) | ||||
−0.943689 | + | 0.330833i | \(0.892670\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −3.94427 | −0.158278 | ||||||||
\(622\) | − 9.90983i | − 0.397348i | ||||||||
\(623\) | − 13.4164i | − 0.537517i | ||||||||
\(624\) | 0.381966 | 0.0152909 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 16.5623 | 0.661963 | ||||||||
\(627\) | 9.47214i | 0.378281i | ||||||||
\(628\) | 4.56231i | 0.182056i | ||||||||
\(629\) | 9.54102 | 0.380425 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −44.8328 | −1.78477 | −0.892383 | − | 0.451279i | \(-0.850968\pi\) | ||||
−0.892383 | + | 0.451279i | \(0.850968\pi\) | |||||||
\(632\) | − 7.23607i | − 0.287835i | ||||||||
\(633\) | 8.50658i | 0.338106i | ||||||||
\(634\) | 8.38197 | 0.332890 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −4.00000 | −0.158610 | ||||||||
\(637\) | − 2.00000i | − 0.0792429i | ||||||||
\(638\) | 40.1246i | 1.58855i | ||||||||
\(639\) | −8.56231 | −0.338720 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −30.3607 | −1.19917 | −0.599587 | − | 0.800309i | \(-0.704669\pi\) | ||||
−0.599587 | + | 0.800309i | \(0.704669\pi\) | |||||||
\(642\) | 0.416408i | 0.0164343i | ||||||||
\(643\) | − 31.7639i | − 1.25265i | −0.779563 | − | 0.626324i | \(-0.784559\pi\) | ||||
0.779563 | − | 0.626324i | \(-0.215441\pi\) | |||||||
\(644\) | −5.29180 | −0.208526 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −6.70820 | −0.263931 | ||||||||
\(647\) | 23.6525i | 0.929875i | 0.885344 | + | 0.464937i | \(0.153923\pi\) | ||||
−0.885344 | + | 0.464937i | \(0.846077\pi\) | |||||||
\(648\) | − 7.70820i | − 0.302807i | ||||||||
\(649\) | 18.9443 | 0.743628 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −0.270510 | −0.0106021 | ||||||||
\(652\) | − 1.85410i | − 0.0726122i | ||||||||
\(653\) | − 8.59675i | − 0.336417i | −0.985751 | − | 0.168208i | \(-0.946202\pi\) | ||||
0.985751 | − | 0.168208i | \(-0.0537981\pi\) | |||||||
\(654\) | 5.72949 | 0.224041 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 1.47214 | 0.0574773 | ||||||||
\(657\) | 22.0000i | 0.858302i | ||||||||
\(658\) | − 35.8328i | − 1.39691i | ||||||||
\(659\) | 25.6525 | 0.999279 | 0.499639 | − | 0.866234i | \(-0.333466\pi\) | ||||
0.499639 | + | 0.866234i | \(0.333466\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −27.2705 | −1.06070 | −0.530350 | − | 0.847779i | \(-0.677939\pi\) | ||||
−0.530350 | + | 0.847779i | \(0.677939\pi\) | |||||||
\(662\) | − 15.5623i | − 0.604846i | ||||||||
\(663\) | − 0.437694i | − 0.0169986i | ||||||||
\(664\) | −4.52786 | −0.175715 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −23.7639 | −0.920834 | ||||||||
\(667\) | − 16.7082i | − 0.646944i | ||||||||
\(668\) | 13.3820i | 0.517764i | ||||||||
\(669\) | −3.43769 | −0.132909 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −37.5066 | −1.44793 | ||||||||
\(672\) | 1.14590i | 0.0442040i | ||||||||
\(673\) | 3.23607i | 0.124741i | 0.998053 | + | 0.0623706i | \(0.0198661\pi\) | ||||
−0.998053 | + | 0.0623706i | \(0.980134\pi\) | |||||||
\(674\) | −4.58359 | −0.176553 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −12.0000 | −0.461538 | ||||||||
\(677\) | − 8.38197i | − 0.322145i | −0.986943 | − | 0.161073i | \(-0.948505\pi\) | ||||
0.986943 | − | 0.161073i | \(-0.0514953\pi\) | |||||||
\(678\) | 1.43769i | 0.0552143i | ||||||||
\(679\) | 28.6869 | 1.10090 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −11.2148 | −0.429751 | ||||||||
\(682\) | − 1.00000i | − 0.0382920i | ||||||||
\(683\) | − 11.3607i | − 0.434704i | −0.976093 | − | 0.217352i | \(-0.930258\pi\) | ||||
0.976093 | − | 0.217352i | \(-0.0697420\pi\) | |||||||
\(684\) | 16.7082 | 0.638854 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −15.0000 | −0.572703 | ||||||||
\(687\) | − 0.978714i | − 0.0373403i | ||||||||
\(688\) | − 6.23607i | − 0.237748i | ||||||||
\(689\) | −10.4721 | −0.398957 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −32.2705 | −1.22763 | −0.613814 | − | 0.789451i | \(-0.710366\pi\) | ||||
−0.613814 | + | 0.789451i | \(0.710366\pi\) | |||||||
\(692\) | 1.23607i | 0.0469883i | ||||||||
\(693\) | 36.2705i | 1.37780i | ||||||||
\(694\) | −21.0902 | −0.800572 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −3.61803 | −0.137141 | ||||||||
\(697\) | − 1.68692i | − 0.0638966i | ||||||||
\(698\) | 17.7639i | 0.672375i | ||||||||
\(699\) | 5.45898 | 0.206478 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 18.1803 | 0.686662 | 0.343331 | − | 0.939214i | \(-0.388445\pi\) | ||||
0.343331 | + | 0.939214i | \(0.388445\pi\) | |||||||
\(702\) | 2.23607i | 0.0843949i | ||||||||
\(703\) | − 48.7426i | − 1.83836i | ||||||||
\(704\) | −4.23607 | −0.159653 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 21.2361 | 0.799230 | ||||||||
\(707\) | 1.85410i | 0.0697307i | ||||||||
\(708\) | 1.70820i | 0.0641982i | ||||||||
\(709\) | −12.2361 | −0.459535 | −0.229768 | − | 0.973246i | \(-0.573797\pi\) | ||||
−0.229768 | + | 0.973246i | \(0.573797\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 20.6525 | 0.774528 | ||||||||
\(712\) | 4.47214i | 0.167600i | ||||||||
\(713\) | 0.416408i | 0.0155946i | ||||||||
\(714\) | 1.31308 | 0.0491409 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 11.1803 | 0.417829 | ||||||||
\(717\) | − 2.63932i | − 0.0985672i | ||||||||
\(718\) | 8.09017i | 0.301922i | ||||||||
\(719\) | −11.5066 | −0.429123 | −0.214561 | − | 0.976710i | \(-0.568832\pi\) | ||||
−0.214561 | + | 0.976710i | \(0.568832\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 39.4377 | 1.46874 | ||||||||
\(722\) | 15.2705i | 0.568310i | ||||||||
\(723\) | − 5.96556i | − 0.221861i | ||||||||
\(724\) | −5.41641 | −0.201299 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 2.65248 | 0.0984426 | ||||||||
\(727\) | − 2.65248i | − 0.0983749i | −0.998790 | − | 0.0491874i | \(-0.984337\pi\) | ||||
0.998790 | − | 0.0491874i | \(-0.0156632\pi\) | |||||||
\(728\) | 3.00000i | 0.111187i | ||||||||
\(729\) | 19.4377 | 0.719915 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −7.14590 | −0.264301 | ||||||||
\(732\) | − 3.38197i | − 0.125001i | ||||||||
\(733\) | 31.7771i | 1.17371i | 0.809691 | + | 0.586857i | \(0.199635\pi\) | ||||
−0.809691 | + | 0.586857i | \(0.800365\pi\) | |||||||
\(734\) | 35.5410 | 1.31184 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1.76393 | 0.0650194 | ||||||||
\(737\) | 43.3607i | 1.59721i | ||||||||
\(738\) | 4.20163i | 0.154664i | ||||||||
\(739\) | −30.0000 | −1.10357 | −0.551784 | − | 0.833987i | \(-0.686053\pi\) | ||||
−0.551784 | + | 0.833987i | \(0.686053\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −2.23607 | −0.0821440 | ||||||||
\(742\) | − 31.4164i | − 1.15333i | ||||||||
\(743\) | 15.2705i | 0.560221i | 0.959968 | + | 0.280110i | \(0.0903711\pi\) | ||||
−0.959968 | + | 0.280110i | \(0.909629\pi\) | |||||||
\(744\) | 0.0901699 | 0.00330579 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 11.7639 | 0.430708 | ||||||||
\(747\) | − 12.9230i | − 0.472827i | ||||||||
\(748\) | 4.85410i | 0.177484i | ||||||||
\(749\) | −3.27051 | −0.119502 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 7.85410 | 0.286600 | 0.143300 | − | 0.989679i | \(-0.454229\pi\) | ||||
0.143300 | + | 0.989679i | \(0.454229\pi\) | |||||||
\(752\) | 11.9443i | 0.435563i | ||||||||
\(753\) | − 0.313082i | − 0.0114094i | ||||||||
\(754\) | −9.47214 | −0.344955 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −6.70820 | −0.243975 | ||||||||
\(757\) | 16.4164i | 0.596664i | 0.954462 | + | 0.298332i | \(0.0964303\pi\) | ||||
−0.954462 | + | 0.298332i | \(0.903570\pi\) | |||||||
\(758\) | − 9.47214i | − 0.344043i | ||||||||
\(759\) | −2.85410 | −0.103597 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 26.9230 | 0.975957 | 0.487979 | − | 0.872856i | \(-0.337734\pi\) | ||||
0.487979 | + | 0.872856i | \(0.337734\pi\) | |||||||
\(762\) | 1.34752i | 0.0488156i | ||||||||
\(763\) | 45.0000i | 1.62911i | ||||||||
\(764\) | 13.6525 | 0.493929 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −11.3262 | −0.409234 | ||||||||
\(767\) | 4.47214i | 0.161479i | ||||||||
\(768\) | − 0.381966i | − 0.0137830i | ||||||||
\(769\) | −3.41641 | −0.123199 | −0.0615994 | − | 0.998101i | \(-0.519620\pi\) | ||||
−0.0615994 | + | 0.998101i | \(0.519620\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −9.83282 | −0.354120 | ||||||||
\(772\) | 14.6525i | 0.527354i | ||||||||
\(773\) | 30.7984i | 1.10774i | 0.832603 | + | 0.553870i | \(0.186850\pi\) | ||||
−0.832603 | + | 0.553870i | \(0.813150\pi\) | |||||||
\(774\) | 17.7984 | 0.639749 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −9.56231 | −0.343267 | ||||||||
\(777\) | 9.54102i | 0.342282i | ||||||||
\(778\) | − 18.2148i | − 0.653032i | ||||||||
\(779\) | −8.61803 | −0.308773 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −12.7082 | −0.454735 | ||||||||
\(782\) | − 2.02129i | − 0.0722810i | ||||||||
\(783\) | − 21.1803i | − 0.756924i | ||||||||
\(784\) | −2.00000 | −0.0714286 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −6.27051 | −0.223662 | ||||||||
\(787\) | 11.4164i | 0.406951i | 0.979080 | + | 0.203475i | \(0.0652237\pi\) | ||||
−0.979080 | + | 0.203475i | \(0.934776\pi\) | |||||||
\(788\) | 12.0000i | 0.427482i | ||||||||
\(789\) | 1.76393 | 0.0627976 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −11.2918 | −0.401490 | ||||||||
\(792\) | − 12.0902i | − 0.429605i | ||||||||
\(793\) | − 8.85410i | − 0.314418i | ||||||||
\(794\) | −10.2361 | −0.363264 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 2.56231 | 0.0908185 | ||||||||
\(797\) | − 5.61803i | − 0.199001i | −0.995038 | − | 0.0995005i | \(-0.968276\pi\) | ||||
0.995038 | − | 0.0995005i | \(-0.0317245\pi\) | |||||||
\(798\) | − 6.70820i | − 0.237468i | ||||||||
\(799\) | 13.6869 | 0.484208 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −12.7639 | −0.450991 | ||||||||
\(802\) | − 14.1803i | − 0.500725i | ||||||||
\(803\) | 32.6525i | 1.15228i | ||||||||
\(804\) | −3.90983 | −0.137889 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0.236068 | 0.00831514 | ||||||||
\(807\) | 0.729490i | 0.0256793i | ||||||||
\(808\) | − 0.618034i | − 0.0217424i | ||||||||
\(809\) | 2.23607 | 0.0786160 | 0.0393080 | − | 0.999227i | \(-0.487485\pi\) | ||||
0.0393080 | + | 0.999227i | \(0.487485\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 40.9443 | 1.43775 | 0.718874 | − | 0.695140i | \(-0.244658\pi\) | ||||
0.718874 | + | 0.695140i | \(0.244658\pi\) | |||||||
\(812\) | − 28.4164i | − 0.997220i | ||||||||
\(813\) | − 10.8885i | − 0.381878i | ||||||||
\(814\) | −35.2705 | −1.23623 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −0.437694 | −0.0153224 | ||||||||
\(817\) | 36.5066i | 1.27720i | ||||||||
\(818\) | 6.70820i | 0.234547i | ||||||||
\(819\) | −8.56231 | −0.299191 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 39.1591 | 1.36666 | 0.683330 | − | 0.730109i | \(-0.260531\pi\) | ||||
0.683330 | + | 0.730109i | \(0.260531\pi\) | |||||||
\(822\) | − 1.94427i | − 0.0678143i | ||||||||
\(823\) | − 20.8328i | − 0.726186i | −0.931753 | − | 0.363093i | \(-0.881721\pi\) | ||||
0.931753 | − | 0.363093i | \(-0.118279\pi\) | |||||||
\(824\) | −13.1459 | −0.457959 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −13.4164 | −0.466817 | ||||||||
\(827\) | 5.03444i | 0.175065i | 0.996162 | + | 0.0875323i | \(0.0278981\pi\) | ||||
−0.996162 | + | 0.0875323i | \(0.972102\pi\) | |||||||
\(828\) | 5.03444i | 0.174959i | ||||||||
\(829\) | −53.4164 | −1.85523 | −0.927614 | − | 0.373540i | \(-0.878144\pi\) | ||||
−0.927614 | + | 0.373540i | \(0.878144\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −0.111456 | −0.00386637 | ||||||||
\(832\) | − 1.00000i | − 0.0346688i | ||||||||
\(833\) | 2.29180i | 0.0794060i | ||||||||
\(834\) | 2.03444 | 0.0704470 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 24.7984 | 0.857670 | ||||||||
\(837\) | 0.527864i | 0.0182457i | ||||||||
\(838\) | − 22.7639i | − 0.786367i | ||||||||
\(839\) | 55.2492 | 1.90742 | 0.953708 | − | 0.300736i | \(-0.0972322\pi\) | ||||
0.953708 | + | 0.300736i | \(0.0972322\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 60.7214 | 2.09384 | ||||||||
\(842\) | 21.2705i | 0.733030i | ||||||||
\(843\) | − 1.21478i | − 0.0418393i | ||||||||
\(844\) | 22.2705 | 0.766583 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −34.0902 | −1.17204 | ||||||||
\(847\) | 20.8328i | 0.715824i | ||||||||
\(848\) | 10.4721i | 0.359615i | ||||||||
\(849\) | −4.69505 | −0.161134 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 14.6869 | 0.503461 | ||||||||
\(852\) | − 1.14590i | − 0.0392578i | ||||||||
\(853\) | − 18.1459i | − 0.621304i | −0.950524 | − | 0.310652i | \(-0.899453\pi\) | ||||
0.950524 | − | 0.310652i | \(-0.100547\pi\) | |||||||
\(854\) | 26.5623 | 0.908943 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 1.09017 | 0.0372612 | ||||||||
\(857\) | 56.3394i | 1.92452i | 0.272137 | + | 0.962259i | \(0.412270\pi\) | ||||
−0.272137 | + | 0.962259i | \(0.587730\pi\) | |||||||
\(858\) | 1.61803i | 0.0552388i | ||||||||
\(859\) | −34.3951 | −1.17355 | −0.586773 | − | 0.809751i | \(-0.699602\pi\) | ||||
−0.586773 | + | 0.809751i | \(0.699602\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 1.68692 | 0.0574900 | ||||||||
\(862\) | 26.0689i | 0.887910i | ||||||||
\(863\) | − 11.2361i | − 0.382480i | −0.981543 | − | 0.191240i | \(-0.938749\pi\) | ||||
0.981543 | − | 0.191240i | \(-0.0612509\pi\) | |||||||
\(864\) | 2.23607 | 0.0760726 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 21.3607 | 0.725865 | ||||||||
\(867\) | − 5.99187i | − 0.203495i | ||||||||
\(868\) | 0.708204i | 0.0240380i | ||||||||
\(869\) | 30.6525 | 1.03981 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −10.2361 | −0.346836 | ||||||||
\(872\) | − 15.0000i | − 0.507964i | ||||||||
\(873\) | − 27.2918i | − 0.923687i | ||||||||
\(874\) | −10.3262 | −0.349290 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −2.94427 | −0.0994777 | ||||||||
\(877\) | − 4.43769i | − 0.149850i | −0.997189 | − | 0.0749251i | \(-0.976128\pi\) | ||||
0.997189 | − | 0.0749251i | \(-0.0238718\pi\) | |||||||
\(878\) | − 25.6525i | − 0.865729i | ||||||||
\(879\) | 3.27051 | 0.110312 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 38.1803 | 1.28633 | 0.643164 | − | 0.765728i | \(-0.277621\pi\) | ||||
0.643164 | + | 0.765728i | \(0.277621\pi\) | |||||||
\(882\) | − 5.70820i | − 0.192205i | ||||||||
\(883\) | − 41.6869i | − 1.40288i | −0.712730 | − | 0.701438i | \(-0.752542\pi\) | ||||
0.712730 | − | 0.701438i | \(-0.247458\pi\) | |||||||
\(884\) | −1.14590 | −0.0385407 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −19.4164 | −0.652307 | ||||||||
\(887\) | − 33.1803i | − 1.11409i | −0.830483 | − | 0.557043i | \(-0.811936\pi\) | ||||
0.830483 | − | 0.557043i | \(-0.188064\pi\) | |||||||
\(888\) | − 3.18034i | − 0.106725i | ||||||||
\(889\) | −10.5836 | −0.354962 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 32.6525 | 1.09390 | ||||||||
\(892\) | 9.00000i | 0.301342i | ||||||||
\(893\) | − 69.9230i | − 2.33988i | ||||||||
\(894\) | −0.854102 | −0.0285654 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 3.00000 | 0.100223 | ||||||||
\(897\) | − 0.673762i | − 0.0224963i | ||||||||
\(898\) | 3.94427i | 0.131622i | ||||||||
\(899\) | −2.23607 | −0.0745770 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 12.0000 | 0.399778 | ||||||||
\(902\) | 6.23607i | 0.207638i | ||||||||
\(903\) | − 7.14590i | − 0.237801i | ||||||||
\(904\) | 3.76393 | 0.125187 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −3.70820 | −0.123197 | ||||||||
\(907\) | − 25.6180i | − 0.850633i | −0.905045 | − | 0.425316i | \(-0.860163\pi\) | ||||
0.905045 | − | 0.425316i | \(-0.139837\pi\) | |||||||
\(908\) | 29.3607i | 0.974368i | ||||||||
\(909\) | 1.76393 | 0.0585059 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −16.4164 | −0.543900 | −0.271950 | − | 0.962311i | \(-0.587669\pi\) | ||||
−0.271950 | + | 0.962311i | \(0.587669\pi\) | |||||||
\(912\) | 2.23607i | 0.0740436i | ||||||||
\(913\) | − 19.1803i | − 0.634777i | ||||||||
\(914\) | 40.2148 | 1.33019 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −2.56231 | −0.0846610 | ||||||||
\(917\) | − 49.2492i | − 1.62635i | ||||||||
\(918\) | − 2.56231i | − 0.0845687i | ||||||||
\(919\) | 5.65248 | 0.186458 | 0.0932290 | − | 0.995645i | \(-0.470281\pi\) | ||||
0.0932290 | + | 0.995645i | \(0.470281\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 8.83282 | 0.291051 | ||||||||
\(922\) | 5.81966i | 0.191660i | ||||||||
\(923\) | − 3.00000i | − 0.0987462i | ||||||||
\(924\) | −4.85410 | −0.159688 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 34.9787 | 1.14947 | ||||||||
\(927\) | − 37.5197i | − 1.23231i | ||||||||
\(928\) | 9.47214i | 0.310938i | ||||||||
\(929\) | 52.8885 | 1.73522 | 0.867608 | − | 0.497248i | \(-0.165656\pi\) | ||||
0.867608 | + | 0.497248i | \(0.165656\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 11.7082 | 0.383721 | ||||||||
\(932\) | − 14.2918i | − 0.468143i | ||||||||
\(933\) | 3.78522i | 0.123922i | ||||||||
\(934\) | −19.1803 | −0.627600 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 2.85410 | 0.0932892 | ||||||||
\(937\) | − 41.9230i | − 1.36956i | −0.728748 | − | 0.684782i | \(-0.759897\pi\) | ||||
0.728748 | − | 0.684782i | \(-0.240103\pi\) | |||||||
\(938\) | − 30.7082i | − 1.00266i | ||||||||
\(939\) | −6.32624 | −0.206449 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −9.38197 | −0.305843 | −0.152922 | − | 0.988238i | \(-0.548868\pi\) | ||||
−0.152922 | + | 0.988238i | \(0.548868\pi\) | |||||||
\(942\) | − 1.74265i | − 0.0567785i | ||||||||
\(943\) | − 2.59675i | − 0.0845617i | ||||||||
\(944\) | 4.47214 | 0.145556 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 26.4164 | 0.858872 | ||||||||
\(947\) | 39.3820i | 1.27974i | 0.768482 | + | 0.639871i | \(0.221012\pi\) | ||||
−0.768482 | + | 0.639871i | \(0.778988\pi\) | |||||||
\(948\) | 2.76393i | 0.0897683i | ||||||||
\(949\) | −7.70820 | −0.250219 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −3.20163 | −0.103820 | ||||||||
\(952\) | − 3.43769i | − 0.111416i | ||||||||
\(953\) | 44.6180i | 1.44532i | 0.691204 | + | 0.722660i | \(0.257081\pi\) | ||||
−0.691204 | + | 0.722660i | \(0.742919\pi\) | |||||||
\(954\) | −29.8885 | −0.967677 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −6.90983 | −0.223480 | ||||||||
\(957\) | − 15.3262i | − 0.495427i | ||||||||
\(958\) | 15.2016i | 0.491142i | ||||||||
\(959\) | 15.2705 | 0.493110 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.9443 | −0.998202 | ||||||||
\(962\) | − 8.32624i | − 0.268449i | ||||||||
\(963\) | 3.11146i | 0.100265i | ||||||||
\(964\) | −15.6180 | −0.503023 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 2.02129 | 0.0650338 | ||||||||
\(967\) | 13.1246i | 0.422059i | 0.977480 | + | 0.211030i | \(0.0676816\pi\) | ||||
−0.977480 | + | 0.211030i | \(0.932318\pi\) | |||||||
\(968\) | − 6.94427i | − 0.223197i | ||||||||
\(969\) | 2.56231 | 0.0823131 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 6.06888 | 0.194760 | 0.0973799 | − | 0.995247i | \(-0.468954\pi\) | ||||
0.0973799 | + | 0.995247i | \(0.468954\pi\) | |||||||
\(972\) | 9.65248i | 0.309603i | ||||||||
\(973\) | 15.9787i | 0.512254i | ||||||||
\(974\) | 22.1246 | 0.708918 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −8.85410 | −0.283413 | ||||||||
\(977\) | − 50.0132i | − 1.60006i | −0.599958 | − | 0.800031i | \(-0.704816\pi\) | ||||
0.599958 | − | 0.800031i | \(-0.295184\pi\) | |||||||
\(978\) | 0.708204i | 0.0226459i | ||||||||
\(979\) | −18.9443 | −0.605462 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 42.8115 | 1.36687 | ||||||||
\(982\) | 19.2361i | 0.613848i | ||||||||
\(983\) | 38.4853i | 1.22749i | 0.789504 | + | 0.613745i | \(0.210338\pi\) | ||||
−0.789504 | + | 0.613745i | \(0.789662\pi\) | |||||||
\(984\) | −0.562306 | −0.0179257 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 10.8541 | 0.345665 | ||||||||
\(987\) | 13.6869i | 0.435659i | ||||||||
\(988\) | 5.85410i | 0.186244i | ||||||||
\(989\) | −11.0000 | −0.349780 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −3.45085 | −0.109620 | −0.0548099 | − | 0.998497i | \(-0.517455\pi\) | ||||
−0.0548099 | + | 0.998497i | \(0.517455\pi\) | |||||||
\(992\) | − 0.236068i | − 0.00749517i | ||||||||
\(993\) | 5.94427i | 0.188636i | ||||||||
\(994\) | 9.00000 | 0.285463 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 1.72949 | 0.0548010 | ||||||||
\(997\) | − 27.2492i | − 0.862992i | −0.902115 | − | 0.431496i | \(-0.857986\pi\) | ||||
0.902115 | − | 0.431496i | \(-0.142014\pi\) | |||||||
\(998\) | − 34.1459i | − 1.08087i | ||||||||
\(999\) | 18.6180 | 0.589049 |
(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 | 1250.2.b.b.1249.4 | 4 | ||
5.2 | odd | 4 | 1250.2.a.a.1.2 | 2 | |||
5.3 | odd | 4 | 1250.2.a.d.1.1 | 2 | |||
5.4 | even | 2 | inner | 1250.2.b.b.1249.1 | 4 | ||
20.3 | even | 4 | 10000.2.a.a.1.2 | 2 | |||
20.7 | even | 4 | 10000.2.a.n.1.1 | 2 | |||
25.2 | odd | 20 | 50.2.d.a.21.1 | ✓ | 4 | ||
25.9 | even | 10 | 250.2.e.b.99.2 | 8 | |||
25.11 | even | 5 | 250.2.e.b.149.2 | 8 | |||
25.12 | odd | 20 | 50.2.d.a.31.1 | yes | 4 | ||
25.13 | odd | 20 | 250.2.d.a.151.1 | 4 | |||
25.14 | even | 10 | 250.2.e.b.149.1 | 8 | |||
25.16 | even | 5 | 250.2.e.b.99.1 | 8 | |||
25.23 | odd | 20 | 250.2.d.a.101.1 | 4 | |||
75.2 | even | 20 | 450.2.h.a.271.1 | 4 | |||
75.62 | even | 20 | 450.2.h.a.181.1 | 4 | |||
100.27 | even | 20 | 400.2.u.c.321.1 | 4 | |||
100.87 | even | 20 | 400.2.u.c.81.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
50.2.d.a.21.1 | ✓ | 4 | 25.2 | odd | 20 | ||
50.2.d.a.31.1 | yes | 4 | 25.12 | odd | 20 | ||
250.2.d.a.101.1 | 4 | 25.23 | odd | 20 | |||
250.2.d.a.151.1 | 4 | 25.13 | odd | 20 | |||
250.2.e.b.99.1 | 8 | 25.16 | even | 5 | |||
250.2.e.b.99.2 | 8 | 25.9 | even | 10 | |||
250.2.e.b.149.1 | 8 | 25.14 | even | 10 | |||
250.2.e.b.149.2 | 8 | 25.11 | even | 5 | |||
400.2.u.c.81.1 | 4 | 100.87 | even | 20 | |||
400.2.u.c.321.1 | 4 | 100.27 | even | 20 | |||
450.2.h.a.181.1 | 4 | 75.62 | even | 20 | |||
450.2.h.a.271.1 | 4 | 75.2 | even | 20 | |||
1250.2.a.a.1.2 | 2 | 5.2 | odd | 4 | |||
1250.2.a.d.1.1 | 2 | 5.3 | odd | 4 | |||
1250.2.b.b.1249.1 | 4 | 5.4 | even | 2 | inner | ||
1250.2.b.b.1249.4 | 4 | 1.1 | even | 1 | trivial | ||
10000.2.a.a.1.2 | 2 | 20.3 | even | 4 | |||
10000.2.a.n.1.1 | 2 | 20.7 | even | 4 |