Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [400,2,Mod(47,400)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(400, base_ring=CyclotomicField(20))
chi = DirichletCharacter(H, H._module([10, 0, 17]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("400.47");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 400 = 2^{4} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 400.bi (of order \(20\), degree \(8\), 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: | \(3.19401608085\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{20})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 8 x^{15} + 32 x^{14} - 64 x^{13} + 66 x^{12} - 28 x^{11} + 160 x^{10} - 392 x^{9} + 419 x^{8} + \cdots + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{9}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{20}]$ |
Embedding invariants
Embedding label | 127.1 | ||
Root | \(1.31377 - 1.31377i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 400.127 |
Dual form | 400.2.bi.c.63.1 |
$q$-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 \(\left(\mathbb{Z}/400\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(177\) | \(351\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{20}\right)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −2.58417 | + | 1.31670i | −1.49197 | + | 0.760198i | −0.994244 | − | 0.107136i | \(-0.965832\pi\) |
−0.497727 | + | 0.867334i | \(0.665832\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −2.23607 | −1.00000 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.62753 | + | 1.62753i | −0.615149 | + | 0.615149i | −0.944283 | − | 0.329134i | \(-0.893243\pi\) |
0.329134 | + | 0.944283i | \(0.393243\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 3.18088 | − | 4.37811i | 1.06029 | − | 1.45937i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.12460 | + | 1.54787i | 0.339079 | + | 0.466702i | 0.944172 | − | 0.329453i | \(-0.106864\pi\) |
−0.605093 | + | 0.796154i | \(0.706864\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.951057 | + | 0.150633i | −0.263776 | + | 0.0417780i | −0.286921 | − | 0.957954i | \(-0.592632\pi\) |
0.0231457 | + | 0.999732i | \(0.492632\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 5.77838 | − | 2.94423i | 1.49197 | − | 0.760198i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.48990 | − | 4.88670i | 0.603889 | − | 1.18520i | −0.363426 | − | 0.931623i | \(-0.618393\pi\) |
0.967315 | − | 0.253576i | \(-0.0816068\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.87751 | − | 5.77838i | −0.430730 | − | 1.32565i | −0.897399 | − | 0.441219i | \(-0.854546\pi\) |
0.466669 | − | 0.884432i | \(-0.345454\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.06285 | − | 6.34879i | 0.450150 | − | 1.38542i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2.55374 | − | 0.404473i | −0.532493 | − | 0.0843385i | −0.115603 | − | 0.993296i | \(-0.536880\pi\) |
−0.416890 | + | 0.908957i | \(0.636880\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 5.00000 | 1.00000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.09417 | + | 6.90832i | −0.210573 | + | 1.32951i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.65063 | + | 0.861243i | 0.492210 | + | 0.159929i | 0.544597 | − | 0.838698i | \(-0.316683\pi\) |
−0.0523865 | + | 0.998627i | \(0.516683\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 9.86654 | − | 3.20583i | 1.77208 | − | 0.575784i | 0.773749 | − | 0.633492i | \(-0.218379\pi\) |
0.998334 | + | 0.0577079i | \(0.0183792\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −4.94424 | − | 2.51921i | −0.860681 | − | 0.438539i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 3.63927 | − | 3.63927i | 0.615149 | − | 0.615149i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.58628 | + | 10.0154i | 0.260782 | + | 1.64651i | 0.676080 | + | 0.736829i | \(0.263678\pi\) |
−0.415297 | + | 0.909686i | \(0.636322\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 2.25935 | − | 1.64152i | 0.361786 | − | 0.262853i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −8.52488 | − | 6.19369i | −1.33136 | − | 0.967292i | −0.999715 | − | 0.0238886i | \(-0.992395\pi\) |
−0.331648 | − | 0.943403i | \(-0.607605\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −6.17421 | − | 6.17421i | −0.941558 | − | 0.941558i | 0.0568258 | − | 0.998384i | \(-0.481902\pi\) |
−0.998384 | + | 0.0568258i | \(0.981902\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −7.11267 | + | 9.78975i | −1.06029 | + | 1.45937i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −0.494291 | − | 0.970102i | −0.0720998 | − | 0.141504i | 0.852143 | − | 0.523309i | \(-0.175303\pi\) |
−0.924243 | + | 0.381805i | \(0.875303\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.70228i | 0.243183i | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 15.9065i | 2.22736i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −4.26445 | − | 8.36946i | −0.585768 | − | 1.14963i | −0.973676 | − | 0.227936i | \(-0.926802\pi\) |
0.387909 | − | 0.921698i | \(-0.373198\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −2.51467 | − | 3.46115i | −0.339079 | − | 0.466702i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 12.4602 | + | 12.4602i | 1.65039 | + | 1.65039i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −7.85962 | − | 5.71035i | −1.02323 | − | 0.743424i | −0.0562914 | − | 0.998414i | \(-0.517928\pi\) |
−0.966944 | + | 0.254991i | \(0.917928\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −0.975062 | + | 0.708424i | −0.124844 | + | 0.0907044i | −0.648455 | − | 0.761253i | \(-0.724585\pi\) |
0.523611 | + | 0.851957i | \(0.324585\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 1.94852 | + | 12.3025i | 0.245491 | + | 1.54997i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 2.12663 | − | 0.336825i | 0.263776 | − | 0.0417780i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 5.77838 | + | 2.94423i | 0.705942 | + | 0.359695i | 0.769819 | − | 0.638263i | \(-0.220347\pi\) |
−0.0638771 | + | 0.997958i | \(0.520347\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 7.13188 | − | 2.31729i | 0.858578 | − | 0.278969i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −8.83270 | − | 2.86992i | −1.04825 | − | 0.340597i | −0.266268 | − | 0.963899i | \(-0.585790\pi\) |
−0.781981 | + | 0.623303i | \(0.785790\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −0.212028 | + | 1.33869i | −0.0248160 | + | 0.156682i | −0.996985 | − | 0.0776007i | \(-0.975274\pi\) |
0.972169 | + | 0.234282i | \(0.0752741\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −12.9209 | + | 6.58350i | −1.49197 | + | 0.760198i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −4.34953 | − | 0.688898i | −0.495675 | − | 0.0785072i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −2.28496 | + | 7.03239i | −0.257078 | + | 0.791206i | 0.736335 | + | 0.676617i | \(0.236555\pi\) |
−0.993413 | + | 0.114588i | \(0.963445\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −1.25180 | − | 3.85265i | −0.139089 | − | 0.428072i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 6.97154 | − | 13.6824i | 0.765225 | − | 1.50184i | −0.0969830 | − | 0.995286i | \(-0.530919\pi\) |
0.862209 | − | 0.506554i | \(-0.169081\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −5.56758 | + | 10.9270i | −0.603889 | + | 1.18520i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −7.98369 | + | 1.26449i | −0.855941 | + | 0.135568i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −1.95788 | − | 2.69479i | −0.207534 | − | 0.285647i | 0.692543 | − | 0.721377i | \(-0.256490\pi\) |
−0.900077 | + | 0.435730i | \(0.856490\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.30272 | − | 1.79303i | 0.136562 | − | 0.187961i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −21.2757 | + | 21.2757i | −2.20619 | + | 2.20619i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 4.19824 | + | 12.9209i | 0.430730 | + | 1.32565i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 2.23955 | − | 1.14111i | 0.227392 | − | 0.115862i | −0.336583 | − | 0.941654i | \(-0.609271\pi\) |
0.563975 | + | 0.825792i | \(0.309271\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 10.3540 | 1.04061 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 2.89806 | 0.288367 | 0.144184 | − | 0.989551i | \(-0.453944\pi\) | ||||
0.144184 | + | 0.989551i | \(0.453944\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −7.80741 | + | 3.97807i | −0.769287 | + | 0.391971i | −0.794152 | − | 0.607720i | \(-0.792084\pi\) |
0.0248649 | + | 0.999691i | \(0.492084\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −4.61267 | + | 14.1963i | −0.450150 | + | 1.38542i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 11.2441 | − | 11.2441i | 1.08701 | − | 1.08701i | 0.0911721 | − | 0.995835i | \(-0.470939\pi\) |
0.995835 | − | 0.0911721i | \(-0.0290613\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 5.03556 | − | 6.93085i | 0.482319 | − | 0.663855i | −0.496629 | − | 0.867963i | \(-0.665429\pi\) |
0.978949 | + | 0.204107i | \(0.0654292\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −17.2864 | − | 23.7927i | −1.64076 | − | 2.25831i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −5.16807 | + | 0.818542i | −0.486171 | + | 0.0770020i | −0.394708 | − | 0.918806i | \(-0.629154\pi\) |
−0.0914631 | + | 0.995808i | \(0.529154\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 5.71035 | + | 0.904430i | 0.532493 | + | 0.0843385i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −2.36571 | + | 4.64297i | −0.218710 | + | 0.429243i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 3.90087 | + | 12.0056i | 0.357592 | + | 1.10056i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 2.26799 | − | 6.98015i | 0.206181 | − | 0.634559i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 30.1850 | + | 4.78083i | 2.72169 | + | 0.431073i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −11.1803 | −1.00000 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2.77391 | − | 17.5138i | 0.246145 | − | 1.55410i | −0.486619 | − | 0.873614i | \(-0.661770\pi\) |
0.732764 | − | 0.680483i | \(-0.238230\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 24.0848 | + | 7.82563i | 2.12055 | + | 0.689008i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 14.5010 | − | 4.71166i | 1.26696 | − | 0.411660i | 0.402989 | − | 0.915205i | \(-0.367971\pi\) |
0.863969 | + | 0.503545i | \(0.167971\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 12.4602 | + | 6.34879i | 1.08044 | + | 0.550510i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 2.44664 | − | 15.4475i | 0.210573 | − | 1.32951i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 0.153395 | + | 0.968498i | 0.0131054 | + | 0.0827443i | 0.993374 | − | 0.114925i | \(-0.0366628\pi\) |
−0.980269 | + | 0.197669i | \(0.936663\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −3.91731 | + | 2.84609i | −0.332262 | + | 0.241403i | −0.741390 | − | 0.671075i | \(-0.765833\pi\) |
0.409128 | + | 0.912477i | \(0.365833\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 2.55467 | + | 1.85607i | 0.215142 | + | 0.156310i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −1.30272 | − | 1.30272i | −0.108939 | − | 0.108939i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −5.92699 | − | 1.92580i | −0.492210 | − | 0.159929i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −2.24140 | − | 4.39899i | −0.184867 | − | 0.362822i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − | 9.16129i | − | 0.750522i | −0.926919 | − | 0.375261i | \(-0.877553\pi\) | ||
0.926919 | − | 0.375261i | \(-0.122447\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 15.6035i | 1.26979i | 0.772597 | + | 0.634897i | \(0.218957\pi\) | ||||
−0.772597 | + | 0.634897i | \(0.781043\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −13.4744 | − | 26.4451i | −1.08934 | − | 2.13796i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −22.0622 | + | 7.16846i | −1.77208 | + | 0.575784i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −5.05644 | − | 5.05644i | −0.403548 | − | 0.403548i | 0.475933 | − | 0.879481i | \(-0.342110\pi\) |
−0.879481 | + | 0.475933i | \(0.842110\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 22.0401 | + | 16.0131i | 1.74790 | + | 1.26992i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 4.81459 | − | 3.49801i | 0.379443 | − | 0.275682i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 0.542005 | + | 3.42208i | 0.0424531 | + | 0.268038i | 0.999780 | − | 0.0209686i | \(-0.00667499\pi\) |
−0.957327 | + | 0.289007i | \(0.906675\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 11.0557 | + | 5.63314i | 0.860681 | + | 0.438539i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −12.2007 | − | 6.21658i | −0.944121 | − | 0.481054i | −0.0870224 | − | 0.996206i | \(-0.527735\pi\) |
−0.857098 | + | 0.515153i | \(0.827735\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −11.4819 | + | 3.73070i | −0.883224 | + | 0.286977i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −31.2705 | − | 10.1604i | −2.39132 | − | 0.776986i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −0.0270578 | + | 0.170836i | −0.00205716 | + | 0.0129884i | −0.988696 | − | 0.149937i | \(-0.952093\pi\) |
0.986638 | + | 0.162925i | \(0.0520930\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −8.13766 | + | 8.13766i | −0.615149 | + | 0.615149i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 27.8294 | + | 4.40775i | 2.09179 | + | 0.331306i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −3.01577 | + | 9.28158i | −0.225409 | + | 0.693738i | 0.772841 | + | 0.634600i | \(0.218835\pi\) |
−0.998250 | + | 0.0591379i | \(0.981165\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −5.57180 | − | 17.1482i | −0.414148 | − | 1.27462i | −0.913010 | − | 0.407936i | \(-0.866249\pi\) |
0.498862 | − | 0.866681i | \(-0.333751\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1.58694 | − | 3.11455i | 0.117310 | − | 0.230234i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −3.54702 | − | 22.3950i | −0.260782 | − | 1.64651i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 10.3641 | − | 1.64152i | 0.757900 | − | 0.120040i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −9.46271 | − | 13.0243i | −0.688311 | − | 0.947379i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 3.50986 | − | 4.83091i | 0.253965 | − | 0.349552i | −0.662930 | − | 0.748681i | \(-0.730687\pi\) |
0.916895 | + | 0.399129i | \(0.130687\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 5.93294 | − | 5.93294i | 0.427062 | − | 0.427062i | −0.460564 | − | 0.887626i | \(-0.652353\pi\) |
0.887626 | + | 0.460564i | \(0.152353\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −5.05207 | + | 3.67054i | −0.361786 | + | 0.262853i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 9.22957 | − | 4.70270i | 0.657580 | − | 0.335054i | −0.0931606 | − | 0.995651i | \(-0.529697\pi\) |
0.750740 | + | 0.660598i | \(0.229697\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −12.1515 | −0.861397 | −0.430698 | − | 0.902496i | \(-0.641733\pi\) | ||||
−0.430698 | + | 0.902496i | \(0.641733\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −18.8090 | −1.32668 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −5.71569 | + | 2.91229i | −0.401163 | + | 0.204403i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 19.0622 | + | 13.8495i | 1.33136 | + | 0.967292i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −9.89399 | + | 9.89399i | −0.687680 | + | 0.687680i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 6.83277 | − | 9.40450i | 0.472632 | − | 0.650523i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 0.265481 | + | 0.365404i | 0.0182765 | + | 0.0251554i | 0.818057 | − | 0.575137i | \(-0.195051\pi\) |
−0.799781 | + | 0.600292i | \(0.795051\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 26.6040 | − | 4.21366i | 1.82288 | − | 0.288715i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 13.8060 | + | 13.8060i | 0.941558 | + | 0.941558i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −10.8405 | + | 21.2757i | −0.735902 | + | 1.44429i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −1.21474 | − | 3.73858i | −0.0820844 | − | 0.252630i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1.63194 | + | 5.02259i | −0.109776 | + | 0.337856i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 8.45289 | + | 1.33881i | 0.566048 | + | 0.0896531i | 0.432898 | − | 0.901443i | \(-0.357491\pi\) |
0.133149 | + | 0.991096i | \(0.457491\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 15.9044 | − | 21.8905i | 1.06029 | − | 1.45937i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −0.623179 | + | 3.93460i | −0.0413619 | + | 0.261149i | −0.999700 | − | 0.0244872i | \(-0.992205\pi\) |
0.958338 | + | 0.285636i | \(0.0922047\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −6.21003 | − | 2.01776i | −0.410371 | − | 0.133337i | 0.0965543 | − | 0.995328i | \(-0.469218\pi\) |
−0.506925 | + | 0.861990i | \(0.669218\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 12.1470 | − | 3.94680i | 0.799214 | − | 0.259680i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −12.7395 | − | 6.49110i | −0.834592 | − | 0.425246i | −0.0161739 | − | 0.999869i | \(-0.505149\pi\) |
−0.818418 | + | 0.574623i | \(0.805149\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.10527 | + | 2.16921i | 0.0720998 | + | 0.141504i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −3.35482 | − | 21.1815i | −0.217919 | − | 1.37589i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −6.67715 | + | 4.85123i | −0.431909 | + | 0.313800i | −0.782412 | − | 0.622762i | \(-0.786011\pi\) |
0.350503 | + | 0.936562i | \(0.386011\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 6.93466 | + | 5.03832i | 0.446700 | + | 0.324547i | 0.788292 | − | 0.615302i | \(-0.210966\pi\) |
−0.341591 | + | 0.939849i | \(0.610966\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −6.52978 | − | 6.52978i | −0.418885 | − | 0.418885i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | − | 3.80642i | − | 0.243183i | ||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2.65603 | + | 5.21275i | 0.168999 | + | 0.331680i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 44.5371i | 2.82242i | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 17.5281i | 1.10636i | 0.833061 | + | 0.553182i | \(0.186586\pi\) | ||||
−0.833061 | + | 0.553182i | \(0.813414\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2.24586 | − | 4.40775i | −0.141196 | − | 0.277113i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | − | 35.5681i | − | 2.22736i | ||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −12.1447 | − | 12.1447i | −0.757568 | − | 0.757568i | 0.218311 | − | 0.975879i | \(-0.429945\pi\) |
−0.975879 | + | 0.218311i | \(0.929945\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −18.8820 | − | 13.7186i | −1.17327 | − | 0.852432i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 12.2020 | − | 8.86524i | 0.755282 | − | 0.548745i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −0.382691 | − | 2.41621i | −0.0235977 | − | 0.148990i | 0.973076 | − | 0.230484i | \(-0.0740309\pi\) |
−0.996674 | + | 0.0814938i | \(0.974031\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 9.53560 | + | 18.7147i | 0.585768 | + | 1.14963i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 8.60771 | + | 4.38585i | 0.526783 | + | 0.268410i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −7.51890 | + | 2.44304i | −0.458436 | + | 0.148955i | −0.529126 | − | 0.848544i | \(-0.677480\pi\) |
0.0706899 | + | 0.997498i | \(0.477480\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 10.8617 | + | 3.52919i | 0.659803 | + | 0.214383i | 0.619731 | − | 0.784814i | \(-0.287242\pi\) |
0.0400712 | + | 0.999197i | \(0.487242\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −1.00555 | + | 6.34879i | −0.0608586 | + | 0.384246i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 5.62298 | + | 7.73937i | 0.339079 | + | 0.466702i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −5.09695 | − | 0.807278i | −0.306246 | − | 0.0485047i | 0.00141993 | − | 0.999999i | \(-0.499548\pi\) |
−0.307666 | + | 0.951494i | \(0.599548\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 17.3488 | − | 53.3941i | 1.03865 | − | 3.19662i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0.292927 | + | 0.901537i | 0.0174746 | + | 0.0537812i | 0.959414 | − | 0.282003i | \(-0.0909988\pi\) |
−0.941939 | + | 0.335784i | \(0.890999\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 2.13911 | − | 4.19824i | 0.127157 | − | 0.249559i | −0.818648 | − | 0.574296i | \(-0.805276\pi\) |
0.945804 | + | 0.324737i | \(0.105276\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −27.8619 | − | 27.8619i | −1.65039 | − | 1.65039i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 23.9549 | − | 3.79409i | 1.41402 | − | 0.223958i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −7.68790 | − | 10.5815i | −0.452229 | − | 0.622440i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −4.28488 | + | 5.89763i | −0.251184 | + | 0.345725i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −17.4021 | + | 17.4021i | −1.01664 | + | 1.01664i | −0.0167798 | + | 0.999859i | \(0.505341\pi\) |
−0.999859 | + | 0.0167798i | \(0.994659\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 17.5746 | + | 12.7687i | 1.02323 | + | 0.743424i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −11.9237 | + | 6.07543i | −0.691884 | + | 0.352532i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 2.48968 | 0.143982 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 20.0974 | 1.15840 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −7.48907 | + | 3.81587i | −0.430236 | + | 0.219216i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 2.18031 | − | 1.58408i | 0.124844 | − | 0.0907044i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −9.15421 | + | 9.15421i | −0.522458 | + | 0.522458i | −0.918313 | − | 0.395855i | \(-0.870448\pi\) |
0.395855 | + | 0.918313i | \(0.370448\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 14.9377 | − | 20.5600i | 0.849778 | − | 1.16962i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 14.5504 | + | 20.0269i | 0.825079 | + | 1.13562i | 0.988819 | + | 0.149120i | \(0.0476441\pi\) |
−0.163740 | + | 0.986504i | \(0.552356\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 24.1995 | − | 3.83282i | 1.36784 | − | 0.216644i | 0.571055 | − | 0.820912i | \(-0.306534\pi\) |
0.796781 | + | 0.604268i | \(0.206534\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −4.35703 | − | 27.5092i | −0.245491 | − | 1.54997i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 5.10607 | − | 10.0212i | 0.286785 | − | 0.562848i | −0.702003 | − | 0.712174i | \(-0.747711\pi\) |
0.988788 | + | 0.149326i | \(0.0477105\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.64780 | + | 5.07140i | 0.0922589 | + | 0.283944i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −14.2515 | + | 43.8618i | −0.795444 | + | 2.44812i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −32.9120 | − | 5.21275i | −1.83127 | − | 0.290045i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −4.75528 | + | 0.753163i | −0.263776 | + | 0.0417780i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −3.88689 | + | 24.5408i | −0.214945 | + | 1.35711i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 2.38335 | + | 0.774396i | 0.131398 | + | 0.0426938i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 20.0332 | − | 6.50919i | 1.10113 | − | 0.357777i | 0.298590 | − | 0.954382i | \(-0.403484\pi\) |
0.802536 | + | 0.596604i | \(0.203484\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 48.8941 | + | 24.9128i | 2.67938 | + | 1.36521i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −12.9209 | − | 6.58350i | −0.705942 | − | 0.359695i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −0.744661 | − | 4.70160i | −0.0405643 | − | 0.256113i | 0.959070 | − | 0.283170i | \(-0.0913862\pi\) |
−0.999634 | + | 0.0270577i | \(0.991386\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 12.2774 | − | 8.92006i | 0.666817 | − | 0.484471i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 16.0581 | + | 11.6669i | 0.869595 | + | 0.631798i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −14.1632 | − | 14.1632i | −0.764743 | − | 0.764743i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −15.9474 | + | 5.18162i | −0.858578 | + | 0.278969i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 2.39689 | + | 4.70415i | 0.128672 | + | 0.252532i | 0.946350 | − | 0.323143i | \(-0.104739\pi\) |
−0.817679 | + | 0.575675i | \(0.804739\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1.87772i | 0.100512i | 0.998736 | + | 0.0502560i | \(0.0160037\pi\) | ||||
−0.998736 | + | 0.0502560i | \(0.983996\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − | 6.73502i | − | 0.359489i | ||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −2.87675 | − | 5.64593i | −0.153114 | − | 0.300503i | 0.801690 | − | 0.597740i | \(-0.203935\pi\) |
−0.954804 | + | 0.297238i | \(0.903935\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 19.7505 | + | 6.41733i | 1.04825 | + | 0.340597i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −25.8884 | − | 25.8884i | −1.37016 | − | 1.37016i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −9.96018 | − | 7.23649i | −0.525678 | − | 0.381928i | 0.293060 | − | 0.956094i | \(-0.405326\pi\) |
−0.818739 | + | 0.574166i | \(0.805326\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −14.4933 | + | 10.5300i | −0.762806 | + | 0.554211i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 3.32990 | + | 21.0242i | 0.174774 | + | 1.10348i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0.474108 | − | 2.99340i | 0.0248160 | − | 0.156682i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −8.31332 | − | 4.23585i | −0.433952 | − | 0.221109i | 0.223348 | − | 0.974739i | \(-0.428301\pi\) |
−0.657300 | + | 0.753629i | \(0.728301\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −54.2333 | + | 17.6215i | −2.82327 | + | 0.917336i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 20.5621 | + | 6.68103i | 1.06753 | + | 0.346862i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −0.744661 | + | 4.70160i | −0.0385571 | + | 0.243440i | −0.999438 | − | 0.0335221i | \(-0.989328\pi\) |
0.960881 | + | 0.276962i | \(0.0893276\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 28.8919 | − | 14.7212i | 1.49197 | − | 0.760198i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −2.65063 | − | 0.419819i | −0.136515 | − | 0.0216218i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −8.61253 | + | 26.5066i | −0.442396 | + | 1.36155i | 0.442918 | + | 0.896562i | \(0.353943\pi\) |
−0.885314 | + | 0.464993i | \(0.846057\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 15.8922 | + | 48.9110i | 0.814180 | + | 2.50579i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −5.76109 | + | 11.3068i | −0.294378 | + | 0.577750i | −0.990067 | − | 0.140593i | \(-0.955099\pi\) |
0.695689 | + | 0.718343i | \(0.255099\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 9.72585 | + | 1.54042i | 0.495675 | + | 0.0785072i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −46.6708 | + | 7.39193i | −2.37241 | + | 0.375753i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 3.10772 | + | 4.27741i | 0.157568 | + | 0.216873i | 0.880501 | − | 0.474045i | \(-0.157207\pi\) |
−0.722933 | + | 0.690918i | \(0.757207\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −8.33510 | + | 11.4723i | −0.421524 | + | 0.580178i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −31.2692 | + | 31.2692i | −1.57732 | + | 1.57732i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 5.10933 | − | 15.7249i | 0.257078 | − | 0.791206i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −24.5503 | + | 12.5090i | −1.23214 | + | 0.627808i | −0.944053 | − | 0.329795i | \(-0.893020\pi\) |
−0.288091 | + | 0.957603i | \(0.593020\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −40.5588 | −2.03048 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −32.1362 | −1.60481 | −0.802403 | − | 0.596783i | \(-0.796445\pi\) | ||||
−0.802403 | + | 0.596783i | \(0.796445\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −8.90073 | + | 4.53515i | −0.443377 | + | 0.225912i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 2.79911 | + | 8.61479i | 0.139089 | + | 0.428072i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −13.7186 | + | 13.7186i | −0.680005 | + | 0.680005i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −17.8888 | + | 24.6219i | −0.884546 | + | 1.21747i | 0.0905950 | + | 0.995888i | \(0.471123\pi\) |
−0.975141 | + | 0.221585i | \(0.928877\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −1.67162 | − | 2.30079i | −0.0824549 | − | 0.113489i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 22.0855 | − | 3.49801i | 1.08676 | − | 0.172126i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −15.5888 | + | 30.5948i | −0.765225 | + | 1.50184i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 6.37555 | − | 12.5127i | 0.312212 | − | 0.612751i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −5.60088 | − | 17.2377i | −0.273621 | − | 0.842118i | −0.989581 | − | 0.143977i | \(-0.954011\pi\) |
0.715960 | − | 0.698141i | \(-0.245989\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 8.04143 | − | 24.7490i | 0.391915 | − | 1.20619i | −0.539423 | − | 0.842035i | \(-0.681358\pi\) |
0.931338 | − | 0.364156i | \(-0.118642\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −5.81949 | − | 0.921717i | −0.282953 | − | 0.0448154i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 12.4495 | − | 24.4335i | 0.603889 | − | 1.18520i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0.433962 | − | 2.73993i | 0.0210009 | − | 0.132594i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 5.08172 | + | 1.65115i | 0.245348 | + | 0.0797184i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −25.3453 | + | 8.23518i | −1.22084 | + | 0.396675i | −0.847388 | − | 0.530975i | \(-0.821826\pi\) |
−0.373452 | + | 0.927650i | \(0.621826\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 27.7248 | + | 14.1265i | 1.33237 | + | 0.678876i | 0.967663 | − | 0.252246i | \(-0.0811693\pi\) |
0.364706 | + | 0.931123i | \(0.381169\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 17.8521 | − | 2.82749i | 0.855941 | − | 0.135568i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 2.45748 | + | 15.5159i | 0.117557 | + | 0.742227i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 7.74387 | − | 5.62625i | 0.369595 | − | 0.268526i | −0.387448 | − | 0.921891i | \(-0.626643\pi\) |
0.757043 | + | 0.653365i | \(0.226643\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 7.45277 | + | 5.41476i | 0.354894 | + | 0.257846i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 9.95720 | + | 9.95720i | 0.473081 | + | 0.473081i | 0.902910 | − | 0.429829i | \(-0.141426\pi\) |
−0.429829 | + | 0.902910i | \(0.641426\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 4.37794 | + | 6.02572i | 0.207534 | + | 0.285647i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 12.0627 | + | 23.6743i | 0.570545 | + | 1.11976i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 24.2916i | 1.14639i | 0.819419 | + | 0.573195i | \(0.194296\pi\) | ||||
−0.819419 | + | 0.573195i | \(0.805704\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 20.1608i | − | 0.949337i | ||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −20.5451 | − | 40.3221i | −0.965294 | − | 1.89450i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −2.91296 | + | 4.00935i | −0.136562 | + | 0.187961i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 19.1711 | + | 19.1711i | 0.896786 | + | 0.896786i | 0.995150 | − | 0.0983649i | \(-0.0313612\pi\) |
−0.0983649 | + | 0.995150i | \(0.531361\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 31.0345 | + | 22.5479i | 1.44857 | + | 1.05245i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −11.1879 | + | 8.12849i | −0.521073 | + | 0.378582i | −0.817008 | − | 0.576626i | \(-0.804369\pi\) |
0.295935 | + | 0.955208i | \(0.404369\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −4.57144 | − | 28.8629i | −0.212453 | − | 1.34137i | −0.831283 | − | 0.555850i | \(-0.812393\pi\) |
0.618830 | − | 0.785525i | \(-0.287607\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 47.5739 | − | 47.5739i | 2.20619 | − | 2.20619i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −1.17085 | − | 0.596577i | −0.0541804 | − | 0.0276063i | 0.426690 | − | 0.904398i | \(-0.359679\pi\) |
−0.480871 | + | 0.876791i | \(0.659679\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −14.1963 | + | 4.61267i | −0.655526 | + | 0.212993i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 19.7245 | + | 6.40889i | 0.908858 | + | 0.295306i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 2.61341 | − | 16.5004i | 0.120165 | − | 0.758689i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −9.38755 | − | 28.8919i | −0.430730 | − | 1.32565i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −50.2071 | − | 7.95202i | −2.29883 | − | 0.364098i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 1.74144 | − | 5.35960i | 0.0795684 | − | 0.244886i | −0.903357 | − | 0.428888i | \(-0.858905\pi\) |
0.982926 | + | 0.184002i | \(0.0589053\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −3.01728 | − | 9.28622i | −0.137576 | − | 0.423415i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −7.83590 | + | 15.3788i | −0.356546 | + | 0.699761i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −5.00778 | + | 2.55159i | −0.227392 | + | 0.115862i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 21.6062 | − | 3.42208i | 0.979070 | − | 0.155069i | 0.353667 | − | 0.935371i | \(-0.384935\pi\) |
0.625403 | + | 0.780302i | \(0.284935\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −5.90649 | − | 8.12959i | −0.267101 | − | 0.367633i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 24.4969 | − | 33.7171i | 1.10553 | − | 1.52163i | 0.277691 | − | 0.960671i | \(-0.410431\pi\) |
0.827841 | − | 0.560963i | \(-0.189569\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 10.8084 | − | 10.8084i | 0.486788 | − | 0.486788i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −23.1522 | −1.04061 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 19.0464 | − | 9.70461i | 0.854347 | − | 0.435311i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 31.4385 | 1.40738 | 0.703690 | − | 0.710508i | \(-0.251535\pi\) | ||||
0.703690 | + | 0.710508i | \(0.251535\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 39.7141 | 1.77430 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 25.4190 | − | 12.9516i | 1.13338 | − | 0.577483i | 0.216351 | − | 0.976316i | \(-0.430584\pi\) |
0.917024 | + | 0.398832i | \(0.130584\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −6.48025 | −0.288367 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 24.7590 | − | 24.7590i | 1.09959 | − | 1.09959i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −11.3987 | + | 15.6889i | −0.505237 | + | 0.695400i | −0.983107 | − | 0.183031i | \(-0.941409\pi\) |
0.477870 | + | 0.878431i | \(0.341409\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1.83368 | − | 2.52384i | −0.0811171 | − | 0.111648i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 41.9732 | − | 6.64791i | 1.85316 | − | 0.293512i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 17.4579 | − | 8.89524i | 0.769287 | − | 0.391971i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0.945717 | − | 1.85607i | 0.0415926 | − | 0.0816300i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −0.155018 | − | 0.477096i | −0.00680453 | − | 0.0209422i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −3.07842 | + | 9.47439i | −0.134868 | + | 0.415081i | −0.995569 | − | 0.0940291i | \(-0.970025\pi\) |
0.860702 | + | 0.509110i | \(0.170025\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −6.66792 | − | 1.05610i | −0.291568 | − | 0.0461798i | 0.00893708 | − | 0.999960i | \(-0.497155\pi\) |
−0.300505 | + | 0.953780i | \(0.597155\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 10.3142 | − | 31.7440i | 0.450150 | − | 1.38542i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 8.90073 | − | 56.1970i | 0.387722 | − | 2.44798i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −15.5163 | − | 5.04155i | −0.674621 | − | 0.219198i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −50.0010 | + | 16.2463i | −2.16986 | + | 0.705030i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 9.04062 | + | 4.60642i | 0.391593 | + | 0.199526i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −25.1426 | + | 25.1426i | −1.08701 | + | 1.08701i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −4.42780 | − | 27.9561i | −0.191074 | − | 1.20639i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −2.63492 | + | 1.91438i | −0.113494 | + | 0.0824582i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −35.9536 | − | 26.1218i | −1.54577 | − | 1.12306i | −0.946587 | − | 0.322449i | \(-0.895494\pi\) |
−0.599179 | − | 0.800615i | \(-0.704506\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 36.9776 | + | 36.9776i | 1.58686 | + | 1.58686i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −11.2599 | + | 15.4979i | −0.482319 | + | 0.663855i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −13.3756 | − | 26.2510i | −0.571897 | − | 1.12241i | −0.978004 | − | 0.208586i | \(-0.933114\pi\) |
0.406107 | − | 0.913826i | \(-0.366886\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 6.52234i | 0.278367i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 16.9334i | − | 0.721385i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −7.72659 | − | 15.1643i | −0.328568 | − | 0.644851i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 38.6536 | + | 53.2022i | 1.64076 | + | 2.25831i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 8.25814 | + | 8.25814i | 0.349908 | + | 0.349908i | 0.860075 | − | 0.510167i | \(-0.170416\pi\) |
−0.510167 | + | 0.860075i | \(0.670416\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 6.80206 | + | 4.94199i | 0.287697 | + | 0.209024i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −24.6213 | + | 17.8884i | −1.03951 | + | 0.755250i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −2.84609 | − | 17.9695i | −0.119949 | − | 0.757325i | −0.972193 | − | 0.234181i | \(-0.924759\pi\) |
0.852244 | − | 0.523144i | \(-0.175241\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 11.5562 | − | 1.83032i | 0.486171 | − | 0.0770020i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 8.30766 | + | 4.23296i | 0.348889 | + | 0.177768i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 22.1612 | − | 7.20061i | 0.929046 | − | 0.301865i | 0.194873 | − | 0.980828i | \(-0.437570\pi\) |
0.734172 | + | 0.678963i | \(0.237570\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −4.48095 | − | 1.45595i | −0.187522 | − | 0.0609296i | 0.213751 | − | 0.976888i | \(-0.431432\pi\) |
−0.401273 | + | 0.915959i | \(0.631432\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −2.70922 | + | 17.1053i | −0.113179 | + | 0.714585i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −12.7687 | − | 2.02237i | −0.532493 | − | 0.0843385i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −25.3479 | − | 4.01471i | −1.05525 | − | 0.167135i | −0.395380 | − | 0.918517i | \(-0.629387\pi\) |
−0.659867 | + | 0.751383i | \(0.729387\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −7.51982 | + | 23.1436i | −0.312513 | + | 0.961816i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 10.9222 | + | 33.6149i | 0.453128 | + | 1.39458i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 8.15908 | − | 16.0131i | 0.337915 | − | 0.663195i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 5.28989 | − | 10.3820i | 0.218710 | − | 0.429243i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −3.46115 | + | 0.548193i | −0.142857 | + | 0.0226263i | −0.227453 | − | 0.973789i | \(-0.573040\pi\) |
0.0845963 | + | 0.996415i | \(0.473040\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −37.0490 | − | 50.9936i | −1.52658 | − | 2.10116i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −17.6587 | + | 24.3052i | −0.726383 | + | 0.999781i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −9.16670 | + | 9.16670i | −0.376431 | + | 0.376431i | −0.869813 | − | 0.493382i | \(-0.835761\pi\) |
0.493382 | + | 0.869813i | \(0.335761\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −8.72261 | − | 26.8454i | −0.357592 | − | 1.10056i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 31.4015 | − | 15.9999i | 1.28518 | − | 0.654832i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 1.02128 | 0.0417284 | 0.0208642 | − | 0.999782i | \(-0.493358\pi\) | ||||
0.0208642 | + | 0.999782i | \(0.493358\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 24.7175 | 1.00825 | 0.504124 | − | 0.863631i | \(-0.331816\pi\) | ||||
0.504124 | + | 0.863631i | \(0.331816\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 31.2705 | − | 15.9331i | 1.27343 | − | 0.648847i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −5.07138 | + | 15.6081i | −0.206181 | + | 0.634559i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 15.6989 | − | 15.6989i | 0.637199 | − | 0.637199i | −0.312664 | − | 0.949864i | \(-0.601222\pi\) |
0.949864 | + | 0.312664i | \(0.101222\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 10.9357 | − | 15.0517i | 0.443137 | − | 0.609926i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0.616228 | + | 0.848165i | 0.0249299 | + | 0.0343131i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 24.4360 | − | 3.87028i | 0.986961 | − | 0.156319i | 0.357971 | − | 0.933733i | \(-0.383469\pi\) |
0.628990 | + | 0.777413i | \(0.283469\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −67.4957 | − | 10.6903i | −2.72169 | − | 0.431073i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 20.2483 | − | 39.7395i | 0.815166 | − | 1.59985i | 0.0151422 | − | 0.999885i | \(-0.495180\pi\) |
0.800024 | − | 0.599968i | \(-0.204820\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 5.01747 | + | 15.4422i | 0.201669 | + | 0.620674i | 0.999834 | + | 0.0182344i | \(0.00580452\pi\) |
−0.798165 | + | 0.602439i | \(0.794195\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 5.58846 | − | 17.1995i | 0.224257 | − | 0.690193i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 7.57235 | + | 1.19934i | 0.303380 | + | 0.0480507i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 25.0000 | 1.00000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −5.27413 | + | 33.2995i | −0.210628 | + | 1.32986i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 52.8917 | + | 17.1856i | 2.10893 | + | 0.685233i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −33.0642 | + | 10.7432i | −1.31626 | + | 0.427680i | −0.881210 | − | 0.472725i | \(-0.843270\pi\) |
−0.435053 | + | 0.900405i | \(0.643270\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −1.16718 | − | 0.594706i | −0.0463911 | − | 0.0236374i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −6.20265 | + | 39.1620i | −0.246145 | + | 1.55410i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −0.256419 | − | 1.61897i | −0.0101597 | − | 0.0641458i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −40.6606 | + | 29.5416i | −1.60851 | + | 1.16865i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 24.7800 | + | 18.0037i | 0.978751 | + | 0.711104i | 0.957429 | − | 0.288668i | \(-0.0932125\pi\) |
0.0213220 | + | 0.999773i | \(0.493212\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 14.8959 | + | 14.8959i | 0.587438 | + | 0.587438i | 0.936937 | − | 0.349499i | \(-0.113648\pi\) |
−0.349499 | + | 0.936937i | \(0.613648\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −53.8553 | − | 17.4986i | −2.12055 | − | 0.689008i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 6.63750 | + | 13.0268i | 0.260947 | + | 0.512137i | 0.983891 | − | 0.178769i | \(-0.0572116\pi\) |
−0.722944 | + | 0.690907i | \(0.757212\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 18.5875i | − | 0.729625i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | − | 69.2537i | − | 2.71427i | ||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 11.8246 | + | 23.2070i | 0.462731 | + | 0.908161i | 0.997984 | + | 0.0634688i | \(0.0202163\pi\) |
−0.535253 | + | 0.844692i | \(0.679784\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −32.4252 | + | 10.5356i | −1.26696 | + | 0.411660i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 5.18649 | + | 5.18649i | 0.202344 | + | 0.202344i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −24.4969 | − | 17.7981i | −0.954265 | − | 0.693314i | −0.00245356 | − | 0.999997i | \(-0.500781\pi\) |
−0.951812 | + | 0.306683i | \(0.900781\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 22.1513 | − | 16.0939i | 0.861587 | − | 0.625980i | −0.0667289 | − | 0.997771i | \(-0.521256\pi\) |
0.928316 | + | 0.371791i | \(0.121256\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −2.39604 | − | 15.1280i | −0.0930545 | − | 0.587523i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −27.8619 | − | 14.1963i | −1.08044 | − | 0.550510i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −6.42069 | − | 3.27150i | −0.248610 | − | 0.126673i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −23.6065 | + | 7.67022i | −0.912681 | + | 0.296548i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −2.19310 | − | 0.712582i | −0.0846638 | − | 0.0275089i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 2.72840 | − | 17.2265i | 0.105172 | − | 0.664031i | −0.877626 | − | 0.479347i | \(-0.840874\pi\) |
0.982798 | − | 0.184684i | \(-0.0591263\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −5.47085 | + | 34.5416i | −0.210573 | + | 1.32951i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −30.9741 | − | 4.90581i | −1.19043 | − | 0.188546i | −0.470377 | − | 0.882465i | \(-0.655882\pi\) |
−0.720052 | + | 0.693920i | \(0.755882\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −1.78775 | + | 5.50212i | −0.0686075 | + | 0.211152i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −3.57029 | − | 10.9882i | −0.136814 | − | 0.421069i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −12.0790 | + | 23.7064i | −0.462191 | + | 0.907101i | 0.535836 | + | 0.844322i | \(0.319996\pi\) |
−0.998027 | + | 0.0627792i | \(0.980004\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −0.343002 | − | 2.16563i | −0.0131054 | − | 0.0827443i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 18.7046 | − | 2.96251i | 0.713624 | − | 0.113027i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 5.31645 | + | 7.31746i | 0.202541 | + | 0.278773i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −12.0424 | + | 16.5750i | −0.458115 | + | 0.630541i | −0.974116 | − | 0.226047i | \(-0.927420\pi\) |
0.516002 | + | 0.856588i | \(0.327420\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −16.8514 | + | 16.8514i | −0.640132 | + | 0.640132i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 8.75938 | − | 6.36406i | 0.332262 | − | 0.241403i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −51.4928 | + | 26.2369i | −1.95043 | + | 0.993793i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 41.4679 | 1.56846 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 0.0556153 | 0.00210056 | 0.00105028 | − | 0.999999i | \(-0.499666\pi\) | ||||
0.00105028 | + | 0.999999i | \(0.499666\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 54.8943 | − | 27.9700i | 2.07038 | − | 1.05491i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −5.71241 | − | 4.15031i | −0.215142 | − | 0.156310i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −4.71668 | + | 4.71668i | −0.177389 | + | 0.177389i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 26.2864 | − | 36.1801i | 0.987206 | − | 1.35877i | 0.0543509 | − | 0.998522i | \(-0.482691\pi\) |
0.932855 | − | 0.360251i | \(-0.117309\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 23.5204 | + | 32.3730i | 0.882082 | + | 1.21408i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −26.4933 | + | 4.19612i | −0.992181 | + | 0.157146i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 2.91296 | + | 2.91296i | 0.108939 | + | 0.108939i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 10.8673 | − | 21.3282i | 0.405845 | − | 0.796517i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 6.24759 | + | 19.2281i | 0.232996 | + | 0.717087i | 0.997381 | + | 0.0723273i | \(0.0230426\pi\) |
−0.764385 | + | 0.644760i | \(0.776957\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 6.23236 | − | 19.1812i | 0.232105 | − | 0.714347i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −24.5543 | − | 3.88902i | −0.913184 | − | 0.144634i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 13.2532 | + | 4.30621i | 0.492210 | + | 0.159929i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1.18294 | − | 7.46881i | 0.0438729 | − | 0.277003i | −0.955993 | − | 0.293390i | \(-0.905217\pi\) |
0.999866 | + | 0.0163874i | \(0.00521652\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 37.0298 | + | 12.0317i | 1.37147 | + | 0.445619i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −45.5447 | + | 14.7984i | −1.68453 | + | 0.547337i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −4.47992 | − | 2.28263i | −0.165470 | − | 0.0843110i | 0.369294 | − | 0.929313i | \(-0.379599\pi\) |
−0.534764 | + | 0.845002i | \(0.679599\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 5.01191 | + | 9.83643i | 0.184867 | + | 0.362822i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 1.94105 | + | 12.2553i | 0.0714994 | + | 0.451429i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 25.4921 | − | 18.5211i | 0.937743 | − | 0.681310i | −0.0101332 | − | 0.999949i | \(-0.503226\pi\) |
0.947876 | + | 0.318638i | \(0.103226\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −13.7273 | − | 9.97345i | −0.504284 | − | 0.366384i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −4.53704 | − | 4.53704i | −0.166448 | − | 0.166448i | 0.618968 | − | 0.785416i | \(-0.287551\pi\) |
−0.785416 | + | 0.618968i | \(0.787551\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 20.4853i | 0.750522i | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −37.7274 | − | 74.0443i | −1.38037 | − | 2.70914i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 36.6002i | 1.33734i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 45.1400i | − | 1.64718i | −0.567184 | − | 0.823591i | \(-0.691967\pi\) | ||
0.567184 | − | 0.823591i | \(-0.308033\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −23.0793 | − | 45.2956i | −0.841055 | − | 1.65066i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − | 34.8905i | − | 1.26979i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −11.2118 | − | 11.2118i | −0.407500 | − | 0.407500i | 0.473366 | − | 0.880866i | \(-0.343039\pi\) |
−0.880866 | + | 0.473366i | \(0.843039\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 11.6074 | + | 8.43324i | 0.421321 | + | 0.306107i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 16.6208 | − | 12.0757i | 0.602503 | − | 0.437744i | −0.244263 | − | 0.969709i | \(-0.578546\pi\) |
0.846767 | + | 0.531965i | \(0.178546\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 3.08465 | + | 19.4757i | 0.111672 | + | 0.705068i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 30.1297 | + | 59.1329i | 1.08934 | + | 2.13796i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 8.33510 | + | 4.24695i | 0.300963 | + | 0.153348i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −22.0022 | + | 7.14894i | −0.793419 | + | 0.257797i | −0.677559 | − | 0.735468i | \(-0.736962\pi\) |
−0.115859 | + | 0.993266i | \(0.536962\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 47.3751 | + | 15.3931i | 1.70617 | + | 0.554369i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −6.27729 | + | 39.6333i | −0.225779 | + | 1.42551i | 0.570857 | + | 0.821050i | \(0.306611\pi\) |
−0.796635 | + | 0.604460i | \(0.793389\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 49.3327 | − | 16.0292i | 1.77208 | − | 0.575784i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 66.8577 | + | 10.5892i | 2.39850 | + | 0.379886i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −19.7839 | + | 60.8887i | −0.708833 | + | 2.18157i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −5.49095 | − | 16.8994i | −0.196482 | − | 0.604708i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −8.84998 | + | 17.3691i | −0.316273 | + | 0.620720i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 11.3065 | + | 11.3065i | 0.403548 | + | 0.403548i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −14.5622 | + | 2.30642i | −0.519085 | + | 0.0822150i | −0.410479 | − | 0.911870i | \(-0.634639\pi\) |
−0.108606 | + | 0.994085i | \(0.534639\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 4.17037 | + | 5.74002i | 0.148469 | + | 0.204350i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 7.07900 | − | 9.74341i | 0.251700 | − | 0.346436i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0.820627 | − | 0.820627i | 0.0291413 | − | 0.0291413i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −49.2833 | − | 35.8064i | −1.74790 | − | 1.26992i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 17.3154 | − | 8.82266i | 0.613344 | − | 0.312515i | −0.119580 | − | 0.992825i | \(-0.538155\pi\) |
0.732924 | + | 0.680310i | \(0.238155\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −5.97133 | −0.211251 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −18.0258 | −0.636911 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −2.31057 | + | 1.17729i | −0.0815382 | + | 0.0415458i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −10.7658 | + | 7.82178i | −0.379443 | + | 0.275682i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 16.2134 | − | 16.2134i | 0.570738 | − | 0.570738i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 12.0110 | − | 16.5317i | 0.422284 | − | 0.581224i | −0.543877 | − | 0.839165i | \(-0.683044\pi\) |
0.966161 | + | 0.257941i | \(0.0830441\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 7.49205 | + | 10.3119i | 0.263081 | + | 0.362101i | 0.920039 | − | 0.391827i | \(-0.128157\pi\) |
−0.656957 | + | 0.753928i | \(0.728157\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −32.7154 | + | 5.18162i | −1.14738 | + | 0.181727i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −1.21196 | − | 7.65201i | −0.0424531 | − | 0.268038i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −24.0848 | + | 47.2691i | −0.842621 | + | 1.65374i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −3.70631 | − | 11.4069i | −0.129509 | − | 0.398588i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −13.2734 | + | 40.8514i | −0.463246 | + | 1.42572i | 0.397929 | + | 0.917416i | \(0.369729\pi\) |
−0.861175 | + | 0.508309i | \(0.830271\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −14.1588 | − | 2.24253i | −0.493545 | − | 0.0781698i | −0.0952992 | − | 0.995449i | \(-0.530381\pi\) |
−0.398246 | + | 0.917279i | \(0.630381\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −24.7212 | − | 12.5961i | −0.860681 | − | 0.438539i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −3.59722 | + | 22.7120i | −0.125088 | + | 0.789773i | 0.842770 | + | 0.538274i | \(0.180923\pi\) |
−0.967858 | + | 0.251499i | \(0.919077\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −53.7472 | − | 17.4635i | −1.86672 | − | 0.606533i | −0.992695 | − | 0.120648i | \(-0.961503\pi\) |
−0.874022 | − | 0.485886i | \(-0.838497\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 14.2343 | − | 4.62502i | 0.493784 | − | 0.160440i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 8.31854 | + | 4.23851i | 0.288220 | + | 0.146856i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 27.2817 | + | 13.9007i | 0.944121 | + | 0.481054i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 11.3512 | + | 71.6689i | 0.392356 | + | 2.47724i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 45.5611 | − | 33.1021i | 1.57294 | − | 1.14281i | 0.648678 | − | 0.761063i | \(-0.275322\pi\) |
0.924266 | − | 0.381748i | \(-0.124678\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −17.1774 | − | 12.4801i | −0.592323 | − | 0.430348i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −1.94403 | − | 1.94403i | −0.0669559 | − | 0.0669559i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 25.6743 | − | 8.34210i | 0.883224 | − | 0.286977i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 7.66920 | + | 15.0516i | 0.263517 | + | 0.517181i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 13.6655i | 0.469000i | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 26.2183i | − | 0.898751i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 2.05888 | + | 4.04078i | 0.0704948 | + | 0.138354i | 0.923564 | − | 0.383443i | \(-0.125262\pi\) |
−0.853070 | + | 0.521797i | \(0.825262\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 69.9230 | + | 22.7194i | 2.39132 | + | 0.776986i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 31.5213 | + | 31.5213i | 1.07675 | + | 1.07675i | 0.996799 | + | 0.0799464i | \(0.0254749\pi\) |
0.0799464 | + | 0.996799i | \(0.474525\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −44.9222 | − | 32.6379i | −1.53272 | − | 1.11359i | −0.954700 | − | 0.297570i | \(-0.903824\pi\) |
−0.578025 | − | 0.816019i | \(-0.696176\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −56.9080 | + | 41.3461i | −1.93942 | + | 1.40907i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −5.82545 | − | 36.7804i | −0.198301 | − | 1.25202i | −0.863113 | − | 0.505010i | \(-0.831489\pi\) |
0.664813 | − | 0.747010i | \(-0.268511\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0.0605030 | − | 0.382001i | 0.00205716 | − | 0.0129884i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 33.7995 | + | 17.2217i | 1.14789 | + | 0.584880i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −13.4549 | + | 4.37177i | −0.456427 | + | 0.148302i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −5.93906 | − | 1.92972i | −0.201238 | − | 0.0653860i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 2.12785 | − | 13.4347i | 0.0720168 | − | 0.454696i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 18.1964 | − | 18.1964i | 0.615149 | − | 0.615149i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 33.6877 | + | 5.33560i | 1.13755 | + | 0.180170i | 0.696668 | − | 0.717394i | \(-0.254665\pi\) |
0.440884 | + | 0.897564i | \(0.354665\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 22.0566 | − | 67.8832i | 0.743950 | − | 2.28964i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −10.0398 | − | 30.8993i | −0.338250 | − | 1.04103i | −0.965099 | − | 0.261885i | \(-0.915656\pi\) |
0.626849 | − | 0.779140i | \(-0.284344\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −19.0062 | + | 37.3018i | −0.639611 | + | 1.25531i | 0.312606 | + | 0.949883i | \(0.398798\pi\) |
−0.952216 | + | 0.305424i | \(0.901202\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −62.2284 | − | 9.85602i | −2.09179 | − | 0.331306i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −15.7111 | + | 2.48840i | −0.527528 | + | 0.0835522i | −0.414517 | − | 0.910042i | \(-0.636049\pi\) |
−0.113011 | + | 0.993594i | \(0.536049\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 23.9896 | + | 33.0189i | 0.804586 | + | 1.10742i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 4.55565 | − | 6.27031i | 0.152620 | − | 0.210063i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −4.67758 | + | 4.67758i | −0.156529 | + | 0.156529i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 6.74346 | − | 20.7542i | 0.225409 | − | 0.693738i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −6.43376 | + | 3.27817i | −0.214817 | + | 0.109455i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 28.9136 | 0.964321 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −51.5171 | −1.71628 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −51.9352 | + | 26.4623i | −1.72830 | + | 0.880611i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 12.4589 | + | 38.3446i | 0.414148 | + | 1.27462i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −26.6340 | + | 26.6340i | −0.884368 | + | 0.884368i | −0.993975 | − | 0.109607i | \(-0.965041\pi\) |
0.109607 | + | 0.993975i | \(0.465041\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 9.21837 | − | 12.6880i | 0.305754 | − | 0.420834i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 10.7990 | + | 14.8635i | 0.357786 | + | 0.492450i | 0.949530 | − | 0.313676i | \(-0.101560\pi\) |
−0.591744 | + | 0.806126i | \(0.701560\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 29.0188 | − | 4.59613i | 0.960383 | − | 0.152110i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −3.54852 | + | 6.96435i | −0.117310 | + | 0.230234i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −15.9325 | + | 31.2692i | −0.526136 | + | 1.03260i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −3.79079 | − | 11.6668i | −0.125047 | − | 0.384854i | 0.868863 | − | 0.495053i | \(-0.164851\pi\) |
−0.993910 | + | 0.110199i | \(0.964851\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 11.6027 | − | 35.7094i | 0.382322 | − | 1.17666i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 8.83270 | + | 1.39896i | 0.290732 | + | 0.0460474i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 7.93138 | + | 50.0768i | 0.260782 | + | 1.64651i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −7.41801 | + | 46.8354i | −0.243639 | + | 1.53828i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −22.8891 | − | 7.43712i | −0.750967 | − | 0.244004i | −0.0915697 | − | 0.995799i | \(-0.529188\pi\) |
−0.659397 | + | 0.751795i | \(0.729188\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 9.83643 | − | 3.19605i | 0.322376 | − | 0.104746i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −63.9703 | − | 32.5945i | −2.09429 | − | 1.06710i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −23.1749 | + | 3.67054i | −0.757900 | + | 0.120040i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −4.35021 | − | 27.4661i | −0.142115 | − | 0.897280i | −0.950973 | − | 0.309275i | \(-0.899914\pi\) |
0.808858 | − | 0.588005i | \(-0.200086\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −57.4889 | + | 41.7682i | −1.87608 | + | 1.36305i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 26.2811 | + | 19.0943i | 0.856739 | + | 0.622458i | 0.926996 | − | 0.375071i | \(-0.122382\pi\) |
−0.0702566 | + | 0.997529i | \(0.522382\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 19.2652 | + | 19.2652i | 0.627361 | + | 0.627361i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 21.1593 | + | 29.1232i | 0.688311 | + | 0.947379i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 19.6510 | + | 38.5672i | 0.638570 | + | 1.25327i | 0.952708 | + | 0.303888i | \(0.0982847\pi\) |
−0.314137 | + | 0.949378i | \(0.601715\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 1.30511i | − | 0.0423656i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 32.6197i | 1.05777i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −17.2271 | − | 33.8100i | −0.558039 | − | 1.09521i | −0.981885 | − | 0.189479i | \(-0.939320\pi\) |
0.423845 | − | 0.905735i | \(-0.360680\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −7.84829 | + | 10.8022i | −0.253965 | + | 0.349552i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −10.9357 | − | 10.9357i | −0.353501 | − | 0.353501i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −1.82592 | − | 1.32661i | −0.0589619 | − | 0.0428383i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 61.9917 | − | 45.0396i | 1.99973 | − | 1.45289i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −13.4617 | − | 84.9940i | −0.433798 | − | 2.73889i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −13.2665 | + | 13.2665i | −0.427062 | + | 0.427062i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −34.9580 | − | 17.8120i | −1.12417 | − | 0.572795i | −0.209832 | − | 0.977738i | \(-0.567292\pi\) |
−0.914342 | + | 0.404942i | \(0.867292\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 91.9139 | − | 29.8646i | 2.95270 | − | 0.959391i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 17.7840 | + | 5.77838i | 0.570717 | + | 0.185437i | 0.580138 | − | 0.814519i | \(-0.302999\pi\) |
−0.00942088 | + | 0.999956i | \(0.502999\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1.74344 | − | 11.0077i | 0.0558922 | − | 0.352889i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 11.2968 | − | 8.20758i | 0.361786 | − | 0.262853i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 39.6220 | + | 6.27550i | 1.26762 | + | 0.200771i | 0.753786 | − | 0.657119i | \(-0.228225\pi\) |
0.513832 | + | 0.857891i | \(0.328225\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1.96937 | − | 6.06109i | 0.0629413 | − | 0.193713i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −14.3265 | − | 44.0924i | −0.457410 | − | 1.40776i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −14.9499 | + | 29.3408i | −0.476827 | + | 0.935826i | 0.519841 | + | 0.854263i | \(0.325991\pi\) |
−0.996668 | + | 0.0815629i | \(0.974009\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −20.6379 | + | 10.5156i | −0.657580 | + | 0.335054i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −7.17862 | + | 1.13698i | −0.228498 | + | 0.0361905i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 13.2701 | + | 18.2647i | 0.421963 | + | 0.580782i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −5.75905 | + | 7.92666i | −0.182942 | + | 0.251799i | −0.890632 | − | 0.454725i | \(-0.849738\pi\) |
0.707690 | + | 0.706524i | \(0.249738\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −43.1986 | + | 43.1986i | −1.37087 | + | 1.37087i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 27.1716 | 0.861397 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 19.0371 | − | 9.69989i | 0.602911 | − | 0.307198i | −0.125762 | − | 0.992060i | \(-0.540138\pi\) |
0.728673 | + | 0.684862i | \(0.240138\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −70.9249 | −2.24397 |
(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 | 400.2.bi.c.127.1 | yes | 16 | |
4.3 | odd | 2 | inner | 400.2.bi.c.127.2 | yes | 16 | |
25.13 | odd | 20 | inner | 400.2.bi.c.63.2 | yes | 16 | |
100.63 | even | 20 | inner | 400.2.bi.c.63.1 | ✓ | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
400.2.bi.c.63.1 | ✓ | 16 | 100.63 | even | 20 | inner | |
400.2.bi.c.63.2 | yes | 16 | 25.13 | odd | 20 | inner | |
400.2.bi.c.127.1 | yes | 16 | 1.1 | even | 1 | trivial | |
400.2.bi.c.127.2 | yes | 16 | 4.3 | odd | 2 | inner |