Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1850,2,Mod(149,1850)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1850, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1850.149");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1850 = 2 \cdot 5^{2} \cdot 37 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1850.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: | \(14.7723243739\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(i, \sqrt{33})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 17x^{2} + 64 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 370) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 149.4 | ||
Root | \(3.37228i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1850.149 |
Dual form | 1850.2.b.m.149.1 |
$q$-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 \(\left(\mathbb{Z}/1850\mathbb{Z}\right)^\times\).
\(n\) | \(1001\) | \(1777\) |
\(\chi(n)\) | \(1\) | \(-1\) |
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 | ||||||||
\(3\) | − 2.00000i | − 1.15470i | −0.816497 | − | 0.577350i | \(-0.804087\pi\) | ||||
0.816497 | − | 0.577350i | \(-0.195913\pi\) | |||||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 2.00000 | 0.816497 | ||||||||
\(7\) | 1.37228i | 0.518674i | 0.965787 | + | 0.259337i | \(0.0835040\pi\) | ||||
−0.965787 | + | 0.259337i | \(0.916496\pi\) | |||||||
\(8\) | − 1.00000i | − 0.353553i | ||||||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.37228 | −1.01678 | −0.508391 | − | 0.861127i | \(-0.669759\pi\) | ||||
−0.508391 | + | 0.861127i | \(0.669759\pi\) | |||||||
\(12\) | 2.00000i | 0.577350i | ||||||||
\(13\) | 4.74456i | 1.31590i | 0.753059 | + | 0.657952i | \(0.228577\pi\) | ||||
−0.753059 | + | 0.657952i | \(0.771423\pi\) | |||||||
\(14\) | −1.37228 | −0.366758 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | − 5.37228i | − 1.30297i | −0.758662 | − | 0.651485i | \(-0.774146\pi\) | ||||
0.758662 | − | 0.651485i | \(-0.225854\pi\) | |||||||
\(18\) | − 1.00000i | − 0.235702i | ||||||||
\(19\) | 2.00000 | 0.458831 | 0.229416 | − | 0.973329i | \(-0.426318\pi\) | ||||
0.229416 | + | 0.973329i | \(0.426318\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.74456 | 0.598913 | ||||||||
\(22\) | − 3.37228i | − 0.718973i | ||||||||
\(23\) | − 6.74456i | − 1.40634i | −0.711022 | − | 0.703169i | \(-0.751768\pi\) | ||||
0.711022 | − | 0.703169i | \(-0.248232\pi\) | |||||||
\(24\) | −2.00000 | −0.408248 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −4.74456 | −0.930485 | ||||||||
\(27\) | − 4.00000i | − 0.769800i | ||||||||
\(28\) | − 1.37228i | − 0.259337i | ||||||||
\(29\) | −8.11684 | −1.50726 | −0.753630 | − | 0.657299i | \(-0.771699\pi\) | ||||
−0.753630 | + | 0.657299i | \(0.771699\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.62772 | −0.471952 | −0.235976 | − | 0.971759i | \(-0.575829\pi\) | ||||
−0.235976 | + | 0.971759i | \(0.575829\pi\) | |||||||
\(32\) | 1.00000i | 0.176777i | ||||||||
\(33\) | 6.74456i | 1.17408i | ||||||||
\(34\) | 5.37228 | 0.921339 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | 1.00000i | 0.164399i | ||||||||
\(38\) | 2.00000i | 0.324443i | ||||||||
\(39\) | 9.48913 | 1.51948 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 5.37228 | 0.839009 | 0.419505 | − | 0.907753i | \(-0.362204\pi\) | ||||
0.419505 | + | 0.907753i | \(0.362204\pi\) | |||||||
\(42\) | 2.74456i | 0.423495i | ||||||||
\(43\) | − 7.37228i | − 1.12426i | −0.827048 | − | 0.562131i | \(-0.809982\pi\) | ||||
0.827048 | − | 0.562131i | \(-0.190018\pi\) | |||||||
\(44\) | 3.37228 | 0.508391 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 6.74456 | 0.994432 | ||||||||
\(47\) | − 8.74456i | − 1.27553i | −0.770233 | − | 0.637763i | \(-0.779860\pi\) | ||||
0.770233 | − | 0.637763i | \(-0.220140\pi\) | |||||||
\(48\) | − 2.00000i | − 0.288675i | ||||||||
\(49\) | 5.11684 | 0.730978 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −10.7446 | −1.50454 | ||||||||
\(52\) | − 4.74456i | − 0.657952i | ||||||||
\(53\) | − 1.37228i | − 0.188497i | −0.995549 | − | 0.0942487i | \(-0.969955\pi\) | ||||
0.995549 | − | 0.0942487i | \(-0.0300449\pi\) | |||||||
\(54\) | 4.00000 | 0.544331 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 1.37228 | 0.183379 | ||||||||
\(57\) | − 4.00000i | − 0.529813i | ||||||||
\(58\) | − 8.11684i | − 1.06579i | ||||||||
\(59\) | −12.7446 | −1.65920 | −0.829600 | − | 0.558358i | \(-0.811432\pi\) | ||||
−0.829600 | + | 0.558358i | \(0.811432\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −5.37228 | −0.687850 | −0.343925 | − | 0.938997i | \(-0.611757\pi\) | ||||
−0.343925 | + | 0.938997i | \(0.611757\pi\) | |||||||
\(62\) | − 2.62772i | − 0.333721i | ||||||||
\(63\) | − 1.37228i | − 0.172891i | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −6.74456 | −0.830198 | ||||||||
\(67\) | 4.74456i | 0.579641i | 0.957081 | + | 0.289820i | \(0.0935955\pi\) | ||||
−0.957081 | + | 0.289820i | \(0.906404\pi\) | |||||||
\(68\) | 5.37228i | 0.651485i | ||||||||
\(69\) | −13.4891 | −1.62390 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −6.74456 | −0.800432 | −0.400216 | − | 0.916421i | \(-0.631065\pi\) | ||||
−0.400216 | + | 0.916421i | \(0.631065\pi\) | |||||||
\(72\) | 1.00000i | 0.117851i | ||||||||
\(73\) | − 8.74456i | − 1.02347i | −0.859142 | − | 0.511737i | \(-0.829002\pi\) | ||||
0.859142 | − | 0.511737i | \(-0.170998\pi\) | |||||||
\(74\) | −1.00000 | −0.116248 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −2.00000 | −0.229416 | ||||||||
\(77\) | − 4.62772i | − 0.527377i | ||||||||
\(78\) | 9.48913i | 1.07443i | ||||||||
\(79\) | 4.74456 | 0.533805 | 0.266903 | − | 0.963724i | \(-0.414000\pi\) | ||||
0.266903 | + | 0.963724i | \(0.414000\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −11.0000 | −1.22222 | ||||||||
\(82\) | 5.37228i | 0.593269i | ||||||||
\(83\) | 0.744563i | 0.0817264i | 0.999165 | + | 0.0408632i | \(0.0130108\pi\) | ||||
−0.999165 | + | 0.0408632i | \(0.986989\pi\) | |||||||
\(84\) | −2.74456 | −0.299456 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 7.37228 | 0.794974 | ||||||||
\(87\) | 16.2337i | 1.74043i | ||||||||
\(88\) | 3.37228i | 0.359486i | ||||||||
\(89\) | −10.0000 | −1.06000 | −0.529999 | − | 0.847998i | \(-0.677808\pi\) | ||||
−0.529999 | + | 0.847998i | \(0.677808\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −6.51087 | −0.682525 | ||||||||
\(92\) | 6.74456i | 0.703169i | ||||||||
\(93\) | 5.25544i | 0.544963i | ||||||||
\(94\) | 8.74456 | 0.901933 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 2.00000 | 0.204124 | ||||||||
\(97\) | − 0.116844i | − 0.0118637i | −0.999982 | − | 0.00593185i | \(-0.998112\pi\) | ||||
0.999982 | − | 0.00593185i | \(-0.00188818\pi\) | |||||||
\(98\) | 5.11684i | 0.516879i | ||||||||
\(99\) | 3.37228 | 0.338927 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −11.4891 | −1.14321 | −0.571605 | − | 0.820529i | \(-0.693679\pi\) | ||||
−0.571605 | + | 0.820529i | \(0.693679\pi\) | |||||||
\(102\) | − 10.7446i | − 1.06387i | ||||||||
\(103\) | 9.48913i | 0.934991i | 0.883995 | + | 0.467496i | \(0.154844\pi\) | ||||
−0.883995 | + | 0.467496i | \(0.845156\pi\) | |||||||
\(104\) | 4.74456 | 0.465243 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 1.37228 | 0.133288 | ||||||||
\(107\) | − 3.48913i | − 0.337306i | −0.985675 | − | 0.168653i | \(-0.946058\pi\) | ||||
0.985675 | − | 0.168653i | \(-0.0539418\pi\) | |||||||
\(108\) | 4.00000i | 0.384900i | ||||||||
\(109\) | −0.116844 | −0.0111916 | −0.00559581 | − | 0.999984i | \(-0.501781\pi\) | ||||
−0.00559581 | + | 0.999984i | \(0.501781\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 2.00000 | 0.189832 | ||||||||
\(112\) | 1.37228i | 0.129668i | ||||||||
\(113\) | − 17.3723i | − 1.63425i | −0.576463 | − | 0.817123i | \(-0.695567\pi\) | ||||
0.576463 | − | 0.817123i | \(-0.304433\pi\) | |||||||
\(114\) | 4.00000 | 0.374634 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 8.11684 | 0.753630 | ||||||||
\(117\) | − 4.74456i | − 0.438635i | ||||||||
\(118\) | − 12.7446i | − 1.17323i | ||||||||
\(119\) | 7.37228 | 0.675816 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0.372281 | 0.0338438 | ||||||||
\(122\) | − 5.37228i | − 0.486383i | ||||||||
\(123\) | − 10.7446i | − 0.968805i | ||||||||
\(124\) | 2.62772 | 0.235976 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 1.37228 | 0.122253 | ||||||||
\(127\) | − 16.7446i | − 1.48584i | −0.669380 | − | 0.742920i | \(-0.733440\pi\) | ||||
0.669380 | − | 0.742920i | \(-0.266560\pi\) | |||||||
\(128\) | − 1.00000i | − 0.0883883i | ||||||||
\(129\) | −14.7446 | −1.29819 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −3.25544 | −0.284429 | −0.142214 | − | 0.989836i | \(-0.545422\pi\) | ||||
−0.142214 | + | 0.989836i | \(0.545422\pi\) | |||||||
\(132\) | − 6.74456i | − 0.587039i | ||||||||
\(133\) | 2.74456i | 0.237984i | ||||||||
\(134\) | −4.74456 | −0.409868 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −5.37228 | −0.460669 | ||||||||
\(137\) | 16.7446i | 1.43058i | 0.698825 | + | 0.715292i | \(0.253706\pi\) | ||||
−0.698825 | + | 0.715292i | \(0.746294\pi\) | |||||||
\(138\) | − 13.4891i | − 1.14827i | ||||||||
\(139\) | 1.88316 | 0.159727 | 0.0798636 | − | 0.996806i | \(-0.474552\pi\) | ||||
0.0798636 | + | 0.996806i | \(0.474552\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −17.4891 | −1.47285 | ||||||||
\(142\) | − 6.74456i | − 0.565991i | ||||||||
\(143\) | − 16.0000i | − 1.33799i | ||||||||
\(144\) | −1.00000 | −0.0833333 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 8.74456 | 0.723705 | ||||||||
\(147\) | − 10.2337i | − 0.844060i | ||||||||
\(148\) | − 1.00000i | − 0.0821995i | ||||||||
\(149\) | 11.4891 | 0.941226 | 0.470613 | − | 0.882340i | \(-0.344033\pi\) | ||||
0.470613 | + | 0.882340i | \(0.344033\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −20.0000 | −1.62758 | −0.813788 | − | 0.581161i | \(-0.802599\pi\) | ||||
−0.813788 | + | 0.581161i | \(0.802599\pi\) | |||||||
\(152\) | − 2.00000i | − 0.162221i | ||||||||
\(153\) | 5.37228i | 0.434323i | ||||||||
\(154\) | 4.62772 | 0.372912 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −9.48913 | −0.759738 | ||||||||
\(157\) | 17.3723i | 1.38646i | 0.720717 | + | 0.693229i | \(0.243813\pi\) | ||||
−0.720717 | + | 0.693229i | \(0.756187\pi\) | |||||||
\(158\) | 4.74456i | 0.377457i | ||||||||
\(159\) | −2.74456 | −0.217658 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 9.25544 | 0.729431 | ||||||||
\(162\) | − 11.0000i | − 0.864242i | ||||||||
\(163\) | − 19.3723i | − 1.51735i | −0.651467 | − | 0.758677i | \(-0.725846\pi\) | ||||
0.651467 | − | 0.758677i | \(-0.274154\pi\) | |||||||
\(164\) | −5.37228 | −0.419505 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −0.744563 | −0.0577893 | ||||||||
\(167\) | 1.48913i | 0.115232i | 0.998339 | + | 0.0576160i | \(0.0183499\pi\) | ||||
−0.998339 | + | 0.0576160i | \(0.981650\pi\) | |||||||
\(168\) | − 2.74456i | − 0.211748i | ||||||||
\(169\) | −9.51087 | −0.731606 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −2.00000 | −0.152944 | ||||||||
\(172\) | 7.37228i | 0.562131i | ||||||||
\(173\) | − 22.8614i | − 1.73812i | −0.494706 | − | 0.869060i | \(-0.664724\pi\) | ||||
0.494706 | − | 0.869060i | \(-0.335276\pi\) | |||||||
\(174\) | −16.2337 | −1.23067 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −3.37228 | −0.254195 | ||||||||
\(177\) | 25.4891i | 1.91588i | ||||||||
\(178\) | − 10.0000i | − 0.749532i | ||||||||
\(179\) | 26.2337 | 1.96080 | 0.980399 | − | 0.197023i | \(-0.0631272\pi\) | ||||
0.980399 | + | 0.197023i | \(0.0631272\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 7.48913 | 0.556662 | 0.278331 | − | 0.960485i | \(-0.410219\pi\) | ||||
0.278331 | + | 0.960485i | \(0.410219\pi\) | |||||||
\(182\) | − 6.51087i | − 0.482618i | ||||||||
\(183\) | 10.7446i | 0.794261i | ||||||||
\(184\) | −6.74456 | −0.497216 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −5.25544 | −0.385347 | ||||||||
\(187\) | 18.1168i | 1.32483i | ||||||||
\(188\) | 8.74456i | 0.637763i | ||||||||
\(189\) | 5.48913 | 0.399275 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 18.6277 | 1.34785 | 0.673927 | − | 0.738798i | \(-0.264606\pi\) | ||||
0.673927 | + | 0.738798i | \(0.264606\pi\) | |||||||
\(192\) | 2.00000i | 0.144338i | ||||||||
\(193\) | − 2.00000i | − 0.143963i | −0.997406 | − | 0.0719816i | \(-0.977068\pi\) | ||||
0.997406 | − | 0.0719816i | \(-0.0229323\pi\) | |||||||
\(194\) | 0.116844 | 0.00838891 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −5.11684 | −0.365489 | ||||||||
\(197\) | 27.4891i | 1.95852i | 0.202610 | + | 0.979260i | \(0.435058\pi\) | ||||
−0.202610 | + | 0.979260i | \(0.564942\pi\) | |||||||
\(198\) | 3.37228i | 0.239658i | ||||||||
\(199\) | 11.2554 | 0.797877 | 0.398938 | − | 0.916978i | \(-0.369379\pi\) | ||||
0.398938 | + | 0.916978i | \(0.369379\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 9.48913 | 0.669311 | ||||||||
\(202\) | − 11.4891i | − 0.808372i | ||||||||
\(203\) | − 11.1386i | − 0.781776i | ||||||||
\(204\) | 10.7446 | 0.752270 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −9.48913 | −0.661139 | ||||||||
\(207\) | 6.74456i | 0.468780i | ||||||||
\(208\) | 4.74456i | 0.328976i | ||||||||
\(209\) | −6.74456 | −0.466531 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −14.1168 | −0.971844 | −0.485922 | − | 0.874002i | \(-0.661516\pi\) | ||||
−0.485922 | + | 0.874002i | \(0.661516\pi\) | |||||||
\(212\) | 1.37228i | 0.0942487i | ||||||||
\(213\) | 13.4891i | 0.924260i | ||||||||
\(214\) | 3.48913 | 0.238512 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −4.00000 | −0.272166 | ||||||||
\(217\) | − 3.60597i | − 0.244789i | ||||||||
\(218\) | − 0.116844i | − 0.00791367i | ||||||||
\(219\) | −17.4891 | −1.18181 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 25.4891 | 1.71458 | ||||||||
\(222\) | 2.00000i | 0.134231i | ||||||||
\(223\) | 1.37228i | 0.0918948i | 0.998944 | + | 0.0459474i | \(0.0146307\pi\) | ||||
−0.998944 | + | 0.0459474i | \(0.985369\pi\) | |||||||
\(224\) | −1.37228 | −0.0916894 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 17.3723 | 1.15559 | ||||||||
\(227\) | − 11.3723i | − 0.754805i | −0.926049 | − | 0.377402i | \(-0.876817\pi\) | ||||
0.926049 | − | 0.377402i | \(-0.123183\pi\) | |||||||
\(228\) | 4.00000i | 0.264906i | ||||||||
\(229\) | 10.0000 | 0.660819 | 0.330409 | − | 0.943838i | \(-0.392813\pi\) | ||||
0.330409 | + | 0.943838i | \(0.392813\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −9.25544 | −0.608963 | ||||||||
\(232\) | 8.11684i | 0.532897i | ||||||||
\(233\) | − 6.23369i | − 0.408382i | −0.978931 | − | 0.204191i | \(-0.934544\pi\) | ||||
0.978931 | − | 0.204191i | \(-0.0654564\pi\) | |||||||
\(234\) | 4.74456 | 0.310162 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 12.7446 | 0.829600 | ||||||||
\(237\) | − 9.48913i | − 0.616385i | ||||||||
\(238\) | 7.37228i | 0.477874i | ||||||||
\(239\) | −17.6060 | −1.13884 | −0.569418 | − | 0.822048i | \(-0.692831\pi\) | ||||
−0.569418 | + | 0.822048i | \(0.692831\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −10.2337 | −0.659210 | −0.329605 | − | 0.944119i | \(-0.606916\pi\) | ||||
−0.329605 | + | 0.944119i | \(0.606916\pi\) | |||||||
\(242\) | 0.372281i | 0.0239311i | ||||||||
\(243\) | 10.0000i | 0.641500i | ||||||||
\(244\) | 5.37228 | 0.343925 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 10.7446 | 0.685048 | ||||||||
\(247\) | 9.48913i | 0.603779i | ||||||||
\(248\) | 2.62772i | 0.166860i | ||||||||
\(249\) | 1.48913 | 0.0943695 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 11.4891 | 0.725187 | 0.362594 | − | 0.931947i | \(-0.381891\pi\) | ||||
0.362594 | + | 0.931947i | \(0.381891\pi\) | |||||||
\(252\) | 1.37228i | 0.0864456i | ||||||||
\(253\) | 22.7446i | 1.42994i | ||||||||
\(254\) | 16.7446 | 1.05065 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | − 20.9783i | − 1.30859i | −0.756241 | − | 0.654294i | \(-0.772966\pi\) | ||||
0.756241 | − | 0.654294i | \(-0.227034\pi\) | |||||||
\(258\) | − 14.7446i | − 0.917956i | ||||||||
\(259\) | −1.37228 | −0.0852694 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 8.11684 | 0.502420 | ||||||||
\(262\) | − 3.25544i | − 0.201122i | ||||||||
\(263\) | − 0.116844i | − 0.00720491i | −0.999994 | − | 0.00360245i | \(-0.998853\pi\) | ||||
0.999994 | − | 0.00360245i | \(-0.00114670\pi\) | |||||||
\(264\) | 6.74456 | 0.415099 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −2.74456 | −0.168280 | ||||||||
\(267\) | 20.0000i | 1.22398i | ||||||||
\(268\) | − 4.74456i | − 0.289820i | ||||||||
\(269\) | −10.0000 | −0.609711 | −0.304855 | − | 0.952399i | \(-0.598608\pi\) | ||||
−0.304855 | + | 0.952399i | \(0.598608\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −6.74456 | −0.409703 | −0.204852 | − | 0.978793i | \(-0.565671\pi\) | ||||
−0.204852 | + | 0.978793i | \(0.565671\pi\) | |||||||
\(272\) | − 5.37228i | − 0.325742i | ||||||||
\(273\) | 13.0217i | 0.788112i | ||||||||
\(274\) | −16.7446 | −1.01158 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 13.4891 | 0.811950 | ||||||||
\(277\) | 0.744563i | 0.0447364i | 0.999750 | + | 0.0223682i | \(0.00712062\pi\) | ||||
−0.999750 | + | 0.0223682i | \(0.992879\pi\) | |||||||
\(278\) | 1.88316i | 0.112944i | ||||||||
\(279\) | 2.62772 | 0.157317 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 24.7446 | 1.47614 | 0.738068 | − | 0.674726i | \(-0.235738\pi\) | ||||
0.738068 | + | 0.674726i | \(0.235738\pi\) | |||||||
\(282\) | − 17.4891i | − 1.04146i | ||||||||
\(283\) | − 5.48913i | − 0.326295i | −0.986602 | − | 0.163147i | \(-0.947835\pi\) | ||||
0.986602 | − | 0.163147i | \(-0.0521646\pi\) | |||||||
\(284\) | 6.74456 | 0.400216 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 16.0000 | 0.946100 | ||||||||
\(287\) | 7.37228i | 0.435172i | ||||||||
\(288\) | − 1.00000i | − 0.0589256i | ||||||||
\(289\) | −11.8614 | −0.697730 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −0.233688 | −0.0136990 | ||||||||
\(292\) | 8.74456i | 0.511737i | ||||||||
\(293\) | 18.8614i | 1.10190i | 0.834540 | + | 0.550948i | \(0.185734\pi\) | ||||
−0.834540 | + | 0.550948i | \(0.814266\pi\) | |||||||
\(294\) | 10.2337 | 0.596841 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 1.00000 | 0.0581238 | ||||||||
\(297\) | 13.4891i | 0.782718i | ||||||||
\(298\) | 11.4891i | 0.665547i | ||||||||
\(299\) | 32.0000 | 1.85061 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 10.1168 | 0.583125 | ||||||||
\(302\) | − 20.0000i | − 1.15087i | ||||||||
\(303\) | 22.9783i | 1.32007i | ||||||||
\(304\) | 2.00000 | 0.114708 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −5.37228 | −0.307113 | ||||||||
\(307\) | − 23.4891i | − 1.34060i | −0.742092 | − | 0.670298i | \(-0.766166\pi\) | ||||
0.742092 | − | 0.670298i | \(-0.233834\pi\) | |||||||
\(308\) | 4.62772i | 0.263689i | ||||||||
\(309\) | 18.9783 | 1.07963 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −1.37228 | −0.0778149 | −0.0389075 | − | 0.999243i | \(-0.512388\pi\) | ||||
−0.0389075 | + | 0.999243i | \(0.512388\pi\) | |||||||
\(312\) | − 9.48913i | − 0.537216i | ||||||||
\(313\) | 3.48913i | 0.197217i | 0.995126 | + | 0.0986085i | \(0.0314392\pi\) | ||||
−0.995126 | + | 0.0986085i | \(0.968561\pi\) | |||||||
\(314\) | −17.3723 | −0.980375 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −4.74456 | −0.266903 | ||||||||
\(317\) | 25.3723i | 1.42505i | 0.701647 | + | 0.712525i | \(0.252448\pi\) | ||||
−0.701647 | + | 0.712525i | \(0.747552\pi\) | |||||||
\(318\) | − 2.74456i | − 0.153907i | ||||||||
\(319\) | 27.3723 | 1.53255 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −6.97825 | −0.389488 | ||||||||
\(322\) | 9.25544i | 0.515785i | ||||||||
\(323\) | − 10.7446i | − 0.597843i | ||||||||
\(324\) | 11.0000 | 0.611111 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 19.3723 | 1.07293 | ||||||||
\(327\) | 0.233688i | 0.0129230i | ||||||||
\(328\) | − 5.37228i | − 0.296635i | ||||||||
\(329\) | 12.0000 | 0.661581 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 23.4891 | 1.29108 | 0.645540 | − | 0.763727i | \(-0.276633\pi\) | ||||
0.645540 | + | 0.763727i | \(0.276633\pi\) | |||||||
\(332\) | − 0.744563i | − 0.0408632i | ||||||||
\(333\) | − 1.00000i | − 0.0547997i | ||||||||
\(334\) | −1.48913 | −0.0814813 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 2.74456 | 0.149728 | ||||||||
\(337\) | − 7.25544i | − 0.395229i | −0.980280 | − | 0.197614i | \(-0.936681\pi\) | ||||
0.980280 | − | 0.197614i | \(-0.0633194\pi\) | |||||||
\(338\) | − 9.51087i | − 0.517323i | ||||||||
\(339\) | −34.7446 | −1.88707 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 8.86141 | 0.479872 | ||||||||
\(342\) | − 2.00000i | − 0.108148i | ||||||||
\(343\) | 16.6277i | 0.897812i | ||||||||
\(344\) | −7.37228 | −0.397487 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 22.8614 | 1.22904 | ||||||||
\(347\) | − 22.9783i | − 1.23354i | −0.787145 | − | 0.616769i | \(-0.788441\pi\) | ||||
0.787145 | − | 0.616769i | \(-0.211559\pi\) | |||||||
\(348\) | − 16.2337i | − 0.870217i | ||||||||
\(349\) | 22.0000 | 1.17763 | 0.588817 | − | 0.808267i | \(-0.299594\pi\) | ||||
0.588817 | + | 0.808267i | \(0.299594\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 18.9783 | 1.01298 | ||||||||
\(352\) | − 3.37228i | − 0.179743i | ||||||||
\(353\) | 22.8614i | 1.21679i | 0.793634 | + | 0.608395i | \(0.208186\pi\) | ||||
−0.793634 | + | 0.608395i | \(0.791814\pi\) | |||||||
\(354\) | −25.4891 | −1.35473 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 10.0000 | 0.529999 | ||||||||
\(357\) | − 14.7446i | − 0.780365i | ||||||||
\(358\) | 26.2337i | 1.38649i | ||||||||
\(359\) | 30.9783 | 1.63497 | 0.817485 | − | 0.575950i | \(-0.195368\pi\) | ||||
0.817485 | + | 0.575950i | \(0.195368\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −15.0000 | −0.789474 | ||||||||
\(362\) | 7.48913i | 0.393620i | ||||||||
\(363\) | − 0.744563i | − 0.0390794i | ||||||||
\(364\) | 6.51087 | 0.341263 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −10.7446 | −0.561627 | ||||||||
\(367\) | 3.88316i | 0.202699i | 0.994851 | + | 0.101350i | \(0.0323160\pi\) | ||||
−0.994851 | + | 0.101350i | \(0.967684\pi\) | |||||||
\(368\) | − 6.74456i | − 0.351585i | ||||||||
\(369\) | −5.37228 | −0.279670 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.88316 | 0.0977686 | ||||||||
\(372\) | − 5.25544i | − 0.272482i | ||||||||
\(373\) | 31.4891i | 1.63045i | 0.579148 | + | 0.815223i | \(0.303385\pi\) | ||||
−0.579148 | + | 0.815223i | \(0.696615\pi\) | |||||||
\(374\) | −18.1168 | −0.936800 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −8.74456 | −0.450966 | ||||||||
\(377\) | − 38.5109i | − 1.98341i | ||||||||
\(378\) | 5.48913i | 0.282330i | ||||||||
\(379\) | 8.00000 | 0.410932 | 0.205466 | − | 0.978664i | \(-0.434129\pi\) | ||||
0.205466 | + | 0.978664i | \(0.434129\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −33.4891 | −1.71570 | ||||||||
\(382\) | 18.6277i | 0.953077i | ||||||||
\(383\) | 13.4891i | 0.689262i | 0.938738 | + | 0.344631i | \(0.111996\pi\) | ||||
−0.938738 | + | 0.344631i | \(0.888004\pi\) | |||||||
\(384\) | −2.00000 | −0.102062 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 2.00000 | 0.101797 | ||||||||
\(387\) | 7.37228i | 0.374754i | ||||||||
\(388\) | 0.116844i | 0.00593185i | ||||||||
\(389\) | −14.8614 | −0.753503 | −0.376752 | − | 0.926314i | \(-0.622959\pi\) | ||||
−0.376752 | + | 0.926314i | \(0.622959\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −36.2337 | −1.83242 | ||||||||
\(392\) | − 5.11684i | − 0.258440i | ||||||||
\(393\) | 6.51087i | 0.328430i | ||||||||
\(394\) | −27.4891 | −1.38488 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −3.37228 | −0.169464 | ||||||||
\(397\) | 24.9783i | 1.25362i | 0.779171 | + | 0.626811i | \(0.215640\pi\) | ||||
−0.779171 | + | 0.626811i | \(0.784360\pi\) | |||||||
\(398\) | 11.2554i | 0.564184i | ||||||||
\(399\) | 5.48913 | 0.274800 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 10.0000 | 0.499376 | 0.249688 | − | 0.968326i | \(-0.419672\pi\) | ||||
0.249688 | + | 0.968326i | \(0.419672\pi\) | |||||||
\(402\) | 9.48913i | 0.473275i | ||||||||
\(403\) | − 12.4674i | − 0.621044i | ||||||||
\(404\) | 11.4891 | 0.571605 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 11.1386 | 0.552799 | ||||||||
\(407\) | − 3.37228i | − 0.167158i | ||||||||
\(408\) | 10.7446i | 0.531935i | ||||||||
\(409\) | −6.23369 | −0.308236 | −0.154118 | − | 0.988052i | \(-0.549254\pi\) | ||||
−0.154118 | + | 0.988052i | \(0.549254\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 33.4891 | 1.65190 | ||||||||
\(412\) | − 9.48913i | − 0.467496i | ||||||||
\(413\) | − 17.4891i | − 0.860584i | ||||||||
\(414\) | −6.74456 | −0.331477 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −4.74456 | −0.232621 | ||||||||
\(417\) | − 3.76631i | − 0.184437i | ||||||||
\(418\) | − 6.74456i | − 0.329887i | ||||||||
\(419\) | −13.4891 | −0.658987 | −0.329493 | − | 0.944158i | \(-0.606878\pi\) | ||||
−0.329493 | + | 0.944158i | \(0.606878\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −7.48913 | −0.364998 | −0.182499 | − | 0.983206i | \(-0.558419\pi\) | ||||
−0.182499 | + | 0.983206i | \(0.558419\pi\) | |||||||
\(422\) | − 14.1168i | − 0.687197i | ||||||||
\(423\) | 8.74456i | 0.425175i | ||||||||
\(424\) | −1.37228 | −0.0666439 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −13.4891 | −0.653550 | ||||||||
\(427\) | − 7.37228i | − 0.356770i | ||||||||
\(428\) | 3.48913i | 0.168653i | ||||||||
\(429\) | −32.0000 | −1.54497 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −1.37228 | −0.0661005 | −0.0330502 | − | 0.999454i | \(-0.510522\pi\) | ||||
−0.0330502 | + | 0.999454i | \(0.510522\pi\) | |||||||
\(432\) | − 4.00000i | − 0.192450i | ||||||||
\(433\) | − 12.9783i | − 0.623695i | −0.950132 | − | 0.311847i | \(-0.899052\pi\) | ||||
0.950132 | − | 0.311847i | \(-0.100948\pi\) | |||||||
\(434\) | 3.60597 | 0.173092 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0.116844 | 0.00559581 | ||||||||
\(437\) | − 13.4891i | − 0.645272i | ||||||||
\(438\) | − 17.4891i | − 0.835663i | ||||||||
\(439\) | 13.3723 | 0.638224 | 0.319112 | − | 0.947717i | \(-0.396615\pi\) | ||||
0.319112 | + | 0.947717i | \(0.396615\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −5.11684 | −0.243659 | ||||||||
\(442\) | 25.4891i | 1.21239i | ||||||||
\(443\) | 16.9783i | 0.806661i | 0.915054 | + | 0.403331i | \(0.132148\pi\) | ||||
−0.915054 | + | 0.403331i | \(0.867852\pi\) | |||||||
\(444\) | −2.00000 | −0.0949158 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −1.37228 | −0.0649794 | ||||||||
\(447\) | − 22.9783i | − 1.08683i | ||||||||
\(448\) | − 1.37228i | − 0.0648342i | ||||||||
\(449\) | −18.0000 | −0.849473 | −0.424736 | − | 0.905317i | \(-0.639633\pi\) | ||||
−0.424736 | + | 0.905317i | \(0.639633\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −18.1168 | −0.853089 | ||||||||
\(452\) | 17.3723i | 0.817123i | ||||||||
\(453\) | 40.0000i | 1.87936i | ||||||||
\(454\) | 11.3723 | 0.533728 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −4.00000 | −0.187317 | ||||||||
\(457\) | 18.8614i | 0.882299i | 0.897434 | + | 0.441150i | \(0.145429\pi\) | ||||
−0.897434 | + | 0.441150i | \(0.854571\pi\) | |||||||
\(458\) | 10.0000i | 0.467269i | ||||||||
\(459\) | −21.4891 | −1.00303 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −39.0951 | −1.82084 | −0.910420 | − | 0.413685i | \(-0.864241\pi\) | ||||
−0.910420 | + | 0.413685i | \(0.864241\pi\) | |||||||
\(462\) | − 9.25544i | − 0.430602i | ||||||||
\(463\) | 5.48913i | 0.255101i | 0.991832 | + | 0.127551i | \(0.0407115\pi\) | ||||
−0.991832 | + | 0.127551i | \(0.959288\pi\) | |||||||
\(464\) | −8.11684 | −0.376815 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 6.23369 | 0.288770 | ||||||||
\(467\) | 30.3505i | 1.40446i | 0.711953 | + | 0.702228i | \(0.247811\pi\) | ||||
−0.711953 | + | 0.702228i | \(0.752189\pi\) | |||||||
\(468\) | 4.74456i | 0.219317i | ||||||||
\(469\) | −6.51087 | −0.300644 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 34.7446 | 1.60094 | ||||||||
\(472\) | 12.7446i | 0.586616i | ||||||||
\(473\) | 24.8614i | 1.14313i | ||||||||
\(474\) | 9.48913 | 0.435850 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −7.37228 | −0.337908 | ||||||||
\(477\) | 1.37228i | 0.0628324i | ||||||||
\(478\) | − 17.6060i | − 0.805278i | ||||||||
\(479\) | −3.25544 | −0.148745 | −0.0743724 | − | 0.997231i | \(-0.523695\pi\) | ||||
−0.0743724 | + | 0.997231i | \(0.523695\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −4.74456 | −0.216333 | ||||||||
\(482\) | − 10.2337i | − 0.466132i | ||||||||
\(483\) | − 18.5109i | − 0.842274i | ||||||||
\(484\) | −0.372281 | −0.0169219 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −10.0000 | −0.453609 | ||||||||
\(487\) | − 37.7228i | − 1.70938i | −0.519136 | − | 0.854692i | \(-0.673746\pi\) | ||||
0.519136 | − | 0.854692i | \(-0.326254\pi\) | |||||||
\(488\) | 5.37228i | 0.243192i | ||||||||
\(489\) | −38.7446 | −1.75209 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 14.9783 | 0.675959 | 0.337979 | − | 0.941153i | \(-0.390257\pi\) | ||||
0.337979 | + | 0.941153i | \(0.390257\pi\) | |||||||
\(492\) | 10.7446i | 0.484402i | ||||||||
\(493\) | 43.6060i | 1.96391i | ||||||||
\(494\) | −9.48913 | −0.426936 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −2.62772 | −0.117988 | ||||||||
\(497\) | − 9.25544i | − 0.415163i | ||||||||
\(498\) | 1.48913i | 0.0667293i | ||||||||
\(499\) | 24.9783 | 1.11818 | 0.559090 | − | 0.829107i | \(-0.311151\pi\) | ||||
0.559090 | + | 0.829107i | \(0.311151\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 2.97825 | 0.133058 | ||||||||
\(502\) | 11.4891i | 0.512785i | ||||||||
\(503\) | − 29.4891i | − 1.31486i | −0.753518 | − | 0.657428i | \(-0.771645\pi\) | ||||
0.753518 | − | 0.657428i | \(-0.228355\pi\) | |||||||
\(504\) | −1.37228 | −0.0611263 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −22.7446 | −1.01112 | ||||||||
\(507\) | 19.0217i | 0.844786i | ||||||||
\(508\) | 16.7446i | 0.742920i | ||||||||
\(509\) | 11.2554 | 0.498888 | 0.249444 | − | 0.968389i | \(-0.419752\pi\) | ||||
0.249444 | + | 0.968389i | \(0.419752\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 12.0000 | 0.530849 | ||||||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | − 8.00000i | − 0.353209i | ||||||||
\(514\) | 20.9783 | 0.925311 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 14.7446 | 0.649093 | ||||||||
\(517\) | 29.4891i | 1.29693i | ||||||||
\(518\) | − 1.37228i | − 0.0602946i | ||||||||
\(519\) | −45.7228 | −2.00701 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 27.0951 | 1.18706 | 0.593529 | − | 0.804813i | \(-0.297734\pi\) | ||||
0.593529 | + | 0.804813i | \(0.297734\pi\) | |||||||
\(522\) | 8.11684i | 0.355265i | ||||||||
\(523\) | − 28.0000i | − 1.22435i | −0.790721 | − | 0.612177i | \(-0.790294\pi\) | ||||
0.790721 | − | 0.612177i | \(-0.209706\pi\) | |||||||
\(524\) | 3.25544 | 0.142214 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0.116844 | 0.00509464 | ||||||||
\(527\) | 14.1168i | 0.614939i | ||||||||
\(528\) | 6.74456i | 0.293519i | ||||||||
\(529\) | −22.4891 | −0.977788 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 12.7446 | 0.553067 | ||||||||
\(532\) | − 2.74456i | − 0.118992i | ||||||||
\(533\) | 25.4891i | 1.10406i | ||||||||
\(534\) | −20.0000 | −0.865485 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 4.74456 | 0.204934 | ||||||||
\(537\) | − 52.4674i | − 2.26413i | ||||||||
\(538\) | − 10.0000i | − 0.431131i | ||||||||
\(539\) | −17.2554 | −0.743244 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 30.0000 | 1.28980 | 0.644900 | − | 0.764267i | \(-0.276899\pi\) | ||||
0.644900 | + | 0.764267i | \(0.276899\pi\) | |||||||
\(542\) | − 6.74456i | − 0.289704i | ||||||||
\(543\) | − 14.9783i | − 0.642778i | ||||||||
\(544\) | 5.37228 | 0.230335 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −13.0217 | −0.557279 | ||||||||
\(547\) | 39.3723i | 1.68344i | 0.539916 | + | 0.841719i | \(0.318456\pi\) | ||||
−0.539916 | + | 0.841719i | \(0.681544\pi\) | |||||||
\(548\) | − 16.7446i | − 0.715292i | ||||||||
\(549\) | 5.37228 | 0.229283 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −16.2337 | −0.691578 | ||||||||
\(552\) | 13.4891i | 0.574135i | ||||||||
\(553\) | 6.51087i | 0.276871i | ||||||||
\(554\) | −0.744563 | −0.0316334 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −1.88316 | −0.0798636 | ||||||||
\(557\) | 8.74456i | 0.370519i | 0.982690 | + | 0.185260i | \(0.0593126\pi\) | ||||
−0.982690 | + | 0.185260i | \(0.940687\pi\) | |||||||
\(558\) | 2.62772i | 0.111240i | ||||||||
\(559\) | 34.9783 | 1.47942 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 36.2337 | 1.52979 | ||||||||
\(562\) | 24.7446i | 1.04379i | ||||||||
\(563\) | − 33.0951i | − 1.39479i | −0.716686 | − | 0.697396i | \(-0.754342\pi\) | ||||
0.716686 | − | 0.697396i | \(-0.245658\pi\) | |||||||
\(564\) | 17.4891 | 0.736425 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 5.48913 | 0.230725 | ||||||||
\(567\) | − 15.0951i | − 0.633934i | ||||||||
\(568\) | 6.74456i | 0.282996i | ||||||||
\(569\) | 32.9783 | 1.38252 | 0.691260 | − | 0.722606i | \(-0.257056\pi\) | ||||
0.691260 | + | 0.722606i | \(0.257056\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −27.6060 | −1.15527 | −0.577637 | − | 0.816294i | \(-0.696025\pi\) | ||||
−0.577637 | + | 0.816294i | \(0.696025\pi\) | |||||||
\(572\) | 16.0000i | 0.668994i | ||||||||
\(573\) | − 37.2554i | − 1.55637i | ||||||||
\(574\) | −7.37228 | −0.307713 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | − 7.48913i | − 0.311776i | −0.987775 | − | 0.155888i | \(-0.950176\pi\) | ||||
0.987775 | − | 0.155888i | \(-0.0498240\pi\) | |||||||
\(578\) | − 11.8614i | − 0.493369i | ||||||||
\(579\) | −4.00000 | −0.166234 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −1.02175 | −0.0423893 | ||||||||
\(582\) | − 0.233688i | − 0.00968668i | ||||||||
\(583\) | 4.62772i | 0.191661i | ||||||||
\(584\) | −8.74456 | −0.361853 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −18.8614 | −0.779158 | ||||||||
\(587\) | 47.8397i | 1.97455i | 0.159010 | + | 0.987277i | \(0.449170\pi\) | ||||
−0.159010 | + | 0.987277i | \(0.550830\pi\) | |||||||
\(588\) | 10.2337i | 0.422030i | ||||||||
\(589\) | −5.25544 | −0.216547 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 54.9783 | 2.26150 | ||||||||
\(592\) | 1.00000i | 0.0410997i | ||||||||
\(593\) | 10.2337i | 0.420247i | 0.977675 | + | 0.210124i | \(0.0673866\pi\) | ||||
−0.977675 | + | 0.210124i | \(0.932613\pi\) | |||||||
\(594\) | −13.4891 | −0.553466 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −11.4891 | −0.470613 | ||||||||
\(597\) | − 22.5109i | − 0.921309i | ||||||||
\(598\) | 32.0000i | 1.30858i | ||||||||
\(599\) | −17.4891 | −0.714586 | −0.357293 | − | 0.933992i | \(-0.616300\pi\) | ||||
−0.357293 | + | 0.933992i | \(0.616300\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −5.37228 | −0.219140 | −0.109570 | − | 0.993979i | \(-0.534947\pi\) | ||||
−0.109570 | + | 0.993979i | \(0.534947\pi\) | |||||||
\(602\) | 10.1168i | 0.412332i | ||||||||
\(603\) | − 4.74456i | − 0.193214i | ||||||||
\(604\) | 20.0000 | 0.813788 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −22.9783 | −0.933428 | ||||||||
\(607\) | 17.7228i | 0.719347i | 0.933078 | + | 0.359673i | \(0.117112\pi\) | ||||
−0.933078 | + | 0.359673i | \(0.882888\pi\) | |||||||
\(608\) | 2.00000i | 0.0811107i | ||||||||
\(609\) | −22.2772 | −0.902717 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 41.4891 | 1.67847 | ||||||||
\(612\) | − 5.37228i | − 0.217162i | ||||||||
\(613\) | − 43.0951i | − 1.74059i | −0.492527 | − | 0.870297i | \(-0.663927\pi\) | ||||
0.492527 | − | 0.870297i | \(-0.336073\pi\) | |||||||
\(614\) | 23.4891 | 0.947944 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −4.62772 | −0.186456 | ||||||||
\(617\) | − 31.7228i | − 1.27711i | −0.769575 | − | 0.638556i | \(-0.779532\pi\) | ||||
0.769575 | − | 0.638556i | \(-0.220468\pi\) | |||||||
\(618\) | 18.9783i | 0.763417i | ||||||||
\(619\) | −30.1168 | −1.21050 | −0.605249 | − | 0.796036i | \(-0.706926\pi\) | ||||
−0.605249 | + | 0.796036i | \(0.706926\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −26.9783 | −1.08260 | ||||||||
\(622\) | − 1.37228i | − 0.0550235i | ||||||||
\(623\) | − 13.7228i | − 0.549793i | ||||||||
\(624\) | 9.48913 | 0.379869 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −3.48913 | −0.139453 | ||||||||
\(627\) | 13.4891i | 0.538704i | ||||||||
\(628\) | − 17.3723i | − 0.693229i | ||||||||
\(629\) | 5.37228 | 0.214207 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −19.0951 | −0.760164 | −0.380082 | − | 0.924953i | \(-0.624104\pi\) | ||||
−0.380082 | + | 0.924953i | \(0.624104\pi\) | |||||||
\(632\) | − 4.74456i | − 0.188729i | ||||||||
\(633\) | 28.2337i | 1.12219i | ||||||||
\(634\) | −25.3723 | −1.00766 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 2.74456 | 0.108829 | ||||||||
\(637\) | 24.2772i | 0.961897i | ||||||||
\(638\) | 27.3723i | 1.08368i | ||||||||
\(639\) | 6.74456 | 0.266811 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −49.6060 | −1.95932 | −0.979659 | − | 0.200670i | \(-0.935688\pi\) | ||||
−0.979659 | + | 0.200670i | \(0.935688\pi\) | |||||||
\(642\) | − 6.97825i | − 0.275410i | ||||||||
\(643\) | − 3.37228i | − 0.132990i | −0.997787 | − | 0.0664949i | \(-0.978818\pi\) | ||||
0.997787 | − | 0.0664949i | \(-0.0211816\pi\) | |||||||
\(644\) | −9.25544 | −0.364715 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 10.7446 | 0.422739 | ||||||||
\(647\) | − 13.4891i | − 0.530312i | −0.964205 | − | 0.265156i | \(-0.914577\pi\) | ||||
0.964205 | − | 0.265156i | \(-0.0854235\pi\) | |||||||
\(648\) | 11.0000i | 0.432121i | ||||||||
\(649\) | 42.9783 | 1.68704 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −7.21194 | −0.282658 | ||||||||
\(652\) | 19.3723i | 0.758677i | ||||||||
\(653\) | − 0.510875i | − 0.0199921i | −0.999950 | − | 0.00999604i | \(-0.996818\pi\) | ||||
0.999950 | − | 0.00999604i | \(-0.00318189\pi\) | |||||||
\(654\) | −0.233688 | −0.00913792 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 5.37228 | 0.209752 | ||||||||
\(657\) | 8.74456i | 0.341158i | ||||||||
\(658\) | 12.0000i | 0.467809i | ||||||||
\(659\) | −12.0000 | −0.467454 | −0.233727 | − | 0.972302i | \(-0.575092\pi\) | ||||
−0.233727 | + | 0.972302i | \(0.575092\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 4.35053 | 0.169216 | 0.0846080 | − | 0.996414i | \(-0.473036\pi\) | ||||
0.0846080 | + | 0.996414i | \(0.473036\pi\) | |||||||
\(662\) | 23.4891i | 0.912931i | ||||||||
\(663\) | − 50.9783i | − 1.97983i | ||||||||
\(664\) | 0.744563 | 0.0288946 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 1.00000 | 0.0387492 | ||||||||
\(667\) | 54.7446i | 2.11972i | ||||||||
\(668\) | − 1.48913i | − 0.0576160i | ||||||||
\(669\) | 2.74456 | 0.106111 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 18.1168 | 0.699393 | ||||||||
\(672\) | 2.74456i | 0.105874i | ||||||||
\(673\) | 8.51087i | 0.328070i | 0.986455 | + | 0.164035i | \(0.0524510\pi\) | ||||
−0.986455 | + | 0.164035i | \(0.947549\pi\) | |||||||
\(674\) | 7.25544 | 0.279469 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 9.51087 | 0.365803 | ||||||||
\(677\) | − 42.0000i | − 1.61419i | −0.590421 | − | 0.807096i | \(-0.701038\pi\) | ||||
0.590421 | − | 0.807096i | \(-0.298962\pi\) | |||||||
\(678\) | − 34.7446i | − 1.33436i | ||||||||
\(679\) | 0.160343 | 0.00615339 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −22.7446 | −0.871574 | ||||||||
\(682\) | 8.86141i | 0.339321i | ||||||||
\(683\) | − 8.62772i | − 0.330130i | −0.986283 | − | 0.165065i | \(-0.947217\pi\) | ||||
0.986283 | − | 0.165065i | \(-0.0527835\pi\) | |||||||
\(684\) | 2.00000 | 0.0764719 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −16.6277 | −0.634849 | ||||||||
\(687\) | − 20.0000i | − 0.763048i | ||||||||
\(688\) | − 7.37228i | − 0.281066i | ||||||||
\(689\) | 6.51087 | 0.248045 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 22.3505 | 0.850254 | 0.425127 | − | 0.905134i | \(-0.360229\pi\) | ||||
0.425127 | + | 0.905134i | \(0.360229\pi\) | |||||||
\(692\) | 22.8614i | 0.869060i | ||||||||
\(693\) | 4.62772i | 0.175792i | ||||||||
\(694\) | 22.9783 | 0.872242 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 16.2337 | 0.615336 | ||||||||
\(697\) | − 28.8614i | − 1.09320i | ||||||||
\(698\) | 22.0000i | 0.832712i | ||||||||
\(699\) | −12.4674 | −0.471559 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −26.4674 | −0.999659 | −0.499829 | − | 0.866124i | \(-0.666604\pi\) | ||||
−0.499829 | + | 0.866124i | \(0.666604\pi\) | |||||||
\(702\) | 18.9783i | 0.716288i | ||||||||
\(703\) | 2.00000i | 0.0754314i | ||||||||
\(704\) | 3.37228 | 0.127098 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −22.8614 | −0.860400 | ||||||||
\(707\) | − 15.7663i | − 0.592953i | ||||||||
\(708\) | − 25.4891i | − 0.957940i | ||||||||
\(709\) | −40.1168 | −1.50662 | −0.753310 | − | 0.657666i | \(-0.771544\pi\) | ||||
−0.753310 | + | 0.657666i | \(0.771544\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −4.74456 | −0.177935 | ||||||||
\(712\) | 10.0000i | 0.374766i | ||||||||
\(713\) | 17.7228i | 0.663725i | ||||||||
\(714\) | 14.7446 | 0.551801 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −26.2337 | −0.980399 | ||||||||
\(717\) | 35.2119i | 1.31501i | ||||||||
\(718\) | 30.9783i | 1.15610i | ||||||||
\(719\) | 34.7446 | 1.29575 | 0.647877 | − | 0.761745i | \(-0.275657\pi\) | ||||
0.647877 | + | 0.761745i | \(0.275657\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −13.0217 | −0.484955 | ||||||||
\(722\) | − 15.0000i | − 0.558242i | ||||||||
\(723\) | 20.4674i | 0.761190i | ||||||||
\(724\) | −7.48913 | −0.278331 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0.744563 | 0.0276333 | ||||||||
\(727\) | − 48.0000i | − 1.78022i | −0.455744 | − | 0.890111i | \(-0.650627\pi\) | ||||
0.455744 | − | 0.890111i | \(-0.349373\pi\) | |||||||
\(728\) | 6.51087i | 0.241309i | ||||||||
\(729\) | −13.0000 | −0.481481 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −39.6060 | −1.46488 | ||||||||
\(732\) | − 10.7446i | − 0.397130i | ||||||||
\(733\) | 29.3723i | 1.08489i | 0.840091 | + | 0.542445i | \(0.182501\pi\) | ||||
−0.840091 | + | 0.542445i | \(0.817499\pi\) | |||||||
\(734\) | −3.88316 | −0.143330 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 6.74456 | 0.248608 | ||||||||
\(737\) | − 16.0000i | − 0.589368i | ||||||||
\(738\) | − 5.37228i | − 0.197756i | ||||||||
\(739\) | 36.8614 | 1.35597 | 0.677984 | − | 0.735076i | \(-0.262854\pi\) | ||||
0.677984 | + | 0.735076i | \(0.262854\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 18.9783 | 0.697183 | ||||||||
\(742\) | 1.88316i | 0.0691328i | ||||||||
\(743\) | 5.37228i | 0.197090i | 0.995133 | + | 0.0985449i | \(0.0314188\pi\) | ||||
−0.995133 | + | 0.0985449i | \(0.968581\pi\) | |||||||
\(744\) | 5.25544 | 0.192674 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −31.4891 | −1.15290 | ||||||||
\(747\) | − 0.744563i | − 0.0272421i | ||||||||
\(748\) | − 18.1168i | − 0.662417i | ||||||||
\(749\) | 4.78806 | 0.174952 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 10.7446 | 0.392075 | 0.196037 | − | 0.980596i | \(-0.437193\pi\) | ||||
0.196037 | + | 0.980596i | \(0.437193\pi\) | |||||||
\(752\) | − 8.74456i | − 0.318881i | ||||||||
\(753\) | − 22.9783i | − 0.837374i | ||||||||
\(754\) | 38.5109 | 1.40248 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −5.48913 | −0.199638 | ||||||||
\(757\) | 43.9565i | 1.59763i | 0.601579 | + | 0.798813i | \(0.294538\pi\) | ||||
−0.601579 | + | 0.798813i | \(0.705462\pi\) | |||||||
\(758\) | 8.00000i | 0.290573i | ||||||||
\(759\) | 45.4891 | 1.65115 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 5.37228 | 0.194745 | 0.0973725 | − | 0.995248i | \(-0.468956\pi\) | ||||
0.0973725 | + | 0.995248i | \(0.468956\pi\) | |||||||
\(762\) | − 33.4891i | − 1.21318i | ||||||||
\(763\) | − 0.160343i | − 0.00580480i | ||||||||
\(764\) | −18.6277 | −0.673927 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −13.4891 | −0.487382 | ||||||||
\(767\) | − 60.4674i | − 2.18335i | ||||||||
\(768\) | − 2.00000i | − 0.0721688i | ||||||||
\(769\) | −46.2337 | −1.66723 | −0.833615 | − | 0.552346i | \(-0.813733\pi\) | ||||
−0.833615 | + | 0.552346i | \(0.813733\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −41.9565 | −1.51103 | ||||||||
\(772\) | 2.00000i | 0.0719816i | ||||||||
\(773\) | 24.3505i | 0.875828i | 0.899017 | + | 0.437914i | \(0.144283\pi\) | ||||
−0.899017 | + | 0.437914i | \(0.855717\pi\) | |||||||
\(774\) | −7.37228 | −0.264991 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −0.116844 | −0.00419445 | ||||||||
\(777\) | 2.74456i | 0.0984606i | ||||||||
\(778\) | − 14.8614i | − 0.532807i | ||||||||
\(779\) | 10.7446 | 0.384964 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 22.7446 | 0.813864 | ||||||||
\(782\) | − 36.2337i | − 1.29571i | ||||||||
\(783\) | 32.4674i | 1.16029i | ||||||||
\(784\) | 5.11684 | 0.182744 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −6.51087 | −0.232235 | ||||||||
\(787\) | − 22.0000i | − 0.784215i | −0.919919 | − | 0.392108i | \(-0.871746\pi\) | ||||
0.919919 | − | 0.392108i | \(-0.128254\pi\) | |||||||
\(788\) | − 27.4891i | − 0.979260i | ||||||||
\(789\) | −0.233688 | −0.00831951 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 23.8397 | 0.847641 | ||||||||
\(792\) | − 3.37228i | − 0.119829i | ||||||||
\(793\) | − 25.4891i | − 0.905145i | ||||||||
\(794\) | −24.9783 | −0.886445 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −11.2554 | −0.398938 | ||||||||
\(797\) | − 27.4891i | − 0.973715i | −0.873481 | − | 0.486857i | \(-0.838143\pi\) | ||||
0.873481 | − | 0.486857i | \(-0.161857\pi\) | |||||||
\(798\) | 5.48913i | 0.194313i | ||||||||
\(799\) | −46.9783 | −1.66197 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 10.0000 | 0.353333 | ||||||||
\(802\) | 10.0000i | 0.353112i | ||||||||
\(803\) | 29.4891i | 1.04065i | ||||||||
\(804\) | −9.48913 | −0.334656 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 12.4674 | 0.439145 | ||||||||
\(807\) | 20.0000i | 0.704033i | ||||||||
\(808\) | 11.4891i | 0.404186i | ||||||||
\(809\) | 51.4891 | 1.81026 | 0.905131 | − | 0.425134i | \(-0.139773\pi\) | ||||
0.905131 | + | 0.425134i | \(0.139773\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 49.4891 | 1.73780 | 0.868899 | − | 0.494989i | \(-0.164828\pi\) | ||||
0.868899 | + | 0.494989i | \(0.164828\pi\) | |||||||
\(812\) | 11.1386i | 0.390888i | ||||||||
\(813\) | 13.4891i | 0.473084i | ||||||||
\(814\) | 3.37228 | 0.118198 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −10.7446 | −0.376135 | ||||||||
\(817\) | − 14.7446i | − 0.515847i | ||||||||
\(818\) | − 6.23369i | − 0.217956i | ||||||||
\(819\) | 6.51087 | 0.227508 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −32.7446 | −1.14279 | −0.571397 | − | 0.820674i | \(-0.693598\pi\) | ||||
−0.571397 | + | 0.820674i | \(0.693598\pi\) | |||||||
\(822\) | 33.4891i | 1.16807i | ||||||||
\(823\) | 39.7228i | 1.38465i | 0.721586 | + | 0.692325i | \(0.243414\pi\) | ||||
−0.721586 | + | 0.692325i | \(0.756586\pi\) | |||||||
\(824\) | 9.48913 | 0.330569 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 17.4891 | 0.608524 | ||||||||
\(827\) | − 54.3505i | − 1.88995i | −0.327138 | − | 0.944977i | \(-0.606084\pi\) | ||||
0.327138 | − | 0.944977i | \(-0.393916\pi\) | |||||||
\(828\) | − 6.74456i | − 0.234390i | ||||||||
\(829\) | 40.3505 | 1.40143 | 0.700716 | − | 0.713440i | \(-0.252864\pi\) | ||||
0.700716 | + | 0.713440i | \(0.252864\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 1.48913 | 0.0516572 | ||||||||
\(832\) | − 4.74456i | − 0.164488i | ||||||||
\(833\) | − 27.4891i | − 0.952442i | ||||||||
\(834\) | 3.76631 | 0.130417 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 6.74456 | 0.233266 | ||||||||
\(837\) | 10.5109i | 0.363309i | ||||||||
\(838\) | − 13.4891i | − 0.465974i | ||||||||
\(839\) | 29.4891 | 1.01808 | 0.509039 | − | 0.860744i | \(-0.330001\pi\) | ||||
0.509039 | + | 0.860744i | \(0.330001\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 36.8832 | 1.27183 | ||||||||
\(842\) | − 7.48913i | − 0.258092i | ||||||||
\(843\) | − 49.4891i | − 1.70450i | ||||||||
\(844\) | 14.1168 | 0.485922 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −8.74456 | −0.300644 | ||||||||
\(847\) | 0.510875i | 0.0175539i | ||||||||
\(848\) | − 1.37228i | − 0.0471243i | ||||||||
\(849\) | −10.9783 | −0.376773 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 6.74456 | 0.231201 | ||||||||
\(852\) | − 13.4891i | − 0.462130i | ||||||||
\(853\) | − 35.4891i | − 1.21512i | −0.794272 | − | 0.607562i | \(-0.792148\pi\) | ||||
0.794272 | − | 0.607562i | \(-0.207852\pi\) | |||||||
\(854\) | 7.37228 | 0.252274 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −3.48913 | −0.119256 | ||||||||
\(857\) | − 29.1386i | − 0.995355i | −0.867362 | − | 0.497678i | \(-0.834186\pi\) | ||||
0.867362 | − | 0.497678i | \(-0.165814\pi\) | |||||||
\(858\) | − 32.0000i | − 1.09246i | ||||||||
\(859\) | 19.7228 | 0.672934 | 0.336467 | − | 0.941695i | \(-0.390768\pi\) | ||||
0.336467 | + | 0.941695i | \(0.390768\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 14.7446 | 0.502493 | ||||||||
\(862\) | − 1.37228i | − 0.0467401i | ||||||||
\(863\) | − 53.8397i | − 1.83272i | −0.400352 | − | 0.916362i | \(-0.631112\pi\) | ||||
0.400352 | − | 0.916362i | \(-0.368888\pi\) | |||||||
\(864\) | 4.00000 | 0.136083 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 12.9783 | 0.441019 | ||||||||
\(867\) | 23.7228i | 0.805669i | ||||||||
\(868\) | 3.60597i | 0.122395i | ||||||||
\(869\) | −16.0000 | −0.542763 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −22.5109 | −0.762752 | ||||||||
\(872\) | 0.116844i | 0.00395684i | ||||||||
\(873\) | 0.116844i | 0.00395457i | ||||||||
\(874\) | 13.4891 | 0.456276 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 17.4891 | 0.590903 | ||||||||
\(877\) | 49.3723i | 1.66718i | 0.552381 | + | 0.833592i | \(0.313719\pi\) | ||||
−0.552381 | + | 0.833592i | \(0.686281\pi\) | |||||||
\(878\) | 13.3723i | 0.451293i | ||||||||
\(879\) | 37.7228 | 1.27236 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1.37228 | 0.0462333 | 0.0231167 | − | 0.999733i | \(-0.492641\pi\) | ||||
0.0231167 | + | 0.999733i | \(0.492641\pi\) | |||||||
\(882\) | − 5.11684i | − 0.172293i | ||||||||
\(883\) | 11.3723i | 0.382708i | 0.981521 | + | 0.191354i | \(0.0612878\pi\) | ||||
−0.981521 | + | 0.191354i | \(0.938712\pi\) | |||||||
\(884\) | −25.4891 | −0.857292 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −16.9783 | −0.570395 | ||||||||
\(887\) | − 25.3723i | − 0.851918i | −0.904743 | − | 0.425959i | \(-0.859937\pi\) | ||||
0.904743 | − | 0.425959i | \(-0.140063\pi\) | |||||||
\(888\) | − 2.00000i | − 0.0671156i | ||||||||
\(889\) | 22.9783 | 0.770666 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 37.0951 | 1.24273 | ||||||||
\(892\) | − 1.37228i | − 0.0459474i | ||||||||
\(893\) | − 17.4891i | − 0.585251i | ||||||||
\(894\) | 22.9783 | 0.768508 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 1.37228 | 0.0458447 | ||||||||
\(897\) | − 64.0000i | − 2.13690i | ||||||||
\(898\) | − 18.0000i | − 0.600668i | ||||||||
\(899\) | 21.3288 | 0.711355 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −7.37228 | −0.245606 | ||||||||
\(902\) | − 18.1168i | − 0.603225i | ||||||||
\(903\) | − 20.2337i | − 0.673335i | ||||||||
\(904\) | −17.3723 | −0.577793 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −40.0000 | −1.32891 | ||||||||
\(907\) | 40.4674i | 1.34370i | 0.740689 | + | 0.671849i | \(0.234499\pi\) | ||||
−0.740689 | + | 0.671849i | \(0.765501\pi\) | |||||||
\(908\) | 11.3723i | 0.377402i | ||||||||
\(909\) | 11.4891 | 0.381070 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 17.7663 | 0.588624 | 0.294312 | − | 0.955709i | \(-0.404909\pi\) | ||||
0.294312 | + | 0.955709i | \(0.404909\pi\) | |||||||
\(912\) | − 4.00000i | − 0.132453i | ||||||||
\(913\) | − 2.51087i | − 0.0830978i | ||||||||
\(914\) | −18.8614 | −0.623880 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −10.0000 | −0.330409 | ||||||||
\(917\) | − 4.46738i | − 0.147526i | ||||||||
\(918\) | − 21.4891i | − 0.709247i | ||||||||
\(919\) | −7.72281 | −0.254752 | −0.127376 | − | 0.991854i | \(-0.540656\pi\) | ||||
−0.127376 | + | 0.991854i | \(0.540656\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −46.9783 | −1.54799 | ||||||||
\(922\) | − 39.0951i | − 1.28753i | ||||||||
\(923\) | − 32.0000i | − 1.05329i | ||||||||
\(924\) | 9.25544 | 0.304482 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −5.48913 | −0.180384 | ||||||||
\(927\) | − 9.48913i | − 0.311664i | ||||||||
\(928\) | − 8.11684i | − 0.266448i | ||||||||
\(929\) | −31.0951 | −1.02020 | −0.510098 | − | 0.860116i | \(-0.670391\pi\) | ||||
−0.510098 | + | 0.860116i | \(0.670391\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 10.2337 | 0.335396 | ||||||||
\(932\) | 6.23369i | 0.204191i | ||||||||
\(933\) | 2.74456i | 0.0898529i | ||||||||
\(934\) | −30.3505 | −0.993100 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −4.74456 | −0.155081 | ||||||||
\(937\) | 36.9783i | 1.20803i | 0.796974 | + | 0.604013i | \(0.206433\pi\) | ||||
−0.796974 | + | 0.604013i | \(0.793567\pi\) | |||||||
\(938\) | − 6.51087i | − 0.212588i | ||||||||
\(939\) | 6.97825 | 0.227727 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 18.0000 | 0.586783 | 0.293392 | − | 0.955992i | \(-0.405216\pi\) | ||||
0.293392 | + | 0.955992i | \(0.405216\pi\) | |||||||
\(942\) | 34.7446i | 1.13204i | ||||||||
\(943\) | − 36.2337i | − 1.17993i | ||||||||
\(944\) | −12.7446 | −0.414800 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −24.8614 | −0.808314 | ||||||||
\(947\) | 37.0951i | 1.20543i | 0.797957 | + | 0.602714i | \(0.205914\pi\) | ||||
−0.797957 | + | 0.602714i | \(0.794086\pi\) | |||||||
\(948\) | 9.48913i | 0.308192i | ||||||||
\(949\) | 41.4891 | 1.34679 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 50.7446 | 1.64551 | ||||||||
\(952\) | − 7.37228i | − 0.238937i | ||||||||
\(953\) | − 46.2337i | − 1.49766i | −0.662764 | − | 0.748828i | \(-0.730617\pi\) | ||||
0.662764 | − | 0.748828i | \(-0.269383\pi\) | |||||||
\(954\) | −1.37228 | −0.0444292 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 17.6060 | 0.569418 | ||||||||
\(957\) | − 54.7446i | − 1.76964i | ||||||||
\(958\) | − 3.25544i | − 0.105178i | ||||||||
\(959\) | −22.9783 | −0.742006 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −24.0951 | −0.777261 | ||||||||
\(962\) | − 4.74456i | − 0.152971i | ||||||||
\(963\) | 3.48913i | 0.112435i | ||||||||
\(964\) | 10.2337 | 0.329605 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 18.5109 | 0.595578 | ||||||||
\(967\) | − 28.0000i | − 0.900419i | −0.892923 | − | 0.450210i | \(-0.851349\pi\) | ||||
0.892923 | − | 0.450210i | \(-0.148651\pi\) | |||||||
\(968\) | − 0.372281i | − 0.0119656i | ||||||||
\(969\) | −21.4891 | −0.690330 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −19.6060 | −0.629185 | −0.314593 | − | 0.949227i | \(-0.601868\pi\) | ||||
−0.314593 | + | 0.949227i | \(0.601868\pi\) | |||||||
\(972\) | − 10.0000i | − 0.320750i | ||||||||
\(973\) | 2.58422i | 0.0828463i | ||||||||
\(974\) | 37.7228 | 1.20872 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −5.37228 | −0.171963 | ||||||||
\(977\) | − 11.8832i | − 0.380176i | −0.981767 | − | 0.190088i | \(-0.939123\pi\) | ||||
0.981767 | − | 0.190088i | \(-0.0608773\pi\) | |||||||
\(978\) | − 38.7446i | − 1.23891i | ||||||||
\(979\) | 33.7228 | 1.07779 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0.116844 | 0.00373054 | ||||||||
\(982\) | 14.9783i | 0.477975i | ||||||||
\(983\) | − 30.8614i | − 0.984326i | −0.870503 | − | 0.492163i | \(-0.836206\pi\) | ||||
0.870503 | − | 0.492163i | \(-0.163794\pi\) | |||||||
\(984\) | −10.7446 | −0.342524 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −43.6060 | −1.38870 | ||||||||
\(987\) | − 24.0000i | − 0.763928i | ||||||||
\(988\) | − 9.48913i | − 0.301889i | ||||||||
\(989\) | −49.7228 | −1.58109 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 25.6060 | 0.813400 | 0.406700 | − | 0.913562i | \(-0.366679\pi\) | ||||
0.406700 | + | 0.913562i | \(0.366679\pi\) | |||||||
\(992\) | − 2.62772i | − 0.0834302i | ||||||||
\(993\) | − 46.9783i | − 1.49081i | ||||||||
\(994\) | 9.25544 | 0.293565 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −1.48913 | −0.0471847 | ||||||||
\(997\) | 26.2337i | 0.830829i | 0.909632 | + | 0.415415i | \(0.136363\pi\) | ||||
−0.909632 | + | 0.415415i | \(0.863637\pi\) | |||||||
\(998\) | 24.9783i | 0.790673i | ||||||||
\(999\) | 4.00000 | 0.126554 |
(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 | 1850.2.b.m.149.4 | 4 | ||
5.2 | odd | 4 | 1850.2.a.q.1.1 | 2 | |||
5.3 | odd | 4 | 370.2.a.f.1.2 | ✓ | 2 | ||
5.4 | even | 2 | inner | 1850.2.b.m.149.1 | 4 | ||
15.8 | even | 4 | 3330.2.a.bb.1.2 | 2 | |||
20.3 | even | 4 | 2960.2.a.o.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
370.2.a.f.1.2 | ✓ | 2 | 5.3 | odd | 4 | ||
1850.2.a.q.1.1 | 2 | 5.2 | odd | 4 | |||
1850.2.b.m.149.1 | 4 | 5.4 | even | 2 | inner | ||
1850.2.b.m.149.4 | 4 | 1.1 | even | 1 | trivial | ||
2960.2.a.o.1.1 | 2 | 20.3 | even | 4 | |||
3330.2.a.bb.1.2 | 2 | 15.8 | even | 4 |