Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [729,2,Mod(244,729)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(729, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("729.244");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 729 = 3^{6} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 729.c (of order \(3\), degree \(2\), 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: | \(5.82109430735\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{3})\) |
Coefficient field: | 12.0.1952986685049.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 6 x^{11} + 27 x^{10} - 80 x^{9} + 186 x^{8} - 330 x^{7} + 463 x^{6} - 504 x^{5} + 420 x^{4} + \cdots + 3 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{4}]\) |
Coefficient ring index: | \( 3^{3} \) |
Twist minimal: | no (minimal twist has level 27) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 487.4 | ||
Root | \(0.500000 + 0.258654i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 729.487 |
Dual form | 729.2.c.b.244.4 |
$q$-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 \(\left(\mathbb{Z}/729\mathbb{Z}\right)^\times\).
\(n\) | \(2\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.207733 | + | 0.359804i | −0.146889 | + | 0.254420i | −0.930076 | − | 0.367366i | \(-0.880260\pi\) |
0.783187 | + | 0.621786i | \(0.213593\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0.913694 | + | 1.58256i | 0.456847 | + | 0.791282i | ||||
\(5\) | 1.10759 | + | 1.91841i | 0.495331 | + | 0.857938i | 0.999986 | − | 0.00538314i | \(-0.00171351\pi\) |
−0.504655 | + | 0.863321i | \(0.668380\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.659815 | − | 1.14283i | 0.249386 | − | 0.431950i | −0.713969 | − | 0.700177i | \(-0.753104\pi\) |
0.963356 | + | 0.268227i | \(0.0864377\pi\) | |||||||
\(8\) | −1.59015 | −0.562203 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −0.920335 | −0.291036 | ||||||||
\(11\) | −2.60759 | + | 4.51648i | −0.786219 | + | 1.36177i | 0.142049 | + | 0.989860i | \(0.454631\pi\) |
−0.928268 | + | 0.371912i | \(0.878702\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.00902926 | + | 0.0156391i | 0.00250427 | + | 0.00433752i | 0.867275 | − | 0.497830i | \(-0.165870\pi\) |
−0.864771 | + | 0.502167i | \(0.832536\pi\) | |||||||
\(14\) | 0.274131 | + | 0.474808i | 0.0732645 | + | 0.126898i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −1.49706 | + | 2.59299i | −0.374265 | + | 0.648246i | ||||
\(17\) | 3.13280 | 0.759814 | 0.379907 | − | 0.925025i | \(-0.375956\pi\) | ||||
0.379907 | + | 0.925025i | \(0.375956\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.417352 | 0.0957472 | 0.0478736 | − | 0.998853i | \(-0.484756\pi\) | ||||
0.0478736 | + | 0.998853i | \(0.484756\pi\) | |||||||
\(20\) | −2.02400 | + | 3.50568i | −0.452581 | + | 0.783893i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −1.08337 | − | 1.87645i | −0.230975 | − | 0.400060i | ||||
\(23\) | −0.517193 | − | 0.895805i | −0.107842 | − | 0.186788i | 0.807054 | − | 0.590478i | \(-0.201061\pi\) |
−0.914896 | + | 0.403690i | \(0.867727\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0.0464738 | − | 0.0804949i | 0.00929475 | − | 0.0160990i | ||||
\(26\) | −0.00750270 | −0.00147140 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 2.41147 | 0.455726 | ||||||||
\(29\) | −3.90361 | + | 6.76125i | −0.724882 | + | 1.25553i | 0.234140 | + | 0.972203i | \(0.424773\pi\) |
−0.959022 | + | 0.283330i | \(0.908561\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.86483 | − | 3.22998i | −0.334934 | − | 0.580122i | 0.648538 | − | 0.761182i | \(-0.275381\pi\) |
−0.983472 | + | 0.181060i | \(0.942047\pi\) | |||||||
\(32\) | −2.21213 | − | 3.83152i | −0.391053 | − | 0.677323i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −0.650785 | + | 1.12719i | −0.111609 | + | 0.193312i | ||||
\(35\) | 2.92322 | 0.494115 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.42476 | 0.727426 | 0.363713 | − | 0.931511i | \(-0.381509\pi\) | ||||
0.363713 | + | 0.931511i | \(0.381509\pi\) | |||||||
\(38\) | −0.0866979 | + | 0.150165i | −0.0140643 | + | 0.0243600i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −1.76124 | − | 3.05056i | −0.278477 | − | 0.482335i | ||||
\(41\) | −1.83747 | − | 3.18259i | −0.286965 | − | 0.497037i | 0.686119 | − | 0.727489i | \(-0.259313\pi\) |
−0.973084 | + | 0.230452i | \(0.925980\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.15394 | − | 7.19483i | 0.633469 | − | 1.09720i | −0.353368 | − | 0.935484i | \(-0.614964\pi\) |
0.986837 | − | 0.161717i | \(-0.0517031\pi\) | |||||||
\(44\) | −9.53017 | −1.43673 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0.429753 | 0.0633636 | ||||||||
\(47\) | −3.54895 | + | 6.14697i | −0.517668 | + | 0.896628i | 0.482121 | + | 0.876105i | \(0.339867\pi\) |
−0.999789 | + | 0.0205231i | \(0.993467\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 2.62929 | + | 4.55406i | 0.375613 | + | 0.650580i | ||||
\(50\) | 0.0193083 | + | 0.0334429i | 0.00273060 | + | 0.00472954i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −0.0165000 | + | 0.0285788i | −0.00228813 | + | 0.00396316i | ||||
\(53\) | 1.30057 | 0.178648 | 0.0893238 | − | 0.996003i | \(-0.471529\pi\) | ||||
0.0893238 | + | 0.996003i | \(0.471529\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −11.5526 | −1.55775 | ||||||||
\(56\) | −1.04920 | + | 1.81728i | −0.140206 | + | 0.242844i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −1.62182 | − | 2.80907i | −0.212955 | − | 0.368849i | ||||
\(59\) | −1.85091 | − | 3.20586i | −0.240967 | − | 0.417368i | 0.720023 | − | 0.693950i | \(-0.244131\pi\) |
−0.960990 | + | 0.276583i | \(0.910798\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3.45712 | + | 5.98791i | −0.442639 | + | 0.766673i | −0.997884 | − | 0.0650137i | \(-0.979291\pi\) |
0.555246 | + | 0.831686i | \(0.312624\pi\) | |||||||
\(62\) | 1.54955 | 0.196793 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −4.15011 | −0.518764 | ||||||||
\(65\) | −0.0200015 | + | 0.0346436i | −0.00248088 | + | 0.00429701i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 5.51340 | + | 9.54949i | 0.673569 | + | 1.16666i | 0.976885 | + | 0.213765i | \(0.0685728\pi\) |
−0.303316 | + | 0.952890i | \(0.598094\pi\) | |||||||
\(68\) | 2.86242 | + | 4.95785i | 0.347119 | + | 0.601228i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −0.607251 | + | 1.05179i | −0.0725803 | + | 0.125713i | ||||
\(71\) | 6.08428 | 0.722071 | 0.361035 | − | 0.932552i | \(-0.382423\pi\) | ||||
0.361035 | + | 0.932552i | \(0.382423\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −0.546973 | −0.0640183 | −0.0320092 | − | 0.999488i | \(-0.510191\pi\) | ||||
−0.0320092 | + | 0.999488i | \(0.510191\pi\) | |||||||
\(74\) | −0.919169 | + | 1.59205i | −0.106851 | + | 0.185072i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0.381332 | + | 0.660487i | 0.0437418 | + | 0.0757630i | ||||
\(77\) | 3.44106 | + | 5.96008i | 0.392145 | + | 0.679215i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −0.244572 | + | 0.423611i | −0.0275165 | + | 0.0476600i | −0.879456 | − | 0.475981i | \(-0.842093\pi\) |
0.851939 | + | 0.523641i | \(0.175427\pi\) | |||||||
\(80\) | −6.63254 | −0.741540 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 1.52681 | 0.168608 | ||||||||
\(83\) | 2.30684 | − | 3.99556i | 0.253208 | − | 0.438569i | −0.711199 | − | 0.702991i | \(-0.751848\pi\) |
0.964407 | + | 0.264421i | \(0.0851809\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 3.46986 | + | 6.00998i | 0.376360 | + | 0.651874i | ||||
\(86\) | 1.72582 | + | 2.98921i | 0.186100 | + | 0.322335i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 4.14647 | − | 7.18189i | 0.442015 | − | 0.765592i | ||||
\(89\) | 3.37307 | 0.357544 | 0.178772 | − | 0.983891i | \(-0.442788\pi\) | ||||
0.178772 | + | 0.983891i | \(0.442788\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.0238305 | 0.00249812 | ||||||||
\(92\) | 0.945113 | − | 1.63698i | 0.0985348 | − | 0.170667i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −1.47447 | − | 2.55386i | −0.152080 | − | 0.263410i | ||||
\(95\) | 0.462257 | + | 0.800652i | 0.0474265 | + | 0.0821452i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −4.97068 | + | 8.60947i | −0.504696 | + | 0.874159i | 0.495289 | + | 0.868728i | \(0.335062\pi\) |
−0.999985 | + | 0.00543103i | \(0.998271\pi\) | |||||||
\(98\) | −2.18476 | −0.220694 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0.169851 | 0.0169851 | ||||||||
\(101\) | 6.89974 | − | 11.9507i | 0.686550 | − | 1.18914i | −0.286397 | − | 0.958111i | \(-0.592458\pi\) |
0.972947 | − | 0.231029i | \(-0.0742092\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −2.28256 | − | 3.95351i | −0.224907 | − | 0.389551i | 0.731384 | − | 0.681966i | \(-0.238875\pi\) |
−0.956292 | + | 0.292415i | \(0.905541\pi\) | |||||||
\(104\) | −0.0143579 | − | 0.0248686i | −0.00140791 | − | 0.00243856i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −0.270172 | + | 0.467952i | −0.0262415 | + | 0.0454515i | ||||
\(107\) | 11.2965 | 1.09207 | 0.546035 | − | 0.837762i | \(-0.316136\pi\) | ||||
0.546035 | + | 0.837762i | \(0.316136\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 14.5032 | 1.38915 | 0.694577 | − | 0.719419i | \(-0.255592\pi\) | ||||
0.694577 | + | 0.719419i | \(0.255592\pi\) | |||||||
\(110\) | 2.39986 | − | 4.15668i | 0.228818 | − | 0.396324i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 1.97557 | + | 3.42178i | 0.186673 | + | 0.323328i | ||||
\(113\) | 6.27921 | + | 10.8759i | 0.590699 | + | 1.02312i | 0.994139 | + | 0.108114i | \(0.0344811\pi\) |
−0.403440 | + | 0.915006i | \(0.632186\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.14568 | − | 1.98438i | 0.106835 | − | 0.185044i | ||||
\(116\) | −14.2668 | −1.32464 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 1.53798 | 0.141582 | ||||||||
\(119\) | 2.06706 | − | 3.58026i | 0.189487 | − | 0.328202i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −8.09909 | − | 14.0280i | −0.736281 | − | 1.27528i | ||||
\(122\) | −1.43632 | − | 2.48777i | −0.130038 | − | 0.225232i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 3.40777 | − | 5.90243i | 0.306027 | − | 0.530054i | ||||
\(125\) | 11.2818 | 1.00908 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −8.39499 | −0.744935 | −0.372467 | − | 0.928045i | \(-0.621488\pi\) | ||||
−0.372467 | + | 0.928045i | \(0.621488\pi\) | |||||||
\(128\) | 5.28637 | − | 9.15627i | 0.467254 | − | 0.809307i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −0.00830995 | − | 0.0143932i | −0.000728831 | − | 0.00126237i | ||||
\(131\) | −7.76745 | − | 13.4536i | −0.678645 | − | 1.17545i | −0.975389 | − | 0.220491i | \(-0.929234\pi\) |
0.296744 | − | 0.954957i | \(-0.404099\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.275375 | − | 0.476964i | 0.0238781 | − | 0.0413580i | ||||
\(134\) | −4.58126 | −0.395761 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −4.98162 | −0.427170 | ||||||||
\(137\) | 6.00370 | − | 10.3987i | 0.512930 | − | 0.888421i | −0.486957 | − | 0.873426i | \(-0.661893\pi\) |
0.999888 | − | 0.0149956i | \(-0.00477344\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −3.07256 | − | 5.32183i | −0.260611 | − | 0.451392i | 0.705793 | − | 0.708418i | \(-0.250591\pi\) |
−0.966404 | + | 0.257026i | \(0.917257\pi\) | |||||||
\(140\) | 2.67093 | + | 4.62619i | 0.225735 | + | 0.390985i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −1.26391 | + | 2.18915i | −0.106065 | + | 0.183709i | ||||
\(143\) | −0.0941785 | −0.00787561 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −17.2945 | −1.43623 | ||||||||
\(146\) | 0.113624 | − | 0.196803i | 0.00940362 | − | 0.0162876i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 4.04287 | + | 7.00246i | 0.332322 | + | 0.575599i | ||||
\(149\) | 0.441410 | + | 0.764545i | 0.0361617 | + | 0.0626340i | 0.883540 | − | 0.468356i | \(-0.155154\pi\) |
−0.847378 | + | 0.530990i | \(0.821820\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −4.11274 | + | 7.12347i | −0.334690 | + | 0.579700i | −0.983425 | − | 0.181314i | \(-0.941965\pi\) |
0.648735 | + | 0.761014i | \(0.275298\pi\) | |||||||
\(152\) | −0.663653 | −0.0538294 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −2.85929 | −0.230408 | ||||||||
\(155\) | 4.13095 | − | 7.15502i | 0.331806 | − | 0.574705i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −6.27991 | − | 10.8771i | −0.501192 | − | 0.868089i | −0.999999 | − | 0.00137640i | \(-0.999562\pi\) |
0.498808 | − | 0.866713i | \(-0.333771\pi\) | |||||||
\(158\) | −0.101611 | − | 0.175996i | −0.00808377 | − | 0.0140015i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 4.90028 | − | 8.48753i | 0.387401 | − | 0.670998i | ||||
\(161\) | −1.36501 | −0.107578 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 3.31466 | 0.259624 | 0.129812 | − | 0.991539i | \(-0.458563\pi\) | ||||
0.129812 | + | 0.991539i | \(0.458563\pi\) | |||||||
\(164\) | 3.35777 | − | 5.81583i | 0.262198 | − | 0.454140i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0.958412 | + | 1.66002i | 0.0743872 | + | 0.128842i | ||||
\(167\) | −10.2815 | − | 17.8081i | −0.795606 | − | 1.37803i | −0.922454 | − | 0.386107i | \(-0.873820\pi\) |
0.126848 | − | 0.991922i | \(-0.459514\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 6.49984 | − | 11.2580i | 0.499987 | − | 0.866004i | ||||
\(170\) | −2.88322 | −0.221133 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 15.1817 | 1.15759 | ||||||||
\(173\) | 7.01663 | − | 12.1532i | 0.533465 | − | 0.923988i | −0.465771 | − | 0.884905i | \(-0.654223\pi\) |
0.999236 | − | 0.0390830i | \(-0.0124437\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −0.0613281 | − | 0.106223i | −0.00463597 | − | 0.00802974i | ||||
\(176\) | −7.80745 | − | 13.5229i | −0.588509 | − | 1.01933i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −0.700697 | + | 1.21364i | −0.0525195 | + | 0.0909664i | ||||
\(179\) | −10.1900 | −0.761636 | −0.380818 | − | 0.924650i | \(-0.624358\pi\) | ||||
−0.380818 | + | 0.924650i | \(0.624358\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 24.0547 | 1.78797 | 0.893987 | − | 0.448093i | \(-0.147897\pi\) | ||||
0.893987 | + | 0.448093i | \(0.147897\pi\) | |||||||
\(182\) | −0.00495039 | + | 0.00857433i | −0.000366948 | + | 0.000635572i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0.822415 | + | 1.42446i | 0.0606292 | + | 0.105013i | ||||
\(185\) | 4.90083 | + | 8.48849i | 0.360316 | + | 0.624086i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −8.16906 | + | 14.1492i | −0.597381 | + | 1.03469i | ||||
\(188\) | −12.9706 | −0.945981 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −0.384104 | −0.0278658 | ||||||||
\(191\) | 5.47318 | − | 9.47983i | 0.396026 | − | 0.685937i | −0.597206 | − | 0.802088i | \(-0.703722\pi\) |
0.993232 | + | 0.116151i | \(0.0370558\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 5.40298 | + | 9.35824i | 0.388915 | + | 0.673621i | 0.992304 | − | 0.123826i | \(-0.0395166\pi\) |
−0.603389 | + | 0.797447i | \(0.706183\pi\) | |||||||
\(194\) | −2.06515 | − | 3.57694i | −0.148269 | − | 0.256810i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −4.80473 | + | 8.32204i | −0.343195 | + | 0.594431i | ||||
\(197\) | 22.0734 | 1.57266 | 0.786331 | − | 0.617806i | \(-0.211978\pi\) | ||||
0.786331 | + | 0.617806i | \(0.211978\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 12.8868 | 0.913518 | 0.456759 | − | 0.889590i | \(-0.349010\pi\) | ||||
0.456759 | + | 0.889590i | \(0.349010\pi\) | |||||||
\(200\) | −0.0739003 | + | 0.127999i | −0.00522554 | + | 0.00905090i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 2.86661 | + | 4.96512i | 0.201694 | + | 0.349344i | ||||
\(203\) | 5.15132 | + | 8.92235i | 0.361552 | + | 0.626226i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 4.07034 | − | 7.05003i | 0.284285 | − | 0.492396i | ||||
\(206\) | 1.89665 | 0.132146 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −0.0540694 | −0.00374904 | ||||||||
\(209\) | −1.08829 | + | 1.88497i | −0.0752783 | + | 0.130386i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 11.9978 | + | 20.7808i | 0.825964 | + | 1.43061i | 0.901181 | + | 0.433444i | \(0.142702\pi\) |
−0.0752168 | + | 0.997167i | \(0.523965\pi\) | |||||||
\(212\) | 1.18833 | + | 2.05824i | 0.0816146 | + | 0.141361i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −2.34665 | + | 4.06452i | −0.160414 | + | 0.277845i | ||||
\(215\) | 18.4035 | 1.25511 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −4.92177 | −0.334112 | ||||||||
\(218\) | −3.01279 | + | 5.21831i | −0.204052 | + | 0.353428i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −10.5556 | − | 18.2828i | −0.711655 | − | 1.23262i | ||||
\(221\) | 0.0282868 | + | 0.0489942i | 0.00190278 | + | 0.00329571i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −10.8311 | + | 18.7600i | −0.725303 | + | 1.25626i | 0.233546 | + | 0.972346i | \(0.424967\pi\) |
−0.958849 | + | 0.283916i | \(0.908366\pi\) | |||||||
\(224\) | −5.83838 | −0.390093 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −5.21760 | −0.347070 | ||||||||
\(227\) | 10.8209 | − | 18.7424i | 0.718211 | − | 1.24398i | −0.243497 | − | 0.969902i | \(-0.578295\pi\) |
0.961708 | − | 0.274076i | \(-0.0883720\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 5.40268 | + | 9.35772i | 0.357019 | + | 0.618375i | 0.987461 | − | 0.157861i | \(-0.0504598\pi\) |
−0.630442 | + | 0.776236i | \(0.717126\pi\) | |||||||
\(230\) | 0.475991 | + | 0.824441i | 0.0313859 | + | 0.0543620i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 6.20733 | − | 10.7514i | 0.407531 | − | 0.705865i | ||||
\(233\) | −7.63900 | −0.500447 | −0.250224 | − | 0.968188i | \(-0.580504\pi\) | ||||
−0.250224 | + | 0.968188i | \(0.580504\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −15.7232 | −1.02567 | ||||||||
\(236\) | 3.38232 | − | 5.85835i | 0.220170 | − | 0.381346i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0.858795 | + | 1.48748i | 0.0556674 | + | 0.0964188i | ||||
\(239\) | −1.61575 | − | 2.79855i | −0.104514 | − | 0.181023i | 0.809026 | − | 0.587773i | \(-0.199995\pi\) |
−0.913540 | + | 0.406750i | \(0.866662\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 13.2725 | − | 22.9886i | 0.854955 | − | 1.48083i | −0.0217316 | − | 0.999764i | \(-0.506918\pi\) |
0.876687 | − | 0.481062i | \(-0.159749\pi\) | |||||||
\(242\) | 6.72979 | 0.432608 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −12.6350 | −0.808873 | ||||||||
\(245\) | −5.82437 | + | 10.0881i | −0.372105 | + | 0.644505i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0.00376838 | + | 0.00652703i | 0.000239776 | + | 0.000415305i | ||||
\(248\) | 2.96536 | + | 5.13616i | 0.188301 | + | 0.326147i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −2.34361 | + | 4.05925i | −0.148223 | + | 0.256730i | ||||
\(251\) | 4.49930 | 0.283993 | 0.141997 | − | 0.989867i | \(-0.454648\pi\) | ||||
0.141997 | + | 0.989867i | \(0.454648\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 5.39452 | 0.339150 | ||||||||
\(254\) | 1.74392 | − | 3.02055i | 0.109423 | − | 0.189526i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −1.95380 | − | 3.38409i | −0.122113 | − | 0.211506i | ||||
\(257\) | 6.86771 | + | 11.8952i | 0.428396 | + | 0.742003i | 0.996731 | − | 0.0807940i | \(-0.0257456\pi\) |
−0.568335 | + | 0.822797i | \(0.692412\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2.91952 | − | 5.05676i | 0.181410 | − | 0.314211i | ||||
\(260\) | −0.0731010 | −0.00453353 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 6.45423 | 0.398743 | ||||||||
\(263\) | −12.1013 | + | 20.9600i | −0.746197 | + | 1.29245i | 0.203437 | + | 0.979088i | \(0.434789\pi\) |
−0.949634 | + | 0.313363i | \(0.898544\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1.44051 | + | 2.49503i | 0.0884897 | + | 0.153269i | ||||
\(266\) | 0.114409 | + | 0.198162i | 0.00701487 | + | 0.0121501i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −10.0751 | + | 17.4506i | −0.615436 | + | 1.06597i | ||||
\(269\) | −12.0062 | −0.732032 | −0.366016 | − | 0.930609i | \(-0.619278\pi\) | ||||
−0.366016 | + | 0.930609i | \(0.619278\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 3.71777 | 0.225839 | 0.112919 | − | 0.993604i | \(-0.463980\pi\) | ||||
0.112919 | + | 0.993604i | \(0.463980\pi\) | |||||||
\(272\) | −4.68999 | + | 8.12329i | −0.284372 | + | 0.492547i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 2.49433 | + | 4.32031i | 0.150688 | + | 0.261000i | ||||
\(275\) | 0.242369 | + | 0.419796i | 0.0146154 | + | 0.0253146i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 11.7416 | − | 20.3370i | 0.705482 | − | 1.22193i | −0.261035 | − | 0.965329i | \(-0.584064\pi\) |
0.966517 | − | 0.256601i | \(-0.0826027\pi\) | |||||||
\(278\) | 2.55309 | 0.153124 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −4.64837 | −0.277793 | ||||||||
\(281\) | −10.1859 | + | 17.6424i | −0.607638 | + | 1.05246i | 0.383991 | + | 0.923337i | \(0.374549\pi\) |
−0.991629 | + | 0.129123i | \(0.958784\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −5.79997 | − | 10.0458i | −0.344772 | − | 0.597163i | 0.640540 | − | 0.767925i | \(-0.278711\pi\) |
−0.985312 | + | 0.170761i | \(0.945377\pi\) | |||||||
\(284\) | 5.55917 | + | 9.62876i | 0.329876 | + | 0.571362i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0.0195640 | − | 0.0338858i | 0.00115684 | − | 0.00200371i | ||||
\(287\) | −4.84956 | −0.286260 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −7.18559 | −0.422682 | ||||||||
\(290\) | 3.59263 | − | 6.22262i | 0.210967 | − | 0.365405i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −0.499766 | − | 0.865620i | −0.0292466 | − | 0.0506566i | ||||
\(293\) | 15.7871 | + | 27.3440i | 0.922291 | + | 1.59745i | 0.795861 | + | 0.605479i | \(0.207019\pi\) |
0.126430 | + | 0.991976i | \(0.459648\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 4.10010 | − | 7.10158i | 0.238717 | − | 0.413470i | ||||
\(296\) | −7.03603 | −0.408961 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −0.366782 | −0.0212471 | ||||||||
\(299\) | 0.00933974 | − | 0.0161769i | 0.000540131 | − | 0.000935535i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −5.48166 | − | 9.49451i | −0.315957 | − | 0.547254i | ||||
\(302\) | −1.70870 | − | 2.95956i | −0.0983248 | − | 0.170304i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −0.624802 | + | 1.08219i | −0.0358348 | + | 0.0620678i | ||||
\(305\) | −15.3163 | −0.877010 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −8.12054 | −0.463464 | −0.231732 | − | 0.972780i | \(-0.574439\pi\) | ||||
−0.231732 | + | 0.972780i | \(0.574439\pi\) | |||||||
\(308\) | −6.28814 | + | 10.8914i | −0.358300 | + | 0.620594i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 1.71627 | + | 2.97267i | 0.0974776 | + | 0.168836i | ||||
\(311\) | −11.9243 | − | 20.6535i | −0.676164 | − | 1.17115i | −0.976127 | − | 0.217199i | \(-0.930308\pi\) |
0.299963 | − | 0.953951i | \(-0.403026\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −13.4552 | + | 23.3051i | −0.760535 | + | 1.31728i | 0.182040 | + | 0.983291i | \(0.441730\pi\) |
−0.942575 | + | 0.333994i | \(0.891604\pi\) | |||||||
\(314\) | 5.21818 | 0.294479 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −0.893856 | −0.0502833 | ||||||||
\(317\) | −4.16617 | + | 7.21601i | −0.233995 | + | 0.405292i | −0.958980 | − | 0.283473i | \(-0.908513\pi\) |
0.724985 | + | 0.688765i | \(0.241847\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −20.3581 | − | 35.2612i | −1.13983 | − | 1.97425i | ||||
\(320\) | −4.59664 | − | 7.96161i | −0.256960 | − | 0.445068i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0.283557 | − | 0.491135i | 0.0158020 | − | 0.0273699i | ||||
\(323\) | 1.30748 | 0.0727501 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0.00167849 | 9.31061e−5 | ||||||||
\(326\) | −0.688565 | + | 1.19263i | −0.0381361 | + | 0.0660536i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 2.92185 | + | 5.06080i | 0.161332 | + | 0.279436i | ||||
\(329\) | 4.68330 | + | 8.11172i | 0.258199 | + | 0.447214i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 3.21013 | − | 5.56011i | 0.176445 | − | 0.305611i | −0.764216 | − | 0.644961i | \(-0.776874\pi\) |
0.940660 | + | 0.339350i | \(0.110207\pi\) | |||||||
\(332\) | 8.43096 | 0.462709 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 8.54322 | 0.467464 | ||||||||
\(335\) | −12.2132 | + | 21.1539i | −0.667279 | + | 1.15576i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −3.73745 | − | 6.47345i | −0.203592 | − | 0.352631i | 0.746091 | − | 0.665844i | \(-0.231928\pi\) |
−0.949683 | + | 0.313212i | \(0.898595\pi\) | |||||||
\(338\) | 2.70046 | + | 4.67734i | 0.146886 | + | 0.254414i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −6.34079 | + | 10.9826i | −0.343877 | + | 0.595613i | ||||
\(341\) | 19.4509 | 1.05333 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 16.1768 | 0.873464 | ||||||||
\(344\) | −6.60538 | + | 11.4409i | −0.356138 | + | 0.616850i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 2.91517 | + | 5.04923i | 0.156721 | + | 0.271448i | ||||
\(347\) | −15.7272 | − | 27.2404i | −0.844283 | − | 1.46234i | −0.886243 | − | 0.463222i | \(-0.846693\pi\) |
0.0419596 | − | 0.999119i | \(-0.486640\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −5.92647 | + | 10.2650i | −0.317237 | + | 0.549470i | −0.979910 | − | 0.199438i | \(-0.936088\pi\) |
0.662674 | + | 0.748908i | \(0.269422\pi\) | |||||||
\(350\) | 0.0509595 | 0.00272390 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 23.0733 | 1.22981 | ||||||||
\(353\) | −4.10354 | + | 7.10754i | −0.218409 | + | 0.378296i | −0.954322 | − | 0.298780i | \(-0.903420\pi\) |
0.735912 | + | 0.677077i | \(0.236754\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 6.73891 | + | 11.6721i | 0.357664 | + | 0.619492i | ||||
\(356\) | 3.08195 | + | 5.33809i | 0.163343 | + | 0.282918i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 2.11680 | − | 3.66640i | 0.111876 | − | 0.193775i | ||||
\(359\) | −17.7273 | −0.935611 | −0.467806 | − | 0.883831i | \(-0.654955\pi\) | ||||
−0.467806 | + | 0.883831i | \(0.654955\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.8258 | −0.990832 | ||||||||
\(362\) | −4.99696 | + | 8.65499i | −0.262635 | + | 0.454896i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0.0217738 | + | 0.0377134i | 0.00114126 | + | 0.00197672i | ||||
\(365\) | −0.605824 | − | 1.04932i | −0.0317103 | − | 0.0549238i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 10.1598 | − | 17.5972i | 0.530335 | − | 0.918568i | −0.469038 | − | 0.883178i | \(-0.655399\pi\) |
0.999374 | − | 0.0353899i | \(-0.0112673\pi\) | |||||||
\(368\) | 3.09708 | 0.161446 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −4.07226 | −0.211707 | ||||||||
\(371\) | 0.858138 | − | 1.48634i | 0.0445523 | − | 0.0771668i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 4.84072 | + | 8.38437i | 0.250643 | + | 0.434126i | 0.963703 | − | 0.266977i | \(-0.0860247\pi\) |
−0.713060 | + | 0.701103i | \(0.752691\pi\) | |||||||
\(374\) | −3.39397 | − | 5.87852i | −0.175498 | − | 0.303971i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 5.64337 | − | 9.77461i | 0.291035 | − | 0.504087i | ||||
\(377\) | −0.140987 | −0.00726119 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −4.12905 | −0.212095 | −0.106048 | − | 0.994361i | \(-0.533820\pi\) | ||||
−0.106048 | + | 0.994361i | \(0.533820\pi\) | |||||||
\(380\) | −0.844722 | + | 1.46310i | −0.0433333 | + | 0.0750555i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 2.27392 | + | 3.93855i | 0.116344 | + | 0.201514i | ||||
\(383\) | 2.37509 | + | 4.11378i | 0.121362 | + | 0.210204i | 0.920305 | − | 0.391202i | \(-0.127941\pi\) |
−0.798943 | + | 0.601406i | \(0.794607\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −7.62258 | + | 13.2027i | −0.388483 | + | 0.672872i | ||||
\(386\) | −4.48951 | −0.228510 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −18.1667 | −0.922275 | ||||||||
\(389\) | −10.9067 | + | 18.8909i | −0.552990 | + | 0.957806i | 0.445067 | + | 0.895497i | \(0.353180\pi\) |
−0.998057 | + | 0.0623089i | \(0.980154\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.62026 | − | 2.80637i | −0.0819401 | − | 0.141924i | ||||
\(392\) | −4.18097 | − | 7.24165i | −0.211171 | − | 0.365758i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −4.58537 | + | 7.94209i | −0.231007 | + | 0.400117i | ||||
\(395\) | −1.08355 | −0.0545191 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −34.8490 | −1.74902 | −0.874512 | − | 0.485005i | \(-0.838818\pi\) | ||||
−0.874512 | + | 0.485005i | \(0.838818\pi\) | |||||||
\(398\) | −2.67701 | + | 4.63671i | −0.134186 | + | 0.232417i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0.139148 | + | 0.241012i | 0.00695740 | + | 0.0120506i | ||||
\(401\) | −9.41304 | − | 16.3039i | −0.470065 | − | 0.814176i | 0.529349 | − | 0.848404i | \(-0.322436\pi\) |
−0.999414 | + | 0.0342279i | \(0.989103\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0.0336761 | − | 0.0583287i | 0.00167753 | − | 0.00290556i | ||||
\(404\) | 25.2170 | 1.25459 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −4.28040 | −0.212433 | ||||||||
\(407\) | −11.5380 | + | 19.9843i | −0.571916 | + | 0.990587i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 3.17998 | + | 5.50788i | 0.157240 | + | 0.272347i | 0.933872 | − | 0.357607i | \(-0.116407\pi\) |
−0.776633 | + | 0.629954i | \(0.783074\pi\) | |||||||
\(410\) | 1.69109 | + | 2.92905i | 0.0835169 | + | 0.144656i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 4.17112 | − | 7.22459i | 0.205496 | − | 0.355930i | ||||
\(413\) | −4.88502 | −0.240376 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 10.2201 | 0.501687 | ||||||||
\(416\) | 0.0399478 | − | 0.0691916i | 0.00195860 | − | 0.00339240i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −0.452146 | − | 0.783139i | −0.0221152 | − | 0.0383046i | ||||
\(419\) | −12.1590 | − | 21.0600i | −0.594005 | − | 1.02885i | −0.993686 | − | 0.112193i | \(-0.964212\pi\) |
0.399681 | − | 0.916654i | \(-0.369121\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 3.99502 | − | 6.91957i | 0.194705 | − | 0.337239i | −0.752099 | − | 0.659051i | \(-0.770958\pi\) |
0.946804 | + | 0.321811i | \(0.104292\pi\) | |||||||
\(422\) | −9.96937 | −0.485302 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −2.06811 | −0.100436 | ||||||||
\(425\) | 0.145593 | − | 0.252174i | 0.00706229 | − | 0.0122322i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 4.56211 | + | 7.90181i | 0.220776 | + | 0.382396i | ||||
\(428\) | 10.3215 | + | 17.8774i | 0.498909 | + | 0.864136i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −3.82301 | + | 6.62166i | −0.184362 | + | 0.319325i | ||||
\(431\) | −9.87124 | −0.475481 | −0.237740 | − | 0.971329i | \(-0.576407\pi\) | ||||
−0.237740 | + | 0.971329i | \(0.576407\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −6.10369 | −0.293325 | −0.146662 | − | 0.989187i | \(-0.546853\pi\) | ||||
−0.146662 | + | 0.989187i | \(0.546853\pi\) | |||||||
\(434\) | 1.02242 | − | 1.77088i | 0.0490775 | − | 0.0850047i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 13.2515 | + | 22.9522i | 0.634630 | + | 1.09921i | ||||
\(437\) | −0.215852 | − | 0.373866i | −0.0103256 | − | 0.0178844i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 7.56701 | − | 13.1064i | 0.361154 | − | 0.625537i | −0.626997 | − | 0.779021i | \(-0.715716\pi\) |
0.988151 | + | 0.153485i | \(0.0490496\pi\) | |||||||
\(440\) | 18.3704 | 0.875774 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −0.0235044 | −0.00111799 | ||||||||
\(443\) | −0.361397 | + | 0.625957i | −0.0171705 | + | 0.0297401i | −0.874483 | − | 0.485056i | \(-0.838799\pi\) |
0.857312 | + | 0.514796i | \(0.172132\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 3.73598 | + | 6.47092i | 0.177103 | + | 0.306751i | ||||
\(446\) | −4.49995 | − | 7.79414i | −0.213079 | − | 0.369063i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −2.73831 | + | 4.74288i | −0.129373 | + | 0.224080i | ||||
\(449\) | −1.66845 | −0.0787389 | −0.0393695 | − | 0.999225i | \(-0.512535\pi\) | ||||
−0.0393695 | + | 0.999225i | \(0.512535\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 19.1655 | 0.902468 | ||||||||
\(452\) | −11.4746 | + | 19.8745i | −0.539718 | + | 0.934819i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 4.49573 | + | 7.78684i | 0.210995 | + | 0.365455i | ||||
\(455\) | 0.0263946 | + | 0.0457167i | 0.00123740 | + | 0.00214323i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −5.54172 | + | 9.59855i | −0.259231 | + | 0.449001i | −0.966036 | − | 0.258407i | \(-0.916802\pi\) |
0.706805 | + | 0.707408i | \(0.250136\pi\) | |||||||
\(458\) | −4.48926 | −0.209769 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 4.18720 | 0.195229 | ||||||||
\(461\) | −10.9422 | + | 18.9524i | −0.509629 | + | 0.882703i | 0.490309 | + | 0.871549i | \(0.336884\pi\) |
−0.999938 | + | 0.0111543i | \(0.996449\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −12.4259 | − | 21.5222i | −0.577479 | − | 1.00022i | −0.995767 | − | 0.0919086i | \(-0.970703\pi\) |
0.418289 | − | 0.908314i | \(-0.362630\pi\) | |||||||
\(464\) | −11.6879 | − | 20.2440i | −0.542597 | − | 0.939805i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 1.58687 | − | 2.74854i | 0.0735105 | − | 0.127324i | ||||
\(467\) | 11.8355 | 0.547683 | 0.273842 | − | 0.961775i | \(-0.411706\pi\) | ||||
0.273842 | + | 0.961775i | \(0.411706\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 14.5513 | 0.671916 | ||||||||
\(470\) | 3.26623 | − | 5.65727i | 0.150660 | − | 0.260951i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 2.94322 | + | 5.09780i | 0.135473 | + | 0.234645i | ||||
\(473\) | 21.6636 | + | 37.5224i | 0.996091 | + | 1.72528i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0.0193959 | − | 0.0335947i | 0.000889946 | − | 0.00154143i | ||||
\(476\) | 7.55465 | 0.346267 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 1.34258 | 0.0614080 | ||||||||
\(479\) | 1.44368 | − | 2.50052i | 0.0659632 | − | 0.114252i | −0.831158 | − | 0.556037i | \(-0.812321\pi\) |
0.897121 | + | 0.441785i | \(0.145655\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0.0399523 | + | 0.0691994i | 0.00182167 | + | 0.00315522i | ||||
\(482\) | 5.51426 | + | 9.55099i | 0.251168 | + | 0.435035i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 14.8002 | − | 25.6347i | 0.672735 | − | 1.16521i | ||||
\(485\) | −22.0220 | −0.999966 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 8.75903 | 0.396910 | 0.198455 | − | 0.980110i | \(-0.436408\pi\) | ||||
0.198455 | + | 0.980110i | \(0.436408\pi\) | |||||||
\(488\) | 5.49734 | − | 9.52167i | 0.248853 | − | 0.431026i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −2.41983 | − | 4.19127i | −0.109317 | − | 0.189342i | ||||
\(491\) | −11.2865 | − | 19.5488i | −0.509354 | − | 0.882226i | −0.999941 | − | 0.0108346i | \(-0.996551\pi\) |
0.490588 | − | 0.871392i | \(-0.336782\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −12.2292 | + | 21.1816i | −0.550776 | + | 0.953972i | ||||
\(494\) | −0.00313127 | −0.000140883 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 11.1671 | 0.501416 | ||||||||
\(497\) | 4.01449 | − | 6.95331i | 0.180075 | − | 0.311899i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 12.6664 | + | 21.9389i | 0.567026 | + | 0.982118i | 0.996858 | + | 0.0792092i | \(0.0252395\pi\) |
−0.429832 | + | 0.902909i | \(0.641427\pi\) | |||||||
\(500\) | 10.3081 | + | 17.8542i | 0.460994 | + | 0.798465i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −0.934653 | + | 1.61887i | −0.0417156 | + | 0.0722536i | ||||
\(503\) | −3.74414 | −0.166943 | −0.0834714 | − | 0.996510i | \(-0.526601\pi\) | ||||
−0.0834714 | + | 0.996510i | \(0.526601\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 30.5684 | 1.36028 | ||||||||
\(506\) | −1.12062 | + | 1.94097i | −0.0498176 | + | 0.0862867i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −7.67045 | − | 13.2856i | −0.340321 | − | 0.589454i | ||||
\(509\) | 12.1749 | + | 21.0876i | 0.539645 | + | 0.934692i | 0.998923 | + | 0.0463997i | \(0.0147748\pi\) |
−0.459278 | + | 0.888292i | \(0.651892\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −0.360901 | + | 0.625098i | −0.0159653 | + | 0.0276527i | ||||
\(512\) | 22.7690 | 1.00626 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −5.70660 | −0.251707 | ||||||||
\(515\) | 5.05630 | − | 8.75776i | 0.222807 | − | 0.385913i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −18.5085 | − | 32.0576i | −0.814001 | − | 1.40989i | ||||
\(518\) | 1.21296 | + | 2.10091i | 0.0532945 | + | 0.0923087i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0.0318054 | − | 0.0550885i | 0.00139476 | − | 0.00241579i | ||||
\(521\) | −19.6209 | −0.859608 | −0.429804 | − | 0.902922i | \(-0.641417\pi\) | ||||
−0.429804 | + | 0.902922i | \(0.641417\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 20.8154 | 0.910194 | 0.455097 | − | 0.890442i | \(-0.349605\pi\) | ||||
0.455097 | + | 0.890442i | \(0.349605\pi\) | |||||||
\(524\) | 14.1941 | − | 24.5850i | 0.620074 | − | 1.07400i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −5.02767 | − | 8.70819i | −0.219217 | − | 0.379695i | ||||
\(527\) | −5.84214 | − | 10.1189i | −0.254488 | − | 0.440785i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 10.9650 | − | 18.9920i | 0.476740 | − | 0.825738i | ||||
\(530\) | −1.19696 | −0.0519928 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 1.00643 | 0.0436345 | ||||||||
\(533\) | 0.0331820 | − | 0.0574729i | 0.00143727 | − | 0.00248943i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 12.5119 | + | 21.6712i | 0.540936 | + | 0.936929i | ||||
\(536\) | −8.76713 | − | 15.1851i | −0.378682 | − | 0.655897i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 2.49409 | − | 4.31989i | 0.107528 | − | 0.186244i | ||||
\(539\) | −27.4245 | −1.18126 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −30.6272 | −1.31676 | −0.658382 | − | 0.752684i | \(-0.728759\pi\) | ||||
−0.658382 | + | 0.752684i | \(0.728759\pi\) | |||||||
\(542\) | −0.772305 | + | 1.33767i | −0.0331733 | + | 0.0574579i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −6.93015 | − | 12.0034i | −0.297128 | − | 0.514640i | ||||
\(545\) | 16.0636 | + | 27.8230i | 0.688090 | + | 1.19181i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −11.3238 | + | 19.6135i | −0.484172 | + | 0.838611i | −0.999835 | − | 0.0181808i | \(-0.994213\pi\) |
0.515662 | + | 0.856792i | \(0.327546\pi\) | |||||||
\(548\) | 21.9422 | 0.937323 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −0.201393 | −0.00858741 | ||||||||
\(551\) | −1.62918 | + | 2.82182i | −0.0694055 | + | 0.120214i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0.322744 | + | 0.559010i | 0.0137245 | + | 0.0237715i | ||||
\(554\) | 4.87822 | + | 8.44933i | 0.207256 | + | 0.358978i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 5.61476 | − | 9.72504i | 0.238119 | − | 0.412434i | ||||
\(557\) | −36.4518 | −1.54451 | −0.772256 | − | 0.635311i | \(-0.780872\pi\) | ||||
−0.772256 | + | 0.635311i | \(0.780872\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0.150028 | 0.00634550 | ||||||||
\(560\) | −4.37625 | + | 7.57988i | −0.184930 | + | 0.320308i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −4.23188 | − | 7.32984i | −0.178511 | − | 0.309191i | ||||
\(563\) | 13.2581 | + | 22.9637i | 0.558763 | + | 0.967806i | 0.997600 | + | 0.0692393i | \(0.0220572\pi\) |
−0.438837 | + | 0.898567i | \(0.644609\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −13.9096 | + | 24.0922i | −0.585183 | + | 1.01357i | ||||
\(566\) | 4.81938 | 0.202574 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −9.67492 | −0.405950 | ||||||||
\(569\) | 11.4837 | − | 19.8904i | 0.481422 | − | 0.833847i | −0.518351 | − | 0.855168i | \(-0.673454\pi\) |
0.999773 | + | 0.0213210i | \(0.00678720\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 2.39900 | + | 4.15519i | 0.100395 | + | 0.173889i | 0.911848 | − | 0.410529i | \(-0.134656\pi\) |
−0.811452 | + | 0.584419i | \(0.801323\pi\) | |||||||
\(572\) | −0.0860504 | − | 0.149044i | −0.00359795 | − | 0.00623183i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 1.00741 | − | 1.74489i | 0.0420486 | − | 0.0728304i | ||||
\(575\) | −0.0961436 | −0.00400947 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −4.31333 | −0.179566 | −0.0897831 | − | 0.995961i | \(-0.528617\pi\) | ||||
−0.0897831 | + | 0.995961i | \(0.528617\pi\) | |||||||
\(578\) | 1.49269 | − | 2.58541i | 0.0620876 | − | 0.107539i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −15.8018 | − | 27.3696i | −0.656136 | − | 1.13646i | ||||
\(581\) | −3.04417 | − | 5.27265i | −0.126293 | − | 0.218746i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −3.39137 | + | 5.87402i | −0.140456 | + | 0.243277i | ||||
\(584\) | 0.869769 | 0.0359913 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −13.1180 | −0.541899 | ||||||||
\(587\) | 20.9111 | − | 36.2191i | 0.863094 | − | 1.49492i | −0.00583407 | − | 0.999983i | \(-0.501857\pi\) |
0.868928 | − | 0.494939i | \(-0.164810\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −0.778292 | − | 1.34804i | −0.0320690 | − | 0.0555451i | ||||
\(590\) | 1.70345 | + | 2.95047i | 0.0701301 | + | 0.121469i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −6.62413 | + | 11.4733i | −0.272250 | + | 0.471551i | ||||
\(593\) | 31.5370 | 1.29507 | 0.647536 | − | 0.762035i | \(-0.275800\pi\) | ||||
0.647536 | + | 0.762035i | \(0.275800\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 9.15786 | 0.375436 | ||||||||
\(596\) | −0.806628 | + | 1.39712i | −0.0330408 | + | 0.0572283i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0.00388035 | + | 0.00672096i | 0.000158679 | + | 0.000274840i | ||||
\(599\) | −6.31515 | − | 10.9382i | −0.258030 | − | 0.446921i | 0.707684 | − | 0.706529i | \(-0.249740\pi\) |
−0.965714 | + | 0.259608i | \(0.916407\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −10.2715 | + | 17.7907i | −0.418983 | + | 0.725699i | −0.995837 | − | 0.0911474i | \(-0.970947\pi\) |
0.576855 | + | 0.816847i | \(0.304280\pi\) | |||||||
\(602\) | 4.55489 | 0.185643 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −15.0311 | −0.611608 | ||||||||
\(605\) | 17.9410 | − | 31.0747i | 0.729405 | − | 1.26337i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −6.45628 | − | 11.1826i | −0.262052 | − | 0.453888i | 0.704735 | − | 0.709471i | \(-0.251066\pi\) |
−0.966787 | + | 0.255583i | \(0.917733\pi\) | |||||||
\(608\) | −0.923237 | − | 1.59909i | −0.0374422 | − | 0.0648518i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 3.18171 | − | 5.51088i | 0.128824 | − | 0.223129i | ||||
\(611\) | −0.128178 | −0.00518552 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −31.1598 | −1.25853 | −0.629265 | − | 0.777191i | \(-0.716644\pi\) | ||||
−0.629265 | + | 0.777191i | \(0.716644\pi\) | |||||||
\(614\) | 1.68690 | − | 2.92180i | 0.0680779 | − | 0.117914i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −5.47180 | − | 9.47743i | −0.220465 | − | 0.381857i | ||||
\(617\) | −3.57039 | − | 6.18410i | −0.143739 | − | 0.248962i | 0.785163 | − | 0.619289i | \(-0.212579\pi\) |
−0.928902 | + | 0.370327i | \(0.879246\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 5.01545 | − | 8.68702i | 0.201588 | − | 0.349161i | −0.747452 | − | 0.664316i | \(-0.768723\pi\) |
0.949040 | + | 0.315155i | \(0.102056\pi\) | |||||||
\(620\) | 15.0977 | 0.606338 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 9.90827 | 0.397285 | ||||||||
\(623\) | 2.22560 | − | 3.85485i | 0.0891667 | − | 0.154441i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 12.2633 | + | 21.2407i | 0.490532 | + | 0.849627i | ||||
\(626\) | −5.59020 | − | 9.68250i | −0.223429 | − | 0.386991i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 11.4758 | − | 19.8767i | 0.457936 | − | 0.793168i | ||||
\(629\) | 13.8619 | 0.552708 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −7.07560 | −0.281675 | −0.140838 | − | 0.990033i | \(-0.544980\pi\) | ||||
−0.140838 | + | 0.990033i | \(0.544980\pi\) | |||||||
\(632\) | 0.388906 | − | 0.673606i | 0.0154699 | − | 0.0267946i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −1.73090 | − | 2.99801i | −0.0687429 | − | 0.119066i | ||||
\(635\) | −9.29823 | − | 16.1050i | −0.368989 | − | 0.639108i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −0.0474811 | + | 0.0822396i | −0.00188127 | + | 0.00325845i | ||||
\(638\) | 16.9162 | 0.669718 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 23.4206 | 0.925781 | ||||||||
\(641\) | −2.50561 | + | 4.33984i | −0.0989655 | + | 0.171413i | −0.911257 | − | 0.411839i | \(-0.864887\pi\) |
0.812291 | + | 0.583252i | \(0.198220\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −0.819202 | − | 1.41890i | −0.0323062 | − | 0.0559559i | 0.849420 | − | 0.527717i | \(-0.176952\pi\) |
−0.881726 | + | 0.471761i | \(0.843618\pi\) | |||||||
\(644\) | −1.24720 | − | 2.16021i | −0.0491465 | − | 0.0851242i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −0.271607 | + | 0.470437i | −0.0106862 | + | 0.0185091i | ||||
\(647\) | −34.4927 | −1.35605 | −0.678024 | − | 0.735040i | \(-0.737164\pi\) | ||||
−0.678024 | + | 0.735040i | \(0.737164\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 19.3056 | 0.757813 | ||||||||
\(650\) | −0.000348679 | 0 | 0.000603929i | −1.36763e−5 | 0 | 2.36881e-5i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 3.02858 | + | 5.24566i | 0.118609 | + | 0.205436i | ||||
\(653\) | 19.3803 | + | 33.5677i | 0.758410 | + | 1.31360i | 0.943661 | + | 0.330913i | \(0.107357\pi\) |
−0.185252 | + | 0.982691i | \(0.559310\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 17.2064 | − | 29.8023i | 0.672308 | − | 1.16447i | ||||
\(656\) | 11.0032 | 0.429604 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −3.89151 | −0.151707 | ||||||||
\(659\) | 4.69596 | − | 8.13364i | 0.182929 | − | 0.316842i | −0.759948 | − | 0.649984i | \(-0.774776\pi\) |
0.942877 | + | 0.333142i | \(0.108109\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 12.0737 | + | 20.9123i | 0.469613 | + | 0.813394i | 0.999396 | − | 0.0347394i | \(-0.0110601\pi\) |
−0.529783 | + | 0.848133i | \(0.677727\pi\) | |||||||
\(662\) | 1.33370 | + | 2.31004i | 0.0518357 | + | 0.0897821i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −3.66821 | + | 6.35353i | −0.142354 | + | 0.246565i | ||||
\(665\) | 1.22001 | 0.0473101 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 8.07569 | 0.312692 | ||||||||
\(668\) | 18.7883 | − | 32.5422i | 0.726940 | − | 1.25910i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −5.07417 | − | 8.78873i | −0.196032 | − | 0.339538i | ||||
\(671\) | −18.0295 | − | 31.2280i | −0.696022 | − | 1.20555i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 13.2331 | − | 22.9203i | 0.510097 | − | 0.883514i | −0.489834 | − | 0.871816i | \(-0.662943\pi\) |
0.999932 | − | 0.0116988i | \(-0.00372393\pi\) | |||||||
\(674\) | 3.10557 | 0.119622 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 23.7554 | 0.913671 | ||||||||
\(677\) | 15.5334 | − | 26.9047i | 0.596998 | − | 1.03403i | −0.396264 | − | 0.918137i | \(-0.629693\pi\) |
0.993262 | − | 0.115894i | \(-0.0369733\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 6.55945 | + | 11.3613i | 0.251729 | + | 0.436007i | ||||
\(680\) | −5.51760 | − | 9.55677i | −0.211590 | − | 0.366485i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −4.04060 | + | 6.99852i | −0.154722 | + | 0.267987i | ||||
\(683\) | −38.1361 | −1.45924 | −0.729619 | − | 0.683854i | \(-0.760303\pi\) | ||||
−0.729619 | + | 0.683854i | \(0.760303\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 26.5986 | 1.01628 | ||||||||
\(686\) | −3.36045 | + | 5.82047i | −0.128303 | + | 0.222227i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 12.4374 | + | 21.5422i | 0.474171 | + | 0.821288i | ||||
\(689\) | 0.0117432 | + | 0.0203399i | 0.000447381 | + | 0.000774887i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −16.4648 | + | 28.5178i | −0.626349 | + | 1.08487i | 0.361929 | + | 0.932206i | \(0.382118\pi\) |
−0.988278 | + | 0.152663i | \(0.951215\pi\) | |||||||
\(692\) | 25.6442 | 0.974847 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 13.0683 | 0.496065 | ||||||||
\(695\) | 6.80629 | − | 11.7888i | 0.258177 | − | 0.447176i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −5.75642 | − | 9.97041i | −0.218040 | − | 0.377656i | ||||
\(698\) | −2.46225 | − | 4.26474i | −0.0931975 | − | 0.161423i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0.112070 | − | 0.194111i | 0.00423586 | − | 0.00733672i | ||||
\(701\) | 2.30710 | 0.0871381 | 0.0435690 | − | 0.999050i | \(-0.486127\pi\) | ||||
0.0435690 | + | 0.999050i | \(0.486127\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.84668 | 0.0696490 | ||||||||
\(704\) | 10.8218 | − | 18.7439i | 0.407862 | − | 0.706438i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −1.70488 | − | 2.95294i | −0.0641641 | − | 0.111136i | ||||
\(707\) | −9.10510 | − | 15.7705i | −0.342433 | − | 0.593111i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 5.57603 | − | 9.65797i | 0.209412 | − | 0.362713i | −0.742117 | − | 0.670270i | \(-0.766178\pi\) |
0.951530 | + | 0.307557i | \(0.0995116\pi\) | |||||||
\(710\) | −5.59958 | −0.210148 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −5.36368 | −0.201012 | ||||||||
\(713\) | −1.92896 | + | 3.34105i | −0.0722400 | + | 0.125123i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −0.104312 | − | 0.180673i | −0.00390103 | − | 0.00675678i | ||||
\(716\) | −9.31053 | − | 16.1263i | −0.347951 | − | 0.602669i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 3.68255 | − | 6.37836i | 0.137431 | − | 0.238038i | ||||
\(719\) | 32.1700 | 1.19974 | 0.599869 | − | 0.800098i | \(-0.295219\pi\) | ||||
0.599869 | + | 0.800098i | \(0.295219\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −6.02426 | −0.224355 | ||||||||
\(722\) | 3.91075 | − | 6.77361i | 0.145543 | − | 0.252088i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 21.9787 | + | 38.0681i | 0.816830 | + | 1.41479i | ||||
\(725\) | 0.362831 | + | 0.628442i | 0.0134752 | + | 0.0233397i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 2.68275 | − | 4.64667i | 0.0994979 | − | 0.172335i | −0.811979 | − | 0.583687i | \(-0.801610\pi\) |
0.911477 | + | 0.411351i | \(0.134943\pi\) | |||||||
\(728\) | −0.0378942 | −0.00140445 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0.503399 | 0.0186316 | ||||||||
\(731\) | 13.0134 | − | 22.5399i | 0.481319 | − | 0.833669i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 7.29818 | + | 12.6408i | 0.269564 | + | 0.466899i | 0.968749 | − | 0.248042i | \(-0.0797870\pi\) |
−0.699185 | + | 0.714941i | \(0.746454\pi\) | |||||||
\(734\) | 4.22104 | + | 7.31105i | 0.155801 | + | 0.269856i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −2.28820 | + | 3.96327i | −0.0843440 | + | 0.146088i | ||||
\(737\) | −57.5068 | −2.11829 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −43.2165 | −1.58975 | −0.794873 | − | 0.606776i | \(-0.792463\pi\) | ||||
−0.794873 | + | 0.606776i | \(0.792463\pi\) | |||||||
\(740\) | −8.95572 | + | 15.5118i | −0.329219 | + | 0.570224i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0.356527 | + | 0.617523i | 0.0130885 | + | 0.0226700i | ||||
\(743\) | 4.05610 | + | 7.02538i | 0.148804 | + | 0.257736i | 0.930786 | − | 0.365565i | \(-0.119124\pi\) |
−0.781982 | + | 0.623301i | \(0.785791\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −0.977806 | + | 1.69361i | −0.0358240 | + | 0.0620491i | ||||
\(746\) | −4.02231 | −0.147267 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −29.8561 | −1.09165 | ||||||||
\(749\) | 7.45357 | − | 12.9100i | 0.272348 | − | 0.471720i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −4.37773 | − | 7.58245i | −0.159746 | − | 0.276687i | 0.775031 | − | 0.631923i | \(-0.217734\pi\) |
−0.934777 | + | 0.355235i | \(0.884401\pi\) | |||||||
\(752\) | −10.6260 | − | 18.4048i | −0.387490 | − | 0.671153i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0.0292876 | − | 0.0507277i | 0.00106659 | − | 0.00184739i | ||||
\(755\) | −18.2210 | −0.663129 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −32.1511 | −1.16855 | −0.584276 | − | 0.811555i | \(-0.698622\pi\) | ||||
−0.584276 | + | 0.811555i | \(0.698622\pi\) | |||||||
\(758\) | 0.857741 | − | 1.48565i | 0.0311546 | − | 0.0539613i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −0.735058 | − | 1.27316i | −0.0266633 | − | 0.0461823i | ||||
\(761\) | −12.2730 | − | 21.2574i | −0.444894 | − | 0.770580i | 0.553151 | − | 0.833081i | \(-0.313425\pi\) |
−0.998045 | + | 0.0625018i | \(0.980092\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 9.56941 | − | 16.5747i | 0.346436 | − | 0.600045i | ||||
\(764\) | 20.0033 | 0.723693 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −1.97354 | −0.0713069 | ||||||||
\(767\) | 0.0334246 | − | 0.0578931i | 0.00120689 | − | 0.00209040i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −15.7072 | − | 27.2057i | −0.566416 | − | 0.981061i | −0.996916 | − | 0.0784710i | \(-0.974996\pi\) |
0.430500 | − | 0.902590i | \(-0.358337\pi\) | |||||||
\(770\) | −3.16693 | − | 5.48528i | −0.114128 | − | 0.197676i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −9.87335 | + | 17.1011i | −0.355349 | + | 0.615483i | ||||
\(773\) | −28.7145 | −1.03279 | −0.516395 | − | 0.856351i | \(-0.672726\pi\) | ||||
−0.516395 | + | 0.856351i | \(0.672726\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −0.346663 | −0.0124525 | ||||||||
\(776\) | 7.90413 | − | 13.6904i | 0.283742 | − | 0.491455i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −4.53135 | − | 7.84853i | −0.162457 | − | 0.281383i | ||||
\(779\) | −0.766872 | − | 1.32826i | −0.0274761 | − | 0.0475899i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −15.8653 | + | 27.4795i | −0.567706 | + | 0.983295i | ||||
\(782\) | 1.34633 | 0.0481446 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −15.7448 | −0.562315 | ||||||||
\(785\) | 13.9112 | − | 24.0949i | 0.496511 | − | 0.859983i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 19.4080 | + | 33.6157i | 0.691821 | + | 1.19827i | 0.971241 | + | 0.238100i | \(0.0765246\pi\) |
−0.279420 | + | 0.960169i | \(0.590142\pi\) | |||||||
\(788\) | 20.1683 | + | 34.9325i | 0.718466 | + | 1.24442i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0.225088 | − | 0.389864i | 0.00800828 | − | 0.0138708i | ||||
\(791\) | 16.5725 | 0.589249 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −0.124861 | −0.00443394 | ||||||||
\(794\) | 7.23930 | − | 12.5388i | 0.256913 | − | 0.444987i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 11.7746 | + | 20.3941i | 0.417338 | + | 0.722851i | ||||
\(797\) | −2.01705 | − | 3.49363i | −0.0714476 | − | 0.123751i | 0.828088 | − | 0.560598i | \(-0.189429\pi\) |
−0.899536 | + | 0.436847i | \(0.856095\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −11.1181 | + | 19.2572i | −0.393332 | + | 0.681271i | ||||
\(800\) | −0.411224 | −0.0145390 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 7.82160 | 0.276190 | ||||||||
\(803\) | 1.42628 | − | 2.47039i | 0.0503324 | − | 0.0871783i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −1.51187 | − | 2.61864i | −0.0532865 | − | 0.0922949i | ||||
\(806\) | 0.0139913 | + | 0.0242336i | 0.000492822 | + | 0.000853593i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −10.9716 | + | 19.0034i | −0.385981 | + | 0.668538i | ||||
\(809\) | 29.9454 | 1.05283 | 0.526413 | − | 0.850229i | \(-0.323537\pi\) | ||||
0.526413 | + | 0.850229i | \(0.323537\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 20.2173 | 0.709927 | 0.354963 | − | 0.934880i | \(-0.384493\pi\) | ||||
0.354963 | + | 0.934880i | \(0.384493\pi\) | |||||||
\(812\) | −9.41346 | + | 16.3046i | −0.330348 | + | 0.572179i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −4.79364 | − | 8.30282i | −0.168017 | − | 0.291014i | ||||
\(815\) | 3.67129 | + | 6.35887i | 0.128600 | + | 0.222741i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.73365 | − | 3.00278i | 0.0606529 | − | 0.105054i | ||||
\(818\) | −2.64235 | −0.0923875 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 14.8762 | 0.519499 | ||||||||
\(821\) | 13.4368 | − | 23.2733i | 0.468948 | − | 0.812242i | −0.530422 | − | 0.847734i | \(-0.677966\pi\) |
0.999370 | + | 0.0354918i | \(0.0112998\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −11.5272 | − | 19.9656i | −0.401812 | − | 0.695958i | 0.592133 | − | 0.805840i | \(-0.298286\pi\) |
−0.993945 | + | 0.109882i | \(0.964953\pi\) | |||||||
\(824\) | 3.62961 | + | 6.28667i | 0.126444 | + | 0.219007i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 1.01478 | − | 1.75765i | 0.0353087 | − | 0.0611565i | ||||
\(827\) | 5.10953 | 0.177676 | 0.0888378 | − | 0.996046i | \(-0.471685\pi\) | ||||
0.0888378 | + | 0.996046i | \(0.471685\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −30.5982 | −1.06272 | −0.531360 | − | 0.847146i | \(-0.678319\pi\) | ||||
−0.531360 | + | 0.847146i | \(0.678319\pi\) | |||||||
\(830\) | −2.12306 | + | 3.67725i | −0.0736926 | + | 0.127639i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −0.0374725 | − | 0.0649042i | −0.00129912 | − | 0.00225015i | ||||
\(833\) | 8.23703 | + | 14.2669i | 0.285396 | + | 0.494320i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 22.7754 | − | 39.4482i | 0.788176 | − | 1.36516i | ||||
\(836\) | −3.97744 | −0.137563 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 10.1033 | 0.349013 | ||||||||
\(839\) | −28.1543 | + | 48.7648i | −0.971996 | + | 1.68355i | −0.282485 | + | 0.959272i | \(0.591159\pi\) |
−0.689512 | + | 0.724275i | \(0.742175\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −15.9764 | − | 27.6719i | −0.550909 | − | 0.954203i | ||||
\(842\) | 1.65980 | + | 2.87485i | 0.0572003 | + | 0.0990739i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −21.9247 | + | 37.9746i | −0.754678 | + | 1.30714i | ||||
\(845\) | 28.7967 | 0.990637 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −21.3756 | −0.734474 | ||||||||
\(848\) | −1.94704 | + | 3.37237i | −0.0668616 | + | 0.115808i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0.0604889 | + | 0.104770i | 0.00207475 | + | 0.00359357i | ||||
\(851\) | −2.28845 | − | 3.96372i | −0.0784472 | − | 0.135875i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 22.7725 | − | 39.4431i | 0.779715 | − | 1.35051i | −0.152390 | − | 0.988320i | \(-0.548697\pi\) |
0.932106 | − | 0.362186i | \(-0.117970\pi\) | |||||||
\(854\) | −3.79081 | −0.129719 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −17.9631 | −0.613966 | ||||||||
\(857\) | −8.74459 | + | 15.1461i | −0.298709 | + | 0.517380i | −0.975841 | − | 0.218482i | \(-0.929889\pi\) |
0.677131 | + | 0.735862i | \(0.263223\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −9.17301 | − | 15.8881i | −0.312979 | − | 0.542096i | 0.666027 | − | 0.745928i | \(-0.267994\pi\) |
−0.979006 | + | 0.203832i | \(0.934660\pi\) | |||||||
\(860\) | 16.8152 | + | 29.1247i | 0.573392 | + | 0.993144i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 2.05058 | − | 3.55171i | 0.0698431 | − | 0.120972i | ||||
\(863\) | −4.65373 | −0.158415 | −0.0792073 | − | 0.996858i | \(-0.525239\pi\) | ||||
−0.0792073 | + | 0.996858i | \(0.525239\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 31.0863 | 1.05697 | ||||||||
\(866\) | 1.26794 | − | 2.19613i | 0.0430863 | − | 0.0746277i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −4.49699 | − | 7.78902i | −0.152638 | − | 0.264377i | ||||
\(869\) | −1.27549 | − | 2.20921i | −0.0432680 | − | 0.0749424i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −0.0995638 | + | 0.172450i | −0.00337359 | + | 0.00584323i | ||||
\(872\) | −23.0622 | −0.780986 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0.179358 | 0.00606688 | ||||||||
\(875\) | 7.44392 | − | 12.8932i | 0.251650 | − | 0.435871i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1.83355 | + | 3.17580i | 0.0619145 | + | 0.107239i | 0.895321 | − | 0.445421i | \(-0.146946\pi\) |
−0.833407 | + | 0.552660i | \(0.813613\pi\) | |||||||
\(878\) | 3.14384 | + | 5.44529i | 0.106099 | + | 0.183770i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 17.2950 | − | 29.9558i | 0.583013 | − | 1.00981i | ||||
\(881\) | −38.3008 | −1.29039 | −0.645193 | − | 0.764020i | \(-0.723223\pi\) | ||||
−0.645193 | + | 0.764020i | \(0.723223\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 22.6142 | 0.761027 | 0.380513 | − | 0.924775i | \(-0.375747\pi\) | ||||
0.380513 | + | 0.924775i | \(0.375747\pi\) | |||||||
\(884\) | −0.0516910 | + | 0.0895314i | −0.00173856 | + | 0.00301127i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −0.150148 | − | 0.260064i | −0.00504433 | − | 0.00873703i | ||||
\(887\) | −0.948279 | − | 1.64247i | −0.0318401 | − | 0.0551486i | 0.849666 | − | 0.527321i | \(-0.176803\pi\) |
−0.881506 | + | 0.472172i | \(0.843470\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −5.53914 | + | 9.59406i | −0.185777 | + | 0.321775i | ||||
\(890\) | −3.10435 | −0.104058 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −39.5852 | −1.32541 | ||||||||
\(893\) | −1.48116 | + | 2.56545i | −0.0495653 | + | 0.0858496i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −11.2864 | − | 19.5486i | −0.377262 | − | 0.653436i | ||||
\(896\) | −6.97605 | − | 12.0829i | −0.233054 | − | 0.403661i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0.346592 | − | 0.600315i | 0.0115659 | − | 0.0200328i | ||||
\(899\) | 29.1183 | 0.971150 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 4.07443 | 0.135739 | ||||||||
\(902\) | −3.98131 | + | 6.89583i | −0.132563 | + | 0.229606i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −9.98489 | − | 17.2943i | −0.332093 | − | 0.575201i | ||||
\(905\) | 26.6429 | + | 46.1468i | 0.885638 | + | 1.53397i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −3.26547 | + | 5.65596i | −0.108428 | + | 0.187803i | −0.915134 | − | 0.403151i | \(-0.867915\pi\) |
0.806705 | + | 0.590954i | \(0.201248\pi\) | |||||||
\(908\) | 39.5481 | 1.31245 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −0.0219321 | −0.000727042 | ||||||||
\(911\) | −21.5186 | + | 37.2712i | −0.712942 | + | 1.23485i | 0.250806 | + | 0.968037i | \(0.419304\pi\) |
−0.963748 | + | 0.266814i | \(0.914029\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 12.0306 | + | 20.8376i | 0.398154 | + | 0.689623i | ||||
\(914\) | −2.30240 | − | 3.98787i | −0.0761566 | − | 0.131907i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −9.87279 | + | 17.1002i | −0.326206 | + | 0.565006i | ||||
\(917\) | −20.5003 | −0.676980 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −16.7911 | −0.553887 | −0.276943 | − | 0.960886i | \(-0.589321\pi\) | ||||
−0.276943 | + | 0.960886i | \(0.589321\pi\) | |||||||
\(920\) | −1.82180 | + | 3.15545i | −0.0600631 | + | 0.104032i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −4.54611 | − | 7.87410i | −0.149718 | − | 0.259320i | ||||
\(923\) | 0.0549365 | + | 0.0951528i | 0.00180826 | + | 0.00313199i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0.205635 | − | 0.356170i | 0.00676124 | − | 0.0117108i | ||||
\(926\) | 10.3251 | 0.339302 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 34.5412 | 1.13387 | ||||||||
\(929\) | −5.80000 | + | 10.0459i | −0.190292 | + | 0.329595i | −0.945347 | − | 0.326066i | \(-0.894277\pi\) |
0.755055 | + | 0.655661i | \(0.227610\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.09734 | + | 1.90065i | 0.0359639 | + | 0.0622912i | ||||
\(932\) | −6.97971 | − | 12.0892i | −0.228628 | − | 0.395995i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −2.45863 | + | 4.25848i | −0.0804489 | + | 0.139342i | ||||
\(935\) | −36.1920 | −1.18360 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 47.7953 | 1.56140 | 0.780702 | − | 0.624904i | \(-0.214862\pi\) | ||||
0.780702 | + | 0.624904i | \(0.214862\pi\) | |||||||
\(938\) | −3.02278 | + | 5.23561i | −0.0986974 | + | 0.170949i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −14.3662 | − | 24.8830i | −0.468573 | − | 0.811593i | ||||
\(941\) | 5.63018 | + | 9.75175i | 0.183538 | + | 0.317898i | 0.943083 | − | 0.332557i | \(-0.107911\pi\) |
−0.759545 | + | 0.650455i | \(0.774578\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1.90065 | + | 3.29203i | −0.0618938 | + | 0.107203i | ||||
\(944\) | 11.0837 | 0.360743 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −18.0010 | −0.585261 | ||||||||
\(947\) | 3.66595 | − | 6.34961i | 0.119127 | − | 0.206335i | −0.800295 | − | 0.599607i | \(-0.795324\pi\) |
0.919422 | + | 0.393272i | \(0.128657\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −0.00493876 | − | 0.00855418i | −0.000160319 | − | 0.000277681i | ||||
\(950\) | 0.00805835 | + | 0.0139575i | 0.000261447 | + | 0.000452840i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −3.28694 | + | 5.69315i | −0.106530 | + | 0.184516i | ||||
\(953\) | 24.8753 | 0.805791 | 0.402895 | − | 0.915246i | \(-0.368004\pi\) | ||||
0.402895 | + | 0.915246i | \(0.368004\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 24.2483 | 0.784655 | ||||||||
\(956\) | 2.95259 | − | 5.11404i | 0.0954937 | − | 0.165400i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0.599799 | + | 1.03888i | 0.0193786 | + | 0.0335647i | ||||
\(959\) | −7.92265 | − | 13.7224i | −0.255836 | − | 0.443121i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 8.54480 | − | 14.8000i | 0.275639 | − | 0.477420i | ||||
\(962\) | −0.0331976 | −0.00107034 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 48.5079 | 1.56233 | ||||||||
\(965\) | −11.9686 | + | 20.7303i | −0.385283 | + | 0.667330i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 17.0150 | + | 29.4708i | 0.547165 | + | 0.947718i | 0.998467 | + | 0.0553465i | \(0.0176264\pi\) |
−0.451302 | + | 0.892371i | \(0.649040\pi\) | |||||||
\(968\) | 12.8788 | + | 22.3067i | 0.413939 | + | 0.716964i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 4.57469 | − | 7.92360i | 0.146885 | − | 0.254411i | ||||
\(971\) | 34.2476 | 1.09906 | 0.549530 | − | 0.835474i | \(-0.314807\pi\) | ||||
0.549530 | + | 0.835474i | \(0.314807\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −8.10928 | −0.259971 | ||||||||
\(974\) | −1.81954 | + | 3.15154i | −0.0583018 | + | 0.100982i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −10.3510 | − | 17.9285i | −0.331329 | − | 0.573878i | ||||
\(977\) | −11.7087 | − | 20.2800i | −0.374593 | − | 0.648814i | 0.615673 | − | 0.788002i | \(-0.288884\pi\) |
−0.990266 | + | 0.139188i | \(0.955551\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −8.79558 | + | 15.2344i | −0.281108 | + | 0.486893i | ||||
\(980\) | −21.2868 | −0.679980 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 9.37834 | 0.299275 | ||||||||
\(983\) | −16.6016 | + | 28.7547i | −0.529508 | + | 0.917134i | 0.469900 | + | 0.882720i | \(0.344290\pi\) |
−0.999408 | + | 0.0344144i | \(0.989043\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 24.4483 | + | 42.3457i | 0.778988 | + | 1.34925i | ||||
\(986\) | −5.08083 | − | 8.80025i | −0.161806 | − | 0.280257i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −0.00688630 | + | 0.0119274i | −0.000219082 | + | 0.000379462i | ||||
\(989\) | −8.59355 | −0.273259 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −28.1806 | −0.895187 | −0.447594 | − | 0.894237i | \(-0.647719\pi\) | ||||
−0.447594 | + | 0.894237i | \(0.647719\pi\) | |||||||
\(992\) | −8.25050 | + | 14.2903i | −0.261954 | + | 0.453717i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 1.66789 | + | 2.88887i | 0.0529022 | + | 0.0916292i | ||||
\(995\) | 14.2733 | + | 24.7221i | 0.452494 | + | 0.783742i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 22.4754 | − | 38.9285i | 0.711802 | − | 1.23288i | −0.252379 | − | 0.967629i | \(-0.581213\pi\) |
0.964180 | − | 0.265248i | \(-0.0854538\pi\) | |||||||
\(998\) | −10.5249 | −0.333161 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 729.2.c.b.487.4 | 12 | ||
3.2 | odd | 2 | 729.2.c.e.487.3 | 12 | |||
9.2 | odd | 6 | 729.2.a.a.1.4 | 6 | |||
9.4 | even | 3 | inner | 729.2.c.b.244.4 | 12 | ||
9.5 | odd | 6 | 729.2.c.e.244.3 | 12 | |||
9.7 | even | 3 | 729.2.a.d.1.3 | 6 | |||
27.2 | odd | 18 | 27.2.e.a.22.2 | yes | 12 | ||
27.4 | even | 9 | 243.2.e.b.55.2 | 12 | |||
27.5 | odd | 18 | 27.2.e.a.16.2 | ✓ | 12 | ||
27.7 | even | 9 | 243.2.e.a.28.1 | 12 | |||
27.11 | odd | 18 | 243.2.e.c.190.1 | 12 | |||
27.13 | even | 9 | 243.2.e.a.217.1 | 12 | |||
27.14 | odd | 18 | 243.2.e.d.217.2 | 12 | |||
27.16 | even | 9 | 243.2.e.b.190.2 | 12 | |||
27.20 | odd | 18 | 243.2.e.d.28.2 | 12 | |||
27.22 | even | 9 | 81.2.e.a.46.1 | 12 | |||
27.23 | odd | 18 | 243.2.e.c.55.1 | 12 | |||
27.25 | even | 9 | 81.2.e.a.37.1 | 12 | |||
108.59 | even | 18 | 432.2.u.c.97.1 | 12 | |||
108.83 | even | 18 | 432.2.u.c.49.1 | 12 | |||
135.2 | even | 36 | 675.2.u.b.49.2 | 24 | |||
135.29 | odd | 18 | 675.2.l.c.76.1 | 12 | |||
135.32 | even | 36 | 675.2.u.b.124.3 | 24 | |||
135.59 | odd | 18 | 675.2.l.c.151.1 | 12 | |||
135.83 | even | 36 | 675.2.u.b.49.3 | 24 | |||
135.113 | even | 36 | 675.2.u.b.124.2 | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
27.2.e.a.16.2 | ✓ | 12 | 27.5 | odd | 18 | ||
27.2.e.a.22.2 | yes | 12 | 27.2 | odd | 18 | ||
81.2.e.a.37.1 | 12 | 27.25 | even | 9 | |||
81.2.e.a.46.1 | 12 | 27.22 | even | 9 | |||
243.2.e.a.28.1 | 12 | 27.7 | even | 9 | |||
243.2.e.a.217.1 | 12 | 27.13 | even | 9 | |||
243.2.e.b.55.2 | 12 | 27.4 | even | 9 | |||
243.2.e.b.190.2 | 12 | 27.16 | even | 9 | |||
243.2.e.c.55.1 | 12 | 27.23 | odd | 18 | |||
243.2.e.c.190.1 | 12 | 27.11 | odd | 18 | |||
243.2.e.d.28.2 | 12 | 27.20 | odd | 18 | |||
243.2.e.d.217.2 | 12 | 27.14 | odd | 18 | |||
432.2.u.c.49.1 | 12 | 108.83 | even | 18 | |||
432.2.u.c.97.1 | 12 | 108.59 | even | 18 | |||
675.2.l.c.76.1 | 12 | 135.29 | odd | 18 | |||
675.2.l.c.151.1 | 12 | 135.59 | odd | 18 | |||
675.2.u.b.49.2 | 24 | 135.2 | even | 36 | |||
675.2.u.b.49.3 | 24 | 135.83 | even | 36 | |||
675.2.u.b.124.2 | 24 | 135.113 | even | 36 | |||
675.2.u.b.124.3 | 24 | 135.32 | even | 36 | |||
729.2.a.a.1.4 | 6 | 9.2 | odd | 6 | |||
729.2.a.d.1.3 | 6 | 9.7 | even | 3 | |||
729.2.c.b.244.4 | 12 | 9.4 | even | 3 | inner | ||
729.2.c.b.487.4 | 12 | 1.1 | even | 1 | trivial | ||
729.2.c.e.244.3 | 12 | 9.5 | odd | 6 | |||
729.2.c.e.487.3 | 12 | 3.2 | odd | 2 |