Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [390,2,Mod(139,390)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(390, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 3, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("390.139");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 390 = 2 \cdot 3 \cdot 5 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 390.y (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(3.11416567883\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\Q(\zeta_{12})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 139.2 | ||
Root | \(0.866025 + 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 390.139 |
Dual form | 390.2.y.c.289.2 |
$q$-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 \(\left(\mathbb{Z}/390\mathbb{Z}\right)^\times\).
\(n\) | \(131\) | \(157\) | \(301\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(e\left(\frac{2}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.866025 | + | 0.500000i | 0.612372 | + | 0.353553i | ||||
\(3\) | −0.866025 | − | 0.500000i | −0.500000 | − | 0.288675i | ||||
\(4\) | 0.500000 | + | 0.866025i | 0.250000 | + | 0.433013i | ||||
\(5\) | 1.23205 | − | 1.86603i | 0.550990 | − | 0.834512i | ||||
\(6\) | −0.500000 | − | 0.866025i | −0.204124 | − | 0.353553i | ||||
\(7\) | 0.633975 | − | 0.366025i | 0.239620 | − | 0.138345i | −0.375382 | − | 0.926870i | \(-0.622489\pi\) |
0.615002 | + | 0.788526i | \(0.289155\pi\) | |||||||
\(8\) | 1.00000i | 0.353553i | ||||||||
\(9\) | 0.500000 | + | 0.866025i | 0.166667 | + | 0.288675i | ||||
\(10\) | 2.00000 | − | 1.00000i | 0.632456 | − | 0.316228i | ||||
\(11\) | 1.36603 | − | 2.36603i | 0.411872 | − | 0.713384i | −0.583222 | − | 0.812313i | \(-0.698208\pi\) |
0.995094 | + | 0.0989291i | \(0.0315417\pi\) | |||||||
\(12\) | − | 1.00000i | − | 0.288675i | ||||||
\(13\) | −1.59808 | − | 3.23205i | −0.443227 | − | 0.896410i | ||||
\(14\) | 0.732051 | 0.195649 | ||||||||
\(15\) | −2.00000 | + | 1.00000i | −0.516398 | + | 0.258199i | ||||
\(16\) | −0.500000 | + | 0.866025i | −0.125000 | + | 0.216506i | ||||
\(17\) | 2.13397 | − | 1.23205i | 0.517565 | − | 0.298816i | −0.218373 | − | 0.975865i | \(-0.570075\pi\) |
0.735938 | + | 0.677049i | \(0.236742\pi\) | |||||||
\(18\) | 1.00000i | 0.235702i | ||||||||
\(19\) | 2.36603 | + | 4.09808i | 0.542803 | + | 0.940163i | 0.998742 | + | 0.0501517i | \(0.0159705\pi\) |
−0.455938 | + | 0.890011i | \(0.650696\pi\) | |||||||
\(20\) | 2.23205 | + | 0.133975i | 0.499102 | + | 0.0299576i | ||||
\(21\) | −0.732051 | −0.159747 | ||||||||
\(22\) | 2.36603 | − | 1.36603i | 0.504438 | − | 0.291238i | ||||
\(23\) | 3.63397 | + | 2.09808i | 0.757736 | + | 0.437479i | 0.828482 | − | 0.560015i | \(-0.189205\pi\) |
−0.0707462 | + | 0.997494i | \(0.522538\pi\) | |||||||
\(24\) | 0.500000 | − | 0.866025i | 0.102062 | − | 0.176777i | ||||
\(25\) | −1.96410 | − | 4.59808i | −0.392820 | − | 0.919615i | ||||
\(26\) | 0.232051 | − | 3.59808i | 0.0455089 | − | 0.705641i | ||||
\(27\) | − | 1.00000i | − | 0.192450i | ||||||
\(28\) | 0.633975 | + | 0.366025i | 0.119810 | + | 0.0691723i | ||||
\(29\) | 0.232051 | − | 0.401924i | 0.0430908 | − | 0.0746354i | −0.843676 | − | 0.536853i | \(-0.819613\pi\) |
0.886766 | + | 0.462218i | \(0.152946\pi\) | |||||||
\(30\) | −2.23205 | − | 0.133975i | −0.407515 | − | 0.0244603i | ||||
\(31\) | 4.00000 | 0.718421 | 0.359211 | − | 0.933257i | \(-0.383046\pi\) | ||||
0.359211 | + | 0.933257i | \(0.383046\pi\) | |||||||
\(32\) | −0.866025 | + | 0.500000i | −0.153093 | + | 0.0883883i | ||||
\(33\) | −2.36603 | + | 1.36603i | −0.411872 | + | 0.237795i | ||||
\(34\) | 2.46410 | 0.422590 | ||||||||
\(35\) | 0.0980762 | − | 1.63397i | 0.0165779 | − | 0.276192i | ||||
\(36\) | −0.500000 | + | 0.866025i | −0.0833333 | + | 0.144338i | ||||
\(37\) | −5.13397 | − | 2.96410i | −0.844020 | − | 0.487295i | 0.0146085 | − | 0.999893i | \(-0.495350\pi\) |
−0.858629 | + | 0.512598i | \(0.828683\pi\) | |||||||
\(38\) | 4.73205i | 0.767640i | ||||||||
\(39\) | −0.232051 | + | 3.59808i | −0.0371579 | + | 0.576153i | ||||
\(40\) | 1.86603 | + | 1.23205i | 0.295045 | + | 0.194804i | ||||
\(41\) | −0.598076 | + | 1.03590i | −0.0934038 | + | 0.161780i | −0.908941 | − | 0.416924i | \(-0.863108\pi\) |
0.815538 | + | 0.578704i | \(0.196441\pi\) | |||||||
\(42\) | −0.633975 | − | 0.366025i | −0.0978244 | − | 0.0564789i | ||||
\(43\) | −5.83013 | + | 3.36603i | −0.889086 | + | 0.513314i | −0.873643 | − | 0.486567i | \(-0.838249\pi\) |
−0.0154426 | + | 0.999881i | \(0.504916\pi\) | |||||||
\(44\) | 2.73205 | 0.411872 | ||||||||
\(45\) | 2.23205 | + | 0.133975i | 0.332734 | + | 0.0199718i | ||||
\(46\) | 2.09808 | + | 3.63397i | 0.309344 | + | 0.535800i | ||||
\(47\) | 9.66025i | 1.40909i | 0.709658 | + | 0.704546i | \(0.248850\pi\) | ||||
−0.709658 | + | 0.704546i | \(0.751150\pi\) | |||||||
\(48\) | 0.866025 | − | 0.500000i | 0.125000 | − | 0.0721688i | ||||
\(49\) | −3.23205 | + | 5.59808i | −0.461722 | + | 0.799725i | ||||
\(50\) | 0.598076 | − | 4.96410i | 0.0845807 | − | 0.702030i | ||||
\(51\) | −2.46410 | −0.345043 | ||||||||
\(52\) | 2.00000 | − | 3.00000i | 0.277350 | − | 0.416025i | ||||
\(53\) | 4.26795i | 0.586248i | 0.956074 | + | 0.293124i | \(0.0946949\pi\) | ||||
−0.956074 | + | 0.293124i | \(0.905305\pi\) | |||||||
\(54\) | 0.500000 | − | 0.866025i | 0.0680414 | − | 0.117851i | ||||
\(55\) | −2.73205 | − | 5.46410i | −0.368390 | − | 0.736779i | ||||
\(56\) | 0.366025 | + | 0.633975i | 0.0489122 | + | 0.0847184i | ||||
\(57\) | − | 4.73205i | − | 0.626775i | ||||||
\(58\) | 0.401924 | − | 0.232051i | 0.0527752 | − | 0.0304698i | ||||
\(59\) | 4.19615 | + | 7.26795i | 0.546293 | + | 0.946206i | 0.998524 | + | 0.0543060i | \(0.0172946\pi\) |
−0.452232 | + | 0.891900i | \(0.649372\pi\) | |||||||
\(60\) | −1.86603 | − | 1.23205i | −0.240903 | − | 0.159057i | ||||
\(61\) | −7.06218 | − | 12.2321i | −0.904219 | − | 1.56615i | −0.821962 | − | 0.569542i | \(-0.807120\pi\) |
−0.0822573 | − | 0.996611i | \(-0.526213\pi\) | |||||||
\(62\) | 3.46410 | + | 2.00000i | 0.439941 | + | 0.254000i | ||||
\(63\) | 0.633975 | + | 0.366025i | 0.0798733 | + | 0.0461149i | ||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | −8.00000 | − | 1.00000i | −0.992278 | − | 0.124035i | ||||
\(66\) | −2.73205 | −0.336292 | ||||||||
\(67\) | −8.36603 | − | 4.83013i | −1.02207 | − | 0.590094i | −0.107369 | − | 0.994219i | \(-0.534243\pi\) |
−0.914704 | + | 0.404125i | \(0.867576\pi\) | |||||||
\(68\) | 2.13397 | + | 1.23205i | 0.258782 | + | 0.149408i | ||||
\(69\) | −2.09808 | − | 3.63397i | −0.252579 | − | 0.437479i | ||||
\(70\) | 0.901924 | − | 1.36603i | 0.107801 | − | 0.163271i | ||||
\(71\) | −2.36603 | − | 4.09808i | −0.280796 | − | 0.486352i | 0.690785 | − | 0.723060i | \(-0.257265\pi\) |
−0.971581 | + | 0.236708i | \(0.923932\pi\) | |||||||
\(72\) | −0.866025 | + | 0.500000i | −0.102062 | + | 0.0589256i | ||||
\(73\) | 12.6603i | 1.48177i | 0.671632 | + | 0.740885i | \(0.265594\pi\) | ||||
−0.671632 | + | 0.740885i | \(0.734406\pi\) | |||||||
\(74\) | −2.96410 | − | 5.13397i | −0.344570 | − | 0.596812i | ||||
\(75\) | −0.598076 | + | 4.96410i | −0.0690599 | + | 0.573205i | ||||
\(76\) | −2.36603 | + | 4.09808i | −0.271402 | + | 0.470082i | ||||
\(77\) | − | 2.00000i | − | 0.227921i | ||||||
\(78\) | −2.00000 | + | 3.00000i | −0.226455 | + | 0.339683i | ||||
\(79\) | −12.0000 | −1.35011 | −0.675053 | − | 0.737769i | \(-0.735879\pi\) | ||||
−0.675053 | + | 0.737769i | \(0.735879\pi\) | |||||||
\(80\) | 1.00000 | + | 2.00000i | 0.111803 | + | 0.223607i | ||||
\(81\) | −0.500000 | + | 0.866025i | −0.0555556 | + | 0.0962250i | ||||
\(82\) | −1.03590 | + | 0.598076i | −0.114396 | + | 0.0660465i | ||||
\(83\) | 8.73205i | 0.958467i | 0.877687 | + | 0.479234i | \(0.159085\pi\) | ||||
−0.877687 | + | 0.479234i | \(0.840915\pi\) | |||||||
\(84\) | −0.366025 | − | 0.633975i | −0.0399366 | − | 0.0691723i | ||||
\(85\) | 0.330127 | − | 5.50000i | 0.0358073 | − | 0.596559i | ||||
\(86\) | −6.73205 | −0.725936 | ||||||||
\(87\) | −0.401924 | + | 0.232051i | −0.0430908 | + | 0.0248785i | ||||
\(88\) | 2.36603 | + | 1.36603i | 0.252219 | + | 0.145619i | ||||
\(89\) | 4.46410 | − | 7.73205i | 0.473194 | − | 0.819596i | −0.526335 | − | 0.850277i | \(-0.676434\pi\) |
0.999529 | + | 0.0306813i | \(0.00976769\pi\) | |||||||
\(90\) | 1.86603 | + | 1.23205i | 0.196696 | + | 0.129870i | ||||
\(91\) | −2.19615 | − | 1.46410i | −0.230219 | − | 0.153480i | ||||
\(92\) | 4.19615i | 0.437479i | ||||||||
\(93\) | −3.46410 | − | 2.00000i | −0.359211 | − | 0.207390i | ||||
\(94\) | −4.83013 | + | 8.36603i | −0.498190 | + | 0.862890i | ||||
\(95\) | 10.5622 | + | 0.633975i | 1.08366 | + | 0.0650444i | ||||
\(96\) | 1.00000 | 0.102062 | ||||||||
\(97\) | 8.66025 | − | 5.00000i | 0.879316 | − | 0.507673i | 0.00888289 | − | 0.999961i | \(-0.497172\pi\) |
0.870433 | + | 0.492287i | \(0.163839\pi\) | |||||||
\(98\) | −5.59808 | + | 3.23205i | −0.565491 | + | 0.326486i | ||||
\(99\) | 2.73205 | 0.274581 | ||||||||
\(100\) | 3.00000 | − | 4.00000i | 0.300000 | − | 0.400000i | ||||
\(101\) | −0.0358984 | + | 0.0621778i | −0.00357202 | + | 0.00618692i | −0.867806 | − | 0.496903i | \(-0.834470\pi\) |
0.864234 | + | 0.503090i | \(0.167804\pi\) | |||||||
\(102\) | −2.13397 | − | 1.23205i | −0.211295 | − | 0.121991i | ||||
\(103\) | 12.7321i | 1.25453i | 0.778807 | + | 0.627263i | \(0.215825\pi\) | ||||
−0.778807 | + | 0.627263i | \(0.784175\pi\) | |||||||
\(104\) | 3.23205 | − | 1.59808i | 0.316929 | − | 0.156704i | ||||
\(105\) | −0.901924 | + | 1.36603i | −0.0880187 | + | 0.133310i | ||||
\(106\) | −2.13397 | + | 3.69615i | −0.207270 | + | 0.359002i | ||||
\(107\) | 4.09808 | + | 2.36603i | 0.396176 | + | 0.228732i | 0.684833 | − | 0.728700i | \(-0.259875\pi\) |
−0.288657 | + | 0.957433i | \(0.593209\pi\) | |||||||
\(108\) | 0.866025 | − | 0.500000i | 0.0833333 | − | 0.0481125i | ||||
\(109\) | −10.0000 | −0.957826 | −0.478913 | − | 0.877862i | \(-0.658969\pi\) | ||||
−0.478913 | + | 0.877862i | \(0.658969\pi\) | |||||||
\(110\) | 0.366025 | − | 6.09808i | 0.0348992 | − | 0.581429i | ||||
\(111\) | 2.96410 | + | 5.13397i | 0.281340 | + | 0.487295i | ||||
\(112\) | 0.732051i | 0.0691723i | ||||||||
\(113\) | 7.79423 | − | 4.50000i | 0.733219 | − | 0.423324i | −0.0863794 | − | 0.996262i | \(-0.527530\pi\) |
0.819599 | + | 0.572938i | \(0.194196\pi\) | |||||||
\(114\) | 2.36603 | − | 4.09808i | 0.221599 | − | 0.383820i | ||||
\(115\) | 8.39230 | − | 4.19615i | 0.782586 | − | 0.391293i | ||||
\(116\) | 0.464102 | 0.0430908 | ||||||||
\(117\) | 2.00000 | − | 3.00000i | 0.184900 | − | 0.277350i | ||||
\(118\) | 8.39230i | 0.772574i | ||||||||
\(119\) | 0.901924 | − | 1.56218i | 0.0826792 | − | 0.143205i | ||||
\(120\) | −1.00000 | − | 2.00000i | −0.0912871 | − | 0.182574i | ||||
\(121\) | 1.76795 | + | 3.06218i | 0.160723 | + | 0.278380i | ||||
\(122\) | − | 14.1244i | − | 1.27876i | ||||||
\(123\) | 1.03590 | − | 0.598076i | 0.0934038 | − | 0.0539267i | ||||
\(124\) | 2.00000 | + | 3.46410i | 0.179605 | + | 0.311086i | ||||
\(125\) | −11.0000 | − | 2.00000i | −0.983870 | − | 0.178885i | ||||
\(126\) | 0.366025 | + | 0.633975i | 0.0326081 | + | 0.0564789i | ||||
\(127\) | 3.46410 | + | 2.00000i | 0.307389 | + | 0.177471i | 0.645758 | − | 0.763542i | \(-0.276542\pi\) |
−0.338368 | + | 0.941014i | \(0.609875\pi\) | |||||||
\(128\) | −0.866025 | − | 0.500000i | −0.0765466 | − | 0.0441942i | ||||
\(129\) | 6.73205 | 0.592724 | ||||||||
\(130\) | −6.42820 | − | 4.86603i | −0.563791 | − | 0.426779i | ||||
\(131\) | 13.8564 | 1.21064 | 0.605320 | − | 0.795982i | \(-0.293045\pi\) | ||||
0.605320 | + | 0.795982i | \(0.293045\pi\) | |||||||
\(132\) | −2.36603 | − | 1.36603i | −0.205936 | − | 0.118897i | ||||
\(133\) | 3.00000 | + | 1.73205i | 0.260133 | + | 0.150188i | ||||
\(134\) | −4.83013 | − | 8.36603i | −0.417259 | − | 0.722715i | ||||
\(135\) | −1.86603 | − | 1.23205i | −0.160602 | − | 0.106038i | ||||
\(136\) | 1.23205 | + | 2.13397i | 0.105647 | + | 0.182987i | ||||
\(137\) | −9.99038 | + | 5.76795i | −0.853536 | + | 0.492789i | −0.861842 | − | 0.507176i | \(-0.830689\pi\) |
0.00830645 | + | 0.999966i | \(0.497356\pi\) | |||||||
\(138\) | − | 4.19615i | − | 0.357200i | ||||||
\(139\) | −7.46410 | − | 12.9282i | −0.633097 | − | 1.09656i | −0.986915 | − | 0.161242i | \(-0.948450\pi\) |
0.353818 | − | 0.935314i | \(-0.384883\pi\) | |||||||
\(140\) | 1.46410 | − | 0.732051i | 0.123739 | − | 0.0618696i | ||||
\(141\) | 4.83013 | − | 8.36603i | 0.406770 | − | 0.704546i | ||||
\(142\) | − | 4.73205i | − | 0.397105i | ||||||
\(143\) | −9.83013 | − | 0.633975i | −0.822037 | − | 0.0530156i | ||||
\(144\) | −1.00000 | −0.0833333 | ||||||||
\(145\) | −0.464102 | − | 0.928203i | −0.0385415 | − | 0.0770831i | ||||
\(146\) | −6.33013 | + | 10.9641i | −0.523885 | + | 0.907396i | ||||
\(147\) | 5.59808 | − | 3.23205i | 0.461722 | − | 0.266575i | ||||
\(148\) | − | 5.92820i | − | 0.487295i | ||||||
\(149\) | 3.03590 | + | 5.25833i | 0.248710 | + | 0.430779i | 0.963168 | − | 0.268899i | \(-0.0866599\pi\) |
−0.714458 | + | 0.699679i | \(0.753327\pi\) | |||||||
\(150\) | −3.00000 | + | 4.00000i | −0.244949 | + | 0.326599i | ||||
\(151\) | 19.1244 | 1.55632 | 0.778159 | − | 0.628067i | \(-0.216154\pi\) | ||||
0.778159 | + | 0.628067i | \(0.216154\pi\) | |||||||
\(152\) | −4.09808 | + | 2.36603i | −0.332398 | + | 0.191910i | ||||
\(153\) | 2.13397 | + | 1.23205i | 0.172522 | + | 0.0996054i | ||||
\(154\) | 1.00000 | − | 1.73205i | 0.0805823 | − | 0.139573i | ||||
\(155\) | 4.92820 | − | 7.46410i | 0.395843 | − | 0.599531i | ||||
\(156\) | −3.23205 | + | 1.59808i | −0.258771 | + | 0.127948i | ||||
\(157\) | 11.3923i | 0.909205i | 0.890694 | + | 0.454602i | \(0.150219\pi\) | ||||
−0.890694 | + | 0.454602i | \(0.849781\pi\) | |||||||
\(158\) | −10.3923 | − | 6.00000i | −0.826767 | − | 0.477334i | ||||
\(159\) | 2.13397 | − | 3.69615i | 0.169235 | − | 0.293124i | ||||
\(160\) | −0.133975 | + | 2.23205i | −0.0105916 | + | 0.176459i | ||||
\(161\) | 3.07180 | 0.242092 | ||||||||
\(162\) | −0.866025 | + | 0.500000i | −0.0680414 | + | 0.0392837i | ||||
\(163\) | −5.66025 | + | 3.26795i | −0.443345 | + | 0.255966i | −0.705016 | − | 0.709192i | \(-0.749060\pi\) |
0.261670 | + | 0.965157i | \(0.415727\pi\) | |||||||
\(164\) | −1.19615 | −0.0934038 | ||||||||
\(165\) | −0.366025 | + | 6.09808i | −0.0284950 | + | 0.474735i | ||||
\(166\) | −4.36603 | + | 7.56218i | −0.338869 | + | 0.586939i | ||||
\(167\) | 12.0000 | + | 6.92820i | 0.928588 | + | 0.536120i | 0.886365 | − | 0.462988i | \(-0.153223\pi\) |
0.0422232 | + | 0.999108i | \(0.486556\pi\) | |||||||
\(168\) | − | 0.732051i | − | 0.0564789i | ||||||
\(169\) | −7.89230 | + | 10.3301i | −0.607100 | + | 0.794625i | ||||
\(170\) | 3.03590 | − | 4.59808i | 0.232843 | − | 0.352656i | ||||
\(171\) | −2.36603 | + | 4.09808i | −0.180934 | + | 0.313388i | ||||
\(172\) | −5.83013 | − | 3.36603i | −0.444543 | − | 0.256657i | ||||
\(173\) | 19.7321 | − | 11.3923i | 1.50020 | − | 0.866141i | 0.500200 | − | 0.865910i | \(-0.333260\pi\) |
1.00000 | 0.000231036i | \(-7.35409e-5\pi\) | ||||||||
\(174\) | −0.464102 | −0.0351835 | ||||||||
\(175\) | −2.92820 | − | 2.19615i | −0.221351 | − | 0.166014i | ||||
\(176\) | 1.36603 | + | 2.36603i | 0.102968 | + | 0.178346i | ||||
\(177\) | − | 8.39230i | − | 0.630804i | ||||||
\(178\) | 7.73205 | − | 4.46410i | 0.579542 | − | 0.334599i | ||||
\(179\) | 3.90192 | − | 6.75833i | 0.291643 | − | 0.505141i | −0.682555 | − | 0.730834i | \(-0.739131\pi\) |
0.974199 | + | 0.225693i | \(0.0724646\pi\) | |||||||
\(180\) | 1.00000 | + | 2.00000i | 0.0745356 | + | 0.149071i | ||||
\(181\) | 8.12436 | 0.603879 | 0.301939 | − | 0.953327i | \(-0.402366\pi\) | ||||
0.301939 | + | 0.953327i | \(0.402366\pi\) | |||||||
\(182\) | −1.16987 | − | 2.36603i | −0.0867168 | − | 0.175381i | ||||
\(183\) | 14.1244i | 1.04410i | ||||||||
\(184\) | −2.09808 | + | 3.63397i | −0.154672 | + | 0.267900i | ||||
\(185\) | −11.8564 | + | 5.92820i | −0.871700 | + | 0.435850i | ||||
\(186\) | −2.00000 | − | 3.46410i | −0.146647 | − | 0.254000i | ||||
\(187\) | − | 6.73205i | − | 0.492296i | ||||||
\(188\) | −8.36603 | + | 4.83013i | −0.610155 | + | 0.352273i | ||||
\(189\) | −0.366025 | − | 0.633975i | −0.0266244 | − | 0.0461149i | ||||
\(190\) | 8.83013 | + | 5.83013i | 0.640605 | + | 0.422962i | ||||
\(191\) | 1.26795 | + | 2.19615i | 0.0917456 | + | 0.158908i | 0.908246 | − | 0.418437i | \(-0.137422\pi\) |
−0.816500 | + | 0.577345i | \(0.804089\pi\) | |||||||
\(192\) | 0.866025 | + | 0.500000i | 0.0625000 | + | 0.0360844i | ||||
\(193\) | −5.76795 | − | 3.33013i | −0.415186 | − | 0.239708i | 0.277830 | − | 0.960630i | \(-0.410385\pi\) |
−0.693016 | + | 0.720923i | \(0.743718\pi\) | |||||||
\(194\) | 10.0000 | 0.717958 | ||||||||
\(195\) | 6.42820 | + | 4.86603i | 0.460333 | + | 0.348463i | ||||
\(196\) | −6.46410 | −0.461722 | ||||||||
\(197\) | −15.4641 | − | 8.92820i | −1.10177 | − | 0.636108i | −0.165086 | − | 0.986279i | \(-0.552790\pi\) |
−0.936686 | + | 0.350171i | \(0.886123\pi\) | |||||||
\(198\) | 2.36603 | + | 1.36603i | 0.168146 | + | 0.0970792i | ||||
\(199\) | 5.02628 | + | 8.70577i | 0.356304 | + | 0.617136i | 0.987340 | − | 0.158617i | \(-0.0507036\pi\) |
−0.631037 | + | 0.775753i | \(0.717370\pi\) | |||||||
\(200\) | 4.59808 | − | 1.96410i | 0.325133 | − | 0.138883i | ||||
\(201\) | 4.83013 | + | 8.36603i | 0.340691 | + | 0.590094i | ||||
\(202\) | −0.0621778 | + | 0.0358984i | −0.00437482 | + | 0.00252580i | ||||
\(203\) | − | 0.339746i | − | 0.0238455i | ||||||
\(204\) | −1.23205 | − | 2.13397i | −0.0862608 | − | 0.149408i | ||||
\(205\) | 1.19615 | + | 2.39230i | 0.0835429 | + | 0.167086i | ||||
\(206\) | −6.36603 | + | 11.0263i | −0.443542 | + | 0.768237i | ||||
\(207\) | 4.19615i | 0.291653i | ||||||||
\(208\) | 3.59808 | + | 0.232051i | 0.249482 | + | 0.0160898i | ||||
\(209\) | 12.9282 | 0.894263 | ||||||||
\(210\) | −1.46410 | + | 0.732051i | −0.101033 | + | 0.0505163i | ||||
\(211\) | 7.26795 | − | 12.5885i | 0.500346 | − | 0.866625i | −0.499654 | − | 0.866225i | \(-0.666539\pi\) |
1.00000 | 0.000399869i | \(-0.000127282\pi\) | ||||||||
\(212\) | −3.69615 | + | 2.13397i | −0.253853 | + | 0.146562i | ||||
\(213\) | 4.73205i | 0.324235i | ||||||||
\(214\) | 2.36603 | + | 4.09808i | 0.161738 | + | 0.280139i | ||||
\(215\) | −0.901924 | + | 15.0263i | −0.0615107 | + | 1.02478i | ||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | 2.53590 | − | 1.46410i | 0.172148 | − | 0.0993897i | ||||
\(218\) | −8.66025 | − | 5.00000i | −0.586546 | − | 0.338643i | ||||
\(219\) | 6.33013 | − | 10.9641i | 0.427750 | − | 0.740885i | ||||
\(220\) | 3.36603 | − | 5.09808i | 0.226937 | − | 0.343712i | ||||
\(221\) | −7.39230 | − | 4.92820i | −0.497260 | − | 0.331507i | ||||
\(222\) | 5.92820i | 0.397875i | ||||||||
\(223\) | −17.6603 | − | 10.1962i | −1.18262 | − | 0.682785i | −0.225999 | − | 0.974127i | \(-0.572565\pi\) |
−0.956619 | + | 0.291343i | \(0.905898\pi\) | |||||||
\(224\) | −0.366025 | + | 0.633975i | −0.0244561 | + | 0.0423592i | ||||
\(225\) | 3.00000 | − | 4.00000i | 0.200000 | − | 0.266667i | ||||
\(226\) | 9.00000 | 0.598671 | ||||||||
\(227\) | −5.36603 | + | 3.09808i | −0.356156 | + | 0.205627i | −0.667393 | − | 0.744706i | \(-0.732590\pi\) |
0.311237 | + | 0.950332i | \(0.399257\pi\) | |||||||
\(228\) | 4.09808 | − | 2.36603i | 0.271402 | − | 0.156694i | ||||
\(229\) | 12.7846 | 0.844831 | 0.422415 | − | 0.906402i | \(-0.361182\pi\) | ||||
0.422415 | + | 0.906402i | \(0.361182\pi\) | |||||||
\(230\) | 9.36603 | + | 0.562178i | 0.617577 | + | 0.0370689i | ||||
\(231\) | −1.00000 | + | 1.73205i | −0.0657952 | + | 0.113961i | ||||
\(232\) | 0.401924 | + | 0.232051i | 0.0263876 | + | 0.0152349i | ||||
\(233\) | − | 8.39230i | − | 0.549798i | −0.961473 | − | 0.274899i | \(-0.911356\pi\) | ||
0.961473 | − | 0.274899i | \(-0.0886444\pi\) | |||||||
\(234\) | 3.23205 | − | 1.59808i | 0.211286 | − | 0.104470i | ||||
\(235\) | 18.0263 | + | 11.9019i | 1.17590 | + | 0.776396i | ||||
\(236\) | −4.19615 | + | 7.26795i | −0.273146 | + | 0.473103i | ||||
\(237\) | 10.3923 | + | 6.00000i | 0.675053 | + | 0.389742i | ||||
\(238\) | 1.56218 | − | 0.901924i | 0.101261 | − | 0.0584630i | ||||
\(239\) | −26.5885 | −1.71986 | −0.859932 | − | 0.510408i | \(-0.829494\pi\) | ||||
−0.859932 | + | 0.510408i | \(0.829494\pi\) | |||||||
\(240\) | 0.133975 | − | 2.23205i | 0.00864802 | − | 0.144078i | ||||
\(241\) | −5.69615 | − | 9.86603i | −0.366921 | − | 0.635527i | 0.622161 | − | 0.782889i | \(-0.286255\pi\) |
−0.989083 | + | 0.147363i | \(0.952922\pi\) | |||||||
\(242\) | 3.53590i | 0.227296i | ||||||||
\(243\) | 0.866025 | − | 0.500000i | 0.0555556 | − | 0.0320750i | ||||
\(244\) | 7.06218 | − | 12.2321i | 0.452110 | − | 0.783077i | ||||
\(245\) | 6.46410 | + | 12.9282i | 0.412976 | + | 0.825953i | ||||
\(246\) | 1.19615 | 0.0762639 | ||||||||
\(247\) | 9.46410 | − | 14.1962i | 0.602186 | − | 0.903280i | ||||
\(248\) | 4.00000i | 0.254000i | ||||||||
\(249\) | 4.36603 | − | 7.56218i | 0.276686 | − | 0.479234i | ||||
\(250\) | −8.52628 | − | 7.23205i | −0.539249 | − | 0.457395i | ||||
\(251\) | 7.26795 | + | 12.5885i | 0.458749 | + | 0.794576i | 0.998895 | − | 0.0469948i | \(-0.0149644\pi\) |
−0.540146 | + | 0.841571i | \(0.681631\pi\) | |||||||
\(252\) | 0.732051i | 0.0461149i | ||||||||
\(253\) | 9.92820 | − | 5.73205i | 0.624181 | − | 0.360371i | ||||
\(254\) | 2.00000 | + | 3.46410i | 0.125491 | + | 0.217357i | ||||
\(255\) | −3.03590 | + | 4.59808i | −0.190115 | + | 0.287943i | ||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | −2.59808 | − | 1.50000i | −0.162064 | − | 0.0935674i | 0.416775 | − | 0.909010i | \(-0.363160\pi\) |
−0.578838 | + | 0.815442i | \(0.696494\pi\) | |||||||
\(258\) | 5.83013 | + | 3.36603i | 0.362968 | + | 0.209560i | ||||
\(259\) | −4.33975 | −0.269659 | ||||||||
\(260\) | −3.13397 | − | 7.42820i | −0.194361 | − | 0.460678i | ||||
\(261\) | 0.464102 | 0.0287272 | ||||||||
\(262\) | 12.0000 | + | 6.92820i | 0.741362 | + | 0.428026i | ||||
\(263\) | −6.16987 | − | 3.56218i | −0.380451 | − | 0.219653i | 0.297564 | − | 0.954702i | \(-0.403826\pi\) |
−0.678014 | + | 0.735049i | \(0.737159\pi\) | |||||||
\(264\) | −1.36603 | − | 2.36603i | −0.0840731 | − | 0.145619i | ||||
\(265\) | 7.96410 | + | 5.25833i | 0.489231 | + | 0.323017i | ||||
\(266\) | 1.73205 | + | 3.00000i | 0.106199 | + | 0.183942i | ||||
\(267\) | −7.73205 | + | 4.46410i | −0.473194 | + | 0.273199i | ||||
\(268\) | − | 9.66025i | − | 0.590094i | ||||||
\(269\) | −8.19615 | − | 14.1962i | −0.499728 | − | 0.865555i | 0.500272 | − | 0.865868i | \(-0.333233\pi\) |
−1.00000 | 0.000313781i | \(0.999900\pi\) | ||||||||
\(270\) | −1.00000 | − | 2.00000i | −0.0608581 | − | 0.121716i | ||||
\(271\) | 10.9282 | − | 18.9282i | 0.663841 | − | 1.14981i | −0.315757 | − | 0.948840i | \(-0.602258\pi\) |
0.979598 | − | 0.200966i | \(-0.0644082\pi\) | |||||||
\(272\) | 2.46410i | 0.149408i | ||||||||
\(273\) | 1.16987 | + | 2.36603i | 0.0708039 | + | 0.143198i | ||||
\(274\) | −11.5359 | −0.696909 | ||||||||
\(275\) | −13.5622 | − | 1.63397i | −0.817830 | − | 0.0985324i | ||||
\(276\) | 2.09808 | − | 3.63397i | 0.126289 | − | 0.218740i | ||||
\(277\) | 19.3301 | − | 11.1603i | 1.16143 | − | 0.670555i | 0.209787 | − | 0.977747i | \(-0.432723\pi\) |
0.951647 | + | 0.307192i | \(0.0993895\pi\) | |||||||
\(278\) | − | 14.9282i | − | 0.895334i | ||||||
\(279\) | 2.00000 | + | 3.46410i | 0.119737 | + | 0.207390i | ||||
\(280\) | 1.63397 | + | 0.0980762i | 0.0976487 | + | 0.00586117i | ||||
\(281\) | −1.73205 | −0.103325 | −0.0516627 | − | 0.998665i | \(-0.516452\pi\) | ||||
−0.0516627 | + | 0.998665i | \(0.516452\pi\) | |||||||
\(282\) | 8.36603 | − | 4.83013i | 0.498190 | − | 0.287630i | ||||
\(283\) | 8.36603 | + | 4.83013i | 0.497309 | + | 0.287121i | 0.727601 | − | 0.686000i | \(-0.240635\pi\) |
−0.230293 | + | 0.973121i | \(0.573968\pi\) | |||||||
\(284\) | 2.36603 | − | 4.09808i | 0.140398 | − | 0.243176i | ||||
\(285\) | −8.83013 | − | 5.83013i | −0.523052 | − | 0.345347i | ||||
\(286\) | −8.19615 | − | 5.46410i | −0.484649 | − | 0.323099i | ||||
\(287\) | 0.875644i | 0.0516877i | ||||||||
\(288\) | −0.866025 | − | 0.500000i | −0.0510310 | − | 0.0294628i | ||||
\(289\) | −5.46410 | + | 9.46410i | −0.321418 | + | 0.556712i | ||||
\(290\) | 0.0621778 | − | 1.03590i | 0.00365121 | − | 0.0608300i | ||||
\(291\) | −10.0000 | −0.586210 | ||||||||
\(292\) | −10.9641 | + | 6.33013i | −0.641626 | + | 0.370443i | ||||
\(293\) | 8.89230 | − | 5.13397i | 0.519494 | − | 0.299930i | −0.217234 | − | 0.976120i | \(-0.569703\pi\) |
0.736728 | + | 0.676190i | \(0.236370\pi\) | |||||||
\(294\) | 6.46410 | 0.376994 | ||||||||
\(295\) | 18.7321 | + | 1.12436i | 1.09062 | + | 0.0654625i | ||||
\(296\) | 2.96410 | − | 5.13397i | 0.172285 | − | 0.298406i | ||||
\(297\) | −2.36603 | − | 1.36603i | −0.137291 | − | 0.0792648i | ||||
\(298\) | 6.07180i | 0.351730i | ||||||||
\(299\) | 0.973721 | − | 15.0981i | 0.0563117 | − | 0.873144i | ||||
\(300\) | −4.59808 | + | 1.96410i | −0.265470 | + | 0.113397i | ||||
\(301\) | −2.46410 | + | 4.26795i | −0.142028 | + | 0.246001i | ||||
\(302\) | 16.5622 | + | 9.56218i | 0.953046 | + | 0.550242i | ||||
\(303\) | 0.0621778 | − | 0.0358984i | 0.00357202 | − | 0.00206231i | ||||
\(304\) | −4.73205 | −0.271402 | ||||||||
\(305\) | −31.5263 | − | 1.89230i | −1.80519 | − | 0.108353i | ||||
\(306\) | 1.23205 | + | 2.13397i | 0.0704317 | + | 0.121991i | ||||
\(307\) | 22.7321i | 1.29739i | 0.761050 | + | 0.648693i | \(0.224684\pi\) | ||||
−0.761050 | + | 0.648693i | \(0.775316\pi\) | |||||||
\(308\) | 1.73205 | − | 1.00000i | 0.0986928 | − | 0.0569803i | ||||
\(309\) | 6.36603 | − | 11.0263i | 0.362151 | − | 0.627263i | ||||
\(310\) | 8.00000 | − | 4.00000i | 0.454369 | − | 0.227185i | ||||
\(311\) | −21.1244 | −1.19785 | −0.598926 | − | 0.800804i | \(-0.704406\pi\) | ||||
−0.598926 | + | 0.800804i | \(0.704406\pi\) | |||||||
\(312\) | −3.59808 | − | 0.232051i | −0.203701 | − | 0.0131373i | ||||
\(313\) | − | 14.0000i | − | 0.791327i | −0.918396 | − | 0.395663i | \(-0.870515\pi\) | ||
0.918396 | − | 0.395663i | \(-0.129485\pi\) | |||||||
\(314\) | −5.69615 | + | 9.86603i | −0.321452 | + | 0.556772i | ||||
\(315\) | 1.46410 | − | 0.732051i | 0.0824928 | − | 0.0412464i | ||||
\(316\) | −6.00000 | − | 10.3923i | −0.337526 | − | 0.584613i | ||||
\(317\) | − | 26.2679i | − | 1.47536i | −0.675153 | − | 0.737678i | \(-0.735923\pi\) | ||
0.675153 | − | 0.737678i | \(-0.264077\pi\) | |||||||
\(318\) | 3.69615 | − | 2.13397i | 0.207270 | − | 0.119667i | ||||
\(319\) | −0.633975 | − | 1.09808i | −0.0354958 | − | 0.0614805i | ||||
\(320\) | −1.23205 | + | 1.86603i | −0.0688737 | + | 0.104314i | ||||
\(321\) | −2.36603 | − | 4.09808i | −0.132059 | − | 0.228732i | ||||
\(322\) | 2.66025 | + | 1.53590i | 0.148250 | + | 0.0855923i | ||||
\(323\) | 10.0981 | + | 5.83013i | 0.561872 | + | 0.324397i | ||||
\(324\) | −1.00000 | −0.0555556 | ||||||||
\(325\) | −11.7224 | + | 13.6962i | −0.650244 | + | 0.759726i | ||||
\(326\) | −6.53590 | −0.361990 | ||||||||
\(327\) | 8.66025 | + | 5.00000i | 0.478913 | + | 0.276501i | ||||
\(328\) | −1.03590 | − | 0.598076i | −0.0571979 | − | 0.0330232i | ||||
\(329\) | 3.53590 | + | 6.12436i | 0.194940 | + | 0.337647i | ||||
\(330\) | −3.36603 | + | 5.09808i | −0.185294 | + | 0.280640i | ||||
\(331\) | −6.39230 | − | 11.0718i | −0.351353 | − | 0.608561i | 0.635134 | − | 0.772402i | \(-0.280945\pi\) |
−0.986487 | + | 0.163841i | \(0.947612\pi\) | |||||||
\(332\) | −7.56218 | + | 4.36603i | −0.415028 | + | 0.239617i | ||||
\(333\) | − | 5.92820i | − | 0.324864i | ||||||
\(334\) | 6.92820 | + | 12.0000i | 0.379094 | + | 0.656611i | ||||
\(335\) | −19.3205 | + | 9.66025i | −1.05559 | + | 0.527796i | ||||
\(336\) | 0.366025 | − | 0.633975i | 0.0199683 | − | 0.0345861i | ||||
\(337\) | 27.0526i | 1.47365i | 0.676085 | + | 0.736823i | \(0.263675\pi\) | ||||
−0.676085 | + | 0.736823i | \(0.736325\pi\) | |||||||
\(338\) | −12.0000 | + | 5.00000i | −0.652714 | + | 0.271964i | ||||
\(339\) | −9.00000 | −0.488813 | ||||||||
\(340\) | 4.92820 | − | 2.46410i | 0.267269 | − | 0.133635i | ||||
\(341\) | 5.46410 | − | 9.46410i | 0.295898 | − | 0.512510i | ||||
\(342\) | −4.09808 | + | 2.36603i | −0.221599 | + | 0.127940i | ||||
\(343\) | 9.85641i | 0.532196i | ||||||||
\(344\) | −3.36603 | − | 5.83013i | −0.181484 | − | 0.314339i | ||||
\(345\) | −9.36603 | − | 0.562178i | −0.504250 | − | 0.0302666i | ||||
\(346\) | 22.7846 | 1.22491 | ||||||||
\(347\) | −10.0981 | + | 5.83013i | −0.542093 | + | 0.312978i | −0.745927 | − | 0.666028i | \(-0.767993\pi\) |
0.203834 | + | 0.979006i | \(0.434660\pi\) | |||||||
\(348\) | −0.401924 | − | 0.232051i | −0.0215454 | − | 0.0124392i | ||||
\(349\) | −16.4641 | + | 28.5167i | −0.881303 | + | 1.52646i | −0.0314101 | + | 0.999507i | \(0.510000\pi\) |
−0.849893 | + | 0.526955i | \(0.823334\pi\) | |||||||
\(350\) | −1.43782 | − | 3.36603i | −0.0768548 | − | 0.179922i | ||||
\(351\) | −3.23205 | + | 1.59808i | −0.172514 | + | 0.0852990i | ||||
\(352\) | 2.73205i | 0.145619i | ||||||||
\(353\) | −20.1340 | − | 11.6244i | −1.07162 | − | 0.618702i | −0.142999 | − | 0.989723i | \(-0.545675\pi\) |
−0.928625 | + | 0.371021i | \(0.879008\pi\) | |||||||
\(354\) | 4.19615 | − | 7.26795i | 0.223023 | − | 0.386287i | ||||
\(355\) | −10.5622 | − | 0.633975i | −0.560582 | − | 0.0336479i | ||||
\(356\) | 8.92820 | 0.473194 | ||||||||
\(357\) | −1.56218 | + | 0.901924i | −0.0826792 | + | 0.0477349i | ||||
\(358\) | 6.75833 | − | 3.90192i | 0.357189 | − | 0.206223i | ||||
\(359\) | −33.1244 | −1.74824 | −0.874118 | − | 0.485713i | \(-0.838560\pi\) | ||||
−0.874118 | + | 0.485713i | \(0.838560\pi\) | |||||||
\(360\) | −0.133975 | + | 2.23205i | −0.00706108 | + | 0.117639i | ||||
\(361\) | −1.69615 | + | 2.93782i | −0.0892712 | + | 0.154622i | ||||
\(362\) | 7.03590 | + | 4.06218i | 0.369799 | + | 0.213503i | ||||
\(363\) | − | 3.53590i | − | 0.185587i | ||||||
\(364\) | 0.169873 | − | 2.63397i | 0.00890376 | − | 0.138058i | ||||
\(365\) | 23.6244 | + | 15.5981i | 1.23656 | + | 0.816441i | ||||
\(366\) | −7.06218 | + | 12.2321i | −0.369146 | + | 0.639380i | ||||
\(367\) | −16.4378 | − | 9.49038i | −0.858047 | − | 0.495394i | 0.00531057 | − | 0.999986i | \(-0.498310\pi\) |
−0.863358 | + | 0.504592i | \(0.831643\pi\) | |||||||
\(368\) | −3.63397 | + | 2.09808i | −0.189434 | + | 0.109370i | ||||
\(369\) | −1.19615 | −0.0622692 | ||||||||
\(370\) | −13.2321 | − | 0.794229i | −0.687902 | − | 0.0412900i | ||||
\(371\) | 1.56218 | + | 2.70577i | 0.0811042 | + | 0.140477i | ||||
\(372\) | − | 4.00000i | − | 0.207390i | ||||||
\(373\) | 26.3827 | − | 15.2321i | 1.36604 | − | 0.788686i | 0.375624 | − | 0.926772i | \(-0.377429\pi\) |
0.990420 | + | 0.138087i | \(0.0440952\pi\) | |||||||
\(374\) | 3.36603 | − | 5.83013i | 0.174053 | − | 0.301469i | ||||
\(375\) | 8.52628 | + | 7.23205i | 0.440295 | + | 0.373461i | ||||
\(376\) | −9.66025 | −0.498190 | ||||||||
\(377\) | −1.66987 | − | 0.107695i | −0.0860028 | − | 0.00554658i | ||||
\(378\) | − | 0.732051i | − | 0.0376526i | ||||||
\(379\) | −11.1244 | + | 19.2679i | −0.571420 | + | 0.989728i | 0.425001 | + | 0.905193i | \(0.360274\pi\) |
−0.996421 | + | 0.0845351i | \(0.973060\pi\) | |||||||
\(380\) | 4.73205 | + | 9.46410i | 0.242749 | + | 0.485498i | ||||
\(381\) | −2.00000 | − | 3.46410i | −0.102463 | − | 0.177471i | ||||
\(382\) | 2.53590i | 0.129748i | ||||||||
\(383\) | 11.3205 | − | 6.53590i | 0.578451 | − | 0.333969i | −0.182067 | − | 0.983286i | \(-0.558279\pi\) |
0.760518 | + | 0.649317i | \(0.224945\pi\) | |||||||
\(384\) | 0.500000 | + | 0.866025i | 0.0255155 | + | 0.0441942i | ||||
\(385\) | −3.73205 | − | 2.46410i | −0.190203 | − | 0.125582i | ||||
\(386\) | −3.33013 | − | 5.76795i | −0.169499 | − | 0.293581i | ||||
\(387\) | −5.83013 | − | 3.36603i | −0.296362 | − | 0.171105i | ||||
\(388\) | 8.66025 | + | 5.00000i | 0.439658 | + | 0.253837i | ||||
\(389\) | 37.9282 | 1.92304 | 0.961518 | − | 0.274742i | \(-0.0885923\pi\) | ||||
0.961518 | + | 0.274742i | \(0.0885923\pi\) | |||||||
\(390\) | 3.13397 | + | 7.42820i | 0.158695 | + | 0.376142i | ||||
\(391\) | 10.3397 | 0.522903 | ||||||||
\(392\) | −5.59808 | − | 3.23205i | −0.282746 | − | 0.163243i | ||||
\(393\) | −12.0000 | − | 6.92820i | −0.605320 | − | 0.349482i | ||||
\(394\) | −8.92820 | − | 15.4641i | −0.449796 | − | 0.779070i | ||||
\(395\) | −14.7846 | + | 22.3923i | −0.743894 | + | 1.12668i | ||||
\(396\) | 1.36603 | + | 2.36603i | 0.0686454 | + | 0.118897i | ||||
\(397\) | −13.2679 | + | 7.66025i | −0.665899 | + | 0.384457i | −0.794521 | − | 0.607237i | \(-0.792278\pi\) |
0.128622 | + | 0.991694i | \(0.458945\pi\) | |||||||
\(398\) | 10.0526i | 0.503889i | ||||||||
\(399\) | −1.73205 | − | 3.00000i | −0.0867110 | − | 0.150188i | ||||
\(400\) | 4.96410 | + | 0.598076i | 0.248205 | + | 0.0299038i | ||||
\(401\) | −14.5263 | + | 25.1603i | −0.725408 | + | 1.25644i | 0.233398 | + | 0.972381i | \(0.425015\pi\) |
−0.958806 | + | 0.284062i | \(0.908318\pi\) | |||||||
\(402\) | 9.66025i | 0.481810i | ||||||||
\(403\) | −6.39230 | − | 12.9282i | −0.318423 | − | 0.644000i | ||||
\(404\) | −0.0717968 | −0.00357202 | ||||||||
\(405\) | 1.00000 | + | 2.00000i | 0.0496904 | + | 0.0993808i | ||||
\(406\) | 0.169873 | − | 0.294229i | 0.00843065 | − | 0.0146023i | ||||
\(407\) | −14.0263 | + | 8.09808i | −0.695257 | + | 0.401407i | ||||
\(408\) | − | 2.46410i | − | 0.121991i | ||||||
\(409\) | 14.9641 | + | 25.9186i | 0.739927 | + | 1.28159i | 0.952528 | + | 0.304452i | \(0.0984734\pi\) |
−0.212600 | + | 0.977139i | \(0.568193\pi\) | |||||||
\(410\) | −0.160254 | + | 2.66987i | −0.00791438 | + | 0.131856i | ||||
\(411\) | 11.5359 | 0.569024 | ||||||||
\(412\) | −11.0263 | + | 6.36603i | −0.543226 | + | 0.313632i | ||||
\(413\) | 5.32051 | + | 3.07180i | 0.261805 | + | 0.151153i | ||||
\(414\) | −2.09808 | + | 3.63397i | −0.103115 | + | 0.178600i | ||||
\(415\) | 16.2942 | + | 10.7583i | 0.799852 | + | 0.528106i | ||||
\(416\) | 3.00000 | + | 2.00000i | 0.147087 | + | 0.0980581i | ||||
\(417\) | 14.9282i | 0.731037i | ||||||||
\(418\) | 11.1962 | + | 6.46410i | 0.547622 | + | 0.316170i | ||||
\(419\) | −6.73205 | + | 11.6603i | −0.328882 | + | 0.569641i | −0.982290 | − | 0.187365i | \(-0.940005\pi\) |
0.653408 | + | 0.757006i | \(0.273339\pi\) | |||||||
\(420\) | −1.63397 | − | 0.0980762i | −0.0797298 | − | 0.00478563i | ||||
\(421\) | −21.0526 | −1.02604 | −0.513019 | − | 0.858377i | \(-0.671473\pi\) | ||||
−0.513019 | + | 0.858377i | \(0.671473\pi\) | |||||||
\(422\) | 12.5885 | − | 7.26795i | 0.612797 | − | 0.353798i | ||||
\(423\) | −8.36603 | + | 4.83013i | −0.406770 | + | 0.234849i | ||||
\(424\) | −4.26795 | −0.207270 | ||||||||
\(425\) | −9.85641 | − | 7.39230i | −0.478106 | − | 0.358579i | ||||
\(426\) | −2.36603 | + | 4.09808i | −0.114634 | + | 0.198552i | ||||
\(427\) | −8.95448 | − | 5.16987i | −0.433338 | − | 0.250188i | ||||
\(428\) | 4.73205i | 0.228732i | ||||||||
\(429\) | 8.19615 | + | 5.46410i | 0.395714 | + | 0.263809i | ||||
\(430\) | −8.29423 | + | 12.5622i | −0.399983 | + | 0.605802i | ||||
\(431\) | 9.09808 | − | 15.7583i | 0.438239 | − | 0.759052i | −0.559315 | − | 0.828955i | \(-0.688936\pi\) |
0.997554 | + | 0.0699032i | \(0.0222691\pi\) | |||||||
\(432\) | 0.866025 | + | 0.500000i | 0.0416667 | + | 0.0240563i | ||||
\(433\) | −21.8205 | + | 12.5981i | −1.04863 | + | 0.605425i | −0.922265 | − | 0.386559i | \(-0.873663\pi\) |
−0.126362 | + | 0.991984i | \(0.540330\pi\) | |||||||
\(434\) | 2.92820 | 0.140558 | ||||||||
\(435\) | −0.0621778 | + | 1.03590i | −0.00298120 | + | 0.0496675i | ||||
\(436\) | −5.00000 | − | 8.66025i | −0.239457 | − | 0.414751i | ||||
\(437\) | 19.8564i | 0.949861i | ||||||||
\(438\) | 10.9641 | − | 6.33013i | 0.523885 | − | 0.302465i | ||||
\(439\) | 10.0981 | − | 17.4904i | 0.481955 | − | 0.834770i | −0.517831 | − | 0.855483i | \(-0.673260\pi\) |
0.999785 | + | 0.0207128i | \(0.00659358\pi\) | |||||||
\(440\) | 5.46410 | − | 2.73205i | 0.260491 | − | 0.130245i | ||||
\(441\) | −6.46410 | −0.307814 | ||||||||
\(442\) | −3.93782 | − | 7.96410i | −0.187303 | − | 0.378814i | ||||
\(443\) | − | 34.6410i | − | 1.64584i | −0.568154 | − | 0.822922i | \(-0.692342\pi\) | ||
0.568154 | − | 0.822922i | \(-0.307658\pi\) | |||||||
\(444\) | −2.96410 | + | 5.13397i | −0.140670 | + | 0.243648i | ||||
\(445\) | −8.92820 | − | 17.8564i | −0.423237 | − | 0.846475i | ||||
\(446\) | −10.1962 | − | 17.6603i | −0.482802 | − | 0.836237i | ||||
\(447\) | − | 6.07180i | − | 0.287186i | ||||||
\(448\) | −0.633975 | + | 0.366025i | −0.0299525 | + | 0.0172931i | ||||
\(449\) | 9.92820 | + | 17.1962i | 0.468541 | + | 0.811537i | 0.999353 | − | 0.0359526i | \(-0.0114465\pi\) |
−0.530813 | + | 0.847489i | \(0.678113\pi\) | |||||||
\(450\) | 4.59808 | − | 1.96410i | 0.216755 | − | 0.0925886i | ||||
\(451\) | 1.63397 | + | 2.83013i | 0.0769409 | + | 0.133265i | ||||
\(452\) | 7.79423 | + | 4.50000i | 0.366610 | + | 0.211662i | ||||
\(453\) | −16.5622 | − | 9.56218i | −0.778159 | − | 0.449270i | ||||
\(454\) | −6.19615 | −0.290800 | ||||||||
\(455\) | −5.43782 | + | 2.29423i | −0.254929 | + | 0.107555i | ||||
\(456\) | 4.73205 | 0.221599 | ||||||||
\(457\) | −16.6244 | − | 9.59808i | −0.777655 | − | 0.448979i | 0.0579439 | − | 0.998320i | \(-0.481546\pi\) |
−0.835598 | + | 0.549341i | \(0.814879\pi\) | |||||||
\(458\) | 11.0718 | + | 6.39230i | 0.517351 | + | 0.298693i | ||||
\(459\) | −1.23205 | − | 2.13397i | −0.0575072 | − | 0.0996054i | ||||
\(460\) | 7.83013 | + | 5.16987i | 0.365082 | + | 0.241047i | ||||
\(461\) | −19.9641 | − | 34.5788i | −0.929821 | − | 1.61050i | −0.783618 | − | 0.621242i | \(-0.786628\pi\) |
−0.146202 | − | 0.989255i | \(-0.546705\pi\) | |||||||
\(462\) | −1.73205 | + | 1.00000i | −0.0805823 | + | 0.0465242i | ||||
\(463\) | − | 23.6603i | − | 1.09959i | −0.835301 | − | 0.549793i | \(-0.814707\pi\) | ||
0.835301 | − | 0.549793i | \(-0.185293\pi\) | |||||||
\(464\) | 0.232051 | + | 0.401924i | 0.0107727 | + | 0.0186588i | ||||
\(465\) | −8.00000 | + | 4.00000i | −0.370991 | + | 0.185496i | ||||
\(466\) | 4.19615 | − | 7.26795i | 0.194383 | − | 0.336681i | ||||
\(467\) | − | 16.0526i | − | 0.742824i | −0.928468 | − | 0.371412i | \(-0.878874\pi\) | ||
0.928468 | − | 0.371412i | \(-0.121126\pi\) | |||||||
\(468\) | 3.59808 | + | 0.232051i | 0.166321 | + | 0.0107266i | ||||
\(469\) | −7.07180 | −0.326545 | ||||||||
\(470\) | 9.66025 | + | 19.3205i | 0.445594 | + | 0.891189i | ||||
\(471\) | 5.69615 | − | 9.86603i | 0.262465 | − | 0.454602i | ||||
\(472\) | −7.26795 | + | 4.19615i | −0.334534 | + | 0.193144i | ||||
\(473\) | 18.3923i | 0.845679i | ||||||||
\(474\) | 6.00000 | + | 10.3923i | 0.275589 | + | 0.477334i | ||||
\(475\) | 14.1962 | − | 18.9282i | 0.651364 | − | 0.868486i | ||||
\(476\) | 1.80385 | 0.0826792 | ||||||||
\(477\) | −3.69615 | + | 2.13397i | −0.169235 | + | 0.0977080i | ||||
\(478\) | −23.0263 | − | 13.2942i | −1.05320 | − | 0.608064i | ||||
\(479\) | −8.00000 | + | 13.8564i | −0.365529 | + | 0.633115i | −0.988861 | − | 0.148842i | \(-0.952445\pi\) |
0.623332 | + | 0.781958i | \(0.285779\pi\) | |||||||
\(480\) | 1.23205 | − | 1.86603i | 0.0562352 | − | 0.0851720i | ||||
\(481\) | −1.37564 | + | 21.3301i | −0.0627240 | + | 0.972570i | ||||
\(482\) | − | 11.3923i | − | 0.518905i | ||||||
\(483\) | −2.66025 | − | 1.53590i | −0.121046 | − | 0.0698858i | ||||
\(484\) | −1.76795 | + | 3.06218i | −0.0803613 | + | 0.139190i | ||||
\(485\) | 1.33975 | − | 22.3205i | 0.0608347 | − | 1.01352i | ||||
\(486\) | 1.00000 | 0.0453609 | ||||||||
\(487\) | 17.7058 | − | 10.2224i | 0.802325 | − | 0.463223i | −0.0419584 | − | 0.999119i | \(-0.513360\pi\) |
0.844284 | + | 0.535897i | \(0.180026\pi\) | |||||||
\(488\) | 12.2321 | − | 7.06218i | 0.553719 | − | 0.319690i | ||||
\(489\) | 6.53590 | 0.295564 | ||||||||
\(490\) | −0.866025 | + | 14.4282i | −0.0391230 | + | 0.651800i | ||||
\(491\) | −16.0981 | + | 27.8827i | −0.726496 | + | 1.25833i | 0.231859 | + | 0.972749i | \(0.425519\pi\) |
−0.958355 | + | 0.285579i | \(0.907814\pi\) | |||||||
\(492\) | 1.03590 | + | 0.598076i | 0.0467019 | + | 0.0269634i | ||||
\(493\) | − | 1.14359i | − | 0.0515049i | ||||||
\(494\) | 15.2942 | − | 7.56218i | 0.688120 | − | 0.340238i | ||||
\(495\) | 3.36603 | − | 5.09808i | 0.151292 | − | 0.229141i | ||||
\(496\) | −2.00000 | + | 3.46410i | −0.0898027 | + | 0.155543i | ||||
\(497\) | −3.00000 | − | 1.73205i | −0.134568 | − | 0.0776931i | ||||
\(498\) | 7.56218 | − | 4.36603i | 0.338869 | − | 0.195646i | ||||
\(499\) | −19.6077 | −0.877761 | −0.438880 | − | 0.898545i | \(-0.644625\pi\) | ||||
−0.438880 | + | 0.898545i | \(0.644625\pi\) | |||||||
\(500\) | −3.76795 | − | 10.5263i | −0.168508 | − | 0.470750i | ||||
\(501\) | −6.92820 | − | 12.0000i | −0.309529 | − | 0.536120i | ||||
\(502\) | 14.5359i | 0.648769i | ||||||||
\(503\) | 27.8827 | − | 16.0981i | 1.24323 | − | 0.717778i | 0.273478 | − | 0.961878i | \(-0.411826\pi\) |
0.969750 | + | 0.244101i | \(0.0784927\pi\) | |||||||
\(504\) | −0.366025 | + | 0.633975i | −0.0163041 | + | 0.0282395i | ||||
\(505\) | 0.0717968 | + | 0.143594i | 0.00319491 | + | 0.00638983i | ||||
\(506\) | 11.4641 | 0.509641 | ||||||||
\(507\) | 12.0000 | − | 5.00000i | 0.532939 | − | 0.222058i | ||||
\(508\) | 4.00000i | 0.177471i | ||||||||
\(509\) | 12.3564 | − | 21.4019i | 0.547688 | − | 0.948624i | −0.450744 | − | 0.892653i | \(-0.648841\pi\) |
0.998432 | − | 0.0559705i | \(-0.0178253\pi\) | |||||||
\(510\) | −4.92820 | + | 2.46410i | −0.218225 | + | 0.109112i | ||||
\(511\) | 4.63397 | + | 8.02628i | 0.204995 | + | 0.355062i | ||||
\(512\) | − | 1.00000i | − | 0.0441942i | ||||||
\(513\) | 4.09808 | − | 2.36603i | 0.180934 | − | 0.104463i | ||||
\(514\) | −1.50000 | − | 2.59808i | −0.0661622 | − | 0.114596i | ||||
\(515\) | 23.7583 | + | 15.6865i | 1.04692 | + | 0.691231i | ||||
\(516\) | 3.36603 | + | 5.83013i | 0.148181 | + | 0.256657i | ||||
\(517\) | 22.8564 | + | 13.1962i | 1.00522 | + | 0.580366i | ||||
\(518\) | −3.75833 | − | 2.16987i | −0.165132 | − | 0.0953387i | ||||
\(519\) | −22.7846 | −1.00013 | ||||||||
\(520\) | 1.00000 | − | 8.00000i | 0.0438529 | − | 0.350823i | ||||
\(521\) | 39.4449 | 1.72811 | 0.864055 | − | 0.503397i | \(-0.167917\pi\) | ||||
0.864055 | + | 0.503397i | \(0.167917\pi\) | |||||||
\(522\) | 0.401924 | + | 0.232051i | 0.0175917 | + | 0.0101566i | ||||
\(523\) | −19.4378 | − | 11.2224i | −0.849957 | − | 0.490723i | 0.0106796 | − | 0.999943i | \(-0.496601\pi\) |
−0.860636 | + | 0.509220i | \(0.829934\pi\) | |||||||
\(524\) | 6.92820 | + | 12.0000i | 0.302660 | + | 0.524222i | ||||
\(525\) | 1.43782 | + | 3.36603i | 0.0627517 | + | 0.146905i | ||||
\(526\) | −3.56218 | − | 6.16987i | −0.155318 | − | 0.269019i | ||||
\(527\) | 8.53590 | − | 4.92820i | 0.371830 | − | 0.214676i | ||||
\(528\) | − | 2.73205i | − | 0.118897i | ||||||
\(529\) | −2.69615 | − | 4.66987i | −0.117224 | − | 0.203038i | ||||
\(530\) | 4.26795 | + | 8.53590i | 0.185388 | + | 0.370776i | ||||
\(531\) | −4.19615 | + | 7.26795i | −0.182098 | + | 0.315402i | ||||
\(532\) | 3.46410i | 0.150188i | ||||||||
\(533\) | 4.30385 | + | 0.277568i | 0.186420 | + | 0.0120228i | ||||
\(534\) | −8.92820 | −0.386361 | ||||||||
\(535\) | 9.46410 | − | 4.73205i | 0.409169 | − | 0.204584i | ||||
\(536\) | 4.83013 | − | 8.36603i | 0.208630 | − | 0.361357i | ||||
\(537\) | −6.75833 | + | 3.90192i | −0.291643 | + | 0.168380i | ||||
\(538\) | − | 16.3923i | − | 0.706722i | ||||||
\(539\) | 8.83013 | + | 15.2942i | 0.380340 | + | 0.658769i | ||||
\(540\) | 0.133975 | − | 2.23205i | 0.00576535 | − | 0.0960522i | ||||
\(541\) | 9.19615 | 0.395373 | 0.197687 | − | 0.980265i | \(-0.436657\pi\) | ||||
0.197687 | + | 0.980265i | \(0.436657\pi\) | |||||||
\(542\) | 18.9282 | − | 10.9282i | 0.813036 | − | 0.469407i | ||||
\(543\) | −7.03590 | − | 4.06218i | −0.301939 | − | 0.174325i | ||||
\(544\) | −1.23205 | + | 2.13397i | −0.0528237 | + | 0.0914934i | ||||
\(545\) | −12.3205 | + | 18.6603i | −0.527753 | + | 0.799317i | ||||
\(546\) | −0.169873 | + | 2.63397i | −0.00726989 | + | 0.112724i | ||||
\(547\) | − | 36.1962i | − | 1.54764i | −0.633408 | − | 0.773818i | \(-0.718345\pi\) | ||
0.633408 | − | 0.773818i | \(-0.281655\pi\) | |||||||
\(548\) | −9.99038 | − | 5.76795i | −0.426768 | − | 0.246395i | ||||
\(549\) | 7.06218 | − | 12.2321i | 0.301406 | − | 0.522051i | ||||
\(550\) | −10.9282 | − | 8.19615i | −0.465980 | − | 0.349485i | ||||
\(551\) | 2.19615 | 0.0935592 | ||||||||
\(552\) | 3.63397 | − | 2.09808i | 0.154672 | − | 0.0893001i | ||||
\(553\) | −7.60770 | + | 4.39230i | −0.323512 | + | 0.186780i | ||||
\(554\) | 22.3205 | 0.948308 | ||||||||
\(555\) | 13.2321 | + | 0.794229i | 0.561669 | + | 0.0337131i | ||||
\(556\) | 7.46410 | − | 12.9282i | 0.316548 | − | 0.548278i | ||||
\(557\) | 2.30385 | + | 1.33013i | 0.0976172 | + | 0.0563593i | 0.548014 | − | 0.836469i | \(-0.315384\pi\) |
−0.450397 | + | 0.892829i | \(0.648717\pi\) | |||||||
\(558\) | 4.00000i | 0.169334i | ||||||||
\(559\) | 20.1962 | + | 13.4641i | 0.854206 | + | 0.569471i | ||||
\(560\) | 1.36603 | + | 0.901924i | 0.0577251 | + | 0.0381132i | ||||
\(561\) | −3.36603 | + | 5.83013i | −0.142114 | + | 0.246148i | ||||
\(562\) | −1.50000 | − | 0.866025i | −0.0632737 | − | 0.0365311i | ||||
\(563\) | 6.92820 | − | 4.00000i | 0.291989 | − | 0.168580i | −0.346850 | − | 0.937921i | \(-0.612749\pi\) |
0.638838 | + | 0.769341i | \(0.279415\pi\) | |||||||
\(564\) | 9.66025 | 0.406770 | ||||||||
\(565\) | 1.20577 | − | 20.0885i | 0.0507272 | − | 0.845128i | ||||
\(566\) | 4.83013 | + | 8.36603i | 0.203025 | + | 0.351650i | ||||
\(567\) | 0.732051i | 0.0307432i | ||||||||
\(568\) | 4.09808 | − | 2.36603i | 0.171951 | − | 0.0992762i | ||||
\(569\) | 22.9282 | − | 39.7128i | 0.961200 | − | 1.66485i | 0.241706 | − | 0.970350i | \(-0.422293\pi\) |
0.719494 | − | 0.694498i | \(-0.244374\pi\) | |||||||
\(570\) | −4.73205 | − | 9.46410i | −0.198204 | − | 0.396408i | ||||
\(571\) | −8.33975 | −0.349008 | −0.174504 | − | 0.984657i | \(-0.555832\pi\) | ||||
−0.174504 | + | 0.984657i | \(0.555832\pi\) | |||||||
\(572\) | −4.36603 | − | 8.83013i | −0.182553 | − | 0.369206i | ||||
\(573\) | − | 2.53590i | − | 0.105939i | ||||||
\(574\) | −0.437822 | + | 0.758330i | −0.0182743 | + | 0.0316521i | ||||
\(575\) | 2.50962 | − | 20.8301i | 0.104658 | − | 0.868676i | ||||
\(576\) | −0.500000 | − | 0.866025i | −0.0208333 | − | 0.0360844i | ||||
\(577\) | 27.9808i | 1.16485i | 0.812883 | + | 0.582427i | \(0.197897\pi\) | ||||
−0.812883 | + | 0.582427i | \(0.802103\pi\) | |||||||
\(578\) | −9.46410 | + | 5.46410i | −0.393655 | + | 0.227277i | ||||
\(579\) | 3.33013 | + | 5.76795i | 0.138395 | + | 0.239708i | ||||
\(580\) | 0.571797 | − | 0.866025i | 0.0237426 | − | 0.0359597i | ||||
\(581\) | 3.19615 | + | 5.53590i | 0.132599 | + | 0.229668i | ||||
\(582\) | −8.66025 | − | 5.00000i | −0.358979 | − | 0.207257i | ||||
\(583\) | 10.0981 | + | 5.83013i | 0.418220 | + | 0.241459i | ||||
\(584\) | −12.6603 | −0.523885 | ||||||||
\(585\) | −3.13397 | − | 7.42820i | −0.129574 | − | 0.307118i | ||||
\(586\) | 10.2679 | 0.424165 | ||||||||
\(587\) | 32.7846 | + | 18.9282i | 1.35317 | + | 0.781251i | 0.988692 | − | 0.149963i | \(-0.0479155\pi\) |
0.364474 | + | 0.931214i | \(0.381249\pi\) | |||||||
\(588\) | 5.59808 | + | 3.23205i | 0.230861 | + | 0.133288i | ||||
\(589\) | 9.46410 | + | 16.3923i | 0.389962 | + | 0.675433i | ||||
\(590\) | 15.6603 | + | 10.3397i | 0.644722 | + | 0.425681i | ||||
\(591\) | 8.92820 | + | 15.4641i | 0.367257 | + | 0.636108i | ||||
\(592\) | 5.13397 | − | 2.96410i | 0.211005 | − | 0.121824i | ||||
\(593\) | − | 1.39230i | − | 0.0571751i | −0.999591 | − | 0.0285876i | \(-0.990899\pi\) | ||
0.999591 | − | 0.0285876i | \(-0.00910094\pi\) | |||||||
\(594\) | −1.36603 | − | 2.36603i | −0.0560487 | − | 0.0970792i | ||||
\(595\) | −1.80385 | − | 3.60770i | −0.0739505 | − | 0.147901i | ||||
\(596\) | −3.03590 | + | 5.25833i | −0.124355 | + | 0.215390i | ||||
\(597\) | − | 10.0526i | − | 0.411424i | ||||||
\(598\) | 8.39230 | − | 12.5885i | 0.343187 | − | 0.514780i | ||||
\(599\) | 32.7846 | 1.33954 | 0.669771 | − | 0.742567i | \(-0.266392\pi\) | ||||
0.669771 | + | 0.742567i | \(0.266392\pi\) | |||||||
\(600\) | −4.96410 | − | 0.598076i | −0.202659 | − | 0.0244164i | ||||
\(601\) | −8.50000 | + | 14.7224i | −0.346722 | + | 0.600541i | −0.985665 | − | 0.168714i | \(-0.946039\pi\) |
0.638943 | + | 0.769254i | \(0.279372\pi\) | |||||||
\(602\) | −4.26795 | + | 2.46410i | −0.173949 | + | 0.100429i | ||||
\(603\) | − | 9.66025i | − | 0.393396i | ||||||
\(604\) | 9.56218 | + | 16.5622i | 0.389079 | + | 0.673905i | ||||
\(605\) | 7.89230 | + | 0.473721i | 0.320868 | + | 0.0192595i | ||||
\(606\) | 0.0717968 | 0.00291654 | ||||||||
\(607\) | −23.9090 | + | 13.8038i | −0.970435 | + | 0.560281i | −0.899369 | − | 0.437191i | \(-0.855973\pi\) |
−0.0710661 | + | 0.997472i | \(0.522640\pi\) | |||||||
\(608\) | −4.09808 | − | 2.36603i | −0.166199 | − | 0.0959550i | ||||
\(609\) | −0.169873 | + | 0.294229i | −0.00688360 | + | 0.0119227i | ||||
\(610\) | −26.3564 | − | 17.4019i | −1.06714 | − | 0.704583i | ||||
\(611\) | 31.2224 | − | 15.4378i | 1.26312 | − | 0.624547i | ||||
\(612\) | 2.46410i | 0.0996054i | ||||||||
\(613\) | 17.1340 | + | 9.89230i | 0.692035 | + | 0.399546i | 0.804374 | − | 0.594123i | \(-0.202501\pi\) |
−0.112339 | + | 0.993670i | \(0.535834\pi\) | |||||||
\(614\) | −11.3660 | + | 19.6865i | −0.458695 | + | 0.794484i | ||||
\(615\) | 0.160254 | − | 2.66987i | 0.00646207 | − | 0.107660i | ||||
\(616\) | 2.00000 | 0.0805823 | ||||||||
\(617\) | −19.6699 | + | 11.3564i | −0.791879 | + | 0.457192i | −0.840624 | − | 0.541620i | \(-0.817811\pi\) |
0.0487445 | + | 0.998811i | \(0.484478\pi\) | |||||||
\(618\) | 11.0263 | − | 6.36603i | 0.443542 | − | 0.256079i | ||||
\(619\) | −40.1051 | −1.61196 | −0.805980 | − | 0.591942i | \(-0.798361\pi\) | ||||
−0.805980 | + | 0.591942i | \(0.798361\pi\) | |||||||
\(620\) | 8.92820 | + | 0.535898i | 0.358565 | + | 0.0215222i | ||||
\(621\) | 2.09808 | − | 3.63397i | 0.0841929 | − | 0.145826i | ||||
\(622\) | −18.2942 | − | 10.5622i | −0.733532 | − | 0.423505i | ||||
\(623\) | − | 6.53590i | − | 0.261855i | ||||||
\(624\) | −3.00000 | − | 2.00000i | −0.120096 | − | 0.0800641i | ||||
\(625\) | −17.2846 | + | 18.0622i | −0.691384 | + | 0.722487i | ||||
\(626\) | 7.00000 | − | 12.1244i | 0.279776 | − | 0.484587i | ||||
\(627\) | −11.1962 | − | 6.46410i | −0.447131 | − | 0.258151i | ||||
\(628\) | −9.86603 | + | 5.69615i | −0.393697 | + | 0.227301i | ||||
\(629\) | −14.6077 | −0.582447 | ||||||||
\(630\) | 1.63397 | + | 0.0980762i | 0.0650991 | + | 0.00390745i | ||||
\(631\) | 8.92820 | + | 15.4641i | 0.355426 | + | 0.615616i | 0.987191 | − | 0.159544i | \(-0.0510024\pi\) |
−0.631765 | + | 0.775160i | \(0.717669\pi\) | |||||||
\(632\) | − | 12.0000i | − | 0.477334i | ||||||
\(633\) | −12.5885 | + | 7.26795i | −0.500346 | + | 0.288875i | ||||
\(634\) | 13.1340 | − | 22.7487i | 0.521617 | − | 0.903467i | ||||
\(635\) | 8.00000 | − | 4.00000i | 0.317470 | − | 0.158735i | ||||
\(636\) | 4.26795 | 0.169235 | ||||||||
\(637\) | 23.2583 | + | 1.50000i | 0.921529 | + | 0.0594322i | ||||
\(638\) | − | 1.26795i | − | 0.0501986i | ||||||
\(639\) | 2.36603 | − | 4.09808i | 0.0935985 | − | 0.162117i | ||||
\(640\) | −2.00000 | + | 1.00000i | −0.0790569 | + | 0.0395285i | ||||
\(641\) | 14.5263 | + | 25.1603i | 0.573754 | + | 0.993770i | 0.996176 | + | 0.0873711i | \(0.0278466\pi\) |
−0.422422 | + | 0.906399i | \(0.638820\pi\) | |||||||
\(642\) | − | 4.73205i | − | 0.186759i | ||||||
\(643\) | 28.3923 | − | 16.3923i | 1.11968 | − | 0.646449i | 0.178363 | − | 0.983965i | \(-0.442920\pi\) |
0.941320 | + | 0.337515i | \(0.109586\pi\) | |||||||
\(644\) | 1.53590 | + | 2.66025i | 0.0605229 | + | 0.104829i | ||||
\(645\) | 8.29423 | − | 12.5622i | 0.326585 | − | 0.494635i | ||||
\(646\) | 5.83013 | + | 10.0981i | 0.229383 | + | 0.397303i | ||||
\(647\) | 9.80385 | + | 5.66025i | 0.385429 | + | 0.222528i | 0.680178 | − | 0.733047i | \(-0.261903\pi\) |
−0.294749 | + | 0.955575i | \(0.595236\pi\) | |||||||
\(648\) | −0.866025 | − | 0.500000i | −0.0340207 | − | 0.0196419i | ||||
\(649\) | 22.9282 | 0.900011 | ||||||||
\(650\) | −17.0000 | + | 6.00000i | −0.666795 | + | 0.235339i | ||||
\(651\) | −2.92820 | −0.114765 | ||||||||
\(652\) | −5.66025 | − | 3.26795i | −0.221673 | − | 0.127983i | ||||
\(653\) | 31.7321 | + | 18.3205i | 1.24177 | + | 0.716937i | 0.969455 | − | 0.245271i | \(-0.0788769\pi\) |
0.272317 | + | 0.962208i | \(0.412210\pi\) | |||||||
\(654\) | 5.00000 | + | 8.66025i | 0.195515 | + | 0.338643i | ||||
\(655\) | 17.0718 | − | 25.8564i | 0.667050 | − | 1.01029i | ||||
\(656\) | −0.598076 | − | 1.03590i | −0.0233510 | − | 0.0404450i | ||||
\(657\) | −10.9641 | + | 6.33013i | −0.427750 | + | 0.246962i | ||||
\(658\) | 7.07180i | 0.275687i | ||||||||
\(659\) | −17.2679 | − | 29.9090i | −0.672664 | − | 1.16509i | −0.977146 | − | 0.212570i | \(-0.931817\pi\) |
0.304482 | − | 0.952518i | \(-0.401517\pi\) | |||||||
\(660\) | −5.46410 | + | 2.73205i | −0.212690 | + | 0.106345i | ||||
\(661\) | −3.25833 | + | 5.64359i | −0.126734 | + | 0.219510i | −0.922410 | − | 0.386213i | \(-0.873783\pi\) |
0.795675 | + | 0.605724i | \(0.207116\pi\) | |||||||
\(662\) | − | 12.7846i | − | 0.496888i | ||||||
\(663\) | 3.93782 | + | 7.96410i | 0.152932 | + | 0.309300i | ||||
\(664\) | −8.73205 | −0.338869 | ||||||||
\(665\) | 6.92820 | − | 3.46410i | 0.268664 | − | 0.134332i | ||||
\(666\) | 2.96410 | − | 5.13397i | 0.114857 | − | 0.198937i | ||||
\(667\) | 1.68653 | − | 0.973721i | 0.0653028 | − | 0.0377026i | ||||
\(668\) | 13.8564i | 0.536120i | ||||||||
\(669\) | 10.1962 | + | 17.6603i | 0.394206 | + | 0.682785i | ||||
\(670\) | −21.5622 | − | 1.29423i | −0.833020 | − | 0.0500004i | ||||
\(671\) | −38.5885 | −1.48969 | ||||||||
\(672\) | 0.633975 | − | 0.366025i | 0.0244561 | − | 0.0141197i | ||||
\(673\) | −11.8923 | − | 6.86603i | −0.458415 | − | 0.264666i | 0.252963 | − | 0.967476i | \(-0.418595\pi\) |
−0.711377 | + | 0.702810i | \(0.751928\pi\) | |||||||
\(674\) | −13.5263 | + | 23.4282i | −0.521013 | + | 0.902421i | ||||
\(675\) | −4.59808 | + | 1.96410i | −0.176980 | + | 0.0755983i | ||||
\(676\) | −12.8923 | − | 1.66987i | −0.495858 | − | 0.0642259i | ||||
\(677\) | − | 20.6410i | − | 0.793299i | −0.917970 | − | 0.396649i | \(-0.870173\pi\) | ||
0.917970 | − | 0.396649i | \(-0.129827\pi\) | |||||||
\(678\) | −7.79423 | − | 4.50000i | −0.299336 | − | 0.172821i | ||||
\(679\) | 3.66025 | − | 6.33975i | 0.140468 | − | 0.243297i | ||||
\(680\) | 5.50000 | + | 0.330127i | 0.210915 | + | 0.0126598i | ||||
\(681\) | 6.19615 | 0.237437 | ||||||||
\(682\) | 9.46410 | − | 5.46410i | 0.362399 | − | 0.209231i | ||||
\(683\) | −11.3205 | + | 6.53590i | −0.433167 | + | 0.250089i | −0.700695 | − | 0.713461i | \(-0.747127\pi\) |
0.267528 | + | 0.963550i | \(0.413793\pi\) | |||||||
\(684\) | −4.73205 | −0.180934 | ||||||||
\(685\) | −1.54552 | + | 25.7487i | −0.0590512 | + | 0.983808i | ||||
\(686\) | −4.92820 | + | 8.53590i | −0.188160 | + | 0.325902i | ||||
\(687\) | −11.0718 | − | 6.39230i | −0.422415 | − | 0.243882i | ||||
\(688\) | − | 6.73205i | − | 0.256657i | ||||||
\(689\) | 13.7942 | − | 6.82051i | 0.525518 | − | 0.259841i | ||||
\(690\) | −7.83013 | − | 5.16987i | −0.298088 | − | 0.196814i | ||||
\(691\) | −4.70577 | + | 8.15064i | −0.179016 | + | 0.310065i | −0.941544 | − | 0.336891i | \(-0.890625\pi\) |
0.762528 | + | 0.646955i | \(0.223958\pi\) | |||||||
\(692\) | 19.7321 | + | 11.3923i | 0.750100 | + | 0.433070i | ||||
\(693\) | 1.73205 | − | 1.00000i | 0.0657952 | − | 0.0379869i | ||||
\(694\) | −11.6603 | −0.442617 | ||||||||
\(695\) | −33.3205 | − | 2.00000i | −1.26392 | − | 0.0758643i | ||||
\(696\) | −0.232051 | − | 0.401924i | −0.00879586 | − | 0.0152349i | ||||
\(697\) | 2.94744i | 0.111642i | ||||||||
\(698\) | −28.5167 | + | 16.4641i | −1.07937 | + | 0.623175i | ||||
\(699\) | −4.19615 | + | 7.26795i | −0.158713 | + | 0.274899i | ||||
\(700\) | 0.437822 | − | 3.63397i | 0.0165481 | − | 0.137351i | ||||
\(701\) | −6.53590 | −0.246857 | −0.123429 | − | 0.992353i | \(-0.539389\pi\) | ||||
−0.123429 | + | 0.992353i | \(0.539389\pi\) | |||||||
\(702\) | −3.59808 | − | 0.232051i | −0.135801 | − | 0.00875819i | ||||
\(703\) | − | 28.0526i | − | 1.05802i | ||||||
\(704\) | −1.36603 | + | 2.36603i | −0.0514840 | + | 0.0891729i | ||||
\(705\) | −9.66025 | − | 19.3205i | −0.363826 | − | 0.727652i | ||||
\(706\) | −11.6244 | − | 20.1340i | −0.437488 | − | 0.757752i | ||||
\(707\) | 0.0525589i | 0.00197668i | ||||||||
\(708\) | 7.26795 | − | 4.19615i | 0.273146 | − | 0.157701i | ||||
\(709\) | −0.526279 | − | 0.911543i | −0.0197648 | − | 0.0342337i | 0.855974 | − | 0.517019i | \(-0.172958\pi\) |
−0.875739 | + | 0.482785i | \(0.839625\pi\) | |||||||
\(710\) | −8.83013 | − | 5.83013i | −0.331389 | − | 0.218801i | ||||
\(711\) | −6.00000 | − | 10.3923i | −0.225018 | − | 0.389742i | ||||
\(712\) | 7.73205 | + | 4.46410i | 0.289771 | + | 0.167299i | ||||
\(713\) | 14.5359 | + | 8.39230i | 0.544374 | + | 0.314294i | ||||
\(714\) | −1.80385 | −0.0675073 | ||||||||
\(715\) | −13.2942 | + | 17.5622i | −0.497176 | + | 0.656788i | ||||
\(716\) | 7.80385 | 0.291643 | ||||||||
\(717\) | 23.0263 | + | 13.2942i | 0.859932 | + | 0.496482i | ||||
\(718\) | −28.6865 | − | 16.5622i | −1.07057 | − | 0.618095i | ||||
\(719\) | −5.80385 | − | 10.0526i | −0.216447 | − | 0.374897i | 0.737272 | − | 0.675596i | \(-0.236114\pi\) |
−0.953719 | + | 0.300699i | \(0.902780\pi\) | |||||||
\(720\) | −1.23205 | + | 1.86603i | −0.0459158 | + | 0.0695427i | ||||
\(721\) | 4.66025 | + | 8.07180i | 0.173557 | + | 0.300609i | ||||
\(722\) | −2.93782 | + | 1.69615i | −0.109334 | + | 0.0631243i | ||||
\(723\) | 11.3923i | 0.423684i | ||||||||
\(724\) | 4.06218 | + | 7.03590i | 0.150970 | + | 0.261487i | ||||
\(725\) | −2.30385 | − | 0.277568i | −0.0855628 | − | 0.0103086i | ||||
\(726\) | 1.76795 | − | 3.06218i | 0.0656147 | − | 0.113648i | ||||
\(727\) | 16.7321i | 0.620557i | 0.950646 | + | 0.310279i | \(0.100422\pi\) | ||||
−0.950646 | + | 0.310279i | \(0.899578\pi\) | |||||||
\(728\) | 1.46410 | − | 2.19615i | 0.0542632 | − | 0.0813948i | ||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 12.6603 | + | 25.3205i | 0.468577 | + | 0.937154i | ||||
\(731\) | −8.29423 | + | 14.3660i | −0.306773 | + | 0.531347i | ||||
\(732\) | −12.2321 | + | 7.06218i | −0.452110 | + | 0.261026i | ||||
\(733\) | 24.6077i | 0.908906i | 0.890771 | + | 0.454453i | \(0.150165\pi\) | ||||
−0.890771 | + | 0.454453i | \(0.849835\pi\) | |||||||
\(734\) | −9.49038 | − | 16.4378i | −0.350296 | − | 0.606731i | ||||
\(735\) | 0.866025 | − | 14.4282i | 0.0319438 | − | 0.532192i | ||||
\(736\) | −4.19615 | −0.154672 | ||||||||
\(737\) | −22.8564 | + | 13.1962i | −0.841927 | + | 0.486087i | ||||
\(738\) | −1.03590 | − | 0.598076i | −0.0381319 | − | 0.0220155i | ||||
\(739\) | 14.9282 | − | 25.8564i | 0.549143 | − | 0.951143i | −0.449191 | − | 0.893436i | \(-0.648288\pi\) |
0.998334 | − | 0.0577074i | \(-0.0183790\pi\) | |||||||
\(740\) | −11.0622 | − | 7.30385i | −0.406654 | − | 0.268495i | ||||
\(741\) | −15.2942 | + | 7.56218i | −0.561848 | + | 0.277804i | ||||
\(742\) | 3.12436i | 0.114699i | ||||||||
\(743\) | 12.5885 | + | 7.26795i | 0.461826 | + | 0.266635i | 0.712812 | − | 0.701356i | \(-0.247421\pi\) |
−0.250986 | + | 0.967991i | \(0.580755\pi\) | |||||||
\(744\) | 2.00000 | − | 3.46410i | 0.0733236 | − | 0.127000i | ||||
\(745\) | 13.5526 | + | 0.813467i | 0.496527 | + | 0.0298031i | ||||
\(746\) | 30.4641 | 1.11537 | ||||||||
\(747\) | −7.56218 | + | 4.36603i | −0.276686 | + | 0.159745i | ||||
\(748\) | 5.83013 | − | 3.36603i | 0.213171 | − | 0.123074i | ||||
\(749\) | 3.46410 | 0.126576 | ||||||||
\(750\) | 3.76795 | + | 10.5263i | 0.137586 | + | 0.384365i | ||||
\(751\) | 1.02628 | − | 1.77757i | 0.0374495 | − | 0.0648644i | −0.846693 | − | 0.532081i | \(-0.821410\pi\) |
0.884143 | + | 0.467217i | \(0.154743\pi\) | |||||||
\(752\) | −8.36603 | − | 4.83013i | −0.305078 | − | 0.176137i | ||||
\(753\) | − | 14.5359i | − | 0.529718i | ||||||
\(754\) | −1.39230 | − | 0.928203i | −0.0507048 | − | 0.0338032i | ||||
\(755\) | 23.5622 | − | 35.6865i | 0.857515 | − | 1.29877i | ||||
\(756\) | 0.366025 | − | 0.633975i | 0.0133122 | − | 0.0230574i | ||||
\(757\) | 31.2679 | + | 18.0526i | 1.13645 | + | 0.656131i | 0.945550 | − | 0.325477i | \(-0.105525\pi\) |
0.190903 | + | 0.981609i | \(0.438858\pi\) | |||||||
\(758\) | −19.2679 | + | 11.1244i | −0.699843 | + | 0.404055i | ||||
\(759\) | −11.4641 | −0.416121 | ||||||||
\(760\) | −0.633975 | + | 10.5622i | −0.0229967 | + | 0.383130i | ||||
\(761\) | −18.4641 | − | 31.9808i | −0.669323 | − | 1.15930i | −0.978094 | − | 0.208165i | \(-0.933251\pi\) |
0.308771 | − | 0.951137i | \(-0.400082\pi\) | |||||||
\(762\) | − | 4.00000i | − | 0.144905i | ||||||
\(763\) | −6.33975 | + | 3.66025i | −0.229514 | + | 0.132510i | ||||
\(764\) | −1.26795 | + | 2.19615i | −0.0458728 | + | 0.0794540i | ||||
\(765\) | 4.92820 | − | 2.46410i | 0.178180 | − | 0.0890898i | ||||
\(766\) | 13.0718 | 0.472303 | ||||||||
\(767\) | 16.7846 | − | 25.1769i | 0.606057 | − | 0.909086i | ||||
\(768\) | 1.00000i | 0.0360844i | ||||||||
\(769\) | 19.2679 | − | 33.3731i | 0.694820 | − | 1.20346i | −0.275421 | − | 0.961324i | \(-0.588817\pi\) |
0.970241 | − | 0.242140i | \(-0.0778493\pi\) | |||||||
\(770\) | −2.00000 | − | 4.00000i | −0.0720750 | − | 0.144150i | ||||
\(771\) | 1.50000 | + | 2.59808i | 0.0540212 | + | 0.0935674i | ||||
\(772\) | − | 6.66025i | − | 0.239708i | ||||||
\(773\) | −24.8038 | + | 14.3205i | −0.892132 | + | 0.515073i | −0.874639 | − | 0.484774i | \(-0.838902\pi\) |
−0.0174930 | + | 0.999847i | \(0.505568\pi\) | |||||||
\(774\) | −3.36603 | − | 5.83013i | −0.120989 | − | 0.209560i | ||||
\(775\) | −7.85641 | − | 18.3923i | −0.282210 | − | 0.660671i | ||||
\(776\) | 5.00000 | + | 8.66025i | 0.179490 | + | 0.310885i | ||||
\(777\) | 3.75833 | + | 2.16987i | 0.134829 | + | 0.0778438i | ||||
\(778\) | 32.8468 | + | 18.9641i | 1.17761 | + | 0.679896i | ||||
\(779\) | −5.66025 | −0.202800 | ||||||||
\(780\) | −1.00000 | + | 8.00000i | −0.0358057 | + | 0.286446i | ||||
\(781\) | −12.9282 | −0.462607 | ||||||||
\(782\) | 8.95448 | + | 5.16987i | 0.320212 | + | 0.184874i | ||||
\(783\) | −0.401924 | − | 0.232051i | −0.0143636 | − | 0.00829282i | ||||
\(784\) | −3.23205 | − | 5.59808i | −0.115430 | − | 0.199931i | ||||
\(785\) | 21.2583 | + | 14.0359i | 0.758742 | + | 0.500963i | ||||
\(786\) | −6.92820 | − | 12.0000i | −0.247121 | − | 0.428026i | ||||
\(787\) | −13.2679 | + | 7.66025i | −0.472951 | + | 0.273059i | −0.717474 | − | 0.696585i | \(-0.754702\pi\) |
0.244523 | + | 0.969643i | \(0.421369\pi\) | |||||||
\(788\) | − | 17.8564i | − | 0.636108i | ||||||
\(789\) | 3.56218 | + | 6.16987i | 0.126817 | + | 0.219653i | ||||
\(790\) | −24.0000 | + | 12.0000i | −0.853882 | + | 0.426941i | ||||
\(791\) | 3.29423 | − | 5.70577i | 0.117129 | − | 0.202874i | ||||
\(792\) | 2.73205i | 0.0970792i | ||||||||
\(793\) | −28.2487 | + | 42.3731i | −1.00314 | + | 1.50471i | ||||
\(794\) | −15.3205 | −0.543704 | ||||||||
\(795\) | −4.26795 | − | 8.53590i | −0.151369 | − | 0.302737i | ||||
\(796\) | −5.02628 | + | 8.70577i | −0.178152 | + | 0.308568i | ||||
\(797\) | 12.9282 | − | 7.46410i | 0.457940 | − | 0.264392i | −0.253237 | − | 0.967404i | \(-0.581495\pi\) |
0.711178 | + | 0.703012i | \(0.248162\pi\) | |||||||
\(798\) | − | 3.46410i | − | 0.122628i | ||||||
\(799\) | 11.9019 | + | 20.6147i | 0.421060 | + | 0.729297i | ||||
\(800\) | 4.00000 | + | 3.00000i | 0.141421 | + | 0.106066i | ||||
\(801\) | 8.92820 | 0.315463 | ||||||||
\(802\) | −25.1603 | + | 14.5263i | −0.888439 | + | 0.512941i | ||||
\(803\) | 29.9545 | + | 17.2942i | 1.05707 | + | 0.610300i | ||||
\(804\) | −4.83013 | + | 8.36603i | −0.170345 | + | 0.295047i | ||||
\(805\) | 3.78461 | − | 5.73205i | 0.133390 | − | 0.202028i | ||||
\(806\) | 0.928203 | − | 14.3923i | 0.0326946 | − | 0.506947i | ||||
\(807\) | 16.3923i | 0.577036i | ||||||||
\(808\) | −0.0621778 | − | 0.0358984i | −0.00218741 | − | 0.00126290i | ||||
\(809\) | −24.9904 | + | 43.2846i | −0.878615 | + | 1.52181i | −0.0257537 | + | 0.999668i | \(0.508199\pi\) |
−0.852861 | + | 0.522138i | \(0.825135\pi\) | |||||||
\(810\) | −0.133975 | + | 2.23205i | −0.00470739 | + | 0.0784263i | ||||
\(811\) | −6.14359 | −0.215731 | −0.107865 | − | 0.994166i | \(-0.534402\pi\) | ||||
−0.107865 | + | 0.994166i | \(0.534402\pi\) | |||||||
\(812\) | 0.294229 | − | 0.169873i | 0.0103254 | − | 0.00596137i | ||||
\(813\) | −18.9282 | + | 10.9282i | −0.663841 | + | 0.383269i | ||||
\(814\) | −16.1962 | −0.567675 | ||||||||
\(815\) | −0.875644 | + | 14.5885i | −0.0306725 | + | 0.511011i | ||||
\(816\) | 1.23205 | − | 2.13397i | 0.0431304 | − | 0.0747041i | ||||
\(817\) | −27.5885 | − | 15.9282i | −0.965198 | − | 0.557257i | ||||
\(818\) | 29.9282i | 1.04642i | ||||||||
\(819\) | 0.169873 | − | 2.63397i | 0.00593584 | − | 0.0920385i | ||||
\(820\) | −1.47372 | + | 2.23205i | −0.0514646 | + | 0.0779466i | ||||
\(821\) | 19.1244 | − | 33.1244i | 0.667445 | − | 1.15605i | −0.311172 | − | 0.950354i | \(-0.600721\pi\) |
0.978616 | − | 0.205694i | \(-0.0659452\pi\) | |||||||
\(822\) | 9.99038 | + | 5.76795i | 0.348455 | + | 0.201180i | ||||
\(823\) | −16.9808 | + | 9.80385i | −0.591912 | + | 0.341741i | −0.765853 | − | 0.643015i | \(-0.777683\pi\) |
0.173941 | + | 0.984756i | \(0.444350\pi\) | |||||||
\(824\) | −12.7321 | −0.443542 | ||||||||
\(825\) | 10.9282 | + | 8.19615i | 0.380471 | + | 0.285353i | ||||
\(826\) | 3.07180 | + | 5.32051i | 0.106881 | + | 0.185124i | ||||
\(827\) | − | 7.21539i | − | 0.250904i | −0.992100 | − | 0.125452i | \(-0.959962\pi\) | ||
0.992100 | − | 0.125452i | \(-0.0400381\pi\) | |||||||
\(828\) | −3.63397 | + | 2.09808i | −0.126289 | + | 0.0729132i | ||||
\(829\) | 21.0622 | − | 36.4808i | 0.731520 | − | 1.26703i | −0.224714 | − | 0.974425i | \(-0.572145\pi\) |
0.956234 | − | 0.292604i | \(-0.0945219\pi\) | |||||||
\(830\) | 8.73205 | + | 17.4641i | 0.303094 | + | 0.606188i | ||||
\(831\) | −22.3205 | −0.774290 | ||||||||
\(832\) | 1.59808 | + | 3.23205i | 0.0554033 | + | 0.112051i | ||||
\(833\) | 15.9282i | 0.551880i | ||||||||
\(834\) | −7.46410 | + | 12.9282i | −0.258461 | + | 0.447667i | ||||
\(835\) | 27.7128 | − | 13.8564i | 0.959041 | − | 0.479521i | ||||
\(836\) | 6.46410 | + | 11.1962i | 0.223566 | + | 0.387227i | ||||
\(837\) | − | 4.00000i | − | 0.138260i | ||||||
\(838\) | −11.6603 | + | 6.73205i | −0.402797 | + | 0.232555i | ||||
\(839\) | −14.0526 | − | 24.3397i | −0.485148 | − | 0.840301i | 0.514706 | − | 0.857367i | \(-0.327901\pi\) |
−0.999854 | + | 0.0170653i | \(0.994568\pi\) | |||||||
\(840\) | −1.36603 | − | 0.901924i | −0.0471324 | − | 0.0311193i | ||||
\(841\) | 14.3923 | + | 24.9282i | 0.496286 | + | 0.859593i | ||||
\(842\) | −18.2321 | − | 10.5263i | −0.628318 | − | 0.362760i | ||||
\(843\) | 1.50000 | + | 0.866025i | 0.0516627 | + | 0.0298275i | ||||
\(844\) | 14.5359 | 0.500346 | ||||||||
\(845\) | 9.55256 | + | 27.4545i | 0.328618 | + | 0.944463i | ||||
\(846\) | −9.66025 | −0.332126 | ||||||||
\(847\) | 2.24167 | + | 1.29423i | 0.0770247 | + | 0.0444702i | ||||
\(848\) | −3.69615 | − | 2.13397i | −0.126926 | − | 0.0732810i | ||||
\(849\) | −4.83013 | − | 8.36603i | −0.165770 | − | 0.287121i | ||||
\(850\) | −4.83975 | − | 11.3301i | −0.166002 | − | 0.388620i | ||||
\(851\) | −12.4378 | − | 21.5429i | −0.426363 | − | 0.738482i | ||||
\(852\) | −4.09808 | + | 2.36603i | −0.140398 | + | 0.0810587i | ||||
\(853\) | − | 25.9282i | − | 0.887765i | −0.896085 | − | 0.443882i | \(-0.853601\pi\) | ||
0.896085 | − | 0.443882i | \(-0.146399\pi\) | |||||||
\(854\) | −5.16987 | − | 8.95448i | −0.176909 | − | 0.306416i | ||||
\(855\) | 4.73205 | + | 9.46410i | 0.161833 | + | 0.323665i | ||||
\(856\) | −2.36603 | + | 4.09808i | −0.0808691 | + | 0.140069i | ||||
\(857\) | 9.92820i | 0.339141i | 0.985518 | + | 0.169570i | \(0.0542380\pi\) | ||||
−0.985518 | + | 0.169570i | \(0.945762\pi\) | |||||||
\(858\) | 4.36603 | + | 8.83013i | 0.149054 | + | 0.301456i | ||||
\(859\) | −42.3013 | −1.44330 | −0.721650 | − | 0.692258i | \(-0.756616\pi\) | ||||
−0.721650 | + | 0.692258i | \(0.756616\pi\) | |||||||
\(860\) | −13.4641 | + | 6.73205i | −0.459122 | + | 0.229561i | ||||
\(861\) | 0.437822 | − | 0.758330i | 0.0149209 | − | 0.0258438i | ||||
\(862\) | 15.7583 | − | 9.09808i | 0.536731 | − | 0.309882i | ||||
\(863\) | − | 3.12436i | − | 0.106354i | −0.998585 | − | 0.0531772i | \(-0.983065\pi\) | ||
0.998585 | − | 0.0531772i | \(-0.0169348\pi\) | |||||||
\(864\) | 0.500000 | + | 0.866025i | 0.0170103 | + | 0.0294628i | ||||
\(865\) | 3.05256 | − | 50.8564i | 0.103790 | − | 1.72917i | ||||
\(866\) | −25.1962 | −0.856200 | ||||||||
\(867\) | 9.46410 | − | 5.46410i | 0.321418 | − | 0.185571i | ||||
\(868\) | 2.53590 | + | 1.46410i | 0.0860740 | + | 0.0496948i | ||||
\(869\) | −16.3923 | + | 28.3923i | −0.556071 | + | 0.963143i | ||||
\(870\) | −0.571797 | + | 0.866025i | −0.0193857 | + | 0.0293610i | ||||
\(871\) | −2.24167 | + | 34.7583i | −0.0759561 | + | 1.17774i | ||||
\(872\) | − | 10.0000i | − | 0.338643i | ||||||
\(873\) | 8.66025 | + | 5.00000i | 0.293105 | + | 0.169224i | ||||
\(874\) | −9.92820 | + | 17.1962i | −0.335826 | + | 0.581669i | ||||
\(875\) | −7.70577 | + | 2.75833i | −0.260503 | + | 0.0932486i | ||||
\(876\) | 12.6603 | 0.427750 | ||||||||
\(877\) | 14.2583 | − | 8.23205i | 0.481470 | − | 0.277977i | −0.239559 | − | 0.970882i | \(-0.577003\pi\) |
0.721029 | + | 0.692905i | \(0.243670\pi\) | |||||||
\(878\) | 17.4904 | − | 10.0981i | 0.590272 | − | 0.340794i | ||||
\(879\) | −10.2679 | −0.346329 | ||||||||
\(880\) | 6.09808 | + | 0.366025i | 0.205566 | + | 0.0123387i | ||||
\(881\) | −21.0622 | + | 36.4808i | −0.709603 | + | 1.22907i | 0.255402 | + | 0.966835i | \(0.417792\pi\) |
−0.965005 | + | 0.262233i | \(0.915541\pi\) | |||||||
\(882\) | −5.59808 | − | 3.23205i | −0.188497 | − | 0.108829i | ||||
\(883\) | 30.2487i | 1.01795i | 0.860781 | + | 0.508975i | \(0.169975\pi\) | ||||
−0.860781 | + | 0.508975i | \(0.830025\pi\) | |||||||
\(884\) | 0.571797 | − | 8.86603i | 0.0192316 | − | 0.298197i | ||||
\(885\) | −15.6603 | − | 10.3397i | −0.526414 | − | 0.347567i | ||||
\(886\) | 17.3205 | − | 30.0000i | 0.581894 | − | 1.00787i | ||||
\(887\) | 37.1769 | + | 21.4641i | 1.24828 | + | 0.720694i | 0.970766 | − | 0.240028i | \(-0.0771566\pi\) |
0.277513 | + | 0.960722i | \(0.410490\pi\) | |||||||
\(888\) | −5.13397 | + | 2.96410i | −0.172285 | + | 0.0994687i | ||||
\(889\) | 2.92820 | 0.0982088 | ||||||||
\(890\) | 1.19615 | − | 19.9282i | 0.0400951 | − | 0.667995i | ||||
\(891\) | 1.36603 | + | 2.36603i | 0.0457636 | + | 0.0792648i | ||||
\(892\) | − | 20.3923i | − | 0.682785i | ||||||
\(893\) | −39.5885 | + | 22.8564i | −1.32478 | + | 0.764860i | ||||
\(894\) | 3.03590 | − | 5.25833i | 0.101536 | − | 0.175865i | ||||
\(895\) | −7.80385 | − | 15.6077i | −0.260854 | − | 0.521708i | ||||
\(896\) | −0.732051 | −0.0244561 | ||||||||
\(897\) | −8.39230 | + | 12.5885i | −0.280211 | + | 0.420316i | ||||
\(898\) | 19.8564i | 0.662617i | ||||||||
\(899\) | 0.928203 | − | 1.60770i | 0.0309573 | − | 0.0536196i | ||||
\(900\) | 4.96410 | + | 0.598076i | 0.165470 | + | 0.0199359i | ||||
\(901\) | 5.25833 | + | 9.10770i | 0.175180 | + | 0.303421i | ||||
\(902\) | 3.26795i | 0.108811i | ||||||||
\(903\) | 4.26795 | − | 2.46410i | 0.142028 | − | 0.0820002i | ||||
\(904\) | 4.50000 | + | 7.79423i | 0.149668 | + | 0.259232i | ||||
\(905\) | 10.0096 | − | 15.1603i | 0.332731 | − | 0.503944i | ||||
\(906\) | −9.56218 | − | 16.5622i | −0.317682 | − | 0.550242i | ||||
\(907\) | −6.00000 | − | 3.46410i | −0.199227 | − | 0.115024i | 0.397068 | − | 0.917789i | \(-0.370028\pi\) |
−0.596295 | + | 0.802766i | \(0.703361\pi\) | |||||||
\(908\) | −5.36603 | − | 3.09808i | −0.178078 | − | 0.102813i | ||||
\(909\) | −0.0717968 | −0.00238135 | ||||||||
\(910\) | −5.85641 | − | 0.732051i | −0.194138 | − | 0.0242672i | ||||
\(911\) | −32.1051 | −1.06369 | −0.531845 | − | 0.846842i | \(-0.678501\pi\) | ||||
−0.531845 | + | 0.846842i | \(0.678501\pi\) | |||||||
\(912\) | 4.09808 | + | 2.36603i | 0.135701 | + | 0.0783469i | ||||
\(913\) | 20.6603 | + | 11.9282i | 0.683755 | + | 0.394766i | ||||
\(914\) | −9.59808 | − | 16.6244i | −0.317476 | − | 0.549885i | ||||
\(915\) | 26.3564 | + | 17.4019i | 0.871316 | + | 0.575290i | ||||
\(916\) | 6.39230 | + | 11.0718i | 0.211208 | + | 0.365822i | ||||
\(917\) | 8.78461 | − | 5.07180i | 0.290093 | − | 0.167485i | ||||
\(918\) | − | 2.46410i | − | 0.0813275i | ||||||
\(919\) | −25.2679 | − | 43.7654i | −0.833513 | − | 1.44369i | −0.895236 | − | 0.445593i | \(-0.852993\pi\) |
0.0617229 | − | 0.998093i | \(-0.480341\pi\) | |||||||
\(920\) | 4.19615 | + | 8.39230i | 0.138343 | + | 0.276686i | ||||
\(921\) | 11.3660 | − | 19.6865i | 0.374523 | − | 0.648693i | ||||
\(922\) | − | 39.9282i | − | 1.31497i | ||||||
\(923\) | −9.46410 | + | 14.1962i | −0.311515 | + | 0.467272i | ||||
\(924\) | −2.00000 | −0.0657952 | ||||||||
\(925\) | −3.54552 | + | 29.4282i | −0.116576 | + | 0.967593i | ||||
\(926\) | 11.8301 | − | 20.4904i | 0.388762 | − | 0.673356i | ||||
\(927\) | −11.0263 | + | 6.36603i | −0.362151 | + | 0.209088i | ||||
\(928\) | 0.464102i | 0.0152349i | ||||||||
\(929\) | 4.20577 | + | 7.28461i | 0.137987 | + | 0.239000i | 0.926734 | − | 0.375717i | \(-0.122603\pi\) |
−0.788748 | + | 0.614717i | \(0.789270\pi\) | |||||||
\(930\) | −8.92820 | − | 0.535898i | −0.292767 | − | 0.0175728i | ||||
\(931\) | −30.5885 | −1.00250 | ||||||||
\(932\) | 7.26795 | − | 4.19615i | 0.238070 | − | 0.137450i | ||||
\(933\) | 18.2942 | + | 10.5622i | 0.598926 | + | 0.345790i | ||||
\(934\) | 8.02628 | − | 13.9019i | 0.262628 | − | 0.454885i | ||||
\(935\) | −12.5622 | − | 8.29423i | −0.410827 | − | 0.271250i | ||||
\(936\) | 3.00000 | + | 2.00000i | 0.0980581 | + | 0.0653720i | ||||
\(937\) | − | 21.0526i | − | 0.687757i | −0.939014 | − | 0.343879i | \(-0.888259\pi\) | ||
0.939014 | − | 0.343879i | \(-0.111741\pi\) | |||||||
\(938\) | −6.12436 | − | 3.53590i | −0.199967 | − | 0.115451i | ||||
\(939\) | −7.00000 | + | 12.1244i | −0.228436 | + | 0.395663i | ||||
\(940\) | −1.29423 | + | 21.5622i | −0.0422131 | + | 0.703281i | ||||
\(941\) | −8.39230 | −0.273581 | −0.136791 | − | 0.990600i | \(-0.543679\pi\) | ||||
−0.136791 | + | 0.990600i | \(0.543679\pi\) | |||||||
\(942\) | 9.86603 | − | 5.69615i | 0.321452 | − | 0.185591i | ||||
\(943\) | −4.34679 | + | 2.50962i | −0.141551 | + | 0.0817244i | ||||
\(944\) | −8.39230 | −0.273146 | ||||||||
\(945\) | −1.63397 | − | 0.0980762i | −0.0531532 | − | 0.00319042i | ||||
\(946\) | −9.19615 | + | 15.9282i | −0.298993 | + | 0.517871i | ||||
\(947\) | −24.0000 | − | 13.8564i | −0.779895 | − | 0.450273i | 0.0564979 | − | 0.998403i | \(-0.482007\pi\) |
−0.836393 | + | 0.548130i | \(0.815340\pi\) | |||||||
\(948\) | 12.0000i | 0.389742i | ||||||||
\(949\) | 40.9186 | − | 20.2321i | 1.32827 | − | 0.656760i | ||||
\(950\) | 21.7583 | − | 9.29423i | 0.705933 | − | 0.301545i | ||||
\(951\) | −13.1340 | + | 22.7487i | −0.425898 | + | 0.737678i | ||||
\(952\) | 1.56218 | + | 0.901924i | 0.0506305 | + | 0.0292315i | ||||
\(953\) | 15.3397 | − | 8.85641i | 0.496903 | − | 0.286887i | −0.230531 | − | 0.973065i | \(-0.574046\pi\) |
0.727434 | + | 0.686178i | \(0.240713\pi\) | |||||||
\(954\) | −4.26795 | −0.138180 | ||||||||
\(955\) | 5.66025 | + | 0.339746i | 0.183162 | + | 0.0109939i | ||||
\(956\) | −13.2942 | − | 23.0263i | −0.429966 | − | 0.744723i | ||||
\(957\) | 1.26795i | 0.0409870i | ||||||||
\(958\) | −13.8564 | + | 8.00000i | −0.447680 | + | 0.258468i | ||||
\(959\) | −4.22243 | + | 7.31347i | −0.136349 | + | 0.236164i | ||||
\(960\) | 2.00000 | − | 1.00000i | 0.0645497 | − | 0.0322749i | ||||
\(961\) | −15.0000 | −0.483871 | ||||||||
\(962\) | −11.8564 | + | 17.7846i | −0.382266 | + | 0.573399i | ||||
\(963\) | 4.73205i | 0.152488i | ||||||||
\(964\) | 5.69615 | − | 9.86603i | 0.183461 | − | 0.317763i | ||||
\(965\) | −13.3205 | + | 6.66025i | −0.428802 | + | 0.214401i | ||||
\(966\) | −1.53590 | − | 2.66025i | −0.0494167 | − | 0.0855923i | ||||
\(967\) | − | 14.5885i | − | 0.469133i | −0.972100 | − | 0.234567i | \(-0.924633\pi\) | ||
0.972100 | − | 0.234567i | \(-0.0753671\pi\) | |||||||
\(968\) | −3.06218 | + | 1.76795i | −0.0984221 | + | 0.0568240i | ||||
\(969\) | −5.83013 | − | 10.0981i | −0.187291 | − | 0.324397i | ||||
\(970\) | 12.3205 | − | 18.6603i | 0.395588 | − | 0.599145i | ||||
\(971\) | 20.5359 | + | 35.5692i | 0.659028 | + | 1.14147i | 0.980868 | + | 0.194676i | \(0.0623656\pi\) |
−0.321839 | + | 0.946794i | \(0.604301\pi\) | |||||||
\(972\) | 0.866025 | + | 0.500000i | 0.0277778 | + | 0.0160375i | ||||
\(973\) | −9.46410 | − | 5.46410i | −0.303405 | − | 0.175171i | ||||
\(974\) | 20.4449 | 0.655096 | ||||||||
\(975\) | 17.0000 | − | 6.00000i | 0.544436 | − | 0.192154i | ||||
\(976\) | 14.1244 | 0.452110 | ||||||||
\(977\) | −23.5981 | − | 13.6244i | −0.754969 | − | 0.435882i | 0.0725173 | − | 0.997367i | \(-0.476897\pi\) |
−0.827487 | + | 0.561485i | \(0.810230\pi\) | |||||||
\(978\) | 5.66025 | + | 3.26795i | 0.180995 | + | 0.104497i | ||||
\(979\) | −12.1962 | − | 21.1244i | −0.389791 | − | 0.675137i | ||||
\(980\) | −7.96410 | + | 12.0622i | −0.254404 | + | 0.385312i | ||||
\(981\) | −5.00000 | − | 8.66025i | −0.159638 | − | 0.276501i | ||||
\(982\) | −27.8827 | + | 16.0981i | −0.889772 | + | 0.513710i | ||||
\(983\) | 23.7128i | 0.756321i | 0.925740 | + | 0.378161i | \(0.123443\pi\) | ||||
−0.925740 | + | 0.378161i | \(0.876557\pi\) | |||||||
\(984\) | 0.598076 | + | 1.03590i | 0.0190660 | + | 0.0330232i | ||||
\(985\) | −35.7128 | + | 17.8564i | −1.13790 | + | 0.568952i | ||||
\(986\) | 0.571797 | − | 0.990381i | 0.0182097 | − | 0.0315402i | ||||
\(987\) | − | 7.07180i | − | 0.225098i | ||||||
\(988\) | 17.0263 | + | 1.09808i | 0.541678 | + | 0.0349345i | ||||
\(989\) | −28.2487 | −0.898257 | ||||||||
\(990\) | 5.46410 | − | 2.73205i | 0.173661 | − | 0.0868303i | ||||
\(991\) | 15.0263 | − | 26.0263i | 0.477325 | − | 0.826752i | −0.522337 | − | 0.852739i | \(-0.674940\pi\) |
0.999662 | + | 0.0259873i | \(0.00827294\pi\) | |||||||
\(992\) | −3.46410 | + | 2.00000i | −0.109985 | + | 0.0635001i | ||||
\(993\) | 12.7846i | 0.405707i | ||||||||
\(994\) | −1.73205 | − | 3.00000i | −0.0549373 | − | 0.0951542i | ||||
\(995\) | 22.4378 | + | 1.34679i | 0.711327 | + | 0.0426960i | ||||
\(996\) | 8.73205 | 0.276686 | ||||||||
\(997\) | 1.79423 | − | 1.03590i | 0.0568238 | − | 0.0328072i | −0.471319 | − | 0.881963i | \(-0.656222\pi\) |
0.528143 | + | 0.849156i | \(0.322889\pi\) | |||||||
\(998\) | −16.9808 | − | 9.80385i | −0.537517 | − | 0.310335i | ||||
\(999\) | −2.96410 | + | 5.13397i | −0.0937800 | + | 0.162432i |
(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 | 390.2.y.c.139.2 | yes | 4 | |
3.2 | odd | 2 | 1170.2.bp.e.919.1 | 4 | |||
5.2 | odd | 4 | 1950.2.i.y.451.2 | 4 | |||
5.3 | odd | 4 | 1950.2.i.bh.451.1 | 4 | |||
5.4 | even | 2 | 390.2.y.b.139.1 | ✓ | 4 | ||
13.3 | even | 3 | 390.2.y.b.289.1 | yes | 4 | ||
15.14 | odd | 2 | 1170.2.bp.d.919.2 | 4 | |||
39.29 | odd | 6 | 1170.2.bp.d.289.2 | 4 | |||
65.3 | odd | 12 | 1950.2.i.bh.601.1 | 4 | |||
65.29 | even | 6 | inner | 390.2.y.c.289.2 | yes | 4 | |
65.42 | odd | 12 | 1950.2.i.y.601.2 | 4 | |||
195.29 | odd | 6 | 1170.2.bp.e.289.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
390.2.y.b.139.1 | ✓ | 4 | 5.4 | even | 2 | ||
390.2.y.b.289.1 | yes | 4 | 13.3 | even | 3 | ||
390.2.y.c.139.2 | yes | 4 | 1.1 | even | 1 | trivial | |
390.2.y.c.289.2 | yes | 4 | 65.29 | even | 6 | inner | |
1170.2.bp.d.289.2 | 4 | 39.29 | odd | 6 | |||
1170.2.bp.d.919.2 | 4 | 15.14 | odd | 2 | |||
1170.2.bp.e.289.1 | 4 | 195.29 | odd | 6 | |||
1170.2.bp.e.919.1 | 4 | 3.2 | odd | 2 | |||
1950.2.i.y.451.2 | 4 | 5.2 | odd | 4 | |||
1950.2.i.y.601.2 | 4 | 65.42 | odd | 12 | |||
1950.2.i.bh.451.1 | 4 | 5.3 | odd | 4 | |||
1950.2.i.bh.601.1 | 4 | 65.3 | odd | 12 |