Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [525,2,Mod(32,525)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(525, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([6, 3, 8]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("525.32");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 525 = 3 \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 525.bf (of order \(12\), degree \(4\), 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: | \(4.19214610612\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{12})\) |
Coefficient field: | \(\Q(\zeta_{24})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{12}]$ |
Embedding invariants
Embedding label | 32.2 | ||
Root | \(0.258819 + 0.965926i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 525.32 |
Dual form | 525.2.bf.d.443.2 |
$q$-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 \(\left(\mathbb{Z}/525\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(176\) | \(451\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(-1\) | \(e\left(\frac{2}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.36603 | + | 0.366025i | 0.965926 | + | 0.258819i | 0.707107 | − | 0.707107i | \(-0.250000\pi\) |
0.258819 | + | 0.965926i | \(0.416667\pi\) | |||||||
\(3\) | −1.10721 | + | 1.33195i | −0.639246 | + | 0.769002i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −2.00000 | + | 1.41421i | −0.816497 | + | 0.577350i | ||||
\(7\) | −1.15539 | − | 2.38014i | −0.436698 | − | 0.899608i | ||||
\(8\) | −2.00000 | − | 2.00000i | −0.707107 | − | 0.707107i | ||||
\(9\) | −0.548188 | − | 2.94949i | −0.182729 | − | 0.983163i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.67423 | − | 2.12132i | −1.10782 | − | 0.639602i | −0.169559 | − | 0.985520i | \(-0.554234\pi\) |
−0.938265 | + | 0.345918i | \(0.887568\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.53553 | + | 3.53553i | −0.980581 | + | 0.980581i | −0.999815 | − | 0.0192343i | \(-0.993877\pi\) |
0.0192343 | + | 0.999815i | \(0.493877\pi\) | |||||||
\(14\) | −0.707107 | − | 3.67423i | −0.188982 | − | 0.981981i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −2.00000 | − | 3.46410i | −0.500000 | − | 0.866025i | ||||
\(17\) | −0.366025 | − | 1.36603i | −0.0887742 | − | 0.331310i | 0.907228 | − | 0.420639i | \(-0.138194\pi\) |
−0.996002 | + | 0.0893296i | \(0.971528\pi\) | |||||||
\(18\) | 0.330749 | − | 4.22973i | 0.0779583 | − | 0.996957i | ||||
\(19\) | 6.06218 | − | 3.50000i | 1.39076 | − | 0.802955i | 0.397360 | − | 0.917663i | \(-0.369927\pi\) |
0.993399 | + | 0.114708i | \(0.0365932\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 4.44949 | + | 1.09638i | 0.970958 | + | 0.239249i | ||||
\(22\) | −4.24264 | − | 4.24264i | −0.904534 | − | 0.904534i | ||||
\(23\) | −1.09808 | + | 4.09808i | −0.228965 | + | 0.854508i | 0.751812 | + | 0.659377i | \(0.229180\pi\) |
−0.980777 | + | 0.195131i | \(0.937487\pi\) | |||||||
\(24\) | 4.87832 | − | 0.449490i | 0.995782 | − | 0.0917517i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −6.12372 | + | 3.53553i | −1.20096 | + | 0.693375i | ||||
\(27\) | 4.53553 | + | 2.53553i | 0.872864 | + | 0.487964i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −7.07107 | −1.31306 | −0.656532 | − | 0.754298i | \(-0.727977\pi\) | ||||
−0.656532 | + | 0.754298i | \(0.727977\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.500000 | − | 0.866025i | 0.0898027 | − | 0.155543i | −0.817625 | − | 0.575751i | \(-0.804710\pi\) |
0.907428 | + | 0.420208i | \(0.138043\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 6.89363 | − | 2.54516i | 1.20003 | − | 0.443056i | ||||
\(34\) | − | 2.00000i | − | 0.342997i | ||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −0.258819 | + | 0.965926i | −0.0425496 | + | 0.158797i | −0.983932 | − | 0.178545i | \(-0.942861\pi\) |
0.941382 | + | 0.337342i | \(0.109528\pi\) | |||||||
\(38\) | 9.56218 | − | 2.56218i | 1.55119 | − | 0.415640i | ||||
\(39\) | −0.794593 | − | 8.62372i | −0.127237 | − | 1.38090i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 7.07107i | − | 1.10432i | −0.833740 | − | 0.552158i | \(-0.813805\pi\) | ||
0.833740 | − | 0.552158i | \(-0.186195\pi\) | |||||||
\(42\) | 5.67681 | + | 3.12630i | 0.875951 | + | 0.482399i | ||||
\(43\) | 3.53553 | − | 3.53553i | 0.539164 | − | 0.539164i | −0.384120 | − | 0.923283i | \(-0.625495\pi\) |
0.923283 | + | 0.384120i | \(0.125495\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −3.00000 | + | 5.19615i | −0.442326 | + | 0.766131i | ||||
\(47\) | −5.46410 | − | 1.46410i | −0.797021 | − | 0.213561i | −0.162745 | − | 0.986668i | \(-0.552035\pi\) |
−0.634276 | + | 0.773107i | \(0.718702\pi\) | |||||||
\(48\) | 6.82843 | + | 1.17157i | 0.985599 | + | 0.169102i | ||||
\(49\) | −4.33013 | + | 5.50000i | −0.618590 | + | 0.785714i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 2.22474 | + | 1.02494i | 0.311527 | + | 0.143521i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −2.73205 | + | 0.732051i | −0.375276 | + | 0.100555i | −0.441527 | − | 0.897248i | \(-0.645563\pi\) |
0.0662507 | + | 0.997803i | \(0.478896\pi\) | |||||||
\(54\) | 5.26758 | + | 5.12372i | 0.716827 | + | 0.697251i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −2.44949 | + | 7.07107i | −0.327327 | + | 0.944911i | ||||
\(57\) | −2.05025 | + | 11.9497i | −0.271563 | + | 1.58278i | ||||
\(58\) | −9.65926 | − | 2.58819i | −1.26832 | − | 0.339846i | ||||
\(59\) | −0.707107 | + | 1.22474i | −0.0920575 | + | 0.159448i | −0.908377 | − | 0.418153i | \(-0.862678\pi\) |
0.816319 | + | 0.577601i | \(0.196011\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.00000 | − | 3.46410i | −0.256074 | − | 0.443533i | 0.709113 | − | 0.705095i | \(-0.249096\pi\) |
−0.965187 | + | 0.261562i | \(0.915762\pi\) | |||||||
\(62\) | 1.00000 | − | 1.00000i | 0.127000 | − | 0.127000i | ||||
\(63\) | −6.38682 | + | 4.71259i | −0.804664 | + | 0.593730i | ||||
\(64\) | 8.00000i | 1.00000i | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 10.3485 | − | 0.953512i | 1.27381 | − | 0.117369i | ||||
\(67\) | −0.965926 | + | 0.258819i | −0.118007 | + | 0.0316198i | −0.317339 | − | 0.948312i | \(-0.602789\pi\) |
0.199332 | + | 0.979932i | \(0.436123\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −4.24264 | − | 6.00000i | −0.510754 | − | 0.722315i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 7.07107i | − | 0.839181i | −0.907713 | − | 0.419591i | \(-0.862174\pi\) | ||
0.907713 | − | 0.419591i | \(-0.137826\pi\) | |||||||
\(72\) | −4.80260 | + | 6.99536i | −0.565992 | + | 0.824411i | ||||
\(73\) | 1.81173 | + | 6.76148i | 0.212047 | + | 0.791371i | 0.987185 | + | 0.159579i | \(0.0510137\pi\) |
−0.775138 | + | 0.631792i | \(0.782320\pi\) | |||||||
\(74\) | −0.707107 | + | 1.22474i | −0.0821995 | + | 0.142374i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −0.803848 | + | 11.1962i | −0.0916069 | + | 1.27592i | ||||
\(78\) | 2.07107 | − | 12.0711i | 0.234502 | − | 1.36678i | ||||
\(79\) | 6.06218 | − | 3.50000i | 0.682048 | − | 0.393781i | −0.118578 | − | 0.992945i | \(-0.537834\pi\) |
0.800626 | + | 0.599164i | \(0.204500\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −8.39898 | + | 3.23375i | −0.933220 | + | 0.359306i | ||||
\(82\) | 2.58819 | − | 9.65926i | 0.285818 | − | 1.06669i | ||||
\(83\) | 1.00000 | + | 1.00000i | 0.109764 | + | 0.109764i | 0.759856 | − | 0.650092i | \(-0.225269\pi\) |
−0.650092 | + | 0.759856i | \(0.725269\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 6.12372 | − | 3.53553i | 0.660338 | − | 0.381246i | ||||
\(87\) | 7.82913 | − | 9.41832i | 0.839371 | − | 1.00975i | ||||
\(88\) | 3.10583 | + | 11.5911i | 0.331082 | + | 1.23562i | ||||
\(89\) | 7.77817 | + | 13.4722i | 0.824485 | + | 1.42805i | 0.902312 | + | 0.431083i | \(0.141868\pi\) |
−0.0778275 | + | 0.996967i | \(0.524798\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 12.5000 | + | 4.33013i | 1.31036 | + | 0.453921i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0.599900 | + | 1.62484i | 0.0622068 | + | 0.168489i | ||||
\(94\) | −6.92820 | − | 4.00000i | −0.714590 | − | 0.412568i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −7.07107 | − | 7.07107i | −0.717958 | − | 0.717958i | 0.250229 | − | 0.968187i | \(-0.419494\pi\) |
−0.968187 | + | 0.250229i | \(0.919494\pi\) | |||||||
\(98\) | −7.92820 | + | 5.92820i | −0.800869 | + | 0.598839i | ||||
\(99\) | −4.24264 | + | 12.0000i | −0.426401 | + | 1.20605i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 8.57321 | + | 4.94975i | 0.853067 | + | 0.492518i | 0.861684 | − | 0.507445i | \(-0.169410\pi\) |
−0.00861771 | + | 0.999963i | \(0.502743\pi\) | |||||||
\(102\) | 2.66390 | + | 2.21441i | 0.263766 | + | 0.219260i | ||||
\(103\) | −2.89778 | − | 0.776457i | −0.285526 | − | 0.0765066i | 0.113213 | − | 0.993571i | \(-0.463886\pi\) |
−0.398740 | + | 0.917064i | \(0.630552\pi\) | |||||||
\(104\) | 14.1421 | 1.38675 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −4.00000 | −0.388514 | ||||||||
\(107\) | 15.0263 | + | 4.02628i | 1.45265 | + | 0.389235i | 0.896943 | − | 0.442146i | \(-0.145783\pi\) |
0.555702 | + | 0.831381i | \(0.312449\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −14.7224 | − | 8.50000i | −1.41015 | − | 0.814152i | −0.414751 | − | 0.909935i | \(-0.636131\pi\) |
−0.995402 | + | 0.0957826i | \(0.969465\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −1.00000 | − | 1.41421i | −0.0949158 | − | 0.134231i | ||||
\(112\) | −5.93426 | + | 8.76268i | −0.560734 | + | 0.827996i | ||||
\(113\) | −14.0000 | − | 14.0000i | −1.31701 | − | 1.31701i | −0.916132 | − | 0.400878i | \(-0.868705\pi\) |
−0.400878 | − | 0.916132i | \(-0.631295\pi\) | |||||||
\(114\) | −7.17461 | + | 15.5732i | −0.671964 | + | 1.45857i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 12.3662 | + | 8.48988i | 1.14325 | + | 0.784890i | ||||
\(118\) | −1.41421 | + | 1.41421i | −0.130189 | + | 0.130189i | ||||
\(119\) | −2.82843 | + | 2.44949i | −0.259281 | + | 0.224544i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 3.50000 | + | 6.06218i | 0.318182 | + | 0.551107i | ||||
\(122\) | −1.46410 | − | 5.46410i | −0.132554 | − | 0.494697i | ||||
\(123\) | 9.41832 | + | 7.82913i | 0.849221 | + | 0.705929i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −10.4495 | + | 4.09978i | −0.930915 | + | 0.365237i | ||||
\(127\) | −10.6066 | − | 10.6066i | −0.941184 | − | 0.941184i | 0.0571802 | − | 0.998364i | \(-0.481789\pi\) |
−0.998364 | + | 0.0571802i | \(0.981789\pi\) | |||||||
\(128\) | −2.92820 | + | 10.9282i | −0.258819 | + | 0.965926i | ||||
\(129\) | 0.794593 | + | 8.62372i | 0.0699600 | + | 0.759277i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 14.6969 | − | 8.48528i | 1.28408 | − | 0.741362i | 0.306486 | − | 0.951875i | \(-0.400847\pi\) |
0.977591 | + | 0.210513i | \(0.0675133\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −15.3347 | − | 10.3849i | −1.32969 | − | 0.900489i | ||||
\(134\) | −1.41421 | −0.122169 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −2.00000 | + | 3.46410i | −0.171499 | + | 0.297044i | ||||
\(137\) | −4.02628 | − | 15.0263i | −0.343988 | − | 1.28378i | −0.893790 | − | 0.448486i | \(-0.851963\pi\) |
0.549801 | − | 0.835295i | \(-0.314703\pi\) | |||||||
\(138\) | −3.59940 | − | 9.74907i | −0.306401 | − | 0.829896i | ||||
\(139\) | 11.0000i | 0.933008i | 0.884519 | + | 0.466504i | \(0.154487\pi\) | ||||
−0.884519 | + | 0.466504i | \(0.845513\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 8.00000 | − | 5.65685i | 0.673722 | − | 0.476393i | ||||
\(142\) | 2.58819 | − | 9.65926i | 0.217196 | − | 0.810587i | ||||
\(143\) | 20.4904 | − | 5.49038i | 1.71349 | − | 0.459129i | ||||
\(144\) | −9.12096 | + | 7.79796i | −0.760080 | + | 0.649830i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 9.89949i | 0.819288i | ||||||||
\(147\) | −2.53139 | − | 11.8572i | −0.208785 | − | 0.977961i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 4.24264 | + | 7.34847i | 0.347571 | + | 0.602010i | 0.985817 | − | 0.167822i | \(-0.0536733\pi\) |
−0.638247 | + | 0.769832i | \(0.720340\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 3.00000 | − | 5.19615i | 0.244137 | − | 0.422857i | −0.717752 | − | 0.696299i | \(-0.754829\pi\) |
0.961888 | + | 0.273442i | \(0.0881622\pi\) | |||||||
\(152\) | −19.1244 | − | 5.12436i | −1.55119 | − | 0.415640i | ||||
\(153\) | −3.82843 | + | 1.82843i | −0.309510 | + | 0.147820i | ||||
\(154\) | −5.19615 | + | 15.0000i | −0.418718 | + | 1.20873i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 3.86370 | − | 1.03528i | 0.308357 | − | 0.0826240i | −0.101322 | − | 0.994854i | \(-0.532307\pi\) |
0.409679 | + | 0.912230i | \(0.365641\pi\) | |||||||
\(158\) | 9.56218 | − | 2.56218i | 0.760726 | − | 0.203836i | ||||
\(159\) | 2.04989 | − | 4.44949i | 0.162567 | − | 0.352867i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 11.0227 | − | 2.12132i | 0.868711 | − | 0.167183i | ||||
\(162\) | −12.6569 | + | 1.34315i | −0.994416 | + | 0.105527i | ||||
\(163\) | 1.93185 | + | 0.517638i | 0.151314 | + | 0.0405445i | 0.333681 | − | 0.942686i | \(-0.391709\pi\) |
−0.182367 | + | 0.983231i | \(0.558376\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 1.00000 | + | 1.73205i | 0.0776151 | + | 0.134433i | ||||
\(167\) | 7.00000 | − | 7.00000i | 0.541676 | − | 0.541676i | −0.382344 | − | 0.924020i | \(-0.624883\pi\) |
0.924020 | + | 0.382344i | \(0.124883\pi\) | |||||||
\(168\) | −6.70623 | − | 11.0917i | −0.517397 | − | 0.855746i | ||||
\(169\) | − | 12.0000i | − | 0.923077i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −13.6464 | − | 15.9617i | −1.04357 | − | 1.22062i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 0.732051 | − | 2.73205i | 0.0556568 | − | 0.207714i | −0.932498 | − | 0.361176i | \(-0.882375\pi\) |
0.988155 | + | 0.153462i | \(0.0490422\pi\) | |||||||
\(174\) | 14.1421 | − | 10.0000i | 1.07211 | − | 0.758098i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 16.9706i | 1.27920i | ||||||||
\(177\) | −0.848387 | − | 2.29788i | −0.0637687 | − | 0.172719i | ||||
\(178\) | 5.69402 | + | 21.2504i | 0.426785 | + | 1.59278i | ||||
\(179\) | 9.89949 | − | 17.1464i | 0.739923 | − | 1.28158i | −0.212607 | − | 0.977138i | \(-0.568195\pi\) |
0.952529 | − | 0.304446i | \(-0.0984714\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −3.00000 | −0.222988 | −0.111494 | − | 0.993765i | \(-0.535564\pi\) | ||||
−0.111494 | + | 0.993765i | \(0.535564\pi\) | |||||||
\(182\) | 15.4904 | + | 10.4904i | 1.14822 | + | 0.777599i | ||||
\(183\) | 6.82843 | + | 1.17157i | 0.504772 | + | 0.0866052i | ||||
\(184\) | 10.3923 | − | 6.00000i | 0.766131 | − | 0.442326i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0.224745 | + | 2.43916i | 0.0164791 | + | 0.178848i | ||||
\(187\) | −1.55291 | + | 5.79555i | −0.113560 | + | 0.423813i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0.794593 | − | 13.7247i | 0.0577981 | − | 0.998328i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −9.79796 | + | 5.65685i | −0.708955 | + | 0.409316i | −0.810674 | − | 0.585498i | \(-0.800899\pi\) |
0.101719 | + | 0.994813i | \(0.467566\pi\) | |||||||
\(192\) | −10.6556 | − | 8.85765i | −0.769002 | − | 0.639246i | ||||
\(193\) | −5.95284 | − | 22.2163i | −0.428495 | − | 1.59916i | −0.756171 | − | 0.654374i | \(-0.772932\pi\) |
0.327677 | − | 0.944790i | \(-0.393734\pi\) | |||||||
\(194\) | −7.07107 | − | 12.2474i | −0.507673 | − | 0.879316i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −3.00000 | + | 3.00000i | −0.213741 | + | 0.213741i | −0.805855 | − | 0.592113i | \(-0.798294\pi\) |
0.592113 | + | 0.805855i | \(0.298294\pi\) | |||||||
\(198\) | −10.1879 | + | 14.8394i | −0.724020 | + | 1.05459i | ||||
\(199\) | −1.73205 | − | 1.00000i | −0.122782 | − | 0.0708881i | 0.437351 | − | 0.899291i | \(-0.355917\pi\) |
−0.560133 | + | 0.828403i | \(0.689250\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0.724745 | − | 1.57313i | 0.0511196 | − | 0.110960i | ||||
\(202\) | 9.89949 | + | 9.89949i | 0.696526 | + | 0.696526i | ||||
\(203\) | 8.16987 | + | 16.8301i | 0.573413 | + | 1.18124i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −3.67423 | − | 2.12132i | −0.255996 | − | 0.147799i | ||||
\(207\) | 12.6892 | + | 0.992248i | 0.881959 | + | 0.0689660i | ||||
\(208\) | 19.3185 | + | 5.17638i | 1.33950 | + | 0.358917i | ||||
\(209\) | −29.6985 | −2.05429 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2.00000 | 0.137686 | 0.0688428 | − | 0.997628i | \(-0.478069\pi\) | ||||
0.0688428 | + | 0.997628i | \(0.478069\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 9.41832 | + | 7.82913i | 0.645332 | + | 0.536443i | ||||
\(214\) | 19.0526 | + | 11.0000i | 1.30241 | + | 0.751945i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −4.00000 | − | 14.1421i | −0.272166 | − | 0.962250i | ||||
\(217\) | −2.63896 | − | 0.189469i | −0.179144 | − | 0.0128620i | ||||
\(218\) | −17.0000 | − | 17.0000i | −1.15139 | − | 1.15139i | ||||
\(219\) | −11.0119 | − | 5.07321i | −0.744117 | − | 0.342816i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 6.12372 | + | 3.53553i | 0.411926 | + | 0.237826i | ||||
\(222\) | −0.848387 | − | 2.29788i | −0.0569400 | − | 0.154223i | ||||
\(223\) | 7.07107 | − | 7.07107i | 0.473514 | − | 0.473514i | −0.429536 | − | 0.903050i | \(-0.641323\pi\) |
0.903050 | + | 0.429536i | \(0.141323\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −14.0000 | − | 24.2487i | −0.931266 | − | 1.61300i | ||||
\(227\) | 3.29423 | + | 12.2942i | 0.218646 | + | 0.815997i | 0.984851 | + | 0.173401i | \(0.0554757\pi\) |
−0.766206 | + | 0.642595i | \(0.777858\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −2.59808 | + | 1.50000i | −0.171686 | + | 0.0991228i | −0.583380 | − | 0.812199i | \(-0.698270\pi\) |
0.411695 | + | 0.911322i | \(0.364937\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −14.0227 | − | 13.4671i | −0.922626 | − | 0.886073i | ||||
\(232\) | 14.1421 | + | 14.1421i | 0.928477 | + | 0.928477i | ||||
\(233\) | 0.732051 | − | 2.73205i | 0.0479582 | − | 0.178983i | −0.937792 | − | 0.347197i | \(-0.887133\pi\) |
0.985750 | + | 0.168215i | \(0.0538001\pi\) | |||||||
\(234\) | 13.7850 | + | 16.1237i | 0.901152 | + | 1.05404i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −2.05025 | + | 11.9497i | −0.133178 | + | 0.776220i | ||||
\(238\) | −4.76028 | + | 2.31079i | −0.308563 | + | 0.149786i | ||||
\(239\) | 28.2843 | 1.82956 | 0.914779 | − | 0.403955i | \(-0.132365\pi\) | ||||
0.914779 | + | 0.403955i | \(0.132365\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −12.0000 | + | 20.7846i | −0.772988 | + | 1.33885i | 0.162930 | + | 0.986638i | \(0.447905\pi\) |
−0.935918 | + | 0.352217i | \(0.885428\pi\) | |||||||
\(242\) | 2.56218 | + | 9.56218i | 0.164703 | + | 0.614680i | ||||
\(243\) | 4.99221 | − | 14.7675i | 0.320250 | − | 0.947333i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 10.0000 | + | 14.1421i | 0.637577 | + | 0.901670i | ||||
\(247\) | −9.05867 | + | 33.8074i | −0.576389 | + | 2.15111i | ||||
\(248\) | −2.73205 | + | 0.732051i | −0.173485 | + | 0.0464853i | ||||
\(249\) | −2.43916 | + | 0.224745i | −0.154575 | + | 0.0142426i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 7.07107i | 0.446322i | 0.974782 | + | 0.223161i | \(0.0716375\pi\) | ||||
−0.974782 | + | 0.223161i | \(0.928362\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 12.7279 | − | 12.7279i | 0.800198 | − | 0.800198i | ||||
\(254\) | −10.6066 | − | 18.3712i | −0.665517 | − | 1.15271i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −12.2942 | − | 3.29423i | −0.766893 | − | 0.205488i | −0.145894 | − | 0.989300i | \(-0.546606\pi\) |
−0.620998 | + | 0.783812i | \(0.713273\pi\) | |||||||
\(258\) | −2.07107 | + | 12.0711i | −0.128939 | + | 0.751512i | ||||
\(259\) | 2.59808 | − | 0.500000i | 0.161437 | − | 0.0310685i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 3.87628 | + | 20.8560i | 0.239935 | + | 1.29096i | ||||
\(262\) | 23.1822 | − | 6.21166i | 1.43220 | − | 0.383757i | ||||
\(263\) | −16.3923 | + | 4.39230i | −1.01079 | + | 0.270841i | −0.725961 | − | 0.687736i | \(-0.758605\pi\) |
−0.284832 | + | 0.958577i | \(0.591938\pi\) | |||||||
\(264\) | −18.8776 | − | 8.69694i | −1.16184 | − | 0.535260i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −17.1464 | − | 19.7990i | −1.05131 | − | 1.21395i | ||||
\(267\) | −26.5563 | − | 4.55635i | −1.62522 | − | 0.278844i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 2.82843 | − | 4.89898i | 0.172452 | − | 0.298696i | −0.766824 | − | 0.641857i | \(-0.778164\pi\) |
0.939277 | + | 0.343161i | \(0.111498\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −7.00000 | − | 12.1244i | −0.425220 | − | 0.736502i | 0.571221 | − | 0.820796i | \(-0.306470\pi\) |
−0.996441 | + | 0.0842940i | \(0.973137\pi\) | |||||||
\(272\) | −4.00000 | + | 4.00000i | −0.242536 | + | 0.242536i | ||||
\(273\) | −19.6076 | + | 11.8550i | −1.18671 | + | 0.717500i | ||||
\(274\) | − | 22.0000i | − | 1.32907i | ||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 8.69333 | − | 2.32937i | 0.522332 | − | 0.139958i | 0.0119868 | − | 0.999928i | \(-0.496184\pi\) |
0.510345 | + | 0.859970i | \(0.329518\pi\) | |||||||
\(278\) | −4.02628 | + | 15.0263i | −0.241480 | + | 0.901216i | ||||
\(279\) | −2.82843 | − | 1.00000i | −0.169334 | − | 0.0598684i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 14.1421i | 0.843649i | 0.906677 | + | 0.421825i | \(0.138610\pi\) | ||||
−0.906677 | + | 0.421825i | \(0.861390\pi\) | |||||||
\(282\) | 12.9988 | − | 4.79920i | 0.774065 | − | 0.285788i | ||||
\(283\) | −5.95284 | − | 22.2163i | −0.353859 | − | 1.32062i | −0.881914 | − | 0.471411i | \(-0.843745\pi\) |
0.528054 | − | 0.849211i | \(-0.322922\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 30.0000 | 1.77394 | ||||||||
\(287\) | −16.8301 | + | 8.16987i | −0.993451 | + | 0.482252i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 12.9904 | − | 7.50000i | 0.764140 | − | 0.441176i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 17.2474 | − | 1.58919i | 1.01106 | − | 0.0931597i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 16.0000 | + | 16.0000i | 0.934730 | + | 0.934730i | 0.997997 | − | 0.0632667i | \(-0.0201519\pi\) |
−0.0632667 | + | 0.997997i | \(0.520152\pi\) | |||||||
\(294\) | 0.882079 | − | 17.1237i | 0.0514439 | − | 0.998676i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 2.44949 | − | 1.41421i | 0.142374 | − | 0.0821995i | ||||
\(297\) | −11.2859 | − | 18.9375i | −0.654876 | − | 1.09886i | ||||
\(298\) | 3.10583 | + | 11.5911i | 0.179916 | + | 0.671455i | ||||
\(299\) | −10.6066 | − | 18.3712i | −0.613396 | − | 1.06243i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −12.5000 | − | 4.33013i | −0.720488 | − | 0.249584i | ||||
\(302\) | 6.00000 | − | 6.00000i | 0.345261 | − | 0.345261i | ||||
\(303\) | −16.0851 | + | 5.93871i | −0.924067 | + | 0.341170i | ||||
\(304\) | −24.2487 | − | 14.0000i | −1.39076 | − | 0.802955i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −5.89898 | + | 1.09638i | −0.337222 | + | 0.0626757i | ||||
\(307\) | 10.6066 | + | 10.6066i | 0.605351 | + | 0.605351i | 0.941727 | − | 0.336377i | \(-0.109202\pi\) |
−0.336377 | + | 0.941727i | \(0.609202\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 4.24264 | − | 3.00000i | 0.241355 | − | 0.170664i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −28.1691 | − | 16.2635i | −1.59732 | − | 0.922216i | −0.992000 | − | 0.126237i | \(-0.959710\pi\) |
−0.605325 | − | 0.795979i | \(-0.706957\pi\) | |||||||
\(312\) | −15.6583 | + | 18.8366i | −0.886475 | + | 1.06641i | ||||
\(313\) | 16.4207 | + | 4.39992i | 0.928155 | + | 0.248698i | 0.691068 | − | 0.722790i | \(-0.257141\pi\) |
0.237087 | + | 0.971488i | \(0.423807\pi\) | |||||||
\(314\) | 5.65685 | 0.319235 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 1.36603 | + | 0.366025i | 0.0767236 | + | 0.0205580i | 0.296977 | − | 0.954885i | \(-0.404022\pi\) |
−0.220253 | + | 0.975443i | \(0.570688\pi\) | |||||||
\(318\) | 4.42883 | − | 5.32780i | 0.248356 | − | 0.298768i | ||||
\(319\) | 25.9808 | + | 15.0000i | 1.45464 | + | 0.839839i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −22.0000 | + | 15.5563i | −1.22792 | + | 0.868271i | ||||
\(322\) | 15.8338 | + | 1.13681i | 0.882380 | + | 0.0633521i | ||||
\(323\) | −7.00000 | − | 7.00000i | −0.389490 | − | 0.389490i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 2.44949 | + | 1.41421i | 0.135665 | + | 0.0783260i | ||||
\(327\) | 27.6224 | − | 10.1983i | 1.52752 | − | 0.563968i | ||||
\(328\) | −14.1421 | + | 14.1421i | −0.780869 | + | 0.780869i | ||||
\(329\) | 2.82843 | + | 14.6969i | 0.155936 | + | 0.810268i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 0.500000 | + | 0.866025i | 0.0274825 | + | 0.0476011i | 0.879440 | − | 0.476011i | \(-0.157918\pi\) |
−0.851957 | + | 0.523612i | \(0.824584\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 2.99087 | + | 0.233875i | 0.163899 | + | 0.0128163i | ||||
\(334\) | 12.1244 | − | 7.00000i | 0.663415 | − | 0.383023i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −5.10102 | − | 17.6062i | −0.278283 | − | 0.960499i | ||||
\(337\) | −3.53553 | − | 3.53553i | −0.192593 | − | 0.192593i | 0.604223 | − | 0.796815i | \(-0.293484\pi\) |
−0.796815 | + | 0.604223i | \(0.793484\pi\) | |||||||
\(338\) | 4.39230 | − | 16.3923i | 0.238910 | − | 0.891624i | ||||
\(339\) | 34.1482 | − | 3.14643i | 1.85468 | − | 0.170891i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −3.67423 | + | 2.12132i | −0.198971 | + | 0.114876i | ||||
\(342\) | −12.7990 | − | 26.7990i | −0.692090 | − | 1.44912i | ||||
\(343\) | 18.0938 | + | 3.95164i | 0.976972 | + | 0.213368i | ||||
\(344\) | −14.1421 | −0.762493 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 2.00000 | − | 3.46410i | 0.107521 | − | 0.186231i | ||||
\(347\) | −5.85641 | − | 21.8564i | −0.314388 | − | 1.17331i | −0.924558 | − | 0.381042i | \(-0.875565\pi\) |
0.610169 | − | 0.792271i | \(-0.291101\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 26.0000i | 1.39175i | 0.718164 | + | 0.695874i | \(0.244983\pi\) | ||||
−0.718164 | + | 0.695874i | \(0.755017\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −25.0000 | + | 7.07107i | −1.33440 | + | 0.377426i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 4.09808 | − | 1.09808i | 0.218119 | − | 0.0584447i | −0.148105 | − | 0.988972i | \(-0.547317\pi\) |
0.366223 | + | 0.930527i | \(0.380651\pi\) | |||||||
\(354\) | −0.317837 | − | 3.44949i | −0.0168929 | − | 0.183338i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −0.130948 | − | 6.47942i | −0.00693052 | − | 0.342927i | ||||
\(358\) | 19.7990 | − | 19.7990i | 1.04641 | − | 1.04641i | ||||
\(359\) | 0.707107 | + | 1.22474i | 0.0373197 | + | 0.0646396i | 0.884082 | − | 0.467332i | \(-0.154785\pi\) |
−0.846762 | + | 0.531971i | \(0.821451\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 15.0000 | − | 25.9808i | 0.789474 | − | 1.36741i | ||||
\(362\) | −4.09808 | − | 1.09808i | −0.215390 | − | 0.0577136i | ||||
\(363\) | −11.9497 | − | 2.05025i | −0.627199 | − | 0.107610i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 8.89898 | + | 4.09978i | 0.465157 | + | 0.214299i | ||||
\(367\) | −20.2844 | + | 5.43520i | −1.05884 | + | 0.283715i | −0.745900 | − | 0.666058i | \(-0.767980\pi\) |
−0.312939 | + | 0.949773i | \(0.601314\pi\) | |||||||
\(368\) | 16.3923 | − | 4.39230i | 0.854508 | − | 0.228965i | ||||
\(369\) | −20.8560 | + | 3.87628i | −1.08572 | + | 0.201791i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 4.89898 | + | 5.65685i | 0.254342 | + | 0.293689i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −22.2163 | − | 5.95284i | −1.15032 | − | 0.308226i | −0.367224 | − | 0.930132i | \(-0.619692\pi\) |
−0.783092 | + | 0.621906i | \(0.786359\pi\) | |||||||
\(374\) | −4.24264 | + | 7.34847i | −0.219382 | + | 0.379980i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 8.00000 | + | 13.8564i | 0.412568 | + | 0.714590i | ||||
\(377\) | 25.0000 | − | 25.0000i | 1.28757 | − | 1.28757i | ||||
\(378\) | 6.10904 | − | 18.4575i | 0.314215 | − | 0.949352i | ||||
\(379\) | − | 9.00000i | − | 0.462299i | −0.972918 | − | 0.231149i | \(-0.925751\pi\) | ||
0.972918 | − | 0.231149i | \(-0.0742486\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 25.8712 | − | 2.38378i | 1.32542 | − | 0.122125i | ||||
\(382\) | −15.4548 | + | 4.14110i | −0.790737 | + | 0.211877i | ||||
\(383\) | 4.39230 | − | 16.3923i | 0.224436 | − | 0.837608i | −0.758193 | − | 0.652030i | \(-0.773918\pi\) |
0.982630 | − | 0.185578i | \(-0.0594157\pi\) | |||||||
\(384\) | −11.3137 | − | 16.0000i | −0.577350 | − | 0.816497i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | − | 32.5269i | − | 1.65558i | ||||||
\(387\) | −12.3662 | − | 8.48988i | −0.628607 | − | 0.431565i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −14.8492 | + | 25.7196i | −0.752886 | + | 1.30404i | 0.193532 | + | 0.981094i | \(0.438006\pi\) |
−0.946418 | + | 0.322944i | \(0.895328\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 6.00000 | 0.303433 | ||||||||
\(392\) | 19.6603 | − | 2.33975i | 0.992993 | − | 0.118175i | ||||
\(393\) | −4.97056 | + | 28.9706i | −0.250732 | + | 1.46137i | ||||
\(394\) | −5.19615 | + | 3.00000i | −0.261778 | + | 0.151138i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −0.258819 | + | 0.965926i | −0.0129898 | + | 0.0484784i | −0.972117 | − | 0.234498i | \(-0.924655\pi\) |
0.959127 | + | 0.282977i | \(0.0913219\pi\) | |||||||
\(398\) | −2.00000 | − | 2.00000i | −0.100251 | − | 0.100251i | ||||
\(399\) | 30.8109 | − | 8.92679i | 1.54248 | − | 0.446898i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −22.0454 | + | 12.7279i | −1.10090 | + | 0.635602i | −0.936456 | − | 0.350785i | \(-0.885915\pi\) |
−0.164439 | + | 0.986387i | \(0.552581\pi\) | |||||||
\(402\) | 1.56583 | − | 1.88366i | 0.0780963 | − | 0.0939486i | ||||
\(403\) | 1.29410 | + | 4.82963i | 0.0644635 | + | 0.240581i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 5.00000 | + | 25.9808i | 0.248146 | + | 1.28940i | ||||
\(407\) | 3.00000 | − | 3.00000i | 0.148704 | − | 0.148704i | ||||
\(408\) | −2.39960 | − | 6.49938i | −0.118798 | − | 0.321767i | ||||
\(409\) | −32.0429 | − | 18.5000i | −1.58442 | − | 0.914766i | −0.994203 | − | 0.107523i | \(-0.965708\pi\) |
−0.590219 | − | 0.807243i | \(-0.700959\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 24.4722 | + | 11.2744i | 1.20712 | + | 0.556124i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 3.73205 | + | 0.267949i | 0.183642 | + | 0.0131849i | ||||
\(414\) | 16.9706 | + | 6.00000i | 0.834058 | + | 0.294884i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −14.6515 | − | 12.1793i | −0.717485 | − | 0.596421i | ||||
\(418\) | −40.5689 | − | 10.8704i | −1.98429 | − | 0.531689i | ||||
\(419\) | 14.1421 | 0.690889 | 0.345444 | − | 0.938439i | \(-0.387728\pi\) | ||||
0.345444 | + | 0.938439i | \(0.387728\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −23.0000 | −1.12095 | −0.560476 | − | 0.828171i | \(-0.689382\pi\) | ||||
−0.560476 | + | 0.828171i | \(0.689382\pi\) | |||||||
\(422\) | 2.73205 | + | 0.732051i | 0.132994 | + | 0.0356357i | ||||
\(423\) | −1.32300 | + | 16.9189i | −0.0643263 | + | 0.822626i | ||||
\(424\) | 6.92820 | + | 4.00000i | 0.336463 | + | 0.194257i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 10.0000 | + | 14.1421i | 0.484502 | + | 0.685189i | ||||
\(427\) | −5.93426 | + | 8.76268i | −0.287179 | + | 0.424056i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −15.3742 | + | 33.3712i | −0.742271 | + | 1.61118i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 2.44949 | + | 1.41421i | 0.117988 | + | 0.0681203i | 0.557832 | − | 0.829954i | \(-0.311633\pi\) |
−0.439845 | + | 0.898074i | \(0.644967\pi\) | |||||||
\(432\) | −0.287721 | − | 20.7826i | −0.0138430 | − | 0.999904i | ||||
\(433\) | 10.6066 | − | 10.6066i | 0.509721 | − | 0.509721i | −0.404720 | − | 0.914441i | \(-0.632631\pi\) |
0.914441 | + | 0.404720i | \(0.132631\pi\) | |||||||
\(434\) | −3.53553 | − | 1.22474i | −0.169711 | − | 0.0587896i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 7.68653 | + | 28.6865i | 0.367697 | + | 1.37226i | ||||
\(438\) | −13.1856 | − | 10.9608i | −0.630034 | − | 0.523727i | ||||
\(439\) | −32.9090 | + | 19.0000i | −1.57066 | + | 0.906821i | −0.574571 | + | 0.818455i | \(0.694831\pi\) |
−0.996088 | + | 0.0883659i | \(0.971836\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 18.5959 | + | 9.75663i | 0.885520 | + | 0.464601i | ||||
\(442\) | 7.07107 | + | 7.07107i | 0.336336 | + | 0.336336i | ||||
\(443\) | −2.92820 | + | 10.9282i | −0.139123 | + | 0.519215i | 0.860824 | + | 0.508903i | \(0.169949\pi\) |
−0.999947 | + | 0.0103113i | \(0.996718\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 12.2474 | − | 7.07107i | 0.579934 | − | 0.334825i | ||||
\(447\) | −14.4853 | − | 2.48528i | −0.685130 | − | 0.117550i | ||||
\(448\) | 19.0411 | − | 9.24316i | 0.899608 | − | 0.436698i | ||||
\(449\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −15.0000 | + | 25.9808i | −0.706322 | + | 1.22339i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 3.59940 | + | 9.74907i | 0.169115 | + | 0.458051i | ||||
\(454\) | 18.0000i | 0.844782i | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 28.0000 | − | 19.7990i | 1.31122 | − | 0.927173i | ||||
\(457\) | 7.50575 | − | 28.0118i | 0.351104 | − | 1.31034i | −0.534212 | − | 0.845350i | \(-0.679392\pi\) |
0.885317 | − | 0.464989i | \(-0.153942\pi\) | |||||||
\(458\) | −4.09808 | + | 1.09808i | −0.191491 | + | 0.0513097i | ||||
\(459\) | 1.80348 | − | 7.12372i | 0.0841794 | − | 0.332507i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 7.07107i | − | 0.329332i | −0.986349 | − | 0.164666i | \(-0.947345\pi\) | ||
0.986349 | − | 0.164666i | \(-0.0526547\pi\) | |||||||
\(462\) | −14.2261 | − | 23.5291i | −0.661856 | − | 1.09467i | ||||
\(463\) | −17.6777 | + | 17.6777i | −0.821551 | + | 0.821551i | −0.986330 | − | 0.164779i | \(-0.947309\pi\) |
0.164779 | + | 0.986330i | \(0.447309\pi\) | |||||||
\(464\) | 14.1421 | + | 24.4949i | 0.656532 | + | 1.13715i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 2.00000 | − | 3.46410i | 0.0926482 | − | 0.160471i | ||||
\(467\) | −5.46410 | − | 1.46410i | −0.252848 | − | 0.0677505i | 0.130168 | − | 0.991492i | \(-0.458448\pi\) |
−0.383017 | + | 0.923741i | \(0.625115\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1.73205 | + | 2.00000i | 0.0799787 | + | 0.0923514i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −2.89898 | + | 6.29253i | −0.133578 | + | 0.289944i | ||||
\(472\) | 3.86370 | − | 1.03528i | 0.177841 | − | 0.0476524i | ||||
\(473\) | −20.4904 | + | 5.49038i | −0.942149 | + | 0.252448i | ||||
\(474\) | −7.17461 | + | 15.5732i | −0.329541 | + | 0.715301i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 3.65685 | + | 7.65685i | 0.167436 | + | 0.350583i | ||||
\(478\) | 38.6370 | + | 10.3528i | 1.76722 | + | 0.473524i | ||||
\(479\) | −4.24264 | + | 7.34847i | −0.193851 | + | 0.335760i | −0.946523 | − | 0.322635i | \(-0.895431\pi\) |
0.752672 | + | 0.658396i | \(0.228765\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2.50000 | − | 4.33013i | −0.113990 | − | 0.197437i | ||||
\(482\) | −24.0000 | + | 24.0000i | −1.09317 | + | 1.09317i | ||||
\(483\) | −9.37891 | + | 17.0304i | −0.426755 | + | 0.774912i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 12.2247 | − | 18.3455i | 0.554526 | − | 0.832167i | ||||
\(487\) | 28.0118 | − | 7.50575i | 1.26934 | − | 0.340118i | 0.439561 | − | 0.898213i | \(-0.355134\pi\) |
0.829777 | + | 0.558095i | \(0.188467\pi\) | |||||||
\(488\) | −2.92820 | + | 10.9282i | −0.132554 | + | 0.494697i | ||||
\(489\) | −2.82843 | + | 2.00000i | −0.127906 | + | 0.0904431i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 14.1421i | − | 0.638226i | −0.947717 | − | 0.319113i | \(-0.896615\pi\) | ||
0.947717 | − | 0.319113i | \(-0.103385\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 2.58819 | + | 9.65926i | 0.116566 | + | 0.435031i | ||||
\(494\) | −24.7487 | + | 42.8661i | −1.11350 | + | 1.92864i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −4.00000 | −0.179605 | ||||||||
\(497\) | −16.8301 | + | 8.16987i | −0.754934 | + | 0.366469i | ||||
\(498\) | −3.41421 | − | 0.585786i | −0.152995 | − | 0.0262497i | ||||
\(499\) | 23.3827 | − | 13.5000i | 1.04675 | − | 0.604343i | 0.125014 | − | 0.992155i | \(-0.460102\pi\) |
0.921739 | + | 0.387812i | \(0.126769\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1.57321 | + | 17.0741i | 0.0702860 | + | 0.762815i | ||||
\(502\) | −2.58819 | + | 9.65926i | −0.115517 | + | 0.431114i | ||||
\(503\) | −24.0000 | − | 24.0000i | −1.07011 | − | 1.07011i | −0.997350 | − | 0.0727574i | \(-0.976820\pi\) |
−0.0727574 | − | 0.997350i | \(-0.523180\pi\) | |||||||
\(504\) | 22.1988 | + | 3.34847i | 0.988814 | + | 0.149153i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 22.0454 | − | 12.7279i | 0.980038 | − | 0.565825i | ||||
\(507\) | 15.9834 | + | 13.2865i | 0.709848 | + | 0.590073i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 4.24264 | + | 7.34847i | 0.188052 | + | 0.325715i | 0.944601 | − | 0.328222i | \(-0.106449\pi\) |
−0.756549 | + | 0.653937i | \(0.773116\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 14.0000 | − | 12.1244i | 0.619324 | − | 0.536350i | ||||
\(512\) | 16.0000 | − | 16.0000i | 0.707107 | − | 0.707107i | ||||
\(513\) | 36.3696 | − | 0.503511i | 1.60576 | − | 0.0222306i | ||||
\(514\) | −15.5885 | − | 9.00000i | −0.687577 | − | 0.396973i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 16.9706 | + | 16.9706i | 0.746364 | + | 0.746364i | ||||
\(518\) | 3.73205 | + | 0.267949i | 0.163977 | + | 0.0117730i | ||||
\(519\) | 2.82843 | + | 4.00000i | 0.124154 | + | 0.175581i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 26.9444 | + | 15.5563i | 1.18046 | + | 0.681536i | 0.956120 | − | 0.292976i | \(-0.0946456\pi\) |
0.224335 | + | 0.974512i | \(0.427979\pi\) | |||||||
\(522\) | −2.33875 | + | 29.9087i | −0.102364 | + | 1.30907i | ||||
\(523\) | 6.76148 | + | 1.81173i | 0.295659 | + | 0.0792216i | 0.403599 | − | 0.914936i | \(-0.367759\pi\) |
−0.107941 | + | 0.994157i | \(0.534426\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −24.0000 | −1.04645 | ||||||||
\(527\) | −1.36603 | − | 0.366025i | −0.0595050 | − | 0.0159443i | ||||
\(528\) | −22.6040 | − | 18.7899i | −0.983711 | − | 0.817726i | ||||
\(529\) | 4.33013 | + | 2.50000i | 0.188266 | + | 0.108696i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 4.00000 | + | 1.41421i | 0.173585 | + | 0.0613716i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 25.0000 | + | 25.0000i | 1.08287 | + | 1.08287i | ||||
\(534\) | −34.6089 | − | 15.9444i | −1.49767 | − | 0.689981i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 2.44949 | + | 1.41421i | 0.105802 | + | 0.0610847i | ||||
\(537\) | 11.8774 | + | 32.1703i | 0.512549 | + | 1.38825i | ||||
\(538\) | 5.65685 | − | 5.65685i | 0.243884 | − | 0.243884i | ||||
\(539\) | 27.5772 | − | 11.0227i | 1.18783 | − | 0.474781i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 5.50000 | + | 9.52628i | 0.236463 | + | 0.409567i | 0.959697 | − | 0.281037i | \(-0.0906783\pi\) |
−0.723234 | + | 0.690604i | \(0.757345\pi\) | |||||||
\(542\) | −5.12436 | − | 19.1244i | −0.220110 | − | 0.821461i | ||||
\(543\) | 3.32162 | − | 3.99585i | 0.142544 | − | 0.171478i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −31.1237 | + | 9.01742i | −1.33197 | + | 0.385910i | ||||
\(547\) | 7.07107 | + | 7.07107i | 0.302337 | + | 0.302337i | 0.841928 | − | 0.539591i | \(-0.181421\pi\) |
−0.539591 | + | 0.841928i | \(0.681421\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −9.12096 | + | 7.79796i | −0.389273 | + | 0.332809i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −42.8661 | + | 24.7487i | −1.82616 | + | 1.05433i | ||||
\(552\) | −3.51472 | + | 20.4853i | −0.149596 | + | 0.871911i | ||||
\(553\) | −15.3347 | − | 10.3849i | −0.652098 | − | 0.441613i | ||||
\(554\) | 12.7279 | 0.540758 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 5.12436 | + | 19.1244i | 0.217126 | + | 0.810325i | 0.985407 | + | 0.170213i | \(0.0544455\pi\) |
−0.768281 | + | 0.640112i | \(0.778888\pi\) | |||||||
\(558\) | −3.49768 | − | 2.40130i | −0.148069 | − | 0.101655i | ||||
\(559\) | 25.0000i | 1.05739i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −6.00000 | − | 8.48528i | −0.253320 | − | 0.358249i | ||||
\(562\) | −5.17638 | + | 19.3185i | −0.218352 | + | 0.814902i | ||||
\(563\) | −30.0526 | + | 8.05256i | −1.26656 | + | 0.339375i | −0.828714 | − | 0.559673i | \(-0.810927\pi\) |
−0.437851 | + | 0.899048i | \(0.644260\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | − | 32.5269i | − | 1.36721i | ||||||
\(567\) | 17.4009 | + | 16.2545i | 0.730770 | + | 0.682624i | ||||
\(568\) | −14.1421 | + | 14.1421i | −0.593391 | + | 0.593391i | ||||
\(569\) | 0.707107 | + | 1.22474i | 0.0296435 | + | 0.0513440i | 0.880467 | − | 0.474108i | \(-0.157229\pi\) |
−0.850823 | + | 0.525452i | \(0.823896\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 0.500000 | − | 0.866025i | 0.0209243 | − | 0.0362420i | −0.855374 | − | 0.518012i | \(-0.826672\pi\) |
0.876298 | + | 0.481770i | \(0.160006\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 3.31371 | − | 19.3137i | 0.138432 | − | 0.806842i | ||||
\(574\) | −25.9808 | + | 5.00000i | −1.08442 | + | 0.208696i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 23.5959 | − | 4.38551i | 0.983163 | − | 0.182729i | ||||
\(577\) | −10.6252 | + | 2.84701i | −0.442332 | + | 0.118523i | −0.473109 | − | 0.881004i | \(-0.656868\pi\) |
0.0307771 | + | 0.999526i | \(0.490202\pi\) | |||||||
\(578\) | 20.4904 | − | 5.49038i | 0.852287 | − | 0.228370i | ||||
\(579\) | 36.1820 | + | 16.6691i | 1.50367 | + | 0.692745i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1.22474 | − | 3.53553i | 0.0508110 | − | 0.146679i | ||||
\(582\) | 24.1421 | + | 4.14214i | 1.00072 | + | 0.171697i | ||||
\(583\) | 11.5911 | + | 3.10583i | 0.480055 | + | 0.128630i | ||||
\(584\) | 9.89949 | − | 17.1464i | 0.409644 | − | 0.709524i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 16.0000 | + | 27.7128i | 0.660954 | + | 1.14481i | ||||
\(587\) | −13.0000 | + | 13.0000i | −0.536567 | + | 0.536567i | −0.922519 | − | 0.385952i | \(-0.873873\pi\) |
0.385952 | + | 0.922519i | \(0.373873\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 7.00000i | − | 0.288430i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −0.674235 | − | 7.31747i | −0.0277343 | − | 0.301001i | ||||
\(592\) | 3.86370 | − | 1.03528i | 0.158797 | − | 0.0425496i | ||||
\(593\) | −4.75833 | + | 17.7583i | −0.195401 | + | 0.729247i | 0.796761 | + | 0.604294i | \(0.206545\pi\) |
−0.992163 | + | 0.124953i | \(0.960122\pi\) | |||||||
\(594\) | −8.48528 | − | 30.0000i | −0.348155 | − | 1.23091i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 3.24969 | − | 1.19980i | 0.133001 | − | 0.0491046i | ||||
\(598\) | −7.76457 | − | 28.9778i | −0.317517 | − | 1.18499i | ||||
\(599\) | 9.89949 | − | 17.1464i | 0.404482 | − | 0.700584i | −0.589779 | − | 0.807565i | \(-0.700785\pi\) |
0.994261 | + | 0.106981i | \(0.0341184\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 7.00000 | 0.285536 | 0.142768 | − | 0.989756i | \(-0.454400\pi\) | ||||
0.142768 | + | 0.989756i | \(0.454400\pi\) | |||||||
\(602\) | −15.4904 | − | 10.4904i | −0.631341 | − | 0.427556i | ||||
\(603\) | 1.29289 | + | 2.70711i | 0.0526507 | + | 0.110242i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −24.1464 | + | 2.22486i | −0.980882 | + | 0.0903788i | ||||
\(607\) | −10.6116 | + | 39.6030i | −0.430711 | + | 1.60743i | 0.320416 | + | 0.947277i | \(0.396177\pi\) |
−0.751127 | + | 0.660158i | \(0.770489\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −31.4626 | − | 7.75255i | −1.27493 | − | 0.314149i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 24.4949 | − | 14.1421i | 0.990957 | − | 0.572130i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 0.517638 | + | 1.93185i | 0.0209072 | + | 0.0780268i | 0.975591 | − | 0.219594i | \(-0.0704734\pi\) |
−0.954684 | + | 0.297621i | \(0.903807\pi\) | |||||||
\(614\) | 10.6066 | + | 18.3712i | 0.428048 | + | 0.741400i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 24.0000 | − | 20.7846i | 0.966988 | − | 0.837436i | ||||
\(617\) | −8.00000 | + | 8.00000i | −0.322068 | + | 0.322068i | −0.849560 | − | 0.527492i | \(-0.823132\pi\) |
0.527492 | + | 0.849560i | \(0.323132\pi\) | |||||||
\(618\) | 6.89363 | − | 2.54516i | 0.277303 | − | 0.102381i | ||||
\(619\) | 2.59808 | + | 1.50000i | 0.104425 | + | 0.0602901i | 0.551303 | − | 0.834305i | \(-0.314131\pi\) |
−0.446878 | + | 0.894595i | \(0.647464\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −15.3712 | + | 15.8028i | −0.616824 | + | 0.634143i | ||||
\(622\) | −32.5269 | − | 32.5269i | −1.30421 | − | 1.30421i | ||||
\(623\) | 23.0788 | − | 34.0788i | 0.924634 | − | 1.36534i | ||||
\(624\) | −28.2843 | + | 20.0000i | −1.13228 | + | 0.800641i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 20.8207 | + | 12.0208i | 0.832161 | + | 0.480448i | ||||
\(627\) | 32.8824 | − | 39.5569i | 1.31319 | − | 1.57975i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 1.41421 | 0.0563884 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 12.0000 | 0.477712 | 0.238856 | − | 0.971055i | \(-0.423228\pi\) | ||||
0.238856 | + | 0.971055i | \(0.423228\pi\) | |||||||
\(632\) | −19.1244 | − | 5.12436i | −0.760726 | − | 0.203836i | ||||
\(633\) | −2.21441 | + | 2.66390i | −0.0880150 | + | 0.105881i | ||||
\(634\) | 1.73205 | + | 1.00000i | 0.0687885 | + | 0.0397151i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −4.13613 | − | 34.7547i | −0.163879 | − | 1.37703i | ||||
\(638\) | 30.0000 | + | 30.0000i | 1.18771 | + | 1.18771i | ||||
\(639\) | −20.8560 | + | 3.87628i | −0.825052 | + | 0.153343i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 8.57321 | + | 4.94975i | 0.338622 | + | 0.195503i | 0.659662 | − | 0.751562i | \(-0.270699\pi\) |
−0.321041 | + | 0.947065i | \(0.604033\pi\) | |||||||
\(642\) | −35.7466 | + | 13.1978i | −1.41080 | + | 0.520876i | ||||
\(643\) | 17.6777 | − | 17.6777i | 0.697139 | − | 0.697139i | −0.266653 | − | 0.963793i | \(-0.585918\pi\) |
0.963793 | + | 0.266653i | \(0.0859179\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −7.00000 | − | 12.1244i | −0.275411 | − | 0.477026i | ||||
\(647\) | −0.366025 | − | 1.36603i | −0.0143899 | − | 0.0537040i | 0.958358 | − | 0.285571i | \(-0.0921832\pi\) |
−0.972747 | + | 0.231867i | \(0.925517\pi\) | |||||||
\(648\) | 23.2655 | + | 10.3305i | 0.913954 | + | 0.405819i | ||||
\(649\) | 5.19615 | − | 3.00000i | 0.203967 | − | 0.117760i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 3.17423 | − | 3.30518i | 0.124408 | − | 0.129540i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 9.88269 | − | 36.8827i | 0.386739 | − | 1.44333i | −0.448667 | − | 0.893699i | \(-0.648101\pi\) |
0.835407 | − | 0.549632i | \(-0.185232\pi\) | |||||||
\(654\) | 41.4657 | − | 3.82066i | 1.62144 | − | 0.149400i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −24.4949 | + | 14.1421i | −0.956365 | + | 0.552158i | ||||
\(657\) | 18.9497 | − | 9.05025i | 0.739300 | − | 0.353084i | ||||
\(658\) | −1.51575 | + | 21.1117i | −0.0590901 | + | 0.823018i | ||||
\(659\) | −28.2843 | −1.10180 | −0.550899 | − | 0.834572i | \(-0.685715\pi\) | ||||
−0.550899 | + | 0.834572i | \(0.685715\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −9.50000 | + | 16.4545i | −0.369507 | + | 0.640005i | −0.989489 | − | 0.144611i | \(-0.953807\pi\) |
0.619981 | + | 0.784617i | \(0.287140\pi\) | |||||||
\(662\) | 0.366025 | + | 1.36603i | 0.0142260 | + | 0.0530921i | ||||
\(663\) | −11.4894 | + | 4.24194i | −0.446211 | + | 0.164743i | ||||
\(664\) | − | 4.00000i | − | 0.155230i | ||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 4.00000 | + | 1.41421i | 0.154997 | + | 0.0547997i | ||||
\(667\) | 7.76457 | − | 28.9778i | 0.300645 | − | 1.12202i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 1.58919 | + | 17.2474i | 0.0614415 | + | 0.666825i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 16.9706i | 0.655141i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −17.6777 | + | 17.6777i | −0.681424 | + | 0.681424i | −0.960321 | − | 0.278897i | \(-0.910031\pi\) |
0.278897 | + | 0.960321i | \(0.410031\pi\) | |||||||
\(674\) | −3.53553 | − | 6.12372i | −0.136184 | − | 0.235877i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 42.3468 | + | 11.3468i | 1.62752 | + | 0.436092i | 0.953198 | − | 0.302346i | \(-0.0977698\pi\) |
0.674321 | + | 0.738438i | \(0.264436\pi\) | |||||||
\(678\) | 47.7990 | + | 8.20101i | 1.83571 | + | 0.314958i | ||||
\(679\) | −8.66025 | + | 25.0000i | −0.332350 | + | 0.959412i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −20.0227 | − | 9.22450i | −0.767272 | − | 0.353483i | ||||
\(682\) | −5.79555 | + | 1.55291i | −0.221923 | + | 0.0594642i | ||||
\(683\) | −23.2224 | + | 6.22243i | −0.888582 | + | 0.238095i | −0.674106 | − | 0.738635i | \(-0.735471\pi\) |
−0.214476 | + | 0.976729i | \(0.568804\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 23.2702 | + | 12.0208i | 0.888459 | + | 0.458957i | ||||
\(687\) | 0.878680 | − | 5.12132i | 0.0335237 | − | 0.195391i | ||||
\(688\) | −19.3185 | − | 5.17638i | −0.736512 | − | 0.197348i | ||||
\(689\) | 7.07107 | − | 12.2474i | 0.269386 | − | 0.466591i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −14.5000 | − | 25.1147i | −0.551606 | − | 0.955410i | −0.998159 | − | 0.0606524i | \(-0.980682\pi\) |
0.446553 | − | 0.894757i | \(-0.352651\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 33.4636 | − | 3.76666i | 1.27118 | − | 0.143084i | ||||
\(694\) | − | 32.0000i | − | 1.21470i | ||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −34.4949 | + | 3.17837i | −1.30753 | + | 0.120476i | ||||
\(697\) | −9.65926 | + | 2.58819i | −0.365870 | + | 0.0980347i | ||||
\(698\) | −9.51666 | + | 35.5167i | −0.360211 | + | 1.34433i | ||||
\(699\) | 2.82843 | + | 4.00000i | 0.106981 | + | 0.151294i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 21.2132i | 0.801212i | 0.916250 | + | 0.400606i | \(0.131200\pi\) | ||||
−0.916250 | + | 0.400606i | \(0.868800\pi\) | |||||||
\(702\) | −36.7388 | + | 0.508623i | −1.38662 | + | 0.0191967i | ||||
\(703\) | 1.81173 | + | 6.76148i | 0.0683308 | + | 0.255014i | ||||
\(704\) | 16.9706 | − | 29.3939i | 0.639602 | − | 1.10782i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 6.00000 | 0.225813 | ||||||||
\(707\) | 1.87564 | − | 26.1244i | 0.0705409 | − | 0.982508i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 27.7128 | − | 16.0000i | 1.04078 | − | 0.600893i | 0.120723 | − | 0.992686i | \(-0.461479\pi\) |
0.920053 | + | 0.391794i | \(0.128145\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −13.6464 | − | 15.9617i | −0.511781 | − | 0.598609i | ||||
\(712\) | 11.3880 | − | 42.5007i | 0.426785 | − | 1.59278i | ||||
\(713\) | 3.00000 | + | 3.00000i | 0.112351 | + | 0.112351i | ||||
\(714\) | 2.19275 | − | 8.89898i | 0.0820617 | − | 0.333036i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −31.3165 | + | 37.6733i | −1.16954 | + | 1.40693i | ||||
\(718\) | 0.517638 | + | 1.93185i | 0.0193181 | + | 0.0720961i | ||||
\(719\) | −9.89949 | − | 17.1464i | −0.369189 | − | 0.639454i | 0.620250 | − | 0.784404i | \(-0.287031\pi\) |
−0.989439 | + | 0.144950i | \(0.953698\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1.50000 | + | 7.79423i | 0.0558629 | + | 0.290272i | ||||
\(722\) | 30.0000 | − | 30.0000i | 1.11648 | − | 1.11648i | ||||
\(723\) | −14.3976 | − | 38.9963i | −0.535453 | − | 1.45029i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −15.5732 | − | 7.17461i | −0.577976 | − | 0.266275i | ||||
\(727\) | −17.6777 | − | 17.6777i | −0.655628 | − | 0.655628i | 0.298714 | − | 0.954343i | \(-0.403442\pi\) |
−0.954343 | + | 0.298714i | \(0.903442\pi\) | |||||||
\(728\) | −16.3397 | − | 33.6603i | −0.605591 | − | 1.24753i | ||||
\(729\) | 14.1421 | + | 23.0000i | 0.523783 | + | 0.851852i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −6.12372 | − | 3.53553i | −0.226494 | − | 0.130766i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −31.8756 | − | 8.54103i | −1.17735 | − | 0.315470i | −0.383475 | − | 0.923551i | \(-0.625273\pi\) |
−0.793875 | + | 0.608081i | \(0.791940\pi\) | |||||||
\(734\) | −29.6985 | −1.09619 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 4.09808 | + | 1.09808i | 0.150955 | + | 0.0404482i | ||||
\(738\) | −29.9087 | − | 2.33875i | −1.10095 | − | 0.0860906i | ||||
\(739\) | −6.06218 | − | 3.50000i | −0.223001 | − | 0.128750i | 0.384338 | − | 0.923192i | \(-0.374430\pi\) |
−0.607339 | + | 0.794443i | \(0.707763\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −35.0000 | − | 49.4975i | −1.28576 | − | 1.81834i | ||||
\(742\) | 4.62158 | + | 9.52056i | 0.169663 | + | 0.349511i | ||||
\(743\) | 11.0000 | + | 11.0000i | 0.403551 | + | 0.403551i | 0.879482 | − | 0.475931i | \(-0.157889\pi\) |
−0.475931 | + | 0.879482i | \(0.657889\pi\) | |||||||
\(744\) | 2.04989 | − | 4.44949i | 0.0751525 | − | 0.163126i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −28.1691 | − | 16.2635i | −1.03135 | − | 0.595447i | ||||
\(747\) | 2.40130 | − | 3.49768i | 0.0878590 | − | 0.127973i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −7.77817 | − | 40.4166i | −0.284208 | − | 1.47679i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −19.5000 | − | 33.7750i | −0.711565 | − | 1.23247i | −0.964269 | − | 0.264923i | \(-0.914653\pi\) |
0.252704 | − | 0.967544i | \(-0.418680\pi\) | |||||||
\(752\) | 5.85641 | + | 21.8564i | 0.213561 | + | 0.797021i | ||||
\(753\) | −9.41832 | − | 7.82913i | −0.343223 | − | 0.285309i | ||||
\(754\) | 43.3013 | − | 25.0000i | 1.57694 | − | 0.910446i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −14.1421 | − | 14.1421i | −0.514005 | − | 0.514005i | 0.401746 | − | 0.915751i | \(-0.368403\pi\) |
−0.915751 | + | 0.401746i | \(0.868403\pi\) | |||||||
\(758\) | 3.29423 | − | 12.2942i | 0.119652 | − | 0.446546i | ||||
\(759\) | 2.86054 | + | 31.0454i | 0.103831 | + | 1.12688i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 20.8207 | − | 12.0208i | 0.754748 | − | 0.435754i | −0.0726586 | − | 0.997357i | \(-0.523148\pi\) |
0.827407 | + | 0.561603i | \(0.189815\pi\) | |||||||
\(762\) | 36.2132 | + | 6.21320i | 1.31187 | + | 0.225081i | ||||
\(763\) | −3.22097 | + | 44.8623i | −0.116607 | + | 1.62412i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 12.0000 | − | 20.7846i | 0.433578 | − | 0.750978i | ||||
\(767\) | −1.83013 | − | 6.83013i | −0.0660821 | − | 0.246622i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 29.0000i | − | 1.04577i | −0.852404 | − | 0.522883i | \(-0.824856\pi\) | ||
0.852404 | − | 0.522883i | \(-0.175144\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 18.0000 | − | 12.7279i | 0.648254 | − | 0.458385i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 17.7583 | − | 4.75833i | 0.638723 | − | 0.171145i | 0.0750979 | − | 0.997176i | \(-0.476073\pi\) |
0.563625 | + | 0.826031i | \(0.309406\pi\) | |||||||
\(774\) | −13.7850 | − | 16.1237i | −0.495491 | − | 0.579555i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 28.2843i | 1.01535i | ||||||||
\(777\) | −2.21063 | + | 4.01411i | −0.0793059 | + | 0.144006i | ||||
\(778\) | −29.6985 | + | 29.6985i | −1.06474 | + | 1.06474i | ||||
\(779\) | −24.7487 | − | 42.8661i | −0.886716 | − | 1.53584i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −15.0000 | + | 25.9808i | −0.536742 | + | 0.929665i | ||||
\(782\) | 8.19615 | + | 2.19615i | 0.293094 | + | 0.0785343i | ||||
\(783\) | −32.0711 | − | 17.9289i | −1.14613 | − | 0.640728i | ||||
\(784\) | 27.7128 | + | 4.00000i | 0.989743 | + | 0.142857i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −17.3939 | + | 37.7552i | −0.620419 | + | 1.34668i | ||||
\(787\) | −25.1141 | + | 6.72930i | −0.895220 | + | 0.239873i | −0.676962 | − | 0.736018i | \(-0.736704\pi\) |
−0.218258 | + | 0.975891i | \(0.570037\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 12.2993 | − | 26.6969i | 0.437868 | − | 0.950436i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −17.1464 | + | 49.4975i | −0.609657 | + | 1.75993i | ||||
\(792\) | 32.4853 | − | 15.5147i | 1.15431 | − | 0.551292i | ||||
\(793\) | 19.3185 | + | 5.17638i | 0.686021 | + | 0.183819i | ||||
\(794\) | −0.707107 | + | 1.22474i | −0.0250943 | + | 0.0434646i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 17.0000 | − | 17.0000i | 0.602171 | − | 0.602171i | −0.338717 | − | 0.940888i | \(-0.609993\pi\) |
0.940888 | + | 0.338717i | \(0.109993\pi\) | |||||||
\(798\) | 45.3559 | − | 0.916639i | 1.60558 | − | 0.0324487i | ||||
\(799\) | 8.00000i | 0.283020i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 35.4722 | − | 30.3269i | 1.25335 | − | 1.07155i | ||||
\(802\) | −34.7733 | + | 9.31749i | −1.22789 | + | 0.329012i | ||||
\(803\) | 7.68653 | − | 28.6865i | 0.271252 | − | 1.01233i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 7.07107i | 0.249068i | ||||||||
\(807\) | 3.39355 | + | 9.19151i | 0.119459 | + | 0.323556i | ||||
\(808\) | −7.24693 | − | 27.0459i | −0.254946 | − | 0.951472i | ||||
\(809\) | 9.89949 | − | 17.1464i | 0.348048 | − | 0.602836i | −0.637855 | − | 0.770157i | \(-0.720178\pi\) |
0.985903 | + | 0.167320i | \(0.0535114\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −18.0000 | −0.632065 | −0.316033 | − | 0.948748i | \(-0.602351\pi\) | ||||
−0.316033 | + | 0.948748i | \(0.602351\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 23.8995 | + | 4.10051i | 0.838192 | + | 0.143811i | ||||
\(814\) | 5.19615 | − | 3.00000i | 0.182125 | − | 0.105150i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −0.898979 | − | 9.75663i | −0.0314706 | − | 0.341550i | ||||
\(817\) | 9.05867 | − | 33.8074i | 0.316923 | − | 1.18277i | ||||
\(818\) | −37.0000 | − | 37.0000i | −1.29367 | − | 1.29367i | ||||
\(819\) | 5.91931 | − | 39.2423i | 0.206838 | − | 1.37124i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −15.9217 | + | 9.19239i | −0.555671 | + | 0.320817i | −0.751406 | − | 0.659840i | \(-0.770624\pi\) |
0.195735 | + | 0.980657i | \(0.437291\pi\) | |||||||
\(822\) | 29.3029 | + | 24.3585i | 1.02206 | + | 0.849602i | ||||
\(823\) | −7.24693 | − | 27.0459i | −0.252612 | − | 0.942762i | −0.969403 | − | 0.245474i | \(-0.921057\pi\) |
0.716791 | − | 0.697288i | \(-0.245610\pi\) | |||||||
\(824\) | 4.24264 | + | 7.34847i | 0.147799 | + | 0.255996i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 5.00000 | + | 1.73205i | 0.173972 | + | 0.0602658i | ||||
\(827\) | −18.0000 | + | 18.0000i | −0.625921 | + | 0.625921i | −0.947039 | − | 0.321118i | \(-0.895941\pi\) |
0.321118 | + | 0.947039i | \(0.395941\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −6.06218 | − | 3.50000i | −0.210548 | − | 0.121560i | 0.391018 | − | 0.920383i | \(-0.372123\pi\) |
−0.601566 | + | 0.798823i | \(0.705456\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −6.52270 | + | 14.1582i | −0.226270 | + | 0.491142i | ||||
\(832\) | −28.2843 | − | 28.2843i | −0.980581 | − | 0.980581i | ||||
\(833\) | 9.09808 | + | 3.90192i | 0.315230 | + | 0.135194i | ||||
\(834\) | −15.5563 | − | 22.0000i | −0.538672 | − | 0.761798i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 4.46360 | − | 2.66012i | 0.154285 | − | 0.0919472i | ||||
\(838\) | 19.3185 | + | 5.17638i | 0.667347 | + | 0.178815i | ||||
\(839\) | 35.3553 | 1.22060 | 0.610301 | − | 0.792170i | \(-0.291049\pi\) | ||||
0.610301 | + | 0.792170i | \(0.291049\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 21.0000 | 0.724138 | ||||||||
\(842\) | −31.4186 | − | 8.41858i | −1.08276 | − | 0.290124i | ||||
\(843\) | −18.8366 | − | 15.6583i | −0.648768 | − | 0.539299i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −8.00000 | + | 22.6274i | −0.275046 | + | 0.777947i | ||||
\(847\) | 10.3849 | − | 15.3347i | 0.356831 | − | 0.526906i | ||||
\(848\) | 8.00000 | + | 8.00000i | 0.274721 | + | 0.274721i | ||||
\(849\) | 36.1820 | + | 16.6691i | 1.24176 | + | 0.572083i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −3.67423 | − | 2.12132i | −0.125951 | − | 0.0727179i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −38.8909 | + | 38.8909i | −1.33160 | + | 1.33160i | −0.427657 | + | 0.903941i | \(0.640661\pi\) |
−0.903941 | + | 0.427657i | \(0.859339\pi\) | |||||||
\(854\) | −11.3137 | + | 9.79796i | −0.387147 | + | 0.335279i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −22.0000 | − | 38.1051i | −0.751945 | − | 1.30241i | ||||
\(857\) | −7.68653 | − | 28.6865i | −0.262567 | − | 0.979913i | −0.963723 | − | 0.266905i | \(-0.913999\pi\) |
0.701156 | − | 0.713008i | \(-0.252668\pi\) | |||||||
\(858\) | −33.2162 | + | 39.9585i | −1.13398 | + | 1.36416i | ||||
\(859\) | 19.0526 | − | 11.0000i | 0.650065 | − | 0.375315i | −0.138416 | − | 0.990374i | \(-0.544201\pi\) |
0.788481 | + | 0.615059i | \(0.210868\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 7.75255 | − | 31.4626i | 0.264206 | − | 1.07224i | ||||
\(862\) | 2.82843 | + | 2.82843i | 0.0963366 | + | 0.0963366i | ||||
\(863\) | −10.2487 | + | 38.2487i | −0.348870 | + | 1.30200i | 0.539155 | + | 0.842207i | \(0.318744\pi\) |
−0.888025 | + | 0.459795i | \(0.847923\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 18.3712 | − | 10.6066i | 0.624278 | − | 0.360427i | ||||
\(867\) | −4.39340 | + | 25.6066i | −0.149208 | + | 0.869646i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −29.6985 | −1.00745 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 2.50000 | − | 4.33013i | 0.0847093 | − | 0.146721i | ||||
\(872\) | 12.4449 | + | 46.4449i | 0.421436 | + | 1.57282i | ||||
\(873\) | −16.9798 | + | 24.7323i | −0.574678 | + | 0.837062i | ||||
\(874\) | 42.0000i | 1.42067i | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 6.21166 | − | 23.1822i | 0.209753 | − | 0.782808i | −0.778195 | − | 0.628022i | \(-0.783865\pi\) |
0.987948 | − | 0.154786i | \(-0.0494687\pi\) | |||||||
\(878\) | −51.9090 | + | 13.9090i | −1.75184 | + | 0.469405i | ||||
\(879\) | −39.0265 | + | 3.59592i | −1.31633 | + | 0.121287i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(882\) | 21.8313 | + | 20.1344i | 0.735099 | + | 0.677960i | ||||
\(883\) | −10.6066 | + | 10.6066i | −0.356941 | + | 0.356941i | −0.862684 | − | 0.505743i | \(-0.831218\pi\) |
0.505743 | + | 0.862684i | \(0.331218\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −8.00000 | + | 13.8564i | −0.268765 | + | 0.465515i | ||||
\(887\) | 28.6865 | + | 7.68653i | 0.963200 | + | 0.258089i | 0.705954 | − | 0.708258i | \(-0.250518\pi\) |
0.257245 | + | 0.966346i | \(0.417185\pi\) | |||||||
\(888\) | −0.828427 | + | 4.82843i | −0.0278002 | + | 0.162031i | ||||
\(889\) | −12.9904 | + | 37.5000i | −0.435683 | + | 1.25771i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 37.7196 | + | 5.93537i | 1.26366 | + | 0.198842i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −38.2487 | + | 10.2487i | −1.27994 | + | 0.342960i | ||||
\(894\) | −18.8776 | − | 8.69694i | −0.631361 | − | 0.290869i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 29.3939 | − | 5.65685i | 0.981981 | − | 0.188982i | ||||
\(897\) | 36.2132 | + | 6.21320i | 1.20912 | + | 0.207453i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −3.53553 | + | 6.12372i | −0.117917 | + | 0.204238i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 2.00000 | + | 3.46410i | 0.0666297 | + | 0.115406i | ||||
\(902\) | −30.0000 | + | 30.0000i | −0.998891 | + | 0.998891i | ||||
\(903\) | 19.6076 | − | 11.8550i | 0.652500 | − | 0.394511i | ||||
\(904\) | 56.0000i | 1.86253i | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 1.34847 | + | 14.6349i | 0.0447999 | + | 0.486213i | ||||
\(907\) | −49.2622 | + | 13.1998i | −1.63573 | + | 0.438291i | −0.955567 | − | 0.294774i | \(-0.904756\pi\) |
−0.680158 | + | 0.733065i | \(0.738089\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 9.89949 | − | 28.0000i | 0.328346 | − | 0.928701i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 35.3553i | − | 1.17137i | −0.810537 | − | 0.585687i | \(-0.800825\pi\) | ||
0.810537 | − | 0.585687i | \(-0.199175\pi\) | |||||||
\(912\) | 45.4956 | − | 16.7972i | 1.50651 | − | 0.556211i | ||||
\(913\) | −1.55291 | − | 5.79555i | −0.0513940 | − | 0.191805i | ||||
\(914\) | 20.5061 | − | 35.5176i | 0.678281 | − | 1.17482i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −37.1769 | − | 25.1769i | −1.22769 | − | 0.831415i | ||||
\(918\) | 5.07107 | − | 9.07107i | 0.167370 | − | 0.299390i | ||||
\(919\) | −11.2583 | + | 6.50000i | −0.371378 | + | 0.214415i | −0.674060 | − | 0.738676i | \(-0.735451\pi\) |
0.302682 | + | 0.953092i | \(0.402118\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −25.8712 | + | 2.38378i | −0.852484 | + | 0.0785482i | ||||
\(922\) | 2.58819 | − | 9.65926i | 0.0852375 | − | 0.318111i | ||||
\(923\) | 25.0000 | + | 25.0000i | 0.822885 | + | 0.822885i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −30.6186 | + | 17.6777i | −1.00619 | + | 0.580924i | ||||
\(927\) | −0.701625 | + | 8.97261i | −0.0230444 | + | 0.294699i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 7.77817 | + | 13.4722i | 0.255194 | + | 0.442008i | 0.964948 | − | 0.262441i | \(-0.0845275\pi\) |
−0.709754 | + | 0.704449i | \(0.751194\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −7.00000 | + | 48.4974i | −0.229416 | + | 1.58944i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 52.8512 | − | 19.5129i | 1.73027 | − | 0.638824i | ||||
\(934\) | −6.92820 | − | 4.00000i | −0.226698 | − | 0.130884i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −7.75255 | − | 41.7121i | −0.253400 | − | 1.36340i | ||||
\(937\) | 10.6066 | + | 10.6066i | 0.346503 | + | 0.346503i | 0.858805 | − | 0.512302i | \(-0.171207\pi\) |
−0.512302 | + | 0.858805i | \(0.671207\pi\) | |||||||
\(938\) | 1.63397 | + | 3.36603i | 0.0533512 | + | 0.109905i | ||||
\(939\) | −24.0416 | + | 17.0000i | −0.784569 | + | 0.554774i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −15.9217 | − | 9.19239i | −0.519032 | − | 0.299663i | 0.217506 | − | 0.976059i | \(-0.430208\pi\) |
−0.736539 | + | 0.676396i | \(0.763541\pi\) | |||||||
\(942\) | −6.26330 | + | 7.53465i | −0.204070 | + | 0.245492i | ||||
\(943\) | 28.9778 | + | 7.76457i | 0.943646 | + | 0.252849i | ||||
\(944\) | 5.65685 | 0.184115 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −30.0000 | −0.975384 | ||||||||
\(947\) | 15.0263 | + | 4.02628i | 0.488288 | + | 0.130837i | 0.494559 | − | 0.869144i | \(-0.335329\pi\) |
−0.00627092 | + | 0.999980i | \(0.501996\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −30.3109 | − | 17.5000i | −0.983933 | − | 0.568074i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −2.00000 | + | 1.41421i | −0.0648544 | + | 0.0458590i | ||||
\(952\) | 10.5558 | + | 0.757875i | 0.342117 | + | 0.0245629i | ||||
\(953\) | 36.0000 | + | 36.0000i | 1.16615 | + | 1.16615i | 0.983103 | + | 0.183051i | \(0.0585973\pi\) |
0.183051 | + | 0.983103i | \(0.441403\pi\) | |||||||
\(954\) | 2.19275 | + | 11.7980i | 0.0709930 | + | 0.381973i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −48.7453 | + | 17.9970i | −1.57571 | + | 0.581761i | ||||
\(958\) | −8.48528 | + | 8.48528i | −0.274147 | + | 0.274147i | ||||
\(959\) | −31.1127 | + | 26.9444i | −1.00468 | + | 0.870080i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 15.0000 | + | 25.9808i | 0.483871 | + | 0.838089i | ||||
\(962\) | −1.83013 | − | 6.83013i | −0.0590057 | − | 0.220212i | ||||
\(963\) | 3.63824 | − | 46.5270i | 0.117241 | − | 1.49931i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −19.0454 | + | 19.8311i | −0.612776 | + | 0.638055i | ||||
\(967\) | 24.7487 | + | 24.7487i | 0.795866 | + | 0.795866i | 0.982441 | − | 0.186575i | \(-0.0597387\pi\) |
−0.186575 | + | 0.982441i | \(0.559739\pi\) | |||||||
\(968\) | 5.12436 | − | 19.1244i | 0.164703 | − | 0.614680i | ||||
\(969\) | 17.0741 | − | 1.57321i | 0.548499 | − | 0.0505389i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 39.1918 | − | 22.6274i | 1.25773 | − | 0.726148i | 0.285094 | − | 0.958500i | \(-0.407975\pi\) |
0.972632 | + | 0.232351i | \(0.0746419\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 26.1815 | − | 12.7093i | 0.839341 | − | 0.407443i | ||||
\(974\) | 41.0122 | 1.31412 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −8.00000 | + | 13.8564i | −0.256074 | + | 0.443533i | ||||
\(977\) | −4.02628 | − | 15.0263i | −0.128812 | − | 0.480733i | 0.871135 | − | 0.491044i | \(-0.163385\pi\) |
−0.999947 | + | 0.0103108i | \(0.996718\pi\) | |||||||
\(978\) | −4.59575 | + | 1.69677i | −0.146956 | + | 0.0542569i | ||||
\(979\) | − | 66.0000i | − | 2.10937i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −17.0000 | + | 48.0833i | −0.542768 | + | 1.53518i | ||||
\(982\) | 5.17638 | − | 19.3185i | 0.165185 | − | 0.616479i | ||||
\(983\) | −36.8827 | + | 9.88269i | −1.17637 | + | 0.315209i | −0.793488 | − | 0.608586i | \(-0.791737\pi\) |
−0.382887 | + | 0.923795i | \(0.625070\pi\) | |||||||
\(984\) | −3.17837 | − | 34.4949i | −0.101323 | − | 1.09966i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 14.1421i | 0.450377i | ||||||||
\(987\) | −22.7073 | − | 12.5052i | −0.722780 | − | 0.398045i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 10.6066 | + | 18.3712i | 0.337270 | + | 0.584169i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 20.5000 | − | 35.5070i | 0.651204 | − | 1.12792i | −0.331627 | − | 0.943411i | \(-0.607598\pi\) |
0.982831 | − | 0.184508i | \(-0.0590691\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −1.70711 | − | 0.292893i | −0.0541734 | − | 0.00929469i | ||||
\(994\) | −25.9808 | + | 5.00000i | −0.824060 | + | 0.158590i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 37.6711 | − | 10.0939i | 1.19306 | − | 0.319678i | 0.392963 | − | 0.919554i | \(-0.371450\pi\) |
0.800093 | + | 0.599876i | \(0.204783\pi\) | |||||||
\(998\) | 36.8827 | − | 9.88269i | 1.16750 | − | 0.312831i | ||||
\(999\) | −3.62302 | + | 3.72474i | −0.114627 | + | 0.117846i |
(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 | 525.2.bf.d.32.2 | yes | 8 | |
3.2 | odd | 2 | 525.2.bf.a.32.2 | yes | 8 | ||
5.2 | odd | 4 | inner | 525.2.bf.d.368.2 | yes | 8 | |
5.3 | odd | 4 | 525.2.bf.a.368.1 | yes | 8 | ||
5.4 | even | 2 | 525.2.bf.a.32.1 | ✓ | 8 | ||
7.2 | even | 3 | inner | 525.2.bf.d.107.1 | yes | 8 | |
15.2 | even | 4 | 525.2.bf.a.368.2 | yes | 8 | ||
15.8 | even | 4 | inner | 525.2.bf.d.368.1 | yes | 8 | |
15.14 | odd | 2 | inner | 525.2.bf.d.32.1 | yes | 8 | |
21.2 | odd | 6 | 525.2.bf.a.107.1 | yes | 8 | ||
35.2 | odd | 12 | inner | 525.2.bf.d.443.1 | yes | 8 | |
35.9 | even | 6 | 525.2.bf.a.107.2 | yes | 8 | ||
35.23 | odd | 12 | 525.2.bf.a.443.2 | yes | 8 | ||
105.2 | even | 12 | 525.2.bf.a.443.1 | yes | 8 | ||
105.23 | even | 12 | inner | 525.2.bf.d.443.2 | yes | 8 | |
105.44 | odd | 6 | inner | 525.2.bf.d.107.2 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
525.2.bf.a.32.1 | ✓ | 8 | 5.4 | even | 2 | ||
525.2.bf.a.32.2 | yes | 8 | 3.2 | odd | 2 | ||
525.2.bf.a.107.1 | yes | 8 | 21.2 | odd | 6 | ||
525.2.bf.a.107.2 | yes | 8 | 35.9 | even | 6 | ||
525.2.bf.a.368.1 | yes | 8 | 5.3 | odd | 4 | ||
525.2.bf.a.368.2 | yes | 8 | 15.2 | even | 4 | ||
525.2.bf.a.443.1 | yes | 8 | 105.2 | even | 12 | ||
525.2.bf.a.443.2 | yes | 8 | 35.23 | odd | 12 | ||
525.2.bf.d.32.1 | yes | 8 | 15.14 | odd | 2 | inner | |
525.2.bf.d.32.2 | yes | 8 | 1.1 | even | 1 | trivial | |
525.2.bf.d.107.1 | yes | 8 | 7.2 | even | 3 | inner | |
525.2.bf.d.107.2 | yes | 8 | 105.44 | odd | 6 | inner | |
525.2.bf.d.368.1 | yes | 8 | 15.8 | even | 4 | inner | |
525.2.bf.d.368.2 | yes | 8 | 5.2 | odd | 4 | inner | |
525.2.bf.d.443.1 | yes | 8 | 35.2 | odd | 12 | inner | |
525.2.bf.d.443.2 | yes | 8 | 105.23 | even | 12 | inner |