Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1734,2,Mod(829,1734)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1734, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1734.829");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1734 = 2 \cdot 3 \cdot 17^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1734.f (of order \(4\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(13.8460597105\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(i)\) |
Coefficient field: | \(\Q(\zeta_{8})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 102) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 1483.1 | ||
Root | \(0.707107 - 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1734.1483 |
Dual form | 1734.2.f.g.829.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1734\mathbb{Z}\right)^\times\).
\(n\) | \(1157\) | \(1159\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{3}{4}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 1.00000i | − | 0.707107i | ||||||
\(3\) | −0.707107 | + | 0.707107i | −0.408248 | + | 0.408248i | ||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | 2.82843 | − | 2.82843i | 1.26491 | − | 1.26491i | 0.316228 | − | 0.948683i | \(-0.397584\pi\) |
0.948683 | − | 0.316228i | \(-0.102416\pi\) | |||||||
\(6\) | 0.707107 | + | 0.707107i | 0.288675 | + | 0.288675i | ||||
\(7\) | 1.41421 | + | 1.41421i | 0.534522 | + | 0.534522i | 0.921915 | − | 0.387392i | \(-0.126624\pi\) |
−0.387392 | + | 0.921915i | \(0.626624\pi\) | |||||||
\(8\) | 1.00000i | 0.353553i | ||||||||
\(9\) | − | 1.00000i | − | 0.333333i | ||||||
\(10\) | −2.82843 | − | 2.82843i | −0.894427 | − | 0.894427i | ||||
\(11\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(12\) | 0.707107 | − | 0.707107i | 0.204124 | − | 0.204124i | ||||
\(13\) | 6.00000 | 1.66410 | 0.832050 | − | 0.554700i | \(-0.187167\pi\) | ||||
0.832050 | + | 0.554700i | \(0.187167\pi\) | |||||||
\(14\) | 1.41421 | − | 1.41421i | 0.377964 | − | 0.377964i | ||||
\(15\) | 4.00000i | 1.03280i | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 0 | 0 | ||||||||
\(18\) | −1.00000 | −0.235702 | ||||||||
\(19\) | 4.00000i | 0.917663i | 0.888523 | + | 0.458831i | \(0.151732\pi\) | ||||
−0.888523 | + | 0.458831i | \(0.848268\pi\) | |||||||
\(20\) | −2.82843 | + | 2.82843i | −0.632456 | + | 0.632456i | ||||
\(21\) | −2.00000 | −0.436436 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4.24264 | + | 4.24264i | 0.884652 | + | 0.884652i | 0.994003 | − | 0.109351i | \(-0.0348774\pi\) |
−0.109351 | + | 0.994003i | \(0.534877\pi\) | |||||||
\(24\) | −0.707107 | − | 0.707107i | −0.144338 | − | 0.144338i | ||||
\(25\) | − | 11.0000i | − | 2.20000i | ||||||
\(26\) | − | 6.00000i | − | 1.17670i | ||||||
\(27\) | 0.707107 | + | 0.707107i | 0.136083 | + | 0.136083i | ||||
\(28\) | −1.41421 | − | 1.41421i | −0.267261 | − | 0.267261i | ||||
\(29\) | 2.82843 | − | 2.82843i | 0.525226 | − | 0.525226i | −0.393919 | − | 0.919145i | \(-0.628881\pi\) |
0.919145 | + | 0.393919i | \(0.128881\pi\) | |||||||
\(30\) | 4.00000 | 0.730297 | ||||||||
\(31\) | −4.24264 | + | 4.24264i | −0.762001 | + | 0.762001i | −0.976684 | − | 0.214683i | \(-0.931128\pi\) |
0.214683 | + | 0.976684i | \(0.431128\pi\) | |||||||
\(32\) | − | 1.00000i | − | 0.176777i | ||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 8.00000 | 1.35225 | ||||||||
\(36\) | 1.00000i | 0.166667i | ||||||||
\(37\) | −2.82843 | + | 2.82843i | −0.464991 | + | 0.464991i | −0.900287 | − | 0.435297i | \(-0.856644\pi\) |
0.435297 | + | 0.900287i | \(0.356644\pi\) | |||||||
\(38\) | 4.00000 | 0.648886 | ||||||||
\(39\) | −4.24264 | + | 4.24264i | −0.679366 | + | 0.679366i | ||||
\(40\) | 2.82843 | + | 2.82843i | 0.447214 | + | 0.447214i | ||||
\(41\) | 7.07107 | + | 7.07107i | 1.10432 | + | 1.10432i | 0.993884 | + | 0.110432i | \(0.0352233\pi\) |
0.110432 | + | 0.993884i | \(0.464777\pi\) | |||||||
\(42\) | 2.00000i | 0.308607i | ||||||||
\(43\) | 4.00000i | 0.609994i | 0.952353 | + | 0.304997i | \(0.0986555\pi\) | ||||
−0.952353 | + | 0.304997i | \(0.901344\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −2.82843 | − | 2.82843i | −0.421637 | − | 0.421637i | ||||
\(46\) | 4.24264 | − | 4.24264i | 0.625543 | − | 0.625543i | ||||
\(47\) | −4.00000 | −0.583460 | −0.291730 | − | 0.956501i | \(-0.594231\pi\) | ||||
−0.291730 | + | 0.956501i | \(0.594231\pi\) | |||||||
\(48\) | −0.707107 | + | 0.707107i | −0.102062 | + | 0.102062i | ||||
\(49\) | − | 3.00000i | − | 0.428571i | ||||||
\(50\) | −11.0000 | −1.55563 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −6.00000 | −0.832050 | ||||||||
\(53\) | − | 2.00000i | − | 0.274721i | −0.990521 | − | 0.137361i | \(-0.956138\pi\) | ||
0.990521 | − | 0.137361i | \(-0.0438619\pi\) | |||||||
\(54\) | 0.707107 | − | 0.707107i | 0.0962250 | − | 0.0962250i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −1.41421 | + | 1.41421i | −0.188982 | + | 0.188982i | ||||
\(57\) | −2.82843 | − | 2.82843i | −0.374634 | − | 0.374634i | ||||
\(58\) | −2.82843 | − | 2.82843i | −0.371391 | − | 0.371391i | ||||
\(59\) | − | 12.0000i | − | 1.56227i | −0.624364 | − | 0.781133i | \(-0.714642\pi\) | ||
0.624364 | − | 0.781133i | \(-0.285358\pi\) | |||||||
\(60\) | − | 4.00000i | − | 0.516398i | ||||||
\(61\) | 2.82843 | + | 2.82843i | 0.362143 | + | 0.362143i | 0.864601 | − | 0.502458i | \(-0.167571\pi\) |
−0.502458 | + | 0.864601i | \(0.667571\pi\) | |||||||
\(62\) | 4.24264 | + | 4.24264i | 0.538816 | + | 0.538816i | ||||
\(63\) | 1.41421 | − | 1.41421i | 0.178174 | − | 0.178174i | ||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 16.9706 | − | 16.9706i | 2.10494 | − | 2.10494i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −12.0000 | −1.46603 | −0.733017 | − | 0.680211i | \(-0.761888\pi\) | ||||
−0.733017 | + | 0.680211i | \(0.761888\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −6.00000 | −0.722315 | ||||||||
\(70\) | − | 8.00000i | − | 0.956183i | ||||||
\(71\) | −4.24264 | + | 4.24264i | −0.503509 | + | 0.503509i | −0.912526 | − | 0.409018i | \(-0.865871\pi\) |
0.409018 | + | 0.912526i | \(0.365871\pi\) | |||||||
\(72\) | 1.00000 | 0.117851 | ||||||||
\(73\) | −1.41421 | + | 1.41421i | −0.165521 | + | 0.165521i | −0.785007 | − | 0.619486i | \(-0.787341\pi\) |
0.619486 | + | 0.785007i | \(0.287341\pi\) | |||||||
\(74\) | 2.82843 | + | 2.82843i | 0.328798 | + | 0.328798i | ||||
\(75\) | 7.77817 | + | 7.77817i | 0.898146 | + | 0.898146i | ||||
\(76\) | − | 4.00000i | − | 0.458831i | ||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 4.24264 | + | 4.24264i | 0.480384 | + | 0.480384i | ||||
\(79\) | 7.07107 | + | 7.07107i | 0.795557 | + | 0.795557i | 0.982391 | − | 0.186834i | \(-0.0598227\pi\) |
−0.186834 | + | 0.982391i | \(0.559823\pi\) | |||||||
\(80\) | 2.82843 | − | 2.82843i | 0.316228 | − | 0.316228i | ||||
\(81\) | −1.00000 | −0.111111 | ||||||||
\(82\) | 7.07107 | − | 7.07107i | 0.780869 | − | 0.780869i | ||||
\(83\) | − | 12.0000i | − | 1.31717i | −0.752506 | − | 0.658586i | \(-0.771155\pi\) | ||
0.752506 | − | 0.658586i | \(-0.228845\pi\) | |||||||
\(84\) | 2.00000 | 0.218218 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 4.00000 | 0.431331 | ||||||||
\(87\) | 4.00000i | 0.428845i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 2.00000 | 0.212000 | 0.106000 | − | 0.994366i | \(-0.466196\pi\) | ||||
0.106000 | + | 0.994366i | \(0.466196\pi\) | |||||||
\(90\) | −2.82843 | + | 2.82843i | −0.298142 | + | 0.298142i | ||||
\(91\) | 8.48528 | + | 8.48528i | 0.889499 | + | 0.889499i | ||||
\(92\) | −4.24264 | − | 4.24264i | −0.442326 | − | 0.442326i | ||||
\(93\) | − | 6.00000i | − | 0.622171i | ||||||
\(94\) | 4.00000i | 0.412568i | ||||||||
\(95\) | 11.3137 | + | 11.3137i | 1.16076 | + | 1.16076i | ||||
\(96\) | 0.707107 | + | 0.707107i | 0.0721688 | + | 0.0721688i | ||||
\(97\) | −4.24264 | + | 4.24264i | −0.430775 | + | 0.430775i | −0.888892 | − | 0.458117i | \(-0.848524\pi\) |
0.458117 | + | 0.888892i | \(0.348524\pi\) | |||||||
\(98\) | −3.00000 | −0.303046 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 11.0000i | 1.10000i | ||||||||
\(101\) | 14.0000 | 1.39305 | 0.696526 | − | 0.717532i | \(-0.254728\pi\) | ||||
0.696526 | + | 0.717532i | \(0.254728\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 4.00000 | 0.394132 | 0.197066 | − | 0.980390i | \(-0.436859\pi\) | ||||
0.197066 | + | 0.980390i | \(0.436859\pi\) | |||||||
\(104\) | 6.00000i | 0.588348i | ||||||||
\(105\) | −5.65685 | + | 5.65685i | −0.552052 | + | 0.552052i | ||||
\(106\) | −2.00000 | −0.194257 | ||||||||
\(107\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(108\) | −0.707107 | − | 0.707107i | −0.0680414 | − | 0.0680414i | ||||
\(109\) | −11.3137 | − | 11.3137i | −1.08366 | − | 1.08366i | −0.996165 | − | 0.0874915i | \(-0.972115\pi\) |
−0.0874915 | − | 0.996165i | \(-0.527885\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − | 4.00000i | − | 0.379663i | ||||||
\(112\) | 1.41421 | + | 1.41421i | 0.133631 | + | 0.133631i | ||||
\(113\) | 1.41421 | + | 1.41421i | 0.133038 | + | 0.133038i | 0.770490 | − | 0.637452i | \(-0.220012\pi\) |
−0.637452 | + | 0.770490i | \(0.720012\pi\) | |||||||
\(114\) | −2.82843 | + | 2.82843i | −0.264906 | + | 0.264906i | ||||
\(115\) | 24.0000 | 2.23801 | ||||||||
\(116\) | −2.82843 | + | 2.82843i | −0.262613 | + | 0.262613i | ||||
\(117\) | − | 6.00000i | − | 0.554700i | ||||||
\(118\) | −12.0000 | −1.10469 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −4.00000 | −0.365148 | ||||||||
\(121\) | − | 11.0000i | − | 1.00000i | ||||||
\(122\) | 2.82843 | − | 2.82843i | 0.256074 | − | 0.256074i | ||||
\(123\) | −10.0000 | −0.901670 | ||||||||
\(124\) | 4.24264 | − | 4.24264i | 0.381000 | − | 0.381000i | ||||
\(125\) | −16.9706 | − | 16.9706i | −1.51789 | − | 1.51789i | ||||
\(126\) | −1.41421 | − | 1.41421i | −0.125988 | − | 0.125988i | ||||
\(127\) | − | 8.00000i | − | 0.709885i | −0.934888 | − | 0.354943i | \(-0.884500\pi\) | ||
0.934888 | − | 0.354943i | \(-0.115500\pi\) | |||||||
\(128\) | 1.00000i | 0.0883883i | ||||||||
\(129\) | −2.82843 | − | 2.82843i | −0.249029 | − | 0.249029i | ||||
\(130\) | −16.9706 | − | 16.9706i | −1.48842 | − | 1.48842i | ||||
\(131\) | 11.3137 | − | 11.3137i | 0.988483 | − | 0.988483i | −0.0114511 | − | 0.999934i | \(-0.503645\pi\) |
0.999934 | + | 0.0114511i | \(0.00364509\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −5.65685 | + | 5.65685i | −0.490511 | + | 0.490511i | ||||
\(134\) | 12.0000i | 1.03664i | ||||||||
\(135\) | 4.00000 | 0.344265 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −6.00000 | −0.512615 | −0.256307 | − | 0.966595i | \(-0.582506\pi\) | ||||
−0.256307 | + | 0.966595i | \(0.582506\pi\) | |||||||
\(138\) | 6.00000i | 0.510754i | ||||||||
\(139\) | 5.65685 | − | 5.65685i | 0.479808 | − | 0.479808i | −0.425262 | − | 0.905070i | \(-0.639818\pi\) |
0.905070 | + | 0.425262i | \(0.139818\pi\) | |||||||
\(140\) | −8.00000 | −0.676123 | ||||||||
\(141\) | 2.82843 | − | 2.82843i | 0.238197 | − | 0.238197i | ||||
\(142\) | 4.24264 | + | 4.24264i | 0.356034 | + | 0.356034i | ||||
\(143\) | 0 | 0 | ||||||||
\(144\) | − | 1.00000i | − | 0.0833333i | ||||||
\(145\) | − | 16.0000i | − | 1.32873i | ||||||
\(146\) | 1.41421 | + | 1.41421i | 0.117041 | + | 0.117041i | ||||
\(147\) | 2.12132 | + | 2.12132i | 0.174964 | + | 0.174964i | ||||
\(148\) | 2.82843 | − | 2.82843i | 0.232495 | − | 0.232495i | ||||
\(149\) | 6.00000 | 0.491539 | 0.245770 | − | 0.969328i | \(-0.420959\pi\) | ||||
0.245770 | + | 0.969328i | \(0.420959\pi\) | |||||||
\(150\) | 7.77817 | − | 7.77817i | 0.635085 | − | 0.635085i | ||||
\(151\) | − | 24.0000i | − | 1.95309i | −0.215308 | − | 0.976546i | \(-0.569076\pi\) | ||
0.215308 | − | 0.976546i | \(-0.430924\pi\) | |||||||
\(152\) | −4.00000 | −0.324443 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 24.0000i | 1.92773i | ||||||||
\(156\) | 4.24264 | − | 4.24264i | 0.339683 | − | 0.339683i | ||||
\(157\) | −6.00000 | −0.478852 | −0.239426 | − | 0.970915i | \(-0.576959\pi\) | ||||
−0.239426 | + | 0.970915i | \(0.576959\pi\) | |||||||
\(158\) | 7.07107 | − | 7.07107i | 0.562544 | − | 0.562544i | ||||
\(159\) | 1.41421 | + | 1.41421i | 0.112154 | + | 0.112154i | ||||
\(160\) | −2.82843 | − | 2.82843i | −0.223607 | − | 0.223607i | ||||
\(161\) | 12.0000i | 0.945732i | ||||||||
\(162\) | 1.00000i | 0.0785674i | ||||||||
\(163\) | −8.48528 | − | 8.48528i | −0.664619 | − | 0.664619i | 0.291847 | − | 0.956465i | \(-0.405730\pi\) |
−0.956465 | + | 0.291847i | \(0.905730\pi\) | |||||||
\(164\) | −7.07107 | − | 7.07107i | −0.552158 | − | 0.552158i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −12.0000 | −0.931381 | ||||||||
\(167\) | −1.41421 | + | 1.41421i | −0.109435 | + | 0.109435i | −0.759704 | − | 0.650269i | \(-0.774656\pi\) |
0.650269 | + | 0.759704i | \(0.274656\pi\) | |||||||
\(168\) | − | 2.00000i | − | 0.154303i | ||||||
\(169\) | 23.0000 | 1.76923 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 4.00000 | 0.305888 | ||||||||
\(172\) | − | 4.00000i | − | 0.304997i | ||||||
\(173\) | −2.82843 | + | 2.82843i | −0.215041 | + | 0.215041i | −0.806405 | − | 0.591364i | \(-0.798590\pi\) |
0.591364 | + | 0.806405i | \(0.298590\pi\) | |||||||
\(174\) | 4.00000 | 0.303239 | ||||||||
\(175\) | 15.5563 | − | 15.5563i | 1.17595 | − | 1.17595i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 8.48528 | + | 8.48528i | 0.637793 | + | 0.637793i | ||||
\(178\) | − | 2.00000i | − | 0.149906i | ||||||
\(179\) | 12.0000i | 0.896922i | 0.893802 | + | 0.448461i | \(0.148028\pi\) | ||||
−0.893802 | + | 0.448461i | \(0.851972\pi\) | |||||||
\(180\) | 2.82843 | + | 2.82843i | 0.210819 | + | 0.210819i | ||||
\(181\) | −14.1421 | − | 14.1421i | −1.05118 | − | 1.05118i | −0.998618 | − | 0.0525588i | \(-0.983262\pi\) |
−0.0525588 | − | 0.998618i | \(-0.516738\pi\) | |||||||
\(182\) | 8.48528 | − | 8.48528i | 0.628971 | − | 0.628971i | ||||
\(183\) | −4.00000 | −0.295689 | ||||||||
\(184\) | −4.24264 | + | 4.24264i | −0.312772 | + | 0.312772i | ||||
\(185\) | 16.0000i | 1.17634i | ||||||||
\(186\) | −6.00000 | −0.439941 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 4.00000 | 0.291730 | ||||||||
\(189\) | 2.00000i | 0.145479i | ||||||||
\(190\) | 11.3137 | − | 11.3137i | 0.820783 | − | 0.820783i | ||||
\(191\) | 4.00000 | 0.289430 | 0.144715 | − | 0.989473i | \(-0.453773\pi\) | ||||
0.144715 | + | 0.989473i | \(0.453773\pi\) | |||||||
\(192\) | 0.707107 | − | 0.707107i | 0.0510310 | − | 0.0510310i | ||||
\(193\) | 4.24264 | + | 4.24264i | 0.305392 | + | 0.305392i | 0.843119 | − | 0.537727i | \(-0.180717\pi\) |
−0.537727 | + | 0.843119i | \(0.680717\pi\) | |||||||
\(194\) | 4.24264 | + | 4.24264i | 0.304604 | + | 0.304604i | ||||
\(195\) | 24.0000i | 1.71868i | ||||||||
\(196\) | 3.00000i | 0.214286i | ||||||||
\(197\) | −5.65685 | − | 5.65685i | −0.403034 | − | 0.403034i | 0.476267 | − | 0.879301i | \(-0.341990\pi\) |
−0.879301 | + | 0.476267i | \(0.841990\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −9.89949 | + | 9.89949i | −0.701757 | + | 0.701757i | −0.964787 | − | 0.263031i | \(-0.915278\pi\) |
0.263031 | + | 0.964787i | \(0.415278\pi\) | |||||||
\(200\) | 11.0000 | 0.777817 | ||||||||
\(201\) | 8.48528 | − | 8.48528i | 0.598506 | − | 0.598506i | ||||
\(202\) | − | 14.0000i | − | 0.985037i | ||||||
\(203\) | 8.00000 | 0.561490 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 40.0000 | 2.79372 | ||||||||
\(206\) | − | 4.00000i | − | 0.278693i | ||||||
\(207\) | 4.24264 | − | 4.24264i | 0.294884 | − | 0.294884i | ||||
\(208\) | 6.00000 | 0.416025 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 5.65685 | + | 5.65685i | 0.390360 | + | 0.390360i | ||||
\(211\) | −5.65685 | − | 5.65685i | −0.389434 | − | 0.389434i | 0.485052 | − | 0.874486i | \(-0.338801\pi\) |
−0.874486 | + | 0.485052i | \(0.838801\pi\) | |||||||
\(212\) | 2.00000i | 0.137361i | ||||||||
\(213\) | − | 6.00000i | − | 0.411113i | ||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 11.3137 | + | 11.3137i | 0.771589 | + | 0.771589i | ||||
\(216\) | −0.707107 | + | 0.707107i | −0.0481125 | + | 0.0481125i | ||||
\(217\) | −12.0000 | −0.814613 | ||||||||
\(218\) | −11.3137 | + | 11.3137i | −0.766261 | + | 0.766261i | ||||
\(219\) | − | 2.00000i | − | 0.135147i | ||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −4.00000 | −0.268462 | ||||||||
\(223\) | − | 4.00000i | − | 0.267860i | −0.990991 | − | 0.133930i | \(-0.957240\pi\) | ||
0.990991 | − | 0.133930i | \(-0.0427597\pi\) | |||||||
\(224\) | 1.41421 | − | 1.41421i | 0.0944911 | − | 0.0944911i | ||||
\(225\) | −11.0000 | −0.733333 | ||||||||
\(226\) | 1.41421 | − | 1.41421i | 0.0940721 | − | 0.0940721i | ||||
\(227\) | 2.82843 | + | 2.82843i | 0.187729 | + | 0.187729i | 0.794714 | − | 0.606984i | \(-0.207621\pi\) |
−0.606984 | + | 0.794714i | \(0.707621\pi\) | |||||||
\(228\) | 2.82843 | + | 2.82843i | 0.187317 | + | 0.187317i | ||||
\(229\) | 2.00000i | 0.132164i | 0.997814 | + | 0.0660819i | \(0.0210498\pi\) | ||||
−0.997814 | + | 0.0660819i | \(0.978950\pi\) | |||||||
\(230\) | − | 24.0000i | − | 1.58251i | ||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 2.82843 | + | 2.82843i | 0.185695 | + | 0.185695i | ||||
\(233\) | 4.24264 | − | 4.24264i | 0.277945 | − | 0.277945i | −0.554343 | − | 0.832288i | \(-0.687031\pi\) |
0.832288 | + | 0.554343i | \(0.187031\pi\) | |||||||
\(234\) | −6.00000 | −0.392232 | ||||||||
\(235\) | −11.3137 | + | 11.3137i | −0.738025 | + | 0.738025i | ||||
\(236\) | 12.0000i | 0.781133i | ||||||||
\(237\) | −10.0000 | −0.649570 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −20.0000 | −1.29369 | −0.646846 | − | 0.762620i | \(-0.723912\pi\) | ||||
−0.646846 | + | 0.762620i | \(0.723912\pi\) | |||||||
\(240\) | 4.00000i | 0.258199i | ||||||||
\(241\) | −12.7279 | + | 12.7279i | −0.819878 | + | 0.819878i | −0.986090 | − | 0.166212i | \(-0.946846\pi\) |
0.166212 | + | 0.986090i | \(0.446846\pi\) | |||||||
\(242\) | −11.0000 | −0.707107 | ||||||||
\(243\) | 0.707107 | − | 0.707107i | 0.0453609 | − | 0.0453609i | ||||
\(244\) | −2.82843 | − | 2.82843i | −0.181071 | − | 0.181071i | ||||
\(245\) | −8.48528 | − | 8.48528i | −0.542105 | − | 0.542105i | ||||
\(246\) | 10.0000i | 0.637577i | ||||||||
\(247\) | 24.0000i | 1.52708i | ||||||||
\(248\) | −4.24264 | − | 4.24264i | −0.269408 | − | 0.269408i | ||||
\(249\) | 8.48528 | + | 8.48528i | 0.537733 | + | 0.537733i | ||||
\(250\) | −16.9706 | + | 16.9706i | −1.07331 | + | 1.07331i | ||||
\(251\) | −12.0000 | −0.757433 | −0.378717 | − | 0.925513i | \(-0.623635\pi\) | ||||
−0.378717 | + | 0.925513i | \(0.623635\pi\) | |||||||
\(252\) | −1.41421 | + | 1.41421i | −0.0890871 | + | 0.0890871i | ||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −8.00000 | −0.501965 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 18.0000i | 1.12281i | 0.827541 | + | 0.561405i | \(0.189739\pi\) | ||||
−0.827541 | + | 0.561405i | \(0.810261\pi\) | |||||||
\(258\) | −2.82843 | + | 2.82843i | −0.176090 | + | 0.176090i | ||||
\(259\) | −8.00000 | −0.497096 | ||||||||
\(260\) | −16.9706 | + | 16.9706i | −1.05247 | + | 1.05247i | ||||
\(261\) | −2.82843 | − | 2.82843i | −0.175075 | − | 0.175075i | ||||
\(262\) | −11.3137 | − | 11.3137i | −0.698963 | − | 0.698963i | ||||
\(263\) | 12.0000i | 0.739952i | 0.929041 | + | 0.369976i | \(0.120634\pi\) | ||||
−0.929041 | + | 0.369976i | \(0.879366\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −5.65685 | − | 5.65685i | −0.347498 | − | 0.347498i | ||||
\(266\) | 5.65685 | + | 5.65685i | 0.346844 | + | 0.346844i | ||||
\(267\) | −1.41421 | + | 1.41421i | −0.0865485 | + | 0.0865485i | ||||
\(268\) | 12.0000 | 0.733017 | ||||||||
\(269\) | −8.48528 | + | 8.48528i | −0.517357 | + | 0.517357i | −0.916771 | − | 0.399414i | \(-0.869214\pi\) |
0.399414 | + | 0.916771i | \(0.369214\pi\) | |||||||
\(270\) | − | 4.00000i | − | 0.243432i | ||||||
\(271\) | −16.0000 | −0.971931 | −0.485965 | − | 0.873978i | \(-0.661532\pi\) | ||||
−0.485965 | + | 0.873978i | \(0.661532\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −12.0000 | −0.726273 | ||||||||
\(274\) | 6.00000i | 0.362473i | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 6.00000 | 0.361158 | ||||||||
\(277\) | 5.65685 | − | 5.65685i | 0.339887 | − | 0.339887i | −0.516437 | − | 0.856325i | \(-0.672742\pi\) |
0.856325 | + | 0.516437i | \(0.172742\pi\) | |||||||
\(278\) | −5.65685 | − | 5.65685i | −0.339276 | − | 0.339276i | ||||
\(279\) | 4.24264 | + | 4.24264i | 0.254000 | + | 0.254000i | ||||
\(280\) | 8.00000i | 0.478091i | ||||||||
\(281\) | 18.0000i | 1.07379i | 0.843649 | + | 0.536895i | \(0.180403\pi\) | ||||
−0.843649 | + | 0.536895i | \(0.819597\pi\) | |||||||
\(282\) | −2.82843 | − | 2.82843i | −0.168430 | − | 0.168430i | ||||
\(283\) | 22.6274 | + | 22.6274i | 1.34506 | + | 1.34506i | 0.890941 | + | 0.454120i | \(0.150046\pi\) |
0.454120 | + | 0.890941i | \(0.349954\pi\) | |||||||
\(284\) | 4.24264 | − | 4.24264i | 0.251754 | − | 0.251754i | ||||
\(285\) | −16.0000 | −0.947758 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 20.0000i | 1.18056i | ||||||||
\(288\) | −1.00000 | −0.0589256 | ||||||||
\(289\) | 0 | 0 | ||||||||
\(290\) | −16.0000 | −0.939552 | ||||||||
\(291\) | − | 6.00000i | − | 0.351726i | ||||||
\(292\) | 1.41421 | − | 1.41421i | 0.0827606 | − | 0.0827606i | ||||
\(293\) | −2.00000 | −0.116841 | −0.0584206 | − | 0.998292i | \(-0.518606\pi\) | ||||
−0.0584206 | + | 0.998292i | \(0.518606\pi\) | |||||||
\(294\) | 2.12132 | − | 2.12132i | 0.123718 | − | 0.123718i | ||||
\(295\) | −33.9411 | − | 33.9411i | −1.97613 | − | 1.97613i | ||||
\(296\) | −2.82843 | − | 2.82843i | −0.164399 | − | 0.164399i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | − | 6.00000i | − | 0.347571i | ||||||
\(299\) | 25.4558 | + | 25.4558i | 1.47215 | + | 1.47215i | ||||
\(300\) | −7.77817 | − | 7.77817i | −0.449073 | − | 0.449073i | ||||
\(301\) | −5.65685 | + | 5.65685i | −0.326056 | + | 0.326056i | ||||
\(302\) | −24.0000 | −1.38104 | ||||||||
\(303\) | −9.89949 | + | 9.89949i | −0.568711 | + | 0.568711i | ||||
\(304\) | 4.00000i | 0.229416i | ||||||||
\(305\) | 16.0000 | 0.916157 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −12.0000 | −0.684876 | −0.342438 | − | 0.939540i | \(-0.611253\pi\) | ||||
−0.342438 | + | 0.939540i | \(0.611253\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −2.82843 | + | 2.82843i | −0.160904 | + | 0.160904i | ||||
\(310\) | 24.0000 | 1.36311 | ||||||||
\(311\) | −21.2132 | + | 21.2132i | −1.20289 | + | 1.20289i | −0.229607 | + | 0.973283i | \(0.573744\pi\) |
−0.973283 | + | 0.229607i | \(0.926256\pi\) | |||||||
\(312\) | −4.24264 | − | 4.24264i | −0.240192 | − | 0.240192i | ||||
\(313\) | 18.3848 | + | 18.3848i | 1.03917 | + | 1.03917i | 0.999201 | + | 0.0399680i | \(0.0127256\pi\) |
0.0399680 | + | 0.999201i | \(0.487274\pi\) | |||||||
\(314\) | 6.00000i | 0.338600i | ||||||||
\(315\) | − | 8.00000i | − | 0.450749i | ||||||
\(316\) | −7.07107 | − | 7.07107i | −0.397779 | − | 0.397779i | ||||
\(317\) | −11.3137 | − | 11.3137i | −0.635441 | − | 0.635441i | 0.313986 | − | 0.949428i | \(-0.398335\pi\) |
−0.949428 | + | 0.313986i | \(0.898335\pi\) | |||||||
\(318\) | 1.41421 | − | 1.41421i | 0.0793052 | − | 0.0793052i | ||||
\(319\) | 0 | 0 | ||||||||
\(320\) | −2.82843 | + | 2.82843i | −0.158114 | + | 0.158114i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 12.0000 | 0.668734 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | − | 66.0000i | − | 3.66102i | ||||||
\(326\) | −8.48528 | + | 8.48528i | −0.469956 | + | 0.469956i | ||||
\(327\) | 16.0000 | 0.884802 | ||||||||
\(328\) | −7.07107 | + | 7.07107i | −0.390434 | + | 0.390434i | ||||
\(329\) | −5.65685 | − | 5.65685i | −0.311872 | − | 0.311872i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 20.0000i | − | 1.09930i | −0.835395 | − | 0.549650i | \(-0.814761\pi\) | ||
0.835395 | − | 0.549650i | \(-0.185239\pi\) | |||||||
\(332\) | 12.0000i | 0.658586i | ||||||||
\(333\) | 2.82843 | + | 2.82843i | 0.154997 | + | 0.154997i | ||||
\(334\) | 1.41421 | + | 1.41421i | 0.0773823 | + | 0.0773823i | ||||
\(335\) | −33.9411 | + | 33.9411i | −1.85440 | + | 1.85440i | ||||
\(336\) | −2.00000 | −0.109109 | ||||||||
\(337\) | −4.24264 | + | 4.24264i | −0.231111 | + | 0.231111i | −0.813156 | − | 0.582045i | \(-0.802253\pi\) |
0.582045 | + | 0.813156i | \(0.302253\pi\) | |||||||
\(338\) | − | 23.0000i | − | 1.25104i | ||||||
\(339\) | −2.00000 | −0.108625 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | − | 4.00000i | − | 0.216295i | ||||||
\(343\) | 14.1421 | − | 14.1421i | 0.763604 | − | 0.763604i | ||||
\(344\) | −4.00000 | −0.215666 | ||||||||
\(345\) | −16.9706 | + | 16.9706i | −0.913664 | + | 0.913664i | ||||
\(346\) | 2.82843 | + | 2.82843i | 0.152057 | + | 0.152057i | ||||
\(347\) | 2.82843 | + | 2.82843i | 0.151838 | + | 0.151838i | 0.778938 | − | 0.627100i | \(-0.215758\pi\) |
−0.627100 | + | 0.778938i | \(0.715758\pi\) | |||||||
\(348\) | − | 4.00000i | − | 0.214423i | ||||||
\(349\) | 30.0000i | 1.60586i | 0.596071 | + | 0.802932i | \(0.296728\pi\) | ||||
−0.596071 | + | 0.802932i | \(0.703272\pi\) | |||||||
\(350\) | −15.5563 | − | 15.5563i | −0.831522 | − | 0.831522i | ||||
\(351\) | 4.24264 | + | 4.24264i | 0.226455 | + | 0.226455i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −14.0000 | −0.745145 | −0.372572 | − | 0.928003i | \(-0.621524\pi\) | ||||
−0.372572 | + | 0.928003i | \(0.621524\pi\) | |||||||
\(354\) | 8.48528 | − | 8.48528i | 0.450988 | − | 0.450988i | ||||
\(355\) | 24.0000i | 1.27379i | ||||||||
\(356\) | −2.00000 | −0.106000 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 12.0000 | 0.634220 | ||||||||
\(359\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(360\) | 2.82843 | − | 2.82843i | 0.149071 | − | 0.149071i | ||||
\(361\) | 3.00000 | 0.157895 | ||||||||
\(362\) | −14.1421 | + | 14.1421i | −0.743294 | + | 0.743294i | ||||
\(363\) | 7.77817 | + | 7.77817i | 0.408248 | + | 0.408248i | ||||
\(364\) | −8.48528 | − | 8.48528i | −0.444750 | − | 0.444750i | ||||
\(365\) | 8.00000i | 0.418739i | ||||||||
\(366\) | 4.00000i | 0.209083i | ||||||||
\(367\) | −7.07107 | − | 7.07107i | −0.369107 | − | 0.369107i | 0.498045 | − | 0.867151i | \(-0.334052\pi\) |
−0.867151 | + | 0.498045i | \(0.834052\pi\) | |||||||
\(368\) | 4.24264 | + | 4.24264i | 0.221163 | + | 0.221163i | ||||
\(369\) | 7.07107 | − | 7.07107i | 0.368105 | − | 0.368105i | ||||
\(370\) | 16.0000 | 0.831800 | ||||||||
\(371\) | 2.82843 | − | 2.82843i | 0.146845 | − | 0.146845i | ||||
\(372\) | 6.00000i | 0.311086i | ||||||||
\(373\) | −14.0000 | −0.724893 | −0.362446 | − | 0.932005i | \(-0.618058\pi\) | ||||
−0.362446 | + | 0.932005i | \(0.618058\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 24.0000 | 1.23935 | ||||||||
\(376\) | − | 4.00000i | − | 0.206284i | ||||||
\(377\) | 16.9706 | − | 16.9706i | 0.874028 | − | 0.874028i | ||||
\(378\) | 2.00000 | 0.102869 | ||||||||
\(379\) | 2.82843 | − | 2.82843i | 0.145287 | − | 0.145287i | −0.630722 | − | 0.776009i | \(-0.717241\pi\) |
0.776009 | + | 0.630722i | \(0.217241\pi\) | |||||||
\(380\) | −11.3137 | − | 11.3137i | −0.580381 | − | 0.580381i | ||||
\(381\) | 5.65685 | + | 5.65685i | 0.289809 | + | 0.289809i | ||||
\(382\) | − | 4.00000i | − | 0.204658i | ||||||
\(383\) | − | 28.0000i | − | 1.43073i | −0.698749 | − | 0.715367i | \(-0.746260\pi\) | ||
0.698749 | − | 0.715367i | \(-0.253740\pi\) | |||||||
\(384\) | −0.707107 | − | 0.707107i | −0.0360844 | − | 0.0360844i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 4.24264 | − | 4.24264i | 0.215945 | − | 0.215945i | ||||
\(387\) | 4.00000 | 0.203331 | ||||||||
\(388\) | 4.24264 | − | 4.24264i | 0.215387 | − | 0.215387i | ||||
\(389\) | − | 14.0000i | − | 0.709828i | −0.934899 | − | 0.354914i | \(-0.884510\pi\) | ||
0.934899 | − | 0.354914i | \(-0.115490\pi\) | |||||||
\(390\) | 24.0000 | 1.21529 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 3.00000 | 0.151523 | ||||||||
\(393\) | 16.0000i | 0.807093i | ||||||||
\(394\) | −5.65685 | + | 5.65685i | −0.284988 | + | 0.284988i | ||||
\(395\) | 40.0000 | 2.01262 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 14.1421 | + | 14.1421i | 0.709773 | + | 0.709773i | 0.966487 | − | 0.256714i | \(-0.0826398\pi\) |
−0.256714 | + | 0.966487i | \(0.582640\pi\) | |||||||
\(398\) | 9.89949 | + | 9.89949i | 0.496217 | + | 0.496217i | ||||
\(399\) | − | 8.00000i | − | 0.400501i | ||||||
\(400\) | − | 11.0000i | − | 0.550000i | ||||||
\(401\) | −21.2132 | − | 21.2132i | −1.05934 | − | 1.05934i | −0.998125 | − | 0.0612120i | \(-0.980503\pi\) |
−0.0612120 | − | 0.998125i | \(-0.519497\pi\) | |||||||
\(402\) | −8.48528 | − | 8.48528i | −0.423207 | − | 0.423207i | ||||
\(403\) | −25.4558 | + | 25.4558i | −1.26805 | + | 1.26805i | ||||
\(404\) | −14.0000 | −0.696526 | ||||||||
\(405\) | −2.82843 | + | 2.82843i | −0.140546 | + | 0.140546i | ||||
\(406\) | − | 8.00000i | − | 0.397033i | ||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −26.0000 | −1.28562 | −0.642809 | − | 0.766027i | \(-0.722231\pi\) | ||||
−0.642809 | + | 0.766027i | \(0.722231\pi\) | |||||||
\(410\) | − | 40.0000i | − | 1.97546i | ||||||
\(411\) | 4.24264 | − | 4.24264i | 0.209274 | − | 0.209274i | ||||
\(412\) | −4.00000 | −0.197066 | ||||||||
\(413\) | 16.9706 | − | 16.9706i | 0.835067 | − | 0.835067i | ||||
\(414\) | −4.24264 | − | 4.24264i | −0.208514 | − | 0.208514i | ||||
\(415\) | −33.9411 | − | 33.9411i | −1.66610 | − | 1.66610i | ||||
\(416\) | − | 6.00000i | − | 0.294174i | ||||||
\(417\) | 8.00000i | 0.391762i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −8.48528 | − | 8.48528i | −0.414533 | − | 0.414533i | 0.468781 | − | 0.883314i | \(-0.344693\pi\) |
−0.883314 | + | 0.468781i | \(0.844693\pi\) | |||||||
\(420\) | 5.65685 | − | 5.65685i | 0.276026 | − | 0.276026i | ||||
\(421\) | −34.0000 | −1.65706 | −0.828529 | − | 0.559946i | \(-0.810822\pi\) | ||||
−0.828529 | + | 0.559946i | \(0.810822\pi\) | |||||||
\(422\) | −5.65685 | + | 5.65685i | −0.275371 | + | 0.275371i | ||||
\(423\) | 4.00000i | 0.194487i | ||||||||
\(424\) | 2.00000 | 0.0971286 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −6.00000 | −0.290701 | ||||||||
\(427\) | 8.00000i | 0.387147i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 11.3137 | − | 11.3137i | 0.545595 | − | 0.545595i | ||||
\(431\) | 9.89949 | + | 9.89949i | 0.476842 | + | 0.476842i | 0.904120 | − | 0.427278i | \(-0.140528\pi\) |
−0.427278 | + | 0.904120i | \(0.640528\pi\) | |||||||
\(432\) | 0.707107 | + | 0.707107i | 0.0340207 | + | 0.0340207i | ||||
\(433\) | 18.0000i | 0.865025i | 0.901628 | + | 0.432512i | \(0.142373\pi\) | ||||
−0.901628 | + | 0.432512i | \(0.857627\pi\) | |||||||
\(434\) | 12.0000i | 0.576018i | ||||||||
\(435\) | 11.3137 | + | 11.3137i | 0.542451 | + | 0.542451i | ||||
\(436\) | 11.3137 | + | 11.3137i | 0.541828 | + | 0.541828i | ||||
\(437\) | −16.9706 | + | 16.9706i | −0.811812 | + | 0.811812i | ||||
\(438\) | −2.00000 | −0.0955637 | ||||||||
\(439\) | −7.07107 | + | 7.07107i | −0.337484 | + | 0.337484i | −0.855419 | − | 0.517936i | \(-0.826701\pi\) |
0.517936 | + | 0.855419i | \(0.326701\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −3.00000 | −0.142857 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 12.0000 | 0.570137 | 0.285069 | − | 0.958507i | \(-0.407984\pi\) | ||||
0.285069 | + | 0.958507i | \(0.407984\pi\) | |||||||
\(444\) | 4.00000i | 0.189832i | ||||||||
\(445\) | 5.65685 | − | 5.65685i | 0.268161 | − | 0.268161i | ||||
\(446\) | −4.00000 | −0.189405 | ||||||||
\(447\) | −4.24264 | + | 4.24264i | −0.200670 | + | 0.200670i | ||||
\(448\) | −1.41421 | − | 1.41421i | −0.0668153 | − | 0.0668153i | ||||
\(449\) | 18.3848 | + | 18.3848i | 0.867631 | + | 0.867631i | 0.992210 | − | 0.124579i | \(-0.0397579\pi\) |
−0.124579 | + | 0.992210i | \(0.539758\pi\) | |||||||
\(450\) | 11.0000i | 0.518545i | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | −1.41421 | − | 1.41421i | −0.0665190 | − | 0.0665190i | ||||
\(453\) | 16.9706 | + | 16.9706i | 0.797347 | + | 0.797347i | ||||
\(454\) | 2.82843 | − | 2.82843i | 0.132745 | − | 0.132745i | ||||
\(455\) | 48.0000 | 2.25027 | ||||||||
\(456\) | 2.82843 | − | 2.82843i | 0.132453 | − | 0.132453i | ||||
\(457\) | 22.0000i | 1.02912i | 0.857455 | + | 0.514558i | \(0.172044\pi\) | ||||
−0.857455 | + | 0.514558i | \(0.827956\pi\) | |||||||
\(458\) | 2.00000 | 0.0934539 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −24.0000 | −1.11901 | ||||||||
\(461\) | − | 10.0000i | − | 0.465746i | −0.972507 | − | 0.232873i | \(-0.925187\pi\) | ||
0.972507 | − | 0.232873i | \(-0.0748127\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 4.00000 | 0.185896 | 0.0929479 | − | 0.995671i | \(-0.470371\pi\) | ||||
0.0929479 | + | 0.995671i | \(0.470371\pi\) | |||||||
\(464\) | 2.82843 | − | 2.82843i | 0.131306 | − | 0.131306i | ||||
\(465\) | −16.9706 | − | 16.9706i | −0.786991 | − | 0.786991i | ||||
\(466\) | −4.24264 | − | 4.24264i | −0.196537 | − | 0.196537i | ||||
\(467\) | 36.0000i | 1.66588i | 0.553362 | + | 0.832941i | \(0.313345\pi\) | ||||
−0.553362 | + | 0.832941i | \(0.686655\pi\) | |||||||
\(468\) | 6.00000i | 0.277350i | ||||||||
\(469\) | −16.9706 | − | 16.9706i | −0.783628 | − | 0.783628i | ||||
\(470\) | 11.3137 | + | 11.3137i | 0.521862 | + | 0.521862i | ||||
\(471\) | 4.24264 | − | 4.24264i | 0.195491 | − | 0.195491i | ||||
\(472\) | 12.0000 | 0.552345 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 10.0000i | 0.459315i | ||||||||
\(475\) | 44.0000 | 2.01886 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −2.00000 | −0.0915737 | ||||||||
\(478\) | 20.0000i | 0.914779i | ||||||||
\(479\) | 7.07107 | − | 7.07107i | 0.323085 | − | 0.323085i | −0.526864 | − | 0.849949i | \(-0.676632\pi\) |
0.849949 | + | 0.526864i | \(0.176632\pi\) | |||||||
\(480\) | 4.00000 | 0.182574 | ||||||||
\(481\) | −16.9706 | + | 16.9706i | −0.773791 | + | 0.773791i | ||||
\(482\) | 12.7279 | + | 12.7279i | 0.579741 | + | 0.579741i | ||||
\(483\) | −8.48528 | − | 8.48528i | −0.386094 | − | 0.386094i | ||||
\(484\) | 11.0000i | 0.500000i | ||||||||
\(485\) | 24.0000i | 1.08978i | ||||||||
\(486\) | −0.707107 | − | 0.707107i | −0.0320750 | − | 0.0320750i | ||||
\(487\) | −26.8701 | − | 26.8701i | −1.21760 | − | 1.21760i | −0.968471 | − | 0.249128i | \(-0.919856\pi\) |
−0.249128 | − | 0.968471i | \(-0.580144\pi\) | |||||||
\(488\) | −2.82843 | + | 2.82843i | −0.128037 | + | 0.128037i | ||||
\(489\) | 12.0000 | 0.542659 | ||||||||
\(490\) | −8.48528 | + | 8.48528i | −0.383326 | + | 0.383326i | ||||
\(491\) | − | 20.0000i | − | 0.902587i | −0.892375 | − | 0.451294i | \(-0.850963\pi\) | ||
0.892375 | − | 0.451294i | \(-0.149037\pi\) | |||||||
\(492\) | 10.0000 | 0.450835 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 24.0000 | 1.07981 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −4.24264 | + | 4.24264i | −0.190500 | + | 0.190500i | ||||
\(497\) | −12.0000 | −0.538274 | ||||||||
\(498\) | 8.48528 | − | 8.48528i | 0.380235 | − | 0.380235i | ||||
\(499\) | 22.6274 | + | 22.6274i | 1.01294 | + | 1.01294i | 0.999915 | + | 0.0130272i | \(0.00414679\pi\) |
0.0130272 | + | 0.999915i | \(0.495853\pi\) | |||||||
\(500\) | 16.9706 | + | 16.9706i | 0.758947 | + | 0.758947i | ||||
\(501\) | − | 2.00000i | − | 0.0893534i | ||||||
\(502\) | 12.0000i | 0.535586i | ||||||||
\(503\) | 18.3848 | + | 18.3848i | 0.819737 | + | 0.819737i | 0.986070 | − | 0.166333i | \(-0.0531927\pi\) |
−0.166333 | + | 0.986070i | \(0.553193\pi\) | |||||||
\(504\) | 1.41421 | + | 1.41421i | 0.0629941 | + | 0.0629941i | ||||
\(505\) | 39.5980 | − | 39.5980i | 1.76209 | − | 1.76209i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −16.2635 | + | 16.2635i | −0.722285 | + | 0.722285i | ||||
\(508\) | 8.00000i | 0.354943i | ||||||||
\(509\) | 26.0000 | 1.15243 | 0.576215 | − | 0.817298i | \(-0.304529\pi\) | ||||
0.576215 | + | 0.817298i | \(0.304529\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −4.00000 | −0.176950 | ||||||||
\(512\) | − | 1.00000i | − | 0.0441942i | ||||||
\(513\) | −2.82843 | + | 2.82843i | −0.124878 | + | 0.124878i | ||||
\(514\) | 18.0000 | 0.793946 | ||||||||
\(515\) | 11.3137 | − | 11.3137i | 0.498542 | − | 0.498542i | ||||
\(516\) | 2.82843 | + | 2.82843i | 0.124515 | + | 0.124515i | ||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 8.00000i | 0.351500i | ||||||||
\(519\) | − | 4.00000i | − | 0.175581i | ||||||
\(520\) | 16.9706 | + | 16.9706i | 0.744208 | + | 0.744208i | ||||
\(521\) | −7.07107 | − | 7.07107i | −0.309789 | − | 0.309789i | 0.535039 | − | 0.844828i | \(-0.320297\pi\) |
−0.844828 | + | 0.535039i | \(0.820297\pi\) | |||||||
\(522\) | −2.82843 | + | 2.82843i | −0.123797 | + | 0.123797i | ||||
\(523\) | 20.0000 | 0.874539 | 0.437269 | − | 0.899331i | \(-0.355946\pi\) | ||||
0.437269 | + | 0.899331i | \(0.355946\pi\) | |||||||
\(524\) | −11.3137 | + | 11.3137i | −0.494242 | + | 0.494242i | ||||
\(525\) | 22.0000i | 0.960159i | ||||||||
\(526\) | 12.0000 | 0.523225 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 13.0000i | 0.565217i | ||||||||
\(530\) | −5.65685 | + | 5.65685i | −0.245718 | + | 0.245718i | ||||
\(531\) | −12.0000 | −0.520756 | ||||||||
\(532\) | 5.65685 | − | 5.65685i | 0.245256 | − | 0.245256i | ||||
\(533\) | 42.4264 | + | 42.4264i | 1.83769 | + | 1.83769i | ||||
\(534\) | 1.41421 | + | 1.41421i | 0.0611990 | + | 0.0611990i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | − | 12.0000i | − | 0.518321i | ||||||
\(537\) | −8.48528 | − | 8.48528i | −0.366167 | − | 0.366167i | ||||
\(538\) | 8.48528 | + | 8.48528i | 0.365826 | + | 0.365826i | ||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −4.00000 | −0.172133 | ||||||||
\(541\) | −8.48528 | + | 8.48528i | −0.364811 | + | 0.364811i | −0.865581 | − | 0.500770i | \(-0.833050\pi\) |
0.500770 | + | 0.865581i | \(0.333050\pi\) | |||||||
\(542\) | 16.0000i | 0.687259i | ||||||||
\(543\) | 20.0000 | 0.858282 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −64.0000 | −2.74146 | ||||||||
\(546\) | 12.0000i | 0.513553i | ||||||||
\(547\) | −5.65685 | + | 5.65685i | −0.241870 | + | 0.241870i | −0.817623 | − | 0.575754i | \(-0.804709\pi\) |
0.575754 | + | 0.817623i | \(0.304709\pi\) | |||||||
\(548\) | 6.00000 | 0.256307 | ||||||||
\(549\) | 2.82843 | − | 2.82843i | 0.120714 | − | 0.120714i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 11.3137 | + | 11.3137i | 0.481980 | + | 0.481980i | ||||
\(552\) | − | 6.00000i | − | 0.255377i | ||||||
\(553\) | 20.0000i | 0.850487i | ||||||||
\(554\) | −5.65685 | − | 5.65685i | −0.240337 | − | 0.240337i | ||||
\(555\) | −11.3137 | − | 11.3137i | −0.480240 | − | 0.480240i | ||||
\(556\) | −5.65685 | + | 5.65685i | −0.239904 | + | 0.239904i | ||||
\(557\) | −14.0000 | −0.593199 | −0.296600 | − | 0.955002i | \(-0.595853\pi\) | ||||
−0.296600 | + | 0.955002i | \(0.595853\pi\) | |||||||
\(558\) | 4.24264 | − | 4.24264i | 0.179605 | − | 0.179605i | ||||
\(559\) | 24.0000i | 1.01509i | ||||||||
\(560\) | 8.00000 | 0.338062 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 18.0000 | 0.759284 | ||||||||
\(563\) | − | 4.00000i | − | 0.168580i | −0.996441 | − | 0.0842900i | \(-0.973138\pi\) | ||
0.996441 | − | 0.0842900i | \(-0.0268622\pi\) | |||||||
\(564\) | −2.82843 | + | 2.82843i | −0.119098 | + | 0.119098i | ||||
\(565\) | 8.00000 | 0.336563 | ||||||||
\(566\) | 22.6274 | − | 22.6274i | 0.951101 | − | 0.951101i | ||||
\(567\) | −1.41421 | − | 1.41421i | −0.0593914 | − | 0.0593914i | ||||
\(568\) | −4.24264 | − | 4.24264i | −0.178017 | − | 0.178017i | ||||
\(569\) | 6.00000i | 0.251533i | 0.992060 | + | 0.125767i | \(0.0401390\pi\) | ||||
−0.992060 | + | 0.125767i | \(0.959861\pi\) | |||||||
\(570\) | 16.0000i | 0.670166i | ||||||||
\(571\) | −31.1127 | − | 31.1127i | −1.30203 | − | 1.30203i | −0.927024 | − | 0.375002i | \(-0.877642\pi\) |
−0.375002 | − | 0.927024i | \(-0.622358\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −2.82843 | + | 2.82843i | −0.118159 | + | 0.118159i | ||||
\(574\) | 20.0000 | 0.834784 | ||||||||
\(575\) | 46.6690 | − | 46.6690i | 1.94623 | − | 1.94623i | ||||
\(576\) | 1.00000i | 0.0416667i | ||||||||
\(577\) | −30.0000 | −1.24892 | −0.624458 | − | 0.781058i | \(-0.714680\pi\) | ||||
−0.624458 | + | 0.781058i | \(0.714680\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −6.00000 | −0.249351 | ||||||||
\(580\) | 16.0000i | 0.664364i | ||||||||
\(581\) | 16.9706 | − | 16.9706i | 0.704058 | − | 0.704058i | ||||
\(582\) | −6.00000 | −0.248708 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | −1.41421 | − | 1.41421i | −0.0585206 | − | 0.0585206i | ||||
\(585\) | −16.9706 | − | 16.9706i | −0.701646 | − | 0.701646i | ||||
\(586\) | 2.00000i | 0.0826192i | ||||||||
\(587\) | − | 36.0000i | − | 1.48588i | −0.669359 | − | 0.742940i | \(-0.733431\pi\) | ||
0.669359 | − | 0.742940i | \(-0.266569\pi\) | |||||||
\(588\) | −2.12132 | − | 2.12132i | −0.0874818 | − | 0.0874818i | ||||
\(589\) | −16.9706 | − | 16.9706i | −0.699260 | − | 0.699260i | ||||
\(590\) | −33.9411 | + | 33.9411i | −1.39733 | + | 1.39733i | ||||
\(591\) | 8.00000 | 0.329076 | ||||||||
\(592\) | −2.82843 | + | 2.82843i | −0.116248 | + | 0.116248i | ||||
\(593\) | − | 30.0000i | − | 1.23195i | −0.787765 | − | 0.615976i | \(-0.788762\pi\) | ||
0.787765 | − | 0.615976i | \(-0.211238\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −6.00000 | −0.245770 | ||||||||
\(597\) | − | 14.0000i | − | 0.572982i | ||||||
\(598\) | 25.4558 | − | 25.4558i | 1.04097 | − | 1.04097i | ||||
\(599\) | 16.0000 | 0.653742 | 0.326871 | − | 0.945069i | \(-0.394006\pi\) | ||||
0.326871 | + | 0.945069i | \(0.394006\pi\) | |||||||
\(600\) | −7.77817 | + | 7.77817i | −0.317543 | + | 0.317543i | ||||
\(601\) | −26.8701 | − | 26.8701i | −1.09605 | − | 1.09605i | −0.994868 | − | 0.101185i | \(-0.967737\pi\) |
−0.101185 | − | 0.994868i | \(-0.532263\pi\) | |||||||
\(602\) | 5.65685 | + | 5.65685i | 0.230556 | + | 0.230556i | ||||
\(603\) | 12.0000i | 0.488678i | ||||||||
\(604\) | 24.0000i | 0.976546i | ||||||||
\(605\) | −31.1127 | − | 31.1127i | −1.26491 | − | 1.26491i | ||||
\(606\) | 9.89949 | + | 9.89949i | 0.402139 | + | 0.402139i | ||||
\(607\) | 26.8701 | − | 26.8701i | 1.09062 | − | 1.09062i | 0.0951600 | − | 0.995462i | \(-0.469664\pi\) |
0.995462 | − | 0.0951600i | \(-0.0303363\pi\) | |||||||
\(608\) | 4.00000 | 0.162221 | ||||||||
\(609\) | −5.65685 | + | 5.65685i | −0.229227 | + | 0.229227i | ||||
\(610\) | − | 16.0000i | − | 0.647821i | ||||||
\(611\) | −24.0000 | −0.970936 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 30.0000 | 1.21169 | 0.605844 | − | 0.795583i | \(-0.292835\pi\) | ||||
0.605844 | + | 0.795583i | \(0.292835\pi\) | |||||||
\(614\) | 12.0000i | 0.484281i | ||||||||
\(615\) | −28.2843 | + | 28.2843i | −1.14053 | + | 1.14053i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 4.24264 | − | 4.24264i | 0.170802 | − | 0.170802i | −0.616530 | − | 0.787332i | \(-0.711462\pi\) |
0.787332 | + | 0.616530i | \(0.211462\pi\) | |||||||
\(618\) | 2.82843 | + | 2.82843i | 0.113776 | + | 0.113776i | ||||
\(619\) | 14.1421 | + | 14.1421i | 0.568420 | + | 0.568420i | 0.931686 | − | 0.363265i | \(-0.118338\pi\) |
−0.363265 | + | 0.931686i | \(0.618338\pi\) | |||||||
\(620\) | − | 24.0000i | − | 0.963863i | ||||||
\(621\) | 6.00000i | 0.240772i | ||||||||
\(622\) | 21.2132 | + | 21.2132i | 0.850572 | + | 0.850572i | ||||
\(623\) | 2.82843 | + | 2.82843i | 0.113319 | + | 0.113319i | ||||
\(624\) | −4.24264 | + | 4.24264i | −0.169842 | + | 0.169842i | ||||
\(625\) | −41.0000 | −1.64000 | ||||||||
\(626\) | 18.3848 | − | 18.3848i | 0.734803 | − | 0.734803i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 6.00000 | 0.239426 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | −8.00000 | −0.318728 | ||||||||
\(631\) | 20.0000i | 0.796187i | 0.917345 | + | 0.398094i | \(0.130328\pi\) | ||||
−0.917345 | + | 0.398094i | \(0.869672\pi\) | |||||||
\(632\) | −7.07107 | + | 7.07107i | −0.281272 | + | 0.281272i | ||||
\(633\) | 8.00000 | 0.317971 | ||||||||
\(634\) | −11.3137 | + | 11.3137i | −0.449325 | + | 0.449325i | ||||
\(635\) | −22.6274 | − | 22.6274i | −0.897942 | − | 0.897942i | ||||
\(636\) | −1.41421 | − | 1.41421i | −0.0560772 | − | 0.0560772i | ||||
\(637\) | − | 18.0000i | − | 0.713186i | ||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 4.24264 | + | 4.24264i | 0.167836 | + | 0.167836i | ||||
\(640\) | 2.82843 | + | 2.82843i | 0.111803 | + | 0.111803i | ||||
\(641\) | 1.41421 | − | 1.41421i | 0.0558581 | − | 0.0558581i | −0.678626 | − | 0.734484i | \(-0.737424\pi\) |
0.734484 | + | 0.678626i | \(0.237424\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 2.82843 | − | 2.82843i | 0.111542 | − | 0.111542i | −0.649133 | − | 0.760675i | \(-0.724868\pi\) |
0.760675 | + | 0.649133i | \(0.224868\pi\) | |||||||
\(644\) | − | 12.0000i | − | 0.472866i | ||||||
\(645\) | −16.0000 | −0.629999 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 28.0000 | 1.10079 | 0.550397 | − | 0.834903i | \(-0.314476\pi\) | ||||
0.550397 | + | 0.834903i | \(0.314476\pi\) | |||||||
\(648\) | − | 1.00000i | − | 0.0392837i | ||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | −66.0000 | −2.58873 | ||||||||
\(651\) | 8.48528 | − | 8.48528i | 0.332564 | − | 0.332564i | ||||
\(652\) | 8.48528 | + | 8.48528i | 0.332309 | + | 0.332309i | ||||
\(653\) | −14.1421 | − | 14.1421i | −0.553425 | − | 0.553425i | 0.374003 | − | 0.927428i | \(-0.377985\pi\) |
−0.927428 | + | 0.374003i | \(0.877985\pi\) | |||||||
\(654\) | − | 16.0000i | − | 0.625650i | ||||||
\(655\) | − | 64.0000i | − | 2.50069i | ||||||
\(656\) | 7.07107 | + | 7.07107i | 0.276079 | + | 0.276079i | ||||
\(657\) | 1.41421 | + | 1.41421i | 0.0551737 | + | 0.0551737i | ||||
\(658\) | −5.65685 | + | 5.65685i | −0.220527 | + | 0.220527i | ||||
\(659\) | −12.0000 | −0.467454 | −0.233727 | − | 0.972302i | \(-0.575092\pi\) | ||||
−0.233727 | + | 0.972302i | \(0.575092\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 14.0000i | − | 0.544537i | −0.962221 | − | 0.272268i | \(-0.912226\pi\) | ||
0.962221 | − | 0.272268i | \(-0.0877739\pi\) | |||||||
\(662\) | −20.0000 | −0.777322 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 12.0000 | 0.465690 | ||||||||
\(665\) | 32.0000i | 1.24091i | ||||||||
\(666\) | 2.82843 | − | 2.82843i | 0.109599 | − | 0.109599i | ||||
\(667\) | 24.0000 | 0.929284 | ||||||||
\(668\) | 1.41421 | − | 1.41421i | 0.0547176 | − | 0.0547176i | ||||
\(669\) | 2.82843 | + | 2.82843i | 0.109353 | + | 0.109353i | ||||
\(670\) | 33.9411 | + | 33.9411i | 1.31126 | + | 1.31126i | ||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 2.00000i | 0.0771517i | ||||||||
\(673\) | 18.3848 | + | 18.3848i | 0.708681 | + | 0.708681i | 0.966258 | − | 0.257577i | \(-0.0829240\pi\) |
−0.257577 | + | 0.966258i | \(0.582924\pi\) | |||||||
\(674\) | 4.24264 | + | 4.24264i | 0.163420 | + | 0.163420i | ||||
\(675\) | 7.77817 | − | 7.77817i | 0.299382 | − | 0.299382i | ||||
\(676\) | −23.0000 | −0.884615 | ||||||||
\(677\) | 5.65685 | − | 5.65685i | 0.217411 | − | 0.217411i | −0.589996 | − | 0.807406i | \(-0.700871\pi\) |
0.807406 | + | 0.589996i | \(0.200871\pi\) | |||||||
\(678\) | 2.00000i | 0.0768095i | ||||||||
\(679\) | −12.0000 | −0.460518 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −4.00000 | −0.153280 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 8.48528 | − | 8.48528i | 0.324680 | − | 0.324680i | −0.525879 | − | 0.850559i | \(-0.676264\pi\) |
0.850559 | + | 0.525879i | \(0.176264\pi\) | |||||||
\(684\) | −4.00000 | −0.152944 | ||||||||
\(685\) | −16.9706 | + | 16.9706i | −0.648412 | + | 0.648412i | ||||
\(686\) | −14.1421 | − | 14.1421i | −0.539949 | − | 0.539949i | ||||
\(687\) | −1.41421 | − | 1.41421i | −0.0539556 | − | 0.0539556i | ||||
\(688\) | 4.00000i | 0.152499i | ||||||||
\(689\) | − | 12.0000i | − | 0.457164i | ||||||
\(690\) | 16.9706 | + | 16.9706i | 0.646058 | + | 0.646058i | ||||
\(691\) | 11.3137 | + | 11.3137i | 0.430394 | + | 0.430394i | 0.888762 | − | 0.458368i | \(-0.151566\pi\) |
−0.458368 | + | 0.888762i | \(0.651566\pi\) | |||||||
\(692\) | 2.82843 | − | 2.82843i | 0.107521 | − | 0.107521i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 2.82843 | − | 2.82843i | 0.107366 | − | 0.107366i | ||||
\(695\) | − | 32.0000i | − | 1.21383i | ||||||
\(696\) | −4.00000 | −0.151620 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 30.0000 | 1.13552 | ||||||||
\(699\) | 6.00000i | 0.226941i | ||||||||
\(700\) | −15.5563 | + | 15.5563i | −0.587975 | + | 0.587975i | ||||
\(701\) | 18.0000 | 0.679851 | 0.339925 | − | 0.940452i | \(-0.389598\pi\) | ||||
0.339925 | + | 0.940452i | \(0.389598\pi\) | |||||||
\(702\) | 4.24264 | − | 4.24264i | 0.160128 | − | 0.160128i | ||||
\(703\) | −11.3137 | − | 11.3137i | −0.426705 | − | 0.426705i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | − | 16.0000i | − | 0.602595i | ||||||
\(706\) | 14.0000i | 0.526897i | ||||||||
\(707\) | 19.7990 | + | 19.7990i | 0.744618 | + | 0.744618i | ||||
\(708\) | −8.48528 | − | 8.48528i | −0.318896 | − | 0.318896i | ||||
\(709\) | 11.3137 | − | 11.3137i | 0.424895 | − | 0.424895i | −0.461990 | − | 0.886885i | \(-0.652864\pi\) |
0.886885 | + | 0.461990i | \(0.152864\pi\) | |||||||
\(710\) | 24.0000 | 0.900704 | ||||||||
\(711\) | 7.07107 | − | 7.07107i | 0.265186 | − | 0.265186i | ||||
\(712\) | 2.00000i | 0.0749532i | ||||||||
\(713\) | −36.0000 | −1.34821 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | − | 12.0000i | − | 0.448461i | ||||||
\(717\) | 14.1421 | − | 14.1421i | 0.528148 | − | 0.528148i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −29.6985 | + | 29.6985i | −1.10757 | + | 1.10757i | −0.114097 | + | 0.993470i | \(0.536397\pi\) |
−0.993470 | + | 0.114097i | \(0.963603\pi\) | |||||||
\(720\) | −2.82843 | − | 2.82843i | −0.105409 | − | 0.105409i | ||||
\(721\) | 5.65685 | + | 5.65685i | 0.210672 | + | 0.210672i | ||||
\(722\) | − | 3.00000i | − | 0.111648i | ||||||
\(723\) | − | 18.0000i | − | 0.669427i | ||||||
\(724\) | 14.1421 | + | 14.1421i | 0.525588 | + | 0.525588i | ||||
\(725\) | −31.1127 | − | 31.1127i | −1.15550 | − | 1.15550i | ||||
\(726\) | 7.77817 | − | 7.77817i | 0.288675 | − | 0.288675i | ||||
\(727\) | 8.00000 | 0.296704 | 0.148352 | − | 0.988935i | \(-0.452603\pi\) | ||||
0.148352 | + | 0.988935i | \(0.452603\pi\) | |||||||
\(728\) | −8.48528 | + | 8.48528i | −0.314485 | + | 0.314485i | ||||
\(729\) | 1.00000i | 0.0370370i | ||||||||
\(730\) | 8.00000 | 0.296093 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 4.00000 | 0.147844 | ||||||||
\(733\) | 18.0000i | 0.664845i | 0.943131 | + | 0.332423i | \(0.107866\pi\) | ||||
−0.943131 | + | 0.332423i | \(0.892134\pi\) | |||||||
\(734\) | −7.07107 | + | 7.07107i | −0.260998 | + | 0.260998i | ||||
\(735\) | 12.0000 | 0.442627 | ||||||||
\(736\) | 4.24264 | − | 4.24264i | 0.156386 | − | 0.156386i | ||||
\(737\) | 0 | 0 | ||||||||
\(738\) | −7.07107 | − | 7.07107i | −0.260290 | − | 0.260290i | ||||
\(739\) | 12.0000i | 0.441427i | 0.975339 | + | 0.220714i | \(0.0708386\pi\) | ||||
−0.975339 | + | 0.220714i | \(0.929161\pi\) | |||||||
\(740\) | − | 16.0000i | − | 0.588172i | ||||||
\(741\) | −16.9706 | − | 16.9706i | −0.623429 | − | 0.623429i | ||||
\(742\) | −2.82843 | − | 2.82843i | −0.103835 | − | 0.103835i | ||||
\(743\) | −26.8701 | + | 26.8701i | −0.985767 | + | 0.985767i | −0.999900 | − | 0.0141333i | \(-0.995501\pi\) |
0.0141333 | + | 0.999900i | \(0.495501\pi\) | |||||||
\(744\) | 6.00000 | 0.219971 | ||||||||
\(745\) | 16.9706 | − | 16.9706i | 0.621753 | − | 0.621753i | ||||
\(746\) | 14.0000i | 0.512576i | ||||||||
\(747\) | −12.0000 | −0.439057 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | − | 24.0000i | − | 0.876356i | ||||||
\(751\) | −24.0416 | + | 24.0416i | −0.877292 | + | 0.877292i | −0.993254 | − | 0.115962i | \(-0.963005\pi\) |
0.115962 | + | 0.993254i | \(0.463005\pi\) | |||||||
\(752\) | −4.00000 | −0.145865 | ||||||||
\(753\) | 8.48528 | − | 8.48528i | 0.309221 | − | 0.309221i | ||||
\(754\) | −16.9706 | − | 16.9706i | −0.618031 | − | 0.618031i | ||||
\(755\) | −67.8823 | − | 67.8823i | −2.47049 | − | 2.47049i | ||||
\(756\) | − | 2.00000i | − | 0.0727393i | ||||||
\(757\) | − | 14.0000i | − | 0.508839i | −0.967094 | − | 0.254419i | \(-0.918116\pi\) | ||
0.967094 | − | 0.254419i | \(-0.0818843\pi\) | |||||||
\(758\) | −2.82843 | − | 2.82843i | −0.102733 | − | 0.102733i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −11.3137 | + | 11.3137i | −0.410391 | + | 0.410391i | ||||
\(761\) | −10.0000 | −0.362500 | −0.181250 | − | 0.983437i | \(-0.558014\pi\) | ||||
−0.181250 | + | 0.983437i | \(0.558014\pi\) | |||||||
\(762\) | 5.65685 | − | 5.65685i | 0.204926 | − | 0.204926i | ||||
\(763\) | − | 32.0000i | − | 1.15848i | ||||||
\(764\) | −4.00000 | −0.144715 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −28.0000 | −1.01168 | ||||||||
\(767\) | − | 72.0000i | − | 2.59977i | ||||||
\(768\) | −0.707107 | + | 0.707107i | −0.0255155 | + | 0.0255155i | ||||
\(769\) | −26.0000 | −0.937584 | −0.468792 | − | 0.883309i | \(-0.655311\pi\) | ||||
−0.468792 | + | 0.883309i | \(0.655311\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −12.7279 | − | 12.7279i | −0.458385 | − | 0.458385i | ||||
\(772\) | −4.24264 | − | 4.24264i | −0.152696 | − | 0.152696i | ||||
\(773\) | − | 42.0000i | − | 1.51064i | −0.655359 | − | 0.755318i | \(-0.727483\pi\) | ||
0.655359 | − | 0.755318i | \(-0.272517\pi\) | |||||||
\(774\) | − | 4.00000i | − | 0.143777i | ||||||
\(775\) | 46.6690 | + | 46.6690i | 1.67640 | + | 1.67640i | ||||
\(776\) | −4.24264 | − | 4.24264i | −0.152302 | − | 0.152302i | ||||
\(777\) | 5.65685 | − | 5.65685i | 0.202939 | − | 0.202939i | ||||
\(778\) | −14.0000 | −0.501924 | ||||||||
\(779\) | −28.2843 | + | 28.2843i |