Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [289,2,Mod(38,289)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(289, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("289.38");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 289 = 17^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 289.c (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: | \(2.30767661842\) |
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: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 17) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 38.1 | ||
Root | \(-0.707107 + 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 289.38 |
Dual form | 289.2.c.a.251.1 |
$q$-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 \(\left(\mathbb{Z}/289\mathbb{Z}\right)^\times\).
\(n\) | \(3\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) |
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 | −0.935414 | − | 0.353553i | \(-0.884973\pi\) | ||
0.935414 | − | 0.353553i | \(-0.115027\pi\) | |||||||
\(3\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −1.41421 | + | 1.41421i | −0.632456 | + | 0.632456i | −0.948683 | − | 0.316228i | \(-0.897584\pi\) |
0.316228 | + | 0.948683i | \(0.397584\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.82843 | + | 2.82843i | 1.06904 | + | 1.06904i | 0.997433 | + | 0.0716124i | \(0.0228145\pi\) |
0.0716124 | + | 0.997433i | \(0.477186\pi\) | |||||||
\(8\) | − | 3.00000i | − | 1.06066i | ||||||
\(9\) | 3.00000i | 1.00000i | ||||||||
\(10\) | 1.41421 | + | 1.41421i | 0.447214 | + | 0.447214i | ||||
\(11\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.00000 | 0.554700 | 0.277350 | − | 0.960769i | \(-0.410544\pi\) | ||||
0.277350 | + | 0.960769i | \(0.410544\pi\) | |||||||
\(14\) | 2.82843 | − | 2.82843i | 0.755929 | − | 0.755929i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −1.00000 | −0.250000 | ||||||||
\(17\) | 0 | 0 | ||||||||
\(18\) | 3.00000 | 0.707107 | ||||||||
\(19\) | − | 4.00000i | − | 0.917663i | −0.888523 | − | 0.458831i | \(-0.848268\pi\) | ||
0.888523 | − | 0.458831i | \(-0.151732\pi\) | |||||||
\(20\) | −1.41421 | + | 1.41421i | −0.316228 | + | 0.316228i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2.82843 | − | 2.82843i | −0.589768 | − | 0.589768i | 0.347801 | − | 0.937568i | \(-0.386929\pi\) |
−0.937568 | + | 0.347801i | \(0.886929\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000i | 0.200000i | ||||||||
\(26\) | − | 2.00000i | − | 0.392232i | ||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 2.82843 | + | 2.82843i | 0.534522 | + | 0.534522i | ||||
\(29\) | 4.24264 | − | 4.24264i | 0.787839 | − | 0.787839i | −0.193301 | − | 0.981140i | \(-0.561919\pi\) |
0.981140 | + | 0.193301i | \(0.0619194\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.82843 | + | 2.82843i | −0.508001 | + | 0.508001i | −0.913912 | − | 0.405912i | \(-0.866954\pi\) |
0.405912 | + | 0.913912i | \(0.366954\pi\) | |||||||
\(32\) | − | 5.00000i | − | 0.883883i | ||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −8.00000 | −1.35225 | ||||||||
\(36\) | 3.00000i | 0.500000i | ||||||||
\(37\) | 1.41421 | − | 1.41421i | 0.232495 | − | 0.232495i | −0.581238 | − | 0.813733i | \(-0.697432\pi\) |
0.813733 | + | 0.581238i | \(0.197432\pi\) | |||||||
\(38\) | −4.00000 | −0.648886 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 4.24264 | + | 4.24264i | 0.670820 | + | 0.670820i | ||||
\(41\) | −4.24264 | − | 4.24264i | −0.662589 | − | 0.662589i | 0.293400 | − | 0.955990i | \(-0.405213\pi\) |
−0.955990 | + | 0.293400i | \(0.905213\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 4.00000i | − | 0.609994i | −0.952353 | − | 0.304997i | \(-0.901344\pi\) | ||
0.952353 | − | 0.304997i | \(-0.0986555\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −4.24264 | − | 4.24264i | −0.632456 | − | 0.632456i | ||||
\(46\) | −2.82843 | + | 2.82843i | −0.417029 | + | 0.417029i | ||||
\(47\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 9.00000i | 1.28571i | ||||||||
\(50\) | 1.00000 | 0.141421 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 2.00000 | 0.277350 | ||||||||
\(53\) | 6.00000i | 0.824163i | 0.911147 | + | 0.412082i | \(0.135198\pi\) | ||||
−0.911147 | + | 0.412082i | \(0.864802\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 8.48528 | − | 8.48528i | 1.13389 | − | 1.13389i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −4.24264 | − | 4.24264i | −0.557086 | − | 0.557086i | ||||
\(59\) | 12.0000i | 1.56227i | 0.624364 | + | 0.781133i | \(0.285358\pi\) | ||||
−0.624364 | + | 0.781133i | \(0.714642\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −7.07107 | − | 7.07107i | −0.905357 | − | 0.905357i | 0.0905357 | − | 0.995893i | \(-0.471142\pi\) |
−0.995893 | + | 0.0905357i | \(0.971142\pi\) | |||||||
\(62\) | 2.82843 | + | 2.82843i | 0.359211 | + | 0.359211i | ||||
\(63\) | −8.48528 | + | 8.48528i | −1.06904 | + | 1.06904i | ||||
\(64\) | −7.00000 | −0.875000 | ||||||||
\(65\) | −2.82843 | + | 2.82843i | −0.350823 | + | 0.350823i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 4.00000 | 0.488678 | 0.244339 | − | 0.969690i | \(-0.421429\pi\) | ||||
0.244339 | + | 0.969690i | \(0.421429\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 8.00000i | 0.956183i | ||||||||
\(71\) | 2.82843 | − | 2.82843i | 0.335673 | − | 0.335673i | −0.519063 | − | 0.854736i | \(-0.673719\pi\) |
0.854736 | + | 0.519063i | \(0.173719\pi\) | |||||||
\(72\) | 9.00000 | 1.06066 | ||||||||
\(73\) | −4.24264 | + | 4.24264i | −0.496564 | + | 0.496564i | −0.910366 | − | 0.413803i | \(-0.864200\pi\) |
0.413803 | + | 0.910366i | \(0.364200\pi\) | |||||||
\(74\) | −1.41421 | − | 1.41421i | −0.164399 | − | 0.164399i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | − | 4.00000i | − | 0.458831i | ||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −8.48528 | − | 8.48528i | −0.954669 | − | 0.954669i | 0.0443474 | − | 0.999016i | \(-0.485879\pi\) |
−0.999016 | + | 0.0443474i | \(0.985879\pi\) | |||||||
\(80\) | 1.41421 | − | 1.41421i | 0.158114 | − | 0.158114i | ||||
\(81\) | −9.00000 | −1.00000 | ||||||||
\(82\) | −4.24264 | + | 4.24264i | −0.468521 | + | 0.468521i | ||||
\(83\) | − | 4.00000i | − | 0.439057i | −0.975606 | − | 0.219529i | \(-0.929548\pi\) | ||
0.975606 | − | 0.219529i | \(-0.0704519\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −4.00000 | −0.431331 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −10.0000 | −1.06000 | −0.529999 | − | 0.847998i | \(-0.677808\pi\) | ||||
−0.529999 | + | 0.847998i | \(0.677808\pi\) | |||||||
\(90\) | −4.24264 | + | 4.24264i | −0.447214 | + | 0.447214i | ||||
\(91\) | 5.65685 | + | 5.65685i | 0.592999 | + | 0.592999i | ||||
\(92\) | −2.82843 | − | 2.82843i | −0.294884 | − | 0.294884i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 5.65685 | + | 5.65685i | 0.580381 | + | 0.580381i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1.41421 | − | 1.41421i | 0.143592 | − | 0.143592i | −0.631657 | − | 0.775248i | \(-0.717625\pi\) |
0.775248 | + | 0.631657i | \(0.217625\pi\) | |||||||
\(98\) | 9.00000 | 0.909137 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 1.00000i | 0.100000i | ||||||||
\(101\) | −10.0000 | −0.995037 | −0.497519 | − | 0.867453i | \(-0.665755\pi\) | ||||
−0.497519 | + | 0.867453i | \(0.665755\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 8.00000 | 0.788263 | 0.394132 | − | 0.919054i | \(-0.371045\pi\) | ||||
0.394132 | + | 0.919054i | \(0.371045\pi\) | |||||||
\(104\) | − | 6.00000i | − | 0.588348i | ||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 6.00000 | 0.582772 | ||||||||
\(107\) | 5.65685 | − | 5.65685i | 0.546869 | − | 0.546869i | −0.378665 | − | 0.925534i | \(-0.623617\pi\) |
0.925534 | + | 0.378665i | \(0.123617\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 4.24264 | + | 4.24264i | 0.406371 | + | 0.406371i | 0.880471 | − | 0.474100i | \(-0.157226\pi\) |
−0.474100 | + | 0.880471i | \(0.657226\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −2.82843 | − | 2.82843i | −0.267261 | − | 0.267261i | ||||
\(113\) | 9.89949 | + | 9.89949i | 0.931266 | + | 0.931266i | 0.997785 | − | 0.0665190i | \(-0.0211893\pi\) |
−0.0665190 | + | 0.997785i | \(0.521189\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 8.00000 | 0.746004 | ||||||||
\(116\) | 4.24264 | − | 4.24264i | 0.393919 | − | 0.393919i | ||||
\(117\) | 6.00000i | 0.554700i | ||||||||
\(118\) | 12.0000 | 1.10469 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | − | 11.0000i | − | 1.00000i | ||||||
\(122\) | −7.07107 | + | 7.07107i | −0.640184 | + | 0.640184i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −2.82843 | + | 2.82843i | −0.254000 | + | 0.254000i | ||||
\(125\) | −8.48528 | − | 8.48528i | −0.758947 | − | 0.758947i | ||||
\(126\) | 8.48528 | + | 8.48528i | 0.755929 | + | 0.755929i | ||||
\(127\) | − | 8.00000i | − | 0.709885i | −0.934888 | − | 0.354943i | \(-0.884500\pi\) | ||
0.934888 | − | 0.354943i | \(-0.115500\pi\) | |||||||
\(128\) | − | 3.00000i | − | 0.265165i | ||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 2.82843 | + | 2.82843i | 0.248069 | + | 0.248069i | ||||
\(131\) | 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 | ||||||||
\(133\) | 11.3137 | − | 11.3137i | 0.981023 | − | 0.981023i | ||||
\(134\) | − | 4.00000i | − | 0.345547i | ||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −6.00000 | −0.512615 | −0.256307 | − | 0.966595i | \(-0.582506\pi\) | ||||
−0.256307 | + | 0.966595i | \(0.582506\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 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 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −2.82843 | − | 2.82843i | −0.237356 | − | 0.237356i | ||||
\(143\) | 0 | 0 | ||||||||
\(144\) | − | 3.00000i | − | 0.250000i | ||||||
\(145\) | 12.0000i | 0.996546i | ||||||||
\(146\) | 4.24264 | + | 4.24264i | 0.351123 | + | 0.351123i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 1.41421 | − | 1.41421i | 0.116248 | − | 0.116248i | ||||
\(149\) | 10.0000 | 0.819232 | 0.409616 | − | 0.912258i | \(-0.365663\pi\) | ||||
0.409616 | + | 0.912258i | \(0.365663\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 16.0000i | − | 1.30206i | −0.759051 | − | 0.651031i | \(-0.774337\pi\) | ||
0.759051 | − | 0.651031i | \(-0.225663\pi\) | |||||||
\(152\) | −12.0000 | −0.973329 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − | 8.00000i | − | 0.642575i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2.00000 | 0.159617 | 0.0798087 | − | 0.996810i | \(-0.474569\pi\) | ||||
0.0798087 | + | 0.996810i | \(0.474569\pi\) | |||||||
\(158\) | −8.48528 | + | 8.48528i | −0.675053 | + | 0.675053i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 7.07107 | + | 7.07107i | 0.559017 | + | 0.559017i | ||||
\(161\) | − | 16.0000i | − | 1.26098i | ||||||
\(162\) | 9.00000i | 0.707107i | ||||||||
\(163\) | 16.9706 | + | 16.9706i | 1.32924 | + | 1.32924i | 0.906036 | + | 0.423201i | \(0.139094\pi\) |
0.423201 | + | 0.906036i | \(0.360906\pi\) | |||||||
\(164\) | −4.24264 | − | 4.24264i | −0.331295 | − | 0.331295i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −4.00000 | −0.310460 | ||||||||
\(167\) | 2.82843 | − | 2.82843i | 0.218870 | − | 0.218870i | −0.589152 | − | 0.808022i | \(-0.700538\pi\) |
0.808022 | + | 0.589152i | \(0.200538\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −9.00000 | −0.692308 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 12.0000 | 0.917663 | ||||||||
\(172\) | − | 4.00000i | − | 0.304997i | ||||||
\(173\) | −15.5563 | + | 15.5563i | −1.18273 | + | 1.18273i | −0.203692 | + | 0.979035i | \(0.565294\pi\) |
−0.979035 | + | 0.203692i | \(0.934706\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −2.82843 | + | 2.82843i | −0.213809 | + | 0.213809i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 10.0000i | 0.749532i | ||||||||
\(179\) | − | 12.0000i | − | 0.896922i | −0.893802 | − | 0.448461i | \(-0.851972\pi\) | ||
0.893802 | − | 0.448461i | \(-0.148028\pi\) | |||||||
\(180\) | −4.24264 | − | 4.24264i | −0.316228 | − | 0.316228i | ||||
\(181\) | 1.41421 | + | 1.41421i | 0.105118 | + | 0.105118i | 0.757710 | − | 0.652592i | \(-0.226318\pi\) |
−0.652592 | + | 0.757710i | \(0.726318\pi\) | |||||||
\(182\) | 5.65685 | − | 5.65685i | 0.419314 | − | 0.419314i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −8.48528 | + | 8.48528i | −0.625543 | + | 0.625543i | ||||
\(185\) | 4.00000i | 0.294086i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 5.65685 | − | 5.65685i | 0.410391 | − | 0.410391i | ||||
\(191\) | 16.0000 | 1.15772 | 0.578860 | − | 0.815427i | \(-0.303498\pi\) | ||||
0.578860 | + | 0.815427i | \(0.303498\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1.41421 | − | 1.41421i | −0.101797 | − | 0.101797i | 0.654374 | − | 0.756171i | \(-0.272932\pi\) |
−0.756171 | + | 0.654374i | \(0.772932\pi\) | |||||||
\(194\) | −1.41421 | − | 1.41421i | −0.101535 | − | 0.101535i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 9.00000i | 0.642857i | ||||||||
\(197\) | −12.7279 | − | 12.7279i | −0.906827 | − | 0.906827i | 0.0891879 | − | 0.996015i | \(-0.471573\pi\) |
−0.996015 | + | 0.0891879i | \(0.971573\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −14.1421 | + | 14.1421i | −1.00251 | + | 1.00251i | −0.00251257 | + | 0.999997i | \(0.500800\pi\) |
−0.999997 | + | 0.00251257i | \(0.999200\pi\) | |||||||
\(200\) | 3.00000 | 0.212132 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 10.0000i | 0.703598i | ||||||||
\(203\) | 24.0000 | 1.68447 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 12.0000 | 0.838116 | ||||||||
\(206\) | − | 8.00000i | − | 0.557386i | ||||||
\(207\) | 8.48528 | − | 8.48528i | 0.589768 | − | 0.589768i | ||||
\(208\) | −2.00000 | −0.138675 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 5.65685 | + | 5.65685i | 0.389434 | + | 0.389434i | 0.874486 | − | 0.485052i | \(-0.161199\pi\) |
−0.485052 | + | 0.874486i | \(0.661199\pi\) | |||||||
\(212\) | 6.00000i | 0.412082i | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −5.65685 | − | 5.65685i | −0.386695 | − | 0.386695i | ||||
\(215\) | 5.65685 | + | 5.65685i | 0.385794 | + | 0.385794i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −16.0000 | −1.08615 | ||||||||
\(218\) | 4.24264 | − | 4.24264i | 0.287348 | − | 0.287348i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 24.0000i | 1.60716i | 0.595198 | + | 0.803579i | \(0.297074\pi\) | ||||
−0.595198 | + | 0.803579i | \(0.702926\pi\) | |||||||
\(224\) | 14.1421 | − | 14.1421i | 0.944911 | − | 0.944911i | ||||
\(225\) | −3.00000 | −0.200000 | ||||||||
\(226\) | 9.89949 | − | 9.89949i | 0.658505 | − | 0.658505i | ||||
\(227\) | 16.9706 | + | 16.9706i | 1.12638 | + | 1.12638i | 0.990762 | + | 0.135614i | \(0.0433007\pi\) |
0.135614 | + | 0.990762i | \(0.456699\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 6.00000i | − | 0.396491i | −0.980152 | − | 0.198246i | \(-0.936476\pi\) | ||
0.980152 | − | 0.198246i | \(-0.0635244\pi\) | |||||||
\(230\) | − | 8.00000i | − | 0.527504i | ||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −12.7279 | − | 12.7279i | −0.835629 | − | 0.835629i | ||||
\(233\) | −4.24264 | + | 4.24264i | −0.277945 | + | 0.277945i | −0.832288 | − | 0.554343i | \(-0.812969\pi\) |
0.554343 | + | 0.832288i | \(0.312969\pi\) | |||||||
\(234\) | 6.00000 | 0.392232 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 12.0000i | 0.781133i | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −16.0000 | −1.03495 | −0.517477 | − | 0.855697i | \(-0.673129\pi\) | ||||
−0.517477 | + | 0.855697i | \(0.673129\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −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 | 0 | ||||||||
\(244\) | −7.07107 | − | 7.07107i | −0.452679 | − | 0.452679i | ||||
\(245\) | −12.7279 | − | 12.7279i | −0.813157 | − | 0.813157i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 8.00000i | − | 0.509028i | ||||||
\(248\) | 8.48528 | + | 8.48528i | 0.538816 | + | 0.538816i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −8.48528 | + | 8.48528i | −0.536656 | + | 0.536656i | ||||
\(251\) | −12.0000 | −0.757433 | −0.378717 | − | 0.925513i | \(-0.623635\pi\) | ||||
−0.378717 | + | 0.925513i | \(0.623635\pi\) | |||||||
\(252\) | −8.48528 | + | 8.48528i | −0.534522 | + | 0.534522i | ||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −8.00000 | −0.501965 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −17.0000 | −1.06250 | ||||||||
\(257\) | 18.0000i | 1.12281i | 0.827541 | + | 0.561405i | \(0.189739\pi\) | ||||
−0.827541 | + | 0.561405i | \(0.810261\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 8.00000 | 0.497096 | ||||||||
\(260\) | −2.82843 | + | 2.82843i | −0.175412 | + | 0.175412i | ||||
\(261\) | 12.7279 | + | 12.7279i | 0.787839 | + | 0.787839i | ||||
\(262\) | −11.3137 | − | 11.3137i | −0.698963 | − | 0.698963i | ||||
\(263\) | 16.0000i | 0.986602i | 0.869859 | + | 0.493301i | \(0.164210\pi\) | ||||
−0.869859 | + | 0.493301i | \(0.835790\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −8.48528 | − | 8.48528i | −0.521247 | − | 0.521247i | ||||
\(266\) | −11.3137 | − | 11.3137i | −0.693688 | − | 0.693688i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 4.00000 | 0.244339 | ||||||||
\(269\) | −15.5563 | + | 15.5563i | −0.948487 | + | 0.948487i | −0.998737 | − | 0.0502494i | \(-0.983998\pi\) |
0.0502494 | + | 0.998737i | \(0.483998\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −16.0000 | −0.971931 | −0.485965 | − | 0.873978i | \(-0.661532\pi\) | ||||
−0.485965 | + | 0.873978i | \(0.661532\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 6.00000i | 0.362473i | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 9.89949 | − | 9.89949i | 0.594803 | − | 0.594803i | −0.344122 | − | 0.938925i | \(-0.611823\pi\) |
0.938925 | + | 0.344122i | \(0.111823\pi\) | |||||||
\(278\) | −5.65685 | − | 5.65685i | −0.339276 | − | 0.339276i | ||||
\(279\) | −8.48528 | − | 8.48528i | −0.508001 | − | 0.508001i | ||||
\(280\) | 24.0000i | 1.43427i | ||||||||
\(281\) | 6.00000i | 0.357930i | 0.983855 | + | 0.178965i | \(0.0572749\pi\) | ||||
−0.983855 | + | 0.178965i | \(0.942725\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 11.3137 | + | 11.3137i | 0.672530 | + | 0.672530i | 0.958299 | − | 0.285769i | \(-0.0922488\pi\) |
−0.285769 | + | 0.958299i | \(0.592249\pi\) | |||||||
\(284\) | 2.82843 | − | 2.82843i | 0.167836 | − | 0.167836i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 24.0000i | − | 1.41668i | ||||||
\(288\) | 15.0000 | 0.883883 | ||||||||
\(289\) | 0 | 0 | ||||||||
\(290\) | 12.0000 | 0.704664 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −4.24264 | + | 4.24264i | −0.248282 | + | 0.248282i | ||||
\(293\) | −6.00000 | −0.350524 | −0.175262 | − | 0.984522i | \(-0.556077\pi\) | ||||
−0.175262 | + | 0.984522i | \(0.556077\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −16.9706 | − | 16.9706i | −0.988064 | − | 0.988064i | ||||
\(296\) | −4.24264 | − | 4.24264i | −0.246598 | − | 0.246598i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | − | 10.0000i | − | 0.579284i | ||||||
\(299\) | −5.65685 | − | 5.65685i | −0.327144 | − | 0.327144i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 11.3137 | − | 11.3137i | 0.652111 | − | 0.652111i | ||||
\(302\) | −16.0000 | −0.920697 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 4.00000i | 0.229416i | ||||||||
\(305\) | 20.0000 | 1.14520 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −12.0000 | −0.684876 | −0.342438 | − | 0.939540i | \(-0.611253\pi\) | ||||
−0.342438 | + | 0.939540i | \(0.611253\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −8.00000 | −0.454369 | ||||||||
\(311\) | 19.7990 | − | 19.7990i | 1.12270 | − | 1.12270i | 0.131363 | − | 0.991334i | \(-0.458065\pi\) |
0.991334 | − | 0.131363i | \(-0.0419355\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −15.5563 | − | 15.5563i | −0.879297 | − | 0.879297i | 0.114165 | − | 0.993462i | \(-0.463581\pi\) |
−0.993462 | + | 0.114165i | \(0.963581\pi\) | |||||||
\(314\) | − | 2.00000i | − | 0.112867i | ||||||
\(315\) | − | 24.0000i | − | 1.35225i | ||||||
\(316\) | −8.48528 | − | 8.48528i | −0.477334 | − | 0.477334i | ||||
\(317\) | 7.07107 | + | 7.07107i | 0.397151 | + | 0.397151i | 0.877227 | − | 0.480076i | \(-0.159391\pi\) |
−0.480076 | + | 0.877227i | \(0.659391\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 9.89949 | − | 9.89949i | 0.553399 | − | 0.553399i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −16.0000 | −0.891645 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | −9.00000 | −0.500000 | ||||||||
\(325\) | 2.00000i | 0.110940i | ||||||||
\(326\) | 16.9706 | − | 16.9706i | 0.939913 | − | 0.939913i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −12.7279 | + | 12.7279i | −0.702782 | + | 0.702782i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 4.00000i | − | 0.219860i | −0.993939 | − | 0.109930i | \(-0.964937\pi\) | ||
0.993939 | − | 0.109930i | \(-0.0350627\pi\) | |||||||
\(332\) | − | 4.00000i | − | 0.219529i | ||||||
\(333\) | 4.24264 | + | 4.24264i | 0.232495 | + | 0.232495i | ||||
\(334\) | −2.82843 | − | 2.82843i | −0.154765 | − | 0.154765i | ||||
\(335\) | −5.65685 | + | 5.65685i | −0.309067 | + | 0.309067i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 9.89949 | − | 9.89949i | 0.539260 | − | 0.539260i | −0.384052 | − | 0.923312i | \(-0.625472\pi\) |
0.923312 | + | 0.384052i | \(0.125472\pi\) | |||||||
\(338\) | 9.00000i | 0.489535i | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | − | 12.0000i | − | 0.648886i | ||||||
\(343\) | −5.65685 | + | 5.65685i | −0.305441 | + | 0.305441i | ||||
\(344\) | −12.0000 | −0.646997 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 15.5563 | + | 15.5563i | 0.836315 | + | 0.836315i | ||||
\(347\) | 22.6274 | + | 22.6274i | 1.21470 | + | 1.21470i | 0.969462 | + | 0.245241i | \(0.0788672\pi\) |
0.245241 | + | 0.969462i | \(0.421133\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 18.0000i | 0.963518i | 0.876304 | + | 0.481759i | \(0.160002\pi\) | ||||
−0.876304 | + | 0.481759i | \(0.839998\pi\) | |||||||
\(350\) | 2.82843 | + | 2.82843i | 0.151186 | + | 0.151186i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 30.0000 | 1.59674 | 0.798369 | − | 0.602168i | \(-0.205696\pi\) | ||||
0.798369 | + | 0.602168i | \(0.205696\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 8.00000i | 0.424596i | ||||||||
\(356\) | −10.0000 | −0.529999 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −12.0000 | −0.634220 | ||||||||
\(359\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(360\) | −12.7279 | + | 12.7279i | −0.670820 | + | 0.670820i | ||||
\(361\) | 3.00000 | 0.157895 | ||||||||
\(362\) | 1.41421 | − | 1.41421i | 0.0743294 | − | 0.0743294i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 5.65685 | + | 5.65685i | 0.296500 | + | 0.296500i | ||||
\(365\) | − | 12.0000i | − | 0.628109i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 19.7990 | + | 19.7990i | 1.03350 | + | 1.03350i | 0.999419 | + | 0.0340797i | \(0.0108500\pi\) |
0.0340797 | + | 0.999419i | \(0.489150\pi\) | |||||||
\(368\) | 2.82843 | + | 2.82843i | 0.147442 | + | 0.147442i | ||||
\(369\) | 12.7279 | − | 12.7279i | 0.662589 | − | 0.662589i | ||||
\(370\) | 4.00000 | 0.207950 | ||||||||
\(371\) | −16.9706 | + | 16.9706i | −0.881068 | + | 0.881068i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 6.00000 | 0.310668 | 0.155334 | − | 0.987862i | \(-0.450355\pi\) | ||||
0.155334 | + | 0.987862i | \(0.450355\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 8.48528 | − | 8.48528i | 0.437014 | − | 0.437014i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −5.65685 | + | 5.65685i | −0.290573 | + | 0.290573i | −0.837307 | − | 0.546734i | \(-0.815871\pi\) |
0.546734 | + | 0.837307i | \(0.315871\pi\) | |||||||
\(380\) | 5.65685 | + | 5.65685i | 0.290191 | + | 0.290191i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | − | 16.0000i | − | 0.818631i | ||||||
\(383\) | 24.0000i | 1.22634i | 0.789950 | + | 0.613171i | \(0.210106\pi\) | ||||
−0.789950 | + | 0.613171i | \(0.789894\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −1.41421 | + | 1.41421i | −0.0719816 | + | 0.0719816i | ||||
\(387\) | 12.0000 | 0.609994 | ||||||||
\(388\) | 1.41421 | − | 1.41421i | 0.0717958 | − | 0.0717958i | ||||
\(389\) | 6.00000i | 0.304212i | 0.988364 | + | 0.152106i | \(0.0486055\pi\) | ||||
−0.988364 | + | 0.152106i | \(0.951394\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 27.0000 | 1.36371 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −12.7279 | + | 12.7279i | −0.641223 | + | 0.641223i | ||||
\(395\) | 24.0000 | 1.20757 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −4.24264 | − | 4.24264i | −0.212932 | − | 0.212932i | 0.592580 | − | 0.805512i | \(-0.298110\pi\) |
−0.805512 | + | 0.592580i | \(0.798110\pi\) | |||||||
\(398\) | 14.1421 | + | 14.1421i | 0.708881 | + | 0.708881i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | − | 1.00000i | − | 0.0500000i | ||||||
\(401\) | −9.89949 | − | 9.89949i | −0.494357 | − | 0.494357i | 0.415319 | − | 0.909676i | \(-0.363670\pi\) |
−0.909676 | + | 0.415319i | \(0.863670\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −5.65685 | + | 5.65685i | −0.281788 | + | 0.281788i | ||||
\(404\) | −10.0000 | −0.497519 | ||||||||
\(405\) | 12.7279 | − | 12.7279i | 0.632456 | − | 0.632456i | ||||
\(406\) | − | 24.0000i | − | 1.19110i | ||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 26.0000 | 1.28562 | 0.642809 | − | 0.766027i | \(-0.277769\pi\) | ||||
0.642809 | + | 0.766027i | \(0.277769\pi\) | |||||||
\(410\) | − | 12.0000i | − | 0.592638i | ||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 8.00000 | 0.394132 | ||||||||
\(413\) | −33.9411 | + | 33.9411i | −1.67013 | + | 1.67013i | ||||
\(414\) | −8.48528 | − | 8.48528i | −0.417029 | − | 0.417029i | ||||
\(415\) | 5.65685 | + | 5.65685i | 0.277684 | + | 0.277684i | ||||
\(416\) | − | 10.0000i | − | 0.490290i | ||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −5.65685 | − | 5.65685i | −0.276355 | − | 0.276355i | 0.555297 | − | 0.831652i | \(-0.312605\pi\) |
−0.831652 | + | 0.555297i | \(0.812605\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −22.0000 | −1.07221 | −0.536107 | − | 0.844150i | \(-0.680106\pi\) | ||||
−0.536107 | + | 0.844150i | \(0.680106\pi\) | |||||||
\(422\) | 5.65685 | − | 5.65685i | 0.275371 | − | 0.275371i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 18.0000 | 0.874157 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 40.0000i | − | 1.93574i | ||||||
\(428\) | 5.65685 | − | 5.65685i | 0.273434 | − | 0.273434i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 5.65685 | − | 5.65685i | 0.272798 | − | 0.272798i | ||||
\(431\) | −8.48528 | − | 8.48528i | −0.408722 | − | 0.408722i | 0.472571 | − | 0.881293i | \(-0.343326\pi\) |
−0.881293 | + | 0.472571i | \(0.843326\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 2.00000i | − | 0.0961139i | −0.998845 | − | 0.0480569i | \(-0.984697\pi\) | ||
0.998845 | − | 0.0480569i | \(-0.0153029\pi\) | |||||||
\(434\) | 16.0000i | 0.768025i | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 4.24264 | + | 4.24264i | 0.203186 | + | 0.203186i | ||||
\(437\) | −11.3137 | + | 11.3137i | −0.541208 | + | 0.541208i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 14.1421 | − | 14.1421i | 0.674967 | − | 0.674967i | −0.283890 | − | 0.958857i | \(-0.591625\pi\) |
0.958857 | + | 0.283890i | \(0.0916249\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −27.0000 | −1.28571 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 28.0000 | 1.33032 | 0.665160 | − | 0.746701i | \(-0.268363\pi\) | ||||
0.665160 | + | 0.746701i | \(0.268363\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 14.1421 | − | 14.1421i | 0.670402 | − | 0.670402i | ||||
\(446\) | 24.0000 | 1.13643 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −19.7990 | − | 19.7990i | −0.935414 | − | 0.935414i | ||||
\(449\) | 24.0416 | + | 24.0416i | 1.13459 | + | 1.13459i | 0.989404 | + | 0.145191i | \(0.0463797\pi\) |
0.145191 | + | 0.989404i | \(0.453620\pi\) | |||||||
\(450\) | 3.00000i | 0.141421i | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 9.89949 | + | 9.89949i | 0.465633 | + | 0.465633i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 16.9706 | − | 16.9706i | 0.796468 | − | 0.796468i | ||||
\(455\) | −16.0000 | −0.750092 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 6.00000i | − | 0.280668i | −0.990104 | − | 0.140334i | \(-0.955182\pi\) | ||
0.990104 | − | 0.140334i | \(-0.0448177\pi\) | |||||||
\(458\) | −6.00000 | −0.280362 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 8.00000 | 0.373002 | ||||||||
\(461\) | − | 2.00000i | − | 0.0931493i | −0.998915 | − | 0.0465746i | \(-0.985169\pi\) | ||
0.998915 | − | 0.0465746i | \(-0.0148305\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −32.0000 | −1.48717 | −0.743583 | − | 0.668644i | \(-0.766875\pi\) | ||||
−0.743583 | + | 0.668644i | \(0.766875\pi\) | |||||||
\(464\) | −4.24264 | + | 4.24264i | −0.196960 | + | 0.196960i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 4.24264 | + | 4.24264i | 0.196537 | + | 0.196537i | ||||
\(467\) | − | 12.0000i | − | 0.555294i | −0.960683 | − | 0.277647i | \(-0.910445\pi\) | ||
0.960683 | − | 0.277647i | \(-0.0895545\pi\) | |||||||
\(468\) | 6.00000i | 0.277350i | ||||||||
\(469\) | 11.3137 | + | 11.3137i | 0.522419 | + | 0.522419i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 36.0000 | 1.65703 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 4.00000 | 0.183533 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −18.0000 | −0.824163 | ||||||||
\(478\) | 16.0000i | 0.731823i | ||||||||
\(479\) | −25.4558 | + | 25.4558i | −1.16311 | + | 1.16311i | −0.179316 | + | 0.983792i | \(0.557388\pi\) |
−0.983792 | + | 0.179316i | \(0.942612\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2.82843 | − | 2.82843i | 0.128965 | − | 0.128965i | ||||
\(482\) | 12.7279 | + | 12.7279i | 0.579741 | + | 0.579741i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | − | 11.0000i | − | 0.500000i | ||||||
\(485\) | 4.00000i | 0.181631i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −14.1421 | − | 14.1421i | −0.640841 | − | 0.640841i | 0.309921 | − | 0.950762i | \(-0.399697\pi\) |
−0.950762 | + | 0.309921i | \(0.899697\pi\) | |||||||
\(488\) | −21.2132 | + | 21.2132i | −0.960277 | + | 0.960277i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −12.7279 | + | 12.7279i | −0.574989 | + | 0.574989i | ||||
\(491\) | 20.0000i | 0.902587i | 0.892375 | + | 0.451294i | \(0.149037\pi\) | ||||
−0.892375 | + | 0.451294i | \(0.850963\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | −8.00000 | −0.359937 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 2.82843 | − | 2.82843i | 0.127000 | − | 0.127000i | ||||
\(497\) | 16.0000 | 0.717698 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 28.2843 | + | 28.2843i | 1.26618 | + | 1.26618i | 0.948047 | + | 0.318131i | \(0.103055\pi\) |
0.318131 | + | 0.948047i | \(0.396945\pi\) | |||||||
\(500\) | −8.48528 | − | 8.48528i | −0.379473 | − | 0.379473i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 12.0000i | 0.535586i | ||||||||
\(503\) | −8.48528 | − | 8.48528i | −0.378340 | − | 0.378340i | 0.492163 | − | 0.870503i | \(-0.336206\pi\) |
−0.870503 | + | 0.492163i | \(0.836206\pi\) | |||||||
\(504\) | 25.4558 | + | 25.4558i | 1.13389 | + | 1.13389i | ||||
\(505\) | 14.1421 | − | 14.1421i | 0.629317 | − | 0.629317i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | − | 8.00000i | − | 0.354943i | ||||||
\(509\) | −2.00000 | −0.0886484 | −0.0443242 | − | 0.999017i | \(-0.514113\pi\) | ||||
−0.0443242 | + | 0.999017i | \(0.514113\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −24.0000 | −1.06170 | ||||||||
\(512\) | 11.0000i | 0.486136i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 18.0000 | 0.793946 | ||||||||
\(515\) | −11.3137 | + | 11.3137i | −0.498542 | + | 0.498542i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | − | 8.00000i | − | 0.351500i | ||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 8.48528 | + | 8.48528i | 0.372104 | + | 0.372104i | ||||
\(521\) | −18.3848 | − | 18.3848i | −0.805452 | − | 0.805452i | 0.178490 | − | 0.983942i | \(-0.442879\pi\) |
−0.983942 | + | 0.178490i | \(0.942879\pi\) | |||||||
\(522\) | 12.7279 | − | 12.7279i | 0.557086 | − | 0.557086i | ||||
\(523\) | 36.0000 | 1.57417 | 0.787085 | − | 0.616844i | \(-0.211589\pi\) | ||||
0.787085 | + | 0.616844i | \(0.211589\pi\) | |||||||
\(524\) | 11.3137 | − | 11.3137i | 0.494242 | − | 0.494242i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 16.0000 | 0.697633 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | − | 7.00000i | − | 0.304348i | ||||||
\(530\) | −8.48528 | + | 8.48528i | −0.368577 | + | 0.368577i | ||||
\(531\) | −36.0000 | −1.56227 | ||||||||
\(532\) | 11.3137 | − | 11.3137i | 0.490511 | − | 0.490511i | ||||
\(533\) | −8.48528 | − | 8.48528i | −0.367538 | − | 0.367538i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 16.0000i | 0.691740i | ||||||||
\(536\) | − | 12.0000i | − | 0.518321i | ||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 15.5563 | + | 15.5563i | 0.670682 | + | 0.670682i | ||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −4.24264 | + | 4.24264i | −0.182405 | + | 0.182405i | −0.792403 | − | 0.609998i | \(-0.791170\pi\) |
0.609998 | + | 0.792403i | \(0.291170\pi\) | |||||||
\(542\) | 16.0000i | 0.687259i | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −12.0000 | −0.514024 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 22.6274 | − | 22.6274i | 0.967478 | − | 0.967478i | −0.0320091 | − | 0.999488i | \(-0.510191\pi\) |
0.999488 | + | 0.0320091i | \(0.0101906\pi\) | |||||||
\(548\) | −6.00000 | −0.256307 | ||||||||
\(549\) | 21.2132 | − | 21.2132i | 0.905357 | − | 0.905357i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −16.9706 | − | 16.9706i | −0.722970 | − | 0.722970i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 48.0000i | − | 2.04117i | ||||||
\(554\) | −9.89949 | − | 9.89949i | −0.420589 | − | 0.420589i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 5.65685 | − | 5.65685i | 0.239904 | − | 0.239904i | ||||
\(557\) | −30.0000 | −1.27114 | −0.635570 | − | 0.772043i | \(-0.719235\pi\) | ||||
−0.635570 | + | 0.772043i | \(0.719235\pi\) | |||||||
\(558\) | −8.48528 | + | 8.48528i | −0.359211 | + | 0.359211i | ||||
\(559\) | − | 8.00000i | − | 0.338364i | ||||||
\(560\) | 8.00000 | 0.338062 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 6.00000 | 0.253095 | ||||||||
\(563\) | − | 4.00000i | − | 0.168580i | −0.996441 | − | 0.0842900i | \(-0.973138\pi\) | ||
0.996441 | − | 0.0842900i | \(-0.0268622\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −28.0000 | −1.17797 | ||||||||
\(566\) | 11.3137 | − | 11.3137i | 0.475551 | − | 0.475551i | ||||
\(567\) | −25.4558 | − | 25.4558i | −1.06904 | − | 1.06904i | ||||
\(568\) | −8.48528 | − | 8.48528i | −0.356034 | − | 0.356034i | ||||
\(569\) | 38.0000i | 1.59304i | 0.604610 | + | 0.796521i | \(0.293329\pi\) | ||||
−0.604610 | + | 0.796521i | \(0.706671\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −22.6274 | − | 22.6274i | −0.946928 | − | 0.946928i | 0.0517330 | − | 0.998661i | \(-0.483526\pi\) |
−0.998661 | + | 0.0517330i | \(0.983526\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −24.0000 | −1.00174 | ||||||||
\(575\) | 2.82843 | − | 2.82843i | 0.117954 | − | 0.117954i | ||||
\(576\) | − | 21.0000i | − | 0.875000i | ||||||
\(577\) | −14.0000 | −0.582828 | −0.291414 | − | 0.956597i | \(-0.594126\pi\) | ||||
−0.291414 | + | 0.956597i | \(0.594126\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 12.0000i | 0.498273i | ||||||||
\(581\) | 11.3137 | − | 11.3137i | 0.469372 | − | 0.469372i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 12.7279 | + | 12.7279i | 0.526685 | + | 0.526685i | ||||
\(585\) | −8.48528 | − | 8.48528i | −0.350823 | − | 0.350823i | ||||
\(586\) | 6.00000i | 0.247858i | ||||||||
\(587\) | − | 4.00000i | − | 0.165098i | −0.996587 | − | 0.0825488i | \(-0.973694\pi\) | ||
0.996587 | − | 0.0825488i | \(-0.0263060\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 11.3137 | + | 11.3137i | 0.466173 | + | 0.466173i | ||||
\(590\) | −16.9706 | + | 16.9706i | −0.698667 | + | 0.698667i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −1.41421 | + | 1.41421i | −0.0581238 | + | 0.0581238i | ||||
\(593\) | 18.0000i | 0.739171i | 0.929197 | + | 0.369586i | \(0.120500\pi\) | ||||
−0.929197 | + | 0.369586i | \(0.879500\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 10.0000 | 0.409616 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −5.65685 | + | 5.65685i | −0.231326 | + | 0.231326i | ||||
\(599\) | 24.0000 | 0.980613 | 0.490307 | − | 0.871550i | \(-0.336885\pi\) | ||||
0.490307 | + | 0.871550i | \(0.336885\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −7.07107 | − | 7.07107i | −0.288435 | − | 0.288435i | 0.548026 | − | 0.836461i | \(-0.315379\pi\) |
−0.836461 | + | 0.548026i | \(0.815379\pi\) | |||||||
\(602\) | −11.3137 | − | 11.3137i | −0.461112 | − | 0.461112i | ||||
\(603\) | 12.0000i | 0.488678i | ||||||||
\(604\) | − | 16.0000i | − | 0.651031i | ||||||
\(605\) | 15.5563 | + | 15.5563i | 0.632456 | + | 0.632456i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 14.1421 | − | 14.1421i | 0.574012 | − | 0.574012i | −0.359235 | − | 0.933247i | \(-0.616962\pi\) |
0.933247 | + | 0.359235i | \(0.116962\pi\) | |||||||
\(608\) | −20.0000 | −0.811107 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | − | 20.0000i | − | 0.809776i | ||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −26.0000 | −1.05013 | −0.525065 | − | 0.851062i | \(-0.675959\pi\) | ||||
−0.525065 | + | 0.851062i | \(0.675959\pi\) | |||||||
\(614\) | 12.0000i | 0.484281i | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −4.24264 | + | 4.24264i | −0.170802 | + | 0.170802i | −0.787332 | − | 0.616530i | \(-0.788538\pi\) |
0.616530 | + | 0.787332i | \(0.288538\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −33.9411 | − | 33.9411i | −1.36421 | − | 1.36421i | −0.868474 | − | 0.495735i | \(-0.834899\pi\) |
−0.495735 | − | 0.868474i | \(-0.665101\pi\) | |||||||
\(620\) | − | 8.00000i | − | 0.321288i | ||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −19.7990 | − | 19.7990i | −0.793867 | − | 0.793867i | ||||
\(623\) | −28.2843 | − | 28.2843i | −1.13319 | − | 1.13319i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 19.0000 | 0.760000 | ||||||||
\(626\) | −15.5563 | + | 15.5563i | −0.621757 | + | 0.621757i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 2.00000 | 0.0798087 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | −24.0000 | −0.956183 | ||||||||
\(631\) | 16.0000i | 0.636950i | 0.947931 | + | 0.318475i | \(0.103171\pi\) | ||||
−0.947931 | + | 0.318475i | \(0.896829\pi\) | |||||||
\(632\) | −25.4558 | + | 25.4558i | −1.01258 | + | 1.01258i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 7.07107 | − | 7.07107i | 0.280828 | − | 0.280828i | ||||
\(635\) | 11.3137 | + | 11.3137i | 0.448971 | + | 0.448971i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 18.0000i | 0.713186i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 8.48528 | + | 8.48528i | 0.335673 | + | 0.335673i | ||||
\(640\) | 4.24264 | + | 4.24264i | 0.167705 | + | 0.167705i | ||||
\(641\) | −21.2132 | + | 21.2132i | −0.837871 | + | 0.837871i | −0.988578 | − | 0.150707i | \(-0.951845\pi\) |
0.150707 | + | 0.988578i | \(0.451845\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −22.6274 | + | 22.6274i | −0.892338 | + | 0.892338i | −0.994743 | − | 0.102405i | \(-0.967346\pi\) |
0.102405 | + | 0.994743i | \(0.467346\pi\) | |||||||
\(644\) | − | 16.0000i | − | 0.630488i | ||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 8.00000 | 0.314512 | 0.157256 | − | 0.987558i | \(-0.449735\pi\) | ||||
0.157256 | + | 0.987558i | \(0.449735\pi\) | |||||||
\(648\) | 27.0000i | 1.06066i | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 2.00000 | 0.0784465 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 16.9706 | + | 16.9706i | 0.664619 | + | 0.664619i | ||||
\(653\) | 4.24264 | + | 4.24264i | 0.166027 | + | 0.166027i | 0.785231 | − | 0.619203i | \(-0.212544\pi\) |
−0.619203 | + | 0.785231i | \(0.712544\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 32.0000i | 1.25034i | ||||||||
\(656\) | 4.24264 | + | 4.24264i | 0.165647 | + | 0.165647i | ||||
\(657\) | −12.7279 | − | 12.7279i | −0.496564 | − | 0.496564i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −4.00000 | −0.155818 | −0.0779089 | − | 0.996960i | \(-0.524824\pi\) | ||||
−0.0779089 | + | 0.996960i | \(0.524824\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 38.0000i | 1.47803i | 0.673690 | + | 0.739014i | \(0.264708\pi\) | ||||
−0.673690 | + | 0.739014i | \(0.735292\pi\) | |||||||
\(662\) | −4.00000 | −0.155464 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −12.0000 | −0.465690 | ||||||||
\(665\) | 32.0000i | 1.24091i | ||||||||
\(666\) | 4.24264 | − | 4.24264i | 0.164399 | − | 0.164399i | ||||
\(667\) | −24.0000 | −0.929284 | ||||||||
\(668\) | 2.82843 | − | 2.82843i | 0.109435 | − | 0.109435i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 5.65685 | + | 5.65685i | 0.218543 | + | 0.218543i | ||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1.41421 | + | 1.41421i | 0.0545139 | + | 0.0545139i | 0.733838 | − | 0.679324i | \(-0.237727\pi\) |
−0.679324 | + | 0.733838i | \(0.737727\pi\) | |||||||
\(674\) | −9.89949 | − | 9.89949i | −0.381314 | − | 0.381314i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −9.00000 | −0.346154 | ||||||||
\(677\) | −21.2132 | + | 21.2132i | −0.815290 | + | 0.815290i | −0.985421 | − | 0.170132i | \(-0.945581\pi\) |
0.170132 | + | 0.985421i | \(0.445581\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 8.00000 | 0.307012 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 28.2843 | − | 28.2843i | 1.08227 | − | 1.08227i | 0.0859698 | − | 0.996298i | \(-0.472601\pi\) |
0.996298 | − | 0.0859698i | \(-0.0273989\pi\) | |||||||
\(684\) | 12.0000 | 0.458831 | ||||||||
\(685\) | 8.48528 | − | 8.48528i | 0.324206 | − | 0.324206i | ||||
\(686\) | 5.65685 | + | 5.65685i | 0.215980 | + | 0.215980i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 4.00000i | 0.152499i | ||||||||
\(689\) | 12.0000i | 0.457164i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 5.65685 | + | 5.65685i | 0.215197 | + | 0.215197i | 0.806471 | − | 0.591274i | \(-0.201375\pi\) |
−0.591274 | + | 0.806471i | \(0.701375\pi\) | |||||||
\(692\) | −15.5563 | + | 15.5563i | −0.591364 | + | 0.591364i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 22.6274 | − | 22.6274i | 0.858925 | − | 0.858925i | ||||
\(695\) | 16.0000i | 0.606915i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 18.0000 | 0.681310 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −2.82843 | + | 2.82843i | −0.106904 | + | 0.106904i | ||||
\(701\) | 18.0000 | 0.679851 | 0.339925 | − | 0.940452i | \(-0.389598\pi\) | ||||
0.339925 | + | 0.940452i | \(0.389598\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −5.65685 | − | 5.65685i | −0.213352 | − | 0.213352i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | − | 30.0000i | − | 1.12906i | ||||||
\(707\) | −28.2843 | − | 28.2843i | −1.06374 | − | 1.06374i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −24.0416 | + | 24.0416i | −0.902902 | + | 0.902902i | −0.995686 | − | 0.0927839i | \(-0.970423\pi\) |
0.0927839 | + | 0.995686i | \(0.470423\pi\) | |||||||
\(710\) | 8.00000 | 0.300235 | ||||||||
\(711\) | 25.4558 | − | 25.4558i | 0.954669 | − | 0.954669i | ||||
\(712\) | 30.0000i | 1.12430i | ||||||||
\(713\) | 16.0000 | 0.599205 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | − | 12.0000i | − | 0.448461i | ||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 2.82843 | − | 2.82843i | 0.105483 | − | 0.105483i | −0.652396 | − | 0.757878i | \(-0.726236\pi\) |
0.757878 | + | 0.652396i | \(0.226236\pi\) | |||||||
\(720\) | 4.24264 | + | 4.24264i | 0.158114 | + | 0.158114i | ||||
\(721\) | 22.6274 | + | 22.6274i | 0.842689 | + | 0.842689i | ||||
\(722\) | − | 3.00000i | − | 0.111648i | ||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 1.41421 | + | 1.41421i | 0.0525588 | + | 0.0525588i | ||||
\(725\) | 4.24264 | + | 4.24264i | 0.157568 | + | 0.157568i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −40.0000 | −1.48352 | −0.741759 | − | 0.670667i | \(-0.766008\pi\) | ||||
−0.741759 | + | 0.670667i | \(0.766008\pi\) | |||||||
\(728\) | 16.9706 | − | 16.9706i | 0.628971 | − | 0.628971i | ||||
\(729\) | − | 27.0000i | − | 1.00000i | ||||||
\(730\) | −12.0000 | −0.444140 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 50.0000i | − | 1.84679i | −0.383849 | − | 0.923396i | \(-0.625402\pi\) | ||
0.383849 | − | 0.923396i | \(-0.374598\pi\) | |||||||
\(734\) | 19.7990 | − | 19.7990i | 0.730794 | − | 0.730794i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −14.1421 | + | 14.1421i | −0.521286 | + | 0.521286i | ||||
\(737\) | 0 | 0 | ||||||||
\(738\) | −12.7279 | − | 12.7279i | −0.468521 | − | 0.468521i | ||||
\(739\) | − | 28.0000i | − | 1.03000i | −0.857191 | − | 0.514998i | \(-0.827793\pi\) | ||
0.857191 | − | 0.514998i | \(-0.172207\pi\) | |||||||
\(740\) | 4.00000i | 0.147043i | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 16.9706 | + | 16.9706i | 0.623009 | + | 0.623009i | ||||
\(743\) | 8.48528 | − | 8.48528i | 0.311295 | − | 0.311295i | −0.534116 | − | 0.845411i | \(-0.679356\pi\) |
0.845411 | + | 0.534116i | \(0.179356\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −14.1421 | + | 14.1421i | −0.518128 | + | 0.518128i | ||||
\(746\) | − | 6.00000i | − | 0.219676i | ||||||
\(747\) | 12.0000 | 0.439057 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 32.0000 | 1.16925 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −14.1421 | + | 14.1421i | −0.516054 | + | 0.516054i | −0.916375 | − | 0.400321i | \(-0.868899\pi\) |
0.400321 | + | 0.916375i | \(0.368899\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −8.48528 | − | 8.48528i | −0.309016 | − | 0.309016i | ||||
\(755\) | 22.6274 | + | 22.6274i | 0.823496 | + | 0.823496i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 22.0000i | − | 0.799604i | −0.916602 | − | 0.399802i | \(-0.869079\pi\) | ||
0.916602 | − | 0.399802i | \(-0.130921\pi\) | |||||||
\(758\) | 5.65685 | + | 5.65685i | 0.205466 | + | 0.205466i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 16.9706 | − | 16.9706i | 0.615587 | − | 0.615587i | ||||
\(761\) | 22.0000 | 0.797499 | 0.398750 | − | 0.917060i | \(-0.369444\pi\) | ||||
0.398750 | + | 0.917060i | \(0.369444\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 24.0000i | 0.868858i | ||||||||
\(764\) | 16.0000 | 0.578860 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 24.0000 | 0.867155 | ||||||||
\(767\) | 24.0000i | 0.866590i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 14.0000 | 0.504853 | 0.252426 | − | 0.967616i | \(-0.418771\pi\) | ||||
0.252426 | + | 0.967616i | \(0.418771\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −1.41421 | − | 1.41421i | −0.0508987 | − | 0.0508987i | ||||
\(773\) | 26.0000i | 0.935155i | 0.883952 | + | 0.467578i | \(0.154873\pi\) | ||||
−0.883952 | + | 0.467578i | \(0.845127\pi\) | |||||||
\(774\) | − | 12.0000i | − | 0.431331i | ||||||
\(775\) | −2.82843 | − | 2.82843i | −0.101600 | − | 0.101600i | ||||
\(776\) | −4.24264 | − | 4.24264i | −0.152302 | − | 0.152302i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 6.00000 | 0.215110 | ||||||||
\(779\) | −16.9706 | + | 16.9706i | −0.608034 | + | 0.608034i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | − | 9.00000i | − | 0.321429i | ||||||
\(785\) | −2.82843 | + | 2.82843i | −0.100951 | + | 0.100951i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −22.6274 | + | 22.6274i | −0.806580 | + | 0.806580i | −0.984115 | − | 0.177534i | \(-0.943188\pi\) |
0.177534 | + | 0.984115i | \(0.443188\pi\) | |||||||
\(788\) | −12.7279 | − | 12.7279i | −0.453413 | − | 0.453413i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | − | 24.0000i | − | 0.853882i | ||||||
\(791\) | 56.0000i | 1.99113i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −14.1421 | − | 14.1421i | −0.502202 | − | 0.502202i | ||||
\(794\) | −4.24264 | + | 4.24264i | −0.150566 | + | 0.150566i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −14.1421 | + | 14.1421i | −0.501255 | + | 0.501255i | ||||
\(797\) | − | 50.0000i | − | 1.77109i | −0.464553 | − | 0.885545i | \(-0.653785\pi\) | ||
0.464553 | − | 0.885545i | \(-0.346215\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 5.00000 | 0.176777 | ||||||||
\(801\) | − | 30.0000i | − | 1.06000i | ||||||
\(802\) | −9.89949 | + | 9.89949i | −0.349563 | + | 0.349563i | ||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 22.6274 | + | 22.6274i | 0.797512 | + | 0.797512i | ||||
\(806\) | 5.65685 | + | 5.65685i | 0.199254 | + | 0.199254i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 30.0000i | 1.05540i | ||||||||
\(809\) | 18.3848 | + | 18.3848i | 0.646374 | + | 0.646374i | 0.952115 | − | 0.305741i | \(-0.0989040\pi\) |
−0.305741 | + | 0.952115i | \(0.598904\pi\) | |||||||
\(810\) | −12.7279 | − | 12.7279i | −0.447214 | − | 0.447214i | ||||
\(811\) | 28.2843 | − | 28.2843i | 0.993195 | − | 0.993195i | −0.00678191 | − | 0.999977i | \(-0.502159\pi\) |
0.999977 | + | 0.00678191i | \(0.00215876\pi\) | |||||||
\(812\) | 24.0000 | 0.842235 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −48.0000 | −1.68137 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −16.0000 | −0.559769 | ||||||||
\(818\) | − | 26.0000i | − | 0.909069i | ||||||
\(819\) | −16.9706 | + | 16.9706i | −0.592999 | + | 0.592999i | ||||
\(820\) | 12.0000 | 0.419058 | ||||||||
\(821\) | −12.7279 | + | 12.7279i | −0.444208 | + | 0.444208i | −0.893423 | − | 0.449216i | \(-0.851703\pi\) |
0.449216 | + | 0.893423i | \(0.351703\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 14.1421 | + | 14.1421i | 0.492964 | + | 0.492964i | 0.909239 | − | 0.416275i | \(-0.136665\pi\) |
−0.416275 | + | 0.909239i | \(0.636665\pi\) | |||||||
\(824\) | − | 24.0000i | − | 0.836080i | ||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 33.9411 | + | 33.9411i | 1.18096 | + | 1.18096i | ||||
\(827\) | 33.9411 | + | 33.9411i | 1.18025 | + | 1.18025i | 0.979680 | + | 0.200569i | \(0.0642791\pi\) |
0.200569 | + | 0.979680i | \(0.435721\pi\) | |||||||
\(828\) | 8.48528 | − | 8.48528i | 0.294884 | − | 0.294884i | ||||
\(829\) | 34.0000 | 1.18087 | 0.590434 | − | 0.807086i | \(-0.298956\pi\) | ||||
0.590434 | + | 0.807086i | \(0.298956\pi\) | |||||||
\(830\) | 5.65685 | − | 5.65685i | 0.196352 | − | 0.196352i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −14.0000 | −0.485363 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 8.00000i | 0.276851i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −5.65685 | + | 5.65685i | −0.195413 | + | 0.195413i | ||||
\(839\) | −14.1421 | − | 14.1421i | −0.488241 | − | 0.488241i | 0.419510 | − | 0.907751i | \(-0.362202\pi\) |
−0.907751 | + | 0.419510i | \(0.862202\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | − | 7.00000i | − | 0.241379i | ||||||
\(842\) | 22.0000i | 0.758170i | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 5.65685 | + | 5.65685i | 0.194717 | + | 0.194717i | ||||
\(845\) | 12.7279 | − | 12.7279i | 0.437854 | − | 0.437854i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 31.1127 | − | 31.1127i | 1.06904 | − | 1.06904i | ||||
\(848\) | − | 6.00000i | − | 0.206041i | ||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −8.00000 | −0.274236 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −9.89949 | + | 9.89949i | −0.338952 | + | 0.338952i | −0.855973 | − | 0.517021i | \(-0.827041\pi\) |
0.517021 | + | 0.855973i | \(0.327041\pi\) | |||||||
\(854\) | −40.0000 | −1.36877 | ||||||||
\(855\) | −16.9706 | + | 16.9706i | −0.580381 | + | 0.580381i | ||||
\(856\) | −16.9706 | − | 16.9706i | −0.580042 | − | 0.580042i | ||||
\(857\) | 7.07107 | + | 7.07107i | 0.241543 | + | 0.241543i | 0.817488 | − | 0.575945i | \(-0.195366\pi\) |
−0.575945 | + | 0.817488i | \(0.695366\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 52.0000i | − | 1.77422i | −0.461561 | − | 0.887109i | \(-0.652710\pi\) | ||
0.461561 | − | 0.887109i | \(-0.347290\pi\) | |||||||
\(860\) | 5.65685 | + | 5.65685i | 0.192897 | + | 0.192897i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −8.48528 | + | 8.48528i | −0.289010 | + | 0.289010i | ||||
\(863\) | −16.0000 | −0.544646 | −0.272323 | − | 0.962206i | \(-0.587792\pi\) | ||||
−0.272323 | + | 0.962206i | \(0.587792\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | − | 44.0000i | − | 1.49604i | ||||||
\(866\) | −2.00000 | −0.0679628 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −16.0000 | −0.543075 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 8.00000 | 0.271070 | ||||||||
\(872\) | 12.7279 | − | 12.7279i | 0.431022 | − | 0.431022i | ||||
\(873\) | 4.24264 | + | 4.24264i | 0.143592 | + | 0.143592i | ||||
\(874\) | 11.3137 | + | 11.3137i | 0.382692 | + | 0.382692i | ||||
\(875\) | − | 48.0000i | − | 1.62270i | ||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 4.24264 | + | 4.24264i | 0.143264 | + | 0.143264i | 0.775101 | − | 0.631837i | \(-0.217699\pi\) |
−0.631837 | + | 0.775101i | \(0.717699\pi\) | |||||||
\(878\) | −14.1421 | − | 14.1421i | −0.477274 | − | 0.477274i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 32.5269 | − | 32.5269i | 1.09586 | − | 1.09586i | 0.100970 | − | 0.994889i | \(-0.467805\pi\) |
0.994889 | − | 0.100970i | \(-0.0321946\pi\) | |||||||
\(882\) | 27.0000i | 0.909137i | ||||||||
\(883\) | −12.0000 | −0.403832 | −0.201916 | − | 0.979403i | \(-0.564717\pi\) | ||||
−0.201916 | + | 0.979403i | \(0.564717\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | − | 28.0000i | − | 0.940678i | ||||||
\(887\) | −8.48528 | + | 8.48528i | −0.284908 | + | 0.284908i | −0.835063 | − | 0.550155i | \(-0.814569\pi\) |
0.550155 | + | 0.835063i | \(0.314569\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 22.6274 | − | 22.6274i | 0.758899 | − | 0.758899i | ||||
\(890\) | −14.1421 | − | 14.1421i | −0.474045 | − | 0.474045i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 24.0000i | 0.803579i | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 16.9706 | + | 16.9706i | 0.567263 | + | 0.567263i | ||||
\(896\) | 8.48528 | − | 8.48528i | 0.283473 | − | 0.283473i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 24.0416 | − | 24.0416i | 0.802280 | − | 0.802280i | ||||
\(899\) | 24.0000i | 0.800445i | ||||||||
\(900\) | −3.00000 | −0.100000 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 29.6985 | − | 29.6985i | 0.987757 | − | 0.987757i | ||||
\(905\) | −4.00000 | −0.132964 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −22.6274 | − | 22.6274i | −0.751331 | − | 0.751331i | 0.223397 | − | 0.974728i | \(-0.428286\pi\) |
−0.974728 | + | 0.223397i | \(0.928286\pi\) | |||||||
\(908\) | 16.9706 | + | 16.9706i | 0.563188 | + | 0.563188i | ||||
\(909\) | − | 30.0000i | − | 0.995037i | ||||||
\(910\) | 16.0000i | 0.530395i | ||||||||
\(911\) | −2.82843 | − | 2.82843i | −0.0937100 | − | 0.0937100i | 0.658698 | − | 0.752408i | \(-0.271108\pi\) |
−0.752408 | + | 0.658698i | \(0.771108\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | −6.00000 | −0.198462 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | − | 6.00000i | − | 0.198246i | ||||||
\(917\) | 64.0000 | 2.11347 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 24.0000 | 0.791687 | 0.395843 | − | 0.918318i | \(-0.370452\pi\) | ||||
0.395843 | + | 0.918318i | \(0.370452\pi\) | |||||||
\(920\) | − | 24.0000i | − | 0.791257i | ||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −2.00000 | −0.0658665 | ||||||||
\(923\) | 5.65685 | − | 5.65685i | 0.186198 | − | 0.186198i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.41421 | + | 1.41421i | 0.0464991 | + | 0.0464991i | ||||
\(926\) | 32.0000i | 1.05159i | ||||||||
\(927\) | 24.0000i | 0.788263i | ||||||||
\(928\) | −21.2132 | − | 21.2132i | −0.696358 | − | 0.696358i | ||||
\(929\) | 21.2132 | + | 21.2132i | 0.695983 | + | 0.695983i | 0.963542 | − | 0.267559i | \(-0.0862170\pi\) |
−0.267559 | + | 0.963542i | \(0.586217\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 36.0000 | 1.17985 | ||||||||
\(932\) | −4.24264 | + | 4.24264i | −0.138972 | + | 0.138972i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −12.0000 | −0.392652 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 18.0000 | 0.588348 | ||||||||
\(937\) | 10.0000i | 0.326686i | 0.986569 | + | 0.163343i | \(0.0522277\pi\) | ||||
−0.986569 | + | 0.163343i | \(0.947772\pi\) | |||||||
\(938\) | 11.3137 | − | 11.3137i | 0.369406 | − | 0.369406i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −4.24264 | − | 4.24264i | −0.138306 | − | 0.138306i | 0.634564 | − | 0.772870i | \(-0.281180\pi\) |
−0.772870 | + | 0.634564i | \(0.781180\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 24.0000i | 0.781548i | ||||||||
\(944\) | − | 12.0000i | − | 0.390567i | ||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 22.6274 | − | 22.6274i | 0.735292 | − | 0.735292i | −0.236371 | − | 0.971663i | \(-0.575958\pi\) |
0.971663 | + | 0.236371i | \(0.0759580\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −8.48528 | + | 8.48528i | −0.275444 | + | 0.275444i | ||||
\(950\) | − | 4.00000i | − | 0.129777i | ||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −22.0000 | −0.712650 | −0.356325 | − | 0.934362i | \(-0.615970\pi\) | ||||
−0.356325 | + | 0.934362i | \(0.615970\pi\) | |||||||
\(954\) | 18.0000i | 0.582772i | ||||||||
\(955\) | −22.6274 | + | 22.6274i | −0.732206 | + | 0.732206i | ||||
\(956\) | −16.0000 | −0.517477 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 25.4558 | + | 25.4558i | 0.822441 | + | 0.822441i | ||||
\(959\) | −16.9706 | − | 16.9706i | −0.548008 | − | 0.548008i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 15.0000i | 0.483871i | ||||||||
\(962\) | −2.82843 | − | 2.82843i | −0.0911922 | − | 0.0911922i | ||||
\(963\) | 16.9706 | + | 16.9706i | 0.546869 | + | 0.546869i | ||||
\(964\) | −12.7279 | + | 12.7279i | −0.409939 | + | 0.409939i | ||||
\(965\) | 4.00000 | 0.128765 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(968\) | −33.0000 | −1.06066 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 4.00000 | 0.128432 | ||||||||
\(971\) | − | 12.0000i | − | 0.385098i | −0.981287 | − | 0.192549i | \(-0.938325\pi\) | ||
0.981287 | − | 0.192549i | \(-0.0616755\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 32.0000 | 1.02587 | ||||||||
\(974\) | −14.1421 | + | 14.1421i | −0.453143 | + | 0.453143i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 7.07107 | + | 7.07107i | 0.226339 | + | 0.226339i | ||||
\(977\) | − | 18.0000i | − | 0.575871i | −0.957650 | − | 0.287936i | \(-0.907031\pi\) | ||
0.957650 | − | 0.287936i | \(-0.0929689\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | −12.7279 | − | 12.7279i | −0.406579 | − | 0.406579i | ||||
\(981\) | −12.7279 | + | 12.7279i | −0.406371 | + | 0.406371i | ||||
\(982\) | 20.0000 | 0.638226 | ||||||||
\(983\) | −8.48528 | + | 8.48528i | −0.270638 | + | 0.270638i | −0.829357 | − | 0.558719i | \(-0.811293\pi\) |
0.558719 | + | 0.829357i | \(0.311293\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 36.0000 | 1.14706 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | − | 8.00000i | − | 0.254514i | ||||||
\(989\) | −11.3137 | + | 11.3137i | −0.359755 | + | 0.359755i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −8.48528 | + | 8.48528i | −0.269544 | + | 0.269544i | −0.828916 | − | 0.559373i | \(-0.811042\pi\) |
0.559373 | + | 0.828916i | \(0.311042\pi\) | |||||||
\(992\) | 14.1421 | + | 14.1421i | 0.449013 | + | 0.449013i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | − | 16.0000i | − | 0.507489i | ||||||
\(995\) | − | 40.0000i | − | 1.26809i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −32.5269 | − | 32.5269i | −1.03014 | − | 1.03014i | −0.999532 | − | 0.0306061i | \(-0.990256\pi\) |
−0.0306061 | − | 0.999532i | \(-0.509744\pi\) | |||||||
\(998\) | 28.2843 | − | 28.2843i | 0.895323 | − | 0.895323i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))