Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1305,2,Mod(289,1305)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1305, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1305.289");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1305 = 3^{2} \cdot 5 \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1305.f (of order \(2\), degree \(1\), 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: | \(10.4204774638\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(i)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 435) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 289.2 | ||
Root | \(-1.00000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1305.289 |
Dual form | 1305.2.f.d.289.1 |
$q$-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 \(\left(\mathbb{Z}/1305\mathbb{Z}\right)^\times\).
\(n\) | \(146\) | \(262\) | \(901\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.00000 | 1.41421 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 2.00000 | 1.00000 | ||||||||
\(5\) | −2.00000 | + | 1.00000i | −0.894427 | + | 0.447214i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 4.00000i | − | 1.51186i | −0.654654 | − | 0.755929i | \(-0.727186\pi\) | ||
0.654654 | − | 0.755929i | \(-0.272814\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −4.00000 | + | 2.00000i | −1.26491 | + | 0.632456i | ||||
\(11\) | 1.00000i | 0.301511i | 0.988571 | + | 0.150756i | \(0.0481707\pi\) | ||||
−0.988571 | + | 0.150756i | \(0.951829\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 2.00000i | − | 0.554700i | −0.960769 | − | 0.277350i | \(-0.910544\pi\) | ||
0.960769 | − | 0.277350i | \(-0.0894562\pi\) | |||||||
\(14\) | − | 8.00000i | − | 2.13809i | ||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −4.00000 | −1.00000 | ||||||||
\(17\) | 6.00000 | 1.45521 | 0.727607 | − | 0.685994i | \(-0.240633\pi\) | ||||
0.727607 | + | 0.685994i | \(0.240633\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 4.00000i | − | 0.917663i | −0.888523 | − | 0.458831i | \(-0.848268\pi\) | ||
0.888523 | − | 0.458831i | \(-0.151732\pi\) | |||||||
\(20\) | −4.00000 | + | 2.00000i | −0.894427 | + | 0.447214i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 2.00000i | 0.426401i | ||||||||
\(23\) | − | 9.00000i | − | 1.87663i | −0.345782 | − | 0.938315i | \(-0.612386\pi\) | ||
0.345782 | − | 0.938315i | \(-0.387614\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 3.00000 | − | 4.00000i | 0.600000 | − | 0.800000i | ||||
\(26\) | − | 4.00000i | − | 0.784465i | ||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | − | 8.00000i | − | 1.51186i | ||||||
\(29\) | 2.00000 | − | 5.00000i | 0.371391 | − | 0.928477i | ||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 2.00000i | − | 0.359211i | −0.983739 | − | 0.179605i | \(-0.942518\pi\) | ||
0.983739 | − | 0.179605i | \(-0.0574821\pi\) | |||||||
\(32\) | −8.00000 | −1.41421 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 12.0000 | 2.05798 | ||||||||
\(35\) | 4.00000 | + | 8.00000i | 0.676123 | + | 1.35225i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.00000 | −0.164399 | −0.0821995 | − | 0.996616i | \(-0.526194\pi\) | ||||
−0.0821995 | + | 0.996616i | \(0.526194\pi\) | |||||||
\(38\) | − | 8.00000i | − | 1.29777i | ||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 9.00000i | 1.40556i | 0.711405 | + | 0.702782i | \(0.248059\pi\) | ||||
−0.711405 | + | 0.702782i | \(0.751941\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.00000 | −0.152499 | −0.0762493 | − | 0.997089i | \(-0.524294\pi\) | ||||
−0.0762493 | + | 0.997089i | \(0.524294\pi\) | |||||||
\(44\) | 2.00000i | 0.301511i | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | − | 18.0000i | − | 2.65396i | ||||||
\(47\) | −8.00000 | −1.16692 | −0.583460 | − | 0.812142i | \(-0.698301\pi\) | ||||
−0.583460 | + | 0.812142i | \(0.698301\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −9.00000 | −1.28571 | ||||||||
\(50\) | 6.00000 | − | 8.00000i | 0.848528 | − | 1.13137i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | − | 4.00000i | − | 0.554700i | ||||||
\(53\) | 9.00000i | 1.23625i | 0.786082 | + | 0.618123i | \(0.212106\pi\) | ||||
−0.786082 | + | 0.618123i | \(0.787894\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.00000 | − | 2.00000i | −0.134840 | − | 0.269680i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 4.00000 | − | 10.0000i | 0.525226 | − | 1.31306i | ||||
\(59\) | −8.00000 | −1.04151 | −0.520756 | − | 0.853706i | \(-0.674350\pi\) | ||||
−0.520756 | + | 0.853706i | \(0.674350\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 6.00000i | − | 0.768221i | −0.923287 | − | 0.384111i | \(-0.874508\pi\) | ||
0.923287 | − | 0.384111i | \(-0.125492\pi\) | |||||||
\(62\) | − | 4.00000i | − | 0.508001i | ||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −8.00000 | −1.00000 | ||||||||
\(65\) | 2.00000 | + | 4.00000i | 0.248069 | + | 0.496139i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 12.0000i | 1.46603i | 0.680211 | + | 0.733017i | \(0.261888\pi\) | ||||
−0.680211 | + | 0.733017i | \(0.738112\pi\) | |||||||
\(68\) | 12.0000 | 1.45521 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 8.00000 | + | 16.0000i | 0.956183 | + | 1.91237i | ||||
\(71\) | −2.00000 | −0.237356 | −0.118678 | − | 0.992933i | \(-0.537866\pi\) | ||||
−0.118678 | + | 0.992933i | \(0.537866\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 15.0000 | 1.75562 | 0.877809 | − | 0.479012i | \(-0.159005\pi\) | ||||
0.877809 | + | 0.479012i | \(0.159005\pi\) | |||||||
\(74\) | −2.00000 | −0.232495 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | − | 8.00000i | − | 0.917663i | ||||||
\(77\) | 4.00000 | 0.455842 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 4.00000i | 0.450035i | 0.974355 | + | 0.225018i | \(0.0722440\pi\) | ||||
−0.974355 | + | 0.225018i | \(0.927756\pi\) | |||||||
\(80\) | 8.00000 | − | 4.00000i | 0.894427 | − | 0.447214i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 18.0000i | 1.98777i | ||||||||
\(83\) | − | 7.00000i | − | 0.768350i | −0.923260 | − | 0.384175i | \(-0.874486\pi\) | ||
0.923260 | − | 0.384175i | \(-0.125514\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −12.0000 | + | 6.00000i | −1.30158 | + | 0.650791i | ||||
\(86\) | −2.00000 | −0.215666 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 2.00000i | − | 0.212000i | −0.994366 | − | 0.106000i | \(-0.966196\pi\) | ||
0.994366 | − | 0.106000i | \(-0.0338043\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −8.00000 | −0.838628 | ||||||||
\(92\) | − | 18.0000i | − | 1.87663i | ||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −16.0000 | −1.65027 | ||||||||
\(95\) | 4.00000 | + | 8.00000i | 0.410391 | + | 0.820783i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 11.0000 | 1.11688 | 0.558440 | − | 0.829545i | \(-0.311400\pi\) | ||||
0.558440 | + | 0.829545i | \(0.311400\pi\) | |||||||
\(98\) | −18.0000 | −1.81827 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 6.00000 | − | 8.00000i | 0.600000 | − | 0.800000i | ||||
\(101\) | − | 3.00000i | − | 0.298511i | −0.988799 | − | 0.149256i | \(-0.952312\pi\) | ||
0.988799 | − | 0.149256i | \(-0.0476877\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 6.00000i | 0.591198i | 0.955312 | + | 0.295599i | \(0.0955191\pi\) | ||||
−0.955312 | + | 0.295599i | \(0.904481\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 18.0000i | 1.74831i | ||||||||
\(107\) | 4.00000i | 0.386695i | 0.981130 | + | 0.193347i | \(0.0619344\pi\) | ||||
−0.981130 | + | 0.193347i | \(0.938066\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1.00000 | −0.0957826 | −0.0478913 | − | 0.998853i | \(-0.515250\pi\) | ||||
−0.0478913 | + | 0.998853i | \(0.515250\pi\) | |||||||
\(110\) | −2.00000 | − | 4.00000i | −0.190693 | − | 0.381385i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 16.0000i | 1.51186i | ||||||||
\(113\) | 8.00000 | 0.752577 | 0.376288 | − | 0.926503i | \(-0.377200\pi\) | ||||
0.376288 | + | 0.926503i | \(0.377200\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 9.00000 | + | 18.0000i | 0.839254 | + | 1.67851i | ||||
\(116\) | 4.00000 | − | 10.0000i | 0.371391 | − | 0.928477i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −16.0000 | −1.47292 | ||||||||
\(119\) | − | 24.0000i | − | 2.20008i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 10.0000 | 0.909091 | ||||||||
\(122\) | − | 12.0000i | − | 1.08643i | ||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | − | 4.00000i | − | 0.359211i | ||||||
\(125\) | −2.00000 | + | 11.0000i | −0.178885 | + | 0.983870i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 7.00000 | 0.621150 | 0.310575 | − | 0.950549i | \(-0.399478\pi\) | ||||
0.310575 | + | 0.950549i | \(0.399478\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 4.00000 | + | 8.00000i | 0.350823 | + | 0.701646i | ||||
\(131\) | − | 20.0000i | − | 1.74741i | −0.486458 | − | 0.873704i | \(-0.661711\pi\) | ||
0.486458 | − | 0.873704i | \(-0.338289\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −16.0000 | −1.38738 | ||||||||
\(134\) | 24.0000i | 2.07328i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 16.0000 | 1.36697 | 0.683486 | − | 0.729964i | \(-0.260463\pi\) | ||||
0.683486 | + | 0.729964i | \(0.260463\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 11.0000 | 0.933008 | 0.466504 | − | 0.884519i | \(-0.345513\pi\) | ||||
0.466504 | + | 0.884519i | \(0.345513\pi\) | |||||||
\(140\) | 8.00000 | + | 16.0000i | 0.676123 | + | 1.35225i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −4.00000 | −0.335673 | ||||||||
\(143\) | 2.00000 | 0.167248 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1.00000 | + | 12.0000i | 0.0830455 | + | 0.996546i | ||||
\(146\) | 30.0000 | 2.48282 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −2.00000 | −0.164399 | ||||||||
\(149\) | −14.0000 | −1.14692 | −0.573462 | − | 0.819232i | \(-0.694400\pi\) | ||||
−0.573462 | + | 0.819232i | \(0.694400\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −17.0000 | −1.38344 | −0.691720 | − | 0.722166i | \(-0.743147\pi\) | ||||
−0.691720 | + | 0.722166i | \(0.743147\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 8.00000 | 0.644658 | ||||||||
\(155\) | 2.00000 | + | 4.00000i | 0.160644 | + | 0.321288i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 14.0000 | 1.11732 | 0.558661 | − | 0.829396i | \(-0.311315\pi\) | ||||
0.558661 | + | 0.829396i | \(0.311315\pi\) | |||||||
\(158\) | 8.00000i | 0.636446i | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 16.0000 | − | 8.00000i | 1.26491 | − | 0.632456i | ||||
\(161\) | −36.0000 | −2.83720 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −13.0000 | −1.01824 | −0.509119 | − | 0.860696i | \(-0.670029\pi\) | ||||
−0.509119 | + | 0.860696i | \(0.670029\pi\) | |||||||
\(164\) | 18.0000i | 1.40556i | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | − | 14.0000i | − | 1.08661i | ||||||
\(167\) | 24.0000i | 1.85718i | 0.371113 | + | 0.928588i | \(0.378976\pi\) | ||||
−0.371113 | + | 0.928588i | \(0.621024\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 9.00000 | 0.692308 | ||||||||
\(170\) | −24.0000 | + | 12.0000i | −1.84072 | + | 0.920358i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −2.00000 | −0.152499 | ||||||||
\(173\) | − | 21.0000i | − | 1.59660i | −0.602260 | − | 0.798300i | \(-0.705733\pi\) | ||
0.602260 | − | 0.798300i | \(-0.294267\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −16.0000 | − | 12.0000i | −1.20949 | − | 0.907115i | ||||
\(176\) | − | 4.00000i | − | 0.301511i | ||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | − | 4.00000i | − | 0.299813i | ||||||
\(179\) | −6.00000 | −0.448461 | −0.224231 | − | 0.974536i | \(-0.571987\pi\) | ||||
−0.224231 | + | 0.974536i | \(0.571987\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −7.00000 | −0.520306 | −0.260153 | − | 0.965567i | \(-0.583773\pi\) | ||||
−0.260153 | + | 0.965567i | \(0.583773\pi\) | |||||||
\(182\) | −16.0000 | −1.18600 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 2.00000 | − | 1.00000i | 0.147043 | − | 0.0735215i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 6.00000i | 0.438763i | ||||||||
\(188\) | −16.0000 | −1.16692 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 8.00000 | + | 16.0000i | 0.580381 | + | 1.16076i | ||||
\(191\) | − | 3.00000i | − | 0.217072i | −0.994092 | − | 0.108536i | \(-0.965384\pi\) | ||
0.994092 | − | 0.108536i | \(-0.0346163\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 6.00000 | 0.431889 | 0.215945 | − | 0.976406i | \(-0.430717\pi\) | ||||
0.215945 | + | 0.976406i | \(0.430717\pi\) | |||||||
\(194\) | 22.0000 | 1.57951 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −18.0000 | −1.28571 | ||||||||
\(197\) | 23.0000i | 1.63868i | 0.573306 | + | 0.819341i | \(0.305660\pi\) | ||||
−0.573306 | + | 0.819341i | \(0.694340\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −19.0000 | −1.34687 | −0.673437 | − | 0.739244i | \(-0.735183\pi\) | ||||
−0.673437 | + | 0.739244i | \(0.735183\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | − | 6.00000i | − | 0.422159i | ||||||
\(203\) | −20.0000 | − | 8.00000i | −1.40372 | − | 0.561490i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −9.00000 | − | 18.0000i | −0.628587 | − | 1.25717i | ||||
\(206\) | 12.0000i | 0.836080i | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 8.00000i | 0.554700i | ||||||||
\(209\) | 4.00000 | 0.276686 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2.00000i | 0.137686i | 0.997628 | + | 0.0688428i | \(0.0219307\pi\) | ||||
−0.997628 | + | 0.0688428i | \(0.978069\pi\) | |||||||
\(212\) | 18.0000i | 1.23625i | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 8.00000i | 0.546869i | ||||||||
\(215\) | 2.00000 | − | 1.00000i | 0.136399 | − | 0.0681994i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −8.00000 | −0.543075 | ||||||||
\(218\) | −2.00000 | −0.135457 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −2.00000 | − | 4.00000i | −0.134840 | − | 0.269680i | ||||
\(221\) | − | 12.0000i | − | 0.807207i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 4.00000i | − | 0.267860i | −0.990991 | − | 0.133930i | \(-0.957240\pi\) | ||
0.990991 | − | 0.133930i | \(-0.0427597\pi\) | |||||||
\(224\) | 32.0000i | 2.13809i | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 16.0000 | 1.06430 | ||||||||
\(227\) | − | 7.00000i | − | 0.464606i | −0.972643 | − | 0.232303i | \(-0.925374\pi\) | ||
0.972643 | − | 0.232303i | \(-0.0746261\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 4.00000i | − | 0.264327i | −0.991228 | − | 0.132164i | \(-0.957808\pi\) | ||
0.991228 | − | 0.132164i | \(-0.0421925\pi\) | |||||||
\(230\) | 18.0000 | + | 36.0000i | 1.18688 | + | 2.37377i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 1.00000i | − | 0.0655122i | −0.999463 | − | 0.0327561i | \(-0.989572\pi\) | ||
0.999463 | − | 0.0327561i | \(-0.0104285\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 16.0000 | − | 8.00000i | 1.04372 | − | 0.521862i | ||||
\(236\) | −16.0000 | −1.04151 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | − | 48.0000i | − | 3.11138i | ||||||
\(239\) | 26.0000 | 1.68180 | 0.840900 | − | 0.541190i | \(-0.182026\pi\) | ||||
0.840900 | + | 0.541190i | \(0.182026\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 11.0000 | 0.708572 | 0.354286 | − | 0.935137i | \(-0.384724\pi\) | ||||
0.354286 | + | 0.935137i | \(0.384724\pi\) | |||||||
\(242\) | 20.0000 | 1.28565 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | − | 12.0000i | − | 0.768221i | ||||||
\(245\) | 18.0000 | − | 9.00000i | 1.14998 | − | 0.574989i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −8.00000 | −0.509028 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −4.00000 | + | 22.0000i | −0.252982 | + | 1.39140i | ||||
\(251\) | 12.0000i | 0.757433i | 0.925513 | + | 0.378717i | \(0.123635\pi\) | ||||
−0.925513 | + | 0.378717i | \(0.876365\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 9.00000 | 0.565825 | ||||||||
\(254\) | 14.0000 | 0.878438 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 16.0000 | 1.00000 | ||||||||
\(257\) | − | 15.0000i | − | 0.935674i | −0.883815 | − | 0.467837i | \(-0.845033\pi\) | ||
0.883815 | − | 0.467837i | \(-0.154967\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 4.00000i | 0.248548i | ||||||||
\(260\) | 4.00000 | + | 8.00000i | 0.248069 | + | 0.496139i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | − | 40.0000i | − | 2.47121i | ||||||
\(263\) | −26.0000 | −1.60323 | −0.801614 | − | 0.597841i | \(-0.796025\pi\) | ||||
−0.801614 | + | 0.597841i | \(0.796025\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −9.00000 | − | 18.0000i | −0.552866 | − | 1.10573i | ||||
\(266\) | −32.0000 | −1.96205 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 24.0000i | 1.46603i | ||||||||
\(269\) | − | 10.0000i | − | 0.609711i | −0.952399 | − | 0.304855i | \(-0.901392\pi\) | ||
0.952399 | − | 0.304855i | \(-0.0986081\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 2.00000i | − | 0.121491i | −0.998153 | − | 0.0607457i | \(-0.980652\pi\) | ||
0.998153 | − | 0.0607457i | \(-0.0193479\pi\) | |||||||
\(272\) | −24.0000 | −1.45521 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 32.0000 | 1.93319 | ||||||||
\(275\) | 4.00000 | + | 3.00000i | 0.241209 | + | 0.180907i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2.00000i | 0.120168i | 0.998193 | + | 0.0600842i | \(0.0191369\pi\) | ||||
−0.998193 | + | 0.0600842i | \(0.980863\pi\) | |||||||
\(278\) | 22.0000 | 1.31947 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 24.0000 | 1.43172 | 0.715860 | − | 0.698244i | \(-0.246035\pi\) | ||||
0.715860 | + | 0.698244i | \(0.246035\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 22.0000i | 1.30776i | 0.756596 | + | 0.653882i | \(0.226861\pi\) | ||||
−0.756596 | + | 0.653882i | \(0.773139\pi\) | |||||||
\(284\) | −4.00000 | −0.237356 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 4.00000 | 0.236525 | ||||||||
\(287\) | 36.0000 | 2.12501 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 19.0000 | 1.11765 | ||||||||
\(290\) | 2.00000 | + | 24.0000i | 0.117444 | + | 1.40933i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 30.0000 | 1.75562 | ||||||||
\(293\) | −2.00000 | −0.116841 | −0.0584206 | − | 0.998292i | \(-0.518606\pi\) | ||||
−0.0584206 | + | 0.998292i | \(0.518606\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 16.0000 | − | 8.00000i | 0.931556 | − | 0.465778i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −28.0000 | −1.62200 | ||||||||
\(299\) | −18.0000 | −1.04097 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 4.00000i | 0.230556i | ||||||||
\(302\) | −34.0000 | −1.95648 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 16.0000i | 0.917663i | ||||||||
\(305\) | 6.00000 | + | 12.0000i | 0.343559 | + | 0.687118i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 15.0000 | 0.856095 | 0.428048 | − | 0.903756i | \(-0.359202\pi\) | ||||
0.428048 | + | 0.903756i | \(0.359202\pi\) | |||||||
\(308\) | 8.00000 | 0.455842 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 4.00000 | + | 8.00000i | 0.227185 | + | 0.454369i | ||||
\(311\) | − | 23.0000i | − | 1.30421i | −0.758129 | − | 0.652105i | \(-0.773886\pi\) | ||
0.758129 | − | 0.652105i | \(-0.226114\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 8.00000i | − | 0.452187i | −0.974106 | − | 0.226093i | \(-0.927405\pi\) | ||
0.974106 | − | 0.226093i | \(-0.0725954\pi\) | |||||||
\(314\) | 28.0000 | 1.58013 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 8.00000i | 0.450035i | ||||||||
\(317\) | 12.0000 | 0.673987 | 0.336994 | − | 0.941507i | \(-0.390590\pi\) | ||||
0.336994 | + | 0.941507i | \(0.390590\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 5.00000 | + | 2.00000i | 0.279946 | + | 0.111979i | ||||
\(320\) | 16.0000 | − | 8.00000i | 0.894427 | − | 0.447214i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −72.0000 | −4.01240 | ||||||||
\(323\) | − | 24.0000i | − | 1.33540i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −8.00000 | − | 6.00000i | −0.443760 | − | 0.332820i | ||||
\(326\) | −26.0000 | −1.44001 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 32.0000i | 1.76422i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 32.0000i | 1.75888i | 0.476011 | + | 0.879440i | \(0.342082\pi\) | ||||
−0.476011 | + | 0.879440i | \(0.657918\pi\) | |||||||
\(332\) | − | 14.0000i | − | 0.768350i | ||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 48.0000i | 2.62644i | ||||||||
\(335\) | −12.0000 | − | 24.0000i | −0.655630 | − | 1.31126i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −10.0000 | −0.544735 | −0.272367 | − | 0.962193i | \(-0.587807\pi\) | ||||
−0.272367 | + | 0.962193i | \(0.587807\pi\) | |||||||
\(338\) | 18.0000 | 0.979071 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −24.0000 | + | 12.0000i | −1.30158 | + | 0.650791i | ||||
\(341\) | 2.00000 | 0.108306 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 8.00000i | 0.431959i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | − | 42.0000i | − | 2.25793i | ||||||
\(347\) | 19.0000i | 1.01997i | 0.860182 | + | 0.509987i | \(0.170350\pi\) | ||||
−0.860182 | + | 0.509987i | \(0.829650\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −11.0000 | −0.588817 | −0.294408 | − | 0.955680i | \(-0.595123\pi\) | ||||
−0.294408 | + | 0.955680i | \(0.595123\pi\) | |||||||
\(350\) | −32.0000 | − | 24.0000i | −1.71047 | − | 1.28285i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | − | 8.00000i | − | 0.426401i | ||||||
\(353\) | − | 18.0000i | − | 0.958043i | −0.877803 | − | 0.479022i | \(-0.840992\pi\) | ||
0.877803 | − | 0.479022i | \(-0.159008\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 4.00000 | − | 2.00000i | 0.212298 | − | 0.106149i | ||||
\(356\) | − | 4.00000i | − | 0.212000i | ||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −12.0000 | −0.634220 | ||||||||
\(359\) | − | 21.0000i | − | 1.10834i | −0.832404 | − | 0.554169i | \(-0.813036\pi\) | ||
0.832404 | − | 0.554169i | \(-0.186964\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 3.00000 | 0.157895 | ||||||||
\(362\) | −14.0000 | −0.735824 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −16.0000 | −0.838628 | ||||||||
\(365\) | −30.0000 | + | 15.0000i | −1.57027 | + | 0.785136i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 27.0000 | 1.40939 | 0.704694 | − | 0.709511i | \(-0.251084\pi\) | ||||
0.704694 | + | 0.709511i | \(0.251084\pi\) | |||||||
\(368\) | 36.0000i | 1.87663i | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 4.00000 | − | 2.00000i | 0.207950 | − | 0.103975i | ||||
\(371\) | 36.0000 | 1.86903 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 2.00000i | 0.103556i | 0.998659 | + | 0.0517780i | \(0.0164888\pi\) | ||||
−0.998659 | + | 0.0517780i | \(0.983511\pi\) | |||||||
\(374\) | 12.0000i | 0.620505i | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −10.0000 | − | 4.00000i | −0.515026 | − | 0.206010i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 22.0000i | 1.13006i | 0.825069 | + | 0.565032i | \(0.191136\pi\) | ||||
−0.825069 | + | 0.565032i | \(0.808864\pi\) | |||||||
\(380\) | 8.00000 | + | 16.0000i | 0.410391 | + | 0.820783i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | − | 6.00000i | − | 0.306987i | ||||||
\(383\) | − | 27.0000i | − | 1.37964i | −0.723983 | − | 0.689818i | \(-0.757691\pi\) | ||
0.723983 | − | 0.689818i | \(-0.242309\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −8.00000 | + | 4.00000i | −0.407718 | + | 0.203859i | ||||
\(386\) | 12.0000 | 0.610784 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 22.0000 | 1.11688 | ||||||||
\(389\) | 3.00000i | 0.152106i | 0.997104 | + | 0.0760530i | \(0.0242318\pi\) | ||||
−0.997104 | + | 0.0760530i | \(0.975768\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 54.0000i | − | 2.73090i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 46.0000i | 2.31745i | ||||||||
\(395\) | −4.00000 | − | 8.00000i | −0.201262 | − | 0.402524i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 16.0000i | − | 0.803017i | −0.915855 | − | 0.401508i | \(-0.868486\pi\) | ||
0.915855 | − | 0.401508i | \(-0.131514\pi\) | |||||||
\(398\) | −38.0000 | −1.90477 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −12.0000 | + | 16.0000i | −0.600000 | + | 0.800000i | ||||
\(401\) | 12.0000 | 0.599251 | 0.299626 | − | 0.954057i | \(-0.403138\pi\) | ||||
0.299626 | + | 0.954057i | \(0.403138\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −4.00000 | −0.199254 | ||||||||
\(404\) | − | 6.00000i | − | 0.298511i | ||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −40.0000 | − | 16.0000i | −1.98517 | − | 0.794067i | ||||
\(407\) | − | 1.00000i | − | 0.0495682i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 14.0000i | − | 0.692255i | −0.938187 | − | 0.346128i | \(-0.887496\pi\) | ||
0.938187 | − | 0.346128i | \(-0.112504\pi\) | |||||||
\(410\) | −18.0000 | − | 36.0000i | −0.888957 | − | 1.77791i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 12.0000i | 0.591198i | ||||||||
\(413\) | 32.0000i | 1.57462i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 7.00000 | + | 14.0000i | 0.343616 | + | 0.687233i | ||||
\(416\) | 16.0000i | 0.784465i | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 8.00000 | 0.391293 | ||||||||
\(419\) | −30.0000 | −1.46560 | −0.732798 | − | 0.680446i | \(-0.761786\pi\) | ||||
−0.732798 | + | 0.680446i | \(0.761786\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 22.0000i | − | 1.07221i | −0.844150 | − | 0.536107i | \(-0.819894\pi\) | ||
0.844150 | − | 0.536107i | \(-0.180106\pi\) | |||||||
\(422\) | 4.00000i | 0.194717i | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 18.0000 | − | 24.0000i | 0.873128 | − | 1.16417i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −24.0000 | −1.16144 | ||||||||
\(428\) | 8.00000i | 0.386695i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 4.00000 | − | 2.00000i | 0.192897 | − | 0.0964486i | ||||
\(431\) | 6.00000 | 0.289010 | 0.144505 | − | 0.989504i | \(-0.453841\pi\) | ||||
0.144505 | + | 0.989504i | \(0.453841\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 7.00000 | 0.336399 | 0.168199 | − | 0.985753i | \(-0.446205\pi\) | ||||
0.168199 | + | 0.985753i | \(0.446205\pi\) | |||||||
\(434\) | −16.0000 | −0.768025 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −2.00000 | −0.0957826 | ||||||||
\(437\) | −36.0000 | −1.72211 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | − | 24.0000i | − | 1.14156i | ||||||
\(443\) | −4.00000 | −0.190046 | −0.0950229 | − | 0.995475i | \(-0.530292\pi\) | ||||
−0.0950229 | + | 0.995475i | \(0.530292\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 2.00000 | + | 4.00000i | 0.0948091 | + | 0.189618i | ||||
\(446\) | − | 8.00000i | − | 0.378811i | ||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 32.0000i | 1.51186i | ||||||||
\(449\) | 15.0000i | 0.707894i | 0.935266 | + | 0.353947i | \(0.115161\pi\) | ||||
−0.935266 | + | 0.353947i | \(0.884839\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −9.00000 | −0.423793 | ||||||||
\(452\) | 16.0000 | 0.752577 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | − | 14.0000i | − | 0.657053i | ||||||
\(455\) | 16.0000 | − | 8.00000i | 0.750092 | − | 0.375046i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 10.0000i | 0.467780i | 0.972263 | + | 0.233890i | \(0.0751456\pi\) | ||||
−0.972263 | + | 0.233890i | \(0.924854\pi\) | |||||||
\(458\) | − | 8.00000i | − | 0.373815i | ||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 18.0000 | + | 36.0000i | 0.839254 | + | 1.67851i | ||||
\(461\) | 33.0000i | 1.53696i | 0.639872 | + | 0.768482i | \(0.278987\pi\) | ||||
−0.639872 | + | 0.768482i | \(0.721013\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 2.00000i | 0.0929479i | 0.998920 | + | 0.0464739i | \(0.0147984\pi\) | ||||
−0.998920 | + | 0.0464739i | \(0.985202\pi\) | |||||||
\(464\) | −8.00000 | + | 20.0000i | −0.371391 | + | 0.928477i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | − | 2.00000i | − | 0.0926482i | ||||||
\(467\) | 18.0000 | 0.832941 | 0.416470 | − | 0.909149i | \(-0.363267\pi\) | ||||
0.416470 | + | 0.909149i | \(0.363267\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 48.0000 | 2.21643 | ||||||||
\(470\) | 32.0000 | − | 16.0000i | 1.47605 | − | 0.738025i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 1.00000i | − | 0.0459800i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −16.0000 | − | 12.0000i | −0.734130 | − | 0.550598i | ||||
\(476\) | − | 48.0000i | − | 2.20008i | ||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 52.0000 | 2.37842 | ||||||||
\(479\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2.00000i | 0.0911922i | ||||||||
\(482\) | 22.0000 | 1.00207 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 20.0000 | 0.909091 | ||||||||
\(485\) | −22.0000 | + | 11.0000i | −0.998969 | + | 0.499484i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 4.00000i | 0.181257i | 0.995885 | + | 0.0906287i | \(0.0288876\pi\) | ||||
−0.995885 | + | 0.0906287i | \(0.971112\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 36.0000 | − | 18.0000i | 1.62631 | − | 0.813157i | ||||
\(491\) | − | 8.00000i | − | 0.361035i | −0.983572 | − | 0.180517i | \(-0.942223\pi\) | ||
0.983572 | − | 0.180517i | \(-0.0577772\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 12.0000 | − | 30.0000i | 0.540453 | − | 1.35113i | ||||
\(494\) | −16.0000 | −0.719874 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 8.00000i | 0.359211i | ||||||||
\(497\) | 8.00000i | 0.358849i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −12.0000 | −0.537194 | −0.268597 | − | 0.963253i | \(-0.586560\pi\) | ||||
−0.268597 | + | 0.963253i | \(0.586560\pi\) | |||||||
\(500\) | −4.00000 | + | 22.0000i | −0.178885 | + | 0.983870i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 24.0000i | 1.07117i | ||||||||
\(503\) | 8.00000 | 0.356702 | 0.178351 | − | 0.983967i | \(-0.442924\pi\) | ||||
0.178351 | + | 0.983967i | \(0.442924\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 3.00000 | + | 6.00000i | 0.133498 | + | 0.266996i | ||||
\(506\) | 18.0000 | 0.800198 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 14.0000 | 0.621150 | ||||||||
\(509\) | 28.0000 | 1.24108 | 0.620539 | − | 0.784176i | \(-0.286914\pi\) | ||||
0.620539 | + | 0.784176i | \(0.286914\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 60.0000i | − | 2.65424i | ||||||
\(512\) | 32.0000 | 1.41421 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | − | 30.0000i | − | 1.32324i | ||||||
\(515\) | −6.00000 | − | 12.0000i | −0.264392 | − | 0.528783i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 8.00000i | − | 0.351840i | ||||||
\(518\) | 8.00000i | 0.351500i | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 8.00000 | 0.350486 | 0.175243 | − | 0.984525i | \(-0.443929\pi\) | ||||
0.175243 | + | 0.984525i | \(0.443929\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 2.00000i | 0.0874539i | 0.999044 | + | 0.0437269i | \(0.0139232\pi\) | ||||
−0.999044 | + | 0.0437269i | \(0.986077\pi\) | |||||||
\(524\) | − | 40.0000i | − | 1.74741i | ||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −52.0000 | −2.26731 | ||||||||
\(527\) | − | 12.0000i | − | 0.522728i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −58.0000 | −2.52174 | ||||||||
\(530\) | −18.0000 | − | 36.0000i | −0.781870 | − | 1.56374i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −32.0000 | −1.38738 | ||||||||
\(533\) | 18.0000 | 0.779667 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −4.00000 | − | 8.00000i | −0.172935 | − | 0.345870i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | − | 20.0000i | − | 0.862261i | ||||||
\(539\) | − | 9.00000i | − | 0.387657i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 32.0000i | 1.37579i | 0.725811 | + | 0.687894i | \(0.241464\pi\) | ||||
−0.725811 | + | 0.687894i | \(0.758536\pi\) | |||||||
\(542\) | − | 4.00000i | − | 0.171815i | ||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −48.0000 | −2.05798 | ||||||||
\(545\) | 2.00000 | − | 1.00000i | 0.0856706 | − | 0.0428353i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 26.0000i | − | 1.11168i | −0.831289 | − | 0.555840i | \(-0.812397\pi\) | ||
0.831289 | − | 0.555840i | \(-0.187603\pi\) | |||||||
\(548\) | 32.0000 | 1.36697 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 8.00000 | + | 6.00000i | 0.341121 | + | 0.255841i | ||||
\(551\) | −20.0000 | − | 8.00000i | −0.852029 | − | 0.340811i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 16.0000 | 0.680389 | ||||||||
\(554\) | 4.00000i | 0.169944i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 22.0000 | 0.933008 | ||||||||
\(557\) | 45.0000i | 1.90671i | 0.301849 | + | 0.953356i | \(0.402396\pi\) | ||||
−0.301849 | + | 0.953356i | \(0.597604\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 2.00000i | 0.0845910i | ||||||||
\(560\) | −16.0000 | − | 32.0000i | −0.676123 | − | 1.35225i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 48.0000 | 2.02476 | ||||||||
\(563\) | 36.0000 | 1.51722 | 0.758610 | − | 0.651546i | \(-0.225879\pi\) | ||||
0.758610 | + | 0.651546i | \(0.225879\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −16.0000 | + | 8.00000i | −0.673125 | + | 0.336563i | ||||
\(566\) | 44.0000i | 1.84946i | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 38.0000i | − | 1.59304i | −0.604610 | − | 0.796521i | \(-0.706671\pi\) | ||
0.604610 | − | 0.796521i | \(-0.293329\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −23.0000 | −0.962520 | −0.481260 | − | 0.876578i | \(-0.659821\pi\) | ||||
−0.481260 | + | 0.876578i | \(0.659821\pi\) | |||||||
\(572\) | 4.00000 | 0.167248 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 72.0000 | 3.00522 | ||||||||
\(575\) | −36.0000 | − | 27.0000i | −1.50130 | − | 1.12598i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −34.0000 | −1.41544 | −0.707719 | − | 0.706494i | \(-0.750276\pi\) | ||||
−0.707719 | + | 0.706494i | \(0.750276\pi\) | |||||||
\(578\) | 38.0000 | 1.58059 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 2.00000 | + | 24.0000i | 0.0830455 | + | 0.996546i | ||||
\(581\) | −28.0000 | −1.16164 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −9.00000 | −0.372742 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −4.00000 | −0.165238 | ||||||||
\(587\) | − | 12.0000i | − | 0.495293i | −0.968850 | − | 0.247647i | \(-0.920343\pi\) | ||
0.968850 | − | 0.247647i | \(-0.0796572\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −8.00000 | −0.329634 | ||||||||
\(590\) | 32.0000 | − | 16.0000i | 1.31742 | − | 0.658710i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 4.00000 | 0.164399 | ||||||||
\(593\) | 14.0000i | 0.574911i | 0.957794 | + | 0.287456i | \(0.0928094\pi\) | ||||
−0.957794 | + | 0.287456i | \(0.907191\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 24.0000 | + | 48.0000i | 0.983904 | + | 1.96781i | ||||
\(596\) | −28.0000 | −1.14692 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −36.0000 | −1.47215 | ||||||||
\(599\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 26.0000i | 1.06056i | 0.847822 | + | 0.530281i | \(0.177914\pi\) | ||||
−0.847822 | + | 0.530281i | \(0.822086\pi\) | |||||||
\(602\) | 8.00000i | 0.326056i | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −34.0000 | −1.38344 | ||||||||
\(605\) | −20.0000 | + | 10.0000i | −0.813116 | + | 0.406558i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 40.0000 | 1.62355 | 0.811775 | − | 0.583970i | \(-0.198502\pi\) | ||||
0.811775 | + | 0.583970i | \(0.198502\pi\) | |||||||
\(608\) | 32.0000i | 1.29777i | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 12.0000 | + | 24.0000i | 0.485866 | + | 0.971732i | ||||
\(611\) | 16.0000i | 0.647291i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 6.00000i | 0.242338i | 0.992632 | + | 0.121169i | \(0.0386643\pi\) | ||||
−0.992632 | + | 0.121169i | \(0.961336\pi\) | |||||||
\(614\) | 30.0000 | 1.21070 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −36.0000 | −1.44931 | −0.724653 | − | 0.689114i | \(-0.758000\pi\) | ||||
−0.724653 | + | 0.689114i | \(0.758000\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 10.0000i | − | 0.401934i | −0.979598 | − | 0.200967i | \(-0.935592\pi\) | ||
0.979598 | − | 0.200967i | \(-0.0644084\pi\) | |||||||
\(620\) | 4.00000 | + | 8.00000i | 0.160644 | + | 0.321288i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | − | 46.0000i | − | 1.84443i | ||||||
\(623\) | −8.00000 | −0.320513 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −7.00000 | − | 24.0000i | −0.280000 | − | 0.960000i | ||||
\(626\) | − | 16.0000i | − | 0.639489i | ||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 28.0000 | 1.11732 | ||||||||
\(629\) | −6.00000 | −0.239236 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 32.0000 | 1.27390 | 0.636950 | − | 0.770905i | \(-0.280196\pi\) | ||||
0.636950 | + | 0.770905i | \(0.280196\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 24.0000 | 0.953162 | ||||||||
\(635\) | −14.0000 | + | 7.00000i | −0.555573 | + | 0.277787i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 18.0000i | 0.713186i | ||||||||
\(638\) | 10.0000 | + | 4.00000i | 0.395904 | + | 0.158362i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 33.0000i | 1.30342i | 0.758468 | + | 0.651711i | \(0.225948\pi\) | ||||
−0.758468 | + | 0.651711i | \(0.774052\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 24.0000i | 0.946468i | 0.880937 | + | 0.473234i | \(0.156913\pi\) | ||||
−0.880937 | + | 0.473234i | \(0.843087\pi\) | |||||||
\(644\) | −72.0000 | −2.83720 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | − | 48.0000i | − | 1.88853i | ||||||
\(647\) | 17.0000i | 0.668339i | 0.942513 | + | 0.334169i | \(0.108456\pi\) | ||||
−0.942513 | + | 0.334169i | \(0.891544\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 8.00000i | − | 0.314027i | ||||||
\(650\) | −16.0000 | − | 12.0000i | −0.627572 | − | 0.470679i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −26.0000 | −1.01824 | ||||||||
\(653\) | 24.0000 | 0.939193 | 0.469596 | − | 0.882881i | \(-0.344399\pi\) | ||||
0.469596 | + | 0.882881i | \(0.344399\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 20.0000 | + | 40.0000i | 0.781465 | + | 1.56293i | ||||
\(656\) | − | 36.0000i | − | 1.40556i | ||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 64.0000i | 2.49498i | ||||||||
\(659\) | − | 29.0000i | − | 1.12968i | −0.825201 | − | 0.564840i | \(-0.808938\pi\) | ||
0.825201 | − | 0.564840i | \(-0.191062\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −5.00000 | −0.194477 | −0.0972387 | − | 0.995261i | \(-0.531001\pi\) | ||||
−0.0972387 | + | 0.995261i | \(0.531001\pi\) | |||||||
\(662\) | 64.0000i | 2.48743i | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 32.0000 | − | 16.0000i | 1.24091 | − | 0.620453i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −45.0000 | − | 18.0000i | −1.74241 | − | 0.696963i | ||||
\(668\) | 48.0000i | 1.85718i | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −24.0000 | − | 48.0000i | −0.927201 | − | 1.85440i | ||||
\(671\) | 6.00000 | 0.231627 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 32.0000i | 1.23351i | 0.787155 | + | 0.616755i | \(0.211553\pi\) | ||||
−0.787155 | + | 0.616755i | \(0.788447\pi\) | |||||||
\(674\) | −20.0000 | −0.770371 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 18.0000 | 0.692308 | ||||||||
\(677\) | 18.0000 | 0.691796 | 0.345898 | − | 0.938272i | \(-0.387574\pi\) | ||||
0.345898 | + | 0.938272i | \(0.387574\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 44.0000i | − | 1.68857i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 4.00000 | 0.153168 | ||||||||
\(683\) | − | 9.00000i | − | 0.344375i | −0.985064 | − | 0.172188i | \(-0.944916\pi\) | ||
0.985064 | − | 0.172188i | \(-0.0550836\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −32.0000 | + | 16.0000i | −1.22266 | + | 0.611329i | ||||
\(686\) | 16.0000i | 0.610883i | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 4.00000 | 0.152499 | ||||||||
\(689\) | 18.0000 | 0.685745 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 20.0000 | 0.760836 | 0.380418 | − | 0.924815i | \(-0.375780\pi\) | ||||
0.380418 | + | 0.924815i | \(0.375780\pi\) | |||||||
\(692\) | − | 42.0000i | − | 1.59660i | ||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 38.0000i | 1.44246i | ||||||||
\(695\) | −22.0000 | + | 11.0000i | −0.834508 | + | 0.417254i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 54.0000i | 2.04540i | ||||||||
\(698\) | −22.0000 | −0.832712 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −32.0000 | − | 24.0000i | −1.20949 | − | 0.907115i | ||||
\(701\) | −6.00000 | −0.226617 | −0.113308 | − | 0.993560i | \(-0.536145\pi\) | ||||
−0.113308 | + | 0.993560i | \(0.536145\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 4.00000i | 0.150863i | ||||||||
\(704\) | − | 8.00000i | − | 0.301511i | ||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | − | 36.0000i | − | 1.35488i | ||||||
\(707\) | −12.0000 | −0.451306 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 19.0000 | 0.713560 | 0.356780 | − | 0.934188i | \(-0.383875\pi\) | ||||
0.356780 | + | 0.934188i | \(0.383875\pi\) | |||||||
\(710\) | 8.00000 | − | 4.00000i | 0.300235 | − | 0.150117i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −18.0000 | −0.674105 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −4.00000 | + | 2.00000i | −0.149592 | + | 0.0747958i | ||||
\(716\) | −12.0000 | −0.448461 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | − | 42.0000i | − | 1.56743i | ||||||
\(719\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 24.0000 | 0.893807 | ||||||||
\(722\) | 6.00000 | 0.223297 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −14.0000 | −0.520306 | ||||||||
\(725\) | −14.0000 | − | 23.0000i | −0.519947 | − | 0.854199i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −60.0000 | + | 30.0000i | −2.22070 | + | 1.11035i | ||||
\(731\) | −6.00000 | −0.221918 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 2.00000 | 0.0738717 | 0.0369358 | − | 0.999318i | \(-0.488240\pi\) | ||||
0.0369358 | + | 0.999318i | \(0.488240\pi\) | |||||||
\(734\) | 54.0000 | 1.99318 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 72.0000i | 2.65396i | ||||||||
\(737\) | −12.0000 | −0.442026 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 10.0000i | 0.367856i | 0.982940 | + | 0.183928i | \(0.0588813\pi\) | ||||
−0.982940 | + | 0.183928i | \(0.941119\pi\) | |||||||
\(740\) | 4.00000 | − | 2.00000i | 0.147043 | − | 0.0735215i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 72.0000 | 2.64320 | ||||||||
\(743\) | −6.00000 | −0.220119 | −0.110059 | − | 0.993925i | \(-0.535104\pi\) | ||||
−0.110059 | + | 0.993925i | \(0.535104\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 28.0000 | − | 14.0000i | 1.02584 | − | 0.512920i | ||||
\(746\) | 4.00000i | 0.146450i | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 12.0000i | 0.438763i | ||||||||
\(749\) | 16.0000 | 0.584627 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 28.0000i | 1.02173i | 0.859660 | + | 0.510867i | \(0.170676\pi\) | ||||
−0.859660 | + | 0.510867i | \(0.829324\pi\) | |||||||
\(752\) | 32.0000 | 1.16692 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −20.0000 | − | 8.00000i | −0.728357 | − | 0.291343i | ||||
\(755\) | 34.0000 | − | 17.0000i | 1.23739 | − | 0.618693i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −33.0000 | −1.19941 | −0.599703 | − | 0.800223i | \(-0.704714\pi\) | ||||
−0.599703 | + | 0.800223i | \(0.704714\pi\) | |||||||
\(758\) | 44.0000i | 1.59815i | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 34.0000 | 1.23250 | 0.616250 | − | 0.787551i | \(-0.288651\pi\) | ||||
0.616250 | + | 0.787551i | \(0.288651\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 4.00000i | 0.144810i | ||||||||
\(764\) | − | 6.00000i | − | 0.217072i | ||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | − | 54.0000i | − | 1.95110i | ||||||
\(767\) | 16.0000i | 0.577727i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 14.0000i | − | 0.504853i | −0.967616 | − | 0.252426i | \(-0.918771\pi\) | ||
0.967616 | − | 0.252426i | \(-0.0812286\pi\) | |||||||
\(770\) | −16.0000 | + | 8.00000i | −0.576600 | + | 0.288300i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 12.0000 | 0.431889 | ||||||||
\(773\) | −24.0000 | −0.863220 | −0.431610 | − | 0.902060i | \(-0.642054\pi\) | ||||
−0.431610 | + | 0.902060i | \(0.642054\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −8.00000 | − | 6.00000i | −0.287368 | − | 0.215526i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 6.00000i | 0.215110i | ||||||||
\(779\) | 36.0000 | 1.28983 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − | 2.00000i | − | 0.0715656i | ||||||
\(782\) | − | 108.000i | − | 3.86207i | ||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 36.0000 | 1.28571 | ||||||||
\(785\) | −28.0000 | + | 14.0000i | −0.999363 | + | 0.499681i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 42.0000i | − | 1.49714i | −0.663057 | − | 0.748569i | \(-0.730741\pi\) | ||
0.663057 | − | 0.748569i | \(-0.269259\pi\) | |||||||
\(788\) | 46.0000i | 1.63868i | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −8.00000 | − | 16.0000i | −0.284627 | − | 0.569254i | ||||