Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1024,2,Mod(257,1024)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1024, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1024.257");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1024 = 2^{10} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1024.e (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: | \(8.17668116698\) |
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: | \(\Z[a_1, \ldots, a_{9}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 128) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 257.2 | ||
Root | \(0.707107 + 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1024.257 |
Dual form | 1024.2.e.i.769.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1024\mathbb{Z}\right)^\times\).
\(n\) | \(5\) | \(1023\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.41421 | + | 1.41421i | 0.816497 | + | 0.816497i | 0.985599 | − | 0.169102i | \(-0.0540867\pi\) |
−0.169102 | + | 0.985599i | \(0.554087\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −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 | ||||||||
\(7\) | 4.00000i | 1.51186i | 0.654654 | + | 0.755929i | \(0.272814\pi\) | ||||
−0.654654 | + | 0.755929i | \(0.727186\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000i | 0.333333i | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.41421 | + | 1.41421i | −0.426401 | + | 0.426401i | −0.887401 | − | 0.460999i | \(-0.847491\pi\) |
0.460999 | + | 0.887401i | \(0.347491\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.41421 | − | 1.41421i | −0.392232 | − | 0.392232i | 0.483250 | − | 0.875482i | \(-0.339456\pi\) |
−0.875482 | + | 0.483250i | \(0.839456\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −4.00000 | −1.03280 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.00000 | 0.485071 | 0.242536 | − | 0.970143i | \(-0.422021\pi\) | ||||
0.242536 | + | 0.970143i | \(0.422021\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.41421 | − | 1.41421i | −0.324443 | − | 0.324443i | 0.526026 | − | 0.850469i | \(-0.323682\pi\) |
−0.850469 | + | 0.526026i | \(0.823682\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −5.65685 | + | 5.65685i | −1.23443 | + | 1.23443i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4.00000i | 0.834058i | 0.908893 | + | 0.417029i | \(0.136929\pi\) | ||||
−0.908893 | + | 0.417029i | \(0.863071\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000i | 0.200000i | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 2.82843 | − | 2.82843i | 0.544331 | − | 0.544331i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −4.24264 | − | 4.24264i | −0.787839 | − | 0.787839i | 0.193301 | − | 0.981140i | \(-0.438081\pi\) |
−0.981140 | + | 0.193301i | \(0.938081\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −4.00000 | −0.696311 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −5.65685 | − | 5.65685i | −0.956183 | − | 0.956183i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −7.07107 | + | 7.07107i | −1.16248 | + | 1.16248i | −0.178545 | + | 0.983932i | \(0.557139\pi\) |
−0.983932 | + | 0.178545i | \(0.942861\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | − | 4.00000i | − | 0.640513i | ||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 6.00000i | − | 0.937043i | −0.883452 | − | 0.468521i | \(-0.844787\pi\) | ||
0.883452 | − | 0.468521i | \(-0.155213\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.24264 | − | 4.24264i | 0.646997 | − | 0.646997i | −0.305269 | − | 0.952266i | \(-0.598747\pi\) |
0.952266 | + | 0.305269i | \(0.0987465\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.41421 | − | 1.41421i | −0.210819 | − | 0.210819i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 8.00000 | 1.16692 | 0.583460 | − | 0.812142i | \(-0.301699\pi\) | ||||
0.583460 | + | 0.812142i | \(0.301699\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −9.00000 | −1.28571 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 2.82843 | + | 2.82843i | 0.396059 | + | 0.396059i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −4.24264 | + | 4.24264i | −0.582772 | + | 0.582772i | −0.935664 | − | 0.352892i | \(-0.885198\pi\) |
0.352892 | + | 0.935664i | \(0.385198\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 4.00000i | − | 0.539360i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 4.00000i | − | 0.529813i | ||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −9.89949 | + | 9.89949i | −1.28880 | + | 1.28880i | −0.353291 | + | 0.935513i | \(0.614937\pi\) |
−0.935513 | + | 0.353291i | \(0.885063\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.41421 | + | 1.41421i | 0.181071 | + | 0.181071i | 0.791823 | − | 0.610751i | \(-0.209132\pi\) |
−0.610751 | + | 0.791823i | \(0.709132\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −4.00000 | −0.503953 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 4.00000 | 0.496139 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 7.07107 | + | 7.07107i | 0.863868 | + | 0.863868i | 0.991785 | − | 0.127917i | \(-0.0408290\pi\) |
−0.127917 | + | 0.991785i | \(0.540829\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −5.65685 | + | 5.65685i | −0.681005 | + | 0.681005i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 12.0000i | − | 1.42414i | −0.702109 | − | 0.712069i | \(-0.747758\pi\) | ||
0.702109 | − | 0.712069i | \(-0.252242\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 14.0000i | 1.63858i | 0.573382 | + | 0.819288i | \(0.305631\pi\) | ||||
−0.573382 | + | 0.819288i | \(0.694369\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1.41421 | + | 1.41421i | −0.163299 | + | 0.163299i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −5.65685 | − | 5.65685i | −0.644658 | − | 0.644658i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 8.00000 | 0.900070 | 0.450035 | − | 0.893011i | \(-0.351411\pi\) | ||||
0.450035 | + | 0.893011i | \(0.351411\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 11.0000 | 1.22222 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 4.24264 | + | 4.24264i | 0.465690 | + | 0.465690i | 0.900515 | − | 0.434825i | \(-0.143190\pi\) |
−0.434825 | + | 0.900515i | \(0.643190\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2.82843 | + | 2.82843i | −0.306786 | + | 0.306786i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − | 12.0000i | − | 1.28654i | ||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 2.00000i | 0.212000i | 0.994366 | + | 0.106000i | \(0.0338043\pi\) | ||||
−0.994366 | + | 0.106000i | \(0.966196\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 5.65685 | − | 5.65685i | 0.592999 | − | 0.592999i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 4.00000 | 0.410391 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −2.00000 | −0.203069 | −0.101535 | − | 0.994832i | \(-0.532375\pi\) | ||||
−0.101535 | + | 0.994832i | \(0.532375\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −1.41421 | − | 1.41421i | −0.142134 | − | 0.142134i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 4.24264 | − | 4.24264i | 0.422159 | − | 0.422159i | −0.463788 | − | 0.885946i | \(-0.653510\pi\) |
0.885946 | + | 0.463788i | \(0.153510\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 4.00000i | 0.394132i | 0.980390 | + | 0.197066i | \(0.0631413\pi\) | ||||
−0.980390 | + | 0.197066i | \(0.936859\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | − | 16.0000i | − | 1.56144i | ||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −1.41421 | + | 1.41421i | −0.136717 | + | 0.136717i | −0.772153 | − | 0.635436i | \(-0.780820\pi\) |
0.635436 | + | 0.772153i | \(0.280820\pi\) | |||||||
\(108\) | 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 | ||||||||
\(111\) | −20.0000 | −1.89832 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −2.00000 | −0.188144 | −0.0940721 | − | 0.995565i | \(-0.529988\pi\) | ||||
−0.0940721 | + | 0.995565i | \(0.529988\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −5.65685 | − | 5.65685i | −0.527504 | − | 0.527504i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 1.41421 | − | 1.41421i | 0.130744 | − | 0.130744i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 8.00000i | 0.733359i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 7.00000i | 0.636364i | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 8.48528 | − | 8.48528i | 0.765092 | − | 0.765092i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −8.48528 | − | 8.48528i | −0.758947 | − | 0.758947i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 16.0000 | 1.41977 | 0.709885 | − | 0.704317i | \(-0.248747\pi\) | ||||
0.709885 | + | 0.704317i | \(0.248747\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 12.0000 | 1.05654 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −4.24264 | − | 4.24264i | −0.370681 | − | 0.370681i | 0.497044 | − | 0.867725i | \(-0.334419\pi\) |
−0.867725 | + | 0.497044i | \(0.834419\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 5.65685 | − | 5.65685i | 0.490511 | − | 0.490511i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 8.00000i | 0.688530i | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 10.0000i | 0.854358i | 0.904167 | + | 0.427179i | \(0.140493\pi\) | ||||
−0.904167 | + | 0.427179i | \(0.859507\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −7.07107 | + | 7.07107i | −0.599760 | + | 0.599760i | −0.940249 | − | 0.340489i | \(-0.889408\pi\) |
0.340489 | + | 0.940249i | \(0.389408\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 11.3137 | + | 11.3137i | 0.952786 | + | 0.952786i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 4.00000 | 0.334497 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 12.0000 | 0.996546 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −12.7279 | − | 12.7279i | −1.04978 | − | 1.04978i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 12.7279 | − | 12.7279i | 1.04271 | − | 1.04271i | 0.0436658 | − | 0.999046i | \(-0.486096\pi\) |
0.999046 | − | 0.0436658i | \(-0.0139037\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 4.00000i | 0.325515i | 0.986666 | + | 0.162758i | \(0.0520389\pi\) | ||||
−0.986666 | + | 0.162758i | \(0.947961\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 2.00000i | 0.161690i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 12.7279 | + | 12.7279i | 1.01580 | + | 1.01580i | 0.999873 | + | 0.0159256i | \(0.00506949\pi\) |
0.0159256 | + | 0.999873i | \(0.494931\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −12.0000 | −0.951662 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −16.0000 | −1.26098 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1.41421 | + | 1.41421i | 0.110770 | + | 0.110770i | 0.760319 | − | 0.649550i | \(-0.225042\pi\) |
−0.649550 | + | 0.760319i | \(0.725042\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 5.65685 | − | 5.65685i | 0.440386 | − | 0.440386i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 20.0000i | 1.54765i | 0.633402 | + | 0.773823i | \(0.281658\pi\) | ||||
−0.633402 | + | 0.773823i | \(0.718342\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 9.00000i | − | 0.692308i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.41421 | − | 1.41421i | 0.108148 | − | 0.108148i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −12.7279 | − | 12.7279i | −0.967686 | − | 0.967686i | 0.0318080 | − | 0.999494i | \(-0.489873\pi\) |
−0.999494 | + | 0.0318080i | \(0.989873\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −4.00000 | −0.302372 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −28.0000 | −2.10461 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 4.24264 | + | 4.24264i | 0.317110 | + | 0.317110i | 0.847656 | − | 0.530546i | \(-0.178013\pi\) |
−0.530546 | + | 0.847656i | \(0.678013\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1.41421 | − | 1.41421i | 0.105118 | − | 0.105118i | −0.652592 | − | 0.757710i | \(-0.726318\pi\) |
0.757710 | + | 0.652592i | \(0.226318\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 4.00000i | 0.295689i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − | 20.0000i | − | 1.47043i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −2.82843 | + | 2.82843i | −0.206835 | + | 0.206835i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 11.3137 | + | 11.3137i | 0.822951 | + | 0.822951i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −16.0000 | −1.15772 | −0.578860 | − | 0.815427i | \(-0.696502\pi\) | ||||
−0.578860 | + | 0.815427i | \(0.696502\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −2.00000 | −0.143963 | −0.0719816 | − | 0.997406i | \(-0.522932\pi\) | ||||
−0.0719816 | + | 0.997406i | \(0.522932\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 5.65685 | + | 5.65685i | 0.405096 | + | 0.405096i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 9.89949 | − | 9.89949i | 0.705310 | − | 0.705310i | −0.260235 | − | 0.965545i | \(-0.583800\pi\) |
0.965545 | + | 0.260235i | \(0.0838002\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 4.00000i | 0.283552i | 0.989899 | + | 0.141776i | \(0.0452813\pi\) | ||||
−0.989899 | + | 0.141776i | \(0.954719\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 20.0000i | 1.41069i | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 16.9706 | − | 16.9706i | 1.19110 | − | 1.19110i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 8.48528 | + | 8.48528i | 0.592638 | + | 0.592638i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −4.00000 | −0.278019 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 4.00000 | 0.276686 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 15.5563 | + | 15.5563i | 1.07094 | + | 1.07094i | 0.997283 | + | 0.0736598i | \(0.0234679\pi\) |
0.0736598 | + | 0.997283i | \(0.476532\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 16.9706 | − | 16.9706i | 1.16280 | − | 1.16280i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 12.0000i | 0.818393i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −19.7990 | + | 19.7990i | −1.33789 | + | 1.33789i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −2.82843 | − | 2.82843i | −0.190261 | − | 0.190261i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −1.00000 | −0.0666667 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 12.7279 | + | 12.7279i | 0.844782 | + | 0.844782i | 0.989476 | − | 0.144695i | \(-0.0462199\pi\) |
−0.144695 | + | 0.989476i | \(0.546220\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 9.89949 | − | 9.89949i | 0.654177 | − | 0.654177i | −0.299819 | − | 0.953996i | \(-0.596926\pi\) |
0.953996 | + | 0.299819i | \(0.0969263\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | − | 16.0000i | − | 1.05272i | ||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 18.0000i | − | 1.17922i | −0.807688 | − | 0.589610i | \(-0.799282\pi\) | ||
0.807688 | − | 0.589610i | \(-0.200718\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −11.3137 | + | 11.3137i | −0.738025 | + | 0.738025i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 11.3137 | + | 11.3137i | 0.734904 | + | 0.734904i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 24.0000 | 1.55243 | 0.776215 | − | 0.630468i | \(-0.217137\pi\) | ||||
0.776215 | + | 0.630468i | \(0.217137\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2.00000 | 0.128831 | 0.0644157 | − | 0.997923i | \(-0.479482\pi\) | ||||
0.0644157 | + | 0.997923i | \(0.479482\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 7.07107 | + | 7.07107i | 0.453609 | + | 0.453609i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 12.7279 | − | 12.7279i | 0.813157 | − | 0.813157i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 4.00000i | 0.254514i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 12.0000i | 0.760469i | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 12.7279 | − | 12.7279i | 0.803379 | − | 0.803379i | −0.180243 | − | 0.983622i | \(-0.557688\pi\) |
0.983622 | + | 0.180243i | \(0.0576884\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −5.65685 | − | 5.65685i | −0.355643 | − | 0.355643i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −8.00000 | −0.500979 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 18.0000 | 1.12281 | 0.561405 | − | 0.827541i | \(-0.310261\pi\) | ||||
0.561405 | + | 0.827541i | \(0.310261\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −28.2843 | − | 28.2843i | −1.75750 | − | 1.75750i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 4.24264 | − | 4.24264i | 0.262613 | − | 0.262613i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 12.0000i | − | 0.739952i | −0.929041 | − | 0.369976i | \(-0.879366\pi\) | ||
0.929041 | − | 0.369976i | \(-0.120634\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 12.0000i | − | 0.737154i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −2.82843 | + | 2.82843i | −0.173097 | + | 0.173097i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −7.07107 | − | 7.07107i | −0.431131 | − | 0.431131i | 0.457882 | − | 0.889013i | \(-0.348608\pi\) |
−0.889013 | + | 0.457882i | \(0.848608\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −8.00000 | −0.485965 | −0.242983 | − | 0.970031i | \(-0.578126\pi\) | ||||
−0.242983 | + | 0.970031i | \(0.578126\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 16.0000 | 0.968364 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −1.41421 | − | 1.41421i | −0.0852803 | − | 0.0852803i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −4.24264 | + | 4.24264i | −0.254916 | + | 0.254916i | −0.822982 | − | 0.568067i | \(-0.807691\pi\) |
0.568067 | + | 0.822982i | \(0.307691\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 18.0000i | 1.07379i | 0.843649 | + | 0.536895i | \(0.180403\pi\) | ||||
−0.843649 | + | 0.536895i | \(0.819597\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −4.24264 | + | 4.24264i | −0.252199 | + | 0.252199i | −0.821872 | − | 0.569673i | \(-0.807070\pi\) |
0.569673 | + | 0.821872i | \(0.307070\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 5.65685 | + | 5.65685i | 0.335083 | + | 0.335083i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 24.0000 | 1.41668 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −13.0000 | −0.764706 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −2.82843 | − | 2.82843i | −0.165805 | − | 0.165805i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 9.89949 | − | 9.89949i | 0.578335 | − | 0.578335i | −0.356110 | − | 0.934444i | \(-0.615897\pi\) |
0.934444 | + | 0.356110i | \(0.115897\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 28.0000i | − | 1.63022i | ||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 8.00000i | 0.464207i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 5.65685 | − | 5.65685i | 0.327144 | − | 0.327144i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 16.9706 | + | 16.9706i | 0.978167 | + | 0.978167i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 12.0000 | 0.689382 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −4.00000 | −0.229039 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −12.7279 | − | 12.7279i | −0.726421 | − | 0.726421i | 0.243484 | − | 0.969905i | \(-0.421710\pi\) |
−0.969905 | + | 0.243484i | \(0.921710\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −5.65685 | + | 5.65685i | −0.321807 | + | 0.321807i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 28.0000i | − | 1.58773i | −0.608091 | − | 0.793867i | \(-0.708065\pi\) | ||
0.608091 | − | 0.793867i | \(-0.291935\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 10.0000i | − | 0.565233i | −0.959233 | − | 0.282617i | \(-0.908798\pi\) | ||
0.959233 | − | 0.282617i | \(-0.0912024\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 5.65685 | − | 5.65685i | 0.318728 | − | 0.318728i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −4.24264 | − | 4.24264i | −0.238290 | − | 0.238290i | 0.577851 | − | 0.816142i | \(-0.303891\pi\) |
−0.816142 | + | 0.577851i | \(0.803891\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 12.0000 | 0.671871 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −4.00000 | −0.223258 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −2.82843 | − | 2.82843i | −0.157378 | − | 0.157378i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.41421 | − | 1.41421i | 0.0784465 | − | 0.0784465i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 12.0000i | 0.663602i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 32.0000i | 1.76422i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 9.89949 | − | 9.89949i | 0.544125 | − | 0.544125i | −0.380610 | − | 0.924736i | \(-0.624286\pi\) |
0.924736 | + | 0.380610i | \(0.124286\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −7.07107 | − | 7.07107i | −0.387492 | − | 0.387492i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −20.0000 | −1.09272 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 14.0000 | 0.762629 | 0.381314 | − | 0.924445i | \(-0.375472\pi\) | ||||
0.381314 | + | 0.924445i | \(0.375472\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −2.82843 | − | 2.82843i | −0.153619 | − | 0.153619i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 8.00000i | − | 0.431959i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | − | 16.0000i | − | 0.861411i | ||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 12.7279 | − | 12.7279i | 0.683271 | − | 0.683271i | −0.277465 | − | 0.960736i | \(-0.589494\pi\) |
0.960736 | + | 0.277465i | \(0.0894943\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 7.07107 | + | 7.07107i | 0.378506 | + | 0.378506i | 0.870563 | − | 0.492057i | \(-0.163755\pi\) |
−0.492057 | + | 0.870563i | \(0.663755\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −8.00000 | −0.427008 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 18.0000 | 0.958043 | 0.479022 | − | 0.877803i | \(-0.340992\pi\) | ||||
0.479022 | + | 0.877803i | \(0.340992\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 16.9706 | + | 16.9706i | 0.900704 | + | 0.900704i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −11.3137 | + | 11.3137i | −0.598785 | + | 0.598785i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 4.00000i | 0.211112i | 0.994413 | + | 0.105556i | \(0.0336622\pi\) | ||||
−0.994413 | + | 0.105556i | \(0.966338\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | − | 15.0000i | − | 0.789474i | ||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −9.89949 | + | 9.89949i | −0.519589 | + | 0.519589i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −19.7990 | − | 19.7990i | −1.03633 | − | 1.03633i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 8.00000 | 0.417597 | 0.208798 | − | 0.977959i | \(-0.433045\pi\) | ||||
0.208798 | + | 0.977959i | \(0.433045\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 6.00000 | 0.312348 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −16.9706 | − | 16.9706i | −0.881068 | − | 0.881068i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 7.07107 | − | 7.07107i | 0.366126 | − | 0.366126i | −0.499936 | − | 0.866062i | \(-0.666643\pi\) |
0.866062 | + | 0.499936i | \(0.166643\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | − | 24.0000i | − | 1.23935i | ||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 12.0000i | 0.618031i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1.41421 | − | 1.41421i | 0.0726433 | − | 0.0726433i | −0.669852 | − | 0.742495i | \(-0.733642\pi\) |
0.742495 | + | 0.669852i | \(0.233642\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 22.6274 | + | 22.6274i | 1.15924 | + | 1.15924i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 16.0000 | 0.815436 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 4.24264 | + | 4.24264i | 0.215666 | + | 0.215666i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −7.07107 | + | 7.07107i | −0.358517 | + | 0.358517i | −0.863266 | − | 0.504749i | \(-0.831585\pi\) |
0.504749 | + | 0.863266i | \(0.331585\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 8.00000i | 0.404577i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 12.0000i | − | 0.605320i | ||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −11.3137 | + | 11.3137i | −0.569254 | + | 0.569254i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 4.24264 | + | 4.24264i | 0.212932 | + | 0.212932i | 0.805512 | − | 0.592580i | \(-0.201890\pi\) |
−0.592580 | + | 0.805512i | \(0.701890\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 16.0000 | 0.801002 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −30.0000 | −1.49813 | −0.749064 | − | 0.662497i | \(-0.769497\pi\) | ||||
−0.749064 | + | 0.662497i | \(0.769497\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −15.5563 | + | 15.5563i | −0.773001 | + | 0.773001i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 20.0000i | − | 0.991363i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 10.0000i | − | 0.494468i | −0.968956 | − | 0.247234i | \(-0.920478\pi\) | ||
0.968956 | − | 0.247234i | \(-0.0795217\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −14.1421 | + | 14.1421i | −0.697580 | + | 0.697580i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −39.5980 | − | 39.5980i | −1.94849 | − | 1.94849i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −12.0000 | −0.589057 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −20.0000 | −0.979404 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 18.3848 | + | 18.3848i | 0.898155 | + | 0.898155i | 0.995273 | − | 0.0971178i | \(-0.0309624\pi\) |
−0.0971178 | + | 0.995273i | \(0.530962\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −24.0416 | + | 24.0416i | −1.17172 | + | 1.17172i | −0.189917 | + | 0.981800i | \(0.560822\pi\) |
−0.981800 | + | 0.189917i | \(0.939178\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 8.00000i | 0.388973i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 2.00000i | 0.0970143i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −5.65685 | + | 5.65685i | −0.273754 | + | 0.273754i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 5.65685 | + | 5.65685i | 0.273115 | + | 0.273115i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −40.0000 | −1.92673 | −0.963366 | − | 0.268190i | \(-0.913575\pi\) | ||||
−0.963366 | + | 0.268190i | \(0.913575\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −30.0000 | −1.44171 | −0.720854 | − | 0.693087i | \(-0.756250\pi\) | ||||
−0.720854 | + | 0.693087i | \(0.756250\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 16.9706 | + | 16.9706i | 0.813676 | + | 0.813676i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 5.65685 | − | 5.65685i | 0.270604 | − | 0.270604i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 36.0000i | 1.71819i | 0.511819 | + | 0.859093i | \(0.328972\pi\) | ||||
−0.511819 | + | 0.859093i | \(0.671028\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | − | 9.00000i | − | 0.428571i | ||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −4.24264 | + | 4.24264i | −0.201574 | + | 0.201574i | −0.800674 | − | 0.599100i | \(-0.795525\pi\) |
0.599100 | + | 0.800674i | \(0.295525\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −2.82843 | − | 2.82843i | −0.134080 | − | 0.134080i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 36.0000 | 1.70274 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −34.0000 | −1.60456 | −0.802280 | − | 0.596948i | \(-0.796380\pi\) | ||||
−0.802280 | + | 0.596948i | \(0.796380\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 8.48528 | + | 8.48528i | 0.399556 | + | 0.399556i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −5.65685 | + | 5.65685i | −0.265782 | + | 0.265782i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 16.0000i | 0.750092i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 6.00000i | − | 0.280668i | −0.990104 | − | 0.140334i | \(-0.955182\pi\) | ||
0.990104 | − | 0.140334i | \(-0.0448177\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 5.65685 | − | 5.65685i | 0.264039 | − | 0.264039i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −7.07107 | − | 7.07107i | −0.329332 | − | 0.329332i | 0.523000 | − | 0.852333i | \(-0.324813\pi\) |
−0.852333 | + | 0.523000i | \(0.824813\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 8.00000 | 0.371792 | 0.185896 | − | 0.982569i | \(-0.440481\pi\) | ||||
0.185896 | + | 0.982569i | \(0.440481\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 9.89949 | + | 9.89949i | 0.458094 | + | 0.458094i | 0.898029 | − | 0.439935i | \(-0.144999\pi\) |
−0.439935 | + | 0.898029i | \(0.644999\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −28.2843 | + | 28.2843i | −1.30605 | + | 1.30605i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 36.0000i | 1.65879i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 12.0000i | 0.551761i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.41421 | − | 1.41421i | 0.0648886 | − | 0.0648886i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −4.24264 | − | 4.24264i | −0.194257 | − | 0.194257i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 20.0000 | 0.911922 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −22.6274 | − | 22.6274i | −1.02958 | − | 1.02958i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 2.82843 | − | 2.82843i | 0.128432 | − | 0.128432i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 20.0000i | 0.906287i | 0.891438 | + | 0.453143i | \(0.149697\pi\) | ||||
−0.891438 | + | 0.453143i | \(0.850303\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 4.00000i | 0.180886i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −7.07107 | + | 7.07107i | −0.319113 | + | 0.319113i | −0.848426 | − | 0.529313i | \(-0.822450\pi\) |
0.529313 | + | 0.848426i | \(0.322450\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −8.48528 | − | 8.48528i | −0.382158 | − | 0.382158i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 4.00000 | 0.179787 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 48.0000 | 2.15309 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 15.5563 | + | 15.5563i | 0.696398 | + | 0.696398i | 0.963632 | − | 0.267234i | \(-0.0861096\pi\) |
−0.267234 | + | 0.963632i | \(0.586110\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −28.2843 | + | 28.2843i | −1.26365 | + | 1.26365i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 20.0000i | 0.891756i | 0.895094 | + | 0.445878i | \(0.147108\pi\) | ||||
−0.895094 | + | 0.445878i | \(0.852892\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 12.0000i | 0.533993i | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 12.7279 | − | 12.7279i | 0.565267 | − | 0.565267i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −9.89949 | − | 9.89949i | −0.438787 | − | 0.438787i | 0.452816 | − | 0.891604i | \(-0.350419\pi\) |
−0.891604 | + | 0.452816i | \(0.850419\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −56.0000 | −2.47729 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −8.00000 | −0.353209 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −5.65685 | − | 5.65685i | −0.249271 | − | 0.249271i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −11.3137 | + | 11.3137i | −0.497576 | + | 0.497576i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 36.0000i | − | 1.58022i | ||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 22.0000i | − | 0.963837i | −0.876216 | − | 0.481919i | \(-0.839940\pi\) | ||
0.876216 | − | 0.481919i | \(-0.160060\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 9.89949 | − | 9.89949i | 0.432875 | − | 0.432875i | −0.456730 | − | 0.889605i | \(-0.650980\pi\) |
0.889605 | + | 0.456730i | \(0.150980\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −5.65685 | − | 5.65685i | −0.246885 | − | 0.246885i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 7.00000 | 0.304348 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −9.89949 | − | 9.89949i | −0.429601 | − | 0.429601i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −8.48528 | + | 8.48528i | −0.367538 | + | 0.367538i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 4.00000i | − | 0.172935i | ||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 12.0000i | 0.517838i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 12.7279 | − | 12.7279i | 0.548230 | − | 0.548230i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 24.0416 | + | 24.0416i | 1.03363 | + | 1.03363i | 0.999414 | + | 0.0342160i | \(0.0108934\pi\) |
0.0342160 | + | 0.999414i | \(0.489107\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 4.00000 | 0.171656 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −12.0000 | −0.514024 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −26.8701 | − | 26.8701i | −1.14888 | − | 1.14888i | −0.986773 | − | 0.162108i | \(-0.948171\pi\) |
−0.162108 | − | 0.986773i | \(-0.551829\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −1.41421 | + | 1.41421i | −0.0603572 | + | 0.0603572i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 12.0000i | 0.511217i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 32.0000i | 1.36078i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 28.2843 | − | 28.2843i | 1.20060 | − | 1.20060i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −1.41421 | − | 1.41421i | −0.0599222 | − | 0.0599222i | 0.676511 | − | 0.736433i | \(-0.263491\pi\) |
−0.736433 | + | 0.676511i | \(0.763491\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −12.0000 | −0.507546 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −8.00000 | −0.337760 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −12.7279 | − | 12.7279i | −0.536418 | − | 0.536418i | 0.386057 | − | 0.922475i | \(-0.373837\pi\) |
−0.922475 | + | 0.386057i | \(0.873837\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 2.82843 | − | 2.82843i | 0.118993 | − | 0.118993i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 44.0000i | 1.84783i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 26.0000i | − | 1.08998i | −0.838444 | − | 0.544988i | \(-0.816534\pi\) | ||
0.838444 | − | 0.544988i | \(-0.183466\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −26.8701 | + | 26.8701i | −1.12448 | + | 1.12448i | −0.133417 | + | 0.991060i | \(0.542595\pi\) |
−0.991060 | + | 0.133417i | \(0.957405\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −22.6274 | − | 22.6274i | −0.945274 | − | 0.945274i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −4.00000 | −0.166812 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 2.00000 | 0.0832611 | 0.0416305 | − | 0.999133i | \(-0.486745\pi\) | ||||
0.0416305 | + | 0.999133i | \(0.486745\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −2.82843 | − | 2.82843i | −0.117545 | − | 0.117545i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −16.9706 | + | 16.9706i | −0.704058 | + | 0.704058i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 12.0000i | − | 0.496989i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 4.00000i | 0.165380i | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −24.0416 | + | 24.0416i | −0.992304 | + | 0.992304i | −0.999971 | − | 0.00766632i | \(-0.997560\pi\) |
0.00766632 | + | 0.999971i | \(0.497560\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 28.0000 | 1.15177 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −18.0000 | −0.739171 | −0.369586 | − | 0.929197i | \(-0.620500\pi\) | ||||
−0.369586 | + | 0.929197i | \(0.620500\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −11.3137 | − | 11.3137i | −0.463817 | − | 0.463817i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −5.65685 | + | 5.65685i | −0.231520 | + | 0.231520i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 12.0000i | − | 0.490307i | −0.969484 | − | 0.245153i | \(-0.921162\pi\) | ||
0.969484 | − | 0.245153i | \(-0.0788383\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 30.0000i | − | 1.22373i | −0.790964 | − | 0.611863i | \(-0.790420\pi\) | ||
0.790964 | − | 0.611863i | \(-0.209580\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −7.07107 | + | 7.07107i | −0.287956 | + | 0.287956i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −9.89949 | − | 9.89949i | −0.402472 | − | 0.402472i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −16.0000 | −0.649420 | −0.324710 | − | 0.945814i | \(-0.605267\pi\) | ||||
−0.324710 | + | 0.945814i | \(0.605267\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 48.0000 | 1.94506 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −11.3137 | − | 11.3137i | −0.457704 | − | 0.457704i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −24.0416 | + | 24.0416i | −0.971032 | + | 0.971032i | −0.999592 | − | 0.0285598i | \(-0.990908\pi\) |
0.0285598 | + | 0.999592i | \(0.490908\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 24.0000i | 0.967773i | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 2.00000i | − | 0.0805170i | −0.999189 | − | 0.0402585i | \(-0.987182\pi\) | ||
0.999189 | − | 0.0402585i | \(-0.0128181\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 32.5269 | − | 32.5269i | 1.30737 | − | 1.30737i | 0.384058 | − | 0.923309i | \(-0.374526\pi\) |
0.923309 | − | 0.384058i | \(-0.125474\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 11.3137 | + | 11.3137i | 0.454003 | + | 0.454003i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −8.00000 | −0.320513 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 19.0000 | 0.760000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 5.65685 | + | 5.65685i | 0.225913 | + | 0.225913i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −14.1421 | + | 14.1421i | −0.563884 | + | 0.563884i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 44.0000i | − | 1.75161i | −0.482663 | − | 0.875806i | \(-0.660330\pi\) | ||
0.482663 | − | 0.875806i | \(-0.339670\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 44.0000i | 1.74884i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −22.6274 | + | 22.6274i | −0.897942 | + | 0.897942i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 12.7279 | + | 12.7279i | 0.504299 | + | 0.504299i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 12.0000 | 0.474713 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 30.0000 | 1.18493 | 0.592464 | − | 0.805597i | \(-0.298155\pi\) | ||||
0.592464 | + | 0.805597i | \(0.298155\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 29.6985 | + | 29.6985i | 1.17119 | + | 1.17119i | 0.981925 | + | 0.189269i | \(0.0606117\pi\) |
0.189269 | + | 0.981925i | \(0.439388\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −16.9706 | + | 16.9706i | −0.668215 | + | 0.668215i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 12.0000i | − | 0.471769i | −0.971781 | − | 0.235884i | \(-0.924201\pi\) | ||
0.971781 | − | 0.235884i | \(-0.0757987\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 28.0000i | − | 1.09910i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −29.6985 | − | 29.6985i | −1.16219 | − | 1.16219i | −0.983995 | − | 0.178197i | \(-0.942974\pi\) |
−0.178197 | − | 0.983995i | \(-0.557026\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 12.0000 | 0.468879 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −14.0000 | −0.546192 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 4.24264 | + | 4.24264i | 0.165270 | + | 0.165270i | 0.784897 | − | 0.619627i | \(-0.212716\pi\) |
−0.619627 | + | 0.784897i | \(0.712716\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 24.0416 | − | 24.0416i | 0.935111 | − | 0.935111i | −0.0629083 | − | 0.998019i | \(-0.520038\pi\) |
0.998019 | + | 0.0629083i | \(0.0200376\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | − | 8.00000i | − | 0.310694i | ||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 16.0000i | 0.620453i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 16.9706 | − | 16.9706i | 0.657103 | − | 0.657103i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −4.00000 | −0.154418 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −2.00000 | −0.0770943 | −0.0385472 | − | 0.999257i | \(-0.512273\pi\) | ||||
−0.0385472 | + | 0.999257i | \(0.512273\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 2.82843 | + | 2.82843i | 0.108866 | + | 0.108866i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 15.5563 | − | 15.5563i | 0.597879 | − | 0.597879i | −0.341869 | − | 0.939748i | \(-0.611060\pi\) |
0.939748 | + | 0.341869i | \(0.111060\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 8.00000i | − | 0.307012i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 36.0000i | 1.37952i | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −29.6985 | + | 29.6985i | −1.13638 | + | 1.13638i | −0.147287 | + | 0.989094i | \(0.547054\pi\) |
−0.989094 | + | 0.147287i | \(0.952946\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −14.1421 | − | 14.1421i | −0.540343 | − | 0.540343i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 28.0000 | 1.06827 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 12.0000 | 0.457164 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 4.24264 | + | 4.24264i | 0.161398 | + | 0.161398i | 0.783186 | − | 0.621788i | \(-0.213593\pi\) |
−0.621788 | + | 0.783186i | \(0.713593\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 5.65685 | − | 5.65685i | 0.214886 | − | 0.214886i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − | 20.0000i | − | 0.758643i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 12.0000i | − | 0.454532i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 25.4558 | − | 25.4558i | 0.962828 | − | 0.962828i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1.41421 | + | 1.41421i | 0.0534141 | + | 0.0534141i | 0.733309 | − | 0.679895i | \(-0.237975\pi\) |
−0.679895 | + | 0.733309i | \(0.737975\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 20.0000 | 0.754314 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −32.0000 | −1.20519 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 16.9706 | + | 16.9706i | 0.638244 | + | 0.638244i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 15.5563 | − | 15.5563i | 0.584231 | − | 0.584231i | −0.351832 | − | 0.936063i | \(-0.614441\pi\) |
0.936063 | + | 0.351832i | \(0.114441\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 8.00000i | 0.300023i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −5.65685 | + | 5.65685i | −0.211554 | + | 0.211554i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 33.9411 | + | 33.9411i | 1.26755 | + | 1.26755i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −24.0000 | −0.895049 | −0.447524 | − | 0.894272i | \(-0.647694\pi\) | ||||
−0.447524 | + | 0.894272i | \(0.647694\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −16.0000 | −0.595871 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 2.82843 | + | 2.82843i | 0.105190 | + | 0.105190i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 4.24264 | − | 4.24264i | 0.157568 | − | 0.157568i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 12.0000i | − | 0.445055i | −0.974926 | − | 0.222528i | \(-0.928569\pi\) | ||
0.974926 | − | 0.222528i | \(-0.0714308\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | − | 13.0000i | − | 0.481481i | ||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 8.48528 | − | 8.48528i | 0.313839 | − | 0.313839i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −4.24264 | − | 4.24264i | −0.156706 | − | 0.156706i | 0.624400 | − | 0.781105i | \(-0.285344\pi\) |
−0.781105 | + | 0.624400i | \(0.785344\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 36.0000 | 1.32788 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −20.0000 | −0.736709 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 12.7279 | + | 12.7279i | 0.468204 | + | 0.468204i | 0.901332 | − | 0.433128i | \(-0.142590\pi\) |
−0.433128 | + | 0.901332i | \(0.642590\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −5.65685 | + | 5.65685i | −0.207810 | + | 0.207810i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 44.0000i | − | 1.61420i | −0.590412 | − | 0.807102i | \(-0.701035\pi\) | ||
0.590412 | − | 0.807102i | \(-0.298965\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 36.0000i | 1.31894i | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −4.24264 | + | 4.24264i | −0.155230 | + | 0.155230i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −5.65685 | − | 5.65685i | −0.206697 | − | 0.206697i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −8.00000 | −0.291924 | −0.145962 | − | 0.989290i | \(-0.546628\pi\) | ||||
−0.145962 | + | 0.989290i | \(0.546628\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 36.0000 | 1.31191 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −5.65685 | − | 5.65685i | −0.205874 | − | 0.205874i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −32.5269 | + | 32.5269i | −1.18221 | + | 1.18221i | −0.203040 | + | 0.979170i | \(0.565082\pi\) |
−0.979170 | + | 0.203040i | \(0.934918\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | − | 16.0000i | − | 0.580763i | ||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 10.0000i | − | 0.362500i | −0.983437 | − | 0.181250i | \(-0.941986\pi\) | ||
0.983437 | − | 0.181250i | \(-0.0580143\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −16.9706 | + | 16.9706i | −0.614376 | + | 0.614376i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −2.82843 | − | 2.82843i | −0.102262 | − | 0.102262i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 28.0000 | 1.01102 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −34.0000 | −1.22607 | −0.613036 | − | 0.790055i | \(-0.710052\pi\) | ||||
−0.613036 | + | 0.790055i | \(0.710052\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 25.4558 | + | 25.4558i | 0.916770 | + | 0.916770i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 38.1838 | − | 38.1838i | 1.37337 | − | 1.37337i | 0.517985 | − | 0.855390i | \(-0.326682\pi\) |
0.855390 | − | 0.517985i | \(-0.173318\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | − | 80.0000i | − | 2.86998i | ||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −8.48528 | + | 8.48528i | −0.304017 | + | 0.304017i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 16.9706 | + | 16.9706i | 0.607254 | + | 0.607254i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −24.0000 | −0.857690 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −36.0000 | −1.28490 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 15.5563 | + | 15.5563i | 0.554524 | + | 0.554524i | 0.927743 | − | 0.373219i | \(-0.121746\pi\) |
−0.373219 | + | 0.927743i | \(0.621746\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 16.9706 | − | 16.9706i | 0.604168 | − | 0.604168i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 8.00000i | − | 0.284447i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 4.00000i | − | 0.142044i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 16.9706 | − | 16.9706i | 0.601884 | − | 0.601884i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 12.7279 | + | 12.7279i | 0.450846 | + | 0.450846i | 0.895635 | − | 0.444789i | \(-0.146721\pi\) |
−0.444789 | + | 0.895635i | \(0.646721\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 16.0000 | 0.566039 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −2.00000 | −0.0706665 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −19.7990 | − | 19.7990i | −0.698691 | − | 0.698691i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 22.6274 | − | 22.6274i | 0.797512 | − | 0.797512i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − | 20.0000i | − | 0.704033i | ||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 6.00000i | − | 0.210949i | −0.994422 | − | 0.105474i | \(-0.966364\pi\) | ||
0.994422 | − | 0.105474i | \(-0.0336361\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −12.7279 | + | 12.7279i | −0.446938 | + | 0.446938i | −0.894335 | − | 0.447397i | \(-0.852351\pi\) |
0.447397 | + | 0.894335i | \(0.352351\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −11.3137 | − | 11.3137i | −0.396789 | − | 0.396789i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −4.00000 | −0.140114 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −12.0000 | −0.419827 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 5.65685 | + | 5.65685i | 0.197666 | + | 0.197666i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 7.07107 | − | 7.07107i | 0.246782 | − | 0.246782i | −0.572867 | − | 0.819649i | \(-0.694169\pi\) |
0.819649 | + | 0.572867i | \(0.194169\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 28.0000i | − | 0.976019i | −0.872838 | − | 0.488009i | \(-0.837723\pi\) | ||
0.872838 | − | 0.488009i | \(-0.162277\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | − | 4.00000i | − | 0.139262i | ||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −15.5563 | + | 15.5563i | −0.540947 | + | 0.540947i | −0.923807 | − | 0.382859i | \(-0.874939\pi\) |
0.382859 | + | 0.923807i | \(0.374939\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −9.89949 | − | 9.89949i | −0.343824 | − | 0.343824i | 0.513979 | − | 0.857803i | \(-0.328171\pi\) |
−0.857803 | + | 0.513979i | \(0.828171\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −12.0000 | −0.416275 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −18.0000 | −0.623663 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −28.2843 | − | 28.2843i | −0.978818 | − | 0.978818i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 36.0000i | 1.24286i | 0.783470 | + | 0.621429i | \(0.213448\pi\) | ||||
−0.783470 | + | 0.621429i | \(0.786552\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 7.00000i | 0.241379i | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −25.4558 | + | 25.4558i | −0.876746 | + | 0.876746i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 12.7279 | + | 12.7279i | 0.437854 | + | 0.437854i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −28.0000 | −0.962091 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −12.0000 | −0.411839 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −28.2843 | − | 28.2843i | −0.969572 | − | 0.969572i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 18.3848 | − | 18.3848i | 0.629483 | − | 0.629483i | −0.318455 | − | 0.947938i | \(-0.603164\pi\) |
0.947938 | + | 0.318455i | \(0.103164\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 4.00000i | 0.136797i | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 6.00000i | 0.204956i | 0.994735 | + | 0.102478i | \(0.0326771\pi\) | ||||
−0.994735 | + | 0.102478i | \(0.967323\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 35.3553 | − | 35.3553i | 1.20631 | − | 1.20631i | 0.234095 | − | 0.972214i | \(-0.424787\pi\) |
0.972214 | − | 0.234095i | \(-0.0752126\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 33.9411 | + | 33.9411i | 1.15671 | + | 1.15671i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −32.0000 | −1.08929 | −0.544646 | − | 0.838666i | \(-0.683336\pi\) | ||||
−0.544646 | + | 0.838666i | \(0.683336\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 36.0000 | 1.22404 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −18.3848 | − | 18.3848i | −0.624380 | − | 0.624380i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −11.3137 | + | 11.3137i | −0.383791 | + | 0.383791i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 20.0000i | − | 0.677674i | ||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − | 2.00000i | − | 0.0676897i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 33.9411 | − | 33.9411i | 1.14742 | − | 1.14742i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 15.5563 | + | 15.5563i | 0.525301 | + | 0.525301i | 0.919167 | − | 0.393867i | \(-0.128863\pi\) |
−0.393867 | + | 0.919167i | \(0.628863\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 28.0000 | 0.944417 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 46.0000 | 1.54978 | 0.774890 | − | 0.632096i | \(-0.217805\pi\) | ||||
0.774890 | + | 0.632096i | \(0.217805\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −24.0416 | − | 24.0416i | −0.809065 | − | 0.809065i | 0.175427 | − | 0.984492i | \(-0.443869\pi\) |
−0.984492 | + | 0.175427i | \(0.943869\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 39.5980 | − | 39.5980i | 1.33107 | − | 1.33107i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 36.0000i | 1.20876i | 0.796696 | + | 0.604381i | \(0.206579\pi\) | ||||
−0.796696 | + | 0.604381i | \(0.793421\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 64.0000i | 2.14649i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −15.5563 | + | 15.5563i | −0.521157 | + | 0.521157i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −11.3137 | − | 11.3137i | −0.378599 | − | 0.378599i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −12.0000 | −0.401116 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 16.0000 | 0.534224 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −8.48528 | + | 8.48528i | −0.282686 | + | 0.282686i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 48.0000i | 1.59734i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 4.00000i | 0.132964i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 26.8701 | − | 26.8701i | 0.892206 | − | 0.892206i | −0.102525 | − | 0.994730i | \(-0.532692\pi\) |
0.994730 | + | 0.102525i | \(0.0326921\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 4.24264 | + | 4.24264i | 0.140720 | + | 0.140720i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 24.0000 | 0.795155 | 0.397578 | − | 0.917568i | \(-0.369851\pi\) | ||||
0.397578 | + | 0.917568i | \(0.369851\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −12.0000 | −0.397142 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −5.65685 | − | 5.65685i | −0.187010 | − | 0.187010i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 16.9706 | − | 16.9706i | 0.560417 | − | 0.560417i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 36.0000i | 1.18753i | 0.804638 | + | 0.593765i | \(0.202359\pi\) | ||||
−0.804638 | + | 0.593765i | \(0.797641\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | − | 36.0000i | − | 1.18624i | ||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −16.9706 | + | 16.9706i | −0.558593 | + | 0.558593i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −7.07107 | − | 7.07107i | −0.232495 | − | 0.232495i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −4.00000 | −0.131377 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 30.0000 | 0.984268 | 0.492134 | − | 0.870519i | \(-0.336217\pi\) | ||||
0.492134 | + | 0.870519i | \(0.336217\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 12.7279 | + | 12.7279i | 0.417141 | + | 0.417141i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 39.5980 | − | 39.5980i | 1.29638 | − | 1.29638i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − | 8.00000i | − | 0.261628i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 46.0000i | 1.50275i | 0.659873 | + | 0.751377i | \(0.270610\pi\) | ||||
−0.659873 | + | 0.751377i | \(0.729390\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 14.1421 | − | 14.1421i | 0.461511 | − | 0.461511i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 26.8701 | + | 26.8701i | 0.875939 | + | 0.875939i | 0.993112 | − | 0.117173i | \(-0.0373831\pi\) |
−0.117173 | + | 0.993112i | \(0.537383\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 24.0000 | 0.781548 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −32.0000 | −1.04096 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 9.89949 | + | 9.89949i | 0.321690 | + | 0.321690i | 0.849415 | − | 0.527725i | \(-0.176955\pi\) |
−0.527725 | + | 0.849415i | \(0.676955\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 19.7990 | − | 19.7990i | 0.642702 | − | 0.642702i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 12.0000i | − | 0.389127i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 58.0000i | − | 1.87880i | −0.342817 | − | 0.939402i | \(-0.611381\pi\) | ||
0.342817 | − | 0.939402i | \(-0.388619\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 22.6274 | − | 22.6274i | 0.732206 | − | 0.732206i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 16.9706 | + | 16.9706i | 0.548580 | + | 0.548580i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −40.0000 | −1.29167 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −31.0000 | −1.00000 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −1.41421 | − | 1.41421i | −0.0455724 | − | 0.0455724i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 2.82843 | − | 2.82843i | 0.0910503 | − | 0.0910503i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 28.0000i | − | 0.900419i | −0.892923 | − | 0.450210i | \(-0.851349\pi\) | ||
0.892923 | − | 0.450210i | \(-0.148651\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | − | 8.00000i | − | 0.256997i | ||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 26.8701 | − | 26.8701i | 0.862301 | − | 0.862301i | −0.129304 | − | 0.991605i | \(-0.541274\pi\) |
0.991605 | + | 0.129304i | \(0.0412743\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −28.2843 | − | 28.2843i | −0.906752 | − | 0.906752i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 4.00000 | 0.128103 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −30.0000 | −0.959785 | −0.479893 | − | 0.877327i | \(-0.659324\pi\) | ||||
−0.479893 | + | 0.877327i | \(0.659324\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −2.82843 | − | 2.82843i | −0.0903969 | − | 0.0903969i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −4.24264 | + | 4.24264i | −0.135457 | + | 0.135457i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 20.0000i | 0.637901i | 0.947771 | + | 0.318950i | \(0.103330\pi\) | ||||
−0.947771 | + | 0.318950i | \(0.896670\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 28.0000i | 0.892154i | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −45.2548 | + | 45.2548i | −1.44048 | + | 1.44048i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 16.9706 | + | 16.9706i | 0.539633 | + | 0.539633i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 16.0000 | 0.508257 | 0.254128 | − | 0.967170i | \(-0.418211\pi\) | ||||
0.254128 | + | 0.967170i | \(0.418211\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 28.0000 | 0.888553 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −5.65685 | − | 5.65685i | −0.179334 | − | 0.179334i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 38.1838 | − | 38.1838i | 1.20929 | − | 1.20929i | 0.238036 | − | 0.971256i | \(-0.423497\pi\) |
0.971256 | − | 0.238036i | \(-0.0765035\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 40.0000i | 1.26554i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))