Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1110,2,Mod(889,1110)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1110, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1110.889");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1110 = 2 \cdot 3 \cdot 5 \cdot 37 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1110.d (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: | \(8.86339462436\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.0.5161984.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 4x^{3} + 25x^{2} - 20x + 8 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 889.5 | ||
Root | \(-1.75233 - 1.75233i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1110.889 |
Dual form | 1110.2.d.i.889.2 |
$q$-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 \(\left(\mathbb{Z}/1110\mathbb{Z}\right)^\times\).
\(n\) | \(371\) | \(631\) | \(667\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000i | 0.707107i | ||||||||
\(3\) | 1.00000i | 0.577350i | ||||||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | 1.38900 | + | 1.75233i | 0.621181 | + | 0.783667i | ||||
\(6\) | −1.00000 | −0.408248 | ||||||||
\(7\) | 2.50466i | 0.946674i | 0.880881 | + | 0.473337i | \(0.156951\pi\) | ||||
−0.880881 | + | 0.473337i | \(0.843049\pi\) | |||||||
\(8\) | − | 1.00000i | − | 0.353553i | ||||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | −1.75233 | + | 1.38900i | −0.554136 | + | 0.439242i | ||||
\(11\) | −3.77801 | −1.13911 | −0.569556 | − | 0.821952i | \(-0.692885\pi\) | ||||
−0.569556 | + | 0.821952i | \(0.692885\pi\) | |||||||
\(12\) | − | 1.00000i | − | 0.288675i | ||||||
\(13\) | − | 1.36333i | − | 0.378119i | −0.981966 | − | 0.189060i | \(-0.939456\pi\) | ||
0.981966 | − | 0.189060i | \(-0.0605439\pi\) | |||||||
\(14\) | −2.50466 | −0.669400 | ||||||||
\(15\) | −1.75233 | + | 1.38900i | −0.452450 | + | 0.358639i | ||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 0.221992i | 0.0538410i | 0.999638 | + | 0.0269205i | \(0.00857010\pi\) | ||||
−0.999638 | + | 0.0269205i | \(0.991430\pi\) | |||||||
\(18\) | − | 1.00000i | − | 0.235702i | ||||||
\(19\) | −6.14134 | −1.40892 | −0.704460 | − | 0.709744i | \(-0.748811\pi\) | ||||
−0.704460 | + | 0.709744i | \(0.748811\pi\) | |||||||
\(20\) | −1.38900 | − | 1.75233i | −0.310591 | − | 0.391833i | ||||
\(21\) | −2.50466 | −0.546563 | ||||||||
\(22\) | − | 3.77801i | − | 0.805474i | ||||||
\(23\) | 0.867993i | 0.180989i | 0.995897 | + | 0.0904945i | \(0.0288447\pi\) | ||||
−0.995897 | + | 0.0904945i | \(0.971155\pi\) | |||||||
\(24\) | 1.00000 | 0.204124 | ||||||||
\(25\) | −1.14134 | + | 4.86799i | −0.228267 | + | 0.973599i | ||||
\(26\) | 1.36333 | 0.267371 | ||||||||
\(27\) | − | 1.00000i | − | 0.192450i | ||||||
\(28\) | − | 2.50466i | − | 0.473337i | ||||||
\(29\) | −0.646000 | −0.119959 | −0.0599796 | − | 0.998200i | \(-0.519104\pi\) | ||||
−0.0599796 | + | 0.998200i | \(0.519104\pi\) | |||||||
\(30\) | −1.38900 | − | 1.75233i | −0.253596 | − | 0.319931i | ||||
\(31\) | 3.86799 | 0.694712 | 0.347356 | − | 0.937733i | \(-0.387080\pi\) | ||||
0.347356 | + | 0.937733i | \(0.387080\pi\) | |||||||
\(32\) | 1.00000i | 0.176777i | ||||||||
\(33\) | − | 3.77801i | − | 0.657667i | ||||||
\(34\) | −0.221992 | −0.0380713 | ||||||||
\(35\) | −4.38900 | + | 3.47899i | −0.741877 | + | 0.588056i | ||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | 1.00000i | 0.164399i | ||||||||
\(38\) | − | 6.14134i | − | 0.996256i | ||||||
\(39\) | 1.36333 | 0.218307 | ||||||||
\(40\) | 1.75233 | − | 1.38900i | 0.277068 | − | 0.219621i | ||||
\(41\) | −0.910015 | −0.142121 | −0.0710603 | − | 0.997472i | \(-0.522638\pi\) | ||||
−0.0710603 | + | 0.997472i | \(0.522638\pi\) | |||||||
\(42\) | − | 2.50466i | − | 0.386478i | ||||||
\(43\) | 4.59465i | 0.700677i | 0.936623 | + | 0.350339i | \(0.113934\pi\) | ||||
−0.936623 | + | 0.350339i | \(0.886066\pi\) | |||||||
\(44\) | 3.77801 | 0.569556 | ||||||||
\(45\) | −1.38900 | − | 1.75233i | −0.207060 | − | 0.261222i | ||||
\(46\) | −0.867993 | −0.127979 | ||||||||
\(47\) | − | 0.778008i | − | 0.113484i | −0.998389 | − | 0.0567421i | \(-0.981929\pi\) | ||
0.998389 | − | 0.0567421i | \(-0.0180713\pi\) | |||||||
\(48\) | 1.00000i | 0.144338i | ||||||||
\(49\) | 0.726656 | 0.103808 | ||||||||
\(50\) | −4.86799 | − | 1.14134i | −0.688438 | − | 0.161409i | ||||
\(51\) | −0.221992 | −0.0310851 | ||||||||
\(52\) | 1.36333i | 0.189060i | ||||||||
\(53\) | − | 2.27334i | − | 0.312268i | −0.987736 | − | 0.156134i | \(-0.950097\pi\) | ||
0.987736 | − | 0.156134i | \(-0.0499031\pi\) | |||||||
\(54\) | 1.00000 | 0.136083 | ||||||||
\(55\) | −5.24767 | − | 6.62032i | −0.707595 | − | 0.892684i | ||||
\(56\) | 2.50466 | 0.334700 | ||||||||
\(57\) | − | 6.14134i | − | 0.813440i | ||||||
\(58\) | − | 0.646000i | − | 0.0848240i | ||||||
\(59\) | −7.78734 | −1.01382 | −0.506912 | − | 0.861998i | \(-0.669213\pi\) | ||||
−0.506912 | + | 0.861998i | \(0.669213\pi\) | |||||||
\(60\) | 1.75233 | − | 1.38900i | 0.226225 | − | 0.179320i | ||||
\(61\) | 9.42401 | 1.20662 | 0.603310 | − | 0.797507i | \(-0.293848\pi\) | ||||
0.603310 | + | 0.797507i | \(0.293848\pi\) | |||||||
\(62\) | 3.86799i | 0.491236i | ||||||||
\(63\) | − | 2.50466i | − | 0.315558i | ||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 2.38900 | − | 1.89367i | 0.296319 | − | 0.234881i | ||||
\(66\) | 3.77801 | 0.465041 | ||||||||
\(67\) | 10.7267i | 1.31047i | 0.755425 | + | 0.655235i | \(0.227430\pi\) | ||||
−0.755425 | + | 0.655235i | \(0.772570\pi\) | |||||||
\(68\) | − | 0.221992i | − | 0.0269205i | ||||||
\(69\) | −0.867993 | −0.104494 | ||||||||
\(70\) | −3.47899 | − | 4.38900i | −0.415819 | − | 0.524586i | ||||
\(71\) | −11.2406 | −1.33402 | −0.667010 | − | 0.745049i | \(-0.732426\pi\) | ||||
−0.667010 | + | 0.745049i | \(0.732426\pi\) | |||||||
\(72\) | 1.00000i | 0.117851i | ||||||||
\(73\) | − | 2.86799i | − | 0.335673i | −0.985815 | − | 0.167837i | \(-0.946322\pi\) | ||
0.985815 | − | 0.167837i | \(-0.0536781\pi\) | |||||||
\(74\) | −1.00000 | −0.116248 | ||||||||
\(75\) | −4.86799 | − | 1.14134i | −0.562107 | − | 0.131790i | ||||
\(76\) | 6.14134 | 0.704460 | ||||||||
\(77\) | − | 9.46264i | − | 1.07837i | ||||||
\(78\) | 1.36333i | 0.154367i | ||||||||
\(79\) | 0.495336 | 0.0557296 | 0.0278648 | − | 0.999612i | \(-0.491129\pi\) | ||||
0.0278648 | + | 0.999612i | \(0.491129\pi\) | |||||||
\(80\) | 1.38900 | + | 1.75233i | 0.155295 | + | 0.195917i | ||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | − | 0.910015i | − | 0.100494i | ||||||
\(83\) | − | 1.08066i | − | 0.118617i | −0.998240 | − | 0.0593087i | \(-0.981110\pi\) | ||
0.998240 | − | 0.0593087i | \(-0.0188896\pi\) | |||||||
\(84\) | 2.50466 | 0.273281 | ||||||||
\(85\) | −0.389004 | + | 0.308348i | −0.0421934 | + | 0.0334450i | ||||
\(86\) | −4.59465 | −0.495454 | ||||||||
\(87\) | − | 0.646000i | − | 0.0692585i | ||||||
\(88\) | 3.77801i | 0.402737i | ||||||||
\(89\) | 0.0899847 | 0.00953836 | 0.00476918 | − | 0.999989i | \(-0.498482\pi\) | ||||
0.00476918 | + | 0.999989i | \(0.498482\pi\) | |||||||
\(90\) | 1.75233 | − | 1.38900i | 0.184712 | − | 0.146414i | ||||
\(91\) | 3.41468 | 0.357956 | ||||||||
\(92\) | − | 0.867993i | − | 0.0904945i | ||||||
\(93\) | 3.86799i | 0.401092i | ||||||||
\(94\) | 0.778008 | 0.0802454 | ||||||||
\(95\) | −8.53034 | − | 10.7617i | −0.875194 | − | 1.10412i | ||||
\(96\) | −1.00000 | −0.102062 | ||||||||
\(97\) | 4.46603i | 0.453457i | 0.973958 | + | 0.226728i | \(0.0728030\pi\) | ||||
−0.973958 | + | 0.226728i | \(0.927197\pi\) | |||||||
\(98\) | 0.726656i | 0.0734034i | ||||||||
\(99\) | 3.77801 | 0.379704 | ||||||||
\(100\) | 1.14134 | − | 4.86799i | 0.114134 | − | 0.486799i | ||||
\(101\) | −6.56534 | −0.653276 | −0.326638 | − | 0.945149i | \(-0.605916\pi\) | ||||
−0.326638 | + | 0.945149i | \(0.605916\pi\) | |||||||
\(102\) | − | 0.221992i | − | 0.0219805i | ||||||
\(103\) | − | 16.9580i | − | 1.67092i | −0.549552 | − | 0.835460i | \(-0.685202\pi\) | ||
0.549552 | − | 0.835460i | \(-0.314798\pi\) | |||||||
\(104\) | −1.36333 | −0.133685 | ||||||||
\(105\) | −3.47899 | − | 4.38900i | −0.339515 | − | 0.428323i | ||||
\(106\) | 2.27334 | 0.220807 | ||||||||
\(107\) | 15.8260i | 1.52995i | 0.644057 | + | 0.764977i | \(0.277250\pi\) | ||||
−0.644057 | + | 0.764977i | \(0.722750\pi\) | |||||||
\(108\) | 1.00000i | 0.0962250i | ||||||||
\(109\) | −0.948649 | −0.0908641 | −0.0454320 | − | 0.998967i | \(-0.514466\pi\) | ||||
−0.0454320 | + | 0.998967i | \(0.514466\pi\) | |||||||
\(110\) | 6.62032 | − | 5.24767i | 0.631223 | − | 0.500345i | ||||
\(111\) | −1.00000 | −0.0949158 | ||||||||
\(112\) | 2.50466i | 0.236669i | ||||||||
\(113\) | 0.311977i | 0.0293483i | 0.999892 | + | 0.0146742i | \(0.00467110\pi\) | ||||
−0.999892 | + | 0.0146742i | \(0.995329\pi\) | |||||||
\(114\) | 6.14134 | 0.575189 | ||||||||
\(115\) | −1.52101 | + | 1.20565i | −0.141835 | + | 0.112427i | ||||
\(116\) | 0.646000 | 0.0599796 | ||||||||
\(117\) | 1.36333i | 0.126040i | ||||||||
\(118\) | − | 7.78734i | − | 0.716882i | ||||||
\(119\) | −0.556016 | −0.0509699 | ||||||||
\(120\) | 1.38900 | + | 1.75233i | 0.126798 | + | 0.159965i | ||||
\(121\) | 3.27334 | 0.297577 | ||||||||
\(122\) | 9.42401i | 0.853210i | ||||||||
\(123\) | − | 0.910015i | − | 0.0820533i | ||||||
\(124\) | −3.86799 | −0.347356 | ||||||||
\(125\) | −10.1157 | + | 4.76166i | −0.904772 | + | 0.425896i | ||||
\(126\) | 2.50466 | 0.223133 | ||||||||
\(127\) | − | 3.09931i | − | 0.275020i | −0.990500 | − | 0.137510i | \(-0.956090\pi\) | ||
0.990500 | − | 0.137510i | \(-0.0439099\pi\) | |||||||
\(128\) | − | 1.00000i | − | 0.0883883i | ||||||
\(129\) | −4.59465 | −0.404536 | ||||||||
\(130\) | 1.89367 | + | 2.38900i | 0.166086 | + | 0.209530i | ||||
\(131\) | −11.3434 | −0.991073 | −0.495537 | − | 0.868587i | \(-0.665029\pi\) | ||||
−0.495537 | + | 0.868587i | \(0.665029\pi\) | |||||||
\(132\) | 3.77801i | 0.328833i | ||||||||
\(133\) | − | 15.3820i | − | 1.33379i | ||||||
\(134\) | −10.7267 | −0.926642 | ||||||||
\(135\) | 1.75233 | − | 1.38900i | 0.150817 | − | 0.119546i | ||||
\(136\) | 0.221992 | 0.0190357 | ||||||||
\(137\) | 10.4953i | 0.896677i | 0.893864 | + | 0.448339i | \(0.147984\pi\) | ||||
−0.893864 | + | 0.448339i | \(0.852016\pi\) | |||||||
\(138\) | − | 0.867993i | − | 0.0738884i | ||||||
\(139\) | 18.8773 | 1.60115 | 0.800577 | − | 0.599230i | \(-0.204527\pi\) | ||||
0.800577 | + | 0.599230i | \(0.204527\pi\) | |||||||
\(140\) | 4.38900 | − | 3.47899i | 0.370939 | − | 0.294028i | ||||
\(141\) | 0.778008 | 0.0655201 | ||||||||
\(142\) | − | 11.2406i | − | 0.943294i | ||||||
\(143\) | 5.15066i | 0.430720i | ||||||||
\(144\) | −1.00000 | −0.0833333 | ||||||||
\(145\) | −0.897297 | − | 1.13201i | −0.0745165 | − | 0.0940081i | ||||
\(146\) | 2.86799 | 0.237357 | ||||||||
\(147\) | 0.726656i | 0.0599336i | ||||||||
\(148\) | − | 1.00000i | − | 0.0821995i | ||||||
\(149\) | 17.0280 | 1.39499 | 0.697493 | − | 0.716591i | \(-0.254299\pi\) | ||||
0.697493 | + | 0.716591i | \(0.254299\pi\) | |||||||
\(150\) | 1.14134 | − | 4.86799i | 0.0931897 | − | 0.397470i | ||||
\(151\) | 22.3727 | 1.82066 | 0.910331 | − | 0.413882i | \(-0.135827\pi\) | ||||
0.910331 | + | 0.413882i | \(0.135827\pi\) | |||||||
\(152\) | 6.14134i | 0.498128i | ||||||||
\(153\) | − | 0.221992i | − | 0.0179470i | ||||||
\(154\) | 9.46264 | 0.762521 | ||||||||
\(155\) | 5.37266 | + | 6.77801i | 0.431542 | + | 0.544423i | ||||
\(156\) | −1.36333 | −0.109154 | ||||||||
\(157\) | 16.9800i | 1.35515i | 0.735452 | + | 0.677577i | \(0.236970\pi\) | ||||
−0.735452 | + | 0.677577i | \(0.763030\pi\) | |||||||
\(158\) | 0.495336i | 0.0394068i | ||||||||
\(159\) | 2.27334 | 0.180288 | ||||||||
\(160\) | −1.75233 | + | 1.38900i | −0.138534 | + | 0.109810i | ||||
\(161\) | −2.17403 | −0.171338 | ||||||||
\(162\) | 1.00000i | 0.0785674i | ||||||||
\(163\) | − | 7.00000i | − | 0.548282i | −0.961689 | − | 0.274141i | \(-0.911606\pi\) | ||
0.961689 | − | 0.274141i | \(-0.0883936\pi\) | |||||||
\(164\) | 0.910015 | 0.0710603 | ||||||||
\(165\) | 6.62032 | − | 5.24767i | 0.515392 | − | 0.408530i | ||||
\(166\) | 1.08066 | 0.0838752 | ||||||||
\(167\) | 23.4333i | 1.81333i | 0.421856 | + | 0.906663i | \(0.361379\pi\) | ||||
−0.421856 | + | 0.906663i | \(0.638621\pi\) | |||||||
\(168\) | 2.50466i | 0.193239i | ||||||||
\(169\) | 11.1413 | 0.857026 | ||||||||
\(170\) | −0.308348 | − | 0.389004i | −0.0236492 | − | 0.0298352i | ||||
\(171\) | 6.14134 | 0.469640 | ||||||||
\(172\) | − | 4.59465i | − | 0.350339i | ||||||
\(173\) | 7.28267i | 0.553691i | 0.960914 | + | 0.276846i | \(0.0892891\pi\) | ||||
−0.960914 | + | 0.276846i | \(0.910711\pi\) | |||||||
\(174\) | 0.646000 | 0.0489732 | ||||||||
\(175\) | −12.1927 | − | 2.85866i | −0.921681 | − | 0.216095i | ||||
\(176\) | −3.77801 | −0.284778 | ||||||||
\(177\) | − | 7.78734i | − | 0.585332i | ||||||
\(178\) | 0.0899847i | 0.00674464i | ||||||||
\(179\) | −1.82003 | −0.136035 | −0.0680177 | − | 0.997684i | \(-0.521667\pi\) | ||||
−0.0680177 | + | 0.997684i | \(0.521667\pi\) | |||||||
\(180\) | 1.38900 | + | 1.75233i | 0.103530 | + | 0.130611i | ||||
\(181\) | 0.212663 | 0.0158071 | 0.00790357 | − | 0.999969i | \(-0.497484\pi\) | ||||
0.00790357 | + | 0.999969i | \(0.497484\pi\) | |||||||
\(182\) | 3.41468i | 0.253113i | ||||||||
\(183\) | 9.42401i | 0.696643i | ||||||||
\(184\) | 0.867993 | 0.0639893 | ||||||||
\(185\) | −1.75233 | + | 1.38900i | −0.128834 | + | 0.102122i | ||||
\(186\) | −3.86799 | −0.283615 | ||||||||
\(187\) | − | 0.838688i | − | 0.0613309i | ||||||
\(188\) | 0.778008i | 0.0567421i | ||||||||
\(189\) | 2.50466 | 0.182188 | ||||||||
\(190\) | 10.7617 | − | 8.53034i | 0.780733 | − | 0.618856i | ||||
\(191\) | −2.00933 | −0.145390 | −0.0726950 | − | 0.997354i | \(-0.523160\pi\) | ||||
−0.0726950 | + | 0.997354i | \(0.523160\pi\) | |||||||
\(192\) | − | 1.00000i | − | 0.0721688i | ||||||
\(193\) | 6.00000i | 0.431889i | 0.976406 | + | 0.215945i | \(0.0692831\pi\) | ||||
−0.976406 | + | 0.215945i | \(0.930717\pi\) | |||||||
\(194\) | −4.46603 | −0.320642 | ||||||||
\(195\) | 1.89367 | + | 2.38900i | 0.135608 | + | 0.171080i | ||||
\(196\) | −0.726656 | −0.0519040 | ||||||||
\(197\) | 2.76529i | 0.197019i | 0.995136 | + | 0.0985094i | \(0.0314074\pi\) | ||||
−0.995136 | + | 0.0985094i | \(0.968593\pi\) | |||||||
\(198\) | 3.77801i | 0.268491i | ||||||||
\(199\) | −1.98134 | −0.140454 | −0.0702268 | − | 0.997531i | \(-0.522372\pi\) | ||||
−0.0702268 | + | 0.997531i | \(0.522372\pi\) | |||||||
\(200\) | 4.86799 | + | 1.14134i | 0.344219 | + | 0.0807047i | ||||
\(201\) | −10.7267 | −0.756600 | ||||||||
\(202\) | − | 6.56534i | − | 0.461936i | ||||||
\(203\) | − | 1.61801i | − | 0.113562i | ||||||
\(204\) | 0.221992 | 0.0155426 | ||||||||
\(205\) | −1.26401 | − | 1.59465i | −0.0882826 | − | 0.111375i | ||||
\(206\) | 16.9580 | 1.18152 | ||||||||
\(207\) | − | 0.867993i | − | 0.0603297i | ||||||
\(208\) | − | 1.36333i | − | 0.0945298i | ||||||
\(209\) | 23.2020 | 1.60492 | ||||||||
\(210\) | 4.38900 | − | 3.47899i | 0.302870 | − | 0.240073i | ||||
\(211\) | −20.9473 | −1.44207 | −0.721037 | − | 0.692897i | \(-0.756334\pi\) | ||||
−0.721037 | + | 0.692897i | \(0.756334\pi\) | |||||||
\(212\) | 2.27334i | 0.156134i | ||||||||
\(213\) | − | 11.2406i | − | 0.770197i | ||||||
\(214\) | −15.8260 | −1.08184 | ||||||||
\(215\) | −8.05135 | + | 6.38199i | −0.549098 | + | 0.435248i | ||||
\(216\) | −1.00000 | −0.0680414 | ||||||||
\(217\) | 9.68802i | 0.657666i | ||||||||
\(218\) | − | 0.948649i | − | 0.0642506i | ||||||
\(219\) | 2.86799 | 0.193801 | ||||||||
\(220\) | 5.24767 | + | 6.62032i | 0.353798 | + | 0.446342i | ||||
\(221\) | 0.302648 | 0.0203583 | ||||||||
\(222\) | − | 1.00000i | − | 0.0671156i | ||||||
\(223\) | 20.1507i | 1.34939i | 0.738097 | + | 0.674694i | \(0.235724\pi\) | ||||
−0.738097 | + | 0.674694i | \(0.764276\pi\) | |||||||
\(224\) | −2.50466 | −0.167350 | ||||||||
\(225\) | 1.14134 | − | 4.86799i | 0.0760891 | − | 0.324533i | ||||
\(226\) | −0.311977 | −0.0207524 | ||||||||
\(227\) | 28.4520i | 1.88843i | 0.329337 | + | 0.944213i | \(0.393175\pi\) | ||||
−0.329337 | + | 0.944213i | \(0.606825\pi\) | |||||||
\(228\) | 6.14134i | 0.406720i | ||||||||
\(229\) | −18.6940 | −1.23533 | −0.617666 | − | 0.786441i | \(-0.711922\pi\) | ||||
−0.617666 | + | 0.786441i | \(0.711922\pi\) | |||||||
\(230\) | −1.20565 | − | 1.52101i | −0.0794979 | − | 0.100293i | ||||
\(231\) | 9.46264 | 0.622596 | ||||||||
\(232\) | 0.646000i | 0.0424120i | ||||||||
\(233\) | − | 9.00933i | − | 0.590221i | −0.955463 | − | 0.295110i | \(-0.904644\pi\) | ||
0.955463 | − | 0.295110i | \(-0.0953564\pi\) | |||||||
\(234\) | −1.36333 | −0.0891236 | ||||||||
\(235\) | 1.36333 | − | 1.08066i | 0.0889337 | − | 0.0704942i | ||||
\(236\) | 7.78734 | 0.506912 | ||||||||
\(237\) | 0.495336i | 0.0321755i | ||||||||
\(238\) | − | 0.556016i | − | 0.0360411i | ||||||
\(239\) | −16.1693 | −1.04591 | −0.522953 | − | 0.852361i | \(-0.675170\pi\) | ||||
−0.522953 | + | 0.852361i | \(0.675170\pi\) | |||||||
\(240\) | −1.75233 | + | 1.38900i | −0.113113 | + | 0.0896598i | ||||
\(241\) | 10.3527 | 0.666875 | 0.333437 | − | 0.942772i | \(-0.391791\pi\) | ||||
0.333437 | + | 0.942772i | \(0.391791\pi\) | |||||||
\(242\) | 3.27334i | 0.210418i | ||||||||
\(243\) | 1.00000i | 0.0641500i | ||||||||
\(244\) | −9.42401 | −0.603310 | ||||||||
\(245\) | 1.00933 | + | 1.27334i | 0.0644836 | + | 0.0813509i | ||||
\(246\) | 0.910015 | 0.0580205 | ||||||||
\(247\) | 8.37266i | 0.532739i | ||||||||
\(248\) | − | 3.86799i | − | 0.245618i | ||||||
\(249\) | 1.08066 | 0.0684838 | ||||||||
\(250\) | −4.76166 | − | 10.1157i | −0.301154 | − | 0.639771i | ||||
\(251\) | 8.38538 | 0.529280 | 0.264640 | − | 0.964347i | \(-0.414747\pi\) | ||||
0.264640 | + | 0.964347i | \(0.414747\pi\) | |||||||
\(252\) | 2.50466i | 0.157779i | ||||||||
\(253\) | − | 3.27928i | − | 0.206167i | ||||||
\(254\) | 3.09931 | 0.194468 | ||||||||
\(255\) | −0.308348 | − | 0.389004i | −0.0193095 | − | 0.0243604i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 6.55263i | 0.408742i | 0.978894 | + | 0.204371i | \(0.0655148\pi\) | ||||
−0.978894 | + | 0.204371i | \(0.934485\pi\) | |||||||
\(258\) | − | 4.59465i | − | 0.286050i | ||||||
\(259\) | −2.50466 | −0.155632 | ||||||||
\(260\) | −2.38900 | + | 1.89367i | −0.148160 | + | 0.117440i | ||||
\(261\) | 0.646000 | 0.0399864 | ||||||||
\(262\) | − | 11.3434i | − | 0.700795i | ||||||
\(263\) | 15.4754i | 0.954252i | 0.878835 | + | 0.477126i | \(0.158321\pi\) | ||||
−0.878835 | + | 0.477126i | \(0.841679\pi\) | |||||||
\(264\) | −3.77801 | −0.232520 | ||||||||
\(265\) | 3.98365 | − | 3.15768i | 0.244714 | − | 0.193975i | ||||
\(266\) | 15.3820 | 0.943130 | ||||||||
\(267\) | 0.0899847i | 0.00550698i | ||||||||
\(268\) | − | 10.7267i | − | 0.655235i | ||||||
\(269\) | 3.31198 | 0.201935 | 0.100967 | − | 0.994890i | \(-0.467806\pi\) | ||||
0.100967 | + | 0.994890i | \(0.467806\pi\) | |||||||
\(270\) | 1.38900 | + | 1.75233i | 0.0845321 | + | 0.106644i | ||||
\(271\) | 32.1986 | 1.95593 | 0.977964 | − | 0.208775i | \(-0.0669477\pi\) | ||||
0.977964 | + | 0.208775i | \(0.0669477\pi\) | |||||||
\(272\) | 0.221992i | 0.0134602i | ||||||||
\(273\) | 3.41468i | 0.206666i | ||||||||
\(274\) | −10.4953 | −0.634046 | ||||||||
\(275\) | 4.31198 | − | 18.3913i | 0.260022 | − | 1.10904i | ||||
\(276\) | 0.867993 | 0.0522470 | ||||||||
\(277\) | 20.6553i | 1.24106i | 0.784183 | + | 0.620529i | \(0.213082\pi\) | ||||
−0.784183 | + | 0.620529i | \(0.786918\pi\) | |||||||
\(278\) | 18.8773i | 1.13219i | ||||||||
\(279\) | −3.86799 | −0.231571 | ||||||||
\(280\) | 3.47899 | + | 4.38900i | 0.207909 | + | 0.262293i | ||||
\(281\) | −9.80731 | −0.585055 | −0.292528 | − | 0.956257i | \(-0.594496\pi\) | ||||
−0.292528 | + | 0.956257i | \(0.594496\pi\) | |||||||
\(282\) | 0.778008i | 0.0463297i | ||||||||
\(283\) | 18.6040i | 1.10589i | 0.833217 | + | 0.552946i | \(0.186496\pi\) | ||||
−0.833217 | + | 0.552946i | \(0.813504\pi\) | |||||||
\(284\) | 11.2406 | 0.667010 | ||||||||
\(285\) | 10.7617 | − | 8.53034i | 0.637466 | − | 0.505294i | ||||
\(286\) | −5.15066 | −0.304565 | ||||||||
\(287\) | − | 2.27928i | − | 0.134542i | ||||||
\(288\) | − | 1.00000i | − | 0.0589256i | ||||||
\(289\) | 16.9507 | 0.997101 | ||||||||
\(290\) | 1.13201 | − | 0.897297i | 0.0664738 | − | 0.0526911i | ||||
\(291\) | −4.46603 | −0.261803 | ||||||||
\(292\) | 2.86799i | 0.167837i | ||||||||
\(293\) | − | 27.8480i | − | 1.62690i | −0.581636 | − | 0.813449i | \(-0.697587\pi\) | ||
0.581636 | − | 0.813449i | \(-0.302413\pi\) | |||||||
\(294\) | −0.726656 | −0.0423795 | ||||||||
\(295\) | −10.8166 | − | 13.6460i | −0.629769 | − | 0.794501i | ||||
\(296\) | 1.00000 | 0.0581238 | ||||||||
\(297\) | 3.77801i | 0.219222i | ||||||||
\(298\) | 17.0280i | 0.986405i | ||||||||
\(299\) | 1.18336 | 0.0684354 | ||||||||
\(300\) | 4.86799 | + | 1.14134i | 0.281054 | + | 0.0658951i | ||||
\(301\) | −11.5081 | −0.663313 | ||||||||
\(302\) | 22.3727i | 1.28740i | ||||||||
\(303\) | − | 6.56534i | − | 0.377169i | ||||||
\(304\) | −6.14134 | −0.352230 | ||||||||
\(305\) | 13.0900 | + | 16.5140i | 0.749530 | + | 0.945588i | ||||
\(306\) | 0.221992 | 0.0126904 | ||||||||
\(307\) | 6.05135i | 0.345369i | 0.984977 | + | 0.172684i | \(0.0552441\pi\) | ||||
−0.984977 | + | 0.172684i | \(0.944756\pi\) | |||||||
\(308\) | 9.46264i | 0.539184i | ||||||||
\(309\) | 16.9580 | 0.964706 | ||||||||
\(310\) | −6.77801 | + | 5.37266i | −0.384965 | + | 0.305146i | ||||
\(311\) | −28.3306 | −1.60648 | −0.803241 | − | 0.595654i | \(-0.796893\pi\) | ||||
−0.803241 | + | 0.595654i | \(0.796893\pi\) | |||||||
\(312\) | − | 1.36333i | − | 0.0771833i | ||||||
\(313\) | − | 1.50466i | − | 0.0850487i | −0.999095 | − | 0.0425243i | \(-0.986460\pi\) | ||
0.999095 | − | 0.0425243i | \(-0.0135400\pi\) | |||||||
\(314\) | −16.9800 | −0.958238 | ||||||||
\(315\) | 4.38900 | − | 3.47899i | 0.247292 | − | 0.196019i | ||||
\(316\) | −0.495336 | −0.0278648 | ||||||||
\(317\) | − | 20.0480i | − | 1.12601i | −0.826455 | − | 0.563003i | \(-0.809646\pi\) | ||
0.826455 | − | 0.563003i | \(-0.190354\pi\) | |||||||
\(318\) | 2.27334i | 0.127483i | ||||||||
\(319\) | 2.44059 | 0.136647 | ||||||||
\(320\) | −1.38900 | − | 1.75233i | −0.0776477 | − | 0.0979583i | ||||
\(321\) | −15.8260 | −0.883320 | ||||||||
\(322\) | − | 2.17403i | − | 0.121154i | ||||||
\(323\) | − | 1.36333i | − | 0.0758576i | ||||||
\(324\) | −1.00000 | −0.0555556 | ||||||||
\(325\) | 6.63667 | + | 1.55602i | 0.368136 | + | 0.0863122i | ||||
\(326\) | 7.00000 | 0.387694 | ||||||||
\(327\) | − | 0.948649i | − | 0.0524604i | ||||||
\(328\) | 0.910015i | 0.0502472i | ||||||||
\(329\) | 1.94865 | 0.107432 | ||||||||
\(330\) | 5.24767 | + | 6.62032i | 0.288875 | + | 0.364437i | ||||
\(331\) | 21.5747 | 1.18585 | 0.592926 | − | 0.805257i | \(-0.297973\pi\) | ||||
0.592926 | + | 0.805257i | \(0.297973\pi\) | |||||||
\(332\) | 1.08066i | 0.0593087i | ||||||||
\(333\) | − | 1.00000i | − | 0.0547997i | ||||||
\(334\) | −23.4333 | −1.28222 | ||||||||
\(335\) | −18.7967 | + | 14.8994i | −1.02697 | + | 0.814039i | ||||
\(336\) | −2.50466 | −0.136641 | ||||||||
\(337\) | 12.4427i | 0.677795i | 0.940823 | + | 0.338898i | \(0.110054\pi\) | ||||
−0.940823 | + | 0.338898i | \(0.889946\pi\) | |||||||
\(338\) | 11.1413i | 0.606009i | ||||||||
\(339\) | −0.311977 | −0.0169443 | ||||||||
\(340\) | 0.389004 | − | 0.308348i | 0.0210967 | − | 0.0167225i | ||||
\(341\) | −14.6133 | −0.791355 | ||||||||
\(342\) | 6.14134i | 0.332085i | ||||||||
\(343\) | 19.3527i | 1.04495i | ||||||||
\(344\) | 4.59465 | 0.247727 | ||||||||
\(345\) | −1.20565 | − | 1.52101i | −0.0649098 | − | 0.0818885i | ||||
\(346\) | −7.28267 | −0.391519 | ||||||||
\(347\) | − | 12.0700i | − | 0.647952i | −0.946065 | − | 0.323976i | \(-0.894980\pi\) | ||
0.946065 | − | 0.323976i | \(-0.105020\pi\) | |||||||
\(348\) | 0.646000i | 0.0346293i | ||||||||
\(349\) | 19.3434 | 1.03543 | 0.517713 | − | 0.855554i | \(-0.326784\pi\) | ||||
0.517713 | + | 0.855554i | \(0.326784\pi\) | |||||||
\(350\) | 2.85866 | − | 12.1927i | 0.152802 | − | 0.651727i | ||||
\(351\) | −1.36333 | −0.0727691 | ||||||||
\(352\) | − | 3.77801i | − | 0.201368i | ||||||
\(353\) | − | 5.48262i | − | 0.291810i | −0.989299 | − | 0.145905i | \(-0.953391\pi\) | ||
0.989299 | − | 0.145905i | \(-0.0466094\pi\) | |||||||
\(354\) | 7.78734 | 0.413892 | ||||||||
\(355\) | −15.6133 | − | 19.6974i | −0.828668 | − | 1.04543i | ||||
\(356\) | −0.0899847 | −0.00476918 | ||||||||
\(357\) | − | 0.556016i | − | 0.0294275i | ||||||
\(358\) | − | 1.82003i | − | 0.0961916i | ||||||
\(359\) | 1.60737 | 0.0848336 | 0.0424168 | − | 0.999100i | \(-0.486494\pi\) | ||||
0.0424168 | + | 0.999100i | \(0.486494\pi\) | |||||||
\(360\) | −1.75233 | + | 1.38900i | −0.0923560 | + | 0.0732069i | ||||
\(361\) | 18.7160 | 0.985053 | ||||||||
\(362\) | 0.212663i | 0.0111773i | ||||||||
\(363\) | 3.27334i | 0.171806i | ||||||||
\(364\) | −3.41468 | −0.178978 | ||||||||
\(365\) | 5.02568 | − | 3.98365i | 0.263056 | − | 0.208514i | ||||
\(366\) | −9.42401 | −0.492601 | ||||||||
\(367\) | − | 7.51399i | − | 0.392227i | −0.980581 | − | 0.196114i | \(-0.937168\pi\) | ||
0.980581 | − | 0.196114i | \(-0.0628321\pi\) | |||||||
\(368\) | 0.867993i | 0.0452472i | ||||||||
\(369\) | 0.910015 | 0.0473735 | ||||||||
\(370\) | −1.38900 | − | 1.75233i | −0.0722109 | − | 0.0910994i | ||||
\(371\) | 5.69396 | 0.295616 | ||||||||
\(372\) | − | 3.86799i | − | 0.200546i | ||||||
\(373\) | 12.5140i | 0.647950i | 0.946066 | + | 0.323975i | \(0.105019\pi\) | ||||
−0.946066 | + | 0.323975i | \(0.894981\pi\) | |||||||
\(374\) | 0.838688 | 0.0433675 | ||||||||
\(375\) | −4.76166 | − | 10.1157i | −0.245891 | − | 0.522370i | ||||
\(376\) | −0.778008 | −0.0401227 | ||||||||
\(377\) | 0.880711i | 0.0453589i | ||||||||
\(378\) | 2.50466i | 0.128826i | ||||||||
\(379\) | −37.6260 | −1.93272 | −0.966360 | − | 0.257195i | \(-0.917202\pi\) | ||||
−0.966360 | + | 0.257195i | \(0.917202\pi\) | |||||||
\(380\) | 8.53034 | + | 10.7617i | 0.437597 | + | 0.552062i | ||||
\(381\) | 3.09931 | 0.158783 | ||||||||
\(382\) | − | 2.00933i | − | 0.102806i | ||||||
\(383\) | − | 14.2440i | − | 0.727836i | −0.931431 | − | 0.363918i | \(-0.881439\pi\) | ||
0.931431 | − | 0.363918i | \(-0.118561\pi\) | |||||||
\(384\) | 1.00000 | 0.0510310 | ||||||||
\(385\) | 16.5817 | − | 13.1436i | 0.845081 | − | 0.669862i | ||||
\(386\) | −6.00000 | −0.305392 | ||||||||
\(387\) | − | 4.59465i | − | 0.233559i | ||||||
\(388\) | − | 4.46603i | − | 0.226728i | ||||||
\(389\) | −0.697352 | −0.0353571 | −0.0176786 | − | 0.999844i | \(-0.505628\pi\) | ||||
−0.0176786 | + | 0.999844i | \(0.505628\pi\) | |||||||
\(390\) | −2.38900 | + | 1.89367i | −0.120972 | + | 0.0958896i | ||||
\(391\) | −0.192688 | −0.00974463 | ||||||||
\(392\) | − | 0.726656i | − | 0.0367017i | ||||||
\(393\) | − | 11.3434i | − | 0.572196i | ||||||
\(394\) | −2.76529 | −0.139313 | ||||||||
\(395\) | 0.688023 | + | 0.867993i | 0.0346182 | + | 0.0436734i | ||||
\(396\) | −3.77801 | −0.189852 | ||||||||
\(397\) | − | 28.4040i | − | 1.42556i | −0.701389 | − | 0.712779i | \(-0.747436\pi\) | ||
0.701389 | − | 0.712779i | \(-0.252564\pi\) | |||||||
\(398\) | − | 1.98134i | − | 0.0993157i | ||||||
\(399\) | 15.3820 | 0.770062 | ||||||||
\(400\) | −1.14134 | + | 4.86799i | −0.0570668 | + | 0.243400i | ||||
\(401\) | 22.7580 | 1.13648 | 0.568241 | − | 0.822862i | \(-0.307624\pi\) | ||||
0.568241 | + | 0.822862i | \(0.307624\pi\) | |||||||
\(402\) | − | 10.7267i | − | 0.534997i | ||||||
\(403\) | − | 5.27334i | − | 0.262684i | ||||||
\(404\) | 6.56534 | 0.326638 | ||||||||
\(405\) | 1.38900 | + | 1.75233i | 0.0690202 | + | 0.0870741i | ||||
\(406\) | 1.61801 | 0.0803007 | ||||||||
\(407\) | − | 3.77801i | − | 0.187269i | ||||||
\(408\) | 0.221992i | 0.0109902i | ||||||||
\(409\) | 16.3527 | 0.808588 | 0.404294 | − | 0.914629i | \(-0.367517\pi\) | ||||
0.404294 | + | 0.914629i | \(0.367517\pi\) | |||||||
\(410\) | 1.59465 | − | 1.26401i | 0.0787541 | − | 0.0624252i | ||||
\(411\) | −10.4953 | −0.517697 | ||||||||
\(412\) | 16.9580i | 0.835460i | ||||||||
\(413\) | − | 19.5047i | − | 0.959762i | ||||||
\(414\) | 0.867993 | 0.0426595 | ||||||||
\(415\) | 1.89367 | − | 1.50104i | 0.0929565 | − | 0.0736829i | ||||
\(416\) | 1.36333 | 0.0668427 | ||||||||
\(417\) | 18.8773i | 0.924426i | ||||||||
\(418\) | 23.2020i | 1.13485i | ||||||||
\(419\) | −11.2020 | −0.547254 | −0.273627 | − | 0.961836i | \(-0.588223\pi\) | ||||
−0.273627 | + | 0.961836i | \(0.588223\pi\) | |||||||
\(420\) | 3.47899 | + | 4.38900i | 0.169757 | + | 0.214161i | ||||
\(421\) | 13.8200 | 0.673547 | 0.336774 | − | 0.941586i | \(-0.390664\pi\) | ||||
0.336774 | + | 0.941586i | \(0.390664\pi\) | |||||||
\(422\) | − | 20.9473i | − | 1.01970i | ||||||
\(423\) | 0.778008i | 0.0378280i | ||||||||
\(424\) | −2.27334 | −0.110403 | ||||||||
\(425\) | −1.08066 | − | 0.253368i | −0.0524195 | − | 0.0122901i | ||||
\(426\) | 11.2406 | 0.544611 | ||||||||
\(427\) | 23.6040i | 1.14228i | ||||||||
\(428\) | − | 15.8260i | − | 0.764977i | ||||||
\(429\) | −5.15066 | −0.248676 | ||||||||
\(430\) | −6.38199 | − | 8.05135i | −0.307767 | − | 0.388271i | ||||
\(431\) | 36.1493 | 1.74125 | 0.870626 | − | 0.491945i | \(-0.163714\pi\) | ||||
0.870626 | + | 0.491945i | \(0.163714\pi\) | |||||||
\(432\) | − | 1.00000i | − | 0.0481125i | ||||||
\(433\) | − | 19.4147i | − | 0.933010i | −0.884519 | − | 0.466505i | \(-0.845513\pi\) | ||
0.884519 | − | 0.466505i | \(-0.154487\pi\) | |||||||
\(434\) | −9.68802 | −0.465040 | ||||||||
\(435\) | 1.13201 | − | 0.897297i | 0.0542756 | − | 0.0430221i | ||||
\(436\) | 0.948649 | 0.0454320 | ||||||||
\(437\) | − | 5.33063i | − | 0.254999i | ||||||
\(438\) | 2.86799i | 0.137038i | ||||||||
\(439\) | 24.2207 | 1.15599 | 0.577995 | − | 0.816040i | \(-0.303835\pi\) | ||||
0.577995 | + | 0.816040i | \(0.303835\pi\) | |||||||
\(440\) | −6.62032 | + | 5.24767i | −0.315612 | + | 0.250173i | ||||
\(441\) | −0.726656 | −0.0346027 | ||||||||
\(442\) | 0.302648i | 0.0143955i | ||||||||
\(443\) | − | 22.0373i | − | 1.04702i | −0.852018 | − | 0.523512i | \(-0.824621\pi\) | ||
0.852018 | − | 0.523512i | \(-0.175379\pi\) | |||||||
\(444\) | 1.00000 | 0.0474579 | ||||||||
\(445\) | 0.124989 | + | 0.157683i | 0.00592505 | + | 0.00747490i | ||||
\(446\) | −20.1507 | −0.954162 | ||||||||
\(447\) | 17.0280i | 0.805396i | ||||||||
\(448\) | − | 2.50466i | − | 0.118334i | ||||||
\(449\) | −1.63328 | −0.0770794 | −0.0385397 | − | 0.999257i | \(-0.512271\pi\) | ||||
−0.0385397 | + | 0.999257i | \(0.512271\pi\) | |||||||
\(450\) | 4.86799 | + | 1.14134i | 0.229479 | + | 0.0538031i | ||||
\(451\) | 3.43804 | 0.161891 | ||||||||
\(452\) | − | 0.311977i | − | 0.0146742i | ||||||
\(453\) | 22.3727i | 1.05116i | ||||||||
\(454\) | −28.4520 | −1.33532 | ||||||||
\(455\) | 4.74300 | + | 5.98365i | 0.222355 | + | 0.280518i | ||||
\(456\) | −6.14134 | −0.287594 | ||||||||
\(457\) | − | 14.2279i | − | 0.665555i | −0.943005 | − | 0.332777i | \(-0.892014\pi\) | ||
0.943005 | − | 0.332777i | \(-0.107986\pi\) | |||||||
\(458\) | − | 18.6940i | − | 0.873512i | ||||||
\(459\) | 0.221992 | 0.0103617 | ||||||||
\(460\) | 1.52101 | − | 1.20565i | 0.0709175 | − | 0.0562135i | ||||
\(461\) | −20.8587 | −0.971485 | −0.485742 | − | 0.874102i | \(-0.661451\pi\) | ||||
−0.485742 | + | 0.874102i | \(0.661451\pi\) | |||||||
\(462\) | 9.46264i | 0.440242i | ||||||||
\(463\) | − | 0.0326940i | − | 0.00151942i | −1.00000 | 0.000759709i | \(-0.999758\pi\) | |||
1.00000 | 0.000759709i | \(-0.000241823\pi\) | ||||||||
\(464\) | −0.646000 | −0.0299898 | ||||||||
\(465\) | −6.77801 | + | 5.37266i | −0.314323 | + | 0.249151i | ||||
\(466\) | 9.00933 | 0.417349 | ||||||||
\(467\) | 16.1834i | 0.748877i | 0.927252 | + | 0.374438i | \(0.122164\pi\) | ||||
−0.927252 | + | 0.374438i | \(0.877836\pi\) | |||||||
\(468\) | − | 1.36333i | − | 0.0630199i | ||||||
\(469\) | −26.8667 | −1.24059 | ||||||||
\(470\) | 1.08066 | + | 1.36333i | 0.0498469 | + | 0.0628856i | ||||
\(471\) | −16.9800 | −0.782398 | ||||||||
\(472\) | 7.78734i | 0.358441i | ||||||||
\(473\) | − | 17.3586i | − | 0.798150i | ||||||
\(474\) | −0.495336 | −0.0227515 | ||||||||
\(475\) | 7.00933 | − | 29.8960i | 0.321610 | − | 1.37172i | ||||
\(476\) | 0.556016 | 0.0254849 | ||||||||
\(477\) | 2.27334i | 0.104089i | ||||||||
\(478\) | − | 16.1693i | − | 0.739568i | ||||||
\(479\) | 1.15066 | 0.0525752 | 0.0262876 | − | 0.999654i | \(-0.491631\pi\) | ||||
0.0262876 | + | 0.999654i | \(0.491631\pi\) | |||||||
\(480\) | −1.38900 | − | 1.75233i | −0.0633991 | − | 0.0799827i | ||||
\(481\) | 1.36333 | 0.0621624 | ||||||||
\(482\) | 10.3527i | 0.471552i | ||||||||
\(483\) | − | 2.17403i | − | 0.0989218i | ||||||
\(484\) | −3.27334 | −0.148788 | ||||||||
\(485\) | −7.82597 | + | 6.20333i | −0.355359 | + | 0.281679i | ||||
\(486\) | −1.00000 | −0.0453609 | ||||||||
\(487\) | 3.71733i | 0.168448i | 0.996447 | + | 0.0842241i | \(0.0268412\pi\) | ||||
−0.996447 | + | 0.0842241i | \(0.973159\pi\) | |||||||
\(488\) | − | 9.42401i | − | 0.426605i | ||||||
\(489\) | 7.00000 | 0.316551 | ||||||||
\(490\) | −1.27334 | + | 1.00933i | −0.0575238 | + | 0.0455968i | ||||
\(491\) | 10.9966 | 0.496270 | 0.248135 | − | 0.968725i | \(-0.420182\pi\) | ||||
0.248135 | + | 0.968725i | \(0.420182\pi\) | |||||||
\(492\) | 0.910015i | 0.0410267i | ||||||||
\(493\) | − | 0.143407i | − | 0.00645873i | ||||||
\(494\) | −8.37266 | −0.376704 | ||||||||
\(495\) | 5.24767 | + | 6.62032i | 0.235865 | + | 0.297561i | ||||
\(496\) | 3.86799 | 0.173678 | ||||||||
\(497\) | − | 28.1541i | − | 1.26288i | ||||||
\(498\) | 1.08066i | 0.0484254i | ||||||||
\(499\) | −29.5547 | −1.32305 | −0.661525 | − | 0.749923i | \(-0.730090\pi\) | ||||
−0.661525 | + | 0.749923i | \(0.730090\pi\) | |||||||
\(500\) | 10.1157 | − | 4.76166i | 0.452386 | − | 0.212948i | ||||
\(501\) | −23.4333 | −1.04692 | ||||||||
\(502\) | 8.38538i | 0.374258i | ||||||||
\(503\) | − | 9.11203i | − | 0.406285i | −0.979149 | − | 0.203143i | \(-0.934884\pi\) | ||
0.979149 | − | 0.203143i | \(-0.0651155\pi\) | |||||||
\(504\) | −2.50466 | −0.111567 | ||||||||
\(505\) | −9.11929 | − | 11.5047i | −0.405803 | − | 0.511951i | ||||
\(506\) | 3.27928 | 0.145782 | ||||||||
\(507\) | 11.1413i | 0.494804i | ||||||||
\(508\) | 3.09931i | 0.137510i | ||||||||
\(509\) | 21.8001 | 0.966270 | 0.483135 | − | 0.875546i | \(-0.339498\pi\) | ||||
0.483135 | + | 0.875546i | \(0.339498\pi\) | |||||||
\(510\) | 0.389004 | − | 0.308348i | 0.0172254 | − | 0.0136539i | ||||
\(511\) | 7.18336 | 0.317773 | ||||||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | 6.14134i | 0.271147i | ||||||||
\(514\) | −6.55263 | −0.289024 | ||||||||
\(515\) | 29.7160 | − | 23.5547i | 1.30944 | − | 1.03794i | ||||
\(516\) | 4.59465 | 0.202268 | ||||||||
\(517\) | 2.93932i | 0.129271i | ||||||||
\(518\) | − | 2.50466i | − | 0.110049i | ||||||
\(519\) | −7.28267 | −0.319674 | ||||||||
\(520\) | −1.89367 | − | 2.38900i | −0.0830428 | − | 0.104765i | ||||
\(521\) | −11.4499 | −0.501630 | −0.250815 | − | 0.968035i | \(-0.580699\pi\) | ||||
−0.250815 | + | 0.968035i | \(0.580699\pi\) | |||||||
\(522\) | 0.646000i | 0.0282747i | ||||||||
\(523\) | 10.8294i | 0.473535i | 0.971566 | + | 0.236767i | \(0.0760879\pi\) | ||||
−0.971566 | + | 0.236767i | \(0.923912\pi\) | |||||||
\(524\) | 11.3434 | 0.495537 | ||||||||
\(525\) | 2.85866 | − | 12.1927i | 0.124762 | − | 0.532133i | ||||
\(526\) | −15.4754 | −0.674758 | ||||||||
\(527\) | 0.858664i | 0.0374040i | ||||||||
\(528\) | − | 3.77801i | − | 0.164417i | ||||||
\(529\) | 22.2466 | 0.967243 | ||||||||
\(530\) | 3.15768 | + | 3.98365i | 0.137161 | + | 0.173039i | ||||
\(531\) | 7.78734 | 0.337942 | ||||||||
\(532\) | 15.3820i | 0.666894i | ||||||||
\(533\) | 1.24065i | 0.0537385i | ||||||||
\(534\) | −0.0899847 | −0.00389402 | ||||||||
\(535\) | −27.7324 | + | 21.9823i | −1.19897 | + | 0.950379i | ||||
\(536\) | 10.7267 | 0.463321 | ||||||||
\(537\) | − | 1.82003i | − | 0.0785401i | ||||||
\(538\) | 3.31198i | 0.142789i | ||||||||
\(539\) | −2.74531 | −0.118249 | ||||||||
\(540\) | −1.75233 | + | 1.38900i | −0.0754084 | + | 0.0597732i | ||||
\(541\) | −7.64600 | −0.328727 | −0.164364 | − | 0.986400i | \(-0.552557\pi\) | ||||
−0.164364 | + | 0.986400i | \(0.552557\pi\) | |||||||
\(542\) | 32.1986i | 1.38305i | ||||||||
\(543\) | 0.212663i | 0.00912626i | ||||||||
\(544\) | −0.221992 | −0.00951783 | ||||||||
\(545\) | −1.31768 | − | 1.66235i | −0.0564431 | − | 0.0712071i | ||||
\(546\) | −3.41468 | −0.146135 | ||||||||
\(547\) | − | 41.1400i | − | 1.75902i | −0.475880 | − | 0.879510i | \(-0.657870\pi\) | ||
0.475880 | − | 0.879510i | \(-0.342130\pi\) | |||||||
\(548\) | − | 10.4953i | − | 0.448339i | ||||||
\(549\) | −9.42401 | −0.402207 | ||||||||
\(550\) | 18.3913 | + | 4.31198i | 0.784208 | + | 0.183863i | ||||
\(551\) | 3.96731 | 0.169013 | ||||||||
\(552\) | 0.867993i | 0.0369442i | ||||||||
\(553\) | 1.24065i | 0.0527578i | ||||||||
\(554\) | −20.6553 | −0.877561 | ||||||||
\(555\) | −1.38900 | − | 1.75233i | −0.0589599 | − | 0.0743824i | ||||
\(556\) | −18.8773 | −0.800577 | ||||||||
\(557\) | − | 17.1820i | − | 0.728026i | −0.931394 | − | 0.364013i | \(-0.881406\pi\) | ||
0.931394 | − | 0.364013i | \(-0.118594\pi\) | |||||||
\(558\) | − | 3.86799i | − | 0.163745i | ||||||
\(559\) | 6.26401 | 0.264940 | ||||||||
\(560\) | −4.38900 | + | 3.47899i | −0.185469 | + | 0.147014i | ||||
\(561\) | 0.838688 | 0.0354094 | ||||||||
\(562\) | − | 9.80731i | − | 0.413697i | ||||||
\(563\) | − | 27.3140i | − | 1.15115i | −0.817749 | − | 0.575575i | \(-0.804778\pi\) | ||
0.817749 | − | 0.575575i | \(-0.195222\pi\) | |||||||
\(564\) | −0.778008 | −0.0327600 | ||||||||
\(565\) | −0.546687 | + | 0.433337i | −0.0229993 | + | 0.0182306i | ||||
\(566\) | −18.6040 | −0.781984 | ||||||||
\(567\) | 2.50466i | 0.105186i | ||||||||
\(568\) | 11.2406i | 0.471647i | ||||||||
\(569\) | 28.1341 | 1.17944 | 0.589721 | − | 0.807607i | \(-0.299238\pi\) | ||||
0.589721 | + | 0.807607i | \(0.299238\pi\) | |||||||
\(570\) | 8.53034 | + | 10.7617i | 0.357297 | + | 0.450756i | ||||
\(571\) | −5.93800 | −0.248498 | −0.124249 | − | 0.992251i | \(-0.539652\pi\) | ||||
−0.124249 | + | 0.992251i | \(0.539652\pi\) | |||||||
\(572\) | − | 5.15066i | − | 0.215360i | ||||||
\(573\) | − | 2.00933i | − | 0.0839409i | ||||||
\(574\) | 2.27928 | 0.0951354 | ||||||||
\(575\) | −4.22538 | − | 0.990671i | −0.176211 | − | 0.0413138i | ||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | 2.46264i | 0.102521i | 0.998685 | + | 0.0512606i | \(0.0163239\pi\) | ||||
−0.998685 | + | 0.0512606i | \(0.983676\pi\) | |||||||
\(578\) | 16.9507i | 0.705057i | ||||||||
\(579\) | −6.00000 | −0.249351 | ||||||||
\(580\) | 0.897297 | + | 1.13201i | 0.0372582 | + | 0.0470040i | ||||
\(581\) | 2.70668 | 0.112292 | ||||||||
\(582\) | − | 4.46603i | − | 0.185123i | ||||||
\(583\) | 8.58871i | 0.355708i | ||||||||
\(584\) | −2.86799 | −0.118678 | ||||||||
\(585\) | −2.38900 | + | 1.89367i | −0.0987732 | + | 0.0782935i | ||||
\(586\) | 27.8480 | 1.15039 | ||||||||
\(587\) | 20.8187i | 0.859280i | 0.903000 | + | 0.429640i | \(0.141360\pi\) | ||||
−0.903000 | + | 0.429640i | \(0.858640\pi\) | |||||||
\(588\) | − | 0.726656i | − | 0.0299668i | ||||||
\(589\) | −23.7546 | −0.978793 | ||||||||
\(590\) | 13.6460 | − | 10.8166i | 0.561797 | − | 0.445314i | ||||
\(591\) | −2.76529 | −0.113749 | ||||||||
\(592\) | 1.00000i | 0.0410997i | ||||||||
\(593\) | 25.4533i | 1.04524i | 0.852565 | + | 0.522621i | \(0.175046\pi\) | ||||
−0.852565 | + | 0.522621i | \(0.824954\pi\) | |||||||
\(594\) | −3.77801 | −0.155014 | ||||||||
\(595\) | −0.772308 | − | 0.974324i | −0.0316615 | − | 0.0399434i | ||||
\(596\) | −17.0280 | −0.697493 | ||||||||
\(597\) | − | 1.98134i | − | 0.0810910i | ||||||
\(598\) | 1.18336i | 0.0483911i | ||||||||
\(599\) | 27.8247 | 1.13688 | 0.568442 | − | 0.822723i | \(-0.307546\pi\) | ||||
0.568442 | + | 0.822723i | \(0.307546\pi\) | |||||||
\(600\) | −1.14134 | + | 4.86799i | −0.0465949 | + | 0.198735i | ||||
\(601\) | −10.1120 | −0.412478 | −0.206239 | − | 0.978502i | \(-0.566122\pi\) | ||||
−0.206239 | + | 0.978502i | \(0.566122\pi\) | |||||||
\(602\) | − | 11.5081i | − | 0.469033i | ||||||
\(603\) | − | 10.7267i | − | 0.436823i | ||||||
\(604\) | −22.3727 | −0.910331 | ||||||||
\(605\) | 4.54669 | + | 5.73599i | 0.184849 | + | 0.233201i | ||||
\(606\) | 6.56534 | 0.266699 | ||||||||
\(607\) | − | 19.5933i | − | 0.795269i | −0.917544 | − | 0.397634i | \(-0.869831\pi\) | ||
0.917544 | − | 0.397634i | \(-0.130169\pi\) | |||||||
\(608\) | − | 6.14134i | − | 0.249064i | ||||||
\(609\) | 1.61801 | 0.0655653 | ||||||||
\(610\) | −16.5140 | + | 13.0900i | −0.668632 | + | 0.529998i | ||||
\(611\) | −1.06068 | −0.0429105 | ||||||||
\(612\) | 0.221992i | 0.00897350i | ||||||||
\(613\) | 12.1693i | 0.491514i | 0.969331 | + | 0.245757i | \(0.0790366\pi\) | ||||
−0.969331 | + | 0.245757i | \(0.920963\pi\) | |||||||
\(614\) | −6.05135 | −0.244213 | ||||||||
\(615\) | 1.59465 | − | 1.26401i | 0.0643025 | − | 0.0509700i | ||||
\(616\) | −9.46264 | −0.381261 | ||||||||
\(617\) | − | 27.1634i | − | 1.09356i | −0.837277 | − | 0.546778i | \(-0.815854\pi\) | ||
0.837277 | − | 0.546778i | \(-0.184146\pi\) | |||||||
\(618\) | 16.9580i | 0.682150i | ||||||||
\(619\) | −33.1273 | −1.33150 | −0.665749 | − | 0.746176i | \(-0.731888\pi\) | ||||
−0.665749 | + | 0.746176i | \(0.731888\pi\) | |||||||
\(620\) | −5.37266 | − | 6.77801i | −0.215771 | − | 0.272211i | ||||
\(621\) | 0.867993 | 0.0348313 | ||||||||
\(622\) | − | 28.3306i | − | 1.13595i | ||||||
\(623\) | 0.225382i | 0.00902972i | ||||||||
\(624\) | 1.36333 | 0.0545768 | ||||||||
\(625\) | −22.3947 | − | 11.1120i | −0.895788 | − | 0.444481i | ||||
\(626\) | 1.50466 | 0.0601385 | ||||||||
\(627\) | 23.2020i | 0.926599i | ||||||||
\(628\) | − | 16.9800i | − | 0.677577i | ||||||
\(629\) | −0.221992 | −0.00885141 | ||||||||
\(630\) | 3.47899 | + | 4.38900i | 0.138606 | + | 0.174862i | ||||
\(631\) | −28.5547 | −1.13674 | −0.568372 | − | 0.822772i | \(-0.692427\pi\) | ||||
−0.568372 | + | 0.822772i | \(0.692427\pi\) | |||||||
\(632\) | − | 0.495336i | − | 0.0197034i | ||||||
\(633\) | − | 20.9473i | − | 0.832582i | ||||||
\(634\) | 20.0480 | 0.796206 | ||||||||
\(635\) | 5.43103 | − | 4.30496i | 0.215524 | − | 0.170837i | ||||
\(636\) | −2.27334 | −0.0901439 | ||||||||
\(637\) | − | 0.990671i | − | 0.0392518i | ||||||
\(638\) | 2.44059i | 0.0966241i | ||||||||
\(639\) | 11.2406 | 0.444673 | ||||||||
\(640\) | 1.75233 | − | 1.38900i | 0.0692670 | − | 0.0549052i | ||||
\(641\) | −41.2373 | −1.62877 | −0.814387 | − | 0.580322i | \(-0.802927\pi\) | ||||
−0.814387 | + | 0.580322i | \(0.802927\pi\) | |||||||
\(642\) | − | 15.8260i | − | 0.624601i | ||||||
\(643\) | − | 12.7360i | − | 0.502258i | −0.967954 | − | 0.251129i | \(-0.919198\pi\) | ||
0.967954 | − | 0.251129i | \(-0.0808019\pi\) | |||||||
\(644\) | 2.17403 | 0.0856688 | ||||||||
\(645\) | −6.38199 | − | 8.05135i | −0.251290 | − | 0.317022i | ||||
\(646\) | 1.36333 | 0.0536394 | ||||||||
\(647\) | − | 28.6040i | − | 1.12454i | −0.826954 | − | 0.562269i | \(-0.809928\pi\) | ||
0.826954 | − | 0.562269i | \(-0.190072\pi\) | |||||||
\(648\) | − | 1.00000i | − | 0.0392837i | ||||||
\(649\) | 29.4206 | 1.15486 | ||||||||
\(650\) | −1.55602 | + | 6.63667i | −0.0610320 | + | 0.260312i | ||||
\(651\) | −9.68802 | −0.379704 | ||||||||
\(652\) | 7.00000i | 0.274141i | ||||||||
\(653\) | − | 25.2920i | − | 0.989752i | −0.868963 | − | 0.494876i | \(-0.835213\pi\) | ||
0.868963 | − | 0.494876i | \(-0.164787\pi\) | |||||||
\(654\) | 0.948649 | 0.0370951 | ||||||||
\(655\) | −15.7560 | − | 19.8773i | −0.615636 | − | 0.776671i | ||||
\(656\) | −0.910015 | −0.0355301 | ||||||||
\(657\) | 2.86799i | 0.111891i | ||||||||
\(658\) | 1.94865i | 0.0759662i | ||||||||
\(659\) | 28.4626 | 1.10875 | 0.554374 | − | 0.832268i | \(-0.312958\pi\) | ||||
0.554374 | + | 0.832268i | \(0.312958\pi\) | |||||||
\(660\) | −6.62032 | + | 5.24767i | −0.257696 | + | 0.204265i | ||||
\(661\) | 15.8994 | 0.618414 | 0.309207 | − | 0.950995i | \(-0.399936\pi\) | ||||
0.309207 | + | 0.950995i | \(0.399936\pi\) | |||||||
\(662\) | 21.5747i | 0.838523i | ||||||||
\(663\) | 0.302648i | 0.0117539i | ||||||||
\(664\) | −1.08066 | −0.0419376 | ||||||||
\(665\) | 26.9543 | − | 21.3656i | 1.04524 | − | 0.828524i | ||||
\(666\) | 1.00000 | 0.0387492 | ||||||||
\(667\) | − | 0.560724i | − | 0.0217113i | ||||||
\(668\) | − | 23.4333i | − | 0.906663i | ||||||
\(669\) | −20.1507 | −0.779070 | ||||||||
\(670\) | −14.8994 | − | 18.7967i | −0.575613 | − | 0.726179i | ||||
\(671\) | −35.6040 | −1.37448 | ||||||||
\(672\) | − | 2.50466i | − | 0.0966195i | ||||||
\(673\) | − | 27.5946i | − | 1.06370i | −0.846840 | − | 0.531848i | \(-0.821498\pi\) | ||
0.846840 | − | 0.531848i | \(-0.178502\pi\) | |||||||
\(674\) | −12.4427 | −0.479274 | ||||||||
\(675\) | 4.86799 | + | 1.14134i | 0.187369 | + | 0.0439300i | ||||
\(676\) | −11.1413 | −0.428513 | ||||||||
\(677\) | − | 4.34674i | − | 0.167059i | −0.996505 | − | 0.0835294i | \(-0.973381\pi\) | ||
0.996505 | − | 0.0835294i | \(-0.0266193\pi\) | |||||||
\(678\) | − | 0.311977i | − | 0.0119814i | ||||||
\(679\) | −11.1859 | −0.429276 | ||||||||
\(680\) | 0.308348 | + | 0.389004i | 0.0118246 | + | 0.0149176i | ||||
\(681\) | −28.4520 | −1.09028 | ||||||||
\(682\) | − | 14.6133i | − | 0.559572i | ||||||
\(683\) | 14.5620i | 0.557198i | 0.960408 | + | 0.278599i | \(0.0898700\pi\) | ||||
−0.960408 | + | 0.278599i | \(0.910130\pi\) | |||||||
\(684\) | −6.14134 | −0.234820 | ||||||||
\(685\) | −18.3913 | + | 14.5781i | −0.702696 | + | 0.556999i | ||||
\(686\) | −19.3527 | −0.738889 | ||||||||
\(687\) | − | 18.6940i | − | 0.713219i | ||||||
\(688\) | 4.59465i | 0.175169i | ||||||||
\(689\) | −3.09931 | −0.118074 | ||||||||
\(690\) | 1.52101 | − | 1.20565i | 0.0579039 | − | 0.0458981i | ||||
\(691\) | −43.9567 | −1.67219 | −0.836095 | − | 0.548585i | \(-0.815167\pi\) | ||||
−0.836095 | + | 0.548585i | \(0.815167\pi\) | |||||||
\(692\) | − | 7.28267i | − | 0.276846i | ||||||
\(693\) | 9.46264i | 0.359456i | ||||||||
\(694\) | 12.0700 | 0.458171 | ||||||||
\(695\) | 26.2207 | + | 33.0793i | 0.994607 | + | 1.25477i | ||||
\(696\) | −0.646000 | −0.0244866 | ||||||||
\(697\) | − | 0.202016i | − | 0.00765191i | ||||||
\(698\) | 19.3434i | 0.732157i | ||||||||
\(699\) | 9.00933 | 0.340764 | ||||||||
\(700\) | 12.1927 | + | 2.85866i | 0.460840 | + | 0.108047i | ||||
\(701\) | −20.8667 | −0.788123 | −0.394062 | − | 0.919084i | \(-0.628930\pi\) | ||||
−0.394062 | + | 0.919084i | \(0.628930\pi\) | |||||||
\(702\) | − | 1.36333i | − | 0.0514555i | ||||||
\(703\) | − | 6.14134i | − | 0.231625i | ||||||
\(704\) | 3.77801 | 0.142389 | ||||||||
\(705\) | 1.08066 | + | 1.36333i | 0.0406999 | + | 0.0513459i | ||||
\(706\) | 5.48262 | 0.206341 | ||||||||
\(707\) | − | 16.4440i | − | 0.618440i | ||||||
\(708\) | 7.78734i | 0.292666i | ||||||||
\(709\) | 31.6167 | 1.18739 | 0.593695 | − | 0.804690i | \(-0.297669\pi\) | ||||
0.593695 | + | 0.804690i | \(0.297669\pi\) | |||||||
\(710\) | 19.6974 | − | 15.6133i | 0.739228 | − | 0.585957i | ||||
\(711\) | −0.495336 | −0.0185765 | ||||||||
\(712\) | − | 0.0899847i | − | 0.00337232i | ||||||
\(713\) | 3.35739i | 0.125735i | ||||||||
\(714\) | 0.556016 | 0.0208084 | ||||||||
\(715\) | −9.02568 | + | 7.15429i | −0.337541 | + | 0.267555i | ||||
\(716\) | 1.82003 | 0.0680177 | ||||||||
\(717\) | − | 16.1693i | − | 0.603854i | ||||||
\(718\) | 1.60737i | 0.0599864i | ||||||||
\(719\) | −16.9953 | −0.633817 | −0.316909 | − | 0.948456i | \(-0.602645\pi\) | ||||
−0.316909 | + | 0.948456i | \(0.602645\pi\) | |||||||
\(720\) | −1.38900 | − | 1.75233i | −0.0517651 | − | 0.0653056i | ||||
\(721\) | 42.4740 | 1.58182 | ||||||||
\(722\) | 18.7160i | 0.696538i | ||||||||
\(723\) | 10.3527i | 0.385020i | ||||||||
\(724\) | −0.212663 | −0.00790357 | ||||||||
\(725\) | 0.737304 | − | 3.14473i | 0.0273828 | − | 0.116792i | ||||
\(726\) | −3.27334 | −0.121485 | ||||||||
\(727\) | 1.40196i | 0.0519959i | 0.999662 | + | 0.0259979i | \(0.00827633\pi\) | ||||
−0.999662 | + | 0.0259979i | \(0.991724\pi\) | |||||||
\(728\) | − | 3.41468i | − | 0.126556i | ||||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 3.98365 | + | 5.02568i | 0.147442 | + | 0.186009i | ||||
\(731\) | −1.01998 | −0.0377252 | ||||||||
\(732\) | − | 9.42401i | − | 0.348321i | ||||||
\(733\) | 19.8094i | 0.731676i | 0.930678 | + | 0.365838i | \(0.119218\pi\) | ||||
−0.930678 | + | 0.365838i | \(0.880782\pi\) | |||||||
\(734\) | 7.51399 | 0.277347 | ||||||||
\(735\) | −1.27334 | + | 1.00933i | −0.0469680 | + | 0.0372297i | ||||
\(736\) | −0.867993 | −0.0319946 | ||||||||
\(737\) | − | 40.5254i | − | 1.49277i | ||||||
\(738\) | 0.910015i | 0.0334981i | ||||||||
\(739\) | −18.3561 | −0.675239 | −0.337619 | − | 0.941283i | \(-0.609622\pi\) | ||||
−0.337619 | + | 0.941283i | \(0.609622\pi\) | |||||||
\(740\) | 1.75233 | − | 1.38900i | 0.0644170 | − | 0.0510608i | ||||
\(741\) | −8.37266 | −0.307577 | ||||||||
\(742\) | 5.69396i | 0.209032i | ||||||||
\(743\) | 30.6273i | 1.12361i | 0.827270 | + | 0.561804i | \(0.189893\pi\) | ||||
−0.827270 | + | 0.561804i | \(0.810107\pi\) | |||||||
\(744\) | 3.86799 | 0.141807 | ||||||||
\(745\) | 23.6519 | + | 29.8387i | 0.866540 | + | 1.09320i | ||||
\(746\) | −12.5140 | −0.458170 | ||||||||
\(747\) | 1.08066i | 0.0395391i | ||||||||
\(748\) | 0.838688i | 0.0306655i | ||||||||
\(749\) | −39.6387 | −1.44837 | ||||||||
\(750\) | 10.1157 | − | 4.76166i | 0.369372 | − | 0.173871i | ||||
\(751\) | −20.6680 | −0.754188 | −0.377094 | − | 0.926175i | \(-0.623077\pi\) | ||||
−0.377094 | + | 0.926175i | \(0.623077\pi\) | |||||||
\(752\) | − | 0.778008i | − | 0.0283710i | ||||||
\(753\) | 8.38538i | 0.305580i | ||||||||
\(754\) | −0.880711 | −0.0320736 | ||||||||
\(755\) | 31.0757 | + | 39.2043i | 1.13096 | + | 1.42679i | ||||
\(756\) | −2.50466 | −0.0910938 | ||||||||
\(757\) | 1.78866i | 0.0650098i | 0.999472 | + | 0.0325049i | \(0.0103484\pi\) | ||||
−0.999472 | + | 0.0325049i | \(0.989652\pi\) | |||||||
\(758\) | − | 37.6260i | − | 1.36664i | ||||||
\(759\) | 3.27928 | 0.119030 | ||||||||
\(760\) | −10.7617 | + | 8.53034i | −0.390366 | + | 0.309428i | ||||
\(761\) | −45.5853 | −1.65247 | −0.826233 | − | 0.563328i | \(-0.809521\pi\) | ||||
−0.826233 | + | 0.563328i | \(0.809521\pi\) | |||||||
\(762\) | 3.09931i | 0.112276i | ||||||||
\(763\) | − | 2.37605i | − | 0.0860187i | ||||||
\(764\) | 2.00933 | 0.0726950 | ||||||||
\(765\) | 0.389004 | − | 0.308348i | 0.0140645 | − | 0.0111483i | ||||
\(766\) | 14.2440 | 0.514658 | ||||||||
\(767\) | 10.6167i | 0.383347i | ||||||||
\(768\) | 1.00000i | 0.0360844i | ||||||||
\(769\) | 26.0887 | 0.940781 | 0.470391 | − | 0.882458i | \(-0.344113\pi\) | ||||
0.470391 | + | 0.882458i | \(0.344113\pi\) | |||||||
\(770\) | 13.1436 | + | 16.5817i | 0.473664 | + | 0.597563i | ||||
\(771\) | −6.55263 | −0.235987 | ||||||||
\(772\) | − | 6.00000i | − | 0.215945i | ||||||
\(773\) | − | 17.8294i | − | 0.641277i | −0.947202 | − | 0.320639i | \(-0.896102\pi\) | ||
0.947202 | − | 0.320639i | \(-0.103898\pi\) | |||||||
\(774\) | 4.59465 | 0.165151 | ||||||||
\(775\) | −4.41468 | + | 18.8294i | −0.158580 | + | 0.676371i | ||||
\(776\) | 4.46603 | 0.160321 | ||||||||
\(777\) | − | 2.50466i | − | 0.0898543i | ||||||
\(778\) | − | 0.697352i | − | 0.0250013i | ||||||
\(779\) | 5.58871 | 0.200236 | ||||||||
\(780\) | −1.89367 | − | 2.38900i | −0.0678042 | − | 0.0855401i | ||||
\(781\) | 42.4673 | 1.51960 | ||||||||
\(782\) | − | 0.192688i | − | 0.00689049i | ||||||
\(783\) | 0.646000i | 0.0230862i | ||||||||
\(784\) | 0.726656 | 0.0259520 | ||||||||
\(785\) | −29.7546 | + | 23.5853i | −1.06199 | + | 0.841796i | ||||
\(786\) | 11.3434 | 0.404604 | ||||||||
\(787\) | 22.1027i | 0.787876i | 0.919137 | + | 0.393938i | \(0.128888\pi\) | ||||
−0.919137 | + | 0.393938i | \(0.871112\pi\) | |||||||
\(788\) | − | 2.76529i | − | 0.0985094i | ||||||
\(789\) | −15.4754 | −0.550937 | ||||||||
\(790\) | −0.867993 | + | 0.688023i | −0.0308818 | + | 0.0244788i | ||||
\(791\) | −0.781397 | −0.0277833 | ||||||||
\(792\) | − | 3.77801i | − | 0.134246i | ||||||
\(793\) | − | 12.8480i | − | 0.456246i | ||||||
\(794\) | 28.4040 | 1.00802 | ||||||||
\(795\) | 3.15768 | + | 3.98365i | 0.111991 | + | 0.141286i | ||||
\(796\) | 1.98134 | 0.0702268 | ||||||||
\(797\) | 37.6633i | 1.33410i | 0.745011 | + | 0.667052i | \(0.232444\pi\) | ||||
−0.745011 | + | 0.667052i | \(0.767556\pi\) | |||||||
\(798\) | 15.3820i | 0.544516i | ||||||||
\(799\) | 0.172712 | 0.00611010 | ||||||||
\(800\) | −4.86799 | − | 1.14134i | −0.172110 | − | 0.0403523i | ||||
\(801\) | −0.0899847 | −0.00317945 | ||||||||
\(802\) | 22.7580i | 0.803614i | ||||||||
\(803\) | 10.8353i | 0.382369i | ||||||||
\(804\) | 10.7267 | 0.378300 | ||||||||
\(805\) | −3.01974 | − | 3.80962i | −0.106432 | − | 0.134272i | ||||
\(806\) | 5.27334 | 0.185746 | ||||||||
\(807\) | 3.31198i | 0.116587i | ||||||||
\(808\) | 6.56534i | 0.230968i | ||||||||
\(809\) | 31.3047 | 1.10062 | 0.550308 | − | 0.834962i | \(-0.314510\pi\) | ||||
0.550308 | + | 0.834962i | \(0.314510\pi\) | |||||||
\(810\) | −1.75233 | + | 1.38900i | −0.0615707 | + | 0.0488046i | ||||
\(811\) | 3.67738 | 0.129130 | 0.0645651 | − | 0.997913i | \(-0.479434\pi\) | ||||
0.0645651 | + | 0.997913i | \(0.479434\pi\) | |||||||
\(812\) | 1.61801i | 0.0567812i | ||||||||
\(813\) | 32.1986i | 1.12926i | ||||||||
\(814\) | 3.77801 | 0.132419 | ||||||||
\(815\) | 12.2663 | − | 9.72303i | 0.429671 | − | 0.340583i | ||||
\(816\) | −0.221992 | −0.00777128 | ||||||||
\(817\) | − | 28.2173i | − | 0.987198i | ||||||
\(818\) | 16.3527i | 0.571758i | ||||||||
\(819\) | −3.41468 | −0.119319 | ||||||||
\(820\) | 1.26401 | + | 1.59465i | 0.0441413 | + | 0.0556876i | ||||
\(821\) | 9.51738 | 0.332159 | 0.166079 | − | 0.986112i | \(-0.446889\pi\) | ||||
0.166079 | + | 0.986112i | \(0.446889\pi\) | |||||||
\(822\) | − | 10.4953i | − | 0.366067i | ||||||
\(823\) | 49.2580i | 1.71703i | 0.512792 | + | 0.858513i | \(0.328611\pi\) | ||||
−0.512792 | + | 0.858513i | \(0.671389\pi\) | |||||||
\(824\) | −16.9580 | −0.590759 | ||||||||
\(825\) | 18.3913 | + | 4.31198i | 0.640303 | + | 0.150124i | ||||
\(826\) | 19.5047 | 0.678654 | ||||||||
\(827\) | − | 41.2487i | − | 1.43436i | −0.696890 | − | 0.717178i | \(-0.745433\pi\) | ||
0.696890 | − | 0.717178i | \(-0.254567\pi\) | |||||||
\(828\) | 0.867993i | 0.0301648i | ||||||||
\(829\) | 19.4113 | 0.674182 | 0.337091 | − | 0.941472i | \(-0.390557\pi\) | ||||
0.337091 | + | 0.941472i | \(0.390557\pi\) | |||||||
\(830\) | 1.50104 | + | 1.89367i | 0.0521017 | + | 0.0657302i | ||||
\(831\) | −20.6553 | −0.716525 | ||||||||
\(832\) | 1.36333i | 0.0472649i | ||||||||
\(833\) | 0.161312i | 0.00558913i | ||||||||
\(834\) | −18.8773 | −0.653668 | ||||||||
\(835\) | −41.0630 | + | 32.5490i | −1.42104 | + | 1.12640i | ||||
\(836\) | −23.2020 | −0.802459 | ||||||||
\(837\) | − | 3.86799i | − | 0.133697i | ||||||
\(838\) | − | 11.2020i | − | 0.386967i | ||||||
\(839\) | 31.8646 | 1.10009 | 0.550044 | − | 0.835136i | \(-0.314611\pi\) | ||||
0.550044 | + | 0.835136i | \(0.314611\pi\) | |||||||
\(840\) | −4.38900 | + | 3.47899i | −0.151435 | + | 0.120037i | ||||
\(841\) | −28.5827 | −0.985610 | ||||||||
\(842\) | 13.8200i | 0.476270i | ||||||||
\(843\) | − | 9.80731i | − | 0.337782i | ||||||
\(844\) | 20.9473 | 0.721037 | ||||||||
\(845\) | 15.4754 | + | 19.5233i | 0.532369 | + | 0.671623i | ||||
\(846\) | −0.778008 | −0.0267485 | ||||||||
\(847\) | 8.19863i | 0.281708i | ||||||||
\(848\) | − | 2.27334i | − | 0.0780669i | ||||||
\(849\) | −18.6040 | −0.638487 | ||||||||
\(850\) | 0.253368 | − | 1.08066i | 0.00869044 | − | 0.0370662i | ||||
\(851\) | −0.867993 | −0.0297544 | ||||||||
\(852\) | 11.2406i | 0.385098i | ||||||||
\(853\) | 51.7860i | 1.77312i | 0.462614 | + | 0.886560i | \(0.346912\pi\) | ||||
−0.462614 | + | 0.886560i | \(0.653088\pi\) | |||||||
\(854\) | −23.6040 | −0.807711 | ||||||||
\(855\) | 8.53034 | + | 10.7617i | 0.291731 | + | 0.368041i | ||||
\(856\) | 15.8260 | 0.540921 | ||||||||
\(857\) | − | 50.1753i | − | 1.71395i | −0.515354 | − | 0.856977i | \(-0.672340\pi\) | ||
0.515354 | − | 0.856977i | \(-0.327660\pi\) | |||||||
\(858\) | − | 5.15066i | − | 0.175841i | ||||||
\(859\) | 44.5199 | 1.51900 | 0.759500 | − | 0.650507i | \(-0.225444\pi\) | ||||
0.759500 | + | 0.650507i | \(0.225444\pi\) | |||||||
\(860\) | 8.05135 | − | 6.38199i | 0.274549 | − | 0.217624i | ||||
\(861\) | 2.27928 | 0.0776778 | ||||||||
\(862\) | 36.1493i | 1.23125i | ||||||||
\(863\) | − | 9.25130i | − | 0.314918i | −0.987526 | − | 0.157459i | \(-0.949670\pi\) | ||
0.987526 | − | 0.157459i | \(-0.0503302\pi\) | |||||||
\(864\) | 1.00000 | 0.0340207 | ||||||||
\(865\) | −12.7617 | + | 10.1157i | −0.433909 | + | 0.343943i | ||||
\(866\) | 19.4147 | 0.659738 | ||||||||
\(867\) | 16.9507i | 0.575677i | ||||||||
\(868\) | − | 9.68802i | − | 0.328833i | ||||||
\(869\) | −1.87138 | −0.0634823 | ||||||||
\(870\) | 0.897297 | + | 1.13201i | 0.0304212 | + | 0.0383786i | ||||
\(871\) | 14.6240 | 0.495514 | ||||||||
\(872\) | 0.948649i | 0.0321253i | ||||||||
\(873\) | − | 4.46603i | − | 0.151152i | ||||||
\(874\) | 5.33063 | 0.180311 | ||||||||
\(875\) | −11.9264 | − | 25.3363i | −0.403185 | − | 0.856524i | ||||
\(876\) | −2.86799 | −0.0969005 | ||||||||
\(877\) | 48.5220i | 1.63847i | 0.573457 | + | 0.819236i | \(0.305602\pi\) | ||||
−0.573457 | + | 0.819236i | \(0.694398\pi\) | |||||||
\(878\) | 24.2207i | 0.817408i | ||||||||
\(879\) | 27.8480 | 0.939290 | ||||||||
\(880\) | −5.24767 | − | 6.62032i | −0.176899 | − | 0.223171i | ||||
\(881\) | 42.5293 | 1.43285 | 0.716424 | − | 0.697666i | \(-0.245778\pi\) | ||||
0.716424 | + | 0.697666i | \(0.245778\pi\) | |||||||
\(882\) | − | 0.726656i | − | 0.0244678i | ||||||
\(883\) | − | 52.0466i | − | 1.75151i | −0.482757 | − | 0.875755i | \(-0.660364\pi\) | ||
0.482757 | − | 0.875755i | \(-0.339636\pi\) | |||||||
\(884\) | −0.302648 | −0.0101792 | ||||||||
\(885\) | 13.6460 | − | 10.8166i | 0.458705 | − | 0.363597i | ||||
\(886\) | 22.0373 | 0.740358 | ||||||||
\(887\) | − | 34.3120i | − | 1.15208i | −0.817420 | − | 0.576042i | \(-0.804597\pi\) | ||
0.817420 | − | 0.576042i | \(-0.195403\pi\) | |||||||
\(888\) | 1.00000i | 0.0335578i | ||||||||
\(889\) | 7.76274 | 0.260354 | ||||||||
\(890\) | −0.157683 | + | 0.124989i | −0.00528555 | + | 0.00418964i | ||||
\(891\) | −3.77801 | −0.126568 | ||||||||
\(892\) | − | 20.1507i | − | 0.674694i | ||||||
\(893\) | 4.77801i | 0.159890i | ||||||||
\(894\) | −17.0280 | −0.569501 | ||||||||
\(895\) | −2.52803 | − | 3.18930i | −0.0845027 | − | 0.106606i | ||||
\(896\) | 2.50466 | 0.0836750 | ||||||||
\(897\) | 1.18336i | 0.0395112i | ||||||||
\(898\) | − | 1.63328i | − | 0.0545033i | ||||||
\(899\) | −2.49873 | −0.0833371 | ||||||||
\(900\) | −1.14134 | + | 4.86799i | −0.0380445 | + | 0.162266i | ||||
\(901\) | 0.504664 | 0.0168128 | ||||||||
\(902\) | 3.43804i | 0.114474i | ||||||||
\(903\) | − | 11.5081i | − | 0.382964i | ||||||
\(904\) | 0.311977 | 0.0103762 | ||||||||
\(905\) | 0.295390 | + | 0.372657i | 0.00981911 | + | 0.0123875i | ||||
\(906\) | −22.3727 | −0.743282 | ||||||||
\(907\) | 5.99868i | 0.199183i | 0.995028 | + | 0.0995915i | \(0.0317536\pi\) | ||||
−0.995028 | + | 0.0995915i | \(0.968246\pi\) | |||||||
\(908\) | − | 28.4520i | − | 0.944213i | ||||||
\(909\) | 6.56534 | 0.217759 | ||||||||
\(910\) | −5.98365 | + | 4.74300i | −0.198356 | + | 0.157229i | ||||
\(911\) | 36.3599 | 1.20466 | 0.602329 | − | 0.798248i | \(-0.294239\pi\) | ||||
0.602329 | + | 0.798248i | \(0.294239\pi\) | |||||||
\(912\) | − | 6.14134i | − | 0.203360i | ||||||
\(913\) | 4.08273i | 0.135119i | ||||||||
\(914\) | 14.2279 | 0.470618 | ||||||||
\(915\) | −16.5140 | + | 13.0900i | −0.545936 | + | 0.432742i | ||||
\(916\) | 18.6940 | 0.617666 | ||||||||
\(917\) | − | 28.4113i | − | 0.938223i | ||||||
\(918\) | 0.221992i | 0.00732683i | ||||||||
\(919\) | 19.6074 | 0.646787 | 0.323394 | − | 0.946265i | \(-0.395176\pi\) | ||||
0.323394 | + | 0.946265i | \(0.395176\pi\) | |||||||
\(920\) | 1.20565 | + | 1.52101i | 0.0397489 | + | 0.0501463i | ||||
\(921\) | −6.05135 | −0.199399 | ||||||||
\(922\) | − | 20.8587i | − | 0.686944i | ||||||
\(923\) | 15.3247i | 0.504418i | ||||||||
\(924\) | −9.46264 | −0.311298 | ||||||||
\(925\) | −4.86799 | − | 1.14134i | −0.160059 | − | 0.0375269i | ||||
\(926\) | 0.0326940 | 0.00107439 | ||||||||
\(927\) | 16.9580i | 0.556973i | ||||||||
\(928\) | − | 0.646000i | − | 0.0212060i | ||||||
\(929\) | 39.0827 | 1.28226 | 0.641131 | − | 0.767431i | \(-0.278465\pi\) | ||||
0.641131 | + | 0.767431i | \(0.278465\pi\) | |||||||
\(930\) | −5.37266 | − | 6.77801i | −0.176176 | − | 0.222260i | ||||
\(931\) | −4.46264 | −0.146257 | ||||||||
\(932\) | 9.00933i | 0.295110i | ||||||||
\(933\) | − | 28.3306i | − | 0.927503i | ||||||
\(934\) | −16.1834 | −0.529536 | ||||||||
\(935\) | 1.46966 | − | 1.16494i | 0.0480630 | − | 0.0380976i | ||||
\(936\) | 1.36333 | 0.0445618 | ||||||||
\(937\) | − | 38.0187i | − | 1.24202i | −0.783804 | − | 0.621008i | \(-0.786724\pi\) | ||
0.783804 | − | 0.621008i | \(-0.213276\pi\) | |||||||
\(938\) | − | 26.8667i | − | 0.877228i | ||||||
\(939\) | 1.50466 | 0.0491029 | ||||||||
\(940\) | −1.36333 | + | 1.08066i | −0.0444669 | + | 0.0352471i | ||||
\(941\) | −41.9600 | −1.36786 | −0.683929 | − | 0.729548i | \(-0.739730\pi\) | ||||
−0.683929 | + | 0.729548i | \(0.739730\pi\) | |||||||
\(942\) | − | 16.9800i | − | 0.553239i | ||||||
\(943\) | − | 0.789887i | − | 0.0257222i | ||||||
\(944\) | −7.78734 | −0.253456 | ||||||||
\(945\) | 3.47899 | + | 4.38900i | 0.113172 | + | 0.142774i | ||||
\(946\) | 17.3586 | 0.564377 | ||||||||
\(947\) | 11.7139i | 0.380652i | 0.981721 | + | 0.190326i | \(0.0609545\pi\) | ||||
−0.981721 | + | 0.190326i | \(0.939046\pi\) | |||||||
\(948\) | − | 0.495336i | − | 0.0160878i | ||||||
\(949\) | −3.91002 | −0.126924 | ||||||||
\(950\) | 29.8960 | + | 7.00933i | 0.969954 | + | 0.227413i | ||||
\(951\) | 20.0480 | 0.650100 | ||||||||
\(952\) | 0.556016i | 0.0180206i | ||||||||
\(953\) | − | 46.6354i | − | 1.51067i | −0.655340 | − | 0.755334i | \(-0.727475\pi\) | ||
0.655340 | − | 0.755334i | \(-0.272525\pi\) | |||||||
\(954\) | −2.27334 | −0.0736022 | ||||||||
\(955\) | −2.79097 | − | 3.52101i | −0.0903135 | − | 0.113937i | ||||
\(956\) | 16.1693 | 0.522953 | ||||||||
\(957\) | 2.44059i | 0.0788932i | ||||||||
\(958\) | 1.15066i | 0.0371763i | ||||||||
\(959\) | −26.2873 | −0.848861 | ||||||||
\(960\) | 1.75233 | − | 1.38900i | 0.0565563 | − | 0.0448299i | ||||
\(961\) | −16.0386 | −0.517375 | ||||||||
\(962\) | 1.36333i | 0.0439555i | ||||||||
\(963\) | − | 15.8260i | − | 0.509985i | ||||||
\(964\) | −10.3527 | −0.333437 | ||||||||
\(965\) | −10.5140 | + | 8.33402i | −0.338457 | + | 0.268282i | ||||
\(966\) | 2.17403 | 0.0699483 | ||||||||
\(967\) | 54.6727i | 1.75815i | 0.476679 | + | 0.879077i | \(0.341840\pi\) | ||||
−0.476679 | + | 0.879077i | \(0.658160\pi\) | |||||||
\(968\) | − | 3.27334i | − | 0.105209i | ||||||
\(969\) | 1.36333 | 0.0437964 | ||||||||
\(970\) | −6.20333 | − | 7.82597i | −0.199177 | − | 0.251277i | ||||
\(971\) | 26.2466 | 0.842293 | 0.421147 | − | 0.906993i | \(-0.361628\pi\) | ||||
0.421147 | + | 0.906993i | \(0.361628\pi\) | |||||||
\(972\) | − | 1.00000i | − | 0.0320750i | ||||||
\(973\) | 47.2814i | 1.51577i | ||||||||
\(974\) | −3.71733 | −0.119111 | ||||||||
\(975\) | −1.55602 | + | 6.63667i | −0.0498324 | + | 0.212544i | ||||
\(976\) | 9.42401 | 0.301655 | ||||||||
\(977\) | 36.3620i | 1.16332i | 0.813431 | + | 0.581662i | \(0.197597\pi\) | ||||
−0.813431 | + | 0.581662i | \(0.802403\pi\) | |||||||
\(978\) | 7.00000i | 0.223835i | ||||||||
\(979\) | −0.339963 | −0.0108653 | ||||||||
\(980\) | −1.00933 | − | 1.27334i | −0.0322418 | − | 0.0406755i | ||||
\(981\) | 0.948649 | 0.0302880 | ||||||||
\(982\) | 10.9966i | 0.350916i | ||||||||
\(983\) | 54.6506i | 1.74308i | 0.490321 | + | 0.871542i | \(0.336880\pi\) | ||||
−0.490321 | + | 0.871542i | \(0.663120\pi\) | |||||||
\(984\) | −0.910015 | −0.0290102 | ||||||||
\(985\) | −4.84571 | + | 3.84100i | −0.154397 | + | 0.122384i | ||||
\(986\) | 0.143407 | 0.00456701 | ||||||||
\(987\) | 1.94865i | 0.0620262i | ||||||||
\(988\) | − | 8.37266i | − | 0.266370i | ||||||
\(989\) | −3.98812 | −0.126815 | ||||||||
\(990\) | −6.62032 | + | 5.24767i | −0.210408 | + | 0.166782i | ||||
\(991\) | 4.05474 | 0.128803 | 0.0644015 | − | 0.997924i | \(-0.479486\pi\) | ||||
0.0644015 | + | 0.997924i | \(0.479486\pi\) | |||||||
\(992\) | 3.86799i | 0.122809i | ||||||||
\(993\) | 21.5747i | 0.684652i | ||||||||
\(994\) | 28.1541 | 0.892992 | ||||||||
\(995\) | −2.75209 | − | 3.47197i | −0.0872472 | − | 0.110069i | ||||
\(996\) | −1.08066 | −0.0342419 | ||||||||
\(997\) | − | 20.7326i | − | 0.656608i | −0.944572 | − | 0.328304i | \(-0.893523\pi\) | ||
0.944572 | − | 0.328304i | \(-0.106477\pi\) | |||||||
\(998\) | − | 29.5547i | − | 0.935538i | ||||||
\(999\) | 1.00000 | 0.0316386 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1110.2.d.i.889.5 | yes | 6 | |
3.2 | odd | 2 | 3330.2.d.n.1999.2 | 6 | |||
5.2 | odd | 4 | 5550.2.a.cf.1.1 | 3 | |||
5.3 | odd | 4 | 5550.2.a.cg.1.3 | 3 | |||
5.4 | even | 2 | inner | 1110.2.d.i.889.2 | ✓ | 6 | |
15.14 | odd | 2 | 3330.2.d.n.1999.5 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1110.2.d.i.889.2 | ✓ | 6 | 5.4 | even | 2 | inner | |
1110.2.d.i.889.5 | yes | 6 | 1.1 | even | 1 | trivial | |
3330.2.d.n.1999.2 | 6 | 3.2 | odd | 2 | |||
3330.2.d.n.1999.5 | 6 | 15.14 | odd | 2 | |||
5550.2.a.cf.1.1 | 3 | 5.2 | odd | 4 | |||
5550.2.a.cg.1.3 | 3 | 5.3 | odd | 4 |