Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [7200,2,Mod(1151,7200)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(7200, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 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("7200.1151");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 7200 = 2^{5} \cdot 3^{2} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 7200.h (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: | \(57.4922894553\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | 12.0.426337261060096.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 4x^{9} - 3x^{8} + 4x^{7} + 8x^{6} + 8x^{5} - 12x^{4} - 32x^{3} + 64 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{41}]\) |
Coefficient ring index: | \( 2^{15} \) |
Twist minimal: | no (minimal twist has level 1440) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1151.6 | ||
Root | \(1.19252 - 0.760198i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 7200.1151 |
Dual form | 7200.2.h.m.1151.8 |
$q$-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 \(\left(\mathbb{Z}/7200\mathbb{Z}\right)^\times\).
\(n\) | \(577\) | \(901\) | \(6401\) | \(6751\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − 0.864641i | − 0.326804i | −0.986560 | − | 0.163402i | \(-0.947753\pi\) | ||||
0.986560 | − | 0.163402i | \(-0.0522467\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.90543 | 1.17753 | 0.588766 | − | 0.808304i | \(-0.299614\pi\) | ||||
0.588766 | + | 0.808304i | \(0.299614\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.13536 | 0.314892 | 0.157446 | − | 0.987528i | \(-0.449674\pi\) | ||||
0.157446 | + | 0.987528i | \(0.449674\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − 3.71400i | − 0.900779i | −0.892832 | − | 0.450389i | \(-0.851285\pi\) | ||||
0.892832 | − | 0.450389i | \(-0.148715\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.72928i | 0.396724i | 0.980129 | + | 0.198362i | \(0.0635622\pi\) | ||||
−0.980129 | + | 0.198362i | \(0.936438\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 9.03365 | 1.88365 | 0.941823 | − | 0.336109i | \(-0.109111\pi\) | ||||
0.941823 | + | 0.336109i | \(0.109111\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − 1.26843i | − 0.235542i | −0.993041 | − | 0.117771i | \(-0.962425\pi\) | ||||
0.993041 | − | 0.117771i | \(-0.0375748\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.25240i | 0.584148i | 0.956396 | + | 0.292074i | \(0.0943453\pi\) | ||||
−0.956396 | + | 0.292074i | \(0.905655\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 6.38776 | 1.05014 | 0.525070 | − | 0.851059i | \(-0.324039\pi\) | ||||
0.525070 | + | 0.851059i | \(0.324039\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 6.39665i | 0.998989i | 0.866317 | + | 0.499494i | \(0.166481\pi\) | ||||
−0.866317 | + | 0.499494i | \(0.833519\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.77551i | 0.728259i | 0.931348 | + | 0.364129i | \(0.118633\pi\) | ||||
−0.931348 | + | 0.364129i | \(0.881367\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −4.59958 | −0.670918 | −0.335459 | − | 0.942055i | \(-0.608891\pi\) | ||||
−0.335459 | + | 0.942055i | \(0.608891\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.25240 | 0.893199 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 8.98801i | 1.23460i | 0.786729 | + | 0.617299i | \(0.211773\pi\) | ||||
−0.786729 | + | 0.617299i | \(0.788227\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −8.50501 | −1.10726 | −0.553629 | − | 0.832763i | \(-0.686758\pi\) | ||||
−0.553629 | + | 0.832763i | \(0.686758\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −9.04623 | −1.15825 | −0.579125 | − | 0.815238i | \(-0.696606\pi\) | ||||
−0.579125 | + | 0.815238i | \(0.696606\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − 11.0462i | − 1.34951i | −0.738041 | − | 0.674756i | \(-0.764249\pi\) | ||||
0.738041 | − | 0.674756i | \(-0.235751\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −8.10243 | −0.961581 | −0.480791 | − | 0.876835i | \(-0.659650\pi\) | ||||
−0.480791 | + | 0.876835i | \(0.659650\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 4.47689 | 0.523980 | 0.261990 | − | 0.965071i | \(-0.415621\pi\) | ||||
0.261990 | + | 0.965071i | \(0.415621\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − 3.37680i | − 0.384822i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − 14.2986i | − 1.60872i | −0.594142 | − | 0.804360i | \(-0.702508\pi\) | ||||
0.594142 | − | 0.804360i | \(-0.297492\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 8.10243 | 0.889357 | 0.444679 | − | 0.895690i | \(-0.353318\pi\) | ||||
0.444679 | + | 0.895690i | \(0.353318\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − 3.56822i | − 0.378231i | −0.981955 | − | 0.189115i | \(-0.939438\pi\) | ||||
0.981955 | − | 0.189115i | \(-0.0605620\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − 0.981678i | − 0.102908i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 10.9817 | 1.11502 | 0.557510 | − | 0.830170i | \(-0.311757\pi\) | ||||
0.557510 | + | 0.830170i | \(0.311757\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 0.885578i | 0.0881183i | 0.999029 | + | 0.0440591i | \(0.0140290\pi\) | ||||
−0.999029 | + | 0.0440591i | \(0.985971\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − 18.1816i | − 1.79149i | −0.444573 | − | 0.895743i | \(-0.646645\pi\) | ||||
0.444573 | − | 0.895743i | \(-0.353355\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −2.44557 | −0.236423 | −0.118211 | − | 0.992988i | \(-0.537716\pi\) | ||||
−0.118211 | + | 0.992988i | \(0.537716\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 3.25240 | 0.311523 | 0.155762 | − | 0.987795i | \(-0.450217\pi\) | ||||
0.155762 | + | 0.987795i | \(0.450217\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 17.5646i | 1.65234i | 0.563424 | + | 0.826168i | \(0.309484\pi\) | ||||
−0.563424 | + | 0.826168i | \(0.690516\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −3.21128 | −0.294378 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 4.25240 | 0.386581 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2.18159i | 0.193585i | 0.995305 | + | 0.0967923i | \(0.0308583\pi\) | ||||
−0.995305 | + | 0.0967923i | \(0.969142\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 22.2643 | 1.94524 | 0.972620 | − | 0.232400i | \(-0.0746578\pi\) | ||||
0.972620 | + | 0.232400i | \(0.0746578\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.49521 | 0.129651 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 6.92529i | 0.591667i | 0.955240 | + | 0.295834i | \(0.0955974\pi\) | ||||
−0.955240 | + | 0.295834i | \(0.904403\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 18.2986i | 1.55207i | 0.630690 | + | 0.776035i | \(0.282772\pi\) | ||||
−0.630690 | + | 0.776035i | \(0.717228\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 4.43407 | 0.370795 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − 8.98801i | − 0.736326i | −0.929761 | − | 0.368163i | \(-0.879987\pi\) | ||||
0.929761 | − | 0.368163i | \(-0.120013\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 6.29862i | 0.512575i | 0.966601 | + | 0.256287i | \(0.0824994\pi\) | ||||
−0.966601 | + | 0.256287i | \(0.917501\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −11.1633 | −0.890926 | −0.445463 | − | 0.895300i | \(-0.646961\pi\) | ||||
−0.445463 | + | 0.895300i | \(0.646961\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − 7.81086i | − 0.615582i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − 17.7293i | − 1.38866i | −0.719655 | − | 0.694332i | \(-0.755700\pi\) | ||||
0.719655 | − | 0.694332i | \(-0.244300\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1.51435 | 0.117184 | 0.0585920 | − | 0.998282i | \(-0.481339\pi\) | ||||
0.0585920 | + | 0.998282i | \(0.481339\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −11.7110 | −0.900843 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 15.4106i | 1.17164i | 0.810440 | + | 0.585822i | \(0.199228\pi\) | ||||
−0.810440 | + | 0.585822i | \(0.800772\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 9.56229 | 0.714719 | 0.357359 | − | 0.933967i | \(-0.383677\pi\) | ||||
0.357359 | + | 0.933967i | \(0.383677\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 14.2986 | 1.06281 | 0.531404 | − | 0.847118i | \(-0.321665\pi\) | ||||
0.531404 | + | 0.847118i | \(0.321665\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 14.5048i | − 1.06070i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −19.1246 | −1.38381 | −0.691903 | − | 0.721991i | \(-0.743227\pi\) | ||||
−0.691903 | + | 0.721991i | \(0.743227\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 22.5048 | 1.61993 | 0.809965 | − | 0.586478i | \(-0.199486\pi\) | ||||
0.809965 | + | 0.586478i | \(0.199486\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 9.91923i | 0.706716i | 0.935488 | + | 0.353358i | \(0.114960\pi\) | ||||
−0.935488 | + | 0.353358i | \(0.885040\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − 3.66473i | − 0.259786i | −0.991528 | − | 0.129893i | \(-0.958537\pi\) | ||||
0.991528 | − | 0.129893i | \(-0.0414634\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −1.09674 | −0.0769759 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 6.75359i | 0.467156i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − 2.29862i | − 0.158244i | −0.996865 | − | 0.0791219i | \(-0.974788\pi\) | ||||
0.996865 | − | 0.0791219i | \(-0.0252116\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2.81215 | 0.190901 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − 4.21673i | − 0.283648i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − 15.1354i | − 1.01354i | −0.862082 | − | 0.506769i | \(-0.830840\pi\) | ||||
0.862082 | − | 0.506769i | \(-0.169160\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 26.1697 | 1.73695 | 0.868473 | − | 0.495737i | \(-0.165102\pi\) | ||||
0.868473 | + | 0.495737i | \(0.165102\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −9.75719 | −0.644773 | −0.322387 | − | 0.946608i | \(-0.604485\pi\) | ||||
−0.322387 | + | 0.946608i | \(0.604485\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − 8.02202i | − 0.525540i | −0.964858 | − | 0.262770i | \(-0.915364\pi\) | ||||
0.964858 | − | 0.262770i | \(-0.0846361\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 17.0100 | 1.10029 | 0.550144 | − | 0.835070i | \(-0.314573\pi\) | ||||
0.550144 | + | 0.835070i | \(0.314573\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −21.0096 | −1.35335 | −0.676673 | − | 0.736284i | \(-0.736579\pi\) | ||||
−0.676673 | + | 0.736284i | \(0.736579\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.96336i | 0.124925i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 8.46555 | 0.534341 | 0.267170 | − | 0.963649i | \(-0.413911\pi\) | ||||
0.267170 | + | 0.963649i | \(0.413911\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 35.2803 | 2.21805 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 11.8164i | 0.737089i | 0.929610 | + | 0.368544i | \(0.120144\pi\) | ||||
−0.929610 | + | 0.368544i | \(0.879856\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − 5.52311i | − 0.343190i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 7.93691 | 0.489411 | 0.244705 | − | 0.969597i | \(-0.421309\pi\) | ||||
0.244705 | + | 0.969597i | \(0.421309\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 29.9750i | 1.82761i | 0.406154 | + | 0.913805i | \(0.366870\pi\) | ||||
−0.406154 | + | 0.913805i | \(0.633130\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − 26.8401i | − 1.63042i | −0.579167 | − | 0.815209i | \(-0.696622\pi\) | ||||
0.579167 | − | 0.815209i | \(-0.303378\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 24.9571 | 1.49953 | 0.749763 | − | 0.661706i | \(-0.230167\pi\) | ||||
0.749763 | + | 0.661706i | \(0.230167\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − 1.12265i | − 0.0669716i | −0.999439 | − | 0.0334858i | \(-0.989339\pi\) | ||||
0.999439 | − | 0.0334858i | \(-0.0106609\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 25.9634i | − 1.54336i | −0.636010 | − | 0.771681i | \(-0.719416\pi\) | ||||
0.636010 | − | 0.771681i | \(-0.280584\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 5.53080 | 0.326473 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 3.20617 | 0.188598 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − 16.6728i | − 0.974037i | −0.873392 | − | 0.487018i | \(-0.838085\pi\) | ||||
0.873392 | − | 0.487018i | \(-0.161915\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 10.2564 | 0.593145 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 4.12910 | 0.237997 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 21.0096i | 1.19908i | 0.800345 | + | 0.599540i | \(0.204650\pi\) | ||||
−0.800345 | + | 0.599540i | \(0.795350\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −34.7463 | −1.97028 | −0.985141 | − | 0.171748i | \(-0.945058\pi\) | ||||
−0.985141 | + | 0.171748i | \(0.945058\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 9.49521 | 0.536701 | 0.268350 | − | 0.963321i | \(-0.413521\pi\) | ||||
0.268350 | + | 0.963321i | \(0.413521\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 16.2505i | 0.912719i | 0.889795 | + | 0.456360i | \(0.150847\pi\) | ||||
−0.889795 | + | 0.456360i | \(0.849153\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − 4.95377i | − 0.277358i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 6.42256 | 0.357361 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 3.97699i | 0.219258i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 20.7755i | 1.14193i | 0.820976 | + | 0.570963i | \(0.193430\pi\) | ||||
−0.820976 | + | 0.570963i | \(0.806570\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −28.1204 | −1.53181 | −0.765907 | − | 0.642951i | \(-0.777710\pi\) | ||||
−0.765907 | + | 0.642951i | \(0.777710\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 12.7020i | 0.687852i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − 11.4586i | − 0.618704i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 18.8330 | 1.01101 | 0.505504 | − | 0.862824i | \(-0.331306\pi\) | ||||
0.505504 | + | 0.862824i | \(0.331306\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 11.5510 | 0.618312 | 0.309156 | − | 0.951011i | \(-0.399953\pi\) | ||||
0.309156 | + | 0.951011i | \(0.399953\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 2.61727i | 0.139303i | 0.997571 | + | 0.0696515i | \(0.0221887\pi\) | ||||
−0.997571 | + | 0.0696515i | \(0.977811\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −20.8044 | −1.09802 | −0.549008 | − | 0.835817i | \(-0.684994\pi\) | ||||
−0.549008 | + | 0.835817i | \(0.684994\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 16.0096 | 0.842610 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − 15.3694i | − 0.802278i | −0.916017 | − | 0.401139i | \(-0.868614\pi\) | ||||
0.916017 | − | 0.401139i | \(-0.131386\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 7.77140 | 0.403471 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 29.3049 | 1.51735 | 0.758675 | − | 0.651470i | \(-0.225847\pi\) | ||||
0.758675 | + | 0.651470i | \(0.225847\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − 1.44012i | − 0.0741702i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 11.7938i | 0.605808i | 0.953021 | + | 0.302904i | \(0.0979562\pi\) | ||||
−0.953021 | + | 0.302904i | \(0.902044\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 16.6790 | 0.852257 | 0.426128 | − | 0.904663i | \(-0.359877\pi\) | ||||
0.426128 | + | 0.904663i | \(0.359877\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − 23.2214i | − 1.17737i | −0.808361 | − | 0.588687i | \(-0.799645\pi\) | ||||
0.808361 | − | 0.588687i | \(-0.200355\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − 33.5510i | − 1.69675i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 2.02458 | 0.101611 | 0.0508054 | − | 0.998709i | \(-0.483821\pi\) | ||||
0.0508054 | + | 0.998709i | \(0.483821\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − 28.9722i | − 1.44680i | −0.690427 | − | 0.723402i | \(-0.742577\pi\) | ||||
0.690427 | − | 0.723402i | \(-0.257423\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 3.69264i | 0.183943i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 24.9469 | 1.23657 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −25.8863 | −1.27999 | −0.639997 | − | 0.768377i | \(-0.721065\pi\) | ||||
−0.639997 | + | 0.768377i | \(0.721065\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 7.35378i | 0.361856i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 12.7736 | 0.624030 | 0.312015 | − | 0.950077i | \(-0.398996\pi\) | ||||
0.312015 | + | 0.950077i | \(0.398996\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 18.1695 | 0.885528 | 0.442764 | − | 0.896638i | \(-0.353998\pi\) | ||||
0.442764 | + | 0.896638i | \(0.353998\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 7.82174i | 0.378520i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −2.40611 | −0.115898 | −0.0579491 | − | 0.998320i | \(-0.518456\pi\) | ||||
−0.0579491 | + | 0.998320i | \(0.518456\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 31.4094 | 1.50944 | 0.754720 | − | 0.656047i | \(-0.227773\pi\) | ||||
0.754720 | + | 0.656047i | \(0.227773\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 15.6217i | 0.747289i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 18.1695i | 0.867184i | 0.901109 | + | 0.433592i | \(0.142754\pi\) | ||||
−0.901109 | + | 0.433592i | \(0.857246\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 18.8330 | 0.894783 | 0.447392 | − | 0.894338i | \(-0.352353\pi\) | ||||
0.447392 | + | 0.894338i | \(0.352353\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − 20.9216i | − 0.987353i | −0.869646 | − | 0.493677i | \(-0.835653\pi\) | ||||
0.869646 | − | 0.493677i | \(-0.164347\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 24.9817i | 1.17634i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 35.5789 | 1.66431 | 0.832156 | − | 0.554542i | \(-0.187106\pi\) | ||||
0.832156 | + | 0.554542i | \(0.187106\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − 14.0617i | − 0.654920i | −0.944865 | − | 0.327460i | \(-0.893807\pi\) | ||||
0.944865 | − | 0.327460i | \(-0.106193\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − 33.0987i | − 1.53823i | −0.639112 | − | 0.769114i | \(-0.720698\pi\) | ||||
0.639112 | − | 0.769114i | \(-0.279302\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −32.0092 | −1.48121 | −0.740604 | − | 0.671942i | \(-0.765460\pi\) | ||||
−0.740604 | + | 0.671942i | \(0.765460\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −9.55102 | −0.441025 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 18.6504i | 0.857548i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −28.6153 | −1.30747 | −0.653733 | − | 0.756725i | \(-0.726798\pi\) | ||||
−0.653733 | + | 0.756725i | \(0.726798\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 7.25240 | 0.330681 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − 2.18159i | − 0.0988572i | −0.998778 | − | 0.0494286i | \(-0.984260\pi\) | ||||
0.998778 | − | 0.0494286i | \(-0.0157400\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 28.2127 | 1.27322 | 0.636611 | − | 0.771185i | \(-0.280336\pi\) | ||||
0.636611 | + | 0.771185i | \(0.280336\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −4.71096 | −0.212171 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 7.00569i | 0.314248i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − 0.234074i | − 0.0104786i | −0.999986 | − | 0.00523930i | \(-0.998332\pi\) | ||||
0.999986 | − | 0.00523930i | \(-0.00166773\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −15.3302 | −0.683538 | −0.341769 | − | 0.939784i | \(-0.611026\pi\) | ||||
−0.341769 | + | 0.939784i | \(0.611026\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 22.7473i | 1.00826i | 0.863629 | + | 0.504128i | \(0.168186\pi\) | ||||
−0.863629 | + | 0.504128i | \(0.831814\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − 3.87090i | − 0.171238i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −17.9634 | −0.790027 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 23.9898i | 1.05101i | 0.850790 | + | 0.525506i | \(0.176124\pi\) | ||||
−0.850790 | + | 0.525506i | \(0.823876\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 28.3632i | − 1.24024i | −0.784509 | − | 0.620118i | \(-0.787085\pi\) | ||||
0.784509 | − | 0.620118i | \(-0.212915\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 12.0794 | 0.526188 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 58.6068 | 2.54812 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 7.26249i | 0.314574i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 24.4183 | 1.05177 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −36.8034 | −1.58230 | −0.791151 | − | 0.611621i | \(-0.790518\pi\) | ||||
−0.791151 | + | 0.611621i | \(0.790518\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − 24.2341i | − 1.03617i | −0.855328 | − | 0.518087i | \(-0.826644\pi\) | ||||
0.855328 | − | 0.518087i | \(-0.173356\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 2.19347 | 0.0934452 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −12.3632 | −0.525736 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − 43.3515i | − 1.83686i | −0.395584 | − | 0.918430i | \(-0.629458\pi\) | ||||
0.395584 | − | 0.918430i | \(-0.370542\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 5.42192i | 0.229323i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −2.62815 | −0.110763 | −0.0553817 | − | 0.998465i | \(-0.517638\pi\) | ||||
−0.0553817 | + | 0.998465i | \(0.517638\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 23.6588i | 0.991828i | 0.868372 | + | 0.495914i | \(0.165167\pi\) | ||||
−0.868372 | + | 0.495914i | \(0.834833\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 35.6926i | 1.49369i | 0.664998 | + | 0.746845i | \(0.268432\pi\) | ||||
−0.664998 | + | 0.746845i | \(0.731568\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −0.646409 | −0.0269104 | −0.0134552 | − | 0.999909i | \(-0.504283\pi\) | ||||
−0.0134552 | + | 0.999909i | \(0.504283\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − 7.00569i | − 0.290645i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 35.1020i | 1.45378i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −22.3753 | −0.923528 | −0.461764 | − | 0.887003i | \(-0.652783\pi\) | ||||
−0.461764 | + | 0.887003i | \(0.652783\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −5.62431 | −0.231746 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 20.4325i | 0.839061i | 0.907741 | + | 0.419530i | \(0.137805\pi\) | ||||
−0.907741 | + | 0.419530i | \(0.862195\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −6.13100 | −0.250506 | −0.125253 | − | 0.992125i | \(-0.539974\pi\) | ||||
−0.125253 | + | 0.992125i | \(0.539974\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −1.79383 | −0.0731720 | −0.0365860 | − | 0.999331i | \(-0.511648\pi\) | ||||
−0.0365860 | + | 0.999331i | \(0.511648\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − 16.6864i | − 0.677279i | −0.940916 | − | 0.338640i | \(-0.890033\pi\) | ||||
0.940916 | − | 0.338640i | \(-0.109967\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −5.22218 | −0.211267 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −23.5264 | −0.950224 | −0.475112 | − | 0.879925i | \(-0.657592\pi\) | ||||
−0.475112 | + | 0.879925i | \(0.657592\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 23.3127i | 0.938535i | 0.883056 | + | 0.469267i | \(0.155482\pi\) | ||||
−0.883056 | + | 0.469267i | \(0.844518\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − 32.3911i | − 1.30191i | −0.759117 | − | 0.650954i | \(-0.774369\pi\) | ||||
0.759117 | − | 0.650954i | \(-0.225631\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −3.08523 | −0.123607 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − 23.7242i | − 0.945944i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − 19.2524i | − 0.766426i | −0.923660 | − | 0.383213i | \(-0.874818\pi\) | ||||
0.923660 | − | 0.383213i | \(-0.125182\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 7.09871 | 0.281261 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 25.9435i | 1.02471i | 0.858774 | + | 0.512354i | \(0.171226\pi\) | ||||
−0.858774 | + | 0.512354i | \(0.828774\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 11.2803i | − 0.444852i | −0.974950 | − | 0.222426i | \(-0.928602\pi\) | ||||
0.974950 | − | 0.222426i | \(-0.0713975\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −11.6053 | −0.456250 | −0.228125 | − | 0.973632i | \(-0.573260\pi\) | ||||
−0.228125 | + | 0.973632i | \(0.573260\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −33.2158 | −1.30383 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 35.4145i | 1.38588i | 0.720996 | + | 0.692939i | \(0.243684\pi\) | ||||
−0.720996 | + | 0.692939i | \(0.756316\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 12.0079 | 0.467760 | 0.233880 | − | 0.972265i | \(-0.424858\pi\) | ||||
0.233880 | + | 0.972265i | \(0.424858\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −3.08287 | −0.119910 | −0.0599549 | − | 0.998201i | \(-0.519096\pi\) | ||||
−0.0599549 | + | 0.998201i | \(0.519096\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − 11.4586i | − 0.443677i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −35.3294 | −1.36388 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −25.7851 | −0.993942 | −0.496971 | − | 0.867767i | \(-0.665555\pi\) | ||||
−0.496971 | + | 0.867767i | \(0.665555\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 2.16019i | 0.0830227i | 0.999138 | + | 0.0415114i | \(0.0132173\pi\) | ||||
−0.999138 | + | 0.0415114i | \(0.986783\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − 9.49521i | − 0.364393i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 28.3632 | 1.08529 | 0.542644 | − | 0.839963i | \(-0.317423\pi\) | ||||
0.542644 | + | 0.839963i | \(0.317423\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 10.2046i | 0.388765i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 37.9142i | 1.44232i | 0.692766 | + | 0.721162i | \(0.256392\pi\) | ||||
−0.692766 | + | 0.721162i | \(0.743608\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 23.7572 | 0.899868 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 12.9650i | 0.489681i | 0.969563 | + | 0.244841i | \(0.0787356\pi\) | ||||
−0.969563 | + | 0.244841i | \(0.921264\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 11.0462i | 0.416616i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0.765707 | 0.0287974 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 26.8401 | 1.00800 | 0.504000 | − | 0.863704i | \(-0.331861\pi\) | ||||
0.504000 | + | 0.863704i | \(0.331861\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 29.3810i | 1.10033i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −40.7342 | −1.51913 | −0.759564 | − | 0.650432i | \(-0.774588\pi\) | ||||
−0.759564 | + | 0.650432i | \(0.774588\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −15.7205 | −0.585464 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − 24.9205i | − 0.924248i | −0.886815 | − | 0.462124i | \(-0.847087\pi\) | ||||
0.886815 | − | 0.462124i | \(-0.152913\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 17.7363 | 0.656000 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 11.2278 | 0.414709 | 0.207354 | − | 0.978266i | \(-0.433515\pi\) | ||||
0.207354 | + | 0.978266i | \(0.433515\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − 43.1403i | − 1.58909i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 3.22449i | 0.118615i | 0.998240 | + | 0.0593074i | \(0.0188892\pi\) | ||||
−0.998240 | + | 0.0593074i | \(0.981111\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 14.5645 | 0.534318 | 0.267159 | − | 0.963652i | \(-0.413915\pi\) | ||||
0.267159 | + | 0.963652i | \(0.413915\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 2.11454i | 0.0772637i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − 52.8034i | − 1.92682i | −0.268025 | − | 0.963412i | \(-0.586371\pi\) | ||||
0.268025 | − | 0.963412i | \(-0.413629\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 8.82800 | 0.320859 | 0.160429 | − | 0.987047i | \(-0.448712\pi\) | ||||
0.160429 | + | 0.987047i | \(0.448712\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 32.6577i | 1.18384i | 0.805997 | + | 0.591920i | \(0.201630\pi\) | ||||
−0.805997 | + | 0.591920i | \(0.798370\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − 2.81215i | − 0.101807i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −9.65625 | −0.348667 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 7.83048 | 0.282374 | 0.141187 | − | 0.989983i | \(-0.454908\pi\) | ||||
0.141187 | + | 0.989983i | \(0.454908\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − 8.14807i | − 0.293066i | −0.989206 | − | 0.146533i | \(-0.953189\pi\) | ||||
0.989206 | − | 0.146533i | \(-0.0468114\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −11.0616 | −0.396323 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −31.6435 | −1.13229 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 35.2803i | 1.25761i | 0.777564 | + | 0.628803i | \(0.216455\pi\) | ||||
−0.777564 | + | 0.628803i | \(0.783545\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 15.1871 | 0.539989 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −10.2707 | −0.364724 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 4.67999i | 0.165774i | 0.996559 | + | 0.0828868i | \(0.0264140\pi\) | ||||
−0.996559 | + | 0.0828868i | \(0.973586\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 17.0829i | 0.604349i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 17.4842 | 0.617003 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − 19.2294i | − 0.676070i | −0.941133 | − | 0.338035i | \(-0.890238\pi\) | ||||
0.941133 | − | 0.338035i | \(-0.109762\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 18.7110i | 0.657031i | 0.944499 | + | 0.328515i | \(0.106548\pi\) | ||||
−0.944499 | + | 0.328515i | \(0.893452\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −8.25820 | −0.288918 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 6.92529i | 0.241694i | 0.992671 | + | 0.120847i | \(0.0385611\pi\) | ||||
−0.992671 | + | 0.120847i | \(0.961439\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 23.6035i | 0.822767i | 0.911462 | + | 0.411383i | \(0.134954\pi\) | ||||
−0.911462 | + | 0.411383i | \(0.865046\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −29.3810 | −1.02168 | −0.510839 | − | 0.859676i | \(-0.670665\pi\) | ||||
−0.510839 | + | 0.859676i | \(0.670665\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −16.2062 | −0.562863 | −0.281432 | − | 0.959581i | \(-0.590809\pi\) | ||||
−0.281432 | + | 0.959581i | \(0.590809\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − 23.2214i | − 0.804575i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −9.49073 | −0.327656 | −0.163828 | − | 0.986489i | \(-0.552384\pi\) | ||||
−0.163828 | + | 0.986489i | \(0.552384\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 27.3911 | 0.944520 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − 3.67680i | − 0.126336i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 57.7047 | 1.97809 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −32.3511 | −1.10768 | −0.553840 | − | 0.832623i | \(-0.686838\pi\) | ||||
−0.553840 | + | 0.832623i | \(0.686838\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − 3.80529i | − 0.129986i | −0.997886 | − | 0.0649932i | \(-0.979297\pi\) | ||||
0.997886 | − | 0.0649932i | \(-0.0207026\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − 2.29862i | − 0.0784281i | −0.999231 | − | 0.0392140i | \(-0.987515\pi\) | ||||
0.999231 | − | 0.0392140i | \(-0.0124854\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −9.79936 | −0.333574 | −0.166787 | − | 0.985993i | \(-0.553339\pi\) | ||||
−0.166787 | + | 0.985993i | \(0.553339\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − 55.8423i | − 1.89432i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − 12.5414i | − 0.424950i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 23.7047 | 0.800451 | 0.400225 | − | 0.916417i | \(-0.368932\pi\) | ||||
0.400225 | + | 0.916417i | \(0.368932\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − 37.1660i | − 1.25215i | −0.779762 | − | 0.626077i | \(-0.784660\pi\) | ||||
0.779762 | − | 0.626077i | \(-0.215340\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 17.7293i | 0.596638i | 0.954466 | + | 0.298319i | \(0.0964259\pi\) | ||||
−0.954466 | + | 0.298319i | \(0.903574\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −34.6202 | −1.16243 | −0.581217 | − | 0.813749i | \(-0.697423\pi\) | ||||
−0.581217 | + | 0.813749i | \(0.697423\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.88629 | 0.0632641 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − 7.95397i | − 0.266170i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 4.12544 | 0.137591 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 33.3815 | 1.11210 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 7.76593i | 0.257863i | 0.991653 | + | 0.128932i | \(0.0411548\pi\) | ||||
−0.991653 | + | 0.128932i | \(0.958845\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 4.30802 | 0.142731 | 0.0713655 | − | 0.997450i | \(-0.477264\pi\) | ||||
0.0713655 | + | 0.997450i | \(0.477264\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 31.6435 | 1.04725 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − 19.2506i | − 0.635712i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − 27.2524i | − 0.898974i | −0.893287 | − | 0.449487i | \(-0.851607\pi\) | ||||
0.893287 | − | 0.449487i | \(-0.148393\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −9.19917 | −0.302794 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − 37.3662i | − 1.22595i | −0.790104 | − | 0.612973i | \(-0.789973\pi\) | ||||
0.790104 | − | 0.612973i | \(-0.210027\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 10.8122i | 0.354354i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −35.4586 | −1.15838 | −0.579190 | − | 0.815192i | \(-0.696631\pi\) | ||||
−0.579190 | + | 0.815192i | \(0.696631\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − 11.1420i | − 0.363219i | −0.983371 | − | 0.181610i | \(-0.941869\pi\) | ||||
0.983371 | − | 0.181610i | \(-0.0581307\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 57.7851i | 1.88174i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 31.4956 | 1.02347 | 0.511734 | − | 0.859144i | \(-0.329003\pi\) | ||||
0.511734 | + | 0.859144i | \(0.329003\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 5.08287 | 0.164997 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − 41.1062i | − 1.33156i | −0.746149 | − | 0.665779i | \(-0.768099\pi\) | ||||
0.746149 | − | 0.665779i | \(-0.231901\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 5.98788 | 0.193359 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 20.4219 | 0.658772 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 18.4157i | 0.592208i | 0.955156 | + | 0.296104i | \(0.0956875\pi\) | ||||
−0.955156 | + | 0.296104i | \(0.904313\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 11.3853 | 0.365371 | 0.182685 | − | 0.983171i | \(-0.441521\pi\) | ||||
0.182685 | + | 0.983171i | \(0.441521\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 15.8217 | 0.507222 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − 43.4822i | − 1.39112i | −0.718469 | − | 0.695559i | \(-0.755157\pi\) | ||||
0.718469 | − | 0.695559i | \(-0.244843\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − 13.9354i | − 0.445379i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 5.36529 | 0.171126 | 0.0855631 | − | 0.996333i | \(-0.472731\pi\) | ||||
0.0855631 | + | 0.996333i | \(0.472731\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 43.1403i | 1.37178i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 24.9325i | 0.792008i | 0.918249 | + | 0.396004i | \(0.129603\pi\) | ||||
−0.918249 | + | 0.396004i | \(0.870397\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 10.5169 | 0.333072 | 0.166536 | − | 0.986035i | \(-0.446742\pi\) | ||||
0.166536 | + | 0.986035i | \(0.446742\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 7200.2.h.m.1151.6 | 12 | ||
3.2 | odd | 2 | inner | 7200.2.h.m.1151.5 | 12 | ||
4.3 | odd | 2 | inner | 7200.2.h.m.1151.7 | 12 | ||
5.2 | odd | 4 | 1440.2.o.a.1439.10 | yes | 12 | ||
5.3 | odd | 4 | 1440.2.o.b.1439.4 | yes | 12 | ||
5.4 | even | 2 | 7200.2.h.l.1151.8 | 12 | |||
12.11 | even | 2 | inner | 7200.2.h.m.1151.8 | 12 | ||
15.2 | even | 4 | 1440.2.o.a.1439.3 | ✓ | 12 | ||
15.8 | even | 4 | 1440.2.o.b.1439.9 | yes | 12 | ||
15.14 | odd | 2 | 7200.2.h.l.1151.7 | 12 | |||
20.3 | even | 4 | 1440.2.o.a.1439.4 | yes | 12 | ||
20.7 | even | 4 | 1440.2.o.b.1439.10 | yes | 12 | ||
20.19 | odd | 2 | 7200.2.h.l.1151.5 | 12 | |||
40.3 | even | 4 | 2880.2.o.f.2879.9 | 12 | |||
40.13 | odd | 4 | 2880.2.o.e.2879.9 | 12 | |||
40.27 | even | 4 | 2880.2.o.e.2879.3 | 12 | |||
40.37 | odd | 4 | 2880.2.o.f.2879.3 | 12 | |||
60.23 | odd | 4 | 1440.2.o.a.1439.9 | yes | 12 | ||
60.47 | odd | 4 | 1440.2.o.b.1439.3 | yes | 12 | ||
60.59 | even | 2 | 7200.2.h.l.1151.6 | 12 | |||
120.53 | even | 4 | 2880.2.o.e.2879.4 | 12 | |||
120.77 | even | 4 | 2880.2.o.f.2879.10 | 12 | |||
120.83 | odd | 4 | 2880.2.o.f.2879.4 | 12 | |||
120.107 | odd | 4 | 2880.2.o.e.2879.10 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1440.2.o.a.1439.3 | ✓ | 12 | 15.2 | even | 4 | ||
1440.2.o.a.1439.4 | yes | 12 | 20.3 | even | 4 | ||
1440.2.o.a.1439.9 | yes | 12 | 60.23 | odd | 4 | ||
1440.2.o.a.1439.10 | yes | 12 | 5.2 | odd | 4 | ||
1440.2.o.b.1439.3 | yes | 12 | 60.47 | odd | 4 | ||
1440.2.o.b.1439.4 | yes | 12 | 5.3 | odd | 4 | ||
1440.2.o.b.1439.9 | yes | 12 | 15.8 | even | 4 | ||
1440.2.o.b.1439.10 | yes | 12 | 20.7 | even | 4 | ||
2880.2.o.e.2879.3 | 12 | 40.27 | even | 4 | |||
2880.2.o.e.2879.4 | 12 | 120.53 | even | 4 | |||
2880.2.o.e.2879.9 | 12 | 40.13 | odd | 4 | |||
2880.2.o.e.2879.10 | 12 | 120.107 | odd | 4 | |||
2880.2.o.f.2879.3 | 12 | 40.37 | odd | 4 | |||
2880.2.o.f.2879.4 | 12 | 120.83 | odd | 4 | |||
2880.2.o.f.2879.9 | 12 | 40.3 | even | 4 | |||
2880.2.o.f.2879.10 | 12 | 120.77 | even | 4 | |||
7200.2.h.l.1151.5 | 12 | 20.19 | odd | 2 | |||
7200.2.h.l.1151.6 | 12 | 60.59 | even | 2 | |||
7200.2.h.l.1151.7 | 12 | 15.14 | odd | 2 | |||
7200.2.h.l.1151.8 | 12 | 5.4 | even | 2 | |||
7200.2.h.m.1151.5 | 12 | 3.2 | odd | 2 | inner | ||
7200.2.h.m.1151.6 | 12 | 1.1 | even | 1 | trivial | ||
7200.2.h.m.1151.7 | 12 | 4.3 | odd | 2 | inner | ||
7200.2.h.m.1151.8 | 12 | 12.11 | even | 2 | inner |