Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [504,2,Mod(289,504)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(504, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 0, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("504.289");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 504 = 2^{3} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 504.s (of order \(3\), degree \(2\), 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: | \(4.02446026187\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 289.1 | ||
Root | \(0.500000 + 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 504.289 |
Dual form | 504.2.s.f.361.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/504\mathbb{Z}\right)^\times\).
\(n\) | \(73\) | \(127\) | \(253\) | \(281\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) | \(1\) | \(1\) |
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 | ||||||||
\(5\) | 0.500000 | − | 0.866025i | 0.223607 | − | 0.387298i | −0.732294 | − | 0.680989i | \(-0.761550\pi\) |
0.955901 | + | 0.293691i | \(0.0948835\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.50000 | − | 0.866025i | −0.944911 | − | 0.327327i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.50000 | − | 4.33013i | −0.753778 | − | 1.30558i | −0.945979 | − | 0.324227i | \(-0.894896\pi\) |
0.192201 | − | 0.981356i | \(-0.438437\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.00000 | 0.554700 | 0.277350 | − | 0.960769i | \(-0.410544\pi\) | ||||
0.277350 | + | 0.960769i | \(0.410544\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −3.00000 | − | 5.19615i | −0.727607 | − | 1.26025i | −0.957892 | − | 0.287129i | \(-0.907299\pi\) |
0.230285 | − | 0.973123i | \(-0.426034\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.00000 | + | 1.73205i | −0.229416 | + | 0.397360i | −0.957635 | − | 0.287984i | \(-0.907015\pi\) |
0.728219 | + | 0.685344i | \(0.240348\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 3.00000 | − | 5.19615i | 0.625543 | − | 1.08347i | −0.362892 | − | 0.931831i | \(-0.618211\pi\) |
0.988436 | − | 0.151642i | \(-0.0484560\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.00000 | + | 3.46410i | 0.400000 | + | 0.692820i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −3.00000 | −0.557086 | −0.278543 | − | 0.960424i | \(-0.589851\pi\) | ||||
−0.278543 | + | 0.960424i | \(0.589851\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.50000 | − | 4.33013i | −0.449013 | − | 0.777714i | 0.549309 | − | 0.835619i | \(-0.314891\pi\) |
−0.998322 | + | 0.0579057i | \(0.981558\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −2.00000 | + | 1.73205i | −0.338062 | + | 0.292770i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.00000 | − | 1.73205i | 0.164399 | − | 0.284747i | −0.772043 | − | 0.635571i | \(-0.780765\pi\) |
0.936442 | + | 0.350823i | \(0.114098\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 8.00000 | 1.24939 | 0.624695 | − | 0.780869i | \(-0.285223\pi\) | ||||
0.624695 | + | 0.780869i | \(0.285223\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −4.00000 | −0.609994 | −0.304997 | − | 0.952353i | \(-0.598656\pi\) | ||||
−0.304997 | + | 0.952353i | \(0.598656\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −2.00000 | + | 3.46410i | −0.291730 | + | 0.505291i | −0.974219 | − | 0.225605i | \(-0.927564\pi\) |
0.682489 | + | 0.730896i | \(0.260898\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 5.50000 | + | 4.33013i | 0.785714 | + | 0.618590i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −4.50000 | − | 7.79423i | −0.618123 | − | 1.07062i | −0.989828 | − | 0.142269i | \(-0.954560\pi\) |
0.371706 | − | 0.928351i | \(-0.378773\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −5.00000 | −0.674200 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 1.50000 | + | 2.59808i | 0.195283 | + | 0.338241i | 0.946993 | − | 0.321253i | \(-0.104104\pi\) |
−0.751710 | + | 0.659494i | \(0.770771\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 6.00000 | − | 10.3923i | 0.768221 | − | 1.33060i | −0.170305 | − | 0.985391i | \(-0.554475\pi\) |
0.938527 | − | 0.345207i | \(-0.112191\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1.00000 | − | 1.73205i | 0.124035 | − | 0.214834i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.00000 | − | 1.73205i | −0.122169 | − | 0.211604i | 0.798454 | − | 0.602056i | \(-0.205652\pi\) |
−0.920623 | + | 0.390453i | \(0.872318\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −8.00000 | −0.949425 | −0.474713 | − | 0.880141i | \(-0.657448\pi\) | ||||
−0.474713 | + | 0.880141i | \(0.657448\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 7.00000 | + | 12.1244i | 0.819288 | + | 1.41905i | 0.906208 | + | 0.422833i | \(0.138964\pi\) |
−0.0869195 | + | 0.996215i | \(0.527702\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 2.50000 | + | 12.9904i | 0.284901 | + | 1.48039i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −0.500000 | + | 0.866025i | −0.0562544 | + | 0.0974355i | −0.892781 | − | 0.450490i | \(-0.851249\pi\) |
0.836527 | + | 0.547926i | \(0.184582\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 17.0000 | 1.86599 | 0.932996 | − | 0.359886i | \(-0.117184\pi\) | ||||
0.932996 | + | 0.359886i | \(0.117184\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −6.00000 | −0.650791 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −9.00000 | + | 15.5885i | −0.953998 | + | 1.65237i | −0.217354 | + | 0.976093i | \(0.569742\pi\) |
−0.736644 | + | 0.676280i | \(0.763591\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −5.00000 | − | 1.73205i | −0.524142 | − | 0.181568i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1.00000 | + | 1.73205i | 0.102598 | + | 0.177705i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 3.00000 | 0.304604 | 0.152302 | − | 0.988334i | \(-0.451331\pi\) | ||||
0.152302 | + | 0.988334i | \(0.451331\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 5.00000 | + | 8.66025i | 0.497519 | + | 0.861727i | 0.999996 | − | 0.00286291i | \(-0.000911295\pi\) |
−0.502477 | + | 0.864590i | \(0.667578\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −4.00000 | + | 6.92820i | −0.394132 | + | 0.682656i | −0.992990 | − | 0.118199i | \(-0.962288\pi\) |
0.598858 | + | 0.800855i | \(0.295621\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −1.50000 | + | 2.59808i | −0.145010 | + | 0.251166i | −0.929377 | − | 0.369132i | \(-0.879655\pi\) |
0.784366 | + | 0.620298i | \(0.212988\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −7.00000 | − | 12.1244i | −0.670478 | − | 1.16130i | −0.977769 | − | 0.209687i | \(-0.932756\pi\) |
0.307290 | − | 0.951616i | \(-0.400578\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 8.00000 | 0.752577 | 0.376288 | − | 0.926503i | \(-0.377200\pi\) | ||||
0.376288 | + | 0.926503i | \(0.377200\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −3.00000 | − | 5.19615i | −0.279751 | − | 0.484544i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 3.00000 | + | 15.5885i | 0.275010 | + | 1.42899i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −7.00000 | + | 12.1244i | −0.636364 | + | 1.10221i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 9.00000 | 0.804984 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 19.0000 | 1.68598 | 0.842989 | − | 0.537931i | \(-0.180794\pi\) | ||||
0.842989 | + | 0.537931i | \(0.180794\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −8.50000 | + | 14.7224i | −0.742648 | + | 1.28630i | 0.208637 | + | 0.977993i | \(0.433097\pi\) |
−0.951285 | + | 0.308312i | \(0.900236\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 4.00000 | − | 3.46410i | 0.346844 | − | 0.300376i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −3.00000 | − | 5.19615i | −0.256307 | − | 0.443937i | 0.708942 | − | 0.705266i | \(-0.249173\pi\) |
−0.965250 | + | 0.261329i | \(0.915839\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 10.0000 | 0.848189 | 0.424094 | − | 0.905618i | \(-0.360592\pi\) | ||||
0.424094 | + | 0.905618i | \(0.360592\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −5.00000 | − | 8.66025i | −0.418121 | − | 0.724207i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1.50000 | + | 2.59808i | −0.124568 | + | 0.215758i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 3.00000 | − | 5.19615i | 0.245770 | − | 0.425685i | −0.716578 | − | 0.697507i | \(-0.754293\pi\) |
0.962348 | + | 0.271821i | \(0.0876260\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 7.50000 | + | 12.9904i | 0.610341 | + | 1.05714i | 0.991183 | + | 0.132502i | \(0.0423010\pi\) |
−0.380841 | + | 0.924640i | \(0.624366\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −5.00000 | −0.401610 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −6.00000 | − | 10.3923i | −0.478852 | − | 0.829396i | 0.520854 | − | 0.853646i | \(-0.325614\pi\) |
−0.999706 | + | 0.0242497i | \(0.992280\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −12.0000 | + | 10.3923i | −0.945732 | + | 0.819028i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 9.00000 | − | 15.5885i | 0.704934 | − | 1.22098i | −0.261781 | − | 0.965127i | \(-0.584310\pi\) |
0.966715 | − | 0.255855i | \(-0.0823569\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 22.0000 | 1.70241 | 0.851206 | − | 0.524832i | \(-0.175872\pi\) | ||||
0.851206 | + | 0.524832i | \(0.175872\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −9.00000 | −0.692308 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 3.00000 | − | 5.19615i | 0.228086 | − | 0.395056i | −0.729155 | − | 0.684349i | \(-0.760087\pi\) |
0.957241 | + | 0.289292i | \(0.0934200\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −2.00000 | − | 10.3923i | −0.151186 | − | 0.785584i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −10.0000 | − | 17.3205i | −0.747435 | − | 1.29460i | −0.949048 | − | 0.315130i | \(-0.897952\pi\) |
0.201613 | − | 0.979465i | \(-0.435382\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −20.0000 | −1.48659 | −0.743294 | − | 0.668965i | \(-0.766738\pi\) | ||||
−0.743294 | + | 0.668965i | \(0.766738\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −1.00000 | − | 1.73205i | −0.0735215 | − | 0.127343i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −15.0000 | + | 25.9808i | −1.09691 | + | 1.89990i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 2.00000 | − | 3.46410i | 0.144715 | − | 0.250654i | −0.784552 | − | 0.620063i | \(-0.787107\pi\) |
0.929267 | + | 0.369410i | \(0.120440\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −0.500000 | − | 0.866025i | −0.0359908 | − | 0.0623379i | 0.847469 | − | 0.530845i | \(-0.178125\pi\) |
−0.883460 | + | 0.468507i | \(0.844792\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −18.0000 | −1.28245 | −0.641223 | − | 0.767354i | \(-0.721573\pi\) | ||||
−0.641223 | + | 0.767354i | \(0.721573\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 7.50000 | + | 2.59808i | 0.526397 | + | 0.182349i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 4.00000 | − | 6.92820i | 0.279372 | − | 0.483887i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 10.0000 | 0.691714 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 24.0000 | 1.65223 | 0.826114 | − | 0.563503i | \(-0.190547\pi\) | ||||
0.826114 | + | 0.563503i | \(0.190547\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −2.00000 | + | 3.46410i | −0.136399 | + | 0.236250i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2.50000 | + | 12.9904i | 0.169711 | + | 0.881845i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −6.00000 | − | 10.3923i | −0.403604 | − | 0.699062i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 3.00000 | 0.200895 | 0.100447 | − | 0.994942i | \(-0.467973\pi\) | ||||
0.100447 | + | 0.994942i | \(0.467973\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −3.50000 | − | 6.06218i | −0.232303 | − | 0.402361i | 0.726182 | − | 0.687502i | \(-0.241293\pi\) |
−0.958485 | + | 0.285141i | \(0.907959\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 10.0000 | − | 17.3205i | 0.660819 | − | 1.14457i | −0.319582 | − | 0.947559i | \(-0.603543\pi\) |
0.980401 | − | 0.197013i | \(-0.0631241\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 11.0000 | − | 19.0526i | 0.720634 | − | 1.24817i | −0.240112 | − | 0.970745i | \(-0.577184\pi\) |
0.960746 | − | 0.277429i | \(-0.0894825\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2.00000 | + | 3.46410i | 0.130466 | + | 0.225973i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 2.00000 | 0.129369 | 0.0646846 | − | 0.997906i | \(-0.479396\pi\) | ||||
0.0646846 | + | 0.997906i | \(0.479396\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 8.50000 | + | 14.7224i | 0.547533 | + | 0.948355i | 0.998443 | + | 0.0557856i | \(0.0177663\pi\) |
−0.450910 | + | 0.892570i | \(0.648900\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 6.50000 | − | 2.59808i | 0.415270 | − | 0.165985i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2.00000 | + | 3.46410i | −0.127257 | + | 0.220416i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −15.0000 | −0.946792 | −0.473396 | − | 0.880850i | \(-0.656972\pi\) | ||||
−0.473396 | + | 0.880850i | \(0.656972\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −30.0000 | −1.88608 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −1.00000 | + | 1.73205i | −0.0623783 | + | 0.108042i | −0.895528 | − | 0.445005i | \(-0.853202\pi\) |
0.833150 | + | 0.553047i | \(0.186535\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −4.00000 | + | 3.46410i | −0.248548 | + | 0.215249i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −12.0000 | − | 20.7846i | −0.739952 | − | 1.28163i | −0.952517 | − | 0.304487i | \(-0.901515\pi\) |
0.212565 | − | 0.977147i | \(-0.431818\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −9.00000 | −0.552866 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −12.5000 | − | 21.6506i | −0.762138 | − | 1.32006i | −0.941746 | − | 0.336324i | \(-0.890816\pi\) |
0.179608 | − | 0.983738i | \(-0.442517\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 7.50000 | − | 12.9904i | 0.455593 | − | 0.789109i | −0.543130 | − | 0.839649i | \(-0.682761\pi\) |
0.998722 | + | 0.0505395i | \(0.0160941\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 10.0000 | − | 17.3205i | 0.603023 | − | 1.04447i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −14.0000 | − | 24.2487i | −0.841178 | − | 1.45696i | −0.888899 | − | 0.458103i | \(-0.848529\pi\) |
0.0477206 | − | 0.998861i | \(-0.484804\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −18.0000 | −1.07379 | −0.536895 | − | 0.843649i | \(-0.680403\pi\) | ||||
−0.536895 | + | 0.843649i | \(0.680403\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −2.00000 | − | 3.46410i | −0.118888 | − | 0.205919i | 0.800439 | − | 0.599414i | \(-0.204600\pi\) |
−0.919327 | + | 0.393494i | \(0.871266\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −20.0000 | − | 6.92820i | −1.18056 | − | 0.408959i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −9.50000 | + | 16.4545i | −0.558824 | + | 0.967911i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 21.0000 | 1.22683 | 0.613417 | − | 0.789760i | \(-0.289795\pi\) | ||||
0.613417 | + | 0.789760i | \(0.289795\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 3.00000 | 0.174667 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 6.00000 | − | 10.3923i | 0.346989 | − | 0.601003i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 10.0000 | + | 3.46410i | 0.576390 | + | 0.199667i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −6.00000 | − | 10.3923i | −0.343559 | − | 0.595062i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 34.0000 | 1.94048 | 0.970241 | − | 0.242140i | \(-0.0778494\pi\) | ||||
0.970241 | + | 0.242140i | \(0.0778494\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 2.00000 | + | 3.46410i | 0.113410 | + | 0.196431i | 0.917143 | − | 0.398559i | \(-0.130489\pi\) |
−0.803733 | + | 0.594990i | \(0.797156\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 11.5000 | − | 19.9186i | 0.650018 | − | 1.12586i | −0.333099 | − | 0.942892i | \(-0.608094\pi\) |
0.983118 | − | 0.182973i | \(-0.0585722\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −4.50000 | + | 7.79423i | −0.252745 | + | 0.437767i | −0.964281 | − | 0.264883i | \(-0.914667\pi\) |
0.711535 | + | 0.702650i | \(0.248000\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 7.50000 | + | 12.9904i | 0.419919 | + | 0.727322i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 12.0000 | 0.667698 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 4.00000 | + | 6.92820i | 0.221880 | + | 0.384308i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 8.00000 | − | 6.92820i | 0.441054 | − | 0.381964i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −4.00000 | + | 6.92820i | −0.219860 | + | 0.380808i | −0.954765 | − | 0.297361i | \(-0.903893\pi\) |
0.734905 | + | 0.678170i | \(0.237227\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −2.00000 | −0.109272 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −19.0000 | −1.03500 | −0.517498 | − | 0.855684i | \(-0.673136\pi\) | ||||
−0.517498 | + | 0.855684i | \(0.673136\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −12.5000 | + | 21.6506i | −0.676913 | + | 1.17245i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −10.0000 | − | 15.5885i | −0.539949 | − | 0.841698i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 6.00000 | + | 10.3923i | 0.322097 | + | 0.557888i | 0.980921 | − | 0.194409i | \(-0.0622790\pi\) |
−0.658824 | + | 0.752297i | \(0.728946\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 6.00000 | 0.321173 | 0.160586 | − | 0.987022i | \(-0.448662\pi\) | ||||
0.160586 | + | 0.987022i | \(0.448662\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 4.00000 | + | 6.92820i | 0.212899 | + | 0.368751i | 0.952620 | − | 0.304162i | \(-0.0983763\pi\) |
−0.739722 | + | 0.672913i | \(0.765043\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −4.00000 | + | 6.92820i | −0.212298 | + | 0.367711i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −3.00000 | + | 5.19615i | −0.158334 | + | 0.274242i | −0.934268 | − | 0.356572i | \(-0.883946\pi\) |
0.775934 | + | 0.630814i | \(0.217279\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 7.50000 | + | 12.9904i | 0.394737 | + | 0.683704i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 14.0000 | 0.732793 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −3.50000 | − | 6.06218i | −0.182699 | − | 0.316443i | 0.760100 | − | 0.649806i | \(-0.225150\pi\) |
−0.942799 | + | 0.333363i | \(0.891817\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 4.50000 | + | 23.3827i | 0.233628 | + | 1.21397i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −2.00000 | + | 3.46410i | −0.103556 | + | 0.179364i | −0.913147 | − | 0.407630i | \(-0.866355\pi\) |
0.809591 | + | 0.586994i | \(0.199689\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −6.00000 | −0.309016 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −4.00000 | −0.205466 | −0.102733 | − | 0.994709i | \(-0.532759\pi\) | ||||
−0.102733 | + | 0.994709i | \(0.532759\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 9.00000 | − | 15.5885i | 0.459879 | − | 0.796533i | −0.539076 | − | 0.842257i | \(-0.681226\pi\) |
0.998954 | + | 0.0457244i | \(0.0145596\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 12.5000 | + | 4.33013i | 0.637059 | + | 0.220684i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 7.00000 | + | 12.1244i | 0.354914 | + | 0.614729i | 0.987103 | − | 0.160085i | \(-0.0511768\pi\) |
−0.632189 | + | 0.774814i | \(0.717843\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −36.0000 | −1.82060 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0.500000 | + | 0.866025i | 0.0251577 | + | 0.0435745i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 4.00000 | − | 6.92820i | 0.200754 | − | 0.347717i | −0.748017 | − | 0.663679i | \(-0.768994\pi\) |
0.948772 | + | 0.315963i | \(0.102327\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −12.0000 | + | 20.7846i | −0.599251 | + | 1.03793i | 0.393680 | + | 0.919247i | \(0.371202\pi\) |
−0.992932 | + | 0.118686i | \(0.962132\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −5.00000 | − | 8.66025i | −0.249068 | − | 0.431398i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −10.0000 | −0.495682 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 2.50000 | + | 4.33013i | 0.123617 | + | 0.214111i | 0.921192 | − | 0.389109i | \(-0.127217\pi\) |
−0.797574 | + | 0.603220i | \(0.793884\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −1.50000 | − | 7.79423i | −0.0738102 | − | 0.383529i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 8.50000 | − | 14.7224i | 0.417249 | − | 0.722696i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −4.00000 | −0.195413 | −0.0977064 | − | 0.995215i | \(-0.531151\pi\) | ||||
−0.0977064 | + | 0.995215i | \(0.531151\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 16.0000 | 0.779792 | 0.389896 | − | 0.920859i | \(-0.372511\pi\) | ||||
0.389896 | + | 0.920859i | \(0.372511\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 12.0000 | − | 20.7846i | 0.582086 | − | 1.00820i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −24.0000 | + | 20.7846i | −1.16144 | + | 1.00584i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 16.0000 | + | 27.7128i | 0.770693 | + | 1.33488i | 0.937184 | + | 0.348836i | \(0.113423\pi\) |
−0.166491 | + | 0.986043i | \(0.553244\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 10.0000 | 0.480569 | 0.240285 | − | 0.970702i | \(-0.422759\pi\) | ||||
0.240285 | + | 0.970702i | \(0.422759\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 6.00000 | + | 10.3923i | 0.287019 | + | 0.497131i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −16.5000 | + | 28.5788i | −0.787502 | + | 1.36399i | 0.139991 | + | 0.990153i | \(0.455293\pi\) |
−0.927493 | + | 0.373841i | \(0.878041\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −4.50000 | + | 7.79423i | −0.213801 | + | 0.370315i | −0.952901 | − | 0.303281i | \(-0.901918\pi\) |
0.739100 | + | 0.673596i | \(0.235251\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 9.00000 | + | 15.5885i | 0.426641 | + | 0.738964i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 10.0000 | 0.471929 | 0.235965 | − | 0.971762i | \(-0.424175\pi\) | ||||
0.235965 | + | 0.971762i | \(0.424175\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −20.0000 | − | 34.6410i | −0.941763 | − | 1.63118i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −4.00000 | + | 3.46410i | −0.187523 | + | 0.162400i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 14.5000 | − | 25.1147i | 0.678281 | − | 1.17482i | −0.297217 | − | 0.954810i | \(-0.596058\pi\) |
0.975498 | − | 0.220008i | \(-0.0706083\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −30.0000 | −1.39724 | −0.698620 | − | 0.715493i | \(-0.746202\pi\) | ||||
−0.698620 | + | 0.715493i | \(0.746202\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 20.0000 | 0.929479 | 0.464739 | − | 0.885448i | \(-0.346148\pi\) | ||||
0.464739 | + | 0.885448i | \(0.346148\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −14.0000 | + | 24.2487i | −0.647843 | + | 1.12210i | 0.335794 | + | 0.941935i | \(0.390995\pi\) |
−0.983637 | + | 0.180161i | \(0.942338\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1.00000 | + | 5.19615i | 0.0461757 | + | 0.239936i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 10.0000 | + | 17.3205i | 0.459800 | + | 0.796398i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −8.00000 | −0.367065 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 12.0000 | + | 20.7846i | 0.548294 | + | 0.949673i | 0.998392 | + | 0.0566937i | \(0.0180558\pi\) |
−0.450098 | + | 0.892979i | \(0.648611\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2.00000 | − | 3.46410i | 0.0911922 | − | 0.157949i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 1.50000 | − | 2.59808i | 0.0681115 | − | 0.117973i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 12.5000 | + | 21.6506i | 0.566429 | + | 0.981084i | 0.996915 | + | 0.0784867i | \(0.0250088\pi\) |
−0.430486 | + | 0.902597i | \(0.641658\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 9.00000 | 0.406164 | 0.203082 | − | 0.979162i | \(-0.434904\pi\) | ||||
0.203082 | + | 0.979162i | \(0.434904\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 9.00000 | + | 15.5885i | 0.405340 | + | 0.702069i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 20.0000 | + | 6.92820i | 0.897123 | + | 0.310772i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 17.0000 | − | 29.4449i | 0.761025 | − | 1.31813i | −0.181298 | − | 0.983428i | \(-0.558030\pi\) |
0.942323 | − | 0.334705i | \(-0.108637\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 10.0000 | 0.445878 | 0.222939 | − | 0.974832i | \(-0.428435\pi\) | ||||
0.222939 | + | 0.974832i | \(0.428435\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 10.0000 | 0.444994 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −6.50000 | + | 11.2583i | −0.288107 | + | 0.499017i | −0.973358 | − | 0.229291i | \(-0.926359\pi\) |
0.685251 | + | 0.728307i | \(0.259693\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −7.00000 | − | 36.3731i | −0.309662 | − | 1.60905i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 4.00000 | + | 6.92820i | 0.176261 | + | 0.305293i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 20.0000 | 0.879599 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 12.0000 | + | 20.7846i | 0.525730 | + | 0.910590i | 0.999551 | + | 0.0299693i | \(0.00954094\pi\) |
−0.473821 | + | 0.880621i | \(0.657126\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −17.0000 | + | 29.4449i | −0.743358 | + | 1.28753i | 0.207600 | + | 0.978214i | \(0.433435\pi\) |
−0.950958 | + | 0.309320i | \(0.899899\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −15.0000 | + | 25.9808i | −0.653410 | + | 1.13174i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −6.50000 | − | 11.2583i | −0.282609 | − | 0.489493i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 16.0000 | 0.693037 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1.50000 | + | 2.59808i | 0.0648507 | + | 0.112325i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 5.00000 | − | 34.6410i | 0.215365 | − | 1.49209i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −16.0000 | + | 27.7128i | −0.687894 | + | 1.19147i | 0.284624 | + | 0.958639i | \(0.408131\pi\) |
−0.972518 | + | 0.232828i | \(0.925202\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −14.0000 | −0.599694 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −18.0000 | −0.769624 | −0.384812 | − | 0.922995i | \(-0.625734\pi\) | ||||
−0.384812 | + | 0.922995i | \(0.625734\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 3.00000 | − | 5.19615i | 0.127804 | − | 0.221364i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 2.00000 | − | 1.73205i | 0.0850487 | − | 0.0736543i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 18.5000 | + | 32.0429i | 0.783870 | + | 1.35770i | 0.929672 | + | 0.368389i | \(0.120091\pi\) |
−0.145802 | + | 0.989314i | \(0.546576\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −8.00000 | −0.338364 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −2.50000 | − | 4.33013i | −0.105362 | − | 0.182493i | 0.808524 | − | 0.588463i | \(-0.200267\pi\) |
−0.913886 | + | 0.405970i | \(0.866934\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 4.00000 | − | 6.92820i | 0.168281 | − | 0.291472i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −7.00000 | + | 12.1244i | −0.293455 | + | 0.508279i | −0.974624 | − | 0.223847i | \(-0.928139\pi\) |
0.681169 | + | 0.732126i | \(0.261472\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −20.0000 | − | 34.6410i | −0.836974 | − | 1.44968i | −0.892413 | − | 0.451219i | \(-0.850989\pi\) |
0.0554391 | − | 0.998462i | \(-0.482344\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 24.0000 | 1.00087 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −3.50000 | − | 6.06218i | −0.145707 | − | 0.252372i | 0.783930 | − | 0.620850i | \(-0.213212\pi\) |
−0.929636 | + | 0.368478i | \(0.879879\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −42.5000 | − | 14.7224i | −1.76320 | − | 0.610789i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −22.5000 | + | 38.9711i | −0.931855 | + | 1.61402i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −21.0000 | −0.866763 | −0.433381 | − | 0.901211i | \(-0.642680\pi\) | ||||
−0.433381 | + | 0.901211i | \(0.642680\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 10.0000 | 0.412043 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 13.0000 | − | 22.5167i | 0.533846 | − | 0.924648i | −0.465372 | − | 0.885115i | \(-0.654080\pi\) |
0.999218 | − | 0.0395334i | \(-0.0125871\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 15.0000 | + | 5.19615i | 0.614940 | + | 0.213021i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 3.00000 | + | 5.19615i | 0.122577 | + | 0.212309i | 0.920783 | − | 0.390075i | \(-0.127551\pi\) |
−0.798206 | + | 0.602384i | \(0.794218\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −1.00000 | −0.0407909 | −0.0203954 | − | 0.999792i | \(-0.506493\pi\) | ||||
−0.0203954 | + | 0.999792i | \(0.506493\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 7.00000 | + | 12.1244i | 0.284590 | + | 0.492925i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 12.5000 | − | 21.6506i | 0.507359 | − | 0.878772i | −0.492604 | − | 0.870253i | \(-0.663955\pi\) |
0.999964 | − | 0.00851879i | \(-0.00271165\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −4.00000 | + | 6.92820i | −0.161823 | + | 0.280285i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 3.00000 | + | 5.19615i | 0.121169 | + | 0.209871i | 0.920229 | − | 0.391381i | \(-0.128002\pi\) |
−0.799060 | + | 0.601251i | \(0.794669\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −20.0000 | −0.805170 | −0.402585 | − | 0.915383i | \(-0.631888\pi\) | ||||
−0.402585 | + | 0.915383i | \(0.631888\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −2.00000 | − | 3.46410i | −0.0803868 | − | 0.139234i | 0.823029 | − | 0.567999i | \(-0.192282\pi\) |
−0.903416 | + | 0.428765i | \(0.858949\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 36.0000 | − | 31.1769i | 1.44231 | − | 1.24908i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −5.50000 | + | 9.52628i | −0.220000 | + | 0.381051i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −12.0000 | −0.478471 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −9.00000 | −0.358284 | −0.179142 | − | 0.983823i | \(-0.557332\pi\) | ||||
−0.179142 | + | 0.983823i | \(0.557332\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 9.50000 | − | 16.4545i | 0.376996 | − | 0.652976i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 11.0000 | + | 8.66025i | 0.435836 | + | 0.343132i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −6.00000 | − | 10.3923i | −0.236986 | − | 0.410471i | 0.722862 | − | 0.690992i | \(-0.242826\pi\) |
−0.959848 | + | 0.280521i | \(0.909493\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 22.0000 | 0.867595 | 0.433798 | − | 0.901010i | \(-0.357173\pi\) | ||||
0.433798 | + | 0.901010i | \(0.357173\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −14.0000 | − | 24.2487i | −0.550397 | − | 0.953315i | −0.998246 | − | 0.0592060i | \(-0.981143\pi\) |
0.447849 | − | 0.894109i | \(-0.352190\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 7.50000 | − | 12.9904i | 0.294401 | − | 0.509917i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 14.5000 | − | 25.1147i | 0.567429 | − | 0.982816i | −0.429390 | − | 0.903119i | \(-0.641272\pi\) |
0.996819 | − | 0.0796966i | \(-0.0253951\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 8.50000 | + | 14.7224i | 0.332122 | + | 0.575253i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −36.0000 | −1.40236 | −0.701180 | − | 0.712984i | \(-0.747343\pi\) | ||||
−0.701180 | + | 0.712984i | \(0.747343\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 20.0000 | + | 34.6410i | 0.777910 | + | 1.34738i | 0.933144 | + | 0.359502i | \(0.117053\pi\) |
−0.155235 | + | 0.987878i | \(0.549613\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −1.00000 | − | 5.19615i | −0.0387783 | − | 0.201498i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −9.00000 | + | 15.5885i | −0.348481 | + | 0.603587i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −60.0000 | −2.31627 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1.00000 | 0.0385472 | 0.0192736 | − | 0.999814i | \(-0.493865\pi\) | ||||
0.0192736 | + | 0.999814i | \(0.493865\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 22.5000 | − | 38.9711i | 0.864745 | − | 1.49778i | −0.00255466 | − | 0.999997i | \(-0.500813\pi\) |
0.867300 | − | 0.497786i | \(-0.165853\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −7.50000 | − | 2.59808i | −0.287824 | − | 0.0997050i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 10.5000 | + | 18.1865i | 0.401771 | + | 0.695888i | 0.993940 | − | 0.109926i | \(-0.0350613\pi\) |
−0.592168 | + | 0.805814i | \(0.701728\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −6.00000 | −0.229248 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −9.00000 | − | 15.5885i | −0.342873 | − | 0.593873i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 4.00000 | − | 6.92820i | 0.152167 | − | 0.263561i | −0.779857 | − | 0.625958i | \(-0.784708\pi\) |
0.932024 | + | 0.362397i | \(0.118041\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 5.00000 | − | 8.66025i | 0.189661 | − | 0.328502i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −24.0000 | − | 41.5692i | −0.909065 | − | 1.57455i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 45.0000 | 1.69963 | 0.849813 | − | 0.527084i | \(-0.176715\pi\) | ||||
0.849813 | + | 0.527084i | \(0.176715\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 2.00000 | + | 3.46410i | 0.0754314 | + | 0.130651i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −5.00000 | − | 25.9808i | −0.188044 | − | 0.977107i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 9.00000 | − | 15.5885i | 0.338002 | − | 0.585437i | −0.646055 | − | 0.763291i | \(-0.723582\pi\) |
0.984057 | + | 0.177854i | \(0.0569156\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −30.0000 | −1.12351 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −10.0000 | −0.373979 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 5.00000 | − | 8.66025i | 0.186469 | − | 0.322973i | −0.757602 | − | 0.652717i | \(-0.773629\pi\) |
0.944070 | + | 0.329744i | \(0.106962\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 16.0000 | − | 13.8564i | 0.595871 | − | 0.516040i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −6.00000 | − | 10.3923i | −0.222834 | − | 0.385961i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −35.0000 | −1.29808 | −0.649039 | − | 0.760755i | \(-0.724829\pi\) | ||||
−0.649039 | + | 0.760755i | \(0.724829\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 12.0000 | + | 20.7846i | 0.443836 | + | 0.768747i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −10.0000 | + | 17.3205i | −0.369358 | + | 0.639748i | −0.989465 | − | 0.144770i | \(-0.953756\pi\) |
0.620107 | + | 0.784517i | \(0.287089\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −5.00000 | + | 8.66025i | −0.184177 | + | 0.319005i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −17.0000 | − | 29.4449i | −0.625355 | − | 1.08315i | −0.988472 | − | 0.151403i | \(-0.951621\pi\) |
0.363117 | − | 0.931744i | \(-0.381713\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 2.00000 | 0.0733729 | 0.0366864 | − | 0.999327i | \(-0.488320\pi\) | ||||
0.0366864 | + | 0.999327i | \(0.488320\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −3.00000 | − | 5.19615i | −0.109911 | − | 0.190372i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 6.00000 | − | 5.19615i | 0.219235 | − | 0.189863i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 14.5000 | − | 25.1147i | 0.529113 | − | 0.916450i | −0.470311 | − | 0.882501i | \(-0.655858\pi\) |
0.999424 | − | 0.0339490i | \(-0.0108084\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 15.0000 | 0.545906 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −20.0000 | −0.726912 | −0.363456 | − | 0.931611i | \(-0.618403\pi\) | ||||
−0.363456 | + | 0.931611i | \(0.618403\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 9.00000 | − | 15.5885i | 0.326250 | − | 0.565081i | −0.655515 | − | 0.755182i | \(-0.727548\pi\) |
0.981764 | + | 0.190101i | \(0.0608816\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 7.00000 | + | 36.3731i | 0.253417 | + | 1.31679i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 3.00000 | + | 5.19615i | 0.108324 | + | 0.187622i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −19.0000 | −0.685158 | −0.342579 | − | 0.939489i | \(-0.611300\pi\) | ||||
−0.342579 | + | 0.939489i | \(0.611300\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −19.0000 | − | 32.9090i | −0.683383 | − | 1.18365i | −0.973942 | − | 0.226796i | \(-0.927175\pi\) |
0.290560 | − | 0.956857i | \(-0.406159\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 10.0000 | − | 17.3205i | 0.359211 | − | 0.622171i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −8.00000 | + | 13.8564i | −0.286630 | + | 0.496457i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 20.0000 | + | 34.6410i | 0.715656 | + | 1.23955i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −12.0000 | −0.428298 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 20.0000 | + | 34.6410i | 0.712923 | + | 1.23482i | 0.963755 | + | 0.266788i | \(0.0859624\pi\) |
−0.250832 | + | 0.968031i | \(0.580704\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −20.0000 | − | 6.92820i | −0.711118 | − | 0.246339i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 12.0000 | − | 20.7846i | 0.426132 | − | 0.738083i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −33.0000 | −1.16892 | −0.584460 | − | 0.811423i | \(-0.698694\pi\) | ||||
−0.584460 | + | 0.811423i | \(0.698694\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 24.0000 | 0.849059 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 35.0000 | − | 60.6218i | 1.23512 | − | 2.13930i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 3.00000 | + | 15.5885i | 0.105736 | + | 0.549421i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 14.0000 | + | 24.2487i | 0.492214 | + | 0.852539i | 0.999960 | − | 0.00896753i | \(-0.00285449\pi\) |
−0.507746 | + | 0.861507i | \(0.669521\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 34.0000 | 1.19390 | 0.596951 | − | 0.802278i | \(-0.296379\pi\) | ||||
0.596951 | + | 0.802278i | \(0.296379\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −9.00000 | − | 15.5885i | −0.315256 | − | 0.546040i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 4.00000 | − | 6.92820i | 0.139942 | − | 0.242387i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −14.5000 | + | 25.1147i | −0.506053 | + | 0.876510i | 0.493922 | + | 0.869506i | \(0.335563\pi\) |
−0.999975 | + | 0.00700413i | \(0.997770\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 12.0000 | + | 20.7846i | 0.418294 | + | 0.724506i | 0.995768 | − | 0.0919029i | \(-0.0292950\pi\) |
−0.577474 | + | 0.816409i | \(0.695962\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 41.0000 | 1.42571 | 0.712855 | − | 0.701312i | \(-0.247402\pi\) | ||||
0.712855 | + | 0.701312i | \(0.247402\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −13.0000 | − | 22.5167i | −0.451509 | − | 0.782036i | 0.546971 | − | 0.837151i | \(-0.315781\pi\) |
−0.998480 | + | 0.0551154i | \(0.982447\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 6.00000 | − | 41.5692i | 0.207888 | − | 1.44029i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 11.0000 | − | 19.0526i | 0.380671 | − | 0.659341i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −30.0000 | −1.03572 | −0.517858 | − | 0.855467i | \(-0.673270\pi\) | ||||
−0.517858 | + | 0.855467i | \(0.673270\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −20.0000 | −0.689655 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −4.50000 | + | 7.79423i | −0.154805 | + | 0.268130i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 28.0000 | − | 24.2487i | 0.962091 | − | 0.833196i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −6.00000 | − | 10.3923i | −0.205677 | − | 0.356244i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −22.0000 | −0.753266 | −0.376633 | − | 0.926363i | \(-0.622918\pi\) | ||||
−0.376633 | + | 0.926363i | \(0.622918\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −6.00000 | − | 10.3923i | −0.204956 | − | 0.354994i | 0.745163 | − | 0.666883i | \(-0.232372\pi\) |
−0.950119 | + | 0.311888i | \(0.899038\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −16.0000 | + | 27.7128i | −0.545913 | + | 0.945549i | 0.452636 | + | 0.891695i | \(0.350484\pi\) |
−0.998549 | + | 0.0538535i | \(0.982850\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 19.0000 | − | 32.9090i | 0.646768 | − | 1.12023i | −0.337123 | − | 0.941461i | \(-0.609454\pi\) |
0.983890 | − | 0.178774i | \(-0.0572129\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −3.00000 | − | 5.19615i | −0.102003 | − | 0.176674i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 5.00000 | 0.169613 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −2.00000 | − | 3.46410i | −0.0677674 | − | 0.117377i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −22.5000 | − | 7.79423i | −0.760639 | − | 0.263493i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −12.0000 | + | 20.7846i | −0.405211 | + | 0.701846i | −0.994346 | − | 0.106188i | \(-0.966135\pi\) |
0.589135 | + | 0.808035i | \(0.299469\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −18.0000 | −0.606435 | −0.303218 | − | 0.952921i | \(-0.598061\pi\) | ||||
−0.303218 | + | 0.952921i | \(0.598061\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 28.0000 | 0.942275 | 0.471138 | − | 0.882060i | \(-0.343844\pi\) | ||||
0.471138 | + | 0.882060i | \(0.343844\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −13.0000 | + | 22.5167i | −0.436497 | + | 0.756035i | −0.997417 | − | 0.0718351i | \(-0.977114\pi\) |
0.560919 | + | 0.827871i | \(0.310448\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −47.5000 | − | 16.4545i | −1.59310 | − | 0.551866i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −4.00000 | − | 6.92820i | −0.133855 | − | 0.231843i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −20.0000 | −0.668526 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 7.50000 | + | 12.9904i | 0.250139 | + | 0.433253i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −27.0000 | + | 46.7654i | −0.899500 | + | 1.55798i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −10.0000 | + | 17.3205i | −0.332411 | + | 0.575753i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 11.0000 | + | 19.0526i | 0.365249 | + | 0.632630i | 0.988816 | − | 0.149140i | \(-0.0476505\pi\) |
−0.623567 | + | 0.781770i | \(0.714317\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −24.0000 | −0.795155 | −0.397578 | − | 0.917568i | \(-0.630149\pi\) | ||||
−0.397578 | + | 0.917568i | \(0.630149\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −42.5000 | − | 73.6122i | −1.40654 | − | 2.43621i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 34.0000 | − | 29.4449i | 1.12278 | − | 0.972355i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −22.0000 | + | 38.1051i | −0.725713 | + | 1.25697i | 0.232967 | + | 0.972485i | \(0.425157\pi\) |
−0.958680 | + | 0.284487i | \(0.908177\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −16.0000 | −0.526646 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 8.00000 | 0.263038 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 4.00000 | − | 6.92820i | 0.131236 | − | 0.227307i | −0.792917 | − | 0.609329i | \(-0.791439\pi\) |
0.924153 | + | 0.382022i | \(0.124772\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −13.0000 | + | 5.19615i | −0.426058 | + | 0.170297i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 15.0000 | + | 25.9808i | 0.490552 | + | 0.849662i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −5.00000 | −0.163343 | −0.0816714 | − | 0.996659i | \(-0.526026\pi\) | ||||
−0.0816714 | + | 0.996659i | \(0.526026\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 10.5000 | + | 18.1865i | 0.342290 | + | 0.592864i | 0.984858 | − | 0.173365i | \(-0.0554641\pi\) |
−0.642567 | + | 0.766229i | \(0.722131\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 24.0000 | − | 41.5692i | 0.781548 | − | 1.35368i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −14.0000 | + | 24.2487i | −0.454939 | + | 0.787977i | −0.998685 | − | 0.0512727i | \(-0.983672\pi\) |
0.543746 | + | 0.839250i | \(0.317006\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 14.0000 | + | 24.2487i | 0.454459 | + | 0.787146i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 60.0000 | 1.94359 | 0.971795 | − | 0.235826i | \(-0.0757795\pi\) | ||||
0.971795 | + | 0.235826i | \(0.0757795\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −2.00000 | − | 3.46410i | −0.0647185 | − | 0.112096i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 3.00000 | + | 15.5885i | 0.0968751 | + | 0.503378i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 3.00000 | − | 5.19615i | 0.0967742 | − | 0.167618i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −1.00000 | −0.0321911 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 17.0000 | 0.546683 | 0.273342 | − | 0.961917i | \(-0.411871\pi\) | ||||
0.273342 | + | 0.961917i | \(0.411871\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −7.50000 | + | 12.9904i | −0.240686 | + | 0.416881i | −0.960910 | − | 0.276861i | \(-0.910706\pi\) |
0.720224 | + | 0.693742i | \(0.244039\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −25.0000 | − | 8.66025i | −0.801463 | − | 0.277635i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 14.0000 | + | 24.2487i | 0.447900 | + | 0.775785i | 0.998249 | − | 0.0591494i | \(-0.0188388\pi\) |
−0.550349 | + | 0.834934i | \(0.685506\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 90.0000 | 2.87641 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 24.0000 | + | 41.5692i | 0.765481 | + | 1.32585i | 0.939992 | + | 0.341197i | \(0.110832\pi\) |
−0.174511 | + | 0.984655i | \(0.555834\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −9.00000 | + | 15.5885i | −0.286764 | + | 0.496690i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −12.0000 | + | 20.7846i | −0.381578 | + | 0.660912i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 3.50000 | + | 6.06218i | 0.111181 | + | 0.192571i | 0.916247 | − | 0.400614i | \(-0.131203\pi\) |
−0.805066 | + | 0.593186i | \(0.797870\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 7.00000 | + | 12.1244i | 0.221692 | + | 0.383982i | 0.955322 | − | 0.295567i | \(-0.0955086\pi\) |
−0.733630 | + | 0.679549i | \(0.762175\pi\) | |||||||
\(998\) | 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 | 504.2.s.f.289.1 | yes | 2 | |
3.2 | odd | 2 | 504.2.s.b.289.1 | ✓ | 2 | ||
4.3 | odd | 2 | 1008.2.s.l.289.1 | 2 | |||
7.2 | even | 3 | 3528.2.a.l.1.1 | 1 | |||
7.3 | odd | 6 | 3528.2.s.l.361.1 | 2 | |||
7.4 | even | 3 | inner | 504.2.s.f.361.1 | yes | 2 | |
7.5 | odd | 6 | 3528.2.a.s.1.1 | 1 | |||
7.6 | odd | 2 | 3528.2.s.l.3313.1 | 2 | |||
12.11 | even | 2 | 1008.2.s.h.289.1 | 2 | |||
21.2 | odd | 6 | 3528.2.a.o.1.1 | 1 | |||
21.5 | even | 6 | 3528.2.a.h.1.1 | 1 | |||
21.11 | odd | 6 | 504.2.s.b.361.1 | yes | 2 | ||
21.17 | even | 6 | 3528.2.s.r.361.1 | 2 | |||
21.20 | even | 2 | 3528.2.s.r.3313.1 | 2 | |||
28.11 | odd | 6 | 1008.2.s.l.865.1 | 2 | |||
28.19 | even | 6 | 7056.2.a.bh.1.1 | 1 | |||
28.23 | odd | 6 | 7056.2.a.r.1.1 | 1 | |||
84.11 | even | 6 | 1008.2.s.h.865.1 | 2 | |||
84.23 | even | 6 | 7056.2.a.bm.1.1 | 1 | |||
84.47 | odd | 6 | 7056.2.a.v.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
504.2.s.b.289.1 | ✓ | 2 | 3.2 | odd | 2 | ||
504.2.s.b.361.1 | yes | 2 | 21.11 | odd | 6 | ||
504.2.s.f.289.1 | yes | 2 | 1.1 | even | 1 | trivial | |
504.2.s.f.361.1 | yes | 2 | 7.4 | even | 3 | inner | |
1008.2.s.h.289.1 | 2 | 12.11 | even | 2 | |||
1008.2.s.h.865.1 | 2 | 84.11 | even | 6 | |||
1008.2.s.l.289.1 | 2 | 4.3 | odd | 2 | |||
1008.2.s.l.865.1 | 2 | 28.11 | odd | 6 | |||
3528.2.a.h.1.1 | 1 | 21.5 | even | 6 | |||
3528.2.a.l.1.1 | 1 | 7.2 | even | 3 | |||
3528.2.a.o.1.1 | 1 | 21.2 | odd | 6 | |||
3528.2.a.s.1.1 | 1 | 7.5 | odd | 6 | |||
3528.2.s.l.361.1 | 2 | 7.3 | odd | 6 | |||
3528.2.s.l.3313.1 | 2 | 7.6 | odd | 2 | |||
3528.2.s.r.361.1 | 2 | 21.17 | even | 6 | |||
3528.2.s.r.3313.1 | 2 | 21.20 | even | 2 | |||
7056.2.a.r.1.1 | 1 | 28.23 | odd | 6 | |||
7056.2.a.v.1.1 | 1 | 84.47 | odd | 6 | |||
7056.2.a.bh.1.1 | 1 | 28.19 | even | 6 | |||
7056.2.a.bm.1.1 | 1 | 84.23 | even | 6 |