Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3024,2,Mod(1889,3024)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3024, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3024.1889");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3024 = 2^{4} \cdot 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3024.k (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(24.1467615712\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 24x^{14} + 230x^{12} - 1052x^{10} + 2139x^{8} - 1244x^{6} + 1134x^{4} - 104x^{2} + 169 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{20} \) |
Twist minimal: | no (minimal twist has level 1512) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1889.6 | ||
Root | \(-2.32849 + 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3024.1889 |
Dual form | 3024.2.k.k.1889.5 |
$q$-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 \(\left(\mathbb{Z}/3024\mathbb{Z}\right)^\times\).
\(n\) | \(757\) | \(785\) | \(1135\) | \(2593\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) | \(-1\) |
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 | ||||||||
\(5\) | −1.10598 | −0.494608 | −0.247304 | − | 0.968938i | \(-0.579545\pi\) | ||||
−0.247304 | + | 0.968938i | \(0.579545\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.64465 | + | 0.0763047i | 0.999584 | + | 0.0288405i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 3.42810i | − | 1.03361i | −0.856103 | − | 0.516805i | \(-0.827121\pi\) | ||
0.856103 | − | 0.516805i | \(-0.172879\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 4.98427i | − | 1.38239i | −0.722670 | − | 0.691194i | \(-0.757085\pi\) | ||
0.722670 | − | 0.691194i | \(-0.242915\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 6.38903 | 1.54957 | 0.774783 | − | 0.632227i | \(-0.217859\pi\) | ||||
0.774783 | + | 0.632227i | \(0.217859\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 4.65697i | − | 1.06838i | −0.845363 | − | 0.534192i | \(-0.820616\pi\) | ||
0.845363 | − | 0.534192i | \(-0.179384\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 8.98172i | 1.87282i | 0.350909 | + | 0.936410i | \(0.385873\pi\) | ||||
−0.350909 | + | 0.936410i | \(0.614127\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.77681 | −0.755363 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.51249i | 0.280862i | 0.990090 | + | 0.140431i | \(0.0448488\pi\) | ||||
−0.990090 | + | 0.140431i | \(0.955151\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 6.71632i | − | 1.20629i | −0.797633 | − | 0.603143i | \(-0.793915\pi\) | ||
0.797633 | − | 0.603143i | \(-0.206085\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −2.92492 | − | 0.0843913i | −0.494402 | − | 0.0142647i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2.83122 | −0.465449 | −0.232725 | − | 0.972543i | \(-0.574764\pi\) | ||||
−0.232725 | + | 0.972543i | \(0.574764\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 10.1147 | 1.57965 | 0.789826 | − | 0.613331i | \(-0.210171\pi\) | ||||
0.789826 | + | 0.613331i | \(0.210171\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −10.8973 | −1.66183 | −0.830914 | − | 0.556401i | \(-0.812182\pi\) | ||||
−0.830914 | + | 0.556401i | \(0.812182\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −12.8935 | −1.88070 | −0.940352 | − | 0.340202i | \(-0.889504\pi\) | ||||
−0.940352 | + | 0.340202i | \(0.889504\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.98836 | + | 0.403599i | 0.998336 | + | 0.0576570i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 3.02497i | 0.415512i | 0.978181 | + | 0.207756i | \(0.0666160\pi\) | ||||
−0.978181 | + | 0.207756i | \(0.933384\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 3.79140i | 0.511232i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −9.54791 | −1.24303 | −0.621516 | − | 0.783402i | \(-0.713483\pi\) | ||||
−0.621516 | + | 0.783402i | \(0.713483\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 9.16134i | − | 1.17299i | −0.809953 | − | 0.586495i | \(-0.800508\pi\) | ||
0.809953 | − | 0.586495i | \(-0.199492\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 5.51249i | 0.683740i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 5.07938 | 0.620545 | 0.310272 | − | 0.950648i | \(-0.399580\pi\) | ||||
0.310272 | + | 0.950648i | \(0.399580\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 8.94058i | − | 1.06105i | −0.847669 | − | 0.530526i | \(-0.821994\pi\) | ||
0.847669 | − | 0.530526i | \(-0.178006\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 7.79378i | − | 0.912193i | −0.889930 | − | 0.456097i | \(-0.849247\pi\) | ||
0.889930 | − | 0.456097i | \(-0.150753\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0.261580 | − | 9.06612i | 0.0298098 | − | 1.03318i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.05440 | 0.231138 | 0.115569 | − | 0.993299i | \(-0.463131\pi\) | ||||
0.115569 | + | 0.993299i | \(0.463131\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −5.73444 | −0.629436 | −0.314718 | − | 0.949185i | \(-0.601910\pi\) | ||||
−0.314718 | + | 0.949185i | \(0.601910\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −7.06612 | −0.766428 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −6.47681 | −0.686541 | −0.343270 | − | 0.939237i | \(-0.611535\pi\) | ||||
−0.343270 | + | 0.939237i | \(0.611535\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.380323 | − | 13.1816i | 0.0398687 | − | 1.38181i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 5.15051i | 0.528431i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 8.04062i | 0.816401i | 0.912892 | + | 0.408201i | \(0.133844\pi\) | ||||
−0.912892 | + | 0.408201i | \(0.866156\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 13.3172 | 1.32511 | 0.662557 | − | 0.749012i | \(-0.269471\pi\) | ||||
0.662557 | + | 0.749012i | \(0.269471\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 6.86893i | 0.676816i | 0.941000 | + | 0.338408i | \(0.109888\pi\) | ||||
−0.941000 | + | 0.338408i | \(0.890112\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 6.09109i | − | 0.588848i | −0.955675 | − | 0.294424i | \(-0.904872\pi\) | ||
0.955675 | − | 0.294424i | \(-0.0951278\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 14.6580 | 1.40398 | 0.701990 | − | 0.712187i | \(-0.252295\pi\) | ||||
0.701990 | + | 0.712187i | \(0.252295\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 18.1322i | − | 1.70574i | −0.522126 | − | 0.852868i | \(-0.674861\pi\) | ||
0.522126 | − | 0.852868i | \(-0.325139\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − | 9.93358i | − | 0.926311i | ||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 16.8967 | + | 0.487513i | 1.54892 | + | 0.0446902i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −0.751840 | −0.0683491 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 9.70696 | 0.868217 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 7.23490 | 0.641993 | 0.320997 | − | 0.947080i | \(-0.395982\pi\) | ||||
0.320997 | + | 0.947080i | \(0.395982\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 14.5823 | 1.27406 | 0.637029 | − | 0.770840i | \(-0.280163\pi\) | ||||
0.637029 | + | 0.770840i | \(0.280163\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.355349 | − | 12.3161i | 0.0308127 | − | 1.06794i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 5.17492i | − | 0.442123i | −0.975260 | − | 0.221062i | \(-0.929048\pi\) | ||
0.975260 | − | 0.221062i | \(-0.0709522\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 11.2419i | − | 0.953523i | −0.879033 | − | 0.476761i | \(-0.841811\pi\) | ||
0.879033 | − | 0.476761i | \(-0.158189\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −17.0865 | −1.42885 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 1.67278i | − | 0.138917i | ||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 7.66243i | 0.627731i | 0.949467 | + | 0.313866i | \(0.101624\pi\) | ||||
−0.949467 | + | 0.313866i | \(0.898376\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −9.28930 | −0.755953 | −0.377976 | − | 0.925815i | \(-0.623380\pi\) | ||||
−0.377976 | + | 0.925815i | \(0.623380\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 7.42810i | 0.596639i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 13.8404i | − | 1.10458i | −0.833651 | − | 0.552292i | \(-0.813754\pi\) | ||
0.833651 | − | 0.552292i | \(-0.186246\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −0.685348 | + | 23.7535i | −0.0540130 | + | 1.87204i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 15.6580 | 1.22643 | 0.613214 | − | 0.789917i | \(-0.289876\pi\) | ||||
0.613214 | + | 0.789917i | \(0.289876\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −3.81347 | −0.295095 | −0.147548 | − | 0.989055i | \(-0.547138\pi\) | ||||
−0.147548 | + | 0.989055i | \(0.547138\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −11.8429 | −0.910995 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −6.36140 | −0.483649 | −0.241824 | − | 0.970320i | \(-0.577746\pi\) | ||||
−0.241824 | + | 0.970320i | \(0.577746\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −9.98836 | − | 0.288189i | −0.755049 | − | 0.0217850i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 4.04114i | − | 0.302049i | −0.988530 | − | 0.151025i | \(-0.951743\pi\) | ||
0.988530 | − | 0.151025i | \(-0.0482573\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 2.84357i | − | 0.211361i | −0.994400 | − | 0.105681i | \(-0.966298\pi\) | ||
0.994400 | − | 0.105681i | \(-0.0337021\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 3.13126 | 0.230215 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 21.9022i | − | 1.60165i | ||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 13.1505i | − | 0.951537i | −0.879570 | − | 0.475769i | \(-0.842170\pi\) | ||
0.879570 | − | 0.475769i | \(-0.157830\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −9.97671 | −0.718139 | −0.359070 | − | 0.933311i | \(-0.616906\pi\) | ||||
−0.359070 | + | 0.933311i | \(0.616906\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 15.4448i | 1.10040i | 0.835034 | + | 0.550199i | \(0.185448\pi\) | ||||
−0.835034 | + | 0.550199i | \(0.814552\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2.25521i | 0.159868i | 0.996800 | + | 0.0799338i | \(0.0254709\pi\) | ||||
−0.996800 | + | 0.0799338i | \(0.974529\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −0.115410 | + | 4.00000i | −0.00810019 | + | 0.280745i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −11.1866 | −0.781308 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −15.9646 | −1.10429 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −5.81796 | −0.400525 | −0.200262 | − | 0.979742i | \(-0.564179\pi\) | ||||
−0.200262 | + | 0.979742i | \(0.564179\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 12.0522 | 0.821953 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0.512487 | − | 17.7623i | 0.0347899 | − | 1.20578i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 31.8446i | − | 2.14210i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1.52241i | 0.101948i | 0.998700 | + | 0.0509741i | \(0.0162326\pi\) | ||||
−0.998700 | + | 0.0509741i | \(0.983767\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −18.2803 | −1.21331 | −0.606654 | − | 0.794966i | \(-0.707488\pi\) | ||||
−0.606654 | + | 0.794966i | \(0.707488\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 10.2738i | 0.678909i | 0.940622 | + | 0.339454i | \(0.110242\pi\) | ||||
−0.940622 | + | 0.339454i | \(0.889758\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 16.0000i | − | 1.04819i | −0.851658 | − | 0.524097i | \(-0.824403\pi\) | ||
0.851658 | − | 0.524097i | \(-0.175597\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 14.2599 | 0.930212 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 21.1161i | 1.36588i | 0.730472 | + | 0.682942i | \(0.239300\pi\) | ||||
−0.730472 | + | 0.682942i | \(0.760700\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 22.9594i | − | 1.47894i | −0.673188 | − | 0.739471i | \(-0.735076\pi\) | ||
0.673188 | − | 0.739471i | \(-0.264924\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −7.72896 | − | 0.446371i | −0.493785 | − | 0.0285176i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −23.2116 | −1.47692 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 9.66332 | 0.609943 | 0.304972 | − | 0.952361i | \(-0.401353\pi\) | ||||
0.304972 | + | 0.952361i | \(0.401353\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 30.7902 | 1.93576 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −9.34471 | −0.582907 | −0.291453 | − | 0.956585i | \(-0.594139\pi\) | ||||
−0.291453 | + | 0.956585i | \(0.594139\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −7.48758 | − | 0.216035i | −0.465256 | − | 0.0134238i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 16.8129i | − | 1.03673i | −0.855159 | − | 0.518365i | \(-0.826541\pi\) | ||
0.855159 | − | 0.518365i | \(-0.173459\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 3.34555i | − | 0.205516i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −6.93981 | −0.423127 | −0.211564 | − | 0.977364i | \(-0.567856\pi\) | ||||
−0.211564 | + | 0.977364i | \(0.567856\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2.35168i | 0.142855i | 0.997446 | + | 0.0714273i | \(0.0227554\pi\) | ||||
−0.997446 | + | 0.0714273i | \(0.977245\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 12.9473i | 0.780750i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1.87948 | −0.112927 | −0.0564635 | − | 0.998405i | \(-0.517982\pi\) | ||||
−0.0564635 | + | 0.998405i | \(0.517982\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 15.3072i | 0.913148i | 0.889685 | + | 0.456574i | \(0.150924\pi\) | ||||
−0.889685 | + | 0.456574i | \(0.849076\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 30.3294i | − | 1.80289i | −0.432889 | − | 0.901447i | \(-0.642506\pi\) | ||
0.432889 | − | 0.901447i | \(-0.357494\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 26.7499 | + | 0.771800i | 1.57899 | + | 0.0455579i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 23.8196 | 1.40116 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −14.1585 | −0.827148 | −0.413574 | − | 0.910471i | \(-0.635720\pi\) | ||||
−0.413574 | + | 0.910471i | \(0.635720\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 10.5598 | 0.614813 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 44.7673 | 2.58896 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −28.8196 | − | 0.831518i | −1.66114 | − | 0.0479279i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 10.1322i | 0.580170i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 0.267126i | − | 0.0152457i | −0.999971 | − | 0.00762283i | \(-0.997574\pi\) | ||
0.999971 | − | 0.00762283i | \(-0.00242645\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −0.962946 | −0.0546037 | −0.0273018 | − | 0.999627i | \(-0.508692\pi\) | ||||
−0.0273018 | + | 0.999627i | \(0.508692\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 6.67306i | 0.377184i | 0.982056 | + | 0.188592i | \(0.0603923\pi\) | ||||
−0.982056 | + | 0.188592i | \(0.939608\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 14.1499i | 0.794740i | 0.917658 | + | 0.397370i | \(0.130077\pi\) | ||||
−0.917658 | + | 0.397370i | \(0.869923\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 5.18495 | 0.290301 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 29.7535i | − | 1.65553i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 18.8247i | 1.04420i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −34.0987 | − | 0.983832i | −1.87992 | − | 0.0542404i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −12.5054 | −0.687357 | −0.343679 | − | 0.939087i | \(-0.611673\pi\) | ||||
−0.343679 | + | 0.939087i | \(0.611673\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −5.61768 | −0.306926 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 17.1322 | 0.933252 | 0.466626 | − | 0.884455i | \(-0.345469\pi\) | ||||
0.466626 | + | 0.884455i | \(0.345469\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −23.0242 | −1.24683 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 18.4510 | + | 1.60062i | 0.996258 | + | 0.0864255i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 6.83178i | 0.366749i | 0.983043 | + | 0.183375i | \(0.0587021\pi\) | ||||
−0.983043 | + | 0.183375i | \(0.941298\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 32.1708i | 1.72206i | 0.508552 | + | 0.861031i | \(0.330181\pi\) | ||||
−0.508552 | + | 0.861031i | \(0.669819\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 18.7317 | 0.996988 | 0.498494 | − | 0.866893i | \(-0.333887\pi\) | ||||
0.498494 | + | 0.866893i | \(0.333887\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 9.88808i | 0.524805i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 15.9589i | 0.842276i | 0.906996 | + | 0.421138i | \(0.138369\pi\) | ||||
−0.906996 | + | 0.421138i | \(0.861631\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −2.68741 | −0.141443 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 8.61974i | 0.451178i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 25.9175i | 1.35288i | 0.736498 | + | 0.676440i | \(0.236478\pi\) | ||||
−0.736498 | + | 0.676440i | \(0.763522\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −0.230820 | + | 8.00000i | −0.0119836 | + | 0.415339i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −18.2848 | −0.946753 | −0.473377 | − | 0.880860i | \(-0.656965\pi\) | ||||
−0.473377 | + | 0.880860i | \(0.656965\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 7.53864 | 0.388260 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 22.3454 | 1.14781 | 0.573903 | − | 0.818923i | \(-0.305429\pi\) | ||||
0.573903 | + | 0.818923i | \(0.305429\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 22.7042 | 1.16013 | 0.580066 | − | 0.814570i | \(-0.303027\pi\) | ||||
0.580066 | + | 0.814570i | \(0.303027\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −0.289301 | + | 10.0269i | −0.0147442 | + | 0.511019i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 17.7947i | 0.902225i | 0.892467 | + | 0.451113i | \(0.148973\pi\) | ||||
−0.892467 | + | 0.451113i | \(0.851027\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 57.3845i | 2.90206i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −2.27212 | −0.114323 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 17.8124i | − | 0.893979i | −0.894539 | − | 0.446989i | \(-0.852496\pi\) | ||
0.894539 | − | 0.446989i | \(-0.147504\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 29.0195i | − | 1.44917i | −0.689187 | − | 0.724583i | \(-0.742032\pi\) | ||
0.689187 | − | 0.724583i | \(-0.257968\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −33.4759 | −1.66756 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 9.70568i | 0.481093i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 21.6502i | − | 1.07053i | −0.844683 | − | 0.535266i | \(-0.820211\pi\) | ||
0.844683 | − | 0.535266i | \(-0.179789\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −25.2509 | − | 0.728551i | −1.24251 | − | 0.0358496i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 6.34216 | 0.311324 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 6.66535 | 0.325624 | 0.162812 | − | 0.986657i | \(-0.447944\pi\) | ||||
0.162812 | + | 0.986657i | \(0.447944\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −3.16878 | −0.154437 | −0.0772185 | − | 0.997014i | \(-0.524604\pi\) | ||||
−0.0772185 | + | 0.997014i | \(0.524604\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −24.1302 | −1.17048 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0.699054 | − | 24.2285i | 0.0338296 | − | 1.17250i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 2.84949i | 0.137255i | 0.997642 | + | 0.0686276i | \(0.0218620\pi\) | ||||
−0.997642 | + | 0.0686276i | \(0.978138\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 32.2375i | 1.54923i | 0.632431 | + | 0.774617i | \(0.282057\pi\) | ||||
−0.632431 | + | 0.774617i | \(0.717943\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 41.8277 | 2.00089 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 37.6052i | 1.79480i | 0.441221 | + | 0.897398i | \(0.354545\pi\) | ||||
−0.441221 | + | 0.897398i | \(0.645455\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − | 12.7407i | − | 0.605328i | −0.953097 | − | 0.302664i | \(-0.902124\pi\) | ||
0.953097 | − | 0.302664i | \(-0.0978760\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 7.16321 | 0.339569 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 8.18218i | − | 0.386141i | −0.981185 | − | 0.193070i | \(-0.938155\pi\) | ||
0.981185 | − | 0.193070i | \(-0.0618446\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 34.6742i | − | 1.63274i | ||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −0.420629 | + | 14.5786i | −0.0197194 | + | 0.683455i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 9.37313 | 0.438457 | 0.219228 | − | 0.975674i | \(-0.429646\pi\) | ||||
0.219228 | + | 0.975674i | \(0.429646\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 17.7688 | 0.827574 | 0.413787 | − | 0.910374i | \(-0.364206\pi\) | ||||
0.413787 | + | 0.910374i | \(0.364206\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −0.231992 | −0.0107816 | −0.00539079 | − | 0.999985i | \(-0.501716\pi\) | ||||
−0.00539079 | + | 0.999985i | \(0.501716\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −6.57569 | −0.304287 | −0.152143 | − | 0.988358i | \(-0.548618\pi\) | ||||
−0.152143 | + | 0.988358i | \(0.548618\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 13.4332 | + | 0.387581i | 0.620287 | + | 0.0178968i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 37.3571i | 1.71768i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 17.5885i | 0.807017i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 16.3544 | 0.747253 | 0.373626 | − | 0.927579i | \(-0.378114\pi\) | ||||
0.373626 | + | 0.927579i | \(0.378114\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 14.1115i | 0.643431i | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − | 8.89274i | − | 0.403799i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 13.1617 | 0.596412 | 0.298206 | − | 0.954502i | \(-0.403612\pi\) | ||||
0.298206 | + | 0.954502i | \(0.403612\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 15.4692i | 0.698117i | 0.937101 | + | 0.349058i | \(0.113499\pi\) | ||||
−0.937101 | + | 0.349058i | \(0.886501\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 9.66332i | 0.435214i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0.682209 | − | 23.6447i | 0.0306013 | − | 1.06061i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 8.94728 | 0.400535 | 0.200268 | − | 0.979741i | \(-0.435819\pi\) | ||||
0.200268 | + | 0.979741i | \(0.435819\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −27.5654 | −1.22908 | −0.614539 | − | 0.788886i | \(-0.710658\pi\) | ||||
−0.614539 | + | 0.788886i | \(0.710658\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −14.7286 | −0.655412 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 2.68961 | 0.119215 | 0.0596075 | − | 0.998222i | \(-0.481015\pi\) | ||||
0.0596075 | + | 0.998222i | \(0.481015\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0.594703 | − | 20.6118i | 0.0263081 | − | 0.911814i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − | 7.59688i | − | 0.334758i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 44.2000i | 1.94391i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 32.5721 | 1.42701 | 0.713505 | − | 0.700651i | \(-0.247107\pi\) | ||||
0.713505 | + | 0.700651i | \(0.247107\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 9.00962i | 0.393963i | 0.980407 | + | 0.196982i | \(0.0631139\pi\) | ||||
−0.980407 | + | 0.196982i | \(0.936886\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 42.9107i | − | 1.86922i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −57.6714 | −2.50745 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 50.4144i | − | 2.18369i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 6.73661i | 0.291249i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1.38358 | − | 23.9568i | 0.0595948 | − | 1.03189i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 21.9884 | 0.945356 | 0.472678 | − | 0.881235i | \(-0.343287\pi\) | ||||
0.472678 | + | 0.881235i | \(0.343287\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −16.2114 | −0.694420 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −1.28930 | −0.0551266 | −0.0275633 | − | 0.999620i | \(-0.508775\pi\) | ||||
−0.0275633 | + | 0.999620i | \(0.508775\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 7.04361 | 0.300068 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 5.43318 | + | 0.156761i | 0.231042 | + | 0.00666614i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 7.44482i | − | 0.315447i | −0.987483 | − | 0.157724i | \(-0.949584\pi\) | ||
0.987483 | − | 0.157724i | \(-0.0504155\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 54.3152i | 2.29729i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −29.2542 | −1.23292 | −0.616458 | − | 0.787388i | \(-0.711433\pi\) | ||||
−0.616458 | + | 0.787388i | \(0.711433\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 20.0538i | 0.843671i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 26.4698i | 1.10967i | 0.831960 | + | 0.554836i | \(0.187219\pi\) | ||||
−0.831960 | + | 0.554836i | \(0.812781\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −29.6626 | −1.24134 | −0.620670 | − | 0.784072i | \(-0.713139\pi\) | ||||
−0.620670 | + | 0.784072i | \(0.713139\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 33.9223i | − | 1.41466i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 1.65473i | − | 0.0688875i | −0.999407 | − | 0.0344437i | \(-0.989034\pi\) | ||
0.999407 | − | 0.0344437i | \(-0.0109660\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −15.1656 | − | 0.437565i | −0.629174 | − | 0.0181532i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 10.3699 | 0.429477 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 9.45826 | 0.390384 | 0.195192 | − | 0.980765i | \(-0.437467\pi\) | ||||
0.195192 | + | 0.980765i | \(0.437467\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −31.2777 | −1.28878 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 3.17049 | 0.130196 | 0.0650981 | − | 0.997879i | \(-0.479264\pi\) | ||||
0.0650981 | + | 0.997879i | \(0.479264\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −18.6874 | − | 0.539178i | −0.766109 | − | 0.0221042i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 23.2827i | − | 0.951307i | −0.879633 | − | 0.475653i | \(-0.842212\pi\) | ||
0.879633 | − | 0.475653i | \(-0.157788\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 23.0358i | − | 0.939649i | −0.882760 | − | 0.469825i | \(-0.844317\pi\) | ||
0.882760 | − | 0.469825i | \(-0.155683\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0.831518 | 0.0338060 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 0.737290i | 0.0299257i | 0.999888 | + | 0.0149628i | \(0.00476300\pi\) | ||||
−0.999888 | + | 0.0149628i | \(0.995237\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 64.2645i | 2.59986i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 36.4494 | 1.47218 | 0.736089 | − | 0.676885i | \(-0.236670\pi\) | ||||
0.736089 | + | 0.676885i | \(0.236670\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 8.19990i | 0.330115i | 0.986284 | + | 0.165058i | \(0.0527810\pi\) | ||||
−0.986284 | + | 0.165058i | \(0.947219\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 18.3236i | − | 0.736487i | −0.929729 | − | 0.368243i | \(-0.879959\pi\) | ||
0.929729 | − | 0.368243i | \(-0.120041\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −17.1289 | − | 0.494212i | −0.686255 | − | 0.0198002i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 8.14840 | 0.325936 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −18.0887 | −0.721244 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 6.47425 | 0.257736 | 0.128868 | − | 0.991662i | \(-0.458866\pi\) | ||||
0.128868 | + | 0.991662i | \(0.458866\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −8.00163 | −0.317535 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 2.01164 | − | 34.8318i | 0.0797043 | − | 1.38009i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 30.9519i | − | 1.22253i | −0.791428 | − | 0.611263i | \(-0.790662\pi\) | ||
0.791428 | − | 0.611263i | \(-0.209338\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 11.2017i | 0.441754i | 0.975302 | + | 0.220877i | \(0.0708919\pi\) | ||||
−0.975302 | + | 0.220877i | \(0.929108\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −32.3689 | −1.27255 | −0.636276 | − | 0.771461i | \(-0.719526\pi\) | ||||
−0.636276 | + | 0.771461i | \(0.719526\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 32.7311i | 1.28481i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 44.9373i | 1.75853i | 0.476332 | + | 0.879265i | \(0.341966\pi\) | ||||
−0.476332 | + | 0.879265i | \(0.658034\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −16.1276 | −0.630159 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 11.5969i | 0.451750i | 0.974156 | + | 0.225875i | \(0.0725241\pi\) | ||||
−0.974156 | + | 0.225875i | \(0.927476\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 13.9488i | 0.542547i | 0.962502 | + | 0.271274i | \(0.0874448\pi\) | ||||
−0.962502 | + | 0.271274i | \(0.912555\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −0.393008 | + | 13.6213i | −0.0152402 | + | 0.528211i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −13.5847 | −0.526003 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −31.4059 | −1.21241 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −16.9194 | −0.652195 | −0.326097 | − | 0.945336i | \(-0.605734\pi\) | ||||
−0.326097 | + | 0.945336i | \(0.605734\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −19.6171 | −0.753947 | −0.376973 | − | 0.926224i | \(-0.623035\pi\) | ||||
−0.376973 | + | 0.926224i | \(0.623035\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −0.613537 | + | 21.2646i | −0.0235454 | + | 0.816062i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 41.4738i | 1.58695i | 0.608602 | + | 0.793476i | \(0.291731\pi\) | ||||
−0.608602 | + | 0.793476i | \(0.708269\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 5.72335i | 0.218678i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 15.0773 | 0.574399 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 20.2864i | − | 0.771733i | −0.922555 | − | 0.385866i | \(-0.873903\pi\) | ||
0.922555 | − | 0.385866i | \(-0.126097\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 12.4332i | 0.471620i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 64.6231 | 2.44777 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 13.4302i | 0.507252i | 0.967302 | + | 0.253626i | \(0.0816232\pi\) | ||||
−0.967302 | + | 0.253626i | \(0.918377\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 13.1849i | 0.497278i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 35.2194 | + | 1.01617i | 1.32456 | + | 0.0382169i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 37.0046 | 1.38974 | 0.694868 | − | 0.719137i | \(-0.255463\pi\) | ||||
0.694868 | + | 0.719137i | \(0.255463\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 60.3241 | 2.25916 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 18.8973 | 0.706720 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 29.3967 | 1.09631 | 0.548156 | − | 0.836376i | \(-0.315330\pi\) | ||||
0.548156 | + | 0.836376i | \(0.315330\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −0.524132 | + | 18.1659i | −0.0195197 | + | 0.676534i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − | 5.71238i | − | 0.212153i | ||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 19.8248i | 0.735261i | 0.929972 | + | 0.367631i | \(0.119831\pi\) | ||||
−0.929972 | + | 0.367631i | \(0.880169\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −69.6233 | −2.57511 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 11.8040i | − | 0.435991i | −0.975950 | − | 0.217996i | \(-0.930048\pi\) | ||
0.975950 | − | 0.217996i | \(-0.0699518\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 17.4126i | − | 0.641401i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 43.8446 | 1.61285 | 0.806425 | − | 0.591336i | \(-0.201399\pi\) | ||||
0.806425 | + | 0.591336i | \(0.201399\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 25.4603i | − | 0.934049i | −0.884244 | − | 0.467024i | \(-0.845326\pi\) | ||
0.884244 | − | 0.467024i | \(-0.154674\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − | 8.47448i | − | 0.310481i | ||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0.464779 | − | 16.1088i | 0.0169827 | − | 0.588603i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 22.4277 | 0.818397 | 0.409199 | − | 0.912445i | \(-0.365808\pi\) | ||||
0.409199 | + | 0.912445i | \(0.365808\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 10.2738 | 0.373900 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −9.44806 | −0.343395 | −0.171698 | − | 0.985150i | \(-0.554925\pi\) | ||||
−0.171698 | + | 0.985150i | \(0.554925\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 25.6274 | 0.928991 | 0.464496 | − | 0.885575i | \(-0.346236\pi\) | ||||
0.464496 | + | 0.885575i | \(0.346236\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 38.7652 | + | 1.11847i | 1.40340 | + | 0.0404915i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 47.5893i | 1.71835i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 33.4382i | 1.20581i | 0.797812 | + | 0.602906i | \(0.205991\pi\) | ||||
−0.797812 | + | 0.602906i | \(0.794009\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 51.5205 | 1.85306 | 0.926531 | − | 0.376218i | \(-0.122776\pi\) | ||||
0.926531 | + | 0.376218i | \(0.122776\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 25.3663i | 0.911184i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − | 47.1039i | − | 1.68767i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −30.6492 | −1.09671 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 15.3072i | 0.546336i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 14.7759i | 0.526703i | 0.964700 | + | 0.263352i | \(0.0848279\pi\) | ||||
−0.964700 | + | 0.263352i | \(0.915172\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1.38358 | − | 47.9534i | 0.0491943 | − | 1.70503i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −45.6626 | −1.62153 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 23.9822 | 0.849493 | 0.424747 | − | 0.905312i | \(-0.360363\pi\) | ||||
0.424747 | + | 0.905312i | \(0.360363\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −82.3766 | −2.91428 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −26.7178 | −0.942852 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0.757980 | − | 26.2709i | 0.0267153 | − | 0.925926i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 48.3821i | − | 1.70102i | −0.525956 | − | 0.850512i | \(-0.676292\pi\) | ||
0.525956 | − | 0.850512i | \(-0.323708\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 6.70030i | − | 0.235279i | −0.993056 | − | 0.117640i | \(-0.962467\pi\) | ||
0.993056 | − | 0.117640i | \(-0.0375328\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −17.3174 | −0.606601 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 50.7486i | 1.77547i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 15.3803i | 0.536775i | 0.963311 | + | 0.268387i | \(0.0864907\pi\) | ||||
−0.963311 | + | 0.268387i | \(0.913509\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 22.3466 | 0.778954 | 0.389477 | − | 0.921036i | \(-0.372656\pi\) | ||||
0.389477 | + | 0.921036i | \(0.372656\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 22.0013i | 0.765059i | 0.923943 | + | 0.382529i | \(0.124947\pi\) | ||||
−0.923943 | + | 0.382529i | \(0.875053\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 35.8055i | − | 1.24358i | −0.783185 | − | 0.621789i | \(-0.786406\pi\) | ||
0.783185 | − | 0.621789i | \(-0.213594\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 44.6488 | + | 2.57860i | 1.54699 | + | 0.0893433i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 4.21761 | 0.145956 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −17.9278 | −0.618937 | −0.309468 | − | 0.950910i | \(-0.600151\pi\) | ||||
−0.309468 | + | 0.950910i | \(0.600151\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 26.7124 | 0.921117 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 13.0980 | 0.450585 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1.98836 | − | 0.0573690i | −0.0683207 | − | 0.00197122i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 25.4292i | − | 0.871702i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 56.3175i | 1.92828i | 0.265401 | + | 0.964138i | \(0.414496\pi\) | ||||
−0.265401 | + | 0.964138i | \(0.585504\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −12.4692 | −0.425939 | −0.212970 | − | 0.977059i | \(-0.568314\pi\) | ||||
−0.212970 | + | 0.977059i | \(0.568314\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 6.69514i | 0.228435i | 0.993456 | + | 0.114218i | \(0.0364361\pi\) | ||||
−0.993456 | + | 0.114218i | \(0.963564\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 46.1734i | 1.57176i | 0.618379 | + | 0.785880i | \(0.287790\pi\) | ||||
−0.618379 | + | 0.785880i | \(0.712210\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 7.03557 | 0.239216 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 7.04269i | − | 0.238907i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 25.3170i | − | 0.857833i | ||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 25.6715 | + | 0.740687i | 0.867855 | + | 0.0250398i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −55.3250 | −1.86819 | −0.934096 | − | 0.357021i | \(-0.883792\pi\) | ||||
−0.934096 | + | 0.357021i | \(0.883792\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 6.38954 | 0.215269 | 0.107634 | − | 0.994191i | \(-0.465672\pi\) | ||||
0.107634 | + | 0.994191i | \(0.465672\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −20.0855 | −0.675931 | −0.337966 | − | 0.941158i | \(-0.609739\pi\) | ||||
−0.337966 | + | 0.941158i | \(0.609739\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 1.80420 | 0.0605793 | 0.0302896 | − | 0.999541i | \(-0.490357\pi\) | ||||
0.0302896 | + | 0.999541i | \(0.490357\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 19.1338 | + | 0.552057i | 0.641726 | + | 0.0185154i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 60.0445i | 2.00931i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 4.46941i | 0.149396i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 10.1583 | 0.338800 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 19.3266i | 0.643864i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 3.14493i | 0.104541i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 9.24272 | 0.306900 | 0.153450 | − | 0.988156i | \(-0.450962\pi\) | ||||
0.153450 | + | 0.988156i | \(0.450962\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 20.7986i | 0.689087i | 0.938770 | + | 0.344543i | \(0.111966\pi\) | ||||
−0.938770 | + | 0.344543i | \(0.888034\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 19.6582i | 0.650591i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 38.5650 | + | 1.11270i | 1.27353 | + | 0.0367444i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −26.0499 | −0.859309 | −0.429654 | − | 0.902993i | \(-0.641365\pi\) | ||||
−0.429654 | + | 0.902993i | \(0.641365\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −44.5623 | −1.46678 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 10.6930 | 0.351583 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −0.539178 | −0.0176899 | −0.00884493 | − | 0.999961i | \(-0.502815\pi\) | ||||
−0.00884493 | + | 0.999961i | \(0.502815\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.87955 | − | 32.5446i | 0.0615997 | − | 1.06661i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 24.2233i | 0.792187i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 43.7537i | 1.42937i | 0.699446 | + | 0.714686i | \(0.253430\pi\) | ||||
−0.699446 | + | 0.714686i | \(0.746570\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −28.2021 | −0.919361 | −0.459681 | − | 0.888084i | \(-0.652036\pi\) | ||||
−0.459681 | + | 0.888084i | \(0.652036\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 90.8475i | 2.95840i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 54.7252i | − | 1.77833i | −0.457586 | − | 0.889165i | \(-0.651286\pi\) | ||
0.457586 | − | 0.889165i | \(-0.348714\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −38.8463 | −1.26100 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 40.1999i | 1.30220i | 0.758991 | + | 0.651101i | \(0.225693\pi\) | ||||
−0.758991 | + | 0.651101i | \(0.774307\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 14.5442i | 0.470638i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0.394871 | − | 13.6859i | 0.0127511 | − | 0.441939i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −14.1089 | −0.455127 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 11.0340 | 0.355197 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −13.8180 | −0.444356 | −0.222178 | − | 0.975006i | \(-0.571317\pi\) | ||||
−0.222178 | + | 0.975006i | \(0.571317\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −53.6151 | −1.72059 | −0.860296 | − | 0.509795i | \(-0.829721\pi\) | ||||
−0.860296 | + | 0.509795i | \(0.829721\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0.857808 | − | 29.7308i | 0.0275001 | − | 0.953126i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 30.1122i | 0.963374i | 0.876343 | + | 0.481687i | \(0.159976\pi\) | ||||
−0.876343 | + | 0.481687i | \(0.840024\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 22.2031i | 0.709615i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −18.1329 | −0.578349 | −0.289174 | − | 0.957276i | \(-0.593381\pi\) | ||||
−0.289174 | + | 0.957276i | \(0.593381\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − | 17.0816i | − | 0.544266i | ||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 97.8768i | − | 3.11230i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 23.2116 | 0.737341 | 0.368671 | − | 0.929560i | \(-0.379813\pi\) | ||||
0.368671 | + | 0.929560i | \(0.379813\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − | 2.49421i | − | 0.0790718i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 6.08067i | − | 0.192577i | −0.995353 | − | 0.0962883i | \(-0.969303\pi\) | ||
0.995353 | − | 0.0962883i | \(-0.0306971\pi\) | |||||||
\(998\) | 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 | 3024.2.k.k.1889.6 | 16 | ||
3.2 | odd | 2 | inner | 3024.2.k.k.1889.12 | 16 | ||
4.3 | odd | 2 | 1512.2.k.a.377.5 | ✓ | 16 | ||
7.6 | odd | 2 | inner | 3024.2.k.k.1889.11 | 16 | ||
12.11 | even | 2 | 1512.2.k.a.377.11 | yes | 16 | ||
21.20 | even | 2 | inner | 3024.2.k.k.1889.5 | 16 | ||
28.27 | even | 2 | 1512.2.k.a.377.12 | yes | 16 | ||
84.83 | odd | 2 | 1512.2.k.a.377.6 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1512.2.k.a.377.5 | ✓ | 16 | 4.3 | odd | 2 | ||
1512.2.k.a.377.6 | yes | 16 | 84.83 | odd | 2 | ||
1512.2.k.a.377.11 | yes | 16 | 12.11 | even | 2 | ||
1512.2.k.a.377.12 | yes | 16 | 28.27 | even | 2 | ||
3024.2.k.k.1889.5 | 16 | 21.20 | even | 2 | inner | ||
3024.2.k.k.1889.6 | 16 | 1.1 | even | 1 | trivial | ||
3024.2.k.k.1889.11 | 16 | 7.6 | odd | 2 | inner | ||
3024.2.k.k.1889.12 | 16 | 3.2 | odd | 2 | inner |