Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4014,2,Mod(4013,4014)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4014, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("4014.4013");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4014 = 2 \cdot 3^{2} \cdot 223 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4014.d (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(32.0519513713\) |
Analytic rank: | \(0\) |
Dimension: | \(72\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 4013.14 | ||
Character | \(\chi\) | \(=\) | 4014.4013 |
Dual form | 4014.2.d.a.4013.13 |
$q$-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 \(\left(\mathbb{Z}/4014\mathbb{Z}\right)^\times\).
\(n\) | \(893\) | \(2233\) |
\(\chi(n)\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000i | 0.707107i | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | 2.29842 | 1.02788 | 0.513942 | − | 0.857825i | \(-0.328185\pi\) | ||||
0.513942 | + | 0.857825i | \(0.328185\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.05558 | 0.776937 | 0.388468 | − | 0.921462i | \(-0.373004\pi\) | ||||
0.388468 | + | 0.921462i | \(0.373004\pi\) | |||||||
\(8\) | − | 1.00000i | − | 0.353553i | ||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 2.29842i | 0.726824i | ||||||||
\(11\) | 0.573894 | 0.173036 | 0.0865178 | − | 0.996250i | \(-0.472426\pi\) | ||||
0.0865178 | + | 0.996250i | \(0.472426\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 5.56690i | 1.54398i | 0.635635 | + | 0.771990i | \(0.280738\pi\) | ||||
−0.635635 | + | 0.771990i | \(0.719262\pi\) | |||||||
\(14\) | 2.05558i | 0.549377i | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 5.74146i | 1.39251i | 0.717795 | + | 0.696255i | \(0.245152\pi\) | ||||
−0.717795 | + | 0.696255i | \(0.754848\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.17599 | 0.958037 | 0.479018 | − | 0.877805i | \(-0.340993\pi\) | ||||
0.479018 | + | 0.877805i | \(0.340993\pi\) | |||||||
\(20\) | −2.29842 | −0.513942 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0.573894i | 0.122355i | ||||||||
\(23\) | 2.06070 | 0.429685 | 0.214843 | − | 0.976649i | \(-0.431076\pi\) | ||||
0.214843 | + | 0.976649i | \(0.431076\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0.282734 | 0.0565469 | ||||||||
\(26\) | −5.56690 | −1.09176 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −2.05558 | −0.388468 | ||||||||
\(29\) | 3.14750i | 0.584477i | 0.956346 | + | 0.292238i | \(0.0944001\pi\) | ||||
−0.956346 | + | 0.292238i | \(0.905600\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.78812 | 0.500761 | 0.250381 | − | 0.968147i | \(-0.419444\pi\) | ||||
0.250381 | + | 0.968147i | \(0.419444\pi\) | |||||||
\(32\) | 1.00000i | 0.176777i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −5.74146 | −0.984653 | ||||||||
\(35\) | 4.72459 | 0.798601 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.611051 | 0.100456 | 0.0502281 | − | 0.998738i | \(-0.484005\pi\) | ||||
0.0502281 | + | 0.998738i | \(0.484005\pi\) | |||||||
\(38\) | 4.17599i | 0.677434i | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | − | 2.29842i | − | 0.363412i | ||||||
\(41\) | 1.16658i | 0.182189i | 0.995842 | + | 0.0910945i | \(0.0290365\pi\) | ||||
−0.995842 | + | 0.0910945i | \(0.970963\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −9.54102 | −1.45499 | −0.727496 | − | 0.686112i | \(-0.759316\pi\) | ||||
−0.727496 | + | 0.686112i | \(0.759316\pi\) | |||||||
\(44\) | −0.573894 | −0.0865178 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 2.06070i | 0.303833i | ||||||||
\(47\) | − | 6.02089i | − | 0.878237i | −0.898429 | − | 0.439118i | \(-0.855291\pi\) | ||
0.898429 | − | 0.439118i | \(-0.144709\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −2.77458 | −0.396369 | ||||||||
\(50\) | 0.282734i | 0.0399847i | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | − | 5.56690i | − | 0.771990i | ||||||
\(53\) | − | 6.82999i | − | 0.938171i | −0.883153 | − | 0.469086i | \(-0.844584\pi\) | ||
0.883153 | − | 0.469086i | \(-0.155416\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.31905 | 0.177861 | ||||||||
\(56\) | − | 2.05558i | − | 0.274689i | ||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −3.14750 | −0.413287 | ||||||||
\(59\) | −1.99536 | −0.259773 | −0.129887 | − | 0.991529i | \(-0.541461\pi\) | ||||
−0.129887 | + | 0.991529i | \(0.541461\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 14.1655i | 1.81371i | 0.421443 | + | 0.906855i | \(0.361524\pi\) | ||||
−0.421443 | + | 0.906855i | \(0.638476\pi\) | |||||||
\(62\) | 2.78812i | 0.354092i | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 12.7951i | 1.58703i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 6.44119i | − | 0.786917i | −0.919342 | − | 0.393458i | \(-0.871279\pi\) | ||
0.919342 | − | 0.393458i | \(-0.128721\pi\) | |||||||
\(68\) | − | 5.74146i | − | 0.696255i | ||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 4.72459i | 0.564697i | ||||||||
\(71\) | −0.0503915 | −0.00598037 | −0.00299018 | − | 0.999996i | \(-0.500952\pi\) | ||||
−0.00299018 | + | 0.999996i | \(0.500952\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −0.158279 | −0.0185252 | −0.00926259 | − | 0.999957i | \(-0.502948\pi\) | ||||
−0.00926259 | + | 0.999957i | \(0.502948\pi\) | |||||||
\(74\) | 0.611051i | 0.0710332i | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −4.17599 | −0.479018 | ||||||||
\(77\) | 1.17969 | 0.134438 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 3.77417i | − | 0.424628i | −0.977202 | − | 0.212314i | \(-0.931900\pi\) | ||
0.977202 | − | 0.212314i | \(-0.0680999\pi\) | |||||||
\(80\) | 2.29842 | 0.256971 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −1.16658 | −0.128827 | ||||||||
\(83\) | − | 3.37366i | − | 0.370308i | −0.982710 | − | 0.185154i | \(-0.940722\pi\) | ||
0.982710 | − | 0.185154i | \(-0.0592783\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 13.1963i | 1.43134i | ||||||||
\(86\) | − | 9.54102i | − | 1.02883i | ||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | − | 0.573894i | − | 0.0611773i | ||||||
\(89\) | − | 8.91850i | − | 0.945359i | −0.881234 | − | 0.472680i | \(-0.843287\pi\) | ||
0.881234 | − | 0.472680i | \(-0.156713\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 11.4432i | 1.19957i | ||||||||
\(92\) | −2.06070 | −0.214843 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 6.02089 | 0.621007 | ||||||||
\(95\) | 9.59817 | 0.984751 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 9.51962i | 0.966571i | 0.875463 | + | 0.483285i | \(0.160557\pi\) | ||||
−0.875463 | + | 0.483285i | \(0.839443\pi\) | |||||||
\(98\) | − | 2.77458i | − | 0.280275i | ||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −0.282734 | −0.0282734 | ||||||||
\(101\) | − | 5.99617i | − | 0.596641i | −0.954466 | − | 0.298321i | \(-0.903574\pi\) | ||
0.954466 | − | 0.298321i | \(-0.0964265\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 12.1527i | 1.19744i | 0.800957 | + | 0.598721i | \(0.204324\pi\) | ||||
−0.800957 | + | 0.598721i | \(0.795676\pi\) | |||||||
\(104\) | 5.56690 | 0.545879 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 6.82999 | 0.663387 | ||||||||
\(107\) | −15.0973 | −1.45951 | −0.729755 | − | 0.683709i | \(-0.760366\pi\) | ||||
−0.729755 | + | 0.683709i | \(0.760366\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 9.61079 | 0.920547 | 0.460273 | − | 0.887777i | \(-0.347751\pi\) | ||||
0.460273 | + | 0.887777i | \(0.347751\pi\) | |||||||
\(110\) | 1.31905i | 0.125766i | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 2.05558 | 0.194234 | ||||||||
\(113\) | 7.55260 | 0.710489 | 0.355245 | − | 0.934773i | \(-0.384398\pi\) | ||||
0.355245 | + | 0.934773i | \(0.384398\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 4.73635 | 0.441667 | ||||||||
\(116\) | − | 3.14750i | − | 0.292238i | ||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | − | 1.99536i | − | 0.183687i | ||||||
\(119\) | 11.8020i | 1.08189i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.6706 | −0.970059 | ||||||||
\(122\) | −14.1655 | −1.28249 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −2.78812 | −0.250381 | ||||||||
\(125\) | −10.8423 | −0.969761 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 5.15057 | 0.457039 | 0.228520 | − | 0.973539i | \(-0.426611\pi\) | ||||
0.228520 | + | 0.973539i | \(0.426611\pi\) | |||||||
\(128\) | − | 1.00000i | − | 0.0883883i | ||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −12.7951 | −1.12220 | ||||||||
\(131\) | 4.12258i | 0.360191i | 0.983649 | + | 0.180096i | \(0.0576408\pi\) | ||||
−0.983649 | + | 0.180096i | \(0.942359\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 8.58408 | 0.744334 | ||||||||
\(134\) | 6.44119 | 0.556434 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 5.74146 | 0.492326 | ||||||||
\(137\) | 19.9960 | 1.70838 | 0.854188 | − | 0.519964i | \(-0.174055\pi\) | ||||
0.854188 | + | 0.519964i | \(0.174055\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 17.2958 | 1.46701 | 0.733503 | − | 0.679686i | \(-0.237884\pi\) | ||||
0.733503 | + | 0.679686i | \(0.237884\pi\) | |||||||
\(140\) | −4.72459 | −0.399301 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | − | 0.0503915i | − | 0.00422876i | ||||||
\(143\) | 3.19481i | 0.267163i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 7.23428i | 0.600775i | ||||||||
\(146\) | − | 0.158279i | − | 0.0130993i | ||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −0.611051 | −0.0502281 | ||||||||
\(149\) | −7.18737 | −0.588812 | −0.294406 | − | 0.955680i | \(-0.595122\pi\) | ||||
−0.294406 | + | 0.955680i | \(0.595122\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 19.2437i | 1.56603i | 0.622000 | + | 0.783017i | \(0.286320\pi\) | ||||
−0.622000 | + | 0.783017i | \(0.713680\pi\) | |||||||
\(152\) | − | 4.17599i | − | 0.338717i | ||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 1.17969i | 0.0950619i | ||||||||
\(155\) | 6.40827 | 0.514725 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 2.53661i | − | 0.202444i | −0.994864 | − | 0.101222i | \(-0.967725\pi\) | ||
0.994864 | − | 0.101222i | \(-0.0322752\pi\) | |||||||
\(158\) | 3.77417 | 0.300257 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 2.29842i | 0.181706i | ||||||||
\(161\) | 4.23593 | 0.333838 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 0.731953i | − | 0.0573310i | −0.999589 | − | 0.0286655i | \(-0.990874\pi\) | ||
0.999589 | − | 0.0286655i | \(-0.00912576\pi\) | |||||||
\(164\) | − | 1.16658i | − | 0.0910945i | ||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 3.37366 | 0.261847 | ||||||||
\(167\) | 6.96980 | 0.539339 | 0.269670 | − | 0.962953i | \(-0.413086\pi\) | ||||
0.269670 | + | 0.962953i | \(0.413086\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −17.9903 | −1.38387 | ||||||||
\(170\) | −13.1963 | −1.01211 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 9.54102 | 0.727496 | ||||||||
\(173\) | 18.9794 | 1.44298 | 0.721488 | − | 0.692427i | \(-0.243458\pi\) | ||||
0.721488 | + | 0.692427i | \(0.243458\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0.581184 | 0.0439334 | ||||||||
\(176\) | 0.573894 | 0.0432589 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 8.91850 | 0.668470 | ||||||||
\(179\) | − | 6.60748i | − | 0.493866i | −0.969033 | − | 0.246933i | \(-0.920577\pi\) | ||
0.969033 | − | 0.246933i | \(-0.0794228\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 12.1359 | 0.902052 | 0.451026 | − | 0.892511i | \(-0.351058\pi\) | ||||
0.451026 | + | 0.892511i | \(0.351058\pi\) | |||||||
\(182\) | −11.4432 | −0.848227 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | − | 2.06070i | − | 0.151917i | ||||||
\(185\) | 1.40445 | 0.103257 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 3.29499i | 0.240954i | ||||||||
\(188\) | 6.02089i | 0.439118i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 9.59817i | 0.696324i | ||||||||
\(191\) | 3.80003 | 0.274961 | 0.137480 | − | 0.990504i | \(-0.456100\pi\) | ||||
0.137480 | + | 0.990504i | \(0.456100\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 16.9361i | 1.21909i | 0.792751 | + | 0.609545i | \(0.208648\pi\) | ||||
−0.792751 | + | 0.609545i | \(0.791352\pi\) | |||||||
\(194\) | −9.51962 | −0.683469 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 2.77458 | 0.198185 | ||||||||
\(197\) | 5.10372i | 0.363625i | 0.983333 | + | 0.181812i | \(0.0581964\pi\) | ||||
−0.983333 | + | 0.181812i | \(0.941804\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 16.5465 | 1.17295 | 0.586475 | − | 0.809967i | \(-0.300515\pi\) | ||||
0.586475 | + | 0.809967i | \(0.300515\pi\) | |||||||
\(200\) | − | 0.282734i | − | 0.0199923i | ||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 5.99617 | 0.421889 | ||||||||
\(203\) | 6.46995i | 0.454101i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2.68129i | 0.187269i | ||||||||
\(206\) | −12.1527 | −0.846720 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 5.56690i | 0.385995i | ||||||||
\(209\) | 2.39657 | 0.165775 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 5.75275 | 0.396036 | 0.198018 | − | 0.980198i | \(-0.436550\pi\) | ||||
0.198018 | + | 0.980198i | \(0.436550\pi\) | |||||||
\(212\) | 6.82999i | 0.469086i | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | − | 15.0973i | − | 1.03203i | ||||||
\(215\) | −21.9293 | −1.49556 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 5.73121 | 0.389060 | ||||||||
\(218\) | 9.61079i | 0.650925i | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −1.31905 | −0.0889303 | ||||||||
\(221\) | −31.9621 | −2.15001 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 2.79911 | − | 14.6685i | 0.187442 | − | 0.982276i | ||||
\(224\) | 2.05558i | 0.137344i | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 7.55260i | 0.502392i | ||||||||
\(227\) | 3.42425i | 0.227276i | 0.993522 | + | 0.113638i | \(0.0362503\pi\) | ||||
−0.993522 | + | 0.113638i | \(0.963750\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2.30551i | 0.152352i | 0.997094 | + | 0.0761760i | \(0.0242711\pi\) | ||||
−0.997094 | + | 0.0761760i | \(0.975729\pi\) | |||||||
\(230\) | 4.73635i | 0.312305i | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 3.14750 | 0.206644 | ||||||||
\(233\) | −19.6834 | −1.28950 | −0.644752 | − | 0.764392i | \(-0.723039\pi\) | ||||
−0.644752 | + | 0.764392i | \(0.723039\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − | 13.8385i | − | 0.902726i | ||||||
\(236\) | 1.99536 | 0.129887 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −11.8020 | −0.765013 | ||||||||
\(239\) | − | 29.8970i | − | 1.93388i | −0.255008 | − | 0.966939i | \(-0.582078\pi\) | ||
0.255008 | − | 0.966939i | \(-0.417922\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −25.4297 | −1.63807 | −0.819037 | − | 0.573741i | \(-0.805492\pi\) | ||||
−0.819037 | + | 0.573741i | \(0.805492\pi\) | |||||||
\(242\) | − | 10.6706i | − | 0.685935i | ||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | − | 14.1655i | − | 0.906855i | ||||||
\(245\) | −6.37716 | −0.407422 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 23.2473i | 1.47919i | ||||||||
\(248\) | − | 2.78812i | − | 0.177046i | ||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | − | 10.8423i | − | 0.685725i | ||||||
\(251\) | − | 17.3937i | − | 1.09788i | −0.835862 | − | 0.548939i | \(-0.815032\pi\) | ||
0.835862 | − | 0.548939i | \(-0.184968\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.18262 | 0.0743508 | ||||||||
\(254\) | 5.15057i | 0.323176i | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 4.90233i | 0.305799i | 0.988242 | + | 0.152900i | \(0.0488611\pi\) | ||||
−0.988242 | + | 0.152900i | \(0.951139\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1.25606 | 0.0780481 | ||||||||
\(260\) | − | 12.7951i | − | 0.793516i | ||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −4.12258 | −0.254694 | ||||||||
\(263\) | −13.0032 | −0.801814 | −0.400907 | − | 0.916119i | \(-0.631305\pi\) | ||||
−0.400907 | + | 0.916119i | \(0.631305\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 15.6982i | − | 0.964332i | ||||||
\(266\) | 8.58408i | 0.526324i | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 6.44119i | 0.393458i | ||||||||
\(269\) | −25.2677 | −1.54060 | −0.770299 | − | 0.637682i | \(-0.779893\pi\) | ||||
−0.770299 | + | 0.637682i | \(0.779893\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 25.4047i | 1.54323i | 0.636093 | + | 0.771613i | \(0.280550\pi\) | ||||
−0.636093 | + | 0.771613i | \(0.719450\pi\) | |||||||
\(272\) | 5.74146i | 0.348127i | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 19.9960i | 1.20800i | ||||||||
\(275\) | 0.162260 | 0.00978463 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 9.06338i | 0.544566i | 0.962217 | + | 0.272283i | \(0.0877787\pi\) | ||||
−0.962217 | + | 0.272283i | \(0.912221\pi\) | |||||||
\(278\) | 17.2958i | 1.03733i | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | − | 4.72459i | − | 0.282348i | ||||||
\(281\) | − | 23.4026i | − | 1.39608i | −0.716056 | − | 0.698042i | \(-0.754055\pi\) | ||
0.716056 | − | 0.698042i | \(-0.245945\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 22.1892 | 1.31901 | 0.659504 | − | 0.751701i | \(-0.270766\pi\) | ||||
0.659504 | + | 0.751701i | \(0.270766\pi\) | |||||||
\(284\) | 0.0503915 | 0.00299018 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −3.19481 | −0.188913 | ||||||||
\(287\) | 2.39800i | 0.141549i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −15.9644 | −0.939082 | ||||||||
\(290\) | −7.23428 | −0.424812 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0.158279 | 0.00926259 | ||||||||
\(293\) | 18.0925 | 1.05697 | 0.528487 | − | 0.848941i | \(-0.322760\pi\) | ||||
0.528487 | + | 0.848941i | \(0.322760\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −4.58617 | −0.267017 | ||||||||
\(296\) | − | 0.611051i | − | 0.0355166i | ||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | − | 7.18737i | − | 0.416353i | ||||||
\(299\) | 11.4717i | 0.663425i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −19.6123 | −1.13044 | ||||||||
\(302\) | −19.2437 | −1.10735 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 4.17599 | 0.239509 | ||||||||
\(305\) | 32.5583i | 1.86428i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 19.3483i | 1.10426i | 0.833757 | + | 0.552132i | \(0.186186\pi\) | ||||
−0.833757 | + | 0.552132i | \(0.813814\pi\) | |||||||
\(308\) | −1.17969 | −0.0672189 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 6.40827i | 0.363965i | ||||||||
\(311\) | 4.22237 | 0.239429 | 0.119714 | − | 0.992808i | \(-0.461802\pi\) | ||||
0.119714 | + | 0.992808i | \(0.461802\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 18.6943i | 1.05666i | 0.849038 | + | 0.528331i | \(0.177182\pi\) | ||||
−0.849038 | + | 0.528331i | \(0.822818\pi\) | |||||||
\(314\) | 2.53661 | 0.143149 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 3.77417i | 0.212314i | ||||||||
\(317\) | − | 26.7226i | − | 1.50089i | −0.660932 | − | 0.750445i | \(-0.729839\pi\) | ||
0.660932 | − | 0.750445i | \(-0.270161\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.80633i | 0.101135i | ||||||||
\(320\) | −2.29842 | −0.128486 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 4.23593i | 0.236059i | ||||||||
\(323\) | 23.9763i | 1.33408i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.57395i | 0.0873072i | ||||||||
\(326\) | 0.731953 | 0.0405391 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 1.16658 | 0.0644135 | ||||||||
\(329\) | − | 12.3764i | − | 0.682334i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 2.01859i | − | 0.110952i | −0.998460 | − | 0.0554758i | \(-0.982332\pi\) | ||
0.998460 | − | 0.0554758i | \(-0.0176676\pi\) | |||||||
\(332\) | 3.37366i | 0.185154i | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 6.96980i | 0.381370i | ||||||||
\(335\) | − | 14.8046i | − | 0.808860i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 12.2132i | − | 0.665293i | −0.943052 | − | 0.332646i | \(-0.892058\pi\) | ||
0.943052 | − | 0.332646i | \(-0.107942\pi\) | |||||||
\(338\) | − | 17.9903i | − | 0.978545i | ||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | − | 13.1963i | − | 0.715670i | ||||||
\(341\) | 1.60009 | 0.0866495 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −20.0925 | −1.08489 | ||||||||
\(344\) | 9.54102i | 0.514417i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 18.9794i | 1.02034i | ||||||||
\(347\) | 27.1269i | 1.45625i | 0.685445 | + | 0.728124i | \(0.259608\pi\) | ||||
−0.685445 | + | 0.728124i | \(0.740392\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 5.01163 | 0.268266 | 0.134133 | − | 0.990963i | \(-0.457175\pi\) | ||||
0.134133 | + | 0.990963i | \(0.457175\pi\) | |||||||
\(350\) | 0.581184i | 0.0310656i | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0.573894i | 0.0305887i | ||||||||
\(353\) | − | 21.8446i | − | 1.16267i | −0.813665 | − | 0.581334i | \(-0.802531\pi\) | ||
0.813665 | − | 0.581334i | \(-0.197469\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −0.115821 | −0.00614713 | ||||||||
\(356\) | 8.91850i | 0.472680i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 6.60748 | 0.349216 | ||||||||
\(359\) | 17.1656i | 0.905966i | 0.891519 | + | 0.452983i | \(0.149640\pi\) | ||||
−0.891519 | + | 0.452983i | \(0.850360\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.56114 | −0.0821655 | ||||||||
\(362\) | 12.1359i | 0.637847i | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | − | 11.4432i | − | 0.599787i | ||||||
\(365\) | −0.363792 | −0.0190417 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −14.9021 | −0.777885 | −0.388942 | − | 0.921262i | \(-0.627160\pi\) | ||||
−0.388942 | + | 0.921262i | \(0.627160\pi\) | |||||||
\(368\) | 2.06070 | 0.107421 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 1.40445i | 0.0730139i | ||||||||
\(371\) | − | 14.0396i | − | 0.728900i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 4.47759i | 0.231841i | 0.993258 | + | 0.115920i | \(0.0369818\pi\) | ||||
−0.993258 | + | 0.115920i | \(0.963018\pi\) | |||||||
\(374\) | −3.29499 | −0.170380 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −6.02089 | −0.310504 | ||||||||
\(377\) | −17.5218 | −0.902420 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −9.65998 | −0.496200 | −0.248100 | − | 0.968734i | \(-0.579806\pi\) | ||||
−0.248100 | + | 0.968734i | \(0.579806\pi\) | |||||||
\(380\) | −9.59817 | −0.492376 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 3.80003i | 0.194427i | ||||||||
\(383\) | 24.1856 | 1.23583 | 0.617914 | − | 0.786246i | \(-0.287978\pi\) | ||||
0.617914 | + | 0.786246i | \(0.287978\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 2.71142 | 0.138187 | ||||||||
\(386\) | −16.9361 | −0.862027 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | − | 9.51962i | − | 0.483285i | ||||||
\(389\) | 9.66092i | 0.489828i | 0.969545 | + | 0.244914i | \(0.0787598\pi\) | ||||
−0.969545 | + | 0.244914i | \(0.921240\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 11.8314i | 0.598340i | ||||||||
\(392\) | 2.77458i | 0.140138i | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −5.10372 | −0.257122 | ||||||||
\(395\) | − | 8.67463i | − | 0.436468i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 10.7987i | − | 0.541971i | −0.962583 | − | 0.270986i | \(-0.912650\pi\) | ||
0.962583 | − | 0.270986i | \(-0.0873496\pi\) | |||||||
\(398\) | 16.5465i | 0.829401i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0.282734 | 0.0141367 | ||||||||
\(401\) | − | 18.3928i | − | 0.918492i | −0.888309 | − | 0.459246i | \(-0.848120\pi\) | ||
0.888309 | − | 0.459246i | \(-0.151880\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 15.5212i | 0.773165i | ||||||||
\(404\) | 5.99617i | 0.298321i | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −6.46995 | −0.321098 | ||||||||
\(407\) | 0.350678 | 0.0173825 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 12.4348i | 0.614863i | 0.951570 | + | 0.307432i | \(0.0994695\pi\) | ||||
−0.951570 | + | 0.307432i | \(0.900530\pi\) | |||||||
\(410\) | −2.68129 | −0.132419 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | − | 12.1527i | − | 0.598721i | ||||||
\(413\) | −4.10162 | −0.201827 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 7.75409i | − | 0.380634i | ||||||
\(416\) | −5.56690 | −0.272940 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 2.39657i | 0.117220i | ||||||||
\(419\) | 0.593093i | 0.0289745i | 0.999895 | + | 0.0144873i | \(0.00461160\pi\) | ||||
−0.999895 | + | 0.0144873i | \(0.995388\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 20.2952i | − | 0.989128i | −0.869141 | − | 0.494564i | \(-0.835328\pi\) | ||
0.869141 | − | 0.494564i | \(-0.164672\pi\) | |||||||
\(422\) | 5.75275i | 0.280040i | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −6.82999 | −0.331694 | ||||||||
\(425\) | 1.62331i | 0.0787421i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 29.1184i | 1.40914i | ||||||||
\(428\) | 15.0973 | 0.729755 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | − | 21.9293i | − | 1.05752i | ||||||
\(431\) | 31.7299 | 1.52838 | 0.764188 | − | 0.644994i | \(-0.223140\pi\) | ||||
0.764188 | + | 0.644994i | \(0.223140\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 13.9906 | 0.672344 | 0.336172 | − | 0.941801i | \(-0.390868\pi\) | ||||
0.336172 | + | 0.941801i | \(0.390868\pi\) | |||||||
\(434\) | 5.73121i | 0.275107i | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −9.61079 | −0.460273 | ||||||||
\(437\) | 8.60544 | 0.411654 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 1.26903i | − | 0.0605673i | −0.999541 | − | 0.0302836i | \(-0.990359\pi\) | ||
0.999541 | − | 0.0302836i | \(-0.00964105\pi\) | |||||||
\(440\) | − | 1.31905i | − | 0.0628832i | ||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | − | 31.9621i | − | 1.52028i | ||||||
\(443\) | − | 15.2558i | − | 0.724827i | −0.932017 | − | 0.362413i | \(-0.881953\pi\) | ||
0.932017 | − | 0.362413i | \(-0.118047\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − | 20.4985i | − | 0.971720i | ||||||
\(446\) | 14.6685 | + | 2.79911i | 0.694574 | + | 0.132542i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −2.05558 | −0.0971171 | ||||||||
\(449\) | 4.87862 | 0.230236 | 0.115118 | − | 0.993352i | \(-0.463275\pi\) | ||||
0.115118 | + | 0.993352i | \(0.463275\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0.669493i | 0.0315252i | ||||||||
\(452\) | −7.55260 | −0.355245 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −3.42425 | −0.160708 | ||||||||
\(455\) | 26.3013i | 1.23302i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 31.9179i | − | 1.49306i | −0.665353 | − | 0.746529i | \(-0.731719\pi\) | ||
0.665353 | − | 0.746529i | \(-0.268281\pi\) | |||||||
\(458\) | −2.30551 | −0.107729 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −4.73635 | −0.220833 | ||||||||
\(461\) | 4.76109i | 0.221746i | 0.993835 | + | 0.110873i | \(0.0353647\pi\) | ||||
−0.993835 | + | 0.110873i | \(0.964635\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 33.0970 | 1.53815 | 0.769073 | − | 0.639161i | \(-0.220718\pi\) | ||||
0.769073 | + | 0.639161i | \(0.220718\pi\) | |||||||
\(464\) | 3.14750i | 0.146119i | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | − | 19.6834i | − | 0.911817i | ||||||
\(467\) | 4.79469 | 0.221872 | 0.110936 | − | 0.993828i | \(-0.464615\pi\) | ||||
0.110936 | + | 0.993828i | \(0.464615\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 13.2404i | − | 0.611385i | ||||||
\(470\) | 13.8385 | 0.638324 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 1.99536i | 0.0918437i | ||||||||
\(473\) | −5.47554 | −0.251765 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.18070 | 0.0541740 | ||||||||
\(476\) | − | 11.8020i | − | 0.540946i | ||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 29.8970 | 1.36746 | ||||||||
\(479\) | 21.0657i | 0.962516i | 0.876579 | + | 0.481258i | \(0.159820\pi\) | ||||
−0.876579 | + | 0.481258i | \(0.840180\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 3.40166i | 0.155102i | ||||||||
\(482\) | − | 25.4297i | − | 1.15829i | ||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 10.6706 | 0.485029 | ||||||||
\(485\) | 21.8801i | 0.993523i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 15.3348 | 0.694888 | 0.347444 | − | 0.937701i | \(-0.387050\pi\) | ||||
0.347444 | + | 0.937701i | \(0.387050\pi\) | |||||||
\(488\) | 14.1655 | 0.641243 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | − | 6.37716i | − | 0.288091i | ||||||
\(491\) | 12.7519 | 0.575487 | 0.287744 | − | 0.957707i | \(-0.407095\pi\) | ||||
0.287744 | + | 0.957707i | \(0.407095\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −18.0713 | −0.813889 | ||||||||
\(494\) | −23.2473 | −1.04594 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 2.78812 | 0.125190 | ||||||||
\(497\) | −0.103584 | −0.00464637 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −19.5666 | −0.875923 | −0.437962 | − | 0.898994i | \(-0.644299\pi\) | ||||
−0.437962 | + | 0.898994i | \(0.644299\pi\) | |||||||
\(500\) | 10.8423 | 0.484880 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 17.3937 | 0.776317 | ||||||||
\(503\) | −4.83916 | −0.215767 | −0.107884 | − | 0.994164i | \(-0.534407\pi\) | ||||
−0.107884 | + | 0.994164i | \(0.534407\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 13.7817i | − | 0.613279i | ||||||
\(506\) | 1.18262i | 0.0525740i | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −5.15057 | −0.228520 | ||||||||
\(509\) | − | 18.1515i | − | 0.804549i | −0.915519 | − | 0.402275i | \(-0.868220\pi\) | ||
0.915519 | − | 0.402275i | \(-0.131780\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −0.325356 | −0.0143929 | ||||||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −4.90233 | −0.216233 | ||||||||
\(515\) | 27.9320i | 1.23083i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 3.45535i | − | 0.151966i | ||||||
\(518\) | 1.25606i | 0.0551883i | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 12.7951 | 0.561101 | ||||||||
\(521\) | −4.91449 | −0.215308 | −0.107654 | − | 0.994188i | \(-0.534334\pi\) | ||||
−0.107654 | + | 0.994188i | \(0.534334\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 14.4996i | 0.634024i | 0.948422 | + | 0.317012i | \(0.102680\pi\) | ||||
−0.948422 | + | 0.317012i | \(0.897320\pi\) | |||||||
\(524\) | − | 4.12258i | − | 0.180096i | ||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | − | 13.0032i | − | 0.566968i | ||||||
\(527\) | 16.0079i | 0.697315i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −18.7535 | −0.815371 | ||||||||
\(530\) | 15.6982 | 0.681885 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −8.58408 | −0.372167 | ||||||||
\(533\) | −6.49422 | −0.281296 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −34.6999 | −1.50021 | ||||||||
\(536\) | −6.44119 | −0.278217 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | − | 25.2677i | − | 1.08937i | ||||||
\(539\) | −1.59232 | −0.0685860 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − | 13.0502i | − | 0.561070i | −0.959844 | − | 0.280535i | \(-0.909488\pi\) | ||
0.959844 | − | 0.280535i | \(-0.0905119\pi\) | |||||||
\(542\) | −25.4047 | −1.09122 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −5.74146 | −0.246163 | ||||||||
\(545\) | 22.0896 | 0.946216 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −31.4676 | −1.34546 | −0.672729 | − | 0.739889i | \(-0.734878\pi\) | ||||
−0.672729 | + | 0.739889i | \(0.734878\pi\) | |||||||
\(548\) | −19.9960 | −0.854188 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0.162260i | 0.00691878i | ||||||||
\(551\) | 13.1439i | 0.559950i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 7.75812i | − | 0.329909i | ||||||
\(554\) | −9.06338 | −0.385066 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −17.2958 | −0.733503 | ||||||||
\(557\) | 9.01148 | 0.381829 | 0.190914 | − | 0.981607i | \(-0.438855\pi\) | ||||
0.190914 | + | 0.981607i | \(0.438855\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 53.1139i | − | 2.24648i | ||||||
\(560\) | 4.72459 | 0.199650 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 23.4026 | 0.987181 | ||||||||
\(563\) | 19.4520 | 0.819804 | 0.409902 | − | 0.912130i | \(-0.365563\pi\) | ||||
0.409902 | + | 0.912130i | \(0.365563\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 17.3591 | 0.730301 | ||||||||
\(566\) | 22.1892i | 0.932680i | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0.0503915i | 0.00211438i | ||||||||
\(569\) | −20.0444 | −0.840306 | −0.420153 | − | 0.907453i | \(-0.638024\pi\) | ||||
−0.420153 | + | 0.907453i | \(0.638024\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 11.4368i | − | 0.478614i | −0.970944 | − | 0.239307i | \(-0.923080\pi\) | ||
0.970944 | − | 0.239307i | \(-0.0769202\pi\) | |||||||
\(572\) | − | 3.19481i | − | 0.133582i | ||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −2.39800 | −0.100091 | ||||||||
\(575\) | 0.582630 | 0.0242974 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 24.5788 | 1.02323 | 0.511615 | − | 0.859215i | \(-0.329047\pi\) | ||||
0.511615 | + | 0.859215i | \(0.329047\pi\) | |||||||
\(578\) | − | 15.9644i | − | 0.664031i | ||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | − | 7.23428i | − | 0.300387i | ||||||
\(581\) | − | 6.93484i | − | 0.287706i | ||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 3.91969i | − | 0.162337i | ||||||
\(584\) | 0.158279i | 0.00654964i | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 18.0925i | 0.747394i | ||||||||
\(587\) | 22.7676 | 0.939719 | 0.469860 | − | 0.882741i | \(-0.344305\pi\) | ||||
0.469860 | + | 0.882741i | \(0.344305\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 11.6432 | 0.479748 | ||||||||
\(590\) | − | 4.58617i | − | 0.188810i | ||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0.611051 | 0.0251140 | ||||||||
\(593\) | 6.60487 | 0.271229 | 0.135615 | − | 0.990762i | \(-0.456699\pi\) | ||||
0.135615 | + | 0.990762i | \(0.456699\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 27.1261i | 1.11206i | ||||||||
\(596\) | 7.18737 | 0.294406 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −11.4717 | −0.469112 | ||||||||
\(599\) | − | 26.3843i | − | 1.07803i | −0.842295 | − | 0.539017i | \(-0.818796\pi\) | ||
0.842295 | − | 0.539017i | \(-0.181204\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 12.7513i | − | 0.520135i | −0.965590 | − | 0.260068i | \(-0.916255\pi\) | ||
0.965590 | − | 0.260068i | \(-0.0837448\pi\) | |||||||
\(602\) | − | 19.6123i | − | 0.799339i | ||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | − | 19.2437i | − | 0.783017i | ||||||
\(605\) | −24.5256 | −0.997108 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 14.5815i | − | 0.591844i | −0.955212 | − | 0.295922i | \(-0.904373\pi\) | ||
0.955212 | − | 0.295922i | \(-0.0956268\pi\) | |||||||
\(608\) | 4.17599i | 0.169359i | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −32.5583 | −1.31825 | ||||||||
\(611\) | 33.5177 | 1.35598 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 9.68272i | 0.391081i | 0.980696 | + | 0.195541i | \(0.0626461\pi\) | ||||
−0.980696 | + | 0.195541i | \(0.937354\pi\) | |||||||
\(614\) | −19.3483 | −0.780833 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | − | 1.17969i | − | 0.0475309i | ||||||
\(617\) | 17.1345i | 0.689809i | 0.938638 | + | 0.344905i | \(0.112089\pi\) | ||||
−0.938638 | + | 0.344905i | \(0.887911\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 9.04916i | − | 0.363717i | −0.983325 | − | 0.181858i | \(-0.941789\pi\) | ||
0.983325 | − | 0.181858i | \(-0.0582112\pi\) | |||||||
\(620\) | −6.40827 | −0.257362 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 4.22237i | 0.169302i | ||||||||
\(623\) | − | 18.3327i | − | 0.734485i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −26.3337 | −1.05335 | ||||||||
\(626\) | −18.6943 | −0.747173 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 2.53661i | 0.101222i | ||||||||
\(629\) | 3.50833i | 0.139886i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 2.23782i | − | 0.0890861i | −0.999007 | − | 0.0445431i | \(-0.985817\pi\) | ||
0.999007 | − | 0.0445431i | \(-0.0141832\pi\) | |||||||
\(632\) | −3.77417 | −0.150129 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 26.7226 | 1.06129 | ||||||||
\(635\) | 11.8382 | 0.469784 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − | 15.4458i | − | 0.611986i | ||||||
\(638\) | −1.80633 | −0.0715135 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | − | 2.29842i | − | 0.0908530i | ||||||
\(641\) | −13.1675 | −0.520085 | −0.260043 | − | 0.965597i | \(-0.583737\pi\) | ||||
−0.260043 | + | 0.965597i | \(0.583737\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 11.5968 | 0.457333 | 0.228666 | − | 0.973505i | \(-0.426563\pi\) | ||||
0.228666 | + | 0.973505i | \(0.426563\pi\) | |||||||
\(644\) | −4.23593 | −0.166919 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −23.9763 | −0.943334 | ||||||||
\(647\) | 16.0490i | 0.630951i | 0.948934 | + | 0.315475i | \(0.102164\pi\) | ||||
−0.948934 | + | 0.315475i | \(0.897836\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1.14512 | −0.0449500 | ||||||||
\(650\) | −1.57395 | −0.0617355 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0.731953i | 0.0286655i | ||||||||
\(653\) | 15.4365 | 0.604077 | 0.302039 | − | 0.953296i | \(-0.402333\pi\) | ||||
0.302039 | + | 0.953296i | \(0.402333\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 9.47542i | 0.370235i | ||||||||
\(656\) | 1.16658i | 0.0455473i | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 12.3764 | 0.482483 | ||||||||
\(659\) | 7.18458i | 0.279872i | 0.990161 | + | 0.139936i | \(0.0446896\pi\) | ||||
−0.990161 | + | 0.139936i | \(0.955310\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 10.6665i | 0.414877i | 0.978248 | + | 0.207439i | \(0.0665127\pi\) | ||||
−0.978248 | + | 0.207439i | \(0.933487\pi\) | |||||||
\(662\) | 2.01859 | 0.0784546 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −3.37366 | −0.130924 | ||||||||
\(665\) | 19.7298 | 0.765090 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 6.48605i | 0.251141i | ||||||||
\(668\) | −6.96980 | −0.269670 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 14.8046 | 0.571950 | ||||||||
\(671\) | 8.12952i | 0.313836i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 8.15548 | 0.314371 | 0.157185 | − | 0.987569i | \(-0.449758\pi\) | ||||
0.157185 | + | 0.987569i | \(0.449758\pi\) | |||||||
\(674\) | 12.2132 | 0.470433 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 17.9903 | 0.691936 | ||||||||
\(677\) | − | 32.2397i | − | 1.23907i | −0.784968 | − | 0.619536i | \(-0.787321\pi\) | ||
0.784968 | − | 0.619536i | \(-0.212679\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 19.5684i | 0.750965i | ||||||||
\(680\) | 13.1963 | 0.506055 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 1.60009i | 0.0612705i | ||||||||
\(683\) | − | 44.5137i | − | 1.70327i | −0.524136 | − | 0.851635i | \(-0.675612\pi\) | ||
0.524136 | − | 0.851635i | \(-0.324388\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 45.9593 | 1.75601 | ||||||||
\(686\) | − | 20.0925i | − | 0.767134i | ||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −9.54102 | −0.363748 | ||||||||
\(689\) | 38.0218 | 1.44852 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 45.7153i | − | 1.73909i | −0.493853 | − | 0.869546i | \(-0.664412\pi\) | ||
0.493853 | − | 0.869546i | \(-0.335588\pi\) | |||||||
\(692\) | −18.9794 | −0.721488 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −27.1269 | −1.02972 | ||||||||
\(695\) | 39.7529 | 1.50791 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −6.69787 | −0.253700 | ||||||||
\(698\) | 5.01163i | 0.189693i | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −0.581184 | −0.0219667 | ||||||||
\(701\) | − | 2.02374i | − | 0.0764355i | −0.999269 | − | 0.0382178i | \(-0.987832\pi\) | ||
0.999269 | − | 0.0382178i | \(-0.0121681\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 2.55174 | 0.0962407 | ||||||||
\(704\) | −0.573894 | −0.0216295 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 21.8446 | 0.822131 | ||||||||
\(707\) | − | 12.3256i | − | 0.463553i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 33.0662i | − | 1.24183i | −0.783879 | − | 0.620914i | \(-0.786762\pi\) | ||
0.783879 | − | 0.620914i | \(-0.213238\pi\) | |||||||
\(710\) | − | 0.115821i | − | 0.00434668i | ||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −8.91850 | −0.334235 | ||||||||
\(713\) | 5.74547 | 0.215170 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 7.34301i | 0.274613i | ||||||||
\(716\) | 6.60748i | 0.246933i | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −17.1656 | −0.640615 | ||||||||
\(719\) | − | 22.6224i | − | 0.843672i | −0.906672 | − | 0.421836i | \(-0.861386\pi\) | ||
0.906672 | − | 0.421836i | \(-0.138614\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 24.9809i | 0.930337i | ||||||||
\(722\) | − | 1.56114i | − | 0.0580998i | ||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −12.1359 | −0.451026 | ||||||||
\(725\) | 0.889908i | 0.0330503i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 44.0215 | 1.63267 | 0.816334 | − | 0.577580i | \(-0.196003\pi\) | ||||
0.816334 | + | 0.577580i | \(0.196003\pi\) | |||||||
\(728\) | 11.4432 | 0.424114 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | − | 0.363792i | − | 0.0134645i | ||||||
\(731\) | − | 54.7794i | − | 2.02609i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −3.97676 | −0.146885 | −0.0734425 | − | 0.997299i | \(-0.523399\pi\) | ||||
−0.0734425 | + | 0.997299i | \(0.523399\pi\) | |||||||
\(734\) | − | 14.9021i | − | 0.550048i | ||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 2.06070i | 0.0759583i | ||||||||
\(737\) | − | 3.69656i | − | 0.136165i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 32.7168i | − | 1.20351i | −0.798682 | − | 0.601753i | \(-0.794469\pi\) | ||
0.798682 | − | 0.601753i | \(-0.205531\pi\) | |||||||
\(740\) | −1.40445 | −0.0516287 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 14.0396 | 0.515410 | ||||||||
\(743\) | − | 12.0003i | − | 0.440250i | −0.975472 | − | 0.220125i | \(-0.929353\pi\) | ||
0.975472 | − | 0.220125i | \(-0.0706465\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −16.5196 | −0.605231 | ||||||||
\(746\) | −4.47759 | −0.163936 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | − | 3.29499i | − | 0.120477i | ||||||
\(749\) | −31.0337 | −1.13395 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −44.2429 | −1.61444 | −0.807222 | − | 0.590247i | \(-0.799030\pi\) | ||||
−0.807222 | + | 0.590247i | \(0.799030\pi\) | |||||||
\(752\) | − | 6.02089i | − | 0.219559i | ||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | − | 17.5218i | − | 0.638107i | ||||||
\(755\) | 44.2302i | 1.60970i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 27.8975i | 1.01395i | 0.861960 | + | 0.506976i | \(0.169237\pi\) | ||||
−0.861960 | + | 0.506976i | \(0.830763\pi\) | |||||||
\(758\) | − | 9.65998i | − | 0.350866i | ||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | − | 9.59817i | − | 0.348162i | ||||||
\(761\) | 37.2469 | 1.35020 | 0.675099 | − | 0.737727i | \(-0.264101\pi\) | ||||
0.675099 | + | 0.737727i | \(0.264101\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 19.7558 | 0.715207 | ||||||||
\(764\) | −3.80003 | −0.137480 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 24.1856i | 0.873862i | ||||||||
\(767\) | − | 11.1079i | − | 0.401085i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 29.6601 | 1.06957 | 0.534785 | − | 0.844988i | \(-0.320392\pi\) | ||||
0.534785 | + | 0.844988i | \(0.320392\pi\) | |||||||
\(770\) | 2.71142i | 0.0977126i | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | − | 16.9361i | − | 0.609545i | ||||||
\(773\) | 12.2136 | 0.439292 | 0.219646 | − | 0.975580i | \(-0.429510\pi\) | ||||
0.219646 | + | 0.975580i | \(0.429510\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0.788298 | 0.0283165 | ||||||||
\(776\) | 9.51962 | 0.341734 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −9.66092 | −0.346361 | ||||||||
\(779\) | 4.87162i | 0.174544i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −0.0289194 | −0.00103482 | ||||||||
\(782\) | −11.8314 | −0.423091 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −2.77458 | −0.0990923 | ||||||||
\(785\) | − | 5.83020i | − | 0.208089i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 26.5060i | 0.944836i | 0.881375 | + | 0.472418i | \(0.156619\pi\) | ||||
−0.881375 | + | 0.472418i | \(0.843381\pi\) | |||||||
\(788\) | − | 5.10372i | − | 0.181812i | ||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 8.67463 | 0.308630 | ||||||||
\(791\) | 15.5250 | 0.552005 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −78.8580 | −2.80033 | ||||||||
\(794\) | 10.7987 | 0.383232 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −16.5465 | −0.586475 | ||||||||
\(797\) | 3.63008i | 0.128584i | 0.997931 | + | 0.0642920i | \(0.0204789\pi\) | ||||
−0.997931 | + | 0.0642920i | \(0.979521\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 34.5687 | 1.22295 | ||||||||
\(800\) | 0.282734i | 0.00999617i | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 18.3928 | 0.649472 | ||||||||
\(803\) | −0.0908355 | −0.00320552 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 9.73595 | 0.343147 | ||||||||
\(806\) | −15.5212 | −0.546710 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −5.99617 | −0.210945 | ||||||||
\(809\) | −39.6296 | −1.39330 | −0.696652 | − | 0.717409i | \(-0.745328\pi\) | ||||
−0.696652 | + | 0.717409i | \(0.745328\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 55.6661i | 1.95470i | 0.211631 | + | 0.977350i | \(0.432123\pi\) | ||||
−0.211631 | + | 0.977350i | \(0.567877\pi\) | |||||||
\(812\) | − | 6.46995i | − | 0.227051i | ||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0.350678i | 0.0122913i | ||||||||
\(815\) | − | 1.68233i | − | 0.0589296i | ||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −39.8432 | −1.39394 | ||||||||
\(818\) | −12.4348 | −0.434774 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | − | 2.68129i | − | 0.0936346i | ||||||
\(821\) | 2.41117i | 0.0841503i | 0.999114 | + | 0.0420752i | \(0.0133969\pi\) | ||||
−0.999114 | + | 0.0420752i | \(0.986603\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 23.8371i | − | 0.830909i | −0.909614 | − | 0.415455i | \(-0.863623\pi\) | ||
0.909614 | − | 0.415455i | \(-0.136377\pi\) | |||||||
\(824\) | 12.1527 | 0.423360 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | − | 4.10162i | − | 0.142714i | ||||||
\(827\) | −9.39474 | −0.326687 | −0.163344 | − | 0.986569i | \(-0.552228\pi\) | ||||
−0.163344 | + | 0.986569i | \(0.552228\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 20.9559i | − | 0.727827i | −0.931433 | − | 0.363914i | \(-0.881440\pi\) | ||
0.931433 | − | 0.363914i | \(-0.118560\pi\) | |||||||
\(830\) | 7.75409 | 0.269149 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | − | 5.56690i | − | 0.192997i | ||||||
\(833\) | − | 15.9302i | − | 0.551948i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 16.0195 | 0.554378 | ||||||||
\(836\) | −2.39657 | −0.0828873 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −0.593093 | −0.0204881 | ||||||||
\(839\) | 30.0123 | 1.03614 | 0.518070 | − | 0.855338i | \(-0.326651\pi\) | ||||
0.518070 | + | 0.855338i | \(0.326651\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 19.0932 | 0.658387 | ||||||||
\(842\) | 20.2952 | 0.699419 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −5.75275 | −0.198018 | ||||||||
\(845\) | −41.3493 | −1.42246 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −21.9344 | −0.753674 | ||||||||
\(848\) | − | 6.82999i | − | 0.234543i | ||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −1.62331 | −0.0556791 | ||||||||
\(851\) | 1.25919 | 0.0431645 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 33.7315i | − | 1.15495i | −0.816410 | − | 0.577473i | \(-0.804039\pi\) | ||
0.816410 | − | 0.577473i | \(-0.195961\pi\) | |||||||
\(854\) | −29.1184 | −0.996411 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 15.0973i | 0.516015i | ||||||||
\(857\) | 39.2212i | 1.33977i | 0.742464 | + | 0.669886i | \(0.233657\pi\) | ||||
−0.742464 | + | 0.669886i | \(0.766343\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 41.8288i | − | 1.42718i | −0.700563 | − | 0.713590i | \(-0.747068\pi\) | ||
0.700563 | − | 0.713590i | \(-0.252932\pi\) | |||||||
\(860\) | 21.9293 | 0.747782 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 31.7299i | 1.08072i | ||||||||
\(863\) | 25.1998 | 0.857812 | 0.428906 | − | 0.903349i | \(-0.358899\pi\) | ||||
0.428906 | + | 0.903349i | \(0.358899\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 43.6226 | 1.48321 | ||||||||
\(866\) | 13.9906i | 0.475419i | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −5.73121 | −0.194530 | ||||||||
\(869\) | − | 2.16598i | − | 0.0734757i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 35.8574 | 1.21498 | ||||||||
\(872\) | − | 9.61079i | − | 0.325462i | ||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 8.60544i | 0.291083i | ||||||||
\(875\) | −22.2871 | −0.753443 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 22.7485i | − | 0.768161i | −0.923300 | − | 0.384080i | \(-0.874519\pi\) | ||
0.923300 | − | 0.384080i | \(-0.125481\pi\) | |||||||
\(878\) | 1.26903 | 0.0428275 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 1.31905 | 0.0444652 | ||||||||
\(881\) | 0.622341i | 0.0209672i | 0.999945 | + | 0.0104836i | \(0.00333709\pi\) | ||||
−0.999945 | + | 0.0104836i | \(0.996663\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 31.7943i | − | 1.06996i | −0.844864 | − | 0.534981i | \(-0.820319\pi\) | ||
0.844864 | − | 0.534981i | \(-0.179681\pi\) | |||||||
\(884\) | 31.9621 | 1.07500 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 15.2558 | 0.512530 | ||||||||
\(887\) | 35.2267i | 1.18280i | 0.806380 | + | 0.591398i | \(0.201424\pi\) | ||||
−0.806380 | + | 0.591398i | \(0.798576\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 10.5874 | 0.355091 | ||||||||
\(890\) | 20.4985 | 0.687110 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −2.79911 | + | 14.6685i | −0.0937211 | + | 0.491138i | ||||
\(893\) | − | 25.1431i | − | 0.841383i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 15.1868i | − | 0.507637i | ||||||
\(896\) | − | 2.05558i | − | 0.0686722i | ||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 4.87862i | 0.162802i | ||||||||
\(899\) | 8.77562i | 0.292683i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 39.2141 | 1.30641 | ||||||||
\(902\) | −0.669493 | −0.0222917 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | − | 7.55260i | − | 0.251196i | ||||||
\(905\) | 27.8933 | 0.927206 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −16.4251 | −0.545387 | −0.272693 | − | 0.962101i | \(-0.587914\pi\) | ||||
−0.272693 | + | 0.962101i | \(0.587914\pi\) | |||||||
\(908\) | − | 3.42425i | − | 0.113638i | ||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −26.3013 | −0.871880 | ||||||||
\(911\) | − | 13.4933i | − | 0.447054i | −0.974698 | − | 0.223527i | \(-0.928243\pi\) | ||
0.974698 | − | 0.223527i | \(-0.0717571\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 1.93613i | − | 0.0640764i | ||||||
\(914\) | 31.9179 | 1.05575 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | − | 2.30551i | − | 0.0761760i | ||||||
\(917\) | 8.47430i | 0.279846i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 9.58044i | 0.316029i | 0.987437 | + | 0.158015i | \(0.0505094\pi\) | ||||
−0.987437 | + | 0.158015i | \(0.949491\pi\) | |||||||
\(920\) | − | 4.73635i | − | 0.156153i | ||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −4.76109 | −0.156798 | ||||||||
\(923\) | − | 0.280524i | − | 0.00923356i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0.172765 | 0.00568048 | ||||||||
\(926\) | 33.0970i | 1.08763i | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −3.14750 | −0.103322 | ||||||||
\(929\) | − | 45.1222i | − | 1.48041i | −0.672381 | − | 0.740206i | \(-0.734728\pi\) | ||
0.672381 | − | 0.740206i | \(-0.265272\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −11.5866 | −0.379736 | ||||||||
\(932\) | 19.6834 | 0.644752 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 4.79469i | 0.156887i | ||||||||
\(935\) | 7.57328i | 0.247673i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 26.4298i | − | 0.863424i | −0.902011 | − | 0.431712i | \(-0.857910\pi\) | ||
0.902011 | − | 0.431712i | \(-0.142090\pi\) | |||||||
\(938\) | 13.2404 | 0.432314 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 13.8385i | 0.451363i | ||||||||
\(941\) | 35.8595i | 1.16899i | 0.811398 | + | 0.584494i | \(0.198707\pi\) | ||||
−0.811398 | + | 0.584494i | \(0.801293\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 2.40397i | 0.0782839i | ||||||||
\(944\) | −1.99536 | −0.0649433 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | − | 5.47554i | − | 0.178025i | ||||||
\(947\) | − | 3.01303i | − | 0.0979104i | −0.998801 | − | 0.0489552i | \(-0.984411\pi\) | ||
0.998801 | − | 0.0489552i | \(-0.0155892\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 0.881124i | − | 0.0286025i | ||||||
\(950\) | 1.18070i | 0.0383068i | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 11.8020 | 0.382507 | ||||||||
\(953\) | −54.5051 | −1.76559 | −0.882797 | − | 0.469755i | \(-0.844342\pi\) | ||||
−0.882797 | + | 0.469755i | \(0.844342\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 8.73407 | 0.282628 | ||||||||
\(956\) | 29.8970i | 0.966939i | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −21.0657 | −0.680601 | ||||||||
\(959\) | 41.1035 | 1.32730 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −23.2264 | −0.749238 | ||||||||
\(962\) | −3.40166 | −0.109674 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 25.4297 | 0.819037 | ||||||||
\(965\) | 38.9264i | 1.25308i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 49.4002i | 1.58860i | 0.607524 | + | 0.794302i | \(0.292163\pi\) | ||||
−0.607524 | + | 0.794302i | \(0.707837\pi\) | |||||||
\(968\) | 10.6706i | 0.342968i | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −21.8801 | −0.702527 | ||||||||
\(971\) | 4.20429 | 0.134922 | 0.0674611 | − | 0.997722i | \(-0.478510\pi\) | ||||
0.0674611 | + | 0.997722i | \(0.478510\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 35.5528 | 1.13977 | ||||||||
\(974\) | 15.3348i | 0.491360i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 14.1655i | 0.453428i | ||||||||
\(977\) | −33.2141 | −1.06261 | −0.531307 | − | 0.847180i | \(-0.678299\pi\) | ||||
−0.531307 | + | 0.847180i | \(0.678299\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 5.11828i | − | 0.163581i | ||||||
\(980\) | 6.37716 | 0.203711 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 12.7519i | 0.406931i | ||||||||
\(983\) | −5.12760 | −0.163545 | −0.0817725 | − | 0.996651i | \(-0.526058\pi\) | ||||
−0.0817725 | + | 0.996651i | \(0.526058\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 11.7305i | 0.373764i | ||||||||
\(986\) | − | 18.0713i | − | 0.575507i | ||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | − | 23.2473i | − | 0.739594i | ||||||
\(989\) | −19.6612 | −0.625188 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 0.444200i | 0.0141105i | 0.999975 | + | 0.00705523i | \(0.00224577\pi\) | ||||
−0.999975 | + | 0.00705523i | \(0.997754\pi\) | |||||||
\(992\) | 2.78812i | 0.0885229i | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | − | 0.103584i | − | 0.00328548i | ||||||
\(995\) | 38.0308 | 1.20566 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −8.42401 | −0.266791 | −0.133396 | − | 0.991063i | \(-0.542588\pi\) | ||||
−0.133396 | + | 0.991063i | \(0.542588\pi\) | |||||||
\(998\) | − | 19.5666i | − | 0.619371i | ||||||
\(999\) | 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 | 4014.2.d.a.4013.14 | yes | 72 | |
3.2 | odd | 2 | inner | 4014.2.d.a.4013.61 | yes | 72 | |
223.222 | odd | 2 | inner | 4014.2.d.a.4013.62 | yes | 72 | |
669.668 | even | 2 | inner | 4014.2.d.a.4013.13 | ✓ | 72 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4014.2.d.a.4013.13 | ✓ | 72 | 669.668 | even | 2 | inner | |
4014.2.d.a.4013.14 | yes | 72 | 1.1 | even | 1 | trivial | |
4014.2.d.a.4013.61 | yes | 72 | 3.2 | odd | 2 | inner | |
4014.2.d.a.4013.62 | yes | 72 | 223.222 | odd | 2 | inner |