Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6300,2,Mod(1457,6300)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6300, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 2, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6300.1457");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6300 = 2^{2} \cdot 3^{2} \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6300.v (of order \(4\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(50.3057532734\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(i)\) |
Coefficient field: | \(\Q(\zeta_{8})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 5993.2 | ||
Root | \(-0.707107 - 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6300.5993 |
Dual form | 6300.2.v.b.1457.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/6300\mathbb{Z}\right)^\times\).
\(n\) | \(2801\) | \(3151\) | \(3277\) | \(3601\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(e\left(\frac{3}{4}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.707107 | − | 0.707107i | 0.267261 | − | 0.267261i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 5.41421i | 1.63245i | 0.577736 | + | 0.816223i | \(0.303936\pi\) | ||||
−0.577736 | + | 0.816223i | \(0.696064\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.41421 | − | 3.41421i | −0.946932 | − | 0.946932i | 0.0517287 | − | 0.998661i | \(-0.483527\pi\) |
−0.998661 | + | 0.0517287i | \(0.983527\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −2.82843 | − | 2.82843i | −0.685994 | − | 0.685994i | 0.275350 | − | 0.961344i | \(-0.411206\pi\) |
−0.961344 | + | 0.275350i | \(0.911206\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.82843i | 0.648886i | 0.945905 | + | 0.324443i | \(0.105177\pi\) | ||||
−0.945905 | + | 0.324443i | \(0.894823\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.82843 | + | 1.82843i | −0.381253 | + | 0.381253i | −0.871554 | − | 0.490300i | \(-0.836887\pi\) |
0.490300 | + | 0.871554i | \(0.336887\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.41421 | 0.262613 | 0.131306 | − | 0.991342i | \(-0.458083\pi\) | ||||
0.131306 | + | 0.991342i | \(0.458083\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.82843 | −0.508001 | −0.254000 | − | 0.967204i | \(-0.581746\pi\) | ||||
−0.254000 | + | 0.967204i | \(0.581746\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 5.41421 | − | 5.41421i | 0.890091 | − | 0.890091i | −0.104440 | − | 0.994531i | \(-0.533305\pi\) |
0.994531 | + | 0.104440i | \(0.0333050\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 1.17157i | − | 0.182969i | −0.995807 | − | 0.0914845i | \(-0.970839\pi\) | ||
0.995807 | − | 0.0914845i | \(-0.0291612\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −6.82843 | − | 6.82843i | −1.04133 | − | 1.04133i | −0.999108 | − | 0.0422169i | \(-0.986558\pi\) |
−0.0422169 | − | 0.999108i | \(-0.513442\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 6.82843 | + | 6.82843i | 0.996028 | + | 0.996028i | 0.999992 | − | 0.00396368i | \(-0.00126168\pi\) |
−0.00396368 | + | 0.999992i | \(0.501262\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | − | 1.00000i | − | 0.142857i | ||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 7.82843 | − | 7.82843i | 1.07532 | − | 1.07532i | 0.0783948 | − | 0.996922i | \(-0.475021\pi\) |
0.996922 | − | 0.0783948i | \(-0.0249795\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −4.00000 | −0.520756 | −0.260378 | − | 0.965507i | \(-0.583847\pi\) | ||||
−0.260378 | + | 0.965507i | \(0.583847\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 13.3137 | 1.70465 | 0.852323 | − | 0.523016i | \(-0.175193\pi\) | ||||
0.852323 | + | 0.523016i | \(0.175193\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −2.58579 | + | 2.58579i | −0.315904 | + | 0.315904i | −0.847192 | − | 0.531287i | \(-0.821708\pi\) |
0.531287 | + | 0.847192i | \(0.321708\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 8.24264i | − | 0.978221i | −0.872222 | − | 0.489111i | \(-0.837321\pi\) | ||
0.872222 | − | 0.489111i | \(-0.162679\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 1.75736 | + | 1.75736i | 0.205683 | + | 0.205683i | 0.802430 | − | 0.596746i | \(-0.203540\pi\) |
−0.596746 | + | 0.802430i | \(0.703540\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 3.82843 | + | 3.82843i | 0.436290 | + | 0.436290i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 9.65685i | − | 1.08648i | −0.839577 | − | 0.543240i | \(-0.817197\pi\) | ||
0.839577 | − | 0.543240i | \(-0.182803\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 1.17157 | − | 1.17157i | 0.128597 | − | 0.128597i | −0.639879 | − | 0.768476i | \(-0.721016\pi\) |
0.768476 | + | 0.639879i | \(0.221016\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 10.8284 | 1.14781 | 0.573905 | − | 0.818922i | \(-0.305428\pi\) | ||||
0.573905 | + | 0.818922i | \(0.305428\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −4.82843 | −0.506157 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 6.24264 | − | 6.24264i | 0.633844 | − | 0.633844i | −0.315186 | − | 0.949030i | \(-0.602067\pi\) |
0.949030 | + | 0.315186i | \(0.102067\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 6.82843i | 0.679454i | 0.940524 | + | 0.339727i | \(0.110335\pi\) | ||||
−0.940524 | + | 0.339727i | \(0.889665\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 5.17157 | + | 5.17157i | 0.509570 | + | 0.509570i | 0.914394 | − | 0.404824i | \(-0.132667\pi\) |
−0.404824 | + | 0.914394i | \(0.632667\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 4.17157 | + | 4.17157i | 0.403281 | + | 0.403281i | 0.879388 | − | 0.476106i | \(-0.157952\pi\) |
−0.476106 | + | 0.879388i | \(0.657952\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 11.3137i | − | 1.08366i | −0.840489 | − | 0.541828i | \(-0.817732\pi\) | ||
0.840489 | − | 0.541828i | \(-0.182268\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 13.8284 | − | 13.8284i | 1.30087 | − | 1.30087i | 0.373063 | − | 0.927806i | \(-0.378308\pi\) |
0.927806 | − | 0.373063i | \(-0.121692\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −4.00000 | −0.366679 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −18.3137 | −1.66488 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −6.58579 | + | 6.58579i | −0.584394 | + | 0.584394i | −0.936108 | − | 0.351714i | \(-0.885599\pi\) |
0.351714 | + | 0.936108i | \(0.385599\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 20.4853i | − | 1.78981i | −0.446259 | − | 0.894904i | \(-0.647244\pi\) | ||
0.446259 | − | 0.894904i | \(-0.352756\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.00000 | + | 2.00000i | 0.173422 | + | 0.173422i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 5.82843 | + | 5.82843i | 0.497956 | + | 0.497956i | 0.910801 | − | 0.412845i | \(-0.135465\pi\) |
−0.412845 | + | 0.910801i | \(0.635465\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 16.4853i | 1.39826i | 0.714993 | + | 0.699132i | \(0.246430\pi\) | ||||
−0.714993 | + | 0.699132i | \(0.753570\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 18.4853 | − | 18.4853i | 1.54582 | − | 1.54582i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 1.41421 | 0.115857 | 0.0579284 | − | 0.998321i | \(-0.481550\pi\) | ||||
0.0579284 | + | 0.998321i | \(0.481550\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −13.3137 | −1.08345 | −0.541727 | − | 0.840554i | \(-0.682229\pi\) | ||||
−0.541727 | + | 0.840554i | \(0.682229\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −3.41421 | + | 3.41421i | −0.272484 | + | 0.272484i | −0.830099 | − | 0.557615i | \(-0.811716\pi\) |
0.557615 | + | 0.830099i | \(0.311716\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 2.58579i | 0.203789i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −15.0711 | − | 15.0711i | −1.18046 | − | 1.18046i | −0.979626 | − | 0.200831i | \(-0.935636\pi\) |
−0.200831 | − | 0.979626i | \(-0.564364\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 17.6569 | + | 17.6569i | 1.36633 | + | 1.36633i | 0.865611 | + | 0.500718i | \(0.166931\pi\) |
0.500718 | + | 0.865611i | \(0.333069\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 10.3137i | 0.793362i | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 10.0000 | − | 10.0000i | 0.760286 | − | 0.760286i | −0.216088 | − | 0.976374i | \(-0.569330\pi\) |
0.976374 | + | 0.216088i | \(0.0693298\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −3.07107 | −0.229542 | −0.114771 | − | 0.993392i | \(-0.536613\pi\) | ||||
−0.114771 | + | 0.993392i | \(0.536613\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 19.6569 | 1.46108 | 0.730541 | − | 0.682869i | \(-0.239268\pi\) | ||||
0.730541 | + | 0.682869i | \(0.239268\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 15.3137 | − | 15.3137i | 1.11985 | − | 1.11985i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 4.92893i | 0.356645i | 0.983972 | + | 0.178323i | \(0.0570670\pi\) | ||||
−0.983972 | + | 0.178323i | \(0.942933\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −12.7279 | − | 12.7279i | −0.916176 | − | 0.916176i | 0.0805728 | − | 0.996749i | \(-0.474325\pi\) |
−0.996749 | + | 0.0805728i | \(0.974325\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −17.1421 | − | 17.1421i | −1.22133 | − | 1.22133i | −0.967161 | − | 0.254166i | \(-0.918199\pi\) |
−0.254166 | − | 0.967161i | \(-0.581801\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 2.82843i | − | 0.200502i | −0.994962 | − | 0.100251i | \(-0.968035\pi\) | ||
0.994962 | − | 0.100251i | \(-0.0319646\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1.00000 | − | 1.00000i | 0.0701862 | − | 0.0701862i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −15.3137 | −1.05927 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 10.9706 | 0.755245 | 0.377622 | − | 0.925960i | \(-0.376742\pi\) | ||||
0.377622 | + | 0.925960i | \(0.376742\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −2.00000 | + | 2.00000i | −0.135769 | + | 0.135769i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 19.3137i | 1.29918i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1.17157 | + | 1.17157i | 0.0784543 | + | 0.0784543i | 0.745245 | − | 0.666791i | \(-0.232333\pi\) |
−0.666791 | + | 0.745245i | \(0.732333\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 12.8284 | + | 12.8284i | 0.851453 | + | 0.851453i | 0.990312 | − | 0.138859i | \(-0.0443436\pi\) |
−0.138859 | + | 0.990312i | \(0.544344\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 17.3137i | 1.14412i | 0.820211 | + | 0.572061i | \(0.193856\pi\) | ||||
−0.820211 | + | 0.572061i | \(0.806144\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 10.1716 | − | 10.1716i | 0.666362 | − | 0.666362i | −0.290510 | − | 0.956872i | \(-0.593825\pi\) |
0.956872 | + | 0.290510i | \(0.0938250\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 8.24264 | 0.533172 | 0.266586 | − | 0.963811i | \(-0.414104\pi\) | ||||
0.266586 | + | 0.963811i | \(0.414104\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −7.65685 | −0.493221 | −0.246611 | − | 0.969115i | \(-0.579317\pi\) | ||||
−0.246611 | + | 0.969115i | \(0.579317\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 9.65685 | − | 9.65685i | 0.614451 | − | 0.614451i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 20.9706i | 1.32365i | 0.749658 | + | 0.661825i | \(0.230218\pi\) | ||||
−0.749658 | + | 0.661825i | \(0.769782\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −9.89949 | − | 9.89949i | −0.622376 | − | 0.622376i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 8.82843 | + | 8.82843i | 0.550702 | + | 0.550702i | 0.926643 | − | 0.375941i | \(-0.122681\pi\) |
−0.375941 | + | 0.926643i | \(0.622681\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 7.65685i | − | 0.475774i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −3.48528 | + | 3.48528i | −0.214912 | + | 0.214912i | −0.806350 | − | 0.591438i | \(-0.798560\pi\) |
0.591438 | + | 0.806350i | \(0.298560\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −15.3137 | −0.933693 | −0.466847 | − | 0.884338i | \(-0.654610\pi\) | ||||
−0.466847 | + | 0.884338i | \(0.654610\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 18.1421 | 1.10206 | 0.551028 | − | 0.834487i | \(-0.314236\pi\) | ||||
0.551028 | + | 0.834487i | \(0.314236\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 9.65685 | − | 9.65685i | 0.580224 | − | 0.580224i | −0.354741 | − | 0.934965i | \(-0.615431\pi\) |
0.934965 | + | 0.354741i | \(0.115431\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 17.8995i | − | 1.06779i | −0.845549 | − | 0.533897i | \(-0.820727\pi\) | ||
0.845549 | − | 0.533897i | \(-0.179273\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −20.4853 | − | 20.4853i | −1.21772 | − | 1.21772i | −0.968427 | − | 0.249296i | \(-0.919801\pi\) |
−0.249296 | − | 0.968427i | \(-0.580199\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −0.828427 | − | 0.828427i | −0.0489005 | − | 0.0489005i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | − | 1.00000i | − | 0.0588235i | ||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 1.51472 | − | 1.51472i | 0.0884908 | − | 0.0884908i | −0.661476 | − | 0.749967i | \(-0.730070\pi\) |
0.749967 | + | 0.661476i | \(0.230070\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 12.4853 | 0.722042 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −9.65685 | −0.556612 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 16.4853 | − | 16.4853i | 0.940865 | − | 0.940865i | −0.0574818 | − | 0.998347i | \(-0.518307\pi\) |
0.998347 | + | 0.0574818i | \(0.0183071\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 4.48528i | 0.254337i | 0.991881 | + | 0.127168i | \(0.0405889\pi\) | ||||
−0.991881 | + | 0.127168i | \(0.959411\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −23.8995 | − | 23.8995i | −1.35088 | − | 1.35088i | −0.884679 | − | 0.466200i | \(-0.845623\pi\) |
−0.466200 | − | 0.884679i | \(-0.654377\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 9.48528 | + | 9.48528i | 0.532746 | + | 0.532746i | 0.921389 | − | 0.388642i | \(-0.127056\pi\) |
−0.388642 | + | 0.921389i | \(0.627056\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 7.65685i | 0.428702i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 8.00000 | − | 8.00000i | 0.445132 | − | 0.445132i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 9.65685 | 0.532400 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −4.34315 | −0.238721 | −0.119360 | − | 0.992851i | \(-0.538084\pi\) | ||||
−0.119360 | + | 0.992851i | \(0.538084\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 3.75736 | − | 3.75736i | 0.204676 | − | 0.204676i | −0.597324 | − | 0.802000i | \(-0.703769\pi\) |
0.802000 | + | 0.597324i | \(0.203769\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 15.3137i | − | 0.829284i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −0.707107 | − | 0.707107i | −0.0381802 | − | 0.0381802i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −5.14214 | − | 5.14214i | −0.276044 | − | 0.276044i | 0.555483 | − | 0.831528i | \(-0.312533\pi\) |
−0.831528 | + | 0.555483i | \(0.812533\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 14.9706i | − | 0.801356i | −0.916219 | − | 0.400678i | \(-0.868775\pi\) | ||
0.916219 | − | 0.400678i | \(-0.131225\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 6.34315 | − | 6.34315i | 0.337612 | − | 0.337612i | −0.517856 | − | 0.855468i | \(-0.673270\pi\) |
0.855468 | + | 0.517856i | \(0.173270\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −7.27208 | −0.383806 | −0.191903 | − | 0.981414i | \(-0.561466\pi\) | ||||
−0.191903 | + | 0.981414i | \(0.561466\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 11.0000 | 0.578947 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 12.9706 | − | 12.9706i | 0.677058 | − | 0.677058i | −0.282276 | − | 0.959333i | \(-0.591089\pi\) |
0.959333 | + | 0.282276i | \(0.0910892\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 11.0711i | − | 0.574781i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −0.485281 | − | 0.485281i | −0.0251269 | − | 0.0251269i | 0.694432 | − | 0.719559i | \(-0.255656\pi\) |
−0.719559 | + | 0.694432i | \(0.755656\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −4.82843 | − | 4.82843i | −0.248677 | − | 0.248677i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 17.3137i | − | 0.889345i | −0.895693 | − | 0.444673i | \(-0.853320\pi\) | ||
0.895693 | − | 0.444673i | \(-0.146680\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 2.00000 | − | 2.00000i | 0.102195 | − | 0.102195i | −0.654161 | − | 0.756356i | \(-0.726978\pi\) |
0.756356 | + | 0.654161i | \(0.226978\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −31.0711 | −1.57537 | −0.787683 | − | 0.616081i | \(-0.788719\pi\) | ||||
−0.787683 | + | 0.616081i | \(0.788719\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 10.3431 | 0.523075 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −13.0711 | + | 13.0711i | −0.656018 | + | 0.656018i | −0.954435 | − | 0.298417i | \(-0.903541\pi\) |
0.298417 | + | 0.954435i | \(0.403541\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 15.5563i | − | 0.776847i | −0.921481 | − | 0.388424i | \(-0.873020\pi\) | ||
0.921481 | − | 0.388424i | \(-0.126980\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 9.65685 | + | 9.65685i | 0.481042 | + | 0.481042i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 29.3137 | + | 29.3137i | 1.45303 | + | 1.45303i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 3.65685i | − | 0.180820i | −0.995905 | − | 0.0904099i | \(-0.971182\pi\) | ||
0.995905 | − | 0.0904099i | \(-0.0288177\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −2.82843 | + | 2.82843i | −0.139178 | + | 0.139178i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −0.970563 | −0.0474151 | −0.0237075 | − | 0.999719i | \(-0.507547\pi\) | ||||
−0.0237075 | + | 0.999719i | \(0.507547\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −21.3137 | −1.03877 | −0.519383 | − | 0.854541i | \(-0.673838\pi\) | ||||
−0.519383 | + | 0.854541i | \(0.673838\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 9.41421 | − | 9.41421i | 0.455586 | − | 0.455586i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 8.72792i | 0.420409i | 0.977657 | + | 0.210205i | \(0.0674130\pi\) | ||||
−0.977657 | + | 0.210205i | \(0.932587\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −10.7279 | − | 10.7279i | −0.515551 | − | 0.515551i | 0.400671 | − | 0.916222i | \(-0.368777\pi\) |
−0.916222 | + | 0.400671i | \(0.868777\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −5.17157 | − | 5.17157i | −0.247390 | − | 0.247390i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 14.8284i | − | 0.707722i | −0.935298 | − | 0.353861i | \(-0.884869\pi\) | ||
0.935298 | − | 0.353861i | \(-0.115131\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 13.4853 | − | 13.4853i | 0.640705 | − | 0.640705i | −0.310024 | − | 0.950729i | \(-0.600337\pi\) |
0.950729 | + | 0.310024i | \(0.100337\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 29.2132 | 1.37866 | 0.689328 | − | 0.724449i | \(-0.257906\pi\) | ||||
0.689328 | + | 0.724449i | \(0.257906\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 6.34315 | 0.298687 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −15.7574 | + | 15.7574i | −0.737098 | + | 0.737098i | −0.972015 | − | 0.234917i | \(-0.924518\pi\) |
0.234917 | + | 0.972015i | \(0.424518\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 23.1127i | 1.07647i | 0.842796 | + | 0.538233i | \(0.180908\pi\) | ||||
−0.842796 | + | 0.538233i | \(0.819092\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 3.75736 | + | 3.75736i | 0.174619 | + | 0.174619i | 0.789005 | − | 0.614386i | \(-0.210596\pi\) |
−0.614386 | + | 0.789005i | \(0.710596\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 7.17157 | + | 7.17157i | 0.331861 | + | 0.331861i | 0.853293 | − | 0.521432i | \(-0.174602\pi\) |
−0.521432 | + | 0.853293i | \(0.674602\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 3.65685i | 0.168858i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 36.9706 | − | 36.9706i | 1.69991 | − | 1.69991i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 42.1421 | 1.92552 | 0.962762 | − | 0.270352i | \(-0.0871399\pi\) | ||||
0.962762 | + | 0.270352i | \(0.0871399\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −36.9706 | −1.68571 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 4.00000 | − | 4.00000i | 0.181257 | − | 0.181257i | −0.610646 | − | 0.791904i | \(-0.709090\pi\) |
0.791904 | + | 0.610646i | \(0.209090\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 9.21320i | − | 0.415786i | −0.978152 | − | 0.207893i | \(-0.933339\pi\) | ||
0.978152 | − | 0.207893i | \(-0.0666606\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −4.00000 | − | 4.00000i | −0.180151 | − | 0.180151i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −5.82843 | − | 5.82843i | −0.261441 | − | 0.261441i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 18.0000i | − | 0.805791i | −0.915246 | − | 0.402895i | \(-0.868004\pi\) | ||
0.915246 | − | 0.402895i | \(-0.131996\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 30.2843 | − | 30.2843i | 1.35031 | − | 1.35031i | 0.464996 | − | 0.885313i | \(-0.346056\pi\) |
0.885313 | − | 0.464996i | \(-0.153944\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −6.34315 | −0.281155 | −0.140577 | − | 0.990070i | \(-0.544896\pi\) | ||||
−0.140577 | + | 0.990070i | \(0.544896\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 2.48528 | 0.109942 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −36.9706 | + | 36.9706i | −1.62596 | + | 1.62596i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 4.00000i | 0.175243i | 0.996154 | + | 0.0876216i | \(0.0279266\pi\) | ||||
−0.996154 | + | 0.0876216i | \(0.972073\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 10.8284 | + | 10.8284i | 0.473494 | + | 0.473494i | 0.903043 | − | 0.429549i | \(-0.141328\pi\) |
−0.429549 | + | 0.903043i | \(0.641328\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 8.00000 | + | 8.00000i | 0.348485 | + | 0.348485i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 16.3137i | 0.709292i | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −4.00000 | + | 4.00000i | −0.173259 | + | 0.173259i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 5.41421 | 0.233207 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −18.0000 | −0.773880 | −0.386940 | − | 0.922105i | \(-0.626468\pi\) | ||||
−0.386940 | + | 0.922105i | \(0.626468\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 25.2132 | − | 25.2132i | 1.07804 | − | 1.07804i | 0.0813534 | − | 0.996685i | \(-0.474076\pi\) |
0.996685 | − | 0.0813534i | \(-0.0259242\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 4.00000i | 0.170406i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −6.82843 | − | 6.82843i | −0.290374 | − | 0.290374i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 11.1421 | + | 11.1421i | 0.472107 | + | 0.472107i | 0.902596 | − | 0.430489i | \(-0.141659\pi\) |
−0.430489 | + | 0.902596i | \(0.641659\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 46.6274i | 1.97213i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −28.6274 | + | 28.6274i | −1.20650 | + | 1.20650i | −0.234349 | + | 0.972152i | \(0.575296\pi\) |
−0.972152 | + | 0.234349i | \(0.924704\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 47.5563 | 1.99367 | 0.996833 | − | 0.0795242i | \(-0.0253401\pi\) | ||||
0.996833 | + | 0.0795242i | \(0.0253401\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 16.0000 | 0.669579 | 0.334790 | − | 0.942293i | \(-0.391335\pi\) | ||||
0.334790 | + | 0.942293i | \(0.391335\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −5.07107 | + | 5.07107i | −0.211111 | + | 0.211111i | −0.804739 | − | 0.593628i | \(-0.797695\pi\) |
0.593628 | + | 0.804739i | \(0.297695\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − | 1.65685i | − | 0.0687379i | ||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 42.3848 | + | 42.3848i | 1.75540 | + | 1.75540i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −14.9706 | − | 14.9706i | −0.617901 | − | 0.617901i | 0.327091 | − | 0.944993i | \(-0.393931\pi\) |
−0.944993 | + | 0.327091i | \(0.893931\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 8.00000i | − | 0.329634i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 4.68629 | − | 4.68629i | 0.192443 | − | 0.192443i | −0.604308 | − | 0.796751i | \(-0.706550\pi\) |
0.796751 | + | 0.604308i | \(0.206550\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 4.92893 | 0.201391 | 0.100695 | − | 0.994917i | \(-0.467893\pi\) | ||||
0.100695 | + | 0.994917i | \(0.467893\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 46.9706 | 1.91597 | 0.957985 | − | 0.286820i | \(-0.0925980\pi\) | ||||
0.957985 | + | 0.286820i | \(0.0925980\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −2.82843 | + | 2.82843i | −0.114802 | + | 0.114802i | −0.762174 | − | 0.647372i | \(-0.775868\pi\) |
0.647372 | + | 0.762174i | \(0.275868\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 46.6274i | − | 1.88634i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −9.65685 | − | 9.65685i | −0.390037 | − | 0.390037i | 0.484664 | − | 0.874701i | \(-0.338942\pi\) |
−0.874701 | + | 0.484664i | \(0.838942\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 15.1421 | + | 15.1421i | 0.609599 | + | 0.609599i | 0.942841 | − | 0.333242i | \(-0.108143\pi\) |
−0.333242 | + | 0.942841i | \(0.608143\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 6.82843i | 0.274458i | 0.990539 | + | 0.137229i | \(0.0438196\pi\) | ||||
−0.990539 | + | 0.137229i | \(0.956180\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 7.65685 | − | 7.65685i | 0.306765 | − | 0.306765i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −30.6274 | −1.22120 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −28.9706 | −1.15330 | −0.576650 | − | 0.816991i | \(-0.695640\pi\) | ||||
−0.576650 | + | 0.816991i | \(0.695640\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −3.41421 | + | 3.41421i | −0.135276 | + | 0.135276i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 22.1005i | − | 0.872917i | −0.899724 | − | 0.436459i | \(-0.856232\pi\) | ||
0.899724 | − | 0.436459i | \(-0.143768\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −9.65685 | − | 9.65685i | −0.380829 | − | 0.380829i | 0.490572 | − | 0.871401i | \(-0.336788\pi\) |
−0.871401 | + | 0.490572i | \(0.836788\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 12.0000 | + | 12.0000i | 0.471769 | + | 0.471769i | 0.902487 | − | 0.430718i | \(-0.141740\pi\) |
−0.430718 | + | 0.902487i | \(0.641740\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 21.6569i | − | 0.850106i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 13.1421 | − | 13.1421i | 0.514292 | − | 0.514292i | −0.401547 | − | 0.915838i | \(-0.631527\pi\) |
0.915838 | + | 0.401547i | \(0.131527\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −35.0711 | −1.36617 | −0.683087 | − | 0.730337i | \(-0.739363\pi\) | ||||
−0.683087 | + | 0.730337i | \(0.739363\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 43.9411 | 1.70911 | 0.854556 | − | 0.519360i | \(-0.173829\pi\) | ||||
0.854556 | + | 0.519360i | \(0.173829\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −2.58579 | + | 2.58579i | −0.100122 | + | 0.100122i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 72.0833i | 2.78274i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 21.8995 | + | 21.8995i | 0.844163 | + | 0.844163i | 0.989397 | − | 0.145234i | \(-0.0463935\pi\) |
−0.145234 | + | 0.989397i | \(0.546393\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −30.4853 | − | 30.4853i | −1.17164 | − | 1.17164i | −0.981818 | − | 0.189827i | \(-0.939207\pi\) |
−0.189827 | − | 0.981818i | \(-0.560793\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 8.82843i | − | 0.338804i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −35.1421 | + | 35.1421i | −1.34468 | + | 1.34468i | −0.453338 | + | 0.891339i | \(0.649767\pi\) |
−0.891339 | + | 0.453338i | \(0.850233\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −53.4558 | −2.03651 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −45.4558 | −1.72922 | −0.864611 | − | 0.502442i | \(-0.832435\pi\) | ||||
−0.864611 | + | 0.502442i | \(0.832435\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −3.31371 | + | 3.31371i | −0.125516 | + | 0.125516i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 11.2721i | 0.425741i | 0.977080 | + | 0.212870i | \(0.0682812\pi\) | ||||
−0.977080 | + | 0.212870i | \(0.931719\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 15.3137 | + | 15.3137i | 0.577567 | + | 0.577567i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 4.82843 | + | 4.82843i | 0.181592 | + | 0.181592i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 22.6274i | 0.849790i | 0.905243 | + | 0.424895i | \(0.139689\pi\) | ||||
−0.905243 | + | 0.424895i | \(0.860311\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 5.17157 | − | 5.17157i | 0.193677 | − | 0.193677i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −20.0000 | −0.745874 | −0.372937 | − | 0.927857i | \(-0.621649\pi\) | ||||
−0.372937 | + | 0.927857i | \(0.621649\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 7.31371 | 0.272377 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 16.9706 | − | 16.9706i | 0.629403 | − | 0.629403i | −0.318515 | − | 0.947918i | \(-0.603184\pi\) |
0.947918 | + | 0.318515i | \(0.103184\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 38.6274i | 1.42869i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −18.2426 | − | 18.2426i | −0.673807 | − | 0.673807i | 0.284784 | − | 0.958592i | \(-0.408078\pi\) |
−0.958592 | + | 0.284784i | \(0.908078\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −14.0000 | − | 14.0000i | −0.515697 | − | 0.515697i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 43.3137i | 1.59332i | 0.604427 | + | 0.796660i | \(0.293402\pi\) | ||||
−0.604427 | + | 0.796660i | \(0.706598\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −13.8284 | + | 13.8284i | −0.507316 | + | 0.507316i | −0.913702 | − | 0.406386i | \(-0.866789\pi\) |
0.406386 | + | 0.913702i | \(0.366789\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 5.89949 | 0.215563 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 14.9706 | 0.546284 | 0.273142 | − | 0.961974i | \(-0.411937\pi\) | ||||
0.273142 | + | 0.961974i | \(0.411937\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 8.92893 | − | 8.92893i | 0.324528 | − | 0.324528i | −0.525973 | − | 0.850501i | \(-0.676299\pi\) |
0.850501 | + | 0.525973i | \(0.176299\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 17.8579i | 0.647347i | 0.946169 | + | 0.323674i | \(0.104918\pi\) | ||||
−0.946169 | + | 0.323674i | \(0.895082\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −8.00000 | − | 8.00000i | −0.289619 | − | 0.289619i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 13.6569 | + | 13.6569i | 0.493120 | + | 0.493120i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 25.5980i | − | 0.923087i | −0.887118 | − | 0.461543i | \(-0.847296\pi\) | ||
0.887118 | − | 0.461543i | \(-0.152704\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −10.0000 | + | 10.0000i | −0.359675 | + | 0.359675i | −0.863693 | − | 0.504018i | \(-0.831854\pi\) |
0.504018 | + | 0.863693i | \(0.331854\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 3.31371 | 0.118726 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 44.6274 | 1.59689 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 6.34315 | − | 6.34315i | 0.226109 | − | 0.226109i | −0.584956 | − | 0.811065i | \(-0.698888\pi\) |
0.811065 | + | 0.584956i | \(0.198888\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 19.5563i | − | 0.695344i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −45.4558 | − | 45.4558i | −1.61418 | − | 1.61418i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −10.6863 | − | 10.6863i | −0.378528 | − | 0.378528i | 0.492043 | − | 0.870571i | \(-0.336250\pi\) |
−0.870571 | + | 0.492043i | \(0.836250\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 38.6274i | − | 1.36654i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −9.51472 | + | 9.51472i | −0.335767 | + | 0.335767i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 11.7574 | 0.413367 | 0.206683 | − | 0.978408i | \(-0.433733\pi\) | ||||
0.206683 | + | 0.978408i | \(0.433733\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −5.45584 | −0.191581 | −0.0957903 | − | 0.995402i | \(-0.530538\pi\) | ||||
−0.0957903 | + | 0.995402i | \(0.530538\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 19.3137 | − | 19.3137i | 0.675701 | − | 0.675701i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 49.0122i | − | 1.71054i | −0.518185 | − | 0.855269i | \(-0.673392\pi\) | ||
0.518185 | − | 0.855269i | \(-0.326608\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −14.5858 | − | 14.5858i | −0.508429 | − | 0.508429i | 0.405615 | − | 0.914044i | \(-0.367057\pi\) |
−0.914044 | + | 0.405615i | \(0.867057\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 25.1421 | + | 25.1421i | 0.874278 | + | 0.874278i | 0.992935 | − | 0.118658i | \(-0.0378591\pi\) |
−0.118658 | + | 0.992935i | \(0.537859\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 37.3137i | 1.29596i | 0.761658 | + | 0.647979i | \(0.224386\pi\) | ||||
−0.761658 | + | 0.647979i | \(0.775614\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −2.82843 | + | 2.82843i | −0.0979992 | + | 0.0979992i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −36.7696 | −1.26943 | −0.634713 | − | 0.772748i | \(-0.718882\pi\) | ||||
−0.634713 | + | 0.772748i | \(0.718882\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −27.0000 | −0.931034 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −12.9497 | + | 12.9497i | −0.444959 | + | 0.444959i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 19.7990i | 0.678701i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 32.8701 | + | 32.8701i | 1.12545 | + | 1.12545i | 0.990908 | + | 0.134541i | \(0.0429561\pi\) |
0.134541 | + | 0.990908i | \(0.457044\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −17.3137 | − | 17.3137i | −0.591425 | − | 0.591425i | 0.346591 | − | 0.938016i | \(-0.387339\pi\) |
−0.938016 | + | 0.346591i | \(0.887339\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 46.4264i | − | 1.58405i | −0.610490 | − | 0.792024i | \(-0.709027\pi\) | ||
0.610490 | − | 0.792024i | \(-0.290973\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −31.1421 | + | 31.1421i | −1.06009 | + | 1.06009i | −0.0620154 | + | 0.998075i | \(0.519753\pi\) |
−0.998075 | + | 0.0620154i | \(0.980247\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 52.2843 | 1.77362 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 17.6569 | 0.598280 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −29.9411 | + | 29.9411i | −1.01104 | + | 1.01104i | −0.0111016 | + | 0.999938i | \(0.503534\pi\) |
−0.999938 | + | 0.0111016i | \(0.996466\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 42.9117i | 1.44573i | 0.690988 | + | 0.722866i | \(0.257176\pi\) | ||||
−0.690988 | + | 0.722866i | \(0.742824\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −1.85786 | − | 1.85786i | −0.0625221 | − | 0.0625221i | 0.675154 | − | 0.737676i | \(-0.264077\pi\) |
−0.737676 | + | 0.675154i | \(0.764077\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −39.1127 | − | 39.1127i | −1.31328 | − | 1.31328i | −0.918986 | − | 0.394290i | \(-0.870991\pi\) |
−0.394290 | − | 0.918986i | \(-0.629009\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 9.31371i | 0.312372i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −19.3137 | + | 19.3137i | −0.646309 | + | 0.646309i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −4.00000 | −0.133407 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −44.2843 | −1.47532 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 17.4558 | − | 17.4558i | 0.579612 | − | 0.579612i | −0.355184 | − | 0.934796i | \(-0.615582\pi\) |
0.934796 | + | 0.355184i | \(0.115582\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 52.5269i | − | 1.74029i | −0.492792 | − | 0.870147i | \(-0.664024\pi\) | ||
0.492792 | − | 0.870147i | \(-0.335976\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 6.34315 | + | 6.34315i | 0.209927 | + | 0.209927i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −14.4853 | − | 14.4853i | −0.478346 | − | 0.478346i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 15.6569i | − | 0.516472i | −0.966082 | − | 0.258236i | \(-0.916859\pi\) | ||
0.966082 | − | 0.258236i | \(-0.0831412\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −28.1421 | + | 28.1421i | −0.926310 | + | 0.926310i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 2.82843 | 0.0927977 | 0.0463988 | − | 0.998923i | \(-0.485225\pi\) | ||||
0.0463988 | + | 0.998923i | \(0.485225\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2.82843 | 0.0926980 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −12.3848 | + | 12.3848i | −0.404593 | + | 0.404593i | −0.879848 | − | 0.475255i | \(-0.842356\pi\) |
0.475255 | + | 0.879848i | \(0.342356\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 51.3137i | − | 1.67278i | −0.548136 | − | 0.836390i | \(-0.684662\pi\) | ||
0.548136 | − | 0.836390i | \(-0.315338\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 2.14214 | + | 2.14214i | 0.0697575 | + | 0.0697575i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −21.1421 | − | 21.1421i | −0.687027 | − | 0.687027i | 0.274547 | − | 0.961574i | \(-0.411472\pi\) |
−0.961574 | + | 0.274547i | \(0.911472\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 12.0000i | − | 0.389536i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −24.7990 | + | 24.7990i | −0.803318 | + | 0.803318i | −0.983613 | − | 0.180295i | \(-0.942295\pi\) |
0.180295 | + | 0.983613i | \(0.442295\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 8.24264 | 0.266169 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −23.0000 | −0.741935 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −16.2426 | + | 16.2426i | −0.522328 | + | 0.522328i | −0.918274 | − | 0.395946i | \(-0.870417\pi\) |
0.395946 | + | 0.918274i | \(0.370417\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 4.20101i | 0.134817i | 0.997725 | + | 0.0674084i | \(0.0214730\pi\) | ||||
−0.997725 | + | 0.0674084i | \(0.978527\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 11.6569 | + | 11.6569i | 0.373702 | + | 0.373702i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −38.7990 | − | 38.7990i | −1.24129 | − | 1.24129i | −0.959466 | − | 0.281823i | \(-0.909061\pi\) |
−0.281823 | − | 0.959466i | \(-0.590939\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 58.6274i | 1.87374i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −2.20101 | + | 2.20101i | −0.0702013 | + | 0.0702013i | −0.741336 | − | 0.671134i | \(-0.765807\pi\) |
0.671134 | + | 0.741336i | \(0.265807\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 24.9706 | 0.794018 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 34.2843 | 1.08908 | 0.544538 | − | 0.838736i | \(-0.316705\pi\) | ||||
0.544538 | + | 0.838736i | \(0.316705\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 23.4142 | − | 23.4142i | 0.741536 | − | 0.741536i | −0.231338 | − | 0.972873i | \(-0.574310\pi\) |
0.972873 | + | 0.231338i | \(0.0743103\pi\) | |||||||
\(998\) | 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 | 6300.2.v.b.5993.2 | yes | 4 | |
3.2 | odd | 2 | 6300.2.v.a.5993.2 | yes | 4 | ||
5.2 | odd | 4 | 6300.2.v.a.1457.2 | ✓ | 4 | ||
5.3 | odd | 4 | 6300.2.v.d.1457.1 | yes | 4 | ||
5.4 | even | 2 | 6300.2.v.c.5993.1 | yes | 4 | ||
15.2 | even | 4 | inner | 6300.2.v.b.1457.2 | yes | 4 | |
15.8 | even | 4 | 6300.2.v.c.1457.1 | yes | 4 | ||
15.14 | odd | 2 | 6300.2.v.d.5993.1 | yes | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6300.2.v.a.1457.2 | ✓ | 4 | 5.2 | odd | 4 | ||
6300.2.v.a.5993.2 | yes | 4 | 3.2 | odd | 2 | ||
6300.2.v.b.1457.2 | yes | 4 | 15.2 | even | 4 | inner | |
6300.2.v.b.5993.2 | yes | 4 | 1.1 | even | 1 | trivial | |
6300.2.v.c.1457.1 | yes | 4 | 15.8 | even | 4 | ||
6300.2.v.c.5993.1 | yes | 4 | 5.4 | even | 2 | ||
6300.2.v.d.1457.1 | yes | 4 | 5.3 | odd | 4 | ||
6300.2.v.d.5993.1 | yes | 4 | 15.14 | odd | 2 |