Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [805,2,Mod(484,805)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(805, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("805.484");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 805 = 5 \cdot 7 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 805.c (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: | \(6.42795736271\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(i)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 484.2 | ||
Root | \(1.00000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 805.484 |
Dual form | 805.2.c.a.484.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/805\mathbb{Z}\right)^\times\).
\(n\) | \(162\) | \(281\) | \(346\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(3\) | 1.00000i | 0.577350i | 0.957427 | + | 0.288675i | \(0.0932147\pi\) | ||||
−0.957427 | + | 0.288675i | \(0.906785\pi\) | |||||||
\(4\) | 2.00000 | 1.00000 | ||||||||
\(5\) | 2.00000 | − | 1.00000i | 0.894427 | − | 0.447214i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000i | 0.377964i | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.00000 | 0.666667 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.00000 | −0.301511 | −0.150756 | − | 0.988571i | \(-0.548171\pi\) | ||||
−0.150756 | + | 0.988571i | \(0.548171\pi\) | |||||||
\(12\) | 2.00000i | 0.577350i | ||||||||
\(13\) | 1.00000i | 0.277350i | 0.990338 | + | 0.138675i | \(0.0442844\pi\) | ||||
−0.990338 | + | 0.138675i | \(0.955716\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.00000 | + | 2.00000i | 0.258199 | + | 0.516398i | ||||
\(16\) | 4.00000 | 1.00000 | ||||||||
\(17\) | − | 1.00000i | − | 0.242536i | −0.992620 | − | 0.121268i | \(-0.961304\pi\) | ||
0.992620 | − | 0.121268i | \(-0.0386960\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.00000 | −0.458831 | −0.229416 | − | 0.973329i | \(-0.573682\pi\) | ||||
−0.229416 | + | 0.973329i | \(0.573682\pi\) | |||||||
\(20\) | 4.00000 | − | 2.00000i | 0.894427 | − | 0.447214i | ||||
\(21\) | −1.00000 | −0.218218 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.00000i | 0.208514i | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 3.00000 | − | 4.00000i | 0.600000 | − | 0.800000i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.00000i | 0.962250i | ||||||||
\(28\) | 2.00000i | 0.377964i | ||||||||
\(29\) | −7.00000 | −1.29987 | −0.649934 | − | 0.759991i | \(-0.725203\pi\) | ||||
−0.649934 | + | 0.759991i | \(0.725203\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.00000 | 0.718421 | 0.359211 | − | 0.933257i | \(-0.383046\pi\) | ||||
0.359211 | + | 0.933257i | \(0.383046\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − | 1.00000i | − | 0.174078i | ||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.00000 | + | 2.00000i | 0.169031 | + | 0.338062i | ||||
\(36\) | 4.00000 | 0.666667 | ||||||||
\(37\) | − | 8.00000i | − | 1.31519i | −0.753371 | − | 0.657596i | \(-0.771573\pi\) | ||
0.753371 | − | 0.657596i | \(-0.228427\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1.00000 | −0.160128 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −6.00000 | −0.937043 | −0.468521 | − | 0.883452i | \(-0.655213\pi\) | ||||
−0.468521 | + | 0.883452i | \(0.655213\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 8.00000i | − | 1.21999i | −0.792406 | − | 0.609994i | \(-0.791172\pi\) | ||
0.792406 | − | 0.609994i | \(-0.208828\pi\) | |||||||
\(44\) | −2.00000 | −0.301511 | ||||||||
\(45\) | 4.00000 | − | 2.00000i | 0.596285 | − | 0.298142i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 7.00000i | 1.02105i | 0.859861 | + | 0.510527i | \(0.170550\pi\) | ||||
−0.859861 | + | 0.510527i | \(0.829450\pi\) | |||||||
\(48\) | 4.00000i | 0.577350i | ||||||||
\(49\) | −1.00000 | −0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.00000 | 0.140028 | ||||||||
\(52\) | 2.00000i | 0.277350i | ||||||||
\(53\) | 4.00000i | 0.549442i | 0.961524 | + | 0.274721i | \(0.0885855\pi\) | ||||
−0.961524 | + | 0.274721i | \(0.911414\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −2.00000 | + | 1.00000i | −0.269680 | + | 0.134840i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 2.00000i | − | 0.264906i | ||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 4.00000 | 0.520756 | 0.260378 | − | 0.965507i | \(-0.416153\pi\) | ||||
0.260378 | + | 0.965507i | \(0.416153\pi\) | |||||||
\(60\) | 2.00000 | + | 4.00000i | 0.258199 | + | 0.516398i | ||||
\(61\) | −10.0000 | −1.28037 | −0.640184 | − | 0.768221i | \(-0.721142\pi\) | ||||
−0.640184 | + | 0.768221i | \(0.721142\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 2.00000i | 0.251976i | ||||||||
\(64\) | 8.00000 | 1.00000 | ||||||||
\(65\) | 1.00000 | + | 2.00000i | 0.124035 | + | 0.248069i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 14.0000i | 1.71037i | 0.518321 | + | 0.855186i | \(0.326557\pi\) | ||||
−0.518321 | + | 0.855186i | \(0.673443\pi\) | |||||||
\(68\) | − | 2.00000i | − | 0.242536i | ||||||
\(69\) | −1.00000 | −0.120386 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2.00000i | 0.234082i | 0.993127 | + | 0.117041i | \(0.0373409\pi\) | ||||
−0.993127 | + | 0.117041i | \(0.962659\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 4.00000 | + | 3.00000i | 0.461880 | + | 0.346410i | ||||
\(76\) | −4.00000 | −0.458831 | ||||||||
\(77\) | − | 1.00000i | − | 0.113961i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 15.0000 | 1.68763 | 0.843816 | − | 0.536633i | \(-0.180304\pi\) | ||||
0.843816 | + | 0.536633i | \(0.180304\pi\) | |||||||
\(80\) | 8.00000 | − | 4.00000i | 0.894427 | − | 0.447214i | ||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 8.00000i | − | 0.878114i | −0.898459 | − | 0.439057i | \(-0.855313\pi\) | ||
0.898459 | − | 0.439057i | \(-0.144687\pi\) | |||||||
\(84\) | −2.00000 | −0.218218 | ||||||||
\(85\) | −1.00000 | − | 2.00000i | −0.108465 | − | 0.216930i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − | 7.00000i | − | 0.750479i | ||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −6.00000 | −0.635999 | −0.317999 | − | 0.948091i | \(-0.603011\pi\) | ||||
−0.317999 | + | 0.948091i | \(0.603011\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.00000 | −0.104828 | ||||||||
\(92\) | 2.00000i | 0.208514i | ||||||||
\(93\) | 4.00000i | 0.414781i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −4.00000 | + | 2.00000i | −0.410391 | + | 0.205196i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 7.00000i | 0.710742i | 0.934725 | + | 0.355371i | \(0.115646\pi\) | ||||
−0.934725 | + | 0.355371i | \(0.884354\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −2.00000 | −0.201008 | ||||||||
\(100\) | 6.00000 | − | 8.00000i | 0.600000 | − | 0.800000i | ||||
\(101\) | −4.00000 | −0.398015 | −0.199007 | − | 0.979998i | \(-0.563772\pi\) | ||||
−0.199007 | + | 0.979998i | \(0.563772\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 7.00000i | 0.689730i | 0.938652 | + | 0.344865i | \(0.112075\pi\) | ||||
−0.938652 | + | 0.344865i | \(0.887925\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −2.00000 | + | 1.00000i | −0.195180 | + | 0.0975900i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(108\) | 10.0000i | 0.962250i | ||||||||
\(109\) | 5.00000 | 0.478913 | 0.239457 | − | 0.970907i | \(-0.423031\pi\) | ||||
0.239457 | + | 0.970907i | \(0.423031\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 8.00000 | 0.759326 | ||||||||
\(112\) | 4.00000i | 0.377964i | ||||||||
\(113\) | − | 18.0000i | − | 1.69330i | −0.532152 | − | 0.846649i | \(-0.678617\pi\) | ||
0.532152 | − | 0.846649i | \(-0.321383\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.00000 | + | 2.00000i | 0.0932505 | + | 0.186501i | ||||
\(116\) | −14.0000 | −1.29987 | ||||||||
\(117\) | 2.00000i | 0.184900i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1.00000 | 0.0916698 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.0000 | −0.909091 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − | 6.00000i | − | 0.541002i | ||||||
\(124\) | 8.00000 | 0.718421 | ||||||||
\(125\) | 2.00000 | − | 11.0000i | 0.178885 | − | 0.983870i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 2.00000i | − | 0.177471i | −0.996055 | − | 0.0887357i | \(-0.971717\pi\) | ||
0.996055 | − | 0.0887357i | \(-0.0282826\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 8.00000 | 0.704361 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −20.0000 | −1.74741 | −0.873704 | − | 0.486458i | \(-0.838289\pi\) | ||||
−0.873704 | + | 0.486458i | \(0.838289\pi\) | |||||||
\(132\) | − | 2.00000i | − | 0.174078i | ||||||
\(133\) | − | 2.00000i | − | 0.173422i | ||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 5.00000 | + | 10.0000i | 0.430331 | + | 0.860663i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 10.0000i | − | 0.854358i | −0.904167 | − | 0.427179i | \(-0.859507\pi\) | ||
0.904167 | − | 0.427179i | \(-0.140493\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −4.00000 | −0.339276 | −0.169638 | − | 0.985506i | \(-0.554260\pi\) | ||||
−0.169638 | + | 0.985506i | \(0.554260\pi\) | |||||||
\(140\) | 2.00000 | + | 4.00000i | 0.169031 | + | 0.338062i | ||||
\(141\) | −7.00000 | −0.589506 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 1.00000i | − | 0.0836242i | ||||||
\(144\) | 8.00000 | 0.666667 | ||||||||
\(145\) | −14.0000 | + | 7.00000i | −1.16264 | + | 0.581318i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | − | 1.00000i | − | 0.0824786i | ||||||
\(148\) | − | 16.0000i | − | 1.31519i | ||||||
\(149\) | −14.0000 | −1.14692 | −0.573462 | − | 0.819232i | \(-0.694400\pi\) | ||||
−0.573462 | + | 0.819232i | \(0.694400\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1.00000 | −0.0813788 | −0.0406894 | − | 0.999172i | \(-0.512955\pi\) | ||||
−0.0406894 | + | 0.999172i | \(0.512955\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − | 2.00000i | − | 0.161690i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 8.00000 | − | 4.00000i | 0.642575 | − | 0.321288i | ||||
\(156\) | −2.00000 | −0.160128 | ||||||||
\(157\) | − | 18.0000i | − | 1.43656i | −0.695756 | − | 0.718278i | \(-0.744931\pi\) | ||
0.695756 | − | 0.718278i | \(-0.255069\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −4.00000 | −0.317221 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1.00000 | −0.0788110 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 4.00000i | − | 0.313304i | −0.987654 | − | 0.156652i | \(-0.949930\pi\) | ||
0.987654 | − | 0.156652i | \(-0.0500701\pi\) | |||||||
\(164\) | −12.0000 | −0.937043 | ||||||||
\(165\) | −1.00000 | − | 2.00000i | −0.0778499 | − | 0.155700i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 3.00000i | 0.232147i | 0.993241 | + | 0.116073i | \(0.0370308\pi\) | ||||
−0.993241 | + | 0.116073i | \(0.962969\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 12.0000 | 0.923077 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −4.00000 | −0.305888 | ||||||||
\(172\) | − | 16.0000i | − | 1.21999i | ||||||
\(173\) | 7.00000i | 0.532200i | 0.963945 | + | 0.266100i | \(0.0857352\pi\) | ||||
−0.963945 | + | 0.266100i | \(0.914265\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 4.00000 | + | 3.00000i | 0.302372 | + | 0.226779i | ||||
\(176\) | −4.00000 | −0.301511 | ||||||||
\(177\) | 4.00000i | 0.300658i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 4.00000 | 0.298974 | 0.149487 | − | 0.988764i | \(-0.452238\pi\) | ||||
0.149487 | + | 0.988764i | \(0.452238\pi\) | |||||||
\(180\) | 8.00000 | − | 4.00000i | 0.596285 | − | 0.298142i | ||||
\(181\) | −16.0000 | −1.18927 | −0.594635 | − | 0.803996i | \(-0.702704\pi\) | ||||
−0.594635 | + | 0.803996i | \(0.702704\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 10.0000i | − | 0.739221i | ||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −8.00000 | − | 16.0000i | −0.588172 | − | 1.17634i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.00000i | 0.0731272i | ||||||||
\(188\) | 14.0000i | 1.02105i | ||||||||
\(189\) | −5.00000 | −0.363696 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −25.0000 | −1.80894 | −0.904468 | − | 0.426541i | \(-0.859732\pi\) | ||||
−0.904468 | + | 0.426541i | \(0.859732\pi\) | |||||||
\(192\) | 8.00000i | 0.577350i | ||||||||
\(193\) | − | 14.0000i | − | 1.00774i | −0.863779 | − | 0.503871i | \(-0.831909\pi\) | ||
0.863779 | − | 0.503871i | \(-0.168091\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −2.00000 | + | 1.00000i | −0.143223 | + | 0.0716115i | ||||
\(196\) | −2.00000 | −0.142857 | ||||||||
\(197\) | − | 18.0000i | − | 1.28245i | −0.767354 | − | 0.641223i | \(-0.778427\pi\) | ||
0.767354 | − | 0.641223i | \(-0.221573\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −12.0000 | −0.850657 | −0.425329 | − | 0.905039i | \(-0.639842\pi\) | ||||
−0.425329 | + | 0.905039i | \(0.639842\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −14.0000 | −0.987484 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − | 7.00000i | − | 0.491304i | ||||||
\(204\) | 2.00000 | 0.140028 | ||||||||
\(205\) | −12.0000 | + | 6.00000i | −0.838116 | + | 0.419058i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 2.00000i | 0.139010i | ||||||||
\(208\) | 4.00000i | 0.277350i | ||||||||
\(209\) | 2.00000 | 0.138343 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −5.00000 | −0.344214 | −0.172107 | − | 0.985078i | \(-0.555058\pi\) | ||||
−0.172107 | + | 0.985078i | \(0.555058\pi\) | |||||||
\(212\) | 8.00000i | 0.549442i | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −8.00000 | − | 16.0000i | −0.545595 | − | 1.09119i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 4.00000i | 0.271538i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −2.00000 | −0.135147 | ||||||||
\(220\) | −4.00000 | + | 2.00000i | −0.269680 | + | 0.134840i | ||||
\(221\) | 1.00000 | 0.0672673 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 25.0000i | 1.67412i | 0.547108 | + | 0.837062i | \(0.315729\pi\) | ||||
−0.547108 | + | 0.837062i | \(0.684271\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 6.00000 | − | 8.00000i | 0.400000 | − | 0.533333i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − | 15.0000i | − | 0.995585i | −0.867296 | − | 0.497792i | \(-0.834144\pi\) | ||
0.867296 | − | 0.497792i | \(-0.165856\pi\) | |||||||
\(228\) | − | 4.00000i | − | 0.264906i | ||||||
\(229\) | 14.0000 | 0.925146 | 0.462573 | − | 0.886581i | \(-0.346926\pi\) | ||||
0.462573 | + | 0.886581i | \(0.346926\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1.00000 | 0.0657952 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 10.0000i | 0.655122i | 0.944830 | + | 0.327561i | \(0.106227\pi\) | ||||
−0.944830 | + | 0.327561i | \(0.893773\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 7.00000 | + | 14.0000i | 0.456630 | + | 0.913259i | ||||
\(236\) | 8.00000 | 0.520756 | ||||||||
\(237\) | 15.0000i | 0.974355i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 9.00000 | 0.582162 | 0.291081 | − | 0.956698i | \(-0.405985\pi\) | ||||
0.291081 | + | 0.956698i | \(0.405985\pi\) | |||||||
\(240\) | 4.00000 | + | 8.00000i | 0.258199 | + | 0.516398i | ||||
\(241\) | 10.0000 | 0.644157 | 0.322078 | − | 0.946713i | \(-0.395619\pi\) | ||||
0.322078 | + | 0.946713i | \(0.395619\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 16.0000i | 1.02640i | ||||||||
\(244\) | −20.0000 | −1.28037 | ||||||||
\(245\) | −2.00000 | + | 1.00000i | −0.127775 | + | 0.0638877i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 2.00000i | − | 0.127257i | ||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 8.00000 | 0.506979 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −12.0000 | −0.757433 | −0.378717 | − | 0.925513i | \(-0.623635\pi\) | ||||
−0.378717 | + | 0.925513i | \(0.623635\pi\) | |||||||
\(252\) | 4.00000i | 0.251976i | ||||||||
\(253\) | − | 1.00000i | − | 0.0628695i | ||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 2.00000 | − | 1.00000i | 0.125245 | − | 0.0626224i | ||||
\(256\) | 16.0000 | 1.00000 | ||||||||
\(257\) | 18.0000i | 1.12281i | 0.827541 | + | 0.561405i | \(0.189739\pi\) | ||||
−0.827541 | + | 0.561405i | \(0.810261\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 8.00000 | 0.497096 | ||||||||
\(260\) | 2.00000 | + | 4.00000i | 0.124035 | + | 0.248069i | ||||
\(261\) | −14.0000 | −0.866578 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 2.00000i | 0.123325i | 0.998097 | + | 0.0616626i | \(0.0196403\pi\) | ||||
−0.998097 | + | 0.0616626i | \(0.980360\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 4.00000 | + | 8.00000i | 0.245718 | + | 0.491436i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − | 6.00000i | − | 0.367194i | ||||||
\(268\) | 28.0000i | 1.71037i | ||||||||
\(269\) | 6.00000 | 0.365826 | 0.182913 | − | 0.983129i | \(-0.441447\pi\) | ||||
0.182913 | + | 0.983129i | \(0.441447\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 10.0000 | 0.607457 | 0.303728 | − | 0.952759i | \(-0.401768\pi\) | ||||
0.303728 | + | 0.952759i | \(0.401768\pi\) | |||||||
\(272\) | − | 4.00000i | − | 0.242536i | ||||||
\(273\) | − | 1.00000i | − | 0.0605228i | ||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −3.00000 | + | 4.00000i | −0.180907 | + | 0.241209i | ||||
\(276\) | −2.00000 | −0.120386 | ||||||||
\(277\) | − | 24.0000i | − | 1.44202i | −0.692925 | − | 0.721010i | \(-0.743678\pi\) | ||
0.692925 | − | 0.721010i | \(-0.256322\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 8.00000 | 0.478947 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 9.00000 | 0.536895 | 0.268447 | − | 0.963294i | \(-0.413489\pi\) | ||||
0.268447 | + | 0.963294i | \(0.413489\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 17.0000i | 1.01055i | 0.862960 | + | 0.505273i | \(0.168608\pi\) | ||||
−0.862960 | + | 0.505273i | \(0.831392\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −2.00000 | − | 4.00000i | −0.118470 | − | 0.236940i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 6.00000i | − | 0.354169i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 16.0000 | 0.941176 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −7.00000 | −0.410347 | ||||||||
\(292\) | 4.00000i | 0.234082i | ||||||||
\(293\) | − | 27.0000i | − | 1.57736i | −0.614806 | − | 0.788678i | \(-0.710766\pi\) | ||
0.614806 | − | 0.788678i | \(-0.289234\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 8.00000 | − | 4.00000i | 0.465778 | − | 0.232889i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − | 5.00000i | − | 0.290129i | ||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −1.00000 | −0.0578315 | ||||||||
\(300\) | 8.00000 | + | 6.00000i | 0.461880 | + | 0.346410i | ||||
\(301\) | 8.00000 | 0.461112 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − | 4.00000i | − | 0.229794i | ||||||
\(304\) | −8.00000 | −0.458831 | ||||||||
\(305\) | −20.0000 | + | 10.0000i | −1.14520 | + | 0.572598i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 9.00000i | 0.513657i | 0.966457 | + | 0.256829i | \(0.0826776\pi\) | ||||
−0.966457 | + | 0.256829i | \(0.917322\pi\) | |||||||
\(308\) | − | 2.00000i | − | 0.113961i | ||||||
\(309\) | −7.00000 | −0.398216 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −18.0000 | −1.02069 | −0.510343 | − | 0.859971i | \(-0.670482\pi\) | ||||
−0.510343 | + | 0.859971i | \(0.670482\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 9.00000i | − | 0.508710i | −0.967111 | − | 0.254355i | \(-0.918137\pi\) | ||
0.967111 | − | 0.254355i | \(-0.0818632\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 2.00000 | + | 4.00000i | 0.112687 | + | 0.225374i | ||||
\(316\) | 30.0000 | 1.68763 | ||||||||
\(317\) | 6.00000i | 0.336994i | 0.985702 | + | 0.168497i | \(0.0538913\pi\) | ||||
−0.985702 | + | 0.168497i | \(0.946109\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 7.00000 | 0.391925 | ||||||||
\(320\) | 16.0000 | − | 8.00000i | 0.894427 | − | 0.447214i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 2.00000i | 0.111283i | ||||||||
\(324\) | 2.00000 | 0.111111 | ||||||||
\(325\) | 4.00000 | + | 3.00000i | 0.221880 | + | 0.166410i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 5.00000i | 0.276501i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −7.00000 | −0.385922 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −4.00000 | −0.219860 | −0.109930 | − | 0.993939i | \(-0.535063\pi\) | ||||
−0.109930 | + | 0.993939i | \(0.535063\pi\) | |||||||
\(332\) | − | 16.0000i | − | 0.878114i | ||||||
\(333\) | − | 16.0000i | − | 0.876795i | ||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 14.0000 | + | 28.0000i | 0.764902 | + | 1.52980i | ||||
\(336\) | −4.00000 | −0.218218 | ||||||||
\(337\) | 10.0000i | 0.544735i | 0.962193 | + | 0.272367i | \(0.0878066\pi\) | ||||
−0.962193 | + | 0.272367i | \(0.912193\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 18.0000 | 0.977626 | ||||||||
\(340\) | −2.00000 | − | 4.00000i | −0.108465 | − | 0.216930i | ||||
\(341\) | −4.00000 | −0.216612 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 1.00000i | − | 0.0539949i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −2.00000 | + | 1.00000i | −0.107676 | + | 0.0538382i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − | 8.00000i | − | 0.429463i | −0.976673 | − | 0.214731i | \(-0.931112\pi\) | ||
0.976673 | − | 0.214731i | \(-0.0688876\pi\) | |||||||
\(348\) | − | 14.0000i | − | 0.750479i | ||||||
\(349\) | 10.0000 | 0.535288 | 0.267644 | − | 0.963518i | \(-0.413755\pi\) | ||||
0.267644 | + | 0.963518i | \(0.413755\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −5.00000 | −0.266880 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 9.00000i | − | 0.479022i | −0.970894 | − | 0.239511i | \(-0.923013\pi\) | ||
0.970894 | − | 0.239511i | \(-0.0769871\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −12.0000 | −0.635999 | ||||||||
\(357\) | 1.00000i | 0.0529256i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −15.0000 | −0.789474 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − | 10.0000i | − | 0.524864i | ||||||
\(364\) | −2.00000 | −0.104828 | ||||||||
\(365\) | 2.00000 | + | 4.00000i | 0.104685 | + | 0.209370i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 23.0000i | − | 1.20059i | −0.799779 | − | 0.600295i | \(-0.795050\pi\) | ||
0.799779 | − | 0.600295i | \(-0.204950\pi\) | |||||||
\(368\) | 4.00000i | 0.208514i | ||||||||
\(369\) | −12.0000 | −0.624695 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −4.00000 | −0.207670 | ||||||||
\(372\) | 8.00000i | 0.414781i | ||||||||
\(373\) | 14.0000i | 0.724893i | 0.932005 | + | 0.362446i | \(0.118058\pi\) | ||||
−0.932005 | + | 0.362446i | \(0.881942\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 11.0000 | + | 2.00000i | 0.568038 | + | 0.103280i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 7.00000i | − | 0.360518i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 28.0000 | 1.43826 | 0.719132 | − | 0.694874i | \(-0.244540\pi\) | ||||
0.719132 | + | 0.694874i | \(0.244540\pi\) | |||||||
\(380\) | −8.00000 | + | 4.00000i | −0.410391 | + | 0.205196i | ||||
\(381\) | 2.00000 | 0.102463 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1.00000 | − | 2.00000i | −0.0509647 | − | 0.101929i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − | 16.0000i | − | 0.813326i | ||||||
\(388\) | 14.0000i | 0.710742i | ||||||||
\(389\) | 29.0000 | 1.47036 | 0.735179 | − | 0.677873i | \(-0.237098\pi\) | ||||
0.735179 | + | 0.677873i | \(0.237098\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.00000 | 0.0505722 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 20.0000i | − | 1.00887i | ||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 30.0000 | − | 15.0000i | 1.50946 | − | 0.754732i | ||||
\(396\) | −4.00000 | −0.201008 | ||||||||
\(397\) | 33.0000i | 1.65622i | 0.560564 | + | 0.828111i | \(0.310584\pi\) | ||||
−0.560564 | + | 0.828111i | \(0.689416\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 2.00000 | 0.100125 | ||||||||
\(400\) | 12.0000 | − | 16.0000i | 0.600000 | − | 0.800000i | ||||
\(401\) | −5.00000 | −0.249688 | −0.124844 | − | 0.992176i | \(-0.539843\pi\) | ||||
−0.124844 | + | 0.992176i | \(0.539843\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 4.00000i | 0.199254i | ||||||||
\(404\) | −8.00000 | −0.398015 | ||||||||
\(405\) | 2.00000 | − | 1.00000i | 0.0993808 | − | 0.0496904i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 8.00000i | 0.396545i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −4.00000 | −0.197787 | −0.0988936 | − | 0.995098i | \(-0.531530\pi\) | ||||
−0.0988936 | + | 0.995098i | \(0.531530\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 10.0000 | 0.493264 | ||||||||
\(412\) | 14.0000i | 0.689730i | ||||||||
\(413\) | 4.00000i | 0.196827i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −8.00000 | − | 16.0000i | −0.392705 | − | 0.785409i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | − | 4.00000i | − | 0.195881i | ||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −12.0000 | −0.586238 | −0.293119 | − | 0.956076i | \(-0.594693\pi\) | ||||
−0.293119 | + | 0.956076i | \(0.594693\pi\) | |||||||
\(420\) | −4.00000 | + | 2.00000i | −0.195180 | + | 0.0975900i | ||||
\(421\) | −5.00000 | −0.243685 | −0.121843 | − | 0.992549i | \(-0.538880\pi\) | ||||
−0.121843 | + | 0.992549i | \(0.538880\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 14.0000i | 0.680703i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −4.00000 | − | 3.00000i | −0.194029 | − | 0.145521i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 10.0000i | − | 0.483934i | ||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 1.00000 | 0.0482805 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 11.0000 | 0.529851 | 0.264926 | − | 0.964269i | \(-0.414653\pi\) | ||||
0.264926 | + | 0.964269i | \(0.414653\pi\) | |||||||
\(432\) | 20.0000i | 0.962250i | ||||||||
\(433\) | 30.0000i | 1.44171i | 0.693087 | + | 0.720854i | \(0.256250\pi\) | ||||
−0.693087 | + | 0.720854i | \(0.743750\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −7.00000 | − | 14.0000i | −0.335624 | − | 0.671249i | ||||
\(436\) | 10.0000 | 0.478913 | ||||||||
\(437\) | − | 2.00000i | − | 0.0956730i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 34.0000 | 1.62273 | 0.811366 | − | 0.584539i | \(-0.198725\pi\) | ||||
0.811366 | + | 0.584539i | \(0.198725\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2.00000 | −0.0952381 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 40.0000i | 1.90046i | 0.311553 | + | 0.950229i | \(0.399151\pi\) | ||||
−0.311553 | + | 0.950229i | \(0.600849\pi\) | |||||||
\(444\) | 16.0000 | 0.759326 | ||||||||
\(445\) | −12.0000 | + | 6.00000i | −0.568855 | + | 0.284427i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − | 14.0000i | − | 0.662177i | ||||||
\(448\) | 8.00000i | 0.377964i | ||||||||
\(449\) | −15.0000 | −0.707894 | −0.353947 | − | 0.935266i | \(-0.615161\pi\) | ||||
−0.353947 | + | 0.935266i | \(0.615161\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 6.00000 | 0.282529 | ||||||||
\(452\) | − | 36.0000i | − | 1.69330i | ||||||
\(453\) | − | 1.00000i | − | 0.0469841i | ||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −2.00000 | + | 1.00000i | −0.0937614 | + | 0.0468807i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 2.00000i | − | 0.0935561i | −0.998905 | − | 0.0467780i | \(-0.985105\pi\) | ||
0.998905 | − | 0.0467780i | \(-0.0148953\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 5.00000 | 0.233380 | ||||||||
\(460\) | 2.00000 | + | 4.00000i | 0.0932505 | + | 0.186501i | ||||
\(461\) | 28.0000 | 1.30409 | 0.652045 | − | 0.758180i | \(-0.273911\pi\) | ||||
0.652045 | + | 0.758180i | \(0.273911\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 30.0000i | − | 1.39422i | −0.716965 | − | 0.697109i | \(-0.754469\pi\) | ||
0.716965 | − | 0.697109i | \(-0.245531\pi\) | |||||||
\(464\) | −28.0000 | −1.29987 | ||||||||
\(465\) | 4.00000 | + | 8.00000i | 0.185496 | + | 0.370991i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 27.0000i | 1.24941i | 0.780860 | + | 0.624705i | \(0.214781\pi\) | ||||
−0.780860 | + | 0.624705i | \(0.785219\pi\) | |||||||
\(468\) | 4.00000i | 0.184900i | ||||||||
\(469\) | −14.0000 | −0.646460 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 18.0000 | 0.829396 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 8.00000i | 0.367840i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −6.00000 | + | 8.00000i | −0.275299 | + | 0.367065i | ||||
\(476\) | 2.00000 | 0.0916698 | ||||||||
\(477\) | 8.00000i | 0.366295i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 10.0000 | 0.456912 | 0.228456 | − | 0.973554i | \(-0.426632\pi\) | ||||
0.228456 | + | 0.973554i | \(0.426632\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 8.00000 | 0.364769 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | − | 1.00000i | − | 0.0455016i | ||||||
\(484\) | −20.0000 | −0.909091 | ||||||||
\(485\) | 7.00000 | + | 14.0000i | 0.317854 | + | 0.635707i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 14.0000i | 0.634401i | 0.948359 | + | 0.317200i | \(0.102743\pi\) | ||||
−0.948359 | + | 0.317200i | \(0.897257\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 4.00000 | 0.180886 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 15.0000 | 0.676941 | 0.338470 | − | 0.940977i | \(-0.390091\pi\) | ||||
0.338470 | + | 0.940977i | \(0.390091\pi\) | |||||||
\(492\) | − | 12.0000i | − | 0.541002i | ||||||
\(493\) | 7.00000i | 0.315264i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −4.00000 | + | 2.00000i | −0.179787 | + | 0.0898933i | ||||
\(496\) | 16.0000 | 0.718421 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −25.0000 | −1.11915 | −0.559577 | − | 0.828778i | \(-0.689036\pi\) | ||||
−0.559577 | + | 0.828778i | \(0.689036\pi\) | |||||||
\(500\) | 4.00000 | − | 22.0000i | 0.178885 | − | 0.983870i | ||||
\(501\) | −3.00000 | −0.134030 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 5.00000i | 0.222939i | 0.993768 | + | 0.111469i | \(0.0355557\pi\) | ||||
−0.993768 | + | 0.111469i | \(0.964444\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −8.00000 | + | 4.00000i | −0.355995 | + | 0.177998i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 12.0000i | 0.532939i | ||||||||
\(508\) | − | 4.00000i | − | 0.177471i | ||||||
\(509\) | 8.00000 | 0.354594 | 0.177297 | − | 0.984157i | \(-0.443265\pi\) | ||||
0.177297 | + | 0.984157i | \(0.443265\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −2.00000 | −0.0884748 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | − | 10.0000i | − | 0.441511i | ||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 7.00000 | + | 14.0000i | 0.308457 | + | 0.616914i | ||||
\(516\) | 16.0000 | 0.704361 | ||||||||
\(517\) | − | 7.00000i | − | 0.307860i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −7.00000 | −0.307266 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 12.0000 | 0.525730 | 0.262865 | − | 0.964833i | \(-0.415333\pi\) | ||||
0.262865 | + | 0.964833i | \(0.415333\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 24.0000i | − | 1.04945i | −0.851273 | − | 0.524723i | \(-0.824169\pi\) | ||
0.851273 | − | 0.524723i | \(-0.175831\pi\) | |||||||
\(524\) | −40.0000 | −1.74741 | ||||||||
\(525\) | −3.00000 | + | 4.00000i | −0.130931 | + | 0.174574i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 4.00000i | − | 0.174243i | ||||||
\(528\) | − | 4.00000i | − | 0.174078i | ||||||
\(529\) | −1.00000 | −0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 8.00000 | 0.347170 | ||||||||
\(532\) | − | 4.00000i | − | 0.173422i | ||||||
\(533\) | − | 6.00000i | − | 0.259889i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 4.00000i | 0.172613i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1.00000 | 0.0430730 | ||||||||
\(540\) | 10.0000 | + | 20.0000i | 0.430331 | + | 0.860663i | ||||
\(541\) | 43.0000 | 1.84871 | 0.924357 | − | 0.381528i | \(-0.124602\pi\) | ||||
0.924357 | + | 0.381528i | \(0.124602\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − | 16.0000i | − | 0.686626i | ||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 10.0000 | − | 5.00000i | 0.428353 | − | 0.214176i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 38.0000i | 1.62476i | 0.583127 | + | 0.812381i | \(0.301829\pi\) | ||||
−0.583127 | + | 0.812381i | \(0.698171\pi\) | |||||||
\(548\) | − | 20.0000i | − | 0.854358i | ||||||
\(549\) | −20.0000 | −0.853579 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 14.0000 | 0.596420 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 15.0000i | 0.637865i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 16.0000 | − | 8.00000i | 0.679162 | − | 0.339581i | ||||
\(556\) | −8.00000 | −0.339276 | ||||||||
\(557\) | 42.0000i | 1.77960i | 0.456354 | + | 0.889799i | \(0.349155\pi\) | ||||
−0.456354 | + | 0.889799i | \(0.650845\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 8.00000 | 0.338364 | ||||||||
\(560\) | 4.00000 | + | 8.00000i | 0.169031 | + | 0.338062i | ||||
\(561\) | −1.00000 | −0.0422200 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − | 4.00000i | − | 0.168580i | −0.996441 | − | 0.0842900i | \(-0.973138\pi\) | ||
0.996441 | − | 0.0842900i | \(-0.0268622\pi\) | |||||||
\(564\) | −14.0000 | −0.589506 | ||||||||
\(565\) | −18.0000 | − | 36.0000i | −0.757266 | − | 1.51453i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 1.00000i | 0.0419961i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 10.0000 | 0.419222 | 0.209611 | − | 0.977785i | \(-0.432780\pi\) | ||||
0.209611 | + | 0.977785i | \(0.432780\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −36.0000 | −1.50655 | −0.753277 | − | 0.657704i | \(-0.771528\pi\) | ||||
−0.753277 | + | 0.657704i | \(0.771528\pi\) | |||||||
\(572\) | − | 2.00000i | − | 0.0836242i | ||||||
\(573\) | − | 25.0000i | − | 1.04439i | ||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 4.00000 | + | 3.00000i | 0.166812 | + | 0.125109i | ||||
\(576\) | 16.0000 | 0.666667 | ||||||||
\(577\) | 3.00000i | 0.124892i | 0.998048 | + | 0.0624458i | \(0.0198901\pi\) | ||||
−0.998048 | + | 0.0624458i | \(0.980110\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 14.0000 | 0.581820 | ||||||||
\(580\) | −28.0000 | + | 14.0000i | −1.16264 | + | 0.581318i | ||||
\(581\) | 8.00000 | 0.331896 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 4.00000i | − | 0.165663i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 2.00000 | + | 4.00000i | 0.0826898 | + | 0.165380i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 28.0000i | 1.15568i | 0.816149 | + | 0.577842i | \(0.196105\pi\) | ||||
−0.816149 | + | 0.577842i | \(0.803895\pi\) | |||||||
\(588\) | − | 2.00000i | − | 0.0824786i | ||||||
\(589\) | −8.00000 | −0.329634 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 18.0000 | 0.740421 | ||||||||
\(592\) | − | 32.0000i | − | 1.31519i | ||||||
\(593\) | 37.0000i | 1.51941i | 0.650269 | + | 0.759704i | \(0.274656\pi\) | ||||
−0.650269 | + | 0.759704i | \(0.725344\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 2.00000 | − | 1.00000i | 0.0819920 | − | 0.0409960i | ||||
\(596\) | −28.0000 | −1.14692 | ||||||||
\(597\) | − | 12.0000i | − | 0.491127i | ||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −25.0000 | −1.02147 | −0.510736 | − | 0.859738i | \(-0.670627\pi\) | ||||
−0.510736 | + | 0.859738i | \(0.670627\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 10.0000 | 0.407909 | 0.203954 | − | 0.978980i | \(-0.434621\pi\) | ||||
0.203954 | + | 0.978980i | \(0.434621\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 28.0000i | 1.14025i | ||||||||
\(604\) | −2.00000 | −0.0813788 | ||||||||
\(605\) | −20.0000 | + | 10.0000i | −0.813116 | + | 0.406558i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 25.0000i | 1.01472i | 0.861735 | + | 0.507359i | \(0.169378\pi\) | ||||
−0.861735 | + | 0.507359i | \(0.830622\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 7.00000 | 0.283654 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −7.00000 | −0.283190 | ||||||||
\(612\) | − | 4.00000i | − | 0.161690i | ||||||
\(613\) | 46.0000i | 1.85792i | 0.370177 | + | 0.928961i | \(0.379297\pi\) | ||||
−0.370177 | + | 0.928961i | \(0.620703\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −6.00000 | − | 12.0000i | −0.241943 | − | 0.483887i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 28.0000i | − | 1.12724i | −0.826035 | − | 0.563619i | \(-0.809409\pi\) | ||
0.826035 | − | 0.563619i | \(-0.190591\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −22.0000 | −0.884255 | −0.442127 | − | 0.896952i | \(-0.645776\pi\) | ||||
−0.442127 | + | 0.896952i | \(0.645776\pi\) | |||||||
\(620\) | 16.0000 | − | 8.00000i | 0.642575 | − | 0.321288i | ||||
\(621\) | −5.00000 | −0.200643 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − | 6.00000i | − | 0.240385i | ||||||
\(624\) | −4.00000 | −0.160128 | ||||||||
\(625\) | −7.00000 | − | 24.0000i | −0.280000 | − | 0.960000i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 2.00000i | 0.0798723i | ||||||||
\(628\) | − | 36.0000i | − | 1.43656i | ||||||
\(629\) | −8.00000 | −0.318981 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 7.00000 | 0.278666 | 0.139333 | − | 0.990246i | \(-0.455504\pi\) | ||||
0.139333 | + | 0.990246i | \(0.455504\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | − | 5.00000i | − | 0.198732i | ||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −2.00000 | − | 4.00000i | −0.0793676 | − | 0.158735i | ||||
\(636\) | −8.00000 | −0.317221 | ||||||||
\(637\) | − | 1.00000i | − | 0.0396214i | ||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −18.0000 | −0.710957 | −0.355479 | − | 0.934684i | \(-0.615682\pi\) | ||||
−0.355479 | + | 0.934684i | \(0.615682\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 49.0000i | − | 1.93237i | −0.257847 | − | 0.966186i | \(-0.583013\pi\) | ||
0.257847 | − | 0.966186i | \(-0.416987\pi\) | |||||||
\(644\) | −2.00000 | −0.0788110 | ||||||||
\(645\) | 16.0000 | − | 8.00000i | 0.629999 | − | 0.315000i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 48.0000i | − | 1.88707i | −0.331266 | − | 0.943537i | \(-0.607476\pi\) | ||
0.331266 | − | 0.943537i | \(-0.392524\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −4.00000 | −0.157014 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −4.00000 | −0.156772 | ||||||||
\(652\) | − | 8.00000i | − | 0.313304i | ||||||
\(653\) | 6.00000i | 0.234798i | 0.993085 | + | 0.117399i | \(0.0374557\pi\) | ||||
−0.993085 | + | 0.117399i | \(0.962544\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −40.0000 | + | 20.0000i | −1.56293 | + | 0.781465i | ||||
\(656\) | −24.0000 | −0.937043 | ||||||||
\(657\) | 4.00000i | 0.156055i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 41.0000 | 1.59713 | 0.798567 | − | 0.601906i | \(-0.205592\pi\) | ||||
0.798567 | + | 0.601906i | \(0.205592\pi\) | |||||||
\(660\) | −2.00000 | − | 4.00000i | −0.0778499 | − | 0.155700i | ||||
\(661\) | 20.0000 | 0.777910 | 0.388955 | − | 0.921257i | \(-0.372836\pi\) | ||||
0.388955 | + | 0.921257i | \(0.372836\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 1.00000i | 0.0388368i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −2.00000 | − | 4.00000i | −0.0775567 | − | 0.155113i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 7.00000i | − | 0.271041i | ||||||
\(668\) | 6.00000i | 0.232147i | ||||||||
\(669\) | −25.0000 | −0.966556 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 10.0000 | 0.386046 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 20.0000 | + | 15.0000i | 0.769800 | + | 0.577350i | ||||
\(676\) | 24.0000 | 0.923077 | ||||||||
\(677\) | 21.0000i | 0.807096i | 0.914959 | + | 0.403548i | \(0.132223\pi\) | ||||
−0.914959 | + | 0.403548i | \(0.867777\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −7.00000 | −0.268635 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 15.0000 | 0.574801 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 12.0000i | 0.459167i | 0.973289 | + | 0.229584i | \(0.0737364\pi\) | ||||
−0.973289 | + | 0.229584i | \(0.926264\pi\) | |||||||
\(684\) | −8.00000 | −0.305888 | ||||||||
\(685\) | −10.0000 | − | 20.0000i | −0.382080 | − | 0.764161i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 14.0000i | 0.534133i | ||||||||
\(688\) | − | 32.0000i | − | 1.21999i | ||||||
\(689\) | −4.00000 | −0.152388 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 18.0000 | 0.684752 | 0.342376 | − | 0.939563i | \(-0.388768\pi\) | ||||
0.342376 | + | 0.939563i | \(0.388768\pi\) | |||||||
\(692\) | 14.0000i | 0.532200i | ||||||||
\(693\) | − | 2.00000i | − | 0.0759737i | ||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −8.00000 | + | 4.00000i | −0.303457 | + | 0.151729i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 6.00000i | 0.227266i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −10.0000 | −0.378235 | ||||||||
\(700\) | 8.00000 | + | 6.00000i | 0.302372 | + | 0.226779i | ||||
\(701\) | −15.0000 | −0.566542 | −0.283271 | − | 0.959040i | \(-0.591420\pi\) | ||||
−0.283271 | + | 0.959040i | \(0.591420\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 16.0000i | 0.603451i | ||||||||
\(704\) | −8.00000 | −0.301511 | ||||||||
\(705\) | −14.0000 | + | 7.00000i | −0.527271 | + | 0.263635i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − | 4.00000i | − | 0.150435i | ||||||
\(708\) | 8.00000i | 0.300658i | ||||||||
\(709\) | 19.0000 | 0.713560 | 0.356780 | − | 0.934188i | \(-0.383875\pi\) | ||||
0.356780 | + | 0.934188i | \(0.383875\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 30.0000 | 1.12509 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 4.00000i | 0.149801i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1.00000 | − | 2.00000i | −0.0373979 | − | 0.0747958i | ||||
\(716\) | 8.00000 | 0.298974 | ||||||||
\(717\) | 9.00000i | 0.336111i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −30.0000 | −1.11881 | −0.559406 | − | 0.828894i | \(-0.688971\pi\) | ||||
−0.559406 | + | 0.828894i | \(0.688971\pi\) | |||||||
\(720\) | 16.0000 | − | 8.00000i | 0.596285 | − | 0.298142i | ||||
\(721\) | −7.00000 | −0.260694 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 10.0000i | 0.371904i | ||||||||
\(724\) | −32.0000 | −1.18927 | ||||||||
\(725\) | −21.0000 | + | 28.0000i | −0.779920 | + | 1.03989i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 8.00000i | 0.296704i | 0.988935 | + | 0.148352i | \(0.0473968\pi\) | ||||
−0.988935 | + | 0.148352i | \(0.952603\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −13.0000 | −0.481481 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −8.00000 | −0.295891 | ||||||||
\(732\) | − | 20.0000i | − | 0.739221i | ||||||
\(733\) | 3.00000i | 0.110808i | 0.998464 | + | 0.0554038i | \(0.0176446\pi\) | ||||
−0.998464 | + | 0.0554038i | \(0.982355\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −1.00000 | − | 2.00000i | −0.0368856 | − | 0.0737711i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 14.0000i | − | 0.515697i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 43.0000 | 1.58178 | 0.790890 | − | 0.611958i | \(-0.209618\pi\) | ||||
0.790890 | + | 0.611958i | \(0.209618\pi\) | |||||||
\(740\) | −16.0000 | − | 32.0000i | −0.588172 | − | 1.17634i | ||||
\(741\) | 2.00000 | 0.0734718 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 24.0000i | − | 0.880475i | −0.897881 | − | 0.440237i | \(-0.854894\pi\) | ||
0.897881 | − | 0.440237i | \(-0.145106\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −28.0000 | + | 14.0000i | −1.02584 | + | 0.512920i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − | 16.0000i | − | 0.585409i | ||||||
\(748\) | 2.00000i | 0.0731272i | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −7.00000 | −0.255434 | −0.127717 | − | 0.991811i | \(-0.540765\pi\) | ||||
−0.127717 | + | 0.991811i | \(0.540765\pi\) | |||||||
\(752\) | 28.0000i | 1.02105i | ||||||||
\(753\) | − | 12.0000i | − | 0.437304i | ||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −2.00000 | + | 1.00000i | −0.0727875 | + | 0.0363937i | ||||
\(756\) | −10.0000 | −0.363696 | ||||||||
\(757\) | 8.00000i | 0.290765i | 0.989376 | + | 0.145382i | \(0.0464413\pi\) | ||||
−0.989376 | + | 0.145382i | \(0.953559\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 1.00000 | 0.0362977 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −28.0000 | −1.01500 | −0.507500 | − | 0.861652i | \(-0.669430\pi\) | ||||
−0.507500 | + | 0.861652i | \(0.669430\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 5.00000i | 0.181012i | ||||||||
\(764\) | −50.0000 | −1.80894 | ||||||||
\(765\) | −2.00000 | − | 4.00000i | −0.0723102 | − | 0.144620i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 4.00000i | 0.144432i | ||||||||
\(768\) | 16.0000i | 0.577350i | ||||||||
\(769\) | 2.00000 | 0.0721218 | 0.0360609 | − | 0.999350i | \(-0.488519\pi\) | ||||
0.0360609 | + | 0.999350i | \(0.488519\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −18.0000 | −0.648254 | ||||||||
\(772\) | − | 28.0000i | − | 1.00774i | ||||||
\(773\) | − | 49.0000i | − | 1.76241i | −0.472737 | − | 0.881204i | \(-0.656734\pi\) | ||
0.472737 | − | 0.881204i | \(-0.343266\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 12.0000 | − | 16.0000i | 0.431053 | − | 0.574737i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 8.00000i | 0.286998i | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 12.0000 | 0.429945 | ||||||||
\(780\) | −4.00000 | + | 2.00000i | −0.143223 | + | 0.0716115i | ||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − | 35.0000i | − | 1.25080i | ||||||
\(784\) | −4.00000 | −0.142857 | ||||||||
\(785\) | −18.0000 | − | 36.0000i | −0.642448 | − | 1.28490i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 35.0000i | − | 1.24762i | −0.781578 | − | 0.623808i | \(-0.785585\pi\) | ||
0.781578 | − | 0.623808i | \(-0.214415\pi\) | |||||||
\(788\) | − | 36.0000i | − | 1.28245i | ||||||
\(789\) | −2.00000 | −0.0712019 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 18.0000 | 0.640006 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 10.0000i | − | 0.355110i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −8.00000 | + | 4.00000i | −0.283731 | + | 0.141865i | ||||
\(796\) | −24.0000 | −0.850657 | ||||||||
\(797\) | − | 17.0000i | − | 0.602171i | −0.953597 | − | 0.301085i | \(-0.902651\pi\) | ||
0.953597 | − | 0.301085i | \(-0.0973489\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 7.00000 | 0.247642 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −12.0000 | −0.423999 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − | 2.00000i | − | 0.0705785i | ||||||
\(804\) | −28.0000 | −0.987484 | ||||||||
\(805\) | −2.00000 | + | 1.00000i | −0.0704907 | + | 0.0352454i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 6.00000i | 0.211210i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −9.00000 | −0.316423 | −0.158212 | − | 0.987405i | \(-0.550573\pi\) | ||||
−0.158212 | + | 0.987405i | \(0.550573\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −2.00000 | −0.0702295 | −0.0351147 | − | 0.999383i | \(-0.511180\pi\) | ||||
−0.0351147 | + | 0.999383i | \(0.511180\pi\) | |||||||
\(812\) | − | 14.0000i | − | 0.491304i | ||||||
\(813\) | 10.0000i | 0.350715i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −4.00000 | − | 8.00000i | −0.140114 | − | 0.280228i | ||||
\(816\) | 4.00000 | 0.140028 | ||||||||
\(817\) | 16.0000i | 0.559769i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −2.00000 | −0.0698857 | ||||||||
\(820\) | −24.0000 | + | 12.0000i | −0.838116 | + | 0.419058i | ||||
\(821\) | −47.0000 | −1.64031 | −0.820156 | − | 0.572140i | \(-0.806113\pi\) | ||||
−0.820156 | + | 0.572140i | \(0.806113\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 28.0000i | 0.976019i | 0.872838 | + | 0.488009i | \(0.162277\pi\) | ||||
−0.872838 | + | 0.488009i | \(0.837723\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −4.00000 | − | 3.00000i | −0.139262 | − | 0.104447i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 32.0000i | 1.11275i | 0.830932 | + | 0.556375i | \(0.187808\pi\) | ||||
−0.830932 | + | 0.556375i | \(0.812192\pi\) | |||||||
\(828\) | 4.00000i | 0.139010i | ||||||||
\(829\) | 46.0000 | 1.59765 | 0.798823 | − | 0.601566i | \(-0.205456\pi\) | ||||
0.798823 | + | 0.601566i | \(0.205456\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 24.0000 | 0.832551 | ||||||||
\(832\) | 8.00000i | 0.277350i | ||||||||
\(833\) | 1.00000i | 0.0346479i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 3.00000 | + | 6.00000i | 0.103819 | + | 0.207639i | ||||
\(836\) | 4.00000 | 0.138343 | ||||||||
\(837\) | 20.0000i | 0.691301i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 40.0000 | 1.38095 | 0.690477 | − | 0.723355i | \(-0.257401\pi\) | ||||
0.690477 | + | 0.723355i | \(0.257401\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 20.0000 | 0.689655 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 9.00000i | 0.309976i | ||||||||
\(844\) | −10.0000 | −0.344214 | ||||||||
\(845\) | 24.0000 | − | 12.0000i | 0.825625 | − | 0.412813i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 10.0000i | − | 0.343604i | ||||||
\(848\) | 16.0000i | 0.549442i | ||||||||
\(849\) | −17.0000 | −0.583438 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 8.00000 | 0.274236 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 38.0000i | − | 1.30110i | −0.759465 | − | 0.650548i | \(-0.774539\pi\) | ||
0.759465 | − | 0.650548i | \(-0.225461\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −8.00000 | + | 4.00000i | −0.273594 | + | 0.136797i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 42.0000i | 1.43469i | 0.696717 | + | 0.717346i | \(0.254643\pi\) | ||||
−0.696717 | + | 0.717346i | \(0.745357\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −36.0000 | −1.22830 | −0.614152 | − | 0.789188i | \(-0.710502\pi\) | ||||
−0.614152 | + | 0.789188i | \(0.710502\pi\) | |||||||
\(860\) | −16.0000 | − | 32.0000i | −0.545595 | − | 1.09119i | ||||
\(861\) | 6.00000 | 0.204479 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 36.0000i | 1.22545i | 0.790295 | + | 0.612727i | \(0.209928\pi\) | ||||
−0.790295 | + | 0.612727i | \(0.790072\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 7.00000 | + | 14.0000i | 0.238007 | + | 0.476014i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 16.0000i | 0.543388i | ||||||||
\(868\) | 8.00000i | 0.271538i | ||||||||
\(869\) | −15.0000 | −0.508840 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −14.0000 | −0.474372 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 14.0000i | 0.473828i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 11.0000 | + | 2.00000i | 0.371868 | + | 0.0676123i | ||||
\(876\) | −4.00000 | −0.135147 | ||||||||
\(877\) | − | 46.0000i | − | 1.55331i | −0.629926 | − | 0.776655i | \(-0.716915\pi\) | ||
0.629926 | − | 0.776655i | \(-0.283085\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 27.0000 | 0.910687 | ||||||||
\(880\) | −8.00000 | + | 4.00000i | −0.269680 | + | 0.134840i | ||||
\(881\) | 42.0000 | 1.41502 | 0.707508 | − | 0.706705i | \(-0.249819\pi\) | ||||
0.707508 | + | 0.706705i | \(0.249819\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 8.00000i | 0.269221i | 0.990899 | + | 0.134611i | \(0.0429784\pi\) | ||||
−0.990899 | + | 0.134611i | \(0.957022\pi\) | |||||||
\(884\) | 2.00000 | 0.0672673 | ||||||||
\(885\) | 4.00000 | + | 8.00000i | 0.134459 | + | 0.268917i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 40.0000i | − | 1.34307i | −0.740973 | − | 0.671534i | \(-0.765636\pi\) | ||
0.740973 | − | 0.671534i | \(-0.234364\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 2.00000 | 0.0670778 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1.00000 | −0.0335013 | ||||||||
\(892\) | 50.0000i | 1.67412i | ||||||||
\(893\) | − | 14.0000i | − | 0.468492i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 8.00000 | − | 4.00000i | 0.267411 | − | 0.133705i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | − | 1.00000i | − | 0.0333890i | ||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −28.0000 | −0.933852 | ||||||||
\(900\) | 12.0000 | − | 16.0000i | 0.400000 | − | 0.533333i | ||||
\(901\) | 4.00000 | 0.133259 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 8.00000i | 0.266223i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −32.0000 | + | 16.0000i | −1.06372 | + | 0.531858i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 40.0000i | − | 1.32818i | −0.747653 | − | 0.664089i | \(-0.768820\pi\) | ||
0.747653 | − | 0.664089i | \(-0.231180\pi\) | |||||||
\(908\) | − | 30.0000i | − | 0.995585i | ||||||
\(909\) | −8.00000 | −0.265343 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 44.0000 | 1.45779 | 0.728893 | − | 0.684628i | \(-0.240035\pi\) | ||||
0.728893 | + | 0.684628i | \(0.240035\pi\) | |||||||
\(912\) | − | 8.00000i | − | 0.264906i | ||||||
\(913\) | 8.00000i | 0.264761i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −10.0000 | − | 20.0000i | −0.330590 | − | 0.661180i | ||||
\(916\) | 28.0000 | 0.925146 | ||||||||
\(917\) | − | 20.0000i | − | 0.660458i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 27.0000 | 0.890648 | 0.445324 | − | 0.895370i | \(-0.353089\pi\) | ||||
0.445324 | + | 0.895370i | \(0.353089\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −9.00000 | −0.296560 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 2.00000 | 0.0657952 | ||||||||
\(925\) | −32.0000 | − | 24.0000i | −1.05215 | − | 0.789115i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 14.0000i | 0.459820i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 4.00000 | 0.131236 | 0.0656179 | − | 0.997845i | \(-0.479098\pi\) | ||||
0.0656179 | + | 0.997845i | \(0.479098\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2.00000 | 0.0655474 | ||||||||
\(932\) | 20.0000i | 0.655122i | ||||||||
\(933\) | − | 18.0000i | − | 0.589294i | ||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 1.00000 | + | 2.00000i | 0.0327035 | + | 0.0654070i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 29.0000i | − | 0.947389i | −0.880689 | − | 0.473694i | \(-0.842920\pi\) | ||
0.880689 | − | 0.473694i | \(-0.157080\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 9.00000 | 0.293704 | ||||||||
\(940\) | 14.0000 | + | 28.0000i | 0.456630 | + | 0.913259i | ||||
\(941\) | 60.0000 | 1.95594 | 0.977972 | − | 0.208736i | \(-0.0669349\pi\) | ||||
0.977972 | + | 0.208736i | \(0.0669349\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 6.00000i | − | 0.195387i | ||||||
\(944\) | 16.0000 | 0.520756 | ||||||||
\(945\) | −10.0000 | + | 5.00000i | −0.325300 | + | 0.162650i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 18.0000i | − | 0.584921i | −0.956278 | − | 0.292461i | \(-0.905526\pi\) | ||
0.956278 | − | 0.292461i | \(-0.0944741\pi\) | |||||||
\(948\) | 30.0000i | 0.974355i | ||||||||
\(949\) | −2.00000 | −0.0649227 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −6.00000 | −0.194563 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 40.0000i | 1.29573i | 0.761756 | + | 0.647864i | \(0.224337\pi\) | ||||
−0.761756 | + | 0.647864i | \(0.775663\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −50.0000 | + | 25.0000i | −1.61796 | + | 0.808981i | ||||
\(956\) | 18.0000 | 0.582162 | ||||||||
\(957\) | 7.00000i | 0.226278i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 10.0000 | 0.322917 | ||||||||
\(960\) | 8.00000 | + | 16.0000i | 0.258199 | + | 0.516398i | ||||
\(961\) | −15.0000 | −0.483871 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 20.0000 | 0.644157 | ||||||||
\(965\) | −14.0000 | − | 28.0000i | −0.450676 | − | 0.901352i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 2.00000i | 0.0643157i | 0.999483 | + | 0.0321578i | \(0.0102379\pi\) | ||||
−0.999483 | + | 0.0321578i | \(0.989762\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −2.00000 | −0.0642493 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 18.0000 | 0.577647 | 0.288824 | − | 0.957382i | \(-0.406736\pi\) | ||||
0.288824 | + | 0.957382i | \(0.406736\pi\) | |||||||
\(972\) | 32.0000i | 1.02640i | ||||||||
\(973\) | − | 4.00000i | − | 0.128234i | ||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −3.00000 | + | 4.00000i | −0.0960769 | + | 0.128103i | ||||
\(976\) | −40.0000 | −1.28037 | ||||||||
\(977\) | − | 18.0000i | − | 0.575871i | −0.957650 | − | 0.287936i | \(-0.907031\pi\) | ||
0.957650 | − | 0.287936i | \(-0.0929689\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 6.00000 | 0.191761 | ||||||||
\(980\) | −4.00000 | + | 2.00000i | −0.127775 | + | 0.0638877i | ||||
\(981\) | 10.0000 | 0.319275 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 21.0000i | 0.669796i | 0.942254 | + | 0.334898i | \(0.108702\pi\) | ||||
−0.942254 | + | 0.334898i | \(0.891298\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −18.0000 | − | 36.0000i | −0.573528 | − | 1.14706i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | − | 7.00000i | − | 0.222812i | ||||||
\(988\) | − | 4.00000i | − | 0.127257i | ||||||
\(989\) | 8.00000 | 0.254385 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − | 4.00000i | − | 0.126936i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −24.0000 | + | 12.0000i | −0.760851 | + | 0.380426i | ||||
\(996\) | 16.0000 | 0.506979 | ||||||||
\(997\) | 17.0000i | 0.538395i | 0.963085 | + | 0.269198i | \(0.0867585\pi\) | ||||
−0.963085 | + | 0.269198i | \(0.913241\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 40.0000 | 1.26554 |
(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 | 805.2.c.a.484.2 | yes | 2 | |
5.2 | odd | 4 | 4025.2.a.d.1.1 | 1 | |||
5.3 | odd | 4 | 4025.2.a.c.1.1 | 1 | |||
5.4 | even | 2 | inner | 805.2.c.a.484.1 | ✓ | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
805.2.c.a.484.1 | ✓ | 2 | 5.4 | even | 2 | inner | |
805.2.c.a.484.2 | yes | 2 | 1.1 | even | 1 | trivial | |
4025.2.a.c.1.1 | 1 | 5.3 | odd | 4 | |||
4025.2.a.d.1.1 | 1 | 5.2 | odd | 4 |