Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3360,2,Mod(1,3360)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3360, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 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("3360.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3360 = 2^{5} \cdot 3 \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3360.a (trivial) |
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: | yes |
Analytic conductor: | \(26.8297350792\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{10})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(1.61803\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3360.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
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 | ||||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.47214 | 1.24035 | 0.620174 | − | 0.784465i | \(-0.287062\pi\) | ||||
0.620174 | + | 0.784465i | \(0.287062\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.00000 | −0.258199 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 4.47214 | 1.08465 | 0.542326 | − | 0.840168i | \(-0.317544\pi\) | ||||
0.542326 | + | 0.840168i | \(0.317544\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.00000 | 0.218218 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.47214 | 0.515476 | 0.257738 | − | 0.966215i | \(-0.417023\pi\) | ||||
0.257738 | + | 0.966215i | \(0.417023\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −0.472136 | −0.0876734 | −0.0438367 | − | 0.999039i | \(-0.513958\pi\) | ||||
−0.0438367 | + | 0.999039i | \(0.513958\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.47214 | −0.444009 | −0.222004 | − | 0.975046i | \(-0.571260\pi\) | ||||
−0.222004 | + | 0.975046i | \(0.571260\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1.00000 | −0.169031 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −0.472136 | −0.0776187 | −0.0388093 | − | 0.999247i | \(-0.512356\pi\) | ||||
−0.0388093 | + | 0.999247i | \(0.512356\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −4.47214 | −0.716115 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −6.94427 | −1.08451 | −0.542257 | − | 0.840213i | \(-0.682430\pi\) | ||||
−0.542257 | + | 0.840213i | \(0.682430\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.52786 | −0.232997 | −0.116499 | − | 0.993191i | \(-0.537167\pi\) | ||||
−0.116499 | + | 0.993191i | \(0.537167\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.00000 | 0.149071 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −6.47214 | −0.944058 | −0.472029 | − | 0.881583i | \(-0.656478\pi\) | ||||
−0.472029 | + | 0.881583i | \(0.656478\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −4.47214 | −0.626224 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 2.00000 | 0.274721 | 0.137361 | − | 0.990521i | \(-0.456138\pi\) | ||||
0.137361 | + | 0.990521i | \(0.456138\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 4.00000 | 0.520756 | 0.260378 | − | 0.965507i | \(-0.416153\pi\) | ||||
0.260378 | + | 0.965507i | \(0.416153\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.52786 | 0.451697 | 0.225848 | − | 0.974162i | \(-0.427485\pi\) | ||||
0.225848 | + | 0.974162i | \(0.427485\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −1.00000 | −0.125988 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 4.47214 | 0.554700 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 6.47214 | 0.790697 | 0.395349 | − | 0.918531i | \(-0.370624\pi\) | ||||
0.395349 | + | 0.918531i | \(0.370624\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −2.47214 | −0.297610 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 11.4164 | 1.35488 | 0.677439 | − | 0.735579i | \(-0.263090\pi\) | ||||
0.677439 | + | 0.735579i | \(0.263090\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −0.472136 | −0.0552593 | −0.0276297 | − | 0.999618i | \(-0.508796\pi\) | ||||
−0.0276297 | + | 0.999618i | \(0.508796\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1.00000 | −0.115470 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 4.94427 | 0.556274 | 0.278137 | − | 0.960541i | \(-0.410283\pi\) | ||||
0.278137 | + | 0.960541i | \(0.410283\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −0.944272 | −0.103647 | −0.0518237 | − | 0.998656i | \(-0.516503\pi\) | ||||
−0.0518237 | + | 0.998656i | \(0.516503\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 4.47214 | 0.485071 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0.472136 | 0.0506183 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 10.9443 | 1.16009 | 0.580045 | − | 0.814584i | \(-0.303035\pi\) | ||||
0.580045 | + | 0.814584i | \(0.303035\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −4.47214 | −0.468807 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 2.47214 | 0.256349 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 4.47214 | 0.454077 | 0.227038 | − | 0.973886i | \(-0.427096\pi\) | ||||
0.227038 | + | 0.973886i | \(0.427096\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 10.9443 | 1.08900 | 0.544498 | − | 0.838762i | \(-0.316720\pi\) | ||||
0.544498 | + | 0.838762i | \(0.316720\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −17.8885 | −1.76261 | −0.881305 | − | 0.472547i | \(-0.843335\pi\) | ||||
−0.881305 | + | 0.472547i | \(0.843335\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1.00000 | 0.0975900 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −2.47214 | −0.238990 | −0.119495 | − | 0.992835i | \(-0.538128\pi\) | ||||
−0.119495 | + | 0.992835i | \(0.538128\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 14.0000 | 1.34096 | 0.670478 | − | 0.741929i | \(-0.266089\pi\) | ||||
0.670478 | + | 0.741929i | \(0.266089\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0.472136 | 0.0448132 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −2.00000 | −0.188144 | −0.0940721 | − | 0.995565i | \(-0.529988\pi\) | ||||
−0.0940721 | + | 0.995565i | \(0.529988\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2.47214 | 0.230528 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 4.47214 | 0.413449 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −4.47214 | −0.409960 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −11.0000 | −1.00000 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 6.94427 | 0.626144 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 1.52786 | 0.134521 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 16.9443 | 1.48043 | 0.740214 | − | 0.672371i | \(-0.234724\pi\) | ||||
0.740214 | + | 0.672371i | \(0.234724\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −1.00000 | −0.0860663 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −6.94427 | −0.593289 | −0.296645 | − | 0.954988i | \(-0.595868\pi\) | ||||
−0.296645 | + | 0.954988i | \(0.595868\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 6.47214 | 0.545052 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −0.472136 | −0.0392088 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −1.00000 | −0.0824786 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 12.4721 | 1.02176 | 0.510879 | − | 0.859653i | \(-0.329320\pi\) | ||||
0.510879 | + | 0.859653i | \(0.329320\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 3.05573 | 0.248672 | 0.124336 | − | 0.992240i | \(-0.460320\pi\) | ||||
0.124336 | + | 0.992240i | \(0.460320\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 4.47214 | 0.361551 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −2.47214 | −0.198567 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 7.52786 | 0.600789 | 0.300394 | − | 0.953815i | \(-0.402882\pi\) | ||||
0.300394 | + | 0.953815i | \(0.402882\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −2.00000 | −0.158610 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −2.47214 | −0.194832 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −6.47214 | −0.506937 | −0.253468 | − | 0.967344i | \(-0.581571\pi\) | ||||
−0.253468 | + | 0.967344i | \(0.581571\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1.52786 | 0.118230 | 0.0591148 | − | 0.998251i | \(-0.481172\pi\) | ||||
0.0591148 | + | 0.998251i | \(0.481172\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 7.00000 | 0.538462 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 6.00000 | 0.456172 | 0.228086 | − | 0.973641i | \(-0.426753\pi\) | ||||
0.228086 | + | 0.973641i | \(0.426753\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.00000 | −0.0755929 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −4.00000 | −0.300658 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 16.0000 | 1.19590 | 0.597948 | − | 0.801535i | \(-0.295983\pi\) | ||||
0.597948 | + | 0.801535i | \(0.295983\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 13.4164 | 0.997234 | 0.498617 | − | 0.866822i | \(-0.333841\pi\) | ||||
0.498617 | + | 0.866822i | \(0.333841\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −3.52786 | −0.260787 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −0.472136 | −0.0347121 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 1.00000 | 0.0727393 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −3.41641 | −0.247203 | −0.123601 | − | 0.992332i | \(-0.539444\pi\) | ||||
−0.123601 | + | 0.992332i | \(0.539444\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1.05573 | −0.0759930 | −0.0379965 | − | 0.999278i | \(-0.512098\pi\) | ||||
−0.0379965 | + | 0.999278i | \(0.512098\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −4.47214 | −0.320256 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −2.94427 | −0.209771 | −0.104885 | − | 0.994484i | \(-0.533448\pi\) | ||||
−0.104885 | + | 0.994484i | \(0.533448\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 15.4164 | 1.09284 | 0.546420 | − | 0.837511i | \(-0.315990\pi\) | ||||
0.546420 | + | 0.837511i | \(0.315990\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −6.47214 | −0.456509 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0.472136 | 0.0331374 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −6.94427 | −0.485009 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 2.47214 | 0.171825 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −8.00000 | −0.550743 | −0.275371 | − | 0.961338i | \(-0.588801\pi\) | ||||
−0.275371 | + | 0.961338i | \(0.588801\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −11.4164 | −0.782239 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −1.52786 | −0.104199 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2.47214 | 0.167820 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0.472136 | 0.0319040 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 20.0000 | 1.34535 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 9.88854 | 0.662186 | 0.331093 | − | 0.943598i | \(-0.392583\pi\) | ||||
0.331093 | + | 0.943598i | \(0.392583\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 16.9443 | 1.12463 | 0.562315 | − | 0.826923i | \(-0.309911\pi\) | ||||
0.562315 | + | 0.826923i | \(0.309911\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 11.5279 | 0.761783 | 0.380891 | − | 0.924620i | \(-0.375617\pi\) | ||||
0.380891 | + | 0.924620i | \(0.375617\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −14.9443 | −0.979032 | −0.489516 | − | 0.871994i | \(-0.662826\pi\) | ||||
−0.489516 | + | 0.871994i | \(0.662826\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −6.47214 | −0.422196 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −4.94427 | −0.321165 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −24.3607 | −1.57576 | −0.787881 | − | 0.615828i | \(-0.788822\pi\) | ||||
−0.787881 | + | 0.615828i | \(0.788822\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −6.00000 | −0.386494 | −0.193247 | − | 0.981150i | \(-0.561902\pi\) | ||||
−0.193247 | + | 0.981150i | \(0.561902\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1.00000 | 0.0638877 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0.944272 | 0.0598408 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 24.9443 | 1.57447 | 0.787234 | − | 0.616654i | \(-0.211512\pi\) | ||||
0.787234 | + | 0.616654i | \(0.211512\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −4.47214 | −0.280056 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −0.472136 | −0.0294510 | −0.0147255 | − | 0.999892i | \(-0.504687\pi\) | ||||
−0.0147255 | + | 0.999892i | \(0.504687\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0.472136 | 0.0293371 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −0.472136 | −0.0292245 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 18.4721 | 1.13904 | 0.569520 | − | 0.821977i | \(-0.307129\pi\) | ||||
0.569520 | + | 0.821977i | \(0.307129\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2.00000 | 0.122859 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −10.9443 | −0.669779 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 22.0000 | 1.34136 | 0.670682 | − | 0.741745i | \(-0.266002\pi\) | ||||
0.670682 | + | 0.741745i | \(0.266002\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 20.3607 | 1.23682 | 0.618412 | − | 0.785854i | \(-0.287776\pi\) | ||||
0.618412 | + | 0.785854i | \(0.287776\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 4.47214 | 0.270666 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 4.47214 | 0.268705 | 0.134352 | − | 0.990934i | \(-0.457105\pi\) | ||||
0.134352 | + | 0.990934i | \(0.457105\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −2.47214 | −0.148003 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 3.88854 | 0.231971 | 0.115986 | − | 0.993251i | \(-0.462997\pi\) | ||||
0.115986 | + | 0.993251i | \(0.462997\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −29.8885 | −1.77669 | −0.888345 | − | 0.459177i | \(-0.848144\pi\) | ||||
−0.888345 | + | 0.459177i | \(0.848144\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 6.94427 | 0.409907 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 3.00000 | 0.176471 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −4.47214 | −0.262161 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −22.9443 | −1.34042 | −0.670209 | − | 0.742172i | \(-0.733796\pi\) | ||||
−0.670209 | + | 0.742172i | \(0.733796\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 4.00000 | 0.232889 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 11.0557 | 0.639369 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.52786 | 0.0880646 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −10.9443 | −0.628732 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 3.52786 | 0.202005 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 7.05573 | 0.402692 | 0.201346 | − | 0.979520i | \(-0.435468\pi\) | ||||
0.201346 | + | 0.979520i | \(0.435468\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 17.8885 | 1.01764 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −1.88854 | −0.107089 | −0.0535447 | − | 0.998565i | \(-0.517052\pi\) | ||||
−0.0535447 | + | 0.998565i | \(0.517052\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −8.47214 | −0.478873 | −0.239437 | − | 0.970912i | \(-0.576963\pi\) | ||||
−0.239437 | + | 0.970912i | \(0.576963\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −1.00000 | −0.0563436 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 19.8885 | 1.11705 | 0.558526 | − | 0.829487i | \(-0.311367\pi\) | ||||
0.558526 | + | 0.829487i | \(0.311367\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 2.47214 | 0.137981 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 4.47214 | 0.248069 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −14.0000 | −0.774202 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 6.47214 | 0.356820 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −32.0000 | −1.75888 | −0.879440 | − | 0.476011i | \(-0.842082\pi\) | ||||
−0.879440 | + | 0.476011i | \(0.842082\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −0.472136 | −0.0258729 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 6.47214 | 0.353611 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −10.9443 | −0.596172 | −0.298086 | − | 0.954539i | \(-0.596348\pi\) | ||||
−0.298086 | + | 0.954539i | \(0.596348\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 2.00000 | 0.108625 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −2.47214 | −0.133095 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 18.4721 | 0.991636 | 0.495818 | − | 0.868426i | \(-0.334868\pi\) | ||||
0.495818 | + | 0.868426i | \(0.334868\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 24.4721 | 1.30996 | 0.654982 | − | 0.755645i | \(-0.272676\pi\) | ||||
0.654982 | + | 0.755645i | \(0.272676\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −4.47214 | −0.238705 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 9.41641 | 0.501185 | 0.250592 | − | 0.968093i | \(-0.419375\pi\) | ||||
0.250592 | + | 0.968093i | \(0.419375\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 11.4164 | 0.605920 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 4.47214 | 0.236691 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 11.4164 | 0.602535 | 0.301267 | − | 0.953540i | \(-0.402590\pi\) | ||||
0.301267 | + | 0.953540i | \(0.402590\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −19.0000 | −1.00000 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 11.0000 | 0.577350 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −0.472136 | −0.0247127 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 3.05573 | 0.159508 | 0.0797539 | − | 0.996815i | \(-0.474587\pi\) | ||||
0.0797539 | + | 0.996815i | \(0.474587\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −6.94427 | −0.361504 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −2.00000 | −0.103835 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −29.4164 | −1.52312 | −0.761562 | − | 0.648092i | \(-0.775567\pi\) | ||||
−0.761562 | + | 0.648092i | \(0.775567\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1.00000 | −0.0516398 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −2.11146 | −0.108746 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −36.9443 | −1.89770 | −0.948850 | − | 0.315728i | \(-0.897751\pi\) | ||||
−0.948850 | + | 0.315728i | \(0.897751\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 3.41641 | 0.174570 | 0.0872851 | − | 0.996183i | \(-0.472181\pi\) | ||||
0.0872851 | + | 0.996183i | \(0.472181\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −1.52786 | −0.0776657 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 15.5279 | 0.787294 | 0.393647 | − | 0.919262i | \(-0.371213\pi\) | ||||
0.393647 | + | 0.919262i | \(0.371213\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 11.0557 | 0.559112 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −16.9443 | −0.854725 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 4.94427 | 0.248773 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 25.4164 | 1.27561 | 0.637806 | − | 0.770197i | \(-0.279842\pi\) | ||||
0.637806 | + | 0.770197i | \(0.279842\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −9.05573 | −0.452221 | −0.226111 | − | 0.974102i | \(-0.572601\pi\) | ||||
−0.226111 | + | 0.974102i | \(0.572601\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −11.0557 | −0.550725 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1.00000 | 0.0496904 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 22.9443 | 1.13452 | 0.567261 | − | 0.823538i | \(-0.308003\pi\) | ||||
0.567261 | + | 0.823538i | \(0.308003\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 6.94427 | 0.342536 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −4.00000 | −0.196827 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −0.944272 | −0.0463525 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 32.9443 | 1.60943 | 0.804717 | − | 0.593659i | \(-0.202317\pi\) | ||||
0.804717 | + | 0.593659i | \(0.202317\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −11.8885 | −0.579412 | −0.289706 | − | 0.957116i | \(-0.593558\pi\) | ||||
−0.289706 | + | 0.957116i | \(0.593558\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −6.47214 | −0.314686 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 4.47214 | 0.216930 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −3.52786 | −0.170725 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 25.5279 | 1.22963 | 0.614817 | − | 0.788670i | \(-0.289230\pi\) | ||||
0.614817 | + | 0.788670i | \(0.289230\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −26.3607 | −1.26681 | −0.633407 | − | 0.773819i | \(-0.718344\pi\) | ||||
−0.633407 | + | 0.773819i | \(0.718344\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0.472136 | 0.0226372 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −21.5279 | −1.02747 | −0.513734 | − | 0.857949i | \(-0.671738\pi\) | ||||
−0.513734 | + | 0.857949i | \(0.671738\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 10.4721 | 0.497546 | 0.248773 | − | 0.968562i | \(-0.419973\pi\) | ||||
0.248773 | + | 0.968562i | \(0.419973\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 10.9443 | 0.518808 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −12.4721 | −0.589912 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −20.8328 | −0.983161 | −0.491581 | − | 0.870832i | \(-0.663581\pi\) | ||||
−0.491581 | + | 0.870832i | \(0.663581\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −3.05573 | −0.143571 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −4.47214 | −0.209657 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −17.0557 | −0.797833 | −0.398917 | − | 0.916987i | \(-0.630614\pi\) | ||||
−0.398917 | + | 0.916987i | \(0.630614\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −4.47214 | −0.208741 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −24.8328 | −1.15658 | −0.578290 | − | 0.815831i | \(-0.696280\pi\) | ||||
−0.578290 | + | 0.815831i | \(0.696280\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −20.9443 | −0.973363 | −0.486681 | − | 0.873580i | \(-0.661793\pi\) | ||||
−0.486681 | + | 0.873580i | \(0.661793\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 2.47214 | 0.114643 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −5.88854 | −0.272489 | −0.136245 | − | 0.990675i | \(-0.543503\pi\) | ||||
−0.136245 | + | 0.990675i | \(0.543503\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −6.47214 | −0.298855 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −7.52786 | −0.346866 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 2.00000 | 0.0915737 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 25.8885 | 1.18288 | 0.591439 | − | 0.806350i | \(-0.298560\pi\) | ||||
0.591439 | + | 0.806350i | \(0.298560\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2.11146 | −0.0962741 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 2.47214 | 0.112486 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 4.47214 | 0.203069 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 36.9443 | 1.67410 | 0.837052 | − | 0.547123i | \(-0.184277\pi\) | ||||
0.837052 | + | 0.547123i | \(0.184277\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 6.47214 | 0.292680 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −2.11146 | −0.0950952 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −11.4164 | −0.512096 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −28.9443 | −1.29572 | −0.647862 | − | 0.761758i | \(-0.724337\pi\) | ||||
−0.647862 | + | 0.761758i | \(0.724337\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −1.52786 | −0.0682599 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 30.4721 | 1.35869 | 0.679343 | − | 0.733821i | \(-0.262265\pi\) | ||||
0.679343 | + | 0.733821i | \(0.262265\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 10.9443 | 0.487014 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −7.00000 | −0.310881 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 22.0000 | 0.975133 | 0.487566 | − | 0.873086i | \(-0.337885\pi\) | ||||
0.487566 | + | 0.873086i | \(0.337885\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0.472136 | 0.0208861 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −17.8885 | −0.788263 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −6.00000 | −0.263371 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −34.0000 | −1.48957 | −0.744784 | − | 0.667306i | \(-0.767447\pi\) | ||||
−0.744784 | + | 0.667306i | \(0.767447\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −7.05573 | −0.308525 | −0.154263 | − | 0.988030i | \(-0.549300\pi\) | ||||
−0.154263 | + | 0.988030i | \(0.549300\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 1.00000 | 0.0436436 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −11.0557 | −0.481595 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −16.8885 | −0.734285 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 4.00000 | 0.173585 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −31.0557 | −1.34517 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −2.47214 | −0.106880 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −16.0000 | −0.690451 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 2.94427 | 0.126584 | 0.0632921 | − | 0.997995i | \(-0.479840\pi\) | ||||
0.0632921 | + | 0.997995i | \(0.479840\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −13.4164 | −0.575753 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 14.0000 | 0.599694 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −11.4164 | −0.488130 | −0.244065 | − | 0.969759i | \(-0.578481\pi\) | ||||
−0.244065 | + | 0.969759i | \(0.578481\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 3.52786 | 0.150566 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −4.94427 | −0.210252 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0.472136 | 0.0200411 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 10.0000 | 0.423714 | 0.211857 | − | 0.977301i | \(-0.432049\pi\) | ||||
0.211857 | + | 0.977301i | \(0.432049\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −6.83282 | −0.288997 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −12.0000 | −0.505740 | −0.252870 | − | 0.967500i | \(-0.581374\pi\) | ||||
−0.252870 | + | 0.967500i | \(0.581374\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −2.00000 | −0.0841406 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −1.00000 | −0.0419961 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −20.8328 | −0.873357 | −0.436679 | − | 0.899618i | \(-0.643845\pi\) | ||||
−0.436679 | + | 0.899618i | \(0.643845\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −12.9443 | −0.541701 | −0.270850 | − | 0.962621i | \(-0.587305\pi\) | ||||
−0.270850 | + | 0.962621i | \(0.587305\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 3.41641 | 0.142722 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 2.47214 | 0.103095 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −2.36068 | −0.0982764 | −0.0491382 | − | 0.998792i | \(-0.515647\pi\) | ||||
−0.0491382 | + | 0.998792i | \(0.515647\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 1.05573 | 0.0438746 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0.944272 | 0.0391750 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 4.47214 | 0.184900 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 29.8885 | 1.23363 | 0.616816 | − | 0.787107i | \(-0.288422\pi\) | ||||
0.616816 | + | 0.787107i | \(0.288422\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 2.94427 | 0.121111 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −3.52786 | −0.144872 | −0.0724360 | − | 0.997373i | \(-0.523077\pi\) | ||||
−0.0724360 | + | 0.997373i | \(0.523077\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −4.47214 | −0.183340 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −15.4164 | −0.630952 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 6.47214 | 0.264444 | 0.132222 | − | 0.991220i | \(-0.457789\pi\) | ||||
0.132222 | + | 0.991220i | \(0.457789\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −26.9443 | −1.09908 | −0.549540 | − | 0.835467i | \(-0.685197\pi\) | ||||
−0.549540 | + | 0.835467i | \(0.685197\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 6.47214 | 0.263566 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −11.0000 | −0.447214 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −25.8885 | −1.05078 | −0.525392 | − | 0.850860i | \(-0.676081\pi\) | ||||
−0.525392 | + | 0.850860i | \(0.676081\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −0.472136 | −0.0191319 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −28.9443 | −1.17096 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −32.4721 | −1.31154 | −0.655769 | − | 0.754962i | \(-0.727655\pi\) | ||||
−0.655769 | + | 0.754962i | \(0.727655\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 6.94427 | 0.280020 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −21.0557 | −0.847672 | −0.423836 | − | 0.905739i | \(-0.639317\pi\) | ||||
−0.423836 | + | 0.905739i | \(0.639317\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −27.0557 | −1.08746 | −0.543731 | − | 0.839260i | \(-0.682989\pi\) | ||||
−0.543731 | + | 0.839260i | \(0.682989\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −2.47214 | −0.0992034 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −10.9443 | −0.438473 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −2.11146 | −0.0841893 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1.88854 | 0.0751817 | 0.0375909 | − | 0.999293i | \(-0.488032\pi\) | ||||
0.0375909 | + | 0.999293i | \(0.488032\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 8.00000 | 0.317971 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 4.47214 | 0.177192 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 11.4164 | 0.451626 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −10.9443 | −0.432273 | −0.216136 | − | 0.976363i | \(-0.569346\pi\) | ||||
−0.216136 | + | 0.976363i | \(0.569346\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 12.0000 | 0.473234 | 0.236617 | − | 0.971603i | \(-0.423961\pi\) | ||||
0.236617 | + | 0.971603i | \(0.423961\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 1.52786 | 0.0601596 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 4.58359 | 0.180200 | 0.0900998 | − | 0.995933i | \(-0.471281\pi\) | ||||
0.0900998 | + | 0.995933i | \(0.471281\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −2.47214 | −0.0968906 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −4.11146 | −0.160894 | −0.0804469 | − | 0.996759i | \(-0.525635\pi\) | ||||
−0.0804469 | + | 0.996759i | \(0.525635\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 16.9443 | 0.662067 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −0.472136 | −0.0184198 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 30.8328 | 1.20108 | 0.600538 | − | 0.799596i | \(-0.294953\pi\) | ||||
0.600538 | + | 0.799596i | \(0.294953\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −46.3607 | −1.80322 | −0.901611 | − | 0.432548i | \(-0.857614\pi\) | ||||
−0.901611 | + | 0.432548i | \(0.857614\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −20.0000 | −0.776736 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1.16718 | −0.0451936 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −9.88854 | −0.382313 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 45.7771 | 1.76458 | 0.882289 | − | 0.470709i | \(-0.156002\pi\) | ||||
0.882289 | + | 0.470709i | \(0.156002\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −1.00000 | −0.0384900 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −11.8885 | −0.456914 | −0.228457 | − | 0.973554i | \(-0.573368\pi\) | ||||
−0.228457 | + | 0.973554i | \(0.573368\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −4.47214 | −0.171625 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −16.9443 | −0.649306 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −12.3607 | −0.472968 | −0.236484 | − | 0.971635i | \(-0.575995\pi\) | ||||
−0.236484 | + | 0.971635i | \(0.575995\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −6.94427 | −0.265327 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −11.5279 | −0.439815 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 8.94427 | 0.340750 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −25.8885 | −0.984847 | −0.492423 | − | 0.870356i | \(-0.663889\pi\) | ||||
−0.492423 | + | 0.870356i | \(0.663889\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −31.0557 | −1.17632 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 14.9443 | 0.565244 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 9.41641 | 0.355653 | 0.177826 | − | 0.984062i | \(-0.443093\pi\) | ||||
0.177826 | + | 0.984062i | \(0.443093\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 6.47214 | 0.243755 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −10.9443 | −0.411602 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 12.8328 | 0.481947 | 0.240973 | − | 0.970532i | \(-0.422533\pi\) | ||||
0.240973 | + | 0.970532i | \(0.422533\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 4.94427 | 0.185425 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −6.11146 | −0.228876 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 24.3607 | 0.909766 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −16.0000 | −0.596699 | −0.298350 | − | 0.954457i | \(-0.596436\pi\) | ||||
−0.298350 | + | 0.954457i | \(0.596436\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 17.8885 | 0.666204 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 6.00000 | 0.223142 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −0.472136 | −0.0175347 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 28.9443 | 1.07348 | 0.536742 | − | 0.843747i | \(-0.319655\pi\) | ||||
0.536742 | + | 0.843747i | \(0.319655\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −6.83282 | −0.252721 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −29.4164 | −1.08652 | −0.543260 | − | 0.839565i | \(-0.682810\pi\) | ||||
−0.543260 | + | 0.839565i | \(0.682810\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −1.00000 | −0.0368856 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −16.0000 | −0.588570 | −0.294285 | − | 0.955718i | \(-0.595081\pi\) | ||||
−0.294285 | + | 0.955718i | \(0.595081\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −7.41641 | −0.272082 | −0.136041 | − | 0.990703i | \(-0.543438\pi\) | ||||
−0.136041 | + | 0.990703i | \(0.543438\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 12.4721 | 0.456944 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −0.944272 | −0.0345491 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 2.47214 | 0.0903299 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −11.0557 | −0.403429 | −0.201715 | − | 0.979444i | \(-0.564651\pi\) | ||||
−0.201715 | + | 0.979444i | \(0.564651\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −24.9443 | −0.909020 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 3.05573 | 0.111209 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −11.5279 | −0.418987 | −0.209494 | − | 0.977810i | \(-0.567182\pi\) | ||||
−0.209494 | + | 0.977810i | \(0.567182\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −35.8885 | −1.30096 | −0.650479 | − | 0.759524i | \(-0.725432\pi\) | ||||
−0.650479 | + | 0.759524i | \(0.725432\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −14.0000 | −0.506834 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 4.47214 | 0.161690 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 17.8885 | 0.645918 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 18.0000 | 0.649097 | 0.324548 | − | 0.945869i | \(-0.394788\pi\) | ||||
0.324548 | + | 0.945869i | \(0.394788\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0.472136 | 0.0170036 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −38.9443 | −1.40073 | −0.700364 | − | 0.713786i | \(-0.746979\pi\) | ||||
−0.700364 | + | 0.713786i | \(0.746979\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −2.47214 | −0.0888017 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −0.472136 | −0.0169378 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0.472136 | 0.0168728 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 7.52786 | 0.268681 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 47.7771 | 1.70307 | 0.851535 | − | 0.524298i | \(-0.175672\pi\) | ||||
0.851535 | + | 0.524298i | \(0.175672\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −18.4721 | −0.657625 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 2.00000 | 0.0711118 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 15.7771 | 0.560261 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −2.00000 | −0.0709327 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −42.0000 | −1.48772 | −0.743858 | − | 0.668338i | \(-0.767006\pi\) | ||||
−0.743858 | + | 0.668338i | \(0.767006\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −28.9443 | −1.02397 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 10.9443 | 0.386697 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −2.47214 | −0.0871313 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −22.0000 | −0.774437 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 40.8328 | 1.43561 | 0.717803 | − | 0.696247i | \(-0.245148\pi\) | ||||
0.717803 | + | 0.696247i | \(0.245148\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 43.7771 | 1.53722 | 0.768611 | − | 0.639717i | \(-0.220948\pi\) | ||||
0.768611 | + | 0.639717i | \(0.220948\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −20.3607 | −0.714080 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −6.47214 | −0.226709 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −4.47214 | −0.156269 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −31.3050 | −1.09255 | −0.546275 | − | 0.837606i | \(-0.683955\pi\) | ||||
−0.546275 | + | 0.837606i | \(0.683955\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 20.9443 | 0.730071 | 0.365036 | − | 0.930994i | \(-0.381057\pi\) | ||||
0.365036 | + | 0.930994i | \(0.381057\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −15.4164 | −0.536081 | −0.268041 | − | 0.963408i | \(-0.586376\pi\) | ||||
−0.268041 | + | 0.963408i | \(0.586376\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 6.58359 | 0.228658 | 0.114329 | − | 0.993443i | \(-0.463528\pi\) | ||||
0.114329 | + | 0.993443i | \(0.463528\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −4.47214 | −0.155137 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 4.47214 | 0.154950 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1.52786 | 0.0528739 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 2.47214 | 0.0854495 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 14.1115 | 0.487182 | 0.243591 | − | 0.969878i | \(-0.421675\pi\) | ||||
0.243591 | + | 0.969878i | \(0.421675\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.7771 | −0.992313 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −3.88854 | −0.133929 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 7.00000 | 0.240807 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 11.0000 | 0.377964 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 29.8885 | 1.02577 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1.16718 | −0.0400106 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −40.4721 | −1.38574 | −0.692870 | − | 0.721063i | \(-0.743654\pi\) | ||||
−0.692870 | + | 0.721063i | \(0.743654\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −26.3607 | −0.900464 | −0.450232 | − | 0.892912i | \(-0.648659\pi\) | ||||
−0.450232 | + | 0.892912i | \(0.648659\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −12.9443 | −0.441653 | −0.220826 | − | 0.975313i | \(-0.570875\pi\) | ||||
−0.220826 | + | 0.975313i | \(0.570875\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −6.94427 | −0.236660 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 3.63932 | 0.123884 | 0.0619420 | − | 0.998080i | \(-0.480271\pi\) | ||||
0.0619420 | + | 0.998080i | \(0.480271\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 6.00000 | 0.204006 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −3.00000 | −0.101885 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 28.9443 | 0.980739 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 4.47214 | 0.151359 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −1.00000 | −0.0338062 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −15.3050 | −0.516811 | −0.258406 | − | 0.966036i | \(-0.583197\pi\) | ||||
−0.258406 | + | 0.966036i | \(0.583197\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 22.9443 | 0.773891 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 20.8328 | 0.701875 | 0.350938 | − | 0.936399i | \(-0.385863\pi\) | ||||
0.350938 | + | 0.936399i | \(0.385863\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 37.3050 | 1.25541 | 0.627706 | − | 0.778451i | \(-0.283994\pi\) | ||||
0.627706 | + | 0.778451i | \(0.283994\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −4.00000 | −0.134459 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −51.4164 | −1.72639 | −0.863197 | − | 0.504867i | \(-0.831541\pi\) | ||||
−0.863197 | + | 0.504867i | \(0.831541\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 16.0000 | 0.534821 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −11.0557 | −0.369140 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 1.16718 | 0.0389278 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 8.94427 | 0.297977 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −1.52786 | −0.0508441 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 13.4164 | 0.445976 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −8.36068 | −0.277612 | −0.138806 | − | 0.990320i | \(-0.544326\pi\) | ||||
−0.138806 | + | 0.990320i | \(0.544326\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 10.9443 | 0.362999 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −27.4164 | −0.908346 | −0.454173 | − | 0.890913i | \(-0.650065\pi\) | ||||
−0.454173 | + | 0.890913i | \(0.650065\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −3.52786 | −0.116628 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −16.9443 | −0.559549 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −32.7214 | −1.07938 | −0.539689 | − | 0.841864i | \(-0.681458\pi\) | ||||
−0.539689 | + | 0.841864i | \(0.681458\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −7.05573 | −0.232494 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 51.0557 | 1.68052 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −0.472136 | −0.0155237 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −17.8885 | −0.587537 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 39.8885 | 1.30870 | 0.654350 | − | 0.756192i | \(-0.272942\pi\) | ||||
0.654350 | + | 0.756192i | \(0.272942\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 1.88854 | 0.0618281 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −31.3050 | −1.02269 | −0.511344 | − | 0.859376i | \(-0.670852\pi\) | ||||
−0.511344 | + | 0.859376i | \(0.670852\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 8.47214 | 0.276478 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −2.00000 | −0.0651981 | −0.0325991 | − | 0.999469i | \(-0.510378\pi\) | ||||
−0.0325991 | + | 0.999469i | \(0.510378\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −17.1672 | −0.559040 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 1.00000 | 0.0325300 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −11.6393 | −0.378227 | −0.189114 | − | 0.981955i | \(-0.560561\pi\) | ||||
−0.189114 | + | 0.981955i | \(0.560561\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −2.11146 | −0.0685408 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −19.8885 | −0.644930 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −29.7771 | −0.964574 | −0.482287 | − | 0.876013i | \(-0.660194\pi\) | ||||
−0.482287 | + | 0.876013i | \(0.660194\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −3.41641 | −0.110552 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 6.94427 | 0.224242 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −24.8885 | −0.802856 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −2.47214 | −0.0796635 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −1.05573 | −0.0339851 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 20.9443 | 0.673522 | 0.336761 | − | 0.941590i | \(-0.390668\pi\) | ||||
0.336761 | + | 0.941590i | \(0.390668\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 12.0000 | 0.385098 | 0.192549 | − | 0.981287i | \(-0.438325\pi\) | ||||
0.192549 | + | 0.981287i | \(0.438325\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −4.47214 | −0.143223 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 28.8328 | 0.922443 | 0.461222 | − | 0.887285i | \(-0.347411\pi\) | ||||
0.461222 | + | 0.887285i | \(0.347411\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 14.0000 | 0.446986 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 50.2492 | 1.60270 | 0.801351 | − | 0.598195i | \(-0.204115\pi\) | ||||
0.801351 | + | 0.598195i | \(0.204115\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −2.94427 | −0.0938123 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −6.47214 | −0.206010 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −3.77709 | −0.120104 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 19.0557 | 0.605325 | 0.302663 | − | 0.953098i | \(-0.402124\pi\) | ||||
0.302663 | + | 0.953098i | \(0.402124\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 32.0000 | 1.01549 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 15.4164 | 0.488733 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 9.41641 | 0.298221 | 0.149110 | − | 0.988821i | \(-0.452359\pi\) | ||||
0.149110 | + | 0.988821i | \(0.452359\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0.472136 | 0.0149377 |
(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 | 3360.2.a.bd.1.2 | ✓ | 2 | |
4.3 | odd | 2 | 3360.2.a.bh.1.2 | yes | 2 | ||
8.3 | odd | 2 | 6720.2.a.cp.1.1 | 2 | |||
8.5 | even | 2 | 6720.2.a.cv.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3360.2.a.bd.1.2 | ✓ | 2 | 1.1 | even | 1 | trivial | |
3360.2.a.bh.1.2 | yes | 2 | 4.3 | odd | 2 | ||
6720.2.a.cp.1.1 | 2 | 8.3 | odd | 2 | |||
6720.2.a.cv.1.1 | 2 | 8.5 | even | 2 |