Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [7280,2,Mod(1,7280)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(7280, 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("7280.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 7280 = 2^{4} \cdot 5 \cdot 7 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 7280.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: | \(58.1310926715\) |
Analytic rank: | \(1\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.1101.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 9x + 12 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 3640) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(2.68740\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 7280.1 |
$q$-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 | ||||||||
\(3\) | 2.68740 | 1.55157 | 0.775785 | − | 0.630997i | \(-0.217354\pi\) | ||||
0.775785 | + | 0.630997i | \(0.217354\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 4.22212 | 1.40737 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.00000 | −0.277350 | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −2.68740 | −0.693884 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.22212 | 0.296407 | 0.148203 | − | 0.988957i | \(-0.452651\pi\) | ||||
0.148203 | + | 0.988957i | \(0.452651\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.777884 | 0.178459 | 0.0892294 | − | 0.996011i | \(-0.471560\pi\) | ||||
0.0892294 | + | 0.996011i | \(0.471560\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.68740 | −0.586439 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −7.81903 | −1.63038 | −0.815190 | − | 0.579193i | \(-0.803368\pi\) | ||||
−0.815190 | + | 0.579193i | \(0.803368\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 3.28432 | 0.632067 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −7.13163 | −1.32431 | −0.662155 | − | 0.749367i | \(-0.730358\pi\) | ||||
−0.662155 | + | 0.749367i | \(0.730358\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.31260 | −0.235750 | −0.117875 | − | 0.993028i | \(-0.537608\pi\) | ||||
−0.117875 | + | 0.993028i | \(0.537608\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.00000 | 0.169031 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −8.50643 | −1.39845 | −0.699224 | − | 0.714902i | \(-0.746471\pi\) | ||||
−0.699224 | + | 0.714902i | \(0.746471\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −2.68740 | −0.430328 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.22212 | 0.190863 | 0.0954313 | − | 0.995436i | \(-0.469577\pi\) | ||||
0.0954313 | + | 0.995436i | \(0.469577\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.37480 | −0.209655 | −0.104827 | − | 0.994490i | \(-0.533429\pi\) | ||||
−0.104827 | + | 0.994490i | \(0.533429\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −4.22212 | −0.629396 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 3.81903 | 0.557063 | 0.278532 | − | 0.960427i | \(-0.410152\pi\) | ||||
0.278532 | + | 0.960427i | \(0.410152\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 3.28432 | 0.459896 | ||||||||
\(52\) | 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 | ||||||||
\(57\) | 2.09048 | 0.276891 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 4.06220 | 0.528853 | 0.264427 | − | 0.964406i | \(-0.414817\pi\) | ||||
0.264427 | + | 0.964406i | \(0.414817\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −10.0000 | −1.28037 | −0.640184 | − | 0.768221i | \(-0.721142\pi\) | ||||
−0.640184 | + | 0.768221i | \(0.721142\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −4.22212 | −0.531937 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1.00000 | 0.124035 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −12.4159 | −1.51685 | −0.758425 | − | 0.651761i | \(-0.774031\pi\) | ||||
−0.758425 | + | 0.651761i | \(0.774031\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −21.0129 | −2.52965 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −5.37480 | −0.637871 | −0.318936 | − | 0.947776i | \(-0.603325\pi\) | ||||
−0.318936 | + | 0.947776i | \(0.603325\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −0.930566 | −0.108915 | −0.0544573 | − | 0.998516i | \(-0.517343\pi\) | ||||
−0.0544573 | + | 0.998516i | \(0.517343\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 2.68740 | 0.310314 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −0.777884 | −0.0875187 | −0.0437594 | − | 0.999042i | \(-0.513933\pi\) | ||||
−0.0437594 | + | 0.999042i | \(0.513933\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −3.84008 | −0.426676 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 7.81903 | 0.858250 | 0.429125 | − | 0.903245i | \(-0.358822\pi\) | ||||
0.429125 | + | 0.903245i | \(0.358822\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.22212 | −0.132557 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −19.1655 | −2.05476 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −13.8812 | −1.47141 | −0.735704 | − | 0.677303i | \(-0.763148\pi\) | ||||
−0.735704 | + | 0.677303i | \(0.763148\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.00000 | 0.104828 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −3.52748 | −0.365783 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −0.777884 | −0.0798092 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 19.0129 | 1.93046 | 0.965232 | − | 0.261395i | \(-0.0841826\pi\) | ||||
0.965232 | + | 0.261395i | \(0.0841826\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 9.81903 | 0.977030 | 0.488515 | − | 0.872555i | \(-0.337539\pi\) | ||||
0.488515 | + | 0.872555i | \(0.337539\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 12.4159 | 1.22338 | 0.611690 | − | 0.791098i | \(-0.290490\pi\) | ||||
0.611690 | + | 0.791098i | \(0.290490\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 2.68740 | 0.262263 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −13.1938 | −1.27550 | −0.637748 | − | 0.770245i | \(-0.720134\pi\) | ||||
−0.637748 | + | 0.770245i | \(0.720134\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 9.63806 | 0.923159 | 0.461580 | − | 0.887099i | \(-0.347283\pi\) | ||||
0.461580 | + | 0.887099i | \(0.347283\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −22.8602 | −2.16979 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −11.0129 | −1.03600 | −0.518002 | − | 0.855380i | \(-0.673324\pi\) | ||||
−0.518002 | + | 0.855380i | \(0.673324\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 7.81903 | 0.729128 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −4.22212 | −0.390335 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −1.22212 | −0.112031 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −11.0000 | −1.00000 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 3.28432 | 0.296137 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −10.9306 | −0.969931 | −0.484965 | − | 0.874533i | \(-0.661168\pi\) | ||||
−0.484965 | + | 0.874533i | \(0.661168\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −3.69463 | −0.325294 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2.93057 | −0.256045 | −0.128022 | − | 0.991771i | \(-0.540863\pi\) | ||||
−0.128022 | + | 0.991771i | \(0.540863\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −0.777884 | −0.0674511 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −3.28432 | −0.282669 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 8.86837 | 0.757676 | 0.378838 | − | 0.925463i | \(-0.376324\pi\) | ||||
0.378838 | + | 0.925463i | \(0.376324\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2.44423 | 0.207317 | 0.103659 | − | 0.994613i | \(-0.466945\pi\) | ||||
0.103659 | + | 0.994613i | \(0.466945\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 10.2633 | 0.864323 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 7.13163 | 0.592250 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 2.68740 | 0.221653 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 2.00000 | 0.163846 | 0.0819232 | − | 0.996639i | \(-0.473894\pi\) | ||||
0.0819232 | + | 0.996639i | \(0.473894\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2.26326 | 0.184182 | 0.0920909 | − | 0.995751i | \(-0.470645\pi\) | ||||
0.0920909 | + | 0.995751i | \(0.470645\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 5.15992 | 0.417155 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1.31260 | 0.105431 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −5.75683 | −0.459445 | −0.229723 | − | 0.973256i | \(-0.573782\pi\) | ||||
−0.229723 | + | 0.973256i | \(0.573782\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 5.37480 | 0.426249 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 7.81903 | 0.616226 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −10.6874 | −0.837102 | −0.418551 | − | 0.908193i | \(-0.637462\pi\) | ||||
−0.418551 | + | 0.908193i | \(0.637462\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −0.486334 | −0.0376336 | −0.0188168 | − | 0.999823i | \(-0.505990\pi\) | ||||
−0.0188168 | + | 0.999823i | \(0.505990\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 3.28432 | 0.251158 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 9.39490 | 0.714281 | 0.357140 | − | 0.934051i | \(-0.383752\pi\) | ||||
0.357140 | + | 0.934051i | \(0.383752\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.00000 | −0.0755929 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 10.9168 | 0.820553 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −11.2221 | −0.838780 | −0.419390 | − | 0.907806i | \(-0.637756\pi\) | ||||
−0.419390 | + | 0.907806i | \(0.637756\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −15.0129 | −1.11590 | −0.557949 | − | 0.829875i | \(-0.688411\pi\) | ||||
−0.557949 | + | 0.829875i | \(0.688411\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −26.8740 | −1.98658 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 8.50643 | 0.625405 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −3.28432 | −0.238899 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −14.6874 | −1.06274 | −0.531371 | − | 0.847139i | \(-0.678323\pi\) | ||||
−0.531371 | + | 0.847139i | \(0.678323\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 19.6663 | 1.41561 | 0.707807 | − | 0.706405i | \(-0.249684\pi\) | ||||
0.707807 | + | 0.706405i | \(0.249684\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 2.68740 | 0.192449 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 26.3676 | 1.87861 | 0.939306 | − | 0.343082i | \(-0.111471\pi\) | ||||
0.939306 | + | 0.343082i | \(0.111471\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 13.0129 | 0.922457 | 0.461229 | − | 0.887281i | \(-0.347409\pi\) | ||||
0.461229 | + | 0.887281i | \(0.347409\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −33.3666 | −2.35350 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 7.13163 | 0.500542 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1.22212 | −0.0853563 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −33.0129 | −2.29455 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −23.1655 | −1.59478 | −0.797391 | − | 0.603463i | \(-0.793787\pi\) | ||||
−0.797391 | + | 0.603463i | \(0.793787\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −14.4442 | −0.989703 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 1.37480 | 0.0937605 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.31260 | 0.0891051 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −2.50080 | −0.168989 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1.22212 | −0.0822084 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −17.1938 | −1.15138 | −0.575692 | − | 0.817667i | \(-0.695267\pi\) | ||||
−0.575692 | + | 0.817667i | \(0.695267\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 4.22212 | 0.281474 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −15.8190 | −1.04995 | −0.524973 | − | 0.851119i | \(-0.675925\pi\) | ||||
−0.524973 | + | 0.851119i | \(0.675925\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −6.77788 | −0.447895 | −0.223948 | − | 0.974601i | \(-0.571894\pi\) | ||||
−0.223948 | + | 0.974601i | \(0.571894\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −2.18097 | −0.142880 | −0.0714400 | − | 0.997445i | \(-0.522759\pi\) | ||||
−0.0714400 | + | 0.997445i | \(0.522759\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −3.81903 | −0.249126 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −2.09048 | −0.135792 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 3.81903 | 0.247033 | 0.123516 | − | 0.992343i | \(-0.460583\pi\) | ||||
0.123516 | + | 0.992343i | \(0.460583\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2.11058 | −0.135955 | −0.0679773 | − | 0.997687i | \(-0.521655\pi\) | ||||
−0.0679773 | + | 0.997687i | \(0.521655\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −20.1728 | −1.29408 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −1.00000 | −0.0638877 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −0.777884 | −0.0494955 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 21.0129 | 1.33164 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −3.51367 | −0.221781 | −0.110890 | − | 0.993833i | \(-0.535370\pi\) | ||||
−0.110890 | + | 0.993833i | \(0.535370\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −3.28432 | −0.205672 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 31.4992 | 1.96487 | 0.982433 | − | 0.186616i | \(-0.0597520\pi\) | ||||
0.982433 | + | 0.186616i | \(0.0597520\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 8.50643 | 0.528564 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −30.1106 | −1.86380 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −8.18097 | −0.504460 | −0.252230 | − | 0.967667i | \(-0.581164\pi\) | ||||
−0.252230 | + | 0.967667i | \(0.581164\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −2.00000 | −0.122859 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −37.3044 | −2.28299 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 12.5686 | 0.766323 | 0.383161 | − | 0.923681i | \(-0.374835\pi\) | ||||
0.383161 | + | 0.923681i | \(0.374835\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −7.63806 | −0.463979 | −0.231990 | − | 0.972718i | \(-0.574524\pi\) | ||||
−0.231990 | + | 0.972718i | \(0.574524\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 2.68740 | 0.162649 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 8.56863 | 0.514839 | 0.257420 | − | 0.966300i | \(-0.417128\pi\) | ||||
0.257420 | + | 0.966300i | \(0.417128\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −5.54195 | −0.331788 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 31.7204 | 1.89228 | 0.946139 | − | 0.323761i | \(-0.104947\pi\) | ||||
0.946139 | + | 0.323761i | \(0.104947\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −7.16555 | −0.425947 | −0.212974 | − | 0.977058i | \(-0.568315\pi\) | ||||
−0.212974 | + | 0.977058i | \(0.568315\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −2.09048 | −0.123830 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −1.22212 | −0.0721393 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −15.5064 | −0.912143 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 51.0952 | 2.99525 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 3.19383 | 0.186586 | 0.0932928 | − | 0.995639i | \(-0.470261\pi\) | ||||
0.0932928 | + | 0.995639i | \(0.470261\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −4.06220 | −0.236510 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 7.81903 | 0.452186 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.37480 | 0.0792421 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 26.3877 | 1.51593 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 10.0000 | 0.572598 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −15.8190 | −0.902840 | −0.451420 | − | 0.892312i | \(-0.649082\pi\) | ||||
−0.451420 | + | 0.892312i | \(0.649082\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 33.3666 | 1.89816 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −19.9434 | −1.13089 | −0.565444 | − | 0.824787i | \(-0.691295\pi\) | ||||
−0.565444 | + | 0.824787i | \(0.691295\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −5.39490 | −0.304938 | −0.152469 | − | 0.988308i | \(-0.548722\pi\) | ||||
−0.152469 | + | 0.988308i | \(0.548722\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 4.22212 | 0.237889 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −10.8885 | −0.611557 | −0.305779 | − | 0.952103i | \(-0.598917\pi\) | ||||
−0.305779 | + | 0.952103i | \(0.598917\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −35.4571 | −1.97902 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0.950664 | 0.0528964 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1.00000 | −0.0554700 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 25.9013 | 1.43235 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −3.81903 | −0.210550 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −7.63806 | −0.419826 | −0.209913 | − | 0.977720i | \(-0.567318\pi\) | ||||
−0.209913 | + | 0.977720i | \(0.567318\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −35.9151 | −1.96814 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 12.4159 | 0.678356 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 12.7496 | 0.694515 | 0.347257 | − | 0.937770i | \(-0.387113\pi\) | ||||
0.347257 | + | 0.937770i | \(0.387113\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −29.5960 | −1.60743 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 21.0129 | 1.13129 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 28.3456 | 1.52167 | 0.760835 | − | 0.648946i | \(-0.224790\pi\) | ||||
0.760835 | + | 0.648946i | \(0.224790\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 6.64530 | 0.355715 | 0.177857 | − | 0.984056i | \(-0.443083\pi\) | ||||
0.177857 | + | 0.984056i | \(0.443083\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −3.28432 | −0.175304 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −4.13887 | −0.220290 | −0.110145 | − | 0.993916i | \(-0.535131\pi\) | ||||
−0.110145 | + | 0.993916i | \(0.535131\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 5.37480 | 0.285265 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −3.28432 | −0.173824 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −29.7204 | −1.56858 | −0.784290 | − | 0.620394i | \(-0.786973\pi\) | ||||
−0.784290 | + | 0.620394i | \(0.786973\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.3949 | −0.968152 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −29.5614 | −1.55157 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0.930566 | 0.0487081 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −4.36194 | −0.227691 | −0.113846 | − | 0.993498i | \(-0.536317\pi\) | ||||
−0.113846 | + | 0.993498i | \(0.536317\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 5.15992 | 0.268615 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −2.00000 | −0.103835 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −24.8740 | −1.28793 | −0.643963 | − | 0.765056i | \(-0.722711\pi\) | ||||
−0.643963 | + | 0.765056i | \(0.722711\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −2.68740 | −0.138777 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 7.13163 | 0.367298 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 19.4571 | 0.999444 | 0.499722 | − | 0.866186i | \(-0.333436\pi\) | ||||
0.499722 | + | 0.866186i | \(0.333436\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −29.3748 | −1.50492 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 3.69463 | 0.188787 | 0.0943935 | − | 0.995535i | \(-0.469909\pi\) | ||||
0.0943935 | + | 0.995535i | \(0.469909\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −5.80456 | −0.295062 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 12.6390 | 0.640824 | 0.320412 | − | 0.947278i | \(-0.396179\pi\) | ||||
0.320412 | + | 0.947278i | \(0.396179\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −9.55577 | −0.483256 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −7.87560 | −0.397272 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0.777884 | 0.0391396 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −1.69463 | −0.0850513 | −0.0425256 | − | 0.999095i | \(-0.513540\pi\) | ||||
−0.0425256 | + | 0.999095i | \(0.513540\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −2.09048 | −0.104655 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −33.5815 | −1.67698 | −0.838490 | − | 0.544917i | \(-0.816561\pi\) | ||||
−0.838490 | + | 0.544917i | \(0.816561\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.31260 | 0.0653853 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 3.84008 | 0.190815 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −26.8885 | −1.32955 | −0.664775 | − | 0.747044i | \(-0.731472\pi\) | ||||
−0.664775 | + | 0.747044i | \(0.731472\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 23.8328 | 1.17559 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −4.06220 | −0.199888 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −7.81903 | −0.383821 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 6.56863 | 0.321667 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −5.55577 | −0.271417 | −0.135708 | − | 0.990749i | \(-0.543331\pi\) | ||||
−0.135708 | + | 0.990749i | \(0.543331\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 4.74960 | 0.231481 | 0.115741 | − | 0.993279i | \(-0.463076\pi\) | ||||
0.115741 | + | 0.993279i | \(0.463076\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 16.1244 | 0.783995 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 1.22212 | 0.0592814 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 10.0000 | 0.483934 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −16.8319 | −0.810764 | −0.405382 | − | 0.914147i | \(-0.632861\pi\) | ||||
−0.405382 | + | 0.914147i | \(0.632861\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −30.4159 | −1.46170 | −0.730849 | − | 0.682540i | \(-0.760875\pi\) | ||||
−0.730849 | + | 0.682540i | \(0.760875\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 19.1655 | 0.918918 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −6.08230 | −0.290956 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 3.11153 | 0.148505 | 0.0742527 | − | 0.997239i | \(-0.476343\pi\) | ||||
0.0742527 | + | 0.997239i | \(0.476343\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 4.22212 | 0.201053 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 7.81903 | 0.371493 | 0.185747 | − | 0.982598i | \(-0.440530\pi\) | ||||
0.185747 | + | 0.982598i | \(0.440530\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 13.8812 | 0.658033 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 5.37480 | 0.254219 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 31.0129 | 1.46359 | 0.731794 | − | 0.681526i | \(-0.238683\pi\) | ||||
0.731794 | + | 0.681526i | \(0.238683\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 6.08230 | 0.285771 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −1.00000 | −0.0468807 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 0.868368 | 0.0406205 | 0.0203103 | − | 0.999794i | \(-0.493535\pi\) | ||||
0.0203103 | + | 0.999794i | \(0.493535\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 4.01382 | 0.187349 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −14.3676 | −0.669164 | −0.334582 | − | 0.942367i | \(-0.608595\pi\) | ||||
−0.334582 | + | 0.942367i | \(0.608595\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 4.11058 | 0.191035 | 0.0955175 | − | 0.995428i | \(-0.469549\pi\) | ||||
0.0955175 | + | 0.995428i | \(0.469549\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 3.52748 | 0.163583 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −14.5548 | −0.673517 | −0.336758 | − | 0.941591i | \(-0.609331\pi\) | ||||
−0.336758 | + | 0.941591i | \(0.609331\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 12.4159 | 0.573315 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −15.4709 | −0.712862 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0.777884 | 0.0356917 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 8.44423 | 0.386635 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −24.9507 | −1.14002 | −0.570012 | − | 0.821636i | \(-0.693062\pi\) | ||||
−0.570012 | + | 0.821636i | \(0.693062\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 8.50643 | 0.387860 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 21.0129 | 0.956118 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −19.0129 | −0.863330 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 23.1737 | 1.05010 | 0.525051 | − | 0.851071i | \(-0.324046\pi\) | ||||
0.525051 | + | 0.851071i | \(0.324046\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −28.7213 | −1.29882 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 22.3877 | 1.01034 | 0.505171 | − | 0.863020i | \(-0.331430\pi\) | ||||
0.505171 | + | 0.863020i | \(0.331430\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −8.71568 | −0.392535 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 5.37480 | 0.241093 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 36.5265 | 1.63515 | 0.817576 | − | 0.575821i | \(-0.195317\pi\) | ||||
0.817576 | + | 0.575821i | \(0.195317\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −1.30697 | −0.0583912 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −4.36194 | −0.194489 | −0.0972446 | − | 0.995261i | \(-0.531003\pi\) | ||||
−0.0972446 | + | 0.995261i | \(0.531003\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −9.81903 | −0.436941 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 2.68740 | 0.119352 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 9.58405 | 0.424806 | 0.212403 | − | 0.977182i | \(-0.431871\pi\) | ||||
0.212403 | + | 0.977182i | \(0.431871\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0.930566 | 0.0411658 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 2.55481 | 0.112798 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −12.4159 | −0.547112 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 25.2478 | 1.10826 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 21.0952 | 0.924196 | 0.462098 | − | 0.886829i | \(-0.347097\pi\) | ||||
0.462098 | + | 0.886829i | \(0.347097\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −6.13887 | −0.268434 | −0.134217 | − | 0.990952i | \(-0.542852\pi\) | ||||
−0.134217 | + | 0.990952i | \(0.542852\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −2.68740 | −0.117288 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −1.60415 | −0.0698779 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 38.1373 | 1.65814 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 17.1511 | 0.744293 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −1.22212 | −0.0529357 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 13.1938 | 0.570419 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −30.1583 | −1.30143 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −31.1938 | −1.34113 | −0.670564 | − | 0.741852i | \(-0.733948\pi\) | ||||
−0.670564 | + | 0.741852i | \(0.733948\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −40.3456 | −1.73139 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −9.63806 | −0.412849 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −5.06943 | −0.216753 | −0.108377 | − | 0.994110i | \(-0.534565\pi\) | ||||
−0.108377 | + | 0.994110i | \(0.534565\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −42.2212 | −1.80196 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −5.54758 | −0.236335 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0.777884 | 0.0330790 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 22.8602 | 0.970361 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −2.11058 | −0.0894282 | −0.0447141 | − | 0.999000i | \(-0.514238\pi\) | ||||
−0.0447141 | + | 0.999000i | \(0.514238\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1.37480 | 0.0581478 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 10.6390 | 0.448381 | 0.224191 | − | 0.974545i | \(-0.428026\pi\) | ||||
0.224191 | + | 0.974545i | \(0.428026\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 11.0129 | 0.463315 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 3.84008 | 0.161268 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 12.0201 | 0.503909 | 0.251954 | − | 0.967739i | \(-0.418927\pi\) | ||||
0.251954 | + | 0.967739i | \(0.418927\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 18.6874 | 0.782043 | 0.391022 | − | 0.920381i | \(-0.372122\pi\) | ||||
0.391022 | + | 0.920381i | \(0.372122\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −39.4709 | −1.64892 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −7.81903 | −0.326076 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 43.8448 | 1.82528 | 0.912641 | − | 0.408763i | \(-0.134040\pi\) | ||||
0.912641 | + | 0.408763i | \(0.134040\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 52.8513 | 2.19643 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −7.81903 | −0.324388 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 4.22212 | 0.174563 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 7.33270 | 0.302653 | 0.151326 | − | 0.988484i | \(-0.451646\pi\) | ||||
0.151326 | + | 0.988484i | \(0.451646\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1.02105 | −0.0420716 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 70.8602 | 2.91480 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −5.45710 | −0.224096 | −0.112048 | − | 0.993703i | \(-0.535741\pi\) | ||||
−0.112048 | + | 0.993703i | \(0.535741\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1.22212 | 0.0501019 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 34.9708 | 1.43126 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −0.361936 | −0.0147883 | −0.00739415 | − | 0.999973i | \(-0.502354\pi\) | ||||
−0.00739415 | + | 0.999973i | \(0.502354\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 12.8740 | 0.525141 | 0.262571 | − | 0.964913i | \(-0.415430\pi\) | ||||
0.262571 | + | 0.964913i | \(0.415430\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −52.4216 | −2.13477 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 11.0000 | 0.447214 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 18.6874 | 0.758498 | 0.379249 | − | 0.925295i | \(-0.376182\pi\) | ||||
0.379249 | + | 0.925295i | \(0.376182\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 19.1655 | 0.776627 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −3.81903 | −0.154501 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 28.3877 | 1.14657 | 0.573283 | − | 0.819357i | \(-0.305669\pi\) | ||||
0.573283 | + | 0.819357i | \(0.305669\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −3.28432 | −0.132436 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 32.3337 | 1.30170 | 0.650852 | − | 0.759205i | \(-0.274412\pi\) | ||||
0.650852 | + | 0.759205i | \(0.274412\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 43.7003 | 1.75646 | 0.878231 | − | 0.478237i | \(-0.158724\pi\) | ||||
0.878231 | + | 0.478237i | \(0.158724\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −25.6802 | −1.03051 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 13.8812 | 0.556140 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −10.3958 | −0.414510 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 3.33270 | 0.132673 | 0.0663363 | − | 0.997797i | \(-0.478869\pi\) | ||||
0.0663363 | + | 0.997797i | \(0.478869\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −62.2551 | −2.47442 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 10.9306 | 0.433766 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.00000 | −0.0396214 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −22.6930 | −0.897722 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 4.99276 | 0.197202 | 0.0986012 | − | 0.995127i | \(-0.468563\pi\) | ||||
0.0986012 | + | 0.995127i | \(0.468563\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 2.20669 | 0.0870235 | 0.0435118 | − | 0.999053i | \(-0.486145\pi\) | ||||
0.0435118 | + | 0.999053i | \(0.486145\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 3.69463 | 0.145476 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −5.31260 | −0.208860 | −0.104430 | − | 0.994532i | \(-0.533302\pi\) | ||||
−0.104430 | + | 0.994532i | \(0.533302\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 3.52748 | 0.138253 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −28.6930 | −1.12284 | −0.561422 | − | 0.827529i | \(-0.689746\pi\) | ||||
−0.561422 | + | 0.827529i | \(0.689746\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 2.93057 | 0.114507 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −3.92896 | −0.153283 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −40.9425 | −1.59489 | −0.797446 | − | 0.603390i | \(-0.793816\pi\) | ||||
−0.797446 | + | 0.603390i | \(0.793816\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 22.9425 | 0.892359 | 0.446179 | − | 0.894944i | \(-0.352784\pi\) | ||||
0.446179 | + | 0.894944i | \(0.352784\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −3.28432 | −0.127552 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0.777884 | 0.0301650 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 55.7625 | 2.15913 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −46.2067 | −1.78645 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 3.68016 | 0.141860 | 0.0709300 | − | 0.997481i | \(-0.477403\pi\) | ||||
0.0709300 | + | 0.997481i | \(0.477403\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 3.28432 | 0.126413 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 28.3877 | 1.09103 | 0.545513 | − | 0.838102i | \(-0.316335\pi\) | ||||
0.545513 | + | 0.838102i | \(0.316335\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −19.0129 | −0.729647 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −42.5121 | −1.62907 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 13.6098 | 0.520764 | 0.260382 | − | 0.965506i | \(-0.416152\pi\) | ||||
0.260382 | + | 0.965506i | \(0.416152\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −8.86837 | −0.338843 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −18.2149 | −0.694941 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −2.00000 | −0.0761939 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 9.43700 | 0.359000 | 0.179500 | − | 0.983758i | \(-0.442552\pi\) | ||||
0.179500 | + | 0.983758i | \(0.442552\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −2.44423 | −0.0927150 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.49357 | 0.0565729 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −5.86113 | −0.221688 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 18.4725 | 0.697697 | 0.348849 | − | 0.937179i | \(-0.386573\pi\) | ||||
0.348849 | + | 0.937179i | \(0.386573\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −6.61701 | −0.249565 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −10.2633 | −0.386537 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −9.81903 | −0.369283 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 27.6802 | 1.03955 | 0.519775 | − | 0.854303i | \(-0.326016\pi\) | ||||
0.519775 | + | 0.854303i | \(0.326016\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −3.28432 | −0.123171 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 10.2633 | 0.384362 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 10.2633 | 0.383289 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 41.8046 | 1.55905 | 0.779524 | − | 0.626373i | \(-0.215461\pi\) | ||||
0.779524 | + | 0.626373i | \(0.215461\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −12.4159 | −0.462394 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −5.67198 | −0.210943 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −7.13163 | −0.264862 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −23.5759 | −0.874380 | −0.437190 | − | 0.899369i | \(-0.644026\pi\) | ||||
−0.437190 | + | 0.899369i | \(0.644026\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −42.6921 | −1.58119 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1.68016 | −0.0621431 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −2.52653 | −0.0933195 | −0.0466597 | − | 0.998911i | \(-0.514858\pi\) | ||||
−0.0466597 | + | 0.998911i | \(0.514858\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −2.68740 | −0.0991262 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −6.80617 | −0.250369 | −0.125184 | − | 0.992133i | \(-0.539952\pi\) | ||||
−0.125184 | + | 0.992133i | \(0.539952\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −2.09048 | −0.0767958 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −50.4417 | −1.85053 | −0.925263 | − | 0.379327i | \(-0.876156\pi\) | ||||
−0.925263 | + | 0.379327i | \(0.876156\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −2.00000 | −0.0732743 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 33.0129 | 1.20788 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 13.1938 | 0.482092 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 32.4643 | 1.18464 | 0.592320 | − | 0.805703i | \(-0.298212\pi\) | ||||
0.592320 | + | 0.805703i | \(0.298212\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −9.44263 | −0.344108 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −2.26326 | −0.0823686 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −5.63806 | −0.204919 | −0.102459 | − | 0.994737i | \(-0.532671\pi\) | ||||
−0.102459 | + | 0.994737i | \(0.532671\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 36.7552 | 1.33238 | 0.666188 | − | 0.745784i | \(-0.267925\pi\) | ||||
0.666188 | + | 0.745784i | \(0.267925\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −9.63806 | −0.348921 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −5.15992 | −0.186557 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −4.06220 | −0.146677 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 34.2488 | 1.23504 | 0.617522 | − | 0.786554i | \(-0.288137\pi\) | ||||
0.617522 | + | 0.786554i | \(0.288137\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 84.6509 | 3.04863 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 33.8869 | 1.21883 | 0.609413 | − | 0.792853i | \(-0.291405\pi\) | ||||
0.609413 | + | 0.792853i | \(0.291405\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1.31260 | −0.0471500 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 22.8602 | 0.820104 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0.950664 | 0.0340611 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −23.4225 | −0.837053 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 5.75683 | 0.205470 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 6.50080 | 0.231729 | 0.115864 | − | 0.993265i | \(-0.463036\pi\) | ||||
0.115864 | + | 0.993265i | \(0.463036\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −21.9855 | −0.782706 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 11.0129 | 0.391572 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 10.0000 | 0.355110 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −5.37480 | −0.190624 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 6.76970 | 0.239795 | 0.119897 | − | 0.992786i | \(-0.461743\pi\) | ||||
0.119897 | + | 0.992786i | \(0.461743\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 4.66730 | 0.165117 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −58.6082 | −2.07082 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −7.81903 | −0.275585 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 33.7769 | 1.18900 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 6.72131 | 0.236309 | 0.118154 | − | 0.992995i | \(-0.462302\pi\) | ||||
0.118154 | + | 0.992995i | \(0.462302\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −30.9142 | −1.08554 | −0.542772 | − | 0.839880i | \(-0.682625\pi\) | ||||
−0.542772 | + | 0.839880i | \(0.682625\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −20.5265 | −0.719897 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 10.6874 | 0.374363 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1.06943 | −0.0374147 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 4.22212 | 0.147533 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −10.6673 | −0.372291 | −0.186146 | − | 0.982522i | \(-0.559600\pi\) | ||||
−0.186146 | + | 0.982522i | \(0.559600\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −6.50080 | −0.226604 | −0.113302 | − | 0.993561i | \(-0.536143\pi\) | ||||
−0.113302 | + | 0.993561i | \(0.536143\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −33.1373 | −1.15230 | −0.576148 | − | 0.817346i | \(-0.695445\pi\) | ||||
−0.576148 | + | 0.817346i | \(0.695445\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 30.9563 | 1.07516 | 0.537578 | − | 0.843214i | \(-0.319339\pi\) | ||||
0.537578 | + | 0.843214i | \(0.319339\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 23.0273 | 0.798809 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 1.22212 | 0.0423438 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0.486334 | 0.0168303 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −4.31099 | −0.149010 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 31.6381 | 1.09227 | 0.546134 | − | 0.837698i | \(-0.316099\pi\) | ||||
0.546134 | + | 0.837698i | \(0.316099\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 21.8602 | 0.753799 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 85.2453 | 2.93600 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −1.00000 | −0.0344010 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 11.0000 | 0.377964 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −19.2567 | −0.660888 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 66.5121 | 2.28000 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −36.9306 | −1.26448 | −0.632239 | − | 0.774773i | \(-0.717864\pi\) | ||||
−0.632239 | + | 0.774773i | \(0.717864\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −3.28432 | −0.112321 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −21.6437 | −0.739334 | −0.369667 | − | 0.929164i | \(-0.620528\pi\) | ||||
−0.369667 | + | 0.929164i | \(0.620528\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −26.0823 | −0.889916 | −0.444958 | − | 0.895551i | \(-0.646781\pi\) | ||||
−0.444958 | + | 0.895551i | \(0.646781\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −3.28432 | −0.111929 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 42.8036 | 1.45705 | 0.728526 | − | 0.685018i | \(-0.240206\pi\) | ||||
0.728526 | + | 0.685018i | \(0.240206\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −9.39490 | −0.319436 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −41.6720 | −1.41525 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 12.4159 | 0.420698 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 80.2745 | 2.71688 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 1.00000 | 0.0338062 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 2.99905 | 0.101271 | 0.0506353 | − | 0.998717i | \(-0.483875\pi\) | ||||
0.0506353 | + | 0.998717i | \(0.483875\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 8.58310 | 0.289501 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 33.0386 | 1.11310 | 0.556549 | − | 0.830815i | \(-0.312125\pi\) | ||||
0.556549 | + | 0.830815i | \(0.312125\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −32.5265 | −1.09460 | −0.547302 | − | 0.836935i | \(-0.684345\pi\) | ||||
−0.547302 | + | 0.836935i | \(0.684345\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −10.9168 | −0.366963 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 19.0493 | 0.639614 | 0.319807 | − | 0.947483i | \(-0.396382\pi\) | ||||
0.319807 | + | 0.947483i | \(0.396382\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 10.9306 | 0.366599 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 2.97076 | 0.0994128 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 11.2221 | 0.375114 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 21.0129 | 0.701599 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 9.36098 | 0.312206 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 2.44423 | 0.0814292 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 3.69463 | 0.122950 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 15.0129 | 0.499044 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −33.8611 | −1.12434 | −0.562170 | − | 0.827022i | \(-0.690033\pi\) | ||||
−0.562170 | + | 0.827022i | \(0.690033\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 41.4571 | 1.37505 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 2.19288 | 0.0726533 | 0.0363267 | − | 0.999340i | \(-0.488434\pi\) | ||||
0.0363267 | + | 0.999340i | \(0.488434\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 26.8740 | 0.888427 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 2.93057 | 0.0967758 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 24.9507 | 0.823046 | 0.411523 | − | 0.911399i | \(-0.364997\pi\) | ||||
0.411523 | + | 0.911399i | \(0.364997\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −42.5121 | −1.40082 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 5.37480 | 0.176914 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −8.50643 | −0.279690 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 52.4216 | 1.72175 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −24.0201 | −0.788074 | −0.394037 | − | 0.919095i | \(-0.628922\pi\) | ||||
−0.394037 | + | 0.919095i | \(0.628922\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0.777884 | 0.0254941 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −53.5960 | −1.75465 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −27.6663 | −0.903820 | −0.451910 | − | 0.892063i | \(-0.649257\pi\) | ||||
−0.451910 | + | 0.892063i | \(0.649257\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −14.4982 | −0.473132 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −24.8036 | −0.808575 | −0.404287 | − | 0.914632i | \(-0.632480\pi\) | ||||
−0.404287 | + | 0.914632i | \(0.632480\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −9.55577 | −0.311179 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 3.28432 | 0.106839 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 28.0540 | 0.911633 | 0.455816 | − | 0.890074i | \(-0.349347\pi\) | ||||
0.455816 | + | 0.890074i | \(0.349347\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0.930566 | 0.0302075 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −29.2617 | −0.948874 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −52.4555 | −1.69920 | −0.849600 | − | 0.527428i | \(-0.823157\pi\) | ||||
−0.849600 | + | 0.527428i | \(0.823157\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 14.6874 | 0.475273 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −8.86837 | −0.286375 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −29.2771 | −0.944422 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −55.7059 | −1.79510 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −19.6663 | −0.633082 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −30.2011 | −0.971201 | −0.485600 | − | 0.874181i | \(-0.661399\pi\) | ||||
−0.485600 | + | 0.874181i | \(0.661399\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 2.55481 | 0.0820725 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −17.8611 | −0.573191 | −0.286596 | − | 0.958052i | \(-0.592524\pi\) | ||||
−0.286596 | + | 0.958052i | \(0.592524\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −2.44423 | −0.0783585 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −2.68740 | −0.0860657 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 15.7506 | 0.503905 | 0.251952 | − | 0.967740i | \(-0.418927\pi\) | ||||
0.251952 | + | 0.967740i | \(0.418927\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 40.6930 | 1.29923 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 38.9306 | 1.24169 | 0.620846 | − | 0.783932i | \(-0.286789\pi\) | ||||
0.620846 | + | 0.783932i | \(0.286789\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −26.3676 | −0.840140 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −10.2633 | −0.326683 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 10.7496 | 0.341817 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −53.9151 | −1.71267 | −0.856335 | − | 0.516420i | \(-0.827264\pi\) | ||||
−0.856335 | + | 0.516420i | \(0.827264\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −20.5265 | −0.651390 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −13.0129 | −0.412535 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −62.0540 | −1.96527 | −0.982635 | − | 0.185548i | \(-0.940594\pi\) | ||||
−0.982635 | + | 0.185548i | \(0.940594\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −27.9378 | −0.883913 |
(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 | 7280.2.a.bn.1.3 | 3 | ||
4.3 | odd | 2 | 3640.2.a.p.1.1 | ✓ | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3640.2.a.p.1.1 | ✓ | 3 | 4.3 | odd | 2 | ||
7280.2.a.bn.1.3 | 3 | 1.1 | even | 1 | trivial |