Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4200,2,Mod(1,4200)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4200, 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("4200.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4200 = 2^{3} \cdot 3 \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4200.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: | \(33.5371688489\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.148.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 3x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 840) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(0.311108\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4200.1 |
$q$-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 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.80642 | −1.14768 | −0.573840 | − | 0.818967i | \(-0.694547\pi\) | ||||
−0.573840 | + | 0.818967i | \(0.694547\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.622216 | 0.172572 | 0.0862858 | − | 0.996270i | \(-0.472500\pi\) | ||||
0.0862858 | + | 0.996270i | \(0.472500\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −4.42864 | −1.07410 | −0.537051 | − | 0.843550i | \(-0.680462\pi\) | ||||
−0.537051 | + | 0.843550i | \(0.680462\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.622216 | 0.142746 | 0.0713730 | − | 0.997450i | \(-0.477262\pi\) | ||||
0.0713730 | + | 0.997450i | \(0.477262\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.00000 | 0.218218 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.62222 | 0.546770 | 0.273385 | − | 0.961905i | \(-0.411857\pi\) | ||||
0.273385 | + | 0.961905i | \(0.411857\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 9.61285 | 1.78506 | 0.892531 | − | 0.450987i | \(-0.148928\pi\) | ||||
0.892531 | + | 0.450987i | \(0.148928\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.622216 | −0.111753 | −0.0558766 | − | 0.998438i | \(-0.517795\pi\) | ||||
−0.0558766 | + | 0.998438i | \(0.517795\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −3.80642 | −0.662613 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.24443 | −0.204583 | −0.102292 | − | 0.994754i | \(-0.532617\pi\) | ||||
−0.102292 | + | 0.994754i | \(0.532617\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0.622216 | 0.0996342 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 4.62222 | 0.721869 | 0.360934 | − | 0.932591i | \(-0.382458\pi\) | ||||
0.360934 | + | 0.932591i | \(0.382458\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −4.85728 | −0.740728 | −0.370364 | − | 0.928887i | \(-0.620767\pi\) | ||||
−0.370364 | + | 0.928887i | \(0.620767\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 11.6128 | 1.69391 | 0.846954 | − | 0.531666i | \(-0.178434\pi\) | ||||
0.846954 | + | 0.531666i | \(0.178434\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −4.42864 | −0.620134 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 13.4795 | 1.85155 | 0.925775 | − | 0.378074i | \(-0.123413\pi\) | ||||
0.925775 | + | 0.378074i | \(0.123413\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0.622216 | 0.0824145 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 11.6128 | 1.51186 | 0.755932 | − | 0.654650i | \(-0.227184\pi\) | ||||
0.755932 | + | 0.654650i | \(0.227184\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −8.10171 | −1.03732 | −0.518659 | − | 0.854981i | \(-0.673569\pi\) | ||||
−0.518659 | + | 0.854981i | \(0.673569\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 1.00000 | 0.125988 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 2.62222 | 0.315678 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.56199 | 0.304053 | 0.152026 | − | 0.988376i | \(-0.451420\pi\) | ||||
0.152026 | + | 0.988376i | \(0.451420\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 10.9906 | 1.28636 | 0.643178 | − | 0.765717i | \(-0.277615\pi\) | ||||
0.643178 | + | 0.765717i | \(0.277615\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −3.80642 | −0.433782 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −6.75557 | −0.760061 | −0.380030 | − | 0.924974i | \(-0.624086\pi\) | ||||
−0.380030 | + | 0.924974i | \(0.624086\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 11.6128 | 1.27468 | 0.637338 | − | 0.770585i | \(-0.280036\pi\) | ||||
0.637338 | + | 0.770585i | \(0.280036\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 9.61285 | 1.03061 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −8.23506 | −0.872915 | −0.436457 | − | 0.899725i | \(-0.643767\pi\) | ||||
−0.436457 | + | 0.899725i | \(0.643767\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.622216 | 0.0652259 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −0.622216 | −0.0645208 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 4.23506 | 0.430006 | 0.215003 | − | 0.976613i | \(-0.431024\pi\) | ||||
0.215003 | + | 0.976613i | \(0.431024\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −3.80642 | −0.382560 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 18.7239 | 1.86310 | 0.931550 | − | 0.363613i | \(-0.118457\pi\) | ||||
0.931550 | + | 0.363613i | \(0.118457\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −0.857279 | −0.0844702 | −0.0422351 | − | 0.999108i | \(-0.513448\pi\) | ||||
−0.0422351 | + | 0.999108i | \(0.513448\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −11.0923 | −1.07234 | −0.536169 | − | 0.844111i | \(-0.680129\pi\) | ||||
−0.536169 | + | 0.844111i | \(0.680129\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 5.61285 | 0.537613 | 0.268807 | − | 0.963194i | \(-0.413371\pi\) | ||||
0.268807 | + | 0.963194i | \(0.413371\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −1.24443 | −0.118116 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 16.2351 | 1.52727 | 0.763633 | − | 0.645650i | \(-0.223414\pi\) | ||||
0.763633 | + | 0.645650i | \(0.223414\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0.622216 | 0.0575239 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −4.42864 | −0.405973 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 3.48886 | 0.317169 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 4.62222 | 0.416771 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 15.3461 | 1.36175 | 0.680875 | − | 0.732400i | \(-0.261600\pi\) | ||||
0.680875 | + | 0.732400i | \(0.261600\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −4.85728 | −0.427660 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −4.00000 | −0.349482 | −0.174741 | − | 0.984614i | \(-0.555909\pi\) | ||||
−0.174741 | + | 0.984614i | \(0.555909\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.622216 | 0.0539529 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −17.0923 | −1.46030 | −0.730149 | − | 0.683288i | \(-0.760549\pi\) | ||||
−0.730149 | + | 0.683288i | \(0.760549\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −13.4795 | −1.14332 | −0.571658 | − | 0.820492i | \(-0.693700\pi\) | ||||
−0.571658 | + | 0.820492i | \(0.693700\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 11.6128 | 0.977978 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −2.36842 | −0.198057 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 1.00000 | 0.0824786 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −9.34614 | −0.765666 | −0.382833 | − | 0.923818i | \(-0.625051\pi\) | ||||
−0.382833 | + | 0.923818i | \(0.625051\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −7.14272 | −0.581266 | −0.290633 | − | 0.956835i | \(-0.593866\pi\) | ||||
−0.290633 | + | 0.956835i | \(0.593866\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −4.42864 | −0.358034 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −6.99063 | −0.557913 | −0.278957 | − | 0.960304i | \(-0.589989\pi\) | ||||
−0.278957 | + | 0.960304i | \(0.589989\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 13.4795 | 1.06899 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 2.62222 | 0.206660 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 15.6128 | 1.22289 | 0.611446 | − | 0.791286i | \(-0.290588\pi\) | ||||
0.611446 | + | 0.791286i | \(0.290588\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −1.51114 | −0.116935 | −0.0584677 | − | 0.998289i | \(-0.518621\pi\) | ||||
−0.0584677 | + | 0.998289i | \(0.518621\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.6128 | −0.970219 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0.622216 | 0.0475820 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −6.53035 | −0.496493 | −0.248247 | − | 0.968697i | \(-0.579854\pi\) | ||||
−0.248247 | + | 0.968697i | \(0.579854\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 11.6128 | 0.872875 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −6.29529 | −0.470532 | −0.235266 | − | 0.971931i | \(-0.575596\pi\) | ||||
−0.235266 | + | 0.971931i | \(0.575596\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −6.85728 | −0.509698 | −0.254849 | − | 0.966981i | \(-0.582026\pi\) | ||||
−0.254849 | + | 0.966981i | \(0.582026\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −8.10171 | −0.598896 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 16.8573 | 1.23273 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 1.00000 | 0.0727393 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −10.5620 | −0.764239 | −0.382119 | − | 0.924113i | \(-0.624806\pi\) | ||||
−0.382119 | + | 0.924113i | \(0.624806\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 5.24443 | 0.377502 | 0.188751 | − | 0.982025i | \(-0.439556\pi\) | ||||
0.188751 | + | 0.982025i | \(0.439556\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 17.7462 | 1.26436 | 0.632182 | − | 0.774820i | \(-0.282159\pi\) | ||||
0.632182 | + | 0.774820i | \(0.282159\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −20.2351 | −1.43443 | −0.717213 | − | 0.696854i | \(-0.754582\pi\) | ||||
−0.717213 | + | 0.696854i | \(0.754582\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 9.61285 | 0.674690 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 2.62222 | 0.182257 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −2.36842 | −0.163827 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 21.3274 | 1.46824 | 0.734120 | − | 0.679020i | \(-0.237595\pi\) | ||||
0.734120 | + | 0.679020i | \(0.237595\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 2.56199 | 0.175545 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −0.622216 | −0.0422387 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 10.9906 | 0.742678 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −2.75557 | −0.185360 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −9.71456 | −0.650535 | −0.325267 | − | 0.945622i | \(-0.605454\pi\) | ||||
−0.325267 | + | 0.945622i | \(0.605454\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −11.3461 | −0.753070 | −0.376535 | − | 0.926402i | \(-0.622885\pi\) | ||||
−0.376535 | + | 0.926402i | \(0.622885\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1.34614 | 0.0889555 | 0.0444778 | − | 0.999010i | \(-0.485838\pi\) | ||||
0.0444778 | + | 0.999010i | \(0.485838\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −3.80642 | −0.250444 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 15.3778 | 1.00743 | 0.503716 | − | 0.863869i | \(-0.331966\pi\) | ||||
0.503716 | + | 0.863869i | \(0.331966\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −6.75557 | −0.438821 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 7.53972 | 0.487704 | 0.243852 | − | 0.969812i | \(-0.421589\pi\) | ||||
0.243852 | + | 0.969812i | \(0.421589\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 23.9813 | 1.54477 | 0.772385 | − | 0.635155i | \(-0.219064\pi\) | ||||
0.772385 | + | 0.635155i | \(0.219064\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0.387152 | 0.0246339 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 11.6128 | 0.735934 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 14.1017 | 0.890092 | 0.445046 | − | 0.895508i | \(-0.353187\pi\) | ||||
0.445046 | + | 0.895508i | \(0.353187\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −9.98126 | −0.627517 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 17.0192 | 1.06163 | 0.530815 | − | 0.847488i | \(-0.321886\pi\) | ||||
0.530815 | + | 0.847488i | \(0.321886\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1.24443 | −0.0773252 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 9.61285 | 0.595020 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 12.6035 | 0.777164 | 0.388582 | − | 0.921414i | \(-0.372965\pi\) | ||||
0.388582 | + | 0.921414i | \(0.372965\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −8.23506 | −0.503978 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 3.76494 | 0.229552 | 0.114776 | − | 0.993391i | \(-0.463385\pi\) | ||||
0.114776 | + | 0.993391i | \(0.463385\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −17.8666 | −1.08532 | −0.542661 | − | 0.839952i | \(-0.682583\pi\) | ||||
−0.542661 | + | 0.839952i | \(0.682583\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0.622216 | 0.0376582 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1.24443 | −0.0747706 | −0.0373853 | − | 0.999301i | \(-0.511903\pi\) | ||||
−0.0373853 | + | 0.999301i | \(0.511903\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −0.622216 | −0.0372511 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −8.95899 | −0.534448 | −0.267224 | − | 0.963634i | \(-0.586106\pi\) | ||||
−0.267224 | + | 0.963634i | \(0.586106\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 30.5718 | 1.81731 | 0.908654 | − | 0.417551i | \(-0.137111\pi\) | ||||
0.908654 | + | 0.417551i | \(0.137111\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 4.62222 | 0.272841 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 2.61285 | 0.153697 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 4.23506 | 0.248264 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −5.67307 | −0.331424 | −0.165712 | − | 0.986174i | \(-0.552992\pi\) | ||||
−0.165712 | + | 0.986174i | \(0.552992\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −3.80642 | −0.220871 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 1.63158 | 0.0943569 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −4.85728 | −0.279969 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 18.7239 | 1.07566 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −4.85728 | −0.277220 | −0.138610 | − | 0.990347i | \(-0.544263\pi\) | ||||
−0.138610 | + | 0.990347i | \(0.544263\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −0.857279 | −0.0487689 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −34.5718 | −1.96039 | −0.980195 | − | 0.198037i | \(-0.936543\pi\) | ||||
−0.980195 | + | 0.198037i | \(0.936543\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −6.33677 | −0.358176 | −0.179088 | − | 0.983833i | \(-0.557315\pi\) | ||||
−0.179088 | + | 0.983833i | \(0.557315\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 15.9684 | 0.896872 | 0.448436 | − | 0.893815i | \(-0.351981\pi\) | ||||
0.448436 | + | 0.893815i | \(0.351981\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −36.5906 | −2.04868 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −11.0923 | −0.619114 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −2.75557 | −0.153324 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 5.61285 | 0.310391 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 11.6128 | 0.640237 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −27.6128 | −1.51774 | −0.758870 | − | 0.651243i | \(-0.774248\pi\) | ||||
−0.758870 | + | 0.651243i | \(0.774248\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −1.24443 | −0.0681944 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 16.0000 | 0.871576 | 0.435788 | − | 0.900049i | \(-0.356470\pi\) | ||||
0.435788 | + | 0.900049i | \(0.356470\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 16.2351 | 0.881768 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 2.36842 | 0.128257 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −11.8666 | −0.637035 | −0.318517 | − | 0.947917i | \(-0.603185\pi\) | ||||
−0.318517 | + | 0.947917i | \(0.603185\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 21.8163 | 1.16780 | 0.583899 | − | 0.811826i | \(-0.301526\pi\) | ||||
0.583899 | + | 0.811826i | \(0.301526\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0.622216 | 0.0332114 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −2.79706 | −0.148872 | −0.0744361 | − | 0.997226i | \(-0.523716\pi\) | ||||
−0.0744361 | + | 0.997226i | \(0.523716\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −4.42864 | −0.234388 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −13.0509 | −0.688798 | −0.344399 | − | 0.938823i | \(-0.611917\pi\) | ||||
−0.344399 | + | 0.938823i | \(0.611917\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.6128 | −0.979624 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 3.48886 | 0.183118 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −10.4889 | −0.547514 | −0.273757 | − | 0.961799i | \(-0.588266\pi\) | ||||
−0.273757 | + | 0.961799i | \(0.588266\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 4.62222 | 0.240623 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 13.4795 | 0.699820 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 30.1847 | 1.56290 | 0.781452 | − | 0.623966i | \(-0.214479\pi\) | ||||
0.781452 | + | 0.623966i | \(0.214479\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 5.98126 | 0.308051 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −12.8573 | −0.660434 | −0.330217 | − | 0.943905i | \(-0.607122\pi\) | ||||
−0.330217 | + | 0.943905i | \(0.607122\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 15.3461 | 0.786207 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −24.4701 | −1.25037 | −0.625183 | − | 0.780479i | \(-0.714975\pi\) | ||||
−0.625183 | + | 0.780479i | \(0.714975\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −4.85728 | −0.246909 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −1.61285 | −0.0817746 | −0.0408873 | − | 0.999164i | \(-0.513018\pi\) | ||||
−0.0408873 | + | 0.999164i | \(0.513018\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −11.6128 | −0.587287 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −4.00000 | −0.201773 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 22.2163 | 1.11501 | 0.557503 | − | 0.830175i | \(-0.311760\pi\) | ||||
0.557503 | + | 0.830175i | \(0.311760\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0.622216 | 0.0311497 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 19.9813 | 0.997817 | 0.498908 | − | 0.866655i | \(-0.333734\pi\) | ||||
0.498908 | + | 0.866655i | \(0.333734\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −0.387152 | −0.0192854 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 4.73683 | 0.234796 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −5.73329 | −0.283493 | −0.141747 | − | 0.989903i | \(-0.545272\pi\) | ||||
−0.141747 | + | 0.989903i | \(0.545272\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −17.0923 | −0.843103 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 11.6128 | 0.571431 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −13.4795 | −0.660094 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 26.3684 | 1.28818 | 0.644091 | − | 0.764949i | \(-0.277236\pi\) | ||||
0.644091 | + | 0.764949i | \(0.277236\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −19.3274 | −0.941960 | −0.470980 | − | 0.882144i | \(-0.656100\pi\) | ||||
−0.470980 | + | 0.882144i | \(0.656100\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 11.6128 | 0.564636 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −8.10171 | −0.392069 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −2.36842 | −0.114348 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −26.9491 | −1.29809 | −0.649047 | − | 0.760748i | \(-0.724832\pi\) | ||||
−0.649047 | + | 0.760748i | \(0.724832\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −2.13335 | −0.102522 | −0.0512612 | − | 0.998685i | \(-0.516324\pi\) | ||||
−0.0512612 | + | 0.998685i | \(0.516324\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 1.63158 | 0.0780492 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −10.5205 | −0.502116 | −0.251058 | − | 0.967972i | \(-0.580779\pi\) | ||||
−0.251058 | + | 0.967972i | \(0.580779\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −6.88892 | −0.327303 | −0.163651 | − | 0.986518i | \(-0.552327\pi\) | ||||
−0.163651 | + | 0.986518i | \(0.552327\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −9.34614 | −0.442057 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 39.9180 | 1.88385 | 0.941923 | − | 0.335829i | \(-0.109016\pi\) | ||||
0.941923 | + | 0.335829i | \(0.109016\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −17.5941 | −0.828474 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −7.14272 | −0.335594 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −8.47013 | −0.396216 | −0.198108 | − | 0.980180i | \(-0.563480\pi\) | ||||
−0.198108 | + | 0.980180i | \(0.563480\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −4.42864 | −0.206711 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 40.1146 | 1.86832 | 0.934162 | − | 0.356849i | \(-0.116149\pi\) | ||||
0.934162 | + | 0.356849i | \(0.116149\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 33.5941 | 1.56125 | 0.780625 | − | 0.624999i | \(-0.214901\pi\) | ||||
0.780625 | + | 0.624999i | \(0.214901\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 11.3461 | 0.525037 | 0.262518 | − | 0.964927i | \(-0.415447\pi\) | ||||
0.262518 | + | 0.964927i | \(0.415447\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −6.99063 | −0.322111 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 18.4889 | 0.850119 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 13.4795 | 0.617184 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 36.2864 | 1.65797 | 0.828984 | − | 0.559273i | \(-0.188919\pi\) | ||||
0.828984 | + | 0.559273i | \(0.188919\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −0.774305 | −0.0353053 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 2.62222 | 0.119315 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −38.8385 | −1.75994 | −0.879971 | − | 0.475027i | \(-0.842438\pi\) | ||||
−0.879971 | + | 0.475027i | \(0.842438\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 15.6128 | 0.706037 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −28.7467 | −1.29732 | −0.648660 | − | 0.761079i | \(-0.724670\pi\) | ||||
−0.648660 | + | 0.761079i | \(0.724670\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −42.5718 | −1.91734 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 2.56199 | 0.114921 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −5.63158 | −0.252104 | −0.126052 | − | 0.992024i | \(-0.540231\pi\) | ||||
−0.126052 | + | 0.992024i | \(0.540231\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −1.51114 | −0.0675126 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −34.9590 | −1.55874 | −0.779372 | − | 0.626561i | \(-0.784462\pi\) | ||||
−0.779372 | + | 0.626561i | \(0.784462\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −12.6128 | −0.560156 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −10.9906 | −0.487151 | −0.243576 | − | 0.969882i | \(-0.578320\pi\) | ||||
−0.243576 | + | 0.969882i | \(0.578320\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 10.9906 | 0.486197 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0.622216 | 0.0274715 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −44.2034 | −1.94406 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −6.53035 | −0.286651 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 6.90766 | 0.302630 | 0.151315 | − | 0.988486i | \(-0.451649\pi\) | ||||
0.151315 | + | 0.988486i | \(0.451649\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 37.7146 | 1.64914 | 0.824571 | − | 0.565758i | \(-0.191416\pi\) | ||||
0.824571 | + | 0.565758i | \(0.191416\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 2.75557 | 0.120034 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −16.1240 | −0.701043 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 11.6128 | 0.503955 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 2.87601 | 0.124574 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −6.29529 | −0.271662 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −3.80642 | −0.163954 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −3.12399 | −0.134311 | −0.0671553 | − | 0.997743i | \(-0.521392\pi\) | ||||
−0.0671553 | + | 0.997743i | \(0.521392\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −6.85728 | −0.294274 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −5.51114 | −0.235639 | −0.117820 | − | 0.993035i | \(-0.537590\pi\) | ||||
−0.117820 | + | 0.993035i | \(0.537590\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −8.10171 | −0.345773 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 5.98126 | 0.254810 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −6.75557 | −0.287276 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 36.7052 | 1.55525 | 0.777624 | − | 0.628729i | \(-0.216425\pi\) | ||||
0.777624 | + | 0.628729i | \(0.216425\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −3.02227 | −0.127829 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 16.8573 | 0.711715 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −27.4924 | −1.15867 | −0.579333 | − | 0.815091i | \(-0.696687\pi\) | ||||
−0.579333 | + | 0.815091i | \(0.696687\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 1.00000 | 0.0419961 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 23.2444 | 0.974457 | 0.487229 | − | 0.873274i | \(-0.338008\pi\) | ||||
0.487229 | + | 0.873274i | \(0.338008\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −25.5111 | −1.06761 | −0.533804 | − | 0.845608i | \(-0.679238\pi\) | ||||
−0.533804 | + | 0.845608i | \(0.679238\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −10.5620 | −0.441234 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 26.0701 | 1.08531 | 0.542656 | − | 0.839955i | \(-0.317419\pi\) | ||||
0.542656 | + | 0.839955i | \(0.317419\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 5.24443 | 0.217951 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 11.6128 | 0.481782 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −51.3087 | −2.12499 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −12.2667 | −0.506301 | −0.253151 | − | 0.967427i | \(-0.581467\pi\) | ||||
−0.253151 | + | 0.967427i | \(0.581467\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −0.387152 | −0.0159523 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 17.7462 | 0.729981 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −14.9175 | −0.612588 | −0.306294 | − | 0.951937i | \(-0.599089\pi\) | ||||
−0.306294 | + | 0.951937i | \(0.599089\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −20.2351 | −0.828166 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −26.5620 | −1.08529 | −0.542647 | − | 0.839961i | \(-0.682578\pi\) | ||||
−0.542647 | + | 0.839961i | \(0.682578\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 39.7146 | 1.61999 | 0.809995 | − | 0.586436i | \(-0.199470\pi\) | ||||
0.809995 | + | 0.586436i | \(0.199470\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 6.28544 | 0.255118 | 0.127559 | − | 0.991831i | \(-0.459286\pi\) | ||||
0.127559 | + | 0.991831i | \(0.459286\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 9.61285 | 0.389532 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 7.22570 | 0.292320 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −45.7146 | −1.84639 | −0.923197 | − | 0.384328i | \(-0.874433\pi\) | ||||
−0.923197 | + | 0.384328i | \(0.874433\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 4.88892 | 0.196821 | 0.0984103 | − | 0.995146i | \(-0.468624\pi\) | ||||
0.0984103 | + | 0.995146i | \(0.468624\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 12.2351 | 0.491769 | 0.245884 | − | 0.969299i | \(-0.420922\pi\) | ||||
0.245884 | + | 0.969299i | \(0.420922\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 2.62222 | 0.105226 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −8.23506 | −0.329931 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −2.36842 | −0.0945854 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 5.51114 | 0.219743 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1.24443 | 0.0495400 | 0.0247700 | − | 0.999693i | \(-0.492115\pi\) | ||||
0.0247700 | + | 0.999693i | \(0.492115\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 21.3274 | 0.847688 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0.622216 | 0.0246531 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 2.56199 | 0.101351 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −48.1847 | −1.90318 | −0.951590 | − | 0.307369i | \(-0.900551\pi\) | ||||
−0.951590 | + | 0.307369i | \(0.900551\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 4.85728 | 0.191552 | 0.0957762 | − | 0.995403i | \(-0.469467\pi\) | ||||
0.0957762 | + | 0.995403i | \(0.469467\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 0.203420 | 0.00799728 | 0.00399864 | − | 0.999992i | \(-0.498727\pi\) | ||||
0.00399864 | + | 0.999992i | \(0.498727\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −44.2034 | −1.73514 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −0.622216 | −0.0243866 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −27.3145 | −1.06890 | −0.534449 | − | 0.845200i | \(-0.679481\pi\) | ||||
−0.534449 | + | 0.845200i | \(0.679481\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 10.9906 | 0.428785 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 33.3176 | 1.29787 | 0.648934 | − | 0.760845i | \(-0.275215\pi\) | ||||
0.648934 | + | 0.760845i | \(0.275215\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 14.5906 | 0.567508 | 0.283754 | − | 0.958897i | \(-0.408420\pi\) | ||||
0.283754 | + | 0.958897i | \(0.408420\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −2.75557 | −0.107017 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 25.2070 | 0.976017 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −9.71456 | −0.375587 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 30.8385 | 1.19051 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 4.53341 | 0.174750 | 0.0873751 | − | 0.996175i | \(-0.472152\pi\) | ||||
0.0873751 | + | 0.996175i | \(0.472152\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −27.2672 | −1.04796 | −0.523981 | − | 0.851730i | \(-0.675554\pi\) | ||||
−0.523981 | + | 0.851730i | \(0.675554\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 4.23506 | 0.162527 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −11.3461 | −0.434785 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −29.5812 | −1.13189 | −0.565947 | − | 0.824442i | \(-0.691489\pi\) | ||||
−0.565947 | + | 0.824442i | \(0.691489\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 1.34614 | 0.0513585 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 8.38715 | 0.319525 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 2.99063 | 0.113769 | 0.0568845 | − | 0.998381i | \(-0.481883\pi\) | ||||
0.0568845 | + | 0.998381i | \(0.481883\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −3.80642 | −0.144594 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −20.4701 | −0.775361 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 15.3778 | 0.581641 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −41.0420 | −1.55013 | −0.775067 | − | 0.631879i | \(-0.782284\pi\) | ||||
−0.775067 | + | 0.631879i | \(0.782284\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −0.774305 | −0.0292035 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 18.7239 | 0.704186 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −41.4291 | −1.55590 | −0.777952 | − | 0.628324i | \(-0.783741\pi\) | ||||
−0.777952 | + | 0.628324i | \(0.783741\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −6.75557 | −0.253354 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −1.63158 | −0.0611033 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 7.53972 | 0.281576 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −18.9590 | −0.707051 | −0.353525 | − | 0.935425i | \(-0.615017\pi\) | ||||
−0.353525 | + | 0.935425i | \(0.615017\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −0.857279 | −0.0319267 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 23.9813 | 0.891873 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 41.7975 | 1.55018 | 0.775092 | − | 0.631848i | \(-0.217703\pi\) | ||||
0.775092 | + | 0.631848i | \(0.217703\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 21.5111 | 0.795618 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 15.3145 | 0.565654 | 0.282827 | − | 0.959171i | \(-0.408728\pi\) | ||||
0.282827 | + | 0.959171i | \(0.408728\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −32.7368 | −1.20424 | −0.602122 | − | 0.798404i | \(-0.705678\pi\) | ||||
−0.602122 | + | 0.798404i | \(0.705678\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0.387152 | 0.0142224 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −37.3778 | −1.37126 | −0.685629 | − | 0.727951i | \(-0.740473\pi\) | ||||
−0.685629 | + | 0.727951i | \(0.740473\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 11.6128 | 0.424892 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −11.0923 | −0.405305 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 20.3497 | 0.742570 | 0.371285 | − | 0.928519i | \(-0.378917\pi\) | ||||
0.371285 | + | 0.928519i | \(0.378917\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 14.1017 | 0.513895 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −6.95899 | −0.252929 | −0.126464 | − | 0.991971i | \(-0.540363\pi\) | ||||
−0.126464 | + | 0.991971i | \(0.540363\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −9.98126 | −0.362297 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 48.6419 | 1.76327 | 0.881634 | − | 0.471934i | \(-0.156444\pi\) | ||||
0.881634 | + | 0.471934i | \(0.156444\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 5.61285 | 0.203199 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 7.22570 | 0.260905 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −24.6923 | −0.890426 | −0.445213 | − | 0.895425i | \(-0.646872\pi\) | ||||
−0.445213 | + | 0.895425i | \(0.646872\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 17.0192 | 0.612932 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 36.0415 | 1.29632 | 0.648161 | − | 0.761503i | \(-0.275538\pi\) | ||||
0.648161 | + | 0.761503i | \(0.275538\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −1.24443 | −0.0446437 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 2.87601 | 0.103044 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −9.75203 | −0.348955 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 9.61285 | 0.343535 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −32.2034 | −1.14793 | −0.573964 | − | 0.818881i | \(-0.694595\pi\) | ||||
−0.573964 | + | 0.818881i | \(0.694595\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 12.6035 | 0.448696 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 16.2351 | 0.577252 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −5.04101 | −0.179012 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −17.5526 | −0.621746 | −0.310873 | − | 0.950451i | \(-0.600621\pi\) | ||||
−0.310873 | + | 0.950451i | \(0.600621\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −51.4291 | −1.81943 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −8.23506 | −0.290972 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −41.8350 | −1.47633 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 3.76494 | 0.132532 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 46.1659 | 1.62311 | 0.811554 | − | 0.584277i | \(-0.198622\pi\) | ||||
0.811554 | + | 0.584277i | \(0.198622\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 18.5205 | 0.650343 | 0.325171 | − | 0.945655i | \(-0.394578\pi\) | ||||
0.325171 | + | 0.945655i | \(0.394578\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −17.8666 | −0.626611 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −3.02227 | −0.105736 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0.622216 | 0.0217420 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 43.0607 | 1.50283 | 0.751414 | − | 0.659831i | \(-0.229372\pi\) | ||||
0.751414 | + | 0.659831i | \(0.229372\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 14.5718 | 0.507942 | 0.253971 | − | 0.967212i | \(-0.418263\pi\) | ||||
0.253971 | + | 0.967212i | \(0.418263\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −55.8292 | −1.94137 | −0.970685 | − | 0.240354i | \(-0.922736\pi\) | ||||
−0.970685 | + | 0.240354i | \(0.922736\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −37.3087 | −1.29578 | −0.647892 | − | 0.761732i | \(-0.724349\pi\) | ||||
−0.647892 | + | 0.761732i | \(0.724349\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −1.24443 | −0.0431688 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −4.42864 | −0.153443 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −0.622216 | −0.0215069 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −51.0420 | −1.76216 | −0.881082 | − | 0.472963i | \(-0.843184\pi\) | ||||
−0.881082 | + | 0.472963i | \(0.843184\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 63.4068 | 2.18644 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −8.95899 | −0.308564 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 3.48886 | 0.119879 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 30.5718 | 1.04922 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −3.26317 | −0.111860 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 26.4197 | 0.904595 | 0.452297 | − | 0.891867i | \(-0.350605\pi\) | ||||
0.452297 | + | 0.891867i | \(0.350605\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −0.161933 | −0.00553154 | −0.00276577 | − | 0.999996i | \(-0.500880\pi\) | ||||
−0.00276577 | + | 0.999996i | \(0.500880\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 51.3403 | 1.75171 | 0.875854 | − | 0.482575i | \(-0.160299\pi\) | ||||
0.875854 | + | 0.482575i | \(0.160299\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 4.62222 | 0.157525 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 12.8702 | 0.438106 | 0.219053 | − | 0.975713i | \(-0.429703\pi\) | ||||
0.219053 | + | 0.975713i | \(0.429703\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 2.61285 | 0.0887370 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 25.7146 | 0.872307 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 4.23506 | 0.143335 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −43.2257 | −1.45963 | −0.729814 | − | 0.683646i | \(-0.760393\pi\) | ||||
−0.729814 | + | 0.683646i | \(0.760393\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −5.67307 | −0.191348 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −16.5018 | −0.555959 | −0.277979 | − | 0.960587i | \(-0.589665\pi\) | ||||
−0.277979 | + | 0.960587i | \(0.589665\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −46.1847 | −1.55424 | −0.777119 | − | 0.629353i | \(-0.783320\pi\) | ||||
−0.777119 | + | 0.629353i | \(0.783320\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −37.3274 | −1.25333 | −0.626666 | − | 0.779288i | \(-0.715581\pi\) | ||||
−0.626666 | + | 0.779288i | \(0.715581\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 15.3461 | 0.514693 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −3.80642 | −0.127520 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 7.22570 | 0.241799 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 1.63158 | 0.0544770 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −5.98126 | −0.199486 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −59.6958 | −1.98876 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −4.85728 | −0.161640 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 24.6735 | 0.819272 | 0.409636 | − | 0.912249i | \(-0.365656\pi\) | ||||
0.409636 | + | 0.912249i | \(0.365656\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 18.7239 | 0.621033 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 29.4380 | 0.975325 | 0.487662 | − | 0.873032i | \(-0.337850\pi\) | ||||
0.487662 | + | 0.873032i | \(0.337850\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −44.2034 | −1.46292 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −4.00000 | −0.132092 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 40.0197 | 1.32013 | 0.660064 | − | 0.751209i | \(-0.270529\pi\) | ||||
0.660064 | + | 0.751209i | \(0.270529\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −4.85728 | −0.160053 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 1.59411 | 0.0524708 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −0.857279 | −0.0281567 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −22.4572 | −0.736797 | −0.368399 | − | 0.929668i | \(-0.620094\pi\) | ||||
−0.368399 | + | 0.929668i | \(0.620094\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0.622216 | 0.0203923 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −34.5718 | −1.13183 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −33.8292 | −1.10515 | −0.552575 | − | 0.833463i | \(-0.686355\pi\) | ||||
−0.552575 | + | 0.833463i | \(0.686355\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −6.33677 | −0.206793 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 47.8479 | 1.55980 | 0.779899 | − | 0.625906i | \(-0.215271\pi\) | ||||
0.779899 | + | 0.625906i | \(0.215271\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 12.1204 | 0.394696 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 44.8069 | 1.45603 | 0.728014 | − | 0.685562i | \(-0.240443\pi\) | ||||
0.728014 | + | 0.685562i | \(0.240443\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 6.83854 | 0.221989 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 15.9684 | 0.517809 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 15.7017 | 0.508626 | 0.254313 | − | 0.967122i | \(-0.418151\pi\) | ||||
0.254313 | + | 0.967122i | \(0.418151\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −36.5906 | −1.18281 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −17.0923 | −0.551941 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.6128 | −0.987511 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −11.0923 | −0.357446 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −46.9590 | −1.51010 | −0.755050 | − | 0.655668i | \(-0.772387\pi\) | ||||
−0.755050 | + | 0.655668i | \(0.772387\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −2.75557 | −0.0885216 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −18.7556 | −0.601895 | −0.300947 | − | 0.953641i | \(-0.597303\pi\) | ||||
−0.300947 | + | 0.953641i | \(0.597303\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −13.4795 | −0.432133 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 37.8292 | 1.21026 | 0.605131 | − | 0.796126i | \(-0.293121\pi\) | ||||
0.605131 | + | 0.796126i | \(0.293121\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 31.3461 | 1.00183 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 5.61285 | 0.179204 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −17.6316 | −0.562360 | −0.281180 | − | 0.959655i | \(-0.590726\pi\) | ||||
−0.281180 | + | 0.959655i | \(0.590726\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 11.6128 | 0.369641 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −12.7368 | −0.405008 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −37.1240 | −1.17928 | −0.589641 | − | 0.807665i | \(-0.700731\pi\) | ||||
−0.589641 | + | 0.807665i | \(0.700731\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −27.6128 | −0.876267 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 42.4197 | 1.34345 | 0.671723 | − | 0.740802i | \(-0.265554\pi\) | ||||
0.671723 | + | 0.740802i | \(0.265554\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −1.24443 | −0.0393721 |
(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 | 4200.2.a.bq.1.1 | 3 | ||
4.3 | odd | 2 | 8400.2.a.dh.1.3 | 3 | |||
5.2 | odd | 4 | 840.2.t.e.169.2 | ✓ | 6 | ||
5.3 | odd | 4 | 840.2.t.e.169.5 | yes | 6 | ||
5.4 | even | 2 | 4200.2.a.bo.1.1 | 3 | |||
15.2 | even | 4 | 2520.2.t.j.1009.4 | 6 | |||
15.8 | even | 4 | 2520.2.t.j.1009.3 | 6 | |||
20.3 | even | 4 | 1680.2.t.i.1009.2 | 6 | |||
20.7 | even | 4 | 1680.2.t.i.1009.5 | 6 | |||
20.19 | odd | 2 | 8400.2.a.dk.1.3 | 3 | |||
60.23 | odd | 4 | 5040.2.t.ba.1009.3 | 6 | |||
60.47 | odd | 4 | 5040.2.t.ba.1009.4 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
840.2.t.e.169.2 | ✓ | 6 | 5.2 | odd | 4 | ||
840.2.t.e.169.5 | yes | 6 | 5.3 | odd | 4 | ||
1680.2.t.i.1009.2 | 6 | 20.3 | even | 4 | |||
1680.2.t.i.1009.5 | 6 | 20.7 | even | 4 | |||
2520.2.t.j.1009.3 | 6 | 15.8 | even | 4 | |||
2520.2.t.j.1009.4 | 6 | 15.2 | even | 4 | |||
4200.2.a.bo.1.1 | 3 | 5.4 | even | 2 | |||
4200.2.a.bq.1.1 | 3 | 1.1 | even | 1 | trivial | ||
5040.2.t.ba.1009.3 | 6 | 60.23 | odd | 4 | |||
5040.2.t.ba.1009.4 | 6 | 60.47 | odd | 4 | |||
8400.2.a.dh.1.3 | 3 | 4.3 | odd | 2 | |||
8400.2.a.dk.1.3 | 3 | 20.19 | odd | 2 |