Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2646,2,Mod(2645,2646)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2646, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2646.2645");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2646 = 2 \cdot 3^{3} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2646.d (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(21.1284163748\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\Q(\zeta_{48})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - x^{8} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{14} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 2645.12 | ||
Root | \(-0.608761 - 0.793353i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2646.2645 |
Dual form | 2646.2.d.e.2645.4 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2646\mathbb{Z}\right)^\times\).
\(n\) | \(785\) | \(1081\) |
\(\chi(n)\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000i | 0.707107i | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | −0.601731 | −0.269102 | −0.134551 | − | 0.990907i | \(-0.542959\pi\) | ||||
−0.134551 | + | 0.990907i | \(0.542959\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | − 1.00000i | − 0.353553i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | − 0.601731i | − 0.190284i | ||||||||
\(11\) | − 1.20041i | − 0.361938i | −0.983489 | − | 0.180969i | \(-0.942077\pi\) | ||||
0.983489 | − | 0.180969i | \(-0.0579234\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.649659i | 0.180183i | 0.995933 | + | 0.0900914i | \(0.0287159\pi\) | ||||
−0.995933 | + | 0.0900914i | \(0.971284\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −0.564050 | −0.136802 | −0.0684011 | − | 0.997658i | \(-0.521790\pi\) | ||||
−0.0684011 | + | 0.997658i | \(0.521790\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − 0.249245i | − 0.0571807i | −0.999591 | − | 0.0285904i | \(-0.990898\pi\) | ||||
0.999591 | − | 0.0285904i | \(-0.00910184\pi\) | |||||||
\(20\) | 0.601731 | 0.134551 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 1.20041 | 0.255929 | ||||||||
\(23\) | 3.95367i | 0.824397i | 0.911094 | + | 0.412198i | \(0.135239\pi\) | ||||
−0.911094 | + | 0.412198i | \(0.864761\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.63792 | −0.927584 | ||||||||
\(26\) | −0.649659 | −0.127409 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − 1.37199i | − 0.254771i | −0.991853 | − | 0.127386i | \(-0.959341\pi\) | ||||
0.991853 | − | 0.127386i | \(-0.0406586\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − 7.11169i | − 1.27730i | −0.769498 | − | 0.638649i | \(-0.779494\pi\) | ||||
0.769498 | − | 0.638649i | \(-0.220506\pi\) | |||||||
\(32\) | 1.00000i | 0.176777i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | − 0.564050i | − 0.0967337i | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 5.17738 | 0.851155 | 0.425578 | − | 0.904922i | \(-0.360071\pi\) | ||||
0.425578 | + | 0.904922i | \(0.360071\pi\) | |||||||
\(38\) | 0.249245 | 0.0404329 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0.601731i | 0.0951420i | ||||||||
\(41\) | −7.32326 | −1.14370 | −0.571850 | − | 0.820358i | \(-0.693774\pi\) | ||||
−0.571850 | + | 0.820358i | \(0.693774\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 9.36414 | 1.42802 | 0.714009 | − | 0.700136i | \(-0.246877\pi\) | ||||
0.714009 | + | 0.700136i | \(0.246877\pi\) | |||||||
\(44\) | 1.20041i | 0.180969i | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −3.95367 | −0.582937 | ||||||||
\(47\) | −9.12845 | −1.33152 | −0.665760 | − | 0.746166i | \(-0.731893\pi\) | ||||
−0.665760 | + | 0.746166i | \(0.731893\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | − 4.63792i | − 0.655901i | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | − 0.649659i | − 0.0900914i | ||||||||
\(53\) | − 10.3178i | − 1.41726i | −0.705580 | − | 0.708630i | \(-0.749313\pi\) | ||||
0.705580 | − | 0.708630i | \(-0.250687\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.722325i | 0.0973983i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 1.37199 | 0.180151 | ||||||||
\(59\) | −7.26508 | −0.945833 | −0.472916 | − | 0.881107i | \(-0.656799\pi\) | ||||
−0.472916 | + | 0.881107i | \(0.656799\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.865467i | 0.110812i | 0.998464 | + | 0.0554059i | \(0.0176453\pi\) | ||||
−0.998464 | + | 0.0554059i | \(0.982355\pi\) | |||||||
\(62\) | 7.11169 | 0.903186 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | − 0.390920i | − 0.0484876i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −9.37779 | −1.14568 | −0.572840 | − | 0.819668i | \(-0.694158\pi\) | ||||
−0.572840 | + | 0.819668i | \(0.694158\pi\) | |||||||
\(68\) | 0.564050 | 0.0684011 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − 4.28897i | − 0.509007i | −0.967072 | − | 0.254504i | \(-0.918088\pi\) | ||||
0.967072 | − | 0.254504i | \(-0.0819121\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − 15.7896i | − 1.84803i | −0.382356 | − | 0.924015i | \(-0.624887\pi\) | ||||
0.382356 | − | 0.924015i | \(-0.375113\pi\) | |||||||
\(74\) | 5.17738i | 0.601858i | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0.249245i | 0.0285904i | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 12.1462 | 1.36656 | 0.683279 | − | 0.730157i | \(-0.260553\pi\) | ||||
0.683279 | + | 0.730157i | \(0.260553\pi\) | |||||||
\(80\) | −0.601731 | −0.0672755 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | − 7.32326i | − 0.808718i | ||||||||
\(83\) | −5.58632 | −0.613178 | −0.306589 | − | 0.951842i | \(-0.599188\pi\) | ||||
−0.306589 | + | 0.951842i | \(0.599188\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.339406 | 0.0368138 | ||||||||
\(86\) | 9.36414i | 1.00976i | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −1.20041 | −0.127964 | ||||||||
\(89\) | −7.62781 | −0.808547 | −0.404273 | − | 0.914638i | \(-0.632476\pi\) | ||||
−0.404273 | + | 0.914638i | \(0.632476\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | − 3.95367i | − 0.412198i | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | − 9.12845i | − 0.941528i | ||||||||
\(95\) | 0.149978i | 0.0153875i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − 13.2012i | − 1.34038i | −0.742191 | − | 0.670189i | \(-0.766213\pi\) | ||||
0.742191 | − | 0.670189i | \(-0.233787\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 4.63792 | 0.463792 | ||||||||
\(101\) | 5.20842 | 0.518257 | 0.259129 | − | 0.965843i | \(-0.416565\pi\) | ||||
0.259129 | + | 0.965843i | \(0.416565\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − 6.31086i | − 0.621828i | −0.950438 | − | 0.310914i | \(-0.899365\pi\) | ||||
0.950438 | − | 0.310914i | \(-0.100635\pi\) | |||||||
\(104\) | 0.649659 | 0.0637043 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 10.3178 | 1.00215 | ||||||||
\(107\) | − 14.7551i | − 1.42643i | −0.700948 | − | 0.713213i | \(-0.747239\pi\) | ||||
0.700948 | − | 0.713213i | \(-0.252761\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1.94812 | −0.186596 | −0.0932982 | − | 0.995638i | \(-0.529741\pi\) | ||||
−0.0932982 | + | 0.995638i | \(0.529741\pi\) | |||||||
\(110\) | −0.722325 | −0.0688710 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 8.35305i | 0.785789i | 0.919584 | + | 0.392894i | \(0.128526\pi\) | ||||
−0.919584 | + | 0.392894i | \(0.871474\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − 2.37904i | − 0.221847i | ||||||||
\(116\) | 1.37199i | 0.127386i | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | − 7.26508i | − 0.668805i | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 9.55901 | 0.869001 | ||||||||
\(122\) | −0.865467 | −0.0783557 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 7.11169i | 0.638649i | ||||||||
\(125\) | 5.79943 | 0.518717 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.09410 | 0.0970861 | 0.0485431 | − | 0.998821i | \(-0.484542\pi\) | ||||
0.0485431 | + | 0.998821i | \(0.484542\pi\) | |||||||
\(128\) | − 1.00000i | − 0.0883883i | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0.390920 | 0.0342859 | ||||||||
\(131\) | 6.60896 | 0.577427 | 0.288714 | − | 0.957415i | \(-0.406772\pi\) | ||||
0.288714 | + | 0.957415i | \(0.406772\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | − 9.37779i | − 0.810117i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0.564050i | 0.0483669i | ||||||||
\(137\) | − 9.61488i | − 0.821455i | −0.911758 | − | 0.410727i | \(-0.865275\pi\) | ||||
0.911758 | − | 0.410727i | \(-0.134725\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − 1.95858i | − 0.166125i | −0.996544 | − | 0.0830623i | \(-0.973530\pi\) | ||||
0.996544 | − | 0.0830623i | \(-0.0264701\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 4.28897 | 0.359923 | ||||||||
\(143\) | 0.779858 | 0.0652150 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0.825566i | 0.0685595i | ||||||||
\(146\) | 15.7896 | 1.30675 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −5.17738 | −0.425578 | ||||||||
\(149\) | 16.4159i | 1.34484i | 0.740168 | + | 0.672422i | \(0.234746\pi\) | ||||
−0.740168 | + | 0.672422i | \(0.765254\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −7.35039 | −0.598166 | −0.299083 | − | 0.954227i | \(-0.596681\pi\) | ||||
−0.299083 | + | 0.954227i | \(0.596681\pi\) | |||||||
\(152\) | −0.249245 | −0.0202164 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 4.27932i | 0.343724i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − 13.3202i | − 1.06307i | −0.847036 | − | 0.531535i | \(-0.821615\pi\) | ||||
0.847036 | − | 0.531535i | \(-0.178385\pi\) | |||||||
\(158\) | 12.1462i | 0.966303i | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | − 0.601731i | − 0.0475710i | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 11.5302 | 0.903113 | 0.451556 | − | 0.892243i | \(-0.350869\pi\) | ||||
0.451556 | + | 0.892243i | \(0.350869\pi\) | |||||||
\(164\) | 7.32326 | 0.571850 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | − 5.58632i | − 0.433582i | ||||||||
\(167\) | −25.7937 | −1.99598 | −0.997990 | − | 0.0633754i | \(-0.979813\pi\) | ||||
−0.997990 | + | 0.0633754i | \(0.979813\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 12.5779 | 0.967534 | ||||||||
\(170\) | 0.339406i | 0.0260313i | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −9.36414 | −0.714009 | ||||||||
\(173\) | −4.04800 | −0.307764 | −0.153882 | − | 0.988089i | \(-0.549178\pi\) | ||||
−0.153882 | + | 0.988089i | \(0.549178\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | − 1.20041i | − 0.0904845i | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | − 7.62781i | − 0.571729i | ||||||||
\(179\) | − 8.94172i | − 0.668336i | −0.942514 | − | 0.334168i | \(-0.891545\pi\) | ||||
0.942514 | − | 0.334168i | \(-0.108455\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − 1.77776i | − 0.132140i | −0.997815 | − | 0.0660699i | \(-0.978954\pi\) | ||||
0.997815 | − | 0.0660699i | \(-0.0210460\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 3.95367 | 0.291468 | ||||||||
\(185\) | −3.11539 | −0.229048 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0.677092i | 0.0495139i | ||||||||
\(188\) | 9.12845 | 0.665760 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −0.149978 | −0.0108806 | ||||||||
\(191\) | − 18.7745i | − 1.35848i | −0.733918 | − | 0.679238i | \(-0.762310\pi\) | ||||
0.733918 | − | 0.679238i | \(-0.237690\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −7.34315 | −0.528571 | −0.264286 | − | 0.964444i | \(-0.585136\pi\) | ||||
−0.264286 | + | 0.964444i | \(0.585136\pi\) | |||||||
\(194\) | 13.2012 | 0.947790 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 14.8593i | 1.05868i | 0.848409 | + | 0.529342i | \(0.177561\pi\) | ||||
−0.848409 | + | 0.529342i | \(0.822439\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − 14.9366i | − 1.05883i | −0.848364 | − | 0.529413i | \(-0.822412\pi\) | ||||
0.848364 | − | 0.529413i | \(-0.177588\pi\) | |||||||
\(200\) | 4.63792i | 0.327950i | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 5.20842i | 0.366463i | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 4.40663 | 0.307772 | ||||||||
\(206\) | 6.31086 | 0.439699 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0.649659i | 0.0450457i | ||||||||
\(209\) | −0.299197 | −0.0206959 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −6.38537 | −0.439587 | −0.219794 | − | 0.975546i | \(-0.570538\pi\) | ||||
−0.219794 | + | 0.975546i | \(0.570538\pi\) | |||||||
\(212\) | 10.3178i | 0.708630i | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 14.7551 | 1.00864 | ||||||||
\(215\) | −5.63469 | −0.384283 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | − 1.94812i | − 0.131944i | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | − 0.722325i | − 0.0486991i | ||||||||
\(221\) | − 0.366440i | − 0.0246494i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − 13.1867i | − 0.883047i | −0.897250 | − | 0.441523i | \(-0.854438\pi\) | ||||
0.897250 | − | 0.441523i | \(-0.145562\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −8.35305 | −0.555637 | ||||||||
\(227\) | −6.70481 | −0.445014 | −0.222507 | − | 0.974931i | \(-0.571424\pi\) | ||||
−0.222507 | + | 0.974931i | \(0.571424\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − 14.7600i | − 0.975368i | −0.873020 | − | 0.487684i | \(-0.837842\pi\) | ||||
0.873020 | − | 0.487684i | \(-0.162158\pi\) | |||||||
\(230\) | 2.37904 | 0.156870 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −1.37199 | −0.0900753 | ||||||||
\(233\) | − 20.9327i | − 1.37135i | −0.727910 | − | 0.685673i | \(-0.759508\pi\) | ||||
0.727910 | − | 0.685673i | \(-0.240492\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 5.49287 | 0.358315 | ||||||||
\(236\) | 7.26508 | 0.472916 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 15.3681i | 0.994082i | 0.867727 | + | 0.497041i | \(0.165580\pi\) | ||||
−0.867727 | + | 0.497041i | \(0.834420\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 13.4328i | 0.865283i | 0.901566 | + | 0.432641i | \(0.142418\pi\) | ||||
−0.901566 | + | 0.432641i | \(0.857582\pi\) | |||||||
\(242\) | 9.55901i | 0.614476i | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | − 0.865467i | − 0.0554059i | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0.161924 | 0.0103030 | ||||||||
\(248\) | −7.11169 | −0.451593 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 5.79943i | 0.366788i | ||||||||
\(251\) | 3.61325 | 0.228066 | 0.114033 | − | 0.993477i | \(-0.463623\pi\) | ||||
0.114033 | + | 0.993477i | \(0.463623\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 4.74603 | 0.298381 | ||||||||
\(254\) | 1.09410i | 0.0686502i | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 31.3932 | 1.95825 | 0.979126 | − | 0.203254i | \(-0.0651518\pi\) | ||||
0.979126 | + | 0.203254i | \(0.0651518\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0.390920i | 0.0242438i | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 6.60896i | 0.408303i | ||||||||
\(263\) | 3.96187i | 0.244300i | 0.992512 | + | 0.122150i | \(0.0389788\pi\) | ||||
−0.992512 | + | 0.122150i | \(0.961021\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 6.20854i | 0.381388i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 9.37779 | 0.572840 | ||||||||
\(269\) | 21.5509 | 1.31398 | 0.656990 | − | 0.753899i | \(-0.271829\pi\) | ||||
0.656990 | + | 0.753899i | \(0.271829\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 6.18603i | 0.375774i | 0.982191 | + | 0.187887i | \(0.0601639\pi\) | ||||
−0.982191 | + | 0.187887i | \(0.939836\pi\) | |||||||
\(272\) | −0.564050 | −0.0342005 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 9.61488 | 0.580856 | ||||||||
\(275\) | 5.56742i | 0.335728i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −11.1419 | −0.669451 | −0.334725 | − | 0.942316i | \(-0.608644\pi\) | ||||
−0.334725 | + | 0.942316i | \(0.608644\pi\) | |||||||
\(278\) | 1.95858 | 0.117468 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 15.4122i | 0.919413i | 0.888071 | + | 0.459707i | \(0.152045\pi\) | ||||
−0.888071 | + | 0.459707i | \(0.847955\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 0.871470i | 0.0518035i | 0.999664 | + | 0.0259018i | \(0.00824571\pi\) | ||||
−0.999664 | + | 0.0259018i | \(0.991754\pi\) | |||||||
\(284\) | 4.28897i | 0.254504i | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0.779858i | 0.0461140i | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.6818 | −0.981285 | ||||||||
\(290\) | −0.825566 | −0.0484789 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 15.7896i | 0.924015i | ||||||||
\(293\) | −26.3170 | −1.53745 | −0.768727 | − | 0.639577i | \(-0.779109\pi\) | ||||
−0.768727 | + | 0.639577i | \(0.779109\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 4.37162 | 0.254526 | ||||||||
\(296\) | − 5.17738i | − 0.300929i | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −16.4159 | −0.950948 | ||||||||
\(299\) | −2.56853 | −0.148542 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | − 7.35039i | − 0.422967i | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | − 0.249245i | − 0.0142952i | ||||||||
\(305\) | − 0.520778i | − 0.0298197i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 25.0183i | 1.42787i | 0.700211 | + | 0.713936i | \(0.253089\pi\) | ||||
−0.700211 | + | 0.713936i | \(0.746911\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −4.27932 | −0.243049 | ||||||||
\(311\) | −27.2433 | −1.54483 | −0.772413 | − | 0.635120i | \(-0.780950\pi\) | ||||
−0.772413 | + | 0.635120i | \(0.780950\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − 0.936585i | − 0.0529389i | −0.999650 | − | 0.0264694i | \(-0.991574\pi\) | ||||
0.999650 | − | 0.0264694i | \(-0.00842647\pi\) | |||||||
\(314\) | 13.3202 | 0.751704 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −12.1462 | −0.683279 | ||||||||
\(317\) | − 8.93218i | − 0.501681i | −0.968028 | − | 0.250841i | \(-0.919293\pi\) | ||||
0.968028 | − | 0.250841i | \(-0.0807070\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1.64695 | −0.0922114 | ||||||||
\(320\) | 0.601731 | 0.0336378 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0.140587i | 0.00782245i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − 3.01306i | − 0.167135i | ||||||||
\(326\) | 11.5302i | 0.638597i | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 7.32326i | 0.404359i | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −13.6805 | −0.751949 | −0.375974 | − | 0.926630i | \(-0.622692\pi\) | ||||
−0.375974 | + | 0.926630i | \(0.622692\pi\) | |||||||
\(332\) | 5.58632 | 0.306589 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | − 25.7937i | − 1.41137i | ||||||||
\(335\) | 5.64290 | 0.308305 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −11.3662 | −0.619157 | −0.309578 | − | 0.950874i | \(-0.600188\pi\) | ||||
−0.309578 | + | 0.950874i | \(0.600188\pi\) | |||||||
\(338\) | 12.5779i | 0.684150i | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −0.339406 | −0.0184069 | ||||||||
\(341\) | −8.53696 | −0.462303 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | − 9.36414i | − 0.504881i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | − 4.04800i | − 0.217622i | ||||||||
\(347\) | 15.1885i | 0.815360i | 0.913125 | + | 0.407680i | \(0.133662\pi\) | ||||
−0.913125 | + | 0.407680i | \(0.866338\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − 1.64664i | − 0.0881425i | −0.999028 | − | 0.0440713i | \(-0.985967\pi\) | ||||
0.999028 | − | 0.0440713i | \(-0.0140329\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 1.20041 | 0.0639822 | ||||||||
\(353\) | 18.2235 | 0.969937 | 0.484968 | − | 0.874532i | \(-0.338831\pi\) | ||||
0.484968 | + | 0.874532i | \(0.338831\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 2.58081i | 0.136975i | ||||||||
\(356\) | 7.62781 | 0.404273 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 8.94172 | 0.472585 | ||||||||
\(359\) | − 27.7530i | − 1.46475i | −0.680902 | − | 0.732374i | \(-0.738412\pi\) | ||||
0.680902 | − | 0.732374i | \(-0.261588\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 18.9379 | 0.996730 | ||||||||
\(362\) | 1.77776 | 0.0934369 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 9.50107i | 0.497309i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 30.5271i | 1.59350i | 0.604309 | + | 0.796750i | \(0.293449\pi\) | ||||
−0.604309 | + | 0.796750i | \(0.706551\pi\) | |||||||
\(368\) | 3.95367i | 0.206099i | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | − 3.11539i | − 0.161961i | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −12.2467 | −0.634112 | −0.317056 | − | 0.948407i | \(-0.602694\pi\) | ||||
−0.317056 | + | 0.948407i | \(0.602694\pi\) | |||||||
\(374\) | −0.677092 | −0.0350116 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 9.12845i | 0.470764i | ||||||||
\(377\) | 0.891322 | 0.0459054 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 3.76316 | 0.193301 | 0.0966503 | − | 0.995318i | \(-0.469187\pi\) | ||||
0.0966503 | + | 0.995318i | \(0.469187\pi\) | |||||||
\(380\) | − 0.149978i | − 0.00769373i | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 18.7745 | 0.960588 | ||||||||
\(383\) | 25.3157 | 1.29357 | 0.646787 | − | 0.762671i | \(-0.276112\pi\) | ||||
0.646787 | + | 0.762671i | \(0.276112\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | − 7.34315i | − 0.373756i | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 13.2012i | 0.670189i | ||||||||
\(389\) | − 30.7667i | − 1.55993i | −0.625822 | − | 0.779966i | \(-0.715236\pi\) | ||||
0.625822 | − | 0.779966i | \(-0.284764\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − 2.23007i | − 0.112779i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −14.8593 | −0.748602 | ||||||||
\(395\) | −7.30876 | −0.367744 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 34.8793i | 1.75054i | 0.483631 | + | 0.875272i | \(0.339318\pi\) | ||||
−0.483631 | + | 0.875272i | \(0.660682\pi\) | |||||||
\(398\) | 14.9366 | 0.748703 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −4.63792 | −0.231896 | ||||||||
\(401\) | 31.8975i | 1.59288i | 0.604716 | + | 0.796441i | \(0.293287\pi\) | ||||
−0.604716 | + | 0.796441i | \(0.706713\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 4.62017 | 0.230147 | ||||||||
\(404\) | −5.20842 | −0.259129 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − 6.21499i | − 0.308065i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 26.3923i | 1.30502i | 0.757782 | + | 0.652508i | \(0.226283\pi\) | ||||
−0.757782 | + | 0.652508i | \(0.773717\pi\) | |||||||
\(410\) | 4.40663i | 0.217628i | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 6.31086i | 0.310914i | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 3.36146 | 0.165008 | ||||||||
\(416\) | −0.649659 | −0.0318521 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | − 0.299197i | − 0.0146342i | ||||||||
\(419\) | −23.9692 | −1.17097 | −0.585485 | − | 0.810683i | \(-0.699096\pi\) | ||||
−0.585485 | + | 0.810683i | \(0.699096\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −15.5279 | −0.756782 | −0.378391 | − | 0.925646i | \(-0.623523\pi\) | ||||
−0.378391 | + | 0.925646i | \(0.623523\pi\) | |||||||
\(422\) | − 6.38537i | − 0.310835i | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −10.3178 | −0.501077 | ||||||||
\(425\) | 2.61602 | 0.126896 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 14.7551i | 0.713213i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | − 5.63469i | − 0.271729i | ||||||||
\(431\) | 15.3414i | 0.738967i | 0.929237 | + | 0.369484i | \(0.120465\pi\) | ||||
−0.929237 | + | 0.369484i | \(0.879535\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 13.1662i | 0.632727i | 0.948638 | + | 0.316364i | \(0.102462\pi\) | ||||
−0.948638 | + | 0.316364i | \(0.897538\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 1.94812 | 0.0932982 | ||||||||
\(437\) | 0.985432 | 0.0471396 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − 19.7473i | − 0.942486i | −0.882003 | − | 0.471243i | \(-0.843805\pi\) | ||||
0.882003 | − | 0.471243i | \(-0.156195\pi\) | |||||||
\(440\) | 0.722325 | 0.0344355 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0.366440 | 0.0174298 | ||||||||
\(443\) | − 24.2237i | − 1.15090i | −0.817836 | − | 0.575452i | \(-0.804826\pi\) | ||||
0.817836 | − | 0.575452i | \(-0.195174\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 4.58989 | 0.217582 | ||||||||
\(446\) | 13.1867 | 0.624408 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 16.9561i | 0.800208i | 0.916470 | + | 0.400104i | \(0.131026\pi\) | ||||
−0.916470 | + | 0.400104i | \(0.868974\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 8.79093i | 0.413949i | ||||||||
\(452\) | − 8.35305i | − 0.392894i | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | − 6.70481i | − 0.314672i | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −5.24264 | −0.245240 | −0.122620 | − | 0.992454i | \(-0.539130\pi\) | ||||
−0.122620 | + | 0.992454i | \(0.539130\pi\) | |||||||
\(458\) | 14.7600 | 0.689689 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 2.37904i | 0.110923i | ||||||||
\(461\) | 18.7628 | 0.873869 | 0.436935 | − | 0.899493i | \(-0.356064\pi\) | ||||
0.436935 | + | 0.899493i | \(0.356064\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −3.27122 | −0.152027 | −0.0760133 | − | 0.997107i | \(-0.524219\pi\) | ||||
−0.0760133 | + | 0.997107i | \(0.524219\pi\) | |||||||
\(464\) | − 1.37199i | − 0.0636928i | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 20.9327 | 0.969688 | ||||||||
\(467\) | −35.0751 | −1.62308 | −0.811541 | − | 0.584295i | \(-0.801371\pi\) | ||||
−0.811541 | + | 0.584295i | \(0.801371\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 5.49287i | 0.253367i | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 7.26508i | 0.334402i | ||||||||
\(473\) | − 11.2408i | − 0.516854i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.15598i | 0.0530399i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −15.3681 | −0.702922 | ||||||||
\(479\) | −7.79415 | −0.356124 | −0.178062 | − | 0.984019i | \(-0.556983\pi\) | ||||
−0.178062 | + | 0.984019i | \(0.556983\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 3.36353i | 0.153364i | ||||||||
\(482\) | −13.4328 | −0.611847 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −9.55901 | −0.434500 | ||||||||
\(485\) | 7.94356i | 0.360699i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 29.1383 | 1.32038 | 0.660191 | − | 0.751098i | \(-0.270475\pi\) | ||||
0.660191 | + | 0.751098i | \(0.270475\pi\) | |||||||
\(488\) | 0.865467 | 0.0391779 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − 19.7492i | − 0.891268i | −0.895215 | − | 0.445634i | \(-0.852978\pi\) | ||||
0.895215 | − | 0.445634i | \(-0.147022\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0.773868i | 0.0348533i | ||||||||
\(494\) | 0.161924i | 0.00728531i | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | − 7.11169i | − 0.319324i | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −31.6108 | −1.41509 | −0.707546 | − | 0.706667i | \(-0.750198\pi\) | ||||
−0.707546 | + | 0.706667i | \(0.750198\pi\) | |||||||
\(500\) | −5.79943 | −0.259358 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 3.61325i | 0.161267i | ||||||||
\(503\) | 13.8811 | 0.618930 | 0.309465 | − | 0.950911i | \(-0.399850\pi\) | ||||
0.309465 | + | 0.950911i | \(0.399850\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −3.13407 | −0.139464 | ||||||||
\(506\) | 4.74603i | 0.210987i | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −1.09410 | −0.0485431 | ||||||||
\(509\) | −14.6657 | −0.650047 | −0.325023 | − | 0.945706i | \(-0.605372\pi\) | ||||
−0.325023 | + | 0.945706i | \(0.605372\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 31.3932i | 1.38469i | ||||||||
\(515\) | 3.79744i | 0.167335i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 10.9579i | 0.481928i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −0.390920 | −0.0171430 | ||||||||
\(521\) | 39.5873 | 1.73435 | 0.867175 | − | 0.498004i | \(-0.165934\pi\) | ||||
0.867175 | + | 0.498004i | \(0.165934\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 1.68035i | − 0.0734767i | −0.999325 | − | 0.0367384i | \(-0.988303\pi\) | ||||
0.999325 | − | 0.0367384i | \(-0.0116968\pi\) | |||||||
\(524\) | −6.60896 | −0.288714 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −3.96187 | −0.172746 | ||||||||
\(527\) | 4.01135i | 0.174737i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 7.36850 | 0.320370 | ||||||||
\(530\) | −6.20854 | −0.269682 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − 4.75762i | − 0.206075i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 8.87857i | 0.383854i | ||||||||
\(536\) | 9.37779i | 0.405059i | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 21.5509i | 0.929125i | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −17.2062 | −0.739753 | −0.369876 | − | 0.929081i | \(-0.620600\pi\) | ||||
−0.369876 | + | 0.929081i | \(0.620600\pi\) | |||||||
\(542\) | −6.18603 | −0.265713 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | − 0.564050i | − 0.0241834i | ||||||||
\(545\) | 1.17225 | 0.0502135 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −43.6062 | −1.86447 | −0.932233 | − | 0.361859i | \(-0.882142\pi\) | ||||
−0.932233 | + | 0.361859i | \(0.882142\pi\) | |||||||
\(548\) | 9.61488i | 0.410727i | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −5.56742 | −0.237395 | ||||||||
\(551\) | −0.341961 | −0.0145680 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | − 11.1419i | − 0.473373i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 1.95858i | 0.0830623i | ||||||||
\(557\) | − 37.4256i | − 1.58577i | −0.609369 | − | 0.792886i | \(-0.708577\pi\) | ||||
0.609369 | − | 0.792886i | \(-0.291423\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 6.08350i | 0.257304i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −15.4122 | −0.650123 | ||||||||
\(563\) | −25.6620 | −1.08152 | −0.540762 | − | 0.841176i | \(-0.681864\pi\) | ||||
−0.540762 | + | 0.841176i | \(0.681864\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − 5.02629i | − 0.211457i | ||||||||
\(566\) | −0.871470 | −0.0366306 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −4.28897 | −0.179961 | ||||||||
\(569\) | 13.2717i | 0.556380i | 0.960526 | + | 0.278190i | \(0.0897345\pi\) | ||||
−0.960526 | + | 0.278190i | \(0.910265\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 20.7867 | 0.869897 | 0.434948 | − | 0.900455i | \(-0.356767\pi\) | ||||
0.434948 | + | 0.900455i | \(0.356767\pi\) | |||||||
\(572\) | −0.779858 | −0.0326075 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − 18.3368i | − 0.764697i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 16.1318i | 0.671576i | 0.941938 | + | 0.335788i | \(0.109003\pi\) | ||||
−0.941938 | + | 0.335788i | \(0.890997\pi\) | |||||||
\(578\) | − 16.6818i | − 0.693873i | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | − 0.825566i | − 0.0342798i | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −12.3856 | −0.512960 | ||||||||
\(584\) | −15.7896 | −0.653377 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | − 26.3170i | − 1.08714i | ||||||||
\(587\) | −18.0600 | −0.745417 | −0.372708 | − | 0.927949i | \(-0.621571\pi\) | ||||
−0.372708 | + | 0.927949i | \(0.621571\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1.77255 | −0.0730368 | ||||||||
\(590\) | 4.37162i | 0.179977i | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 5.17738 | 0.212789 | ||||||||
\(593\) | −6.69679 | −0.275004 | −0.137502 | − | 0.990501i | \(-0.543907\pi\) | ||||
−0.137502 | + | 0.990501i | \(0.543907\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | − 16.4159i | − 0.672422i | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | − 2.56853i | − 0.105035i | ||||||||
\(599\) | − 3.28379i | − 0.134172i | −0.997747 | − | 0.0670860i | \(-0.978630\pi\) | ||||
0.997747 | − | 0.0670860i | \(-0.0213702\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 4.59868i | 0.187584i | 0.995592 | + | 0.0937920i | \(0.0298989\pi\) | ||||
−0.995592 | + | 0.0937920i | \(0.970101\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 7.35039 | 0.299083 | ||||||||
\(605\) | −5.75195 | −0.233850 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 27.1633i | 1.10252i | 0.834333 | + | 0.551261i | \(0.185853\pi\) | ||||
−0.834333 | + | 0.551261i | \(0.814147\pi\) | |||||||
\(608\) | 0.249245 | 0.0101082 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0.520778 | 0.0210857 | ||||||||
\(611\) | − 5.93037i | − 0.239917i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 32.9907 | 1.33248 | 0.666241 | − | 0.745736i | \(-0.267902\pi\) | ||||
0.666241 | + | 0.745736i | \(0.267902\pi\) | |||||||
\(614\) | −25.0183 | −1.00966 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 20.1479i | 0.811125i | 0.914067 | + | 0.405563i | \(0.132924\pi\) | ||||
−0.914067 | + | 0.405563i | \(0.867076\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 16.0966i | 0.646975i | 0.946232 | + | 0.323488i | \(0.104855\pi\) | ||||
−0.946232 | + | 0.323488i | \(0.895145\pi\) | |||||||
\(620\) | − 4.27932i | − 0.171862i | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | − 27.2433i | − 1.09236i | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 19.6999 | 0.787996 | ||||||||
\(626\) | 0.936585 | 0.0374334 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 13.3202i | 0.531535i | ||||||||
\(629\) | −2.92030 | −0.116440 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −2.81684 | −0.112137 | −0.0560684 | − | 0.998427i | \(-0.517856\pi\) | ||||
−0.0560684 | + | 0.998427i | \(0.517856\pi\) | |||||||
\(632\) | − 12.1462i | − 0.483151i | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 8.93218 | 0.354742 | ||||||||
\(635\) | −0.658356 | −0.0261261 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | − 1.64695i | − 0.0652033i | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0.601731i | 0.0237855i | ||||||||
\(641\) | 17.2433i | 0.681068i | 0.940232 | + | 0.340534i | \(0.110608\pi\) | ||||
−0.940232 | + | 0.340534i | \(0.889392\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 43.9469i | − 1.73310i | −0.499093 | − | 0.866549i | \(-0.666333\pi\) | ||||
0.499093 | − | 0.866549i | \(-0.333667\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −0.140587 | −0.00553131 | ||||||||
\(647\) | −15.4124 | −0.605922 | −0.302961 | − | 0.953003i | \(-0.597975\pi\) | ||||
−0.302961 | + | 0.953003i | \(0.597975\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 8.72109i | 0.342333i | ||||||||
\(650\) | 3.01306 | 0.118182 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −11.5302 | −0.451556 | ||||||||
\(653\) | 34.4687i | 1.34886i | 0.738337 | + | 0.674432i | \(0.235611\pi\) | ||||
−0.738337 | + | 0.674432i | \(0.764389\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −3.97681 | −0.155387 | ||||||||
\(656\) | −7.32326 | −0.285925 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − 16.2348i | − 0.632418i | −0.948690 | − | 0.316209i | \(-0.897590\pi\) | ||||
0.948690 | − | 0.316209i | \(-0.102410\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 47.2554i | 1.83802i | 0.394230 | + | 0.919012i | \(0.371011\pi\) | ||||
−0.394230 | + | 0.919012i | \(0.628989\pi\) | |||||||
\(662\) | − 13.6805i | − 0.531708i | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 5.58632i | 0.216791i | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 5.42438 | 0.210033 | ||||||||
\(668\) | 25.7937 | 0.997990 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 5.64290i | 0.218004i | ||||||||
\(671\) | 1.03892 | 0.0401070 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −16.2598 | −0.626769 | −0.313384 | − | 0.949626i | \(-0.601463\pi\) | ||||
−0.313384 | + | 0.949626i | \(0.601463\pi\) | |||||||
\(674\) | − 11.3662i | − 0.437810i | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −12.5779 | −0.483767 | ||||||||
\(677\) | −12.9879 | −0.499165 | −0.249582 | − | 0.968354i | \(-0.580293\pi\) | ||||
−0.249582 | + | 0.968354i | \(0.580293\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | − 0.339406i | − 0.0130156i | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | − 8.53696i | − 0.326897i | ||||||||
\(683\) | 30.7325i | 1.17595i | 0.808880 | + | 0.587974i | \(0.200074\pi\) | ||||
−0.808880 | + | 0.587974i | \(0.799926\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 5.78557i | 0.221055i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 9.36414 | 0.357005 | ||||||||
\(689\) | 6.70306 | 0.255366 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − 16.0781i | − 0.611638i | −0.952090 | − | 0.305819i | \(-0.901070\pi\) | ||||
0.952090 | − | 0.305819i | \(-0.0989302\pi\) | |||||||
\(692\) | 4.04800 | 0.153882 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −15.1885 | −0.576546 | ||||||||
\(695\) | 1.17854i | 0.0447045i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 4.13068 | 0.156461 | ||||||||
\(698\) | 1.64664 | 0.0623262 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − 37.8263i | − 1.42868i | −0.699799 | − | 0.714339i | \(-0.746727\pi\) | ||||
0.699799 | − | 0.714339i | \(-0.253273\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − 1.29043i | − 0.0486697i | ||||||||
\(704\) | 1.20041i | 0.0452423i | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 18.2235i | 0.685849i | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −41.7113 | −1.56650 | −0.783251 | − | 0.621706i | \(-0.786440\pi\) | ||||
−0.783251 | + | 0.621706i | \(0.786440\pi\) | |||||||
\(710\) | −2.58081 | −0.0968559 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 7.62781i | 0.285864i | ||||||||
\(713\) | 28.1173 | 1.05300 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −0.469265 | −0.0175495 | ||||||||
\(716\) | 8.94172i | 0.334168i | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 27.7530 | 1.03573 | ||||||||
\(719\) | 2.06421 | 0.0769820 | 0.0384910 | − | 0.999259i | \(-0.487745\pi\) | ||||
0.0384910 | + | 0.999259i | \(0.487745\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 18.9379i | 0.704795i | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 1.77776i | 0.0660699i | ||||||||
\(725\) | 6.36316i | 0.236322i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 31.5303i | 1.16939i | 0.811251 | + | 0.584697i | \(0.198787\pi\) | ||||
−0.811251 | + | 0.584697i | \(0.801213\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −9.50107 | −0.351650 | ||||||||
\(731\) | −5.28184 | −0.195356 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 40.4015i | − 1.49226i | −0.665799 | − | 0.746131i | \(-0.731909\pi\) | ||||
0.665799 | − | 0.746131i | \(-0.268091\pi\) | |||||||
\(734\) | −30.5271 | −1.12677 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −3.95367 | −0.145734 | ||||||||
\(737\) | 11.2572i | 0.414665i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 40.5607 | 1.49205 | 0.746025 | − | 0.665918i | \(-0.231960\pi\) | ||||
0.746025 | + | 0.665918i | \(0.231960\pi\) | |||||||
\(740\) | 3.11539 | 0.114524 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − 29.9301i | − 1.09803i | −0.835812 | − | 0.549015i | \(-0.815003\pi\) | ||||
0.835812 | − | 0.549015i | \(-0.184997\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − 9.87796i | − 0.361900i | ||||||||
\(746\) | − 12.2467i | − 0.448385i | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | − 0.677092i | − 0.0247570i | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −39.8892 | −1.45558 | −0.727790 | − | 0.685800i | \(-0.759452\pi\) | ||||
−0.727790 | + | 0.685800i | \(0.759452\pi\) | |||||||
\(752\) | −9.12845 | −0.332880 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0.891322i | 0.0324600i | ||||||||
\(755\) | 4.42296 | 0.160968 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −17.9258 | −0.651525 | −0.325762 | − | 0.945452i | \(-0.605621\pi\) | ||||
−0.325762 | + | 0.945452i | \(0.605621\pi\) | |||||||
\(758\) | 3.76316i | 0.136684i | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0.149978 | 0.00544029 | ||||||||
\(761\) | 15.6453 | 0.567142 | 0.283571 | − | 0.958951i | \(-0.408481\pi\) | ||||
0.283571 | + | 0.958951i | \(0.408481\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 18.7745i | 0.679238i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 25.3157i | 0.914695i | ||||||||
\(767\) | − 4.71982i | − 0.170423i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 2.25067i | 0.0811613i | 0.999176 | + | 0.0405806i | \(0.0129208\pi\) | ||||
−0.999176 | + | 0.0405806i | \(0.987079\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 7.34315 | 0.264286 | ||||||||
\(773\) | −21.9049 | −0.787866 | −0.393933 | − | 0.919139i | \(-0.628886\pi\) | ||||
−0.393933 | + | 0.919139i | \(0.628886\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 32.9835i | 1.18480i | ||||||||
\(776\) | −13.2012 | −0.473895 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 30.7667 | 1.10304 | ||||||||
\(779\) | 1.82528i | 0.0653976i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −5.14854 | −0.184229 | ||||||||
\(782\) | 2.23007 | 0.0797470 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 8.01519i | 0.286075i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 16.8406i | 0.600301i | 0.953892 | + | 0.300151i | \(0.0970369\pi\) | ||||
−0.953892 | + | 0.300151i | \(0.902963\pi\) | |||||||
\(788\) | − 14.8593i | − 0.529342i | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | − 7.30876i | − 0.260034i | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −0.562258 | −0.0199664 | ||||||||
\(794\) | −34.8793 | −1.23782 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 14.9366i | 0.529413i | ||||||||
\(797\) | 13.8756 | 0.491500 | 0.245750 | − | 0.969333i | \(-0.420966\pi\) | ||||
0.245750 | + | 0.969333i | \(0.420966\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 5.14890 | 0.182155 | ||||||||
\(800\) | − 4.63792i | − 0.163975i | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −31.8975 | −1.12634 | ||||||||
\(803\) | −18.9540 | −0.668872 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 4.62017i | 0.162739i | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | − 5.20842i | − 0.183232i | ||||||||
\(809\) | − 16.0990i | − 0.566010i | −0.959118 | − | 0.283005i | \(-0.908669\pi\) | ||||
0.959118 | − | 0.283005i | \(-0.0913313\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 8.57333i | 0.301050i | 0.988606 | + | 0.150525i | \(0.0480965\pi\) | ||||
−0.988606 | + | 0.150525i | \(0.951904\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 6.21499 | 0.217835 | ||||||||
\(815\) | −6.93806 | −0.243030 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − 2.33397i | − 0.0816551i | ||||||||
\(818\) | −26.3923 | −0.922786 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −4.40663 | −0.153886 | ||||||||
\(821\) | 41.2485i | 1.43958i | 0.694191 | + | 0.719791i | \(0.255762\pi\) | ||||
−0.694191 | + | 0.719791i | \(0.744238\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −25.1482 | −0.876611 | −0.438305 | − | 0.898826i | \(-0.644421\pi\) | ||||
−0.438305 | + | 0.898826i | \(0.644421\pi\) | |||||||
\(824\) | −6.31086 | −0.219849 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − 12.8906i | − 0.448249i | −0.974561 | − | 0.224125i | \(-0.928048\pi\) | ||||
0.974561 | − | 0.224125i | \(-0.0719523\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − 24.5664i | − 0.853228i | −0.904434 | − | 0.426614i | \(-0.859706\pi\) | ||||
0.904434 | − | 0.426614i | \(-0.140294\pi\) | |||||||
\(830\) | 3.36146i | 0.116678i | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | − 0.649659i | − 0.0225229i | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 15.5209 | 0.537122 | ||||||||
\(836\) | 0.299197 | 0.0103479 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | − 23.9692i | − 0.828001i | ||||||||
\(839\) | −20.4459 | −0.705872 | −0.352936 | − | 0.935647i | \(-0.614817\pi\) | ||||
−0.352936 | + | 0.935647i | \(0.614817\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 27.1177 | 0.935092 | ||||||||
\(842\) | − 15.5279i | − 0.535126i | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 6.38537 | 0.219794 | ||||||||
\(845\) | −7.56853 | −0.260366 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | − 10.3178i | − 0.354315i | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 2.61602i | 0.0897287i | ||||||||
\(851\) | 20.4696i | 0.701690i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 3.15935i | − 0.108174i | −0.998536 | − | 0.0540870i | \(-0.982775\pi\) | ||||
0.998536 | − | 0.0540870i | \(-0.0172248\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −14.7551 | −0.504318 | ||||||||
\(857\) | 38.2349 | 1.30608 | 0.653040 | − | 0.757323i | \(-0.273493\pi\) | ||||
0.653040 | + | 0.757323i | \(0.273493\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 21.9370i | 0.748480i | 0.927332 | + | 0.374240i | \(0.122096\pi\) | ||||
−0.927332 | + | 0.374240i | \(0.877904\pi\) | |||||||
\(860\) | 5.63469 | 0.192141 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −15.3414 | −0.522529 | ||||||||
\(863\) | − 1.54212i | − 0.0524942i | −0.999655 | − | 0.0262471i | \(-0.991644\pi\) | ||||
0.999655 | − | 0.0262471i | \(-0.00835568\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 2.43581 | 0.0828200 | ||||||||
\(866\) | −13.1662 | −0.447406 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − 14.5805i | − 0.494610i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − 6.09236i | − 0.206432i | ||||||||
\(872\) | 1.94812i | 0.0659718i | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0.985432i | 0.0333327i | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 45.3364 | 1.53090 | 0.765451 | − | 0.643494i | \(-0.222516\pi\) | ||||
0.765451 | + | 0.643494i | \(0.222516\pi\) | |||||||
\(878\) | 19.7473 | 0.666439 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0.722325i | 0.0243496i | ||||||||
\(881\) | 31.3187 | 1.05516 | 0.527578 | − | 0.849507i | \(-0.323100\pi\) | ||||
0.527578 | + | 0.849507i | \(0.323100\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 31.9125 | 1.07394 | 0.536971 | − | 0.843601i | \(-0.319568\pi\) | ||||
0.536971 | + | 0.843601i | \(0.319568\pi\) | |||||||
\(884\) | 0.366440i | 0.0123247i | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 24.2237 | 0.813811 | ||||||||
\(887\) | −43.0139 | −1.44426 | −0.722132 | − | 0.691755i | \(-0.756838\pi\) | ||||
−0.722132 | + | 0.691755i | \(0.756838\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 4.58989i | 0.153853i | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 13.1867i | 0.441523i | ||||||||
\(893\) | 2.27522i | 0.0761373i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 5.38051i | 0.179851i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −16.9561 | −0.565832 | ||||||||
\(899\) | −9.75714 | −0.325419 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 5.81976i | 0.193884i | ||||||||
\(902\) | −8.79093 | −0.292706 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 8.35305 | 0.277818 | ||||||||
\(905\) | 1.06973i | 0.0355591i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −40.6686 | −1.35038 | −0.675189 | − | 0.737645i | \(-0.735938\pi\) | ||||
−0.675189 | + | 0.737645i | \(0.735938\pi\) | |||||||
\(908\) | 6.70481 | 0.222507 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − 16.4174i | − 0.543932i | −0.962307 | − | 0.271966i | \(-0.912326\pi\) | ||||
0.962307 | − | 0.271966i | \(-0.0876739\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 6.70589i | 0.221932i | ||||||||
\(914\) | − 5.24264i | − 0.173411i | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 14.7600i | 0.487684i | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 6.36995 | 0.210125 | 0.105063 | − | 0.994466i | \(-0.466496\pi\) | ||||
0.105063 | + | 0.994466i | \(0.466496\pi\) | |||||||
\(920\) | −2.37904 | −0.0784348 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 18.7628i | 0.617919i | ||||||||
\(923\) | 2.78637 | 0.0917144 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −24.0123 | −0.789518 | ||||||||
\(926\) | − 3.27122i | − 0.107499i | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 1.37199 | 0.0450376 | ||||||||
\(929\) | 43.2708 | 1.41967 | 0.709834 | − | 0.704369i | \(-0.248770\pi\) | ||||
0.709834 | + | 0.704369i | \(0.248770\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 20.9327i | 0.685673i | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | − 35.0751i | − 1.14769i | ||||||||
\(935\) | − 0.407427i | − 0.0133243i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − 41.8956i | − 1.36867i | −0.729168 | − | 0.684335i | \(-0.760093\pi\) | ||||
0.729168 | − | 0.684335i | \(-0.239907\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −5.49287 | −0.179158 | ||||||||
\(941\) | 39.7919 | 1.29718 | 0.648590 | − | 0.761138i | \(-0.275359\pi\) | ||||
0.648590 | + | 0.761138i | \(0.275359\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − 28.9537i | − 0.942863i | ||||||||
\(944\) | −7.26508 | −0.236458 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 11.2408 | 0.365471 | ||||||||
\(947\) | − 20.0515i | − 0.651587i | −0.945441 | − | 0.325794i | \(-0.894369\pi\) | ||||
0.945441 | − | 0.325794i | \(-0.105631\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 10.2578 | 0.332983 | ||||||||
\(950\) | −1.15598 | −0.0375049 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 26.4300i | 0.856153i | 0.903743 | + | 0.428076i | \(0.140809\pi\) | ||||
−0.903743 | + | 0.428076i | \(0.859191\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 11.2972i | 0.365569i | ||||||||
\(956\) | − 15.3681i | − 0.497041i | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | − 7.79415i | − 0.251817i | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −19.5762 | −0.631489 | ||||||||
\(962\) | −3.36353 | −0.108444 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | − 13.4328i | − 0.432641i | ||||||||
\(965\) | 4.41860 | 0.142240 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −17.7780 | −0.571702 | −0.285851 | − | 0.958274i | \(-0.592276\pi\) | ||||
−0.285851 | + | 0.958274i | \(0.592276\pi\) | |||||||
\(968\) | − 9.55901i | − 0.307238i | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −7.94356 | −0.255052 | ||||||||
\(971\) | 46.5597 | 1.49417 | 0.747086 | − | 0.664728i | \(-0.231452\pi\) | ||||
0.747086 | + | 0.664728i | \(0.231452\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 29.1383i | 0.933651i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0.865467i | 0.0277029i | ||||||||
\(977\) | − 16.9303i | − 0.541647i | −0.962629 | − | 0.270824i | \(-0.912704\pi\) | ||||
0.962629 | − | 0.270824i | \(-0.0872960\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 9.15652i | 0.292644i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 19.7492 | 0.630222 | ||||||||
\(983\) | −41.6087 | −1.32711 | −0.663556 | − | 0.748126i | \(-0.730954\pi\) | ||||
−0.663556 | + | 0.748126i | \(0.730954\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − 8.94131i | − 0.284894i | ||||||||
\(986\) | −0.773868 | −0.0246450 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −0.161924 | −0.00515149 | ||||||||
\(989\) | 37.0227i | 1.17725i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −7.67254 | −0.243726 | −0.121863 | − | 0.992547i | \(-0.538887\pi\) | ||||
−0.121863 | + | 0.992547i | \(0.538887\pi\) | |||||||
\(992\) | 7.11169 | 0.225796 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 8.98780i | 0.284932i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 2.76497i | 0.0875673i | 0.999041 | + | 0.0437837i | \(0.0139412\pi\) | ||||
−0.999041 | + | 0.0437837i | \(0.986059\pi\) | |||||||
\(998\) | − 31.6108i | − 1.00062i | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 2646.2.d.e.2645.12 | yes | 16 | |
3.2 | odd | 2 | inner | 2646.2.d.e.2645.5 | yes | 16 | |
7.6 | odd | 2 | inner | 2646.2.d.e.2645.13 | yes | 16 | |
21.20 | even | 2 | inner | 2646.2.d.e.2645.4 | ✓ | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2646.2.d.e.2645.4 | ✓ | 16 | 21.20 | even | 2 | inner | |
2646.2.d.e.2645.5 | yes | 16 | 3.2 | odd | 2 | inner | |
2646.2.d.e.2645.12 | yes | 16 | 1.1 | even | 1 | trivial | |
2646.2.d.e.2645.13 | yes | 16 | 7.6 | odd | 2 | inner |