Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3800,2,Mod(1,3800)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3800, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("3800.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3800 = 2^{3} \cdot 5^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3800.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: | \(30.3431527681\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{6} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 2x^{5} - 12x^{4} + 16x^{3} + 33x^{2} - 4x - 7 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(-0.471016\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3800.1 |
$q$-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 | ||||||||
\(3\) | −0.471016 | −0.271941 | −0.135971 | − | 0.990713i | \(-0.543415\pi\) | ||||
−0.135971 | + | 0.990713i | \(0.543415\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.567324 | −0.214428 | −0.107214 | − | 0.994236i | \(-0.534193\pi\) | ||||
−0.107214 | + | 0.994236i | \(0.534193\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.77814 | −0.926048 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.37804 | 1.32003 | 0.660014 | − | 0.751253i | \(-0.270550\pi\) | ||||
0.660014 | + | 0.751253i | \(0.270550\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.165457 | 0.0458895 | 0.0229448 | − | 0.999737i | \(-0.492696\pi\) | ||||
0.0229448 | + | 0.999737i | \(0.492696\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 7.94693 | 1.92741 | 0.963707 | − | 0.266963i | \(-0.0860200\pi\) | ||||
0.963707 | + | 0.266963i | \(0.0860200\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.00000 | 0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.267219 | 0.0583119 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −3.87445 | −0.807879 | −0.403939 | − | 0.914786i | \(-0.632359\pi\) | ||||
−0.403939 | + | 0.914786i | \(0.632359\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 2.72160 | 0.523772 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.53231 | 0.655934 | 0.327967 | − | 0.944689i | \(-0.393636\pi\) | ||||
0.327967 | + | 0.944689i | \(0.393636\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.20380 | 0.575419 | 0.287709 | − | 0.957718i | \(-0.407106\pi\) | ||||
0.287709 | + | 0.957718i | \(0.407106\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −2.06213 | −0.358970 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −10.1779 | −1.67323 | −0.836617 | − | 0.547788i | \(-0.815470\pi\) | ||||
−0.836617 | + | 0.547788i | \(0.815470\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −0.0779330 | −0.0124793 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −5.97409 | −0.932996 | −0.466498 | − | 0.884522i | \(-0.654485\pi\) | ||||
−0.466498 | + | 0.884522i | \(0.654485\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −12.0904 | −1.84376 | −0.921881 | − | 0.387472i | \(-0.873348\pi\) | ||||
−0.921881 | + | 0.387472i | \(0.873348\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 5.46140 | 0.796627 | 0.398314 | − | 0.917249i | \(-0.369596\pi\) | ||||
0.398314 | + | 0.917249i | \(0.369596\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.67814 | −0.954020 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −3.74313 | −0.524143 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 2.00333 | 0.275179 | 0.137589 | − | 0.990489i | \(-0.456065\pi\) | ||||
0.137589 | + | 0.990489i | \(0.456065\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −0.471016 | −0.0623876 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 8.32164 | 1.08339 | 0.541693 | − | 0.840577i | \(-0.317784\pi\) | ||||
0.541693 | + | 0.840577i | \(0.317784\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 11.8181 | 1.51315 | 0.756573 | − | 0.653909i | \(-0.226872\pi\) | ||||
0.756573 | + | 0.653909i | \(0.226872\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 1.57611 | 0.198571 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −8.79599 | −1.07460 | −0.537300 | − | 0.843391i | \(-0.680556\pi\) | ||||
−0.537300 | + | 0.843391i | \(0.680556\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1.82493 | 0.219696 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0.720031 | 0.0854520 | 0.0427260 | − | 0.999087i | \(-0.486396\pi\) | ||||
0.0427260 | + | 0.999087i | \(0.486396\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −4.54017 | −0.531386 | −0.265693 | − | 0.964058i | \(-0.585601\pi\) | ||||
−0.265693 | + | 0.964058i | \(0.585601\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −2.48377 | −0.283051 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 11.7123 | 1.31774 | 0.658870 | − | 0.752257i | \(-0.271035\pi\) | ||||
0.658870 | + | 0.752257i | \(0.271035\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 7.05251 | 0.783613 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 6.72351 | 0.738001 | 0.369000 | − | 0.929429i | \(-0.379700\pi\) | ||||
0.369000 | + | 0.929429i | \(0.379700\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −1.66378 | −0.178376 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 8.11941 | 0.860656 | 0.430328 | − | 0.902673i | \(-0.358398\pi\) | ||||
0.430328 | + | 0.902673i | \(0.358398\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.0938678 | −0.00984002 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −1.50904 | −0.156480 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 13.6321 | 1.38413 | 0.692065 | − | 0.721835i | \(-0.256701\pi\) | ||||
0.692065 | + | 0.721835i | \(0.256701\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −12.1628 | −1.22241 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 19.2686 | 1.91730 | 0.958649 | − | 0.284590i | \(-0.0918575\pi\) | ||||
0.958649 | + | 0.284590i | \(0.0918575\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 19.2069 | 1.89251 | 0.946257 | − | 0.323417i | \(-0.104832\pi\) | ||||
0.946257 | + | 0.323417i | \(0.104832\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 12.0091 | 1.16096 | 0.580480 | − | 0.814275i | \(-0.302865\pi\) | ||||
0.580480 | + | 0.814275i | \(0.302865\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −15.0032 | −1.43704 | −0.718521 | − | 0.695505i | \(-0.755180\pi\) | ||||
−0.718521 | + | 0.695505i | \(0.755180\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 4.79395 | 0.455022 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −8.13049 | −0.764852 | −0.382426 | − | 0.923986i | \(-0.624911\pi\) | ||||
−0.382426 | + | 0.923986i | \(0.624911\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −0.459664 | −0.0424959 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −4.50848 | −0.413292 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 8.16722 | 0.742474 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 2.81389 | 0.253720 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 8.37051 | 0.742762 | 0.371381 | − | 0.928480i | \(-0.378884\pi\) | ||||
0.371381 | + | 0.928480i | \(0.378884\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 5.69476 | 0.501395 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −5.03206 | −0.439653 | −0.219826 | − | 0.975539i | \(-0.570549\pi\) | ||||
−0.219826 | + | 0.975539i | \(0.570549\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −0.567324 | −0.0491932 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −20.6498 | −1.76423 | −0.882115 | − | 0.471033i | \(-0.843881\pi\) | ||||
−0.882115 | + | 0.471033i | \(0.843881\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 11.4726 | 0.973092 | 0.486546 | − | 0.873655i | \(-0.338257\pi\) | ||||
0.486546 | + | 0.873655i | \(0.338257\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −2.57241 | −0.216636 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0.724378 | 0.0605755 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 3.14551 | 0.259438 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 13.0611 | 1.07001 | 0.535003 | − | 0.844850i | \(-0.320311\pi\) | ||||
0.535003 | + | 0.844850i | \(0.320311\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 17.8177 | 1.44998 | 0.724992 | − | 0.688758i | \(-0.241844\pi\) | ||||
0.724992 | + | 0.688758i | \(0.241844\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −22.0777 | −1.78488 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 11.3959 | 0.909490 | 0.454745 | − | 0.890622i | \(-0.349730\pi\) | ||||
0.454745 | + | 0.890622i | \(0.349730\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −0.943601 | −0.0748324 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 2.19807 | 0.173232 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −16.5741 | −1.29819 | −0.649093 | − | 0.760709i | \(-0.724851\pi\) | ||||
−0.649093 | + | 0.760709i | \(0.724851\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 19.3378 | 1.49640 | 0.748200 | − | 0.663473i | \(-0.230918\pi\) | ||||
0.748200 | + | 0.663473i | \(0.230918\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.9726 | −0.997894 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −2.77814 | −0.212450 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −9.31290 | −0.708046 | −0.354023 | − | 0.935237i | \(-0.615187\pi\) | ||||
−0.354023 | + | 0.935237i | \(0.615187\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −3.91963 | −0.294617 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 24.1703 | 1.80658 | 0.903288 | − | 0.429035i | \(-0.141146\pi\) | ||||
0.903288 | + | 0.429035i | \(0.141146\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 18.6981 | 1.38982 | 0.694910 | − | 0.719097i | \(-0.255444\pi\) | ||||
0.694910 | + | 0.719097i | \(0.255444\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −5.56649 | −0.411487 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 34.7920 | 2.54424 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −1.54403 | −0.112312 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 6.27452 | 0.454008 | 0.227004 | − | 0.973894i | \(-0.427107\pi\) | ||||
0.227004 | + | 0.973894i | \(0.427107\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −8.49096 | −0.611193 | −0.305596 | − | 0.952161i | \(-0.598856\pi\) | ||||
−0.305596 | + | 0.952161i | \(0.598856\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −5.97358 | −0.425600 | −0.212800 | − | 0.977096i | \(-0.568258\pi\) | ||||
−0.212800 | + | 0.977096i | \(0.568258\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 19.8763 | 1.40899 | 0.704497 | − | 0.709707i | \(-0.251173\pi\) | ||||
0.704497 | + | 0.709707i | \(0.251173\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 4.14305 | 0.292228 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −2.00397 | −0.140651 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 10.7638 | 0.748135 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 4.37804 | 0.302835 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2.84905 | −0.196137 | −0.0980685 | − | 0.995180i | \(-0.531266\pi\) | ||||
−0.0980685 | + | 0.995180i | \(0.531266\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −0.339146 | −0.0232379 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1.81759 | −0.123386 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 2.13849 | 0.144506 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.31488 | 0.0884481 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0.883914 | 0.0591912 | 0.0295956 | − | 0.999562i | \(-0.490578\pi\) | ||||
0.0295956 | + | 0.999562i | \(0.490578\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −1.02836 | −0.0682549 | −0.0341275 | − | 0.999417i | \(-0.510865\pi\) | ||||
−0.0341275 | + | 0.999417i | \(0.510865\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −24.5878 | −1.62481 | −0.812404 | − | 0.583095i | \(-0.801842\pi\) | ||||
−0.812404 | + | 0.583095i | \(0.801842\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1.16989 | 0.0769734 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 5.23585 | 0.343012 | 0.171506 | − | 0.985183i | \(-0.445137\pi\) | ||||
0.171506 | + | 0.985183i | \(0.445137\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −5.51669 | −0.358348 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −12.8124 | −0.828767 | −0.414384 | − | 0.910102i | \(-0.636003\pi\) | ||||
−0.414384 | + | 0.910102i | \(0.636003\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −11.9996 | −0.772962 | −0.386481 | − | 0.922297i | \(-0.626309\pi\) | ||||
−0.386481 | + | 0.922297i | \(0.626309\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −11.4866 | −0.736869 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0.165457 | 0.0105278 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −3.16688 | −0.200693 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 23.7189 | 1.49713 | 0.748563 | − | 0.663064i | \(-0.230744\pi\) | ||||
0.748563 | + | 0.663064i | \(0.230744\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −16.9625 | −1.06642 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 2.11678 | 0.132041 | 0.0660206 | − | 0.997818i | \(-0.478970\pi\) | ||||
0.0660206 | + | 0.997818i | \(0.478970\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 5.77416 | 0.358789 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −9.81327 | −0.607426 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 1.95674 | 0.120658 | 0.0603288 | − | 0.998179i | \(-0.480785\pi\) | ||||
0.0603288 | + | 0.998179i | \(0.480785\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −3.82437 | −0.234048 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −22.8278 | −1.39184 | −0.695919 | − | 0.718120i | \(-0.745003\pi\) | ||||
−0.695919 | + | 0.718120i | \(0.745003\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −15.8203 | −0.961014 | −0.480507 | − | 0.876991i | \(-0.659547\pi\) | ||||
−0.480507 | + | 0.876991i | \(0.659547\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0.0442133 | 0.00267591 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −9.47924 | −0.569553 | −0.284776 | − | 0.958594i | \(-0.591919\pi\) | ||||
−0.284776 | + | 0.958594i | \(0.591919\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −8.90061 | −0.532866 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 13.3160 | 0.794367 | 0.397183 | − | 0.917739i | \(-0.369988\pi\) | ||||
0.397183 | + | 0.917739i | \(0.369988\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 9.20676 | 0.547285 | 0.273643 | − | 0.961831i | \(-0.411771\pi\) | ||||
0.273643 | + | 0.961831i | \(0.411771\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 3.38924 | 0.200061 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 46.1537 | 2.71492 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −6.42094 | −0.376402 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −10.3435 | −0.604273 | −0.302137 | − | 0.953265i | \(-0.597700\pi\) | ||||
−0.302137 | + | 0.953265i | \(0.597700\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 11.9153 | 0.691394 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −0.641056 | −0.0370732 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 6.85915 | 0.395355 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −9.07583 | −0.521393 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −22.0642 | −1.25927 | −0.629636 | − | 0.776891i | \(-0.716796\pi\) | ||||
−0.629636 | + | 0.776891i | \(0.716796\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −9.04677 | −0.514653 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −31.4064 | −1.78089 | −0.890447 | − | 0.455087i | \(-0.849608\pi\) | ||||
−0.890447 | + | 0.455087i | \(0.849608\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 15.1428 | 0.855924 | 0.427962 | − | 0.903797i | \(-0.359232\pi\) | ||||
0.427962 | + | 0.903797i | \(0.359232\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 18.5791 | 1.04350 | 0.521752 | − | 0.853097i | \(-0.325279\pi\) | ||||
0.521752 | + | 0.853097i | \(0.325279\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 15.4646 | 0.865852 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −5.65646 | −0.315713 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 7.94693 | 0.442179 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 7.06673 | 0.390791 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −3.09839 | −0.170820 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 22.8001 | 1.25320 | 0.626602 | − | 0.779339i | \(-0.284445\pi\) | ||||
0.626602 | + | 0.779339i | \(0.284445\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 28.2756 | 1.54950 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −28.9306 | −1.57595 | −0.787976 | − | 0.615706i | \(-0.788871\pi\) | ||||
−0.787976 | + | 0.615706i | \(0.788871\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 3.82959 | 0.207995 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 14.0263 | 0.759569 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 7.75994 | 0.418997 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 20.2803 | 1.08870 | 0.544352 | − | 0.838857i | \(-0.316776\pi\) | ||||
0.544352 | + | 0.838857i | \(0.316776\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 20.4355 | 1.09389 | 0.546943 | − | 0.837170i | \(-0.315792\pi\) | ||||
0.546943 | + | 0.837170i | \(0.315792\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0.450308 | 0.0240357 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −7.50588 | −0.399498 | −0.199749 | − | 0.979847i | \(-0.564013\pi\) | ||||
−0.199749 | + | 0.979847i | \(0.564013\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 2.12357 | 0.112391 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −18.4383 | −0.973135 | −0.486567 | − | 0.873643i | \(-0.661751\pi\) | ||||
−0.486567 | + | 0.873643i | \(0.661751\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −3.84689 | −0.201909 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 12.0105 | 0.626943 | 0.313471 | − | 0.949598i | \(-0.398508\pi\) | ||||
0.313471 | + | 0.949598i | \(0.398508\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 16.5969 | 0.863999 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1.13654 | −0.0590061 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 15.0719 | 0.780395 | 0.390197 | − | 0.920731i | \(-0.372407\pi\) | ||||
0.390197 | + | 0.920731i | \(0.372407\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0.584446 | 0.0301005 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −8.50216 | −0.436727 | −0.218363 | − | 0.975868i | \(-0.570072\pi\) | ||||
−0.218363 | + | 0.975868i | \(0.570072\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −3.94264 | −0.201988 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 34.9232 | 1.78449 | 0.892247 | − | 0.451547i | \(-0.149128\pi\) | ||||
0.892247 | + | 0.451547i | \(0.149128\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 33.5888 | 1.70741 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −10.7455 | −0.544820 | −0.272410 | − | 0.962181i | \(-0.587821\pi\) | ||||
−0.272410 | + | 0.962181i | \(0.587821\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −30.7900 | −1.55712 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 2.37018 | 0.119560 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −1.45462 | −0.0730051 | −0.0365025 | − | 0.999334i | \(-0.511622\pi\) | ||||
−0.0365025 | + | 0.999334i | \(0.511622\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0.267219 | 0.0133777 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 11.5379 | 0.576176 | 0.288088 | − | 0.957604i | \(-0.406980\pi\) | ||||
0.288088 | + | 0.957604i | \(0.406980\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0.530091 | 0.0264057 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −44.5592 | −2.20872 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −20.5596 | −1.01661 | −0.508304 | − | 0.861178i | \(-0.669727\pi\) | ||||
−0.508304 | + | 0.861178i | \(0.669727\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 9.72639 | 0.479767 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −4.72107 | −0.232308 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −5.40377 | −0.264624 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −11.0760 | −0.541096 | −0.270548 | − | 0.962706i | \(-0.587205\pi\) | ||||
−0.270548 | + | 0.962706i | \(0.587205\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 18.9178 | 0.921999 | 0.461000 | − | 0.887400i | \(-0.347491\pi\) | ||||
0.461000 | + | 0.887400i | \(0.347491\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −15.1726 | −0.737715 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −6.70467 | −0.324461 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −0.341194 | −0.0164730 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 5.23923 | 0.252365 | 0.126182 | − | 0.992007i | \(-0.459728\pi\) | ||||
0.126182 | + | 0.992007i | \(0.459728\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 8.26963 | 0.397413 | 0.198707 | − | 0.980059i | \(-0.436326\pi\) | ||||
0.198707 | + | 0.980059i | \(0.436326\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −3.87445 | −0.185340 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 26.2786 | 1.25421 | 0.627104 | − | 0.778936i | \(-0.284240\pi\) | ||||
0.627104 | + | 0.778936i | \(0.284240\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 18.5528 | 0.883469 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 9.03372 | 0.429205 | 0.214602 | − | 0.976701i | \(-0.431154\pi\) | ||||
0.214602 | + | 0.976701i | \(0.431154\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −6.15198 | −0.290979 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −10.5553 | −0.498135 | −0.249067 | − | 0.968486i | \(-0.580124\pi\) | ||||
−0.249067 | + | 0.968486i | \(0.580124\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −26.1548 | −1.23158 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −8.39242 | −0.394310 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −13.7694 | −0.644105 | −0.322053 | − | 0.946722i | \(-0.604373\pi\) | ||||
−0.322053 | + | 0.946722i | \(0.604373\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 21.6284 | 1.00953 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −0.0771895 | −0.00359507 | −0.00179754 | − | 0.999998i | \(-0.500572\pi\) | ||||
−0.00179754 | + | 0.999998i | \(0.500572\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −7.73598 | −0.359521 | −0.179761 | − | 0.983710i | \(-0.557532\pi\) | ||||
−0.179761 | + | 0.983710i | \(0.557532\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 9.11290 | 0.421695 | 0.210847 | − | 0.977519i | \(-0.432378\pi\) | ||||
0.210847 | + | 0.977519i | \(0.432378\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 4.99017 | 0.230425 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −5.36764 | −0.247328 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −52.9321 | −2.43382 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −5.56554 | −0.254828 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 14.8868 | 0.680197 | 0.340099 | − | 0.940390i | \(-0.389540\pi\) | ||||
0.340099 | + | 0.940390i | \(0.389540\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.68400 | −0.0767840 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −1.03533 | −0.0471090 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −37.1917 | −1.68532 | −0.842658 | − | 0.538449i | \(-0.819011\pi\) | ||||
−0.842658 | + | 0.538449i | \(0.819011\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 7.80668 | 0.353030 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −6.94872 | −0.313591 | −0.156796 | − | 0.987631i | \(-0.550116\pi\) | ||||
−0.156796 | + | 0.987631i | \(0.550116\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 28.0711 | 1.26426 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −0.408491 | −0.0183233 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 12.2261 | 0.547314 | 0.273657 | − | 0.961827i | \(-0.411767\pi\) | ||||
0.273657 | + | 0.961827i | \(0.411767\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −9.10840 | −0.406933 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −28.0625 | −1.25125 | −0.625623 | − | 0.780126i | \(-0.715155\pi\) | ||||
−0.625623 | + | 0.780126i | \(0.715155\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 6.11032 | 0.271369 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 3.23221 | 0.143265 | 0.0716326 | − | 0.997431i | \(-0.477179\pi\) | ||||
0.0716326 | + | 0.997431i | \(0.477179\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 2.57575 | 0.113944 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 2.72160 | 0.120162 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 23.9102 | 1.05157 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 4.38653 | 0.192547 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −27.8354 | −1.21949 | −0.609745 | − | 0.792598i | \(-0.708728\pi\) | ||||
−0.609745 | + | 0.792598i | \(0.708728\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −10.1695 | −0.444682 | −0.222341 | − | 0.974969i | \(-0.571370\pi\) | ||||
−0.222341 | + | 0.974969i | \(0.571370\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 25.4604 | 1.10907 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −7.98863 | −0.347332 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −23.1187 | −1.00327 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −0.988456 | −0.0428148 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −11.3846 | −0.491283 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −29.2372 | −1.25933 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 27.4801 | 1.18146 | 0.590731 | − | 0.806869i | \(-0.298840\pi\) | ||||
0.590731 | + | 0.806869i | \(0.298840\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −8.80711 | −0.377949 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 5.84680 | 0.249991 | 0.124995 | − | 0.992157i | \(-0.460108\pi\) | ||||
0.124995 | + | 0.992157i | \(0.460108\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −32.8322 | −1.40125 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 3.53231 | 0.150482 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −6.64468 | −0.282561 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −12.2691 | −0.519860 | −0.259930 | − | 0.965628i | \(-0.583699\pi\) | ||||
−0.259930 | + | 0.965628i | \(0.583699\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −2.00044 | −0.0846095 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −16.3876 | −0.691884 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 17.3234 | 0.730096 | 0.365048 | − | 0.930989i | \(-0.381053\pi\) | ||||
0.365048 | + | 0.930989i | \(0.381053\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −4.00106 | −0.168029 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −10.3824 | −0.435252 | −0.217626 | − | 0.976032i | \(-0.569831\pi\) | ||||
−0.217626 | + | 0.976032i | \(0.569831\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 10.3852 | 0.434607 | 0.217304 | − | 0.976104i | \(-0.430274\pi\) | ||||
0.217304 | + | 0.976104i | \(0.430274\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −2.95540 | −0.123464 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −16.6524 | −0.693248 | −0.346624 | − | 0.938004i | \(-0.612672\pi\) | ||||
−0.346624 | + | 0.938004i | \(0.612672\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 3.99938 | 0.166209 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −3.81441 | −0.158248 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 8.77065 | 0.363243 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 13.4077 | 0.553393 | 0.276697 | − | 0.960957i | \(-0.410760\pi\) | ||||
0.276697 | + | 0.960957i | \(0.410760\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 3.20380 | 0.132010 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 2.81365 | 0.115738 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −20.8050 | −0.854361 | −0.427180 | − | 0.904166i | \(-0.640493\pi\) | ||||
−0.427180 | + | 0.904166i | \(0.640493\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −9.36207 | −0.383164 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 9.75788 | 0.398696 | 0.199348 | − | 0.979929i | \(-0.436118\pi\) | ||||
0.199348 | + | 0.979929i | \(0.436118\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 3.27717 | 0.133679 | 0.0668393 | − | 0.997764i | \(-0.478709\pi\) | ||||
0.0668393 | + | 0.997764i | \(0.478709\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 24.4365 | 0.995132 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 31.1984 | 1.26630 | 0.633151 | − | 0.774028i | \(-0.281761\pi\) | ||||
0.633151 | + | 0.774028i | \(0.281761\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0.943901 | 0.0382488 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0.903628 | 0.0365569 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 30.3455 | 1.22564 | 0.612821 | − | 0.790222i | \(-0.290035\pi\) | ||||
0.612821 | + | 0.790222i | \(0.290035\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −40.7447 | −1.64032 | −0.820159 | − | 0.572135i | \(-0.806115\pi\) | ||||
−0.820159 | + | 0.572135i | \(0.806115\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −13.7115 | −0.551113 | −0.275557 | − | 0.961285i | \(-0.588862\pi\) | ||||
−0.275557 | + | 0.961285i | \(0.588862\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −10.5447 | −0.423144 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −4.60634 | −0.184549 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −2.06213 | −0.0823534 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −80.8830 | −3.22501 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −32.3748 | −1.28882 | −0.644411 | − | 0.764680i | \(-0.722897\pi\) | ||||
−0.644411 | + | 0.764680i | \(0.722897\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 1.34195 | 0.0533378 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.10495 | −0.0437796 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −2.00035 | −0.0791326 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 0.701397 | 0.0277035 | 0.0138518 | − | 0.999904i | \(-0.495591\pi\) | ||||
0.0138518 | + | 0.999904i | \(0.495591\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 12.5736 | 0.495856 | 0.247928 | − | 0.968778i | \(-0.420250\pi\) | ||||
0.247928 | + | 0.968778i | \(0.420250\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 36.4494 | 1.43297 | 0.716487 | − | 0.697600i | \(-0.245749\pi\) | ||||
0.716487 | + | 0.697600i | \(0.245749\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 36.4325 | 1.43010 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0.856115 | 0.0335538 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 44.2535 | 1.73177 | 0.865887 | − | 0.500240i | \(-0.166755\pi\) | ||||
0.865887 | + | 0.500240i | \(0.166755\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 12.6132 | 0.492089 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −18.4958 | −0.720493 | −0.360247 | − | 0.932857i | \(-0.617307\pi\) | ||||
−0.360247 | + | 0.932857i | \(0.617307\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 15.3505 | 0.597067 | 0.298533 | − | 0.954399i | \(-0.403503\pi\) | ||||
0.298533 | + | 0.954399i | \(0.403503\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −0.619328 | −0.0240527 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −13.6858 | −0.529915 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −0.416338 | −0.0160965 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 51.7399 | 1.99740 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 34.1219 | 1.31530 | 0.657651 | − | 0.753322i | \(-0.271550\pi\) | ||||
0.657651 | + | 0.753322i | \(0.271550\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −13.7808 | −0.529639 | −0.264819 | − | 0.964298i | \(-0.585312\pi\) | ||||
−0.264819 | + | 0.964298i | \(0.585312\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −7.73382 | −0.296797 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0.484376 | 0.0185613 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 35.8693 | 1.37250 | 0.686250 | − | 0.727366i | \(-0.259256\pi\) | ||||
0.686250 | + | 0.727366i | \(0.259256\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 11.5813 | 0.441853 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0.331465 | 0.0126278 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 17.5888 | 0.669111 | 0.334555 | − | 0.942376i | \(-0.391414\pi\) | ||||
0.334555 | + | 0.942376i | \(0.391414\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 6.90026 | 0.262119 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −47.4757 | −1.79827 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −2.46617 | −0.0932792 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −40.3585 | −1.52432 | −0.762159 | − | 0.647389i | \(-0.775861\pi\) | ||||
−0.762159 | + | 0.647389i | \(0.775861\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −10.1779 | −0.383866 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −10.9315 | −0.411123 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 20.5258 | 0.770862 | 0.385431 | − | 0.922737i | \(-0.374053\pi\) | ||||
0.385431 | + | 0.922737i | \(0.374053\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −32.5385 | −1.22029 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −12.4130 | −0.464869 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 6.03486 | 0.225376 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −29.8673 | −1.11386 | −0.556930 | − | 0.830559i | \(-0.688021\pi\) | ||||
−0.556930 | + | 0.830559i | \(0.688021\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −10.8965 | −0.405808 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 5.65200 | 0.210200 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −26.4630 | −0.981458 | −0.490729 | − | 0.871312i | \(-0.663269\pi\) | ||||
−0.490729 | + | 0.871312i | \(0.663269\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −15.7471 | −0.583228 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −96.0813 | −3.55369 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 30.5488 | 1.12834 | 0.564172 | − | 0.825657i | \(-0.309196\pi\) | ||||
0.564172 | + | 0.825657i | \(0.309196\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −38.5092 | −1.41850 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −34.4001 | −1.26543 | −0.632714 | − | 0.774386i | \(-0.718059\pi\) | ||||
−0.632714 | + | 0.774386i | \(0.718059\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −0.0779330 | −0.00286294 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −21.9370 | −0.804790 | −0.402395 | − | 0.915466i | \(-0.631822\pi\) | ||||
−0.402395 | + | 0.915466i | \(0.631822\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −18.6789 | −0.683424 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −6.81303 | −0.248943 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −45.4750 | −1.65941 | −0.829703 | − | 0.558206i | \(-0.811490\pi\) | ||||
−0.829703 | + | 0.558206i | \(0.811490\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −11.1720 | −0.407130 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −8.91122 | −0.323884 | −0.161942 | − | 0.986800i | \(-0.551776\pi\) | ||||
−0.161942 | + | 0.986800i | \(0.551776\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 7.98961 | 0.290005 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −48.1068 | −1.74387 | −0.871934 | − | 0.489623i | \(-0.837134\pi\) | ||||
−0.871934 | + | 0.489623i | \(0.837134\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 8.51165 | 0.308142 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 1.37687 | 0.0497161 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −11.2615 | −0.406099 | −0.203049 | − | 0.979169i | \(-0.565085\pi\) | ||||
−0.203049 | + | 0.979169i | \(0.565085\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −0.997039 | −0.0359075 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −20.4897 | −0.736964 | −0.368482 | − | 0.929635i | \(-0.620122\pi\) | ||||
−0.368482 | + | 0.929635i | \(0.620122\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −2.71972 | −0.0975695 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −5.97409 | −0.214044 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 3.15232 | 0.112799 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 9.61354 | 0.343560 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −5.45356 | −0.194398 | −0.0971992 | − | 0.995265i | \(-0.530988\pi\) | ||||
−0.0971992 | + | 0.995265i | \(0.530988\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −0.921655 | −0.0328118 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 4.61262 | 0.164006 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1.95538 | 0.0694376 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 4.96228 | 0.175773 | 0.0878864 | − | 0.996131i | \(-0.471989\pi\) | ||||
0.0878864 | + | 0.996131i | \(0.471989\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 43.4014 | 1.53543 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −22.5569 | −0.797008 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −19.8770 | −0.701445 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 10.7523 | 0.378498 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −18.4521 | −0.648741 | −0.324370 | − | 0.945930i | \(-0.605152\pi\) | ||||
−0.324370 | + | 0.945930i | \(0.605152\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 31.3590 | 1.10116 | 0.550582 | − | 0.834781i | \(-0.314406\pi\) | ||||
0.550582 | + | 0.834781i | \(0.314406\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 7.45161 | 0.261339 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −12.0904 | −0.422988 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0.260778 | 0.00911233 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −52.9504 | −1.84798 | −0.923991 | − | 0.382413i | \(-0.875093\pi\) | ||||
−0.923991 | + | 0.382413i | \(0.875093\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 46.0815 | 1.60630 | 0.803150 | − | 0.595776i | \(-0.203155\pi\) | ||||
0.803150 | + | 0.595776i | \(0.203155\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 10.9170 | 0.379622 | 0.189811 | − | 0.981821i | \(-0.439212\pi\) | ||||
0.189811 | + | 0.981821i | \(0.439212\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 48.6141 | 1.68844 | 0.844219 | − | 0.535998i | \(-0.180064\pi\) | ||||
0.844219 | + | 0.535998i | \(0.180064\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 4.46488 | 0.154885 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −53.0707 | −1.83879 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 8.71945 | 0.301388 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −35.2171 | −1.21583 | −0.607915 | − | 0.794002i | \(-0.707994\pi\) | ||||
−0.607915 | + | 0.794002i | \(0.707994\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −16.5228 | −0.569750 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −6.27206 | −0.216021 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −4.63346 | −0.159208 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −4.33653 | −0.148829 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 39.4337 | 1.35177 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −7.77006 | −0.266042 | −0.133021 | − | 0.991113i | \(-0.542468\pi\) | ||||
−0.133021 | + | 0.991113i | \(0.542468\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 20.8792 | 0.713219 | 0.356610 | − | 0.934253i | \(-0.383933\pi\) | ||||
0.356610 | + | 0.934253i | \(0.383933\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 5.48065 | 0.186997 | 0.0934987 | − | 0.995619i | \(-0.470195\pi\) | ||||
0.0934987 | + | 0.995619i | \(0.470195\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −1.59639 | −0.0544048 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 23.9562 | 0.815479 | 0.407740 | − | 0.913098i | \(-0.366317\pi\) | ||||
0.407740 | + | 0.913098i | \(0.366317\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −21.7391 | −0.738300 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 51.2770 | 1.73945 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1.45536 | −0.0493129 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −37.8719 | −1.28177 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −18.0925 | −0.610941 | −0.305471 | − | 0.952201i | \(-0.598814\pi\) | ||||
−0.305471 | + | 0.952201i | \(0.598814\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 4.87195 | 0.164327 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 6.10173 | 0.205572 | 0.102786 | − | 0.994703i | \(-0.467224\pi\) | ||||
0.102786 | + | 0.994703i | \(0.467224\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 11.8538 | 0.398914 | 0.199457 | − | 0.979907i | \(-0.436082\pi\) | ||||
0.199457 | + | 0.979907i | \(0.436082\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −46.7513 | −1.56976 | −0.784878 | − | 0.619651i | \(-0.787274\pi\) | ||||
−0.784878 | + | 0.619651i | \(0.787274\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −4.74879 | −0.159269 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 30.8762 | 1.03439 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 5.46140 | 0.182759 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0.301948 | 0.0100817 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 11.3168 | 0.377437 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 15.9203 | 0.530383 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −3.23077 | −0.107513 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −36.8753 | −1.22442 | −0.612212 | − | 0.790693i | \(-0.709720\pi\) | ||||
−0.612212 | + | 0.790693i | \(0.709720\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −53.5310 | −1.77551 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −24.9642 | −0.827099 | −0.413550 | − | 0.910482i | \(-0.635711\pi\) | ||||
−0.413550 | + | 0.910482i | \(0.635711\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 29.4358 | 0.974182 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 2.85481 | 0.0942740 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −8.45204 | −0.278807 | −0.139404 | − | 0.990236i | \(-0.544519\pi\) | ||||
−0.139404 | + | 0.990236i | \(0.544519\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 10.3926 | 0.342448 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0.119134 | 0.00392135 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −53.3596 | −1.75256 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 34.3786 | 1.12793 | 0.563963 | − | 0.825800i | \(-0.309276\pi\) | ||||
0.563963 | + | 0.825800i | \(0.309276\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −6.67814 | −0.218867 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 14.7929 | 0.484299 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 5.23838 | 0.171130 | 0.0855652 | − | 0.996333i | \(-0.472730\pi\) | ||||
0.0855652 | + | 0.996333i | \(0.472730\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −7.13252 | −0.232761 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 14.3720 | 0.468514 | 0.234257 | − | 0.972175i | \(-0.424734\pi\) | ||||
0.234257 | + | 0.972175i | \(0.424734\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 23.1463 | 0.753748 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −27.8865 | −0.906190 | −0.453095 | − | 0.891462i | \(-0.649680\pi\) | ||||
−0.453095 | + | 0.891462i | \(0.649680\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −0.751203 | −0.0243851 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −8.75104 | −0.283772 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 18.8741 | 0.611392 | 0.305696 | − | 0.952129i | \(-0.401111\pi\) | ||||
0.305696 | + | 0.952129i | \(0.401111\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −7.28408 | −0.235461 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 11.7151 | 0.378301 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −20.7357 | −0.668893 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −33.3629 | −1.07510 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 2.87426 | 0.0924301 | 0.0462150 | − | 0.998932i | \(-0.485284\pi\) | ||||
0.0462150 | + | 0.998932i | \(0.485284\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −3.74313 | −0.120247 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −50.4156 | −1.61791 | −0.808956 | − | 0.587869i | \(-0.799967\pi\) | ||||
−0.808956 | + | 0.587869i | \(0.799967\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −6.50867 | −0.208658 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 48.5411 | 1.55297 | 0.776484 | − | 0.630137i | \(-0.217001\pi\) | ||||
0.776484 | + | 0.630137i | \(0.217001\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 35.5471 | 1.13609 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 41.6809 | 1.33077 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −5.00431 | −0.159613 | −0.0798063 | − | 0.996810i | \(-0.525430\pi\) | ||||
−0.0798063 | + | 0.996810i | \(0.525430\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 1.45939 | 0.0464529 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 46.8435 | 1.48954 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −43.9761 | −1.39695 | −0.698474 | − | 0.715635i | \(-0.746137\pi\) | ||||
−0.698474 | + | 0.715635i | \(0.746137\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −10.7392 | −0.340798 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 11.4138 | 0.361478 | 0.180739 | − | 0.983531i | \(-0.442151\pi\) | ||||
0.180739 | + | 0.983531i | \(0.442151\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −27.7001 | −0.876393 |
(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 | 3800.2.a.bd.1.3 | yes | 6 | |
4.3 | odd | 2 | 7600.2.a.ci.1.4 | 6 | |||
5.2 | odd | 4 | 3800.2.d.p.3649.7 | 12 | |||
5.3 | odd | 4 | 3800.2.d.p.3649.6 | 12 | |||
5.4 | even | 2 | 3800.2.a.bb.1.4 | ✓ | 6 | ||
20.19 | odd | 2 | 7600.2.a.cm.1.3 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3800.2.a.bb.1.4 | ✓ | 6 | 5.4 | even | 2 | ||
3800.2.a.bd.1.3 | yes | 6 | 1.1 | even | 1 | trivial | |
3800.2.d.p.3649.6 | 12 | 5.3 | odd | 4 | |||
3800.2.d.p.3649.7 | 12 | 5.2 | odd | 4 | |||
7600.2.a.ci.1.4 | 6 | 4.3 | odd | 2 | |||
7600.2.a.cm.1.3 | 6 | 20.19 | odd | 2 |