Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4140,2,Mod(1,4140)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4140, 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("4140.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4140 = 2^{2} \cdot 3^{2} \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4140.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(33.0580664368\) |
Analytic rank: | \(0\) |
Dimension: | \(5\) |
Coefficient field: | 5.5.14345904.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{5} - 2x^{4} - 13x^{3} + 34x^{2} - 11x - 12 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(3.18817\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4140.1 |
$q$-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 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.334658 | −0.126489 | −0.0632445 | − | 0.997998i | \(-0.520145\pi\) | ||||
−0.0632445 | + | 0.997998i | \(0.520145\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.12122 | −0.639572 | −0.319786 | − | 0.947490i | \(-0.603611\pi\) | ||||
−0.319786 | + | 0.947490i | \(0.603611\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.25511 | −0.625456 | −0.312728 | − | 0.949843i | \(-0.601243\pi\) | ||||
−0.312728 | + | 0.949843i | \(0.601243\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −6.93838 | −1.68280 | −0.841402 | − | 0.540410i | \(-0.818269\pi\) | ||||
−0.841402 | + | 0.540410i | \(0.818269\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.12122 | 0.945473 | 0.472736 | − | 0.881204i | \(-0.343266\pi\) | ||||
0.472736 | + | 0.881204i | \(0.343266\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.00000 | 0.208514 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.92046 | 0.356620 | 0.178310 | − | 0.983974i | \(-0.442937\pi\) | ||||
0.178310 | + | 0.983974i | \(0.442937\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.440822 | 0.0791740 | 0.0395870 | − | 0.999216i | \(-0.487396\pi\) | ||||
0.0395870 | + | 0.999216i | \(0.487396\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −0.334658 | −0.0565676 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 6.04168 | 0.993246 | 0.496623 | − | 0.867966i | \(-0.334573\pi\) | ||||
0.496623 | + | 0.867966i | \(0.334573\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 10.2493 | 1.60067 | 0.800334 | − | 0.599554i | \(-0.204655\pi\) | ||||
0.800334 | + | 0.599554i | \(0.204655\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −5.50042 | −0.838806 | −0.419403 | − | 0.907800i | \(-0.637761\pi\) | ||||
−0.419403 | + | 0.907800i | \(0.637761\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 4.65664 | 0.679241 | 0.339621 | − | 0.940562i | \(-0.389701\pi\) | ||||
0.339621 | + | 0.940562i | \(0.389701\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.88800 | −0.984001 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 4.40296 | 0.604792 | 0.302396 | − | 0.953182i | \(-0.402213\pi\) | ||||
0.302396 | + | 0.953182i | \(0.402213\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −2.12122 | −0.286025 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 10.8322 | 1.41023 | 0.705117 | − | 0.709091i | \(-0.250894\pi\) | ||||
0.705117 | + | 0.709091i | \(0.250894\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 13.7555 | 1.76122 | 0.880608 | − | 0.473846i | \(-0.157135\pi\) | ||||
0.880608 | + | 0.473846i | \(0.157135\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −2.25511 | −0.279713 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 6.87008 | 0.839314 | 0.419657 | − | 0.907683i | \(-0.362150\pi\) | ||||
0.419657 | + | 0.907683i | \(0.362150\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −5.57997 | −0.662220 | −0.331110 | − | 0.943592i | \(-0.607423\pi\) | ||||
−0.331110 | + | 0.943592i | \(0.607423\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 6.25511 | 0.732106 | 0.366053 | − | 0.930594i | \(-0.380709\pi\) | ||||
0.366053 | + | 0.930594i | \(0.380709\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0.709884 | 0.0808988 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 16.7052 | 1.87948 | 0.939739 | − | 0.341893i | \(-0.111068\pi\) | ||||
0.939739 | + | 0.341893i | \(0.111068\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −10.2770 | −1.12805 | −0.564024 | − | 0.825758i | \(-0.690748\pi\) | ||||
−0.564024 | + | 0.825758i | \(0.690748\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −6.93838 | −0.752573 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −1.33068 | −0.141052 | −0.0705261 | − | 0.997510i | \(-0.522468\pi\) | ||||
−0.0705261 | + | 0.997510i | \(0.522468\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.754693 | 0.0791133 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 4.12122 | 0.422828 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 18.4122 | 1.86947 | 0.934737 | − | 0.355341i | \(-0.115635\pi\) | ||||
0.934737 | + | 0.355341i | \(0.115635\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 3.33179 | 0.331526 | 0.165763 | − | 0.986166i | \(-0.446991\pi\) | ||||
0.165763 | + | 0.986166i | \(0.446991\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 5.25798 | 0.518084 | 0.259042 | − | 0.965866i | \(-0.416593\pi\) | ||||
0.259042 | + | 0.965866i | \(0.416593\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −0.768640 | −0.0743073 | −0.0371536 | − | 0.999310i | \(-0.511829\pi\) | ||||
−0.0371536 | + | 0.999310i | \(0.511829\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 4.12122 | 0.394741 | 0.197371 | − | 0.980329i | \(-0.436760\pi\) | ||||
0.197371 | + | 0.980329i | \(0.436760\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −10.5979 | −0.996965 | −0.498483 | − | 0.866900i | \(-0.666109\pi\) | ||||
−0.498483 | + | 0.866900i | \(0.666109\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.00000 | 0.0932505 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 2.32199 | 0.212856 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −6.50042 | −0.590947 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −6.29096 | −0.558232 | −0.279116 | − | 0.960257i | \(-0.590041\pi\) | ||||
−0.279116 | + | 0.960257i | \(0.590041\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 4.66932 | 0.407960 | 0.203980 | − | 0.978975i | \(-0.434612\pi\) | ||||
0.203980 | + | 0.978975i | \(0.434612\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.37920 | −0.119592 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −16.2172 | −1.38553 | −0.692766 | − | 0.721162i | \(-0.743608\pi\) | ||||
−0.692766 | + | 0.721162i | \(0.743608\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 11.8880 | 1.00833 | 0.504164 | − | 0.863608i | \(-0.331801\pi\) | ||||
0.504164 | + | 0.863608i | \(0.331801\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 4.78360 | 0.400024 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1.92046 | 0.159485 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −12.3637 | −1.01287 | −0.506435 | − | 0.862278i | \(-0.669037\pi\) | ||||
−0.506435 | + | 0.862278i | \(0.669037\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 0.499578 | 0.0406551 | 0.0203276 | − | 0.999793i | \(-0.493529\pi\) | ||||
0.0203276 | + | 0.999793i | \(0.493529\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0.440822 | 0.0354077 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0.0668715 | 0.00533692 | 0.00266846 | − | 0.999996i | \(-0.499151\pi\) | ||||
0.00266846 | + | 0.999996i | \(0.499151\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −0.334658 | −0.0263748 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 21.8768 | 1.71352 | 0.856760 | − | 0.515715i | \(-0.172474\pi\) | ||||
0.856760 | + | 0.515715i | \(0.172474\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −10.4500 | −0.808649 | −0.404324 | − | 0.914616i | \(-0.632493\pi\) | ||||
−0.404324 | + | 0.914616i | \(0.632493\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −7.91446 | −0.608805 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −0.722557 | −0.0549350 | −0.0274675 | − | 0.999623i | \(-0.508744\pi\) | ||||
−0.0274675 | + | 0.999623i | \(0.508744\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −0.334658 | −0.0252978 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −20.6546 | −1.54380 | −0.771899 | − | 0.635745i | \(-0.780693\pi\) | ||||
−0.771899 | + | 0.635745i | \(0.780693\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −9.62858 | −0.715687 | −0.357844 | − | 0.933782i | \(-0.616488\pi\) | ||||
−0.357844 | + | 0.933782i | \(0.616488\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 6.04168 | 0.444193 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 14.7178 | 1.07627 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 20.2658 | 1.46638 | 0.733190 | − | 0.680024i | \(-0.238031\pi\) | ||||
0.733190 | + | 0.680024i | \(0.238031\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 7.36653 | 0.530254 | 0.265127 | − | 0.964213i | \(-0.414586\pi\) | ||||
0.265127 | + | 0.964213i | \(0.414586\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 1.17955 | 0.0840391 | 0.0420196 | − | 0.999117i | \(-0.486621\pi\) | ||||
0.0420196 | + | 0.999117i | \(0.486621\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 17.4140 | 1.23445 | 0.617224 | − | 0.786787i | \(-0.288257\pi\) | ||||
0.617224 | + | 0.786787i | \(0.288257\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −0.642697 | −0.0451085 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 10.2493 | 0.715841 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −8.74202 | −0.604698 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 16.4515 | 1.13257 | 0.566283 | − | 0.824211i | \(-0.308381\pi\) | ||||
0.566283 | + | 0.824211i | \(0.308381\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −5.50042 | −0.375126 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −0.147525 | −0.0100146 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 15.6468 | 1.05252 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −5.87676 | −0.393537 | −0.196768 | − | 0.980450i | \(-0.563045\pi\) | ||||
−0.196768 | + | 0.980450i | \(0.563045\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 10.0913 | 0.669783 | 0.334892 | − | 0.942257i | \(-0.391300\pi\) | ||||
0.334892 | + | 0.942257i | \(0.391300\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −25.4578 | −1.68230 | −0.841150 | − | 0.540801i | \(-0.818121\pi\) | ||||
−0.841150 | + | 0.540801i | \(0.818121\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −0.828404 | −0.0542706 | −0.0271353 | − | 0.999632i | \(-0.508638\pi\) | ||||
−0.0271353 | + | 0.999632i | \(0.508638\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 4.65664 | 0.303766 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 8.59247 | 0.555801 | 0.277900 | − | 0.960610i | \(-0.410361\pi\) | ||||
0.277900 | + | 0.960610i | \(0.410361\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −15.1221 | −0.974098 | −0.487049 | − | 0.873375i | \(-0.661927\pi\) | ||||
−0.487049 | + | 0.873375i | \(0.661927\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −6.88800 | −0.440058 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −9.29382 | −0.591352 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 19.8014 | 1.24985 | 0.624925 | − | 0.780685i | \(-0.285129\pi\) | ||||
0.624925 | + | 0.780685i | \(0.285129\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2.12122 | −0.133360 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −27.4705 | −1.71356 | −0.856781 | − | 0.515680i | \(-0.827539\pi\) | ||||
−0.856781 | + | 0.515680i | \(0.827539\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −2.02190 | −0.125635 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 23.9587 | 1.47736 | 0.738678 | − | 0.674059i | \(-0.235450\pi\) | ||||
0.738678 | + | 0.674059i | \(0.235450\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 4.40296 | 0.270471 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −15.1000 | −0.920663 | −0.460332 | − | 0.887747i | \(-0.652270\pi\) | ||||
−0.460332 | + | 0.887747i | \(0.652270\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 24.1837 | 1.46905 | 0.734527 | − | 0.678579i | \(-0.237404\pi\) | ||||
0.734527 | + | 0.678579i | \(0.237404\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −2.12122 | −0.127914 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −18.9001 | −1.13560 | −0.567798 | − | 0.823168i | \(-0.692205\pi\) | ||||
−0.567798 | + | 0.823168i | \(0.692205\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −15.7914 | −0.942035 | −0.471017 | − | 0.882124i | \(-0.656113\pi\) | ||||
−0.471017 | + | 0.882124i | \(0.656113\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 30.2415 | 1.79767 | 0.898836 | − | 0.438285i | \(-0.144414\pi\) | ||||
0.898836 | + | 0.438285i | \(0.144414\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −3.43001 | −0.202467 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 31.1411 | 1.83183 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 32.1063 | 1.87567 | 0.937834 | − | 0.347085i | \(-0.112828\pi\) | ||||
0.937834 | + | 0.347085i | \(0.112828\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 10.8322 | 0.630676 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −2.25511 | −0.130417 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.84076 | 0.106100 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 13.7555 | 0.787640 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −24.4102 | −1.39316 | −0.696581 | − | 0.717478i | \(-0.745296\pi\) | ||||
−0.696581 | + | 0.717478i | \(0.745296\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −0.351141 | −0.0199114 | −0.00995569 | − | 0.999950i | \(-0.503169\pi\) | ||||
−0.00995569 | + | 0.999950i | \(0.503169\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 34.6236 | 1.95704 | 0.978521 | − | 0.206149i | \(-0.0660931\pi\) | ||||
0.978521 | + | 0.206149i | \(0.0660931\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 12.3385 | 0.692997 | 0.346499 | − | 0.938050i | \(-0.387371\pi\) | ||||
0.346499 | + | 0.938050i | \(0.387371\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −4.07371 | −0.228084 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −28.5946 | −1.59105 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −2.25511 | −0.125091 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −1.55838 | −0.0859165 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 16.3118 | 0.896580 | 0.448290 | − | 0.893888i | \(-0.352033\pi\) | ||||
0.448290 | + | 0.893888i | \(0.352033\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 6.87008 | 0.375353 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 20.9476 | 1.14109 | 0.570544 | − | 0.821267i | \(-0.306732\pi\) | ||||
0.570544 | + | 0.821267i | \(0.306732\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −0.935081 | −0.0506375 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 4.64774 | 0.250954 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 0.752671 | 0.0404055 | 0.0202027 | − | 0.999796i | \(-0.493569\pi\) | ||||
0.0202027 | + | 0.999796i | \(0.493569\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −20.4204 | −1.09308 | −0.546539 | − | 0.837433i | \(-0.684055\pi\) | ||||
−0.546539 | + | 0.837433i | \(0.684055\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −1.24261 | −0.0661373 | −0.0330686 | − | 0.999453i | \(-0.510528\pi\) | ||||
−0.0330686 | + | 0.999453i | \(0.510528\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −5.57997 | −0.296154 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −12.6394 | −0.667082 | −0.333541 | − | 0.942736i | \(-0.608244\pi\) | ||||
−0.333541 | + | 0.942736i | \(0.608244\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −2.01554 | −0.106081 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 6.25511 | 0.327408 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 25.7622 | 1.34478 | 0.672389 | − | 0.740198i | \(-0.265268\pi\) | ||||
0.672389 | + | 0.740198i | \(0.265268\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1.47349 | −0.0764996 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −18.7557 | −0.971133 | −0.485567 | − | 0.874200i | \(-0.661387\pi\) | ||||
−0.485567 | + | 0.874200i | \(0.661387\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −4.33085 | −0.223050 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 6.56347 | 0.337143 | 0.168571 | − | 0.985689i | \(-0.446085\pi\) | ||||
0.168571 | + | 0.985689i | \(0.446085\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −33.0101 | −1.68674 | −0.843368 | − | 0.537337i | \(-0.819430\pi\) | ||||
−0.843368 | + | 0.537337i | \(0.819430\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0.709884 | 0.0361790 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 22.5819 | 1.14495 | 0.572474 | − | 0.819923i | \(-0.305984\pi\) | ||||
0.572474 | + | 0.819923i | \(0.305984\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −6.93838 | −0.350889 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 16.7052 | 0.840528 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −17.2549 | −0.866001 | −0.433001 | − | 0.901394i | \(-0.642545\pi\) | ||||
−0.433001 | + | 0.901394i | \(0.642545\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 7.96416 | 0.397711 | 0.198855 | − | 0.980029i | \(-0.436278\pi\) | ||||
0.198855 | + | 0.980029i | \(0.436278\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −0.994105 | −0.0495199 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −12.8157 | −0.635252 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −3.42528 | −0.169369 | −0.0846847 | − | 0.996408i | \(-0.526988\pi\) | ||||
−0.0846847 | + | 0.996408i | \(0.526988\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −3.62509 | −0.178379 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −10.2770 | −0.504479 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −33.3141 | −1.62750 | −0.813751 | − | 0.581214i | \(-0.802578\pi\) | ||||
−0.813751 | + | 0.581214i | \(0.802578\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 6.42485 | 0.313128 | 0.156564 | − | 0.987668i | \(-0.449958\pi\) | ||||
0.156564 | + | 0.987668i | \(0.449958\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −6.93838 | −0.336561 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −4.60340 | −0.222774 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 22.3733 | 1.07768 | 0.538842 | − | 0.842407i | \(-0.318862\pi\) | ||||
0.538842 | + | 0.842407i | \(0.318862\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −28.5150 | −1.37035 | −0.685173 | − | 0.728381i | \(-0.740273\pi\) | ||||
−0.685173 | + | 0.728381i | \(0.740273\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 4.12122 | 0.197145 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 17.4947 | 0.834976 | 0.417488 | − | 0.908682i | \(-0.362911\pi\) | ||||
0.417488 | + | 0.908682i | \(0.362911\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 3.90397 | 0.185483 | 0.0927417 | − | 0.995690i | \(-0.470437\pi\) | ||||
0.0927417 | + | 0.995690i | \(0.470437\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1.33068 | −0.0630804 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 14.6615 | 0.691917 | 0.345959 | − | 0.938250i | \(-0.387554\pi\) | ||||
0.345959 | + | 0.938250i | \(0.387554\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −21.7410 | −1.02374 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0.754693 | 0.0353805 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −0.435257 | −0.0203605 | −0.0101802 | − | 0.999948i | \(-0.503241\pi\) | ||||
−0.0101802 | + | 0.999948i | \(0.503241\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 32.0970 | 1.49491 | 0.747454 | − | 0.664314i | \(-0.231276\pi\) | ||||
0.747454 | + | 0.664314i | \(0.231276\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −17.0357 | −0.791715 | −0.395858 | − | 0.918312i | \(-0.629553\pi\) | ||||
−0.395858 | + | 0.918312i | \(0.629553\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −18.1352 | −0.839196 | −0.419598 | − | 0.907710i | \(-0.637829\pi\) | ||||
−0.419598 | + | 0.907710i | \(0.637829\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −2.29913 | −0.106164 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 11.6676 | 0.536477 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 4.12122 | 0.189095 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 22.2046 | 1.01455 | 0.507276 | − | 0.861783i | \(-0.330652\pi\) | ||||
0.507276 | + | 0.861783i | \(0.330652\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −13.6247 | −0.621232 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 18.4122 | 0.836054 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 7.98733 | 0.361940 | 0.180970 | − | 0.983489i | \(-0.442076\pi\) | ||||
0.180970 | + | 0.983489i | \(0.442076\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 13.3122 | 0.600770 | 0.300385 | − | 0.953818i | \(-0.402885\pi\) | ||||
0.300385 | + | 0.953818i | \(0.402885\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −13.3249 | −0.600121 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 1.86738 | 0.0837635 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −14.9732 | −0.670293 | −0.335147 | − | 0.942166i | \(-0.608786\pi\) | ||||
−0.335147 | + | 0.942166i | \(0.608786\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −42.2038 | −1.88178 | −0.940888 | − | 0.338718i | \(-0.890007\pi\) | ||||
−0.940888 | + | 0.338718i | \(0.890007\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 3.33179 | 0.148263 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −12.5966 | −0.558335 | −0.279168 | − | 0.960242i | \(-0.590058\pi\) | ||||
−0.279168 | + | 0.960242i | \(0.590058\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −2.09333 | −0.0926033 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 5.25798 | 0.231694 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −9.87777 | −0.434424 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 39.6602 | 1.73754 | 0.868772 | − | 0.495212i | \(-0.164910\pi\) | ||||
0.868772 | + | 0.495212i | \(0.164910\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −7.62063 | −0.333227 | −0.166614 | − | 0.986022i | \(-0.553283\pi\) | ||||
−0.166614 | + | 0.986022i | \(0.553283\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −3.05859 | −0.133234 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −23.1133 | −1.00115 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −0.768640 | −0.0332312 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 14.6110 | 0.629339 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 16.1020 | 0.692277 | 0.346139 | − | 0.938183i | \(-0.387493\pi\) | ||||
0.346139 | + | 0.938183i | \(0.387493\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 4.12122 | 0.176534 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 30.8139 | 1.31751 | 0.658753 | − | 0.752359i | \(-0.271084\pi\) | ||||
0.658753 | + | 0.752359i | \(0.271084\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 7.91462 | 0.337174 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −5.59052 | −0.237733 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −9.54954 | −0.404627 | −0.202313 | − | 0.979321i | \(-0.564846\pi\) | ||||
−0.202313 | + | 0.979321i | \(0.564846\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 12.4041 | 0.524637 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 31.6843 | 1.33533 | 0.667667 | − | 0.744460i | \(-0.267293\pi\) | ||||
0.667667 | + | 0.744460i | \(0.267293\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −10.5979 | −0.445856 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −40.3500 | −1.69156 | −0.845780 | − | 0.533533i | \(-0.820864\pi\) | ||||
−0.845780 | + | 0.533533i | \(0.820864\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 19.4732 | 0.814928 | 0.407464 | − | 0.913221i | \(-0.366413\pi\) | ||||
0.407464 | + | 0.913221i | \(0.366413\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1.00000 | 0.0417029 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 5.17381 | 0.215389 | 0.107694 | − | 0.994184i | \(-0.465653\pi\) | ||||
0.107694 | + | 0.994184i | \(0.465653\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 3.43929 | 0.142686 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −9.33964 | −0.386808 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −20.1892 | −0.833298 | −0.416649 | − | 0.909068i | \(-0.636796\pi\) | ||||
−0.416649 | + | 0.909068i | \(0.636796\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.81673 | 0.0748569 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 40.1978 | 1.65073 | 0.825364 | − | 0.564602i | \(-0.190970\pi\) | ||||
0.825364 | + | 0.564602i | \(0.190970\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 2.32199 | 0.0951921 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 11.1599 | 0.455982 | 0.227991 | − | 0.973663i | \(-0.426784\pi\) | ||||
0.227991 | + | 0.973663i | \(0.426784\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −3.60669 | −0.147120 | −0.0735599 | − | 0.997291i | \(-0.523436\pi\) | ||||
−0.0735599 | + | 0.997291i | \(0.523436\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −6.50042 | −0.264280 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −30.3968 | −1.23377 | −0.616884 | − | 0.787054i | \(-0.711605\pi\) | ||||
−0.616884 | + | 0.787054i | \(0.711605\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −10.5013 | −0.424836 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −27.2908 | −1.10226 | −0.551132 | − | 0.834418i | \(-0.685804\pi\) | ||||
−0.551132 | + | 0.834418i | \(0.685804\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −14.7815 | −0.595081 | −0.297541 | − | 0.954709i | \(-0.596166\pi\) | ||||
−0.297541 | + | 0.954709i | \(0.596166\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −25.3266 | −1.01796 | −0.508982 | − | 0.860777i | \(-0.669978\pi\) | ||||
−0.508982 | + | 0.860777i | \(0.669978\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0.445324 | 0.0178415 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −41.9194 | −1.67144 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −4.76519 | −0.189699 | −0.0948497 | − | 0.995492i | \(-0.530237\pi\) | ||||
−0.0948497 | + | 0.995492i | \(0.530237\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −6.29096 | −0.249649 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 15.5332 | 0.615449 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 12.8964 | 0.509377 | 0.254688 | − | 0.967023i | \(-0.418027\pi\) | ||||
0.254688 | + | 0.967023i | \(0.418027\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −12.0474 | −0.475103 | −0.237552 | − | 0.971375i | \(-0.576345\pi\) | ||||
−0.237552 | + | 0.971375i | \(0.576345\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −33.9728 | −1.33561 | −0.667804 | − | 0.744337i | \(-0.732766\pi\) | ||||
−0.667804 | + | 0.744337i | \(0.732766\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −22.9775 | −0.901947 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −20.4722 | −0.801140 | −0.400570 | − | 0.916266i | \(-0.631188\pi\) | ||||
−0.400570 | + | 0.916266i | \(0.631188\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 4.66932 | 0.182445 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −4.08538 | −0.159144 | −0.0795718 | − | 0.996829i | \(-0.525355\pi\) | ||||
−0.0795718 | + | 0.996829i | \(0.525355\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 23.5770 | 0.917040 | 0.458520 | − | 0.888684i | \(-0.348380\pi\) | ||||
0.458520 | + | 0.888684i | \(0.348380\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −1.37920 | −0.0534831 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.92046 | 0.0743604 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −29.1785 | −1.12642 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 14.3385 | 0.552707 | 0.276354 | − | 0.961056i | \(-0.410874\pi\) | ||||
0.276354 | + | 0.961056i | \(0.410874\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −22.2265 | −0.854233 | −0.427116 | − | 0.904197i | \(-0.640471\pi\) | ||||
−0.427116 | + | 0.904197i | \(0.640471\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −6.16179 | −0.236468 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −8.17176 | −0.312684 | −0.156342 | − | 0.987703i | \(-0.549970\pi\) | ||||
−0.156342 | + | 0.987703i | \(0.549970\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −16.2172 | −0.619629 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −9.92917 | −0.378271 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 3.55081 | 0.135079 | 0.0675396 | − | 0.997717i | \(-0.478485\pi\) | ||||
0.0675396 | + | 0.997717i | \(0.478485\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 11.8880 | 0.450938 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −71.1134 | −2.69361 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 40.2484 | 1.52016 | 0.760080 | − | 0.649830i | \(-0.225160\pi\) | ||||
0.760080 | + | 0.649830i | \(0.225160\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 24.8991 | 0.939087 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −1.11501 | −0.0419343 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1.81099 | 0.0680133 | 0.0340067 | − | 0.999422i | \(-0.489173\pi\) | ||||
0.0340067 | + | 0.999422i | \(0.489173\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0.440822 | 0.0165089 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 4.78360 | 0.178896 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 51.6544 | 1.92638 | 0.963191 | − | 0.268817i | \(-0.0866328\pi\) | ||||
0.963191 | + | 0.268817i | \(0.0866328\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1.75963 | −0.0655319 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 1.92046 | 0.0713239 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 40.1715 | 1.48988 | 0.744940 | − | 0.667132i | \(-0.232478\pi\) | ||||
0.744940 | + | 0.667132i | \(0.232478\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 38.1640 | 1.41155 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −25.2890 | −0.934071 | −0.467035 | − | 0.884239i | \(-0.654678\pi\) | ||||
−0.467035 | + | 0.884239i | \(0.654678\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −14.5730 | −0.536802 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 8.09730 | 0.297864 | 0.148932 | − | 0.988847i | \(-0.452416\pi\) | ||||
0.148932 | + | 0.988847i | \(0.452416\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −6.97954 | −0.256055 | −0.128027 | − | 0.991771i | \(-0.540865\pi\) | ||||
−0.128027 | + | 0.991771i | \(0.540865\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −12.3637 | −0.452970 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0.257232 | 0.00939905 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −5.03076 | −0.183575 | −0.0917875 | − | 0.995779i | \(-0.529258\pi\) | ||||
−0.0917875 | + | 0.995779i | \(0.529258\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0.499578 | 0.0181815 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −3.84977 | −0.139922 | −0.0699612 | − | 0.997550i | \(-0.522288\pi\) | ||||
−0.0699612 | + | 0.997550i | \(0.522288\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −41.4084 | −1.50105 | −0.750527 | − | 0.660840i | \(-0.770200\pi\) | ||||
−0.750527 | + | 0.660840i | \(0.770200\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −1.37920 | −0.0499304 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −24.4279 | −0.882040 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −20.2299 | −0.729510 | −0.364755 | − | 0.931104i | \(-0.618847\pi\) | ||||
−0.364755 | + | 0.931104i | \(0.618847\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −27.6528 | −0.994601 | −0.497300 | − | 0.867578i | \(-0.665675\pi\) | ||||
−0.497300 | + | 0.867578i | \(0.665675\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0.440822 | 0.0158348 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 42.2396 | 1.51339 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 11.8363 | 0.423538 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0.0668715 | 0.00238674 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −3.56252 | −0.126990 | −0.0634951 | − | 0.997982i | \(-0.520225\pi\) | ||||
−0.0634951 | + | 0.997982i | \(0.520225\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 3.54667 | 0.126105 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −31.0203 | −1.10156 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −7.20920 | −0.255363 | −0.127681 | − | 0.991815i | \(-0.540753\pi\) | ||||
−0.127681 | + | 0.991815i | \(0.540753\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −32.3096 | −1.14303 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −13.2685 | −0.468234 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −0.334658 | −0.0117952 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 30.2452 | 1.06337 | 0.531683 | − | 0.846943i | \(-0.321560\pi\) | ||||
0.531683 | + | 0.846943i | \(0.321560\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 3.32739 | 0.116840 | 0.0584202 | − | 0.998292i | \(-0.481394\pi\) | ||||
0.0584202 | + | 0.998292i | \(0.481394\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 21.8768 | 0.766309 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −22.6685 | −0.793069 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 2.50531 | 0.0874359 | 0.0437179 | − | 0.999044i | \(-0.486080\pi\) | ||||
0.0437179 | + | 0.999044i | \(0.486080\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 12.8639 | 0.448408 | 0.224204 | − | 0.974542i | \(-0.428022\pi\) | ||||
0.224204 | + | 0.974542i | \(0.428022\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −52.5222 | −1.82637 | −0.913187 | − | 0.407541i | \(-0.866387\pi\) | ||||
−0.913187 | + | 0.407541i | \(0.866387\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −29.6030 | −1.02815 | −0.514077 | − | 0.857744i | \(-0.671865\pi\) | ||||
−0.514077 | + | 0.857744i | \(0.671865\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 47.7916 | 1.65588 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −10.4500 | −0.361639 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −51.6360 | −1.78267 | −0.891336 | − | 0.453343i | \(-0.850231\pi\) | ||||
−0.891336 | + | 0.453343i | \(0.850231\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −25.3118 | −0.872822 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −7.91446 | −0.272266 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 2.17542 | 0.0747483 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 6.04168 | 0.207106 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −19.3687 | −0.663173 | −0.331587 | − | 0.943425i | \(-0.607584\pi\) | ||||
−0.331587 | + | 0.943425i | \(0.607584\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 24.9929 | 0.853741 | 0.426870 | − | 0.904313i | \(-0.359616\pi\) | ||||
0.426870 | + | 0.904313i | \(0.359616\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 33.4904 | 1.14268 | 0.571339 | − | 0.820715i | \(-0.306424\pi\) | ||||
0.571339 | + | 0.820715i | \(0.306424\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −12.4269 | −0.423016 | −0.211508 | − | 0.977376i | \(-0.567837\pi\) | ||||
−0.211508 | + | 0.977376i | \(0.567837\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −0.722557 | −0.0245677 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −35.4353 | −1.20206 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −15.4928 | −0.524954 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −0.334658 | −0.0113135 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −49.8039 | −1.68176 | −0.840879 | − | 0.541223i | \(-0.817962\pi\) | ||||
−0.840879 | + | 0.541223i | \(0.817962\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 14.6372 | 0.493139 | 0.246570 | − | 0.969125i | \(-0.420697\pi\) | ||||
0.246570 | + | 0.969125i | \(0.420697\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −19.1495 | −0.644431 | −0.322216 | − | 0.946666i | \(-0.604428\pi\) | ||||
−0.322216 | + | 0.946666i | \(0.604428\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −7.38614 | −0.248002 | −0.124001 | − | 0.992282i | \(-0.539573\pi\) | ||||
−0.124001 | + | 0.992282i | \(0.539573\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 2.10532 | 0.0706102 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 19.1911 | 0.642204 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −20.6546 | −0.690408 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0.846580 | 0.0282350 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −30.5494 | −1.01775 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −9.62858 | −0.320065 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −34.0630 | −1.13104 | −0.565521 | − | 0.824734i | \(-0.691325\pi\) | ||||
−0.565521 | + | 0.824734i | \(0.691325\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 13.8330 | 0.458306 | 0.229153 | − | 0.973390i | \(-0.426404\pi\) | ||||
0.229153 | + | 0.973390i | \(0.426404\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 21.7998 | 0.721468 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −1.56263 | −0.0516024 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 26.5797 | 0.876783 | 0.438392 | − | 0.898784i | \(-0.355548\pi\) | ||||
0.438392 | + | 0.898784i | \(0.355548\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 12.5835 | 0.414190 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 6.04168 | 0.198649 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −33.2511 | −1.09093 | −0.545467 | − | 0.838132i | \(-0.683648\pi\) | ||||
−0.545467 | + | 0.838132i | \(0.683648\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −28.3870 | −0.930346 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 14.7178 | 0.481325 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −1.26964 | −0.0414775 | −0.0207387 | − | 0.999785i | \(-0.506602\pi\) | ||||
−0.0207387 | + | 0.999785i | \(0.506602\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 39.8534 | 1.29918 | 0.649592 | − | 0.760283i | \(-0.274940\pi\) | ||||
0.649592 | + | 0.760283i | \(0.274940\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 10.2493 | 0.333763 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 20.8798 | 0.678503 | 0.339251 | − | 0.940696i | \(-0.389826\pi\) | ||||
0.339251 | + | 0.940696i | \(0.389826\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −14.1060 | −0.457900 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 3.38902 | 0.109781 | 0.0548906 | − | 0.998492i | \(-0.482519\pi\) | ||||
0.0548906 | + | 0.998492i | \(0.482519\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 20.2658 | 0.655785 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 5.42724 | 0.175255 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.8057 | −0.993731 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 7.36653 | 0.237137 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 61.7169 | 1.98468 | 0.992340 | − | 0.123536i | \(-0.0394235\pi\) | ||||
0.992340 | + | 0.123536i | \(0.0394235\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 46.2441 | 1.48404 | 0.742022 | − | 0.670375i | \(-0.233867\pi\) | ||||
0.742022 | + | 0.670375i | \(0.233867\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −3.97842 | −0.127542 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −13.9871 | −0.447486 | −0.223743 | − | 0.974648i | \(-0.571828\pi\) | ||||
−0.223743 | + | 0.974648i | \(0.571828\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 2.82267 | 0.0902130 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 32.2324 | 1.02805 | 0.514026 | − | 0.857774i | \(-0.328153\pi\) | ||||
0.514026 | + | 0.857774i | \(0.328153\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1.17955 | 0.0375834 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −5.50042 | −0.174903 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −34.1460 | −1.08468 | −0.542342 | − | 0.840158i | \(-0.682462\pi\) | ||||
−0.542342 | + | 0.840158i | \(0.682462\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 17.4140 | 0.552062 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 32.4286 | 1.02702 | 0.513511 | − | 0.858083i | \(-0.328344\pi\) | ||||
0.513511 | + | 0.858083i | \(0.328344\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 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 | 4140.2.a.u.1.2 | yes | 5 | |
3.2 | odd | 2 | 4140.2.a.t.1.2 | ✓ | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4140.2.a.t.1.2 | ✓ | 5 | 3.2 | odd | 2 | ||
4140.2.a.u.1.2 | yes | 5 | 1.1 | even | 1 | trivial |