Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2900,2,Mod(1,2900)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2900, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("2900.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2900 = 2^{2} \cdot 5^{2} \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2900.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: | \(23.1566165862\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.564.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 5x + 3 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 580) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-2.08613\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2900.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.35194 | −0.780542 | −0.390271 | − | 0.920700i | \(-0.627619\pi\) | ||||
−0.390271 | + | 0.920700i | \(0.627619\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.648061 | 0.244944 | 0.122472 | − | 0.992472i | \(-0.460918\pi\) | ||||
0.122472 | + | 0.992472i | \(0.460918\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.17226 | −0.390753 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.35194 | 1.01065 | 0.505324 | − | 0.862930i | \(-0.331373\pi\) | ||||
0.505324 | + | 0.862930i | \(0.331373\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −4.17226 | −1.15718 | −0.578588 | − | 0.815620i | \(-0.696396\pi\) | ||||
−0.578588 | + | 0.815620i | \(0.696396\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −4.82032 | −1.16910 | −0.584550 | − | 0.811358i | \(-0.698729\pi\) | ||||
−0.584550 | + | 0.811358i | \(0.698729\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 6.82032 | 1.56469 | 0.782344 | − | 0.622846i | \(-0.214024\pi\) | ||||
0.782344 | + | 0.622846i | \(0.214024\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.876139 | −0.191189 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −5.52420 | −1.15188 | −0.575938 | − | 0.817494i | \(-0.695363\pi\) | ||||
−0.575938 | + | 0.817494i | \(0.695363\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.64064 | 1.08554 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.00000 | −0.185695 | ||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.82032 | −0.506545 | −0.253272 | − | 0.967395i | \(-0.581507\pi\) | ||||
−0.253272 | + | 0.967395i | \(0.581507\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −4.53162 | −0.788853 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 10.2281 | 1.68149 | 0.840743 | − | 0.541435i | \(-0.182119\pi\) | ||||
0.840743 | + | 0.541435i | \(0.182119\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 5.64064 | 0.903226 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 8.17226 | 1.27629 | 0.638146 | − | 0.769915i | \(-0.279701\pi\) | ||||
0.638146 | + | 0.769915i | \(0.279701\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5.69646 | 0.868702 | 0.434351 | − | 0.900744i | \(-0.356978\pi\) | ||||
0.434351 | + | 0.900744i | \(0.356978\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 2.64806 | 0.386259 | 0.193130 | − | 0.981173i | \(-0.438136\pi\) | ||||
0.193130 | + | 0.981173i | \(0.438136\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.58002 | −0.940002 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 6.51678 | 0.912532 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 2.87614 | 0.395068 | 0.197534 | − | 0.980296i | \(-0.436707\pi\) | ||||
0.197534 | + | 0.980296i | \(0.436707\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −9.22066 | −1.22131 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −13.2207 | −1.72118 | −0.860592 | − | 0.509296i | \(-0.829906\pi\) | ||||
−0.860592 | + | 0.509296i | \(0.829906\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.12386 | −0.143896 | −0.0719478 | − | 0.997408i | \(-0.522922\pi\) | ||||
−0.0719478 | + | 0.997408i | \(0.522922\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −0.759696 | −0.0957127 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.52420 | −0.186211 | −0.0931053 | − | 0.995656i | \(-0.529679\pi\) | ||||
−0.0931053 | + | 0.995656i | \(0.529679\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 7.46838 | 0.899088 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −8.87614 | −1.05340 | −0.526702 | − | 0.850050i | \(-0.676572\pi\) | ||||
−0.526702 | + | 0.850050i | \(0.676572\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −9.69646 | −1.13488 | −0.567442 | − | 0.823413i | \(-0.692067\pi\) | ||||
−0.567442 | + | 0.823413i | \(0.692067\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 2.17226 | 0.247552 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 8.99258 | 1.01174 | 0.505872 | − | 0.862608i | \(-0.331171\pi\) | ||||
0.505872 | + | 0.862608i | \(0.331171\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −4.10902 | −0.456558 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −1.94418 | −0.213402 | −0.106701 | − | 0.994291i | \(-0.534029\pi\) | ||||
−0.106701 | + | 0.994291i | \(0.534029\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 1.35194 | 0.144943 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 17.0484 | 1.80713 | 0.903563 | − | 0.428455i | \(-0.140942\pi\) | ||||
0.903563 | + | 0.428455i | \(0.140942\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.70388 | −0.283443 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 3.81290 | 0.395380 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 13.3519 | 1.35568 | 0.677842 | − | 0.735208i | \(-0.262915\pi\) | ||||
0.677842 | + | 0.735208i | \(0.262915\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −3.92935 | −0.394914 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 18.4562 | 1.83646 | 0.918228 | − | 0.396052i | \(-0.129620\pi\) | ||||
0.918228 | + | 0.396052i | \(0.129620\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 14.8203 | 1.46029 | 0.730145 | − | 0.683292i | \(-0.239453\pi\) | ||||
0.730145 | + | 0.683292i | \(0.239453\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 3.35194 | 0.324044 | 0.162022 | − | 0.986787i | \(-0.448198\pi\) | ||||
0.162022 | + | 0.986787i | \(0.448198\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 2.76450 | 0.264791 | 0.132396 | − | 0.991197i | \(-0.457733\pi\) | ||||
0.132396 | + | 0.991197i | \(0.457733\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −13.8277 | −1.31247 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −7.94418 | −0.747326 | −0.373663 | − | 0.927565i | \(-0.621898\pi\) | ||||
−0.373663 | + | 0.927565i | \(0.621898\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 4.89098 | 0.452171 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −3.12386 | −0.286364 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0.235496 | 0.0214088 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −11.0484 | −0.996201 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 17.6965 | 1.57031 | 0.785153 | − | 0.619301i | \(-0.212584\pi\) | ||||
0.785153 | + | 0.619301i | \(0.212584\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −7.70127 | −0.678059 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 5.52420 | 0.482652 | 0.241326 | − | 0.970444i | \(-0.422418\pi\) | ||||
0.241326 | + | 0.970444i | \(0.422418\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 4.41998 | 0.383261 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 3.86872 | 0.330527 | 0.165264 | − | 0.986249i | \(-0.447153\pi\) | ||||
0.165264 | + | 0.986249i | \(0.447153\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 5.64064 | 0.478433 | 0.239217 | − | 0.970966i | \(-0.423109\pi\) | ||||
0.239217 | + | 0.970966i | \(0.423109\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −3.58002 | −0.301492 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −13.9852 | −1.16950 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 8.89578 | 0.733712 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 18.0000 | 1.47462 | 0.737309 | − | 0.675556i | \(-0.236096\pi\) | ||||
0.737309 | + | 0.675556i | \(0.236096\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −17.2207 | −1.40140 | −0.700699 | − | 0.713457i | \(-0.747128\pi\) | ||||
−0.700699 | + | 0.713457i | \(0.747128\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 5.65067 | 0.456830 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 5.69646 | 0.454627 | 0.227314 | − | 0.973822i | \(-0.427006\pi\) | ||||
0.227314 | + | 0.973822i | \(0.427006\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −3.88836 | −0.308367 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −3.58002 | −0.282145 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −16.4003 | −1.28457 | −0.642287 | − | 0.766464i | \(-0.722014\pi\) | ||||
−0.642287 | + | 0.766464i | \(0.722014\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 23.2765 | 1.80119 | 0.900594 | − | 0.434661i | \(-0.143132\pi\) | ||||
0.900594 | + | 0.434661i | \(0.143132\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 4.40776 | 0.339058 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −7.99519 | −0.611408 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 13.9245 | 1.05866 | 0.529332 | − | 0.848415i | \(-0.322443\pi\) | ||||
0.529332 | + | 0.848415i | \(0.322443\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 17.8735 | 1.34346 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −4.34452 | −0.324725 | −0.162362 | − | 0.986731i | \(-0.551911\pi\) | ||||
−0.162362 | + | 0.986731i | \(0.551911\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 20.5168 | 1.52500 | 0.762500 | − | 0.646988i | \(-0.223972\pi\) | ||||
0.762500 | + | 0.646988i | \(0.223972\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1.51939 | 0.112317 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −16.1574 | −1.18155 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 3.65548 | 0.265897 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −9.10422 | −0.658758 | −0.329379 | − | 0.944198i | \(-0.606839\pi\) | ||||
−0.329379 | + | 0.944198i | \(0.606839\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 25.1648 | 1.81140 | 0.905702 | − | 0.423914i | \(-0.139344\pi\) | ||||
0.905702 | + | 0.423914i | \(0.139344\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 0.703878 | 0.0501493 | 0.0250746 | − | 0.999686i | \(-0.492018\pi\) | ||||
0.0250746 | + | 0.999686i | \(0.492018\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −5.22066 | −0.370083 | −0.185041 | − | 0.982731i | \(-0.559242\pi\) | ||||
−0.185041 | + | 0.982731i | \(0.559242\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 2.06063 | 0.145345 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −0.648061 | −0.0454850 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 6.47580 | 0.450099 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 22.8613 | 1.58135 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −13.1042 | −0.902131 | −0.451066 | − | 0.892491i | \(-0.648956\pi\) | ||||
−0.451066 | + | 0.892491i | \(0.648956\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 12.0000 | 0.822226 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1.82774 | −0.124075 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 13.1090 | 0.885826 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 20.1116 | 1.35285 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 20.5726 | 1.37764 | 0.688822 | − | 0.724931i | \(-0.258128\pi\) | ||||
0.688822 | + | 0.724931i | \(0.258128\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 9.41256 | 0.624734 | 0.312367 | − | 0.949962i | \(-0.398878\pi\) | ||||
0.312367 | + | 0.949962i | \(0.398878\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2.00000 | 0.132164 | 0.0660819 | − | 0.997814i | \(-0.478950\pi\) | ||||
0.0660819 | + | 0.997814i | \(0.478950\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −2.93676 | −0.193225 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −10.3445 | −0.677692 | −0.338846 | − | 0.940842i | \(-0.610037\pi\) | ||||
−0.338846 | + | 0.940842i | \(0.610037\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −12.1574 | −0.789710 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 20.8761 | 1.35037 | 0.675183 | − | 0.737651i | \(-0.264065\pi\) | ||||
0.675183 | + | 0.737651i | \(0.264065\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 21.1600 | 1.36304 | 0.681519 | − | 0.731801i | \(-0.261320\pi\) | ||||
0.681519 | + | 0.731801i | \(0.261320\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −11.3668 | −0.729179 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −28.4562 | −1.81062 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 2.62842 | 0.166569 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −8.64806 | −0.545861 | −0.272930 | − | 0.962034i | \(-0.587993\pi\) | ||||
−0.272930 | + | 0.962034i | \(0.587993\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −18.5168 | −1.16414 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −27.4535 | −1.71251 | −0.856253 | − | 0.516557i | \(-0.827213\pi\) | ||||
−0.856253 | + | 0.516557i | \(0.827213\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 6.62842 | 0.411870 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1.17226 | 0.0725611 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 11.3371 | 0.699076 | 0.349538 | − | 0.936922i | \(-0.386339\pi\) | ||||
0.349538 | + | 0.936922i | \(0.386339\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −23.0484 | −1.41054 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −20.1723 | −1.22992 | −0.614962 | − | 0.788557i | \(-0.710829\pi\) | ||||
−0.614962 | + | 0.788557i | \(0.710829\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −10.7449 | −0.652704 | −0.326352 | − | 0.945248i | \(-0.605819\pi\) | ||||
−0.326352 | + | 0.945248i | \(0.605819\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 3.65548 | 0.221240 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 12.6284 | 0.758768 | 0.379384 | − | 0.925239i | \(-0.376136\pi\) | ||||
0.379384 | + | 0.925239i | \(0.376136\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 3.30615 | 0.197934 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 6.76450 | 0.403536 | 0.201768 | − | 0.979433i | \(-0.435331\pi\) | ||||
0.201768 | + | 0.979433i | \(0.435331\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −1.06804 | −0.0634886 | −0.0317443 | − | 0.999496i | \(-0.510106\pi\) | ||||
−0.0317443 | + | 0.999496i | \(0.510106\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 5.29612 | 0.312620 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 6.23550 | 0.366794 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −18.0510 | −1.05817 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −5.46357 | −0.319185 | −0.159593 | − | 0.987183i | \(-0.551018\pi\) | ||||
−0.159593 | + | 0.987183i | \(0.551018\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 18.9071 | 1.09710 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 23.0484 | 1.33292 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 3.69165 | 0.212783 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −24.9516 | −1.43343 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −6.30354 | −0.359762 | −0.179881 | − | 0.983688i | \(-0.557571\pi\) | ||||
−0.179881 | + | 0.983688i | \(0.557571\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −20.0362 | −1.13982 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 24.6842 | 1.39971 | 0.699857 | − | 0.714283i | \(-0.253247\pi\) | ||||
0.699857 | + | 0.714283i | \(0.253247\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 24.1723 | 1.36630 | 0.683148 | − | 0.730280i | \(-0.260610\pi\) | ||||
0.683148 | + | 0.730280i | \(0.260610\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −1.42740 | −0.0801708 | −0.0400854 | − | 0.999196i | \(-0.512763\pi\) | ||||
−0.0400854 | + | 0.999196i | \(0.512763\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −3.35194 | −0.187673 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −4.53162 | −0.252930 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −32.8761 | −1.82928 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −3.73744 | −0.206681 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 1.71610 | 0.0946119 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 34.2132 | 1.88053 | 0.940265 | − | 0.340444i | \(-0.110577\pi\) | ||||
0.940265 | + | 0.340444i | \(0.110577\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −11.9900 | −0.657046 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −4.40034 | −0.239702 | −0.119851 | − | 0.992792i | \(-0.538242\pi\) | ||||
−0.119851 | + | 0.992792i | \(0.538242\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 10.7401 | 0.583320 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −9.45355 | −0.511938 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −8.80068 | −0.475192 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −12.9926 | −0.697478 | −0.348739 | − | 0.937220i | \(-0.613390\pi\) | ||||
−0.348739 | + | 0.937220i | \(0.613390\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −20.0968 | −1.07576 | −0.537878 | − | 0.843022i | \(-0.680774\pi\) | ||||
−0.537878 | + | 0.843022i | \(0.680774\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −23.5342 | −1.25616 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 17.8129 | 0.948085 | 0.474043 | − | 0.880502i | \(-0.342794\pi\) | ||||
0.474043 | + | 0.880502i | \(0.342794\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 4.22327 | 0.223519 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 5.52420 | 0.291556 | 0.145778 | − | 0.989317i | \(-0.453431\pi\) | ||||
0.145778 | + | 0.989317i | \(0.453431\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 27.5168 | 1.44825 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −0.318377 | −0.0167104 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 20.0558 | 1.04691 | 0.523453 | − | 0.852055i | \(-0.324644\pi\) | ||||
0.523453 | + | 0.852055i | \(0.324644\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −9.58002 | −0.498716 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.86391 | 0.0967695 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1.88836 | 0.0977758 | 0.0488879 | − | 0.998804i | \(-0.484432\pi\) | ||||
0.0488879 | + | 0.998804i | \(0.484432\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 4.17226 | 0.214882 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −15.0894 | −0.775089 | −0.387545 | − | 0.921851i | \(-0.626677\pi\) | ||||
−0.387545 | + | 0.921851i | \(0.626677\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −23.9245 | −1.22569 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −17.3371 | −0.885885 | −0.442942 | − | 0.896550i | \(-0.646065\pi\) | ||||
−0.442942 | + | 0.896550i | \(0.646065\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −6.67773 | −0.339448 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −0.890976 | −0.0451743 | −0.0225871 | − | 0.999745i | \(-0.507190\pi\) | ||||
−0.0225871 | + | 0.999745i | \(0.507190\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 26.6284 | 1.34666 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −7.46838 | −0.376730 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −5.39292 | −0.270663 | −0.135331 | − | 0.990800i | \(-0.543210\pi\) | ||||
−0.135331 | + | 0.990800i | \(0.543210\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −5.97555 | −0.299152 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 5.23550 | 0.261448 | 0.130724 | − | 0.991419i | \(-0.458270\pi\) | ||||
0.130724 | + | 0.991419i | \(0.458270\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 11.7671 | 0.586162 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 34.2839 | 1.69939 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −16.0606 | −0.794147 | −0.397073 | − | 0.917787i | \(-0.629974\pi\) | ||||
−0.397073 | + | 0.917787i | \(0.629974\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −5.23027 | −0.257990 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −8.56779 | −0.421593 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −7.62581 | −0.373437 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −19.9245 | −0.973377 | −0.486689 | − | 0.873575i | \(-0.661795\pi\) | ||||
−0.486689 | + | 0.873575i | \(0.661795\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −15.5652 | −0.758600 | −0.379300 | − | 0.925274i | \(-0.623835\pi\) | ||||
−0.379300 | + | 0.925274i | \(0.623835\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −3.10422 | −0.150932 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −0.728330 | −0.0352464 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 18.9071 | 0.912843 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −13.4078 | −0.645829 | −0.322914 | − | 0.946428i | \(-0.604663\pi\) | ||||
−0.322914 | + | 0.946428i | \(0.604663\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 34.6842 | 1.66682 | 0.833409 | − | 0.552657i | \(-0.186386\pi\) | ||||
0.833409 | + | 0.552657i | \(0.186386\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −37.6768 | −1.80233 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −15.2355 | −0.727151 | −0.363575 | − | 0.931565i | \(-0.618444\pi\) | ||||
−0.363575 | + | 0.931565i | \(0.618444\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 7.71349 | 0.367309 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −5.00742 | −0.237910 | −0.118955 | − | 0.992900i | \(-0.537954\pi\) | ||||
−0.118955 | + | 0.992900i | \(0.537954\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −24.3349 | −1.15100 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −17.8129 | −0.840643 | −0.420321 | − | 0.907375i | \(-0.638083\pi\) | ||||
−0.420321 | + | 0.907375i | \(0.638083\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 27.3929 | 1.28988 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 23.2813 | 1.09385 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −24.4051 | −1.14162 | −0.570812 | − | 0.821081i | \(-0.693372\pi\) | ||||
−0.570812 | + | 0.821081i | \(0.693372\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −27.1897 | −1.26911 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −7.98516 | −0.371906 | −0.185953 | − | 0.982559i | \(-0.559537\pi\) | ||||
−0.185953 | + | 0.982559i | \(0.559537\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −11.6210 | −0.540074 | −0.270037 | − | 0.962850i | \(-0.587036\pi\) | ||||
−0.270037 | + | 0.962850i | \(0.587036\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −1.24030 | −0.0573944 | −0.0286972 | − | 0.999588i | \(-0.509136\pi\) | ||||
−0.0286972 | + | 0.999588i | \(0.509136\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −0.987774 | −0.0456112 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −7.70127 | −0.354856 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 19.0942 | 0.877952 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −3.37158 | −0.154374 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 19.6965 | 0.899954 | 0.449977 | − | 0.893040i | \(-0.351432\pi\) | ||||
0.449977 | + | 0.893040i | \(0.351432\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −42.6742 | −1.94578 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 4.83997 | 0.220226 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 15.0894 | 0.683765 | 0.341883 | − | 0.939743i | \(-0.388936\pi\) | ||||
0.341883 | + | 0.939743i | \(0.388936\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 22.1723 | 1.00266 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −12.2281 | −0.551845 | −0.275923 | − | 0.961180i | \(-0.588983\pi\) | ||||
−0.275923 | + | 0.961180i | \(0.588983\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 4.82032 | 0.217096 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −5.75228 | −0.258025 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −5.52901 | −0.247512 | −0.123756 | − | 0.992313i | \(-0.539494\pi\) | ||||
−0.123756 | + | 0.992313i | \(0.539494\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −31.4684 | −1.40590 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −24.2887 | −1.08298 | −0.541490 | − | 0.840707i | \(-0.682140\pi\) | ||||
−0.541490 | + | 0.840707i | \(0.682140\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −5.95902 | −0.264649 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −9.58002 | −0.424627 | −0.212313 | − | 0.977202i | \(-0.568100\pi\) | ||||
−0.212313 | + | 0.977202i | \(0.568100\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −6.28390 | −0.277983 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 38.4710 | 1.69854 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 8.87614 | 0.390372 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −18.8251 | −0.826331 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −21.5800 | −0.945438 | −0.472719 | − | 0.881213i | \(-0.656727\pi\) | ||||
−0.472719 | + | 0.881213i | \(0.656727\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 42.2132 | 1.84586 | 0.922928 | − | 0.384972i | \(-0.125789\pi\) | ||||
0.922928 | + | 0.384972i | \(0.125789\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 13.5949 | 0.592201 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 7.51678 | 0.326817 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 15.4981 | 0.672558 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −34.0968 | −1.47690 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 5.87353 | 0.253461 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −22.0558 | −0.950011 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 36.5530 | 1.57153 | 0.785767 | − | 0.618522i | \(-0.212268\pi\) | ||||
0.785767 | + | 0.618522i | \(0.212268\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −27.7374 | −1.19033 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −26.6236 | −1.13834 | −0.569172 | − | 0.822219i | \(-0.692736\pi\) | ||||
−0.569172 | + | 0.822219i | \(0.692736\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 1.31746 | 0.0562277 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −6.82032 | −0.290555 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 5.82774 | 0.247821 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −22.2233 | −0.941630 | −0.470815 | − | 0.882232i | \(-0.656040\pi\) | ||||
−0.470815 | + | 0.882232i | \(0.656040\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −23.7671 | −1.00524 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 21.8439 | 0.922248 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −1.11905 | −0.0471625 | −0.0235812 | − | 0.999722i | \(-0.507507\pi\) | ||||
−0.0235812 | + | 0.999722i | \(0.507507\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −2.66290 | −0.111831 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −10.5316 | −0.441508 | −0.220754 | − | 0.975329i | \(-0.570852\pi\) | ||||
−0.220754 | + | 0.975329i | \(0.570852\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −1.18449 | −0.0495692 | −0.0247846 | − | 0.999693i | \(-0.507890\pi\) | ||||
−0.0247846 | + | 0.999693i | \(0.507890\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 12.3083 | 0.514189 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −11.8687 | −0.494101 | −0.247051 | − | 0.969003i | \(-0.579461\pi\) | ||||
−0.247051 | + | 0.969003i | \(0.579461\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −34.0213 | −1.41388 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −1.25995 | −0.0522715 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 9.64064 | 0.399275 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −32.4610 | −1.33981 | −0.669904 | − | 0.742448i | \(-0.733665\pi\) | ||||
−0.669904 | + | 0.742448i | \(0.733665\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −19.2355 | −0.792585 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −0.951601 | −0.0391436 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −9.12386 | −0.374672 | −0.187336 | − | 0.982296i | \(-0.559985\pi\) | ||||
−0.187336 | + | 0.982296i | \(0.559985\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 7.05801 | 0.288865 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −30.2887 | −1.23756 | −0.618781 | − | 0.785563i | \(-0.712373\pi\) | ||||
−0.618781 | + | 0.785563i | \(0.712373\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 20.5168 | 0.836897 | 0.418448 | − | 0.908241i | \(-0.362574\pi\) | ||||
0.418448 | + | 0.908241i | \(0.362574\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 1.78676 | 0.0727624 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 13.9293 | 0.565375 | 0.282687 | − | 0.959212i | \(-0.408774\pi\) | ||||
0.282687 | + | 0.959212i | \(0.408774\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0.876139 | 0.0355029 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −11.0484 | −0.446970 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −19.7523 | −0.797787 | −0.398893 | − | 0.916997i | \(-0.630606\pi\) | ||||
−0.398893 | + | 0.916997i | \(0.630606\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 37.2010 | 1.49766 | 0.748828 | − | 0.662764i | \(-0.230617\pi\) | ||||
0.748828 | + | 0.662764i | \(0.230617\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 7.46357 | 0.299986 | 0.149993 | − | 0.988687i | \(-0.452075\pi\) | ||||
0.149993 | + | 0.988687i | \(0.452075\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −31.1600 | −1.25041 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 11.0484 | 0.442645 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −30.9071 | −1.23431 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −49.3026 | −1.96582 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 44.4562 | 1.76977 | 0.884886 | − | 0.465808i | \(-0.154236\pi\) | ||||
0.884886 | + | 0.465808i | \(0.154236\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 17.7161 | 0.704152 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 27.4535 | 1.08775 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 10.4051 | 0.411621 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −40.7401 | −1.60914 | −0.804568 | − | 0.593861i | \(-0.797603\pi\) | ||||
−0.804568 | + | 0.593861i | \(0.797603\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −20.3493 | −0.802499 | −0.401250 | − | 0.915969i | \(-0.631424\pi\) | ||||
−0.401250 | + | 0.915969i | \(0.631424\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −41.7933 | −1.64306 | −0.821531 | − | 0.570163i | \(-0.806880\pi\) | ||||
−0.821531 | + | 0.570163i | \(0.806880\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −44.3148 | −1.73951 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 2.47099 | 0.0968458 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −23.7933 | −0.931102 | −0.465551 | − | 0.885021i | \(-0.654144\pi\) | ||||
−0.465551 | + | 0.885021i | \(0.654144\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 11.3668 | 0.443460 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 7.50936 | 0.292523 | 0.146262 | − | 0.989246i | \(-0.453276\pi\) | ||||
0.146262 | + | 0.989246i | \(0.453276\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 45.9245 | 1.78626 | 0.893129 | − | 0.449801i | \(-0.148505\pi\) | ||||
0.893129 | + | 0.449801i | \(0.148505\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −27.1897 | −1.05596 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 5.52420 | 0.213898 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −27.8129 | −1.07531 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −3.76711 | −0.145428 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −7.29612 | −0.281245 | −0.140622 | − | 0.990063i | \(-0.544910\pi\) | ||||
−0.140622 | + | 0.990063i | \(0.544910\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −36.2494 | −1.39318 | −0.696589 | − | 0.717470i | \(-0.745300\pi\) | ||||
−0.696589 | + | 0.717470i | \(0.745300\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 8.65287 | 0.332067 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −12.7252 | −0.487631 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 5.40295 | 0.206738 | 0.103369 | − | 0.994643i | \(-0.467038\pi\) | ||||
0.103369 | + | 0.994643i | \(0.467038\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −2.70388 | −0.103159 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −12.0000 | −0.457164 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −36.0458 | −1.37125 | −0.685623 | − | 0.727957i | \(-0.740470\pi\) | ||||
−0.685623 | + | 0.727957i | \(0.740470\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −2.54645 | −0.0967318 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −39.3929 | −1.49211 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 13.9852 | 0.528967 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 3.33229 | 0.125859 | 0.0629295 | − | 0.998018i | \(-0.479956\pi\) | ||||
0.0629295 | + | 0.998018i | \(0.479956\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 69.7588 | 2.63100 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 11.9607 | 0.449829 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 7.48322 | 0.281038 | 0.140519 | − | 0.990078i | \(-0.455123\pi\) | ||||
0.140519 | + | 0.990078i | \(0.455123\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −10.5416 | −0.395343 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 15.5800 | 0.583476 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −28.2233 | −1.05402 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −39.6620 | −1.47914 | −0.739571 | − | 0.673078i | \(-0.764972\pi\) | ||||
−0.739571 | + | 0.673078i | \(0.764972\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 9.60447 | 0.357689 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −28.6071 | −1.06391 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 8.05582 | 0.298774 | 0.149387 | − | 0.988779i | \(-0.452270\pi\) | ||||
0.149387 | + | 0.988779i | \(0.452270\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 27.6943 | 1.02571 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −27.4588 | −1.01560 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 28.9320 | 1.06863 | 0.534313 | − | 0.845287i | \(-0.320570\pi\) | ||||
0.534313 | + | 0.845287i | \(0.320570\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −5.10902 | −0.188193 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 36.0772 | 1.32712 | 0.663560 | − | 0.748123i | \(-0.269045\pi\) | ||||
0.663560 | + | 0.748123i | \(0.269045\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 38.4710 | 1.41327 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 40.9681 | 1.50297 | 0.751487 | − | 0.659747i | \(-0.229337\pi\) | ||||
0.751487 | + | 0.659747i | \(0.229337\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 2.27909 | 0.0833875 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 2.17226 | 0.0793727 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 23.2861 | 0.849722 | 0.424861 | − | 0.905259i | \(-0.360323\pi\) | ||||
0.424861 | + | 0.905259i | \(0.360323\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 11.6917 | 0.426067 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −27.3275 | −0.993234 | −0.496617 | − | 0.867970i | \(-0.665425\pi\) | ||||
−0.496617 | + | 0.867970i | \(0.665425\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 25.0336 | 0.908661 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 44.5626 | 1.61539 | 0.807696 | − | 0.589599i | \(-0.200714\pi\) | ||||
0.807696 | + | 0.589599i | \(0.200714\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1.79157 | 0.0648591 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 55.1600 | 1.99171 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 51.6110 | 1.86114 | 0.930570 | − | 0.366115i | \(-0.119312\pi\) | ||||
0.930570 | + | 0.366115i | \(0.119312\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 37.1155 | 1.33668 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 19.6358 | 0.706252 | 0.353126 | − | 0.935576i | \(-0.385119\pi\) | ||||
0.353126 | + | 0.935576i | \(0.385119\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −8.96122 | −0.321482 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 55.7374 | 1.99700 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −29.7523 | −1.06462 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −5.64064 | −0.201580 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −37.3371 | −1.33092 | −0.665462 | − | 0.746432i | \(-0.731765\pi\) | ||||
−0.665462 | + | 0.746432i | \(0.731765\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −15.3271 | −0.545658 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −5.14831 | −0.183053 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 4.68904 | 0.166513 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 11.2159 | 0.397286 | 0.198643 | − | 0.980072i | \(-0.436347\pi\) | ||||
0.198643 | + | 0.980072i | \(0.436347\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −12.7645 | −0.451576 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −19.9852 | −0.706141 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −32.5019 | −1.14697 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 27.2717 | 0.960008 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 11.1749 | 0.392888 | 0.196444 | − | 0.980515i | \(-0.437061\pi\) | ||||
0.196444 | + | 0.980515i | \(0.437061\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 17.6406 | 0.619447 | 0.309723 | − | 0.950827i | \(-0.399764\pi\) | ||||
0.309723 | + | 0.950827i | \(0.399764\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 14.5264 | 0.509463 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 38.8517 | 1.35925 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 3.16965 | 0.110757 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 24.2477 | 0.846251 | 0.423126 | − | 0.906071i | \(-0.360933\pi\) | ||||
0.423126 | + | 0.906071i | \(0.360933\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −16.9777 | −0.591807 | −0.295903 | − | 0.955218i | \(-0.595621\pi\) | ||||
−0.295903 | + | 0.955218i | \(0.595621\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 5.58482 | 0.194203 | 0.0971017 | − | 0.995274i | \(-0.469043\pi\) | ||||
0.0971017 | + | 0.995274i | \(0.469043\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 18.6136 | 0.646476 | 0.323238 | − | 0.946318i | \(-0.395229\pi\) | ||||
0.323238 | + | 0.946318i | \(0.395229\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −17.0729 | −0.592251 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 31.7178 | 1.09896 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −15.9084 | −0.549876 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −15.9293 | −0.549942 | −0.274971 | − | 0.961453i | \(-0.588668\pi\) | ||||
−0.274971 | + | 0.961453i | \(0.588668\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.00000 | 0.0344828 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −9.14520 | −0.314977 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0.152616 | 0.00524395 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 1.44393 | 0.0495555 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −56.5019 | −1.93686 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 27.0288 | 0.925447 | 0.462723 | − | 0.886503i | \(-0.346872\pi\) | ||||
0.462723 | + | 0.886503i | \(0.346872\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −30.2691 | −1.03397 | −0.516986 | − | 0.855994i | \(-0.672946\pi\) | ||||
−0.516986 | + | 0.855994i | \(0.672946\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −41.4487 | −1.41421 | −0.707106 | − | 0.707107i | \(-0.750000\pi\) | ||||
−0.707106 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −7.16003 | −0.244013 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −42.2494 | −1.43819 | −0.719093 | − | 0.694913i | \(-0.755443\pi\) | ||||
−0.719093 | + | 0.694913i | \(0.755443\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −8.43001 | −0.286298 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 30.1426 | 1.02252 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 6.35936 | 0.215479 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −15.6519 | −0.529738 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −37.8129 | −1.27685 | −0.638426 | − | 0.769684i | \(-0.720414\pi\) | ||||
−0.638426 | + | 0.769684i | \(0.720414\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 7.38642 | 0.249138 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −5.35675 | −0.180473 | −0.0902367 | − | 0.995920i | \(-0.528762\pi\) | ||||
−0.0902367 | + | 0.995920i | \(0.528762\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −8.53643 | −0.287274 | −0.143637 | − | 0.989630i | \(-0.545880\pi\) | ||||
−0.143637 | + | 0.989630i | \(0.545880\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 22.7597 | 0.764196 | 0.382098 | − | 0.924122i | \(-0.375202\pi\) | ||||
0.382098 | + | 0.924122i | \(0.375202\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 11.4684 | 0.384637 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −13.7732 | −0.461420 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 18.0606 | 0.604376 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −31.1600 | −1.04040 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 2.82032 | 0.0940630 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −13.8639 | −0.461874 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −4.99089 | −0.166086 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −3.94418 | −0.130964 | −0.0654822 | − | 0.997854i | \(-0.520859\pi\) | ||||
−0.0654822 | + | 0.997854i | \(0.520859\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −21.6354 | −0.717602 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −40.6546 | −1.34695 | −0.673473 | − | 0.739212i | \(-0.735198\pi\) | ||||
−0.673473 | + | 0.739212i | \(0.735198\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −6.51678 | −0.215674 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 3.58002 | 0.118223 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 27.3471 | 0.902099 | 0.451049 | − | 0.892499i | \(-0.351050\pi\) | ||||
0.451049 | + | 0.892499i | \(0.351050\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 8.52200 | 0.280810 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 37.0336 | 1.21897 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −17.3733 | −0.570613 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 20.9368 | 0.686913 | 0.343456 | − | 0.939169i | \(-0.388402\pi\) | ||||
0.343456 | + | 0.939169i | \(0.388402\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −44.8778 | −1.47081 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −33.3716 | −1.09254 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −36.4051 | −1.18930 | −0.594652 | − | 0.803983i | \(-0.702710\pi\) | ||||
−0.594652 | + | 0.803983i | \(0.702710\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −32.6794 | −1.06645 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 28.0968 | 0.915929 | 0.457965 | − | 0.888970i | \(-0.348579\pi\) | ||||
0.457965 | + | 0.888970i | \(0.348579\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −45.1452 | −1.47013 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 10.8809 | 0.353583 | 0.176792 | − | 0.984248i | \(-0.443428\pi\) | ||||
0.176792 | + | 0.984248i | \(0.443428\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 40.4562 | 1.31326 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 1.92976 | 0.0625767 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −38.8103 | −1.25719 | −0.628594 | − | 0.777733i | \(-0.716369\pi\) | ||||
−0.628594 | + | 0.777733i | \(0.716369\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 4.53162 | 0.146486 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 2.50717 | 0.0809606 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −23.0458 | −0.743413 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −3.92935 | −0.126621 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −47.1862 | −1.51741 | −0.758703 | − | 0.651437i | \(-0.774166\pi\) | ||||
−0.758703 | + | 0.651437i | \(0.774166\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 44.4465 | 1.42783 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 40.0772 | 1.28614 | 0.643069 | − | 0.765809i | \(-0.277661\pi\) | ||||
0.643069 | + | 0.765809i | \(0.277661\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 3.65548 | 0.117189 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −2.29873 | −0.0735430 | −0.0367715 | − | 0.999324i | \(-0.511707\pi\) | ||||
−0.0367715 | + | 0.999324i | \(0.511707\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 57.1452 | 1.82637 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −3.24072 | −0.103468 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 8.89578 | 0.283731 | 0.141866 | − | 0.989886i | \(-0.454690\pi\) | ||||
0.141866 | + | 0.989886i | \(0.454690\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −2.32007 | −0.0738486 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −31.4684 | −1.00064 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 37.5652 | 1.19330 | 0.596649 | − | 0.802503i | \(-0.296499\pi\) | ||||
0.596649 | + | 0.802503i | \(0.296499\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −46.2542 | −1.46783 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 25.8081 | 0.817351 | 0.408675 | − | 0.912680i | \(-0.365991\pi\) | ||||
0.408675 | + | 0.912680i | \(0.365991\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 57.6929 | 1.82532 |
(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 | 2900.2.a.g.1.2 | 3 | ||
5.2 | odd | 4 | 2900.2.c.f.349.4 | 6 | |||
5.3 | odd | 4 | 2900.2.c.f.349.3 | 6 | |||
5.4 | even | 2 | 580.2.a.c.1.2 | ✓ | 3 | ||
15.14 | odd | 2 | 5220.2.a.x.1.2 | 3 | |||
20.19 | odd | 2 | 2320.2.a.m.1.2 | 3 | |||
40.19 | odd | 2 | 9280.2.a.bw.1.2 | 3 | |||
40.29 | even | 2 | 9280.2.a.bk.1.2 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
580.2.a.c.1.2 | ✓ | 3 | 5.4 | even | 2 | ||
2320.2.a.m.1.2 | 3 | 20.19 | odd | 2 | |||
2900.2.a.g.1.2 | 3 | 1.1 | even | 1 | trivial | ||
2900.2.c.f.349.3 | 6 | 5.3 | odd | 4 | |||
2900.2.c.f.349.4 | 6 | 5.2 | odd | 4 | |||
5220.2.a.x.1.2 | 3 | 15.14 | odd | 2 | |||
9280.2.a.bk.1.2 | 3 | 40.29 | even | 2 | |||
9280.2.a.bw.1.2 | 3 | 40.19 | odd | 2 |