Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [9280,2,Mod(1,9280)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(9280, 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("9280.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 9280 = 2^{6} \cdot 5 \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 9280.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: | \(74.1011730757\) |
Analytic rank: | \(1\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{8} - 15x^{6} + 57x^{4} - 40x^{2} + 4 \)
|
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 2^{3} \) |
Twist minimal: | no (minimal twist has level 4640) |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(-0.346147\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 9280.1 |
$q$-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 | ||||||||
\(3\) | −0.346147 | −0.199848 | −0.0999241 | − | 0.994995i | \(-0.531860\pi\) | ||||
−0.0999241 | + | 0.994995i | \(0.531860\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.09203 | −0.412749 | −0.206375 | − | 0.978473i | \(-0.566167\pi\) | ||||
−0.206375 | + | 0.978473i | \(0.566167\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.88018 | −0.960061 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −5.77789 | −1.74210 | −0.871050 | − | 0.491195i | \(-0.836560\pi\) | ||||
−0.871050 | + | 0.491195i | \(0.836560\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.497822 | −0.138071 | −0.0690355 | − | 0.997614i | \(-0.521992\pi\) | ||||
−0.0690355 | + | 0.997614i | \(0.521992\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.346147 | 0.0893748 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 4.15482 | 1.00769 | 0.503846 | − | 0.863793i | \(-0.331918\pi\) | ||||
0.503846 | + | 0.863793i | \(0.331918\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.48837 | 1.02970 | 0.514851 | − | 0.857280i | \(-0.327847\pi\) | ||||
0.514851 | + | 0.857280i | \(0.327847\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.378004 | 0.0824872 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0.346147 | 0.0721767 | 0.0360883 | − | 0.999349i | \(-0.488510\pi\) | ||||
0.0360883 | + | 0.999349i | \(0.488510\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 2.03541 | 0.391715 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.00000 | 0.185695 | ||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 9.77145 | 1.75500 | 0.877502 | − | 0.479572i | \(-0.159208\pi\) | ||||
0.877502 | + | 0.479572i | \(0.159208\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 2.00000 | 0.348155 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.09203 | 0.184587 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2.27464 | −0.373948 | −0.186974 | − | 0.982365i | \(-0.559868\pi\) | ||||
−0.186974 | + | 0.982365i | \(0.559868\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0.172320 | 0.0275932 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0.446365 | 0.0697105 | 0.0348552 | − | 0.999392i | \(-0.488903\pi\) | ||||
0.0348552 | + | 0.999392i | \(0.488903\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5.25791 | 0.801824 | 0.400912 | − | 0.916116i | \(-0.368693\pi\) | ||||
0.400912 | + | 0.916116i | \(0.368693\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 2.88018 | 0.429352 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −2.20924 | −0.322250 | −0.161125 | − | 0.986934i | \(-0.551512\pi\) | ||||
−0.161125 | + | 0.986934i | \(0.551512\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.80746 | −0.829638 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1.43818 | −0.201385 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −13.1942 | −1.81236 | −0.906180 | − | 0.422892i | \(-0.861015\pi\) | ||||
−0.906180 | + | 0.422892i | \(0.861015\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 5.77789 | 0.779090 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −1.55364 | −0.205784 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −1.26586 | −0.164801 | −0.0824005 | − | 0.996599i | \(-0.526259\pi\) | ||||
−0.0824005 | + | 0.996599i | \(0.526259\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.81182 | 0.488054 | 0.244027 | − | 0.969768i | \(-0.421531\pi\) | ||||
0.244027 | + | 0.969768i | \(0.421531\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 3.14525 | 0.396265 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0.497822 | 0.0617472 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 11.1860 | 1.36658 | 0.683292 | − | 0.730145i | \(-0.260548\pi\) | ||||
0.683292 | + | 0.730145i | \(0.260548\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −0.119818 | −0.0144244 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 4.16588 | 0.494399 | 0.247200 | − | 0.968965i | \(-0.420490\pi\) | ||||
0.247200 | + | 0.968965i | \(0.420490\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 13.4688 | 1.57641 | 0.788203 | − | 0.615415i | \(-0.211012\pi\) | ||||
0.788203 | + | 0.615415i | \(0.211012\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −0.346147 | −0.0399696 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 6.30964 | 0.719051 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −3.22251 | −0.362560 | −0.181280 | − | 0.983431i | \(-0.558024\pi\) | ||||
−0.181280 | + | 0.983431i | \(0.558024\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 7.93600 | 0.881777 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 1.26435 | 0.138781 | 0.0693903 | − | 0.997590i | \(-0.477895\pi\) | ||||
0.0693903 | + | 0.997590i | \(0.477895\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −4.15482 | −0.450654 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −0.346147 | −0.0371109 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 13.6236 | 1.44410 | 0.722052 | − | 0.691839i | \(-0.243199\pi\) | ||||
0.722052 | + | 0.691839i | \(0.243199\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.543638 | 0.0569887 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −3.38236 | −0.350734 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −4.48837 | −0.460497 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −7.09082 | −0.719963 | −0.359982 | − | 0.932959i | \(-0.617217\pi\) | ||||
−0.359982 | + | 0.932959i | \(0.617217\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 16.6414 | 1.67252 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −8.50653 | −0.846432 | −0.423216 | − | 0.906029i | \(-0.639099\pi\) | ||||
−0.423216 | + | 0.906029i | \(0.639099\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 3.59382 | 0.354110 | 0.177055 | − | 0.984201i | \(-0.443343\pi\) | ||||
0.177055 | + | 0.984201i | \(0.443343\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −0.378004 | −0.0368894 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −12.8201 | −1.23937 | −0.619684 | − | 0.784851i | \(-0.712739\pi\) | ||||
−0.619684 | + | 0.784851i | \(0.712739\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −4.99564 | −0.478496 | −0.239248 | − | 0.970959i | \(-0.576901\pi\) | ||||
−0.239248 | + | 0.970959i | \(0.576901\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0.787360 | 0.0747329 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −7.09082 | −0.667048 | −0.333524 | − | 0.942742i | \(-0.608238\pi\) | ||||
−0.333524 | + | 0.942742i | \(0.608238\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −0.346147 | −0.0322784 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 1.43382 | 0.132556 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −4.53720 | −0.415924 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 22.3840 | 2.03491 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −0.154508 | −0.0139315 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −2.20924 | −0.196038 | −0.0980190 | − | 0.995185i | \(-0.531251\pi\) | ||||
−0.0980190 | + | 0.995185i | \(0.531251\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −1.82001 | −0.160243 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −6.67243 | −0.582973 | −0.291487 | − | 0.956575i | \(-0.594150\pi\) | ||||
−0.291487 | + | 0.956575i | \(0.594150\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −4.90144 | −0.425009 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −2.03541 | −0.175180 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 10.8425 | 0.926335 | 0.463167 | − | 0.886271i | \(-0.346713\pi\) | ||||
0.463167 | + | 0.886271i | \(0.346713\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 6.96499 | 0.590763 | 0.295381 | − | 0.955379i | \(-0.404553\pi\) | ||||
0.295381 | + | 0.955379i | \(0.404553\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0.764721 | 0.0644011 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 2.87636 | 0.240533 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1.00000 | −0.0830455 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 2.01024 | 0.165802 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −6.44636 | −0.528107 | −0.264053 | − | 0.964508i | \(-0.585060\pi\) | ||||
−0.264053 | + | 0.964508i | \(0.585060\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −18.2534 | −1.48544 | −0.742720 | − | 0.669603i | \(-0.766464\pi\) | ||||
−0.742720 | + | 0.669603i | \(0.766464\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −11.9666 | −0.967446 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −9.77145 | −0.784862 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −15.8983 | −1.26882 | −0.634411 | − | 0.772996i | \(-0.718757\pi\) | ||||
−0.634411 | + | 0.772996i | \(0.718757\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 4.56713 | 0.362197 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −0.378004 | −0.0297909 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 18.3233 | 1.43519 | 0.717595 | − | 0.696461i | \(-0.245243\pi\) | ||||
0.717595 | + | 0.696461i | \(0.245243\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −2.00000 | −0.155700 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −9.67639 | −0.748781 | −0.374391 | − | 0.927271i | \(-0.622148\pi\) | ||||
−0.374391 | + | 0.927271i | \(0.622148\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.7522 | −0.980936 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −12.9273 | −0.988576 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −15.5722 | −1.18393 | −0.591966 | − | 0.805963i | \(-0.701648\pi\) | ||||
−0.591966 | + | 0.805963i | \(0.701648\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.09203 | −0.0825499 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0.438174 | 0.0329352 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −20.6634 | −1.54445 | −0.772226 | − | 0.635348i | \(-0.780857\pi\) | ||||
−0.772226 | + | 0.635348i | \(0.780857\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −21.0657 | −1.56580 | −0.782899 | − | 0.622149i | \(-0.786260\pi\) | ||||
−0.782899 | + | 0.622149i | \(0.786260\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −1.31945 | −0.0975366 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 2.27464 | 0.167235 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −24.0061 | −1.75550 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −2.22273 | −0.161680 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 7.14467 | 0.516970 | 0.258485 | − | 0.966015i | \(-0.416777\pi\) | ||||
0.258485 | + | 0.966015i | \(0.416777\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1.67390 | −0.120490 | −0.0602451 | − | 0.998184i | \(-0.519188\pi\) | ||||
−0.0602451 | + | 0.998184i | \(0.519188\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −0.172320 | −0.0123401 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −8.97874 | −0.639709 | −0.319854 | − | 0.947467i | \(-0.603634\pi\) | ||||
−0.319854 | + | 0.947467i | \(0.603634\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 12.1530 | 0.861504 | 0.430752 | − | 0.902470i | \(-0.358248\pi\) | ||||
0.430752 | + | 0.902470i | \(0.358248\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −3.87199 | −0.273109 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −1.09203 | −0.0766457 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −0.446365 | −0.0311755 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −0.996967 | −0.0692940 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −25.9333 | −1.79384 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −6.42286 | −0.442168 | −0.221084 | − | 0.975255i | \(-0.570959\pi\) | ||||
−0.221084 | + | 0.975255i | \(0.570959\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −1.44201 | −0.0988048 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −5.25791 | −0.358587 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −10.6707 | −0.724377 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −4.66219 | −0.315042 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −2.06836 | −0.139133 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −10.0152 | −0.670666 | −0.335333 | − | 0.942100i | \(-0.608849\pi\) | ||||
−0.335333 | + | 0.942100i | \(0.608849\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −2.88018 | −0.192012 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −15.4973 | −1.02859 | −0.514295 | − | 0.857614i | \(-0.671946\pi\) | ||||
−0.514295 | + | 0.857614i | \(0.671946\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −8.87583 | −0.586531 | −0.293266 | − | 0.956031i | \(-0.594742\pi\) | ||||
−0.293266 | + | 0.956031i | \(0.594742\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −2.18407 | −0.143701 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −1.45072 | −0.0950399 | −0.0475199 | − | 0.998870i | \(-0.515132\pi\) | ||||
−0.0475199 | + | 0.998870i | \(0.515132\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2.20924 | 0.144115 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 1.11546 | 0.0724570 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 29.2240 | 1.89035 | 0.945173 | − | 0.326569i | \(-0.105893\pi\) | ||||
0.945173 | + | 0.326569i | \(0.105893\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 4.04274 | 0.260416 | 0.130208 | − | 0.991487i | \(-0.458435\pi\) | ||||
0.130208 | + | 0.991487i | \(0.458435\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −8.85325 | −0.567936 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 5.80746 | 0.371025 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2.23441 | −0.142172 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −0.437652 | −0.0277351 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 5.67071 | 0.357932 | 0.178966 | − | 0.983855i | \(-0.442725\pi\) | ||||
0.178966 | + | 0.983855i | \(0.442725\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2.00000 | −0.125739 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 1.43818 | 0.0900623 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 2.11163 | 0.131720 | 0.0658598 | − | 0.997829i | \(-0.479021\pi\) | ||||
0.0658598 | + | 0.997829i | \(0.479021\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2.48398 | 0.154347 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −2.88018 | −0.178279 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 12.3804 | 0.763410 | 0.381705 | − | 0.924284i | \(-0.375337\pi\) | ||||
0.381705 | + | 0.924284i | \(0.375337\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 13.1942 | 0.810512 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −4.71579 | −0.288601 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 9.95019 | 0.606674 | 0.303337 | − | 0.952883i | \(-0.401899\pi\) | ||||
0.303337 | + | 0.952883i | \(0.401899\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 6.81784 | 0.414154 | 0.207077 | − | 0.978325i | \(-0.433605\pi\) | ||||
0.207077 | + | 0.978325i | \(0.433605\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −0.188179 | −0.0113891 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −5.77789 | −0.348420 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.30529 | 0.0784271 | 0.0392135 | − | 0.999231i | \(-0.487515\pi\) | ||||
0.0392135 | + | 0.999231i | \(0.487515\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −28.1436 | −1.68491 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 3.88889 | 0.231992 | 0.115996 | − | 0.993250i | \(-0.462994\pi\) | ||||
0.115996 | + | 0.993250i | \(0.462994\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 15.8419 | 0.941703 | 0.470852 | − | 0.882212i | \(-0.343947\pi\) | ||||
0.470852 | + | 0.882212i | \(0.343947\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 1.55364 | 0.0920294 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −0.487445 | −0.0287730 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 0.262543 | 0.0154437 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 2.45447 | 0.143883 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −19.5886 | −1.14438 | −0.572190 | − | 0.820121i | \(-0.693906\pi\) | ||||
−0.572190 | + | 0.820121i | \(0.693906\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1.26586 | 0.0737012 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −11.7604 | −0.682406 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −0.172320 | −0.00996550 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −5.74181 | −0.330953 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 2.94451 | 0.169158 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −3.81182 | −0.218264 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 20.1627 | 1.15075 | 0.575373 | − | 0.817891i | \(-0.304857\pi\) | ||||
0.575373 | + | 0.817891i | \(0.304857\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1.24399 | −0.0707682 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −25.1990 | −1.42891 | −0.714453 | − | 0.699683i | \(-0.753325\pi\) | ||||
−0.714453 | + | 0.699683i | \(0.753325\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −27.4540 | −1.55179 | −0.775896 | − | 0.630860i | \(-0.782702\pi\) | ||||
−0.775896 | + | 0.630860i | \(0.782702\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −3.14525 | −0.177215 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 26.2079 | 1.47198 | 0.735992 | − | 0.676990i | \(-0.236716\pi\) | ||||
0.735992 | + | 0.676990i | \(0.236716\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −5.77789 | −0.323500 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 4.43765 | 0.247686 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 18.6484 | 1.03762 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −0.497822 | −0.0276142 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 1.72923 | 0.0956265 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 2.41256 | 0.133009 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 27.4424 | 1.50837 | 0.754185 | − | 0.656662i | \(-0.228032\pi\) | ||||
0.754185 | + | 0.656662i | \(0.228032\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 6.55138 | 0.359013 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −11.1860 | −0.611155 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −9.81227 | −0.534508 | −0.267254 | − | 0.963626i | \(-0.586116\pi\) | ||||
−0.267254 | + | 0.963626i | \(0.586116\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 2.45447 | 0.133308 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −56.4584 | −3.05739 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 13.9862 | 0.755182 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0.119818 | 0.00645078 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 13.2750 | 0.712638 | 0.356319 | − | 0.934364i | \(-0.384032\pi\) | ||||
0.356319 | + | 0.934364i | \(0.384032\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −25.3840 | −1.35877 | −0.679387 | − | 0.733780i | \(-0.737754\pi\) | ||||
−0.679387 | + | 0.733780i | \(0.737754\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.01327 | −0.0540844 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −25.1860 | −1.34052 | −0.670258 | − | 0.742129i | \(-0.733816\pi\) | ||||
−0.670258 | + | 0.742129i | \(0.733816\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −4.16588 | −0.221102 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 1.57054 | 0.0831217 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 13.5959 | 0.717567 | 0.358783 | − | 0.933421i | \(-0.383192\pi\) | ||||
0.358783 | + | 0.933421i | \(0.383192\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.14543 | 0.0602860 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −7.74816 | −0.406673 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −13.4688 | −0.704990 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −25.9627 | −1.35524 | −0.677622 | − | 0.735410i | \(-0.736989\pi\) | ||||
−0.677622 | + | 0.735410i | \(0.736989\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −1.28561 | −0.0669263 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 14.4085 | 0.748051 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −16.4469 | −0.851588 | −0.425794 | − | 0.904820i | \(-0.640005\pi\) | ||||
−0.425794 | + | 0.904820i | \(0.640005\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0.346147 | 0.0178750 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −0.497822 | −0.0256391 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 28.8894 | 1.48395 | 0.741976 | − | 0.670427i | \(-0.233889\pi\) | ||||
0.741976 | + | 0.670427i | \(0.233889\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0.764721 | 0.0391778 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −28.3574 | −1.44899 | −0.724497 | − | 0.689278i | \(-0.757928\pi\) | ||||
−0.724497 | + | 0.689278i | \(0.757928\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −6.30964 | −0.321569 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −15.1438 | −0.769800 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −20.2067 | −1.02452 | −0.512261 | − | 0.858830i | \(-0.671192\pi\) | ||||
−0.512261 | + | 0.858830i | \(0.671192\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.43818 | 0.0727319 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 2.30964 | 0.116506 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 3.22251 | 0.162142 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −16.2598 | −0.816058 | −0.408029 | − | 0.912969i | \(-0.633784\pi\) | ||||
−0.408029 | + | 0.912969i | \(0.633784\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 1.69662 | 0.0849373 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 18.8862 | 0.943131 | 0.471566 | − | 0.881831i | \(-0.343689\pi\) | ||||
0.471566 | + | 0.881831i | \(0.343689\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −4.86444 | −0.242315 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −7.93600 | −0.394343 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 13.1426 | 0.651455 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −6.00871 | −0.297112 | −0.148556 | − | 0.988904i | \(-0.547462\pi\) | ||||
−0.148556 | + | 0.988904i | \(0.547462\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −3.75309 | −0.185126 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 1.38236 | 0.0680215 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −1.26435 | −0.0620646 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −2.41091 | −0.118063 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 8.70633 | 0.425332 | 0.212666 | − | 0.977125i | \(-0.431785\pi\) | ||||
0.212666 | + | 0.977125i | \(0.431785\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 19.4540 | 0.948131 | 0.474065 | − | 0.880490i | \(-0.342786\pi\) | ||||
0.474065 | + | 0.880490i | \(0.342786\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 6.36300 | 0.309380 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 4.15482 | 0.201538 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −4.16263 | −0.201444 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −0.995644 | −0.0480701 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 19.1952 | 0.924603 | 0.462301 | − | 0.886723i | \(-0.347024\pi\) | ||||
0.462301 | + | 0.886723i | \(0.347024\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 27.2210 | 1.30816 | 0.654079 | − | 0.756426i | \(-0.273056\pi\) | ||||
0.654079 | + | 0.756426i | \(0.273056\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0.346147 | 0.0165965 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 1.55364 | 0.0743205 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 20.4374 | 0.975426 | 0.487713 | − | 0.873004i | \(-0.337831\pi\) | ||||
0.487713 | + | 0.873004i | \(0.337831\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 16.7266 | 0.796503 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −19.9962 | −0.950050 | −0.475025 | − | 0.879972i | \(-0.657561\pi\) | ||||
−0.475025 | + | 0.879972i | \(0.657561\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −13.6236 | −0.645823 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 2.23139 | 0.105541 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 17.1357 | 0.808682 | 0.404341 | − | 0.914608i | \(-0.367501\pi\) | ||||
0.404341 | + | 0.914608i | \(0.367501\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −2.57905 | −0.121443 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 6.31836 | 0.296862 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −0.543638 | −0.0254861 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 26.8347 | 1.25528 | 0.627638 | − | 0.778505i | \(-0.284022\pi\) | ||||
0.627638 | + | 0.778505i | \(0.284022\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 8.45676 | 0.394728 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −6.81453 | −0.317384 | −0.158692 | − | 0.987328i | \(-0.550728\pi\) | ||||
−0.158692 | + | 0.987328i | \(0.550728\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −26.5153 | −1.23227 | −0.616134 | − | 0.787641i | \(-0.711302\pi\) | ||||
−0.616134 | + | 0.787641i | \(0.711302\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 3.38236 | 0.156853 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −19.1879 | −0.887910 | −0.443955 | − | 0.896049i | \(-0.646425\pi\) | ||||
−0.443955 | + | 0.896049i | \(0.646425\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −12.2154 | −0.564057 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 5.50315 | 0.253572 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −30.3797 | −1.39686 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 4.48837 | 0.205940 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 38.0016 | 1.73998 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −7.72978 | −0.353183 | −0.176591 | − | 0.984284i | \(-0.556507\pi\) | ||||
−0.176591 | + | 0.984284i | \(0.556507\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.13237 | 0.0516314 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0.130845 | 0.00595365 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 7.09082 | 0.321977 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 18.0500 | 0.817925 | 0.408963 | − | 0.912551i | \(-0.365891\pi\) | ||||
0.408963 | + | 0.912551i | \(0.365891\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −6.34255 | −0.286820 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 38.4634 | 1.73583 | 0.867915 | − | 0.496713i | \(-0.165460\pi\) | ||||
0.867915 | + | 0.496713i | \(0.165460\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 4.15482 | 0.187124 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −16.6414 | −0.747974 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −4.54928 | −0.204063 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −29.2356 | −1.30876 | −0.654382 | − | 0.756164i | \(-0.727071\pi\) | ||||
−0.654382 | + | 0.756164i | \(0.727071\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 3.34945 | 0.149643 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −12.6209 | −0.562738 | −0.281369 | − | 0.959600i | \(-0.590789\pi\) | ||||
−0.281369 | + | 0.959600i | \(0.590789\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 8.50653 | 0.378536 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 4.41413 | 0.196038 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −27.1444 | −1.20315 | −0.601577 | − | 0.798815i | \(-0.705461\pi\) | ||||
−0.601577 | + | 0.798815i | \(0.705461\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −14.7084 | −0.650661 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 9.13566 | 0.403349 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −3.59382 | −0.158363 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 12.7647 | 0.561392 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 5.39027 | 0.236606 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −16.7478 | −0.733735 | −0.366868 | − | 0.930273i | \(-0.619570\pi\) | ||||
−0.366868 | + | 0.930273i | \(0.619570\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 13.8123 | 0.603971 | 0.301986 | − | 0.953312i | \(-0.402350\pi\) | ||||
0.301986 | + | 0.953312i | \(0.402350\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0.378004 | 0.0164974 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 40.5986 | 1.76850 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.8802 | −0.994791 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 3.64591 | 0.158219 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −0.222210 | −0.00962499 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 12.8201 | 0.554263 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 7.15256 | 0.308656 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 33.5549 | 1.44531 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −32.6024 | −1.40169 | −0.700843 | − | 0.713316i | \(-0.747193\pi\) | ||||
−0.700843 | + | 0.713316i | \(0.747193\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 7.29182 | 0.312922 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 4.99564 | 0.213990 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −9.78625 | −0.418430 | −0.209215 | − | 0.977870i | \(-0.567091\pi\) | ||||
−0.209215 | + | 0.977870i | \(0.567091\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −10.9787 | −0.468561 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 4.48837 | 0.191211 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 3.51908 | 0.149647 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −0.787360 | −0.0334216 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 35.8731 | 1.51999 | 0.759996 | − | 0.649927i | \(-0.225201\pi\) | ||||
0.759996 | + | 0.649927i | \(0.225201\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −2.61750 | −0.110709 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 8.30964 | 0.350833 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 18.3469 | 0.773231 | 0.386616 | − | 0.922241i | \(-0.373644\pi\) | ||||
0.386616 | + | 0.922241i | \(0.373644\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 7.09082 | 0.298313 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −8.66637 | −0.363953 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −30.0787 | −1.26097 | −0.630483 | − | 0.776203i | \(-0.717143\pi\) | ||||
−0.630483 | + | 0.776203i | \(0.717143\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −37.4727 | −1.56818 | −0.784092 | − | 0.620645i | \(-0.786871\pi\) | ||||
−0.784092 | + | 0.620645i | \(0.786871\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −2.47311 | −0.103315 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0.346147 | 0.0144353 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 11.2447 | 0.468122 | 0.234061 | − | 0.972222i | \(-0.424799\pi\) | ||||
0.234061 | + | 0.972222i | \(0.424799\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0.579417 | 0.0240797 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −1.38071 | −0.0572817 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 76.2345 | 3.15731 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −1.43382 | −0.0592811 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 20.3645 | 0.840534 | 0.420267 | − | 0.907400i | \(-0.361936\pi\) | ||||
0.420267 | + | 0.907400i | \(0.361936\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 43.8579 | 1.80713 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 3.10797 | 0.127845 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −28.8589 | −1.18509 | −0.592547 | − | 0.805536i | \(-0.701878\pi\) | ||||
−0.592547 | + | 0.805536i | \(0.701878\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 4.53720 | 0.186007 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −4.20673 | −0.172170 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −20.9201 | −0.854773 | −0.427387 | − | 0.904069i | \(-0.640566\pi\) | ||||
−0.427387 | + | 0.904069i | \(0.640566\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 5.69907 | 0.232470 | 0.116235 | − | 0.993222i | \(-0.462917\pi\) | ||||
0.116235 | + | 0.993222i | \(0.462917\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −32.2176 | −1.31200 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −22.3840 | −0.910039 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 34.1074 | 1.38438 | 0.692188 | − | 0.721717i | \(-0.256647\pi\) | ||||
0.692188 | + | 0.721717i | \(0.256647\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0.378004 | 0.0153175 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1.09981 | 0.0444934 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −12.9787 | −0.524206 | −0.262103 | − | 0.965040i | \(-0.584416\pi\) | ||||
−0.262103 | + | 0.965040i | \(0.584416\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0.154508 | 0.00623036 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 9.22919 | 0.371553 | 0.185777 | − | 0.982592i | \(-0.440520\pi\) | ||||
0.185777 | + | 0.982592i | \(0.440520\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −43.7166 | −1.75712 | −0.878559 | − | 0.477635i | \(-0.841494\pi\) | ||||
−0.878559 | + | 0.477635i | \(0.841494\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0.704551 | 0.0282726 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −14.8775 | −0.596053 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 8.97673 | 0.358496 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −9.45072 | −0.376825 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −37.6835 | −1.50016 | −0.750078 | − | 0.661349i | \(-0.769984\pi\) | ||||
−0.750078 | + | 0.661349i | \(0.769984\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 2.22325 | 0.0883664 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 2.20924 | 0.0876709 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 2.89108 | 0.114549 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −11.9985 | −0.474653 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −28.5864 | −1.12909 | −0.564547 | − | 0.825401i | \(-0.690949\pi\) | ||||
−0.564547 | + | 0.825401i | \(0.690949\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −12.7251 | −0.501828 | −0.250914 | − | 0.968009i | \(-0.580731\pi\) | ||||
−0.250914 | + | 0.968009i | \(0.580731\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 1.82001 | 0.0716629 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 33.4503 | 1.31507 | 0.657534 | − | 0.753425i | \(-0.271600\pi\) | ||||
0.657534 | + | 0.753425i | \(0.271600\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 7.31400 | 0.287100 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 3.69365 | 0.144765 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 11.7954 | 0.461588 | 0.230794 | − | 0.973003i | \(-0.425868\pi\) | ||||
0.230794 | + | 0.973003i | \(0.425868\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 6.67243 | 0.260713 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −38.7927 | −1.51345 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −11.2780 | −0.439329 | −0.219665 | − | 0.975575i | \(-0.570496\pi\) | ||||
−0.219665 | + | 0.975575i | \(0.570496\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −16.6531 | −0.647730 | −0.323865 | − | 0.946103i | \(-0.604982\pi\) | ||||
−0.323865 | + | 0.946103i | \(0.604982\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0.715957 | 0.0278055 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 4.90144 | 0.190070 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0.346147 | 0.0134029 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 3.46672 | 0.134031 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −22.0243 | −0.850238 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −10.6531 | −0.410647 | −0.205323 | − | 0.978694i | \(-0.565825\pi\) | ||||
−0.205323 | + | 0.978694i | \(0.565825\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 2.03541 | 0.0783429 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 39.5557 | 1.52025 | 0.760125 | − | 0.649777i | \(-0.225138\pi\) | ||||
0.760125 | + | 0.649777i | \(0.225138\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 7.74340 | 0.297165 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 5.36433 | 0.205562 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −39.1678 | −1.49871 | −0.749357 | − | 0.662166i | \(-0.769638\pi\) | ||||
−0.749357 | + | 0.662166i | \(0.769638\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −10.8425 | −0.414269 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 3.07234 | 0.117217 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 6.56835 | 0.250234 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −16.0841 | −0.611868 | −0.305934 | − | 0.952053i | \(-0.598969\pi\) | ||||
−0.305934 | + | 0.952053i | \(0.598969\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −18.1729 | −0.690332 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −6.96499 | −0.264197 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.85457 | 0.0702467 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0.502163 | 0.0189935 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −8.85892 | −0.334597 | −0.167298 | − | 0.985906i | \(-0.553504\pi\) | ||||
−0.167298 | + | 0.985906i | \(0.553504\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −10.2094 | −0.385055 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −0.764721 | −0.0288010 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 9.28941 | 0.349364 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 6.66181 | 0.250189 | 0.125095 | − | 0.992145i | \(-0.460077\pi\) | ||||
0.125095 | + | 0.992145i | \(0.460077\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 9.28141 | 0.348080 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 3.38236 | 0.126670 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −2.87636 | −0.107570 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −10.1158 | −0.377782 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −33.2736 | −1.24090 | −0.620449 | − | 0.784247i | \(-0.713050\pi\) | ||||
−0.620449 | + | 0.784247i | \(0.713050\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −3.92457 | −0.146159 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −1.39938 | −0.0520437 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 1.00000 | 0.0371391 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 10.1964 | 0.378162 | 0.189081 | − | 0.981961i | \(-0.439449\pi\) | ||||
0.189081 | + | 0.981961i | \(0.439449\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −20.7435 | −0.768276 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 21.8457 | 0.807992 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 48.8697 | 1.80504 | 0.902522 | − | 0.430643i | \(-0.141713\pi\) | ||||
0.902522 | + | 0.430643i | \(0.141713\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −2.01024 | −0.0741487 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −64.6313 | −2.38072 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −45.6511 | −1.67930 | −0.839651 | − | 0.543127i | \(-0.817240\pi\) | ||||
−0.839651 | + | 0.543127i | \(0.817240\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0.773434 | 0.0284128 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −3.35335 | −0.123023 | −0.0615113 | − | 0.998106i | \(-0.519592\pi\) | ||||
−0.0615113 | + | 0.998106i | \(0.519592\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 6.44636 | 0.236177 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −3.64156 | −0.133238 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 14.0000 | 0.511549 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −17.9812 | −0.656145 | −0.328072 | − | 0.944653i | \(-0.606399\pi\) | ||||
−0.328072 | + | 0.944653i | \(0.606399\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −1.96290 | −0.0715320 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 18.2534 | 0.664309 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 25.1181 | 0.912932 | 0.456466 | − | 0.889741i | \(-0.349115\pi\) | ||||
0.456466 | + | 0.889741i | \(0.349115\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0.692294 | 0.0251287 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −42.1656 | −1.52850 | −0.764251 | − | 0.644918i | \(-0.776891\pi\) | ||||
−0.764251 | + | 0.644918i | \(0.776891\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 5.45541 | 0.197499 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 11.9666 | 0.432655 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0.630173 | 0.0227542 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 0.181635 | 0.00654991 | 0.00327495 | − | 0.999995i | \(-0.498958\pi\) | ||||
0.00327495 | + | 0.999995i | \(0.498958\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −0.730934 | −0.0263239 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 17.5557 | 0.631436 | 0.315718 | − | 0.948853i | \(-0.397755\pi\) | ||||
0.315718 | + | 0.948853i | \(0.397755\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 9.77145 | 0.351001 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −0.859823 | −0.0308460 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 2.00345 | 0.0717810 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −24.0700 | −0.861293 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 2.03541 | 0.0727396 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 15.8983 | 0.567434 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 12.3210 | 0.439196 | 0.219598 | − | 0.975590i | \(-0.429525\pi\) | ||||
0.219598 | + | 0.975590i | \(0.429525\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −4.28545 | −0.152566 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 7.74340 | 0.275324 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −1.89761 | −0.0673860 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −4.56713 | −0.161979 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −2.66300 | −0.0943284 | −0.0471642 | − | 0.998887i | \(-0.515018\pi\) | ||||
−0.0471642 | + | 0.998887i | \(0.515018\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −9.17898 | −0.324729 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −39.2386 | −1.38643 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −77.8214 | −2.74626 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0.378004 | 0.0133229 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −3.44423 | −0.121243 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −26.4826 | −0.931077 | −0.465539 | − | 0.885028i | \(-0.654139\pi\) | ||||
−0.465539 | + | 0.885028i | \(0.654139\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 20.9695 | 0.736340 | 0.368170 | − | 0.929758i | \(-0.379984\pi\) | ||||
0.368170 | + | 0.929758i | \(0.379984\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −2.35998 | −0.0827680 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −18.3233 | −0.641836 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 23.5994 | 0.825640 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −1.56578 | −0.0547126 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −6.44636 | −0.224980 | −0.112490 | − | 0.993653i | \(-0.535883\pi\) | ||||
−0.112490 | + | 0.993653i | \(0.535883\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −26.3577 | −0.918773 | −0.459386 | − | 0.888237i | \(-0.651931\pi\) | ||||
−0.459386 | + | 0.888237i | \(0.651931\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 2.00000 | 0.0696311 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 35.7116 | 1.24182 | 0.620908 | − | 0.783884i | \(-0.286764\pi\) | ||||
0.620908 | + | 0.783884i | \(0.286764\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 5.31348 | 0.184545 | 0.0922724 | − | 0.995734i | \(-0.470587\pi\) | ||||
0.0922724 | + | 0.995734i | \(0.470587\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −0.451821 | −0.0156735 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −24.1290 | −0.836020 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 9.67639 | 0.334865 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 19.8889 | 0.687461 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −23.9865 | −0.828108 | −0.414054 | − | 0.910252i | \(-0.635887\pi\) | ||||
−0.414054 | + | 0.910252i | \(0.635887\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.00000 | 0.0344828 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −1.34613 | −0.0463632 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 12.7522 | 0.438688 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −24.4441 | −0.839908 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −5.48363 | −0.188198 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −0.787360 | −0.0269904 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −16.6968 | −0.571688 | −0.285844 | − | 0.958276i | \(-0.592274\pi\) | ||||
−0.285844 | + | 0.958276i | \(0.592274\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 12.9273 | 0.442105 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −28.8589 | −0.985802 | −0.492901 | − | 0.870085i | \(-0.664064\pi\) | ||||
−0.492901 | + | 0.870085i | \(0.664064\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −2.39635 | −0.0817625 | −0.0408812 | − | 0.999164i | \(-0.513017\pi\) | ||||
−0.0408812 | + | 0.999164i | \(0.513017\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0.168728 | 0.00575022 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −11.6493 | −0.396548 | −0.198274 | − | 0.980147i | \(-0.563534\pi\) | ||||
−0.198274 | + | 0.980147i | \(0.563534\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 15.5722 | 0.529470 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −0.0908783 | −0.00308639 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 18.6193 | 0.631616 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −5.56862 | −0.188685 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 20.4228 | 0.691209 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 1.09203 | 0.0369174 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 42.2331 | 1.42611 | 0.713055 | − | 0.701108i | \(-0.247311\pi\) | ||||
0.713055 | + | 0.701108i | \(0.247311\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 6.78055 | 0.228702 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 8.49895 | 0.286337 | 0.143168 | − | 0.989698i | \(-0.454271\pi\) | ||||
0.143168 | + | 0.989698i | \(0.454271\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 52.5509 | 1.76848 | 0.884239 | − | 0.467034i | \(-0.154677\pi\) | ||||
0.884239 | + | 0.467034i | \(0.154677\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −0.438174 | −0.0147291 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −18.1331 | −0.608851 | −0.304426 | − | 0.952536i | \(-0.598465\pi\) | ||||
−0.304426 | + | 0.952536i | \(0.598465\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 2.41256 | 0.0809146 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −45.8533 | −1.53614 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −9.91586 | −0.331822 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 20.6634 | 0.690700 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0.0596479 | 0.00199159 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 9.77145 | 0.325896 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −54.8195 | −1.82630 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 1.98751 | 0.0661403 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 21.0657 | 0.700246 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 19.8329 | 0.658539 | 0.329270 | − | 0.944236i | \(-0.393197\pi\) | ||||
0.329270 | + | 0.944236i | \(0.393197\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 24.5004 | 0.812626 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 33.2248 | 1.10079 | 0.550394 | − | 0.834905i | \(-0.314478\pi\) | ||||
0.550394 | + | 0.834905i | \(0.314478\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −7.30529 | −0.241770 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 1.31945 | 0.0436197 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 7.28651 | 0.240622 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −54.8075 | −1.80793 | −0.903966 | − | 0.427605i | \(-0.859358\pi\) | ||||
−0.903966 | + | 0.427605i | \(0.859358\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −6.97926 | −0.229974 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −2.07387 | −0.0682622 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −2.27464 | −0.0747897 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −10.3509 | −0.339967 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −26.5749 | −0.871894 | −0.435947 | − | 0.899972i | \(-0.643586\pi\) | ||||
−0.435947 | + | 0.899972i | \(0.643586\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −26.0660 | −0.854280 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 8.72258 | 0.285564 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 24.0061 | 0.785083 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1.47491 | 0.0481834 | 0.0240917 | − | 0.999710i | \(-0.492331\pi\) | ||||
0.0240917 | + | 0.999710i | \(0.492331\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 9.50313 | 0.310123 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −16.9047 | −0.551079 | −0.275539 | − | 0.961290i | \(-0.588856\pi\) | ||||
−0.275539 | + | 0.961290i | \(0.588856\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0.154508 | 0.00503147 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 2.22273 | 0.0723055 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 12.4544 | 0.404715 | 0.202357 | − | 0.979312i | \(-0.435140\pi\) | ||||
0.202357 | + | 0.979312i | \(0.435140\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −6.70507 | −0.217656 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −9.07180 | −0.294173 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −21.5033 | −0.696560 | −0.348280 | − | 0.937390i | \(-0.613234\pi\) | ||||
−0.348280 | + | 0.937390i | \(0.613234\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −7.14467 | −0.231196 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 2.00000 | 0.0646508 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −11.8403 | −0.382344 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 64.4813 | 2.08004 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 36.9243 | 1.18987 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 1.67390 | 0.0538849 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −2.45922 | −0.0790833 | −0.0395416 | − | 0.999218i | \(-0.512590\pi\) | ||||
−0.0395416 | + | 0.999218i | \(0.512590\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −6.45508 | −0.207367 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 46.0525 | 1.47790 | 0.738948 | − | 0.673762i | \(-0.235323\pi\) | ||||
0.738948 | + | 0.673762i | \(0.235323\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −7.60599 | −0.243837 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0.172320 | 0.00551864 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −61.4124 | −1.96476 | −0.982378 | − | 0.186903i | \(-0.940155\pi\) | ||||
−0.982378 | + | 0.186903i | \(0.940155\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −78.7159 | −2.51577 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 14.3884 | 0.459385 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −17.6457 | −0.562810 | −0.281405 | − | 0.959589i | \(-0.590801\pi\) | ||||
−0.281405 | + | 0.959589i | \(0.590801\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 8.97874 | 0.286086 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −0.835100 | −0.0265815 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 1.82001 | 0.0578730 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 48.4193 | 1.53809 | 0.769045 | − | 0.639195i | \(-0.220732\pi\) | ||||
0.769045 | + | 0.639195i | \(0.220732\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −9.49911 | −0.301445 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −12.1530 | −0.385276 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 28.3972 | 0.899349 | 0.449675 | − | 0.893192i | \(-0.351540\pi\) | ||||
0.449675 | + | 0.893192i | \(0.351540\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −4.62982 | −0.146481 |
(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 | 9280.2.a.cs.1.4 | 8 | ||
4.3 | odd | 2 | inner | 9280.2.a.cs.1.5 | 8 | ||
8.3 | odd | 2 | 4640.2.a.y.1.4 | ✓ | 8 | ||
8.5 | even | 2 | 4640.2.a.y.1.5 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4640.2.a.y.1.4 | ✓ | 8 | 8.3 | odd | 2 | ||
4640.2.a.y.1.5 | yes | 8 | 8.5 | even | 2 | ||
9280.2.a.cs.1.4 | 8 | 1.1 | even | 1 | trivial | ||
9280.2.a.cs.1.5 | 8 | 4.3 | odd | 2 | inner |