Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4400,2,Mod(1,4400)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4400, 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("4400.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4400 = 2^{4} \cdot 5^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4400.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: | \(35.1341768894\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.54764.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} - 9x^{2} + 3x + 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 440) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-2.67673\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4400.1 |
$q$-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 | ||||||||
\(3\) | −2.67673 | −1.54541 | −0.772706 | − | 0.634764i | \(-0.781097\pi\) | ||||
−0.772706 | + | 0.634764i | \(0.781097\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 4.38559 | 1.65760 | 0.828799 | − | 0.559546i | \(-0.189025\pi\) | ||||
0.828799 | + | 0.559546i | \(0.189025\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 4.16490 | 1.38830 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −4.00000 | −1.10940 | −0.554700 | − | 0.832050i | \(-0.687167\pi\) | ||||
−0.554700 | + | 0.832050i | \(0.687167\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −5.87995 | −1.42610 | −0.713049 | − | 0.701114i | \(-0.752686\pi\) | ||||
−0.713049 | + | 0.701114i | \(0.752686\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.526486 | 0.120784 | 0.0603920 | − | 0.998175i | \(-0.480765\pi\) | ||||
0.0603920 | + | 0.998175i | \(0.480765\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −11.7391 | −2.56167 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 6.15025 | 1.28242 | 0.641208 | − | 0.767367i | \(-0.278434\pi\) | ||||
0.641208 | + | 0.767367i | \(0.278434\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −3.11812 | −0.600083 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −0.967873 | −0.179730 | −0.0898648 | − | 0.995954i | \(-0.528643\pi\) | ||||
−0.0898648 | + | 0.995954i | \(0.528643\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 9.60629 | 1.72534 | 0.862670 | − | 0.505767i | \(-0.168791\pi\) | ||||
0.862670 | + | 0.505767i | \(0.168791\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 2.67673 | 0.465959 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.76466 | −0.290108 | −0.145054 | − | 0.989424i | \(-0.546336\pi\) | ||||
−0.145054 | + | 0.989424i | \(0.546336\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 10.7069 | 1.71448 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2.50564 | 0.391315 | 0.195658 | − | 0.980672i | \(-0.437316\pi\) | ||||
0.195658 | + | 0.980672i | \(0.437316\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −3.85911 | −0.588508 | −0.294254 | − | 0.955727i | \(-0.595071\pi\) | ||||
−0.294254 | + | 0.955727i | \(0.595071\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −4.91208 | −0.716500 | −0.358250 | − | 0.933626i | \(-0.616626\pi\) | ||||
−0.358250 | + | 0.933626i | \(0.616626\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 12.2334 | 1.74763 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 15.7391 | 2.20391 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 5.29767 | 0.727691 | 0.363845 | − | 0.931459i | \(-0.381464\pi\) | ||||
0.363845 | + | 0.931459i | \(0.381464\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −1.40926 | −0.186661 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 2.63841 | 0.343492 | 0.171746 | − | 0.985141i | \(-0.445059\pi\) | ||||
0.171746 | + | 0.985141i | \(0.445059\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 8.96787 | 1.14822 | 0.574109 | − | 0.818779i | \(-0.305348\pi\) | ||||
0.574109 | + | 0.818779i | \(0.305348\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 18.2655 | 2.30124 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −7.97440 | −0.974228 | −0.487114 | − | 0.873338i | \(-0.661950\pi\) | ||||
−0.487114 | + | 0.873338i | \(0.661950\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −16.4626 | −1.98186 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −13.8718 | −1.64628 | −0.823142 | − | 0.567836i | \(-0.807781\pi\) | ||||
−0.823142 | + | 0.567836i | \(0.807781\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −12.7712 | −1.49475 | −0.747377 | − | 0.664400i | \(-0.768687\pi\) | ||||
−0.747377 | + | 0.664400i | \(0.768687\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −4.38559 | −0.499785 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 13.2768 | 1.49376 | 0.746880 | − | 0.664959i | \(-0.231551\pi\) | ||||
0.746880 | + | 0.664959i | \(0.231551\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −4.14832 | −0.460924 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −7.61901 | −0.836295 | −0.418147 | − | 0.908379i | \(-0.637320\pi\) | ||||
−0.418147 | + | 0.908379i | \(0.637320\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 2.59074 | 0.277756 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 2.83510 | 0.300520 | 0.150260 | − | 0.988646i | \(-0.451989\pi\) | ||||
0.150260 | + | 0.988646i | \(0.451989\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −17.5424 | −1.83894 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −25.7135 | −2.66636 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 10.4800 | 1.06409 | 0.532044 | − | 0.846717i | \(-0.321424\pi\) | ||||
0.532044 | + | 0.846717i | \(0.321424\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −4.16490 | −0.418588 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 8.70693 | 0.866372 | 0.433186 | − | 0.901305i | \(-0.357389\pi\) | ||||
0.433186 | + | 0.901305i | \(0.357389\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 15.6190 | 1.53899 | 0.769493 | − | 0.638655i | \(-0.220509\pi\) | ||||
0.769493 | + | 0.638655i | \(0.220509\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 7.08792 | 0.685215 | 0.342608 | − | 0.939479i | \(-0.388690\pi\) | ||||
0.342608 | + | 0.939479i | \(0.388690\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −15.5424 | −1.48869 | −0.744344 | − | 0.667796i | \(-0.767238\pi\) | ||||
−0.744344 | + | 0.667796i | \(0.767238\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 4.72351 | 0.448336 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −8.11530 | −0.763423 | −0.381711 | − | 0.924282i | \(-0.624665\pi\) | ||||
−0.381711 | + | 0.924282i | \(0.624665\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −16.6596 | −1.54018 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −25.7871 | −2.36390 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −6.70693 | −0.604744 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 4.32980 | 0.384207 | 0.192104 | − | 0.981375i | \(-0.438469\pi\) | ||||
0.192104 | + | 0.981375i | \(0.438469\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 10.3298 | 0.909488 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 17.6748 | 1.54425 | 0.772127 | − | 0.635468i | \(-0.219193\pi\) | ||||
0.772127 | + | 0.635468i | \(0.219193\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.30895 | 0.200211 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −18.4800 | −1.57886 | −0.789428 | − | 0.613843i | \(-0.789623\pi\) | ||||
−0.789428 | + | 0.613843i | \(0.789623\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 5.55861 | 0.471475 | 0.235738 | − | 0.971817i | \(-0.424249\pi\) | ||||
0.235738 | + | 0.971817i | \(0.424249\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 13.1483 | 1.10729 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 4.00000 | 0.334497 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −32.7456 | −2.70081 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 20.9516 | 1.71642 | 0.858212 | − | 0.513295i | \(-0.171575\pi\) | ||||
0.858212 | + | 0.513295i | \(0.171575\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1.67020 | 0.135919 | 0.0679596 | − | 0.997688i | \(-0.478351\pi\) | ||||
0.0679596 | + | 0.997688i | \(0.478351\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −24.4894 | −1.97985 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 8.94228 | 0.713671 | 0.356836 | − | 0.934167i | \(-0.383856\pi\) | ||||
0.356836 | + | 0.934167i | \(0.383856\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −14.1804 | −1.12458 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 26.9725 | 2.12573 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −9.43856 | −0.739285 | −0.369643 | − | 0.929174i | \(-0.620520\pi\) | ||||
−0.369643 | + | 0.929174i | \(0.620520\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 8.96787 | 0.693955 | 0.346977 | − | 0.937873i | \(-0.387208\pi\) | ||||
0.346977 | + | 0.937873i | \(0.387208\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 3.00000 | 0.230769 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 2.19276 | 0.167684 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −2.64653 | −0.201212 | −0.100606 | − | 0.994926i | \(-0.532078\pi\) | ||||
−0.100606 | + | 0.994926i | \(0.532078\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −7.06232 | −0.530837 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −20.2225 | −1.51150 | −0.755749 | − | 0.654861i | \(-0.772727\pi\) | ||||
−0.755749 | + | 0.654861i | \(0.772727\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 15.3453 | 1.14061 | 0.570305 | − | 0.821433i | \(-0.306825\pi\) | ||||
0.570305 | + | 0.821433i | \(0.306825\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −24.0046 | −1.77447 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 5.87995 | 0.429985 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −13.6748 | −0.994696 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 5.62713 | 0.407165 | 0.203582 | − | 0.979058i | \(-0.434742\pi\) | ||||
0.203582 | + | 0.979058i | \(0.434742\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 7.23342 | 0.520673 | 0.260336 | − | 0.965518i | \(-0.416167\pi\) | ||||
0.260336 | + | 0.965518i | \(0.416167\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −5.35347 | −0.381419 | −0.190709 | − | 0.981647i | \(-0.561079\pi\) | ||||
−0.190709 | + | 0.981647i | \(0.561079\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −7.23342 | −0.512763 | −0.256382 | − | 0.966576i | \(-0.582530\pi\) | ||||
−0.256382 | + | 0.966576i | \(0.582530\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 21.3453 | 1.50558 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −4.24470 | −0.297919 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 25.6152 | 1.78038 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −0.526486 | −0.0364178 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 12.2447 | 0.842960 | 0.421480 | − | 0.906838i | \(-0.361511\pi\) | ||||
0.421480 | + | 0.906838i | \(0.361511\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 37.1312 | 2.54419 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 42.1292 | 2.85992 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 34.1850 | 2.31001 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 23.5198 | 1.58211 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 19.4525 | 1.30264 | 0.651318 | − | 0.758805i | \(-0.274216\pi\) | ||||
0.651318 | + | 0.758805i | \(0.274216\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 3.90080 | 0.258905 | 0.129452 | − | 0.991586i | \(-0.458678\pi\) | ||||
0.129452 | + | 0.991586i | \(0.458678\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 13.4096 | 0.886131 | 0.443066 | − | 0.896489i | \(-0.353891\pi\) | ||||
0.443066 | + | 0.896489i | \(0.353891\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 11.7391 | 0.772373 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 3.36192 | 0.220247 | 0.110123 | − | 0.993918i | \(-0.464875\pi\) | ||||
0.110123 | + | 0.993918i | \(0.464875\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −35.5385 | −2.30847 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 13.2768 | 0.858806 | 0.429403 | − | 0.903113i | \(-0.358724\pi\) | ||||
0.429403 | + | 0.903113i | \(0.358724\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −17.7437 | −1.14297 | −0.571485 | − | 0.820613i | \(-0.693632\pi\) | ||||
−0.571485 | + | 0.820613i | \(0.693632\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 20.4583 | 1.31240 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2.10594 | −0.133998 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 20.3940 | 1.29242 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −8.57416 | −0.541196 | −0.270598 | − | 0.962692i | \(-0.587221\pi\) | ||||
−0.270598 | + | 0.962692i | \(0.587221\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −6.15025 | −0.386663 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 2.70693 | 0.168854 | 0.0844269 | − | 0.996430i | \(-0.473094\pi\) | ||||
0.0844269 | + | 0.996430i | \(0.473094\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −7.73906 | −0.480882 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −4.03109 | −0.249518 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 14.3213 | 0.883092 | 0.441546 | − | 0.897239i | \(-0.354430\pi\) | ||||
0.441546 | + | 0.897239i | \(0.354430\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −7.58881 | −0.464428 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −11.9357 | −0.727735 | −0.363868 | − | 0.931451i | \(-0.618544\pi\) | ||||
−0.363868 | + | 0.931451i | \(0.618544\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 24.4195 | 1.48338 | 0.741689 | − | 0.670744i | \(-0.234025\pi\) | ||||
0.741689 | + | 0.670744i | \(0.234025\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 46.9562 | 2.84192 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 23.0074 | 1.38238 | 0.691191 | − | 0.722672i | \(-0.257086\pi\) | ||||
0.691191 | + | 0.722672i | \(0.257086\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 40.0092 | 2.39529 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −10.6596 | −0.635898 | −0.317949 | − | 0.948108i | \(-0.602994\pi\) | ||||
−0.317949 | + | 0.948108i | \(0.602994\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 10.3771 | 0.616857 | 0.308428 | − | 0.951248i | \(-0.400197\pi\) | ||||
0.308428 | + | 0.951248i | \(0.400197\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 10.9887 | 0.648644 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 17.5738 | 1.03375 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −28.0523 | −1.64445 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 22.7069 | 1.32655 | 0.663277 | − | 0.748374i | \(-0.269165\pi\) | ||||
0.663277 | + | 0.748374i | \(0.269165\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 3.11812 | 0.180932 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −24.6010 | −1.42271 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −16.9245 | −0.975510 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −23.3061 | −1.33890 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −5.49436 | −0.313580 | −0.156790 | − | 0.987632i | \(-0.550115\pi\) | ||||
−0.156790 | + | 0.987632i | \(0.550115\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −41.8079 | −2.37837 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 24.2447 | 1.37479 | 0.687395 | − | 0.726283i | \(-0.258754\pi\) | ||||
0.687395 | + | 0.726283i | \(0.258754\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 11.7562 | 0.664500 | 0.332250 | − | 0.943191i | \(-0.392192\pi\) | ||||
0.332250 | + | 0.943191i | \(0.392192\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 9.05387 | 0.508516 | 0.254258 | − | 0.967136i | \(-0.418169\pi\) | ||||
0.254258 | + | 0.967136i | \(0.418169\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0.967873 | 0.0541905 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −18.9725 | −1.05894 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −3.09571 | −0.172250 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 41.6028 | 2.30064 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −21.5424 | −1.18767 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 3.29733 | 0.181238 | 0.0906190 | − | 0.995886i | \(-0.471115\pi\) | ||||
0.0906190 | + | 0.995886i | \(0.471115\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −7.34961 | −0.402756 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 3.17302 | 0.172845 | 0.0864227 | − | 0.996259i | \(-0.472456\pi\) | ||||
0.0864227 | + | 0.996259i | \(0.472456\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 21.7225 | 1.17980 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −9.60629 | −0.520210 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 22.9516 | 1.23927 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −4.44139 | −0.238426 | −0.119213 | − | 0.992869i | \(-0.538037\pi\) | ||||
−0.119213 | + | 0.992869i | \(0.538037\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 29.2380 | 1.56508 | 0.782538 | − | 0.622603i | \(-0.213925\pi\) | ||||
0.782538 | + | 0.622603i | \(0.213925\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 12.4725 | 0.665732 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −1.04927 | −0.0558469 | −0.0279234 | − | 0.999610i | \(-0.508889\pi\) | ||||
−0.0279234 | + | 0.999610i | \(0.508889\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 69.0251 | 3.65319 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −9.69565 | −0.511717 | −0.255858 | − | 0.966714i | \(-0.582358\pi\) | ||||
−0.255858 | + | 0.966714i | \(0.582358\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.7228 | −0.985411 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −2.67673 | −0.140492 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 11.3921 | 0.594664 | 0.297332 | − | 0.954774i | \(-0.403903\pi\) | ||||
0.297332 | + | 0.954774i | \(0.403903\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 10.4357 | 0.543263 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 23.2334 | 1.20622 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 6.47634 | 0.335332 | 0.167666 | − | 0.985844i | \(-0.446377\pi\) | ||||
0.167666 | + | 0.985844i | \(0.446377\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 3.87149 | 0.199392 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 33.4993 | 1.72074 | 0.860372 | − | 0.509667i | \(-0.170232\pi\) | ||||
0.860372 | + | 0.509667i | \(0.170232\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −11.5897 | −0.593759 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 30.8702 | 1.57740 | 0.788698 | − | 0.614781i | \(-0.210756\pi\) | ||||
0.788698 | + | 0.614781i | \(0.210756\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −16.0728 | −0.817026 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −23.3453 | −1.18366 | −0.591828 | − | 0.806064i | \(-0.701594\pi\) | ||||
−0.591828 | + | 0.806064i | \(0.701594\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −36.1632 | −1.82885 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −47.3107 | −2.38651 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −19.4781 | −0.977579 | −0.488789 | − | 0.872402i | \(-0.662561\pi\) | ||||
−0.488789 | + | 0.872402i | \(0.662561\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −6.18045 | −0.309409 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 2.24470 | 0.112095 | 0.0560474 | − | 0.998428i | \(-0.482150\pi\) | ||||
0.0560474 | + | 0.998428i | \(0.482150\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −38.4251 | −1.91409 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1.76466 | 0.0874707 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 29.4781 | 1.45760 | 0.728799 | − | 0.684727i | \(-0.240079\pi\) | ||||
0.728799 | + | 0.684727i | \(0.240079\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 49.4661 | 2.43998 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 11.5710 | 0.569372 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −14.8789 | −0.728624 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −7.64831 | −0.373644 | −0.186822 | − | 0.982394i | \(-0.559819\pi\) | ||||
−0.186822 | + | 0.982394i | \(0.559819\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 29.4781 | 1.43668 | 0.718338 | − | 0.695695i | \(-0.244903\pi\) | ||||
0.718338 | + | 0.695695i | \(0.244903\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −20.4583 | −0.994717 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 39.3294 | 1.90328 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −10.7069 | −0.516935 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 2.08970 | 0.100657 | 0.0503286 | − | 0.998733i | \(-0.483973\pi\) | ||||
0.0503286 | + | 0.998733i | \(0.483973\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 5.17777 | 0.248828 | 0.124414 | − | 0.992230i | \(-0.460295\pi\) | ||||
0.124414 | + | 0.992230i | \(0.460295\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 3.23802 | 0.154895 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −27.6066 | −1.31759 | −0.658796 | − | 0.752322i | \(-0.728934\pi\) | ||||
−0.658796 | + | 0.752322i | \(0.728934\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 50.9509 | 2.42623 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −14.1502 | −0.672299 | −0.336149 | − | 0.941809i | \(-0.609125\pi\) | ||||
−0.336149 | + | 0.941809i | \(0.609125\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −56.0819 | −2.65258 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −6.46257 | −0.304987 | −0.152494 | − | 0.988304i | \(-0.548730\pi\) | ||||
−0.152494 | + | 0.988304i | \(0.548730\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −2.50564 | −0.117986 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −4.47069 | −0.210051 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 38.5582 | 1.80368 | 0.901839 | − | 0.432071i | \(-0.142217\pi\) | ||||
0.901839 | + | 0.432071i | \(0.142217\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 18.3344 | 0.855776 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −18.4234 | −0.858064 | −0.429032 | − | 0.903289i | \(-0.641145\pi\) | ||||
−0.429032 | + | 0.903289i | \(0.641145\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 7.09163 | 0.329576 | 0.164788 | − | 0.986329i | \(-0.447306\pi\) | ||||
0.164788 | + | 0.986329i | \(0.447306\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 40.4328 | 1.87101 | 0.935503 | − | 0.353319i | \(-0.114947\pi\) | ||||
0.935503 | + | 0.353319i | \(0.114947\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −34.9725 | −1.61488 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −23.9361 | −1.10292 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 3.85911 | 0.177442 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 22.0643 | 1.01025 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 10.7486 | 0.491117 | 0.245559 | − | 0.969382i | \(-0.421029\pi\) | ||||
0.245559 | + | 0.969382i | \(0.421029\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 7.05862 | 0.321845 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −72.1981 | −3.28513 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −38.6396 | −1.75093 | −0.875465 | − | 0.483282i | \(-0.839445\pi\) | ||||
−0.875465 | + | 0.483282i | \(0.839445\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 25.2645 | 1.14250 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −32.9460 | −1.48683 | −0.743416 | − | 0.668830i | \(-0.766796\pi\) | ||||
−0.743416 | + | 0.668830i | \(0.766796\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 5.69105 | 0.256312 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −60.8362 | −2.72888 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −26.9562 | −1.20673 | −0.603363 | − | 0.797466i | \(-0.706173\pi\) | ||||
−0.603363 | + | 0.797466i | \(0.706173\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −24.0046 | −1.07245 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 14.0766 | 0.627646 | 0.313823 | − | 0.949481i | \(-0.398390\pi\) | ||||
0.313823 | + | 0.949481i | \(0.398390\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −8.03020 | −0.356634 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 1.28109 | 0.0567833 | 0.0283917 | − | 0.999597i | \(-0.490961\pi\) | ||||
0.0283917 | + | 0.999597i | \(0.490961\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −56.0092 | −2.47770 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −1.64165 | −0.0724804 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 4.91208 | 0.216033 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 7.08407 | 0.310956 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −29.2394 | −1.28100 | −0.640501 | − | 0.767958i | \(-0.721273\pi\) | ||||
−0.640501 | + | 0.767958i | \(0.721273\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −2.50564 | −0.109564 | −0.0547820 | − | 0.998498i | \(-0.517446\pi\) | ||||
−0.0547820 | + | 0.998498i | \(0.517446\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −56.4845 | −2.46050 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 14.8255 | 0.644589 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 10.9887 | 0.476870 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −10.0226 | −0.434125 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 54.1301 | 2.33589 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −12.2334 | −0.526931 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −3.27222 | −0.140684 | −0.0703420 | − | 0.997523i | \(-0.522409\pi\) | ||||
−0.0703420 | + | 0.997523i | \(0.522409\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −41.0754 | −1.76271 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 3.03673 | 0.129841 | 0.0649205 | − | 0.997890i | \(-0.479321\pi\) | ||||
0.0649205 | + | 0.997890i | \(0.479321\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 37.3503 | 1.59407 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −0.509572 | −0.0217085 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 58.2267 | 2.47605 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 1.52366 | 0.0645596 | 0.0322798 | − | 0.999479i | \(-0.489723\pi\) | ||||
0.0322798 | + | 0.999479i | \(0.489723\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 15.4364 | 0.652891 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −15.7391 | −0.664504 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 27.9195 | 1.17667 | 0.588333 | − | 0.808618i | \(-0.299784\pi\) | ||||
0.588333 | + | 0.808618i | \(0.299784\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −18.1928 | −0.764027 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −13.7437 | −0.576164 | −0.288082 | − | 0.957606i | \(-0.593018\pi\) | ||||
−0.288082 | + | 0.957606i | \(0.593018\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1.42618 | 0.0596836 | 0.0298418 | − | 0.999555i | \(-0.490500\pi\) | ||||
0.0298418 | + | 0.999555i | \(0.490500\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −15.0623 | −0.629238 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −6.35154 | −0.264418 | −0.132209 | − | 0.991222i | \(-0.542207\pi\) | ||||
−0.132209 | + | 0.991222i | \(0.542207\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −19.3619 | −0.804654 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −33.4139 | −1.38624 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −5.29767 | −0.219407 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 22.1681 | 0.914974 | 0.457487 | − | 0.889216i | \(-0.348750\pi\) | ||||
0.457487 | + | 0.889216i | \(0.348750\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 5.05757 | 0.208394 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 14.3298 | 0.589449 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −1.05297 | −0.0432403 | −0.0216202 | − | 0.999766i | \(-0.506882\pi\) | ||||
−0.0216202 | + | 0.999766i | \(0.506882\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 19.3619 | 0.792431 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 5.12747 | 0.209503 | 0.104751 | − | 0.994498i | \(-0.466595\pi\) | ||||
0.104751 | + | 0.994498i | \(0.466595\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −1.71821 | −0.0700874 | −0.0350437 | − | 0.999386i | \(-0.511157\pi\) | ||||
−0.0350437 | + | 0.999386i | \(0.511157\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −33.2126 | −1.35252 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 4.42728 | 0.179698 | 0.0898489 | − | 0.995955i | \(-0.471362\pi\) | ||||
0.0898489 | + | 0.995955i | \(0.471362\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 11.3619 | 0.460408 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 19.6483 | 0.794886 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 33.8334 | 1.36652 | 0.683258 | − | 0.730177i | \(-0.260562\pi\) | ||||
0.683258 | + | 0.730177i | \(0.260562\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −40.3778 | −1.62555 | −0.812775 | − | 0.582578i | \(-0.802044\pi\) | ||||
−0.812775 | + | 0.582578i | \(0.802044\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 1.62713 | 0.0653999 | 0.0327000 | − | 0.999465i | \(-0.489589\pi\) | ||||
0.0327000 | + | 0.999465i | \(0.489589\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −19.1772 | −0.769555 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 12.4336 | 0.498142 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 1.40926 | 0.0562805 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 10.3761 | 0.413722 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −3.71223 | −0.147781 | −0.0738907 | − | 0.997266i | \(-0.523542\pi\) | ||||
−0.0738907 | + | 0.997266i | \(0.523542\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −32.7758 | −1.30272 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −48.9337 | −1.93882 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −57.7748 | −2.28553 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 32.5562 | 1.28589 | 0.642946 | − | 0.765911i | \(-0.277712\pi\) | ||||
0.642946 | + | 0.765911i | \(0.277712\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 27.9017 | 1.10034 | 0.550168 | − | 0.835054i | \(-0.314564\pi\) | ||||
0.550168 | + | 0.835054i | \(0.314564\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 28.7873 | 1.13174 | 0.565872 | − | 0.824493i | \(-0.308540\pi\) | ||||
0.565872 | + | 0.824493i | \(0.308540\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −2.63841 | −0.103567 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −112.769 | −4.41976 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −34.7152 | −1.35851 | −0.679256 | − | 0.733901i | \(-0.737697\pi\) | ||||
−0.679256 | + | 0.733901i | \(0.737697\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −53.1907 | −2.07517 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 25.5632 | 0.995801 | 0.497901 | − | 0.867234i | \(-0.334104\pi\) | ||||
0.497901 | + | 0.867234i | \(0.334104\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1.40960 | 0.0548269 | 0.0274135 | − | 0.999624i | \(-0.491273\pi\) | ||||
0.0274135 | + | 0.999624i | \(0.491273\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −62.9562 | −2.44502 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −5.95266 | −0.230488 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −52.0692 | −2.01311 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −8.96787 | −0.346201 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −0.0557959 | −0.00215078 | −0.00107539 | − | 0.999999i | \(-0.500342\pi\) | ||||
−0.00107539 | + | 0.999999i | \(0.500342\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −20.8316 | −0.800623 | −0.400311 | − | 0.916379i | \(-0.631098\pi\) | ||||
−0.400311 | + | 0.916379i | \(0.631098\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 45.9612 | 1.76383 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −10.4414 | −0.400115 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 21.5085 | 0.822999 | 0.411499 | − | 0.911410i | \(-0.365005\pi\) | ||||
0.411499 | + | 0.911410i | \(0.365005\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −35.8939 | −1.36944 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −21.1907 | −0.807301 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −5.49862 | −0.209178 | −0.104589 | − | 0.994516i | \(-0.533353\pi\) | ||||
−0.104589 | + | 0.994516i | \(0.533353\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −18.2655 | −0.693851 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −14.7330 | −0.558054 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −8.99897 | −0.340372 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −6.00460 | −0.226791 | −0.113395 | − | 0.993550i | \(-0.536173\pi\) | ||||
−0.113395 | + | 0.993550i | \(0.536173\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −0.929066 | −0.0350404 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 38.1850 | 1.43610 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 17.7168 | 0.665369 | 0.332685 | − | 0.943038i | \(-0.392046\pi\) | ||||
0.332685 | + | 0.943038i | \(0.392046\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 55.2966 | 2.07379 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 59.0810 | 2.21260 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −35.5385 | −1.32721 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −30.5308 | −1.13860 | −0.569302 | − | 0.822128i | \(-0.692787\pi\) | ||||
−0.569302 | + | 0.822128i | \(0.692787\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 68.4986 | 2.55102 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 47.4950 | 1.76636 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −43.9063 | −1.62839 | −0.814197 | − | 0.580589i | \(-0.802823\pi\) | ||||
−0.814197 | + | 0.580589i | \(0.802823\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −42.3165 | −1.56728 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 22.6914 | 0.839270 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 20.6427 | 0.762455 | 0.381227 | − | 0.924481i | \(-0.375502\pi\) | ||||
0.381227 | + | 0.924481i | \(0.375502\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 7.97440 | 0.293741 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 7.73446 | 0.284517 | 0.142258 | − | 0.989830i | \(-0.454564\pi\) | ||||
0.142258 | + | 0.989830i | \(0.454564\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 5.63705 | 0.207082 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −29.1755 | −1.07034 | −0.535172 | − | 0.844743i | \(-0.679753\pi\) | ||||
−0.535172 | + | 0.844743i | \(0.679753\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −31.7324 | −1.16103 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 31.0847 | 1.13581 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 9.38310 | 0.342394 | 0.171197 | − | 0.985237i | \(-0.445237\pi\) | ||||
0.171197 | + | 0.985237i | \(0.445237\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 22.9507 | 0.836371 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −12.8997 | −0.468847 | −0.234424 | − | 0.972135i | \(-0.575320\pi\) | ||||
−0.234424 | + | 0.972135i | \(0.575320\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 16.4626 | 0.597553 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 15.6963 | 0.568991 | 0.284496 | − | 0.958677i | \(-0.408174\pi\) | ||||
0.284496 | + | 0.958677i | \(0.408174\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −68.1625 | −2.46765 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −10.5536 | −0.381070 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 34.1123 | 1.23012 | 0.615060 | − | 0.788480i | \(-0.289132\pi\) | ||||
0.615060 | + | 0.788480i | \(0.289132\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −7.24573 | −0.260949 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 52.2539 | 1.87944 | 0.939721 | − | 0.341942i | \(-0.111085\pi\) | ||||
0.939721 | + | 0.341942i | \(0.111085\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 20.7154 | 0.743160 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1.31918 | 0.0472647 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 13.8718 | 0.496373 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 3.01795 | 0.107853 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 6.89902 | 0.245924 | 0.122962 | − | 0.992411i | \(-0.460761\pi\) | ||||
0.122962 | + | 0.992411i | \(0.460761\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −38.3344 | −1.36474 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −35.5904 | −1.26545 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −35.8715 | −1.27383 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 0.544296 | 0.0192800 | 0.00963998 | − | 0.999954i | \(-0.496931\pi\) | ||||
0.00963998 | + | 0.999954i | \(0.496931\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 28.8828 | 1.02180 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 11.8079 | 0.417212 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 12.7712 | 0.450685 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 31.9488 | 1.12465 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 26.3354 | 0.925905 | 0.462952 | − | 0.886383i | \(-0.346790\pi\) | ||||
0.462952 | + | 0.886383i | \(0.346790\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 24.4686 | 0.859207 | 0.429604 | − | 0.903018i | \(-0.358653\pi\) | ||||
0.429604 | + | 0.903018i | \(0.358653\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −65.3645 | −2.29243 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −2.03176 | −0.0710824 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −73.0622 | −2.55300 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 42.8503 | 1.49549 | 0.747743 | − | 0.663989i | \(-0.231138\pi\) | ||||
0.747743 | + | 0.663989i | \(0.231138\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 18.7417 | 0.653296 | 0.326648 | − | 0.945146i | \(-0.394081\pi\) | ||||
0.326648 | + | 0.945146i | \(0.394081\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −30.6681 | −1.06644 | −0.533218 | − | 0.845978i | \(-0.679017\pi\) | ||||
−0.533218 | + | 0.845978i | \(0.679017\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −19.8758 | −0.690314 | −0.345157 | − | 0.938545i | \(-0.612174\pi\) | ||||
−0.345157 | + | 0.938545i | \(0.612174\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −61.5847 | −2.13635 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −71.9319 | −2.49229 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −29.9536 | −1.03535 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 48.3178 | 1.66812 | 0.834058 | − | 0.551677i | \(-0.186012\pi\) | ||||
0.834058 | + | 0.551677i | \(0.186012\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.0632 | −0.967697 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 28.5329 | 0.982725 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 4.38559 | 0.150691 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −27.7768 | −0.953298 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −10.8531 | −0.372038 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −39.4686 | −1.35138 | −0.675690 | − | 0.737186i | \(-0.736154\pi\) | ||||
−0.675690 | + | 0.737186i | \(0.736154\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −16.7666 | −0.572736 | −0.286368 | − | 0.958120i | \(-0.592448\pi\) | ||||
−0.286368 | + | 0.958120i | \(0.592448\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −0.350976 | −0.0119751 | −0.00598757 | − | 0.999982i | \(-0.501906\pi\) | ||||
−0.00598757 | + | 0.999982i | \(0.501906\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −29.4139 | −1.00242 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −35.2087 | −1.19852 | −0.599259 | − | 0.800555i | \(-0.704538\pi\) | ||||
−0.599259 | + | 0.800555i | \(0.704538\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −47.0404 | −1.59758 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −13.2768 | −0.450385 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 31.8976 | 1.08081 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 43.6483 | 1.47727 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 8.61790 | 0.291006 | 0.145503 | − | 0.989358i | \(-0.453520\pi\) | ||||
0.145503 | + | 0.989358i | \(0.453520\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −60.7804 | −2.05007 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −42.5162 | −1.43241 | −0.716204 | − | 0.697891i | \(-0.754122\pi\) | ||||
−0.716204 | + | 0.697891i | \(0.754122\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 25.1568 | 0.846593 | 0.423296 | − | 0.905991i | \(-0.360873\pi\) | ||||
0.423296 | + | 0.905991i | \(0.360873\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 6.27505 | 0.210696 | 0.105348 | − | 0.994435i | \(-0.466404\pi\) | ||||
0.105348 | + | 0.994435i | \(0.466404\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 18.9887 | 0.636861 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 4.14832 | 0.138974 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −2.58614 | −0.0865418 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 65.8503 | 2.19868 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −9.29767 | −0.310095 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −31.1500 | −1.03776 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 45.3023 | 1.50757 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 11.0925 | 0.368321 | 0.184161 | − | 0.982896i | \(-0.441043\pi\) | ||||
0.184161 | + | 0.982896i | \(0.441043\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 36.2635 | 1.20278 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 32.8175 | 1.08729 | 0.543646 | − | 0.839315i | \(-0.317044\pi\) | ||||
0.543646 | + | 0.839315i | \(0.317044\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 7.61901 | 0.252152 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 77.5145 | 2.55975 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −0.658922 | −0.0217358 | −0.0108679 | − | 0.999941i | \(-0.503459\pi\) | ||||
−0.0108679 | + | 0.999941i | \(0.503459\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 14.7069 | 0.484610 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 55.4873 | 1.82639 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 65.0516 | 2.13657 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −28.0519 | −0.920354 | −0.460177 | − | 0.887827i | \(-0.652214\pi\) | ||||
−0.460177 | + | 0.887827i | \(0.652214\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 6.44072 | 0.211086 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −64.8966 | −2.12462 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −26.6652 | −0.871115 | −0.435558 | − | 0.900161i | \(-0.643449\pi\) | ||||
−0.435558 | + | 0.900161i | \(0.643449\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −31.4682 | −1.02693 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −0.222135 | −0.00724139 | −0.00362069 | − | 0.999993i | \(-0.501153\pi\) | ||||
−0.00362069 | + | 0.999993i | \(0.501153\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 15.4103 | 0.501829 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −4.99028 | −0.162162 | −0.0810812 | − | 0.996707i | \(-0.525837\pi\) | ||||
−0.0810812 | + | 0.996707i | \(0.525837\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 51.0847 | 1.65828 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −24.2348 | −0.785867 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 9.66807 | 0.313179 | 0.156590 | − | 0.987664i | \(-0.449950\pi\) | ||||
0.156590 | + | 0.987664i | \(0.449950\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −2.59074 | −0.0837467 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −81.0459 | −2.61711 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 61.2807 | 1.97680 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 29.5205 | 0.951284 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −19.8033 | −0.636832 | −0.318416 | − | 0.947951i | \(-0.603151\pi\) | ||||
−0.318416 | + | 0.947951i | \(0.603151\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 8.28639 | 0.266197 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −39.0410 | −1.25289 | −0.626443 | − | 0.779468i | \(-0.715490\pi\) | ||||
−0.626443 | + | 0.779468i | \(0.715490\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 24.3778 | 0.781517 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 50.8314 | 1.62624 | 0.813121 | − | 0.582095i | \(-0.197767\pi\) | ||||
0.813121 | + | 0.582095i | \(0.197767\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −2.83510 | −0.0906103 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −64.7324 | −2.06675 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −21.7569 | −0.693936 | −0.346968 | − | 0.937877i | \(-0.612789\pi\) | ||||
−0.346968 | + | 0.937877i | \(0.612789\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 57.6632 | 1.83544 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −23.7345 | −0.754712 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 33.0622 | 1.05025 | 0.525127 | − | 0.851024i | \(-0.324018\pi\) | ||||
0.525127 | + | 0.851024i | \(0.324018\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −8.82608 | −0.280087 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 19.4008 | 0.614430 | 0.307215 | − | 0.951640i | \(-0.400603\pi\) | ||||
0.307215 | + | 0.951640i | \(0.400603\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 5.50241 | 0.174088 |
(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 | 4400.2.a.ce.1.1 | 4 | ||
4.3 | odd | 2 | 2200.2.a.x.1.4 | 4 | |||
5.2 | odd | 4 | 880.2.b.j.529.7 | 8 | |||
5.3 | odd | 4 | 880.2.b.j.529.2 | 8 | |||
5.4 | even | 2 | 4400.2.a.cb.1.4 | 4 | |||
20.3 | even | 4 | 440.2.b.d.89.7 | yes | 8 | ||
20.7 | even | 4 | 440.2.b.d.89.2 | ✓ | 8 | ||
20.19 | odd | 2 | 2200.2.a.y.1.1 | 4 | |||
60.23 | odd | 4 | 3960.2.d.f.3169.2 | 8 | |||
60.47 | odd | 4 | 3960.2.d.f.3169.1 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
440.2.b.d.89.2 | ✓ | 8 | 20.7 | even | 4 | ||
440.2.b.d.89.7 | yes | 8 | 20.3 | even | 4 | ||
880.2.b.j.529.2 | 8 | 5.3 | odd | 4 | |||
880.2.b.j.529.7 | 8 | 5.2 | odd | 4 | |||
2200.2.a.x.1.4 | 4 | 4.3 | odd | 2 | |||
2200.2.a.y.1.1 | 4 | 20.19 | odd | 2 | |||
3960.2.d.f.3169.1 | 8 | 60.47 | odd | 4 | |||
3960.2.d.f.3169.2 | 8 | 60.23 | odd | 4 | |||
4400.2.a.cb.1.4 | 4 | 5.4 | even | 2 | |||
4400.2.a.ce.1.1 | 4 | 1.1 | even | 1 | trivial |