Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1305,4,Mod(1,1305)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1305, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1305.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1305 = 3^{2} \cdot 5 \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1305.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: | \(76.9974925575\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{6} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - x^{5} - 49x^{4} + 27x^{3} + 692x^{2} - 82x - 2588 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 435) |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(5.42717\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1305.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −5.42717 | −1.91879 | −0.959397 | − | 0.282060i | \(-0.908982\pi\) | ||||
−0.959397 | + | 0.282060i | \(0.908982\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 21.4542 | 2.68177 | ||||||||
\(5\) | 5.00000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −10.2400 | −0.552906 | −0.276453 | − | 0.961027i | \(-0.589159\pi\) | ||||
−0.276453 | + | 0.961027i | \(0.589159\pi\) | |||||||
\(8\) | −73.0180 | −3.22697 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −27.1358 | −0.858111 | ||||||||
\(11\) | −12.6318 | −0.346239 | −0.173119 | − | 0.984901i | \(-0.555385\pi\) | ||||
−0.173119 | + | 0.984901i | \(0.555385\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 84.2342 | 1.79710 | 0.898552 | − | 0.438866i | \(-0.144620\pi\) | ||||
0.898552 | + | 0.438866i | \(0.144620\pi\) | |||||||
\(14\) | 55.5740 | 1.06091 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 224.647 | 3.51012 | ||||||||
\(17\) | −6.89181 | −0.0983241 | −0.0491621 | − | 0.998791i | \(-0.515655\pi\) | ||||
−0.0491621 | + | 0.998791i | \(0.515655\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −79.7045 | −0.962393 | −0.481196 | − | 0.876613i | \(-0.659798\pi\) | ||||
−0.481196 | + | 0.876613i | \(0.659798\pi\) | |||||||
\(20\) | 107.271 | 1.19932 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 68.5548 | 0.664361 | ||||||||
\(23\) | 73.8181 | 0.669223 | 0.334612 | − | 0.942356i | \(-0.391395\pi\) | ||||
0.334612 | + | 0.942356i | \(0.391395\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 25.0000 | 0.200000 | ||||||||
\(26\) | −457.153 | −3.44827 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −219.690 | −1.48277 | ||||||||
\(29\) | −29.0000 | −0.185695 | ||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.254654 | 0.00147540 | 0.000737698 | − | 1.00000i | \(-0.499765\pi\) | ||||
0.000737698 | 1.00000i | \(0.499765\pi\) | ||||||||
\(32\) | −635.056 | −3.50822 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 37.4030 | 0.188664 | ||||||||
\(35\) | −51.1998 | −0.247267 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 40.4065 | 0.179535 | 0.0897674 | − | 0.995963i | \(-0.471388\pi\) | ||||
0.0897674 | + | 0.995963i | \(0.471388\pi\) | |||||||
\(38\) | 432.570 | 1.84663 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −365.090 | −1.44314 | ||||||||
\(41\) | −208.354 | −0.793645 | −0.396822 | − | 0.917895i | \(-0.629887\pi\) | ||||
−0.396822 | + | 0.917895i | \(0.629887\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −194.427 | −0.689531 | −0.344766 | − | 0.938689i | \(-0.612042\pi\) | ||||
−0.344766 | + | 0.938689i | \(0.612042\pi\) | |||||||
\(44\) | −271.004 | −0.928532 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −400.623 | −1.28410 | ||||||||
\(47\) | 522.168 | 1.62055 | 0.810277 | − | 0.586047i | \(-0.199317\pi\) | ||||
0.810277 | + | 0.586047i | \(0.199317\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −238.143 | −0.694295 | ||||||||
\(50\) | −135.679 | −0.383759 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 1807.17 | 4.81942 | ||||||||
\(53\) | 294.893 | 0.764276 | 0.382138 | − | 0.924105i | \(-0.375188\pi\) | ||||
0.382138 | + | 0.924105i | \(0.375188\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −63.1589 | −0.154843 | ||||||||
\(56\) | 747.701 | 1.78421 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 157.388 | 0.356311 | ||||||||
\(59\) | 196.229 | 0.432997 | 0.216498 | − | 0.976283i | \(-0.430536\pi\) | ||||
0.216498 | + | 0.976283i | \(0.430536\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 189.313 | 0.397360 | 0.198680 | − | 0.980064i | \(-0.436334\pi\) | ||||
0.198680 | + | 0.980064i | \(0.436334\pi\) | |||||||
\(62\) | −1.38205 | −0.00283098 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1649.38 | 3.22144 | ||||||||
\(65\) | 421.171 | 0.803690 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −570.840 | −1.04088 | −0.520442 | − | 0.853897i | \(-0.674233\pi\) | ||||
−0.520442 | + | 0.853897i | \(0.674233\pi\) | |||||||
\(68\) | −147.858 | −0.263683 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 277.870 | 0.474454 | ||||||||
\(71\) | 1126.87 | 1.88358 | 0.941792 | − | 0.336196i | \(-0.109141\pi\) | ||||
0.941792 | + | 0.336196i | \(0.109141\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 581.431 | 0.932210 | 0.466105 | − | 0.884729i | \(-0.345657\pi\) | ||||
0.466105 | + | 0.884729i | \(0.345657\pi\) | |||||||
\(74\) | −219.293 | −0.344490 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −1709.99 | −2.58092 | ||||||||
\(77\) | 129.349 | 0.191437 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −255.631 | −0.364060 | −0.182030 | − | 0.983293i | \(-0.558267\pi\) | ||||
−0.182030 | + | 0.983293i | \(0.558267\pi\) | |||||||
\(80\) | 1123.24 | 1.56977 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 1130.77 | 1.52284 | ||||||||
\(83\) | 983.081 | 1.30009 | 0.650043 | − | 0.759897i | \(-0.274751\pi\) | ||||
0.650043 | + | 0.759897i | \(0.274751\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −34.4591 | −0.0439719 | ||||||||
\(86\) | 1055.19 | 1.32307 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 922.347 | 1.11730 | ||||||||
\(89\) | −678.642 | −0.808268 | −0.404134 | − | 0.914700i | \(-0.632427\pi\) | ||||
−0.404134 | + | 0.914700i | \(0.632427\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −862.555 | −0.993630 | ||||||||
\(92\) | 1583.70 | 1.79470 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −2833.89 | −3.10951 | ||||||||
\(95\) | −398.523 | −0.430395 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −30.8442 | −0.0322861 | −0.0161431 | − | 0.999870i | \(-0.505139\pi\) | ||||
−0.0161431 | + | 0.999870i | \(0.505139\pi\) | |||||||
\(98\) | 1292.44 | 1.33221 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 536.354 | 0.536354 | ||||||||
\(101\) | −1749.78 | −1.72386 | −0.861930 | − | 0.507028i | \(-0.830744\pi\) | ||||
−0.861930 | + | 0.507028i | \(0.830744\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1912.26 | 1.82933 | 0.914663 | − | 0.404217i | \(-0.132456\pi\) | ||||
0.914663 | + | 0.404217i | \(0.132456\pi\) | |||||||
\(104\) | −6150.61 | −5.79920 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −1600.43 | −1.46649 | ||||||||
\(107\) | −1719.25 | −1.55333 | −0.776663 | − | 0.629916i | \(-0.783089\pi\) | ||||
−0.776663 | + | 0.629916i | \(0.783089\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −779.425 | −0.684911 | −0.342456 | − | 0.939534i | \(-0.611259\pi\) | ||||
−0.342456 | + | 0.939534i | \(0.611259\pi\) | |||||||
\(110\) | 342.774 | 0.297111 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −2300.38 | −1.94076 | ||||||||
\(113\) | −766.529 | −0.638132 | −0.319066 | − | 0.947732i | \(-0.603369\pi\) | ||||
−0.319066 | + | 0.947732i | \(0.603369\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 369.090 | 0.299286 | ||||||||
\(116\) | −622.170 | −0.497992 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −1064.97 | −0.830831 | ||||||||
\(119\) | 70.5719 | 0.0543640 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1171.44 | −0.880119 | ||||||||
\(122\) | −1027.43 | −0.762453 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 5.46339 | 0.00395667 | ||||||||
\(125\) | 125.000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1363.54 | −0.952715 | −0.476358 | − | 0.879252i | \(-0.658043\pi\) | ||||
−0.476358 | + | 0.879252i | \(0.658043\pi\) | |||||||
\(128\) | −3870.99 | −2.67305 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −2285.77 | −1.54211 | ||||||||
\(131\) | 1346.83 | 0.898269 | 0.449134 | − | 0.893464i | \(-0.351732\pi\) | ||||
0.449134 | + | 0.893464i | \(0.351732\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 816.171 | 0.532113 | ||||||||
\(134\) | 3098.05 | 1.99724 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 503.226 | 0.317289 | ||||||||
\(137\) | 2508.42 | 1.56430 | 0.782148 | − | 0.623093i | \(-0.214124\pi\) | ||||
0.782148 | + | 0.623093i | \(0.214124\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1363.95 | 0.832292 | 0.416146 | − | 0.909298i | \(-0.363380\pi\) | ||||
0.416146 | + | 0.909298i | \(0.363380\pi\) | |||||||
\(140\) | −1098.45 | −0.663113 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −6115.69 | −3.61421 | ||||||||
\(143\) | −1064.03 | −0.622227 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −145.000 | −0.0830455 | ||||||||
\(146\) | −3155.52 | −1.78872 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 866.887 | 0.481471 | ||||||||
\(149\) | −2792.25 | −1.53523 | −0.767617 | − | 0.640909i | \(-0.778558\pi\) | ||||
−0.767617 | + | 0.640909i | \(0.778558\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 306.493 | 0.165179 | 0.0825897 | − | 0.996584i | \(-0.473681\pi\) | ||||
0.0825897 | + | 0.996584i | \(0.473681\pi\) | |||||||
\(152\) | 5819.86 | 3.10561 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −701.999 | −0.367329 | ||||||||
\(155\) | 1.27327 | 0.000659817 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1828.15 | −0.929315 | −0.464657 | − | 0.885491i | \(-0.653822\pi\) | ||||
−0.464657 | + | 0.885491i | \(0.653822\pi\) | |||||||
\(158\) | 1387.35 | 0.698556 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −3175.28 | −1.56892 | ||||||||
\(161\) | −755.894 | −0.370018 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2101.15 | 1.00966 | 0.504830 | − | 0.863219i | \(-0.331555\pi\) | ||||
0.504830 | + | 0.863219i | \(0.331555\pi\) | |||||||
\(164\) | −4470.06 | −2.12837 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −5335.35 | −2.49460 | ||||||||
\(167\) | −1564.53 | −0.724950 | −0.362475 | − | 0.931994i | \(-0.618068\pi\) | ||||
−0.362475 | + | 0.931994i | \(0.618068\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 4898.40 | 2.22959 | ||||||||
\(170\) | 187.015 | 0.0843730 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −4171.27 | −1.84916 | ||||||||
\(173\) | 2695.23 | 1.18448 | 0.592239 | − | 0.805762i | \(-0.298244\pi\) | ||||
0.592239 | + | 0.805762i | \(0.298244\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −255.999 | −0.110581 | ||||||||
\(176\) | −2837.70 | −1.21534 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 3683.10 | 1.55090 | ||||||||
\(179\) | 3604.16 | 1.50496 | 0.752480 | − | 0.658615i | \(-0.228857\pi\) | ||||
0.752480 | + | 0.658615i | \(0.228857\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2658.32 | −1.09166 | −0.545832 | − | 0.837894i | \(-0.683786\pi\) | ||||
−0.545832 | + | 0.837894i | \(0.683786\pi\) | |||||||
\(182\) | 4681.23 | 1.90657 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −5390.05 | −2.15956 | ||||||||
\(185\) | 202.033 | 0.0802904 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 87.0559 | 0.0340436 | ||||||||
\(188\) | 11202.7 | 4.34595 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 2162.85 | 0.825840 | ||||||||
\(191\) | 145.942 | 0.0552877 | 0.0276439 | − | 0.999618i | \(-0.491200\pi\) | ||||
0.0276439 | + | 0.999618i | \(0.491200\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1151.46 | 0.429451 | 0.214725 | − | 0.976674i | \(-0.431114\pi\) | ||||
0.214725 | + | 0.976674i | \(0.431114\pi\) | |||||||
\(194\) | 167.397 | 0.0619504 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −5109.16 | −1.86194 | ||||||||
\(197\) | −4328.08 | −1.56529 | −0.782647 | − | 0.622466i | \(-0.786131\pi\) | ||||
−0.782647 | + | 0.622466i | \(0.786131\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1532.72 | 0.545988 | 0.272994 | − | 0.962016i | \(-0.411986\pi\) | ||||
0.272994 | + | 0.962016i | \(0.411986\pi\) | |||||||
\(200\) | −1825.45 | −0.645394 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 9496.36 | 3.30773 | ||||||||
\(203\) | 296.959 | 0.102672 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1041.77 | −0.354929 | ||||||||
\(206\) | −10378.2 | −3.51010 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 18923.0 | 6.30805 | ||||||||
\(209\) | 1006.81 | 0.333218 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 5345.39 | 1.74404 | 0.872019 | − | 0.489472i | \(-0.162810\pi\) | ||||
0.872019 | + | 0.489472i | \(0.162810\pi\) | |||||||
\(212\) | 6326.67 | 2.04961 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 9330.65 | 2.98051 | ||||||||
\(215\) | −972.135 | −0.308368 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −2.60765 | −0.000815755 0 | ||||||||
\(218\) | 4230.07 | 1.31420 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −1355.02 | −0.415252 | ||||||||
\(221\) | −580.526 | −0.176699 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 3783.05 | 1.13602 | 0.568008 | − | 0.823023i | \(-0.307714\pi\) | ||||
0.568008 | + | 0.823023i | \(0.307714\pi\) | |||||||
\(224\) | 6502.95 | 1.93972 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 4160.08 | 1.22444 | ||||||||
\(227\) | 4348.46 | 1.27144 | 0.635721 | − | 0.771919i | \(-0.280703\pi\) | ||||
0.635721 | + | 0.771919i | \(0.280703\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −3068.67 | −0.885517 | −0.442759 | − | 0.896641i | \(-0.646000\pi\) | ||||
−0.442759 | + | 0.896641i | \(0.646000\pi\) | |||||||
\(230\) | −2003.12 | −0.574268 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 2117.52 | 0.599233 | ||||||||
\(233\) | 275.696 | 0.0775170 | 0.0387585 | − | 0.999249i | \(-0.487660\pi\) | ||||
0.0387585 | + | 0.999249i | \(0.487660\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2610.84 | 0.724734 | ||||||||
\(236\) | 4209.92 | 1.16120 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −383.006 | −0.104313 | ||||||||
\(239\) | −3132.87 | −0.847901 | −0.423950 | − | 0.905685i | \(-0.639357\pi\) | ||||
−0.423950 | + | 0.905685i | \(0.639357\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 5699.61 | 1.52342 | 0.761710 | − | 0.647918i | \(-0.224360\pi\) | ||||
0.761710 | + | 0.647918i | \(0.224360\pi\) | |||||||
\(242\) | 6357.59 | 1.68877 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 4061.54 | 1.06563 | ||||||||
\(245\) | −1190.72 | −0.310498 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −6713.85 | −1.72952 | ||||||||
\(248\) | −18.5943 | −0.00476105 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −678.396 | −0.171622 | ||||||||
\(251\) | −1714.12 | −0.431054 | −0.215527 | − | 0.976498i | \(-0.569147\pi\) | ||||
−0.215527 | + | 0.976498i | \(0.569147\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −932.454 | −0.231711 | ||||||||
\(254\) | 7400.17 | 1.82806 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 7813.52 | 1.90760 | ||||||||
\(257\) | 803.085 | 0.194922 | 0.0974612 | − | 0.995239i | \(-0.468928\pi\) | ||||
0.0974612 | + | 0.995239i | \(0.468928\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −413.761 | −0.0992659 | ||||||||
\(260\) | 9035.87 | 2.15531 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −7309.48 | −1.72359 | ||||||||
\(263\) | 1694.24 | 0.397230 | 0.198615 | − | 0.980078i | \(-0.436356\pi\) | ||||
0.198615 | + | 0.980078i | \(0.436356\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1474.46 | 0.341794 | ||||||||
\(266\) | −4429.50 | −1.02101 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −12246.9 | −2.79141 | ||||||||
\(269\) | −3364.95 | −0.762693 | −0.381347 | − | 0.924432i | \(-0.624540\pi\) | ||||
−0.381347 | + | 0.924432i | \(0.624540\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 8044.10 | 1.80312 | 0.901558 | − | 0.432658i | \(-0.142424\pi\) | ||||
0.901558 | + | 0.432658i | \(0.142424\pi\) | |||||||
\(272\) | −1548.23 | −0.345129 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −13613.6 | −3.00156 | ||||||||
\(275\) | −315.795 | −0.0692477 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −6971.54 | −1.51220 | −0.756100 | − | 0.654456i | \(-0.772898\pi\) | ||||
−0.756100 | + | 0.654456i | \(0.772898\pi\) | |||||||
\(278\) | −7402.38 | −1.59700 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 3738.51 | 0.797923 | ||||||||
\(281\) | 1916.94 | 0.406957 | 0.203478 | − | 0.979079i | \(-0.434775\pi\) | ||||
0.203478 | + | 0.979079i | \(0.434775\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 2036.63 | 0.427792 | 0.213896 | − | 0.976856i | \(-0.431385\pi\) | ||||
0.213896 | + | 0.976856i | \(0.431385\pi\) | |||||||
\(284\) | 24176.0 | 5.05134 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 5774.66 | 1.19393 | ||||||||
\(287\) | 2133.54 | 0.438811 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −4865.50 | −0.990332 | ||||||||
\(290\) | 786.939 | 0.159347 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 12474.1 | 2.49997 | ||||||||
\(293\) | 1754.55 | 0.349836 | 0.174918 | − | 0.984583i | \(-0.444034\pi\) | ||||
0.174918 | + | 0.984583i | \(0.444034\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 981.143 | 0.193642 | ||||||||
\(296\) | −2950.40 | −0.579353 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 15154.0 | 2.94580 | ||||||||
\(299\) | 6218.01 | 1.20266 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1990.92 | 0.381246 | ||||||||
\(302\) | −1663.39 | −0.316945 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −17905.4 | −3.37811 | ||||||||
\(305\) | 946.563 | 0.177705 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 8909.41 | 1.65631 | 0.828154 | − | 0.560500i | \(-0.189391\pi\) | ||||
0.828154 | + | 0.560500i | \(0.189391\pi\) | |||||||
\(308\) | 2775.07 | 0.513391 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −6.91026 | −0.00126605 | ||||||||
\(311\) | 7422.88 | 1.35342 | 0.676709 | − | 0.736251i | \(-0.263405\pi\) | ||||
0.676709 | + | 0.736251i | \(0.263405\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1453.62 | −0.262504 | −0.131252 | − | 0.991349i | \(-0.541900\pi\) | ||||
−0.131252 | + | 0.991349i | \(0.541900\pi\) | |||||||
\(314\) | 9921.69 | 1.78316 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −5484.35 | −0.976326 | ||||||||
\(317\) | −5203.30 | −0.921912 | −0.460956 | − | 0.887423i | \(-0.652493\pi\) | ||||
−0.460956 | + | 0.887423i | \(0.652493\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 366.322 | 0.0642949 | ||||||||
\(320\) | 8246.88 | 1.44067 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 4102.37 | 0.709987 | ||||||||
\(323\) | 549.309 | 0.0946264 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 2105.86 | 0.359421 | ||||||||
\(326\) | −11403.3 | −1.93733 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 15213.6 | 2.56107 | ||||||||
\(329\) | −5346.98 | −0.896014 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −10985.0 | −1.82414 | −0.912070 | − | 0.410035i | \(-0.865516\pi\) | ||||
−0.912070 | + | 0.410035i | \(0.865516\pi\) | |||||||
\(332\) | 21091.2 | 3.48653 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 8490.94 | 1.39103 | ||||||||
\(335\) | −2854.20 | −0.465498 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2295.27 | 0.371013 | 0.185507 | − | 0.982643i | \(-0.440607\pi\) | ||||
0.185507 | + | 0.982643i | \(0.440607\pi\) | |||||||
\(338\) | −26584.4 | −4.27812 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −739.290 | −0.117922 | ||||||||
\(341\) | −3.21674 | −0.000510839 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 5950.88 | 0.936786 | ||||||||
\(344\) | 14196.7 | 2.22510 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −14627.5 | −2.27277 | ||||||||
\(347\) | 5313.01 | 0.821952 | 0.410976 | − | 0.911646i | \(-0.365188\pi\) | ||||
0.410976 | + | 0.911646i | \(0.365188\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 2086.08 | 0.319958 | 0.159979 | − | 0.987120i | \(-0.448857\pi\) | ||||
0.159979 | + | 0.987120i | \(0.448857\pi\) | |||||||
\(350\) | 1389.35 | 0.212182 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 8021.89 | 1.21468 | ||||||||
\(353\) | −5382.37 | −0.811543 | −0.405772 | − | 0.913975i | \(-0.632997\pi\) | ||||
−0.405772 | + | 0.913975i | \(0.632997\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 5634.33 | 0.842364 | ||||||||
\(356\) | −14559.7 | −2.16759 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −19560.4 | −2.88771 | ||||||||
\(359\) | 7990.36 | 1.17469 | 0.587347 | − | 0.809335i | \(-0.300173\pi\) | ||||
0.587347 | + | 0.809335i | \(0.300173\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −506.193 | −0.0737998 | ||||||||
\(362\) | 14427.1 | 2.09468 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −18505.4 | −2.66469 | ||||||||
\(365\) | 2907.16 | 0.416897 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −429.201 | −0.0610466 | −0.0305233 | − | 0.999534i | \(-0.509717\pi\) | ||||
−0.0305233 | + | 0.999534i | \(0.509717\pi\) | |||||||
\(368\) | 16583.0 | 2.34905 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −1096.46 | −0.154061 | ||||||||
\(371\) | −3019.69 | −0.422572 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 6270.80 | 0.870482 | 0.435241 | − | 0.900314i | \(-0.356663\pi\) | ||||
0.435241 | + | 0.900314i | \(0.356663\pi\) | |||||||
\(374\) | −472.467 | −0.0653227 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −38127.7 | −5.22948 | ||||||||
\(377\) | −2442.79 | −0.333714 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 10417.0 | 1.41183 | 0.705917 | − | 0.708294i | \(-0.250535\pi\) | ||||
0.705917 | + | 0.708294i | \(0.250535\pi\) | |||||||
\(380\) | −8549.96 | −1.15422 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −792.049 | −0.106086 | ||||||||
\(383\) | −10769.3 | −1.43677 | −0.718387 | − | 0.695644i | \(-0.755119\pi\) | ||||
−0.718387 | + | 0.695644i | \(0.755119\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 646.745 | 0.0856134 | ||||||||
\(386\) | −6249.18 | −0.824028 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −661.736 | −0.0865839 | ||||||||
\(389\) | 11121.7 | 1.44960 | 0.724798 | − | 0.688961i | \(-0.241933\pi\) | ||||
0.724798 | + | 0.688961i | \(0.241933\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −508.740 | −0.0658008 | ||||||||
\(392\) | 17388.7 | 2.24047 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 23489.2 | 3.00348 | ||||||||
\(395\) | −1278.16 | −0.162813 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 11286.7 | 1.42686 | 0.713432 | − | 0.700724i | \(-0.247140\pi\) | ||||
0.713432 | + | 0.700724i | \(0.247140\pi\) | |||||||
\(398\) | −8318.33 | −1.04764 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 5616.19 | 0.702023 | ||||||||
\(401\) | 15418.0 | 1.92005 | 0.960023 | − | 0.279922i | \(-0.0903086\pi\) | ||||
0.960023 | + | 0.279922i | \(0.0903086\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 21.4506 | 0.00265144 | ||||||||
\(404\) | −37540.1 | −4.62299 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −1611.65 | −0.197006 | ||||||||
\(407\) | −510.406 | −0.0621619 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 13849.5 | 1.67437 | 0.837183 | − | 0.546922i | \(-0.184201\pi\) | ||||
0.837183 | + | 0.546922i | \(0.184201\pi\) | |||||||
\(410\) | 5653.86 | 0.681035 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 41025.9 | 4.90583 | ||||||||
\(413\) | −2009.37 | −0.239406 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 4915.40 | 0.581416 | ||||||||
\(416\) | −53493.4 | −6.30464 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −5464.13 | −0.639376 | ||||||||
\(419\) | 2793.33 | 0.325688 | 0.162844 | − | 0.986652i | \(-0.447933\pi\) | ||||
0.162844 | + | 0.986652i | \(0.447933\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −3643.79 | −0.421823 | −0.210911 | − | 0.977505i | \(-0.567643\pi\) | ||||
−0.210911 | + | 0.977505i | \(0.567643\pi\) | |||||||
\(422\) | −29010.4 | −3.34645 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −21532.4 | −2.46629 | ||||||||
\(425\) | −172.295 | −0.0196648 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −1938.55 | −0.219703 | ||||||||
\(428\) | −36885.0 | −4.16566 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 5275.94 | 0.591694 | ||||||||
\(431\) | −5834.03 | −0.652007 | −0.326004 | − | 0.945369i | \(-0.605702\pi\) | ||||
−0.326004 | + | 0.945369i | \(0.605702\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 7919.15 | 0.878915 | 0.439457 | − | 0.898263i | \(-0.355171\pi\) | ||||
0.439457 | + | 0.898263i | \(0.355171\pi\) | |||||||
\(434\) | 14.1522 | 0.00156527 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −16721.9 | −1.83677 | ||||||||
\(437\) | −5883.63 | −0.644056 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 11696.0 | 1.27158 | 0.635788 | − | 0.771864i | \(-0.280675\pi\) | ||||
0.635788 | + | 0.771864i | \(0.280675\pi\) | |||||||
\(440\) | 4611.73 | 0.499672 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 3150.61 | 0.339049 | ||||||||
\(443\) | 2786.16 | 0.298814 | 0.149407 | − | 0.988776i | \(-0.452264\pi\) | ||||
0.149407 | + | 0.988776i | \(0.452264\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −3393.21 | −0.361468 | ||||||||
\(446\) | −20531.2 | −2.17978 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −16889.5 | −1.78115 | ||||||||
\(449\) | −11013.8 | −1.15762 | −0.578811 | − | 0.815462i | \(-0.696483\pi\) | ||||
−0.578811 | + | 0.815462i | \(0.696483\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2631.88 | 0.274790 | ||||||||
\(452\) | −16445.2 | −1.71132 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −23599.8 | −2.43963 | ||||||||
\(455\) | −4312.77 | −0.444365 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 12773.5 | 1.30748 | 0.653739 | − | 0.756720i | \(-0.273199\pi\) | ||||
0.653739 | + | 0.756720i | \(0.273199\pi\) | |||||||
\(458\) | 16654.2 | 1.69912 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 7918.52 | 0.802615 | ||||||||
\(461\) | 13343.4 | 1.34808 | 0.674039 | − | 0.738696i | \(-0.264558\pi\) | ||||
0.674039 | + | 0.738696i | \(0.264558\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 17265.4 | 1.73303 | 0.866514 | − | 0.499153i | \(-0.166355\pi\) | ||||
0.866514 | + | 0.499153i | \(0.166355\pi\) | |||||||
\(464\) | −6514.78 | −0.651812 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −1496.25 | −0.148739 | ||||||||
\(467\) | 16016.7 | 1.58708 | 0.793538 | − | 0.608521i | \(-0.208237\pi\) | ||||
0.793538 | + | 0.608521i | \(0.208237\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 5845.38 | 0.575511 | ||||||||
\(470\) | −14169.5 | −1.39062 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −14328.2 | −1.39727 | ||||||||
\(473\) | 2455.96 | 0.238742 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1992.61 | −0.192479 | ||||||||
\(476\) | 1514.06 | 0.145792 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 17002.6 | 1.62695 | ||||||||
\(479\) | 5847.01 | 0.557738 | 0.278869 | − | 0.960329i | \(-0.410040\pi\) | ||||
0.278869 | + | 0.960329i | \(0.410040\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 3403.61 | 0.322643 | ||||||||
\(482\) | −30932.7 | −2.92313 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −25132.2 | −2.36028 | ||||||||
\(485\) | −154.221 | −0.0144388 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −342.662 | −0.0318840 | −0.0159420 | − | 0.999873i | \(-0.505075\pi\) | ||||
−0.0159420 | + | 0.999873i | \(0.505075\pi\) | |||||||
\(488\) | −13823.2 | −1.28227 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 6462.22 | 0.595782 | ||||||||
\(491\) | 1673.48 | 0.153815 | 0.0769073 | − | 0.997038i | \(-0.475495\pi\) | ||||
0.0769073 | + | 0.997038i | \(0.475495\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 199.863 | 0.0182583 | ||||||||
\(494\) | 36437.2 | 3.31859 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 57.2074 | 0.00517881 | ||||||||
\(497\) | −11539.1 | −1.04144 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 10918.2 | 0.979487 | 0.489743 | − | 0.871867i | \(-0.337090\pi\) | ||||
0.489743 | + | 0.871867i | \(0.337090\pi\) | |||||||
\(500\) | 2681.77 | 0.239865 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 9302.84 | 0.827103 | ||||||||
\(503\) | −16957.6 | −1.50319 | −0.751595 | − | 0.659625i | \(-0.770715\pi\) | ||||
−0.751595 | + | 0.659625i | \(0.770715\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −8748.91 | −0.770933 | ||||||||
\(506\) | 5060.58 | 0.444606 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −29253.6 | −2.55496 | ||||||||
\(509\) | 226.179 | 0.0196959 | 0.00984795 | − | 0.999952i | \(-0.496865\pi\) | ||||
0.00984795 | + | 0.999952i | \(0.496865\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −5953.83 | −0.515425 | ||||||||
\(512\) | −11437.3 | −0.987234 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −4358.48 | −0.374016 | ||||||||
\(515\) | 9561.30 | 0.818100 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −6595.91 | −0.561099 | ||||||||
\(518\) | 2245.55 | 0.190471 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −30753.0 | −2.59348 | ||||||||
\(521\) | 2051.24 | 0.172489 | 0.0862443 | − | 0.996274i | \(-0.472513\pi\) | ||||
0.0862443 | + | 0.996274i | \(0.472513\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −11922.9 | −0.996852 | −0.498426 | − | 0.866932i | \(-0.666088\pi\) | ||||
−0.498426 | + | 0.866932i | \(0.666088\pi\) | |||||||
\(524\) | 28895.1 | 2.40895 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −9194.94 | −0.762203 | ||||||||
\(527\) | −1.75503 | −0.000145067 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −6717.89 | −0.552140 | ||||||||
\(530\) | −8002.16 | −0.655833 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 17510.3 | 1.42700 | ||||||||
\(533\) | −17550.5 | −1.42626 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −8596.24 | −0.694669 | ||||||||
\(536\) | 41681.6 | 3.35890 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 18262.1 | 1.46345 | ||||||||
\(539\) | 3008.17 | 0.240392 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 12876.2 | 1.02327 | 0.511635 | − | 0.859203i | \(-0.329040\pi\) | ||||
0.511635 | + | 0.859203i | \(0.329040\pi\) | |||||||
\(542\) | −43656.7 | −3.45981 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 4376.69 | 0.344943 | ||||||||
\(545\) | −3897.12 | −0.306302 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 9065.39 | 0.708607 | 0.354304 | − | 0.935130i | \(-0.384718\pi\) | ||||
0.354304 | + | 0.935130i | \(0.384718\pi\) | |||||||
\(548\) | 53816.0 | 4.19508 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 1713.87 | 0.132872 | ||||||||
\(551\) | 2311.43 | 0.178712 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 2617.65 | 0.201291 | ||||||||
\(554\) | 37835.7 | 2.90160 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 29262.4 | 2.23202 | ||||||||
\(557\) | 19520.2 | 1.48492 | 0.742458 | − | 0.669893i | \(-0.233660\pi\) | ||||
0.742458 | + | 0.669893i | \(0.233660\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −16377.4 | −1.23916 | ||||||||
\(560\) | −11501.9 | −0.867936 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −10403.5 | −0.780866 | ||||||||
\(563\) | −9786.46 | −0.732593 | −0.366297 | − | 0.930498i | \(-0.619374\pi\) | ||||
−0.366297 | + | 0.930498i | \(0.619374\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −3832.64 | −0.285381 | ||||||||
\(566\) | −11053.1 | −0.820844 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −82281.5 | −6.07826 | ||||||||
\(569\) | −13236.9 | −0.975257 | −0.487628 | − | 0.873051i | \(-0.662138\pi\) | ||||
−0.487628 | + | 0.873051i | \(0.662138\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −21385.2 | −1.56733 | −0.783663 | − | 0.621186i | \(-0.786651\pi\) | ||||
−0.783663 | + | 0.621186i | \(0.786651\pi\) | |||||||
\(572\) | −22827.8 | −1.66867 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −11579.1 | −0.841987 | ||||||||
\(575\) | 1845.45 | 0.133845 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 1531.13 | 0.110471 | 0.0552356 | − | 0.998473i | \(-0.482409\pi\) | ||||
0.0552356 | + | 0.998473i | \(0.482409\pi\) | |||||||
\(578\) | 26405.9 | 1.90024 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −3110.85 | −0.222709 | ||||||||
\(581\) | −10066.7 | −0.718825 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −3725.02 | −0.264622 | ||||||||
\(584\) | −42454.9 | −3.00821 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −9522.25 | −0.671263 | ||||||||
\(587\) | −2742.12 | −0.192810 | −0.0964050 | − | 0.995342i | \(-0.530734\pi\) | ||||
−0.0964050 | + | 0.995342i | \(0.530734\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −20.2971 | −0.00141991 | ||||||||
\(590\) | −5324.83 | −0.371559 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 9077.22 | 0.630188 | ||||||||
\(593\) | 8476.47 | 0.586993 | 0.293497 | − | 0.955960i | \(-0.405181\pi\) | ||||
0.293497 | + | 0.955960i | \(0.405181\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 352.859 | 0.0243123 | ||||||||
\(596\) | −59905.3 | −4.11714 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −33746.2 | −2.30767 | ||||||||
\(599\) | 14839.1 | 1.01220 | 0.506100 | − | 0.862475i | \(-0.331087\pi\) | ||||
0.506100 | + | 0.862475i | \(0.331087\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −13198.6 | −0.895814 | −0.447907 | − | 0.894080i | \(-0.647830\pi\) | ||||
−0.447907 | + | 0.894080i | \(0.647830\pi\) | |||||||
\(602\) | −10805.1 | −0.731532 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 6575.56 | 0.442973 | ||||||||
\(605\) | −5857.19 | −0.393601 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 2310.67 | 0.154509 | 0.0772547 | − | 0.997011i | \(-0.475385\pi\) | ||||
0.0772547 | + | 0.997011i | \(0.475385\pi\) | |||||||
\(608\) | 50616.8 | 3.37629 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −5137.15 | −0.340979 | ||||||||
\(611\) | 43984.4 | 2.91231 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −3944.92 | −0.259925 | −0.129962 | − | 0.991519i | \(-0.541486\pi\) | ||||
−0.129962 | + | 0.991519i | \(0.541486\pi\) | |||||||
\(614\) | −48352.9 | −3.17811 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −9444.80 | −0.617762 | ||||||||
\(617\) | 26587.7 | 1.73482 | 0.867408 | − | 0.497598i | \(-0.165784\pi\) | ||||
0.867408 | + | 0.497598i | \(0.165784\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 8691.35 | 0.564353 | 0.282177 | − | 0.959362i | \(-0.408944\pi\) | ||||
0.282177 | + | 0.959362i | \(0.408944\pi\) | |||||||
\(620\) | 27.3170 | 0.00176948 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −40285.2 | −2.59693 | ||||||||
\(623\) | 6949.26 | 0.446896 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 625.000 | 0.0400000 | ||||||||
\(626\) | 7889.06 | 0.503690 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −39221.5 | −2.49221 | ||||||||
\(629\) | −278.474 | −0.0176526 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −19396.9 | −1.22374 | −0.611869 | − | 0.790959i | \(-0.709582\pi\) | ||||
−0.611869 | + | 0.790959i | \(0.709582\pi\) | |||||||
\(632\) | 18665.7 | 1.17481 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 28239.2 | 1.76896 | ||||||||
\(635\) | −6817.71 | −0.426067 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −20059.8 | −1.24772 | ||||||||
\(638\) | −1988.09 | −0.123369 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −19355.0 | −1.19543 | ||||||||
\(641\) | 11088.7 | 0.683273 | 0.341636 | − | 0.939832i | \(-0.389019\pi\) | ||||
0.341636 | + | 0.939832i | \(0.389019\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −3896.33 | −0.238968 | −0.119484 | − | 0.992836i | \(-0.538124\pi\) | ||||
−0.119484 | + | 0.992836i | \(0.538124\pi\) | |||||||
\(644\) | −16217.1 | −0.992302 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −2981.19 | −0.181569 | ||||||||
\(647\) | −14565.2 | −0.885034 | −0.442517 | − | 0.896760i | \(-0.645914\pi\) | ||||
−0.442517 | + | 0.896760i | \(0.645914\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −2478.72 | −0.149920 | ||||||||
\(650\) | −11428.8 | −0.689655 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 45078.3 | 2.70767 | ||||||||
\(653\) | −27443.4 | −1.64463 | −0.822314 | − | 0.569034i | \(-0.807317\pi\) | ||||
−0.822314 | + | 0.569034i | \(0.807317\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 6734.16 | 0.401718 | ||||||||
\(656\) | −46806.2 | −2.78579 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 29019.0 | 1.71927 | ||||||||
\(659\) | −10355.6 | −0.612135 | −0.306068 | − | 0.952010i | \(-0.599013\pi\) | ||||
−0.306068 | + | 0.952010i | \(0.599013\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 9704.01 | 0.571017 | 0.285508 | − | 0.958376i | \(-0.407838\pi\) | ||||
0.285508 | + | 0.958376i | \(0.407838\pi\) | |||||||
\(662\) | 59617.4 | 3.50015 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −71782.6 | −4.19534 | ||||||||
\(665\) | 4080.85 | 0.237968 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −2140.72 | −0.124272 | ||||||||
\(668\) | −33565.6 | −1.94415 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 15490.2 | 0.893194 | ||||||||
\(671\) | −2391.35 | −0.137582 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 16876.5 | 0.966629 | 0.483315 | − | 0.875447i | \(-0.339433\pi\) | ||||
0.483315 | + | 0.875447i | \(0.339433\pi\) | |||||||
\(674\) | −12456.8 | −0.711898 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 105091. | 5.97924 | ||||||||
\(677\) | 1095.44 | 0.0621880 | 0.0310940 | − | 0.999516i | \(-0.490101\pi\) | ||||
0.0310940 | + | 0.999516i | \(0.490101\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 315.843 | 0.0178512 | ||||||||
\(680\) | 2516.13 | 0.141896 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 17.4578 | 0.000980195 0 | ||||||||
\(683\) | 23004.5 | 1.28879 | 0.644394 | − | 0.764693i | \(-0.277110\pi\) | ||||
0.644394 | + | 0.764693i | \(0.277110\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 12542.1 | 0.699574 | ||||||||
\(686\) | −32296.4 | −1.79750 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −43677.5 | −2.42034 | ||||||||
\(689\) | 24840.0 | 1.37348 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 4973.91 | 0.273830 | 0.136915 | − | 0.990583i | \(-0.456281\pi\) | ||||
0.136915 | + | 0.990583i | \(0.456281\pi\) | |||||||
\(692\) | 57824.0 | 3.17650 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −28834.6 | −1.57716 | ||||||||
\(695\) | 6819.75 | 0.372212 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1435.94 | 0.0780344 | ||||||||
\(698\) | −11321.5 | −0.613933 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −5492.24 | −0.296553 | ||||||||
\(701\) | −19281.6 | −1.03888 | −0.519440 | − | 0.854507i | \(-0.673859\pi\) | ||||
−0.519440 | + | 0.854507i | \(0.673859\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −3220.58 | −0.172783 | ||||||||
\(704\) | −20834.6 | −1.11539 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 29211.0 | 1.55718 | ||||||||
\(707\) | 17917.7 | 0.953132 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 35391.4 | 1.87468 | 0.937342 | − | 0.348412i | \(-0.113279\pi\) | ||||
0.937342 | + | 0.348412i | \(0.113279\pi\) | |||||||
\(710\) | −30578.5 | −1.61632 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 49553.0 | 2.60826 | ||||||||
\(713\) | 18.7981 | 0.000987369 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −5320.14 | −0.278268 | ||||||||
\(716\) | 77324.3 | 4.03596 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −43365.0 | −2.25399 | ||||||||
\(719\) | 19325.0 | 1.00237 | 0.501183 | − | 0.865341i | \(-0.332898\pi\) | ||||
0.501183 | + | 0.865341i | \(0.332898\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −19581.5 | −1.01145 | ||||||||
\(722\) | 2747.19 | 0.141607 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −57032.0 | −2.92759 | ||||||||
\(725\) | −725.000 | −0.0371391 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 16887.9 | 0.861537 | 0.430768 | − | 0.902462i | \(-0.358243\pi\) | ||||
0.430768 | + | 0.902462i | \(0.358243\pi\) | |||||||
\(728\) | 62982.0 | 3.20641 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −15777.6 | −0.799940 | ||||||||
\(731\) | 1339.95 | 0.0677975 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 6698.16 | 0.337520 | 0.168760 | − | 0.985657i | \(-0.446024\pi\) | ||||
0.168760 | + | 0.985657i | \(0.446024\pi\) | |||||||
\(734\) | 2329.35 | 0.117136 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −46878.6 | −2.34778 | ||||||||
\(737\) | 7210.73 | 0.360394 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 4934.50 | 0.245627 | 0.122814 | − | 0.992430i | \(-0.460808\pi\) | ||||
0.122814 | + | 0.992430i | \(0.460808\pi\) | |||||||
\(740\) | 4334.44 | 0.215320 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 16388.4 | 0.810829 | ||||||||
\(743\) | 5140.65 | 0.253825 | 0.126913 | − | 0.991914i | \(-0.459493\pi\) | ||||
0.126913 | + | 0.991914i | \(0.459493\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −13961.2 | −0.686578 | ||||||||
\(746\) | −34032.7 | −1.67027 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 1867.71 | 0.0912971 | ||||||||
\(749\) | 17605.0 | 0.858843 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 9625.37 | 0.467690 | 0.233845 | − | 0.972274i | \(-0.424869\pi\) | ||||
0.233845 | + | 0.972274i | \(0.424869\pi\) | |||||||
\(752\) | 117304. | 5.68834 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 13257.4 | 0.640328 | ||||||||
\(755\) | 1532.47 | 0.0738704 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −5128.83 | −0.246249 | −0.123125 | − | 0.992391i | \(-0.539291\pi\) | ||||
−0.123125 | + | 0.992391i | \(0.539291\pi\) | |||||||
\(758\) | −56534.8 | −2.70902 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 29099.3 | 1.38887 | ||||||||
\(761\) | 25024.7 | 1.19204 | 0.596022 | − | 0.802968i | \(-0.296747\pi\) | ||||
0.596022 | + | 0.802968i | \(0.296747\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 7981.28 | 0.378692 | ||||||||
\(764\) | 3131.05 | 0.148269 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 58446.7 | 2.75687 | ||||||||
\(767\) | 16529.2 | 0.778140 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −26474.8 | −1.24149 | −0.620746 | − | 0.784012i | \(-0.713170\pi\) | ||||
−0.620746 | + | 0.784012i | \(0.713170\pi\) | |||||||
\(770\) | −3509.99 | −0.164274 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 24703.6 | 1.15169 | ||||||||
\(773\) | 24685.1 | 1.14859 | 0.574295 | − | 0.818648i | \(-0.305276\pi\) | ||||
0.574295 | + | 0.818648i | \(0.305276\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 6.36636 | 0.000295079 0 | ||||||||
\(776\) | 2252.18 | 0.104186 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −60359.4 | −2.78148 | ||||||||
\(779\) | 16606.8 | 0.763798 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −14234.3 | −0.652170 | ||||||||
\(782\) | 2761.02 | 0.126258 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −53498.3 | −2.43706 | ||||||||
\(785\) | −9140.76 | −0.415602 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −35383.4 | −1.60265 | −0.801323 | − | 0.598232i | \(-0.795870\pi\) | ||||
−0.801323 | + | 0.598232i | \(0.795870\pi\) | |||||||
\(788\) | −92855.3 | −4.19776 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 6936.77 | 0.312404 | ||||||||
\(791\) | 7849.22 | 0.352827 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 15946.6 | 0.714098 | ||||||||
\(794\) | −61255.0 | −2.73786 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 32883.2 | 1.46421 | ||||||||
\(797\) | 24869.4 | 1.10529 | 0.552647 | − | 0.833415i | \(-0.313618\pi\) | ||||
0.552647 | + | 0.833415i | \(0.313618\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −3598.69 | −0.159340 | ||||||||
\(800\) | −15876.4 | −0.701644 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −83676.1 | −3.68417 | ||||||||
\(803\) | −7344.51 | −0.322767 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −3779.47 | −0.165477 | ||||||||
\(806\) | −116.416 | −0.00508757 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 127765. | 5.56284 | ||||||||
\(809\) | −834.568 | −0.0362693 | −0.0181346 | − | 0.999836i | \(-0.505773\pi\) | ||||
−0.0181346 | + | 0.999836i | \(0.505773\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −17419.5 | −0.754232 | −0.377116 | − | 0.926166i | \(-0.623084\pi\) | ||||
−0.377116 | + | 0.926166i | \(0.623084\pi\) | |||||||
\(812\) | 6371.00 | 0.275343 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 2770.06 | 0.119276 | ||||||||
\(815\) | 10505.7 | 0.451533 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 15496.7 | 0.663600 | ||||||||
\(818\) | −75163.8 | −3.21276 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −22350.3 | −0.951837 | ||||||||
\(821\) | −20163.7 | −0.857148 | −0.428574 | − | 0.903507i | \(-0.640984\pi\) | ||||
−0.428574 | + | 0.903507i | \(0.640984\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 10456.9 | 0.442898 | 0.221449 | − | 0.975172i | \(-0.428921\pi\) | ||||
0.221449 | + | 0.975172i | \(0.428921\pi\) | |||||||
\(824\) | −139629. | −5.90318 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 10905.2 | 0.459371 | ||||||||
\(827\) | 10943.6 | 0.460154 | 0.230077 | − | 0.973172i | \(-0.426102\pi\) | ||||
0.230077 | + | 0.973172i | \(0.426102\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −33775.8 | −1.41506 | −0.707528 | − | 0.706685i | \(-0.750190\pi\) | ||||
−0.707528 | + | 0.706685i | \(0.750190\pi\) | |||||||
\(830\) | −26676.7 | −1.11562 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 138934. | 5.78926 | ||||||||
\(833\) | 1641.24 | 0.0682660 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −7822.63 | −0.324207 | ||||||||
\(836\) | 21600.3 | 0.893613 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −15159.9 | −0.624927 | ||||||||
\(839\) | −39087.3 | −1.60840 | −0.804198 | − | 0.594361i | \(-0.797405\pi\) | ||||
−0.804198 | + | 0.594361i | \(0.797405\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 841.000 | 0.0344828 | ||||||||
\(842\) | 19775.4 | 0.809391 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 114681. | 4.67711 | ||||||||
\(845\) | 24492.0 | 0.997101 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 11995.5 | 0.486623 | ||||||||
\(848\) | 66246.9 | 2.68270 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 935.076 | 0.0377327 | ||||||||
\(851\) | 2982.73 | 0.120149 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 47274.9 | 1.89761 | 0.948806 | − | 0.315859i | \(-0.102293\pi\) | ||||
0.948806 | + | 0.315859i | \(0.102293\pi\) | |||||||
\(854\) | 10520.9 | 0.421565 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 125536. | 5.01254 | ||||||||
\(857\) | −15482.0 | −0.617099 | −0.308550 | − | 0.951208i | \(-0.599844\pi\) | ||||
−0.308550 | + | 0.951208i | \(0.599844\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −32719.1 | −1.29960 | −0.649802 | − | 0.760103i | \(-0.725148\pi\) | ||||
−0.649802 | + | 0.760103i | \(0.725148\pi\) | |||||||
\(860\) | −20856.3 | −0.826971 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 31662.2 | 1.25107 | ||||||||
\(863\) | 1741.34 | 0.0686858 | 0.0343429 | − | 0.999410i | \(-0.489066\pi\) | ||||
0.0343429 | + | 0.999410i | \(0.489066\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 13476.2 | 0.529715 | ||||||||
\(866\) | −42978.6 | −1.68646 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −55.9449 | −0.00218767 | ||||||||
\(869\) | 3229.08 | 0.126052 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −48084.3 | −1.87058 | ||||||||
\(872\) | 56912.0 | 2.21019 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 31931.5 | 1.23581 | ||||||||
\(875\) | −1280.00 | −0.0494534 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 11848.6 | 0.456213 | 0.228106 | − | 0.973636i | \(-0.426747\pi\) | ||||
0.228106 | + | 0.973636i | \(0.426747\pi\) | |||||||
\(878\) | −63476.4 | −2.43989 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −14188.5 | −0.543516 | ||||||||
\(881\) | 29332.3 | 1.12171 | 0.560857 | − | 0.827913i | \(-0.310472\pi\) | ||||
0.560857 | + | 0.827913i | \(0.310472\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −25723.3 | −0.980360 | −0.490180 | − | 0.871621i | \(-0.663069\pi\) | ||||
−0.490180 | + | 0.871621i | \(0.663069\pi\) | |||||||
\(884\) | −12454.7 | −0.473865 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −15121.0 | −0.573362 | ||||||||
\(887\) | −10959.8 | −0.414875 | −0.207437 | − | 0.978248i | \(-0.566512\pi\) | ||||
−0.207437 | + | 0.978248i | \(0.566512\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 13962.6 | 0.526762 | ||||||||
\(890\) | 18415.5 | 0.693583 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 81162.1 | 3.04653 | ||||||||
\(893\) | −41619.2 | −1.55961 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 18020.8 | 0.673039 | ||||||||
\(896\) | 39638.8 | 1.47795 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 59773.6 | 2.22124 | ||||||||
\(899\) | −7.38497 | −0.000273974 0 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −2032.34 | −0.0751467 | ||||||||
\(902\) | −14283.7 | −0.527266 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 55970.3 | 2.05923 | ||||||||
\(905\) | −13291.6 | −0.488207 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −3053.42 | −0.111783 | −0.0558915 | − | 0.998437i | \(-0.517800\pi\) | ||||
−0.0558915 | + | 0.998437i | \(0.517800\pi\) | |||||||
\(908\) | 93292.4 | 3.40971 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 23406.2 | 0.852644 | ||||||||
\(911\) | 32880.5 | 1.19581 | 0.597903 | − | 0.801568i | \(-0.296001\pi\) | ||||
0.597903 | + | 0.801568i | \(0.296001\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −12418.1 | −0.450140 | ||||||||
\(914\) | −69323.8 | −2.50878 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −65835.7 | −2.37475 | ||||||||
\(917\) | −13791.5 | −0.496658 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −49962.9 | −1.79339 | −0.896694 | − | 0.442650i | \(-0.854038\pi\) | ||||
−0.896694 | + | 0.442650i | \(0.854038\pi\) | |||||||
\(920\) | −26950.2 | −0.965786 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −72416.8 | −2.58668 | ||||||||
\(923\) | 94920.7 | 3.38500 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1010.16 | 0.0359070 | ||||||||
\(926\) | −93702.3 | −3.32532 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 18416.6 | 0.651460 | ||||||||
\(929\) | 48163.6 | 1.70096 | 0.850482 | − | 0.526004i | \(-0.176310\pi\) | ||||
0.850482 | + | 0.526004i | \(0.176310\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 18981.1 | 0.668185 | ||||||||
\(932\) | 5914.83 | 0.207883 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −86925.3 | −3.04527 | ||||||||
\(935\) | 435.279 | 0.0152248 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 32244.1 | 1.12419 | 0.562097 | − | 0.827071i | \(-0.309995\pi\) | ||||
0.562097 | + | 0.827071i | \(0.309995\pi\) | |||||||
\(938\) | −31723.9 | −1.10429 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 56013.4 | 1.94357 | ||||||||
\(941\) | −37391.5 | −1.29535 | −0.647677 | − | 0.761915i | \(-0.724260\pi\) | ||||
−0.647677 | + | 0.761915i | \(0.724260\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −15380.3 | −0.531125 | ||||||||
\(944\) | 44082.3 | 1.51987 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −13328.9 | −0.458097 | ||||||||
\(947\) | −17887.8 | −0.613807 | −0.306903 | − | 0.951741i | \(-0.599293\pi\) | ||||
−0.306903 | + | 0.951741i | \(0.599293\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 48976.4 | 1.67528 | ||||||||
\(950\) | 10814.2 | 0.369327 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −5153.02 | −0.175431 | ||||||||
\(953\) | −20302.3 | −0.690090 | −0.345045 | − | 0.938586i | \(-0.612136\pi\) | ||||
−0.345045 | + | 0.938586i | \(0.612136\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 729.708 | 0.0247254 | ||||||||
\(956\) | −67213.0 | −2.27387 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −31732.7 | −1.07018 | ||||||||
\(959\) | −25686.1 | −0.864908 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −29790.9 | −0.999998 | ||||||||
\(962\) | −18472.0 | −0.619085 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 122280. | 4.08546 | ||||||||
\(965\) | 5757.31 | 0.192056 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −19313.4 | −0.642273 | −0.321137 | − | 0.947033i | \(-0.604065\pi\) | ||||
−0.321137 | + | 0.947033i | \(0.604065\pi\) | |||||||
\(968\) | 85536.0 | 2.84012 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 836.983 | 0.0277050 | ||||||||
\(971\) | 25297.3 | 0.836077 | 0.418038 | − | 0.908429i | \(-0.362718\pi\) | ||||
0.418038 | + | 0.908429i | \(0.362718\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −13966.8 | −0.460179 | ||||||||
\(974\) | 1859.68 | 0.0611787 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 42528.6 | 1.39478 | ||||||||
\(977\) | −21461.4 | −0.702776 | −0.351388 | − | 0.936230i | \(-0.614290\pi\) | ||||
−0.351388 | + | 0.936230i | \(0.614290\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 8572.45 | 0.279854 | ||||||||
\(980\) | −25545.8 | −0.832684 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −9082.24 | −0.295138 | ||||||||
\(983\) | −14059.8 | −0.456193 | −0.228096 | − | 0.973639i | \(-0.573250\pi\) | ||||
−0.228096 | + | 0.973639i | \(0.573250\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −21640.4 | −0.700021 | ||||||||
\(986\) | −1084.69 | −0.0350340 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −144040. | −4.63818 | ||||||||
\(989\) | −14352.2 | −0.461450 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −60932.3 | −1.95316 | −0.976578 | − | 0.215162i | \(-0.930972\pi\) | ||||
−0.976578 | + | 0.215162i | \(0.930972\pi\) | |||||||
\(992\) | −161.720 | −0.00517601 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 62624.5 | 1.99832 | ||||||||
\(995\) | 7663.60 | 0.244173 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −4183.32 | −0.132886 | −0.0664428 | − | 0.997790i | \(-0.521165\pi\) | ||||
−0.0664428 | + | 0.997790i | \(0.521165\pi\) | |||||||
\(998\) | −59254.7 | −1.87943 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1305.4.a.h.1.1 | 6 | ||
3.2 | odd | 2 | 435.4.a.h.1.6 | ✓ | 6 | ||
15.14 | odd | 2 | 2175.4.a.k.1.1 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
435.4.a.h.1.6 | ✓ | 6 | 3.2 | odd | 2 | ||
1305.4.a.h.1.1 | 6 | 1.1 | even | 1 | trivial | ||
2175.4.a.k.1.1 | 6 | 15.14 | odd | 2 |