Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [5625,2,Mod(1,5625)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5625, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("5625.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 5625 = 3^{2} \cdot 5^{4} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 5625.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: | \(44.9158511370\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.8.46980000000.2 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 15x^{6} + 80x^{4} - 180x^{2} + 145 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.8 | ||
Root | \(2.44055\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 5625.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.44055 | 1.72573 | 0.862866 | − | 0.505434i | \(-0.168667\pi\) | ||||
0.862866 | + | 0.505434i | \(0.168667\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 3.95630 | 1.97815 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.591023 | 0.223386 | 0.111693 | − | 0.993743i | \(-0.464373\pi\) | ||||
0.111693 | + | 0.993743i | \(0.464373\pi\) | |||||||
\(8\) | 4.77444 | 1.68802 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.26423 | 1.28571 | 0.642856 | − | 0.765987i | \(-0.277749\pi\) | ||||
0.642856 | + | 0.765987i | \(0.277749\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 5.06316 | 1.40427 | 0.702134 | − | 0.712045i | \(-0.252231\pi\) | ||||
0.702134 | + | 0.712045i | \(0.252231\pi\) | |||||||
\(14\) | 1.44242 | 0.385504 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 3.73968 | 0.934920 | ||||||||
\(17\) | 5.39132 | 1.30759 | 0.653793 | − | 0.756673i | \(-0.273177\pi\) | ||||
0.653793 | + | 0.756673i | \(0.273177\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −5.73968 | −1.31677 | −0.658387 | − | 0.752680i | \(-0.728761\pi\) | ||||
−0.658387 | + | 0.752680i | \(0.728761\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 10.4071 | 2.21879 | ||||||||
\(23\) | −2.12522 | −0.443140 | −0.221570 | − | 0.975145i | \(-0.571118\pi\) | ||||
−0.221570 | + | 0.975145i | \(0.571118\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 12.3569 | 2.42339 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 2.33826 | 0.441890 | ||||||||
\(29\) | 9.48296 | 1.76094 | 0.880471 | − | 0.474101i | \(-0.157227\pi\) | ||||
0.880471 | + | 0.474101i | \(0.157227\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.38761 | −0.249223 | −0.124611 | − | 0.992206i | \(-0.539768\pi\) | ||||
−0.124611 | + | 0.992206i | \(0.539768\pi\) | |||||||
\(32\) | −0.421994 | −0.0745986 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 13.1578 | 2.25654 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −11.3502 | −1.86595 | −0.932977 | − | 0.359935i | \(-0.882799\pi\) | ||||
−0.932977 | + | 0.359935i | \(0.882799\pi\) | |||||||
\(38\) | −14.0080 | −2.27240 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −0.403551 | −0.0630240 | −0.0315120 | − | 0.999503i | \(-0.510032\pi\) | ||||
−0.0315120 | + | 0.999503i | \(0.510032\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5.30211 | 0.808565 | 0.404282 | − | 0.914634i | \(-0.367521\pi\) | ||||
0.404282 | + | 0.914634i | \(0.367521\pi\) | |||||||
\(44\) | 16.8705 | 2.54333 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −5.18672 | −0.764740 | ||||||||
\(47\) | −8.60289 | −1.25486 | −0.627430 | − | 0.778673i | \(-0.715893\pi\) | ||||
−0.627430 | + | 0.778673i | \(0.715893\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.65069 | −0.950099 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 20.0314 | 2.77785 | ||||||||
\(53\) | −0.337629 | −0.0463769 | −0.0231884 | − | 0.999731i | \(-0.507382\pi\) | ||||
−0.0231884 | + | 0.999731i | \(0.507382\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 2.82180 | 0.377079 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 23.1437 | 3.03891 | ||||||||
\(59\) | −2.73744 | −0.356384 | −0.178192 | − | 0.983996i | \(-0.557025\pi\) | ||||
−0.178192 | + | 0.983996i | \(0.557025\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 9.01478 | 1.15422 | 0.577112 | − | 0.816665i | \(-0.304179\pi\) | ||||
0.577112 | + | 0.816665i | \(0.304179\pi\) | |||||||
\(62\) | −3.38654 | −0.430091 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −8.50926 | −1.06366 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −5.86133 | −0.716075 | −0.358038 | − | 0.933707i | \(-0.616554\pi\) | ||||
−0.358038 | + | 0.933707i | \(0.616554\pi\) | |||||||
\(68\) | 21.3296 | 2.58660 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 10.7281 | 1.27319 | 0.636596 | − | 0.771197i | \(-0.280342\pi\) | ||||
0.636596 | + | 0.771197i | \(0.280342\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 5.02136 | 0.587706 | 0.293853 | − | 0.955851i | \(-0.405062\pi\) | ||||
0.293853 | + | 0.955851i | \(0.405062\pi\) | |||||||
\(74\) | −27.7007 | −3.22014 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −22.7079 | −2.60477 | ||||||||
\(77\) | 2.52026 | 0.287210 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 8.44321 | 0.949936 | 0.474968 | − | 0.880003i | \(-0.342460\pi\) | ||||
0.474968 | + | 0.880003i | \(0.342460\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −0.984886 | −0.108762 | ||||||||
\(83\) | 11.0136 | 1.20890 | 0.604450 | − | 0.796643i | \(-0.293393\pi\) | ||||
0.604450 | + | 0.796643i | \(0.293393\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 12.9401 | 1.39537 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 20.3593 | 2.17031 | ||||||||
\(89\) | −13.1464 | −1.39351 | −0.696756 | − | 0.717308i | \(-0.745374\pi\) | ||||
−0.696756 | + | 0.717308i | \(0.745374\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.99244 | 0.313693 | ||||||||
\(92\) | −8.40801 | −0.876595 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −20.9958 | −2.16555 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 7.24927 | 0.736052 | 0.368026 | − | 0.929815i | \(-0.380034\pi\) | ||||
0.368026 | + | 0.929815i | \(0.380034\pi\) | |||||||
\(98\) | −16.2314 | −1.63962 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −10.2203 | −1.01696 | −0.508478 | − | 0.861075i | \(-0.669792\pi\) | ||||
−0.508478 | + | 0.861075i | \(0.669792\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 11.6781 | 1.15068 | 0.575339 | − | 0.817915i | \(-0.304870\pi\) | ||||
0.575339 | + | 0.817915i | \(0.304870\pi\) | |||||||
\(104\) | 24.1738 | 2.37043 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −0.824000 | −0.0800340 | ||||||||
\(107\) | −1.07495 | −0.103920 | −0.0519598 | − | 0.998649i | \(-0.516547\pi\) | ||||
−0.0519598 | + | 0.998649i | \(0.516547\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −0.279773 | −0.0267974 | −0.0133987 | − | 0.999910i | \(-0.504265\pi\) | ||||
−0.0133987 | + | 0.999910i | \(0.504265\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 2.21024 | 0.208848 | ||||||||
\(113\) | −13.6813 | −1.28703 | −0.643513 | − | 0.765436i | \(-0.722524\pi\) | ||||
−0.643513 | + | 0.765436i | \(0.722524\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 37.5174 | 3.48340 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −6.68086 | −0.615023 | ||||||||
\(119\) | 3.18639 | 0.292096 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 7.18363 | 0.653057 | ||||||||
\(122\) | 22.0011 | 1.99188 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −5.48981 | −0.492999 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 14.9264 | 1.32450 | 0.662252 | − | 0.749281i | \(-0.269601\pi\) | ||||
0.662252 | + | 0.749281i | \(0.269601\pi\) | |||||||
\(128\) | −19.9233 | −1.76099 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 20.2324 | 1.76771 | 0.883856 | − | 0.467758i | \(-0.154938\pi\) | ||||
0.883856 | + | 0.467758i | \(0.154938\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −3.39228 | −0.294148 | ||||||||
\(134\) | −14.3049 | −1.23575 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 25.7405 | 2.20723 | ||||||||
\(137\) | 8.00831 | 0.684196 | 0.342098 | − | 0.939664i | \(-0.388862\pi\) | ||||
0.342098 | + | 0.939664i | \(0.388862\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 10.0009 | 0.848261 | 0.424131 | − | 0.905601i | \(-0.360580\pi\) | ||||
0.424131 | + | 0.905601i | \(0.360580\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 26.1825 | 2.19719 | ||||||||
\(143\) | 21.5905 | 1.80548 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 12.2549 | 1.01422 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −44.9046 | −3.69113 | ||||||||
\(149\) | −20.2500 | −1.65895 | −0.829474 | − | 0.558546i | \(-0.811360\pi\) | ||||
−0.829474 | + | 0.558546i | \(0.811360\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −0.0600683 | −0.00488829 | −0.00244414 | − | 0.999997i | \(-0.500778\pi\) | ||||
−0.00244414 | + | 0.999997i | \(0.500778\pi\) | |||||||
\(152\) | −27.4038 | −2.22274 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 6.15082 | 0.495647 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 3.69886 | 0.295201 | 0.147601 | − | 0.989047i | \(-0.452845\pi\) | ||||
0.147601 | + | 0.989047i | \(0.452845\pi\) | |||||||
\(158\) | 20.6061 | 1.63933 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1.25606 | −0.0989910 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 4.88965 | 0.382987 | 0.191493 | − | 0.981494i | \(-0.438667\pi\) | ||||
0.191493 | + | 0.981494i | \(0.438667\pi\) | |||||||
\(164\) | −1.59656 | −0.124671 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 26.8793 | 2.08624 | ||||||||
\(167\) | −16.3419 | −1.26457 | −0.632286 | − | 0.774735i | \(-0.717883\pi\) | ||||
−0.632286 | + | 0.774735i | \(0.717883\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 12.6356 | 0.971968 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 20.9767 | 1.59946 | ||||||||
\(173\) | 11.1117 | 0.844811 | 0.422405 | − | 0.906407i | \(-0.361186\pi\) | ||||
0.422405 | + | 0.906407i | \(0.361186\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 15.9468 | 1.20204 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −32.0844 | −2.40483 | ||||||||
\(179\) | −18.0527 | −1.34932 | −0.674659 | − | 0.738129i | \(-0.735709\pi\) | ||||
−0.674659 | + | 0.738129i | \(0.735709\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −3.11291 | −0.231381 | −0.115690 | − | 0.993285i | \(-0.536908\pi\) | ||||
−0.115690 | + | 0.993285i | \(0.536908\pi\) | |||||||
\(182\) | 7.30321 | 0.541350 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −10.1467 | −0.748028 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 22.9898 | 1.68118 | ||||||||
\(188\) | −34.0356 | −2.48230 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −15.0422 | −1.08842 | −0.544208 | − | 0.838950i | \(-0.683170\pi\) | ||||
−0.544208 | + | 0.838950i | \(0.683170\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −5.39017 | −0.387993 | −0.193996 | − | 0.981002i | \(-0.562145\pi\) | ||||
−0.193996 | + | 0.981002i | \(0.562145\pi\) | |||||||
\(194\) | 17.6922 | 1.27023 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −26.3121 | −1.87944 | ||||||||
\(197\) | −12.5879 | −0.896848 | −0.448424 | − | 0.893821i | \(-0.648015\pi\) | ||||
−0.448424 | + | 0.893821i | \(0.648015\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 16.6365 | 1.17933 | 0.589666 | − | 0.807648i | \(-0.299260\pi\) | ||||
0.589666 | + | 0.807648i | \(0.299260\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −24.9431 | −1.75499 | ||||||||
\(203\) | 5.60465 | 0.393369 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 28.5010 | 1.98576 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 18.9346 | 1.31288 | ||||||||
\(209\) | −24.4753 | −1.69299 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −23.3539 | −1.60775 | −0.803874 | − | 0.594799i | \(-0.797232\pi\) | ||||
−0.803874 | + | 0.594799i | \(0.797232\pi\) | |||||||
\(212\) | −1.33576 | −0.0917403 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −2.62348 | −0.179337 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −0.820111 | −0.0556728 | ||||||||
\(218\) | −0.682800 | −0.0462451 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 27.2971 | 1.83620 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0.829977 | 0.0555794 | 0.0277897 | − | 0.999614i | \(-0.491153\pi\) | ||||
0.0277897 | + | 0.999614i | \(0.491153\pi\) | |||||||
\(224\) | −0.249408 | −0.0166643 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −33.3898 | −2.22106 | ||||||||
\(227\) | 22.7061 | 1.50706 | 0.753530 | − | 0.657413i | \(-0.228349\pi\) | ||||
0.753530 | + | 0.657413i | \(0.228349\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −27.7726 | −1.83527 | −0.917633 | − | 0.397429i | \(-0.869903\pi\) | ||||
−0.917633 | + | 0.397429i | \(0.869903\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 45.2758 | 2.97250 | ||||||||
\(233\) | 1.14087 | 0.0747411 | 0.0373706 | − | 0.999301i | \(-0.488102\pi\) | ||||
0.0373706 | + | 0.999301i | \(0.488102\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −10.8301 | −0.704981 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 7.77656 | 0.504079 | ||||||||
\(239\) | −7.82335 | −0.506051 | −0.253025 | − | 0.967460i | \(-0.581426\pi\) | ||||
−0.253025 | + | 0.967460i | \(0.581426\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −0.865353 | −0.0557423 | −0.0278711 | − | 0.999612i | \(-0.508873\pi\) | ||||
−0.0278711 | + | 0.999612i | \(0.508873\pi\) | |||||||
\(242\) | 17.5320 | 1.12700 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 35.6651 | 2.28323 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −29.0609 | −1.84910 | ||||||||
\(248\) | −6.62508 | −0.420693 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 6.09930 | 0.384984 | 0.192492 | − | 0.981299i | \(-0.438343\pi\) | ||||
0.192492 | + | 0.981299i | \(0.438343\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −9.06243 | −0.569750 | ||||||||
\(254\) | 36.4287 | 2.28574 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −31.6054 | −1.97533 | ||||||||
\(257\) | −18.2063 | −1.13568 | −0.567839 | − | 0.823140i | \(-0.692220\pi\) | ||||
−0.567839 | + | 0.823140i | \(0.692220\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −6.70820 | −0.416828 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 49.3782 | 3.05060 | ||||||||
\(263\) | 11.7262 | 0.723071 | 0.361536 | − | 0.932358i | \(-0.382253\pi\) | ||||
0.361536 | + | 0.932358i | \(0.382253\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −8.27904 | −0.507621 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −23.1891 | −1.41650 | ||||||||
\(269\) | −12.0486 | −0.734617 | −0.367309 | − | 0.930099i | \(-0.619721\pi\) | ||||
−0.367309 | + | 0.930099i | \(0.619721\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −19.0195 | −1.15535 | −0.577675 | − | 0.816267i | \(-0.696040\pi\) | ||||
−0.577675 | + | 0.816267i | \(0.696040\pi\) | |||||||
\(272\) | 20.1618 | 1.22249 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 19.5447 | 1.18074 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −7.22640 | −0.434192 | −0.217096 | − | 0.976150i | \(-0.569658\pi\) | ||||
−0.217096 | + | 0.976150i | \(0.569658\pi\) | |||||||
\(278\) | 24.4076 | 1.46387 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −19.2675 | −1.14940 | −0.574700 | − | 0.818364i | \(-0.694881\pi\) | ||||
−0.574700 | + | 0.818364i | \(0.694881\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 23.2436 | 1.38169 | 0.690843 | − | 0.723004i | \(-0.257239\pi\) | ||||
0.690843 | + | 0.723004i | \(0.257239\pi\) | |||||||
\(284\) | 42.4436 | 2.51856 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 52.6926 | 3.11578 | ||||||||
\(287\) | −0.238508 | −0.0140787 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 12.0663 | 0.709783 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 19.8660 | 1.16257 | ||||||||
\(293\) | −16.9450 | −0.989936 | −0.494968 | − | 0.868911i | \(-0.664820\pi\) | ||||
−0.494968 | + | 0.868911i | \(0.664820\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −54.1907 | −3.14977 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −49.4213 | −2.86290 | ||||||||
\(299\) | −10.7603 | −0.622286 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 3.13367 | 0.180622 | ||||||||
\(302\) | −0.146600 | −0.00843587 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −21.4646 | −1.23108 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 7.48318 | 0.427088 | 0.213544 | − | 0.976933i | \(-0.431499\pi\) | ||||
0.213544 | + | 0.976933i | \(0.431499\pi\) | |||||||
\(308\) | 9.97087 | 0.568143 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 29.3081 | 1.66191 | 0.830955 | − | 0.556339i | \(-0.187794\pi\) | ||||
0.830955 | + | 0.556339i | \(0.187794\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −20.6261 | −1.16585 | −0.582927 | − | 0.812524i | \(-0.698093\pi\) | ||||
−0.582927 | + | 0.812524i | \(0.698093\pi\) | |||||||
\(314\) | 9.02727 | 0.509438 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 33.4039 | 1.87911 | ||||||||
\(317\) | 29.7154 | 1.66898 | 0.834490 | − | 0.551023i | \(-0.185762\pi\) | ||||
0.834490 | + | 0.551023i | \(0.185762\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 40.4375 | 2.26406 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −3.06547 | −0.170832 | ||||||||
\(323\) | −30.9445 | −1.72180 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 11.9334 | 0.660932 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −1.92673 | −0.106386 | ||||||||
\(329\) | −5.08451 | −0.280318 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 33.8462 | 1.86036 | 0.930178 | − | 0.367109i | \(-0.119652\pi\) | ||||
0.930178 | + | 0.367109i | \(0.119652\pi\) | |||||||
\(332\) | 43.5731 | 2.39138 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −39.8832 | −2.18231 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −5.39168 | −0.293704 | −0.146852 | − | 0.989159i | \(-0.546914\pi\) | ||||
−0.146852 | + | 0.989159i | \(0.546914\pi\) | |||||||
\(338\) | 30.8378 | 1.67735 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −5.91710 | −0.320429 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −8.06787 | −0.435624 | ||||||||
\(344\) | 25.3146 | 1.36487 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 27.1188 | 1.45792 | ||||||||
\(347\) | −20.1190 | −1.08004 | −0.540022 | − | 0.841651i | \(-0.681584\pi\) | ||||
−0.540022 | + | 0.841651i | \(0.681584\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −15.9106 | −0.851672 | −0.425836 | − | 0.904800i | \(-0.640020\pi\) | ||||
−0.425836 | + | 0.904800i | \(0.640020\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −1.79948 | −0.0959124 | ||||||||
\(353\) | −7.21261 | −0.383888 | −0.191944 | − | 0.981406i | \(-0.561479\pi\) | ||||
−0.191944 | + | 0.981406i | \(0.561479\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −52.0109 | −2.75657 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −44.0584 | −2.32856 | ||||||||
\(359\) | 3.37048 | 0.177887 | 0.0889436 | − | 0.996037i | \(-0.471651\pi\) | ||||
0.0889436 | + | 0.996037i | \(0.471651\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 13.9439 | 0.733892 | ||||||||
\(362\) | −7.59722 | −0.399301 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 11.8390 | 0.620532 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −5.37420 | −0.280531 | −0.140266 | − | 0.990114i | \(-0.544796\pi\) | ||||
−0.140266 | + | 0.990114i | \(0.544796\pi\) | |||||||
\(368\) | −7.94765 | −0.414300 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −0.199546 | −0.0103599 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −16.0783 | −0.832505 | −0.416252 | − | 0.909249i | \(-0.636657\pi\) | ||||
−0.416252 | + | 0.909249i | \(0.636657\pi\) | |||||||
\(374\) | 56.1078 | 2.90127 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −41.0740 | −2.11823 | ||||||||
\(377\) | 48.0137 | 2.47283 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −27.6162 | −1.41855 | −0.709274 | − | 0.704933i | \(-0.750977\pi\) | ||||
−0.709274 | + | 0.704933i | \(0.750977\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −36.7113 | −1.87831 | ||||||||
\(383\) | −23.2577 | −1.18841 | −0.594207 | − | 0.804312i | \(-0.702534\pi\) | ||||
−0.594207 | + | 0.804312i | \(0.702534\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −13.1550 | −0.669571 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 28.6803 | 1.45602 | ||||||||
\(389\) | 12.8126 | 0.649624 | 0.324812 | − | 0.945779i | \(-0.394699\pi\) | ||||
0.324812 | + | 0.945779i | \(0.394699\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −11.4578 | −0.579443 | ||||||||
\(392\) | −31.7533 | −1.60379 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −30.7214 | −1.54772 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −10.8608 | −0.545085 | −0.272543 | − | 0.962144i | \(-0.587865\pi\) | ||||
−0.272543 | + | 0.962144i | \(0.587865\pi\) | |||||||
\(398\) | 40.6023 | 2.03521 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −23.0220 | −1.14966 | −0.574831 | − | 0.818272i | \(-0.694932\pi\) | ||||
−0.574831 | + | 0.818272i | \(0.694932\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −7.02570 | −0.349975 | ||||||||
\(404\) | −40.4345 | −2.01169 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 13.6784 | 0.678849 | ||||||||
\(407\) | −48.3996 | −2.39908 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −20.3469 | −1.00609 | −0.503044 | − | 0.864261i | \(-0.667787\pi\) | ||||
−0.503044 | + | 0.864261i | \(0.667787\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 46.2020 | 2.27621 | ||||||||
\(413\) | −1.61789 | −0.0796111 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −2.13662 | −0.104756 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −59.7332 | −2.92165 | ||||||||
\(419\) | −21.6227 | −1.05634 | −0.528169 | − | 0.849140i | \(-0.677121\pi\) | ||||
−0.528169 | + | 0.849140i | \(0.677121\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −5.15561 | −0.251269 | −0.125635 | − | 0.992077i | \(-0.540097\pi\) | ||||
−0.125635 | + | 0.992077i | \(0.540097\pi\) | |||||||
\(422\) | −56.9964 | −2.77454 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −1.61199 | −0.0782850 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 5.32794 | 0.257837 | ||||||||
\(428\) | −4.25283 | −0.205568 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 1.21065 | 0.0583150 | 0.0291575 | − | 0.999575i | \(-0.490718\pi\) | ||||
0.0291575 | + | 0.999575i | \(0.490718\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −0.0648649 | −0.00311721 | −0.00155860 | − | 0.999999i | \(-0.500496\pi\) | ||||
−0.00155860 | + | 0.999999i | \(0.500496\pi\) | |||||||
\(434\) | −2.00152 | −0.0960762 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −1.10686 | −0.0530092 | ||||||||
\(437\) | 12.1981 | 0.583514 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −11.7704 | −0.561770 | −0.280885 | − | 0.959741i | \(-0.590628\pi\) | ||||
−0.280885 | + | 0.959741i | \(0.590628\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 66.6200 | 3.16879 | ||||||||
\(443\) | −19.1683 | −0.910716 | −0.455358 | − | 0.890309i | \(-0.650489\pi\) | ||||
−0.455358 | + | 0.890309i | \(0.650489\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 2.02560 | 0.0959151 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −5.02917 | −0.237606 | ||||||||
\(449\) | 0.536369 | 0.0253128 | 0.0126564 | − | 0.999920i | \(-0.495971\pi\) | ||||
0.0126564 | + | 0.999920i | \(0.495971\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.72083 | −0.0810308 | ||||||||
\(452\) | −54.1271 | −2.54593 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 55.4155 | 2.60078 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 35.1952 | 1.64636 | 0.823181 | − | 0.567779i | \(-0.192197\pi\) | ||||
0.823181 | + | 0.567779i | \(0.192197\pi\) | |||||||
\(458\) | −67.7805 | −3.16718 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −1.79752 | −0.0837188 | −0.0418594 | − | 0.999124i | \(-0.513328\pi\) | ||||
−0.0418594 | + | 0.999124i | \(0.513328\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 15.8682 | 0.737460 | 0.368730 | − | 0.929537i | \(-0.379793\pi\) | ||||
0.368730 | + | 0.929537i | \(0.379793\pi\) | |||||||
\(464\) | 35.4632 | 1.64634 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 2.78436 | 0.128983 | ||||||||
\(467\) | 41.1577 | 1.90455 | 0.952275 | − | 0.305240i | \(-0.0987368\pi\) | ||||
0.952275 | + | 0.305240i | \(0.0987368\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −3.46418 | −0.159961 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −13.0697 | −0.601584 | ||||||||
\(473\) | 22.6094 | 1.03958 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 12.6063 | 0.577809 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −19.0933 | −0.873307 | ||||||||
\(479\) | −15.1052 | −0.690176 | −0.345088 | − | 0.938570i | \(-0.612151\pi\) | ||||
−0.345088 | + | 0.938570i | \(0.612151\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −57.4677 | −2.62030 | ||||||||
\(482\) | −2.11194 | −0.0961962 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 28.4205 | 1.29184 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −4.90873 | −0.222436 | −0.111218 | − | 0.993796i | \(-0.535475\pi\) | ||||
−0.111218 | + | 0.993796i | \(0.535475\pi\) | |||||||
\(488\) | 43.0405 | 1.94835 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −43.7750 | −1.97554 | −0.987769 | − | 0.155925i | \(-0.950164\pi\) | ||||
−0.987769 | + | 0.155925i | \(0.950164\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 51.1257 | 2.30258 | ||||||||
\(494\) | −70.9247 | −3.19105 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −5.18923 | −0.233003 | ||||||||
\(497\) | 6.34056 | 0.284413 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 6.00199 | 0.268686 | 0.134343 | − | 0.990935i | \(-0.457108\pi\) | ||||
0.134343 | + | 0.990935i | \(0.457108\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 14.8857 | 0.664379 | ||||||||
\(503\) | −28.8130 | −1.28471 | −0.642354 | − | 0.766408i | \(-0.722042\pi\) | ||||
−0.642354 | + | 0.766408i | \(0.722042\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −22.1173 | −0.983235 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 59.0532 | 2.62006 | ||||||||
\(509\) | 12.3745 | 0.548492 | 0.274246 | − | 0.961660i | \(-0.411572\pi\) | ||||
0.274246 | + | 0.961660i | \(0.411572\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 2.96774 | 0.131285 | ||||||||
\(512\) | −37.2879 | −1.64791 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −44.4334 | −1.95987 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −36.6847 | −1.61339 | ||||||||
\(518\) | −16.3717 | −0.719332 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 16.0357 | 0.702535 | 0.351268 | − | 0.936275i | \(-0.385751\pi\) | ||||
0.351268 | + | 0.936275i | \(0.385751\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 34.7701 | 1.52039 | 0.760195 | − | 0.649695i | \(-0.225103\pi\) | ||||
0.760195 | + | 0.649695i | \(0.225103\pi\) | |||||||
\(524\) | 80.0453 | 3.49680 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 28.6185 | 1.24783 | ||||||||
\(527\) | −7.48106 | −0.325880 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −18.4834 | −0.803627 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −13.4209 | −0.581869 | ||||||||
\(533\) | −2.04324 | −0.0885026 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −27.9846 | −1.20875 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −29.4053 | −1.26775 | ||||||||
\(539\) | −28.3601 | −1.22155 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −10.0421 | −0.431745 | −0.215872 | − | 0.976422i | \(-0.569260\pi\) | ||||
−0.215872 | + | 0.976422i | \(0.569260\pi\) | |||||||
\(542\) | −46.4180 | −1.99382 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −2.27510 | −0.0975442 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 34.1914 | 1.46192 | 0.730959 | − | 0.682421i | \(-0.239073\pi\) | ||||
0.730959 | + | 0.682421i | \(0.239073\pi\) | |||||||
\(548\) | 31.6832 | 1.35344 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −54.4292 | −2.31876 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 4.99013 | 0.212202 | ||||||||
\(554\) | −17.6364 | −0.749299 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 39.5663 | 1.67799 | ||||||||
\(557\) | 1.35501 | 0.0574135 | 0.0287068 | − | 0.999588i | \(-0.490861\pi\) | ||||
0.0287068 | + | 0.999588i | \(0.490861\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 26.8454 | 1.13544 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −47.0233 | −1.98356 | ||||||||
\(563\) | 14.5306 | 0.612391 | 0.306195 | − | 0.951969i | \(-0.400944\pi\) | ||||
0.306195 | + | 0.951969i | \(0.400944\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 56.7271 | 2.38442 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 51.2207 | 2.14917 | ||||||||
\(569\) | −19.6012 | −0.821727 | −0.410863 | − | 0.911697i | \(-0.634773\pi\) | ||||
−0.410863 | + | 0.911697i | \(0.634773\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 32.8810 | 1.37603 | 0.688013 | − | 0.725698i | \(-0.258483\pi\) | ||||
0.688013 | + | 0.725698i | \(0.258483\pi\) | |||||||
\(572\) | 85.4182 | 3.57151 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −0.582090 | −0.0242960 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 7.26819 | 0.302579 | 0.151289 | − | 0.988490i | \(-0.451657\pi\) | ||||
0.151289 | + | 0.988490i | \(0.451657\pi\) | |||||||
\(578\) | 29.4485 | 1.22490 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 6.50929 | 0.270051 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1.43972 | −0.0596273 | ||||||||
\(584\) | 23.9742 | 0.992060 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −41.3551 | −1.70836 | ||||||||
\(587\) | −9.51042 | −0.392537 | −0.196268 | − | 0.980550i | \(-0.562882\pi\) | ||||
−0.196268 | + | 0.980550i | \(0.562882\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 7.96446 | 0.328170 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −42.4460 | −1.74452 | ||||||||
\(593\) | −9.75081 | −0.400418 | −0.200209 | − | 0.979753i | \(-0.564162\pi\) | ||||
−0.200209 | + | 0.979753i | \(0.564162\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −80.1151 | −3.28164 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −26.2612 | −1.07390 | ||||||||
\(599\) | 6.63034 | 0.270908 | 0.135454 | − | 0.990784i | \(-0.456751\pi\) | ||||
0.135454 | + | 0.990784i | \(0.456751\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −25.8619 | −1.05493 | −0.527465 | − | 0.849577i | \(-0.676857\pi\) | ||||
−0.527465 | + | 0.849577i | \(0.676857\pi\) | |||||||
\(602\) | 7.64789 | 0.311705 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −0.237648 | −0.00966975 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 11.3597 | 0.461075 | 0.230537 | − | 0.973063i | \(-0.425952\pi\) | ||||
0.230537 | + | 0.973063i | \(0.425952\pi\) | |||||||
\(608\) | 2.42211 | 0.0982295 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −43.5578 | −1.76216 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 30.2599 | 1.22218 | 0.611092 | − | 0.791559i | \(-0.290730\pi\) | ||||
0.611092 | + | 0.791559i | \(0.290730\pi\) | |||||||
\(614\) | 18.2631 | 0.737039 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 12.0328 | 0.484816 | ||||||||
\(617\) | −33.1940 | −1.33634 | −0.668170 | − | 0.744009i | \(-0.732922\pi\) | ||||
−0.668170 | + | 0.744009i | \(0.732922\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −11.1705 | −0.448979 | −0.224489 | − | 0.974477i | \(-0.572071\pi\) | ||||
−0.224489 | + | 0.974477i | \(0.572071\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 71.5280 | 2.86801 | ||||||||
\(623\) | −7.76980 | −0.311291 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −50.3390 | −2.01195 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 14.6338 | 0.583952 | ||||||||
\(629\) | −61.1923 | −2.43990 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −13.7542 | −0.547546 | −0.273773 | − | 0.961794i | \(-0.588272\pi\) | ||||
−0.273773 | + | 0.961794i | \(0.588272\pi\) | |||||||
\(632\) | 40.3116 | 1.60351 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 72.5219 | 2.88021 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −33.6735 | −1.33419 | ||||||||
\(638\) | 98.6898 | 3.90717 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −26.6242 | −1.05159 | −0.525797 | − | 0.850610i | \(-0.676233\pi\) | ||||
−0.525797 | + | 0.850610i | \(0.676233\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −21.6827 | −0.855082 | −0.427541 | − | 0.903996i | \(-0.640620\pi\) | ||||
−0.427541 | + | 0.903996i | \(0.640620\pi\) | |||||||
\(644\) | −4.96933 | −0.195819 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −75.5216 | −2.97136 | ||||||||
\(647\) | −13.6216 | −0.535520 | −0.267760 | − | 0.963486i | \(-0.586283\pi\) | ||||
−0.267760 | + | 0.963486i | \(0.586283\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −11.6731 | −0.458208 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 19.3449 | 0.757604 | ||||||||
\(653\) | 30.4783 | 1.19271 | 0.596355 | − | 0.802721i | \(-0.296615\pi\) | ||||
0.596355 | + | 0.802721i | \(0.296615\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −1.50915 | −0.0589224 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −12.4090 | −0.483753 | ||||||||
\(659\) | −17.7054 | −0.689705 | −0.344852 | − | 0.938657i | \(-0.612071\pi\) | ||||
−0.344852 | + | 0.938657i | \(0.612071\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 7.21561 | 0.280655 | 0.140327 | − | 0.990105i | \(-0.455184\pi\) | ||||
0.140327 | + | 0.990105i | \(0.455184\pi\) | |||||||
\(662\) | 82.6035 | 3.21047 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 52.5838 | 2.04065 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −20.1534 | −0.780343 | ||||||||
\(668\) | −64.6533 | −2.50151 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 38.4411 | 1.48400 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 41.3984 | 1.59579 | 0.797896 | − | 0.602796i | \(-0.205947\pi\) | ||||
0.797896 | + | 0.602796i | \(0.205947\pi\) | |||||||
\(674\) | −13.1587 | −0.506853 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 49.9901 | 1.92270 | ||||||||
\(677\) | 4.67244 | 0.179576 | 0.0897882 | − | 0.995961i | \(-0.471381\pi\) | ||||
0.0897882 | + | 0.995961i | \(0.471381\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 4.28449 | 0.164423 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −14.4410 | −0.552974 | ||||||||
\(683\) | −0.695173 | −0.0266001 | −0.0133000 | − | 0.999912i | \(-0.504234\pi\) | ||||
−0.0133000 | + | 0.999912i | \(0.504234\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −19.6901 | −0.751770 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 19.8282 | 0.755944 | ||||||||
\(689\) | −1.70947 | −0.0651255 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 16.0208 | 0.609461 | 0.304731 | − | 0.952439i | \(-0.401434\pi\) | ||||
0.304731 | + | 0.952439i | \(0.401434\pi\) | |||||||
\(692\) | 43.9614 | 1.67116 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −49.1015 | −1.86387 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −2.17567 | −0.0824094 | ||||||||
\(698\) | −38.8305 | −1.46976 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −33.8563 | −1.27873 | −0.639367 | − | 0.768902i | \(-0.720803\pi\) | ||||
−0.639367 | + | 0.768902i | \(0.720803\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 65.1463 | 2.45704 | ||||||||
\(704\) | −36.2854 | −1.36756 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −17.6028 | −0.662488 | ||||||||
\(707\) | −6.04042 | −0.227173 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −14.4041 | −0.540959 | −0.270479 | − | 0.962726i | \(-0.587182\pi\) | ||||
−0.270479 | + | 0.962726i | \(0.587182\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −62.7666 | −2.35228 | ||||||||
\(713\) | 2.94899 | 0.110440 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −71.4216 | −2.66915 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 8.22584 | 0.306985 | ||||||||
\(719\) | −28.5156 | −1.06345 | −0.531726 | − | 0.846916i | \(-0.678457\pi\) | ||||
−0.531726 | + | 0.846916i | \(0.678457\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 6.90203 | 0.257045 | ||||||||
\(722\) | 34.0309 | 1.26650 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −12.3156 | −0.457705 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 47.5108 | 1.76208 | 0.881040 | − | 0.473042i | \(-0.156844\pi\) | ||||
0.881040 | + | 0.473042i | \(0.156844\pi\) | |||||||
\(728\) | 14.2872 | 0.529520 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 28.5854 | 1.05727 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 24.3105 | 0.897928 | 0.448964 | − | 0.893550i | \(-0.351793\pi\) | ||||
0.448964 | + | 0.893550i | \(0.351793\pi\) | |||||||
\(734\) | −13.1160 | −0.484121 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0.896830 | 0.0330576 | ||||||||
\(737\) | −24.9940 | −0.920667 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 41.7625 | 1.53626 | 0.768130 | − | 0.640294i | \(-0.221187\pi\) | ||||
0.768130 | + | 0.640294i | \(0.221187\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −0.487003 | −0.0178784 | ||||||||
\(743\) | −19.7341 | −0.723972 | −0.361986 | − | 0.932183i | \(-0.617901\pi\) | ||||
−0.361986 | + | 0.932183i | \(0.617901\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −39.2400 | −1.43668 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 90.9544 | 3.32562 | ||||||||
\(749\) | −0.635321 | −0.0232141 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 18.2348 | 0.665397 | 0.332699 | − | 0.943033i | \(-0.392041\pi\) | ||||
0.332699 | + | 0.943033i | \(0.392041\pi\) | |||||||
\(752\) | −32.1721 | −1.17319 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 117.180 | 4.26744 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −15.5166 | −0.563962 | −0.281981 | − | 0.959420i | \(-0.590992\pi\) | ||||
−0.281981 | + | 0.959420i | \(0.590992\pi\) | |||||||
\(758\) | −67.3988 | −2.44803 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 11.7633 | 0.426419 | 0.213210 | − | 0.977006i | \(-0.431608\pi\) | ||||
0.213210 | + | 0.977006i | \(0.431608\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −0.165352 | −0.00598615 | ||||||||
\(764\) | −59.5114 | −2.15305 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −56.7617 | −2.05088 | ||||||||
\(767\) | −13.8601 | −0.500459 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −9.10438 | −0.328312 | −0.164156 | − | 0.986434i | \(-0.552490\pi\) | ||||
−0.164156 | + | 0.986434i | \(0.552490\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −21.3251 | −0.767507 | ||||||||
\(773\) | 25.6603 | 0.922937 | 0.461468 | − | 0.887157i | \(-0.347323\pi\) | ||||
0.461468 | + | 0.887157i | \(0.347323\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 34.6112 | 1.24247 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 31.2698 | 1.12108 | ||||||||
\(779\) | 2.31625 | 0.0829883 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 45.7471 | 1.63696 | ||||||||
\(782\) | −27.9632 | −0.999963 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −24.8715 | −0.888267 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −32.6096 | −1.16241 | −0.581204 | − | 0.813758i | \(-0.697418\pi\) | ||||
−0.581204 | + | 0.813758i | \(0.697418\pi\) | |||||||
\(788\) | −49.8013 | −1.77410 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −8.08594 | −0.287503 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 45.6433 | 1.62084 | ||||||||
\(794\) | −26.5062 | −0.940671 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 65.8190 | 2.33289 | ||||||||
\(797\) | −29.7470 | −1.05369 | −0.526846 | − | 0.849961i | \(-0.676626\pi\) | ||||
−0.526846 | + | 0.849961i | \(0.676626\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −46.3809 | −1.64084 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −56.1863 | −1.98401 | ||||||||
\(803\) | 21.4122 | 0.755621 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −17.1466 | −0.603963 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −48.7961 | −1.71664 | ||||||||
\(809\) | −28.9282 | −1.01706 | −0.508530 | − | 0.861044i | \(-0.669811\pi\) | ||||
−0.508530 | + | 0.861044i | \(0.669811\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 9.02896 | 0.317050 | 0.158525 | − | 0.987355i | \(-0.449326\pi\) | ||||
0.158525 | + | 0.987355i | \(0.449326\pi\) | |||||||
\(812\) | 22.1736 | 0.778142 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −118.122 | −4.14017 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −30.4324 | −1.06470 | ||||||||
\(818\) | −49.6576 | −1.73624 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 22.0570 | 0.769796 | 0.384898 | − | 0.922959i | \(-0.374237\pi\) | ||||
0.384898 | + | 0.922959i | \(0.374237\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −17.9828 | −0.626840 | −0.313420 | − | 0.949615i | \(-0.601475\pi\) | ||||
−0.313420 | + | 0.949615i | \(0.601475\pi\) | |||||||
\(824\) | 55.7564 | 1.94237 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −3.94854 | −0.137387 | ||||||||
\(827\) | 13.4856 | 0.468939 | 0.234470 | − | 0.972123i | \(-0.424665\pi\) | ||||
0.234470 | + | 0.972123i | \(0.424665\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 34.6056 | 1.20190 | 0.600952 | − | 0.799285i | \(-0.294788\pi\) | ||||
0.600952 | + | 0.799285i | \(0.294788\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −43.0837 | −1.49366 | ||||||||
\(833\) | −35.8560 | −1.24234 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −96.8315 | −3.34899 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −52.7713 | −1.82295 | ||||||||
\(839\) | 25.5209 | 0.881080 | 0.440540 | − | 0.897733i | \(-0.354787\pi\) | ||||
0.440540 | + | 0.897733i | \(0.354787\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 60.9265 | 2.10091 | ||||||||
\(842\) | −12.5825 | −0.433623 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −92.3949 | −3.18036 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 4.24569 | 0.145884 | ||||||||
\(848\) | −1.26262 | −0.0433587 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 24.1216 | 0.826878 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −3.05949 | −0.104755 | −0.0523775 | − | 0.998627i | \(-0.516680\pi\) | ||||
−0.0523775 | + | 0.998627i | \(0.516680\pi\) | |||||||
\(854\) | 13.0031 | 0.444958 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −5.13229 | −0.175418 | ||||||||
\(857\) | 29.0297 | 0.991635 | 0.495817 | − | 0.868427i | \(-0.334869\pi\) | ||||
0.495817 | + | 0.868427i | \(0.334869\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −11.5059 | −0.392576 | −0.196288 | − | 0.980546i | \(-0.562889\pi\) | ||||
−0.196288 | + | 0.980546i | \(0.562889\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 2.95466 | 0.100636 | ||||||||
\(863\) | 10.0121 | 0.340816 | 0.170408 | − | 0.985374i | \(-0.445491\pi\) | ||||
0.170408 | + | 0.985374i | \(0.445491\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −0.158306 | −0.00537946 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −3.24460 | −0.110129 | ||||||||
\(869\) | 36.0038 | 1.22134 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −29.6768 | −1.00556 | ||||||||
\(872\) | −1.33576 | −0.0452345 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 29.7701 | 1.00699 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 16.6844 | 0.563392 | 0.281696 | − | 0.959504i | \(-0.409103\pi\) | ||||
0.281696 | + | 0.959504i | \(0.409103\pi\) | |||||||
\(878\) | −28.7262 | −0.969464 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 9.74584 | 0.328346 | 0.164173 | − | 0.986432i | \(-0.447505\pi\) | ||||
0.164173 | + | 0.986432i | \(0.447505\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 19.7999 | 0.666319 | 0.333160 | − | 0.942870i | \(-0.391885\pi\) | ||||
0.333160 | + | 0.942870i | \(0.391885\pi\) | |||||||
\(884\) | 107.995 | 3.63228 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −46.7813 | −1.57165 | ||||||||
\(887\) | 16.0655 | 0.539427 | 0.269714 | − | 0.962941i | \(-0.413071\pi\) | ||||
0.269714 | + | 0.962941i | \(0.413071\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 8.82184 | 0.295875 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 3.28364 | 0.109944 | ||||||||
\(893\) | 49.3779 | 1.65237 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −11.7751 | −0.393380 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 1.30904 | 0.0436831 | ||||||||
\(899\) | −13.1587 | −0.438866 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1.82026 | −0.0606418 | ||||||||
\(902\) | −4.19978 | −0.139837 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −65.3204 | −2.17252 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 17.0483 | 0.566080 | 0.283040 | − | 0.959108i | \(-0.408657\pi\) | ||||
0.283040 | + | 0.959108i | \(0.408657\pi\) | |||||||
\(908\) | 89.8322 | 2.98119 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 30.9582 | 1.02569 | 0.512846 | − | 0.858481i | \(-0.328591\pi\) | ||||
0.512846 | + | 0.858481i | \(0.328591\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 46.9645 | 1.55430 | ||||||||
\(914\) | 85.8957 | 2.84118 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −109.877 | −3.63043 | ||||||||
\(917\) | 11.9578 | 0.394882 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 17.0914 | 0.563794 | 0.281897 | − | 0.959445i | \(-0.409036\pi\) | ||||
0.281897 | + | 0.959445i | \(0.409036\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −4.38694 | −0.144476 | ||||||||
\(923\) | 54.3181 | 1.78790 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 38.7273 | 1.27266 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −4.00175 | −0.131364 | ||||||||
\(929\) | 3.86068 | 0.126665 | 0.0633323 | − | 0.997992i | \(-0.479827\pi\) | ||||
0.0633323 | + | 0.997992i | \(0.479827\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 38.1729 | 1.25106 | ||||||||
\(932\) | 4.51363 | 0.147849 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 100.447 | 3.28674 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 7.05231 | 0.230389 | 0.115194 | − | 0.993343i | \(-0.463251\pi\) | ||||
0.115194 | + | 0.993343i | \(0.463251\pi\) | |||||||
\(938\) | −8.45451 | −0.276050 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −11.6549 | −0.379937 | −0.189969 | − | 0.981790i | \(-0.560839\pi\) | ||||
−0.189969 | + | 0.981790i | \(0.560839\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0.857635 | 0.0279284 | ||||||||
\(944\) | −10.2371 | −0.333191 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 55.1794 | 1.79404 | ||||||||
\(947\) | −31.9057 | −1.03680 | −0.518398 | − | 0.855140i | \(-0.673471\pi\) | ||||
−0.518398 | + | 0.855140i | \(0.673471\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 25.4240 | 0.825297 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 15.2132 | 0.493064 | ||||||||
\(953\) | 26.3431 | 0.853337 | 0.426668 | − | 0.904408i | \(-0.359687\pi\) | ||||
0.426668 | + | 0.904408i | \(0.359687\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −30.9515 | −1.00104 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −36.8651 | −1.19106 | ||||||||
\(959\) | 4.73310 | 0.152840 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −29.0745 | −0.937888 | ||||||||
\(962\) | −140.253 | −4.52193 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −3.42359 | −0.110266 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −2.32875 | −0.0748876 | −0.0374438 | − | 0.999299i | \(-0.511922\pi\) | ||||
−0.0374438 | + | 0.999299i | \(0.511922\pi\) | |||||||
\(968\) | 34.2978 | 1.10237 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −43.6099 | −1.39951 | −0.699755 | − | 0.714383i | \(-0.746707\pi\) | ||||
−0.699755 | + | 0.714383i | \(0.746707\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 5.91073 | 0.189489 | ||||||||
\(974\) | −11.9800 | −0.383864 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 33.7124 | 1.07911 | ||||||||
\(977\) | 36.5836 | 1.17041 | 0.585207 | − | 0.810884i | \(-0.301013\pi\) | ||||
0.585207 | + | 0.810884i | \(0.301013\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −56.0591 | −1.79166 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −106.835 | −3.40925 | ||||||||
\(983\) | 26.5522 | 0.846885 | 0.423442 | − | 0.905923i | \(-0.360822\pi\) | ||||
0.423442 | + | 0.905923i | \(0.360822\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 124.775 | 3.97364 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −114.974 | −3.65780 | ||||||||
\(989\) | −11.2682 | −0.358307 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −52.9441 | −1.68182 | −0.840912 | − | 0.541172i | \(-0.817981\pi\) | ||||
−0.840912 | + | 0.541172i | \(0.817981\pi\) | |||||||
\(992\) | 0.585564 | 0.0185917 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 15.4745 | 0.490820 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −49.7519 | −1.57566 | −0.787828 | − | 0.615895i | \(-0.788795\pi\) | ||||
−0.787828 | + | 0.615895i | \(0.788795\pi\) | |||||||
\(998\) | 14.6482 | 0.463680 | ||||||||
\(999\) | 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 | 5625.2.a.ba.1.8 | yes | 8 | |
3.2 | odd | 2 | inner | 5625.2.a.ba.1.1 | yes | 8 | |
5.4 | even | 2 | 5625.2.a.y.1.1 | ✓ | 8 | ||
15.14 | odd | 2 | 5625.2.a.y.1.8 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
5625.2.a.y.1.1 | ✓ | 8 | 5.4 | even | 2 | ||
5625.2.a.y.1.8 | yes | 8 | 15.14 | odd | 2 | ||
5625.2.a.ba.1.1 | yes | 8 | 3.2 | odd | 2 | inner | |
5625.2.a.ba.1.8 | yes | 8 | 1.1 | even | 1 | trivial |