Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2475,2,Mod(1,2475)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2475, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2475.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2475 = 3^{2} \cdot 5^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2475.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: | \(19.7629745003\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{17}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 4 \) |
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 | 1.2 | ||
Root | \(-1.56155\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2475.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.56155 | 1.10418 | 0.552092 | − | 0.833783i | \(-0.313830\pi\) | ||||
0.552092 | + | 0.833783i | \(0.313830\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0.438447 | 0.219224 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | −0.377964 | −0.188982 | − | 0.981981i | \(-0.560519\pi\) | ||||
−0.188982 | + | 0.981981i | \(0.560519\pi\) | |||||||
\(8\) | −2.43845 | −0.862121 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.56155 | 1.26515 | 0.632574 | − | 0.774500i | \(-0.281999\pi\) | ||||
0.632574 | + | 0.774500i | \(0.281999\pi\) | |||||||
\(14\) | −1.56155 | −0.417343 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −4.68466 | −1.17116 | ||||||||
\(17\) | −5.56155 | −1.34887 | −0.674437 | − | 0.738332i | \(-0.735614\pi\) | ||||
−0.674437 | + | 0.738332i | \(0.735614\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.00000 | 0.688247 | 0.344124 | − | 0.938924i | \(-0.388176\pi\) | ||||
0.344124 | + | 0.938924i | \(0.388176\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −1.56155 | −0.332924 | ||||||||
\(23\) | −2.43845 | −0.508451 | −0.254226 | − | 0.967145i | \(-0.581821\pi\) | ||||
−0.254226 | + | 0.967145i | \(0.581821\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 7.12311 | 1.39696 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −0.438447 | −0.0828587 | ||||||||
\(29\) | −3.12311 | −0.579946 | −0.289973 | − | 0.957035i | \(-0.593646\pi\) | ||||
−0.289973 | + | 0.957035i | \(0.593646\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −7.68466 | −1.38021 | −0.690103 | − | 0.723711i | \(-0.742435\pi\) | ||||
−0.690103 | + | 0.723711i | \(0.742435\pi\) | |||||||
\(32\) | −2.43845 | −0.431061 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −8.68466 | −1.48941 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −9.80776 | −1.61239 | −0.806193 | − | 0.591652i | \(-0.798476\pi\) | ||||
−0.806193 | + | 0.591652i | \(0.798476\pi\) | |||||||
\(38\) | 4.68466 | 0.759952 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 4.68466 | 0.731621 | 0.365810 | − | 0.930689i | \(-0.380792\pi\) | ||||
0.365810 | + | 0.930689i | \(0.380792\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 7.68466 | 1.17190 | 0.585950 | − | 0.810347i | \(-0.300722\pi\) | ||||
0.585950 | + | 0.810347i | \(0.300722\pi\) | |||||||
\(44\) | −0.438447 | −0.0660984 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −3.80776 | −0.561424 | ||||||||
\(47\) | −9.56155 | −1.39470 | −0.697348 | − | 0.716733i | \(-0.745637\pi\) | ||||
−0.697348 | + | 0.716733i | \(0.745637\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.00000 | −0.857143 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 2.00000 | 0.277350 | ||||||||
\(53\) | −7.12311 | −0.978434 | −0.489217 | − | 0.872162i | \(-0.662717\pi\) | ||||
−0.489217 | + | 0.872162i | \(0.662717\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 2.43845 | 0.325851 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −4.87689 | −0.640368 | ||||||||
\(59\) | 6.43845 | 0.838214 | 0.419107 | − | 0.907937i | \(-0.362343\pi\) | ||||
0.419107 | + | 0.907937i | \(0.362343\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3.43845 | −0.440248 | −0.220124 | − | 0.975472i | \(-0.570646\pi\) | ||||
−0.220124 | + | 0.975472i | \(0.570646\pi\) | |||||||
\(62\) | −12.0000 | −1.52400 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 5.56155 | 0.695194 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −5.68466 | −0.694492 | −0.347246 | − | 0.937774i | \(-0.612883\pi\) | ||||
−0.347246 | + | 0.937774i | \(0.612883\pi\) | |||||||
\(68\) | −2.43845 | −0.295705 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −11.8078 | −1.40132 | −0.700662 | − | 0.713493i | \(-0.747112\pi\) | ||||
−0.700662 | + | 0.713493i | \(0.747112\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0.246211 | 0.0288168 | 0.0144084 | − | 0.999896i | \(-0.495413\pi\) | ||||
0.0144084 | + | 0.999896i | \(0.495413\pi\) | |||||||
\(74\) | −15.3153 | −1.78037 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 1.31534 | 0.150880 | ||||||||
\(77\) | 1.00000 | 0.113961 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −3.31534 | −0.373005 | −0.186503 | − | 0.982454i | \(-0.559715\pi\) | ||||
−0.186503 | + | 0.982454i | \(0.559715\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 7.31534 | 0.807844 | ||||||||
\(83\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 12.0000 | 1.29399 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 2.43845 | 0.259939 | ||||||||
\(89\) | −8.87689 | −0.940949 | −0.470474 | − | 0.882414i | \(-0.655917\pi\) | ||||
−0.470474 | + | 0.882414i | \(0.655917\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −4.56155 | −0.478181 | ||||||||
\(92\) | −1.06913 | −0.111465 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −14.9309 | −1.54000 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 6.12311 | 0.621707 | 0.310854 | − | 0.950458i | \(-0.399385\pi\) | ||||
0.310854 | + | 0.950458i | \(0.399385\pi\) | |||||||
\(98\) | −9.36932 | −0.946444 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 5.56155 | 0.553395 | 0.276698 | − | 0.960957i | \(-0.410760\pi\) | ||||
0.276698 | + | 0.960957i | \(0.410760\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0.876894 | 0.0864030 | 0.0432015 | − | 0.999066i | \(-0.486244\pi\) | ||||
0.0432015 | + | 0.999066i | \(0.486244\pi\) | |||||||
\(104\) | −11.1231 | −1.09071 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −11.1231 | −1.08037 | ||||||||
\(107\) | 0.876894 | 0.0847726 | 0.0423863 | − | 0.999101i | \(-0.486504\pi\) | ||||
0.0423863 | + | 0.999101i | \(0.486504\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 12.8078 | 1.22676 | 0.613381 | − | 0.789787i | \(-0.289809\pi\) | ||||
0.613381 | + | 0.789787i | \(0.289809\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 4.68466 | 0.442659 | ||||||||
\(113\) | 0.876894 | 0.0824913 | 0.0412456 | − | 0.999149i | \(-0.486867\pi\) | ||||
0.0412456 | + | 0.999149i | \(0.486867\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −1.36932 | −0.127138 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 10.0540 | 0.925543 | ||||||||
\(119\) | 5.56155 | 0.509827 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | −5.36932 | −0.486115 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −3.36932 | −0.302574 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −15.8078 | −1.40271 | −0.701356 | − | 0.712811i | \(-0.747422\pi\) | ||||
−0.701356 | + | 0.712811i | \(0.747422\pi\) | |||||||
\(128\) | 13.5616 | 1.19868 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 16.4924 | 1.44095 | 0.720475 | − | 0.693481i | \(-0.243924\pi\) | ||||
0.720475 | + | 0.693481i | \(0.243924\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −3.00000 | −0.260133 | ||||||||
\(134\) | −8.87689 | −0.766847 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 13.5616 | 1.16289 | ||||||||
\(137\) | −21.3693 | −1.82570 | −0.912852 | − | 0.408291i | \(-0.866125\pi\) | ||||
−0.912852 | + | 0.408291i | \(0.866125\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 8.00000 | 0.678551 | 0.339276 | − | 0.940687i | \(-0.389818\pi\) | ||||
0.339276 | + | 0.940687i | \(0.389818\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −18.4384 | −1.54732 | ||||||||
\(143\) | −4.56155 | −0.381456 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0.384472 | 0.0318191 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −4.30019 | −0.353473 | ||||||||
\(149\) | −11.8078 | −0.967330 | −0.483665 | − | 0.875253i | \(-0.660695\pi\) | ||||
−0.483665 | + | 0.875253i | \(0.660695\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −4.31534 | −0.351178 | −0.175589 | − | 0.984464i | \(-0.556183\pi\) | ||||
−0.175589 | + | 0.984464i | \(0.556183\pi\) | |||||||
\(152\) | −7.31534 | −0.593353 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 1.56155 | 0.125834 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 9.68466 | 0.772920 | 0.386460 | − | 0.922306i | \(-0.373698\pi\) | ||||
0.386460 | + | 0.922306i | \(0.373698\pi\) | |||||||
\(158\) | −5.17708 | −0.411866 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 2.43845 | 0.192177 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 17.6847 | 1.38517 | 0.692585 | − | 0.721337i | \(-0.256472\pi\) | ||||
0.692585 | + | 0.721337i | \(0.256472\pi\) | |||||||
\(164\) | 2.05398 | 0.160389 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −9.36932 | −0.725020 | −0.362510 | − | 0.931980i | \(-0.618080\pi\) | ||||
−0.362510 | + | 0.931980i | \(0.618080\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 7.80776 | 0.600597 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 3.36932 | 0.256908 | ||||||||
\(173\) | −17.5616 | −1.33518 | −0.667590 | − | 0.744529i | \(-0.732674\pi\) | ||||
−0.667590 | + | 0.744529i | \(0.732674\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 4.68466 | 0.353119 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −13.8617 | −1.03898 | ||||||||
\(179\) | 10.4384 | 0.780206 | 0.390103 | − | 0.920771i | \(-0.372439\pi\) | ||||
0.390103 | + | 0.920771i | \(0.372439\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 20.1231 | 1.49574 | 0.747869 | − | 0.663846i | \(-0.231077\pi\) | ||||
0.747869 | + | 0.663846i | \(0.231077\pi\) | |||||||
\(182\) | −7.12311 | −0.528000 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 5.94602 | 0.438347 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 5.56155 | 0.406701 | ||||||||
\(188\) | −4.19224 | −0.305750 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 26.9309 | 1.94865 | 0.974325 | − | 0.225148i | \(-0.0722864\pi\) | ||||
0.974325 | + | 0.225148i | \(0.0722864\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −13.4384 | −0.967321 | −0.483660 | − | 0.875256i | \(-0.660693\pi\) | ||||
−0.483660 | + | 0.875256i | \(0.660693\pi\) | |||||||
\(194\) | 9.56155 | 0.686479 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −2.63068 | −0.187906 | ||||||||
\(197\) | 10.9309 | 0.778792 | 0.389396 | − | 0.921070i | \(-0.372684\pi\) | ||||
0.389396 | + | 0.921070i | \(0.372684\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 6.80776 | 0.482590 | 0.241295 | − | 0.970452i | \(-0.422428\pi\) | ||||
0.241295 | + | 0.970452i | \(0.422428\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 8.68466 | 0.611050 | ||||||||
\(203\) | 3.12311 | 0.219199 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 1.36932 | 0.0954048 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −21.3693 | −1.48170 | ||||||||
\(209\) | −3.00000 | −0.207514 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 15.6847 | 1.07978 | 0.539888 | − | 0.841737i | \(-0.318467\pi\) | ||||
0.539888 | + | 0.841737i | \(0.318467\pi\) | |||||||
\(212\) | −3.12311 | −0.214496 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 1.36932 | 0.0936046 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 7.68466 | 0.521669 | ||||||||
\(218\) | 20.0000 | 1.35457 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −25.3693 | −1.70652 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1.19224 | −0.0798380 | −0.0399190 | − | 0.999203i | \(-0.512710\pi\) | ||||
−0.0399190 | + | 0.999203i | \(0.512710\pi\) | |||||||
\(224\) | 2.43845 | 0.162926 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 1.36932 | 0.0910856 | ||||||||
\(227\) | 12.4924 | 0.829151 | 0.414576 | − | 0.910015i | \(-0.363930\pi\) | ||||
0.414576 | + | 0.910015i | \(0.363930\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 0.123106 | 0.00813505 | 0.00406752 | − | 0.999992i | \(-0.498705\pi\) | ||||
0.00406752 | + | 0.999992i | \(0.498705\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 7.61553 | 0.499984 | ||||||||
\(233\) | −4.19224 | −0.274643 | −0.137321 | − | 0.990527i | \(-0.543849\pi\) | ||||
−0.137321 | + | 0.990527i | \(0.543849\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 2.82292 | 0.183756 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 8.68466 | 0.562943 | ||||||||
\(239\) | 16.4924 | 1.06681 | 0.533403 | − | 0.845861i | \(-0.320913\pi\) | ||||
0.533403 | + | 0.845861i | \(0.320913\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 23.0540 | 1.48504 | 0.742519 | − | 0.669826i | \(-0.233631\pi\) | ||||
0.742519 | + | 0.669826i | \(0.233631\pi\) | |||||||
\(242\) | 1.56155 | 0.100380 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −1.50758 | −0.0965128 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 13.6847 | 0.870734 | ||||||||
\(248\) | 18.7386 | 1.18990 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −12.0000 | −0.757433 | −0.378717 | − | 0.925513i | \(-0.623635\pi\) | ||||
−0.378717 | + | 0.925513i | \(0.623635\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2.43845 | 0.153304 | ||||||||
\(254\) | −24.6847 | −1.54885 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 10.0540 | 0.628373 | ||||||||
\(257\) | −1.75379 | −0.109398 | −0.0546992 | − | 0.998503i | \(-0.517420\pi\) | ||||
−0.0546992 | + | 0.998503i | \(0.517420\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 9.80776 | 0.609425 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 25.7538 | 1.59107 | ||||||||
\(263\) | −21.3693 | −1.31769 | −0.658844 | − | 0.752279i | \(-0.728954\pi\) | ||||
−0.658844 | + | 0.752279i | \(0.728954\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −4.68466 | −0.287235 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −2.49242 | −0.152249 | ||||||||
\(269\) | −4.49242 | −0.273908 | −0.136954 | − | 0.990577i | \(-0.543731\pi\) | ||||
−0.136954 | + | 0.990577i | \(0.543731\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 17.1771 | 1.04343 | 0.521717 | − | 0.853119i | \(-0.325292\pi\) | ||||
0.521717 | + | 0.853119i | \(0.325292\pi\) | |||||||
\(272\) | 26.0540 | 1.57975 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −33.3693 | −2.01591 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −22.1771 | −1.33249 | −0.666246 | − | 0.745732i | \(-0.732100\pi\) | ||||
−0.666246 | + | 0.745732i | \(0.732100\pi\) | |||||||
\(278\) | 12.4924 | 0.749246 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −23.8078 | −1.42025 | −0.710126 | − | 0.704075i | \(-0.751362\pi\) | ||||
−0.710126 | + | 0.704075i | \(0.751362\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −23.8769 | −1.41933 | −0.709667 | − | 0.704537i | \(-0.751155\pi\) | ||||
−0.709667 | + | 0.704537i | \(0.751155\pi\) | |||||||
\(284\) | −5.17708 | −0.307203 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −7.12311 | −0.421198 | ||||||||
\(287\) | −4.68466 | −0.276527 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 13.9309 | 0.819463 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0.107951 | 0.00631733 | ||||||||
\(293\) | −30.9309 | −1.80700 | −0.903500 | − | 0.428587i | \(-0.859011\pi\) | ||||
−0.903500 | + | 0.428587i | \(0.859011\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 23.9157 | 1.39007 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −18.4384 | −1.06811 | ||||||||
\(299\) | −11.1231 | −0.643266 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −7.68466 | −0.442936 | ||||||||
\(302\) | −6.73863 | −0.387765 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −14.0540 | −0.806051 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −5.93087 | −0.338493 | −0.169246 | − | 0.985574i | \(-0.554133\pi\) | ||||
−0.169246 | + | 0.985574i | \(0.554133\pi\) | |||||||
\(308\) | 0.438447 | 0.0249828 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −30.2462 | −1.71511 | −0.857553 | − | 0.514396i | \(-0.828016\pi\) | ||||
−0.857553 | + | 0.514396i | \(0.828016\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 14.7538 | 0.833933 | 0.416967 | − | 0.908922i | \(-0.363093\pi\) | ||||
0.416967 | + | 0.908922i | \(0.363093\pi\) | |||||||
\(314\) | 15.1231 | 0.853446 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −1.45360 | −0.0817715 | ||||||||
\(317\) | −15.1231 | −0.849398 | −0.424699 | − | 0.905335i | \(-0.639620\pi\) | ||||
−0.424699 | + | 0.905335i | \(0.639620\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 3.12311 | 0.174860 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 3.80776 | 0.212198 | ||||||||
\(323\) | −16.6847 | −0.928359 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 27.6155 | 1.52948 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −11.4233 | −0.630746 | ||||||||
\(329\) | 9.56155 | 0.527145 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 6.24621 | 0.343323 | 0.171661 | − | 0.985156i | \(-0.445086\pi\) | ||||
0.171661 | + | 0.985156i | \(0.445086\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −14.6307 | −0.800555 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1.68466 | −0.0917692 | −0.0458846 | − | 0.998947i | \(-0.514611\pi\) | ||||
−0.0458846 | + | 0.998947i | \(0.514611\pi\) | |||||||
\(338\) | 12.1922 | 0.663170 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 7.68466 | 0.416148 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 13.0000 | 0.701934 | ||||||||
\(344\) | −18.7386 | −1.01032 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −27.4233 | −1.47429 | ||||||||
\(347\) | 2.63068 | 0.141222 | 0.0706112 | − | 0.997504i | \(-0.477505\pi\) | ||||
0.0706112 | + | 0.997504i | \(0.477505\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 31.3693 | 1.67916 | 0.839581 | − | 0.543235i | \(-0.182801\pi\) | ||||
0.839581 | + | 0.543235i | \(0.182801\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 2.43845 | 0.129970 | ||||||||
\(353\) | 29.8617 | 1.58938 | 0.794690 | − | 0.607015i | \(-0.207633\pi\) | ||||
0.794690 | + | 0.607015i | \(0.207633\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −3.89205 | −0.206278 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 16.3002 | 0.861492 | ||||||||
\(359\) | 9.75379 | 0.514785 | 0.257393 | − | 0.966307i | \(-0.417137\pi\) | ||||
0.257393 | + | 0.966307i | \(0.417137\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −10.0000 | −0.526316 | ||||||||
\(362\) | 31.4233 | 1.65157 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −2.00000 | −0.104828 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 23.0540 | 1.20341 | 0.601704 | − | 0.798719i | \(-0.294489\pi\) | ||||
0.601704 | + | 0.798719i | \(0.294489\pi\) | |||||||
\(368\) | 11.4233 | 0.595480 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 7.12311 | 0.369813 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −6.80776 | −0.352493 | −0.176246 | − | 0.984346i | \(-0.556396\pi\) | ||||
−0.176246 | + | 0.984346i | \(0.556396\pi\) | |||||||
\(374\) | 8.68466 | 0.449073 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 23.3153 | 1.20240 | ||||||||
\(377\) | −14.2462 | −0.733717 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 29.3002 | 1.50505 | 0.752525 | − | 0.658564i | \(-0.228836\pi\) | ||||
0.752525 | + | 0.658564i | \(0.228836\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 42.0540 | 2.15167 | ||||||||
\(383\) | −5.75379 | −0.294005 | −0.147002 | − | 0.989136i | \(-0.546963\pi\) | ||||
−0.147002 | + | 0.989136i | \(0.546963\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −20.9848 | −1.06810 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 2.68466 | 0.136293 | ||||||||
\(389\) | 33.8617 | 1.71686 | 0.858429 | − | 0.512932i | \(-0.171441\pi\) | ||||
0.858429 | + | 0.512932i | \(0.171441\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 13.5616 | 0.685837 | ||||||||
\(392\) | 14.6307 | 0.738961 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 17.0691 | 0.859930 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −32.5616 | −1.63422 | −0.817109 | − | 0.576484i | \(-0.804424\pi\) | ||||
−0.817109 | + | 0.576484i | \(0.804424\pi\) | |||||||
\(398\) | 10.6307 | 0.532868 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −35.6155 | −1.77855 | −0.889277 | − | 0.457368i | \(-0.848792\pi\) | ||||
−0.889277 | + | 0.457368i | \(0.848792\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −35.0540 | −1.74616 | ||||||||
\(404\) | 2.43845 | 0.121317 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 4.87689 | 0.242036 | ||||||||
\(407\) | 9.80776 | 0.486153 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −29.0540 | −1.43663 | −0.718313 | − | 0.695720i | \(-0.755086\pi\) | ||||
−0.718313 | + | 0.695720i | \(0.755086\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0.384472 | 0.0189416 | ||||||||
\(413\) | −6.43845 | −0.316815 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −11.1231 | −0.545355 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −4.68466 | −0.229134 | ||||||||
\(419\) | 29.5616 | 1.44418 | 0.722088 | − | 0.691801i | \(-0.243182\pi\) | ||||
0.722088 | + | 0.691801i | \(0.243182\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 20.0540 | 0.977371 | 0.488685 | − | 0.872460i | \(-0.337477\pi\) | ||||
0.488685 | + | 0.872460i | \(0.337477\pi\) | |||||||
\(422\) | 24.4924 | 1.19227 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 17.3693 | 0.843529 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 3.43845 | 0.166398 | ||||||||
\(428\) | 0.384472 | 0.0185841 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −38.2462 | −1.84226 | −0.921128 | − | 0.389261i | \(-0.872730\pi\) | ||||
−0.921128 | + | 0.389261i | \(0.872730\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 11.9309 | 0.573361 | 0.286681 | − | 0.958026i | \(-0.407448\pi\) | ||||
0.286681 | + | 0.958026i | \(0.407448\pi\) | |||||||
\(434\) | 12.0000 | 0.576018 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 5.61553 | 0.268935 | ||||||||
\(437\) | −7.31534 | −0.349940 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −37.7386 | −1.80117 | −0.900583 | − | 0.434683i | \(-0.856860\pi\) | ||||
−0.900583 | + | 0.434683i | \(0.856860\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −39.6155 | −1.88432 | ||||||||
\(443\) | 28.3002 | 1.34458 | 0.672291 | − | 0.740287i | \(-0.265310\pi\) | ||||
0.672291 | + | 0.740287i | \(0.265310\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −1.86174 | −0.0881559 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −5.56155 | −0.262759 | ||||||||
\(449\) | 4.49242 | 0.212011 | 0.106005 | − | 0.994366i | \(-0.466194\pi\) | ||||
0.106005 | + | 0.994366i | \(0.466194\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −4.68466 | −0.220592 | ||||||||
\(452\) | 0.384472 | 0.0180840 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 19.5076 | 0.915536 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 11.3693 | 0.531834 | 0.265917 | − | 0.963996i | \(-0.414325\pi\) | ||||
0.265917 | + | 0.963996i | \(0.414325\pi\) | |||||||
\(458\) | 0.192236 | 0.00898260 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 41.8617 | 1.94970 | 0.974848 | − | 0.222872i | \(-0.0715431\pi\) | ||||
0.974848 | + | 0.222872i | \(0.0715431\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 18.2462 | 0.847973 | 0.423987 | − | 0.905668i | \(-0.360630\pi\) | ||||
0.423987 | + | 0.905668i | \(0.360630\pi\) | |||||||
\(464\) | 14.6307 | 0.679212 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −6.54640 | −0.303256 | ||||||||
\(467\) | 14.2462 | 0.659236 | 0.329618 | − | 0.944114i | \(-0.393080\pi\) | ||||
0.329618 | + | 0.944114i | \(0.393080\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 5.68466 | 0.262493 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −15.6998 | −0.722642 | ||||||||
\(473\) | −7.68466 | −0.353341 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 2.43845 | 0.111766 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 25.7538 | 1.17795 | ||||||||
\(479\) | −21.3693 | −0.976389 | −0.488195 | − | 0.872735i | \(-0.662344\pi\) | ||||
−0.488195 | + | 0.872735i | \(0.662344\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −44.7386 | −2.03991 | ||||||||
\(482\) | 36.0000 | 1.63976 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0.438447 | 0.0199294 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −25.0540 | −1.13530 | −0.567652 | − | 0.823269i | \(-0.692148\pi\) | ||||
−0.567652 | + | 0.823269i | \(0.692148\pi\) | |||||||
\(488\) | 8.38447 | 0.379547 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −16.4924 | −0.744293 | −0.372146 | − | 0.928174i | \(-0.621378\pi\) | ||||
−0.372146 | + | 0.928174i | \(0.621378\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 17.3693 | 0.782275 | ||||||||
\(494\) | 21.3693 | 0.961451 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 36.0000 | 1.61645 | ||||||||
\(497\) | 11.8078 | 0.529651 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −16.8078 | −0.752419 | −0.376209 | − | 0.926535i | \(-0.622773\pi\) | ||||
−0.376209 | + | 0.926535i | \(0.622773\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −18.7386 | −0.836346 | ||||||||
\(503\) | −16.4924 | −0.735361 | −0.367680 | − | 0.929952i | \(-0.619848\pi\) | ||||
−0.367680 | + | 0.929952i | \(0.619848\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 3.80776 | 0.169276 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −6.93087 | −0.307508 | ||||||||
\(509\) | −8.87689 | −0.393461 | −0.196731 | − | 0.980458i | \(-0.563032\pi\) | ||||
−0.196731 | + | 0.980458i | \(0.563032\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −0.246211 | −0.0108917 | ||||||||
\(512\) | −11.4233 | −0.504843 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −2.73863 | −0.120796 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 9.56155 | 0.420517 | ||||||||
\(518\) | 15.3153 | 0.672917 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 15.6155 | 0.684129 | 0.342064 | − | 0.939677i | \(-0.388874\pi\) | ||||
0.342064 | + | 0.939677i | \(0.388874\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 7.24621 | 0.316855 | 0.158427 | − | 0.987371i | \(-0.449358\pi\) | ||||
0.158427 | + | 0.987371i | \(0.449358\pi\) | |||||||
\(524\) | 7.23106 | 0.315890 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −33.3693 | −1.45497 | ||||||||
\(527\) | 42.7386 | 1.86172 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −17.0540 | −0.741477 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −1.31534 | −0.0570273 | ||||||||
\(533\) | 21.3693 | 0.925608 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 13.8617 | 0.598736 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −7.01515 | −0.302445 | ||||||||
\(539\) | 6.00000 | 0.258438 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −19.6847 | −0.846310 | −0.423155 | − | 0.906057i | \(-0.639077\pi\) | ||||
−0.423155 | + | 0.906057i | \(0.639077\pi\) | |||||||
\(542\) | 26.8229 | 1.15214 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 13.5616 | 0.581447 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 8.68466 | 0.371329 | 0.185665 | − | 0.982613i | \(-0.440556\pi\) | ||||
0.185665 | + | 0.982613i | \(0.440556\pi\) | |||||||
\(548\) | −9.36932 | −0.400237 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −9.36932 | −0.399146 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 3.31534 | 0.140983 | ||||||||
\(554\) | −34.6307 | −1.47132 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 3.50758 | 0.148754 | ||||||||
\(557\) | 7.12311 | 0.301816 | 0.150908 | − | 0.988548i | \(-0.451780\pi\) | ||||
0.150908 | + | 0.988548i | \(0.451780\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 35.0540 | 1.48263 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −37.1771 | −1.56822 | ||||||||
\(563\) | 19.1231 | 0.805943 | 0.402971 | − | 0.915213i | \(-0.367977\pi\) | ||||
0.402971 | + | 0.915213i | \(0.367977\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −37.2850 | −1.56721 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 28.7926 | 1.20811 | ||||||||
\(569\) | 9.06913 | 0.380198 | 0.190099 | − | 0.981765i | \(-0.439119\pi\) | ||||
0.190099 | + | 0.981765i | \(0.439119\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 0.946025 | 0.0395899 | 0.0197950 | − | 0.999804i | \(-0.493699\pi\) | ||||
0.0197950 | + | 0.999804i | \(0.493699\pi\) | |||||||
\(572\) | −2.00000 | −0.0836242 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −7.31534 | −0.305336 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 3.63068 | 0.151147 | 0.0755737 | − | 0.997140i | \(-0.475921\pi\) | ||||
0.0755737 | + | 0.997140i | \(0.475921\pi\) | |||||||
\(578\) | 21.7538 | 0.904838 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 7.12311 | 0.295009 | ||||||||
\(584\) | −0.600373 | −0.0248436 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −48.3002 | −1.99526 | ||||||||
\(587\) | 47.8078 | 1.97324 | 0.986619 | − | 0.163044i | \(-0.0521313\pi\) | ||||
0.986619 | + | 0.163044i | \(0.0521313\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −23.0540 | −0.949923 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 45.9460 | 1.88837 | ||||||||
\(593\) | −40.1080 | −1.64704 | −0.823518 | − | 0.567290i | \(-0.807992\pi\) | ||||
−0.823518 | + | 0.567290i | \(0.807992\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −5.17708 | −0.212061 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −17.3693 | −0.710284 | ||||||||
\(599\) | −21.1771 | −0.865272 | −0.432636 | − | 0.901569i | \(-0.642416\pi\) | ||||
−0.432636 | + | 0.901569i | \(0.642416\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −24.4233 | −0.996247 | −0.498123 | − | 0.867106i | \(-0.665977\pi\) | ||||
−0.498123 | + | 0.867106i | \(0.665977\pi\) | |||||||
\(602\) | −12.0000 | −0.489083 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −1.89205 | −0.0769864 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 10.2462 | 0.415881 | 0.207940 | − | 0.978141i | \(-0.433324\pi\) | ||||
0.207940 | + | 0.978141i | \(0.433324\pi\) | |||||||
\(608\) | −7.31534 | −0.296676 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −43.6155 | −1.76450 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 46.1080 | 1.86228 | 0.931141 | − | 0.364659i | \(-0.118814\pi\) | ||||
0.931141 | + | 0.364659i | \(0.118814\pi\) | |||||||
\(614\) | −9.26137 | −0.373758 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −2.43845 | −0.0982478 | ||||||||
\(617\) | −38.2462 | −1.53973 | −0.769867 | − | 0.638204i | \(-0.779678\pi\) | ||||
−0.769867 | + | 0.638204i | \(0.779678\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −38.1771 | −1.53447 | −0.767233 | − | 0.641368i | \(-0.778367\pi\) | ||||
−0.767233 | + | 0.641368i | \(0.778367\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −47.2311 | −1.89379 | ||||||||
\(623\) | 8.87689 | 0.355645 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 23.0388 | 0.920816 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 4.24621 | 0.169442 | ||||||||
\(629\) | 54.5464 | 2.17491 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −10.3153 | −0.410647 | −0.205324 | − | 0.978694i | \(-0.565825\pi\) | ||||
−0.205324 | + | 0.978694i | \(0.565825\pi\) | |||||||
\(632\) | 8.08429 | 0.321576 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −23.6155 | −0.937892 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −27.3693 | −1.08441 | ||||||||
\(638\) | 4.87689 | 0.193078 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −6.73863 | −0.266160 | −0.133080 | − | 0.991105i | \(-0.542487\pi\) | ||||
−0.133080 | + | 0.991105i | \(0.542487\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 9.36932 | 0.369490 | 0.184745 | − | 0.982787i | \(-0.440854\pi\) | ||||
0.184745 | + | 0.982787i | \(0.440854\pi\) | |||||||
\(644\) | 1.06913 | 0.0421296 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −26.0540 | −1.02508 | ||||||||
\(647\) | 20.1922 | 0.793839 | 0.396919 | − | 0.917853i | \(-0.370079\pi\) | ||||
0.396919 | + | 0.917853i | \(0.370079\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −6.43845 | −0.252731 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 7.75379 | 0.303662 | ||||||||
\(653\) | −40.4924 | −1.58459 | −0.792295 | − | 0.610138i | \(-0.791114\pi\) | ||||
−0.792295 | + | 0.610138i | \(0.791114\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −21.9460 | −0.856848 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 14.9309 | 0.582066 | ||||||||
\(659\) | 33.3693 | 1.29988 | 0.649942 | − | 0.759984i | \(-0.274793\pi\) | ||||
0.649942 | + | 0.759984i | \(0.274793\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −13.8078 | −0.537060 | −0.268530 | − | 0.963271i | \(-0.586538\pi\) | ||||
−0.268530 | + | 0.963271i | \(0.586538\pi\) | |||||||
\(662\) | 9.75379 | 0.379092 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 7.61553 | 0.294874 | ||||||||
\(668\) | −4.10795 | −0.158941 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 3.43845 | 0.132740 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −35.3693 | −1.36339 | −0.681693 | − | 0.731638i | \(-0.738756\pi\) | ||||
−0.681693 | + | 0.731638i | \(0.738756\pi\) | |||||||
\(674\) | −2.63068 | −0.101330 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 3.42329 | 0.131665 | ||||||||
\(677\) | −20.8769 | −0.802364 | −0.401182 | − | 0.915998i | \(-0.631401\pi\) | ||||
−0.401182 | + | 0.915998i | \(0.631401\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −6.12311 | −0.234983 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 12.0000 | 0.459504 | ||||||||
\(683\) | 0.192236 | 0.00735570 | 0.00367785 | − | 0.999993i | \(-0.498829\pi\) | ||||
0.00367785 | + | 0.999993i | \(0.498829\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 20.3002 | 0.775065 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −36.0000 | −1.37249 | ||||||||
\(689\) | −32.4924 | −1.23786 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −20.4924 | −0.779568 | −0.389784 | − | 0.920906i | \(-0.627450\pi\) | ||||
−0.389784 | + | 0.920906i | \(0.627450\pi\) | |||||||
\(692\) | −7.69981 | −0.292703 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 4.10795 | 0.155936 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −26.0540 | −0.986865 | ||||||||
\(698\) | 48.9848 | 1.85410 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 26.9309 | 1.01716 | 0.508582 | − | 0.861013i | \(-0.330170\pi\) | ||||
0.508582 | + | 0.861013i | \(0.330170\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −29.4233 | −1.10972 | ||||||||
\(704\) | −5.56155 | −0.209609 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 46.6307 | 1.75497 | ||||||||
\(707\) | −5.56155 | −0.209164 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −2.12311 | −0.0797349 | −0.0398675 | − | 0.999205i | \(-0.512694\pi\) | ||||
−0.0398675 | + | 0.999205i | \(0.512694\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 21.6458 | 0.811212 | ||||||||
\(713\) | 18.7386 | 0.701767 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 4.57671 | 0.171040 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 15.2311 | 0.568418 | ||||||||
\(719\) | 32.9848 | 1.23013 | 0.615064 | − | 0.788478i | \(-0.289130\pi\) | ||||
0.615064 | + | 0.788478i | \(0.289130\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −0.876894 | −0.0326573 | ||||||||
\(722\) | −15.6155 | −0.581150 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 8.82292 | 0.327901 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −7.05398 | −0.261617 | −0.130809 | − | 0.991408i | \(-0.541757\pi\) | ||||
−0.130809 | + | 0.991408i | \(0.541757\pi\) | |||||||
\(728\) | 11.1231 | 0.412250 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −42.7386 | −1.58075 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −2.00000 | −0.0738717 | −0.0369358 | − | 0.999318i | \(-0.511760\pi\) | ||||
−0.0369358 | + | 0.999318i | \(0.511760\pi\) | |||||||
\(734\) | 36.0000 | 1.32878 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 5.94602 | 0.219173 | ||||||||
\(737\) | 5.68466 | 0.209397 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 0.684658 | 0.0251856 | 0.0125928 | − | 0.999921i | \(-0.495991\pi\) | ||||
0.0125928 | + | 0.999921i | \(0.495991\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 11.1231 | 0.408342 | ||||||||
\(743\) | 9.86174 | 0.361792 | 0.180896 | − | 0.983502i | \(-0.442100\pi\) | ||||
0.180896 | + | 0.983502i | \(0.442100\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −10.6307 | −0.389217 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 2.43845 | 0.0891585 | ||||||||
\(749\) | −0.876894 | −0.0320410 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −22.7386 | −0.829745 | −0.414872 | − | 0.909880i | \(-0.636174\pi\) | ||||
−0.414872 | + | 0.909880i | \(0.636174\pi\) | |||||||
\(752\) | 44.7926 | 1.63342 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −22.2462 | −0.810159 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 47.3002 | 1.71915 | 0.859577 | − | 0.511006i | \(-0.170727\pi\) | ||||
0.859577 | + | 0.511006i | \(0.170727\pi\) | |||||||
\(758\) | 45.7538 | 1.66185 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 45.3693 | 1.64464 | 0.822318 | − | 0.569028i | \(-0.192680\pi\) | ||||
0.822318 | + | 0.569028i | \(0.192680\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −12.8078 | −0.463672 | ||||||||
\(764\) | 11.8078 | 0.427190 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −8.98485 | −0.324636 | ||||||||
\(767\) | 29.3693 | 1.06046 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −31.0540 | −1.11983 | −0.559917 | − | 0.828548i | \(-0.689167\pi\) | ||||
−0.559917 | + | 0.828548i | \(0.689167\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −5.89205 | −0.212059 | ||||||||
\(773\) | −15.5076 | −0.557769 | −0.278884 | − | 0.960325i | \(-0.589965\pi\) | ||||
−0.278884 | + | 0.960325i | \(0.589965\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −14.9309 | −0.535987 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 52.8769 | 1.89573 | ||||||||
\(779\) | 14.0540 | 0.503536 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 11.8078 | 0.422515 | ||||||||
\(782\) | 21.1771 | 0.757291 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 28.1080 | 1.00386 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −53.7386 | −1.91558 | −0.957788 | − | 0.287476i | \(-0.907184\pi\) | ||||
−0.957788 | + | 0.287476i | \(0.907184\pi\) | |||||||
\(788\) | 4.79261 | 0.170730 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −0.876894 | −0.0311788 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −15.6847 | −0.556979 | ||||||||
\(794\) | −50.8466 | −1.80448 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 2.98485 | 0.105795 | ||||||||
\(797\) | −51.1231 | −1.81087 | −0.905437 | − | 0.424481i | \(-0.860456\pi\) | ||||
−0.905437 | + | 0.424481i | \(0.860456\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 53.1771 | 1.88127 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −55.6155 | −1.96385 | ||||||||
\(803\) | −0.246211 | −0.00868861 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −54.7386 | −1.92809 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −13.5616 | −0.477094 | ||||||||
\(809\) | 7.31534 | 0.257194 | 0.128597 | − | 0.991697i | \(-0.458953\pi\) | ||||
0.128597 | + | 0.991697i | \(0.458953\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −1.00000 | −0.0351147 | −0.0175574 | − | 0.999846i | \(-0.505589\pi\) | ||||
−0.0175574 | + | 0.999846i | \(0.505589\pi\) | |||||||
\(812\) | 1.36932 | 0.0480536 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 15.3153 | 0.536802 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 23.0540 | 0.806557 | ||||||||
\(818\) | −45.3693 | −1.58630 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −16.8769 | −0.589008 | −0.294504 | − | 0.955650i | \(-0.595154\pi\) | ||||
−0.294504 | + | 0.955650i | \(0.595154\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 37.0540 | 1.29162 | 0.645810 | − | 0.763498i | \(-0.276520\pi\) | ||||
0.645810 | + | 0.763498i | \(0.276520\pi\) | |||||||
\(824\) | −2.13826 | −0.0744898 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −10.0540 | −0.349823 | ||||||||
\(827\) | −26.2462 | −0.912670 | −0.456335 | − | 0.889808i | \(-0.650838\pi\) | ||||
−0.456335 | + | 0.889808i | \(0.650838\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −0.738634 | −0.0256538 | −0.0128269 | − | 0.999918i | \(-0.504083\pi\) | ||||
−0.0128269 | + | 0.999918i | \(0.504083\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 25.3693 | 0.879523 | ||||||||
\(833\) | 33.3693 | 1.15618 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −1.31534 | −0.0454920 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 46.1619 | 1.59464 | ||||||||
\(839\) | −12.4924 | −0.431286 | −0.215643 | − | 0.976472i | \(-0.569185\pi\) | ||||
−0.215643 | + | 0.976472i | \(0.569185\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −19.2462 | −0.663662 | ||||||||
\(842\) | 31.3153 | 1.07920 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 6.87689 | 0.236712 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1.00000 | −0.0343604 | ||||||||
\(848\) | 33.3693 | 1.14591 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 23.9157 | 0.819820 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −26.4233 | −0.904716 | −0.452358 | − | 0.891836i | \(-0.649417\pi\) | ||||
−0.452358 | + | 0.891836i | \(0.649417\pi\) | |||||||
\(854\) | 5.36932 | 0.183734 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −2.13826 | −0.0730842 | ||||||||
\(857\) | −9.56155 | −0.326616 | −0.163308 | − | 0.986575i | \(-0.552216\pi\) | ||||
−0.163308 | + | 0.986575i | \(0.552216\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −34.3542 | −1.17215 | −0.586074 | − | 0.810257i | \(-0.699327\pi\) | ||||
−0.586074 | + | 0.810257i | \(0.699327\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −59.7235 | −2.03419 | ||||||||
\(863\) | −14.2462 | −0.484947 | −0.242473 | − | 0.970158i | \(-0.577959\pi\) | ||||
−0.242473 | + | 0.970158i | \(0.577959\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 18.6307 | 0.633096 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 3.36932 | 0.114362 | ||||||||
\(869\) | 3.31534 | 0.112465 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −25.9309 | −0.878634 | ||||||||
\(872\) | −31.2311 | −1.05762 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −11.4233 | −0.386399 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 23.0540 | 0.778477 | 0.389239 | − | 0.921137i | \(-0.372738\pi\) | ||||
0.389239 | + | 0.921137i | \(0.372738\pi\) | |||||||
\(878\) | −58.9309 | −1.98882 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −26.2462 | −0.884257 | −0.442129 | − | 0.896952i | \(-0.645777\pi\) | ||||
−0.442129 | + | 0.896952i | \(0.645777\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 16.0691 | 0.540769 | 0.270385 | − | 0.962752i | \(-0.412849\pi\) | ||||
0.270385 | + | 0.962752i | \(0.412849\pi\) | |||||||
\(884\) | −11.1231 | −0.374111 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 44.1922 | 1.48467 | ||||||||
\(887\) | 29.8617 | 1.00266 | 0.501330 | − | 0.865256i | \(-0.332844\pi\) | ||||
0.501330 | + | 0.865256i | \(0.332844\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 15.8078 | 0.530175 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −0.522732 | −0.0175024 | ||||||||
\(893\) | −28.6847 | −0.959895 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −13.5616 | −0.453060 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 7.01515 | 0.234099 | ||||||||
\(899\) | 24.0000 | 0.800445 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 39.6155 | 1.31978 | ||||||||
\(902\) | −7.31534 | −0.243574 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −2.13826 | −0.0711175 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 28.1080 | 0.933309 | 0.466655 | − | 0.884440i | \(-0.345459\pi\) | ||||
0.466655 | + | 0.884440i | \(0.345459\pi\) | |||||||
\(908\) | 5.47727 | 0.181770 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 54.1619 | 1.79446 | 0.897232 | − | 0.441559i | \(-0.145574\pi\) | ||||
0.897232 | + | 0.441559i | \(0.145574\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 17.7538 | 0.587243 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0.0539753 | 0.00178339 | ||||||||
\(917\) | −16.4924 | −0.544628 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −33.1080 | −1.09213 | −0.546065 | − | 0.837743i | \(-0.683875\pi\) | ||||
−0.546065 | + | 0.837743i | \(0.683875\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 65.3693 | 2.15282 | ||||||||
\(923\) | −53.8617 | −1.77288 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 28.4924 | 0.936319 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 7.61553 | 0.249992 | ||||||||
\(929\) | −59.2311 | −1.94331 | −0.971654 | − | 0.236408i | \(-0.924030\pi\) | ||||
−0.971654 | + | 0.236408i | \(0.924030\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −18.0000 | −0.589926 | ||||||||
\(932\) | −1.83807 | −0.0602081 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 22.2462 | 0.727918 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −22.3153 | −0.729010 | −0.364505 | − | 0.931201i | \(-0.618762\pi\) | ||||
−0.364505 | + | 0.931201i | \(0.618762\pi\) | |||||||
\(938\) | 8.87689 | 0.289841 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 14.8229 | 0.483213 | 0.241607 | − | 0.970374i | \(-0.422326\pi\) | ||||
0.241607 | + | 0.970374i | \(0.422326\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −11.4233 | −0.371994 | ||||||||
\(944\) | −30.1619 | −0.981687 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −12.0000 | −0.390154 | ||||||||
\(947\) | −13.1771 | −0.428198 | −0.214099 | − | 0.976812i | \(-0.568681\pi\) | ||||
−0.214099 | + | 0.976812i | \(0.568681\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1.12311 | 0.0364576 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −13.5616 | −0.439532 | ||||||||
\(953\) | −15.8078 | −0.512064 | −0.256032 | − | 0.966668i | \(-0.582415\pi\) | ||||
−0.256032 | + | 0.966668i | \(0.582415\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 7.23106 | 0.233869 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −33.3693 | −1.07811 | ||||||||
\(959\) | 21.3693 | 0.690051 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 28.0540 | 0.904967 | ||||||||
\(962\) | −69.8617 | −2.25243 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 10.1080 | 0.325555 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −44.0000 | −1.41494 | −0.707472 | − | 0.706741i | \(-0.750165\pi\) | ||||
−0.707472 | + | 0.706741i | \(0.750165\pi\) | |||||||
\(968\) | −2.43845 | −0.0783747 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −37.1771 | −1.19307 | −0.596535 | − | 0.802587i | \(-0.703456\pi\) | ||||
−0.596535 | + | 0.802587i | \(0.703456\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −8.00000 | −0.256468 | ||||||||
\(974\) | −39.1231 | −1.25359 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 16.1080 | 0.515603 | ||||||||
\(977\) | −15.6155 | −0.499585 | −0.249793 | − | 0.968299i | \(-0.580362\pi\) | ||||
−0.249793 | + | 0.968299i | \(0.580362\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 8.87689 | 0.283707 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −25.7538 | −0.821836 | ||||||||
\(983\) | 6.93087 | 0.221060 | 0.110530 | − | 0.993873i | \(-0.464745\pi\) | ||||
0.110530 | + | 0.993873i | \(0.464745\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 27.1231 | 0.863776 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 6.00000 | 0.190885 | ||||||||
\(989\) | −18.7386 | −0.595854 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 49.6847 | 1.57829 | 0.789143 | − | 0.614210i | \(-0.210525\pi\) | ||||
0.789143 | + | 0.614210i | \(0.210525\pi\) | |||||||
\(992\) | 18.7386 | 0.594952 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 18.4384 | 0.584832 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 28.7386 | 0.910162 | 0.455081 | − | 0.890450i | \(-0.349610\pi\) | ||||
0.455081 | + | 0.890450i | \(0.349610\pi\) | |||||||
\(998\) | −26.2462 | −0.830809 | ||||||||
\(999\) | 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 | 2475.2.a.p.1.2 | ✓ | 2 | |
3.2 | odd | 2 | 2475.2.a.u.1.1 | yes | 2 | ||
5.2 | odd | 4 | 2475.2.c.i.199.3 | 4 | |||
5.3 | odd | 4 | 2475.2.c.i.199.2 | 4 | |||
5.4 | even | 2 | 2475.2.a.v.1.1 | yes | 2 | ||
15.2 | even | 4 | 2475.2.c.j.199.2 | 4 | |||
15.8 | even | 4 | 2475.2.c.j.199.3 | 4 | |||
15.14 | odd | 2 | 2475.2.a.q.1.2 | yes | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2475.2.a.p.1.2 | ✓ | 2 | 1.1 | even | 1 | trivial | |
2475.2.a.q.1.2 | yes | 2 | 15.14 | odd | 2 | ||
2475.2.a.u.1.1 | yes | 2 | 3.2 | odd | 2 | ||
2475.2.a.v.1.1 | yes | 2 | 5.4 | even | 2 | ||
2475.2.c.i.199.2 | 4 | 5.3 | odd | 4 | |||
2475.2.c.i.199.3 | 4 | 5.2 | odd | 4 | |||
2475.2.c.j.199.2 | 4 | 15.2 | even | 4 | |||
2475.2.c.j.199.3 | 4 | 15.8 | even | 4 |