Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2850,2,Mod(1,2850)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2850, 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("2850.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2850 = 2 \cdot 3 \cdot 5^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2850.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: | \(22.7573645761\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{6}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 6 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(2.44949\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2850.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 1.00000 | 0.408248 | ||||||||
\(7\) | 4.44949 | 1.68175 | 0.840875 | − | 0.541230i | \(-0.182041\pi\) | ||||
0.840875 | + | 0.541230i | \(0.182041\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.44949 | 1.04006 | 0.520030 | − | 0.854148i | \(-0.325921\pi\) | ||||
0.520030 | + | 0.854148i | \(0.325921\pi\) | |||||||
\(12\) | 1.00000 | 0.288675 | ||||||||
\(13\) | −2.44949 | −0.679366 | −0.339683 | − | 0.940540i | \(-0.610320\pi\) | ||||
−0.339683 | + | 0.940540i | \(0.610320\pi\) | |||||||
\(14\) | 4.44949 | 1.18918 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 4.44949 | 1.07916 | 0.539580 | − | 0.841934i | \(-0.318583\pi\) | ||||
0.539580 | + | 0.841934i | \(0.318583\pi\) | |||||||
\(18\) | 1.00000 | 0.235702 | ||||||||
\(19\) | 1.00000 | 0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 4.44949 | 0.970958 | ||||||||
\(22\) | 3.44949 | 0.735434 | ||||||||
\(23\) | −1.00000 | −0.208514 | −0.104257 | − | 0.994550i | \(-0.533247\pi\) | ||||
−0.104257 | + | 0.994550i | \(0.533247\pi\) | |||||||
\(24\) | 1.00000 | 0.204124 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −2.44949 | −0.480384 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 4.44949 | 0.840875 | ||||||||
\(29\) | −4.34847 | −0.807490 | −0.403745 | − | 0.914871i | \(-0.632292\pi\) | ||||
−0.403745 | + | 0.914871i | \(0.632292\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.00000 | −0.538816 | −0.269408 | − | 0.963026i | \(-0.586828\pi\) | ||||
−0.269408 | + | 0.963026i | \(0.586828\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 3.44949 | 0.600479 | ||||||||
\(34\) | 4.44949 | 0.763081 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | −7.79796 | −1.28198 | −0.640988 | − | 0.767551i | \(-0.721475\pi\) | ||||
−0.640988 | + | 0.767551i | \(0.721475\pi\) | |||||||
\(38\) | 1.00000 | 0.162221 | ||||||||
\(39\) | −2.44949 | −0.392232 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −0.898979 | −0.140397 | −0.0701985 | − | 0.997533i | \(-0.522363\pi\) | ||||
−0.0701985 | + | 0.997533i | \(0.522363\pi\) | |||||||
\(42\) | 4.44949 | 0.686571 | ||||||||
\(43\) | −2.44949 | −0.373544 | −0.186772 | − | 0.982403i | \(-0.559803\pi\) | ||||
−0.186772 | + | 0.982403i | \(0.559803\pi\) | |||||||
\(44\) | 3.44949 | 0.520030 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −1.00000 | −0.147442 | ||||||||
\(47\) | −7.79796 | −1.13745 | −0.568725 | − | 0.822528i | \(-0.692563\pi\) | ||||
−0.568725 | + | 0.822528i | \(0.692563\pi\) | |||||||
\(48\) | 1.00000 | 0.144338 | ||||||||
\(49\) | 12.7980 | 1.82828 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 4.44949 | 0.623053 | ||||||||
\(52\) | −2.44949 | −0.339683 | ||||||||
\(53\) | −7.44949 | −1.02327 | −0.511633 | − | 0.859204i | \(-0.670959\pi\) | ||||
−0.511633 | + | 0.859204i | \(0.670959\pi\) | |||||||
\(54\) | 1.00000 | 0.136083 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 4.44949 | 0.594588 | ||||||||
\(57\) | 1.00000 | 0.132453 | ||||||||
\(58\) | −4.34847 | −0.570982 | ||||||||
\(59\) | 6.44949 | 0.839652 | 0.419826 | − | 0.907605i | \(-0.362091\pi\) | ||||
0.419826 | + | 0.907605i | \(0.362091\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −9.44949 | −1.20988 | −0.604942 | − | 0.796270i | \(-0.706804\pi\) | ||||
−0.604942 | + | 0.796270i | \(0.706804\pi\) | |||||||
\(62\) | −3.00000 | −0.381000 | ||||||||
\(63\) | 4.44949 | 0.560583 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 3.44949 | 0.424603 | ||||||||
\(67\) | 15.2474 | 1.86277 | 0.931386 | − | 0.364033i | \(-0.118600\pi\) | ||||
0.931386 | + | 0.364033i | \(0.118600\pi\) | |||||||
\(68\) | 4.44949 | 0.539580 | ||||||||
\(69\) | −1.00000 | −0.120386 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −1.55051 | −0.184012 | −0.0920059 | − | 0.995758i | \(-0.529328\pi\) | ||||
−0.0920059 | + | 0.995758i | \(0.529328\pi\) | |||||||
\(72\) | 1.00000 | 0.117851 | ||||||||
\(73\) | −1.00000 | −0.117041 | −0.0585206 | − | 0.998286i | \(-0.518638\pi\) | ||||
−0.0585206 | + | 0.998286i | \(0.518638\pi\) | |||||||
\(74\) | −7.79796 | −0.906494 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 1.00000 | 0.114708 | ||||||||
\(77\) | 15.3485 | 1.74912 | ||||||||
\(78\) | −2.44949 | −0.277350 | ||||||||
\(79\) | −5.00000 | −0.562544 | −0.281272 | − | 0.959628i | \(-0.590756\pi\) | ||||
−0.281272 | + | 0.959628i | \(0.590756\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −0.898979 | −0.0992757 | ||||||||
\(83\) | 8.34847 | 0.916364 | 0.458182 | − | 0.888859i | \(-0.348501\pi\) | ||||
0.458182 | + | 0.888859i | \(0.348501\pi\) | |||||||
\(84\) | 4.44949 | 0.485479 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −2.44949 | −0.264135 | ||||||||
\(87\) | −4.34847 | −0.466205 | ||||||||
\(88\) | 3.44949 | 0.367717 | ||||||||
\(89\) | 2.10102 | 0.222708 | 0.111354 | − | 0.993781i | \(-0.464481\pi\) | ||||
0.111354 | + | 0.993781i | \(0.464481\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −10.8990 | −1.14252 | ||||||||
\(92\) | −1.00000 | −0.104257 | ||||||||
\(93\) | −3.00000 | −0.311086 | ||||||||
\(94\) | −7.79796 | −0.804298 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 1.00000 | 0.102062 | ||||||||
\(97\) | 1.55051 | 0.157430 | 0.0787152 | − | 0.996897i | \(-0.474918\pi\) | ||||
0.0787152 | + | 0.996897i | \(0.474918\pi\) | |||||||
\(98\) | 12.7980 | 1.29279 | ||||||||
\(99\) | 3.44949 | 0.346687 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1.55051 | −0.154282 | −0.0771408 | − | 0.997020i | \(-0.524579\pi\) | ||||
−0.0771408 | + | 0.997020i | \(0.524579\pi\) | |||||||
\(102\) | 4.44949 | 0.440565 | ||||||||
\(103\) | 1.89898 | 0.187112 | 0.0935560 | − | 0.995614i | \(-0.470177\pi\) | ||||
0.0935560 | + | 0.995614i | \(0.470177\pi\) | |||||||
\(104\) | −2.44949 | −0.240192 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −7.44949 | −0.723558 | ||||||||
\(107\) | 17.3485 | 1.67714 | 0.838570 | − | 0.544794i | \(-0.183392\pi\) | ||||
0.838570 | + | 0.544794i | \(0.183392\pi\) | |||||||
\(108\) | 1.00000 | 0.0962250 | ||||||||
\(109\) | −2.89898 | −0.277672 | −0.138836 | − | 0.990315i | \(-0.544336\pi\) | ||||
−0.138836 | + | 0.990315i | \(0.544336\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −7.79796 | −0.740150 | ||||||||
\(112\) | 4.44949 | 0.420437 | ||||||||
\(113\) | −16.7980 | −1.58022 | −0.790110 | − | 0.612966i | \(-0.789976\pi\) | ||||
−0.790110 | + | 0.612966i | \(0.789976\pi\) | |||||||
\(114\) | 1.00000 | 0.0936586 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −4.34847 | −0.403745 | ||||||||
\(117\) | −2.44949 | −0.226455 | ||||||||
\(118\) | 6.44949 | 0.593724 | ||||||||
\(119\) | 19.7980 | 1.81488 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0.898979 | 0.0817254 | ||||||||
\(122\) | −9.44949 | −0.855517 | ||||||||
\(123\) | −0.898979 | −0.0810583 | ||||||||
\(124\) | −3.00000 | −0.269408 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 4.44949 | 0.396392 | ||||||||
\(127\) | 0.101021 | 0.00896412 | 0.00448206 | − | 0.999990i | \(-0.498573\pi\) | ||||
0.00448206 | + | 0.999990i | \(0.498573\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | −2.44949 | −0.215666 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 9.24745 | 0.807953 | 0.403977 | − | 0.914769i | \(-0.367628\pi\) | ||||
0.403977 | + | 0.914769i | \(0.367628\pi\) | |||||||
\(132\) | 3.44949 | 0.300240 | ||||||||
\(133\) | 4.44949 | 0.385820 | ||||||||
\(134\) | 15.2474 | 1.31718 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 4.44949 | 0.381541 | ||||||||
\(137\) | −4.89898 | −0.418548 | −0.209274 | − | 0.977857i | \(-0.567110\pi\) | ||||
−0.209274 | + | 0.977857i | \(0.567110\pi\) | |||||||
\(138\) | −1.00000 | −0.0851257 | ||||||||
\(139\) | −22.2474 | −1.88700 | −0.943502 | − | 0.331367i | \(-0.892490\pi\) | ||||
−0.943502 | + | 0.331367i | \(0.892490\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −7.79796 | −0.656707 | ||||||||
\(142\) | −1.55051 | −0.130116 | ||||||||
\(143\) | −8.44949 | −0.706582 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −1.00000 | −0.0827606 | ||||||||
\(147\) | 12.7980 | 1.05556 | ||||||||
\(148\) | −7.79796 | −0.640988 | ||||||||
\(149\) | 5.79796 | 0.474987 | 0.237494 | − | 0.971389i | \(-0.423674\pi\) | ||||
0.237494 | + | 0.971389i | \(0.423674\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −23.7980 | −1.93665 | −0.968325 | − | 0.249692i | \(-0.919671\pi\) | ||||
−0.968325 | + | 0.249692i | \(0.919671\pi\) | |||||||
\(152\) | 1.00000 | 0.0811107 | ||||||||
\(153\) | 4.44949 | 0.359720 | ||||||||
\(154\) | 15.3485 | 1.23681 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −2.44949 | −0.196116 | ||||||||
\(157\) | −4.89898 | −0.390981 | −0.195491 | − | 0.980706i | \(-0.562630\pi\) | ||||
−0.195491 | + | 0.980706i | \(0.562630\pi\) | |||||||
\(158\) | −5.00000 | −0.397779 | ||||||||
\(159\) | −7.44949 | −0.590783 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −4.44949 | −0.350669 | ||||||||
\(162\) | 1.00000 | 0.0785674 | ||||||||
\(163\) | 19.7980 | 1.55070 | 0.775348 | − | 0.631534i | \(-0.217575\pi\) | ||||
0.775348 | + | 0.631534i | \(0.217575\pi\) | |||||||
\(164\) | −0.898979 | −0.0701985 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 8.34847 | 0.647967 | ||||||||
\(167\) | 18.0000 | 1.39288 | 0.696441 | − | 0.717614i | \(-0.254766\pi\) | ||||
0.696441 | + | 0.717614i | \(0.254766\pi\) | |||||||
\(168\) | 4.44949 | 0.343286 | ||||||||
\(169\) | −7.00000 | −0.538462 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.00000 | 0.0764719 | ||||||||
\(172\) | −2.44949 | −0.186772 | ||||||||
\(173\) | −1.65153 | −0.125564 | −0.0627818 | − | 0.998027i | \(-0.519997\pi\) | ||||
−0.0627818 | + | 0.998027i | \(0.519997\pi\) | |||||||
\(174\) | −4.34847 | −0.329657 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 3.44949 | 0.260015 | ||||||||
\(177\) | 6.44949 | 0.484773 | ||||||||
\(178\) | 2.10102 | 0.157478 | ||||||||
\(179\) | 25.7980 | 1.92823 | 0.964115 | − | 0.265485i | \(-0.0855321\pi\) | ||||
0.964115 | + | 0.265485i | \(0.0855321\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −14.4495 | −1.07402 | −0.537011 | − | 0.843575i | \(-0.680447\pi\) | ||||
−0.537011 | + | 0.843575i | \(0.680447\pi\) | |||||||
\(182\) | −10.8990 | −0.807886 | ||||||||
\(183\) | −9.44949 | −0.698526 | ||||||||
\(184\) | −1.00000 | −0.0737210 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −3.00000 | −0.219971 | ||||||||
\(187\) | 15.3485 | 1.12239 | ||||||||
\(188\) | −7.79796 | −0.568725 | ||||||||
\(189\) | 4.44949 | 0.323653 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −0.101021 | −0.00730959 | −0.00365479 | − | 0.999993i | \(-0.501163\pi\) | ||||
−0.00365479 | + | 0.999993i | \(0.501163\pi\) | |||||||
\(192\) | 1.00000 | 0.0721688 | ||||||||
\(193\) | −15.3485 | −1.10481 | −0.552403 | − | 0.833577i | \(-0.686289\pi\) | ||||
−0.552403 | + | 0.833577i | \(0.686289\pi\) | |||||||
\(194\) | 1.55051 | 0.111320 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 12.7980 | 0.914140 | ||||||||
\(197\) | 27.3485 | 1.94850 | 0.974249 | − | 0.225475i | \(-0.0723935\pi\) | ||||
0.974249 | + | 0.225475i | \(0.0723935\pi\) | |||||||
\(198\) | 3.44949 | 0.245145 | ||||||||
\(199\) | −10.0000 | −0.708881 | −0.354441 | − | 0.935079i | \(-0.615329\pi\) | ||||
−0.354441 | + | 0.935079i | \(0.615329\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 15.2474 | 1.07547 | ||||||||
\(202\) | −1.55051 | −0.109094 | ||||||||
\(203\) | −19.3485 | −1.35800 | ||||||||
\(204\) | 4.44949 | 0.311527 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 1.89898 | 0.132308 | ||||||||
\(207\) | −1.00000 | −0.0695048 | ||||||||
\(208\) | −2.44949 | −0.169842 | ||||||||
\(209\) | 3.44949 | 0.238606 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −3.65153 | −0.251382 | −0.125691 | − | 0.992069i | \(-0.540115\pi\) | ||||
−0.125691 | + | 0.992069i | \(0.540115\pi\) | |||||||
\(212\) | −7.44949 | −0.511633 | ||||||||
\(213\) | −1.55051 | −0.106239 | ||||||||
\(214\) | 17.3485 | 1.18592 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | −13.3485 | −0.906153 | ||||||||
\(218\) | −2.89898 | −0.196344 | ||||||||
\(219\) | −1.00000 | −0.0675737 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −10.8990 | −0.733145 | ||||||||
\(222\) | −7.79796 | −0.523365 | ||||||||
\(223\) | 16.1010 | 1.07820 | 0.539102 | − | 0.842240i | \(-0.318764\pi\) | ||||
0.539102 | + | 0.842240i | \(0.318764\pi\) | |||||||
\(224\) | 4.44949 | 0.297294 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −16.7980 | −1.11738 | ||||||||
\(227\) | 29.5959 | 1.96435 | 0.982175 | − | 0.187969i | \(-0.0601903\pi\) | ||||
0.982175 | + | 0.187969i | \(0.0601903\pi\) | |||||||
\(228\) | 1.00000 | 0.0662266 | ||||||||
\(229\) | 7.24745 | 0.478925 | 0.239462 | − | 0.970906i | \(-0.423029\pi\) | ||||
0.239462 | + | 0.970906i | \(0.423029\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 15.3485 | 1.00986 | ||||||||
\(232\) | −4.34847 | −0.285491 | ||||||||
\(233\) | 6.24745 | 0.409284 | 0.204642 | − | 0.978837i | \(-0.434397\pi\) | ||||
0.204642 | + | 0.978837i | \(0.434397\pi\) | |||||||
\(234\) | −2.44949 | −0.160128 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 6.44949 | 0.419826 | ||||||||
\(237\) | −5.00000 | −0.324785 | ||||||||
\(238\) | 19.7980 | 1.28331 | ||||||||
\(239\) | −8.69694 | −0.562558 | −0.281279 | − | 0.959626i | \(-0.590759\pi\) | ||||
−0.281279 | + | 0.959626i | \(0.590759\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −4.44949 | −0.286617 | −0.143308 | − | 0.989678i | \(-0.545774\pi\) | ||||
−0.143308 | + | 0.989678i | \(0.545774\pi\) | |||||||
\(242\) | 0.898979 | 0.0577886 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | −9.44949 | −0.604942 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −0.898979 | −0.0573168 | ||||||||
\(247\) | −2.44949 | −0.155857 | ||||||||
\(248\) | −3.00000 | −0.190500 | ||||||||
\(249\) | 8.34847 | 0.529063 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −18.0000 | −1.13615 | −0.568075 | − | 0.822977i | \(-0.692312\pi\) | ||||
−0.568075 | + | 0.822977i | \(0.692312\pi\) | |||||||
\(252\) | 4.44949 | 0.280292 | ||||||||
\(253\) | −3.44949 | −0.216868 | ||||||||
\(254\) | 0.101021 | 0.00633859 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −21.4949 | −1.34081 | −0.670407 | − | 0.741993i | \(-0.733881\pi\) | ||||
−0.670407 | + | 0.741993i | \(0.733881\pi\) | |||||||
\(258\) | −2.44949 | −0.152499 | ||||||||
\(259\) | −34.6969 | −2.15596 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −4.34847 | −0.269163 | ||||||||
\(262\) | 9.24745 | 0.571309 | ||||||||
\(263\) | −6.79796 | −0.419180 | −0.209590 | − | 0.977789i | \(-0.567213\pi\) | ||||
−0.209590 | + | 0.977789i | \(0.567213\pi\) | |||||||
\(264\) | 3.44949 | 0.212301 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 4.44949 | 0.272816 | ||||||||
\(267\) | 2.10102 | 0.128580 | ||||||||
\(268\) | 15.2474 | 0.931386 | ||||||||
\(269\) | −2.89898 | −0.176754 | −0.0883769 | − | 0.996087i | \(-0.528168\pi\) | ||||
−0.0883769 | + | 0.996087i | \(0.528168\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 22.9444 | 1.39377 | 0.696886 | − | 0.717182i | \(-0.254568\pi\) | ||||
0.696886 | + | 0.717182i | \(0.254568\pi\) | |||||||
\(272\) | 4.44949 | 0.269790 | ||||||||
\(273\) | −10.8990 | −0.659636 | ||||||||
\(274\) | −4.89898 | −0.295958 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −1.00000 | −0.0601929 | ||||||||
\(277\) | 21.0454 | 1.26450 | 0.632248 | − | 0.774766i | \(-0.282132\pi\) | ||||
0.632248 | + | 0.774766i | \(0.282132\pi\) | |||||||
\(278\) | −22.2474 | −1.33431 | ||||||||
\(279\) | −3.00000 | −0.179605 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 7.00000 | 0.417585 | 0.208792 | − | 0.977960i | \(-0.433047\pi\) | ||||
0.208792 | + | 0.977960i | \(0.433047\pi\) | |||||||
\(282\) | −7.79796 | −0.464362 | ||||||||
\(283\) | 29.7980 | 1.77130 | 0.885652 | − | 0.464349i | \(-0.153712\pi\) | ||||
0.885652 | + | 0.464349i | \(0.153712\pi\) | |||||||
\(284\) | −1.55051 | −0.0920059 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −8.44949 | −0.499629 | ||||||||
\(287\) | −4.00000 | −0.236113 | ||||||||
\(288\) | 1.00000 | 0.0589256 | ||||||||
\(289\) | 2.79796 | 0.164586 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1.55051 | 0.0908925 | ||||||||
\(292\) | −1.00000 | −0.0585206 | ||||||||
\(293\) | −23.2474 | −1.35813 | −0.679065 | − | 0.734078i | \(-0.737615\pi\) | ||||
−0.679065 | + | 0.734078i | \(0.737615\pi\) | |||||||
\(294\) | 12.7980 | 0.746392 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −7.79796 | −0.453247 | ||||||||
\(297\) | 3.44949 | 0.200160 | ||||||||
\(298\) | 5.79796 | 0.335867 | ||||||||
\(299\) | 2.44949 | 0.141658 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −10.8990 | −0.628207 | ||||||||
\(302\) | −23.7980 | −1.36942 | ||||||||
\(303\) | −1.55051 | −0.0890745 | ||||||||
\(304\) | 1.00000 | 0.0573539 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 4.44949 | 0.254360 | ||||||||
\(307\) | −16.3485 | −0.933056 | −0.466528 | − | 0.884506i | \(-0.654495\pi\) | ||||
−0.466528 | + | 0.884506i | \(0.654495\pi\) | |||||||
\(308\) | 15.3485 | 0.874560 | ||||||||
\(309\) | 1.89898 | 0.108029 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −23.7980 | −1.34946 | −0.674729 | − | 0.738065i | \(-0.735740\pi\) | ||||
−0.674729 | + | 0.738065i | \(0.735740\pi\) | |||||||
\(312\) | −2.44949 | −0.138675 | ||||||||
\(313\) | 31.8990 | 1.80304 | 0.901518 | − | 0.432741i | \(-0.142453\pi\) | ||||
0.901518 | + | 0.432741i | \(0.142453\pi\) | |||||||
\(314\) | −4.89898 | −0.276465 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −5.00000 | −0.281272 | ||||||||
\(317\) | 15.2474 | 0.856382 | 0.428191 | − | 0.903688i | \(-0.359151\pi\) | ||||
0.428191 | + | 0.903688i | \(0.359151\pi\) | |||||||
\(318\) | −7.44949 | −0.417747 | ||||||||
\(319\) | −15.0000 | −0.839839 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 17.3485 | 0.968297 | ||||||||
\(322\) | −4.44949 | −0.247960 | ||||||||
\(323\) | 4.44949 | 0.247576 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 19.7980 | 1.09651 | ||||||||
\(327\) | −2.89898 | −0.160314 | ||||||||
\(328\) | −0.898979 | −0.0496378 | ||||||||
\(329\) | −34.6969 | −1.91290 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −22.3485 | −1.22838 | −0.614191 | − | 0.789157i | \(-0.710518\pi\) | ||||
−0.614191 | + | 0.789157i | \(0.710518\pi\) | |||||||
\(332\) | 8.34847 | 0.458182 | ||||||||
\(333\) | −7.79796 | −0.427326 | ||||||||
\(334\) | 18.0000 | 0.984916 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 4.44949 | 0.242740 | ||||||||
\(337\) | −24.8990 | −1.35633 | −0.678167 | − | 0.734908i | \(-0.737225\pi\) | ||||
−0.678167 | + | 0.734908i | \(0.737225\pi\) | |||||||
\(338\) | −7.00000 | −0.380750 | ||||||||
\(339\) | −16.7980 | −0.912340 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −10.3485 | −0.560401 | ||||||||
\(342\) | 1.00000 | 0.0540738 | ||||||||
\(343\) | 25.7980 | 1.39296 | ||||||||
\(344\) | −2.44949 | −0.132068 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −1.65153 | −0.0887868 | ||||||||
\(347\) | −23.5959 | −1.26670 | −0.633348 | − | 0.773867i | \(-0.718320\pi\) | ||||
−0.633348 | + | 0.773867i | \(0.718320\pi\) | |||||||
\(348\) | −4.34847 | −0.233102 | ||||||||
\(349\) | −25.9444 | −1.38877 | −0.694386 | − | 0.719603i | \(-0.744324\pi\) | ||||
−0.694386 | + | 0.719603i | \(0.744324\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −2.44949 | −0.130744 | ||||||||
\(352\) | 3.44949 | 0.183858 | ||||||||
\(353\) | −18.2474 | −0.971214 | −0.485607 | − | 0.874177i | \(-0.661401\pi\) | ||||
−0.485607 | + | 0.874177i | \(0.661401\pi\) | |||||||
\(354\) | 6.44949 | 0.342787 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 2.10102 | 0.111354 | ||||||||
\(357\) | 19.7980 | 1.04782 | ||||||||
\(358\) | 25.7980 | 1.36346 | ||||||||
\(359\) | −22.8990 | −1.20856 | −0.604281 | − | 0.796771i | \(-0.706540\pi\) | ||||
−0.604281 | + | 0.796771i | \(0.706540\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | −14.4495 | −0.759448 | ||||||||
\(363\) | 0.898979 | 0.0471842 | ||||||||
\(364\) | −10.8990 | −0.571262 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −9.44949 | −0.493933 | ||||||||
\(367\) | −5.55051 | −0.289734 | −0.144867 | − | 0.989451i | \(-0.546275\pi\) | ||||
−0.144867 | + | 0.989451i | \(0.546275\pi\) | |||||||
\(368\) | −1.00000 | −0.0521286 | ||||||||
\(369\) | −0.898979 | −0.0467990 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −33.1464 | −1.72088 | ||||||||
\(372\) | −3.00000 | −0.155543 | ||||||||
\(373\) | −22.4495 | −1.16239 | −0.581195 | − | 0.813764i | \(-0.697415\pi\) | ||||
−0.581195 | + | 0.813764i | \(0.697415\pi\) | |||||||
\(374\) | 15.3485 | 0.793650 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −7.79796 | −0.402149 | ||||||||
\(377\) | 10.6515 | 0.548582 | ||||||||
\(378\) | 4.44949 | 0.228857 | ||||||||
\(379\) | −1.30306 | −0.0669338 | −0.0334669 | − | 0.999440i | \(-0.510655\pi\) | ||||
−0.0334669 | + | 0.999440i | \(0.510655\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0.101021 | 0.00517544 | ||||||||
\(382\) | −0.101021 | −0.00516866 | ||||||||
\(383\) | 16.2474 | 0.830206 | 0.415103 | − | 0.909774i | \(-0.363746\pi\) | ||||
0.415103 | + | 0.909774i | \(0.363746\pi\) | |||||||
\(384\) | 1.00000 | 0.0510310 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −15.3485 | −0.781217 | ||||||||
\(387\) | −2.44949 | −0.124515 | ||||||||
\(388\) | 1.55051 | 0.0787152 | ||||||||
\(389\) | 21.5959 | 1.09496 | 0.547478 | − | 0.836820i | \(-0.315588\pi\) | ||||
0.547478 | + | 0.836820i | \(0.315588\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −4.44949 | −0.225020 | ||||||||
\(392\) | 12.7980 | 0.646395 | ||||||||
\(393\) | 9.24745 | 0.466472 | ||||||||
\(394\) | 27.3485 | 1.37780 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 3.44949 | 0.173343 | ||||||||
\(397\) | 23.9444 | 1.20173 | 0.600867 | − | 0.799349i | \(-0.294822\pi\) | ||||
0.600867 | + | 0.799349i | \(0.294822\pi\) | |||||||
\(398\) | −10.0000 | −0.501255 | ||||||||
\(399\) | 4.44949 | 0.222753 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 11.2020 | 0.559403 | 0.279702 | − | 0.960087i | \(-0.409764\pi\) | ||||
0.279702 | + | 0.960087i | \(0.409764\pi\) | |||||||
\(402\) | 15.2474 | 0.760474 | ||||||||
\(403\) | 7.34847 | 0.366053 | ||||||||
\(404\) | −1.55051 | −0.0771408 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −19.3485 | −0.960248 | ||||||||
\(407\) | −26.8990 | −1.33333 | ||||||||
\(408\) | 4.44949 | 0.220283 | ||||||||
\(409\) | −22.8990 | −1.13228 | −0.566141 | − | 0.824309i | \(-0.691564\pi\) | ||||
−0.566141 | + | 0.824309i | \(0.691564\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −4.89898 | −0.241649 | ||||||||
\(412\) | 1.89898 | 0.0935560 | ||||||||
\(413\) | 28.6969 | 1.41208 | ||||||||
\(414\) | −1.00000 | −0.0491473 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −2.44949 | −0.120096 | ||||||||
\(417\) | −22.2474 | −1.08946 | ||||||||
\(418\) | 3.44949 | 0.168720 | ||||||||
\(419\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 22.0000 | 1.07221 | 0.536107 | − | 0.844150i | \(-0.319894\pi\) | ||||
0.536107 | + | 0.844150i | \(0.319894\pi\) | |||||||
\(422\) | −3.65153 | −0.177754 | ||||||||
\(423\) | −7.79796 | −0.379150 | ||||||||
\(424\) | −7.44949 | −0.361779 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −1.55051 | −0.0751225 | ||||||||
\(427\) | −42.0454 | −2.03472 | ||||||||
\(428\) | 17.3485 | 0.838570 | ||||||||
\(429\) | −8.44949 | −0.407945 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −5.10102 | −0.245708 | −0.122854 | − | 0.992425i | \(-0.539205\pi\) | ||||
−0.122854 | + | 0.992425i | \(0.539205\pi\) | |||||||
\(432\) | 1.00000 | 0.0481125 | ||||||||
\(433\) | 4.65153 | 0.223538 | 0.111769 | − | 0.993734i | \(-0.464348\pi\) | ||||
0.111769 | + | 0.993734i | \(0.464348\pi\) | |||||||
\(434\) | −13.3485 | −0.640747 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −2.89898 | −0.138836 | ||||||||
\(437\) | −1.00000 | −0.0478365 | ||||||||
\(438\) | −1.00000 | −0.0477818 | ||||||||
\(439\) | −12.1010 | −0.577550 | −0.288775 | − | 0.957397i | \(-0.593248\pi\) | ||||
−0.288775 | + | 0.957397i | \(0.593248\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 12.7980 | 0.609427 | ||||||||
\(442\) | −10.8990 | −0.518412 | ||||||||
\(443\) | 21.2474 | 1.00950 | 0.504748 | − | 0.863267i | \(-0.331585\pi\) | ||||
0.504748 | + | 0.863267i | \(0.331585\pi\) | |||||||
\(444\) | −7.79796 | −0.370075 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 16.1010 | 0.762405 | ||||||||
\(447\) | 5.79796 | 0.274234 | ||||||||
\(448\) | 4.44949 | 0.210219 | ||||||||
\(449\) | −15.0000 | −0.707894 | −0.353947 | − | 0.935266i | \(-0.615161\pi\) | ||||
−0.353947 | + | 0.935266i | \(0.615161\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −3.10102 | −0.146021 | ||||||||
\(452\) | −16.7980 | −0.790110 | ||||||||
\(453\) | −23.7980 | −1.11813 | ||||||||
\(454\) | 29.5959 | 1.38901 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 1.00000 | 0.0468293 | ||||||||
\(457\) | −24.8990 | −1.16473 | −0.582363 | − | 0.812929i | \(-0.697872\pi\) | ||||
−0.582363 | + | 0.812929i | \(0.697872\pi\) | |||||||
\(458\) | 7.24745 | 0.338651 | ||||||||
\(459\) | 4.44949 | 0.207684 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 12.0000 | 0.558896 | 0.279448 | − | 0.960161i | \(-0.409849\pi\) | ||||
0.279448 | + | 0.960161i | \(0.409849\pi\) | |||||||
\(462\) | 15.3485 | 0.714075 | ||||||||
\(463\) | −14.6969 | −0.683025 | −0.341512 | − | 0.939877i | \(-0.610939\pi\) | ||||
−0.341512 | + | 0.939877i | \(0.610939\pi\) | |||||||
\(464\) | −4.34847 | −0.201873 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 6.24745 | 0.289407 | ||||||||
\(467\) | −6.34847 | −0.293772 | −0.146886 | − | 0.989153i | \(-0.546925\pi\) | ||||
−0.146886 | + | 0.989153i | \(0.546925\pi\) | |||||||
\(468\) | −2.44949 | −0.113228 | ||||||||
\(469\) | 67.8434 | 3.13272 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −4.89898 | −0.225733 | ||||||||
\(472\) | 6.44949 | 0.296862 | ||||||||
\(473\) | −8.44949 | −0.388508 | ||||||||
\(474\) | −5.00000 | −0.229658 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 19.7980 | 0.907438 | ||||||||
\(477\) | −7.44949 | −0.341089 | ||||||||
\(478\) | −8.69694 | −0.397789 | ||||||||
\(479\) | 16.5959 | 0.758287 | 0.379143 | − | 0.925338i | \(-0.376219\pi\) | ||||
0.379143 | + | 0.925338i | \(0.376219\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 19.1010 | 0.870932 | ||||||||
\(482\) | −4.44949 | −0.202669 | ||||||||
\(483\) | −4.44949 | −0.202459 | ||||||||
\(484\) | 0.898979 | 0.0408627 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 1.00000 | 0.0453609 | ||||||||
\(487\) | −32.0000 | −1.45006 | −0.725029 | − | 0.688718i | \(-0.758174\pi\) | ||||
−0.725029 | + | 0.688718i | \(0.758174\pi\) | |||||||
\(488\) | −9.44949 | −0.427758 | ||||||||
\(489\) | 19.7980 | 0.895295 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 43.5959 | 1.96746 | 0.983728 | − | 0.179664i | \(-0.0575009\pi\) | ||||
0.983728 | + | 0.179664i | \(0.0575009\pi\) | |||||||
\(492\) | −0.898979 | −0.0405291 | ||||||||
\(493\) | −19.3485 | −0.871411 | ||||||||
\(494\) | −2.44949 | −0.110208 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −3.00000 | −0.134704 | ||||||||
\(497\) | −6.89898 | −0.309462 | ||||||||
\(498\) | 8.34847 | 0.374104 | ||||||||
\(499\) | −23.8434 | −1.06738 | −0.533688 | − | 0.845682i | \(-0.679194\pi\) | ||||
−0.533688 | + | 0.845682i | \(0.679194\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 18.0000 | 0.804181 | ||||||||
\(502\) | −18.0000 | −0.803379 | ||||||||
\(503\) | 29.7980 | 1.32863 | 0.664313 | − | 0.747455i | \(-0.268724\pi\) | ||||
0.664313 | + | 0.747455i | \(0.268724\pi\) | |||||||
\(504\) | 4.44949 | 0.198196 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −3.44949 | −0.153349 | ||||||||
\(507\) | −7.00000 | −0.310881 | ||||||||
\(508\) | 0.101021 | 0.00448206 | ||||||||
\(509\) | −30.1464 | −1.33622 | −0.668108 | − | 0.744064i | \(-0.732896\pi\) | ||||
−0.668108 | + | 0.744064i | \(0.732896\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −4.44949 | −0.196834 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 1.00000 | 0.0441511 | ||||||||
\(514\) | −21.4949 | −0.948099 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −2.44949 | −0.107833 | ||||||||
\(517\) | −26.8990 | −1.18302 | ||||||||
\(518\) | −34.6969 | −1.52450 | ||||||||
\(519\) | −1.65153 | −0.0724942 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 15.6969 | 0.687695 | 0.343848 | − | 0.939025i | \(-0.388270\pi\) | ||||
0.343848 | + | 0.939025i | \(0.388270\pi\) | |||||||
\(522\) | −4.34847 | −0.190327 | ||||||||
\(523\) | −33.3939 | −1.46021 | −0.730106 | − | 0.683334i | \(-0.760529\pi\) | ||||
−0.730106 | + | 0.683334i | \(0.760529\pi\) | |||||||
\(524\) | 9.24745 | 0.403977 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −6.79796 | −0.296405 | ||||||||
\(527\) | −13.3485 | −0.581468 | ||||||||
\(528\) | 3.44949 | 0.150120 | ||||||||
\(529\) | −22.0000 | −0.956522 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 6.44949 | 0.279884 | ||||||||
\(532\) | 4.44949 | 0.192910 | ||||||||
\(533\) | 2.20204 | 0.0953810 | ||||||||
\(534\) | 2.10102 | 0.0909200 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 15.2474 | 0.658589 | ||||||||
\(537\) | 25.7980 | 1.11326 | ||||||||
\(538\) | −2.89898 | −0.124984 | ||||||||
\(539\) | 44.1464 | 1.90152 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 22.1464 | 0.952149 | 0.476075 | − | 0.879405i | \(-0.342059\pi\) | ||||
0.476075 | + | 0.879405i | \(0.342059\pi\) | |||||||
\(542\) | 22.9444 | 0.985546 | ||||||||
\(543\) | −14.4495 | −0.620087 | ||||||||
\(544\) | 4.44949 | 0.190770 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −10.8990 | −0.466433 | ||||||||
\(547\) | −46.6413 | −1.99424 | −0.997120 | − | 0.0758461i | \(-0.975834\pi\) | ||||
−0.997120 | + | 0.0758461i | \(0.975834\pi\) | |||||||
\(548\) | −4.89898 | −0.209274 | ||||||||
\(549\) | −9.44949 | −0.403294 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −4.34847 | −0.185251 | ||||||||
\(552\) | −1.00000 | −0.0425628 | ||||||||
\(553\) | −22.2474 | −0.946058 | ||||||||
\(554\) | 21.0454 | 0.894134 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −22.2474 | −0.943502 | ||||||||
\(557\) | 27.3485 | 1.15879 | 0.579396 | − | 0.815046i | \(-0.303289\pi\) | ||||
0.579396 | + | 0.815046i | \(0.303289\pi\) | |||||||
\(558\) | −3.00000 | −0.127000 | ||||||||
\(559\) | 6.00000 | 0.253773 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 15.3485 | 0.648013 | ||||||||
\(562\) | 7.00000 | 0.295277 | ||||||||
\(563\) | 6.24745 | 0.263299 | 0.131649 | − | 0.991296i | \(-0.457973\pi\) | ||||
0.131649 | + | 0.991296i | \(0.457973\pi\) | |||||||
\(564\) | −7.79796 | −0.328353 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 29.7980 | 1.25250 | ||||||||
\(567\) | 4.44949 | 0.186861 | ||||||||
\(568\) | −1.55051 | −0.0650580 | ||||||||
\(569\) | −33.1918 | −1.39147 | −0.695737 | − | 0.718297i | \(-0.744922\pi\) | ||||
−0.695737 | + | 0.718297i | \(0.744922\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −10.2474 | −0.428842 | −0.214421 | − | 0.976741i | \(-0.568787\pi\) | ||||
−0.214421 | + | 0.976741i | \(0.568787\pi\) | |||||||
\(572\) | −8.44949 | −0.353291 | ||||||||
\(573\) | −0.101021 | −0.00422019 | ||||||||
\(574\) | −4.00000 | −0.166957 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | 0.101021 | 0.00420554 | 0.00210277 | − | 0.999998i | \(-0.499331\pi\) | ||||
0.00210277 | + | 0.999998i | \(0.499331\pi\) | |||||||
\(578\) | 2.79796 | 0.116380 | ||||||||
\(579\) | −15.3485 | −0.637861 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 37.1464 | 1.54109 | ||||||||
\(582\) | 1.55051 | 0.0642707 | ||||||||
\(583\) | −25.6969 | −1.06426 | ||||||||
\(584\) | −1.00000 | −0.0413803 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −23.2474 | −0.960343 | ||||||||
\(587\) | −33.4495 | −1.38061 | −0.690304 | − | 0.723519i | \(-0.742523\pi\) | ||||
−0.690304 | + | 0.723519i | \(0.742523\pi\) | |||||||
\(588\) | 12.7980 | 0.527779 | ||||||||
\(589\) | −3.00000 | −0.123613 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 27.3485 | 1.12497 | ||||||||
\(592\) | −7.79796 | −0.320494 | ||||||||
\(593\) | 8.49490 | 0.348844 | 0.174422 | − | 0.984671i | \(-0.444194\pi\) | ||||
0.174422 | + | 0.984671i | \(0.444194\pi\) | |||||||
\(594\) | 3.44949 | 0.141534 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 5.79796 | 0.237494 | ||||||||
\(597\) | −10.0000 | −0.409273 | ||||||||
\(598\) | 2.44949 | 0.100167 | ||||||||
\(599\) | 16.4495 | 0.672108 | 0.336054 | − | 0.941843i | \(-0.390908\pi\) | ||||
0.336054 | + | 0.941843i | \(0.390908\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 17.1464 | 0.699417 | 0.349709 | − | 0.936858i | \(-0.386281\pi\) | ||||
0.349709 | + | 0.936858i | \(0.386281\pi\) | |||||||
\(602\) | −10.8990 | −0.444209 | ||||||||
\(603\) | 15.2474 | 0.620924 | ||||||||
\(604\) | −23.7980 | −0.968325 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −1.55051 | −0.0629852 | ||||||||
\(607\) | 46.1918 | 1.87487 | 0.937434 | − | 0.348162i | \(-0.113194\pi\) | ||||
0.937434 | + | 0.348162i | \(0.113194\pi\) | |||||||
\(608\) | 1.00000 | 0.0405554 | ||||||||
\(609\) | −19.3485 | −0.784040 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 19.1010 | 0.772745 | ||||||||
\(612\) | 4.44949 | 0.179860 | ||||||||
\(613\) | 37.1918 | 1.50216 | 0.751082 | − | 0.660209i | \(-0.229532\pi\) | ||||
0.751082 | + | 0.660209i | \(0.229532\pi\) | |||||||
\(614\) | −16.3485 | −0.659771 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 15.3485 | 0.618407 | ||||||||
\(617\) | 28.2929 | 1.13903 | 0.569514 | − | 0.821982i | \(-0.307132\pi\) | ||||
0.569514 | + | 0.821982i | \(0.307132\pi\) | |||||||
\(618\) | 1.89898 | 0.0763882 | ||||||||
\(619\) | 45.1464 | 1.81459 | 0.907294 | − | 0.420497i | \(-0.138144\pi\) | ||||
0.907294 | + | 0.420497i | \(0.138144\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.00000 | −0.0401286 | ||||||||
\(622\) | −23.7980 | −0.954211 | ||||||||
\(623\) | 9.34847 | 0.374539 | ||||||||
\(624\) | −2.44949 | −0.0980581 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 31.8990 | 1.27494 | ||||||||
\(627\) | 3.44949 | 0.137759 | ||||||||
\(628\) | −4.89898 | −0.195491 | ||||||||
\(629\) | −34.6969 | −1.38346 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −28.0000 | −1.11466 | −0.557331 | − | 0.830290i | \(-0.688175\pi\) | ||||
−0.557331 | + | 0.830290i | \(0.688175\pi\) | |||||||
\(632\) | −5.00000 | −0.198889 | ||||||||
\(633\) | −3.65153 | −0.145135 | ||||||||
\(634\) | 15.2474 | 0.605554 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −7.44949 | −0.295391 | ||||||||
\(637\) | −31.3485 | −1.24207 | ||||||||
\(638\) | −15.0000 | −0.593856 | ||||||||
\(639\) | −1.55051 | −0.0613372 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 37.7980 | 1.49293 | 0.746465 | − | 0.665425i | \(-0.231750\pi\) | ||||
0.746465 | + | 0.665425i | \(0.231750\pi\) | |||||||
\(642\) | 17.3485 | 0.684689 | ||||||||
\(643\) | −0.202041 | −0.00796772 | −0.00398386 | − | 0.999992i | \(-0.501268\pi\) | ||||
−0.00398386 | + | 0.999992i | \(0.501268\pi\) | |||||||
\(644\) | −4.44949 | −0.175334 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 4.44949 | 0.175063 | ||||||||
\(647\) | 25.8990 | 1.01819 | 0.509097 | − | 0.860709i | \(-0.329979\pi\) | ||||
0.509097 | + | 0.860709i | \(0.329979\pi\) | |||||||
\(648\) | 1.00000 | 0.0392837 | ||||||||
\(649\) | 22.2474 | 0.873289 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −13.3485 | −0.523168 | ||||||||
\(652\) | 19.7980 | 0.775348 | ||||||||
\(653\) | −14.6969 | −0.575136 | −0.287568 | − | 0.957760i | \(-0.592847\pi\) | ||||
−0.287568 | + | 0.957760i | \(0.592847\pi\) | |||||||
\(654\) | −2.89898 | −0.113359 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −0.898979 | −0.0350993 | ||||||||
\(657\) | −1.00000 | −0.0390137 | ||||||||
\(658\) | −34.6969 | −1.35263 | ||||||||
\(659\) | −18.0454 | −0.702949 | −0.351475 | − | 0.936197i | \(-0.614320\pi\) | ||||
−0.351475 | + | 0.936197i | \(0.614320\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 23.5959 | 0.917775 | 0.458887 | − | 0.888494i | \(-0.348248\pi\) | ||||
0.458887 | + | 0.888494i | \(0.348248\pi\) | |||||||
\(662\) | −22.3485 | −0.868598 | ||||||||
\(663\) | −10.8990 | −0.423281 | ||||||||
\(664\) | 8.34847 | 0.323983 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −7.79796 | −0.302165 | ||||||||
\(667\) | 4.34847 | 0.168373 | ||||||||
\(668\) | 18.0000 | 0.696441 | ||||||||
\(669\) | 16.1010 | 0.622501 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −32.5959 | −1.25835 | ||||||||
\(672\) | 4.44949 | 0.171643 | ||||||||
\(673\) | −45.3485 | −1.74806 | −0.874028 | − | 0.485876i | \(-0.838501\pi\) | ||||
−0.874028 | + | 0.485876i | \(0.838501\pi\) | |||||||
\(674\) | −24.8990 | −0.959073 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −7.00000 | −0.269231 | ||||||||
\(677\) | 22.3485 | 0.858921 | 0.429461 | − | 0.903086i | \(-0.358704\pi\) | ||||
0.429461 | + | 0.903086i | \(0.358704\pi\) | |||||||
\(678\) | −16.7980 | −0.645122 | ||||||||
\(679\) | 6.89898 | 0.264759 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 29.5959 | 1.13412 | ||||||||
\(682\) | −10.3485 | −0.396263 | ||||||||
\(683\) | −35.6413 | −1.36378 | −0.681889 | − | 0.731456i | \(-0.738841\pi\) | ||||
−0.681889 | + | 0.731456i | \(0.738841\pi\) | |||||||
\(684\) | 1.00000 | 0.0382360 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 25.7980 | 0.984971 | ||||||||
\(687\) | 7.24745 | 0.276507 | ||||||||
\(688\) | −2.44949 | −0.0933859 | ||||||||
\(689\) | 18.2474 | 0.695172 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 9.75255 | 0.371005 | 0.185502 | − | 0.982644i | \(-0.440609\pi\) | ||||
0.185502 | + | 0.982644i | \(0.440609\pi\) | |||||||
\(692\) | −1.65153 | −0.0627818 | ||||||||
\(693\) | 15.3485 | 0.583040 | ||||||||
\(694\) | −23.5959 | −0.895689 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −4.34847 | −0.164828 | ||||||||
\(697\) | −4.00000 | −0.151511 | ||||||||
\(698\) | −25.9444 | −0.982010 | ||||||||
\(699\) | 6.24745 | 0.236300 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −32.4949 | −1.22732 | −0.613658 | − | 0.789572i | \(-0.710302\pi\) | ||||
−0.613658 | + | 0.789572i | \(0.710302\pi\) | |||||||
\(702\) | −2.44949 | −0.0924500 | ||||||||
\(703\) | −7.79796 | −0.294106 | ||||||||
\(704\) | 3.44949 | 0.130008 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −18.2474 | −0.686752 | ||||||||
\(707\) | −6.89898 | −0.259463 | ||||||||
\(708\) | 6.44949 | 0.242387 | ||||||||
\(709\) | −12.7526 | −0.478932 | −0.239466 | − | 0.970905i | \(-0.576972\pi\) | ||||
−0.239466 | + | 0.970905i | \(0.576972\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −5.00000 | −0.187515 | ||||||||
\(712\) | 2.10102 | 0.0787391 | ||||||||
\(713\) | 3.00000 | 0.112351 | ||||||||
\(714\) | 19.7980 | 0.740920 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 25.7980 | 0.964115 | ||||||||
\(717\) | −8.69694 | −0.324793 | ||||||||
\(718\) | −22.8990 | −0.854582 | ||||||||
\(719\) | −19.2020 | −0.716115 | −0.358058 | − | 0.933699i | \(-0.616561\pi\) | ||||
−0.358058 | + | 0.933699i | \(0.616561\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 8.44949 | 0.314675 | ||||||||
\(722\) | 1.00000 | 0.0372161 | ||||||||
\(723\) | −4.44949 | −0.165478 | ||||||||
\(724\) | −14.4495 | −0.537011 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0.898979 | 0.0333643 | ||||||||
\(727\) | 22.4949 | 0.834290 | 0.417145 | − | 0.908840i | \(-0.363031\pi\) | ||||
0.417145 | + | 0.908840i | \(0.363031\pi\) | |||||||
\(728\) | −10.8990 | −0.403943 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −10.8990 | −0.403113 | ||||||||
\(732\) | −9.44949 | −0.349263 | ||||||||
\(733\) | 4.14643 | 0.153152 | 0.0765759 | − | 0.997064i | \(-0.475601\pi\) | ||||
0.0765759 | + | 0.997064i | \(0.475601\pi\) | |||||||
\(734\) | −5.55051 | −0.204873 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −1.00000 | −0.0368605 | ||||||||
\(737\) | 52.5959 | 1.93740 | ||||||||
\(738\) | −0.898979 | −0.0330919 | ||||||||
\(739\) | 32.8990 | 1.21021 | 0.605104 | − | 0.796146i | \(-0.293131\pi\) | ||||
0.605104 | + | 0.796146i | \(0.293131\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −2.44949 | −0.0899843 | ||||||||
\(742\) | −33.1464 | −1.21684 | ||||||||
\(743\) | −53.3939 | −1.95883 | −0.979416 | − | 0.201854i | \(-0.935303\pi\) | ||||
−0.979416 | + | 0.201854i | \(0.935303\pi\) | |||||||
\(744\) | −3.00000 | −0.109985 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −22.4495 | −0.821934 | ||||||||
\(747\) | 8.34847 | 0.305455 | ||||||||
\(748\) | 15.3485 | 0.561196 | ||||||||
\(749\) | 77.1918 | 2.82053 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −23.7980 | −0.868400 | −0.434200 | − | 0.900817i | \(-0.642969\pi\) | ||||
−0.434200 | + | 0.900817i | \(0.642969\pi\) | |||||||
\(752\) | −7.79796 | −0.284362 | ||||||||
\(753\) | −18.0000 | −0.655956 | ||||||||
\(754\) | 10.6515 | 0.387906 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 4.44949 | 0.161826 | ||||||||
\(757\) | 48.1464 | 1.74991 | 0.874956 | − | 0.484203i | \(-0.160890\pi\) | ||||
0.874956 | + | 0.484203i | \(0.160890\pi\) | |||||||
\(758\) | −1.30306 | −0.0473293 | ||||||||
\(759\) | −3.44949 | −0.125209 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 51.3485 | 1.86138 | 0.930690 | − | 0.365808i | \(-0.119207\pi\) | ||||
0.930690 | + | 0.365808i | \(0.119207\pi\) | |||||||
\(762\) | 0.101021 | 0.00365959 | ||||||||
\(763\) | −12.8990 | −0.466974 | ||||||||
\(764\) | −0.101021 | −0.00365479 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 16.2474 | 0.587044 | ||||||||
\(767\) | −15.7980 | −0.570431 | ||||||||
\(768\) | 1.00000 | 0.0360844 | ||||||||
\(769\) | −7.89898 | −0.284844 | −0.142422 | − | 0.989806i | \(-0.545489\pi\) | ||||
−0.142422 | + | 0.989806i | \(0.545489\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −21.4949 | −0.774120 | ||||||||
\(772\) | −15.3485 | −0.552403 | ||||||||
\(773\) | 18.4949 | 0.665215 | 0.332608 | − | 0.943065i | \(-0.392072\pi\) | ||||
0.332608 | + | 0.943065i | \(0.392072\pi\) | |||||||
\(774\) | −2.44949 | −0.0880451 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 1.55051 | 0.0556601 | ||||||||
\(777\) | −34.6969 | −1.24475 | ||||||||
\(778\) | 21.5959 | 0.774251 | ||||||||
\(779\) | −0.898979 | −0.0322093 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −5.34847 | −0.191383 | ||||||||
\(782\) | −4.44949 | −0.159113 | ||||||||
\(783\) | −4.34847 | −0.155402 | ||||||||
\(784\) | 12.7980 | 0.457070 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 9.24745 | 0.329846 | ||||||||
\(787\) | −33.4495 | −1.19235 | −0.596173 | − | 0.802856i | \(-0.703313\pi\) | ||||
−0.596173 | + | 0.802856i | \(0.703313\pi\) | |||||||
\(788\) | 27.3485 | 0.974249 | ||||||||
\(789\) | −6.79796 | −0.242014 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −74.7423 | −2.65753 | ||||||||
\(792\) | 3.44949 | 0.122572 | ||||||||
\(793\) | 23.1464 | 0.821954 | ||||||||
\(794\) | 23.9444 | 0.849755 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −10.0000 | −0.354441 | ||||||||
\(797\) | 3.50510 | 0.124157 | 0.0620786 | − | 0.998071i | \(-0.480227\pi\) | ||||
0.0620786 | + | 0.998071i | \(0.480227\pi\) | |||||||
\(798\) | 4.44949 | 0.157510 | ||||||||
\(799\) | −34.6969 | −1.22749 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 2.10102 | 0.0742359 | ||||||||
\(802\) | 11.2020 | 0.395558 | ||||||||
\(803\) | −3.44949 | −0.121730 | ||||||||
\(804\) | 15.2474 | 0.537736 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 7.34847 | 0.258839 | ||||||||
\(807\) | −2.89898 | −0.102049 | ||||||||
\(808\) | −1.55051 | −0.0545468 | ||||||||
\(809\) | −3.55051 | −0.124829 | −0.0624146 | − | 0.998050i | \(-0.519880\pi\) | ||||
−0.0624146 | + | 0.998050i | \(0.519880\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −19.4495 | −0.682964 | −0.341482 | − | 0.939888i | \(-0.610929\pi\) | ||||
−0.341482 | + | 0.939888i | \(0.610929\pi\) | |||||||
\(812\) | −19.3485 | −0.678998 | ||||||||
\(813\) | 22.9444 | 0.804695 | ||||||||
\(814\) | −26.8990 | −0.942809 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 4.44949 | 0.155763 | ||||||||
\(817\) | −2.44949 | −0.0856968 | ||||||||
\(818\) | −22.8990 | −0.800644 | ||||||||
\(819\) | −10.8990 | −0.380841 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −23.1464 | −0.807816 | −0.403908 | − | 0.914800i | \(-0.632348\pi\) | ||||
−0.403908 | + | 0.914800i | \(0.632348\pi\) | |||||||
\(822\) | −4.89898 | −0.170872 | ||||||||
\(823\) | −31.7980 | −1.10841 | −0.554204 | − | 0.832381i | \(-0.686977\pi\) | ||||
−0.554204 | + | 0.832381i | \(0.686977\pi\) | |||||||
\(824\) | 1.89898 | 0.0661541 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 28.6969 | 0.998494 | ||||||||
\(827\) | 0.247449 | 0.00860463 | 0.00430232 | − | 0.999991i | \(-0.498631\pi\) | ||||
0.00430232 | + | 0.999991i | \(0.498631\pi\) | |||||||
\(828\) | −1.00000 | −0.0347524 | ||||||||
\(829\) | −39.6413 | −1.37680 | −0.688400 | − | 0.725331i | \(-0.741687\pi\) | ||||
−0.688400 | + | 0.725331i | \(0.741687\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 21.0454 | 0.730057 | ||||||||
\(832\) | −2.44949 | −0.0849208 | ||||||||
\(833\) | 56.9444 | 1.97301 | ||||||||
\(834\) | −22.2474 | −0.770366 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 3.44949 | 0.119303 | ||||||||
\(837\) | −3.00000 | −0.103695 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 10.6515 | 0.367732 | 0.183866 | − | 0.982951i | \(-0.441139\pi\) | ||||
0.183866 | + | 0.982951i | \(0.441139\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −10.0908 | −0.347959 | ||||||||
\(842\) | 22.0000 | 0.758170 | ||||||||
\(843\) | 7.00000 | 0.241093 | ||||||||
\(844\) | −3.65153 | −0.125691 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −7.79796 | −0.268099 | ||||||||
\(847\) | 4.00000 | 0.137442 | ||||||||
\(848\) | −7.44949 | −0.255817 | ||||||||
\(849\) | 29.7980 | 1.02266 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 7.79796 | 0.267311 | ||||||||
\(852\) | −1.55051 | −0.0531196 | ||||||||
\(853\) | 1.10102 | 0.0376982 | 0.0188491 | − | 0.999822i | \(-0.494000\pi\) | ||||
0.0188491 | + | 0.999822i | \(0.494000\pi\) | |||||||
\(854\) | −42.0454 | −1.43876 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 17.3485 | 0.592958 | ||||||||
\(857\) | −36.4949 | −1.24664 | −0.623321 | − | 0.781966i | \(-0.714217\pi\) | ||||
−0.623321 | + | 0.781966i | \(0.714217\pi\) | |||||||
\(858\) | −8.44949 | −0.288461 | ||||||||
\(859\) | −4.20204 | −0.143372 | −0.0716859 | − | 0.997427i | \(-0.522838\pi\) | ||||
−0.0716859 | + | 0.997427i | \(0.522838\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −4.00000 | −0.136320 | ||||||||
\(862\) | −5.10102 | −0.173741 | ||||||||
\(863\) | −17.3031 | −0.589003 | −0.294502 | − | 0.955651i | \(-0.595154\pi\) | ||||
−0.294502 | + | 0.955651i | \(0.595154\pi\) | |||||||
\(864\) | 1.00000 | 0.0340207 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 4.65153 | 0.158065 | ||||||||
\(867\) | 2.79796 | 0.0950237 | ||||||||
\(868\) | −13.3485 | −0.453077 | ||||||||
\(869\) | −17.2474 | −0.585080 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −37.3485 | −1.26550 | ||||||||
\(872\) | −2.89898 | −0.0981718 | ||||||||
\(873\) | 1.55051 | 0.0524768 | ||||||||
\(874\) | −1.00000 | −0.0338255 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −1.00000 | −0.0337869 | ||||||||
\(877\) | −9.10102 | −0.307320 | −0.153660 | − | 0.988124i | \(-0.549106\pi\) | ||||
−0.153660 | + | 0.988124i | \(0.549106\pi\) | |||||||
\(878\) | −12.1010 | −0.408390 | ||||||||
\(879\) | −23.2474 | −0.784117 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 50.6969 | 1.70802 | 0.854012 | − | 0.520254i | \(-0.174163\pi\) | ||||
0.854012 | + | 0.520254i | \(0.174163\pi\) | |||||||
\(882\) | 12.7980 | 0.430930 | ||||||||
\(883\) | 34.6515 | 1.16612 | 0.583058 | − | 0.812430i | \(-0.301856\pi\) | ||||
0.583058 | + | 0.812430i | \(0.301856\pi\) | |||||||
\(884\) | −10.8990 | −0.366572 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 21.2474 | 0.713822 | ||||||||
\(887\) | −4.89898 | −0.164492 | −0.0822458 | − | 0.996612i | \(-0.526209\pi\) | ||||
−0.0822458 | + | 0.996612i | \(0.526209\pi\) | |||||||
\(888\) | −7.79796 | −0.261682 | ||||||||
\(889\) | 0.449490 | 0.0150754 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 3.44949 | 0.115562 | ||||||||
\(892\) | 16.1010 | 0.539102 | ||||||||
\(893\) | −7.79796 | −0.260949 | ||||||||
\(894\) | 5.79796 | 0.193913 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 4.44949 | 0.148647 | ||||||||
\(897\) | 2.44949 | 0.0817861 | ||||||||
\(898\) | −15.0000 | −0.500556 | ||||||||
\(899\) | 13.0454 | 0.435089 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −33.1464 | −1.10427 | ||||||||
\(902\) | −3.10102 | −0.103253 | ||||||||
\(903\) | −10.8990 | −0.362695 | ||||||||
\(904\) | −16.7980 | −0.558692 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −23.7980 | −0.790634 | ||||||||
\(907\) | −22.0000 | −0.730498 | −0.365249 | − | 0.930910i | \(-0.619016\pi\) | ||||
−0.365249 | + | 0.930910i | \(0.619016\pi\) | |||||||
\(908\) | 29.5959 | 0.982175 | ||||||||
\(909\) | −1.55051 | −0.0514272 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 6.49490 | 0.215186 | 0.107593 | − | 0.994195i | \(-0.465686\pi\) | ||||
0.107593 | + | 0.994195i | \(0.465686\pi\) | |||||||
\(912\) | 1.00000 | 0.0331133 | ||||||||
\(913\) | 28.7980 | 0.953073 | ||||||||
\(914\) | −24.8990 | −0.823585 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 7.24745 | 0.239462 | ||||||||
\(917\) | 41.1464 | 1.35877 | ||||||||
\(918\) | 4.44949 | 0.146855 | ||||||||
\(919\) | 23.8434 | 0.786520 | 0.393260 | − | 0.919427i | \(-0.371347\pi\) | ||||
0.393260 | + | 0.919427i | \(0.371347\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −16.3485 | −0.538700 | ||||||||
\(922\) | 12.0000 | 0.395199 | ||||||||
\(923\) | 3.79796 | 0.125011 | ||||||||
\(924\) | 15.3485 | 0.504928 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −14.6969 | −0.482971 | ||||||||
\(927\) | 1.89898 | 0.0623707 | ||||||||
\(928\) | −4.34847 | −0.142745 | ||||||||
\(929\) | −31.5959 | −1.03663 | −0.518314 | − | 0.855190i | \(-0.673440\pi\) | ||||
−0.518314 | + | 0.855190i | \(0.673440\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 12.7980 | 0.419436 | ||||||||
\(932\) | 6.24745 | 0.204642 | ||||||||
\(933\) | −23.7980 | −0.779110 | ||||||||
\(934\) | −6.34847 | −0.207728 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −2.44949 | −0.0800641 | ||||||||
\(937\) | −19.3939 | −0.633570 | −0.316785 | − | 0.948497i | \(-0.602603\pi\) | ||||
−0.316785 | + | 0.948497i | \(0.602603\pi\) | |||||||
\(938\) | 67.8434 | 2.21516 | ||||||||
\(939\) | 31.8990 | 1.04098 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 36.6413 | 1.19447 | 0.597237 | − | 0.802065i | \(-0.296265\pi\) | ||||
0.597237 | + | 0.802065i | \(0.296265\pi\) | |||||||
\(942\) | −4.89898 | −0.159617 | ||||||||
\(943\) | 0.898979 | 0.0292748 | ||||||||
\(944\) | 6.44949 | 0.209913 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −8.44949 | −0.274717 | ||||||||
\(947\) | 8.00000 | 0.259965 | 0.129983 | − | 0.991516i | \(-0.458508\pi\) | ||||
0.129983 | + | 0.991516i | \(0.458508\pi\) | |||||||
\(948\) | −5.00000 | −0.162392 | ||||||||
\(949\) | 2.44949 | 0.0795138 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 15.2474 | 0.494432 | ||||||||
\(952\) | 19.7980 | 0.641656 | ||||||||
\(953\) | −15.4949 | −0.501929 | −0.250964 | − | 0.967996i | \(-0.580748\pi\) | ||||
−0.250964 | + | 0.967996i | \(0.580748\pi\) | |||||||
\(954\) | −7.44949 | −0.241186 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −8.69694 | −0.281279 | ||||||||
\(957\) | −15.0000 | −0.484881 | ||||||||
\(958\) | 16.5959 | 0.536190 | ||||||||
\(959\) | −21.7980 | −0.703893 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −22.0000 | −0.709677 | ||||||||
\(962\) | 19.1010 | 0.615842 | ||||||||
\(963\) | 17.3485 | 0.559047 | ||||||||
\(964\) | −4.44949 | −0.143308 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −4.44949 | −0.143160 | ||||||||
\(967\) | −34.8990 | −1.12228 | −0.561138 | − | 0.827722i | \(-0.689636\pi\) | ||||
−0.561138 | + | 0.827722i | \(0.689636\pi\) | |||||||
\(968\) | 0.898979 | 0.0288943 | ||||||||
\(969\) | 4.44949 | 0.142938 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 41.6413 | 1.33633 | 0.668167 | − | 0.744011i | \(-0.267079\pi\) | ||||
0.668167 | + | 0.744011i | \(0.267079\pi\) | |||||||
\(972\) | 1.00000 | 0.0320750 | ||||||||
\(973\) | −98.9898 | −3.17347 | ||||||||
\(974\) | −32.0000 | −1.02535 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −9.44949 | −0.302471 | ||||||||
\(977\) | 19.5959 | 0.626929 | 0.313464 | − | 0.949600i | \(-0.398510\pi\) | ||||
0.313464 | + | 0.949600i | \(0.398510\pi\) | |||||||
\(978\) | 19.7980 | 0.633069 | ||||||||
\(979\) | 7.24745 | 0.231629 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −2.89898 | −0.0925573 | ||||||||
\(982\) | 43.5959 | 1.39120 | ||||||||
\(983\) | 50.4495 | 1.60909 | 0.804544 | − | 0.593892i | \(-0.202410\pi\) | ||||
0.804544 | + | 0.593892i | \(0.202410\pi\) | |||||||
\(984\) | −0.898979 | −0.0286584 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −19.3485 | −0.616181 | ||||||||
\(987\) | −34.6969 | −1.10442 | ||||||||
\(988\) | −2.44949 | −0.0779287 | ||||||||
\(989\) | 2.44949 | 0.0778892 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 44.1010 | 1.40092 | 0.700458 | − | 0.713694i | \(-0.252979\pi\) | ||||
0.700458 | + | 0.713694i | \(0.252979\pi\) | |||||||
\(992\) | −3.00000 | −0.0952501 | ||||||||
\(993\) | −22.3485 | −0.709207 | ||||||||
\(994\) | −6.89898 | −0.218822 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 8.34847 | 0.264531 | ||||||||
\(997\) | 39.4495 | 1.24938 | 0.624689 | − | 0.780874i | \(-0.285226\pi\) | ||||
0.624689 | + | 0.780874i | \(0.285226\pi\) | |||||||
\(998\) | −23.8434 | −0.754749 | ||||||||
\(999\) | −7.79796 | −0.246717 |
(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 | 2850.2.a.bj.1.2 | yes | 2 | |
3.2 | odd | 2 | 8550.2.a.bu.1.2 | 2 | |||
5.2 | odd | 4 | 2850.2.d.w.799.4 | 4 | |||
5.3 | odd | 4 | 2850.2.d.w.799.1 | 4 | |||
5.4 | even | 2 | 2850.2.a.bc.1.1 | ✓ | 2 | ||
15.14 | odd | 2 | 8550.2.a.bv.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2850.2.a.bc.1.1 | ✓ | 2 | 5.4 | even | 2 | ||
2850.2.a.bj.1.2 | yes | 2 | 1.1 | even | 1 | trivial | |
2850.2.d.w.799.1 | 4 | 5.3 | odd | 4 | |||
2850.2.d.w.799.4 | 4 | 5.2 | odd | 4 | |||
8550.2.a.bu.1.2 | 2 | 3.2 | odd | 2 | |||
8550.2.a.bv.1.1 | 2 | 15.14 | odd | 2 |