Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2394,2,Mod(1063,2394)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2394, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2394.1063");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2394 = 2 \cdot 3^{2} \cdot 7 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2394.e (of order \(2\), degree \(1\), minimal) |
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: | no |
Analytic conductor: | \(19.1161862439\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + 44x^{14} + 708x^{12} + 5378x^{10} + 20592x^{8} + 38856x^{6} + 33265x^{4} + 10216x^{2} + 900 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | no (minimal twist has level 266) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1063.11 | ||
Root | \(-2.30643i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2394.1063 |
Dual form | 2394.2.e.c.1063.6 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2394\mathbb{Z}\right)^\times\).
\(n\) | \(533\) | \(1009\) | \(1711\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000i | 0.707107i | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | − | 2.68862i | − | 1.20239i | −0.799103 | − | 0.601194i | \(-0.794692\pi\) | ||
0.799103 | − | 0.601194i | \(-0.205308\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.592978 | − | 2.57844i | −0.224125 | − | 0.974560i | ||||
\(8\) | − | 1.00000i | − | 0.353553i | ||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 2.68862 | 0.850217 | ||||||||
\(11\) | 1.22869 | 0.370463 | 0.185231 | − | 0.982695i | \(-0.440697\pi\) | ||||
0.185231 | + | 0.982695i | \(0.440697\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 5.01856 | 1.39190 | 0.695949 | − | 0.718091i | \(-0.254984\pi\) | ||||
0.695949 | + | 0.718091i | \(0.254984\pi\) | |||||||
\(14\) | 2.57844 | − | 0.592978i | 0.689118 | − | 0.158480i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 5.15689i | 1.25073i | 0.780333 | + | 0.625365i | \(0.215050\pi\) | ||||
−0.780333 | + | 0.625365i | \(0.784950\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.75779 | + | 3.37559i | 0.632679 | + | 0.774414i | ||||
\(20\) | 2.68862i | 0.601194i | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 1.22869i | 0.261957i | ||||||||
\(23\) | −3.18596 | −0.664318 | −0.332159 | − | 0.943223i | \(-0.607777\pi\) | ||||
−0.332159 | + | 0.943223i | \(0.607777\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.22869 | −0.445737 | ||||||||
\(26\) | 5.01856i | 0.984221i | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0.592978 | + | 2.57844i | 0.112062 | + | 0.487280i | ||||
\(29\) | − | 4.47509i | − | 0.831003i | −0.909592 | − | 0.415502i | \(-0.863606\pi\) | ||
0.909592 | − | 0.415502i | \(-0.136394\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.61285 | 1.18770 | 0.593852 | − | 0.804574i | \(-0.297607\pi\) | ||||
0.593852 | + | 0.804574i | \(0.297607\pi\) | |||||||
\(32\) | 1.00000i | 0.176777i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −5.15689 | −0.884399 | ||||||||
\(35\) | −6.93246 | + | 1.59429i | −1.17180 | + | 0.269485i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 3.74651i | − | 0.615922i | −0.951399 | − | 0.307961i | \(-0.900353\pi\) | ||
0.951399 | − | 0.307961i | \(-0.0996466\pi\) | |||||||
\(38\) | −3.37559 | + | 2.75779i | −0.547593 | + | 0.447372i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −2.68862 | −0.425108 | ||||||||
\(41\) | −0.873974 | −0.136492 | −0.0682459 | − | 0.997669i | \(-0.521740\pi\) | ||||
−0.0682459 | + | 0.997669i | \(0.521740\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 8.11842 | 1.23805 | 0.619024 | − | 0.785372i | \(-0.287529\pi\) | ||||
0.619024 | + | 0.785372i | \(0.287529\pi\) | |||||||
\(44\) | −1.22869 | −0.185231 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | − | 3.18596i | − | 0.469744i | ||||||
\(47\) | − | 7.36603i | − | 1.07445i | −0.843440 | − | 0.537223i | \(-0.819473\pi\) | ||
0.843440 | − | 0.537223i | \(-0.180527\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.29675 | + | 3.05792i | −0.899536 | + | 0.436846i | ||||
\(50\) | − | 2.22869i | − | 0.315184i | ||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −5.01856 | −0.695949 | ||||||||
\(53\) | − | 1.58536i | − | 0.217766i | −0.994055 | − | 0.108883i | \(-0.965273\pi\) | ||
0.994055 | − | 0.108883i | \(-0.0347273\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 3.30347i | − | 0.445440i | ||||||
\(56\) | −2.57844 | + | 0.592978i | −0.344559 | + | 0.0792400i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 4.47509 | 0.587608 | ||||||||
\(59\) | −2.46827 | −0.321341 | −0.160671 | − | 0.987008i | \(-0.551366\pi\) | ||||
−0.160671 | + | 0.987008i | \(0.551366\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 9.69893i | − | 1.24182i | −0.783882 | − | 0.620910i | \(-0.786763\pi\) | ||
0.783882 | − | 0.620910i | \(-0.213237\pi\) | |||||||
\(62\) | 6.61285i | 0.839833i | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | − | 13.4930i | − | 1.67360i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 0.728584i | − | 0.0890107i | −0.999009 | − | 0.0445053i | \(-0.985829\pi\) | ||
0.999009 | − | 0.0445053i | \(-0.0141712\pi\) | |||||||
\(68\) | − | 5.15689i | − | 0.625365i | ||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −1.59429 | − | 6.93246i | −0.190555 | − | 0.828588i | ||||
\(71\) | − | 5.14323i | − | 0.610389i | −0.952290 | − | 0.305194i | \(-0.901279\pi\) | ||
0.952290 | − | 0.305194i | \(-0.0987214\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 6.11584i | − | 0.715805i | −0.933759 | − | 0.357903i | \(-0.883492\pi\) | ||
0.933759 | − | 0.357903i | \(-0.116508\pi\) | |||||||
\(74\) | 3.74651 | 0.435522 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −2.75779 | − | 3.37559i | −0.316340 | − | 0.387207i | ||||
\(77\) | −0.728584 | − | 3.16810i | −0.0830298 | − | 0.361038i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 9.74651i | − | 1.09657i | −0.836292 | − | 0.548284i | \(-0.815281\pi\) | ||
0.836292 | − | 0.548284i | \(-0.184719\pi\) | |||||||
\(80\) | − | 2.68862i | − | 0.300597i | ||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | − | 0.873974i | − | 0.0965143i | ||||||
\(83\) | 1.81465i | 0.199183i | 0.995028 | + | 0.0995917i | \(0.0317537\pi\) | ||||
−0.995028 | + | 0.0995917i | \(0.968246\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 13.8649 | 1.50386 | ||||||||
\(86\) | 8.11842i | 0.875432i | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | − | 1.22869i | − | 0.130978i | ||||||
\(89\) | 3.38845 | 0.359175 | 0.179588 | − | 0.983742i | \(-0.442524\pi\) | ||||
0.179588 | + | 0.983742i | \(0.442524\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.97590 | − | 12.9401i | −0.311959 | − | 1.35649i | ||||
\(92\) | 3.18596 | 0.332159 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 7.36603 | 0.759748 | ||||||||
\(95\) | 9.07569 | − | 7.41464i | 0.931146 | − | 0.760726i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −3.22440 | −0.327388 | −0.163694 | − | 0.986511i | \(-0.552341\pi\) | ||||
−0.163694 | + | 0.986511i | \(0.552341\pi\) | |||||||
\(98\) | −3.05792 | − | 6.29675i | −0.308897 | − | 0.636068i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 2.22869 | 0.222869 | ||||||||
\(101\) | − | 3.56260i | − | 0.354492i | −0.984167 | − | 0.177246i | \(-0.943281\pi\) | ||
0.984167 | − | 0.177246i | \(-0.0567187\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 8.28917 | 0.816757 | 0.408378 | − | 0.912813i | \(-0.366094\pi\) | ||||
0.408378 | + | 0.912813i | \(0.366094\pi\) | |||||||
\(104\) | − | 5.01856i | − | 0.492110i | ||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 1.58536 | 0.153984 | ||||||||
\(107\) | 17.0509i | 1.64837i | 0.566320 | + | 0.824185i | \(0.308367\pi\) | ||||
−0.566320 | + | 0.824185i | \(0.691633\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 1.58536i | − | 0.151850i | −0.997114 | − | 0.0759249i | \(-0.975809\pi\) | ||
0.997114 | − | 0.0759249i | \(-0.0241909\pi\) | |||||||
\(110\) | 3.30347 | 0.314974 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −0.592978 | − | 2.57844i | −0.0560312 | − | 0.243640i | ||||
\(113\) | − | 10.3223i | − | 0.971040i | −0.874226 | − | 0.485520i | \(-0.838630\pi\) | ||
0.874226 | − | 0.485520i | \(-0.161370\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 8.56583i | 0.798768i | ||||||||
\(116\) | 4.47509i | 0.415502i | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | − | 2.46827i | − | 0.227222i | ||||||
\(119\) | 13.2968 | − | 3.05792i | 1.21891 | − | 0.280319i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −9.49033 | −0.862757 | ||||||||
\(122\) | 9.69893 | 0.878100 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −6.61285 | −0.593852 | ||||||||
\(125\) | − | 7.45101i | − | 0.666439i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 9.80695i | − | 0.870226i | −0.900376 | − | 0.435113i | \(-0.856708\pi\) | ||
0.900376 | − | 0.435113i | \(-0.143292\pi\) | |||||||
\(128\) | − | 1.00000i | − | 0.0883883i | ||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 13.4930 | 1.18342 | ||||||||
\(131\) | 3.56260i | 0.311265i | 0.987815 | + | 0.155633i | \(0.0497416\pi\) | ||||
−0.987815 | + | 0.155633i | \(0.950258\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 7.06847 | − | 9.11245i | 0.612914 | − | 0.790150i | ||||
\(134\) | 0.728584 | 0.0629401 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 5.15689 | 0.442200 | ||||||||
\(137\) | −9.38983 | −0.802228 | −0.401114 | − | 0.916028i | \(-0.631377\pi\) | ||||
−0.401114 | + | 0.916028i | \(0.631377\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 18.4646i | 1.56615i | 0.621928 | + | 0.783075i | \(0.286350\pi\) | ||||
−0.621928 | + | 0.783075i | \(0.713650\pi\) | |||||||
\(140\) | 6.93246 | − | 1.59429i | 0.585900 | − | 0.134742i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 5.14323 | 0.431610 | ||||||||
\(143\) | 6.16624 | 0.515647 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −12.0318 | −0.999189 | ||||||||
\(146\) | 6.11584 | 0.506151 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 3.74651i | 0.307961i | ||||||||
\(149\) | −19.8649 | −1.62740 | −0.813699 | − | 0.581286i | \(-0.802550\pi\) | ||||
−0.813699 | + | 0.581286i | \(0.802550\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 11.7795i | 0.958599i | 0.877651 | + | 0.479300i | \(0.159109\pi\) | ||||
−0.877651 | + | 0.479300i | \(0.840891\pi\) | |||||||
\(152\) | 3.37559 | − | 2.75779i | 0.273797 | − | 0.223686i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 3.16810 | − | 0.728584i | 0.255293 | − | 0.0587110i | ||||
\(155\) | − | 17.7795i | − | 1.42808i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 13.3282i | 1.06371i | 0.846836 | + | 0.531854i | \(0.178504\pi\) | ||||
−0.846836 | + | 0.531854i | \(0.821496\pi\) | |||||||
\(158\) | 9.74651 | 0.775390 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 2.68862 | 0.212554 | ||||||||
\(161\) | 1.88920 | + | 8.21481i | 0.148890 | + | 0.647418i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −9.22869 | −0.722846 | −0.361423 | − | 0.932402i | \(-0.617709\pi\) | ||||
−0.361423 | + | 0.932402i | \(0.617709\pi\) | |||||||
\(164\) | 0.873974 | 0.0682459 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −1.81465 | −0.140844 | ||||||||
\(167\) | −16.1317 | −1.24831 | −0.624155 | − | 0.781300i | \(-0.714557\pi\) | ||||
−0.624155 | + | 0.781300i | \(0.714557\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 12.1860 | 0.937381 | ||||||||
\(170\) | 13.8649i | 1.06339i | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −8.11842 | −0.619024 | ||||||||
\(173\) | 4.00330 | 0.304366 | 0.152183 | − | 0.988352i | \(-0.451370\pi\) | ||||
0.152183 | + | 0.988352i | \(0.451370\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.32156 | + | 5.74654i | 0.0999007 | + | 0.434398i | ||||
\(176\) | 1.22869 | 0.0926157 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 3.38845i | 0.253975i | ||||||||
\(179\) | − | 7.49301i | − | 0.560054i | −0.959992 | − | 0.280027i | \(-0.909657\pi\) | ||
0.959992 | − | 0.280027i | \(-0.0903434\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1.09728 | 0.0815604 | 0.0407802 | − | 0.999168i | \(-0.487016\pi\) | ||||
0.0407802 | + | 0.999168i | \(0.487016\pi\) | |||||||
\(182\) | 12.9401 | − | 2.97590i | 0.959183 | − | 0.220588i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 3.18596i | 0.234872i | ||||||||
\(185\) | −10.0729 | −0.740577 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 6.33620i | 0.463349i | ||||||||
\(188\) | 7.36603i | 0.537223i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 7.41464 | + | 9.07569i | 0.537915 | + | 0.658420i | ||||
\(191\) | −6.01524 | −0.435248 | −0.217624 | − | 0.976033i | \(-0.569831\pi\) | ||||
−0.217624 | + | 0.976033i | \(0.569831\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 19.2725i | − | 1.38726i | −0.720330 | − | 0.693632i | \(-0.756010\pi\) | ||
0.720330 | − | 0.693632i | \(-0.243990\pi\) | |||||||
\(194\) | − | 3.22440i | − | 0.231499i | ||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 6.29675 | − | 3.05792i | 0.449768 | − | 0.218423i | ||||
\(197\) | 0.371912 | 0.0264976 | 0.0132488 | − | 0.999912i | \(-0.495783\pi\) | ||||
0.0132488 | + | 0.999912i | \(0.495783\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 16.3446i | 1.15864i | 0.815100 | + | 0.579320i | \(0.196682\pi\) | ||||
−0.815100 | + | 0.579320i | \(0.803318\pi\) | |||||||
\(200\) | 2.22869i | 0.157592i | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 3.56260 | 0.250663 | ||||||||
\(203\) | −11.5388 | + | 2.65363i | −0.809863 | + | 0.186248i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2.34979i | 0.164116i | ||||||||
\(206\) | 8.28917i | 0.577534i | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 5.01856 | 0.347975 | ||||||||
\(209\) | 3.38845 | + | 4.14754i | 0.234384 | + | 0.286892i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2.44213i | 0.168123i | 0.996461 | + | 0.0840616i | \(0.0267893\pi\) | ||||
−0.996461 | + | 0.0840616i | \(0.973211\pi\) | |||||||
\(212\) | 1.58536i | 0.108883i | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −17.0509 | −1.16557 | ||||||||
\(215\) | − | 21.8274i | − | 1.48861i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −3.92128 | − | 17.0509i | −0.266194 | − | 1.15749i | ||||
\(218\) | 1.58536 | 0.107374 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 3.30347i | 0.222720i | ||||||||
\(221\) | 25.8802i | 1.74089i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −8.80742 | −0.589789 | −0.294894 | − | 0.955530i | \(-0.595284\pi\) | ||||
−0.294894 | + | 0.955530i | \(0.595284\pi\) | |||||||
\(224\) | 2.57844 | − | 0.592978i | 0.172280 | − | 0.0396200i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 10.3223 | 0.686629 | ||||||||
\(227\) | 25.8511 | 1.71580 | 0.857900 | − | 0.513816i | \(-0.171769\pi\) | ||||
0.857900 | + | 0.513816i | \(0.171769\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 5.87721i | − | 0.388377i | −0.980964 | − | 0.194188i | \(-0.937793\pi\) | ||
0.980964 | − | 0.194188i | \(-0.0622073\pi\) | |||||||
\(230\) | −8.56583 | −0.564814 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −4.47509 | −0.293804 | ||||||||
\(233\) | 9.09361 | 0.595742 | 0.297871 | − | 0.954606i | \(-0.403723\pi\) | ||||
0.297871 | + | 0.954606i | \(0.403723\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −19.8045 | −1.29190 | ||||||||
\(236\) | 2.46827 | 0.160671 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 3.05792 | + | 13.2968i | 0.198216 | + | 0.861901i | ||||
\(239\) | −5.64333 | −0.365037 | −0.182518 | − | 0.983202i | \(-0.558425\pi\) | ||||
−0.182518 | + | 0.983202i | \(0.558425\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 22.2248 | 1.43163 | 0.715813 | − | 0.698292i | \(-0.246056\pi\) | ||||
0.715813 | + | 0.698292i | \(0.246056\pi\) | |||||||
\(242\) | − | 9.49033i | − | 0.610062i | ||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 9.69893i | 0.620910i | ||||||||
\(245\) | 8.22160 | + | 16.9296i | 0.525258 | + | 1.08159i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 13.8401 | + | 16.9406i | 0.880626 | + | 1.07791i | ||||
\(248\) | − | 6.61285i | − | 0.419917i | ||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 7.45101 | 0.471244 | ||||||||
\(251\) | 1.37394i | 0.0867223i | 0.999059 | + | 0.0433612i | \(0.0138066\pi\) | ||||
−0.999059 | + | 0.0433612i | \(0.986193\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −3.91454 | −0.246105 | ||||||||
\(254\) | 9.80695 | 0.615343 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 5.81051 | 0.362450 | 0.181225 | − | 0.983442i | \(-0.441994\pi\) | ||||
0.181225 | + | 0.983442i | \(0.441994\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −9.66016 | + | 2.22160i | −0.600253 | + | 0.138043i | ||||
\(260\) | 13.4930i | 0.836801i | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −3.56260 | −0.220098 | ||||||||
\(263\) | 27.3579 | 1.68696 | 0.843481 | − | 0.537159i | \(-0.180502\pi\) | ||||
0.843481 | + | 0.537159i | \(0.180502\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −4.26243 | −0.261839 | ||||||||
\(266\) | 9.11245 | + | 7.06847i | 0.558720 | + | 0.433396i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0.728584i | 0.0445053i | ||||||||
\(269\) | 27.5487 | 1.67967 | 0.839837 | − | 0.542839i | \(-0.182650\pi\) | ||||
0.839837 | + | 0.542839i | \(0.182650\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 30.7284i | − | 1.86662i | −0.359073 | − | 0.933309i | \(-0.616907\pi\) | ||
0.359073 | − | 0.933309i | \(-0.383093\pi\) | |||||||
\(272\) | 5.15689i | 0.312682i | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | − | 9.38983i | − | 0.567261i | ||||||
\(275\) | −2.73836 | −0.165129 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −7.03564 | −0.422731 | −0.211365 | − | 0.977407i | \(-0.567791\pi\) | ||||
−0.211365 | + | 0.977407i | \(0.567791\pi\) | |||||||
\(278\) | −18.4646 | −1.10743 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 1.59429 | + | 6.93246i | 0.0952773 | + | 0.414294i | ||||
\(281\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 18.2947i | 1.08750i | 0.839246 | + | 0.543752i | \(0.182997\pi\) | ||||
−0.839246 | + | 0.543752i | \(0.817003\pi\) | |||||||
\(284\) | 5.14323i | 0.305194i | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 6.16624i | 0.364617i | ||||||||
\(287\) | 0.518248 | + | 2.25349i | 0.0305912 | + | 0.133020i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −9.59351 | −0.564324 | ||||||||
\(290\) | − | 12.0318i | − | 0.706533i | ||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 6.11584i | 0.357903i | ||||||||
\(293\) | 22.6626 | 1.32396 | 0.661980 | − | 0.749521i | \(-0.269716\pi\) | ||||
0.661980 | + | 0.749521i | \(0.269716\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 6.63624i | 0.386377i | ||||||||
\(296\) | −3.74651 | −0.217761 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | − | 19.8649i | − | 1.15074i | ||||||
\(299\) | −15.9889 | −0.924663 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −4.81404 | − | 20.9329i | −0.277477 | − | 1.20655i | ||||
\(302\) | −11.7795 | −0.677832 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 2.75779 | + | 3.37559i | 0.158170 | + | 0.193603i | ||||
\(305\) | −26.0767 | −1.49315 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 3.48353 | 0.198815 | 0.0994077 | − | 0.995047i | \(-0.468305\pi\) | ||||
0.0994077 | + | 0.995047i | \(0.468305\pi\) | |||||||
\(308\) | 0.728584 | + | 3.16810i | 0.0415149 | + | 0.180519i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 17.7795 | 1.00981 | ||||||||
\(311\) | 14.7116i | 0.834217i | 0.908857 | + | 0.417109i | \(0.136957\pi\) | ||||
−0.908857 | + | 0.417109i | \(0.863043\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 9.57518i | − | 0.541221i | −0.962689 | − | 0.270611i | \(-0.912774\pi\) | ||
0.962689 | − | 0.270611i | \(-0.0872256\pi\) | |||||||
\(314\) | −13.3282 | −0.752155 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 9.74651i | 0.548284i | ||||||||
\(317\) | − | 19.2439i | − | 1.08085i | −0.841393 | − | 0.540423i | \(-0.818264\pi\) | ||
0.841393 | − | 0.540423i | \(-0.181736\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 5.49848i | − | 0.307856i | ||||||
\(320\) | 2.68862i | 0.150299i | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −8.21481 | + | 1.88920i | −0.457794 | + | 0.105281i | ||||
\(323\) | −17.4076 | + | 14.2216i | −0.968582 | + | 0.791311i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −11.1848 | −0.620421 | ||||||||
\(326\) | − | 9.22869i | − | 0.511130i | ||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0.873974i | 0.0482572i | ||||||||
\(329\) | −18.9929 | + | 4.36790i | −1.04711 | + | 0.240810i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 29.0509i | 1.59678i | 0.602140 | + | 0.798390i | \(0.294315\pi\) | ||||
−0.602140 | + | 0.798390i | \(0.705685\pi\) | |||||||
\(332\) | − | 1.81465i | − | 0.0995917i | ||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | − | 16.1317i | − | 0.882689i | ||||||
\(335\) | −1.95889 | −0.107025 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 23.7795i | 1.29535i | 0.761917 | + | 0.647675i | \(0.224259\pi\) | ||||
−0.761917 | + | 0.647675i | \(0.775741\pi\) | |||||||
\(338\) | 12.1860i | 0.662829i | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −13.8649 | −0.751931 | ||||||||
\(341\) | 8.12512 | 0.440000 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 11.6185 | + | 14.4226i | 0.627341 | + | 0.778745i | ||||
\(344\) | − | 8.11842i | − | 0.437716i | ||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 4.00330i | 0.215219i | ||||||||
\(347\) | 28.4737 | 1.52855 | 0.764273 | − | 0.644892i | \(-0.223098\pi\) | ||||
0.764273 | + | 0.644892i | \(0.223098\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 19.4236i | − | 1.03972i | −0.854251 | − | 0.519860i | \(-0.825984\pi\) | ||
0.854251 | − | 0.519860i | \(-0.174016\pi\) | |||||||
\(350\) | −5.74654 | + | 1.32156i | −0.307166 | + | 0.0706405i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 1.22869i | 0.0654892i | ||||||||
\(353\) | 19.1000i | 1.01659i | 0.861183 | + | 0.508294i | \(0.169724\pi\) | ||||
−0.861183 | + | 0.508294i | \(0.830276\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −13.8282 | −0.733924 | ||||||||
\(356\) | −3.38845 | −0.179588 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 7.49301 | 0.396018 | ||||||||
\(359\) | −2.59351 | −0.136880 | −0.0684401 | − | 0.997655i | \(-0.521802\pi\) | ||||
−0.0684401 | + | 0.997655i | \(0.521802\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −3.78924 | + | 18.6183i | −0.199433 | + | 0.979911i | ||||
\(362\) | 1.09728i | 0.0576719i | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 2.97590 | + | 12.9401i | 0.155979 | + | 0.678245i | ||||
\(365\) | −16.4432 | −0.860676 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 28.6818i | − | 1.49718i | −0.663034 | − | 0.748589i | \(-0.730732\pi\) | ||
0.663034 | − | 0.748589i | \(-0.269268\pi\) | |||||||
\(368\) | −3.18596 | −0.166079 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | − | 10.0729i | − | 0.523667i | ||||||
\(371\) | −4.08776 | + | 0.940082i | −0.212226 | + | 0.0488066i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 4.47509i | − | 0.231711i | −0.993266 | − | 0.115856i | \(-0.963039\pi\) | ||
0.993266 | − | 0.115856i | \(-0.0369610\pi\) | |||||||
\(374\) | −6.33620 | −0.327637 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −7.36603 | −0.379874 | ||||||||
\(377\) | − | 22.4585i | − | 1.15667i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 11.2714i | − | 0.578974i | −0.957182 | − | 0.289487i | \(-0.906515\pi\) | ||
0.957182 | − | 0.289487i | \(-0.0934847\pi\) | |||||||
\(380\) | −9.07569 | + | 7.41464i | −0.465573 | + | 0.380363i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | − | 6.01524i | − | 0.307766i | ||||||
\(383\) | −3.58832 | −0.183355 | −0.0916773 | − | 0.995789i | \(-0.529223\pi\) | ||||
−0.0916773 | + | 0.995789i | \(0.529223\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −8.51782 | + | 1.95889i | −0.434108 | + | 0.0998341i | ||||
\(386\) | 19.2725 | 0.980943 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 3.22440 | 0.163694 | ||||||||
\(389\) | −3.54263 | −0.179618 | −0.0898092 | − | 0.995959i | \(-0.528626\pi\) | ||||
−0.0898092 | + | 0.995959i | \(0.528626\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 16.4296i | − | 0.830882i | ||||||
\(392\) | 3.05792 | + | 6.29675i | 0.154448 | + | 0.318034i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0.371912i | 0.0187367i | ||||||||
\(395\) | −26.2047 | −1.31850 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 6.99202i | − | 0.350920i | −0.984487 | − | 0.175460i | \(-0.943859\pi\) | ||
0.984487 | − | 0.175460i | \(-0.0561412\pi\) | |||||||
\(398\) | −16.3446 | −0.819283 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −2.22869 | −0.111434 | ||||||||
\(401\) | − | 28.1018i | − | 1.40333i | −0.712505 | − | 0.701667i | \(-0.752439\pi\) | ||
0.712505 | − | 0.701667i | \(-0.247561\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 33.1870 | 1.65316 | ||||||||
\(404\) | 3.56260i | 0.177246i | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −2.65363 | − | 11.5388i | −0.131697 | − | 0.572660i | ||||
\(407\) | − | 4.60328i | − | 0.228176i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 24.2927 | 1.20120 | 0.600598 | − | 0.799551i | \(-0.294929\pi\) | ||||
0.600598 | + | 0.799551i | \(0.294929\pi\) | |||||||
\(410\) | −2.34979 | −0.116048 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −8.28917 | −0.408378 | ||||||||
\(413\) | 1.46363 | + | 6.36429i | 0.0720205 | + | 0.313166i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 4.87890 | 0.239496 | ||||||||
\(416\) | 5.01856i | 0.246055i | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −4.14754 | + | 3.38845i | −0.202863 | + | 0.165735i | ||||
\(419\) | 27.1080i | 1.32431i | 0.749366 | + | 0.662156i | \(0.230358\pi\) | ||||
−0.749366 | + | 0.662156i | \(0.769642\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 14.2216i | − | 0.693118i | −0.938028 | − | 0.346559i | \(-0.887350\pi\) | ||
0.938028 | − | 0.346559i | \(-0.112650\pi\) | |||||||
\(422\) | −2.44213 | −0.118881 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −1.58536 | −0.0769918 | ||||||||
\(425\) | − | 11.4931i | − | 0.557497i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −25.0082 | + | 5.75125i | −1.21023 | + | 0.278323i | ||||
\(428\) | − | 17.0509i | − | 0.824185i | ||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 21.8274 | 1.05261 | ||||||||
\(431\) | 32.0934i | 1.54588i | 0.634476 | + | 0.772942i | \(0.281216\pi\) | ||||
−0.634476 | + | 0.772942i | \(0.718784\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −18.5896 | −0.893359 | −0.446680 | − | 0.894694i | \(-0.647394\pi\) | ||||
−0.446680 | + | 0.894694i | \(0.647394\pi\) | |||||||
\(434\) | 17.0509 | − | 3.92128i | 0.818468 | − | 0.188227i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 1.58536i | 0.0759249i | ||||||||
\(437\) | −8.78618 | − | 10.7545i | −0.420300 | − | 0.514457i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −22.0623 | −1.05298 | −0.526488 | − | 0.850183i | \(-0.676491\pi\) | ||||
−0.526488 | + | 0.850183i | \(0.676491\pi\) | |||||||
\(440\) | −3.30347 | −0.157487 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −25.8802 | −1.23099 | ||||||||
\(443\) | 8.62541 | 0.409805 | 0.204903 | − | 0.978782i | \(-0.434312\pi\) | ||||
0.204903 | + | 0.978782i | \(0.434312\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − | 9.11027i | − | 0.431868i | ||||||
\(446\) | − | 8.80742i | − | 0.417043i | ||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0.592978 | + | 2.57844i | 0.0280156 | + | 0.121820i | ||||
\(449\) | 22.1018i | 1.04305i | 0.853237 | + | 0.521523i | \(0.174636\pi\) | ||||
−0.853237 | + | 0.521523i | \(0.825364\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.07384 | −0.0505651 | ||||||||
\(452\) | 10.3223i | 0.485520i | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 25.8511i | 1.21325i | ||||||||
\(455\) | −34.7910 | + | 8.00106i | −1.63103 | + | 0.375095i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −0.00688586 | −0.000322107 | −0.000161053 | − | 1.00000i | \(-0.500051\pi\) | ||||
−0.000161053 | 1.00000i | \(0.500051\pi\) | ||||||||
\(458\) | 5.87721 | 0.274624 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | − | 8.56583i | − | 0.399384i | ||||||
\(461\) | 16.4758i | 0.767356i | 0.923467 | + | 0.383678i | \(0.125343\pi\) | ||||
−0.923467 | + | 0.383678i | \(0.874657\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −24.7296 | −1.14928 | −0.574642 | − | 0.818405i | \(-0.694859\pi\) | ||||
−0.574642 | + | 0.818405i | \(0.694859\pi\) | |||||||
\(464\) | − | 4.47509i | − | 0.207751i | ||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 9.09361i | 0.421253i | ||||||||
\(467\) | − | 5.00323i | − | 0.231522i | −0.993277 | − | 0.115761i | \(-0.963069\pi\) | ||
0.993277 | − | 0.115761i | \(-0.0369307\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1.87861 | + | 0.432034i | −0.0867463 | + | 0.0199495i | ||||
\(470\) | − | 19.8045i | − | 0.913512i | ||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 2.46827i | 0.113611i | ||||||||
\(473\) | 9.97499 | 0.458650 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −6.14624 | − | 7.52313i | −0.282009 | − | 0.345185i | ||||
\(476\) | −13.2968 | + | 3.05792i | −0.609456 | + | 0.140160i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | − | 5.64333i | − | 0.258120i | ||||||
\(479\) | − | 9.95805i | − | 0.454995i | −0.973779 | − | 0.227498i | \(-0.926946\pi\) | ||
0.973779 | − | 0.227498i | \(-0.0730544\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | − | 18.8021i | − | 0.857301i | ||||||
\(482\) | 22.2248i | 1.01231i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 9.49033 | 0.431379 | ||||||||
\(485\) | 8.66920i | 0.393648i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 39.1845i | 1.77562i | 0.460209 | + | 0.887810i | \(0.347774\pi\) | ||||
−0.460209 | + | 0.887810i | \(0.652226\pi\) | |||||||
\(488\) | −9.69893 | −0.439050 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −16.9296 | + | 8.22160i | −0.764801 | + | 0.371414i | ||||
\(491\) | −28.4737 | −1.28500 | −0.642499 | − | 0.766286i | \(-0.722102\pi\) | ||||
−0.642499 | + | 0.766286i | \(0.722102\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 23.0775 | 1.03936 | ||||||||
\(494\) | −16.9406 | + | 13.8401i | −0.762194 | + | 0.622696i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 6.61285 | 0.296926 | ||||||||
\(497\) | −13.2615 | + | 3.04982i | −0.594861 | + | 0.136803i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −8.52617 | −0.381684 | −0.190842 | − | 0.981621i | \(-0.561122\pi\) | ||||
−0.190842 | + | 0.981621i | \(0.561122\pi\) | |||||||
\(500\) | 7.45101i | 0.333219i | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −1.37394 | −0.0613219 | ||||||||
\(503\) | − | 0.653620i | − | 0.0291435i | −0.999894 | − | 0.0145717i | \(-0.995362\pi\) | ||
0.999894 | − | 0.0145717i | \(-0.00463849\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −9.57847 | −0.426236 | ||||||||
\(506\) | − | 3.91454i | − | 0.174023i | ||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 9.80695i | 0.435113i | ||||||||
\(509\) | 28.2602 | 1.25261 | 0.626305 | − | 0.779578i | \(-0.284567\pi\) | ||||
0.626305 | + | 0.779578i | \(0.284567\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −15.7694 | + | 3.62656i | −0.697596 | + | 0.160430i | ||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 5.81051i | 0.256291i | ||||||||
\(515\) | − | 22.2865i | − | 0.982058i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 9.05054i | − | 0.398042i | ||||||
\(518\) | −2.22160 | − | 9.66016i | −0.0976113 | − | 0.424443i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −13.4930 | −0.591708 | ||||||||
\(521\) | −8.00661 | −0.350776 | −0.175388 | − | 0.984499i | \(-0.556118\pi\) | ||||
−0.175388 | + | 0.984499i | \(0.556118\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 21.6685 | 0.947499 | 0.473750 | − | 0.880660i | \(-0.342900\pi\) | ||||
0.473750 | + | 0.880660i | \(0.342900\pi\) | |||||||
\(524\) | − | 3.56260i | − | 0.155633i | ||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 27.3579i | 1.19286i | ||||||||
\(527\) | 34.1018i | 1.48550i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −12.8497 | −0.558682 | ||||||||
\(530\) | − | 4.26243i | − | 0.185148i | ||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −7.06847 | + | 9.11245i | −0.306457 | + | 0.395075i | ||||
\(533\) | −4.38609 | −0.189983 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 45.8434 | 1.98198 | ||||||||
\(536\) | −0.728584 | −0.0314700 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 27.5487i | 1.18771i | ||||||||
\(539\) | −7.73673 | + | 3.75723i | −0.333245 | + | 0.161835i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −11.2725 | −0.484642 | −0.242321 | − | 0.970196i | \(-0.577909\pi\) | ||||
−0.242321 | + | 0.970196i | \(0.577909\pi\) | |||||||
\(542\) | 30.7284 | 1.31990 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −5.15689 | −0.221100 | ||||||||
\(545\) | −4.26243 | −0.182582 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 17.6586i | − | 0.755026i | −0.926004 | − | 0.377513i | \(-0.876779\pi\) | ||
0.926004 | − | 0.377513i | \(-0.123221\pi\) | |||||||
\(548\) | 9.38983 | 0.401114 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | − | 2.73836i | − | 0.116764i | ||||||
\(551\) | 15.1061 | − | 12.3413i | 0.643540 | − | 0.525759i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −25.1308 | + | 5.77946i | −1.06867 | + | 0.245768i | ||||
\(554\) | − | 7.03564i | − | 0.298916i | ||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | − | 18.4646i | − | 0.783075i | ||||||
\(557\) | −28.0713 | −1.18942 | −0.594709 | − | 0.803941i | \(-0.702733\pi\) | ||||
−0.594709 | + | 0.803941i | \(0.702733\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 40.7428 | 1.72324 | ||||||||
\(560\) | −6.93246 | + | 1.59429i | −0.292950 | + | 0.0673712i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 33.9148 | 1.42934 | 0.714669 | − | 0.699463i | \(-0.246577\pi\) | ||||
0.714669 | + | 0.699463i | \(0.246577\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −27.7527 | −1.16757 | ||||||||
\(566\) | −18.2947 | −0.768982 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −5.14323 | −0.215805 | ||||||||
\(569\) | − | 44.7296i | − | 1.87516i | −0.347764 | − | 0.937582i | \(-0.613059\pi\) | ||
0.347764 | − | 0.937582i | \(-0.386941\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 46.5316 | 1.94729 | 0.973644 | − | 0.228072i | \(-0.0732421\pi\) | ||||
0.973644 | + | 0.228072i | \(0.0732421\pi\) | |||||||
\(572\) | −6.16624 | −0.257823 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −2.25349 | + | 0.518248i | −0.0940590 | + | 0.0216312i | ||||
\(575\) | 7.10050 | 0.296111 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 37.0982i | 1.54442i | 0.635370 | + | 0.772208i | \(0.280848\pi\) | ||||
−0.635370 | + | 0.772208i | \(0.719152\pi\) | |||||||
\(578\) | − | 9.59351i | − | 0.399037i | ||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 12.0318 | 0.499594 | ||||||||
\(581\) | 4.67897 | − | 1.07605i | 0.194116 | − | 0.0446419i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 1.94791i | − | 0.0806741i | ||||||
\(584\) | −6.11584 | −0.253075 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 22.6626i | 0.936182i | ||||||||
\(587\) | − | 21.6532i | − | 0.893724i | −0.894603 | − | 0.446862i | \(-0.852542\pi\) | ||
0.894603 | − | 0.446862i | \(-0.147458\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 18.2368 | + | 22.3223i | 0.751436 | + | 0.919774i | ||||
\(590\) | −6.63624 | −0.273210 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | − | 3.74651i | − | 0.153980i | ||||||
\(593\) | − | 31.3820i | − | 1.28871i | −0.764728 | − | 0.644353i | \(-0.777127\pi\) | ||
0.764728 | − | 0.644353i | \(-0.222873\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −8.22160 | − | 35.7499i | −0.337053 | − | 1.46560i | ||||
\(596\) | 19.8649 | 0.813699 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | − | 15.9889i | − | 0.653835i | ||||||
\(599\) | 18.8568i | 0.770467i | 0.922819 | + | 0.385233i | \(0.125879\pi\) | ||||
−0.922819 | + | 0.385233i | \(0.874121\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 44.1670 | 1.80161 | 0.900806 | − | 0.434222i | \(-0.142977\pi\) | ||||
0.900806 | + | 0.434222i | \(0.142977\pi\) | |||||||
\(602\) | 20.9329 | − | 4.81404i | 0.853161 | − | 0.196206i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | − | 11.7795i | − | 0.479300i | ||||||
\(605\) | 25.5159i | 1.03737i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −18.3263 | −0.743841 | −0.371921 | − | 0.928265i | \(-0.621301\pi\) | ||||
−0.371921 | + | 0.928265i | \(0.621301\pi\) | |||||||
\(608\) | −3.37559 | + | 2.75779i | −0.136898 | + | 0.111843i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | − | 26.0767i | − | 1.05582i | ||||||
\(611\) | − | 36.9669i | − | 1.49552i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −9.82908 | −0.396993 | −0.198496 | − | 0.980102i | \(-0.563606\pi\) | ||||
−0.198496 | + | 0.980102i | \(0.563606\pi\) | |||||||
\(614\) | 3.48353i | 0.140584i | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −3.16810 | + | 0.728584i | −0.127646 | + | 0.0293555i | ||||
\(617\) | −35.0495 | −1.41104 | −0.705519 | − | 0.708691i | \(-0.749286\pi\) | ||||
−0.705519 | + | 0.708691i | \(0.749286\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 0.543970i | 0.0218640i | 0.999940 | + | 0.0109320i | \(0.00347984\pi\) | ||||
−0.999940 | + | 0.0109320i | \(0.996520\pi\) | |||||||
\(620\) | 17.7795i | 0.714040i | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −14.7116 | −0.589881 | ||||||||
\(623\) | −2.00928 | − | 8.73694i | −0.0805000 | − | 0.350038i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −31.1764 | −1.24706 | ||||||||
\(626\) | 9.57518 | 0.382701 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | − | 13.3282i | − | 0.531854i | ||||||
\(629\) | 19.3203 | 0.770351 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 4.77967 | 0.190276 | 0.0951378 | − | 0.995464i | \(-0.469671\pi\) | ||||
0.0951378 | + | 0.995464i | \(0.469671\pi\) | |||||||
\(632\) | −9.74651 | −0.387695 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 19.2439 | 0.764274 | ||||||||
\(635\) | −26.3672 | −1.04635 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −31.6006 | + | 15.3464i | −1.25206 | + | 0.608045i | ||||
\(638\) | 5.49848 | 0.217687 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −2.68862 | −0.106277 | ||||||||
\(641\) | − | 11.7795i | − | 0.465261i | −0.972565 | − | 0.232630i | \(-0.925267\pi\) | ||
0.972565 | − | 0.232630i | \(-0.0747333\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 36.0736i | 1.42260i | 0.702887 | + | 0.711301i | \(0.251894\pi\) | ||||
−0.702887 | + | 0.711301i | \(0.748106\pi\) | |||||||
\(644\) | −1.88920 | − | 8.21481i | −0.0744450 | − | 0.323709i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −14.2216 | − | 17.4076i | −0.559541 | − | 0.684891i | ||||
\(647\) | − | 6.20083i | − | 0.243780i | −0.992544 | − | 0.121890i | \(-0.961105\pi\) | ||
0.992544 | − | 0.121890i | \(-0.0388955\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −3.03273 | −0.119045 | ||||||||
\(650\) | − | 11.1848i | − | 0.438704i | ||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 9.22869 | 0.361423 | ||||||||
\(653\) | 33.6090 | 1.31522 | 0.657610 | − | 0.753359i | \(-0.271567\pi\) | ||||
0.657610 | + | 0.753359i | \(0.271567\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 9.57847 | 0.374262 | ||||||||
\(656\) | −0.873974 | −0.0341230 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −4.36790 | − | 18.9929i | −0.170278 | − | 0.740421i | ||||
\(659\) | 25.7593i | 1.00344i | 0.865030 | + | 0.501719i | \(0.167299\pi\) | ||||
−0.865030 | + | 0.501719i | \(0.832701\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −46.1611 | −1.79546 | −0.897729 | − | 0.440549i | \(-0.854784\pi\) | ||||
−0.897729 | + | 0.440549i | \(0.854784\pi\) | |||||||
\(662\) | −29.0509 | −1.12909 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 1.81465 | 0.0704220 | ||||||||
\(665\) | −24.4999 | − | 19.0044i | −0.950066 | − | 0.736961i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 14.2574i | 0.552050i | ||||||||
\(668\) | 16.1317 | 0.624155 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | − | 1.95889i | − | 0.0756784i | ||||||
\(671\) | − | 11.9169i | − | 0.460048i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 35.4380i | 1.36604i | 0.730402 | + | 0.683018i | \(0.239333\pi\) | ||||
−0.730402 | + | 0.683018i | \(0.760667\pi\) | |||||||
\(674\) | −23.7795 | −0.915951 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −12.1860 | −0.468691 | ||||||||
\(677\) | −12.1788 | −0.468070 | −0.234035 | − | 0.972228i | \(-0.575193\pi\) | ||||
−0.234035 | + | 0.972228i | \(0.575193\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1.91200 | + | 8.31394i | 0.0733758 | + | 0.319060i | ||||
\(680\) | − | 13.8649i | − | 0.531696i | ||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 8.12512i | 0.311127i | ||||||||
\(683\) | − | 19.0519i | − | 0.729002i | −0.931203 | − | 0.364501i | \(-0.881240\pi\) | ||
0.931203 | − | 0.364501i | \(-0.118760\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 25.2457i | 0.964589i | ||||||||
\(686\) | −14.4226 | + | 11.6185i | −0.550656 | + | 0.443597i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 8.11842 | 0.309512 | ||||||||
\(689\) | − | 7.95621i | − | 0.303108i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 27.5487i | 1.04800i | 0.851718 | + | 0.524001i | \(0.175561\pi\) | ||||
−0.851718 | + | 0.524001i | \(0.824439\pi\) | |||||||
\(692\) | −4.00330 | −0.152183 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 28.4737i | 1.08085i | ||||||||
\(695\) | 49.6444 | 1.88312 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 4.50699i | − | 0.170714i | ||||||
\(698\) | 19.4236 | 0.735193 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −1.32156 | − | 5.74654i | −0.0499503 | − | 0.217199i | ||||
\(701\) | −9.50678 | −0.359066 | −0.179533 | − | 0.983752i | \(-0.557459\pi\) | ||||
−0.179533 | + | 0.983752i | \(0.557459\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 12.6467 | − | 10.3321i | 0.476978 | − | 0.389681i | ||||
\(704\) | −1.22869 | −0.0463079 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −19.1000 | −0.718837 | ||||||||
\(707\) | −9.18596 | + | 2.11254i | −0.345473 | + | 0.0794503i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −28.7296 | −1.07896 | −0.539482 | − | 0.841997i | \(-0.681380\pi\) | ||||
−0.539482 | + | 0.841997i | \(0.681380\pi\) | |||||||
\(710\) | − | 13.8282i | − | 0.518963i | ||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | − | 3.38845i | − | 0.126988i | ||||||
\(713\) | −21.0683 | −0.789013 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − | 16.5787i | − | 0.620007i | ||||||
\(716\) | 7.49301i | 0.280027i | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | − | 2.59351i | − | 0.0967889i | ||||||
\(719\) | 14.2000i | 0.529570i | 0.964307 | + | 0.264785i | \(0.0853010\pi\) | ||||
−0.964307 | + | 0.264785i | \(0.914699\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −4.91530 | − | 21.3732i | −0.183055 | − | 0.795979i | ||||
\(722\) | −18.6183 | − | 3.78924i | −0.692902 | − | 0.141021i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −1.09728 | −0.0407802 | ||||||||
\(725\) | 9.97357i | 0.370409i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 7.54541i | 0.279844i | 0.990163 | + | 0.139922i | \(0.0446852\pi\) | ||||
−0.990163 | + | 0.139922i | \(0.955315\pi\) | |||||||
\(728\) | −12.9401 | + | 2.97590i | −0.479591 | + | 0.110294i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | − | 16.4432i | − | 0.608590i | ||||||
\(731\) | 41.8658i | 1.54846i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 35.8186i | − | 1.32299i | −0.749949 | − | 0.661495i | \(-0.769922\pi\) | ||
0.749949 | − | 0.661495i | \(-0.230078\pi\) | |||||||
\(734\) | 28.6818 | 1.05866 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | − | 3.18596i | − | 0.117436i | ||||||
\(737\) | − | 0.895201i | − | 0.0329751i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −50.7272 | −1.86603 | −0.933014 | − | 0.359839i | \(-0.882832\pi\) | ||||
−0.933014 | + | 0.359839i | \(0.882832\pi\) | |||||||
\(740\) | 10.0729 | 0.370289 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −0.940082 | − | 4.08776i | −0.0345115 | − | 0.150066i | ||||
\(743\) | 12.9531i | 0.475202i | 0.971363 | + | 0.237601i | \(0.0763611\pi\) | ||||
−0.971363 | + | 0.237601i | \(0.923639\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 53.4093i | 1.95676i | ||||||||
\(746\) | 4.47509 | 0.163845 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | − | 6.33620i | − | 0.231674i | ||||||
\(749\) | 43.9648 | − | 10.1108i | 1.60644 | − | 0.369441i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 2.41023i | − | 0.0879507i | −0.999033 | − | 0.0439753i | \(-0.985998\pi\) | ||
0.999033 | − | 0.0439753i | \(-0.0140023\pi\) | |||||||
\(752\) | − | 7.36603i | − | 0.268612i | ||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 22.4585 | 0.817891 | ||||||||
\(755\) | 31.6705 | 1.15261 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −36.2727 | −1.31835 | −0.659176 | − | 0.751988i | \(-0.729095\pi\) | ||||
−0.659176 | + | 0.751988i | \(0.729095\pi\) | |||||||
\(758\) | 11.2714 | 0.409396 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −7.41464 | − | 9.07569i | −0.268957 | − | 0.329210i | ||||
\(761\) | 25.0730i | 0.908895i | 0.890773 | + | 0.454448i | \(0.150163\pi\) | ||||
−0.890773 | + | 0.454448i | \(0.849837\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −4.08776 | + | 0.940082i | −0.147987 | + | 0.0340333i | ||||
\(764\) | 6.01524 | 0.217624 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | − | 3.58832i | − | 0.129651i | ||||||
\(767\) | −12.3872 | −0.447274 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 16.9479i | − | 0.611156i | −0.952167 | − | 0.305578i | \(-0.901150\pi\) | ||
0.952167 | − | 0.305578i | \(-0.0988496\pi\) | |||||||
\(770\) | −1.95889 | − | 8.51782i | −0.0705934 | − | 0.306961i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 19.2725i | 0.693632i | ||||||||
\(773\) | −33.8578 | −1.21778 | −0.608889 | − | 0.793255i | \(-0.708385\pi\) | ||||
−0.608889 | + | 0.793255i | \(0.708385\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −14.7380 | −0.529404 | ||||||||
\(776\) | 3.22440i | 0.115749i | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | − | 3.54263i | − | 0.127009i | ||||||
\(779\) | −2.41023 | − | 2.95018i | −0.0863556 | − | 0.105701i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − | 6.31941i | − | 0.226126i | ||||||
\(782\) | 16.4296 | 0.587522 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −6.29675 | + | 3.05792i | −0.224884 | + | 0.109212i | ||||
\(785\) | 35.8345 | 1.27899 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 5.49280 | 0.195797 | 0.0978987 | − | 0.995196i | \(-0.468788\pi\) | ||||
0.0978987 | + | 0.995196i | \(0.468788\pi\) | |||||||
\(788\) | −0.371912 | −0.0132488 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | − | 26.2047i | − | 0.932320i | ||||||
\(791\) | −26.6155 | + | 6.12090i | −0.946337 | + | 0.217634i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 48.6747i | − | 1.72849i | ||||||
\(794\) | 6.99202 | 0.248138 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | − | 16.3446i | − | 0.579320i | ||||||
\(797\) | 25.8511 | 0.915695 | 0.457847 | − | 0.889031i | \(-0.348621\pi\) | ||||
0.457847 | + | 0.889031i | \(0.348621\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 37.9858 | 1.34384 | ||||||||
\(800\) | − | 2.22869i | − | 0.0787960i | ||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 28.1018 | 0.992308 | ||||||||
\(803\) | − | 7.51445i | − | 0.265179i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 22.0865 | − | 5.07935i | 0.778448 | − | 0.179024i | ||||
\(806\) | 33.1870i | 1.16896i | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −3.56260 | −0.125332 | ||||||||
\(809\) | 7.71213 | 0.271144 | 0.135572 | − | 0.990767i | \(-0.456713\pi\) | ||||
0.135572 | + | 0.990767i | \(0.456713\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −20.0280 | −0.703279 | −0.351640 | − | 0.936135i | \(-0.614376\pi\) | ||||
−0.351640 | + | 0.936135i | \(0.614376\pi\) | |||||||
\(812\) | 11.5388 | − | 2.65363i | 0.404932 | − | 0.0931242i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 4.60328 | 0.161345 | ||||||||
\(815\) | 24.8124i | 0.869142i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 22.3889 | + | 27.4045i | 0.783287 | + | 0.958761i | ||||
\(818\) | 24.2927i | 0.849373i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | − | 2.34979i | − | 0.0820581i | ||||||
\(821\) | −28.8151 | −1.00565 | −0.502827 | − | 0.864387i | \(-0.667707\pi\) | ||||
−0.502827 | + | 0.864387i | \(0.667707\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 7.15011 | 0.249237 | 0.124619 | − | 0.992205i | \(-0.460229\pi\) | ||||
0.124619 | + | 0.992205i | \(0.460229\pi\) | |||||||
\(824\) | − | 8.28917i | − | 0.288767i | ||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −6.36429 | + | 1.46363i | −0.221442 | + | 0.0509262i | ||||
\(827\) | 55.7805i | 1.93968i | 0.243745 | + | 0.969839i | \(0.421624\pi\) | ||||
−0.243745 | + | 0.969839i | \(0.578376\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 19.0274 | 0.660847 | 0.330424 | − | 0.943833i | \(-0.392808\pi\) | ||||
0.330424 | + | 0.943833i | \(0.392808\pi\) | |||||||
\(830\) | 4.87890i | 0.169349i | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −5.01856 | −0.173987 | ||||||||
\(833\) | −15.7694 | − | 32.4717i | −0.546376 | − | 1.12508i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 43.3721i | 1.50095i | ||||||||
\(836\) | −3.38845 | − | 4.14754i | −0.117192 | − | 0.143446i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −27.1080 | −0.936430 | ||||||||
\(839\) | 38.2365 | 1.32007 | 0.660035 | − | 0.751235i | \(-0.270541\pi\) | ||||
0.660035 | + | 0.751235i | \(0.270541\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 8.97357 | 0.309433 | ||||||||
\(842\) | 14.2216 | 0.490109 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | − | 2.44213i | − | 0.0840616i | ||||||
\(845\) | − | 32.7634i | − | 1.12710i | ||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 5.62756 | + | 24.4703i | 0.193365 | + | 0.840809i | ||||
\(848\) | − | 1.58536i | − | 0.0544414i | ||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 11.4931 | 0.394210 | ||||||||
\(851\) | 11.9362i | 0.409168i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 2.51866i | − | 0.0862373i | −0.999070 | − | 0.0431186i | \(-0.986271\pi\) | ||
0.999070 | − | 0.0431186i | \(-0.0137293\pi\) | |||||||
\(854\) | −5.75125 | − | 25.0082i | −0.196804 | − | 0.855761i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 17.0509 | 0.582787 | ||||||||
\(857\) | −25.2933 | −0.864004 | −0.432002 | − | 0.901873i | \(-0.642193\pi\) | ||||
−0.432002 | + | 0.901873i | \(0.642193\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 5.27398i | 0.179946i | 0.995944 | + | 0.0899729i | \(0.0286781\pi\) | ||||
−0.995944 | + | 0.0899729i | \(0.971322\pi\) | |||||||
\(860\) | 21.8274i | 0.744307i | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −32.0934 | −1.09311 | ||||||||
\(863\) | 24.7325i | 0.841905i | 0.907083 | + | 0.420953i | \(0.138304\pi\) | ||||
−0.907083 | + | 0.420953i | \(0.861696\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | − | 10.7634i | − | 0.365965i | ||||||
\(866\) | − | 18.5896i | − | 0.631700i | ||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 3.92128 | + | 17.0509i | 0.133097 | + | 0.578745i | ||||
\(869\) | − | 11.9754i | − | 0.406238i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 3.65644i | − | 0.123894i | ||||||
\(872\) | −1.58536 | −0.0536870 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 10.7545 | − | 8.78618i | 0.363776 | − | 0.297197i | ||||
\(875\) | −19.2120 | + | 4.41829i | −0.649485 | + | 0.149365i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 13.1443i | 0.443851i | 0.975064 | + | 0.221926i | \(0.0712342\pi\) | ||||
−0.975064 | + | 0.221926i | \(0.928766\pi\) | |||||||
\(878\) | − | 22.0623i | − | 0.744566i | ||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | − | 3.30347i | − | 0.111360i | ||||||
\(881\) | 29.6341i | 0.998398i | 0.866487 | + | 0.499199i | \(0.166372\pi\) | ||||
−0.866487 | + | 0.499199i | \(0.833628\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 38.9444 | 1.31058 | 0.655291 | − | 0.755377i | \(-0.272546\pi\) | ||||
0.655291 | + | 0.755377i | \(0.272546\pi\) | |||||||
\(884\) | − | 25.8802i | − | 0.870444i | ||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 8.62541i | 0.289776i | ||||||||
\(887\) | 34.5297 | 1.15939 | 0.579696 | − | 0.814833i | \(-0.303171\pi\) | ||||
0.579696 | + | 0.814833i | \(0.303171\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −25.2867 | + | 5.81531i | −0.848088 | + | 0.195039i | ||||
\(890\) | 9.11027 | 0.305377 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 8.80742 | 0.294894 | ||||||||
\(893\) | 24.8647 | − | 20.3139i | 0.832066 | − | 0.679780i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −20.1459 | −0.673402 | ||||||||
\(896\) | −2.57844 | + | 0.592978i | −0.0861398 | + | 0.0198100i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −22.1018 | −0.737545 | ||||||||
\(899\) | − | 29.5931i | − | 0.986986i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 8.17551 | 0.272366 | ||||||||
\(902\) | − | 1.07384i | − | 0.0357550i | ||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −10.3223 | −0.343314 | ||||||||
\(905\) | − | 2.95018i | − | 0.0980673i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 15.2164i | − | 0.505254i | −0.967564 | − | 0.252627i | \(-0.918706\pi\) | ||
0.967564 | − | 0.252627i | \(-0.0812945\pi\) | |||||||
\(908\) | −25.8511 | −0.857900 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −8.00106 | − | 34.7910i | −0.265233 | − | 1.15331i | ||||
\(911\) | 26.0330i | 0.862510i | 0.902230 | + | 0.431255i | \(0.141929\pi\) | ||||
−0.902230 | + | 0.431255i | \(0.858071\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 2.22963i | 0.0737901i | ||||||||
\(914\) | − | 0.00688586i | − | 0.000227764i | ||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 5.87721i | 0.194188i | ||||||||
\(917\) | 9.18596 | − | 2.11254i | 0.303347 | − | 0.0697623i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 15.0154 | 0.495314 | 0.247657 | − | 0.968848i | \(-0.420339\pi\) | ||||
0.247657 | + | 0.968848i | \(0.420339\pi\) | |||||||
\(920\) | 8.56583 | 0.282407 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −16.4758 | −0.542603 | ||||||||
\(923\) | − | 25.8116i | − | 0.849599i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 8.34979i | 0.274539i | ||||||||
\(926\) | − | 24.7296i | − | 0.812667i | ||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 4.47509 | 0.146902 | ||||||||
\(929\) | 19.8480i | 0.651191i | 0.945509 | + | 0.325596i | \(0.105565\pi\) | ||||
−0.945509 | + | 0.325596i | \(0.894435\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −27.6874 | − | 12.8222i | −0.907418 | − | 0.420230i | ||||
\(932\) | −9.09361 | −0.297871 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 5.00323 | 0.163711 | ||||||||
\(935\) | 17.0356 | 0.557125 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 37.4569i | 1.22366i | 0.790988 | + | 0.611832i | \(0.209567\pi\) | ||||
−0.790988 | + | 0.611832i | \(0.790433\pi\) | |||||||
\(938\) | −0.432034 | − | 1.87861i | −0.0141064 | − | 0.0613389i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 19.8045 | 0.645951 | ||||||||
\(941\) | 24.3097 | 0.792474 | 0.396237 | − | 0.918148i | \(-0.370316\pi\) | ||||
0.396237 | + | 0.918148i | \(0.370316\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 2.78444 | 0.0906740 | ||||||||
\(944\) | −2.46827 | −0.0803353 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 9.97499i | 0.324315i | ||||||||
\(947\) | 51.7736 | 1.68242 | 0.841209 | − | 0.540711i | \(-0.181845\pi\) | ||||
0.841209 | + | 0.540711i | \(0.181845\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 30.6927i | − | 0.996328i | ||||||
\(950\) | 7.52313 | − | 6.14624i | 0.244083 | − | 0.199410i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −3.05792 | − | 13.2968i | −0.0991078 | − | 0.430950i | ||||
\(953\) | 45.5398i | 1.47518i | 0.675250 | + | 0.737589i | \(0.264036\pi\) | ||||
−0.675250 | + | 0.737589i | \(0.735964\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 16.1727i | 0.523336i | ||||||||
\(956\) | 5.64333 | 0.182518 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 9.95805 | 0.321730 | ||||||||
\(959\) | 5.56797 | + | 24.2112i | 0.179799 | + | 0.781819i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 12.7298 | 0.410640 | ||||||||
\(962\) | 18.8021 | 0.606203 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −22.2248 | −0.715813 | ||||||||
\(965\) | −51.8164 | −1.66803 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −19.9667 | −0.642085 | −0.321043 | − | 0.947065i | \(-0.604033\pi\) | ||||
−0.321043 | + | 0.947065i | \(0.604033\pi\) | |||||||
\(968\) | 9.49033i | 0.305031i | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −8.66920 | −0.278351 | ||||||||
\(971\) | −54.6758 | −1.75463 | −0.877314 | − | 0.479916i | \(-0.840667\pi\) | ||||
−0.877314 | + | 0.479916i | \(0.840667\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 47.6100 | − | 10.9491i | 1.52631 | − | 0.351013i | ||||
\(974\) | −39.1845 | −1.25555 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | − | 9.69893i | − | 0.310455i | ||||||
\(977\) | − | 7.11574i | − | 0.227653i | −0.993501 | − | 0.113826i | \(-0.963689\pi\) | ||
0.993501 | − | 0.113826i | \(-0.0363107\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 4.16335 | 0.133061 | ||||||||
\(980\) | −8.22160 | − | 16.9296i | −0.262629 | − | 0.540796i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | − | 28.4737i | − | 0.908631i | ||||||
\(983\) | 2.26620 | 0.0722804 | 0.0361402 | − | 0.999347i | \(-0.488494\pi\) | ||||
0.0361402 | + | 0.999347i | \(0.488494\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − | 0.999931i | − | 0.0318605i | ||||||
\(986\) | 23.0775i | 0.734939i | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −13.8401 | − | 16.9406i | −0.440313 | − | 0.538953i | ||||
\(989\) | −25.8649 | −0.822457 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 30.6004i | 0.972054i | 0.873944 | + | 0.486027i | \(0.161554\pi\) | ||||
−0.873944 | + | 0.486027i | \(0.838446\pi\) | |||||||
\(992\) | 6.61285i | 0.209958i | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −3.04982 | − | 13.2615i | −0.0967344 | − | 0.420630i | ||||
\(995\) | 43.9446 | 1.39314 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 41.1959i | 1.30469i | 0.757924 | + | 0.652343i | \(0.226214\pi\) | ||||
−0.757924 | + | 0.652343i | \(0.773786\pi\) | |||||||
\(998\) | − | 8.52617i | − | 0.269891i | ||||||
\(999\) | 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 | 2394.2.e.c.1063.11 | 16 | ||
3.2 | odd | 2 | 266.2.d.a.265.1 | ✓ | 16 | ||
7.6 | odd | 2 | inner | 2394.2.e.c.1063.14 | 16 | ||
12.11 | even | 2 | 2128.2.m.f.1329.16 | 16 | |||
19.18 | odd | 2 | inner | 2394.2.e.c.1063.3 | 16 | ||
21.20 | even | 2 | 266.2.d.a.265.8 | yes | 16 | ||
57.56 | even | 2 | 266.2.d.a.265.16 | yes | 16 | ||
84.83 | odd | 2 | 2128.2.m.f.1329.1 | 16 | |||
133.132 | even | 2 | inner | 2394.2.e.c.1063.6 | 16 | ||
228.227 | odd | 2 | 2128.2.m.f.1329.2 | 16 | |||
399.398 | odd | 2 | 266.2.d.a.265.9 | yes | 16 | ||
1596.1595 | even | 2 | 2128.2.m.f.1329.15 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
266.2.d.a.265.1 | ✓ | 16 | 3.2 | odd | 2 | ||
266.2.d.a.265.8 | yes | 16 | 21.20 | even | 2 | ||
266.2.d.a.265.9 | yes | 16 | 399.398 | odd | 2 | ||
266.2.d.a.265.16 | yes | 16 | 57.56 | even | 2 | ||
2128.2.m.f.1329.1 | 16 | 84.83 | odd | 2 | |||
2128.2.m.f.1329.2 | 16 | 228.227 | odd | 2 | |||
2128.2.m.f.1329.15 | 16 | 1596.1595 | even | 2 | |||
2128.2.m.f.1329.16 | 16 | 12.11 | even | 2 | |||
2394.2.e.c.1063.3 | 16 | 19.18 | odd | 2 | inner | ||
2394.2.e.c.1063.6 | 16 | 133.132 | even | 2 | inner | ||
2394.2.e.c.1063.11 | 16 | 1.1 | even | 1 | trivial | ||
2394.2.e.c.1063.14 | 16 | 7.6 | odd | 2 | inner |