Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2070,2,Mod(829,2070)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2070, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2070.829");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2070 = 2 \cdot 3^{2} \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2070.d (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: | \(16.5290332184\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.0.5161984.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 4x^{3} + 25x^{2} - 20x + 8 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 690) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 829.5 | ||
Root | \(0.432320 - 0.432320i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2070.829 |
Dual form | 2070.2.d.d.829.2 |
$q$-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 \(\left(\mathbb{Z}/2070\mathbb{Z}\right)^\times\).
\(n\) | \(461\) | \(1657\) | \(1891\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) |
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 | ||||||||
\(5\) | −0.432320 | + | 2.19388i | −0.193340 | + | 0.981132i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.00000i | 0.755929i | 0.925820 | + | 0.377964i | \(0.123376\pi\) | ||||
−0.925820 | + | 0.377964i | \(0.876624\pi\) | |||||||
\(8\) | − | 1.00000i | − | 0.353553i | ||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −2.19388 | − | 0.432320i | −0.693765 | − | 0.136712i | ||||
\(11\) | 0.864641 | 0.260699 | 0.130350 | − | 0.991468i | \(-0.458390\pi\) | ||||
0.130350 | + | 0.991468i | \(0.458390\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 5.52311i | − | 1.53184i | −0.642938 | − | 0.765918i | \(-0.722285\pi\) | ||
0.642938 | − | 0.765918i | \(-0.277715\pi\) | |||||||
\(14\) | −2.00000 | −0.534522 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 3.52311i | 0.854481i | 0.904138 | + | 0.427240i | \(0.140514\pi\) | ||||
−0.904138 | + | 0.427240i | \(0.859486\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −8.11704 | −1.86218 | −0.931088 | − | 0.364795i | \(-0.881139\pi\) | ||||
−0.931088 | + | 0.364795i | \(0.881139\pi\) | |||||||
\(20\) | 0.432320 | − | 2.19388i | 0.0966698 | − | 0.490566i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0.864641i | 0.184342i | ||||||||
\(23\) | 1.00000i | 0.208514i | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.62620 | − | 1.89692i | −0.925240 | − | 0.379383i | ||||
\(26\) | 5.52311 | 1.08317 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | − | 2.00000i | − | 0.377964i | ||||||
\(29\) | −2.00000 | −0.371391 | −0.185695 | − | 0.982607i | \(-0.559454\pi\) | ||||
−0.185695 | + | 0.982607i | \(0.559454\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.25240 | −0.584148 | −0.292074 | − | 0.956396i | \(-0.594345\pi\) | ||||
−0.292074 | + | 0.956396i | \(0.594345\pi\) | |||||||
\(32\) | 1.00000i | 0.176777i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −3.52311 | −0.604209 | ||||||||
\(35\) | −4.38776 | − | 0.864641i | −0.741666 | − | 0.146151i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 5.13536i | 0.844248i | 0.906538 | + | 0.422124i | \(0.138715\pi\) | ||||
−0.906538 | + | 0.422124i | \(0.861285\pi\) | |||||||
\(38\) | − | 8.11704i | − | 1.31676i | ||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 2.19388 | + | 0.432320i | 0.346883 | + | 0.0683559i | ||||
\(41\) | −3.52311 | −0.550218 | −0.275109 | − | 0.961413i | \(-0.588714\pi\) | ||||
−0.275109 | + | 0.961413i | \(0.588714\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 1.13536i | − | 0.173141i | −0.996246 | − | 0.0865703i | \(-0.972409\pi\) | ||
0.996246 | − | 0.0865703i | \(-0.0275907\pi\) | |||||||
\(44\) | −0.864641 | −0.130350 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −1.00000 | −0.147442 | ||||||||
\(47\) | − | 5.52311i | − | 0.805629i | −0.915282 | − | 0.402815i | \(-0.868032\pi\) | ||
0.915282 | − | 0.402815i | \(-0.131968\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 3.00000 | 0.428571 | ||||||||
\(50\) | 1.89692 | − | 4.62620i | 0.268264 | − | 0.654243i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 5.52311i | 0.765918i | ||||||||
\(53\) | 1.34153i | 0.184273i | 0.995746 | + | 0.0921364i | \(0.0293696\pi\) | ||||
−0.995746 | + | 0.0921364i | \(0.970630\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −0.373802 | + | 1.89692i | −0.0504034 | + | 0.255780i | ||||
\(56\) | 2.00000 | 0.267261 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | − | 2.00000i | − | 0.262613i | ||||||
\(59\) | −10.9817 | −1.42969 | −0.714846 | − | 0.699282i | \(-0.753503\pi\) | ||||
−0.714846 | + | 0.699282i | \(0.753503\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −5.91087 | −0.756809 | −0.378405 | − | 0.925640i | \(-0.623527\pi\) | ||||
−0.378405 | + | 0.925640i | \(0.623527\pi\) | |||||||
\(62\) | − | 3.25240i | − | 0.413055i | ||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 12.1170 | + | 2.38776i | 1.50293 | + | 0.296165i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 5.91087i | − | 0.722128i | −0.932541 | − | 0.361064i | \(-0.882414\pi\) | ||
0.932541 | − | 0.361064i | \(-0.117586\pi\) | |||||||
\(68\) | − | 3.52311i | − | 0.427240i | ||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0.864641 | − | 4.38776i | 0.103344 | − | 0.524437i | ||||
\(71\) | 5.79383 | 0.687601 | 0.343801 | − | 0.939043i | \(-0.388286\pi\) | ||||
0.343801 | + | 0.939043i | \(0.388286\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 15.2524i | − | 1.78516i | −0.450891 | − | 0.892579i | \(-0.648894\pi\) | ||
0.450891 | − | 0.892579i | \(-0.351106\pi\) | |||||||
\(74\) | −5.13536 | −0.596973 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 8.11704 | 0.931088 | ||||||||
\(77\) | 1.72928i | 0.197070i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 3.79383 | 0.426840 | 0.213420 | − | 0.976961i | \(-0.431540\pi\) | ||||
0.213420 | + | 0.976961i | \(0.431540\pi\) | |||||||
\(80\) | −0.432320 | + | 2.19388i | −0.0483349 | + | 0.245283i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | − | 3.52311i | − | 0.389063i | ||||||
\(83\) | 8.32320i | 0.913590i | 0.889572 | + | 0.456795i | \(0.151003\pi\) | ||||
−0.889572 | + | 0.456795i | \(0.848997\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −7.72928 | − | 1.52311i | −0.838358 | − | 0.165205i | ||||
\(86\) | 1.13536 | 0.122429 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | − | 0.864641i | − | 0.0921710i | ||||||
\(89\) | 4.77551 | 0.506203 | 0.253102 | − | 0.967440i | \(-0.418549\pi\) | ||||
0.253102 | + | 0.967440i | \(0.418549\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 11.0462 | 1.15796 | ||||||||
\(92\) | − | 1.00000i | − | 0.104257i | ||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 5.52311 | 0.569666 | ||||||||
\(95\) | 3.50916 | − | 17.8078i | 0.360032 | − | 1.82704i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 1.04623i | − | 0.106228i | −0.998588 | − | 0.0531142i | \(-0.983085\pi\) | ||
0.998588 | − | 0.0531142i | \(-0.0169147\pi\) | |||||||
\(98\) | 3.00000i | 0.303046i | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 4.62620 | + | 1.89692i | 0.462620 | + | 0.189692i | ||||
\(101\) | −9.04623 | −0.900133 | −0.450067 | − | 0.892995i | \(-0.648600\pi\) | ||||
−0.450067 | + | 0.892995i | \(0.648600\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 11.3169i | − | 1.11509i | −0.830146 | − | 0.557546i | \(-0.811743\pi\) | ||
0.830146 | − | 0.557546i | \(-0.188257\pi\) | |||||||
\(104\) | −5.52311 | −0.541586 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −1.34153 | −0.130301 | ||||||||
\(107\) | − | 5.64015i | − | 0.545254i | −0.962120 | − | 0.272627i | \(-0.912108\pi\) | ||
0.962120 | − | 0.272627i | \(-0.0878925\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 12.1816 | 1.16678 | 0.583392 | − | 0.812191i | \(-0.301725\pi\) | ||||
0.583392 | + | 0.812191i | \(0.301725\pi\) | |||||||
\(110\) | −1.89692 | − | 0.373802i | −0.180864 | − | 0.0356406i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 2.00000i | 0.188982i | ||||||||
\(113\) | 5.79383i | 0.545038i | 0.962150 | + | 0.272519i | \(0.0878567\pi\) | ||||
−0.962150 | + | 0.272519i | \(0.912143\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −2.19388 | − | 0.432320i | −0.204580 | − | 0.0403141i | ||||
\(116\) | 2.00000 | 0.185695 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | − | 10.9817i | − | 1.01095i | ||||||
\(119\) | −7.04623 | −0.645927 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.2524 | −0.932036 | ||||||||
\(122\) | − | 5.91087i | − | 0.535145i | ||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 3.25240 | 0.292074 | ||||||||
\(125\) | 6.16160 | − | 9.32924i | 0.551110 | − | 0.834432i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 0.747604i | 0.0663391i | 0.999450 | + | 0.0331696i | \(0.0105601\pi\) | ||||
−0.999450 | + | 0.0331696i | \(0.989440\pi\) | |||||||
\(128\) | − | 1.00000i | − | 0.0883883i | ||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −2.38776 | + | 12.1170i | −0.209420 | + | 1.06273i | ||||
\(131\) | −19.7572 | −1.72619 | −0.863097 | − | 0.505039i | \(-0.831478\pi\) | ||||
−0.863097 | + | 0.505039i | \(0.831478\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − | 16.2341i | − | 1.40767i | ||||||
\(134\) | 5.91087 | 0.510621 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 3.52311 | 0.302105 | ||||||||
\(137\) | − | 0.476886i | − | 0.0407431i | −0.999792 | − | 0.0203715i | \(-0.993515\pi\) | ||
0.999792 | − | 0.0203715i | \(-0.00648491\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 3.45856 | 0.293352 | 0.146676 | − | 0.989185i | \(-0.453143\pi\) | ||||
0.146676 | + | 0.989185i | \(0.453143\pi\) | |||||||
\(140\) | 4.38776 | + | 0.864641i | 0.370833 | + | 0.0730755i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 5.79383i | 0.486208i | ||||||||
\(143\) | − | 4.77551i | − | 0.399348i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0.864641 | − | 4.38776i | 0.0718045 | − | 0.364383i | ||||
\(146\) | 15.2524 | 1.26230 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | − | 5.13536i | − | 0.422124i | ||||||
\(149\) | −8.86464 | −0.726220 | −0.363110 | − | 0.931746i | \(-0.618285\pi\) | ||||
−0.363110 | + | 0.931746i | \(0.618285\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −6.71096 | −0.546130 | −0.273065 | − | 0.961996i | \(-0.588037\pi\) | ||||
−0.273065 | + | 0.961996i | \(0.588037\pi\) | |||||||
\(152\) | 8.11704i | 0.658379i | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −1.72928 | −0.139349 | ||||||||
\(155\) | 1.40608 | − | 7.13536i | 0.112939 | − | 0.573126i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 14.6864i | − | 1.17210i | −0.810275 | − | 0.586050i | \(-0.800682\pi\) | ||
0.810275 | − | 0.586050i | \(-0.199318\pi\) | |||||||
\(158\) | 3.79383i | 0.301821i | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −2.19388 | − | 0.432320i | −0.173441 | − | 0.0341779i | ||||
\(161\) | −2.00000 | −0.157622 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 23.2803i | 1.82345i | 0.410797 | + | 0.911727i | \(0.365251\pi\) | ||||
−0.410797 | + | 0.911727i | \(0.634749\pi\) | |||||||
\(164\) | 3.52311 | 0.275109 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −8.32320 | −0.646006 | ||||||||
\(167\) | 5.93545i | 0.459299i | 0.973273 | + | 0.229649i | \(0.0737580\pi\) | ||||
−0.973273 | + | 0.229649i | \(0.926242\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −17.5048 | −1.34652 | ||||||||
\(170\) | 1.52311 | − | 7.72928i | 0.116818 | − | 0.592809i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 1.13536i | 0.0865703i | ||||||||
\(173\) | 25.8217i | 1.96319i | 0.190973 | + | 0.981595i | \(0.438836\pi\) | ||||
−0.190973 | + | 0.981595i | \(0.561164\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 3.79383 | − | 9.25240i | 0.286787 | − | 0.699415i | ||||
\(176\) | 0.864641 | 0.0651748 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 4.77551i | 0.357940i | ||||||||
\(179\) | −23.3449 | −1.74488 | −0.872438 | − | 0.488725i | \(-0.837462\pi\) | ||||
−0.872438 | + | 0.488725i | \(0.837462\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 13.3694 | 0.993742 | 0.496871 | − | 0.867824i | \(-0.334482\pi\) | ||||
0.496871 | + | 0.867824i | \(0.334482\pi\) | |||||||
\(182\) | 11.0462i | 0.818801i | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 1.00000 | 0.0737210 | ||||||||
\(185\) | −11.2663 | − | 2.22012i | −0.828318 | − | 0.163227i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 3.04623i | 0.222762i | ||||||||
\(188\) | 5.52311i | 0.402815i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 17.8078 | + | 3.50916i | 1.29191 | + | 0.254581i | ||||
\(191\) | −12.2341 | −0.885227 | −0.442613 | − | 0.896713i | \(-0.645949\pi\) | ||||
−0.442613 | + | 0.896713i | \(0.645949\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 7.45856i | − | 0.536879i | −0.963297 | − | 0.268440i | \(-0.913492\pi\) | ||
0.963297 | − | 0.268440i | \(-0.0865080\pi\) | |||||||
\(194\) | 1.04623 | 0.0751148 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −3.00000 | −0.214286 | ||||||||
\(197\) | − | 2.00000i | − | 0.142494i | −0.997459 | − | 0.0712470i | \(-0.977302\pi\) | ||
0.997459 | − | 0.0712470i | \(-0.0226979\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −22.8401 | −1.61909 | −0.809545 | − | 0.587059i | \(-0.800286\pi\) | ||||
−0.809545 | + | 0.587059i | \(0.800286\pi\) | |||||||
\(200\) | −1.89692 | + | 4.62620i | −0.134132 | + | 0.327122i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | − | 9.04623i | − | 0.636490i | ||||||
\(203\) | − | 4.00000i | − | 0.280745i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.52311 | − | 7.72928i | 0.106379 | − | 0.539836i | ||||
\(206\) | 11.3169 | 0.788489 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | − | 5.52311i | − | 0.382959i | ||||||
\(209\) | −7.01832 | −0.485467 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 24.2341 | 1.66834 | 0.834171 | − | 0.551506i | \(-0.185946\pi\) | ||||
0.834171 | + | 0.551506i | \(0.185946\pi\) | |||||||
\(212\) | − | 1.34153i | − | 0.0921364i | ||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 5.64015 | 0.385553 | ||||||||
\(215\) | 2.49084 | + | 0.490839i | 0.169874 | + | 0.0334749i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 6.50479i | − | 0.441574i | ||||||
\(218\) | 12.1816i | 0.825041i | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0.373802 | − | 1.89692i | 0.0252017 | − | 0.127890i | ||||
\(221\) | 19.4586 | 1.30892 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 13.9634i | − | 0.935055i | −0.883978 | − | 0.467528i | \(-0.845145\pi\) | ||
0.883978 | − | 0.467528i | \(-0.154855\pi\) | |||||||
\(224\) | −2.00000 | −0.133631 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −5.79383 | −0.385400 | ||||||||
\(227\) | 4.45231i | 0.295510i | 0.989024 | + | 0.147755i | \(0.0472047\pi\) | ||||
−0.989024 | + | 0.147755i | \(0.952795\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 4.05249 | 0.267796 | 0.133898 | − | 0.990995i | \(-0.457251\pi\) | ||||
0.133898 | + | 0.990995i | \(0.457251\pi\) | |||||||
\(230\) | 0.432320 | − | 2.19388i | 0.0285064 | − | 0.144660i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 2.00000i | 0.131306i | ||||||||
\(233\) | − | 24.5327i | − | 1.60719i | −0.595176 | − | 0.803595i | \(-0.702918\pi\) | ||
0.595176 | − | 0.803595i | \(-0.297082\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 12.1170 | + | 2.38776i | 0.790428 | + | 0.155760i | ||||
\(236\) | 10.9817 | 0.714846 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | − | 7.04623i | − | 0.456739i | ||||||
\(239\) | 10.7755 | 0.697010 | 0.348505 | − | 0.937307i | \(-0.386689\pi\) | ||||
0.348505 | + | 0.937307i | \(0.386689\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −10.7755 | −0.694112 | −0.347056 | − | 0.937844i | \(-0.612819\pi\) | ||||
−0.347056 | + | 0.937844i | \(0.612819\pi\) | |||||||
\(242\) | − | 10.2524i | − | 0.659049i | ||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 5.91087 | 0.378405 | ||||||||
\(245\) | −1.29696 | + | 6.58163i | −0.0828598 | + | 0.420485i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 44.8313i | 2.85255i | ||||||||
\(248\) | 3.25240i | 0.206527i | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 9.32924 | + | 6.16160i | 0.590033 | + | 0.389694i | ||||
\(251\) | 3.91087 | 0.246852 | 0.123426 | − | 0.992354i | \(-0.460612\pi\) | ||||
0.123426 | + | 0.992354i | \(0.460612\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0.864641i | 0.0543595i | ||||||||
\(254\) | −0.747604 | −0.0469088 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | − | 28.0925i | − | 1.75236i | −0.481985 | − | 0.876180i | \(-0.660084\pi\) | ||
0.481985 | − | 0.876180i | \(-0.339916\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −10.2707 | −0.638191 | ||||||||
\(260\) | −12.1170 | − | 2.38776i | −0.751467 | − | 0.148082i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | − | 19.7572i | − | 1.22060i | ||||||
\(263\) | 29.5510i | 1.82219i | 0.412192 | + | 0.911097i | \(0.364763\pi\) | ||||
−0.412192 | + | 0.911097i | \(0.635237\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −2.94315 | − | 0.579969i | −0.180796 | − | 0.0356272i | ||||
\(266\) | 16.2341 | 0.995375 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 5.91087i | 0.361064i | ||||||||
\(269\) | −17.2803 | −1.05360 | −0.526799 | − | 0.849990i | \(-0.676608\pi\) | ||||
−0.526799 | + | 0.849990i | \(0.676608\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 9.96336 | 0.605231 | 0.302615 | − | 0.953113i | \(-0.402140\pi\) | ||||
0.302615 | + | 0.953113i | \(0.402140\pi\) | |||||||
\(272\) | 3.52311i | 0.213620i | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0.476886 | 0.0288097 | ||||||||
\(275\) | −4.00000 | − | 1.64015i | −0.241209 | − | 0.0989049i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 27.0741i | 1.62673i | 0.581756 | + | 0.813364i | \(0.302366\pi\) | ||||
−0.581756 | + | 0.813364i | \(0.697634\pi\) | |||||||
\(278\) | 3.45856i | 0.207431i | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −0.864641 | + | 4.38776i | −0.0516722 | + | 0.262219i | ||||
\(281\) | 27.2803 | 1.62741 | 0.813703 | − | 0.581281i | \(-0.197448\pi\) | ||||
0.813703 | + | 0.581281i | \(0.197448\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 30.9205i | 1.83803i | 0.394222 | + | 0.919015i | \(0.371014\pi\) | ||||
−0.394222 | + | 0.919015i | \(0.628986\pi\) | |||||||
\(284\) | −5.79383 | −0.343801 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 4.77551 | 0.282382 | ||||||||
\(287\) | − | 7.04623i | − | 0.415926i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 4.58767 | 0.269863 | ||||||||
\(290\) | 4.38776 | + | 0.864641i | 0.257658 | + | 0.0507735i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 15.2524i | 0.892579i | ||||||||
\(293\) | 11.0708i | 0.646764i | 0.946269 | + | 0.323382i | \(0.104820\pi\) | ||||
−0.946269 | + | 0.323382i | \(0.895180\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 4.74760 | − | 24.0925i | 0.276416 | − | 1.40272i | ||||
\(296\) | 5.13536 | 0.298487 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | − | 8.86464i | − | 0.513515i | ||||||
\(299\) | 5.52311 | 0.319410 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2.27072 | 0.130882 | ||||||||
\(302\) | − | 6.71096i | − | 0.386172i | ||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −8.11704 | −0.465544 | ||||||||
\(305\) | 2.55539 | − | 12.9677i | 0.146321 | − | 0.742530i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 4.23407i | 0.241651i | 0.992674 | + | 0.120826i | \(0.0385542\pi\) | ||||
−0.992674 | + | 0.120826i | \(0.961446\pi\) | |||||||
\(308\) | − | 1.72928i | − | 0.0985350i | ||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 7.13536 | + | 1.40608i | 0.405261 | + | 0.0798598i | ||||
\(311\) | 13.2803 | 0.753057 | 0.376528 | − | 0.926405i | \(-0.377118\pi\) | ||||
0.376528 | + | 0.926405i | \(0.377118\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 31.9634i | 1.80668i | 0.428930 | + | 0.903338i | \(0.358891\pi\) | ||||
−0.428930 | + | 0.903338i | \(0.641109\pi\) | |||||||
\(314\) | 14.6864 | 0.828800 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −3.79383 | −0.213420 | ||||||||
\(317\) | 13.2803i | 0.745896i | 0.927852 | + | 0.372948i | \(0.121653\pi\) | ||||
−0.927852 | + | 0.372948i | \(0.878347\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1.72928 | −0.0968212 | ||||||||
\(320\) | 0.432320 | − | 2.19388i | 0.0241674 | − | 0.122641i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | − | 2.00000i | − | 0.111456i | ||||||
\(323\) | − | 28.5972i | − | 1.59119i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −10.4769 | + | 25.5510i | −0.581153 | + | 1.41732i | ||||
\(326\) | −23.2803 | −1.28938 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 3.52311i | 0.194531i | ||||||||
\(329\) | 11.0462 | 0.608998 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −11.8217 | −0.649782 | −0.324891 | − | 0.945752i | \(-0.605328\pi\) | ||||
−0.324891 | + | 0.945752i | \(0.605328\pi\) | |||||||
\(332\) | − | 8.32320i | − | 0.456795i | ||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −5.93545 | −0.324773 | ||||||||
\(335\) | 12.9677 | + | 2.55539i | 0.708502 | + | 0.139616i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 13.2803i | 0.723424i | 0.932290 | + | 0.361712i | \(0.117808\pi\) | ||||
−0.932290 | + | 0.361712i | \(0.882192\pi\) | |||||||
\(338\) | − | 17.5048i | − | 0.952135i | ||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 7.72928 | + | 1.52311i | 0.419179 | + | 0.0826025i | ||||
\(341\) | −2.81215 | −0.152287 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 20.0000i | 1.07990i | ||||||||
\(344\) | −1.13536 | −0.0612145 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −25.8217 | −1.38819 | ||||||||
\(347\) | 24.3632i | 1.30788i | 0.756545 | + | 0.653942i | \(0.226886\pi\) | ||||
−0.756545 | + | 0.653942i | \(0.773114\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −3.49521 | −0.187094 | −0.0935471 | − | 0.995615i | \(-0.529821\pi\) | ||||
−0.0935471 | + | 0.995615i | \(0.529821\pi\) | |||||||
\(350\) | 9.25240 | + | 3.79383i | 0.494561 | + | 0.202789i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0.864641i | 0.0460855i | ||||||||
\(353\) | 31.5789i | 1.68078i | 0.541985 | + | 0.840388i | \(0.317673\pi\) | ||||
−0.541985 | + | 0.840388i | \(0.682327\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −2.50479 | + | 12.7110i | −0.132941 | + | 0.674628i | ||||
\(356\) | −4.77551 | −0.253102 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | − | 23.3449i | − | 1.23381i | ||||||
\(359\) | −21.1878 | −1.11825 | −0.559126 | − | 0.829083i | \(-0.688863\pi\) | ||||
−0.559126 | + | 0.829083i | \(0.688863\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 46.8863 | 2.46770 | ||||||||
\(362\) | 13.3694i | 0.702682i | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −11.0462 | −0.578980 | ||||||||
\(365\) | 33.4619 | + | 6.59392i | 1.75148 | + | 0.345142i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 13.0462i | 0.681008i | 0.940243 | + | 0.340504i | \(0.110598\pi\) | ||||
−0.940243 | + | 0.340504i | \(0.889402\pi\) | |||||||
\(368\) | 1.00000i | 0.0521286i | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 2.22012 | − | 11.2663i | 0.115419 | − | 0.585710i | ||||
\(371\) | −2.68305 | −0.139297 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 18.8646i | − | 0.976774i | −0.872627 | − | 0.488387i | \(-0.837585\pi\) | ||
0.872627 | − | 0.488387i | \(-0.162415\pi\) | |||||||
\(374\) | −3.04623 | −0.157517 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −5.52311 | −0.284833 | ||||||||
\(377\) | 11.0462i | 0.568910i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −26.7509 | −1.37410 | −0.687052 | − | 0.726609i | \(-0.741095\pi\) | ||||
−0.687052 | + | 0.726609i | \(0.741095\pi\) | |||||||
\(380\) | −3.50916 | + | 17.8078i | −0.180016 | + | 0.913520i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | − | 12.2341i | − | 0.625950i | ||||||
\(383\) | − | 22.5048i | − | 1.14994i | −0.818174 | − | 0.574971i | \(-0.805013\pi\) | ||
0.818174 | − | 0.574971i | \(-0.194987\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −3.79383 | − | 0.747604i | −0.193352 | − | 0.0381014i | ||||
\(386\) | 7.45856 | 0.379631 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 1.04623i | 0.0531142i | ||||||||
\(389\) | −7.67680 | −0.389229 | −0.194614 | − | 0.980880i | \(-0.562346\pi\) | ||||
−0.194614 | + | 0.980880i | \(0.562346\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −3.52311 | −0.178172 | ||||||||
\(392\) | − | 3.00000i | − | 0.151523i | ||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 2.00000 | 0.100759 | ||||||||
\(395\) | −1.64015 | + | 8.32320i | −0.0825250 | + | 0.418786i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 31.7938i | − | 1.59569i | −0.602865 | − | 0.797843i | \(-0.705974\pi\) | ||
0.602865 | − | 0.797843i | \(-0.294026\pi\) | |||||||
\(398\) | − | 22.8401i | − | 1.14487i | ||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −4.62620 | − | 1.89692i | −0.231310 | − | 0.0948458i | ||||
\(401\) | 18.0925 | 0.903494 | 0.451747 | − | 0.892146i | \(-0.350801\pi\) | ||||
0.451747 | + | 0.892146i | \(0.350801\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 17.9634i | 0.894818i | ||||||||
\(404\) | 9.04623 | 0.450067 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 4.00000 | 0.198517 | ||||||||
\(407\) | 4.44024i | 0.220095i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −2.00000 | −0.0988936 | −0.0494468 | − | 0.998777i | \(-0.515746\pi\) | ||||
−0.0494468 | + | 0.998777i | \(0.515746\pi\) | |||||||
\(410\) | 7.72928 | + | 1.52311i | 0.381722 | + | 0.0752213i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 11.3169i | 0.557546i | ||||||||
\(413\) | − | 21.9634i | − | 1.08075i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −18.2601 | − | 3.59829i | −0.896353 | − | 0.176633i | ||||
\(416\) | 5.52311 | 0.270793 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | − | 7.01832i | − | 0.343277i | ||||||
\(419\) | 20.4523 | 0.999161 | 0.499580 | − | 0.866268i | \(-0.333488\pi\) | ||||
0.499580 | + | 0.866268i | \(0.333488\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −12.9571 | −0.631490 | −0.315745 | − | 0.948844i | \(-0.602254\pi\) | ||||
−0.315745 | + | 0.948844i | \(0.602254\pi\) | |||||||
\(422\) | 24.2341i | 1.17970i | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 1.34153 | 0.0651503 | ||||||||
\(425\) | 6.68305 | − | 16.2986i | 0.324176 | − | 0.790599i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 11.8217i | − | 0.572094i | ||||||
\(428\) | 5.64015i | 0.272627i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −0.490839 | + | 2.49084i | −0.0236704 | + | 0.120119i | ||||
\(431\) | −33.3728 | −1.60751 | −0.803755 | − | 0.594961i | \(-0.797168\pi\) | ||||
−0.803755 | + | 0.594961i | \(0.797168\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 19.0096i | − | 0.913542i | −0.889584 | − | 0.456771i | \(-0.849006\pi\) | ||
0.889584 | − | 0.456771i | \(-0.150994\pi\) | |||||||
\(434\) | 6.50479 | 0.312240 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −12.1816 | −0.583392 | ||||||||
\(437\) | − | 8.11704i | − | 0.388291i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −32.5972 | −1.55578 | −0.777891 | − | 0.628399i | \(-0.783710\pi\) | ||||
−0.777891 | + | 0.628399i | \(0.783710\pi\) | |||||||
\(440\) | 1.89692 | + | 0.373802i | 0.0904319 | + | 0.0178203i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 19.4586i | 0.925549i | ||||||||
\(443\) | 4.00000i | 0.190046i | 0.995475 | + | 0.0950229i | \(0.0302924\pi\) | ||||
−0.995475 | + | 0.0950229i | \(0.969708\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −2.06455 | + | 10.4769i | −0.0978691 | + | 0.496652i | ||||
\(446\) | 13.9634 | 0.661184 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | − | 2.00000i | − | 0.0944911i | ||||||
\(449\) | 39.5789 | 1.86785 | 0.933923 | − | 0.357475i | \(-0.116362\pi\) | ||||
0.933923 | + | 0.357475i | \(0.116362\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −3.04623 | −0.143441 | ||||||||
\(452\) | − | 5.79383i | − | 0.272519i | ||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −4.45231 | −0.208957 | ||||||||
\(455\) | −4.77551 | + | 24.2341i | −0.223879 | + | 1.13611i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 24.5048i | 1.14629i | 0.819455 | + | 0.573143i | \(0.194276\pi\) | ||||
−0.819455 | + | 0.573143i | \(0.805724\pi\) | |||||||
\(458\) | 4.05249i | 0.189360i | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 2.19388 | + | 0.432320i | 0.102290 | + | 0.0201570i | ||||
\(461\) | −18.2341 | −0.849245 | −0.424623 | − | 0.905370i | \(-0.639593\pi\) | ||||
−0.424623 | + | 0.905370i | \(0.639593\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 4.20617i | 0.195477i | 0.995212 | + | 0.0977386i | \(0.0311609\pi\) | ||||
−0.995212 | + | 0.0977386i | \(0.968839\pi\) | |||||||
\(464\) | −2.00000 | −0.0928477 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 24.5327 | 1.13646 | ||||||||
\(467\) | − | 19.1912i | − | 0.888062i | −0.896012 | − | 0.444031i | \(-0.853548\pi\) | ||
0.896012 | − | 0.444031i | \(-0.146452\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 11.8217 | 0.545877 | ||||||||
\(470\) | −2.38776 | + | 12.1170i | −0.110139 | + | 0.558917i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 10.9817i | 0.505473i | ||||||||
\(473\) | − | 0.981678i | − | 0.0451376i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 37.5510 | + | 15.3973i | 1.72296 | + | 0.706478i | ||||
\(476\) | 7.04623 | 0.322963 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 10.7755i | 0.492860i | ||||||||
\(479\) | −25.6801 | −1.17335 | −0.586677 | − | 0.809821i | \(-0.699564\pi\) | ||||
−0.586677 | + | 0.809821i | \(0.699564\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 28.3632 | 1.29325 | ||||||||
\(482\) | − | 10.7755i | − | 0.490811i | ||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 10.2524 | 0.466018 | ||||||||
\(485\) | 2.29530 | + | 0.452306i | 0.104224 | + | 0.0205382i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 8.74760i | 0.396392i | 0.980162 | + | 0.198196i | \(0.0635082\pi\) | ||||
−0.980162 | + | 0.198196i | \(0.936492\pi\) | |||||||
\(488\) | 5.91087i | 0.267572i | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −6.58163 | − | 1.29696i | −0.297328 | − | 0.0585907i | ||||
\(491\) | −23.8863 | −1.07797 | −0.538987 | − | 0.842314i | \(-0.681193\pi\) | ||||
−0.538987 | + | 0.842314i | \(0.681193\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 7.04623i | − | 0.317346i | ||||||
\(494\) | −44.8313 | −2.01706 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −3.25240 | −0.146037 | ||||||||
\(497\) | 11.5877i | 0.519778i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −29.7293 | −1.33087 | −0.665433 | − | 0.746458i | \(-0.731753\pi\) | ||||
−0.665433 | + | 0.746458i | \(0.731753\pi\) | |||||||
\(500\) | −6.16160 | + | 9.32924i | −0.275555 | + | 0.417216i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 3.91087i | 0.174551i | ||||||||
\(503\) | 0.775511i | 0.0345783i | 0.999851 | + | 0.0172892i | \(0.00550358\pi\) | ||||
−0.999851 | + | 0.0172892i | \(0.994496\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 3.91087 | − | 19.8463i | 0.174031 | − | 0.883150i | ||||
\(506\) | −0.864641 | −0.0384380 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | − | 0.747604i | − | 0.0331696i | ||||||
\(509\) | −26.0000 | −1.15243 | −0.576215 | − | 0.817298i | \(-0.695471\pi\) | ||||
−0.576215 | + | 0.817298i | \(0.695471\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 30.5048 | 1.34945 | ||||||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 28.0925 | 1.23911 | ||||||||
\(515\) | 24.8280 | + | 4.89255i | 1.09405 | + | 0.215591i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 4.77551i | − | 0.210027i | ||||||
\(518\) | − | 10.2707i | − | 0.451269i | ||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 2.38776 | − | 12.1170i | 0.104710 | − | 0.531367i | ||||
\(521\) | −13.4219 | −0.588025 | −0.294012 | − | 0.955802i | \(-0.594991\pi\) | ||||
−0.294012 | + | 0.955802i | \(0.594991\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 41.9667i | 1.83507i | 0.397649 | + | 0.917537i | \(0.369826\pi\) | ||||
−0.397649 | + | 0.917537i | \(0.630174\pi\) | |||||||
\(524\) | 19.7572 | 0.863097 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −29.5510 | −1.28849 | ||||||||
\(527\) | − | 11.4586i | − | 0.499143i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1.00000 | −0.0434783 | ||||||||
\(530\) | 0.579969 | − | 2.94315i | 0.0251923 | − | 0.127842i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 16.2341i | 0.703836i | ||||||||
\(533\) | 19.4586i | 0.842844i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 12.3738 | + | 2.43835i | 0.534966 | + | 0.105419i | ||||
\(536\) | −5.91087 | −0.255311 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | − | 17.2803i | − | 0.745007i | ||||||
\(539\) | 2.59392 | 0.111728 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −1.58767 | −0.0682591 | −0.0341295 | − | 0.999417i | \(-0.510866\pi\) | ||||
−0.0341295 | + | 0.999417i | \(0.510866\pi\) | |||||||
\(542\) | 9.96336i | 0.427963i | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −3.52311 | −0.151052 | ||||||||
\(545\) | −5.26635 | + | 26.7249i | −0.225586 | + | 1.14477i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 20.6464i | − | 0.882777i | −0.897316 | − | 0.441388i | \(-0.854486\pi\) | ||
0.897316 | − | 0.441388i | \(-0.145514\pi\) | |||||||
\(548\) | 0.476886i | 0.0203715i | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 1.64015 | − | 4.00000i | 0.0699363 | − | 0.170561i | ||||
\(551\) | 16.2341 | 0.691595 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 7.58767i | 0.322660i | ||||||||
\(554\) | −27.0741 | −1.15027 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −3.45856 | −0.146676 | ||||||||
\(557\) | − | 9.47063i | − | 0.401283i | −0.979665 | − | 0.200642i | \(-0.935697\pi\) | ||
0.979665 | − | 0.200642i | \(-0.0643027\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −6.27072 | −0.265223 | ||||||||
\(560\) | −4.38776 | − | 0.864641i | −0.185417 | − | 0.0365377i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 27.2803i | 1.15075i | ||||||||
\(563\) | 1.51105i | 0.0636832i | 0.999493 | + | 0.0318416i | \(0.0101372\pi\) | ||||
−0.999493 | + | 0.0318416i | \(0.989863\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −12.7110 | − | 2.50479i | −0.534754 | − | 0.105377i | ||||
\(566\) | −30.9205 | −1.29968 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | − | 5.79383i | − | 0.243104i | ||||||
\(569\) | −20.0000 | −0.838444 | −0.419222 | − | 0.907884i | \(-0.637697\pi\) | ||||
−0.419222 | + | 0.907884i | \(0.637697\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −35.1633 | −1.47154 | −0.735768 | − | 0.677233i | \(-0.763179\pi\) | ||||
−0.735768 | + | 0.677233i | \(0.763179\pi\) | |||||||
\(572\) | 4.77551i | 0.199674i | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 7.04623 | 0.294104 | ||||||||
\(575\) | 1.89692 | − | 4.62620i | 0.0791069 | − | 0.192926i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 22.7110i | − | 0.945470i | −0.881205 | − | 0.472735i | \(-0.843267\pi\) | ||
0.881205 | − | 0.472735i | \(-0.156733\pi\) | |||||||
\(578\) | 4.58767i | 0.190822i | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −0.864641 | + | 4.38776i | −0.0359023 | + | 0.182192i | ||||
\(581\) | −16.6464 | −0.690609 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.15994i | 0.0480398i | ||||||||
\(584\) | −15.2524 | −0.631149 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −11.0708 | −0.457331 | ||||||||
\(587\) | − | 3.76593i | − | 0.155436i | −0.996975 | − | 0.0777182i | \(-0.975237\pi\) | ||
0.996975 | − | 0.0777182i | \(-0.0247634\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 26.3998 | 1.08779 | ||||||||
\(590\) | 24.0925 | + | 4.74760i | 0.991871 | + | 0.195456i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 5.13536i | 0.211062i | ||||||||
\(593\) | 1.04623i | 0.0429635i | 0.999769 | + | 0.0214817i | \(0.00683837\pi\) | ||||
−0.999769 | + | 0.0214817i | \(0.993162\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 3.04623 | − | 15.4586i | 0.124883 | − | 0.633739i | ||||
\(596\) | 8.86464 | 0.363110 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 5.52311i | 0.225857i | ||||||||
\(599\) | −21.2803 | −0.869490 | −0.434745 | − | 0.900554i | \(-0.643161\pi\) | ||||
−0.434745 | + | 0.900554i | \(0.643161\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 30.8034 | 1.25650 | 0.628249 | − | 0.778012i | \(-0.283772\pi\) | ||||
0.628249 | + | 0.778012i | \(0.283772\pi\) | |||||||
\(602\) | 2.27072i | 0.0925476i | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 6.71096 | 0.273065 | ||||||||
\(605\) | 4.43232 | − | 22.4925i | 0.180199 | − | 0.914450i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 22.0925i | − | 0.896705i | −0.893857 | − | 0.448353i | \(-0.852011\pi\) | ||
0.893857 | − | 0.448353i | \(-0.147989\pi\) | |||||||
\(608\) | − | 8.11704i | − | 0.329189i | ||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 12.9677 | + | 2.55539i | 0.525048 | + | 0.103465i | ||||
\(611\) | −30.5048 | −1.23409 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 41.4985i | 1.67611i | 0.545586 | + | 0.838055i | \(0.316307\pi\) | ||||
−0.545586 | + | 0.838055i | \(0.683693\pi\) | |||||||
\(614\) | −4.23407 | −0.170873 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 1.72928 | 0.0696747 | ||||||||
\(617\) | 30.9325i | 1.24530i | 0.782502 | + | 0.622648i | \(0.213943\pi\) | ||||
−0.782502 | + | 0.622648i | \(0.786057\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −14.5660 | −0.585458 | −0.292729 | − | 0.956196i | \(-0.594563\pi\) | ||||
−0.292729 | + | 0.956196i | \(0.594563\pi\) | |||||||
\(620\) | −1.40608 | + | 7.13536i | −0.0564694 | + | 0.286563i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 13.2803i | 0.532492i | ||||||||
\(623\) | 9.55102i | 0.382654i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 17.8034 | + | 17.5510i | 0.712137 | + | 0.702041i | ||||
\(626\) | −31.9634 | −1.27751 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 14.6864i | 0.586050i | ||||||||
\(629\) | −18.0925 | −0.721394 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −38.4036 | −1.52882 | −0.764412 | − | 0.644729i | \(-0.776970\pi\) | ||||
−0.764412 | + | 0.644729i | \(0.776970\pi\) | |||||||
\(632\) | − | 3.79383i | − | 0.150911i | ||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −13.2803 | −0.527428 | ||||||||
\(635\) | −1.64015 | − | 0.323204i | −0.0650874 | − | 0.0128260i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − | 16.5693i | − | 0.656501i | ||||||
\(638\) | − | 1.72928i | − | 0.0684629i | ||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 2.19388 | + | 0.432320i | 0.0867206 | + | 0.0170890i | ||||
\(641\) | 31.9267 | 1.26103 | 0.630515 | − | 0.776177i | \(-0.282844\pi\) | ||||
0.630515 | + | 0.776177i | \(0.282844\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 4.72302i | 0.186258i | 0.995654 | + | 0.0931289i | \(0.0296869\pi\) | ||||
−0.995654 | + | 0.0931289i | \(0.970313\pi\) | |||||||
\(644\) | 2.00000 | 0.0788110 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 28.5972 | 1.12514 | ||||||||
\(647\) | 43.4586i | 1.70853i | 0.519836 | + | 0.854266i | \(0.325993\pi\) | ||||
−0.519836 | + | 0.854266i | \(0.674007\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −9.49521 | −0.372720 | ||||||||
\(650\) | −25.5510 | − | 10.4769i | −1.00219 | − | 0.410937i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | − | 23.2803i | − | 0.911727i | ||||||
\(653\) | 2.36318i | 0.0924782i | 0.998930 | + | 0.0462391i | \(0.0147236\pi\) | ||||
−0.998930 | + | 0.0462391i | \(0.985276\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 8.54144 | − | 43.3449i | 0.333742 | − | 1.69362i | ||||
\(656\) | −3.52311 | −0.137555 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 11.0462i | 0.430627i | ||||||||
\(659\) | −22.4157 | −0.873190 | −0.436595 | − | 0.899658i | \(-0.643816\pi\) | ||||
−0.436595 | + | 0.899658i | \(0.643816\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −14.9937 | −0.583189 | −0.291594 | − | 0.956542i | \(-0.594186\pi\) | ||||
−0.291594 | + | 0.956542i | \(0.594186\pi\) | |||||||
\(662\) | − | 11.8217i | − | 0.459465i | ||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 8.32320 | 0.323003 | ||||||||
\(665\) | 35.6156 | + | 7.01832i | 1.38111 | + | 0.272159i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 2.00000i | − | 0.0774403i | ||||||
\(668\) | − | 5.93545i | − | 0.229649i | ||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −2.55539 | + | 12.9677i | −0.0987233 | + | 0.500987i | ||||
\(671\) | −5.11078 | −0.197299 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 49.2158i | 1.89713i | 0.316586 | + | 0.948564i | \(0.397464\pi\) | ||||
−0.316586 | + | 0.948564i | \(0.602536\pi\) | |||||||
\(674\) | −13.2803 | −0.511538 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 17.5048 | 0.673261 | ||||||||
\(677\) | 5.34153i | 0.205292i | 0.994718 | + | 0.102646i | \(0.0327308\pi\) | ||||
−0.994718 | + | 0.102646i | \(0.967269\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 2.09246 | 0.0803011 | ||||||||
\(680\) | −1.52311 | + | 7.72928i | −0.0584088 | + | 0.296404i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | − | 2.81215i | − | 0.107683i | ||||||
\(683\) | 27.1512i | 1.03891i | 0.854497 | + | 0.519456i | \(0.173865\pi\) | ||||
−0.854497 | + | 0.519456i | \(0.826135\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 1.04623 | + | 0.206167i | 0.0399743 | + | 0.00787725i | ||||
\(686\) | −20.0000 | −0.763604 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | − | 1.13536i | − | 0.0432852i | ||||||
\(689\) | 7.40940 | 0.282276 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 12.1050 | 0.460495 | 0.230247 | − | 0.973132i | \(-0.426046\pi\) | ||||
0.230247 | + | 0.973132i | \(0.426046\pi\) | |||||||
\(692\) | − | 25.8217i | − | 0.981595i | ||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −24.3632 | −0.924814 | ||||||||
\(695\) | −1.49521 | + | 7.58767i | −0.0567165 | + | 0.287817i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 12.4123i | − | 0.470151i | ||||||
\(698\) | − | 3.49521i | − | 0.132296i | ||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −3.79383 | + | 9.25240i | −0.143393 | + | 0.349708i | ||||
\(701\) | −2.59392 | −0.0979711 | −0.0489856 | − | 0.998799i | \(-0.515599\pi\) | ||||
−0.0489856 | + | 0.998799i | \(0.515599\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 41.6839i | − | 1.57214i | ||||||
\(704\) | −0.864641 | −0.0325874 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −31.5789 | −1.18849 | ||||||||
\(707\) | − | 18.0925i | − | 0.680437i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −4.00333 | −0.150348 | −0.0751741 | − | 0.997170i | \(-0.523951\pi\) | ||||
−0.0751741 | + | 0.997170i | \(0.523951\pi\) | |||||||
\(710\) | −12.7110 | − | 2.50479i | −0.477034 | − | 0.0940032i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | − | 4.77551i | − | 0.178970i | ||||||
\(713\) | − | 3.25240i | − | 0.121803i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 10.4769 | + | 2.06455i | 0.391813 | + | 0.0772098i | ||||
\(716\) | 23.3449 | 0.872438 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | − | 21.1878i | − | 0.790723i | ||||||
\(719\) | 20.2707 | 0.755970 | 0.377985 | − | 0.925812i | \(-0.376617\pi\) | ||||
0.377985 | + | 0.925812i | \(0.376617\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 22.6339 | 0.842930 | ||||||||
\(722\) | 46.8863i | 1.74493i | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −13.3694 | −0.496871 | ||||||||
\(725\) | 9.25240 | + | 3.79383i | 0.343625 | + | 0.140899i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 32.6339i | − | 1.21032i | −0.796102 | − | 0.605162i | \(-0.793108\pi\) | ||
0.796102 | − | 0.605162i | \(-0.206892\pi\) | |||||||
\(728\) | − | 11.0462i | − | 0.409400i | ||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −6.59392 | + | 33.4619i | −0.244052 | + | 1.23848i | ||||
\(731\) | 4.00000 | 0.147945 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 1.13536i | 0.0419354i | 0.999780 | + | 0.0209677i | \(0.00667472\pi\) | ||||
−0.999780 | + | 0.0209677i | \(0.993325\pi\) | |||||||
\(734\) | −13.0462 | −0.481545 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −1.00000 | −0.0368605 | ||||||||
\(737\) | − | 5.11078i | − | 0.188258i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 29.4219 | 1.08230 | 0.541151 | − | 0.840925i | \(-0.317989\pi\) | ||||
0.541151 | + | 0.840925i | \(0.317989\pi\) | |||||||
\(740\) | 11.2663 | + | 2.22012i | 0.414159 | + | 0.0816133i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | − | 2.68305i | − | 0.0984980i | ||||||
\(743\) | − | 27.4586i | − | 1.00736i | −0.863891 | − | 0.503678i | \(-0.831980\pi\) | ||
0.863891 | − | 0.503678i | \(-0.168020\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 3.83237 | − | 19.4479i | 0.140407 | − | 0.712517i | ||||
\(746\) | 18.8646 | 0.690684 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | − | 3.04623i | − | 0.111381i | ||||||
\(749\) | 11.2803 | 0.412173 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 4.02791 | 0.146980 | 0.0734902 | − | 0.997296i | \(-0.476586\pi\) | ||||
0.0734902 | + | 0.997296i | \(0.476586\pi\) | |||||||
\(752\) | − | 5.52311i | − | 0.201407i | ||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −11.0462 | −0.402280 | ||||||||
\(755\) | 2.90129 | − | 14.7230i | 0.105589 | − | 0.535826i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 31.5110i | − | 1.14529i | −0.819804 | − | 0.572644i | \(-0.805918\pi\) | ||
0.819804 | − | 0.572644i | \(-0.194082\pi\) | |||||||
\(758\) | − | 26.7509i | − | 0.971638i | ||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −17.8078 | − | 3.50916i | −0.645956 | − | 0.127291i | ||||
\(761\) | 19.9634 | 0.723671 | 0.361836 | − | 0.932242i | \(-0.382150\pi\) | ||||
0.361836 | + | 0.932242i | \(0.382150\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 24.3632i | 0.882006i | ||||||||
\(764\) | 12.2341 | 0.442613 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 22.5048 | 0.813131 | ||||||||
\(767\) | 60.6531i | 2.19006i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 46.4190 | 1.67391 | 0.836956 | − | 0.547271i | \(-0.184333\pi\) | ||||
0.836956 | + | 0.547271i | \(0.184333\pi\) | |||||||
\(770\) | 0.747604 | − | 3.79383i | 0.0269418 | − | 0.136720i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 7.45856i | 0.268440i | ||||||||
\(773\) | − | 29.0342i | − | 1.04429i | −0.852858 | − | 0.522143i | \(-0.825133\pi\) | ||
0.852858 | − | 0.522143i | \(-0.174867\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 15.0462 | + | 6.16952i | 0.540476 | + | 0.221616i | ||||
\(776\) | −1.04623 | −0.0375574 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | − | 7.67680i | − | 0.275226i | ||||||
\(779\) | 28.5972 | 1.02460 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 5.00958 | 0.179257 | ||||||||
\(782\) | − | 3.52311i | − | 0.125986i | ||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 3.00000 | 0.107143 | ||||||||
\(785\) | 32.2201 | + | 6.34922i | 1.14999 | + | 0.226613i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 35.7693i | 1.27504i | 0.770435 | + | 0.637518i | \(0.220039\pi\) | ||||
−0.770435 | + | 0.637518i | \(0.779961\pi\) | |||||||
\(788\) | 2.00000i | 0.0712470i | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −8.32320 | − | 1.64015i | −0.296126 | − | 0.0583540i | ||||
\(791\) | −11.5877 | −0.412010 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 32.6464i | 1.15931i | ||||||||
\(794\) | 31.7938 | 1.12832 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 22.8401 | 0.809545 | ||||||||
\(797\) | 22.8367i | 0.808919i | 0.914556 | + | 0.404459i | \(0.132540\pi\) | ||||
−0.914556 | + | 0.404459i | \(0.867460\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 19.4586 | 0.688394 | ||||||||
\(800\) | 1.89692 | − | 4.62620i | 0.0670661 | − | 0.163561i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 18.0925i | 0.638867i | ||||||||
\(803\) | − | 13.1878i | − | 0.465389i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0.864641 | − | 4.38776i | 0.0304746 | − | 0.154648i | ||||
\(806\) | −17.9634 | −0.632732 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 9.04623i | 0.318245i | ||||||||
\(809\) | −36.9171 | −1.29794 | −0.648969 | − | 0.760815i | \(-0.724799\pi\) | ||||
−0.648969 | + | 0.760815i | \(0.724799\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 51.8217 | 1.81971 | 0.909854 | − | 0.414929i | \(-0.136194\pi\) | ||||
0.909854 | + | 0.414929i | \(0.136194\pi\) | |||||||
\(812\) | 4.00000i | 0.140372i | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −4.44024 | −0.155630 | ||||||||
\(815\) | −51.0741 | − | 10.0646i | −1.78905 | − | 0.352546i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 9.21575i | 0.322418i | ||||||||
\(818\) | − | 2.00000i | − | 0.0699284i | ||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −1.52311 | + | 7.72928i | −0.0531895 | + | 0.269918i | ||||
\(821\) | 17.8709 | 0.623699 | 0.311849 | − | 0.950132i | \(-0.399052\pi\) | ||||
0.311849 | + | 0.950132i | \(0.399052\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 9.00958i | − | 0.314054i | −0.987594 | − | 0.157027i | \(-0.949809\pi\) | ||
0.987594 | − | 0.157027i | \(-0.0501910\pi\) | |||||||
\(824\) | −11.3169 | −0.394245 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 21.9634 | 0.764203 | ||||||||
\(827\) | − | 42.1083i | − | 1.46425i | −0.681171 | − | 0.732125i | \(-0.738529\pi\) | ||
0.681171 | − | 0.732125i | \(-0.261471\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 35.5510 | 1.23474 | 0.617369 | − | 0.786674i | \(-0.288199\pi\) | ||||
0.617369 | + | 0.786674i | \(0.288199\pi\) | |||||||
\(830\) | 3.59829 | − | 18.2601i | 0.124899 | − | 0.633817i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 5.52311i | 0.191480i | ||||||||
\(833\) | 10.5693i | 0.366206i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −13.0216 | − | 2.56602i | −0.450633 | − | 0.0888006i | ||||
\(836\) | 7.01832 | 0.242734 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 20.4523i | 0.706513i | ||||||||
\(839\) | −25.6801 | −0.886576 | −0.443288 | − | 0.896379i | \(-0.646188\pi\) | ||||
−0.443288 | + | 0.896379i | \(0.646188\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −25.0000 | −0.862069 | ||||||||
\(842\) | − | 12.9571i | − | 0.446531i | ||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −24.2341 | −0.834171 | ||||||||
\(845\) | 7.56768 | − | 38.4034i | 0.260336 | − | 1.32112i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 20.5048i | − | 0.704553i | ||||||
\(848\) | 1.34153i | 0.0460682i | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 16.2986 | + | 6.68305i | 0.559038 | + | 0.229227i | ||||
\(851\) | −5.13536 | −0.176038 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 11.6647i | 0.399393i | 0.979858 | + | 0.199696i | \(0.0639956\pi\) | ||||
−0.979858 | + | 0.199696i | \(0.936004\pi\) | |||||||
\(854\) | 11.8217 | 0.404532 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −5.64015 | −0.192776 | ||||||||
\(857\) | − | 41.5423i | − | 1.41906i | −0.704677 | − | 0.709529i | \(-0.748908\pi\) | ||
0.704677 | − | 0.709529i | \(-0.251092\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −21.5510 | −0.735311 | −0.367656 | − | 0.929962i | \(-0.619839\pi\) | ||||
−0.367656 | + | 0.929962i | \(0.619839\pi\) | |||||||
\(860\) | −2.49084 | − | 0.490839i | −0.0849369 | − | 0.0167375i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | − | 33.3728i | − | 1.13668i | ||||||
\(863\) | − | 6.91713i | − | 0.235462i | −0.993046 | − | 0.117731i | \(-0.962438\pi\) | ||
0.993046 | − | 0.117731i | \(-0.0375620\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −56.6497 | − | 11.1633i | −1.92615 | − | 0.379562i | ||||
\(866\) | 19.0096 | 0.645972 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 6.50479i | 0.220787i | ||||||||
\(869\) | 3.28030 | 0.111277 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −32.6464 | −1.10618 | ||||||||
\(872\) | − | 12.1816i | − | 0.412521i | ||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 8.11704 | 0.274563 | ||||||||
\(875\) | 18.6585 | + | 12.3232i | 0.630772 | + | 0.416600i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 2.53270i | 0.0855232i | 0.999085 | + | 0.0427616i | \(0.0136156\pi\) | ||||
−0.999085 | + | 0.0427616i | \(0.986384\pi\) | |||||||
\(878\) | − | 32.5972i | − | 1.10010i | ||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −0.373802 | + | 1.89692i | −0.0126009 | + | 0.0639450i | ||||
\(881\) | 10.8680 | 0.366151 | 0.183076 | − | 0.983099i | \(-0.441395\pi\) | ||||
0.183076 | + | 0.983099i | \(0.441395\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 40.4190i | − | 1.36021i | −0.733116 | − | 0.680104i | \(-0.761935\pi\) | ||
0.733116 | − | 0.680104i | \(-0.238065\pi\) | |||||||
\(884\) | −19.4586 | −0.654462 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −4.00000 | −0.134383 | ||||||||
\(887\) | 7.48647i | 0.251371i | 0.992070 | + | 0.125686i | \(0.0401130\pi\) | ||||
−0.992070 | + | 0.125686i | \(0.959887\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1.49521 | −0.0501477 | ||||||||
\(890\) | −10.4769 | − | 2.06455i | −0.351186 | − | 0.0692039i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 13.9634i | 0.467528i | ||||||||
\(893\) | 44.8313i | 1.50022i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 10.0925 | − | 51.2158i | 0.337354 | − | 1.71195i | ||||
\(896\) | 2.00000 | 0.0668153 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 39.5789i | 1.32077i | ||||||||
\(899\) | 6.50479 | 0.216947 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −4.72635 | −0.157458 | ||||||||
\(902\) | − | 3.04623i | − | 0.101428i | ||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 5.79383 | 0.192700 | ||||||||
\(905\) | −5.77988 | + | 29.3309i | −0.192130 | + | 0.974992i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 22.6864i | − | 0.753289i | −0.926358 | − | 0.376644i | \(-0.877078\pi\) | ||
0.926358 | − | 0.376644i | \(-0.122922\pi\) | |||||||
\(908\) | − | 4.45231i | − | 0.147755i | ||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −24.2341 | − | 4.77551i | −0.803352 | − | 0.158307i | ||||
\(911\) | 35.8217 | 1.18683 | 0.593414 | − | 0.804898i | \(-0.297780\pi\) | ||||
0.593414 | + | 0.804898i | \(0.297780\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 7.19658i | 0.238172i | ||||||||
\(914\) | −24.5048 | −0.810546 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −4.05249 | −0.133898 | ||||||||
\(917\) | − | 39.5144i | − | 1.30488i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 13.2890 | 0.438365 | 0.219182 | − | 0.975684i | \(-0.429661\pi\) | ||||
0.219182 | + | 0.975684i | \(0.429661\pi\) | |||||||
\(920\) | −0.432320 | + | 2.19388i | −0.0142532 | + | 0.0723300i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | − | 18.2341i | − | 0.600507i | ||||||
\(923\) | − | 32.0000i | − | 1.05329i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 9.74135 | − | 23.7572i | 0.320293 | − | 0.781132i | ||||
\(926\) | −4.20617 | −0.138223 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | − | 2.00000i | − | 0.0656532i | ||||||
\(929\) | 41.1299 | 1.34943 | 0.674715 | − | 0.738078i | \(-0.264267\pi\) | ||||
0.674715 | + | 0.738078i | \(0.264267\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −24.3511 | −0.798075 | ||||||||
\(932\) | 24.5327i | 0.803595i | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 19.1912 | 0.627954 | ||||||||
\(935\) | −6.68305 | − | 1.31695i | −0.218559 | − | 0.0430688i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 22.7755i | 0.744043i | 0.928224 | + | 0.372022i | \(0.121335\pi\) | ||||
−0.928224 | + | 0.372022i | \(0.878665\pi\) | |||||||
\(938\) | 11.8217i | 0.385993i | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −12.1170 | − | 2.38776i | −0.395214 | − | 0.0778800i | ||||
\(941\) | 54.7788 | 1.78574 | 0.892870 | − | 0.450315i | \(-0.148688\pi\) | ||||
0.892870 | + | 0.450315i | \(0.148688\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 3.52311i | − | 0.114728i | ||||||
\(944\) | −10.9817 | −0.357423 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0.981678 | 0.0319171 | ||||||||
\(947\) | 11.4094i | 0.370756i | 0.982667 | + | 0.185378i | \(0.0593509\pi\) | ||||
−0.982667 | + | 0.185378i | \(0.940649\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −84.2407 | −2.73457 | ||||||||
\(950\) | −15.3973 | + | 37.5510i | −0.499556 | + | 1.21832i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 7.04623i | 0.228370i | ||||||||
\(953\) | − | 41.6714i | − | 1.34987i | −0.737878 | − | 0.674934i | \(-0.764172\pi\) | ||
0.737878 | − | 0.674934i | \(-0.235828\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 5.28904 | − | 26.8401i | 0.171149 | − | 0.868524i | ||||
\(956\) | −10.7755 | −0.348505 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | − | 25.6801i | − | 0.829687i | ||||||
\(959\) | 0.953771 | 0.0307989 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −20.4219 | −0.658772 | ||||||||
\(962\) | 28.3632i | 0.914465i | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 10.7755 | 0.347056 | ||||||||
\(965\) | 16.3632 | + | 3.22449i | 0.526749 | + | 0.103800i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 3.17533i | − | 0.102112i | −0.998696 | − | 0.0510559i | \(-0.983741\pi\) | ||
0.998696 | − | 0.0510559i | \(-0.0162587\pi\) | |||||||
\(968\) | 10.2524i | 0.329524i | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −0.452306 | + | 2.29530i | −0.0145227 | + | 0.0736976i | ||||
\(971\) | 35.7326 | 1.14671 | 0.573357 | − | 0.819306i | \(-0.305641\pi\) | ||||
0.573357 | + | 0.819306i | \(0.305641\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 6.91713i | 0.221753i | ||||||||
\(974\) | −8.74760 | −0.280291 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −5.91087 | −0.189202 | ||||||||
\(977\) | 2.02791i | 0.0648785i | 0.999474 | + | 0.0324392i | \(0.0103275\pi\) | ||||
−0.999474 | + | 0.0324392i | \(0.989672\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 4.12910 | 0.131967 | ||||||||
\(980\) | 1.29696 | − | 6.58163i | 0.0414299 | − | 0.210243i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | − | 23.8863i | − | 0.762242i | ||||||
\(983\) | 1.67347i | 0.0533754i | 0.999644 | + | 0.0266877i | \(0.00849596\pi\) | ||||
−0.999644 | + | 0.0266877i | \(0.991504\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 4.38776 | + | 0.864641i | 0.139806 | + | 0.0275497i | ||||
\(986\) | 7.04623 | 0.224398 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | − | 44.8313i | − | 1.42627i | ||||||
\(989\) | 1.13536 | 0.0361023 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −55.8496 | −1.77412 | −0.887061 | − | 0.461652i | \(-0.847257\pi\) | ||||
−0.887061 | + | 0.461652i | \(0.847257\pi\) | |||||||
\(992\) | − | 3.25240i | − | 0.103264i | ||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −11.5877 | −0.367538 | ||||||||
\(995\) | 9.87423 | − | 50.1083i | 0.313034 | − | 1.58854i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 44.2062i | − | 1.40002i | −0.714131 | − | 0.700012i | \(-0.753178\pi\) | ||
0.714131 | − | 0.700012i | \(-0.246822\pi\) | |||||||
\(998\) | − | 29.7293i | − | 0.941064i | ||||||
\(999\) | 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 | 2070.2.d.d.829.5 | 6 | ||
3.2 | odd | 2 | 690.2.d.d.139.2 | ✓ | 6 | ||
5.4 | even | 2 | inner | 2070.2.d.d.829.2 | 6 | ||
15.2 | even | 4 | 3450.2.a.br.1.2 | 3 | |||
15.8 | even | 4 | 3450.2.a.bq.1.2 | 3 | |||
15.14 | odd | 2 | 690.2.d.d.139.5 | yes | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
690.2.d.d.139.2 | ✓ | 6 | 3.2 | odd | 2 | ||
690.2.d.d.139.5 | yes | 6 | 15.14 | odd | 2 | ||
2070.2.d.d.829.2 | 6 | 5.4 | even | 2 | inner | ||
2070.2.d.d.829.5 | 6 | 1.1 | even | 1 | trivial | ||
3450.2.a.bq.1.2 | 3 | 15.8 | even | 4 | |||
3450.2.a.br.1.2 | 3 | 15.2 | even | 4 |