Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [630,3,Mod(559,630)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(630, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("630.559");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 630.h (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: | \(17.1662566547\) |
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: | \( x^{16} - 8 x^{15} + 96 x^{14} - 532 x^{13} + 3236 x^{12} - 12864 x^{11} + 49526 x^{10} - 141436 x^{9} + \cdots + 33750 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{14} \) |
Twist minimal: | no (minimal twist has level 210) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 559.2 | ||
Root | \(0.500000 - 4.10071i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 630.559 |
Dual form | 630.3.h.e.559.10 |
$q$-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 \(\left(\mathbb{Z}/630\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(281\) | \(451\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 1.41421i | − | 0.707107i | ||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −2.00000 | −0.500000 | ||||||||
\(5\) | −4.59769 | − | 1.96501i | −0.919538 | − | 0.393001i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 6.81963 | − | 1.57881i | 0.974233 | − | 0.225545i | ||||
\(8\) | 2.82843i | 0.353553i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −2.77894 | + | 6.50212i | −0.277894 | + | 0.650212i | ||||
\(11\) | 8.15965 | 0.741786 | 0.370893 | − | 0.928676i | \(-0.379052\pi\) | ||||
0.370893 | + | 0.928676i | \(0.379052\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 14.6064 | 1.12357 | 0.561785 | − | 0.827284i | \(-0.310115\pi\) | ||||
0.561785 | + | 0.827284i | \(0.310115\pi\) | |||||||
\(14\) | −2.23278 | − | 9.64441i | −0.159484 | − | 0.688887i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 4.00000 | 0.250000 | ||||||||
\(17\) | −5.81421 | −0.342012 | −0.171006 | − | 0.985270i | \(-0.554702\pi\) | ||||
−0.171006 | + | 0.985270i | \(0.554702\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 33.7736i | 1.77756i | 0.458337 | + | 0.888778i | \(0.348445\pi\) | ||||
−0.458337 | + | 0.888778i | \(0.651555\pi\) | |||||||
\(20\) | 9.19538 | + | 3.93001i | 0.459769 | + | 0.196501i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | − | 11.5395i | − | 0.524522i | ||||||
\(23\) | − | 37.2576i | − | 1.61989i | −0.586503 | − | 0.809947i | \(-0.699496\pi\) | ||
0.586503 | − | 0.809947i | \(-0.300504\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 17.2775 | + | 18.0690i | 0.691100 | + | 0.722759i | ||||
\(26\) | − | 20.6566i | − | 0.794483i | ||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −13.6393 | + | 3.15763i | −0.487116 | + | 0.112772i | ||||
\(29\) | 9.25305 | 0.319071 | 0.159535 | − | 0.987192i | \(-0.449000\pi\) | ||||
0.159535 | + | 0.987192i | \(0.449000\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 19.2558i | − | 0.621154i | −0.950548 | − | 0.310577i | \(-0.899478\pi\) | ||
0.950548 | − | 0.310577i | \(-0.100522\pi\) | |||||||
\(32\) | − | 5.65685i | − | 0.176777i | ||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 8.22253i | 0.241839i | ||||||||
\(35\) | −34.4569 | − | 6.14171i | −0.984483 | − | 0.175478i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 63.4350i | − | 1.71446i | −0.514933 | − | 0.857230i | \(-0.672183\pi\) | ||
0.514933 | − | 0.857230i | \(-0.327817\pi\) | |||||||
\(38\) | 47.7631 | 1.25692 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 5.55788 | − | 13.0042i | 0.138947 | − | 0.325106i | ||||
\(41\) | − | 8.25880i | − | 0.201434i | −0.994915 | − | 0.100717i | \(-0.967886\pi\) | ||
0.994915 | − | 0.100717i | \(-0.0321137\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 42.0893i | − | 0.978822i | −0.872053 | − | 0.489411i | \(-0.837212\pi\) | ||
0.872053 | − | 0.489411i | \(-0.162788\pi\) | |||||||
\(44\) | −16.3193 | −0.370893 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −52.6901 | −1.14544 | ||||||||
\(47\) | −23.3380 | −0.496552 | −0.248276 | − | 0.968689i | \(-0.579864\pi\) | ||||
−0.248276 | + | 0.968689i | \(0.579864\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 44.0147 | − | 21.5339i | 0.898259 | − | 0.439466i | ||||
\(50\) | 25.5534 | − | 24.4341i | 0.511068 | − | 0.488682i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −29.2128 | −0.561785 | ||||||||
\(53\) | − | 71.3497i | − | 1.34622i | −0.739542 | − | 0.673110i | \(-0.764958\pi\) | ||
0.739542 | − | 0.673110i | \(-0.235042\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −37.5155 | − | 16.0337i | −0.682100 | − | 0.291523i | ||||
\(56\) | 4.46556 | + | 19.2888i | 0.0797422 | + | 0.344443i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | − | 13.0858i | − | 0.225617i | ||||||
\(59\) | 42.9350i | 0.727712i | 0.931455 | + | 0.363856i | \(0.118540\pi\) | ||||
−0.931455 | + | 0.363856i | \(0.881460\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 34.2864i | − | 0.562072i | −0.959697 | − | 0.281036i | \(-0.909322\pi\) | ||
0.959697 | − | 0.281036i | \(-0.0906781\pi\) | |||||||
\(62\) | −27.2318 | −0.439222 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −8.00000 | −0.125000 | ||||||||
\(65\) | −67.1557 | − | 28.7017i | −1.03316 | − | 0.441564i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 4.99889i | − | 0.0746102i | −0.999304 | − | 0.0373051i | \(-0.988123\pi\) | ||
0.999304 | − | 0.0373051i | \(-0.0118773\pi\) | |||||||
\(68\) | 11.6284 | 0.171006 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −8.68569 | + | 48.7294i | −0.124081 | + | 0.696135i | ||||
\(71\) | 38.8120 | 0.546648 | 0.273324 | − | 0.961922i | \(-0.411877\pi\) | ||||
0.273324 | + | 0.961922i | \(0.411877\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 124.629 | 1.70725 | 0.853626 | − | 0.520886i | \(-0.174398\pi\) | ||||
0.853626 | + | 0.520886i | \(0.174398\pi\) | |||||||
\(74\) | −89.7107 | −1.21231 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | − | 67.5472i | − | 0.888778i | ||||||
\(77\) | 55.6458 | − | 12.8826i | 0.722672 | − | 0.167306i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −56.1842 | −0.711192 | −0.355596 | − | 0.934640i | \(-0.615722\pi\) | ||||
−0.355596 | + | 0.934640i | \(0.615722\pi\) | |||||||
\(80\) | −18.3908 | − | 7.86002i | −0.229884 | − | 0.0982503i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −11.6797 | −0.142435 | ||||||||
\(83\) | 90.3980 | 1.08913 | 0.544566 | − | 0.838718i | \(-0.316694\pi\) | ||||
0.544566 | + | 0.838718i | \(0.316694\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 26.7319 | + | 11.4249i | 0.314493 | + | 0.134411i | ||||
\(86\) | −59.5233 | −0.692131 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 23.0790i | 0.262261i | ||||||||
\(89\) | − | 16.2289i | − | 0.182347i | −0.995835 | − | 0.0911736i | \(-0.970938\pi\) | ||
0.995835 | − | 0.0911736i | \(-0.0290618\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 99.6102 | − | 23.0608i | 1.09462 | − | 0.253415i | ||||
\(92\) | 74.5151i | 0.809947i | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 33.0048i | 0.351115i | ||||||||
\(95\) | 66.3653 | − | 155.280i | 0.698582 | − | 1.63453i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 82.7605 | 0.853201 | 0.426601 | − | 0.904440i | \(-0.359711\pi\) | ||||
0.426601 | + | 0.904440i | \(0.359711\pi\) | |||||||
\(98\) | −30.4535 | − | 62.2462i | −0.310750 | − | 0.635165i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −34.5550 | − | 36.1379i | −0.345550 | − | 0.361379i | ||||
\(101\) | 87.2055i | 0.863420i | 0.902012 | + | 0.431710i | \(0.142090\pi\) | ||||
−0.902012 | + | 0.431710i | \(0.857910\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −187.567 | −1.82104 | −0.910521 | − | 0.413462i | \(-0.864319\pi\) | ||||
−0.910521 | + | 0.413462i | \(0.864319\pi\) | |||||||
\(104\) | 41.3131i | 0.397242i | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −100.904 | −0.951922 | ||||||||
\(107\) | 157.858i | 1.47531i | 0.675180 | + | 0.737653i | \(0.264066\pi\) | ||||
−0.675180 | + | 0.737653i | \(0.735934\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −112.073 | −1.02819 | −0.514097 | − | 0.857732i | \(-0.671873\pi\) | ||||
−0.514097 | + | 0.857732i | \(0.671873\pi\) | |||||||
\(110\) | −22.6751 | + | 53.0550i | −0.206138 | + | 0.482318i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 27.2785 | − | 6.31526i | 0.243558 | − | 0.0563862i | ||||
\(113\) | 141.987i | 1.25653i | 0.778001 | + | 0.628263i | \(0.216234\pi\) | ||||
−0.778001 | + | 0.628263i | \(0.783766\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −73.2113 | + | 171.299i | −0.636620 | + | 1.48955i | ||||
\(116\) | −18.5061 | −0.159535 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 60.7192 | 0.514570 | ||||||||
\(119\) | −39.6507 | + | 9.17955i | −0.333199 | + | 0.0771391i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −54.4202 | −0.449754 | ||||||||
\(122\) | −48.4883 | −0.397445 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 38.5116i | 0.310577i | ||||||||
\(125\) | −43.9310 | − | 117.026i | −0.351448 | − | 0.936207i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 202.414i | − | 1.59381i | −0.604104 | − | 0.796905i | \(-0.706469\pi\) | ||
0.604104 | − | 0.796905i | \(-0.293531\pi\) | |||||||
\(128\) | 11.3137i | 0.0883883i | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −40.5903 | + | 94.9725i | −0.312233 | + | 0.730558i | ||||
\(131\) | − | 141.260i | − | 1.07832i | −0.842203 | − | 0.539160i | \(-0.818742\pi\) | ||
0.842203 | − | 0.539160i | \(-0.181258\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 53.3222 | + | 230.323i | 0.400919 | + | 1.73175i | ||||
\(134\) | −7.06949 | −0.0527574 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | − | 16.4451i | − | 0.120920i | ||||||
\(137\) | − | 50.6430i | − | 0.369657i | −0.982771 | − | 0.184829i | \(-0.940827\pi\) | ||
0.982771 | − | 0.184829i | \(-0.0591730\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 74.0256i | 0.532559i | 0.963896 | + | 0.266279i | \(0.0857943\pi\) | ||||
−0.963896 | + | 0.266279i | \(0.914206\pi\) | |||||||
\(140\) | 68.9138 | + | 12.2834i | 0.492242 | + | 0.0877388i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | − | 54.8885i | − | 0.386538i | ||||||
\(143\) | 119.183 | 0.833448 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −42.5426 | − | 18.1823i | −0.293397 | − | 0.125395i | ||||
\(146\) | − | 176.253i | − | 1.20721i | ||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 126.870i | 0.857230i | ||||||||
\(149\) | 226.979 | 1.52335 | 0.761676 | − | 0.647958i | \(-0.224377\pi\) | ||||
0.761676 | + | 0.647958i | \(0.224377\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 294.426 | 1.94984 | 0.974920 | − | 0.222558i | \(-0.0714406\pi\) | ||||
0.974920 | + | 0.222558i | \(0.0714406\pi\) | |||||||
\(152\) | −95.5261 | −0.628461 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −18.2187 | − | 78.6950i | −0.118303 | − | 0.511006i | ||||
\(155\) | −37.8377 | + | 88.5321i | −0.244114 | + | 0.571175i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −65.8596 | −0.419488 | −0.209744 | − | 0.977756i | \(-0.567263\pi\) | ||||
−0.209744 | + | 0.977756i | \(0.567263\pi\) | |||||||
\(158\) | 79.4564i | 0.502889i | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −11.1158 | + | 26.0085i | −0.0694734 | + | 0.162553i | ||||
\(161\) | −58.8227 | − | 254.083i | −0.365359 | − | 1.57815i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 28.2075i | − | 0.173052i | −0.996250 | − | 0.0865260i | \(-0.972423\pi\) | ||
0.996250 | − | 0.0865260i | \(-0.0275766\pi\) | |||||||
\(164\) | 16.5176i | 0.100717i | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | − | 127.842i | − | 0.770133i | ||||||
\(167\) | −128.461 | −0.769227 | −0.384614 | − | 0.923078i | \(-0.625665\pi\) | ||||
−0.384614 | + | 0.923078i | \(0.625665\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 44.3469 | 0.262408 | ||||||||
\(170\) | 16.1573 | − | 37.8046i | 0.0950431 | − | 0.222380i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 84.1786i | 0.489411i | ||||||||
\(173\) | −112.446 | −0.649976 | −0.324988 | − | 0.945718i | \(-0.605360\pi\) | ||||
−0.324988 | + | 0.945718i | \(0.605360\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 146.354 | + | 95.9457i | 0.836307 | + | 0.548261i | ||||
\(176\) | 32.6386 | 0.185446 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −22.9511 | −0.128939 | ||||||||
\(179\) | 68.9019 | 0.384927 | 0.192464 | − | 0.981304i | \(-0.438352\pi\) | ||||
0.192464 | + | 0.981304i | \(0.438352\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 166.537i | − | 0.920094i | −0.887895 | − | 0.460047i | \(-0.847833\pi\) | ||
0.887895 | − | 0.460047i | \(-0.152167\pi\) | |||||||
\(182\) | −32.6129 | − | 140.870i | −0.179192 | − | 0.774012i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 105.380 | 0.572719 | ||||||||
\(185\) | −124.650 | + | 291.655i | −0.673785 | + | 1.57651i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −47.4419 | −0.253700 | ||||||||
\(188\) | 46.6759 | 0.248276 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −219.600 | − | 93.8547i | −1.15579 | − | 0.493972i | ||||
\(191\) | 148.289 | 0.776382 | 0.388191 | − | 0.921579i | \(-0.373100\pi\) | ||||
0.388191 | + | 0.921579i | \(0.373100\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 35.1886i | 0.182324i | 0.995836 | + | 0.0911622i | \(0.0290582\pi\) | ||||
−0.995836 | + | 0.0911622i | \(0.970942\pi\) | |||||||
\(194\) | − | 117.041i | − | 0.603304i | ||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −88.0294 | + | 43.0677i | −0.449130 | + | 0.219733i | ||||
\(197\) | 193.634i | 0.982915i | 0.870902 | + | 0.491457i | \(0.163536\pi\) | ||||
−0.870902 | + | 0.491457i | \(0.836464\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 181.838i | 0.913759i | 0.889529 | + | 0.456880i | \(0.151033\pi\) | ||||
−0.889529 | + | 0.456880i | \(0.848967\pi\) | |||||||
\(200\) | −51.1068 | + | 48.8682i | −0.255534 | + | 0.244341i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 123.327 | 0.610530 | ||||||||
\(203\) | 63.1023 | − | 14.6088i | 0.310849 | − | 0.0719647i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −16.2286 | + | 37.9714i | −0.0791638 | + | 0.185226i | ||||
\(206\) | 265.260i | 1.28767i | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 58.4256 | 0.280892 | ||||||||
\(209\) | 275.580i | 1.31857i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 175.914 | 0.833717 | 0.416859 | − | 0.908971i | \(-0.363131\pi\) | ||||
0.416859 | + | 0.908971i | \(0.363131\pi\) | |||||||
\(212\) | 142.699i | 0.673110i | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 223.244 | 1.04320 | ||||||||
\(215\) | −82.7058 | + | 193.514i | −0.384678 | + | 0.900064i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −30.4013 | − | 131.317i | −0.140098 | − | 0.605149i | ||||
\(218\) | 158.495i | 0.727042i | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 75.0310 | + | 32.0675i | 0.341050 | + | 0.145761i | ||||
\(221\) | −84.9246 | −0.384274 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 20.5675 | 0.0922308 | 0.0461154 | − | 0.998936i | \(-0.485316\pi\) | ||||
0.0461154 | + | 0.998936i | \(0.485316\pi\) | |||||||
\(224\) | −8.93112 | − | 38.5776i | −0.0398711 | − | 0.172222i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 200.801 | 0.888498 | ||||||||
\(227\) | 414.087 | 1.82417 | 0.912085 | − | 0.410001i | \(-0.134472\pi\) | ||||
0.912085 | + | 0.410001i | \(0.134472\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 195.520i | 0.853799i | 0.904299 | + | 0.426899i | \(0.140394\pi\) | ||||
−0.904299 | + | 0.426899i | \(0.859606\pi\) | |||||||
\(230\) | 242.253 | + | 103.536i | 1.05327 | + | 0.450158i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 26.1716i | 0.112808i | ||||||||
\(233\) | − | 81.3006i | − | 0.348930i | −0.984663 | − | 0.174465i | \(-0.944180\pi\) | ||
0.984663 | − | 0.174465i | \(-0.0558195\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 107.301 | + | 45.8592i | 0.456599 | + | 0.195146i | ||||
\(236\) | − | 85.8700i | − | 0.363856i | ||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 12.9818 | + | 56.0746i | 0.0545456 | + | 0.235608i | ||||
\(239\) | 249.265 | 1.04295 | 0.521475 | − | 0.853267i | \(-0.325382\pi\) | ||||
0.521475 | + | 0.853267i | \(0.325382\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 262.343i | − | 1.08856i | −0.838904 | − | 0.544280i | \(-0.816803\pi\) | ||
0.838904 | − | 0.544280i | \(-0.183197\pi\) | |||||||
\(242\) | 76.9618i | 0.318024i | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 68.5728i | 0.281036i | ||||||||
\(245\) | −244.680 | + | 12.5169i | −0.998694 | + | 0.0510892i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 493.310i | 1.99721i | ||||||||
\(248\) | 54.4636 | 0.219611 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −165.500 | + | 62.1278i | −0.661999 | + | 0.248511i | ||||
\(251\) | 141.917i | 0.565406i | 0.959208 | + | 0.282703i | \(0.0912310\pi\) | ||||
−0.959208 | + | 0.282703i | \(0.908769\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 304.008i | − | 1.20161i | ||||||
\(254\) | −286.257 | −1.12699 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 16.0000 | 0.0625000 | ||||||||
\(257\) | −170.843 | −0.664757 | −0.332379 | − | 0.943146i | \(-0.607851\pi\) | ||||
−0.332379 | + | 0.943146i | \(0.607851\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −100.152 | − | 432.604i | −0.386688 | − | 1.67028i | ||||
\(260\) | 134.311 | + | 57.4033i | 0.516582 | + | 0.220782i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −199.772 | −0.762488 | ||||||||
\(263\) | 383.417i | 1.45786i | 0.684588 | + | 0.728930i | \(0.259982\pi\) | ||||
−0.684588 | + | 0.728930i | \(0.740018\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −140.203 | + | 328.044i | −0.529066 | + | 1.23790i | ||||
\(266\) | 325.726 | − | 75.4090i | 1.22454 | − | 0.283492i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 9.99777i | 0.0373051i | ||||||||
\(269\) | 154.512i | 0.574393i | 0.957872 | + | 0.287196i | \(0.0927232\pi\) | ||||
−0.957872 | + | 0.287196i | \(0.907277\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 320.328i | − | 1.18202i | −0.806664 | − | 0.591010i | \(-0.798729\pi\) | ||
0.806664 | − | 0.591010i | \(-0.201271\pi\) | |||||||
\(272\) | −23.2568 | −0.0855030 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −71.6200 | −0.261387 | ||||||||
\(275\) | 140.978 | + | 147.436i | 0.512648 | + | 0.536132i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 222.854i | 0.804526i | 0.915524 | + | 0.402263i | \(0.131776\pi\) | ||||
−0.915524 | + | 0.402263i | \(0.868224\pi\) | |||||||
\(278\) | 104.688 | 0.376576 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 17.3714 | − | 97.4589i | 0.0620407 | − | 0.348067i | ||||
\(281\) | −218.973 | −0.779263 | −0.389631 | − | 0.920971i | \(-0.627398\pi\) | ||||
−0.389631 | + | 0.920971i | \(0.627398\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 36.3957 | 0.128607 | 0.0643034 | − | 0.997930i | \(-0.479517\pi\) | ||||
0.0643034 | + | 0.997930i | \(0.479517\pi\) | |||||||
\(284\) | −77.6240 | −0.273324 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | − | 168.550i | − | 0.589337i | ||||||
\(287\) | −13.0391 | − | 56.3219i | −0.0454324 | − | 0.196244i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −255.195 | −0.883028 | ||||||||
\(290\) | −25.7136 | + | 60.1644i | −0.0886677 | + | 0.207463i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −249.259 | −0.853626 | ||||||||
\(293\) | 168.440 | 0.574882 | 0.287441 | − | 0.957798i | \(-0.407195\pi\) | ||||
0.287441 | + | 0.957798i | \(0.407195\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 84.3675 | − | 197.402i | 0.285991 | − | 0.669158i | ||||
\(296\) | 179.421 | 0.606153 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | − | 320.997i | − | 1.07717i | ||||||
\(299\) | − | 544.199i | − | 1.82006i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −66.4512 | − | 287.034i | −0.220768 | − | 0.953600i | ||||
\(302\) | − | 416.381i | − | 1.37874i | ||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 135.094i | 0.444389i | ||||||||
\(305\) | −67.3730 | + | 157.638i | −0.220895 | + | 0.516847i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 223.400 | 0.727688 | 0.363844 | − | 0.931460i | \(-0.381464\pi\) | ||||
0.363844 | + | 0.931460i | \(0.381464\pi\) | |||||||
\(308\) | −111.292 | + | 25.7651i | −0.361336 | + | 0.0836530i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 125.203 | + | 53.5106i | 0.403882 | + | 0.172615i | ||||
\(311\) | − | 46.0396i | − | 0.148037i | −0.997257 | − | 0.0740186i | \(-0.976418\pi\) | ||
0.997257 | − | 0.0740186i | \(-0.0235824\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −80.0375 | −0.255711 | −0.127855 | − | 0.991793i | \(-0.540809\pi\) | ||||
−0.127855 | + | 0.991793i | \(0.540809\pi\) | |||||||
\(314\) | 93.1395i | 0.296623i | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 112.368 | 0.355596 | ||||||||
\(317\) | − | 185.237i | − | 0.584343i | −0.956366 | − | 0.292171i | \(-0.905622\pi\) | ||
0.956366 | − | 0.292171i | \(-0.0943777\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 75.5016 | 0.236682 | ||||||||
\(320\) | 36.7815 | + | 15.7200i | 0.114942 | + | 0.0491251i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −359.327 | + | 83.1879i | −1.11592 | + | 0.258348i | ||||
\(323\) | − | 196.367i | − | 0.607946i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 252.362 | + | 263.923i | 0.776499 | + | 0.812070i | ||||
\(326\) | −39.8914 | −0.122366 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 23.3594 | 0.0712177 | ||||||||
\(329\) | −159.156 | + | 36.8463i | −0.483757 | + | 0.111995i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 61.4686 | 0.185706 | 0.0928529 | − | 0.995680i | \(-0.470401\pi\) | ||||
0.0928529 | + | 0.995680i | \(0.470401\pi\) | |||||||
\(332\) | −180.796 | −0.544566 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 181.671i | 0.543926i | ||||||||
\(335\) | −9.82284 | + | 22.9833i | −0.0293219 | + | 0.0686069i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 656.501i | 1.94807i | 0.226387 | + | 0.974037i | \(0.427309\pi\) | ||||
−0.226387 | + | 0.974037i | \(0.572691\pi\) | |||||||
\(338\) | − | 62.7160i | − | 0.185550i | ||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −53.4638 | − | 22.8499i | −0.157247 | − | 0.0672056i | ||||
\(341\) | − | 157.120i | − | 0.460764i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 266.166 | − | 216.344i | 0.775994 | − | 0.630740i | ||||
\(344\) | 119.047 | 0.346066 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 159.022i | 0.459603i | ||||||||
\(347\) | − | 321.323i | − | 0.926002i | −0.886358 | − | 0.463001i | \(-0.846773\pi\) | ||
0.886358 | − | 0.463001i | \(-0.153227\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 185.135i | − | 0.530474i | −0.964183 | − | 0.265237i | \(-0.914550\pi\) | ||
0.964183 | − | 0.265237i | \(-0.0854501\pi\) | |||||||
\(350\) | 135.688 | − | 206.975i | 0.387679 | − | 0.591358i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | − | 46.1579i | − | 0.131130i | ||||||
\(353\) | −597.338 | −1.69218 | −0.846088 | − | 0.533043i | \(-0.821048\pi\) | ||||
−0.846088 | + | 0.533043i | \(0.821048\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −178.446 | − | 76.2658i | −0.502664 | − | 0.214833i | ||||
\(356\) | 32.4578i | 0.0911736i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | − | 97.4421i | − | 0.272185i | ||||||
\(359\) | −239.446 | −0.666982 | −0.333491 | − | 0.942753i | \(-0.608227\pi\) | ||||
−0.333491 | + | 0.942753i | \(0.608227\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −779.655 | −2.15971 | ||||||||
\(362\) | −235.519 | −0.650604 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −199.220 | + | 46.1216i | −0.547309 | + | 0.126708i | ||||
\(365\) | −573.007 | − | 244.898i | −1.56988 | − | 0.670952i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 398.743 | 1.08649 | 0.543246 | − | 0.839573i | \(-0.317195\pi\) | ||||
0.543246 | + | 0.839573i | \(0.317195\pi\) | |||||||
\(368\) | − | 149.030i | − | 0.404973i | ||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 412.462 | + | 176.282i | 1.11476 | + | 0.476438i | ||||
\(371\) | −112.648 | − | 486.578i | −0.303633 | − | 1.31153i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 34.7064i | 0.0930466i | 0.998917 | + | 0.0465233i | \(0.0148142\pi\) | ||||
−0.998917 | + | 0.0465233i | \(0.985186\pi\) | |||||||
\(374\) | 67.0929i | 0.179393i | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | − | 66.0097i | − | 0.175558i | ||||||
\(377\) | 135.154 | 0.358498 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −109.217 | −0.288172 | −0.144086 | − | 0.989565i | \(-0.546024\pi\) | ||||
−0.144086 | + | 0.989565i | \(0.546024\pi\) | |||||||
\(380\) | −132.731 | + | 310.561i | −0.349291 | + | 0.817265i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | − | 209.712i | − | 0.548985i | ||||||
\(383\) | −336.420 | −0.878381 | −0.439191 | − | 0.898394i | \(-0.644735\pi\) | ||||
−0.439191 | + | 0.898394i | \(0.644735\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −281.156 | − | 50.1142i | −0.730276 | − | 0.130167i | ||||
\(386\) | 49.7642 | 0.128923 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −165.521 | −0.426601 | ||||||||
\(389\) | 311.173 | 0.799930 | 0.399965 | − | 0.916530i | \(-0.369022\pi\) | ||||
0.399965 | + | 0.916530i | \(0.369022\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 216.623i | 0.554023i | ||||||||
\(392\) | 60.9069 | + | 124.492i | 0.155375 | + | 0.317583i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 273.840 | 0.695026 | ||||||||
\(395\) | 258.317 | + | 110.402i | 0.653968 | + | 0.279499i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −41.2679 | −0.103949 | −0.0519747 | − | 0.998648i | \(-0.516552\pi\) | ||||
−0.0519747 | + | 0.998648i | \(0.516552\pi\) | |||||||
\(398\) | 257.158 | 0.646125 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 69.1100 | + | 72.2759i | 0.172775 | + | 0.180690i | ||||
\(401\) | 495.642 | 1.23601 | 0.618007 | − | 0.786173i | \(-0.287940\pi\) | ||||
0.618007 | + | 0.786173i | \(0.287940\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 281.258i | − | 0.697910i | ||||||
\(404\) | − | 174.411i | − | 0.431710i | ||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −20.6600 | − | 89.2402i | −0.0508867 | − | 0.219803i | ||||
\(407\) | − | 517.608i | − | 1.27176i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 359.920i | 0.880001i | 0.897998 | + | 0.440000i | \(0.145022\pi\) | ||||
−0.897998 | + | 0.440000i | \(0.854978\pi\) | |||||||
\(410\) | 53.6997 | + | 22.9507i | 0.130975 | + | 0.0559773i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 375.135 | 0.910521 | ||||||||
\(413\) | 67.7863 | + | 292.801i | 0.164132 | + | 0.708960i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −415.622 | − | 177.633i | −1.00150 | − | 0.428030i | ||||
\(416\) | − | 82.6263i | − | 0.198621i | ||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 389.730 | 0.932367 | ||||||||
\(419\) | 482.910i | 1.15253i | 0.817263 | + | 0.576265i | \(0.195490\pi\) | ||||
−0.817263 | + | 0.576265i | \(0.804510\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −523.520 | −1.24351 | −0.621757 | − | 0.783210i | \(-0.713581\pi\) | ||||
−0.621757 | + | 0.783210i | \(0.713581\pi\) | |||||||
\(422\) | − | 248.780i | − | 0.589527i | ||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 201.807 | 0.475961 | ||||||||
\(425\) | −100.455 | − | 105.057i | −0.236365 | − | 0.247192i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −54.1319 | − | 233.821i | −0.126773 | − | 0.547589i | ||||
\(428\) | − | 315.715i | − | 0.737653i | ||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 273.670 | + | 116.964i | 0.636441 | + | 0.272008i | ||||
\(431\) | −517.027 | −1.19960 | −0.599799 | − | 0.800150i | \(-0.704753\pi\) | ||||
−0.599799 | + | 0.800150i | \(0.704753\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −567.712 | −1.31111 | −0.655557 | − | 0.755146i | \(-0.727566\pi\) | ||||
−0.655557 | + | 0.755146i | \(0.727566\pi\) | |||||||
\(434\) | −185.711 | + | 42.9939i | −0.427905 | + | 0.0990644i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 224.146 | 0.514097 | ||||||||
\(437\) | 1258.32 | 2.87945 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 622.875i | 1.41885i | 0.704781 | + | 0.709425i | \(0.251045\pi\) | ||||
−0.704781 | + | 0.709425i | \(0.748955\pi\) | |||||||
\(440\) | 45.3503 | − | 106.110i | 0.103069 | − | 0.241159i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 120.102i | 0.271723i | ||||||||
\(443\) | − | 476.699i | − | 1.07607i | −0.842923 | − | 0.538035i | \(-0.819167\pi\) | ||
0.842923 | − | 0.538035i | \(-0.180833\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −31.8899 | + | 74.6154i | −0.0716626 | + | 0.167675i | ||||
\(446\) | − | 29.0868i | − | 0.0652170i | ||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −54.5570 | + | 12.6305i | −0.121779 | + | 0.0281931i | ||||
\(449\) | −861.931 | −1.91967 | −0.959834 | − | 0.280570i | \(-0.909477\pi\) | ||||
−0.959834 | + | 0.280570i | \(0.909477\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 67.3889i | − | 0.149421i | ||||||
\(452\) | − | 283.975i | − | 0.628263i | ||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | − | 585.607i | − | 1.28988i | ||||||
\(455\) | −503.292 | − | 89.7083i | −1.10614 | − | 0.197161i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 27.5401i | − | 0.0602629i | −0.999546 | − | 0.0301314i | \(-0.990407\pi\) | ||
0.999546 | − | 0.0301314i | \(-0.00959258\pi\) | |||||||
\(458\) | 276.507 | 0.603727 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 146.423 | − | 342.597i | 0.318310 | − | 0.744777i | ||||
\(461\) | − | 378.183i | − | 0.820353i | −0.912006 | − | 0.410176i | \(-0.865467\pi\) | ||
0.912006 | − | 0.410176i | \(-0.134533\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 724.994i | 1.56586i | 0.622108 | + | 0.782931i | \(0.286276\pi\) | ||||
−0.622108 | + | 0.782931i | \(0.713724\pi\) | |||||||
\(464\) | 37.0122 | 0.0797676 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −114.976 | −0.246731 | ||||||||
\(467\) | 371.451 | 0.795398 | 0.397699 | − | 0.917516i | \(-0.369809\pi\) | ||||
0.397699 | + | 0.917516i | \(0.369809\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −7.89231 | − | 34.0905i | −0.0168280 | − | 0.0726877i | ||||
\(470\) | 64.8547 | − | 151.746i | 0.137989 | − | 0.322864i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −121.438 | −0.257285 | ||||||||
\(473\) | − | 343.434i | − | 0.726076i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −610.254 | + | 583.523i | −1.28475 | + | 1.22847i | ||||
\(476\) | 79.3015 | − | 18.3591i | 0.166600 | − | 0.0385695i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | − | 352.514i | − | 0.737477i | ||||||
\(479\) | 860.650i | 1.79677i | 0.439214 | + | 0.898383i | \(0.355257\pi\) | ||||
−0.439214 | + | 0.898383i | \(0.644743\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | − | 926.558i | − | 1.92632i | ||||||
\(482\) | −371.009 | −0.769728 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 108.840 | 0.224877 | ||||||||
\(485\) | −380.507 | − | 162.625i | −0.784551 | − | 0.335309i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 887.173i | − | 1.82171i | −0.412726 | − | 0.910855i | \(-0.635423\pi\) | ||
0.412726 | − | 0.910855i | \(-0.364577\pi\) | |||||||
\(488\) | 96.9766 | 0.198723 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 17.7015 | + | 346.030i | 0.0361255 | + | 0.706183i | ||||
\(491\) | 50.1823 | 0.102204 | 0.0511021 | − | 0.998693i | \(-0.483727\pi\) | ||||
0.0511021 | + | 0.998693i | \(0.483727\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −53.7991 | −0.109126 | ||||||||
\(494\) | 697.646 | 1.41224 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | − | 77.0231i | − | 0.155289i | ||||||
\(497\) | 264.683 | − | 61.2769i | 0.532562 | − | 0.123294i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 160.443 | 0.321529 | 0.160765 | − | 0.986993i | \(-0.448604\pi\) | ||||
0.160765 | + | 0.986993i | \(0.448604\pi\) | |||||||
\(500\) | 87.8620 | + | 234.052i | 0.175724 | + | 0.468104i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 200.701 | 0.399802 | ||||||||
\(503\) | −742.042 | −1.47523 | −0.737616 | − | 0.675220i | \(-0.764049\pi\) | ||||
−0.737616 | + | 0.675220i | \(0.764049\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 171.359 | − | 400.944i | 0.339325 | − | 0.793948i | ||||
\(506\) | −429.933 | −0.849670 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 404.828i | 0.796905i | ||||||||
\(509\) | − | 978.447i | − | 1.92229i | −0.276038 | − | 0.961147i | \(-0.589021\pi\) | ||
0.276038 | − | 0.961147i | \(-0.410979\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 849.927 | − | 196.767i | 1.66326 | − | 0.385062i | ||||
\(512\) | − | 22.6274i | − | 0.0441942i | ||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 241.608i | 0.470054i | ||||||||
\(515\) | 862.377 | + | 368.571i | 1.67452 | + | 0.715672i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −190.429 | −0.368335 | ||||||||
\(518\) | −611.794 | + | 141.637i | −1.18107 | + | 0.273430i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 81.1805 | − | 189.945i | 0.156116 | − | 0.365279i | ||||
\(521\) | 575.650i | 1.10489i | 0.833548 | + | 0.552447i | \(0.186306\pi\) | ||||
−0.833548 | + | 0.552447i | \(0.813694\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −339.090 | −0.648355 | −0.324178 | − | 0.945996i | \(-0.605088\pi\) | ||||
−0.324178 | + | 0.945996i | \(0.605088\pi\) | |||||||
\(524\) | 282.520i | 0.539160i | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 542.234 | 1.03086 | ||||||||
\(527\) | 111.957i | 0.212442i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −859.125 | −1.62406 | ||||||||
\(530\) | 463.924 | + | 198.276i | 0.875328 | + | 0.374106i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −106.644 | − | 460.647i | −0.200459 | − | 0.865877i | ||||
\(533\) | − | 120.631i | − | 0.226325i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 310.191 | − | 725.781i | 0.579797 | − | 1.35660i | ||||
\(536\) | 14.1390 | 0.0263787 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 218.512 | 0.406157 | ||||||||
\(539\) | 359.144 | − | 175.709i | 0.666316 | − | 0.325990i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 35.8638 | 0.0662916 | 0.0331458 | − | 0.999451i | \(-0.489447\pi\) | ||||
0.0331458 | + | 0.999451i | \(0.489447\pi\) | |||||||
\(542\) | −453.012 | −0.835815 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 32.8901i | 0.0604598i | ||||||||
\(545\) | 515.277 | + | 220.224i | 0.945463 | + | 0.404081i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 700.845i | 1.28125i | 0.767853 | + | 0.640626i | \(0.221325\pi\) | ||||
−0.767853 | + | 0.640626i | \(0.778675\pi\) | |||||||
\(548\) | 101.286i | 0.184829i | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 208.507 | − | 199.373i | 0.379103 | − | 0.362497i | ||||
\(551\) | 312.508i | 0.567166i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −383.155 | + | 88.7044i | −0.692867 | + | 0.160406i | ||||
\(554\) | 315.163 | 0.568886 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | − | 148.051i | − | 0.266279i | ||||||
\(557\) | 639.349i | 1.14784i | 0.818910 | + | 0.573922i | \(0.194579\pi\) | ||||
−0.818910 | + | 0.573922i | \(0.805421\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 614.773i | − | 1.09977i | ||||||
\(560\) | −137.828 | − | 24.5669i | −0.246121 | − | 0.0438694i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 309.674i | 0.551022i | ||||||||
\(563\) | 227.519 | 0.404120 | 0.202060 | − | 0.979373i | \(-0.435236\pi\) | ||||
0.202060 | + | 0.979373i | \(0.435236\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 279.006 | − | 652.814i | 0.493816 | − | 1.15542i | ||||
\(566\) | − | 51.4713i | − | 0.0909387i | ||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 109.777i | 0.193269i | ||||||||
\(569\) | −613.901 | −1.07891 | −0.539456 | − | 0.842014i | \(-0.681370\pi\) | ||||
−0.539456 | + | 0.842014i | \(0.681370\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 366.674 | 0.642161 | 0.321081 | − | 0.947052i | \(-0.395954\pi\) | ||||
0.321081 | + | 0.947052i | \(0.395954\pi\) | |||||||
\(572\) | −238.366 | −0.416724 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −79.6513 | + | 18.4401i | −0.138765 | + | 0.0321256i | ||||
\(575\) | 673.206 | − | 643.718i | 1.17079 | − | 1.11951i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −62.1951 | −0.107790 | −0.0538952 | − | 0.998547i | \(-0.517164\pi\) | ||||
−0.0538952 | + | 0.998547i | \(0.517164\pi\) | |||||||
\(578\) | 360.900i | 0.624395i | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 85.0853 | + | 36.3646i | 0.146699 | + | 0.0626975i | ||||
\(581\) | 616.481 | − | 142.722i | 1.06107 | − | 0.245648i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 582.188i | − | 0.998607i | ||||||
\(584\) | 352.505i | 0.603605i | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | − | 238.211i | − | 0.406503i | ||||||
\(587\) | 176.872 | 0.301315 | 0.150658 | − | 0.988586i | \(-0.451861\pi\) | ||||
0.150658 | + | 0.988586i | \(0.451861\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 650.337 | 1.10414 | ||||||||
\(590\) | −279.168 | − | 119.314i | −0.473166 | − | 0.202226i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | − | 253.740i | − | 0.428615i | ||||||
\(593\) | −154.878 | −0.261176 | −0.130588 | − | 0.991437i | \(-0.541687\pi\) | ||||
−0.130588 | + | 0.991437i | \(0.541687\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 200.340 | + | 35.7092i | 0.336705 | + | 0.0600154i | ||||
\(596\) | −453.959 | −0.761676 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −769.613 | −1.28698 | ||||||||
\(599\) | −900.825 | −1.50388 | −0.751940 | − | 0.659231i | \(-0.770882\pi\) | ||||
−0.751940 | + | 0.659231i | \(0.770882\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 682.387i | 1.13542i | 0.823229 | + | 0.567710i | \(0.192170\pi\) | ||||
−0.823229 | + | 0.567710i | \(0.807830\pi\) | |||||||
\(602\) | −405.927 | + | 93.9762i | −0.674297 | + | 0.156107i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −588.851 | −0.974920 | ||||||||
\(605\) | 250.207 | + | 106.936i | 0.413566 | + | 0.176754i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 367.814 | 0.605954 | 0.302977 | − | 0.952998i | \(-0.402019\pi\) | ||||
0.302977 | + | 0.952998i | \(0.402019\pi\) | |||||||
\(608\) | 191.052 | 0.314231 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 222.934 | + | 95.2798i | 0.365466 | + | 0.156196i | ||||
\(611\) | −340.883 | −0.557911 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 117.271i | − | 0.191306i | −0.995415 | − | 0.0956532i | \(-0.969506\pi\) | ||
0.995415 | − | 0.0956532i | \(-0.0304940\pi\) | |||||||
\(614\) | − | 315.936i | − | 0.514553i | ||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 36.4374 | + | 157.390i | 0.0591516 | + | 0.255503i | ||||
\(617\) | 1070.18i | 1.73449i | 0.497881 | + | 0.867245i | \(0.334112\pi\) | ||||
−0.497881 | + | 0.867245i | \(0.665888\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 532.192i | 0.859761i | 0.902886 | + | 0.429880i | \(0.141444\pi\) | ||||
−0.902886 | + | 0.429880i | \(0.858556\pi\) | |||||||
\(620\) | 75.6754 | − | 177.064i | 0.122057 | − | 0.285587i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −65.1098 | −0.104678 | ||||||||
\(623\) | −25.6224 | − | 110.675i | −0.0411275 | − | 0.177649i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −27.9756 | + | 624.374i | −0.0447610 | + | 0.998998i | ||||
\(626\) | 113.190i | 0.180815i | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 131.719 | 0.209744 | ||||||||
\(629\) | 368.825i | 0.586366i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 472.933 | 0.749498 | 0.374749 | − | 0.927126i | \(-0.377729\pi\) | ||||
0.374749 | + | 0.927126i | \(0.377729\pi\) | |||||||
\(632\) | − | 158.913i | − | 0.251444i | ||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −261.964 | −0.413193 | ||||||||
\(635\) | −397.745 | + | 930.636i | −0.626369 | + | 1.46557i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 642.896 | − | 314.532i | 1.00926 | − | 0.493771i | ||||
\(638\) | − | 106.775i | − | 0.167359i | ||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 22.2315 | − | 52.0169i | 0.0347367 | − | 0.0812764i | ||||
\(641\) | 486.990 | 0.759734 | 0.379867 | − | 0.925041i | \(-0.375970\pi\) | ||||
0.379867 | + | 0.925041i | \(0.375970\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −111.425 | −0.173289 | −0.0866447 | − | 0.996239i | \(-0.527614\pi\) | ||||
−0.0866447 | + | 0.996239i | \(0.527614\pi\) | |||||||
\(644\) | 117.645 | + | 508.165i | 0.182679 | + | 0.789077i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −277.704 | −0.429883 | ||||||||
\(647\) | −737.696 | −1.14018 | −0.570090 | − | 0.821583i | \(-0.693092\pi\) | ||||
−0.570090 | + | 0.821583i | \(0.693092\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 350.334i | 0.539806i | ||||||||
\(650\) | 373.243 | − | 356.894i | 0.574220 | − | 0.549068i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 56.4149i | 0.0865260i | ||||||||
\(653\) | 193.734i | 0.296682i | 0.988936 | + | 0.148341i | \(0.0473934\pi\) | ||||
−0.988936 | + | 0.148341i | \(0.952607\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −277.577 | + | 649.469i | −0.423781 | + | 0.991556i | ||||
\(656\) | − | 33.0352i | − | 0.0503585i | ||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 52.1085 | + | 225.081i | 0.0791923 | + | 0.342068i | ||||
\(659\) | 823.339 | 1.24938 | 0.624688 | − | 0.780874i | \(-0.285226\pi\) | ||||
0.624688 | + | 0.780874i | \(0.285226\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 657.833i | 0.995208i | 0.867404 | + | 0.497604i | \(0.165787\pi\) | ||||
−0.867404 | + | 0.497604i | \(0.834213\pi\) | |||||||
\(662\) | − | 86.9298i | − | 0.131314i | ||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 255.684i | 0.385066i | ||||||||
\(665\) | 207.428 | − | 1163.73i | 0.311921 | − | 1.74998i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 344.746i | − | 0.516860i | ||||||
\(668\) | 256.922 | 0.384614 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 32.5033 | + | 13.8916i | 0.0485124 | + | 0.0207337i | ||||
\(671\) | − | 279.765i | − | 0.416937i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 727.300i | 1.08068i | 0.841446 | + | 0.540342i | \(0.181705\pi\) | ||||
−0.841446 | + | 0.540342i | \(0.818295\pi\) | |||||||
\(674\) | 928.433 | 1.37750 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −88.6938 | −0.131204 | ||||||||
\(677\) | 385.964 | 0.570110 | 0.285055 | − | 0.958511i | \(-0.407988\pi\) | ||||
0.285055 | + | 0.958511i | \(0.407988\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 564.396 | − | 130.663i | 0.831217 | − | 0.192435i | ||||
\(680\) | −32.3146 | + | 75.6093i | −0.0475215 | + | 0.111190i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −222.202 | −0.325809 | ||||||||
\(683\) | 236.488i | 0.346249i | 0.984900 | + | 0.173124i | \(0.0553863\pi\) | ||||
−0.984900 | + | 0.173124i | \(0.944614\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −99.5138 | + | 232.841i | −0.145276 | + | 0.339914i | ||||
\(686\) | −305.957 | − | 376.415i | −0.446001 | − | 0.548711i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | − | 168.357i | − | 0.244705i | ||||||
\(689\) | − | 1042.16i | − | 1.51257i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 337.426i | 0.488316i | 0.969735 | + | 0.244158i | \(0.0785116\pi\) | ||||
−0.969735 | + | 0.244158i | \(0.921488\pi\) | |||||||
\(692\) | 224.892 | 0.324988 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −454.419 | −0.654782 | ||||||||
\(695\) | 145.461 | − | 340.347i | 0.209296 | − | 0.489708i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 48.0184i | 0.0688929i | ||||||||
\(698\) | −261.821 | −0.375101 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −292.707 | − | 191.891i | −0.418154 | − | 0.274131i | ||||
\(701\) | −89.2192 | −0.127274 | −0.0636371 | − | 0.997973i | \(-0.520270\pi\) | ||||
−0.0636371 | + | 0.997973i | \(0.520270\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 2142.43 | 3.04755 | ||||||||
\(704\) | −65.2772 | −0.0927232 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 844.764i | 1.19655i | ||||||||
\(707\) | 137.681 | + | 594.709i | 0.194740 | + | 0.841172i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 569.646 | 0.803450 | 0.401725 | − | 0.915760i | \(-0.368411\pi\) | ||||
0.401725 | + | 0.915760i | \(0.368411\pi\) | |||||||
\(710\) | −107.856 | + | 252.360i | −0.151910 | + | 0.355437i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 45.9023 | 0.0644695 | ||||||||
\(713\) | −717.423 | −1.00620 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −547.967 | − | 234.195i | −0.766387 | − | 0.327546i | ||||
\(716\) | −137.804 | −0.192464 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 338.628i | 0.471627i | ||||||||
\(719\) | − | 1261.33i | − | 1.75428i | −0.480233 | − | 0.877141i | \(-0.659448\pi\) | ||
0.480233 | − | 0.877141i | \(-0.340552\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1279.14 | + | 296.134i | −1.77412 | + | 0.410727i | ||||
\(722\) | 1102.60i | 1.52714i | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 333.074i | 0.460047i | ||||||||
\(725\) | 159.870 | + | 167.193i | 0.220510 | + | 0.230611i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −307.746 | −0.423310 | −0.211655 | − | 0.977344i | \(-0.567885\pi\) | ||||
−0.211655 | + | 0.977344i | \(0.567885\pi\) | |||||||
\(728\) | 65.2258 | + | 281.740i | 0.0895958 | + | 0.387006i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −346.337 | + | 810.355i | −0.474435 | + | 1.11008i | ||||
\(731\) | 244.716i | 0.334769i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −633.490 | −0.864243 | −0.432121 | − | 0.901815i | \(-0.642235\pi\) | ||||
−0.432121 | + | 0.901815i | \(0.642235\pi\) | |||||||
\(734\) | − | 563.908i | − | 0.768266i | ||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −210.761 | −0.286359 | ||||||||
\(737\) | − | 40.7891i | − | 0.0553448i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 749.557 | 1.01428 | 0.507142 | − | 0.861862i | \(-0.330702\pi\) | ||||
0.507142 | + | 0.861862i | \(0.330702\pi\) | |||||||
\(740\) | 249.300 | − | 583.309i | 0.336893 | − | 0.788256i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −688.126 | + | 159.308i | −0.927393 | + | 0.214701i | ||||
\(743\) | − | 145.699i | − | 0.196095i | −0.995182 | − | 0.0980476i | \(-0.968740\pi\) | ||
0.995182 | − | 0.0980476i | \(-0.0312597\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −1043.58 | − | 446.016i | −1.40078 | − | 0.598679i | ||||
\(746\) | 49.0822 | 0.0657939 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 94.8837 | 0.126850 | ||||||||
\(749\) | 249.228 | + | 1076.53i | 0.332748 | + | 1.43729i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 156.811 | 0.208803 | 0.104402 | − | 0.994535i | \(-0.466707\pi\) | ||||
0.104402 | + | 0.994535i | \(0.466707\pi\) | |||||||
\(752\) | −93.3518 | −0.124138 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | − | 191.136i | − | 0.253496i | ||||||
\(755\) | −1353.68 | − | 578.548i | −1.79295 | − | 0.766289i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 296.377i | − | 0.391515i | −0.980652 | − | 0.195758i | \(-0.937283\pi\) | ||
0.980652 | − | 0.195758i | \(-0.0627166\pi\) | |||||||
\(758\) | 154.457i | 0.203769i | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 439.199 | + | 187.709i | 0.577894 | + | 0.246986i | ||||
\(761\) | 312.747i | 0.410968i | 0.978660 | + | 0.205484i | \(0.0658769\pi\) | ||||
−0.978660 | + | 0.205484i | \(0.934123\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −764.297 | + | 176.942i | −1.00170 | + | 0.231904i | ||||
\(764\) | −296.578 | −0.388191 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 475.770i | 0.621109i | ||||||||
\(767\) | 627.125i | 0.817634i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 91.1460i | − | 0.118525i | −0.998242 | − | 0.0592627i | \(-0.981125\pi\) | ||
0.998242 | − | 0.0592627i | \(-0.0188750\pi\) | |||||||
\(770\) | −70.8722 | + | 397.615i | −0.0920418 | + | 0.516383i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | − | 70.3772i | − | 0.0911622i | ||||||
\(773\) | −417.539 | −0.540154 | −0.270077 | − | 0.962839i | \(-0.587049\pi\) | ||||
−0.270077 | + | 0.962839i | \(0.587049\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 347.932 | − | 332.692i | 0.448945 | − | 0.429280i | ||||
\(776\) | 234.082i | 0.301652i | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | − | 440.065i | − | 0.565636i | ||||||
\(779\) | 278.929 | 0.358061 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 316.692 | 0.405496 | ||||||||
\(782\) | 306.351 | 0.391754 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 176.059 | − | 86.1354i | 0.224565 | − | 0.109867i | ||||
\(785\) | 302.802 | + | 129.414i | 0.385735 | + | 0.164859i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 318.111 | 0.404207 | 0.202104 | − | 0.979364i | \(-0.435222\pi\) | ||||
0.202104 | + | 0.979364i | \(0.435222\pi\) | |||||||
\(788\) | − | 387.268i | − | 0.491457i | ||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 156.132 | − | 365.316i | 0.197636 | − | 0.462425i | ||||
\(791\) | 224.172 | + | 968.302i | 0.283403 | + | 1.22415i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 500.801i | − | 0.631527i | ||||||
\(794\) | 58.3616i | 0.0735033i | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | − | 363.676i | − | 0.456880i | ||||||
\(797\) | −1188.06 | −1.49067 | −0.745335 | − | 0.666690i | \(-0.767711\pi\) | ||||
−0.745335 | + | 0.666690i | \(0.767711\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 135.692 | 0.169827 | ||||||||
\(800\) | 102.214 | − | 97.7363i | 0.127767 | − | 0.122170i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | − | 700.943i | − | 0.873994i | ||||||
\(803\) | 1016.93 | 1.26642 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −228.825 | + | 1283.78i | −0.284255 | + | 1.59476i | ||||
\(806\) | −397.758 | −0.493497 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −246.654 | −0.305265 | ||||||||
\(809\) | 223.374 | 0.276111 | 0.138055 | − | 0.990425i | \(-0.455915\pi\) | ||||
0.138055 | + | 0.990425i | \(0.455915\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 366.185i | 0.451523i | 0.974183 | + | 0.225761i | \(0.0724870\pi\) | ||||
−0.974183 | + | 0.225761i | \(0.927513\pi\) | |||||||
\(812\) | −126.205 | + | 29.2177i | −0.155424 | + | 0.0359824i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −732.008 | −0.899272 | ||||||||
\(815\) | −55.4278 | + | 129.689i | −0.0680096 | + | 0.159128i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1421.51 | 1.73991 | ||||||||
\(818\) | 509.004 | 0.622255 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 32.4572 | − | 75.9428i | 0.0395819 | − | 0.0926132i | ||||
\(821\) | 1547.39 | 1.88476 | 0.942381 | − | 0.334543i | \(-0.108582\pi\) | ||||
0.942381 | + | 0.334543i | \(0.108582\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1284.25i | 1.56045i | 0.625499 | + | 0.780225i | \(0.284895\pi\) | ||||
−0.625499 | + | 0.780225i | \(0.715105\pi\) | |||||||
\(824\) | − | 530.521i | − | 0.643836i | ||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 414.083 | − | 95.8644i | 0.501311 | − | 0.116059i | ||||
\(827\) | 807.319i | 0.976202i | 0.872787 | + | 0.488101i | \(0.162310\pi\) | ||||
−0.872787 | + | 0.488101i | \(0.837690\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 623.615i | − | 0.752250i | −0.926569 | − | 0.376125i | \(-0.877256\pi\) | ||
0.926569 | − | 0.376125i | \(-0.122744\pi\) | |||||||
\(830\) | −251.210 | + | 587.778i | −0.302663 | + | 0.708166i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −116.851 | −0.140446 | ||||||||
\(833\) | −255.911 | + | 125.202i | −0.307216 | + | 0.150303i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 590.623 | + | 252.426i | 0.707333 | + | 0.302307i | ||||
\(836\) | − | 551.161i | − | 0.659283i | ||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 682.938 | 0.814962 | ||||||||
\(839\) | 1146.31i | 1.36628i | 0.730286 | + | 0.683142i | \(0.239387\pi\) | ||||
−0.730286 | + | 0.683142i | \(0.760613\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −755.381 | −0.898194 | ||||||||
\(842\) | 740.368i | 0.879297i | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −351.829 | −0.416859 | ||||||||
\(845\) | −203.893 | − | 87.1419i | −0.241294 | − | 0.103127i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −371.126 | + | 85.9194i | −0.438165 | + | 0.101440i | ||||
\(848\) | − | 285.399i | − | 0.336555i | ||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −148.573 | + | 142.065i | −0.174791 | + | 0.167135i | ||||
\(851\) | −2363.43 | −2.77724 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −948.920 | −1.11245 | −0.556225 | − | 0.831032i | \(-0.687751\pi\) | ||||
−0.556225 | + | 0.831032i | \(0.687751\pi\) | |||||||
\(854\) | −330.672 | + | 76.5540i | −0.387204 | + | 0.0896417i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −446.489 | −0.521599 | ||||||||
\(857\) | 868.842 | 1.01382 | 0.506909 | − | 0.862000i | \(-0.330788\pi\) | ||||
0.506909 | + | 0.862000i | \(0.330788\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 119.981i | − | 0.139675i | −0.997558 | − | 0.0698377i | \(-0.977752\pi\) | ||
0.997558 | − | 0.0698377i | \(-0.0222482\pi\) | |||||||
\(860\) | 165.412 | − | 387.027i | 0.192339 | − | 0.450032i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 731.187i | 0.848245i | ||||||||
\(863\) | 788.430i | 0.913592i | 0.889571 | + | 0.456796i | \(0.151003\pi\) | ||||
−0.889571 | + | 0.456796i | \(0.848997\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 516.991 | + | 220.957i | 0.597678 | + | 0.255441i | ||||
\(866\) | 802.866i | 0.927097i | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 60.8026 | + | 262.635i | 0.0700491 | + | 0.302574i | ||||
\(869\) | −458.443 | −0.527552 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 73.0157i | − | 0.0838298i | ||||||
\(872\) | − | 316.990i | − | 0.363521i | ||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | − | 1779.53i | − | 2.03608i | ||||||
\(875\) | −484.355 | − | 728.715i | −0.553549 | − | 0.832817i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 234.663i | − | 0.267574i | −0.991010 | − | 0.133787i | \(-0.957286\pi\) | ||
0.991010 | − | 0.133787i | \(-0.0427139\pi\) | |||||||
\(878\) | 880.879 | 1.00328 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −150.062 | − | 64.1350i | −0.170525 | − | 0.0728807i | ||||
\(881\) | 750.816i | 0.852232i | 0.904669 | + | 0.426116i | \(0.140118\pi\) | ||||
−0.904669 | + | 0.426116i | \(0.859882\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 1293.79i | − | 1.46522i | −0.680649 | − | 0.732610i | \(-0.738302\pi\) | ||
0.680649 | − | 0.732610i | \(-0.261698\pi\) | |||||||
\(884\) | 169.849 | 0.192137 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −674.154 | −0.760896 | ||||||||
\(887\) | −728.248 | −0.821024 | −0.410512 | − | 0.911855i | \(-0.634650\pi\) | ||||
−0.410512 | + | 0.911855i | \(0.634650\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −319.574 | − | 1380.39i | −0.359476 | − | 1.55274i | ||||
\(890\) | 105.522 | + | 45.0991i | 0.118564 | + | 0.0506731i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −41.1349 | −0.0461154 | ||||||||
\(893\) | − | 788.206i | − | 0.882650i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −316.790 | − | 135.393i | −0.353955 | − | 0.151277i | ||||
\(896\) | 17.8622 | + | 77.1553i | 0.0199355 | + | 0.0861108i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 1218.95i | 1.35741i | ||||||||
\(899\) | − | 178.175i | − | 0.198192i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 414.842i | 0.460424i | ||||||||
\(902\) | −95.3022 | −0.105657 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −401.601 | −0.444249 | ||||||||
\(905\) | −327.246 | + | 765.685i | −0.361598 | + | 0.846061i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 913.713i | − | 1.00740i | −0.863878 | − | 0.503700i | \(-0.831972\pi\) | ||
0.863878 | − | 0.503700i | \(-0.168028\pi\) | |||||||
\(908\) | −828.173 | −0.912085 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −126.867 | + | 711.762i | −0.139414 | + | 0.782156i | ||||
\(911\) | 1331.32 | 1.46138 | 0.730690 | − | 0.682709i | \(-0.239198\pi\) | ||||
0.730690 | + | 0.682709i | \(0.239198\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 737.615 | 0.807903 | ||||||||
\(914\) | −38.9476 | −0.0426123 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | − | 391.040i | − | 0.426899i | ||||||
\(917\) | −223.023 | − | 963.341i | −0.243210 | − | 1.05053i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −111.140 | −0.120936 | −0.0604678 | − | 0.998170i | \(-0.519259\pi\) | ||||
−0.0604678 | + | 0.998170i | \(0.519259\pi\) | |||||||
\(920\) | −484.506 | − | 207.073i | −0.526637 | − | 0.225079i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −534.831 | −0.580077 | ||||||||
\(923\) | 566.904 | 0.614197 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1146.21 | − | 1096.00i | 1.23914 | − | 1.18486i | ||||
\(926\) | 1025.30 | 1.10723 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | − | 52.3431i | − | 0.0564042i | ||||||
\(929\) | 571.383i | 0.615051i | 0.951540 | + | 0.307526i | \(0.0995010\pi\) | ||||
−0.951540 | + | 0.307526i | \(0.900499\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 727.275 | + | 1486.53i | 0.781176 | + | 1.59671i | ||||
\(932\) | 162.601i | 0.174465i | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | − | 525.311i | − | 0.562431i | ||||||
\(935\) | 218.123 | + | 93.2235i | 0.233287 | + | 0.0997043i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −1657.10 | −1.76852 | −0.884259 | − | 0.466997i | \(-0.845336\pi\) | ||||
−0.884259 | + | 0.466997i | \(0.845336\pi\) | |||||||
\(938\) | −48.2113 | + | 11.1614i | −0.0513980 | + | 0.0118992i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −214.601 | − | 91.7184i | −0.228299 | − | 0.0975728i | ||||
\(941\) | 519.083i | 0.551629i | 0.961211 | + | 0.275815i | \(0.0889476\pi\) | ||||
−0.961211 | + | 0.275815i | \(0.911052\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −307.703 | −0.326302 | ||||||||
\(944\) | 171.740i | 0.181928i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −485.689 | −0.513413 | ||||||||
\(947\) | 558.258i | 0.589502i | 0.955574 | + | 0.294751i | \(0.0952366\pi\) | ||||
−0.955574 | + | 0.294751i | \(0.904763\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1820.39 | 1.91822 | ||||||||
\(950\) | 825.226 | + | 863.029i | 0.868659 | + | 0.908452i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −25.9637 | − | 112.149i | −0.0272728 | − | 0.117804i | ||||
\(953\) | 291.413i | 0.305784i | 0.988243 | + | 0.152892i | \(0.0488587\pi\) | ||||
−0.988243 | + | 0.152892i | \(0.951141\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −681.786 | − | 291.389i | −0.713912 | − | 0.305119i | ||||
\(956\) | −498.530 | −0.521475 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 1217.14 | 1.27050 | ||||||||
\(959\) | −79.9559 | − | 345.367i | −0.0833742 | − | 0.360132i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 590.215 | 0.614167 | ||||||||
\(962\) | −1310.35 | −1.36211 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 524.686i | 0.544280i | ||||||||
\(965\) | 69.1458 | − | 161.786i | 0.0716537 | − | 0.167654i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 323.558i | 0.334600i | 0.985906 | + | 0.167300i | \(0.0535048\pi\) | ||||
−0.985906 | + | 0.167300i | \(0.946495\pi\) | |||||||
\(968\) | − | 153.924i | − | 0.159012i | ||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −229.986 | + | 538.118i | −0.237099 | + | 0.554761i | ||||
\(971\) | − | 219.659i | − | 0.226219i | −0.993583 | − | 0.113110i | \(-0.963919\pi\) | ||
0.993583 | − | 0.113110i | \(-0.0360812\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 116.873 | + | 504.827i | 0.120116 | + | 0.518836i | ||||
\(974\) | −1254.65 | −1.28814 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | − | 137.146i | − | 0.140518i | ||||||
\(977\) | − | 1302.29i | − | 1.33295i | −0.745527 | − | 0.666475i | \(-0.767802\pi\) | ||
0.745527 | − | 0.666475i | \(-0.232198\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 132.422i | − | 0.135263i | ||||||
\(980\) | 489.360 | − | 25.0337i | 0.499347 | − | 0.0255446i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | − | 70.9685i | − | 0.0722693i | ||||||
\(983\) | 649.905 | 0.661144 | 0.330572 | − | 0.943781i | \(-0.392758\pi\) | ||||
0.330572 | + | 0.943781i | \(0.392758\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 380.492 | − | 890.270i | 0.386287 | − | 0.903827i | ||||
\(986\) | 76.0834i | 0.0771637i | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | − | 986.621i | − | 0.998604i | ||||||
\(989\) | −1568.15 | −1.58559 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −575.568 | −0.580795 | −0.290397 | − | 0.956906i | \(-0.593788\pi\) | ||||
−0.290397 | + | 0.956906i | \(0.593788\pi\) | |||||||
\(992\) | −108.927 | −0.109806 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −86.6587 | − | 374.319i | −0.0871818 | − | 0.376578i | ||||
\(995\) | 357.313 | − | 836.035i | 0.359108 | − | 0.840236i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 705.512 | 0.707635 | 0.353817 | − | 0.935315i | \(-0.384883\pi\) | ||||
0.353817 | + | 0.935315i | \(0.384883\pi\) | |||||||
\(998\) | − | 226.901i | − | 0.227355i | ||||||
\(999\) | 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 | 630.3.h.e.559.2 | 16 | ||
3.2 | odd | 2 | 210.3.h.a.139.12 | yes | 16 | ||
5.4 | even | 2 | inner | 630.3.h.e.559.15 | 16 | ||
7.6 | odd | 2 | inner | 630.3.h.e.559.7 | 16 | ||
12.11 | even | 2 | 1680.3.bd.a.769.16 | 16 | |||
15.2 | even | 4 | 1050.3.f.e.601.7 | 16 | |||
15.8 | even | 4 | 1050.3.f.e.601.10 | 16 | |||
15.14 | odd | 2 | 210.3.h.a.139.5 | yes | 16 | ||
21.20 | even | 2 | 210.3.h.a.139.13 | yes | 16 | ||
35.34 | odd | 2 | inner | 630.3.h.e.559.10 | 16 | ||
60.59 | even | 2 | 1680.3.bd.a.769.2 | 16 | |||
84.83 | odd | 2 | 1680.3.bd.a.769.1 | 16 | |||
105.62 | odd | 4 | 1050.3.f.e.601.3 | 16 | |||
105.83 | odd | 4 | 1050.3.f.e.601.14 | 16 | |||
105.104 | even | 2 | 210.3.h.a.139.4 | ✓ | 16 | ||
420.419 | odd | 2 | 1680.3.bd.a.769.15 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
210.3.h.a.139.4 | ✓ | 16 | 105.104 | even | 2 | ||
210.3.h.a.139.5 | yes | 16 | 15.14 | odd | 2 | ||
210.3.h.a.139.12 | yes | 16 | 3.2 | odd | 2 | ||
210.3.h.a.139.13 | yes | 16 | 21.20 | even | 2 | ||
630.3.h.e.559.2 | 16 | 1.1 | even | 1 | trivial | ||
630.3.h.e.559.7 | 16 | 7.6 | odd | 2 | inner | ||
630.3.h.e.559.10 | 16 | 35.34 | odd | 2 | inner | ||
630.3.h.e.559.15 | 16 | 5.4 | even | 2 | inner | ||
1050.3.f.e.601.3 | 16 | 105.62 | odd | 4 | |||
1050.3.f.e.601.7 | 16 | 15.2 | even | 4 | |||
1050.3.f.e.601.10 | 16 | 15.8 | even | 4 | |||
1050.3.f.e.601.14 | 16 | 105.83 | odd | 4 | |||
1680.3.bd.a.769.1 | 16 | 84.83 | odd | 2 | |||
1680.3.bd.a.769.2 | 16 | 60.59 | even | 2 | |||
1680.3.bd.a.769.15 | 16 | 420.419 | odd | 2 | |||
1680.3.bd.a.769.16 | 16 | 12.11 | even | 2 |