Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [7056,2,Mod(881,7056)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(7056, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("7056.881");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 7056 = 2^{4} \cdot 3^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 7056.k (of order \(2\), degree \(1\), not 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: | \(56.3424436662\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\Q(\zeta_{16})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | no (minimal twist has level 1764) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 881.5 | ||
Root | \(-0.382683 - 0.923880i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 7056.881 |
Dual form | 7056.2.k.e.881.6 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/7056\mathbb{Z}\right)^\times\).
\(n\) | \(785\) | \(1765\) | \(4609\) | \(6175\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.765367 | 0.342282 | 0.171141 | − | 0.985247i | \(-0.445255\pi\) | ||||
0.171141 | + | 0.985247i | \(0.445255\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − 2.00000i | − 0.603023i | −0.953463 | − | 0.301511i | \(-0.902509\pi\) | ||||
0.953463 | − | 0.301511i | \(-0.0974911\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 0.317025i | − 0.0879270i | −0.999033 | − | 0.0439635i | \(-0.986001\pi\) | ||||
0.999033 | − | 0.0439635i | \(-0.0139985\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 5.54328 | 1.34444 | 0.672221 | − | 0.740350i | \(-0.265340\pi\) | ||||
0.672221 | + | 0.740350i | \(0.265340\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − 3.69552i | − 0.847810i | −0.905707 | − | 0.423905i | \(-0.860659\pi\) | ||||
0.905707 | − | 0.423905i | \(-0.139341\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − 3.17157i | − 0.661319i | −0.943750 | − | 0.330659i | \(-0.892729\pi\) | ||||
0.943750 | − | 0.330659i | \(-0.107271\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.41421 | −0.882843 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − 6.82843i | − 1.26801i | −0.773330 | − | 0.634004i | \(-0.781410\pi\) | ||||
0.773330 | − | 0.634004i | \(-0.218590\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − 6.75699i | − 1.21359i | −0.794858 | − | 0.606795i | \(-0.792455\pi\) | ||||
0.794858 | − | 0.606795i | \(-0.207545\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −0.242641 | −0.0398899 | −0.0199449 | − | 0.999801i | \(-0.506349\pi\) | ||||
−0.0199449 | + | 0.999801i | \(0.506349\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −2.74444 | −0.428610 | −0.214305 | − | 0.976767i | \(-0.568749\pi\) | ||||
−0.214305 | + | 0.976767i | \(0.568749\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −6.82843 | −1.04133 | −0.520663 | − | 0.853762i | \(-0.674315\pi\) | ||||
−0.520663 | + | 0.853762i | \(0.674315\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −11.9832 | −1.74793 | −0.873967 | − | 0.485985i | \(-0.838461\pi\) | ||||
−0.873967 | + | 0.485985i | \(0.838461\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 12.2426i | 1.68166i | 0.541302 | + | 0.840828i | \(0.317931\pi\) | ||||
−0.541302 | + | 0.840828i | \(0.682069\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − 1.53073i | − 0.206404i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −13.2513 | −1.72518 | −0.862589 | − | 0.505906i | \(-0.831158\pi\) | ||||
−0.862589 | + | 0.505906i | \(0.831158\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.56420i | 0.456349i | 0.973620 | + | 0.228175i | \(0.0732757\pi\) | ||||
−0.973620 | + | 0.228175i | \(0.926724\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − 0.242641i | − 0.0300959i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 4.48528 | 0.547964 | 0.273982 | − | 0.961735i | \(-0.411659\pi\) | ||||
0.273982 | + | 0.961735i | \(0.411659\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 9.31371i | 1.10533i | 0.833402 | + | 0.552667i | \(0.186390\pi\) | ||||
−0.833402 | + | 0.552667i | \(0.813610\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 11.8519i | 1.38716i | 0.720378 | + | 0.693581i | \(0.243968\pi\) | ||||
−0.720378 | + | 0.693581i | \(0.756032\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 11.3137 | 1.27289 | 0.636446 | − | 0.771321i | \(-0.280404\pi\) | ||||
0.636446 | + | 0.771321i | \(0.280404\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −4.32957 | −0.475232 | −0.237616 | − | 0.971359i | \(-0.576366\pi\) | ||||
−0.237616 | + | 0.971359i | \(0.576366\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 4.24264 | 0.460179 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1.66205 | 0.176177 | 0.0880885 | − | 0.996113i | \(-0.471924\pi\) | ||||
0.0880885 | + | 0.996113i | \(0.471924\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | − 2.82843i | − 0.290191i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − 11.8519i | − 1.20338i | −0.798730 | − | 0.601690i | \(-0.794494\pi\) | ||||
0.798730 | − | 0.601690i | \(-0.205506\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 11.8519 | 1.17931 | 0.589655 | − | 0.807655i | \(-0.299264\pi\) | ||||
0.589655 | + | 0.807655i | \(0.299264\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − 8.92177i | − 0.879088i | −0.898221 | − | 0.439544i | \(-0.855140\pi\) | ||||
0.898221 | − | 0.439544i | \(-0.144860\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − 7.17157i | − 0.693302i | −0.937994 | − | 0.346651i | \(-0.887319\pi\) | ||||
0.937994 | − | 0.346651i | \(-0.112681\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −11.0711 | −1.06042 | −0.530208 | − | 0.847868i | \(-0.677886\pi\) | ||||
−0.530208 | + | 0.847868i | \(0.677886\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − 10.5858i | − 0.995827i | −0.867227 | − | 0.497914i | \(-0.834100\pi\) | ||||
0.867227 | − | 0.497914i | \(-0.165900\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − 2.42742i | − 0.226358i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 7.00000 | 0.636364 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −7.20533 | −0.644464 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.17157 | −0.103960 | −0.0519801 | − | 0.998648i | \(-0.516553\pi\) | ||||
−0.0519801 | + | 0.998648i | \(0.516553\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −16.9469 | −1.48065 | −0.740327 | − | 0.672247i | \(-0.765329\pi\) | ||||
−0.740327 | + | 0.672247i | \(0.765329\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 10.8284i | 0.925135i | 0.886584 | + | 0.462567i | \(0.153072\pi\) | ||||
−0.886584 | + | 0.462567i | \(0.846928\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − 15.6788i | − 1.32985i | −0.746908 | − | 0.664927i | \(-0.768462\pi\) | ||||
0.746908 | − | 0.664927i | \(-0.231538\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −0.634051 | −0.0530220 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − 5.22625i | − 0.434017i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − 7.07107i | − 0.579284i | −0.957135 | − | 0.289642i | \(-0.906464\pi\) | ||||
0.957135 | − | 0.289642i | \(-0.0935363\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −10.1421 | −0.825355 | −0.412678 | − | 0.910877i | \(-0.635406\pi\) | ||||
−0.412678 | + | 0.910877i | \(0.635406\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − 5.17157i | − 0.415391i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 6.17733i | 0.493004i | 0.969142 | + | 0.246502i | \(0.0792813\pi\) | ||||
−0.969142 | + | 0.246502i | \(0.920719\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −2.82843 | −0.221540 | −0.110770 | − | 0.993846i | \(-0.535332\pi\) | ||||
−0.110770 | + | 0.993846i | \(0.535332\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −2.42742 | −0.187839 | −0.0939196 | − | 0.995580i | \(-0.529940\pi\) | ||||
−0.0939196 | + | 0.995580i | \(0.529940\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 12.8995 | 0.992269 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −18.7946 | −1.42893 | −0.714464 | − | 0.699672i | \(-0.753329\pi\) | ||||
−0.714464 | + | 0.699672i | \(0.753329\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 9.31371i | 0.696139i | 0.937469 | + | 0.348070i | \(0.113163\pi\) | ||||
−0.937469 | + | 0.348070i | \(0.886837\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1.66205i | 0.123539i | 0.998090 | + | 0.0617696i | \(0.0196744\pi\) | ||||
−0.998090 | + | 0.0617696i | \(0.980326\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −0.185709 | −0.0136536 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 11.0866i | − 0.810729i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − 17.3137i | − 1.25278i | −0.779511 | − | 0.626388i | \(-0.784533\pi\) | ||||
0.779511 | − | 0.626388i | \(-0.215467\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −9.65685 | −0.695116 | −0.347558 | − | 0.937659i | \(-0.612989\pi\) | ||||
−0.347558 | + | 0.937659i | \(0.612989\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 3.07107i | 0.218805i | 0.993998 | + | 0.109402i | \(0.0348937\pi\) | ||||
−0.993998 | + | 0.109402i | \(0.965106\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 7.39104i | 0.523937i | 0.965076 | + | 0.261968i | \(0.0843716\pi\) | ||||
−0.965076 | + | 0.261968i | \(0.915628\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −2.10051 | −0.146706 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −7.39104 | −0.511249 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 18.6274 | 1.28236 | 0.641182 | − | 0.767389i | \(-0.278444\pi\) | ||||
0.641182 | + | 0.767389i | \(0.278444\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −5.22625 | −0.356427 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − 1.75736i | − 0.118213i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 21.8017i | 1.45995i | 0.683474 | + | 0.729975i | \(0.260468\pi\) | ||||
−0.683474 | + | 0.729975i | \(0.739532\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 6.75699 | 0.448477 | 0.224238 | − | 0.974534i | \(-0.428011\pi\) | ||||
0.224238 | + | 0.974534i | \(0.428011\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − 16.1815i | − 1.06930i | −0.845073 | − | 0.534651i | \(-0.820443\pi\) | ||||
0.845073 | − | 0.534651i | \(-0.179557\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − 15.1716i | − 0.993923i | −0.867773 | − | 0.496961i | \(-0.834449\pi\) | ||||
0.867773 | − | 0.496961i | \(-0.165551\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −9.17157 | −0.598287 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − 8.82843i | − 0.571063i | −0.958369 | − | 0.285532i | \(-0.907830\pi\) | ||||
0.958369 | − | 0.285532i | \(-0.0921702\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − 25.5516i | − 1.64592i | −0.568097 | − | 0.822962i | \(-0.692320\pi\) | ||||
0.568097 | − | 0.822962i | \(-0.307680\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1.17157 | −0.0745454 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −25.4972 | −1.60937 | −0.804685 | − | 0.593702i | \(-0.797666\pi\) | ||||
−0.804685 | + | 0.593702i | \(0.797666\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −6.34315 | −0.398790 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −20.5880 | −1.28424 | −0.642122 | − | 0.766603i | \(-0.721946\pi\) | ||||
−0.642122 | + | 0.766603i | \(0.721946\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 19.6569i | 1.21209i | 0.795429 | + | 0.606047i | \(0.207246\pi\) | ||||
−0.795429 | + | 0.606047i | \(0.792754\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 9.37011i | 0.575601i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −17.8979 | −1.09126 | −0.545628 | − | 0.838027i | \(-0.683709\pi\) | ||||
−0.545628 | + | 0.838027i | \(0.683709\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − 5.48888i | − 0.333426i | −0.986005 | − | 0.166713i | \(-0.946685\pi\) | ||||
0.986005 | − | 0.166713i | \(-0.0533153\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 8.82843i | 0.532374i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 12.9706 | 0.779326 | 0.389663 | − | 0.920958i | \(-0.372592\pi\) | ||||
0.389663 | + | 0.920958i | \(0.372592\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 10.4853i | 0.625499i | 0.949836 | + | 0.312750i | \(0.101250\pi\) | ||||
−0.949836 | + | 0.312750i | \(0.898750\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 4.06694i | − 0.241754i | −0.992667 | − | 0.120877i | \(-0.961429\pi\) | ||||
0.992667 | − | 0.120877i | \(-0.0385707\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 13.7279 | 0.807525 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −16.4441 | −0.960676 | −0.480338 | − | 0.877083i | \(-0.659486\pi\) | ||||
−0.480338 | + | 0.877083i | \(0.659486\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −10.1421 | −0.590498 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −1.00547 | −0.0581478 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 2.72792i | 0.156200i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 27.1367i | − 1.54877i | −0.632712 | − | 0.774387i | \(-0.718058\pi\) | ||||
0.632712 | − | 0.774387i | \(-0.281942\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 30.7235 | 1.74217 | 0.871084 | − | 0.491134i | \(-0.163418\pi\) | ||||
0.871084 | + | 0.491134i | \(0.163418\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − 28.8757i | − 1.63215i | −0.577945 | − | 0.816076i | \(-0.696145\pi\) | ||||
0.577945 | − | 0.816076i | \(-0.303855\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − 15.7574i | − 0.885021i | −0.896763 | − | 0.442511i | \(-0.854088\pi\) | ||||
0.896763 | − | 0.442511i | \(-0.145912\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −13.6569 | −0.764637 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − 20.4853i | − 1.13983i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.39942i | 0.0776257i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 27.3137 | 1.50130 | 0.750649 | − | 0.660702i | \(-0.229741\pi\) | ||||
0.750649 | + | 0.660702i | \(0.229741\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 3.43289 | 0.187559 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −27.0711 | −1.47466 | −0.737328 | − | 0.675535i | \(-0.763913\pi\) | ||||
−0.737328 | + | 0.675535i | \(0.763913\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −13.5140 | −0.731823 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 29.7990i | 1.59969i | 0.600204 | + | 0.799847i | \(0.295086\pi\) | ||||
−0.600204 | + | 0.799847i | \(0.704914\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − 31.9372i | − 1.70956i | −0.518993 | − | 0.854779i | \(-0.673693\pi\) | ||||
0.518993 | − | 0.854779i | \(-0.326307\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −21.1451 | −1.12544 | −0.562720 | − | 0.826647i | \(-0.690245\pi\) | ||||
−0.562720 | + | 0.826647i | \(0.690245\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 7.12840i | 0.378336i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − 19.4558i | − 1.02684i | −0.858137 | − | 0.513420i | \(-0.828378\pi\) | ||||
0.858137 | − | 0.513420i | \(-0.171622\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 5.34315 | 0.281218 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 9.07107i | 0.474801i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 36.0585i | 1.88224i | 0.338075 | + | 0.941119i | \(0.390224\pi\) | ||||
−0.338075 | + | 0.941119i | \(0.609776\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 30.6274 | 1.58583 | 0.792914 | − | 0.609334i | \(-0.208563\pi\) | ||||
0.792914 | + | 0.609334i | \(0.208563\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −2.16478 | −0.111492 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 36.2843 | 1.86380 | 0.931899 | − | 0.362718i | \(-0.118151\pi\) | ||||
0.931899 | + | 0.362718i | \(0.118151\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 14.7821 | 0.755329 | 0.377664 | − | 0.925943i | \(-0.376727\pi\) | ||||
0.377664 | + | 0.925943i | \(0.376727\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − 1.17157i | − 0.0594011i | −0.999559 | − | 0.0297006i | \(-0.990545\pi\) | ||||
0.999559 | − | 0.0297006i | \(-0.00945537\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − 17.5809i | − 0.889105i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 8.65914 | 0.435688 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − 14.0167i | − 0.703478i | −0.936098 | − | 0.351739i | \(-0.885590\pi\) | ||||
0.936098 | − | 0.351739i | \(-0.114410\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − 5.51472i | − 0.275392i | −0.990475 | − | 0.137696i | \(-0.956030\pi\) | ||||
0.990475 | − | 0.137696i | \(-0.0439697\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −2.14214 | −0.106707 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0.485281i | 0.0240545i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 1.13679i | 0.0562104i | 0.999605 | + | 0.0281052i | \(0.00894734\pi\) | ||||
−0.999605 | + | 0.0281052i | \(0.991053\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −3.31371 | −0.162664 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −27.6620 | −1.35138 | −0.675688 | − | 0.737187i | \(-0.736154\pi\) | ||||
−0.675688 | + | 0.737187i | \(0.736154\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 15.3137 | 0.746344 | 0.373172 | − | 0.927762i | \(-0.378270\pi\) | ||||
0.373172 | + | 0.927762i | \(0.378270\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −24.4692 | −1.18693 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 33.3137i | 1.60466i | 0.596877 | + | 0.802332i | \(0.296408\pi\) | ||||
−0.596877 | + | 0.802332i | \(0.703592\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − 0.502734i | − 0.0241599i | −0.999927 | − | 0.0120799i | \(-0.996155\pi\) | ||||
0.999927 | − | 0.0120799i | \(-0.00384526\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −11.7206 | −0.560673 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − 13.8854i | − 0.662713i | −0.943506 | − | 0.331357i | \(-0.892494\pi\) | ||||
0.943506 | − | 0.331357i | \(-0.107506\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 29.3137i | 1.39274i | 0.717685 | + | 0.696368i | \(0.245202\pi\) | ||||
−0.717685 | + | 0.696368i | \(0.754798\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1.27208 | 0.0603023 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 11.5563i | 0.545378i | 0.962102 | + | 0.272689i | \(0.0879130\pi\) | ||||
−0.962102 | + | 0.272689i | \(0.912087\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 5.48888i | 0.258461i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −22.0000 | −1.02912 | −0.514558 | − | 0.857455i | \(-0.672044\pi\) | ||||
−0.514558 | + | 0.857455i | \(0.672044\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 5.17186 | 0.240877 | 0.120439 | − | 0.992721i | \(-0.461570\pi\) | ||||
0.120439 | + | 0.992721i | \(0.461570\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 2.82843 | 0.131448 | 0.0657241 | − | 0.997838i | \(-0.479064\pi\) | ||||
0.0657241 | + | 0.997838i | \(0.479064\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −6.23172 | −0.288370 | −0.144185 | − | 0.989551i | \(-0.546056\pi\) | ||||
−0.144185 | + | 0.989551i | \(0.546056\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 13.6569i | 0.627943i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 16.3128i | 0.748483i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 23.3324 | 1.06609 | 0.533043 | − | 0.846088i | \(-0.321048\pi\) | ||||
0.533043 | + | 0.846088i | \(0.321048\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0.0769232i | 0.00350740i | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − 9.07107i | − 0.411896i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −19.7990 | −0.897178 | −0.448589 | − | 0.893738i | \(-0.648073\pi\) | ||||
−0.448589 | + | 0.893738i | \(0.648073\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − 34.4853i | − 1.55630i | −0.628079 | − | 0.778149i | \(-0.716159\pi\) | ||||
0.628079 | − | 0.778149i | \(-0.283841\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − 37.8519i | − 1.70476i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −26.1421 | −1.17028 | −0.585141 | − | 0.810931i | \(-0.698961\pi\) | ||||
−0.585141 | + | 0.810931i | \(0.698961\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 29.5641 | 1.31820 | 0.659100 | − | 0.752055i | \(-0.270937\pi\) | ||||
0.659100 | + | 0.752055i | \(0.270937\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 9.07107 | 0.403657 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −12.9343 | −0.573303 | −0.286652 | − | 0.958035i | \(-0.592542\pi\) | ||||
−0.286652 | + | 0.958035i | \(0.592542\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − 6.82843i | − 0.300896i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 23.9665i | 1.05404i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 2.03347 | 0.0890879 | 0.0445439 | − | 0.999007i | \(-0.485817\pi\) | ||||
0.0445439 | + | 0.999007i | \(0.485817\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 18.2150i | 0.796485i | 0.917280 | + | 0.398242i | \(0.130380\pi\) | ||||
−0.917280 | + | 0.398242i | \(0.869620\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − 37.4558i | − 1.63160i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 12.9411 | 0.562658 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0.870058i | 0.0376864i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − 5.48888i | − 0.237305i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 8.34315 | 0.358700 | 0.179350 | − | 0.983785i | \(-0.442601\pi\) | ||||
0.179350 | + | 0.983785i | \(0.442601\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −8.47343 | −0.362962 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −16.0000 | −0.684111 | −0.342055 | − | 0.939680i | \(-0.611123\pi\) | ||||
−0.342055 | + | 0.939680i | \(0.611123\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −25.2346 | −1.07503 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − 16.7279i | − 0.708785i | −0.935097 | − | 0.354392i | \(-0.884688\pi\) | ||||
0.935097 | − | 0.354392i | \(-0.115312\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 2.16478i | 0.0915606i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −22.0643 | −0.929900 | −0.464950 | − | 0.885337i | \(-0.653928\pi\) | ||||
−0.464950 | + | 0.885337i | \(0.653928\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − 8.10201i | − 0.340854i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − 0.485281i | − 0.0203441i | −0.999948 | − | 0.0101720i | \(-0.996762\pi\) | ||||
0.999948 | − | 0.0101720i | \(-0.00323791\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 2.62742 | 0.109954 | 0.0549770 | − | 0.998488i | \(-0.482491\pi\) | ||||
0.0549770 | + | 0.998488i | \(0.482491\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 14.0000i | 0.583840i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 19.8770i | 0.827491i | 0.910393 | + | 0.413745i | \(0.135780\pi\) | ||||
−0.910393 | + | 0.413745i | \(0.864220\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 24.4853 | 1.01408 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −28.0334 | −1.15706 | −0.578531 | − | 0.815660i | \(-0.696374\pi\) | ||||
−0.578531 | + | 0.815660i | \(0.696374\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −24.9706 | −1.02889 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −30.7779 | −1.26389 | −0.631947 | − | 0.775011i | \(-0.717744\pi\) | ||||
−0.631947 | + | 0.775011i | \(0.717744\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − 9.31371i | − 0.380548i | −0.981731 | − | 0.190274i | \(-0.939062\pi\) | ||||
0.981731 | − | 0.190274i | \(-0.0609376\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − 23.9121i | − 0.975394i | −0.873013 | − | 0.487697i | \(-0.837837\pi\) | ||||
0.873013 | − | 0.487697i | \(-0.162163\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 5.35757 | 0.217816 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − 12.6173i | − 0.512120i | −0.966661 | − | 0.256060i | \(-0.917576\pi\) | ||||
0.966661 | − | 0.256060i | \(-0.0824245\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 3.79899i | 0.153691i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −45.2132 | −1.82614 | −0.913072 | − | 0.407798i | \(-0.866297\pi\) | ||||
−0.913072 | + | 0.407798i | \(0.866297\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − 17.4558i | − 0.702746i | −0.936236 | − | 0.351373i | \(-0.885715\pi\) | ||||
0.936236 | − | 0.351373i | \(-0.114285\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − 1.79337i | − 0.0720815i | −0.999350 | − | 0.0360407i | \(-0.988525\pi\) | ||||
0.999350 | − | 0.0360407i | \(-0.0114746\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 16.5563 | 0.662254 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −1.34502 | −0.0536296 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 12.4853 | 0.497031 | 0.248516 | − | 0.968628i | \(-0.420057\pi\) | ||||
0.248516 | + | 0.968628i | \(0.420057\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −0.896683 | −0.0355838 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − 23.4558i | − 0.926450i | −0.886241 | − | 0.463225i | \(-0.846692\pi\) | ||||
0.886241 | − | 0.463225i | \(-0.153308\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 32.5168i | − 1.28234i | −0.767400 | − | 0.641169i | \(-0.778450\pi\) | ||||
0.767400 | − | 0.641169i | \(-0.221550\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 6.38557 | 0.251043 | 0.125521 | − | 0.992091i | \(-0.459940\pi\) | ||||
0.125521 | + | 0.992091i | \(0.459940\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 26.5027i | 1.04032i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − 5.85786i | − 0.229236i | −0.993410 | − | 0.114618i | \(-0.963436\pi\) | ||||
0.993410 | − | 0.114618i | \(-0.0365644\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −12.9706 | −0.506802 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 2.97056i | 0.115717i | 0.998325 | + | 0.0578583i | \(0.0184272\pi\) | ||||
−0.998325 | + | 0.0578583i | \(0.981573\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 23.3868i | 0.909642i | 0.890583 | + | 0.454821i | \(0.150297\pi\) | ||||
−0.890583 | + | 0.454821i | \(0.849703\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −21.6569 | −0.838557 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 7.12840 | 0.275189 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 20.0416 | 0.772548 | 0.386274 | − | 0.922384i | \(-0.373762\pi\) | ||||
0.386274 | + | 0.922384i | \(0.373762\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 27.9790 | 1.07532 | 0.537661 | − | 0.843161i | \(-0.319308\pi\) | ||||
0.537661 | + | 0.843161i | \(0.319308\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − 46.9706i | − 1.79728i | −0.438688 | − | 0.898639i | \(-0.644557\pi\) | ||||
0.438688 | − | 0.898639i | \(-0.355443\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 8.28772i | 0.316657i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 3.88123 | 0.147863 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − 25.6060i | − 0.974098i | −0.873375 | − | 0.487049i | \(-0.838073\pi\) | ||||
0.873375 | − | 0.487049i | \(-0.161927\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − 12.0000i | − 0.455186i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −15.2132 | −0.576241 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − 15.4558i | − 0.583759i | −0.956455 | − | 0.291880i | \(-0.905719\pi\) | ||||
0.956455 | − | 0.291880i | \(-0.0942807\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0.896683i | 0.0338190i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −30.8701 | −1.15935 | −0.579675 | − | 0.814848i | \(-0.696820\pi\) | ||||
−0.579675 | + | 0.814848i | \(0.696820\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −21.4303 | −0.802570 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −0.485281 | −0.0181485 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −19.6369 | −0.732333 | −0.366167 | − | 0.930549i | \(-0.619330\pi\) | ||||
−0.366167 | + | 0.930549i | \(0.619330\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 30.1421i | 1.11945i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 53.7933i | 1.99508i | 0.0700903 | + | 0.997541i | \(0.477671\pi\) | ||||
−0.0700903 | + | 0.997541i | \(0.522329\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −37.8519 | −1.40000 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 22.3044i | − 0.823833i | −0.911222 | − | 0.411916i | \(-0.864860\pi\) | ||||
0.911222 | − | 0.411916i | \(-0.135140\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − 8.97056i | − 0.330435i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −2.54416 | −0.0935883 | −0.0467941 | − | 0.998905i | \(-0.514900\pi\) | ||||
−0.0467941 | + | 0.998905i | \(0.514900\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 43.6569i | 1.60161i | 0.598922 | + | 0.800807i | \(0.295596\pi\) | ||||
−0.598922 | + | 0.800807i | \(0.704404\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − 5.41196i | − 0.198279i | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 36.2843 | 1.32403 | 0.662016 | − | 0.749490i | \(-0.269701\pi\) | ||||
0.662016 | + | 0.749490i | \(0.269701\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −7.76245 | −0.282505 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 18.1005 | 0.657874 | 0.328937 | − | 0.944352i | \(-0.393310\pi\) | ||||
0.328937 | + | 0.944352i | \(0.393310\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 53.6619 | 1.94524 | 0.972622 | − | 0.232394i | \(-0.0746557\pi\) | ||||
0.972622 | + | 0.232394i | \(0.0746557\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 4.20101i | 0.151690i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 14.2793i | 0.514926i | 0.966288 | + | 0.257463i | \(0.0828866\pi\) | ||||
−0.966288 | + | 0.257463i | \(0.917113\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 33.5767 | 1.20767 | 0.603835 | − | 0.797110i | \(-0.293639\pi\) | ||||
0.603835 | + | 0.797110i | \(0.293639\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 29.8268i | 1.07141i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 10.1421i | 0.363380i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 18.6274 | 0.666541 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 4.72792i | 0.168747i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 50.4692i | − 1.79903i | −0.436889 | − | 0.899515i | \(-0.643920\pi\) | ||||
0.436889 | − | 0.899515i | \(-0.356080\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1.12994 | 0.0401254 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 26.3714 | 0.934122 | 0.467061 | − | 0.884225i | \(-0.345313\pi\) | ||||
0.467061 | + | 0.884225i | \(0.345313\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −66.4264 | −2.35000 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 23.7038 | 0.836490 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 21.2132i | 0.745817i | 0.927868 | + | 0.372908i | \(0.121639\pi\) | ||||
−0.927868 | + | 0.372908i | \(0.878361\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − 42.1814i | − 1.48119i | −0.671951 | − | 0.740595i | \(-0.734544\pi\) | ||||
0.671951 | − | 0.740595i | \(-0.265456\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −2.16478 | −0.0758291 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 25.2346i | 0.882846i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 51.0711i | 1.78239i | 0.453618 | + | 0.891196i | \(0.350133\pi\) | ||||
−0.453618 | + | 0.891196i | \(0.649867\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 40.2843 | 1.40422 | 0.702111 | − | 0.712068i | \(-0.252241\pi\) | ||||
0.702111 | + | 0.712068i | \(0.252241\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − 18.4853i | − 0.642796i | −0.946944 | − | 0.321398i | \(-0.895847\pi\) | ||||
0.946944 | − | 0.321398i | \(-0.104153\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 35.3701i | 1.22845i | 0.789130 | + | 0.614226i | \(0.210532\pi\) | ||||
−0.789130 | + | 0.614226i | \(0.789468\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −1.85786 | −0.0642940 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 32.8882 | 1.13543 | 0.567714 | − | 0.823226i | \(-0.307828\pi\) | ||||
0.567714 | + | 0.823226i | \(0.307828\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −17.6274 | −0.607842 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 9.87285 | 0.339636 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0.769553i | 0.0263799i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 57.2805i | − 1.96125i | −0.195899 | − | 0.980624i | \(-0.562763\pi\) | ||||
0.195899 | − | 0.980624i | \(-0.437237\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 39.6227 | 1.35349 | 0.676743 | − | 0.736219i | \(-0.263391\pi\) | ||||
0.676743 | + | 0.736219i | \(0.263391\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − 13.7766i | − 0.470052i | −0.971989 | − | 0.235026i | \(-0.924483\pi\) | ||||
0.971989 | − | 0.235026i | \(-0.0755175\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 25.1127i | 0.854846i | 0.904052 | + | 0.427423i | \(0.140579\pi\) | ||||
−0.904052 | + | 0.427423i | \(0.859421\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −14.3848 | −0.489097 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − 22.6274i | − 0.767583i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − 1.42195i | − 0.0481809i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 0.928932 | 0.0313678 | 0.0156839 | − | 0.999877i | \(-0.495007\pi\) | ||||
0.0156839 | + | 0.999877i | \(0.495007\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 22.1187 | 0.745198 | 0.372599 | − | 0.927992i | \(-0.378467\pi\) | ||||
0.372599 | + | 0.927992i | \(0.378467\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 21.8579 | 0.735576 | 0.367788 | − | 0.929910i | \(-0.380115\pi\) | ||||
0.367788 | + | 0.929910i | \(0.380115\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −19.8995 | −0.668161 | −0.334081 | − | 0.942545i | \(-0.608426\pi\) | ||||
−0.334081 | + | 0.942545i | \(0.608426\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 44.2843i | 1.48192i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 7.12840i | 0.238276i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −46.1396 | −1.53884 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 67.8644i | 2.26089i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 1.27208i | 0.0422853i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 32.4853 | 1.07866 | 0.539328 | − | 0.842096i | \(-0.318678\pi\) | ||||
0.539328 | + | 0.842096i | \(0.318678\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 42.2843i | 1.40094i | 0.713682 | + | 0.700470i | \(0.247026\pi\) | ||||
−0.713682 | + | 0.700470i | \(0.752974\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 8.65914i | 0.286576i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 15.5147 | 0.511783 | 0.255892 | − | 0.966705i | \(-0.417631\pi\) | ||||
0.255892 | + | 0.966705i | \(0.417631\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 2.95268 | 0.0971887 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.07107 | 0.0352165 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 22.3044 | 0.731784 | 0.365892 | − | 0.930657i | \(-0.380764\pi\) | ||||
0.365892 | + | 0.930657i | \(0.380764\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − 8.48528i | − 0.277498i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 16.5210i | 0.539719i | 0.962900 | + | 0.269860i | \(0.0869773\pi\) | ||||
−0.962900 | + | 0.269860i | \(0.913023\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −2.37302 | −0.0773584 | −0.0386792 | − | 0.999252i | \(-0.512315\pi\) | ||||
−0.0386792 | + | 0.999252i | \(0.512315\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 8.70420i | 0.283448i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − 8.82843i | − 0.286885i | −0.989659 | − | 0.143443i | \(-0.954183\pi\) | ||||
0.989659 | − | 0.143443i | \(-0.0458173\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 3.75736 | 0.121969 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − 58.8701i | − 1.90699i | −0.301412 | − | 0.953494i | \(-0.597458\pi\) | ||||
0.301412 | − | 0.953494i | \(-0.402542\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − 13.2513i | − 0.428803i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −14.6569 | −0.472802 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −7.39104 | −0.237926 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −15.5147 | −0.498920 | −0.249460 | − | 0.968385i | \(-0.580253\pi\) | ||||
−0.249460 | + | 0.968385i | \(0.580253\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −25.2346 | −0.809816 | −0.404908 | − | 0.914357i | \(-0.632696\pi\) | ||||
−0.404908 | + | 0.914357i | \(0.632696\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − 0.485281i | − 0.0155255i | −0.999970 | − | 0.00776276i | \(-0.997529\pi\) | ||||
0.999970 | − | 0.00776276i | \(-0.00247099\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − 3.32410i | − 0.106239i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −7.01962 | −0.223891 | −0.111946 | − | 0.993714i | \(-0.535708\pi\) | ||||
−0.111946 | + | 0.993714i | \(0.535708\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 2.35049i | 0.0748930i | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 21.6569i | 0.688648i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 9.85786 | 0.313145 | 0.156573 | − | 0.987666i | \(-0.449955\pi\) | ||||
0.156573 | + | 0.987666i | \(0.449955\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 5.65685i | 0.179334i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − 15.4705i | − 0.489956i | −0.969529 | − | 0.244978i | \(-0.921219\pi\) | ||||
0.969529 | − | 0.244978i | \(-0.0787808\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 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 | 7056.2.k.e.881.5 | 8 | ||
3.2 | odd | 2 | inner | 7056.2.k.e.881.4 | 8 | ||
4.3 | odd | 2 | 1764.2.f.b.881.6 | yes | 8 | ||
7.6 | odd | 2 | inner | 7056.2.k.e.881.3 | 8 | ||
12.11 | even | 2 | 1764.2.f.b.881.3 | ✓ | 8 | ||
21.20 | even | 2 | inner | 7056.2.k.e.881.6 | 8 | ||
28.3 | even | 6 | 1764.2.t.c.1097.6 | 16 | |||
28.11 | odd | 6 | 1764.2.t.c.1097.4 | 16 | |||
28.19 | even | 6 | 1764.2.t.c.521.5 | 16 | |||
28.23 | odd | 6 | 1764.2.t.c.521.3 | 16 | |||
28.27 | even | 2 | 1764.2.f.b.881.4 | yes | 8 | ||
84.11 | even | 6 | 1764.2.t.c.1097.5 | 16 | |||
84.23 | even | 6 | 1764.2.t.c.521.6 | 16 | |||
84.47 | odd | 6 | 1764.2.t.c.521.4 | 16 | |||
84.59 | odd | 6 | 1764.2.t.c.1097.3 | 16 | |||
84.83 | odd | 2 | 1764.2.f.b.881.5 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1764.2.f.b.881.3 | ✓ | 8 | 12.11 | even | 2 | ||
1764.2.f.b.881.4 | yes | 8 | 28.27 | even | 2 | ||
1764.2.f.b.881.5 | yes | 8 | 84.83 | odd | 2 | ||
1764.2.f.b.881.6 | yes | 8 | 4.3 | odd | 2 | ||
1764.2.t.c.521.3 | 16 | 28.23 | odd | 6 | |||
1764.2.t.c.521.4 | 16 | 84.47 | odd | 6 | |||
1764.2.t.c.521.5 | 16 | 28.19 | even | 6 | |||
1764.2.t.c.521.6 | 16 | 84.23 | even | 6 | |||
1764.2.t.c.1097.3 | 16 | 84.59 | odd | 6 | |||
1764.2.t.c.1097.4 | 16 | 28.11 | odd | 6 | |||
1764.2.t.c.1097.5 | 16 | 84.11 | even | 6 | |||
1764.2.t.c.1097.6 | 16 | 28.3 | even | 6 | |||
7056.2.k.e.881.3 | 8 | 7.6 | odd | 2 | inner | ||
7056.2.k.e.881.4 | 8 | 3.2 | odd | 2 | inner | ||
7056.2.k.e.881.5 | 8 | 1.1 | even | 1 | trivial | ||
7056.2.k.e.881.6 | 8 | 21.20 | even | 2 | inner |