Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1280,3,Mod(1279,1280)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1280, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1280.1279");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1280 = 2^{8} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1280.h (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: | \(34.8774738381\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.493995311104.27 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 10x^{6} + 41x^{4} + 46x^{2} + 64 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{11} \) |
Twist minimal: | no (minimal twist has level 640) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1279.7 | ||
Root | \(0.707107 + 2.24979i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1280.1279 |
Dual form | 1280.3.h.h.1279.8 |
$q$-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 \(\left(\mathbb{Z}/1280\mathbb{Z}\right)^\times\).
\(n\) | \(257\) | \(261\) | \(511\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 3.62258 | 1.20753 | 0.603764 | − | 0.797163i | \(-0.293667\pi\) | ||||
0.603764 | + | 0.797163i | \(0.293667\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.561553 | − | 4.96837i | 0.112311 | − | 0.993673i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −6.45101 | −0.921573 | −0.460786 | − | 0.887511i | \(-0.652433\pi\) | ||||
−0.460786 | + | 0.887511i | \(0.652433\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 4.12311 | 0.458123 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.94566i | 0.358696i | 0.983786 | + | 0.179348i | \(0.0573988\pi\) | ||||
−0.983786 | + | 0.179348i | \(0.942601\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 15.5167i | 1.19359i | 0.802392 | + | 0.596797i | \(0.203560\pi\) | ||||
−0.802392 | + | 0.596797i | \(0.796440\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 2.03427 | − | 17.9983i | 0.135618 | − | 1.19989i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 25.4535i | 1.49726i | 0.662987 | + | 0.748631i | \(0.269289\pi\) | ||||
−0.662987 | + | 0.748631i | \(0.730711\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 32.0510i | 1.68689i | 0.537213 | + | 0.843447i | \(0.319477\pi\) | ||||
−0.537213 | + | 0.843447i | \(0.680523\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −23.3693 | −1.11282 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 15.2845 | 0.664543 | 0.332271 | − | 0.943184i | \(-0.392185\pi\) | ||||
0.332271 | + | 0.943184i | \(0.392185\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −24.3693 | − | 5.58000i | −0.974773 | − | 0.223200i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −17.6670 | −0.654332 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −34.7386 | −1.19788 | −0.598942 | − | 0.800792i | \(-0.704412\pi\) | ||||
−0.598942 | + | 0.800792i | \(0.704412\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 20.2140i | − | 0.652065i | −0.945359 | − | 0.326032i | \(-0.894288\pi\) | ||
0.945359 | − | 0.326032i | \(-0.105712\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 14.2935i | 0.433135i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −3.62258 | + | 32.0510i | −0.103502 | + | 0.915742i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 9.93673i | − | 0.268560i | −0.990943 | − | 0.134280i | \(-0.957128\pi\) | ||
0.990943 | − | 0.134280i | \(-0.0428722\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 56.2106i | 1.44130i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 42.3542 | 1.03303 | 0.516514 | − | 0.856279i | \(-0.327229\pi\) | ||||
0.516514 | + | 0.856279i | \(0.327229\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 52.9460 | 1.23130 | 0.615651 | − | 0.788019i | \(-0.288893\pi\) | ||||
0.615651 | + | 0.788019i | \(0.288893\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 2.31534 | − | 20.4851i | 0.0514520 | − | 0.455224i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −21.6377 | −0.460377 | −0.230189 | − | 0.973146i | \(-0.573934\pi\) | ||||
−0.230189 | + | 0.973146i | \(0.573934\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −7.38447 | −0.150704 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 92.2073i | 1.80799i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 35.3902i | 0.667740i | 0.942619 | + | 0.333870i | \(0.108355\pi\) | ||||
−0.942619 | + | 0.333870i | \(0.891645\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 19.6035 | + | 2.21569i | 0.356427 | + | 0.0402853i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 116.107i | 2.03697i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − | 16.2684i | − | 0.275735i | −0.990451 | − | 0.137867i | \(-0.955975\pi\) | ||
0.990451 | − | 0.137867i | \(-0.0440248\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 77.3390 | 1.26785 | 0.633926 | − | 0.773393i | \(-0.281442\pi\) | ||||
0.633926 | + | 0.773393i | \(0.281442\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −26.5982 | −0.422194 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 77.0928 | + | 8.71346i | 1.18604 | + | 0.134053i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 14.0444 | 0.209617 | 0.104809 | − | 0.994492i | \(-0.466577\pi\) | ||||
0.104809 | + | 0.994492i | \(0.466577\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 55.3693 | 0.802454 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 107.990i | 1.52098i | 0.649347 | + | 0.760492i | \(0.275042\pi\) | ||||
−0.649347 | + | 0.760492i | \(0.724958\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 93.7873i | 1.28476i | 0.766387 | + | 0.642379i | \(0.222052\pi\) | ||||
−0.766387 | + | 0.642379i | \(0.777948\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −88.2799 | − | 20.2140i | −1.17706 | − | 0.269520i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − | 25.4535i | − | 0.330564i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 92.2073i | − | 1.16718i | −0.812048 | − | 0.583590i | \(-0.801647\pi\) | ||
0.812048 | − | 0.583590i | \(-0.198353\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −101.108 | −1.24825 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 26.7509 | 0.322300 | 0.161150 | − | 0.986930i | \(-0.448480\pi\) | ||||
0.161150 | + | 0.986930i | \(0.448480\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 126.462 | + | 14.2935i | 1.48779 | + | 0.168158i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −125.844 | −1.44648 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −27.7538 | −0.311840 | −0.155920 | − | 0.987770i | \(-0.549834\pi\) | ||||
−0.155920 | + | 0.987770i | \(0.549834\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 100.099i | − | 1.09998i | ||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | − | 73.2269i | − | 0.787386i | ||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 159.241 | + | 17.9983i | 1.67622 | + | 0.189456i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 133.534i | 1.37664i | 0.725406 | + | 0.688321i | \(0.241652\pi\) | ||||
−0.725406 | + | 0.688321i | \(0.758348\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 16.2684i | 0.164327i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −148.708 | −1.47236 | −0.736180 | − | 0.676786i | \(-0.763372\pi\) | ||||
−0.736180 | + | 0.676786i | \(0.763372\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 146.089 | 1.41834 | 0.709168 | − | 0.705040i | \(-0.249071\pi\) | ||||
0.709168 | + | 0.705040i | \(0.249071\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −13.1231 | + | 116.107i | −0.124982 | + | 1.10578i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −35.2790 | −0.329710 | −0.164855 | − | 0.986318i | \(-0.552716\pi\) | ||||
−0.164855 | + | 0.986318i | \(0.552716\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 24.1383 | 0.221452 | 0.110726 | − | 0.993851i | \(-0.464682\pi\) | ||||
0.110726 | + | 0.993851i | \(0.464682\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − | 35.9966i | − | 0.324294i | ||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 181.308i | 1.60449i | 0.596993 | + | 0.802246i | \(0.296362\pi\) | ||||
−0.596993 | + | 0.802246i | \(0.703638\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 8.58305 | − | 75.9389i | 0.0746352 | − | 0.660338i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 63.9771i | 0.546813i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − | 164.201i | − | 1.37984i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 105.432 | 0.871337 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 153.431 | 1.24741 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −41.4081 | + | 117.942i | −0.331265 | + | 0.943538i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −191.453 | −1.50751 | −0.753753 | − | 0.657158i | \(-0.771758\pi\) | ||||
−0.753753 | + | 0.657158i | \(0.771758\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 191.801 | 1.48683 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 224.357i | − | 1.71265i | −0.516439 | − | 0.856324i | \(-0.672743\pi\) | ||
0.516439 | − | 0.856324i | \(-0.327257\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − | 206.761i | − | 1.55460i | ||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −9.92093 | + | 87.7759i | −0.0734884 | + | 0.650192i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 55.8000i | − | 0.407299i | −0.979044 | − | 0.203650i | \(-0.934720\pi\) | ||
0.979044 | − | 0.203650i | \(-0.0652803\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 115.395i | − | 0.830183i | −0.909780 | − | 0.415092i | \(-0.863750\pi\) | ||
0.909780 | − | 0.415092i | \(-0.136250\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −78.3845 | −0.555918 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −61.2237 | −0.428138 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −19.5076 | + | 172.594i | −0.134535 | + | 1.19031i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −26.7509 | −0.181979 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −52.6307 | −0.353226 | −0.176613 | − | 0.984280i | \(-0.556514\pi\) | ||||
−0.176613 | + | 0.984280i | \(0.556514\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 231.762i | − | 1.53485i | −0.641138 | − | 0.767425i | \(-0.721538\pi\) | ||
0.641138 | − | 0.767425i | \(-0.278462\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 104.947i | 0.685930i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −100.431 | − | 11.3512i | −0.647939 | − | 0.0732338i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 162.658i | 1.03604i | 0.855370 | + | 0.518018i | \(0.173330\pi\) | ||||
−0.855370 | + | 0.518018i | \(0.826670\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 128.204i | 0.806314i | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −98.6004 | −0.612425 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −293.319 | −1.79951 | −0.899753 | − | 0.436400i | \(-0.856253\pi\) | ||||
−0.899753 | + | 0.436400i | \(0.856253\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 71.0152 | + | 8.02653i | 0.430395 | + | 0.0486457i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −246.934 | −1.47865 | −0.739324 | − | 0.673350i | \(-0.764855\pi\) | ||||
−0.739324 | + | 0.673350i | \(0.764855\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −71.7689 | −0.424668 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 132.150i | 0.772804i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 76.8967i | 0.444490i | 0.974991 | + | 0.222245i | \(0.0713384\pi\) | ||||
−0.974991 | + | 0.222245i | \(0.928662\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 157.207 | + | 35.9966i | 0.898324 | + | 0.205695i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | − | 58.9335i | − | 0.332957i | ||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 284.999i | − | 1.59217i | −0.605183 | − | 0.796086i | \(-0.706900\pi\) | ||
0.605183 | − | 0.796086i | \(-0.293100\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −176.769 | −0.976624 | −0.488312 | − | 0.872669i | \(-0.662387\pi\) | ||||
−0.488312 | + | 0.872669i | \(0.662387\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 280.167 | 1.53097 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −49.3693 | − | 5.58000i | −0.266861 | − | 0.0301622i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −100.431 | −0.537062 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 113.970 | 0.603014 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 265.271i | 1.38885i | 0.719564 | + | 0.694426i | \(0.244341\pi\) | ||||
−0.719564 | + | 0.694426i | \(0.755659\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 82.6273i | 0.428121i | 0.976820 | + | 0.214060i | \(0.0686689\pi\) | ||||
−0.976820 | + | 0.214060i | \(0.931331\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 279.275 | + | 31.5652i | 1.43218 | + | 0.161873i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 180.771i | − | 0.917621i | −0.888534 | − | 0.458811i | \(-0.848276\pi\) | ||
0.888534 | − | 0.458811i | \(-0.151724\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 171.120i | 0.859901i | 0.902852 | + | 0.429951i | \(0.141469\pi\) | ||||
−0.902852 | + | 0.429951i | \(0.858531\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 50.8769 | 0.253119 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 224.099 | 1.10394 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 23.7841 | − | 210.431i | 0.116020 | − | 1.02649i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 63.0196 | 0.304442 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −126.462 | −0.605082 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 96.1529i | − | 0.455701i | −0.973696 | − | 0.227851i | \(-0.926830\pi\) | ||
0.973696 | − | 0.227851i | \(-0.0731698\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 391.202i | 1.83663i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 29.7320 | − | 263.055i | 0.138288 | − | 1.22351i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 130.401i | 0.600925i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 339.752i | 1.55138i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −394.955 | −1.78712 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −79.8803 | −0.358208 | −0.179104 | − | 0.983830i | \(-0.557320\pi\) | ||||
−0.179104 | + | 0.983830i | \(0.557320\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −100.477 | − | 23.0069i | −0.446566 | − | 0.102253i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 229.897 | 1.01276 | 0.506381 | − | 0.862310i | \(-0.330983\pi\) | ||||
0.506381 | + | 0.862310i | \(0.330983\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 132.277 | 0.577627 | 0.288813 | − | 0.957385i | \(-0.406739\pi\) | ||||
0.288813 | + | 0.957385i | \(0.406739\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | − | 92.2073i | − | 0.399166i | ||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 81.2535i | 0.348727i | 0.984681 | + | 0.174364i | \(0.0557868\pi\) | ||||
−0.984681 | + | 0.174364i | \(0.944213\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −12.1507 | + | 107.504i | −0.0517052 | + | 0.457465i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − | 334.028i | − | 1.40940i | ||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 317.050i | 1.32657i | 0.748368 | + | 0.663284i | \(0.230838\pi\) | ||||
−0.748368 | + | 0.663284i | \(0.769162\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 446.725 | 1.85363 | 0.926816 | − | 0.375516i | \(-0.122534\pi\) | ||||
0.926816 | + | 0.375516i | \(0.122534\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −207.269 | −0.852960 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −4.14677 | + | 36.6888i | −0.0169256 | + | 0.149750i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −497.326 | −2.01347 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 96.9072 | 0.389186 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 253.434i | 1.00970i | 0.863208 | + | 0.504848i | \(0.168451\pi\) | ||||
−0.863208 | + | 0.504848i | \(0.831549\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 60.3073i | 0.238369i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 458.119 | + | 51.7793i | 1.79655 | + | 0.203056i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 85.7608i | − | 0.333700i | −0.985982 | − | 0.166850i | \(-0.946641\pi\) | ||
0.985982 | − | 0.166850i | \(-0.0533595\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 64.1020i | 0.247498i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −143.231 | −0.548778 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 302.587 | 1.15052 | 0.575260 | − | 0.817971i | \(-0.304901\pi\) | ||||
0.575260 | + | 0.817971i | \(0.304901\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 175.831 | + | 19.8735i | 0.663515 | + | 0.0749942i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −100.540 | −0.376556 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 173.339 | 0.644383 | 0.322191 | − | 0.946675i | \(-0.395581\pi\) | ||||
0.322191 | + | 0.946675i | \(0.395581\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 195.766i | − | 0.722383i | −0.932492 | − | 0.361191i | \(-0.882370\pi\) | ||
0.932492 | − | 0.361191i | \(-0.117630\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | − | 362.615i | − | 1.32826i | ||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 22.0168 | − | 96.1529i | 0.0800609 | − | 0.349647i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 365.213i | 1.31846i | 0.751943 | + | 0.659228i | \(0.229117\pi\) | ||||
−0.751943 | + | 0.659228i | \(0.770883\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | − | 83.3445i | − | 0.298726i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −268.756 | −0.956426 | −0.478213 | − | 0.878244i | \(-0.658715\pi\) | ||||
−0.478213 | + | 0.878244i | \(0.658715\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −43.6357 | −0.154190 | −0.0770949 | − | 0.997024i | \(-0.524564\pi\) | ||||
−0.0770949 | + | 0.997024i | \(0.524564\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 576.864 | + | 65.2004i | 2.02408 | + | 0.228773i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −273.227 | −0.952011 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −358.879 | −1.24180 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 483.739i | 1.66233i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 226.098i | − | 0.771667i | −0.922569 | − | 0.385833i | \(-0.873914\pi\) | ||
0.922569 | − | 0.385833i | \(-0.126086\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −80.8271 | − | 9.13554i | −0.273990 | − | 0.0309679i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − | 69.7077i | − | 0.234706i | ||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 237.165i | 0.793195i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −341.555 | −1.13473 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −538.708 | −1.77791 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 43.4299 | − | 384.248i | 0.142393 | − | 1.25983i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 172.436 | 0.561682 | 0.280841 | − | 0.959754i | \(-0.409387\pi\) | ||||
0.280841 | + | 0.959754i | \(0.409387\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 529.218 | 1.71268 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 78.9131i | 0.253740i | 0.991919 | + | 0.126870i | \(0.0404931\pi\) | ||||
−0.991919 | + | 0.126870i | \(0.959507\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 338.922i | − | 1.08282i | −0.840760 | − | 0.541408i | \(-0.817891\pi\) | ||
0.840760 | − | 0.541408i | \(-0.182109\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −14.9363 | + | 132.150i | −0.0474168 | + | 0.419522i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 101.278i | 0.319487i | 0.987159 | + | 0.159744i | \(0.0510668\pi\) | ||||
−0.987159 | + | 0.159744i | \(0.948933\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 137.067i | − | 0.429676i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −127.801 | −0.398134 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −815.808 | −2.52572 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 86.5834 | − | 378.132i | 0.266410 | − | 1.16348i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 87.4428 | 0.267409 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 139.585 | 0.424271 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 153.335i | − | 0.463248i | −0.972805 | − | 0.231624i | \(-0.925596\pi\) | ||
0.972805 | − | 0.231624i | \(-0.0744039\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − | 40.9702i | − | 0.123034i | ||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 7.88666 | − | 69.7776i | 0.0235423 | − | 0.208291i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 146.454i | 0.434581i | 0.976107 | + | 0.217291i | \(0.0697219\pi\) | ||||
−0.976107 | + | 0.217291i | \(0.930278\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 656.802i | 1.93747i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 79.7575 | 0.233893 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 363.737 | 1.06046 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 31.0928 | − | 275.095i | 0.0901240 | − | 0.797377i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 332.832 | 0.959169 | 0.479585 | − | 0.877496i | \(-0.340787\pi\) | ||||
0.479585 | + | 0.877496i | \(0.340787\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 307.170 | 0.880145 | 0.440072 | − | 0.897962i | \(-0.354953\pi\) | ||||
0.440072 | + | 0.897962i | \(0.354953\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − | 274.133i | − | 0.781007i | ||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 177.788i | − | 0.503650i | −0.967773 | − | 0.251825i | \(-0.918969\pi\) | ||
0.967773 | − | 0.251825i | \(-0.0810308\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 536.533 | + | 60.6420i | 1.51136 | + | 0.170823i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | − | 594.830i | − | 1.66619i | ||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 447.742i | − | 1.24719i | −0.781746 | − | 0.623596i | \(-0.785671\pi\) | ||
0.781746 | − | 0.623596i | \(-0.214329\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −666.265 | −1.84561 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 381.935 | 1.05216 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 465.970 | + | 52.6665i | 1.27663 | + | 0.144292i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 417.312 | 1.13709 | 0.568545 | − | 0.822652i | \(-0.307506\pi\) | ||||
0.568545 | + | 0.822652i | \(0.307506\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 174.631 | 0.473254 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 228.302i | − | 0.615371i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 206.225i | 0.552882i | 0.961031 | + | 0.276441i | \(0.0891550\pi\) | ||||
−0.961031 | + | 0.276441i | \(0.910845\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −150.004 | + | 427.255i | −0.400012 | + | 1.13935i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 539.030i | − | 1.42979i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 573.943i | − | 1.51436i | −0.653205 | − | 0.757181i | \(-0.726576\pi\) | ||
0.653205 | − | 0.757181i | \(-0.273424\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −693.555 | −1.82035 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 144.219 | 0.376551 | 0.188275 | − | 0.982116i | \(-0.439710\pi\) | ||||
0.188275 | + | 0.982116i | \(0.439710\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −126.462 | − | 14.2935i | −0.328473 | − | 0.0371259i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 218.302 | 0.564087 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −470.358 | −1.20915 | −0.604573 | − | 0.796550i | \(-0.706656\pi\) | ||||
−0.604573 | + | 0.796550i | \(0.706656\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 389.043i | 0.994995i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 812.751i | − | 2.06807i | ||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −458.119 | − | 51.7793i | −1.15980 | − | 0.131087i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 337.011i | 0.848895i | 0.905453 | + | 0.424448i | \(0.139532\pi\) | ||||
−0.905453 | + | 0.424448i | \(0.860468\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | − | 749.009i | − | 1.87722i | ||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 228.739 | 0.570421 | 0.285210 | − | 0.958465i | \(-0.407937\pi\) | ||||
0.285210 | + | 0.958465i | \(0.407937\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 313.655 | 0.778301 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −56.7775 | + | 502.341i | −0.140191 | + | 1.24035i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 39.2069 | 0.0963315 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 576.263 | 1.40896 | 0.704478 | − | 0.709726i | \(-0.251181\pi\) | ||||
0.704478 | + | 0.709726i | \(0.251181\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − | 202.140i | − | 0.491825i | ||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 104.947i | 0.254110i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 15.0220 | − | 132.908i | 0.0361976 | − | 0.320260i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | − | 418.030i | − | 1.00247i | ||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 435.905i | − | 1.04035i | −0.854061 | − | 0.520173i | \(-0.825867\pi\) | ||
0.854061 | − | 0.520173i | \(-0.174133\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −429.616 | −1.02046 | −0.510232 | − | 0.860037i | \(-0.670441\pi\) | ||||
−0.510232 | + | 0.860037i | \(0.670441\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −89.2147 | −0.210909 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 142.030 | − | 620.283i | 0.334189 | − | 1.45949i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −498.915 | −1.16842 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −221.788 | −0.516988 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 690.856i | 1.60291i | 0.598053 | + | 0.801457i | \(0.295941\pi\) | ||||
−0.598053 | + | 0.801457i | \(0.704059\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 70.0935i | − | 0.161879i | −0.996719 | − | 0.0809393i | \(-0.974208\pi\) | ||
0.996719 | − | 0.0809393i | \(-0.0257920\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −70.6678 | + | 625.237i | −0.162455 | + | 1.43733i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 489.883i | 1.12101i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 816.571i | 1.86007i | 0.367469 | + | 0.930036i | \(0.380224\pi\) | ||||
−0.367469 | + | 0.930036i | \(0.619776\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −30.4470 | −0.0690407 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −199.242 | −0.449756 | −0.224878 | − | 0.974387i | \(-0.572198\pi\) | ||||
−0.224878 | + | 0.974387i | \(0.572198\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −15.5852 | + | 137.891i | −0.0350230 | + | 0.309867i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −190.659 | −0.426530 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −3.00187 | −0.00668567 | −0.00334283 | − | 0.999994i | \(-0.501064\pi\) | ||||
−0.00334283 | + | 0.999994i | \(0.501064\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 167.115i | 0.370543i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − | 839.579i | − | 1.85337i | ||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −497.326 | − | 56.2106i | −1.09303 | − | 0.123540i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 345.188i | 0.755336i | 0.925941 | + | 0.377668i | \(0.123274\pi\) | ||||
−0.925941 | + | 0.377668i | \(0.876726\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | − | 449.685i | − | 0.979706i | ||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −799.663 | −1.73463 | −0.867313 | − | 0.497763i | \(-0.834155\pi\) | ||||
−0.867313 | + | 0.497763i | \(0.834155\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −245.737 | −0.530749 | −0.265375 | − | 0.964145i | \(-0.585496\pi\) | ||||
−0.265375 | + | 0.964145i | \(0.585496\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −363.818 | − | 41.1208i | −0.782405 | − | 0.0884318i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −331.439 | −0.709719 | −0.354860 | − | 0.934920i | \(-0.615471\pi\) | ||||
−0.354860 | + | 0.934920i | \(0.615471\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −90.6004 | −0.193178 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 589.240i | 1.25104i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 208.907i | 0.441663i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 178.844 | − | 781.060i | 0.376515 | − | 1.64434i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 145.918i | 0.305907i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − | 310.676i | − | 0.648592i | −0.945956 | − | 0.324296i | \(-0.894873\pi\) | ||
0.945956 | − | 0.324296i | \(-0.105127\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 154.186 | 0.320552 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −357.188 | −0.739520 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 663.447 | + | 74.9865i | 1.36793 | + | 0.154611i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 173.615 | 0.356498 | 0.178249 | − | 0.983985i | \(-0.442957\pi\) | ||||
0.178249 | + | 0.983985i | \(0.442957\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −1062.57 | −2.17295 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 470.930i | − | 0.959125i | −0.877508 | − | 0.479563i | \(-0.840795\pi\) | ||
0.877508 | − | 0.479563i | \(-0.159205\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 884.219i | − | 1.79355i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 80.8271 | + | 9.13554i | 0.163287 | + | 0.0184556i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 696.644i | − | 1.40170i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 114.424i | − | 0.229307i | −0.993406 | − | 0.114653i | \(-0.963424\pi\) | ||
0.993406 | − | 0.114653i | \(-0.0365757\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −894.540 | −1.78551 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 279.067 | 0.554806 | 0.277403 | − | 0.960754i | \(-0.410526\pi\) | ||||
0.277403 | + | 0.960754i | \(0.410526\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −83.5076 | + | 738.837i | −0.165362 | + | 1.46304i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −259.989 | −0.512799 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 332.155 | 0.652564 | 0.326282 | − | 0.945272i | \(-0.394204\pi\) | ||||
0.326282 | + | 0.945272i | \(0.394204\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 605.023i | − | 1.18400i | ||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | − | 566.243i | − | 1.10379i | ||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 82.0364 | − | 725.821i | 0.159294 | − | 1.40936i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 85.3750i | − | 0.165135i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 278.565i | 0.536734i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 746.924 | 1.43364 | 0.716818 | − | 0.697260i | \(-0.245598\pi\) | ||||
0.716818 | + | 0.697260i | \(0.245598\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 584.018 | 1.11667 | 0.558335 | − | 0.829616i | \(-0.311441\pi\) | ||||
0.558335 | + | 0.829616i | \(0.311441\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 569.494 | + | 130.401i | 1.08475 | + | 0.248382i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 514.517 | 0.976312 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −295.384 | −0.558383 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − | 67.0761i | − | 0.126320i | ||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 657.198i | 1.23302i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −19.8110 | + | 175.279i | −0.0370300 | + | 0.327624i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | − | 1032.43i | − | 1.92259i | ||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − | 29.1366i | − | 0.0540567i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −271.905 | −0.502598 | −0.251299 | − | 0.967910i | \(-0.580858\pi\) | ||||
−0.251299 | + | 0.967910i | \(0.580858\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −640.360 | −1.17930 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 13.5549 | − | 119.928i | 0.0248714 | − | 0.220051i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 19.1146 | 0.0349445 | 0.0174722 | − | 0.999847i | \(-0.494438\pi\) | ||||
0.0174722 | + | 0.999847i | \(0.494438\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 318.877 | 0.580832 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 1113.41i | − | 2.02070i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 594.830i | 1.07564i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −178.844 | − | 20.2140i | −0.322242 | − | 0.0364216i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 868.015i | − | 1.55837i | −0.626791 | − | 0.779187i | \(-0.715632\pi\) | ||
0.626791 | − | 0.779187i | \(-0.284368\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 821.548i | 1.46967i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −363.818 | −0.648517 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 912.726 | 1.62118 | 0.810592 | − | 0.585612i | \(-0.199146\pi\) | ||||
0.810592 | + | 0.585612i | \(0.199146\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 900.803 | + | 101.814i | 1.59434 | + | 0.180202i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 652.248 | 1.15035 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −115.434 | −0.202871 | −0.101436 | − | 0.994842i | \(-0.532344\pi\) | ||||
−0.101436 | + | 0.994842i | \(0.532344\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 347.158i | − | 0.607982i | −0.952675 | − | 0.303991i | \(-0.901681\pi\) | ||
0.952675 | − | 0.303991i | \(-0.0983193\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 960.965i | 1.67708i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −372.472 | − | 85.2874i | −0.647778 | − | 0.148326i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 70.4792i | − | 0.122148i | −0.998133 | − | 0.0610738i | \(-0.980547\pi\) | ||
0.998133 | − | 0.0610738i | \(-0.0194525\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 299.324i | 0.516968i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −172.570 | −0.297022 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −139.638 | −0.239515 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 317.862 | + | 35.9265i | 0.543353 | + | 0.0614129i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 461.461 | 0.786134 | 0.393067 | − | 0.919510i | \(-0.371414\pi\) | ||||
0.393067 | + | 0.919510i | \(0.371414\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 647.879 | 1.09996 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | − | 654.859i | − | 1.10805i | ||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 222.428i | − | 0.375090i | −0.982256 | − | 0.187545i | \(-0.939947\pi\) | ||
0.982256 | − | 0.187545i | \(-0.0600531\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −815.808 | − | 92.2073i | −1.37111 | − | 0.154970i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 619.898i | 1.03835i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 206.571i | − | 0.344861i | −0.985022 | − | 0.172430i | \(-0.944838\pi\) | ||
0.985022 | − | 0.172430i | \(-0.0551620\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 102.941 | 0.171283 | 0.0856416 | − | 0.996326i | \(-0.472706\pi\) | ||||
0.0856416 | + | 0.996326i | \(0.472706\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 57.9064 | 0.0960306 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 59.2055 | − | 523.824i | 0.0978604 | − | 0.865824i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 857.703 | 1.41302 | 0.706510 | − | 0.707703i | \(-0.250269\pi\) | ||||
0.706510 | + | 0.707703i | \(0.250269\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 811.818 | 1.33303 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 335.747i | − | 0.549504i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 299.711i | 0.488925i | 0.969659 | + | 0.244462i | \(0.0786115\pi\) | ||||
−0.969659 | + | 0.244462i | \(0.921389\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 86.1599 | − | 762.304i | 0.140097 | − | 1.23952i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 189.334i | − | 0.306863i | −0.988159 | − | 0.153431i | \(-0.950968\pi\) | ||
0.988159 | − | 0.153431i | \(-0.0490324\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 269.762i | 0.435803i | 0.975971 | + | 0.217901i | \(0.0699211\pi\) | ||||
−0.975971 | + | 0.217901i | \(0.930079\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −270.030 | −0.434831 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 179.040 | 0.287384 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 562.727 | + | 271.962i | 0.900364 | + | 0.435138i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −458.119 | −0.730653 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 252.924 | 0.402105 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 569.026i | 0.901785i | 0.892578 | + | 0.450892i | \(0.148894\pi\) | ||||
−0.892578 | + | 0.450892i | \(0.851106\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | − | 348.322i | − | 0.550272i | ||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −107.511 | + | 951.209i | −0.169309 | + | 1.49797i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − | 114.583i | − | 0.179879i | ||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 445.254i | 0.696798i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −173.093 | −0.270036 | −0.135018 | − | 0.990843i | \(-0.543109\pi\) | ||||
−0.135018 | + | 0.990843i | \(0.543109\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −551.298 | −0.857384 | −0.428692 | − | 0.903451i | \(-0.641026\pi\) | ||||
−0.428692 | + | 0.903451i | \(0.641026\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 107.706 | − | 952.938i | 0.166987 | − | 1.47742i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 518.940 | 0.802071 | 0.401036 | − | 0.916062i | \(-0.368650\pi\) | ||||
0.401036 | + | 0.916062i | \(0.368650\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 64.1893 | 0.0989050 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 472.388i | 0.725634i | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − | 150.509i | − | 0.230489i | −0.993337 | − | 0.115245i | \(-0.963235\pi\) | ||
0.993337 | − | 0.115245i | \(-0.0367652\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −1114.69 | − | 125.988i | −1.70181 | − | 0.192348i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 386.695i | 0.588577i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 397.420i | − | 0.603065i | −0.953456 | − | 0.301533i | \(-0.902502\pi\) | ||
0.953456 | − | 0.301533i | \(-0.0974983\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −673.953 | −1.01960 | −0.509798 | − | 0.860294i | \(-0.670280\pi\) | ||||
−0.509798 | + | 0.860294i | \(0.670280\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −1430.76 | −2.15800 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −1027.27 | − | 116.107i | −1.54476 | − | 0.174597i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −530.962 | −0.796045 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −289.373 | −0.432546 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 305.153i | 0.454774i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1132.10i | 1.68217i | 0.540903 | + | 0.841085i | \(0.318083\pi\) | ||||
−0.540903 | + | 0.841085i | \(0.681917\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 430.532 | + | 98.5816i | 0.637825 | + | 0.146047i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 1088.08i | − | 1.60721i | −0.595163 | − | 0.803605i | \(-0.702912\pi\) | ||
0.595163 | − | 0.803605i | \(-0.297088\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 861.431i | − | 1.26868i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 832.820 | 1.22294 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 24.4045 | 0.0357313 | 0.0178657 | − | 0.999840i | \(-0.494313\pi\) | ||||
0.0178657 | + | 0.999840i | \(0.494313\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −277.235 | − | 31.3346i | −0.404722 | − | 0.0457440i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 479.183 | 0.697500 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −549.140 | −0.797010 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 349.646i | 0.506001i | 0.967466 | + | 0.253000i | \(0.0814173\pi\) | ||||
−0.967466 | + | 0.253000i | \(0.918583\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | − | 104.947i | − | 0.151439i | ||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −573.327 | − | 64.8007i | −0.824931 | − | 0.0932384i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1078.06i | 1.54671i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 294.347i | 0.421098i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 819.714 | 1.16935 | 0.584675 | − | 0.811268i | \(-0.301222\pi\) | ||||
0.584675 | + | 0.811268i | \(0.301222\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 318.482 | 0.453033 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −44.0170 | + | 389.443i | −0.0624355 | + | 0.552401i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 959.319 | 1.35689 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 719.231 | 1.01443 | 0.507215 | − | 0.861819i | \(-0.330675\pi\) | ||||
0.507215 | + | 0.861819i | \(0.330675\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − | 380.180i | − | 0.534712i | ||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 308.961i | − | 0.433325i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −34.3803 | + | 304.182i | −0.0480844 | + | 0.425429i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 1148.54i | 1.60187i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 600.046i | 0.834556i | 0.908779 | + | 0.417278i | \(0.137016\pi\) | ||||
−0.908779 | + | 0.417278i | \(0.862984\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −942.419 | −1.30710 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 1618.30 | 2.23831 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 846.557 | + | 193.842i | 1.16766 | + | 0.267368i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 452.279 | 0.622117 | 0.311059 | − | 0.950391i | \(-0.399316\pi\) | ||||
0.311059 | + | 0.950391i | \(0.399316\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 159.121 | 0.218273 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1347.66i | 1.84358i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 773.541i | 1.05531i | 0.849459 | + | 0.527654i | \(0.176928\pi\) | ||||
−0.849459 | + | 0.527654i | \(0.823072\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −15.0220 | + | 132.908i | −0.0204381 | + | 0.180827i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 55.4142i | 0.0751889i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 34.5394i | 0.0467381i | 0.999727 | + | 0.0233690i | \(0.00743927\pi\) | ||||
−0.999727 | + | 0.0233690i | \(0.992561\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −1801.61 | −2.43132 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −396.078 | −0.533079 | −0.266539 | − | 0.963824i | \(-0.585880\pi\) | ||||
−0.266539 | + | 0.963824i | \(0.585880\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −29.5549 | + | 261.488i | −0.0396710 | + | 0.350991i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 110.297 | 0.147653 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 227.585 | 0.303852 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 850.079i | 1.13193i | 0.824429 | + | 0.565965i | \(0.191496\pi\) | ||||
−0.824429 | + | 0.565965i | \(0.808504\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 918.084i | 1.21924i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −1151.48 | − | 130.147i | −1.52514 | − | 0.172380i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 458.313i | − | 0.605433i | −0.953081 | − | 0.302717i | \(-0.902106\pi\) | ||
0.953081 | − | 0.302717i | \(-0.0978936\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 218.468i | 0.287837i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −788.678 | −1.03637 | −0.518185 | − | 0.855268i | \(-0.673392\pi\) | ||||
−0.518185 | + | 0.855268i | \(0.673392\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −155.716 | −0.204084 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 521.417 | + | 58.9335i | 0.681590 | + | 0.0770372i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 252.432 | 0.329116 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 980.098 | 1.27451 | 0.637255 | − | 0.770653i | \(-0.280070\pi\) | ||||
0.637255 | + | 0.770653i | \(0.280070\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | − | 310.676i | − | 0.402951i | ||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 193.305i | − | 0.250071i | −0.992152 | − | 0.125036i | \(-0.960095\pi\) | ||
0.992152 | − | 0.125036i | \(-0.0399045\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −112.794 | + | 492.602i | −0.145541 | + | 0.635615i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 232.215i | 0.298861i | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1357.49i | 1.74261i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −426.091 | −0.545571 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 613.726 | 0.783813 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 808.142 | + | 91.3408i | 1.02948 | + | 0.116358i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −679.927 | −0.863948 | −0.431974 | − | 0.901886i | \(-0.642183\pi\) | ||||
−0.431974 | + | 0.901886i | \(0.642183\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 1096.15 | 1.38928 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 1169.62i | − | 1.47866i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1200.05i | 1.51330i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 636.964 | + | 71.9933i | 0.801212 | + | 0.0905576i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 324.477i | 0.407124i | 0.979062 | + | 0.203562i | \(0.0652518\pi\) | ||||
−0.979062 | + | 0.203562i | \(0.934748\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 550.755i | − | 0.689306i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −114.432 | −0.142861 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −370.052 | −0.460837 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −55.3693 | + | 489.883i | −0.0687818 | + | 0.608550i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 627.935 | 0.778110 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 392.712 | 0.485429 | 0.242714 | − | 0.970098i | \(-0.421962\pi\) | ||||
0.242714 | + | 0.970098i | \(0.421962\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 606.480i | 0.747818i | 0.927465 | + | 0.373909i | \(0.121983\pi\) | ||||
−0.927465 | + | 0.373909i | \(0.878017\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − | 709.178i | − | 0.872297i | ||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −164.714 | + | 1457.32i | −0.202103 | + | 1.78812i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1696.97i | 2.07707i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | − | 412.717i | − | 0.503928i | ||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −750.634 | −0.914293 | −0.457146 | − | 0.889391i | \(-0.651128\pi\) | ||||
−0.457146 | + | 0.889391i | \(0.651128\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 557.389 | 0.677265 | 0.338632 | − | 0.940919i | \(-0.390036\pi\) | ||||
0.338632 | + | 0.940919i | \(0.390036\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 79.7575 | − | 348.322i | 0.0966758 | − | 0.422208i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 1394.76 | 1.68652 | 0.843262 | − | 0.537502i | \(-0.180632\pi\) | ||||
0.843262 | + | 0.537502i | \(0.180632\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −392.570 | −0.473547 | −0.236773 | − | 0.971565i | \(-0.576090\pi\) | ||||
−0.236773 | + | 0.971565i | \(0.576090\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 1323.01i | 1.59207i | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − | 187.960i | − | 0.225643i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −138.667 | + | 1226.86i | −0.166068 | + | 1.46929i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 357.120i | 0.426667i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 10.8057i | − | 0.0128793i | −0.999979 | − | 0.00643963i | \(-0.997950\pi\) | ||
0.999979 | − | 0.00643963i | \(-0.00204981\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 365.773 | 0.434926 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −973.590 | −1.15491 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −40.3021 | + | 356.574i | −0.0476947 | + | 0.421981i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −680.142 | −0.803001 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −158.074 | −0.186188 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 151.878i | − | 0.178470i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 222.965i | 0.261389i | 0.991423 | + | 0.130695i | \(0.0417207\pi\) | ||||
−0.991423 | + | 0.130695i | \(0.958279\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 656.567 | + | 74.2090i | 0.767915 | + | 0.0867941i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 1258.77i | 1.46880i | 0.678714 | + | 0.734402i | \(0.262537\pi\) | ||||
−0.678714 | + | 0.734402i | \(0.737463\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 667.122i | 0.776626i | 0.921527 | + | 0.388313i | \(0.126942\pi\) | ||||
−0.921527 | + | 0.388313i | \(0.873058\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −989.788 | −1.14958 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 235.010 | 0.272317 | 0.136159 | − | 0.990687i | \(-0.456524\pi\) | ||||
0.136159 | + | 0.990687i | \(0.456524\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 382.051 | + | 43.1816i | 0.441678 | + | 0.0499209i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −1300.07 | −1.49950 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 363.818 | 0.418663 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 217.923i | 0.250198i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 550.576i | 0.630671i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 267.124 | − | 760.846i | 0.305285 | − | 0.869539i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 1577.19i | − | 1.79840i | −0.437543 | − | 0.899198i | \(-0.644151\pi\) | ||
0.437543 | − | 0.899198i | \(-0.355849\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | − | 819.060i | − | 0.931809i | ||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −220.324 | −0.250084 | −0.125042 | − | 0.992151i | \(-0.539907\pi\) | ||||
−0.125042 | + | 0.992151i | \(0.539907\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1144.57 | 1.29623 | 0.648115 | − | 0.761542i | \(-0.275558\pi\) | ||||
0.648115 | + | 0.761542i | \(0.275558\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −292.803 | − | 33.0943i | −0.330851 | − | 0.0373946i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 773.413 | 0.871942 | 0.435971 | − | 0.899961i | \(-0.356405\pi\) | ||||
0.435971 | + | 0.899961i | \(0.356405\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1235.07 | 1.38928 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | − | 398.937i | − | 0.447741i | ||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − | 693.510i | − | 0.776607i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −1415.98 | − | 160.042i | −1.58210 | − | 0.178818i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 859.151i | 0.957805i | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 702.207i | 0.781098i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −900.803 | −0.999781 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −1237.31 | −1.37022 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −99.2651 | + | 878.253i | −0.109685 | + | 0.970445i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −271.474 | −0.299310 | −0.149655 | − | 0.988738i | \(-0.547816\pi\) | ||||
−0.149655 | + | 0.988738i | \(0.547816\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −613.140 | −0.674522 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 663.176i | − | 0.727965i | −0.931406 | − | 0.363983i | \(-0.881417\pi\) | ||
0.931406 | − | 0.363983i | \(-0.118583\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 105.550i | 0.115608i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 157.329 | − | 1391.97i | 0.171944 | − | 1.52128i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 1447.33i | 1.57833i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 1017.31i | − | 1.10698i | −0.832856 | − | 0.553490i | \(-0.813296\pi\) | ||
0.832856 | − | 0.553490i | \(-0.186704\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 624.665 | 0.678246 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −1675.65 | −1.81544 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −55.4470 | + | 242.151i | −0.0599427 | + | 0.261785i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 602.338 | 0.649772 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −800.790 | −0.861991 | −0.430996 | − | 0.902354i | \(-0.641838\pi\) | ||||
−0.430996 | + | 0.902354i | \(0.641838\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − | 236.680i | − | 0.254221i | ||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 285.869i | 0.306398i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −56.3971 | + | 498.976i | −0.0603177 | + | 0.533664i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 795.927i | 0.849441i | 0.905324 | + | 0.424721i | \(0.139628\pi\) | ||||
−0.905324 | + | 0.424721i | \(0.860372\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | − | 1227.77i | − | 1.30753i | ||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −159.663 | −0.169674 | −0.0848368 | − | 0.996395i | \(-0.527037\pi\) | ||||
−0.0848368 | + | 0.996395i | \(0.527037\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 647.362 | 0.686492 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 64.0000 | − | 566.243i | 0.0677249 | − | 0.599199i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −138.776 | −0.146543 | −0.0732716 | − | 0.997312i | \(-0.523344\pi\) | ||||
−0.0732716 | + | 0.997312i | \(0.523344\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −1455.27 | −1.53348 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 366.886i | 0.385790i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 141.561i | − | 0.148542i | −0.997238 | − | 0.0742711i | \(-0.976337\pi\) | ||
0.997238 | − | 0.0742711i | \(-0.0236630\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1317.96 | + | 148.963i | 1.38006 | + | 0.155983i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − | 496.535i | − | 0.518846i | ||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 359.966i | 0.375356i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 552.394 | 0.574811 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −145.459 | −0.151048 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 410.523 | + | 46.3996i | 0.425412 | + | 0.0480825i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −278.872 | −0.288389 | −0.144194 | − | 0.989549i | \(-0.546059\pi\) | ||||
−0.144194 | + | 0.989549i | \(0.546059\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −2955.33 | −3.04988 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 88.2616i | − | 0.0908977i | −0.998967 | − | 0.0454488i | \(-0.985528\pi\) | ||
0.998967 | − | 0.0454488i | \(-0.0144718\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 744.417i | 0.765074i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 313.655 | − | 1369.81i | 0.321698 | − | 1.40494i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 521.989i | − | 0.534277i | −0.963658 | − | 0.267139i | \(-0.913922\pi\) | ||
0.963658 | − | 0.267139i | \(-0.0860782\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 109.507i | − | 0.111856i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 99.5246 | 0.101452 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −1819.43 | −1.85090 | −0.925448 | − | 0.378876i | \(-0.876311\pi\) | ||||
−0.925448 | + | 0.378876i | \(0.876311\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −898.138 | − | 101.513i | −0.911815 | − | 0.103059i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 505.659 | 0.512319 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 809.252 | 0.818253 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 593.672i | − | 0.599063i | −0.954086 | − | 0.299532i | \(-0.903170\pi\) | ||
0.954086 | − | 0.299532i | \(-0.0968304\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − | 555.469i | − | 0.559385i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 850.189 | + | 96.0931i | 0.854461 | + | 0.0965760i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 639.235i | 0.641158i | 0.947222 | + | 0.320579i | \(0.103878\pi\) | ||||
−0.947222 | + | 0.320579i | \(0.896122\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 175.552i | 0.175727i |
(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 | 1280.3.h.h.1279.7 | 8 | ||
4.3 | odd | 2 | inner | 1280.3.h.h.1279.1 | 8 | ||
5.4 | even | 2 | inner | 1280.3.h.h.1279.2 | 8 | ||
8.3 | odd | 2 | 1280.3.h.l.1279.8 | 8 | |||
8.5 | even | 2 | 1280.3.h.l.1279.2 | 8 | |||
16.3 | odd | 4 | 640.3.e.i.319.1 | ✓ | 16 | ||
16.5 | even | 4 | 640.3.e.i.319.4 | yes | 16 | ||
16.11 | odd | 4 | 640.3.e.i.319.16 | yes | 16 | ||
16.13 | even | 4 | 640.3.e.i.319.13 | yes | 16 | ||
20.19 | odd | 2 | inner | 1280.3.h.h.1279.8 | 8 | ||
40.19 | odd | 2 | 1280.3.h.l.1279.1 | 8 | |||
40.29 | even | 2 | 1280.3.h.l.1279.7 | 8 | |||
80.19 | odd | 4 | 640.3.e.i.319.15 | yes | 16 | ||
80.29 | even | 4 | 640.3.e.i.319.3 | yes | 16 | ||
80.59 | odd | 4 | 640.3.e.i.319.2 | yes | 16 | ||
80.69 | even | 4 | 640.3.e.i.319.14 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
640.3.e.i.319.1 | ✓ | 16 | 16.3 | odd | 4 | ||
640.3.e.i.319.2 | yes | 16 | 80.59 | odd | 4 | ||
640.3.e.i.319.3 | yes | 16 | 80.29 | even | 4 | ||
640.3.e.i.319.4 | yes | 16 | 16.5 | even | 4 | ||
640.3.e.i.319.13 | yes | 16 | 16.13 | even | 4 | ||
640.3.e.i.319.14 | yes | 16 | 80.69 | even | 4 | ||
640.3.e.i.319.15 | yes | 16 | 80.19 | odd | 4 | ||
640.3.e.i.319.16 | yes | 16 | 16.11 | odd | 4 | ||
1280.3.h.h.1279.1 | 8 | 4.3 | odd | 2 | inner | ||
1280.3.h.h.1279.2 | 8 | 5.4 | even | 2 | inner | ||
1280.3.h.h.1279.7 | 8 | 1.1 | even | 1 | trivial | ||
1280.3.h.h.1279.8 | 8 | 20.19 | odd | 2 | inner | ||
1280.3.h.l.1279.1 | 8 | 40.19 | odd | 2 | |||
1280.3.h.l.1279.2 | 8 | 8.5 | even | 2 | |||
1280.3.h.l.1279.7 | 8 | 40.29 | even | 2 | |||
1280.3.h.l.1279.8 | 8 | 8.3 | odd | 2 |