Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [384,3,Mod(257,384)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(384, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("384.257");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 384 = 2^{7} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 384.e (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(10.4632421514\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 18x^{6} + 99x^{4} + 170x^{2} + 81 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{10}\cdot 3 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 257.3 | ||
Root | \(2.55118i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 384.257 |
Dual form | 384.3.e.a.257.4 |
$q$-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 \(\left(\mathbb{Z}/384\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(133\) | \(257\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) |
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 | ||||||||
\(3\) | −1.57844 | − | 2.55118i | −0.526147 | − | 0.850394i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.31534i | 0.263067i | 0.991312 | + | 0.131534i | \(0.0419902\pi\) | ||||
−0.991312 | + | 0.131534i | \(0.958010\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 10.2329 | 1.46184 | 0.730920 | − | 0.682463i | \(-0.239091\pi\) | ||||
0.730920 | + | 0.682463i | \(0.239091\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −4.01705 | + | 8.05378i | −0.446339 | + | 0.894864i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 16.6620i | 1.51473i | 0.652991 | + | 0.757366i | \(0.273514\pi\) | ||||
−0.652991 | + | 0.757366i | \(0.726486\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −18.7454 | −1.44196 | −0.720978 | − | 0.692958i | \(-0.756307\pi\) | ||||
−0.720978 | + | 0.692958i | \(0.756307\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 3.35566 | − | 2.07618i | 0.223711 | − | 0.138412i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 4.38114i | 0.257714i | 0.991663 | + | 0.128857i | \(0.0411308\pi\) | ||||
−0.991663 | + | 0.128857i | \(0.958869\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 11.5544 | 0.608129 | 0.304064 | − | 0.952652i | \(-0.401656\pi\) | ||||
0.304064 | + | 0.952652i | \(0.401656\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −16.1520 | − | 26.1059i | −0.769143 | − | 1.24314i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 16.7490i | 0.728219i | 0.931356 | + | 0.364109i | \(0.118627\pi\) | ||||
−0.931356 | + | 0.364109i | \(0.881373\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 23.2699 | 0.930796 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 26.8873 | − | 2.46419i | 0.995827 | − | 0.0912663i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 12.5498i | 0.432752i | 0.976310 | + | 0.216376i | \(0.0694237\pi\) | ||||
−0.976310 | + | 0.216376i | \(0.930576\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 20.3167 | 0.655377 | 0.327688 | − | 0.944786i | \(-0.393730\pi\) | ||||
0.327688 | + | 0.944786i | \(0.393730\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 42.5079 | − | 26.3001i | 1.28812 | − | 0.796971i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 13.4597i | 0.384562i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 18.5778 | 0.502103 | 0.251052 | − | 0.967974i | \(-0.419224\pi\) | ||||
0.251052 | + | 0.967974i | \(0.419224\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 29.5885 | + | 47.8230i | 0.758681 | + | 1.22623i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 78.6737i | 1.91887i | 0.281930 | + | 0.959435i | \(0.409025\pi\) | ||||
−0.281930 | + | 0.959435i | \(0.590975\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 36.4860 | 0.848511 | 0.424255 | − | 0.905543i | \(-0.360536\pi\) | ||||
0.424255 | + | 0.905543i | \(0.360536\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −10.5934 | − | 5.28377i | −0.235410 | − | 0.117417i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − | 19.9175i | − | 0.423777i | −0.977294 | − | 0.211888i | \(-0.932039\pi\) | ||
0.977294 | − | 0.211888i | \(-0.0679613\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 55.7118 | 1.13698 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 11.1771 | − | 6.91537i | 0.219158 | − | 0.135596i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 81.3064i | − | 1.53408i | −0.641598 | − | 0.767041i | \(-0.721728\pi\) | ||
0.641598 | − | 0.767041i | \(-0.278272\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −21.9162 | −0.398476 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −18.2380 | − | 29.4775i | −0.319965 | − | 0.517149i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 29.9477i | 0.507589i | 0.967258 | + | 0.253794i | \(0.0816787\pi\) | ||||
−0.967258 | + | 0.253794i | \(0.918321\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −72.0687 | −1.18145 | −0.590727 | − | 0.806872i | \(-0.701159\pi\) | ||||
−0.590727 | + | 0.806872i | \(0.701159\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −41.1060 | + | 82.4133i | −0.652476 | + | 1.30815i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − | 24.6565i | − | 0.379331i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 56.3520 | 0.841074 | 0.420537 | − | 0.907275i | \(-0.361842\pi\) | ||||
0.420537 | + | 0.907275i | \(0.361842\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 42.7298 | − | 26.4374i | 0.619273 | − | 0.383150i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 136.465i | − | 1.92204i | −0.276479 | − | 0.961020i | \(-0.589168\pi\) | ||
0.276479 | − | 0.961020i | \(-0.410832\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −80.8141 | −1.10704 | −0.553521 | − | 0.832835i | \(-0.686716\pi\) | ||||
−0.553521 | + | 0.832835i | \(0.686716\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −36.7301 | − | 59.3657i | −0.489735 | − | 0.791543i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 170.501i | 2.21429i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 86.0317 | 1.08901 | 0.544504 | − | 0.838758i | \(-0.316718\pi\) | ||||
0.544504 | + | 0.838758i | \(0.316718\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −48.7266 | − | 64.7048i | −0.601563 | − | 0.798825i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 80.4263i | 0.968992i | 0.874793 | + | 0.484496i | \(0.160997\pi\) | ||||
−0.874793 | + | 0.484496i | \(0.839003\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −5.76268 | −0.0677962 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 32.0168 | − | 19.8091i | 0.368009 | − | 0.227691i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 131.830i | 1.48124i | 0.671923 | + | 0.740621i | \(0.265468\pi\) | ||||
−0.671923 | + | 0.740621i | \(0.734532\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −191.820 | −2.10791 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −32.0687 | − | 51.8315i | −0.344824 | − | 0.557328i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 15.1980i | 0.159979i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −20.4375 | −0.210696 | −0.105348 | − | 0.994435i | \(-0.533596\pi\) | ||||
−0.105348 | + | 0.994435i | \(0.533596\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −134.192 | − | 66.9323i | −1.35548 | − | 0.676083i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 143.374i | 1.41954i | 0.704431 | + | 0.709772i | \(0.251202\pi\) | ||||
−0.704431 | + | 0.709772i | \(0.748798\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −113.748 | −1.10435 | −0.552173 | − | 0.833730i | \(-0.686201\pi\) | ||||
−0.552173 | + | 0.833730i | \(0.686201\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 34.3381 | − | 21.2453i | 0.327029 | − | 0.202336i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 6.26024i | − | 0.0585069i | −0.999572 | − | 0.0292535i | \(-0.990687\pi\) | ||
0.999572 | − | 0.0292535i | \(-0.00931300\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 147.657 | 1.35465 | 0.677327 | − | 0.735682i | \(-0.263138\pi\) | ||||
0.677327 | + | 0.735682i | \(0.263138\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −29.3240 | − | 47.3954i | −0.264180 | − | 0.426986i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 51.3905i | − | 0.454783i | −0.973803 | − | 0.227392i | \(-0.926980\pi\) | ||
0.973803 | − | 0.227392i | \(-0.0730197\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −22.0306 | −0.191571 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 75.3013 | − | 150.971i | 0.643601 | − | 1.29035i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 44.8317i | 0.376737i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −156.624 | −1.29441 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 200.711 | − | 124.182i | 1.63179 | − | 1.00961i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 63.4912i | 0.507929i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −145.579 | −1.14629 | −0.573147 | − | 0.819452i | \(-0.694278\pi\) | ||||
−0.573147 | + | 0.819452i | \(0.694278\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −57.5909 | − | 93.0823i | −0.446441 | − | 0.721568i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 45.3993i | 0.346560i | 0.984873 | + | 0.173280i | \(0.0554365\pi\) | ||||
−0.984873 | + | 0.173280i | \(0.944563\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 118.235 | 0.888987 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 3.24124 | + | 35.3659i | 0.0240092 | + | 0.261969i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 179.157i | − | 1.30771i | −0.756618 | − | 0.653857i | \(-0.773150\pi\) | ||
0.756618 | − | 0.653857i | \(-0.226850\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −50.8841 | −0.366073 | −0.183036 | − | 0.983106i | \(-0.558593\pi\) | ||||
−0.183036 | + | 0.983106i | \(0.558593\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −50.8131 | + | 31.4386i | −0.360377 | + | 0.222969i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 312.337i | − | 2.18418i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −16.5072 | −0.113843 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −87.9378 | − | 142.131i | −0.598216 | − | 0.966877i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 76.0410i | 0.510342i | 0.966896 | + | 0.255171i | \(0.0821318\pi\) | ||||
−0.966896 | + | 0.255171i | \(0.917868\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −179.918 | −1.19151 | −0.595754 | − | 0.803167i | \(-0.703147\pi\) | ||||
−0.595754 | + | 0.803167i | \(0.703147\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −35.2847 | − | 17.5993i | −0.230619 | − | 0.115028i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 26.7233i | 0.172408i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 67.2180 | 0.428140 | 0.214070 | − | 0.976818i | \(-0.431328\pi\) | ||||
0.214070 | + | 0.976818i | \(0.431328\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −207.427 | + | 128.337i | −1.30457 | + | 0.807153i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 171.391i | 1.06454i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 102.723 | 0.630204 | 0.315102 | − | 0.949058i | \(-0.397961\pi\) | ||||
0.315102 | + | 0.949058i | \(0.397961\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 34.5934 | + | 55.9122i | 0.209657 | + | 0.338862i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 80.7935i | − | 0.483793i | −0.970302 | − | 0.241897i | \(-0.922231\pi\) | ||
0.970302 | − | 0.241897i | \(-0.0777695\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 182.391 | 1.07924 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −46.4148 | + | 93.0569i | −0.271431 | + | 0.544192i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − | 169.185i | − | 0.977950i | −0.872298 | − | 0.488975i | \(-0.837371\pi\) | ||
0.872298 | − | 0.488975i | \(-0.162629\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 238.118 | 1.36067 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 76.4021 | − | 47.2707i | 0.431650 | − | 0.267066i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 170.982i | − | 0.955205i | −0.878576 | − | 0.477602i | \(-0.841506\pi\) | ||
0.878576 | − | 0.477602i | \(-0.158494\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −39.6292 | −0.218946 | −0.109473 | − | 0.993990i | \(-0.534916\pi\) | ||||
−0.109473 | + | 0.993990i | \(0.534916\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 113.756 | + | 183.860i | 0.621618 | + | 1.00470i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 24.4361i | 0.132087i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −72.9988 | −0.390368 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 275.135 | − | 25.2158i | 1.45574 | − | 0.133417i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 239.917i | 1.25611i | 0.778170 | + | 0.628054i | \(0.216148\pi\) | ||||
−0.778170 | + | 0.628054i | \(0.783852\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −13.4972 | −0.0699337 | −0.0349669 | − | 0.999388i | \(-0.511133\pi\) | ||||
−0.0349669 | + | 0.999388i | \(0.511133\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −62.9033 | + | 38.9189i | −0.322581 | + | 0.199584i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 16.6040i | 0.0842843i | 0.999112 | + | 0.0421422i | \(0.0134182\pi\) | ||||
−0.999112 | + | 0.0421422i | \(0.986582\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 143.674 | 0.721979 | 0.360990 | − | 0.932570i | \(-0.382439\pi\) | ||||
0.360990 | + | 0.932570i | \(0.382439\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −88.9483 | − | 143.764i | −0.442529 | − | 0.715244i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 128.421i | 0.632614i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −103.482 | −0.504792 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −134.893 | − | 67.2817i | −0.651657 | − | 0.325032i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 192.521i | 0.921151i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 83.6553 | 0.396471 | 0.198235 | − | 0.980154i | \(-0.436479\pi\) | ||||
0.198235 | + | 0.980154i | \(0.436479\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −348.146 | + | 215.402i | −1.63449 | + | 1.01128i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 47.9913i | 0.223215i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 207.898 | 0.958056 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 127.560 | + | 206.171i | 0.582467 | + | 0.941422i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 82.1263i | − | 0.371612i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 146.898 | 0.658734 | 0.329367 | − | 0.944202i | \(-0.393165\pi\) | ||||
0.329367 | + | 0.944202i | \(0.393165\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −93.4763 | + | 187.410i | −0.415450 | + | 0.832936i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − | 28.5250i | − | 0.125661i | −0.998024 | − | 0.0628304i | \(-0.979987\pi\) | ||
0.998024 | − | 0.0628304i | \(-0.0200127\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −345.118 | −1.50707 | −0.753533 | − | 0.657410i | \(-0.771652\pi\) | ||||
−0.753533 | + | 0.657410i | \(0.771652\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 434.978 | − | 269.125i | 1.88302 | − | 1.16504i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 105.272i | 0.451809i | 0.974149 | + | 0.225905i | \(0.0725338\pi\) | ||||
−0.974149 | + | 0.225905i | \(0.927466\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 26.1982 | 0.111482 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −135.796 | − | 219.482i | −0.572978 | − | 0.926086i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 280.456i | − | 1.17346i | −0.809783 | − | 0.586729i | \(-0.800415\pi\) | ||
0.809783 | − | 0.586729i | \(-0.199585\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −369.833 | −1.53458 | −0.767289 | − | 0.641302i | \(-0.778395\pi\) | ||||
−0.767289 | + | 0.641302i | \(0.778395\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −88.1616 | + | 226.443i | −0.362805 | + | 0.931865i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 73.2798i | 0.299101i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −216.593 | −0.876894 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 205.182 | − | 126.948i | 0.824025 | − | 0.509832i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 27.4959i | − | 0.109545i | −0.998499 | − | 0.0547727i | \(-0.982557\pi\) | ||
0.998499 | − | 0.0547727i | \(-0.0174434\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −279.073 | −1.10306 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 9.09604 | + | 14.7016i | 0.0356708 | + | 0.0576534i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 4.92447i | 0.0191614i | 0.999954 | + | 0.00958068i | \(0.00304967\pi\) | ||||
−0.999954 | + | 0.00958068i | \(0.996950\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 190.105 | 0.733995 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −101.073 | − | 50.4132i | −0.387254 | − | 0.193154i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 263.575i | 1.00219i | 0.865394 | + | 0.501093i | \(0.167068\pi\) | ||||
−0.865394 | + | 0.501093i | \(0.832932\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 106.945 | 0.403567 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 336.323 | − | 208.087i | 1.25964 | − | 0.779351i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 236.023i | − | 0.877409i | −0.898631 | − | 0.438704i | \(-0.855438\pi\) | ||
0.898631 | − | 0.438704i | \(-0.144562\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 433.288 | 1.59885 | 0.799424 | − | 0.600767i | \(-0.205138\pi\) | ||||
0.799424 | + | 0.600767i | \(0.205138\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 302.776 | + | 489.367i | 1.10907 | + | 1.79255i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 387.724i | 1.40991i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 244.067 | 0.881107 | 0.440553 | − | 0.897726i | \(-0.354782\pi\) | ||||
0.440553 | + | 0.897726i | \(0.354782\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −81.6131 | + | 163.626i | −0.292520 | + | 0.586473i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 431.627i | − | 1.53604i | −0.640426 | − | 0.768020i | \(-0.721242\pi\) | ||
0.640426 | − | 0.768020i | \(-0.278758\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −35.1843 | −0.124326 | −0.0621631 | − | 0.998066i | \(-0.519800\pi\) | ||||
−0.0621631 | + | 0.998066i | \(0.519800\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 38.7728 | − | 23.9891i | 0.136045 | − | 0.0841723i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 805.058i | 2.80508i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 269.806 | 0.933583 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 32.2594 | + | 52.1397i | 0.110857 | + | 0.179174i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 214.900i | − | 0.733446i | −0.930330 | − | 0.366723i | \(-0.880480\pi\) | ||
0.930330 | − | 0.366723i | \(-0.119520\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −39.3914 | −0.133530 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 41.0585 | + | 447.998i | 0.138244 | + | 1.50841i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − | 313.968i | − | 1.05006i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 373.356 | 1.24039 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 365.773 | − | 226.307i | 1.20717 | − | 0.746889i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − | 94.7946i | − | 0.310802i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 425.639 | 1.38645 | 0.693223 | − | 0.720723i | \(-0.256190\pi\) | ||||
0.693223 | + | 0.720723i | \(0.256190\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 179.544 | + | 290.191i | 0.581048 | + | 0.939128i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 7.67121i | − | 0.0246663i | −0.999924 | − | 0.0123331i | \(-0.996074\pi\) | ||
0.999924 | − | 0.0123331i | \(-0.00392586\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 313.959 | 1.00306 | 0.501532 | − | 0.865139i | \(-0.332770\pi\) | ||||
0.501532 | + | 0.865139i | \(0.332770\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −108.401 | − | 54.0682i | −0.344131 | − | 0.171645i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 361.930i | − | 1.14174i | −0.821042 | − | 0.570868i | \(-0.806607\pi\) | ||
0.821042 | − | 0.570868i | \(-0.193393\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −209.105 | −0.655503 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −15.9710 | + | 9.88142i | −0.0497539 | + | 0.0307832i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 50.6216i | 0.156723i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −436.204 | −1.34217 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −233.068 | − | 376.701i | −0.712748 | − | 1.15199i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − | 203.813i | − | 0.619493i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −283.000 | −0.854984 | −0.427492 | − | 0.904019i | \(-0.640603\pi\) | ||||
−0.427492 | + | 0.904019i | \(0.640603\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −74.6280 | + | 149.622i | −0.224108 | + | 0.449314i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 74.1218i | 0.221259i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 242.847 | 0.720614 | 0.360307 | − | 0.932834i | \(-0.382672\pi\) | ||||
0.360307 | + | 0.932834i | \(0.382672\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −131.106 | + | 81.1168i | −0.386745 | + | 0.239283i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 338.517i | 0.992720i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 68.6810 | 0.200236 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 34.7740 | + | 56.2041i | 0.100794 | + | 0.162910i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − | 35.8055i | − | 0.103186i | −0.998668 | − | 0.0515929i | \(-0.983570\pi\) | ||
0.998668 | − | 0.0515929i | \(-0.0164298\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −119.019 | −0.341030 | −0.170515 | − | 0.985355i | \(-0.554543\pi\) | ||||
−0.170515 | + | 0.985355i | \(0.554543\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −504.014 | + | 46.1923i | −1.43594 | + | 0.131602i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 158.225i | − | 0.448230i | −0.974563 | − | 0.224115i | \(-0.928051\pi\) | ||
0.974563 | − | 0.224115i | \(-0.0719492\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 179.497 | 0.505626 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 114.374 | − | 70.7641i | 0.320375 | − | 0.198219i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 127.881i | − | 0.356214i | −0.984011 | − | 0.178107i | \(-0.943003\pi\) | ||
0.984011 | − | 0.178107i | \(-0.0569974\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −227.495 | −0.630180 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 247.221 | + | 399.576i | 0.681051 | + | 1.10076i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − | 106.298i | − | 0.291227i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −92.6498 | −0.252452 | −0.126226 | − | 0.992002i | \(-0.540286\pi\) | ||||
−0.126226 | + | 0.992002i | \(0.540286\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −633.620 | − | 316.036i | −1.71713 | − | 0.856466i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 831.998i | − | 2.24258i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −9.37918 | −0.0251453 | −0.0125726 | − | 0.999921i | \(-0.504002\pi\) | ||||
−0.0125726 | + | 0.999921i | \(0.504002\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 161.977 | − | 100.217i | 0.431940 | − | 0.267245i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 235.251i | − | 0.624009i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 353.377 | 0.932392 | 0.466196 | − | 0.884681i | \(-0.345624\pi\) | ||||
0.466196 | + | 0.884681i | \(0.345624\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 229.789 | + | 371.400i | 0.603120 | + | 0.974802i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 106.620i | 0.278382i | 0.990266 | + | 0.139191i | \(0.0444502\pi\) | ||||
−0.990266 | + | 0.139191i | \(0.955550\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −224.266 | −0.582509 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −146.566 | + | 293.850i | −0.378723 | + | 0.759302i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − | 659.144i | − | 1.69446i | −0.531227 | − | 0.847229i | \(-0.678269\pi\) | ||
0.531227 | − | 0.847229i | \(-0.321731\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −73.3799 | −0.187672 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 115.822 | − | 71.6601i | 0.294712 | − | 0.182341i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 113.161i | 0.286483i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 523.170 | 1.31781 | 0.658904 | − | 0.752227i | \(-0.271020\pi\) | ||||
0.658904 | + | 0.752227i | \(0.271020\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −186.627 | − | 301.639i | −0.467738 | − | 0.755989i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 255.566i | 0.637323i | 0.947869 | + | 0.318661i | \(0.103233\pi\) | ||||
−0.947869 | + | 0.318661i | \(0.896767\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −380.845 | −0.945024 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 85.1086 | − | 64.0919i | 0.210145 | − | 0.158252i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 309.545i | 0.760552i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −630.598 | −1.54180 | −0.770902 | − | 0.636954i | \(-0.780194\pi\) | ||||
−0.770902 | + | 0.636954i | \(0.780194\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −457.061 | + | 282.788i | −1.11207 | + | 0.688050i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 306.452i | 0.742014i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −105.788 | −0.254910 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 80.3175 | + | 129.815i | 0.192608 | + | 0.311306i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 475.721i | − | 1.13537i | −0.823245 | − | 0.567686i | \(-0.807839\pi\) | ||
0.823245 | − | 0.567686i | \(-0.192161\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 239.614 | 0.569155 | 0.284578 | − | 0.958653i | \(-0.408147\pi\) | ||||
0.284578 | + | 0.958653i | \(0.408147\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 160.411 | + | 80.0096i | 0.379222 | + | 0.189148i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 101.949i | 0.239879i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −737.470 | −1.72710 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −796.828 | + | 493.006i | −1.85741 | + | 1.14920i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 618.539i | − | 1.43513i | −0.696494 | − | 0.717563i | \(-0.745258\pi\) | ||
0.696494 | − | 0.717563i | \(-0.254742\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 211.763 | 0.489061 | 0.244530 | − | 0.969642i | \(-0.421366\pi\) | ||||
0.244530 | + | 0.969642i | \(0.421366\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 26.0557 | + | 42.1129i | 0.0598981 | + | 0.0968112i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 193.526i | 0.442851i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −56.6884 | −0.129131 | −0.0645654 | − | 0.997913i | \(-0.520566\pi\) | ||||
−0.0645654 | + | 0.997913i | \(0.520566\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −223.797 | + | 448.690i | −0.507476 | + | 1.01744i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − | 687.493i | − | 1.55190i | −0.630792 | − | 0.775952i | \(-0.717270\pi\) | ||
0.630792 | − | 0.775952i | \(-0.282730\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −173.401 | −0.389666 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 193.994 | − | 120.026i | 0.433992 | − | 0.268515i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 490.455i | − | 1.09233i | −0.837679 | − | 0.546163i | \(-0.816088\pi\) | ||
0.837679 | − | 0.546163i | \(-0.183912\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1310.86 | −2.90657 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 283.989 | + | 459.002i | 0.626908 | + | 1.01325i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | − | 252.307i | − | 0.554522i | ||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −537.122 | −1.17532 | −0.587661 | − | 0.809107i | \(-0.699951\pi\) | ||||
−0.587661 | + | 0.809107i | \(0.699951\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 10.7960 | + | 117.797i | 0.0235206 | + | 0.256639i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 129.931i | − | 0.281847i | −0.990021 | − | 0.140923i | \(-0.954993\pi\) | ||
0.990021 | − | 0.140923i | \(-0.0450071\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 262.112 | 0.566118 | 0.283059 | − | 0.959103i | \(-0.408651\pi\) | ||||
0.283059 | + | 0.959103i | \(0.408651\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 68.1759 | − | 42.1811i | 0.146615 | − | 0.0907121i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 418.978i | 0.897169i | 0.893740 | + | 0.448585i | \(0.148072\pi\) | ||||
−0.893740 | + | 0.448585i | \(0.851928\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 576.643 | 1.22952 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −106.100 | − | 171.485i | −0.225264 | − | 0.364087i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 607.931i | 1.28527i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 268.871 | 0.566043 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 654.823 | + | 326.612i | 1.37280 | + | 0.684720i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − | 306.699i | − | 0.640290i | −0.947369 | − | 0.320145i | \(-0.896268\pi\) | ||
0.947369 | − | 0.320145i | \(-0.103732\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −348.249 | −0.724011 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 437.249 | − | 270.530i | 0.905278 | − | 0.560104i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − | 26.8822i | − | 0.0554272i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −387.411 | −0.795506 | −0.397753 | − | 0.917493i | \(-0.630210\pi\) | ||||
−0.397753 | + | 0.917493i | \(0.630210\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −162.143 | − | 262.066i | −0.331580 | − | 0.535922i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 13.1250i | − | 0.0267311i | −0.999911 | − | 0.0133655i | \(-0.995745\pi\) | ||
0.999911 | − | 0.0133655i | \(-0.00425451\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −54.9824 | −0.111526 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 88.0385 | − | 176.508i | 0.177855 | − | 0.356582i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 1396.43i | − | 2.80971i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 239.526 | 0.480012 | 0.240006 | − | 0.970771i | \(-0.422851\pi\) | ||||
0.240006 | + | 0.970771i | \(0.422851\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −206.119 | + | 127.528i | −0.411415 | + | 0.254546i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 595.462i | 1.18382i | 0.806004 | + | 0.591911i | \(0.201626\pi\) | ||||
−0.806004 | + | 0.591911i | \(0.798374\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −188.585 | −0.373436 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −287.893 | − | 465.312i | −0.567837 | − | 0.917775i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 600.556i | 1.17987i | 0.807449 | + | 0.589937i | \(0.200847\pi\) | ||||
−0.807449 | + | 0.589937i | \(0.799153\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −826.961 | −1.61832 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 310.668 | − | 28.4724i | 0.605591 | − | 0.0555017i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − | 149.616i | − | 0.290517i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 331.866 | 0.641908 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −431.622 | + | 267.049i | −0.831642 | + | 0.514545i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 394.528i | − | 0.757251i | −0.925550 | − | 0.378626i | \(-0.876397\pi\) | ||
0.925550 | − | 0.378626i | \(-0.123603\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 639.213 | 1.22221 | 0.611103 | − | 0.791551i | \(-0.290726\pi\) | ||||
0.611103 | + | 0.791551i | \(0.290726\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −375.855 | − | 607.482i | −0.715914 | − | 1.15711i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 89.0102i | 0.168900i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 248.470 | 0.469697 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −241.192 | − | 120.302i | −0.454223 | − | 0.226557i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 1474.77i | − | 2.76692i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 8.23433 | 0.0153913 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −436.205 | + | 269.884i | −0.812300 | + | 0.502578i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 928.273i | 1.72221i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −606.241 | −1.12059 | −0.560296 | − | 0.828292i | \(-0.689313\pi\) | ||||
−0.560296 | + | 0.828292i | \(0.689313\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 62.5524 | + | 101.101i | 0.115198 | + | 0.186190i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 194.219i | 0.356365i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 409.425 | 0.748492 | 0.374246 | − | 0.927330i | \(-0.377902\pi\) | ||||
0.374246 | + | 0.927330i | \(0.377902\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 289.503 | − | 580.425i | 0.527329 | − | 1.05724i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 145.006i | 0.263169i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 880.352 | 1.59196 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 62.3409 | − | 38.5709i | 0.112326 | − | 0.0694972i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 994.040i | 1.78463i | 0.451411 | + | 0.892316i | \(0.350921\pi\) | ||||
−0.451411 | + | 0.892316i | \(0.649079\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −683.945 | −1.22351 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 115.224 | + | 186.233i | 0.205391 | + | 0.331966i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − | 29.5954i | − | 0.0525673i | −0.999655 | − | 0.0262837i | \(-0.991633\pi\) | ||
0.999655 | − | 0.0262837i | \(-0.00836731\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 67.5958 | 0.119639 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −498.614 | − | 662.117i | −0.879389 | − | 1.16775i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 355.324i | 0.624471i | 0.950005 | + | 0.312235i | \(0.101078\pi\) | ||||
−0.950005 | + | 0.312235i | \(0.898922\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 133.482 | 0.233769 | 0.116885 | − | 0.993145i | \(-0.462709\pi\) | ||||
0.116885 | + | 0.993145i | \(0.462709\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 612.071 | − | 378.694i | 1.06819 | − | 0.660898i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 389.748i | 0.677823i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −228.735 | −0.396422 | −0.198211 | − | 0.980159i | \(-0.563513\pi\) | ||||
−0.198211 | + | 0.980159i | \(0.563513\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 21.3046 | + | 34.4338i | 0.0367954 | + | 0.0594712i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 822.993i | 1.41651i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1354.73 | 2.32372 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 198.578 | + | 99.0465i | 0.339450 | + | 0.169310i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 633.349i | − | 1.07896i | −0.841998 | − | 0.539480i | \(-0.818621\pi\) | ||
0.841998 | − | 0.539480i | \(-0.181379\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 234.748 | 0.398553 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 42.3598 | − | 26.2084i | 0.0716748 | − | 0.0443459i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 189.510i | 0.319578i | 0.987151 | + | 0.159789i | \(0.0510813\pi\) | ||||
−0.987151 | + | 0.159789i | \(0.948919\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −58.9688 | −0.0991071 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −226.781 | − | 366.538i | −0.379867 | − | 0.613967i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 340.082i | − | 0.567750i | −0.958861 | − | 0.283875i | \(-0.908380\pi\) | ||
0.958861 | − | 0.283875i | \(-0.0916200\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 528.406 | 0.879211 | 0.439605 | − | 0.898191i | \(-0.355118\pi\) | ||||
0.439605 | + | 0.898191i | \(0.355118\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −226.369 | + | 453.846i | −0.375404 | + | 0.752647i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − | 206.013i | − | 0.340517i | ||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 659.649 | 1.08674 | 0.543368 | − | 0.839495i | \(-0.317149\pi\) | ||||
0.543368 | + | 0.839495i | \(0.317149\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 327.624 | − | 202.704i | 0.537971 | − | 0.332848i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 373.362i | 0.611067i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −67.7073 | −0.110452 | −0.0552262 | − | 0.998474i | \(-0.517588\pi\) | ||||
−0.0552262 | + | 0.998474i | \(0.517588\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 163.341 | + | 264.002i | 0.265595 | + | 0.429272i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 807.698i | 1.30907i | 0.756031 | + | 0.654536i | \(0.227136\pi\) | ||||
−0.756031 | + | 0.654536i | \(0.772864\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 122.858 | 0.198479 | 0.0992393 | − | 0.995064i | \(-0.468359\pi\) | ||||
0.0992393 | + | 0.995064i | \(0.468359\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 41.2728 | + | 450.337i | 0.0664619 | + | 0.725180i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 1349.01i | 2.16534i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 498.235 | 0.797176 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 491.155 | − | 303.882i | 0.783341 | − | 0.484661i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 81.3921i | 0.129399i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 141.286 | 0.223908 | 0.111954 | − | 0.993713i | \(-0.464289\pi\) | ||||
0.111954 | + | 0.993713i | \(0.464289\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −132.045 | − | 213.420i | −0.208602 | − | 0.337156i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − | 191.486i | − | 0.301553i | ||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1044.34 | −1.63947 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 1099.06 | + | 548.186i | 1.71996 | + | 0.857881i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 240.601i | − | 0.375352i | −0.982231 | − | 0.187676i | \(-0.939904\pi\) | ||
0.982231 | − | 0.187676i | \(-0.0600955\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 774.975 | 1.20525 | 0.602624 | − | 0.798025i | \(-0.294122\pi\) | ||||
0.602624 | + | 0.798025i | \(0.294122\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 122.435 | − | 75.7515i | 0.189821 | − | 0.117444i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 823.719i | − | 1.27314i | −0.771220 | − | 0.636568i | \(-0.780353\pi\) | ||
0.771220 | − | 0.636568i | \(-0.219647\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −498.991 | −0.768861 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −328.155 | − | 530.386i | −0.504078 | − | 0.814724i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − | 142.733i | − | 0.218581i | −0.994010 | − | 0.109290i | \(-0.965142\pi\) | ||
0.994010 | − | 0.109290i | \(-0.0348579\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −59.7154 | −0.0911685 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 324.634 | − | 650.859i | 0.494116 | − | 0.990652i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 485.418i | 0.736598i | 0.929707 | + | 0.368299i | \(0.120060\pi\) | ||||
−0.929707 | + | 0.368299i | \(0.879940\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 89.9502 | 0.136082 | 0.0680410 | − | 0.997683i | \(-0.478325\pi\) | ||||
0.0680410 | + | 0.997683i | \(0.478325\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −209.519 | + | 129.632i | −0.316017 | + | 0.195523i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 155.519i | 0.233863i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −210.197 | −0.315138 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −231.869 | − | 374.763i | −0.346591 | − | 0.560184i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 1200.81i | − | 1.78958i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 779.599 | 1.15839 | 0.579197 | − | 0.815188i | \(-0.303366\pi\) | ||||
0.579197 | + | 0.815188i | \(0.303366\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 625.665 | − | 57.3415i | 0.926911 | − | 0.0849503i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 207.151i | − | 0.305984i | −0.988227 | − | 0.152992i | \(-0.951109\pi\) | ||
0.988227 | − | 0.152992i | \(-0.0488909\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −209.134 | −0.308003 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −72.7724 | + | 45.0250i | −0.106861 | + | 0.0661160i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 680.228i | 0.995941i | 0.867194 | + | 0.497970i | \(0.165921\pi\) | ||||
−0.867194 | + | 0.497970i | \(0.834079\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 235.652 | 0.344017 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 544.748 | + | 880.458i | 0.792938 | + | 1.28160i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 1524.12i | 2.21208i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −480.570 | −0.695470 | −0.347735 | − | 0.937593i | \(-0.613049\pi\) | ||||
−0.347735 | + | 0.937593i | \(0.613049\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −1373.17 | − | 684.910i | −1.98149 | − | 0.988326i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − | 66.9297i | − | 0.0963018i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −344.680 | −0.494520 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 268.567 | − | 166.165i | 0.384216 | − | 0.237718i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 854.903i | − | 1.21955i | −0.792575 | − | 0.609774i | \(-0.791260\pi\) | ||
0.792575 | − | 0.609774i | \(-0.208740\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 214.656 | 0.305343 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −41.3523 | − | 66.8364i | −0.0586558 | − | 0.0948034i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 1467.13i | 2.07515i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −990.069 | −1.39643 | −0.698215 | − | 0.715888i | \(-0.746022\pi\) | ||||
−0.698215 | + | 0.715888i | \(0.746022\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −345.593 | + | 692.880i | −0.486067 | + | 0.974514i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 340.285i | 0.477258i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 410.828 | 0.574585 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −715.495 | + | 442.684i | −0.997901 | + | 0.617411i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − | 502.244i | − | 0.698531i | −0.937024 | − | 0.349266i | \(-0.886431\pi\) | ||
0.937024 | − | 0.349266i | \(-0.113569\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1163.97 | −1.61438 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 583.760 | + | 943.511i | 0.807413 | + | 1.30499i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 292.032i | 0.402803i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 718.280 | 0.988005 | 0.494002 | − | 0.869461i | \(-0.335533\pi\) | ||||
0.494002 | + | 0.869461i | \(0.335533\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 716.856 | − | 132.511i | 0.983341 | − | 0.181771i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 159.850i | 0.218673i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −1362.31 | −1.85854 | −0.929272 | − | 0.369397i | \(-0.879564\pi\) | ||||
−0.929272 | + | 0.369397i | \(0.879564\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 186.950 | − | 115.668i | 0.254354 | − | 0.157371i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 938.939i | 1.27400i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −1057.01 | −1.43033 | −0.715164 | − | 0.698957i | \(-0.753648\pi\) | ||||
−0.715164 | + | 0.698957i | \(0.753648\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 341.879 | + | 552.568i | 0.461375 | + | 0.745705i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 88.0799i | 0.118546i | 0.998242 | + | 0.0592731i | \(0.0188783\pi\) | ||||
−0.998242 | + | 0.0592731i | \(0.981122\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −100.019 | −0.134254 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −647.736 | − | 323.076i | −0.867116 | − | 0.432499i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − | 64.0603i | − | 0.0855278i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −11.4389 | −0.0152315 | −0.00761576 | − | 0.999971i | \(-0.502424\pi\) | ||||
−0.00761576 | + | 0.999971i | \(0.502424\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −70.1470 | + | 43.4006i | −0.0931566 | + | 0.0576369i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − | 236.652i | − | 0.313447i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 38.6736 | 0.0510879 | 0.0255440 | − | 0.999674i | \(-0.491868\pi\) | ||||
0.0255440 | + | 0.999674i | \(0.491868\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 440.501 | + | 711.966i | 0.580370 | + | 0.938032i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 814.341i | − | 1.07009i | −0.844822 | − | 0.535047i | \(-0.820294\pi\) | ||
0.844822 | − | 0.535047i | \(-0.179706\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1510.96 | 1.98029 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 23.1489 | − | 46.4113i | 0.0302601 | − | 0.0606684i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 561.383i | − | 0.731921i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 490.085 | 0.637302 | 0.318651 | − | 0.947872i | \(-0.396770\pi\) | ||||
0.318651 | + | 0.947872i | \(0.396770\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 12.5632 | − | 7.77298i | 0.0162947 | − | 0.0100817i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 747.603i | 0.967145i | 0.875304 | + | 0.483572i | \(0.160661\pi\) | ||||
−0.875304 | + | 0.483572i | \(0.839339\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 472.767 | 0.610022 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −300.069 | − | 484.991i | −0.386189 | − | 0.624184i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 909.030i | 1.16692i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 2273.78 | 2.91137 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 30.9251 | + | 337.430i | 0.0394957 | + | 0.430946i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 88.4143i | 0.112630i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −975.671 | −1.23973 | −0.619867 | − | 0.784707i | \(-0.712814\pi\) | ||||
−0.619867 | + | 0.784707i | \(0.712814\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 672.427 | − | 416.037i | 0.852252 | − | 0.527297i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 525.873i | − | 0.664820i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1350.96 | 1.70360 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −168.807 | − | 272.837i | −0.212336 | − | 0.343191i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 417.874i | 0.524309i | 0.965026 | + | 0.262154i | \(0.0844330\pi\) | ||||
−0.965026 | + | 0.262154i | \(0.915567\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 87.2613 | 0.109213 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −1061.73 | − | 529.569i | −1.32551 | − | 0.661135i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − | 1346.53i | − | 1.67687i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −225.437 | −0.280046 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −602.137 | + | 372.548i | −0.746143 | + | 0.461646i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 743.849i | 0.919468i | 0.888057 | + | 0.459734i | \(0.152055\pi\) | ||||
−0.888057 | + | 0.459734i | \(0.847945\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1248.10 | 1.53897 | 0.769483 | − | 0.638667i | \(-0.220514\pi\) | ||||
0.769483 | + | 0.638667i | \(0.220514\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −683.920 | − | 1105.40i | −0.841229 | − | 1.35965i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 135.116i | 0.165786i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 421.575 | 0.516004 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 770.549 | − | 1544.87i | 0.940841 | − | 1.88629i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 202.487i | 0.246635i | 0.992367 | + | 0.123318i | \(0.0393534\pi\) | ||||
−0.992367 | + | 0.123318i | \(0.960647\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 525.426 | 0.638427 | 0.319214 | − | 0.947683i | \(-0.396581\pi\) | ||||
0.319214 | + | 0.947683i | \(0.396581\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 989.154 | − | 611.999i | 1.19897 | − | 0.741817i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 857.247i | − | 1.03657i | −0.855207 | − | 0.518287i | \(-0.826570\pi\) | ||
0.855207 | − | 0.518287i | \(-0.173430\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 578.524 | 0.697857 | 0.348929 | − | 0.937149i | \(-0.386546\pi\) | ||||
0.348929 | + | 0.937149i | \(0.386546\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −385.245 | − | 622.658i | −0.463592 | − | 0.749288i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 244.081i | 0.293015i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 106.271 | 0.127270 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 546.261 | − | 50.0642i | 0.652641 | − | 0.0598138i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 1450.83i | 1.72924i | 0.502425 | + | 0.864621i | \(0.332441\pi\) | ||||
−0.502425 | + | 0.864621i | \(0.667559\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 683.503 | 0.812726 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −1101.16 | + | 681.298i | −1.30624 | + | 0.808183i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 239.905i | 0.283912i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1602.71 | −1.89222 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 55.5364 | + | 89.7616i | 0.0654139 | + | 0.105726i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 311.161i | 0.365641i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −1293.52 | −1.51643 | −0.758216 | − | 0.652004i | \(-0.773929\pi\) | ||||
−0.758216 | + | 0.652004i | \(0.773929\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −122.401 | − | 61.0510i | −0.143159 | − | 0.0714047i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 954.256i | − | 1.11348i | −0.830685 | − | 0.556742i | \(-0.812051\pi\) | ||
0.830685 | − | 0.556742i | \(-0.187949\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1590.52 | −1.85159 | −0.925796 | − | 0.378023i | \(-0.876604\pi\) | ||||
−0.925796 | + | 0.378023i | \(0.876604\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 2053.85 | − | 1270.74i | 2.38542 | − | 1.47588i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 398.552i | − | 0.461821i | −0.972975 | − | 0.230911i | \(-0.925829\pi\) | ||
0.972975 | − | 0.230911i | \(-0.0741705\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 222.536 | 0.257267 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −425.872 | − | 688.323i | −0.491202 | − | 0.793913i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 1433.46i | 1.64956i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1056.34 | −1.21279 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 82.0984 | − | 164.599i | 0.0940417 | − | 0.188544i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 649.697i | 0.742511i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 515.896 | 0.588251 | 0.294125 | − | 0.955767i | \(-0.404972\pi\) | ||||
0.294125 | + | 0.955767i | \(0.404972\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −548.248 | + | 339.207i | −0.623718 | + | 0.385901i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 686.344i | 0.779051i | 0.921016 | + | 0.389526i | \(0.127361\pi\) | ||||
−0.921016 | + | 0.389526i | \(0.872639\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 733.647 | 0.830857 | 0.415429 | − | 0.909626i | \(-0.363632\pi\) | ||||
0.415429 | + | 0.909626i | \(0.363632\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 62.1770 | + | 100.495i | 0.0702564 | + | 0.113553i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 1527.56i | − | 1.72217i | −0.508465 | − | 0.861083i | \(-0.669787\pi\) | ||
0.508465 | − | 0.861083i | \(-0.330213\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1489.70 | −1.67570 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1078.11 | − | 811.885i | 1.21001 | − | 0.911207i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − | 230.136i | − | 0.257711i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 224.899 | 0.251283 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −800.989 | + | 495.580i | −0.892964 | + | 0.552486i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 254.970i | 0.283615i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 356.215 | 0.395355 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −589.321 | − | 952.500i | −0.652626 | − | 1.05482i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 52.1258i | − | 0.0575976i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 174.749 | 0.192667 | 0.0963334 | − | 0.995349i | \(-0.469289\pi\) | ||||
0.0963334 | + | 0.995349i | \(0.469289\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −1154.70 | − | 575.940i | −1.27030 | − | 0.633598i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1459.33i | 1.60190i | 0.598733 | + | 0.800949i | \(0.295671\pi\) | ||||
−0.598733 | + | 0.800949i | \(0.704329\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1340.07 | −1.46776 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −241.838 | + | 149.628i | −0.264304 | + | 0.163527i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 464.566i | 0.506615i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1271.02 | 1.38304 | 0.691521 | − | 0.722356i | \(-0.256941\pi\) | ||||
0.691521 | + | 0.722356i | \(0.256941\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −671.846 | − | 1085.88i | −0.729474 | − | 1.17903i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 2558.09i | 2.77150i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 432.304 | 0.467356 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 456.930 | − | 916.098i | 0.492912 | − | 0.988239i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 1112.35i | − | 1.19736i | −0.800987 | − | 0.598681i | \(-0.795692\pi\) | ||
0.800987 | − | 0.598681i | \(-0.204308\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 643.719 | 0.691427 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −19.5707 | + | 12.1086i | −0.0209761 | + | 0.0129781i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − | 96.0180i | − | 0.102693i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −331.746 | −0.354051 | −0.177026 | − | 0.984206i | \(-0.556648\pi\) | ||||
−0.177026 | + | 0.984206i | \(0.556648\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −495.566 | − | 800.967i | −0.527760 | − | 0.853000i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 36.4001i | 0.0386824i | 0.999813 | + | 0.0193412i | \(0.00615688\pi\) | ||||
−0.999813 | + | 0.0193412i | \(0.993843\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1317.71 | −1.39736 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 33.1672 | + | 361.895i | 0.0350976 | + | 0.382957i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 675.715i | − | 0.713532i | −0.934194 | − | 0.356766i | \(-0.883879\pi\) | ||
0.934194 | − | 0.356766i | \(-0.116121\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1514.89 | 1.59631 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −923.350 | + | 571.286i | −0.970925 | + | 0.600721i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 611.944i | 0.642124i | 0.947058 | + | 0.321062i | \(0.104040\pi\) | ||||
−0.947058 | + | 0.321062i | \(0.895960\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −315.571 | −0.330441 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 330.060 | + | 533.466i | 0.344891 | + | 0.557435i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | − | 1833.29i | − | 1.91167i | ||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −548.233 | −0.570481 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 50.4186 | + | 25.1477i | 0.0523558 | + | 0.0261139i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − | 17.7534i | − | 0.0183973i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1258.24 | −1.30118 | −0.650592 | − | 0.759428i | \(-0.725479\pi\) | ||||
−0.650592 | + | 0.759428i | \(0.725479\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 129.145 | − | 79.9033i | 0.133277 | − | 0.0824595i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 1624.87i | − | 1.67340i | −0.547663 | − | 0.836699i | \(-0.684482\pi\) | ||
0.547663 | − | 0.836699i | \(-0.315518\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −520.691 | −0.535140 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 688.522 | + | 1112.84i | 0.706176 | + | 1.14137i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 850.205i | − | 0.870220i | −0.900377 | − | 0.435110i | \(-0.856710\pi\) | ||
0.900377 | − | 0.435110i | \(-0.143290\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −2196.57 | −2.24368 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −593.147 | + | 1189.20i | −0.604635 | + | 1.21223i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 63.7157i | 0.0648176i | 0.999475 | + | 0.0324088i | \(0.0103178\pi\) | ||||
−0.999475 | + | 0.0324088i | \(0.989682\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −21.8399 | −0.0221725 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −519.965 | + | 321.707i | −0.526813 | + | 0.325945i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 611.105i | 0.617901i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1050.59 | −1.06013 | −0.530066 | − | 0.847957i | \(-0.677833\pi\) | ||||
−0.530066 | + | 0.847957i | \(0.677833\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 446.698 | + | 721.984i | 0.449847 | + | 0.727073i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 188.980i | 0.189929i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 54.6960 | 0.0548606 | 0.0274303 | − | 0.999624i | \(-0.491268\pi\) | ||||
0.0274303 | + | 0.999624i | \(0.491268\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 499.508 | − | 45.7793i | 0.500008 | − | 0.0458251i |
(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 | 384.3.e.a.257.3 | ✓ | 8 | |
3.2 | odd | 2 | inner | 384.3.e.a.257.4 | yes | 8 | |
4.3 | odd | 2 | 384.3.e.d.257.6 | yes | 8 | ||
8.3 | odd | 2 | 384.3.e.b.257.3 | yes | 8 | ||
8.5 | even | 2 | 384.3.e.c.257.6 | yes | 8 | ||
12.11 | even | 2 | 384.3.e.d.257.5 | yes | 8 | ||
16.3 | odd | 4 | 768.3.h.g.641.4 | 16 | |||
16.5 | even | 4 | 768.3.h.h.641.4 | 16 | |||
16.11 | odd | 4 | 768.3.h.g.641.13 | 16 | |||
16.13 | even | 4 | 768.3.h.h.641.13 | 16 | |||
24.5 | odd | 2 | 384.3.e.c.257.5 | yes | 8 | ||
24.11 | even | 2 | 384.3.e.b.257.4 | yes | 8 | ||
48.5 | odd | 4 | 768.3.h.h.641.14 | 16 | |||
48.11 | even | 4 | 768.3.h.g.641.3 | 16 | |||
48.29 | odd | 4 | 768.3.h.h.641.3 | 16 | |||
48.35 | even | 4 | 768.3.h.g.641.14 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
384.3.e.a.257.3 | ✓ | 8 | 1.1 | even | 1 | trivial | |
384.3.e.a.257.4 | yes | 8 | 3.2 | odd | 2 | inner | |
384.3.e.b.257.3 | yes | 8 | 8.3 | odd | 2 | ||
384.3.e.b.257.4 | yes | 8 | 24.11 | even | 2 | ||
384.3.e.c.257.5 | yes | 8 | 24.5 | odd | 2 | ||
384.3.e.c.257.6 | yes | 8 | 8.5 | even | 2 | ||
384.3.e.d.257.5 | yes | 8 | 12.11 | even | 2 | ||
384.3.e.d.257.6 | yes | 8 | 4.3 | odd | 2 | ||
768.3.h.g.641.3 | 16 | 48.11 | even | 4 | |||
768.3.h.g.641.4 | 16 | 16.3 | odd | 4 | |||
768.3.h.g.641.13 | 16 | 16.11 | odd | 4 | |||
768.3.h.g.641.14 | 16 | 48.35 | even | 4 | |||
768.3.h.h.641.3 | 16 | 48.29 | odd | 4 | |||
768.3.h.h.641.4 | 16 | 16.5 | even | 4 | |||
768.3.h.h.641.13 | 16 | 16.13 | even | 4 | |||
768.3.h.h.641.14 | 16 | 48.5 | odd | 4 |