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.b.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 | \(-0.958010\pi\) | ||
0.991312 | − | 0.131534i | \(-0.0419902\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −10.2329 | −1.46184 | −0.730920 | − | 0.682463i | \(-0.760909\pi\) | ||||
−0.730920 | + | 0.682463i | \(0.760909\pi\) | |||||||
\(8\) | 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 | \(-0.243693\pi\) | ||||
0.720978 | + | 0.692958i | \(0.243693\pi\) | |||||||
\(14\) | 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 | \(-0.881373\pi\) | ||
0.931356 | − | 0.364109i | \(-0.118627\pi\) | |||||||
\(24\) | 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 | \(-0.930576\pi\) | ||
0.976310 | − | 0.216376i | \(-0.0694237\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −20.3167 | −0.655377 | −0.327688 | − | 0.944786i | \(-0.606270\pi\) | ||||
−0.327688 | + | 0.944786i | \(0.606270\pi\) | |||||||
\(32\) | 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 | \(-0.580776\pi\) | ||||
−0.251052 | + | 0.967974i | \(0.580776\pi\) | |||||||
\(38\) | 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 | \(0.0679613\pi\) | ||||
−0.977294 | + | 0.211888i | \(0.932039\pi\) | |||||||
\(48\) | 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 | \(0.278272\pi\) | ||||
−0.641598 | + | 0.767041i | \(0.721728\pi\) | |||||||
\(54\) | 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 | \(-0.298841\pi\) | ||||
0.590727 | + | 0.806872i | \(0.298841\pi\) | |||||||
\(62\) | 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 | \(0.410832\pi\) | ||||
−0.276479 | + | 0.961020i | \(0.589168\pi\) | |||||||
\(72\) | 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 | \(-0.683282\pi\) | ||||
−0.544504 | + | 0.838758i | \(0.683282\pi\) | |||||||
\(80\) | 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 | \(-0.748798\pi\) | ||
0.704431 | − | 0.709772i | \(-0.251202\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 113.748 | 1.10435 | 0.552173 | − | 0.833730i | \(-0.313799\pi\) | ||||
0.552173 | + | 0.833730i | \(0.313799\pi\) | |||||||
\(104\) | 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 | \(-0.736862\pi\) | ||||
−0.677327 | + | 0.735682i | \(0.736862\pi\) | |||||||
\(110\) | 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 | \(-0.305722\pi\) | ||||
0.573147 | + | 0.819452i | \(0.305722\pi\) | |||||||
\(128\) | 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 | \(-0.917868\pi\) | ||
0.966896 | − | 0.255171i | \(-0.0821318\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 179.918 | 1.19151 | 0.595754 | − | 0.803167i | \(-0.296853\pi\) | ||||
0.595754 | + | 0.803167i | \(0.296853\pi\) | |||||||
\(152\) | 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 | \(-0.568672\pi\) | ||||
−0.214070 | + | 0.976818i | \(0.568672\pi\) | |||||||
\(158\) | 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 | \(0.0777695\pi\) | ||||
−0.970302 | + | 0.241897i | \(0.922231\pi\) | |||||||
\(168\) | 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 | \(0.162629\pi\) | ||||
−0.872298 | + | 0.488975i | \(0.837371\pi\) | |||||||
\(174\) | 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 | \(-0.465084\pi\) | ||||
0.109473 | + | 0.993990i | \(0.465084\pi\) | |||||||
\(182\) | 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 | \(-0.783852\pi\) | ||
0.778170 | − | 0.628054i | \(-0.216148\pi\) | |||||||
\(192\) | 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 | \(-0.986582\pi\) | ||
0.999112 | − | 0.0421422i | \(-0.0134182\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −143.674 | −0.721979 | −0.360990 | − | 0.932570i | \(-0.617561\pi\) | ||||
−0.360990 | + | 0.932570i | \(0.617561\pi\) | |||||||
\(200\) | 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 | \(-0.606835\pi\) | ||||
−0.329367 | + | 0.944202i | \(0.606835\pi\) | |||||||
\(224\) | 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 | \(-0.228348\pi\) | ||||
0.753533 | + | 0.657410i | \(0.228348\pi\) | |||||||
\(230\) | 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 | \(0.199585\pi\) | ||||
−0.809783 | + | 0.586729i | \(0.800415\pi\) | |||||||
\(240\) | 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 | \(-0.832932\pi\) | ||
0.865394 | − | 0.501093i | \(-0.167068\pi\) | |||||||
\(264\) | 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 | \(0.144562\pi\) | ||||
−0.898631 | + | 0.438704i | \(0.855438\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −433.288 | −1.59885 | −0.799424 | − | 0.600767i | \(-0.794862\pi\) | ||||
−0.799424 | + | 0.600767i | \(0.794862\pi\) | |||||||
\(272\) | 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 | \(-0.645218\pi\) | ||||
−0.440553 | + | 0.897726i | \(0.645218\pi\) | |||||||
\(278\) | 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 | \(0.119520\pi\) | ||||
−0.930330 | + | 0.366723i | \(0.880480\pi\) | |||||||
\(294\) | 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 | \(0.00392586\pi\) | ||||
−0.999924 | + | 0.0123331i | \(0.996074\pi\) | |||||||
\(312\) | 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 | \(0.193393\pi\) | ||||
−0.821042 | + | 0.570868i | \(0.806607\pi\) | |||||||
\(318\) | 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 | \(-0.445457\pi\) | ||||
0.170515 | + | 0.985355i | \(0.445457\pi\) | |||||||
\(350\) | 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 | \(0.0569974\pi\) | ||||
−0.984011 | + | 0.178107i | \(0.943003\pi\) | |||||||
\(360\) | 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 | \(-0.459714\pi\) | ||||
0.126226 | + | 0.992002i | \(0.459714\pi\) | |||||||
\(368\) | 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 | \(-0.495998\pi\) | ||||
0.0125726 | + | 0.999921i | \(0.495998\pi\) | |||||||
\(374\) | 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 | \(-0.955550\pi\) | ||
0.990266 | − | 0.139191i | \(-0.0444502\pi\) | |||||||
\(384\) | 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 | \(0.321731\pi\) | ||||
−0.531227 | + | 0.847229i | \(0.678269\pi\) | |||||||
\(390\) | 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 | \(-0.728980\pi\) | ||||
−0.658904 | + | 0.752227i | \(0.728980\pi\) | |||||||
\(398\) | 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 | \(-0.591853\pi\) | ||||
−0.284578 | + | 0.958653i | \(0.591853\pi\) | |||||||
\(422\) | 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 | \(0.254742\pi\) | ||||
−0.696494 | + | 0.717563i | \(0.745258\pi\) | |||||||
\(432\) | 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 | \(-0.479434\pi\) | ||||
0.0645654 | + | 0.997913i | \(0.479434\pi\) | |||||||
\(440\) | 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 | \(0.0450071\pi\) | ||||
−0.990021 | + | 0.140923i | \(0.954993\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −262.112 | −0.566118 | −0.283059 | − | 0.959103i | \(-0.591349\pi\) | ||||
−0.283059 | + | 0.959103i | \(0.591349\pi\) | |||||||
\(464\) | 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 | \(0.103732\pi\) | ||||
−0.947369 | + | 0.320145i | \(0.896268\pi\) | |||||||
\(480\) | 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 | \(-0.369790\pi\) | ||||
0.397753 | + | 0.917493i | \(0.369790\pi\) | |||||||
\(488\) | 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 | \(-0.798374\pi\) | ||
0.806004 | − | 0.591911i | \(-0.201626\pi\) | |||||||
\(504\) | 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 | \(-0.799153\pi\) | ||
0.807449 | − | 0.589937i | \(-0.200847\pi\) | |||||||
\(510\) | 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 | \(-0.310687\pi\) | ||||
0.560296 | + | 0.828292i | \(0.310687\pi\) | |||||||
\(542\) | 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 | \(-0.649079\pi\) | ||
0.451411 | − | 0.892316i | \(-0.350921\pi\) | |||||||
\(558\) | 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 | \(0.0916200\pi\) | ||||
−0.958861 | + | 0.283875i | \(0.908380\pi\) | |||||||
\(600\) | 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 | \(-0.682851\pi\) | ||||
−0.543368 | + | 0.839495i | \(0.682851\pi\) | |||||||
\(608\) | 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 | \(-0.482412\pi\) | ||||
0.0552262 | + | 0.998474i | \(0.482412\pi\) | |||||||
\(614\) | 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 | \(-0.535711\pi\) | ||||
−0.111954 | + | 0.993713i | \(0.535711\pi\) | |||||||
\(632\) | 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 | \(0.219647\pi\) | ||||
−0.771220 | + | 0.636568i | \(0.780353\pi\) | |||||||
\(648\) | 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 | \(0.0348579\pi\) | ||||
−0.994010 | + | 0.109290i | \(0.965142\pi\) | |||||||
\(654\) | 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 | \(-0.521675\pi\) | ||||
−0.0680410 | + | 0.997683i | \(0.521675\pi\) | |||||||
\(662\) | 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 | \(0.0488909\pi\) | ||||
−0.988227 | + | 0.152992i | \(0.951109\pi\) | |||||||
\(678\) | 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 | \(0.208740\pi\) | ||||
−0.792575 | + | 0.609774i | \(0.791260\pi\) | |||||||
\(702\) | 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 | \(-0.253978\pi\) | ||||
0.698215 | + | 0.715888i | \(0.253978\pi\) | |||||||
\(710\) | 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 | \(0.113569\pi\) | ||||
−0.937024 | + | 0.349266i | \(0.886431\pi\) | |||||||
\(720\) | 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 | \(-0.664467\pi\) | ||||
−0.494002 | + | 0.869461i | \(0.664467\pi\) | |||||||
\(728\) | 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 | \(-0.120436\pi\) | ||||
0.929272 | + | 0.369397i | \(0.120436\pi\) | |||||||
\(734\) | 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 | \(-0.981122\pi\) | ||
0.998242 | − | 0.0592731i | \(-0.0188783\pi\) | |||||||
\(744\) | 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 | \(-0.497576\pi\) | ||||
0.00761576 | + | 0.999971i | \(0.497576\pi\) | |||||||
\(752\) | 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 | \(-0.508132\pi\) | ||||
−0.0255440 | + | 0.999674i | \(0.508132\pi\) | |||||||
\(758\) | 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 | \(-0.839339\pi\) | ||
0.875304 | − | 0.483572i | \(-0.160661\pi\) | |||||||
\(774\) | 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 | \(-0.915567\pi\) | ||
0.965026 | − | 0.262154i | \(-0.0844330\pi\) | |||||||
\(798\) | 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 | \(-0.960647\pi\) | ||
0.992367 | − | 0.123318i | \(-0.0393534\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −525.426 | −0.638427 | −0.319214 | − | 0.947683i | \(-0.603419\pi\) | ||||
−0.319214 | + | 0.947683i | \(0.603419\pi\) | |||||||
\(824\) | 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 | \(-0.613454\pi\) | ||||
−0.348929 | + | 0.937149i | \(0.613454\pi\) | |||||||
\(830\) | 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 | \(-0.667559\pi\) | ||
0.502425 | − | 0.864621i | \(-0.332441\pi\) | |||||||
\(840\) | 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 | \(-0.226071\pi\) | ||||
0.758216 | + | 0.652004i | \(0.226071\pi\) | |||||||
\(854\) | 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 | \(0.0741705\pi\) | ||||
−0.972975 | + | 0.230911i | \(0.925829\pi\) | |||||||
\(864\) | 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 | \(-0.595028\pi\) | ||||
−0.294125 | + | 0.955767i | \(0.595028\pi\) | |||||||
\(878\) | 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 | \(0.330213\pi\) | ||||
−0.508465 | + | 0.861083i | \(0.669787\pi\) | |||||||
\(888\) | 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 | \(-0.704329\pi\) | ||
0.598733 | − | 0.800949i | \(-0.295671\pi\) | |||||||
\(912\) | 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 | \(-0.743059\pi\) | ||||
−0.691521 | + | 0.722356i | \(0.743059\pi\) | |||||||
\(920\) | 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 | \(-0.993843\pi\) | ||
0.999813 | − | 0.0193412i | \(-0.00615688\pi\) | |||||||
\(942\) | 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 | \(-0.274521\pi\) | ||||
0.650592 | + | 0.759428i | \(0.274521\pi\) | |||||||
\(968\) | 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 | \(-0.989682\pi\) | ||
0.999475 | − | 0.0324088i | \(-0.0103178\pi\) | |||||||
\(984\) | 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 | \(-0.322167\pi\) | ||||
0.530066 | + | 0.847957i | \(0.322167\pi\) | |||||||
\(992\) | 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 | \(-0.508732\pi\) | ||||
−0.0274303 | + | 0.999624i | \(0.508732\pi\) | |||||||
\(998\) | 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.b.257.3 | yes | 8 | |
3.2 | odd | 2 | inner | 384.3.e.b.257.4 | yes | 8 | |
4.3 | odd | 2 | 384.3.e.c.257.6 | yes | 8 | ||
8.3 | odd | 2 | 384.3.e.a.257.3 | ✓ | 8 | ||
8.5 | even | 2 | 384.3.e.d.257.6 | yes | 8 | ||
12.11 | even | 2 | 384.3.e.c.257.5 | yes | 8 | ||
16.3 | odd | 4 | 768.3.h.h.641.4 | 16 | |||
16.5 | even | 4 | 768.3.h.g.641.4 | 16 | |||
16.11 | odd | 4 | 768.3.h.h.641.13 | 16 | |||
16.13 | even | 4 | 768.3.h.g.641.13 | 16 | |||
24.5 | odd | 2 | 384.3.e.d.257.5 | yes | 8 | ||
24.11 | even | 2 | 384.3.e.a.257.4 | yes | 8 | ||
48.5 | odd | 4 | 768.3.h.g.641.14 | 16 | |||
48.11 | even | 4 | 768.3.h.h.641.3 | 16 | |||
48.29 | odd | 4 | 768.3.h.g.641.3 | 16 | |||
48.35 | even | 4 | 768.3.h.h.641.14 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
384.3.e.a.257.3 | ✓ | 8 | 8.3 | odd | 2 | ||
384.3.e.a.257.4 | yes | 8 | 24.11 | even | 2 | ||
384.3.e.b.257.3 | yes | 8 | 1.1 | even | 1 | trivial | |
384.3.e.b.257.4 | yes | 8 | 3.2 | odd | 2 | inner | |
384.3.e.c.257.5 | yes | 8 | 12.11 | even | 2 | ||
384.3.e.c.257.6 | yes | 8 | 4.3 | odd | 2 | ||
384.3.e.d.257.5 | yes | 8 | 24.5 | odd | 2 | ||
384.3.e.d.257.6 | yes | 8 | 8.5 | even | 2 | ||
768.3.h.g.641.3 | 16 | 48.29 | odd | 4 | |||
768.3.h.g.641.4 | 16 | 16.5 | even | 4 | |||
768.3.h.g.641.13 | 16 | 16.13 | even | 4 | |||
768.3.h.g.641.14 | 16 | 48.5 | odd | 4 | |||
768.3.h.h.641.3 | 16 | 48.11 | even | 4 | |||
768.3.h.h.641.4 | 16 | 16.3 | odd | 4 | |||
768.3.h.h.641.13 | 16 | 16.11 | odd | 4 | |||
768.3.h.h.641.14 | 16 | 48.35 | even | 4 |