Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [768,3,Mod(641,768)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(768, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("768.641");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 768 = 2^{8} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 768.h (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(20.9264843029\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 4 x^{15} + 14 x^{14} - 28 x^{13} + 50 x^{12} - 104 x^{11} - 66 x^{10} + 640 x^{9} + 555 x^{8} + \cdots + 2401 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{34}\cdot 3^{2} \) |
Twist minimal: | no (minimal twist has level 384) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 641.13 | ||
Root | \(1.57980 - 0.654376i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 768.641 |
Dual form | 768.3.h.h.641.14 |
$q$-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 \(\left(\mathbb{Z}/768\mathbb{Z}\right)^\times\).
\(n\) | \(257\) | \(511\) | \(517\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) |
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 | ||||||||
\(3\) | 2.55118 | − | 1.57844i | 0.850394 | − | 0.526147i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.31534 | 0.263067 | 0.131534 | − | 0.991312i | \(-0.458010\pi\) | ||||
0.131534 | + | 0.991312i | \(0.458010\pi\) | |||||||
\(6\) | 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 | ||||||||
\(11\) | 16.6620 | 1.51473 | 0.757366 | − | 0.652991i | \(-0.226486\pi\) | ||||
0.757366 | + | 0.652991i | \(0.226486\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 18.7454i | − | 1.44196i | −0.692958 | − | 0.720978i | \(-0.743693\pi\) | ||
0.692958 | − | 0.720978i | \(-0.256307\pi\) | |||||||
\(14\) | 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 | ||||||||
\(19\) | 11.5544i | 0.608129i | 0.952652 | + | 0.304064i | \(0.0983438\pi\) | ||||
−0.952652 | + | 0.304064i | \(0.901656\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −26.1059 | + | 16.1520i | −1.24314 | + | 0.769143i | ||||
\(22\) | 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 | ||||||||
\(27\) | −2.46419 | − | 26.8873i | −0.0912663 | − | 0.995827i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −12.5498 | −0.432752 | −0.216376 | − | 0.976310i | \(-0.569424\pi\) | ||||
−0.216376 | + | 0.976310i | \(0.569424\pi\) | |||||||
\(30\) | 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 | ||||||||
\(35\) | −13.4597 | −0.384562 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 18.5778i | − | 0.502103i | −0.967974 | − | 0.251052i | \(-0.919224\pi\) | ||
0.967974 | − | 0.251052i | \(-0.0807764\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −29.5885 | − | 47.8230i | −0.758681 | − | 1.22623i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 78.6737i | − | 1.91887i | −0.281930 | − | 0.959435i | \(-0.590975\pi\) | ||
0.281930 | − | 0.959435i | \(-0.409025\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 36.4860i | − | 0.848511i | −0.905543 | − | 0.424255i | \(-0.860536\pi\) | ||
0.905543 | − | 0.424255i | \(-0.139464\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 5.28377 | − | 10.5934i | 0.117417 | − | 0.235410i | ||||
\(46\) | 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 | ||||||||
\(51\) | 6.91537 | + | 11.1771i | 0.135596 | + | 0.219158i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −81.3064 | −1.53408 | −0.767041 | − | 0.641598i | \(-0.778272\pi\) | ||||
−0.767041 | + | 0.641598i | \(0.778272\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 21.9162 | 0.398476 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 18.2380 | + | 29.4775i | 0.319965 | + | 0.517149i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 29.9477 | 0.507589 | 0.253794 | − | 0.967258i | \(-0.418321\pi\) | ||||
0.253794 | + | 0.967258i | \(0.418321\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 72.0687i | − | 1.18145i | −0.806872 | − | 0.590727i | \(-0.798841\pi\) | ||
0.806872 | − | 0.590727i | \(-0.201159\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −41.1060 | + | 82.4133i | −0.652476 | + | 1.30815i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − | 24.6565i | − | 0.379331i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 56.3520i | 0.841074i | 0.907275 | + | 0.420537i | \(0.138158\pi\) | ||||
−0.907275 | + | 0.420537i | \(0.861842\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −26.4374 | − | 42.7298i | −0.383150 | − | 0.619273i | ||||
\(70\) | 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 | \(-0.313284\pi\) | ||||
0.553521 | + | 0.832835i | \(0.313284\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −59.3657 | + | 36.7301i | −0.791543 | + | 0.489735i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −170.501 | −2.21429 | ||||||||
\(78\) | 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 | ||||||||
\(83\) | −80.4263 | −0.968992 | −0.484496 | − | 0.874793i | \(-0.660997\pi\) | ||||
−0.484496 | + | 0.874793i | \(0.660997\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 5.76268i | 0.0677962i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −32.0168 | + | 19.8091i | −0.368009 | + | 0.227691i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 131.830i | − | 1.48124i | −0.671923 | − | 0.740621i | \(-0.734532\pi\) | ||
0.671923 | − | 0.740621i | \(-0.265468\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 191.820i | 2.10791i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 51.8315 | − | 32.0687i | 0.557328 | − | 0.344824i | ||||
\(94\) | 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 | ||||||||
\(99\) | 66.9323 | − | 134.192i | 0.676083 | − | 1.35548i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 143.374 | 1.41954 | 0.709772 | − | 0.704431i | \(-0.248798\pi\) | ||||
0.709772 | + | 0.704431i | \(0.248798\pi\) | |||||||
\(102\) | 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 | ||||||||
\(107\) | −6.26024 | −0.0585069 | −0.0292535 | − | 0.999572i | \(-0.509313\pi\) | ||||
−0.0292535 | + | 0.999572i | \(0.509313\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 147.657i | 1.35465i | 0.735682 | + | 0.677327i | \(0.236862\pi\) | ||||
−0.735682 | + | 0.677327i | \(0.763138\pi\) | |||||||
\(110\) | 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 | ||||||||
\(115\) | − | 22.0306i | − | 0.191571i | ||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −150.971 | − | 75.3013i | −1.29035 | − | 0.643601i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − | 44.8317i | − | 0.376737i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 156.624 | 1.29441 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −124.182 | − | 200.711i | −1.00961 | − | 1.63179i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −63.4912 | −0.507929 | ||||||||
\(126\) | 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 | ||||||||
\(131\) | −45.3993 | −0.346560 | −0.173280 | − | 0.984873i | \(-0.555437\pi\) | ||||
−0.173280 | + | 0.984873i | \(0.555437\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − | 118.235i | − | 0.888987i | ||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −3.24124 | − | 35.3659i | −0.0240092 | − | 0.261969i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 179.157i | 1.30771i | 0.756618 | + | 0.653857i | \(0.226850\pi\) | ||||
−0.756618 | + | 0.653857i | \(0.773150\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 50.8841i | 0.366073i | 0.983106 | + | 0.183036i | \(0.0585926\pi\) | ||||
−0.983106 | + | 0.183036i | \(0.941407\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −31.4386 | − | 50.8131i | −0.222969 | − | 0.360377i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 312.337i | − | 2.18418i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −16.5072 | −0.113843 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 142.131 | − | 87.9378i | 0.966877 | − | 0.598216i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 76.0410 | 0.510342 | 0.255171 | − | 0.966896i | \(-0.417868\pi\) | ||||
0.255171 | + | 0.966896i | \(0.417868\pi\) | |||||||
\(150\) | 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 | ||||||||
\(155\) | 26.7233 | 0.172408 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 67.2180i | 0.428140i | 0.976818 | + | 0.214070i | \(0.0686720\pi\) | ||||
−0.976818 | + | 0.214070i | \(0.931328\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −207.427 | + | 128.337i | −1.30457 | + | 0.807153i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 171.391i | 1.06454i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 102.723i | 0.630204i | 0.949058 | + | 0.315102i | \(0.102039\pi\) | ||||
−0.949058 | + | 0.315102i | \(0.897961\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 55.9122 | − | 34.5934i | 0.338862 | − | 0.209657i | ||||
\(166\) | 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 | ||||||||
\(171\) | 93.0569 | + | 46.4148i | 0.544192 | + | 0.271431i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 169.185 | 0.977950 | 0.488975 | − | 0.872298i | \(-0.337371\pi\) | ||||
0.488975 | + | 0.872298i | \(0.337371\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 238.118 | 1.36067 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 76.4021 | − | 47.2707i | 0.431650 | − | 0.267066i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 170.982 | 0.955205 | 0.477602 | − | 0.878576i | \(-0.341506\pi\) | ||||
0.477602 | + | 0.878576i | \(0.341506\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 39.6292i | 0.218946i | 0.993990 | + | 0.109473i | \(0.0349163\pi\) | ||||
−0.993990 | + | 0.109473i | \(0.965084\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −113.756 | − | 183.860i | −0.621618 | − | 1.00470i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − | 24.4361i | − | 0.132087i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 72.9988i | 0.390368i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 25.2158 | + | 275.135i | 0.133417 | + | 1.45574i | ||||
\(190\) | 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 | ||||||||
\(195\) | −38.9189 | − | 62.9033i | −0.199584 | − | 0.322581i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 16.6040 | 0.0842843 | 0.0421422 | − | 0.999112i | \(-0.486582\pi\) | ||||
0.0421422 | + | 0.999112i | \(0.486582\pi\) | |||||||
\(198\) | 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 | ||||||||
\(203\) | 128.421 | 0.632614 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − | 103.482i | − | 0.504792i | ||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −134.893 | − | 67.2817i | −0.651657 | − | 0.325032i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 192.521i | 0.921151i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 83.6553i | 0.396471i | 0.980154 | + | 0.198235i | \(0.0635210\pi\) | ||||
−0.980154 | + | 0.198235i | \(0.936479\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 215.402 | + | 348.146i | 1.01128 | + | 1.63449i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − | 47.9913i | − | 0.223215i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −207.898 | −0.958056 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 206.171 | − | 127.560i | 0.941422 | − | 0.582467i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 82.1263 | 0.371612 | ||||||||
\(222\) | 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 | ||||||||
\(227\) | 28.5250 | 0.125661 | 0.0628304 | − | 0.998024i | \(-0.479987\pi\) | ||||
0.0628304 | + | 0.998024i | \(0.479987\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 345.118i | 1.50707i | 0.657410 | + | 0.753533i | \(0.271652\pi\) | ||||
−0.657410 | + | 0.753533i | \(0.728348\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −434.978 | + | 269.125i | −1.88302 | + | 1.16504i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 105.272i | − | 0.451809i | −0.974149 | − | 0.225905i | \(-0.927466\pi\) | ||
0.974149 | − | 0.225905i | \(-0.0725338\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − | 26.1982i | − | 0.111482i | ||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 219.482 | − | 135.796i | 0.926086 | − | 0.572978i | ||||
\(238\) | 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 | ||||||||
\(243\) | −226.443 | − | 88.1616i | −0.931865 | − | 0.362805i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 73.2798 | 0.299101 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 216.593 | 0.876894 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −205.182 | + | 126.948i | −0.824025 | + | 0.509832i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −27.4959 | −0.109545 | −0.0547727 | − | 0.998499i | \(-0.517443\pi\) | ||||
−0.0547727 | + | 0.998499i | \(0.517443\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 279.073i | − | 1.10306i | ||||||
\(254\) | 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 | ||||||||
\(259\) | 190.105i | 0.733995i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −50.4132 | + | 101.073i | −0.193154 | + | 0.387254i | ||||
\(262\) | 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 | ||||||||
\(267\) | −208.087 | − | 336.323i | −0.779351 | − | 1.25964i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 236.023 | 0.877409 | 0.438704 | − | 0.898631i | \(-0.355438\pi\) | ||||
0.438704 | + | 0.898631i | \(0.355438\pi\) | |||||||
\(270\) | 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 | ||||||||
\(275\) | −387.724 | −1.40991 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 244.067i | − | 0.881107i | −0.897726 | − | 0.440553i | \(-0.854782\pi\) | ||
0.897726 | − | 0.440553i | \(-0.145218\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 81.6131 | − | 163.626i | 0.292520 | − | 0.586473i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 431.627i | 1.53604i | 0.640426 | + | 0.768020i | \(0.278758\pi\) | ||||
−0.640426 | + | 0.768020i | \(0.721242\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 35.1843i | 0.124326i | 0.998066 | + | 0.0621631i | \(0.0197999\pi\) | ||||
−0.998066 | + | 0.0621631i | \(0.980200\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 23.9891 | + | 38.7728i | 0.0841723 | + | 0.136045i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 805.058i | 2.80508i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 269.806 | 0.933583 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −52.1397 | + | 32.2594i | −0.179174 | + | 0.110857i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −214.900 | −0.733446 | −0.366723 | − | 0.930330i | \(-0.619520\pi\) | ||||
−0.366723 | + | 0.930330i | \(0.619520\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 39.3914 | 0.133530 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −41.0585 | − | 447.998i | −0.138244 | − | 1.50841i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −313.968 | −1.05006 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 373.356i | 1.24039i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 365.773 | − | 226.307i | 1.20717 | − | 0.746889i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − | 94.7946i | − | 0.310802i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 425.639i | 1.38645i | 0.720723 | + | 0.693223i | \(0.243810\pi\) | ||||
−0.720723 | + | 0.693223i | \(0.756190\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 290.191 | − | 179.544i | 0.939128 | − | 0.581048i | ||||
\(310\) | 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 | \(-0.667230\pi\) | ||||
−0.501532 | + | 0.865139i | \(0.667230\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −54.0682 | + | 108.401i | −0.171645 | + | 0.344131i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 361.930 | 1.14174 | 0.570868 | − | 0.821042i | \(-0.306607\pi\) | ||||
0.570868 | + | 0.821042i | \(0.306607\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −209.105 | −0.655503 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −15.9710 | + | 9.88142i | −0.0497539 | + | 0.0307832i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −50.6216 | −0.156723 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 436.204i | 1.34217i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 233.068 | + | 376.701i | 0.712748 | + | 1.15199i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 203.813i | 0.619493i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 283.000i | 0.854984i | 0.904019 | + | 0.427492i | \(0.140603\pi\) | ||||
−0.904019 | + | 0.427492i | \(0.859397\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −149.622 | − | 74.6280i | −0.449314 | − | 0.224108i | ||||
\(334\) | 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 | ||||||||
\(339\) | −81.1168 | − | 131.106i | −0.239283 | − | 0.386745i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 338.517 | 0.992720 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −68.6810 | −0.200236 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −34.7740 | − | 56.2041i | −0.100794 | − | 0.162910i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −35.8055 | −0.103186 | −0.0515929 | − | 0.998668i | \(-0.516430\pi\) | ||||
−0.0515929 | + | 0.998668i | \(0.516430\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 119.019i | − | 0.341030i | −0.985355 | − | 0.170515i | \(-0.945457\pi\) | ||
0.985355 | − | 0.170515i | \(-0.0545431\pi\) | |||||||
\(350\) | 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 | ||||||||
\(355\) | 179.497i | 0.505626i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −70.7641 | − | 114.374i | −0.198219 | − | 0.320375i | ||||
\(358\) | 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 | ||||||||
\(363\) | 399.576 | − | 247.221i | 1.10076 | − | 0.681051i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 106.298 | 0.291227 | ||||||||
\(366\) | 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 | ||||||||
\(371\) | 831.998 | 2.24258 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 9.37918i | 0.0251453i | 0.999921 | + | 0.0125726i | \(0.00400210\pi\) | ||||
−0.999921 | + | 0.0125726i | \(0.995998\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −161.977 | + | 100.217i | −0.431940 | + | 0.267245i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 235.251i | 0.624009i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 353.377i | − | 0.932392i | −0.884681 | − | 0.466196i | \(-0.845624\pi\) | ||
0.884681 | − | 0.466196i | \(-0.154376\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −371.400 | + | 229.789i | −0.974802 | + | 0.603120i | ||||
\(382\) | 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 | ||||||||
\(387\) | −293.850 | − | 146.566i | −0.759302 | − | 0.378723i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −659.144 | −1.69446 | −0.847229 | − | 0.531227i | \(-0.821731\pi\) | ||||
−0.847229 | + | 0.531227i | \(0.821731\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 73.3799 | 0.187672 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −115.822 | + | 71.6601i | −0.294712 | + | 0.182341i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 113.161 | 0.286483 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 523.170i | 1.31781i | 0.752227 | + | 0.658904i | \(0.228980\pi\) | ||||
−0.752227 | + | 0.658904i | \(0.771020\pi\) | |||||||
\(398\) | 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 | ||||||||
\(403\) | − | 380.845i | − | 0.945024i | ||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −64.0919 | − | 85.1086i | −0.158252 | − | 0.210145i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 309.545i | − | 0.760552i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 630.598 | 1.54180 | 0.770902 | − | 0.636954i | \(-0.219806\pi\) | ||||
0.770902 | + | 0.636954i | \(0.219806\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 282.788 | + | 457.061i | 0.688050 | + | 1.11207i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −306.452 | −0.742014 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −105.788 | −0.254910 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 80.3175 | + | 129.815i | 0.192608 | + | 0.311306i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 475.721 | 1.13537 | 0.567686 | − | 0.823245i | \(-0.307839\pi\) | ||||
0.567686 | + | 0.823245i | \(0.307839\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 239.614i | − | 0.569155i | −0.958653 | − | 0.284578i | \(-0.908147\pi\) | ||
0.958653 | − | 0.284578i | \(-0.0918534\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −160.411 | − | 80.0096i | −0.379222 | − | 0.189148i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − | 101.949i | − | 0.239879i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 737.470i | 1.72710i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −493.006 | − | 796.828i | −1.14920 | − | 1.85741i | ||||
\(430\) | 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 | ||||||||
\(435\) | −42.1129 | + | 26.0557i | −0.0968112 | + | 0.0598981i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 193.526 | 0.442851 | ||||||||
\(438\) | 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 | ||||||||
\(443\) | −687.493 | −1.55190 | −0.775952 | − | 0.630792i | \(-0.782730\pi\) | ||||
−0.775952 | + | 0.630792i | \(0.782730\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − | 173.401i | − | 0.389666i | ||||||
\(446\) | 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 | ||||||||
\(451\) | − | 1310.86i | − | 2.90657i | ||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 459.002 | − | 283.989i | 1.01325 | − | 0.626908i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 252.307i | 0.554522i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 537.122 | 1.17532 | 0.587661 | − | 0.809107i | \(-0.300049\pi\) | ||||
0.587661 | + | 0.809107i | \(0.300049\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 117.797 | − | 10.7960i | 0.256639 | − | 0.0235206i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 129.931 | 0.281847 | 0.140923 | − | 0.990021i | \(-0.454993\pi\) | ||||
0.140923 | + | 0.990021i | \(0.454993\pi\) | |||||||
\(462\) | 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 | ||||||||
\(467\) | −418.978 | −0.897169 | −0.448585 | − | 0.893740i | \(-0.648072\pi\) | ||||
−0.448585 | + | 0.893740i | \(0.648072\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 576.643i | − | 1.22952i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 106.100 | + | 171.485i | 0.225264 | + | 0.364087i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 607.931i | − | 1.28527i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 268.871i | − | 0.566043i | ||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −326.612 | + | 654.823i | −0.684720 | + | 1.37280i | ||||
\(478\) | 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 | ||||||||
\(483\) | 270.530 | + | 437.249i | 0.560104 | + | 0.905278i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −26.8822 | −0.0554272 | ||||||||
\(486\) | 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 | ||||||||
\(491\) | −13.1250 | −0.0267311 | −0.0133655 | − | 0.999911i | \(-0.504255\pi\) | ||||
−0.0133655 | + | 0.999911i | \(0.504255\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 54.9824i | − | 0.111526i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 88.0385 | − | 176.508i | 0.177855 | − | 0.356582i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 1396.43i | − | 2.80971i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 239.526i | 0.480012i | 0.970771 | + | 0.240006i | \(0.0771494\pi\) | ||||
−0.970771 | + | 0.240006i | \(0.922851\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 127.528 | + | 206.119i | 0.254546 | + | 0.411415i | ||||
\(502\) | 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 | ||||||||
\(507\) | −465.312 | + | 287.893i | −0.917775 | + | 0.567837i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −600.556 | −1.17987 | −0.589937 | − | 0.807449i | \(-0.700847\pi\) | ||||
−0.589937 | + | 0.807449i | \(0.700847\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −826.961 | −1.61832 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 310.668 | − | 28.4724i | 0.605591 | − | 0.0555017i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 149.616 | 0.290517 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 331.866i | − | 0.641908i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 431.622 | − | 267.049i | 0.831642 | − | 0.514545i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 394.528i | 0.757251i | 0.925550 | + | 0.378626i | \(0.123603\pi\) | ||||
−0.925550 | + | 0.378626i | \(0.876397\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 639.213i | − | 1.22221i | −0.791551 | − | 0.611103i | \(-0.790726\pi\) | ||
0.791551 | − | 0.611103i | \(-0.209274\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 607.482 | − | 375.855i | 1.15711 | − | 0.715914i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 89.0102i | 0.168900i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 248.470 | 0.469697 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 120.302 | − | 241.192i | 0.226557 | − | 0.454223i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −1474.77 | −2.76692 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −8.23433 | −0.0153913 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 436.205 | − | 269.884i | 0.812300 | − | 0.502578i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 928.273 | 1.72221 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − | 606.241i | − | 1.12059i | −0.828292 | − | 0.560296i | \(-0.810687\pi\) | ||
0.828292 | − | 0.560296i | \(-0.189313\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 62.5524 | + | 101.101i | 0.115198 | + | 0.186190i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 194.219i | 0.356365i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 409.425i | 0.748492i | 0.927330 | + | 0.374246i | \(0.122098\pi\) | ||||
−0.927330 | + | 0.374246i | \(0.877902\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −580.425 | − | 289.503i | −1.05724 | − | 0.527329i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 145.006i | − | 0.263169i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −880.352 | −1.59196 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −38.5709 | − | 62.3409i | −0.0694972 | − | 0.112326i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −994.040 | −1.78463 | −0.892316 | − | 0.451411i | \(-0.850921\pi\) | ||||
−0.892316 | + | 0.451411i | \(0.850921\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −683.945 | −1.22351 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 115.224 | + | 186.233i | 0.205391 | + | 0.331966i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 29.5954 | 0.0525673 | 0.0262837 | − | 0.999655i | \(-0.491633\pi\) | ||||
0.0262837 | + | 0.999655i | \(0.491633\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − | 67.5958i | − | 0.119639i | ||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 498.614 | + | 662.117i | 0.879389 | + | 1.16775i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 355.324i | − | 0.624471i | −0.950005 | − | 0.312235i | \(-0.898922\pi\) | ||
0.950005 | − | 0.312235i | \(-0.101078\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 133.482i | − | 0.233769i | −0.993145 | − | 0.116885i | \(-0.962709\pi\) | ||
0.993145 | − | 0.116885i | \(-0.0372908\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 378.694 | + | 612.071i | 0.660898 | + | 1.06819i | ||||
\(574\) | 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 | ||||||||
\(579\) | −34.4338 | + | 21.3046i | −0.0594712 | + | 0.0367954i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 822.993 | 1.41651 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1354.73 | −2.32372 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −198.578 | − | 99.0465i | −0.339450 | − | 0.169310i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −633.349 | −1.07896 | −0.539480 | − | 0.841998i | \(-0.681379\pi\) | ||||
−0.539480 | + | 0.841998i | \(0.681379\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 234.748i | 0.398553i | ||||||||
\(590\) | 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 | ||||||||
\(595\) | − | 58.9688i | − | 0.0991071i | ||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −366.538 | + | 226.781i | −0.613967 | + | 0.379867i | ||||
\(598\) | 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 | \(-0.644882\pi\) | ||||
−0.439605 | + | 0.898191i | \(0.644882\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 453.846 | + | 226.369i | 0.752647 | + | 0.375404i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 206.013 | 0.340517 | ||||||||
\(606\) | 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 | ||||||||
\(611\) | −373.362 | −0.611067 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 67.7073i | 0.110452i | 0.998474 | + | 0.0552262i | \(0.0175880\pi\) | ||||
−0.998474 | + | 0.0552262i | \(0.982412\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −163.341 | − | 264.002i | −0.265595 | − | 0.429272i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 807.698i | − | 1.30907i | −0.756031 | − | 0.654536i | \(-0.772864\pi\) | ||
0.756031 | − | 0.654536i | \(-0.227136\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 122.858i | − | 0.198479i | −0.995064 | − | 0.0992393i | \(-0.968359\pi\) | ||
0.995064 | − | 0.0992393i | \(-0.0316409\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −450.337 | + | 41.2728i | −0.725180 | + | 0.0664619i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 1349.01i | 2.16534i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 498.235 | 0.797176 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 303.882 | + | 491.155i | 0.484661 | + | 0.783341i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 81.3921 | 0.129399 | ||||||||
\(630\) | 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 | ||||||||
\(635\) | −191.486 | −0.301553 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − | 1044.34i | − | 1.63947i | ||||||
\(638\) | 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 | ||||||||
\(643\) | 774.975i | 1.20525i | 0.798025 | + | 0.602624i | \(0.205878\pi\) | ||||
−0.798025 | + | 0.602624i | \(0.794122\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −75.7515 | − | 122.435i | −0.117444 | − | 0.189821i | ||||
\(646\) | 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 | ||||||||
\(651\) | −530.386 | + | 328.155i | −0.814724 | + | 0.504078i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 142.733 | 0.218581 | 0.109290 | − | 0.994010i | \(-0.465142\pi\) | ||||
0.109290 | + | 0.994010i | \(0.465142\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −59.7154 | −0.0911685 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 324.634 | − | 650.859i | 0.494116 | − | 0.990652i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −485.418 | −0.736598 | −0.368299 | − | 0.929707i | \(-0.620060\pi\) | ||||
−0.368299 | + | 0.929707i | \(0.620060\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 89.9502i | − | 0.136082i | −0.997683 | − | 0.0680410i | \(-0.978325\pi\) | ||
0.997683 | − | 0.0680410i | \(-0.0216749\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 209.519 | − | 129.632i | 0.316017 | − | 0.195523i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − | 155.519i | − | 0.233863i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 210.197i | 0.315138i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 374.763 | − | 231.869i | 0.560184 | − | 0.346591i | ||||
\(670\) | 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 | ||||||||
\(675\) | 57.3415 | + | 625.665i | 0.0849503 | + | 0.926911i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −207.151 | −0.305984 | −0.152992 | − | 0.988227i | \(-0.548891\pi\) | ||||
−0.152992 | + | 0.988227i | \(0.548891\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 209.134 | 0.308003 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 72.7724 | − | 45.0250i | 0.106861 | − | 0.0661160i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 680.228 | 0.995941 | 0.497970 | − | 0.867194i | \(-0.334079\pi\) | ||||
0.497970 | + | 0.867194i | \(0.334079\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 235.652i | 0.344017i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 544.748 | + | 880.458i | 0.792938 | + | 1.28160i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 1524.12i | 2.21208i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 480.570i | − | 0.695470i | −0.937593 | − | 0.347735i | \(-0.886951\pi\) | ||
0.937593 | − | 0.347735i | \(-0.113049\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −684.910 | + | 1373.17i | −0.988326 | + | 1.98149i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 66.9297i | 0.0963018i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 344.680 | 0.494520 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −166.165 | − | 268.567i | −0.237718 | − | 0.384216i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 854.903 | 1.21955 | 0.609774 | − | 0.792575i | \(-0.291260\pi\) | ||||
0.609774 | + | 0.792575i | \(0.291260\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 214.656 | 0.305343 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −41.3523 | − | 66.8364i | −0.0586558 | − | 0.0948034i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −1467.13 | −2.07515 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 990.069i | 1.39643i | 0.715888 | + | 0.698215i | \(0.246022\pi\) | ||||
−0.715888 | + | 0.698215i | \(0.753978\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 345.593 | − | 692.880i | 0.486067 | − | 0.974514i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 340.285i | − | 0.477258i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − | 410.828i | − | 0.574585i | ||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −442.684 | − | 715.495i | −0.617411 | − | 0.997901i | ||||
\(718\) | 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 | ||||||||
\(723\) | −943.511 | + | 583.760i | −1.30499 | + | 0.807413i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 292.032 | 0.402803 | ||||||||
\(726\) | 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 | ||||||||
\(731\) | 159.850 | 0.218673 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 1362.31i | − | 1.85854i | −0.369397 | − | 0.929272i | \(-0.620436\pi\) | ||
0.369397 | − | 0.929272i | \(-0.379564\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 186.950 | − | 115.668i | 0.254354 | − | 0.157371i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 938.939i | 1.27400i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 1057.01i | − | 1.43033i | −0.698957 | − | 0.715164i | \(-0.746352\pi\) | ||
0.698957 | − | 0.715164i | \(-0.253648\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 552.568 | − | 341.879i | 0.745705 | − | 0.461375i | ||||
\(742\) | 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 | ||||||||
\(747\) | −323.076 | + | 647.736i | −0.432499 | + | 0.867116i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 64.0603 | 0.0855278 | ||||||||
\(750\) | 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 | ||||||||
\(755\) | 236.652 | 0.313447 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 38.6736i | − | 0.0510879i | −0.999674 | − | 0.0255440i | \(-0.991868\pi\) | ||
0.999674 | − | 0.0255440i | \(-0.00813178\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −440.501 | − | 711.966i | −0.580370 | − | 0.938032i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 814.341i | 1.07009i | 0.844822 | + | 0.535047i | \(0.179706\pi\) | ||||
−0.844822 | + | 0.535047i | \(0.820294\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 1510.96i | − | 1.98029i | ||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 46.4113 | + | 23.1489i | 0.0606684 | + | 0.0302601i | ||||
\(766\) | 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 | ||||||||
\(771\) | 7.77298 | + | 12.5632i | 0.0100817 | + | 0.0162947i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 747.603 | 0.967145 | 0.483572 | − | 0.875304i | \(-0.339339\pi\) | ||||
0.483572 | + | 0.875304i | \(0.339339\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −472.767 | −0.610022 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 300.069 | + | 484.991i | 0.386189 | + | 0.624184i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 909.030 | 1.16692 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 2273.78i | 2.91137i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 30.9251 | + | 337.430i | 0.0394957 | + | 0.430946i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 88.4143i | 0.112630i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 975.671i | − | 1.23973i | −0.784707 | − | 0.619867i | \(-0.787186\pi\) | ||
0.784707 | − | 0.619867i | \(-0.212814\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −416.037 | − | 672.427i | −0.527297 | − | 0.852252i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 525.873i | 0.664820i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −1350.96 | −1.70360 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −272.837 | + | 168.807i | −0.343191 | + | 0.212336i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −417.874 | −0.524309 | −0.262154 | − | 0.965026i | \(-0.584433\pi\) | ||||
−0.262154 | + | 0.965026i | \(0.584433\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 87.2613 | 0.109213 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −1061.73 | − | 529.569i | −1.32551 | − | 0.661135i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 1346.53 | 1.67687 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 225.437i | 0.280046i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 602.137 | − | 372.548i | 0.746143 | − | 0.461646i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 743.849i | − | 0.919468i | −0.888057 | − | 0.459734i | \(-0.847945\pi\) | ||
0.888057 | − | 0.459734i | \(-0.152055\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 1248.10i | − | 1.53897i | −0.638667 | − | 0.769483i | \(-0.720514\pi\) | ||
0.638667 | − | 0.769483i | \(-0.279486\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 1105.40 | − | 683.920i | 1.35965 | − | 0.841229i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 135.116i | 0.165786i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 421.575 | 0.516004 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 1544.87 | + | 770.549i | 1.88629 | + | 0.940841i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 202.487 | 0.246635 | 0.123318 | − | 0.992367i | \(-0.460647\pi\) | ||||
0.123318 | + | 0.992367i | \(0.460647\pi\) | |||||||
\(822\) | 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 | ||||||||
\(827\) | −857.247 | −1.03657 | −0.518287 | − | 0.855207i | \(-0.673430\pi\) | ||||
−0.518287 | + | 0.855207i | \(0.673430\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 578.524i | 0.697857i | 0.937149 | + | 0.348929i | \(0.113454\pi\) | ||||
−0.937149 | + | 0.348929i | \(0.886546\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −385.245 | − | 622.658i | −0.463592 | − | 0.749288i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 244.081i | 0.293015i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 106.271i | 0.127270i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −50.0642 | − | 546.261i | −0.0598138 | − | 0.652641i | ||||
\(838\) | 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 | ||||||||
\(843\) | 681.298 | + | 1101.16i | 0.808183 | + | 1.30624i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −239.905 | −0.283912 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1602.71 | −1.89222 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 55.5364 | + | 89.7616i | 0.0654139 | + | 0.105726i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −311.161 | −0.365641 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1293.52i | 1.51643i | 0.652004 | + | 0.758216i | \(0.273929\pi\) | ||||
−0.652004 | + | 0.758216i | \(0.726071\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 122.401 | + | 61.0510i | 0.143159 | + | 0.0714047i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 954.256i | 1.11348i | 0.830685 | + | 0.556742i | \(0.187949\pi\) | ||||
−0.830685 | + | 0.556742i | \(0.812051\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1590.52i | 1.85159i | 0.378023 | + | 0.925796i | \(0.376604\pi\) | ||||
−0.378023 | + | 0.925796i | \(0.623396\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 1270.74 | + | 2053.85i | 1.47588 | + | 2.38542i | ||||
\(862\) | 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 | ||||||||
\(867\) | 688.323 | − | 425.872i | 0.793913 | − | 0.491202i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 1433.46 | 1.64956 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1056.34 | 1.21279 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −82.0984 | + | 164.599i | −0.0940417 | + | 0.188544i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 649.697 | 0.742511 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 515.896i | 0.588251i | 0.955767 | + | 0.294125i | \(0.0950284\pi\) | ||||
−0.955767 | + | 0.294125i | \(0.904972\pi\) | |||||||
\(878\) | 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 | ||||||||
\(883\) | 733.647i | 0.830857i | 0.909626 | + | 0.415429i | \(0.136368\pi\) | ||||
−0.909626 | + | 0.415429i | \(0.863632\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 100.495 | − | 62.1770i | 0.113553 | − | 0.0702564i | ||||
\(886\) | 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 | ||||||||
\(891\) | −811.885 | − | 1078.11i | −0.911207 | − | 1.21001i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 230.136 | 0.257711 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 224.899 | 0.251283 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −800.989 | + | 495.580i | −0.892964 | + | 0.552486i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −254.970 | −0.283615 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 356.215i | − | 0.395355i | ||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 589.321 | + | 952.500i | 0.652626 | + | 1.05482i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 52.1258i | 0.0575976i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 174.749i | − | 0.192667i | −0.995349 | − | 0.0963334i | \(-0.969289\pi\) | ||
0.995349 | − | 0.0963334i | \(-0.0307115\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 575.940 | − | 1154.70i | 0.633598 | − | 1.27030i | ||||
\(910\) | 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 | ||||||||
\(915\) | −149.628 | − | 241.838i | −0.163527 | − | 0.264304i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 464.566 | 0.506615 | ||||||||
\(918\) | 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 | ||||||||
\(923\) | 2558.09 | 2.77150 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 432.304i | 0.467356i | ||||||||
\(926\) | 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 | ||||||||
\(931\) | 643.719i | 0.691427i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 12.1086 | + | 19.5707i | 0.0129781 | + | 0.0209761i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 96.0180i | 0.102693i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 331.746 | 0.354051 | 0.177026 | − | 0.984206i | \(-0.443352\pi\) | ||||
0.177026 | + | 0.984206i | \(0.443352\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −800.967 | + | 495.566i | −0.853000 | + | 0.527760i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −36.4001 | −0.0386824 | −0.0193412 | − | 0.999813i | \(-0.506157\pi\) | ||||
−0.0193412 | + | 0.999813i | \(0.506157\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1317.71 | −1.39736 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 33.1672 | + | 361.895i | 0.0350976 | + | 0.382957i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 675.715 | 0.713532 | 0.356766 | − | 0.934194i | \(-0.383879\pi\) | ||||
0.356766 | + | 0.934194i | \(0.383879\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 1514.89i | − | 1.59631i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 923.350 | − | 571.286i | 0.970925 | − | 0.600721i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 611.944i | − | 0.642124i | −0.947058 | − | 0.321062i | \(-0.895960\pi\) | ||
0.947058 | − | 0.321062i | \(-0.104040\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 315.571i | 0.330441i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −533.466 | + | 330.060i | −0.557435 | + | 0.344891i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | − | 1833.29i | − | 1.91167i | ||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −548.233 | −0.570481 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −25.1477 | + | 50.4186i | −0.0261139 | + | 0.0523558i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −17.7534 | −0.0183973 | ||||||||
\(966\) | 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 | ||||||||
\(971\) | −1624.87 | −1.67340 | −0.836699 | − | 0.547663i | \(-0.815518\pi\) | ||||
−0.836699 | + | 0.547663i | \(0.815518\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 520.691i | − | 0.535140i | ||||||
\(974\) | 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 | ||||||||
\(979\) | − | 2196.57i | − | 2.24368i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 1189.20 | + | 593.147i | 1.21223 | + | 0.604635i | ||||
\(982\) | 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 | ||||||||
\(987\) | 321.707 | + | 519.965i | 0.325945 | + | 0.526813i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −611.105 | −0.617901 | ||||||||
\(990\) | 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 | ||||||||
\(995\) | −188.980 | −0.189929 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 54.6960i | − | 0.0548606i | −0.999624 | − | 0.0274303i | \(-0.991268\pi\) | ||
0.999624 | − | 0.0274303i | \(-0.00873243\pi\) | |||||||
\(998\) | 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 | 768.3.h.h.641.13 | 16 | ||
3.2 | odd | 2 | inner | 768.3.h.h.641.3 | 16 | ||
4.3 | odd | 2 | 768.3.h.g.641.4 | 16 | |||
8.3 | odd | 2 | 768.3.h.g.641.13 | 16 | |||
8.5 | even | 2 | inner | 768.3.h.h.641.4 | 16 | ||
12.11 | even | 2 | 768.3.h.g.641.14 | 16 | |||
16.3 | odd | 4 | 384.3.e.b.257.3 | yes | 8 | ||
16.5 | even | 4 | 384.3.e.a.257.3 | ✓ | 8 | ||
16.11 | odd | 4 | 384.3.e.d.257.6 | yes | 8 | ||
16.13 | even | 4 | 384.3.e.c.257.6 | yes | 8 | ||
24.5 | odd | 2 | inner | 768.3.h.h.641.14 | 16 | ||
24.11 | even | 2 | 768.3.h.g.641.3 | 16 | |||
48.5 | odd | 4 | 384.3.e.a.257.4 | yes | 8 | ||
48.11 | even | 4 | 384.3.e.d.257.5 | yes | 8 | ||
48.29 | odd | 4 | 384.3.e.c.257.5 | yes | 8 | ||
48.35 | even | 4 | 384.3.e.b.257.4 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
384.3.e.a.257.3 | ✓ | 8 | 16.5 | even | 4 | ||
384.3.e.a.257.4 | yes | 8 | 48.5 | odd | 4 | ||
384.3.e.b.257.3 | yes | 8 | 16.3 | odd | 4 | ||
384.3.e.b.257.4 | yes | 8 | 48.35 | even | 4 | ||
384.3.e.c.257.5 | yes | 8 | 48.29 | odd | 4 | ||
384.3.e.c.257.6 | yes | 8 | 16.13 | even | 4 | ||
384.3.e.d.257.5 | yes | 8 | 48.11 | even | 4 | ||
384.3.e.d.257.6 | yes | 8 | 16.11 | odd | 4 | ||
768.3.h.g.641.3 | 16 | 24.11 | even | 2 | |||
768.3.h.g.641.4 | 16 | 4.3 | odd | 2 | |||
768.3.h.g.641.13 | 16 | 8.3 | odd | 2 | |||
768.3.h.g.641.14 | 16 | 12.11 | even | 2 | |||
768.3.h.h.641.3 | 16 | 3.2 | odd | 2 | inner | ||
768.3.h.h.641.4 | 16 | 8.5 | even | 2 | inner | ||
768.3.h.h.641.13 | 16 | 1.1 | even | 1 | trivial | ||
768.3.h.h.641.14 | 16 | 24.5 | odd | 2 | inner |