Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4056,2,Mod(337,4056)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4056, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4056.337");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4056 = 2^{3} \cdot 3 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4056.c (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: | \(32.3873230598\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.649638144.4 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 14x^{6} + 75x^{4} - 170x^{2} + 169 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{8} \) |
Twist minimal: | no (minimal twist has level 312) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 337.3 | ||
Root | \(1.42055 + 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4056.337 |
Dual form | 4056.2.c.p.337.6 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/4056\mathbb{Z}\right)^\times\).
\(n\) | \(1015\) | \(2029\) | \(2705\) | \(3889\) |
\(\chi(n)\) | \(1\) | \(1\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − 1.28657i | − 0.575372i | −0.957725 | − | 0.287686i | \(-0.907114\pi\) | ||||
0.957725 | − | 0.287686i | \(-0.0928859\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.96046i | 0.740983i | 0.928836 | + | 0.370492i | \(0.120811\pi\) | ||||
−0.928836 | + | 0.370492i | \(0.879189\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − 5.51498i | − 1.66283i | −0.555653 | − | 0.831414i | \(-0.687532\pi\) | ||||
0.555653 | − | 0.831414i | \(-0.312468\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | − 1.28657i | − 0.332191i | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1.82247 | −0.442014 | −0.221007 | − | 0.975272i | \(-0.570934\pi\) | ||||
−0.221007 | + | 0.975272i | \(0.570934\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 8.08812i | 1.85554i | 0.373151 | + | 0.927771i | \(0.378277\pi\) | ||||
−0.373151 | + | 0.927771i | \(0.621723\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.96046i | 0.427807i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 6.97908 | 1.45524 | 0.727619 | − | 0.685981i | \(-0.240627\pi\) | ||||
0.727619 | + | 0.685981i | \(0.240627\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 3.34474 | 0.668947 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −2.22841 | −0.413805 | −0.206902 | − | 0.978362i | \(-0.566338\pi\) | ||||
−0.206902 | + | 0.978362i | \(0.566338\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.44548i | 0.798432i | 0.916857 | + | 0.399216i | \(0.130718\pi\) | ||||
−0.916857 | + | 0.399216i | \(0.869282\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − 5.51498i | − 0.960034i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 2.52227 | 0.426341 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.80155i | 0.460572i | 0.973123 | + | 0.230286i | \(0.0739661\pi\) | ||||
−0.973123 | + | 0.230286i | \(0.926034\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 4.58347i | 0.715817i | 0.933757 | + | 0.357909i | \(0.116510\pi\) | ||||
−0.933757 | + | 0.357909i | \(0.883490\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5.39561 | 0.822823 | 0.411411 | − | 0.911450i | \(-0.365036\pi\) | ||||
0.411411 | + | 0.911450i | \(0.365036\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | − 1.28657i | − 0.191791i | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − 5.05816i | − 0.737809i | −0.929467 | − | 0.368905i | \(-0.879733\pi\) | ||||
0.929467 | − | 0.368905i | \(-0.120267\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 3.15661 | 0.450944 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1.82247 | −0.255197 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −2.44649 | −0.336051 | −0.168025 | − | 0.985783i | \(-0.553739\pi\) | ||||
−0.168025 | + | 0.985783i | \(0.553739\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −7.09541 | −0.956745 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 8.08812i | 1.07130i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − 10.0372i | − 1.30674i | −0.757040 | − | 0.653369i | \(-0.773355\pi\) | ||||
0.757040 | − | 0.653369i | \(-0.226645\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 12.9073 | 1.65261 | 0.826304 | − | 0.563224i | \(-0.190439\pi\) | ||||
0.826304 | + | 0.563224i | \(0.190439\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 1.96046i | 0.246994i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − 2.39460i | − 0.292548i | −0.989244 | − | 0.146274i | \(-0.953272\pi\) | ||||
0.989244 | − | 0.146274i | \(-0.0467280\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 6.97908 | 0.840182 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − 15.1181i | − 1.79419i | −0.441843 | − | 0.897093i | \(-0.645675\pi\) | ||||
0.441843 | − | 0.897093i | \(-0.354325\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − 2.62301i | − 0.307000i | −0.988149 | − | 0.153500i | \(-0.950945\pi\) | ||||
0.988149 | − | 0.153500i | \(-0.0490545\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 3.34474 | 0.386217 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 10.8119 | 1.23213 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 6.15661 | 0.692673 | 0.346336 | − | 0.938110i | \(-0.387426\pi\) | ||||
0.346336 | + | 0.938110i | \(0.387426\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 5.59406i | 0.614028i | 0.951705 | + | 0.307014i | \(0.0993299\pi\) | ||||
−0.951705 | + | 0.307014i | \(0.900670\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.34474i | 0.254322i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −2.22841 | −0.238910 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − 15.0300i | − 1.59317i | −0.604525 | − | 0.796586i | \(-0.706637\pi\) | ||||
0.604525 | − | 0.796586i | \(-0.293363\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 4.44548i | 0.460975i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 10.4059 | 1.06763 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − 13.9468i | − 1.41609i | −0.706170 | − | 0.708043i | \(-0.749578\pi\) | ||||
0.706170 | − | 0.708043i | \(-0.250422\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − 5.51498i | − 0.554276i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −5.25836 | −0.523226 | −0.261613 | − | 0.965173i | \(-0.584254\pi\) | ||||
−0.261613 | + | 0.965173i | \(0.584254\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −7.39561 | −0.728711 | −0.364356 | − | 0.931260i | \(-0.618711\pi\) | ||||
−0.364356 | + | 0.931260i | \(0.618711\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 2.52227 | 0.246148 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 7.77030 | 0.751183 | 0.375592 | − | 0.926785i | \(-0.377440\pi\) | ||||
0.375592 | + | 0.926785i | \(0.377440\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 12.4455i | 1.19206i | 0.802962 | + | 0.596030i | \(0.203256\pi\) | ||||
−0.802962 | + | 0.596030i | \(0.796744\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 2.80155i | 0.265911i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 4.17753 | 0.392989 | 0.196495 | − | 0.980505i | \(-0.437044\pi\) | ||||
0.196495 | + | 0.980505i | \(0.437044\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − 8.97908i | − 0.837303i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − 3.57287i | − 0.327525i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −19.4150 | −1.76500 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 4.58347i | 0.413277i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − 10.7361i | − 0.960265i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 4.19845 | 0.372552 | 0.186276 | − | 0.982497i | \(-0.440358\pi\) | ||||
0.186276 | + | 0.982497i | \(0.440358\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 5.39561 | 0.475057 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 11.5013 | 1.00488 | 0.502439 | − | 0.864613i | \(-0.332436\pi\) | ||||
0.502439 | + | 0.864613i | \(0.332436\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −15.8564 | −1.37492 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | − 1.28657i | − 0.110730i | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 8.75970i | 0.748392i | 0.927350 | + | 0.374196i | \(0.122081\pi\) | ||||
−0.927350 | + | 0.374196i | \(0.877919\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 14.9685 | 1.26961 | 0.634805 | − | 0.772672i | \(-0.281080\pi\) | ||||
0.634805 | + | 0.772672i | \(0.281080\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | − 5.05816i | − 0.425974i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2.86700i | 0.238092i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 3.15661 | 0.260353 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 7.78063i | 0.637414i | 0.947853 | + | 0.318707i | \(0.103249\pi\) | ||||
−0.947853 | + | 0.318707i | \(0.896751\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 5.51498i | 0.448802i | 0.974497 | + | 0.224401i | \(0.0720426\pi\) | ||||
−0.974497 | + | 0.224401i | \(0.927957\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −1.82247 | −0.147338 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 5.71942 | 0.459395 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 20.5104 | 1.63691 | 0.818453 | − | 0.574573i | \(-0.194832\pi\) | ||||
0.818453 | + | 0.574573i | \(0.194832\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −2.44649 | −0.194019 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 13.6822i | 1.07831i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − 18.3246i | − 1.43529i | −0.696409 | − | 0.717645i | \(-0.745220\pi\) | ||||
0.696409 | − | 0.717645i | \(-0.254780\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −7.09541 | −0.552377 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 8.17624i | 0.632696i | 0.948643 | + | 0.316348i | \(0.102457\pi\) | ||||
−0.948643 | + | 0.316348i | \(0.897543\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 8.08812i | 0.618514i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −8.57314 | −0.651804 | −0.325902 | − | 0.945404i | \(-0.605668\pi\) | ||||
−0.325902 | + | 0.945404i | \(0.605668\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 6.55721i | 0.495678i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | − 10.0372i | − 0.754445i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 3.73104 | 0.278871 | 0.139436 | − | 0.990231i | \(-0.455471\pi\) | ||||
0.139436 | + | 0.990231i | \(0.455471\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 5.24933 | 0.390179 | 0.195090 | − | 0.980785i | \(-0.437500\pi\) | ||||
0.195090 | + | 0.980785i | \(0.437500\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 12.9073 | 0.954134 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 3.60439 | 0.265000 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 10.0509i | 0.734993i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 1.96046i | 0.142602i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −5.54319 | −0.401091 | −0.200546 | − | 0.979684i | \(-0.564271\pi\) | ||||
−0.200546 | + | 0.979684i | \(0.564271\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 10.1889i | 0.733410i | 0.930337 | + | 0.366705i | \(0.119514\pi\) | ||||
−0.930337 | + | 0.366705i | \(0.880486\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 25.8564i | 1.84219i | 0.389335 | + | 0.921096i | \(0.372705\pi\) | ||||
−0.389335 | + | 0.921096i | \(0.627295\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −12.5419 | −0.889071 | −0.444536 | − | 0.895761i | \(-0.646631\pi\) | ||||
−0.444536 | + | 0.895761i | \(0.646631\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | − 2.39460i | − 0.168902i | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − 4.36869i | − 0.306622i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 5.89696 | 0.411861 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 6.97908 | 0.485079 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 44.6058 | 3.08545 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −12.4099 | −0.854334 | −0.427167 | − | 0.904173i | \(-0.640488\pi\) | ||||
−0.427167 | + | 0.904173i | \(0.640488\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − 15.1181i | − 1.03587i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − 6.94184i | − 0.473429i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −8.71517 | −0.591624 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | − 2.62301i | − 0.177247i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − 19.1835i | − 1.28462i | −0.766443 | − | 0.642312i | \(-0.777975\pi\) | ||||
0.766443 | − | 0.642312i | \(-0.222025\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 3.34474 | 0.222982 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 10.5822i | 0.702364i | 0.936307 | + | 0.351182i | \(0.114220\pi\) | ||||
−0.936307 | + | 0.351182i | \(0.885780\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 19.4595i | 1.28592i | 0.765900 | + | 0.642960i | \(0.222294\pi\) | ||||
−0.765900 | + | 0.642960i | \(0.777706\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 10.8119 | 0.711369 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −27.4243 | −1.79662 | −0.898312 | − | 0.439358i | \(-0.855206\pi\) | ||||
−0.898312 | + | 0.439358i | \(0.855206\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −6.50769 | −0.424515 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 6.15661 | 0.399915 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 2.76100i | 0.178594i | 0.996005 | + | 0.0892971i | \(0.0284621\pi\) | ||||
−0.996005 | + | 0.0892971i | \(0.971538\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 6.17753i | 0.397930i | 0.980007 | + | 0.198965i | \(0.0637580\pi\) | ||||
−0.980007 | + | 0.198965i | \(0.936242\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | − 4.06120i | − 0.259461i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 5.59406i | 0.354509i | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 14.1163 | 0.891015 | 0.445507 | − | 0.895278i | \(-0.353023\pi\) | ||||
0.445507 | + | 0.895278i | \(0.353023\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − 38.4895i | − 2.41981i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 2.34474i | 0.146833i | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 11.6225 | 0.724989 | 0.362494 | − | 0.931986i | \(-0.381925\pi\) | ||||
0.362494 | + | 0.931986i | \(0.381925\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −5.49231 | −0.341276 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −2.22841 | −0.137935 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −8.62402 | −0.531780 | −0.265890 | − | 0.964003i | \(-0.585666\pi\) | ||||
−0.265890 | + | 0.964003i | \(0.585666\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 3.14758i | 0.193354i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − 15.0300i | − 0.919818i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 25.2480 | 1.53940 | 0.769700 | − | 0.638406i | \(-0.220406\pi\) | ||||
0.769700 | + | 0.638406i | \(0.220406\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − 2.99797i | − 0.182114i | −0.995846 | − | 0.0910568i | \(-0.970976\pi\) | ||||
0.995846 | − | 0.0910568i | \(-0.0290245\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − 18.4461i | − 1.11234i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 24.9123 | 1.49684 | 0.748418 | − | 0.663227i | \(-0.230814\pi\) | ||||
0.748418 | + | 0.663227i | \(0.230814\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 4.44548i | 0.266144i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − 8.38198i | − 0.500027i | −0.968242 | − | 0.250013i | \(-0.919565\pi\) | ||||
0.968242 | − | 0.250013i | \(-0.0804351\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 25.8106 | 1.53428 | 0.767140 | − | 0.641480i | \(-0.221679\pi\) | ||||
0.767140 | + | 0.641480i | \(0.221679\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 10.4059 | 0.616394 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −8.98569 | −0.530409 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −13.6786 | −0.804624 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | − 13.9468i | − 0.817577i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − 12.7527i | − 0.745020i | −0.928028 | − | 0.372510i | \(-0.878497\pi\) | ||||
0.928028 | − | 0.372510i | \(-0.121503\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −12.9136 | −0.751860 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − 5.51498i | − 0.320011i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 10.5779i | 0.609698i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −5.25836 | −0.302085 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − 16.6061i | − 0.950864i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 16.6307i | − 0.949167i | −0.880210 | − | 0.474583i | \(-0.842599\pi\) | ||||
0.880210 | − | 0.474583i | \(-0.157401\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −7.39561 | −0.420722 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −19.3940 | −1.09974 | −0.549868 | − | 0.835252i | \(-0.685322\pi\) | ||||
−0.549868 | + | 0.835252i | \(0.685322\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −26.5091 | −1.49838 | −0.749191 | − | 0.662354i | \(-0.769557\pi\) | ||||
−0.749191 | + | 0.662354i | \(0.769557\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 2.52227 | 0.142114 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 8.13569i | 0.456946i | 0.973550 | + | 0.228473i | \(0.0733732\pi\) | ||||
−0.973550 | + | 0.228473i | \(0.926627\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 12.2896i | 0.688086i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 7.77030 | 0.433696 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − 14.7403i | − 0.820175i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 12.4455i | 0.688237i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 9.91631 | 0.546704 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − 31.9861i | − 1.75811i | −0.476717 | − | 0.879057i | \(-0.658173\pi\) | ||||
0.476717 | − | 0.879057i | \(-0.341827\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 2.80155i | 0.153524i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −3.08083 | −0.168324 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 8.14628 | 0.443756 | 0.221878 | − | 0.975074i | \(-0.428781\pi\) | ||||
0.221878 | + | 0.975074i | \(0.428781\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 4.17753 | 0.226892 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 24.5167 | 1.32765 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 19.9116i | 1.07512i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | − 8.97908i | − 0.483417i | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −31.7491 | −1.70438 | −0.852191 | − | 0.523231i | \(-0.824726\pi\) | ||||
−0.852191 | + | 0.523231i | \(0.824726\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − 11.3963i | − 0.610032i | −0.952347 | − | 0.305016i | \(-0.901338\pi\) | ||||
0.952347 | − | 0.305016i | \(-0.0986619\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 22.9551i | 1.22178i | 0.791716 | + | 0.610889i | \(0.209188\pi\) | ||||
−0.791716 | + | 0.610889i | \(0.790812\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −19.4505 | −1.03232 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | − 3.57287i | − 0.189096i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − 8.77558i | − 0.463157i | −0.972816 | − | 0.231579i | \(-0.925611\pi\) | ||||
0.972816 | − | 0.231579i | \(-0.0743891\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −46.4177 | −2.44303 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −19.4150 | −1.01902 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −3.37469 | −0.176639 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −33.6670 | −1.75740 | −0.878701 | − | 0.477372i | \(-0.841589\pi\) | ||||
−0.878701 | + | 0.477372i | \(0.841589\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 4.58347i | 0.238606i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − 4.79623i | − 0.249008i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 6.49231 | 0.336159 | 0.168080 | − | 0.985773i | \(-0.446243\pi\) | ||||
0.168080 | + | 0.985773i | \(0.446243\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | − 10.7361i | − 0.554409i | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − 30.5572i | − 1.56962i | −0.619737 | − | 0.784809i | \(-0.712761\pi\) | ||||
0.619737 | − | 0.784809i | \(-0.287239\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 4.19845 | 0.215093 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 7.39163i | 0.377694i | 0.982006 | + | 0.188847i | \(0.0604751\pi\) | ||||
−0.982006 | + | 0.188847i | \(0.939525\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | − 13.9102i | − 0.708932i | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 5.39561 | 0.274274 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 24.8408 | 1.25948 | 0.629739 | − | 0.776807i | \(-0.283162\pi\) | ||||
0.629739 | + | 0.776807i | \(0.283162\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −12.7192 | −0.643235 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 11.5013 | 0.580166 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − 7.92091i | − 0.398544i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 27.0347i | 1.35683i | 0.734678 | + | 0.678416i | \(0.237333\pi\) | ||||
−0.734678 | + | 0.678416i | \(0.762667\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −15.8564 | −0.793813 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 24.7804i | 1.23747i | 0.785599 | + | 0.618736i | \(0.212355\pi\) | ||||
−0.785599 | + | 0.618736i | \(0.787645\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | − 1.28657i | − 0.0639302i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 15.4505 | 0.765851 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 15.6338i | 0.773041i | 0.922281 | + | 0.386520i | \(0.126323\pi\) | ||||
−0.922281 | + | 0.386520i | \(0.873677\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 8.75970i | 0.432084i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 19.6776 | 0.968270 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 7.19716 | 0.353295 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 14.9685 | 0.733010 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −35.3079 | −1.72491 | −0.862453 | − | 0.506137i | \(-0.831073\pi\) | ||||
−0.862453 | + | 0.506137i | \(0.831073\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 36.6693i | 1.78715i | 0.448912 | + | 0.893576i | \(0.351812\pi\) | ||||
−0.448912 | + | 0.893576i | \(0.648188\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | − 5.05816i | − 0.245936i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −6.09568 | −0.295684 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 25.3042i | 1.22455i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 3.22442i | 0.155315i | 0.996980 | + | 0.0776575i | \(0.0247441\pi\) | ||||
−0.996980 | + | 0.0776575i | \(0.975256\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −6.79650 | −0.326619 | −0.163309 | − | 0.986575i | \(-0.552217\pi\) | ||||
−0.163309 | + | 0.986575i | \(0.552217\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 2.86700i | 0.137462i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 56.4476i | 2.70026i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 8.83705 | 0.421769 | 0.210885 | − | 0.977511i | \(-0.432366\pi\) | ||||
0.210885 | + | 0.977511i | \(0.432366\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 3.15661 | 0.150315 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 9.08986 | 0.431872 | 0.215936 | − | 0.976407i | \(-0.430720\pi\) | ||||
0.215936 | + | 0.976407i | \(0.430720\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −19.3371 | −0.916666 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 7.78063i | 0.368011i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − 3.92091i | − 0.185039i | −0.995711 | − | 0.0925197i | \(-0.970508\pi\) | ||||
0.995711 | − | 0.0925197i | \(-0.0294921\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 25.2777 | 1.19028 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 5.51498i | 0.259116i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − 25.0944i | − 1.17387i | −0.809635 | − | 0.586933i | \(-0.800335\pi\) | ||||
0.809635 | − | 0.586933i | \(-0.199665\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −1.82247 | −0.0850656 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 23.1863i | 1.07989i | 0.841699 | + | 0.539947i | \(0.181556\pi\) | ||||
−0.841699 | + | 0.539947i | \(0.818444\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 8.88866i | 0.413091i | 0.978437 | + | 0.206546i | \(0.0662222\pi\) | ||||
−0.978437 | + | 0.206546i | \(0.933778\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 5.71942 | 0.265232 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 23.1760 | 1.07246 | 0.536228 | − | 0.844073i | \(-0.319849\pi\) | ||||
0.536228 | + | 0.844073i | \(0.319849\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 4.69452 | 0.216773 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 20.5104 | 0.945068 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − 29.7567i | − 1.36821i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 27.0526i | 1.24126i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −2.44649 | −0.112017 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − 25.5965i | − 1.16953i | −0.811202 | − | 0.584767i | \(-0.801186\pi\) | ||||
0.811202 | − | 0.584767i | \(-0.198814\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 13.6822i | 0.622561i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −17.9436 | −0.814776 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 23.1115i | 1.04728i | 0.851940 | + | 0.523640i | \(0.175426\pi\) | ||||
−0.851940 | + | 0.523640i | \(0.824574\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − 18.3246i | − 0.828665i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 4.84210 | 0.218521 | 0.109260 | − | 0.994013i | \(-0.465152\pi\) | ||||
0.109260 | + | 0.994013i | \(0.465152\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 4.06120 | 0.182907 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −7.09541 | −0.318915 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 29.6383 | 1.32946 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − 40.8818i | − 1.83012i | −0.403319 | − | 0.915059i | \(-0.632143\pi\) | ||||
0.403319 | − | 0.915059i | \(-0.367857\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 8.17624i | 0.365287i | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 0.937235 | 0.0417892 | 0.0208946 | − | 0.999782i | \(-0.493349\pi\) | ||||
0.0208946 | + | 0.999782i | \(0.493349\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 6.76525i | 0.301050i | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 21.9694i | 0.973778i | 0.873464 | + | 0.486889i | \(0.161868\pi\) | ||||
−0.873464 | + | 0.486889i | \(0.838132\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 5.14230 | 0.227482 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 8.08812i | 0.357099i | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 9.51498i | 0.419280i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −27.8957 | −1.22685 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −8.57314 | −0.376319 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 22.1775 | 0.971615 | 0.485808 | − | 0.874066i | \(-0.338526\pi\) | ||||
0.485808 | + | 0.874066i | \(0.338526\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −14.3042 | −0.625478 | −0.312739 | − | 0.949839i | \(-0.601247\pi\) | ||||
−0.312739 | + | 0.949839i | \(0.601247\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 6.55721i | 0.286180i | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − 8.10175i | − 0.352918i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 25.7075 | 1.11772 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − 10.0372i | − 0.435579i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − 9.99704i | − 0.432210i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 3.73104 | 0.161006 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − 17.4086i | − 0.749843i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 15.3779i | 0.661149i | 0.943780 | + | 0.330575i | \(0.107243\pi\) | ||||
−0.943780 | + | 0.330575i | \(0.892757\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 5.24933 | 0.225270 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 16.0120 | 0.685878 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −11.1503 | −0.476751 | −0.238375 | − | 0.971173i | \(-0.576615\pi\) | ||||
−0.238375 | + | 0.971173i | \(0.576615\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 12.9073 | 0.550869 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − 18.0236i | − 0.767832i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 12.0698i | 0.513259i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 3.60439 | 0.152998 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 13.3092i | 0.563930i | 0.959425 | + | 0.281965i | \(0.0909863\pi\) | ||||
−0.959425 | + | 0.281965i | \(0.909014\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 10.0509i | 0.424348i | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 7.76127 | 0.327098 | 0.163549 | − | 0.986535i | \(-0.447706\pi\) | ||||
0.163549 | + | 0.986535i | \(0.447706\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − 5.37469i | − 0.226115i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 1.96046i | 0.0823314i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −14.2986 | −0.599430 | −0.299715 | − | 0.954029i | \(-0.596892\pi\) | ||||
−0.299715 | + | 0.954029i | \(0.596892\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −29.6121 | −1.23923 | −0.619614 | − | 0.784906i | \(-0.712711\pi\) | ||||
−0.619614 | + | 0.784906i | \(0.712711\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −5.54319 | −0.231570 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 23.3432 | 0.973478 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − 1.23475i | − 0.0514032i | −0.999670 | − | 0.0257016i | \(-0.991818\pi\) | ||||
0.999670 | − | 0.0257016i | \(-0.00818198\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 10.1889i | 0.423435i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −10.9669 | −0.454984 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 13.4923i | 0.558795i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 10.9096i | 0.450286i | 0.974326 | + | 0.225143i | \(0.0722849\pi\) | ||||
−0.974326 | + | 0.225143i | \(0.927715\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −35.9556 | −1.48152 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 25.8564i | 1.06359i | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − 17.2775i | − 0.709503i | −0.934961 | − | 0.354752i | \(-0.884565\pi\) | ||||
0.934961 | − | 0.354752i | \(-0.115435\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −4.59675 | −0.188448 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −12.5419 | −0.513306 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −44.0533 | −1.79997 | −0.899984 | − | 0.435922i | \(-0.856422\pi\) | ||||
−0.899984 | + | 0.435922i | \(0.856422\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −4.34474 | −0.177225 | −0.0886127 | − | 0.996066i | \(-0.528243\pi\) | ||||
−0.0886127 | + | 0.996066i | \(0.528243\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − 2.39460i | − 0.0975158i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 24.9787i | 1.01553i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 30.2089 | 1.22614 | 0.613070 | − | 0.790028i | \(-0.289934\pi\) | ||||
0.613070 | + | 0.790028i | \(0.289934\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | − 4.36869i | − 0.177028i | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − 6.63664i | − 0.268051i | −0.990978 | − | 0.134026i | \(-0.957210\pi\) | ||||
0.990978 | − | 0.134026i | \(-0.0427905\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 5.89696 | 0.237788 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 24.5402i | 0.987949i | 0.869476 | + | 0.493975i | \(0.164456\pi\) | ||||
−0.869476 | + | 0.493975i | \(0.835544\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 33.4563i | 1.34472i | 0.740224 | + | 0.672360i | \(0.234719\pi\) | ||||
−0.740224 | + | 0.672360i | \(0.765281\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 6.97908 | 0.280061 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 29.4656 | 1.18051 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 2.91093 | 0.116437 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 44.6058 | 1.78138 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − 5.10573i | − 0.203579i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − 14.4263i | − 0.574302i | −0.957885 | − | 0.287151i | \(-0.907292\pi\) | ||||
0.957885 | − | 0.287151i | \(-0.0927081\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −12.4099 | −0.493250 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − 5.40161i | − 0.214356i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | − 15.1181i | − 0.598062i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −41.6225 | −1.64399 | −0.821994 | − | 0.569496i | \(-0.807138\pi\) | ||||
−0.821994 | + | 0.569496i | \(0.807138\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 11.6854i | 0.460828i | 0.973093 | + | 0.230414i | \(0.0740081\pi\) | ||||
−0.973093 | + | 0.230414i | \(0.925992\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | − 6.94184i | − 0.273334i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 10.9947 | 0.432247 | 0.216124 | − | 0.976366i | \(-0.430659\pi\) | ||||
0.216124 | + | 0.976366i | \(0.430659\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −55.3552 | −2.17288 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −8.71517 | −0.341574 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 33.1190 | 1.29605 | 0.648024 | − | 0.761620i | \(-0.275596\pi\) | ||||
0.648024 | + | 0.761620i | \(0.275596\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − 14.7973i | − 0.578178i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − 2.62301i | − 0.102333i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −22.1908 | −0.864431 | −0.432216 | − | 0.901770i | \(-0.642268\pi\) | ||||
−0.432216 | + | 0.901770i | \(0.642268\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − 19.8368i | − 0.771561i | −0.922591 | − | 0.385780i | \(-0.873932\pi\) | ||||
0.922591 | − | 0.385780i | \(-0.126068\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 20.4004i | 0.791093i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −15.5522 | −0.602184 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | − 19.1835i | − 0.741678i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − 71.1834i | − 2.74800i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −38.8564 | −1.49780 | −0.748902 | − | 0.662681i | \(-0.769419\pi\) | ||||
−0.748902 | + | 0.662681i | \(0.769419\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 3.34474 | 0.128739 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −40.8864 | −1.57139 | −0.785695 | − | 0.618614i | \(-0.787695\pi\) | ||||
−0.785695 | + | 0.618614i | \(0.787695\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 27.3421 | 1.04930 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 10.5822i | 0.405510i | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − 44.3298i | − 1.69623i | −0.529810 | − | 0.848117i | \(-0.677737\pi\) | ||||
0.529810 | − | 0.848117i | \(-0.322263\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 11.2700 | 0.430604 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 19.4595i | 0.742426i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − 12.7144i | − 0.483680i | −0.970316 | − | 0.241840i | \(-0.922249\pi\) | ||||
0.970316 | − | 0.241840i | \(-0.0777509\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 10.8119 | 0.410709 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − 19.2580i | − 0.730498i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − 8.35323i | − 0.316401i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −27.4243 | −1.03728 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −13.9582 | −0.527192 | −0.263596 | − | 0.964633i | \(-0.584909\pi\) | ||||
−0.263596 | + | 0.964633i | \(0.584909\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −22.6592 | −0.854610 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −6.50769 | −0.245094 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − 10.3088i | − 0.387702i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − 9.38142i | − 0.352327i | −0.984361 | − | 0.176163i | \(-0.943631\pi\) | ||||
0.984361 | − | 0.176163i | \(-0.0563687\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 6.15661 | 0.230891 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 31.0254i | 1.16191i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 2.76100i | 0.103111i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 37.5613 | 1.40080 | 0.700399 | − | 0.713751i | \(-0.253005\pi\) | ||||
0.700399 | + | 0.713751i | \(0.253005\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − 14.4988i | − 0.539963i | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 6.17753i | 0.229745i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −7.45343 | −0.276813 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 25.5864 | 0.948948 | 0.474474 | − | 0.880270i | \(-0.342638\pi\) | ||||
0.474474 | + | 0.880270i | \(0.342638\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −9.83333 | −0.363699 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 27.1633i | 1.00330i | 0.865070 | + | 0.501650i | \(0.167274\pi\) | ||||
−0.865070 | + | 0.501650i | \(0.832726\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | − 4.06120i | − 0.149800i | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −13.2062 | −0.486456 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 16.9363i | 0.623011i | 0.950244 | + | 0.311506i | \(0.100833\pi\) | ||||
−0.950244 | + | 0.311506i | \(0.899167\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − 18.8078i | − 0.689992i | −0.938604 | − | 0.344996i | \(-0.887880\pi\) | ||||
0.938604 | − | 0.344996i | \(-0.112120\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 10.0103 | 0.366750 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 5.59406i | 0.204676i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 15.2333i | 0.556614i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −3.47112 | −0.126663 | −0.0633315 | − | 0.997993i | \(-0.520173\pi\) | ||||
−0.0633315 | + | 0.997993i | \(0.520173\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 14.1163 | 0.514428 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 7.09541 | 0.258228 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −9.76734 | −0.355000 | −0.177500 | − | 0.984121i | \(-0.556801\pi\) | ||||
−0.177500 | + | 0.984121i | \(0.556801\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | − 38.4895i | − 1.39708i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − 12.1762i | − 0.441388i | −0.975343 | − | 0.220694i | \(-0.929168\pi\) | ||||
0.975343 | − | 0.220694i | \(-0.0708323\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −24.3988 | −0.883297 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 2.34474i | 0.0847741i | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − 41.6776i | − 1.50293i | −0.659772 | − | 0.751466i | \(-0.729347\pi\) | ||||
0.659772 | − | 0.751466i | \(-0.270653\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 11.6225 | 0.418572 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 47.0460i | 1.69213i | 0.533082 | + | 0.846064i | \(0.321034\pi\) | ||||
−0.533082 | + | 0.846064i | \(0.678966\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 14.8690i | 0.534109i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −5.49231 | −0.197036 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −37.0716 | −1.32823 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −83.3758 | −2.98342 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −2.22841 | −0.0796367 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − 26.3881i | − 0.941830i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 4.26464i | 0.152018i | 0.997107 | + | 0.0760091i | \(0.0242178\pi\) | ||||
−0.997107 | + | 0.0760091i | \(0.975782\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −8.62402 | −0.307023 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 8.18987i | 0.291198i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 3.14758i | 0.111633i | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 31.5048 | 1.11596 | 0.557979 | − | 0.829855i | \(-0.311577\pi\) | ||||
0.557979 | + | 0.829855i | \(0.311577\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 9.21835i | 0.326122i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | − 15.0300i | − 0.531057i | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −14.4658 | −0.510489 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 17.6031 | 0.620428 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 25.2480 | 0.888773 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −35.9004 | −1.26219 | −0.631096 | − | 0.775705i | \(-0.717395\pi\) | ||||
−0.631096 | + | 0.775705i | \(0.717395\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − 19.1515i | − 0.672502i | −0.941772 | − | 0.336251i | \(-0.890841\pi\) | ||||
0.941772 | − | 0.336251i | \(-0.109159\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − 2.99797i | − 0.105143i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −23.5758 | −0.825825 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 43.6403i | 1.52678i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − 34.6139i | − 1.20803i | −0.796972 | − | 0.604016i | \(-0.793566\pi\) | ||||
0.796972 | − | 0.604016i | \(-0.206434\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −9.42025 | −0.328369 | −0.164185 | − | 0.986430i | \(-0.552499\pi\) | ||||
−0.164185 | + | 0.986430i | \(0.552499\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | − 18.4461i | − 0.642212i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 9.40621i | 0.327086i | 0.986536 | + | 0.163543i | \(0.0522922\pi\) | ||||
−0.986536 | + | 0.163543i | \(0.947708\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 39.3615 | 1.36708 | 0.683541 | − | 0.729912i | \(-0.260439\pi\) | ||||
0.683541 | + | 0.729912i | \(0.260439\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 24.9123 | 0.864199 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −5.75282 | −0.199324 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 10.5193 | 0.364036 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 4.44548i | 0.153658i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 30.5147i | 1.05348i | 0.850025 | + | 0.526742i | \(0.176587\pi\) | ||||
−0.850025 | + | 0.526742i | \(0.823413\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −24.0342 | −0.828766 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − 8.38198i | − 0.288691i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − 38.0622i | − 1.30783i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 25.8106 | 0.885817 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 19.5522i | 0.670241i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1.33219i | 0.0456132i | 0.999740 | + | 0.0228066i | \(0.00726020\pi\) | ||||
−0.999740 | + | 0.0228066i | \(0.992740\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 10.4059 | 0.355876 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −0.771864 | −0.0263664 | −0.0131832 | − | 0.999913i | \(-0.504196\pi\) | ||||
−0.0131832 | + | 0.999913i | \(0.504196\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −5.09036 | −0.173681 | −0.0868404 | − | 0.996222i | \(-0.527677\pi\) | ||||
−0.0868404 | + | 0.996222i | \(0.527677\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −8.98569 | −0.306232 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 23.7264i | 0.807658i | 0.914835 | + | 0.403829i | \(0.132321\pi\) | ||||
−0.914835 | + | 0.403829i | \(0.867679\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 11.0300i | 0.375030i | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −13.6786 | −0.464550 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − 33.9536i | − 1.15180i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − 13.9468i | − 0.472029i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 21.0476 | 0.711540 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 8.02893i | 0.271118i | 0.990769 | + | 0.135559i | \(0.0432830\pi\) | ||||
−0.990769 | + | 0.135559i | \(0.956717\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | − 12.7527i | − 0.430137i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −21.7454 | −0.732621 | −0.366310 | − | 0.930493i | \(-0.619379\pi\) | ||||
−0.366310 | + | 0.930493i | \(0.619379\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 0.00504815 | 0.000169884 0 | 8.49419e−5 | − | 1.00000i | \(-0.499973\pi\) | ||||
8.49419e−5 | 1.00000i | \(0.499973\pi\) | ||||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −12.9136 | −0.434087 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 33.8503 | 1.13658 | 0.568291 | − | 0.822827i | \(-0.307605\pi\) | ||||
0.568291 | + | 0.822827i | \(0.307605\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 8.23088i | 0.276055i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | − 5.51498i | − 0.184759i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 40.9110 | 1.36904 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − 4.80025i | − 0.160455i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − 9.90633i | − 0.330395i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 4.45865 | 0.148539 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 10.5779i | 0.352009i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − 6.75363i | − 0.224498i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −25.2772 | −0.839315 | −0.419658 | − | 0.907682i | \(-0.637850\pi\) | ||||
−0.419658 | + | 0.907682i | \(0.637850\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −5.25836 | −0.174409 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −15.5366 | −0.514750 | −0.257375 | − | 0.966312i | \(-0.582858\pi\) | ||||
−0.257375 | + | 0.966312i | \(0.582858\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 30.8511 | 1.02102 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | − 16.6061i | − 0.548982i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 22.5479i | 0.744597i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −50.5141 | −1.66631 | −0.833154 | − | 0.553041i | \(-0.813467\pi\) | ||||
−0.833154 | + | 0.553041i | \(0.813467\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | − 16.6307i | − 0.548002i | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 9.37044i | 0.308098i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −7.39561 | −0.242904 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 12.3800i | 0.406174i | 0.979161 | + | 0.203087i | \(0.0650974\pi\) | ||||
−0.979161 | + | 0.203087i | \(0.934903\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 25.5310i | 0.836746i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −19.3940 | −0.634933 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 12.9312 | 0.422894 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 17.5721 | 0.574056 | 0.287028 | − | 0.957922i | \(-0.407333\pi\) | ||||
0.287028 | + | 0.957922i | \(0.407333\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −26.5091 | −0.865091 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − 51.8438i | − 1.69006i | −0.534718 | − | 0.845030i | \(-0.679582\pi\) | ||||
0.534718 | − | 0.845030i | \(-0.320418\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 31.9884i | 1.04168i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 2.52227 | 0.0820493 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 22.0146i | 0.715378i | 0.933841 | + | 0.357689i | \(0.116435\pi\) | ||||
−0.933841 | + | 0.357689i | \(0.883565\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 8.13569i | 0.263818i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −25.5432 | −0.827425 | −0.413713 | − | 0.910408i | \(-0.635768\pi\) | ||||
−0.413713 | + | 0.910408i | \(0.635768\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 7.13170i | 0.230777i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 12.2896i | 0.397267i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −17.1730 | −0.554546 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 11.2377 | 0.362507 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 7.77030 | 0.250394 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 13.1087 | 0.421984 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − 14.8939i | − 0.478956i | −0.970902 | − | 0.239478i | \(-0.923024\pi\) | ||||
0.970902 | − | 0.239478i | \(-0.0769763\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | − 14.7403i | − 0.473528i | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −9.88367 | −0.317182 | −0.158591 | − | 0.987344i | \(-0.550695\pi\) | ||||
−0.158591 | + | 0.987344i | \(0.550695\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 29.3451i | 0.940760i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − 49.6527i | − 1.58853i | −0.607572 | − | 0.794265i | \(-0.707856\pi\) | ||||
0.607572 | − | 0.794265i | \(-0.292144\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −82.8898 | −2.64917 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 12.4455i | 0.397354i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 4.41350i | 0.140769i | 0.997520 | + | 0.0703843i | \(0.0224226\pi\) | ||||
−0.997520 | + | 0.0703843i | \(0.977577\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 33.2661 | 1.05995 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 9.91631 | 0.315640 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 37.6564 | 1.19740 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −0.802842 | −0.0255031 | −0.0127516 | − | 0.999919i | \(-0.504059\pi\) | ||||
−0.0127516 | + | 0.999919i | \(0.504059\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − 31.9861i | − 1.01505i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 16.1360i | 0.511547i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 7.94331 | 0.251567 | 0.125784 | − | 0.992058i | \(-0.459856\pi\) | ||||
0.125784 | + | 0.992058i | \(0.459856\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 2.80155i | 0.0886370i |
(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 | 4056.2.c.p.337.3 | 8 | ||
13.3 | even | 3 | 312.2.bf.b.121.2 | yes | 8 | ||
13.4 | even | 6 | 312.2.bf.b.49.3 | ✓ | 8 | ||
13.5 | odd | 4 | 4056.2.a.be.1.1 | 4 | |||
13.8 | odd | 4 | 4056.2.a.bd.1.4 | 4 | |||
13.12 | even | 2 | inner | 4056.2.c.p.337.6 | 8 | ||
39.17 | odd | 6 | 936.2.bi.c.361.2 | 8 | |||
39.29 | odd | 6 | 936.2.bi.c.433.3 | 8 | |||
52.3 | odd | 6 | 624.2.bv.g.433.2 | 8 | |||
52.31 | even | 4 | 8112.2.a.cs.1.1 | 4 | |||
52.43 | odd | 6 | 624.2.bv.g.49.3 | 8 | |||
52.47 | even | 4 | 8112.2.a.cq.1.4 | 4 | |||
156.95 | even | 6 | 1872.2.by.m.1297.2 | 8 | |||
156.107 | even | 6 | 1872.2.by.m.433.3 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
312.2.bf.b.49.3 | ✓ | 8 | 13.4 | even | 6 | ||
312.2.bf.b.121.2 | yes | 8 | 13.3 | even | 3 | ||
624.2.bv.g.49.3 | 8 | 52.43 | odd | 6 | |||
624.2.bv.g.433.2 | 8 | 52.3 | odd | 6 | |||
936.2.bi.c.361.2 | 8 | 39.17 | odd | 6 | |||
936.2.bi.c.433.3 | 8 | 39.29 | odd | 6 | |||
1872.2.by.m.433.3 | 8 | 156.107 | even | 6 | |||
1872.2.by.m.1297.2 | 8 | 156.95 | even | 6 | |||
4056.2.a.bd.1.4 | 4 | 13.8 | odd | 4 | |||
4056.2.a.be.1.1 | 4 | 13.5 | odd | 4 | |||
4056.2.c.p.337.3 | 8 | 1.1 | even | 1 | trivial | ||
4056.2.c.p.337.6 | 8 | 13.12 | even | 2 | inner | ||
8112.2.a.cq.1.4 | 4 | 52.47 | even | 4 | |||
8112.2.a.cs.1.1 | 4 | 52.31 | even | 4 |