Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1110,2,Mod(961,1110)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1110, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("1110.961");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1110 = 2 \cdot 3 \cdot 5 \cdot 37 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1110.h (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(8.86339462436\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 20x^{6} + 132x^{4} + 297x^{2} + 64 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 961.3 | ||
Root | \(-2.87151i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1110.961 |
Dual form | 1110.2.h.g.961.7 |
$q$-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 \(\left(\mathbb{Z}/1110\mathbb{Z}\right)^\times\).
\(n\) | \(371\) | \(631\) | \(667\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 1.00000i | − | 0.707107i | ||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | 1.00000i | 0.447214i | ||||||||
\(6\) | − | 1.00000i | − | 0.408248i | ||||||
\(7\) | 0.374052 | 0.141378 | 0.0706892 | − | 0.997498i | \(-0.477480\pi\) | ||||
0.0706892 | + | 0.997498i | \(0.477480\pi\) | |||||||
\(8\) | 1.00000i | 0.353553i | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 1.00000 | 0.316228 | ||||||||
\(11\) | −6.11707 | −1.84437 | −0.922183 | − | 0.386754i | \(-0.873596\pi\) | ||||
−0.922183 | + | 0.386754i | \(0.873596\pi\) | |||||||
\(12\) | −1.00000 | −0.288675 | ||||||||
\(13\) | 5.44814i | 1.51104i | 0.655124 | + | 0.755522i | \(0.272617\pi\) | ||||
−0.655124 | + | 0.755522i | \(0.727383\pi\) | |||||||
\(14\) | − | 0.374052i | − | 0.0999696i | ||||||
\(15\) | 1.00000i | 0.258199i | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 2.37405i | 0.575792i | 0.957662 | + | 0.287896i | \(0.0929558\pi\) | ||||
−0.957662 | + | 0.287896i | \(0.907044\pi\) | |||||||
\(18\) | − | 1.00000i | − | 0.235702i | ||||||
\(19\) | 1.70513i | 0.391183i | 0.980685 | + | 0.195592i | \(0.0626627\pi\) | ||||
−0.980685 | + | 0.195592i | \(0.937337\pi\) | |||||||
\(20\) | − | 1.00000i | − | 0.223607i | ||||||
\(21\) | 0.374052 | 0.0816248 | ||||||||
\(22\) | 6.11707i | 1.30416i | ||||||||
\(23\) | 5.44814i | 1.13602i | 0.823023 | + | 0.568008i | \(0.192286\pi\) | ||||
−0.823023 | + | 0.568008i | \(0.807714\pi\) | |||||||
\(24\) | 1.00000i | 0.204124i | ||||||||
\(25\) | −1.00000 | −0.200000 | ||||||||
\(26\) | 5.44814 | 1.06847 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | −0.374052 | −0.0706892 | ||||||||
\(29\) | − | 4.41194i | − | 0.819277i | −0.912248 | − | 0.409638i | \(-0.865655\pi\) | ||
0.912248 | − | 0.409638i | \(-0.134345\pi\) | |||||||
\(30\) | 1.00000 | 0.182574 | ||||||||
\(31\) | 3.07409i | 0.552123i | 0.961140 | + | 0.276062i | \(0.0890294\pi\) | ||||
−0.961140 | + | 0.276062i | \(0.910971\pi\) | |||||||
\(32\) | − | 1.00000i | − | 0.176777i | ||||||
\(33\) | −6.11707 | −1.06484 | ||||||||
\(34\) | 2.37405 | 0.407147 | ||||||||
\(35\) | 0.374052i | 0.0632263i | ||||||||
\(36\) | −1.00000 | −0.166667 | ||||||||
\(37\) | 2.70513 | − | 5.44814i | 0.444720 | − | 0.895669i | ||||
\(38\) | 1.70513 | 0.276608 | ||||||||
\(39\) | 5.44814i | 0.872401i | ||||||||
\(40\) | −1.00000 | −0.158114 | ||||||||
\(41\) | 3.07409 | 0.480093 | 0.240046 | − | 0.970761i | \(-0.422837\pi\) | ||||
0.240046 | + | 0.970761i | \(0.422837\pi\) | |||||||
\(42\) | − | 0.374052i | − | 0.0577175i | ||||||
\(43\) | 7.82220i | 1.19287i | 0.802660 | + | 0.596437i | \(0.203417\pi\) | ||||
−0.802660 | + | 0.596437i | \(0.796583\pi\) | |||||||
\(44\) | 6.11707 | 0.922183 | ||||||||
\(45\) | 1.00000i | 0.149071i | ||||||||
\(46\) | 5.44814 | 0.803285 | ||||||||
\(47\) | −13.3874 | −1.95275 | −0.976377 | − | 0.216073i | \(-0.930675\pi\) | ||||
−0.976377 | + | 0.216073i | \(0.930675\pi\) | |||||||
\(48\) | 1.00000 | 0.144338 | ||||||||
\(49\) | −6.86009 | −0.980012 | ||||||||
\(50\) | 1.00000i | 0.141421i | ||||||||
\(51\) | 2.37405i | 0.332434i | ||||||||
\(52\) | − | 5.44814i | − | 0.755522i | ||||||
\(53\) | 2.37405 | 0.326101 | 0.163051 | − | 0.986618i | \(-0.447867\pi\) | ||||
0.163051 | + | 0.986618i | \(0.447867\pi\) | |||||||
\(54\) | − | 1.00000i | − | 0.136083i | ||||||
\(55\) | − | 6.11707i | − | 0.824825i | ||||||
\(56\) | 0.374052i | 0.0499848i | ||||||||
\(57\) | 1.70513i | 0.225850i | ||||||||
\(58\) | −4.41194 | −0.579316 | ||||||||
\(59\) | 10.8963i | 1.41858i | 0.704919 | + | 0.709288i | \(0.250983\pi\) | ||||
−0.704919 | + | 0.709288i | \(0.749017\pi\) | |||||||
\(60\) | − | 1.00000i | − | 0.129099i | ||||||
\(61\) | − | 4.07918i | − | 0.522285i | −0.965300 | − | 0.261143i | \(-0.915901\pi\) | ||
0.965300 | − | 0.261143i | \(-0.0840993\pi\) | |||||||
\(62\) | 3.07409 | 0.390410 | ||||||||
\(63\) | 0.374052 | 0.0471261 | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | −5.44814 | −0.675759 | ||||||||
\(66\) | 6.11707i | 0.752959i | ||||||||
\(67\) | 10.1482 | 1.23980 | 0.619899 | − | 0.784682i | \(-0.287174\pi\) | ||||
0.619899 | + | 0.784682i | \(0.287174\pi\) | |||||||
\(68\) | − | 2.37405i | − | 0.287896i | ||||||
\(69\) | 5.44814i | 0.655880i | ||||||||
\(70\) | 0.374052 | 0.0447077 | ||||||||
\(71\) | 4.74810 | 0.563496 | 0.281748 | − | 0.959488i | \(-0.409086\pi\) | ||||
0.281748 | + | 0.959488i | \(0.409086\pi\) | |||||||
\(72\) | 1.00000i | 0.117851i | ||||||||
\(73\) | 8.19625 | 0.959298 | 0.479649 | − | 0.877460i | \(-0.340764\pi\) | ||||
0.479649 | + | 0.877460i | \(0.340764\pi\) | |||||||
\(74\) | −5.44814 | − | 2.70513i | −0.633334 | − | 0.314465i | ||||
\(75\) | −1.00000 | −0.115470 | ||||||||
\(76\) | − | 1.70513i | − | 0.195592i | ||||||
\(77\) | −2.28810 | −0.260753 | ||||||||
\(78\) | 5.44814 | 0.616881 | ||||||||
\(79\) | 12.1482i | 1.36678i | 0.730055 | + | 0.683389i | \(0.239495\pi\) | ||||
−0.730055 | + | 0.683389i | \(0.760505\pi\) | |||||||
\(80\) | 1.00000i | 0.111803i | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | − | 3.07409i | − | 0.339477i | ||||||
\(83\) | 6.78599 | 0.744859 | 0.372430 | − | 0.928060i | \(-0.378525\pi\) | ||||
0.372430 | + | 0.928060i | \(0.378525\pi\) | |||||||
\(84\) | −0.374052 | −0.0408124 | ||||||||
\(85\) | −2.37405 | −0.257502 | ||||||||
\(86\) | 7.82220 | 0.843489 | ||||||||
\(87\) | − | 4.41194i | − | 0.473010i | ||||||
\(88\) | − | 6.11707i | − | 0.652082i | ||||||
\(89\) | 0.551855i | 0.0584965i | 0.999572 | + | 0.0292483i | \(0.00931134\pi\) | ||||
−0.999572 | + | 0.0292483i | \(0.990689\pi\) | |||||||
\(90\) | 1.00000 | 0.105409 | ||||||||
\(91\) | 2.03789i | 0.213629i | ||||||||
\(92\) | − | 5.44814i | − | 0.568008i | ||||||
\(93\) | 3.07409i | 0.318769i | ||||||||
\(94\) | 13.3874i | 1.38081i | ||||||||
\(95\) | −1.70513 | −0.174942 | ||||||||
\(96\) | − | 1.00000i | − | 0.102062i | ||||||
\(97\) | 8.15496i | 0.828010i | 0.910275 | + | 0.414005i | \(0.135870\pi\) | ||||
−0.910275 | + | 0.414005i | \(0.864130\pi\) | |||||||
\(98\) | 6.86009i | 0.692973i | ||||||||
\(99\) | −6.11707 | −0.614789 | ||||||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | 3.74302 | 0.372444 | 0.186222 | − | 0.982508i | \(-0.440376\pi\) | ||||
0.186222 | + | 0.982508i | \(0.440376\pi\) | |||||||
\(102\) | 2.37405 | 0.235066 | ||||||||
\(103\) | − | 8.49112i | − | 0.836655i | −0.908296 | − | 0.418327i | \(-0.862616\pi\) | ||
0.908296 | − | 0.418327i | \(-0.137384\pi\) | |||||||
\(104\) | −5.44814 | −0.534235 | ||||||||
\(105\) | 0.374052i | 0.0365037i | ||||||||
\(106\) | − | 2.37405i | − | 0.230588i | ||||||
\(107\) | −17.4481 | −1.68678 | −0.843388 | − | 0.537305i | \(-0.819442\pi\) | ||||
−0.843388 | + | 0.537305i | \(0.819442\pi\) | |||||||
\(108\) | −1.00000 | −0.0962250 | ||||||||
\(109\) | − | 8.62086i | − | 0.825729i | −0.910793 | − | 0.412864i | \(-0.864528\pi\) | ||
0.910793 | − | 0.412864i | \(-0.135472\pi\) | |||||||
\(110\) | −6.11707 | −0.583240 | ||||||||
\(111\) | 2.70513 | − | 5.44814i | 0.256759 | − | 0.517115i | ||||
\(112\) | 0.374052 | 0.0353446 | ||||||||
\(113\) | − | 18.7185i | − | 1.76089i | −0.474151 | − | 0.880444i | \(-0.657245\pi\) | ||
0.474151 | − | 0.880444i | \(-0.342755\pi\) | |||||||
\(114\) | 1.70513 | 0.159700 | ||||||||
\(115\) | −5.44814 | −0.508042 | ||||||||
\(116\) | 4.41194i | 0.409638i | ||||||||
\(117\) | 5.44814i | 0.503681i | ||||||||
\(118\) | 10.8963 | 1.00308 | ||||||||
\(119\) | 0.888018i | 0.0814045i | ||||||||
\(120\) | −1.00000 | −0.0912871 | ||||||||
\(121\) | 26.4185 | 2.40168 | ||||||||
\(122\) | −4.07918 | −0.369312 | ||||||||
\(123\) | 3.07409 | 0.277182 | ||||||||
\(124\) | − | 3.07409i | − | 0.276062i | ||||||
\(125\) | − | 1.00000i | − | 0.0894427i | ||||||
\(126\) | − | 0.374052i | − | 0.0333232i | ||||||
\(127\) | 16.1861 | 1.43628 | 0.718141 | − | 0.695898i | \(-0.244993\pi\) | ||||
0.718141 | + | 0.695898i | \(0.244993\pi\) | |||||||
\(128\) | 1.00000i | 0.0883883i | ||||||||
\(129\) | 7.82220i | 0.688706i | ||||||||
\(130\) | 5.44814i | 0.477834i | ||||||||
\(131\) | − | 10.8963i | − | 0.952013i | −0.879442 | − | 0.476007i | \(-0.842084\pi\) | ||
0.879442 | − | 0.476007i | \(-0.157916\pi\) | |||||||
\(132\) | 6.11707 | 0.532422 | ||||||||
\(133\) | 0.637806i | 0.0553048i | ||||||||
\(134\) | − | 10.1482i | − | 0.876670i | ||||||
\(135\) | 1.00000i | 0.0860663i | ||||||||
\(136\) | −2.37405 | −0.203573 | ||||||||
\(137\) | 0.332760 | 0.0284296 | 0.0142148 | − | 0.999899i | \(-0.495475\pi\) | ||||
0.0142148 | + | 0.999899i | \(0.495475\pi\) | |||||||
\(138\) | 5.44814 | 0.463777 | ||||||||
\(139\) | −13.8980 | −1.17881 | −0.589405 | − | 0.807837i | \(-0.700638\pi\) | ||||
−0.589405 | + | 0.807837i | \(0.700638\pi\) | |||||||
\(140\) | − | 0.374052i | − | 0.0316132i | ||||||
\(141\) | −13.3874 | −1.12742 | ||||||||
\(142\) | − | 4.74810i | − | 0.398452i | ||||||
\(143\) | − | 33.3267i | − | 2.78692i | ||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | 4.41194 | 0.366392 | ||||||||
\(146\) | − | 8.19625i | − | 0.678326i | ||||||
\(147\) | −6.86009 | −0.565810 | ||||||||
\(148\) | −2.70513 | + | 5.44814i | −0.222360 | + | 0.447835i | ||||
\(149\) | −11.9014 | −0.974999 | −0.487499 | − | 0.873123i | \(-0.662091\pi\) | ||||
−0.487499 | + | 0.873123i | \(0.662091\pi\) | |||||||
\(150\) | 1.00000i | 0.0816497i | ||||||||
\(151\) | 18.4304 | 1.49984 | 0.749922 | − | 0.661527i | \(-0.230091\pi\) | ||||
0.749922 | + | 0.661527i | \(0.230091\pi\) | |||||||
\(152\) | −1.70513 | −0.138304 | ||||||||
\(153\) | 2.37405i | 0.191931i | ||||||||
\(154\) | 2.28810i | 0.184380i | ||||||||
\(155\) | −3.07409 | −0.246917 | ||||||||
\(156\) | − | 5.44814i | − | 0.436201i | ||||||
\(157\) | 7.98056 | 0.636918 | 0.318459 | − | 0.947937i | \(-0.396835\pi\) | ||||
0.318459 | + | 0.947937i | \(0.396835\pi\) | |||||||
\(158\) | 12.1482 | 0.966458 | ||||||||
\(159\) | 2.37405 | 0.188275 | ||||||||
\(160\) | 1.00000 | 0.0790569 | ||||||||
\(161\) | 2.03789i | 0.160608i | ||||||||
\(162\) | − | 1.00000i | − | 0.0785674i | ||||||
\(163\) | 9.86009i | 0.772301i | 0.922436 | + | 0.386151i | \(0.126196\pi\) | ||||
−0.922436 | + | 0.386151i | \(0.873804\pi\) | |||||||
\(164\) | −3.07409 | −0.240046 | ||||||||
\(165\) | − | 6.11707i | − | 0.476213i | ||||||
\(166\) | − | 6.78599i | − | 0.526695i | ||||||
\(167\) | − | 22.4304i | − | 1.73572i | −0.496813 | − | 0.867858i | \(-0.665496\pi\) | ||
0.496813 | − | 0.867858i | \(-0.334504\pi\) | |||||||
\(168\) | 0.374052i | 0.0288587i | ||||||||
\(169\) | −16.6823 | −1.28325 | ||||||||
\(170\) | 2.37405i | 0.182081i | ||||||||
\(171\) | 1.70513i | 0.130394i | ||||||||
\(172\) | − | 7.82220i | − | 0.596437i | ||||||
\(173\) | −22.7665 | −1.73091 | −0.865454 | − | 0.500988i | \(-0.832970\pi\) | ||||
−0.865454 | + | 0.500988i | \(0.832970\pi\) | |||||||
\(174\) | −4.41194 | −0.334468 | ||||||||
\(175\) | −0.374052 | −0.0282757 | ||||||||
\(176\) | −6.11707 | −0.461091 | ||||||||
\(177\) | 10.8963i | 0.819015i | ||||||||
\(178\) | 0.551855 | 0.0413633 | ||||||||
\(179\) | 11.1304i | 0.831927i | 0.909381 | + | 0.415964i | \(0.136556\pi\) | ||||
−0.909381 | + | 0.415964i | \(0.863444\pi\) | |||||||
\(180\) | − | 1.00000i | − | 0.0745356i | ||||||
\(181\) | −15.3378 | −1.14005 | −0.570027 | − | 0.821626i | \(-0.693067\pi\) | ||||
−0.570027 | + | 0.821626i | \(0.693067\pi\) | |||||||
\(182\) | 2.03789 | 0.151058 | ||||||||
\(183\) | − | 4.07918i | − | 0.301542i | ||||||
\(184\) | −5.44814 | −0.401643 | ||||||||
\(185\) | 5.44814 | + | 2.70513i | 0.400556 | + | 0.198885i | ||||
\(186\) | 3.07409 | 0.225403 | ||||||||
\(187\) | − | 14.5222i | − | 1.06197i | ||||||
\(188\) | 13.3874 | 0.976377 | ||||||||
\(189\) | 0.374052 | 0.0272083 | ||||||||
\(190\) | 1.70513i | 0.123703i | ||||||||
\(191\) | 12.0184i | 0.869624i | 0.900521 | + | 0.434812i | \(0.143185\pi\) | ||||
−0.900521 | + | 0.434812i | \(0.856815\pi\) | |||||||
\(192\) | −1.00000 | −0.0721688 | ||||||||
\(193\) | 17.2291i | 1.24017i | 0.784533 | + | 0.620087i | \(0.212903\pi\) | ||||
−0.784533 | + | 0.620087i | \(0.787097\pi\) | |||||||
\(194\) | 8.15496 | 0.585492 | ||||||||
\(195\) | −5.44814 | −0.390150 | ||||||||
\(196\) | 6.86009 | 0.490006 | ||||||||
\(197\) | 1.88970 | 0.134636 | 0.0673179 | − | 0.997732i | \(-0.478556\pi\) | ||||
0.0673179 | + | 0.997732i | \(0.478556\pi\) | |||||||
\(198\) | 6.11707i | 0.434721i | ||||||||
\(199\) | 14.1584i | 1.00366i | 0.864966 | + | 0.501830i | \(0.167340\pi\) | ||||
−0.864966 | + | 0.501830i | \(0.832660\pi\) | |||||||
\(200\) | − | 1.00000i | − | 0.0707107i | ||||||
\(201\) | 10.1482 | 0.715798 | ||||||||
\(202\) | − | 3.74302i | − | 0.263358i | ||||||
\(203\) | − | 1.65029i | − | 0.115828i | ||||||
\(204\) | − | 2.37405i | − | 0.166217i | ||||||
\(205\) | 3.07409i | 0.214704i | ||||||||
\(206\) | −8.49112 | −0.591604 | ||||||||
\(207\) | 5.44814i | 0.378672i | ||||||||
\(208\) | 5.44814i | 0.377761i | ||||||||
\(209\) | − | 10.4304i | − | 0.721485i | ||||||
\(210\) | 0.374052 | 0.0258120 | ||||||||
\(211\) | 11.1600 | 0.768289 | 0.384145 | − | 0.923273i | \(-0.374496\pi\) | ||||
0.384145 | + | 0.923273i | \(0.374496\pi\) | |||||||
\(212\) | −2.37405 | −0.163051 | ||||||||
\(213\) | 4.74810 | 0.325335 | ||||||||
\(214\) | 17.4481i | 1.19273i | ||||||||
\(215\) | −7.82220 | −0.533469 | ||||||||
\(216\) | 1.00000i | 0.0680414i | ||||||||
\(217\) | 1.14987i | 0.0780583i | ||||||||
\(218\) | −8.62086 | −0.583878 | ||||||||
\(219\) | 8.19625 | 0.553851 | ||||||||
\(220\) | 6.11707i | 0.412413i | ||||||||
\(221\) | −12.9342 | −0.870047 | ||||||||
\(222\) | −5.44814 | − | 2.70513i | −0.365656 | − | 0.181556i | ||||
\(223\) | −10.5703 | −0.707840 | −0.353920 | − | 0.935276i | \(-0.615151\pi\) | ||||
−0.353920 | + | 0.935276i | \(0.615151\pi\) | |||||||
\(224\) | − | 0.374052i | − | 0.0249924i | ||||||
\(225\) | −1.00000 | −0.0666667 | ||||||||
\(226\) | −18.7185 | −1.24514 | ||||||||
\(227\) | − | 2.05633i | − | 0.136484i | −0.997669 | − | 0.0682418i | \(-0.978261\pi\) | ||
0.997669 | − | 0.0682418i | \(-0.0217389\pi\) | |||||||
\(228\) | − | 1.70513i | − | 0.112925i | ||||||
\(229\) | 8.08595 | 0.534335 | 0.267167 | − | 0.963650i | \(-0.413912\pi\) | ||||
0.267167 | + | 0.963650i | \(0.413912\pi\) | |||||||
\(230\) | 5.44814i | 0.359240i | ||||||||
\(231\) | −2.28810 | −0.150546 | ||||||||
\(232\) | 4.41194 | 0.289658 | ||||||||
\(233\) | 22.1253 | 1.44948 | 0.724740 | − | 0.689023i | \(-0.241960\pi\) | ||||
0.724740 | + | 0.689023i | \(0.241960\pi\) | |||||||
\(234\) | 5.44814 | 0.356156 | ||||||||
\(235\) | − | 13.3874i | − | 0.873298i | ||||||
\(236\) | − | 10.8963i | − | 0.709288i | ||||||
\(237\) | 12.1482i | 0.789109i | ||||||||
\(238\) | 0.888018 | 0.0575617 | ||||||||
\(239\) | 5.23245i | 0.338459i | 0.985577 | + | 0.169230i | \(0.0541279\pi\) | ||||
−0.985577 | + | 0.169230i | \(0.945872\pi\) | |||||||
\(240\) | 1.00000i | 0.0645497i | ||||||||
\(241\) | − | 2.50379i | − | 0.161283i | −0.996743 | − | 0.0806417i | \(-0.974303\pi\) | ||
0.996743 | − | 0.0806417i | \(-0.0256970\pi\) | |||||||
\(242\) | − | 26.4185i | − | 1.69825i | ||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 4.07918i | 0.261143i | ||||||||
\(245\) | − | 6.86009i | − | 0.438275i | ||||||
\(246\) | − | 3.07409i | − | 0.195997i | ||||||
\(247\) | −9.28978 | −0.591095 | ||||||||
\(248\) | −3.07409 | −0.195205 | ||||||||
\(249\) | 6.78599 | 0.430045 | ||||||||
\(250\) | −1.00000 | −0.0632456 | ||||||||
\(251\) | 16.9822i | 1.07191i | 0.844247 | + | 0.535955i | \(0.180048\pi\) | ||||
−0.844247 | + | 0.535955i | \(0.819952\pi\) | |||||||
\(252\) | −0.374052 | −0.0235631 | ||||||||
\(253\) | − | 33.3267i | − | 2.09523i | ||||||
\(254\) | − | 16.1861i | − | 1.01560i | ||||||
\(255\) | −2.37405 | −0.148669 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | − | 6.70004i | − | 0.417937i | −0.977922 | − | 0.208969i | \(-0.932989\pi\) | ||
0.977922 | − | 0.208969i | \(-0.0670106\pi\) | |||||||
\(258\) | 7.82220 | 0.486989 | ||||||||
\(259\) | 1.01186 | − | 2.03789i | 0.0628738 | − | 0.126628i | ||||
\(260\) | 5.44814 | 0.337880 | ||||||||
\(261\) | − | 4.41194i | − | 0.273092i | ||||||
\(262\) | −10.8963 | −0.673175 | ||||||||
\(263\) | 8.15496 | 0.502856 | 0.251428 | − | 0.967876i | \(-0.419100\pi\) | ||||
0.251428 | + | 0.967876i | \(0.419100\pi\) | |||||||
\(264\) | − | 6.11707i | − | 0.376480i | ||||||
\(265\) | 2.37405i | 0.145837i | ||||||||
\(266\) | 0.637806 | 0.0391064 | ||||||||
\(267\) | 0.551855i | 0.0337730i | ||||||||
\(268\) | −10.1482 | −0.619899 | ||||||||
\(269\) | −5.34952 | −0.326166 | −0.163083 | − | 0.986612i | \(-0.552144\pi\) | ||||
−0.163083 | + | 0.986612i | \(0.552144\pi\) | |||||||
\(270\) | 1.00000 | 0.0608581 | ||||||||
\(271\) | −27.2888 | −1.65768 | −0.828838 | − | 0.559489i | \(-0.810997\pi\) | ||||
−0.828838 | + | 0.559489i | \(0.810997\pi\) | |||||||
\(272\) | 2.37405i | 0.143948i | ||||||||
\(273\) | 2.03789i | 0.123339i | ||||||||
\(274\) | − | 0.332760i | − | 0.0201028i | ||||||
\(275\) | 6.11707 | 0.368873 | ||||||||
\(276\) | − | 5.44814i | − | 0.327940i | ||||||
\(277\) | 6.78599i | 0.407731i | 0.978999 | + | 0.203865i | \(0.0653505\pi\) | ||||
−0.978999 | + | 0.203865i | \(0.934650\pi\) | |||||||
\(278\) | 13.8980i | 0.833545i | ||||||||
\(279\) | 3.07409i | 0.184041i | ||||||||
\(280\) | −0.374052 | −0.0223539 | ||||||||
\(281\) | − | 18.8719i | − | 1.12581i | −0.826523 | − | 0.562903i | \(-0.809685\pi\) | ||
0.826523 | − | 0.562903i | \(-0.190315\pi\) | |||||||
\(282\) | 13.3874i | 0.797209i | ||||||||
\(283\) | − | 10.5417i | − | 0.626638i | −0.949648 | − | 0.313319i | \(-0.898559\pi\) | ||
0.949648 | − | 0.313319i | \(-0.101441\pi\) | |||||||
\(284\) | −4.74810 | −0.281748 | ||||||||
\(285\) | −1.70513 | −0.101003 | ||||||||
\(286\) | −33.3267 | −1.97065 | ||||||||
\(287\) | 1.14987 | 0.0678747 | ||||||||
\(288\) | − | 1.00000i | − | 0.0589256i | ||||||
\(289\) | 11.3639 | 0.668463 | ||||||||
\(290\) | − | 4.41194i | − | 0.259078i | ||||||
\(291\) | 8.15496i | 0.478052i | ||||||||
\(292\) | −8.19625 | −0.479649 | ||||||||
\(293\) | −8.46000 | −0.494239 | −0.247119 | − | 0.968985i | \(-0.579484\pi\) | ||||
−0.247119 | + | 0.968985i | \(0.579484\pi\) | |||||||
\(294\) | 6.86009i | 0.400088i | ||||||||
\(295\) | −10.8963 | −0.634407 | ||||||||
\(296\) | 5.44814 | + | 2.70513i | 0.316667 | + | 0.157232i | ||||
\(297\) | −6.11707 | −0.354948 | ||||||||
\(298\) | 11.9014i | 0.689428i | ||||||||
\(299\) | −29.6823 | −1.71657 | ||||||||
\(300\) | 1.00000 | 0.0577350 | ||||||||
\(301\) | 2.92591i | 0.168646i | ||||||||
\(302\) | − | 18.4304i | − | 1.06055i | ||||||
\(303\) | 3.74302 | 0.215031 | ||||||||
\(304\) | 1.70513i | 0.0977958i | ||||||||
\(305\) | 4.07918 | 0.233573 | ||||||||
\(306\) | 2.37405 | 0.135716 | ||||||||
\(307\) | −16.4683 | −0.939894 | −0.469947 | − | 0.882695i | \(-0.655727\pi\) | ||||
−0.469947 | + | 0.882695i | \(0.655727\pi\) | |||||||
\(308\) | 2.28810 | 0.130377 | ||||||||
\(309\) | − | 8.49112i | − | 0.483043i | ||||||
\(310\) | 3.07409i | 0.174597i | ||||||||
\(311\) | 21.0741i | 1.19500i | 0.801868 | + | 0.597501i | \(0.203840\pi\) | ||||
−0.801868 | + | 0.597501i | \(0.796160\pi\) | |||||||
\(312\) | −5.44814 | −0.308440 | ||||||||
\(313\) | − | 27.6317i | − | 1.56184i | −0.624633 | − | 0.780919i | \(-0.714751\pi\) | ||
0.624633 | − | 0.780919i | \(-0.285249\pi\) | |||||||
\(314\) | − | 7.98056i | − | 0.450369i | ||||||
\(315\) | 0.374052i | 0.0210754i | ||||||||
\(316\) | − | 12.1482i | − | 0.683389i | ||||||
\(317\) | 16.4119 | 0.921786 | 0.460893 | − | 0.887456i | \(-0.347529\pi\) | ||||
0.460893 | + | 0.887456i | \(0.347529\pi\) | |||||||
\(318\) | − | 2.37405i | − | 0.133130i | ||||||
\(319\) | 26.9881i | 1.51105i | ||||||||
\(320\) | − | 1.00000i | − | 0.0559017i | ||||||
\(321\) | −17.4481 | −0.973860 | ||||||||
\(322\) | 2.03789 | 0.113567 | ||||||||
\(323\) | −4.04806 | −0.225240 | ||||||||
\(324\) | −1.00000 | −0.0555556 | ||||||||
\(325\) | − | 5.44814i | − | 0.302209i | ||||||
\(326\) | 9.86009 | 0.546100 | ||||||||
\(327\) | − | 8.62086i | − | 0.476735i | ||||||
\(328\) | 3.07409i | 0.169738i | ||||||||
\(329\) | −5.00759 | −0.276077 | ||||||||
\(330\) | −6.11707 | −0.336734 | ||||||||
\(331\) | − | 32.9594i | − | 1.81161i | −0.423693 | − | 0.905806i | \(-0.639266\pi\) | ||
0.423693 | − | 0.905806i | \(-0.360734\pi\) | |||||||
\(332\) | −6.78599 | −0.372430 | ||||||||
\(333\) | 2.70513 | − | 5.44814i | 0.148240 | − | 0.298556i | ||||
\(334\) | −22.4304 | −1.22734 | ||||||||
\(335\) | 10.1482i | 0.554455i | ||||||||
\(336\) | 0.374052 | 0.0204062 | ||||||||
\(337\) | 23.1548 | 1.26132 | 0.630660 | − | 0.776059i | \(-0.282784\pi\) | ||||
0.630660 | + | 0.776059i | \(0.282784\pi\) | |||||||
\(338\) | 16.6823i | 0.907397i | ||||||||
\(339\) | − | 18.7185i | − | 1.01665i | ||||||
\(340\) | 2.37405 | 0.128751 | ||||||||
\(341\) | − | 18.8044i | − | 1.01832i | ||||||
\(342\) | 1.70513 | 0.0922028 | ||||||||
\(343\) | −5.18439 | −0.279931 | ||||||||
\(344\) | −7.82220 | −0.421745 | ||||||||
\(345\) | −5.44814 | −0.293318 | ||||||||
\(346\) | 22.7665i | 1.22394i | ||||||||
\(347\) | − | 5.91405i | − | 0.317483i | −0.987320 | − | 0.158741i | \(-0.949256\pi\) | ||
0.987320 | − | 0.158741i | \(-0.0507436\pi\) | |||||||
\(348\) | 4.41194i | 0.236505i | ||||||||
\(349\) | 3.17949 | 0.170194 | 0.0850970 | − | 0.996373i | \(-0.472880\pi\) | ||||
0.0850970 | + | 0.996373i | \(0.472880\pi\) | |||||||
\(350\) | 0.374052i | 0.0199939i | ||||||||
\(351\) | 5.44814i | 0.290800i | ||||||||
\(352\) | 6.11707i | 0.326041i | ||||||||
\(353\) | − | 0.102026i | − | 0.00543031i | −0.999996 | − | 0.00271515i | \(-0.999136\pi\) | ||
0.999996 | − | 0.00271515i | \(-0.000864261\pi\) | |||||||
\(354\) | 10.8963 | 0.579131 | ||||||||
\(355\) | 4.74810i | 0.252003i | ||||||||
\(356\) | − | 0.551855i | − | 0.0292483i | ||||||
\(357\) | 0.888018i | 0.0469989i | ||||||||
\(358\) | 11.1304 | 0.588261 | ||||||||
\(359\) | −13.5720 | −0.716302 | −0.358151 | − | 0.933664i | \(-0.616593\pi\) | ||||
−0.358151 | + | 0.933664i | \(0.616593\pi\) | |||||||
\(360\) | −1.00000 | −0.0527046 | ||||||||
\(361\) | 16.0925 | 0.846976 | ||||||||
\(362\) | 15.3378i | 0.806139i | ||||||||
\(363\) | 26.4185 | 1.38661 | ||||||||
\(364\) | − | 2.03789i | − | 0.106814i | ||||||
\(365\) | 8.19625i | 0.429011i | ||||||||
\(366\) | −4.07918 | −0.213222 | ||||||||
\(367\) | 36.3284 | 1.89632 | 0.948162 | − | 0.317786i | \(-0.102939\pi\) | ||||
0.948162 | + | 0.317786i | \(0.102939\pi\) | |||||||
\(368\) | 5.44814i | 0.284004i | ||||||||
\(369\) | 3.07409 | 0.160031 | ||||||||
\(370\) | 2.70513 | − | 5.44814i | 0.140633 | − | 0.283236i | ||||
\(371\) | 0.888018 | 0.0461036 | ||||||||
\(372\) | − | 3.07409i | − | 0.159384i | ||||||
\(373\) | 8.89629 | 0.460632 | 0.230316 | − | 0.973116i | \(-0.426024\pi\) | ||||
0.230316 | + | 0.973116i | \(0.426024\pi\) | |||||||
\(374\) | −14.5222 | −0.750927 | ||||||||
\(375\) | − | 1.00000i | − | 0.0516398i | ||||||
\(376\) | − | 13.3874i | − | 0.690403i | ||||||
\(377\) | 24.0369 | 1.23796 | ||||||||
\(378\) | − | 0.374052i | − | 0.0192392i | ||||||
\(379\) | −33.2028 | −1.70552 | −0.852758 | − | 0.522307i | \(-0.825072\pi\) | ||||
−0.852758 | + | 0.522307i | \(0.825072\pi\) | |||||||
\(380\) | 1.70513 | 0.0874712 | ||||||||
\(381\) | 16.1861 | 0.829238 | ||||||||
\(382\) | 12.0184 | 0.614917 | ||||||||
\(383\) | − | 27.2407i | − | 1.39194i | −0.718073 | − | 0.695968i | \(-0.754976\pi\) | ||
0.718073 | − | 0.695968i | \(-0.245024\pi\) | |||||||
\(384\) | 1.00000i | 0.0510310i | ||||||||
\(385\) | − | 2.28810i | − | 0.116612i | ||||||
\(386\) | 17.2291 | 0.876936 | ||||||||
\(387\) | 7.82220i | 0.397625i | ||||||||
\(388\) | − | 8.15496i | − | 0.414005i | ||||||
\(389\) | 4.64608i | 0.235565i | 0.993039 | + | 0.117783i | \(0.0375786\pi\) | ||||
−0.993039 | + | 0.117783i | \(0.962421\pi\) | |||||||
\(390\) | 5.44814i | 0.275878i | ||||||||
\(391\) | −12.9342 | −0.654110 | ||||||||
\(392\) | − | 6.86009i | − | 0.346487i | ||||||
\(393\) | − | 10.8963i | − | 0.549645i | ||||||
\(394\) | − | 1.88970i | − | 0.0952018i | ||||||
\(395\) | −12.1482 | −0.611242 | ||||||||
\(396\) | 6.11707 | 0.307394 | ||||||||
\(397\) | −15.5720 | −0.781535 | −0.390768 | − | 0.920489i | \(-0.627790\pi\) | ||||
−0.390768 | + | 0.920489i | \(0.627790\pi\) | |||||||
\(398\) | 14.1584 | 0.709694 | ||||||||
\(399\) | 0.637806i | 0.0319303i | ||||||||
\(400\) | −1.00000 | −0.0500000 | ||||||||
\(401\) | 28.6645i | 1.43144i | 0.698388 | + | 0.715719i | \(0.253901\pi\) | ||||
−0.698388 | + | 0.715719i | \(0.746099\pi\) | |||||||
\(402\) | − | 10.1482i | − | 0.506146i | ||||||
\(403\) | −16.7481 | −0.834282 | ||||||||
\(404\) | −3.74302 | −0.186222 | ||||||||
\(405\) | 1.00000i | 0.0496904i | ||||||||
\(406\) | −1.65029 | −0.0819027 | ||||||||
\(407\) | −16.5475 | + | 33.3267i | −0.820227 | + | 1.65194i | ||||
\(408\) | −2.37405 | −0.117533 | ||||||||
\(409\) | − | 16.9822i | − | 0.839718i | −0.907589 | − | 0.419859i | \(-0.862080\pi\) | ||
0.907589 | − | 0.419859i | \(-0.137920\pi\) | |||||||
\(410\) | 3.07409 | 0.151819 | ||||||||
\(411\) | 0.332760 | 0.0164139 | ||||||||
\(412\) | 8.49112i | 0.418327i | ||||||||
\(413\) | 4.07578i | 0.200556i | ||||||||
\(414\) | 5.44814 | 0.267762 | ||||||||
\(415\) | 6.78599i | 0.333111i | ||||||||
\(416\) | 5.44814 | 0.267117 | ||||||||
\(417\) | −13.8980 | −0.680587 | ||||||||
\(418\) | −10.4304 | −0.510167 | ||||||||
\(419\) | 28.2949 | 1.38229 | 0.691147 | − | 0.722714i | \(-0.257105\pi\) | ||||
0.691147 | + | 0.722714i | \(0.257105\pi\) | |||||||
\(420\) | − | 0.374052i | − | 0.0182519i | ||||||
\(421\) | 11.3150i | 0.551459i | 0.961235 | + | 0.275730i | \(0.0889195\pi\) | ||||
−0.961235 | + | 0.275730i | \(0.911081\pi\) | |||||||
\(422\) | − | 11.1600i | − | 0.543262i | ||||||
\(423\) | −13.3874 | −0.650918 | ||||||||
\(424\) | 2.37405i | 0.115294i | ||||||||
\(425\) | − | 2.37405i | − | 0.115158i | ||||||
\(426\) | − | 4.74810i | − | 0.230046i | ||||||
\(427\) | − | 1.52582i | − | 0.0738398i | ||||||
\(428\) | 17.4481 | 0.843388 | ||||||||
\(429\) | − | 33.3267i | − | 1.60903i | ||||||
\(430\) | 7.82220i | 0.377220i | ||||||||
\(431\) | 13.1844i | 0.635070i | 0.948247 | + | 0.317535i | \(0.102855\pi\) | ||||
−0.948247 | + | 0.317535i | \(0.897145\pi\) | |||||||
\(432\) | 1.00000 | 0.0481125 | ||||||||
\(433\) | 34.9711 | 1.68060 | 0.840301 | − | 0.542120i | \(-0.182378\pi\) | ||||
0.840301 | + | 0.542120i | \(0.182378\pi\) | |||||||
\(434\) | 1.14987 | 0.0551955 | ||||||||
\(435\) | 4.41194 | 0.211536 | ||||||||
\(436\) | 8.62086i | 0.412864i | ||||||||
\(437\) | −9.28978 | −0.444391 | ||||||||
\(438\) | − | 8.19625i | − | 0.391632i | ||||||
\(439\) | − | 3.27134i | − | 0.156133i | −0.996948 | − | 0.0780663i | \(-0.975125\pi\) | ||
0.996948 | − | 0.0780663i | \(-0.0248746\pi\) | |||||||
\(440\) | 6.11707 | 0.291620 | ||||||||
\(441\) | −6.86009 | −0.326671 | ||||||||
\(442\) | 12.9342i | 0.615216i | ||||||||
\(443\) | 21.9645 | 1.04356 | 0.521782 | − | 0.853079i | \(-0.325267\pi\) | ||||
0.521782 | + | 0.853079i | \(0.325267\pi\) | |||||||
\(444\) | −2.70513 | + | 5.44814i | −0.128380 | + | 0.258558i | ||||
\(445\) | −0.551855 | −0.0261604 | ||||||||
\(446\) | 10.5703i | 0.500518i | ||||||||
\(447\) | −11.9014 | −0.562916 | ||||||||
\(448\) | −0.374052 | −0.0176723 | ||||||||
\(449\) | − | 10.8103i | − | 0.510171i | −0.966918 | − | 0.255086i | \(-0.917896\pi\) | ||
0.966918 | − | 0.255086i | \(-0.0821037\pi\) | |||||||
\(450\) | 1.00000i | 0.0471405i | ||||||||
\(451\) | −18.8044 | −0.885466 | ||||||||
\(452\) | 18.7185i | 0.880444i | ||||||||
\(453\) | 18.4304 | 0.865935 | ||||||||
\(454\) | −2.05633 | −0.0965085 | ||||||||
\(455\) | −2.03789 | −0.0955377 | ||||||||
\(456\) | −1.70513 | −0.0798499 | ||||||||
\(457\) | − | 2.74133i | − | 0.128234i | −0.997942 | − | 0.0641171i | \(-0.979577\pi\) | ||
0.997942 | − | 0.0641171i | \(-0.0204231\pi\) | |||||||
\(458\) | − | 8.08595i | − | 0.377832i | ||||||
\(459\) | 2.37405i | 0.110811i | ||||||||
\(460\) | 5.44814 | 0.254021 | ||||||||
\(461\) | 30.9526i | 1.44161i | 0.693139 | + | 0.720804i | \(0.256227\pi\) | ||||
−0.693139 | + | 0.720804i | \(0.743773\pi\) | |||||||
\(462\) | 2.28810i | 0.106452i | ||||||||
\(463\) | 15.7430i | 0.731640i | 0.930686 | + | 0.365820i | \(0.119211\pi\) | ||||
−0.930686 | + | 0.365820i | \(0.880789\pi\) | |||||||
\(464\) | − | 4.41194i | − | 0.204819i | ||||||
\(465\) | −3.07409 | −0.142558 | ||||||||
\(466\) | − | 22.1253i | − | 1.02494i | ||||||
\(467\) | − | 17.7007i | − | 0.819092i | −0.912289 | − | 0.409546i | \(-0.865687\pi\) | ||
0.912289 | − | 0.409546i | \(-0.134313\pi\) | |||||||
\(468\) | − | 5.44814i | − | 0.251841i | ||||||
\(469\) | 3.79595 | 0.175281 | ||||||||
\(470\) | −13.3874 | −0.617515 | ||||||||
\(471\) | 7.98056 | 0.367725 | ||||||||
\(472\) | −10.8963 | −0.501542 | ||||||||
\(473\) | − | 47.8489i | − | 2.20010i | ||||||
\(474\) | 12.1482 | 0.557985 | ||||||||
\(475\) | − | 1.70513i | − | 0.0782366i | ||||||
\(476\) | − | 0.888018i | − | 0.0407023i | ||||||
\(477\) | 2.37405 | 0.108700 | ||||||||
\(478\) | 5.23245 | 0.239327 | ||||||||
\(479\) | − | 4.47945i | − | 0.204671i | −0.994750 | − | 0.102336i | \(-0.967368\pi\) | ||
0.994750 | − | 0.102336i | \(-0.0326315\pi\) | |||||||
\(480\) | 1.00000 | 0.0456435 | ||||||||
\(481\) | 29.6823 | + | 14.7379i | 1.35340 | + | 0.671992i | ||||
\(482\) | −2.50379 | −0.114045 | ||||||||
\(483\) | 2.03789i | 0.0927271i | ||||||||
\(484\) | −26.4185 | −1.20084 | ||||||||
\(485\) | −8.15496 | −0.370298 | ||||||||
\(486\) | − | 1.00000i | − | 0.0453609i | ||||||
\(487\) | 7.32518i | 0.331935i | 0.986131 | + | 0.165968i | \(0.0530747\pi\) | ||||
−0.986131 | + | 0.165968i | \(0.946925\pi\) | |||||||
\(488\) | 4.07918 | 0.184656 | ||||||||
\(489\) | 9.86009i | 0.445888i | ||||||||
\(490\) | −6.86009 | −0.309907 | ||||||||
\(491\) | 32.0015 | 1.44421 | 0.722104 | − | 0.691785i | \(-0.243175\pi\) | ||||
0.722104 | + | 0.691785i | \(0.243175\pi\) | |||||||
\(492\) | −3.07409 | −0.138591 | ||||||||
\(493\) | 10.4742 | 0.471733 | ||||||||
\(494\) | 9.28978i | 0.417967i | ||||||||
\(495\) | − | 6.11707i | − | 0.274942i | ||||||
\(496\) | 3.07409i | 0.138031i | ||||||||
\(497\) | 1.77604 | 0.0796661 | ||||||||
\(498\) | − | 6.78599i | − | 0.304088i | ||||||
\(499\) | 35.4977i | 1.58910i | 0.607202 | + | 0.794548i | \(0.292292\pi\) | ||||
−0.607202 | + | 0.794548i | \(0.707708\pi\) | |||||||
\(500\) | 1.00000i | 0.0447214i | ||||||||
\(501\) | − | 22.4304i | − | 1.00212i | ||||||
\(502\) | 16.9822 | 0.757954 | ||||||||
\(503\) | − | 2.01017i | − | 0.0896292i | −0.998995 | − | 0.0448146i | \(-0.985730\pi\) | ||
0.998995 | − | 0.0448146i | \(-0.0142697\pi\) | |||||||
\(504\) | 0.374052i | 0.0166616i | ||||||||
\(505\) | 3.74302i | 0.166562i | ||||||||
\(506\) | −33.3267 | −1.48155 | ||||||||
\(507\) | −16.6823 | −0.740886 | ||||||||
\(508\) | −16.1861 | −0.718141 | ||||||||
\(509\) | −17.5468 | −0.777747 | −0.388873 | − | 0.921291i | \(-0.627136\pi\) | ||||
−0.388873 | + | 0.921291i | \(0.627136\pi\) | |||||||
\(510\) | 2.37405i | 0.105125i | ||||||||
\(511\) | 3.06582 | 0.135624 | ||||||||
\(512\) | − | 1.00000i | − | 0.0441942i | ||||||
\(513\) | 1.70513i | 0.0752832i | ||||||||
\(514\) | −6.70004 | −0.295526 | ||||||||
\(515\) | 8.49112 | 0.374163 | ||||||||
\(516\) | − | 7.82220i | − | 0.344353i | ||||||
\(517\) | 81.8917 | 3.60159 | ||||||||
\(518\) | −2.03789 | − | 1.01186i | −0.0895397 | − | 0.0444585i | ||||
\(519\) | −22.7665 | −0.999341 | ||||||||
\(520\) | − | 5.44814i | − | 0.238917i | ||||||
\(521\) | 8.55676 | 0.374878 | 0.187439 | − | 0.982276i | \(-0.439981\pi\) | ||||
0.187439 | + | 0.982276i | \(0.439981\pi\) | |||||||
\(522\) | −4.41194 | −0.193105 | ||||||||
\(523\) | − | 13.7202i | − | 0.599941i | −0.953948 | − | 0.299971i | \(-0.903023\pi\) | ||
0.953948 | − | 0.299971i | \(-0.0969769\pi\) | |||||||
\(524\) | 10.8963i | 0.476007i | ||||||||
\(525\) | −0.374052 | −0.0163250 | ||||||||
\(526\) | − | 8.15496i | − | 0.355573i | ||||||
\(527\) | −7.29806 | −0.317908 | ||||||||
\(528\) | −6.11707 | −0.266211 | ||||||||
\(529\) | −6.68228 | −0.290534 | ||||||||
\(530\) | 2.37405 | 0.103122 | ||||||||
\(531\) | 10.8963i | 0.472859i | ||||||||
\(532\) | − | 0.637806i | − | 0.0276524i | ||||||
\(533\) | 16.7481i | 0.725441i | ||||||||
\(534\) | 0.551855 | 0.0238811 | ||||||||
\(535\) | − | 17.4481i | − | 0.754349i | ||||||
\(536\) | 10.1482i | 0.438335i | ||||||||
\(537\) | 11.1304i | 0.480313i | ||||||||
\(538\) | 5.34952i | 0.230634i | ||||||||
\(539\) | 41.9636 | 1.80750 | ||||||||
\(540\) | − | 1.00000i | − | 0.0430331i | ||||||
\(541\) | 21.0430i | 0.904708i | 0.891838 | + | 0.452354i | \(0.149416\pi\) | ||||
−0.891838 | + | 0.452354i | \(0.850584\pi\) | |||||||
\(542\) | 27.2888i | 1.17215i | ||||||||
\(543\) | −15.3378 | −0.658210 | ||||||||
\(544\) | 2.37405 | 0.101787 | ||||||||
\(545\) | 8.62086 | 0.369277 | ||||||||
\(546\) | 2.03789 | 0.0872136 | ||||||||
\(547\) | 29.3461i | 1.25475i | 0.778718 | + | 0.627375i | \(0.215871\pi\) | ||||
−0.778718 | + | 0.627375i | \(0.784129\pi\) | |||||||
\(548\) | −0.332760 | −0.0142148 | ||||||||
\(549\) | − | 4.07918i | − | 0.174095i | ||||||
\(550\) | − | 6.11707i | − | 0.260833i | ||||||
\(551\) | 7.52292 | 0.320487 | ||||||||
\(552\) | −5.44814 | −0.231888 | ||||||||
\(553\) | 4.54405i | 0.193233i | ||||||||
\(554\) | 6.78599 | 0.288309 | ||||||||
\(555\) | 5.44814 | + | 2.70513i | 0.231261 | + | 0.114826i | ||||
\(556\) | 13.8980 | 0.589405 | ||||||||
\(557\) | 19.4370i | 0.823571i | 0.911281 | + | 0.411785i | \(0.135095\pi\) | ||||
−0.911281 | + | 0.411785i | \(0.864905\pi\) | |||||||
\(558\) | 3.07409 | 0.130137 | ||||||||
\(559\) | −42.6165 | −1.80248 | ||||||||
\(560\) | 0.374052i | 0.0158066i | ||||||||
\(561\) | − | 14.5222i | − | 0.613129i | ||||||
\(562\) | −18.8719 | −0.796065 | ||||||||
\(563\) | 43.2981i | 1.82480i | 0.409305 | + | 0.912398i | \(0.365771\pi\) | ||||
−0.409305 | + | 0.912398i | \(0.634229\pi\) | |||||||
\(564\) | 13.3874 | 0.563712 | ||||||||
\(565\) | 18.7185 | 0.787493 | ||||||||
\(566\) | −10.5417 | −0.443100 | ||||||||
\(567\) | 0.374052 | 0.0157087 | ||||||||
\(568\) | 4.74810i | 0.199226i | ||||||||
\(569\) | 28.9240i | 1.21256i | 0.795252 | + | 0.606279i | \(0.207338\pi\) | ||||
−0.795252 | + | 0.606279i | \(0.792662\pi\) | |||||||
\(570\) | 1.70513i | 0.0714200i | ||||||||
\(571\) | −7.07746 | −0.296183 | −0.148091 | − | 0.988974i | \(-0.547313\pi\) | ||||
−0.148091 | + | 0.988974i | \(0.547313\pi\) | |||||||
\(572\) | 33.3267i | 1.39346i | ||||||||
\(573\) | 12.0184i | 0.502078i | ||||||||
\(574\) | − | 1.14987i | − | 0.0479947i | ||||||
\(575\) | − | 5.44814i | − | 0.227203i | ||||||
\(576\) | −1.00000 | −0.0416667 | ||||||||
\(577\) | 2.75060i | 0.114509i | 0.998360 | + | 0.0572545i | \(0.0182347\pi\) | ||||
−0.998360 | + | 0.0572545i | \(0.981765\pi\) | |||||||
\(578\) | − | 11.3639i | − | 0.472675i | ||||||
\(579\) | 17.2291i | 0.716015i | ||||||||
\(580\) | −4.41194 | −0.183196 | ||||||||
\(581\) | 2.53831 | 0.105307 | ||||||||
\(582\) | 8.15496 | 0.338034 | ||||||||
\(583\) | −14.5222 | −0.601450 | ||||||||
\(584\) | 8.19625i | 0.339163i | ||||||||
\(585\) | −5.44814 | −0.225253 | ||||||||
\(586\) | 8.46000i | 0.349480i | ||||||||
\(587\) | 8.64271i | 0.356723i | 0.983965 | + | 0.178361i | \(0.0570796\pi\) | ||||
−0.983965 | + | 0.178361i | \(0.942920\pi\) | |||||||
\(588\) | 6.86009 | 0.282905 | ||||||||
\(589\) | −5.24172 | −0.215981 | ||||||||
\(590\) | 10.8963i | 0.448593i | ||||||||
\(591\) | 1.88970 | 0.0777320 | ||||||||
\(592\) | 2.70513 | − | 5.44814i | 0.111180 | − | 0.223917i | ||||
\(593\) | 32.7253 | 1.34387 | 0.671933 | − | 0.740612i | \(-0.265464\pi\) | ||||
0.671933 | + | 0.740612i | \(0.265464\pi\) | |||||||
\(594\) | 6.11707i | 0.250986i | ||||||||
\(595\) | −0.888018 | −0.0364052 | ||||||||
\(596\) | 11.9014 | 0.487499 | ||||||||
\(597\) | 14.1584i | 0.579463i | ||||||||
\(598\) | 29.6823i | 1.21380i | ||||||||
\(599\) | 21.5584 | 0.880854 | 0.440427 | − | 0.897788i | \(-0.354827\pi\) | ||||
0.440427 | + | 0.897788i | \(0.354827\pi\) | |||||||
\(600\) | − | 1.00000i | − | 0.0408248i | ||||||
\(601\) | 14.5946 | 0.595328 | 0.297664 | − | 0.954671i | \(-0.403792\pi\) | ||||
0.297664 | + | 0.954671i | \(0.403792\pi\) | |||||||
\(602\) | 2.92591 | 0.119251 | ||||||||
\(603\) | 10.1482 | 0.413266 | ||||||||
\(604\) | −18.4304 | −0.749922 | ||||||||
\(605\) | 26.4185i | 1.07407i | ||||||||
\(606\) | − | 3.74302i | − | 0.152050i | ||||||
\(607\) | − | 19.8188i | − | 0.804420i | −0.915547 | − | 0.402210i | \(-0.868242\pi\) | ||
0.915547 | − | 0.402210i | \(-0.131758\pi\) | |||||||
\(608\) | 1.70513 | 0.0691521 | ||||||||
\(609\) | − | 1.65029i | − | 0.0668733i | ||||||
\(610\) | − | 4.07918i | − | 0.165161i | ||||||
\(611\) | − | 72.9365i | − | 2.95070i | ||||||
\(612\) | − | 2.37405i | − | 0.0959654i | ||||||
\(613\) | 43.4666 | 1.75560 | 0.877800 | − | 0.479028i | \(-0.159011\pi\) | ||||
0.877800 | + | 0.479028i | \(0.159011\pi\) | |||||||
\(614\) | 16.4683i | 0.664605i | ||||||||
\(615\) | 3.07409i | 0.123959i | ||||||||
\(616\) | − | 2.28810i | − | 0.0921902i | ||||||
\(617\) | 22.8599 | 0.920305 | 0.460152 | − | 0.887840i | \(-0.347795\pi\) | ||||
0.460152 | + | 0.887840i | \(0.347795\pi\) | |||||||
\(618\) | −8.49112 | −0.341563 | ||||||||
\(619\) | −6.92591 | −0.278376 | −0.139188 | − | 0.990266i | \(-0.544449\pi\) | ||||
−0.139188 | + | 0.990266i | \(0.544449\pi\) | |||||||
\(620\) | 3.07409 | 0.123459 | ||||||||
\(621\) | 5.44814i | 0.218627i | ||||||||
\(622\) | 21.0741 | 0.844994 | ||||||||
\(623\) | 0.206422i | 0.00827014i | ||||||||
\(624\) | 5.44814i | 0.218100i | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −27.6317 | −1.10439 | ||||||||
\(627\) | − | 10.4304i | − | 0.416549i | ||||||
\(628\) | −7.98056 | −0.318459 | ||||||||
\(629\) | 12.9342 | + | 6.42211i | 0.515719 | + | 0.256066i | ||||
\(630\) | 0.374052 | 0.0149026 | ||||||||
\(631\) | 6.95262i | 0.276780i | 0.990378 | + | 0.138390i | \(0.0441927\pi\) | ||||
−0.990378 | + | 0.138390i | \(0.955807\pi\) | |||||||
\(632\) | −12.1482 | −0.483229 | ||||||||
\(633\) | 11.1600 | 0.443572 | ||||||||
\(634\) | − | 16.4119i | − | 0.651801i | ||||||
\(635\) | 16.1861i | 0.642325i | ||||||||
\(636\) | −2.37405 | −0.0941373 | ||||||||
\(637\) | − | 37.3747i | − | 1.48084i | ||||||
\(638\) | 26.9881 | 1.06847 | ||||||||
\(639\) | 4.74810 | 0.187832 | ||||||||
\(640\) | −1.00000 | −0.0395285 | ||||||||
\(641\) | 45.9315 | 1.81419 | 0.907093 | − | 0.420931i | \(-0.138297\pi\) | ||||
0.907093 | + | 0.420931i | \(0.138297\pi\) | |||||||
\(642\) | 17.4481i | 0.688623i | ||||||||
\(643\) | 8.26276i | 0.325851i | 0.986638 | + | 0.162926i | \(0.0520931\pi\) | ||||
−0.986638 | + | 0.162926i | \(0.947907\pi\) | |||||||
\(644\) | − | 2.03789i | − | 0.0803041i | ||||||
\(645\) | −7.82220 | −0.307999 | ||||||||
\(646\) | 4.04806i | 0.159269i | ||||||||
\(647\) | 30.6510i | 1.20501i | 0.798113 | + | 0.602507i | \(0.205832\pi\) | ||||
−0.798113 | + | 0.602507i | \(0.794168\pi\) | |||||||
\(648\) | 1.00000i | 0.0392837i | ||||||||
\(649\) | − | 66.6534i | − | 2.61637i | ||||||
\(650\) | −5.44814 | −0.213694 | ||||||||
\(651\) | 1.14987i | 0.0450670i | ||||||||
\(652\) | − | 9.86009i | − | 0.386151i | ||||||
\(653\) | 27.9645i | 1.09433i | 0.837023 | + | 0.547167i | \(0.184294\pi\) | ||||
−0.837023 | + | 0.547167i | \(0.815706\pi\) | |||||||
\(654\) | −8.62086 | −0.337102 | ||||||||
\(655\) | 10.8963 | 0.425753 | ||||||||
\(656\) | 3.07409 | 0.120023 | ||||||||
\(657\) | 8.19625 | 0.319766 | ||||||||
\(658\) | 5.00759i | 0.195216i | ||||||||
\(659\) | 44.6762 | 1.74034 | 0.870169 | − | 0.492754i | \(-0.164010\pi\) | ||||
0.870169 | + | 0.492754i | \(0.164010\pi\) | |||||||
\(660\) | 6.11707i | 0.238107i | ||||||||
\(661\) | − | 1.13483i | − | 0.0441397i | −0.999756 | − | 0.0220698i | \(-0.992974\pi\) | ||
0.999756 | − | 0.0220698i | \(-0.00702562\pi\) | |||||||
\(662\) | −32.9594 | −1.28100 | ||||||||
\(663\) | −12.9342 | −0.502322 | ||||||||
\(664\) | 6.78599i | 0.263348i | ||||||||
\(665\) | −0.637806 | −0.0247331 | ||||||||
\(666\) | −5.44814 | − | 2.70513i | −0.211111 | − | 0.104822i | ||||
\(667\) | 24.0369 | 0.930712 | ||||||||
\(668\) | 22.4304i | 0.867858i | ||||||||
\(669\) | −10.5703 | −0.408671 | ||||||||
\(670\) | 10.1482 | 0.392059 | ||||||||
\(671\) | 24.9526i | 0.963285i | ||||||||
\(672\) | − | 0.374052i | − | 0.0144294i | ||||||
\(673\) | −43.4850 | −1.67622 | −0.838112 | − | 0.545497i | \(-0.816341\pi\) | ||||
−0.838112 | + | 0.545497i | \(0.816341\pi\) | |||||||
\(674\) | − | 23.1548i | − | 0.891889i | ||||||
\(675\) | −1.00000 | −0.0384900 | ||||||||
\(676\) | 16.6823 | 0.641626 | ||||||||
\(677\) | 5.96548 | 0.229272 | 0.114636 | − | 0.993408i | \(-0.463430\pi\) | ||||
0.114636 | + | 0.993408i | \(0.463430\pi\) | |||||||
\(678\) | −18.7185 | −0.718879 | ||||||||
\(679\) | 3.05038i | 0.117063i | ||||||||
\(680\) | − | 2.37405i | − | 0.0910407i | ||||||
\(681\) | − | 2.05633i | − | 0.0787989i | ||||||
\(682\) | −18.8044 | −0.720059 | ||||||||
\(683\) | − | 40.5348i | − | 1.55102i | −0.631335 | − | 0.775510i | \(-0.717493\pi\) | ||
0.631335 | − | 0.775510i | \(-0.282507\pi\) | |||||||
\(684\) | − | 1.70513i | − | 0.0651972i | ||||||
\(685\) | 0.332760i | 0.0127141i | ||||||||
\(686\) | 5.18439i | 0.197941i | ||||||||
\(687\) | 8.08595 | 0.308498 | ||||||||
\(688\) | 7.82220i | 0.298218i | ||||||||
\(689\) | 12.9342i | 0.492753i | ||||||||
\(690\) | 5.44814i | 0.207407i | ||||||||
\(691\) | −32.4843 | −1.23576 | −0.617881 | − | 0.786271i | \(-0.712009\pi\) | ||||
−0.617881 | + | 0.786271i | \(0.712009\pi\) | |||||||
\(692\) | 22.7665 | 0.865454 | ||||||||
\(693\) | −2.28810 | −0.0869178 | ||||||||
\(694\) | −5.91405 | −0.224494 | ||||||||
\(695\) | − | 13.8980i | − | 0.527180i | ||||||
\(696\) | 4.41194 | 0.167234 | ||||||||
\(697\) | 7.29806i | 0.276434i | ||||||||
\(698\) | − | 3.17949i | − | 0.120345i | ||||||
\(699\) | 22.1253 | 0.836857 | ||||||||
\(700\) | 0.374052 | 0.0141378 | ||||||||
\(701\) | 24.3823i | 0.920908i | 0.887684 | + | 0.460454i | \(0.152313\pi\) | ||||
−0.887684 | + | 0.460454i | \(0.847687\pi\) | |||||||
\(702\) | 5.44814 | 0.205627 | ||||||||
\(703\) | 9.28978 | + | 4.61259i | 0.350371 | + | 0.173967i | ||||
\(704\) | 6.11707 | 0.230546 | ||||||||
\(705\) | − | 13.3874i | − | 0.504199i | ||||||
\(706\) | −0.102026 | −0.00383981 | ||||||||
\(707\) | 1.40008 | 0.0526555 | ||||||||
\(708\) | − | 10.8963i | − | 0.409508i | ||||||
\(709\) | − | 11.8339i | − | 0.444430i | −0.974998 | − | 0.222215i | \(-0.928671\pi\) | ||
0.974998 | − | 0.222215i | \(-0.0713287\pi\) | |||||||
\(710\) | 4.74810 | 0.178193 | ||||||||
\(711\) | 12.1482i | 0.455593i | ||||||||
\(712\) | −0.551855 | −0.0206816 | ||||||||
\(713\) | −16.7481 | −0.627221 | ||||||||
\(714\) | 0.888018 | 0.0332333 | ||||||||
\(715\) | 33.3267 | 1.24635 | ||||||||
\(716\) | − | 11.1304i | − | 0.415964i | ||||||
\(717\) | 5.23245i | 0.195410i | ||||||||
\(718\) | 13.5720i | 0.506502i | ||||||||
\(719\) | 21.2990 | 0.794317 | 0.397159 | − | 0.917750i | \(-0.369996\pi\) | ||||
0.397159 | + | 0.917750i | \(0.369996\pi\) | |||||||
\(720\) | 1.00000i | 0.0372678i | ||||||||
\(721\) | − | 3.17612i | − | 0.118285i | ||||||
\(722\) | − | 16.0925i | − | 0.598902i | ||||||
\(723\) | − | 2.50379i | − | 0.0931171i | ||||||
\(724\) | 15.3378 | 0.570027 | ||||||||
\(725\) | 4.41194i | 0.163855i | ||||||||
\(726\) | − | 26.4185i | − | 0.980484i | ||||||
\(727\) | − | 16.8836i | − | 0.626179i | −0.949724 | − | 0.313089i | \(-0.898636\pi\) | ||
0.949724 | − | 0.313089i | \(-0.101364\pi\) | |||||||
\(728\) | −2.03789 | −0.0755292 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 8.19625 | 0.303357 | ||||||||
\(731\) | −18.5703 | −0.686847 | ||||||||
\(732\) | 4.07918i | 0.150771i | ||||||||
\(733\) | −20.5111 | −0.757593 | −0.378797 | − | 0.925480i | \(-0.623662\pi\) | ||||
−0.378797 | + | 0.925480i | \(0.623662\pi\) | |||||||
\(734\) | − | 36.3284i | − | 1.34090i | ||||||
\(735\) | − | 6.86009i | − | 0.253038i | ||||||
\(736\) | 5.44814 | 0.200821 | ||||||||
\(737\) | −62.0771 | −2.28664 | ||||||||
\(738\) | − | 3.07409i | − | 0.113159i | ||||||
\(739\) | −4.71849 | −0.173572 | −0.0867862 | − | 0.996227i | \(-0.527660\pi\) | ||||
−0.0867862 | + | 0.996227i | \(0.527660\pi\) | |||||||
\(740\) | −5.44814 | − | 2.70513i | −0.200278 | − | 0.0994425i | ||||
\(741\) | −9.28978 | −0.341269 | ||||||||
\(742\) | − | 0.888018i | − | 0.0326002i | ||||||
\(743\) | −54.0098 | −1.98143 | −0.990713 | − | 0.135968i | \(-0.956585\pi\) | ||||
−0.990713 | + | 0.135968i | \(0.956585\pi\) | |||||||
\(744\) | −3.07409 | −0.112702 | ||||||||
\(745\) | − | 11.9014i | − | 0.436033i | ||||||
\(746\) | − | 8.89629i | − | 0.325716i | ||||||
\(747\) | 6.78599 | 0.248286 | ||||||||
\(748\) | 14.5222i | 0.530986i | ||||||||
\(749\) | −6.52651 | −0.238474 | ||||||||
\(750\) | −1.00000 | −0.0365148 | ||||||||
\(751\) | 12.6520 | 0.461677 | 0.230839 | − | 0.972992i | \(-0.425853\pi\) | ||||
0.230839 | + | 0.972992i | \(0.425853\pi\) | |||||||
\(752\) | −13.3874 | −0.488189 | ||||||||
\(753\) | 16.9822i | 0.618867i | ||||||||
\(754\) | − | 24.0369i | − | 0.875372i | ||||||
\(755\) | 18.4304i | 0.670750i | ||||||||
\(756\) | −0.374052 | −0.0136041 | ||||||||
\(757\) | 10.8618i | 0.394778i | 0.980325 | + | 0.197389i | \(0.0632462\pi\) | ||||
−0.980325 | + | 0.197389i | \(0.936754\pi\) | |||||||
\(758\) | 33.2028i | 1.20598i | ||||||||
\(759\) | − | 33.3267i | − | 1.20968i | ||||||
\(760\) | − | 1.70513i | − | 0.0618515i | ||||||
\(761\) | 37.2358 | 1.34980 | 0.674899 | − | 0.737910i | \(-0.264187\pi\) | ||||
0.674899 | + | 0.737910i | \(0.264187\pi\) | |||||||
\(762\) | − | 16.1861i | − | 0.586360i | ||||||
\(763\) | − | 3.22465i | − | 0.116740i | ||||||
\(764\) | − | 12.0184i | − | 0.434812i | ||||||
\(765\) | −2.37405 | −0.0858340 | ||||||||
\(766\) | −27.2407 | −0.984247 | ||||||||
\(767\) | −59.3646 | −2.14353 | ||||||||
\(768\) | 1.00000 | 0.0360844 | ||||||||
\(769\) | − | 15.9039i | − | 0.573508i | −0.958004 | − | 0.286754i | \(-0.907424\pi\) | ||
0.958004 | − | 0.286754i | \(-0.0925763\pi\) | |||||||
\(770\) | −2.28810 | −0.0824574 | ||||||||
\(771\) | − | 6.70004i | − | 0.241296i | ||||||
\(772\) | − | 17.2291i | − | 0.620087i | ||||||
\(773\) | −48.1666 | −1.73243 | −0.866217 | − | 0.499669i | \(-0.833455\pi\) | ||||
−0.866217 | + | 0.499669i | \(0.833455\pi\) | |||||||
\(774\) | 7.82220 | 0.281163 | ||||||||
\(775\) | − | 3.07409i | − | 0.110425i | ||||||
\(776\) | −8.15496 | −0.292746 | ||||||||
\(777\) | 1.01186 | − | 2.03789i | 0.0363002 | − | 0.0731088i | ||||
\(778\) | 4.64608 | 0.166570 | ||||||||
\(779\) | 5.24172i | 0.187804i | ||||||||
\(780\) | 5.44814 | 0.195075 | ||||||||
\(781\) | −29.0445 | −1.03929 | ||||||||
\(782\) | 12.9342i | 0.462525i | ||||||||
\(783\) | − | 4.41194i | − | 0.157670i | ||||||
\(784\) | −6.86009 | −0.245003 | ||||||||
\(785\) | 7.98056i | 0.284838i | ||||||||
\(786\) | −10.8963 | −0.388658 | ||||||||
\(787\) | 3.42380 | 0.122045 | 0.0610226 | − | 0.998136i | \(-0.480564\pi\) | ||||
0.0610226 | + | 0.998136i | \(0.480564\pi\) | |||||||
\(788\) | −1.88970 | −0.0673179 | ||||||||
\(789\) | 8.15496 | 0.290324 | ||||||||
\(790\) | 12.1482i | 0.432213i | ||||||||
\(791\) | − | 7.00168i | − | 0.248951i | ||||||
\(792\) | − | 6.11707i | − | 0.217361i | ||||||
\(793\) | 22.2240 | 0.789196 | ||||||||
\(794\) | 15.5720i | 0.552629i | ||||||||
\(795\) | 2.37405i | 0.0841989i | ||||||||
\(796\) | − | 14.1584i | − | 0.501830i | ||||||
\(797\) | 20.5407i | 0.727588i | 0.931479 | + | 0.363794i | \(0.118519\pi\) | ||||
−0.931479 | + | 0.363794i | \(0.881481\pi\) | |||||||
\(798\) | 0.637806 | 0.0225781 | ||||||||
\(799\) | − | 31.7824i | − | 1.12438i | ||||||
\(800\) | 1.00000i | 0.0353553i | ||||||||
\(801\) | 0.551855i | 0.0194988i | ||||||||
\(802\) | 28.6645 | 1.01218 | ||||||||
\(803\) | −50.1370 | −1.76930 | ||||||||
\(804\) | −10.1482 | −0.357899 | ||||||||
\(805\) | −2.03789 | −0.0718261 | ||||||||
\(806\) | 16.7481i | 0.589927i | ||||||||
\(807\) | −5.34952 | −0.188312 | ||||||||
\(808\) | 3.74302i | 0.131679i | ||||||||
\(809\) | 21.5476i | 0.757575i | 0.925484 | + | 0.378787i | \(0.123659\pi\) | ||||
−0.925484 | + | 0.378787i | \(0.876341\pi\) | |||||||
\(810\) | 1.00000 | 0.0351364 | ||||||||
\(811\) | 0.293372 | 0.0103017 | 0.00515084 | − | 0.999987i | \(-0.498360\pi\) | ||||
0.00515084 | + | 0.999987i | \(0.498360\pi\) | |||||||
\(812\) | 1.65029i | 0.0579140i | ||||||||
\(813\) | −27.2888 | −0.957060 | ||||||||
\(814\) | 33.3267 | + | 16.5475i | 1.16810 | + | 0.579988i | ||||
\(815\) | −9.86009 | −0.345384 | ||||||||
\(816\) | 2.37405i | 0.0831084i | ||||||||
\(817\) | −13.3378 | −0.466632 | ||||||||
\(818\) | −16.9822 | −0.593770 | ||||||||
\(819\) | 2.03789i | 0.0712096i | ||||||||
\(820\) | − | 3.07409i | − | 0.107352i | ||||||
\(821\) | −33.7217 | −1.17689 | −0.588447 | − | 0.808536i | \(-0.700261\pi\) | ||||
−0.588447 | + | 0.808536i | \(0.700261\pi\) | |||||||
\(822\) | − | 0.332760i | − | 0.0116064i | ||||||
\(823\) | −35.0570 | −1.22201 | −0.611005 | − | 0.791626i | \(-0.709235\pi\) | ||||
−0.611005 | + | 0.791626i | \(0.709235\pi\) | |||||||
\(824\) | 8.49112 | 0.295802 | ||||||||
\(825\) | 6.11707 | 0.212969 | ||||||||
\(826\) | 4.07578 | 0.141814 | ||||||||
\(827\) | 30.8044i | 1.07118i | 0.844480 | + | 0.535588i | \(0.179910\pi\) | ||||
−0.844480 | + | 0.535588i | \(0.820090\pi\) | |||||||
\(828\) | − | 5.44814i | − | 0.189336i | ||||||
\(829\) | 27.6133i | 0.959049i | 0.877529 | + | 0.479524i | \(0.159191\pi\) | ||||
−0.877529 | + | 0.479524i | \(0.840809\pi\) | |||||||
\(830\) | 6.78599 | 0.235545 | ||||||||
\(831\) | 6.78599i | 0.235403i | ||||||||
\(832\) | − | 5.44814i | − | 0.188880i | ||||||
\(833\) | − | 16.2862i | − | 0.564283i | ||||||
\(834\) | 13.8980i | 0.481247i | ||||||||
\(835\) | 22.4304 | 0.776236 | ||||||||
\(836\) | 10.4304i | 0.360742i | ||||||||
\(837\) | 3.07409i | 0.106256i | ||||||||
\(838\) | − | 28.2949i | − | 0.977430i | ||||||
\(839\) | 15.1761 | 0.523938 | 0.261969 | − | 0.965076i | \(-0.415628\pi\) | ||||
0.261969 | + | 0.965076i | \(0.415628\pi\) | |||||||
\(840\) | −0.374052 | −0.0129060 | ||||||||
\(841\) | 9.53478 | 0.328786 | ||||||||
\(842\) | 11.3150 | 0.389941 | ||||||||
\(843\) | − | 18.8719i | − | 0.649984i | ||||||
\(844\) | −11.1600 | −0.384145 | ||||||||
\(845\) | − | 16.6823i | − | 0.573888i | ||||||
\(846\) | 13.3874i | 0.460269i | ||||||||
\(847\) | 9.88190 | 0.339546 | ||||||||
\(848\) | 2.37405 | 0.0815253 | ||||||||
\(849\) | − | 10.5417i | − | 0.361790i | ||||||
\(850\) | −2.37405 | −0.0814293 | ||||||||
\(851\) | 29.6823 | + | 14.7379i | 1.01750 | + | 0.505210i | ||||
\(852\) | −4.74810 | −0.162667 | ||||||||
\(853\) | − | 27.4380i | − | 0.939458i | −0.882811 | − | 0.469729i | \(-0.844352\pi\) | ||
0.882811 | − | 0.469729i | \(-0.155648\pi\) | |||||||
\(854\) | −1.52582 | −0.0522126 | ||||||||
\(855\) | −1.70513 | −0.0583142 | ||||||||
\(856\) | − | 17.4481i | − | 0.596365i | ||||||
\(857\) | − | 0.535780i | − | 0.0183019i | −0.999958 | − | 0.00915095i | \(-0.997087\pi\) | ||
0.999958 | − | 0.00915095i | \(-0.00291288\pi\) | |||||||
\(858\) | −33.3267 | −1.13775 | ||||||||
\(859\) | 55.8649i | 1.90608i | 0.302837 | + | 0.953042i | \(0.402066\pi\) | ||||
−0.302837 | + | 0.953042i | \(0.597934\pi\) | |||||||
\(860\) | 7.82220 | 0.266735 | ||||||||
\(861\) | 1.14987 | 0.0391875 | ||||||||
\(862\) | 13.1844 | 0.449062 | ||||||||
\(863\) | 10.5343 | 0.358591 | 0.179296 | − | 0.983795i | \(-0.442618\pi\) | ||||
0.179296 | + | 0.983795i | \(0.442618\pi\) | |||||||
\(864\) | − | 1.00000i | − | 0.0340207i | ||||||
\(865\) | − | 22.7665i | − | 0.774086i | ||||||
\(866\) | − | 34.9711i | − | 1.18837i | ||||||
\(867\) | 11.3639 | 0.385938 | ||||||||
\(868\) | − | 1.14987i | − | 0.0390291i | ||||||
\(869\) | − | 74.3113i | − | 2.52084i | ||||||
\(870\) | − | 4.41194i | − | 0.149579i | ||||||
\(871\) | 55.2888i | 1.87339i | ||||||||
\(872\) | 8.62086 | 0.291939 | ||||||||
\(873\) | 8.15496i | 0.276003i | ||||||||
\(874\) | 9.28978i | 0.314232i | ||||||||
\(875\) | − | 0.374052i | − | 0.0126453i | ||||||
\(876\) | −8.19625 | −0.276926 | ||||||||
\(877\) | −3.99410 | −0.134871 | −0.0674356 | − | 0.997724i | \(-0.521482\pi\) | ||||
−0.0674356 | + | 0.997724i | \(0.521482\pi\) | |||||||
\(878\) | −3.27134 | −0.110402 | ||||||||
\(879\) | −8.46000 | −0.285349 | ||||||||
\(880\) | − | 6.11707i | − | 0.206206i | ||||||
\(881\) | −23.9971 | −0.808483 | −0.404241 | − | 0.914652i | \(-0.632464\pi\) | ||||
−0.404241 | + | 0.914652i | \(0.632464\pi\) | |||||||
\(882\) | 6.86009i | 0.230991i | ||||||||
\(883\) | − | 37.4422i | − | 1.26003i | −0.776582 | − | 0.630016i | \(-0.783048\pi\) | ||
0.776582 | − | 0.630016i | \(-0.216952\pi\) | |||||||
\(884\) | 12.9342 | 0.435023 | ||||||||
\(885\) | −10.8963 | −0.366275 | ||||||||
\(886\) | − | 21.9645i | − | 0.737911i | ||||||
\(887\) | 1.33444 | 0.0448063 | 0.0224031 | − | 0.999749i | \(-0.492868\pi\) | ||||
0.0224031 | + | 0.999749i | \(0.492868\pi\) | |||||||
\(888\) | 5.44814 | + | 2.70513i | 0.182828 | + | 0.0907782i | ||||
\(889\) | 6.05443 | 0.203059 | ||||||||
\(890\) | 0.551855i | 0.0184982i | ||||||||
\(891\) | −6.11707 | −0.204930 | ||||||||
\(892\) | 10.5703 | 0.353920 | ||||||||
\(893\) | − | 22.8272i | − | 0.763885i | ||||||
\(894\) | 11.9014i | 0.398042i | ||||||||
\(895\) | −11.1304 | −0.372049 | ||||||||
\(896\) | 0.374052i | 0.0124962i | ||||||||
\(897\) | −29.6823 | −0.991063 | ||||||||
\(898\) | −10.8103 | −0.360746 | ||||||||
\(899\) | 13.5627 | 0.452342 | ||||||||
\(900\) | 1.00000 | 0.0333333 | ||||||||
\(901\) | 5.63612i | 0.187766i | ||||||||
\(902\) | 18.8044i | 0.626119i | ||||||||
\(903\) | 2.92591i | 0.0973681i | ||||||||
\(904\) | 18.7185 | 0.622568 | ||||||||
\(905\) | − | 15.3378i | − | 0.509847i | ||||||
\(906\) | − | 18.4304i | − | 0.612309i | ||||||
\(907\) | − | 18.9342i | − | 0.628699i | −0.949307 | − | 0.314350i | \(-0.898214\pi\) | ||
0.949307 | − | 0.314350i | \(-0.101786\pi\) | |||||||
\(908\) | 2.05633i | 0.0682418i | ||||||||
\(909\) | 3.74302 | 0.124148 | ||||||||
\(910\) | 2.03789i | 0.0675553i | ||||||||
\(911\) | 37.1338i | 1.23030i | 0.788411 | + | 0.615149i | \(0.210904\pi\) | ||||
−0.788411 | + | 0.615149i | \(0.789096\pi\) | |||||||
\(912\) | 1.70513i | 0.0564624i | ||||||||
\(913\) | −41.5104 | −1.37379 | ||||||||
\(914\) | −2.74133 | −0.0906752 | ||||||||
\(915\) | 4.07918 | 0.134854 | ||||||||
\(916\) | −8.08595 | −0.267167 | ||||||||
\(917\) | − | 4.07578i | − | 0.134594i | ||||||
\(918\) | 2.37405 | 0.0783554 | ||||||||
\(919\) | − | 27.8548i | − | 0.918846i | −0.888218 | − | 0.459423i | \(-0.848056\pi\) | ||
0.888218 | − | 0.459423i | \(-0.151944\pi\) | |||||||
\(920\) | − | 5.44814i | − | 0.179620i | ||||||
\(921\) | −16.4683 | −0.542648 | ||||||||
\(922\) | 30.9526 | 1.01937 | ||||||||
\(923\) | 25.8684i | 0.851467i | ||||||||
\(924\) | 2.28810 | 0.0752730 | ||||||||
\(925\) | −2.70513 | + | 5.44814i | −0.0889441 | + | 0.179134i | ||||
\(926\) | 15.7430 | 0.517348 | ||||||||
\(927\) | − | 8.49112i | − | 0.278885i | ||||||
\(928\) | −4.41194 | −0.144829 | ||||||||
\(929\) | 15.7765 | 0.517610 | 0.258805 | − | 0.965930i | \(-0.416671\pi\) | ||||
0.258805 | + | 0.965930i | \(0.416671\pi\) | |||||||
\(930\) | 3.07409i | 0.100803i | ||||||||
\(931\) | − | 11.6973i | − | 0.383364i | ||||||
\(932\) | −22.1253 | −0.724740 | ||||||||
\(933\) | 21.0741i | 0.689935i | ||||||||
\(934\) | −17.7007 | −0.579185 | ||||||||
\(935\) | 14.5222 | 0.474928 | ||||||||
\(936\) | −5.44814 | −0.178078 | ||||||||
\(937\) | 19.6546 | 0.642087 | 0.321043 | − | 0.947064i | \(-0.395966\pi\) | ||||
0.321043 | + | 0.947064i | \(0.395966\pi\) | |||||||
\(938\) | − | 3.79595i | − | 0.123942i | ||||||
\(939\) | − | 27.6317i | − | 0.901727i | ||||||
\(940\) | 13.3874i | 0.436649i | ||||||||
\(941\) | −3.57111 | −0.116415 | −0.0582075 | − | 0.998305i | \(-0.518539\pi\) | ||||
−0.0582075 | + | 0.998305i | \(0.518539\pi\) | |||||||
\(942\) | − | 7.98056i | − | 0.260021i | ||||||
\(943\) | 16.7481i | 0.545393i | ||||||||
\(944\) | 10.8963i | 0.354644i | ||||||||
\(945\) | 0.374052i | 0.0121679i | ||||||||
\(946\) | −47.8489 | −1.55570 | ||||||||
\(947\) | − | 12.0462i | − | 0.391448i | −0.980659 | − | 0.195724i | \(-0.937294\pi\) | ||
0.980659 | − | 0.195724i | \(-0.0627056\pi\) | |||||||
\(948\) | − | 12.1482i | − | 0.394555i | ||||||
\(949\) | 44.6543i | 1.44954i | ||||||||
\(950\) | −1.70513 | −0.0553217 | ||||||||
\(951\) | 16.4119 | 0.532194 | ||||||||
\(952\) | −0.888018 | −0.0287808 | ||||||||
\(953\) | 11.4632 | 0.371329 | 0.185665 | − | 0.982613i | \(-0.440556\pi\) | ||||
0.185665 | + | 0.982613i | \(0.440556\pi\) | |||||||
\(954\) | − | 2.37405i | − | 0.0768628i | ||||||
\(955\) | −12.0184 | −0.388908 | ||||||||
\(956\) | − | 5.23245i | − | 0.169230i | ||||||
\(957\) | 26.9881i | 0.872403i | ||||||||
\(958\) | −4.47945 | −0.144724 | ||||||||
\(959\) | 0.124470 | 0.00401933 | ||||||||
\(960\) | − | 1.00000i | − | 0.0322749i | ||||||
\(961\) | 21.5500 | 0.695160 | ||||||||
\(962\) | 14.7379 | − | 29.6823i | 0.475170 | − | 0.956995i | ||||
\(963\) | −17.4481 | −0.562259 | ||||||||
\(964\) | 2.50379i | 0.0806417i | ||||||||
\(965\) | −17.2291 | −0.554623 | ||||||||
\(966\) | 2.03789 | 0.0655680 | ||||||||
\(967\) | 55.1211i | 1.77258i | 0.463135 | + | 0.886288i | \(0.346725\pi\) | ||||
−0.463135 | + | 0.886288i | \(0.653275\pi\) | |||||||
\(968\) | 26.4185i | 0.849124i | ||||||||
\(969\) | −4.04806 | −0.130043 | ||||||||
\(970\) | 8.15496i | 0.261840i | ||||||||
\(971\) | 20.6486 | 0.662644 | 0.331322 | − | 0.943518i | \(-0.392505\pi\) | ||||
0.331322 | + | 0.943518i | \(0.392505\pi\) | |||||||
\(972\) | −1.00000 | −0.0320750 | ||||||||
\(973\) | −5.19856 | −0.166658 | ||||||||
\(974\) | 7.32518 | 0.234714 | ||||||||
\(975\) | − | 5.44814i | − | 0.174480i | ||||||
\(976\) | − | 4.07918i | − | 0.130571i | ||||||
\(977\) | − | 14.1768i | − | 0.453556i | −0.973946 | − | 0.226778i | \(-0.927181\pi\) | ||
0.973946 | − | 0.226778i | \(-0.0728192\pi\) | |||||||
\(978\) | 9.86009 | 0.315291 | ||||||||
\(979\) | − | 3.37574i | − | 0.107889i | ||||||
\(980\) | 6.86009i | 0.219137i | ||||||||
\(981\) | − | 8.62086i | − | 0.275243i | ||||||
\(982\) | − | 32.0015i | − | 1.02121i | ||||||
\(983\) | 4.04229 | 0.128929 | 0.0644645 | − | 0.997920i | \(-0.479466\pi\) | ||||
0.0644645 | + | 0.997920i | \(0.479466\pi\) | |||||||
\(984\) | 3.07409i | 0.0979985i | ||||||||
\(985\) | 1.88970i | 0.0602109i | ||||||||
\(986\) | − | 10.4742i | − | 0.333566i | ||||||
\(987\) | −5.00759 | −0.159393 | ||||||||
\(988\) | 9.28978 | 0.295547 | ||||||||
\(989\) | −42.6165 | −1.35512 | ||||||||
\(990\) | −6.11707 | −0.194413 | ||||||||
\(991\) | 16.2147i | 0.515077i | 0.966268 | + | 0.257538i | \(0.0829114\pi\) | ||||
−0.966268 | + | 0.257538i | \(0.917089\pi\) | |||||||
\(992\) | 3.07409 | 0.0976025 | ||||||||
\(993\) | − | 32.9594i | − | 1.04593i | ||||||
\(994\) | − | 1.77604i | − | 0.0563325i | ||||||
\(995\) | −14.1584 | −0.448850 | ||||||||
\(996\) | −6.78599 | −0.215022 | ||||||||
\(997\) | − | 41.0722i | − | 1.30077i | −0.759605 | − | 0.650385i | \(-0.774608\pi\) | ||
0.759605 | − | 0.650385i | \(-0.225392\pi\) | |||||||
\(998\) | 35.4977 | 1.12366 | ||||||||
\(999\) | 2.70513 | − | 5.44814i | 0.0855865 | − | 0.172372i |
(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 | 1110.2.h.g.961.3 | ✓ | 8 | |
3.2 | odd | 2 | 3330.2.h.o.2071.7 | 8 | |||
37.36 | even | 2 | inner | 1110.2.h.g.961.7 | yes | 8 | |
111.110 | odd | 2 | 3330.2.h.o.2071.3 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1110.2.h.g.961.3 | ✓ | 8 | 1.1 | even | 1 | trivial | |
1110.2.h.g.961.7 | yes | 8 | 37.36 | even | 2 | inner | |
3330.2.h.o.2071.3 | 8 | 111.110 | odd | 2 | |||
3330.2.h.o.2071.7 | 8 | 3.2 | odd | 2 |