Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6030,2,Mod(2411,6030)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6030, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 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("6030.2411");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6030 = 2 \cdot 3^{2} \cdot 5 \cdot 67 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6030.d (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: | \(48.1497924188\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 2411.3 | ||
Character | \(\chi\) | \(=\) | 6030.2411 |
Dual form | 6030.2.d.k.2411.22 |
$q$-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 \(\left(\mathbb{Z}/6030\mathbb{Z}\right)^\times\).
\(n\) | \(1207\) | \(3151\) | \(4691\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 3.48375i | − | 1.31674i | −0.752697 | − | 0.658368i | \(-0.771247\pi\) | ||
0.752697 | − | 0.658368i | \(-0.228753\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 1.00000 | 0.316228 | ||||||||
\(11\) | 3.99641 | 1.20496 | 0.602482 | − | 0.798133i | \(-0.294179\pi\) | ||||
0.602482 | + | 0.798133i | \(0.294179\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.23077i | 1.17340i | 0.809803 | + | 0.586702i | \(0.199574\pi\) | ||||
−0.809803 | + | 0.586702i | \(0.800426\pi\) | |||||||
\(14\) | 3.48375i | 0.931072i | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | − | 2.08407i | − | 0.505460i | −0.967537 | − | 0.252730i | \(-0.918671\pi\) | ||
0.967537 | − | 0.252730i | \(-0.0813285\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.38304 | 0.776122 | 0.388061 | − | 0.921634i | \(-0.373145\pi\) | ||||
0.388061 | + | 0.921634i | \(0.373145\pi\) | |||||||
\(20\) | −1.00000 | −0.223607 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −3.99641 | −0.852038 | ||||||||
\(23\) | 3.40101i | 0.709161i | 0.935026 | + | 0.354580i | \(0.115376\pi\) | ||||
−0.935026 | + | 0.354580i | \(0.884624\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | − | 4.23077i | − | 0.829722i | ||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | − | 3.48375i | − | 0.658368i | ||||||
\(29\) | 7.87608i | 1.46255i | 0.682082 | + | 0.731276i | \(0.261075\pi\) | ||||
−0.682082 | + | 0.731276i | \(0.738925\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 4.40560i | − | 0.791269i | −0.918408 | − | 0.395634i | \(-0.870525\pi\) | ||
0.918408 | − | 0.395634i | \(-0.129475\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 2.08407i | 0.357415i | ||||||||
\(35\) | 3.48375i | 0.588862i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 6.85166 | 1.12641 | 0.563203 | − | 0.826319i | \(-0.309569\pi\) | ||||
0.563203 | + | 0.826319i | \(0.309569\pi\) | |||||||
\(38\) | −3.38304 | −0.548801 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 1.00000 | 0.158114 | ||||||||
\(41\) | 3.37181 | 0.526588 | 0.263294 | − | 0.964716i | \(-0.415191\pi\) | ||||
0.263294 | + | 0.964716i | \(0.415191\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.24695i | 0.647654i | 0.946116 | + | 0.323827i | \(0.104970\pi\) | ||||
−0.946116 | + | 0.323827i | \(0.895030\pi\) | |||||||
\(44\) | 3.99641 | 0.602482 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | − | 3.40101i | − | 0.501452i | ||||||
\(47\) | 0.604591i | 0.0881887i | 0.999027 | + | 0.0440943i | \(0.0140402\pi\) | ||||
−0.999027 | + | 0.0440943i | \(0.985960\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.13654 | −0.733791 | ||||||||
\(50\) | −1.00000 | −0.141421 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 4.23077i | 0.586702i | ||||||||
\(53\) | −12.4512 | −1.71031 | −0.855153 | − | 0.518375i | \(-0.826537\pi\) | ||||
−0.855153 | + | 0.518375i | \(0.826537\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −3.99641 | −0.538876 | ||||||||
\(56\) | 3.48375i | 0.465536i | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | − | 7.87608i | − | 1.03418i | ||||||
\(59\) | 6.23827i | 0.812153i | 0.913839 | + | 0.406076i | \(0.133103\pi\) | ||||
−0.913839 | + | 0.406076i | \(0.866897\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 2.59685i | − | 0.332492i | −0.986084 | − | 0.166246i | \(-0.946835\pi\) | ||
0.986084 | − | 0.166246i | \(-0.0531646\pi\) | |||||||
\(62\) | 4.40560i | 0.559511i | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | − | 4.23077i | − | 0.524762i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −7.64991 | − | 2.91185i | −0.934585 | − | 0.355739i | ||||
\(68\) | − | 2.08407i | − | 0.252730i | ||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | − | 3.48375i | − | 0.416388i | ||||||
\(71\) | 8.66350i | 1.02817i | 0.857740 | + | 0.514084i | \(0.171868\pi\) | ||||
−0.857740 | + | 0.514084i | \(0.828132\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 10.3997 | 1.21719 | 0.608596 | − | 0.793480i | \(-0.291733\pi\) | ||||
0.608596 | + | 0.793480i | \(0.291733\pi\) | |||||||
\(74\) | −6.85166 | −0.796489 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 3.38304 | 0.388061 | ||||||||
\(77\) | − | 13.9225i | − | 1.58662i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0.716620i | 0.0806260i | 0.999187 | + | 0.0403130i | \(0.0128355\pi\) | ||||
−0.999187 | + | 0.0403130i | \(0.987164\pi\) | |||||||
\(80\) | −1.00000 | −0.111803 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −3.37181 | −0.372354 | ||||||||
\(83\) | 14.3735i | 1.57769i | 0.614590 | + | 0.788847i | \(0.289322\pi\) | ||||
−0.614590 | + | 0.788847i | \(0.710678\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.08407i | 0.226049i | ||||||||
\(86\) | − | 4.24695i | − | 0.457961i | ||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −3.99641 | −0.426019 | ||||||||
\(89\) | 18.2414i | 1.93358i | 0.255568 | + | 0.966791i | \(0.417738\pi\) | ||||
−0.255568 | + | 0.966791i | \(0.582262\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 14.7389 | 1.54506 | ||||||||
\(92\) | 3.40101i | 0.354580i | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | − | 0.604591i | − | 0.0623588i | ||||||
\(95\) | −3.38304 | −0.347092 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 4.52609i | − | 0.459555i | −0.973243 | − | 0.229777i | \(-0.926200\pi\) | ||
0.973243 | − | 0.229777i | \(-0.0737998\pi\) | |||||||
\(98\) | 5.13654 | 0.518869 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | 1.78667 | 0.177780 | 0.0888900 | − | 0.996041i | \(-0.471668\pi\) | ||||
0.0888900 | + | 0.996041i | \(0.471668\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −4.68292 | −0.461422 | −0.230711 | − | 0.973022i | \(-0.574105\pi\) | ||||
−0.230711 | + | 0.973022i | \(0.574105\pi\) | |||||||
\(104\) | − | 4.23077i | − | 0.414861i | ||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 12.4512 | 1.20937 | ||||||||
\(107\) | 9.29118i | 0.898212i | 0.893478 | + | 0.449106i | \(0.148257\pi\) | ||||
−0.893478 | + | 0.449106i | \(0.851743\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 4.13442i | − | 0.396005i | −0.980201 | − | 0.198003i | \(-0.936555\pi\) | ||
0.980201 | − | 0.198003i | \(-0.0634455\pi\) | |||||||
\(110\) | 3.99641 | 0.381043 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | − | 3.48375i | − | 0.329184i | ||||||
\(113\) | −11.0862 | −1.04290 | −0.521451 | − | 0.853281i | \(-0.674609\pi\) | ||||
−0.521451 | + | 0.853281i | \(0.674609\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − | 3.40101i | − | 0.317146i | ||||||
\(116\) | 7.87608i | 0.731276i | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | − | 6.23827i | − | 0.574279i | ||||||
\(119\) | −7.26038 | −0.665558 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 4.97130 | 0.451936 | ||||||||
\(122\) | 2.59685i | 0.235107i | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | − | 4.40560i | − | 0.395634i | ||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −18.1578 | −1.61125 | −0.805623 | − | 0.592429i | \(-0.798169\pi\) | ||||
−0.805623 | + | 0.592429i | \(0.798169\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 4.23077i | 0.371063i | ||||||||
\(131\) | − | 17.7282i | − | 1.54892i | −0.632622 | − | 0.774461i | \(-0.718021\pi\) | ||
0.632622 | − | 0.774461i | \(-0.281979\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − | 11.7857i | − | 1.02195i | ||||||
\(134\) | 7.64991 | + | 2.91185i | 0.660852 | + | 0.251545i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 2.08407i | 0.178707i | ||||||||
\(137\) | −3.48287 | −0.297562 | −0.148781 | − | 0.988870i | \(-0.547535\pi\) | ||||
−0.148781 | + | 0.988870i | \(0.547535\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 12.1021i | 1.02648i | 0.858244 | + | 0.513242i | \(0.171556\pi\) | ||||
−0.858244 | + | 0.513242i | \(0.828444\pi\) | |||||||
\(140\) | 3.48375i | 0.294431i | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | − | 8.66350i | − | 0.727025i | ||||||
\(143\) | 16.9079i | 1.41391i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 7.87608i | − | 0.654073i | ||||||
\(146\) | −10.3997 | −0.860685 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 6.85166 | 0.563203 | ||||||||
\(149\) | − | 3.95643i | − | 0.324123i | −0.986781 | − | 0.162062i | \(-0.948186\pi\) | ||
0.986781 | − | 0.162062i | \(-0.0518144\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −8.69934 | −0.707942 | −0.353971 | − | 0.935256i | \(-0.615169\pi\) | ||||
−0.353971 | + | 0.935256i | \(0.615169\pi\) | |||||||
\(152\) | −3.38304 | −0.274400 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 13.9225i | 1.12191i | ||||||||
\(155\) | 4.40560i | 0.353866i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −12.4921 | −0.996981 | −0.498491 | − | 0.866895i | \(-0.666112\pi\) | ||||
−0.498491 | + | 0.866895i | \(0.666112\pi\) | |||||||
\(158\) | − | 0.716620i | − | 0.0570112i | ||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 1.00000 | 0.0790569 | ||||||||
\(161\) | 11.8483 | 0.933777 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 11.8292 | 0.926538 | 0.463269 | − | 0.886218i | \(-0.346676\pi\) | ||||
0.463269 | + | 0.886218i | \(0.346676\pi\) | |||||||
\(164\) | 3.37181 | 0.263294 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | − | 14.3735i | − | 1.11560i | ||||||
\(167\) | 16.5249i | 1.27874i | 0.768900 | + | 0.639369i | \(0.220804\pi\) | ||||
−0.768900 | + | 0.639369i | \(0.779196\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −4.89938 | −0.376876 | ||||||||
\(170\) | − | 2.08407i | − | 0.159841i | ||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 4.24695i | 0.323827i | ||||||||
\(173\) | − | 19.1729i | − | 1.45769i | −0.684679 | − | 0.728844i | \(-0.740058\pi\) | ||
0.684679 | − | 0.728844i | \(-0.259942\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − | 3.48375i | − | 0.263347i | ||||||
\(176\) | 3.99641 | 0.301241 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | − | 18.2414i | − | 1.36725i | ||||||
\(179\) | 15.8601 | 1.18544 | 0.592719 | − | 0.805409i | \(-0.298054\pi\) | ||||
0.592719 | + | 0.805409i | \(0.298054\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 13.3117 | 0.989450 | 0.494725 | − | 0.869050i | \(-0.335269\pi\) | ||||
0.494725 | + | 0.869050i | \(0.335269\pi\) | |||||||
\(182\) | −14.7389 | −1.09252 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | − | 3.40101i | − | 0.250726i | ||||||
\(185\) | −6.85166 | −0.503744 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 8.32879i | − | 0.609061i | ||||||
\(188\) | 0.604591i | 0.0440943i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 3.38304 | 0.245431 | ||||||||
\(191\) | 21.3256 | 1.54306 | 0.771532 | − | 0.636190i | \(-0.219491\pi\) | ||||
0.771532 | + | 0.636190i | \(0.219491\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 8.68487 | 0.625151 | 0.312575 | − | 0.949893i | \(-0.398808\pi\) | ||||
0.312575 | + | 0.949893i | \(0.398808\pi\) | |||||||
\(194\) | 4.52609i | 0.324954i | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −5.13654 | −0.366896 | ||||||||
\(197\) | 21.1629 | 1.50779 | 0.753896 | − | 0.656994i | \(-0.228172\pi\) | ||||
0.753896 | + | 0.656994i | \(0.228172\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1.78351 | 0.126430 | 0.0632148 | − | 0.998000i | \(-0.479865\pi\) | ||||
0.0632148 | + | 0.998000i | \(0.479865\pi\) | |||||||
\(200\) | −1.00000 | −0.0707107 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −1.78667 | −0.125709 | ||||||||
\(203\) | 27.4383 | 1.92579 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −3.37181 | −0.235498 | ||||||||
\(206\) | 4.68292 | 0.326275 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 4.23077i | 0.293351i | ||||||||
\(209\) | 13.5200 | 0.935198 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 3.94725 | 0.271740 | 0.135870 | − | 0.990727i | \(-0.456617\pi\) | ||||
0.135870 | + | 0.990727i | \(0.456617\pi\) | |||||||
\(212\) | −12.4512 | −0.855153 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | − | 9.29118i | − | 0.635132i | ||||||
\(215\) | − | 4.24695i | − | 0.289640i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −15.3480 | −1.04189 | ||||||||
\(218\) | 4.13442i | 0.280018i | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −3.99641 | −0.269438 | ||||||||
\(221\) | 8.81720 | 0.593109 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 3.06080 | 0.204967 | 0.102483 | − | 0.994735i | \(-0.467321\pi\) | ||||
0.102483 | + | 0.994735i | \(0.467321\pi\) | |||||||
\(224\) | 3.48375i | 0.232768i | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 11.0862 | 0.737443 | ||||||||
\(227\) | − | 0.309618i | − | 0.0205501i | −0.999947 | − | 0.0102750i | \(-0.996729\pi\) | ||
0.999947 | − | 0.0102750i | \(-0.00327070\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 3.45165i | − | 0.228091i | −0.993476 | − | 0.114046i | \(-0.963619\pi\) | ||
0.993476 | − | 0.114046i | \(-0.0363810\pi\) | |||||||
\(230\) | 3.40101i | 0.224256i | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | − | 7.87608i | − | 0.517090i | ||||||
\(233\) | 13.0421 | 0.854419 | 0.427210 | − | 0.904153i | \(-0.359497\pi\) | ||||
0.427210 | + | 0.904153i | \(0.359497\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − | 0.604591i | − | 0.0394392i | ||||||
\(236\) | 6.23827i | 0.406076i | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 7.26038 | 0.470620 | ||||||||
\(239\) | 8.10257 | 0.524112 | 0.262056 | − | 0.965053i | \(-0.415600\pi\) | ||||
0.262056 | + | 0.965053i | \(0.415600\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 19.6546 | 1.26606 | 0.633031 | − | 0.774127i | \(-0.281811\pi\) | ||||
0.633031 | + | 0.774127i | \(0.281811\pi\) | |||||||
\(242\) | −4.97130 | −0.319567 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | − | 2.59685i | − | 0.166246i | ||||||
\(245\) | 5.13654 | 0.328161 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 14.3128i | 0.910704i | ||||||||
\(248\) | 4.40560i | 0.279756i | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 1.00000 | 0.0632456 | ||||||||
\(251\) | −8.55102 | −0.539736 | −0.269868 | − | 0.962897i | \(-0.586980\pi\) | ||||
−0.269868 | + | 0.962897i | \(0.586980\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 13.5919i | 0.854512i | ||||||||
\(254\) | 18.1578 | 1.13932 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 3.41059i | 0.212747i | 0.994326 | + | 0.106373i | \(0.0339239\pi\) | ||||
−0.994326 | + | 0.106373i | \(0.966076\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 23.8695i | − | 1.48318i | ||||||
\(260\) | − | 4.23077i | − | 0.262381i | ||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 17.7282i | 1.09525i | ||||||||
\(263\) | 25.1417i | 1.55030i | 0.631776 | + | 0.775151i | \(0.282326\pi\) | ||||
−0.631776 | + | 0.775151i | \(0.717674\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 12.4512 | 0.764872 | ||||||||
\(266\) | 11.7857i | 0.722625i | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −7.64991 | − | 2.91185i | −0.467293 | − | 0.177869i | ||||
\(269\) | 1.86659i | 0.113808i | 0.998380 | + | 0.0569041i | \(0.0181229\pi\) | ||||
−0.998380 | + | 0.0569041i | \(0.981877\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 19.0863i | 1.15941i | 0.814825 | + | 0.579706i | \(0.196833\pi\) | ||||
−0.814825 | + | 0.579706i | \(0.803167\pi\) | |||||||
\(272\) | − | 2.08407i | − | 0.126365i | ||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 3.48287 | 0.210408 | ||||||||
\(275\) | 3.99641 | 0.240993 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 12.0262 | 0.722585 | 0.361292 | − | 0.932453i | \(-0.382336\pi\) | ||||
0.361292 | + | 0.932453i | \(0.382336\pi\) | |||||||
\(278\) | − | 12.1021i | − | 0.725834i | ||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | − | 3.48375i | − | 0.208194i | ||||||
\(281\) | −15.6985 | −0.936495 | −0.468247 | − | 0.883597i | \(-0.655114\pi\) | ||||
−0.468247 | + | 0.883597i | \(0.655114\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −20.1358 | −1.19695 | −0.598475 | − | 0.801142i | \(-0.704226\pi\) | ||||
−0.598475 | + | 0.801142i | \(0.704226\pi\) | |||||||
\(284\) | 8.66350i | 0.514084i | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | − | 16.9079i | − | 0.999784i | ||||||
\(287\) | − | 11.7466i | − | 0.693378i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 12.6567 | 0.744510 | ||||||||
\(290\) | 7.87608i | 0.462500i | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 10.3997 | 0.608596 | ||||||||
\(293\) | − | 20.6521i | − | 1.20651i | −0.797550 | − | 0.603253i | \(-0.793871\pi\) | ||
0.797550 | − | 0.603253i | \(-0.206129\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 6.23827i | − | 0.363206i | ||||||
\(296\) | −6.85166 | −0.398245 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 3.95643i | 0.229190i | ||||||||
\(299\) | −14.3889 | −0.832132 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 14.7953 | 0.852789 | ||||||||
\(302\) | 8.69934 | 0.500591 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 3.38304 | 0.194030 | ||||||||
\(305\) | 2.59685i | 0.148695i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 21.6799 | 1.23734 | 0.618669 | − | 0.785652i | \(-0.287672\pi\) | ||||
0.618669 | + | 0.785652i | \(0.287672\pi\) | |||||||
\(308\) | − | 13.9225i | − | 0.793309i | ||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | − | 4.40560i | − | 0.250221i | ||||||
\(311\) | −13.1375 | −0.744961 | −0.372481 | − | 0.928040i | \(-0.621493\pi\) | ||||
−0.372481 | + | 0.928040i | \(0.621493\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 16.0459i | 0.906966i | 0.891265 | + | 0.453483i | \(0.149819\pi\) | ||||
−0.891265 | + | 0.453483i | \(0.850181\pi\) | |||||||
\(314\) | 12.4921 | 0.704972 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0.716620i | 0.0403130i | ||||||||
\(317\) | − | 6.77333i | − | 0.380428i | −0.981743 | − | 0.190214i | \(-0.939082\pi\) | ||
0.981743 | − | 0.190214i | \(-0.0609182\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 31.4761i | 1.76232i | ||||||||
\(320\) | −1.00000 | −0.0559017 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −11.8483 | −0.660280 | ||||||||
\(323\) | − | 7.05047i | − | 0.392299i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 4.23077i | 0.234681i | ||||||||
\(326\) | −11.8292 | −0.655161 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −3.37181 | −0.186177 | ||||||||
\(329\) | 2.10625 | 0.116121 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 7.91254i | − | 0.434912i | −0.976070 | − | 0.217456i | \(-0.930224\pi\) | ||
0.976070 | − | 0.217456i | \(-0.0697759\pi\) | |||||||
\(332\) | 14.3735i | 0.788847i | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | − | 16.5249i | − | 0.904204i | ||||||
\(335\) | 7.64991 | + | 2.91185i | 0.417959 | + | 0.159091i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 3.60081i | 0.196148i | 0.995179 | + | 0.0980742i | \(0.0312683\pi\) | ||||
−0.995179 | + | 0.0980742i | \(0.968732\pi\) | |||||||
\(338\) | 4.89938 | 0.266491 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 2.08407i | 0.113024i | ||||||||
\(341\) | − | 17.6066i | − | 0.953449i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 6.49184i | − | 0.350526i | ||||||
\(344\) | − | 4.24695i | − | 0.228980i | ||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 19.1729i | 1.03074i | ||||||||
\(347\) | 12.3427 | 0.662591 | 0.331295 | − | 0.943527i | \(-0.392514\pi\) | ||||
0.331295 | + | 0.943527i | \(0.392514\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 0.685387 | 0.0366879 | 0.0183440 | − | 0.999832i | \(-0.494161\pi\) | ||||
0.0183440 | + | 0.999832i | \(0.494161\pi\) | |||||||
\(350\) | 3.48375i | 0.186214i | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −3.99641 | −0.213009 | ||||||||
\(353\) | −26.1784 | −1.39334 | −0.696669 | − | 0.717393i | \(-0.745335\pi\) | ||||
−0.696669 | + | 0.717393i | \(0.745335\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − | 8.66350i | − | 0.459811i | ||||||
\(356\) | 18.2414i | 0.966791i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −15.8601 | −0.838231 | ||||||||
\(359\) | − | 13.3188i | − | 0.702940i | −0.936199 | − | 0.351470i | \(-0.885682\pi\) | ||
0.936199 | − | 0.351470i | \(-0.114318\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −7.55507 | −0.397635 | ||||||||
\(362\) | −13.3117 | −0.699647 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 14.7389 | 0.772531 | ||||||||
\(365\) | −10.3997 | −0.544345 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 11.6296i | − | 0.607060i | −0.952822 | − | 0.303530i | \(-0.901835\pi\) | ||
0.952822 | − | 0.303530i | \(-0.0981652\pi\) | |||||||
\(368\) | 3.40101i | 0.177290i | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 6.85166 | 0.356201 | ||||||||
\(371\) | 43.3770i | 2.25202i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 4.54904i | 0.235540i | 0.993041 | + | 0.117770i | \(0.0375746\pi\) | ||||
−0.993041 | + | 0.117770i | \(0.962425\pi\) | |||||||
\(374\) | 8.32879i | 0.430671i | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | − | 0.604591i | − | 0.0311794i | ||||||
\(377\) | −33.3219 | −1.71616 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 22.5627i | 1.15897i | 0.814983 | + | 0.579484i | \(0.196746\pi\) | ||||
−0.814983 | + | 0.579484i | \(0.803254\pi\) | |||||||
\(380\) | −3.38304 | −0.173546 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −21.3256 | −1.09111 | ||||||||
\(383\) | 21.2816 | 1.08744 | 0.543719 | − | 0.839268i | \(-0.317016\pi\) | ||||
0.543719 | + | 0.839268i | \(0.317016\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 13.9225i | 0.709557i | ||||||||
\(386\) | −8.68487 | −0.442048 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | − | 4.52609i | − | 0.229777i | ||||||
\(389\) | − | 21.3579i | − | 1.08289i | −0.840737 | − | 0.541443i | \(-0.817878\pi\) | ||
0.840737 | − | 0.541443i | \(-0.182122\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 7.08794 | 0.358453 | ||||||||
\(392\) | 5.13654 | 0.259434 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −21.1629 | −1.06617 | ||||||||
\(395\) | − | 0.716620i | − | 0.0360571i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −1.91628 | −0.0961754 | −0.0480877 | − | 0.998843i | \(-0.515313\pi\) | ||||
−0.0480877 | + | 0.998843i | \(0.515313\pi\) | |||||||
\(398\) | −1.78351 | −0.0893993 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | −6.89731 | −0.344435 | −0.172218 | − | 0.985059i | \(-0.555093\pi\) | ||||
−0.172218 | + | 0.985059i | \(0.555093\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 18.6391 | 0.928477 | ||||||||
\(404\) | 1.78667 | 0.0888900 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −27.4383 | −1.36174 | ||||||||
\(407\) | 27.3820 | 1.35728 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 32.9734i | 1.63043i | 0.579160 | + | 0.815214i | \(0.303381\pi\) | ||||
−0.579160 | + | 0.815214i | \(0.696619\pi\) | |||||||
\(410\) | 3.37181 | 0.166522 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −4.68292 | −0.230711 | ||||||||
\(413\) | 21.7326 | 1.06939 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 14.3735i | − | 0.705566i | ||||||
\(416\) | − | 4.23077i | − | 0.207430i | ||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −13.5200 | −0.661285 | ||||||||
\(419\) | 8.84340i | 0.432028i | 0.976390 | + | 0.216014i | \(0.0693058\pi\) | ||||
−0.976390 | + | 0.216014i | \(0.930694\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 31.5517 | 1.53774 | 0.768868 | − | 0.639408i | \(-0.220820\pi\) | ||||
0.768868 | + | 0.639408i | \(0.220820\pi\) | |||||||
\(422\) | −3.94725 | −0.192149 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 12.4512 | 0.604685 | ||||||||
\(425\) | − | 2.08407i | − | 0.101092i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −9.04677 | −0.437804 | ||||||||
\(428\) | 9.29118i | 0.449106i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 4.24695i | 0.204806i | ||||||||
\(431\) | 26.2803i | 1.26588i | 0.774202 | + | 0.632939i | \(0.218152\pi\) | ||||
−0.774202 | + | 0.632939i | \(0.781848\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 13.6961i | 0.658193i | 0.944296 | + | 0.329096i | \(0.106744\pi\) | ||||
−0.944296 | + | 0.329096i | \(0.893256\pi\) | |||||||
\(434\) | 15.3480 | 0.736728 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | − | 4.13442i | − | 0.198003i | ||||||
\(437\) | 11.5058i | 0.550395i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 15.2634 | 0.728481 | 0.364241 | − | 0.931305i | \(-0.381329\pi\) | ||||
0.364241 | + | 0.931305i | \(0.381329\pi\) | |||||||
\(440\) | 3.99641 | 0.190521 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −8.81720 | −0.419391 | ||||||||
\(443\) | −22.5273 | −1.07030 | −0.535152 | − | 0.844756i | \(-0.679746\pi\) | ||||
−0.535152 | + | 0.844756i | \(0.679746\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − | 18.2414i | − | 0.864724i | ||||||
\(446\) | −3.06080 | −0.144933 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | − | 3.48375i | − | 0.164592i | ||||||
\(449\) | 29.9612i | 1.41396i | 0.707235 | + | 0.706978i | \(0.249942\pi\) | ||||
−0.707235 | + | 0.706978i | \(0.750058\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 13.4751 | 0.634520 | ||||||||
\(452\) | −11.0862 | −0.521451 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0.309618i | 0.0145311i | ||||||||
\(455\) | −14.7389 | −0.690973 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 22.6809 | 1.06097 | 0.530485 | − | 0.847694i | \(-0.322010\pi\) | ||||
0.530485 | + | 0.847694i | \(0.322010\pi\) | |||||||
\(458\) | 3.45165i | 0.161285i | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | − | 3.40101i | − | 0.158573i | ||||||
\(461\) | 10.5378i | 0.490796i | 0.969422 | + | 0.245398i | \(0.0789186\pi\) | ||||
−0.969422 | + | 0.245398i | \(0.921081\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 20.6778i | 0.960979i | 0.877001 | + | 0.480489i | \(0.159541\pi\) | ||||
−0.877001 | + | 0.480489i | \(0.840459\pi\) | |||||||
\(464\) | 7.87608i | 0.365638i | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −13.0421 | −0.604166 | ||||||||
\(467\) | 5.30865i | 0.245655i | 0.992428 | + | 0.122827i | \(0.0391962\pi\) | ||||
−0.992428 | + | 0.122827i | \(0.960804\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −10.1442 | + | 26.6504i | −0.468414 | + | 1.23060i | ||||
\(470\) | 0.604591i | 0.0278877i | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | − | 6.23827i | − | 0.287139i | ||||||
\(473\) | 16.9726i | 0.780399i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 3.38304 | 0.155224 | ||||||||
\(476\) | −7.26038 | −0.332779 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −8.10257 | −0.370603 | ||||||||
\(479\) | − | 20.1076i | − | 0.918737i | −0.888246 | − | 0.459369i | \(-0.848076\pi\) | ||
0.888246 | − | 0.459369i | \(-0.151924\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 28.9878i | 1.32173i | ||||||||
\(482\) | −19.6546 | −0.895241 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 4.97130 | 0.225968 | ||||||||
\(485\) | 4.52609i | 0.205519i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 22.4926i | − | 1.01923i | −0.860401 | − | 0.509617i | \(-0.829787\pi\) | ||
0.860401 | − | 0.509617i | \(-0.170213\pi\) | |||||||
\(488\) | 2.59685i | 0.117554i | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −5.13654 | −0.232045 | ||||||||
\(491\) | 7.59955i | 0.342963i | 0.985187 | + | 0.171482i | \(0.0548554\pi\) | ||||
−0.985187 | + | 0.171482i | \(0.945145\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 16.4143 | 0.739262 | ||||||||
\(494\) | − | 14.3128i | − | 0.643965i | ||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | − | 4.40560i | − | 0.197817i | ||||||
\(497\) | 30.1815 | 1.35383 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 14.1638i | 0.634058i | 0.948416 | + | 0.317029i | \(0.102685\pi\) | ||||
−0.948416 | + | 0.317029i | \(0.897315\pi\) | |||||||
\(500\) | −1.00000 | −0.0447214 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 8.55102 | 0.381651 | ||||||||
\(503\) | −29.1111 | −1.29800 | −0.649000 | − | 0.760789i | \(-0.724812\pi\) | ||||
−0.649000 | + | 0.760789i | \(0.724812\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1.78667 | −0.0795056 | ||||||||
\(506\) | − | 13.5919i | − | 0.604231i | ||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −18.1578 | −0.805623 | ||||||||
\(509\) | − | 32.9968i | − | 1.46256i | −0.682078 | − | 0.731280i | \(-0.738923\pi\) | ||
0.682078 | − | 0.731280i | \(-0.261077\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 36.2300i | − | 1.60272i | ||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | − | 3.41059i | − | 0.150435i | ||||||
\(515\) | 4.68292 | 0.206354 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 2.41619i | 0.106264i | ||||||||
\(518\) | 23.8695i | 1.04877i | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 4.23077i | 0.185531i | ||||||||
\(521\) | 1.17209 | 0.0513501 | 0.0256750 | − | 0.999670i | \(-0.491826\pi\) | ||||
0.0256750 | + | 0.999670i | \(0.491826\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 33.2501 | 1.45393 | 0.726963 | − | 0.686676i | \(-0.240931\pi\) | ||||
0.726963 | + | 0.686676i | \(0.240931\pi\) | |||||||
\(524\) | − | 17.7282i | − | 0.774461i | ||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | − | 25.1417i | − | 1.09623i | ||||||
\(527\) | −9.18156 | −0.399955 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 11.4331 | 0.497091 | ||||||||
\(530\) | −12.4512 | −0.540846 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | − | 11.7857i | − | 0.510973i | ||||||
\(533\) | 14.2653i | 0.617901i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 9.29118i | − | 0.401693i | ||||||
\(536\) | 7.64991 | + | 2.91185i | 0.330426 | + | 0.125773i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | − | 1.86659i | − | 0.0804745i | ||||||
\(539\) | −20.5277 | −0.884192 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − | 4.00668i | − | 0.172261i | −0.996284 | − | 0.0861304i | \(-0.972550\pi\) | ||
0.996284 | − | 0.0861304i | \(-0.0274502\pi\) | |||||||
\(542\) | − | 19.0863i | − | 0.819829i | ||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 2.08407i | 0.0893536i | ||||||||
\(545\) | 4.13442i | 0.177099i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 6.26255i | − | 0.267767i | −0.990997 | − | 0.133884i | \(-0.957255\pi\) | ||
0.990997 | − | 0.133884i | \(-0.0427449\pi\) | |||||||
\(548\) | −3.48287 | −0.148781 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −3.99641 | −0.170408 | ||||||||
\(551\) | 26.6451i | 1.13512i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 2.49653 | 0.106163 | ||||||||
\(554\) | −12.0262 | −0.510944 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 12.1021i | 0.513242i | ||||||||
\(557\) | − | 2.09611i | − | 0.0888148i | −0.999014 | − | 0.0444074i | \(-0.985860\pi\) | ||
0.999014 | − | 0.0444074i | \(-0.0141400\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −17.9679 | −0.759960 | ||||||||
\(560\) | 3.48375i | 0.147215i | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 15.6985 | 0.662202 | ||||||||
\(563\) | 9.67579 | 0.407786 | 0.203893 | − | 0.978993i | \(-0.434641\pi\) | ||||
0.203893 | + | 0.978993i | \(0.434641\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 11.0862 | 0.466400 | ||||||||
\(566\) | 20.1358 | 0.846371 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | − | 8.66350i | − | 0.363512i | ||||||
\(569\) | − | 4.77375i | − | 0.200126i | −0.994981 | − | 0.100063i | \(-0.968096\pi\) | ||
0.994981 | − | 0.100063i | \(-0.0319044\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 35.3058 | 1.47750 | 0.738752 | − | 0.673978i | \(-0.235416\pi\) | ||||
0.738752 | + | 0.673978i | \(0.235416\pi\) | |||||||
\(572\) | 16.9079i | 0.706954i | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 11.7466i | 0.490292i | ||||||||
\(575\) | 3.40101i | 0.141832i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 19.8356i | − | 0.825769i | −0.910783 | − | 0.412884i | \(-0.864521\pi\) | ||
0.910783 | − | 0.412884i | \(-0.135479\pi\) | |||||||
\(578\) | −12.6567 | −0.526448 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | − | 7.87608i | − | 0.327037i | ||||||
\(581\) | 50.0737 | 2.07741 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −49.7602 | −2.06086 | ||||||||
\(584\) | −10.3997 | −0.430342 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 20.6521i | 0.853129i | ||||||||
\(587\) | −41.6201 | −1.71785 | −0.858923 | − | 0.512104i | \(-0.828866\pi\) | ||||
−0.858923 | + | 0.512104i | \(0.828866\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 14.9043i | − | 0.614121i | ||||||
\(590\) | 6.23827i | 0.256825i | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 6.85166 | 0.281601 | ||||||||
\(593\) | 31.4410 | 1.29113 | 0.645563 | − | 0.763707i | \(-0.276623\pi\) | ||||
0.645563 | + | 0.763707i | \(0.276623\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 7.26038 | 0.297646 | ||||||||
\(596\) | − | 3.95643i | − | 0.162062i | ||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 14.3889 | 0.588406 | ||||||||
\(599\) | −47.2767 | −1.93167 | −0.965837 | − | 0.259152i | \(-0.916557\pi\) | ||||
−0.965837 | + | 0.259152i | \(0.916557\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −28.4147 | −1.15906 | −0.579529 | − | 0.814951i | \(-0.696764\pi\) | ||||
−0.579529 | + | 0.814951i | \(0.696764\pi\) | |||||||
\(602\) | −14.7953 | −0.603013 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −8.69934 | −0.353971 | ||||||||
\(605\) | −4.97130 | −0.202112 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −22.3704 | −0.907986 | −0.453993 | − | 0.891005i | \(-0.650001\pi\) | ||||
−0.453993 | + | 0.891005i | \(0.650001\pi\) | |||||||
\(608\) | −3.38304 | −0.137200 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | − | 2.59685i | − | 0.105143i | ||||||
\(611\) | −2.55788 | −0.103481 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −28.3712 | −1.14590 | −0.572950 | − | 0.819590i | \(-0.694201\pi\) | ||||
−0.572950 | + | 0.819590i | \(0.694201\pi\) | |||||||
\(614\) | −21.6799 | −0.874930 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 13.9225i | 0.560954i | ||||||||
\(617\) | 15.9077i | 0.640418i | 0.947347 | + | 0.320209i | \(0.103753\pi\) | ||||
−0.947347 | + | 0.320209i | \(0.896247\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 28.2806 | 1.13669 | 0.568347 | − | 0.822789i | \(-0.307583\pi\) | ||||
0.568347 | + | 0.822789i | \(0.307583\pi\) | |||||||
\(620\) | 4.40560i | 0.176933i | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 13.1375 | 0.526767 | ||||||||
\(623\) | 63.5485 | 2.54602 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | − | 16.0459i | − | 0.641322i | ||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −12.4921 | −0.498491 | ||||||||
\(629\) | − | 14.2793i | − | 0.569353i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 17.4570i | 0.694952i | 0.937689 | + | 0.347476i | \(0.112961\pi\) | ||||
−0.937689 | + | 0.347476i | \(0.887039\pi\) | |||||||
\(632\) | − | 0.716620i | − | 0.0285056i | ||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 6.77333i | 0.269003i | ||||||||
\(635\) | 18.1578 | 0.720571 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − | 21.7315i | − | 0.861033i | ||||||
\(638\) | − | 31.4761i | − | 1.24615i | ||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 1.00000 | 0.0395285 | ||||||||
\(641\) | 39.8394 | 1.57356 | 0.786781 | − | 0.617232i | \(-0.211746\pi\) | ||||
0.786781 | + | 0.617232i | \(0.211746\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 28.3510 | 1.11806 | 0.559028 | − | 0.829149i | \(-0.311174\pi\) | ||||
0.559028 | + | 0.829149i | \(0.311174\pi\) | |||||||
\(644\) | 11.8483 | 0.466888 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 7.05047i | 0.277397i | ||||||||
\(647\) | 28.3642 | 1.11511 | 0.557556 | − | 0.830140i | \(-0.311739\pi\) | ||||
0.557556 | + | 0.830140i | \(0.311739\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 24.9307i | 0.978614i | ||||||||
\(650\) | − | 4.23077i | − | 0.165944i | ||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 11.8292 | 0.463269 | ||||||||
\(653\) | −7.12955 | −0.279001 | −0.139500 | − | 0.990222i | \(-0.544550\pi\) | ||||
−0.139500 | + | 0.990222i | \(0.544550\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 17.7282i | 0.692699i | ||||||||
\(656\) | 3.37181 | 0.131647 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −2.10625 | −0.0821100 | ||||||||
\(659\) | − | 18.2907i | − | 0.712503i | −0.934390 | − | 0.356252i | \(-0.884055\pi\) | ||
0.934390 | − | 0.356252i | \(-0.115945\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 32.5538i | 1.26620i | 0.774072 | + | 0.633098i | \(0.218217\pi\) | ||||
−0.774072 | + | 0.633098i | \(0.781783\pi\) | |||||||
\(662\) | 7.91254i | 0.307529i | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | − | 14.3735i | − | 0.557799i | ||||||
\(665\) | 11.7857i | 0.457028i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −26.7867 | −1.03718 | ||||||||
\(668\) | 16.5249i | 0.639369i | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −7.64991 | − | 2.91185i | −0.295542 | − | 0.112495i | ||||
\(671\) | − | 10.3781i | − | 0.400641i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 10.1435i | 0.391003i | 0.980703 | + | 0.195501i | \(0.0626334\pi\) | ||||
−0.980703 | + | 0.195501i | \(0.937367\pi\) | |||||||
\(674\) | − | 3.60081i | − | 0.138698i | ||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −4.89938 | −0.188438 | ||||||||
\(677\) | 23.0518 | 0.885952 | 0.442976 | − | 0.896533i | \(-0.353923\pi\) | ||||
0.442976 | + | 0.896533i | \(0.353923\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −15.7678 | −0.605112 | ||||||||
\(680\) | − | 2.08407i | − | 0.0799203i | ||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 17.6066i | 0.674191i | ||||||||
\(683\) | −28.8993 | −1.10580 | −0.552901 | − | 0.833247i | \(-0.686479\pi\) | ||||
−0.552901 | + | 0.833247i | \(0.686479\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 3.48287 | 0.133074 | ||||||||
\(686\) | 6.49184i | 0.247859i | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 4.24695i | 0.161914i | ||||||||
\(689\) | − | 52.6782i | − | 2.00688i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 22.6111 | 0.860167 | 0.430083 | − | 0.902789i | \(-0.358484\pi\) | ||||
0.430083 | + | 0.902789i | \(0.358484\pi\) | |||||||
\(692\) | − | 19.1729i | − | 0.728844i | ||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −12.3427 | −0.468522 | ||||||||
\(695\) | − | 12.1021i | − | 0.459057i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 7.02708i | − | 0.266170i | ||||||
\(698\) | −0.685387 | −0.0259423 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | − | 3.48375i | − | 0.131674i | ||||||
\(701\) | 42.6689 | 1.61158 | 0.805791 | − | 0.592200i | \(-0.201740\pi\) | ||||
0.805791 | + | 0.592200i | \(0.201740\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 23.1794 | 0.874228 | ||||||||
\(704\) | 3.99641 | 0.150620 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 26.1784 | 0.985238 | ||||||||
\(707\) | − | 6.22431i | − | 0.234089i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 25.2920 | 0.949859 | 0.474930 | − | 0.880024i | \(-0.342473\pi\) | ||||
0.474930 | + | 0.880024i | \(0.342473\pi\) | |||||||
\(710\) | 8.66350i | 0.325135i | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | − | 18.2414i | − | 0.683625i | ||||||
\(713\) | 14.9835 | 0.561137 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − | 16.9079i | − | 0.632319i | ||||||
\(716\) | 15.8601 | 0.592719 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 13.3188i | 0.497053i | ||||||||
\(719\) | − | 32.2768i | − | 1.20372i | −0.798601 | − | 0.601860i | \(-0.794426\pi\) | ||
0.798601 | − | 0.601860i | \(-0.205574\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 16.3141i | 0.607570i | ||||||||
\(722\) | 7.55507 | 0.281171 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 13.3117 | 0.494725 | ||||||||
\(725\) | 7.87608i | 0.292510i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 21.0542i | 0.780856i | 0.920634 | + | 0.390428i | \(0.127673\pi\) | ||||
−0.920634 | + | 0.390428i | \(0.872327\pi\) | |||||||
\(728\) | −14.7389 | −0.546262 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 10.3997 | 0.384910 | ||||||||
\(731\) | 8.85093 | 0.327364 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 21.1508i | − | 0.781221i | −0.920556 | − | 0.390611i | \(-0.872264\pi\) | ||
0.920556 | − | 0.390611i | \(-0.127736\pi\) | |||||||
\(734\) | 11.6296i | 0.429256i | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | − | 3.40101i | − | 0.125363i | ||||||
\(737\) | −30.5722 | − | 11.6369i | −1.12614 | − | 0.428652i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 25.7851i | 0.948519i | 0.880385 | + | 0.474260i | \(0.157284\pi\) | ||||
−0.880385 | + | 0.474260i | \(0.842716\pi\) | |||||||
\(740\) | −6.85166 | −0.251872 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | − | 43.3770i | − | 1.59242i | ||||||
\(743\) | 21.0941i | 0.773869i | 0.922107 | + | 0.386935i | \(0.126466\pi\) | ||||
−0.922107 | + | 0.386935i | \(0.873534\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 3.95643i | 0.144952i | ||||||||
\(746\) | − | 4.54904i | − | 0.166552i | ||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | − | 8.32879i | − | 0.304531i | ||||||
\(749\) | 32.3682 | 1.18271 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −37.2197 | −1.35817 | −0.679084 | − | 0.734061i | \(-0.737623\pi\) | ||||
−0.679084 | + | 0.734061i | \(0.737623\pi\) | |||||||
\(752\) | 0.604591i | 0.0220472i | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 33.3219 | 1.21351 | ||||||||
\(755\) | 8.69934 | 0.316601 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 44.7365i | − | 1.62597i | −0.582281 | − | 0.812987i | \(-0.697840\pi\) | ||
0.582281 | − | 0.812987i | \(-0.302160\pi\) | |||||||
\(758\) | − | 22.5627i | − | 0.819514i | ||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 3.38304 | 0.122716 | ||||||||
\(761\) | − | 40.9089i | − | 1.48295i | −0.670982 | − | 0.741474i | \(-0.734127\pi\) | ||
0.670982 | − | 0.741474i | \(-0.265873\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −14.4033 | −0.521434 | ||||||||
\(764\) | 21.3256 | 0.771532 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −21.2816 | −0.768934 | ||||||||
\(767\) | −26.3926 | −0.952983 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 24.5575i | − | 0.885568i | −0.896628 | − | 0.442784i | \(-0.853991\pi\) | ||
0.896628 | − | 0.442784i | \(-0.146009\pi\) | |||||||
\(770\) | − | 13.9225i | − | 0.501732i | ||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 8.68487 | 0.312575 | ||||||||
\(773\) | − | 5.23417i | − | 0.188260i | −0.995560 | − | 0.0941301i | \(-0.969993\pi\) | ||
0.995560 | − | 0.0941301i | \(-0.0300070\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 4.40560i | − | 0.158254i | ||||||
\(776\) | 4.52609i | 0.162477i | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 21.3579i | 0.765717i | ||||||||
\(779\) | 11.4070 | 0.408697 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 34.6229i | 1.23890i | ||||||||
\(782\) | −7.08794 | −0.253464 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −5.13654 | −0.183448 | ||||||||
\(785\) | 12.4921 | 0.445864 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 20.2364i | 0.721348i | 0.932692 | + | 0.360674i | \(0.117453\pi\) | ||||
−0.932692 | + | 0.360674i | \(0.882547\pi\) | |||||||
\(788\) | 21.1629 | 0.753896 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0.716620i | 0.0254962i | ||||||||
\(791\) | 38.6216i | 1.37323i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 10.9866 | 0.390147 | ||||||||
\(794\) | 1.91628 | 0.0680063 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 1.78351 | 0.0632148 | ||||||||
\(797\) | 33.3752i | 1.18221i | 0.806595 | + | 0.591105i | \(0.201308\pi\) | ||||
−0.806595 | + | 0.591105i | \(0.798692\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1.26001 | 0.0445759 | ||||||||
\(800\) | −1.00000 | −0.0353553 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 6.89731 | 0.243552 | ||||||||
\(803\) | 41.5614 | 1.46667 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −11.8483 | −0.417598 | ||||||||
\(806\) | −18.6391 | −0.656533 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −1.78667 | −0.0628547 | ||||||||
\(809\) | 49.3188 | 1.73395 | 0.866977 | − | 0.498347i | \(-0.166060\pi\) | ||||
0.866977 | + | 0.498347i | \(0.166060\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 30.3513i | 1.06578i | 0.846185 | + | 0.532889i | \(0.178894\pi\) | ||||
−0.846185 | + | 0.532889i | \(0.821106\pi\) | |||||||
\(812\) | 27.4383 | 0.962897 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −27.3820 | −0.959740 | ||||||||
\(815\) | −11.8292 | −0.414360 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 14.3676i | 0.502658i | ||||||||
\(818\) | − | 32.9734i | − | 1.15289i | ||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −3.37181 | −0.117749 | ||||||||
\(821\) | 38.7641i | 1.35288i | 0.736500 | + | 0.676438i | \(0.236477\pi\) | ||||
−0.736500 | + | 0.676438i | \(0.763523\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −29.6749 | −1.03440 | −0.517201 | − | 0.855864i | \(-0.673026\pi\) | ||||
−0.517201 | + | 0.855864i | \(0.673026\pi\) | |||||||
\(824\) | 4.68292 | 0.163137 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −21.7326 | −0.756173 | ||||||||
\(827\) | − | 45.0316i | − | 1.56590i | −0.622084 | − | 0.782951i | \(-0.713714\pi\) | ||
0.622084 | − | 0.782951i | \(-0.286286\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 10.3590 | 0.359783 | 0.179891 | − | 0.983686i | \(-0.442425\pi\) | ||||
0.179891 | + | 0.983686i | \(0.442425\pi\) | |||||||
\(830\) | 14.3735i | 0.498911i | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 4.23077i | 0.146675i | ||||||||
\(833\) | 10.7049i | 0.370903i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − | 16.5249i | − | 0.571869i | ||||||
\(836\) | 13.5200 | 0.467599 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | − | 8.84340i | − | 0.305490i | ||||||
\(839\) | − | 34.8547i | − | 1.20332i | −0.798753 | − | 0.601659i | \(-0.794507\pi\) | ||
0.798753 | − | 0.601659i | \(-0.205493\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −33.0327 | −1.13906 | ||||||||
\(842\) | −31.5517 | −1.08734 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 3.94725 | 0.135870 | ||||||||
\(845\) | 4.89938 | 0.168544 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 17.3188i | − | 0.595080i | ||||||
\(848\) | −12.4512 | −0.427577 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 2.08407i | 0.0714829i | ||||||||
\(851\) | 23.3026i | 0.798802i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 40.7371 | 1.39481 | 0.697405 | − | 0.716677i | \(-0.254338\pi\) | ||||
0.697405 | + | 0.716677i | \(0.254338\pi\) | |||||||
\(854\) | 9.04677 | 0.309574 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | − | 9.29118i | − | 0.317566i | ||||||
\(857\) | 24.7367 | 0.844990 | 0.422495 | − | 0.906365i | \(-0.361154\pi\) | ||||
0.422495 | + | 0.906365i | \(0.361154\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 2.15510 | 0.0735310 | 0.0367655 | − | 0.999324i | \(-0.488295\pi\) | ||||
0.0367655 | + | 0.999324i | \(0.488295\pi\) | |||||||
\(860\) | − | 4.24695i | − | 0.144820i | ||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | − | 26.2803i | − | 0.895111i | ||||||
\(863\) | − | 54.0311i | − | 1.83924i | −0.392811 | − | 0.919619i | \(-0.628497\pi\) | ||
0.392811 | − | 0.919619i | \(-0.371503\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 19.1729i | 0.651898i | ||||||||
\(866\) | − | 13.6961i | − | 0.465413i | ||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −15.3480 | −0.520946 | ||||||||
\(869\) | 2.86391i | 0.0971514i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 12.3193 | − | 32.3650i | 0.417425 | − | 1.09665i | ||||
\(872\) | 4.13442i | 0.140009i | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | − | 11.5058i | − | 0.389188i | ||||||
\(875\) | 3.48375i | 0.117772i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −42.5051 | −1.43530 | −0.717648 | − | 0.696406i | \(-0.754781\pi\) | ||||
−0.717648 | + | 0.696406i | \(0.754781\pi\) | |||||||
\(878\) | −15.2634 | −0.515114 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −3.99641 | −0.134719 | ||||||||
\(881\) | 34.6532i | 1.16750i | 0.811935 | + | 0.583748i | \(0.198414\pi\) | ||||
−0.811935 | + | 0.583748i | \(0.801586\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 30.7629i | − | 1.03525i | −0.855607 | − | 0.517627i | \(-0.826816\pi\) | ||
0.855607 | − | 0.517627i | \(-0.173184\pi\) | |||||||
\(884\) | 8.81720 | 0.296555 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 22.5273 | 0.756819 | ||||||||
\(887\) | − | 4.64771i | − | 0.156055i | −0.996951 | − | 0.0780274i | \(-0.975138\pi\) | ||
0.996951 | − | 0.0780274i | \(-0.0248622\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 63.2573i | 2.12158i | ||||||||
\(890\) | 18.2414i | 0.611452i | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 3.06080 | 0.102483 | ||||||||
\(893\) | 2.04535i | 0.0684451i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −15.8601 | −0.530144 | ||||||||
\(896\) | 3.48375i | 0.116384i | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | − | 29.9612i | − | 0.999818i | ||||||
\(899\) | 34.6989 | 1.15727 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 25.9492i | 0.864492i | ||||||||
\(902\) | −13.4751 | −0.448673 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 11.0862 | 0.368722 | ||||||||
\(905\) | −13.3117 | −0.442495 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −18.9881 | −0.630488 | −0.315244 | − | 0.949011i | \(-0.602086\pi\) | ||||
−0.315244 | + | 0.949011i | \(0.602086\pi\) | |||||||
\(908\) | − | 0.309618i | − | 0.0102750i | ||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 14.7389 | 0.488591 | ||||||||
\(911\) | 19.4110i | 0.643115i | 0.946890 | + | 0.321558i | \(0.104206\pi\) | ||||
−0.946890 | + | 0.321558i | \(0.895794\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 57.4423i | 1.90106i | ||||||||
\(914\) | −22.6809 | −0.750219 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | − | 3.45165i | − | 0.114046i | ||||||
\(917\) | −61.7607 | −2.03952 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 22.9752i | − | 0.757882i | −0.925421 | − | 0.378941i | \(-0.876288\pi\) | ||
0.925421 | − | 0.378941i | \(-0.123712\pi\) | |||||||
\(920\) | 3.40101i | 0.112128i | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | − | 10.5378i | − | 0.347045i | ||||||
\(923\) | −36.6532 | −1.20646 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 6.85166 | 0.225281 | ||||||||
\(926\) | − | 20.6778i | − | 0.679515i | ||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | − | 7.87608i | − | 0.258545i | ||||||
\(929\) | 19.4841 | 0.639253 | 0.319626 | − | 0.947544i | \(-0.396443\pi\) | ||||
0.319626 | + | 0.947544i | \(0.396443\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −17.3771 | −0.569511 | ||||||||
\(932\) | 13.0421 | 0.427210 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | − | 5.30865i | − | 0.173704i | ||||||
\(935\) | 8.32879i | 0.272380i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 41.1999i | − | 1.34594i | −0.739669 | − | 0.672971i | \(-0.765018\pi\) | ||
0.739669 | − | 0.672971i | \(-0.234982\pi\) | |||||||
\(938\) | 10.1442 | − | 26.6504i | 0.331219 | − | 0.870167i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | − | 0.604591i | − | 0.0197196i | ||||||
\(941\) | −34.1662 | −1.11379 | −0.556893 | − | 0.830584i | \(-0.688007\pi\) | ||||
−0.556893 | + | 0.830584i | \(0.688007\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 11.4676i | 0.373436i | ||||||||
\(944\) | 6.23827i | 0.203038i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | − | 16.9726i | − | 0.551826i | ||||||
\(947\) | − | 27.1731i | − | 0.883007i | −0.897259 | − | 0.441504i | \(-0.854445\pi\) | ||
0.897259 | − | 0.441504i | \(-0.145555\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 43.9987i | 1.42826i | ||||||||
\(950\) | −3.38304 | −0.109760 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 7.26038 | 0.235310 | ||||||||
\(953\) | − | 19.9691i | − | 0.646863i | −0.946252 | − | 0.323432i | \(-0.895163\pi\) | ||
0.946252 | − | 0.323432i | \(-0.104837\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −21.3256 | −0.690079 | ||||||||
\(956\) | 8.10257 | 0.262056 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 20.1076i | 0.649645i | ||||||||
\(959\) | 12.1335i | 0.391810i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 11.5907 | 0.373894 | ||||||||
\(962\) | − | 28.9878i | − | 0.934603i | ||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 19.6546 | 0.633031 | ||||||||
\(965\) | −8.68487 | −0.279576 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 5.96867 | 0.191939 | 0.0959697 | − | 0.995384i | \(-0.469405\pi\) | ||||
0.0959697 | + | 0.995384i | \(0.469405\pi\) | |||||||
\(968\) | −4.97130 | −0.159784 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | − | 4.52609i | − | 0.145324i | ||||||
\(971\) | 11.5025i | 0.369132i | 0.982820 | + | 0.184566i | \(0.0590880\pi\) | ||||
−0.982820 | + | 0.184566i | \(0.940912\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 42.1606 | 1.35161 | ||||||||
\(974\) | 22.4926i | 0.720708i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | − | 2.59685i | − | 0.0831230i | ||||||
\(977\) | − | 17.8647i | − | 0.571544i | −0.958298 | − | 0.285772i | \(-0.907750\pi\) | ||
0.958298 | − | 0.285772i | \(-0.0922500\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 72.9000i | 2.32990i | ||||||||
\(980\) | 5.13654 | 0.164081 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | − | 7.59955i | − | 0.242511i | ||||||
\(983\) | 42.4866 | 1.35511 | 0.677556 | − | 0.735472i | \(-0.263039\pi\) | ||||
0.677556 | + | 0.735472i | \(0.263039\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −21.1629 | −0.674305 | ||||||||
\(986\) | −16.4143 | −0.522737 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 14.3128i | 0.455352i | ||||||||
\(989\) | −14.4439 | −0.459291 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 31.3474i | 0.995782i | 0.867239 | + | 0.497891i | \(0.165892\pi\) | ||||
−0.867239 | + | 0.497891i | \(0.834108\pi\) | |||||||
\(992\) | 4.40560i | 0.139878i | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −30.1815 | −0.957299 | ||||||||
\(995\) | −1.78351 | −0.0565411 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 50.4135 | 1.59661 | 0.798307 | − | 0.602251i | \(-0.205729\pi\) | ||||
0.798307 | + | 0.602251i | \(0.205729\pi\) | |||||||
\(998\) | − | 14.1638i | − | 0.448347i | ||||||
\(999\) | 0 | 0 |
(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 | 6030.2.d.k.2411.3 | ✓ | 24 | |
3.2 | odd | 2 | 6030.2.d.l.2411.3 | yes | 24 | ||
67.66 | odd | 2 | 6030.2.d.l.2411.22 | yes | 24 | ||
201.200 | even | 2 | inner | 6030.2.d.k.2411.22 | yes | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6030.2.d.k.2411.3 | ✓ | 24 | 1.1 | even | 1 | trivial | |
6030.2.d.k.2411.22 | yes | 24 | 201.200 | even | 2 | inner | |
6030.2.d.l.2411.3 | yes | 24 | 3.2 | odd | 2 | ||
6030.2.d.l.2411.22 | yes | 24 | 67.66 | odd | 2 |