Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [7600,2,Mod(1,7600)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(7600, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("7600.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 7600 = 2^{4} \cdot 5^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 7600.a (trivial) |
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: | yes |
Analytic conductor: | \(60.6863055362\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.257.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 4x + 3 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 950) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(2.19869\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 7600.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −3.03293 | −1.75107 | −0.875533 | − | 0.483159i | \(-0.839489\pi\) | ||||
−0.875533 | + | 0.483159i | \(0.839489\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.46980 | 0.933495 | 0.466747 | − | 0.884391i | \(-0.345426\pi\) | ||||
0.466747 | + | 0.884391i | \(0.345426\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 6.19869 | 2.06623 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.728896 | −0.219770 | −0.109885 | − | 0.993944i | \(-0.535048\pi\) | ||||
−0.109885 | + | 0.993944i | \(0.535048\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 6.23163 | 1.72834 | 0.864171 | − | 0.503198i | \(-0.167843\pi\) | ||||
0.864171 | + | 0.503198i | \(0.167843\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −0.563139 | −0.136581 | −0.0682907 | − | 0.997665i | \(-0.521755\pi\) | ||||
−0.0682907 | + | 0.997665i | \(0.521755\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.00000 | 0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −7.49073 | −1.63461 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4.63555 | 0.966579 | 0.483290 | − | 0.875460i | \(-0.339442\pi\) | ||||
0.483290 | + | 0.875460i | \(0.339442\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −9.70142 | −1.86704 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 10.2316 | 1.89997 | 0.949983 | − | 0.312303i | \(-0.101100\pi\) | ||||
0.949983 | + | 0.312303i | \(0.101100\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −6.06587 | −1.08946 | −0.544731 | − | 0.838611i | \(-0.683368\pi\) | ||||
−0.544731 | + | 0.838611i | \(0.683368\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 2.21069 | 0.384832 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 5.72890 | 0.941825 | 0.470912 | − | 0.882180i | \(-0.343925\pi\) | ||||
0.470912 | + | 0.882180i | \(0.343925\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −18.9001 | −3.02644 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 4.79476 | 0.748816 | 0.374408 | − | 0.927264i | \(-0.377846\pi\) | ||||
0.374408 | + | 0.927264i | \(0.377846\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 8.06587 | 1.23003 | 0.615017 | − | 0.788514i | \(-0.289149\pi\) | ||||
0.615017 | + | 0.788514i | \(0.289149\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 8.12628 | 1.18534 | 0.592670 | − | 0.805446i | \(-0.298074\pi\) | ||||
0.592670 | + | 0.805446i | \(0.298074\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −0.900112 | −0.128587 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.70796 | 0.239163 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 1.53020 | 0.210190 | 0.105095 | − | 0.994462i | \(-0.466485\pi\) | ||||
0.105095 | + | 0.994462i | \(0.466485\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −3.03293 | −0.401722 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 5.76183 | 0.750126 | 0.375063 | − | 0.926999i | \(-0.377621\pi\) | ||||
0.375063 | + | 0.926999i | \(0.377621\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 10.9396 | 1.40067 | 0.700336 | − | 0.713814i | \(-0.253034\pi\) | ||||
0.700336 | + | 0.713814i | \(0.253034\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 15.3095 | 1.92882 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 12.9330 | 1.58002 | 0.790012 | − | 0.613092i | \(-0.210074\pi\) | ||||
0.790012 | + | 0.613092i | \(0.210074\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −14.0593 | −1.69254 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 4.39738 | 0.521873 | 0.260937 | − | 0.965356i | \(-0.415969\pi\) | ||||
0.260937 | + | 0.965356i | \(0.415969\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 4.09334 | 0.479090 | 0.239545 | − | 0.970885i | \(-0.423002\pi\) | ||||
0.239545 | + | 0.970885i | \(0.423002\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −1.80022 | −0.205155 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −15.3370 | −1.72554 | −0.862772 | − | 0.505593i | \(-0.831274\pi\) | ||||
−0.862772 | + | 0.505593i | \(0.831274\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 10.8277 | 1.20308 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 7.85517 | 0.862217 | 0.431109 | − | 0.902300i | \(-0.358123\pi\) | ||||
0.431109 | + | 0.902300i | \(0.358123\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −31.0318 | −3.32696 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −10.0000 | −1.06000 | −0.529999 | − | 0.847998i | \(-0.677808\pi\) | ||||
−0.529999 | + | 0.847998i | \(0.677808\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 15.3908 | 1.61340 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 18.3974 | 1.90772 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −11.0055 | −1.11744 | −0.558718 | − | 0.829358i | \(-0.688706\pi\) | ||||
−0.558718 | + | 0.829358i | \(0.688706\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −4.51820 | −0.454096 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −9.73436 | −0.968605 | −0.484302 | − | 0.874901i | \(-0.660926\pi\) | ||||
−0.484302 | + | 0.874901i | \(0.660926\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −8.33151 | −0.820928 | −0.410464 | − | 0.911877i | \(-0.634633\pi\) | ||||
−0.410464 | + | 0.911877i | \(0.634633\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −15.0264 | −1.45266 | −0.726328 | − | 0.687348i | \(-0.758775\pi\) | ||||
−0.726328 | + | 0.687348i | \(0.758775\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −13.6619 | −1.30858 | −0.654288 | − | 0.756245i | \(-0.727032\pi\) | ||||
−0.654288 | + | 0.756245i | \(0.727032\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −17.3754 | −1.64920 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1.20524 | −0.113379 | −0.0566895 | − | 0.998392i | \(-0.518055\pi\) | ||||
−0.0566895 | + | 0.998392i | \(0.518055\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 38.6279 | 3.57115 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −1.39084 | −0.127498 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.4687 | −0.951701 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −14.5422 | −1.31123 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 9.52366 | 0.845088 | 0.422544 | − | 0.906342i | \(-0.361137\pi\) | ||||
0.422544 | + | 0.906342i | \(0.361137\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −24.4633 | −2.15387 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 17.4028 | 1.52049 | 0.760247 | − | 0.649635i | \(-0.225078\pi\) | ||||
0.760247 | + | 0.649635i | \(0.225078\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.46980 | 0.214158 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −2.25910 | −0.193008 | −0.0965040 | − | 0.995333i | \(-0.530766\pi\) | ||||
−0.0965040 | + | 0.995333i | \(0.530766\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −16.8606 | −1.43010 | −0.715050 | − | 0.699073i | \(-0.753596\pi\) | ||||
−0.715050 | + | 0.699073i | \(0.753596\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −24.6465 | −2.07561 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −4.54221 | −0.379838 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 2.72998 | 0.225165 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −13.0055 | −1.06545 | −0.532724 | − | 0.846289i | \(-0.678832\pi\) | ||||
−0.532724 | + | 0.846289i | \(0.678832\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −17.5895 | −1.43142 | −0.715708 | − | 0.698400i | \(-0.753896\pi\) | ||||
−0.715708 | + | 0.698400i | \(0.753896\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −3.49073 | −0.282209 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −9.52366 | −0.760071 | −0.380035 | − | 0.924972i | \(-0.624088\pi\) | ||||
−0.380035 | + | 0.924972i | \(0.624088\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −4.64101 | −0.368056 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 11.4489 | 0.902297 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 13.1921 | 1.03329 | 0.516644 | − | 0.856200i | \(-0.327181\pi\) | ||||
0.516644 | + | 0.856200i | \(0.327181\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1.81331 | 0.140318 | 0.0701591 | − | 0.997536i | \(-0.477649\pi\) | ||||
0.0701591 | + | 0.997536i | \(0.477649\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 25.8332 | 1.98717 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 6.19869 | 0.474026 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 12.5237 | 0.952156 | 0.476078 | − | 0.879403i | \(-0.342058\pi\) | ||||
0.476078 | + | 0.879403i | \(0.342058\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −17.4753 | −1.31352 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −1.39738 | −0.104445 | −0.0522226 | − | 0.998635i | \(-0.516631\pi\) | ||||
−0.0522226 | + | 0.998635i | \(0.516631\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 5.72890 | 0.425825 | 0.212913 | − | 0.977071i | \(-0.431705\pi\) | ||||
0.212913 | + | 0.977071i | \(0.431705\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −33.1791 | −2.45267 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0.410470 | 0.0300165 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −23.9605 | −1.74287 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 27.0198 | 1.95509 | 0.977544 | − | 0.210733i | \(-0.0675849\pi\) | ||||
0.977544 | + | 0.210733i | \(0.0675849\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 23.0713 | 1.66071 | 0.830355 | − | 0.557234i | \(-0.188138\pi\) | ||||
0.830355 | + | 0.557234i | \(0.188138\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −0.794765 | −0.0566247 | −0.0283123 | − | 0.999599i | \(-0.509013\pi\) | ||||
−0.0283123 | + | 0.999599i | \(0.509013\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −8.07241 | −0.572238 | −0.286119 | − | 0.958194i | \(-0.592365\pi\) | ||||
−0.286119 | + | 0.958194i | \(0.592365\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −39.2251 | −2.76672 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 25.2700 | 1.77361 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 28.7344 | 1.99718 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −0.728896 | −0.0504188 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 11.6410 | 0.801400 | 0.400700 | − | 0.916209i | \(-0.368767\pi\) | ||||
0.400700 | + | 0.916209i | \(0.368767\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −13.3370 | −0.913834 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −14.9815 | −1.01701 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −12.4148 | −0.838917 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −3.50927 | −0.236059 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −15.6554 | −1.04836 | −0.524182 | − | 0.851607i | \(-0.675629\pi\) | ||||
−0.524182 | + | 0.851607i | \(0.675629\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 4.80131 | 0.318674 | 0.159337 | − | 0.987224i | \(-0.449064\pi\) | ||||
0.159337 | + | 0.987224i | \(0.449064\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2.79476 | 0.184683 | 0.0923416 | − | 0.995727i | \(-0.470565\pi\) | ||||
0.0923416 | + | 0.995727i | \(0.470565\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 5.45996 | 0.359239 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −11.5422 | −0.756155 | −0.378078 | − | 0.925774i | \(-0.623415\pi\) | ||||
−0.378078 | + | 0.925774i | \(0.623415\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 46.5160 | 3.02154 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 26.2251 | 1.69636 | 0.848180 | − | 0.529708i | \(-0.177699\pi\) | ||||
0.848180 | + | 0.529708i | \(0.177699\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −12.0659 | −0.777231 | −0.388615 | − | 0.921400i | \(-0.627047\pi\) | ||||
−0.388615 | + | 0.921400i | \(0.627047\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −3.73544 | −0.239629 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 6.23163 | 0.396509 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −23.8242 | −1.50980 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −13.5237 | −0.853606 | −0.426803 | − | 0.904345i | \(-0.640360\pi\) | ||||
−0.426803 | + | 0.904345i | \(0.640360\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −3.37884 | −0.212426 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −22.7398 | −1.41847 | −0.709235 | − | 0.704972i | \(-0.750960\pi\) | ||||
−0.709235 | + | 0.704972i | \(0.750960\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 14.1492 | 0.879188 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 63.4227 | 3.92577 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −6.67395 | −0.411533 | −0.205767 | − | 0.978601i | \(-0.565969\pi\) | ||||
−0.205767 | + | 0.978601i | \(0.565969\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 30.3293 | 1.85613 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −29.7398 | −1.81327 | −0.906634 | − | 0.421917i | \(-0.861357\pi\) | ||||
−0.906634 | + | 0.421917i | \(0.861357\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1.11189 | −0.0675426 | −0.0337713 | − | 0.999430i | \(-0.510752\pi\) | ||||
−0.0337713 | + | 0.999430i | \(0.510752\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −46.6794 | −2.82517 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −13.1263 | −0.788682 | −0.394341 | − | 0.918964i | \(-0.629027\pi\) | ||||
−0.394341 | + | 0.918964i | \(0.629027\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −37.6004 | −2.25108 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 22.9265 | 1.36768 | 0.683840 | − | 0.729632i | \(-0.260309\pi\) | ||||
0.683840 | + | 0.729632i | \(0.260309\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 0.860634 | 0.0511594 | 0.0255797 | − | 0.999673i | \(-0.491857\pi\) | ||||
0.0255797 | + | 0.999673i | \(0.491857\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 11.8421 | 0.699016 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.6829 | −0.981346 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 33.3788 | 1.95670 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −19.8212 | −1.15796 | −0.578982 | − | 0.815340i | \(-0.696550\pi\) | ||||
−0.578982 | + | 0.815340i | \(0.696550\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 7.07133 | 0.410320 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 28.8870 | 1.67058 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 19.9210 | 1.14823 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 29.5237 | 1.69609 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −16.8661 | −0.962599 | −0.481299 | − | 0.876556i | \(-0.659835\pi\) | ||||
−0.481299 | + | 0.876556i | \(0.659835\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 25.2689 | 1.43750 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −10.3250 | −0.585475 | −0.292738 | − | 0.956193i | \(-0.594566\pi\) | ||||
−0.292738 | + | 0.956193i | \(0.594566\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 15.7684 | 0.891281 | 0.445641 | − | 0.895212i | \(-0.352976\pi\) | ||||
0.445641 | + | 0.895212i | \(0.352976\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 2.17230 | 0.122009 | 0.0610043 | − | 0.998138i | \(-0.480570\pi\) | ||||
0.0610043 | + | 0.998138i | \(0.480570\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −7.45779 | −0.417556 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 45.5741 | 2.54370 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −0.563139 | −0.0313339 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 41.4358 | 2.29140 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 20.0702 | 1.10651 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −11.9791 | −0.658429 | −0.329215 | − | 0.944255i | \(-0.606784\pi\) | ||||
−0.329215 | + | 0.944255i | \(0.606784\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 35.5117 | 1.94603 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 11.1921 | 0.609675 | 0.304838 | − | 0.952404i | \(-0.401398\pi\) | ||||
0.304838 | + | 0.952404i | \(0.401398\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 3.65540 | 0.198534 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 4.42139 | 0.239432 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −19.5117 | −1.05353 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −20.3843 | −1.09429 | −0.547143 | − | 0.837039i | \(-0.684285\pi\) | ||||
−0.547143 | + | 0.837039i | \(0.684285\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −0.252557 | −0.0135191 | −0.00675954 | − | 0.999977i | \(-0.502152\pi\) | ||||
−0.00675954 | + | 0.999977i | \(0.502152\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −60.4556 | −3.22688 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 28.6434 | 1.52453 | 0.762267 | − | 0.647263i | \(-0.224086\pi\) | ||||
0.762267 | + | 0.647263i | \(0.224086\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 4.21832 | 0.223257 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 18.5741 | 0.980301 | 0.490151 | − | 0.871638i | \(-0.336942\pi\) | ||||
0.490151 | + | 0.871638i | \(0.336942\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 31.7509 | 1.66649 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −4.79476 | −0.250285 | −0.125142 | − | 0.992139i | \(-0.539939\pi\) | ||||
−0.125142 | + | 0.992139i | \(0.539939\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 29.7213 | 1.54723 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 3.77929 | 0.196211 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −15.9485 | −0.825783 | −0.412892 | − | 0.910780i | \(-0.635481\pi\) | ||||
−0.412892 | + | 0.910780i | \(0.635481\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 63.7597 | 3.28379 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 16.8013 | 0.863025 | 0.431513 | − | 0.902107i | \(-0.357980\pi\) | ||||
0.431513 | + | 0.902107i | \(0.357980\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −28.8846 | −1.47980 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 26.7948 | 1.36915 | 0.684574 | − | 0.728943i | \(-0.259988\pi\) | ||||
0.684574 | + | 0.728943i | \(0.259988\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 49.9978 | 2.54153 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 18.3424 | 0.929998 | 0.464999 | − | 0.885311i | \(-0.346055\pi\) | ||||
0.464999 | + | 0.885311i | \(0.346055\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2.61046 | −0.132017 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −52.7817 | −2.66248 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −21.2162 | −1.06481 | −0.532404 | − | 0.846490i | \(-0.678711\pi\) | ||||
−0.532404 | + | 0.846490i | \(0.678711\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −7.49073 | −0.375005 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −27.8661 | −1.39157 | −0.695783 | − | 0.718252i | \(-0.744943\pi\) | ||||
−0.695783 | + | 0.718252i | \(0.744943\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −37.8002 | −1.88296 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −4.17577 | −0.206985 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −18.0899 | −0.894487 | −0.447243 | − | 0.894412i | \(-0.647594\pi\) | ||||
−0.447243 | + | 0.894412i | \(0.647594\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 6.85171 | 0.337970 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 14.2305 | 0.700239 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 51.1372 | 2.50420 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 15.3370 | 0.749260 | 0.374630 | − | 0.927174i | \(-0.377770\pi\) | ||||
0.374630 | + | 0.927174i | \(0.377770\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −8.42486 | −0.410602 | −0.205301 | − | 0.978699i | \(-0.565817\pi\) | ||||
−0.205301 | + | 0.978699i | \(0.565817\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 50.3723 | 2.44918 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 27.0185 | 1.30752 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 13.7762 | 0.665122 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −16.2766 | −0.784014 | −0.392007 | − | 0.919962i | \(-0.628219\pi\) | ||||
−0.392007 | + | 0.919962i | \(0.628219\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 18.1976 | 0.874521 | 0.437261 | − | 0.899335i | \(-0.355949\pi\) | ||||
0.437261 | + | 0.899335i | \(0.355949\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 4.63555 | 0.221749 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −20.4214 | −0.974660 | −0.487330 | − | 0.873218i | \(-0.662029\pi\) | ||||
−0.487330 | + | 0.873218i | \(0.662029\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −5.57952 | −0.265691 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 21.6685 | 1.02950 | 0.514750 | − | 0.857340i | \(-0.327885\pi\) | ||||
0.514750 | + | 0.857340i | \(0.327885\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 39.4447 | 1.86567 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 23.8133 | 1.12382 | 0.561910 | − | 0.827198i | \(-0.310067\pi\) | ||||
0.561910 | + | 0.827198i | \(0.310067\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −3.49489 | −0.164568 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 53.3479 | 2.50650 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −9.15813 | −0.428399 | −0.214200 | − | 0.976790i | \(-0.568714\pi\) | ||||
−0.214200 | + | 0.976790i | \(0.568714\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 5.46325 | 0.255003 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −7.78931 | −0.362784 | −0.181392 | − | 0.983411i | \(-0.558060\pi\) | ||||
−0.181392 | + | 0.983411i | \(0.558060\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 0.405011 | 0.0188225 | 0.00941123 | − | 0.999956i | \(-0.497004\pi\) | ||||
0.00941123 | + | 0.999956i | \(0.497004\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −1.95814 | −0.0906118 | −0.0453059 | − | 0.998973i | \(-0.514426\pi\) | ||||
−0.0453059 | + | 0.998973i | \(0.514426\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 31.9420 | 1.47494 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 28.8846 | 1.33093 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −5.87918 | −0.270325 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 9.48527 | 0.434301 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 22.9210 | 1.04729 | 0.523645 | − | 0.851937i | \(-0.324572\pi\) | ||||
0.523645 | + | 0.851937i | \(0.324572\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 35.7003 | 1.62780 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −34.7237 | −1.57998 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −23.9450 | −1.08505 | −0.542527 | − | 0.840038i | \(-0.682532\pi\) | ||||
−0.542527 | + | 0.840038i | \(0.682532\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −40.0109 | −1.80936 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −3.86826 | −0.174572 | −0.0872861 | − | 0.996183i | \(-0.527819\pi\) | ||||
−0.0872861 | + | 0.996183i | \(0.527819\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −5.76183 | −0.259500 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 10.8606 | 0.487166 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 7.92104 | 0.354595 | 0.177297 | − | 0.984157i | \(-0.443265\pi\) | ||||
0.177297 | + | 0.984157i | \(0.443265\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −5.49966 | −0.245706 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −16.6949 | −0.744388 | −0.372194 | − | 0.928155i | \(-0.621394\pi\) | ||||
−0.372194 | + | 0.928155i | \(0.621394\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −78.3503 | −3.47966 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 24.4028 | 1.08164 | 0.540818 | − | 0.841139i | \(-0.318115\pi\) | ||||
0.540818 | + | 0.841139i | \(0.318115\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 10.1097 | 0.447228 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −9.70142 | −0.428328 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −5.92321 | −0.260503 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −37.9834 | −1.66729 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 26.0659 | 1.14197 | 0.570983 | − | 0.820962i | \(-0.306562\pi\) | ||||
0.570983 | + | 0.820962i | \(0.306562\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 17.8726 | 0.781516 | 0.390758 | − | 0.920493i | \(-0.372213\pi\) | ||||
0.390758 | + | 0.920493i | \(0.372213\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 3.41593 | 0.148800 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1.51166 | −0.0657243 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 35.7158 | 1.54993 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 29.8792 | 1.29421 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 4.23817 | 0.182891 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0.656088 | 0.0282597 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 23.0604 | 0.991444 | 0.495722 | − | 0.868481i | \(-0.334903\pi\) | ||||
0.495722 | + | 0.868481i | \(0.334903\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −17.3754 | −0.745648 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −27.7584 | −1.18686 | −0.593431 | − | 0.804885i | \(-0.702227\pi\) | ||||
−0.593431 | + | 0.804885i | \(0.702227\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 67.8111 | 2.89411 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 10.2316 | 0.435882 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −37.8792 | −1.61079 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 8.60808 | 0.364736 | 0.182368 | − | 0.983230i | \(-0.441624\pi\) | ||||
0.182368 | + | 0.983230i | \(0.441624\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 50.2635 | 2.12592 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1.24493 | −0.0525609 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 7.93959 | 0.334614 | 0.167307 | − | 0.985905i | \(-0.446493\pi\) | ||||
0.167307 | + | 0.985905i | \(0.446493\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 26.7422 | 1.12307 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −1.65757 | −0.0694889 | −0.0347444 | − | 0.999396i | \(-0.511062\pi\) | ||||
−0.0347444 | + | 0.999396i | \(0.511062\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 14.0528 | 0.588091 | 0.294045 | − | 0.955791i | \(-0.404998\pi\) | ||||
0.294045 | + | 0.955791i | \(0.404998\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −81.9494 | −3.42349 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 1.36445 | 0.0568027 | 0.0284014 | − | 0.999597i | \(-0.490958\pi\) | ||||
0.0284014 | + | 0.999597i | \(0.490958\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −69.9738 | −2.90801 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 19.4007 | 0.804876 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1.11536 | −0.0461935 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −24.6609 | −1.01786 | −0.508931 | − | 0.860807i | \(-0.669959\pi\) | ||||
−0.508931 | + | 0.860807i | \(0.669959\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −6.06587 | −0.249940 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 2.41047 | 0.0991535 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 0.747443 | 0.0306938 | 0.0153469 | − | 0.999882i | \(-0.495115\pi\) | ||||
0.0153469 | + | 0.999882i | \(0.495115\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 24.4831 | 1.00203 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −1.40501 | −0.0574072 | −0.0287036 | − | 0.999588i | \(-0.509138\pi\) | ||||
−0.0287036 | + | 0.999588i | \(0.509138\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 29.7453 | 1.21334 | 0.606668 | − | 0.794956i | \(-0.292506\pi\) | ||||
0.606668 | + | 0.794956i | \(0.292506\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 80.1680 | 3.26469 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 5.66849 | 0.230077 | 0.115038 | − | 0.993361i | \(-0.463301\pi\) | ||||
0.115038 | + | 0.993361i | \(0.463301\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −76.6423 | −3.10570 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 50.6399 | 2.04867 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 2.99454 | 0.120948 | 0.0604742 | − | 0.998170i | \(-0.480739\pi\) | ||||
0.0604742 | + | 0.998170i | \(0.480739\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 32.3370 | 1.30184 | 0.650919 | − | 0.759147i | \(-0.274384\pi\) | ||||
0.650919 | + | 0.759147i | \(0.274384\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 20.9265 | 0.841107 | 0.420554 | − | 0.907268i | \(-0.361836\pi\) | ||||
0.420554 | + | 0.907268i | \(0.361836\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −44.9714 | −1.80464 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −24.6980 | −0.989503 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 2.21069 | 0.0882866 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −3.22617 | −0.128636 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −22.8002 | −0.907663 | −0.453831 | − | 0.891088i | \(-0.649943\pi\) | ||||
−0.453831 | + | 0.891088i | \(0.649943\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −35.3064 | −1.40330 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −5.60916 | −0.222243 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 27.2580 | 1.07831 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 36.3184 | 1.43449 | 0.717246 | − | 0.696820i | \(-0.245402\pi\) | ||||
0.717246 | + | 0.696820i | \(0.245402\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 13.6135 | 0.536865 | 0.268433 | − | 0.963298i | \(-0.413494\pi\) | ||||
0.268433 | + | 0.963298i | \(0.413494\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −0.0724126 | −0.00284683 | −0.00142342 | − | 0.999999i | \(-0.500453\pi\) | ||||
−0.00142342 | + | 0.999999i | \(0.500453\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −4.19978 | −0.164856 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 45.4378 | 1.78085 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 43.5346 | 1.70364 | 0.851820 | − | 0.523835i | \(-0.175499\pi\) | ||||
0.851820 | + | 0.523835i | \(0.175499\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 25.3734 | 0.989910 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 33.4512 | 1.30308 | 0.651538 | − | 0.758616i | \(-0.274124\pi\) | ||||
0.651538 | + | 0.758616i | \(0.274124\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −2.89465 | −0.112589 | −0.0562945 | − | 0.998414i | \(-0.517929\pi\) | ||||
−0.0562945 | + | 0.998414i | \(0.517929\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 10.6434 | 0.413355 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 47.4292 | 1.83647 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 47.4818 | 1.83575 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −7.97382 | −0.307826 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −42.8475 | −1.65165 | −0.825826 | − | 0.563925i | \(-0.809291\pi\) | ||||
−0.825826 | + | 0.563925i | \(0.809291\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −34.4567 | −1.32428 | −0.662139 | − | 0.749381i | \(-0.730351\pi\) | ||||
−0.662139 | + | 0.749381i | \(0.730351\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −27.1812 | −1.04312 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −14.5621 | −0.558019 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −2.73436 | −0.104627 | −0.0523136 | − | 0.998631i | \(-0.516660\pi\) | ||||
−0.0523136 | + | 0.998631i | \(0.516660\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −8.47634 | −0.323393 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 9.53566 | 0.363280 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 4.74198 | 0.180394 | 0.0901968 | − | 0.995924i | \(-0.471250\pi\) | ||||
0.0901968 | + | 0.995924i | \(0.471250\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −11.1590 | −0.423897 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −2.70012 | −0.102274 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 35.0068 | 1.32408 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 33.1372 | 1.25157 | 0.625787 | − | 0.779994i | \(-0.284778\pi\) | ||||
0.625787 | + | 0.779994i | \(0.284778\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 5.72890 | 0.216069 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −24.0419 | −0.904187 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 5.37884 | 0.202006 | 0.101003 | − | 0.994886i | \(-0.467795\pi\) | ||||
0.101003 | + | 0.994886i | \(0.467795\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −95.0692 | −3.56537 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −28.1187 | −1.05305 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −79.5390 | −2.97044 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −33.0857 | −1.23389 | −0.616944 | − | 0.787007i | \(-0.711630\pi\) | ||||
−0.616944 | + | 0.787007i | \(0.711630\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −20.5771 | −0.766332 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 36.5950 | 1.36098 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 2.62463 | 0.0973423 | 0.0486711 | − | 0.998815i | \(-0.484501\pi\) | ||||
0.0486711 | + | 0.998815i | \(0.484501\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −21.1538 | −0.783472 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −4.54221 | −0.168000 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −0.608077 | −0.0224598 | −0.0112299 | − | 0.999937i | \(-0.503575\pi\) | ||||
−0.0112299 | + | 0.999937i | \(0.503575\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −9.42685 | −0.347242 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −36.3974 | −1.33890 | −0.669450 | − | 0.742857i | \(-0.733470\pi\) | ||||
−0.669450 | + | 0.742857i | \(0.733470\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −18.9001 | −0.694313 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −23.0713 | −0.846405 | −0.423202 | − | 0.906035i | \(-0.639094\pi\) | ||||
−0.423202 | + | 0.906035i | \(0.639094\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 48.6918 | 1.78154 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −37.1121 | −1.35605 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −4.75290 | −0.173436 | −0.0867179 | − | 0.996233i | \(-0.527638\pi\) | ||||
−0.0867179 | + | 0.996233i | \(0.527638\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 41.0164 | 1.49472 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −26.8057 | −0.974269 | −0.487135 | − | 0.873327i | \(-0.661958\pi\) | ||||
−0.487135 | + | 0.873327i | \(0.661958\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 10.2478 | 0.371971 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 25.4478 | 0.922481 | 0.461241 | − | 0.887275i | \(-0.347404\pi\) | ||||
0.461241 | + | 0.887275i | \(0.347404\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −33.7422 | −1.22155 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 35.9056 | 1.29648 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −14.6421 | −0.528007 | −0.264004 | − | 0.964522i | \(-0.585043\pi\) | ||||
−0.264004 | + | 0.964522i | \(0.585043\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 68.9684 | 2.48384 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 16.8462 | 0.605917 | 0.302959 | − | 0.953004i | \(-0.402026\pi\) | ||||
0.302959 | + | 0.953004i | \(0.402026\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −42.9136 | −1.53952 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 4.79476 | 0.171790 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −3.20524 | −0.114692 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −99.2613 | −3.54731 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 18.7367 | 0.667893 | 0.333946 | − | 0.942592i | \(-0.391620\pi\) | ||||
0.333946 | + | 0.942592i | \(0.391620\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 20.2416 | 0.720621 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −2.97668 | −0.105839 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 68.1714 | 2.42084 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 37.9900 | 1.34567 | 0.672837 | − | 0.739791i | \(-0.265075\pi\) | ||||
0.672837 | + | 0.739791i | \(0.265075\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −4.57623 | −0.161895 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −61.9869 | −2.19020 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −2.98362 | −0.105290 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 90.1989 | 3.17515 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 21.8857 | 0.769461 | 0.384731 | − | 0.923029i | \(-0.374294\pi\) | ||||
0.384731 | + | 0.923029i | \(0.374294\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −37.8595 | −1.32943 | −0.664714 | − | 0.747098i | \(-0.731447\pi\) | ||||
−0.664714 | + | 0.747098i | \(0.731447\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 3.37229 | 0.118271 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 8.06587 | 0.282189 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 95.4031 | 3.33365 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −20.1976 | −0.704901 | −0.352451 | − | 0.935830i | \(-0.614652\pi\) | ||||
−0.352451 | + | 0.935830i | \(0.614652\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −4.34590 | −0.151489 | −0.0757443 | − | 0.997127i | \(-0.524133\pi\) | ||||
−0.0757443 | + | 0.997127i | \(0.524133\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −56.8375 | −1.97643 | −0.988217 | − | 0.153057i | \(-0.951088\pi\) | ||||
−0.988217 | + | 0.153057i | \(0.951088\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −17.4543 | −0.606214 | −0.303107 | − | 0.952957i | \(-0.598024\pi\) | ||||
−0.303107 | + | 0.952957i | \(0.598024\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 39.8111 | 1.38103 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0.506888 | 0.0175626 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 58.8475 | 2.03407 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −1.77622 | −0.0613219 | −0.0306609 | − | 0.999530i | \(-0.509761\pi\) | ||||
−0.0306609 | + | 0.999530i | \(0.509761\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 75.6862 | 2.60987 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −69.5346 | −2.39490 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −25.8556 | −0.888408 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −2.61025 | −0.0895834 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 26.5566 | 0.910348 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 16.1187 | 0.551892 | 0.275946 | − | 0.961173i | \(-0.411009\pi\) | ||||
0.275946 | + | 0.961173i | \(0.411009\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 47.2031 | 1.61243 | 0.806213 | − | 0.591625i | \(-0.201514\pi\) | ||||
0.806213 | + | 0.591625i | \(0.201514\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −37.3239 | −1.27347 | −0.636737 | − | 0.771081i | \(-0.719716\pi\) | ||||
−0.636737 | + | 0.771081i | \(0.719716\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −35.9163 | −1.22402 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −1.33697 | −0.0455111 | −0.0227555 | − | 0.999741i | \(-0.507244\pi\) | ||||
−0.0227555 | + | 0.999741i | \(0.507244\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 50.5981 | 1.71840 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 11.1791 | 0.379224 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 80.5939 | 2.73082 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −68.2194 | −2.30888 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −13.1647 | −0.444539 | −0.222270 | − | 0.974985i | \(-0.571347\pi\) | ||||
−0.222270 | + | 0.974985i | \(0.571347\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 60.1163 | 2.02767 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −10.2052 | −0.343823 | −0.171912 | − | 0.985112i | \(-0.554994\pi\) | ||||
−0.171912 | + | 0.985112i | \(0.554994\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1.49966 | 0.0504674 | 0.0252337 | − | 0.999682i | \(-0.491967\pi\) | ||||
0.0252337 | + | 0.999682i | \(0.491967\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −46.9505 | −1.57644 | −0.788222 | − | 0.615391i | \(-0.788998\pi\) | ||||
−0.788222 | + | 0.615391i | \(0.788998\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 23.5215 | 0.788886 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −7.89227 | −0.264401 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 8.12628 | 0.271936 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −87.6125 | −2.92529 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −62.0637 | −2.06994 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −0.861719 | −0.0287080 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −60.4192 | −2.01063 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 16.3668 | 0.543452 | 0.271726 | − | 0.962375i | \(-0.412406\pi\) | ||||
0.271726 | + | 0.962375i | \(0.412406\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −60.3403 | −2.00136 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −32.3293 | −1.07112 | −0.535559 | − | 0.844498i | \(-0.679899\pi\) | ||||
−0.535559 | + | 0.844498i | \(0.679899\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −5.72561 | −0.189490 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 42.9815 | 1.41937 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 22.8157 | 0.752620 | 0.376310 | − | 0.926494i | \(-0.377193\pi\) | ||||
0.376310 | + | 0.926494i | \(0.377193\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 51.1538 | 1.68557 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 27.4028 | 0.901976 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −51.6445 | −1.69623 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −27.2436 | −0.893834 | −0.446917 | − | 0.894575i | \(-0.647478\pi\) | ||||
−0.446917 | + | 0.894575i | \(0.647478\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −0.900112 | −0.0295000 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 31.3150 | 1.02521 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 51.5006 | 1.68245 | 0.841225 | − | 0.540685i | \(-0.181835\pi\) | ||||
0.841225 | + | 0.540685i | \(0.181835\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −47.8244 | −1.56069 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −40.8541 | −1.33181 | −0.665903 | − | 0.746039i | \(-0.731953\pi\) | ||||
−0.665903 | + | 0.746039i | \(0.731953\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 22.2264 | 0.723791 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 38.2526 | 1.24304 | 0.621521 | − | 0.783398i | \(-0.286515\pi\) | ||||
0.621521 | + | 0.783398i | \(0.286515\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 25.5082 | 0.828031 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −6.58845 | −0.213645 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −54.1187 | −1.75308 | −0.876538 | − | 0.481334i | \(-0.840153\pi\) | ||||
−0.876538 | + | 0.481334i | \(0.840153\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 22.6190 | 0.731168 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −5.57952 | −0.180172 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 5.79476 | 0.186928 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −93.1440 | −3.00152 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 28.4214 | 0.913970 | 0.456985 | − | 0.889474i | \(-0.348929\pi\) | ||||
0.456985 | + | 0.889474i | \(0.348929\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 1.70796 | 0.0548677 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −30.8057 | −0.988601 | −0.494301 | − | 0.869291i | \(-0.664576\pi\) | ||||
−0.494301 | + | 0.869291i | \(0.664576\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −41.6423 | −1.33499 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −37.6554 | −1.20470 | −0.602351 | − | 0.798231i | \(-0.705769\pi\) | ||||
−0.602351 | + | 0.798231i | \(0.705769\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 7.28896 | 0.232956 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −84.6862 | −2.70382 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −38.7948 | −1.23736 | −0.618680 | − | 0.785643i | \(-0.712332\pi\) | ||||
−0.618680 | + | 0.785643i | \(0.712332\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −60.8717 | −1.93757 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 37.3898 | 1.18893 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 15.0295 | 0.477427 | 0.238713 | − | 0.971090i | \(-0.423274\pi\) | ||||
0.238713 | + | 0.971090i | \(0.423274\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 36.3317 | 1.15295 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −1.18123 | −0.0374099 | −0.0187050 | − | 0.999825i | \(-0.505954\pi\) | ||||
−0.0187050 | + | 0.999825i | \(0.505954\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −55.5784 | −1.75842 |
(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 | 7600.2.a.cb.1.1 | 3 | ||
4.3 | odd | 2 | 950.2.a.k.1.3 | ✓ | 3 | ||
5.4 | even | 2 | 7600.2.a.bm.1.3 | 3 | |||
12.11 | even | 2 | 8550.2.a.co.1.2 | 3 | |||
20.3 | even | 4 | 950.2.b.g.799.6 | 6 | |||
20.7 | even | 4 | 950.2.b.g.799.1 | 6 | |||
20.19 | odd | 2 | 950.2.a.m.1.1 | yes | 3 | ||
60.59 | even | 2 | 8550.2.a.cj.1.2 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
950.2.a.k.1.3 | ✓ | 3 | 4.3 | odd | 2 | ||
950.2.a.m.1.1 | yes | 3 | 20.19 | odd | 2 | ||
950.2.b.g.799.1 | 6 | 20.7 | even | 4 | |||
950.2.b.g.799.6 | 6 | 20.3 | even | 4 | |||
7600.2.a.bm.1.3 | 3 | 5.4 | even | 2 | |||
7600.2.a.cb.1.1 | 3 | 1.1 | even | 1 | trivial | ||
8550.2.a.cj.1.2 | 3 | 60.59 | even | 2 | |||
8550.2.a.co.1.2 | 3 | 12.11 | even | 2 |