Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3332,2,Mod(1,3332)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3332, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("3332.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3332 = 2^{2} \cdot 7^{2} \cdot 17 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3332.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: | \(26.6061539535\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{13}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{2} - x - 3 \)
|
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 476) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-1.30278\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3332.1 |
$q$-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 | ||||||||
\(3\) | −0.302776 | −0.174808 | −0.0874038 | − | 0.996173i | \(-0.527857\pi\) | ||||
−0.0874038 | + | 0.996173i | \(0.527857\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 3.30278 | 1.47705 | 0.738523 | − | 0.674228i | \(-0.235524\pi\) | ||||
0.738523 | + | 0.674228i | \(0.235524\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.90833 | −0.969442 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.60555 | 1.38863 | 0.694313 | − | 0.719673i | \(-0.255708\pi\) | ||||
0.694313 | + | 0.719673i | \(0.255708\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 6.60555 | 1.83205 | 0.916025 | − | 0.401121i | \(-0.131379\pi\) | ||||
0.916025 | + | 0.401121i | \(0.131379\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.00000 | −0.258199 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.00000 | 0.242536 | ||||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 6.00000 | 1.37649 | 0.688247 | − | 0.725476i | \(-0.258380\pi\) | ||||
0.688247 | + | 0.725476i | \(0.258380\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2.60555 | −0.543295 | −0.271647 | − | 0.962397i | \(-0.587568\pi\) | ||||
−0.271647 | + | 0.962397i | \(0.587568\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 5.90833 | 1.18167 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.78890 | 0.344273 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −8.60555 | −1.59801 | −0.799005 | − | 0.601324i | \(-0.794640\pi\) | ||||
−0.799005 | + | 0.601324i | \(0.794640\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.69722 | 1.20286 | 0.601429 | − | 0.798927i | \(-0.294598\pi\) | ||||
0.601429 | + | 0.798927i | \(0.294598\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −1.39445 | −0.242742 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 7.21110 | 1.18550 | 0.592749 | − | 0.805387i | \(-0.298043\pi\) | ||||
0.592749 | + | 0.805387i | \(0.298043\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −2.00000 | −0.320256 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −9.51388 | −1.48582 | −0.742909 | − | 0.669392i | \(-0.766555\pi\) | ||||
−0.742909 | + | 0.669392i | \(0.766555\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −4.30278 | −0.656167 | −0.328084 | − | 0.944649i | \(-0.606403\pi\) | ||||
−0.328084 | + | 0.944649i | \(0.606403\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −9.60555 | −1.43191 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −10.0000 | −1.45865 | −0.729325 | − | 0.684167i | \(-0.760166\pi\) | ||||
−0.729325 | + | 0.684167i | \(0.760166\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.302776 | −0.0423971 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0.697224 | 0.0957711 | 0.0478856 | − | 0.998853i | \(-0.484752\pi\) | ||||
0.0478856 | + | 0.998853i | \(0.484752\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 15.2111 | 2.05106 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −1.81665 | −0.240622 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −5.21110 | −0.678428 | −0.339214 | − | 0.940709i | \(-0.610161\pi\) | ||||
−0.339214 | + | 0.940709i | \(0.610161\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4.30278 | 0.550914 | 0.275457 | − | 0.961313i | \(-0.411171\pi\) | ||||
0.275457 | + | 0.961313i | \(0.411171\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 21.8167 | 2.70602 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.69722 | 0.329518 | 0.164759 | − | 0.986334i | \(-0.447315\pi\) | ||||
0.164759 | + | 0.986334i | \(0.447315\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0.788897 | 0.0949721 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −2.00000 | −0.237356 | −0.118678 | − | 0.992933i | \(-0.537866\pi\) | ||||
−0.118678 | + | 0.992933i | \(0.537866\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 13.5139 | 1.58168 | 0.790840 | − | 0.612023i | \(-0.209644\pi\) | ||||
0.790840 | + | 0.612023i | \(0.209644\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1.78890 | −0.206564 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −6.00000 | −0.675053 | −0.337526 | − | 0.941316i | \(-0.609590\pi\) | ||||
−0.337526 | + | 0.941316i | \(0.609590\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 8.18335 | 0.909261 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −9.21110 | −1.01105 | −0.505525 | − | 0.862812i | \(-0.668701\pi\) | ||||
−0.505525 | + | 0.862812i | \(0.668701\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 3.30278 | 0.358236 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 2.60555 | 0.279344 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 2.00000 | 0.212000 | 0.106000 | − | 0.994366i | \(-0.466196\pi\) | ||||
0.106000 | + | 0.994366i | \(0.466196\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −2.02776 | −0.210269 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 19.8167 | 2.03315 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 2.09167 | 0.212377 | 0.106189 | − | 0.994346i | \(-0.466135\pi\) | ||||
0.106189 | + | 0.994346i | \(0.466135\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −13.3944 | −1.34619 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 12.4222 | 1.23606 | 0.618028 | − | 0.786156i | \(-0.287932\pi\) | ||||
0.618028 | + | 0.786156i | \(0.287932\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −13.2111 | −1.30173 | −0.650864 | − | 0.759194i | \(-0.725593\pi\) | ||||
−0.650864 | + | 0.759194i | \(0.725593\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −9.39445 | −0.908196 | −0.454098 | − | 0.890952i | \(-0.650038\pi\) | ||||
−0.454098 | + | 0.890952i | \(0.650038\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −2.00000 | −0.191565 | −0.0957826 | − | 0.995402i | \(-0.530535\pi\) | ||||
−0.0957826 | + | 0.995402i | \(0.530535\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −2.18335 | −0.207234 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 19.2111 | 1.80723 | 0.903614 | − | 0.428347i | \(-0.140904\pi\) | ||||
0.903614 | + | 0.428347i | \(0.140904\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −8.60555 | −0.802472 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −19.2111 | −1.77607 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 10.2111 | 0.928282 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 2.88057 | 0.259732 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 3.00000 | 0.268328 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −5.11943 | −0.454276 | −0.227138 | − | 0.973863i | \(-0.572937\pi\) | ||||
−0.227138 | + | 0.973863i | \(0.572937\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 1.30278 | 0.114703 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 10.4222 | 0.910592 | 0.455296 | − | 0.890340i | \(-0.349533\pi\) | ||||
0.455296 | + | 0.890340i | \(0.349533\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 5.90833 | 0.508508 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −3.09167 | −0.264139 | −0.132070 | − | 0.991240i | \(-0.542162\pi\) | ||||
−0.132070 | + | 0.991240i | \(0.542162\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1.48612 | 0.126051 | 0.0630256 | − | 0.998012i | \(-0.479925\pi\) | ||||
0.0630256 | + | 0.998012i | \(0.479925\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 3.02776 | 0.254983 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 30.4222 | 2.54403 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −28.4222 | −2.36034 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 4.90833 | 0.402106 | 0.201053 | − | 0.979580i | \(-0.435564\pi\) | ||||
0.201053 | + | 0.979580i | \(0.435564\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 14.1194 | 1.14902 | 0.574511 | − | 0.818497i | \(-0.305192\pi\) | ||||
0.574511 | + | 0.818497i | \(0.305192\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −2.90833 | −0.235124 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 22.1194 | 1.77668 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0.183346 | 0.0146326 | 0.00731631 | − | 0.999973i | \(-0.497671\pi\) | ||||
0.00731631 | + | 0.999973i | \(0.497671\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −0.211103 | −0.0167415 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −21.8167 | −1.70881 | −0.854406 | − | 0.519606i | \(-0.826079\pi\) | ||||
−0.854406 | + | 0.519606i | \(0.826079\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −4.60555 | −0.358542 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 2.11943 | 0.164006 | 0.0820032 | − | 0.996632i | \(-0.473868\pi\) | ||||
0.0820032 | + | 0.996632i | \(0.473868\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 30.6333 | 2.35641 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −17.4500 | −1.33443 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −4.90833 | −0.373173 | −0.186587 | − | 0.982439i | \(-0.559742\pi\) | ||||
−0.186587 | + | 0.982439i | \(0.559742\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 1.57779 | 0.118594 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 11.0917 | 0.829031 | 0.414515 | − | 0.910042i | \(-0.363951\pi\) | ||||
0.414515 | + | 0.910042i | \(0.363951\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 21.6333 | 1.60799 | 0.803996 | − | 0.594635i | \(-0.202704\pi\) | ||||
0.803996 | + | 0.594635i | \(0.202704\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −1.30278 | −0.0963039 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 23.8167 | 1.75104 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 4.60555 | 0.336791 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −23.7250 | −1.71668 | −0.858340 | − | 0.513082i | \(-0.828504\pi\) | ||||
−0.858340 | + | 0.513082i | \(0.828504\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −5.39445 | −0.388301 | −0.194150 | − | 0.980972i | \(-0.562195\pi\) | ||||
−0.194150 | + | 0.980972i | \(0.562195\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −6.60555 | −0.473033 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −23.0278 | −1.64066 | −0.820330 | − | 0.571891i | \(-0.806210\pi\) | ||||
−0.820330 | + | 0.571891i | \(0.806210\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −13.5139 | −0.957973 | −0.478987 | − | 0.877822i | \(-0.658996\pi\) | ||||
−0.478987 | + | 0.877822i | \(0.658996\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −0.816654 | −0.0576023 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −31.4222 | −2.19462 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 7.57779 | 0.526693 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 27.6333 | 1.91144 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −27.0278 | −1.86067 | −0.930334 | − | 0.366714i | \(-0.880483\pi\) | ||||
−0.930334 | + | 0.366714i | \(0.880483\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0.605551 | 0.0414917 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −14.2111 | −0.969189 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −4.09167 | −0.276490 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 6.60555 | 0.444337 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 21.6333 | 1.44867 | 0.724337 | − | 0.689446i | \(-0.242146\pi\) | ||||
0.724337 | + | 0.689446i | \(0.242146\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −17.1833 | −1.14556 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −0.0916731 | −0.00608456 | −0.00304228 | − | 0.999995i | \(-0.500968\pi\) | ||||
−0.00304228 | + | 0.999995i | \(0.500968\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 5.81665 | 0.384375 | 0.192188 | − | 0.981358i | \(-0.438442\pi\) | ||||
0.192188 | + | 0.981358i | \(0.438442\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 13.2111 | 0.865488 | 0.432744 | − | 0.901517i | \(-0.357545\pi\) | ||||
0.432744 | + | 0.901517i | \(0.357545\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −33.0278 | −2.15449 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 1.81665 | 0.118004 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −12.3028 | −0.795800 | −0.397900 | − | 0.917429i | \(-0.630261\pi\) | ||||
−0.397900 | + | 0.917429i | \(0.630261\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −13.9083 | −0.895914 | −0.447957 | − | 0.894055i | \(-0.647848\pi\) | ||||
−0.447957 | + | 0.894055i | \(0.647848\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −7.84441 | −0.503219 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 39.6333 | 2.52181 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 2.78890 | 0.176739 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −8.78890 | −0.554750 | −0.277375 | − | 0.960762i | \(-0.589464\pi\) | ||||
−0.277375 | + | 0.960762i | \(0.589464\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −12.0000 | −0.754434 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −1.00000 | −0.0626224 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 13.8167 | 0.861859 | 0.430930 | − | 0.902386i | \(-0.358186\pi\) | ||||
0.430930 | + | 0.902386i | \(0.358186\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 25.0278 | 1.54918 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 22.4222 | 1.38261 | 0.691306 | − | 0.722562i | \(-0.257036\pi\) | ||||
0.691306 | + | 0.722562i | \(0.257036\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2.30278 | 0.141458 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −0.605551 | −0.0370591 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 6.00000 | 0.365826 | 0.182913 | − | 0.983129i | \(-0.441447\pi\) | ||||
0.182913 | + | 0.983129i | \(0.441447\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 31.8167 | 1.93272 | 0.966362 | − | 0.257186i | \(-0.0827952\pi\) | ||||
0.966362 | + | 0.257186i | \(0.0827952\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 27.2111 | 1.64089 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 25.0278 | 1.50377 | 0.751886 | − | 0.659293i | \(-0.229144\pi\) | ||||
0.751886 | + | 0.659293i | \(0.229144\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −19.4777 | −1.16610 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −16.6972 | −0.996073 | −0.498036 | − | 0.867156i | \(-0.665945\pi\) | ||||
−0.498036 | + | 0.867156i | \(0.665945\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −6.69722 | −0.398109 | −0.199054 | − | 0.979988i | \(-0.563787\pi\) | ||||
−0.199054 | + | 0.979988i | \(0.563787\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −6.00000 | −0.355409 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −0.633308 | −0.0371252 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −1.81665 | −0.106130 | −0.0530650 | − | 0.998591i | \(-0.516899\pi\) | ||||
−0.0530650 | + | 0.998591i | \(0.516899\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −17.2111 | −1.00207 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 8.23886 | 0.478067 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −17.2111 | −0.995344 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −3.76114 | −0.216072 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 14.2111 | 0.813725 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 26.0000 | 1.48390 | 0.741949 | − | 0.670456i | \(-0.233902\pi\) | ||||
0.741949 | + | 0.670456i | \(0.233902\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 4.00000 | 0.227552 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 15.7250 | 0.891682 | 0.445841 | − | 0.895112i | \(-0.352905\pi\) | ||||
0.445841 | + | 0.895112i | \(0.352905\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 5.72498 | 0.323595 | 0.161798 | − | 0.986824i | \(-0.448271\pi\) | ||||
0.161798 | + | 0.986824i | \(0.448271\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −12.6056 | −0.707998 | −0.353999 | − | 0.935246i | \(-0.615178\pi\) | ||||
−0.353999 | + | 0.935246i | \(0.615178\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −39.6333 | −2.21904 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 2.84441 | 0.158759 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 6.00000 | 0.333849 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 39.0278 | 2.16487 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0.605551 | 0.0334871 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −0.275019 | −0.0151164 | −0.00755821 | − | 0.999971i | \(-0.502406\pi\) | ||||
−0.00755821 | + | 0.999971i | \(0.502406\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −20.9722 | −1.14927 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 8.90833 | 0.486714 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 10.7889 | 0.587709 | 0.293854 | − | 0.955850i | \(-0.405062\pi\) | ||||
0.293854 | + | 0.955850i | \(0.405062\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −5.81665 | −0.315917 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 30.8444 | 1.67032 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 2.60555 | 0.140278 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 6.00000 | 0.322097 | 0.161048 | − | 0.986947i | \(-0.448512\pi\) | ||||
0.161048 | + | 0.986947i | \(0.448512\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −19.2111 | −1.02835 | −0.514173 | − | 0.857686i | \(-0.671901\pi\) | ||||
−0.514173 | + | 0.857686i | \(0.671901\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 11.8167 | 0.630726 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −4.60555 | −0.245129 | −0.122564 | − | 0.992461i | \(-0.539112\pi\) | ||||
−0.122564 | + | 0.992461i | \(0.539112\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −6.60555 | −0.350586 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −17.4861 | −0.922882 | −0.461441 | − | 0.887171i | \(-0.652667\pi\) | ||||
−0.461441 | + | 0.887171i | \(0.652667\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 17.0000 | 0.894737 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −3.09167 | −0.162271 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 44.6333 | 2.33621 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −26.7250 | −1.39503 | −0.697516 | − | 0.716569i | \(-0.745712\pi\) | ||||
−0.697516 | + | 0.716569i | \(0.745712\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 27.6695 | 1.44041 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 12.3028 | 0.637014 | 0.318507 | − | 0.947921i | \(-0.396819\pi\) | ||||
0.318507 | + | 0.947921i | \(0.396819\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −0.908327 | −0.0469058 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −56.8444 | −2.92764 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −28.2389 | −1.45053 | −0.725266 | − | 0.688468i | \(-0.758283\pi\) | ||||
−0.725266 | + | 0.688468i | \(0.758283\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1.55004 | 0.0794109 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 3.02776 | 0.154711 | 0.0773556 | − | 0.997004i | \(-0.475352\pi\) | ||||
0.0773556 | + | 0.997004i | \(0.475352\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 12.5139 | 0.636116 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −14.0917 | −0.714476 | −0.357238 | − | 0.934013i | \(-0.616282\pi\) | ||||
−0.357238 | + | 0.934013i | \(0.616282\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2.60555 | −0.131768 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −3.15559 | −0.159178 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −19.8167 | −0.997084 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 6.09167 | 0.305732 | 0.152866 | − | 0.988247i | \(-0.451150\pi\) | ||||
0.152866 | + | 0.988247i | \(0.451150\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 24.0000 | 1.19850 | 0.599251 | − | 0.800561i | \(-0.295465\pi\) | ||||
0.599251 | + | 0.800561i | \(0.295465\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 44.2389 | 2.20369 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 27.0278 | 1.34302 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 33.2111 | 1.64621 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 3.02776 | 0.149713 | 0.0748565 | − | 0.997194i | \(-0.476150\pi\) | ||||
0.0748565 | + | 0.997194i | \(0.476150\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0.936083 | 0.0461736 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −30.4222 | −1.49337 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −0.449961 | −0.0220347 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 1.30278 | 0.0636448 | 0.0318224 | − | 0.999494i | \(-0.489869\pi\) | ||||
0.0318224 | + | 0.999494i | \(0.489869\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −0.908327 | −0.0442691 | −0.0221346 | − | 0.999755i | \(-0.507046\pi\) | ||||
−0.0221346 | + | 0.999755i | \(0.507046\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 29.0833 | 1.41408 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 5.90833 | 0.286596 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −9.21110 | −0.444716 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 18.8444 | 0.907703 | 0.453852 | − | 0.891077i | \(-0.350050\pi\) | ||||
0.453852 | + | 0.891077i | \(0.350050\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −11.6333 | −0.559061 | −0.279531 | − | 0.960137i | \(-0.590179\pi\) | ||||
−0.279531 | + | 0.960137i | \(0.590179\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 8.60555 | 0.412605 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −15.6333 | −0.747843 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 0.302776 | 0.0144507 | 0.00722535 | − | 0.999974i | \(-0.497700\pi\) | ||||
0.00722535 | + | 0.999974i | \(0.497700\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −10.4222 | −0.495174 | −0.247587 | − | 0.968866i | \(-0.579638\pi\) | ||||
−0.247587 | + | 0.968866i | \(0.579638\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 6.60555 | 0.313133 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −1.48612 | −0.0702911 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −32.2389 | −1.52145 | −0.760723 | − | 0.649077i | \(-0.775155\pi\) | ||||
−0.760723 | + | 0.649077i | \(0.775155\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −43.8167 | −2.06325 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −4.27502 | −0.200858 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 6.09167 | 0.284956 | 0.142478 | − | 0.989798i | \(-0.454493\pi\) | ||||
0.142478 | + | 0.989798i | \(0.454493\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 1.78890 | 0.0834986 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −9.21110 | −0.429004 | −0.214502 | − | 0.976724i | \(-0.568813\pi\) | ||||
−0.214502 | + | 0.976724i | \(0.568813\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 36.5416 | 1.69823 | 0.849117 | − | 0.528205i | \(-0.177135\pi\) | ||||
0.849117 | + | 0.528205i | \(0.177135\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −6.69722 | −0.310576 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −17.2111 | −0.796435 | −0.398217 | − | 0.917291i | \(-0.630371\pi\) | ||||
−0.398217 | + | 0.917291i | \(0.630371\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −0.0555128 | −0.00255789 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −19.8167 | −0.911171 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 35.4500 | 1.62656 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −2.02776 | −0.0928446 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 24.3028 | 1.11042 | 0.555211 | − | 0.831709i | \(-0.312637\pi\) | ||||
0.555211 | + | 0.831709i | \(0.312637\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 47.6333 | 2.17189 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 6.90833 | 0.313691 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 13.6333 | 0.617784 | 0.308892 | − | 0.951097i | \(-0.400042\pi\) | ||||
0.308892 | + | 0.951097i | \(0.400042\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 6.60555 | 0.298713 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 30.6972 | 1.38535 | 0.692673 | − | 0.721252i | \(-0.256433\pi\) | ||||
0.692673 | + | 0.721252i | \(0.256433\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −8.60555 | −0.387575 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −44.2389 | −1.98839 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −6.00000 | −0.268597 | −0.134298 | − | 0.990941i | \(-0.542878\pi\) | ||||
−0.134298 | + | 0.990941i | \(0.542878\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −0.641712 | −0.0286696 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −10.8806 | −0.485141 | −0.242570 | − | 0.970134i | \(-0.577991\pi\) | ||||
−0.242570 | + | 0.970134i | \(0.577991\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 41.0278 | 1.82571 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −9.27502 | −0.411918 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −3.39445 | −0.150456 | −0.0752281 | − | 0.997166i | \(-0.523969\pi\) | ||||
−0.0752281 | + | 0.997166i | \(0.523969\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 10.7334 | 0.473891 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −43.6333 | −1.92271 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −46.0555 | −2.02552 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 1.48612 | 0.0652335 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −7.33053 | −0.321156 | −0.160578 | − | 0.987023i | \(-0.551336\pi\) | ||||
−0.160578 | + | 0.987023i | \(0.551336\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −17.0278 | −0.744572 | −0.372286 | − | 0.928118i | \(-0.621426\pi\) | ||||
−0.372286 | + | 0.928118i | \(0.621426\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 6.69722 | 0.291736 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −16.2111 | −0.704831 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 15.1556 | 0.657697 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −62.8444 | −2.72209 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −31.0278 | −1.34145 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −3.35829 | −0.144921 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 3.81665 | 0.164091 | 0.0820454 | − | 0.996629i | \(-0.473855\pi\) | ||||
0.0820454 | + | 0.996629i | \(0.473855\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −6.55004 | −0.281089 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −6.60555 | −0.282951 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −39.4500 | −1.68676 | −0.843379 | − | 0.537319i | \(-0.819437\pi\) | ||||
−0.843379 | + | 0.537319i | \(0.819437\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −12.5139 | −0.534079 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −51.6333 | −2.19965 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −7.21110 | −0.306094 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 11.2111 | 0.475030 | 0.237515 | − | 0.971384i | \(-0.423667\pi\) | ||||
0.237515 | + | 0.971384i | \(0.423667\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −28.4222 | −1.20213 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1.39445 | −0.0588737 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −32.2389 | −1.35871 | −0.679353 | − | 0.733812i | \(-0.737739\pi\) | ||||
−0.679353 | + | 0.733812i | \(0.737739\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 63.4500 | 2.66936 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −41.5139 | −1.74035 | −0.870176 | − | 0.492741i | \(-0.835995\pi\) | ||||
−0.870176 | + | 0.492741i | \(0.835995\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −33.6333 | −1.40751 | −0.703755 | − | 0.710443i | \(-0.748495\pi\) | ||||
−0.703755 | + | 0.710443i | \(0.748495\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 7.18335 | 0.300089 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −15.3944 | −0.641993 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −39.0278 | −1.62475 | −0.812373 | − | 0.583138i | \(-0.801825\pi\) | ||||
−0.812373 | + | 0.583138i | \(0.801825\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 1.63331 | 0.0678779 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 3.21110 | 0.132990 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −63.4500 | −2.62333 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 17.2111 | 0.710378 | 0.355189 | − | 0.934794i | \(-0.384416\pi\) | ||||
0.355189 | + | 0.934794i | \(0.384416\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 40.1833 | 1.65573 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 6.97224 | 0.286800 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −9.63331 | −0.395593 | −0.197796 | − | 0.980243i | \(-0.563378\pi\) | ||||
−0.197796 | + | 0.980243i | \(0.563378\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 4.09167 | 0.167461 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −32.5416 | −1.32962 | −0.664808 | − | 0.747015i | \(-0.731486\pi\) | ||||
−0.664808 | + | 0.747015i | \(0.731486\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −19.2111 | −0.783637 | −0.391819 | − | 0.920042i | \(-0.628154\pi\) | ||||
−0.391819 | + | 0.920042i | \(0.628154\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −7.84441 | −0.319449 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 33.7250 | 1.37112 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 16.0917 | 0.653141 | 0.326570 | − | 0.945173i | \(-0.394107\pi\) | ||||
0.326570 | + | 0.945173i | \(0.394107\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −66.0555 | −2.67232 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −30.9361 | −1.24950 | −0.624748 | − | 0.780826i | \(-0.714798\pi\) | ||||
−0.624748 | + | 0.780826i | \(0.714798\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 9.51388 | 0.383637 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 4.60555 | 0.185413 | 0.0927063 | − | 0.995694i | \(-0.470448\pi\) | ||||
0.0927063 | + | 0.995694i | \(0.470448\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 8.00000 | 0.321547 | 0.160774 | − | 0.986991i | \(-0.448601\pi\) | ||||
0.160774 | + | 0.986991i | \(0.448601\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −4.66106 | −0.187042 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −19.6333 | −0.785332 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −8.36669 | −0.334134 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 7.21110 | 0.287525 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 13.1194 | 0.522276 | 0.261138 | − | 0.965301i | \(-0.415902\pi\) | ||||
0.261138 | + | 0.965301i | \(0.415902\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 8.18335 | 0.325259 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −16.9083 | −0.670986 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 5.81665 | 0.230103 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −7.57779 | −0.299305 | −0.149652 | − | 0.988739i | \(-0.547815\pi\) | ||||
−0.149652 | + | 0.988739i | \(0.547815\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −27.3305 | −1.07781 | −0.538905 | − | 0.842366i | \(-0.681162\pi\) | ||||
−0.538905 | + | 0.842366i | \(0.681162\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 4.30278 | 0.169422 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 27.3944 | 1.07699 | 0.538493 | − | 0.842630i | \(-0.318994\pi\) | ||||
0.538493 | + | 0.842630i | \(0.318994\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −24.0000 | −0.942082 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 2.00000 | 0.0782660 | 0.0391330 | − | 0.999234i | \(-0.487540\pi\) | ||||
0.0391330 | + | 0.999234i | \(0.487540\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 34.4222 | 1.34499 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −39.3028 | −1.53335 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 7.54163 | 0.293780 | 0.146890 | − | 0.989153i | \(-0.453074\pi\) | ||||
0.146890 | + | 0.989153i | \(0.453074\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −15.6333 | −0.608065 | −0.304033 | − | 0.952662i | \(-0.598333\pi\) | ||||
−0.304033 | + | 0.952662i | \(0.598333\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −2.00000 | −0.0776736 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 22.4222 | 0.868191 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −6.55004 | −0.253239 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 19.8167 | 0.765013 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −20.8444 | −0.803493 | −0.401746 | − | 0.915751i | \(-0.631597\pi\) | ||||
−0.401746 | + | 0.915751i | \(0.631597\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 10.5694 | 0.406816 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −22.0000 | −0.845529 | −0.422764 | − | 0.906240i | \(-0.638940\pi\) | ||||
−0.422764 | + | 0.906240i | \(0.638940\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0.0277564 | 0.00106363 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −11.0278 | −0.421965 | −0.210983 | − | 0.977490i | \(-0.567666\pi\) | ||||
−0.210983 | + | 0.977490i | \(0.567666\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −10.2111 | −0.390146 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −1.76114 | −0.0671917 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 4.60555 | 0.175458 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −4.30278 | −0.163685 | −0.0818426 | − | 0.996645i | \(-0.526080\pi\) | ||||
−0.0818426 | + | 0.996645i | \(0.526080\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 4.90833 | 0.186183 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −9.51388 | −0.360364 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −4.00000 | −0.151294 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −11.2111 | −0.423437 | −0.211719 | − | 0.977331i | \(-0.567906\pi\) | ||||
−0.211719 | + | 0.977331i | \(0.567906\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 43.2666 | 1.63183 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 10.0000 | 0.376622 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −24.1833 | −0.908225 | −0.454112 | − | 0.890944i | \(-0.650044\pi\) | ||||
−0.454112 | + | 0.890944i | \(0.650044\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 17.4500 | 0.654425 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −17.4500 | −0.653506 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 100.478 | 3.75765 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 3.72498 | 0.139112 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 2.48612 | 0.0927167 | 0.0463583 | − | 0.998925i | \(-0.485238\pi\) | ||||
0.0463583 | + | 0.998925i | \(0.485238\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 4.21110 | 0.156613 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −50.8444 | −1.88831 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −49.2666 | −1.82720 | −0.913599 | − | 0.406617i | \(-0.866708\pi\) | ||||
−0.913599 | + | 0.406617i | \(0.866708\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −22.1749 | −0.821294 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −4.30278 | −0.159144 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 15.6333 | 0.577429 | 0.288715 | − | 0.957415i | \(-0.406772\pi\) | ||||
0.288715 | + | 0.957415i | \(0.406772\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 12.4222 | 0.457578 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −24.9083 | −0.916268 | −0.458134 | − | 0.888883i | \(-0.651482\pi\) | ||||
−0.458134 | + | 0.888883i | \(0.651482\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −12.0000 | −0.440831 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −33.3944 | −1.22512 | −0.612562 | − | 0.790423i | \(-0.709861\pi\) | ||||
−0.612562 | + | 0.790423i | \(0.709861\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 16.2111 | 0.593929 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 26.7889 | 0.980155 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −51.2111 | −1.86872 | −0.934360 | − | 0.356331i | \(-0.884028\pi\) | ||||
−0.934360 | + | 0.356331i | \(0.884028\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 2.66106 | 0.0969746 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 46.6333 | 1.69716 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 23.0917 | 0.839281 | 0.419641 | − | 0.907690i | \(-0.362156\pi\) | ||||
0.419641 | + | 0.907690i | \(0.362156\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 3.63331 | 0.131881 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −46.6056 | −1.68945 | −0.844725 | − | 0.535201i | \(-0.820236\pi\) | ||||
−0.844725 | + | 0.535201i | \(0.820236\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −9.60555 | −0.347289 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −34.4222 | −1.24291 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −11.8167 | −0.426119 | −0.213060 | − | 0.977039i | \(-0.568343\pi\) | ||||
−0.213060 | + | 0.977039i | \(0.568343\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −4.18335 | −0.150660 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 6.84441 | 0.246176 | 0.123088 | − | 0.992396i | \(-0.460720\pi\) | ||||
0.123088 | + | 0.992396i | \(0.460720\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 39.5694 | 1.42137 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −57.0833 | −2.04522 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −9.21110 | −0.329599 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −15.3944 | −0.550153 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0.605551 | 0.0216131 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 14.4222 | 0.514096 | 0.257048 | − | 0.966399i | \(-0.417250\pi\) | ||||
0.257048 | + | 0.966399i | \(0.417250\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −6.78890 | −0.241691 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 28.4222 | 1.00930 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −0.697224 | −0.0247280 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −14.7889 | −0.523850 | −0.261925 | − | 0.965088i | \(-0.584357\pi\) | ||||
−0.261925 | + | 0.965088i | \(0.584357\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −10.0000 | −0.353775 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −5.81665 | −0.205521 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 62.2389 | 2.19636 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −1.81665 | −0.0639492 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 45.4500 | 1.59794 | 0.798968 | − | 0.601374i | \(-0.205380\pi\) | ||||
0.798968 | + | 0.601374i | \(0.205380\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 38.3583 | 1.34694 | 0.673471 | − | 0.739214i | \(-0.264803\pi\) | ||||
0.673471 | + | 0.739214i | \(0.264803\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −9.63331 | −0.337855 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −72.0555 | −2.52399 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −25.8167 | −0.903210 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 40.4222 | 1.41074 | 0.705372 | − | 0.708837i | \(-0.250780\pi\) | ||||
0.705372 | + | 0.708837i | \(0.250780\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −5.02776 | −0.175257 | −0.0876283 | − | 0.996153i | \(-0.527929\pi\) | ||||
−0.0876283 | + | 0.996153i | \(0.527929\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −8.23886 | −0.286840 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 18.8444 | 0.655284 | 0.327642 | − | 0.944802i | \(-0.393746\pi\) | ||||
0.327642 | + | 0.944802i | \(0.393746\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 29.3944 | 1.02091 | 0.510456 | − | 0.859904i | \(-0.329477\pi\) | ||||
0.510456 | + | 0.859904i | \(0.329477\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −7.57779 | −0.262871 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 7.00000 | 0.242245 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 11.9806 | 0.414112 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −21.2111 | −0.732289 | −0.366144 | − | 0.930558i | \(-0.619322\pi\) | ||||
−0.366144 | + | 0.930558i | \(0.619322\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 45.0555 | 1.55364 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 5.05551 | 0.174121 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 101.175 | 3.48052 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 2.02776 | 0.0695924 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −18.7889 | −0.644075 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 19.2111 | 0.657776 | 0.328888 | − | 0.944369i | \(-0.393326\pi\) | ||||
0.328888 | + | 0.944369i | \(0.393326\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −57.6333 | −1.97102 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −12.5139 | −0.427466 | −0.213733 | − | 0.976892i | \(-0.568562\pi\) | ||||
−0.213733 | + | 0.976892i | \(0.568562\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 45.6333 | 1.55699 | 0.778494 | − | 0.627652i | \(-0.215984\pi\) | ||||
0.778494 | + | 0.627652i | \(0.215984\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 8.93608 | 0.304188 | 0.152094 | − | 0.988366i | \(-0.451398\pi\) | ||||
0.152094 | + | 0.988366i | \(0.451398\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −16.2111 | −0.551194 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −0.302776 | −0.0102828 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −27.6333 | −0.937396 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 17.8167 | 0.603694 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −6.08327 | −0.205887 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −6.18335 | −0.208797 | −0.104398 | − | 0.994536i | \(-0.533292\pi\) | ||||
−0.104398 | + | 0.994536i | \(0.533292\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0.550039 | 0.0185523 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 7.11943 | 0.239860 | 0.119930 | − | 0.992782i | \(-0.461733\pi\) | ||||
0.119930 | + | 0.992782i | \(0.461733\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 55.7250 | 1.87529 | 0.937647 | − | 0.347588i | \(-0.112999\pi\) | ||||
0.937647 | + | 0.347588i | \(0.112999\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 5.21110 | 0.175169 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 12.2750 | 0.412155 | 0.206077 | − | 0.978536i | \(-0.433930\pi\) | ||||
0.206077 | + | 0.978536i | \(0.433930\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 37.6888 | 1.26262 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −60.0000 | −2.00782 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 36.6333 | 1.22452 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 5.21110 | 0.173994 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −57.6333 | −1.92218 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0.697224 | 0.0232279 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 71.4500 | 2.37508 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −3.57779 | −0.118799 | −0.0593994 | − | 0.998234i | \(-0.518919\pi\) | ||||
−0.0593994 | + | 0.998234i | \(0.518919\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −36.1278 | −1.19828 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −10.4222 | −0.345303 | −0.172652 | − | 0.984983i | \(-0.555233\pi\) | ||||
−0.172652 | + | 0.984983i | \(0.555233\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −42.4222 | −1.40397 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −4.30278 | −0.142245 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −10.4861 | −0.345905 | −0.172953 | − | 0.984930i | \(-0.555331\pi\) | ||||
−0.172953 | + | 0.984930i | \(0.555331\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −7.87217 | −0.259397 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −13.2111 | −0.434849 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 42.6056 | 1.40086 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 38.4222 | 1.26195 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 24.6972 | 0.810290 | 0.405145 | − | 0.914253i | \(-0.367221\pi\) | ||||
0.405145 | + | 0.914253i | \(0.367221\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −4.76114 | −0.155873 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 15.2111 | 0.497456 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 25.2111 | 0.823611 | 0.411805 | − | 0.911272i | \(-0.364898\pi\) | ||||
0.411805 | + | 0.911272i | \(0.364898\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −1.73338 | −0.0565669 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 0.669468 | 0.0218240 | 0.0109120 | − | 0.999940i | \(-0.496527\pi\) | ||||
0.0109120 | + | 0.999940i | \(0.496527\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 24.7889 | 0.807238 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 20.2389 | 0.657675 | 0.328837 | − | 0.944387i | \(-0.393343\pi\) | ||||
0.328837 | + | 0.944387i | \(0.393343\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 89.2666 | 2.89772 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 3.81665 | 0.123763 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 26.7527 | 0.866606 | 0.433303 | − | 0.901248i | \(-0.357348\pi\) | ||||
0.433303 | + | 0.901248i | \(0.357348\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −78.3583 | −2.53561 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 12.0000 | 0.387905 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 13.8528 | 0.446865 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 27.3221 | 0.880443 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −17.8167 | −0.573538 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −20.3028 | −0.652893 | −0.326447 | − | 0.945216i | \(-0.605851\pi\) | ||||
−0.326447 | + | 0.945216i | \(0.605851\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −1.81665 | −0.0583593 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 20.2389 | 0.649496 | 0.324748 | − | 0.945801i | \(-0.394721\pi\) | ||||
0.324748 | + | 0.945801i | \(0.394721\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −11.8167 | −0.378436 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 12.5139 | 0.400354 | 0.200177 | − | 0.979760i | \(-0.435848\pi\) | ||||
0.200177 | + | 0.979760i | \(0.435848\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 9.21110 | 0.294388 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 5.81665 | 0.185711 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −14.5139 | −0.462921 | −0.231460 | − | 0.972844i | \(-0.574350\pi\) | ||||
−0.231460 | + | 0.972844i | \(0.574350\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −76.0555 | −2.42333 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 11.2111 | 0.356492 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 6.00000 | 0.190596 | 0.0952981 | − | 0.995449i | \(-0.469620\pi\) | ||||
0.0952981 | + | 0.995449i | \(0.469620\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0.0832691 | 0.00264247 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −44.6333 | −1.41497 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −32.9083 | −1.04222 | −0.521109 | − | 0.853490i | \(-0.674481\pi\) | ||||
−0.521109 | + | 0.853490i | \(0.674481\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 12.8999 | 0.408136 |
(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 | 3332.2.a.n.1.1 | 2 | ||
7.6 | odd | 2 | 476.2.a.a.1.2 | ✓ | 2 | ||
21.20 | even | 2 | 4284.2.a.p.1.2 | 2 | |||
28.27 | even | 2 | 1904.2.a.l.1.1 | 2 | |||
56.13 | odd | 2 | 7616.2.a.z.1.1 | 2 | |||
56.27 | even | 2 | 7616.2.a.m.1.2 | 2 | |||
119.118 | odd | 2 | 8092.2.a.n.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
476.2.a.a.1.2 | ✓ | 2 | 7.6 | odd | 2 | ||
1904.2.a.l.1.1 | 2 | 28.27 | even | 2 | |||
3332.2.a.n.1.1 | 2 | 1.1 | even | 1 | trivial | ||
4284.2.a.p.1.2 | 2 | 21.20 | even | 2 | |||
7616.2.a.m.1.2 | 2 | 56.27 | even | 2 | |||
7616.2.a.z.1.1 | 2 | 56.13 | odd | 2 | |||
8092.2.a.n.1.1 | 2 | 119.118 | odd | 2 |