Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2842,2,Mod(1,2842)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2842, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("2842.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2842 = 2 \cdot 7^{2} \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2842.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: | \(22.6934842544\) |
Analytic rank: | \(0\) |
Dimension: | \(5\) |
Coefficient field: | 5.5.1019601.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{5} - 10x^{3} - x^{2} + 24x + 7 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 406) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-2.48141\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2842.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | −0.714579 | −0.412562 | −0.206281 | − | 0.978493i | \(-0.566136\pi\) | ||||
−0.206281 | + | 0.978493i | \(0.566136\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 0.233169 | 0.104276 | 0.0521381 | − | 0.998640i | \(-0.483396\pi\) | ||||
0.0521381 | + | 0.998640i | \(0.483396\pi\) | |||||||
\(6\) | −0.714579 | −0.291726 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | −2.48938 | −0.829792 | ||||||||
\(10\) | 0.233169 | 0.0737344 | ||||||||
\(11\) | 0.293388 | 0.0884599 | 0.0442299 | − | 0.999021i | \(-0.485917\pi\) | ||||
0.0442299 | + | 0.999021i | \(0.485917\pi\) | |||||||
\(12\) | −0.714579 | −0.206281 | ||||||||
\(13\) | 4.15740 | 1.15305 | 0.576527 | − | 0.817078i | \(-0.304408\pi\) | ||||
0.576527 | + | 0.817078i | \(0.304408\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.166617 | −0.0430204 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 0.609435 | 0.147810 | 0.0739048 | − | 0.997265i | \(-0.476454\pi\) | ||||
0.0739048 | + | 0.997265i | \(0.476454\pi\) | |||||||
\(18\) | −2.48938 | −0.586752 | ||||||||
\(19\) | 6.67740 | 1.53190 | 0.765950 | − | 0.642900i | \(-0.222269\pi\) | ||||
0.765950 | + | 0.642900i | \(0.222269\pi\) | |||||||
\(20\) | 0.233169 | 0.0521381 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0.293388 | 0.0625506 | ||||||||
\(23\) | −1.48774 | −0.310216 | −0.155108 | − | 0.987898i | \(-0.549572\pi\) | ||||
−0.155108 | + | 0.987898i | \(0.549572\pi\) | |||||||
\(24\) | −0.714579 | −0.145863 | ||||||||
\(25\) | −4.94563 | −0.989126 | ||||||||
\(26\) | 4.15740 | 0.815333 | ||||||||
\(27\) | 3.92259 | 0.754903 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.00000 | −0.185695 | ||||||||
\(30\) | −0.166617 | −0.0304200 | ||||||||
\(31\) | −1.35175 | −0.242781 | −0.121391 | − | 0.992605i | \(-0.538735\pi\) | ||||
−0.121391 | + | 0.992605i | \(0.538735\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | −0.209649 | −0.0364952 | ||||||||
\(34\) | 0.609435 | 0.104517 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −2.48938 | −0.414896 | ||||||||
\(37\) | 0.637171 | 0.104750 | 0.0523752 | − | 0.998627i | \(-0.483321\pi\) | ||||
0.0523752 | + | 0.998627i | \(0.483321\pi\) | |||||||
\(38\) | 6.67740 | 1.08322 | ||||||||
\(39\) | −2.97079 | −0.475707 | ||||||||
\(40\) | 0.233169 | 0.0368672 | ||||||||
\(41\) | 3.31605 | 0.517880 | 0.258940 | − | 0.965893i | \(-0.416627\pi\) | ||||
0.258940 | + | 0.965893i | \(0.416627\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −3.29502 | −0.502486 | −0.251243 | − | 0.967924i | \(-0.580839\pi\) | ||||
−0.251243 | + | 0.967924i | \(0.580839\pi\) | |||||||
\(44\) | 0.293388 | 0.0442299 | ||||||||
\(45\) | −0.580445 | −0.0865276 | ||||||||
\(46\) | −1.48774 | −0.219356 | ||||||||
\(47\) | 2.18092 | 0.318119 | 0.159060 | − | 0.987269i | \(-0.449154\pi\) | ||||
0.159060 | + | 0.987269i | \(0.449154\pi\) | |||||||
\(48\) | −0.714579 | −0.103141 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −4.94563 | −0.699418 | ||||||||
\(51\) | −0.435489 | −0.0609807 | ||||||||
\(52\) | 4.15740 | 0.576527 | ||||||||
\(53\) | 11.9922 | 1.64725 | 0.823627 | − | 0.567132i | \(-0.191947\pi\) | ||||
0.823627 | + | 0.567132i | \(0.191947\pi\) | |||||||
\(54\) | 3.92259 | 0.533797 | ||||||||
\(55\) | 0.0684089 | 0.00922426 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −4.77153 | −0.632004 | ||||||||
\(58\) | −1.00000 | −0.131306 | ||||||||
\(59\) | 4.30113 | 0.559960 | 0.279980 | − | 0.960006i | \(-0.409672\pi\) | ||||
0.279980 | + | 0.960006i | \(0.409672\pi\) | |||||||
\(60\) | −0.166617 | −0.0215102 | ||||||||
\(61\) | 3.64803 | 0.467082 | 0.233541 | − | 0.972347i | \(-0.424969\pi\) | ||||
0.233541 | + | 0.972347i | \(0.424969\pi\) | |||||||
\(62\) | −1.35175 | −0.171672 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0.969374 | 0.120236 | ||||||||
\(66\) | −0.209649 | −0.0258060 | ||||||||
\(67\) | 4.95649 | 0.605531 | 0.302766 | − | 0.953065i | \(-0.402090\pi\) | ||||
0.302766 | + | 0.953065i | \(0.402090\pi\) | |||||||
\(68\) | 0.609435 | 0.0739048 | ||||||||
\(69\) | 1.06311 | 0.127983 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 4.21106 | 0.499761 | 0.249881 | − | 0.968277i | \(-0.419609\pi\) | ||||
0.249881 | + | 0.968277i | \(0.419609\pi\) | |||||||
\(72\) | −2.48938 | −0.293376 | ||||||||
\(73\) | 5.84298 | 0.683870 | 0.341935 | − | 0.939724i | \(-0.388918\pi\) | ||||
0.341935 | + | 0.939724i | \(0.388918\pi\) | |||||||
\(74\) | 0.637171 | 0.0740697 | ||||||||
\(75\) | 3.53404 | 0.408076 | ||||||||
\(76\) | 6.67740 | 0.765950 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −2.97079 | −0.336375 | ||||||||
\(79\) | 2.10678 | 0.237031 | 0.118516 | − | 0.992952i | \(-0.462186\pi\) | ||||
0.118516 | + | 0.992952i | \(0.462186\pi\) | |||||||
\(80\) | 0.233169 | 0.0260690 | ||||||||
\(81\) | 4.66513 | 0.518348 | ||||||||
\(82\) | 3.31605 | 0.366196 | ||||||||
\(83\) | 6.73621 | 0.739395 | 0.369697 | − | 0.929152i | \(-0.379461\pi\) | ||||
0.369697 | + | 0.929152i | \(0.379461\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.142101 | 0.0154130 | ||||||||
\(86\) | −3.29502 | −0.355312 | ||||||||
\(87\) | 0.714579 | 0.0766109 | ||||||||
\(88\) | 0.293388 | 0.0312753 | ||||||||
\(89\) | −12.6247 | −1.33821 | −0.669106 | − | 0.743167i | \(-0.733323\pi\) | ||||
−0.669106 | + | 0.743167i | \(0.733323\pi\) | |||||||
\(90\) | −0.580445 | −0.0611842 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −1.48774 | −0.155108 | ||||||||
\(93\) | 0.965932 | 0.100162 | ||||||||
\(94\) | 2.18092 | 0.224944 | ||||||||
\(95\) | 1.55696 | 0.159741 | ||||||||
\(96\) | −0.714579 | −0.0729314 | ||||||||
\(97\) | 5.70498 | 0.579253 | 0.289626 | − | 0.957140i | \(-0.406469\pi\) | ||||
0.289626 | + | 0.957140i | \(0.406469\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −0.730354 | −0.0734033 | ||||||||
\(100\) | −4.94563 | −0.494563 | ||||||||
\(101\) | 15.7339 | 1.56558 | 0.782789 | − | 0.622287i | \(-0.213796\pi\) | ||||
0.782789 | + | 0.622287i | \(0.213796\pi\) | |||||||
\(102\) | −0.435489 | −0.0431199 | ||||||||
\(103\) | −4.89549 | −0.482367 | −0.241184 | − | 0.970479i | \(-0.577536\pi\) | ||||
−0.241184 | + | 0.970479i | \(0.577536\pi\) | |||||||
\(104\) | 4.15740 | 0.407666 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 11.9922 | 1.16478 | ||||||||
\(107\) | 11.2315 | 1.08579 | 0.542894 | − | 0.839801i | \(-0.317329\pi\) | ||||
0.542894 | + | 0.839801i | \(0.317329\pi\) | |||||||
\(108\) | 3.92259 | 0.377452 | ||||||||
\(109\) | 15.1865 | 1.45461 | 0.727304 | − | 0.686316i | \(-0.240773\pi\) | ||||
0.727304 | + | 0.686316i | \(0.240773\pi\) | |||||||
\(110\) | 0.0684089 | 0.00652253 | ||||||||
\(111\) | −0.455309 | −0.0432160 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −10.2976 | −0.968717 | −0.484359 | − | 0.874870i | \(-0.660947\pi\) | ||||
−0.484359 | + | 0.874870i | \(0.660947\pi\) | |||||||
\(114\) | −4.77153 | −0.446895 | ||||||||
\(115\) | −0.346895 | −0.0323481 | ||||||||
\(116\) | −1.00000 | −0.0928477 | ||||||||
\(117\) | −10.3493 | −0.956796 | ||||||||
\(118\) | 4.30113 | 0.395951 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −0.166617 | −0.0152100 | ||||||||
\(121\) | −10.9139 | −0.992175 | ||||||||
\(122\) | 3.64803 | 0.330277 | ||||||||
\(123\) | −2.36958 | −0.213658 | ||||||||
\(124\) | −1.35175 | −0.121391 | ||||||||
\(125\) | −2.31901 | −0.207419 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −15.3053 | −1.35813 | −0.679065 | − | 0.734078i | \(-0.737615\pi\) | ||||
−0.679065 | + | 0.734078i | \(0.737615\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 2.35455 | 0.207307 | ||||||||
\(130\) | 0.969374 | 0.0850198 | ||||||||
\(131\) | 12.2176 | 1.06745 | 0.533726 | − | 0.845657i | \(-0.320791\pi\) | ||||
0.533726 | + | 0.845657i | \(0.320791\pi\) | |||||||
\(132\) | −0.209649 | −0.0182476 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 4.95649 | 0.428175 | ||||||||
\(135\) | 0.914626 | 0.0787184 | ||||||||
\(136\) | 0.609435 | 0.0522586 | ||||||||
\(137\) | 17.8291 | 1.52324 | 0.761622 | − | 0.648022i | \(-0.224404\pi\) | ||||
0.761622 | + | 0.648022i | \(0.224404\pi\) | |||||||
\(138\) | 1.06311 | 0.0904978 | ||||||||
\(139\) | 7.99852 | 0.678426 | 0.339213 | − | 0.940710i | \(-0.389839\pi\) | ||||
0.339213 | + | 0.940710i | \(0.389839\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1.55844 | −0.131244 | ||||||||
\(142\) | 4.21106 | 0.353384 | ||||||||
\(143\) | 1.21973 | 0.101999 | ||||||||
\(144\) | −2.48938 | −0.207448 | ||||||||
\(145\) | −0.233169 | −0.0193636 | ||||||||
\(146\) | 5.84298 | 0.483569 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0.637171 | 0.0523752 | ||||||||
\(149\) | 7.81597 | 0.640309 | 0.320155 | − | 0.947365i | \(-0.396265\pi\) | ||||
0.320155 | + | 0.947365i | \(0.396265\pi\) | |||||||
\(150\) | 3.53404 | 0.288553 | ||||||||
\(151\) | −16.2176 | −1.31977 | −0.659883 | − | 0.751368i | \(-0.729394\pi\) | ||||
−0.659883 | + | 0.751368i | \(0.729394\pi\) | |||||||
\(152\) | 6.67740 | 0.541609 | ||||||||
\(153\) | −1.51711 | −0.122651 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −0.315186 | −0.0253163 | ||||||||
\(156\) | −2.97079 | −0.237853 | ||||||||
\(157\) | −23.6455 | −1.88711 | −0.943556 | − | 0.331212i | \(-0.892543\pi\) | ||||
−0.943556 | + | 0.331212i | \(0.892543\pi\) | |||||||
\(158\) | 2.10678 | 0.167606 | ||||||||
\(159\) | −8.56937 | −0.679595 | ||||||||
\(160\) | 0.233169 | 0.0184336 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 4.66513 | 0.366527 | ||||||||
\(163\) | −13.6125 | −1.06621 | −0.533106 | − | 0.846048i | \(-0.678975\pi\) | ||||
−0.533106 | + | 0.846048i | \(0.678975\pi\) | |||||||
\(164\) | 3.31605 | 0.258940 | ||||||||
\(165\) | −0.0488836 | −0.00380558 | ||||||||
\(166\) | 6.73621 | 0.522831 | ||||||||
\(167\) | −3.59710 | −0.278352 | −0.139176 | − | 0.990268i | \(-0.544445\pi\) | ||||
−0.139176 | + | 0.990268i | \(0.544445\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 4.28394 | 0.329534 | ||||||||
\(170\) | 0.142101 | 0.0108987 | ||||||||
\(171\) | −16.6226 | −1.27116 | ||||||||
\(172\) | −3.29502 | −0.251243 | ||||||||
\(173\) | 12.3956 | 0.942423 | 0.471212 | − | 0.882020i | \(-0.343817\pi\) | ||||
0.471212 | + | 0.882020i | \(0.343817\pi\) | |||||||
\(174\) | 0.714579 | 0.0541721 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0.293388 | 0.0221150 | ||||||||
\(177\) | −3.07350 | −0.231018 | ||||||||
\(178\) | −12.6247 | −0.946259 | ||||||||
\(179\) | 9.58344 | 0.716300 | 0.358150 | − | 0.933664i | \(-0.383408\pi\) | ||||
0.358150 | + | 0.933664i | \(0.383408\pi\) | |||||||
\(180\) | −0.580445 | −0.0432638 | ||||||||
\(181\) | 0.148655 | 0.0110495 | 0.00552473 | − | 0.999985i | \(-0.498241\pi\) | ||||
0.00552473 | + | 0.999985i | \(0.498241\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −2.60680 | −0.192700 | ||||||||
\(184\) | −1.48774 | −0.109678 | ||||||||
\(185\) | 0.148568 | 0.0109230 | ||||||||
\(186\) | 0.965932 | 0.0708256 | ||||||||
\(187\) | 0.178801 | 0.0130752 | ||||||||
\(188\) | 2.18092 | 0.159060 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 1.55696 | 0.112954 | ||||||||
\(191\) | 10.2831 | 0.744058 | 0.372029 | − | 0.928221i | \(-0.378662\pi\) | ||||
0.372029 | + | 0.928221i | \(0.378662\pi\) | |||||||
\(192\) | −0.714579 | −0.0515703 | ||||||||
\(193\) | 12.4681 | 0.897476 | 0.448738 | − | 0.893663i | \(-0.351874\pi\) | ||||
0.448738 | + | 0.893663i | \(0.351874\pi\) | |||||||
\(194\) | 5.70498 | 0.409593 | ||||||||
\(195\) | −0.692694 | −0.0496049 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −19.0312 | −1.35591 | −0.677957 | − | 0.735101i | \(-0.737135\pi\) | ||||
−0.677957 | + | 0.735101i | \(0.737135\pi\) | |||||||
\(198\) | −0.730354 | −0.0519040 | ||||||||
\(199\) | −10.6083 | −0.752005 | −0.376003 | − | 0.926619i | \(-0.622702\pi\) | ||||
−0.376003 | + | 0.926619i | \(0.622702\pi\) | |||||||
\(200\) | −4.94563 | −0.349709 | ||||||||
\(201\) | −3.54180 | −0.249819 | ||||||||
\(202\) | 15.7339 | 1.10703 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −0.435489 | −0.0304903 | ||||||||
\(205\) | 0.773198 | 0.0540025 | ||||||||
\(206\) | −4.89549 | −0.341085 | ||||||||
\(207\) | 3.70355 | 0.257415 | ||||||||
\(208\) | 4.15740 | 0.288264 | ||||||||
\(209\) | 1.95907 | 0.135512 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −8.69020 | −0.598258 | −0.299129 | − | 0.954213i | \(-0.596696\pi\) | ||||
−0.299129 | + | 0.954213i | \(0.596696\pi\) | |||||||
\(212\) | 11.9922 | 0.823627 | ||||||||
\(213\) | −3.00914 | −0.206183 | ||||||||
\(214\) | 11.2315 | 0.767767 | ||||||||
\(215\) | −0.768296 | −0.0523974 | ||||||||
\(216\) | 3.92259 | 0.266899 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 15.1865 | 1.02856 | ||||||||
\(219\) | −4.17527 | −0.282139 | ||||||||
\(220\) | 0.0684089 | 0.00461213 | ||||||||
\(221\) | 2.53366 | 0.170433 | ||||||||
\(222\) | −0.455309 | −0.0305583 | ||||||||
\(223\) | 9.99383 | 0.669236 | 0.334618 | − | 0.942354i | \(-0.391393\pi\) | ||||
0.334618 | + | 0.942354i | \(0.391393\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 12.3115 | 0.820770 | ||||||||
\(226\) | −10.2976 | −0.684986 | ||||||||
\(227\) | −25.3090 | −1.67982 | −0.839910 | − | 0.542726i | \(-0.817392\pi\) | ||||
−0.839910 | + | 0.542726i | \(0.817392\pi\) | |||||||
\(228\) | −4.77153 | −0.316002 | ||||||||
\(229\) | 18.4785 | 1.22109 | 0.610545 | − | 0.791981i | \(-0.290950\pi\) | ||||
0.610545 | + | 0.791981i | \(0.290950\pi\) | |||||||
\(230\) | −0.346895 | −0.0228736 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −1.00000 | −0.0656532 | ||||||||
\(233\) | −9.35908 | −0.613134 | −0.306567 | − | 0.951849i | \(-0.599180\pi\) | ||||
−0.306567 | + | 0.951849i | \(0.599180\pi\) | |||||||
\(234\) | −10.3493 | −0.676557 | ||||||||
\(235\) | 0.508521 | 0.0331723 | ||||||||
\(236\) | 4.30113 | 0.279980 | ||||||||
\(237\) | −1.50546 | −0.0977901 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −17.5424 | −1.13473 | −0.567363 | − | 0.823468i | \(-0.692036\pi\) | ||||
−0.567363 | + | 0.823468i | \(0.692036\pi\) | |||||||
\(240\) | −0.166617 | −0.0107551 | ||||||||
\(241\) | 3.04226 | 0.195969 | 0.0979845 | − | 0.995188i | \(-0.468760\pi\) | ||||
0.0979845 | + | 0.995188i | \(0.468760\pi\) | |||||||
\(242\) | −10.9139 | −0.701574 | ||||||||
\(243\) | −15.1014 | −0.968754 | ||||||||
\(244\) | 3.64803 | 0.233541 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −2.36958 | −0.151079 | ||||||||
\(247\) | 27.7606 | 1.76636 | ||||||||
\(248\) | −1.35175 | −0.0858362 | ||||||||
\(249\) | −4.81355 | −0.305046 | ||||||||
\(250\) | −2.31901 | −0.146667 | ||||||||
\(251\) | −17.2275 | −1.08739 | −0.543694 | − | 0.839283i | \(-0.682975\pi\) | ||||
−0.543694 | + | 0.839283i | \(0.682975\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −0.436486 | −0.0274416 | ||||||||
\(254\) | −15.3053 | −0.960343 | ||||||||
\(255\) | −0.101542 | −0.00635883 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 20.6454 | 1.28783 | 0.643913 | − | 0.765098i | \(-0.277310\pi\) | ||||
0.643913 | + | 0.765098i | \(0.277310\pi\) | |||||||
\(258\) | 2.35455 | 0.146588 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0.969374 | 0.0601180 | ||||||||
\(261\) | 2.48938 | 0.154089 | ||||||||
\(262\) | 12.2176 | 0.754803 | ||||||||
\(263\) | −16.5706 | −1.02179 | −0.510894 | − | 0.859644i | \(-0.670686\pi\) | ||||
−0.510894 | + | 0.859644i | \(0.670686\pi\) | |||||||
\(264\) | −0.209649 | −0.0129030 | ||||||||
\(265\) | 2.79620 | 0.171769 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 9.02132 | 0.552096 | ||||||||
\(268\) | 4.95649 | 0.302766 | ||||||||
\(269\) | −2.62826 | −0.160248 | −0.0801239 | − | 0.996785i | \(-0.525532\pi\) | ||||
−0.0801239 | + | 0.996785i | \(0.525532\pi\) | |||||||
\(270\) | 0.914626 | 0.0556623 | ||||||||
\(271\) | −12.6224 | −0.766756 | −0.383378 | − | 0.923592i | \(-0.625239\pi\) | ||||
−0.383378 | + | 0.923592i | \(0.625239\pi\) | |||||||
\(272\) | 0.609435 | 0.0369524 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 17.8291 | 1.07710 | ||||||||
\(275\) | −1.45099 | −0.0874980 | ||||||||
\(276\) | 1.06311 | 0.0639916 | ||||||||
\(277\) | 19.4595 | 1.16921 | 0.584605 | − | 0.811318i | \(-0.301249\pi\) | ||||
0.584605 | + | 0.811318i | \(0.301249\pi\) | |||||||
\(278\) | 7.99852 | 0.479720 | ||||||||
\(279\) | 3.36502 | 0.201458 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 15.9906 | 0.953917 | 0.476958 | − | 0.878926i | \(-0.341739\pi\) | ||||
0.476958 | + | 0.878926i | \(0.341739\pi\) | |||||||
\(282\) | −1.55844 | −0.0928035 | ||||||||
\(283\) | 27.9827 | 1.66340 | 0.831699 | − | 0.555227i | \(-0.187369\pi\) | ||||
0.831699 | + | 0.555227i | \(0.187369\pi\) | |||||||
\(284\) | 4.21106 | 0.249881 | ||||||||
\(285\) | −1.11257 | −0.0659030 | ||||||||
\(286\) | 1.21973 | 0.0721242 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −2.48938 | −0.146688 | ||||||||
\(289\) | −16.6286 | −0.978152 | ||||||||
\(290\) | −0.233169 | −0.0136921 | ||||||||
\(291\) | −4.07666 | −0.238978 | ||||||||
\(292\) | 5.84298 | 0.341935 | ||||||||
\(293\) | 20.6845 | 1.20840 | 0.604202 | − | 0.796832i | \(-0.293492\pi\) | ||||
0.604202 | + | 0.796832i | \(0.293492\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1.00289 | 0.0583905 | ||||||||
\(296\) | 0.637171 | 0.0370348 | ||||||||
\(297\) | 1.15084 | 0.0667786 | ||||||||
\(298\) | 7.81597 | 0.452767 | ||||||||
\(299\) | −6.18513 | −0.357695 | ||||||||
\(300\) | 3.53404 | 0.204038 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −16.2176 | −0.933215 | ||||||||
\(303\) | −11.2431 | −0.645899 | ||||||||
\(304\) | 6.67740 | 0.382975 | ||||||||
\(305\) | 0.850606 | 0.0487055 | ||||||||
\(306\) | −1.51711 | −0.0867276 | ||||||||
\(307\) | −28.6540 | −1.63537 | −0.817686 | − | 0.575664i | \(-0.804744\pi\) | ||||
−0.817686 | + | 0.575664i | \(0.804744\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 3.49822 | 0.199007 | ||||||||
\(310\) | −0.315186 | −0.0179013 | ||||||||
\(311\) | 10.4647 | 0.593399 | 0.296699 | − | 0.954971i | \(-0.404114\pi\) | ||||
0.296699 | + | 0.954971i | \(0.404114\pi\) | |||||||
\(312\) | −2.97079 | −0.168188 | ||||||||
\(313\) | −31.4172 | −1.77580 | −0.887901 | − | 0.460034i | \(-0.847837\pi\) | ||||
−0.887901 | + | 0.460034i | \(0.847837\pi\) | |||||||
\(314\) | −23.6455 | −1.33439 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 2.10678 | 0.118516 | ||||||||
\(317\) | 12.7478 | 0.715986 | 0.357993 | − | 0.933724i | \(-0.383461\pi\) | ||||
0.357993 | + | 0.933724i | \(0.383461\pi\) | |||||||
\(318\) | −8.56937 | −0.480546 | ||||||||
\(319\) | −0.293388 | −0.0164266 | ||||||||
\(320\) | 0.233169 | 0.0130345 | ||||||||
\(321\) | −8.02577 | −0.447955 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 4.06944 | 0.226430 | ||||||||
\(324\) | 4.66513 | 0.259174 | ||||||||
\(325\) | −20.5610 | −1.14052 | ||||||||
\(326\) | −13.6125 | −0.753926 | ||||||||
\(327\) | −10.8520 | −0.600116 | ||||||||
\(328\) | 3.31605 | 0.183098 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −0.0488836 | −0.00269095 | ||||||||
\(331\) | −10.2619 | −0.564046 | −0.282023 | − | 0.959408i | \(-0.591006\pi\) | ||||
−0.282023 | + | 0.959408i | \(0.591006\pi\) | |||||||
\(332\) | 6.73621 | 0.369697 | ||||||||
\(333\) | −1.58616 | −0.0869210 | ||||||||
\(334\) | −3.59710 | −0.196825 | ||||||||
\(335\) | 1.15570 | 0.0631425 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −26.9868 | −1.47007 | −0.735033 | − | 0.678031i | \(-0.762833\pi\) | ||||
−0.735033 | + | 0.678031i | \(0.762833\pi\) | |||||||
\(338\) | 4.28394 | 0.233016 | ||||||||
\(339\) | 7.35845 | 0.399656 | ||||||||
\(340\) | 0.142101 | 0.00770652 | ||||||||
\(341\) | −0.396588 | −0.0214764 | ||||||||
\(342\) | −16.6226 | −0.898845 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −3.29502 | −0.177656 | ||||||||
\(345\) | 0.247884 | 0.0133456 | ||||||||
\(346\) | 12.3956 | 0.666394 | ||||||||
\(347\) | 0.0299869 | 0.00160978 | 0.000804890 | − | 1.00000i | \(-0.499744\pi\) | ||||
0.000804890 | 1.00000i | \(0.499744\pi\) | ||||||||
\(348\) | 0.714579 | 0.0383054 | ||||||||
\(349\) | 6.30027 | 0.337246 | 0.168623 | − | 0.985681i | \(-0.446068\pi\) | ||||
0.168623 | + | 0.985681i | \(0.446068\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 16.3078 | 0.870444 | ||||||||
\(352\) | 0.293388 | 0.0156376 | ||||||||
\(353\) | 27.6344 | 1.47083 | 0.735415 | − | 0.677617i | \(-0.236987\pi\) | ||||
0.735415 | + | 0.677617i | \(0.236987\pi\) | |||||||
\(354\) | −3.07350 | −0.163355 | ||||||||
\(355\) | 0.981888 | 0.0521132 | ||||||||
\(356\) | −12.6247 | −0.669106 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 9.58344 | 0.506501 | ||||||||
\(359\) | −18.4797 | −0.975322 | −0.487661 | − | 0.873033i | \(-0.662150\pi\) | ||||
−0.487661 | + | 0.873033i | \(0.662150\pi\) | |||||||
\(360\) | −0.580445 | −0.0305921 | ||||||||
\(361\) | 25.5877 | 1.34672 | ||||||||
\(362\) | 0.148655 | 0.00781314 | ||||||||
\(363\) | 7.79886 | 0.409334 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1.36240 | 0.0713113 | ||||||||
\(366\) | −2.60680 | −0.136260 | ||||||||
\(367\) | −17.7335 | −0.925683 | −0.462841 | − | 0.886441i | \(-0.653170\pi\) | ||||
−0.462841 | + | 0.886441i | \(0.653170\pi\) | |||||||
\(368\) | −1.48774 | −0.0775539 | ||||||||
\(369\) | −8.25489 | −0.429732 | ||||||||
\(370\) | 0.148568 | 0.00772370 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0.965932 | 0.0500812 | ||||||||
\(373\) | 14.2392 | 0.737279 | 0.368639 | − | 0.929573i | \(-0.379824\pi\) | ||||
0.368639 | + | 0.929573i | \(0.379824\pi\) | |||||||
\(374\) | 0.178801 | 0.00924558 | ||||||||
\(375\) | 1.65712 | 0.0855731 | ||||||||
\(376\) | 2.18092 | 0.112472 | ||||||||
\(377\) | −4.15740 | −0.214117 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 33.9879 | 1.74584 | 0.872920 | − | 0.487863i | \(-0.162224\pi\) | ||||
0.872920 | + | 0.487863i | \(0.162224\pi\) | |||||||
\(380\) | 1.55696 | 0.0798704 | ||||||||
\(381\) | 10.9369 | 0.560313 | ||||||||
\(382\) | 10.2831 | 0.526128 | ||||||||
\(383\) | −17.0812 | −0.872807 | −0.436404 | − | 0.899751i | \(-0.643748\pi\) | ||||
−0.436404 | + | 0.899751i | \(0.643748\pi\) | |||||||
\(384\) | −0.714579 | −0.0364657 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 12.4681 | 0.634611 | ||||||||
\(387\) | 8.20256 | 0.416959 | ||||||||
\(388\) | 5.70498 | 0.289626 | ||||||||
\(389\) | −11.3176 | −0.573827 | −0.286913 | − | 0.957957i | \(-0.592629\pi\) | ||||
−0.286913 | + | 0.957957i | \(0.592629\pi\) | |||||||
\(390\) | −0.692694 | −0.0350759 | ||||||||
\(391\) | −0.906682 | −0.0458529 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −8.73040 | −0.440391 | ||||||||
\(394\) | −19.0312 | −0.958776 | ||||||||
\(395\) | 0.491235 | 0.0247167 | ||||||||
\(396\) | −0.730354 | −0.0367017 | ||||||||
\(397\) | 10.2515 | 0.514506 | 0.257253 | − | 0.966344i | \(-0.417183\pi\) | ||||
0.257253 | + | 0.966344i | \(0.417183\pi\) | |||||||
\(398\) | −10.6083 | −0.531748 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −4.94563 | −0.247282 | ||||||||
\(401\) | −17.6102 | −0.879410 | −0.439705 | − | 0.898142i | \(-0.644917\pi\) | ||||
−0.439705 | + | 0.898142i | \(0.644917\pi\) | |||||||
\(402\) | −3.54180 | −0.176649 | ||||||||
\(403\) | −5.61976 | −0.279940 | ||||||||
\(404\) | 15.7339 | 0.782789 | ||||||||
\(405\) | 1.08776 | 0.0540513 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0.186939 | 0.00926620 | ||||||||
\(408\) | −0.435489 | −0.0215599 | ||||||||
\(409\) | −38.8959 | −1.92328 | −0.961639 | − | 0.274317i | \(-0.911548\pi\) | ||||
−0.961639 | + | 0.274317i | \(0.911548\pi\) | |||||||
\(410\) | 0.773198 | 0.0381855 | ||||||||
\(411\) | −12.7403 | −0.628433 | ||||||||
\(412\) | −4.89549 | −0.241184 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 3.70355 | 0.182020 | ||||||||
\(415\) | 1.57067 | 0.0771013 | ||||||||
\(416\) | 4.15740 | 0.203833 | ||||||||
\(417\) | −5.71558 | −0.279893 | ||||||||
\(418\) | 1.95907 | 0.0958212 | ||||||||
\(419\) | −12.6437 | −0.617683 | −0.308842 | − | 0.951113i | \(-0.599941\pi\) | ||||
−0.308842 | + | 0.951113i | \(0.599941\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −10.7981 | −0.526267 | −0.263133 | − | 0.964759i | \(-0.584756\pi\) | ||||
−0.263133 | + | 0.964759i | \(0.584756\pi\) | |||||||
\(422\) | −8.69020 | −0.423032 | ||||||||
\(423\) | −5.42912 | −0.263973 | ||||||||
\(424\) | 11.9922 | 0.582392 | ||||||||
\(425\) | −3.01404 | −0.146202 | ||||||||
\(426\) | −3.00914 | −0.145793 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 11.2315 | 0.542894 | ||||||||
\(429\) | −0.871594 | −0.0420810 | ||||||||
\(430\) | −0.768296 | −0.0370505 | ||||||||
\(431\) | −36.1812 | −1.74279 | −0.871394 | − | 0.490583i | \(-0.836784\pi\) | ||||
−0.871394 | + | 0.490583i | \(0.836784\pi\) | |||||||
\(432\) | 3.92259 | 0.188726 | ||||||||
\(433\) | 10.6350 | 0.511084 | 0.255542 | − | 0.966798i | \(-0.417746\pi\) | ||||
0.255542 | + | 0.966798i | \(0.417746\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0.166617 | 0.00798869 | ||||||||
\(436\) | 15.1865 | 0.727304 | ||||||||
\(437\) | −9.93425 | −0.475219 | ||||||||
\(438\) | −4.17527 | −0.199502 | ||||||||
\(439\) | −2.97507 | −0.141992 | −0.0709961 | − | 0.997477i | \(-0.522618\pi\) | ||||
−0.0709961 | + | 0.997477i | \(0.522618\pi\) | |||||||
\(440\) | 0.0684089 | 0.00326127 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 2.53366 | 0.120514 | ||||||||
\(443\) | −27.9429 | −1.32761 | −0.663804 | − | 0.747907i | \(-0.731059\pi\) | ||||
−0.663804 | + | 0.747907i | \(0.731059\pi\) | |||||||
\(444\) | −0.455309 | −0.0216080 | ||||||||
\(445\) | −2.94368 | −0.139544 | ||||||||
\(446\) | 9.99383 | 0.473221 | ||||||||
\(447\) | −5.58513 | −0.264167 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −0.604431 | −0.0285248 | −0.0142624 | − | 0.999898i | \(-0.504540\pi\) | ||||
−0.0142624 | + | 0.999898i | \(0.504540\pi\) | |||||||
\(450\) | 12.3115 | 0.580372 | ||||||||
\(451\) | 0.972889 | 0.0458116 | ||||||||
\(452\) | −10.2976 | −0.484359 | ||||||||
\(453\) | 11.5887 | 0.544486 | ||||||||
\(454\) | −25.3090 | −1.18781 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −4.77153 | −0.223447 | ||||||||
\(457\) | −7.10311 | −0.332270 | −0.166135 | − | 0.986103i | \(-0.553129\pi\) | ||||
−0.166135 | + | 0.986103i | \(0.553129\pi\) | |||||||
\(458\) | 18.4785 | 0.863442 | ||||||||
\(459\) | 2.39057 | 0.111582 | ||||||||
\(460\) | −0.346895 | −0.0161741 | ||||||||
\(461\) | 3.81028 | 0.177462 | 0.0887312 | − | 0.996056i | \(-0.471719\pi\) | ||||
0.0887312 | + | 0.996056i | \(0.471719\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −3.42327 | −0.159093 | −0.0795464 | − | 0.996831i | \(-0.525347\pi\) | ||||
−0.0795464 | + | 0.996831i | \(0.525347\pi\) | |||||||
\(464\) | −1.00000 | −0.0464238 | ||||||||
\(465\) | 0.225225 | 0.0104446 | ||||||||
\(466\) | −9.35908 | −0.433551 | ||||||||
\(467\) | 22.8701 | 1.05830 | 0.529151 | − | 0.848528i | \(-0.322510\pi\) | ||||
0.529151 | + | 0.848528i | \(0.322510\pi\) | |||||||
\(468\) | −10.3493 | −0.478398 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0.508521 | 0.0234563 | ||||||||
\(471\) | 16.8965 | 0.778552 | ||||||||
\(472\) | 4.30113 | 0.197976 | ||||||||
\(473\) | −0.966721 | −0.0444499 | ||||||||
\(474\) | −1.50546 | −0.0691481 | ||||||||
\(475\) | −33.0240 | −1.51524 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −29.8531 | −1.36688 | ||||||||
\(478\) | −17.5424 | −0.802372 | ||||||||
\(479\) | −4.57219 | −0.208909 | −0.104454 | − | 0.994530i | \(-0.533310\pi\) | ||||
−0.104454 | + | 0.994530i | \(0.533310\pi\) | |||||||
\(480\) | −0.166617 | −0.00760501 | ||||||||
\(481\) | 2.64897 | 0.120783 | ||||||||
\(482\) | 3.04226 | 0.138571 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −10.9139 | −0.496087 | ||||||||
\(485\) | 1.33022 | 0.0604022 | ||||||||
\(486\) | −15.1014 | −0.685013 | ||||||||
\(487\) | 21.6569 | 0.981367 | 0.490683 | − | 0.871338i | \(-0.336747\pi\) | ||||
0.490683 | + | 0.871338i | \(0.336747\pi\) | |||||||
\(488\) | 3.64803 | 0.165138 | ||||||||
\(489\) | 9.72719 | 0.439879 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 32.0537 | 1.44656 | 0.723281 | − | 0.690554i | \(-0.242633\pi\) | ||||
0.723281 | + | 0.690554i | \(0.242633\pi\) | |||||||
\(492\) | −2.36958 | −0.106829 | ||||||||
\(493\) | −0.609435 | −0.0274476 | ||||||||
\(494\) | 27.7606 | 1.24901 | ||||||||
\(495\) | −0.170296 | −0.00765422 | ||||||||
\(496\) | −1.35175 | −0.0606954 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −4.81355 | −0.215700 | ||||||||
\(499\) | 24.6113 | 1.10175 | 0.550877 | − | 0.834587i | \(-0.314293\pi\) | ||||
0.550877 | + | 0.834587i | \(0.314293\pi\) | |||||||
\(500\) | −2.31901 | −0.103709 | ||||||||
\(501\) | 2.57041 | 0.114838 | ||||||||
\(502\) | −17.2275 | −0.768900 | ||||||||
\(503\) | −35.0600 | −1.56325 | −0.781623 | − | 0.623751i | \(-0.785608\pi\) | ||||
−0.781623 | + | 0.623751i | \(0.785608\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 3.66864 | 0.163253 | ||||||||
\(506\) | −0.436486 | −0.0194042 | ||||||||
\(507\) | −3.06122 | −0.135953 | ||||||||
\(508\) | −15.3053 | −0.679065 | ||||||||
\(509\) | −31.7592 | −1.40770 | −0.703851 | − | 0.710348i | \(-0.748538\pi\) | ||||
−0.703851 | + | 0.710348i | \(0.748538\pi\) | |||||||
\(510\) | −0.101542 | −0.00449638 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 26.1927 | 1.15644 | ||||||||
\(514\) | 20.6454 | 0.910631 | ||||||||
\(515\) | −1.14148 | −0.0502994 | ||||||||
\(516\) | 2.35455 | 0.103653 | ||||||||
\(517\) | 0.639855 | 0.0281408 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −8.85766 | −0.388808 | ||||||||
\(520\) | 0.969374 | 0.0425099 | ||||||||
\(521\) | −14.1681 | −0.620716 | −0.310358 | − | 0.950620i | \(-0.600449\pi\) | ||||
−0.310358 | + | 0.950620i | \(0.600449\pi\) | |||||||
\(522\) | 2.48938 | 0.108957 | ||||||||
\(523\) | −19.7029 | −0.861547 | −0.430774 | − | 0.902460i | \(-0.641759\pi\) | ||||
−0.430774 | + | 0.902460i | \(0.641759\pi\) | |||||||
\(524\) | 12.2176 | 0.533726 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −16.5706 | −0.722513 | ||||||||
\(527\) | −0.823804 | −0.0358855 | ||||||||
\(528\) | −0.209649 | −0.00912380 | ||||||||
\(529\) | −20.7866 | −0.903766 | ||||||||
\(530\) | 2.79620 | 0.121459 | ||||||||
\(531\) | −10.7071 | −0.464650 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 13.7861 | 0.597143 | ||||||||
\(534\) | 9.02132 | 0.390391 | ||||||||
\(535\) | 2.61883 | 0.113222 | ||||||||
\(536\) | 4.95649 | 0.214088 | ||||||||
\(537\) | −6.84812 | −0.295518 | ||||||||
\(538\) | −2.62826 | −0.113312 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0.914626 | 0.0393592 | ||||||||
\(541\) | −13.2854 | −0.571184 | −0.285592 | − | 0.958351i | \(-0.592190\pi\) | ||||
−0.285592 | + | 0.958351i | \(0.592190\pi\) | |||||||
\(542\) | −12.6224 | −0.542178 | ||||||||
\(543\) | −0.106226 | −0.00455859 | ||||||||
\(544\) | 0.609435 | 0.0261293 | ||||||||
\(545\) | 3.54103 | 0.151681 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −3.77149 | −0.161257 | −0.0806287 | − | 0.996744i | \(-0.525693\pi\) | ||||
−0.0806287 | + | 0.996744i | \(0.525693\pi\) | |||||||
\(548\) | 17.8291 | 0.761622 | ||||||||
\(549\) | −9.08132 | −0.387581 | ||||||||
\(550\) | −1.45099 | −0.0618704 | ||||||||
\(551\) | −6.67740 | −0.284467 | ||||||||
\(552\) | 1.06311 | 0.0452489 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 19.4595 | 0.826757 | ||||||||
\(555\) | −0.106164 | −0.00450640 | ||||||||
\(556\) | 7.99852 | 0.339213 | ||||||||
\(557\) | −41.3443 | −1.75181 | −0.875907 | − | 0.482480i | \(-0.839736\pi\) | ||||
−0.875907 | + | 0.482480i | \(0.839736\pi\) | |||||||
\(558\) | 3.36502 | 0.142452 | ||||||||
\(559\) | −13.6987 | −0.579394 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −0.127767 | −0.00539434 | ||||||||
\(562\) | 15.9906 | 0.674521 | ||||||||
\(563\) | −6.62591 | −0.279249 | −0.139624 | − | 0.990205i | \(-0.544590\pi\) | ||||
−0.139624 | + | 0.990205i | \(0.544590\pi\) | |||||||
\(564\) | −1.55844 | −0.0656220 | ||||||||
\(565\) | −2.40108 | −0.101014 | ||||||||
\(566\) | 27.9827 | 1.17620 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 4.21106 | 0.176692 | ||||||||
\(569\) | −13.9549 | −0.585022 | −0.292511 | − | 0.956262i | \(-0.594491\pi\) | ||||
−0.292511 | + | 0.956262i | \(0.594491\pi\) | |||||||
\(570\) | −1.11257 | −0.0466005 | ||||||||
\(571\) | −2.11161 | −0.0883682 | −0.0441841 | − | 0.999023i | \(-0.514069\pi\) | ||||
−0.0441841 | + | 0.999023i | \(0.514069\pi\) | |||||||
\(572\) | 1.21973 | 0.0509995 | ||||||||
\(573\) | −7.34807 | −0.306970 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 7.35782 | 0.306842 | ||||||||
\(576\) | −2.48938 | −0.103724 | ||||||||
\(577\) | 2.79762 | 0.116466 | 0.0582331 | − | 0.998303i | \(-0.481453\pi\) | ||||
0.0582331 | + | 0.998303i | \(0.481453\pi\) | |||||||
\(578\) | −16.6286 | −0.691658 | ||||||||
\(579\) | −8.90946 | −0.370265 | ||||||||
\(580\) | −0.233169 | −0.00968180 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −4.07666 | −0.168983 | ||||||||
\(583\) | 3.51837 | 0.145716 | ||||||||
\(584\) | 5.84298 | 0.241784 | ||||||||
\(585\) | −2.41314 | −0.0997710 | ||||||||
\(586\) | 20.6845 | 0.854470 | ||||||||
\(587\) | 6.93586 | 0.286274 | 0.143137 | − | 0.989703i | \(-0.454281\pi\) | ||||
0.143137 | + | 0.989703i | \(0.454281\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −9.02617 | −0.371917 | ||||||||
\(590\) | 1.00289 | 0.0412883 | ||||||||
\(591\) | 13.5993 | 0.559399 | ||||||||
\(592\) | 0.637171 | 0.0261876 | ||||||||
\(593\) | 3.39084 | 0.139245 | 0.0696225 | − | 0.997573i | \(-0.477821\pi\) | ||||
0.0696225 | + | 0.997573i | \(0.477821\pi\) | |||||||
\(594\) | 1.15084 | 0.0472196 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 7.81597 | 0.320155 | ||||||||
\(597\) | 7.58049 | 0.310249 | ||||||||
\(598\) | −6.18513 | −0.252929 | ||||||||
\(599\) | −30.7247 | −1.25538 | −0.627689 | − | 0.778464i | \(-0.715999\pi\) | ||||
−0.627689 | + | 0.778464i | \(0.715999\pi\) | |||||||
\(600\) | 3.53404 | 0.144277 | ||||||||
\(601\) | 32.5720 | 1.32864 | 0.664320 | − | 0.747448i | \(-0.268721\pi\) | ||||
0.664320 | + | 0.747448i | \(0.268721\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −12.3386 | −0.502465 | ||||||||
\(604\) | −16.2176 | −0.659883 | ||||||||
\(605\) | −2.54478 | −0.103460 | ||||||||
\(606\) | −11.2431 | −0.456719 | ||||||||
\(607\) | −1.92006 | −0.0779329 | −0.0389664 | − | 0.999241i | \(-0.512407\pi\) | ||||
−0.0389664 | + | 0.999241i | \(0.512407\pi\) | |||||||
\(608\) | 6.67740 | 0.270804 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0.850606 | 0.0344400 | ||||||||
\(611\) | 9.06693 | 0.366809 | ||||||||
\(612\) | −1.51711 | −0.0613257 | ||||||||
\(613\) | −28.8055 | −1.16344 | −0.581722 | − | 0.813388i | \(-0.697621\pi\) | ||||
−0.581722 | + | 0.813388i | \(0.697621\pi\) | |||||||
\(614\) | −28.6540 | −1.15638 | ||||||||
\(615\) | −0.552511 | −0.0222794 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 41.9416 | 1.68850 | 0.844252 | − | 0.535946i | \(-0.180045\pi\) | ||||
0.844252 | + | 0.535946i | \(0.180045\pi\) | |||||||
\(618\) | 3.49822 | 0.140719 | ||||||||
\(619\) | −0.752705 | −0.0302538 | −0.0151269 | − | 0.999886i | \(-0.504815\pi\) | ||||
−0.0151269 | + | 0.999886i | \(0.504815\pi\) | |||||||
\(620\) | −0.315186 | −0.0126582 | ||||||||
\(621\) | −5.83581 | −0.234183 | ||||||||
\(622\) | 10.4647 | 0.419596 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −2.97079 | −0.118927 | ||||||||
\(625\) | 24.1874 | 0.967498 | ||||||||
\(626\) | −31.4172 | −1.25568 | ||||||||
\(627\) | −1.39991 | −0.0559070 | ||||||||
\(628\) | −23.6455 | −0.943556 | ||||||||
\(629\) | 0.388314 | 0.0154831 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −36.3961 | −1.44891 | −0.724453 | − | 0.689325i | \(-0.757907\pi\) | ||||
−0.724453 | + | 0.689325i | \(0.757907\pi\) | |||||||
\(632\) | 2.10678 | 0.0838032 | ||||||||
\(633\) | 6.20983 | 0.246819 | ||||||||
\(634\) | 12.7478 | 0.506279 | ||||||||
\(635\) | −3.56873 | −0.141621 | ||||||||
\(636\) | −8.56937 | −0.339797 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −0.293388 | −0.0116153 | ||||||||
\(639\) | −10.4829 | −0.414698 | ||||||||
\(640\) | 0.233169 | 0.00921680 | ||||||||
\(641\) | −20.4574 | −0.808021 | −0.404010 | − | 0.914754i | \(-0.632384\pi\) | ||||
−0.404010 | + | 0.914754i | \(0.632384\pi\) | |||||||
\(642\) | −8.02577 | −0.316752 | ||||||||
\(643\) | −36.0350 | −1.42108 | −0.710541 | − | 0.703656i | \(-0.751550\pi\) | ||||
−0.710541 | + | 0.703656i | \(0.751550\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0.549008 | 0.0216172 | ||||||||
\(646\) | 4.06944 | 0.160110 | ||||||||
\(647\) | 42.7775 | 1.68176 | 0.840879 | − | 0.541223i | \(-0.182039\pi\) | ||||
0.840879 | + | 0.541223i | \(0.182039\pi\) | |||||||
\(648\) | 4.66513 | 0.183264 | ||||||||
\(649\) | 1.26190 | 0.0495340 | ||||||||
\(650\) | −20.5610 | −0.806467 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −13.6125 | −0.533106 | ||||||||
\(653\) | 28.0322 | 1.09699 | 0.548493 | − | 0.836155i | \(-0.315202\pi\) | ||||
0.548493 | + | 0.836155i | \(0.315202\pi\) | |||||||
\(654\) | −10.8520 | −0.424346 | ||||||||
\(655\) | 2.84875 | 0.111310 | ||||||||
\(656\) | 3.31605 | 0.129470 | ||||||||
\(657\) | −14.5454 | −0.567470 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 36.2772 | 1.41316 | 0.706579 | − | 0.707634i | \(-0.250238\pi\) | ||||
0.706579 | + | 0.707634i | \(0.250238\pi\) | |||||||
\(660\) | −0.0488836 | −0.00190279 | ||||||||
\(661\) | −6.03049 | −0.234559 | −0.117279 | − | 0.993099i | \(-0.537417\pi\) | ||||
−0.117279 | + | 0.993099i | \(0.537417\pi\) | |||||||
\(662\) | −10.2619 | −0.398841 | ||||||||
\(663\) | −1.81050 | −0.0703141 | ||||||||
\(664\) | 6.73621 | 0.261415 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −1.58616 | −0.0614624 | ||||||||
\(667\) | 1.48774 | 0.0576056 | ||||||||
\(668\) | −3.59710 | −0.139176 | ||||||||
\(669\) | −7.14138 | −0.276102 | ||||||||
\(670\) | 1.15570 | 0.0446485 | ||||||||
\(671\) | 1.07029 | 0.0413180 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 16.7412 | 0.645327 | 0.322663 | − | 0.946514i | \(-0.395422\pi\) | ||||
0.322663 | + | 0.946514i | \(0.395422\pi\) | |||||||
\(674\) | −26.9868 | −1.03949 | ||||||||
\(675\) | −19.3997 | −0.746695 | ||||||||
\(676\) | 4.28394 | 0.164767 | ||||||||
\(677\) | 40.9926 | 1.57547 | 0.787737 | − | 0.616011i | \(-0.211252\pi\) | ||||
0.787737 | + | 0.616011i | \(0.211252\pi\) | |||||||
\(678\) | 7.35845 | 0.282600 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0.142101 | 0.00544933 | ||||||||
\(681\) | 18.0853 | 0.693030 | ||||||||
\(682\) | −0.396588 | −0.0151861 | ||||||||
\(683\) | −34.1468 | −1.30659 | −0.653296 | − | 0.757102i | \(-0.726614\pi\) | ||||
−0.653296 | + | 0.757102i | \(0.726614\pi\) | |||||||
\(684\) | −16.6226 | −0.635580 | ||||||||
\(685\) | 4.15719 | 0.158838 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −13.2043 | −0.503776 | ||||||||
\(688\) | −3.29502 | −0.125622 | ||||||||
\(689\) | 49.8563 | 1.89937 | ||||||||
\(690\) | 0.247884 | 0.00943677 | ||||||||
\(691\) | −22.6343 | −0.861051 | −0.430525 | − | 0.902579i | \(-0.641672\pi\) | ||||
−0.430525 | + | 0.902579i | \(0.641672\pi\) | |||||||
\(692\) | 12.3956 | 0.471212 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0.0299869 | 0.00113829 | ||||||||
\(695\) | 1.86500 | 0.0707437 | ||||||||
\(696\) | 0.714579 | 0.0270860 | ||||||||
\(697\) | 2.02091 | 0.0765476 | ||||||||
\(698\) | 6.30027 | 0.238469 | ||||||||
\(699\) | 6.68780 | 0.252956 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −15.1951 | −0.573911 | −0.286955 | − | 0.957944i | \(-0.592643\pi\) | ||||
−0.286955 | + | 0.957944i | \(0.592643\pi\) | |||||||
\(702\) | 16.3078 | 0.615497 | ||||||||
\(703\) | 4.25465 | 0.160467 | ||||||||
\(704\) | 0.293388 | 0.0110575 | ||||||||
\(705\) | −0.363378 | −0.0136856 | ||||||||
\(706\) | 27.6344 | 1.04003 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −3.07350 | −0.115509 | ||||||||
\(709\) | 8.01561 | 0.301033 | 0.150516 | − | 0.988608i | \(-0.451906\pi\) | ||||
0.150516 | + | 0.988608i | \(0.451906\pi\) | |||||||
\(710\) | 0.981888 | 0.0368496 | ||||||||
\(711\) | −5.24457 | −0.196687 | ||||||||
\(712\) | −12.6247 | −0.473129 | ||||||||
\(713\) | 2.01106 | 0.0753146 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0.284403 | 0.0106361 | ||||||||
\(716\) | 9.58344 | 0.358150 | ||||||||
\(717\) | 12.5354 | 0.468145 | ||||||||
\(718\) | −18.4797 | −0.689657 | ||||||||
\(719\) | 2.17601 | 0.0811515 | 0.0405757 | − | 0.999176i | \(-0.487081\pi\) | ||||
0.0405757 | + | 0.999176i | \(0.487081\pi\) | |||||||
\(720\) | −0.580445 | −0.0216319 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 25.5877 | 0.952274 | ||||||||
\(723\) | −2.17393 | −0.0808494 | ||||||||
\(724\) | 0.148655 | 0.00552473 | ||||||||
\(725\) | 4.94563 | 0.183676 | ||||||||
\(726\) | 7.79886 | 0.289443 | ||||||||
\(727\) | −53.7791 | −1.99456 | −0.997278 | − | 0.0737366i | \(-0.976508\pi\) | ||||
−0.997278 | + | 0.0737366i | \(0.976508\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −3.20426 | −0.118676 | ||||||||
\(730\) | 1.36240 | 0.0504247 | ||||||||
\(731\) | −2.00810 | −0.0742724 | ||||||||
\(732\) | −2.60680 | −0.0963502 | ||||||||
\(733\) | 26.7745 | 0.988938 | 0.494469 | − | 0.869195i | \(-0.335363\pi\) | ||||
0.494469 | + | 0.869195i | \(0.335363\pi\) | |||||||
\(734\) | −17.7335 | −0.654556 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −1.48774 | −0.0548389 | ||||||||
\(737\) | 1.45418 | 0.0535652 | ||||||||
\(738\) | −8.25489 | −0.303867 | ||||||||
\(739\) | 29.2936 | 1.07758 | 0.538791 | − | 0.842440i | \(-0.318881\pi\) | ||||
0.538791 | + | 0.842440i | \(0.318881\pi\) | |||||||
\(740\) | 0.148568 | 0.00546148 | ||||||||
\(741\) | −19.8371 | −0.728735 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 6.53498 | 0.239745 | 0.119873 | − | 0.992789i | \(-0.461751\pi\) | ||||
0.119873 | + | 0.992789i | \(0.461751\pi\) | |||||||
\(744\) | 0.965932 | 0.0354128 | ||||||||
\(745\) | 1.82244 | 0.0667690 | ||||||||
\(746\) | 14.2392 | 0.521335 | ||||||||
\(747\) | −16.7690 | −0.613544 | ||||||||
\(748\) | 0.178801 | 0.00653761 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 1.65712 | 0.0605093 | ||||||||
\(751\) | 30.1997 | 1.10200 | 0.551002 | − | 0.834504i | \(-0.314246\pi\) | ||||
0.551002 | + | 0.834504i | \(0.314246\pi\) | |||||||
\(752\) | 2.18092 | 0.0795298 | ||||||||
\(753\) | 12.3104 | 0.448616 | ||||||||
\(754\) | −4.15740 | −0.151403 | ||||||||
\(755\) | −3.78142 | −0.137620 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −26.5008 | −0.963189 | −0.481595 | − | 0.876394i | \(-0.659942\pi\) | ||||
−0.481595 | + | 0.876394i | \(0.659942\pi\) | |||||||
\(758\) | 33.9879 | 1.23450 | ||||||||
\(759\) | 0.311904 | 0.0113214 | ||||||||
\(760\) | 1.55696 | 0.0564769 | ||||||||
\(761\) | 4.37410 | 0.158561 | 0.0792805 | − | 0.996852i | \(-0.474738\pi\) | ||||
0.0792805 | + | 0.996852i | \(0.474738\pi\) | |||||||
\(762\) | 10.9369 | 0.396201 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 10.2831 | 0.372029 | ||||||||
\(765\) | −0.353743 | −0.0127896 | ||||||||
\(766\) | −17.0812 | −0.617168 | ||||||||
\(767\) | 17.8815 | 0.645664 | ||||||||
\(768\) | −0.714579 | −0.0257851 | ||||||||
\(769\) | 43.7523 | 1.57775 | 0.788874 | − | 0.614555i | \(-0.210665\pi\) | ||||
0.788874 | + | 0.614555i | \(0.210665\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −14.7528 | −0.531309 | ||||||||
\(772\) | 12.4681 | 0.448738 | ||||||||
\(773\) | 14.3435 | 0.515901 | 0.257950 | − | 0.966158i | \(-0.416953\pi\) | ||||
0.257950 | + | 0.966158i | \(0.416953\pi\) | |||||||
\(774\) | 8.20256 | 0.294835 | ||||||||
\(775\) | 6.68526 | 0.240142 | ||||||||
\(776\) | 5.70498 | 0.204797 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −11.3176 | −0.405757 | ||||||||
\(779\) | 22.1426 | 0.793340 | ||||||||
\(780\) | −0.692694 | −0.0248024 | ||||||||
\(781\) | 1.23548 | 0.0442088 | ||||||||
\(782\) | −0.906682 | −0.0324229 | ||||||||
\(783\) | −3.92259 | −0.140182 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −5.51338 | −0.196781 | ||||||||
\(786\) | −8.73040 | −0.311403 | ||||||||
\(787\) | −31.6417 | −1.12791 | −0.563953 | − | 0.825807i | \(-0.690720\pi\) | ||||
−0.563953 | + | 0.825807i | \(0.690720\pi\) | |||||||
\(788\) | −19.0312 | −0.677957 | ||||||||
\(789\) | 11.8410 | 0.421551 | ||||||||
\(790\) | 0.491235 | 0.0174773 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −0.730354 | −0.0259520 | ||||||||
\(793\) | 15.1663 | 0.538571 | ||||||||
\(794\) | 10.2515 | 0.363811 | ||||||||
\(795\) | −1.99811 | −0.0708656 | ||||||||
\(796\) | −10.6083 | −0.376003 | ||||||||
\(797\) | −12.6909 | −0.449536 | −0.224768 | − | 0.974412i | \(-0.572162\pi\) | ||||
−0.224768 | + | 0.974412i | \(0.572162\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1.32913 | 0.0470211 | ||||||||
\(800\) | −4.94563 | −0.174855 | ||||||||
\(801\) | 31.4276 | 1.11044 | ||||||||
\(802\) | −17.6102 | −0.621837 | ||||||||
\(803\) | 1.71426 | 0.0604950 | ||||||||
\(804\) | −3.54180 | −0.124910 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −5.61976 | −0.197948 | ||||||||
\(807\) | 1.87810 | 0.0661122 | ||||||||
\(808\) | 15.7339 | 0.553516 | ||||||||
\(809\) | 10.5845 | 0.372132 | 0.186066 | − | 0.982537i | \(-0.440426\pi\) | ||||
0.186066 | + | 0.982537i | \(0.440426\pi\) | |||||||
\(810\) | 1.08776 | 0.0382201 | ||||||||
\(811\) | −47.2614 | −1.65957 | −0.829786 | − | 0.558082i | \(-0.811537\pi\) | ||||
−0.829786 | + | 0.558082i | \(0.811537\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 9.01969 | 0.316334 | ||||||||
\(814\) | 0.186939 | 0.00655219 | ||||||||
\(815\) | −3.17400 | −0.111181 | ||||||||
\(816\) | −0.435489 | −0.0152452 | ||||||||
\(817\) | −22.0022 | −0.769759 | ||||||||
\(818\) | −38.8959 | −1.35996 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0.773198 | 0.0270012 | ||||||||
\(821\) | −0.820326 | −0.0286296 | −0.0143148 | − | 0.999898i | \(-0.504557\pi\) | ||||
−0.0143148 | + | 0.999898i | \(0.504557\pi\) | |||||||
\(822\) | −12.7403 | −0.444369 | ||||||||
\(823\) | 41.1702 | 1.43510 | 0.717551 | − | 0.696506i | \(-0.245263\pi\) | ||||
0.717551 | + | 0.696506i | \(0.245263\pi\) | |||||||
\(824\) | −4.89549 | −0.170543 | ||||||||
\(825\) | 1.03685 | 0.0360984 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −24.2372 | −0.842810 | −0.421405 | − | 0.906872i | \(-0.638463\pi\) | ||||
−0.421405 | + | 0.906872i | \(0.638463\pi\) | |||||||
\(828\) | 3.70355 | 0.128707 | ||||||||
\(829\) | −29.7746 | −1.03411 | −0.517057 | − | 0.855951i | \(-0.672972\pi\) | ||||
−0.517057 | + | 0.855951i | \(0.672972\pi\) | |||||||
\(830\) | 1.57067 | 0.0545188 | ||||||||
\(831\) | −13.9054 | −0.482372 | ||||||||
\(832\) | 4.15740 | 0.144132 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −5.71558 | −0.197914 | ||||||||
\(835\) | −0.838731 | −0.0290255 | ||||||||
\(836\) | 1.95907 | 0.0677559 | ||||||||
\(837\) | −5.30236 | −0.183277 | ||||||||
\(838\) | −12.6437 | −0.436768 | ||||||||
\(839\) | 14.8726 | 0.513459 | 0.256730 | − | 0.966483i | \(-0.417355\pi\) | ||||
0.256730 | + | 0.966483i | \(0.417355\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.00000 | 0.0344828 | ||||||||
\(842\) | −10.7981 | −0.372127 | ||||||||
\(843\) | −11.4265 | −0.393550 | ||||||||
\(844\) | −8.69020 | −0.299129 | ||||||||
\(845\) | 0.998882 | 0.0343626 | ||||||||
\(846\) | −5.42912 | −0.186657 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 11.9922 | 0.411814 | ||||||||
\(849\) | −19.9958 | −0.686255 | ||||||||
\(850\) | −3.01404 | −0.103381 | ||||||||
\(851\) | −0.947946 | −0.0324952 | ||||||||
\(852\) | −3.00914 | −0.103091 | ||||||||
\(853\) | 48.2468 | 1.65194 | 0.825970 | − | 0.563715i | \(-0.190628\pi\) | ||||
0.825970 | + | 0.563715i | \(0.190628\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −3.87586 | −0.132552 | ||||||||
\(856\) | 11.2315 | 0.383884 | ||||||||
\(857\) | −22.2883 | −0.761355 | −0.380677 | − | 0.924708i | \(-0.624309\pi\) | ||||
−0.380677 | + | 0.924708i | \(0.624309\pi\) | |||||||
\(858\) | −0.871594 | −0.0297557 | ||||||||
\(859\) | 33.0107 | 1.12631 | 0.563155 | − | 0.826351i | \(-0.309587\pi\) | ||||
0.563155 | + | 0.826351i | \(0.309587\pi\) | |||||||
\(860\) | −0.768296 | −0.0261987 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −36.1812 | −1.23234 | ||||||||
\(863\) | 2.98200 | 0.101509 | 0.0507543 | − | 0.998711i | \(-0.483837\pi\) | ||||
0.0507543 | + | 0.998711i | \(0.483837\pi\) | |||||||
\(864\) | 3.92259 | 0.133449 | ||||||||
\(865\) | 2.89028 | 0.0982723 | ||||||||
\(866\) | 10.6350 | 0.361391 | ||||||||
\(867\) | 11.8824 | 0.403549 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0.618104 | 0.0209677 | ||||||||
\(870\) | 0.166617 | 0.00564886 | ||||||||
\(871\) | 20.6061 | 0.698211 | ||||||||
\(872\) | 15.1865 | 0.514281 | ||||||||
\(873\) | −14.2018 | −0.480659 | ||||||||
\(874\) | −9.93425 | −0.336031 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −4.17527 | −0.141069 | ||||||||
\(877\) | −9.60117 | −0.324208 | −0.162104 | − | 0.986774i | \(-0.551828\pi\) | ||||
−0.162104 | + | 0.986774i | \(0.551828\pi\) | |||||||
\(878\) | −2.97507 | −0.100404 | ||||||||
\(879\) | −14.7807 | −0.498541 | ||||||||
\(880\) | 0.0684089 | 0.00230606 | ||||||||
\(881\) | 11.0461 | 0.372153 | 0.186076 | − | 0.982535i | \(-0.440423\pi\) | ||||
0.186076 | + | 0.982535i | \(0.440423\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −30.8011 | −1.03654 | −0.518269 | − | 0.855218i | \(-0.673423\pi\) | ||||
−0.518269 | + | 0.855218i | \(0.673423\pi\) | |||||||
\(884\) | 2.53366 | 0.0852163 | ||||||||
\(885\) | −0.716643 | −0.0240897 | ||||||||
\(886\) | −27.9429 | −0.938760 | ||||||||
\(887\) | −39.0735 | −1.31196 | −0.655980 | − | 0.754778i | \(-0.727744\pi\) | ||||
−0.655980 | + | 0.754778i | \(0.727744\pi\) | |||||||
\(888\) | −0.455309 | −0.0152792 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −2.94368 | −0.0986723 | ||||||||
\(891\) | 1.36869 | 0.0458530 | ||||||||
\(892\) | 9.99383 | 0.334618 | ||||||||
\(893\) | 14.5628 | 0.487327 | ||||||||
\(894\) | −5.58513 | −0.186795 | ||||||||
\(895\) | 2.23456 | 0.0746930 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 4.41976 | 0.147572 | ||||||||
\(898\) | −0.604431 | −0.0201701 | ||||||||
\(899\) | 1.35175 | 0.0450834 | ||||||||
\(900\) | 12.3115 | 0.410385 | ||||||||
\(901\) | 7.30846 | 0.243480 | ||||||||
\(902\) | 0.972889 | 0.0323937 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −10.2976 | −0.342493 | ||||||||
\(905\) | 0.0346617 | 0.00115219 | ||||||||
\(906\) | 11.5887 | 0.385009 | ||||||||
\(907\) | −0.412413 | −0.0136939 | −0.00684697 | − | 0.999977i | \(-0.502179\pi\) | ||||
−0.00684697 | + | 0.999977i | \(0.502179\pi\) | |||||||
\(908\) | −25.3090 | −0.839910 | ||||||||
\(909\) | −39.1675 | −1.29911 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 31.6863 | 1.04981 | 0.524907 | − | 0.851160i | \(-0.324100\pi\) | ||||
0.524907 | + | 0.851160i | \(0.324100\pi\) | |||||||
\(912\) | −4.77153 | −0.158001 | ||||||||
\(913\) | 1.97632 | 0.0654068 | ||||||||
\(914\) | −7.10311 | −0.234950 | ||||||||
\(915\) | −0.607825 | −0.0200941 | ||||||||
\(916\) | 18.4785 | 0.610545 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 2.39057 | 0.0789004 | ||||||||
\(919\) | −55.1497 | −1.81922 | −0.909611 | − | 0.415462i | \(-0.863620\pi\) | ||||
−0.909611 | + | 0.415462i | \(0.863620\pi\) | |||||||
\(920\) | −0.346895 | −0.0114368 | ||||||||
\(921\) | 20.4756 | 0.674693 | ||||||||
\(922\) | 3.81028 | 0.125485 | ||||||||
\(923\) | 17.5071 | 0.576252 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −3.15122 | −0.103611 | ||||||||
\(926\) | −3.42327 | −0.112496 | ||||||||
\(927\) | 12.1867 | 0.400265 | ||||||||
\(928\) | −1.00000 | −0.0328266 | ||||||||
\(929\) | 39.6996 | 1.30250 | 0.651251 | − | 0.758863i | \(-0.274245\pi\) | ||||
0.651251 | + | 0.758863i | \(0.274245\pi\) | |||||||
\(930\) | 0.225225 | 0.00738542 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −9.35908 | −0.306567 | ||||||||
\(933\) | −7.47785 | −0.244814 | ||||||||
\(934\) | 22.8701 | 0.748333 | ||||||||
\(935\) | 0.0416908 | 0.00136343 | ||||||||
\(936\) | −10.3493 | −0.338278 | ||||||||
\(937\) | 2.47672 | 0.0809108 | 0.0404554 | − | 0.999181i | \(-0.487119\pi\) | ||||
0.0404554 | + | 0.999181i | \(0.487119\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 22.4500 | 0.732629 | ||||||||
\(940\) | 0.508521 | 0.0165861 | ||||||||
\(941\) | 25.1780 | 0.820780 | 0.410390 | − | 0.911910i | \(-0.365393\pi\) | ||||
0.410390 | + | 0.911910i | \(0.365393\pi\) | |||||||
\(942\) | 16.8965 | 0.550519 | ||||||||
\(943\) | −4.93342 | −0.160654 | ||||||||
\(944\) | 4.30113 | 0.139990 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −0.966721 | −0.0314308 | ||||||||
\(947\) | −38.1720 | −1.24042 | −0.620212 | − | 0.784434i | \(-0.712953\pi\) | ||||
−0.620212 | + | 0.784434i | \(0.712953\pi\) | |||||||
\(948\) | −1.50546 | −0.0488951 | ||||||||
\(949\) | 24.2916 | 0.788539 | ||||||||
\(950\) | −33.0240 | −1.07144 | ||||||||
\(951\) | −9.10929 | −0.295389 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 41.3605 | 1.33980 | 0.669900 | − | 0.742452i | \(-0.266337\pi\) | ||||
0.669900 | + | 0.742452i | \(0.266337\pi\) | |||||||
\(954\) | −29.8531 | −0.966529 | ||||||||
\(955\) | 2.39769 | 0.0775875 | ||||||||
\(956\) | −17.5424 | −0.567363 | ||||||||
\(957\) | 0.209649 | 0.00677699 | ||||||||
\(958\) | −4.57219 | −0.147721 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −0.166617 | −0.00537755 | ||||||||
\(961\) | −29.1728 | −0.941057 | ||||||||
\(962\) | 2.64897 | 0.0854063 | ||||||||
\(963\) | −27.9594 | −0.900978 | ||||||||
\(964\) | 3.04226 | 0.0979845 | ||||||||
\(965\) | 2.90718 | 0.0935853 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 7.05786 | 0.226965 | 0.113483 | − | 0.993540i | \(-0.463799\pi\) | ||||
0.113483 | + | 0.993540i | \(0.463799\pi\) | |||||||
\(968\) | −10.9139 | −0.350787 | ||||||||
\(969\) | −2.90794 | −0.0934164 | ||||||||
\(970\) | 1.33022 | 0.0427108 | ||||||||
\(971\) | 35.4988 | 1.13921 | 0.569605 | − | 0.821919i | \(-0.307096\pi\) | ||||
0.569605 | + | 0.821919i | \(0.307096\pi\) | |||||||
\(972\) | −15.1014 | −0.484377 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 21.6569 | 0.693931 | ||||||||
\(975\) | 14.6924 | 0.470534 | ||||||||
\(976\) | 3.64803 | 0.116771 | ||||||||
\(977\) | 14.8701 | 0.475735 | 0.237868 | − | 0.971298i | \(-0.423552\pi\) | ||||
0.237868 | + | 0.971298i | \(0.423552\pi\) | |||||||
\(978\) | 9.72719 | 0.311041 | ||||||||
\(979\) | −3.70393 | −0.118378 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −37.8050 | −1.20702 | ||||||||
\(982\) | 32.0537 | 1.02287 | ||||||||
\(983\) | 36.7682 | 1.17272 | 0.586362 | − | 0.810049i | \(-0.300560\pi\) | ||||
0.586362 | + | 0.810049i | \(0.300560\pi\) | |||||||
\(984\) | −2.36958 | −0.0755393 | ||||||||
\(985\) | −4.43747 | −0.141390 | ||||||||
\(986\) | −0.609435 | −0.0194084 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 27.7606 | 0.883182 | ||||||||
\(989\) | 4.90214 | 0.155879 | ||||||||
\(990\) | −0.170296 | −0.00541235 | ||||||||
\(991\) | −26.9622 | −0.856483 | −0.428242 | − | 0.903664i | \(-0.640867\pi\) | ||||
−0.428242 | + | 0.903664i | \(0.640867\pi\) | |||||||
\(992\) | −1.35175 | −0.0429181 | ||||||||
\(993\) | 7.33295 | 0.232704 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −2.47353 | −0.0784162 | ||||||||
\(996\) | −4.81355 | −0.152523 | ||||||||
\(997\) | 7.46930 | 0.236555 | 0.118278 | − | 0.992981i | \(-0.462263\pi\) | ||||
0.118278 | + | 0.992981i | \(0.462263\pi\) | |||||||
\(998\) | 24.6113 | 0.779058 | ||||||||
\(999\) | 2.49936 | 0.0790764 |
(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 | 2842.2.a.z.1.2 | 5 | ||
7.2 | even | 3 | 406.2.e.a.291.4 | yes | 10 | ||
7.4 | even | 3 | 406.2.e.a.233.4 | ✓ | 10 | ||
7.6 | odd | 2 | 2842.2.a.x.1.4 | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
406.2.e.a.233.4 | ✓ | 10 | 7.4 | even | 3 | ||
406.2.e.a.291.4 | yes | 10 | 7.2 | even | 3 | ||
2842.2.a.x.1.4 | 5 | 7.6 | odd | 2 | |||
2842.2.a.z.1.2 | 5 | 1.1 | even | 1 | trivial |