Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8085,2,Mod(1,8085)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8085, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8085.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8085 = 3 \cdot 5 \cdot 7^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8085.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: | \(64.5590500342\) |
Analytic rank: | \(0\) |
Dimension: | \(14\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{14} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{14} - 4 x^{13} - 16 x^{12} + 76 x^{11} + 78 x^{10} - 532 x^{9} - 56 x^{8} + 1684 x^{7} - 471 x^{6} - 2352 x^{5} + 950 x^{4} + 1184 x^{3} - 340 x^{2} - 152 x + 14 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.8 | ||
Root | \(0.537407\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8085.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.537407 | 0.380004 | 0.190002 | − | 0.981784i | \(-0.439150\pi\) | ||||
0.190002 | + | 0.981784i | \(0.439150\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | −1.71119 | −0.855597 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 0.537407 | 0.219396 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −1.99442 | −0.705135 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0.537407 | 0.169943 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | −1.71119 | −0.493979 | ||||||||
\(13\) | 1.59143 | 0.441384 | 0.220692 | − | 0.975344i | \(-0.429169\pi\) | ||||
0.220692 | + | 0.975344i | \(0.429169\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.00000 | 0.258199 | ||||||||
\(16\) | 2.35057 | 0.587642 | ||||||||
\(17\) | 0.957367 | 0.232196 | 0.116098 | − | 0.993238i | \(-0.462961\pi\) | ||||
0.116098 | + | 0.993238i | \(0.462961\pi\) | |||||||
\(18\) | 0.537407 | 0.126668 | ||||||||
\(19\) | 0.301599 | 0.0691915 | 0.0345957 | − | 0.999401i | \(-0.488986\pi\) | ||||
0.0345957 | + | 0.999401i | \(0.488986\pi\) | |||||||
\(20\) | −1.71119 | −0.382634 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0.537407 | 0.114576 | ||||||||
\(23\) | 5.18215 | 1.08055 | 0.540276 | − | 0.841488i | \(-0.318320\pi\) | ||||
0.540276 | + | 0.841488i | \(0.318320\pi\) | |||||||
\(24\) | −1.99442 | −0.407110 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0.855247 | 0.167728 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 5.89540 | 1.09475 | 0.547374 | − | 0.836888i | \(-0.315627\pi\) | ||||
0.547374 | + | 0.836888i | \(0.315627\pi\) | |||||||
\(30\) | 0.537407 | 0.0981167 | ||||||||
\(31\) | 2.28121 | 0.409717 | 0.204858 | − | 0.978792i | \(-0.434327\pi\) | ||||
0.204858 | + | 0.978792i | \(0.434327\pi\) | |||||||
\(32\) | 5.25206 | 0.928442 | ||||||||
\(33\) | 1.00000 | 0.174078 | ||||||||
\(34\) | 0.514496 | 0.0882354 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −1.71119 | −0.285199 | ||||||||
\(37\) | −9.90813 | −1.62889 | −0.814444 | − | 0.580243i | \(-0.802958\pi\) | ||||
−0.814444 | + | 0.580243i | \(0.802958\pi\) | |||||||
\(38\) | 0.162081 | 0.0262931 | ||||||||
\(39\) | 1.59143 | 0.254833 | ||||||||
\(40\) | −1.99442 | −0.315346 | ||||||||
\(41\) | 11.2799 | 1.76163 | 0.880813 | − | 0.473465i | \(-0.156997\pi\) | ||||
0.880813 | + | 0.473465i | \(0.156997\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −0.309330 | −0.0471724 | −0.0235862 | − | 0.999722i | \(-0.507508\pi\) | ||||
−0.0235862 | + | 0.999722i | \(0.507508\pi\) | |||||||
\(44\) | −1.71119 | −0.257972 | ||||||||
\(45\) | 1.00000 | 0.149071 | ||||||||
\(46\) | 2.78492 | 0.410615 | ||||||||
\(47\) | −6.44995 | −0.940822 | −0.470411 | − | 0.882447i | \(-0.655894\pi\) | ||||
−0.470411 | + | 0.882447i | \(0.655894\pi\) | |||||||
\(48\) | 2.35057 | 0.339275 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0.537407 | 0.0760009 | ||||||||
\(51\) | 0.957367 | 0.134058 | ||||||||
\(52\) | −2.72325 | −0.377646 | ||||||||
\(53\) | −12.4653 | −1.71224 | −0.856119 | − | 0.516780i | \(-0.827131\pi\) | ||||
−0.856119 | + | 0.516780i | \(0.827131\pi\) | |||||||
\(54\) | 0.537407 | 0.0731319 | ||||||||
\(55\) | 1.00000 | 0.134840 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0.301599 | 0.0399477 | ||||||||
\(58\) | 3.16823 | 0.416009 | ||||||||
\(59\) | 10.5444 | 1.37277 | 0.686385 | − | 0.727239i | \(-0.259197\pi\) | ||||
0.686385 | + | 0.727239i | \(0.259197\pi\) | |||||||
\(60\) | −1.71119 | −0.220914 | ||||||||
\(61\) | −10.9417 | −1.40094 | −0.700471 | − | 0.713681i | \(-0.747026\pi\) | ||||
−0.700471 | + | 0.713681i | \(0.747026\pi\) | |||||||
\(62\) | 1.22594 | 0.155694 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.87864 | −0.234831 | ||||||||
\(65\) | 1.59143 | 0.197393 | ||||||||
\(66\) | 0.537407 | 0.0661503 | ||||||||
\(67\) | −4.92273 | −0.601407 | −0.300703 | − | 0.953718i | \(-0.597221\pi\) | ||||
−0.300703 | + | 0.953718i | \(0.597221\pi\) | |||||||
\(68\) | −1.63824 | −0.198666 | ||||||||
\(69\) | 5.18215 | 0.623857 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −16.6715 | −1.97855 | −0.989274 | − | 0.146070i | \(-0.953337\pi\) | ||||
−0.989274 | + | 0.146070i | \(0.953337\pi\) | |||||||
\(72\) | −1.99442 | −0.235045 | ||||||||
\(73\) | −12.5376 | −1.46742 | −0.733710 | − | 0.679463i | \(-0.762213\pi\) | ||||
−0.733710 | + | 0.679463i | \(0.762213\pi\) | |||||||
\(74\) | −5.32470 | −0.618984 | ||||||||
\(75\) | 1.00000 | 0.115470 | ||||||||
\(76\) | −0.516093 | −0.0592000 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0.855247 | 0.0968376 | ||||||||
\(79\) | 8.17883 | 0.920190 | 0.460095 | − | 0.887870i | \(-0.347815\pi\) | ||||
0.460095 | + | 0.887870i | \(0.347815\pi\) | |||||||
\(80\) | 2.35057 | 0.262802 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 6.06191 | 0.669425 | ||||||||
\(83\) | −4.70769 | −0.516736 | −0.258368 | − | 0.966047i | \(-0.583185\pi\) | ||||
−0.258368 | + | 0.966047i | \(0.583185\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.957367 | 0.103841 | ||||||||
\(86\) | −0.166236 | −0.0179257 | ||||||||
\(87\) | 5.89540 | 0.632053 | ||||||||
\(88\) | −1.99442 | −0.212606 | ||||||||
\(89\) | 15.4510 | 1.63780 | 0.818902 | − | 0.573934i | \(-0.194583\pi\) | ||||
0.818902 | + | 0.573934i | \(0.194583\pi\) | |||||||
\(90\) | 0.537407 | 0.0566477 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −8.86766 | −0.924517 | ||||||||
\(93\) | 2.28121 | 0.236550 | ||||||||
\(94\) | −3.46625 | −0.357516 | ||||||||
\(95\) | 0.301599 | 0.0309434 | ||||||||
\(96\) | 5.25206 | 0.536036 | ||||||||
\(97\) | 18.2513 | 1.85314 | 0.926571 | − | 0.376119i | \(-0.122742\pi\) | ||||
0.926571 | + | 0.376119i | \(0.122742\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.00000 | 0.100504 | ||||||||
\(100\) | −1.71119 | −0.171119 | ||||||||
\(101\) | −10.8839 | −1.08299 | −0.541493 | − | 0.840705i | \(-0.682141\pi\) | ||||
−0.541493 | + | 0.840705i | \(0.682141\pi\) | |||||||
\(102\) | 0.514496 | 0.0509427 | ||||||||
\(103\) | 2.06192 | 0.203167 | 0.101584 | − | 0.994827i | \(-0.467609\pi\) | ||||
0.101584 | + | 0.994827i | \(0.467609\pi\) | |||||||
\(104\) | −3.17399 | −0.311235 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −6.69893 | −0.650658 | ||||||||
\(107\) | 7.26476 | 0.702311 | 0.351155 | − | 0.936317i | \(-0.385789\pi\) | ||||
0.351155 | + | 0.936317i | \(0.385789\pi\) | |||||||
\(108\) | −1.71119 | −0.164660 | ||||||||
\(109\) | 17.0326 | 1.63142 | 0.815711 | − | 0.578459i | \(-0.196346\pi\) | ||||
0.815711 | + | 0.578459i | \(0.196346\pi\) | |||||||
\(110\) | 0.537407 | 0.0512398 | ||||||||
\(111\) | −9.90813 | −0.940439 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 16.2281 | 1.52661 | 0.763304 | − | 0.646039i | \(-0.223576\pi\) | ||||
0.763304 | + | 0.646039i | \(0.223576\pi\) | |||||||
\(114\) | 0.162081 | 0.0151803 | ||||||||
\(115\) | 5.18215 | 0.483238 | ||||||||
\(116\) | −10.0882 | −0.936663 | ||||||||
\(117\) | 1.59143 | 0.147128 | ||||||||
\(118\) | 5.66666 | 0.521658 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −1.99442 | −0.182065 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | −5.88015 | −0.532364 | ||||||||
\(123\) | 11.2799 | 1.01708 | ||||||||
\(124\) | −3.90358 | −0.350552 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 7.49535 | 0.665105 | 0.332553 | − | 0.943085i | \(-0.392090\pi\) | ||||
0.332553 | + | 0.943085i | \(0.392090\pi\) | |||||||
\(128\) | −11.5137 | −1.01768 | ||||||||
\(129\) | −0.309330 | −0.0272350 | ||||||||
\(130\) | 0.855247 | 0.0750101 | ||||||||
\(131\) | 16.3884 | 1.43186 | 0.715932 | − | 0.698170i | \(-0.246002\pi\) | ||||
0.715932 | + | 0.698170i | \(0.246002\pi\) | |||||||
\(132\) | −1.71119 | −0.148940 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −2.64551 | −0.228537 | ||||||||
\(135\) | 1.00000 | 0.0860663 | ||||||||
\(136\) | −1.90940 | −0.163729 | ||||||||
\(137\) | 5.84770 | 0.499603 | 0.249801 | − | 0.968297i | \(-0.419635\pi\) | ||||
0.249801 | + | 0.968297i | \(0.419635\pi\) | |||||||
\(138\) | 2.78492 | 0.237068 | ||||||||
\(139\) | 22.3715 | 1.89752 | 0.948762 | − | 0.315992i | \(-0.102337\pi\) | ||||
0.948762 | + | 0.315992i | \(0.102337\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −6.44995 | −0.543184 | ||||||||
\(142\) | −8.95941 | −0.751857 | ||||||||
\(143\) | 1.59143 | 0.133082 | ||||||||
\(144\) | 2.35057 | 0.195881 | ||||||||
\(145\) | 5.89540 | 0.489586 | ||||||||
\(146\) | −6.73782 | −0.557626 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 16.9547 | 1.39367 | ||||||||
\(149\) | 22.0198 | 1.80393 | 0.901965 | − | 0.431809i | \(-0.142125\pi\) | ||||
0.901965 | + | 0.431809i | \(0.142125\pi\) | |||||||
\(150\) | 0.537407 | 0.0438791 | ||||||||
\(151\) | −0.293489 | −0.0238838 | −0.0119419 | − | 0.999929i | \(-0.503801\pi\) | ||||
−0.0119419 | + | 0.999929i | \(0.503801\pi\) | |||||||
\(152\) | −0.601515 | −0.0487893 | ||||||||
\(153\) | 0.957367 | 0.0773986 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 2.28121 | 0.183231 | ||||||||
\(156\) | −2.72325 | −0.218034 | ||||||||
\(157\) | −4.13745 | −0.330204 | −0.165102 | − | 0.986276i | \(-0.552795\pi\) | ||||
−0.165102 | + | 0.986276i | \(0.552795\pi\) | |||||||
\(158\) | 4.39536 | 0.349676 | ||||||||
\(159\) | −12.4653 | −0.988561 | ||||||||
\(160\) | 5.25206 | 0.415212 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0.537407 | 0.0422227 | ||||||||
\(163\) | −6.19238 | −0.485024 | −0.242512 | − | 0.970148i | \(-0.577971\pi\) | ||||
−0.242512 | + | 0.970148i | \(0.577971\pi\) | |||||||
\(164\) | −19.3021 | −1.50724 | ||||||||
\(165\) | 1.00000 | 0.0778499 | ||||||||
\(166\) | −2.52995 | −0.196362 | ||||||||
\(167\) | 4.74324 | 0.367043 | 0.183522 | − | 0.983016i | \(-0.441250\pi\) | ||||
0.183522 | + | 0.983016i | \(0.441250\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −10.4673 | −0.805180 | ||||||||
\(170\) | 0.514496 | 0.0394601 | ||||||||
\(171\) | 0.301599 | 0.0230638 | ||||||||
\(172\) | 0.529324 | 0.0403606 | ||||||||
\(173\) | −23.5426 | −1.78991 | −0.894956 | − | 0.446154i | \(-0.852793\pi\) | ||||
−0.894956 | + | 0.446154i | \(0.852793\pi\) | |||||||
\(174\) | 3.16823 | 0.240183 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 2.35057 | 0.177181 | ||||||||
\(177\) | 10.5444 | 0.792569 | ||||||||
\(178\) | 8.30348 | 0.622372 | ||||||||
\(179\) | 3.34159 | 0.249762 | 0.124881 | − | 0.992172i | \(-0.460145\pi\) | ||||
0.124881 | + | 0.992172i | \(0.460145\pi\) | |||||||
\(180\) | −1.71119 | −0.127545 | ||||||||
\(181\) | 13.2594 | 0.985560 | 0.492780 | − | 0.870154i | \(-0.335981\pi\) | ||||
0.492780 | + | 0.870154i | \(0.335981\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −10.9417 | −0.808834 | ||||||||
\(184\) | −10.3354 | −0.761935 | ||||||||
\(185\) | −9.90813 | −0.728461 | ||||||||
\(186\) | 1.22594 | 0.0898901 | ||||||||
\(187\) | 0.957367 | 0.0700096 | ||||||||
\(188\) | 11.0371 | 0.804964 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0.162081 | 0.0117586 | ||||||||
\(191\) | 21.6487 | 1.56645 | 0.783223 | − | 0.621741i | \(-0.213574\pi\) | ||||
0.783223 | + | 0.621741i | \(0.213574\pi\) | |||||||
\(192\) | −1.87864 | −0.135579 | ||||||||
\(193\) | 19.5443 | 1.40683 | 0.703416 | − | 0.710779i | \(-0.251657\pi\) | ||||
0.703416 | + | 0.710779i | \(0.251657\pi\) | |||||||
\(194\) | 9.80840 | 0.704202 | ||||||||
\(195\) | 1.59143 | 0.113965 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 14.0102 | 0.998189 | 0.499094 | − | 0.866548i | \(-0.333666\pi\) | ||||
0.499094 | + | 0.866548i | \(0.333666\pi\) | |||||||
\(198\) | 0.537407 | 0.0381919 | ||||||||
\(199\) | −9.00502 | −0.638349 | −0.319174 | − | 0.947696i | \(-0.603406\pi\) | ||||
−0.319174 | + | 0.947696i | \(0.603406\pi\) | |||||||
\(200\) | −1.99442 | −0.141027 | ||||||||
\(201\) | −4.92273 | −0.347222 | ||||||||
\(202\) | −5.84907 | −0.411539 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −1.63824 | −0.114700 | ||||||||
\(205\) | 11.2799 | 0.787823 | ||||||||
\(206\) | 1.10809 | 0.0772045 | ||||||||
\(207\) | 5.18215 | 0.360184 | ||||||||
\(208\) | 3.74077 | 0.259376 | ||||||||
\(209\) | 0.301599 | 0.0208620 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 8.40675 | 0.578745 | 0.289372 | − | 0.957217i | \(-0.406553\pi\) | ||||
0.289372 | + | 0.957217i | \(0.406553\pi\) | |||||||
\(212\) | 21.3305 | 1.46498 | ||||||||
\(213\) | −16.6715 | −1.14232 | ||||||||
\(214\) | 3.90414 | 0.266881 | ||||||||
\(215\) | −0.309330 | −0.0210961 | ||||||||
\(216\) | −1.99442 | −0.135703 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 9.15342 | 0.619948 | ||||||||
\(219\) | −12.5376 | −0.847215 | ||||||||
\(220\) | −1.71119 | −0.115369 | ||||||||
\(221\) | 1.52358 | 0.102487 | ||||||||
\(222\) | −5.32470 | −0.357371 | ||||||||
\(223\) | −3.96213 | −0.265324 | −0.132662 | − | 0.991161i | \(-0.542352\pi\) | ||||
−0.132662 | + | 0.991161i | \(0.542352\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | 8.72109 | 0.580118 | ||||||||
\(227\) | 4.72377 | 0.313527 | 0.156764 | − | 0.987636i | \(-0.449894\pi\) | ||||
0.156764 | + | 0.987636i | \(0.449894\pi\) | |||||||
\(228\) | −0.516093 | −0.0341791 | ||||||||
\(229\) | −3.44504 | −0.227654 | −0.113827 | − | 0.993501i | \(-0.536311\pi\) | ||||
−0.113827 | + | 0.993501i | \(0.536311\pi\) | |||||||
\(230\) | 2.78492 | 0.183632 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −11.7579 | −0.771945 | ||||||||
\(233\) | 17.5457 | 1.14946 | 0.574728 | − | 0.818345i | \(-0.305108\pi\) | ||||
0.574728 | + | 0.818345i | \(0.305108\pi\) | |||||||
\(234\) | 0.855247 | 0.0559092 | ||||||||
\(235\) | −6.44995 | −0.420748 | ||||||||
\(236\) | −18.0436 | −1.17454 | ||||||||
\(237\) | 8.17883 | 0.531272 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −22.3788 | −1.44757 | −0.723783 | − | 0.690027i | \(-0.757598\pi\) | ||||
−0.723783 | + | 0.690027i | \(0.757598\pi\) | |||||||
\(240\) | 2.35057 | 0.151729 | ||||||||
\(241\) | −12.6591 | −0.815442 | −0.407721 | − | 0.913107i | \(-0.633676\pi\) | ||||
−0.407721 | + | 0.913107i | \(0.633676\pi\) | |||||||
\(242\) | 0.537407 | 0.0345459 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 18.7234 | 1.19864 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 6.06191 | 0.386493 | ||||||||
\(247\) | 0.479973 | 0.0305400 | ||||||||
\(248\) | −4.54969 | −0.288906 | ||||||||
\(249\) | −4.70769 | −0.298338 | ||||||||
\(250\) | 0.537407 | 0.0339886 | ||||||||
\(251\) | −9.48355 | −0.598597 | −0.299298 | − | 0.954160i | \(-0.596753\pi\) | ||||
−0.299298 | + | 0.954160i | \(0.596753\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 5.18215 | 0.325799 | ||||||||
\(254\) | 4.02806 | 0.252743 | ||||||||
\(255\) | 0.957367 | 0.0599527 | ||||||||
\(256\) | −2.43027 | −0.151892 | ||||||||
\(257\) | 9.41243 | 0.587131 | 0.293566 | − | 0.955939i | \(-0.405158\pi\) | ||||
0.293566 | + | 0.955939i | \(0.405158\pi\) | |||||||
\(258\) | −0.166236 | −0.0103494 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −2.72325 | −0.168889 | ||||||||
\(261\) | 5.89540 | 0.364916 | ||||||||
\(262\) | 8.80727 | 0.544115 | ||||||||
\(263\) | −9.97123 | −0.614852 | −0.307426 | − | 0.951572i | \(-0.599468\pi\) | ||||
−0.307426 | + | 0.951572i | \(0.599468\pi\) | |||||||
\(264\) | −1.99442 | −0.122748 | ||||||||
\(265\) | −12.4653 | −0.765736 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 15.4510 | 0.945586 | ||||||||
\(268\) | 8.42373 | 0.514562 | ||||||||
\(269\) | 13.9922 | 0.853122 | 0.426561 | − | 0.904459i | \(-0.359725\pi\) | ||||
0.426561 | + | 0.904459i | \(0.359725\pi\) | |||||||
\(270\) | 0.537407 | 0.0327056 | ||||||||
\(271\) | 17.8855 | 1.08646 | 0.543232 | − | 0.839583i | \(-0.317200\pi\) | ||||
0.543232 | + | 0.839583i | \(0.317200\pi\) | |||||||
\(272\) | 2.25036 | 0.136448 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 3.14260 | 0.189851 | ||||||||
\(275\) | 1.00000 | 0.0603023 | ||||||||
\(276\) | −8.86766 | −0.533770 | ||||||||
\(277\) | −4.08065 | −0.245183 | −0.122591 | − | 0.992457i | \(-0.539120\pi\) | ||||
−0.122591 | + | 0.992457i | \(0.539120\pi\) | |||||||
\(278\) | 12.0226 | 0.721067 | ||||||||
\(279\) | 2.28121 | 0.136572 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1.48034 | 0.0883094 | 0.0441547 | − | 0.999025i | \(-0.485941\pi\) | ||||
0.0441547 | + | 0.999025i | \(0.485941\pi\) | |||||||
\(282\) | −3.46625 | −0.206412 | ||||||||
\(283\) | −22.3349 | −1.32767 | −0.663836 | − | 0.747878i | \(-0.731073\pi\) | ||||
−0.663836 | + | 0.747878i | \(0.731073\pi\) | |||||||
\(284\) | 28.5282 | 1.69284 | ||||||||
\(285\) | 0.301599 | 0.0178652 | ||||||||
\(286\) | 0.855247 | 0.0505718 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 5.25206 | 0.309481 | ||||||||
\(289\) | −16.0834 | −0.946085 | ||||||||
\(290\) | 3.16823 | 0.186045 | ||||||||
\(291\) | 18.2513 | 1.06991 | ||||||||
\(292\) | 21.4543 | 1.25552 | ||||||||
\(293\) | −3.68648 | −0.215367 | −0.107683 | − | 0.994185i | \(-0.534343\pi\) | ||||
−0.107683 | + | 0.994185i | \(0.534343\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 10.5444 | 0.613921 | ||||||||
\(296\) | 19.7610 | 1.14859 | ||||||||
\(297\) | 1.00000 | 0.0580259 | ||||||||
\(298\) | 11.8336 | 0.685501 | ||||||||
\(299\) | 8.24703 | 0.476938 | ||||||||
\(300\) | −1.71119 | −0.0987958 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −0.157723 | −0.00907596 | ||||||||
\(303\) | −10.8839 | −0.625262 | ||||||||
\(304\) | 0.708928 | 0.0406598 | ||||||||
\(305\) | −10.9417 | −0.626520 | ||||||||
\(306\) | 0.514496 | 0.0294118 | ||||||||
\(307\) | −2.54070 | −0.145005 | −0.0725027 | − | 0.997368i | \(-0.523099\pi\) | ||||
−0.0725027 | + | 0.997368i | \(0.523099\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 2.06192 | 0.117299 | ||||||||
\(310\) | 1.22594 | 0.0696285 | ||||||||
\(311\) | −5.06535 | −0.287229 | −0.143615 | − | 0.989634i | \(-0.545873\pi\) | ||||
−0.143615 | + | 0.989634i | \(0.545873\pi\) | |||||||
\(312\) | −3.17399 | −0.179692 | ||||||||
\(313\) | 0.628632 | 0.0355324 | 0.0177662 | − | 0.999842i | \(-0.494345\pi\) | ||||
0.0177662 | + | 0.999842i | \(0.494345\pi\) | |||||||
\(314\) | −2.22349 | −0.125479 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −13.9956 | −0.787312 | ||||||||
\(317\) | 0.181949 | 0.0102193 | 0.00510963 | − | 0.999987i | \(-0.498374\pi\) | ||||
0.00510963 | + | 0.999987i | \(0.498374\pi\) | |||||||
\(318\) | −6.69893 | −0.375657 | ||||||||
\(319\) | 5.89540 | 0.330079 | ||||||||
\(320\) | −1.87864 | −0.105019 | ||||||||
\(321\) | 7.26476 | 0.405479 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0.288741 | 0.0160660 | ||||||||
\(324\) | −1.71119 | −0.0950663 | ||||||||
\(325\) | 1.59143 | 0.0882767 | ||||||||
\(326\) | −3.32783 | −0.184311 | ||||||||
\(327\) | 17.0326 | 0.941902 | ||||||||
\(328\) | −22.4969 | −1.24218 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0.537407 | 0.0295833 | ||||||||
\(331\) | 26.8960 | 1.47834 | 0.739170 | − | 0.673519i | \(-0.235218\pi\) | ||||
0.739170 | + | 0.673519i | \(0.235218\pi\) | |||||||
\(332\) | 8.05577 | 0.442118 | ||||||||
\(333\) | −9.90813 | −0.542962 | ||||||||
\(334\) | 2.54905 | 0.139478 | ||||||||
\(335\) | −4.92273 | −0.268957 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −20.1187 | −1.09594 | −0.547969 | − | 0.836499i | \(-0.684599\pi\) | ||||
−0.547969 | + | 0.836499i | \(0.684599\pi\) | |||||||
\(338\) | −5.62523 | −0.305972 | ||||||||
\(339\) | 16.2281 | 0.881388 | ||||||||
\(340\) | −1.63824 | −0.0888461 | ||||||||
\(341\) | 2.28121 | 0.123534 | ||||||||
\(342\) | 0.162081 | 0.00876435 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0.616935 | 0.0332629 | ||||||||
\(345\) | 5.18215 | 0.278997 | ||||||||
\(346\) | −12.6520 | −0.680175 | ||||||||
\(347\) | −2.20167 | −0.118192 | −0.0590958 | − | 0.998252i | \(-0.518822\pi\) | ||||
−0.0590958 | + | 0.998252i | \(0.518822\pi\) | |||||||
\(348\) | −10.0882 | −0.540783 | ||||||||
\(349\) | −24.3330 | −1.30252 | −0.651258 | − | 0.758857i | \(-0.725758\pi\) | ||||
−0.651258 | + | 0.758857i | \(0.725758\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.59143 | 0.0849443 | ||||||||
\(352\) | 5.25206 | 0.279936 | ||||||||
\(353\) | 10.0855 | 0.536795 | 0.268397 | − | 0.963308i | \(-0.413506\pi\) | ||||
0.268397 | + | 0.963308i | \(0.413506\pi\) | |||||||
\(354\) | 5.66666 | 0.301180 | ||||||||
\(355\) | −16.6715 | −0.884834 | ||||||||
\(356\) | −26.4397 | −1.40130 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 1.79580 | 0.0949108 | ||||||||
\(359\) | 10.2313 | 0.539988 | 0.269994 | − | 0.962862i | \(-0.412978\pi\) | ||||
0.269994 | + | 0.962862i | \(0.412978\pi\) | |||||||
\(360\) | −1.99442 | −0.105115 | ||||||||
\(361\) | −18.9090 | −0.995213 | ||||||||
\(362\) | 7.12567 | 0.374517 | ||||||||
\(363\) | 1.00000 | 0.0524864 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −12.5376 | −0.656250 | ||||||||
\(366\) | −5.88015 | −0.307360 | ||||||||
\(367\) | −25.6154 | −1.33711 | −0.668555 | − | 0.743662i | \(-0.733087\pi\) | ||||
−0.668555 | + | 0.743662i | \(0.733087\pi\) | |||||||
\(368\) | 12.1810 | 0.634978 | ||||||||
\(369\) | 11.2799 | 0.587209 | ||||||||
\(370\) | −5.32470 | −0.276818 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −3.90358 | −0.202391 | ||||||||
\(373\) | 25.7975 | 1.33574 | 0.667871 | − | 0.744277i | \(-0.267206\pi\) | ||||
0.667871 | + | 0.744277i | \(0.267206\pi\) | |||||||
\(374\) | 0.514496 | 0.0266040 | ||||||||
\(375\) | 1.00000 | 0.0516398 | ||||||||
\(376\) | 12.8639 | 0.663406 | ||||||||
\(377\) | 9.38212 | 0.483204 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 18.8896 | 0.970293 | 0.485146 | − | 0.874433i | \(-0.338766\pi\) | ||||
0.485146 | + | 0.874433i | \(0.338766\pi\) | |||||||
\(380\) | −0.516093 | −0.0264750 | ||||||||
\(381\) | 7.49535 | 0.383999 | ||||||||
\(382\) | 11.6342 | 0.595257 | ||||||||
\(383\) | −28.7713 | −1.47014 | −0.735072 | − | 0.677990i | \(-0.762851\pi\) | ||||
−0.735072 | + | 0.677990i | \(0.762851\pi\) | |||||||
\(384\) | −11.5137 | −0.587557 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 10.5033 | 0.534602 | ||||||||
\(387\) | −0.309330 | −0.0157241 | ||||||||
\(388\) | −31.2316 | −1.58554 | ||||||||
\(389\) | 15.1536 | 0.768318 | 0.384159 | − | 0.923267i | \(-0.374491\pi\) | ||||
0.384159 | + | 0.923267i | \(0.374491\pi\) | |||||||
\(390\) | 0.855247 | 0.0433071 | ||||||||
\(391\) | 4.96122 | 0.250900 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 16.3884 | 0.826687 | ||||||||
\(394\) | 7.52921 | 0.379316 | ||||||||
\(395\) | 8.17883 | 0.411522 | ||||||||
\(396\) | −1.71119 | −0.0859907 | ||||||||
\(397\) | 2.35650 | 0.118269 | 0.0591346 | − | 0.998250i | \(-0.481166\pi\) | ||||
0.0591346 | + | 0.998250i | \(0.481166\pi\) | |||||||
\(398\) | −4.83936 | −0.242575 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 2.35057 | 0.117528 | ||||||||
\(401\) | 15.4658 | 0.772325 | 0.386163 | − | 0.922431i | \(-0.373800\pi\) | ||||
0.386163 | + | 0.922431i | \(0.373800\pi\) | |||||||
\(402\) | −2.64551 | −0.131946 | ||||||||
\(403\) | 3.63038 | 0.180842 | ||||||||
\(404\) | 18.6244 | 0.926599 | ||||||||
\(405\) | 1.00000 | 0.0496904 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −9.90813 | −0.491128 | ||||||||
\(408\) | −1.90940 | −0.0945292 | ||||||||
\(409\) | −5.06959 | −0.250675 | −0.125338 | − | 0.992114i | \(-0.540001\pi\) | ||||
−0.125338 | + | 0.992114i | \(0.540001\pi\) | |||||||
\(410\) | 6.06191 | 0.299376 | ||||||||
\(411\) | 5.84770 | 0.288446 | ||||||||
\(412\) | −3.52835 | −0.173829 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 2.78492 | 0.136872 | ||||||||
\(415\) | −4.70769 | −0.231091 | ||||||||
\(416\) | 8.35829 | 0.409799 | ||||||||
\(417\) | 22.3715 | 1.09554 | ||||||||
\(418\) | 0.162081 | 0.00792765 | ||||||||
\(419\) | 39.1469 | 1.91245 | 0.956226 | − | 0.292629i | \(-0.0945302\pi\) | ||||
0.956226 | + | 0.292629i | \(0.0945302\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 15.0025 | 0.731177 | 0.365589 | − | 0.930777i | \(-0.380868\pi\) | ||||
0.365589 | + | 0.930777i | \(0.380868\pi\) | |||||||
\(422\) | 4.51785 | 0.219926 | ||||||||
\(423\) | −6.44995 | −0.313607 | ||||||||
\(424\) | 24.8610 | 1.20736 | ||||||||
\(425\) | 0.957367 | 0.0464391 | ||||||||
\(426\) | −8.95941 | −0.434085 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −12.4314 | −0.600895 | ||||||||
\(429\) | 1.59143 | 0.0768350 | ||||||||
\(430\) | −0.166236 | −0.00801663 | ||||||||
\(431\) | −17.0025 | −0.818983 | −0.409492 | − | 0.912314i | \(-0.634294\pi\) | ||||
−0.409492 | + | 0.912314i | \(0.634294\pi\) | |||||||
\(432\) | 2.35057 | 0.113092 | ||||||||
\(433\) | 20.2420 | 0.972768 | 0.486384 | − | 0.873745i | \(-0.338316\pi\) | ||||
0.486384 | + | 0.873745i | \(0.338316\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 5.89540 | 0.282663 | ||||||||
\(436\) | −29.1460 | −1.39584 | ||||||||
\(437\) | 1.56293 | 0.0747650 | ||||||||
\(438\) | −6.73782 | −0.321946 | ||||||||
\(439\) | −9.22630 | −0.440347 | −0.220174 | − | 0.975461i | \(-0.570662\pi\) | ||||
−0.220174 | + | 0.975461i | \(0.570662\pi\) | |||||||
\(440\) | −1.99442 | −0.0950804 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0.818786 | 0.0389457 | ||||||||
\(443\) | 34.2426 | 1.62692 | 0.813458 | − | 0.581624i | \(-0.197582\pi\) | ||||
0.813458 | + | 0.581624i | \(0.197582\pi\) | |||||||
\(444\) | 16.9547 | 0.804636 | ||||||||
\(445\) | 15.4510 | 0.732448 | ||||||||
\(446\) | −2.12928 | −0.100824 | ||||||||
\(447\) | 22.0198 | 1.04150 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −3.40604 | −0.160741 | −0.0803704 | − | 0.996765i | \(-0.525610\pi\) | ||||
−0.0803704 | + | 0.996765i | \(0.525610\pi\) | |||||||
\(450\) | 0.537407 | 0.0253336 | ||||||||
\(451\) | 11.2799 | 0.531150 | ||||||||
\(452\) | −27.7694 | −1.30616 | ||||||||
\(453\) | −0.293489 | −0.0137893 | ||||||||
\(454\) | 2.53859 | 0.119142 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −0.601515 | −0.0281685 | ||||||||
\(457\) | −19.8711 | −0.929529 | −0.464764 | − | 0.885434i | \(-0.653861\pi\) | ||||
−0.464764 | + | 0.885434i | \(0.653861\pi\) | |||||||
\(458\) | −1.85139 | −0.0865097 | ||||||||
\(459\) | 0.957367 | 0.0446861 | ||||||||
\(460\) | −8.86766 | −0.413457 | ||||||||
\(461\) | −16.1882 | −0.753961 | −0.376981 | − | 0.926221i | \(-0.623038\pi\) | ||||
−0.376981 | + | 0.926221i | \(0.623038\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 37.5479 | 1.74500 | 0.872499 | − | 0.488616i | \(-0.162498\pi\) | ||||
0.872499 | + | 0.488616i | \(0.162498\pi\) | |||||||
\(464\) | 13.8575 | 0.643321 | ||||||||
\(465\) | 2.28121 | 0.105788 | ||||||||
\(466\) | 9.42918 | 0.436798 | ||||||||
\(467\) | 16.6119 | 0.768709 | 0.384355 | − | 0.923186i | \(-0.374424\pi\) | ||||
0.384355 | + | 0.923186i | \(0.374424\pi\) | |||||||
\(468\) | −2.72325 | −0.125882 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −3.46625 | −0.159886 | ||||||||
\(471\) | −4.13745 | −0.190644 | ||||||||
\(472\) | −21.0301 | −0.967987 | ||||||||
\(473\) | −0.309330 | −0.0142230 | ||||||||
\(474\) | 4.39536 | 0.201886 | ||||||||
\(475\) | 0.301599 | 0.0138383 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −12.4653 | −0.570746 | ||||||||
\(478\) | −12.0265 | −0.550082 | ||||||||
\(479\) | −27.8995 | −1.27476 | −0.637381 | − | 0.770549i | \(-0.719982\pi\) | ||||
−0.637381 | + | 0.770549i | \(0.719982\pi\) | |||||||
\(480\) | 5.25206 | 0.239723 | ||||||||
\(481\) | −15.7681 | −0.718964 | ||||||||
\(482\) | −6.80308 | −0.309872 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −1.71119 | −0.0777815 | ||||||||
\(485\) | 18.2513 | 0.828751 | ||||||||
\(486\) | 0.537407 | 0.0243773 | ||||||||
\(487\) | 0.319844 | 0.0144935 | 0.00724675 | − | 0.999974i | \(-0.497693\pi\) | ||||
0.00724675 | + | 0.999974i | \(0.497693\pi\) | |||||||
\(488\) | 21.8224 | 0.987852 | ||||||||
\(489\) | −6.19238 | −0.280029 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 24.6414 | 1.11205 | 0.556025 | − | 0.831166i | \(-0.312326\pi\) | ||||
0.556025 | + | 0.831166i | \(0.312326\pi\) | |||||||
\(492\) | −19.3021 | −0.870206 | ||||||||
\(493\) | 5.64406 | 0.254196 | ||||||||
\(494\) | 0.257941 | 0.0116053 | ||||||||
\(495\) | 1.00000 | 0.0449467 | ||||||||
\(496\) | 5.36213 | 0.240767 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −2.52995 | −0.113370 | ||||||||
\(499\) | 18.9623 | 0.848870 | 0.424435 | − | 0.905458i | \(-0.360473\pi\) | ||||
0.424435 | + | 0.905458i | \(0.360473\pi\) | |||||||
\(500\) | −1.71119 | −0.0765269 | ||||||||
\(501\) | 4.74324 | 0.211912 | ||||||||
\(502\) | −5.09653 | −0.227469 | ||||||||
\(503\) | −20.5865 | −0.917906 | −0.458953 | − | 0.888461i | \(-0.651775\pi\) | ||||
−0.458953 | + | 0.888461i | \(0.651775\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −10.8839 | −0.484326 | ||||||||
\(506\) | 2.78492 | 0.123805 | ||||||||
\(507\) | −10.4673 | −0.464871 | ||||||||
\(508\) | −12.8260 | −0.569062 | ||||||||
\(509\) | −24.6176 | −1.09115 | −0.545577 | − | 0.838061i | \(-0.683689\pi\) | ||||
−0.545577 | + | 0.838061i | \(0.683689\pi\) | |||||||
\(510\) | 0.514496 | 0.0227823 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 21.7214 | 0.959959 | ||||||||
\(513\) | 0.301599 | 0.0133159 | ||||||||
\(514\) | 5.05831 | 0.223112 | ||||||||
\(515\) | 2.06192 | 0.0908592 | ||||||||
\(516\) | 0.529324 | 0.0233022 | ||||||||
\(517\) | −6.44995 | −0.283668 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −23.5426 | −1.03341 | ||||||||
\(520\) | −3.17399 | −0.139189 | ||||||||
\(521\) | −24.1063 | −1.05612 | −0.528058 | − | 0.849209i | \(-0.677079\pi\) | ||||
−0.528058 | + | 0.849209i | \(0.677079\pi\) | |||||||
\(522\) | 3.16823 | 0.138670 | ||||||||
\(523\) | −37.5949 | −1.64391 | −0.821955 | − | 0.569553i | \(-0.807116\pi\) | ||||
−0.821955 | + | 0.569553i | \(0.807116\pi\) | |||||||
\(524\) | −28.0438 | −1.22510 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −5.35861 | −0.233647 | ||||||||
\(527\) | 2.18395 | 0.0951345 | ||||||||
\(528\) | 2.35057 | 0.102295 | ||||||||
\(529\) | 3.85465 | 0.167594 | ||||||||
\(530\) | −6.69893 | −0.290983 | ||||||||
\(531\) | 10.5444 | 0.457590 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 17.9512 | 0.777553 | ||||||||
\(534\) | 8.30348 | 0.359327 | ||||||||
\(535\) | 7.26476 | 0.314083 | ||||||||
\(536\) | 9.81799 | 0.424073 | ||||||||
\(537\) | 3.34159 | 0.144200 | ||||||||
\(538\) | 7.51953 | 0.324190 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −1.71119 | −0.0736380 | ||||||||
\(541\) | −14.3326 | −0.616206 | −0.308103 | − | 0.951353i | \(-0.599694\pi\) | ||||
−0.308103 | + | 0.951353i | \(0.599694\pi\) | |||||||
\(542\) | 9.61177 | 0.412861 | ||||||||
\(543\) | 13.2594 | 0.569013 | ||||||||
\(544\) | 5.02815 | 0.215580 | ||||||||
\(545\) | 17.0326 | 0.729595 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 37.3357 | 1.59636 | 0.798179 | − | 0.602421i | \(-0.205797\pi\) | ||||
0.798179 | + | 0.602421i | \(0.205797\pi\) | |||||||
\(548\) | −10.0065 | −0.427458 | ||||||||
\(549\) | −10.9417 | −0.466980 | ||||||||
\(550\) | 0.537407 | 0.0229151 | ||||||||
\(551\) | 1.77804 | 0.0757472 | ||||||||
\(552\) | −10.3354 | −0.439903 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −2.19297 | −0.0931705 | ||||||||
\(555\) | −9.90813 | −0.420577 | ||||||||
\(556\) | −38.2819 | −1.62351 | ||||||||
\(557\) | 1.72433 | 0.0730622 | 0.0365311 | − | 0.999333i | \(-0.488369\pi\) | ||||
0.0365311 | + | 0.999333i | \(0.488369\pi\) | |||||||
\(558\) | 1.22594 | 0.0518980 | ||||||||
\(559\) | −0.492278 | −0.0208211 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0.957367 | 0.0404201 | ||||||||
\(562\) | 0.795543 | 0.0335580 | ||||||||
\(563\) | −27.1865 | −1.14577 | −0.572887 | − | 0.819634i | \(-0.694177\pi\) | ||||
−0.572887 | + | 0.819634i | \(0.694177\pi\) | |||||||
\(564\) | 11.0371 | 0.464746 | ||||||||
\(565\) | 16.2281 | 0.682720 | ||||||||
\(566\) | −12.0029 | −0.504521 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 33.2501 | 1.39514 | ||||||||
\(569\) | 10.1029 | 0.423534 | 0.211767 | − | 0.977320i | \(-0.432078\pi\) | ||||
0.211767 | + | 0.977320i | \(0.432078\pi\) | |||||||
\(570\) | 0.162081 | 0.00678884 | ||||||||
\(571\) | −37.7805 | −1.58106 | −0.790532 | − | 0.612421i | \(-0.790196\pi\) | ||||
−0.790532 | + | 0.612421i | \(0.790196\pi\) | |||||||
\(572\) | −2.72325 | −0.113865 | ||||||||
\(573\) | 21.6487 | 0.904388 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 5.18215 | 0.216110 | ||||||||
\(576\) | −1.87864 | −0.0782768 | ||||||||
\(577\) | 35.9847 | 1.49806 | 0.749031 | − | 0.662535i | \(-0.230519\pi\) | ||||
0.749031 | + | 0.662535i | \(0.230519\pi\) | |||||||
\(578\) | −8.64336 | −0.359516 | ||||||||
\(579\) | 19.5443 | 0.812234 | ||||||||
\(580\) | −10.0882 | −0.418888 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 9.80840 | 0.406571 | ||||||||
\(583\) | −12.4653 | −0.516259 | ||||||||
\(584\) | 25.0054 | 1.03473 | ||||||||
\(585\) | 1.59143 | 0.0657976 | ||||||||
\(586\) | −1.98114 | −0.0818403 | ||||||||
\(587\) | −29.1862 | −1.20464 | −0.602322 | − | 0.798253i | \(-0.705758\pi\) | ||||
−0.602322 | + | 0.798253i | \(0.705758\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0.688009 | 0.0283489 | ||||||||
\(590\) | 5.66666 | 0.233293 | ||||||||
\(591\) | 14.0102 | 0.576305 | ||||||||
\(592\) | −23.2898 | −0.957203 | ||||||||
\(593\) | −20.2522 | −0.831660 | −0.415830 | − | 0.909442i | \(-0.636509\pi\) | ||||
−0.415830 | + | 0.909442i | \(0.636509\pi\) | |||||||
\(594\) | 0.537407 | 0.0220501 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −37.6801 | −1.54344 | ||||||||
\(597\) | −9.00502 | −0.368551 | ||||||||
\(598\) | 4.43202 | 0.181239 | ||||||||
\(599\) | 0.363495 | 0.0148520 | 0.00742600 | − | 0.999972i | \(-0.497636\pi\) | ||||
0.00742600 | + | 0.999972i | \(0.497636\pi\) | |||||||
\(600\) | −1.99442 | −0.0814220 | ||||||||
\(601\) | −31.8648 | −1.29979 | −0.649896 | − | 0.760023i | \(-0.725187\pi\) | ||||
−0.649896 | + | 0.760023i | \(0.725187\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −4.92273 | −0.200469 | ||||||||
\(604\) | 0.502217 | 0.0204349 | ||||||||
\(605\) | 1.00000 | 0.0406558 | ||||||||
\(606\) | −5.84907 | −0.237602 | ||||||||
\(607\) | 39.4818 | 1.60252 | 0.801258 | − | 0.598318i | \(-0.204164\pi\) | ||||
0.801258 | + | 0.598318i | \(0.204164\pi\) | |||||||
\(608\) | 1.58401 | 0.0642402 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −5.88015 | −0.238080 | ||||||||
\(611\) | −10.2647 | −0.415263 | ||||||||
\(612\) | −1.63824 | −0.0662220 | ||||||||
\(613\) | −38.1007 | −1.53887 | −0.769436 | − | 0.638724i | \(-0.779463\pi\) | ||||
−0.769436 | + | 0.638724i | \(0.779463\pi\) | |||||||
\(614\) | −1.36539 | −0.0551027 | ||||||||
\(615\) | 11.2799 | 0.454850 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 22.7915 | 0.917552 | 0.458776 | − | 0.888552i | \(-0.348288\pi\) | ||||
0.458776 | + | 0.888552i | \(0.348288\pi\) | |||||||
\(618\) | 1.10809 | 0.0445740 | ||||||||
\(619\) | 40.4851 | 1.62723 | 0.813617 | − | 0.581401i | \(-0.197495\pi\) | ||||
0.813617 | + | 0.581401i | \(0.197495\pi\) | |||||||
\(620\) | −3.90358 | −0.156772 | ||||||||
\(621\) | 5.18215 | 0.207952 | ||||||||
\(622\) | −2.72215 | −0.109148 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 3.74077 | 0.149751 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0.337832 | 0.0135025 | ||||||||
\(627\) | 0.301599 | 0.0120447 | ||||||||
\(628\) | 7.07997 | 0.282522 | ||||||||
\(629\) | −9.48573 | −0.378221 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −35.2789 | −1.40443 | −0.702216 | − | 0.711964i | \(-0.747806\pi\) | ||||
−0.702216 | + | 0.711964i | \(0.747806\pi\) | |||||||
\(632\) | −16.3120 | −0.648858 | ||||||||
\(633\) | 8.40675 | 0.334138 | ||||||||
\(634\) | 0.0977805 | 0.00388336 | ||||||||
\(635\) | 7.49535 | 0.297444 | ||||||||
\(636\) | 21.3305 | 0.845809 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 3.16823 | 0.125431 | ||||||||
\(639\) | −16.6715 | −0.659516 | ||||||||
\(640\) | −11.5137 | −0.455119 | ||||||||
\(641\) | 8.37635 | 0.330846 | 0.165423 | − | 0.986223i | \(-0.447101\pi\) | ||||
0.165423 | + | 0.986223i | \(0.447101\pi\) | |||||||
\(642\) | 3.90414 | 0.154084 | ||||||||
\(643\) | −6.75016 | −0.266200 | −0.133100 | − | 0.991103i | \(-0.542493\pi\) | ||||
−0.133100 | + | 0.991103i | \(0.542493\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −0.309330 | −0.0121799 | ||||||||
\(646\) | 0.155171 | 0.00610514 | ||||||||
\(647\) | −18.3045 | −0.719625 | −0.359812 | − | 0.933025i | \(-0.617159\pi\) | ||||
−0.359812 | + | 0.933025i | \(0.617159\pi\) | |||||||
\(648\) | −1.99442 | −0.0783483 | ||||||||
\(649\) | 10.5444 | 0.413905 | ||||||||
\(650\) | 0.855247 | 0.0335455 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 10.5964 | 0.414985 | ||||||||
\(653\) | −34.9119 | −1.36621 | −0.683104 | − | 0.730321i | \(-0.739370\pi\) | ||||
−0.683104 | + | 0.730321i | \(0.739370\pi\) | |||||||
\(654\) | 9.15342 | 0.357927 | ||||||||
\(655\) | 16.3884 | 0.640349 | ||||||||
\(656\) | 26.5142 | 1.03521 | ||||||||
\(657\) | −12.5376 | −0.489140 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −22.5509 | −0.878456 | −0.439228 | − | 0.898376i | \(-0.644748\pi\) | ||||
−0.439228 | + | 0.898376i | \(0.644748\pi\) | |||||||
\(660\) | −1.71119 | −0.0666081 | ||||||||
\(661\) | −11.6028 | −0.451297 | −0.225649 | − | 0.974209i | \(-0.572450\pi\) | ||||
−0.225649 | + | 0.974209i | \(0.572450\pi\) | |||||||
\(662\) | 14.4541 | 0.561776 | ||||||||
\(663\) | 1.52358 | 0.0591711 | ||||||||
\(664\) | 9.38912 | 0.364369 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −5.32470 | −0.206328 | ||||||||
\(667\) | 30.5508 | 1.18293 | ||||||||
\(668\) | −8.11660 | −0.314041 | ||||||||
\(669\) | −3.96213 | −0.153185 | ||||||||
\(670\) | −2.64551 | −0.102205 | ||||||||
\(671\) | −10.9417 | −0.422400 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −9.60158 | −0.370114 | −0.185057 | − | 0.982728i | \(-0.559247\pi\) | ||||
−0.185057 | + | 0.982728i | \(0.559247\pi\) | |||||||
\(674\) | −10.8120 | −0.416461 | ||||||||
\(675\) | 1.00000 | 0.0384900 | ||||||||
\(676\) | 17.9117 | 0.688910 | ||||||||
\(677\) | 3.45175 | 0.132662 | 0.0663308 | − | 0.997798i | \(-0.478871\pi\) | ||||
0.0663308 | + | 0.997798i | \(0.478871\pi\) | |||||||
\(678\) | 8.72109 | 0.334931 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −1.90940 | −0.0732220 | ||||||||
\(681\) | 4.72377 | 0.181015 | ||||||||
\(682\) | 1.22594 | 0.0469436 | ||||||||
\(683\) | −4.50424 | −0.172350 | −0.0861750 | − | 0.996280i | \(-0.527464\pi\) | ||||
−0.0861750 | + | 0.996280i | \(0.527464\pi\) | |||||||
\(684\) | −0.516093 | −0.0197333 | ||||||||
\(685\) | 5.84770 | 0.223429 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −3.44504 | −0.131436 | ||||||||
\(688\) | −0.727102 | −0.0277205 | ||||||||
\(689\) | −19.8376 | −0.755753 | ||||||||
\(690\) | 2.78492 | 0.106020 | ||||||||
\(691\) | 16.0030 | 0.608781 | 0.304391 | − | 0.952547i | \(-0.401547\pi\) | ||||
0.304391 | + | 0.952547i | \(0.401547\pi\) | |||||||
\(692\) | 40.2860 | 1.53144 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −1.18319 | −0.0449133 | ||||||||
\(695\) | 22.3715 | 0.848598 | ||||||||
\(696\) | −11.7579 | −0.445683 | ||||||||
\(697\) | 10.7990 | 0.409042 | ||||||||
\(698\) | −13.0767 | −0.494962 | ||||||||
\(699\) | 17.5457 | 0.663639 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −27.0747 | −1.02260 | −0.511299 | − | 0.859403i | \(-0.670835\pi\) | ||||
−0.511299 | + | 0.859403i | \(0.670835\pi\) | |||||||
\(702\) | 0.855247 | 0.0322792 | ||||||||
\(703\) | −2.98828 | −0.112705 | ||||||||
\(704\) | −1.87864 | −0.0708041 | ||||||||
\(705\) | −6.44995 | −0.242919 | ||||||||
\(706\) | 5.42000 | 0.203984 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −18.0436 | −0.678119 | ||||||||
\(709\) | 4.02201 | 0.151050 | 0.0755248 | − | 0.997144i | \(-0.475937\pi\) | ||||
0.0755248 | + | 0.997144i | \(0.475937\pi\) | |||||||
\(710\) | −8.95941 | −0.336241 | ||||||||
\(711\) | 8.17883 | 0.306730 | ||||||||
\(712\) | −30.8158 | −1.15487 | ||||||||
\(713\) | 11.8215 | 0.442720 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.59143 | 0.0595162 | ||||||||
\(716\) | −5.71811 | −0.213696 | ||||||||
\(717\) | −22.3788 | −0.835753 | ||||||||
\(718\) | 5.49838 | 0.205198 | ||||||||
\(719\) | −29.1357 | −1.08658 | −0.543289 | − | 0.839546i | \(-0.682821\pi\) | ||||
−0.543289 | + | 0.839546i | \(0.682821\pi\) | |||||||
\(720\) | 2.35057 | 0.0876006 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −10.1619 | −0.378185 | ||||||||
\(723\) | −12.6591 | −0.470796 | ||||||||
\(724\) | −22.6893 | −0.843242 | ||||||||
\(725\) | 5.89540 | 0.218950 | ||||||||
\(726\) | 0.537407 | 0.0199451 | ||||||||
\(727\) | 13.5927 | 0.504127 | 0.252064 | − | 0.967711i | \(-0.418891\pi\) | ||||
0.252064 | + | 0.967711i | \(0.418891\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −6.73782 | −0.249378 | ||||||||
\(731\) | −0.296143 | −0.0109532 | ||||||||
\(732\) | 18.7234 | 0.692035 | ||||||||
\(733\) | 42.9606 | 1.58679 | 0.793393 | − | 0.608710i | \(-0.208313\pi\) | ||||
0.793393 | + | 0.608710i | \(0.208313\pi\) | |||||||
\(734\) | −13.7659 | −0.508108 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 27.2169 | 1.00323 | ||||||||
\(737\) | −4.92273 | −0.181331 | ||||||||
\(738\) | 6.06191 | 0.223142 | ||||||||
\(739\) | 34.1334 | 1.25562 | 0.627809 | − | 0.778367i | \(-0.283952\pi\) | ||||
0.627809 | + | 0.778367i | \(0.283952\pi\) | |||||||
\(740\) | 16.9547 | 0.623268 | ||||||||
\(741\) | 0.479973 | 0.0176323 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 19.1862 | 0.703874 | 0.351937 | − | 0.936024i | \(-0.385523\pi\) | ||||
0.351937 | + | 0.936024i | \(0.385523\pi\) | |||||||
\(744\) | −4.54969 | −0.166800 | ||||||||
\(745\) | 22.0198 | 0.806742 | ||||||||
\(746\) | 13.8638 | 0.507588 | ||||||||
\(747\) | −4.70769 | −0.172245 | ||||||||
\(748\) | −1.63824 | −0.0599000 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0.537407 | 0.0196233 | ||||||||
\(751\) | 26.8910 | 0.981267 | 0.490633 | − | 0.871366i | \(-0.336765\pi\) | ||||
0.490633 | + | 0.871366i | \(0.336765\pi\) | |||||||
\(752\) | −15.1611 | −0.552867 | ||||||||
\(753\) | −9.48355 | −0.345600 | ||||||||
\(754\) | 5.04202 | 0.183620 | ||||||||
\(755\) | −0.293489 | −0.0106812 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 36.8100 | 1.33788 | 0.668941 | − | 0.743316i | \(-0.266748\pi\) | ||||
0.668941 | + | 0.743316i | \(0.266748\pi\) | |||||||
\(758\) | 10.1514 | 0.368715 | ||||||||
\(759\) | 5.18215 | 0.188100 | ||||||||
\(760\) | −0.601515 | −0.0218192 | ||||||||
\(761\) | −7.34622 | −0.266300 | −0.133150 | − | 0.991096i | \(-0.542509\pi\) | ||||
−0.133150 | + | 0.991096i | \(0.542509\pi\) | |||||||
\(762\) | 4.02806 | 0.145921 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −37.0451 | −1.34025 | ||||||||
\(765\) | 0.957367 | 0.0346137 | ||||||||
\(766\) | −15.4619 | −0.558661 | ||||||||
\(767\) | 16.7808 | 0.605918 | ||||||||
\(768\) | −2.43027 | −0.0876947 | ||||||||
\(769\) | 33.4817 | 1.20738 | 0.603690 | − | 0.797219i | \(-0.293697\pi\) | ||||
0.603690 | + | 0.797219i | \(0.293697\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 9.41243 | 0.338980 | ||||||||
\(772\) | −33.4441 | −1.20368 | ||||||||
\(773\) | −17.1652 | −0.617389 | −0.308694 | − | 0.951161i | \(-0.599892\pi\) | ||||
−0.308694 | + | 0.951161i | \(0.599892\pi\) | |||||||
\(774\) | −0.166236 | −0.00597524 | ||||||||
\(775\) | 2.28121 | 0.0819433 | ||||||||
\(776\) | −36.4009 | −1.30672 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 8.14366 | 0.291964 | ||||||||
\(779\) | 3.40200 | 0.121889 | ||||||||
\(780\) | −2.72325 | −0.0975079 | ||||||||
\(781\) | −16.6715 | −0.596555 | ||||||||
\(782\) | 2.66620 | 0.0953430 | ||||||||
\(783\) | 5.89540 | 0.210684 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −4.13745 | −0.147672 | ||||||||
\(786\) | 8.80727 | 0.314145 | ||||||||
\(787\) | −11.5253 | −0.410834 | −0.205417 | − | 0.978675i | \(-0.565855\pi\) | ||||
−0.205417 | + | 0.978675i | \(0.565855\pi\) | |||||||
\(788\) | −23.9742 | −0.854047 | ||||||||
\(789\) | −9.97123 | −0.354985 | ||||||||
\(790\) | 4.39536 | 0.156380 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −1.99442 | −0.0708687 | ||||||||
\(793\) | −17.4130 | −0.618352 | ||||||||
\(794\) | 1.26640 | 0.0449428 | ||||||||
\(795\) | −12.4653 | −0.442098 | ||||||||
\(796\) | 15.4093 | 0.546169 | ||||||||
\(797\) | 27.8120 | 0.985152 | 0.492576 | − | 0.870269i | \(-0.336055\pi\) | ||||
0.492576 | + | 0.870269i | \(0.336055\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −6.17497 | −0.218455 | ||||||||
\(800\) | 5.25206 | 0.185688 | ||||||||
\(801\) | 15.4510 | 0.545934 | ||||||||
\(802\) | 8.31144 | 0.293487 | ||||||||
\(803\) | −12.5376 | −0.442444 | ||||||||
\(804\) | 8.42373 | 0.297082 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 1.95099 | 0.0687208 | ||||||||
\(807\) | 13.9922 | 0.492550 | ||||||||
\(808\) | 21.7070 | 0.763651 | ||||||||
\(809\) | −9.79928 | −0.344524 | −0.172262 | − | 0.985051i | \(-0.555108\pi\) | ||||
−0.172262 | + | 0.985051i | \(0.555108\pi\) | |||||||
\(810\) | 0.537407 | 0.0188826 | ||||||||
\(811\) | −28.0466 | −0.984849 | −0.492424 | − | 0.870355i | \(-0.663889\pi\) | ||||
−0.492424 | + | 0.870355i | \(0.663889\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 17.8855 | 0.627270 | ||||||||
\(814\) | −5.32470 | −0.186631 | ||||||||
\(815\) | −6.19238 | −0.216909 | ||||||||
\(816\) | 2.25036 | 0.0787783 | ||||||||
\(817\) | −0.0932935 | −0.00326393 | ||||||||
\(818\) | −2.72444 | −0.0952577 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −19.3021 | −0.674059 | ||||||||
\(821\) | 2.89729 | 0.101116 | 0.0505581 | − | 0.998721i | \(-0.483900\pi\) | ||||
0.0505581 | + | 0.998721i | \(0.483900\pi\) | |||||||
\(822\) | 3.14260 | 0.109611 | ||||||||
\(823\) | −5.71777 | −0.199309 | −0.0996544 | − | 0.995022i | \(-0.531774\pi\) | ||||
−0.0996544 | + | 0.995022i | \(0.531774\pi\) | |||||||
\(824\) | −4.11235 | −0.143260 | ||||||||
\(825\) | 1.00000 | 0.0348155 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 14.6027 | 0.507786 | 0.253893 | − | 0.967232i | \(-0.418289\pi\) | ||||
0.253893 | + | 0.967232i | \(0.418289\pi\) | |||||||
\(828\) | −8.86766 | −0.308172 | ||||||||
\(829\) | −18.5862 | −0.645524 | −0.322762 | − | 0.946480i | \(-0.604611\pi\) | ||||
−0.322762 | + | 0.946480i | \(0.604611\pi\) | |||||||
\(830\) | −2.52995 | −0.0878157 | ||||||||
\(831\) | −4.08065 | −0.141556 | ||||||||
\(832\) | −2.98973 | −0.103650 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 12.0226 | 0.416308 | ||||||||
\(835\) | 4.74324 | 0.164147 | ||||||||
\(836\) | −0.516093 | −0.0178495 | ||||||||
\(837\) | 2.28121 | 0.0788500 | ||||||||
\(838\) | 21.0378 | 0.726740 | ||||||||
\(839\) | 7.03801 | 0.242979 | 0.121490 | − | 0.992593i | \(-0.461233\pi\) | ||||
0.121490 | + | 0.992593i | \(0.461233\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 5.75575 | 0.198474 | ||||||||
\(842\) | 8.06246 | 0.277851 | ||||||||
\(843\) | 1.48034 | 0.0509855 | ||||||||
\(844\) | −14.3856 | −0.495172 | ||||||||
\(845\) | −10.4673 | −0.360088 | ||||||||
\(846\) | −3.46625 | −0.119172 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −29.3005 | −1.00618 | ||||||||
\(849\) | −22.3349 | −0.766532 | ||||||||
\(850\) | 0.514496 | 0.0176471 | ||||||||
\(851\) | −51.3454 | −1.76010 | ||||||||
\(852\) | 28.5282 | 0.977361 | ||||||||
\(853\) | 9.35268 | 0.320230 | 0.160115 | − | 0.987098i | \(-0.448814\pi\) | ||||
0.160115 | + | 0.987098i | \(0.448814\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0.301599 | 0.0103145 | ||||||||
\(856\) | −14.4890 | −0.495224 | ||||||||
\(857\) | −50.5947 | −1.72828 | −0.864141 | − | 0.503250i | \(-0.832137\pi\) | ||||
−0.864141 | + | 0.503250i | \(0.832137\pi\) | |||||||
\(858\) | 0.855247 | 0.0291976 | ||||||||
\(859\) | −10.8366 | −0.369740 | −0.184870 | − | 0.982763i | \(-0.559186\pi\) | ||||
−0.184870 | + | 0.982763i | \(0.559186\pi\) | |||||||
\(860\) | 0.529324 | 0.0180498 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −9.13728 | −0.311217 | ||||||||
\(863\) | 34.7467 | 1.18279 | 0.591396 | − | 0.806381i | \(-0.298577\pi\) | ||||
0.591396 | + | 0.806381i | \(0.298577\pi\) | |||||||
\(864\) | 5.25206 | 0.178679 | ||||||||
\(865\) | −23.5426 | −0.800473 | ||||||||
\(866\) | 10.8782 | 0.369656 | ||||||||
\(867\) | −16.0834 | −0.546223 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 8.17883 | 0.277448 | ||||||||
\(870\) | 3.16823 | 0.107413 | ||||||||
\(871\) | −7.83418 | −0.265451 | ||||||||
\(872\) | −33.9701 | −1.15037 | ||||||||
\(873\) | 18.2513 | 0.617714 | ||||||||
\(874\) | 0.839929 | 0.0284110 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 21.4543 | 0.724875 | ||||||||
\(877\) | −40.3760 | −1.36340 | −0.681701 | − | 0.731631i | \(-0.738759\pi\) | ||||
−0.681701 | + | 0.731631i | \(0.738759\pi\) | |||||||
\(878\) | −4.95828 | −0.167334 | ||||||||
\(879\) | −3.68648 | −0.124342 | ||||||||
\(880\) | 2.35057 | 0.0792377 | ||||||||
\(881\) | −45.4623 | −1.53166 | −0.765832 | − | 0.643040i | \(-0.777673\pi\) | ||||
−0.765832 | + | 0.643040i | \(0.777673\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 32.6461 | 1.09863 | 0.549314 | − | 0.835616i | \(-0.314889\pi\) | ||||
0.549314 | + | 0.835616i | \(0.314889\pi\) | |||||||
\(884\) | −2.60715 | −0.0876879 | ||||||||
\(885\) | 10.5444 | 0.354447 | ||||||||
\(886\) | 18.4022 | 0.618235 | ||||||||
\(887\) | 37.1818 | 1.24844 | 0.624222 | − | 0.781247i | \(-0.285416\pi\) | ||||
0.624222 | + | 0.781247i | \(0.285416\pi\) | |||||||
\(888\) | 19.7610 | 0.663136 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 8.30348 | 0.278333 | ||||||||
\(891\) | 1.00000 | 0.0335013 | ||||||||
\(892\) | 6.77997 | 0.227010 | ||||||||
\(893\) | −1.94530 | −0.0650968 | ||||||||
\(894\) | 11.8336 | 0.395774 | ||||||||
\(895\) | 3.34159 | 0.111697 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 8.24703 | 0.275360 | ||||||||
\(898\) | −1.83043 | −0.0610822 | ||||||||
\(899\) | 13.4486 | 0.448537 | ||||||||
\(900\) | −1.71119 | −0.0570398 | ||||||||
\(901\) | −11.9338 | −0.397574 | ||||||||
\(902\) | 6.06191 | 0.201839 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −32.3656 | −1.07647 | ||||||||
\(905\) | 13.2594 | 0.440756 | ||||||||
\(906\) | −0.157723 | −0.00524001 | ||||||||
\(907\) | −19.8449 | −0.658938 | −0.329469 | − | 0.944166i | \(-0.606870\pi\) | ||||
−0.329469 | + | 0.944166i | \(0.606870\pi\) | |||||||
\(908\) | −8.08328 | −0.268253 | ||||||||
\(909\) | −10.8839 | −0.360995 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 11.6268 | 0.385214 | 0.192607 | − | 0.981276i | \(-0.438306\pi\) | ||||
0.192607 | + | 0.981276i | \(0.438306\pi\) | |||||||
\(912\) | 0.708928 | 0.0234750 | ||||||||
\(913\) | −4.70769 | −0.155802 | ||||||||
\(914\) | −10.6789 | −0.353225 | ||||||||
\(915\) | −10.9417 | −0.361721 | ||||||||
\(916\) | 5.89512 | 0.194780 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0.514496 | 0.0169809 | ||||||||
\(919\) | 10.0408 | 0.331214 | 0.165607 | − | 0.986192i | \(-0.447042\pi\) | ||||
0.165607 | + | 0.986192i | \(0.447042\pi\) | |||||||
\(920\) | −10.3354 | −0.340748 | ||||||||
\(921\) | −2.54070 | −0.0837189 | ||||||||
\(922\) | −8.69967 | −0.286509 | ||||||||
\(923\) | −26.5316 | −0.873299 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −9.90813 | −0.325777 | ||||||||
\(926\) | 20.1785 | 0.663107 | ||||||||
\(927\) | 2.06192 | 0.0677225 | ||||||||
\(928\) | 30.9630 | 1.01641 | ||||||||
\(929\) | −26.9895 | −0.885496 | −0.442748 | − | 0.896646i | \(-0.645996\pi\) | ||||
−0.442748 | + | 0.896646i | \(0.645996\pi\) | |||||||
\(930\) | 1.22594 | 0.0402001 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −30.0241 | −0.983471 | ||||||||
\(933\) | −5.06535 | −0.165832 | ||||||||
\(934\) | 8.92738 | 0.292113 | ||||||||
\(935\) | 0.957367 | 0.0313093 | ||||||||
\(936\) | −3.17399 | −0.103745 | ||||||||
\(937\) | 34.3873 | 1.12338 | 0.561691 | − | 0.827347i | \(-0.310151\pi\) | ||||
0.561691 | + | 0.827347i | \(0.310151\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0.628632 | 0.0205146 | ||||||||
\(940\) | 11.0371 | 0.359991 | ||||||||
\(941\) | 30.4791 | 0.993589 | 0.496794 | − | 0.867868i | \(-0.334510\pi\) | ||||
0.496794 | + | 0.867868i | \(0.334510\pi\) | |||||||
\(942\) | −2.22349 | −0.0724454 | ||||||||
\(943\) | 58.4541 | 1.90353 | ||||||||
\(944\) | 24.7854 | 0.806697 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −0.166236 | −0.00540481 | ||||||||
\(947\) | 60.0385 | 1.95099 | 0.975495 | − | 0.220023i | \(-0.0706133\pi\) | ||||
0.975495 | + | 0.220023i | \(0.0706133\pi\) | |||||||
\(948\) | −13.9956 | −0.454555 | ||||||||
\(949\) | −19.9528 | −0.647695 | ||||||||
\(950\) | 0.162081 | 0.00525861 | ||||||||
\(951\) | 0.181949 | 0.00590009 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −11.7675 | −0.381188 | −0.190594 | − | 0.981669i | \(-0.561041\pi\) | ||||
−0.190594 | + | 0.981669i | \(0.561041\pi\) | |||||||
\(954\) | −6.69893 | −0.216886 | ||||||||
\(955\) | 21.6487 | 0.700536 | ||||||||
\(956\) | 38.2945 | 1.23853 | ||||||||
\(957\) | 5.89540 | 0.190571 | ||||||||
\(958\) | −14.9934 | −0.484415 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −1.87864 | −0.0606330 | ||||||||
\(961\) | −25.7961 | −0.832132 | ||||||||
\(962\) | −8.47390 | −0.273210 | ||||||||
\(963\) | 7.26476 | 0.234104 | ||||||||
\(964\) | 21.6621 | 0.697690 | ||||||||
\(965\) | 19.5443 | 0.629154 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −15.6712 | −0.503953 | −0.251976 | − | 0.967733i | \(-0.581081\pi\) | ||||
−0.251976 | + | 0.967733i | \(0.581081\pi\) | |||||||
\(968\) | −1.99442 | −0.0641032 | ||||||||
\(969\) | 0.288741 | 0.00927569 | ||||||||
\(970\) | 9.80840 | 0.314929 | ||||||||
\(971\) | −39.0248 | −1.25237 | −0.626183 | − | 0.779676i | \(-0.715384\pi\) | ||||
−0.626183 | + | 0.779676i | \(0.715384\pi\) | |||||||
\(972\) | −1.71119 | −0.0548866 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0.171886 | 0.00550759 | ||||||||
\(975\) | 1.59143 | 0.0509666 | ||||||||
\(976\) | −25.7192 | −0.823252 | ||||||||
\(977\) | −52.9257 | −1.69324 | −0.846621 | − | 0.532196i | \(-0.821367\pi\) | ||||
−0.846621 | + | 0.532196i | \(0.821367\pi\) | |||||||
\(978\) | −3.32783 | −0.106412 | ||||||||
\(979\) | 15.4510 | 0.493816 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 17.0326 | 0.543808 | ||||||||
\(982\) | 13.2425 | 0.422584 | ||||||||
\(983\) | 7.76273 | 0.247592 | 0.123796 | − | 0.992308i | \(-0.460493\pi\) | ||||
0.123796 | + | 0.992308i | \(0.460493\pi\) | |||||||
\(984\) | −22.4969 | −0.717175 | ||||||||
\(985\) | 14.0102 | 0.446404 | ||||||||
\(986\) | 3.03316 | 0.0965955 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −0.821327 | −0.0261299 | ||||||||
\(989\) | −1.60299 | −0.0509723 | ||||||||
\(990\) | 0.537407 | 0.0170799 | ||||||||
\(991\) | 13.6086 | 0.432290 | 0.216145 | − | 0.976361i | \(-0.430652\pi\) | ||||
0.216145 | + | 0.976361i | \(0.430652\pi\) | |||||||
\(992\) | 11.9810 | 0.380398 | ||||||||
\(993\) | 26.8960 | 0.853520 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −9.00502 | −0.285478 | ||||||||
\(996\) | 8.05577 | 0.255257 | ||||||||
\(997\) | 46.0890 | 1.45965 | 0.729827 | − | 0.683632i | \(-0.239601\pi\) | ||||
0.729827 | + | 0.683632i | \(0.239601\pi\) | |||||||
\(998\) | 10.1905 | 0.322574 | ||||||||
\(999\) | −9.90813 | −0.313480 |
(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 | 8085.2.a.cp.1.8 | yes | 14 | |
7.6 | odd | 2 | 8085.2.a.co.1.8 | ✓ | 14 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8085.2.a.co.1.8 | ✓ | 14 | 7.6 | odd | 2 | ||
8085.2.a.cp.1.8 | yes | 14 | 1.1 | even | 1 | trivial |