Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8034,2,Mod(1,8034)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8034, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8034.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8034 = 2 \cdot 3 \cdot 13 \cdot 103 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8034.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: | \(64.1518129839\) |
Analytic rank: | \(1\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{7} - 12x^{6} + 12x^{5} + 43x^{4} - 38x^{3} - 49x^{2} + 23x + 20 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Root | \(-2.01106\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8034.1 |
$q$-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 | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −0.612396 | −0.273872 | −0.136936 | − | 0.990580i | \(-0.543725\pi\) | ||||
−0.136936 | + | 0.990580i | \(0.543725\pi\) | |||||||
\(6\) | 1.00000 | 0.408248 | ||||||||
\(7\) | −3.48353 | −1.31665 | −0.658326 | − | 0.752733i | \(-0.728735\pi\) | ||||
−0.658326 | + | 0.752733i | \(0.728735\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −0.612396 | −0.193656 | ||||||||
\(11\) | 5.85219 | 1.76450 | 0.882251 | − | 0.470780i | \(-0.156027\pi\) | ||||
0.882251 | + | 0.470780i | \(0.156027\pi\) | |||||||
\(12\) | 1.00000 | 0.288675 | ||||||||
\(13\) | 1.00000 | 0.277350 | ||||||||
\(14\) | −3.48353 | −0.931013 | ||||||||
\(15\) | −0.612396 | −0.158120 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −4.41285 | −1.07027 | −0.535136 | − | 0.844766i | \(-0.679740\pi\) | ||||
−0.535136 | + | 0.844766i | \(0.679740\pi\) | |||||||
\(18\) | 1.00000 | 0.235702 | ||||||||
\(19\) | −6.11628 | −1.40317 | −0.701585 | − | 0.712585i | \(-0.747524\pi\) | ||||
−0.701585 | + | 0.712585i | \(0.747524\pi\) | |||||||
\(20\) | −0.612396 | −0.136936 | ||||||||
\(21\) | −3.48353 | −0.760169 | ||||||||
\(22\) | 5.85219 | 1.24769 | ||||||||
\(23\) | 5.11376 | 1.06629 | 0.533146 | − | 0.846023i | \(-0.321010\pi\) | ||||
0.533146 | + | 0.846023i | \(0.321010\pi\) | |||||||
\(24\) | 1.00000 | 0.204124 | ||||||||
\(25\) | −4.62497 | −0.924994 | ||||||||
\(26\) | 1.00000 | 0.196116 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | −3.48353 | −0.658326 | ||||||||
\(29\) | −7.19584 | −1.33623 | −0.668117 | − | 0.744056i | \(-0.732899\pi\) | ||||
−0.668117 | + | 0.744056i | \(0.732899\pi\) | |||||||
\(30\) | −0.612396 | −0.111808 | ||||||||
\(31\) | −4.63030 | −0.831626 | −0.415813 | − | 0.909450i | \(-0.636503\pi\) | ||||
−0.415813 | + | 0.909450i | \(0.636503\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 5.85219 | 1.01874 | ||||||||
\(34\) | −4.41285 | −0.756797 | ||||||||
\(35\) | 2.13330 | 0.360593 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | −4.90640 | −0.806607 | −0.403304 | − | 0.915066i | \(-0.632138\pi\) | ||||
−0.403304 | + | 0.915066i | \(0.632138\pi\) | |||||||
\(38\) | −6.11628 | −0.992192 | ||||||||
\(39\) | 1.00000 | 0.160128 | ||||||||
\(40\) | −0.612396 | −0.0968282 | ||||||||
\(41\) | −2.73338 | −0.426883 | −0.213441 | − | 0.976956i | \(-0.568467\pi\) | ||||
−0.213441 | + | 0.976956i | \(0.568467\pi\) | |||||||
\(42\) | −3.48353 | −0.537521 | ||||||||
\(43\) | −6.64391 | −1.01319 | −0.506594 | − | 0.862185i | \(-0.669096\pi\) | ||||
−0.506594 | + | 0.862185i | \(0.669096\pi\) | |||||||
\(44\) | 5.85219 | 0.882251 | ||||||||
\(45\) | −0.612396 | −0.0912905 | ||||||||
\(46\) | 5.11376 | 0.753982 | ||||||||
\(47\) | −4.75015 | −0.692880 | −0.346440 | − | 0.938072i | \(-0.612610\pi\) | ||||
−0.346440 | + | 0.938072i | \(0.612610\pi\) | |||||||
\(48\) | 1.00000 | 0.144338 | ||||||||
\(49\) | 5.13499 | 0.733570 | ||||||||
\(50\) | −4.62497 | −0.654070 | ||||||||
\(51\) | −4.41285 | −0.617922 | ||||||||
\(52\) | 1.00000 | 0.138675 | ||||||||
\(53\) | 2.85708 | 0.392450 | 0.196225 | − | 0.980559i | \(-0.437132\pi\) | ||||
0.196225 | + | 0.980559i | \(0.437132\pi\) | |||||||
\(54\) | 1.00000 | 0.136083 | ||||||||
\(55\) | −3.58386 | −0.483247 | ||||||||
\(56\) | −3.48353 | −0.465506 | ||||||||
\(57\) | −6.11628 | −0.810121 | ||||||||
\(58\) | −7.19584 | −0.944860 | ||||||||
\(59\) | 10.0815 | 1.31250 | 0.656251 | − | 0.754543i | \(-0.272141\pi\) | ||||
0.656251 | + | 0.754543i | \(0.272141\pi\) | |||||||
\(60\) | −0.612396 | −0.0790599 | ||||||||
\(61\) | 14.1513 | 1.81188 | 0.905942 | − | 0.423402i | \(-0.139164\pi\) | ||||
0.905942 | + | 0.423402i | \(0.139164\pi\) | |||||||
\(62\) | −4.63030 | −0.588049 | ||||||||
\(63\) | −3.48353 | −0.438884 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −0.612396 | −0.0759583 | ||||||||
\(66\) | 5.85219 | 0.720355 | ||||||||
\(67\) | −4.74317 | −0.579471 | −0.289735 | − | 0.957107i | \(-0.593567\pi\) | ||||
−0.289735 | + | 0.957107i | \(0.593567\pi\) | |||||||
\(68\) | −4.41285 | −0.535136 | ||||||||
\(69\) | 5.11376 | 0.615624 | ||||||||
\(70\) | 2.13330 | 0.254978 | ||||||||
\(71\) | −5.14935 | −0.611116 | −0.305558 | − | 0.952174i | \(-0.598843\pi\) | ||||
−0.305558 | + | 0.952174i | \(0.598843\pi\) | |||||||
\(72\) | 1.00000 | 0.117851 | ||||||||
\(73\) | −2.75511 | −0.322461 | −0.161231 | − | 0.986917i | \(-0.551546\pi\) | ||||
−0.161231 | + | 0.986917i | \(0.551546\pi\) | |||||||
\(74\) | −4.90640 | −0.570358 | ||||||||
\(75\) | −4.62497 | −0.534046 | ||||||||
\(76\) | −6.11628 | −0.701585 | ||||||||
\(77\) | −20.3863 | −2.32323 | ||||||||
\(78\) | 1.00000 | 0.113228 | ||||||||
\(79\) | −14.8772 | −1.67381 | −0.836905 | − | 0.547348i | \(-0.815637\pi\) | ||||
−0.836905 | + | 0.547348i | \(0.815637\pi\) | |||||||
\(80\) | −0.612396 | −0.0684679 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −2.73338 | −0.301852 | ||||||||
\(83\) | 17.5526 | 1.92665 | 0.963325 | − | 0.268338i | \(-0.0864745\pi\) | ||||
0.963325 | + | 0.268338i | \(0.0864745\pi\) | |||||||
\(84\) | −3.48353 | −0.380084 | ||||||||
\(85\) | 2.70241 | 0.293117 | ||||||||
\(86\) | −6.64391 | −0.716432 | ||||||||
\(87\) | −7.19584 | −0.771475 | ||||||||
\(88\) | 5.85219 | 0.623846 | ||||||||
\(89\) | 8.15381 | 0.864302 | 0.432151 | − | 0.901801i | \(-0.357755\pi\) | ||||
0.432151 | + | 0.901801i | \(0.357755\pi\) | |||||||
\(90\) | −0.612396 | −0.0645522 | ||||||||
\(91\) | −3.48353 | −0.365173 | ||||||||
\(92\) | 5.11376 | 0.533146 | ||||||||
\(93\) | −4.63030 | −0.480140 | ||||||||
\(94\) | −4.75015 | −0.489940 | ||||||||
\(95\) | 3.74558 | 0.384289 | ||||||||
\(96\) | 1.00000 | 0.102062 | ||||||||
\(97\) | −16.6216 | −1.68767 | −0.843834 | − | 0.536604i | \(-0.819707\pi\) | ||||
−0.843834 | + | 0.536604i | \(0.819707\pi\) | |||||||
\(98\) | 5.13499 | 0.518713 | ||||||||
\(99\) | 5.85219 | 0.588167 | ||||||||
\(100\) | −4.62497 | −0.462497 | ||||||||
\(101\) | 12.0412 | 1.19815 | 0.599073 | − | 0.800695i | \(-0.295536\pi\) | ||||
0.599073 | + | 0.800695i | \(0.295536\pi\) | |||||||
\(102\) | −4.41285 | −0.436937 | ||||||||
\(103\) | 1.00000 | 0.0985329 | ||||||||
\(104\) | 1.00000 | 0.0980581 | ||||||||
\(105\) | 2.13330 | 0.208189 | ||||||||
\(106\) | 2.85708 | 0.277504 | ||||||||
\(107\) | −11.1516 | −1.07807 | −0.539034 | − | 0.842284i | \(-0.681211\pi\) | ||||
−0.539034 | + | 0.842284i | \(0.681211\pi\) | |||||||
\(108\) | 1.00000 | 0.0962250 | ||||||||
\(109\) | −17.3067 | −1.65768 | −0.828842 | − | 0.559483i | \(-0.811000\pi\) | ||||
−0.828842 | + | 0.559483i | \(0.811000\pi\) | |||||||
\(110\) | −3.58386 | −0.341707 | ||||||||
\(111\) | −4.90640 | −0.465695 | ||||||||
\(112\) | −3.48353 | −0.329163 | ||||||||
\(113\) | −17.6891 | −1.66405 | −0.832026 | − | 0.554737i | \(-0.812819\pi\) | ||||
−0.832026 | + | 0.554737i | \(0.812819\pi\) | |||||||
\(114\) | −6.11628 | −0.572842 | ||||||||
\(115\) | −3.13164 | −0.292027 | ||||||||
\(116\) | −7.19584 | −0.668117 | ||||||||
\(117\) | 1.00000 | 0.0924500 | ||||||||
\(118\) | 10.0815 | 0.928079 | ||||||||
\(119\) | 15.3723 | 1.40918 | ||||||||
\(120\) | −0.612396 | −0.0559038 | ||||||||
\(121\) | 23.2481 | 2.11347 | ||||||||
\(122\) | 14.1513 | 1.28120 | ||||||||
\(123\) | −2.73338 | −0.246461 | ||||||||
\(124\) | −4.63030 | −0.415813 | ||||||||
\(125\) | 5.89429 | 0.527201 | ||||||||
\(126\) | −3.48353 | −0.310338 | ||||||||
\(127\) | 5.50207 | 0.488230 | 0.244115 | − | 0.969746i | \(-0.421503\pi\) | ||||
0.244115 | + | 0.969746i | \(0.421503\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | −6.64391 | −0.584964 | ||||||||
\(130\) | −0.612396 | −0.0537106 | ||||||||
\(131\) | −11.9690 | −1.04574 | −0.522870 | − | 0.852413i | \(-0.675139\pi\) | ||||
−0.522870 | + | 0.852413i | \(0.675139\pi\) | |||||||
\(132\) | 5.85219 | 0.509368 | ||||||||
\(133\) | 21.3063 | 1.84749 | ||||||||
\(134\) | −4.74317 | −0.409748 | ||||||||
\(135\) | −0.612396 | −0.0527066 | ||||||||
\(136\) | −4.41285 | −0.378399 | ||||||||
\(137\) | 21.7646 | 1.85947 | 0.929736 | − | 0.368228i | \(-0.120035\pi\) | ||||
0.929736 | + | 0.368228i | \(0.120035\pi\) | |||||||
\(138\) | 5.11376 | 0.435312 | ||||||||
\(139\) | −20.0706 | −1.70236 | −0.851182 | − | 0.524871i | \(-0.824114\pi\) | ||||
−0.851182 | + | 0.524871i | \(0.824114\pi\) | |||||||
\(140\) | 2.13330 | 0.180297 | ||||||||
\(141\) | −4.75015 | −0.400035 | ||||||||
\(142\) | −5.14935 | −0.432124 | ||||||||
\(143\) | 5.85219 | 0.489385 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | 4.40670 | 0.365956 | ||||||||
\(146\) | −2.75511 | −0.228015 | ||||||||
\(147\) | 5.13499 | 0.423527 | ||||||||
\(148\) | −4.90640 | −0.403304 | ||||||||
\(149\) | 7.12490 | 0.583695 | 0.291847 | − | 0.956465i | \(-0.405730\pi\) | ||||
0.291847 | + | 0.956465i | \(0.405730\pi\) | |||||||
\(150\) | −4.62497 | −0.377627 | ||||||||
\(151\) | −7.40255 | −0.602411 | −0.301206 | − | 0.953559i | \(-0.597389\pi\) | ||||
−0.301206 | + | 0.953559i | \(0.597389\pi\) | |||||||
\(152\) | −6.11628 | −0.496096 | ||||||||
\(153\) | −4.41285 | −0.356758 | ||||||||
\(154\) | −20.3863 | −1.64277 | ||||||||
\(155\) | 2.83557 | 0.227759 | ||||||||
\(156\) | 1.00000 | 0.0800641 | ||||||||
\(157\) | 2.06155 | 0.164530 | 0.0822649 | − | 0.996610i | \(-0.473785\pi\) | ||||
0.0822649 | + | 0.996610i | \(0.473785\pi\) | |||||||
\(158\) | −14.8772 | −1.18356 | ||||||||
\(159\) | 2.85708 | 0.226581 | ||||||||
\(160\) | −0.612396 | −0.0484141 | ||||||||
\(161\) | −17.8139 | −1.40393 | ||||||||
\(162\) | 1.00000 | 0.0785674 | ||||||||
\(163\) | 7.03191 | 0.550782 | 0.275391 | − | 0.961332i | \(-0.411193\pi\) | ||||
0.275391 | + | 0.961332i | \(0.411193\pi\) | |||||||
\(164\) | −2.73338 | −0.213441 | ||||||||
\(165\) | −3.58386 | −0.279003 | ||||||||
\(166\) | 17.5526 | 1.36235 | ||||||||
\(167\) | −5.22098 | −0.404011 | −0.202006 | − | 0.979384i | \(-0.564746\pi\) | ||||
−0.202006 | + | 0.979384i | \(0.564746\pi\) | |||||||
\(168\) | −3.48353 | −0.268760 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 2.70241 | 0.207265 | ||||||||
\(171\) | −6.11628 | −0.467724 | ||||||||
\(172\) | −6.64391 | −0.506594 | ||||||||
\(173\) | −0.772617 | −0.0587410 | −0.0293705 | − | 0.999569i | \(-0.509350\pi\) | ||||
−0.0293705 | + | 0.999569i | \(0.509350\pi\) | |||||||
\(174\) | −7.19584 | −0.545515 | ||||||||
\(175\) | 16.1112 | 1.21789 | ||||||||
\(176\) | 5.85219 | 0.441125 | ||||||||
\(177\) | 10.0815 | 0.757773 | ||||||||
\(178\) | 8.15381 | 0.611154 | ||||||||
\(179\) | −10.5628 | −0.789499 | −0.394750 | − | 0.918789i | \(-0.629169\pi\) | ||||
−0.394750 | + | 0.918789i | \(0.629169\pi\) | |||||||
\(180\) | −0.612396 | −0.0456453 | ||||||||
\(181\) | 10.7815 | 0.801381 | 0.400690 | − | 0.916214i | \(-0.368770\pi\) | ||||
0.400690 | + | 0.916214i | \(0.368770\pi\) | |||||||
\(182\) | −3.48353 | −0.258217 | ||||||||
\(183\) | 14.1513 | 1.04609 | ||||||||
\(184\) | 5.11376 | 0.376991 | ||||||||
\(185\) | 3.00466 | 0.220907 | ||||||||
\(186\) | −4.63030 | −0.339510 | ||||||||
\(187\) | −25.8248 | −1.88850 | ||||||||
\(188\) | −4.75015 | −0.346440 | ||||||||
\(189\) | −3.48353 | −0.253390 | ||||||||
\(190\) | 3.74558 | 0.271733 | ||||||||
\(191\) | 14.9225 | 1.07975 | 0.539875 | − | 0.841745i | \(-0.318471\pi\) | ||||
0.539875 | + | 0.841745i | \(0.318471\pi\) | |||||||
\(192\) | 1.00000 | 0.0721688 | ||||||||
\(193\) | −5.95264 | −0.428480 | −0.214240 | − | 0.976781i | \(-0.568728\pi\) | ||||
−0.214240 | + | 0.976781i | \(0.568728\pi\) | |||||||
\(194\) | −16.6216 | −1.19336 | ||||||||
\(195\) | −0.612396 | −0.0438546 | ||||||||
\(196\) | 5.13499 | 0.366785 | ||||||||
\(197\) | −0.0499995 | −0.00356232 | −0.00178116 | − | 0.999998i | \(-0.500567\pi\) | ||||
−0.00178116 | + | 0.999998i | \(0.500567\pi\) | |||||||
\(198\) | 5.85219 | 0.415897 | ||||||||
\(199\) | −21.6481 | −1.53459 | −0.767296 | − | 0.641293i | \(-0.778398\pi\) | ||||
−0.767296 | + | 0.641293i | \(0.778398\pi\) | |||||||
\(200\) | −4.62497 | −0.327035 | ||||||||
\(201\) | −4.74317 | −0.334558 | ||||||||
\(202\) | 12.0412 | 0.847217 | ||||||||
\(203\) | 25.0669 | 1.75935 | ||||||||
\(204\) | −4.41285 | −0.308961 | ||||||||
\(205\) | 1.67391 | 0.116911 | ||||||||
\(206\) | 1.00000 | 0.0696733 | ||||||||
\(207\) | 5.11376 | 0.355431 | ||||||||
\(208\) | 1.00000 | 0.0693375 | ||||||||
\(209\) | −35.7936 | −2.47590 | ||||||||
\(210\) | 2.13330 | 0.147212 | ||||||||
\(211\) | −22.1750 | −1.52659 | −0.763294 | − | 0.646051i | \(-0.776419\pi\) | ||||
−0.763294 | + | 0.646051i | \(0.776419\pi\) | |||||||
\(212\) | 2.85708 | 0.196225 | ||||||||
\(213\) | −5.14935 | −0.352828 | ||||||||
\(214\) | −11.1516 | −0.762310 | ||||||||
\(215\) | 4.06870 | 0.277483 | ||||||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | 16.1298 | 1.09496 | ||||||||
\(218\) | −17.3067 | −1.17216 | ||||||||
\(219\) | −2.75511 | −0.186173 | ||||||||
\(220\) | −3.58386 | −0.241623 | ||||||||
\(221\) | −4.41285 | −0.296840 | ||||||||
\(222\) | −4.90640 | −0.329296 | ||||||||
\(223\) | 4.05280 | 0.271395 | 0.135698 | − | 0.990750i | \(-0.456672\pi\) | ||||
0.135698 | + | 0.990750i | \(0.456672\pi\) | |||||||
\(224\) | −3.48353 | −0.232753 | ||||||||
\(225\) | −4.62497 | −0.308331 | ||||||||
\(226\) | −17.6891 | −1.17666 | ||||||||
\(227\) | −7.40828 | −0.491705 | −0.245852 | − | 0.969307i | \(-0.579068\pi\) | ||||
−0.245852 | + | 0.969307i | \(0.579068\pi\) | |||||||
\(228\) | −6.11628 | −0.405061 | ||||||||
\(229\) | −1.36046 | −0.0899019 | −0.0449509 | − | 0.998989i | \(-0.514313\pi\) | ||||
−0.0449509 | + | 0.998989i | \(0.514313\pi\) | |||||||
\(230\) | −3.13164 | −0.206494 | ||||||||
\(231\) | −20.3863 | −1.34132 | ||||||||
\(232\) | −7.19584 | −0.472430 | ||||||||
\(233\) | 2.92599 | 0.191688 | 0.0958441 | − | 0.995396i | \(-0.469445\pi\) | ||||
0.0958441 | + | 0.995396i | \(0.469445\pi\) | |||||||
\(234\) | 1.00000 | 0.0653720 | ||||||||
\(235\) | 2.90897 | 0.189760 | ||||||||
\(236\) | 10.0815 | 0.656251 | ||||||||
\(237\) | −14.8772 | −0.966375 | ||||||||
\(238\) | 15.3723 | 0.996438 | ||||||||
\(239\) | −9.80743 | −0.634390 | −0.317195 | − | 0.948360i | \(-0.602741\pi\) | ||||
−0.317195 | + | 0.948360i | \(0.602741\pi\) | |||||||
\(240\) | −0.612396 | −0.0395300 | ||||||||
\(241\) | −3.18594 | −0.205224 | −0.102612 | − | 0.994721i | \(-0.532720\pi\) | ||||
−0.102612 | + | 0.994721i | \(0.532720\pi\) | |||||||
\(242\) | 23.2481 | 1.49445 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 14.1513 | 0.905942 | ||||||||
\(245\) | −3.14465 | −0.200904 | ||||||||
\(246\) | −2.73338 | −0.174274 | ||||||||
\(247\) | −6.11628 | −0.389170 | ||||||||
\(248\) | −4.63030 | −0.294024 | ||||||||
\(249\) | 17.5526 | 1.11235 | ||||||||
\(250\) | 5.89429 | 0.372788 | ||||||||
\(251\) | −17.9970 | −1.13596 | −0.567981 | − | 0.823042i | \(-0.692275\pi\) | ||||
−0.567981 | + | 0.823042i | \(0.692275\pi\) | |||||||
\(252\) | −3.48353 | −0.219442 | ||||||||
\(253\) | 29.9267 | 1.88147 | ||||||||
\(254\) | 5.50207 | 0.345231 | ||||||||
\(255\) | 2.70241 | 0.169231 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −2.17579 | −0.135722 | −0.0678610 | − | 0.997695i | \(-0.521617\pi\) | ||||
−0.0678610 | + | 0.997695i | \(0.521617\pi\) | |||||||
\(258\) | −6.64391 | −0.413632 | ||||||||
\(259\) | 17.0916 | 1.06202 | ||||||||
\(260\) | −0.612396 | −0.0379792 | ||||||||
\(261\) | −7.19584 | −0.445411 | ||||||||
\(262\) | −11.9690 | −0.739449 | ||||||||
\(263\) | 18.6103 | 1.14756 | 0.573779 | − | 0.819010i | \(-0.305477\pi\) | ||||
0.573779 | + | 0.819010i | \(0.305477\pi\) | |||||||
\(264\) | 5.85219 | 0.360177 | ||||||||
\(265\) | −1.74966 | −0.107481 | ||||||||
\(266\) | 21.3063 | 1.30637 | ||||||||
\(267\) | 8.15381 | 0.499005 | ||||||||
\(268\) | −4.74317 | −0.289735 | ||||||||
\(269\) | 10.2151 | 0.622827 | 0.311413 | − | 0.950275i | \(-0.399198\pi\) | ||||
0.311413 | + | 0.950275i | \(0.399198\pi\) | |||||||
\(270\) | −0.612396 | −0.0372692 | ||||||||
\(271\) | −9.90095 | −0.601440 | −0.300720 | − | 0.953713i | \(-0.597227\pi\) | ||||
−0.300720 | + | 0.953713i | \(0.597227\pi\) | |||||||
\(272\) | −4.41285 | −0.267568 | ||||||||
\(273\) | −3.48353 | −0.210833 | ||||||||
\(274\) | 21.7646 | 1.31484 | ||||||||
\(275\) | −27.0662 | −1.63215 | ||||||||
\(276\) | 5.11376 | 0.307812 | ||||||||
\(277\) | −15.2883 | −0.918585 | −0.459292 | − | 0.888285i | \(-0.651897\pi\) | ||||
−0.459292 | + | 0.888285i | \(0.651897\pi\) | |||||||
\(278\) | −20.0706 | −1.20375 | ||||||||
\(279\) | −4.63030 | −0.277209 | ||||||||
\(280\) | 2.13330 | 0.127489 | ||||||||
\(281\) | −29.0625 | −1.73372 | −0.866860 | − | 0.498551i | \(-0.833866\pi\) | ||||
−0.866860 | + | 0.498551i | \(0.833866\pi\) | |||||||
\(282\) | −4.75015 | −0.282867 | ||||||||
\(283\) | −8.88160 | −0.527956 | −0.263978 | − | 0.964529i | \(-0.585035\pi\) | ||||
−0.263978 | + | 0.964529i | \(0.585035\pi\) | |||||||
\(284\) | −5.14935 | −0.305558 | ||||||||
\(285\) | 3.74558 | 0.221869 | ||||||||
\(286\) | 5.85219 | 0.346047 | ||||||||
\(287\) | 9.52182 | 0.562056 | ||||||||
\(288\) | 1.00000 | 0.0589256 | ||||||||
\(289\) | 2.47323 | 0.145484 | ||||||||
\(290\) | 4.40670 | 0.258770 | ||||||||
\(291\) | −16.6216 | −0.974376 | ||||||||
\(292\) | −2.75511 | −0.161231 | ||||||||
\(293\) | 20.6747 | 1.20783 | 0.603914 | − | 0.797050i | \(-0.293607\pi\) | ||||
0.603914 | + | 0.797050i | \(0.293607\pi\) | |||||||
\(294\) | 5.13499 | 0.299479 | ||||||||
\(295\) | −6.17388 | −0.359457 | ||||||||
\(296\) | −4.90640 | −0.285179 | ||||||||
\(297\) | 5.85219 | 0.339579 | ||||||||
\(298\) | 7.12490 | 0.412734 | ||||||||
\(299\) | 5.11376 | 0.295736 | ||||||||
\(300\) | −4.62497 | −0.267023 | ||||||||
\(301\) | 23.1443 | 1.33401 | ||||||||
\(302\) | −7.40255 | −0.425969 | ||||||||
\(303\) | 12.0412 | 0.691750 | ||||||||
\(304\) | −6.11628 | −0.350793 | ||||||||
\(305\) | −8.66617 | −0.496224 | ||||||||
\(306\) | −4.41285 | −0.252266 | ||||||||
\(307\) | 28.7899 | 1.64313 | 0.821563 | − | 0.570117i | \(-0.193102\pi\) | ||||
0.821563 | + | 0.570117i | \(0.193102\pi\) | |||||||
\(308\) | −20.3863 | −1.16162 | ||||||||
\(309\) | 1.00000 | 0.0568880 | ||||||||
\(310\) | 2.83557 | 0.161050 | ||||||||
\(311\) | −14.2384 | −0.807386 | −0.403693 | − | 0.914894i | \(-0.632274\pi\) | ||||
−0.403693 | + | 0.914894i | \(0.632274\pi\) | |||||||
\(312\) | 1.00000 | 0.0566139 | ||||||||
\(313\) | −28.8988 | −1.63346 | −0.816728 | − | 0.577023i | \(-0.804214\pi\) | ||||
−0.816728 | + | 0.577023i | \(0.804214\pi\) | |||||||
\(314\) | 2.06155 | 0.116340 | ||||||||
\(315\) | 2.13330 | 0.120198 | ||||||||
\(316\) | −14.8772 | −0.836905 | ||||||||
\(317\) | 17.5058 | 0.983225 | 0.491613 | − | 0.870814i | \(-0.336408\pi\) | ||||
0.491613 | + | 0.870814i | \(0.336408\pi\) | |||||||
\(318\) | 2.85708 | 0.160217 | ||||||||
\(319\) | −42.1114 | −2.35779 | ||||||||
\(320\) | −0.612396 | −0.0342340 | ||||||||
\(321\) | −11.1516 | −0.622423 | ||||||||
\(322\) | −17.8139 | −0.992732 | ||||||||
\(323\) | 26.9902 | 1.50178 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | −4.62497 | −0.256547 | ||||||||
\(326\) | 7.03191 | 0.389461 | ||||||||
\(327\) | −17.3067 | −0.957064 | ||||||||
\(328\) | −2.73338 | −0.150926 | ||||||||
\(329\) | 16.5473 | 0.912282 | ||||||||
\(330\) | −3.58386 | −0.197285 | ||||||||
\(331\) | 13.6127 | 0.748222 | 0.374111 | − | 0.927384i | \(-0.377948\pi\) | ||||
0.374111 | + | 0.927384i | \(0.377948\pi\) | |||||||
\(332\) | 17.5526 | 0.963325 | ||||||||
\(333\) | −4.90640 | −0.268869 | ||||||||
\(334\) | −5.22098 | −0.285679 | ||||||||
\(335\) | 2.90470 | 0.158701 | ||||||||
\(336\) | −3.48353 | −0.190042 | ||||||||
\(337\) | −18.2169 | −0.992337 | −0.496169 | − | 0.868226i | \(-0.665260\pi\) | ||||
−0.496169 | + | 0.868226i | \(0.665260\pi\) | |||||||
\(338\) | 1.00000 | 0.0543928 | ||||||||
\(339\) | −17.6891 | −0.960741 | ||||||||
\(340\) | 2.70241 | 0.146559 | ||||||||
\(341\) | −27.0974 | −1.46741 | ||||||||
\(342\) | −6.11628 | −0.330731 | ||||||||
\(343\) | 6.49681 | 0.350795 | ||||||||
\(344\) | −6.64391 | −0.358216 | ||||||||
\(345\) | −3.13164 | −0.168602 | ||||||||
\(346\) | −0.772617 | −0.0415362 | ||||||||
\(347\) | 2.22190 | 0.119278 | 0.0596389 | − | 0.998220i | \(-0.481005\pi\) | ||||
0.0596389 | + | 0.998220i | \(0.481005\pi\) | |||||||
\(348\) | −7.19584 | −0.385737 | ||||||||
\(349\) | −10.3813 | −0.555698 | −0.277849 | − | 0.960625i | \(-0.589621\pi\) | ||||
−0.277849 | + | 0.960625i | \(0.589621\pi\) | |||||||
\(350\) | 16.1112 | 0.861182 | ||||||||
\(351\) | 1.00000 | 0.0533761 | ||||||||
\(352\) | 5.85219 | 0.311923 | ||||||||
\(353\) | −19.5439 | −1.04022 | −0.520110 | − | 0.854099i | \(-0.674109\pi\) | ||||
−0.520110 | + | 0.854099i | \(0.674109\pi\) | |||||||
\(354\) | 10.0815 | 0.535827 | ||||||||
\(355\) | 3.15344 | 0.167367 | ||||||||
\(356\) | 8.15381 | 0.432151 | ||||||||
\(357\) | 15.3723 | 0.813588 | ||||||||
\(358\) | −10.5628 | −0.558260 | ||||||||
\(359\) | 16.4233 | 0.866791 | 0.433396 | − | 0.901204i | \(-0.357315\pi\) | ||||
0.433396 | + | 0.901204i | \(0.357315\pi\) | |||||||
\(360\) | −0.612396 | −0.0322761 | ||||||||
\(361\) | 18.4089 | 0.968888 | ||||||||
\(362\) | 10.7815 | 0.566662 | ||||||||
\(363\) | 23.2481 | 1.22021 | ||||||||
\(364\) | −3.48353 | −0.182587 | ||||||||
\(365\) | 1.68722 | 0.0883130 | ||||||||
\(366\) | 14.1513 | 0.739698 | ||||||||
\(367\) | 9.91003 | 0.517299 | 0.258650 | − | 0.965971i | \(-0.416722\pi\) | ||||
0.258650 | + | 0.965971i | \(0.416722\pi\) | |||||||
\(368\) | 5.11376 | 0.266573 | ||||||||
\(369\) | −2.73338 | −0.142294 | ||||||||
\(370\) | 3.00466 | 0.156205 | ||||||||
\(371\) | −9.95273 | −0.516720 | ||||||||
\(372\) | −4.63030 | −0.240070 | ||||||||
\(373\) | −16.0590 | −0.831502 | −0.415751 | − | 0.909478i | \(-0.636481\pi\) | ||||
−0.415751 | + | 0.909478i | \(0.636481\pi\) | |||||||
\(374\) | −25.8248 | −1.33537 | ||||||||
\(375\) | 5.89429 | 0.304380 | ||||||||
\(376\) | −4.75015 | −0.244970 | ||||||||
\(377\) | −7.19584 | −0.370604 | ||||||||
\(378\) | −3.48353 | −0.179174 | ||||||||
\(379\) | −24.6722 | −1.26733 | −0.633663 | − | 0.773609i | \(-0.718449\pi\) | ||||
−0.633663 | + | 0.773609i | \(0.718449\pi\) | |||||||
\(380\) | 3.74558 | 0.192144 | ||||||||
\(381\) | 5.50207 | 0.281880 | ||||||||
\(382\) | 14.9225 | 0.763499 | ||||||||
\(383\) | 13.5806 | 0.693935 | 0.346968 | − | 0.937877i | \(-0.387211\pi\) | ||||
0.346968 | + | 0.937877i | \(0.387211\pi\) | |||||||
\(384\) | 1.00000 | 0.0510310 | ||||||||
\(385\) | 12.4845 | 0.636268 | ||||||||
\(386\) | −5.95264 | −0.302981 | ||||||||
\(387\) | −6.64391 | −0.337729 | ||||||||
\(388\) | −16.6216 | −0.843834 | ||||||||
\(389\) | 35.1204 | 1.78068 | 0.890339 | − | 0.455299i | \(-0.150468\pi\) | ||||
0.890339 | + | 0.455299i | \(0.150468\pi\) | |||||||
\(390\) | −0.612396 | −0.0310099 | ||||||||
\(391\) | −22.5662 | −1.14122 | ||||||||
\(392\) | 5.13499 | 0.259356 | ||||||||
\(393\) | −11.9690 | −0.603758 | ||||||||
\(394\) | −0.0499995 | −0.00251894 | ||||||||
\(395\) | 9.11070 | 0.458409 | ||||||||
\(396\) | 5.85219 | 0.294084 | ||||||||
\(397\) | 26.1141 | 1.31063 | 0.655315 | − | 0.755356i | \(-0.272536\pi\) | ||||
0.655315 | + | 0.755356i | \(0.272536\pi\) | |||||||
\(398\) | −21.6481 | −1.08512 | ||||||||
\(399\) | 21.3063 | 1.06665 | ||||||||
\(400\) | −4.62497 | −0.231249 | ||||||||
\(401\) | −30.5163 | −1.52391 | −0.761955 | − | 0.647630i | \(-0.775760\pi\) | ||||
−0.761955 | + | 0.647630i | \(0.775760\pi\) | |||||||
\(402\) | −4.74317 | −0.236568 | ||||||||
\(403\) | −4.63030 | −0.230652 | ||||||||
\(404\) | 12.0412 | 0.599073 | ||||||||
\(405\) | −0.612396 | −0.0304302 | ||||||||
\(406\) | 25.0669 | 1.24405 | ||||||||
\(407\) | −28.7132 | −1.42326 | ||||||||
\(408\) | −4.41285 | −0.218469 | ||||||||
\(409\) | 7.07618 | 0.349895 | 0.174947 | − | 0.984578i | \(-0.444024\pi\) | ||||
0.174947 | + | 0.984578i | \(0.444024\pi\) | |||||||
\(410\) | 1.67391 | 0.0826686 | ||||||||
\(411\) | 21.7646 | 1.07357 | ||||||||
\(412\) | 1.00000 | 0.0492665 | ||||||||
\(413\) | −35.1193 | −1.72811 | ||||||||
\(414\) | 5.11376 | 0.251327 | ||||||||
\(415\) | −10.7491 | −0.527655 | ||||||||
\(416\) | 1.00000 | 0.0490290 | ||||||||
\(417\) | −20.0706 | −0.982860 | ||||||||
\(418\) | −35.7936 | −1.75072 | ||||||||
\(419\) | −8.13256 | −0.397301 | −0.198651 | − | 0.980070i | \(-0.563656\pi\) | ||||
−0.198651 | + | 0.980070i | \(0.563656\pi\) | |||||||
\(420\) | 2.13330 | 0.104094 | ||||||||
\(421\) | 33.9300 | 1.65365 | 0.826823 | − | 0.562462i | \(-0.190146\pi\) | ||||
0.826823 | + | 0.562462i | \(0.190146\pi\) | |||||||
\(422\) | −22.1750 | −1.07946 | ||||||||
\(423\) | −4.75015 | −0.230960 | ||||||||
\(424\) | 2.85708 | 0.138752 | ||||||||
\(425\) | 20.4093 | 0.989996 | ||||||||
\(426\) | −5.14935 | −0.249487 | ||||||||
\(427\) | −49.2964 | −2.38562 | ||||||||
\(428\) | −11.1516 | −0.539034 | ||||||||
\(429\) | 5.85219 | 0.282546 | ||||||||
\(430\) | 4.06870 | 0.196210 | ||||||||
\(431\) | 25.4352 | 1.22517 | 0.612585 | − | 0.790405i | \(-0.290130\pi\) | ||||
0.612585 | + | 0.790405i | \(0.290130\pi\) | |||||||
\(432\) | 1.00000 | 0.0481125 | ||||||||
\(433\) | 6.45505 | 0.310210 | 0.155105 | − | 0.987898i | \(-0.450428\pi\) | ||||
0.155105 | + | 0.987898i | \(0.450428\pi\) | |||||||
\(434\) | 16.1298 | 0.774255 | ||||||||
\(435\) | 4.40670 | 0.211285 | ||||||||
\(436\) | −17.3067 | −0.828842 | ||||||||
\(437\) | −31.2772 | −1.49619 | ||||||||
\(438\) | −2.75511 | −0.131644 | ||||||||
\(439\) | −5.52037 | −0.263473 | −0.131736 | − | 0.991285i | \(-0.542055\pi\) | ||||
−0.131736 | + | 0.991285i | \(0.542055\pi\) | |||||||
\(440\) | −3.58386 | −0.170854 | ||||||||
\(441\) | 5.13499 | 0.244523 | ||||||||
\(442\) | −4.41285 | −0.209898 | ||||||||
\(443\) | −1.12187 | −0.0533016 | −0.0266508 | − | 0.999645i | \(-0.508484\pi\) | ||||
−0.0266508 | + | 0.999645i | \(0.508484\pi\) | |||||||
\(444\) | −4.90640 | −0.232847 | ||||||||
\(445\) | −4.99336 | −0.236708 | ||||||||
\(446\) | 4.05280 | 0.191906 | ||||||||
\(447\) | 7.12490 | 0.336996 | ||||||||
\(448\) | −3.48353 | −0.164581 | ||||||||
\(449\) | −21.3872 | −1.00932 | −0.504662 | − | 0.863317i | \(-0.668383\pi\) | ||||
−0.504662 | + | 0.863317i | \(0.668383\pi\) | |||||||
\(450\) | −4.62497 | −0.218023 | ||||||||
\(451\) | −15.9963 | −0.753235 | ||||||||
\(452\) | −17.6891 | −0.832026 | ||||||||
\(453\) | −7.40255 | −0.347802 | ||||||||
\(454\) | −7.40828 | −0.347688 | ||||||||
\(455\) | 2.13330 | 0.100011 | ||||||||
\(456\) | −6.11628 | −0.286421 | ||||||||
\(457\) | −35.8670 | −1.67779 | −0.838894 | − | 0.544295i | \(-0.816797\pi\) | ||||
−0.838894 | + | 0.544295i | \(0.816797\pi\) | |||||||
\(458\) | −1.36046 | −0.0635702 | ||||||||
\(459\) | −4.41285 | −0.205974 | ||||||||
\(460\) | −3.13164 | −0.146014 | ||||||||
\(461\) | 18.2746 | 0.851135 | 0.425567 | − | 0.904927i | \(-0.360075\pi\) | ||||
0.425567 | + | 0.904927i | \(0.360075\pi\) | |||||||
\(462\) | −20.3863 | −0.948456 | ||||||||
\(463\) | −12.7228 | −0.591279 | −0.295640 | − | 0.955300i | \(-0.595533\pi\) | ||||
−0.295640 | + | 0.955300i | \(0.595533\pi\) | |||||||
\(464\) | −7.19584 | −0.334058 | ||||||||
\(465\) | 2.83557 | 0.131497 | ||||||||
\(466\) | 2.92599 | 0.135544 | ||||||||
\(467\) | 4.92734 | 0.228010 | 0.114005 | − | 0.993480i | \(-0.463632\pi\) | ||||
0.114005 | + | 0.993480i | \(0.463632\pi\) | |||||||
\(468\) | 1.00000 | 0.0462250 | ||||||||
\(469\) | 16.5230 | 0.762961 | ||||||||
\(470\) | 2.90897 | 0.134181 | ||||||||
\(471\) | 2.06155 | 0.0949913 | ||||||||
\(472\) | 10.0815 | 0.464039 | ||||||||
\(473\) | −38.8814 | −1.78777 | ||||||||
\(474\) | −14.8772 | −0.683330 | ||||||||
\(475\) | 28.2876 | 1.29793 | ||||||||
\(476\) | 15.3723 | 0.704588 | ||||||||
\(477\) | 2.85708 | 0.130817 | ||||||||
\(478\) | −9.80743 | −0.448581 | ||||||||
\(479\) | −37.8264 | −1.72833 | −0.864166 | − | 0.503207i | \(-0.832153\pi\) | ||||
−0.864166 | + | 0.503207i | \(0.832153\pi\) | |||||||
\(480\) | −0.612396 | −0.0279519 | ||||||||
\(481\) | −4.90640 | −0.223713 | ||||||||
\(482\) | −3.18594 | −0.145116 | ||||||||
\(483\) | −17.8139 | −0.810562 | ||||||||
\(484\) | 23.2481 | 1.05673 | ||||||||
\(485\) | 10.1790 | 0.462204 | ||||||||
\(486\) | 1.00000 | 0.0453609 | ||||||||
\(487\) | 33.2028 | 1.50456 | 0.752282 | − | 0.658841i | \(-0.228953\pi\) | ||||
0.752282 | + | 0.658841i | \(0.228953\pi\) | |||||||
\(488\) | 14.1513 | 0.640598 | ||||||||
\(489\) | 7.03191 | 0.317994 | ||||||||
\(490\) | −3.14465 | −0.142061 | ||||||||
\(491\) | −32.9200 | −1.48566 | −0.742828 | − | 0.669482i | \(-0.766516\pi\) | ||||
−0.742828 | + | 0.669482i | \(0.766516\pi\) | |||||||
\(492\) | −2.73338 | −0.123230 | ||||||||
\(493\) | 31.7541 | 1.43013 | ||||||||
\(494\) | −6.11628 | −0.275184 | ||||||||
\(495\) | −3.58386 | −0.161082 | ||||||||
\(496\) | −4.63030 | −0.207907 | ||||||||
\(497\) | 17.9379 | 0.804626 | ||||||||
\(498\) | 17.5526 | 0.786551 | ||||||||
\(499\) | 43.7955 | 1.96055 | 0.980277 | − | 0.197628i | \(-0.0633236\pi\) | ||||
0.980277 | + | 0.197628i | \(0.0633236\pi\) | |||||||
\(500\) | 5.89429 | 0.263601 | ||||||||
\(501\) | −5.22098 | −0.233256 | ||||||||
\(502\) | −17.9970 | −0.803247 | ||||||||
\(503\) | 26.4282 | 1.17838 | 0.589188 | − | 0.807996i | \(-0.299448\pi\) | ||||
0.589188 | + | 0.807996i | \(0.299448\pi\) | |||||||
\(504\) | −3.48353 | −0.155169 | ||||||||
\(505\) | −7.37398 | −0.328138 | ||||||||
\(506\) | 29.9267 | 1.33040 | ||||||||
\(507\) | 1.00000 | 0.0444116 | ||||||||
\(508\) | 5.50207 | 0.244115 | ||||||||
\(509\) | −40.7276 | −1.80522 | −0.902609 | − | 0.430462i | \(-0.858351\pi\) | ||||
−0.902609 | + | 0.430462i | \(0.858351\pi\) | |||||||
\(510\) | 2.70241 | 0.119665 | ||||||||
\(511\) | 9.59751 | 0.424569 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −6.11628 | −0.270040 | ||||||||
\(514\) | −2.17579 | −0.0959700 | ||||||||
\(515\) | −0.612396 | −0.0269854 | ||||||||
\(516\) | −6.64391 | −0.292482 | ||||||||
\(517\) | −27.7988 | −1.22259 | ||||||||
\(518\) | 17.0916 | 0.750962 | ||||||||
\(519\) | −0.772617 | −0.0339141 | ||||||||
\(520\) | −0.612396 | −0.0268553 | ||||||||
\(521\) | −0.959434 | −0.0420336 | −0.0210168 | − | 0.999779i | \(-0.506690\pi\) | ||||
−0.0210168 | + | 0.999779i | \(0.506690\pi\) | |||||||
\(522\) | −7.19584 | −0.314953 | ||||||||
\(523\) | 41.6081 | 1.81939 | 0.909697 | − | 0.415273i | \(-0.136314\pi\) | ||||
0.909697 | + | 0.415273i | \(0.136314\pi\) | |||||||
\(524\) | −11.9690 | −0.522870 | ||||||||
\(525\) | 16.1112 | 0.703152 | ||||||||
\(526\) | 18.6103 | 0.811446 | ||||||||
\(527\) | 20.4328 | 0.890067 | ||||||||
\(528\) | 5.85219 | 0.254684 | ||||||||
\(529\) | 3.15050 | 0.136978 | ||||||||
\(530\) | −1.74966 | −0.0760005 | ||||||||
\(531\) | 10.0815 | 0.437501 | ||||||||
\(532\) | 21.3063 | 0.923743 | ||||||||
\(533\) | −2.73338 | −0.118396 | ||||||||
\(534\) | 8.15381 | 0.352850 | ||||||||
\(535\) | 6.82921 | 0.295252 | ||||||||
\(536\) | −4.74317 | −0.204874 | ||||||||
\(537\) | −10.5628 | −0.455818 | ||||||||
\(538\) | 10.2151 | 0.440405 | ||||||||
\(539\) | 30.0510 | 1.29439 | ||||||||
\(540\) | −0.612396 | −0.0263533 | ||||||||
\(541\) | −1.42268 | −0.0611656 | −0.0305828 | − | 0.999532i | \(-0.509736\pi\) | ||||
−0.0305828 | + | 0.999532i | \(0.509736\pi\) | |||||||
\(542\) | −9.90095 | −0.425282 | ||||||||
\(543\) | 10.7815 | 0.462677 | ||||||||
\(544\) | −4.41285 | −0.189199 | ||||||||
\(545\) | 10.5986 | 0.453993 | ||||||||
\(546\) | −3.48353 | −0.149081 | ||||||||
\(547\) | −5.60579 | −0.239686 | −0.119843 | − | 0.992793i | \(-0.538239\pi\) | ||||
−0.119843 | + | 0.992793i | \(0.538239\pi\) | |||||||
\(548\) | 21.7646 | 0.929736 | ||||||||
\(549\) | 14.1513 | 0.603961 | ||||||||
\(550\) | −27.0662 | −1.15411 | ||||||||
\(551\) | 44.0118 | 1.87496 | ||||||||
\(552\) | 5.11376 | 0.217656 | ||||||||
\(553\) | 51.8250 | 2.20382 | ||||||||
\(554\) | −15.2883 | −0.649537 | ||||||||
\(555\) | 3.00466 | 0.127541 | ||||||||
\(556\) | −20.0706 | −0.851182 | ||||||||
\(557\) | −23.0865 | −0.978208 | −0.489104 | − | 0.872225i | \(-0.662676\pi\) | ||||
−0.489104 | + | 0.872225i | \(0.662676\pi\) | |||||||
\(558\) | −4.63030 | −0.196016 | ||||||||
\(559\) | −6.64391 | −0.281008 | ||||||||
\(560\) | 2.13330 | 0.0901483 | ||||||||
\(561\) | −25.8248 | −1.09033 | ||||||||
\(562\) | −29.0625 | −1.22593 | ||||||||
\(563\) | 15.9022 | 0.670200 | 0.335100 | − | 0.942183i | \(-0.391230\pi\) | ||||
0.335100 | + | 0.942183i | \(0.391230\pi\) | |||||||
\(564\) | −4.75015 | −0.200017 | ||||||||
\(565\) | 10.8327 | 0.455737 | ||||||||
\(566\) | −8.88160 | −0.373322 | ||||||||
\(567\) | −3.48353 | −0.146295 | ||||||||
\(568\) | −5.14935 | −0.216062 | ||||||||
\(569\) | 40.4754 | 1.69682 | 0.848409 | − | 0.529342i | \(-0.177561\pi\) | ||||
0.848409 | + | 0.529342i | \(0.177561\pi\) | |||||||
\(570\) | 3.74558 | 0.156885 | ||||||||
\(571\) | 24.1215 | 1.00945 | 0.504727 | − | 0.863279i | \(-0.331593\pi\) | ||||
0.504727 | + | 0.863279i | \(0.331593\pi\) | |||||||
\(572\) | 5.85219 | 0.244692 | ||||||||
\(573\) | 14.9225 | 0.623394 | ||||||||
\(574\) | 9.52182 | 0.397433 | ||||||||
\(575\) | −23.6510 | −0.986314 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | −1.40846 | −0.0586349 | −0.0293174 | − | 0.999570i | \(-0.509333\pi\) | ||||
−0.0293174 | + | 0.999570i | \(0.509333\pi\) | |||||||
\(578\) | 2.47323 | 0.102873 | ||||||||
\(579\) | −5.95264 | −0.247383 | ||||||||
\(580\) | 4.40670 | 0.182978 | ||||||||
\(581\) | −61.1451 | −2.53673 | ||||||||
\(582\) | −16.6216 | −0.688988 | ||||||||
\(583\) | 16.7202 | 0.692479 | ||||||||
\(584\) | −2.75511 | −0.114007 | ||||||||
\(585\) | −0.612396 | −0.0253194 | ||||||||
\(586\) | 20.6747 | 0.854063 | ||||||||
\(587\) | 2.68345 | 0.110758 | 0.0553789 | − | 0.998465i | \(-0.482363\pi\) | ||||
0.0553789 | + | 0.998465i | \(0.482363\pi\) | |||||||
\(588\) | 5.13499 | 0.211764 | ||||||||
\(589\) | 28.3202 | 1.16691 | ||||||||
\(590\) | −6.17388 | −0.254174 | ||||||||
\(591\) | −0.0499995 | −0.00205670 | ||||||||
\(592\) | −4.90640 | −0.201652 | ||||||||
\(593\) | −3.13502 | −0.128740 | −0.0643698 | − | 0.997926i | \(-0.520504\pi\) | ||||
−0.0643698 | + | 0.997926i | \(0.520504\pi\) | |||||||
\(594\) | 5.85219 | 0.240118 | ||||||||
\(595\) | −9.41393 | −0.385933 | ||||||||
\(596\) | 7.12490 | 0.291847 | ||||||||
\(597\) | −21.6481 | −0.885997 | ||||||||
\(598\) | 5.11376 | 0.209117 | ||||||||
\(599\) | −17.6222 | −0.720023 | −0.360011 | − | 0.932948i | \(-0.617227\pi\) | ||||
−0.360011 | + | 0.932948i | \(0.617227\pi\) | |||||||
\(600\) | −4.62497 | −0.188814 | ||||||||
\(601\) | 18.4794 | 0.753790 | 0.376895 | − | 0.926256i | \(-0.376992\pi\) | ||||
0.376895 | + | 0.926256i | \(0.376992\pi\) | |||||||
\(602\) | 23.1443 | 0.943291 | ||||||||
\(603\) | −4.74317 | −0.193157 | ||||||||
\(604\) | −7.40255 | −0.301206 | ||||||||
\(605\) | −14.2371 | −0.578818 | ||||||||
\(606\) | 12.0412 | 0.489141 | ||||||||
\(607\) | 13.1121 | 0.532203 | 0.266101 | − | 0.963945i | \(-0.414264\pi\) | ||||
0.266101 | + | 0.963945i | \(0.414264\pi\) | |||||||
\(608\) | −6.11628 | −0.248048 | ||||||||
\(609\) | 25.0669 | 1.01576 | ||||||||
\(610\) | −8.66617 | −0.350883 | ||||||||
\(611\) | −4.75015 | −0.192170 | ||||||||
\(612\) | −4.41285 | −0.178379 | ||||||||
\(613\) | −4.83225 | −0.195173 | −0.0975864 | − | 0.995227i | \(-0.531112\pi\) | ||||
−0.0975864 | + | 0.995227i | \(0.531112\pi\) | |||||||
\(614\) | 28.7899 | 1.16187 | ||||||||
\(615\) | 1.67391 | 0.0674986 | ||||||||
\(616\) | −20.3863 | −0.821387 | ||||||||
\(617\) | −22.7084 | −0.914205 | −0.457103 | − | 0.889414i | \(-0.651113\pi\) | ||||
−0.457103 | + | 0.889414i | \(0.651113\pi\) | |||||||
\(618\) | 1.00000 | 0.0402259 | ||||||||
\(619\) | −2.60889 | −0.104860 | −0.0524302 | − | 0.998625i | \(-0.516697\pi\) | ||||
−0.0524302 | + | 0.998625i | \(0.516697\pi\) | |||||||
\(620\) | 2.83557 | 0.113879 | ||||||||
\(621\) | 5.11376 | 0.205208 | ||||||||
\(622\) | −14.2384 | −0.570908 | ||||||||
\(623\) | −28.4040 | −1.13798 | ||||||||
\(624\) | 1.00000 | 0.0400320 | ||||||||
\(625\) | 19.5152 | 0.780609 | ||||||||
\(626\) | −28.8988 | −1.15503 | ||||||||
\(627\) | −35.7936 | −1.42946 | ||||||||
\(628\) | 2.06155 | 0.0822649 | ||||||||
\(629\) | 21.6512 | 0.863290 | ||||||||
\(630\) | 2.13330 | 0.0849927 | ||||||||
\(631\) | −4.76038 | −0.189508 | −0.0947539 | − | 0.995501i | \(-0.530206\pi\) | ||||
−0.0947539 | + | 0.995501i | \(0.530206\pi\) | |||||||
\(632\) | −14.8772 | −0.591781 | ||||||||
\(633\) | −22.1750 | −0.881376 | ||||||||
\(634\) | 17.5058 | 0.695245 | ||||||||
\(635\) | −3.36944 | −0.133712 | ||||||||
\(636\) | 2.85708 | 0.113291 | ||||||||
\(637\) | 5.13499 | 0.203456 | ||||||||
\(638\) | −42.1114 | −1.66721 | ||||||||
\(639\) | −5.14935 | −0.203705 | ||||||||
\(640\) | −0.612396 | −0.0242071 | ||||||||
\(641\) | 2.57178 | 0.101579 | 0.0507895 | − | 0.998709i | \(-0.483826\pi\) | ||||
0.0507895 | + | 0.998709i | \(0.483826\pi\) | |||||||
\(642\) | −11.1516 | −0.440120 | ||||||||
\(643\) | 49.6390 | 1.95757 | 0.978785 | − | 0.204891i | \(-0.0656838\pi\) | ||||
0.978785 | + | 0.204891i | \(0.0656838\pi\) | |||||||
\(644\) | −17.8139 | −0.701967 | ||||||||
\(645\) | 4.06870 | 0.160205 | ||||||||
\(646\) | 26.9902 | 1.06192 | ||||||||
\(647\) | 20.9211 | 0.822492 | 0.411246 | − | 0.911524i | \(-0.365094\pi\) | ||||
0.411246 | + | 0.911524i | \(0.365094\pi\) | |||||||
\(648\) | 1.00000 | 0.0392837 | ||||||||
\(649\) | 58.9989 | 2.31591 | ||||||||
\(650\) | −4.62497 | −0.181406 | ||||||||
\(651\) | 16.1298 | 0.632176 | ||||||||
\(652\) | 7.03191 | 0.275391 | ||||||||
\(653\) | 11.0240 | 0.431402 | 0.215701 | − | 0.976460i | \(-0.430796\pi\) | ||||
0.215701 | + | 0.976460i | \(0.430796\pi\) | |||||||
\(654\) | −17.3067 | −0.676747 | ||||||||
\(655\) | 7.32978 | 0.286398 | ||||||||
\(656\) | −2.73338 | −0.106721 | ||||||||
\(657\) | −2.75511 | −0.107487 | ||||||||
\(658\) | 16.5473 | 0.645081 | ||||||||
\(659\) | −1.31811 | −0.0513464 | −0.0256732 | − | 0.999670i | \(-0.508173\pi\) | ||||
−0.0256732 | + | 0.999670i | \(0.508173\pi\) | |||||||
\(660\) | −3.58386 | −0.139501 | ||||||||
\(661\) | −10.1024 | −0.392940 | −0.196470 | − | 0.980510i | \(-0.562948\pi\) | ||||
−0.196470 | + | 0.980510i | \(0.562948\pi\) | |||||||
\(662\) | 13.6127 | 0.529073 | ||||||||
\(663\) | −4.41285 | −0.171381 | ||||||||
\(664\) | 17.5526 | 0.681173 | ||||||||
\(665\) | −13.0479 | −0.505974 | ||||||||
\(666\) | −4.90640 | −0.190119 | ||||||||
\(667\) | −36.7978 | −1.42481 | ||||||||
\(668\) | −5.22098 | −0.202006 | ||||||||
\(669\) | 4.05280 | 0.156690 | ||||||||
\(670\) | 2.90470 | 0.112218 | ||||||||
\(671\) | 82.8159 | 3.19707 | ||||||||
\(672\) | −3.48353 | −0.134380 | ||||||||
\(673\) | 12.3916 | 0.477662 | 0.238831 | − | 0.971061i | \(-0.423236\pi\) | ||||
0.238831 | + | 0.971061i | \(0.423236\pi\) | |||||||
\(674\) | −18.2169 | −0.701688 | ||||||||
\(675\) | −4.62497 | −0.178015 | ||||||||
\(676\) | 1.00000 | 0.0384615 | ||||||||
\(677\) | −38.3673 | −1.47457 | −0.737287 | − | 0.675580i | \(-0.763893\pi\) | ||||
−0.737287 | + | 0.675580i | \(0.763893\pi\) | |||||||
\(678\) | −17.6891 | −0.679346 | ||||||||
\(679\) | 57.9019 | 2.22207 | ||||||||
\(680\) | 2.70241 | 0.103633 | ||||||||
\(681\) | −7.40828 | −0.283886 | ||||||||
\(682\) | −27.0974 | −1.03761 | ||||||||
\(683\) | 40.7863 | 1.56065 | 0.780323 | − | 0.625377i | \(-0.215055\pi\) | ||||
0.780323 | + | 0.625377i | \(0.215055\pi\) | |||||||
\(684\) | −6.11628 | −0.233862 | ||||||||
\(685\) | −13.3285 | −0.509256 | ||||||||
\(686\) | 6.49681 | 0.248049 | ||||||||
\(687\) | −1.36046 | −0.0519049 | ||||||||
\(688\) | −6.64391 | −0.253297 | ||||||||
\(689\) | 2.85708 | 0.108846 | ||||||||
\(690\) | −3.13164 | −0.119220 | ||||||||
\(691\) | 28.9316 | 1.10061 | 0.550306 | − | 0.834963i | \(-0.314511\pi\) | ||||
0.550306 | + | 0.834963i | \(0.314511\pi\) | |||||||
\(692\) | −0.772617 | −0.0293705 | ||||||||
\(693\) | −20.3863 | −0.774411 | ||||||||
\(694\) | 2.22190 | 0.0843422 | ||||||||
\(695\) | 12.2911 | 0.466229 | ||||||||
\(696\) | −7.19584 | −0.272758 | ||||||||
\(697\) | 12.0620 | 0.456881 | ||||||||
\(698\) | −10.3813 | −0.392938 | ||||||||
\(699\) | 2.92599 | 0.110671 | ||||||||
\(700\) | 16.1112 | 0.608947 | ||||||||
\(701\) | −25.1536 | −0.950038 | −0.475019 | − | 0.879976i | \(-0.657559\pi\) | ||||
−0.475019 | + | 0.879976i | \(0.657559\pi\) | |||||||
\(702\) | 1.00000 | 0.0377426 | ||||||||
\(703\) | 30.0089 | 1.13181 | ||||||||
\(704\) | 5.85219 | 0.220563 | ||||||||
\(705\) | 2.90897 | 0.109558 | ||||||||
\(706\) | −19.5439 | −0.735546 | ||||||||
\(707\) | −41.9459 | −1.57754 | ||||||||
\(708\) | 10.0815 | 0.378887 | ||||||||
\(709\) | 7.09284 | 0.266377 | 0.133189 | − | 0.991091i | \(-0.457478\pi\) | ||||
0.133189 | + | 0.991091i | \(0.457478\pi\) | |||||||
\(710\) | 3.15344 | 0.118347 | ||||||||
\(711\) | −14.8772 | −0.557937 | ||||||||
\(712\) | 8.15381 | 0.305577 | ||||||||
\(713\) | −23.6782 | −0.886756 | ||||||||
\(714\) | 15.3723 | 0.575294 | ||||||||
\(715\) | −3.58386 | −0.134029 | ||||||||
\(716\) | −10.5628 | −0.394750 | ||||||||
\(717\) | −9.80743 | −0.366265 | ||||||||
\(718\) | 16.4233 | 0.612914 | ||||||||
\(719\) | 52.2800 | 1.94971 | 0.974857 | − | 0.222833i | \(-0.0715303\pi\) | ||||
0.974857 | + | 0.222833i | \(0.0715303\pi\) | |||||||
\(720\) | −0.612396 | −0.0228226 | ||||||||
\(721\) | −3.48353 | −0.129733 | ||||||||
\(722\) | 18.4089 | 0.685108 | ||||||||
\(723\) | −3.18594 | −0.118486 | ||||||||
\(724\) | 10.7815 | 0.400690 | ||||||||
\(725\) | 33.2805 | 1.23601 | ||||||||
\(726\) | 23.2481 | 0.862819 | ||||||||
\(727\) | 29.6708 | 1.10043 | 0.550214 | − | 0.835024i | \(-0.314546\pi\) | ||||
0.550214 | + | 0.835024i | \(0.314546\pi\) | |||||||
\(728\) | −3.48353 | −0.129108 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 1.68722 | 0.0624467 | ||||||||
\(731\) | 29.3186 | 1.08439 | ||||||||
\(732\) | 14.1513 | 0.523046 | ||||||||
\(733\) | 26.7669 | 0.988658 | 0.494329 | − | 0.869275i | \(-0.335414\pi\) | ||||
0.494329 | + | 0.869275i | \(0.335414\pi\) | |||||||
\(734\) | 9.91003 | 0.365786 | ||||||||
\(735\) | −3.14465 | −0.115992 | ||||||||
\(736\) | 5.11376 | 0.188496 | ||||||||
\(737\) | −27.7580 | −1.02248 | ||||||||
\(738\) | −2.73338 | −0.100617 | ||||||||
\(739\) | −7.88082 | −0.289901 | −0.144950 | − | 0.989439i | \(-0.546302\pi\) | ||||
−0.144950 | + | 0.989439i | \(0.546302\pi\) | |||||||
\(740\) | 3.00466 | 0.110453 | ||||||||
\(741\) | −6.11628 | −0.224687 | ||||||||
\(742\) | −9.95273 | −0.365376 | ||||||||
\(743\) | 28.1717 | 1.03352 | 0.516759 | − | 0.856131i | \(-0.327138\pi\) | ||||
0.516759 | + | 0.856131i | \(0.327138\pi\) | |||||||
\(744\) | −4.63030 | −0.169755 | ||||||||
\(745\) | −4.36326 | −0.159857 | ||||||||
\(746\) | −16.0590 | −0.587961 | ||||||||
\(747\) | 17.5526 | 0.642216 | ||||||||
\(748\) | −25.8248 | −0.944249 | ||||||||
\(749\) | 38.8470 | 1.41944 | ||||||||
\(750\) | 5.89429 | 0.215229 | ||||||||
\(751\) | −4.01398 | −0.146472 | −0.0732360 | − | 0.997315i | \(-0.523333\pi\) | ||||
−0.0732360 | + | 0.997315i | \(0.523333\pi\) | |||||||
\(752\) | −4.75015 | −0.173220 | ||||||||
\(753\) | −17.9970 | −0.655848 | ||||||||
\(754\) | −7.19584 | −0.262057 | ||||||||
\(755\) | 4.53329 | 0.164983 | ||||||||
\(756\) | −3.48353 | −0.126695 | ||||||||
\(757\) | −33.4646 | −1.21629 | −0.608147 | − | 0.793825i | \(-0.708087\pi\) | ||||
−0.608147 | + | 0.793825i | \(0.708087\pi\) | |||||||
\(758\) | −24.6722 | −0.896135 | ||||||||
\(759\) | 29.9267 | 1.08627 | ||||||||
\(760\) | 3.74558 | 0.135867 | ||||||||
\(761\) | 3.50752 | 0.127147 | 0.0635737 | − | 0.997977i | \(-0.479750\pi\) | ||||
0.0635737 | + | 0.997977i | \(0.479750\pi\) | |||||||
\(762\) | 5.50207 | 0.199319 | ||||||||
\(763\) | 60.2885 | 2.18259 | ||||||||
\(764\) | 14.9225 | 0.539875 | ||||||||
\(765\) | 2.70241 | 0.0977058 | ||||||||
\(766\) | 13.5806 | 0.490686 | ||||||||
\(767\) | 10.0815 | 0.364022 | ||||||||
\(768\) | 1.00000 | 0.0360844 | ||||||||
\(769\) | 8.88559 | 0.320423 | 0.160211 | − | 0.987083i | \(-0.448782\pi\) | ||||
0.160211 | + | 0.987083i | \(0.448782\pi\) | |||||||
\(770\) | 12.4845 | 0.449909 | ||||||||
\(771\) | −2.17579 | −0.0783592 | ||||||||
\(772\) | −5.95264 | −0.214240 | ||||||||
\(773\) | 30.8947 | 1.11120 | 0.555602 | − | 0.831448i | \(-0.312488\pi\) | ||||
0.555602 | + | 0.831448i | \(0.312488\pi\) | |||||||
\(774\) | −6.64391 | −0.238811 | ||||||||
\(775\) | 21.4150 | 0.769250 | ||||||||
\(776\) | −16.6216 | −0.596681 | ||||||||
\(777\) | 17.0916 | 0.613158 | ||||||||
\(778\) | 35.1204 | 1.25913 | ||||||||
\(779\) | 16.7181 | 0.598989 | ||||||||
\(780\) | −0.612396 | −0.0219273 | ||||||||
\(781\) | −30.1350 | −1.07831 | ||||||||
\(782\) | −22.5662 | −0.806967 | ||||||||
\(783\) | −7.19584 | −0.257158 | ||||||||
\(784\) | 5.13499 | 0.183393 | ||||||||
\(785\) | −1.26249 | −0.0450600 | ||||||||
\(786\) | −11.9690 | −0.426921 | ||||||||
\(787\) | 31.7040 | 1.13013 | 0.565063 | − | 0.825048i | \(-0.308852\pi\) | ||||
0.565063 | + | 0.825048i | \(0.308852\pi\) | |||||||
\(788\) | −0.0499995 | −0.00178116 | ||||||||
\(789\) | 18.6103 | 0.662543 | ||||||||
\(790\) | 9.11070 | 0.324144 | ||||||||
\(791\) | 61.6206 | 2.19098 | ||||||||
\(792\) | 5.85219 | 0.207949 | ||||||||
\(793\) | 14.1513 | 0.502526 | ||||||||
\(794\) | 26.1141 | 0.926755 | ||||||||
\(795\) | −1.74966 | −0.0620542 | ||||||||
\(796\) | −21.6481 | −0.767296 | ||||||||
\(797\) | 48.6722 | 1.72406 | 0.862028 | − | 0.506861i | \(-0.169194\pi\) | ||||
0.862028 | + | 0.506861i | \(0.169194\pi\) | |||||||
\(798\) | 21.3063 | 0.754233 | ||||||||
\(799\) | 20.9617 | 0.741571 | ||||||||
\(800\) | −4.62497 | −0.163517 | ||||||||
\(801\) | 8.15381 | 0.288101 | ||||||||
\(802\) | −30.5163 | −1.07757 | ||||||||
\(803\) | −16.1234 | −0.568983 | ||||||||
\(804\) | −4.74317 | −0.167279 | ||||||||
\(805\) | 10.9092 | 0.384498 | ||||||||
\(806\) | −4.63030 | −0.163095 | ||||||||
\(807\) | 10.2151 | 0.359589 | ||||||||
\(808\) | 12.0412 | 0.423608 | ||||||||
\(809\) | 6.54336 | 0.230052 | 0.115026 | − | 0.993362i | \(-0.463305\pi\) | ||||
0.115026 | + | 0.993362i | \(0.463305\pi\) | |||||||
\(810\) | −0.612396 | −0.0215174 | ||||||||
\(811\) | −19.0964 | −0.670565 | −0.335282 | − | 0.942118i | \(-0.608832\pi\) | ||||
−0.335282 | + | 0.942118i | \(0.608832\pi\) | |||||||
\(812\) | 25.0669 | 0.879677 | ||||||||
\(813\) | −9.90095 | −0.347241 | ||||||||
\(814\) | −28.7132 | −1.00640 | ||||||||
\(815\) | −4.30631 | −0.150843 | ||||||||
\(816\) | −4.41285 | −0.154481 | ||||||||
\(817\) | 40.6360 | 1.42168 | ||||||||
\(818\) | 7.07618 | 0.247413 | ||||||||
\(819\) | −3.48353 | −0.121724 | ||||||||
\(820\) | 1.67391 | 0.0584555 | ||||||||
\(821\) | 41.0461 | 1.43252 | 0.716259 | − | 0.697835i | \(-0.245853\pi\) | ||||
0.716259 | + | 0.697835i | \(0.245853\pi\) | |||||||
\(822\) | 21.7646 | 0.759126 | ||||||||
\(823\) | 12.4626 | 0.434420 | 0.217210 | − | 0.976125i | \(-0.430304\pi\) | ||||
0.217210 | + | 0.976125i | \(0.430304\pi\) | |||||||
\(824\) | 1.00000 | 0.0348367 | ||||||||
\(825\) | −27.0662 | −0.942325 | ||||||||
\(826\) | −35.1193 | −1.22196 | ||||||||
\(827\) | 13.2011 | 0.459048 | 0.229524 | − | 0.973303i | \(-0.426283\pi\) | ||||
0.229524 | + | 0.973303i | \(0.426283\pi\) | |||||||
\(828\) | 5.11376 | 0.177715 | ||||||||
\(829\) | −13.7036 | −0.475945 | −0.237972 | − | 0.971272i | \(-0.576483\pi\) | ||||
−0.237972 | + | 0.971272i | \(0.576483\pi\) | |||||||
\(830\) | −10.7491 | −0.373108 | ||||||||
\(831\) | −15.2883 | −0.530345 | ||||||||
\(832\) | 1.00000 | 0.0346688 | ||||||||
\(833\) | −22.6599 | −0.785121 | ||||||||
\(834\) | −20.0706 | −0.694987 | ||||||||
\(835\) | 3.19730 | 0.110647 | ||||||||
\(836\) | −35.7936 | −1.23795 | ||||||||
\(837\) | −4.63030 | −0.160047 | ||||||||
\(838\) | −8.13256 | −0.280935 | ||||||||
\(839\) | 24.5301 | 0.846872 | 0.423436 | − | 0.905926i | \(-0.360824\pi\) | ||||
0.423436 | + | 0.905926i | \(0.360824\pi\) | |||||||
\(840\) | 2.13330 | 0.0736058 | ||||||||
\(841\) | 22.7801 | 0.785520 | ||||||||
\(842\) | 33.9300 | 1.16930 | ||||||||
\(843\) | −29.0625 | −1.00096 | ||||||||
\(844\) | −22.1750 | −0.763294 | ||||||||
\(845\) | −0.612396 | −0.0210670 | ||||||||
\(846\) | −4.75015 | −0.163313 | ||||||||
\(847\) | −80.9856 | −2.78270 | ||||||||
\(848\) | 2.85708 | 0.0981126 | ||||||||
\(849\) | −8.88160 | −0.304816 | ||||||||
\(850\) | 20.4093 | 0.700033 | ||||||||
\(851\) | −25.0901 | −0.860079 | ||||||||
\(852\) | −5.14935 | −0.176414 | ||||||||
\(853\) | 3.99574 | 0.136812 | 0.0684058 | − | 0.997658i | \(-0.478209\pi\) | ||||
0.0684058 | + | 0.997658i | \(0.478209\pi\) | |||||||
\(854\) | −49.2964 | −1.68689 | ||||||||
\(855\) | 3.74558 | 0.128096 | ||||||||
\(856\) | −11.1516 | −0.381155 | ||||||||
\(857\) | 11.1097 | 0.379500 | 0.189750 | − | 0.981832i | \(-0.439232\pi\) | ||||
0.189750 | + | 0.981832i | \(0.439232\pi\) | |||||||
\(858\) | 5.85219 | 0.199790 | ||||||||
\(859\) | 55.0781 | 1.87924 | 0.939620 | − | 0.342220i | \(-0.111179\pi\) | ||||
0.939620 | + | 0.342220i | \(0.111179\pi\) | |||||||
\(860\) | 4.06870 | 0.138742 | ||||||||
\(861\) | 9.52182 | 0.324503 | ||||||||
\(862\) | 25.4352 | 0.866326 | ||||||||
\(863\) | −52.6209 | −1.79124 | −0.895618 | − | 0.444824i | \(-0.853266\pi\) | ||||
−0.895618 | + | 0.444824i | \(0.853266\pi\) | |||||||
\(864\) | 1.00000 | 0.0340207 | ||||||||
\(865\) | 0.473147 | 0.0160875 | ||||||||
\(866\) | 6.45505 | 0.219352 | ||||||||
\(867\) | 2.47323 | 0.0839953 | ||||||||
\(868\) | 16.1298 | 0.547481 | ||||||||
\(869\) | −87.0639 | −2.95344 | ||||||||
\(870\) | 4.40670 | 0.149401 | ||||||||
\(871\) | −4.74317 | −0.160716 | ||||||||
\(872\) | −17.3067 | −0.586080 | ||||||||
\(873\) | −16.6216 | −0.562556 | ||||||||
\(874\) | −31.2772 | −1.05797 | ||||||||
\(875\) | −20.5329 | −0.694140 | ||||||||
\(876\) | −2.75511 | −0.0930865 | ||||||||
\(877\) | −21.1462 | −0.714058 | −0.357029 | − | 0.934093i | \(-0.616210\pi\) | ||||
−0.357029 | + | 0.934093i | \(0.616210\pi\) | |||||||
\(878\) | −5.52037 | −0.186303 | ||||||||
\(879\) | 20.6747 | 0.697339 | ||||||||
\(880\) | −3.58386 | −0.120812 | ||||||||
\(881\) | 15.9866 | 0.538601 | 0.269301 | − | 0.963056i | \(-0.413207\pi\) | ||||
0.269301 | + | 0.963056i | \(0.413207\pi\) | |||||||
\(882\) | 5.13499 | 0.172904 | ||||||||
\(883\) | 19.3224 | 0.650252 | 0.325126 | − | 0.945671i | \(-0.394593\pi\) | ||||
0.325126 | + | 0.945671i | \(0.394593\pi\) | |||||||
\(884\) | −4.41285 | −0.148420 | ||||||||
\(885\) | −6.17388 | −0.207533 | ||||||||
\(886\) | −1.12187 | −0.0376899 | ||||||||
\(887\) | −54.5289 | −1.83090 | −0.915451 | − | 0.402430i | \(-0.868166\pi\) | ||||
−0.915451 | + | 0.402430i | \(0.868166\pi\) | |||||||
\(888\) | −4.90640 | −0.164648 | ||||||||
\(889\) | −19.1666 | −0.642828 | ||||||||
\(890\) | −4.99336 | −0.167378 | ||||||||
\(891\) | 5.85219 | 0.196056 | ||||||||
\(892\) | 4.05280 | 0.135698 | ||||||||
\(893\) | 29.0532 | 0.972229 | ||||||||
\(894\) | 7.12490 | 0.238292 | ||||||||
\(895\) | 6.46860 | 0.216221 | ||||||||
\(896\) | −3.48353 | −0.116377 | ||||||||
\(897\) | 5.11376 | 0.170743 | ||||||||
\(898\) | −21.3872 | −0.713700 | ||||||||
\(899\) | 33.3189 | 1.11125 | ||||||||
\(900\) | −4.62497 | −0.154166 | ||||||||
\(901\) | −12.6079 | −0.420029 | ||||||||
\(902\) | −15.9963 | −0.532618 | ||||||||
\(903\) | 23.1443 | 0.770194 | ||||||||
\(904\) | −17.6891 | −0.588331 | ||||||||
\(905\) | −6.60253 | −0.219475 | ||||||||
\(906\) | −7.40255 | −0.245933 | ||||||||
\(907\) | −10.9245 | −0.362741 | −0.181370 | − | 0.983415i | \(-0.558053\pi\) | ||||
−0.181370 | + | 0.983415i | \(0.558053\pi\) | |||||||
\(908\) | −7.40828 | −0.245852 | ||||||||
\(909\) | 12.0412 | 0.399382 | ||||||||
\(910\) | 2.13330 | 0.0707182 | ||||||||
\(911\) | −25.7835 | −0.854244 | −0.427122 | − | 0.904194i | \(-0.640473\pi\) | ||||
−0.427122 | + | 0.904194i | \(0.640473\pi\) | |||||||
\(912\) | −6.11628 | −0.202530 | ||||||||
\(913\) | 102.721 | 3.39958 | ||||||||
\(914\) | −35.8670 | −1.18638 | ||||||||
\(915\) | −8.66617 | −0.286495 | ||||||||
\(916\) | −1.36046 | −0.0449509 | ||||||||
\(917\) | 41.6945 | 1.37687 | ||||||||
\(918\) | −4.41285 | −0.145646 | ||||||||
\(919\) | −26.0283 | −0.858595 | −0.429298 | − | 0.903163i | \(-0.641239\pi\) | ||||
−0.429298 | + | 0.903163i | \(0.641239\pi\) | |||||||
\(920\) | −3.13164 | −0.103247 | ||||||||
\(921\) | 28.7899 | 0.948660 | ||||||||
\(922\) | 18.2746 | 0.601843 | ||||||||
\(923\) | −5.14935 | −0.169493 | ||||||||
\(924\) | −20.3863 | −0.670660 | ||||||||
\(925\) | 22.6920 | 0.746107 | ||||||||
\(926\) | −12.7228 | −0.418097 | ||||||||
\(927\) | 1.00000 | 0.0328443 | ||||||||
\(928\) | −7.19584 | −0.236215 | ||||||||
\(929\) | −49.0183 | −1.60824 | −0.804119 | − | 0.594469i | \(-0.797362\pi\) | ||||
−0.804119 | + | 0.594469i | \(0.797362\pi\) | |||||||
\(930\) | 2.83557 | 0.0929822 | ||||||||
\(931\) | −31.4071 | −1.02932 | ||||||||
\(932\) | 2.92599 | 0.0958441 | ||||||||
\(933\) | −14.2384 | −0.466145 | ||||||||
\(934\) | 4.92734 | 0.161228 | ||||||||
\(935\) | 15.8150 | 0.517206 | ||||||||
\(936\) | 1.00000 | 0.0326860 | ||||||||
\(937\) | −6.72812 | −0.219798 | −0.109899 | − | 0.993943i | \(-0.535053\pi\) | ||||
−0.109899 | + | 0.993943i | \(0.535053\pi\) | |||||||
\(938\) | 16.5230 | 0.539495 | ||||||||
\(939\) | −28.8988 | −0.943076 | ||||||||
\(940\) | 2.90897 | 0.0948801 | ||||||||
\(941\) | 31.5977 | 1.03006 | 0.515028 | − | 0.857173i | \(-0.327781\pi\) | ||||
0.515028 | + | 0.857173i | \(0.327781\pi\) | |||||||
\(942\) | 2.06155 | 0.0671690 | ||||||||
\(943\) | −13.9779 | −0.455181 | ||||||||
\(944\) | 10.0815 | 0.328125 | ||||||||
\(945\) | 2.13330 | 0.0693962 | ||||||||
\(946\) | −38.8814 | −1.26414 | ||||||||
\(947\) | −17.8014 | −0.578467 | −0.289234 | − | 0.957259i | \(-0.593400\pi\) | ||||
−0.289234 | + | 0.957259i | \(0.593400\pi\) | |||||||
\(948\) | −14.8772 | −0.483187 | ||||||||
\(949\) | −2.75511 | −0.0894347 | ||||||||
\(950\) | 28.2876 | 0.917772 | ||||||||
\(951\) | 17.5058 | 0.567665 | ||||||||
\(952\) | 15.3723 | 0.498219 | ||||||||
\(953\) | 2.08963 | 0.0676898 | 0.0338449 | − | 0.999427i | \(-0.489225\pi\) | ||||
0.0338449 | + | 0.999427i | \(0.489225\pi\) | |||||||
\(954\) | 2.85708 | 0.0925014 | ||||||||
\(955\) | −9.13844 | −0.295713 | ||||||||
\(956\) | −9.80743 | −0.317195 | ||||||||
\(957\) | −42.1114 | −1.36127 | ||||||||
\(958\) | −37.8264 | −1.22211 | ||||||||
\(959\) | −75.8175 | −2.44828 | ||||||||
\(960\) | −0.612396 | −0.0197650 | ||||||||
\(961\) | −9.56033 | −0.308398 | ||||||||
\(962\) | −4.90640 | −0.158189 | ||||||||
\(963\) | −11.1516 | −0.359356 | ||||||||
\(964\) | −3.18594 | −0.102612 | ||||||||
\(965\) | 3.64537 | 0.117349 | ||||||||
\(966\) | −17.8139 | −0.573154 | ||||||||
\(967\) | 4.77847 | 0.153665 | 0.0768326 | − | 0.997044i | \(-0.475519\pi\) | ||||
0.0768326 | + | 0.997044i | \(0.475519\pi\) | |||||||
\(968\) | 23.2481 | 0.747223 | ||||||||
\(969\) | 26.9902 | 0.867051 | ||||||||
\(970\) | 10.1790 | 0.326828 | ||||||||
\(971\) | 50.8623 | 1.63225 | 0.816124 | − | 0.577877i | \(-0.196119\pi\) | ||||
0.816124 | + | 0.577877i | \(0.196119\pi\) | |||||||
\(972\) | 1.00000 | 0.0320750 | ||||||||
\(973\) | 69.9165 | 2.24142 | ||||||||
\(974\) | 33.2028 | 1.06389 | ||||||||
\(975\) | −4.62497 | −0.148118 | ||||||||
\(976\) | 14.1513 | 0.452971 | ||||||||
\(977\) | 42.7067 | 1.36631 | 0.683155 | − | 0.730274i | \(-0.260607\pi\) | ||||
0.683155 | + | 0.730274i | \(0.260607\pi\) | |||||||
\(978\) | 7.03191 | 0.224856 | ||||||||
\(979\) | 47.7176 | 1.52506 | ||||||||
\(980\) | −3.14465 | −0.100452 | ||||||||
\(981\) | −17.3067 | −0.552561 | ||||||||
\(982\) | −32.9200 | −1.05052 | ||||||||
\(983\) | −48.5646 | −1.54897 | −0.774485 | − | 0.632592i | \(-0.781991\pi\) | ||||
−0.774485 | + | 0.632592i | \(0.781991\pi\) | |||||||
\(984\) | −2.73338 | −0.0871370 | ||||||||
\(985\) | 0.0306195 | 0.000975618 0 | ||||||||
\(986\) | 31.7541 | 1.01126 | ||||||||
\(987\) | 16.5473 | 0.526706 | ||||||||
\(988\) | −6.11628 | −0.194585 | ||||||||
\(989\) | −33.9754 | −1.08035 | ||||||||
\(990\) | −3.58386 | −0.113902 | ||||||||
\(991\) | −12.7901 | −0.406292 | −0.203146 | − | 0.979148i | \(-0.565117\pi\) | ||||
−0.203146 | + | 0.979148i | \(0.565117\pi\) | |||||||
\(992\) | −4.63030 | −0.147012 | ||||||||
\(993\) | 13.6127 | 0.431986 | ||||||||
\(994\) | 17.9379 | 0.568957 | ||||||||
\(995\) | 13.2572 | 0.420281 | ||||||||
\(996\) | 17.5526 | 0.556176 | ||||||||
\(997\) | −16.0228 | −0.507447 | −0.253723 | − | 0.967277i | \(-0.581655\pi\) | ||||
−0.253723 | + | 0.967277i | \(0.581655\pi\) | |||||||
\(998\) | 43.7955 | 1.38632 | ||||||||
\(999\) | −4.90640 | −0.155232 |
(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 | 8034.2.a.p.1.5 | ✓ | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8034.2.a.p.1.5 | ✓ | 8 | 1.1 | even | 1 | trivial |