Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4334,2,Mod(1,4334)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4334, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4334.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4334 = 2 \cdot 11 \cdot 197 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4334.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: | \(34.6071642360\) |
Analytic rank: | \(1\) |
Dimension: | \(15\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{15} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{15} - x^{14} - 23 x^{13} + 19 x^{12} + 194 x^{11} - 124 x^{10} - 761 x^{9} + 353 x^{8} + 1417 x^{7} - 465 x^{6} - 1128 x^{5} + 288 x^{4} + 316 x^{3} - 79 x^{2} - 20 x + 4 \)
|
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.13 | ||
Root | \(-1.77498\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4334.1 |
$q$-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 | ||||||||
\(3\) | 1.77498 | 1.02479 | 0.512393 | − | 0.858751i | \(-0.328759\pi\) | ||||
0.512393 | + | 0.858751i | \(0.328759\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −0.781935 | −0.349692 | −0.174846 | − | 0.984596i | \(-0.555943\pi\) | ||||
−0.174846 | + | 0.984596i | \(0.555943\pi\) | |||||||
\(6\) | −1.77498 | −0.724632 | ||||||||
\(7\) | 2.50677 | 0.947472 | 0.473736 | − | 0.880667i | \(-0.342905\pi\) | ||||
0.473736 | + | 0.880667i | \(0.342905\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 0.150553 | 0.0501844 | ||||||||
\(10\) | 0.781935 | 0.247270 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | 1.77498 | 0.512393 | ||||||||
\(13\) | −1.62749 | −0.451385 | −0.225692 | − | 0.974199i | \(-0.572464\pi\) | ||||
−0.225692 | + | 0.974199i | \(0.572464\pi\) | |||||||
\(14\) | −2.50677 | −0.669964 | ||||||||
\(15\) | −1.38792 | −0.358359 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 0.818716 | 0.198568 | 0.0992839 | − | 0.995059i | \(-0.468345\pi\) | ||||
0.0992839 | + | 0.995059i | \(0.468345\pi\) | |||||||
\(18\) | −0.150553 | −0.0354857 | ||||||||
\(19\) | −2.63893 | −0.605413 | −0.302706 | − | 0.953084i | \(-0.597890\pi\) | ||||
−0.302706 | + | 0.953084i | \(0.597890\pi\) | |||||||
\(20\) | −0.781935 | −0.174846 | ||||||||
\(21\) | 4.44947 | 0.970955 | ||||||||
\(22\) | −1.00000 | −0.213201 | ||||||||
\(23\) | −0.372117 | −0.0775918 | −0.0387959 | − | 0.999247i | \(-0.512352\pi\) | ||||
−0.0387959 | + | 0.999247i | \(0.512352\pi\) | |||||||
\(24\) | −1.77498 | −0.362316 | ||||||||
\(25\) | −4.38858 | −0.877715 | ||||||||
\(26\) | 1.62749 | 0.319177 | ||||||||
\(27\) | −5.05771 | −0.973357 | ||||||||
\(28\) | 2.50677 | 0.473736 | ||||||||
\(29\) | −9.27335 | −1.72202 | −0.861009 | − | 0.508590i | \(-0.830167\pi\) | ||||
−0.861009 | + | 0.508590i | \(0.830167\pi\) | |||||||
\(30\) | 1.38792 | 0.253398 | ||||||||
\(31\) | −1.78637 | −0.320842 | −0.160421 | − | 0.987049i | \(-0.551285\pi\) | ||||
−0.160421 | + | 0.987049i | \(0.551285\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 1.77498 | 0.308984 | ||||||||
\(34\) | −0.818716 | −0.140409 | ||||||||
\(35\) | −1.96014 | −0.331323 | ||||||||
\(36\) | 0.150553 | 0.0250922 | ||||||||
\(37\) | −1.76213 | −0.289692 | −0.144846 | − | 0.989454i | \(-0.546269\pi\) | ||||
−0.144846 | + | 0.989454i | \(0.546269\pi\) | |||||||
\(38\) | 2.63893 | 0.428092 | ||||||||
\(39\) | −2.88876 | −0.462572 | ||||||||
\(40\) | 0.781935 | 0.123635 | ||||||||
\(41\) | 1.44923 | 0.226332 | 0.113166 | − | 0.993576i | \(-0.463901\pi\) | ||||
0.113166 | + | 0.993576i | \(0.463901\pi\) | |||||||
\(42\) | −4.44947 | −0.686569 | ||||||||
\(43\) | −6.20306 | −0.945958 | −0.472979 | − | 0.881074i | \(-0.656821\pi\) | ||||
−0.472979 | + | 0.881074i | \(0.656821\pi\) | |||||||
\(44\) | 1.00000 | 0.150756 | ||||||||
\(45\) | −0.117723 | −0.0175491 | ||||||||
\(46\) | 0.372117 | 0.0548657 | ||||||||
\(47\) | −3.71682 | −0.542154 | −0.271077 | − | 0.962558i | \(-0.587380\pi\) | ||||
−0.271077 | + | 0.962558i | \(0.587380\pi\) | |||||||
\(48\) | 1.77498 | 0.256196 | ||||||||
\(49\) | −0.716080 | −0.102297 | ||||||||
\(50\) | 4.38858 | 0.620639 | ||||||||
\(51\) | 1.45320 | 0.203489 | ||||||||
\(52\) | −1.62749 | −0.225692 | ||||||||
\(53\) | −4.17393 | −0.573334 | −0.286667 | − | 0.958030i | \(-0.592547\pi\) | ||||
−0.286667 | + | 0.958030i | \(0.592547\pi\) | |||||||
\(54\) | 5.05771 | 0.688267 | ||||||||
\(55\) | −0.781935 | −0.105436 | ||||||||
\(56\) | −2.50677 | −0.334982 | ||||||||
\(57\) | −4.68405 | −0.620418 | ||||||||
\(58\) | 9.27335 | 1.21765 | ||||||||
\(59\) | 1.81440 | 0.236214 | 0.118107 | − | 0.993001i | \(-0.462317\pi\) | ||||
0.118107 | + | 0.993001i | \(0.462317\pi\) | |||||||
\(60\) | −1.38792 | −0.179180 | ||||||||
\(61\) | −9.44494 | −1.20930 | −0.604650 | − | 0.796491i | \(-0.706687\pi\) | ||||
−0.604650 | + | 0.796491i | \(0.706687\pi\) | |||||||
\(62\) | 1.78637 | 0.226870 | ||||||||
\(63\) | 0.377403 | 0.0475483 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 1.27259 | 0.157846 | ||||||||
\(66\) | −1.77498 | −0.218485 | ||||||||
\(67\) | −5.26558 | −0.643293 | −0.321646 | − | 0.946860i | \(-0.604236\pi\) | ||||
−0.321646 | + | 0.946860i | \(0.604236\pi\) | |||||||
\(68\) | 0.818716 | 0.0992839 | ||||||||
\(69\) | −0.660501 | −0.0795150 | ||||||||
\(70\) | 1.96014 | 0.234281 | ||||||||
\(71\) | 15.4660 | 1.83548 | 0.917740 | − | 0.397182i | \(-0.130012\pi\) | ||||
0.917740 | + | 0.397182i | \(0.130012\pi\) | |||||||
\(72\) | −0.150553 | −0.0177429 | ||||||||
\(73\) | 15.1608 | 1.77444 | 0.887218 | − | 0.461351i | \(-0.152635\pi\) | ||||
0.887218 | + | 0.461351i | \(0.152635\pi\) | |||||||
\(74\) | 1.76213 | 0.204843 | ||||||||
\(75\) | −7.78964 | −0.899470 | ||||||||
\(76\) | −2.63893 | −0.302706 | ||||||||
\(77\) | 2.50677 | 0.285674 | ||||||||
\(78\) | 2.88876 | 0.327088 | ||||||||
\(79\) | −14.1141 | −1.58796 | −0.793978 | − | 0.607946i | \(-0.791994\pi\) | ||||
−0.793978 | + | 0.607946i | \(0.791994\pi\) | |||||||
\(80\) | −0.781935 | −0.0874230 | ||||||||
\(81\) | −9.42899 | −1.04767 | ||||||||
\(82\) | −1.44923 | −0.160041 | ||||||||
\(83\) | 12.5488 | 1.37741 | 0.688707 | − | 0.725040i | \(-0.258179\pi\) | ||||
0.688707 | + | 0.725040i | \(0.258179\pi\) | |||||||
\(84\) | 4.44947 | 0.485477 | ||||||||
\(85\) | −0.640183 | −0.0694376 | ||||||||
\(86\) | 6.20306 | 0.668893 | ||||||||
\(87\) | −16.4600 | −1.76470 | ||||||||
\(88\) | −1.00000 | −0.106600 | ||||||||
\(89\) | −9.46795 | −1.00360 | −0.501800 | − | 0.864983i | \(-0.667329\pi\) | ||||
−0.501800 | + | 0.864983i | \(0.667329\pi\) | |||||||
\(90\) | 0.117723 | 0.0124091 | ||||||||
\(91\) | −4.07975 | −0.427674 | ||||||||
\(92\) | −0.372117 | −0.0387959 | ||||||||
\(93\) | −3.17078 | −0.328794 | ||||||||
\(94\) | 3.71682 | 0.383361 | ||||||||
\(95\) | 2.06348 | 0.211708 | ||||||||
\(96\) | −1.77498 | −0.181158 | ||||||||
\(97\) | −1.58308 | −0.160738 | −0.0803688 | − | 0.996765i | \(-0.525610\pi\) | ||||
−0.0803688 | + | 0.996765i | \(0.525610\pi\) | |||||||
\(98\) | 0.716080 | 0.0723350 | ||||||||
\(99\) | 0.150553 | 0.0151312 | ||||||||
\(100\) | −4.38858 | −0.438858 | ||||||||
\(101\) | 14.9101 | 1.48361 | 0.741806 | − | 0.670614i | \(-0.233969\pi\) | ||||
0.741806 | + | 0.670614i | \(0.233969\pi\) | |||||||
\(102\) | −1.45320 | −0.143889 | ||||||||
\(103\) | 5.87321 | 0.578704 | 0.289352 | − | 0.957223i | \(-0.406560\pi\) | ||||
0.289352 | + | 0.957223i | \(0.406560\pi\) | |||||||
\(104\) | 1.62749 | 0.159589 | ||||||||
\(105\) | −3.47920 | −0.339535 | ||||||||
\(106\) | 4.17393 | 0.405408 | ||||||||
\(107\) | −16.9770 | −1.64122 | −0.820612 | − | 0.571486i | \(-0.806367\pi\) | ||||
−0.820612 | + | 0.571486i | \(0.806367\pi\) | |||||||
\(108\) | −5.05771 | −0.486678 | ||||||||
\(109\) | −3.16635 | −0.303282 | −0.151641 | − | 0.988436i | \(-0.548456\pi\) | ||||
−0.151641 | + | 0.988436i | \(0.548456\pi\) | |||||||
\(110\) | 0.781935 | 0.0745546 | ||||||||
\(111\) | −3.12774 | −0.296872 | ||||||||
\(112\) | 2.50677 | 0.236868 | ||||||||
\(113\) | −0.907314 | −0.0853529 | −0.0426765 | − | 0.999089i | \(-0.513588\pi\) | ||||
−0.0426765 | + | 0.999089i | \(0.513588\pi\) | |||||||
\(114\) | 4.68405 | 0.438702 | ||||||||
\(115\) | 0.290972 | 0.0271333 | ||||||||
\(116\) | −9.27335 | −0.861009 | ||||||||
\(117\) | −0.245024 | −0.0226525 | ||||||||
\(118\) | −1.81440 | −0.167029 | ||||||||
\(119\) | 2.05234 | 0.188137 | ||||||||
\(120\) | 1.38792 | 0.126699 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 9.44494 | 0.855105 | ||||||||
\(123\) | 2.57236 | 0.231942 | ||||||||
\(124\) | −1.78637 | −0.160421 | ||||||||
\(125\) | 7.34126 | 0.656622 | ||||||||
\(126\) | −0.377403 | −0.0336217 | ||||||||
\(127\) | −11.2218 | −0.995778 | −0.497889 | − | 0.867241i | \(-0.665891\pi\) | ||||
−0.497889 | + | 0.867241i | \(0.665891\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −11.0103 | −0.969404 | ||||||||
\(130\) | −1.27259 | −0.111614 | ||||||||
\(131\) | 19.0329 | 1.66291 | 0.831455 | − | 0.555591i | \(-0.187508\pi\) | ||||
0.831455 | + | 0.555591i | \(0.187508\pi\) | |||||||
\(132\) | 1.77498 | 0.154492 | ||||||||
\(133\) | −6.61521 | −0.573612 | ||||||||
\(134\) | 5.26558 | 0.454877 | ||||||||
\(135\) | 3.95480 | 0.340375 | ||||||||
\(136\) | −0.818716 | −0.0702043 | ||||||||
\(137\) | −17.5646 | −1.50065 | −0.750324 | − | 0.661070i | \(-0.770103\pi\) | ||||
−0.750324 | + | 0.661070i | \(0.770103\pi\) | |||||||
\(138\) | 0.660501 | 0.0562256 | ||||||||
\(139\) | 2.44108 | 0.207049 | 0.103525 | − | 0.994627i | \(-0.466988\pi\) | ||||
0.103525 | + | 0.994627i | \(0.466988\pi\) | |||||||
\(140\) | −1.96014 | −0.165662 | ||||||||
\(141\) | −6.59728 | −0.555591 | ||||||||
\(142\) | −15.4660 | −1.29788 | ||||||||
\(143\) | −1.62749 | −0.136098 | ||||||||
\(144\) | 0.150553 | 0.0125461 | ||||||||
\(145\) | 7.25116 | 0.602176 | ||||||||
\(146\) | −15.1608 | −1.25472 | ||||||||
\(147\) | −1.27103 | −0.104833 | ||||||||
\(148\) | −1.76213 | −0.144846 | ||||||||
\(149\) | 11.3385 | 0.928887 | 0.464444 | − | 0.885603i | \(-0.346254\pi\) | ||||
0.464444 | + | 0.885603i | \(0.346254\pi\) | |||||||
\(150\) | 7.78964 | 0.636021 | ||||||||
\(151\) | −1.88511 | −0.153408 | −0.0767040 | − | 0.997054i | \(-0.524440\pi\) | ||||
−0.0767040 | + | 0.997054i | \(0.524440\pi\) | |||||||
\(152\) | 2.63893 | 0.214046 | ||||||||
\(153\) | 0.123260 | 0.00996500 | ||||||||
\(154\) | −2.50677 | −0.202002 | ||||||||
\(155\) | 1.39683 | 0.112196 | ||||||||
\(156\) | −2.88876 | −0.231286 | ||||||||
\(157\) | 15.0113 | 1.19803 | 0.599016 | − | 0.800737i | \(-0.295559\pi\) | ||||
0.599016 | + | 0.800737i | \(0.295559\pi\) | |||||||
\(158\) | 14.1141 | 1.12286 | ||||||||
\(159\) | −7.40865 | −0.587544 | ||||||||
\(160\) | 0.781935 | 0.0618174 | ||||||||
\(161\) | −0.932815 | −0.0735161 | ||||||||
\(162\) | 9.42899 | 0.740812 | ||||||||
\(163\) | −10.5044 | −0.822765 | −0.411382 | − | 0.911463i | \(-0.634954\pi\) | ||||
−0.411382 | + | 0.911463i | \(0.634954\pi\) | |||||||
\(164\) | 1.44923 | 0.113166 | ||||||||
\(165\) | −1.38792 | −0.108049 | ||||||||
\(166\) | −12.5488 | −0.973978 | ||||||||
\(167\) | 1.67807 | 0.129853 | 0.0649266 | − | 0.997890i | \(-0.479319\pi\) | ||||
0.0649266 | + | 0.997890i | \(0.479319\pi\) | |||||||
\(168\) | −4.44947 | −0.343284 | ||||||||
\(169\) | −10.3513 | −0.796252 | ||||||||
\(170\) | 0.640183 | 0.0490998 | ||||||||
\(171\) | −0.397300 | −0.0303823 | ||||||||
\(172\) | −6.20306 | −0.472979 | ||||||||
\(173\) | 6.87018 | 0.522330 | 0.261165 | − | 0.965294i | \(-0.415893\pi\) | ||||
0.261165 | + | 0.965294i | \(0.415893\pi\) | |||||||
\(174\) | 16.4600 | 1.24783 | ||||||||
\(175\) | −11.0012 | −0.831611 | ||||||||
\(176\) | 1.00000 | 0.0753778 | ||||||||
\(177\) | 3.22052 | 0.242069 | ||||||||
\(178\) | 9.46795 | 0.709653 | ||||||||
\(179\) | −15.2669 | −1.14110 | −0.570552 | − | 0.821261i | \(-0.693271\pi\) | ||||
−0.570552 | + | 0.821261i | \(0.693271\pi\) | |||||||
\(180\) | −0.117723 | −0.00877454 | ||||||||
\(181\) | 25.0359 | 1.86091 | 0.930453 | − | 0.366410i | \(-0.119413\pi\) | ||||
0.930453 | + | 0.366410i | \(0.119413\pi\) | |||||||
\(182\) | 4.07975 | 0.302411 | ||||||||
\(183\) | −16.7646 | −1.23927 | ||||||||
\(184\) | 0.372117 | 0.0274329 | ||||||||
\(185\) | 1.37787 | 0.101303 | ||||||||
\(186\) | 3.17078 | 0.232493 | ||||||||
\(187\) | 0.818716 | 0.0598705 | ||||||||
\(188\) | −3.71682 | −0.271077 | ||||||||
\(189\) | −12.6785 | −0.922228 | ||||||||
\(190\) | −2.06348 | −0.149700 | ||||||||
\(191\) | −1.20417 | −0.0871308 | −0.0435654 | − | 0.999051i | \(-0.513872\pi\) | ||||
−0.0435654 | + | 0.999051i | \(0.513872\pi\) | |||||||
\(192\) | 1.77498 | 0.128098 | ||||||||
\(193\) | −14.9340 | −1.07497 | −0.537485 | − | 0.843273i | \(-0.680626\pi\) | ||||
−0.537485 | + | 0.843273i | \(0.680626\pi\) | |||||||
\(194\) | 1.58308 | 0.113659 | ||||||||
\(195\) | 2.25883 | 0.161758 | ||||||||
\(196\) | −0.716080 | −0.0511485 | ||||||||
\(197\) | 1.00000 | 0.0712470 | ||||||||
\(198\) | −0.150553 | −0.0106993 | ||||||||
\(199\) | −15.2442 | −1.08064 | −0.540318 | − | 0.841461i | \(-0.681696\pi\) | ||||
−0.540318 | + | 0.841461i | \(0.681696\pi\) | |||||||
\(200\) | 4.38858 | 0.310319 | ||||||||
\(201\) | −9.34629 | −0.659237 | ||||||||
\(202\) | −14.9101 | −1.04907 | ||||||||
\(203\) | −23.2462 | −1.63156 | ||||||||
\(204\) | 1.45320 | 0.101745 | ||||||||
\(205\) | −1.13321 | −0.0791467 | ||||||||
\(206\) | −5.87321 | −0.409206 | ||||||||
\(207\) | −0.0560234 | −0.00389390 | ||||||||
\(208\) | −1.62749 | −0.112846 | ||||||||
\(209\) | −2.63893 | −0.182539 | ||||||||
\(210\) | 3.47920 | 0.240088 | ||||||||
\(211\) | 1.69924 | 0.116981 | 0.0584904 | − | 0.998288i | \(-0.481371\pi\) | ||||
0.0584904 | + | 0.998288i | \(0.481371\pi\) | |||||||
\(212\) | −4.17393 | −0.286667 | ||||||||
\(213\) | 27.4519 | 1.88097 | ||||||||
\(214\) | 16.9770 | 1.16052 | ||||||||
\(215\) | 4.85039 | 0.330794 | ||||||||
\(216\) | 5.05771 | 0.344134 | ||||||||
\(217\) | −4.47804 | −0.303989 | ||||||||
\(218\) | 3.16635 | 0.214452 | ||||||||
\(219\) | 26.9101 | 1.81842 | ||||||||
\(220\) | −0.781935 | −0.0527181 | ||||||||
\(221\) | −1.33245 | −0.0896305 | ||||||||
\(222\) | 3.12774 | 0.209920 | ||||||||
\(223\) | −17.4207 | −1.16658 | −0.583288 | − | 0.812265i | \(-0.698234\pi\) | ||||
−0.583288 | + | 0.812265i | \(0.698234\pi\) | |||||||
\(224\) | −2.50677 | −0.167491 | ||||||||
\(225\) | −0.660714 | −0.0440476 | ||||||||
\(226\) | 0.907314 | 0.0603536 | ||||||||
\(227\) | 17.0235 | 1.12989 | 0.564945 | − | 0.825129i | \(-0.308897\pi\) | ||||
0.564945 | + | 0.825129i | \(0.308897\pi\) | |||||||
\(228\) | −4.68405 | −0.310209 | ||||||||
\(229\) | 24.1710 | 1.59727 | 0.798634 | − | 0.601818i | \(-0.205557\pi\) | ||||
0.798634 | + | 0.601818i | \(0.205557\pi\) | |||||||
\(230\) | −0.290972 | −0.0191861 | ||||||||
\(231\) | 4.44947 | 0.292754 | ||||||||
\(232\) | 9.27335 | 0.608825 | ||||||||
\(233\) | −8.79647 | −0.576276 | −0.288138 | − | 0.957589i | \(-0.593036\pi\) | ||||
−0.288138 | + | 0.957589i | \(0.593036\pi\) | |||||||
\(234\) | 0.245024 | 0.0160177 | ||||||||
\(235\) | 2.90631 | 0.189587 | ||||||||
\(236\) | 1.81440 | 0.118107 | ||||||||
\(237\) | −25.0522 | −1.62731 | ||||||||
\(238\) | −2.05234 | −0.133033 | ||||||||
\(239\) | 9.49252 | 0.614020 | 0.307010 | − | 0.951706i | \(-0.400671\pi\) | ||||
0.307010 | + | 0.951706i | \(0.400671\pi\) | |||||||
\(240\) | −1.38792 | −0.0895898 | ||||||||
\(241\) | −4.32087 | −0.278332 | −0.139166 | − | 0.990269i | \(-0.544442\pi\) | ||||
−0.139166 | + | 0.990269i | \(0.544442\pi\) | |||||||
\(242\) | −1.00000 | −0.0642824 | ||||||||
\(243\) | −1.56314 | −0.100275 | ||||||||
\(244\) | −9.44494 | −0.604650 | ||||||||
\(245\) | 0.559928 | 0.0357725 | ||||||||
\(246\) | −2.57236 | −0.164008 | ||||||||
\(247\) | 4.29484 | 0.273274 | ||||||||
\(248\) | 1.78637 | 0.113435 | ||||||||
\(249\) | 22.2739 | 1.41155 | ||||||||
\(250\) | −7.34126 | −0.464302 | ||||||||
\(251\) | −18.6422 | −1.17669 | −0.588343 | − | 0.808612i | \(-0.700219\pi\) | ||||
−0.588343 | + | 0.808612i | \(0.700219\pi\) | |||||||
\(252\) | 0.377403 | 0.0237741 | ||||||||
\(253\) | −0.372117 | −0.0233948 | ||||||||
\(254\) | 11.2218 | 0.704121 | ||||||||
\(255\) | −1.13631 | −0.0711586 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 12.1480 | 0.757774 | 0.378887 | − | 0.925443i | \(-0.376307\pi\) | ||||
0.378887 | + | 0.925443i | \(0.376307\pi\) | |||||||
\(258\) | 11.0103 | 0.685472 | ||||||||
\(259\) | −4.41725 | −0.274475 | ||||||||
\(260\) | 1.27259 | 0.0789228 | ||||||||
\(261\) | −1.39613 | −0.0864184 | ||||||||
\(262\) | −19.0329 | −1.17586 | ||||||||
\(263\) | 13.4102 | 0.826910 | 0.413455 | − | 0.910525i | \(-0.364322\pi\) | ||||
0.413455 | + | 0.910525i | \(0.364322\pi\) | |||||||
\(264\) | −1.77498 | −0.109242 | ||||||||
\(265\) | 3.26375 | 0.200490 | ||||||||
\(266\) | 6.61521 | 0.405605 | ||||||||
\(267\) | −16.8054 | −1.02848 | ||||||||
\(268\) | −5.26558 | −0.321646 | ||||||||
\(269\) | −19.4803 | −1.18774 | −0.593868 | − | 0.804563i | \(-0.702400\pi\) | ||||
−0.593868 | + | 0.804563i | \(0.702400\pi\) | |||||||
\(270\) | −3.95480 | −0.240682 | ||||||||
\(271\) | −15.5878 | −0.946893 | −0.473446 | − | 0.880823i | \(-0.656990\pi\) | ||||
−0.473446 | + | 0.880823i | \(0.656990\pi\) | |||||||
\(272\) | 0.818716 | 0.0496420 | ||||||||
\(273\) | −7.24148 | −0.438274 | ||||||||
\(274\) | 17.5646 | 1.06112 | ||||||||
\(275\) | −4.38858 | −0.264641 | ||||||||
\(276\) | −0.660501 | −0.0397575 | ||||||||
\(277\) | −27.0289 | −1.62401 | −0.812004 | − | 0.583651i | \(-0.801623\pi\) | ||||
−0.812004 | + | 0.583651i | \(0.801623\pi\) | |||||||
\(278\) | −2.44108 | −0.146406 | ||||||||
\(279\) | −0.268944 | −0.0161013 | ||||||||
\(280\) | 1.96014 | 0.117141 | ||||||||
\(281\) | 3.39112 | 0.202297 | 0.101149 | − | 0.994871i | \(-0.467748\pi\) | ||||
0.101149 | + | 0.994871i | \(0.467748\pi\) | |||||||
\(282\) | 6.59728 | 0.392862 | ||||||||
\(283\) | 3.95128 | 0.234879 | 0.117440 | − | 0.993080i | \(-0.462531\pi\) | ||||
0.117440 | + | 0.993080i | \(0.462531\pi\) | |||||||
\(284\) | 15.4660 | 0.917740 | ||||||||
\(285\) | 3.66263 | 0.216955 | ||||||||
\(286\) | 1.62749 | 0.0962355 | ||||||||
\(287\) | 3.63291 | 0.214444 | ||||||||
\(288\) | −0.150553 | −0.00887143 | ||||||||
\(289\) | −16.3297 | −0.960571 | ||||||||
\(290\) | −7.25116 | −0.425803 | ||||||||
\(291\) | −2.80994 | −0.164722 | ||||||||
\(292\) | 15.1608 | 0.887218 | ||||||||
\(293\) | 7.09396 | 0.414434 | 0.207217 | − | 0.978295i | \(-0.433559\pi\) | ||||
0.207217 | + | 0.978295i | \(0.433559\pi\) | |||||||
\(294\) | 1.27103 | 0.0741278 | ||||||||
\(295\) | −1.41874 | −0.0826022 | ||||||||
\(296\) | 1.76213 | 0.102422 | ||||||||
\(297\) | −5.05771 | −0.293478 | ||||||||
\(298\) | −11.3385 | −0.656822 | ||||||||
\(299\) | 0.605618 | 0.0350238 | ||||||||
\(300\) | −7.78964 | −0.449735 | ||||||||
\(301\) | −15.5497 | −0.896269 | ||||||||
\(302\) | 1.88511 | 0.108476 | ||||||||
\(303\) | 26.4652 | 1.52038 | ||||||||
\(304\) | −2.63893 | −0.151353 | ||||||||
\(305\) | 7.38533 | 0.422883 | ||||||||
\(306\) | −0.123260 | −0.00704632 | ||||||||
\(307\) | 10.7934 | 0.616013 | 0.308006 | − | 0.951384i | \(-0.400338\pi\) | ||||
0.308006 | + | 0.951384i | \(0.400338\pi\) | |||||||
\(308\) | 2.50677 | 0.142837 | ||||||||
\(309\) | 10.4248 | 0.593048 | ||||||||
\(310\) | −1.39683 | −0.0793346 | ||||||||
\(311\) | −32.2969 | −1.83139 | −0.915693 | − | 0.401878i | \(-0.868358\pi\) | ||||
−0.915693 | + | 0.401878i | \(0.868358\pi\) | |||||||
\(312\) | 2.88876 | 0.163544 | ||||||||
\(313\) | 16.1264 | 0.911518 | 0.455759 | − | 0.890103i | \(-0.349368\pi\) | ||||
0.455759 | + | 0.890103i | \(0.349368\pi\) | |||||||
\(314\) | −15.0113 | −0.847136 | ||||||||
\(315\) | −0.295104 | −0.0166273 | ||||||||
\(316\) | −14.1141 | −0.793978 | ||||||||
\(317\) | 31.5608 | 1.77263 | 0.886317 | − | 0.463080i | \(-0.153256\pi\) | ||||
0.886317 | + | 0.463080i | \(0.153256\pi\) | |||||||
\(318\) | 7.40865 | 0.415456 | ||||||||
\(319\) | −9.27335 | −0.519208 | ||||||||
\(320\) | −0.781935 | −0.0437115 | ||||||||
\(321\) | −30.1337 | −1.68190 | ||||||||
\(322\) | 0.932815 | 0.0519837 | ||||||||
\(323\) | −2.16054 | −0.120216 | ||||||||
\(324\) | −9.42899 | −0.523833 | ||||||||
\(325\) | 7.14237 | 0.396187 | ||||||||
\(326\) | 10.5044 | 0.581782 | ||||||||
\(327\) | −5.62021 | −0.310798 | ||||||||
\(328\) | −1.44923 | −0.0800206 | ||||||||
\(329\) | −9.31723 | −0.513675 | ||||||||
\(330\) | 1.38792 | 0.0764024 | ||||||||
\(331\) | −16.6835 | −0.917008 | −0.458504 | − | 0.888692i | \(-0.651614\pi\) | ||||
−0.458504 | + | 0.888692i | \(0.651614\pi\) | |||||||
\(332\) | 12.5488 | 0.688707 | ||||||||
\(333\) | −0.265294 | −0.0145380 | ||||||||
\(334\) | −1.67807 | −0.0918200 | ||||||||
\(335\) | 4.11734 | 0.224954 | ||||||||
\(336\) | 4.44947 | 0.242739 | ||||||||
\(337\) | 19.5671 | 1.06589 | 0.532945 | − | 0.846150i | \(-0.321085\pi\) | ||||
0.532945 | + | 0.846150i | \(0.321085\pi\) | |||||||
\(338\) | 10.3513 | 0.563035 | ||||||||
\(339\) | −1.61046 | −0.0874684 | ||||||||
\(340\) | −0.640183 | −0.0347188 | ||||||||
\(341\) | −1.78637 | −0.0967376 | ||||||||
\(342\) | 0.397300 | 0.0214835 | ||||||||
\(343\) | −19.3425 | −1.04440 | ||||||||
\(344\) | 6.20306 | 0.334447 | ||||||||
\(345\) | 0.516469 | 0.0278057 | ||||||||
\(346\) | −6.87018 | −0.369343 | ||||||||
\(347\) | −8.13041 | −0.436463 | −0.218232 | − | 0.975897i | \(-0.570029\pi\) | ||||
−0.218232 | + | 0.975897i | \(0.570029\pi\) | |||||||
\(348\) | −16.4600 | −0.882349 | ||||||||
\(349\) | 29.7361 | 1.59174 | 0.795868 | − | 0.605470i | \(-0.207015\pi\) | ||||
0.795868 | + | 0.605470i | \(0.207015\pi\) | |||||||
\(350\) | 11.0012 | 0.588038 | ||||||||
\(351\) | 8.23138 | 0.439358 | ||||||||
\(352\) | −1.00000 | −0.0533002 | ||||||||
\(353\) | −6.94727 | −0.369766 | −0.184883 | − | 0.982761i | \(-0.559191\pi\) | ||||
−0.184883 | + | 0.982761i | \(0.559191\pi\) | |||||||
\(354\) | −3.22052 | −0.171168 | ||||||||
\(355\) | −12.0934 | −0.641853 | ||||||||
\(356\) | −9.46795 | −0.501800 | ||||||||
\(357\) | 3.64286 | 0.192800 | ||||||||
\(358\) | 15.2669 | 0.806883 | ||||||||
\(359\) | 16.6568 | 0.879113 | 0.439557 | − | 0.898215i | \(-0.355136\pi\) | ||||
0.439557 | + | 0.898215i | \(0.355136\pi\) | |||||||
\(360\) | 0.117723 | 0.00620453 | ||||||||
\(361\) | −12.0360 | −0.633475 | ||||||||
\(362\) | −25.0359 | −1.31586 | ||||||||
\(363\) | 1.77498 | 0.0931623 | ||||||||
\(364\) | −4.07975 | −0.213837 | ||||||||
\(365\) | −11.8548 | −0.620506 | ||||||||
\(366\) | 16.7646 | 0.876299 | ||||||||
\(367\) | −29.9141 | −1.56150 | −0.780752 | − | 0.624841i | \(-0.785164\pi\) | ||||
−0.780752 | + | 0.624841i | \(0.785164\pi\) | |||||||
\(368\) | −0.372117 | −0.0193980 | ||||||||
\(369\) | 0.218187 | 0.0113584 | ||||||||
\(370\) | −1.37787 | −0.0716320 | ||||||||
\(371\) | −10.4631 | −0.543218 | ||||||||
\(372\) | −3.17078 | −0.164397 | ||||||||
\(373\) | 0.196826 | 0.0101913 | 0.00509563 | − | 0.999987i | \(-0.498378\pi\) | ||||
0.00509563 | + | 0.999987i | \(0.498378\pi\) | |||||||
\(374\) | −0.818716 | −0.0423348 | ||||||||
\(375\) | 13.0306 | 0.672897 | ||||||||
\(376\) | 3.71682 | 0.191680 | ||||||||
\(377\) | 15.0923 | 0.777293 | ||||||||
\(378\) | 12.6785 | 0.652114 | ||||||||
\(379\) | 36.7410 | 1.88726 | 0.943630 | − | 0.331003i | \(-0.107387\pi\) | ||||
0.943630 | + | 0.331003i | \(0.107387\pi\) | |||||||
\(380\) | 2.06348 | 0.105854 | ||||||||
\(381\) | −19.9186 | −1.02046 | ||||||||
\(382\) | 1.20417 | 0.0616108 | ||||||||
\(383\) | −6.97054 | −0.356178 | −0.178089 | − | 0.984014i | \(-0.556991\pi\) | ||||
−0.178089 | + | 0.984014i | \(0.556991\pi\) | |||||||
\(384\) | −1.77498 | −0.0905791 | ||||||||
\(385\) | −1.96014 | −0.0998978 | ||||||||
\(386\) | 14.9340 | 0.760119 | ||||||||
\(387\) | −0.933890 | −0.0474723 | ||||||||
\(388\) | −1.58308 | −0.0803688 | ||||||||
\(389\) | −9.98330 | −0.506173 | −0.253087 | − | 0.967444i | \(-0.581446\pi\) | ||||
−0.253087 | + | 0.967444i | \(0.581446\pi\) | |||||||
\(390\) | −2.25883 | −0.114380 | ||||||||
\(391\) | −0.304659 | −0.0154072 | ||||||||
\(392\) | 0.716080 | 0.0361675 | ||||||||
\(393\) | 33.7830 | 1.70413 | ||||||||
\(394\) | −1.00000 | −0.0503793 | ||||||||
\(395\) | 11.0363 | 0.555296 | ||||||||
\(396\) | 0.150553 | 0.00756558 | ||||||||
\(397\) | −16.4016 | −0.823171 | −0.411586 | − | 0.911371i | \(-0.635025\pi\) | ||||
−0.411586 | + | 0.911371i | \(0.635025\pi\) | |||||||
\(398\) | 15.2442 | 0.764125 | ||||||||
\(399\) | −11.7419 | −0.587829 | ||||||||
\(400\) | −4.38858 | −0.219429 | ||||||||
\(401\) | 16.9990 | 0.848887 | 0.424444 | − | 0.905454i | \(-0.360470\pi\) | ||||
0.424444 | + | 0.905454i | \(0.360470\pi\) | |||||||
\(402\) | 9.34629 | 0.466151 | ||||||||
\(403\) | 2.90731 | 0.144823 | ||||||||
\(404\) | 14.9101 | 0.741806 | ||||||||
\(405\) | 7.37286 | 0.366360 | ||||||||
\(406\) | 23.2462 | 1.15369 | ||||||||
\(407\) | −1.76213 | −0.0873454 | ||||||||
\(408\) | −1.45320 | −0.0719444 | ||||||||
\(409\) | −7.86890 | −0.389092 | −0.194546 | − | 0.980893i | \(-0.562323\pi\) | ||||
−0.194546 | + | 0.980893i | \(0.562323\pi\) | |||||||
\(410\) | 1.13321 | 0.0559651 | ||||||||
\(411\) | −31.1769 | −1.53784 | ||||||||
\(412\) | 5.87321 | 0.289352 | ||||||||
\(413\) | 4.54828 | 0.223806 | ||||||||
\(414\) | 0.0560234 | 0.00275340 | ||||||||
\(415\) | −9.81237 | −0.481670 | ||||||||
\(416\) | 1.62749 | 0.0797943 | ||||||||
\(417\) | 4.33286 | 0.212181 | ||||||||
\(418\) | 2.63893 | 0.129074 | ||||||||
\(419\) | 12.8174 | 0.626173 | 0.313086 | − | 0.949725i | \(-0.398637\pi\) | ||||
0.313086 | + | 0.949725i | \(0.398637\pi\) | |||||||
\(420\) | −3.47920 | −0.169768 | ||||||||
\(421\) | −6.50870 | −0.317214 | −0.158607 | − | 0.987342i | \(-0.550700\pi\) | ||||
−0.158607 | + | 0.987342i | \(0.550700\pi\) | |||||||
\(422\) | −1.69924 | −0.0827180 | ||||||||
\(423\) | −0.559579 | −0.0272076 | ||||||||
\(424\) | 4.17393 | 0.202704 | ||||||||
\(425\) | −3.59300 | −0.174286 | ||||||||
\(426\) | −27.4519 | −1.33005 | ||||||||
\(427\) | −23.6763 | −1.14578 | ||||||||
\(428\) | −16.9770 | −0.820612 | ||||||||
\(429\) | −2.88876 | −0.139471 | ||||||||
\(430\) | −4.85039 | −0.233907 | ||||||||
\(431\) | 1.23118 | 0.0593040 | 0.0296520 | − | 0.999560i | \(-0.490560\pi\) | ||||
0.0296520 | + | 0.999560i | \(0.490560\pi\) | |||||||
\(432\) | −5.05771 | −0.243339 | ||||||||
\(433\) | −2.24503 | −0.107889 | −0.0539447 | − | 0.998544i | \(-0.517179\pi\) | ||||
−0.0539447 | + | 0.998544i | \(0.517179\pi\) | |||||||
\(434\) | 4.47804 | 0.214953 | ||||||||
\(435\) | 12.8707 | 0.617101 | ||||||||
\(436\) | −3.16635 | −0.151641 | ||||||||
\(437\) | 0.981993 | 0.0469751 | ||||||||
\(438\) | −26.9101 | −1.28581 | ||||||||
\(439\) | 14.6966 | 0.701432 | 0.350716 | − | 0.936482i | \(-0.385938\pi\) | ||||
0.350716 | + | 0.936482i | \(0.385938\pi\) | |||||||
\(440\) | 0.781935 | 0.0372773 | ||||||||
\(441\) | −0.107808 | −0.00513371 | ||||||||
\(442\) | 1.33245 | 0.0633783 | ||||||||
\(443\) | −17.1435 | −0.814512 | −0.407256 | − | 0.913314i | \(-0.633514\pi\) | ||||
−0.407256 | + | 0.913314i | \(0.633514\pi\) | |||||||
\(444\) | −3.12774 | −0.148436 | ||||||||
\(445\) | 7.40332 | 0.350951 | ||||||||
\(446\) | 17.4207 | 0.824894 | ||||||||
\(447\) | 20.1256 | 0.951910 | ||||||||
\(448\) | 2.50677 | 0.118434 | ||||||||
\(449\) | 30.0085 | 1.41619 | 0.708093 | − | 0.706119i | \(-0.249556\pi\) | ||||
0.708093 | + | 0.706119i | \(0.249556\pi\) | |||||||
\(450\) | 0.660714 | 0.0311464 | ||||||||
\(451\) | 1.44923 | 0.0682418 | ||||||||
\(452\) | −0.907314 | −0.0426765 | ||||||||
\(453\) | −3.34603 | −0.157210 | ||||||||
\(454\) | −17.0235 | −0.798953 | ||||||||
\(455\) | 3.19010 | 0.149554 | ||||||||
\(456\) | 4.68405 | 0.219351 | ||||||||
\(457\) | 23.8644 | 1.11633 | 0.558165 | − | 0.829730i | \(-0.311506\pi\) | ||||
0.558165 | + | 0.829730i | \(0.311506\pi\) | |||||||
\(458\) | −24.1710 | −1.12944 | ||||||||
\(459\) | −4.14083 | −0.193277 | ||||||||
\(460\) | 0.290972 | 0.0135666 | ||||||||
\(461\) | 26.3947 | 1.22933 | 0.614663 | − | 0.788790i | \(-0.289292\pi\) | ||||
0.614663 | + | 0.788790i | \(0.289292\pi\) | |||||||
\(462\) | −4.44947 | −0.207008 | ||||||||
\(463\) | −29.1966 | −1.35688 | −0.678440 | − | 0.734656i | \(-0.737343\pi\) | ||||
−0.678440 | + | 0.734656i | \(0.737343\pi\) | |||||||
\(464\) | −9.27335 | −0.430504 | ||||||||
\(465\) | 2.47934 | 0.114977 | ||||||||
\(466\) | 8.79647 | 0.407489 | ||||||||
\(467\) | 11.7938 | 0.545753 | 0.272876 | − | 0.962049i | \(-0.412025\pi\) | ||||
0.272876 | + | 0.962049i | \(0.412025\pi\) | |||||||
\(468\) | −0.245024 | −0.0113262 | ||||||||
\(469\) | −13.1996 | −0.609502 | ||||||||
\(470\) | −2.90631 | −0.134058 | ||||||||
\(471\) | 26.6447 | 1.22772 | ||||||||
\(472\) | −1.81440 | −0.0835143 | ||||||||
\(473\) | −6.20306 | −0.285217 | ||||||||
\(474\) | 25.0522 | 1.15069 | ||||||||
\(475\) | 11.5812 | 0.531380 | ||||||||
\(476\) | 2.05234 | 0.0940687 | ||||||||
\(477\) | −0.628399 | −0.0287724 | ||||||||
\(478\) | −9.49252 | −0.434178 | ||||||||
\(479\) | −15.2391 | −0.696294 | −0.348147 | − | 0.937440i | \(-0.613189\pi\) | ||||
−0.348147 | + | 0.937440i | \(0.613189\pi\) | |||||||
\(480\) | 1.38792 | 0.0633496 | ||||||||
\(481\) | 2.86784 | 0.130762 | ||||||||
\(482\) | 4.32087 | 0.196810 | ||||||||
\(483\) | −1.65573 | −0.0753382 | ||||||||
\(484\) | 1.00000 | 0.0454545 | ||||||||
\(485\) | 1.23787 | 0.0562087 | ||||||||
\(486\) | 1.56314 | 0.0709055 | ||||||||
\(487\) | −37.6125 | −1.70439 | −0.852193 | − | 0.523228i | \(-0.824728\pi\) | ||||
−0.852193 | + | 0.523228i | \(0.824728\pi\) | |||||||
\(488\) | 9.44494 | 0.427552 | ||||||||
\(489\) | −18.6450 | −0.843157 | ||||||||
\(490\) | −0.559928 | −0.0252950 | ||||||||
\(491\) | −10.2636 | −0.463191 | −0.231596 | − | 0.972812i | \(-0.574395\pi\) | ||||
−0.231596 | + | 0.972812i | \(0.574395\pi\) | |||||||
\(492\) | 2.57236 | 0.115971 | ||||||||
\(493\) | −7.59224 | −0.341937 | ||||||||
\(494\) | −4.29484 | −0.193234 | ||||||||
\(495\) | −0.117723 | −0.00529125 | ||||||||
\(496\) | −1.78637 | −0.0802106 | ||||||||
\(497\) | 38.7698 | 1.73907 | ||||||||
\(498\) | −22.2739 | −0.998118 | ||||||||
\(499\) | 15.7335 | 0.704328 | 0.352164 | − | 0.935938i | \(-0.385446\pi\) | ||||
0.352164 | + | 0.935938i | \(0.385446\pi\) | |||||||
\(500\) | 7.34126 | 0.328311 | ||||||||
\(501\) | 2.97854 | 0.133072 | ||||||||
\(502\) | 18.6422 | 0.832042 | ||||||||
\(503\) | 14.4975 | 0.646413 | 0.323207 | − | 0.946328i | \(-0.395239\pi\) | ||||
0.323207 | + | 0.946328i | \(0.395239\pi\) | |||||||
\(504\) | −0.377403 | −0.0168109 | ||||||||
\(505\) | −11.6587 | −0.518807 | ||||||||
\(506\) | 0.372117 | 0.0165426 | ||||||||
\(507\) | −18.3733 | −0.815987 | ||||||||
\(508\) | −11.2218 | −0.497889 | ||||||||
\(509\) | 17.8700 | 0.792075 | 0.396038 | − | 0.918234i | \(-0.370385\pi\) | ||||
0.396038 | + | 0.918234i | \(0.370385\pi\) | |||||||
\(510\) | 1.13631 | 0.0503167 | ||||||||
\(511\) | 38.0047 | 1.68123 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 13.3470 | 0.589283 | ||||||||
\(514\) | −12.1480 | −0.535827 | ||||||||
\(515\) | −4.59247 | −0.202368 | ||||||||
\(516\) | −11.0103 | −0.484702 | ||||||||
\(517\) | −3.71682 | −0.163466 | ||||||||
\(518\) | 4.41725 | 0.194083 | ||||||||
\(519\) | 12.1944 | 0.535276 | ||||||||
\(520\) | −1.27259 | −0.0558069 | ||||||||
\(521\) | 0.778605 | 0.0341113 | 0.0170557 | − | 0.999855i | \(-0.494571\pi\) | ||||
0.0170557 | + | 0.999855i | \(0.494571\pi\) | |||||||
\(522\) | 1.39613 | 0.0611070 | ||||||||
\(523\) | 27.8500 | 1.21780 | 0.608898 | − | 0.793249i | \(-0.291612\pi\) | ||||
0.608898 | + | 0.793249i | \(0.291612\pi\) | |||||||
\(524\) | 19.0329 | 0.831455 | ||||||||
\(525\) | −19.5269 | −0.852222 | ||||||||
\(526\) | −13.4102 | −0.584714 | ||||||||
\(527\) | −1.46253 | −0.0637090 | ||||||||
\(528\) | 1.77498 | 0.0772461 | ||||||||
\(529\) | −22.8615 | −0.993980 | ||||||||
\(530\) | −3.26375 | −0.141768 | ||||||||
\(531\) | 0.273163 | 0.0118543 | ||||||||
\(532\) | −6.61521 | −0.286806 | ||||||||
\(533\) | −2.35862 | −0.102163 | ||||||||
\(534\) | 16.8054 | 0.727242 | ||||||||
\(535\) | 13.2749 | 0.573923 | ||||||||
\(536\) | 5.26558 | 0.227438 | ||||||||
\(537\) | −27.0985 | −1.16939 | ||||||||
\(538\) | 19.4803 | 0.839856 | ||||||||
\(539\) | −0.716080 | −0.0308437 | ||||||||
\(540\) | 3.95480 | 0.170188 | ||||||||
\(541\) | −23.9261 | −1.02866 | −0.514332 | − | 0.857591i | \(-0.671960\pi\) | ||||
−0.514332 | + | 0.857591i | \(0.671960\pi\) | |||||||
\(542\) | 15.5878 | 0.669554 | ||||||||
\(543\) | 44.4383 | 1.90703 | ||||||||
\(544\) | −0.818716 | −0.0351022 | ||||||||
\(545\) | 2.47588 | 0.106055 | ||||||||
\(546\) | 7.24148 | 0.309907 | ||||||||
\(547\) | −20.7243 | −0.886109 | −0.443054 | − | 0.896495i | \(-0.646105\pi\) | ||||
−0.443054 | + | 0.896495i | \(0.646105\pi\) | |||||||
\(548\) | −17.5646 | −0.750324 | ||||||||
\(549\) | −1.42197 | −0.0606880 | ||||||||
\(550\) | 4.38858 | 0.187130 | ||||||||
\(551\) | 24.4718 | 1.04253 | ||||||||
\(552\) | 0.660501 | 0.0281128 | ||||||||
\(553\) | −35.3808 | −1.50454 | ||||||||
\(554\) | 27.0289 | 1.14835 | ||||||||
\(555\) | 2.44569 | 0.103814 | ||||||||
\(556\) | 2.44108 | 0.103525 | ||||||||
\(557\) | −43.5313 | −1.84448 | −0.922240 | − | 0.386619i | \(-0.873643\pi\) | ||||
−0.922240 | + | 0.386619i | \(0.873643\pi\) | |||||||
\(558\) | 0.268944 | 0.0113853 | ||||||||
\(559\) | 10.0954 | 0.426991 | ||||||||
\(560\) | −1.96014 | −0.0828308 | ||||||||
\(561\) | 1.45320 | 0.0613544 | ||||||||
\(562\) | −3.39112 | −0.143046 | ||||||||
\(563\) | 17.4341 | 0.734760 | 0.367380 | − | 0.930071i | \(-0.380255\pi\) | ||||
0.367380 | + | 0.930071i | \(0.380255\pi\) | |||||||
\(564\) | −6.59728 | −0.277796 | ||||||||
\(565\) | 0.709461 | 0.0298472 | ||||||||
\(566\) | −3.95128 | −0.166085 | ||||||||
\(567\) | −23.6364 | −0.992634 | ||||||||
\(568\) | −15.4660 | −0.648940 | ||||||||
\(569\) | −16.5164 | −0.692403 | −0.346202 | − | 0.938160i | \(-0.612529\pi\) | ||||
−0.346202 | + | 0.938160i | \(0.612529\pi\) | |||||||
\(570\) | −3.66263 | −0.153411 | ||||||||
\(571\) | −12.6596 | −0.529787 | −0.264893 | − | 0.964278i | \(-0.585337\pi\) | ||||
−0.264893 | + | 0.964278i | \(0.585337\pi\) | |||||||
\(572\) | −1.62749 | −0.0680488 | ||||||||
\(573\) | −2.13738 | −0.0892903 | ||||||||
\(574\) | −3.63291 | −0.151635 | ||||||||
\(575\) | 1.63307 | 0.0681036 | ||||||||
\(576\) | 0.150553 | 0.00627305 | ||||||||
\(577\) | −35.4381 | −1.47531 | −0.737653 | − | 0.675180i | \(-0.764066\pi\) | ||||
−0.737653 | + | 0.675180i | \(0.764066\pi\) | |||||||
\(578\) | 16.3297 | 0.679226 | ||||||||
\(579\) | −26.5075 | −1.10161 | ||||||||
\(580\) | 7.25116 | 0.301088 | ||||||||
\(581\) | 31.4571 | 1.30506 | ||||||||
\(582\) | 2.80994 | 0.116476 | ||||||||
\(583\) | −4.17393 | −0.172867 | ||||||||
\(584\) | −15.1608 | −0.627358 | ||||||||
\(585\) | 0.191593 | 0.00792138 | ||||||||
\(586\) | −7.09396 | −0.293049 | ||||||||
\(587\) | 6.83618 | 0.282159 | 0.141080 | − | 0.989998i | \(-0.454943\pi\) | ||||
0.141080 | + | 0.989998i | \(0.454943\pi\) | |||||||
\(588\) | −1.27103 | −0.0524163 | ||||||||
\(589\) | 4.71412 | 0.194242 | ||||||||
\(590\) | 1.41874 | 0.0584086 | ||||||||
\(591\) | 1.77498 | 0.0730129 | ||||||||
\(592\) | −1.76213 | −0.0724229 | ||||||||
\(593\) | 3.16742 | 0.130070 | 0.0650352 | − | 0.997883i | \(-0.479284\pi\) | ||||
0.0650352 | + | 0.997883i | \(0.479284\pi\) | |||||||
\(594\) | 5.05771 | 0.207520 | ||||||||
\(595\) | −1.60479 | −0.0657902 | ||||||||
\(596\) | 11.3385 | 0.464444 | ||||||||
\(597\) | −27.0582 | −1.10742 | ||||||||
\(598\) | −0.605618 | −0.0247655 | ||||||||
\(599\) | 4.38361 | 0.179109 | 0.0895547 | − | 0.995982i | \(-0.471456\pi\) | ||||
0.0895547 | + | 0.995982i | \(0.471456\pi\) | |||||||
\(600\) | 7.78964 | 0.318011 | ||||||||
\(601\) | 34.6226 | 1.41228 | 0.706142 | − | 0.708070i | \(-0.250434\pi\) | ||||
0.706142 | + | 0.708070i | \(0.250434\pi\) | |||||||
\(602\) | 15.5497 | 0.633758 | ||||||||
\(603\) | −0.792749 | −0.0322832 | ||||||||
\(604\) | −1.88511 | −0.0767040 | ||||||||
\(605\) | −0.781935 | −0.0317902 | ||||||||
\(606\) | −26.4652 | −1.07507 | ||||||||
\(607\) | 13.4099 | 0.544290 | 0.272145 | − | 0.962256i | \(-0.412267\pi\) | ||||
0.272145 | + | 0.962256i | \(0.412267\pi\) | |||||||
\(608\) | 2.63893 | 0.107023 | ||||||||
\(609\) | −41.2615 | −1.67200 | ||||||||
\(610\) | −7.38533 | −0.299023 | ||||||||
\(611\) | 6.04909 | 0.244720 | ||||||||
\(612\) | 0.123260 | 0.00498250 | ||||||||
\(613\) | −21.9274 | −0.885640 | −0.442820 | − | 0.896610i | \(-0.646022\pi\) | ||||
−0.442820 | + | 0.896610i | \(0.646022\pi\) | |||||||
\(614\) | −10.7934 | −0.435587 | ||||||||
\(615\) | −2.01142 | −0.0811083 | ||||||||
\(616\) | −2.50677 | −0.101001 | ||||||||
\(617\) | −23.5090 | −0.946437 | −0.473219 | − | 0.880945i | \(-0.656908\pi\) | ||||
−0.473219 | + | 0.880945i | \(0.656908\pi\) | |||||||
\(618\) | −10.4248 | −0.419348 | ||||||||
\(619\) | −39.8837 | −1.60306 | −0.801530 | − | 0.597955i | \(-0.795980\pi\) | ||||
−0.801530 | + | 0.597955i | \(0.795980\pi\) | |||||||
\(620\) | 1.39683 | 0.0560980 | ||||||||
\(621\) | 1.88206 | 0.0755245 | ||||||||
\(622\) | 32.2969 | 1.29499 | ||||||||
\(623\) | −23.7340 | −0.950884 | ||||||||
\(624\) | −2.88876 | −0.115643 | ||||||||
\(625\) | 16.2025 | 0.648100 | ||||||||
\(626\) | −16.1264 | −0.644541 | ||||||||
\(627\) | −4.68405 | −0.187063 | ||||||||
\(628\) | 15.0113 | 0.599016 | ||||||||
\(629\) | −1.44268 | −0.0575235 | ||||||||
\(630\) | 0.295104 | 0.0117572 | ||||||||
\(631\) | −32.2398 | −1.28345 | −0.641723 | − | 0.766937i | \(-0.721780\pi\) | ||||
−0.641723 | + | 0.766937i | \(0.721780\pi\) | |||||||
\(632\) | 14.1141 | 0.561428 | ||||||||
\(633\) | 3.01613 | 0.119880 | ||||||||
\(634\) | −31.5608 | −1.25344 | ||||||||
\(635\) | 8.77476 | 0.348216 | ||||||||
\(636\) | −7.40865 | −0.293772 | ||||||||
\(637\) | 1.16541 | 0.0461753 | ||||||||
\(638\) | 9.27335 | 0.367135 | ||||||||
\(639\) | 2.32846 | 0.0921124 | ||||||||
\(640\) | 0.781935 | 0.0309087 | ||||||||
\(641\) | −47.3531 | −1.87033 | −0.935167 | − | 0.354207i | \(-0.884751\pi\) | ||||
−0.935167 | + | 0.354207i | \(0.884751\pi\) | |||||||
\(642\) | 30.1337 | 1.18928 | ||||||||
\(643\) | −42.0430 | −1.65801 | −0.829006 | − | 0.559240i | \(-0.811093\pi\) | ||||
−0.829006 | + | 0.559240i | \(0.811093\pi\) | |||||||
\(644\) | −0.932815 | −0.0367580 | ||||||||
\(645\) | 8.60935 | 0.338993 | ||||||||
\(646\) | 2.16054 | 0.0850052 | ||||||||
\(647\) | −35.8141 | −1.40800 | −0.703998 | − | 0.710202i | \(-0.748604\pi\) | ||||
−0.703998 | + | 0.710202i | \(0.748604\pi\) | |||||||
\(648\) | 9.42899 | 0.370406 | ||||||||
\(649\) | 1.81440 | 0.0712213 | ||||||||
\(650\) | −7.14237 | −0.280147 | ||||||||
\(651\) | −7.94843 | −0.311523 | ||||||||
\(652\) | −10.5044 | −0.411382 | ||||||||
\(653\) | −45.4473 | −1.77849 | −0.889246 | − | 0.457429i | \(-0.848770\pi\) | ||||
−0.889246 | + | 0.457429i | \(0.848770\pi\) | |||||||
\(654\) | 5.62021 | 0.219768 | ||||||||
\(655\) | −14.8825 | −0.581507 | ||||||||
\(656\) | 1.44923 | 0.0565831 | ||||||||
\(657\) | 2.28250 | 0.0890489 | ||||||||
\(658\) | 9.31723 | 0.363223 | ||||||||
\(659\) | −14.6584 | −0.571012 | −0.285506 | − | 0.958377i | \(-0.592162\pi\) | ||||
−0.285506 | + | 0.958377i | \(0.592162\pi\) | |||||||
\(660\) | −1.38792 | −0.0540247 | ||||||||
\(661\) | −34.1543 | −1.32845 | −0.664224 | − | 0.747534i | \(-0.731238\pi\) | ||||
−0.664224 | + | 0.747534i | \(0.731238\pi\) | |||||||
\(662\) | 16.6835 | 0.648422 | ||||||||
\(663\) | −2.36508 | −0.0918520 | ||||||||
\(664\) | −12.5488 | −0.486989 | ||||||||
\(665\) | 5.17267 | 0.200587 | ||||||||
\(666\) | 0.265294 | 0.0102799 | ||||||||
\(667\) | 3.45077 | 0.133615 | ||||||||
\(668\) | 1.67807 | 0.0649266 | ||||||||
\(669\) | −30.9214 | −1.19549 | ||||||||
\(670\) | −4.11734 | −0.159067 | ||||||||
\(671\) | −9.44494 | −0.364618 | ||||||||
\(672\) | −4.44947 | −0.171642 | ||||||||
\(673\) | 38.1298 | 1.46980 | 0.734899 | − | 0.678177i | \(-0.237230\pi\) | ||||
0.734899 | + | 0.678177i | \(0.237230\pi\) | |||||||
\(674\) | −19.5671 | −0.753698 | ||||||||
\(675\) | 22.1962 | 0.854330 | ||||||||
\(676\) | −10.3513 | −0.398126 | ||||||||
\(677\) | 22.3458 | 0.858817 | 0.429408 | − | 0.903110i | \(-0.358722\pi\) | ||||
0.429408 | + | 0.903110i | \(0.358722\pi\) | |||||||
\(678\) | 1.61046 | 0.0618495 | ||||||||
\(679\) | −3.96843 | −0.152294 | ||||||||
\(680\) | 0.640183 | 0.0245499 | ||||||||
\(681\) | 30.2164 | 1.15789 | ||||||||
\(682\) | 1.78637 | 0.0684038 | ||||||||
\(683\) | 41.9925 | 1.60680 | 0.803400 | − | 0.595440i | \(-0.203022\pi\) | ||||
0.803400 | + | 0.595440i | \(0.203022\pi\) | |||||||
\(684\) | −0.397300 | −0.0151911 | ||||||||
\(685\) | 13.7344 | 0.524765 | ||||||||
\(686\) | 19.3425 | 0.738499 | ||||||||
\(687\) | 42.9031 | 1.63686 | ||||||||
\(688\) | −6.20306 | −0.236490 | ||||||||
\(689\) | 6.79304 | 0.258794 | ||||||||
\(690\) | −0.516469 | −0.0196616 | ||||||||
\(691\) | 0.267171 | 0.0101636 | 0.00508182 | − | 0.999987i | \(-0.498382\pi\) | ||||
0.00508182 | + | 0.999987i | \(0.498382\pi\) | |||||||
\(692\) | 6.87018 | 0.261165 | ||||||||
\(693\) | 0.377403 | 0.0143363 | ||||||||
\(694\) | 8.13041 | 0.308626 | ||||||||
\(695\) | −1.90876 | −0.0724035 | ||||||||
\(696\) | 16.4600 | 0.623915 | ||||||||
\(697\) | 1.18651 | 0.0449423 | ||||||||
\(698\) | −29.7361 | −1.12553 | ||||||||
\(699\) | −15.6136 | −0.590559 | ||||||||
\(700\) | −11.0012 | −0.415805 | ||||||||
\(701\) | 9.31232 | 0.351722 | 0.175861 | − | 0.984415i | \(-0.443729\pi\) | ||||
0.175861 | + | 0.984415i | \(0.443729\pi\) | |||||||
\(702\) | −8.23138 | −0.310673 | ||||||||
\(703\) | 4.65013 | 0.175383 | ||||||||
\(704\) | 1.00000 | 0.0376889 | ||||||||
\(705\) | 5.15864 | 0.194286 | ||||||||
\(706\) | 6.94727 | 0.261464 | ||||||||
\(707\) | 37.3763 | 1.40568 | ||||||||
\(708\) | 3.22052 | 0.121034 | ||||||||
\(709\) | 37.3501 | 1.40271 | 0.701356 | − | 0.712811i | \(-0.252578\pi\) | ||||
0.701356 | + | 0.712811i | \(0.252578\pi\) | |||||||
\(710\) | 12.0934 | 0.453858 | ||||||||
\(711\) | −2.12492 | −0.0796906 | ||||||||
\(712\) | 9.46795 | 0.354826 | ||||||||
\(713\) | 0.664741 | 0.0248947 | ||||||||
\(714\) | −3.64286 | −0.136331 | ||||||||
\(715\) | 1.27259 | 0.0475923 | ||||||||
\(716\) | −15.2669 | −0.570552 | ||||||||
\(717\) | 16.8490 | 0.629239 | ||||||||
\(718\) | −16.6568 | −0.621627 | ||||||||
\(719\) | −37.4487 | −1.39660 | −0.698301 | − | 0.715804i | \(-0.746060\pi\) | ||||
−0.698301 | + | 0.715804i | \(0.746060\pi\) | |||||||
\(720\) | −0.117723 | −0.00438727 | ||||||||
\(721\) | 14.7228 | 0.548306 | ||||||||
\(722\) | 12.0360 | 0.447935 | ||||||||
\(723\) | −7.66946 | −0.285230 | ||||||||
\(724\) | 25.0359 | 0.930453 | ||||||||
\(725\) | 40.6968 | 1.51144 | ||||||||
\(726\) | −1.77498 | −0.0658757 | ||||||||
\(727\) | 20.0366 | 0.743115 | 0.371558 | − | 0.928410i | \(-0.378824\pi\) | ||||
0.371558 | + | 0.928410i | \(0.378824\pi\) | |||||||
\(728\) | 4.07975 | 0.151206 | ||||||||
\(729\) | 25.5124 | 0.944905 | ||||||||
\(730\) | 11.8548 | 0.438764 | ||||||||
\(731\) | −5.07855 | −0.187837 | ||||||||
\(732\) | −16.7646 | −0.619637 | ||||||||
\(733\) | −12.2045 | −0.450783 | −0.225392 | − | 0.974268i | \(-0.572366\pi\) | ||||
−0.225392 | + | 0.974268i | \(0.572366\pi\) | |||||||
\(734\) | 29.9141 | 1.10415 | ||||||||
\(735\) | 0.993861 | 0.0366591 | ||||||||
\(736\) | 0.372117 | 0.0137164 | ||||||||
\(737\) | −5.26558 | −0.193960 | ||||||||
\(738\) | −0.218187 | −0.00803157 | ||||||||
\(739\) | 39.4330 | 1.45057 | 0.725284 | − | 0.688450i | \(-0.241709\pi\) | ||||
0.725284 | + | 0.688450i | \(0.241709\pi\) | |||||||
\(740\) | 1.37787 | 0.0506515 | ||||||||
\(741\) | 7.62326 | 0.280047 | ||||||||
\(742\) | 10.4631 | 0.384113 | ||||||||
\(743\) | −26.2310 | −0.962321 | −0.481160 | − | 0.876633i | \(-0.659785\pi\) | ||||
−0.481160 | + | 0.876633i | \(0.659785\pi\) | |||||||
\(744\) | 3.17078 | 0.116246 | ||||||||
\(745\) | −8.86598 | −0.324824 | ||||||||
\(746\) | −0.196826 | −0.00720632 | ||||||||
\(747\) | 1.88927 | 0.0691246 | ||||||||
\(748\) | 0.818716 | 0.0299352 | ||||||||
\(749\) | −42.5574 | −1.55501 | ||||||||
\(750\) | −13.0306 | −0.475810 | ||||||||
\(751\) | 20.7380 | 0.756741 | 0.378370 | − | 0.925654i | \(-0.376485\pi\) | ||||
0.378370 | + | 0.925654i | \(0.376485\pi\) | |||||||
\(752\) | −3.71682 | −0.135538 | ||||||||
\(753\) | −33.0895 | −1.20585 | ||||||||
\(754\) | −15.0923 | −0.549629 | ||||||||
\(755\) | 1.47403 | 0.0536456 | ||||||||
\(756\) | −12.6785 | −0.461114 | ||||||||
\(757\) | −49.6783 | −1.80559 | −0.902795 | − | 0.430072i | \(-0.858488\pi\) | ||||
−0.902795 | + | 0.430072i | \(0.858488\pi\) | |||||||
\(758\) | −36.7410 | −1.33449 | ||||||||
\(759\) | −0.660501 | −0.0239747 | ||||||||
\(760\) | −2.06348 | −0.0748501 | ||||||||
\(761\) | −38.6052 | −1.39944 | −0.699719 | − | 0.714418i | \(-0.746692\pi\) | ||||
−0.699719 | + | 0.714418i | \(0.746692\pi\) | |||||||
\(762\) | 19.9186 | 0.721573 | ||||||||
\(763\) | −7.93733 | −0.287351 | ||||||||
\(764\) | −1.20417 | −0.0435654 | ||||||||
\(765\) | −0.0963815 | −0.00348468 | ||||||||
\(766\) | 6.97054 | 0.251856 | ||||||||
\(767\) | −2.95291 | −0.106623 | ||||||||
\(768\) | 1.77498 | 0.0640491 | ||||||||
\(769\) | −20.8456 | −0.751713 | −0.375856 | − | 0.926678i | \(-0.622651\pi\) | ||||
−0.375856 | + | 0.926678i | \(0.622651\pi\) | |||||||
\(770\) | 1.96014 | 0.0706384 | ||||||||
\(771\) | 21.5625 | 0.776556 | ||||||||
\(772\) | −14.9340 | −0.537485 | ||||||||
\(773\) | 26.9810 | 0.970439 | 0.485219 | − | 0.874392i | \(-0.338740\pi\) | ||||
0.485219 | + | 0.874392i | \(0.338740\pi\) | |||||||
\(774\) | 0.933890 | 0.0335680 | ||||||||
\(775\) | 7.83964 | 0.281608 | ||||||||
\(776\) | 1.58308 | 0.0568293 | ||||||||
\(777\) | −7.84054 | −0.281278 | ||||||||
\(778\) | 9.98330 | 0.357919 | ||||||||
\(779\) | −3.82443 | −0.137025 | ||||||||
\(780\) | 2.25883 | 0.0808789 | ||||||||
\(781\) | 15.4660 | 0.553418 | ||||||||
\(782\) | 0.304659 | 0.0108946 | ||||||||
\(783\) | 46.9019 | 1.67614 | ||||||||
\(784\) | −0.716080 | −0.0255743 | ||||||||
\(785\) | −11.7379 | −0.418942 | ||||||||
\(786\) | −33.7830 | −1.20500 | ||||||||
\(787\) | −28.2984 | −1.00873 | −0.504365 | − | 0.863491i | \(-0.668273\pi\) | ||||
−0.504365 | + | 0.863491i | \(0.668273\pi\) | |||||||
\(788\) | 1.00000 | 0.0356235 | ||||||||
\(789\) | 23.8029 | 0.847405 | ||||||||
\(790\) | −11.0363 | −0.392653 | ||||||||
\(791\) | −2.27443 | −0.0808695 | ||||||||
\(792\) | −0.150553 | −0.00534967 | ||||||||
\(793\) | 15.3716 | 0.545860 | ||||||||
\(794\) | 16.4016 | 0.582070 | ||||||||
\(795\) | 5.79308 | 0.205460 | ||||||||
\(796\) | −15.2442 | −0.540318 | ||||||||
\(797\) | 54.8757 | 1.94380 | 0.971899 | − | 0.235397i | \(-0.0756390\pi\) | ||||
0.971899 | + | 0.235397i | \(0.0756390\pi\) | |||||||
\(798\) | 11.7419 | 0.415658 | ||||||||
\(799\) | −3.04302 | −0.107654 | ||||||||
\(800\) | 4.38858 | 0.155160 | ||||||||
\(801\) | −1.42543 | −0.0503651 | ||||||||
\(802\) | −16.9990 | −0.600254 | ||||||||
\(803\) | 15.1608 | 0.535012 | ||||||||
\(804\) | −9.34629 | −0.329618 | ||||||||
\(805\) | 0.729401 | 0.0257080 | ||||||||
\(806\) | −2.90731 | −0.102406 | ||||||||
\(807\) | −34.5771 | −1.21717 | ||||||||
\(808\) | −14.9101 | −0.524536 | ||||||||
\(809\) | 10.4403 | 0.367061 | 0.183531 | − | 0.983014i | \(-0.441247\pi\) | ||||
0.183531 | + | 0.983014i | \(0.441247\pi\) | |||||||
\(810\) | −7.37286 | −0.259056 | ||||||||
\(811\) | 7.76663 | 0.272723 | 0.136362 | − | 0.990659i | \(-0.456459\pi\) | ||||
0.136362 | + | 0.990659i | \(0.456459\pi\) | |||||||
\(812\) | −23.2462 | −0.815782 | ||||||||
\(813\) | −27.6681 | −0.970361 | ||||||||
\(814\) | 1.76213 | 0.0617625 | ||||||||
\(815\) | 8.21372 | 0.287714 | ||||||||
\(816\) | 1.45320 | 0.0508723 | ||||||||
\(817\) | 16.3695 | 0.572695 | ||||||||
\(818\) | 7.86890 | 0.275130 | ||||||||
\(819\) | −0.614219 | −0.0214626 | ||||||||
\(820\) | −1.13321 | −0.0395733 | ||||||||
\(821\) | 22.4742 | 0.784354 | 0.392177 | − | 0.919890i | \(-0.371722\pi\) | ||||
0.392177 | + | 0.919890i | \(0.371722\pi\) | |||||||
\(822\) | 31.1769 | 1.08742 | ||||||||
\(823\) | 30.8250 | 1.07449 | 0.537246 | − | 0.843426i | \(-0.319465\pi\) | ||||
0.537246 | + | 0.843426i | \(0.319465\pi\) | |||||||
\(824\) | −5.87321 | −0.204603 | ||||||||
\(825\) | −7.78964 | −0.271200 | ||||||||
\(826\) | −4.54828 | −0.158255 | ||||||||
\(827\) | 2.59362 | 0.0901890 | 0.0450945 | − | 0.998983i | \(-0.485641\pi\) | ||||
0.0450945 | + | 0.998983i | \(0.485641\pi\) | |||||||
\(828\) | −0.0560234 | −0.00194695 | ||||||||
\(829\) | 7.86562 | 0.273184 | 0.136592 | − | 0.990627i | \(-0.456385\pi\) | ||||
0.136592 | + | 0.990627i | \(0.456385\pi\) | |||||||
\(830\) | 9.81237 | 0.340592 | ||||||||
\(831\) | −47.9757 | −1.66426 | ||||||||
\(832\) | −1.62749 | −0.0564231 | ||||||||
\(833\) | −0.586266 | −0.0203129 | ||||||||
\(834\) | −4.33286 | −0.150035 | ||||||||
\(835\) | −1.31214 | −0.0454086 | ||||||||
\(836\) | −2.63893 | −0.0912694 | ||||||||
\(837\) | 9.03497 | 0.312294 | ||||||||
\(838\) | −12.8174 | −0.442771 | ||||||||
\(839\) | 23.9608 | 0.827220 | 0.413610 | − | 0.910454i | \(-0.364268\pi\) | ||||
0.413610 | + | 0.910454i | \(0.364268\pi\) | |||||||
\(840\) | 3.47920 | 0.120044 | ||||||||
\(841\) | 56.9950 | 1.96535 | ||||||||
\(842\) | 6.50870 | 0.224305 | ||||||||
\(843\) | 6.01918 | 0.207311 | ||||||||
\(844\) | 1.69924 | 0.0584904 | ||||||||
\(845\) | 8.09403 | 0.278443 | ||||||||
\(846\) | 0.559579 | 0.0192387 | ||||||||
\(847\) | 2.50677 | 0.0861338 | ||||||||
\(848\) | −4.17393 | −0.143334 | ||||||||
\(849\) | 7.01345 | 0.240701 | ||||||||
\(850\) | 3.59300 | 0.123239 | ||||||||
\(851\) | 0.655718 | 0.0224777 | ||||||||
\(852\) | 27.4519 | 0.940486 | ||||||||
\(853\) | −11.5589 | −0.395770 | −0.197885 | − | 0.980225i | \(-0.563407\pi\) | ||||
−0.197885 | + | 0.980225i | \(0.563407\pi\) | |||||||
\(854\) | 23.6763 | 0.810188 | ||||||||
\(855\) | 0.310663 | 0.0106244 | ||||||||
\(856\) | 16.9770 | 0.580260 | ||||||||
\(857\) | 16.9502 | 0.579009 | 0.289504 | − | 0.957177i | \(-0.406510\pi\) | ||||
0.289504 | + | 0.957177i | \(0.406510\pi\) | |||||||
\(858\) | 2.88876 | 0.0986208 | ||||||||
\(859\) | 17.0536 | 0.581860 | 0.290930 | − | 0.956744i | \(-0.406035\pi\) | ||||
0.290930 | + | 0.956744i | \(0.406035\pi\) | |||||||
\(860\) | 4.85039 | 0.165397 | ||||||||
\(861\) | 6.44833 | 0.219759 | ||||||||
\(862\) | −1.23118 | −0.0419343 | ||||||||
\(863\) | 33.8655 | 1.15279 | 0.576397 | − | 0.817170i | \(-0.304458\pi\) | ||||
0.576397 | + | 0.817170i | \(0.304458\pi\) | |||||||
\(864\) | 5.05771 | 0.172067 | ||||||||
\(865\) | −5.37203 | −0.182655 | ||||||||
\(866\) | 2.24503 | 0.0762893 | ||||||||
\(867\) | −28.9849 | −0.984379 | ||||||||
\(868\) | −4.47804 | −0.151995 | ||||||||
\(869\) | −14.1141 | −0.478787 | ||||||||
\(870\) | −12.8707 | −0.436356 | ||||||||
\(871\) | 8.56968 | 0.290372 | ||||||||
\(872\) | 3.16635 | 0.107226 | ||||||||
\(873\) | −0.238338 | −0.00806652 | ||||||||
\(874\) | −0.981993 | −0.0332164 | ||||||||
\(875\) | 18.4029 | 0.622131 | ||||||||
\(876\) | 26.9101 | 0.909208 | ||||||||
\(877\) | 19.9918 | 0.675074 | 0.337537 | − | 0.941312i | \(-0.390406\pi\) | ||||
0.337537 | + | 0.941312i | \(0.390406\pi\) | |||||||
\(878\) | −14.6966 | −0.495987 | ||||||||
\(879\) | 12.5916 | 0.424705 | ||||||||
\(880\) | −0.781935 | −0.0263590 | ||||||||
\(881\) | −41.1816 | −1.38744 | −0.693721 | − | 0.720244i | \(-0.744030\pi\) | ||||
−0.693721 | + | 0.720244i | \(0.744030\pi\) | |||||||
\(882\) | 0.107808 | 0.00363008 | ||||||||
\(883\) | −34.1202 | −1.14824 | −0.574118 | − | 0.818773i | \(-0.694655\pi\) | ||||
−0.574118 | + | 0.818773i | \(0.694655\pi\) | |||||||
\(884\) | −1.33245 | −0.0448152 | ||||||||
\(885\) | −2.51823 | −0.0846495 | ||||||||
\(886\) | 17.1435 | 0.575947 | ||||||||
\(887\) | −27.7652 | −0.932264 | −0.466132 | − | 0.884715i | \(-0.654353\pi\) | ||||
−0.466132 | + | 0.884715i | \(0.654353\pi\) | |||||||
\(888\) | 3.12774 | 0.104960 | ||||||||
\(889\) | −28.1306 | −0.943471 | ||||||||
\(890\) | −7.40332 | −0.248160 | ||||||||
\(891\) | −9.42899 | −0.315883 | ||||||||
\(892\) | −17.4207 | −0.583288 | ||||||||
\(893\) | 9.80844 | 0.328227 | ||||||||
\(894\) | −20.1256 | −0.673102 | ||||||||
\(895\) | 11.9378 | 0.399035 | ||||||||
\(896\) | −2.50677 | −0.0837455 | ||||||||
\(897\) | 1.07496 | 0.0358918 | ||||||||
\(898\) | −30.0085 | −1.00139 | ||||||||
\(899\) | 16.5657 | 0.552496 | ||||||||
\(900\) | −0.660714 | −0.0220238 | ||||||||
\(901\) | −3.41727 | −0.113846 | ||||||||
\(902\) | −1.44923 | −0.0482542 | ||||||||
\(903\) | −27.6004 | −0.918483 | ||||||||
\(904\) | 0.907314 | 0.0301768 | ||||||||
\(905\) | −19.5765 | −0.650744 | ||||||||
\(906\) | 3.34603 | 0.111164 | ||||||||
\(907\) | 18.7838 | 0.623706 | 0.311853 | − | 0.950130i | \(-0.399050\pi\) | ||||
0.311853 | + | 0.950130i | \(0.399050\pi\) | |||||||
\(908\) | 17.0235 | 0.564945 | ||||||||
\(909\) | 2.24476 | 0.0744541 | ||||||||
\(910\) | −3.19010 | −0.105751 | ||||||||
\(911\) | −17.0719 | −0.565617 | −0.282808 | − | 0.959176i | \(-0.591266\pi\) | ||||
−0.282808 | + | 0.959176i | \(0.591266\pi\) | |||||||
\(912\) | −4.68405 | −0.155105 | ||||||||
\(913\) | 12.5488 | 0.415306 | ||||||||
\(914\) | −23.8644 | −0.789365 | ||||||||
\(915\) | 13.1088 | 0.433364 | ||||||||
\(916\) | 24.1710 | 0.798634 | ||||||||
\(917\) | 47.7112 | 1.57556 | ||||||||
\(918\) | 4.14083 | 0.136668 | ||||||||
\(919\) | 57.6392 | 1.90134 | 0.950671 | − | 0.310201i | \(-0.100396\pi\) | ||||
0.950671 | + | 0.310201i | \(0.100396\pi\) | |||||||
\(920\) | −0.290972 | −0.00959305 | ||||||||
\(921\) | 19.1581 | 0.631281 | ||||||||
\(922\) | −26.3947 | −0.869264 | ||||||||
\(923\) | −25.1708 | −0.828507 | ||||||||
\(924\) | 4.44947 | 0.146377 | ||||||||
\(925\) | 7.73323 | 0.254267 | ||||||||
\(926\) | 29.1966 | 0.959458 | ||||||||
\(927\) | 0.884230 | 0.0290419 | ||||||||
\(928\) | 9.27335 | 0.304413 | ||||||||
\(929\) | −6.15552 | −0.201956 | −0.100978 | − | 0.994889i | \(-0.532197\pi\) | ||||
−0.100978 | + | 0.994889i | \(0.532197\pi\) | |||||||
\(930\) | −2.47934 | −0.0813009 | ||||||||
\(931\) | 1.88969 | 0.0619320 | ||||||||
\(932\) | −8.79647 | −0.288138 | ||||||||
\(933\) | −57.3263 | −1.87678 | ||||||||
\(934\) | −11.7938 | −0.385905 | ||||||||
\(935\) | −0.640183 | −0.0209362 | ||||||||
\(936\) | 0.245024 | 0.00800885 | ||||||||
\(937\) | −35.2150 | −1.15042 | −0.575212 | − | 0.818004i | \(-0.695080\pi\) | ||||
−0.575212 | + | 0.818004i | \(0.695080\pi\) | |||||||
\(938\) | 13.1996 | 0.430983 | ||||||||
\(939\) | 28.6240 | 0.934110 | ||||||||
\(940\) | 2.90631 | 0.0947934 | ||||||||
\(941\) | 34.0646 | 1.11047 | 0.555237 | − | 0.831692i | \(-0.312628\pi\) | ||||
0.555237 | + | 0.831692i | \(0.312628\pi\) | |||||||
\(942\) | −26.6447 | −0.868132 | ||||||||
\(943\) | −0.539285 | −0.0175616 | ||||||||
\(944\) | 1.81440 | 0.0590535 | ||||||||
\(945\) | 9.91380 | 0.322496 | ||||||||
\(946\) | 6.20306 | 0.201679 | ||||||||
\(947\) | 24.8820 | 0.808556 | 0.404278 | − | 0.914636i | \(-0.367523\pi\) | ||||
0.404278 | + | 0.914636i | \(0.367523\pi\) | |||||||
\(948\) | −25.0522 | −0.813657 | ||||||||
\(949\) | −24.6740 | −0.800953 | ||||||||
\(950\) | −11.5812 | −0.375743 | ||||||||
\(951\) | 56.0198 | 1.81657 | ||||||||
\(952\) | −2.05234 | −0.0665166 | ||||||||
\(953\) | 28.6111 | 0.926806 | 0.463403 | − | 0.886148i | \(-0.346628\pi\) | ||||
0.463403 | + | 0.886148i | \(0.346628\pi\) | |||||||
\(954\) | 0.628399 | 0.0203452 | ||||||||
\(955\) | 0.941584 | 0.0304689 | ||||||||
\(956\) | 9.49252 | 0.307010 | ||||||||
\(957\) | −16.4600 | −0.532076 | ||||||||
\(958\) | 15.2391 | 0.492355 | ||||||||
\(959\) | −44.0306 | −1.42182 | ||||||||
\(960\) | −1.38792 | −0.0447949 | ||||||||
\(961\) | −27.8089 | −0.897060 | ||||||||
\(962\) | −2.86784 | −0.0924630 | ||||||||
\(963\) | −2.55593 | −0.0823638 | ||||||||
\(964\) | −4.32087 | −0.139166 | ||||||||
\(965\) | 11.6774 | 0.375909 | ||||||||
\(966\) | 1.65573 | 0.0532721 | ||||||||
\(967\) | 52.0373 | 1.67341 | 0.836703 | − | 0.547656i | \(-0.184480\pi\) | ||||
0.836703 | + | 0.547656i | \(0.184480\pi\) | |||||||
\(968\) | −1.00000 | −0.0321412 | ||||||||
\(969\) | −3.83491 | −0.123195 | ||||||||
\(970\) | −1.23787 | −0.0397455 | ||||||||
\(971\) | 28.2403 | 0.906274 | 0.453137 | − | 0.891441i | \(-0.350305\pi\) | ||||
0.453137 | + | 0.891441i | \(0.350305\pi\) | |||||||
\(972\) | −1.56314 | −0.0501377 | ||||||||
\(973\) | 6.11923 | 0.196173 | ||||||||
\(974\) | 37.6125 | 1.20518 | ||||||||
\(975\) | 12.6776 | 0.406007 | ||||||||
\(976\) | −9.44494 | −0.302325 | ||||||||
\(977\) | 39.4882 | 1.26334 | 0.631669 | − | 0.775238i | \(-0.282370\pi\) | ||||
0.631669 | + | 0.775238i | \(0.282370\pi\) | |||||||
\(978\) | 18.6450 | 0.596202 | ||||||||
\(979\) | −9.46795 | −0.302597 | ||||||||
\(980\) | 0.559928 | 0.0178862 | ||||||||
\(981\) | −0.476704 | −0.0152200 | ||||||||
\(982\) | 10.2636 | 0.327526 | ||||||||
\(983\) | 11.0518 | 0.352499 | 0.176250 | − | 0.984346i | \(-0.443603\pi\) | ||||
0.176250 | + | 0.984346i | \(0.443603\pi\) | |||||||
\(984\) | −2.57236 | −0.0820039 | ||||||||
\(985\) | −0.781935 | −0.0249145 | ||||||||
\(986\) | 7.59224 | 0.241786 | ||||||||
\(987\) | −16.5379 | −0.526407 | ||||||||
\(988\) | 4.29484 | 0.136637 | ||||||||
\(989\) | 2.30827 | 0.0733986 | ||||||||
\(990\) | 0.117723 | 0.00374148 | ||||||||
\(991\) | 54.0951 | 1.71839 | 0.859193 | − | 0.511652i | \(-0.170966\pi\) | ||||
0.859193 | + | 0.511652i | \(0.170966\pi\) | |||||||
\(992\) | 1.78637 | 0.0567174 | ||||||||
\(993\) | −29.6129 | −0.939736 | ||||||||
\(994\) | −38.7698 | −1.22970 | ||||||||
\(995\) | 11.9200 | 0.377890 | ||||||||
\(996\) | 22.2739 | 0.705776 | ||||||||
\(997\) | 46.1210 | 1.46067 | 0.730333 | − | 0.683091i | \(-0.239365\pi\) | ||||
0.730333 | + | 0.683091i | \(0.239365\pi\) | |||||||
\(998\) | −15.7335 | −0.498035 | ||||||||
\(999\) | 8.91232 | 0.281973 |
(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 | 4334.2.a.a.1.13 | ✓ | 15 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4334.2.a.a.1.13 | ✓ | 15 | 1.1 | even | 1 | trivial |