Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6031,2,Mod(1,6031)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6031, 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("6031.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6031 = 37 \cdot 163 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6031.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: | \(48.1577774590\) |
Analytic rank: | \(0\) |
Dimension: | \(133\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.12 | ||
Character | \(\chi\) | \(=\) | 6031.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.38561 | −1.68688 | −0.843441 | − | 0.537222i | \(-0.819474\pi\) | ||||
−0.843441 | + | 0.537222i | \(0.819474\pi\) | |||||||
\(3\) | −1.27766 | −0.737657 | −0.368829 | − | 0.929497i | \(-0.620241\pi\) | ||||
−0.368829 | + | 0.929497i | \(0.620241\pi\) | |||||||
\(4\) | 3.69114 | 1.84557 | ||||||||
\(5\) | 1.05833 | 0.473301 | 0.236650 | − | 0.971595i | \(-0.423950\pi\) | ||||
0.236650 | + | 0.971595i | \(0.423950\pi\) | |||||||
\(6\) | 3.04800 | 1.24434 | ||||||||
\(7\) | 3.63452 | 1.37372 | 0.686860 | − | 0.726790i | \(-0.258989\pi\) | ||||
0.686860 | + | 0.726790i | \(0.258989\pi\) | |||||||
\(8\) | −4.03440 | −1.42638 | ||||||||
\(9\) | −1.36759 | −0.455862 | ||||||||
\(10\) | −2.52477 | −0.798403 | ||||||||
\(11\) | 6.37491 | 1.92211 | 0.961055 | − | 0.276359i | \(-0.0891278\pi\) | ||||
0.961055 | + | 0.276359i | \(0.0891278\pi\) | |||||||
\(12\) | −4.71602 | −1.36140 | ||||||||
\(13\) | 3.34884 | 0.928802 | 0.464401 | − | 0.885625i | \(-0.346270\pi\) | ||||
0.464401 | + | 0.885625i | \(0.346270\pi\) | |||||||
\(14\) | −8.67055 | −2.31730 | ||||||||
\(15\) | −1.35219 | −0.349134 | ||||||||
\(16\) | 2.24223 | 0.560557 | ||||||||
\(17\) | −1.62321 | −0.393687 | −0.196843 | − | 0.980435i | \(-0.563069\pi\) | ||||
−0.196843 | + | 0.980435i | \(0.563069\pi\) | |||||||
\(18\) | 3.26253 | 0.768985 | ||||||||
\(19\) | −1.80216 | −0.413444 | −0.206722 | − | 0.978400i | \(-0.566280\pi\) | ||||
−0.206722 | + | 0.978400i | \(0.566280\pi\) | |||||||
\(20\) | 3.90645 | 0.873510 | ||||||||
\(21\) | −4.64368 | −1.01333 | ||||||||
\(22\) | −15.2081 | −3.24237 | ||||||||
\(23\) | 2.14602 | 0.447477 | 0.223738 | − | 0.974649i | \(-0.428174\pi\) | ||||
0.223738 | + | 0.974649i | \(0.428174\pi\) | |||||||
\(24\) | 5.15459 | 1.05218 | ||||||||
\(25\) | −3.87993 | −0.775986 | ||||||||
\(26\) | −7.98904 | −1.56678 | ||||||||
\(27\) | 5.58029 | 1.07393 | ||||||||
\(28\) | 13.4155 | 2.53530 | ||||||||
\(29\) | −8.47687 | −1.57412 | −0.787058 | − | 0.616879i | \(-0.788397\pi\) | ||||
−0.787058 | + | 0.616879i | \(0.788397\pi\) | |||||||
\(30\) | 3.22580 | 0.588947 | ||||||||
\(31\) | −0.456835 | −0.0820501 | −0.0410250 | − | 0.999158i | \(-0.513062\pi\) | ||||
−0.0410250 | + | 0.999158i | \(0.513062\pi\) | |||||||
\(32\) | 2.71971 | 0.480782 | ||||||||
\(33\) | −8.14497 | −1.41786 | ||||||||
\(34\) | 3.87235 | 0.664103 | ||||||||
\(35\) | 3.84653 | 0.650183 | ||||||||
\(36\) | −5.04795 | −0.841325 | ||||||||
\(37\) | −1.00000 | −0.164399 | ||||||||
\(38\) | 4.29926 | 0.697432 | ||||||||
\(39\) | −4.27868 | −0.685138 | ||||||||
\(40\) | −4.26974 | −0.675105 | ||||||||
\(41\) | −3.27551 | −0.511549 | −0.255775 | − | 0.966736i | \(-0.582331\pi\) | ||||
−0.255775 | + | 0.966736i | \(0.582331\pi\) | |||||||
\(42\) | 11.0780 | 1.70937 | ||||||||
\(43\) | −1.63618 | −0.249515 | −0.124757 | − | 0.992187i | \(-0.539815\pi\) | ||||
−0.124757 | + | 0.992187i | \(0.539815\pi\) | |||||||
\(44\) | 23.5307 | 3.54739 | ||||||||
\(45\) | −1.44736 | −0.215760 | ||||||||
\(46\) | −5.11957 | −0.754840 | ||||||||
\(47\) | −0.868467 | −0.126679 | −0.0633395 | − | 0.997992i | \(-0.520175\pi\) | ||||
−0.0633395 | + | 0.997992i | \(0.520175\pi\) | |||||||
\(48\) | −2.86481 | −0.413499 | ||||||||
\(49\) | 6.20974 | 0.887106 | ||||||||
\(50\) | 9.25601 | 1.30900 | ||||||||
\(51\) | 2.07391 | 0.290406 | ||||||||
\(52\) | 12.3610 | 1.71417 | ||||||||
\(53\) | 5.15215 | 0.707703 | 0.353851 | − | 0.935302i | \(-0.384872\pi\) | ||||
0.353851 | + | 0.935302i | \(0.384872\pi\) | |||||||
\(54\) | −13.3124 | −1.81159 | ||||||||
\(55\) | 6.74678 | 0.909736 | ||||||||
\(56\) | −14.6631 | −1.95944 | ||||||||
\(57\) | 2.30255 | 0.304980 | ||||||||
\(58\) | 20.2225 | 2.65535 | ||||||||
\(59\) | 12.0518 | 1.56901 | 0.784506 | − | 0.620121i | \(-0.212917\pi\) | ||||
0.784506 | + | 0.620121i | \(0.212917\pi\) | |||||||
\(60\) | −4.99112 | −0.644351 | ||||||||
\(61\) | 0.335052 | 0.0428991 | 0.0214495 | − | 0.999770i | \(-0.493172\pi\) | ||||
0.0214495 | + | 0.999770i | \(0.493172\pi\) | |||||||
\(62\) | 1.08983 | 0.138409 | ||||||||
\(63\) | −4.97052 | −0.626227 | ||||||||
\(64\) | −10.9726 | −1.37158 | ||||||||
\(65\) | 3.54419 | 0.439603 | ||||||||
\(66\) | 19.4307 | 2.39176 | ||||||||
\(67\) | −2.75376 | −0.336425 | −0.168213 | − | 0.985751i | \(-0.553800\pi\) | ||||
−0.168213 | + | 0.985751i | \(0.553800\pi\) | |||||||
\(68\) | −5.99150 | −0.726577 | ||||||||
\(69\) | −2.74189 | −0.330084 | ||||||||
\(70\) | −9.17633 | −1.09678 | ||||||||
\(71\) | −7.94862 | −0.943328 | −0.471664 | − | 0.881778i | \(-0.656346\pi\) | ||||
−0.471664 | + | 0.881778i | \(0.656346\pi\) | |||||||
\(72\) | 5.51739 | 0.650230 | ||||||||
\(73\) | −4.92432 | −0.576348 | −0.288174 | − | 0.957578i | \(-0.593048\pi\) | ||||
−0.288174 | + | 0.957578i | \(0.593048\pi\) | |||||||
\(74\) | 2.38561 | 0.277322 | ||||||||
\(75\) | 4.95723 | 0.572412 | ||||||||
\(76\) | −6.65203 | −0.763041 | ||||||||
\(77\) | 23.1698 | 2.64044 | ||||||||
\(78\) | 10.2073 | 1.15575 | ||||||||
\(79\) | 11.9529 | 1.34480 | 0.672401 | − | 0.740187i | \(-0.265263\pi\) | ||||
0.672401 | + | 0.740187i | \(0.265263\pi\) | |||||||
\(80\) | 2.37303 | 0.265312 | ||||||||
\(81\) | −3.02695 | −0.336328 | ||||||||
\(82\) | 7.81410 | 0.862923 | ||||||||
\(83\) | 9.43378 | 1.03549 | 0.517746 | − | 0.855535i | \(-0.326771\pi\) | ||||
0.517746 | + | 0.855535i | \(0.326771\pi\) | |||||||
\(84\) | −17.1405 | −1.87018 | ||||||||
\(85\) | −1.71790 | −0.186332 | ||||||||
\(86\) | 3.90328 | 0.420902 | ||||||||
\(87\) | 10.8306 | 1.16116 | ||||||||
\(88\) | −25.7190 | −2.74165 | ||||||||
\(89\) | 10.3818 | 1.10047 | 0.550237 | − | 0.835009i | \(-0.314537\pi\) | ||||
0.550237 | + | 0.835009i | \(0.314537\pi\) | |||||||
\(90\) | 3.45284 | 0.363961 | ||||||||
\(91\) | 12.1714 | 1.27591 | ||||||||
\(92\) | 7.92127 | 0.825849 | ||||||||
\(93\) | 0.583680 | 0.0605248 | ||||||||
\(94\) | 2.07182 | 0.213692 | ||||||||
\(95\) | −1.90729 | −0.195684 | ||||||||
\(96\) | −3.47487 | −0.354652 | ||||||||
\(97\) | −10.0161 | −1.01698 | −0.508490 | − | 0.861068i | \(-0.669796\pi\) | ||||
−0.508490 | + | 0.861068i | \(0.669796\pi\) | |||||||
\(98\) | −14.8140 | −1.49644 | ||||||||
\(99\) | −8.71824 | −0.876216 | ||||||||
\(100\) | −14.3214 | −1.43214 | ||||||||
\(101\) | −11.1360 | −1.10808 | −0.554038 | − | 0.832492i | \(-0.686914\pi\) | ||||
−0.554038 | + | 0.832492i | \(0.686914\pi\) | |||||||
\(102\) | −4.94755 | −0.489880 | ||||||||
\(103\) | 4.02708 | 0.396800 | 0.198400 | − | 0.980121i | \(-0.436425\pi\) | ||||
0.198400 | + | 0.980121i | \(0.436425\pi\) | |||||||
\(104\) | −13.5106 | −1.32482 | ||||||||
\(105\) | −4.91456 | −0.479612 | ||||||||
\(106\) | −12.2910 | −1.19381 | ||||||||
\(107\) | 18.0569 | 1.74563 | 0.872814 | − | 0.488053i | \(-0.162293\pi\) | ||||
0.872814 | + | 0.488053i | \(0.162293\pi\) | |||||||
\(108\) | 20.5976 | 1.98201 | ||||||||
\(109\) | 9.94049 | 0.952126 | 0.476063 | − | 0.879411i | \(-0.342063\pi\) | ||||
0.476063 | + | 0.879411i | \(0.342063\pi\) | |||||||
\(110\) | −16.0952 | −1.53462 | ||||||||
\(111\) | 1.27766 | 0.121270 | ||||||||
\(112\) | 8.14943 | 0.770049 | ||||||||
\(113\) | 6.41720 | 0.603680 | 0.301840 | − | 0.953359i | \(-0.402399\pi\) | ||||
0.301840 | + | 0.953359i | \(0.402399\pi\) | |||||||
\(114\) | −5.49299 | −0.514466 | ||||||||
\(115\) | 2.27121 | 0.211791 | ||||||||
\(116\) | −31.2893 | −2.90514 | ||||||||
\(117\) | −4.57983 | −0.423406 | ||||||||
\(118\) | −28.7509 | −2.64674 | ||||||||
\(119\) | −5.89960 | −0.540816 | ||||||||
\(120\) | 5.45527 | 0.497996 | ||||||||
\(121\) | 29.6395 | 2.69450 | ||||||||
\(122\) | −0.799305 | −0.0723657 | ||||||||
\(123\) | 4.18499 | 0.377348 | ||||||||
\(124\) | −1.68624 | −0.151429 | ||||||||
\(125\) | −9.39792 | −0.840576 | ||||||||
\(126\) | 11.8577 | 1.05637 | ||||||||
\(127\) | −10.0174 | −0.888897 | −0.444448 | − | 0.895804i | \(-0.646600\pi\) | ||||
−0.444448 | + | 0.895804i | \(0.646600\pi\) | |||||||
\(128\) | 20.7370 | 1.83291 | ||||||||
\(129\) | 2.09048 | 0.184056 | ||||||||
\(130\) | −8.45506 | −0.741558 | ||||||||
\(131\) | 17.0598 | 1.49052 | 0.745261 | − | 0.666773i | \(-0.232325\pi\) | ||||
0.745261 | + | 0.666773i | \(0.232325\pi\) | |||||||
\(132\) | −30.0642 | −2.61675 | ||||||||
\(133\) | −6.55000 | −0.567957 | ||||||||
\(134\) | 6.56940 | 0.567510 | ||||||||
\(135\) | 5.90580 | 0.508291 | ||||||||
\(136\) | 6.54869 | 0.561545 | ||||||||
\(137\) | 8.84841 | 0.755971 | 0.377985 | − | 0.925812i | \(-0.376617\pi\) | ||||
0.377985 | + | 0.925812i | \(0.376617\pi\) | |||||||
\(138\) | 6.54107 | 0.556813 | ||||||||
\(139\) | 20.9195 | 1.77437 | 0.887186 | − | 0.461412i | \(-0.152657\pi\) | ||||
0.887186 | + | 0.461412i | \(0.152657\pi\) | |||||||
\(140\) | 14.1981 | 1.19996 | ||||||||
\(141\) | 1.10961 | 0.0934456 | ||||||||
\(142\) | 18.9623 | 1.59128 | ||||||||
\(143\) | 21.3486 | 1.78526 | ||||||||
\(144\) | −3.06644 | −0.255537 | ||||||||
\(145\) | −8.97135 | −0.745030 | ||||||||
\(146\) | 11.7475 | 0.972231 | ||||||||
\(147\) | −7.93394 | −0.654380 | ||||||||
\(148\) | −3.69114 | −0.303410 | ||||||||
\(149\) | −2.23035 | −0.182718 | −0.0913588 | − | 0.995818i | \(-0.529121\pi\) | ||||
−0.0913588 | + | 0.995818i | \(0.529121\pi\) | |||||||
\(150\) | −11.8260 | −0.965591 | ||||||||
\(151\) | 1.12941 | 0.0919099 | 0.0459549 | − | 0.998944i | \(-0.485367\pi\) | ||||
0.0459549 | + | 0.998944i | \(0.485367\pi\) | |||||||
\(152\) | 7.27064 | 0.589727 | ||||||||
\(153\) | 2.21988 | 0.179467 | ||||||||
\(154\) | −55.2740 | −4.45411 | ||||||||
\(155\) | −0.483484 | −0.0388344 | ||||||||
\(156\) | −15.7932 | −1.26447 | ||||||||
\(157\) | −2.00470 | −0.159992 | −0.0799962 | − | 0.996795i | \(-0.525491\pi\) | ||||
−0.0799962 | + | 0.996795i | \(0.525491\pi\) | |||||||
\(158\) | −28.5149 | −2.26852 | ||||||||
\(159\) | −6.58270 | −0.522042 | ||||||||
\(160\) | 2.87836 | 0.227554 | ||||||||
\(161\) | 7.79976 | 0.614707 | ||||||||
\(162\) | 7.22113 | 0.567345 | ||||||||
\(163\) | 1.00000 | 0.0783260 | ||||||||
\(164\) | −12.0904 | −0.944100 | ||||||||
\(165\) | −8.62009 | −0.671073 | ||||||||
\(166\) | −22.5053 | −1.74675 | ||||||||
\(167\) | 3.43488 | 0.265799 | 0.132899 | − | 0.991130i | \(-0.457571\pi\) | ||||
0.132899 | + | 0.991130i | \(0.457571\pi\) | |||||||
\(168\) | 18.7345 | 1.44540 | ||||||||
\(169\) | −1.78524 | −0.137326 | ||||||||
\(170\) | 4.09824 | 0.314321 | ||||||||
\(171\) | 2.46461 | 0.188474 | ||||||||
\(172\) | −6.03936 | −0.460497 | ||||||||
\(173\) | −6.87158 | −0.522437 | −0.261218 | − | 0.965280i | \(-0.584124\pi\) | ||||
−0.261218 | + | 0.965280i | \(0.584124\pi\) | |||||||
\(174\) | −25.8375 | −1.95874 | ||||||||
\(175\) | −14.1017 | −1.06599 | ||||||||
\(176\) | 14.2940 | 1.07745 | ||||||||
\(177\) | −15.3981 | −1.15739 | ||||||||
\(178\) | −24.7670 | −1.85637 | ||||||||
\(179\) | 9.23808 | 0.690486 | 0.345243 | − | 0.938513i | \(-0.387796\pi\) | ||||
0.345243 | + | 0.938513i | \(0.387796\pi\) | |||||||
\(180\) | −5.34241 | −0.398200 | ||||||||
\(181\) | −16.1734 | −1.20216 | −0.601081 | − | 0.799188i | \(-0.705263\pi\) | ||||
−0.601081 | + | 0.799188i | \(0.705263\pi\) | |||||||
\(182\) | −29.0363 | −2.15232 | ||||||||
\(183\) | −0.428083 | −0.0316448 | ||||||||
\(184\) | −8.65791 | −0.638270 | ||||||||
\(185\) | −1.05833 | −0.0778102 | ||||||||
\(186\) | −1.39243 | −0.102098 | ||||||||
\(187\) | −10.3478 | −0.756709 | ||||||||
\(188\) | −3.20563 | −0.233795 | ||||||||
\(189\) | 20.2817 | 1.47527 | ||||||||
\(190\) | 4.55005 | 0.330095 | ||||||||
\(191\) | 6.49253 | 0.469783 | 0.234891 | − | 0.972022i | \(-0.424527\pi\) | ||||
0.234891 | + | 0.972022i | \(0.424527\pi\) | |||||||
\(192\) | 14.0193 | 1.01176 | ||||||||
\(193\) | −17.1509 | −1.23455 | −0.617273 | − | 0.786749i | \(-0.711763\pi\) | ||||
−0.617273 | + | 0.786749i | \(0.711763\pi\) | |||||||
\(194\) | 23.8945 | 1.71553 | ||||||||
\(195\) | −4.52827 | −0.324276 | ||||||||
\(196\) | 22.9210 | 1.63722 | ||||||||
\(197\) | 18.7610 | 1.33667 | 0.668334 | − | 0.743862i | \(-0.267008\pi\) | ||||
0.668334 | + | 0.743862i | \(0.267008\pi\) | |||||||
\(198\) | 20.7983 | 1.47807 | ||||||||
\(199\) | 7.77477 | 0.551139 | 0.275569 | − | 0.961281i | \(-0.411134\pi\) | ||||
0.275569 | + | 0.961281i | \(0.411134\pi\) | |||||||
\(200\) | 15.6532 | 1.10685 | ||||||||
\(201\) | 3.51837 | 0.248166 | ||||||||
\(202\) | 26.5662 | 1.86919 | ||||||||
\(203\) | −30.8094 | −2.16239 | ||||||||
\(204\) | 7.65510 | 0.535964 | ||||||||
\(205\) | −3.46659 | −0.242117 | ||||||||
\(206\) | −9.60705 | −0.669355 | ||||||||
\(207\) | −2.93487 | −0.203988 | ||||||||
\(208\) | 7.50888 | 0.520647 | ||||||||
\(209\) | −11.4886 | −0.794685 | ||||||||
\(210\) | 11.7242 | 0.809049 | ||||||||
\(211\) | 7.92778 | 0.545771 | 0.272885 | − | 0.962047i | \(-0.412022\pi\) | ||||
0.272885 | + | 0.962047i | \(0.412022\pi\) | |||||||
\(212\) | 19.0173 | 1.30611 | ||||||||
\(213\) | 10.1556 | 0.695852 | ||||||||
\(214\) | −43.0768 | −2.94467 | ||||||||
\(215\) | −1.73162 | −0.118096 | ||||||||
\(216\) | −22.5131 | −1.53182 | ||||||||
\(217\) | −1.66038 | −0.112714 | ||||||||
\(218\) | −23.7141 | −1.60612 | ||||||||
\(219\) | 6.29160 | 0.425147 | ||||||||
\(220\) | 24.9033 | 1.67898 | ||||||||
\(221\) | −5.43589 | −0.365657 | ||||||||
\(222\) | −3.04800 | −0.204568 | ||||||||
\(223\) | 22.1897 | 1.48593 | 0.742967 | − | 0.669328i | \(-0.233418\pi\) | ||||
0.742967 | + | 0.669328i | \(0.233418\pi\) | |||||||
\(224\) | 9.88485 | 0.660459 | ||||||||
\(225\) | 5.30614 | 0.353743 | ||||||||
\(226\) | −15.3089 | −1.01834 | ||||||||
\(227\) | 1.90344 | 0.126336 | 0.0631680 | − | 0.998003i | \(-0.479880\pi\) | ||||
0.0631680 | + | 0.998003i | \(0.479880\pi\) | |||||||
\(228\) | 8.49903 | 0.562862 | ||||||||
\(229\) | 7.79373 | 0.515024 | 0.257512 | − | 0.966275i | \(-0.417097\pi\) | ||||
0.257512 | + | 0.966275i | \(0.417097\pi\) | |||||||
\(230\) | −5.41821 | −0.357266 | ||||||||
\(231\) | −29.6031 | −1.94774 | ||||||||
\(232\) | 34.1991 | 2.24528 | ||||||||
\(233\) | −2.40280 | −0.157412 | −0.0787062 | − | 0.996898i | \(-0.525079\pi\) | ||||
−0.0787062 | + | 0.996898i | \(0.525079\pi\) | |||||||
\(234\) | 10.9257 | 0.714235 | ||||||||
\(235\) | −0.919128 | −0.0599573 | ||||||||
\(236\) | 44.4849 | 2.89572 | ||||||||
\(237\) | −15.2717 | −0.992002 | ||||||||
\(238\) | 14.0742 | 0.912292 | ||||||||
\(239\) | −0.587973 | −0.0380328 | −0.0190164 | − | 0.999819i | \(-0.506053\pi\) | ||||
−0.0190164 | + | 0.999819i | \(0.506053\pi\) | |||||||
\(240\) | −3.03192 | −0.195710 | ||||||||
\(241\) | −15.4995 | −0.998410 | −0.499205 | − | 0.866484i | \(-0.666374\pi\) | ||||
−0.499205 | + | 0.866484i | \(0.666374\pi\) | |||||||
\(242\) | −70.7084 | −4.54531 | ||||||||
\(243\) | −12.8735 | −0.825832 | ||||||||
\(244\) | 1.23673 | 0.0791732 | ||||||||
\(245\) | 6.57198 | 0.419868 | ||||||||
\(246\) | −9.98376 | −0.636542 | ||||||||
\(247\) | −6.03516 | −0.384008 | ||||||||
\(248\) | 1.84306 | 0.117034 | ||||||||
\(249\) | −12.0532 | −0.763838 | ||||||||
\(250\) | 22.4198 | 1.41795 | ||||||||
\(251\) | 29.3174 | 1.85050 | 0.925250 | − | 0.379358i | \(-0.123855\pi\) | ||||
0.925250 | + | 0.379358i | \(0.123855\pi\) | |||||||
\(252\) | −18.3469 | −1.15574 | ||||||||
\(253\) | 13.6807 | 0.860099 | ||||||||
\(254\) | 23.8975 | 1.49946 | ||||||||
\(255\) | 2.19489 | 0.137449 | ||||||||
\(256\) | −27.5252 | −1.72032 | ||||||||
\(257\) | −15.6563 | −0.976612 | −0.488306 | − | 0.872673i | \(-0.662385\pi\) | ||||
−0.488306 | + | 0.872673i | \(0.662385\pi\) | |||||||
\(258\) | −4.98707 | −0.310481 | ||||||||
\(259\) | −3.63452 | −0.225838 | ||||||||
\(260\) | 13.0821 | 0.811318 | ||||||||
\(261\) | 11.5929 | 0.717579 | ||||||||
\(262\) | −40.6980 | −2.51433 | ||||||||
\(263\) | −6.19871 | −0.382229 | −0.191114 | − | 0.981568i | \(-0.561210\pi\) | ||||
−0.191114 | + | 0.981568i | \(0.561210\pi\) | |||||||
\(264\) | 32.8601 | 2.02240 | ||||||||
\(265\) | 5.45269 | 0.334956 | ||||||||
\(266\) | 15.6257 | 0.958076 | ||||||||
\(267\) | −13.2645 | −0.811772 | ||||||||
\(268\) | −10.1645 | −0.620896 | ||||||||
\(269\) | −27.5181 | −1.67781 | −0.838903 | − | 0.544281i | \(-0.816802\pi\) | ||||
−0.838903 | + | 0.544281i | \(0.816802\pi\) | |||||||
\(270\) | −14.0889 | −0.857426 | ||||||||
\(271\) | 7.35320 | 0.446675 | 0.223337 | − | 0.974741i | \(-0.428305\pi\) | ||||
0.223337 | + | 0.974741i | \(0.428305\pi\) | |||||||
\(272\) | −3.63962 | −0.220684 | ||||||||
\(273\) | −15.5510 | −0.941187 | ||||||||
\(274\) | −21.1089 | −1.27523 | ||||||||
\(275\) | −24.7342 | −1.49153 | ||||||||
\(276\) | −10.1207 | −0.609193 | ||||||||
\(277\) | −12.0892 | −0.726372 | −0.363186 | − | 0.931717i | \(-0.618311\pi\) | ||||
−0.363186 | + | 0.931717i | \(0.618311\pi\) | |||||||
\(278\) | −49.9059 | −2.99316 | ||||||||
\(279\) | 0.624762 | 0.0374035 | ||||||||
\(280\) | −15.5185 | −0.927405 | ||||||||
\(281\) | 24.9391 | 1.48774 | 0.743872 | − | 0.668322i | \(-0.232987\pi\) | ||||
0.743872 | + | 0.668322i | \(0.232987\pi\) | |||||||
\(282\) | −2.64709 | −0.157632 | ||||||||
\(283\) | 9.67230 | 0.574958 | 0.287479 | − | 0.957787i | \(-0.407183\pi\) | ||||
0.287479 | + | 0.957787i | \(0.407183\pi\) | |||||||
\(284\) | −29.3395 | −1.74098 | ||||||||
\(285\) | 2.43687 | 0.144347 | ||||||||
\(286\) | −50.9294 | −3.01152 | ||||||||
\(287\) | −11.9049 | −0.702726 | ||||||||
\(288\) | −3.71944 | −0.219170 | ||||||||
\(289\) | −14.3652 | −0.845011 | ||||||||
\(290\) | 21.4022 | 1.25678 | ||||||||
\(291\) | 12.7972 | 0.750183 | ||||||||
\(292\) | −18.1764 | −1.06369 | ||||||||
\(293\) | −3.19113 | −0.186428 | −0.0932138 | − | 0.995646i | \(-0.529714\pi\) | ||||
−0.0932138 | + | 0.995646i | \(0.529714\pi\) | |||||||
\(294\) | 18.9273 | 1.10386 | ||||||||
\(295\) | 12.7548 | 0.742615 | ||||||||
\(296\) | 4.03440 | 0.234495 | ||||||||
\(297\) | 35.5739 | 2.06420 | ||||||||
\(298\) | 5.32075 | 0.308223 | ||||||||
\(299\) | 7.18669 | 0.415617 | ||||||||
\(300\) | 18.2978 | 1.05643 | ||||||||
\(301\) | −5.94672 | −0.342763 | ||||||||
\(302\) | −2.69433 | −0.155041 | ||||||||
\(303\) | 14.2280 | 0.817379 | ||||||||
\(304\) | −4.04086 | −0.231759 | ||||||||
\(305\) | 0.354597 | 0.0203042 | ||||||||
\(306\) | −5.29578 | −0.302739 | ||||||||
\(307\) | −0.199609 | −0.0113923 | −0.00569614 | − | 0.999984i | \(-0.501813\pi\) | ||||
−0.00569614 | + | 0.999984i | \(0.501813\pi\) | |||||||
\(308\) | 85.5228 | 4.87311 | ||||||||
\(309\) | −5.14524 | −0.292702 | ||||||||
\(310\) | 1.15340 | 0.0655090 | ||||||||
\(311\) | 24.1056 | 1.36690 | 0.683451 | − | 0.729996i | \(-0.260478\pi\) | ||||
0.683451 | + | 0.729996i | \(0.260478\pi\) | |||||||
\(312\) | 17.2619 | 0.977264 | ||||||||
\(313\) | −6.78884 | −0.383728 | −0.191864 | − | 0.981422i | \(-0.561453\pi\) | ||||
−0.191864 | + | 0.981422i | \(0.561453\pi\) | |||||||
\(314\) | 4.78243 | 0.269888 | ||||||||
\(315\) | −5.26047 | −0.296394 | ||||||||
\(316\) | 44.1197 | 2.48192 | ||||||||
\(317\) | −13.6757 | −0.768105 | −0.384053 | − | 0.923311i | \(-0.625472\pi\) | ||||
−0.384053 | + | 0.923311i | \(0.625472\pi\) | |||||||
\(318\) | 15.7038 | 0.880623 | ||||||||
\(319\) | −54.0393 | −3.02562 | ||||||||
\(320\) | −11.6127 | −0.649170 | ||||||||
\(321\) | −23.0706 | −1.28767 | ||||||||
\(322\) | −18.6072 | −1.03694 | ||||||||
\(323\) | 2.92529 | 0.162768 | ||||||||
\(324\) | −11.1729 | −0.620716 | ||||||||
\(325\) | −12.9933 | −0.720738 | ||||||||
\(326\) | −2.38561 | −0.132127 | ||||||||
\(327\) | −12.7006 | −0.702343 | ||||||||
\(328\) | 13.2147 | 0.729662 | ||||||||
\(329\) | −3.15646 | −0.174021 | ||||||||
\(330\) | 20.5642 | 1.13202 | ||||||||
\(331\) | 22.7086 | 1.24818 | 0.624088 | − | 0.781354i | \(-0.285471\pi\) | ||||
0.624088 | + | 0.781354i | \(0.285471\pi\) | |||||||
\(332\) | 34.8214 | 1.91107 | ||||||||
\(333\) | 1.36759 | 0.0749432 | ||||||||
\(334\) | −8.19428 | −0.448371 | ||||||||
\(335\) | −2.91439 | −0.159230 | ||||||||
\(336\) | −10.4122 | −0.568032 | ||||||||
\(337\) | −27.7135 | −1.50965 | −0.754826 | − | 0.655926i | \(-0.772278\pi\) | ||||
−0.754826 | + | 0.655926i | \(0.772278\pi\) | |||||||
\(338\) | 4.25890 | 0.231653 | ||||||||
\(339\) | −8.19900 | −0.445309 | ||||||||
\(340\) | −6.34101 | −0.343889 | ||||||||
\(341\) | −2.91229 | −0.157709 | ||||||||
\(342\) | −5.87961 | −0.317933 | ||||||||
\(343\) | −2.87220 | −0.155084 | ||||||||
\(344\) | 6.60100 | 0.355902 | ||||||||
\(345\) | −2.90183 | −0.156229 | ||||||||
\(346\) | 16.3929 | 0.881289 | ||||||||
\(347\) | 14.0521 | 0.754357 | 0.377179 | − | 0.926140i | \(-0.376894\pi\) | ||||
0.377179 | + | 0.926140i | \(0.376894\pi\) | |||||||
\(348\) | 39.9771 | 2.14300 | ||||||||
\(349\) | −19.1006 | −1.02243 | −0.511215 | − | 0.859453i | \(-0.670804\pi\) | ||||
−0.511215 | + | 0.859453i | \(0.670804\pi\) | |||||||
\(350\) | 33.6411 | 1.79819 | ||||||||
\(351\) | 18.6875 | 0.997466 | ||||||||
\(352\) | 17.3379 | 0.924115 | ||||||||
\(353\) | 18.0643 | 0.961463 | 0.480732 | − | 0.876868i | \(-0.340371\pi\) | ||||
0.480732 | + | 0.876868i | \(0.340371\pi\) | |||||||
\(354\) | 36.7339 | 1.95238 | ||||||||
\(355\) | −8.41229 | −0.446478 | ||||||||
\(356\) | 38.3208 | 2.03100 | ||||||||
\(357\) | 7.53768 | 0.398936 | ||||||||
\(358\) | −22.0385 | −1.16477 | ||||||||
\(359\) | −14.9244 | −0.787679 | −0.393839 | − | 0.919179i | \(-0.628853\pi\) | ||||
−0.393839 | + | 0.919179i | \(0.628853\pi\) | |||||||
\(360\) | 5.83924 | 0.307755 | ||||||||
\(361\) | −15.7522 | −0.829064 | ||||||||
\(362\) | 38.5835 | 2.02790 | ||||||||
\(363\) | −37.8692 | −1.98762 | ||||||||
\(364\) | 44.9265 | 2.35479 | ||||||||
\(365\) | −5.21157 | −0.272786 | ||||||||
\(366\) | 1.02124 | 0.0533810 | ||||||||
\(367\) | −33.3017 | −1.73834 | −0.869168 | − | 0.494516i | \(-0.835345\pi\) | ||||
−0.869168 | + | 0.494516i | \(0.835345\pi\) | |||||||
\(368\) | 4.81187 | 0.250836 | ||||||||
\(369\) | 4.47955 | 0.233196 | ||||||||
\(370\) | 2.52477 | 0.131257 | ||||||||
\(371\) | 18.7256 | 0.972185 | ||||||||
\(372\) | 2.15444 | 0.111703 | ||||||||
\(373\) | −8.21808 | −0.425516 | −0.212758 | − | 0.977105i | \(-0.568245\pi\) | ||||
−0.212758 | + | 0.977105i | \(0.568245\pi\) | |||||||
\(374\) | 24.6859 | 1.27648 | ||||||||
\(375\) | 12.0073 | 0.620057 | ||||||||
\(376\) | 3.50374 | 0.180692 | ||||||||
\(377\) | −28.3877 | −1.46204 | ||||||||
\(378\) | −48.3842 | −2.48861 | ||||||||
\(379\) | 17.9178 | 0.920377 | 0.460189 | − | 0.887821i | \(-0.347782\pi\) | ||||
0.460189 | + | 0.887821i | \(0.347782\pi\) | |||||||
\(380\) | −7.04007 | −0.361148 | ||||||||
\(381\) | 12.7988 | 0.655701 | ||||||||
\(382\) | −15.4886 | −0.792468 | ||||||||
\(383\) | −6.54536 | −0.334453 | −0.167226 | − | 0.985919i | \(-0.553481\pi\) | ||||
−0.167226 | + | 0.985919i | \(0.553481\pi\) | |||||||
\(384\) | −26.4948 | −1.35206 | ||||||||
\(385\) | 24.5213 | 1.24972 | ||||||||
\(386\) | 40.9153 | 2.08253 | ||||||||
\(387\) | 2.23761 | 0.113744 | ||||||||
\(388\) | −36.9708 | −1.87691 | ||||||||
\(389\) | −16.9083 | −0.857287 | −0.428643 | − | 0.903474i | \(-0.641008\pi\) | ||||
−0.428643 | + | 0.903474i | \(0.641008\pi\) | |||||||
\(390\) | 10.8027 | 0.547016 | ||||||||
\(391\) | −3.48345 | −0.176166 | ||||||||
\(392\) | −25.0526 | −1.26535 | ||||||||
\(393\) | −21.7966 | −1.09949 | ||||||||
\(394\) | −44.7565 | −2.25480 | ||||||||
\(395\) | 12.6501 | 0.636496 | ||||||||
\(396\) | −32.1803 | −1.61712 | ||||||||
\(397\) | 7.76674 | 0.389802 | 0.194901 | − | 0.980823i | \(-0.437562\pi\) | ||||
0.194901 | + | 0.980823i | \(0.437562\pi\) | |||||||
\(398\) | −18.5476 | −0.929706 | ||||||||
\(399\) | 8.36867 | 0.418957 | ||||||||
\(400\) | −8.69970 | −0.434985 | ||||||||
\(401\) | 20.5245 | 1.02494 | 0.512471 | − | 0.858704i | \(-0.328730\pi\) | ||||
0.512471 | + | 0.858704i | \(0.328730\pi\) | |||||||
\(402\) | −8.39345 | −0.418627 | ||||||||
\(403\) | −1.52987 | −0.0762083 | ||||||||
\(404\) | −41.1046 | −2.04503 | ||||||||
\(405\) | −3.20352 | −0.159184 | ||||||||
\(406\) | 73.4992 | 3.64770 | ||||||||
\(407\) | −6.37491 | −0.315993 | ||||||||
\(408\) | −8.36700 | −0.414228 | ||||||||
\(409\) | 10.6232 | 0.525285 | 0.262642 | − | 0.964893i | \(-0.415406\pi\) | ||||
0.262642 | + | 0.964893i | \(0.415406\pi\) | |||||||
\(410\) | 8.26992 | 0.408422 | ||||||||
\(411\) | −11.3053 | −0.557647 | ||||||||
\(412\) | 14.8645 | 0.732322 | ||||||||
\(413\) | 43.8026 | 2.15538 | ||||||||
\(414\) | 7.00146 | 0.344103 | ||||||||
\(415\) | 9.98408 | 0.490099 | ||||||||
\(416\) | 9.10789 | 0.446551 | ||||||||
\(417\) | −26.7281 | −1.30888 | ||||||||
\(418\) | 27.4074 | 1.34054 | ||||||||
\(419\) | 29.3565 | 1.43416 | 0.717079 | − | 0.696992i | \(-0.245479\pi\) | ||||
0.717079 | + | 0.696992i | \(0.245479\pi\) | |||||||
\(420\) | −18.1403 | −0.885157 | ||||||||
\(421\) | 19.2212 | 0.936785 | 0.468393 | − | 0.883520i | \(-0.344833\pi\) | ||||
0.468393 | + | 0.883520i | \(0.344833\pi\) | |||||||
\(422\) | −18.9126 | −0.920651 | ||||||||
\(423\) | 1.18770 | 0.0577481 | ||||||||
\(424\) | −20.7858 | −1.00945 | ||||||||
\(425\) | 6.29795 | 0.305496 | ||||||||
\(426\) | −24.2274 | −1.17382 | ||||||||
\(427\) | 1.21776 | 0.0589313 | ||||||||
\(428\) | 66.6506 | 3.22168 | ||||||||
\(429\) | −27.2762 | −1.31691 | ||||||||
\(430\) | 4.13097 | 0.199213 | ||||||||
\(431\) | −8.03518 | −0.387041 | −0.193520 | − | 0.981096i | \(-0.561991\pi\) | ||||
−0.193520 | + | 0.981096i | \(0.561991\pi\) | |||||||
\(432\) | 12.5123 | 0.601998 | ||||||||
\(433\) | 32.7921 | 1.57589 | 0.787943 | − | 0.615749i | \(-0.211146\pi\) | ||||
0.787943 | + | 0.615749i | \(0.211146\pi\) | |||||||
\(434\) | 3.96102 | 0.190135 | ||||||||
\(435\) | 11.4623 | 0.549577 | ||||||||
\(436\) | 36.6917 | 1.75722 | ||||||||
\(437\) | −3.86748 | −0.185007 | ||||||||
\(438\) | −15.0093 | −0.717173 | ||||||||
\(439\) | 13.1832 | 0.629199 | 0.314599 | − | 0.949225i | \(-0.398130\pi\) | ||||
0.314599 | + | 0.949225i | \(0.398130\pi\) | |||||||
\(440\) | −27.2192 | −1.29763 | ||||||||
\(441\) | −8.49236 | −0.404398 | ||||||||
\(442\) | 12.9679 | 0.616821 | ||||||||
\(443\) | 20.7843 | 0.987493 | 0.493746 | − | 0.869606i | \(-0.335627\pi\) | ||||
0.493746 | + | 0.869606i | \(0.335627\pi\) | |||||||
\(444\) | 4.71602 | 0.223812 | ||||||||
\(445\) | 10.9875 | 0.520855 | ||||||||
\(446\) | −52.9361 | −2.50660 | ||||||||
\(447\) | 2.84963 | 0.134783 | ||||||||
\(448\) | −39.8803 | −1.88417 | ||||||||
\(449\) | 30.9573 | 1.46097 | 0.730483 | − | 0.682931i | \(-0.239295\pi\) | ||||
0.730483 | + | 0.682931i | \(0.239295\pi\) | |||||||
\(450\) | −12.6584 | −0.596722 | ||||||||
\(451\) | −20.8811 | −0.983254 | ||||||||
\(452\) | 23.6868 | 1.11413 | ||||||||
\(453\) | −1.44300 | −0.0677980 | ||||||||
\(454\) | −4.54088 | −0.213114 | ||||||||
\(455\) | 12.8814 | 0.603891 | ||||||||
\(456\) | −9.28941 | −0.435016 | ||||||||
\(457\) | 7.77568 | 0.363731 | 0.181865 | − | 0.983323i | \(-0.441786\pi\) | ||||
0.181865 | + | 0.983323i | \(0.441786\pi\) | |||||||
\(458\) | −18.5928 | −0.868785 | ||||||||
\(459\) | −9.05799 | −0.422791 | ||||||||
\(460\) | 8.38334 | 0.390875 | ||||||||
\(461\) | 26.6159 | 1.23963 | 0.619813 | − | 0.784749i | \(-0.287208\pi\) | ||||
0.619813 | + | 0.784749i | \(0.287208\pi\) | |||||||
\(462\) | 70.6214 | 3.28560 | ||||||||
\(463\) | 9.44524 | 0.438958 | 0.219479 | − | 0.975617i | \(-0.429564\pi\) | ||||
0.219479 | + | 0.975617i | \(0.429564\pi\) | |||||||
\(464\) | −19.0071 | −0.882382 | ||||||||
\(465\) | 0.617728 | 0.0286465 | ||||||||
\(466\) | 5.73213 | 0.265536 | ||||||||
\(467\) | −28.0646 | −1.29868 | −0.649338 | − | 0.760500i | \(-0.724954\pi\) | ||||
−0.649338 | + | 0.760500i | \(0.724954\pi\) | |||||||
\(468\) | −16.9048 | −0.781425 | ||||||||
\(469\) | −10.0086 | −0.462154 | ||||||||
\(470\) | 2.19268 | 0.101141 | ||||||||
\(471\) | 2.56132 | 0.118019 | ||||||||
\(472\) | −48.6218 | −2.23800 | ||||||||
\(473\) | −10.4305 | −0.479595 | ||||||||
\(474\) | 36.4323 | 1.67339 | ||||||||
\(475\) | 6.99227 | 0.320827 | ||||||||
\(476\) | −21.7762 | −0.998113 | ||||||||
\(477\) | −7.04601 | −0.322615 | ||||||||
\(478\) | 1.40267 | 0.0641568 | ||||||||
\(479\) | −20.8581 | −0.953033 | −0.476517 | − | 0.879166i | \(-0.658101\pi\) | ||||
−0.476517 | + | 0.879166i | \(0.658101\pi\) | |||||||
\(480\) | −3.67757 | −0.167857 | ||||||||
\(481\) | −3.34884 | −0.152694 | ||||||||
\(482\) | 36.9757 | 1.68420 | ||||||||
\(483\) | −9.96544 | −0.453443 | ||||||||
\(484\) | 109.404 | 4.97289 | ||||||||
\(485\) | −10.6004 | −0.481338 | ||||||||
\(486\) | 30.7110 | 1.39308 | ||||||||
\(487\) | −42.9596 | −1.94668 | −0.973342 | − | 0.229360i | \(-0.926337\pi\) | ||||
−0.973342 | + | 0.229360i | \(0.926337\pi\) | |||||||
\(488\) | −1.35174 | −0.0611902 | ||||||||
\(489\) | −1.27766 | −0.0577778 | ||||||||
\(490\) | −15.6782 | −0.708268 | ||||||||
\(491\) | 23.4348 | 1.05760 | 0.528798 | − | 0.848748i | \(-0.322643\pi\) | ||||
0.528798 | + | 0.848748i | \(0.322643\pi\) | |||||||
\(492\) | 15.4474 | 0.696422 | ||||||||
\(493\) | 13.7598 | 0.619709 | ||||||||
\(494\) | 14.3975 | 0.647776 | ||||||||
\(495\) | −9.22681 | −0.414714 | ||||||||
\(496\) | −1.02433 | −0.0459938 | ||||||||
\(497\) | −28.8894 | −1.29587 | ||||||||
\(498\) | 28.7541 | 1.28850 | ||||||||
\(499\) | 24.7700 | 1.10886 | 0.554428 | − | 0.832232i | \(-0.312937\pi\) | ||||
0.554428 | + | 0.832232i | \(0.312937\pi\) | |||||||
\(500\) | −34.6890 | −1.55134 | ||||||||
\(501\) | −4.38860 | −0.196068 | ||||||||
\(502\) | −69.9400 | −3.12157 | ||||||||
\(503\) | 11.3696 | 0.506944 | 0.253472 | − | 0.967343i | \(-0.418427\pi\) | ||||
0.253472 | + | 0.967343i | \(0.418427\pi\) | |||||||
\(504\) | 20.0531 | 0.893235 | ||||||||
\(505\) | −11.7856 | −0.524453 | ||||||||
\(506\) | −32.6368 | −1.45088 | ||||||||
\(507\) | 2.28093 | 0.101300 | ||||||||
\(508\) | −36.9755 | −1.64052 | ||||||||
\(509\) | −25.1393 | −1.11428 | −0.557139 | − | 0.830419i | \(-0.688101\pi\) | ||||
−0.557139 | + | 0.830419i | \(0.688101\pi\) | |||||||
\(510\) | −5.23616 | −0.231861 | ||||||||
\(511\) | −17.8975 | −0.791741 | ||||||||
\(512\) | 24.1903 | 1.06907 | ||||||||
\(513\) | −10.0566 | −0.444009 | ||||||||
\(514\) | 37.3498 | 1.64743 | ||||||||
\(515\) | 4.26199 | 0.187806 | ||||||||
\(516\) | 7.71625 | 0.339689 | ||||||||
\(517\) | −5.53640 | −0.243491 | ||||||||
\(518\) | 8.67055 | 0.380962 | ||||||||
\(519\) | 8.77955 | 0.385379 | ||||||||
\(520\) | −14.2987 | −0.627039 | ||||||||
\(521\) | 10.1344 | 0.443997 | 0.221998 | − | 0.975047i | \(-0.428742\pi\) | ||||
0.221998 | + | 0.975047i | \(0.428742\pi\) | |||||||
\(522\) | −27.6560 | −1.21047 | ||||||||
\(523\) | 3.89363 | 0.170257 | 0.0851283 | − | 0.996370i | \(-0.472870\pi\) | ||||
0.0851283 | + | 0.996370i | \(0.472870\pi\) | |||||||
\(524\) | 62.9701 | 2.75086 | ||||||||
\(525\) | 18.0172 | 0.786333 | ||||||||
\(526\) | 14.7877 | 0.644775 | ||||||||
\(527\) | 0.741541 | 0.0323020 | ||||||||
\(528\) | −18.2629 | −0.794791 | ||||||||
\(529\) | −18.3946 | −0.799765 | ||||||||
\(530\) | −13.0080 | −0.565032 | ||||||||
\(531\) | −16.4819 | −0.715253 | ||||||||
\(532\) | −24.1770 | −1.04820 | ||||||||
\(533\) | −10.9692 | −0.475128 | ||||||||
\(534\) | 31.6439 | 1.36936 | ||||||||
\(535\) | 19.1102 | 0.826207 | ||||||||
\(536\) | 11.1098 | 0.479869 | ||||||||
\(537\) | −11.8031 | −0.509342 | ||||||||
\(538\) | 65.6474 | 2.83026 | ||||||||
\(539\) | 39.5866 | 1.70511 | ||||||||
\(540\) | 21.7991 | 0.938086 | ||||||||
\(541\) | 17.9159 | 0.770263 | 0.385132 | − | 0.922862i | \(-0.374156\pi\) | ||||
0.385132 | + | 0.922862i | \(0.374156\pi\) | |||||||
\(542\) | −17.5419 | −0.753488 | ||||||||
\(543\) | 20.6641 | 0.886783 | ||||||||
\(544\) | −4.41467 | −0.189277 | ||||||||
\(545\) | 10.5204 | 0.450642 | ||||||||
\(546\) | 37.0985 | 1.58767 | ||||||||
\(547\) | −14.3505 | −0.613582 | −0.306791 | − | 0.951777i | \(-0.599255\pi\) | ||||
−0.306791 | + | 0.951777i | \(0.599255\pi\) | |||||||
\(548\) | 32.6607 | 1.39520 | ||||||||
\(549\) | −0.458213 | −0.0195561 | ||||||||
\(550\) | 59.0062 | 2.51603 | ||||||||
\(551\) | 15.2767 | 0.650809 | ||||||||
\(552\) | 11.0619 | 0.470824 | ||||||||
\(553\) | 43.4429 | 1.84738 | ||||||||
\(554\) | 28.8402 | 1.22530 | ||||||||
\(555\) | 1.35219 | 0.0573972 | ||||||||
\(556\) | 77.2169 | 3.27473 | ||||||||
\(557\) | 25.2670 | 1.07060 | 0.535298 | − | 0.844663i | \(-0.320199\pi\) | ||||
0.535298 | + | 0.844663i | \(0.320199\pi\) | |||||||
\(558\) | −1.49044 | −0.0630953 | ||||||||
\(559\) | −5.47931 | −0.231750 | ||||||||
\(560\) | 8.62481 | 0.364465 | ||||||||
\(561\) | 13.2210 | 0.558192 | ||||||||
\(562\) | −59.4951 | −2.50965 | ||||||||
\(563\) | −21.0305 | −0.886331 | −0.443165 | − | 0.896440i | \(-0.646145\pi\) | ||||
−0.443165 | + | 0.896440i | \(0.646145\pi\) | |||||||
\(564\) | 4.09571 | 0.172460 | ||||||||
\(565\) | 6.79154 | 0.285722 | ||||||||
\(566\) | −23.0743 | −0.969887 | ||||||||
\(567\) | −11.0015 | −0.462020 | ||||||||
\(568\) | 32.0679 | 1.34554 | ||||||||
\(569\) | −14.2962 | −0.599329 | −0.299664 | − | 0.954045i | \(-0.596875\pi\) | ||||
−0.299664 | + | 0.954045i | \(0.596875\pi\) | |||||||
\(570\) | −5.81341 | −0.243497 | ||||||||
\(571\) | 46.6942 | 1.95409 | 0.977045 | − | 0.213034i | \(-0.0683345\pi\) | ||||
0.977045 | + | 0.213034i | \(0.0683345\pi\) | |||||||
\(572\) | 78.8006 | 3.29482 | ||||||||
\(573\) | −8.29524 | −0.346539 | ||||||||
\(574\) | 28.4005 | 1.18541 | ||||||||
\(575\) | −8.32642 | −0.347236 | ||||||||
\(576\) | 15.0060 | 0.625251 | ||||||||
\(577\) | −1.17680 | −0.0489909 | −0.0244954 | − | 0.999700i | \(-0.507798\pi\) | ||||
−0.0244954 | + | 0.999700i | \(0.507798\pi\) | |||||||
\(578\) | 34.2697 | 1.42543 | ||||||||
\(579\) | 21.9130 | 0.910672 | ||||||||
\(580\) | −33.1145 | −1.37501 | ||||||||
\(581\) | 34.2873 | 1.42248 | ||||||||
\(582\) | −30.5291 | −1.26547 | ||||||||
\(583\) | 32.8445 | 1.36028 | ||||||||
\(584\) | 19.8667 | 0.822089 | ||||||||
\(585\) | −4.84699 | −0.200398 | ||||||||
\(586\) | 7.61279 | 0.314481 | ||||||||
\(587\) | −3.93425 | −0.162384 | −0.0811919 | − | 0.996698i | \(-0.525873\pi\) | ||||
−0.0811919 | + | 0.996698i | \(0.525873\pi\) | |||||||
\(588\) | −29.2853 | −1.20770 | ||||||||
\(589\) | 0.823292 | 0.0339231 | ||||||||
\(590\) | −30.4281 | −1.25270 | ||||||||
\(591\) | −23.9702 | −0.986002 | ||||||||
\(592\) | −2.24223 | −0.0921551 | ||||||||
\(593\) | 25.2795 | 1.03810 | 0.519051 | − | 0.854743i | \(-0.326285\pi\) | ||||
0.519051 | + | 0.854743i | \(0.326285\pi\) | |||||||
\(594\) | −84.8654 | −3.48207 | ||||||||
\(595\) | −6.24374 | −0.255968 | ||||||||
\(596\) | −8.23254 | −0.337218 | ||||||||
\(597\) | −9.93351 | −0.406552 | ||||||||
\(598\) | −17.1447 | −0.701097 | ||||||||
\(599\) | 5.51051 | 0.225153 | 0.112577 | − | 0.993643i | \(-0.464090\pi\) | ||||
0.112577 | + | 0.993643i | \(0.464090\pi\) | |||||||
\(600\) | −19.9995 | −0.816474 | ||||||||
\(601\) | −31.2876 | −1.27625 | −0.638124 | − | 0.769933i | \(-0.720289\pi\) | ||||
−0.638124 | + | 0.769933i | \(0.720289\pi\) | |||||||
\(602\) | 14.1866 | 0.578201 | ||||||||
\(603\) | 3.76600 | 0.153363 | ||||||||
\(604\) | 4.16880 | 0.169626 | ||||||||
\(605\) | 31.3685 | 1.27531 | ||||||||
\(606\) | −33.9426 | −1.37882 | ||||||||
\(607\) | −32.5715 | −1.32204 | −0.661018 | − | 0.750370i | \(-0.729875\pi\) | ||||
−0.661018 | + | 0.750370i | \(0.729875\pi\) | |||||||
\(608\) | −4.90136 | −0.198777 | ||||||||
\(609\) | 39.3639 | 1.59511 | ||||||||
\(610\) | −0.845931 | −0.0342507 | ||||||||
\(611\) | −2.90836 | −0.117660 | ||||||||
\(612\) | 8.19390 | 0.331219 | ||||||||
\(613\) | 37.3315 | 1.50780 | 0.753902 | − | 0.656987i | \(-0.228169\pi\) | ||||
0.753902 | + | 0.656987i | \(0.228169\pi\) | |||||||
\(614\) | 0.476189 | 0.0192174 | ||||||||
\(615\) | 4.42912 | 0.178599 | ||||||||
\(616\) | −93.4761 | −3.76626 | ||||||||
\(617\) | 24.4064 | 0.982565 | 0.491283 | − | 0.871000i | \(-0.336528\pi\) | ||||
0.491283 | + | 0.871000i | \(0.336528\pi\) | |||||||
\(618\) | 12.2745 | 0.493754 | ||||||||
\(619\) | 2.15033 | 0.0864291 | 0.0432145 | − | 0.999066i | \(-0.486240\pi\) | ||||
0.0432145 | + | 0.999066i | \(0.486240\pi\) | |||||||
\(620\) | −1.78461 | −0.0716715 | ||||||||
\(621\) | 11.9754 | 0.480557 | ||||||||
\(622\) | −57.5065 | −2.30580 | ||||||||
\(623\) | 37.7330 | 1.51174 | ||||||||
\(624\) | −9.59379 | −0.384059 | ||||||||
\(625\) | 9.45352 | 0.378141 | ||||||||
\(626\) | 16.1955 | 0.647304 | ||||||||
\(627\) | 14.6786 | 0.586205 | ||||||||
\(628\) | −7.39962 | −0.295277 | ||||||||
\(629\) | 1.62321 | 0.0647217 | ||||||||
\(630\) | 12.5494 | 0.499981 | ||||||||
\(631\) | −5.62209 | −0.223812 | −0.111906 | − | 0.993719i | \(-0.535696\pi\) | ||||
−0.111906 | + | 0.993719i | \(0.535696\pi\) | |||||||
\(632\) | −48.2226 | −1.91819 | ||||||||
\(633\) | −10.1290 | −0.402592 | ||||||||
\(634\) | 32.6250 | 1.29570 | ||||||||
\(635\) | −10.6017 | −0.420716 | ||||||||
\(636\) | −24.2977 | −0.963465 | ||||||||
\(637\) | 20.7955 | 0.823946 | ||||||||
\(638\) | 128.917 | 5.10387 | ||||||||
\(639\) | 10.8704 | 0.430027 | ||||||||
\(640\) | 21.9467 | 0.867518 | ||||||||
\(641\) | 20.9671 | 0.828149 | 0.414075 | − | 0.910243i | \(-0.364105\pi\) | ||||
0.414075 | + | 0.910243i | \(0.364105\pi\) | |||||||
\(642\) | 55.0374 | 2.17215 | ||||||||
\(643\) | −19.7292 | −0.778044 | −0.389022 | − | 0.921229i | \(-0.627187\pi\) | ||||
−0.389022 | + | 0.921229i | \(0.627187\pi\) | |||||||
\(644\) | 28.7900 | 1.13449 | ||||||||
\(645\) | 2.21242 | 0.0871141 | ||||||||
\(646\) | −6.97861 | −0.274570 | ||||||||
\(647\) | 30.9230 | 1.21571 | 0.607854 | − | 0.794048i | \(-0.292030\pi\) | ||||
0.607854 | + | 0.794048i | \(0.292030\pi\) | |||||||
\(648\) | 12.2119 | 0.479730 | ||||||||
\(649\) | 76.8293 | 3.01581 | ||||||||
\(650\) | 30.9969 | 1.21580 | ||||||||
\(651\) | 2.12140 | 0.0831441 | ||||||||
\(652\) | 3.69114 | 0.144556 | ||||||||
\(653\) | 10.4491 | 0.408906 | 0.204453 | − | 0.978876i | \(-0.434459\pi\) | ||||
0.204453 | + | 0.978876i | \(0.434459\pi\) | |||||||
\(654\) | 30.2986 | 1.18477 | ||||||||
\(655\) | 18.0550 | 0.705465 | ||||||||
\(656\) | −7.34446 | −0.286753 | ||||||||
\(657\) | 6.73443 | 0.262735 | ||||||||
\(658\) | 7.53009 | 0.293553 | ||||||||
\(659\) | −28.2674 | −1.10114 | −0.550571 | − | 0.834788i | \(-0.685590\pi\) | ||||
−0.550571 | + | 0.834788i | \(0.685590\pi\) | |||||||
\(660\) | −31.8180 | −1.23851 | ||||||||
\(661\) | 18.2170 | 0.708559 | 0.354280 | − | 0.935140i | \(-0.384726\pi\) | ||||
0.354280 | + | 0.935140i | \(0.384726\pi\) | |||||||
\(662\) | −54.1738 | −2.10553 | ||||||||
\(663\) | 6.94521 | 0.269730 | ||||||||
\(664\) | −38.0596 | −1.47700 | ||||||||
\(665\) | −6.93208 | −0.268815 | ||||||||
\(666\) | −3.26253 | −0.126420 | ||||||||
\(667\) | −18.1916 | −0.704380 | ||||||||
\(668\) | 12.6786 | 0.490550 | ||||||||
\(669\) | −28.3509 | −1.09611 | ||||||||
\(670\) | 6.95261 | 0.268603 | ||||||||
\(671\) | 2.13593 | 0.0824567 | ||||||||
\(672\) | −12.6295 | −0.487193 | ||||||||
\(673\) | −28.8117 | −1.11061 | −0.555305 | − | 0.831647i | \(-0.687398\pi\) | ||||
−0.555305 | + | 0.831647i | \(0.687398\pi\) | |||||||
\(674\) | 66.1136 | 2.54660 | ||||||||
\(675\) | −21.6511 | −0.833353 | ||||||||
\(676\) | −6.58958 | −0.253445 | ||||||||
\(677\) | 14.8273 | 0.569860 | 0.284930 | − | 0.958548i | \(-0.408030\pi\) | ||||
0.284930 | + | 0.958548i | \(0.408030\pi\) | |||||||
\(678\) | 19.5596 | 0.751183 | ||||||||
\(679\) | −36.4037 | −1.39705 | ||||||||
\(680\) | 6.93069 | 0.265780 | ||||||||
\(681\) | −2.43195 | −0.0931927 | ||||||||
\(682\) | 6.94758 | 0.266037 | ||||||||
\(683\) | 9.54038 | 0.365053 | 0.182526 | − | 0.983201i | \(-0.441573\pi\) | ||||
0.182526 | + | 0.983201i | \(0.441573\pi\) | |||||||
\(684\) | 9.09723 | 0.347841 | ||||||||
\(685\) | 9.36457 | 0.357802 | ||||||||
\(686\) | 6.85196 | 0.261609 | ||||||||
\(687\) | −9.95774 | −0.379911 | ||||||||
\(688\) | −3.66869 | −0.139867 | ||||||||
\(689\) | 17.2538 | 0.657316 | ||||||||
\(690\) | 6.92263 | 0.263540 | ||||||||
\(691\) | 22.9783 | 0.874137 | 0.437068 | − | 0.899428i | \(-0.356017\pi\) | ||||
0.437068 | + | 0.899428i | \(0.356017\pi\) | |||||||
\(692\) | −25.3640 | −0.964194 | ||||||||
\(693\) | −31.6866 | −1.20368 | ||||||||
\(694\) | −33.5229 | −1.27251 | ||||||||
\(695\) | 22.1398 | 0.839812 | ||||||||
\(696\) | −43.6948 | −1.65625 | ||||||||
\(697\) | 5.31686 | 0.201390 | ||||||||
\(698\) | 45.5665 | 1.72472 | ||||||||
\(699\) | 3.06995 | 0.116116 | ||||||||
\(700\) | −52.0513 | −1.96735 | ||||||||
\(701\) | 38.7262 | 1.46267 | 0.731334 | − | 0.682019i | \(-0.238898\pi\) | ||||
0.731334 | + | 0.682019i | \(0.238898\pi\) | |||||||
\(702\) | −44.5811 | −1.68261 | ||||||||
\(703\) | 1.80216 | 0.0679699 | ||||||||
\(704\) | −69.9496 | −2.63632 | ||||||||
\(705\) | 1.17433 | 0.0442279 | ||||||||
\(706\) | −43.0943 | −1.62187 | ||||||||
\(707\) | −40.4741 | −1.52218 | ||||||||
\(708\) | −56.8366 | −2.13605 | ||||||||
\(709\) | −11.4267 | −0.429140 | −0.214570 | − | 0.976709i | \(-0.568835\pi\) | ||||
−0.214570 | + | 0.976709i | \(0.568835\pi\) | |||||||
\(710\) | 20.0684 | 0.753155 | ||||||||
\(711\) | −16.3466 | −0.613044 | ||||||||
\(712\) | −41.8845 | −1.56969 | ||||||||
\(713\) | −0.980379 | −0.0367155 | ||||||||
\(714\) | −17.9820 | −0.672958 | ||||||||
\(715\) | 22.5939 | 0.844965 | ||||||||
\(716\) | 34.0990 | 1.27434 | ||||||||
\(717\) | 0.751229 | 0.0280552 | ||||||||
\(718\) | 35.6038 | 1.32872 | ||||||||
\(719\) | −11.6324 | −0.433815 | −0.216907 | − | 0.976192i | \(-0.569597\pi\) | ||||
−0.216907 | + | 0.976192i | \(0.569597\pi\) | |||||||
\(720\) | −3.24532 | −0.120946 | ||||||||
\(721\) | 14.6365 | 0.545092 | ||||||||
\(722\) | 37.5786 | 1.39853 | ||||||||
\(723\) | 19.8031 | 0.736484 | ||||||||
\(724\) | −59.6984 | −2.21867 | ||||||||
\(725\) | 32.8897 | 1.22149 | ||||||||
\(726\) | 90.3413 | 3.35288 | ||||||||
\(727\) | 29.9366 | 1.11029 | 0.555144 | − | 0.831755i | \(-0.312663\pi\) | ||||
0.555144 | + | 0.831755i | \(0.312663\pi\) | |||||||
\(728\) | −49.1045 | −1.81993 | ||||||||
\(729\) | 25.5287 | 0.945509 | ||||||||
\(730\) | 12.4328 | 0.460158 | ||||||||
\(731\) | 2.65587 | 0.0982307 | ||||||||
\(732\) | −1.58011 | −0.0584027 | ||||||||
\(733\) | 42.5192 | 1.57048 | 0.785241 | − | 0.619191i | \(-0.212539\pi\) | ||||
0.785241 | + | 0.619191i | \(0.212539\pi\) | |||||||
\(734\) | 79.4450 | 2.93237 | ||||||||
\(735\) | −8.39675 | −0.309719 | ||||||||
\(736\) | 5.83656 | 0.215139 | ||||||||
\(737\) | −17.5550 | −0.646646 | ||||||||
\(738\) | −10.6865 | −0.393374 | ||||||||
\(739\) | −13.7936 | −0.507407 | −0.253703 | − | 0.967282i | \(-0.581649\pi\) | ||||
−0.253703 | + | 0.967282i | \(0.581649\pi\) | |||||||
\(740\) | −3.90645 | −0.143604 | ||||||||
\(741\) | 7.71088 | 0.283266 | ||||||||
\(742\) | −44.6720 | −1.63996 | ||||||||
\(743\) | −9.17497 | −0.336597 | −0.168299 | − | 0.985736i | \(-0.553827\pi\) | ||||
−0.168299 | + | 0.985736i | \(0.553827\pi\) | |||||||
\(744\) | −2.35480 | −0.0863311 | ||||||||
\(745\) | −2.36046 | −0.0864804 | ||||||||
\(746\) | 19.6051 | 0.717795 | ||||||||
\(747\) | −12.9015 | −0.472041 | ||||||||
\(748\) | −38.1953 | −1.39656 | ||||||||
\(749\) | 65.6282 | 2.39800 | ||||||||
\(750\) | −28.6449 | −1.04596 | ||||||||
\(751\) | −31.8375 | −1.16177 | −0.580884 | − | 0.813986i | \(-0.697293\pi\) | ||||
−0.580884 | + | 0.813986i | \(0.697293\pi\) | |||||||
\(752\) | −1.94730 | −0.0710108 | ||||||||
\(753\) | −37.4577 | −1.36503 | ||||||||
\(754\) | 67.7221 | 2.46629 | ||||||||
\(755\) | 1.19529 | 0.0435010 | ||||||||
\(756\) | 74.8625 | 2.72272 | ||||||||
\(757\) | 28.5958 | 1.03933 | 0.519666 | − | 0.854370i | \(-0.326057\pi\) | ||||
0.519666 | + | 0.854370i | \(0.326057\pi\) | |||||||
\(758\) | −42.7450 | −1.55257 | ||||||||
\(759\) | −17.4793 | −0.634458 | ||||||||
\(760\) | 7.69476 | 0.279118 | ||||||||
\(761\) | −25.7172 | −0.932249 | −0.466124 | − | 0.884719i | \(-0.654350\pi\) | ||||
−0.466124 | + | 0.884719i | \(0.654350\pi\) | |||||||
\(762\) | −30.5329 | −1.10609 | ||||||||
\(763\) | 36.1289 | 1.30795 | ||||||||
\(764\) | 23.9648 | 0.867017 | ||||||||
\(765\) | 2.34938 | 0.0849418 | ||||||||
\(766\) | 15.6147 | 0.564182 | ||||||||
\(767\) | 40.3596 | 1.45730 | ||||||||
\(768\) | 35.1678 | 1.26901 | ||||||||
\(769\) | 16.4920 | 0.594718 | 0.297359 | − | 0.954766i | \(-0.403894\pi\) | ||||
0.297359 | + | 0.954766i | \(0.403894\pi\) | |||||||
\(770\) | −58.4983 | −2.10813 | ||||||||
\(771\) | 20.0034 | 0.720405 | ||||||||
\(772\) | −63.3063 | −2.27844 | ||||||||
\(773\) | 25.1581 | 0.904872 | 0.452436 | − | 0.891797i | \(-0.350555\pi\) | ||||
0.452436 | + | 0.891797i | \(0.350555\pi\) | |||||||
\(774\) | −5.33808 | −0.191873 | ||||||||
\(775\) | 1.77249 | 0.0636697 | ||||||||
\(776\) | 40.4089 | 1.45060 | ||||||||
\(777\) | 4.64368 | 0.166591 | ||||||||
\(778\) | 40.3367 | 1.44614 | ||||||||
\(779\) | 5.90301 | 0.211497 | ||||||||
\(780\) | −16.7145 | −0.598474 | ||||||||
\(781\) | −50.6718 | −1.81318 | ||||||||
\(782\) | 8.31016 | 0.297171 | ||||||||
\(783\) | −47.3034 | −1.69049 | ||||||||
\(784\) | 13.9237 | 0.497274 | ||||||||
\(785\) | −2.12164 | −0.0757245 | ||||||||
\(786\) | 51.9982 | 1.85472 | ||||||||
\(787\) | −28.3678 | −1.01120 | −0.505602 | − | 0.862767i | \(-0.668730\pi\) | ||||
−0.505602 | + | 0.862767i | \(0.668730\pi\) | |||||||
\(788\) | 69.2495 | 2.46691 | ||||||||
\(789\) | 7.91984 | 0.281954 | ||||||||
\(790\) | −30.1782 | −1.07369 | ||||||||
\(791\) | 23.3235 | 0.829287 | ||||||||
\(792\) | 35.1729 | 1.24981 | ||||||||
\(793\) | 1.12204 | 0.0398448 | ||||||||
\(794\) | −18.5284 | −0.657549 | ||||||||
\(795\) | −6.96669 | −0.247083 | ||||||||
\(796\) | 28.6978 | 1.01717 | ||||||||
\(797\) | 27.9988 | 0.991767 | 0.495883 | − | 0.868389i | \(-0.334844\pi\) | ||||
0.495883 | + | 0.868389i | \(0.334844\pi\) | |||||||
\(798\) | −19.9644 | −0.706732 | ||||||||
\(799\) | 1.40971 | 0.0498718 | ||||||||
\(800\) | −10.5523 | −0.373080 | ||||||||
\(801\) | −14.1981 | −0.501664 | ||||||||
\(802\) | −48.9634 | −1.72896 | ||||||||
\(803\) | −31.3921 | −1.10780 | ||||||||
\(804\) | 12.9868 | 0.458008 | ||||||||
\(805\) | 8.25475 | 0.290942 | ||||||||
\(806\) | 3.64968 | 0.128554 | ||||||||
\(807\) | 35.1587 | 1.23765 | ||||||||
\(808\) | 44.9271 | 1.58053 | ||||||||
\(809\) | 17.2548 | 0.606646 | 0.303323 | − | 0.952888i | \(-0.401904\pi\) | ||||
0.303323 | + | 0.952888i | \(0.401904\pi\) | |||||||
\(810\) | 7.64236 | 0.268525 | ||||||||
\(811\) | 29.1635 | 1.02407 | 0.512035 | − | 0.858965i | \(-0.328892\pi\) | ||||
0.512035 | + | 0.858965i | \(0.328892\pi\) | |||||||
\(812\) | −113.722 | −3.99085 | ||||||||
\(813\) | −9.39488 | −0.329493 | ||||||||
\(814\) | 15.2081 | 0.533042 | ||||||||
\(815\) | 1.05833 | 0.0370718 | ||||||||
\(816\) | 4.65019 | 0.162789 | ||||||||
\(817\) | 2.94866 | 0.103161 | ||||||||
\(818\) | −25.3429 | −0.886093 | ||||||||
\(819\) | −16.6455 | −0.581641 | ||||||||
\(820\) | −12.7956 | −0.446843 | ||||||||
\(821\) | −7.24680 | −0.252915 | −0.126457 | − | 0.991972i | \(-0.540361\pi\) | ||||
−0.126457 | + | 0.991972i | \(0.540361\pi\) | |||||||
\(822\) | 26.9700 | 0.940685 | ||||||||
\(823\) | −32.0667 | −1.11777 | −0.558887 | − | 0.829244i | \(-0.688772\pi\) | ||||
−0.558887 | + | 0.829244i | \(0.688772\pi\) | |||||||
\(824\) | −16.2469 | −0.565986 | ||||||||
\(825\) | 31.6019 | 1.10024 | ||||||||
\(826\) | −104.496 | −3.63588 | ||||||||
\(827\) | −39.4316 | −1.37117 | −0.685585 | − | 0.727993i | \(-0.740453\pi\) | ||||
−0.685585 | + | 0.727993i | \(0.740453\pi\) | |||||||
\(828\) | −10.8330 | −0.376473 | ||||||||
\(829\) | −36.3763 | −1.26340 | −0.631701 | − | 0.775212i | \(-0.717643\pi\) | ||||
−0.631701 | + | 0.775212i | \(0.717643\pi\) | |||||||
\(830\) | −23.8181 | −0.826739 | ||||||||
\(831\) | 15.4459 | 0.535813 | ||||||||
\(832\) | −36.7456 | −1.27393 | ||||||||
\(833\) | −10.0797 | −0.349242 | ||||||||
\(834\) | 63.7627 | 2.20792 | ||||||||
\(835\) | 3.63524 | 0.125803 | ||||||||
\(836\) | −42.4061 | −1.46665 | ||||||||
\(837\) | −2.54927 | −0.0881158 | ||||||||
\(838\) | −70.0331 | −2.41925 | ||||||||
\(839\) | −38.4451 | −1.32727 | −0.663636 | − | 0.748055i | \(-0.730988\pi\) | ||||
−0.663636 | + | 0.748055i | \(0.730988\pi\) | |||||||
\(840\) | 19.8273 | 0.684107 | ||||||||
\(841\) | 42.8574 | 1.47784 | ||||||||
\(842\) | −45.8544 | −1.58025 | ||||||||
\(843\) | −31.8637 | −1.09744 | ||||||||
\(844\) | 29.2625 | 1.00726 | ||||||||
\(845\) | −1.88938 | −0.0649967 | ||||||||
\(846\) | −2.83340 | −0.0974142 | ||||||||
\(847\) | 107.726 | 3.70149 | ||||||||
\(848\) | 11.5523 | 0.396708 | ||||||||
\(849\) | −12.3579 | −0.424122 | ||||||||
\(850\) | −15.0245 | −0.515335 | ||||||||
\(851\) | −2.14602 | −0.0735647 | ||||||||
\(852\) | 37.4859 | 1.28424 | ||||||||
\(853\) | −29.1175 | −0.996965 | −0.498483 | − | 0.866900i | \(-0.666109\pi\) | ||||
−0.498483 | + | 0.866900i | \(0.666109\pi\) | |||||||
\(854\) | −2.90509 | −0.0994101 | ||||||||
\(855\) | 2.60838 | 0.0892047 | ||||||||
\(856\) | −72.8488 | −2.48992 | ||||||||
\(857\) | −28.5512 | −0.975290 | −0.487645 | − | 0.873042i | \(-0.662144\pi\) | ||||
−0.487645 | + | 0.873042i | \(0.662144\pi\) | |||||||
\(858\) | 65.0705 | 2.22147 | ||||||||
\(859\) | −8.84258 | −0.301705 | −0.150853 | − | 0.988556i | \(-0.548202\pi\) | ||||
−0.150853 | + | 0.988556i | \(0.548202\pi\) | |||||||
\(860\) | −6.39166 | −0.217954 | ||||||||
\(861\) | 15.2104 | 0.518371 | ||||||||
\(862\) | 19.1688 | 0.652892 | ||||||||
\(863\) | 34.5391 | 1.17572 | 0.587862 | − | 0.808961i | \(-0.299970\pi\) | ||||
0.587862 | + | 0.808961i | \(0.299970\pi\) | |||||||
\(864\) | 15.1768 | 0.516324 | ||||||||
\(865\) | −7.27243 | −0.247270 | ||||||||
\(866\) | −78.2291 | −2.65833 | ||||||||
\(867\) | 18.3538 | 0.623328 | ||||||||
\(868\) | −6.12869 | −0.208021 | ||||||||
\(869\) | 76.1984 | 2.58486 | ||||||||
\(870\) | −27.3447 | −0.927071 | ||||||||
\(871\) | −9.22191 | −0.312472 | ||||||||
\(872\) | −40.1039 | −1.35809 | ||||||||
\(873\) | 13.6979 | 0.463603 | ||||||||
\(874\) | 9.22630 | 0.312084 | ||||||||
\(875\) | −34.1570 | −1.15472 | ||||||||
\(876\) | 23.2232 | 0.784639 | ||||||||
\(877\) | −57.3543 | −1.93672 | −0.968358 | − | 0.249564i | \(-0.919713\pi\) | ||||
−0.968358 | + | 0.249564i | \(0.919713\pi\) | |||||||
\(878\) | −31.4499 | −1.06138 | ||||||||
\(879\) | 4.07717 | 0.137520 | ||||||||
\(880\) | 15.1278 | 0.509959 | ||||||||
\(881\) | 20.3193 | 0.684574 | 0.342287 | − | 0.939595i | \(-0.388798\pi\) | ||||
0.342287 | + | 0.939595i | \(0.388798\pi\) | |||||||
\(882\) | 20.2595 | 0.682172 | ||||||||
\(883\) | 13.0358 | 0.438689 | 0.219344 | − | 0.975648i | \(-0.429608\pi\) | ||||
0.219344 | + | 0.975648i | \(0.429608\pi\) | |||||||
\(884\) | −20.0646 | −0.674846 | ||||||||
\(885\) | −16.2963 | −0.547795 | ||||||||
\(886\) | −49.5833 | −1.66578 | ||||||||
\(887\) | −24.5973 | −0.825896 | −0.412948 | − | 0.910755i | \(-0.635501\pi\) | ||||
−0.412948 | + | 0.910755i | \(0.635501\pi\) | |||||||
\(888\) | −5.15459 | −0.172977 | ||||||||
\(889\) | −36.4083 | −1.22110 | ||||||||
\(890\) | −26.2118 | −0.878621 | ||||||||
\(891\) | −19.2966 | −0.646459 | ||||||||
\(892\) | 81.9054 | 2.74239 | ||||||||
\(893\) | 1.56512 | 0.0523747 | ||||||||
\(894\) | −6.79811 | −0.227363 | ||||||||
\(895\) | 9.77696 | 0.326808 | ||||||||
\(896\) | 75.3691 | 2.51791 | ||||||||
\(897\) | −9.18215 | −0.306583 | ||||||||
\(898\) | −73.8521 | −2.46448 | ||||||||
\(899\) | 3.87254 | 0.129156 | ||||||||
\(900\) | 19.5857 | 0.652857 | ||||||||
\(901\) | −8.36304 | −0.278613 | ||||||||
\(902\) | 49.8142 | 1.65863 | ||||||||
\(903\) | 7.59789 | 0.252842 | ||||||||
\(904\) | −25.8896 | −0.861074 | ||||||||
\(905\) | −17.1169 | −0.568984 | ||||||||
\(906\) | 3.44243 | 0.114367 | ||||||||
\(907\) | −38.6492 | −1.28333 | −0.641663 | − | 0.766987i | \(-0.721755\pi\) | ||||
−0.641663 | + | 0.766987i | \(0.721755\pi\) | |||||||
\(908\) | 7.02588 | 0.233162 | ||||||||
\(909\) | 15.2295 | 0.505129 | ||||||||
\(910\) | −30.7301 | −1.01869 | ||||||||
\(911\) | −37.0511 | −1.22756 | −0.613779 | − | 0.789478i | \(-0.710351\pi\) | ||||
−0.613779 | + | 0.789478i | \(0.710351\pi\) | |||||||
\(912\) | 5.16285 | 0.170959 | ||||||||
\(913\) | 60.1395 | 1.99033 | ||||||||
\(914\) | −18.5497 | −0.613571 | ||||||||
\(915\) | −0.453054 | −0.0149775 | ||||||||
\(916\) | 28.7678 | 0.950514 | ||||||||
\(917\) | 62.0042 | 2.04756 | ||||||||
\(918\) | 21.6088 | 0.713198 | ||||||||
\(919\) | −7.27746 | −0.240061 | −0.120031 | − | 0.992770i | \(-0.538299\pi\) | ||||
−0.120031 | + | 0.992770i | \(0.538299\pi\) | |||||||
\(920\) | −9.16295 | −0.302094 | ||||||||
\(921\) | 0.255032 | 0.00840360 | ||||||||
\(922\) | −63.4952 | −2.09110 | ||||||||
\(923\) | −26.6187 | −0.876165 | ||||||||
\(924\) | −109.269 | −3.59469 | ||||||||
\(925\) | 3.87993 | 0.127571 | ||||||||
\(926\) | −22.5327 | −0.740470 | ||||||||
\(927\) | −5.50738 | −0.180886 | ||||||||
\(928\) | −23.0546 | −0.756806 | ||||||||
\(929\) | −44.2105 | −1.45050 | −0.725249 | − | 0.688486i | \(-0.758275\pi\) | ||||
−0.725249 | + | 0.688486i | \(0.758275\pi\) | |||||||
\(930\) | −1.47366 | −0.0483232 | ||||||||
\(931\) | −11.1910 | −0.366769 | ||||||||
\(932\) | −8.86905 | −0.290515 | ||||||||
\(933\) | −30.7987 | −1.00831 | ||||||||
\(934\) | 66.9513 | 2.19071 | ||||||||
\(935\) | −10.9515 | −0.358151 | ||||||||
\(936\) | 18.4769 | 0.603936 | ||||||||
\(937\) | −21.1418 | −0.690673 | −0.345336 | − | 0.938479i | \(-0.612235\pi\) | ||||
−0.345336 | + | 0.938479i | \(0.612235\pi\) | |||||||
\(938\) | 23.8766 | 0.779599 | ||||||||
\(939\) | 8.67383 | 0.283060 | ||||||||
\(940\) | −3.39263 | −0.110655 | ||||||||
\(941\) | 11.4252 | 0.372450 | 0.186225 | − | 0.982507i | \(-0.440375\pi\) | ||||
0.186225 | + | 0.982507i | \(0.440375\pi\) | |||||||
\(942\) | −6.11032 | −0.199085 | ||||||||
\(943\) | −7.02933 | −0.228906 | ||||||||
\(944\) | 27.0229 | 0.879521 | ||||||||
\(945\) | 21.4648 | 0.698249 | ||||||||
\(946\) | 24.8831 | 0.809019 | ||||||||
\(947\) | 5.31208 | 0.172619 | 0.0863097 | − | 0.996268i | \(-0.472493\pi\) | ||||
0.0863097 | + | 0.996268i | \(0.472493\pi\) | |||||||
\(948\) | −56.3699 | −1.83081 | ||||||||
\(949\) | −16.4908 | −0.535313 | ||||||||
\(950\) | −16.6808 | −0.541198 | ||||||||
\(951\) | 17.4729 | 0.566598 | ||||||||
\(952\) | 23.8013 | 0.771406 | ||||||||
\(953\) | −30.4192 | −0.985376 | −0.492688 | − | 0.870206i | \(-0.663986\pi\) | ||||
−0.492688 | + | 0.870206i | \(0.663986\pi\) | |||||||
\(954\) | 16.8090 | 0.544213 | ||||||||
\(955\) | 6.87126 | 0.222349 | ||||||||
\(956\) | −2.17029 | −0.0701922 | ||||||||
\(957\) | 69.0439 | 2.23187 | ||||||||
\(958\) | 49.7594 | 1.60765 | ||||||||
\(959\) | 32.1597 | 1.03849 | ||||||||
\(960\) | 14.8371 | 0.478865 | ||||||||
\(961\) | −30.7913 | −0.993268 | ||||||||
\(962\) | 7.98904 | 0.257577 | ||||||||
\(963\) | −24.6944 | −0.795765 | ||||||||
\(964\) | −57.2108 | −1.84263 | ||||||||
\(965\) | −18.1513 | −0.584312 | ||||||||
\(966\) | 23.7737 | 0.764905 | ||||||||
\(967\) | 9.93886 | 0.319612 | 0.159806 | − | 0.987148i | \(-0.448913\pi\) | ||||
0.159806 | + | 0.987148i | \(0.448913\pi\) | |||||||
\(968\) | −119.578 | −3.84337 | ||||||||
\(969\) | −3.73753 | −0.120067 | ||||||||
\(970\) | 25.2884 | 0.811960 | ||||||||
\(971\) | 34.1939 | 1.09733 | 0.548667 | − | 0.836041i | \(-0.315135\pi\) | ||||
0.548667 | + | 0.836041i | \(0.315135\pi\) | |||||||
\(972\) | −47.5177 | −1.52413 | ||||||||
\(973\) | 76.0325 | 2.43749 | ||||||||
\(974\) | 102.485 | 3.28382 | ||||||||
\(975\) | 16.6010 | 0.531657 | ||||||||
\(976\) | 0.751265 | 0.0240474 | ||||||||
\(977\) | −12.2301 | −0.391276 | −0.195638 | − | 0.980676i | \(-0.562678\pi\) | ||||
−0.195638 | + | 0.980676i | \(0.562678\pi\) | |||||||
\(978\) | 3.04800 | 0.0974642 | ||||||||
\(979\) | 66.1834 | 2.11523 | ||||||||
\(980\) | 24.2581 | 0.774896 | ||||||||
\(981\) | −13.5945 | −0.434038 | ||||||||
\(982\) | −55.9062 | −1.78404 | ||||||||
\(983\) | −42.8678 | −1.36727 | −0.683636 | − | 0.729823i | \(-0.739602\pi\) | ||||
−0.683636 | + | 0.729823i | \(0.739602\pi\) | |||||||
\(984\) | −16.8839 | −0.538240 | ||||||||
\(985\) | 19.8554 | 0.632646 | ||||||||
\(986\) | −32.8254 | −1.04538 | ||||||||
\(987\) | 4.03288 | 0.128368 | ||||||||
\(988\) | −22.2766 | −0.708714 | ||||||||
\(989\) | −3.51127 | −0.111652 | ||||||||
\(990\) | 22.0116 | 0.699574 | ||||||||
\(991\) | 23.9459 | 0.760665 | 0.380333 | − | 0.924850i | \(-0.375810\pi\) | ||||
0.380333 | + | 0.924850i | \(0.375810\pi\) | |||||||
\(992\) | −1.24246 | −0.0394482 | ||||||||
\(993\) | −29.0138 | −0.920726 | ||||||||
\(994\) | 68.9189 | 2.18598 | ||||||||
\(995\) | 8.22830 | 0.260855 | ||||||||
\(996\) | −44.4899 | −1.40972 | ||||||||
\(997\) | −45.8007 | −1.45052 | −0.725262 | − | 0.688473i | \(-0.758281\pi\) | ||||
−0.725262 | + | 0.688473i | \(0.758281\pi\) | |||||||
\(998\) | −59.0915 | −1.87051 | ||||||||
\(999\) | −5.58029 | −0.176553 |
(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 | 6031.2.a.d.1.12 | ✓ | 133 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6031.2.a.d.1.12 | ✓ | 133 | 1.1 | even | 1 | trivial |