Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2013,2,Mod(1,2013)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2013, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2013.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2013 = 3 \cdot 11 \cdot 61 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2013.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: | \(16.0738859269\) |
Analytic rank: | \(1\) |
Dimension: | \(11\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{11} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{11} - 4x^{10} - 6x^{9} + 37x^{8} - 2x^{7} - 109x^{6} + 55x^{5} + 115x^{4} - 76x^{3} - 29x^{2} + 14x + 3 \) |
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 | 1.8 | ||
Root | \(-0.423080\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2013.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.423080 | 0.299163 | 0.149582 | − | 0.988749i | \(-0.452207\pi\) | ||||
0.149582 | + | 0.988749i | \(0.452207\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | −1.82100 | −0.910501 | ||||||||
\(5\) | −1.36483 | −0.610370 | −0.305185 | − | 0.952293i | \(-0.598718\pi\) | ||||
−0.305185 | + | 0.952293i | \(0.598718\pi\) | |||||||
\(6\) | 0.423080 | 0.172722 | ||||||||
\(7\) | 0.865577 | 0.327157 | 0.163579 | − | 0.986530i | \(-0.447696\pi\) | ||||
0.163579 | + | 0.986530i | \(0.447696\pi\) | |||||||
\(8\) | −1.61659 | −0.571551 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −0.577432 | −0.182600 | ||||||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | −1.82100 | −0.525678 | ||||||||
\(13\) | 2.63744 | 0.731493 | 0.365747 | − | 0.930714i | \(-0.380814\pi\) | ||||
0.365747 | + | 0.930714i | \(0.380814\pi\) | |||||||
\(14\) | 0.366209 | 0.0978733 | ||||||||
\(15\) | −1.36483 | −0.352397 | ||||||||
\(16\) | 2.95806 | 0.739514 | ||||||||
\(17\) | −3.12547 | −0.758037 | −0.379019 | − | 0.925389i | \(-0.623738\pi\) | ||||
−0.379019 | + | 0.925389i | \(0.623738\pi\) | |||||||
\(18\) | 0.423080 | 0.0997210 | ||||||||
\(19\) | −0.281623 | −0.0646088 | −0.0323044 | − | 0.999478i | \(-0.510285\pi\) | ||||
−0.0323044 | + | 0.999478i | \(0.510285\pi\) | |||||||
\(20\) | 2.48536 | 0.555742 | ||||||||
\(21\) | 0.865577 | 0.188884 | ||||||||
\(22\) | −0.423080 | −0.0902010 | ||||||||
\(23\) | 1.73752 | 0.362297 | 0.181149 | − | 0.983456i | \(-0.442018\pi\) | ||||
0.181149 | + | 0.983456i | \(0.442018\pi\) | |||||||
\(24\) | −1.61659 | −0.329985 | ||||||||
\(25\) | −3.13724 | −0.627449 | ||||||||
\(26\) | 1.11585 | 0.218836 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | −1.57622 | −0.297877 | ||||||||
\(29\) | −7.07603 | −1.31399 | −0.656993 | − | 0.753897i | \(-0.728172\pi\) | ||||
−0.656993 | + | 0.753897i | \(0.728172\pi\) | |||||||
\(30\) | −0.577432 | −0.105424 | ||||||||
\(31\) | −4.28304 | −0.769257 | −0.384628 | − | 0.923071i | \(-0.625670\pi\) | ||||
−0.384628 | + | 0.923071i | \(0.625670\pi\) | |||||||
\(32\) | 4.48468 | 0.792787 | ||||||||
\(33\) | −1.00000 | −0.174078 | ||||||||
\(34\) | −1.32232 | −0.226777 | ||||||||
\(35\) | −1.18136 | −0.199687 | ||||||||
\(36\) | −1.82100 | −0.303500 | ||||||||
\(37\) | 3.94276 | 0.648186 | 0.324093 | − | 0.946025i | \(-0.394941\pi\) | ||||
0.324093 | + | 0.946025i | \(0.394941\pi\) | |||||||
\(38\) | −0.119149 | −0.0193286 | ||||||||
\(39\) | 2.63744 | 0.422328 | ||||||||
\(40\) | 2.20637 | 0.348858 | ||||||||
\(41\) | −7.38287 | −1.15301 | −0.576505 | − | 0.817094i | \(-0.695584\pi\) | ||||
−0.576505 | + | 0.817094i | \(0.695584\pi\) | |||||||
\(42\) | 0.366209 | 0.0565072 | ||||||||
\(43\) | 5.77261 | 0.880315 | 0.440157 | − | 0.897921i | \(-0.354923\pi\) | ||||
0.440157 | + | 0.897921i | \(0.354923\pi\) | |||||||
\(44\) | 1.82100 | 0.274527 | ||||||||
\(45\) | −1.36483 | −0.203457 | ||||||||
\(46\) | 0.735109 | 0.108386 | ||||||||
\(47\) | −3.73936 | −0.545441 | −0.272721 | − | 0.962093i | \(-0.587924\pi\) | ||||
−0.272721 | + | 0.962093i | \(0.587924\pi\) | |||||||
\(48\) | 2.95806 | 0.426959 | ||||||||
\(49\) | −6.25078 | −0.892968 | ||||||||
\(50\) | −1.32731 | −0.187709 | ||||||||
\(51\) | −3.12547 | −0.437653 | ||||||||
\(52\) | −4.80278 | −0.666026 | ||||||||
\(53\) | −5.86335 | −0.805393 | −0.402696 | − | 0.915334i | \(-0.631927\pi\) | ||||
−0.402696 | + | 0.915334i | \(0.631927\pi\) | |||||||
\(54\) | 0.423080 | 0.0575739 | ||||||||
\(55\) | 1.36483 | 0.184033 | ||||||||
\(56\) | −1.39928 | −0.186987 | ||||||||
\(57\) | −0.281623 | −0.0373019 | ||||||||
\(58\) | −2.99373 | −0.393096 | ||||||||
\(59\) | −7.96157 | −1.03651 | −0.518254 | − | 0.855227i | \(-0.673418\pi\) | ||||
−0.518254 | + | 0.855227i | \(0.673418\pi\) | |||||||
\(60\) | 2.48536 | 0.320858 | ||||||||
\(61\) | 1.00000 | 0.128037 | ||||||||
\(62\) | −1.81207 | −0.230133 | ||||||||
\(63\) | 0.865577 | 0.109052 | ||||||||
\(64\) | −4.01874 | −0.502342 | ||||||||
\(65\) | −3.59965 | −0.446481 | ||||||||
\(66\) | −0.423080 | −0.0520776 | ||||||||
\(67\) | 4.80971 | 0.587599 | 0.293800 | − | 0.955867i | \(-0.405080\pi\) | ||||
0.293800 | + | 0.955867i | \(0.405080\pi\) | |||||||
\(68\) | 5.69149 | 0.690194 | ||||||||
\(69\) | 1.73752 | 0.209172 | ||||||||
\(70\) | −0.499812 | −0.0597389 | ||||||||
\(71\) | −7.35945 | −0.873406 | −0.436703 | − | 0.899606i | \(-0.643854\pi\) | ||||
−0.436703 | + | 0.899606i | \(0.643854\pi\) | |||||||
\(72\) | −1.61659 | −0.190517 | ||||||||
\(73\) | −16.3671 | −1.91563 | −0.957814 | − | 0.287390i | \(-0.907212\pi\) | ||||
−0.957814 | + | 0.287390i | \(0.907212\pi\) | |||||||
\(74\) | 1.66811 | 0.193913 | ||||||||
\(75\) | −3.13724 | −0.362258 | ||||||||
\(76\) | 0.512837 | 0.0588265 | ||||||||
\(77\) | −0.865577 | −0.0986416 | ||||||||
\(78\) | 1.11585 | 0.126345 | ||||||||
\(79\) | −6.03539 | −0.679035 | −0.339517 | − | 0.940600i | \(-0.610264\pi\) | ||||
−0.339517 | + | 0.940600i | \(0.610264\pi\) | |||||||
\(80\) | −4.03724 | −0.451377 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −3.12355 | −0.344938 | ||||||||
\(83\) | 10.7520 | 1.18019 | 0.590093 | − | 0.807336i | \(-0.299091\pi\) | ||||
0.590093 | + | 0.807336i | \(0.299091\pi\) | |||||||
\(84\) | −1.57622 | −0.171979 | ||||||||
\(85\) | 4.26573 | 0.462683 | ||||||||
\(86\) | 2.44228 | 0.263358 | ||||||||
\(87\) | −7.07603 | −0.758630 | ||||||||
\(88\) | 1.61659 | 0.172329 | ||||||||
\(89\) | −13.8901 | −1.47235 | −0.736175 | − | 0.676791i | \(-0.763370\pi\) | ||||
−0.736175 | + | 0.676791i | \(0.763370\pi\) | |||||||
\(90\) | −0.577432 | −0.0608667 | ||||||||
\(91\) | 2.28290 | 0.239313 | ||||||||
\(92\) | −3.16402 | −0.329872 | ||||||||
\(93\) | −4.28304 | −0.444131 | ||||||||
\(94\) | −1.58205 | −0.163176 | ||||||||
\(95\) | 0.384368 | 0.0394353 | ||||||||
\(96\) | 4.48468 | 0.457716 | ||||||||
\(97\) | 12.3781 | 1.25680 | 0.628402 | − | 0.777888i | \(-0.283709\pi\) | ||||
0.628402 | + | 0.777888i | \(0.283709\pi\) | |||||||
\(98\) | −2.64458 | −0.267143 | ||||||||
\(99\) | −1.00000 | −0.100504 | ||||||||
\(100\) | 5.71293 | 0.571293 | ||||||||
\(101\) | 0.0427311 | 0.00425191 | 0.00212595 | − | 0.999998i | \(-0.499323\pi\) | ||||
0.00212595 | + | 0.999998i | \(0.499323\pi\) | |||||||
\(102\) | −1.32232 | −0.130930 | ||||||||
\(103\) | −14.7060 | −1.44902 | −0.724511 | − | 0.689263i | \(-0.757935\pi\) | ||||
−0.724511 | + | 0.689263i | \(0.757935\pi\) | |||||||
\(104\) | −4.26366 | −0.418086 | ||||||||
\(105\) | −1.18136 | −0.115289 | ||||||||
\(106\) | −2.48067 | −0.240944 | ||||||||
\(107\) | 14.8784 | 1.43835 | 0.719175 | − | 0.694829i | \(-0.244520\pi\) | ||||
0.719175 | + | 0.694829i | \(0.244520\pi\) | |||||||
\(108\) | −1.82100 | −0.175226 | ||||||||
\(109\) | −9.34470 | −0.895060 | −0.447530 | − | 0.894269i | \(-0.647696\pi\) | ||||
−0.447530 | + | 0.894269i | \(0.647696\pi\) | |||||||
\(110\) | 0.577432 | 0.0550560 | ||||||||
\(111\) | 3.94276 | 0.374231 | ||||||||
\(112\) | 2.56043 | 0.241938 | ||||||||
\(113\) | 15.9919 | 1.50440 | 0.752198 | − | 0.658938i | \(-0.228994\pi\) | ||||
0.752198 | + | 0.658938i | \(0.228994\pi\) | |||||||
\(114\) | −0.119149 | −0.0111594 | ||||||||
\(115\) | −2.37141 | −0.221135 | ||||||||
\(116\) | 12.8855 | 1.19639 | ||||||||
\(117\) | 2.63744 | 0.243831 | ||||||||
\(118\) | −3.36839 | −0.310085 | ||||||||
\(119\) | −2.70533 | −0.247997 | ||||||||
\(120\) | 2.20637 | 0.201413 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 0.423080 | 0.0383039 | ||||||||
\(123\) | −7.38287 | −0.665691 | ||||||||
\(124\) | 7.79943 | 0.700410 | ||||||||
\(125\) | 11.1059 | 0.993345 | ||||||||
\(126\) | 0.366209 | 0.0326244 | ||||||||
\(127\) | −17.6871 | −1.56948 | −0.784740 | − | 0.619825i | \(-0.787204\pi\) | ||||
−0.784740 | + | 0.619825i | \(0.787204\pi\) | |||||||
\(128\) | −10.6696 | −0.943069 | ||||||||
\(129\) | 5.77261 | 0.508250 | ||||||||
\(130\) | −1.52294 | −0.133571 | ||||||||
\(131\) | −20.0215 | −1.74929 | −0.874643 | − | 0.484768i | \(-0.838904\pi\) | ||||
−0.874643 | + | 0.484768i | \(0.838904\pi\) | |||||||
\(132\) | 1.82100 | 0.158498 | ||||||||
\(133\) | −0.243767 | −0.0211373 | ||||||||
\(134\) | 2.03489 | 0.175788 | ||||||||
\(135\) | −1.36483 | −0.117466 | ||||||||
\(136\) | 5.05260 | 0.433257 | ||||||||
\(137\) | −16.4175 | −1.40264 | −0.701322 | − | 0.712844i | \(-0.747407\pi\) | ||||
−0.701322 | + | 0.712844i | \(0.747407\pi\) | |||||||
\(138\) | 0.735109 | 0.0625767 | ||||||||
\(139\) | −6.82389 | −0.578795 | −0.289397 | − | 0.957209i | \(-0.593455\pi\) | ||||
−0.289397 | + | 0.957209i | \(0.593455\pi\) | |||||||
\(140\) | 2.15127 | 0.181815 | ||||||||
\(141\) | −3.73936 | −0.314911 | ||||||||
\(142\) | −3.11364 | −0.261291 | ||||||||
\(143\) | −2.63744 | −0.220554 | ||||||||
\(144\) | 2.95806 | 0.246505 | ||||||||
\(145\) | 9.65757 | 0.802017 | ||||||||
\(146\) | −6.92461 | −0.573085 | ||||||||
\(147\) | −6.25078 | −0.515555 | ||||||||
\(148\) | −7.17979 | −0.590175 | ||||||||
\(149\) | 15.0883 | 1.23608 | 0.618039 | − | 0.786148i | \(-0.287927\pi\) | ||||
0.618039 | + | 0.786148i | \(0.287927\pi\) | |||||||
\(150\) | −1.32731 | −0.108374 | ||||||||
\(151\) | −8.59674 | −0.699593 | −0.349797 | − | 0.936826i | \(-0.613749\pi\) | ||||
−0.349797 | + | 0.936826i | \(0.613749\pi\) | |||||||
\(152\) | 0.455270 | 0.0369273 | ||||||||
\(153\) | −3.12547 | −0.252679 | ||||||||
\(154\) | −0.366209 | −0.0295099 | ||||||||
\(155\) | 5.84562 | 0.469531 | ||||||||
\(156\) | −4.80278 | −0.384530 | ||||||||
\(157\) | 9.95066 | 0.794149 | 0.397074 | − | 0.917786i | \(-0.370025\pi\) | ||||
0.397074 | + | 0.917786i | \(0.370025\pi\) | |||||||
\(158\) | −2.55346 | −0.203142 | ||||||||
\(159\) | −5.86335 | −0.464994 | ||||||||
\(160\) | −6.12082 | −0.483893 | ||||||||
\(161\) | 1.50395 | 0.118528 | ||||||||
\(162\) | 0.423080 | 0.0332403 | ||||||||
\(163\) | 21.9852 | 1.72201 | 0.861005 | − | 0.508596i | \(-0.169835\pi\) | ||||
0.861005 | + | 0.508596i | \(0.169835\pi\) | |||||||
\(164\) | 13.4442 | 1.04982 | ||||||||
\(165\) | 1.36483 | 0.106252 | ||||||||
\(166\) | 4.54896 | 0.353068 | ||||||||
\(167\) | 11.4954 | 0.889539 | 0.444770 | − | 0.895645i | \(-0.353286\pi\) | ||||
0.444770 | + | 0.895645i | \(0.353286\pi\) | |||||||
\(168\) | −1.39928 | −0.107957 | ||||||||
\(169\) | −6.04393 | −0.464918 | ||||||||
\(170\) | 1.80474 | 0.138418 | ||||||||
\(171\) | −0.281623 | −0.0215363 | ||||||||
\(172\) | −10.5119 | −0.801528 | ||||||||
\(173\) | −20.5992 | −1.56613 | −0.783065 | − | 0.621940i | \(-0.786345\pi\) | ||||
−0.783065 | + | 0.621940i | \(0.786345\pi\) | |||||||
\(174\) | −2.99373 | −0.226954 | ||||||||
\(175\) | −2.71553 | −0.205274 | ||||||||
\(176\) | −2.95806 | −0.222972 | ||||||||
\(177\) | −7.96157 | −0.598429 | ||||||||
\(178\) | −5.87664 | −0.440473 | ||||||||
\(179\) | −9.33212 | −0.697515 | −0.348758 | − | 0.937213i | \(-0.613396\pi\) | ||||
−0.348758 | + | 0.937213i | \(0.613396\pi\) | |||||||
\(180\) | 2.48536 | 0.185247 | ||||||||
\(181\) | 10.1819 | 0.756814 | 0.378407 | − | 0.925639i | \(-0.376472\pi\) | ||||
0.378407 | + | 0.925639i | \(0.376472\pi\) | |||||||
\(182\) | 0.965852 | 0.0715937 | ||||||||
\(183\) | 1.00000 | 0.0739221 | ||||||||
\(184\) | −2.80886 | −0.207072 | ||||||||
\(185\) | −5.38119 | −0.395633 | ||||||||
\(186\) | −1.81207 | −0.132867 | ||||||||
\(187\) | 3.12547 | 0.228557 | ||||||||
\(188\) | 6.80938 | 0.496625 | ||||||||
\(189\) | 0.865577 | 0.0629614 | ||||||||
\(190\) | 0.162618 | 0.0117976 | ||||||||
\(191\) | 7.53307 | 0.545074 | 0.272537 | − | 0.962145i | \(-0.412137\pi\) | ||||
0.272537 | + | 0.962145i | \(0.412137\pi\) | |||||||
\(192\) | −4.01874 | −0.290027 | ||||||||
\(193\) | 27.2060 | 1.95833 | 0.979165 | − | 0.203067i | \(-0.0650909\pi\) | ||||
0.979165 | + | 0.203067i | \(0.0650909\pi\) | |||||||
\(194\) | 5.23693 | 0.375990 | ||||||||
\(195\) | −3.59965 | −0.257776 | ||||||||
\(196\) | 11.3827 | 0.813049 | ||||||||
\(197\) | 5.30033 | 0.377633 | 0.188817 | − | 0.982012i | \(-0.439535\pi\) | ||||
0.188817 | + | 0.982012i | \(0.439535\pi\) | |||||||
\(198\) | −0.423080 | −0.0300670 | ||||||||
\(199\) | 26.0687 | 1.84796 | 0.923981 | − | 0.382438i | \(-0.124916\pi\) | ||||
0.923981 | + | 0.382438i | \(0.124916\pi\) | |||||||
\(200\) | 5.07164 | 0.358619 | ||||||||
\(201\) | 4.80971 | 0.339251 | ||||||||
\(202\) | 0.0180787 | 0.00127201 | ||||||||
\(203\) | −6.12485 | −0.429880 | ||||||||
\(204\) | 5.69149 | 0.398484 | ||||||||
\(205\) | 10.0763 | 0.703763 | ||||||||
\(206\) | −6.22181 | −0.433494 | ||||||||
\(207\) | 1.73752 | 0.120766 | ||||||||
\(208\) | 7.80169 | 0.540950 | ||||||||
\(209\) | 0.281623 | 0.0194803 | ||||||||
\(210\) | −0.499812 | −0.0344903 | ||||||||
\(211\) | 21.3309 | 1.46848 | 0.734238 | − | 0.678892i | \(-0.237539\pi\) | ||||
0.734238 | + | 0.678892i | \(0.237539\pi\) | |||||||
\(212\) | 10.6772 | 0.733311 | ||||||||
\(213\) | −7.35945 | −0.504261 | ||||||||
\(214\) | 6.29476 | 0.430301 | ||||||||
\(215\) | −7.87862 | −0.537317 | ||||||||
\(216\) | −1.61659 | −0.109995 | ||||||||
\(217\) | −3.70730 | −0.251668 | ||||||||
\(218\) | −3.95356 | −0.267769 | ||||||||
\(219\) | −16.3671 | −1.10599 | ||||||||
\(220\) | −2.48536 | −0.167563 | ||||||||
\(221\) | −8.24322 | −0.554499 | ||||||||
\(222\) | 1.66811 | 0.111956 | ||||||||
\(223\) | 10.5749 | 0.708148 | 0.354074 | − | 0.935217i | \(-0.384796\pi\) | ||||
0.354074 | + | 0.935217i | \(0.384796\pi\) | |||||||
\(224\) | 3.88183 | 0.259366 | ||||||||
\(225\) | −3.13724 | −0.209150 | ||||||||
\(226\) | 6.76588 | 0.450059 | ||||||||
\(227\) | −10.0676 | −0.668210 | −0.334105 | − | 0.942536i | \(-0.608434\pi\) | ||||
−0.334105 | + | 0.942536i | \(0.608434\pi\) | |||||||
\(228\) | 0.512837 | 0.0339635 | ||||||||
\(229\) | −18.2971 | −1.20910 | −0.604552 | − | 0.796566i | \(-0.706648\pi\) | ||||
−0.604552 | + | 0.796566i | \(0.706648\pi\) | |||||||
\(230\) | −1.00330 | −0.0661555 | ||||||||
\(231\) | −0.865577 | −0.0569508 | ||||||||
\(232\) | 11.4391 | 0.751011 | ||||||||
\(233\) | −20.1119 | −1.31758 | −0.658788 | − | 0.752328i | \(-0.728931\pi\) | ||||
−0.658788 | + | 0.752328i | \(0.728931\pi\) | |||||||
\(234\) | 1.11585 | 0.0729452 | ||||||||
\(235\) | 5.10358 | 0.332921 | ||||||||
\(236\) | 14.4981 | 0.943743 | ||||||||
\(237\) | −6.03539 | −0.392041 | ||||||||
\(238\) | −1.14457 | −0.0741916 | ||||||||
\(239\) | −9.24058 | −0.597723 | −0.298862 | − | 0.954296i | \(-0.596607\pi\) | ||||
−0.298862 | + | 0.954296i | \(0.596607\pi\) | |||||||
\(240\) | −4.03724 | −0.260603 | ||||||||
\(241\) | −4.46915 | −0.287884 | −0.143942 | − | 0.989586i | \(-0.545978\pi\) | ||||
−0.143942 | + | 0.989586i | \(0.545978\pi\) | |||||||
\(242\) | 0.423080 | 0.0271966 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | −1.82100 | −0.116578 | ||||||||
\(245\) | 8.53124 | 0.545041 | ||||||||
\(246\) | −3.12355 | −0.199150 | ||||||||
\(247\) | −0.742764 | −0.0472609 | ||||||||
\(248\) | 6.92393 | 0.439670 | ||||||||
\(249\) | 10.7520 | 0.681380 | ||||||||
\(250\) | 4.69871 | 0.297172 | ||||||||
\(251\) | 25.3784 | 1.60187 | 0.800935 | − | 0.598752i | \(-0.204336\pi\) | ||||
0.800935 | + | 0.598752i | \(0.204336\pi\) | |||||||
\(252\) | −1.57622 | −0.0992924 | ||||||||
\(253\) | −1.73752 | −0.109237 | ||||||||
\(254\) | −7.48308 | −0.469530 | ||||||||
\(255\) | 4.26573 | 0.267130 | ||||||||
\(256\) | 3.52337 | 0.220211 | ||||||||
\(257\) | 11.7192 | 0.731022 | 0.365511 | − | 0.930807i | \(-0.380894\pi\) | ||||
0.365511 | + | 0.930807i | \(0.380894\pi\) | |||||||
\(258\) | 2.44228 | 0.152050 | ||||||||
\(259\) | 3.41276 | 0.212059 | ||||||||
\(260\) | 6.55497 | 0.406522 | ||||||||
\(261\) | −7.07603 | −0.437995 | ||||||||
\(262\) | −8.47070 | −0.523321 | ||||||||
\(263\) | 12.2142 | 0.753163 | 0.376581 | − | 0.926384i | \(-0.377100\pi\) | ||||
0.376581 | + | 0.926384i | \(0.377100\pi\) | |||||||
\(264\) | 1.61659 | 0.0994943 | ||||||||
\(265\) | 8.00246 | 0.491587 | ||||||||
\(266\) | −0.103133 | −0.00632348 | ||||||||
\(267\) | −13.8901 | −0.850062 | ||||||||
\(268\) | −8.75849 | −0.535010 | ||||||||
\(269\) | −22.0290 | −1.34313 | −0.671567 | − | 0.740944i | \(-0.734378\pi\) | ||||
−0.671567 | + | 0.740944i | \(0.734378\pi\) | |||||||
\(270\) | −0.577432 | −0.0351414 | ||||||||
\(271\) | 5.27206 | 0.320255 | 0.160127 | − | 0.987096i | \(-0.448810\pi\) | ||||
0.160127 | + | 0.987096i | \(0.448810\pi\) | |||||||
\(272\) | −9.24531 | −0.560579 | ||||||||
\(273\) | 2.28290 | 0.138168 | ||||||||
\(274\) | −6.94594 | −0.419619 | ||||||||
\(275\) | 3.13724 | 0.189183 | ||||||||
\(276\) | −3.16402 | −0.190452 | ||||||||
\(277\) | 25.0372 | 1.50434 | 0.752171 | − | 0.658969i | \(-0.229007\pi\) | ||||
0.752171 | + | 0.658969i | \(0.229007\pi\) | |||||||
\(278\) | −2.88705 | −0.173154 | ||||||||
\(279\) | −4.28304 | −0.256419 | ||||||||
\(280\) | 1.90978 | 0.114131 | ||||||||
\(281\) | 19.6180 | 1.17031 | 0.585157 | − | 0.810920i | \(-0.301033\pi\) | ||||
0.585157 | + | 0.810920i | \(0.301033\pi\) | |||||||
\(282\) | −1.58205 | −0.0942097 | ||||||||
\(283\) | −3.64470 | −0.216655 | −0.108327 | − | 0.994115i | \(-0.534549\pi\) | ||||
−0.108327 | + | 0.994115i | \(0.534549\pi\) | |||||||
\(284\) | 13.4016 | 0.795238 | ||||||||
\(285\) | 0.384368 | 0.0227680 | ||||||||
\(286\) | −1.11585 | −0.0659815 | ||||||||
\(287\) | −6.39044 | −0.377216 | ||||||||
\(288\) | 4.48468 | 0.264262 | ||||||||
\(289\) | −7.23145 | −0.425380 | ||||||||
\(290\) | 4.08593 | 0.239934 | ||||||||
\(291\) | 12.3781 | 0.725617 | ||||||||
\(292\) | 29.8046 | 1.74418 | ||||||||
\(293\) | −5.22920 | −0.305493 | −0.152747 | − | 0.988265i | \(-0.548812\pi\) | ||||
−0.152747 | + | 0.988265i | \(0.548812\pi\) | |||||||
\(294\) | −2.64458 | −0.154235 | ||||||||
\(295\) | 10.8662 | 0.632654 | ||||||||
\(296\) | −6.37384 | −0.370472 | ||||||||
\(297\) | −1.00000 | −0.0580259 | ||||||||
\(298\) | 6.38354 | 0.369789 | ||||||||
\(299\) | 4.58259 | 0.265018 | ||||||||
\(300\) | 5.71293 | 0.329836 | ||||||||
\(301\) | 4.99664 | 0.288001 | ||||||||
\(302\) | −3.63711 | −0.209292 | ||||||||
\(303\) | 0.0427311 | 0.00245484 | ||||||||
\(304\) | −0.833058 | −0.0477792 | ||||||||
\(305\) | −1.36483 | −0.0781498 | ||||||||
\(306\) | −1.32232 | −0.0755922 | ||||||||
\(307\) | −24.2309 | −1.38293 | −0.691467 | − | 0.722408i | \(-0.743035\pi\) | ||||
−0.691467 | + | 0.722408i | \(0.743035\pi\) | |||||||
\(308\) | 1.57622 | 0.0898133 | ||||||||
\(309\) | −14.7060 | −0.836594 | ||||||||
\(310\) | 2.47317 | 0.140466 | ||||||||
\(311\) | 1.91505 | 0.108593 | 0.0542964 | − | 0.998525i | \(-0.482708\pi\) | ||||
0.0542964 | + | 0.998525i | \(0.482708\pi\) | |||||||
\(312\) | −4.26366 | −0.241382 | ||||||||
\(313\) | 18.8745 | 1.06685 | 0.533425 | − | 0.845847i | \(-0.320905\pi\) | ||||
0.533425 | + | 0.845847i | \(0.320905\pi\) | |||||||
\(314\) | 4.20993 | 0.237580 | ||||||||
\(315\) | −1.18136 | −0.0665623 | ||||||||
\(316\) | 10.9905 | 0.618262 | ||||||||
\(317\) | −29.4492 | −1.65403 | −0.827017 | − | 0.562176i | \(-0.809964\pi\) | ||||
−0.827017 | + | 0.562176i | \(0.809964\pi\) | |||||||
\(318\) | −2.48067 | −0.139109 | ||||||||
\(319\) | 7.07603 | 0.396182 | ||||||||
\(320\) | 5.48488 | 0.306614 | ||||||||
\(321\) | 14.8784 | 0.830432 | ||||||||
\(322\) | 0.636294 | 0.0354593 | ||||||||
\(323\) | 0.880205 | 0.0489759 | ||||||||
\(324\) | −1.82100 | −0.101167 | ||||||||
\(325\) | −8.27428 | −0.458975 | ||||||||
\(326\) | 9.30149 | 0.515162 | ||||||||
\(327\) | −9.34470 | −0.516763 | ||||||||
\(328\) | 11.9351 | 0.659005 | ||||||||
\(329\) | −3.23670 | −0.178445 | ||||||||
\(330\) | 0.577432 | 0.0317866 | ||||||||
\(331\) | −12.7781 | −0.702347 | −0.351173 | − | 0.936310i | \(-0.614217\pi\) | ||||
−0.351173 | + | 0.936310i | \(0.614217\pi\) | |||||||
\(332\) | −19.5794 | −1.07456 | ||||||||
\(333\) | 3.94276 | 0.216062 | ||||||||
\(334\) | 4.86347 | 0.266117 | ||||||||
\(335\) | −6.56442 | −0.358653 | ||||||||
\(336\) | 2.56043 | 0.139683 | ||||||||
\(337\) | 28.0453 | 1.52773 | 0.763863 | − | 0.645378i | \(-0.223300\pi\) | ||||
0.763863 | + | 0.645378i | \(0.223300\pi\) | |||||||
\(338\) | −2.55707 | −0.139086 | ||||||||
\(339\) | 15.9919 | 0.868563 | ||||||||
\(340\) | −7.76790 | −0.421273 | ||||||||
\(341\) | 4.28304 | 0.231940 | ||||||||
\(342\) | −0.119149 | −0.00644286 | ||||||||
\(343\) | −11.4696 | −0.619298 | ||||||||
\(344\) | −9.33195 | −0.503145 | ||||||||
\(345\) | −2.37141 | −0.127673 | ||||||||
\(346\) | −8.71513 | −0.468528 | ||||||||
\(347\) | −20.4356 | −1.09704 | −0.548520 | − | 0.836137i | \(-0.684809\pi\) | ||||
−0.548520 | + | 0.836137i | \(0.684809\pi\) | |||||||
\(348\) | 12.8855 | 0.690734 | ||||||||
\(349\) | 17.9641 | 0.961598 | 0.480799 | − | 0.876831i | \(-0.340347\pi\) | ||||
0.480799 | + | 0.876831i | \(0.340347\pi\) | |||||||
\(350\) | −1.14889 | −0.0614105 | ||||||||
\(351\) | 2.63744 | 0.140776 | ||||||||
\(352\) | −4.48468 | −0.239034 | ||||||||
\(353\) | 20.5387 | 1.09317 | 0.546583 | − | 0.837405i | \(-0.315928\pi\) | ||||
0.546583 | + | 0.837405i | \(0.315928\pi\) | |||||||
\(354\) | −3.36839 | −0.179028 | ||||||||
\(355\) | 10.0444 | 0.533101 | ||||||||
\(356\) | 25.2940 | 1.34058 | ||||||||
\(357\) | −2.70533 | −0.143181 | ||||||||
\(358\) | −3.94824 | −0.208671 | ||||||||
\(359\) | −19.6886 | −1.03913 | −0.519564 | − | 0.854432i | \(-0.673905\pi\) | ||||
−0.519564 | + | 0.854432i | \(0.673905\pi\) | |||||||
\(360\) | 2.20637 | 0.116286 | ||||||||
\(361\) | −18.9207 | −0.995826 | ||||||||
\(362\) | 4.30776 | 0.226411 | ||||||||
\(363\) | 1.00000 | 0.0524864 | ||||||||
\(364\) | −4.15717 | −0.217895 | ||||||||
\(365\) | 22.3383 | 1.16924 | ||||||||
\(366\) | 0.423080 | 0.0221148 | ||||||||
\(367\) | −13.8596 | −0.723465 | −0.361733 | − | 0.932282i | \(-0.617815\pi\) | ||||
−0.361733 | + | 0.932282i | \(0.617815\pi\) | |||||||
\(368\) | 5.13968 | 0.267924 | ||||||||
\(369\) | −7.38287 | −0.384337 | ||||||||
\(370\) | −2.27668 | −0.118359 | ||||||||
\(371\) | −5.07518 | −0.263490 | ||||||||
\(372\) | 7.79943 | 0.404382 | ||||||||
\(373\) | 15.4187 | 0.798351 | 0.399175 | − | 0.916875i | \(-0.369296\pi\) | ||||
0.399175 | + | 0.916875i | \(0.369296\pi\) | |||||||
\(374\) | 1.32232 | 0.0683757 | ||||||||
\(375\) | 11.1059 | 0.573508 | ||||||||
\(376\) | 6.04501 | 0.311748 | ||||||||
\(377\) | −18.6626 | −0.961172 | ||||||||
\(378\) | 0.366209 | 0.0188357 | ||||||||
\(379\) | 0.426414 | 0.0219034 | 0.0109517 | − | 0.999940i | \(-0.496514\pi\) | ||||
0.0109517 | + | 0.999940i | \(0.496514\pi\) | |||||||
\(380\) | −0.699935 | −0.0359059 | ||||||||
\(381\) | −17.6871 | −0.906140 | ||||||||
\(382\) | 3.18709 | 0.163066 | ||||||||
\(383\) | 35.5235 | 1.81517 | 0.907584 | − | 0.419870i | \(-0.137924\pi\) | ||||
0.907584 | + | 0.419870i | \(0.137924\pi\) | |||||||
\(384\) | −10.6696 | −0.544481 | ||||||||
\(385\) | 1.18136 | 0.0602079 | ||||||||
\(386\) | 11.5103 | 0.585860 | ||||||||
\(387\) | 5.77261 | 0.293438 | ||||||||
\(388\) | −22.5405 | −1.14432 | ||||||||
\(389\) | −13.9775 | −0.708686 | −0.354343 | − | 0.935115i | \(-0.615296\pi\) | ||||
−0.354343 | + | 0.935115i | \(0.615296\pi\) | |||||||
\(390\) | −1.52294 | −0.0771171 | ||||||||
\(391\) | −5.43055 | −0.274635 | ||||||||
\(392\) | 10.1050 | 0.510377 | ||||||||
\(393\) | −20.0215 | −1.00995 | ||||||||
\(394\) | 2.24247 | 0.112974 | ||||||||
\(395\) | 8.23727 | 0.414462 | ||||||||
\(396\) | 1.82100 | 0.0915088 | ||||||||
\(397\) | 24.6805 | 1.23868 | 0.619338 | − | 0.785124i | \(-0.287401\pi\) | ||||
0.619338 | + | 0.785124i | \(0.287401\pi\) | |||||||
\(398\) | 11.0292 | 0.552842 | ||||||||
\(399\) | −0.243767 | −0.0122036 | ||||||||
\(400\) | −9.28015 | −0.464008 | ||||||||
\(401\) | −38.1654 | −1.90589 | −0.952944 | − | 0.303148i | \(-0.901962\pi\) | ||||
−0.952944 | + | 0.303148i | \(0.901962\pi\) | |||||||
\(402\) | 2.03489 | 0.101491 | ||||||||
\(403\) | −11.2963 | −0.562706 | ||||||||
\(404\) | −0.0778135 | −0.00387137 | ||||||||
\(405\) | −1.36483 | −0.0678189 | ||||||||
\(406\) | −2.59130 | −0.128604 | ||||||||
\(407\) | −3.94276 | −0.195436 | ||||||||
\(408\) | 5.05260 | 0.250141 | ||||||||
\(409\) | −6.08708 | −0.300987 | −0.150493 | − | 0.988611i | \(-0.548086\pi\) | ||||
−0.150493 | + | 0.988611i | \(0.548086\pi\) | |||||||
\(410\) | 4.26310 | 0.210540 | ||||||||
\(411\) | −16.4175 | −0.809817 | ||||||||
\(412\) | 26.7796 | 1.31934 | ||||||||
\(413\) | −6.89135 | −0.339101 | ||||||||
\(414\) | 0.735109 | 0.0361287 | ||||||||
\(415\) | −14.6746 | −0.720349 | ||||||||
\(416\) | 11.8281 | 0.579918 | ||||||||
\(417\) | −6.82389 | −0.334167 | ||||||||
\(418\) | 0.119149 | 0.00582779 | ||||||||
\(419\) | −14.7329 | −0.719752 | −0.359876 | − | 0.933000i | \(-0.617181\pi\) | ||||
−0.359876 | + | 0.933000i | \(0.617181\pi\) | |||||||
\(420\) | 2.15127 | 0.104971 | ||||||||
\(421\) | −12.0408 | −0.586834 | −0.293417 | − | 0.955985i | \(-0.594792\pi\) | ||||
−0.293417 | + | 0.955985i | \(0.594792\pi\) | |||||||
\(422\) | 9.02467 | 0.439314 | ||||||||
\(423\) | −3.73936 | −0.181814 | ||||||||
\(424\) | 9.47864 | 0.460323 | ||||||||
\(425\) | 9.80536 | 0.475630 | ||||||||
\(426\) | −3.11364 | −0.150856 | ||||||||
\(427\) | 0.865577 | 0.0418882 | ||||||||
\(428\) | −27.0936 | −1.30962 | ||||||||
\(429\) | −2.63744 | −0.127337 | ||||||||
\(430\) | −3.33329 | −0.160745 | ||||||||
\(431\) | 26.7332 | 1.28769 | 0.643846 | − | 0.765155i | \(-0.277338\pi\) | ||||
0.643846 | + | 0.765155i | \(0.277338\pi\) | |||||||
\(432\) | 2.95806 | 0.142320 | ||||||||
\(433\) | −33.0285 | −1.58725 | −0.793624 | − | 0.608409i | \(-0.791808\pi\) | ||||
−0.793624 | + | 0.608409i | \(0.791808\pi\) | |||||||
\(434\) | −1.56849 | −0.0752898 | ||||||||
\(435\) | 9.65757 | 0.463045 | ||||||||
\(436\) | 17.0167 | 0.814954 | ||||||||
\(437\) | −0.489326 | −0.0234076 | ||||||||
\(438\) | −6.92461 | −0.330871 | ||||||||
\(439\) | 32.4991 | 1.55110 | 0.775548 | − | 0.631288i | \(-0.217474\pi\) | ||||
0.775548 | + | 0.631288i | \(0.217474\pi\) | |||||||
\(440\) | −2.20637 | −0.105185 | ||||||||
\(441\) | −6.25078 | −0.297656 | ||||||||
\(442\) | −3.48755 | −0.165886 | ||||||||
\(443\) | −23.0625 | −1.09573 | −0.547865 | − | 0.836567i | \(-0.684559\pi\) | ||||
−0.547865 | + | 0.836567i | \(0.684559\pi\) | |||||||
\(444\) | −7.17979 | −0.340738 | ||||||||
\(445\) | 18.9576 | 0.898678 | ||||||||
\(446\) | 4.47404 | 0.211852 | ||||||||
\(447\) | 15.0883 | 0.713650 | ||||||||
\(448\) | −3.47852 | −0.164345 | ||||||||
\(449\) | 27.4385 | 1.29490 | 0.647450 | − | 0.762108i | \(-0.275835\pi\) | ||||
0.647450 | + | 0.762108i | \(0.275835\pi\) | |||||||
\(450\) | −1.32731 | −0.0625698 | ||||||||
\(451\) | 7.38287 | 0.347646 | ||||||||
\(452\) | −29.1214 | −1.36975 | ||||||||
\(453\) | −8.59674 | −0.403910 | ||||||||
\(454\) | −4.25940 | −0.199904 | ||||||||
\(455\) | −3.11577 | −0.146070 | ||||||||
\(456\) | 0.455270 | 0.0213200 | ||||||||
\(457\) | 32.4706 | 1.51891 | 0.759456 | − | 0.650559i | \(-0.225465\pi\) | ||||
0.759456 | + | 0.650559i | \(0.225465\pi\) | |||||||
\(458\) | −7.74113 | −0.361719 | ||||||||
\(459\) | −3.12547 | −0.145884 | ||||||||
\(460\) | 4.31835 | 0.201344 | ||||||||
\(461\) | −26.3178 | −1.22574 | −0.612871 | − | 0.790183i | \(-0.709985\pi\) | ||||
−0.612871 | + | 0.790183i | \(0.709985\pi\) | |||||||
\(462\) | −0.366209 | −0.0170376 | ||||||||
\(463\) | −31.9939 | −1.48688 | −0.743441 | − | 0.668801i | \(-0.766808\pi\) | ||||
−0.743441 | + | 0.668801i | \(0.766808\pi\) | |||||||
\(464\) | −20.9313 | −0.971712 | ||||||||
\(465\) | 5.84562 | 0.271084 | ||||||||
\(466\) | −8.50897 | −0.394170 | ||||||||
\(467\) | −18.9096 | −0.875032 | −0.437516 | − | 0.899211i | \(-0.644142\pi\) | ||||
−0.437516 | + | 0.899211i | \(0.644142\pi\) | |||||||
\(468\) | −4.80278 | −0.222009 | ||||||||
\(469\) | 4.16317 | 0.192237 | ||||||||
\(470\) | 2.15923 | 0.0995976 | ||||||||
\(471\) | 9.95066 | 0.458502 | ||||||||
\(472\) | 12.8706 | 0.592418 | ||||||||
\(473\) | −5.77261 | −0.265425 | ||||||||
\(474\) | −2.55346 | −0.117284 | ||||||||
\(475\) | 0.883522 | 0.0405388 | ||||||||
\(476\) | 4.92642 | 0.225802 | ||||||||
\(477\) | −5.86335 | −0.268464 | ||||||||
\(478\) | −3.90951 | −0.178817 | ||||||||
\(479\) | −37.8765 | −1.73062 | −0.865311 | − | 0.501235i | \(-0.832879\pi\) | ||||
−0.865311 | + | 0.501235i | \(0.832879\pi\) | |||||||
\(480\) | −6.12082 | −0.279376 | ||||||||
\(481\) | 10.3988 | 0.474144 | ||||||||
\(482\) | −1.89081 | −0.0861241 | ||||||||
\(483\) | 1.50395 | 0.0684323 | ||||||||
\(484\) | −1.82100 | −0.0827729 | ||||||||
\(485\) | −16.8940 | −0.767116 | ||||||||
\(486\) | 0.423080 | 0.0191913 | ||||||||
\(487\) | 9.67080 | 0.438226 | 0.219113 | − | 0.975699i | \(-0.429684\pi\) | ||||
0.219113 | + | 0.975699i | \(0.429684\pi\) | |||||||
\(488\) | −1.61659 | −0.0731797 | ||||||||
\(489\) | 21.9852 | 0.994203 | ||||||||
\(490\) | 3.60940 | 0.163056 | ||||||||
\(491\) | 9.63253 | 0.434710 | 0.217355 | − | 0.976093i | \(-0.430257\pi\) | ||||
0.217355 | + | 0.976093i | \(0.430257\pi\) | |||||||
\(492\) | 13.4442 | 0.606112 | ||||||||
\(493\) | 22.1159 | 0.996050 | ||||||||
\(494\) | −0.314249 | −0.0141387 | ||||||||
\(495\) | 1.36483 | 0.0613445 | ||||||||
\(496\) | −12.6695 | −0.568877 | ||||||||
\(497\) | −6.37017 | −0.285741 | ||||||||
\(498\) | 4.54896 | 0.203844 | ||||||||
\(499\) | 28.9699 | 1.29687 | 0.648436 | − | 0.761269i | \(-0.275423\pi\) | ||||
0.648436 | + | 0.761269i | \(0.275423\pi\) | |||||||
\(500\) | −20.2239 | −0.904442 | ||||||||
\(501\) | 11.4954 | 0.513576 | ||||||||
\(502\) | 10.7371 | 0.479220 | ||||||||
\(503\) | 18.9084 | 0.843084 | 0.421542 | − | 0.906809i | \(-0.361489\pi\) | ||||
0.421542 | + | 0.906809i | \(0.361489\pi\) | |||||||
\(504\) | −1.39928 | −0.0623291 | ||||||||
\(505\) | −0.0583206 | −0.00259523 | ||||||||
\(506\) | −0.735109 | −0.0326796 | ||||||||
\(507\) | −6.04393 | −0.268420 | ||||||||
\(508\) | 32.2083 | 1.42901 | ||||||||
\(509\) | −8.63556 | −0.382765 | −0.191382 | − | 0.981516i | \(-0.561297\pi\) | ||||
−0.191382 | + | 0.981516i | \(0.561297\pi\) | |||||||
\(510\) | 1.80474 | 0.0799154 | ||||||||
\(511\) | −14.1670 | −0.626711 | ||||||||
\(512\) | 22.8299 | 1.00895 | ||||||||
\(513\) | −0.281623 | −0.0124340 | ||||||||
\(514\) | 4.95816 | 0.218695 | ||||||||
\(515\) | 20.0711 | 0.884439 | ||||||||
\(516\) | −10.5119 | −0.462762 | ||||||||
\(517\) | 3.73936 | 0.164457 | ||||||||
\(518\) | 1.44387 | 0.0634402 | ||||||||
\(519\) | −20.5992 | −0.904205 | ||||||||
\(520\) | 5.81916 | 0.255187 | ||||||||
\(521\) | −5.59504 | −0.245123 | −0.122562 | − | 0.992461i | \(-0.539111\pi\) | ||||
−0.122562 | + | 0.992461i | \(0.539111\pi\) | |||||||
\(522\) | −2.99373 | −0.131032 | ||||||||
\(523\) | 38.6887 | 1.69174 | 0.845870 | − | 0.533390i | \(-0.179082\pi\) | ||||
0.845870 | + | 0.533390i | \(0.179082\pi\) | |||||||
\(524\) | 36.4592 | 1.59273 | ||||||||
\(525\) | −2.71553 | −0.118515 | ||||||||
\(526\) | 5.16761 | 0.225318 | ||||||||
\(527\) | 13.3865 | 0.583125 | ||||||||
\(528\) | −2.95806 | −0.128733 | ||||||||
\(529\) | −19.9810 | −0.868741 | ||||||||
\(530\) | 3.38569 | 0.147065 | ||||||||
\(531\) | −7.96157 | −0.345503 | ||||||||
\(532\) | 0.443900 | 0.0192455 | ||||||||
\(533\) | −19.4718 | −0.843419 | ||||||||
\(534\) | −5.87664 | −0.254307 | ||||||||
\(535\) | −20.3065 | −0.877925 | ||||||||
\(536\) | −7.77533 | −0.335843 | ||||||||
\(537\) | −9.33212 | −0.402711 | ||||||||
\(538\) | −9.32005 | −0.401816 | ||||||||
\(539\) | 6.25078 | 0.269240 | ||||||||
\(540\) | 2.48536 | 0.106953 | ||||||||
\(541\) | 3.22362 | 0.138594 | 0.0692971 | − | 0.997596i | \(-0.477924\pi\) | ||||
0.0692971 | + | 0.997596i | \(0.477924\pi\) | |||||||
\(542\) | 2.23050 | 0.0958083 | ||||||||
\(543\) | 10.1819 | 0.436947 | ||||||||
\(544\) | −14.0167 | −0.600962 | ||||||||
\(545\) | 12.7539 | 0.546318 | ||||||||
\(546\) | 0.965852 | 0.0413346 | ||||||||
\(547\) | −42.0810 | −1.79925 | −0.899627 | − | 0.436658i | \(-0.856162\pi\) | ||||
−0.899627 | + | 0.436658i | \(0.856162\pi\) | |||||||
\(548\) | 29.8964 | 1.27711 | ||||||||
\(549\) | 1.00000 | 0.0426790 | ||||||||
\(550\) | 1.32731 | 0.0565965 | ||||||||
\(551\) | 1.99278 | 0.0848951 | ||||||||
\(552\) | −2.80886 | −0.119553 | ||||||||
\(553\) | −5.22410 | −0.222151 | ||||||||
\(554\) | 10.5928 | 0.450043 | ||||||||
\(555\) | −5.38119 | −0.228419 | ||||||||
\(556\) | 12.4263 | 0.526994 | ||||||||
\(557\) | −39.2686 | −1.66386 | −0.831932 | − | 0.554878i | \(-0.812765\pi\) | ||||
−0.831932 | + | 0.554878i | \(0.812765\pi\) | |||||||
\(558\) | −1.81207 | −0.0767111 | ||||||||
\(559\) | 15.2249 | 0.643944 | ||||||||
\(560\) | −3.49454 | −0.147671 | ||||||||
\(561\) | 3.12547 | 0.131957 | ||||||||
\(562\) | 8.30000 | 0.350115 | ||||||||
\(563\) | 18.1501 | 0.764935 | 0.382468 | − | 0.923969i | \(-0.375074\pi\) | ||||
0.382468 | + | 0.923969i | \(0.375074\pi\) | |||||||
\(564\) | 6.80938 | 0.286727 | ||||||||
\(565\) | −21.8263 | −0.918237 | ||||||||
\(566\) | −1.54200 | −0.0648151 | ||||||||
\(567\) | 0.865577 | 0.0363508 | ||||||||
\(568\) | 11.8972 | 0.499197 | ||||||||
\(569\) | 10.8482 | 0.454782 | 0.227391 | − | 0.973804i | \(-0.426980\pi\) | ||||
0.227391 | + | 0.973804i | \(0.426980\pi\) | |||||||
\(570\) | 0.162618 | 0.00681133 | ||||||||
\(571\) | 20.0265 | 0.838081 | 0.419041 | − | 0.907967i | \(-0.362366\pi\) | ||||
0.419041 | + | 0.907967i | \(0.362366\pi\) | |||||||
\(572\) | 4.80278 | 0.200814 | ||||||||
\(573\) | 7.53307 | 0.314699 | ||||||||
\(574\) | −2.70367 | −0.112849 | ||||||||
\(575\) | −5.45102 | −0.227323 | ||||||||
\(576\) | −4.01874 | −0.167447 | ||||||||
\(577\) | −34.8606 | −1.45127 | −0.725634 | − | 0.688081i | \(-0.758453\pi\) | ||||
−0.725634 | + | 0.688081i | \(0.758453\pi\) | |||||||
\(578\) | −3.05949 | −0.127258 | ||||||||
\(579\) | 27.2060 | 1.13064 | ||||||||
\(580\) | −17.5865 | −0.730238 | ||||||||
\(581\) | 9.30668 | 0.386106 | ||||||||
\(582\) | 5.23693 | 0.217078 | ||||||||
\(583\) | 5.86335 | 0.242835 | ||||||||
\(584\) | 26.4590 | 1.09488 | ||||||||
\(585\) | −3.59965 | −0.148827 | ||||||||
\(586\) | −2.21237 | −0.0913922 | ||||||||
\(587\) | −14.8050 | −0.611066 | −0.305533 | − | 0.952181i | \(-0.598835\pi\) | ||||
−0.305533 | + | 0.952181i | \(0.598835\pi\) | |||||||
\(588\) | 11.3827 | 0.469414 | ||||||||
\(589\) | 1.20620 | 0.0497008 | ||||||||
\(590\) | 4.59727 | 0.189267 | ||||||||
\(591\) | 5.30033 | 0.218027 | ||||||||
\(592\) | 11.6629 | 0.479343 | ||||||||
\(593\) | 15.7941 | 0.648586 | 0.324293 | − | 0.945957i | \(-0.394874\pi\) | ||||
0.324293 | + | 0.945957i | \(0.394874\pi\) | |||||||
\(594\) | −0.423080 | −0.0173592 | ||||||||
\(595\) | 3.69231 | 0.151370 | ||||||||
\(596\) | −27.4757 | −1.12545 | ||||||||
\(597\) | 26.0687 | 1.06692 | ||||||||
\(598\) | 1.93880 | 0.0792836 | ||||||||
\(599\) | 21.0304 | 0.859279 | 0.429640 | − | 0.903000i | \(-0.358641\pi\) | ||||
0.429640 | + | 0.903000i | \(0.358641\pi\) | |||||||
\(600\) | 5.07164 | 0.207049 | ||||||||
\(601\) | −26.1583 | −1.06702 | −0.533510 | − | 0.845794i | \(-0.679127\pi\) | ||||
−0.533510 | + | 0.845794i | \(0.679127\pi\) | |||||||
\(602\) | 2.11398 | 0.0861593 | ||||||||
\(603\) | 4.80971 | 0.195866 | ||||||||
\(604\) | 15.6547 | 0.636980 | ||||||||
\(605\) | −1.36483 | −0.0554882 | ||||||||
\(606\) | 0.0180787 | 0.000734397 0 | ||||||||
\(607\) | 37.7328 | 1.53153 | 0.765764 | − | 0.643122i | \(-0.222361\pi\) | ||||
0.765764 | + | 0.643122i | \(0.222361\pi\) | |||||||
\(608\) | −1.26299 | −0.0512210 | ||||||||
\(609\) | −6.12485 | −0.248191 | ||||||||
\(610\) | −0.577432 | −0.0233795 | ||||||||
\(611\) | −9.86232 | −0.398987 | ||||||||
\(612\) | 5.69149 | 0.230065 | ||||||||
\(613\) | 34.1803 | 1.38053 | 0.690264 | − | 0.723558i | \(-0.257494\pi\) | ||||
0.690264 | + | 0.723558i | \(0.257494\pi\) | |||||||
\(614\) | −10.2516 | −0.413722 | ||||||||
\(615\) | 10.0763 | 0.406317 | ||||||||
\(616\) | 1.39928 | 0.0563788 | ||||||||
\(617\) | 19.5940 | 0.788826 | 0.394413 | − | 0.918933i | \(-0.370948\pi\) | ||||
0.394413 | + | 0.918933i | \(0.370948\pi\) | |||||||
\(618\) | −6.22181 | −0.250278 | ||||||||
\(619\) | −27.3391 | −1.09885 | −0.549425 | − | 0.835543i | \(-0.685153\pi\) | ||||
−0.549425 | + | 0.835543i | \(0.685153\pi\) | |||||||
\(620\) | −10.6449 | −0.427509 | ||||||||
\(621\) | 1.73752 | 0.0697242 | ||||||||
\(622\) | 0.810222 | 0.0324869 | ||||||||
\(623\) | −12.0230 | −0.481690 | ||||||||
\(624\) | 7.80169 | 0.312318 | ||||||||
\(625\) | 0.528524 | 0.0211410 | ||||||||
\(626\) | 7.98543 | 0.319162 | ||||||||
\(627\) | 0.281623 | 0.0112470 | ||||||||
\(628\) | −18.1202 | −0.723074 | ||||||||
\(629\) | −12.3230 | −0.491349 | ||||||||
\(630\) | −0.499812 | −0.0199130 | ||||||||
\(631\) | 29.4107 | 1.17082 | 0.585411 | − | 0.810737i | \(-0.300933\pi\) | ||||
0.585411 | + | 0.810737i | \(0.300933\pi\) | |||||||
\(632\) | 9.75676 | 0.388103 | ||||||||
\(633\) | 21.3309 | 0.847825 | ||||||||
\(634\) | −12.4594 | −0.494826 | ||||||||
\(635\) | 24.1399 | 0.957963 | ||||||||
\(636\) | 10.6772 | 0.423378 | ||||||||
\(637\) | −16.4860 | −0.653200 | ||||||||
\(638\) | 2.99373 | 0.118523 | ||||||||
\(639\) | −7.35945 | −0.291135 | ||||||||
\(640\) | 14.5622 | 0.575621 | ||||||||
\(641\) | −36.2587 | −1.43213 | −0.716066 | − | 0.698032i | \(-0.754059\pi\) | ||||
−0.716066 | + | 0.698032i | \(0.754059\pi\) | |||||||
\(642\) | 6.29476 | 0.248434 | ||||||||
\(643\) | 5.46621 | 0.215566 | 0.107783 | − | 0.994174i | \(-0.465625\pi\) | ||||
0.107783 | + | 0.994174i | \(0.465625\pi\) | |||||||
\(644\) | −2.73871 | −0.107920 | ||||||||
\(645\) | −7.87862 | −0.310220 | ||||||||
\(646\) | 0.372397 | 0.0146518 | ||||||||
\(647\) | 8.88569 | 0.349333 | 0.174666 | − | 0.984628i | \(-0.444115\pi\) | ||||
0.174666 | + | 0.984628i | \(0.444115\pi\) | |||||||
\(648\) | −1.61659 | −0.0635057 | ||||||||
\(649\) | 7.96157 | 0.312519 | ||||||||
\(650\) | −3.50069 | −0.137308 | ||||||||
\(651\) | −3.70730 | −0.145301 | ||||||||
\(652\) | −40.0350 | −1.56789 | ||||||||
\(653\) | 42.2586 | 1.65371 | 0.826853 | − | 0.562418i | \(-0.190129\pi\) | ||||
0.826853 | + | 0.562418i | \(0.190129\pi\) | |||||||
\(654\) | −3.95356 | −0.154596 | ||||||||
\(655\) | 27.3259 | 1.06771 | ||||||||
\(656\) | −21.8390 | −0.852668 | ||||||||
\(657\) | −16.3671 | −0.638542 | ||||||||
\(658\) | −1.36938 | −0.0533842 | ||||||||
\(659\) | −32.6335 | −1.27122 | −0.635610 | − | 0.772010i | \(-0.719251\pi\) | ||||
−0.635610 | + | 0.772010i | \(0.719251\pi\) | |||||||
\(660\) | −2.48536 | −0.0967423 | ||||||||
\(661\) | 10.9510 | 0.425943 | 0.212971 | − | 0.977058i | \(-0.431686\pi\) | ||||
0.212971 | + | 0.977058i | \(0.431686\pi\) | |||||||
\(662\) | −5.40615 | −0.210116 | ||||||||
\(663\) | −8.24322 | −0.320140 | ||||||||
\(664\) | −17.3816 | −0.674537 | ||||||||
\(665\) | 0.332700 | 0.0129015 | ||||||||
\(666\) | 1.66811 | 0.0646378 | ||||||||
\(667\) | −12.2947 | −0.476054 | ||||||||
\(668\) | −20.9331 | −0.809927 | ||||||||
\(669\) | 10.5749 | 0.408850 | ||||||||
\(670\) | −2.77728 | −0.107296 | ||||||||
\(671\) | −1.00000 | −0.0386046 | ||||||||
\(672\) | 3.88183 | 0.149745 | ||||||||
\(673\) | 11.8740 | 0.457709 | 0.228854 | − | 0.973461i | \(-0.426502\pi\) | ||||
0.228854 | + | 0.973461i | \(0.426502\pi\) | |||||||
\(674\) | 11.8654 | 0.457039 | ||||||||
\(675\) | −3.13724 | −0.120753 | ||||||||
\(676\) | 11.0060 | 0.423308 | ||||||||
\(677\) | 4.07190 | 0.156496 | 0.0782478 | − | 0.996934i | \(-0.475067\pi\) | ||||
0.0782478 | + | 0.996934i | \(0.475067\pi\) | |||||||
\(678\) | 6.76588 | 0.259842 | ||||||||
\(679\) | 10.7142 | 0.411173 | ||||||||
\(680\) | −6.89594 | −0.264447 | ||||||||
\(681\) | −10.0676 | −0.385791 | ||||||||
\(682\) | 1.81207 | 0.0693878 | ||||||||
\(683\) | −35.2353 | −1.34824 | −0.674120 | − | 0.738622i | \(-0.735477\pi\) | ||||
−0.674120 | + | 0.738622i | \(0.735477\pi\) | |||||||
\(684\) | 0.512837 | 0.0196088 | ||||||||
\(685\) | 22.4071 | 0.856132 | ||||||||
\(686\) | −4.85255 | −0.185271 | ||||||||
\(687\) | −18.2971 | −0.698076 | ||||||||
\(688\) | 17.0757 | 0.651005 | ||||||||
\(689\) | −15.4642 | −0.589140 | ||||||||
\(690\) | −1.00330 | −0.0381949 | ||||||||
\(691\) | −29.7507 | −1.13177 | −0.565885 | − | 0.824484i | \(-0.691465\pi\) | ||||
−0.565885 | + | 0.824484i | \(0.691465\pi\) | |||||||
\(692\) | 37.5112 | 1.42596 | ||||||||
\(693\) | −0.865577 | −0.0328805 | ||||||||
\(694\) | −8.64590 | −0.328194 | ||||||||
\(695\) | 9.31344 | 0.353279 | ||||||||
\(696\) | 11.4391 | 0.433596 | ||||||||
\(697\) | 23.0749 | 0.874025 | ||||||||
\(698\) | 7.60027 | 0.287675 | ||||||||
\(699\) | −20.1119 | −0.760703 | ||||||||
\(700\) | 4.94498 | 0.186903 | ||||||||
\(701\) | 36.1389 | 1.36495 | 0.682475 | − | 0.730909i | \(-0.260904\pi\) | ||||
0.682475 | + | 0.730909i | \(0.260904\pi\) | |||||||
\(702\) | 1.11585 | 0.0421150 | ||||||||
\(703\) | −1.11037 | −0.0418786 | ||||||||
\(704\) | 4.01874 | 0.151462 | ||||||||
\(705\) | 5.10358 | 0.192212 | ||||||||
\(706\) | 8.68954 | 0.327035 | ||||||||
\(707\) | 0.0369871 | 0.00139104 | ||||||||
\(708\) | 14.4981 | 0.544870 | ||||||||
\(709\) | −5.65735 | −0.212466 | −0.106233 | − | 0.994341i | \(-0.533879\pi\) | ||||
−0.106233 | + | 0.994341i | \(0.533879\pi\) | |||||||
\(710\) | 4.24958 | 0.159484 | ||||||||
\(711\) | −6.03539 | −0.226345 | ||||||||
\(712\) | 22.4547 | 0.841524 | ||||||||
\(713\) | −7.44186 | −0.278700 | ||||||||
\(714\) | −1.14457 | −0.0428346 | ||||||||
\(715\) | 3.59965 | 0.134619 | ||||||||
\(716\) | 16.9938 | 0.635089 | ||||||||
\(717\) | −9.24058 | −0.345096 | ||||||||
\(718\) | −8.32988 | −0.310868 | ||||||||
\(719\) | −19.1968 | −0.715920 | −0.357960 | − | 0.933737i | \(-0.616528\pi\) | ||||
−0.357960 | + | 0.933737i | \(0.616528\pi\) | |||||||
\(720\) | −4.03724 | −0.150459 | ||||||||
\(721\) | −12.7291 | −0.474058 | ||||||||
\(722\) | −8.00497 | −0.297914 | ||||||||
\(723\) | −4.46915 | −0.166210 | ||||||||
\(724\) | −18.5412 | −0.689080 | ||||||||
\(725\) | 22.1992 | 0.824459 | ||||||||
\(726\) | 0.423080 | 0.0157020 | ||||||||
\(727\) | 27.1989 | 1.00875 | 0.504375 | − | 0.863485i | \(-0.331723\pi\) | ||||
0.504375 | + | 0.863485i | \(0.331723\pi\) | |||||||
\(728\) | −3.69052 | −0.136780 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 9.45090 | 0.349794 | ||||||||
\(731\) | −18.0421 | −0.667311 | ||||||||
\(732\) | −1.82100 | −0.0673062 | ||||||||
\(733\) | 12.3262 | 0.455277 | 0.227638 | − | 0.973746i | \(-0.426900\pi\) | ||||
0.227638 | + | 0.973746i | \(0.426900\pi\) | |||||||
\(734\) | −5.86372 | −0.216434 | ||||||||
\(735\) | 8.53124 | 0.314679 | ||||||||
\(736\) | 7.79221 | 0.287225 | ||||||||
\(737\) | −4.80971 | −0.177168 | ||||||||
\(738\) | −3.12355 | −0.114979 | ||||||||
\(739\) | −45.4141 | −1.67059 | −0.835293 | − | 0.549806i | \(-0.814702\pi\) | ||||
−0.835293 | + | 0.549806i | \(0.814702\pi\) | |||||||
\(740\) | 9.79917 | 0.360225 | ||||||||
\(741\) | −0.742764 | −0.0272861 | ||||||||
\(742\) | −2.14721 | −0.0788265 | ||||||||
\(743\) | 38.0717 | 1.39672 | 0.698358 | − | 0.715749i | \(-0.253914\pi\) | ||||
0.698358 | + | 0.715749i | \(0.253914\pi\) | |||||||
\(744\) | 6.92393 | 0.253844 | ||||||||
\(745\) | −20.5929 | −0.754464 | ||||||||
\(746\) | 6.52336 | 0.238837 | ||||||||
\(747\) | 10.7520 | 0.393395 | ||||||||
\(748\) | −5.69149 | −0.208101 | ||||||||
\(749\) | 12.8784 | 0.470567 | ||||||||
\(750\) | 4.69871 | 0.171572 | ||||||||
\(751\) | 12.2499 | 0.447006 | 0.223503 | − | 0.974703i | \(-0.428251\pi\) | ||||
0.223503 | + | 0.974703i | \(0.428251\pi\) | |||||||
\(752\) | −11.0612 | −0.403362 | ||||||||
\(753\) | 25.3784 | 0.924840 | ||||||||
\(754\) | −7.89577 | −0.287547 | ||||||||
\(755\) | 11.7331 | 0.427010 | ||||||||
\(756\) | −1.57622 | −0.0573265 | ||||||||
\(757\) | 1.84173 | 0.0669390 | 0.0334695 | − | 0.999440i | \(-0.489344\pi\) | ||||
0.0334695 | + | 0.999440i | \(0.489344\pi\) | |||||||
\(758\) | 0.180408 | 0.00655270 | ||||||||
\(759\) | −1.73752 | −0.0630679 | ||||||||
\(760\) | −0.621365 | −0.0225393 | ||||||||
\(761\) | 36.8876 | 1.33717 | 0.668587 | − | 0.743634i | \(-0.266900\pi\) | ||||
0.668587 | + | 0.743634i | \(0.266900\pi\) | |||||||
\(762\) | −7.48308 | −0.271084 | ||||||||
\(763\) | −8.08856 | −0.292825 | ||||||||
\(764\) | −13.7177 | −0.496291 | ||||||||
\(765\) | 4.26573 | 0.154228 | ||||||||
\(766\) | 15.0293 | 0.543031 | ||||||||
\(767\) | −20.9982 | −0.758199 | ||||||||
\(768\) | 3.52337 | 0.127139 | ||||||||
\(769\) | −18.9650 | −0.683894 | −0.341947 | − | 0.939719i | \(-0.611086\pi\) | ||||
−0.341947 | + | 0.939719i | \(0.611086\pi\) | |||||||
\(770\) | 0.499812 | 0.0180120 | ||||||||
\(771\) | 11.7192 | 0.422056 | ||||||||
\(772\) | −49.5422 | −1.78306 | ||||||||
\(773\) | 34.9730 | 1.25789 | 0.628946 | − | 0.777449i | \(-0.283487\pi\) | ||||
0.628946 | + | 0.777449i | \(0.283487\pi\) | |||||||
\(774\) | 2.44228 | 0.0877859 | ||||||||
\(775\) | 13.4369 | 0.482669 | ||||||||
\(776\) | −20.0103 | −0.718329 | ||||||||
\(777\) | 3.41276 | 0.122432 | ||||||||
\(778\) | −5.91360 | −0.212013 | ||||||||
\(779\) | 2.07919 | 0.0744947 | ||||||||
\(780\) | 6.55497 | 0.234706 | ||||||||
\(781\) | 7.35945 | 0.263342 | ||||||||
\(782\) | −2.29756 | −0.0821606 | ||||||||
\(783\) | −7.07603 | −0.252877 | ||||||||
\(784\) | −18.4902 | −0.660363 | ||||||||
\(785\) | −13.5809 | −0.484724 | ||||||||
\(786\) | −8.47070 | −0.302140 | ||||||||
\(787\) | −3.25717 | −0.116106 | −0.0580529 | − | 0.998314i | \(-0.518489\pi\) | ||||
−0.0580529 | + | 0.998314i | \(0.518489\pi\) | |||||||
\(788\) | −9.65192 | −0.343835 | ||||||||
\(789\) | 12.2142 | 0.434839 | ||||||||
\(790\) | 3.48503 | 0.123992 | ||||||||
\(791\) | 13.8423 | 0.492174 | ||||||||
\(792\) | 1.61659 | 0.0574431 | ||||||||
\(793\) | 2.63744 | 0.0936581 | ||||||||
\(794\) | 10.4418 | 0.370566 | ||||||||
\(795\) | 8.00246 | 0.283818 | ||||||||
\(796\) | −47.4712 | −1.68257 | ||||||||
\(797\) | −23.1563 | −0.820238 | −0.410119 | − | 0.912032i | \(-0.634513\pi\) | ||||
−0.410119 | + | 0.912032i | \(0.634513\pi\) | |||||||
\(798\) | −0.103133 | −0.00365087 | ||||||||
\(799\) | 11.6872 | 0.413465 | ||||||||
\(800\) | −14.0695 | −0.497433 | ||||||||
\(801\) | −13.8901 | −0.490784 | ||||||||
\(802\) | −16.1470 | −0.570171 | ||||||||
\(803\) | 16.3671 | 0.577583 | ||||||||
\(804\) | −8.75849 | −0.308888 | ||||||||
\(805\) | −2.05264 | −0.0723460 | ||||||||
\(806\) | −4.77922 | −0.168341 | ||||||||
\(807\) | −22.0290 | −0.775459 | ||||||||
\(808\) | −0.0690788 | −0.00243018 | ||||||||
\(809\) | 1.91012 | 0.0671564 | 0.0335782 | − | 0.999436i | \(-0.489310\pi\) | ||||
0.0335782 | + | 0.999436i | \(0.489310\pi\) | |||||||
\(810\) | −0.577432 | −0.0202889 | ||||||||
\(811\) | −7.87730 | −0.276609 | −0.138305 | − | 0.990390i | \(-0.544165\pi\) | ||||
−0.138305 | + | 0.990390i | \(0.544165\pi\) | |||||||
\(812\) | 11.1534 | 0.391406 | ||||||||
\(813\) | 5.27206 | 0.184899 | ||||||||
\(814\) | −1.66811 | −0.0584671 | ||||||||
\(815\) | −30.0060 | −1.05106 | ||||||||
\(816\) | −9.24531 | −0.323651 | ||||||||
\(817\) | −1.62570 | −0.0568761 | ||||||||
\(818\) | −2.57532 | −0.0900440 | ||||||||
\(819\) | 2.28290 | 0.0797711 | ||||||||
\(820\) | −18.3491 | −0.640777 | ||||||||
\(821\) | −10.6394 | −0.371318 | −0.185659 | − | 0.982614i | \(-0.559442\pi\) | ||||
−0.185659 | + | 0.982614i | \(0.559442\pi\) | |||||||
\(822\) | −6.94594 | −0.242267 | ||||||||
\(823\) | −2.50922 | −0.0874658 | −0.0437329 | − | 0.999043i | \(-0.513925\pi\) | ||||
−0.0437329 | + | 0.999043i | \(0.513925\pi\) | |||||||
\(824\) | 23.7736 | 0.828191 | ||||||||
\(825\) | 3.13724 | 0.109225 | ||||||||
\(826\) | −2.91560 | −0.101447 | ||||||||
\(827\) | −5.89475 | −0.204980 | −0.102490 | − | 0.994734i | \(-0.532681\pi\) | ||||
−0.102490 | + | 0.994734i | \(0.532681\pi\) | |||||||
\(828\) | −3.16402 | −0.109957 | ||||||||
\(829\) | −15.3165 | −0.531964 | −0.265982 | − | 0.963978i | \(-0.585696\pi\) | ||||
−0.265982 | + | 0.963978i | \(0.585696\pi\) | |||||||
\(830\) | −6.20855 | −0.215502 | ||||||||
\(831\) | 25.0372 | 0.868532 | ||||||||
\(832\) | −10.5992 | −0.367460 | ||||||||
\(833\) | 19.5366 | 0.676903 | ||||||||
\(834\) | −2.88705 | −0.0999705 | ||||||||
\(835\) | −15.6892 | −0.542948 | ||||||||
\(836\) | −0.512837 | −0.0177368 | ||||||||
\(837\) | −4.28304 | −0.148044 | ||||||||
\(838\) | −6.23322 | −0.215323 | ||||||||
\(839\) | −35.8612 | −1.23807 | −0.619033 | − | 0.785365i | \(-0.712475\pi\) | ||||
−0.619033 | + | 0.785365i | \(0.712475\pi\) | |||||||
\(840\) | 1.90978 | 0.0658937 | ||||||||
\(841\) | 21.0702 | 0.726560 | ||||||||
\(842\) | −5.09424 | −0.175559 | ||||||||
\(843\) | 19.6180 | 0.675681 | ||||||||
\(844\) | −38.8435 | −1.33705 | ||||||||
\(845\) | 8.24892 | 0.283772 | ||||||||
\(846\) | −1.58205 | −0.0543920 | ||||||||
\(847\) | 0.865577 | 0.0297416 | ||||||||
\(848\) | −17.3441 | −0.595600 | ||||||||
\(849\) | −3.64470 | −0.125086 | ||||||||
\(850\) | 4.14845 | 0.142291 | ||||||||
\(851\) | 6.85062 | 0.234836 | ||||||||
\(852\) | 13.4016 | 0.459131 | ||||||||
\(853\) | 1.26182 | 0.0432041 | 0.0216020 | − | 0.999767i | \(-0.493123\pi\) | ||||
0.0216020 | + | 0.999767i | \(0.493123\pi\) | |||||||
\(854\) | 0.366209 | 0.0125314 | ||||||||
\(855\) | 0.384368 | 0.0131451 | ||||||||
\(856\) | −24.0523 | −0.822091 | ||||||||
\(857\) | 30.6772 | 1.04791 | 0.523956 | − | 0.851745i | \(-0.324455\pi\) | ||||
0.523956 | + | 0.851745i | \(0.324455\pi\) | |||||||
\(858\) | −1.11585 | −0.0380944 | ||||||||
\(859\) | 5.82456 | 0.198731 | 0.0993657 | − | 0.995051i | \(-0.468319\pi\) | ||||
0.0993657 | + | 0.995051i | \(0.468319\pi\) | |||||||
\(860\) | 14.3470 | 0.489228 | ||||||||
\(861\) | −6.39044 | −0.217786 | ||||||||
\(862\) | 11.3103 | 0.385230 | ||||||||
\(863\) | 47.2448 | 1.60823 | 0.804116 | − | 0.594472i | \(-0.202639\pi\) | ||||
0.804116 | + | 0.594472i | \(0.202639\pi\) | |||||||
\(864\) | 4.48468 | 0.152572 | ||||||||
\(865\) | 28.1144 | 0.955918 | ||||||||
\(866\) | −13.9737 | −0.474846 | ||||||||
\(867\) | −7.23145 | −0.245593 | ||||||||
\(868\) | 6.75101 | 0.229144 | ||||||||
\(869\) | 6.03539 | 0.204737 | ||||||||
\(870\) | 4.08593 | 0.138526 | ||||||||
\(871\) | 12.6853 | 0.429825 | ||||||||
\(872\) | 15.1066 | 0.511573 | ||||||||
\(873\) | 12.3781 | 0.418935 | ||||||||
\(874\) | −0.207024 | −0.00700269 | ||||||||
\(875\) | 9.61304 | 0.324980 | ||||||||
\(876\) | 29.8046 | 1.00700 | ||||||||
\(877\) | −26.3489 | −0.889740 | −0.444870 | − | 0.895595i | \(-0.646750\pi\) | ||||
−0.444870 | + | 0.895595i | \(0.646750\pi\) | |||||||
\(878\) | 13.7497 | 0.464031 | ||||||||
\(879\) | −5.22920 | −0.176376 | ||||||||
\(880\) | 4.03724 | 0.136095 | ||||||||
\(881\) | −3.59627 | −0.121162 | −0.0605808 | − | 0.998163i | \(-0.519295\pi\) | ||||
−0.0605808 | + | 0.998163i | \(0.519295\pi\) | |||||||
\(882\) | −2.64458 | −0.0890477 | ||||||||
\(883\) | −9.91315 | −0.333604 | −0.166802 | − | 0.985990i | \(-0.553344\pi\) | ||||
−0.166802 | + | 0.985990i | \(0.553344\pi\) | |||||||
\(884\) | 15.0109 | 0.504872 | ||||||||
\(885\) | 10.8662 | 0.365263 | ||||||||
\(886\) | −9.75728 | −0.327802 | ||||||||
\(887\) | −15.1609 | −0.509052 | −0.254526 | − | 0.967066i | \(-0.581919\pi\) | ||||
−0.254526 | + | 0.967066i | \(0.581919\pi\) | |||||||
\(888\) | −6.37384 | −0.213892 | ||||||||
\(889\) | −15.3096 | −0.513467 | ||||||||
\(890\) | 8.02061 | 0.268851 | ||||||||
\(891\) | −1.00000 | −0.0335013 | ||||||||
\(892\) | −19.2569 | −0.644770 | ||||||||
\(893\) | 1.05309 | 0.0352403 | ||||||||
\(894\) | 6.38354 | 0.213498 | ||||||||
\(895\) | 12.7367 | 0.425742 | ||||||||
\(896\) | −9.23536 | −0.308532 | ||||||||
\(897\) | 4.58259 | 0.153008 | ||||||||
\(898\) | 11.6087 | 0.387386 | ||||||||
\(899\) | 30.3069 | 1.01079 | ||||||||
\(900\) | 5.71293 | 0.190431 | ||||||||
\(901\) | 18.3257 | 0.610518 | ||||||||
\(902\) | 3.12355 | 0.104003 | ||||||||
\(903\) | 4.99664 | 0.166278 | ||||||||
\(904\) | −25.8524 | −0.859839 | ||||||||
\(905\) | −13.8965 | −0.461936 | ||||||||
\(906\) | −3.63711 | −0.120835 | ||||||||
\(907\) | −37.2166 | −1.23576 | −0.617879 | − | 0.786273i | \(-0.712008\pi\) | ||||
−0.617879 | + | 0.786273i | \(0.712008\pi\) | |||||||
\(908\) | 18.3331 | 0.608406 | ||||||||
\(909\) | 0.0427311 | 0.00141730 | ||||||||
\(910\) | −1.31822 | −0.0436986 | ||||||||
\(911\) | −9.44668 | −0.312982 | −0.156491 | − | 0.987679i | \(-0.550018\pi\) | ||||
−0.156491 | + | 0.987679i | \(0.550018\pi\) | |||||||
\(912\) | −0.833058 | −0.0275853 | ||||||||
\(913\) | −10.7520 | −0.355839 | ||||||||
\(914\) | 13.7377 | 0.454402 | ||||||||
\(915\) | −1.36483 | −0.0451198 | ||||||||
\(916\) | 33.3190 | 1.10089 | ||||||||
\(917\) | −17.3301 | −0.572291 | ||||||||
\(918\) | −1.32232 | −0.0436432 | ||||||||
\(919\) | −32.5338 | −1.07319 | −0.536596 | − | 0.843839i | \(-0.680290\pi\) | ||||
−0.536596 | + | 0.843839i | \(0.680290\pi\) | |||||||
\(920\) | 3.83360 | 0.126390 | ||||||||
\(921\) | −24.2309 | −0.798437 | ||||||||
\(922\) | −11.1345 | −0.366697 | ||||||||
\(923\) | −19.4101 | −0.638891 | ||||||||
\(924\) | 1.57622 | 0.0518538 | ||||||||
\(925\) | −12.3694 | −0.406704 | ||||||||
\(926\) | −13.5360 | −0.444820 | ||||||||
\(927\) | −14.7060 | −0.483008 | ||||||||
\(928\) | −31.7337 | −1.04171 | ||||||||
\(929\) | −28.2779 | −0.927767 | −0.463883 | − | 0.885896i | \(-0.653544\pi\) | ||||
−0.463883 | + | 0.885896i | \(0.653544\pi\) | |||||||
\(930\) | 2.47317 | 0.0810983 | ||||||||
\(931\) | 1.76037 | 0.0576936 | ||||||||
\(932\) | 36.6239 | 1.19966 | ||||||||
\(933\) | 1.91505 | 0.0626961 | ||||||||
\(934\) | −8.00029 | −0.261777 | ||||||||
\(935\) | −4.26573 | −0.139504 | ||||||||
\(936\) | −4.26366 | −0.139362 | ||||||||
\(937\) | 10.7114 | 0.349927 | 0.174964 | − | 0.984575i | \(-0.444019\pi\) | ||||
0.174964 | + | 0.984575i | \(0.444019\pi\) | |||||||
\(938\) | 1.76136 | 0.0575103 | ||||||||
\(939\) | 18.8745 | 0.615946 | ||||||||
\(940\) | −9.29364 | −0.303125 | ||||||||
\(941\) | 1.24454 | 0.0405708 | 0.0202854 | − | 0.999794i | \(-0.493543\pi\) | ||||
0.0202854 | + | 0.999794i | \(0.493543\pi\) | |||||||
\(942\) | 4.20993 | 0.137167 | ||||||||
\(943\) | −12.8279 | −0.417733 | ||||||||
\(944\) | −23.5508 | −0.766513 | ||||||||
\(945\) | −1.18136 | −0.0384298 | ||||||||
\(946\) | −2.44228 | −0.0794053 | ||||||||
\(947\) | −31.5849 | −1.02637 | −0.513186 | − | 0.858277i | \(-0.671535\pi\) | ||||
−0.513186 | + | 0.858277i | \(0.671535\pi\) | |||||||
\(948\) | 10.9905 | 0.356954 | ||||||||
\(949\) | −43.1673 | −1.40127 | ||||||||
\(950\) | 0.373801 | 0.0121277 | ||||||||
\(951\) | −29.4492 | −0.954957 | ||||||||
\(952\) | 4.37342 | 0.141743 | ||||||||
\(953\) | 8.16979 | 0.264645 | 0.132323 | − | 0.991207i | \(-0.457756\pi\) | ||||
0.132323 | + | 0.991207i | \(0.457756\pi\) | |||||||
\(954\) | −2.48067 | −0.0803146 | ||||||||
\(955\) | −10.2813 | −0.332697 | ||||||||
\(956\) | 16.8271 | 0.544228 | ||||||||
\(957\) | 7.07603 | 0.228736 | ||||||||
\(958\) | −16.0248 | −0.517738 | ||||||||
\(959\) | −14.2106 | −0.458885 | ||||||||
\(960\) | 5.48488 | 0.177024 | ||||||||
\(961\) | −12.6556 | −0.408244 | ||||||||
\(962\) | 4.39952 | 0.141846 | ||||||||
\(963\) | 14.8784 | 0.479450 | ||||||||
\(964\) | 8.13834 | 0.262118 | ||||||||
\(965\) | −37.1315 | −1.19531 | ||||||||
\(966\) | 0.636294 | 0.0204724 | ||||||||
\(967\) | −8.87766 | −0.285486 | −0.142743 | − | 0.989760i | \(-0.545592\pi\) | ||||
−0.142743 | + | 0.989760i | \(0.545592\pi\) | |||||||
\(968\) | −1.61659 | −0.0519592 | ||||||||
\(969\) | 0.880205 | 0.0282763 | ||||||||
\(970\) | −7.14751 | −0.229493 | ||||||||
\(971\) | −3.89090 | −0.124865 | −0.0624324 | − | 0.998049i | \(-0.519886\pi\) | ||||
−0.0624324 | + | 0.998049i | \(0.519886\pi\) | |||||||
\(972\) | −1.82100 | −0.0584087 | ||||||||
\(973\) | −5.90660 | −0.189357 | ||||||||
\(974\) | 4.09153 | 0.131101 | ||||||||
\(975\) | −8.27428 | −0.264989 | ||||||||
\(976\) | 2.95806 | 0.0946851 | ||||||||
\(977\) | 52.3391 | 1.67447 | 0.837237 | − | 0.546840i | \(-0.184169\pi\) | ||||
0.837237 | + | 0.546840i | \(0.184169\pi\) | |||||||
\(978\) | 9.30149 | 0.297429 | ||||||||
\(979\) | 13.8901 | 0.443930 | ||||||||
\(980\) | −15.5354 | −0.496260 | ||||||||
\(981\) | −9.34470 | −0.298353 | ||||||||
\(982\) | 4.07533 | 0.130049 | ||||||||
\(983\) | 3.51579 | 0.112136 | 0.0560682 | − | 0.998427i | \(-0.482144\pi\) | ||||
0.0560682 | + | 0.998427i | \(0.482144\pi\) | |||||||
\(984\) | 11.9351 | 0.380477 | ||||||||
\(985\) | −7.23404 | −0.230496 | ||||||||
\(986\) | 9.35681 | 0.297981 | ||||||||
\(987\) | −3.23670 | −0.103025 | ||||||||
\(988\) | 1.35258 | 0.0430312 | ||||||||
\(989\) | 10.0300 | 0.318936 | ||||||||
\(990\) | 0.577432 | 0.0183520 | ||||||||
\(991\) | −59.0461 | −1.87566 | −0.937831 | − | 0.347092i | \(-0.887169\pi\) | ||||
−0.937831 | + | 0.347092i | \(0.887169\pi\) | |||||||
\(992\) | −19.2081 | −0.609857 | ||||||||
\(993\) | −12.7781 | −0.405500 | ||||||||
\(994\) | −2.69509 | −0.0854832 | ||||||||
\(995\) | −35.5793 | −1.12794 | ||||||||
\(996\) | −19.5794 | −0.620398 | ||||||||
\(997\) | 2.67568 | 0.0847396 | 0.0423698 | − | 0.999102i | \(-0.486509\pi\) | ||||
0.0423698 | + | 0.999102i | \(0.486509\pi\) | |||||||
\(998\) | 12.2566 | 0.387976 | ||||||||
\(999\) | 3.94276 | 0.124744 |
(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 | 2013.2.a.a.1.8 | ✓ | 11 | |
3.2 | odd | 2 | 6039.2.a.d.1.4 | 11 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2013.2.a.a.1.8 | ✓ | 11 | 1.1 | even | 1 | trivial | |
6039.2.a.d.1.4 | 11 | 3.2 | odd | 2 |