Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4010,2,Mod(1,4010)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4010, 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("4010.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4010 = 2 \cdot 5 \cdot 401 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4010.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: | \(32.0200112105\) |
Analytic rank: | \(1\) |
Dimension: | \(15\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{15} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{15} - 7 x^{14} - 7 x^{13} + 133 x^{12} - 99 x^{11} - 941 x^{10} + 1290 x^{9} + 3031 x^{8} - 5452 x^{7} - 4098 x^{6} + 9986 x^{5} + 850 x^{4} - 7216 x^{3} + 1688 x^{2} + \cdots - 512 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.11 | ||
Root | \(0.698269\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4010.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | 1.23027 | 0.710297 | 0.355149 | − | 0.934810i | \(-0.384430\pi\) | ||||
0.355149 | + | 0.934810i | \(0.384430\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | −1.23027 | −0.502256 | ||||||||
\(7\) | 3.50539 | 1.32491 | 0.662456 | − | 0.749101i | \(-0.269514\pi\) | ||||
0.662456 | + | 0.749101i | \(0.269514\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | −1.48643 | −0.495478 | ||||||||
\(10\) | 1.00000 | 0.316228 | ||||||||
\(11\) | −1.86568 | −0.562523 | −0.281262 | − | 0.959631i | \(-0.590753\pi\) | ||||
−0.281262 | + | 0.959631i | \(0.590753\pi\) | |||||||
\(12\) | 1.23027 | 0.355149 | ||||||||
\(13\) | −6.67672 | −1.85179 | −0.925895 | − | 0.377781i | \(-0.876687\pi\) | ||||
−0.925895 | + | 0.377781i | \(0.876687\pi\) | |||||||
\(14\) | −3.50539 | −0.936855 | ||||||||
\(15\) | −1.23027 | −0.317655 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 6.33119 | 1.53554 | 0.767770 | − | 0.640726i | \(-0.221367\pi\) | ||||
0.767770 | + | 0.640726i | \(0.221367\pi\) | |||||||
\(18\) | 1.48643 | 0.350356 | ||||||||
\(19\) | 4.59396 | 1.05393 | 0.526963 | − | 0.849888i | \(-0.323330\pi\) | ||||
0.526963 | + | 0.849888i | \(0.323330\pi\) | |||||||
\(20\) | −1.00000 | −0.223607 | ||||||||
\(21\) | 4.31258 | 0.941082 | ||||||||
\(22\) | 1.86568 | 0.397764 | ||||||||
\(23\) | −8.71861 | −1.81796 | −0.908978 | − | 0.416843i | \(-0.863136\pi\) | ||||
−0.908978 | + | 0.416843i | \(0.863136\pi\) | |||||||
\(24\) | −1.23027 | −0.251128 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 6.67672 | 1.30941 | ||||||||
\(27\) | −5.51953 | −1.06223 | ||||||||
\(28\) | 3.50539 | 0.662456 | ||||||||
\(29\) | 9.04127 | 1.67892 | 0.839461 | − | 0.543421i | \(-0.182871\pi\) | ||||
0.839461 | + | 0.543421i | \(0.182871\pi\) | |||||||
\(30\) | 1.23027 | 0.224616 | ||||||||
\(31\) | −8.47326 | −1.52184 | −0.760921 | − | 0.648844i | \(-0.775253\pi\) | ||||
−0.760921 | + | 0.648844i | \(0.775253\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | −2.29529 | −0.399559 | ||||||||
\(34\) | −6.33119 | −1.08579 | ||||||||
\(35\) | −3.50539 | −0.592519 | ||||||||
\(36\) | −1.48643 | −0.247739 | ||||||||
\(37\) | −3.07987 | −0.506327 | −0.253164 | − | 0.967424i | \(-0.581471\pi\) | ||||
−0.253164 | + | 0.967424i | \(0.581471\pi\) | |||||||
\(38\) | −4.59396 | −0.745239 | ||||||||
\(39\) | −8.21418 | −1.31532 | ||||||||
\(40\) | 1.00000 | 0.158114 | ||||||||
\(41\) | −3.18575 | −0.497531 | −0.248765 | − | 0.968564i | \(-0.580025\pi\) | ||||
−0.248765 | + | 0.968564i | \(0.580025\pi\) | |||||||
\(42\) | −4.31258 | −0.665445 | ||||||||
\(43\) | −2.83884 | −0.432919 | −0.216460 | − | 0.976292i | \(-0.569451\pi\) | ||||
−0.216460 | + | 0.976292i | \(0.569451\pi\) | |||||||
\(44\) | −1.86568 | −0.281262 | ||||||||
\(45\) | 1.48643 | 0.221584 | ||||||||
\(46\) | 8.71861 | 1.28549 | ||||||||
\(47\) | 8.62657 | 1.25831 | 0.629157 | − | 0.777278i | \(-0.283400\pi\) | ||||
0.629157 | + | 0.777278i | \(0.283400\pi\) | |||||||
\(48\) | 1.23027 | 0.177574 | ||||||||
\(49\) | 5.28775 | 0.755393 | ||||||||
\(50\) | −1.00000 | −0.141421 | ||||||||
\(51\) | 7.78908 | 1.09069 | ||||||||
\(52\) | −6.67672 | −0.925895 | ||||||||
\(53\) | 6.47876 | 0.889926 | 0.444963 | − | 0.895549i | \(-0.353217\pi\) | ||||
0.444963 | + | 0.895549i | \(0.353217\pi\) | |||||||
\(54\) | 5.51953 | 0.751113 | ||||||||
\(55\) | 1.86568 | 0.251568 | ||||||||
\(56\) | −3.50539 | −0.468427 | ||||||||
\(57\) | 5.65182 | 0.748602 | ||||||||
\(58\) | −9.04127 | −1.18718 | ||||||||
\(59\) | −5.42917 | −0.706818 | −0.353409 | − | 0.935469i | \(-0.614978\pi\) | ||||
−0.353409 | + | 0.935469i | \(0.614978\pi\) | |||||||
\(60\) | −1.23027 | −0.158827 | ||||||||
\(61\) | −4.38698 | −0.561696 | −0.280848 | − | 0.959752i | \(-0.590616\pi\) | ||||
−0.280848 | + | 0.959752i | \(0.590616\pi\) | |||||||
\(62\) | 8.47326 | 1.07611 | ||||||||
\(63\) | −5.21053 | −0.656464 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 6.67672 | 0.828146 | ||||||||
\(66\) | 2.29529 | 0.282531 | ||||||||
\(67\) | 2.27426 | 0.277845 | 0.138923 | − | 0.990303i | \(-0.455636\pi\) | ||||
0.138923 | + | 0.990303i | \(0.455636\pi\) | |||||||
\(68\) | 6.33119 | 0.767770 | ||||||||
\(69\) | −10.7263 | −1.29129 | ||||||||
\(70\) | 3.50539 | 0.418974 | ||||||||
\(71\) | −0.782381 | −0.0928515 | −0.0464258 | − | 0.998922i | \(-0.514783\pi\) | ||||
−0.0464258 | + | 0.998922i | \(0.514783\pi\) | |||||||
\(72\) | 1.48643 | 0.175178 | ||||||||
\(73\) | −1.86149 | −0.217871 | −0.108936 | − | 0.994049i | \(-0.534744\pi\) | ||||
−0.108936 | + | 0.994049i | \(0.534744\pi\) | |||||||
\(74\) | 3.07987 | 0.358027 | ||||||||
\(75\) | 1.23027 | 0.142059 | ||||||||
\(76\) | 4.59396 | 0.526963 | ||||||||
\(77\) | −6.53993 | −0.745294 | ||||||||
\(78\) | 8.21418 | 0.930073 | ||||||||
\(79\) | −8.08705 | −0.909864 | −0.454932 | − | 0.890526i | \(-0.650337\pi\) | ||||
−0.454932 | + | 0.890526i | \(0.650337\pi\) | |||||||
\(80\) | −1.00000 | −0.111803 | ||||||||
\(81\) | −2.33122 | −0.259024 | ||||||||
\(82\) | 3.18575 | 0.351808 | ||||||||
\(83\) | −15.8885 | −1.74399 | −0.871994 | − | 0.489516i | \(-0.837173\pi\) | ||||
−0.871994 | + | 0.489516i | \(0.837173\pi\) | |||||||
\(84\) | 4.31258 | 0.470541 | ||||||||
\(85\) | −6.33119 | −0.686714 | ||||||||
\(86\) | 2.83884 | 0.306120 | ||||||||
\(87\) | 11.1232 | 1.19253 | ||||||||
\(88\) | 1.86568 | 0.198882 | ||||||||
\(89\) | −11.8551 | −1.25664 | −0.628321 | − | 0.777954i | \(-0.716257\pi\) | ||||
−0.628321 | + | 0.777954i | \(0.716257\pi\) | |||||||
\(90\) | −1.48643 | −0.156684 | ||||||||
\(91\) | −23.4045 | −2.45346 | ||||||||
\(92\) | −8.71861 | −0.908978 | ||||||||
\(93\) | −10.4244 | −1.08096 | ||||||||
\(94\) | −8.62657 | −0.889762 | ||||||||
\(95\) | −4.59396 | −0.471330 | ||||||||
\(96\) | −1.23027 | −0.125564 | ||||||||
\(97\) | −15.0823 | −1.53137 | −0.765686 | − | 0.643215i | \(-0.777600\pi\) | ||||
−0.765686 | + | 0.643215i | \(0.777600\pi\) | |||||||
\(98\) | −5.28775 | −0.534144 | ||||||||
\(99\) | 2.77321 | 0.278718 | ||||||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | 7.22136 | 0.718553 | 0.359276 | − | 0.933231i | \(-0.383024\pi\) | ||||
0.359276 | + | 0.933231i | \(0.383024\pi\) | |||||||
\(102\) | −7.78908 | −0.771234 | ||||||||
\(103\) | −7.70292 | −0.758991 | −0.379496 | − | 0.925194i | \(-0.623902\pi\) | ||||
−0.379496 | + | 0.925194i | \(0.623902\pi\) | |||||||
\(104\) | 6.67672 | 0.654707 | ||||||||
\(105\) | −4.31258 | −0.420865 | ||||||||
\(106\) | −6.47876 | −0.629273 | ||||||||
\(107\) | −0.576866 | −0.0557678 | −0.0278839 | − | 0.999611i | \(-0.508877\pi\) | ||||
−0.0278839 | + | 0.999611i | \(0.508877\pi\) | |||||||
\(108\) | −5.51953 | −0.531117 | ||||||||
\(109\) | −20.1187 | −1.92703 | −0.963513 | − | 0.267663i | \(-0.913749\pi\) | ||||
−0.963513 | + | 0.267663i | \(0.913749\pi\) | |||||||
\(110\) | −1.86568 | −0.177885 | ||||||||
\(111\) | −3.78907 | −0.359643 | ||||||||
\(112\) | 3.50539 | 0.331228 | ||||||||
\(113\) | 7.13357 | 0.671070 | 0.335535 | − | 0.942028i | \(-0.391083\pi\) | ||||
0.335535 | + | 0.942028i | \(0.391083\pi\) | |||||||
\(114\) | −5.65182 | −0.529341 | ||||||||
\(115\) | 8.71861 | 0.813015 | ||||||||
\(116\) | 9.04127 | 0.839461 | ||||||||
\(117\) | 9.92450 | 0.917520 | ||||||||
\(118\) | 5.42917 | 0.499796 | ||||||||
\(119\) | 22.1933 | 2.03445 | ||||||||
\(120\) | 1.23027 | 0.112308 | ||||||||
\(121\) | −7.51924 | −0.683568 | ||||||||
\(122\) | 4.38698 | 0.397179 | ||||||||
\(123\) | −3.91934 | −0.353395 | ||||||||
\(124\) | −8.47326 | −0.760921 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 5.21053 | 0.464190 | ||||||||
\(127\) | 3.36741 | 0.298809 | 0.149405 | − | 0.988776i | \(-0.452264\pi\) | ||||
0.149405 | + | 0.988776i | \(0.452264\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −3.49254 | −0.307501 | ||||||||
\(130\) | −6.67672 | −0.585587 | ||||||||
\(131\) | 2.27447 | 0.198722 | 0.0993609 | − | 0.995051i | \(-0.468320\pi\) | ||||
0.0993609 | + | 0.995051i | \(0.468320\pi\) | |||||||
\(132\) | −2.29529 | −0.199779 | ||||||||
\(133\) | 16.1036 | 1.39636 | ||||||||
\(134\) | −2.27426 | −0.196466 | ||||||||
\(135\) | 5.51953 | 0.475045 | ||||||||
\(136\) | −6.33119 | −0.542895 | ||||||||
\(137\) | −1.03381 | −0.0883241 | −0.0441621 | − | 0.999024i | \(-0.514062\pi\) | ||||
−0.0441621 | + | 0.999024i | \(0.514062\pi\) | |||||||
\(138\) | 10.7263 | 0.913080 | ||||||||
\(139\) | −1.19908 | −0.101705 | −0.0508524 | − | 0.998706i | \(-0.516194\pi\) | ||||
−0.0508524 | + | 0.998706i | \(0.516194\pi\) | |||||||
\(140\) | −3.50539 | −0.296259 | ||||||||
\(141\) | 10.6130 | 0.893777 | ||||||||
\(142\) | 0.782381 | 0.0656559 | ||||||||
\(143\) | 12.4566 | 1.04167 | ||||||||
\(144\) | −1.48643 | −0.123869 | ||||||||
\(145\) | −9.04127 | −0.750836 | ||||||||
\(146\) | 1.86149 | 0.154058 | ||||||||
\(147\) | 6.50537 | 0.536554 | ||||||||
\(148\) | −3.07987 | −0.253164 | ||||||||
\(149\) | 3.22469 | 0.264177 | 0.132088 | − | 0.991238i | \(-0.457832\pi\) | ||||
0.132088 | + | 0.991238i | \(0.457832\pi\) | |||||||
\(150\) | −1.23027 | −0.100451 | ||||||||
\(151\) | −8.09195 | −0.658514 | −0.329257 | − | 0.944240i | \(-0.606798\pi\) | ||||
−0.329257 | + | 0.944240i | \(0.606798\pi\) | |||||||
\(152\) | −4.59396 | −0.372619 | ||||||||
\(153\) | −9.41089 | −0.760825 | ||||||||
\(154\) | 6.53993 | 0.527003 | ||||||||
\(155\) | 8.47326 | 0.680589 | ||||||||
\(156\) | −8.21418 | −0.657661 | ||||||||
\(157\) | 9.24673 | 0.737970 | 0.368985 | − | 0.929435i | \(-0.379705\pi\) | ||||
0.368985 | + | 0.929435i | \(0.379705\pi\) | |||||||
\(158\) | 8.08705 | 0.643371 | ||||||||
\(159\) | 7.97063 | 0.632112 | ||||||||
\(160\) | 1.00000 | 0.0790569 | ||||||||
\(161\) | −30.5621 | −2.40863 | ||||||||
\(162\) | 2.33122 | 0.183158 | ||||||||
\(163\) | −3.93017 | −0.307834 | −0.153917 | − | 0.988084i | \(-0.549189\pi\) | ||||
−0.153917 | + | 0.988084i | \(0.549189\pi\) | |||||||
\(164\) | −3.18575 | −0.248765 | ||||||||
\(165\) | 2.29529 | 0.178688 | ||||||||
\(166\) | 15.8885 | 1.23319 | ||||||||
\(167\) | 17.6116 | 1.36283 | 0.681415 | − | 0.731898i | \(-0.261365\pi\) | ||||
0.681415 | + | 0.731898i | \(0.261365\pi\) | |||||||
\(168\) | −4.31258 | −0.332723 | ||||||||
\(169\) | 31.5786 | 2.42913 | ||||||||
\(170\) | 6.33119 | 0.485580 | ||||||||
\(171\) | −6.82861 | −0.522197 | ||||||||
\(172\) | −2.83884 | −0.216460 | ||||||||
\(173\) | −8.62140 | −0.655473 | −0.327736 | − | 0.944769i | \(-0.606286\pi\) | ||||
−0.327736 | + | 0.944769i | \(0.606286\pi\) | |||||||
\(174\) | −11.1232 | −0.843248 | ||||||||
\(175\) | 3.50539 | 0.264983 | ||||||||
\(176\) | −1.86568 | −0.140631 | ||||||||
\(177\) | −6.67935 | −0.502051 | ||||||||
\(178\) | 11.8551 | 0.888580 | ||||||||
\(179\) | −12.5525 | −0.938216 | −0.469108 | − | 0.883141i | \(-0.655424\pi\) | ||||
−0.469108 | + | 0.883141i | \(0.655424\pi\) | |||||||
\(180\) | 1.48643 | 0.110792 | ||||||||
\(181\) | 15.6152 | 1.16067 | 0.580334 | − | 0.814379i | \(-0.302922\pi\) | ||||
0.580334 | + | 0.814379i | \(0.302922\pi\) | |||||||
\(182\) | 23.4045 | 1.73486 | ||||||||
\(183\) | −5.39718 | −0.398971 | ||||||||
\(184\) | 8.71861 | 0.642745 | ||||||||
\(185\) | 3.07987 | 0.226436 | ||||||||
\(186\) | 10.4244 | 0.764355 | ||||||||
\(187\) | −11.8120 | −0.863776 | ||||||||
\(188\) | 8.62657 | 0.629157 | ||||||||
\(189\) | −19.3481 | −1.40737 | ||||||||
\(190\) | 4.59396 | 0.333281 | ||||||||
\(191\) | 13.2113 | 0.955940 | 0.477970 | − | 0.878376i | \(-0.341373\pi\) | ||||
0.477970 | + | 0.878376i | \(0.341373\pi\) | |||||||
\(192\) | 1.23027 | 0.0887872 | ||||||||
\(193\) | −21.5214 | −1.54914 | −0.774572 | − | 0.632485i | \(-0.782035\pi\) | ||||
−0.774572 | + | 0.632485i | \(0.782035\pi\) | |||||||
\(194\) | 15.0823 | 1.08284 | ||||||||
\(195\) | 8.21418 | 0.588230 | ||||||||
\(196\) | 5.28775 | 0.377697 | ||||||||
\(197\) | −13.5788 | −0.967452 | −0.483726 | − | 0.875219i | \(-0.660717\pi\) | ||||
−0.483726 | + | 0.875219i | \(0.660717\pi\) | |||||||
\(198\) | −2.77321 | −0.197083 | ||||||||
\(199\) | −9.76276 | −0.692064 | −0.346032 | − | 0.938223i | \(-0.612471\pi\) | ||||
−0.346032 | + | 0.938223i | \(0.612471\pi\) | |||||||
\(200\) | −1.00000 | −0.0707107 | ||||||||
\(201\) | 2.79796 | 0.197353 | ||||||||
\(202\) | −7.22136 | −0.508093 | ||||||||
\(203\) | 31.6932 | 2.22442 | ||||||||
\(204\) | 7.78908 | 0.545345 | ||||||||
\(205\) | 3.18575 | 0.222503 | ||||||||
\(206\) | 7.70292 | 0.536688 | ||||||||
\(207\) | 12.9596 | 0.900757 | ||||||||
\(208\) | −6.67672 | −0.462948 | ||||||||
\(209\) | −8.57085 | −0.592858 | ||||||||
\(210\) | 4.31258 | 0.297596 | ||||||||
\(211\) | 0.164687 | 0.0113375 | 0.00566875 | − | 0.999984i | \(-0.498196\pi\) | ||||
0.00566875 | + | 0.999984i | \(0.498196\pi\) | |||||||
\(212\) | 6.47876 | 0.444963 | ||||||||
\(213\) | −0.962541 | −0.0659522 | ||||||||
\(214\) | 0.576866 | 0.0394338 | ||||||||
\(215\) | 2.83884 | 0.193607 | ||||||||
\(216\) | 5.51953 | 0.375556 | ||||||||
\(217\) | −29.7021 | −2.01631 | ||||||||
\(218\) | 20.1187 | 1.36261 | ||||||||
\(219\) | −2.29014 | −0.154753 | ||||||||
\(220\) | 1.86568 | 0.125784 | ||||||||
\(221\) | −42.2716 | −2.84350 | ||||||||
\(222\) | 3.78907 | 0.254306 | ||||||||
\(223\) | 22.9746 | 1.53849 | 0.769247 | − | 0.638952i | \(-0.220632\pi\) | ||||
0.769247 | + | 0.638952i | \(0.220632\pi\) | |||||||
\(224\) | −3.50539 | −0.234214 | ||||||||
\(225\) | −1.48643 | −0.0990955 | ||||||||
\(226\) | −7.13357 | −0.474518 | ||||||||
\(227\) | −9.13036 | −0.606003 | −0.303002 | − | 0.952990i | \(-0.597989\pi\) | ||||
−0.303002 | + | 0.952990i | \(0.597989\pi\) | |||||||
\(228\) | 5.65182 | 0.374301 | ||||||||
\(229\) | 15.1182 | 0.999042 | 0.499521 | − | 0.866302i | \(-0.333509\pi\) | ||||
0.499521 | + | 0.866302i | \(0.333509\pi\) | |||||||
\(230\) | −8.71861 | −0.574888 | ||||||||
\(231\) | −8.04589 | −0.529380 | ||||||||
\(232\) | −9.04127 | −0.593588 | ||||||||
\(233\) | −7.18355 | −0.470610 | −0.235305 | − | 0.971922i | \(-0.575609\pi\) | ||||
−0.235305 | + | 0.971922i | \(0.575609\pi\) | |||||||
\(234\) | −9.92450 | −0.648785 | ||||||||
\(235\) | −8.62657 | −0.562735 | ||||||||
\(236\) | −5.42917 | −0.353409 | ||||||||
\(237\) | −9.94927 | −0.646274 | ||||||||
\(238\) | −22.1933 | −1.43858 | ||||||||
\(239\) | 9.40800 | 0.608553 | 0.304276 | − | 0.952584i | \(-0.401585\pi\) | ||||
0.304276 | + | 0.952584i | \(0.401585\pi\) | |||||||
\(240\) | −1.23027 | −0.0794137 | ||||||||
\(241\) | −18.3916 | −1.18471 | −0.592355 | − | 0.805677i | \(-0.701802\pi\) | ||||
−0.592355 | + | 0.805677i | \(0.701802\pi\) | |||||||
\(242\) | 7.51924 | 0.483355 | ||||||||
\(243\) | 13.6906 | 0.878249 | ||||||||
\(244\) | −4.38698 | −0.280848 | ||||||||
\(245\) | −5.28775 | −0.337822 | ||||||||
\(246\) | 3.91934 | 0.249888 | ||||||||
\(247\) | −30.6726 | −1.95165 | ||||||||
\(248\) | 8.47326 | 0.538053 | ||||||||
\(249\) | −19.5472 | −1.23875 | ||||||||
\(250\) | 1.00000 | 0.0632456 | ||||||||
\(251\) | −0.0298497 | −0.00188409 | −0.000942047 | − | 1.00000i | \(-0.500300\pi\) | ||||
−0.000942047 | 1.00000i | \(0.500300\pi\) | ||||||||
\(252\) | −5.21053 | −0.328232 | ||||||||
\(253\) | 16.2661 | 1.02264 | ||||||||
\(254\) | −3.36741 | −0.211290 | ||||||||
\(255\) | −7.78908 | −0.487771 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −17.3843 | −1.08440 | −0.542201 | − | 0.840249i | \(-0.682409\pi\) | ||||
−0.542201 | + | 0.840249i | \(0.682409\pi\) | |||||||
\(258\) | 3.49254 | 0.217436 | ||||||||
\(259\) | −10.7961 | −0.670839 | ||||||||
\(260\) | 6.67672 | 0.414073 | ||||||||
\(261\) | −13.4392 | −0.831868 | ||||||||
\(262\) | −2.27447 | −0.140517 | ||||||||
\(263\) | −1.69511 | −0.104525 | −0.0522625 | − | 0.998633i | \(-0.516643\pi\) | ||||
−0.0522625 | + | 0.998633i | \(0.516643\pi\) | |||||||
\(264\) | 2.29529 | 0.141265 | ||||||||
\(265\) | −6.47876 | −0.397987 | ||||||||
\(266\) | −16.1036 | −0.987376 | ||||||||
\(267\) | −14.5850 | −0.892589 | ||||||||
\(268\) | 2.27426 | 0.138923 | ||||||||
\(269\) | 26.8529 | 1.63725 | 0.818626 | − | 0.574327i | \(-0.194736\pi\) | ||||
0.818626 | + | 0.574327i | \(0.194736\pi\) | |||||||
\(270\) | −5.51953 | −0.335908 | ||||||||
\(271\) | 24.6974 | 1.50026 | 0.750132 | − | 0.661289i | \(-0.229990\pi\) | ||||
0.750132 | + | 0.661289i | \(0.229990\pi\) | |||||||
\(272\) | 6.33119 | 0.383885 | ||||||||
\(273\) | −28.7939 | −1.74269 | ||||||||
\(274\) | 1.03381 | 0.0624546 | ||||||||
\(275\) | −1.86568 | −0.112505 | ||||||||
\(276\) | −10.7263 | −0.645645 | ||||||||
\(277\) | −25.3607 | −1.52378 | −0.761888 | − | 0.647708i | \(-0.775727\pi\) | ||||
−0.761888 | + | 0.647708i | \(0.775727\pi\) | |||||||
\(278\) | 1.19908 | 0.0719162 | ||||||||
\(279\) | 12.5949 | 0.754039 | ||||||||
\(280\) | 3.50539 | 0.209487 | ||||||||
\(281\) | 12.4409 | 0.742160 | 0.371080 | − | 0.928601i | \(-0.378988\pi\) | ||||
0.371080 | + | 0.928601i | \(0.378988\pi\) | |||||||
\(282\) | −10.6130 | −0.631996 | ||||||||
\(283\) | −16.5614 | −0.984470 | −0.492235 | − | 0.870462i | \(-0.663820\pi\) | ||||
−0.492235 | + | 0.870462i | \(0.663820\pi\) | |||||||
\(284\) | −0.782381 | −0.0464258 | ||||||||
\(285\) | −5.65182 | −0.334785 | ||||||||
\(286\) | −12.4566 | −0.736575 | ||||||||
\(287\) | −11.1673 | −0.659185 | ||||||||
\(288\) | 1.48643 | 0.0875889 | ||||||||
\(289\) | 23.0840 | 1.35788 | ||||||||
\(290\) | 9.04127 | 0.530922 | ||||||||
\(291\) | −18.5553 | −1.08773 | ||||||||
\(292\) | −1.86149 | −0.108936 | ||||||||
\(293\) | 3.84987 | 0.224912 | 0.112456 | − | 0.993657i | \(-0.464128\pi\) | ||||
0.112456 | + | 0.993657i | \(0.464128\pi\) | |||||||
\(294\) | −6.50537 | −0.379401 | ||||||||
\(295\) | 5.42917 | 0.316099 | ||||||||
\(296\) | 3.07987 | 0.179014 | ||||||||
\(297\) | 10.2977 | 0.597531 | ||||||||
\(298\) | −3.22469 | −0.186801 | ||||||||
\(299\) | 58.2118 | 3.36647 | ||||||||
\(300\) | 1.23027 | 0.0710297 | ||||||||
\(301\) | −9.95124 | −0.573580 | ||||||||
\(302\) | 8.09195 | 0.465639 | ||||||||
\(303\) | 8.88424 | 0.510386 | ||||||||
\(304\) | 4.59396 | 0.263482 | ||||||||
\(305\) | 4.38698 | 0.251198 | ||||||||
\(306\) | 9.41089 | 0.537985 | ||||||||
\(307\) | −21.1164 | −1.20517 | −0.602587 | − | 0.798053i | \(-0.705863\pi\) | ||||
−0.602587 | + | 0.798053i | \(0.705863\pi\) | |||||||
\(308\) | −6.53993 | −0.372647 | ||||||||
\(309\) | −9.47668 | −0.539110 | ||||||||
\(310\) | −8.47326 | −0.481249 | ||||||||
\(311\) | 17.9731 | 1.01916 | 0.509581 | − | 0.860423i | \(-0.329801\pi\) | ||||
0.509581 | + | 0.860423i | \(0.329801\pi\) | |||||||
\(312\) | 8.21418 | 0.465036 | ||||||||
\(313\) | 26.9382 | 1.52264 | 0.761319 | − | 0.648377i | \(-0.224552\pi\) | ||||
0.761319 | + | 0.648377i | \(0.224552\pi\) | |||||||
\(314\) | −9.24673 | −0.521823 | ||||||||
\(315\) | 5.21053 | 0.293580 | ||||||||
\(316\) | −8.08705 | −0.454932 | ||||||||
\(317\) | 8.62087 | 0.484196 | 0.242098 | − | 0.970252i | \(-0.422164\pi\) | ||||
0.242098 | + | 0.970252i | \(0.422164\pi\) | |||||||
\(318\) | −7.97063 | −0.446971 | ||||||||
\(319\) | −16.8681 | −0.944432 | ||||||||
\(320\) | −1.00000 | −0.0559017 | ||||||||
\(321\) | −0.709702 | −0.0396117 | ||||||||
\(322\) | 30.5621 | 1.70316 | ||||||||
\(323\) | 29.0852 | 1.61835 | ||||||||
\(324\) | −2.33122 | −0.129512 | ||||||||
\(325\) | −6.67672 | −0.370358 | ||||||||
\(326\) | 3.93017 | 0.217672 | ||||||||
\(327\) | −24.7515 | −1.36876 | ||||||||
\(328\) | 3.18575 | 0.175904 | ||||||||
\(329\) | 30.2395 | 1.66716 | ||||||||
\(330\) | −2.29529 | −0.126352 | ||||||||
\(331\) | −19.3529 | −1.06373 | −0.531866 | − | 0.846828i | \(-0.678509\pi\) | ||||
−0.531866 | + | 0.846828i | \(0.678509\pi\) | |||||||
\(332\) | −15.8885 | −0.871994 | ||||||||
\(333\) | 4.57802 | 0.250874 | ||||||||
\(334\) | −17.6116 | −0.963666 | ||||||||
\(335\) | −2.27426 | −0.124256 | ||||||||
\(336\) | 4.31258 | 0.235270 | ||||||||
\(337\) | −22.5312 | −1.22735 | −0.613675 | − | 0.789559i | \(-0.710310\pi\) | ||||
−0.613675 | + | 0.789559i | \(0.710310\pi\) | |||||||
\(338\) | −31.5786 | −1.71765 | ||||||||
\(339\) | 8.77623 | 0.476659 | ||||||||
\(340\) | −6.33119 | −0.343357 | ||||||||
\(341\) | 15.8084 | 0.856072 | ||||||||
\(342\) | 6.82861 | 0.369249 | ||||||||
\(343\) | −6.00209 | −0.324083 | ||||||||
\(344\) | 2.83884 | 0.153060 | ||||||||
\(345\) | 10.7263 | 0.577482 | ||||||||
\(346\) | 8.62140 | 0.463489 | ||||||||
\(347\) | −8.34036 | −0.447734 | −0.223867 | − | 0.974620i | \(-0.571868\pi\) | ||||
−0.223867 | + | 0.974620i | \(0.571868\pi\) | |||||||
\(348\) | 11.1232 | 0.596267 | ||||||||
\(349\) | 2.91112 | 0.155828 | 0.0779142 | − | 0.996960i | \(-0.475174\pi\) | ||||
0.0779142 | + | 0.996960i | \(0.475174\pi\) | |||||||
\(350\) | −3.50539 | −0.187371 | ||||||||
\(351\) | 36.8524 | 1.96703 | ||||||||
\(352\) | 1.86568 | 0.0994410 | ||||||||
\(353\) | −31.4044 | −1.67149 | −0.835745 | − | 0.549118i | \(-0.814964\pi\) | ||||
−0.835745 | + | 0.549118i | \(0.814964\pi\) | |||||||
\(354\) | 6.67935 | 0.355004 | ||||||||
\(355\) | 0.782381 | 0.0415245 | ||||||||
\(356\) | −11.8551 | −0.628321 | ||||||||
\(357\) | 27.3038 | 1.44507 | ||||||||
\(358\) | 12.5525 | 0.663419 | ||||||||
\(359\) | −15.7995 | −0.833865 | −0.416933 | − | 0.908937i | \(-0.636895\pi\) | ||||
−0.416933 | + | 0.908937i | \(0.636895\pi\) | |||||||
\(360\) | −1.48643 | −0.0783419 | ||||||||
\(361\) | 2.10448 | 0.110762 | ||||||||
\(362\) | −15.6152 | −0.820716 | ||||||||
\(363\) | −9.25071 | −0.485536 | ||||||||
\(364\) | −23.4045 | −1.22673 | ||||||||
\(365\) | 1.86149 | 0.0974350 | ||||||||
\(366\) | 5.39718 | 0.282115 | ||||||||
\(367\) | −10.9877 | −0.573554 | −0.286777 | − | 0.957997i | \(-0.592584\pi\) | ||||
−0.286777 | + | 0.957997i | \(0.592584\pi\) | |||||||
\(368\) | −8.71861 | −0.454489 | ||||||||
\(369\) | 4.73541 | 0.246515 | ||||||||
\(370\) | −3.07987 | −0.160115 | ||||||||
\(371\) | 22.7106 | 1.17907 | ||||||||
\(372\) | −10.4244 | −0.540480 | ||||||||
\(373\) | −11.7560 | −0.608702 | −0.304351 | − | 0.952560i | \(-0.598440\pi\) | ||||
−0.304351 | + | 0.952560i | \(0.598440\pi\) | |||||||
\(374\) | 11.8120 | 0.610782 | ||||||||
\(375\) | −1.23027 | −0.0635309 | ||||||||
\(376\) | −8.62657 | −0.444881 | ||||||||
\(377\) | −60.3661 | −3.10901 | ||||||||
\(378\) | 19.3481 | 0.995159 | ||||||||
\(379\) | −8.20803 | −0.421618 | −0.210809 | − | 0.977527i | \(-0.567610\pi\) | ||||
−0.210809 | + | 0.977527i | \(0.567610\pi\) | |||||||
\(380\) | −4.59396 | −0.235665 | ||||||||
\(381\) | 4.14283 | 0.212243 | ||||||||
\(382\) | −13.2113 | −0.675951 | ||||||||
\(383\) | 6.79756 | 0.347339 | 0.173670 | − | 0.984804i | \(-0.444438\pi\) | ||||
0.173670 | + | 0.984804i | \(0.444438\pi\) | |||||||
\(384\) | −1.23027 | −0.0627820 | ||||||||
\(385\) | 6.53993 | 0.333306 | ||||||||
\(386\) | 21.5214 | 1.09541 | ||||||||
\(387\) | 4.21975 | 0.214502 | ||||||||
\(388\) | −15.0823 | −0.765686 | ||||||||
\(389\) | −15.0416 | −0.762641 | −0.381320 | − | 0.924443i | \(-0.624531\pi\) | ||||
−0.381320 | + | 0.924443i | \(0.624531\pi\) | |||||||
\(390\) | −8.21418 | −0.415941 | ||||||||
\(391\) | −55.1992 | −2.79154 | ||||||||
\(392\) | −5.28775 | −0.267072 | ||||||||
\(393\) | 2.79822 | 0.141152 | ||||||||
\(394\) | 13.5788 | 0.684092 | ||||||||
\(395\) | 8.08705 | 0.406904 | ||||||||
\(396\) | 2.77321 | 0.139359 | ||||||||
\(397\) | −15.9858 | −0.802307 | −0.401153 | − | 0.916011i | \(-0.631391\pi\) | ||||
−0.401153 | + | 0.916011i | \(0.631391\pi\) | |||||||
\(398\) | 9.76276 | 0.489363 | ||||||||
\(399\) | 19.8118 | 0.991832 | ||||||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | −1.00000 | −0.0499376 | ||||||||
\(402\) | −2.79796 | −0.139550 | ||||||||
\(403\) | 56.5736 | 2.81813 | ||||||||
\(404\) | 7.22136 | 0.359276 | ||||||||
\(405\) | 2.33122 | 0.115839 | ||||||||
\(406\) | −31.6932 | −1.57291 | ||||||||
\(407\) | 5.74604 | 0.284821 | ||||||||
\(408\) | −7.78908 | −0.385617 | ||||||||
\(409\) | 32.7944 | 1.62158 | 0.810790 | − | 0.585337i | \(-0.199038\pi\) | ||||
0.810790 | + | 0.585337i | \(0.199038\pi\) | |||||||
\(410\) | −3.18575 | −0.157333 | ||||||||
\(411\) | −1.27186 | −0.0627364 | ||||||||
\(412\) | −7.70292 | −0.379496 | ||||||||
\(413\) | −19.0314 | −0.936472 | ||||||||
\(414\) | −12.9596 | −0.636931 | ||||||||
\(415\) | 15.8885 | 0.779935 | ||||||||
\(416\) | 6.67672 | 0.327353 | ||||||||
\(417\) | −1.47520 | −0.0722407 | ||||||||
\(418\) | 8.57085 | 0.419214 | ||||||||
\(419\) | −20.1649 | −0.985122 | −0.492561 | − | 0.870278i | \(-0.663939\pi\) | ||||
−0.492561 | + | 0.870278i | \(0.663939\pi\) | |||||||
\(420\) | −4.31258 | −0.210432 | ||||||||
\(421\) | −25.9559 | −1.26501 | −0.632507 | − | 0.774554i | \(-0.717974\pi\) | ||||
−0.632507 | + | 0.774554i | \(0.717974\pi\) | |||||||
\(422\) | −0.164687 | −0.00801682 | ||||||||
\(423\) | −12.8228 | −0.623466 | ||||||||
\(424\) | −6.47876 | −0.314636 | ||||||||
\(425\) | 6.33119 | 0.307108 | ||||||||
\(426\) | 0.962541 | 0.0466352 | ||||||||
\(427\) | −15.3781 | −0.744198 | ||||||||
\(428\) | −0.576866 | −0.0278839 | ||||||||
\(429\) | 15.3250 | 0.739899 | ||||||||
\(430\) | −2.83884 | −0.136901 | ||||||||
\(431\) | 11.7637 | 0.566640 | 0.283320 | − | 0.959025i | \(-0.408564\pi\) | ||||
0.283320 | + | 0.959025i | \(0.408564\pi\) | |||||||
\(432\) | −5.51953 | −0.265558 | ||||||||
\(433\) | −19.7689 | −0.950033 | −0.475017 | − | 0.879977i | \(-0.657558\pi\) | ||||
−0.475017 | + | 0.879977i | \(0.657558\pi\) | |||||||
\(434\) | 29.7021 | 1.42575 | ||||||||
\(435\) | −11.1232 | −0.533317 | ||||||||
\(436\) | −20.1187 | −0.963513 | ||||||||
\(437\) | −40.0530 | −1.91599 | ||||||||
\(438\) | 2.29014 | 0.109427 | ||||||||
\(439\) | −1.15129 | −0.0549481 | −0.0274741 | − | 0.999623i | \(-0.508746\pi\) | ||||
−0.0274741 | + | 0.999623i | \(0.508746\pi\) | |||||||
\(440\) | −1.86568 | −0.0889427 | ||||||||
\(441\) | −7.85989 | −0.374280 | ||||||||
\(442\) | 42.2716 | 2.01066 | ||||||||
\(443\) | 24.9362 | 1.18475 | 0.592377 | − | 0.805661i | \(-0.298190\pi\) | ||||
0.592377 | + | 0.805661i | \(0.298190\pi\) | |||||||
\(444\) | −3.78907 | −0.179821 | ||||||||
\(445\) | 11.8551 | 0.561987 | ||||||||
\(446\) | −22.9746 | −1.08788 | ||||||||
\(447\) | 3.96724 | 0.187644 | ||||||||
\(448\) | 3.50539 | 0.165614 | ||||||||
\(449\) | 4.63346 | 0.218666 | 0.109333 | − | 0.994005i | \(-0.465128\pi\) | ||||
0.109333 | + | 0.994005i | \(0.465128\pi\) | |||||||
\(450\) | 1.48643 | 0.0700711 | ||||||||
\(451\) | 5.94359 | 0.279873 | ||||||||
\(452\) | 7.13357 | 0.335535 | ||||||||
\(453\) | −9.95530 | −0.467741 | ||||||||
\(454\) | 9.13036 | 0.428509 | ||||||||
\(455\) | 23.4045 | 1.09722 | ||||||||
\(456\) | −5.65182 | −0.264671 | ||||||||
\(457\) | 39.7724 | 1.86048 | 0.930238 | − | 0.366956i | \(-0.119600\pi\) | ||||
0.930238 | + | 0.366956i | \(0.119600\pi\) | |||||||
\(458\) | −15.1182 | −0.706429 | ||||||||
\(459\) | −34.9452 | −1.63110 | ||||||||
\(460\) | 8.71861 | 0.406508 | ||||||||
\(461\) | 17.5872 | 0.819117 | 0.409559 | − | 0.912284i | \(-0.365683\pi\) | ||||
0.409559 | + | 0.912284i | \(0.365683\pi\) | |||||||
\(462\) | 8.04589 | 0.374329 | ||||||||
\(463\) | 7.95209 | 0.369565 | 0.184783 | − | 0.982779i | \(-0.440842\pi\) | ||||
0.184783 | + | 0.982779i | \(0.440842\pi\) | |||||||
\(464\) | 9.04127 | 0.419730 | ||||||||
\(465\) | 10.4244 | 0.483420 | ||||||||
\(466\) | 7.18355 | 0.332772 | ||||||||
\(467\) | −19.3310 | −0.894534 | −0.447267 | − | 0.894401i | \(-0.647603\pi\) | ||||
−0.447267 | + | 0.894401i | \(0.647603\pi\) | |||||||
\(468\) | 9.92450 | 0.458760 | ||||||||
\(469\) | 7.97217 | 0.368121 | ||||||||
\(470\) | 8.62657 | 0.397914 | ||||||||
\(471\) | 11.3760 | 0.524178 | ||||||||
\(472\) | 5.42917 | 0.249898 | ||||||||
\(473\) | 5.29636 | 0.243527 | ||||||||
\(474\) | 9.94927 | 0.456985 | ||||||||
\(475\) | 4.59396 | 0.210785 | ||||||||
\(476\) | 22.1933 | 1.01723 | ||||||||
\(477\) | −9.63024 | −0.440939 | ||||||||
\(478\) | −9.40800 | −0.430312 | ||||||||
\(479\) | 23.6652 | 1.08129 | 0.540645 | − | 0.841251i | \(-0.318180\pi\) | ||||
0.540645 | + | 0.841251i | \(0.318180\pi\) | |||||||
\(480\) | 1.23027 | 0.0561539 | ||||||||
\(481\) | 20.5634 | 0.937611 | ||||||||
\(482\) | 18.3916 | 0.837716 | ||||||||
\(483\) | −37.5997 | −1.71085 | ||||||||
\(484\) | −7.51924 | −0.341784 | ||||||||
\(485\) | 15.0823 | 0.684850 | ||||||||
\(486\) | −13.6906 | −0.621016 | ||||||||
\(487\) | −23.8703 | −1.08167 | −0.540833 | − | 0.841130i | \(-0.681891\pi\) | ||||
−0.540833 | + | 0.841130i | \(0.681891\pi\) | |||||||
\(488\) | 4.38698 | 0.198589 | ||||||||
\(489\) | −4.83517 | −0.218654 | ||||||||
\(490\) | 5.28775 | 0.238876 | ||||||||
\(491\) | 0.223451 | 0.0100842 | 0.00504209 | − | 0.999987i | \(-0.498395\pi\) | ||||
0.00504209 | + | 0.999987i | \(0.498395\pi\) | |||||||
\(492\) | −3.91934 | −0.176697 | ||||||||
\(493\) | 57.2420 | 2.57805 | ||||||||
\(494\) | 30.6726 | 1.38003 | ||||||||
\(495\) | −2.77321 | −0.124646 | ||||||||
\(496\) | −8.47326 | −0.380461 | ||||||||
\(497\) | −2.74255 | −0.123020 | ||||||||
\(498\) | 19.5472 | 0.875929 | ||||||||
\(499\) | −6.97246 | −0.312130 | −0.156065 | − | 0.987747i | \(-0.549881\pi\) | ||||
−0.156065 | + | 0.987747i | \(0.549881\pi\) | |||||||
\(500\) | −1.00000 | −0.0447214 | ||||||||
\(501\) | 21.6671 | 0.968014 | ||||||||
\(502\) | 0.0298497 | 0.00133226 | ||||||||
\(503\) | −38.4956 | −1.71644 | −0.858218 | − | 0.513286i | \(-0.828428\pi\) | ||||
−0.858218 | + | 0.513286i | \(0.828428\pi\) | |||||||
\(504\) | 5.21053 | 0.232095 | ||||||||
\(505\) | −7.22136 | −0.321346 | ||||||||
\(506\) | −16.2661 | −0.723118 | ||||||||
\(507\) | 38.8503 | 1.72540 | ||||||||
\(508\) | 3.36741 | 0.149405 | ||||||||
\(509\) | 34.8707 | 1.54562 | 0.772809 | − | 0.634639i | \(-0.218851\pi\) | ||||
0.772809 | + | 0.634639i | \(0.218851\pi\) | |||||||
\(510\) | 7.78908 | 0.344906 | ||||||||
\(511\) | −6.52526 | −0.288660 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −25.3565 | −1.11952 | ||||||||
\(514\) | 17.3843 | 0.766788 | ||||||||
\(515\) | 7.70292 | 0.339431 | ||||||||
\(516\) | −3.49254 | −0.153751 | ||||||||
\(517\) | −16.0944 | −0.707831 | ||||||||
\(518\) | 10.7961 | 0.474355 | ||||||||
\(519\) | −10.6067 | −0.465581 | ||||||||
\(520\) | −6.67672 | −0.292794 | ||||||||
\(521\) | −15.7666 | −0.690745 | −0.345373 | − | 0.938466i | \(-0.612248\pi\) | ||||
−0.345373 | + | 0.938466i | \(0.612248\pi\) | |||||||
\(522\) | 13.4392 | 0.588219 | ||||||||
\(523\) | −35.2794 | −1.54266 | −0.771331 | − | 0.636435i | \(-0.780408\pi\) | ||||
−0.771331 | + | 0.636435i | \(0.780408\pi\) | |||||||
\(524\) | 2.27447 | 0.0993609 | ||||||||
\(525\) | 4.31258 | 0.188216 | ||||||||
\(526\) | 1.69511 | 0.0739103 | ||||||||
\(527\) | −53.6458 | −2.33685 | ||||||||
\(528\) | −2.29529 | −0.0998897 | ||||||||
\(529\) | 53.0142 | 2.30497 | ||||||||
\(530\) | 6.47876 | 0.281419 | ||||||||
\(531\) | 8.07010 | 0.350212 | ||||||||
\(532\) | 16.1036 | 0.698181 | ||||||||
\(533\) | 21.2704 | 0.921323 | ||||||||
\(534\) | 14.5850 | 0.631156 | ||||||||
\(535\) | 0.576866 | 0.0249401 | ||||||||
\(536\) | −2.27426 | −0.0982331 | ||||||||
\(537\) | −15.4429 | −0.666412 | ||||||||
\(538\) | −26.8529 | −1.15771 | ||||||||
\(539\) | −9.86525 | −0.424926 | ||||||||
\(540\) | 5.51953 | 0.237523 | ||||||||
\(541\) | 30.9354 | 1.33001 | 0.665007 | − | 0.746837i | \(-0.268428\pi\) | ||||
0.665007 | + | 0.746837i | \(0.268428\pi\) | |||||||
\(542\) | −24.6974 | −1.06085 | ||||||||
\(543\) | 19.2109 | 0.824419 | ||||||||
\(544\) | −6.33119 | −0.271448 | ||||||||
\(545\) | 20.1187 | 0.861792 | ||||||||
\(546\) | 28.7939 | 1.23227 | ||||||||
\(547\) | 22.2158 | 0.949880 | 0.474940 | − | 0.880018i | \(-0.342470\pi\) | ||||
0.474940 | + | 0.880018i | \(0.342470\pi\) | |||||||
\(548\) | −1.03381 | −0.0441621 | ||||||||
\(549\) | 6.52096 | 0.278308 | ||||||||
\(550\) | 1.86568 | 0.0795528 | ||||||||
\(551\) | 41.5352 | 1.76946 | ||||||||
\(552\) | 10.7263 | 0.456540 | ||||||||
\(553\) | −28.3483 | −1.20549 | ||||||||
\(554\) | 25.3607 | 1.07747 | ||||||||
\(555\) | 3.78907 | 0.160837 | ||||||||
\(556\) | −1.19908 | −0.0508524 | ||||||||
\(557\) | −20.7416 | −0.878848 | −0.439424 | − | 0.898280i | \(-0.644818\pi\) | ||||
−0.439424 | + | 0.898280i | \(0.644818\pi\) | |||||||
\(558\) | −12.5949 | −0.533186 | ||||||||
\(559\) | 18.9542 | 0.801675 | ||||||||
\(560\) | −3.50539 | −0.148130 | ||||||||
\(561\) | −14.5319 | −0.613538 | ||||||||
\(562\) | −12.4409 | −0.524787 | ||||||||
\(563\) | −13.0881 | −0.551596 | −0.275798 | − | 0.961216i | \(-0.588942\pi\) | ||||
−0.275798 | + | 0.961216i | \(0.588942\pi\) | |||||||
\(564\) | 10.6130 | 0.446889 | ||||||||
\(565\) | −7.13357 | −0.300112 | ||||||||
\(566\) | 16.5614 | 0.696126 | ||||||||
\(567\) | −8.17183 | −0.343185 | ||||||||
\(568\) | 0.782381 | 0.0328280 | ||||||||
\(569\) | 34.4569 | 1.44451 | 0.722254 | − | 0.691627i | \(-0.243106\pi\) | ||||
0.722254 | + | 0.691627i | \(0.243106\pi\) | |||||||
\(570\) | 5.65182 | 0.236729 | ||||||||
\(571\) | 12.3441 | 0.516585 | 0.258292 | − | 0.966067i | \(-0.416840\pi\) | ||||
0.258292 | + | 0.966067i | \(0.416840\pi\) | |||||||
\(572\) | 12.4566 | 0.520837 | ||||||||
\(573\) | 16.2535 | 0.679001 | ||||||||
\(574\) | 11.1673 | 0.466114 | ||||||||
\(575\) | −8.71861 | −0.363591 | ||||||||
\(576\) | −1.48643 | −0.0619347 | ||||||||
\(577\) | 26.1431 | 1.08835 | 0.544176 | − | 0.838971i | \(-0.316842\pi\) | ||||
0.544176 | + | 0.838971i | \(0.316842\pi\) | |||||||
\(578\) | −23.0840 | −0.960166 | ||||||||
\(579\) | −26.4772 | −1.10035 | ||||||||
\(580\) | −9.04127 | −0.375418 | ||||||||
\(581\) | −55.6953 | −2.31063 | ||||||||
\(582\) | 18.5553 | 0.769141 | ||||||||
\(583\) | −12.0873 | −0.500604 | ||||||||
\(584\) | 1.86149 | 0.0770291 | ||||||||
\(585\) | −9.92450 | −0.410328 | ||||||||
\(586\) | −3.84987 | −0.159037 | ||||||||
\(587\) | 14.5314 | 0.599774 | 0.299887 | − | 0.953975i | \(-0.403051\pi\) | ||||
0.299887 | + | 0.953975i | \(0.403051\pi\) | |||||||
\(588\) | 6.50537 | 0.268277 | ||||||||
\(589\) | −38.9258 | −1.60391 | ||||||||
\(590\) | −5.42917 | −0.223515 | ||||||||
\(591\) | −16.7057 | −0.687179 | ||||||||
\(592\) | −3.07987 | −0.126582 | ||||||||
\(593\) | −6.08413 | −0.249845 | −0.124923 | − | 0.992166i | \(-0.539868\pi\) | ||||
−0.124923 | + | 0.992166i | \(0.539868\pi\) | |||||||
\(594\) | −10.2977 | −0.422518 | ||||||||
\(595\) | −22.1933 | −0.909836 | ||||||||
\(596\) | 3.22469 | 0.132088 | ||||||||
\(597\) | −12.0108 | −0.491571 | ||||||||
\(598\) | −58.2118 | −2.38046 | ||||||||
\(599\) | −1.43166 | −0.0584961 | −0.0292481 | − | 0.999572i | \(-0.509311\pi\) | ||||
−0.0292481 | + | 0.999572i | \(0.509311\pi\) | |||||||
\(600\) | −1.23027 | −0.0502256 | ||||||||
\(601\) | 41.2129 | 1.68111 | 0.840554 | − | 0.541728i | \(-0.182230\pi\) | ||||
0.840554 | + | 0.541728i | \(0.182230\pi\) | |||||||
\(602\) | 9.95124 | 0.405582 | ||||||||
\(603\) | −3.38054 | −0.137666 | ||||||||
\(604\) | −8.09195 | −0.329257 | ||||||||
\(605\) | 7.51924 | 0.305701 | ||||||||
\(606\) | −8.88424 | −0.360897 | ||||||||
\(607\) | −3.96130 | −0.160784 | −0.0803921 | − | 0.996763i | \(-0.525617\pi\) | ||||
−0.0803921 | + | 0.996763i | \(0.525617\pi\) | |||||||
\(608\) | −4.59396 | −0.186310 | ||||||||
\(609\) | 38.9912 | 1.58000 | ||||||||
\(610\) | −4.38698 | −0.177624 | ||||||||
\(611\) | −57.5972 | −2.33013 | ||||||||
\(612\) | −9.41089 | −0.380413 | ||||||||
\(613\) | −42.6106 | −1.72103 | −0.860514 | − | 0.509427i | \(-0.829857\pi\) | ||||
−0.860514 | + | 0.509427i | \(0.829857\pi\) | |||||||
\(614\) | 21.1164 | 0.852187 | ||||||||
\(615\) | 3.91934 | 0.158043 | ||||||||
\(616\) | 6.53993 | 0.263501 | ||||||||
\(617\) | 7.67455 | 0.308966 | 0.154483 | − | 0.987995i | \(-0.450629\pi\) | ||||
0.154483 | + | 0.987995i | \(0.450629\pi\) | |||||||
\(618\) | 9.47668 | 0.381208 | ||||||||
\(619\) | −49.5915 | −1.99325 | −0.996625 | − | 0.0820940i | \(-0.973839\pi\) | ||||
−0.996625 | + | 0.0820940i | \(0.973839\pi\) | |||||||
\(620\) | 8.47326 | 0.340294 | ||||||||
\(621\) | 48.1226 | 1.93110 | ||||||||
\(622\) | −17.9731 | −0.720656 | ||||||||
\(623\) | −41.5569 | −1.66494 | ||||||||
\(624\) | −8.21418 | −0.328830 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −26.9382 | −1.07667 | ||||||||
\(627\) | −10.5445 | −0.421106 | ||||||||
\(628\) | 9.24673 | 0.368985 | ||||||||
\(629\) | −19.4992 | −0.777485 | ||||||||
\(630\) | −5.21053 | −0.207592 | ||||||||
\(631\) | 6.23601 | 0.248252 | 0.124126 | − | 0.992266i | \(-0.460387\pi\) | ||||
0.124126 | + | 0.992266i | \(0.460387\pi\) | |||||||
\(632\) | 8.08705 | 0.321686 | ||||||||
\(633\) | 0.202609 | 0.00805300 | ||||||||
\(634\) | −8.62087 | −0.342378 | ||||||||
\(635\) | −3.36741 | −0.133632 | ||||||||
\(636\) | 7.97063 | 0.316056 | ||||||||
\(637\) | −35.3049 | −1.39883 | ||||||||
\(638\) | 16.8681 | 0.667814 | ||||||||
\(639\) | 1.16296 | 0.0460058 | ||||||||
\(640\) | 1.00000 | 0.0395285 | ||||||||
\(641\) | −23.6154 | −0.932753 | −0.466376 | − | 0.884586i | \(-0.654441\pi\) | ||||
−0.466376 | + | 0.884586i | \(0.654441\pi\) | |||||||
\(642\) | 0.709702 | 0.0280097 | ||||||||
\(643\) | 33.9364 | 1.33832 | 0.669161 | − | 0.743117i | \(-0.266654\pi\) | ||||
0.669161 | + | 0.743117i | \(0.266654\pi\) | |||||||
\(644\) | −30.5621 | −1.20432 | ||||||||
\(645\) | 3.49254 | 0.137519 | ||||||||
\(646\) | −29.0852 | −1.14434 | ||||||||
\(647\) | 23.3364 | 0.917449 | 0.458724 | − | 0.888579i | \(-0.348307\pi\) | ||||
0.458724 | + | 0.888579i | \(0.348307\pi\) | |||||||
\(648\) | 2.33122 | 0.0915790 | ||||||||
\(649\) | 10.1291 | 0.397602 | ||||||||
\(650\) | 6.67672 | 0.261883 | ||||||||
\(651\) | −36.5416 | −1.43218 | ||||||||
\(652\) | −3.93017 | −0.153917 | ||||||||
\(653\) | 41.8439 | 1.63748 | 0.818739 | − | 0.574165i | \(-0.194673\pi\) | ||||
0.818739 | + | 0.574165i | \(0.194673\pi\) | |||||||
\(654\) | 24.7515 | 0.967860 | ||||||||
\(655\) | −2.27447 | −0.0888711 | ||||||||
\(656\) | −3.18575 | −0.124383 | ||||||||
\(657\) | 2.76698 | 0.107950 | ||||||||
\(658\) | −30.2395 | −1.17886 | ||||||||
\(659\) | −11.0508 | −0.430478 | −0.215239 | − | 0.976561i | \(-0.569053\pi\) | ||||
−0.215239 | + | 0.976561i | \(0.569053\pi\) | |||||||
\(660\) | 2.29529 | 0.0893441 | ||||||||
\(661\) | −49.4459 | −1.92322 | −0.961612 | − | 0.274412i | \(-0.911517\pi\) | ||||
−0.961612 | + | 0.274412i | \(0.911517\pi\) | |||||||
\(662\) | 19.3529 | 0.752173 | ||||||||
\(663\) | −52.0055 | −2.01973 | ||||||||
\(664\) | 15.8885 | 0.616593 | ||||||||
\(665\) | −16.1036 | −0.624472 | ||||||||
\(666\) | −4.57802 | −0.177394 | ||||||||
\(667\) | −78.8273 | −3.05221 | ||||||||
\(668\) | 17.6116 | 0.681415 | ||||||||
\(669\) | 28.2650 | 1.09279 | ||||||||
\(670\) | 2.27426 | 0.0878624 | ||||||||
\(671\) | 8.18470 | 0.315967 | ||||||||
\(672\) | −4.31258 | −0.166361 | ||||||||
\(673\) | 35.1239 | 1.35393 | 0.676963 | − | 0.736017i | \(-0.263296\pi\) | ||||
0.676963 | + | 0.736017i | \(0.263296\pi\) | |||||||
\(674\) | 22.5312 | 0.867868 | ||||||||
\(675\) | −5.51953 | −0.212447 | ||||||||
\(676\) | 31.5786 | 1.21456 | ||||||||
\(677\) | 0.724062 | 0.0278280 | 0.0139140 | − | 0.999903i | \(-0.495571\pi\) | ||||
0.0139140 | + | 0.999903i | \(0.495571\pi\) | |||||||
\(678\) | −8.77623 | −0.337049 | ||||||||
\(679\) | −52.8692 | −2.02893 | ||||||||
\(680\) | 6.33119 | 0.242790 | ||||||||
\(681\) | −11.2328 | −0.430443 | ||||||||
\(682\) | −15.8084 | −0.605334 | ||||||||
\(683\) | −12.9178 | −0.494287 | −0.247144 | − | 0.968979i | \(-0.579492\pi\) | ||||
−0.247144 | + | 0.968979i | \(0.579492\pi\) | |||||||
\(684\) | −6.82861 | −0.261099 | ||||||||
\(685\) | 1.03381 | 0.0394998 | ||||||||
\(686\) | 6.00209 | 0.229161 | ||||||||
\(687\) | 18.5995 | 0.709617 | ||||||||
\(688\) | −2.83884 | −0.108230 | ||||||||
\(689\) | −43.2569 | −1.64796 | ||||||||
\(690\) | −10.7263 | −0.408342 | ||||||||
\(691\) | 24.6577 | 0.938022 | 0.469011 | − | 0.883192i | \(-0.344610\pi\) | ||||
0.469011 | + | 0.883192i | \(0.344610\pi\) | |||||||
\(692\) | −8.62140 | −0.327736 | ||||||||
\(693\) | 9.72116 | 0.369277 | ||||||||
\(694\) | 8.34036 | 0.316596 | ||||||||
\(695\) | 1.19908 | 0.0454838 | ||||||||
\(696\) | −11.1232 | −0.421624 | ||||||||
\(697\) | −20.1696 | −0.763978 | ||||||||
\(698\) | −2.91112 | −0.110187 | ||||||||
\(699\) | −8.83772 | −0.334273 | ||||||||
\(700\) | 3.50539 | 0.132491 | ||||||||
\(701\) | 13.8211 | 0.522017 | 0.261009 | − | 0.965336i | \(-0.415945\pi\) | ||||
0.261009 | + | 0.965336i | \(0.415945\pi\) | |||||||
\(702\) | −36.8524 | −1.39090 | ||||||||
\(703\) | −14.1488 | −0.533632 | ||||||||
\(704\) | −1.86568 | −0.0703154 | ||||||||
\(705\) | −10.6130 | −0.399709 | ||||||||
\(706\) | 31.4044 | 1.18192 | ||||||||
\(707\) | 25.3137 | 0.952019 | ||||||||
\(708\) | −6.67935 | −0.251025 | ||||||||
\(709\) | 33.3561 | 1.25272 | 0.626358 | − | 0.779536i | \(-0.284545\pi\) | ||||
0.626358 | + | 0.779536i | \(0.284545\pi\) | |||||||
\(710\) | −0.782381 | −0.0293622 | ||||||||
\(711\) | 12.0209 | 0.450817 | ||||||||
\(712\) | 11.8551 | 0.444290 | ||||||||
\(713\) | 73.8751 | 2.76664 | ||||||||
\(714\) | −27.3038 | −1.02182 | ||||||||
\(715\) | −12.4566 | −0.465851 | ||||||||
\(716\) | −12.5525 | −0.469108 | ||||||||
\(717\) | 11.5744 | 0.432253 | ||||||||
\(718\) | 15.7995 | 0.589632 | ||||||||
\(719\) | 34.6507 | 1.29225 | 0.646126 | − | 0.763231i | \(-0.276388\pi\) | ||||
0.646126 | + | 0.763231i | \(0.276388\pi\) | |||||||
\(720\) | 1.48643 | 0.0553961 | ||||||||
\(721\) | −27.0017 | −1.00560 | ||||||||
\(722\) | −2.10448 | −0.0783205 | ||||||||
\(723\) | −22.6267 | −0.841496 | ||||||||
\(724\) | 15.6152 | 0.580334 | ||||||||
\(725\) | 9.04127 | 0.335784 | ||||||||
\(726\) | 9.25071 | 0.343326 | ||||||||
\(727\) | 43.9121 | 1.62861 | 0.814305 | − | 0.580438i | \(-0.197118\pi\) | ||||
0.814305 | + | 0.580438i | \(0.197118\pi\) | |||||||
\(728\) | 23.4045 | 0.867429 | ||||||||
\(729\) | 23.8368 | 0.882843 | ||||||||
\(730\) | −1.86149 | −0.0688969 | ||||||||
\(731\) | −17.9732 | −0.664764 | ||||||||
\(732\) | −5.39718 | −0.199486 | ||||||||
\(733\) | −28.7870 | −1.06327 | −0.531635 | − | 0.846973i | \(-0.678422\pi\) | ||||
−0.531635 | + | 0.846973i | \(0.678422\pi\) | |||||||
\(734\) | 10.9877 | 0.405564 | ||||||||
\(735\) | −6.50537 | −0.239954 | ||||||||
\(736\) | 8.71861 | 0.321372 | ||||||||
\(737\) | −4.24304 | −0.156294 | ||||||||
\(738\) | −4.73541 | −0.174313 | ||||||||
\(739\) | −27.5448 | −1.01325 | −0.506626 | − | 0.862166i | \(-0.669107\pi\) | ||||
−0.506626 | + | 0.862166i | \(0.669107\pi\) | |||||||
\(740\) | 3.07987 | 0.113218 | ||||||||
\(741\) | −37.7356 | −1.38625 | ||||||||
\(742\) | −22.7106 | −0.833732 | ||||||||
\(743\) | −0.848185 | −0.0311169 | −0.0155584 | − | 0.999879i | \(-0.504953\pi\) | ||||
−0.0155584 | + | 0.999879i | \(0.504953\pi\) | |||||||
\(744\) | 10.4244 | 0.382177 | ||||||||
\(745\) | −3.22469 | −0.118144 | ||||||||
\(746\) | 11.7560 | 0.430417 | ||||||||
\(747\) | 23.6172 | 0.864107 | ||||||||
\(748\) | −11.8120 | −0.431888 | ||||||||
\(749\) | −2.02214 | −0.0738874 | ||||||||
\(750\) | 1.23027 | 0.0449232 | ||||||||
\(751\) | −50.2099 | −1.83218 | −0.916092 | − | 0.400967i | \(-0.868674\pi\) | ||||
−0.916092 | + | 0.400967i | \(0.868674\pi\) | |||||||
\(752\) | 8.62657 | 0.314578 | ||||||||
\(753\) | −0.0367232 | −0.00133827 | ||||||||
\(754\) | 60.3661 | 2.19840 | ||||||||
\(755\) | 8.09195 | 0.294496 | ||||||||
\(756\) | −19.3481 | −0.703683 | ||||||||
\(757\) | 19.6196 | 0.713087 | 0.356544 | − | 0.934279i | \(-0.383955\pi\) | ||||
0.356544 | + | 0.934279i | \(0.383955\pi\) | |||||||
\(758\) | 8.20803 | 0.298129 | ||||||||
\(759\) | 20.0118 | 0.726381 | ||||||||
\(760\) | 4.59396 | 0.166640 | ||||||||
\(761\) | −23.5857 | −0.854981 | −0.427490 | − | 0.904020i | \(-0.640602\pi\) | ||||
−0.427490 | + | 0.904020i | \(0.640602\pi\) | |||||||
\(762\) | −4.14283 | −0.150079 | ||||||||
\(763\) | −70.5240 | −2.55314 | ||||||||
\(764\) | 13.2113 | 0.477970 | ||||||||
\(765\) | 9.41089 | 0.340251 | ||||||||
\(766\) | −6.79756 | −0.245606 | ||||||||
\(767\) | 36.2491 | 1.30888 | ||||||||
\(768\) | 1.23027 | 0.0443936 | ||||||||
\(769\) | 36.8895 | 1.33027 | 0.665134 | − | 0.746724i | \(-0.268374\pi\) | ||||
0.665134 | + | 0.746724i | \(0.268374\pi\) | |||||||
\(770\) | −6.53993 | −0.235683 | ||||||||
\(771\) | −21.3874 | −0.770248 | ||||||||
\(772\) | −21.5214 | −0.774572 | ||||||||
\(773\) | −14.4421 | −0.519445 | −0.259722 | − | 0.965683i | \(-0.583631\pi\) | ||||
−0.259722 | + | 0.965683i | \(0.583631\pi\) | |||||||
\(774\) | −4.21975 | −0.151676 | ||||||||
\(775\) | −8.47326 | −0.304369 | ||||||||
\(776\) | 15.0823 | 0.541422 | ||||||||
\(777\) | −13.2822 | −0.476495 | ||||||||
\(778\) | 15.0416 | 0.539269 | ||||||||
\(779\) | −14.6352 | −0.524361 | ||||||||
\(780\) | 8.21418 | 0.294115 | ||||||||
\(781\) | 1.45967 | 0.0522311 | ||||||||
\(782\) | 55.1992 | 1.97392 | ||||||||
\(783\) | −49.9035 | −1.78341 | ||||||||
\(784\) | 5.28775 | 0.188848 | ||||||||
\(785\) | −9.24673 | −0.330030 | ||||||||
\(786\) | −2.79822 | −0.0998092 | ||||||||
\(787\) | 53.8269 | 1.91872 | 0.959360 | − | 0.282184i | \(-0.0910590\pi\) | ||||
0.959360 | + | 0.282184i | \(0.0910590\pi\) | |||||||
\(788\) | −13.5788 | −0.483726 | ||||||||
\(789\) | −2.08544 | −0.0742438 | ||||||||
\(790\) | −8.08705 | −0.287724 | ||||||||
\(791\) | 25.0059 | 0.889109 | ||||||||
\(792\) | −2.77321 | −0.0985416 | ||||||||
\(793\) | 29.2907 | 1.04014 | ||||||||
\(794\) | 15.9858 | 0.567317 | ||||||||
\(795\) | −7.97063 | −0.282689 | ||||||||
\(796\) | −9.76276 | −0.346032 | ||||||||
\(797\) | −27.4417 | −0.972036 | −0.486018 | − | 0.873949i | \(-0.661551\pi\) | ||||
−0.486018 | + | 0.873949i | \(0.661551\pi\) | |||||||
\(798\) | −19.8118 | −0.701331 | ||||||||
\(799\) | 54.6164 | 1.93219 | ||||||||
\(800\) | −1.00000 | −0.0353553 | ||||||||
\(801\) | 17.6219 | 0.622638 | ||||||||
\(802\) | 1.00000 | 0.0353112 | ||||||||
\(803\) | 3.47295 | 0.122558 | ||||||||
\(804\) | 2.79796 | 0.0986764 | ||||||||
\(805\) | 30.5621 | 1.07717 | ||||||||
\(806\) | −56.5736 | −1.99272 | ||||||||
\(807\) | 33.0364 | 1.16294 | ||||||||
\(808\) | −7.22136 | −0.254047 | ||||||||
\(809\) | 52.0779 | 1.83096 | 0.915480 | − | 0.402363i | \(-0.131811\pi\) | ||||
0.915480 | + | 0.402363i | \(0.131811\pi\) | |||||||
\(810\) | −2.33122 | −0.0819107 | ||||||||
\(811\) | 54.4632 | 1.91246 | 0.956231 | − | 0.292611i | \(-0.0945242\pi\) | ||||
0.956231 | + | 0.292611i | \(0.0945242\pi\) | |||||||
\(812\) | 31.6932 | 1.11221 | ||||||||
\(813\) | 30.3846 | 1.06563 | ||||||||
\(814\) | −5.74604 | −0.201399 | ||||||||
\(815\) | 3.93017 | 0.137668 | ||||||||
\(816\) | 7.78908 | 0.272672 | ||||||||
\(817\) | −13.0415 | −0.456265 | ||||||||
\(818\) | −32.7944 | −1.14663 | ||||||||
\(819\) | 34.7892 | 1.21563 | ||||||||
\(820\) | 3.18575 | 0.111251 | ||||||||
\(821\) | −35.7966 | −1.24931 | −0.624655 | − | 0.780901i | \(-0.714760\pi\) | ||||
−0.624655 | + | 0.780901i | \(0.714760\pi\) | |||||||
\(822\) | 1.27186 | 0.0443613 | ||||||||
\(823\) | 39.5956 | 1.38022 | 0.690108 | − | 0.723706i | \(-0.257563\pi\) | ||||
0.690108 | + | 0.723706i | \(0.257563\pi\) | |||||||
\(824\) | 7.70292 | 0.268344 | ||||||||
\(825\) | −2.29529 | −0.0799118 | ||||||||
\(826\) | 19.0314 | 0.662186 | ||||||||
\(827\) | −44.2405 | −1.53839 | −0.769197 | − | 0.639011i | \(-0.779344\pi\) | ||||
−0.769197 | + | 0.639011i | \(0.779344\pi\) | |||||||
\(828\) | 12.9596 | 0.450378 | ||||||||
\(829\) | −48.5432 | −1.68597 | −0.842987 | − | 0.537934i | \(-0.819205\pi\) | ||||
−0.842987 | + | 0.537934i | \(0.819205\pi\) | |||||||
\(830\) | −15.8885 | −0.551498 | ||||||||
\(831\) | −31.2005 | −1.08233 | ||||||||
\(832\) | −6.67672 | −0.231474 | ||||||||
\(833\) | 33.4778 | 1.15994 | ||||||||
\(834\) | 1.47520 | 0.0510819 | ||||||||
\(835\) | −17.6116 | −0.609476 | ||||||||
\(836\) | −8.57085 | −0.296429 | ||||||||
\(837\) | 46.7684 | 1.61655 | ||||||||
\(838\) | 20.1649 | 0.696586 | ||||||||
\(839\) | −4.76663 | −0.164562 | −0.0822812 | − | 0.996609i | \(-0.526221\pi\) | ||||
−0.0822812 | + | 0.996609i | \(0.526221\pi\) | |||||||
\(840\) | 4.31258 | 0.148798 | ||||||||
\(841\) | 52.7445 | 1.81878 | ||||||||
\(842\) | 25.9559 | 0.894501 | ||||||||
\(843\) | 15.3056 | 0.527154 | ||||||||
\(844\) | 0.164687 | 0.00566875 | ||||||||
\(845\) | −31.5786 | −1.08634 | ||||||||
\(846\) | 12.8228 | 0.440857 | ||||||||
\(847\) | −26.3579 | −0.905667 | ||||||||
\(848\) | 6.47876 | 0.222482 | ||||||||
\(849\) | −20.3750 | −0.699267 | ||||||||
\(850\) | −6.33119 | −0.217158 | ||||||||
\(851\) | 26.8522 | 0.920481 | ||||||||
\(852\) | −0.962541 | −0.0329761 | ||||||||
\(853\) | −1.64798 | −0.0564258 | −0.0282129 | − | 0.999602i | \(-0.508982\pi\) | ||||
−0.0282129 | + | 0.999602i | \(0.508982\pi\) | |||||||
\(854\) | 15.3781 | 0.526227 | ||||||||
\(855\) | 6.82861 | 0.233534 | ||||||||
\(856\) | 0.576866 | 0.0197169 | ||||||||
\(857\) | −2.42222 | −0.0827414 | −0.0413707 | − | 0.999144i | \(-0.513172\pi\) | ||||
−0.0413707 | + | 0.999144i | \(0.513172\pi\) | |||||||
\(858\) | −15.3250 | −0.523188 | ||||||||
\(859\) | −23.4226 | −0.799170 | −0.399585 | − | 0.916696i | \(-0.630846\pi\) | ||||
−0.399585 | + | 0.916696i | \(0.630846\pi\) | |||||||
\(860\) | 2.83884 | 0.0968037 | ||||||||
\(861\) | −13.7388 | −0.468217 | ||||||||
\(862\) | −11.7637 | −0.400675 | ||||||||
\(863\) | 47.6593 | 1.62234 | 0.811171 | − | 0.584809i | \(-0.198830\pi\) | ||||
0.811171 | + | 0.584809i | \(0.198830\pi\) | |||||||
\(864\) | 5.51953 | 0.187778 | ||||||||
\(865\) | 8.62140 | 0.293136 | ||||||||
\(866\) | 19.7689 | 0.671775 | ||||||||
\(867\) | 28.3995 | 0.964499 | ||||||||
\(868\) | −29.7021 | −1.00815 | ||||||||
\(869\) | 15.0878 | 0.511820 | ||||||||
\(870\) | 11.1232 | 0.377112 | ||||||||
\(871\) | −15.1846 | −0.514511 | ||||||||
\(872\) | 20.1187 | 0.681306 | ||||||||
\(873\) | 22.4188 | 0.758760 | ||||||||
\(874\) | 40.0530 | 1.35481 | ||||||||
\(875\) | −3.50539 | −0.118504 | ||||||||
\(876\) | −2.29014 | −0.0773767 | ||||||||
\(877\) | 50.6235 | 1.70944 | 0.854718 | − | 0.519093i | \(-0.173730\pi\) | ||||
0.854718 | + | 0.519093i | \(0.173730\pi\) | |||||||
\(878\) | 1.15129 | 0.0388542 | ||||||||
\(879\) | 4.73639 | 0.159754 | ||||||||
\(880\) | 1.86568 | 0.0628920 | ||||||||
\(881\) | −4.73175 | −0.159417 | −0.0797084 | − | 0.996818i | \(-0.525399\pi\) | ||||
−0.0797084 | + | 0.996818i | \(0.525399\pi\) | |||||||
\(882\) | 7.85989 | 0.264656 | ||||||||
\(883\) | −5.98415 | −0.201383 | −0.100691 | − | 0.994918i | \(-0.532105\pi\) | ||||
−0.100691 | + | 0.994918i | \(0.532105\pi\) | |||||||
\(884\) | −42.2716 | −1.42175 | ||||||||
\(885\) | 6.67935 | 0.224524 | ||||||||
\(886\) | −24.9362 | −0.837747 | ||||||||
\(887\) | −33.5805 | −1.12752 | −0.563762 | − | 0.825937i | \(-0.690646\pi\) | ||||
−0.563762 | + | 0.825937i | \(0.690646\pi\) | |||||||
\(888\) | 3.78907 | 0.127153 | ||||||||
\(889\) | 11.8041 | 0.395896 | ||||||||
\(890\) | −11.8551 | −0.397385 | ||||||||
\(891\) | 4.34931 | 0.145707 | ||||||||
\(892\) | 22.9746 | 0.769247 | ||||||||
\(893\) | 39.6301 | 1.32617 | ||||||||
\(894\) | −3.96724 | −0.132685 | ||||||||
\(895\) | 12.5525 | 0.419583 | ||||||||
\(896\) | −3.50539 | −0.117107 | ||||||||
\(897\) | 71.6163 | 2.39120 | ||||||||
\(898\) | −4.63346 | −0.154621 | ||||||||
\(899\) | −76.6090 | −2.55505 | ||||||||
\(900\) | −1.48643 | −0.0495478 | ||||||||
\(901\) | 41.0183 | 1.36652 | ||||||||
\(902\) | −5.94359 | −0.197900 | ||||||||
\(903\) | −12.2427 | −0.407412 | ||||||||
\(904\) | −7.13357 | −0.237259 | ||||||||
\(905\) | −15.6152 | −0.519066 | ||||||||
\(906\) | 9.95530 | 0.330743 | ||||||||
\(907\) | 12.2532 | 0.406862 | 0.203431 | − | 0.979089i | \(-0.434791\pi\) | ||||
0.203431 | + | 0.979089i | \(0.434791\pi\) | |||||||
\(908\) | −9.13036 | −0.303002 | ||||||||
\(909\) | −10.7341 | −0.356027 | ||||||||
\(910\) | −23.4045 | −0.775852 | ||||||||
\(911\) | 53.0914 | 1.75900 | 0.879499 | − | 0.475901i | \(-0.157878\pi\) | ||||
0.879499 | + | 0.475901i | \(0.157878\pi\) | |||||||
\(912\) | 5.65182 | 0.187150 | ||||||||
\(913\) | 29.6428 | 0.981034 | ||||||||
\(914\) | −39.7724 | −1.31556 | ||||||||
\(915\) | 5.39718 | 0.178425 | ||||||||
\(916\) | 15.1182 | 0.499521 | ||||||||
\(917\) | 7.97292 | 0.263289 | ||||||||
\(918\) | 34.9452 | 1.15336 | ||||||||
\(919\) | 14.2286 | 0.469357 | 0.234678 | − | 0.972073i | \(-0.424596\pi\) | ||||
0.234678 | + | 0.972073i | \(0.424596\pi\) | |||||||
\(920\) | −8.71861 | −0.287444 | ||||||||
\(921\) | −25.9788 | −0.856032 | ||||||||
\(922\) | −17.5872 | −0.579203 | ||||||||
\(923\) | 5.22374 | 0.171942 | ||||||||
\(924\) | −8.04589 | −0.264690 | ||||||||
\(925\) | −3.07987 | −0.101265 | ||||||||
\(926\) | −7.95209 | −0.261322 | ||||||||
\(927\) | 11.4499 | 0.376063 | ||||||||
\(928\) | −9.04127 | −0.296794 | ||||||||
\(929\) | 31.1373 | 1.02158 | 0.510790 | − | 0.859705i | \(-0.329353\pi\) | ||||
0.510790 | + | 0.859705i | \(0.329353\pi\) | |||||||
\(930\) | −10.4244 | −0.341830 | ||||||||
\(931\) | 24.2917 | 0.796129 | ||||||||
\(932\) | −7.18355 | −0.235305 | ||||||||
\(933\) | 22.1118 | 0.723908 | ||||||||
\(934\) | 19.3310 | 0.632531 | ||||||||
\(935\) | 11.8120 | 0.386293 | ||||||||
\(936\) | −9.92450 | −0.324392 | ||||||||
\(937\) | 0.167810 | 0.00548210 | 0.00274105 | − | 0.999996i | \(-0.499127\pi\) | ||||
0.00274105 | + | 0.999996i | \(0.499127\pi\) | |||||||
\(938\) | −7.97217 | −0.260301 | ||||||||
\(939\) | 33.1413 | 1.08153 | ||||||||
\(940\) | −8.62657 | −0.281368 | ||||||||
\(941\) | −0.306413 | −0.00998878 | −0.00499439 | − | 0.999988i | \(-0.501590\pi\) | ||||
−0.00499439 | + | 0.999988i | \(0.501590\pi\) | |||||||
\(942\) | −11.3760 | −0.370650 | ||||||||
\(943\) | 27.7753 | 0.904490 | ||||||||
\(944\) | −5.42917 | −0.176704 | ||||||||
\(945\) | 19.3481 | 0.629394 | ||||||||
\(946\) | −5.29636 | −0.172200 | ||||||||
\(947\) | −50.7816 | −1.65018 | −0.825091 | − | 0.565000i | \(-0.808876\pi\) | ||||
−0.825091 | + | 0.565000i | \(0.808876\pi\) | |||||||
\(948\) | −9.94927 | −0.323137 | ||||||||
\(949\) | 12.4287 | 0.403452 | ||||||||
\(950\) | −4.59396 | −0.149048 | ||||||||
\(951\) | 10.6060 | 0.343923 | ||||||||
\(952\) | −22.1933 | −0.719288 | ||||||||
\(953\) | 37.2224 | 1.20575 | 0.602876 | − | 0.797835i | \(-0.294021\pi\) | ||||
0.602876 | + | 0.797835i | \(0.294021\pi\) | |||||||
\(954\) | 9.63024 | 0.311791 | ||||||||
\(955\) | −13.2113 | −0.427509 | ||||||||
\(956\) | 9.40800 | 0.304276 | ||||||||
\(957\) | −20.7523 | −0.670828 | ||||||||
\(958\) | −23.6652 | −0.764588 | ||||||||
\(959\) | −3.62390 | −0.117022 | ||||||||
\(960\) | −1.23027 | −0.0397068 | ||||||||
\(961\) | 40.7962 | 1.31601 | ||||||||
\(962\) | −20.5634 | −0.662991 | ||||||||
\(963\) | 0.857473 | 0.0276317 | ||||||||
\(964\) | −18.3916 | −0.592355 | ||||||||
\(965\) | 21.5214 | 0.692799 | ||||||||
\(966\) | 37.5997 | 1.20975 | ||||||||
\(967\) | 47.0212 | 1.51210 | 0.756050 | − | 0.654513i | \(-0.227126\pi\) | ||||
0.756050 | + | 0.654513i | \(0.227126\pi\) | |||||||
\(968\) | 7.51924 | 0.241678 | ||||||||
\(969\) | 35.7827 | 1.14951 | ||||||||
\(970\) | −15.0823 | −0.484262 | ||||||||
\(971\) | −12.4900 | −0.400824 | −0.200412 | − | 0.979712i | \(-0.564228\pi\) | ||||
−0.200412 | + | 0.979712i | \(0.564228\pi\) | |||||||
\(972\) | 13.6906 | 0.439125 | ||||||||
\(973\) | −4.20325 | −0.134750 | ||||||||
\(974\) | 23.8703 | 0.764854 | ||||||||
\(975\) | −8.21418 | −0.263064 | ||||||||
\(976\) | −4.38698 | −0.140424 | ||||||||
\(977\) | −7.95194 | −0.254405 | −0.127202 | − | 0.991877i | \(-0.540600\pi\) | ||||
−0.127202 | + | 0.991877i | \(0.540600\pi\) | |||||||
\(978\) | 4.83517 | 0.154612 | ||||||||
\(979\) | 22.1179 | 0.706890 | ||||||||
\(980\) | −5.28775 | −0.168911 | ||||||||
\(981\) | 29.9051 | 0.954798 | ||||||||
\(982\) | −0.223451 | −0.00713060 | ||||||||
\(983\) | 16.9641 | 0.541071 | 0.270535 | − | 0.962710i | \(-0.412799\pi\) | ||||
0.270535 | + | 0.962710i | \(0.412799\pi\) | |||||||
\(984\) | 3.91934 | 0.124944 | ||||||||
\(985\) | 13.5788 | 0.432658 | ||||||||
\(986\) | −57.2420 | −1.82296 | ||||||||
\(987\) | 37.2027 | 1.18418 | ||||||||
\(988\) | −30.6726 | −0.975826 | ||||||||
\(989\) | 24.7508 | 0.787028 | ||||||||
\(990\) | 2.77321 | 0.0881383 | ||||||||
\(991\) | 44.8176 | 1.42368 | 0.711839 | − | 0.702342i | \(-0.247862\pi\) | ||||
0.711839 | + | 0.702342i | \(0.247862\pi\) | |||||||
\(992\) | 8.47326 | 0.269026 | ||||||||
\(993\) | −23.8093 | −0.755567 | ||||||||
\(994\) | 2.74255 | 0.0869884 | ||||||||
\(995\) | 9.76276 | 0.309500 | ||||||||
\(996\) | −19.5472 | −0.619375 | ||||||||
\(997\) | −38.1285 | −1.20754 | −0.603771 | − | 0.797158i | \(-0.706336\pi\) | ||||
−0.603771 | + | 0.797158i | \(0.706336\pi\) | |||||||
\(998\) | 6.97246 | 0.220709 | ||||||||
\(999\) | 16.9994 | 0.537838 |
(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 | 4010.2.a.k.1.11 | ✓ | 15 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4010.2.a.k.1.11 | ✓ | 15 | 1.1 | even | 1 | trivial |