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: | \(0\) |
Dimension: | \(14\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{14} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{14} - x^{13} - 21 x^{12} + 20 x^{11} + 167 x^{10} - 148 x^{9} - 627 x^{8} + 497 x^{7} + 1123 x^{6} + \cdots - 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(2.63401\) 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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.63401 | −1.86252 | −0.931262 | − | 0.364351i | \(-0.881291\pi\) | ||||
−0.931262 | + | 0.364351i | \(0.881291\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 4.93799 | 2.46899 | ||||||||
\(5\) | 2.62502 | 1.17394 | 0.586972 | − | 0.809607i | \(-0.300320\pi\) | ||||
0.586972 | + | 0.809607i | \(0.300320\pi\) | |||||||
\(6\) | 2.63401 | 1.07533 | ||||||||
\(7\) | 5.18852 | 1.96107 | 0.980537 | − | 0.196333i | \(-0.0629034\pi\) | ||||
0.980537 | + | 0.196333i | \(0.0629034\pi\) | |||||||
\(8\) | −7.73867 | −2.73603 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −6.91432 | −2.18650 | ||||||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | −4.93799 | −1.42547 | ||||||||
\(13\) | −3.47280 | −0.963182 | −0.481591 | − | 0.876396i | \(-0.659941\pi\) | ||||
−0.481591 | + | 0.876396i | \(0.659941\pi\) | |||||||
\(14\) | −13.6666 | −3.65255 | ||||||||
\(15\) | −2.62502 | −0.677777 | ||||||||
\(16\) | 10.5077 | 2.62694 | ||||||||
\(17\) | 1.94870 | 0.472630 | 0.236315 | − | 0.971677i | \(-0.424060\pi\) | ||||
0.236315 | + | 0.971677i | \(0.424060\pi\) | |||||||
\(18\) | −2.63401 | −0.620841 | ||||||||
\(19\) | −0.343156 | −0.0787255 | −0.0393627 | − | 0.999225i | \(-0.512533\pi\) | ||||
−0.0393627 | + | 0.999225i | \(0.512533\pi\) | |||||||
\(20\) | 12.9623 | 2.89846 | ||||||||
\(21\) | −5.18852 | −1.13223 | ||||||||
\(22\) | 2.63401 | 0.561572 | ||||||||
\(23\) | −4.48645 | −0.935489 | −0.467744 | − | 0.883864i | \(-0.654933\pi\) | ||||
−0.467744 | + | 0.883864i | \(0.654933\pi\) | |||||||
\(24\) | 7.73867 | 1.57965 | ||||||||
\(25\) | 1.89073 | 0.378146 | ||||||||
\(26\) | 9.14738 | 1.79395 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 25.6208 | 4.84188 | ||||||||
\(29\) | −5.47498 | −1.01668 | −0.508339 | − | 0.861157i | \(-0.669740\pi\) | ||||
−0.508339 | + | 0.861157i | \(0.669740\pi\) | |||||||
\(30\) | 6.91432 | 1.26238 | ||||||||
\(31\) | 2.40756 | 0.432410 | 0.216205 | − | 0.976348i | \(-0.430632\pi\) | ||||
0.216205 | + | 0.976348i | \(0.430632\pi\) | |||||||
\(32\) | −12.2001 | −2.15669 | ||||||||
\(33\) | 1.00000 | 0.174078 | ||||||||
\(34\) | −5.13290 | −0.880284 | ||||||||
\(35\) | 13.6200 | 2.30219 | ||||||||
\(36\) | 4.93799 | 0.822998 | ||||||||
\(37\) | 10.3461 | 1.70089 | 0.850444 | − | 0.526065i | \(-0.176333\pi\) | ||||
0.850444 | + | 0.526065i | \(0.176333\pi\) | |||||||
\(38\) | 0.903876 | 0.146628 | ||||||||
\(39\) | 3.47280 | 0.556093 | ||||||||
\(40\) | −20.3142 | −3.21195 | ||||||||
\(41\) | −0.436542 | −0.0681764 | −0.0340882 | − | 0.999419i | \(-0.510853\pi\) | ||||
−0.0340882 | + | 0.999419i | \(0.510853\pi\) | |||||||
\(42\) | 13.6666 | 2.10880 | ||||||||
\(43\) | 6.40802 | 0.977214 | 0.488607 | − | 0.872504i | \(-0.337505\pi\) | ||||
0.488607 | + | 0.872504i | \(0.337505\pi\) | |||||||
\(44\) | −4.93799 | −0.744430 | ||||||||
\(45\) | 2.62502 | 0.391315 | ||||||||
\(46\) | 11.8173 | 1.74237 | ||||||||
\(47\) | 4.42685 | 0.645723 | 0.322861 | − | 0.946446i | \(-0.395355\pi\) | ||||
0.322861 | + | 0.946446i | \(0.395355\pi\) | |||||||
\(48\) | −10.5077 | −1.51666 | ||||||||
\(49\) | 19.9207 | 2.84581 | ||||||||
\(50\) | −4.98019 | −0.704306 | ||||||||
\(51\) | −1.94870 | −0.272873 | ||||||||
\(52\) | −17.1487 | −2.37809 | ||||||||
\(53\) | 2.47102 | 0.339420 | 0.169710 | − | 0.985494i | \(-0.445717\pi\) | ||||
0.169710 | + | 0.985494i | \(0.445717\pi\) | |||||||
\(54\) | 2.63401 | 0.358443 | ||||||||
\(55\) | −2.62502 | −0.353958 | ||||||||
\(56\) | −40.1522 | −5.36557 | ||||||||
\(57\) | 0.343156 | 0.0454522 | ||||||||
\(58\) | 14.4211 | 1.89359 | ||||||||
\(59\) | 13.7469 | 1.78970 | 0.894849 | − | 0.446369i | \(-0.147283\pi\) | ||||
0.894849 | + | 0.446369i | \(0.147283\pi\) | |||||||
\(60\) | −12.9623 | −1.67343 | ||||||||
\(61\) | 1.00000 | 0.128037 | ||||||||
\(62\) | −6.34152 | −0.805374 | ||||||||
\(63\) | 5.18852 | 0.653691 | ||||||||
\(64\) | 11.1197 | 1.38996 | ||||||||
\(65\) | −9.11617 | −1.13072 | ||||||||
\(66\) | −2.63401 | −0.324224 | ||||||||
\(67\) | 2.76619 | 0.337944 | 0.168972 | − | 0.985621i | \(-0.445955\pi\) | ||||
0.168972 | + | 0.985621i | \(0.445955\pi\) | |||||||
\(68\) | 9.62267 | 1.16692 | ||||||||
\(69\) | 4.48645 | 0.540105 | ||||||||
\(70\) | −35.8750 | −4.28789 | ||||||||
\(71\) | −16.0977 | −1.91045 | −0.955225 | − | 0.295881i | \(-0.904387\pi\) | ||||
−0.955225 | + | 0.295881i | \(0.904387\pi\) | |||||||
\(72\) | −7.73867 | −0.912012 | ||||||||
\(73\) | −3.11724 | −0.364845 | −0.182422 | − | 0.983220i | \(-0.558394\pi\) | ||||
−0.182422 | + | 0.983220i | \(0.558394\pi\) | |||||||
\(74\) | −27.2517 | −3.16794 | ||||||||
\(75\) | −1.89073 | −0.218323 | ||||||||
\(76\) | −1.69450 | −0.194373 | ||||||||
\(77\) | −5.18852 | −0.591286 | ||||||||
\(78\) | −9.14738 | −1.03574 | ||||||||
\(79\) | −5.15429 | −0.579903 | −0.289952 | − | 0.957041i | \(-0.593639\pi\) | ||||
−0.289952 | + | 0.957041i | \(0.593639\pi\) | |||||||
\(80\) | 27.5830 | 3.08388 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 1.14985 | 0.126980 | ||||||||
\(83\) | 2.12536 | 0.233289 | 0.116644 | − | 0.993174i | \(-0.462786\pi\) | ||||
0.116644 | + | 0.993174i | \(0.462786\pi\) | |||||||
\(84\) | −25.6208 | −2.79546 | ||||||||
\(85\) | 5.11538 | 0.554841 | ||||||||
\(86\) | −16.8788 | −1.82008 | ||||||||
\(87\) | 5.47498 | 0.586979 | ||||||||
\(88\) | 7.73867 | 0.824946 | ||||||||
\(89\) | 3.14440 | 0.333305 | 0.166653 | − | 0.986016i | \(-0.446704\pi\) | ||||
0.166653 | + | 0.986016i | \(0.446704\pi\) | |||||||
\(90\) | −6.91432 | −0.728833 | ||||||||
\(91\) | −18.0187 | −1.88887 | ||||||||
\(92\) | −22.1540 | −2.30972 | ||||||||
\(93\) | −2.40756 | −0.249652 | ||||||||
\(94\) | −11.6604 | −1.20267 | ||||||||
\(95\) | −0.900792 | −0.0924193 | ||||||||
\(96\) | 12.2001 | 1.24517 | ||||||||
\(97\) | 6.51443 | 0.661440 | 0.330720 | − | 0.943729i | \(-0.392708\pi\) | ||||
0.330720 | + | 0.943729i | \(0.392708\pi\) | |||||||
\(98\) | −52.4712 | −5.30039 | ||||||||
\(99\) | −1.00000 | −0.100504 | ||||||||
\(100\) | 9.33640 | 0.933640 | ||||||||
\(101\) | 11.1124 | 1.10572 | 0.552862 | − | 0.833273i | \(-0.313536\pi\) | ||||
0.552862 | + | 0.833273i | \(0.313536\pi\) | |||||||
\(102\) | 5.13290 | 0.508232 | ||||||||
\(103\) | −0.504742 | −0.0497337 | −0.0248668 | − | 0.999691i | \(-0.507916\pi\) | ||||
−0.0248668 | + | 0.999691i | \(0.507916\pi\) | |||||||
\(104\) | 26.8749 | 2.63530 | ||||||||
\(105\) | −13.6200 | −1.32917 | ||||||||
\(106\) | −6.50868 | −0.632178 | ||||||||
\(107\) | 7.83003 | 0.756957 | 0.378479 | − | 0.925610i | \(-0.376447\pi\) | ||||
0.378479 | + | 0.925610i | \(0.376447\pi\) | |||||||
\(108\) | −4.93799 | −0.475158 | ||||||||
\(109\) | −5.69464 | −0.545448 | −0.272724 | − | 0.962092i | \(-0.587925\pi\) | ||||
−0.272724 | + | 0.962092i | \(0.587925\pi\) | |||||||
\(110\) | 6.91432 | 0.659254 | ||||||||
\(111\) | −10.3461 | −0.982008 | ||||||||
\(112\) | 54.5196 | 5.15162 | ||||||||
\(113\) | 16.5161 | 1.55370 | 0.776850 | − | 0.629686i | \(-0.216816\pi\) | ||||
0.776850 | + | 0.629686i | \(0.216816\pi\) | |||||||
\(114\) | −0.903876 | −0.0846557 | ||||||||
\(115\) | −11.7770 | −1.09821 | ||||||||
\(116\) | −27.0354 | −2.51017 | ||||||||
\(117\) | −3.47280 | −0.321061 | ||||||||
\(118\) | −36.2095 | −3.33335 | ||||||||
\(119\) | 10.1109 | 0.926862 | ||||||||
\(120\) | 20.3142 | 1.85442 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | −2.63401 | −0.238472 | ||||||||
\(123\) | 0.436542 | 0.0393617 | ||||||||
\(124\) | 11.8885 | 1.06762 | ||||||||
\(125\) | −8.16190 | −0.730022 | ||||||||
\(126\) | −13.6666 | −1.21752 | ||||||||
\(127\) | 15.2576 | 1.35390 | 0.676948 | − | 0.736031i | \(-0.263302\pi\) | ||||
0.676948 | + | 0.736031i | \(0.263302\pi\) | |||||||
\(128\) | −4.88904 | −0.432134 | ||||||||
\(129\) | −6.40802 | −0.564195 | ||||||||
\(130\) | 24.0121 | 2.10600 | ||||||||
\(131\) | −2.57715 | −0.225167 | −0.112583 | − | 0.993642i | \(-0.535913\pi\) | ||||
−0.112583 | + | 0.993642i | \(0.535913\pi\) | |||||||
\(132\) | 4.93799 | 0.429797 | ||||||||
\(133\) | −1.78047 | −0.154387 | ||||||||
\(134\) | −7.28616 | −0.629428 | ||||||||
\(135\) | −2.62502 | −0.225926 | ||||||||
\(136\) | −15.0804 | −1.29313 | ||||||||
\(137\) | 14.4185 | 1.23185 | 0.615926 | − | 0.787804i | \(-0.288782\pi\) | ||||
0.615926 | + | 0.787804i | \(0.288782\pi\) | |||||||
\(138\) | −11.8173 | −1.00596 | ||||||||
\(139\) | 11.3125 | 0.959516 | 0.479758 | − | 0.877401i | \(-0.340724\pi\) | ||||
0.479758 | + | 0.877401i | \(0.340724\pi\) | |||||||
\(140\) | 67.2552 | 5.68410 | ||||||||
\(141\) | −4.42685 | −0.372808 | ||||||||
\(142\) | 42.4015 | 3.55826 | ||||||||
\(143\) | 3.47280 | 0.290410 | ||||||||
\(144\) | 10.5077 | 0.875645 | ||||||||
\(145\) | −14.3719 | −1.19352 | ||||||||
\(146\) | 8.21082 | 0.679532 | ||||||||
\(147\) | −19.9207 | −1.64303 | ||||||||
\(148\) | 51.0889 | 4.19948 | ||||||||
\(149\) | −4.30768 | −0.352899 | −0.176449 | − | 0.984310i | \(-0.556461\pi\) | ||||
−0.176449 | + | 0.984310i | \(0.556461\pi\) | |||||||
\(150\) | 4.98019 | 0.406631 | ||||||||
\(151\) | −12.6896 | −1.03267 | −0.516334 | − | 0.856387i | \(-0.672704\pi\) | ||||
−0.516334 | + | 0.856387i | \(0.672704\pi\) | |||||||
\(152\) | 2.65558 | 0.215396 | ||||||||
\(153\) | 1.94870 | 0.157543 | ||||||||
\(154\) | 13.6666 | 1.10128 | ||||||||
\(155\) | 6.31989 | 0.507626 | ||||||||
\(156\) | 17.1487 | 1.37299 | ||||||||
\(157\) | 10.8043 | 0.862274 | 0.431137 | − | 0.902286i | \(-0.358113\pi\) | ||||
0.431137 | + | 0.902286i | \(0.358113\pi\) | |||||||
\(158\) | 13.5764 | 1.08008 | ||||||||
\(159\) | −2.47102 | −0.195964 | ||||||||
\(160\) | −32.0255 | −2.53184 | ||||||||
\(161\) | −23.2780 | −1.83456 | ||||||||
\(162\) | −2.63401 | −0.206947 | ||||||||
\(163\) | 25.0214 | 1.95983 | 0.979913 | − | 0.199427i | \(-0.0639080\pi\) | ||||
0.979913 | + | 0.199427i | \(0.0639080\pi\) | |||||||
\(164\) | −2.15564 | −0.168327 | ||||||||
\(165\) | 2.62502 | 0.204358 | ||||||||
\(166\) | −5.59821 | −0.434506 | ||||||||
\(167\) | −21.9141 | −1.69576 | −0.847882 | − | 0.530185i | \(-0.822123\pi\) | ||||
−0.847882 | + | 0.530185i | \(0.822123\pi\) | |||||||
\(168\) | 40.1522 | 3.09781 | ||||||||
\(169\) | −0.939647 | −0.0722805 | ||||||||
\(170\) | −13.4740 | −1.03340 | ||||||||
\(171\) | −0.343156 | −0.0262418 | ||||||||
\(172\) | 31.6427 | 2.41273 | ||||||||
\(173\) | −19.3446 | −1.47075 | −0.735373 | − | 0.677663i | \(-0.762993\pi\) | ||||
−0.735373 | + | 0.677663i | \(0.762993\pi\) | |||||||
\(174\) | −14.4211 | −1.09326 | ||||||||
\(175\) | 9.81008 | 0.741572 | ||||||||
\(176\) | −10.5077 | −0.792051 | ||||||||
\(177\) | −13.7469 | −1.03328 | ||||||||
\(178\) | −8.28236 | −0.620789 | ||||||||
\(179\) | 20.9873 | 1.56866 | 0.784331 | − | 0.620343i | \(-0.213007\pi\) | ||||
0.784331 | + | 0.620343i | \(0.213007\pi\) | |||||||
\(180\) | 12.9623 | 0.966154 | ||||||||
\(181\) | −26.3913 | −1.96165 | −0.980826 | − | 0.194886i | \(-0.937566\pi\) | ||||
−0.980826 | + | 0.194886i | \(0.937566\pi\) | |||||||
\(182\) | 47.4613 | 3.51807 | ||||||||
\(183\) | −1.00000 | −0.0739221 | ||||||||
\(184\) | 34.7191 | 2.55953 | ||||||||
\(185\) | 27.1587 | 1.99675 | ||||||||
\(186\) | 6.34152 | 0.464983 | ||||||||
\(187\) | −1.94870 | −0.142503 | ||||||||
\(188\) | 21.8597 | 1.59429 | ||||||||
\(189\) | −5.18852 | −0.377409 | ||||||||
\(190\) | 2.37269 | 0.172133 | ||||||||
\(191\) | 20.2002 | 1.46164 | 0.730818 | − | 0.682572i | \(-0.239139\pi\) | ||||
0.730818 | + | 0.682572i | \(0.239139\pi\) | |||||||
\(192\) | −11.1197 | −0.802492 | ||||||||
\(193\) | −16.2353 | −1.16864 | −0.584321 | − | 0.811523i | \(-0.698639\pi\) | ||||
−0.584321 | + | 0.811523i | \(0.698639\pi\) | |||||||
\(194\) | −17.1591 | −1.23195 | ||||||||
\(195\) | 9.11617 | 0.652823 | ||||||||
\(196\) | 98.3681 | 7.02629 | ||||||||
\(197\) | 10.8231 | 0.771112 | 0.385556 | − | 0.922685i | \(-0.374010\pi\) | ||||
0.385556 | + | 0.922685i | \(0.374010\pi\) | |||||||
\(198\) | 2.63401 | 0.187191 | ||||||||
\(199\) | 17.1207 | 1.21366 | 0.606828 | − | 0.794833i | \(-0.292442\pi\) | ||||
0.606828 | + | 0.794833i | \(0.292442\pi\) | |||||||
\(200\) | −14.6317 | −1.03462 | ||||||||
\(201\) | −2.76619 | −0.195112 | ||||||||
\(202\) | −29.2701 | −2.05944 | ||||||||
\(203\) | −28.4070 | −1.99378 | ||||||||
\(204\) | −9.62267 | −0.673722 | ||||||||
\(205\) | −1.14593 | −0.0800353 | ||||||||
\(206\) | 1.32949 | 0.0926301 | ||||||||
\(207\) | −4.48645 | −0.311830 | ||||||||
\(208\) | −36.4913 | −2.53022 | ||||||||
\(209\) | 0.343156 | 0.0237366 | ||||||||
\(210\) | 35.8750 | 2.47561 | ||||||||
\(211\) | 6.07527 | 0.418239 | 0.209119 | − | 0.977890i | \(-0.432940\pi\) | ||||
0.209119 | + | 0.977890i | \(0.432940\pi\) | |||||||
\(212\) | 12.2019 | 0.838027 | ||||||||
\(213\) | 16.0977 | 1.10300 | ||||||||
\(214\) | −20.6243 | −1.40985 | ||||||||
\(215\) | 16.8212 | 1.14719 | ||||||||
\(216\) | 7.73867 | 0.526550 | ||||||||
\(217\) | 12.4917 | 0.847989 | ||||||||
\(218\) | 14.9997 | 1.01591 | ||||||||
\(219\) | 3.11724 | 0.210643 | ||||||||
\(220\) | −12.9623 | −0.873919 | ||||||||
\(221\) | −6.76746 | −0.455229 | ||||||||
\(222\) | 27.2517 | 1.82901 | ||||||||
\(223\) | −24.7908 | −1.66011 | −0.830057 | − | 0.557679i | \(-0.811692\pi\) | ||||
−0.830057 | + | 0.557679i | \(0.811692\pi\) | |||||||
\(224\) | −63.3004 | −4.22944 | ||||||||
\(225\) | 1.89073 | 0.126049 | ||||||||
\(226\) | −43.5034 | −2.89380 | ||||||||
\(227\) | 25.6959 | 1.70549 | 0.852747 | − | 0.522324i | \(-0.174935\pi\) | ||||
0.852747 | + | 0.522324i | \(0.174935\pi\) | |||||||
\(228\) | 1.69450 | 0.112221 | ||||||||
\(229\) | −1.69139 | −0.111770 | −0.0558852 | − | 0.998437i | \(-0.517798\pi\) | ||||
−0.0558852 | + | 0.998437i | \(0.517798\pi\) | |||||||
\(230\) | 31.0207 | 2.04545 | ||||||||
\(231\) | 5.18852 | 0.341379 | ||||||||
\(232\) | 42.3691 | 2.78167 | ||||||||
\(233\) | −8.61616 | −0.564463 | −0.282232 | − | 0.959346i | \(-0.591075\pi\) | ||||
−0.282232 | + | 0.959346i | \(0.591075\pi\) | |||||||
\(234\) | 9.14738 | 0.597983 | ||||||||
\(235\) | 11.6206 | 0.758043 | ||||||||
\(236\) | 67.8822 | 4.41875 | ||||||||
\(237\) | 5.15429 | 0.334807 | ||||||||
\(238\) | −26.6321 | −1.72630 | ||||||||
\(239\) | −13.2629 | −0.857905 | −0.428953 | − | 0.903327i | \(-0.641117\pi\) | ||||
−0.428953 | + | 0.903327i | \(0.641117\pi\) | |||||||
\(240\) | −27.5830 | −1.78048 | ||||||||
\(241\) | 2.12784 | 0.137066 | 0.0685332 | − | 0.997649i | \(-0.478168\pi\) | ||||
0.0685332 | + | 0.997649i | \(0.478168\pi\) | |||||||
\(242\) | −2.63401 | −0.169320 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 4.93799 | 0.316122 | ||||||||
\(245\) | 52.2922 | 3.34083 | ||||||||
\(246\) | −1.14985 | −0.0733120 | ||||||||
\(247\) | 1.19171 | 0.0758270 | ||||||||
\(248\) | −18.6313 | −1.18309 | ||||||||
\(249\) | −2.12536 | −0.134689 | ||||||||
\(250\) | 21.4985 | 1.35968 | ||||||||
\(251\) | 1.21883 | 0.0769321 | 0.0384661 | − | 0.999260i | \(-0.487753\pi\) | ||||
0.0384661 | + | 0.999260i | \(0.487753\pi\) | |||||||
\(252\) | 25.6208 | 1.61396 | ||||||||
\(253\) | 4.48645 | 0.282060 | ||||||||
\(254\) | −40.1887 | −2.52166 | ||||||||
\(255\) | −5.11538 | −0.320338 | ||||||||
\(256\) | −9.36155 | −0.585097 | ||||||||
\(257\) | −10.0350 | −0.625964 | −0.312982 | − | 0.949759i | \(-0.601328\pi\) | ||||
−0.312982 | + | 0.949759i | \(0.601328\pi\) | |||||||
\(258\) | 16.8788 | 1.05083 | ||||||||
\(259\) | 53.6809 | 3.33557 | ||||||||
\(260\) | −45.0155 | −2.79175 | ||||||||
\(261\) | −5.47498 | −0.338893 | ||||||||
\(262\) | 6.78823 | 0.419378 | ||||||||
\(263\) | −15.4701 | −0.953925 | −0.476963 | − | 0.878924i | \(-0.658262\pi\) | ||||
−0.476963 | + | 0.878924i | \(0.658262\pi\) | |||||||
\(264\) | −7.73867 | −0.476283 | ||||||||
\(265\) | 6.48647 | 0.398461 | ||||||||
\(266\) | 4.68977 | 0.287549 | ||||||||
\(267\) | −3.14440 | −0.192434 | ||||||||
\(268\) | 13.6594 | 0.834381 | ||||||||
\(269\) | −11.4654 | −0.699059 | −0.349530 | − | 0.936925i | \(-0.613659\pi\) | ||||
−0.349530 | + | 0.936925i | \(0.613659\pi\) | |||||||
\(270\) | 6.91432 | 0.420792 | ||||||||
\(271\) | −10.6925 | −0.649521 | −0.324760 | − | 0.945796i | \(-0.605284\pi\) | ||||
−0.324760 | + | 0.945796i | \(0.605284\pi\) | |||||||
\(272\) | 20.4765 | 1.24157 | ||||||||
\(273\) | 18.0187 | 1.09054 | ||||||||
\(274\) | −37.9783 | −2.29435 | ||||||||
\(275\) | −1.89073 | −0.114015 | ||||||||
\(276\) | 22.1540 | 1.33351 | ||||||||
\(277\) | −31.4466 | −1.88944 | −0.944720 | − | 0.327877i | \(-0.893667\pi\) | ||||
−0.944720 | + | 0.327877i | \(0.893667\pi\) | |||||||
\(278\) | −29.7973 | −1.78712 | ||||||||
\(279\) | 2.40756 | 0.144137 | ||||||||
\(280\) | −105.400 | −6.29888 | ||||||||
\(281\) | 15.8197 | 0.943723 | 0.471861 | − | 0.881673i | \(-0.343582\pi\) | ||||
0.471861 | + | 0.881673i | \(0.343582\pi\) | |||||||
\(282\) | 11.6604 | 0.694364 | ||||||||
\(283\) | −17.7131 | −1.05293 | −0.526467 | − | 0.850196i | \(-0.676484\pi\) | ||||
−0.526467 | + | 0.850196i | \(0.676484\pi\) | |||||||
\(284\) | −79.4904 | −4.71689 | ||||||||
\(285\) | 0.900792 | 0.0533583 | ||||||||
\(286\) | −9.14738 | −0.540896 | ||||||||
\(287\) | −2.26500 | −0.133699 | ||||||||
\(288\) | −12.2001 | −0.718898 | ||||||||
\(289\) | −13.2026 | −0.776621 | ||||||||
\(290\) | 37.8557 | 2.22296 | ||||||||
\(291\) | −6.51443 | −0.381883 | ||||||||
\(292\) | −15.3929 | −0.900799 | ||||||||
\(293\) | −6.92077 | −0.404316 | −0.202158 | − | 0.979353i | \(-0.564795\pi\) | ||||
−0.202158 | + | 0.979353i | \(0.564795\pi\) | |||||||
\(294\) | 52.4712 | 3.06018 | ||||||||
\(295\) | 36.0860 | 2.10101 | ||||||||
\(296\) | −80.0651 | −4.65369 | ||||||||
\(297\) | 1.00000 | 0.0580259 | ||||||||
\(298\) | 11.3465 | 0.657282 | ||||||||
\(299\) | 15.5805 | 0.901046 | ||||||||
\(300\) | −9.33640 | −0.539037 | ||||||||
\(301\) | 33.2481 | 1.91639 | ||||||||
\(302\) | 33.4246 | 1.92337 | ||||||||
\(303\) | −11.1124 | −0.638390 | ||||||||
\(304\) | −3.60580 | −0.206807 | ||||||||
\(305\) | 2.62502 | 0.150308 | ||||||||
\(306\) | −5.13290 | −0.293428 | ||||||||
\(307\) | 15.9515 | 0.910401 | 0.455201 | − | 0.890389i | \(-0.349568\pi\) | ||||
0.455201 | + | 0.890389i | \(0.349568\pi\) | |||||||
\(308\) | −25.6208 | −1.45988 | ||||||||
\(309\) | 0.504742 | 0.0287138 | ||||||||
\(310\) | −16.6466 | −0.945465 | ||||||||
\(311\) | −13.8655 | −0.786239 | −0.393119 | − | 0.919487i | \(-0.628604\pi\) | ||||
−0.393119 | + | 0.919487i | \(0.628604\pi\) | |||||||
\(312\) | −26.8749 | −1.52149 | ||||||||
\(313\) | 18.1128 | 1.02380 | 0.511898 | − | 0.859046i | \(-0.328943\pi\) | ||||
0.511898 | + | 0.859046i | \(0.328943\pi\) | |||||||
\(314\) | −28.4585 | −1.60601 | ||||||||
\(315\) | 13.6200 | 0.767398 | ||||||||
\(316\) | −25.4518 | −1.43178 | ||||||||
\(317\) | 22.4082 | 1.25857 | 0.629286 | − | 0.777174i | \(-0.283348\pi\) | ||||
0.629286 | + | 0.777174i | \(0.283348\pi\) | |||||||
\(318\) | 6.50868 | 0.364988 | ||||||||
\(319\) | 5.47498 | 0.306540 | ||||||||
\(320\) | 29.1893 | 1.63173 | ||||||||
\(321\) | −7.83003 | −0.437029 | ||||||||
\(322\) | 61.3144 | 3.41692 | ||||||||
\(323\) | −0.668710 | −0.0372080 | ||||||||
\(324\) | 4.93799 | 0.274333 | ||||||||
\(325\) | −6.56613 | −0.364223 | ||||||||
\(326\) | −65.9065 | −3.65022 | ||||||||
\(327\) | 5.69464 | 0.314914 | ||||||||
\(328\) | 3.37826 | 0.186533 | ||||||||
\(329\) | 22.9688 | 1.26631 | ||||||||
\(330\) | −6.91432 | −0.380621 | ||||||||
\(331\) | −1.51172 | −0.0830916 | −0.0415458 | − | 0.999137i | \(-0.513228\pi\) | ||||
−0.0415458 | + | 0.999137i | \(0.513228\pi\) | |||||||
\(332\) | 10.4950 | 0.575988 | ||||||||
\(333\) | 10.3461 | 0.566963 | ||||||||
\(334\) | 57.7219 | 3.15840 | ||||||||
\(335\) | 7.26130 | 0.396727 | ||||||||
\(336\) | −54.5196 | −2.97429 | ||||||||
\(337\) | −2.97052 | −0.161815 | −0.0809074 | − | 0.996722i | \(-0.525782\pi\) | ||||
−0.0809074 | + | 0.996722i | \(0.525782\pi\) | |||||||
\(338\) | 2.47503 | 0.134624 | ||||||||
\(339\) | −16.5161 | −0.897029 | ||||||||
\(340\) | 25.2597 | 1.36990 | ||||||||
\(341\) | −2.40756 | −0.130377 | ||||||||
\(342\) | 0.903876 | 0.0488760 | ||||||||
\(343\) | 67.0392 | 3.61978 | ||||||||
\(344\) | −49.5896 | −2.67369 | ||||||||
\(345\) | 11.7770 | 0.634053 | ||||||||
\(346\) | 50.9539 | 2.73930 | ||||||||
\(347\) | 34.9082 | 1.87397 | 0.936985 | − | 0.349369i | \(-0.113604\pi\) | ||||
0.936985 | + | 0.349369i | \(0.113604\pi\) | |||||||
\(348\) | 27.0354 | 1.44925 | ||||||||
\(349\) | −7.36747 | −0.394371 | −0.197186 | − | 0.980366i | \(-0.563180\pi\) | ||||
−0.197186 | + | 0.980366i | \(0.563180\pi\) | |||||||
\(350\) | −25.8398 | −1.38120 | ||||||||
\(351\) | 3.47280 | 0.185364 | ||||||||
\(352\) | 12.2001 | 0.650268 | ||||||||
\(353\) | 30.1994 | 1.60735 | 0.803675 | − | 0.595068i | \(-0.202875\pi\) | ||||
0.803675 | + | 0.595068i | \(0.202875\pi\) | |||||||
\(354\) | 36.2095 | 1.92451 | ||||||||
\(355\) | −42.2569 | −2.24276 | ||||||||
\(356\) | 15.5270 | 0.822929 | ||||||||
\(357\) | −10.1109 | −0.535124 | ||||||||
\(358\) | −55.2806 | −2.92167 | ||||||||
\(359\) | −28.2798 | −1.49255 | −0.746274 | − | 0.665639i | \(-0.768159\pi\) | ||||
−0.746274 | + | 0.665639i | \(0.768159\pi\) | |||||||
\(360\) | −20.3142 | −1.07065 | ||||||||
\(361\) | −18.8822 | −0.993802 | ||||||||
\(362\) | 69.5149 | 3.65362 | ||||||||
\(363\) | −1.00000 | −0.0524864 | ||||||||
\(364\) | −88.9760 | −4.66361 | ||||||||
\(365\) | −8.18281 | −0.428308 | ||||||||
\(366\) | 2.63401 | 0.137682 | ||||||||
\(367\) | 9.06316 | 0.473093 | 0.236547 | − | 0.971620i | \(-0.423984\pi\) | ||||
0.236547 | + | 0.971620i | \(0.423984\pi\) | |||||||
\(368\) | −47.1424 | −2.45747 | ||||||||
\(369\) | −0.436542 | −0.0227255 | ||||||||
\(370\) | −71.5362 | −3.71899 | ||||||||
\(371\) | 12.8209 | 0.665629 | ||||||||
\(372\) | −11.8885 | −0.616390 | ||||||||
\(373\) | 4.76411 | 0.246676 | 0.123338 | − | 0.992365i | \(-0.460640\pi\) | ||||
0.123338 | + | 0.992365i | \(0.460640\pi\) | |||||||
\(374\) | 5.13290 | 0.265416 | ||||||||
\(375\) | 8.16190 | 0.421479 | ||||||||
\(376\) | −34.2580 | −1.76672 | ||||||||
\(377\) | 19.0135 | 0.979245 | ||||||||
\(378\) | 13.6666 | 0.702933 | ||||||||
\(379\) | 24.6033 | 1.26379 | 0.631893 | − | 0.775056i | \(-0.282278\pi\) | ||||
0.631893 | + | 0.775056i | \(0.282278\pi\) | |||||||
\(380\) | −4.44810 | −0.228183 | ||||||||
\(381\) | −15.2576 | −0.781672 | ||||||||
\(382\) | −53.2075 | −2.72233 | ||||||||
\(383\) | 1.16351 | 0.0594524 | 0.0297262 | − | 0.999558i | \(-0.490536\pi\) | ||||
0.0297262 | + | 0.999558i | \(0.490536\pi\) | |||||||
\(384\) | 4.88904 | 0.249493 | ||||||||
\(385\) | −13.6200 | −0.694137 | ||||||||
\(386\) | 42.7638 | 2.17662 | ||||||||
\(387\) | 6.40802 | 0.325738 | ||||||||
\(388\) | 32.1682 | 1.63309 | ||||||||
\(389\) | 4.68535 | 0.237557 | 0.118778 | − | 0.992921i | \(-0.462102\pi\) | ||||
0.118778 | + | 0.992921i | \(0.462102\pi\) | |||||||
\(390\) | −24.0121 | −1.21590 | ||||||||
\(391\) | −8.74275 | −0.442140 | ||||||||
\(392\) | −154.160 | −7.78624 | ||||||||
\(393\) | 2.57715 | 0.130000 | ||||||||
\(394\) | −28.5080 | −1.43621 | ||||||||
\(395\) | −13.5301 | −0.680774 | ||||||||
\(396\) | −4.93799 | −0.248143 | ||||||||
\(397\) | −32.1659 | −1.61436 | −0.807180 | − | 0.590306i | \(-0.799007\pi\) | ||||
−0.807180 | + | 0.590306i | \(0.799007\pi\) | |||||||
\(398\) | −45.0961 | −2.26046 | ||||||||
\(399\) | 1.78047 | 0.0891351 | ||||||||
\(400\) | 19.8673 | 0.993365 | ||||||||
\(401\) | −37.0986 | −1.85262 | −0.926309 | − | 0.376765i | \(-0.877036\pi\) | ||||
−0.926309 | + | 0.376765i | \(0.877036\pi\) | |||||||
\(402\) | 7.28616 | 0.363401 | ||||||||
\(403\) | −8.36097 | −0.416490 | ||||||||
\(404\) | 54.8729 | 2.73003 | ||||||||
\(405\) | 2.62502 | 0.130438 | ||||||||
\(406\) | 74.8242 | 3.71346 | ||||||||
\(407\) | −10.3461 | −0.512837 | ||||||||
\(408\) | 15.0804 | 0.746590 | ||||||||
\(409\) | −22.4268 | −1.10893 | −0.554467 | − | 0.832206i | \(-0.687078\pi\) | ||||
−0.554467 | + | 0.832206i | \(0.687078\pi\) | |||||||
\(410\) | 3.01839 | 0.149068 | ||||||||
\(411\) | −14.4185 | −0.711210 | ||||||||
\(412\) | −2.49241 | −0.122792 | ||||||||
\(413\) | 71.3262 | 3.50973 | ||||||||
\(414\) | 11.8173 | 0.580790 | ||||||||
\(415\) | 5.57912 | 0.273868 | ||||||||
\(416\) | 42.3685 | 2.07729 | ||||||||
\(417\) | −11.3125 | −0.553977 | ||||||||
\(418\) | −0.903876 | −0.0442100 | ||||||||
\(419\) | −8.94385 | −0.436936 | −0.218468 | − | 0.975844i | \(-0.570106\pi\) | ||||
−0.218468 | + | 0.975844i | \(0.570106\pi\) | |||||||
\(420\) | −67.2552 | −3.28172 | ||||||||
\(421\) | −40.0168 | −1.95030 | −0.975151 | − | 0.221543i | \(-0.928891\pi\) | ||||
−0.975151 | + | 0.221543i | \(0.928891\pi\) | |||||||
\(422\) | −16.0023 | −0.778980 | ||||||||
\(423\) | 4.42685 | 0.215241 | ||||||||
\(424\) | −19.1224 | −0.928666 | ||||||||
\(425\) | 3.68447 | 0.178723 | ||||||||
\(426\) | −42.4015 | −2.05436 | ||||||||
\(427\) | 5.18852 | 0.251090 | ||||||||
\(428\) | 38.6646 | 1.86892 | ||||||||
\(429\) | −3.47280 | −0.167668 | ||||||||
\(430\) | −44.3071 | −2.13668 | ||||||||
\(431\) | −1.04053 | −0.0501205 | −0.0250603 | − | 0.999686i | \(-0.507978\pi\) | ||||
−0.0250603 | + | 0.999686i | \(0.507978\pi\) | |||||||
\(432\) | −10.5077 | −0.505554 | ||||||||
\(433\) | −15.4980 | −0.744785 | −0.372393 | − | 0.928075i | \(-0.621463\pi\) | ||||
−0.372393 | + | 0.928075i | \(0.621463\pi\) | |||||||
\(434\) | −32.9031 | −1.57940 | ||||||||
\(435\) | 14.3719 | 0.689081 | ||||||||
\(436\) | −28.1201 | −1.34671 | ||||||||
\(437\) | 1.53955 | 0.0736468 | ||||||||
\(438\) | −8.21082 | −0.392328 | ||||||||
\(439\) | 22.0242 | 1.05116 | 0.525579 | − | 0.850745i | \(-0.323849\pi\) | ||||
0.525579 | + | 0.850745i | \(0.323849\pi\) | |||||||
\(440\) | 20.3142 | 0.968440 | ||||||||
\(441\) | 19.9207 | 0.948604 | ||||||||
\(442\) | 17.8255 | 0.847874 | ||||||||
\(443\) | 27.4427 | 1.30384 | 0.651921 | − | 0.758287i | \(-0.273964\pi\) | ||||
0.651921 | + | 0.758287i | \(0.273964\pi\) | |||||||
\(444\) | −51.0889 | −2.42457 | ||||||||
\(445\) | 8.25410 | 0.391282 | ||||||||
\(446\) | 65.2991 | 3.09200 | ||||||||
\(447\) | 4.30768 | 0.203746 | ||||||||
\(448\) | 57.6945 | 2.72581 | ||||||||
\(449\) | −31.7031 | −1.49616 | −0.748081 | − | 0.663607i | \(-0.769025\pi\) | ||||
−0.748081 | + | 0.663607i | \(0.769025\pi\) | |||||||
\(450\) | −4.98019 | −0.234769 | ||||||||
\(451\) | 0.436542 | 0.0205560 | ||||||||
\(452\) | 81.5561 | 3.83607 | ||||||||
\(453\) | 12.6896 | 0.596211 | ||||||||
\(454\) | −67.6830 | −3.17652 | ||||||||
\(455\) | −47.2994 | −2.21743 | ||||||||
\(456\) | −2.65558 | −0.124359 | ||||||||
\(457\) | −6.80691 | −0.318414 | −0.159207 | − | 0.987245i | \(-0.550894\pi\) | ||||
−0.159207 | + | 0.987245i | \(0.550894\pi\) | |||||||
\(458\) | 4.45514 | 0.208175 | ||||||||
\(459\) | −1.94870 | −0.0909577 | ||||||||
\(460\) | −58.1547 | −2.71148 | ||||||||
\(461\) | 3.68797 | 0.171766 | 0.0858830 | − | 0.996305i | \(-0.472629\pi\) | ||||
0.0858830 | + | 0.996305i | \(0.472629\pi\) | |||||||
\(462\) | −13.6666 | −0.635827 | ||||||||
\(463\) | 6.47116 | 0.300740 | 0.150370 | − | 0.988630i | \(-0.451953\pi\) | ||||
0.150370 | + | 0.988630i | \(0.451953\pi\) | |||||||
\(464\) | −57.5296 | −2.67075 | ||||||||
\(465\) | −6.31989 | −0.293078 | ||||||||
\(466\) | 22.6950 | 1.05133 | ||||||||
\(467\) | −14.4505 | −0.668692 | −0.334346 | − | 0.942450i | \(-0.608515\pi\) | ||||
−0.334346 | + | 0.942450i | \(0.608515\pi\) | |||||||
\(468\) | −17.1487 | −0.792697 | ||||||||
\(469\) | 14.3524 | 0.662733 | ||||||||
\(470\) | −30.6087 | −1.41187 | ||||||||
\(471\) | −10.8043 | −0.497834 | ||||||||
\(472\) | −106.383 | −4.89668 | ||||||||
\(473\) | −6.40802 | −0.294641 | ||||||||
\(474\) | −13.5764 | −0.623587 | ||||||||
\(475\) | −0.648816 | −0.0297697 | ||||||||
\(476\) | 49.9274 | 2.28842 | ||||||||
\(477\) | 2.47102 | 0.113140 | ||||||||
\(478\) | 34.9345 | 1.59787 | ||||||||
\(479\) | −26.3992 | −1.20621 | −0.603106 | − | 0.797661i | \(-0.706070\pi\) | ||||
−0.603106 | + | 0.797661i | \(0.706070\pi\) | |||||||
\(480\) | 32.0255 | 1.46176 | ||||||||
\(481\) | −35.9300 | −1.63827 | ||||||||
\(482\) | −5.60475 | −0.255289 | ||||||||
\(483\) | 23.2780 | 1.05919 | ||||||||
\(484\) | 4.93799 | 0.224454 | ||||||||
\(485\) | 17.1005 | 0.776494 | ||||||||
\(486\) | 2.63401 | 0.119481 | ||||||||
\(487\) | 1.02748 | 0.0465596 | 0.0232798 | − | 0.999729i | \(-0.492589\pi\) | ||||
0.0232798 | + | 0.999729i | \(0.492589\pi\) | |||||||
\(488\) | −7.73867 | −0.350313 | ||||||||
\(489\) | −25.0214 | −1.13151 | ||||||||
\(490\) | −137.738 | −6.22237 | ||||||||
\(491\) | 26.4321 | 1.19286 | 0.596432 | − | 0.802664i | \(-0.296584\pi\) | ||||
0.596432 | + | 0.802664i | \(0.296584\pi\) | |||||||
\(492\) | 2.15564 | 0.0971837 | ||||||||
\(493\) | −10.6691 | −0.480512 | ||||||||
\(494\) | −3.13898 | −0.141229 | ||||||||
\(495\) | −2.62502 | −0.117986 | ||||||||
\(496\) | 25.2980 | 1.13591 | ||||||||
\(497\) | −83.5234 | −3.74653 | ||||||||
\(498\) | 5.59821 | 0.250862 | ||||||||
\(499\) | −21.5904 | −0.966520 | −0.483260 | − | 0.875477i | \(-0.660547\pi\) | ||||
−0.483260 | + | 0.875477i | \(0.660547\pi\) | |||||||
\(500\) | −40.3033 | −1.80242 | ||||||||
\(501\) | 21.9141 | 0.979050 | ||||||||
\(502\) | −3.21042 | −0.143288 | ||||||||
\(503\) | −21.8467 | −0.974095 | −0.487048 | − | 0.873375i | \(-0.661926\pi\) | ||||
−0.487048 | + | 0.873375i | \(0.661926\pi\) | |||||||
\(504\) | −40.1522 | −1.78852 | ||||||||
\(505\) | 29.1703 | 1.29806 | ||||||||
\(506\) | −11.8173 | −0.525344 | ||||||||
\(507\) | 0.939647 | 0.0417312 | ||||||||
\(508\) | 75.3420 | 3.34276 | ||||||||
\(509\) | 39.4287 | 1.74765 | 0.873823 | − | 0.486245i | \(-0.161634\pi\) | ||||
0.873823 | + | 0.486245i | \(0.161634\pi\) | |||||||
\(510\) | 13.4740 | 0.596637 | ||||||||
\(511\) | −16.1738 | −0.715488 | ||||||||
\(512\) | 34.4365 | 1.52189 | ||||||||
\(513\) | 0.343156 | 0.0151507 | ||||||||
\(514\) | 26.4322 | 1.16587 | ||||||||
\(515\) | −1.32496 | −0.0583846 | ||||||||
\(516\) | −31.6427 | −1.39299 | ||||||||
\(517\) | −4.42685 | −0.194693 | ||||||||
\(518\) | −141.396 | −6.21258 | ||||||||
\(519\) | 19.3446 | 0.849135 | ||||||||
\(520\) | 70.5471 | 3.09370 | ||||||||
\(521\) | 4.56305 | 0.199911 | 0.0999555 | − | 0.994992i | \(-0.468130\pi\) | ||||
0.0999555 | + | 0.994992i | \(0.468130\pi\) | |||||||
\(522\) | 14.4211 | 0.631195 | ||||||||
\(523\) | 6.29112 | 0.275092 | 0.137546 | − | 0.990495i | \(-0.456079\pi\) | ||||
0.137546 | + | 0.990495i | \(0.456079\pi\) | |||||||
\(524\) | −12.7259 | −0.555935 | ||||||||
\(525\) | −9.81008 | −0.428147 | ||||||||
\(526\) | 40.7482 | 1.77671 | ||||||||
\(527\) | 4.69162 | 0.204370 | ||||||||
\(528\) | 10.5077 | 0.457291 | ||||||||
\(529\) | −2.87181 | −0.124861 | ||||||||
\(530\) | −17.0854 | −0.742143 | ||||||||
\(531\) | 13.7469 | 0.596566 | ||||||||
\(532\) | −8.79195 | −0.381179 | ||||||||
\(533\) | 1.51602 | 0.0656663 | ||||||||
\(534\) | 8.28236 | 0.358413 | ||||||||
\(535\) | 20.5540 | 0.888626 | ||||||||
\(536\) | −21.4066 | −0.924626 | ||||||||
\(537\) | −20.9873 | −0.905667 | ||||||||
\(538\) | 30.2000 | 1.30201 | ||||||||
\(539\) | −19.9207 | −0.858045 | ||||||||
\(540\) | −12.9623 | −0.557809 | ||||||||
\(541\) | 14.4263 | 0.620233 | 0.310117 | − | 0.950699i | \(-0.399632\pi\) | ||||
0.310117 | + | 0.950699i | \(0.399632\pi\) | |||||||
\(542\) | 28.1640 | 1.20975 | ||||||||
\(543\) | 26.3913 | 1.13256 | ||||||||
\(544\) | −23.7744 | −1.01932 | ||||||||
\(545\) | −14.9486 | −0.640326 | ||||||||
\(546\) | −47.4613 | −2.03116 | ||||||||
\(547\) | 9.30055 | 0.397663 | 0.198831 | − | 0.980034i | \(-0.436285\pi\) | ||||
0.198831 | + | 0.980034i | \(0.436285\pi\) | |||||||
\(548\) | 71.1982 | 3.04144 | ||||||||
\(549\) | 1.00000 | 0.0426790 | ||||||||
\(550\) | 4.98019 | 0.212356 | ||||||||
\(551\) | 1.87877 | 0.0800384 | ||||||||
\(552\) | −34.7191 | −1.47774 | ||||||||
\(553\) | −26.7431 | −1.13723 | ||||||||
\(554\) | 82.8304 | 3.51913 | ||||||||
\(555\) | −27.1587 | −1.15282 | ||||||||
\(556\) | 55.8611 | 2.36904 | ||||||||
\(557\) | −4.86880 | −0.206298 | −0.103149 | − | 0.994666i | \(-0.532892\pi\) | ||||
−0.103149 | + | 0.994666i | \(0.532892\pi\) | |||||||
\(558\) | −6.34152 | −0.268458 | ||||||||
\(559\) | −22.2538 | −0.941235 | ||||||||
\(560\) | 143.115 | 6.04771 | ||||||||
\(561\) | 1.94870 | 0.0822743 | ||||||||
\(562\) | −41.6691 | −1.75771 | ||||||||
\(563\) | 14.5434 | 0.612929 | 0.306465 | − | 0.951882i | \(-0.400854\pi\) | ||||
0.306465 | + | 0.951882i | \(0.400854\pi\) | |||||||
\(564\) | −21.8597 | −0.920461 | ||||||||
\(565\) | 43.3550 | 1.82396 | ||||||||
\(566\) | 46.6564 | 1.96111 | ||||||||
\(567\) | 5.18852 | 0.217897 | ||||||||
\(568\) | 124.575 | 5.22706 | ||||||||
\(569\) | 25.4145 | 1.06543 | 0.532717 | − | 0.846294i | \(-0.321171\pi\) | ||||
0.532717 | + | 0.846294i | \(0.321171\pi\) | |||||||
\(570\) | −2.37269 | −0.0993811 | ||||||||
\(571\) | 3.21902 | 0.134712 | 0.0673560 | − | 0.997729i | \(-0.478544\pi\) | ||||
0.0673560 | + | 0.997729i | \(0.478544\pi\) | |||||||
\(572\) | 17.1487 | 0.717021 | ||||||||
\(573\) | −20.2002 | −0.843876 | ||||||||
\(574\) | 5.96603 | 0.249017 | ||||||||
\(575\) | −8.48266 | −0.353751 | ||||||||
\(576\) | 11.1197 | 0.463319 | ||||||||
\(577\) | 16.5724 | 0.689918 | 0.344959 | − | 0.938618i | \(-0.387893\pi\) | ||||
0.344959 | + | 0.938618i | \(0.387893\pi\) | |||||||
\(578\) | 34.7756 | 1.44647 | ||||||||
\(579\) | 16.2353 | 0.674715 | ||||||||
\(580\) | −70.9684 | −2.94680 | ||||||||
\(581\) | 11.0275 | 0.457497 | ||||||||
\(582\) | 17.1591 | 0.711266 | ||||||||
\(583\) | −2.47102 | −0.102339 | ||||||||
\(584\) | 24.1233 | 0.998228 | ||||||||
\(585\) | −9.11617 | −0.376907 | ||||||||
\(586\) | 18.2294 | 0.753048 | ||||||||
\(587\) | 7.08569 | 0.292458 | 0.146229 | − | 0.989251i | \(-0.453286\pi\) | ||||
0.146229 | + | 0.989251i | \(0.453286\pi\) | |||||||
\(588\) | −98.3681 | −4.05663 | ||||||||
\(589\) | −0.826169 | −0.0340417 | ||||||||
\(590\) | −95.0507 | −3.91317 | ||||||||
\(591\) | −10.8231 | −0.445201 | ||||||||
\(592\) | 108.714 | 4.46812 | ||||||||
\(593\) | −10.7052 | −0.439612 | −0.219806 | − | 0.975544i | \(-0.570542\pi\) | ||||
−0.219806 | + | 0.975544i | \(0.570542\pi\) | |||||||
\(594\) | −2.63401 | −0.108075 | ||||||||
\(595\) | 26.5412 | 1.08809 | ||||||||
\(596\) | −21.2713 | −0.871305 | ||||||||
\(597\) | −17.1207 | −0.700705 | ||||||||
\(598\) | −41.0392 | −1.67822 | ||||||||
\(599\) | −15.1212 | −0.617836 | −0.308918 | − | 0.951089i | \(-0.599967\pi\) | ||||
−0.308918 | + | 0.951089i | \(0.599967\pi\) | |||||||
\(600\) | 14.6317 | 0.597338 | ||||||||
\(601\) | −0.515149 | −0.0210134 | −0.0105067 | − | 0.999945i | \(-0.503344\pi\) | ||||
−0.0105067 | + | 0.999945i | \(0.503344\pi\) | |||||||
\(602\) | −87.5757 | −3.56932 | ||||||||
\(603\) | 2.76619 | 0.112648 | ||||||||
\(604\) | −62.6613 | −2.54965 | ||||||||
\(605\) | 2.62502 | 0.106722 | ||||||||
\(606\) | 29.2701 | 1.18902 | ||||||||
\(607\) | 33.0600 | 1.34186 | 0.670932 | − | 0.741519i | \(-0.265894\pi\) | ||||
0.670932 | + | 0.741519i | \(0.265894\pi\) | |||||||
\(608\) | 4.18654 | 0.169787 | ||||||||
\(609\) | 28.4070 | 1.15111 | ||||||||
\(610\) | −6.91432 | −0.279953 | ||||||||
\(611\) | −15.3736 | −0.621949 | ||||||||
\(612\) | 9.62267 | 0.388973 | ||||||||
\(613\) | 10.2485 | 0.413933 | 0.206966 | − | 0.978348i | \(-0.433641\pi\) | ||||
0.206966 | + | 0.978348i | \(0.433641\pi\) | |||||||
\(614\) | −42.0164 | −1.69564 | ||||||||
\(615\) | 1.14593 | 0.0462084 | ||||||||
\(616\) | 40.1522 | 1.61778 | ||||||||
\(617\) | 29.1352 | 1.17294 | 0.586469 | − | 0.809971i | \(-0.300517\pi\) | ||||
0.586469 | + | 0.809971i | \(0.300517\pi\) | |||||||
\(618\) | −1.32949 | −0.0534800 | ||||||||
\(619\) | −13.3947 | −0.538377 | −0.269188 | − | 0.963088i | \(-0.586755\pi\) | ||||
−0.269188 | + | 0.963088i | \(0.586755\pi\) | |||||||
\(620\) | 31.2075 | 1.25332 | ||||||||
\(621\) | 4.48645 | 0.180035 | ||||||||
\(622\) | 36.5217 | 1.46439 | ||||||||
\(623\) | 16.3147 | 0.653636 | ||||||||
\(624\) | 36.4913 | 1.46082 | ||||||||
\(625\) | −30.8788 | −1.23515 | ||||||||
\(626\) | −47.7092 | −1.90684 | ||||||||
\(627\) | −0.343156 | −0.0137043 | ||||||||
\(628\) | 53.3513 | 2.12895 | ||||||||
\(629\) | 20.1615 | 0.803891 | ||||||||
\(630\) | −35.8750 | −1.42930 | ||||||||
\(631\) | −24.1306 | −0.960622 | −0.480311 | − | 0.877098i | \(-0.659476\pi\) | ||||
−0.480311 | + | 0.877098i | \(0.659476\pi\) | |||||||
\(632\) | 39.8874 | 1.58664 | ||||||||
\(633\) | −6.07527 | −0.241470 | ||||||||
\(634\) | −59.0234 | −2.34412 | ||||||||
\(635\) | 40.0516 | 1.58940 | ||||||||
\(636\) | −12.2019 | −0.483835 | ||||||||
\(637\) | −69.1806 | −2.74104 | ||||||||
\(638\) | −14.4211 | −0.570938 | ||||||||
\(639\) | −16.0977 | −0.636817 | ||||||||
\(640\) | −12.8338 | −0.507302 | ||||||||
\(641\) | 31.1854 | 1.23175 | 0.615874 | − | 0.787845i | \(-0.288803\pi\) | ||||
0.615874 | + | 0.787845i | \(0.288803\pi\) | |||||||
\(642\) | 20.6243 | 0.813977 | ||||||||
\(643\) | 31.3001 | 1.23436 | 0.617178 | − | 0.786824i | \(-0.288276\pi\) | ||||
0.617178 | + | 0.786824i | \(0.288276\pi\) | |||||||
\(644\) | −114.946 | −4.52952 | ||||||||
\(645\) | −16.8212 | −0.662333 | ||||||||
\(646\) | 1.76139 | 0.0693008 | ||||||||
\(647\) | −25.8036 | −1.01445 | −0.507223 | − | 0.861815i | \(-0.669328\pi\) | ||||
−0.507223 | + | 0.861815i | \(0.669328\pi\) | |||||||
\(648\) | −7.73867 | −0.304004 | ||||||||
\(649\) | −13.7469 | −0.539614 | ||||||||
\(650\) | 17.2952 | 0.678375 | ||||||||
\(651\) | −12.4917 | −0.489587 | ||||||||
\(652\) | 123.555 | 4.83880 | ||||||||
\(653\) | −39.3780 | −1.54098 | −0.770491 | − | 0.637451i | \(-0.779989\pi\) | ||||
−0.770491 | + | 0.637451i | \(0.779989\pi\) | |||||||
\(654\) | −14.9997 | −0.586536 | ||||||||
\(655\) | −6.76507 | −0.264333 | ||||||||
\(656\) | −4.58707 | −0.179095 | ||||||||
\(657\) | −3.11724 | −0.121615 | ||||||||
\(658\) | −60.4999 | −2.35853 | ||||||||
\(659\) | −17.3863 | −0.677275 | −0.338637 | − | 0.940917i | \(-0.609966\pi\) | ||||
−0.338637 | + | 0.940917i | \(0.609966\pi\) | |||||||
\(660\) | 12.9623 | 0.504557 | ||||||||
\(661\) | 10.6188 | 0.413025 | 0.206512 | − | 0.978444i | \(-0.433789\pi\) | ||||
0.206512 | + | 0.978444i | \(0.433789\pi\) | |||||||
\(662\) | 3.98188 | 0.154760 | ||||||||
\(663\) | 6.76746 | 0.262826 | ||||||||
\(664\) | −16.4475 | −0.638286 | ||||||||
\(665\) | −4.67377 | −0.181241 | ||||||||
\(666\) | −27.2517 | −1.05598 | ||||||||
\(667\) | 24.5632 | 0.951090 | ||||||||
\(668\) | −108.212 | −4.18683 | ||||||||
\(669\) | 24.7908 | 0.958467 | ||||||||
\(670\) | −19.1263 | −0.738914 | ||||||||
\(671\) | −1.00000 | −0.0386046 | ||||||||
\(672\) | 63.3004 | 2.44187 | ||||||||
\(673\) | −25.4524 | −0.981117 | −0.490559 | − | 0.871408i | \(-0.663207\pi\) | ||||
−0.490559 | + | 0.871408i | \(0.663207\pi\) | |||||||
\(674\) | 7.82438 | 0.301384 | ||||||||
\(675\) | −1.89073 | −0.0727742 | ||||||||
\(676\) | −4.63996 | −0.178460 | ||||||||
\(677\) | 29.4870 | 1.13328 | 0.566638 | − | 0.823967i | \(-0.308244\pi\) | ||||
0.566638 | + | 0.823967i | \(0.308244\pi\) | |||||||
\(678\) | 43.5034 | 1.67074 | ||||||||
\(679\) | 33.8002 | 1.29713 | ||||||||
\(680\) | −39.5863 | −1.51807 | ||||||||
\(681\) | −25.6959 | −0.984667 | ||||||||
\(682\) | 6.34152 | 0.242829 | ||||||||
\(683\) | 10.3877 | 0.397475 | 0.198737 | − | 0.980053i | \(-0.436316\pi\) | ||||
0.198737 | + | 0.980053i | \(0.436316\pi\) | |||||||
\(684\) | −1.69450 | −0.0647909 | ||||||||
\(685\) | 37.8487 | 1.44613 | ||||||||
\(686\) | −176.582 | −6.74192 | ||||||||
\(687\) | 1.69139 | 0.0645306 | ||||||||
\(688\) | 67.3338 | 2.56708 | ||||||||
\(689\) | −8.58136 | −0.326924 | ||||||||
\(690\) | −31.0207 | −1.18094 | ||||||||
\(691\) | −8.92858 | −0.339659 | −0.169830 | − | 0.985473i | \(-0.554322\pi\) | ||||
−0.169830 | + | 0.985473i | \(0.554322\pi\) | |||||||
\(692\) | −95.5236 | −3.63126 | ||||||||
\(693\) | −5.18852 | −0.197095 | ||||||||
\(694\) | −91.9484 | −3.49031 | ||||||||
\(695\) | 29.6956 | 1.12642 | ||||||||
\(696\) | −42.3691 | −1.60600 | ||||||||
\(697\) | −0.850690 | −0.0322222 | ||||||||
\(698\) | 19.4059 | 0.734526 | ||||||||
\(699\) | 8.61616 | 0.325893 | ||||||||
\(700\) | 48.4420 | 1.83094 | ||||||||
\(701\) | 45.5207 | 1.71929 | 0.859646 | − | 0.510891i | \(-0.170684\pi\) | ||||
0.859646 | + | 0.510891i | \(0.170684\pi\) | |||||||
\(702\) | −9.14738 | −0.345246 | ||||||||
\(703\) | −3.55033 | −0.133903 | ||||||||
\(704\) | −11.1197 | −0.419088 | ||||||||
\(705\) | −11.6206 | −0.437656 | ||||||||
\(706\) | −79.5453 | −2.99373 | ||||||||
\(707\) | 57.6568 | 2.16841 | ||||||||
\(708\) | −67.8822 | −2.55117 | ||||||||
\(709\) | 16.4201 | 0.616670 | 0.308335 | − | 0.951278i | \(-0.400228\pi\) | ||||
0.308335 | + | 0.951278i | \(0.400228\pi\) | |||||||
\(710\) | 111.305 | 4.17720 | ||||||||
\(711\) | −5.15429 | −0.193301 | ||||||||
\(712\) | −24.3335 | −0.911935 | ||||||||
\(713\) | −10.8014 | −0.404515 | ||||||||
\(714\) | 26.6321 | 0.996681 | ||||||||
\(715\) | 9.11617 | 0.340926 | ||||||||
\(716\) | 103.635 | 3.87301 | ||||||||
\(717\) | 13.2629 | 0.495312 | ||||||||
\(718\) | 74.4890 | 2.77991 | ||||||||
\(719\) | 17.6047 | 0.656545 | 0.328273 | − | 0.944583i | \(-0.393534\pi\) | ||||
0.328273 | + | 0.944583i | \(0.393534\pi\) | |||||||
\(720\) | 27.5830 | 1.02796 | ||||||||
\(721\) | −2.61886 | −0.0975314 | ||||||||
\(722\) | 49.7359 | 1.85098 | ||||||||
\(723\) | −2.12784 | −0.0791353 | ||||||||
\(724\) | −130.320 | −4.84331 | ||||||||
\(725\) | −10.3517 | −0.384452 | ||||||||
\(726\) | 2.63401 | 0.0977571 | ||||||||
\(727\) | 26.0709 | 0.966914 | 0.483457 | − | 0.875368i | \(-0.339381\pi\) | ||||
0.483457 | + | 0.875368i | \(0.339381\pi\) | |||||||
\(728\) | 139.441 | 5.16802 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 21.5536 | 0.797733 | ||||||||
\(731\) | 12.4873 | 0.461860 | ||||||||
\(732\) | −4.93799 | −0.182513 | ||||||||
\(733\) | −30.5781 | −1.12943 | −0.564715 | − | 0.825286i | \(-0.691014\pi\) | ||||
−0.564715 | + | 0.825286i | \(0.691014\pi\) | |||||||
\(734\) | −23.8724 | −0.881147 | ||||||||
\(735\) | −52.2922 | −1.92883 | ||||||||
\(736\) | 54.7351 | 2.01756 | ||||||||
\(737\) | −2.76619 | −0.101894 | ||||||||
\(738\) | 1.14985 | 0.0423267 | ||||||||
\(739\) | −50.2330 | −1.84785 | −0.923926 | − | 0.382571i | \(-0.875039\pi\) | ||||
−0.923926 | + | 0.382571i | \(0.875039\pi\) | |||||||
\(740\) | 134.109 | 4.92996 | ||||||||
\(741\) | −1.19171 | −0.0437787 | ||||||||
\(742\) | −33.7704 | −1.23975 | ||||||||
\(743\) | 31.2350 | 1.14590 | 0.572950 | − | 0.819590i | \(-0.305799\pi\) | ||||
0.572950 | + | 0.819590i | \(0.305799\pi\) | |||||||
\(744\) | 18.6313 | 0.683057 | ||||||||
\(745\) | −11.3077 | −0.414284 | ||||||||
\(746\) | −12.5487 | −0.459440 | ||||||||
\(747\) | 2.12536 | 0.0777629 | ||||||||
\(748\) | −9.62267 | −0.351840 | ||||||||
\(749\) | 40.6262 | 1.48445 | ||||||||
\(750\) | −21.4985 | −0.785014 | ||||||||
\(751\) | −6.93821 | −0.253179 | −0.126590 | − | 0.991955i | \(-0.540403\pi\) | ||||
−0.126590 | + | 0.991955i | \(0.540403\pi\) | |||||||
\(752\) | 46.5162 | 1.69627 | ||||||||
\(753\) | −1.21883 | −0.0444168 | ||||||||
\(754\) | −50.0817 | −1.82387 | ||||||||
\(755\) | −33.3105 | −1.21229 | ||||||||
\(756\) | −25.6208 | −0.931820 | ||||||||
\(757\) | −42.3758 | −1.54017 | −0.770086 | − | 0.637939i | \(-0.779787\pi\) | ||||
−0.770086 | + | 0.637939i | \(0.779787\pi\) | |||||||
\(758\) | −64.8052 | −2.35383 | ||||||||
\(759\) | −4.48645 | −0.162848 | ||||||||
\(760\) | 6.97094 | 0.252863 | ||||||||
\(761\) | −38.5976 | −1.39916 | −0.699582 | − | 0.714553i | \(-0.746630\pi\) | ||||
−0.699582 | + | 0.714553i | \(0.746630\pi\) | |||||||
\(762\) | 40.1887 | 1.45588 | ||||||||
\(763\) | −29.5467 | −1.06966 | ||||||||
\(764\) | 99.7484 | 3.60877 | ||||||||
\(765\) | 5.11538 | 0.184947 | ||||||||
\(766\) | −3.06468 | −0.110731 | ||||||||
\(767\) | −47.7404 | −1.72381 | ||||||||
\(768\) | 9.36155 | 0.337806 | ||||||||
\(769\) | −8.52482 | −0.307413 | −0.153706 | − | 0.988117i | \(-0.549121\pi\) | ||||
−0.153706 | + | 0.988117i | \(0.549121\pi\) | |||||||
\(770\) | 35.8750 | 1.29285 | ||||||||
\(771\) | 10.0350 | 0.361401 | ||||||||
\(772\) | −80.1696 | −2.88537 | ||||||||
\(773\) | −44.8848 | −1.61439 | −0.807197 | − | 0.590283i | \(-0.799016\pi\) | ||||
−0.807197 | + | 0.590283i | \(0.799016\pi\) | |||||||
\(774\) | −16.8788 | −0.606694 | ||||||||
\(775\) | 4.55204 | 0.163514 | ||||||||
\(776\) | −50.4131 | −1.80972 | ||||||||
\(777\) | −53.6809 | −1.92579 | ||||||||
\(778\) | −12.3412 | −0.442455 | ||||||||
\(779\) | 0.149802 | 0.00536722 | ||||||||
\(780\) | 45.0155 | 1.61182 | ||||||||
\(781\) | 16.0977 | 0.576022 | ||||||||
\(782\) | 23.0285 | 0.823496 | ||||||||
\(783\) | 5.47498 | 0.195660 | ||||||||
\(784\) | 209.321 | 7.47577 | ||||||||
\(785\) | 28.3614 | 1.01226 | ||||||||
\(786\) | −6.78823 | −0.242128 | ||||||||
\(787\) | −13.9456 | −0.497106 | −0.248553 | − | 0.968618i | \(-0.579955\pi\) | ||||
−0.248553 | + | 0.968618i | \(0.579955\pi\) | |||||||
\(788\) | 53.4442 | 1.90387 | ||||||||
\(789\) | 15.4701 | 0.550749 | ||||||||
\(790\) | 35.6384 | 1.26796 | ||||||||
\(791\) | 85.6938 | 3.04692 | ||||||||
\(792\) | 7.73867 | 0.274982 | ||||||||
\(793\) | −3.47280 | −0.123323 | ||||||||
\(794\) | 84.7251 | 3.00678 | ||||||||
\(795\) | −6.48647 | −0.230051 | ||||||||
\(796\) | 84.5420 | 2.99651 | ||||||||
\(797\) | 23.5528 | 0.834282 | 0.417141 | − | 0.908842i | \(-0.363032\pi\) | ||||
0.417141 | + | 0.908842i | \(0.363032\pi\) | |||||||
\(798\) | −4.68977 | −0.166016 | ||||||||
\(799\) | 8.62662 | 0.305188 | ||||||||
\(800\) | −23.0671 | −0.815545 | ||||||||
\(801\) | 3.14440 | 0.111102 | ||||||||
\(802\) | 97.7180 | 3.45054 | ||||||||
\(803\) | 3.11724 | 0.110005 | ||||||||
\(804\) | −13.6594 | −0.481730 | ||||||||
\(805\) | −61.1052 | −2.15367 | ||||||||
\(806\) | 22.0229 | 0.775722 | ||||||||
\(807\) | 11.4654 | 0.403602 | ||||||||
\(808\) | −85.9952 | −3.02530 | ||||||||
\(809\) | −32.6289 | −1.14717 | −0.573586 | − | 0.819145i | \(-0.694448\pi\) | ||||
−0.573586 | + | 0.819145i | \(0.694448\pi\) | |||||||
\(810\) | −6.91432 | −0.242944 | ||||||||
\(811\) | 8.24758 | 0.289612 | 0.144806 | − | 0.989460i | \(-0.453744\pi\) | ||||
0.144806 | + | 0.989460i | \(0.453744\pi\) | |||||||
\(812\) | −140.273 | −4.92263 | ||||||||
\(813\) | 10.6925 | 0.375001 | ||||||||
\(814\) | 27.2517 | 0.955171 | ||||||||
\(815\) | 65.6816 | 2.30073 | ||||||||
\(816\) | −20.4765 | −0.716820 | ||||||||
\(817\) | −2.19895 | −0.0769316 | ||||||||
\(818\) | 59.0723 | 2.06542 | ||||||||
\(819\) | −18.0187 | −0.629624 | ||||||||
\(820\) | −5.65859 | −0.197607 | ||||||||
\(821\) | 53.7676 | 1.87650 | 0.938251 | − | 0.345954i | \(-0.112445\pi\) | ||||
0.938251 | + | 0.345954i | \(0.112445\pi\) | |||||||
\(822\) | 37.9783 | 1.32465 | ||||||||
\(823\) | −8.85638 | −0.308714 | −0.154357 | − | 0.988015i | \(-0.549331\pi\) | ||||
−0.154357 | + | 0.988015i | \(0.549331\pi\) | |||||||
\(824\) | 3.90603 | 0.136073 | ||||||||
\(825\) | 1.89073 | 0.0658268 | ||||||||
\(826\) | −187.874 | −6.53696 | ||||||||
\(827\) | −1.91639 | −0.0666395 | −0.0333198 | − | 0.999445i | \(-0.510608\pi\) | ||||
−0.0333198 | + | 0.999445i | \(0.510608\pi\) | |||||||
\(828\) | −22.1540 | −0.769905 | ||||||||
\(829\) | −35.4299 | −1.23053 | −0.615266 | − | 0.788320i | \(-0.710951\pi\) | ||||
−0.615266 | + | 0.788320i | \(0.710951\pi\) | |||||||
\(830\) | −14.6954 | −0.510086 | ||||||||
\(831\) | 31.4466 | 1.09087 | ||||||||
\(832\) | −38.6164 | −1.33878 | ||||||||
\(833\) | 38.8195 | 1.34502 | ||||||||
\(834\) | 29.7973 | 1.03180 | ||||||||
\(835\) | −57.5250 | −1.99073 | ||||||||
\(836\) | 1.69450 | 0.0586056 | ||||||||
\(837\) | −2.40756 | −0.0832174 | ||||||||
\(838\) | 23.5582 | 0.813803 | ||||||||
\(839\) | −11.2612 | −0.388781 | −0.194391 | − | 0.980924i | \(-0.562273\pi\) | ||||
−0.194391 | + | 0.980924i | \(0.562273\pi\) | |||||||
\(840\) | 105.400 | 3.63666 | ||||||||
\(841\) | 0.975363 | 0.0336332 | ||||||||
\(842\) | 105.405 | 3.63248 | ||||||||
\(843\) | −15.8197 | −0.544859 | ||||||||
\(844\) | 29.9996 | 1.03263 | ||||||||
\(845\) | −2.46659 | −0.0848533 | ||||||||
\(846\) | −11.6604 | −0.400891 | ||||||||
\(847\) | 5.18852 | 0.178279 | ||||||||
\(848\) | 25.9648 | 0.891635 | ||||||||
\(849\) | 17.7131 | 0.607912 | ||||||||
\(850\) | −9.70492 | −0.332876 | ||||||||
\(851\) | −46.4172 | −1.59116 | ||||||||
\(852\) | 79.4904 | 2.72330 | ||||||||
\(853\) | 5.79874 | 0.198545 | 0.0992725 | − | 0.995060i | \(-0.468348\pi\) | ||||
0.0992725 | + | 0.995060i | \(0.468348\pi\) | |||||||
\(854\) | −13.6666 | −0.467661 | ||||||||
\(855\) | −0.900792 | −0.0308064 | ||||||||
\(856\) | −60.5940 | −2.07106 | ||||||||
\(857\) | 40.4860 | 1.38298 | 0.691488 | − | 0.722388i | \(-0.256956\pi\) | ||||
0.691488 | + | 0.722388i | \(0.256956\pi\) | |||||||
\(858\) | 9.14738 | 0.312286 | ||||||||
\(859\) | 19.1302 | 0.652715 | 0.326357 | − | 0.945246i | \(-0.394179\pi\) | ||||
0.326357 | + | 0.945246i | \(0.394179\pi\) | |||||||
\(860\) | 83.0627 | 2.83242 | ||||||||
\(861\) | 2.26500 | 0.0771911 | ||||||||
\(862\) | 2.74076 | 0.0933506 | ||||||||
\(863\) | 25.2855 | 0.860727 | 0.430364 | − | 0.902656i | \(-0.358385\pi\) | ||||
0.430364 | + | 0.902656i | \(0.358385\pi\) | |||||||
\(864\) | 12.2001 | 0.415056 | ||||||||
\(865\) | −50.7801 | −1.72657 | ||||||||
\(866\) | 40.8218 | 1.38718 | ||||||||
\(867\) | 13.2026 | 0.448382 | ||||||||
\(868\) | 61.6836 | 2.09368 | ||||||||
\(869\) | 5.15429 | 0.174847 | ||||||||
\(870\) | −37.8557 | −1.28343 | ||||||||
\(871\) | −9.60643 | −0.325501 | ||||||||
\(872\) | 44.0690 | 1.49236 | ||||||||
\(873\) | 6.51443 | 0.220480 | ||||||||
\(874\) | −4.05519 | −0.137169 | ||||||||
\(875\) | −42.3481 | −1.43163 | ||||||||
\(876\) | 15.3929 | 0.520077 | ||||||||
\(877\) | −31.4779 | −1.06293 | −0.531466 | − | 0.847080i | \(-0.678359\pi\) | ||||
−0.531466 | + | 0.847080i | \(0.678359\pi\) | |||||||
\(878\) | −58.0119 | −1.95781 | ||||||||
\(879\) | 6.92077 | 0.233432 | ||||||||
\(880\) | −27.5830 | −0.929824 | ||||||||
\(881\) | −7.07691 | −0.238427 | −0.119214 | − | 0.992869i | \(-0.538037\pi\) | ||||
−0.119214 | + | 0.992869i | \(0.538037\pi\) | |||||||
\(882\) | −52.4712 | −1.76680 | ||||||||
\(883\) | 39.1958 | 1.31904 | 0.659521 | − | 0.751686i | \(-0.270759\pi\) | ||||
0.659521 | + | 0.751686i | \(0.270759\pi\) | |||||||
\(884\) | −33.4176 | −1.12396 | ||||||||
\(885\) | −36.0860 | −1.21302 | ||||||||
\(886\) | −72.2842 | −2.42843 | ||||||||
\(887\) | −33.0652 | −1.11022 | −0.555111 | − | 0.831776i | \(-0.687324\pi\) | ||||
−0.555111 | + | 0.831776i | \(0.687324\pi\) | |||||||
\(888\) | 80.0651 | 2.68681 | ||||||||
\(889\) | 79.1645 | 2.65509 | ||||||||
\(890\) | −21.7414 | −0.728772 | ||||||||
\(891\) | −1.00000 | −0.0335013 | ||||||||
\(892\) | −122.417 | −4.09881 | ||||||||
\(893\) | −1.51910 | −0.0508348 | ||||||||
\(894\) | −11.3465 | −0.379482 | ||||||||
\(895\) | 55.0920 | 1.84152 | ||||||||
\(896\) | −25.3669 | −0.847448 | ||||||||
\(897\) | −15.5805 | −0.520219 | ||||||||
\(898\) | 83.5062 | 2.78664 | ||||||||
\(899\) | −13.1813 | −0.439622 | ||||||||
\(900\) | 9.33640 | 0.311213 | ||||||||
\(901\) | 4.81528 | 0.160420 | ||||||||
\(902\) | −1.14985 | −0.0382859 | ||||||||
\(903\) | −33.2481 | −1.10643 | ||||||||
\(904\) | −127.812 | −4.25098 | ||||||||
\(905\) | −69.2778 | −2.30287 | ||||||||
\(906\) | −33.4246 | −1.11046 | ||||||||
\(907\) | −49.4081 | −1.64057 | −0.820285 | − | 0.571955i | \(-0.806185\pi\) | ||||
−0.820285 | + | 0.571955i | \(0.806185\pi\) | |||||||
\(908\) | 126.886 | 4.21085 | ||||||||
\(909\) | 11.1124 | 0.368575 | ||||||||
\(910\) | 124.587 | 4.13002 | ||||||||
\(911\) | 11.0990 | 0.367725 | 0.183863 | − | 0.982952i | \(-0.441140\pi\) | ||||
0.183863 | + | 0.982952i | \(0.441140\pi\) | |||||||
\(912\) | 3.60580 | 0.119400 | ||||||||
\(913\) | −2.12536 | −0.0703392 | ||||||||
\(914\) | 17.9294 | 0.593053 | ||||||||
\(915\) | −2.62502 | −0.0867805 | ||||||||
\(916\) | −8.35207 | −0.275960 | ||||||||
\(917\) | −13.3716 | −0.441569 | ||||||||
\(918\) | 5.13290 | 0.169411 | ||||||||
\(919\) | 9.02754 | 0.297791 | 0.148895 | − | 0.988853i | \(-0.452428\pi\) | ||||
0.148895 | + | 0.988853i | \(0.452428\pi\) | |||||||
\(920\) | 91.1384 | 3.00475 | ||||||||
\(921\) | −15.9515 | −0.525620 | ||||||||
\(922\) | −9.71414 | −0.319918 | ||||||||
\(923\) | 55.9043 | 1.84011 | ||||||||
\(924\) | 25.6208 | 0.842863 | ||||||||
\(925\) | 19.5617 | 0.643184 | ||||||||
\(926\) | −17.0451 | −0.560136 | ||||||||
\(927\) | −0.504742 | −0.0165779 | ||||||||
\(928\) | 66.7953 | 2.19266 | ||||||||
\(929\) | −22.1504 | −0.726732 | −0.363366 | − | 0.931646i | \(-0.618373\pi\) | ||||
−0.363366 | + | 0.931646i | \(0.618373\pi\) | |||||||
\(930\) | 16.6466 | 0.545864 | ||||||||
\(931\) | −6.83591 | −0.224038 | ||||||||
\(932\) | −42.5465 | −1.39366 | ||||||||
\(933\) | 13.8655 | 0.453935 | ||||||||
\(934\) | 38.0628 | 1.24545 | ||||||||
\(935\) | −5.11538 | −0.167291 | ||||||||
\(936\) | 26.8749 | 0.878433 | ||||||||
\(937\) | −32.4015 | −1.05851 | −0.529255 | − | 0.848463i | \(-0.677529\pi\) | ||||
−0.529255 | + | 0.848463i | \(0.677529\pi\) | |||||||
\(938\) | −37.8044 | −1.23436 | ||||||||
\(939\) | −18.1128 | −0.591089 | ||||||||
\(940\) | 57.3822 | 1.87160 | ||||||||
\(941\) | −23.0935 | −0.752826 | −0.376413 | − | 0.926452i | \(-0.622843\pi\) | ||||
−0.376413 | + | 0.926452i | \(0.622843\pi\) | |||||||
\(942\) | 28.4585 | 0.927228 | ||||||||
\(943\) | 1.95852 | 0.0637782 | ||||||||
\(944\) | 144.449 | 4.70142 | ||||||||
\(945\) | −13.6200 | −0.443057 | ||||||||
\(946\) | 16.8788 | 0.548776 | ||||||||
\(947\) | −19.1527 | −0.622378 | −0.311189 | − | 0.950348i | \(-0.600727\pi\) | ||||
−0.311189 | + | 0.950348i | \(0.600727\pi\) | |||||||
\(948\) | 25.4518 | 0.826637 | ||||||||
\(949\) | 10.8255 | 0.351412 | ||||||||
\(950\) | 1.70899 | 0.0554468 | ||||||||
\(951\) | −22.4082 | −0.726636 | ||||||||
\(952\) | −78.2448 | −2.53593 | ||||||||
\(953\) | −18.1232 | −0.587067 | −0.293534 | − | 0.955949i | \(-0.594831\pi\) | ||||
−0.293534 | + | 0.955949i | \(0.594831\pi\) | |||||||
\(954\) | −6.50868 | −0.210726 | ||||||||
\(955\) | 53.0260 | 1.71588 | ||||||||
\(956\) | −65.4920 | −2.11816 | ||||||||
\(957\) | −5.47498 | −0.176981 | ||||||||
\(958\) | 69.5358 | 2.24660 | ||||||||
\(959\) | 74.8104 | 2.41575 | ||||||||
\(960\) | −29.1893 | −0.942081 | ||||||||
\(961\) | −25.2037 | −0.813021 | ||||||||
\(962\) | 94.6397 | 3.05131 | ||||||||
\(963\) | 7.83003 | 0.252319 | ||||||||
\(964\) | 10.5073 | 0.338416 | ||||||||
\(965\) | −42.6180 | −1.37192 | ||||||||
\(966\) | −61.3144 | −1.97276 | ||||||||
\(967\) | −40.9282 | −1.31616 | −0.658082 | − | 0.752947i | \(-0.728632\pi\) | ||||
−0.658082 | + | 0.752947i | \(0.728632\pi\) | |||||||
\(968\) | −7.73867 | −0.248730 | ||||||||
\(969\) | 0.668710 | 0.0214821 | ||||||||
\(970\) | −45.0429 | −1.44624 | ||||||||
\(971\) | 13.7378 | 0.440866 | 0.220433 | − | 0.975402i | \(-0.429253\pi\) | ||||
0.220433 | + | 0.975402i | \(0.429253\pi\) | |||||||
\(972\) | −4.93799 | −0.158386 | ||||||||
\(973\) | 58.6952 | 1.88168 | ||||||||
\(974\) | −2.70639 | −0.0867183 | ||||||||
\(975\) | 6.56613 | 0.210284 | ||||||||
\(976\) | 10.5077 | 0.336345 | ||||||||
\(977\) | −25.1855 | −0.805755 | −0.402878 | − | 0.915254i | \(-0.631990\pi\) | ||||
−0.402878 | + | 0.915254i | \(0.631990\pi\) | |||||||
\(978\) | 65.9065 | 2.10746 | ||||||||
\(979\) | −3.14440 | −0.100495 | ||||||||
\(980\) | 258.218 | 8.24848 | ||||||||
\(981\) | −5.69464 | −0.181816 | ||||||||
\(982\) | −69.6223 | −2.22174 | ||||||||
\(983\) | 0.0437437 | 0.00139521 | 0.000697604 | − | 1.00000i | \(-0.499778\pi\) | ||||
0.000697604 | 1.00000i | \(0.499778\pi\) | ||||||||
\(984\) | −3.37826 | −0.107695 | ||||||||
\(985\) | 28.4108 | 0.905242 | ||||||||
\(986\) | 28.1025 | 0.894965 | ||||||||
\(987\) | −22.9688 | −0.731105 | ||||||||
\(988\) | 5.88467 | 0.187216 | ||||||||
\(989\) | −28.7492 | −0.914172 | ||||||||
\(990\) | 6.91432 | 0.219751 | ||||||||
\(991\) | 12.7220 | 0.404126 | 0.202063 | − | 0.979373i | \(-0.435235\pi\) | ||||
0.202063 | + | 0.979373i | \(0.435235\pi\) | |||||||
\(992\) | −29.3725 | −0.932576 | ||||||||
\(993\) | 1.51172 | 0.0479729 | ||||||||
\(994\) | 220.001 | 6.97801 | ||||||||
\(995\) | 44.9423 | 1.42477 | ||||||||
\(996\) | −10.4950 | −0.332547 | ||||||||
\(997\) | −56.0727 | −1.77584 | −0.887920 | − | 0.459997i | \(-0.847850\pi\) | ||||
−0.887920 | + | 0.459997i | \(0.847850\pi\) | |||||||
\(998\) | 56.8693 | 1.80017 | ||||||||
\(999\) | −10.3461 | −0.327336 |
(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.h.1.1 | ✓ | 14 | |
3.2 | odd | 2 | 6039.2.a.j.1.14 | 14 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2013.2.a.h.1.1 | ✓ | 14 | 1.1 | even | 1 | trivial | |
6039.2.a.j.1.14 | 14 | 3.2 | odd | 2 |