Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4019,2,Mod(1,4019)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4019, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4019.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4019 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4019.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: | \(32.0918765724\) |
Analytic rank: | \(0\) |
Dimension: | \(186\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.20 | ||
Character | \(\chi\) | \(=\) | 4019.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.34165 | −1.65580 | −0.827898 | − | 0.560878i | \(-0.810464\pi\) | ||||
−0.827898 | + | 0.560878i | \(0.810464\pi\) | |||||||
\(3\) | −0.437788 | −0.252757 | −0.126378 | − | 0.991982i | \(-0.540335\pi\) | ||||
−0.126378 | + | 0.991982i | \(0.540335\pi\) | |||||||
\(4\) | 3.48332 | 1.74166 | ||||||||
\(5\) | 0.358726 | 0.160427 | 0.0802135 | − | 0.996778i | \(-0.474440\pi\) | ||||
0.0802135 | + | 0.996778i | \(0.474440\pi\) | |||||||
\(6\) | 1.02515 | 0.418514 | ||||||||
\(7\) | 3.39349 | 1.28262 | 0.641310 | − | 0.767282i | \(-0.278391\pi\) | ||||
0.641310 | + | 0.767282i | \(0.278391\pi\) | |||||||
\(8\) | −3.47342 | −1.22804 | ||||||||
\(9\) | −2.80834 | −0.936114 | ||||||||
\(10\) | −0.840010 | −0.265634 | ||||||||
\(11\) | −1.11610 | −0.336517 | −0.168259 | − | 0.985743i | \(-0.553814\pi\) | ||||
−0.168259 | + | 0.985743i | \(0.553814\pi\) | |||||||
\(12\) | −1.52496 | −0.440217 | ||||||||
\(13\) | −4.45688 | −1.23612 | −0.618059 | − | 0.786132i | \(-0.712081\pi\) | ||||
−0.618059 | + | 0.786132i | \(0.712081\pi\) | |||||||
\(14\) | −7.94637 | −2.12376 | ||||||||
\(15\) | −0.157046 | −0.0405490 | ||||||||
\(16\) | 1.16689 | 0.291724 | ||||||||
\(17\) | 6.33668 | 1.53687 | 0.768435 | − | 0.639928i | \(-0.221036\pi\) | ||||
0.768435 | + | 0.639928i | \(0.221036\pi\) | |||||||
\(18\) | 6.57615 | 1.55001 | ||||||||
\(19\) | −2.34535 | −0.538060 | −0.269030 | − | 0.963132i | \(-0.586703\pi\) | ||||
−0.269030 | + | 0.963132i | \(0.586703\pi\) | |||||||
\(20\) | 1.24956 | 0.279410 | ||||||||
\(21\) | −1.48563 | −0.324191 | ||||||||
\(22\) | 2.61352 | 0.557204 | ||||||||
\(23\) | −0.282972 | −0.0590037 | −0.0295019 | − | 0.999565i | \(-0.509392\pi\) | ||||
−0.0295019 | + | 0.999565i | \(0.509392\pi\) | |||||||
\(24\) | 1.52062 | 0.310396 | ||||||||
\(25\) | −4.87132 | −0.974263 | ||||||||
\(26\) | 10.4365 | 2.04676 | ||||||||
\(27\) | 2.54282 | 0.489366 | ||||||||
\(28\) | 11.8206 | 2.23389 | ||||||||
\(29\) | −9.05378 | −1.68125 | −0.840623 | − | 0.541621i | \(-0.817811\pi\) | ||||
−0.840623 | + | 0.541621i | \(0.817811\pi\) | |||||||
\(30\) | 0.367746 | 0.0671409 | ||||||||
\(31\) | −0.329502 | −0.0591804 | −0.0295902 | − | 0.999562i | \(-0.509420\pi\) | ||||
−0.0295902 | + | 0.999562i | \(0.509420\pi\) | |||||||
\(32\) | 4.21439 | 0.745006 | ||||||||
\(33\) | 0.488616 | 0.0850571 | ||||||||
\(34\) | −14.8383 | −2.54474 | ||||||||
\(35\) | 1.21733 | 0.205767 | ||||||||
\(36\) | −9.78236 | −1.63039 | ||||||||
\(37\) | 0.0658927 | 0.0108327 | 0.00541634 | − | 0.999985i | \(-0.498276\pi\) | ||||
0.00541634 | + | 0.999985i | \(0.498276\pi\) | |||||||
\(38\) | 5.49199 | 0.890918 | ||||||||
\(39\) | 1.95117 | 0.312437 | ||||||||
\(40\) | −1.24601 | −0.197011 | ||||||||
\(41\) | −10.2733 | −1.60442 | −0.802208 | − | 0.597045i | \(-0.796342\pi\) | ||||
−0.802208 | + | 0.597045i | \(0.796342\pi\) | |||||||
\(42\) | 3.47882 | 0.536794 | ||||||||
\(43\) | 7.73519 | 1.17961 | 0.589803 | − | 0.807547i | \(-0.299205\pi\) | ||||
0.589803 | + | 0.807547i | \(0.299205\pi\) | |||||||
\(44\) | −3.88774 | −0.586099 | ||||||||
\(45\) | −1.00742 | −0.150178 | ||||||||
\(46\) | 0.662621 | 0.0976981 | ||||||||
\(47\) | −11.0036 | −1.60505 | −0.802524 | − | 0.596621i | \(-0.796510\pi\) | ||||
−0.802524 | + | 0.596621i | \(0.796510\pi\) | |||||||
\(48\) | −0.510852 | −0.0737351 | ||||||||
\(49\) | 4.51580 | 0.645114 | ||||||||
\(50\) | 11.4069 | 1.61318 | ||||||||
\(51\) | −2.77412 | −0.388454 | ||||||||
\(52\) | −15.5248 | −2.15290 | ||||||||
\(53\) | 1.11064 | 0.152558 | 0.0762788 | − | 0.997087i | \(-0.475696\pi\) | ||||
0.0762788 | + | 0.997087i | \(0.475696\pi\) | |||||||
\(54\) | −5.95439 | −0.810291 | ||||||||
\(55\) | −0.400374 | −0.0539865 | ||||||||
\(56\) | −11.7870 | −1.57511 | ||||||||
\(57\) | 1.02676 | 0.135998 | ||||||||
\(58\) | 21.2008 | 2.78380 | ||||||||
\(59\) | 14.2019 | 1.84893 | 0.924466 | − | 0.381265i | \(-0.124511\pi\) | ||||
0.924466 | + | 0.381265i | \(0.124511\pi\) | |||||||
\(60\) | −0.547041 | −0.0706227 | ||||||||
\(61\) | 6.80698 | 0.871545 | 0.435772 | − | 0.900057i | \(-0.356475\pi\) | ||||
0.435772 | + | 0.900057i | \(0.356475\pi\) | |||||||
\(62\) | 0.771579 | 0.0979906 | ||||||||
\(63\) | −9.53009 | −1.20068 | ||||||||
\(64\) | −12.2024 | −1.52530 | ||||||||
\(65\) | −1.59880 | −0.198307 | ||||||||
\(66\) | −1.14417 | −0.140837 | ||||||||
\(67\) | 11.3700 | 1.38906 | 0.694530 | − | 0.719463i | \(-0.255612\pi\) | ||||
0.694530 | + | 0.719463i | \(0.255612\pi\) | |||||||
\(68\) | 22.0727 | 2.67671 | ||||||||
\(69\) | 0.123882 | 0.0149136 | ||||||||
\(70\) | −2.85057 | −0.340708 | ||||||||
\(71\) | 5.88288 | 0.698169 | 0.349085 | − | 0.937091i | \(-0.386493\pi\) | ||||
0.349085 | + | 0.937091i | \(0.386493\pi\) | |||||||
\(72\) | 9.75456 | 1.14959 | ||||||||
\(73\) | 8.90981 | 1.04281 | 0.521407 | − | 0.853308i | \(-0.325407\pi\) | ||||
0.521407 | + | 0.853308i | \(0.325407\pi\) | |||||||
\(74\) | −0.154298 | −0.0179367 | ||||||||
\(75\) | 2.13260 | 0.246252 | ||||||||
\(76\) | −8.16961 | −0.937118 | ||||||||
\(77\) | −3.78749 | −0.431624 | ||||||||
\(78\) | −4.56895 | −0.517332 | ||||||||
\(79\) | 8.35937 | 0.940503 | 0.470252 | − | 0.882532i | \(-0.344163\pi\) | ||||
0.470252 | + | 0.882532i | \(0.344163\pi\) | |||||||
\(80\) | 0.418595 | 0.0468003 | ||||||||
\(81\) | 7.31181 | 0.812423 | ||||||||
\(82\) | 24.0564 | 2.65659 | ||||||||
\(83\) | 6.63373 | 0.728146 | 0.364073 | − | 0.931370i | \(-0.381386\pi\) | ||||
0.364073 | + | 0.931370i | \(0.381386\pi\) | |||||||
\(84\) | −5.17493 | −0.564631 | ||||||||
\(85\) | 2.27313 | 0.246555 | ||||||||
\(86\) | −18.1131 | −1.95319 | ||||||||
\(87\) | 3.96363 | 0.424946 | ||||||||
\(88\) | 3.87669 | 0.413257 | ||||||||
\(89\) | −7.80016 | −0.826816 | −0.413408 | − | 0.910546i | \(-0.635662\pi\) | ||||
−0.413408 | + | 0.910546i | \(0.635662\pi\) | |||||||
\(90\) | 2.35904 | 0.248664 | ||||||||
\(91\) | −15.1244 | −1.58547 | ||||||||
\(92\) | −0.985682 | −0.102764 | ||||||||
\(93\) | 0.144252 | 0.0149582 | ||||||||
\(94\) | 25.7667 | 2.65763 | ||||||||
\(95\) | −0.841337 | −0.0863194 | ||||||||
\(96\) | −1.84501 | −0.188305 | ||||||||
\(97\) | 19.0062 | 1.92979 | 0.964895 | − | 0.262635i | \(-0.0845914\pi\) | ||||
0.964895 | + | 0.262635i | \(0.0845914\pi\) | |||||||
\(98\) | −10.5744 | −1.06818 | ||||||||
\(99\) | 3.13440 | 0.315019 | ||||||||
\(100\) | −16.9684 | −1.69684 | ||||||||
\(101\) | 14.1883 | 1.41179 | 0.705894 | − | 0.708317i | \(-0.250545\pi\) | ||||
0.705894 | + | 0.708317i | \(0.250545\pi\) | |||||||
\(102\) | 6.49601 | 0.643201 | ||||||||
\(103\) | 0.329243 | 0.0324413 | 0.0162206 | − | 0.999868i | \(-0.494837\pi\) | ||||
0.0162206 | + | 0.999868i | \(0.494837\pi\) | |||||||
\(104\) | 15.4806 | 1.51800 | ||||||||
\(105\) | −0.532934 | −0.0520090 | ||||||||
\(106\) | −2.60072 | −0.252604 | ||||||||
\(107\) | 3.18162 | 0.307579 | 0.153790 | − | 0.988104i | \(-0.450852\pi\) | ||||
0.153790 | + | 0.988104i | \(0.450852\pi\) | |||||||
\(108\) | 8.85747 | 0.852310 | ||||||||
\(109\) | 0.00227135 | 0.000217556 0 | 0.000108778 | − | 1.00000i | \(-0.499965\pi\) | ||||
0.000108778 | 1.00000i | \(0.499965\pi\) | ||||||||
\(110\) | 0.937537 | 0.0893906 | ||||||||
\(111\) | −0.0288470 | −0.00273804 | ||||||||
\(112\) | 3.95985 | 0.374170 | ||||||||
\(113\) | −14.7948 | −1.39178 | −0.695889 | − | 0.718149i | \(-0.744990\pi\) | ||||
−0.695889 | + | 0.718149i | \(0.744990\pi\) | |||||||
\(114\) | −2.40432 | −0.225186 | ||||||||
\(115\) | −0.101509 | −0.00946579 | ||||||||
\(116\) | −31.5372 | −2.92816 | ||||||||
\(117\) | 12.5165 | 1.15715 | ||||||||
\(118\) | −33.2559 | −3.06145 | ||||||||
\(119\) | 21.5035 | 1.97122 | ||||||||
\(120\) | 0.545486 | 0.0497958 | ||||||||
\(121\) | −9.75432 | −0.886756 | ||||||||
\(122\) | −15.9396 | −1.44310 | ||||||||
\(123\) | 4.49751 | 0.405527 | ||||||||
\(124\) | −1.14776 | −0.103072 | ||||||||
\(125\) | −3.54109 | −0.316725 | ||||||||
\(126\) | 22.3161 | 1.98808 | ||||||||
\(127\) | 8.19744 | 0.727405 | 0.363703 | − | 0.931515i | \(-0.381512\pi\) | ||||
0.363703 | + | 0.931515i | \(0.381512\pi\) | |||||||
\(128\) | 20.1450 | 1.78058 | ||||||||
\(129\) | −3.38637 | −0.298153 | ||||||||
\(130\) | 3.74383 | 0.328355 | ||||||||
\(131\) | −16.6557 | −1.45522 | −0.727609 | − | 0.685992i | \(-0.759368\pi\) | ||||
−0.727609 | + | 0.685992i | \(0.759368\pi\) | |||||||
\(132\) | 1.70201 | 0.148141 | ||||||||
\(133\) | −7.95893 | −0.690126 | ||||||||
\(134\) | −26.6244 | −2.30000 | ||||||||
\(135\) | 0.912175 | 0.0785075 | ||||||||
\(136\) | −22.0100 | −1.88734 | ||||||||
\(137\) | 2.44283 | 0.208705 | 0.104353 | − | 0.994540i | \(-0.466723\pi\) | ||||
0.104353 | + | 0.994540i | \(0.466723\pi\) | |||||||
\(138\) | −0.290087 | −0.0246939 | ||||||||
\(139\) | −3.01871 | −0.256044 | −0.128022 | − | 0.991771i | \(-0.540863\pi\) | ||||
−0.128022 | + | 0.991771i | \(0.540863\pi\) | |||||||
\(140\) | 4.24037 | 0.358376 | ||||||||
\(141\) | 4.81726 | 0.405687 | ||||||||
\(142\) | −13.7756 | −1.15603 | ||||||||
\(143\) | 4.97434 | 0.415975 | ||||||||
\(144\) | −3.27704 | −0.273087 | ||||||||
\(145\) | −3.24782 | −0.269717 | ||||||||
\(146\) | −20.8636 | −1.72669 | ||||||||
\(147\) | −1.97696 | −0.163057 | ||||||||
\(148\) | 0.229525 | 0.0188669 | ||||||||
\(149\) | −17.6155 | −1.44312 | −0.721558 | − | 0.692354i | \(-0.756574\pi\) | ||||
−0.721558 | + | 0.692354i | \(0.756574\pi\) | |||||||
\(150\) | −4.99381 | −0.407743 | ||||||||
\(151\) | 6.53463 | 0.531781 | 0.265890 | − | 0.964003i | \(-0.414334\pi\) | ||||
0.265890 | + | 0.964003i | \(0.414334\pi\) | |||||||
\(152\) | 8.14639 | 0.660759 | ||||||||
\(153\) | −17.7956 | −1.43869 | ||||||||
\(154\) | 8.86896 | 0.714681 | ||||||||
\(155\) | −0.118201 | −0.00949413 | ||||||||
\(156\) | 6.79655 | 0.544160 | ||||||||
\(157\) | 21.0609 | 1.68084 | 0.840419 | − | 0.541936i | \(-0.182309\pi\) | ||||
0.840419 | + | 0.541936i | \(0.182309\pi\) | |||||||
\(158\) | −19.5747 | −1.55728 | ||||||||
\(159\) | −0.486223 | −0.0385600 | ||||||||
\(160\) | 1.51181 | 0.119519 | ||||||||
\(161\) | −0.960263 | −0.0756793 | ||||||||
\(162\) | −17.1217 | −1.34521 | ||||||||
\(163\) | −8.74516 | −0.684974 | −0.342487 | − | 0.939523i | \(-0.611269\pi\) | ||||
−0.342487 | + | 0.939523i | \(0.611269\pi\) | |||||||
\(164\) | −35.7851 | −2.79435 | ||||||||
\(165\) | 0.175279 | 0.0136455 | ||||||||
\(166\) | −15.5339 | −1.20566 | ||||||||
\(167\) | 3.65416 | 0.282767 | 0.141384 | − | 0.989955i | \(-0.454845\pi\) | ||||
0.141384 | + | 0.989955i | \(0.454845\pi\) | |||||||
\(168\) | 5.16022 | 0.398120 | ||||||||
\(169\) | 6.86382 | 0.527986 | ||||||||
\(170\) | −5.32287 | −0.408246 | ||||||||
\(171\) | 6.58654 | 0.503685 | ||||||||
\(172\) | 26.9442 | 2.05447 | ||||||||
\(173\) | −23.6903 | −1.80114 | −0.900571 | − | 0.434709i | \(-0.856851\pi\) | ||||
−0.900571 | + | 0.434709i | \(0.856851\pi\) | |||||||
\(174\) | −9.28144 | −0.703624 | ||||||||
\(175\) | −16.5308 | −1.24961 | ||||||||
\(176\) | −1.30237 | −0.0981701 | ||||||||
\(177\) | −6.21742 | −0.467330 | ||||||||
\(178\) | 18.2653 | 1.36904 | ||||||||
\(179\) | 21.3915 | 1.59887 | 0.799436 | − | 0.600751i | \(-0.205132\pi\) | ||||
0.799436 | + | 0.600751i | \(0.205132\pi\) | |||||||
\(180\) | −3.50919 | −0.261559 | ||||||||
\(181\) | 12.7464 | 0.947436 | 0.473718 | − | 0.880677i | \(-0.342912\pi\) | ||||
0.473718 | + | 0.880677i | \(0.342912\pi\) | |||||||
\(182\) | 35.4161 | 2.62521 | ||||||||
\(183\) | −2.98001 | −0.220289 | ||||||||
\(184\) | 0.982881 | 0.0724589 | ||||||||
\(185\) | 0.0236374 | 0.00173786 | ||||||||
\(186\) | −0.337788 | −0.0247678 | ||||||||
\(187\) | −7.07238 | −0.517183 | ||||||||
\(188\) | −38.3293 | −2.79545 | ||||||||
\(189\) | 8.62905 | 0.627671 | ||||||||
\(190\) | 1.97012 | 0.142927 | ||||||||
\(191\) | −2.71538 | −0.196478 | −0.0982389 | − | 0.995163i | \(-0.531321\pi\) | ||||
−0.0982389 | + | 0.995163i | \(0.531321\pi\) | |||||||
\(192\) | 5.34207 | 0.385530 | ||||||||
\(193\) | −6.32621 | −0.455371 | −0.227685 | − | 0.973735i | \(-0.573116\pi\) | ||||
−0.227685 | + | 0.973735i | \(0.573116\pi\) | |||||||
\(194\) | −44.5059 | −3.19534 | ||||||||
\(195\) | 0.699935 | 0.0501234 | ||||||||
\(196\) | 15.7300 | 1.12357 | ||||||||
\(197\) | 10.2970 | 0.733632 | 0.366816 | − | 0.930294i | \(-0.380448\pi\) | ||||
0.366816 | + | 0.930294i | \(0.380448\pi\) | |||||||
\(198\) | −7.33966 | −0.521607 | ||||||||
\(199\) | 11.2383 | 0.796664 | 0.398332 | − | 0.917241i | \(-0.369589\pi\) | ||||
0.398332 | + | 0.917241i | \(0.369589\pi\) | |||||||
\(200\) | 16.9201 | 1.19643 | ||||||||
\(201\) | −4.97762 | −0.351095 | ||||||||
\(202\) | −33.2240 | −2.33763 | ||||||||
\(203\) | −30.7240 | −2.15640 | ||||||||
\(204\) | −9.66315 | −0.676556 | ||||||||
\(205\) | −3.68529 | −0.257392 | ||||||||
\(206\) | −0.770972 | −0.0537161 | ||||||||
\(207\) | 0.794682 | 0.0552342 | ||||||||
\(208\) | −5.20071 | −0.360605 | ||||||||
\(209\) | 2.61765 | 0.181067 | ||||||||
\(210\) | 1.24794 | 0.0861163 | ||||||||
\(211\) | 28.1377 | 1.93708 | 0.968541 | − | 0.248855i | \(-0.0800543\pi\) | ||||
0.968541 | + | 0.248855i | \(0.0800543\pi\) | |||||||
\(212\) | 3.86870 | 0.265704 | ||||||||
\(213\) | −2.57545 | −0.176467 | ||||||||
\(214\) | −7.45025 | −0.509288 | ||||||||
\(215\) | 2.77481 | 0.189241 | ||||||||
\(216\) | −8.83229 | −0.600961 | ||||||||
\(217\) | −1.11816 | −0.0759059 | ||||||||
\(218\) | −0.00531870 | −0.000360228 0 | ||||||||
\(219\) | −3.90060 | −0.263578 | ||||||||
\(220\) | −1.39463 | −0.0940262 | ||||||||
\(221\) | −28.2418 | −1.89975 | ||||||||
\(222\) | 0.0675496 | 0.00453363 | ||||||||
\(223\) | 20.4221 | 1.36756 | 0.683782 | − | 0.729686i | \(-0.260334\pi\) | ||||
0.683782 | + | 0.729686i | \(0.260334\pi\) | |||||||
\(224\) | 14.3015 | 0.955559 | ||||||||
\(225\) | 13.6803 | 0.912021 | ||||||||
\(226\) | 34.6443 | 2.30450 | ||||||||
\(227\) | −14.3892 | −0.955043 | −0.477522 | − | 0.878620i | \(-0.658465\pi\) | ||||
−0.477522 | + | 0.878620i | \(0.658465\pi\) | |||||||
\(228\) | 3.57655 | 0.236863 | ||||||||
\(229\) | −13.3730 | −0.883715 | −0.441857 | − | 0.897085i | \(-0.645680\pi\) | ||||
−0.441857 | + | 0.897085i | \(0.645680\pi\) | |||||||
\(230\) | 0.237699 | 0.0156734 | ||||||||
\(231\) | 1.65811 | 0.109096 | ||||||||
\(232\) | 31.4476 | 2.06464 | ||||||||
\(233\) | 3.15750 | 0.206855 | 0.103427 | − | 0.994637i | \(-0.467019\pi\) | ||||
0.103427 | + | 0.994637i | \(0.467019\pi\) | |||||||
\(234\) | −29.3092 | −1.91600 | ||||||||
\(235\) | −3.94729 | −0.257493 | ||||||||
\(236\) | 49.4699 | 3.22021 | ||||||||
\(237\) | −3.65963 | −0.237719 | ||||||||
\(238\) | −50.3536 | −3.26394 | ||||||||
\(239\) | 9.95161 | 0.643716 | 0.321858 | − | 0.946788i | \(-0.395693\pi\) | ||||
0.321858 | + | 0.946788i | \(0.395693\pi\) | |||||||
\(240\) | −0.183256 | −0.0118291 | ||||||||
\(241\) | −1.63636 | −0.105407 | −0.0527036 | − | 0.998610i | \(-0.516784\pi\) | ||||
−0.0527036 | + | 0.998610i | \(0.516784\pi\) | |||||||
\(242\) | 22.8412 | 1.46829 | ||||||||
\(243\) | −10.8295 | −0.694712 | ||||||||
\(244\) | 23.7109 | 1.51794 | ||||||||
\(245\) | 1.61993 | 0.103494 | ||||||||
\(246\) | −10.5316 | −0.671470 | ||||||||
\(247\) | 10.4529 | 0.665105 | ||||||||
\(248\) | 1.14450 | 0.0726759 | ||||||||
\(249\) | −2.90416 | −0.184044 | ||||||||
\(250\) | 8.29200 | 0.524432 | ||||||||
\(251\) | 1.02428 | 0.0646520 | 0.0323260 | − | 0.999477i | \(-0.489709\pi\) | ||||
0.0323260 | + | 0.999477i | \(0.489709\pi\) | |||||||
\(252\) | −33.1964 | −2.09118 | ||||||||
\(253\) | 0.315825 | 0.0198558 | ||||||||
\(254\) | −19.1955 | −1.20444 | ||||||||
\(255\) | −0.995148 | −0.0623186 | ||||||||
\(256\) | −22.7677 | −1.42298 | ||||||||
\(257\) | −6.80941 | −0.424759 | −0.212380 | − | 0.977187i | \(-0.568121\pi\) | ||||
−0.212380 | + | 0.977187i | \(0.568121\pi\) | |||||||
\(258\) | 7.92970 | 0.493681 | ||||||||
\(259\) | 0.223606 | 0.0138942 | ||||||||
\(260\) | −5.56913 | −0.345383 | ||||||||
\(261\) | 25.4261 | 1.57384 | ||||||||
\(262\) | 39.0019 | 2.40954 | ||||||||
\(263\) | 10.4225 | 0.642678 | 0.321339 | − | 0.946964i | \(-0.395867\pi\) | ||||
0.321339 | + | 0.946964i | \(0.395867\pi\) | |||||||
\(264\) | −1.69717 | −0.104454 | ||||||||
\(265\) | 0.398414 | 0.0244744 | ||||||||
\(266\) | 18.6370 | 1.14271 | ||||||||
\(267\) | 3.41482 | 0.208983 | ||||||||
\(268\) | 39.6052 | 2.41927 | ||||||||
\(269\) | −21.5507 | −1.31397 | −0.656984 | − | 0.753905i | \(-0.728168\pi\) | ||||
−0.656984 | + | 0.753905i | \(0.728168\pi\) | |||||||
\(270\) | −2.13599 | −0.129992 | ||||||||
\(271\) | 4.26267 | 0.258939 | 0.129469 | − | 0.991583i | \(-0.458673\pi\) | ||||
0.129469 | + | 0.991583i | \(0.458673\pi\) | |||||||
\(272\) | 7.39423 | 0.448341 | ||||||||
\(273\) | 6.62128 | 0.400738 | ||||||||
\(274\) | −5.72026 | −0.345573 | ||||||||
\(275\) | 5.43689 | 0.327857 | ||||||||
\(276\) | 0.431520 | 0.0259744 | ||||||||
\(277\) | 15.9214 | 0.956625 | 0.478313 | − | 0.878190i | \(-0.341249\pi\) | ||||
0.478313 | + | 0.878190i | \(0.341249\pi\) | |||||||
\(278\) | 7.06876 | 0.423956 | ||||||||
\(279\) | 0.925355 | 0.0553996 | ||||||||
\(280\) | −4.22831 | −0.252690 | ||||||||
\(281\) | 8.00350 | 0.477449 | 0.238724 | − | 0.971087i | \(-0.423271\pi\) | ||||
0.238724 | + | 0.971087i | \(0.423271\pi\) | |||||||
\(282\) | −11.2803 | −0.671734 | ||||||||
\(283\) | 2.40190 | 0.142778 | 0.0713890 | − | 0.997449i | \(-0.477257\pi\) | ||||
0.0713890 | + | 0.997449i | \(0.477257\pi\) | |||||||
\(284\) | 20.4920 | 1.21597 | ||||||||
\(285\) | 0.368327 | 0.0218178 | ||||||||
\(286\) | −11.6482 | −0.688770 | ||||||||
\(287\) | −34.8623 | −2.05786 | ||||||||
\(288\) | −11.8354 | −0.697410 | ||||||||
\(289\) | 23.1535 | 1.36197 | ||||||||
\(290\) | 7.60527 | 0.446597 | ||||||||
\(291\) | −8.32069 | −0.487768 | ||||||||
\(292\) | 31.0357 | 1.81623 | ||||||||
\(293\) | −19.5879 | −1.14433 | −0.572167 | − | 0.820137i | \(-0.693897\pi\) | ||||
−0.572167 | + | 0.820137i | \(0.693897\pi\) | |||||||
\(294\) | 4.62935 | 0.269989 | ||||||||
\(295\) | 5.09459 | 0.296619 | ||||||||
\(296\) | −0.228873 | −0.0133030 | ||||||||
\(297\) | −2.83805 | −0.164680 | ||||||||
\(298\) | 41.2493 | 2.38951 | ||||||||
\(299\) | 1.26117 | 0.0729355 | ||||||||
\(300\) | 7.42854 | 0.428887 | ||||||||
\(301\) | 26.2493 | 1.51299 | ||||||||
\(302\) | −15.3018 | −0.880520 | ||||||||
\(303\) | −6.21146 | −0.356839 | ||||||||
\(304\) | −2.73677 | −0.156965 | ||||||||
\(305\) | 2.44184 | 0.139819 | ||||||||
\(306\) | 41.6710 | 2.38217 | ||||||||
\(307\) | 11.7220 | 0.669009 | 0.334504 | − | 0.942394i | \(-0.391431\pi\) | ||||
0.334504 | + | 0.942394i | \(0.391431\pi\) | |||||||
\(308\) | −13.1930 | −0.751743 | ||||||||
\(309\) | −0.144138 | −0.00819975 | ||||||||
\(310\) | 0.276785 | 0.0157203 | ||||||||
\(311\) | 23.6782 | 1.34267 | 0.671334 | − | 0.741155i | \(-0.265721\pi\) | ||||
0.671334 | + | 0.741155i | \(0.265721\pi\) | |||||||
\(312\) | −6.77724 | −0.383685 | ||||||||
\(313\) | 18.1630 | 1.02663 | 0.513316 | − | 0.858200i | \(-0.328417\pi\) | ||||
0.513316 | + | 0.858200i | \(0.328417\pi\) | |||||||
\(314\) | −49.3171 | −2.78313 | ||||||||
\(315\) | −3.41869 | −0.192621 | ||||||||
\(316\) | 29.1184 | 1.63804 | ||||||||
\(317\) | 19.7993 | 1.11204 | 0.556019 | − | 0.831170i | \(-0.312328\pi\) | ||||
0.556019 | + | 0.831170i | \(0.312328\pi\) | |||||||
\(318\) | 1.13856 | 0.0638475 | ||||||||
\(319\) | 10.1049 | 0.565768 | ||||||||
\(320\) | −4.37732 | −0.244700 | ||||||||
\(321\) | −1.39288 | −0.0777427 | ||||||||
\(322\) | 2.24860 | 0.125310 | ||||||||
\(323\) | −14.8617 | −0.826928 | ||||||||
\(324\) | 25.4694 | 1.41497 | ||||||||
\(325\) | 21.7109 | 1.20430 | ||||||||
\(326\) | 20.4781 | 1.13418 | ||||||||
\(327\) | −0.000994368 0 | −5.49887e−5 0 | ||||||||
\(328\) | 35.6834 | 1.97029 | ||||||||
\(329\) | −37.3408 | −2.05867 | ||||||||
\(330\) | −0.410442 | −0.0225941 | ||||||||
\(331\) | −11.4205 | −0.627727 | −0.313864 | − | 0.949468i | \(-0.601623\pi\) | ||||
−0.313864 | + | 0.949468i | \(0.601623\pi\) | |||||||
\(332\) | 23.1074 | 1.26818 | ||||||||
\(333\) | −0.185049 | −0.0101406 | ||||||||
\(334\) | −8.55676 | −0.468205 | ||||||||
\(335\) | 4.07869 | 0.222843 | ||||||||
\(336\) | −1.73357 | −0.0945741 | ||||||||
\(337\) | −11.2706 | −0.613949 | −0.306974 | − | 0.951718i | \(-0.599317\pi\) | ||||
−0.306974 | + | 0.951718i | \(0.599317\pi\) | |||||||
\(338\) | −16.0727 | −0.874237 | ||||||||
\(339\) | 6.47698 | 0.351781 | ||||||||
\(340\) | 7.91804 | 0.429416 | ||||||||
\(341\) | 0.367758 | 0.0199152 | ||||||||
\(342\) | −15.4234 | −0.834001 | ||||||||
\(343\) | −8.43012 | −0.455184 | ||||||||
\(344\) | −26.8676 | −1.44860 | ||||||||
\(345\) | 0.0444395 | 0.00239254 | ||||||||
\(346\) | 55.4745 | 2.98232 | ||||||||
\(347\) | −20.1839 | −1.08353 | −0.541764 | − | 0.840531i | \(-0.682243\pi\) | ||||
−0.541764 | + | 0.840531i | \(0.682243\pi\) | |||||||
\(348\) | 13.8066 | 0.740112 | ||||||||
\(349\) | 2.08367 | 0.111537 | 0.0557683 | − | 0.998444i | \(-0.482239\pi\) | ||||
0.0557683 | + | 0.998444i | \(0.482239\pi\) | |||||||
\(350\) | 38.7093 | 2.06910 | ||||||||
\(351\) | −11.3331 | −0.604914 | ||||||||
\(352\) | −4.70369 | −0.250707 | ||||||||
\(353\) | 9.91563 | 0.527756 | 0.263878 | − | 0.964556i | \(-0.414998\pi\) | ||||
0.263878 | + | 0.964556i | \(0.414998\pi\) | |||||||
\(354\) | 14.5590 | 0.773804 | ||||||||
\(355\) | 2.11034 | 0.112005 | ||||||||
\(356\) | −27.1705 | −1.44003 | ||||||||
\(357\) | −9.41395 | −0.498239 | ||||||||
\(358\) | −50.0913 | −2.64741 | ||||||||
\(359\) | 26.0532 | 1.37503 | 0.687517 | − | 0.726168i | \(-0.258701\pi\) | ||||
0.687517 | + | 0.726168i | \(0.258701\pi\) | |||||||
\(360\) | 3.49921 | 0.184425 | ||||||||
\(361\) | −13.4993 | −0.710491 | ||||||||
\(362\) | −29.8477 | −1.56876 | ||||||||
\(363\) | 4.27032 | 0.224134 | ||||||||
\(364\) | −52.6832 | −2.76135 | ||||||||
\(365\) | 3.19618 | 0.167296 | ||||||||
\(366\) | 6.97814 | 0.364753 | ||||||||
\(367\) | −6.74178 | −0.351918 | −0.175959 | − | 0.984397i | \(-0.556303\pi\) | ||||
−0.175959 | + | 0.984397i | \(0.556303\pi\) | |||||||
\(368\) | −0.330198 | −0.0172128 | ||||||||
\(369\) | 28.8509 | 1.50192 | ||||||||
\(370\) | −0.0553505 | −0.00287754 | ||||||||
\(371\) | 3.76894 | 0.195673 | ||||||||
\(372\) | 0.502477 | 0.0260522 | ||||||||
\(373\) | 13.2044 | 0.683696 | 0.341848 | − | 0.939755i | \(-0.388947\pi\) | ||||
0.341848 | + | 0.939755i | \(0.388947\pi\) | |||||||
\(374\) | 16.5610 | 0.856350 | ||||||||
\(375\) | 1.55025 | 0.0800544 | ||||||||
\(376\) | 38.2203 | 1.97106 | ||||||||
\(377\) | 40.3517 | 2.07822 | ||||||||
\(378\) | −20.2062 | −1.03929 | ||||||||
\(379\) | −2.26102 | −0.116141 | −0.0580704 | − | 0.998312i | \(-0.518495\pi\) | ||||
−0.0580704 | + | 0.998312i | \(0.518495\pi\) | |||||||
\(380\) | −2.93065 | −0.150339 | ||||||||
\(381\) | −3.58874 | −0.183857 | ||||||||
\(382\) | 6.35846 | 0.325327 | ||||||||
\(383\) | −9.86894 | −0.504279 | −0.252140 | − | 0.967691i | \(-0.581134\pi\) | ||||
−0.252140 | + | 0.967691i | \(0.581134\pi\) | |||||||
\(384\) | −8.81923 | −0.450054 | ||||||||
\(385\) | −1.35867 | −0.0692441 | ||||||||
\(386\) | 14.8138 | 0.754001 | ||||||||
\(387\) | −21.7231 | −1.10425 | ||||||||
\(388\) | 66.2049 | 3.36104 | ||||||||
\(389\) | 12.8695 | 0.652507 | 0.326254 | − | 0.945282i | \(-0.394214\pi\) | ||||
0.326254 | + | 0.945282i | \(0.394214\pi\) | |||||||
\(390\) | −1.63900 | −0.0829941 | ||||||||
\(391\) | −1.79310 | −0.0906810 | ||||||||
\(392\) | −15.6853 | −0.792226 | ||||||||
\(393\) | 7.29167 | 0.367816 | ||||||||
\(394\) | −24.1120 | −1.21474 | ||||||||
\(395\) | 2.99872 | 0.150882 | ||||||||
\(396\) | 10.9181 | 0.548656 | ||||||||
\(397\) | 9.16350 | 0.459903 | 0.229951 | − | 0.973202i | \(-0.426143\pi\) | ||||
0.229951 | + | 0.973202i | \(0.426143\pi\) | |||||||
\(398\) | −26.3162 | −1.31911 | ||||||||
\(399\) | 3.48432 | 0.174434 | ||||||||
\(400\) | −5.68431 | −0.284216 | ||||||||
\(401\) | −5.55171 | −0.277239 | −0.138620 | − | 0.990346i | \(-0.544267\pi\) | ||||
−0.138620 | + | 0.990346i | \(0.544267\pi\) | |||||||
\(402\) | 11.6559 | 0.581341 | ||||||||
\(403\) | 1.46855 | 0.0731539 | ||||||||
\(404\) | 49.4224 | 2.45886 | ||||||||
\(405\) | 2.62293 | 0.130335 | ||||||||
\(406\) | 71.9447 | 3.57056 | ||||||||
\(407\) | −0.0735429 | −0.00364539 | ||||||||
\(408\) | 9.63569 | 0.477038 | ||||||||
\(409\) | −11.3015 | −0.558824 | −0.279412 | − | 0.960171i | \(-0.590140\pi\) | ||||
−0.279412 | + | 0.960171i | \(0.590140\pi\) | |||||||
\(410\) | 8.62965 | 0.426188 | ||||||||
\(411\) | −1.06944 | −0.0527517 | ||||||||
\(412\) | 1.14686 | 0.0565017 | ||||||||
\(413\) | 48.1941 | 2.37148 | ||||||||
\(414\) | −1.86087 | −0.0914566 | ||||||||
\(415\) | 2.37969 | 0.116814 | ||||||||
\(416\) | −18.7830 | −0.920915 | ||||||||
\(417\) | 1.32155 | 0.0647168 | ||||||||
\(418\) | −6.12962 | −0.299809 | ||||||||
\(419\) | 37.8498 | 1.84908 | 0.924541 | − | 0.381083i | \(-0.124449\pi\) | ||||
0.924541 | + | 0.381083i | \(0.124449\pi\) | |||||||
\(420\) | −1.85638 | −0.0905821 | ||||||||
\(421\) | 6.54301 | 0.318887 | 0.159443 | − | 0.987207i | \(-0.449030\pi\) | ||||
0.159443 | + | 0.987207i | \(0.449030\pi\) | |||||||
\(422\) | −65.8887 | −3.20741 | ||||||||
\(423\) | 30.9020 | 1.50251 | ||||||||
\(424\) | −3.85771 | −0.187347 | ||||||||
\(425\) | −30.8680 | −1.49732 | ||||||||
\(426\) | 6.03080 | 0.292193 | ||||||||
\(427\) | 23.0994 | 1.11786 | ||||||||
\(428\) | 11.0826 | 0.535699 | ||||||||
\(429\) | −2.17770 | −0.105141 | ||||||||
\(430\) | −6.49764 | −0.313344 | ||||||||
\(431\) | 15.1655 | 0.730496 | 0.365248 | − | 0.930910i | \(-0.380984\pi\) | ||||
0.365248 | + | 0.930910i | \(0.380984\pi\) | |||||||
\(432\) | 2.96720 | 0.142760 | ||||||||
\(433\) | −5.51206 | −0.264892 | −0.132446 | − | 0.991190i | \(-0.542283\pi\) | ||||
−0.132446 | + | 0.991190i | \(0.542283\pi\) | |||||||
\(434\) | 2.61835 | 0.125685 | ||||||||
\(435\) | 1.42186 | 0.0681728 | ||||||||
\(436\) | 0.00791184 | 0.000378908 0 | ||||||||
\(437\) | 0.663668 | 0.0317475 | ||||||||
\(438\) | 9.13385 | 0.436432 | ||||||||
\(439\) | −5.86387 | −0.279867 | −0.139934 | − | 0.990161i | \(-0.544689\pi\) | ||||
−0.139934 | + | 0.990161i | \(0.544689\pi\) | |||||||
\(440\) | 1.39067 | 0.0662976 | ||||||||
\(441\) | −12.6819 | −0.603900 | ||||||||
\(442\) | 66.1325 | 3.14560 | ||||||||
\(443\) | 12.0408 | 0.572078 | 0.286039 | − | 0.958218i | \(-0.407661\pi\) | ||||
0.286039 | + | 0.958218i | \(0.407661\pi\) | |||||||
\(444\) | −0.100483 | −0.00476873 | ||||||||
\(445\) | −2.79812 | −0.132644 | ||||||||
\(446\) | −47.8214 | −2.26441 | ||||||||
\(447\) | 7.71184 | 0.364757 | ||||||||
\(448\) | −41.4088 | −1.95638 | ||||||||
\(449\) | −28.5061 | −1.34529 | −0.672643 | − | 0.739967i | \(-0.734841\pi\) | ||||
−0.672643 | + | 0.739967i | \(0.734841\pi\) | |||||||
\(450\) | −32.0345 | −1.51012 | ||||||||
\(451\) | 11.4660 | 0.539914 | ||||||||
\(452\) | −51.5351 | −2.42401 | ||||||||
\(453\) | −2.86078 | −0.134411 | ||||||||
\(454\) | 33.6944 | 1.58136 | ||||||||
\(455\) | −5.42551 | −0.254352 | ||||||||
\(456\) | −3.56639 | −0.167011 | ||||||||
\(457\) | −0.275369 | −0.0128812 | −0.00644060 | − | 0.999979i | \(-0.502050\pi\) | ||||
−0.00644060 | + | 0.999979i | \(0.502050\pi\) | |||||||
\(458\) | 31.3150 | 1.46325 | ||||||||
\(459\) | 16.1130 | 0.752092 | ||||||||
\(460\) | −0.353590 | −0.0164862 | ||||||||
\(461\) | 27.5656 | 1.28386 | 0.641928 | − | 0.766765i | \(-0.278135\pi\) | ||||
0.641928 | + | 0.766765i | \(0.278135\pi\) | |||||||
\(462\) | −3.88272 | −0.180641 | ||||||||
\(463\) | −16.0011 | −0.743633 | −0.371816 | − | 0.928306i | \(-0.621265\pi\) | ||||
−0.371816 | + | 0.928306i | \(0.621265\pi\) | |||||||
\(464\) | −10.5648 | −0.490459 | ||||||||
\(465\) | 0.0517469 | 0.00239971 | ||||||||
\(466\) | −7.39376 | −0.342510 | ||||||||
\(467\) | −6.64048 | −0.307285 | −0.153642 | − | 0.988127i | \(-0.549100\pi\) | ||||
−0.153642 | + | 0.988127i | \(0.549100\pi\) | |||||||
\(468\) | 43.5989 | 2.01536 | ||||||||
\(469\) | 38.5839 | 1.78164 | ||||||||
\(470\) | 9.24317 | 0.426356 | ||||||||
\(471\) | −9.22018 | −0.424844 | ||||||||
\(472\) | −49.3293 | −2.27056 | ||||||||
\(473\) | −8.63326 | −0.396958 | ||||||||
\(474\) | 8.56957 | 0.393614 | ||||||||
\(475\) | 11.4249 | 0.524212 | ||||||||
\(476\) | 74.9035 | 3.43320 | ||||||||
\(477\) | −3.11905 | −0.142811 | ||||||||
\(478\) | −23.3032 | −1.06586 | ||||||||
\(479\) | 5.90173 | 0.269657 | 0.134829 | − | 0.990869i | \(-0.456952\pi\) | ||||
0.134829 | + | 0.990869i | \(0.456952\pi\) | |||||||
\(480\) | −0.661852 | −0.0302093 | ||||||||
\(481\) | −0.293676 | −0.0133905 | ||||||||
\(482\) | 3.83178 | 0.174533 | ||||||||
\(483\) | 0.420391 | 0.0191285 | ||||||||
\(484\) | −33.9774 | −1.54443 | ||||||||
\(485\) | 6.81802 | 0.309591 | ||||||||
\(486\) | 25.3589 | 1.15030 | ||||||||
\(487\) | −13.2061 | −0.598427 | −0.299214 | − | 0.954186i | \(-0.596724\pi\) | ||||
−0.299214 | + | 0.954186i | \(0.596724\pi\) | |||||||
\(488\) | −23.6435 | −1.07029 | ||||||||
\(489\) | 3.82852 | 0.173132 | ||||||||
\(490\) | −3.79332 | −0.171365 | ||||||||
\(491\) | 15.9325 | 0.719026 | 0.359513 | − | 0.933140i | \(-0.382943\pi\) | ||||
0.359513 | + | 0.933140i | \(0.382943\pi\) | |||||||
\(492\) | 15.6663 | 0.706291 | ||||||||
\(493\) | −57.3709 | −2.58385 | ||||||||
\(494\) | −24.4771 | −1.10128 | ||||||||
\(495\) | 1.12439 | 0.0505375 | ||||||||
\(496\) | −0.384494 | −0.0172643 | ||||||||
\(497\) | 19.9635 | 0.895486 | ||||||||
\(498\) | 6.80054 | 0.304739 | ||||||||
\(499\) | −9.87843 | −0.442219 | −0.221110 | − | 0.975249i | \(-0.570968\pi\) | ||||
−0.221110 | + | 0.975249i | \(0.570968\pi\) | |||||||
\(500\) | −12.3348 | −0.551628 | ||||||||
\(501\) | −1.59975 | −0.0714714 | ||||||||
\(502\) | −2.39851 | −0.107051 | ||||||||
\(503\) | −22.9873 | −1.02495 | −0.512477 | − | 0.858701i | \(-0.671272\pi\) | ||||
−0.512477 | + | 0.858701i | \(0.671272\pi\) | |||||||
\(504\) | 33.1020 | 1.47448 | ||||||||
\(505\) | 5.08971 | 0.226489 | ||||||||
\(506\) | −0.739553 | −0.0328771 | ||||||||
\(507\) | −3.00490 | −0.133452 | ||||||||
\(508\) | 28.5543 | 1.26689 | ||||||||
\(509\) | 11.6725 | 0.517373 | 0.258687 | − | 0.965961i | \(-0.416710\pi\) | ||||
0.258687 | + | 0.965961i | \(0.416710\pi\) | |||||||
\(510\) | 2.33029 | 0.103187 | ||||||||
\(511\) | 30.2354 | 1.33753 | ||||||||
\(512\) | 13.0240 | 0.575584 | ||||||||
\(513\) | −5.96380 | −0.263308 | ||||||||
\(514\) | 15.9453 | 0.703315 | ||||||||
\(515\) | 0.118108 | 0.00520446 | ||||||||
\(516\) | −11.7958 | −0.519282 | ||||||||
\(517\) | 12.2812 | 0.540126 | ||||||||
\(518\) | −0.523608 | −0.0230060 | ||||||||
\(519\) | 10.3713 | 0.455251 | ||||||||
\(520\) | 5.55331 | 0.243529 | ||||||||
\(521\) | 12.1587 | 0.532684 | 0.266342 | − | 0.963879i | \(-0.414185\pi\) | ||||
0.266342 | + | 0.963879i | \(0.414185\pi\) | |||||||
\(522\) | −59.5391 | −2.60595 | ||||||||
\(523\) | 10.2136 | 0.446607 | 0.223304 | − | 0.974749i | \(-0.428316\pi\) | ||||
0.223304 | + | 0.974749i | \(0.428316\pi\) | |||||||
\(524\) | −58.0173 | −2.53450 | ||||||||
\(525\) | 7.23697 | 0.315847 | ||||||||
\(526\) | −24.4058 | −1.06414 | ||||||||
\(527\) | −2.08795 | −0.0909525 | ||||||||
\(528\) | 0.570163 | 0.0248132 | ||||||||
\(529\) | −22.9199 | −0.996519 | ||||||||
\(530\) | −0.932945 | −0.0405245 | ||||||||
\(531\) | −39.8838 | −1.73081 | ||||||||
\(532\) | −27.7235 | −1.20197 | ||||||||
\(533\) | 45.7868 | 1.98325 | ||||||||
\(534\) | −7.99630 | −0.346034 | ||||||||
\(535\) | 1.14133 | 0.0493440 | ||||||||
\(536\) | −39.4927 | −1.70582 | ||||||||
\(537\) | −9.36492 | −0.404126 | ||||||||
\(538\) | 50.4641 | 2.17566 | ||||||||
\(539\) | −5.04009 | −0.217092 | ||||||||
\(540\) | 3.17740 | 0.136734 | ||||||||
\(541\) | 12.4937 | 0.537147 | 0.268573 | − | 0.963259i | \(-0.413448\pi\) | ||||
0.268573 | + | 0.963259i | \(0.413448\pi\) | |||||||
\(542\) | −9.98168 | −0.428750 | ||||||||
\(543\) | −5.58024 | −0.239471 | ||||||||
\(544\) | 26.7052 | 1.14498 | ||||||||
\(545\) | 0.000814791 0 | 3.49018e−5 0 | ||||||||
\(546\) | −15.5047 | −0.663541 | ||||||||
\(547\) | −1.80967 | −0.0773758 | −0.0386879 | − | 0.999251i | \(-0.512318\pi\) | ||||
−0.0386879 | + | 0.999251i | \(0.512318\pi\) | |||||||
\(548\) | 8.50917 | 0.363494 | ||||||||
\(549\) | −19.1163 | −0.815865 | ||||||||
\(550\) | −12.7313 | −0.542864 | ||||||||
\(551\) | 21.2343 | 0.904611 | ||||||||
\(552\) | −0.430293 | −0.0183145 | ||||||||
\(553\) | 28.3675 | 1.20631 | ||||||||
\(554\) | −37.2824 | −1.58398 | ||||||||
\(555\) | −0.0103482 | −0.000439255 0 | ||||||||
\(556\) | −10.5151 | −0.445942 | ||||||||
\(557\) | 11.5872 | 0.490964 | 0.245482 | − | 0.969401i | \(-0.421054\pi\) | ||||
0.245482 | + | 0.969401i | \(0.421054\pi\) | |||||||
\(558\) | −2.16686 | −0.0917304 | ||||||||
\(559\) | −34.4749 | −1.45813 | ||||||||
\(560\) | 1.42050 | 0.0600271 | ||||||||
\(561\) | 3.09620 | 0.130722 | ||||||||
\(562\) | −18.7414 | −0.790558 | ||||||||
\(563\) | −29.6044 | −1.24768 | −0.623838 | − | 0.781553i | \(-0.714428\pi\) | ||||
−0.623838 | + | 0.781553i | \(0.714428\pi\) | |||||||
\(564\) | 16.7801 | 0.706569 | ||||||||
\(565\) | −5.30728 | −0.223279 | ||||||||
\(566\) | −5.62440 | −0.236411 | ||||||||
\(567\) | 24.8126 | 1.04203 | ||||||||
\(568\) | −20.4337 | −0.857380 | ||||||||
\(569\) | −5.15781 | −0.216227 | −0.108113 | − | 0.994139i | \(-0.534481\pi\) | ||||
−0.108113 | + | 0.994139i | \(0.534481\pi\) | |||||||
\(570\) | −0.862493 | −0.0361258 | ||||||||
\(571\) | −28.9582 | −1.21186 | −0.605932 | − | 0.795516i | \(-0.707200\pi\) | ||||
−0.605932 | + | 0.795516i | \(0.707200\pi\) | |||||||
\(572\) | 17.3272 | 0.724488 | ||||||||
\(573\) | 1.18876 | 0.0496611 | ||||||||
\(574\) | 81.6353 | 3.40739 | ||||||||
\(575\) | 1.37845 | 0.0574851 | ||||||||
\(576\) | 34.2685 | 1.42786 | ||||||||
\(577\) | 37.8112 | 1.57410 | 0.787051 | − | 0.616888i | \(-0.211607\pi\) | ||||
0.787051 | + | 0.616888i | \(0.211607\pi\) | |||||||
\(578\) | −54.2173 | −2.25514 | ||||||||
\(579\) | 2.76954 | 0.115098 | ||||||||
\(580\) | −11.3132 | −0.469756 | ||||||||
\(581\) | 22.5115 | 0.933935 | ||||||||
\(582\) | 19.4842 | 0.807644 | ||||||||
\(583\) | −1.23958 | −0.0513383 | ||||||||
\(584\) | −30.9475 | −1.28062 | ||||||||
\(585\) | 4.48997 | 0.185638 | ||||||||
\(586\) | 45.8679 | 1.89478 | ||||||||
\(587\) | −11.0475 | −0.455981 | −0.227990 | − | 0.973663i | \(-0.573215\pi\) | ||||
−0.227990 | + | 0.973663i | \(0.573215\pi\) | |||||||
\(588\) | −6.88640 | −0.283990 | ||||||||
\(589\) | 0.772798 | 0.0318426 | ||||||||
\(590\) | −11.9297 | −0.491140 | ||||||||
\(591\) | −4.50791 | −0.185430 | ||||||||
\(592\) | 0.0768898 | 0.00316015 | ||||||||
\(593\) | 10.6953 | 0.439202 | 0.219601 | − | 0.975590i | \(-0.429524\pi\) | ||||
0.219601 | + | 0.975590i | \(0.429524\pi\) | |||||||
\(594\) | 6.64571 | 0.272677 | ||||||||
\(595\) | 7.71385 | 0.316237 | ||||||||
\(596\) | −61.3604 | −2.51342 | ||||||||
\(597\) | −4.92000 | −0.201362 | ||||||||
\(598\) | −2.95322 | −0.120766 | ||||||||
\(599\) | 6.57106 | 0.268486 | 0.134243 | − | 0.990948i | \(-0.457140\pi\) | ||||
0.134243 | + | 0.990948i | \(0.457140\pi\) | |||||||
\(600\) | −7.40743 | −0.302407 | ||||||||
\(601\) | 41.6967 | 1.70084 | 0.850422 | − | 0.526100i | \(-0.176346\pi\) | ||||
0.850422 | + | 0.526100i | \(0.176346\pi\) | |||||||
\(602\) | −61.4667 | −2.50520 | ||||||||
\(603\) | −31.9307 | −1.30032 | ||||||||
\(604\) | 22.7622 | 0.926182 | ||||||||
\(605\) | −3.49912 | −0.142260 | ||||||||
\(606\) | 14.5451 | 0.590853 | ||||||||
\(607\) | −1.69124 | −0.0686454 | −0.0343227 | − | 0.999411i | \(-0.510927\pi\) | ||||
−0.0343227 | + | 0.999411i | \(0.510927\pi\) | |||||||
\(608\) | −9.88421 | −0.400858 | ||||||||
\(609\) | 13.4506 | 0.545044 | ||||||||
\(610\) | −5.71793 | −0.231512 | ||||||||
\(611\) | 49.0420 | 1.98403 | ||||||||
\(612\) | −61.9877 | −2.50570 | ||||||||
\(613\) | −11.0082 | −0.444618 | −0.222309 | − | 0.974976i | \(-0.571359\pi\) | ||||
−0.222309 | + | 0.974976i | \(0.571359\pi\) | |||||||
\(614\) | −27.4488 | −1.10774 | ||||||||
\(615\) | 1.61337 | 0.0650575 | ||||||||
\(616\) | 13.1555 | 0.530052 | ||||||||
\(617\) | 21.9853 | 0.885096 | 0.442548 | − | 0.896745i | \(-0.354075\pi\) | ||||
0.442548 | + | 0.896745i | \(0.354075\pi\) | |||||||
\(618\) | 0.337522 | 0.0135771 | ||||||||
\(619\) | 24.9238 | 1.00177 | 0.500887 | − | 0.865513i | \(-0.333007\pi\) | ||||
0.500887 | + | 0.865513i | \(0.333007\pi\) | |||||||
\(620\) | −0.411732 | −0.0165356 | ||||||||
\(621\) | −0.719547 | −0.0288744 | ||||||||
\(622\) | −55.4461 | −2.22319 | ||||||||
\(623\) | −26.4698 | −1.06049 | ||||||||
\(624\) | 2.27681 | 0.0911453 | ||||||||
\(625\) | 23.0863 | 0.923452 | ||||||||
\(626\) | −42.5313 | −1.69989 | ||||||||
\(627\) | −1.14597 | −0.0457658 | ||||||||
\(628\) | 73.3618 | 2.92745 | ||||||||
\(629\) | 0.417540 | 0.0166484 | ||||||||
\(630\) | 8.00537 | 0.318942 | ||||||||
\(631\) | −19.8290 | −0.789382 | −0.394691 | − | 0.918814i | \(-0.629148\pi\) | ||||
−0.394691 | + | 0.918814i | \(0.629148\pi\) | |||||||
\(632\) | −29.0356 | −1.15498 | ||||||||
\(633\) | −12.3184 | −0.489611 | ||||||||
\(634\) | −46.3629 | −1.84131 | ||||||||
\(635\) | 2.94063 | 0.116695 | ||||||||
\(636\) | −1.69367 | −0.0671584 | ||||||||
\(637\) | −20.1264 | −0.797437 | ||||||||
\(638\) | −23.6622 | −0.936797 | ||||||||
\(639\) | −16.5211 | −0.653566 | ||||||||
\(640\) | 7.22653 | 0.285654 | ||||||||
\(641\) | −3.79896 | −0.150050 | −0.0750250 | − | 0.997182i | \(-0.523904\pi\) | ||||
−0.0750250 | + | 0.997182i | \(0.523904\pi\) | |||||||
\(642\) | 3.26163 | 0.128726 | ||||||||
\(643\) | 47.1945 | 1.86117 | 0.930585 | − | 0.366075i | \(-0.119299\pi\) | ||||
0.930585 | + | 0.366075i | \(0.119299\pi\) | |||||||
\(644\) | −3.34491 | −0.131808 | ||||||||
\(645\) | −1.21478 | −0.0478319 | ||||||||
\(646\) | 34.8009 | 1.36922 | ||||||||
\(647\) | 6.92533 | 0.272263 | 0.136131 | − | 0.990691i | \(-0.456533\pi\) | ||||
0.136131 | + | 0.990691i | \(0.456533\pi\) | |||||||
\(648\) | −25.3970 | −0.997689 | ||||||||
\(649\) | −15.8508 | −0.622198 | ||||||||
\(650\) | −50.8393 | −1.99408 | ||||||||
\(651\) | 0.489518 | 0.0191857 | ||||||||
\(652\) | −30.4622 | −1.19299 | ||||||||
\(653\) | 32.2940 | 1.26376 | 0.631880 | − | 0.775066i | \(-0.282283\pi\) | ||||
0.631880 | + | 0.775066i | \(0.282283\pi\) | |||||||
\(654\) | 0.00232846 | 9.10501e−5 0 | ||||||||
\(655\) | −5.97484 | −0.233456 | ||||||||
\(656\) | −11.9878 | −0.468046 | ||||||||
\(657\) | −25.0218 | −0.976193 | ||||||||
\(658\) | 87.4391 | 3.40873 | ||||||||
\(659\) | 5.06870 | 0.197449 | 0.0987243 | − | 0.995115i | \(-0.468524\pi\) | ||||
0.0987243 | + | 0.995115i | \(0.468524\pi\) | |||||||
\(660\) | 0.610553 | 0.0237658 | ||||||||
\(661\) | 13.0491 | 0.507550 | 0.253775 | − | 0.967263i | \(-0.418328\pi\) | ||||
0.253775 | + | 0.967263i | \(0.418328\pi\) | |||||||
\(662\) | 26.7428 | 1.03939 | ||||||||
\(663\) | 12.3639 | 0.480175 | ||||||||
\(664\) | −23.0418 | −0.894193 | ||||||||
\(665\) | −2.85507 | −0.110715 | ||||||||
\(666\) | 0.433320 | 0.0167908 | ||||||||
\(667\) | 2.56197 | 0.0991997 | ||||||||
\(668\) | 12.7286 | 0.492485 | ||||||||
\(669\) | −8.94054 | −0.345661 | ||||||||
\(670\) | −9.55087 | −0.368982 | ||||||||
\(671\) | −7.59728 | −0.293290 | ||||||||
\(672\) | −6.26102 | −0.241524 | ||||||||
\(673\) | −45.0455 | −1.73638 | −0.868189 | − | 0.496234i | \(-0.834716\pi\) | ||||
−0.868189 | + | 0.496234i | \(0.834716\pi\) | |||||||
\(674\) | 26.3918 | 1.01657 | ||||||||
\(675\) | −12.3869 | −0.476771 | ||||||||
\(676\) | 23.9089 | 0.919573 | ||||||||
\(677\) | 32.1256 | 1.23469 | 0.617344 | − | 0.786693i | \(-0.288208\pi\) | ||||
0.617344 | + | 0.786693i | \(0.288208\pi\) | |||||||
\(678\) | −15.1668 | −0.582479 | ||||||||
\(679\) | 64.4975 | 2.47519 | ||||||||
\(680\) | −7.89554 | −0.302780 | ||||||||
\(681\) | 6.29941 | 0.241394 | ||||||||
\(682\) | −0.861161 | −0.0329756 | ||||||||
\(683\) | 50.4661 | 1.93103 | 0.965515 | − | 0.260346i | \(-0.0838367\pi\) | ||||
0.965515 | + | 0.260346i | \(0.0838367\pi\) | |||||||
\(684\) | 22.9431 | 0.877250 | ||||||||
\(685\) | 0.876306 | 0.0334819 | ||||||||
\(686\) | 19.7404 | 0.753691 | ||||||||
\(687\) | 5.85455 | 0.223365 | ||||||||
\(688\) | 9.02615 | 0.344119 | ||||||||
\(689\) | −4.94998 | −0.188579 | ||||||||
\(690\) | −0.104062 | −0.00396156 | ||||||||
\(691\) | 48.7678 | 1.85522 | 0.927608 | − | 0.373556i | \(-0.121861\pi\) | ||||
0.927608 | + | 0.373556i | \(0.121861\pi\) | |||||||
\(692\) | −82.5211 | −3.13698 | ||||||||
\(693\) | 10.6366 | 0.404049 | ||||||||
\(694\) | 47.2636 | 1.79410 | ||||||||
\(695\) | −1.08289 | −0.0410763 | ||||||||
\(696\) | −13.7674 | −0.521851 | ||||||||
\(697\) | −65.0984 | −2.46578 | ||||||||
\(698\) | −4.87924 | −0.184682 | ||||||||
\(699\) | −1.38232 | −0.0522840 | ||||||||
\(700\) | −57.5820 | −2.17640 | ||||||||
\(701\) | 22.0662 | 0.833428 | 0.416714 | − | 0.909038i | \(-0.363182\pi\) | ||||
0.416714 | + | 0.909038i | \(0.363182\pi\) | |||||||
\(702\) | 26.5381 | 1.00161 | ||||||||
\(703\) | −0.154541 | −0.00582864 | ||||||||
\(704\) | 13.6191 | 0.513290 | ||||||||
\(705\) | 1.72808 | 0.0650831 | ||||||||
\(706\) | −23.2189 | −0.873856 | ||||||||
\(707\) | 48.1479 | 1.81079 | ||||||||
\(708\) | −21.6573 | −0.813931 | ||||||||
\(709\) | 24.3535 | 0.914614 | 0.457307 | − | 0.889309i | \(-0.348814\pi\) | ||||
0.457307 | + | 0.889309i | \(0.348814\pi\) | |||||||
\(710\) | −4.94168 | −0.185458 | ||||||||
\(711\) | −23.4760 | −0.880418 | ||||||||
\(712\) | 27.0933 | 1.01536 | ||||||||
\(713\) | 0.0932399 | 0.00349186 | ||||||||
\(714\) | 22.0442 | 0.824983 | ||||||||
\(715\) | 1.78442 | 0.0667336 | ||||||||
\(716\) | 74.5134 | 2.78470 | ||||||||
\(717\) | −4.35669 | −0.162704 | ||||||||
\(718\) | −61.0074 | −2.27678 | ||||||||
\(719\) | 40.9178 | 1.52598 | 0.762989 | − | 0.646412i | \(-0.223731\pi\) | ||||
0.762989 | + | 0.646412i | \(0.223731\pi\) | |||||||
\(720\) | −1.17556 | −0.0438105 | ||||||||
\(721\) | 1.11728 | 0.0416098 | ||||||||
\(722\) | 31.6107 | 1.17643 | ||||||||
\(723\) | 0.716379 | 0.0266424 | ||||||||
\(724\) | 44.4000 | 1.65011 | ||||||||
\(725\) | 44.1038 | 1.63798 | ||||||||
\(726\) | −9.99959 | −0.371120 | ||||||||
\(727\) | 22.8789 | 0.848531 | 0.424265 | − | 0.905538i | \(-0.360532\pi\) | ||||
0.424265 | + | 0.905538i | \(0.360532\pi\) | |||||||
\(728\) | 52.5335 | 1.94702 | ||||||||
\(729\) | −17.1944 | −0.636830 | ||||||||
\(730\) | −7.48432 | −0.277007 | ||||||||
\(731\) | 49.0154 | 1.81290 | ||||||||
\(732\) | −10.3803 | −0.383669 | ||||||||
\(733\) | −37.7703 | −1.39508 | −0.697538 | − | 0.716548i | \(-0.745721\pi\) | ||||
−0.697538 | + | 0.716548i | \(0.745721\pi\) | |||||||
\(734\) | 15.7869 | 0.582705 | ||||||||
\(735\) | −0.709187 | −0.0261588 | ||||||||
\(736\) | −1.19255 | −0.0439581 | ||||||||
\(737\) | −12.6900 | −0.467443 | ||||||||
\(738\) | −67.5586 | −2.48687 | ||||||||
\(739\) | −4.84983 | −0.178404 | −0.0892019 | − | 0.996014i | \(-0.528432\pi\) | ||||
−0.0892019 | + | 0.996014i | \(0.528432\pi\) | |||||||
\(740\) | 0.0823367 | 0.00302676 | ||||||||
\(741\) | −4.57617 | −0.168110 | ||||||||
\(742\) | −8.82553 | −0.323995 | ||||||||
\(743\) | −9.93345 | −0.364423 | −0.182211 | − | 0.983259i | \(-0.558326\pi\) | ||||
−0.182211 | + | 0.983259i | \(0.558326\pi\) | |||||||
\(744\) | −0.501049 | −0.0183693 | ||||||||
\(745\) | −6.31912 | −0.231515 | ||||||||
\(746\) | −30.9200 | −1.13206 | ||||||||
\(747\) | −18.6298 | −0.681628 | ||||||||
\(748\) | −24.6354 | −0.900759 | ||||||||
\(749\) | 10.7968 | 0.394507 | ||||||||
\(750\) | −3.63014 | −0.132554 | ||||||||
\(751\) | 4.98144 | 0.181775 | 0.0908876 | − | 0.995861i | \(-0.471030\pi\) | ||||
0.0908876 | + | 0.995861i | \(0.471030\pi\) | |||||||
\(752\) | −12.8401 | −0.468230 | ||||||||
\(753\) | −0.448417 | −0.0163412 | ||||||||
\(754\) | −94.4894 | −3.44110 | ||||||||
\(755\) | 2.34414 | 0.0853120 | ||||||||
\(756\) | 30.0578 | 1.09319 | ||||||||
\(757\) | 39.4946 | 1.43545 | 0.717727 | − | 0.696324i | \(-0.245182\pi\) | ||||
0.717727 | + | 0.696324i | \(0.245182\pi\) | |||||||
\(758\) | 5.29452 | 0.192306 | ||||||||
\(759\) | −0.138264 | −0.00501868 | ||||||||
\(760\) | 2.92232 | 0.106004 | ||||||||
\(761\) | −16.3169 | −0.591488 | −0.295744 | − | 0.955267i | \(-0.595568\pi\) | ||||
−0.295744 | + | 0.955267i | \(0.595568\pi\) | |||||||
\(762\) | 8.40357 | 0.304429 | ||||||||
\(763\) | 0.00770781 | 0.000279041 0 | ||||||||
\(764\) | −9.45854 | −0.342198 | ||||||||
\(765\) | −6.38372 | −0.230804 | ||||||||
\(766\) | 23.1096 | 0.834984 | ||||||||
\(767\) | −63.2963 | −2.28550 | ||||||||
\(768\) | 9.96742 | 0.359668 | ||||||||
\(769\) | 11.2026 | 0.403977 | 0.201989 | − | 0.979388i | \(-0.435260\pi\) | ||||
0.201989 | + | 0.979388i | \(0.435260\pi\) | |||||||
\(770\) | 3.18153 | 0.114654 | ||||||||
\(771\) | 2.98108 | 0.107361 | ||||||||
\(772\) | −22.0362 | −0.793101 | ||||||||
\(773\) | −44.0784 | −1.58539 | −0.792695 | − | 0.609618i | \(-0.791323\pi\) | ||||
−0.792695 | + | 0.609618i | \(0.791323\pi\) | |||||||
\(774\) | 50.8678 | 1.82841 | ||||||||
\(775\) | 1.60511 | 0.0576573 | ||||||||
\(776\) | −66.0167 | −2.36986 | ||||||||
\(777\) | −0.0978921 | −0.00351186 | ||||||||
\(778\) | −30.1358 | −1.08042 | ||||||||
\(779\) | 24.0944 | 0.863272 | ||||||||
\(780\) | 2.43810 | 0.0872979 | ||||||||
\(781\) | −6.56589 | −0.234946 | ||||||||
\(782\) | 4.19881 | 0.150149 | ||||||||
\(783\) | −23.0221 | −0.822744 | ||||||||
\(784\) | 5.26946 | 0.188195 | ||||||||
\(785\) | 7.55507 | 0.269652 | ||||||||
\(786\) | −17.0745 | −0.609029 | ||||||||
\(787\) | 1.98422 | 0.0707297 | 0.0353648 | − | 0.999374i | \(-0.488741\pi\) | ||||
0.0353648 | + | 0.999374i | \(0.488741\pi\) | |||||||
\(788\) | 35.8678 | 1.27774 | ||||||||
\(789\) | −4.56284 | −0.162441 | ||||||||
\(790\) | −7.02196 | −0.249830 | ||||||||
\(791\) | −50.2061 | −1.78512 | ||||||||
\(792\) | −10.8871 | −0.386856 | ||||||||
\(793\) | −30.3379 | −1.07733 | ||||||||
\(794\) | −21.4577 | −0.761505 | ||||||||
\(795\) | −0.174421 | −0.00618606 | ||||||||
\(796\) | 39.1467 | 1.38752 | ||||||||
\(797\) | −28.2809 | −1.00176 | −0.500880 | − | 0.865517i | \(-0.666990\pi\) | ||||
−0.500880 | + | 0.865517i | \(0.666990\pi\) | |||||||
\(798\) | −8.15906 | −0.288827 | ||||||||
\(799\) | −69.7266 | −2.46675 | ||||||||
\(800\) | −20.5296 | −0.725832 | ||||||||
\(801\) | 21.9055 | 0.773994 | ||||||||
\(802\) | 13.0002 | 0.459052 | ||||||||
\(803\) | −9.94425 | −0.350925 | ||||||||
\(804\) | −17.3387 | −0.611488 | ||||||||
\(805\) | −0.344471 | −0.0121410 | ||||||||
\(806\) | −3.43884 | −0.121128 | ||||||||
\(807\) | 9.43461 | 0.332114 | ||||||||
\(808\) | −49.2820 | −1.73373 | ||||||||
\(809\) | 16.4780 | 0.579337 | 0.289668 | − | 0.957127i | \(-0.406455\pi\) | ||||
0.289668 | + | 0.957127i | \(0.406455\pi\) | |||||||
\(810\) | −6.14199 | −0.215808 | ||||||||
\(811\) | −40.5809 | −1.42499 | −0.712494 | − | 0.701679i | \(-0.752434\pi\) | ||||
−0.712494 | + | 0.701679i | \(0.752434\pi\) | |||||||
\(812\) | −107.021 | −3.75572 | ||||||||
\(813\) | −1.86614 | −0.0654485 | ||||||||
\(814\) | 0.172212 | 0.00603602 | ||||||||
\(815\) | −3.13711 | −0.109888 | ||||||||
\(816\) | −3.23710 | −0.113321 | ||||||||
\(817\) | −18.1417 | −0.634699 | ||||||||
\(818\) | 26.4642 | 0.925299 | ||||||||
\(819\) | 42.4745 | 1.48418 | ||||||||
\(820\) | −12.8371 | −0.448289 | ||||||||
\(821\) | 50.5083 | 1.76275 | 0.881376 | − | 0.472416i | \(-0.156618\pi\) | ||||
0.881376 | + | 0.472416i | \(0.156618\pi\) | |||||||
\(822\) | 2.50426 | 0.0873460 | ||||||||
\(823\) | 25.7541 | 0.897731 | 0.448865 | − | 0.893599i | \(-0.351828\pi\) | ||||
0.448865 | + | 0.893599i | \(0.351828\pi\) | |||||||
\(824\) | −1.14360 | −0.0398392 | ||||||||
\(825\) | −2.38020 | −0.0828680 | ||||||||
\(826\) | −112.854 | −3.92668 | ||||||||
\(827\) | −10.2641 | −0.356917 | −0.178459 | − | 0.983947i | \(-0.557111\pi\) | ||||
−0.178459 | + | 0.983947i | \(0.557111\pi\) | |||||||
\(828\) | 2.76813 | 0.0961993 | ||||||||
\(829\) | −25.1531 | −0.873605 | −0.436802 | − | 0.899558i | \(-0.643889\pi\) | ||||
−0.436802 | + | 0.899558i | \(0.643889\pi\) | |||||||
\(830\) | −5.57240 | −0.193421 | ||||||||
\(831\) | −6.97020 | −0.241794 | ||||||||
\(832\) | 54.3847 | 1.88545 | ||||||||
\(833\) | 28.6152 | 0.991456 | ||||||||
\(834\) | −3.09462 | −0.107158 | ||||||||
\(835\) | 1.31084 | 0.0453635 | ||||||||
\(836\) | 9.11812 | 0.315357 | ||||||||
\(837\) | −0.837865 | −0.0289609 | ||||||||
\(838\) | −88.6309 | −3.06170 | ||||||||
\(839\) | −14.5706 | −0.503034 | −0.251517 | − | 0.967853i | \(-0.580929\pi\) | ||||
−0.251517 | + | 0.967853i | \(0.580929\pi\) | |||||||
\(840\) | 1.85110 | 0.0638692 | ||||||||
\(841\) | 52.9710 | 1.82658 | ||||||||
\(842\) | −15.3214 | −0.528011 | ||||||||
\(843\) | −3.50383 | −0.120678 | ||||||||
\(844\) | 98.0128 | 3.37374 | ||||||||
\(845\) | 2.46223 | 0.0847032 | ||||||||
\(846\) | −72.3617 | −2.48785 | ||||||||
\(847\) | −33.1012 | −1.13737 | ||||||||
\(848\) | 1.29599 | 0.0445046 | ||||||||
\(849\) | −1.05152 | −0.0360881 | ||||||||
\(850\) | 72.2819 | 2.47925 | ||||||||
\(851\) | −0.0186458 | −0.000639169 0 | ||||||||
\(852\) | −8.97113 | −0.307346 | ||||||||
\(853\) | −48.1849 | −1.64982 | −0.824910 | − | 0.565263i | \(-0.808774\pi\) | ||||
−0.824910 | + | 0.565263i | \(0.808774\pi\) | |||||||
\(854\) | −54.0908 | −1.85095 | ||||||||
\(855\) | 2.36276 | 0.0808048 | ||||||||
\(856\) | −11.0511 | −0.377720 | ||||||||
\(857\) | −7.96120 | −0.271949 | −0.135975 | − | 0.990712i | \(-0.543417\pi\) | ||||
−0.135975 | + | 0.990712i | \(0.543417\pi\) | |||||||
\(858\) | 5.09942 | 0.174091 | ||||||||
\(859\) | −49.9784 | −1.70524 | −0.852620 | − | 0.522531i | \(-0.824988\pi\) | ||||
−0.852620 | + | 0.522531i | \(0.824988\pi\) | |||||||
\(860\) | 9.66557 | 0.329593 | ||||||||
\(861\) | 15.2623 | 0.520137 | ||||||||
\(862\) | −35.5123 | −1.20955 | ||||||||
\(863\) | −20.6894 | −0.704274 | −0.352137 | − | 0.935948i | \(-0.614545\pi\) | ||||
−0.352137 | + | 0.935948i | \(0.614545\pi\) | |||||||
\(864\) | 10.7164 | 0.364581 | ||||||||
\(865\) | −8.49833 | −0.288952 | ||||||||
\(866\) | 12.9073 | 0.438608 | ||||||||
\(867\) | −10.1363 | −0.344247 | ||||||||
\(868\) | −3.89493 | −0.132202 | ||||||||
\(869\) | −9.32991 | −0.316496 | ||||||||
\(870\) | −3.32949 | −0.112880 | ||||||||
\(871\) | −50.6746 | −1.71704 | ||||||||
\(872\) | −0.00788935 | −0.000267167 0 | ||||||||
\(873\) | −53.3760 | −1.80650 | ||||||||
\(874\) | −1.55408 | −0.0525674 | ||||||||
\(875\) | −12.0167 | −0.406238 | ||||||||
\(876\) | −13.5871 | −0.459064 | ||||||||
\(877\) | 16.7222 | 0.564668 | 0.282334 | − | 0.959316i | \(-0.408891\pi\) | ||||
0.282334 | + | 0.959316i | \(0.408891\pi\) | |||||||
\(878\) | 13.7311 | 0.463403 | ||||||||
\(879\) | 8.57532 | 0.289238 | ||||||||
\(880\) | −0.467195 | −0.0157491 | ||||||||
\(881\) | −12.6555 | −0.426374 | −0.213187 | − | 0.977011i | \(-0.568384\pi\) | ||||
−0.213187 | + | 0.977011i | \(0.568384\pi\) | |||||||
\(882\) | 29.6966 | 0.999936 | ||||||||
\(883\) | 24.3092 | 0.818070 | 0.409035 | − | 0.912519i | \(-0.365865\pi\) | ||||
0.409035 | + | 0.912519i | \(0.365865\pi\) | |||||||
\(884\) | −98.3754 | −3.30872 | ||||||||
\(885\) | −2.23035 | −0.0749724 | ||||||||
\(886\) | −28.1954 | −0.947244 | ||||||||
\(887\) | 38.9644 | 1.30830 | 0.654148 | − | 0.756367i | \(-0.273028\pi\) | ||||
0.654148 | + | 0.756367i | \(0.273028\pi\) | |||||||
\(888\) | 0.100198 | 0.00336242 | ||||||||
\(889\) | 27.8180 | 0.932985 | ||||||||
\(890\) | 6.55222 | 0.219631 | ||||||||
\(891\) | −8.16073 | −0.273395 | ||||||||
\(892\) | 71.1368 | 2.38184 | ||||||||
\(893\) | 25.8074 | 0.863612 | ||||||||
\(894\) | −18.0584 | −0.603964 | ||||||||
\(895\) | 7.67367 | 0.256502 | ||||||||
\(896\) | 68.3619 | 2.28381 | ||||||||
\(897\) | −0.552126 | −0.0184349 | ||||||||
\(898\) | 66.7513 | 2.22752 | ||||||||
\(899\) | 2.98324 | 0.0994967 | ||||||||
\(900\) | 47.6530 | 1.58843 | ||||||||
\(901\) | 7.03774 | 0.234461 | ||||||||
\(902\) | −26.8494 | −0.893988 | ||||||||
\(903\) | −11.4916 | −0.382418 | ||||||||
\(904\) | 51.3886 | 1.70916 | ||||||||
\(905\) | 4.57248 | 0.151994 | ||||||||
\(906\) | 6.69895 | 0.222558 | ||||||||
\(907\) | −31.5800 | −1.04860 | −0.524299 | − | 0.851534i | \(-0.675673\pi\) | ||||
−0.524299 | + | 0.851534i | \(0.675673\pi\) | |||||||
\(908\) | −50.1222 | −1.66336 | ||||||||
\(909\) | −39.8456 | −1.32159 | ||||||||
\(910\) | 12.7047 | 0.421155 | ||||||||
\(911\) | −50.3164 | −1.66706 | −0.833528 | − | 0.552477i | \(-0.813683\pi\) | ||||
−0.833528 | + | 0.552477i | \(0.813683\pi\) | |||||||
\(912\) | 1.19813 | 0.0396739 | ||||||||
\(913\) | −7.40392 | −0.245034 | ||||||||
\(914\) | 0.644817 | 0.0213287 | ||||||||
\(915\) | −1.06901 | −0.0353403 | ||||||||
\(916\) | −46.5826 | −1.53913 | ||||||||
\(917\) | −56.5211 | −1.86649 | ||||||||
\(918\) | −37.7311 | −1.24531 | ||||||||
\(919\) | −10.9756 | −0.362051 | −0.181026 | − | 0.983478i | \(-0.557942\pi\) | ||||
−0.181026 | + | 0.983478i | \(0.557942\pi\) | |||||||
\(920\) | 0.352585 | 0.0116244 | ||||||||
\(921\) | −5.13174 | −0.169097 | ||||||||
\(922\) | −64.5489 | −2.12581 | ||||||||
\(923\) | −26.2193 | −0.863019 | ||||||||
\(924\) | 5.77575 | 0.190008 | ||||||||
\(925\) | −0.320984 | −0.0105539 | ||||||||
\(926\) | 37.4689 | 1.23130 | ||||||||
\(927\) | −0.924627 | −0.0303687 | ||||||||
\(928\) | −38.1562 | −1.25254 | ||||||||
\(929\) | 4.81786 | 0.158069 | 0.0790345 | − | 0.996872i | \(-0.474816\pi\) | ||||
0.0790345 | + | 0.996872i | \(0.474816\pi\) | |||||||
\(930\) | −0.121173 | −0.00397342 | ||||||||
\(931\) | −10.5911 | −0.347110 | ||||||||
\(932\) | 10.9986 | 0.360271 | ||||||||
\(933\) | −10.3660 | −0.339369 | ||||||||
\(934\) | 15.5497 | 0.508801 | ||||||||
\(935\) | −2.53704 | −0.0829702 | ||||||||
\(936\) | −43.4749 | −1.42102 | ||||||||
\(937\) | −48.8481 | −1.59580 | −0.797900 | − | 0.602790i | \(-0.794056\pi\) | ||||
−0.797900 | + | 0.602790i | \(0.794056\pi\) | |||||||
\(938\) | −90.3499 | −2.95003 | ||||||||
\(939\) | −7.95153 | −0.259488 | ||||||||
\(940\) | −13.7497 | −0.448466 | ||||||||
\(941\) | −53.4332 | −1.74187 | −0.870937 | − | 0.491396i | \(-0.836487\pi\) | ||||
−0.870937 | + | 0.491396i | \(0.836487\pi\) | |||||||
\(942\) | 21.5904 | 0.703454 | ||||||||
\(943\) | 2.90705 | 0.0946665 | ||||||||
\(944\) | 16.5721 | 0.539377 | ||||||||
\(945\) | 3.09546 | 0.100695 | ||||||||
\(946\) | 20.2161 | 0.657281 | ||||||||
\(947\) | 38.0769 | 1.23733 | 0.618666 | − | 0.785654i | \(-0.287673\pi\) | ||||
0.618666 | + | 0.785654i | \(0.287673\pi\) | |||||||
\(948\) | −12.7477 | −0.414025 | ||||||||
\(949\) | −39.7100 | −1.28904 | ||||||||
\(950\) | −26.7532 | −0.867988 | ||||||||
\(951\) | −8.66787 | −0.281075 | ||||||||
\(952\) | −74.6907 | −2.42074 | ||||||||
\(953\) | −20.0787 | −0.650414 | −0.325207 | − | 0.945643i | \(-0.605434\pi\) | ||||
−0.325207 | + | 0.945643i | \(0.605434\pi\) | |||||||
\(954\) | 7.30371 | 0.236466 | ||||||||
\(955\) | −0.974076 | −0.0315204 | ||||||||
\(956\) | 34.6647 | 1.12114 | ||||||||
\(957\) | −4.42382 | −0.143002 | ||||||||
\(958\) | −13.8198 | −0.446497 | ||||||||
\(959\) | 8.28973 | 0.267689 | ||||||||
\(960\) | 1.91634 | 0.0618495 | ||||||||
\(961\) | −30.8914 | −0.996498 | ||||||||
\(962\) | 0.687686 | 0.0221719 | ||||||||
\(963\) | −8.93508 | −0.287929 | ||||||||
\(964\) | −5.69997 | −0.183584 | ||||||||
\(965\) | −2.26937 | −0.0730537 | ||||||||
\(966\) | −0.984409 | −0.0316729 | ||||||||
\(967\) | 13.6347 | 0.438464 | 0.219232 | − | 0.975673i | \(-0.429645\pi\) | ||||
0.219232 | + | 0.975673i | \(0.429645\pi\) | |||||||
\(968\) | 33.8809 | 1.08897 | ||||||||
\(969\) | 6.50628 | 0.209012 | ||||||||
\(970\) | −15.9654 | −0.512619 | ||||||||
\(971\) | −30.7116 | −0.985581 | −0.492790 | − | 0.870148i | \(-0.664023\pi\) | ||||
−0.492790 | + | 0.870148i | \(0.664023\pi\) | |||||||
\(972\) | −37.7226 | −1.20995 | ||||||||
\(973\) | −10.2440 | −0.328407 | ||||||||
\(974\) | 30.9241 | 0.990873 | ||||||||
\(975\) | −9.50476 | −0.304396 | ||||||||
\(976\) | 7.94303 | 0.254250 | ||||||||
\(977\) | −30.2357 | −0.967327 | −0.483663 | − | 0.875254i | \(-0.660694\pi\) | ||||
−0.483663 | + | 0.875254i | \(0.660694\pi\) | |||||||
\(978\) | −8.96506 | −0.286671 | ||||||||
\(979\) | 8.70578 | 0.278238 | ||||||||
\(980\) | 5.64275 | 0.180251 | ||||||||
\(981\) | −0.00637872 | −0.000203657 0 | ||||||||
\(982\) | −37.3084 | −1.19056 | ||||||||
\(983\) | −12.2019 | −0.389181 | −0.194591 | − | 0.980885i | \(-0.562338\pi\) | ||||
−0.194591 | + | 0.980885i | \(0.562338\pi\) | |||||||
\(984\) | −15.6218 | −0.498004 | ||||||||
\(985\) | 3.69380 | 0.117694 | ||||||||
\(986\) | 134.343 | 4.27834 | ||||||||
\(987\) | 16.3473 | 0.520342 | ||||||||
\(988\) | 36.4110 | 1.15839 | ||||||||
\(989\) | −2.18884 | −0.0696011 | ||||||||
\(990\) | −2.63292 | −0.0836798 | ||||||||
\(991\) | −32.1730 | −1.02201 | −0.511005 | − | 0.859578i | \(-0.670726\pi\) | ||||
−0.511005 | + | 0.859578i | \(0.670726\pi\) | |||||||
\(992\) | −1.38865 | −0.0440897 | ||||||||
\(993\) | 4.99975 | 0.158662 | ||||||||
\(994\) | −46.7475 | −1.48274 | ||||||||
\(995\) | 4.03148 | 0.127806 | ||||||||
\(996\) | −10.1161 | −0.320542 | ||||||||
\(997\) | 34.1417 | 1.08128 | 0.540640 | − | 0.841254i | \(-0.318182\pi\) | ||||
0.540640 | + | 0.841254i | \(0.318182\pi\) | |||||||
\(998\) | 23.1318 | 0.732225 | ||||||||
\(999\) | 0.167553 | 0.00530115 |
(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 | 4019.2.a.b.1.20 | ✓ | 186 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4019.2.a.b.1.20 | ✓ | 186 | 1.1 | even | 1 | trivial |