Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3525,2,Mod(1,3525)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3525, 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("3525.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3525 = 3 \cdot 5^{2} \cdot 47 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3525.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: | \(28.1472667125\) |
Analytic rank: | \(1\) |
Dimension: | \(10\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} - 3x^{9} - 9x^{8} + 29x^{7} + 25x^{6} - 91x^{5} - 21x^{4} + 101x^{3} + 6x^{2} - 30x - 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 705) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.9 | ||
Root | \(-1.88719\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3525.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.88719 | 1.33444 | 0.667222 | − | 0.744859i | \(-0.267483\pi\) | ||||
0.667222 | + | 0.744859i | \(0.267483\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 1.56149 | 0.780743 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 1.88719 | 0.770442 | ||||||||
\(7\) | −1.44822 | −0.547376 | −0.273688 | − | 0.961818i | \(-0.588244\pi\) | ||||
−0.273688 | + | 0.961818i | \(0.588244\pi\) | |||||||
\(8\) | −0.827559 | −0.292586 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.859846 | 0.259253 | 0.129627 | − | 0.991563i | \(-0.458622\pi\) | ||||
0.129627 | + | 0.991563i | \(0.458622\pi\) | |||||||
\(12\) | 1.56149 | 0.450762 | ||||||||
\(13\) | −2.84255 | −0.788380 | −0.394190 | − | 0.919029i | \(-0.628975\pi\) | ||||
−0.394190 | + | 0.919029i | \(0.628975\pi\) | |||||||
\(14\) | −2.73307 | −0.730443 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −4.68473 | −1.17118 | ||||||||
\(17\) | −5.63243 | −1.36606 | −0.683032 | − | 0.730389i | \(-0.739339\pi\) | ||||
−0.683032 | + | 0.730389i | \(0.739339\pi\) | |||||||
\(18\) | 1.88719 | 0.444815 | ||||||||
\(19\) | −6.59805 | −1.51370 | −0.756848 | − | 0.653590i | \(-0.773262\pi\) | ||||
−0.756848 | + | 0.653590i | \(0.773262\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.44822 | −0.316028 | ||||||||
\(22\) | 1.62269 | 0.345959 | ||||||||
\(23\) | 0.190099 | 0.0396384 | 0.0198192 | − | 0.999804i | \(-0.493691\pi\) | ||||
0.0198192 | + | 0.999804i | \(0.493691\pi\) | |||||||
\(24\) | −0.827559 | −0.168925 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −5.36442 | −1.05205 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | −2.26138 | −0.427360 | ||||||||
\(29\) | −10.3976 | −1.93078 | −0.965391 | − | 0.260807i | \(-0.916011\pi\) | ||||
−0.965391 | + | 0.260807i | \(0.916011\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 7.02308 | 1.26138 | 0.630692 | − | 0.776034i | \(-0.282771\pi\) | ||||
0.630692 | + | 0.776034i | \(0.282771\pi\) | |||||||
\(32\) | −7.18586 | −1.27029 | ||||||||
\(33\) | 0.859846 | 0.149680 | ||||||||
\(34\) | −10.6295 | −1.82294 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.56149 | 0.260248 | ||||||||
\(37\) | 5.67710 | 0.933309 | 0.466655 | − | 0.884440i | \(-0.345459\pi\) | ||||
0.466655 | + | 0.884440i | \(0.345459\pi\) | |||||||
\(38\) | −12.4518 | −2.01994 | ||||||||
\(39\) | −2.84255 | −0.455172 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −8.12459 | −1.26885 | −0.634424 | − | 0.772986i | \(-0.718762\pi\) | ||||
−0.634424 | + | 0.772986i | \(0.718762\pi\) | |||||||
\(42\) | −2.73307 | −0.421722 | ||||||||
\(43\) | 4.91032 | 0.748817 | 0.374409 | − | 0.927264i | \(-0.377846\pi\) | ||||
0.374409 | + | 0.927264i | \(0.377846\pi\) | |||||||
\(44\) | 1.34264 | 0.202410 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0.358753 | 0.0528952 | ||||||||
\(47\) | −1.00000 | −0.145865 | ||||||||
\(48\) | −4.68473 | −0.676183 | ||||||||
\(49\) | −4.90265 | −0.700379 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −5.63243 | −0.788697 | ||||||||
\(52\) | −4.43860 | −0.615522 | ||||||||
\(53\) | 3.85125 | 0.529010 | 0.264505 | − | 0.964384i | \(-0.414791\pi\) | ||||
0.264505 | + | 0.964384i | \(0.414791\pi\) | |||||||
\(54\) | 1.88719 | 0.256814 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 1.19849 | 0.160155 | ||||||||
\(57\) | −6.59805 | −0.873933 | ||||||||
\(58\) | −19.6222 | −2.57652 | ||||||||
\(59\) | 15.1067 | 1.96672 | 0.983360 | − | 0.181665i | \(-0.0581487\pi\) | ||||
0.983360 | + | 0.181665i | \(0.0581487\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −10.1814 | −1.30359 | −0.651796 | − | 0.758395i | \(-0.725984\pi\) | ||||
−0.651796 | + | 0.758395i | \(0.725984\pi\) | |||||||
\(62\) | 13.2539 | 1.68325 | ||||||||
\(63\) | −1.44822 | −0.182459 | ||||||||
\(64\) | −4.19162 | −0.523953 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 1.62269 | 0.199740 | ||||||||
\(67\) | 10.1209 | 1.23646 | 0.618230 | − | 0.785998i | \(-0.287850\pi\) | ||||
0.618230 | + | 0.785998i | \(0.287850\pi\) | |||||||
\(68\) | −8.79496 | −1.06654 | ||||||||
\(69\) | 0.190099 | 0.0228852 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −0.840275 | −0.0997223 | −0.0498611 | − | 0.998756i | \(-0.515878\pi\) | ||||
−0.0498611 | + | 0.998756i | \(0.515878\pi\) | |||||||
\(72\) | −0.827559 | −0.0975287 | ||||||||
\(73\) | −4.72701 | −0.553254 | −0.276627 | − | 0.960977i | \(-0.589217\pi\) | ||||
−0.276627 | + | 0.960977i | \(0.589217\pi\) | |||||||
\(74\) | 10.7138 | 1.24545 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −10.3028 | −1.18181 | ||||||||
\(77\) | −1.24525 | −0.141909 | ||||||||
\(78\) | −5.36442 | −0.607401 | ||||||||
\(79\) | −13.2708 | −1.49308 | −0.746541 | − | 0.665340i | \(-0.768287\pi\) | ||||
−0.746541 | + | 0.665340i | \(0.768287\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −15.3326 | −1.69321 | ||||||||
\(83\) | 0.110350 | 0.0121125 | 0.00605624 | − | 0.999982i | \(-0.498072\pi\) | ||||
0.00605624 | + | 0.999982i | \(0.498072\pi\) | |||||||
\(84\) | −2.26138 | −0.246737 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 9.26671 | 0.999255 | ||||||||
\(87\) | −10.3976 | −1.11474 | ||||||||
\(88\) | −0.711573 | −0.0758539 | ||||||||
\(89\) | 14.5928 | 1.54683 | 0.773416 | − | 0.633899i | \(-0.218546\pi\) | ||||
0.773416 | + | 0.633899i | \(0.218546\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 4.11663 | 0.431541 | ||||||||
\(92\) | 0.296837 | 0.0309474 | ||||||||
\(93\) | 7.02308 | 0.728260 | ||||||||
\(94\) | −1.88719 | −0.194649 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −7.18586 | −0.733404 | ||||||||
\(97\) | −1.88445 | −0.191337 | −0.0956685 | − | 0.995413i | \(-0.530499\pi\) | ||||
−0.0956685 | + | 0.995413i | \(0.530499\pi\) | |||||||
\(98\) | −9.25224 | −0.934617 | ||||||||
\(99\) | 0.859846 | 0.0864177 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −3.61387 | −0.359594 | −0.179797 | − | 0.983704i | \(-0.557544\pi\) | ||||
−0.179797 | + | 0.983704i | \(0.557544\pi\) | |||||||
\(102\) | −10.6295 | −1.05247 | ||||||||
\(103\) | 1.46000 | 0.143858 | 0.0719289 | − | 0.997410i | \(-0.477085\pi\) | ||||
0.0719289 | + | 0.997410i | \(0.477085\pi\) | |||||||
\(104\) | 2.35237 | 0.230669 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 7.26805 | 0.705935 | ||||||||
\(107\) | 15.0739 | 1.45724 | 0.728622 | − | 0.684916i | \(-0.240161\pi\) | ||||
0.728622 | + | 0.684916i | \(0.240161\pi\) | |||||||
\(108\) | 1.56149 | 0.150254 | ||||||||
\(109\) | 5.90985 | 0.566061 | 0.283031 | − | 0.959111i | \(-0.408660\pi\) | ||||
0.283031 | + | 0.959111i | \(0.408660\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 5.67710 | 0.538846 | ||||||||
\(112\) | 6.78453 | 0.641078 | ||||||||
\(113\) | −20.3228 | −1.91181 | −0.955904 | − | 0.293678i | \(-0.905121\pi\) | ||||
−0.955904 | + | 0.293678i | \(0.905121\pi\) | |||||||
\(114\) | −12.4518 | −1.16622 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −16.2357 | −1.50744 | ||||||||
\(117\) | −2.84255 | −0.262793 | ||||||||
\(118\) | 28.5092 | 2.62448 | ||||||||
\(119\) | 8.15700 | 0.747751 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.2607 | −0.932788 | ||||||||
\(122\) | −19.2142 | −1.73957 | ||||||||
\(123\) | −8.12459 | −0.732569 | ||||||||
\(124\) | 10.9665 | 0.984816 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −2.73307 | −0.243481 | ||||||||
\(127\) | 4.27301 | 0.379169 | 0.189584 | − | 0.981864i | \(-0.439286\pi\) | ||||
0.189584 | + | 0.981864i | \(0.439286\pi\) | |||||||
\(128\) | 6.46134 | 0.571107 | ||||||||
\(129\) | 4.91032 | 0.432330 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −12.5152 | −1.09346 | −0.546730 | − | 0.837309i | \(-0.684127\pi\) | ||||
−0.546730 | + | 0.837309i | \(0.684127\pi\) | |||||||
\(132\) | 1.34264 | 0.116862 | ||||||||
\(133\) | 9.55544 | 0.828562 | ||||||||
\(134\) | 19.1000 | 1.64999 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 4.66116 | 0.399691 | ||||||||
\(137\) | −7.69232 | −0.657200 | −0.328600 | − | 0.944469i | \(-0.606577\pi\) | ||||
−0.328600 | + | 0.944469i | \(0.606577\pi\) | |||||||
\(138\) | 0.358753 | 0.0305391 | ||||||||
\(139\) | −6.47935 | −0.549571 | −0.274786 | − | 0.961505i | \(-0.588607\pi\) | ||||
−0.274786 | + | 0.961505i | \(0.588607\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1.00000 | −0.0842152 | ||||||||
\(142\) | −1.58576 | −0.133074 | ||||||||
\(143\) | −2.44415 | −0.204390 | ||||||||
\(144\) | −4.68473 | −0.390394 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −8.92076 | −0.738287 | ||||||||
\(147\) | −4.90265 | −0.404364 | ||||||||
\(148\) | 8.86471 | 0.728675 | ||||||||
\(149\) | 16.7246 | 1.37013 | 0.685066 | − | 0.728481i | \(-0.259773\pi\) | ||||
0.685066 | + | 0.728481i | \(0.259773\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 16.0916 | 1.30951 | 0.654757 | − | 0.755839i | \(-0.272771\pi\) | ||||
0.654757 | + | 0.755839i | \(0.272771\pi\) | |||||||
\(152\) | 5.46028 | 0.442887 | ||||||||
\(153\) | −5.63243 | −0.455355 | ||||||||
\(154\) | −2.35002 | −0.189370 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −4.43860 | −0.355372 | ||||||||
\(157\) | 7.85429 | 0.626840 | 0.313420 | − | 0.949615i | \(-0.398525\pi\) | ||||
0.313420 | + | 0.949615i | \(0.398525\pi\) | |||||||
\(158\) | −25.0445 | −1.99244 | ||||||||
\(159\) | 3.85125 | 0.305424 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −0.275305 | −0.0216971 | ||||||||
\(162\) | 1.88719 | 0.148272 | ||||||||
\(163\) | 2.33379 | 0.182797 | 0.0913983 | − | 0.995814i | \(-0.470866\pi\) | ||||
0.0913983 | + | 0.995814i | \(0.470866\pi\) | |||||||
\(164\) | −12.6864 | −0.990644 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0.208251 | 0.0161634 | ||||||||
\(167\) | −10.0546 | −0.778052 | −0.389026 | − | 0.921227i | \(-0.627188\pi\) | ||||
−0.389026 | + | 0.921227i | \(0.627188\pi\) | |||||||
\(168\) | 1.19849 | 0.0924654 | ||||||||
\(169\) | −4.91994 | −0.378457 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −6.59805 | −0.504566 | ||||||||
\(172\) | 7.66740 | 0.584634 | ||||||||
\(173\) | −2.50875 | −0.190737 | −0.0953684 | − | 0.995442i | \(-0.530403\pi\) | ||||
−0.0953684 | + | 0.995442i | \(0.530403\pi\) | |||||||
\(174\) | −19.6222 | −1.48756 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −4.02815 | −0.303633 | ||||||||
\(177\) | 15.1067 | 1.13549 | ||||||||
\(178\) | 27.5394 | 2.06416 | ||||||||
\(179\) | −15.3483 | −1.14718 | −0.573592 | − | 0.819141i | \(-0.694450\pi\) | ||||
−0.573592 | + | 0.819141i | \(0.694450\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −17.0869 | −1.27006 | −0.635028 | − | 0.772489i | \(-0.719012\pi\) | ||||
−0.635028 | + | 0.772489i | \(0.719012\pi\) | |||||||
\(182\) | 7.76887 | 0.575867 | ||||||||
\(183\) | −10.1814 | −0.752629 | ||||||||
\(184\) | −0.157318 | −0.0115976 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 13.2539 | 0.971823 | ||||||||
\(187\) | −4.84302 | −0.354156 | ||||||||
\(188\) | −1.56149 | −0.113883 | ||||||||
\(189\) | −1.44822 | −0.105343 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 2.59051 | 0.187443 | 0.0937213 | − | 0.995598i | \(-0.470124\pi\) | ||||
0.0937213 | + | 0.995598i | \(0.470124\pi\) | |||||||
\(192\) | −4.19162 | −0.302504 | ||||||||
\(193\) | 10.1692 | 0.731994 | 0.365997 | − | 0.930616i | \(-0.380728\pi\) | ||||
0.365997 | + | 0.930616i | \(0.380728\pi\) | |||||||
\(194\) | −3.55632 | −0.255329 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −7.65543 | −0.546816 | ||||||||
\(197\) | −19.8628 | −1.41517 | −0.707584 | − | 0.706629i | \(-0.750215\pi\) | ||||
−0.707584 | + | 0.706629i | \(0.750215\pi\) | |||||||
\(198\) | 1.62269 | 0.115320 | ||||||||
\(199\) | −4.72329 | −0.334825 | −0.167413 | − | 0.985887i | \(-0.553541\pi\) | ||||
−0.167413 | + | 0.985887i | \(0.553541\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 10.1209 | 0.713870 | ||||||||
\(202\) | −6.82007 | −0.479858 | ||||||||
\(203\) | 15.0580 | 1.05686 | ||||||||
\(204\) | −8.79496 | −0.615770 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 2.75529 | 0.191970 | ||||||||
\(207\) | 0.190099 | 0.0132128 | ||||||||
\(208\) | 13.3166 | 0.923338 | ||||||||
\(209\) | −5.67331 | −0.392431 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −17.7581 | −1.22252 | −0.611261 | − | 0.791429i | \(-0.709337\pi\) | ||||
−0.611261 | + | 0.791429i | \(0.709337\pi\) | |||||||
\(212\) | 6.01368 | 0.413021 | ||||||||
\(213\) | −0.840275 | −0.0575747 | ||||||||
\(214\) | 28.4472 | 1.94461 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −0.827559 | −0.0563082 | ||||||||
\(217\) | −10.1710 | −0.690451 | ||||||||
\(218\) | 11.1530 | 0.755377 | ||||||||
\(219\) | −4.72701 | −0.319421 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 16.0104 | 1.07698 | ||||||||
\(222\) | 10.7138 | 0.719061 | ||||||||
\(223\) | −27.7580 | −1.85882 | −0.929408 | − | 0.369053i | \(-0.879682\pi\) | ||||
−0.929408 | + | 0.369053i | \(0.879682\pi\) | |||||||
\(224\) | 10.4067 | 0.695328 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −38.3530 | −2.55120 | ||||||||
\(227\) | 19.9112 | 1.32155 | 0.660775 | − | 0.750584i | \(-0.270228\pi\) | ||||
0.660775 | + | 0.750584i | \(0.270228\pi\) | |||||||
\(228\) | −10.3028 | −0.682317 | ||||||||
\(229\) | 15.9729 | 1.05552 | 0.527760 | − | 0.849394i | \(-0.323032\pi\) | ||||
0.527760 | + | 0.849394i | \(0.323032\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −1.24525 | −0.0819312 | ||||||||
\(232\) | 8.60461 | 0.564920 | ||||||||
\(233\) | 15.9896 | 1.04752 | 0.523758 | − | 0.851867i | \(-0.324530\pi\) | ||||
0.523758 | + | 0.851867i | \(0.324530\pi\) | |||||||
\(234\) | −5.36442 | −0.350683 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 23.5889 | 1.53550 | ||||||||
\(237\) | −13.2708 | −0.862031 | ||||||||
\(238\) | 15.3938 | 0.997832 | ||||||||
\(239\) | −16.2400 | −1.05048 | −0.525239 | − | 0.850955i | \(-0.676024\pi\) | ||||
−0.525239 | + | 0.850955i | \(0.676024\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.73011 | −0.111446 | −0.0557231 | − | 0.998446i | \(-0.517746\pi\) | ||||
−0.0557231 | + | 0.998446i | \(0.517746\pi\) | |||||||
\(242\) | −19.3638 | −1.24475 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | −15.8981 | −1.01777 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −15.3326 | −0.977573 | ||||||||
\(247\) | 18.7553 | 1.19337 | ||||||||
\(248\) | −5.81202 | −0.369063 | ||||||||
\(249\) | 0.110350 | 0.00699315 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −0.650330 | −0.0410484 | −0.0205242 | − | 0.999789i | \(-0.506534\pi\) | ||||
−0.0205242 | + | 0.999789i | \(0.506534\pi\) | |||||||
\(252\) | −2.26138 | −0.142453 | ||||||||
\(253\) | 0.163456 | 0.0102764 | ||||||||
\(254\) | 8.06399 | 0.505980 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 20.5770 | 1.28606 | ||||||||
\(257\) | −30.7586 | −1.91867 | −0.959336 | − | 0.282268i | \(-0.908913\pi\) | ||||
−0.959336 | + | 0.282268i | \(0.908913\pi\) | |||||||
\(258\) | 9.26671 | 0.576920 | ||||||||
\(259\) | −8.22170 | −0.510871 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −10.3976 | −0.643594 | ||||||||
\(262\) | −23.6186 | −1.45916 | ||||||||
\(263\) | 11.7992 | 0.727569 | 0.363784 | − | 0.931483i | \(-0.381485\pi\) | ||||
0.363784 | + | 0.931483i | \(0.381485\pi\) | |||||||
\(264\) | −0.711573 | −0.0437943 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 18.0329 | 1.10567 | ||||||||
\(267\) | 14.5928 | 0.893064 | ||||||||
\(268\) | 15.8036 | 0.965357 | ||||||||
\(269\) | 10.7027 | 0.652555 | 0.326278 | − | 0.945274i | \(-0.394206\pi\) | ||||
0.326278 | + | 0.945274i | \(0.394206\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −18.8506 | −1.14509 | −0.572547 | − | 0.819872i | \(-0.694045\pi\) | ||||
−0.572547 | + | 0.819872i | \(0.694045\pi\) | |||||||
\(272\) | 26.3864 | 1.59991 | ||||||||
\(273\) | 4.11663 | 0.249150 | ||||||||
\(274\) | −14.5169 | −0.876997 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0.296837 | 0.0178675 | ||||||||
\(277\) | 20.6129 | 1.23851 | 0.619255 | − | 0.785190i | \(-0.287435\pi\) | ||||
0.619255 | + | 0.785190i | \(0.287435\pi\) | |||||||
\(278\) | −12.2278 | −0.733373 | ||||||||
\(279\) | 7.02308 | 0.420461 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −11.2673 | −0.672149 | −0.336074 | − | 0.941835i | \(-0.609099\pi\) | ||||
−0.336074 | + | 0.941835i | \(0.609099\pi\) | |||||||
\(282\) | −1.88719 | −0.112381 | ||||||||
\(283\) | −12.1394 | −0.721615 | −0.360808 | − | 0.932640i | \(-0.617499\pi\) | ||||
−0.360808 | + | 0.932640i | \(0.617499\pi\) | |||||||
\(284\) | −1.31208 | −0.0778575 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −4.61258 | −0.272747 | ||||||||
\(287\) | 11.7662 | 0.694537 | ||||||||
\(288\) | −7.18586 | −0.423431 | ||||||||
\(289\) | 14.7242 | 0.866131 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −1.88445 | −0.110468 | ||||||||
\(292\) | −7.38115 | −0.431949 | ||||||||
\(293\) | −4.03918 | −0.235971 | −0.117986 | − | 0.993015i | \(-0.537644\pi\) | ||||
−0.117986 | + | 0.993015i | \(0.537644\pi\) | |||||||
\(294\) | −9.25224 | −0.539602 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −4.69813 | −0.273073 | ||||||||
\(297\) | 0.859846 | 0.0498933 | ||||||||
\(298\) | 31.5625 | 1.82837 | ||||||||
\(299\) | −0.540365 | −0.0312501 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −7.11123 | −0.409885 | ||||||||
\(302\) | 30.3679 | 1.74747 | ||||||||
\(303\) | −3.61387 | −0.207612 | ||||||||
\(304\) | 30.9101 | 1.77282 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −10.6295 | −0.607646 | ||||||||
\(307\) | 15.3270 | 0.874756 | 0.437378 | − | 0.899278i | \(-0.355907\pi\) | ||||
0.437378 | + | 0.899278i | \(0.355907\pi\) | |||||||
\(308\) | −1.94444 | −0.110795 | ||||||||
\(309\) | 1.46000 | 0.0830563 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −7.92368 | −0.449311 | −0.224655 | − | 0.974438i | \(-0.572126\pi\) | ||||
−0.224655 | + | 0.974438i | \(0.572126\pi\) | |||||||
\(312\) | 2.35237 | 0.133177 | ||||||||
\(313\) | 6.41853 | 0.362797 | 0.181398 | − | 0.983410i | \(-0.441938\pi\) | ||||
0.181398 | + | 0.983410i | \(0.441938\pi\) | |||||||
\(314\) | 14.8225 | 0.836484 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −20.7222 | −1.16571 | ||||||||
\(317\) | 24.5794 | 1.38052 | 0.690260 | − | 0.723562i | \(-0.257496\pi\) | ||||
0.690260 | + | 0.723562i | \(0.257496\pi\) | |||||||
\(318\) | 7.26805 | 0.407572 | ||||||||
\(319\) | −8.94031 | −0.500561 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 15.0739 | 0.841341 | ||||||||
\(322\) | −0.519553 | −0.0289536 | ||||||||
\(323\) | 37.1630 | 2.06781 | ||||||||
\(324\) | 1.56149 | 0.0867492 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 4.40431 | 0.243932 | ||||||||
\(327\) | 5.90985 | 0.326815 | ||||||||
\(328\) | 6.72357 | 0.371247 | ||||||||
\(329\) | 1.44822 | 0.0798430 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 9.57831 | 0.526472 | 0.263236 | − | 0.964732i | \(-0.415210\pi\) | ||||
0.263236 | + | 0.964732i | \(0.415210\pi\) | |||||||
\(332\) | 0.172310 | 0.00945674 | ||||||||
\(333\) | 5.67710 | 0.311103 | ||||||||
\(334\) | −18.9750 | −1.03827 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 6.78453 | 0.370127 | ||||||||
\(337\) | 25.0697 | 1.36563 | 0.682816 | − | 0.730590i | \(-0.260755\pi\) | ||||
0.682816 | + | 0.730590i | \(0.260755\pi\) | |||||||
\(338\) | −9.28486 | −0.505030 | ||||||||
\(339\) | −20.3228 | −1.10378 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 6.03877 | 0.327018 | ||||||||
\(342\) | −12.4518 | −0.673315 | ||||||||
\(343\) | 17.2377 | 0.930747 | ||||||||
\(344\) | −4.06358 | −0.219094 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −4.73449 | −0.254528 | ||||||||
\(347\) | 13.1076 | 0.703651 | 0.351825 | − | 0.936066i | \(-0.385561\pi\) | ||||
0.351825 | + | 0.936066i | \(0.385561\pi\) | |||||||
\(348\) | −16.2357 | −0.870324 | ||||||||
\(349\) | 5.51525 | 0.295225 | 0.147612 | − | 0.989045i | \(-0.452841\pi\) | ||||
0.147612 | + | 0.989045i | \(0.452841\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −2.84255 | −0.151724 | ||||||||
\(352\) | −6.17873 | −0.329328 | ||||||||
\(353\) | −2.08998 | −0.111238 | −0.0556191 | − | 0.998452i | \(-0.517713\pi\) | ||||
−0.0556191 | + | 0.998452i | \(0.517713\pi\) | |||||||
\(354\) | 28.5092 | 1.51524 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 22.7864 | 1.20768 | ||||||||
\(357\) | 8.15700 | 0.431714 | ||||||||
\(358\) | −28.9651 | −1.53085 | ||||||||
\(359\) | 13.2830 | 0.701048 | 0.350524 | − | 0.936554i | \(-0.386004\pi\) | ||||
0.350524 | + | 0.936554i | \(0.386004\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 24.5343 | 1.29128 | ||||||||
\(362\) | −32.2462 | −1.69482 | ||||||||
\(363\) | −10.2607 | −0.538545 | ||||||||
\(364\) | 6.42807 | 0.336922 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −19.2142 | −1.00434 | ||||||||
\(367\) | −0.628588 | −0.0328120 | −0.0164060 | − | 0.999865i | \(-0.505222\pi\) | ||||
−0.0164060 | + | 0.999865i | \(0.505222\pi\) | |||||||
\(368\) | −0.890563 | −0.0464238 | ||||||||
\(369\) | −8.12459 | −0.422949 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −5.57747 | −0.289568 | ||||||||
\(372\) | 10.9665 | 0.568584 | ||||||||
\(373\) | −2.38412 | −0.123445 | −0.0617225 | − | 0.998093i | \(-0.519659\pi\) | ||||
−0.0617225 | + | 0.998093i | \(0.519659\pi\) | |||||||
\(374\) | −9.13969 | −0.472602 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0.827559 | 0.0426781 | ||||||||
\(377\) | 29.5556 | 1.52219 | ||||||||
\(378\) | −2.73307 | −0.140574 | ||||||||
\(379\) | −23.4179 | −1.20290 | −0.601449 | − | 0.798911i | \(-0.705410\pi\) | ||||
−0.601449 | + | 0.798911i | \(0.705410\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 4.27301 | 0.218913 | ||||||||
\(382\) | 4.88878 | 0.250132 | ||||||||
\(383\) | 27.1633 | 1.38798 | 0.693989 | − | 0.719986i | \(-0.255852\pi\) | ||||
0.693989 | + | 0.719986i | \(0.255852\pi\) | |||||||
\(384\) | 6.46134 | 0.329729 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 19.1912 | 0.976806 | ||||||||
\(387\) | 4.91032 | 0.249606 | ||||||||
\(388\) | −2.94254 | −0.149385 | ||||||||
\(389\) | −23.7025 | −1.20176 | −0.600882 | − | 0.799338i | \(-0.705184\pi\) | ||||
−0.600882 | + | 0.799338i | \(0.705184\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.07072 | −0.0541485 | ||||||||
\(392\) | 4.05724 | 0.204921 | ||||||||
\(393\) | −12.5152 | −0.631309 | ||||||||
\(394\) | −37.4849 | −1.88846 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 1.34264 | 0.0674701 | ||||||||
\(397\) | −3.84692 | −0.193072 | −0.0965358 | − | 0.995330i | \(-0.530776\pi\) | ||||
−0.0965358 | + | 0.995330i | \(0.530776\pi\) | |||||||
\(398\) | −8.91374 | −0.446806 | ||||||||
\(399\) | 9.55544 | 0.478370 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −16.9168 | −0.844786 | −0.422393 | − | 0.906413i | \(-0.638810\pi\) | ||||
−0.422393 | + | 0.906413i | \(0.638810\pi\) | |||||||
\(402\) | 19.1000 | 0.952620 | ||||||||
\(403\) | −19.9634 | −0.994450 | ||||||||
\(404\) | −5.64302 | −0.280750 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 28.4173 | 1.41033 | ||||||||
\(407\) | 4.88143 | 0.241964 | ||||||||
\(408\) | 4.66116 | 0.230762 | ||||||||
\(409\) | 25.8955 | 1.28045 | 0.640224 | − | 0.768188i | \(-0.278842\pi\) | ||||
0.640224 | + | 0.768188i | \(0.278842\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −7.69232 | −0.379434 | ||||||||
\(412\) | 2.27976 | 0.112316 | ||||||||
\(413\) | −21.8778 | −1.07654 | ||||||||
\(414\) | 0.358753 | 0.0176317 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 20.4261 | 1.00147 | ||||||||
\(417\) | −6.47935 | −0.317295 | ||||||||
\(418\) | −10.7066 | −0.523677 | ||||||||
\(419\) | −36.2498 | −1.77092 | −0.885460 | − | 0.464716i | \(-0.846156\pi\) | ||||
−0.885460 | + | 0.464716i | \(0.846156\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 35.1728 | 1.71422 | 0.857108 | − | 0.515137i | \(-0.172259\pi\) | ||||
0.857108 | + | 0.515137i | \(0.172259\pi\) | |||||||
\(422\) | −33.5130 | −1.63139 | ||||||||
\(423\) | −1.00000 | −0.0486217 | ||||||||
\(424\) | −3.18714 | −0.154781 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −1.58576 | −0.0768303 | ||||||||
\(427\) | 14.7449 | 0.713555 | ||||||||
\(428\) | 23.5376 | 1.13773 | ||||||||
\(429\) | −2.44415 | −0.118005 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −27.3100 | −1.31548 | −0.657739 | − | 0.753246i | \(-0.728487\pi\) | ||||
−0.657739 | + | 0.753246i | \(0.728487\pi\) | |||||||
\(432\) | −4.68473 | −0.225394 | ||||||||
\(433\) | −16.1935 | −0.778211 | −0.389105 | − | 0.921193i | \(-0.627216\pi\) | ||||
−0.389105 | + | 0.921193i | \(0.627216\pi\) | |||||||
\(434\) | −19.1946 | −0.921369 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 9.22815 | 0.441948 | ||||||||
\(437\) | −1.25428 | −0.0600005 | ||||||||
\(438\) | −8.92076 | −0.426250 | ||||||||
\(439\) | −12.2351 | −0.583948 | −0.291974 | − | 0.956426i | \(-0.594312\pi\) | ||||
−0.291974 | + | 0.956426i | \(0.594312\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −4.90265 | −0.233460 | ||||||||
\(442\) | 30.2147 | 1.43717 | ||||||||
\(443\) | −23.1034 | −1.09768 | −0.548838 | − | 0.835929i | \(-0.684930\pi\) | ||||
−0.548838 | + | 0.835929i | \(0.684930\pi\) | |||||||
\(444\) | 8.86471 | 0.420701 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −52.3847 | −2.48049 | ||||||||
\(447\) | 16.7246 | 0.791046 | ||||||||
\(448\) | 6.07040 | 0.286799 | ||||||||
\(449\) | −11.6166 | −0.548223 | −0.274112 | − | 0.961698i | \(-0.588384\pi\) | ||||
−0.274112 | + | 0.961698i | \(0.588384\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −6.98589 | −0.328953 | ||||||||
\(452\) | −31.7338 | −1.49263 | ||||||||
\(453\) | 16.0916 | 0.756048 | ||||||||
\(454\) | 37.5761 | 1.76353 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 5.46028 | 0.255701 | ||||||||
\(457\) | 2.55111 | 0.119336 | 0.0596680 | − | 0.998218i | \(-0.480996\pi\) | ||||
0.0596680 | + | 0.998218i | \(0.480996\pi\) | |||||||
\(458\) | 30.1439 | 1.40853 | ||||||||
\(459\) | −5.63243 | −0.262899 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 2.45274 | 0.114235 | 0.0571176 | − | 0.998367i | \(-0.481809\pi\) | ||||
0.0571176 | + | 0.998367i | \(0.481809\pi\) | |||||||
\(462\) | −2.35002 | −0.109333 | ||||||||
\(463\) | 36.6395 | 1.70278 | 0.851392 | − | 0.524530i | \(-0.175759\pi\) | ||||
0.851392 | + | 0.524530i | \(0.175759\pi\) | |||||||
\(464\) | 48.7099 | 2.26130 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 30.1755 | 1.39785 | ||||||||
\(467\) | −27.2894 | −1.26280 | −0.631401 | − | 0.775457i | \(-0.717520\pi\) | ||||
−0.631401 | + | 0.775457i | \(0.717520\pi\) | |||||||
\(468\) | −4.43860 | −0.205174 | ||||||||
\(469\) | −14.6572 | −0.676808 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 7.85429 | 0.361906 | ||||||||
\(472\) | −12.5017 | −0.575435 | ||||||||
\(473\) | 4.22212 | 0.194133 | ||||||||
\(474\) | −25.0445 | −1.15033 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 12.7370 | 0.583801 | ||||||||
\(477\) | 3.85125 | 0.176337 | ||||||||
\(478\) | −30.6479 | −1.40180 | ||||||||
\(479\) | −8.83826 | −0.403831 | −0.201915 | − | 0.979403i | \(-0.564717\pi\) | ||||
−0.201915 | + | 0.979403i | \(0.564717\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −16.1374 | −0.735803 | ||||||||
\(482\) | −3.26505 | −0.148719 | ||||||||
\(483\) | −0.275305 | −0.0125268 | ||||||||
\(484\) | −16.0219 | −0.728268 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 1.88719 | 0.0856047 | ||||||||
\(487\) | −3.60971 | −0.163572 | −0.0817858 | − | 0.996650i | \(-0.526062\pi\) | ||||
−0.0817858 | + | 0.996650i | \(0.526062\pi\) | |||||||
\(488\) | 8.42569 | 0.381413 | ||||||||
\(489\) | 2.33379 | 0.105538 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 28.7874 | 1.29916 | 0.649578 | − | 0.760295i | \(-0.274946\pi\) | ||||
0.649578 | + | 0.760295i | \(0.274946\pi\) | |||||||
\(492\) | −12.6864 | −0.571948 | ||||||||
\(493\) | 58.5636 | 2.63757 | ||||||||
\(494\) | 35.3947 | 1.59248 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −32.9013 | −1.47731 | ||||||||
\(497\) | 1.21690 | 0.0545856 | ||||||||
\(498\) | 0.208251 | 0.00933197 | ||||||||
\(499\) | 3.94447 | 0.176579 | 0.0882893 | − | 0.996095i | \(-0.471860\pi\) | ||||
0.0882893 | + | 0.996095i | \(0.471860\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −10.0546 | −0.449208 | ||||||||
\(502\) | −1.22730 | −0.0547769 | ||||||||
\(503\) | −16.5560 | −0.738198 | −0.369099 | − | 0.929390i | \(-0.620334\pi\) | ||||
−0.369099 | + | 0.929390i | \(0.620334\pi\) | |||||||
\(504\) | 1.19849 | 0.0533849 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0.308472 | 0.0137133 | ||||||||
\(507\) | −4.91994 | −0.218502 | ||||||||
\(508\) | 6.67225 | 0.296033 | ||||||||
\(509\) | −8.73370 | −0.387115 | −0.193557 | − | 0.981089i | \(-0.562003\pi\) | ||||
−0.193557 | + | 0.981089i | \(0.562003\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 6.84575 | 0.302838 | ||||||||
\(512\) | 25.9101 | 1.14507 | ||||||||
\(513\) | −6.59805 | −0.291311 | ||||||||
\(514\) | −58.0474 | −2.56036 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 7.66740 | 0.337539 | ||||||||
\(517\) | −0.859846 | −0.0378160 | ||||||||
\(518\) | −15.5159 | −0.681730 | ||||||||
\(519\) | −2.50875 | −0.110122 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 13.1791 | 0.577388 | 0.288694 | − | 0.957421i | \(-0.406779\pi\) | ||||
0.288694 | + | 0.957421i | \(0.406779\pi\) | |||||||
\(522\) | −19.6222 | −0.858841 | ||||||||
\(523\) | −2.57258 | −0.112491 | −0.0562454 | − | 0.998417i | \(-0.517913\pi\) | ||||
−0.0562454 | + | 0.998417i | \(0.517913\pi\) | |||||||
\(524\) | −19.5423 | −0.853711 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 22.2673 | 0.970900 | ||||||||
\(527\) | −39.5570 | −1.72313 | ||||||||
\(528\) | −4.02815 | −0.175303 | ||||||||
\(529\) | −22.9639 | −0.998429 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 15.1067 | 0.655574 | ||||||||
\(532\) | 14.9207 | 0.646894 | ||||||||
\(533\) | 23.0945 | 1.00033 | ||||||||
\(534\) | 27.5394 | 1.19174 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −8.37560 | −0.361771 | ||||||||
\(537\) | −15.3483 | −0.662327 | ||||||||
\(538\) | 20.1980 | 0.870799 | ||||||||
\(539\) | −4.21553 | −0.181576 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −20.2219 | −0.869407 | −0.434704 | − | 0.900574i | \(-0.643147\pi\) | ||||
−0.434704 | + | 0.900574i | \(0.643147\pi\) | |||||||
\(542\) | −35.5747 | −1.52807 | ||||||||
\(543\) | −17.0869 | −0.733268 | ||||||||
\(544\) | 40.4738 | 1.73530 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 7.76887 | 0.332477 | ||||||||
\(547\) | −15.1716 | −0.648693 | −0.324346 | − | 0.945938i | \(-0.605144\pi\) | ||||
−0.324346 | + | 0.945938i | \(0.605144\pi\) | |||||||
\(548\) | −12.0115 | −0.513104 | ||||||||
\(549\) | −10.1814 | −0.434531 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 68.6038 | 2.92262 | ||||||||
\(552\) | −0.157318 | −0.00669590 | ||||||||
\(553\) | 19.2191 | 0.817277 | ||||||||
\(554\) | 38.9005 | 1.65272 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −10.1174 | −0.429074 | ||||||||
\(557\) | −11.8437 | −0.501835 | −0.250918 | − | 0.968008i | \(-0.580732\pi\) | ||||
−0.250918 | + | 0.968008i | \(0.580732\pi\) | |||||||
\(558\) | 13.2539 | 0.561082 | ||||||||
\(559\) | −13.9578 | −0.590353 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −4.84302 | −0.204472 | ||||||||
\(562\) | −21.2635 | −0.896945 | ||||||||
\(563\) | −16.0440 | −0.676174 | −0.338087 | − | 0.941115i | \(-0.609780\pi\) | ||||
−0.338087 | + | 0.941115i | \(0.609780\pi\) | |||||||
\(564\) | −1.56149 | −0.0657504 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −22.9094 | −0.962956 | ||||||||
\(567\) | −1.44822 | −0.0608196 | ||||||||
\(568\) | 0.695377 | 0.0291774 | ||||||||
\(569\) | 25.6910 | 1.07702 | 0.538511 | − | 0.842619i | \(-0.318987\pi\) | ||||
0.538511 | + | 0.842619i | \(0.318987\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −10.8543 | −0.454239 | −0.227119 | − | 0.973867i | \(-0.572931\pi\) | ||||
−0.227119 | + | 0.973867i | \(0.572931\pi\) | |||||||
\(572\) | −3.81651 | −0.159576 | ||||||||
\(573\) | 2.59051 | 0.108220 | ||||||||
\(574\) | 22.2051 | 0.926821 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −4.19162 | −0.174651 | ||||||||
\(577\) | −10.2698 | −0.427536 | −0.213768 | − | 0.976884i | \(-0.568574\pi\) | ||||
−0.213768 | + | 0.976884i | \(0.568574\pi\) | |||||||
\(578\) | 27.7874 | 1.15580 | ||||||||
\(579\) | 10.1692 | 0.422617 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −0.159811 | −0.00663009 | ||||||||
\(582\) | −3.55632 | −0.147414 | ||||||||
\(583\) | 3.31148 | 0.137148 | ||||||||
\(584\) | 3.91187 | 0.161875 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −7.62270 | −0.314891 | ||||||||
\(587\) | 6.33798 | 0.261596 | 0.130798 | − | 0.991409i | \(-0.458246\pi\) | ||||
0.130798 | + | 0.991409i | \(0.458246\pi\) | |||||||
\(588\) | −7.65543 | −0.315705 | ||||||||
\(589\) | −46.3387 | −1.90935 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −19.8628 | −0.817048 | ||||||||
\(592\) | −26.5957 | −1.09308 | ||||||||
\(593\) | 22.6796 | 0.931339 | 0.465669 | − | 0.884959i | \(-0.345814\pi\) | ||||
0.465669 | + | 0.884959i | \(0.345814\pi\) | |||||||
\(594\) | 1.62269 | 0.0665799 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 26.1152 | 1.06972 | ||||||||
\(597\) | −4.72329 | −0.193311 | ||||||||
\(598\) | −1.01977 | −0.0417015 | ||||||||
\(599\) | 6.52930 | 0.266780 | 0.133390 | − | 0.991064i | \(-0.457414\pi\) | ||||
0.133390 | + | 0.991064i | \(0.457414\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 9.56925 | 0.390338 | 0.195169 | − | 0.980770i | \(-0.437474\pi\) | ||||
0.195169 | + | 0.980770i | \(0.437474\pi\) | |||||||
\(602\) | −13.4203 | −0.546969 | ||||||||
\(603\) | 10.1209 | 0.412153 | ||||||||
\(604\) | 25.1268 | 1.02239 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −6.82007 | −0.277046 | ||||||||
\(607\) | 40.9145 | 1.66067 | 0.830334 | − | 0.557266i | \(-0.188150\pi\) | ||||
0.830334 | + | 0.557266i | \(0.188150\pi\) | |||||||
\(608\) | 47.4127 | 1.92284 | ||||||||
\(609\) | 15.0580 | 0.610181 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 2.84255 | 0.114997 | ||||||||
\(612\) | −8.79496 | −0.355515 | ||||||||
\(613\) | 25.6984 | 1.03795 | 0.518973 | − | 0.854790i | \(-0.326314\pi\) | ||||
0.518973 | + | 0.854790i | \(0.326314\pi\) | |||||||
\(614\) | 28.9249 | 1.16731 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 1.03052 | 0.0415206 | ||||||||
\(617\) | −20.1936 | −0.812963 | −0.406481 | − | 0.913659i | \(-0.633244\pi\) | ||||
−0.406481 | + | 0.913659i | \(0.633244\pi\) | |||||||
\(618\) | 2.75529 | 0.110834 | ||||||||
\(619\) | −20.4156 | −0.820572 | −0.410286 | − | 0.911957i | \(-0.634571\pi\) | ||||
−0.410286 | + | 0.911957i | \(0.634571\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0.190099 | 0.00762841 | ||||||||
\(622\) | −14.9535 | −0.599580 | ||||||||
\(623\) | −21.1336 | −0.846699 | ||||||||
\(624\) | 13.3166 | 0.533089 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 12.1130 | 0.484132 | ||||||||
\(627\) | −5.67331 | −0.226570 | ||||||||
\(628\) | 12.2644 | 0.489401 | ||||||||
\(629\) | −31.9758 | −1.27496 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −22.2092 | −0.884135 | −0.442067 | − | 0.896982i | \(-0.645755\pi\) | ||||
−0.442067 | + | 0.896982i | \(0.645755\pi\) | |||||||
\(632\) | 10.9824 | 0.436855 | ||||||||
\(633\) | −17.7581 | −0.705823 | ||||||||
\(634\) | 46.3861 | 1.84223 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 6.01368 | 0.238458 | ||||||||
\(637\) | 13.9360 | 0.552165 | ||||||||
\(638\) | −16.8721 | −0.667972 | ||||||||
\(639\) | −0.840275 | −0.0332408 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 21.0709 | 0.832249 | 0.416124 | − | 0.909308i | \(-0.363388\pi\) | ||||
0.416124 | + | 0.909308i | \(0.363388\pi\) | |||||||
\(642\) | 28.4472 | 1.12272 | ||||||||
\(643\) | 25.6183 | 1.01029 | 0.505144 | − | 0.863035i | \(-0.331439\pi\) | ||||
0.505144 | + | 0.863035i | \(0.331439\pi\) | |||||||
\(644\) | −0.429885 | −0.0169399 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 70.1337 | 2.75937 | ||||||||
\(647\) | 37.3646 | 1.46896 | 0.734478 | − | 0.678633i | \(-0.237427\pi\) | ||||
0.734478 | + | 0.678633i | \(0.237427\pi\) | |||||||
\(648\) | −0.827559 | −0.0325096 | ||||||||
\(649\) | 12.9894 | 0.509879 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −10.1710 | −0.398632 | ||||||||
\(652\) | 3.64418 | 0.142717 | ||||||||
\(653\) | −42.1304 | −1.64869 | −0.824344 | − | 0.566089i | \(-0.808456\pi\) | ||||
−0.824344 | + | 0.566089i | \(0.808456\pi\) | |||||||
\(654\) | 11.1530 | 0.436117 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 38.0615 | 1.48605 | ||||||||
\(657\) | −4.72701 | −0.184418 | ||||||||
\(658\) | 2.73307 | 0.106546 | ||||||||
\(659\) | −37.4208 | −1.45771 | −0.728853 | − | 0.684670i | \(-0.759946\pi\) | ||||
−0.728853 | + | 0.684670i | \(0.759946\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 3.81349 | 0.148328 | 0.0741639 | − | 0.997246i | \(-0.476371\pi\) | ||||
0.0741639 | + | 0.997246i | \(0.476371\pi\) | |||||||
\(662\) | 18.0761 | 0.702547 | ||||||||
\(663\) | 16.0104 | 0.621793 | ||||||||
\(664\) | −0.0913211 | −0.00354395 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 10.7138 | 0.415150 | ||||||||
\(667\) | −1.97657 | −0.0765330 | ||||||||
\(668\) | −15.7002 | −0.607458 | ||||||||
\(669\) | −27.7580 | −1.07319 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −8.75441 | −0.337960 | ||||||||
\(672\) | 10.4067 | 0.401448 | ||||||||
\(673\) | −16.5907 | −0.639524 | −0.319762 | − | 0.947498i | \(-0.603603\pi\) | ||||
−0.319762 | + | 0.947498i | \(0.603603\pi\) | |||||||
\(674\) | 47.3113 | 1.82236 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −7.68241 | −0.295477 | ||||||||
\(677\) | −44.5604 | −1.71260 | −0.856298 | − | 0.516482i | \(-0.827241\pi\) | ||||
−0.856298 | + | 0.516482i | \(0.827241\pi\) | |||||||
\(678\) | −38.3530 | −1.47294 | ||||||||
\(679\) | 2.72910 | 0.104733 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 19.9112 | 0.762997 | ||||||||
\(682\) | 11.3963 | 0.436387 | ||||||||
\(683\) | −7.32263 | −0.280193 | −0.140096 | − | 0.990138i | \(-0.544741\pi\) | ||||
−0.140096 | + | 0.990138i | \(0.544741\pi\) | |||||||
\(684\) | −10.3028 | −0.393936 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 32.5308 | 1.24203 | ||||||||
\(687\) | 15.9729 | 0.609404 | ||||||||
\(688\) | −23.0036 | −0.877002 | ||||||||
\(689\) | −10.9474 | −0.417061 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 33.4388 | 1.27207 | 0.636037 | − | 0.771659i | \(-0.280573\pi\) | ||||
0.636037 | + | 0.771659i | \(0.280573\pi\) | |||||||
\(692\) | −3.91738 | −0.148916 | ||||||||
\(693\) | −1.24525 | −0.0473030 | ||||||||
\(694\) | 24.7365 | 0.938983 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 8.60461 | 0.326157 | ||||||||
\(697\) | 45.7611 | 1.73333 | ||||||||
\(698\) | 10.4083 | 0.393961 | ||||||||
\(699\) | 15.9896 | 0.604783 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −48.6669 | −1.83812 | −0.919062 | − | 0.394113i | \(-0.871052\pi\) | ||||
−0.919062 | + | 0.394113i | \(0.871052\pi\) | |||||||
\(702\) | −5.36442 | −0.202467 | ||||||||
\(703\) | −37.4578 | −1.41275 | ||||||||
\(704\) | −3.60415 | −0.135837 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −3.94418 | −0.148441 | ||||||||
\(707\) | 5.23369 | 0.196833 | ||||||||
\(708\) | 23.5889 | 0.886524 | ||||||||
\(709\) | 22.6001 | 0.848765 | 0.424382 | − | 0.905483i | \(-0.360491\pi\) | ||||
0.424382 | + | 0.905483i | \(0.360491\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −13.2708 | −0.497694 | ||||||||
\(712\) | −12.0764 | −0.452582 | ||||||||
\(713\) | 1.33508 | 0.0499992 | ||||||||
\(714\) | 15.3938 | 0.576099 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −23.9661 | −0.895656 | ||||||||
\(717\) | −16.2400 | −0.606493 | ||||||||
\(718\) | 25.0675 | 0.935510 | ||||||||
\(719\) | 0.480330 | 0.0179133 | 0.00895665 | − | 0.999960i | \(-0.497149\pi\) | ||||
0.00895665 | + | 0.999960i | \(0.497149\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −2.11440 | −0.0787443 | ||||||||
\(722\) | 46.3009 | 1.72314 | ||||||||
\(723\) | −1.73011 | −0.0643435 | ||||||||
\(724\) | −26.6809 | −0.991588 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −19.3638 | −0.718659 | ||||||||
\(727\) | −14.6427 | −0.543067 | −0.271533 | − | 0.962429i | \(-0.587531\pi\) | ||||
−0.271533 | + | 0.962429i | \(0.587531\pi\) | |||||||
\(728\) | −3.40676 | −0.126263 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −27.6570 | −1.02293 | ||||||||
\(732\) | −15.8981 | −0.587610 | ||||||||
\(733\) | −40.2801 | −1.48778 | −0.743890 | − | 0.668302i | \(-0.767021\pi\) | ||||
−0.743890 | + | 0.668302i | \(0.767021\pi\) | |||||||
\(734\) | −1.18627 | −0.0437859 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −1.36602 | −0.0503523 | ||||||||
\(737\) | 8.70237 | 0.320556 | ||||||||
\(738\) | −15.3326 | −0.564402 | ||||||||
\(739\) | 7.24682 | 0.266579 | 0.133289 | − | 0.991077i | \(-0.457446\pi\) | ||||
0.133289 | + | 0.991077i | \(0.457446\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 18.7553 | 0.688992 | ||||||||
\(742\) | −10.5257 | −0.386412 | ||||||||
\(743\) | −21.4774 | −0.787930 | −0.393965 | − | 0.919126i | \(-0.628897\pi\) | ||||
−0.393965 | + | 0.919126i | \(0.628897\pi\) | |||||||
\(744\) | −5.81202 | −0.213079 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −4.49928 | −0.164730 | ||||||||
\(747\) | 0.110350 | 0.00403750 | ||||||||
\(748\) | −7.56230 | −0.276505 | ||||||||
\(749\) | −21.8303 | −0.797661 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −4.27938 | −0.156157 | −0.0780783 | − | 0.996947i | \(-0.524878\pi\) | ||||
−0.0780783 | + | 0.996947i | \(0.524878\pi\) | |||||||
\(752\) | 4.68473 | 0.170835 | ||||||||
\(753\) | −0.650330 | −0.0236993 | ||||||||
\(754\) | 55.7770 | 2.03128 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −2.26138 | −0.0822455 | ||||||||
\(757\) | 30.3315 | 1.10242 | 0.551209 | − | 0.834367i | \(-0.314167\pi\) | ||||
0.551209 | + | 0.834367i | \(0.314167\pi\) | |||||||
\(758\) | −44.1941 | −1.60520 | ||||||||
\(759\) | 0.163456 | 0.00593307 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −24.5189 | −0.888809 | −0.444405 | − | 0.895826i | \(-0.646585\pi\) | ||||
−0.444405 | + | 0.895826i | \(0.646585\pi\) | |||||||
\(762\) | 8.06399 | 0.292128 | ||||||||
\(763\) | −8.55877 | −0.309848 | ||||||||
\(764\) | 4.04504 | 0.146345 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 51.2622 | 1.85218 | ||||||||
\(767\) | −42.9414 | −1.55052 | ||||||||
\(768\) | 20.5770 | 0.742509 | ||||||||
\(769\) | 38.6946 | 1.39536 | 0.697682 | − | 0.716408i | \(-0.254215\pi\) | ||||
0.697682 | + | 0.716408i | \(0.254215\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −30.7586 | −1.10775 | ||||||||
\(772\) | 15.8791 | 0.571500 | ||||||||
\(773\) | 17.7072 | 0.636882 | 0.318441 | − | 0.947943i | \(-0.396841\pi\) | ||||
0.318441 | + | 0.947943i | \(0.396841\pi\) | |||||||
\(774\) | 9.26671 | 0.333085 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 1.55949 | 0.0559826 | ||||||||
\(777\) | −8.22170 | −0.294952 | ||||||||
\(778\) | −44.7311 | −1.60369 | ||||||||
\(779\) | 53.6064 | 1.92065 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −0.722507 | −0.0258533 | ||||||||
\(782\) | −2.02065 | −0.0722582 | ||||||||
\(783\) | −10.3976 | −0.371579 | ||||||||
\(784\) | 22.9676 | 0.820272 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −23.6186 | −0.842447 | ||||||||
\(787\) | −40.2262 | −1.43391 | −0.716954 | − | 0.697121i | \(-0.754464\pi\) | ||||
−0.716954 | + | 0.697121i | \(0.754464\pi\) | |||||||
\(788\) | −31.0155 | −1.10488 | ||||||||
\(789\) | 11.7992 | 0.420062 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 29.4319 | 1.04648 | ||||||||
\(792\) | −0.711573 | −0.0252846 | ||||||||
\(793\) | 28.9410 | 1.02773 | ||||||||
\(794\) | −7.25988 | −0.257643 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −7.37535 | −0.261412 | ||||||||
\(797\) | −2.98055 | −0.105576 | −0.0527882 | − | 0.998606i | \(-0.516811\pi\) | ||||
−0.0527882 | + | 0.998606i | \(0.516811\pi\) | |||||||
\(798\) | 18.0329 | 0.638359 | ||||||||
\(799\) | 5.63243 | 0.199261 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 14.5928 | 0.515611 | ||||||||
\(802\) | −31.9253 | −1.12732 | ||||||||
\(803\) | −4.06450 | −0.143433 | ||||||||
\(804\) | 15.8036 | 0.557349 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −37.6748 | −1.32704 | ||||||||
\(807\) | 10.7027 | 0.376753 | ||||||||
\(808\) | 2.99069 | 0.105212 | ||||||||
\(809\) | −26.4486 | −0.929883 | −0.464941 | − | 0.885342i | \(-0.653925\pi\) | ||||
−0.464941 | + | 0.885342i | \(0.653925\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 22.0553 | 0.774466 | 0.387233 | − | 0.921982i | \(-0.373431\pi\) | ||||
0.387233 | + | 0.921982i | \(0.373431\pi\) | |||||||
\(812\) | 23.5129 | 0.825139 | ||||||||
\(813\) | −18.8506 | −0.661121 | ||||||||
\(814\) | 9.21219 | 0.322887 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 26.3864 | 0.923709 | ||||||||
\(817\) | −32.3986 | −1.13348 | ||||||||
\(818\) | 48.8696 | 1.70869 | ||||||||
\(819\) | 4.11663 | 0.143847 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −20.8576 | −0.727936 | −0.363968 | − | 0.931411i | \(-0.618578\pi\) | ||||
−0.363968 | + | 0.931411i | \(0.618578\pi\) | |||||||
\(822\) | −14.5169 | −0.506334 | ||||||||
\(823\) | 46.5050 | 1.62106 | 0.810532 | − | 0.585695i | \(-0.199178\pi\) | ||||
0.810532 | + | 0.585695i | \(0.199178\pi\) | |||||||
\(824\) | −1.20823 | −0.0420908 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −41.2876 | −1.43658 | ||||||||
\(827\) | 10.7596 | 0.374147 | 0.187073 | − | 0.982346i | \(-0.440100\pi\) | ||||
0.187073 | + | 0.982346i | \(0.440100\pi\) | |||||||
\(828\) | 0.296837 | 0.0103158 | ||||||||
\(829\) | −11.8086 | −0.410128 | −0.205064 | − | 0.978749i | \(-0.565740\pi\) | ||||
−0.205064 | + | 0.978749i | \(0.565740\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 20.6129 | 0.715054 | ||||||||
\(832\) | 11.9149 | 0.413074 | ||||||||
\(833\) | 27.6138 | 0.956763 | ||||||||
\(834\) | −12.2278 | −0.423413 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −8.85879 | −0.306388 | ||||||||
\(837\) | 7.02308 | 0.242753 | ||||||||
\(838\) | −68.4103 | −2.36319 | ||||||||
\(839\) | −1.61587 | −0.0557859 | −0.0278930 | − | 0.999611i | \(-0.508880\pi\) | ||||
−0.0278930 | + | 0.999611i | \(0.508880\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 79.1097 | 2.72792 | ||||||||
\(842\) | 66.3777 | 2.28753 | ||||||||
\(843\) | −11.2673 | −0.388065 | ||||||||
\(844\) | −27.7291 | −0.954475 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −1.88719 | −0.0648829 | ||||||||
\(847\) | 14.8597 | 0.510586 | ||||||||
\(848\) | −18.0421 | −0.619568 | ||||||||
\(849\) | −12.1394 | −0.416625 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1.07921 | 0.0369949 | ||||||||
\(852\) | −1.31208 | −0.0449510 | ||||||||
\(853\) | 41.0468 | 1.40542 | 0.702708 | − | 0.711478i | \(-0.251974\pi\) | ||||
0.702708 | + | 0.711478i | \(0.251974\pi\) | |||||||
\(854\) | 27.8264 | 0.952200 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −12.4745 | −0.426370 | ||||||||
\(857\) | 10.9047 | 0.372499 | 0.186249 | − | 0.982503i | \(-0.440367\pi\) | ||||
0.186249 | + | 0.982503i | \(0.440367\pi\) | |||||||
\(858\) | −4.61258 | −0.157471 | ||||||||
\(859\) | 4.70526 | 0.160541 | 0.0802707 | − | 0.996773i | \(-0.474422\pi\) | ||||
0.0802707 | + | 0.996773i | \(0.474422\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 11.7662 | 0.400991 | ||||||||
\(862\) | −51.5392 | −1.75543 | ||||||||
\(863\) | −29.9360 | −1.01903 | −0.509517 | − | 0.860461i | \(-0.670176\pi\) | ||||
−0.509517 | + | 0.860461i | \(0.670176\pi\) | |||||||
\(864\) | −7.18586 | −0.244468 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −30.5602 | −1.03848 | ||||||||
\(867\) | 14.7242 | 0.500061 | ||||||||
\(868\) | −15.8818 | −0.539065 | ||||||||
\(869\) | −11.4108 | −0.387086 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −28.7690 | −0.974800 | ||||||||
\(872\) | −4.89075 | −0.165622 | ||||||||
\(873\) | −1.88445 | −0.0637790 | ||||||||
\(874\) | −2.36707 | −0.0800673 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −7.38115 | −0.249386 | ||||||||
\(877\) | −31.0724 | −1.04924 | −0.524620 | − | 0.851336i | \(-0.675793\pi\) | ||||
−0.524620 | + | 0.851336i | \(0.675793\pi\) | |||||||
\(878\) | −23.0899 | −0.779246 | ||||||||
\(879\) | −4.03918 | −0.136238 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −4.98410 | −0.167919 | −0.0839593 | − | 0.996469i | \(-0.526757\pi\) | ||||
−0.0839593 | + | 0.996469i | \(0.526757\pi\) | |||||||
\(882\) | −9.25224 | −0.311539 | ||||||||
\(883\) | −40.1396 | −1.35080 | −0.675402 | − | 0.737450i | \(-0.736030\pi\) | ||||
−0.675402 | + | 0.737450i | \(0.736030\pi\) | |||||||
\(884\) | 25.0001 | 0.840843 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −43.6005 | −1.46479 | ||||||||
\(887\) | −17.2649 | −0.579698 | −0.289849 | − | 0.957072i | \(-0.593605\pi\) | ||||
−0.289849 | + | 0.957072i | \(0.593605\pi\) | |||||||
\(888\) | −4.69813 | −0.157659 | ||||||||
\(889\) | −6.18827 | −0.207548 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0.859846 | 0.0288059 | ||||||||
\(892\) | −43.3438 | −1.45126 | ||||||||
\(893\) | 6.59805 | 0.220795 | ||||||||
\(894\) | 31.5625 | 1.05561 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −9.35744 | −0.312610 | ||||||||
\(897\) | −0.540365 | −0.0180423 | ||||||||
\(898\) | −21.9228 | −0.731574 | ||||||||
\(899\) | −73.0231 | −2.43546 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −21.6919 | −0.722662 | ||||||||
\(902\) | −13.1837 | −0.438969 | ||||||||
\(903\) | −7.11123 | −0.236647 | ||||||||
\(904\) | 16.8183 | 0.559369 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 30.3679 | 1.00890 | ||||||||
\(907\) | −19.9543 | −0.662571 | −0.331286 | − | 0.943531i | \(-0.607482\pi\) | ||||
−0.331286 | + | 0.943531i | \(0.607482\pi\) | |||||||
\(908\) | 31.0910 | 1.03179 | ||||||||
\(909\) | −3.61387 | −0.119865 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −51.6225 | −1.71033 | −0.855164 | − | 0.518357i | \(-0.826544\pi\) | ||||
−0.855164 | + | 0.518357i | \(0.826544\pi\) | |||||||
\(912\) | 30.9101 | 1.02354 | ||||||||
\(913\) | 0.0948840 | 0.00314020 | ||||||||
\(914\) | 4.81443 | 0.159247 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 24.9415 | 0.824089 | ||||||||
\(917\) | 18.1248 | 0.598534 | ||||||||
\(918\) | −10.6295 | −0.350824 | ||||||||
\(919\) | 51.2100 | 1.68926 | 0.844630 | − | 0.535350i | \(-0.179820\pi\) | ||||
0.844630 | + | 0.535350i | \(0.179820\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 15.3270 | 0.505041 | ||||||||
\(922\) | 4.62878 | 0.152441 | ||||||||
\(923\) | 2.38852 | 0.0786191 | ||||||||
\(924\) | −1.94444 | −0.0639672 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 69.1458 | 2.27227 | ||||||||
\(927\) | 1.46000 | 0.0479526 | ||||||||
\(928\) | 74.7156 | 2.45266 | ||||||||
\(929\) | 8.78390 | 0.288190 | 0.144095 | − | 0.989564i | \(-0.453973\pi\) | ||||
0.144095 | + | 0.989564i | \(0.453973\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 32.3480 | 1.06016 | ||||||||
\(932\) | 24.9676 | 0.817841 | ||||||||
\(933\) | −7.92368 | −0.259410 | ||||||||
\(934\) | −51.5002 | −1.68514 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 2.35237 | 0.0768897 | ||||||||
\(937\) | 5.50915 | 0.179976 | 0.0899881 | − | 0.995943i | \(-0.471317\pi\) | ||||
0.0899881 | + | 0.995943i | \(0.471317\pi\) | |||||||
\(938\) | −27.6610 | −0.903164 | ||||||||
\(939\) | 6.41853 | 0.209461 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 31.9819 | 1.04258 | 0.521290 | − | 0.853379i | \(-0.325451\pi\) | ||||
0.521290 | + | 0.853379i | \(0.325451\pi\) | |||||||
\(942\) | 14.8225 | 0.482944 | ||||||||
\(943\) | −1.54448 | −0.0502950 | ||||||||
\(944\) | −70.7707 | −2.30339 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 7.96794 | 0.259060 | ||||||||
\(947\) | 14.9787 | 0.486742 | 0.243371 | − | 0.969933i | \(-0.421747\pi\) | ||||
0.243371 | + | 0.969933i | \(0.421747\pi\) | |||||||
\(948\) | −20.7222 | −0.673025 | ||||||||
\(949\) | 13.4367 | 0.436175 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 24.5794 | 0.797043 | ||||||||
\(952\) | −6.75040 | −0.218782 | ||||||||
\(953\) | −25.8993 | −0.838961 | −0.419481 | − | 0.907764i | \(-0.637788\pi\) | ||||
−0.419481 | + | 0.907764i | \(0.637788\pi\) | |||||||
\(954\) | 7.26805 | 0.235312 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −25.3585 | −0.820153 | ||||||||
\(957\) | −8.94031 | −0.288999 | ||||||||
\(958\) | −16.6795 | −0.538890 | ||||||||
\(959\) | 11.1402 | 0.359735 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 18.3237 | 0.591088 | ||||||||
\(962\) | −30.4544 | −0.981888 | ||||||||
\(963\) | 15.0739 | 0.485748 | ||||||||
\(964\) | −2.70154 | −0.0870109 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −0.519553 | −0.0167164 | ||||||||
\(967\) | −14.3077 | −0.460105 | −0.230053 | − | 0.973178i | \(-0.573890\pi\) | ||||
−0.230053 | + | 0.973178i | \(0.573890\pi\) | |||||||
\(968\) | 8.49130 | 0.272921 | ||||||||
\(969\) | 37.1630 | 1.19385 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 6.01930 | 0.193168 | 0.0965842 | − | 0.995325i | \(-0.469208\pi\) | ||||
0.0965842 | + | 0.995325i | \(0.469208\pi\) | |||||||
\(972\) | 1.56149 | 0.0500847 | ||||||||
\(973\) | 9.38353 | 0.300822 | ||||||||
\(974\) | −6.81221 | −0.218277 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 47.6970 | 1.52674 | ||||||||
\(977\) | 3.45052 | 0.110392 | 0.0551959 | − | 0.998476i | \(-0.482422\pi\) | ||||
0.0551959 | + | 0.998476i | \(0.482422\pi\) | |||||||
\(978\) | 4.40431 | 0.140834 | ||||||||
\(979\) | 12.5475 | 0.401021 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 5.90985 | 0.188687 | ||||||||
\(982\) | 54.3272 | 1.73365 | ||||||||
\(983\) | 20.5372 | 0.655034 | 0.327517 | − | 0.944845i | \(-0.393788\pi\) | ||||
0.327517 | + | 0.944845i | \(0.393788\pi\) | |||||||
\(984\) | 6.72357 | 0.214340 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 110.521 | 3.51969 | ||||||||
\(987\) | 1.44822 | 0.0460974 | ||||||||
\(988\) | 29.2861 | 0.931714 | ||||||||
\(989\) | 0.933447 | 0.0296819 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 17.3370 | 0.550726 | 0.275363 | − | 0.961340i | \(-0.411202\pi\) | ||||
0.275363 | + | 0.961340i | \(0.411202\pi\) | |||||||
\(992\) | −50.4669 | −1.60233 | ||||||||
\(993\) | 9.57831 | 0.303958 | ||||||||
\(994\) | 2.29653 | 0.0728415 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0.172310 | 0.00545985 | ||||||||
\(997\) | −60.2724 | −1.90884 | −0.954422 | − | 0.298459i | \(-0.903527\pi\) | ||||
−0.954422 | + | 0.298459i | \(0.903527\pi\) | |||||||
\(998\) | 7.44396 | 0.235634 | ||||||||
\(999\) | 5.67710 | 0.179615 |
(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 | 3525.2.a.bf.1.9 | 10 | ||
5.2 | odd | 4 | 705.2.c.b.424.17 | yes | 20 | ||
5.3 | odd | 4 | 705.2.c.b.424.4 | ✓ | 20 | ||
5.4 | even | 2 | 3525.2.a.bg.1.2 | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
705.2.c.b.424.4 | ✓ | 20 | 5.3 | odd | 4 | ||
705.2.c.b.424.17 | yes | 20 | 5.2 | odd | 4 | ||
3525.2.a.bf.1.9 | 10 | 1.1 | even | 1 | trivial | ||
3525.2.a.bg.1.2 | 10 | 5.4 | even | 2 |