Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [169,2,Mod(1,169)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(169, 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("169.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 169 = 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 169.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: | \(1.34947179416\) |
Analytic rank: | \(1\) |
Dimension: | \(3\) |
Coefficient field: | \(\Q(\zeta_{14})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 2x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(1.80194\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 169.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.24698 | −1.58885 | −0.794427 | − | 0.607359i | \(-0.792229\pi\) | ||||
−0.794427 | + | 0.607359i | \(0.792229\pi\) | |||||||
\(3\) | −0.554958 | −0.320405 | −0.160203 | − | 0.987084i | \(-0.551215\pi\) | ||||
−0.160203 | + | 0.987084i | \(0.551215\pi\) | |||||||
\(4\) | 3.04892 | 1.52446 | ||||||||
\(5\) | −1.44504 | −0.646242 | −0.323121 | − | 0.946358i | \(-0.604732\pi\) | ||||
−0.323121 | + | 0.946358i | \(0.604732\pi\) | |||||||
\(6\) | 1.24698 | 0.509077 | ||||||||
\(7\) | 2.04892 | 0.774418 | 0.387209 | − | 0.921992i | \(-0.373439\pi\) | ||||
0.387209 | + | 0.921992i | \(0.373439\pi\) | |||||||
\(8\) | −2.35690 | −0.833289 | ||||||||
\(9\) | −2.69202 | −0.897340 | ||||||||
\(10\) | 3.24698 | 1.02679 | ||||||||
\(11\) | −2.55496 | −0.770349 | −0.385174 | − | 0.922844i | \(-0.625859\pi\) | ||||
−0.385174 | + | 0.922844i | \(0.625859\pi\) | |||||||
\(12\) | −1.69202 | −0.488445 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | −4.60388 | −1.23044 | ||||||||
\(15\) | 0.801938 | 0.207059 | ||||||||
\(16\) | −0.801938 | −0.200484 | ||||||||
\(17\) | −5.29590 | −1.28444 | −0.642222 | − | 0.766519i | \(-0.721987\pi\) | ||||
−0.642222 | + | 0.766519i | \(0.721987\pi\) | |||||||
\(18\) | 6.04892 | 1.42574 | ||||||||
\(19\) | −5.85086 | −1.34228 | −0.671139 | − | 0.741331i | \(-0.734195\pi\) | ||||
−0.671139 | + | 0.741331i | \(0.734195\pi\) | |||||||
\(20\) | −4.40581 | −0.985170 | ||||||||
\(21\) | −1.13706 | −0.248128 | ||||||||
\(22\) | 5.74094 | 1.22397 | ||||||||
\(23\) | −1.89008 | −0.394110 | −0.197055 | − | 0.980392i | \(-0.563138\pi\) | ||||
−0.197055 | + | 0.980392i | \(0.563138\pi\) | |||||||
\(24\) | 1.30798 | 0.266990 | ||||||||
\(25\) | −2.91185 | −0.582371 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 3.15883 | 0.607918 | ||||||||
\(28\) | 6.24698 | 1.18057 | ||||||||
\(29\) | 2.26875 | 0.421296 | 0.210648 | − | 0.977562i | \(-0.432443\pi\) | ||||
0.210648 | + | 0.977562i | \(0.432443\pi\) | |||||||
\(30\) | −1.80194 | −0.328987 | ||||||||
\(31\) | −4.26875 | −0.766690 | −0.383345 | − | 0.923605i | \(-0.625228\pi\) | ||||
−0.383345 | + | 0.923605i | \(0.625228\pi\) | |||||||
\(32\) | 6.51573 | 1.15183 | ||||||||
\(33\) | 1.41789 | 0.246824 | ||||||||
\(34\) | 11.8998 | 2.04079 | ||||||||
\(35\) | −2.96077 | −0.500462 | ||||||||
\(36\) | −8.20775 | −1.36796 | ||||||||
\(37\) | 5.35690 | 0.880668 | 0.440334 | − | 0.897834i | \(-0.354860\pi\) | ||||
0.440334 | + | 0.897834i | \(0.354860\pi\) | |||||||
\(38\) | 13.1468 | 2.13268 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 3.40581 | 0.538506 | ||||||||
\(41\) | 1.27413 | 0.198985 | 0.0994926 | − | 0.995038i | \(-0.468278\pi\) | ||||
0.0994926 | + | 0.995038i | \(0.468278\pi\) | |||||||
\(42\) | 2.55496 | 0.394239 | ||||||||
\(43\) | 6.13706 | 0.935893 | 0.467947 | − | 0.883757i | \(-0.344994\pi\) | ||||
0.467947 | + | 0.883757i | \(0.344994\pi\) | |||||||
\(44\) | −7.78986 | −1.17437 | ||||||||
\(45\) | 3.89008 | 0.579899 | ||||||||
\(46\) | 4.24698 | 0.626183 | ||||||||
\(47\) | −2.95108 | −0.430460 | −0.215230 | − | 0.976563i | \(-0.569050\pi\) | ||||
−0.215230 | + | 0.976563i | \(0.569050\pi\) | |||||||
\(48\) | 0.445042 | 0.0642363 | ||||||||
\(49\) | −2.80194 | −0.400277 | ||||||||
\(50\) | 6.54288 | 0.925302 | ||||||||
\(51\) | 2.93900 | 0.411542 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 5.52111 | 0.758382 | 0.379191 | − | 0.925318i | \(-0.376202\pi\) | ||||
0.379191 | + | 0.925318i | \(0.376202\pi\) | |||||||
\(54\) | −7.09783 | −0.965893 | ||||||||
\(55\) | 3.69202 | 0.497832 | ||||||||
\(56\) | −4.82908 | −0.645314 | ||||||||
\(57\) | 3.24698 | 0.430073 | ||||||||
\(58\) | −5.09783 | −0.669378 | ||||||||
\(59\) | −12.2078 | −1.58931 | −0.794657 | − | 0.607059i | \(-0.792349\pi\) | ||||
−0.794657 | + | 0.607059i | \(0.792349\pi\) | |||||||
\(60\) | 2.44504 | 0.315654 | ||||||||
\(61\) | 8.56465 | 1.09659 | 0.548295 | − | 0.836285i | \(-0.315277\pi\) | ||||
0.548295 | + | 0.836285i | \(0.315277\pi\) | |||||||
\(62\) | 9.59179 | 1.21816 | ||||||||
\(63\) | −5.51573 | −0.694917 | ||||||||
\(64\) | −13.0368 | −1.62960 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −3.18598 | −0.392167 | ||||||||
\(67\) | 0.576728 | 0.0704586 | 0.0352293 | − | 0.999379i | \(-0.488784\pi\) | ||||
0.0352293 | + | 0.999379i | \(0.488784\pi\) | |||||||
\(68\) | −16.1468 | −1.95808 | ||||||||
\(69\) | 1.04892 | 0.126275 | ||||||||
\(70\) | 6.65279 | 0.795161 | ||||||||
\(71\) | −4.59419 | −0.545230 | −0.272615 | − | 0.962123i | \(-0.587888\pi\) | ||||
−0.272615 | + | 0.962123i | \(0.587888\pi\) | |||||||
\(72\) | 6.34481 | 0.747744 | ||||||||
\(73\) | −10.5526 | −1.23508 | −0.617542 | − | 0.786538i | \(-0.711872\pi\) | ||||
−0.617542 | + | 0.786538i | \(0.711872\pi\) | |||||||
\(74\) | −12.0368 | −1.39925 | ||||||||
\(75\) | 1.61596 | 0.186595 | ||||||||
\(76\) | −17.8388 | −2.04625 | ||||||||
\(77\) | −5.23490 | −0.596572 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −15.7778 | −1.77514 | −0.887569 | − | 0.460674i | \(-0.847608\pi\) | ||||
−0.887569 | + | 0.460674i | \(0.847608\pi\) | |||||||
\(80\) | 1.15883 | 0.129562 | ||||||||
\(81\) | 6.32304 | 0.702560 | ||||||||
\(82\) | −2.86294 | −0.316158 | ||||||||
\(83\) | 7.72348 | 0.847762 | 0.423881 | − | 0.905718i | \(-0.360667\pi\) | ||||
0.423881 | + | 0.905718i | \(0.360667\pi\) | |||||||
\(84\) | −3.46681 | −0.378260 | ||||||||
\(85\) | 7.65279 | 0.830062 | ||||||||
\(86\) | −13.7899 | −1.48700 | ||||||||
\(87\) | −1.25906 | −0.134986 | ||||||||
\(88\) | 6.02177 | 0.641923 | ||||||||
\(89\) | 6.61356 | 0.701036 | 0.350518 | − | 0.936556i | \(-0.386005\pi\) | ||||
0.350518 | + | 0.936556i | \(0.386005\pi\) | |||||||
\(90\) | −8.74094 | −0.921376 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −5.76271 | −0.600804 | ||||||||
\(93\) | 2.36898 | 0.245652 | ||||||||
\(94\) | 6.63102 | 0.683938 | ||||||||
\(95\) | 8.45473 | 0.867437 | ||||||||
\(96\) | −3.61596 | −0.369052 | ||||||||
\(97\) | 11.9269 | 1.21100 | 0.605498 | − | 0.795847i | \(-0.292974\pi\) | ||||
0.605498 | + | 0.795847i | \(0.292974\pi\) | |||||||
\(98\) | 6.29590 | 0.635982 | ||||||||
\(99\) | 6.87800 | 0.691265 | ||||||||
\(100\) | −8.87800 | −0.887800 | ||||||||
\(101\) | 13.0640 | 1.29991 | 0.649957 | − | 0.759971i | \(-0.274787\pi\) | ||||
0.649957 | + | 0.759971i | \(0.274787\pi\) | |||||||
\(102\) | −6.60388 | −0.653881 | ||||||||
\(103\) | 9.16852 | 0.903401 | 0.451701 | − | 0.892170i | \(-0.350818\pi\) | ||||
0.451701 | + | 0.892170i | \(0.350818\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1.64310 | 0.160351 | ||||||||
\(106\) | −12.4058 | −1.20496 | ||||||||
\(107\) | −6.89977 | −0.667026 | −0.333513 | − | 0.942745i | \(-0.608234\pi\) | ||||
−0.333513 | + | 0.942745i | \(0.608234\pi\) | |||||||
\(108\) | 9.63102 | 0.926746 | ||||||||
\(109\) | 0.121998 | 0.0116853 | 0.00584264 | − | 0.999983i | \(-0.498140\pi\) | ||||
0.00584264 | + | 0.999983i | \(0.498140\pi\) | |||||||
\(110\) | −8.29590 | −0.790983 | ||||||||
\(111\) | −2.97285 | −0.282171 | ||||||||
\(112\) | −1.64310 | −0.155259 | ||||||||
\(113\) | 7.30798 | 0.687477 | 0.343738 | − | 0.939065i | \(-0.388307\pi\) | ||||
0.343738 | + | 0.939065i | \(0.388307\pi\) | |||||||
\(114\) | −7.29590 | −0.683323 | ||||||||
\(115\) | 2.73125 | 0.254690 | ||||||||
\(116\) | 6.91723 | 0.642249 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 27.4306 | 2.52519 | ||||||||
\(119\) | −10.8509 | −0.994696 | ||||||||
\(120\) | −1.89008 | −0.172540 | ||||||||
\(121\) | −4.47219 | −0.406563 | ||||||||
\(122\) | −19.2446 | −1.74232 | ||||||||
\(123\) | −0.707087 | −0.0637559 | ||||||||
\(124\) | −13.0151 | −1.16879 | ||||||||
\(125\) | 11.4330 | 1.02260 | ||||||||
\(126\) | 12.3937 | 1.10412 | ||||||||
\(127\) | −18.9705 | −1.68336 | −0.841678 | − | 0.539980i | \(-0.818432\pi\) | ||||
−0.841678 | + | 0.539980i | \(0.818432\pi\) | |||||||
\(128\) | 16.2620 | 1.43738 | ||||||||
\(129\) | −3.40581 | −0.299865 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 3.25667 | 0.284536 | 0.142268 | − | 0.989828i | \(-0.454560\pi\) | ||||
0.142268 | + | 0.989828i | \(0.454560\pi\) | |||||||
\(132\) | 4.32304 | 0.376273 | ||||||||
\(133\) | −11.9879 | −1.03948 | ||||||||
\(134\) | −1.29590 | −0.111948 | ||||||||
\(135\) | −4.56465 | −0.392862 | ||||||||
\(136\) | 12.4819 | 1.07031 | ||||||||
\(137\) | 0.792249 | 0.0676864 | 0.0338432 | − | 0.999427i | \(-0.489225\pi\) | ||||
0.0338432 | + | 0.999427i | \(0.489225\pi\) | |||||||
\(138\) | −2.35690 | −0.200632 | ||||||||
\(139\) | −11.3394 | −0.961799 | −0.480899 | − | 0.876776i | \(-0.659690\pi\) | ||||
−0.480899 | + | 0.876776i | \(0.659690\pi\) | |||||||
\(140\) | −9.02715 | −0.762933 | ||||||||
\(141\) | 1.63773 | 0.137922 | ||||||||
\(142\) | 10.3230 | 0.866291 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 2.15883 | 0.179903 | ||||||||
\(145\) | −3.27844 | −0.272260 | ||||||||
\(146\) | 23.7114 | 1.96237 | ||||||||
\(147\) | 1.55496 | 0.128251 | ||||||||
\(148\) | 16.3327 | 1.34254 | ||||||||
\(149\) | 8.40581 | 0.688631 | 0.344316 | − | 0.938854i | \(-0.388111\pi\) | ||||
0.344316 | + | 0.938854i | \(0.388111\pi\) | |||||||
\(150\) | −3.63102 | −0.296472 | ||||||||
\(151\) | 14.1293 | 1.14983 | 0.574913 | − | 0.818215i | \(-0.305036\pi\) | ||||
0.574913 | + | 0.818215i | \(0.305036\pi\) | |||||||
\(152\) | 13.7899 | 1.11851 | ||||||||
\(153\) | 14.2567 | 1.15258 | ||||||||
\(154\) | 11.7627 | 0.947866 | ||||||||
\(155\) | 6.16852 | 0.495468 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −9.43296 | −0.752832 | −0.376416 | − | 0.926451i | \(-0.622844\pi\) | ||||
−0.376416 | + | 0.926451i | \(0.622844\pi\) | |||||||
\(158\) | 35.4523 | 2.82044 | ||||||||
\(159\) | −3.06398 | −0.242990 | ||||||||
\(160\) | −9.41550 | −0.744361 | ||||||||
\(161\) | −3.87263 | −0.305206 | ||||||||
\(162\) | −14.2078 | −1.11627 | ||||||||
\(163\) | 8.70410 | 0.681758 | 0.340879 | − | 0.940107i | \(-0.389275\pi\) | ||||
0.340879 | + | 0.940107i | \(0.389275\pi\) | |||||||
\(164\) | 3.88471 | 0.303345 | ||||||||
\(165\) | −2.04892 | −0.159508 | ||||||||
\(166\) | −17.3545 | −1.34697 | ||||||||
\(167\) | −23.8538 | −1.84587 | −0.922933 | − | 0.384961i | \(-0.874215\pi\) | ||||
−0.922933 | + | 0.384961i | \(0.874215\pi\) | |||||||
\(168\) | 2.67994 | 0.206762 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | −17.1957 | −1.31885 | ||||||||
\(171\) | 15.7506 | 1.20448 | ||||||||
\(172\) | 18.7114 | 1.42673 | ||||||||
\(173\) | −18.8552 | −1.43353 | −0.716766 | − | 0.697314i | \(-0.754378\pi\) | ||||
−0.716766 | + | 0.697314i | \(0.754378\pi\) | |||||||
\(174\) | 2.82908 | 0.214472 | ||||||||
\(175\) | −5.96615 | −0.450998 | ||||||||
\(176\) | 2.04892 | 0.154443 | ||||||||
\(177\) | 6.77479 | 0.509224 | ||||||||
\(178\) | −14.8605 | −1.11384 | ||||||||
\(179\) | 6.02177 | 0.450088 | 0.225044 | − | 0.974349i | \(-0.427747\pi\) | ||||
0.225044 | + | 0.974349i | \(0.427747\pi\) | |||||||
\(180\) | 11.8605 | 0.884033 | ||||||||
\(181\) | −4.77777 | −0.355129 | −0.177565 | − | 0.984109i | \(-0.556822\pi\) | ||||
−0.177565 | + | 0.984109i | \(0.556822\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −4.75302 | −0.351353 | ||||||||
\(184\) | 4.45473 | 0.328407 | ||||||||
\(185\) | −7.74094 | −0.569125 | ||||||||
\(186\) | −5.32304 | −0.390305 | ||||||||
\(187\) | 13.5308 | 0.989470 | ||||||||
\(188\) | −8.99761 | −0.656218 | ||||||||
\(189\) | 6.47219 | 0.470782 | ||||||||
\(190\) | −18.9976 | −1.37823 | ||||||||
\(191\) | 18.4306 | 1.33359 | 0.666795 | − | 0.745242i | \(-0.267666\pi\) | ||||
0.666795 | + | 0.745242i | \(0.267666\pi\) | |||||||
\(192\) | 7.23490 | 0.522134 | ||||||||
\(193\) | 6.05429 | 0.435798 | 0.217899 | − | 0.975971i | \(-0.430080\pi\) | ||||
0.217899 | + | 0.975971i | \(0.430080\pi\) | |||||||
\(194\) | −26.7995 | −1.92410 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −8.54288 | −0.610205 | ||||||||
\(197\) | −11.4155 | −0.813321 | −0.406660 | − | 0.913579i | \(-0.633307\pi\) | ||||
−0.406660 | + | 0.913579i | \(0.633307\pi\) | |||||||
\(198\) | −15.4547 | −1.09832 | ||||||||
\(199\) | −13.9051 | −0.985710 | −0.492855 | − | 0.870111i | \(-0.664047\pi\) | ||||
−0.492855 | + | 0.870111i | \(0.664047\pi\) | |||||||
\(200\) | 6.86294 | 0.485283 | ||||||||
\(201\) | −0.320060 | −0.0225753 | ||||||||
\(202\) | −29.3545 | −2.06538 | ||||||||
\(203\) | 4.64848 | 0.326259 | ||||||||
\(204\) | 8.96077 | 0.627379 | ||||||||
\(205\) | −1.84117 | −0.128593 | ||||||||
\(206\) | −20.6015 | −1.43537 | ||||||||
\(207\) | 5.08815 | 0.353651 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 14.9487 | 1.03402 | ||||||||
\(210\) | −3.69202 | −0.254774 | ||||||||
\(211\) | −13.2446 | −0.911795 | −0.455897 | − | 0.890032i | \(-0.650682\pi\) | ||||
−0.455897 | + | 0.890032i | \(0.650682\pi\) | |||||||
\(212\) | 16.8334 | 1.15612 | ||||||||
\(213\) | 2.54958 | 0.174694 | ||||||||
\(214\) | 15.5036 | 1.05981 | ||||||||
\(215\) | −8.86831 | −0.604814 | ||||||||
\(216\) | −7.44504 | −0.506571 | ||||||||
\(217\) | −8.74632 | −0.593739 | ||||||||
\(218\) | −0.274127 | −0.0185662 | ||||||||
\(219\) | 5.85623 | 0.395727 | ||||||||
\(220\) | 11.2567 | 0.758924 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 6.67994 | 0.448328 | ||||||||
\(223\) | −7.33513 | −0.491196 | −0.245598 | − | 0.969372i | \(-0.578984\pi\) | ||||
−0.245598 | + | 0.969372i | \(0.578984\pi\) | |||||||
\(224\) | 13.3502 | 0.891997 | ||||||||
\(225\) | 7.83877 | 0.522585 | ||||||||
\(226\) | −16.4209 | −1.09230 | ||||||||
\(227\) | −8.67456 | −0.575751 | −0.287875 | − | 0.957668i | \(-0.592949\pi\) | ||||
−0.287875 | + | 0.957668i | \(0.592949\pi\) | |||||||
\(228\) | 9.89977 | 0.655628 | ||||||||
\(229\) | −13.6866 | −0.904439 | −0.452219 | − | 0.891907i | \(-0.649368\pi\) | ||||
−0.452219 | + | 0.891907i | \(0.649368\pi\) | |||||||
\(230\) | −6.13706 | −0.404666 | ||||||||
\(231\) | 2.90515 | 0.191145 | ||||||||
\(232\) | −5.34721 | −0.351061 | ||||||||
\(233\) | −5.08815 | −0.333336 | −0.166668 | − | 0.986013i | \(-0.553301\pi\) | ||||
−0.166668 | + | 0.986013i | \(0.553301\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 4.26444 | 0.278181 | ||||||||
\(236\) | −37.2204 | −2.42284 | ||||||||
\(237\) | 8.75600 | 0.568764 | ||||||||
\(238\) | 24.3817 | 1.58043 | ||||||||
\(239\) | −10.9239 | −0.706611 | −0.353305 | − | 0.935508i | \(-0.614942\pi\) | ||||
−0.353305 | + | 0.935508i | \(0.614942\pi\) | |||||||
\(240\) | −0.643104 | −0.0415122 | ||||||||
\(241\) | 11.9148 | 0.767502 | 0.383751 | − | 0.923437i | \(-0.374632\pi\) | ||||
0.383751 | + | 0.923437i | \(0.374632\pi\) | |||||||
\(242\) | 10.0489 | 0.645969 | ||||||||
\(243\) | −12.9855 | −0.833022 | ||||||||
\(244\) | 26.1129 | 1.67171 | ||||||||
\(245\) | 4.04892 | 0.258676 | ||||||||
\(246\) | 1.58881 | 0.101299 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 10.0610 | 0.638874 | ||||||||
\(249\) | −4.28621 | −0.271627 | ||||||||
\(250\) | −25.6896 | −1.62475 | ||||||||
\(251\) | 22.3478 | 1.41058 | 0.705290 | − | 0.708919i | \(-0.250817\pi\) | ||||
0.705290 | + | 0.708919i | \(0.250817\pi\) | |||||||
\(252\) | −16.8170 | −1.05937 | ||||||||
\(253\) | 4.82908 | 0.303602 | ||||||||
\(254\) | 42.6262 | 2.67461 | ||||||||
\(255\) | −4.24698 | −0.265956 | ||||||||
\(256\) | −10.4668 | −0.654176 | ||||||||
\(257\) | −18.6601 | −1.16398 | −0.581992 | − | 0.813194i | \(-0.697727\pi\) | ||||
−0.581992 | + | 0.813194i | \(0.697727\pi\) | |||||||
\(258\) | 7.65279 | 0.476442 | ||||||||
\(259\) | 10.9758 | 0.682005 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −6.10752 | −0.378046 | ||||||||
\(262\) | −7.31767 | −0.452087 | ||||||||
\(263\) | 14.3991 | 0.887887 | 0.443944 | − | 0.896055i | \(-0.353579\pi\) | ||||
0.443944 | + | 0.896055i | \(0.353579\pi\) | |||||||
\(264\) | −3.34183 | −0.205675 | ||||||||
\(265\) | −7.97823 | −0.490099 | ||||||||
\(266\) | 26.9366 | 1.65159 | ||||||||
\(267\) | −3.67025 | −0.224616 | ||||||||
\(268\) | 1.75840 | 0.107411 | ||||||||
\(269\) | 0.652793 | 0.0398015 | 0.0199007 | − | 0.999802i | \(-0.493665\pi\) | ||||
0.0199007 | + | 0.999802i | \(0.493665\pi\) | |||||||
\(270\) | 10.2567 | 0.624201 | ||||||||
\(271\) | −1.99569 | −0.121229 | −0.0606147 | − | 0.998161i | \(-0.519306\pi\) | ||||
−0.0606147 | + | 0.998161i | \(0.519306\pi\) | |||||||
\(272\) | 4.24698 | 0.257511 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −1.78017 | −0.107544 | ||||||||
\(275\) | 7.43967 | 0.448629 | ||||||||
\(276\) | 3.19806 | 0.192501 | ||||||||
\(277\) | 11.7845 | 0.708061 | 0.354030 | − | 0.935234i | \(-0.384811\pi\) | ||||
0.354030 | + | 0.935234i | \(0.384811\pi\) | |||||||
\(278\) | 25.4795 | 1.52816 | ||||||||
\(279\) | 11.4916 | 0.687982 | ||||||||
\(280\) | 6.97823 | 0.417029 | ||||||||
\(281\) | −6.47219 | −0.386098 | −0.193049 | − | 0.981189i | \(-0.561838\pi\) | ||||
−0.193049 | + | 0.981189i | \(0.561838\pi\) | |||||||
\(282\) | −3.67994 | −0.219137 | ||||||||
\(283\) | 6.58104 | 0.391202 | 0.195601 | − | 0.980684i | \(-0.437334\pi\) | ||||
0.195601 | + | 0.980684i | \(0.437334\pi\) | |||||||
\(284\) | −14.0073 | −0.831180 | ||||||||
\(285\) | −4.69202 | −0.277931 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 2.61058 | 0.154098 | ||||||||
\(288\) | −17.5405 | −1.03358 | ||||||||
\(289\) | 11.0465 | 0.649796 | ||||||||
\(290\) | 7.36658 | 0.432581 | ||||||||
\(291\) | −6.61894 | −0.388009 | ||||||||
\(292\) | −32.1739 | −1.88284 | ||||||||
\(293\) | −24.3381 | −1.42185 | −0.710924 | − | 0.703269i | \(-0.751723\pi\) | ||||
−0.710924 | + | 0.703269i | \(0.751723\pi\) | |||||||
\(294\) | −3.49396 | −0.203772 | ||||||||
\(295\) | 17.6407 | 1.02708 | ||||||||
\(296\) | −12.6256 | −0.733851 | ||||||||
\(297\) | −8.07069 | −0.468309 | ||||||||
\(298\) | −18.8877 | −1.09413 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 4.92692 | 0.284456 | ||||||||
\(301\) | 12.5743 | 0.724773 | ||||||||
\(302\) | −31.7482 | −1.82691 | ||||||||
\(303\) | −7.24996 | −0.416500 | ||||||||
\(304\) | 4.69202 | 0.269106 | ||||||||
\(305\) | −12.3763 | −0.708663 | ||||||||
\(306\) | −32.0344 | −1.83129 | ||||||||
\(307\) | −14.0737 | −0.803227 | −0.401613 | − | 0.915809i | \(-0.631550\pi\) | ||||
−0.401613 | + | 0.915809i | \(0.631550\pi\) | |||||||
\(308\) | −15.9608 | −0.909449 | ||||||||
\(309\) | −5.08815 | −0.289455 | ||||||||
\(310\) | −13.8605 | −0.787226 | ||||||||
\(311\) | −29.7700 | −1.68810 | −0.844051 | − | 0.536263i | \(-0.819836\pi\) | ||||
−0.844051 | + | 0.536263i | \(0.819836\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −7.47889 | −0.422732 | −0.211366 | − | 0.977407i | \(-0.567791\pi\) | ||||
−0.211366 | + | 0.977407i | \(0.567791\pi\) | |||||||
\(314\) | 21.1957 | 1.19614 | ||||||||
\(315\) | 7.97046 | 0.449085 | ||||||||
\(316\) | −48.1051 | −2.70613 | ||||||||
\(317\) | 30.0301 | 1.68666 | 0.843330 | − | 0.537396i | \(-0.180592\pi\) | ||||
0.843330 | + | 0.537396i | \(0.180592\pi\) | |||||||
\(318\) | 6.88471 | 0.386075 | ||||||||
\(319\) | −5.79656 | −0.324545 | ||||||||
\(320\) | 18.8388 | 1.05312 | ||||||||
\(321\) | 3.82908 | 0.213719 | ||||||||
\(322\) | 8.70171 | 0.484927 | ||||||||
\(323\) | 30.9855 | 1.72408 | ||||||||
\(324\) | 19.2784 | 1.07102 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −19.5579 | −1.08321 | ||||||||
\(327\) | −0.0677037 | −0.00374402 | ||||||||
\(328\) | −3.00298 | −0.165812 | ||||||||
\(329\) | −6.04652 | −0.333356 | ||||||||
\(330\) | 4.60388 | 0.253435 | ||||||||
\(331\) | −15.7168 | −0.863872 | −0.431936 | − | 0.901904i | \(-0.642169\pi\) | ||||
−0.431936 | + | 0.901904i | \(0.642169\pi\) | |||||||
\(332\) | 23.5483 | 1.29238 | ||||||||
\(333\) | −14.4209 | −0.790259 | ||||||||
\(334\) | 53.5991 | 2.93281 | ||||||||
\(335\) | −0.833397 | −0.0455333 | ||||||||
\(336\) | 0.911854 | 0.0497457 | ||||||||
\(337\) | 1.95407 | 0.106445 | 0.0532224 | − | 0.998583i | \(-0.483051\pi\) | ||||
0.0532224 | + | 0.998583i | \(0.483051\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −4.05562 | −0.220271 | ||||||||
\(340\) | 23.3327 | 1.26540 | ||||||||
\(341\) | 10.9065 | 0.590619 | ||||||||
\(342\) | −35.3913 | −1.91374 | ||||||||
\(343\) | −20.0834 | −1.08440 | ||||||||
\(344\) | −14.4644 | −0.779869 | ||||||||
\(345\) | −1.51573 | −0.0816041 | ||||||||
\(346\) | 42.3672 | 2.27767 | ||||||||
\(347\) | −17.1250 | −0.919317 | −0.459659 | − | 0.888096i | \(-0.652028\pi\) | ||||
−0.459659 | + | 0.888096i | \(0.652028\pi\) | |||||||
\(348\) | −3.83877 | −0.205780 | ||||||||
\(349\) | −10.4668 | −0.560276 | −0.280138 | − | 0.959960i | \(-0.590380\pi\) | ||||
−0.280138 | + | 0.959960i | \(0.590380\pi\) | |||||||
\(350\) | 13.4058 | 0.716571 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −16.6474 | −0.887310 | ||||||||
\(353\) | 15.5308 | 0.826621 | 0.413310 | − | 0.910590i | \(-0.364372\pi\) | ||||
0.413310 | + | 0.910590i | \(0.364372\pi\) | |||||||
\(354\) | −15.2228 | −0.809084 | ||||||||
\(355\) | 6.63879 | 0.352351 | ||||||||
\(356\) | 20.1642 | 1.06870 | ||||||||
\(357\) | 6.02177 | 0.318706 | ||||||||
\(358\) | −13.5308 | −0.715125 | ||||||||
\(359\) | −21.4263 | −1.13083 | −0.565417 | − | 0.824805i | \(-0.691285\pi\) | ||||
−0.565417 | + | 0.824805i | \(0.691285\pi\) | |||||||
\(360\) | −9.16852 | −0.483224 | ||||||||
\(361\) | 15.2325 | 0.801711 | ||||||||
\(362\) | 10.7356 | 0.564249 | ||||||||
\(363\) | 2.48188 | 0.130265 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 15.2489 | 0.798164 | ||||||||
\(366\) | 10.6799 | 0.558249 | ||||||||
\(367\) | 34.3032 | 1.79061 | 0.895306 | − | 0.445452i | \(-0.146957\pi\) | ||||
0.895306 | + | 0.445452i | \(0.146957\pi\) | |||||||
\(368\) | 1.51573 | 0.0790129 | ||||||||
\(369\) | −3.42998 | −0.178557 | ||||||||
\(370\) | 17.3937 | 0.904257 | ||||||||
\(371\) | 11.3123 | 0.587305 | ||||||||
\(372\) | 7.22282 | 0.374486 | ||||||||
\(373\) | −12.5961 | −0.652202 | −0.326101 | − | 0.945335i | \(-0.605735\pi\) | ||||
−0.326101 | + | 0.945335i | \(0.605735\pi\) | |||||||
\(374\) | −30.4034 | −1.57212 | ||||||||
\(375\) | −6.34481 | −0.327645 | ||||||||
\(376\) | 6.95539 | 0.358697 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | −14.5429 | −0.748005 | ||||||||
\(379\) | 16.5386 | 0.849529 | 0.424765 | − | 0.905304i | \(-0.360357\pi\) | ||||
0.424765 | + | 0.905304i | \(0.360357\pi\) | |||||||
\(380\) | 25.7778 | 1.32237 | ||||||||
\(381\) | 10.5278 | 0.539356 | ||||||||
\(382\) | −41.4131 | −2.11888 | ||||||||
\(383\) | 7.53617 | 0.385080 | 0.192540 | − | 0.981289i | \(-0.438327\pi\) | ||||
0.192540 | + | 0.981289i | \(0.438327\pi\) | |||||||
\(384\) | −9.02475 | −0.460543 | ||||||||
\(385\) | 7.56465 | 0.385530 | ||||||||
\(386\) | −13.6039 | −0.692419 | ||||||||
\(387\) | −16.5211 | −0.839815 | ||||||||
\(388\) | 36.3642 | 1.84611 | ||||||||
\(389\) | 35.5555 | 1.80274 | 0.901369 | − | 0.433052i | \(-0.142563\pi\) | ||||
0.901369 | + | 0.433052i | \(0.142563\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 10.0097 | 0.506212 | ||||||||
\(392\) | 6.60388 | 0.333546 | ||||||||
\(393\) | −1.80731 | −0.0911670 | ||||||||
\(394\) | 25.6504 | 1.29225 | ||||||||
\(395\) | 22.7995 | 1.14717 | ||||||||
\(396\) | 20.9705 | 1.05381 | ||||||||
\(397\) | 1.35152 | 0.0678308 | 0.0339154 | − | 0.999425i | \(-0.489202\pi\) | ||||
0.0339154 | + | 0.999425i | \(0.489202\pi\) | |||||||
\(398\) | 31.2446 | 1.56615 | ||||||||
\(399\) | 6.65279 | 0.333056 | ||||||||
\(400\) | 2.33513 | 0.116756 | ||||||||
\(401\) | 0.579121 | 0.0289199 | 0.0144600 | − | 0.999895i | \(-0.495397\pi\) | ||||
0.0144600 | + | 0.999895i | \(0.495397\pi\) | |||||||
\(402\) | 0.719169 | 0.0358689 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 39.8310 | 1.98167 | ||||||||
\(405\) | −9.13706 | −0.454024 | ||||||||
\(406\) | −10.4450 | −0.518379 | ||||||||
\(407\) | −13.6866 | −0.678422 | ||||||||
\(408\) | −6.92692 | −0.342934 | ||||||||
\(409\) | −15.1575 | −0.749490 | −0.374745 | − | 0.927128i | \(-0.622270\pi\) | ||||
−0.374745 | + | 0.927128i | \(0.622270\pi\) | |||||||
\(410\) | 4.13706 | 0.204315 | ||||||||
\(411\) | −0.439665 | −0.0216871 | ||||||||
\(412\) | 27.9541 | 1.37720 | ||||||||
\(413\) | −25.0127 | −1.23079 | ||||||||
\(414\) | −11.4330 | −0.561899 | ||||||||
\(415\) | −11.1608 | −0.547860 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 6.29291 | 0.308165 | ||||||||
\(418\) | −33.5894 | −1.64291 | ||||||||
\(419\) | −35.7235 | −1.74521 | −0.872603 | − | 0.488430i | \(-0.837570\pi\) | ||||
−0.872603 | + | 0.488430i | \(0.837570\pi\) | |||||||
\(420\) | 5.00969 | 0.244448 | ||||||||
\(421\) | −35.0465 | −1.70806 | −0.854032 | − | 0.520221i | \(-0.825849\pi\) | ||||
−0.854032 | + | 0.520221i | \(0.825849\pi\) | |||||||
\(422\) | 29.7603 | 1.44871 | ||||||||
\(423\) | 7.94438 | 0.386269 | ||||||||
\(424\) | −13.0127 | −0.631951 | ||||||||
\(425\) | 15.4209 | 0.748022 | ||||||||
\(426\) | −5.72886 | −0.277564 | ||||||||
\(427\) | 17.5483 | 0.849220 | ||||||||
\(428\) | −21.0368 | −1.01685 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 19.9269 | 0.960961 | ||||||||
\(431\) | −34.2814 | −1.65128 | −0.825639 | − | 0.564199i | \(-0.809185\pi\) | ||||
−0.825639 | + | 0.564199i | \(0.809185\pi\) | |||||||
\(432\) | −2.53319 | −0.121878 | ||||||||
\(433\) | 13.7385 | 0.660232 | 0.330116 | − | 0.943940i | \(-0.392912\pi\) | ||||
0.330116 | + | 0.943940i | \(0.392912\pi\) | |||||||
\(434\) | 19.6528 | 0.943364 | ||||||||
\(435\) | 1.81940 | 0.0872334 | ||||||||
\(436\) | 0.371961 | 0.0178137 | ||||||||
\(437\) | 11.0586 | 0.529005 | ||||||||
\(438\) | −13.1588 | −0.628753 | ||||||||
\(439\) | 10.2403 | 0.488742 | 0.244371 | − | 0.969682i | \(-0.421419\pi\) | ||||
0.244371 | + | 0.969682i | \(0.421419\pi\) | |||||||
\(440\) | −8.70171 | −0.414838 | ||||||||
\(441\) | 7.54288 | 0.359185 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 12.1763 | 0.578513 | 0.289257 | − | 0.957252i | \(-0.406592\pi\) | ||||
0.289257 | + | 0.957252i | \(0.406592\pi\) | |||||||
\(444\) | −9.06398 | −0.430158 | ||||||||
\(445\) | −9.55688 | −0.453039 | ||||||||
\(446\) | 16.4819 | 0.780440 | ||||||||
\(447\) | −4.66487 | −0.220641 | ||||||||
\(448\) | −26.7114 | −1.26199 | ||||||||
\(449\) | −12.9051 | −0.609032 | −0.304516 | − | 0.952507i | \(-0.598495\pi\) | ||||
−0.304516 | + | 0.952507i | \(0.598495\pi\) | |||||||
\(450\) | −17.6136 | −0.830311 | ||||||||
\(451\) | −3.25534 | −0.153288 | ||||||||
\(452\) | 22.2814 | 1.04803 | ||||||||
\(453\) | −7.84117 | −0.368410 | ||||||||
\(454\) | 19.4916 | 0.914785 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −7.65279 | −0.358375 | ||||||||
\(457\) | 4.65710 | 0.217850 | 0.108925 | − | 0.994050i | \(-0.465259\pi\) | ||||
0.108925 | + | 0.994050i | \(0.465259\pi\) | |||||||
\(458\) | 30.7536 | 1.43702 | ||||||||
\(459\) | −16.7289 | −0.780836 | ||||||||
\(460\) | 8.32736 | 0.388265 | ||||||||
\(461\) | −31.5405 | −1.46899 | −0.734493 | − | 0.678616i | \(-0.762580\pi\) | ||||
−0.734493 | + | 0.678616i | \(0.762580\pi\) | |||||||
\(462\) | −6.52781 | −0.303701 | ||||||||
\(463\) | 17.6504 | 0.820284 | 0.410142 | − | 0.912022i | \(-0.365479\pi\) | ||||
0.410142 | + | 0.912022i | \(0.365479\pi\) | |||||||
\(464\) | −1.81940 | −0.0844633 | ||||||||
\(465\) | −3.42327 | −0.158750 | ||||||||
\(466\) | 11.4330 | 0.529622 | ||||||||
\(467\) | −32.1726 | −1.48877 | −0.744385 | − | 0.667751i | \(-0.767257\pi\) | ||||
−0.744385 | + | 0.667751i | \(0.767257\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1.18167 | 0.0545644 | ||||||||
\(470\) | −9.58211 | −0.441990 | ||||||||
\(471\) | 5.23490 | 0.241211 | ||||||||
\(472\) | 28.7724 | 1.32436 | ||||||||
\(473\) | −15.6799 | −0.720964 | ||||||||
\(474\) | −19.6746 | −0.903683 | ||||||||
\(475\) | 17.0368 | 0.781704 | ||||||||
\(476\) | −33.0834 | −1.51637 | ||||||||
\(477\) | −14.8629 | −0.680527 | ||||||||
\(478\) | 24.5459 | 1.12270 | ||||||||
\(479\) | −34.8998 | −1.59461 | −0.797306 | − | 0.603576i | \(-0.793742\pi\) | ||||
−0.797306 | + | 0.603576i | \(0.793742\pi\) | |||||||
\(480\) | 5.22521 | 0.238497 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −26.7724 | −1.21945 | ||||||||
\(483\) | 2.14914 | 0.0977895 | ||||||||
\(484\) | −13.6353 | −0.619788 | ||||||||
\(485\) | −17.2349 | −0.782596 | ||||||||
\(486\) | 29.1782 | 1.32355 | ||||||||
\(487\) | 41.8351 | 1.89573 | 0.947864 | − | 0.318676i | \(-0.103238\pi\) | ||||
0.947864 | + | 0.318676i | \(0.103238\pi\) | |||||||
\(488\) | −20.1860 | −0.913776 | ||||||||
\(489\) | −4.83041 | −0.218439 | ||||||||
\(490\) | −9.09783 | −0.410998 | ||||||||
\(491\) | 21.8455 | 0.985873 | 0.492936 | − | 0.870065i | \(-0.335924\pi\) | ||||
0.492936 | + | 0.870065i | \(0.335924\pi\) | |||||||
\(492\) | −2.15585 | −0.0971932 | ||||||||
\(493\) | −12.0151 | −0.541131 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −9.93900 | −0.446725 | ||||||||
\(496\) | 3.42327 | 0.153709 | ||||||||
\(497\) | −9.41311 | −0.422236 | ||||||||
\(498\) | 9.63102 | 0.431576 | ||||||||
\(499\) | 23.5472 | 1.05412 | 0.527058 | − | 0.849829i | \(-0.323295\pi\) | ||||
0.527058 | + | 0.849829i | \(0.323295\pi\) | |||||||
\(500\) | 34.8582 | 1.55890 | ||||||||
\(501\) | 13.2379 | 0.591425 | ||||||||
\(502\) | −50.2150 | −2.24121 | ||||||||
\(503\) | −7.08682 | −0.315986 | −0.157993 | − | 0.987440i | \(-0.550502\pi\) | ||||
−0.157993 | + | 0.987440i | \(0.550502\pi\) | |||||||
\(504\) | 13.0000 | 0.579066 | ||||||||
\(505\) | −18.8780 | −0.840060 | ||||||||
\(506\) | −10.8509 | −0.482379 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −57.8394 | −2.56621 | ||||||||
\(509\) | 7.61894 | 0.337704 | 0.168852 | − | 0.985641i | \(-0.445994\pi\) | ||||
0.168852 | + | 0.985641i | \(0.445994\pi\) | |||||||
\(510\) | 9.54288 | 0.422566 | ||||||||
\(511\) | −21.6213 | −0.956471 | ||||||||
\(512\) | −9.00538 | −0.397985 | ||||||||
\(513\) | −18.4819 | −0.815995 | ||||||||
\(514\) | 41.9288 | 1.84940 | ||||||||
\(515\) | −13.2489 | −0.583816 | ||||||||
\(516\) | −10.3840 | −0.457132 | ||||||||
\(517\) | 7.53989 | 0.331604 | ||||||||
\(518\) | −24.6625 | −1.08361 | ||||||||
\(519\) | 10.4638 | 0.459311 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −39.5133 | −1.73111 | −0.865555 | − | 0.500813i | \(-0.833034\pi\) | ||||
−0.865555 | + | 0.500813i | \(0.833034\pi\) | |||||||
\(522\) | 13.7235 | 0.600660 | ||||||||
\(523\) | −15.8194 | −0.691734 | −0.345867 | − | 0.938284i | \(-0.612415\pi\) | ||||
−0.345867 | + | 0.938284i | \(0.612415\pi\) | |||||||
\(524\) | 9.92931 | 0.433764 | ||||||||
\(525\) | 3.31096 | 0.144502 | ||||||||
\(526\) | −32.3545 | −1.41072 | ||||||||
\(527\) | 22.6069 | 0.984770 | ||||||||
\(528\) | −1.13706 | −0.0494843 | ||||||||
\(529\) | −19.4276 | −0.844678 | ||||||||
\(530\) | 17.9269 | 0.778696 | ||||||||
\(531\) | 32.8635 | 1.42616 | ||||||||
\(532\) | −36.5502 | −1.58465 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 8.24698 | 0.356882 | ||||||||
\(535\) | 9.97046 | 0.431061 | ||||||||
\(536\) | −1.35929 | −0.0587123 | ||||||||
\(537\) | −3.34183 | −0.144211 | ||||||||
\(538\) | −1.46681 | −0.0632388 | ||||||||
\(539\) | 7.15883 | 0.308353 | ||||||||
\(540\) | −13.9172 | −0.598902 | ||||||||
\(541\) | 34.4819 | 1.48249 | 0.741246 | − | 0.671234i | \(-0.234235\pi\) | ||||
0.741246 | + | 0.671234i | \(0.234235\pi\) | |||||||
\(542\) | 4.48427 | 0.192616 | ||||||||
\(543\) | 2.65146 | 0.113785 | ||||||||
\(544\) | −34.5066 | −1.47946 | ||||||||
\(545\) | −0.176292 | −0.00755152 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 36.8582 | 1.57594 | 0.787970 | − | 0.615713i | \(-0.211132\pi\) | ||||
0.787970 | + | 0.615713i | \(0.211132\pi\) | |||||||
\(548\) | 2.41550 | 0.103185 | ||||||||
\(549\) | −23.0562 | −0.984015 | ||||||||
\(550\) | −16.7168 | −0.712806 | ||||||||
\(551\) | −13.2741 | −0.565497 | ||||||||
\(552\) | −2.47219 | −0.105223 | ||||||||
\(553\) | −32.3274 | −1.37470 | ||||||||
\(554\) | −26.4795 | −1.12501 | ||||||||
\(555\) | 4.29590 | 0.182351 | ||||||||
\(556\) | −34.5730 | −1.46622 | ||||||||
\(557\) | 1.27652 | 0.0540879 | 0.0270439 | − | 0.999634i | \(-0.491391\pi\) | ||||
0.0270439 | + | 0.999634i | \(0.491391\pi\) | |||||||
\(558\) | −25.8213 | −1.09310 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 2.37435 | 0.100335 | ||||||||
\(561\) | −7.50902 | −0.317031 | ||||||||
\(562\) | 14.5429 | 0.613454 | ||||||||
\(563\) | −9.12737 | −0.384673 | −0.192336 | − | 0.981329i | \(-0.561607\pi\) | ||||
−0.192336 | + | 0.981329i | \(0.561607\pi\) | |||||||
\(564\) | 4.99330 | 0.210256 | ||||||||
\(565\) | −10.5603 | −0.444277 | ||||||||
\(566\) | −14.7875 | −0.621563 | ||||||||
\(567\) | 12.9554 | 0.544075 | ||||||||
\(568\) | 10.8280 | 0.454334 | ||||||||
\(569\) | −5.72156 | −0.239860 | −0.119930 | − | 0.992782i | \(-0.538267\pi\) | ||||
−0.119930 | + | 0.992782i | \(0.538267\pi\) | |||||||
\(570\) | 10.5429 | 0.441593 | ||||||||
\(571\) | 7.60148 | 0.318112 | 0.159056 | − | 0.987270i | \(-0.449155\pi\) | ||||
0.159056 | + | 0.987270i | \(0.449155\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −10.2282 | −0.427289 | ||||||||
\(574\) | −5.86592 | −0.244839 | ||||||||
\(575\) | 5.50365 | 0.229518 | ||||||||
\(576\) | 35.0954 | 1.46231 | ||||||||
\(577\) | 45.1564 | 1.87989 | 0.939944 | − | 0.341330i | \(-0.110877\pi\) | ||||
0.939944 | + | 0.341330i | \(0.110877\pi\) | |||||||
\(578\) | −24.8213 | −1.03243 | ||||||||
\(579\) | −3.35988 | −0.139632 | ||||||||
\(580\) | −9.99569 | −0.415048 | ||||||||
\(581\) | 15.8248 | 0.656522 | ||||||||
\(582\) | 14.8726 | 0.616490 | ||||||||
\(583\) | −14.1062 | −0.584219 | ||||||||
\(584\) | 24.8713 | 1.02918 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 54.6872 | 2.25911 | ||||||||
\(587\) | −32.4040 | −1.33746 | −0.668728 | − | 0.743507i | \(-0.733161\pi\) | ||||
−0.668728 | + | 0.743507i | \(0.733161\pi\) | |||||||
\(588\) | 4.74094 | 0.195513 | ||||||||
\(589\) | 24.9758 | 1.02911 | ||||||||
\(590\) | −39.6383 | −1.63188 | ||||||||
\(591\) | 6.33513 | 0.260592 | ||||||||
\(592\) | −4.29590 | −0.176560 | ||||||||
\(593\) | 36.6848 | 1.50647 | 0.753233 | − | 0.657754i | \(-0.228493\pi\) | ||||
0.753233 | + | 0.657754i | \(0.228493\pi\) | |||||||
\(594\) | 18.1347 | 0.744075 | ||||||||
\(595\) | 15.6799 | 0.642815 | ||||||||
\(596\) | 25.6286 | 1.04979 | ||||||||
\(597\) | 7.71678 | 0.315827 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −9.99223 | −0.408271 | −0.204136 | − | 0.978943i | \(-0.565438\pi\) | ||||
−0.204136 | + | 0.978943i | \(0.565438\pi\) | |||||||
\(600\) | −3.80864 | −0.155487 | ||||||||
\(601\) | −1.81163 | −0.0738978 | −0.0369489 | − | 0.999317i | \(-0.511764\pi\) | ||||
−0.0369489 | + | 0.999317i | \(0.511764\pi\) | |||||||
\(602\) | −28.2543 | −1.15156 | ||||||||
\(603\) | −1.55257 | −0.0632253 | ||||||||
\(604\) | 43.0790 | 1.75286 | ||||||||
\(605\) | 6.46250 | 0.262738 | ||||||||
\(606\) | 16.2905 | 0.661757 | ||||||||
\(607\) | 11.2161 | 0.455248 | 0.227624 | − | 0.973749i | \(-0.426904\pi\) | ||||
0.227624 | + | 0.973749i | \(0.426904\pi\) | |||||||
\(608\) | −38.1226 | −1.54608 | ||||||||
\(609\) | −2.57971 | −0.104535 | ||||||||
\(610\) | 27.8092 | 1.12596 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 43.4674 | 1.75707 | ||||||||
\(613\) | −20.8944 | −0.843917 | −0.421958 | − | 0.906615i | \(-0.638657\pi\) | ||||
−0.421958 | + | 0.906615i | \(0.638657\pi\) | |||||||
\(614\) | 31.6233 | 1.27621 | ||||||||
\(615\) | 1.02177 | 0.0412018 | ||||||||
\(616\) | 12.3381 | 0.497117 | ||||||||
\(617\) | 12.0992 | 0.487094 | 0.243547 | − | 0.969889i | \(-0.421689\pi\) | ||||
0.243547 | + | 0.969889i | \(0.421689\pi\) | |||||||
\(618\) | 11.4330 | 0.459901 | ||||||||
\(619\) | −10.5526 | −0.424143 | −0.212072 | − | 0.977254i | \(-0.568021\pi\) | ||||
−0.212072 | + | 0.977254i | \(0.568021\pi\) | |||||||
\(620\) | 18.8073 | 0.755320 | ||||||||
\(621\) | −5.97046 | −0.239586 | ||||||||
\(622\) | 66.8926 | 2.68215 | ||||||||
\(623\) | 13.5506 | 0.542895 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −1.96184 | −0.0784735 | ||||||||
\(626\) | 16.8049 | 0.671660 | ||||||||
\(627\) | −8.29590 | −0.331306 | ||||||||
\(628\) | −28.7603 | −1.14766 | ||||||||
\(629\) | −28.3696 | −1.13117 | ||||||||
\(630\) | −17.9095 | −0.713530 | ||||||||
\(631\) | −13.8514 | −0.551417 | −0.275709 | − | 0.961241i | \(-0.588913\pi\) | ||||
−0.275709 | + | 0.961241i | \(0.588913\pi\) | |||||||
\(632\) | 37.1866 | 1.47920 | ||||||||
\(633\) | 7.35019 | 0.292144 | ||||||||
\(634\) | −67.4771 | −2.67986 | ||||||||
\(635\) | 27.4131 | 1.08786 | ||||||||
\(636\) | −9.34183 | −0.370428 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 13.0248 | 0.515655 | ||||||||
\(639\) | 12.3676 | 0.489257 | ||||||||
\(640\) | −23.4993 | −0.928893 | ||||||||
\(641\) | 34.9608 | 1.38087 | 0.690434 | − | 0.723396i | \(-0.257420\pi\) | ||||
0.690434 | + | 0.723396i | \(0.257420\pi\) | |||||||
\(642\) | −8.60388 | −0.339568 | ||||||||
\(643\) | 33.3980 | 1.31709 | 0.658545 | − | 0.752541i | \(-0.271172\pi\) | ||||
0.658545 | + | 0.752541i | \(0.271172\pi\) | |||||||
\(644\) | −11.8073 | −0.465273 | ||||||||
\(645\) | 4.92154 | 0.193786 | ||||||||
\(646\) | −69.6238 | −2.73931 | ||||||||
\(647\) | 2.32842 | 0.0915397 | 0.0457698 | − | 0.998952i | \(-0.485426\pi\) | ||||
0.0457698 | + | 0.998952i | \(0.485426\pi\) | |||||||
\(648\) | −14.9028 | −0.585436 | ||||||||
\(649\) | 31.1903 | 1.22433 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 4.85384 | 0.190237 | ||||||||
\(652\) | 26.5381 | 1.03931 | ||||||||
\(653\) | 14.5714 | 0.570221 | 0.285111 | − | 0.958495i | \(-0.407970\pi\) | ||||
0.285111 | + | 0.958495i | \(0.407970\pi\) | |||||||
\(654\) | 0.152129 | 0.00594871 | ||||||||
\(655\) | −4.70602 | −0.183879 | ||||||||
\(656\) | −1.02177 | −0.0398934 | ||||||||
\(657\) | 28.4077 | 1.10829 | ||||||||
\(658\) | 13.5864 | 0.529654 | ||||||||
\(659\) | 11.1395 | 0.433932 | 0.216966 | − | 0.976179i | \(-0.430384\pi\) | ||||
0.216966 | + | 0.976179i | \(0.430384\pi\) | |||||||
\(660\) | −6.24698 | −0.243163 | ||||||||
\(661\) | −13.8498 | −0.538694 | −0.269347 | − | 0.963043i | \(-0.586808\pi\) | ||||
−0.269347 | + | 0.963043i | \(0.586808\pi\) | |||||||
\(662\) | 35.3153 | 1.37257 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −18.2034 | −0.706430 | ||||||||
\(665\) | 17.3230 | 0.671759 | ||||||||
\(666\) | 32.4034 | 1.25561 | ||||||||
\(667\) | −4.28813 | −0.166037 | ||||||||
\(668\) | −72.7284 | −2.81395 | ||||||||
\(669\) | 4.07069 | 0.157382 | ||||||||
\(670\) | 1.87263 | 0.0723458 | ||||||||
\(671\) | −21.8823 | −0.844757 | ||||||||
\(672\) | −7.40880 | −0.285801 | ||||||||
\(673\) | −6.52973 | −0.251703 | −0.125851 | − | 0.992049i | \(-0.540166\pi\) | ||||
−0.125851 | + | 0.992049i | \(0.540166\pi\) | |||||||
\(674\) | −4.39075 | −0.169125 | ||||||||
\(675\) | −9.19806 | −0.354034 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −11.3104 | −0.434693 | −0.217346 | − | 0.976095i | \(-0.569740\pi\) | ||||
−0.217346 | + | 0.976095i | \(0.569740\pi\) | |||||||
\(678\) | 9.11290 | 0.349979 | ||||||||
\(679\) | 24.4373 | 0.937816 | ||||||||
\(680\) | −18.0368 | −0.691681 | ||||||||
\(681\) | 4.81402 | 0.184474 | ||||||||
\(682\) | −24.5066 | −0.938407 | ||||||||
\(683\) | 14.1793 | 0.542555 | 0.271277 | − | 0.962501i | \(-0.412554\pi\) | ||||
0.271277 | + | 0.962501i | \(0.412554\pi\) | |||||||
\(684\) | 48.0224 | 1.83618 | ||||||||
\(685\) | −1.14483 | −0.0437418 | ||||||||
\(686\) | 45.1269 | 1.72295 | ||||||||
\(687\) | 7.59551 | 0.289787 | ||||||||
\(688\) | −4.92154 | −0.187632 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 3.40581 | 0.129657 | ||||||||
\(691\) | 30.7952 | 1.17151 | 0.585753 | − | 0.810490i | \(-0.300799\pi\) | ||||
0.585753 | + | 0.810490i | \(0.300799\pi\) | |||||||
\(692\) | −57.4878 | −2.18536 | ||||||||
\(693\) | 14.0925 | 0.535328 | ||||||||
\(694\) | 38.4795 | 1.46066 | ||||||||
\(695\) | 16.3860 | 0.621555 | ||||||||
\(696\) | 2.96748 | 0.112482 | ||||||||
\(697\) | −6.74764 | −0.255585 | ||||||||
\(698\) | 23.5187 | 0.890196 | ||||||||
\(699\) | 2.82371 | 0.106802 | ||||||||
\(700\) | −18.1903 | −0.687528 | ||||||||
\(701\) | 6.73184 | 0.254258 | 0.127129 | − | 0.991886i | \(-0.459424\pi\) | ||||
0.127129 | + | 0.991886i | \(0.459424\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −31.3424 | −1.18210 | ||||||||
\(704\) | 33.3086 | 1.25536 | ||||||||
\(705\) | −2.36658 | −0.0891307 | ||||||||
\(706\) | −34.8974 | −1.31338 | ||||||||
\(707\) | 26.7670 | 1.00668 | ||||||||
\(708\) | 20.6558 | 0.776292 | ||||||||
\(709\) | −47.6252 | −1.78860 | −0.894300 | − | 0.447467i | \(-0.852326\pi\) | ||||
−0.894300 | + | 0.447467i | \(0.852326\pi\) | |||||||
\(710\) | −14.9172 | −0.559834 | ||||||||
\(711\) | 42.4741 | 1.59290 | ||||||||
\(712\) | −15.5875 | −0.584166 | ||||||||
\(713\) | 8.06829 | 0.302160 | ||||||||
\(714\) | −13.5308 | −0.506377 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 18.3599 | 0.686141 | ||||||||
\(717\) | 6.06233 | 0.226402 | ||||||||
\(718\) | 48.1444 | 1.79673 | ||||||||
\(719\) | −5.99330 | −0.223512 | −0.111756 | − | 0.993736i | \(-0.535648\pi\) | ||||
−0.111756 | + | 0.993736i | \(0.535648\pi\) | |||||||
\(720\) | −3.11960 | −0.116261 | ||||||||
\(721\) | 18.7855 | 0.699610 | ||||||||
\(722\) | −34.2271 | −1.27380 | ||||||||
\(723\) | −6.61224 | −0.245912 | ||||||||
\(724\) | −14.5670 | −0.541380 | ||||||||
\(725\) | −6.60627 | −0.245351 | ||||||||
\(726\) | −5.57673 | −0.206972 | ||||||||
\(727\) | −24.1226 | −0.894657 | −0.447329 | − | 0.894370i | \(-0.647625\pi\) | ||||
−0.447329 | + | 0.894370i | \(0.647625\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −11.7627 | −0.435656 | ||||||||
\(730\) | −34.2640 | −1.26817 | ||||||||
\(731\) | −32.5013 | −1.20210 | ||||||||
\(732\) | −14.4916 | −0.535624 | ||||||||
\(733\) | 36.0646 | 1.33208 | 0.666038 | − | 0.745918i | \(-0.267989\pi\) | ||||
0.666038 | + | 0.745918i | \(0.267989\pi\) | |||||||
\(734\) | −77.0786 | −2.84502 | ||||||||
\(735\) | −2.24698 | −0.0828811 | ||||||||
\(736\) | −12.3153 | −0.453947 | ||||||||
\(737\) | −1.47352 | −0.0542777 | ||||||||
\(738\) | 7.70709 | 0.283702 | ||||||||
\(739\) | 27.5254 | 1.01254 | 0.506269 | − | 0.862375i | \(-0.331024\pi\) | ||||
0.506269 | + | 0.862375i | \(0.331024\pi\) | |||||||
\(740\) | −23.6015 | −0.867608 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −25.4185 | −0.933142 | ||||||||
\(743\) | −10.4692 | −0.384078 | −0.192039 | − | 0.981387i | \(-0.561510\pi\) | ||||
−0.192039 | + | 0.981387i | \(0.561510\pi\) | |||||||
\(744\) | −5.58343 | −0.204699 | ||||||||
\(745\) | −12.1468 | −0.445023 | ||||||||
\(746\) | 28.3032 | 1.03625 | ||||||||
\(747\) | −20.7918 | −0.760731 | ||||||||
\(748\) | 41.2543 | 1.50841 | ||||||||
\(749\) | −14.1371 | −0.516557 | ||||||||
\(750\) | 14.2567 | 0.520580 | ||||||||
\(751\) | 4.06770 | 0.148433 | 0.0742163 | − | 0.997242i | \(-0.476354\pi\) | ||||
0.0742163 | + | 0.997242i | \(0.476354\pi\) | |||||||
\(752\) | 2.36658 | 0.0863005 | ||||||||
\(753\) | −12.4021 | −0.451957 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −20.4174 | −0.743066 | ||||||||
\(756\) | 19.7332 | 0.717688 | ||||||||
\(757\) | 20.4336 | 0.742670 | 0.371335 | − | 0.928499i | \(-0.378900\pi\) | ||||
0.371335 | + | 0.928499i | \(0.378900\pi\) | |||||||
\(758\) | −37.1618 | −1.34978 | ||||||||
\(759\) | −2.67994 | −0.0972757 | ||||||||
\(760\) | −19.9269 | −0.722825 | ||||||||
\(761\) | −27.0237 | −0.979608 | −0.489804 | − | 0.871833i | \(-0.662932\pi\) | ||||
−0.489804 | + | 0.871833i | \(0.662932\pi\) | |||||||
\(762\) | −23.6558 | −0.856958 | ||||||||
\(763\) | 0.249964 | 0.00904929 | ||||||||
\(764\) | 56.1933 | 2.03300 | ||||||||
\(765\) | −20.6015 | −0.744848 | ||||||||
\(766\) | −16.9336 | −0.611837 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 5.80864 | 0.209601 | ||||||||
\(769\) | −37.9407 | −1.36818 | −0.684088 | − | 0.729400i | \(-0.739799\pi\) | ||||
−0.684088 | + | 0.729400i | \(0.739799\pi\) | |||||||
\(770\) | −16.9976 | −0.612551 | ||||||||
\(771\) | 10.3556 | 0.372947 | ||||||||
\(772\) | 18.4590 | 0.664355 | ||||||||
\(773\) | −16.3375 | −0.587620 | −0.293810 | − | 0.955864i | \(-0.594923\pi\) | ||||
−0.293810 | + | 0.955864i | \(0.594923\pi\) | |||||||
\(774\) | 37.1226 | 1.33434 | ||||||||
\(775\) | 12.4300 | 0.446498 | ||||||||
\(776\) | −28.1105 | −1.00911 | ||||||||
\(777\) | −6.09113 | −0.218518 | ||||||||
\(778\) | −79.8926 | −2.86429 | ||||||||
\(779\) | −7.45473 | −0.267093 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 11.7380 | 0.420017 | ||||||||
\(782\) | −22.4916 | −0.804297 | ||||||||
\(783\) | 7.16660 | 0.256114 | ||||||||
\(784\) | 2.24698 | 0.0802493 | ||||||||
\(785\) | 13.6310 | 0.486512 | ||||||||
\(786\) | 4.06100 | 0.144851 | ||||||||
\(787\) | −18.6907 | −0.666251 | −0.333126 | − | 0.942882i | \(-0.608103\pi\) | ||||
−0.333126 | + | 0.942882i | \(0.608103\pi\) | |||||||
\(788\) | −34.8049 | −1.23987 | ||||||||
\(789\) | −7.99090 | −0.284484 | ||||||||
\(790\) | −51.2301 | −1.82269 | ||||||||
\(791\) | 14.9734 | 0.532394 | ||||||||
\(792\) | −16.2107 | −0.576023 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −3.03684 | −0.107773 | ||||||||
\(795\) | 4.42758 | 0.157030 | ||||||||
\(796\) | −42.3957 | −1.50267 | ||||||||
\(797\) | 29.2519 | 1.03615 | 0.518077 | − | 0.855334i | \(-0.326648\pi\) | ||||
0.518077 | + | 0.855334i | \(0.326648\pi\) | |||||||
\(798\) | −14.9487 | −0.529178 | ||||||||
\(799\) | 15.6286 | 0.552901 | ||||||||
\(800\) | −18.9729 | −0.670792 | ||||||||
\(801\) | −17.8039 | −0.629068 | ||||||||
\(802\) | −1.30127 | −0.0459496 | ||||||||
\(803\) | 26.9614 | 0.951446 | ||||||||
\(804\) | −0.975837 | −0.0344151 | ||||||||
\(805\) | 5.59611 | 0.197237 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −0.362273 | −0.0127526 | ||||||||
\(808\) | −30.7904 | −1.08320 | ||||||||
\(809\) | −6.65087 | −0.233832 | −0.116916 | − | 0.993142i | \(-0.537301\pi\) | ||||
−0.116916 | + | 0.993142i | \(0.537301\pi\) | |||||||
\(810\) | 20.5308 | 0.721379 | ||||||||
\(811\) | 3.89200 | 0.136667 | 0.0683333 | − | 0.997663i | \(-0.478232\pi\) | ||||
0.0683333 | + | 0.997663i | \(0.478232\pi\) | |||||||
\(812\) | 14.1728 | 0.497369 | ||||||||
\(813\) | 1.10752 | 0.0388425 | ||||||||
\(814\) | 30.7536 | 1.07791 | ||||||||
\(815\) | −12.5778 | −0.440581 | ||||||||
\(816\) | −2.35690 | −0.0825079 | ||||||||
\(817\) | −35.9071 | −1.25623 | ||||||||
\(818\) | 34.0586 | 1.19083 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −5.61356 | −0.196034 | ||||||||
\(821\) | 45.9982 | 1.60535 | 0.802674 | − | 0.596418i | \(-0.203410\pi\) | ||||
0.802674 | + | 0.596418i | \(0.203410\pi\) | |||||||
\(822\) | 0.987918 | 0.0344576 | ||||||||
\(823\) | 7.95300 | 0.277224 | 0.138612 | − | 0.990347i | \(-0.455736\pi\) | ||||
0.138612 | + | 0.990347i | \(0.455736\pi\) | |||||||
\(824\) | −21.6093 | −0.752794 | ||||||||
\(825\) | −4.12870 | −0.143743 | ||||||||
\(826\) | 56.2030 | 1.95555 | ||||||||
\(827\) | 27.9648 | 0.972432 | 0.486216 | − | 0.873839i | \(-0.338377\pi\) | ||||
0.486216 | + | 0.873839i | \(0.338377\pi\) | |||||||
\(828\) | 15.5133 | 0.539126 | ||||||||
\(829\) | 27.6310 | 0.959665 | 0.479833 | − | 0.877360i | \(-0.340697\pi\) | ||||
0.479833 | + | 0.877360i | \(0.340697\pi\) | |||||||
\(830\) | 25.0780 | 0.870470 | ||||||||
\(831\) | −6.53989 | −0.226866 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 14.8388 | 0.514133 | ||||||||
\(834\) | −14.1400 | −0.489630 | ||||||||
\(835\) | 34.4698 | 1.19288 | ||||||||
\(836\) | 45.5773 | 1.57632 | ||||||||
\(837\) | −13.4843 | −0.466085 | ||||||||
\(838\) | 80.2699 | 2.77288 | ||||||||
\(839\) | 28.6848 | 0.990311 | 0.495155 | − | 0.868804i | \(-0.335111\pi\) | ||||
0.495155 | + | 0.868804i | \(0.335111\pi\) | |||||||
\(840\) | −3.87263 | −0.133618 | ||||||||
\(841\) | −23.8528 | −0.822509 | ||||||||
\(842\) | 78.7488 | 2.71386 | ||||||||
\(843\) | 3.59179 | 0.123708 | ||||||||
\(844\) | −40.3817 | −1.38999 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −17.8509 | −0.613725 | ||||||||
\(847\) | −9.16315 | −0.314849 | ||||||||
\(848\) | −4.42758 | −0.152044 | ||||||||
\(849\) | −3.65220 | −0.125343 | ||||||||
\(850\) | −34.6504 | −1.18850 | ||||||||
\(851\) | −10.1250 | −0.347080 | ||||||||
\(852\) | 7.77346 | 0.266314 | ||||||||
\(853\) | −43.2078 | −1.47941 | −0.739703 | − | 0.672934i | \(-0.765034\pi\) | ||||
−0.739703 | + | 0.672934i | \(0.765034\pi\) | |||||||
\(854\) | −39.4306 | −1.34929 | ||||||||
\(855\) | −22.7603 | −0.778386 | ||||||||
\(856\) | 16.2620 | 0.555825 | ||||||||
\(857\) | 35.1685 | 1.20133 | 0.600667 | − | 0.799499i | \(-0.294902\pi\) | ||||
0.600667 | + | 0.799499i | \(0.294902\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 27.3793 | 0.934168 | 0.467084 | − | 0.884213i | \(-0.345305\pi\) | ||||
0.467084 | + | 0.884213i | \(0.345305\pi\) | |||||||
\(860\) | −27.0388 | −0.922014 | ||||||||
\(861\) | −1.44876 | −0.0493737 | ||||||||
\(862\) | 77.0297 | 2.62364 | ||||||||
\(863\) | −41.3913 | −1.40898 | −0.704489 | − | 0.709715i | \(-0.748824\pi\) | ||||
−0.704489 | + | 0.709715i | \(0.748824\pi\) | |||||||
\(864\) | 20.5821 | 0.700217 | ||||||||
\(865\) | 27.2465 | 0.926409 | ||||||||
\(866\) | −30.8702 | −1.04901 | ||||||||
\(867\) | −6.13036 | −0.208198 | ||||||||
\(868\) | −26.6668 | −0.905130 | ||||||||
\(869\) | 40.3116 | 1.36748 | ||||||||
\(870\) | −4.08815 | −0.138601 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −0.287536 | −0.00973721 | ||||||||
\(873\) | −32.1075 | −1.08668 | ||||||||
\(874\) | −24.8485 | −0.840512 | ||||||||
\(875\) | 23.4252 | 0.791916 | ||||||||
\(876\) | 17.8552 | 0.603270 | ||||||||
\(877\) | −24.7472 | −0.835653 | −0.417826 | − | 0.908527i | \(-0.637208\pi\) | ||||
−0.417826 | + | 0.908527i | \(0.637208\pi\) | |||||||
\(878\) | −23.0097 | −0.776539 | ||||||||
\(879\) | 13.5066 | 0.455567 | ||||||||
\(880\) | −2.96077 | −0.0998076 | ||||||||
\(881\) | −28.5875 | −0.963137 | −0.481568 | − | 0.876409i | \(-0.659933\pi\) | ||||
−0.481568 | + | 0.876409i | \(0.659933\pi\) | |||||||
\(882\) | −16.9487 | −0.570692 | ||||||||
\(883\) | 9.61702 | 0.323639 | 0.161819 | − | 0.986820i | \(-0.448264\pi\) | ||||
0.161819 | + | 0.986820i | \(0.448264\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −9.78986 | −0.329082 | ||||||||
\(886\) | −27.3599 | −0.919173 | ||||||||
\(887\) | 15.9661 | 0.536091 | 0.268045 | − | 0.963406i | \(-0.413622\pi\) | ||||
0.268045 | + | 0.963406i | \(0.413622\pi\) | |||||||
\(888\) | 7.00670 | 0.235130 | ||||||||
\(889\) | −38.8689 | −1.30362 | ||||||||
\(890\) | 21.4741 | 0.719814 | ||||||||
\(891\) | −16.1551 | −0.541217 | ||||||||
\(892\) | −22.3642 | −0.748809 | ||||||||
\(893\) | 17.2664 | 0.577797 | ||||||||
\(894\) | 10.4819 | 0.350566 | ||||||||
\(895\) | −8.70171 | −0.290866 | ||||||||
\(896\) | 33.3196 | 1.11313 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 28.9976 | 0.967663 | ||||||||
\(899\) | −9.68473 | −0.323004 | ||||||||
\(900\) | 23.8998 | 0.796659 | ||||||||
\(901\) | −29.2392 | −0.974099 | ||||||||
\(902\) | 7.31468 | 0.243552 | ||||||||
\(903\) | −6.97823 | −0.232221 | ||||||||
\(904\) | −17.2241 | −0.572867 | ||||||||
\(905\) | 6.90408 | 0.229500 | ||||||||
\(906\) | 17.6189 | 0.585350 | ||||||||
\(907\) | −28.8364 | −0.957496 | −0.478748 | − | 0.877952i | \(-0.658909\pi\) | ||||
−0.478748 | + | 0.877952i | \(0.658909\pi\) | |||||||
\(908\) | −26.4480 | −0.877709 | ||||||||
\(909\) | −35.1685 | −1.16647 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 38.5633 | 1.27766 | 0.638830 | − | 0.769348i | \(-0.279419\pi\) | ||||
0.638830 | + | 0.769348i | \(0.279419\pi\) | |||||||
\(912\) | −2.60388 | −0.0862229 | ||||||||
\(913\) | −19.7332 | −0.653073 | ||||||||
\(914\) | −10.4644 | −0.346132 | ||||||||
\(915\) | 6.86831 | 0.227059 | ||||||||
\(916\) | −41.7294 | −1.37878 | ||||||||
\(917\) | 6.67264 | 0.220350 | ||||||||
\(918\) | 37.5894 | 1.24064 | ||||||||
\(919\) | 8.87502 | 0.292760 | 0.146380 | − | 0.989228i | \(-0.453238\pi\) | ||||
0.146380 | + | 0.989228i | \(0.453238\pi\) | |||||||
\(920\) | −6.43727 | −0.212231 | ||||||||
\(921\) | 7.81030 | 0.257358 | ||||||||
\(922\) | 70.8708 | 2.33401 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 8.85756 | 0.291392 | ||||||||
\(925\) | −15.5985 | −0.512875 | ||||||||
\(926\) | −39.6601 | −1.30331 | ||||||||
\(927\) | −24.6819 | −0.810659 | ||||||||
\(928\) | 14.7826 | 0.485261 | ||||||||
\(929\) | 24.2295 | 0.794945 | 0.397472 | − | 0.917614i | \(-0.369887\pi\) | ||||
0.397472 | + | 0.917614i | \(0.369887\pi\) | |||||||
\(930\) | 7.69202 | 0.252231 | ||||||||
\(931\) | 16.3937 | 0.537283 | ||||||||
\(932\) | −15.5133 | −0.508156 | ||||||||
\(933\) | 16.5211 | 0.540877 | ||||||||
\(934\) | 72.2911 | 2.36544 | ||||||||
\(935\) | −19.5526 | −0.639437 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 17.2644 | 0.564005 | 0.282002 | − | 0.959414i | \(-0.409001\pi\) | ||||
0.282002 | + | 0.959414i | \(0.409001\pi\) | |||||||
\(938\) | −2.65519 | −0.0866949 | ||||||||
\(939\) | 4.15047 | 0.135446 | ||||||||
\(940\) | 13.0019 | 0.424076 | ||||||||
\(941\) | 4.34050 | 0.141496 | 0.0707482 | − | 0.997494i | \(-0.477461\pi\) | ||||
0.0707482 | + | 0.997494i | \(0.477461\pi\) | |||||||
\(942\) | −11.7627 | −0.383250 | ||||||||
\(943\) | −2.40821 | −0.0784220 | ||||||||
\(944\) | 9.78986 | 0.318633 | ||||||||
\(945\) | −9.35258 | −0.304240 | ||||||||
\(946\) | 35.2325 | 1.14551 | ||||||||
\(947\) | −45.0146 | −1.46278 | −0.731389 | − | 0.681961i | \(-0.761128\pi\) | ||||
−0.731389 | + | 0.681961i | \(0.761128\pi\) | |||||||
\(948\) | 26.6963 | 0.867057 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | −38.2814 | −1.24201 | ||||||||
\(951\) | −16.6655 | −0.540415 | ||||||||
\(952\) | 25.5743 | 0.828869 | ||||||||
\(953\) | −46.8859 | −1.51878 | −0.759391 | − | 0.650634i | \(-0.774503\pi\) | ||||
−0.759391 | + | 0.650634i | \(0.774503\pi\) | |||||||
\(954\) | 33.3967 | 1.08126 | ||||||||
\(955\) | −26.6329 | −0.861822 | ||||||||
\(956\) | −33.3062 | −1.07720 | ||||||||
\(957\) | 3.21685 | 0.103986 | ||||||||
\(958\) | 78.4191 | 2.53361 | ||||||||
\(959\) | 1.62325 | 0.0524176 | ||||||||
\(960\) | −10.4547 | −0.337425 | ||||||||
\(961\) | −12.7778 | −0.412186 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 18.5743 | 0.598550 | ||||||||
\(964\) | 36.3274 | 1.17003 | ||||||||
\(965\) | −8.74871 | −0.281631 | ||||||||
\(966\) | −4.82908 | −0.155373 | ||||||||
\(967\) | 6.29457 | 0.202420 | 0.101210 | − | 0.994865i | \(-0.467729\pi\) | ||||
0.101210 | + | 0.994865i | \(0.467729\pi\) | |||||||
\(968\) | 10.5405 | 0.338784 | ||||||||
\(969\) | −17.1957 | −0.552404 | ||||||||
\(970\) | 38.7265 | 1.24343 | ||||||||
\(971\) | −41.8068 | −1.34165 | −0.670823 | − | 0.741618i | \(-0.734059\pi\) | ||||
−0.670823 | + | 0.741618i | \(0.734059\pi\) | |||||||
\(972\) | −39.5918 | −1.26991 | ||||||||
\(973\) | −23.2336 | −0.744834 | ||||||||
\(974\) | −94.0025 | −3.01203 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −6.86831 | −0.219849 | ||||||||
\(977\) | 23.7530 | 0.759926 | 0.379963 | − | 0.925002i | \(-0.375937\pi\) | ||||
0.379963 | + | 0.925002i | \(0.375937\pi\) | |||||||
\(978\) | 10.8538 | 0.347067 | ||||||||
\(979\) | −16.8974 | −0.540043 | ||||||||
\(980\) | 12.3448 | 0.394341 | ||||||||
\(981\) | −0.328421 | −0.0104857 | ||||||||
\(982\) | −49.0863 | −1.56641 | ||||||||
\(983\) | −55.7251 | −1.77736 | −0.888678 | − | 0.458532i | \(-0.848375\pi\) | ||||
−0.888678 | + | 0.458532i | \(0.848375\pi\) | |||||||
\(984\) | 1.66653 | 0.0531270 | ||||||||
\(985\) | 16.4959 | 0.525602 | ||||||||
\(986\) | 26.9976 | 0.859779 | ||||||||
\(987\) | 3.35557 | 0.106809 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −11.5996 | −0.368845 | ||||||||
\(990\) | 22.3327 | 0.709781 | ||||||||
\(991\) | −35.5512 | −1.12932 | −0.564661 | − | 0.825323i | \(-0.690993\pi\) | ||||
−0.564661 | + | 0.825323i | \(0.690993\pi\) | |||||||
\(992\) | −27.8140 | −0.883096 | ||||||||
\(993\) | 8.72215 | 0.276789 | ||||||||
\(994\) | 21.1511 | 0.670871 | ||||||||
\(995\) | 20.0935 | 0.637007 | ||||||||
\(996\) | −13.0683 | −0.414085 | ||||||||
\(997\) | 6.61058 | 0.209359 | 0.104680 | − | 0.994506i | \(-0.466618\pi\) | ||||
0.104680 | + | 0.994506i | \(0.466618\pi\) | |||||||
\(998\) | −52.9101 | −1.67484 | ||||||||
\(999\) | 16.9215 | 0.535374 |
(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 | 169.2.a.b.1.1 | ✓ | 3 | |
3.2 | odd | 2 | 1521.2.a.r.1.3 | 3 | |||
4.3 | odd | 2 | 2704.2.a.z.1.2 | 3 | |||
5.4 | even | 2 | 4225.2.a.bg.1.3 | 3 | |||
7.6 | odd | 2 | 8281.2.a.bf.1.1 | 3 | |||
13.2 | odd | 12 | 169.2.e.b.147.1 | 12 | |||
13.3 | even | 3 | 169.2.c.c.22.3 | 6 | |||
13.4 | even | 6 | 169.2.c.b.146.1 | 6 | |||
13.5 | odd | 4 | 169.2.b.b.168.6 | 6 | |||
13.6 | odd | 12 | 169.2.e.b.23.6 | 12 | |||
13.7 | odd | 12 | 169.2.e.b.23.1 | 12 | |||
13.8 | odd | 4 | 169.2.b.b.168.1 | 6 | |||
13.9 | even | 3 | 169.2.c.c.146.3 | 6 | |||
13.10 | even | 6 | 169.2.c.b.22.1 | 6 | |||
13.11 | odd | 12 | 169.2.e.b.147.6 | 12 | |||
13.12 | even | 2 | 169.2.a.c.1.3 | yes | 3 | ||
39.5 | even | 4 | 1521.2.b.l.1351.1 | 6 | |||
39.8 | even | 4 | 1521.2.b.l.1351.6 | 6 | |||
39.38 | odd | 2 | 1521.2.a.o.1.1 | 3 | |||
52.31 | even | 4 | 2704.2.f.o.337.4 | 6 | |||
52.47 | even | 4 | 2704.2.f.o.337.3 | 6 | |||
52.51 | odd | 2 | 2704.2.a.ba.1.2 | 3 | |||
65.64 | even | 2 | 4225.2.a.bb.1.1 | 3 | |||
91.90 | odd | 2 | 8281.2.a.bj.1.3 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
169.2.a.b.1.1 | ✓ | 3 | 1.1 | even | 1 | trivial | |
169.2.a.c.1.3 | yes | 3 | 13.12 | even | 2 | ||
169.2.b.b.168.1 | 6 | 13.8 | odd | 4 | |||
169.2.b.b.168.6 | 6 | 13.5 | odd | 4 | |||
169.2.c.b.22.1 | 6 | 13.10 | even | 6 | |||
169.2.c.b.146.1 | 6 | 13.4 | even | 6 | |||
169.2.c.c.22.3 | 6 | 13.3 | even | 3 | |||
169.2.c.c.146.3 | 6 | 13.9 | even | 3 | |||
169.2.e.b.23.1 | 12 | 13.7 | odd | 12 | |||
169.2.e.b.23.6 | 12 | 13.6 | odd | 12 | |||
169.2.e.b.147.1 | 12 | 13.2 | odd | 12 | |||
169.2.e.b.147.6 | 12 | 13.11 | odd | 12 | |||
1521.2.a.o.1.1 | 3 | 39.38 | odd | 2 | |||
1521.2.a.r.1.3 | 3 | 3.2 | odd | 2 | |||
1521.2.b.l.1351.1 | 6 | 39.5 | even | 4 | |||
1521.2.b.l.1351.6 | 6 | 39.8 | even | 4 | |||
2704.2.a.z.1.2 | 3 | 4.3 | odd | 2 | |||
2704.2.a.ba.1.2 | 3 | 52.51 | odd | 2 | |||
2704.2.f.o.337.3 | 6 | 52.47 | even | 4 | |||
2704.2.f.o.337.4 | 6 | 52.31 | even | 4 | |||
4225.2.a.bb.1.1 | 3 | 65.64 | even | 2 | |||
4225.2.a.bg.1.3 | 3 | 5.4 | even | 2 | |||
8281.2.a.bf.1.1 | 3 | 7.6 | odd | 2 | |||
8281.2.a.bj.1.3 | 3 | 91.90 | odd | 2 |