Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1859,2,Mod(1,1859)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1859, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1859.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1859 = 11 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1859.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: | \(14.8441897358\) |
Analytic rank: | \(1\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.361.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 6x + 7 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 143) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(2.28514\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1859.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.50702 | −1.77273 | −0.886365 | − | 0.462987i | \(-0.846778\pi\) | ||||
−0.886365 | + | 0.462987i | \(0.846778\pi\) | |||||||
\(3\) | 2.28514 | 1.31933 | 0.659664 | − | 0.751561i | \(-0.270699\pi\) | ||||
0.659664 | + | 0.751561i | \(0.270699\pi\) | |||||||
\(4\) | 4.28514 | 2.14257 | ||||||||
\(5\) | 1.22188 | 0.546440 | 0.273220 | − | 0.961952i | \(-0.411911\pi\) | ||||
0.273220 | + | 0.961952i | \(0.411911\pi\) | |||||||
\(6\) | −5.72889 | −2.33881 | ||||||||
\(7\) | −0.778124 | −0.294103 | −0.147052 | − | 0.989129i | \(-0.546978\pi\) | ||||
−0.147052 | + | 0.989129i | \(0.546978\pi\) | |||||||
\(8\) | −5.72889 | −2.02547 | ||||||||
\(9\) | 2.22188 | 0.740625 | ||||||||
\(10\) | −3.06327 | −0.968690 | ||||||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | 9.79216 | 2.82675 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 1.95077 | 0.521365 | ||||||||
\(15\) | 2.79216 | 0.720933 | ||||||||
\(16\) | 5.79216 | 1.44804 | ||||||||
\(17\) | −4.28514 | −1.03930 | −0.519650 | − | 0.854379i | \(-0.673938\pi\) | ||||
−0.519650 | + | 0.854379i | \(0.673938\pi\) | |||||||
\(18\) | −5.57028 | −1.31293 | ||||||||
\(19\) | −8.29918 | −1.90396 | −0.951981 | − | 0.306156i | \(-0.900957\pi\) | ||||
−0.951981 | + | 0.306156i | \(0.900957\pi\) | |||||||
\(20\) | 5.23591 | 1.17079 | ||||||||
\(21\) | −1.77812 | −0.388018 | ||||||||
\(22\) | 2.50702 | 0.534498 | ||||||||
\(23\) | −2.72889 | −0.569014 | −0.284507 | − | 0.958674i | \(-0.591830\pi\) | ||||
−0.284507 | + | 0.958674i | \(0.591830\pi\) | |||||||
\(24\) | −13.0913 | −2.67226 | ||||||||
\(25\) | −3.50702 | −0.701404 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.77812 | −0.342200 | ||||||||
\(28\) | −3.33437 | −0.630137 | ||||||||
\(29\) | 7.36245 | 1.36717 | 0.683586 | − | 0.729870i | \(-0.260419\pi\) | ||||
0.683586 | + | 0.729870i | \(0.260419\pi\) | |||||||
\(30\) | −7.00000 | −1.27802 | ||||||||
\(31\) | 1.44375 | 0.259306 | 0.129653 | − | 0.991559i | \(-0.458614\pi\) | ||||
0.129653 | + | 0.991559i | \(0.458614\pi\) | |||||||
\(32\) | −3.06327 | −0.541514 | ||||||||
\(33\) | −2.28514 | −0.397792 | ||||||||
\(34\) | 10.7429 | 1.84240 | ||||||||
\(35\) | −0.950771 | −0.160710 | ||||||||
\(36\) | 9.52106 | 1.58684 | ||||||||
\(37\) | 0.792161 | 0.130230 | 0.0651152 | − | 0.997878i | \(-0.479258\pi\) | ||||
0.0651152 | + | 0.997878i | \(0.479258\pi\) | |||||||
\(38\) | 20.8062 | 3.37521 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −7.00000 | −1.10680 | ||||||||
\(41\) | −9.74293 | −1.52159 | −0.760795 | − | 0.648992i | \(-0.775191\pi\) | ||||
−0.760795 | + | 0.648992i | \(0.775191\pi\) | |||||||
\(42\) | 4.45779 | 0.687852 | ||||||||
\(43\) | −9.67967 | −1.47614 | −0.738068 | − | 0.674727i | \(-0.764261\pi\) | ||||
−0.738068 | + | 0.674727i | \(0.764261\pi\) | |||||||
\(44\) | −4.28514 | −0.646010 | ||||||||
\(45\) | 2.71486 | 0.404707 | ||||||||
\(46\) | 6.84139 | 1.00871 | ||||||||
\(47\) | 3.38049 | 0.493095 | 0.246547 | − | 0.969131i | \(-0.420704\pi\) | ||||
0.246547 | + | 0.969131i | \(0.420704\pi\) | |||||||
\(48\) | 13.2359 | 1.91044 | ||||||||
\(49\) | −6.39452 | −0.913503 | ||||||||
\(50\) | 8.79216 | 1.24340 | ||||||||
\(51\) | −9.79216 | −1.37118 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 1.79216 | 0.246172 | 0.123086 | − | 0.992396i | \(-0.460721\pi\) | ||||
0.123086 | + | 0.992396i | \(0.460721\pi\) | |||||||
\(54\) | 4.45779 | 0.606628 | ||||||||
\(55\) | −1.22188 | −0.164758 | ||||||||
\(56\) | 4.45779 | 0.595697 | ||||||||
\(57\) | −18.9648 | −2.51195 | ||||||||
\(58\) | −18.4578 | −2.42363 | ||||||||
\(59\) | −5.20784 | −0.678003 | −0.339001 | − | 0.940786i | \(-0.610089\pi\) | ||||
−0.339001 | + | 0.940786i | \(0.610089\pi\) | |||||||
\(60\) | 11.9648 | 1.54465 | ||||||||
\(61\) | −14.5211 | −1.85923 | −0.929615 | − | 0.368531i | \(-0.879861\pi\) | ||||
−0.929615 | + | 0.368531i | \(0.879861\pi\) | |||||||
\(62\) | −3.61951 | −0.459679 | ||||||||
\(63\) | −1.72889 | −0.217820 | ||||||||
\(64\) | −3.90466 | −0.488082 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 5.72889 | 0.705178 | ||||||||
\(67\) | −6.06327 | −0.740746 | −0.370373 | − | 0.928883i | \(-0.620770\pi\) | ||||
−0.370373 | + | 0.928883i | \(0.620770\pi\) | |||||||
\(68\) | −18.3624 | −2.22677 | ||||||||
\(69\) | −6.23591 | −0.750716 | ||||||||
\(70\) | 2.38360 | 0.284895 | ||||||||
\(71\) | 6.50702 | 0.772241 | 0.386121 | − | 0.922448i | \(-0.373815\pi\) | ||||
0.386121 | + | 0.922448i | \(0.373815\pi\) | |||||||
\(72\) | −12.7289 | −1.50011 | ||||||||
\(73\) | 2.00000 | 0.234082 | 0.117041 | − | 0.993127i | \(-0.462659\pi\) | ||||
0.117041 | + | 0.993127i | \(0.462659\pi\) | |||||||
\(74\) | −1.98596 | −0.230863 | ||||||||
\(75\) | −8.01404 | −0.925381 | ||||||||
\(76\) | −35.5632 | −4.07938 | ||||||||
\(77\) | 0.778124 | 0.0886754 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 13.5843 | 1.52836 | 0.764178 | − | 0.645006i | \(-0.223145\pi\) | ||||
0.764178 | + | 0.645006i | \(0.223145\pi\) | |||||||
\(80\) | 7.07730 | 0.791267 | ||||||||
\(81\) | −10.7289 | −1.19210 | ||||||||
\(82\) | 24.4257 | 2.69737 | ||||||||
\(83\) | 13.3624 | 1.46672 | 0.733360 | − | 0.679841i | \(-0.237951\pi\) | ||||
0.733360 | + | 0.679841i | \(0.237951\pi\) | |||||||
\(84\) | −7.61951 | −0.831357 | ||||||||
\(85\) | −5.23591 | −0.567915 | ||||||||
\(86\) | 24.2671 | 2.61679 | ||||||||
\(87\) | 16.8242 | 1.80375 | ||||||||
\(88\) | 5.72889 | 0.610702 | ||||||||
\(89\) | 4.77812 | 0.506480 | 0.253240 | − | 0.967403i | \(-0.418504\pi\) | ||||
0.253240 | + | 0.967403i | \(0.418504\pi\) | |||||||
\(90\) | −6.80620 | −0.717436 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −11.6937 | −1.21915 | ||||||||
\(93\) | 3.29918 | 0.342109 | ||||||||
\(94\) | −8.47494 | −0.874123 | ||||||||
\(95\) | −10.1406 | −1.04040 | ||||||||
\(96\) | −7.00000 | −0.714435 | ||||||||
\(97\) | 4.14057 | 0.420411 | 0.210206 | − | 0.977657i | \(-0.432587\pi\) | ||||
0.210206 | + | 0.977657i | \(0.432587\pi\) | |||||||
\(98\) | 16.0312 | 1.61939 | ||||||||
\(99\) | −2.22188 | −0.223307 | ||||||||
\(100\) | −15.0281 | −1.50281 | ||||||||
\(101\) | 4.82424 | 0.480030 | 0.240015 | − | 0.970769i | \(-0.422848\pi\) | ||||
0.240015 | + | 0.970769i | \(0.422848\pi\) | |||||||
\(102\) | 24.5491 | 2.43073 | ||||||||
\(103\) | 9.76008 | 0.961690 | 0.480845 | − | 0.876806i | \(-0.340330\pi\) | ||||
0.480845 | + | 0.876806i | \(0.340330\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −2.17265 | −0.212029 | ||||||||
\(106\) | −4.49298 | −0.436397 | ||||||||
\(107\) | 2.36245 | 0.228386 | 0.114193 | − | 0.993459i | \(-0.463572\pi\) | ||||
0.114193 | + | 0.993459i | \(0.463572\pi\) | |||||||
\(108\) | −7.61951 | −0.733188 | ||||||||
\(109\) | 2.86946 | 0.274845 | 0.137422 | − | 0.990513i | \(-0.456118\pi\) | ||||
0.137422 | + | 0.990513i | \(0.456118\pi\) | |||||||
\(110\) | 3.06327 | 0.292071 | ||||||||
\(111\) | 1.81020 | 0.171817 | ||||||||
\(112\) | −4.50702 | −0.425873 | ||||||||
\(113\) | −5.60236 | −0.527026 | −0.263513 | − | 0.964656i | \(-0.584881\pi\) | ||||
−0.263513 | + | 0.964656i | \(0.584881\pi\) | |||||||
\(114\) | 47.5451 | 4.45301 | ||||||||
\(115\) | −3.33437 | −0.310932 | ||||||||
\(116\) | 31.5491 | 2.92926 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 13.0561 | 1.20192 | ||||||||
\(119\) | 3.33437 | 0.305661 | ||||||||
\(120\) | −15.9960 | −1.46023 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 36.4046 | 3.29591 | ||||||||
\(123\) | −22.2640 | −2.00748 | ||||||||
\(124\) | 6.18668 | 0.555581 | ||||||||
\(125\) | −10.3945 | −0.929714 | ||||||||
\(126\) | 4.33437 | 0.386137 | ||||||||
\(127\) | 7.23591 | 0.642083 | 0.321042 | − | 0.947065i | \(-0.395967\pi\) | ||||
0.321042 | + | 0.947065i | \(0.395967\pi\) | |||||||
\(128\) | 15.9156 | 1.40675 | ||||||||
\(129\) | −22.1194 | −1.94751 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −10.3484 | −0.904145 | −0.452072 | − | 0.891981i | \(-0.649315\pi\) | ||||
−0.452072 | + | 0.891981i | \(0.649315\pi\) | |||||||
\(132\) | −9.79216 | −0.852298 | ||||||||
\(133\) | 6.45779 | 0.559961 | ||||||||
\(134\) | 15.2007 | 1.31314 | ||||||||
\(135\) | −2.17265 | −0.186992 | ||||||||
\(136\) | 24.5491 | 2.10507 | ||||||||
\(137\) | 4.93673 | 0.421774 | 0.210887 | − | 0.977510i | \(-0.432365\pi\) | ||||
0.210887 | + | 0.977510i | \(0.432365\pi\) | |||||||
\(138\) | 15.6336 | 1.33082 | ||||||||
\(139\) | 16.4718 | 1.39712 | 0.698561 | − | 0.715550i | \(-0.253824\pi\) | ||||
0.698561 | + | 0.715550i | \(0.253824\pi\) | |||||||
\(140\) | −4.07419 | −0.344332 | ||||||||
\(141\) | 7.72489 | 0.650553 | ||||||||
\(142\) | −16.3132 | −1.36897 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 12.8695 | 1.07246 | ||||||||
\(145\) | 8.99600 | 0.747077 | ||||||||
\(146\) | −5.01404 | −0.414965 | ||||||||
\(147\) | −14.6124 | −1.20521 | ||||||||
\(148\) | 3.39452 | 0.279028 | ||||||||
\(149\) | 1.90466 | 0.156036 | 0.0780178 | − | 0.996952i | \(-0.475141\pi\) | ||||
0.0780178 | + | 0.996952i | \(0.475141\pi\) | |||||||
\(150\) | 20.0913 | 1.64045 | ||||||||
\(151\) | −18.4086 | −1.49807 | −0.749034 | − | 0.662532i | \(-0.769482\pi\) | ||||
−0.749034 | + | 0.662532i | \(0.769482\pi\) | |||||||
\(152\) | 47.5451 | 3.85642 | ||||||||
\(153\) | −9.52106 | −0.769732 | ||||||||
\(154\) | −1.95077 | −0.157198 | ||||||||
\(155\) | 1.76409 | 0.141695 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −12.1054 | −0.966114 | −0.483057 | − | 0.875589i | \(-0.660474\pi\) | ||||
−0.483057 | + | 0.875589i | \(0.660474\pi\) | |||||||
\(158\) | −34.0561 | −2.70936 | ||||||||
\(159\) | 4.09534 | 0.324782 | ||||||||
\(160\) | −3.74293 | −0.295905 | ||||||||
\(161\) | 2.12342 | 0.167349 | ||||||||
\(162\) | 26.8975 | 2.11327 | ||||||||
\(163\) | −1.91869 | −0.150284 | −0.0751418 | − | 0.997173i | \(-0.523941\pi\) | ||||
−0.0751418 | + | 0.997173i | \(0.523941\pi\) | |||||||
\(164\) | −41.7499 | −3.26012 | ||||||||
\(165\) | −2.79216 | −0.217369 | ||||||||
\(166\) | −33.4999 | −2.60010 | ||||||||
\(167\) | 7.06015 | 0.546331 | 0.273165 | − | 0.961967i | \(-0.411929\pi\) | ||||
0.273165 | + | 0.961967i | \(0.411929\pi\) | |||||||
\(168\) | 10.1867 | 0.785920 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 13.1265 | 1.00676 | ||||||||
\(171\) | −18.4397 | −1.41012 | ||||||||
\(172\) | −41.4787 | −3.16272 | ||||||||
\(173\) | 1.64759 | 0.125264 | 0.0626319 | − | 0.998037i | \(-0.480051\pi\) | ||||
0.0626319 | + | 0.998037i | \(0.480051\pi\) | |||||||
\(174\) | −42.1787 | −3.19756 | ||||||||
\(175\) | 2.72889 | 0.206285 | ||||||||
\(176\) | −5.79216 | −0.436601 | ||||||||
\(177\) | −11.9007 | −0.894508 | ||||||||
\(178\) | −11.9788 | −0.897852 | ||||||||
\(179\) | 7.33437 | 0.548197 | 0.274098 | − | 0.961702i | \(-0.411621\pi\) | ||||
0.274098 | + | 0.961702i | \(0.411621\pi\) | |||||||
\(180\) | 11.6336 | 0.867114 | ||||||||
\(181\) | 11.7750 | 0.875230 | 0.437615 | − | 0.899163i | \(-0.355823\pi\) | ||||
0.437615 | + | 0.899163i | \(0.355823\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −33.1827 | −2.45293 | ||||||||
\(184\) | 15.6336 | 1.15252 | ||||||||
\(185\) | 0.967923 | 0.0711631 | ||||||||
\(186\) | −8.27111 | −0.606467 | ||||||||
\(187\) | 4.28514 | 0.313361 | ||||||||
\(188\) | 14.4859 | 1.05649 | ||||||||
\(189\) | 1.38360 | 0.100642 | ||||||||
\(190\) | 25.4226 | 1.84435 | ||||||||
\(191\) | 14.7429 | 1.06676 | 0.533381 | − | 0.845875i | \(-0.320921\pi\) | ||||
0.533381 | + | 0.845875i | \(0.320921\pi\) | |||||||
\(192\) | −8.92270 | −0.643940 | ||||||||
\(193\) | 8.90154 | 0.640747 | 0.320374 | − | 0.947291i | \(-0.396192\pi\) | ||||
0.320374 | + | 0.947291i | \(0.396192\pi\) | |||||||
\(194\) | −10.3805 | −0.745275 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −27.4014 | −1.95725 | ||||||||
\(197\) | 6.11250 | 0.435497 | 0.217749 | − | 0.976005i | \(-0.430129\pi\) | ||||
0.217749 | + | 0.976005i | \(0.430129\pi\) | |||||||
\(198\) | 5.57028 | 0.395863 | ||||||||
\(199\) | 9.34529 | 0.662470 | 0.331235 | − | 0.943548i | \(-0.392535\pi\) | ||||
0.331235 | + | 0.943548i | \(0.392535\pi\) | |||||||
\(200\) | 20.0913 | 1.42067 | ||||||||
\(201\) | −13.8554 | −0.977287 | ||||||||
\(202\) | −12.0945 | −0.850963 | ||||||||
\(203\) | −5.72889 | −0.402090 | ||||||||
\(204\) | −41.9608 | −2.93784 | ||||||||
\(205\) | −11.9047 | −0.831457 | ||||||||
\(206\) | −24.4687 | −1.70482 | ||||||||
\(207\) | −6.06327 | −0.421426 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 8.29918 | 0.574066 | ||||||||
\(210\) | 5.44687 | 0.375870 | ||||||||
\(211\) | −5.18668 | −0.357066 | −0.178533 | − | 0.983934i | \(-0.557135\pi\) | ||||
−0.178533 | + | 0.983934i | \(0.557135\pi\) | |||||||
\(212\) | 7.67967 | 0.527442 | ||||||||
\(213\) | 14.8695 | 1.01884 | ||||||||
\(214\) | −5.92270 | −0.404867 | ||||||||
\(215\) | −11.8274 | −0.806619 | ||||||||
\(216\) | 10.1867 | 0.693116 | ||||||||
\(217\) | −1.12342 | −0.0762626 | ||||||||
\(218\) | −7.19380 | −0.487226 | ||||||||
\(219\) | 4.57028 | 0.308831 | ||||||||
\(220\) | −5.23591 | −0.353005 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −4.53821 | −0.304585 | ||||||||
\(223\) | −16.8343 | −1.12731 | −0.563653 | − | 0.826012i | \(-0.690605\pi\) | ||||
−0.563653 | + | 0.826012i | \(0.690605\pi\) | |||||||
\(224\) | 2.38360 | 0.159261 | ||||||||
\(225\) | −7.79216 | −0.519477 | ||||||||
\(226\) | 14.0452 | 0.934275 | ||||||||
\(227\) | 17.6164 | 1.16924 | 0.584621 | − | 0.811307i | \(-0.301243\pi\) | ||||
0.584621 | + | 0.811307i | \(0.301243\pi\) | |||||||
\(228\) | −81.2669 | −5.38203 | ||||||||
\(229\) | −26.8554 | −1.77466 | −0.887328 | − | 0.461138i | \(-0.847441\pi\) | ||||
−0.887328 | + | 0.461138i | \(0.847441\pi\) | |||||||
\(230\) | 8.35933 | 0.551198 | ||||||||
\(231\) | 1.77812 | 0.116992 | ||||||||
\(232\) | −42.1787 | −2.76917 | ||||||||
\(233\) | −27.1406 | −1.77804 | −0.889019 | − | 0.457870i | \(-0.848612\pi\) | ||||
−0.889019 | + | 0.457870i | \(0.848612\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 4.13054 | 0.269446 | ||||||||
\(236\) | −22.3163 | −1.45267 | ||||||||
\(237\) | 31.0421 | 2.01640 | ||||||||
\(238\) | −8.35933 | −0.541855 | ||||||||
\(239\) | −0.746047 | −0.0482577 | −0.0241289 | − | 0.999709i | \(-0.507681\pi\) | ||||
−0.0241289 | + | 0.999709i | \(0.507681\pi\) | |||||||
\(240\) | 16.1726 | 1.04394 | ||||||||
\(241\) | −16.1726 | −1.04177 | −0.520886 | − | 0.853626i | \(-0.674398\pi\) | ||||
−0.520886 | + | 0.853626i | \(0.674398\pi\) | |||||||
\(242\) | −2.50702 | −0.161157 | ||||||||
\(243\) | −19.1827 | −1.23057 | ||||||||
\(244\) | −62.2248 | −3.98353 | ||||||||
\(245\) | −7.81332 | −0.499174 | ||||||||
\(246\) | 55.8162 | 3.55871 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −8.27111 | −0.525216 | ||||||||
\(249\) | 30.5351 | 1.93508 | ||||||||
\(250\) | 26.0593 | 1.64813 | ||||||||
\(251\) | −11.0281 | −0.696086 | −0.348043 | − | 0.937479i | \(-0.613154\pi\) | ||||
−0.348043 | + | 0.937479i | \(0.613154\pi\) | |||||||
\(252\) | −7.40856 | −0.466695 | ||||||||
\(253\) | 2.72889 | 0.171564 | ||||||||
\(254\) | −18.1406 | −1.13824 | ||||||||
\(255\) | −11.9648 | −0.749265 | ||||||||
\(256\) | −32.0913 | −2.00571 | ||||||||
\(257\) | 18.8523 | 1.17597 | 0.587987 | − | 0.808870i | \(-0.299920\pi\) | ||||
0.587987 | + | 0.808870i | \(0.299920\pi\) | |||||||
\(258\) | 55.4538 | 3.45240 | ||||||||
\(259\) | −0.616399 | −0.0383012 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 16.3584 | 1.01256 | ||||||||
\(262\) | 25.9437 | 1.60280 | ||||||||
\(263\) | −15.5522 | −0.958993 | −0.479496 | − | 0.877544i | \(-0.659181\pi\) | ||||
−0.479496 | + | 0.877544i | \(0.659181\pi\) | |||||||
\(264\) | 13.0913 | 0.805716 | ||||||||
\(265\) | 2.18980 | 0.134518 | ||||||||
\(266\) | −16.1898 | −0.992660 | ||||||||
\(267\) | 10.9187 | 0.668213 | ||||||||
\(268\) | −25.9820 | −1.58710 | ||||||||
\(269\) | −5.22188 | −0.318383 | −0.159192 | − | 0.987248i | \(-0.550889\pi\) | ||||
−0.159192 | + | 0.987248i | \(0.550889\pi\) | |||||||
\(270\) | 5.44687 | 0.331486 | ||||||||
\(271\) | −25.9367 | −1.57554 | −0.787772 | − | 0.615967i | \(-0.788766\pi\) | ||||
−0.787772 | + | 0.615967i | \(0.788766\pi\) | |||||||
\(272\) | −24.8202 | −1.50495 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −12.3765 | −0.747691 | ||||||||
\(275\) | 3.50702 | 0.211481 | ||||||||
\(276\) | −26.7218 | −1.60846 | ||||||||
\(277\) | −17.7741 | −1.06794 | −0.533972 | − | 0.845502i | \(-0.679301\pi\) | ||||
−0.533972 | + | 0.845502i | \(0.679301\pi\) | |||||||
\(278\) | −41.2952 | −2.47672 | ||||||||
\(279\) | 3.20784 | 0.192048 | ||||||||
\(280\) | 5.44687 | 0.325513 | ||||||||
\(281\) | −7.41168 | −0.442143 | −0.221072 | − | 0.975258i | \(-0.570955\pi\) | ||||
−0.221072 | + | 0.975258i | \(0.570955\pi\) | |||||||
\(282\) | −19.3664 | −1.15326 | ||||||||
\(283\) | 9.31722 | 0.553851 | 0.276926 | − | 0.960891i | \(-0.410684\pi\) | ||||
0.276926 | + | 0.960891i | \(0.410684\pi\) | |||||||
\(284\) | 27.8835 | 1.65458 | ||||||||
\(285\) | −23.1726 | −1.37263 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 7.58121 | 0.447505 | ||||||||
\(288\) | −6.80620 | −0.401059 | ||||||||
\(289\) | 1.36245 | 0.0801439 | ||||||||
\(290\) | −22.5531 | −1.32437 | ||||||||
\(291\) | 9.46179 | 0.554660 | ||||||||
\(292\) | 8.57028 | 0.501538 | ||||||||
\(293\) | 28.7530 | 1.67977 | 0.839883 | − | 0.542767i | \(-0.182623\pi\) | ||||
0.839883 | + | 0.542767i | \(0.182623\pi\) | |||||||
\(294\) | 36.6336 | 2.13651 | ||||||||
\(295\) | −6.36333 | −0.370488 | ||||||||
\(296\) | −4.53821 | −0.263778 | ||||||||
\(297\) | 1.77812 | 0.103177 | ||||||||
\(298\) | −4.77501 | −0.276609 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −34.3413 | −1.98270 | ||||||||
\(301\) | 7.53198 | 0.434136 | ||||||||
\(302\) | 46.1506 | 2.65567 | ||||||||
\(303\) | 11.0241 | 0.633316 | ||||||||
\(304\) | −48.0702 | −2.75701 | ||||||||
\(305\) | −17.7429 | −1.01596 | ||||||||
\(306\) | 23.8695 | 1.36453 | ||||||||
\(307\) | 0.792161 | 0.0452110 | 0.0226055 | − | 0.999744i | \(-0.492804\pi\) | ||||
0.0226055 | + | 0.999744i | \(0.492804\pi\) | |||||||
\(308\) | 3.33437 | 0.189993 | ||||||||
\(309\) | 22.3032 | 1.26878 | ||||||||
\(310\) | −4.42260 | −0.251187 | ||||||||
\(311\) | 25.8022 | 1.46311 | 0.731554 | − | 0.681783i | \(-0.238795\pi\) | ||||
0.731554 | + | 0.681783i | \(0.238795\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −26.2780 | −1.48532 | −0.742661 | − | 0.669668i | \(-0.766437\pi\) | ||||
−0.742661 | + | 0.669668i | \(0.766437\pi\) | |||||||
\(314\) | 30.3484 | 1.71266 | ||||||||
\(315\) | −2.11250 | −0.119026 | ||||||||
\(316\) | 58.2108 | 3.27461 | ||||||||
\(317\) | −10.9788 | −0.616633 | −0.308317 | − | 0.951284i | \(-0.599766\pi\) | ||||
−0.308317 | + | 0.951284i | \(0.599766\pi\) | |||||||
\(318\) | −10.2671 | −0.575751 | ||||||||
\(319\) | −7.36245 | −0.412218 | ||||||||
\(320\) | −4.77101 | −0.266707 | ||||||||
\(321\) | 5.39853 | 0.301316 | ||||||||
\(322\) | −5.32345 | −0.296664 | ||||||||
\(323\) | 35.5632 | 1.97879 | ||||||||
\(324\) | −45.9748 | −2.55416 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 4.81020 | 0.266412 | ||||||||
\(327\) | 6.55714 | 0.362610 | ||||||||
\(328\) | 55.8162 | 3.08194 | ||||||||
\(329\) | −2.63044 | −0.145021 | ||||||||
\(330\) | 7.00000 | 0.385337 | ||||||||
\(331\) | −10.0561 | −0.552736 | −0.276368 | − | 0.961052i | \(-0.589131\pi\) | ||||
−0.276368 | + | 0.961052i | \(0.589131\pi\) | |||||||
\(332\) | 57.2600 | 3.14255 | ||||||||
\(333\) | 1.76008 | 0.0964520 | ||||||||
\(334\) | −17.6999 | −0.968497 | ||||||||
\(335\) | −7.40856 | −0.404773 | ||||||||
\(336\) | −10.2992 | −0.561866 | ||||||||
\(337\) | 19.7398 | 1.07530 | 0.537648 | − | 0.843169i | \(-0.319313\pi\) | ||||
0.537648 | + | 0.843169i | \(0.319313\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −12.8022 | −0.695320 | ||||||||
\(340\) | −22.4366 | −1.21680 | ||||||||
\(341\) | −1.44375 | −0.0781836 | ||||||||
\(342\) | 46.2288 | 2.49977 | ||||||||
\(343\) | 10.4226 | 0.562767 | ||||||||
\(344\) | 55.4538 | 2.98987 | ||||||||
\(345\) | −7.61951 | −0.410221 | ||||||||
\(346\) | −4.13054 | −0.222059 | ||||||||
\(347\) | 18.3132 | 0.983105 | 0.491553 | − | 0.870848i | \(-0.336430\pi\) | ||||
0.491553 | + | 0.870848i | \(0.336430\pi\) | |||||||
\(348\) | 72.0943 | 3.86466 | ||||||||
\(349\) | −17.3765 | −0.930142 | −0.465071 | − | 0.885273i | \(-0.653971\pi\) | ||||
−0.465071 | + | 0.885273i | \(0.653971\pi\) | |||||||
\(350\) | −6.84139 | −0.365688 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 3.06327 | 0.163273 | ||||||||
\(353\) | −33.7670 | −1.79724 | −0.898618 | − | 0.438732i | \(-0.855428\pi\) | ||||
−0.898618 | + | 0.438732i | \(0.855428\pi\) | |||||||
\(354\) | 29.8352 | 1.58572 | ||||||||
\(355\) | 7.95077 | 0.421983 | ||||||||
\(356\) | 20.4749 | 1.08517 | ||||||||
\(357\) | 7.61951 | 0.403267 | ||||||||
\(358\) | −18.3874 | −0.971805 | ||||||||
\(359\) | 4.72889 | 0.249582 | 0.124791 | − | 0.992183i | \(-0.460174\pi\) | ||||
0.124791 | + | 0.992183i | \(0.460174\pi\) | |||||||
\(360\) | −15.5531 | −0.819722 | ||||||||
\(361\) | 49.8764 | 2.62507 | ||||||||
\(362\) | −29.5202 | −1.55155 | ||||||||
\(363\) | 2.28514 | 0.119939 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 2.44375 | 0.127912 | ||||||||
\(366\) | 83.1896 | 4.34839 | ||||||||
\(367\) | 6.42660 | 0.335466 | 0.167733 | − | 0.985832i | \(-0.446355\pi\) | ||||
0.167733 | + | 0.985832i | \(0.446355\pi\) | |||||||
\(368\) | −15.8062 | −0.823955 | ||||||||
\(369\) | −21.6476 | −1.12693 | ||||||||
\(370\) | −2.42660 | −0.126153 | ||||||||
\(371\) | −1.39452 | −0.0724000 | ||||||||
\(372\) | 14.1375 | 0.732993 | ||||||||
\(373\) | −4.41168 | −0.228428 | −0.114214 | − | 0.993456i | \(-0.536435\pi\) | ||||
−0.114214 | + | 0.993456i | \(0.536435\pi\) | |||||||
\(374\) | −10.7429 | −0.555504 | ||||||||
\(375\) | −23.7530 | −1.22660 | ||||||||
\(376\) | −19.3664 | −0.998748 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | −3.46871 | −0.178411 | ||||||||
\(379\) | −19.5070 | −1.00201 | −0.501004 | − | 0.865445i | \(-0.667036\pi\) | ||||
−0.501004 | + | 0.865445i | \(0.667036\pi\) | |||||||
\(380\) | −43.4538 | −2.22913 | ||||||||
\(381\) | 16.5351 | 0.847118 | ||||||||
\(382\) | −36.9608 | −1.89108 | ||||||||
\(383\) | −27.6304 | −1.41185 | −0.705925 | − | 0.708287i | \(-0.749468\pi\) | ||||
−0.705925 | + | 0.708287i | \(0.749468\pi\) | |||||||
\(384\) | 36.3694 | 1.85597 | ||||||||
\(385\) | 0.950771 | 0.0484558 | ||||||||
\(386\) | −22.3163 | −1.13587 | ||||||||
\(387\) | −21.5070 | −1.09326 | ||||||||
\(388\) | 17.7429 | 0.900761 | ||||||||
\(389\) | −28.9960 | −1.47016 | −0.735078 | − | 0.677983i | \(-0.762854\pi\) | ||||
−0.735078 | + | 0.677983i | \(0.762854\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 11.6937 | 0.591376 | ||||||||
\(392\) | 36.6336 | 1.85027 | ||||||||
\(393\) | −23.6476 | −1.19286 | ||||||||
\(394\) | −15.3241 | −0.772019 | ||||||||
\(395\) | 16.5984 | 0.835154 | ||||||||
\(396\) | −9.52106 | −0.478451 | ||||||||
\(397\) | −34.6585 | −1.73946 | −0.869730 | − | 0.493527i | \(-0.835707\pi\) | ||||
−0.869730 | + | 0.493527i | \(0.835707\pi\) | |||||||
\(398\) | −23.4288 | −1.17438 | ||||||||
\(399\) | 14.7570 | 0.738773 | ||||||||
\(400\) | −20.3132 | −1.01566 | ||||||||
\(401\) | 14.5874 | 0.728462 | 0.364231 | − | 0.931309i | \(-0.381332\pi\) | ||||
0.364231 | + | 0.931309i | \(0.381332\pi\) | |||||||
\(402\) | 34.7358 | 1.73246 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 20.6725 | 1.02850 | ||||||||
\(405\) | −13.1094 | −0.651410 | ||||||||
\(406\) | 14.3624 | 0.712796 | ||||||||
\(407\) | −0.792161 | −0.0392660 | ||||||||
\(408\) | 56.0983 | 2.77728 | ||||||||
\(409\) | −16.6015 | −0.820890 | −0.410445 | − | 0.911885i | \(-0.634627\pi\) | ||||
−0.410445 | + | 0.911885i | \(0.634627\pi\) | |||||||
\(410\) | 29.8452 | 1.47395 | ||||||||
\(411\) | 11.2811 | 0.556458 | ||||||||
\(412\) | 41.8234 | 2.06049 | ||||||||
\(413\) | 4.05234 | 0.199403 | ||||||||
\(414\) | 15.2007 | 0.747075 | ||||||||
\(415\) | 16.3273 | 0.801473 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 37.6405 | 1.84326 | ||||||||
\(418\) | −20.8062 | −1.01766 | ||||||||
\(419\) | −22.2952 | −1.08919 | −0.544595 | − | 0.838699i | \(-0.683317\pi\) | ||||
−0.544595 | + | 0.838699i | \(0.683317\pi\) | |||||||
\(420\) | −9.31010 | −0.454286 | ||||||||
\(421\) | 3.45779 | 0.168522 | 0.0842612 | − | 0.996444i | \(-0.473147\pi\) | ||||
0.0842612 | + | 0.996444i | \(0.473147\pi\) | |||||||
\(422\) | 13.0031 | 0.632982 | ||||||||
\(423\) | 7.51102 | 0.365198 | ||||||||
\(424\) | −10.2671 | −0.498615 | ||||||||
\(425\) | 15.0281 | 0.728969 | ||||||||
\(426\) | −37.2780 | −1.80613 | ||||||||
\(427\) | 11.2992 | 0.546806 | ||||||||
\(428\) | 10.1234 | 0.489334 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 29.6514 | 1.42992 | ||||||||
\(431\) | −25.8804 | −1.24661 | −0.623307 | − | 0.781977i | \(-0.714211\pi\) | ||||
−0.623307 | + | 0.781977i | \(0.714211\pi\) | |||||||
\(432\) | −10.2992 | −0.495520 | ||||||||
\(433\) | 14.3805 | 0.691082 | 0.345541 | − | 0.938404i | \(-0.387695\pi\) | ||||
0.345541 | + | 0.938404i | \(0.387695\pi\) | |||||||
\(434\) | 2.81643 | 0.135193 | ||||||||
\(435\) | 20.5571 | 0.985639 | ||||||||
\(436\) | 12.2961 | 0.588875 | ||||||||
\(437\) | 22.6476 | 1.08338 | ||||||||
\(438\) | −11.4578 | −0.547474 | ||||||||
\(439\) | 4.56628 | 0.217937 | 0.108968 | − | 0.994045i | \(-0.465245\pi\) | ||||
0.108968 | + | 0.994045i | \(0.465245\pi\) | |||||||
\(440\) | 7.00000 | 0.333712 | ||||||||
\(441\) | −14.2078 | −0.676564 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 18.1718 | 0.863366 | 0.431683 | − | 0.902025i | \(-0.357920\pi\) | ||||
0.431683 | + | 0.902025i | \(0.357920\pi\) | |||||||
\(444\) | 7.75697 | 0.368129 | ||||||||
\(445\) | 5.83828 | 0.276761 | ||||||||
\(446\) | 42.2038 | 1.99841 | ||||||||
\(447\) | 4.35241 | 0.205862 | ||||||||
\(448\) | 3.03831 | 0.143546 | ||||||||
\(449\) | 12.6295 | 0.596025 | 0.298013 | − | 0.954562i | \(-0.403676\pi\) | ||||
0.298013 | + | 0.954562i | \(0.403676\pi\) | |||||||
\(450\) | 19.5351 | 0.920893 | ||||||||
\(451\) | 9.74293 | 0.458777 | ||||||||
\(452\) | −24.0069 | −1.12919 | ||||||||
\(453\) | −42.0662 | −1.97644 | ||||||||
\(454\) | −44.1646 | −2.07275 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 108.647 | 5.08788 | ||||||||
\(457\) | 25.7882 | 1.20632 | 0.603160 | − | 0.797621i | \(-0.293908\pi\) | ||||
0.603160 | + | 0.797621i | \(0.293908\pi\) | |||||||
\(458\) | 67.3271 | 3.14599 | ||||||||
\(459\) | 7.61951 | 0.355648 | ||||||||
\(460\) | −14.2883 | −0.666193 | ||||||||
\(461\) | 12.6336 | 0.588403 | 0.294202 | − | 0.955743i | \(-0.404946\pi\) | ||||
0.294202 | + | 0.955743i | \(0.404946\pi\) | |||||||
\(462\) | −4.45779 | −0.207395 | ||||||||
\(463\) | 3.47494 | 0.161494 | 0.0807471 | − | 0.996735i | \(-0.474269\pi\) | ||||
0.0807471 | + | 0.996735i | \(0.474269\pi\) | |||||||
\(464\) | 42.6445 | 1.97972 | ||||||||
\(465\) | 4.03119 | 0.186942 | ||||||||
\(466\) | 68.0419 | 3.15198 | ||||||||
\(467\) | −18.7258 | −0.866526 | −0.433263 | − | 0.901268i | \(-0.642638\pi\) | ||||
−0.433263 | + | 0.901268i | \(0.642638\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 4.71797 | 0.217856 | ||||||||
\(470\) | −10.3553 | −0.477656 | ||||||||
\(471\) | −27.6625 | −1.27462 | ||||||||
\(472\) | 29.8352 | 1.37327 | ||||||||
\(473\) | 9.67967 | 0.445072 | ||||||||
\(474\) | −77.8232 | −3.57454 | ||||||||
\(475\) | 29.1054 | 1.33545 | ||||||||
\(476\) | 14.2883 | 0.654901 | ||||||||
\(477\) | 3.98196 | 0.182321 | ||||||||
\(478\) | 1.87035 | 0.0855479 | ||||||||
\(479\) | −9.28514 | −0.424249 | −0.212124 | − | 0.977243i | \(-0.568038\pi\) | ||||
−0.212124 | + | 0.977243i | \(0.568038\pi\) | |||||||
\(480\) | −8.55313 | −0.390395 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 40.5451 | 1.84678 | ||||||||
\(483\) | 4.85231 | 0.220788 | ||||||||
\(484\) | 4.28514 | 0.194779 | ||||||||
\(485\) | 5.05926 | 0.229729 | ||||||||
\(486\) | 48.0913 | 2.18147 | ||||||||
\(487\) | 39.9296 | 1.80938 | 0.904692 | − | 0.426067i | \(-0.140101\pi\) | ||||
0.904692 | + | 0.426067i | \(0.140101\pi\) | |||||||
\(488\) | 83.1896 | 3.76582 | ||||||||
\(489\) | −4.38449 | −0.198273 | ||||||||
\(490\) | 19.5881 | 0.884901 | ||||||||
\(491\) | −41.1827 | −1.85855 | −0.929274 | − | 0.369391i | \(-0.879566\pi\) | ||||
−0.929274 | + | 0.369391i | \(0.879566\pi\) | |||||||
\(492\) | −95.4044 | −4.30116 | ||||||||
\(493\) | −31.5491 | −1.42090 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −2.71486 | −0.122024 | ||||||||
\(496\) | 8.36245 | 0.375485 | ||||||||
\(497\) | −5.06327 | −0.227119 | ||||||||
\(498\) | −76.5520 | −3.43038 | ||||||||
\(499\) | −19.3132 | −0.864578 | −0.432289 | − | 0.901735i | \(-0.642294\pi\) | ||||
−0.432289 | + | 0.901735i | \(0.642294\pi\) | |||||||
\(500\) | −44.5420 | −1.99198 | ||||||||
\(501\) | 16.1335 | 0.720790 | ||||||||
\(502\) | 27.6476 | 1.23397 | ||||||||
\(503\) | 19.6897 | 0.877920 | 0.438960 | − | 0.898507i | \(-0.355347\pi\) | ||||
0.438960 | + | 0.898507i | \(0.355347\pi\) | |||||||
\(504\) | 9.90466 | 0.441188 | ||||||||
\(505\) | 5.89462 | 0.262307 | ||||||||
\(506\) | −6.84139 | −0.304137 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 31.0069 | 1.37571 | ||||||||
\(509\) | −13.4749 | −0.597266 | −0.298633 | − | 0.954368i | \(-0.596531\pi\) | ||||
−0.298633 | + | 0.954368i | \(0.596531\pi\) | |||||||
\(510\) | 29.9960 | 1.32825 | ||||||||
\(511\) | −1.55625 | −0.0688443 | ||||||||
\(512\) | 48.6224 | 2.14883 | ||||||||
\(513\) | 14.7570 | 0.651536 | ||||||||
\(514\) | −47.2631 | −2.08469 | ||||||||
\(515\) | 11.9256 | 0.525505 | ||||||||
\(516\) | −94.7848 | −4.17267 | ||||||||
\(517\) | −3.38049 | −0.148674 | ||||||||
\(518\) | 1.54532 | 0.0678977 | ||||||||
\(519\) | 3.76497 | 0.165264 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 19.4266 | 0.851095 | 0.425547 | − | 0.904936i | \(-0.360082\pi\) | ||||
0.425547 | + | 0.904936i | \(0.360082\pi\) | |||||||
\(522\) | −41.0109 | −1.79500 | ||||||||
\(523\) | 10.9227 | 0.477616 | 0.238808 | − | 0.971067i | \(-0.423243\pi\) | ||||
0.238808 | + | 0.971067i | \(0.423243\pi\) | |||||||
\(524\) | −44.3444 | −1.93719 | ||||||||
\(525\) | 6.23591 | 0.272158 | ||||||||
\(526\) | 38.9898 | 1.70003 | ||||||||
\(527\) | −6.18668 | −0.269496 | ||||||||
\(528\) | −13.2359 | −0.576019 | ||||||||
\(529\) | −15.5531 | −0.676223 | ||||||||
\(530\) | −5.48987 | −0.238465 | ||||||||
\(531\) | −11.5712 | −0.502146 | ||||||||
\(532\) | 27.6725 | 1.19976 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | −27.3734 | −1.18456 | ||||||||
\(535\) | 2.88662 | 0.124799 | ||||||||
\(536\) | 34.7358 | 1.50036 | ||||||||
\(537\) | 16.7601 | 0.723251 | ||||||||
\(538\) | 13.0913 | 0.564408 | ||||||||
\(539\) | 6.39452 | 0.275432 | ||||||||
\(540\) | −9.31010 | −0.400643 | ||||||||
\(541\) | 16.9820 | 0.730111 | 0.365056 | − | 0.930986i | \(-0.381050\pi\) | ||||
0.365056 | + | 0.930986i | \(0.381050\pi\) | |||||||
\(542\) | 65.0239 | 2.79301 | ||||||||
\(543\) | 26.9076 | 1.15471 | ||||||||
\(544\) | 13.1265 | 0.562795 | ||||||||
\(545\) | 3.50613 | 0.150186 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1.13345 | 0.0484629 | 0.0242315 | − | 0.999706i | \(-0.492286\pi\) | ||||
0.0242315 | + | 0.999706i | \(0.492286\pi\) | |||||||
\(548\) | 21.1546 | 0.903680 | ||||||||
\(549\) | −32.2640 | −1.37699 | ||||||||
\(550\) | −8.79216 | −0.374899 | ||||||||
\(551\) | −61.1023 | −2.60304 | ||||||||
\(552\) | 35.7249 | 1.52055 | ||||||||
\(553\) | −10.5703 | −0.449494 | ||||||||
\(554\) | 44.5601 | 1.89318 | ||||||||
\(555\) | 2.21184 | 0.0938874 | ||||||||
\(556\) | 70.5841 | 2.99343 | ||||||||
\(557\) | 20.2671 | 0.858745 | 0.429372 | − | 0.903128i | \(-0.358735\pi\) | ||||
0.429372 | + | 0.903128i | \(0.358735\pi\) | |||||||
\(558\) | −8.04211 | −0.340450 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −5.50702 | −0.232714 | ||||||||
\(561\) | 9.79216 | 0.413425 | ||||||||
\(562\) | 18.5812 | 0.783801 | ||||||||
\(563\) | 0.313217 | 0.0132005 | 0.00660026 | − | 0.999978i | \(-0.497899\pi\) | ||||
0.00660026 | + | 0.999978i | \(0.497899\pi\) | |||||||
\(564\) | 33.1023 | 1.39386 | ||||||||
\(565\) | −6.84539 | −0.287988 | ||||||||
\(566\) | −23.3584 | −0.981829 | ||||||||
\(567\) | 8.34841 | 0.350600 | ||||||||
\(568\) | −37.2780 | −1.56415 | ||||||||
\(569\) | −11.0842 | −0.464675 | −0.232337 | − | 0.972635i | \(-0.574637\pi\) | ||||
−0.232337 | + | 0.972635i | \(0.574637\pi\) | |||||||
\(570\) | 58.0943 | 2.43330 | ||||||||
\(571\) | 41.7037 | 1.74525 | 0.872624 | − | 0.488393i | \(-0.162417\pi\) | ||||
0.872624 | + | 0.488393i | \(0.162417\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 33.6897 | 1.40741 | ||||||||
\(574\) | −19.0062 | −0.793305 | ||||||||
\(575\) | 9.57028 | 0.399108 | ||||||||
\(576\) | −8.67566 | −0.361486 | ||||||||
\(577\) | −19.1867 | −0.798752 | −0.399376 | − | 0.916787i | \(-0.630773\pi\) | ||||
−0.399376 | + | 0.916787i | \(0.630773\pi\) | |||||||
\(578\) | −3.41568 | −0.142073 | ||||||||
\(579\) | 20.3413 | 0.845355 | ||||||||
\(580\) | 38.5491 | 1.60067 | ||||||||
\(581\) | −10.3976 | −0.431367 | ||||||||
\(582\) | −23.7209 | −0.983263 | ||||||||
\(583\) | −1.79216 | −0.0742237 | ||||||||
\(584\) | −11.4578 | −0.474127 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −72.0842 | −2.97777 | ||||||||
\(587\) | 12.5843 | 0.519411 | 0.259705 | − | 0.965688i | \(-0.416375\pi\) | ||||
0.259705 | + | 0.965688i | \(0.416375\pi\) | |||||||
\(588\) | −62.6162 | −2.58225 | ||||||||
\(589\) | −11.9820 | −0.493708 | ||||||||
\(590\) | 15.9530 | 0.656775 | ||||||||
\(591\) | 13.9679 | 0.574564 | ||||||||
\(592\) | 4.58832 | 0.188579 | ||||||||
\(593\) | 13.7117 | 0.563074 | 0.281537 | − | 0.959550i | \(-0.409156\pi\) | ||||
0.281537 | + | 0.959550i | \(0.409156\pi\) | |||||||
\(594\) | −4.45779 | −0.182905 | ||||||||
\(595\) | 4.07419 | 0.167025 | ||||||||
\(596\) | 8.16172 | 0.334317 | ||||||||
\(597\) | 21.3553 | 0.874015 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −15.3905 | −0.628840 | −0.314420 | − | 0.949284i | \(-0.601810\pi\) | ||||
−0.314420 | + | 0.949284i | \(0.601810\pi\) | |||||||
\(600\) | 45.9116 | 1.87433 | ||||||||
\(601\) | −16.2148 | −0.661414 | −0.330707 | − | 0.943734i | \(-0.607287\pi\) | ||||
−0.330707 | + | 0.943734i | \(0.607287\pi\) | |||||||
\(602\) | −18.8828 | −0.769606 | ||||||||
\(603\) | −13.4718 | −0.548615 | ||||||||
\(604\) | −78.8833 | −3.20972 | ||||||||
\(605\) | 1.22188 | 0.0496763 | ||||||||
\(606\) | −27.6376 | −1.12270 | ||||||||
\(607\) | 2.68278 | 0.108891 | 0.0544453 | − | 0.998517i | \(-0.482661\pi\) | ||||
0.0544453 | + | 0.998517i | \(0.482661\pi\) | |||||||
\(608\) | 25.4226 | 1.03102 | ||||||||
\(609\) | −13.0913 | −0.530488 | ||||||||
\(610\) | 44.4819 | 1.80102 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | −40.7991 | −1.64921 | ||||||||
\(613\) | 36.0913 | 1.45772 | 0.728858 | − | 0.684665i | \(-0.240052\pi\) | ||||
0.728858 | + | 0.684665i | \(0.240052\pi\) | |||||||
\(614\) | −1.98596 | −0.0801469 | ||||||||
\(615\) | −27.2038 | −1.09696 | ||||||||
\(616\) | −4.45779 | −0.179609 | ||||||||
\(617\) | 19.1718 | 0.771826 | 0.385913 | − | 0.922535i | \(-0.373886\pi\) | ||||
0.385913 | + | 0.922535i | \(0.373886\pi\) | |||||||
\(618\) | −55.9145 | −2.24921 | ||||||||
\(619\) | −6.38049 | −0.256453 | −0.128227 | − | 0.991745i | \(-0.540929\pi\) | ||||
−0.128227 | + | 0.991745i | \(0.540929\pi\) | |||||||
\(620\) | 7.55936 | 0.303591 | ||||||||
\(621\) | 4.85231 | 0.194717 | ||||||||
\(622\) | −64.6866 | −2.59370 | ||||||||
\(623\) | −3.71797 | −0.148957 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 4.83427 | 0.193371 | ||||||||
\(626\) | 65.8795 | 2.63307 | ||||||||
\(627\) | 18.9648 | 0.757381 | ||||||||
\(628\) | −51.8733 | −2.06997 | ||||||||
\(629\) | −3.39452 | −0.135349 | ||||||||
\(630\) | 5.29607 | 0.211000 | ||||||||
\(631\) | 20.9007 | 0.832042 | 0.416021 | − | 0.909355i | \(-0.363424\pi\) | ||||
0.416021 | + | 0.909355i | \(0.363424\pi\) | |||||||
\(632\) | −77.8232 | −3.09564 | ||||||||
\(633\) | −11.8523 | −0.471087 | ||||||||
\(634\) | 27.5242 | 1.09312 | ||||||||
\(635\) | 8.84139 | 0.350860 | ||||||||
\(636\) | 17.5491 | 0.695868 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 18.4578 | 0.730751 | ||||||||
\(639\) | 14.4578 | 0.571941 | ||||||||
\(640\) | 19.4469 | 0.768705 | ||||||||
\(641\) | 19.1085 | 0.754740 | 0.377370 | − | 0.926063i | \(-0.376828\pi\) | ||||
0.377370 | + | 0.926063i | \(0.376828\pi\) | |||||||
\(642\) | −13.5342 | −0.534152 | ||||||||
\(643\) | 3.50702 | 0.138303 | 0.0691517 | − | 0.997606i | \(-0.477971\pi\) | ||||
0.0691517 | + | 0.997606i | \(0.477971\pi\) | |||||||
\(644\) | 9.09915 | 0.358557 | ||||||||
\(645\) | −27.0272 | −1.06419 | ||||||||
\(646\) | −89.1575 | −3.50786 | ||||||||
\(647\) | 20.8343 | 0.819080 | 0.409540 | − | 0.912292i | \(-0.365689\pi\) | ||||
0.409540 | + | 0.912292i | \(0.365689\pi\) | |||||||
\(648\) | 61.4647 | 2.41456 | ||||||||
\(649\) | 5.20784 | 0.204426 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −2.56717 | −0.100615 | ||||||||
\(652\) | −8.22188 | −0.321994 | ||||||||
\(653\) | −12.6757 | −0.496037 | −0.248019 | − | 0.968755i | \(-0.579779\pi\) | ||||
−0.248019 | + | 0.968755i | \(0.579779\pi\) | |||||||
\(654\) | −16.4389 | −0.642810 | ||||||||
\(655\) | −12.6445 | −0.494060 | ||||||||
\(656\) | −56.4326 | −2.20332 | ||||||||
\(657\) | 4.44375 | 0.173367 | ||||||||
\(658\) | 6.59455 | 0.257082 | ||||||||
\(659\) | 4.37960 | 0.170605 | 0.0853025 | − | 0.996355i | \(-0.472814\pi\) | ||||
0.0853025 | + | 0.996355i | \(0.472814\pi\) | |||||||
\(660\) | −11.9648 | −0.465730 | ||||||||
\(661\) | 1.12253 | 0.0436614 | 0.0218307 | − | 0.999762i | \(-0.493051\pi\) | ||||
0.0218307 | + | 0.999762i | \(0.493051\pi\) | |||||||
\(662\) | 25.2110 | 0.979852 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −76.5520 | −2.97080 | ||||||||
\(665\) | 7.89062 | 0.305985 | ||||||||
\(666\) | −4.41256 | −0.170983 | ||||||||
\(667\) | −20.0913 | −0.777940 | ||||||||
\(668\) | 30.2538 | 1.17055 | ||||||||
\(669\) | −38.4687 | −1.48729 | ||||||||
\(670\) | 18.5734 | 0.717553 | ||||||||
\(671\) | 14.5211 | 0.560579 | ||||||||
\(672\) | 5.44687 | 0.210117 | ||||||||
\(673\) | 18.0492 | 0.695747 | 0.347873 | − | 0.937542i | \(-0.386904\pi\) | ||||
0.347873 | + | 0.937542i | \(0.386904\pi\) | |||||||
\(674\) | −49.4881 | −1.90621 | ||||||||
\(675\) | 6.23591 | 0.240020 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −26.7037 | −1.02631 | −0.513154 | − | 0.858297i | \(-0.671523\pi\) | ||||
−0.513154 | + | 0.858297i | \(0.671523\pi\) | |||||||
\(678\) | 32.0953 | 1.23261 | ||||||||
\(679\) | −3.22188 | −0.123644 | ||||||||
\(680\) | 29.9960 | 1.15029 | ||||||||
\(681\) | 40.2560 | 1.54261 | ||||||||
\(682\) | 3.61951 | 0.138598 | ||||||||
\(683\) | −30.9788 | −1.18537 | −0.592686 | − | 0.805433i | \(-0.701933\pi\) | ||||
−0.592686 | + | 0.805433i | \(0.701933\pi\) | |||||||
\(684\) | −79.0170 | −3.02129 | ||||||||
\(685\) | 6.03208 | 0.230474 | ||||||||
\(686\) | −26.1296 | −0.997635 | ||||||||
\(687\) | −61.3685 | −2.34135 | ||||||||
\(688\) | −56.0662 | −2.13750 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 19.1023 | 0.727211 | ||||||||
\(691\) | 2.33126 | 0.0886852 | 0.0443426 | − | 0.999016i | \(-0.485881\pi\) | ||||
0.0443426 | + | 0.999016i | \(0.485881\pi\) | |||||||
\(692\) | 7.06015 | 0.268387 | ||||||||
\(693\) | 1.72889 | 0.0656753 | ||||||||
\(694\) | −45.9116 | −1.74278 | ||||||||
\(695\) | 20.1265 | 0.763443 | ||||||||
\(696\) | −96.3843 | −3.65344 | ||||||||
\(697\) | 41.7499 | 1.58139 | ||||||||
\(698\) | 43.5632 | 1.64889 | ||||||||
\(699\) | −62.0201 | −2.34581 | ||||||||
\(700\) | 11.6937 | 0.441980 | ||||||||
\(701\) | −22.5834 | −0.852965 | −0.426482 | − | 0.904496i | \(-0.640247\pi\) | ||||
−0.426482 | + | 0.904496i | \(0.640247\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −6.57429 | −0.247954 | ||||||||
\(704\) | 3.90466 | 0.147162 | ||||||||
\(705\) | 9.43886 | 0.355488 | ||||||||
\(706\) | 84.6545 | 3.18601 | ||||||||
\(707\) | −3.75385 | −0.141178 | ||||||||
\(708\) | −50.9960 | −1.91655 | ||||||||
\(709\) | 15.7218 | 0.590444 | 0.295222 | − | 0.955429i | \(-0.404606\pi\) | ||||
0.295222 | + | 0.955429i | \(0.404606\pi\) | |||||||
\(710\) | −19.9327 | −0.748062 | ||||||||
\(711\) | 30.1827 | 1.13194 | ||||||||
\(712\) | −27.3734 | −1.02586 | ||||||||
\(713\) | −3.93985 | −0.147548 | ||||||||
\(714\) | −19.1023 | −0.714884 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 31.4288 | 1.17455 | ||||||||
\(717\) | −1.70482 | −0.0636678 | ||||||||
\(718\) | −11.8554 | −0.442441 | ||||||||
\(719\) | −29.8303 | −1.11248 | −0.556241 | − | 0.831021i | \(-0.687757\pi\) | ||||
−0.556241 | + | 0.831021i | \(0.687757\pi\) | |||||||
\(720\) | 15.7249 | 0.586032 | ||||||||
\(721\) | −7.59455 | −0.282836 | ||||||||
\(722\) | −125.041 | −4.65355 | ||||||||
\(723\) | −36.9568 | −1.37444 | ||||||||
\(724\) | 50.4576 | 1.87524 | ||||||||
\(725\) | −25.8202 | −0.958939 | ||||||||
\(726\) | −5.72889 | −0.212619 | ||||||||
\(727\) | −36.6053 | −1.35761 | −0.678807 | − | 0.734316i | \(-0.737503\pi\) | ||||
−0.678807 | + | 0.734316i | \(0.737503\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −11.6485 | −0.431425 | ||||||||
\(730\) | −6.12653 | −0.226753 | ||||||||
\(731\) | 41.4787 | 1.53415 | ||||||||
\(732\) | −142.193 | −5.25559 | ||||||||
\(733\) | −29.8695 | −1.10325 | −0.551627 | − | 0.834091i | \(-0.685993\pi\) | ||||
−0.551627 | + | 0.834091i | \(0.685993\pi\) | |||||||
\(734\) | −16.1116 | −0.594690 | ||||||||
\(735\) | −17.8545 | −0.658575 | ||||||||
\(736\) | 8.35933 | 0.308129 | ||||||||
\(737\) | 6.06327 | 0.223343 | ||||||||
\(738\) | 54.2709 | 1.99774 | ||||||||
\(739\) | −30.2569 | −1.11302 | −0.556508 | − | 0.830842i | \(-0.687859\pi\) | ||||
−0.556508 | + | 0.830842i | \(0.687859\pi\) | |||||||
\(740\) | 4.14769 | 0.152472 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 3.49610 | 0.128346 | ||||||||
\(743\) | −39.2419 | −1.43965 | −0.719824 | − | 0.694157i | \(-0.755777\pi\) | ||||
−0.719824 | + | 0.694157i | \(0.755777\pi\) | |||||||
\(744\) | −18.9007 | −0.692932 | ||||||||
\(745\) | 2.32725 | 0.0852640 | ||||||||
\(746\) | 11.0602 | 0.404941 | ||||||||
\(747\) | 29.6897 | 1.08629 | ||||||||
\(748\) | 18.3624 | 0.671398 | ||||||||
\(749\) | −1.83828 | −0.0671691 | ||||||||
\(750\) | 59.5491 | 2.17443 | ||||||||
\(751\) | 6.82335 | 0.248988 | 0.124494 | − | 0.992220i | \(-0.460269\pi\) | ||||
0.124494 | + | 0.992220i | \(0.460269\pi\) | |||||||
\(752\) | 19.5803 | 0.714021 | ||||||||
\(753\) | −25.2007 | −0.918365 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −22.4930 | −0.818603 | ||||||||
\(756\) | 5.92893 | 0.215633 | ||||||||
\(757\) | −0.752967 | −0.0273670 | −0.0136835 | − | 0.999906i | \(-0.504356\pi\) | ||||
−0.0136835 | + | 0.999906i | \(0.504356\pi\) | |||||||
\(758\) | 48.9045 | 1.77629 | ||||||||
\(759\) | 6.23591 | 0.226349 | ||||||||
\(760\) | 58.0943 | 2.10730 | ||||||||
\(761\) | −34.9748 | −1.26784 | −0.633919 | − | 0.773400i | \(-0.718555\pi\) | ||||
−0.633919 | + | 0.773400i | \(0.718555\pi\) | |||||||
\(762\) | −41.4538 | −1.50171 | ||||||||
\(763\) | −2.23280 | −0.0808327 | ||||||||
\(764\) | 63.1756 | 2.28561 | ||||||||
\(765\) | −11.6336 | −0.420612 | ||||||||
\(766\) | 69.2700 | 2.50283 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −73.3333 | −2.64619 | ||||||||
\(769\) | −15.4649 | −0.557679 | −0.278839 | − | 0.960338i | \(-0.589950\pi\) | ||||
−0.278839 | + | 0.960338i | \(0.589950\pi\) | |||||||
\(770\) | −2.38360 | −0.0858990 | ||||||||
\(771\) | 43.0802 | 1.55150 | ||||||||
\(772\) | 38.1444 | 1.37285 | ||||||||
\(773\) | 36.1366 | 1.29974 | 0.649871 | − | 0.760045i | \(-0.274823\pi\) | ||||
0.649871 | + | 0.760045i | \(0.274823\pi\) | |||||||
\(774\) | 53.9185 | 1.93806 | ||||||||
\(775\) | −5.06327 | −0.181878 | ||||||||
\(776\) | −23.7209 | −0.851530 | ||||||||
\(777\) | −1.40856 | −0.0505318 | ||||||||
\(778\) | 72.6935 | 2.60619 | ||||||||
\(779\) | 80.8583 | 2.89705 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −6.50702 | −0.232839 | ||||||||
\(782\) | −29.3163 | −1.04835 | ||||||||
\(783\) | −13.0913 | −0.467846 | ||||||||
\(784\) | −37.0381 | −1.32279 | ||||||||
\(785\) | −14.7913 | −0.527923 | ||||||||
\(786\) | 59.2849 | 2.11462 | ||||||||
\(787\) | 22.9499 | 0.818075 | 0.409037 | − | 0.912518i | \(-0.365865\pi\) | ||||
0.409037 | + | 0.912518i | \(0.365865\pi\) | |||||||
\(788\) | 26.1929 | 0.933084 | ||||||||
\(789\) | −35.5391 | −1.26523 | ||||||||
\(790\) | −41.6124 | −1.48050 | ||||||||
\(791\) | 4.35933 | 0.155000 | ||||||||
\(792\) | 12.7289 | 0.452302 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 86.8895 | 3.08359 | ||||||||
\(795\) | 5.00400 | 0.177474 | ||||||||
\(796\) | 40.0459 | 1.41939 | ||||||||
\(797\) | 43.4498 | 1.53907 | 0.769535 | − | 0.638604i | \(-0.220488\pi\) | ||||
0.769535 | + | 0.638604i | \(0.220488\pi\) | |||||||
\(798\) | −36.9960 | −1.30964 | ||||||||
\(799\) | −14.4859 | −0.512473 | ||||||||
\(800\) | 10.7429 | 0.379820 | ||||||||
\(801\) | 10.6164 | 0.375112 | ||||||||
\(802\) | −36.5710 | −1.29137 | ||||||||
\(803\) | −2.00000 | −0.0705785 | ||||||||
\(804\) | −59.3725 | −2.09391 | ||||||||
\(805\) | 2.59455 | 0.0914460 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −11.9327 | −0.420052 | ||||||||
\(808\) | −27.6376 | −0.972286 | ||||||||
\(809\) | −43.1094 | −1.51565 | −0.757823 | − | 0.652461i | \(-0.773737\pi\) | ||||
−0.757823 | + | 0.652461i | \(0.773737\pi\) | |||||||
\(810\) | 32.8655 | 1.15477 | ||||||||
\(811\) | 17.9428 | 0.630056 | 0.315028 | − | 0.949082i | \(-0.397986\pi\) | ||||
0.315028 | + | 0.949082i | \(0.397986\pi\) | |||||||
\(812\) | −24.5491 | −0.861506 | ||||||||
\(813\) | −59.2691 | −2.07866 | ||||||||
\(814\) | 1.98596 | 0.0696080 | ||||||||
\(815\) | −2.34441 | −0.0821210 | ||||||||
\(816\) | −56.7178 | −1.98552 | ||||||||
\(817\) | 80.3333 | 2.81051 | ||||||||
\(818\) | 41.6202 | 1.45522 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −51.0131 | −1.78146 | ||||||||
\(821\) | −15.6647 | −0.546703 | −0.273352 | − | 0.961914i | \(-0.588132\pi\) | ||||
−0.273352 | + | 0.961914i | \(0.588132\pi\) | |||||||
\(822\) | −28.2820 | −0.986449 | ||||||||
\(823\) | 3.69771 | 0.128894 | 0.0644470 | − | 0.997921i | \(-0.479472\pi\) | ||||
0.0644470 | + | 0.997921i | \(0.479472\pi\) | |||||||
\(824\) | −55.9145 | −1.94787 | ||||||||
\(825\) | 8.01404 | 0.279013 | ||||||||
\(826\) | −10.1593 | −0.353487 | ||||||||
\(827\) | 42.3201 | 1.47162 | 0.735808 | − | 0.677191i | \(-0.236803\pi\) | ||||
0.735808 | + | 0.677191i | \(0.236803\pi\) | |||||||
\(828\) | −25.9820 | −0.902936 | ||||||||
\(829\) | 7.15461 | 0.248490 | 0.124245 | − | 0.992252i | \(-0.460349\pi\) | ||||
0.124245 | + | 0.992252i | \(0.460349\pi\) | |||||||
\(830\) | −40.9327 | −1.42080 | ||||||||
\(831\) | −40.6164 | −1.40897 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 27.4014 | 0.949404 | ||||||||
\(834\) | −94.3654 | −3.26761 | ||||||||
\(835\) | 8.62663 | 0.298537 | ||||||||
\(836\) | 35.5632 | 1.22998 | ||||||||
\(837\) | −2.56717 | −0.0887344 | ||||||||
\(838\) | 55.8944 | 1.93084 | ||||||||
\(839\) | −2.76008 | −0.0952887 | −0.0476443 | − | 0.998864i | \(-0.515171\pi\) | ||||
−0.0476443 | + | 0.998864i | \(0.515171\pi\) | |||||||
\(840\) | 12.4469 | 0.429458 | ||||||||
\(841\) | 25.2056 | 0.869159 | ||||||||
\(842\) | −8.66874 | −0.298745 | ||||||||
\(843\) | −16.9367 | −0.583332 | ||||||||
\(844\) | −22.2257 | −0.765040 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −18.8303 | −0.647398 | ||||||||
\(847\) | −0.778124 | −0.0267367 | ||||||||
\(848\) | 10.3805 | 0.356467 | ||||||||
\(849\) | 21.2912 | 0.730711 | ||||||||
\(850\) | −37.6757 | −1.29226 | ||||||||
\(851\) | −2.16172 | −0.0741030 | ||||||||
\(852\) | 63.7178 | 2.18294 | ||||||||
\(853\) | −46.1615 | −1.58054 | −0.790270 | − | 0.612758i | \(-0.790060\pi\) | ||||
−0.790270 | + | 0.612758i | \(0.790060\pi\) | |||||||
\(854\) | −28.3273 | −0.969339 | ||||||||
\(855\) | −22.5311 | −0.770547 | ||||||||
\(856\) | −13.5342 | −0.462590 | ||||||||
\(857\) | 26.2680 | 0.897297 | 0.448649 | − | 0.893708i | \(-0.351905\pi\) | ||||
0.448649 | + | 0.893708i | \(0.351905\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −32.0381 | −1.09313 | −0.546563 | − | 0.837418i | \(-0.684064\pi\) | ||||
−0.546563 | + | 0.837418i | \(0.684064\pi\) | |||||||
\(860\) | −50.6819 | −1.72824 | ||||||||
\(861\) | 17.3241 | 0.590405 | ||||||||
\(862\) | 64.8826 | 2.20991 | ||||||||
\(863\) | 24.2078 | 0.824044 | 0.412022 | − | 0.911174i | \(-0.364823\pi\) | ||||
0.412022 | + | 0.911174i | \(0.364823\pi\) | |||||||
\(864\) | 5.44687 | 0.185306 | ||||||||
\(865\) | 2.01315 | 0.0684491 | ||||||||
\(866\) | −36.0521 | −1.22510 | ||||||||
\(867\) | 3.11338 | 0.105736 | ||||||||
\(868\) | −4.81401 | −0.163398 | ||||||||
\(869\) | −13.5843 | −0.460817 | ||||||||
\(870\) | −51.5371 | −1.74727 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −16.4389 | −0.556690 | ||||||||
\(873\) | 9.19983 | 0.311367 | ||||||||
\(874\) | −56.7779 | −1.92054 | ||||||||
\(875\) | 8.08823 | 0.273432 | ||||||||
\(876\) | 19.5843 | 0.661693 | ||||||||
\(877\) | −1.05635 | −0.0356703 | −0.0178351 | − | 0.999841i | \(-0.505677\pi\) | ||||
−0.0178351 | + | 0.999841i | \(0.505677\pi\) | |||||||
\(878\) | −11.4478 | −0.386343 | ||||||||
\(879\) | 65.7046 | 2.21616 | ||||||||
\(880\) | −7.07730 | −0.238576 | ||||||||
\(881\) | −24.1655 | −0.814157 | −0.407079 | − | 0.913393i | \(-0.633453\pi\) | ||||
−0.407079 | + | 0.913393i | \(0.633453\pi\) | |||||||
\(882\) | 35.6193 | 1.19936 | ||||||||
\(883\) | 5.84831 | 0.196811 | 0.0984057 | − | 0.995146i | \(-0.468626\pi\) | ||||
0.0984057 | + | 0.995146i | \(0.468626\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −14.5411 | −0.488795 | ||||||||
\(886\) | −45.5569 | −1.53052 | ||||||||
\(887\) | −8.67566 | −0.291300 | −0.145650 | − | 0.989336i | \(-0.546527\pi\) | ||||
−0.145650 | + | 0.989336i | \(0.546527\pi\) | |||||||
\(888\) | −10.3705 | −0.348010 | ||||||||
\(889\) | −5.63044 | −0.188839 | ||||||||
\(890\) | −14.6367 | −0.490622 | ||||||||
\(891\) | 10.7289 | 0.359431 | ||||||||
\(892\) | −72.1373 | −2.41533 | ||||||||
\(893\) | −28.0553 | −0.938834 | ||||||||
\(894\) | −10.9116 | −0.364938 | ||||||||
\(895\) | 8.96169 | 0.299556 | ||||||||
\(896\) | −12.3843 | −0.413730 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −31.6625 | −1.05659 | ||||||||
\(899\) | 10.6295 | 0.354515 | ||||||||
\(900\) | −33.3905 | −1.11302 | ||||||||
\(901\) | −7.67967 | −0.255847 | ||||||||
\(902\) | −24.4257 | −0.813287 | ||||||||
\(903\) | 17.2116 | 0.572768 | ||||||||
\(904\) | 32.0953 | 1.06748 | ||||||||
\(905\) | 14.3876 | 0.478260 | ||||||||
\(906\) | 105.461 | 3.50370 | ||||||||
\(907\) | −15.5952 | −0.517832 | −0.258916 | − | 0.965900i | \(-0.583365\pi\) | ||||
−0.258916 | + | 0.965900i | \(0.583365\pi\) | |||||||
\(908\) | 75.4888 | 2.50518 | ||||||||
\(909\) | 10.7189 | 0.355522 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 24.5672 | 0.813947 | 0.406973 | − | 0.913440i | \(-0.366584\pi\) | ||||
0.406973 | + | 0.913440i | \(0.366584\pi\) | |||||||
\(912\) | −109.847 | −3.63741 | ||||||||
\(913\) | −13.3624 | −0.442232 | ||||||||
\(914\) | −64.6514 | −2.13848 | ||||||||
\(915\) | −40.5451 | −1.34038 | ||||||||
\(916\) | −115.079 | −3.80233 | ||||||||
\(917\) | 8.05234 | 0.265912 | ||||||||
\(918\) | −19.1023 | −0.630469 | ||||||||
\(919\) | 17.2811 | 0.570052 | 0.285026 | − | 0.958520i | \(-0.407998\pi\) | ||||
0.285026 | + | 0.958520i | \(0.407998\pi\) | |||||||
\(920\) | 19.1023 | 0.629783 | ||||||||
\(921\) | 1.81020 | 0.0596482 | ||||||||
\(922\) | −31.6725 | −1.04308 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 7.61951 | 0.250664 | ||||||||
\(925\) | −2.77812 | −0.0913441 | ||||||||
\(926\) | −8.71174 | −0.286286 | ||||||||
\(927\) | 21.6857 | 0.712252 | ||||||||
\(928\) | −22.5531 | −0.740343 | ||||||||
\(929\) | 48.2569 | 1.58326 | 0.791628 | − | 0.611003i | \(-0.209234\pi\) | ||||
0.791628 | + | 0.611003i | \(0.209234\pi\) | |||||||
\(930\) | −10.1063 | −0.331398 | ||||||||
\(931\) | 53.0693 | 1.73928 | ||||||||
\(932\) | −116.301 | −3.80957 | ||||||||
\(933\) | 58.9617 | 1.93032 | ||||||||
\(934\) | 46.9459 | 1.53612 | ||||||||
\(935\) | 5.23591 | 0.171233 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −17.7209 | −0.578916 | −0.289458 | − | 0.957191i | \(-0.593475\pi\) | ||||
−0.289458 | + | 0.957191i | \(0.593475\pi\) | |||||||
\(938\) | −11.8280 | −0.386199 | ||||||||
\(939\) | −60.0490 | −1.95963 | ||||||||
\(940\) | 17.6999 | 0.577308 | ||||||||
\(941\) | −7.96392 | −0.259616 | −0.129808 | − | 0.991539i | \(-0.541436\pi\) | ||||
−0.129808 | + | 0.991539i | \(0.541436\pi\) | |||||||
\(942\) | 69.3504 | 2.25956 | ||||||||
\(943\) | 26.5874 | 0.865806 | ||||||||
\(944\) | −30.1646 | −0.981775 | ||||||||
\(945\) | 1.69059 | 0.0549948 | ||||||||
\(946\) | −24.2671 | −0.788992 | ||||||||
\(947\) | −15.5632 | −0.505735 | −0.252867 | − | 0.967501i | \(-0.581374\pi\) | ||||
−0.252867 | + | 0.967501i | \(0.581374\pi\) | |||||||
\(948\) | 133.020 | 4.32028 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | −72.9677 | −2.36739 | ||||||||
\(951\) | −25.0882 | −0.813541 | ||||||||
\(952\) | −19.1023 | −0.619108 | ||||||||
\(953\) | −31.8483 | −1.03167 | −0.515834 | − | 0.856689i | \(-0.672518\pi\) | ||||
−0.515834 | + | 0.856689i | \(0.672518\pi\) | |||||||
\(954\) | −9.98285 | −0.323207 | ||||||||
\(955\) | 18.0140 | 0.582921 | ||||||||
\(956\) | −3.19692 | −0.103396 | ||||||||
\(957\) | −16.8242 | −0.543850 | ||||||||
\(958\) | 23.2780 | 0.752079 | ||||||||
\(959\) | −3.84139 | −0.124045 | ||||||||
\(960\) | −10.9024 | −0.351874 | ||||||||
\(961\) | −28.9156 | −0.932761 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 5.24906 | 0.169149 | ||||||||
\(964\) | −69.3021 | −2.23207 | ||||||||
\(965\) | 10.8766 | 0.350130 | ||||||||
\(966\) | −12.1648 | −0.391397 | ||||||||
\(967\) | 46.1023 | 1.48255 | 0.741274 | − | 0.671202i | \(-0.234222\pi\) | ||||
0.741274 | + | 0.671202i | \(0.234222\pi\) | |||||||
\(968\) | −5.72889 | −0.184134 | ||||||||
\(969\) | 81.2669 | 2.61067 | ||||||||
\(970\) | −12.6837 | −0.407248 | ||||||||
\(971\) | −14.7882 | −0.474575 | −0.237287 | − | 0.971440i | \(-0.576258\pi\) | ||||
−0.237287 | + | 0.971440i | \(0.576258\pi\) | |||||||
\(972\) | −82.2005 | −2.63658 | ||||||||
\(973\) | −12.8171 | −0.410898 | ||||||||
\(974\) | −100.104 | −3.20755 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −84.1083 | −2.69224 | ||||||||
\(977\) | −1.35933 | −0.0434889 | −0.0217444 | − | 0.999764i | \(-0.506922\pi\) | ||||
−0.0217444 | + | 0.999764i | \(0.506922\pi\) | |||||||
\(978\) | 10.9920 | 0.351485 | ||||||||
\(979\) | −4.77812 | −0.152710 | ||||||||
\(980\) | −33.4812 | −1.06952 | ||||||||
\(981\) | 6.37560 | 0.203557 | ||||||||
\(982\) | 103.246 | 3.29470 | ||||||||
\(983\) | −27.4709 | −0.876187 | −0.438093 | − | 0.898929i | \(-0.644346\pi\) | ||||
−0.438093 | + | 0.898929i | \(0.644346\pi\) | |||||||
\(984\) | 127.548 | 4.06608 | ||||||||
\(985\) | 7.46871 | 0.237973 | ||||||||
\(986\) | 79.0943 | 2.51887 | ||||||||
\(987\) | −6.01092 | −0.191330 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 26.4148 | 0.839941 | ||||||||
\(990\) | 6.80620 | 0.216315 | ||||||||
\(991\) | 0.173535 | 0.00551253 | 0.00275626 | − | 0.999996i | \(-0.499123\pi\) | ||||
0.00275626 | + | 0.999996i | \(0.499123\pi\) | |||||||
\(992\) | −4.42260 | −0.140418 | ||||||||
\(993\) | −22.9797 | −0.729240 | ||||||||
\(994\) | 12.6937 | 0.402620 | ||||||||
\(995\) | 11.4188 | 0.362000 | ||||||||
\(996\) | 130.847 | 4.14605 | ||||||||
\(997\) | 44.1896 | 1.39950 | 0.699749 | − | 0.714388i | \(-0.253295\pi\) | ||||
0.699749 | + | 0.714388i | \(0.253295\pi\) | |||||||
\(998\) | 48.4186 | 1.53266 | ||||||||
\(999\) | −1.40856 | −0.0445649 |
(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 | 1859.2.a.g.1.1 | 3 | ||
13.4 | even | 6 | 143.2.e.b.133.1 | yes | 6 | ||
13.10 | even | 6 | 143.2.e.b.100.1 | ✓ | 6 | ||
13.12 | even | 2 | 1859.2.a.f.1.3 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
143.2.e.b.100.1 | ✓ | 6 | 13.10 | even | 6 | ||
143.2.e.b.133.1 | yes | 6 | 13.4 | even | 6 | ||
1859.2.a.f.1.3 | 3 | 13.12 | even | 2 | |||
1859.2.a.g.1.1 | 3 | 1.1 | even | 1 | trivial |