Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1815,2,Mod(1,1815)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1815, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1815.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1815 = 3 \cdot 5 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1815.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: | \(14.4928479669\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.725.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} - 3x^{2} + x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 165) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(-0.477260\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1815.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.77222 | 1.96026 | 0.980129 | − | 0.198362i | \(-0.0635622\pi\) | ||||
0.980129 | + | 0.198362i | \(0.0635622\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 5.68522 | 2.84261 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 2.77222 | 1.13176 | ||||||||
\(7\) | −2.27759 | −0.860849 | −0.430424 | − | 0.902627i | \(-0.641636\pi\) | ||||
−0.430424 | + | 0.902627i | \(0.641636\pi\) | |||||||
\(8\) | 10.2163 | 3.61199 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −2.77222 | −0.876654 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 5.68522 | 1.64118 | ||||||||
\(13\) | −0.435737 | −0.120852 | −0.0604258 | − | 0.998173i | \(-0.519246\pi\) | ||||
−0.0604258 | + | 0.998173i | \(0.519246\pi\) | |||||||
\(14\) | −6.31399 | −1.68748 | ||||||||
\(15\) | −1.00000 | −0.258199 | ||||||||
\(16\) | 16.9513 | 4.23782 | ||||||||
\(17\) | 5.00000 | 1.21268 | 0.606339 | − | 0.795206i | \(-0.292637\pi\) | ||||
0.606339 | + | 0.795206i | \(0.292637\pi\) | |||||||
\(18\) | 2.77222 | 0.653419 | ||||||||
\(19\) | 4.69596 | 1.07733 | 0.538663 | − | 0.842521i | \(-0.318930\pi\) | ||||
0.538663 | + | 0.842521i | \(0.318930\pi\) | |||||||
\(20\) | −5.68522 | −1.27125 | ||||||||
\(21\) | −2.27759 | −0.497011 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −0.845811 | −0.176364 | −0.0881819 | − | 0.996104i | \(-0.528106\pi\) | ||||
−0.0881819 | + | 0.996104i | \(0.528106\pi\) | |||||||
\(24\) | 10.2163 | 2.08538 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | −1.20796 | −0.236900 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | −12.9486 | −2.44706 | ||||||||
\(29\) | −2.65711 | −0.493413 | −0.246707 | − | 0.969090i | \(-0.579348\pi\) | ||||
−0.246707 | + | 0.969090i | \(0.579348\pi\) | |||||||
\(30\) | −2.77222 | −0.506136 | ||||||||
\(31\) | −4.66785 | −0.838370 | −0.419185 | − | 0.907901i | \(-0.637684\pi\) | ||||
−0.419185 | + | 0.907901i | \(0.637684\pi\) | |||||||
\(32\) | 26.5602 | 4.69523 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 13.8611 | 2.37716 | ||||||||
\(35\) | 2.27759 | 0.384983 | ||||||||
\(36\) | 5.68522 | 0.947537 | ||||||||
\(37\) | −8.86239 | −1.45697 | −0.728484 | − | 0.685063i | \(-0.759775\pi\) | ||||
−0.728484 | + | 0.685063i | \(0.759775\pi\) | |||||||
\(38\) | 13.0182 | 2.11184 | ||||||||
\(39\) | −0.435737 | −0.0697737 | ||||||||
\(40\) | −10.2163 | −1.61533 | ||||||||
\(41\) | −4.29417 | −0.670637 | −0.335319 | − | 0.942105i | \(-0.608844\pi\) | ||||
−0.335319 | + | 0.942105i | \(0.608844\pi\) | |||||||
\(42\) | −6.31399 | −0.974270 | ||||||||
\(43\) | 7.00317 | 1.06797 | 0.533986 | − | 0.845493i | \(-0.320693\pi\) | ||||
0.533986 | + | 0.845493i | \(0.320693\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.00000 | −0.149071 | ||||||||
\(46\) | −2.34478 | −0.345718 | ||||||||
\(47\) | 0.468179 | 0.0682909 | 0.0341455 | − | 0.999417i | \(-0.489129\pi\) | ||||
0.0341455 | + | 0.999417i | \(0.489129\pi\) | |||||||
\(48\) | 16.9513 | 2.44671 | ||||||||
\(49\) | −1.81258 | −0.258940 | ||||||||
\(50\) | 2.77222 | 0.392052 | ||||||||
\(51\) | 5.00000 | 0.700140 | ||||||||
\(52\) | −2.47726 | −0.343534 | ||||||||
\(53\) | −10.8386 | −1.48880 | −0.744399 | − | 0.667735i | \(-0.767264\pi\) | ||||
−0.744399 | + | 0.667735i | \(0.767264\pi\) | |||||||
\(54\) | 2.77222 | 0.377252 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −23.2684 | −3.10938 | ||||||||
\(57\) | 4.69596 | 0.621995 | ||||||||
\(58\) | −7.36611 | −0.967217 | ||||||||
\(59\) | 3.93598 | 0.512421 | 0.256211 | − | 0.966621i | \(-0.417526\pi\) | ||||
0.256211 | + | 0.966621i | \(0.417526\pi\) | |||||||
\(60\) | −5.68522 | −0.733959 | ||||||||
\(61\) | 2.96549 | 0.379692 | 0.189846 | − | 0.981814i | \(-0.439201\pi\) | ||||
0.189846 | + | 0.981814i | \(0.439201\pi\) | |||||||
\(62\) | −12.9403 | −1.64342 | ||||||||
\(63\) | −2.27759 | −0.286950 | ||||||||
\(64\) | 39.7283 | 4.96604 | ||||||||
\(65\) | 0.435737 | 0.0540465 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −2.47048 | −0.301817 | −0.150909 | − | 0.988548i | \(-0.548220\pi\) | ||||
−0.150909 | + | 0.988548i | \(0.548220\pi\) | |||||||
\(68\) | 28.4261 | 3.44717 | ||||||||
\(69\) | −0.845811 | −0.101824 | ||||||||
\(70\) | 6.31399 | 0.754666 | ||||||||
\(71\) | −11.3140 | −1.34272 | −0.671362 | − | 0.741130i | \(-0.734290\pi\) | ||||
−0.671362 | + | 0.741130i | \(0.734290\pi\) | |||||||
\(72\) | 10.2163 | 1.20400 | ||||||||
\(73\) | 8.42910 | 0.986552 | 0.493276 | − | 0.869873i | \(-0.335799\pi\) | ||||
0.493276 | + | 0.869873i | \(0.335799\pi\) | |||||||
\(74\) | −24.5685 | −2.85603 | ||||||||
\(75\) | 1.00000 | 0.115470 | ||||||||
\(76\) | 26.6975 | 3.06242 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −1.20796 | −0.136775 | ||||||||
\(79\) | −10.8707 | −1.22305 | −0.611524 | − | 0.791226i | \(-0.709443\pi\) | ||||
−0.611524 | + | 0.791226i | \(0.709443\pi\) | |||||||
\(80\) | −16.9513 | −1.89521 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −11.9044 | −1.31462 | ||||||||
\(83\) | −5.92050 | −0.649859 | −0.324930 | − | 0.945738i | \(-0.605341\pi\) | ||||
−0.324930 | + | 0.945738i | \(0.605341\pi\) | |||||||
\(84\) | −12.9486 | −1.41281 | ||||||||
\(85\) | −5.00000 | −0.542326 | ||||||||
\(86\) | 19.4143 | 2.09350 | ||||||||
\(87\) | −2.65711 | −0.284872 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 5.89958 | 0.625354 | 0.312677 | − | 0.949859i | \(-0.398774\pi\) | ||||
0.312677 | + | 0.949859i | \(0.398774\pi\) | |||||||
\(90\) | −2.77222 | −0.292218 | ||||||||
\(91\) | 0.992430 | 0.104035 | ||||||||
\(92\) | −4.80862 | −0.501333 | ||||||||
\(93\) | −4.66785 | −0.484033 | ||||||||
\(94\) | 1.29790 | 0.133868 | ||||||||
\(95\) | −4.69596 | −0.481795 | ||||||||
\(96\) | 26.5602 | 2.71079 | ||||||||
\(97\) | −8.64803 | −0.878074 | −0.439037 | − | 0.898469i | \(-0.644680\pi\) | ||||
−0.439037 | + | 0.898469i | \(0.644680\pi\) | |||||||
\(98\) | −5.02487 | −0.507589 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 5.68522 | 0.568522 | ||||||||
\(101\) | −5.68126 | −0.565307 | −0.282653 | − | 0.959222i | \(-0.591215\pi\) | ||||
−0.282653 | + | 0.959222i | \(0.591215\pi\) | |||||||
\(102\) | 13.8611 | 1.37245 | ||||||||
\(103\) | −1.29613 | −0.127711 | −0.0638557 | − | 0.997959i | \(-0.520340\pi\) | ||||
−0.0638557 | + | 0.997959i | \(0.520340\pi\) | |||||||
\(104\) | −4.45160 | −0.436515 | ||||||||
\(105\) | 2.27759 | 0.222270 | ||||||||
\(106\) | −30.0471 | −2.91843 | ||||||||
\(107\) | −12.2008 | −1.17949 | −0.589746 | − | 0.807589i | \(-0.700772\pi\) | ||||
−0.589746 | + | 0.807589i | \(0.700772\pi\) | |||||||
\(108\) | 5.68522 | 0.547061 | ||||||||
\(109\) | −12.1644 | −1.16514 | −0.582568 | − | 0.812782i | \(-0.697952\pi\) | ||||
−0.582568 | + | 0.812782i | \(0.697952\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −8.86239 | −0.841181 | ||||||||
\(112\) | −38.6081 | −3.64812 | ||||||||
\(113\) | 0.142052 | 0.0133632 | 0.00668158 | − | 0.999978i | \(-0.497873\pi\) | ||||
0.00668158 | + | 0.999978i | \(0.497873\pi\) | |||||||
\(114\) | 13.0182 | 1.21927 | ||||||||
\(115\) | 0.845811 | 0.0788723 | ||||||||
\(116\) | −15.1063 | −1.40258 | ||||||||
\(117\) | −0.435737 | −0.0402839 | ||||||||
\(118\) | 10.9114 | 1.00448 | ||||||||
\(119\) | −11.3880 | −1.04393 | ||||||||
\(120\) | −10.2163 | −0.932612 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | 8.22100 | 0.744294 | ||||||||
\(123\) | −4.29417 | −0.387193 | ||||||||
\(124\) | −26.5377 | −2.38316 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | −6.31399 | −0.562495 | ||||||||
\(127\) | −0.503713 | −0.0446973 | −0.0223486 | − | 0.999750i | \(-0.507114\pi\) | ||||
−0.0223486 | + | 0.999750i | \(0.507114\pi\) | |||||||
\(128\) | 57.0153 | 5.03949 | ||||||||
\(129\) | 7.00317 | 0.616594 | ||||||||
\(130\) | 1.20796 | 0.105945 | ||||||||
\(131\) | 19.1098 | 1.66963 | 0.834816 | − | 0.550529i | \(-0.185574\pi\) | ||||
0.834816 | + | 0.550529i | \(0.185574\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −10.6955 | −0.927415 | ||||||||
\(134\) | −6.84872 | −0.591640 | ||||||||
\(135\) | −1.00000 | −0.0860663 | ||||||||
\(136\) | 51.0813 | 4.38018 | ||||||||
\(137\) | 12.3448 | 1.05469 | 0.527343 | − | 0.849653i | \(-0.323188\pi\) | ||||
0.527343 | + | 0.849653i | \(0.323188\pi\) | |||||||
\(138\) | −2.34478 | −0.199601 | ||||||||
\(139\) | −7.73236 | −0.655850 | −0.327925 | − | 0.944704i | \(-0.606349\pi\) | ||||
−0.327925 | + | 0.944704i | \(0.606349\pi\) | |||||||
\(140\) | 12.9486 | 1.09436 | ||||||||
\(141\) | 0.468179 | 0.0394278 | ||||||||
\(142\) | −31.3649 | −2.63208 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 16.9513 | 1.41261 | ||||||||
\(145\) | 2.65711 | 0.220661 | ||||||||
\(146\) | 23.3673 | 1.93390 | ||||||||
\(147\) | −1.81258 | −0.149499 | ||||||||
\(148\) | −50.3847 | −4.14159 | ||||||||
\(149\) | 7.60895 | 0.623350 | 0.311675 | − | 0.950189i | \(-0.399110\pi\) | ||||
0.311675 | + | 0.950189i | \(0.399110\pi\) | |||||||
\(150\) | 2.77222 | 0.226351 | ||||||||
\(151\) | −2.67425 | −0.217627 | −0.108814 | − | 0.994062i | \(-0.534705\pi\) | ||||
−0.108814 | + | 0.994062i | \(0.534705\pi\) | |||||||
\(152\) | 47.9751 | 3.89129 | ||||||||
\(153\) | 5.00000 | 0.404226 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 4.66785 | 0.374931 | ||||||||
\(156\) | −2.47726 | −0.198340 | ||||||||
\(157\) | 20.2000 | 1.61213 | 0.806067 | − | 0.591825i | \(-0.201592\pi\) | ||||
0.806067 | + | 0.591825i | \(0.201592\pi\) | |||||||
\(158\) | −30.1360 | −2.39749 | ||||||||
\(159\) | −10.8386 | −0.859558 | ||||||||
\(160\) | −26.5602 | −2.09977 | ||||||||
\(161\) | 1.92641 | 0.151823 | ||||||||
\(162\) | 2.77222 | 0.217806 | ||||||||
\(163\) | −9.79582 | −0.767268 | −0.383634 | − | 0.923485i | \(-0.625328\pi\) | ||||
−0.383634 | + | 0.923485i | \(0.625328\pi\) | |||||||
\(164\) | −24.4133 | −1.90636 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −16.4129 | −1.27389 | ||||||||
\(167\) | 25.5776 | 1.97925 | 0.989627 | − | 0.143658i | \(-0.0458865\pi\) | ||||
0.989627 | + | 0.143658i | \(0.0458865\pi\) | |||||||
\(168\) | −23.2684 | −1.79520 | ||||||||
\(169\) | −12.8101 | −0.985395 | ||||||||
\(170\) | −13.8611 | −1.06310 | ||||||||
\(171\) | 4.69596 | 0.359109 | ||||||||
\(172\) | 39.8145 | 3.03583 | ||||||||
\(173\) | −6.75406 | −0.513502 | −0.256751 | − | 0.966478i | \(-0.582652\pi\) | ||||
−0.256751 | + | 0.966478i | \(0.582652\pi\) | |||||||
\(174\) | −7.36611 | −0.558423 | ||||||||
\(175\) | −2.27759 | −0.172170 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 3.93598 | 0.295846 | ||||||||
\(178\) | 16.3550 | 1.22586 | ||||||||
\(179\) | 6.52195 | 0.487473 | 0.243737 | − | 0.969841i | \(-0.421627\pi\) | ||||
0.243737 | + | 0.969841i | \(0.421627\pi\) | |||||||
\(180\) | −5.68522 | −0.423751 | ||||||||
\(181\) | 13.7522 | 1.02219 | 0.511095 | − | 0.859524i | \(-0.329240\pi\) | ||||
0.511095 | + | 0.859524i | \(0.329240\pi\) | |||||||
\(182\) | 2.75124 | 0.203935 | ||||||||
\(183\) | 2.96549 | 0.219215 | ||||||||
\(184\) | −8.64102 | −0.637024 | ||||||||
\(185\) | 8.86239 | 0.651576 | ||||||||
\(186\) | −12.9403 | −0.948830 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 2.66170 | 0.194124 | ||||||||
\(189\) | −2.27759 | −0.165670 | ||||||||
\(190\) | −13.0182 | −0.944442 | ||||||||
\(191\) | −19.4360 | −1.40634 | −0.703171 | − | 0.711020i | \(-0.748233\pi\) | ||||
−0.703171 | + | 0.711020i | \(0.748233\pi\) | |||||||
\(192\) | 39.7283 | 2.86715 | ||||||||
\(193\) | 22.6124 | 1.62767 | 0.813836 | − | 0.581094i | \(-0.197375\pi\) | ||||
0.813836 | + | 0.581094i | \(0.197375\pi\) | |||||||
\(194\) | −23.9743 | −1.72125 | ||||||||
\(195\) | 0.435737 | 0.0312038 | ||||||||
\(196\) | −10.3049 | −0.736065 | ||||||||
\(197\) | 23.0300 | 1.64082 | 0.820410 | − | 0.571776i | \(-0.193745\pi\) | ||||
0.820410 | + | 0.571776i | \(0.193745\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −19.6216 | −1.39094 | −0.695468 | − | 0.718557i | \(-0.744803\pi\) | ||||
−0.695468 | + | 0.718557i | \(0.744803\pi\) | |||||||
\(200\) | 10.2163 | 0.722398 | ||||||||
\(201\) | −2.47048 | −0.174254 | ||||||||
\(202\) | −15.7497 | −1.10815 | ||||||||
\(203\) | 6.05181 | 0.424754 | ||||||||
\(204\) | 28.4261 | 1.99023 | ||||||||
\(205\) | 4.29417 | 0.299918 | ||||||||
\(206\) | −3.59316 | −0.250347 | ||||||||
\(207\) | −0.845811 | −0.0587879 | ||||||||
\(208\) | −7.38630 | −0.512148 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 6.31399 | 0.435707 | ||||||||
\(211\) | 0.0499252 | 0.00343699 | 0.00171850 | − | 0.999999i | \(-0.499453\pi\) | ||||
0.00171850 | + | 0.999999i | \(0.499453\pi\) | |||||||
\(212\) | −61.6199 | −4.23207 | ||||||||
\(213\) | −11.3140 | −0.775222 | ||||||||
\(214\) | −33.8232 | −2.31211 | ||||||||
\(215\) | −7.00317 | −0.477612 | ||||||||
\(216\) | 10.2163 | 0.695128 | ||||||||
\(217\) | 10.6314 | 0.721710 | ||||||||
\(218\) | −33.7223 | −2.28397 | ||||||||
\(219\) | 8.42910 | 0.569586 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −2.17868 | −0.146554 | ||||||||
\(222\) | −24.5685 | −1.64893 | ||||||||
\(223\) | 0.754962 | 0.0505560 | 0.0252780 | − | 0.999680i | \(-0.491953\pi\) | ||||
0.0252780 | + | 0.999680i | \(0.491953\pi\) | |||||||
\(224\) | −60.4934 | −4.04188 | ||||||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | 0.393801 | 0.0261952 | ||||||||
\(227\) | 8.28399 | 0.549828 | 0.274914 | − | 0.961469i | \(-0.411351\pi\) | ||||
0.274914 | + | 0.961469i | \(0.411351\pi\) | |||||||
\(228\) | 26.6975 | 1.76809 | ||||||||
\(229\) | −2.87622 | −0.190066 | −0.0950330 | − | 0.995474i | \(-0.530296\pi\) | ||||
−0.0950330 | + | 0.995474i | \(0.530296\pi\) | |||||||
\(230\) | 2.34478 | 0.154610 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −27.1457 | −1.78220 | ||||||||
\(233\) | −5.17868 | −0.339267 | −0.169633 | − | 0.985507i | \(-0.554258\pi\) | ||||
−0.169633 | + | 0.985507i | \(0.554258\pi\) | |||||||
\(234\) | −1.20796 | −0.0789668 | ||||||||
\(235\) | −0.468179 | −0.0305406 | ||||||||
\(236\) | 22.3769 | 1.45661 | ||||||||
\(237\) | −10.8707 | −0.706127 | ||||||||
\(238\) | −31.5700 | −2.04638 | ||||||||
\(239\) | 10.8328 | 0.700714 | 0.350357 | − | 0.936616i | \(-0.386060\pi\) | ||||
0.350357 | + | 0.936616i | \(0.386060\pi\) | |||||||
\(240\) | −16.9513 | −1.09420 | ||||||||
\(241\) | −2.96526 | −0.191009 | −0.0955045 | − | 0.995429i | \(-0.530446\pi\) | ||||
−0.0955045 | + | 0.995429i | \(0.530446\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 16.8595 | 1.07932 | ||||||||
\(245\) | 1.81258 | 0.115801 | ||||||||
\(246\) | −11.9044 | −0.758997 | ||||||||
\(247\) | −2.04620 | −0.130197 | ||||||||
\(248\) | −47.6879 | −3.02818 | ||||||||
\(249\) | −5.92050 | −0.375196 | ||||||||
\(250\) | −2.77222 | −0.175331 | ||||||||
\(251\) | −17.6144 | −1.11181 | −0.555906 | − | 0.831245i | \(-0.687629\pi\) | ||||
−0.555906 | + | 0.831245i | \(0.687629\pi\) | |||||||
\(252\) | −12.9486 | −0.815685 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −1.39640 | −0.0876182 | ||||||||
\(255\) | −5.00000 | −0.313112 | ||||||||
\(256\) | 78.6025 | 4.91266 | ||||||||
\(257\) | 20.9647 | 1.30774 | 0.653871 | − | 0.756606i | \(-0.273144\pi\) | ||||
0.653871 | + | 0.756606i | \(0.273144\pi\) | |||||||
\(258\) | 19.4143 | 1.20868 | ||||||||
\(259\) | 20.1849 | 1.25423 | ||||||||
\(260\) | 2.47726 | 0.153633 | ||||||||
\(261\) | −2.65711 | −0.164471 | ||||||||
\(262\) | 52.9766 | 3.27291 | ||||||||
\(263\) | 8.43471 | 0.520107 | 0.260053 | − | 0.965594i | \(-0.416260\pi\) | ||||
0.260053 | + | 0.965594i | \(0.416260\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 10.8386 | 0.665811 | ||||||||
\(266\) | −29.6502 | −1.81797 | ||||||||
\(267\) | 5.89958 | 0.361049 | ||||||||
\(268\) | −14.0452 | −0.857949 | ||||||||
\(269\) | 9.64346 | 0.587972 | 0.293986 | − | 0.955810i | \(-0.405018\pi\) | ||||
0.293986 | + | 0.955810i | \(0.405018\pi\) | |||||||
\(270\) | −2.77222 | −0.168712 | ||||||||
\(271\) | 10.2278 | 0.621293 | 0.310647 | − | 0.950525i | \(-0.399454\pi\) | ||||
0.310647 | + | 0.950525i | \(0.399454\pi\) | |||||||
\(272\) | 84.7564 | 5.13911 | ||||||||
\(273\) | 0.992430 | 0.0600646 | ||||||||
\(274\) | 34.2225 | 2.06746 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −4.80862 | −0.289445 | ||||||||
\(277\) | −5.83903 | −0.350833 | −0.175417 | − | 0.984494i | \(-0.556127\pi\) | ||||
−0.175417 | + | 0.984494i | \(0.556127\pi\) | |||||||
\(278\) | −21.4358 | −1.28563 | ||||||||
\(279\) | −4.66785 | −0.279457 | ||||||||
\(280\) | 23.2684 | 1.39056 | ||||||||
\(281\) | 14.4139 | 0.859858 | 0.429929 | − | 0.902863i | \(-0.358539\pi\) | ||||
0.429929 | + | 0.902863i | \(0.358539\pi\) | |||||||
\(282\) | 1.29790 | 0.0772886 | ||||||||
\(283\) | −10.6334 | −0.632093 | −0.316046 | − | 0.948744i | \(-0.602356\pi\) | ||||
−0.316046 | + | 0.948744i | \(0.602356\pi\) | |||||||
\(284\) | −64.3225 | −3.81684 | ||||||||
\(285\) | −4.69596 | −0.278164 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 9.78037 | 0.577317 | ||||||||
\(288\) | 26.5602 | 1.56508 | ||||||||
\(289\) | 8.00000 | 0.470588 | ||||||||
\(290\) | 7.36611 | 0.432553 | ||||||||
\(291\) | −8.64803 | −0.506957 | ||||||||
\(292\) | 47.9213 | 2.80438 | ||||||||
\(293\) | −8.39576 | −0.490485 | −0.245243 | − | 0.969462i | \(-0.578868\pi\) | ||||
−0.245243 | + | 0.969462i | \(0.578868\pi\) | |||||||
\(294\) | −5.02487 | −0.293057 | ||||||||
\(295\) | −3.93598 | −0.229162 | ||||||||
\(296\) | −90.5404 | −5.26256 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 21.0937 | 1.22193 | ||||||||
\(299\) | 0.368551 | 0.0213139 | ||||||||
\(300\) | 5.68522 | 0.328236 | ||||||||
\(301\) | −15.9504 | −0.919363 | ||||||||
\(302\) | −7.41362 | −0.426606 | ||||||||
\(303\) | −5.68126 | −0.326380 | ||||||||
\(304\) | 79.6025 | 4.56552 | ||||||||
\(305\) | −2.96549 | −0.169803 | ||||||||
\(306\) | 13.8611 | 0.792387 | ||||||||
\(307\) | 4.51902 | 0.257914 | 0.128957 | − | 0.991650i | \(-0.458837\pi\) | ||||
0.128957 | + | 0.991650i | \(0.458837\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1.29613 | −0.0737343 | ||||||||
\(310\) | 12.9403 | 0.734961 | ||||||||
\(311\) | 23.9970 | 1.36074 | 0.680372 | − | 0.732867i | \(-0.261818\pi\) | ||||
0.680372 | + | 0.732867i | \(0.261818\pi\) | |||||||
\(312\) | −4.45160 | −0.252022 | ||||||||
\(313\) | −25.8686 | −1.46218 | −0.731090 | − | 0.682281i | \(-0.760988\pi\) | ||||
−0.731090 | + | 0.682281i | \(0.760988\pi\) | |||||||
\(314\) | 55.9988 | 3.16020 | ||||||||
\(315\) | 2.27759 | 0.128328 | ||||||||
\(316\) | −61.8022 | −3.47665 | ||||||||
\(317\) | 2.90319 | 0.163060 | 0.0815298 | − | 0.996671i | \(-0.474019\pi\) | ||||
0.0815298 | + | 0.996671i | \(0.474019\pi\) | |||||||
\(318\) | −30.0471 | −1.68496 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | −39.7283 | −2.22088 | ||||||||
\(321\) | −12.2008 | −0.680980 | ||||||||
\(322\) | 5.34044 | 0.297611 | ||||||||
\(323\) | 23.4798 | 1.30645 | ||||||||
\(324\) | 5.68522 | 0.315846 | ||||||||
\(325\) | −0.435737 | −0.0241703 | ||||||||
\(326\) | −27.1562 | −1.50404 | ||||||||
\(327\) | −12.1644 | −0.672691 | ||||||||
\(328\) | −43.8703 | −2.42233 | ||||||||
\(329\) | −1.06632 | −0.0587881 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 10.9837 | 0.603720 | 0.301860 | − | 0.953352i | \(-0.402392\pi\) | ||||
0.301860 | + | 0.953352i | \(0.402392\pi\) | |||||||
\(332\) | −33.6593 | −1.84730 | ||||||||
\(333\) | −8.86239 | −0.485656 | ||||||||
\(334\) | 70.9068 | 3.87985 | ||||||||
\(335\) | 2.47048 | 0.134977 | ||||||||
\(336\) | −38.6081 | −2.10624 | ||||||||
\(337\) | 12.8462 | 0.699775 | 0.349887 | − | 0.936792i | \(-0.386220\pi\) | ||||
0.349887 | + | 0.936792i | \(0.386220\pi\) | |||||||
\(338\) | −35.5125 | −1.93163 | ||||||||
\(339\) | 0.142052 | 0.00771522 | ||||||||
\(340\) | −28.4261 | −1.54162 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 13.0182 | 0.703946 | ||||||||
\(343\) | 20.0715 | 1.08376 | ||||||||
\(344\) | 71.5461 | 3.85751 | ||||||||
\(345\) | 0.845811 | 0.0455369 | ||||||||
\(346\) | −18.7238 | −1.00660 | ||||||||
\(347\) | −1.88971 | −0.101445 | −0.0507225 | − | 0.998713i | \(-0.516152\pi\) | ||||
−0.0507225 | + | 0.998713i | \(0.516152\pi\) | |||||||
\(348\) | −15.1063 | −0.809781 | ||||||||
\(349\) | 23.7787 | 1.27284 | 0.636422 | − | 0.771341i | \(-0.280414\pi\) | ||||
0.636422 | + | 0.771341i | \(0.280414\pi\) | |||||||
\(350\) | −6.31399 | −0.337497 | ||||||||
\(351\) | −0.435737 | −0.0232579 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −20.2294 | −1.07670 | −0.538352 | − | 0.842720i | \(-0.680953\pi\) | ||||
−0.538352 | + | 0.842720i | \(0.680953\pi\) | |||||||
\(354\) | 10.9114 | 0.579935 | ||||||||
\(355\) | 11.3140 | 0.600484 | ||||||||
\(356\) | 33.5404 | 1.77764 | ||||||||
\(357\) | −11.3880 | −0.602715 | ||||||||
\(358\) | 18.0803 | 0.955573 | ||||||||
\(359\) | −18.5897 | −0.981129 | −0.490565 | − | 0.871405i | \(-0.663209\pi\) | ||||
−0.490565 | + | 0.871405i | \(0.663209\pi\) | |||||||
\(360\) | −10.2163 | −0.538444 | ||||||||
\(361\) | 3.05200 | 0.160632 | ||||||||
\(362\) | 38.1241 | 2.00376 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 5.64219 | 0.295731 | ||||||||
\(365\) | −8.42910 | −0.441199 | ||||||||
\(366\) | 8.22100 | 0.429718 | ||||||||
\(367\) | 5.90811 | 0.308401 | 0.154200 | − | 0.988040i | \(-0.450720\pi\) | ||||
0.154200 | + | 0.988040i | \(0.450720\pi\) | |||||||
\(368\) | −14.3376 | −0.747398 | ||||||||
\(369\) | −4.29417 | −0.223546 | ||||||||
\(370\) | 24.5685 | 1.27726 | ||||||||
\(371\) | 24.6859 | 1.28163 | ||||||||
\(372\) | −26.5377 | −1.37592 | ||||||||
\(373\) | −1.66992 | −0.0864650 | −0.0432325 | − | 0.999065i | \(-0.513766\pi\) | ||||
−0.0432325 | + | 0.999065i | \(0.513766\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1.00000 | −0.0516398 | ||||||||
\(376\) | 4.78303 | 0.246666 | ||||||||
\(377\) | 1.15780 | 0.0596298 | ||||||||
\(378\) | −6.31399 | −0.324757 | ||||||||
\(379\) | 8.43518 | 0.433286 | 0.216643 | − | 0.976251i | \(-0.430489\pi\) | ||||
0.216643 | + | 0.976251i | \(0.430489\pi\) | |||||||
\(380\) | −26.6975 | −1.36956 | ||||||||
\(381\) | −0.503713 | −0.0258060 | ||||||||
\(382\) | −53.8810 | −2.75679 | ||||||||
\(383\) | 21.8815 | 1.11809 | 0.559047 | − | 0.829136i | \(-0.311167\pi\) | ||||
0.559047 | + | 0.829136i | \(0.311167\pi\) | |||||||
\(384\) | 57.0153 | 2.90955 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 62.6865 | 3.19066 | ||||||||
\(387\) | 7.00317 | 0.355991 | ||||||||
\(388\) | −49.1660 | −2.49602 | ||||||||
\(389\) | −0.392092 | −0.0198799 | −0.00993993 | − | 0.999951i | \(-0.503164\pi\) | ||||
−0.00993993 | + | 0.999951i | \(0.503164\pi\) | |||||||
\(390\) | 1.20796 | 0.0611674 | ||||||||
\(391\) | −4.22906 | −0.213873 | ||||||||
\(392\) | −18.5178 | −0.935288 | ||||||||
\(393\) | 19.1098 | 0.963962 | ||||||||
\(394\) | 63.8443 | 3.21643 | ||||||||
\(395\) | 10.8707 | 0.546963 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 35.7823 | 1.79586 | 0.897932 | − | 0.440134i | \(-0.145069\pi\) | ||||
0.897932 | + | 0.440134i | \(0.145069\pi\) | |||||||
\(398\) | −54.3954 | −2.72659 | ||||||||
\(399\) | −10.6955 | −0.535443 | ||||||||
\(400\) | 16.9513 | 0.847564 | ||||||||
\(401\) | 30.4165 | 1.51893 | 0.759463 | − | 0.650551i | \(-0.225462\pi\) | ||||
0.759463 | + | 0.650551i | \(0.225462\pi\) | |||||||
\(402\) | −6.84872 | −0.341583 | ||||||||
\(403\) | 2.03395 | 0.101318 | ||||||||
\(404\) | −32.2992 | −1.60695 | ||||||||
\(405\) | −1.00000 | −0.0496904 | ||||||||
\(406\) | 16.7770 | 0.832627 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 51.0813 | 2.52890 | ||||||||
\(409\) | −16.2697 | −0.804486 | −0.402243 | − | 0.915533i | \(-0.631769\pi\) | ||||
−0.402243 | + | 0.915533i | \(0.631769\pi\) | |||||||
\(410\) | 11.9044 | 0.587917 | ||||||||
\(411\) | 12.3448 | 0.608923 | ||||||||
\(412\) | −7.36878 | −0.363034 | ||||||||
\(413\) | −8.96456 | −0.441117 | ||||||||
\(414\) | −2.34478 | −0.115239 | ||||||||
\(415\) | 5.92050 | 0.290626 | ||||||||
\(416\) | −11.5733 | −0.567427 | ||||||||
\(417\) | −7.73236 | −0.378655 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −40.0703 | −1.95756 | −0.978781 | − | 0.204910i | \(-0.934310\pi\) | ||||
−0.978781 | + | 0.204910i | \(0.934310\pi\) | |||||||
\(420\) | 12.9486 | 0.631827 | ||||||||
\(421\) | −19.3943 | −0.945219 | −0.472609 | − | 0.881272i | \(-0.656688\pi\) | ||||
−0.472609 | + | 0.881272i | \(0.656688\pi\) | |||||||
\(422\) | 0.138404 | 0.00673739 | ||||||||
\(423\) | 0.468179 | 0.0227636 | ||||||||
\(424\) | −110.730 | −5.37753 | ||||||||
\(425\) | 5.00000 | 0.242536 | ||||||||
\(426\) | −31.3649 | −1.51963 | ||||||||
\(427\) | −6.75417 | −0.326857 | ||||||||
\(428\) | −69.3640 | −3.35284 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −19.4143 | −0.936243 | ||||||||
\(431\) | 33.9444 | 1.63505 | 0.817523 | − | 0.575896i | \(-0.195347\pi\) | ||||
0.817523 | + | 0.575896i | \(0.195347\pi\) | |||||||
\(432\) | 16.9513 | 0.815569 | ||||||||
\(433\) | −13.1155 | −0.630290 | −0.315145 | − | 0.949044i | \(-0.602053\pi\) | ||||
−0.315145 | + | 0.949044i | \(0.602053\pi\) | |||||||
\(434\) | 29.4727 | 1.41474 | ||||||||
\(435\) | 2.65711 | 0.127399 | ||||||||
\(436\) | −69.1571 | −3.31202 | ||||||||
\(437\) | −3.97189 | −0.190001 | ||||||||
\(438\) | 23.3673 | 1.11654 | ||||||||
\(439\) | −9.64731 | −0.460441 | −0.230220 | − | 0.973138i | \(-0.573945\pi\) | ||||
−0.230220 | + | 0.973138i | \(0.573945\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1.81258 | −0.0863133 | ||||||||
\(442\) | −6.03980 | −0.287284 | ||||||||
\(443\) | −8.91410 | −0.423521 | −0.211761 | − | 0.977322i | \(-0.567920\pi\) | ||||
−0.211761 | + | 0.977322i | \(0.567920\pi\) | |||||||
\(444\) | −50.3847 | −2.39115 | ||||||||
\(445\) | −5.89958 | −0.279667 | ||||||||
\(446\) | 2.09292 | 0.0991028 | ||||||||
\(447\) | 7.60895 | 0.359891 | ||||||||
\(448\) | −90.4849 | −4.27501 | ||||||||
\(449\) | −12.4368 | −0.586931 | −0.293465 | − | 0.955970i | \(-0.594809\pi\) | ||||
−0.293465 | + | 0.955970i | \(0.594809\pi\) | |||||||
\(450\) | 2.77222 | 0.130684 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 0.807599 | 0.0379863 | ||||||||
\(453\) | −2.67425 | −0.125647 | ||||||||
\(454\) | 22.9651 | 1.07780 | ||||||||
\(455\) | −0.992430 | −0.0465259 | ||||||||
\(456\) | 47.9751 | 2.24664 | ||||||||
\(457\) | −38.1583 | −1.78497 | −0.892484 | − | 0.451078i | \(-0.851040\pi\) | ||||
−0.892484 | + | 0.451078i | \(0.851040\pi\) | |||||||
\(458\) | −7.97353 | −0.372578 | ||||||||
\(459\) | 5.00000 | 0.233380 | ||||||||
\(460\) | 4.80862 | 0.224203 | ||||||||
\(461\) | 34.3847 | 1.60145 | 0.800726 | − | 0.599030i | \(-0.204447\pi\) | ||||
0.800726 | + | 0.599030i | \(0.204447\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −40.2561 | −1.87086 | −0.935430 | − | 0.353511i | \(-0.884988\pi\) | ||||
−0.935430 | + | 0.353511i | \(0.884988\pi\) | |||||||
\(464\) | −45.0415 | −2.09100 | ||||||||
\(465\) | 4.66785 | 0.216466 | ||||||||
\(466\) | −14.3565 | −0.665051 | ||||||||
\(467\) | 15.1161 | 0.699490 | 0.349745 | − | 0.936845i | \(-0.386268\pi\) | ||||
0.349745 | + | 0.936845i | \(0.386268\pi\) | |||||||
\(468\) | −2.47726 | −0.114511 | ||||||||
\(469\) | 5.62674 | 0.259819 | ||||||||
\(470\) | −1.29790 | −0.0598675 | ||||||||
\(471\) | 20.2000 | 0.930766 | ||||||||
\(472\) | 40.2110 | 1.85086 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | −30.1360 | −1.38419 | ||||||||
\(475\) | 4.69596 | 0.215465 | ||||||||
\(476\) | −64.7430 | −2.96749 | ||||||||
\(477\) | −10.8386 | −0.496266 | ||||||||
\(478\) | 30.0309 | 1.37358 | ||||||||
\(479\) | −28.8045 | −1.31611 | −0.658055 | − | 0.752970i | \(-0.728621\pi\) | ||||
−0.658055 | + | 0.752970i | \(0.728621\pi\) | |||||||
\(480\) | −26.5602 | −1.21230 | ||||||||
\(481\) | 3.86167 | 0.176077 | ||||||||
\(482\) | −8.22035 | −0.374427 | ||||||||
\(483\) | 1.92641 | 0.0876548 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 8.64803 | 0.392687 | ||||||||
\(486\) | 2.77222 | 0.125751 | ||||||||
\(487\) | 28.8525 | 1.30743 | 0.653716 | − | 0.756740i | \(-0.273209\pi\) | ||||
0.653716 | + | 0.756740i | \(0.273209\pi\) | |||||||
\(488\) | 30.2962 | 1.37144 | ||||||||
\(489\) | −9.79582 | −0.442982 | ||||||||
\(490\) | 5.02487 | 0.227001 | ||||||||
\(491\) | −14.9367 | −0.674084 | −0.337042 | − | 0.941490i | \(-0.609426\pi\) | ||||
−0.337042 | + | 0.941490i | \(0.609426\pi\) | |||||||
\(492\) | −24.4133 | −1.10064 | ||||||||
\(493\) | −13.2856 | −0.598351 | ||||||||
\(494\) | −5.67253 | −0.255219 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −79.1260 | −3.55286 | ||||||||
\(497\) | 25.7686 | 1.15588 | ||||||||
\(498\) | −16.4129 | −0.735481 | ||||||||
\(499\) | 22.1990 | 0.993764 | 0.496882 | − | 0.867818i | \(-0.334478\pi\) | ||||
0.496882 | + | 0.867818i | \(0.334478\pi\) | |||||||
\(500\) | −5.68522 | −0.254251 | ||||||||
\(501\) | 25.5776 | 1.14272 | ||||||||
\(502\) | −48.8311 | −2.17944 | ||||||||
\(503\) | 0.155356 | 0.00692698 | 0.00346349 | − | 0.999994i | \(-0.498898\pi\) | ||||
0.00346349 | + | 0.999994i | \(0.498898\pi\) | |||||||
\(504\) | −23.2684 | −1.03646 | ||||||||
\(505\) | 5.68126 | 0.252813 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −12.8101 | −0.568918 | ||||||||
\(508\) | −2.86372 | −0.127057 | ||||||||
\(509\) | −18.6375 | −0.826095 | −0.413047 | − | 0.910710i | \(-0.635536\pi\) | ||||
−0.413047 | + | 0.910710i | \(0.635536\pi\) | |||||||
\(510\) | −13.8611 | −0.613780 | ||||||||
\(511\) | −19.1980 | −0.849272 | ||||||||
\(512\) | 103.873 | 4.59058 | ||||||||
\(513\) | 4.69596 | 0.207332 | ||||||||
\(514\) | 58.1188 | 2.56351 | ||||||||
\(515\) | 1.29613 | 0.0571143 | ||||||||
\(516\) | 39.8145 | 1.75274 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 55.9571 | 2.45861 | ||||||||
\(519\) | −6.75406 | −0.296470 | ||||||||
\(520\) | 4.45160 | 0.195215 | ||||||||
\(521\) | 31.3888 | 1.37517 | 0.687585 | − | 0.726104i | \(-0.258671\pi\) | ||||
0.687585 | + | 0.726104i | \(0.258671\pi\) | |||||||
\(522\) | −7.36611 | −0.322406 | ||||||||
\(523\) | −23.9841 | −1.04875 | −0.524377 | − | 0.851486i | \(-0.675702\pi\) | ||||
−0.524377 | + | 0.851486i | \(0.675702\pi\) | |||||||
\(524\) | 108.643 | 4.74611 | ||||||||
\(525\) | −2.27759 | −0.0994022 | ||||||||
\(526\) | 23.3829 | 1.01954 | ||||||||
\(527\) | −23.3392 | −1.01667 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.2846 | −0.968896 | ||||||||
\(530\) | 30.0471 | 1.30516 | ||||||||
\(531\) | 3.93598 | 0.170807 | ||||||||
\(532\) | −60.8061 | −2.63628 | ||||||||
\(533\) | 1.87113 | 0.0810476 | ||||||||
\(534\) | 16.3550 | 0.707748 | ||||||||
\(535\) | 12.2008 | 0.527485 | ||||||||
\(536\) | −25.2390 | −1.09016 | ||||||||
\(537\) | 6.52195 | 0.281443 | ||||||||
\(538\) | 26.7338 | 1.15258 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −5.68522 | −0.244653 | ||||||||
\(541\) | 9.97322 | 0.428782 | 0.214391 | − | 0.976748i | \(-0.431223\pi\) | ||||
0.214391 | + | 0.976748i | \(0.431223\pi\) | |||||||
\(542\) | 28.3537 | 1.21789 | ||||||||
\(543\) | 13.7522 | 0.590162 | ||||||||
\(544\) | 132.801 | 5.69380 | ||||||||
\(545\) | 12.1644 | 0.521064 | ||||||||
\(546\) | 2.75124 | 0.117742 | ||||||||
\(547\) | −40.0167 | −1.71099 | −0.855496 | − | 0.517809i | \(-0.826748\pi\) | ||||
−0.855496 | + | 0.517809i | \(0.826748\pi\) | |||||||
\(548\) | 70.1828 | 2.99806 | ||||||||
\(549\) | 2.96549 | 0.126564 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −12.4777 | −0.531567 | ||||||||
\(552\) | −8.64102 | −0.367786 | ||||||||
\(553\) | 24.7590 | 1.05286 | ||||||||
\(554\) | −16.1871 | −0.687724 | ||||||||
\(555\) | 8.86239 | 0.376188 | ||||||||
\(556\) | −43.9601 | −1.86433 | ||||||||
\(557\) | −7.76046 | −0.328821 | −0.164411 | − | 0.986392i | \(-0.552572\pi\) | ||||
−0.164411 | + | 0.986392i | \(0.552572\pi\) | |||||||
\(558\) | −12.9403 | −0.547807 | ||||||||
\(559\) | −3.05154 | −0.129066 | ||||||||
\(560\) | 38.6081 | 1.63149 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 39.9584 | 1.68554 | ||||||||
\(563\) | 18.4355 | 0.776964 | 0.388482 | − | 0.921456i | \(-0.373000\pi\) | ||||
0.388482 | + | 0.921456i | \(0.373000\pi\) | |||||||
\(564\) | 2.66170 | 0.112078 | ||||||||
\(565\) | −0.142052 | −0.00597619 | ||||||||
\(566\) | −29.4783 | −1.23906 | ||||||||
\(567\) | −2.27759 | −0.0956498 | ||||||||
\(568\) | −115.587 | −4.84990 | ||||||||
\(569\) | 11.0239 | 0.462148 | 0.231074 | − | 0.972936i | \(-0.425776\pi\) | ||||
0.231074 | + | 0.972936i | \(0.425776\pi\) | |||||||
\(570\) | −13.0182 | −0.545274 | ||||||||
\(571\) | −38.1338 | −1.59585 | −0.797926 | − | 0.602756i | \(-0.794069\pi\) | ||||
−0.797926 | + | 0.602756i | \(0.794069\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −19.4360 | −0.811952 | ||||||||
\(574\) | 27.1134 | 1.13169 | ||||||||
\(575\) | −0.845811 | −0.0352728 | ||||||||
\(576\) | 39.7283 | 1.65535 | ||||||||
\(577\) | 11.0122 | 0.458446 | 0.229223 | − | 0.973374i | \(-0.426382\pi\) | ||||
0.229223 | + | 0.973374i | \(0.426382\pi\) | |||||||
\(578\) | 22.1778 | 0.922474 | ||||||||
\(579\) | 22.6124 | 0.939737 | ||||||||
\(580\) | 15.1063 | 0.627253 | ||||||||
\(581\) | 13.4845 | 0.559430 | ||||||||
\(582\) | −23.9743 | −0.993765 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 86.1138 | 3.56341 | ||||||||
\(585\) | 0.435737 | 0.0180155 | ||||||||
\(586\) | −23.2749 | −0.961478 | ||||||||
\(587\) | 11.8440 | 0.488853 | 0.244427 | − | 0.969668i | \(-0.421400\pi\) | ||||
0.244427 | + | 0.969668i | \(0.421400\pi\) | |||||||
\(588\) | −10.3049 | −0.424967 | ||||||||
\(589\) | −21.9200 | −0.903198 | ||||||||
\(590\) | −10.9114 | −0.449216 | ||||||||
\(591\) | 23.0300 | 0.947327 | ||||||||
\(592\) | −150.229 | −6.17437 | ||||||||
\(593\) | 9.25062 | 0.379877 | 0.189939 | − | 0.981796i | \(-0.439171\pi\) | ||||
0.189939 | + | 0.981796i | \(0.439171\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 11.3880 | 0.466861 | ||||||||
\(596\) | 43.2586 | 1.77194 | ||||||||
\(597\) | −19.6216 | −0.803058 | ||||||||
\(598\) | 1.02171 | 0.0417807 | ||||||||
\(599\) | 23.6834 | 0.967678 | 0.483839 | − | 0.875157i | \(-0.339242\pi\) | ||||
0.483839 | + | 0.875157i | \(0.339242\pi\) | |||||||
\(600\) | 10.2163 | 0.417077 | ||||||||
\(601\) | 36.2731 | 1.47961 | 0.739806 | − | 0.672821i | \(-0.234917\pi\) | ||||
0.739806 | + | 0.672821i | \(0.234917\pi\) | |||||||
\(602\) | −44.2179 | −1.80219 | ||||||||
\(603\) | −2.47048 | −0.100606 | ||||||||
\(604\) | −15.2037 | −0.618630 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −15.7497 | −0.639789 | ||||||||
\(607\) | −24.5068 | −0.994699 | −0.497350 | − | 0.867550i | \(-0.665693\pi\) | ||||
−0.497350 | + | 0.867550i | \(0.665693\pi\) | |||||||
\(608\) | 124.726 | 5.05830 | ||||||||
\(609\) | 6.05181 | 0.245232 | ||||||||
\(610\) | −8.22100 | −0.332858 | ||||||||
\(611\) | −0.204003 | −0.00825307 | ||||||||
\(612\) | 28.4261 | 1.14906 | ||||||||
\(613\) | 4.64498 | 0.187609 | 0.0938044 | − | 0.995591i | \(-0.470097\pi\) | ||||
0.0938044 | + | 0.995591i | \(0.470097\pi\) | |||||||
\(614\) | 12.5277 | 0.505578 | ||||||||
\(615\) | 4.29417 | 0.173158 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 41.7419 | 1.68047 | 0.840233 | − | 0.542226i | \(-0.182418\pi\) | ||||
0.840233 | + | 0.542226i | \(0.182418\pi\) | |||||||
\(618\) | −3.59316 | −0.144538 | ||||||||
\(619\) | −44.2019 | −1.77663 | −0.888313 | − | 0.459239i | \(-0.848122\pi\) | ||||
−0.888313 | + | 0.459239i | \(0.848122\pi\) | |||||||
\(620\) | 26.5377 | 1.06578 | ||||||||
\(621\) | −0.845811 | −0.0339412 | ||||||||
\(622\) | 66.5250 | 2.66741 | ||||||||
\(623\) | −13.4368 | −0.538335 | ||||||||
\(624\) | −7.38630 | −0.295689 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −71.7136 | −2.86625 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 114.841 | 4.58267 | ||||||||
\(629\) | −44.3120 | −1.76683 | ||||||||
\(630\) | 6.31399 | 0.251555 | ||||||||
\(631\) | −16.1161 | −0.641572 | −0.320786 | − | 0.947152i | \(-0.603947\pi\) | ||||
−0.320786 | + | 0.947152i | \(0.603947\pi\) | |||||||
\(632\) | −111.058 | −4.41764 | ||||||||
\(633\) | 0.0499252 | 0.00198435 | ||||||||
\(634\) | 8.04830 | 0.319639 | ||||||||
\(635\) | 0.503713 | 0.0199892 | ||||||||
\(636\) | −61.6199 | −2.44339 | ||||||||
\(637\) | 0.789807 | 0.0312933 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −11.3140 | −0.447575 | ||||||||
\(640\) | −57.0153 | −2.25373 | ||||||||
\(641\) | −9.20985 | −0.363767 | −0.181884 | − | 0.983320i | \(-0.558219\pi\) | ||||
−0.181884 | + | 0.983320i | \(0.558219\pi\) | |||||||
\(642\) | −33.8232 | −1.33490 | ||||||||
\(643\) | 4.01530 | 0.158348 | 0.0791741 | − | 0.996861i | \(-0.474772\pi\) | ||||
0.0791741 | + | 0.996861i | \(0.474772\pi\) | |||||||
\(644\) | 10.9521 | 0.431572 | ||||||||
\(645\) | −7.00317 | −0.275749 | ||||||||
\(646\) | 65.0912 | 2.56098 | ||||||||
\(647\) | 14.2693 | 0.560984 | 0.280492 | − | 0.959856i | \(-0.409502\pi\) | ||||
0.280492 | + | 0.959856i | \(0.409502\pi\) | |||||||
\(648\) | 10.2163 | 0.401332 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | −1.20796 | −0.0473801 | ||||||||
\(651\) | 10.6314 | 0.416679 | ||||||||
\(652\) | −55.6914 | −2.18104 | ||||||||
\(653\) | −6.52172 | −0.255215 | −0.127607 | − | 0.991825i | \(-0.540730\pi\) | ||||
−0.127607 | + | 0.991825i | \(0.540730\pi\) | |||||||
\(654\) | −33.7223 | −1.31865 | ||||||||
\(655\) | −19.1098 | −0.746682 | ||||||||
\(656\) | −72.7917 | −2.84204 | ||||||||
\(657\) | 8.42910 | 0.328851 | ||||||||
\(658\) | −2.95608 | −0.115240 | ||||||||
\(659\) | 6.74928 | 0.262915 | 0.131457 | − | 0.991322i | \(-0.458034\pi\) | ||||
0.131457 | + | 0.991322i | \(0.458034\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 9.65248 | 0.375438 | 0.187719 | − | 0.982223i | \(-0.439891\pi\) | ||||
0.187719 | + | 0.982223i | \(0.439891\pi\) | |||||||
\(662\) | 30.4493 | 1.18345 | ||||||||
\(663\) | −2.17868 | −0.0846131 | ||||||||
\(664\) | −60.4853 | −2.34728 | ||||||||
\(665\) | 10.6955 | 0.414752 | ||||||||
\(666\) | −24.5685 | −0.952011 | ||||||||
\(667\) | 2.24741 | 0.0870202 | ||||||||
\(668\) | 145.414 | 5.62625 | ||||||||
\(669\) | 0.754962 | 0.0291885 | ||||||||
\(670\) | 6.84872 | 0.264589 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | −60.4934 | −2.33358 | ||||||||
\(673\) | −28.3594 | −1.09318 | −0.546588 | − | 0.837402i | \(-0.684074\pi\) | ||||
−0.546588 | + | 0.837402i | \(0.684074\pi\) | |||||||
\(674\) | 35.6124 | 1.37174 | ||||||||
\(675\) | 1.00000 | 0.0384900 | ||||||||
\(676\) | −72.8284 | −2.80109 | ||||||||
\(677\) | −5.08697 | −0.195508 | −0.0977540 | − | 0.995211i | \(-0.531166\pi\) | ||||
−0.0977540 | + | 0.995211i | \(0.531166\pi\) | |||||||
\(678\) | 0.393801 | 0.0151238 | ||||||||
\(679\) | 19.6967 | 0.755889 | ||||||||
\(680\) | −51.0813 | −1.95888 | ||||||||
\(681\) | 8.28399 | 0.317443 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 17.3612 | 0.664310 | 0.332155 | − | 0.943225i | \(-0.392224\pi\) | ||||
0.332155 | + | 0.943225i | \(0.392224\pi\) | |||||||
\(684\) | 26.6975 | 1.02081 | ||||||||
\(685\) | −12.3448 | −0.471670 | ||||||||
\(686\) | 55.6425 | 2.12444 | ||||||||
\(687\) | −2.87622 | −0.109735 | ||||||||
\(688\) | 118.713 | 4.52588 | ||||||||
\(689\) | 4.72279 | 0.179924 | ||||||||
\(690\) | 2.34478 | 0.0892641 | ||||||||
\(691\) | −42.9791 | −1.63500 | −0.817500 | − | 0.575928i | \(-0.804641\pi\) | ||||
−0.817500 | + | 0.575928i | \(0.804641\pi\) | |||||||
\(692\) | −38.3983 | −1.45969 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −5.23870 | −0.198858 | ||||||||
\(695\) | 7.73236 | 0.293305 | ||||||||
\(696\) | −27.1457 | −1.02896 | ||||||||
\(697\) | −21.4709 | −0.813267 | ||||||||
\(698\) | 65.9198 | 2.49510 | ||||||||
\(699\) | −5.17868 | −0.195876 | ||||||||
\(700\) | −12.9486 | −0.489411 | ||||||||
\(701\) | −14.3882 | −0.543436 | −0.271718 | − | 0.962377i | \(-0.587592\pi\) | ||||
−0.271718 | + | 0.962377i | \(0.587592\pi\) | |||||||
\(702\) | −1.20796 | −0.0455915 | ||||||||
\(703\) | −41.6174 | −1.56963 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −0.468179 | −0.0176326 | ||||||||
\(706\) | −56.0805 | −2.11062 | ||||||||
\(707\) | 12.9396 | 0.486644 | ||||||||
\(708\) | 22.3769 | 0.840976 | ||||||||
\(709\) | 51.1751 | 1.92192 | 0.960961 | − | 0.276682i | \(-0.0892349\pi\) | ||||
0.960961 | + | 0.276682i | \(0.0892349\pi\) | |||||||
\(710\) | 31.3649 | 1.17710 | ||||||||
\(711\) | −10.8707 | −0.407682 | ||||||||
\(712\) | 60.2716 | 2.25877 | ||||||||
\(713\) | 3.94812 | 0.147858 | ||||||||
\(714\) | −31.5700 | −1.18148 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 37.0787 | 1.38570 | ||||||||
\(717\) | 10.8328 | 0.404557 | ||||||||
\(718\) | −51.5349 | −1.92327 | ||||||||
\(719\) | 52.0371 | 1.94066 | 0.970328 | − | 0.241793i | \(-0.0777354\pi\) | ||||
0.970328 | + | 0.241793i | \(0.0777354\pi\) | |||||||
\(720\) | −16.9513 | −0.631737 | ||||||||
\(721\) | 2.95205 | 0.109940 | ||||||||
\(722\) | 8.46084 | 0.314880 | ||||||||
\(723\) | −2.96526 | −0.110279 | ||||||||
\(724\) | 78.1841 | 2.90569 | ||||||||
\(725\) | −2.65711 | −0.0986826 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −18.2951 | −0.678528 | −0.339264 | − | 0.940691i | \(-0.610178\pi\) | ||||
−0.339264 | + | 0.940691i | \(0.610178\pi\) | |||||||
\(728\) | 10.1389 | 0.375773 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −23.3673 | −0.864864 | ||||||||
\(731\) | 35.0158 | 1.29511 | ||||||||
\(732\) | 16.8595 | 0.623144 | ||||||||
\(733\) | 37.5153 | 1.38566 | 0.692830 | − | 0.721101i | \(-0.256364\pi\) | ||||
0.692830 | + | 0.721101i | \(0.256364\pi\) | |||||||
\(734\) | 16.3786 | 0.604545 | ||||||||
\(735\) | 1.81258 | 0.0668580 | ||||||||
\(736\) | −22.4649 | −0.828069 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | −11.9044 | −0.438207 | ||||||||
\(739\) | −27.3138 | −1.00475 | −0.502377 | − | 0.864649i | \(-0.667541\pi\) | ||||
−0.502377 | + | 0.864649i | \(0.667541\pi\) | |||||||
\(740\) | 50.3847 | 1.85218 | ||||||||
\(741\) | −2.04620 | −0.0751691 | ||||||||
\(742\) | 68.4349 | 2.51233 | ||||||||
\(743\) | 18.8234 | 0.690562 | 0.345281 | − | 0.938499i | \(-0.387784\pi\) | ||||
0.345281 | + | 0.938499i | \(0.387784\pi\) | |||||||
\(744\) | −47.6879 | −1.74832 | ||||||||
\(745\) | −7.60895 | −0.278770 | ||||||||
\(746\) | −4.62938 | −0.169494 | ||||||||
\(747\) | −5.92050 | −0.216620 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 27.7884 | 1.01536 | ||||||||
\(750\) | −2.77222 | −0.101227 | ||||||||
\(751\) | −25.1894 | −0.919174 | −0.459587 | − | 0.888133i | \(-0.652003\pi\) | ||||
−0.459587 | + | 0.888133i | \(0.652003\pi\) | |||||||
\(752\) | 7.93624 | 0.289405 | ||||||||
\(753\) | −17.6144 | −0.641905 | ||||||||
\(754\) | 3.20968 | 0.116890 | ||||||||
\(755\) | 2.67425 | 0.0973259 | ||||||||
\(756\) | −12.9486 | −0.470936 | ||||||||
\(757\) | 45.7939 | 1.66441 | 0.832204 | − | 0.554470i | \(-0.187079\pi\) | ||||
0.832204 | + | 0.554470i | \(0.187079\pi\) | |||||||
\(758\) | 23.3842 | 0.849352 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −47.9751 | −1.74024 | ||||||||
\(761\) | 8.01793 | 0.290650 | 0.145325 | − | 0.989384i | \(-0.453577\pi\) | ||||
0.145325 | + | 0.989384i | \(0.453577\pi\) | |||||||
\(762\) | −1.39640 | −0.0505864 | ||||||||
\(763\) | 27.7055 | 1.00300 | ||||||||
\(764\) | −110.498 | −3.99768 | ||||||||
\(765\) | −5.00000 | −0.180775 | ||||||||
\(766\) | 60.6605 | 2.19175 | ||||||||
\(767\) | −1.71505 | −0.0619269 | ||||||||
\(768\) | 78.6025 | 2.83632 | ||||||||
\(769\) | 40.0439 | 1.44402 | 0.722010 | − | 0.691883i | \(-0.243218\pi\) | ||||
0.722010 | + | 0.691883i | \(0.243218\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 20.9647 | 0.755025 | ||||||||
\(772\) | 128.556 | 4.62684 | ||||||||
\(773\) | −23.8250 | −0.856925 | −0.428462 | − | 0.903560i | \(-0.640945\pi\) | ||||
−0.428462 | + | 0.903560i | \(0.640945\pi\) | |||||||
\(774\) | 19.4143 | 0.697834 | ||||||||
\(775\) | −4.66785 | −0.167674 | ||||||||
\(776\) | −88.3504 | −3.17160 | ||||||||
\(777\) | 20.1849 | 0.724130 | ||||||||
\(778\) | −1.08697 | −0.0389697 | ||||||||
\(779\) | −20.1652 | −0.722495 | ||||||||
\(780\) | 2.47726 | 0.0887001 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | −11.7239 | −0.419245 | ||||||||
\(783\) | −2.65711 | −0.0949574 | ||||||||
\(784\) | −30.7255 | −1.09734 | ||||||||
\(785\) | −20.2000 | −0.720968 | ||||||||
\(786\) | 52.9766 | 1.88961 | ||||||||
\(787\) | −9.48879 | −0.338239 | −0.169119 | − | 0.985596i | \(-0.554092\pi\) | ||||
−0.169119 | + | 0.985596i | \(0.554092\pi\) | |||||||
\(788\) | 130.931 | 4.66421 | ||||||||
\(789\) | 8.43471 | 0.300284 | ||||||||
\(790\) | 30.1360 | 1.07219 | ||||||||
\(791\) | −0.323537 | −0.0115037 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −1.29217 | −0.0458864 | ||||||||
\(794\) | 99.1966 | 3.52036 | ||||||||
\(795\) | 10.8386 | 0.384406 | ||||||||
\(796\) | −111.553 | −3.95389 | ||||||||
\(797\) | −23.7639 | −0.841759 | −0.420880 | − | 0.907117i | \(-0.638279\pi\) | ||||
−0.420880 | + | 0.907117i | \(0.638279\pi\) | |||||||
\(798\) | −29.6502 | −1.04961 | ||||||||
\(799\) | 2.34090 | 0.0828149 | ||||||||
\(800\) | 26.5602 | 0.939046 | ||||||||
\(801\) | 5.89958 | 0.208451 | ||||||||
\(802\) | 84.3212 | 2.97749 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | −14.0452 | −0.495337 | ||||||||
\(805\) | −1.92641 | −0.0678971 | ||||||||
\(806\) | 5.63857 | 0.198610 | ||||||||
\(807\) | 9.64346 | 0.339466 | ||||||||
\(808\) | −58.0412 | −2.04188 | ||||||||
\(809\) | −18.4128 | −0.647361 | −0.323680 | − | 0.946167i | \(-0.604920\pi\) | ||||
−0.323680 | + | 0.946167i | \(0.604920\pi\) | |||||||
\(810\) | −2.77222 | −0.0974060 | ||||||||
\(811\) | 23.6451 | 0.830293 | 0.415147 | − | 0.909755i | \(-0.363730\pi\) | ||||
0.415147 | + | 0.909755i | \(0.363730\pi\) | |||||||
\(812\) | 34.4059 | 1.20741 | ||||||||
\(813\) | 10.2278 | 0.358704 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 9.79582 | 0.343133 | ||||||||
\(816\) | 84.7564 | 2.96707 | ||||||||
\(817\) | 32.8866 | 1.15056 | ||||||||
\(818\) | −45.1033 | −1.57700 | ||||||||
\(819\) | 0.992430 | 0.0346783 | ||||||||
\(820\) | 24.4133 | 0.852550 | ||||||||
\(821\) | 26.3153 | 0.918409 | 0.459204 | − | 0.888331i | \(-0.348135\pi\) | ||||
0.459204 | + | 0.888331i | \(0.348135\pi\) | |||||||
\(822\) | 34.2225 | 1.19365 | ||||||||
\(823\) | 40.4318 | 1.40936 | 0.704681 | − | 0.709524i | \(-0.251090\pi\) | ||||
0.704681 | + | 0.709524i | \(0.251090\pi\) | |||||||
\(824\) | −13.2416 | −0.461293 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −24.8517 | −0.864703 | ||||||||
\(827\) | 16.5927 | 0.576984 | 0.288492 | − | 0.957482i | \(-0.406846\pi\) | ||||
0.288492 | + | 0.957482i | \(0.406846\pi\) | |||||||
\(828\) | −4.80862 | −0.167111 | ||||||||
\(829\) | −34.3073 | −1.19154 | −0.595770 | − | 0.803155i | \(-0.703153\pi\) | ||||
−0.595770 | + | 0.803155i | \(0.703153\pi\) | |||||||
\(830\) | 16.4129 | 0.569701 | ||||||||
\(831\) | −5.83903 | −0.202554 | ||||||||
\(832\) | −17.3111 | −0.600154 | ||||||||
\(833\) | −9.06289 | −0.314011 | ||||||||
\(834\) | −21.4358 | −0.742261 | ||||||||
\(835\) | −25.5776 | −0.885150 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −4.66785 | −0.161344 | ||||||||
\(838\) | −111.084 | −3.83732 | ||||||||
\(839\) | −3.38811 | −0.116971 | −0.0584853 | − | 0.998288i | \(-0.518627\pi\) | ||||
−0.0584853 | + | 0.998288i | \(0.518627\pi\) | |||||||
\(840\) | 23.2684 | 0.802838 | ||||||||
\(841\) | −21.9398 | −0.756543 | ||||||||
\(842\) | −53.7652 | −1.85287 | ||||||||
\(843\) | 14.4139 | 0.496439 | ||||||||
\(844\) | 0.283836 | 0.00977003 | ||||||||
\(845\) | 12.8101 | 0.440682 | ||||||||
\(846\) | 1.29790 | 0.0446226 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −183.729 | −6.30926 | ||||||||
\(849\) | −10.6334 | −0.364939 | ||||||||
\(850\) | 13.8611 | 0.475432 | ||||||||
\(851\) | 7.49591 | 0.256956 | ||||||||
\(852\) | −64.3225 | −2.20365 | ||||||||
\(853\) | 16.4060 | 0.561732 | 0.280866 | − | 0.959747i | \(-0.409378\pi\) | ||||
0.280866 | + | 0.959747i | \(0.409378\pi\) | |||||||
\(854\) | −18.7241 | −0.640725 | ||||||||
\(855\) | −4.69596 | −0.160598 | ||||||||
\(856\) | −124.646 | −4.26032 | ||||||||
\(857\) | −3.37817 | −0.115396 | −0.0576981 | − | 0.998334i | \(-0.518376\pi\) | ||||
−0.0576981 | + | 0.998334i | \(0.518376\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −2.32376 | −0.0792855 | −0.0396428 | − | 0.999214i | \(-0.512622\pi\) | ||||
−0.0396428 | + | 0.999214i | \(0.512622\pi\) | |||||||
\(860\) | −39.8145 | −1.35766 | ||||||||
\(861\) | 9.78037 | 0.333314 | ||||||||
\(862\) | 94.1015 | 3.20511 | ||||||||
\(863\) | −20.2652 | −0.689837 | −0.344918 | − | 0.938633i | \(-0.612093\pi\) | ||||
−0.344918 | + | 0.938633i | \(0.612093\pi\) | |||||||
\(864\) | 26.5602 | 0.903598 | ||||||||
\(865\) | 6.75406 | 0.229645 | ||||||||
\(866\) | −36.3591 | −1.23553 | ||||||||
\(867\) | 8.00000 | 0.271694 | ||||||||
\(868\) | 60.4421 | 2.05154 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 7.36611 | 0.249734 | ||||||||
\(871\) | 1.07648 | 0.0364751 | ||||||||
\(872\) | −124.274 | −4.20846 | ||||||||
\(873\) | −8.64803 | −0.292691 | ||||||||
\(874\) | −11.0110 | −0.372452 | ||||||||
\(875\) | 2.27759 | 0.0769966 | ||||||||
\(876\) | 47.9213 | 1.61911 | ||||||||
\(877\) | −16.6208 | −0.561244 | −0.280622 | − | 0.959818i | \(-0.590541\pi\) | ||||
−0.280622 | + | 0.959818i | \(0.590541\pi\) | |||||||
\(878\) | −26.7445 | −0.902583 | ||||||||
\(879\) | −8.39576 | −0.283182 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −29.8895 | −1.00700 | −0.503502 | − | 0.863994i | \(-0.667955\pi\) | ||||
−0.503502 | + | 0.863994i | \(0.667955\pi\) | |||||||
\(882\) | −5.02487 | −0.169196 | ||||||||
\(883\) | 14.0135 | 0.471593 | 0.235796 | − | 0.971803i | \(-0.424230\pi\) | ||||
0.235796 | + | 0.971803i | \(0.424230\pi\) | |||||||
\(884\) | −12.3863 | −0.416596 | ||||||||
\(885\) | −3.93598 | −0.132307 | ||||||||
\(886\) | −24.7119 | −0.830211 | ||||||||
\(887\) | 28.6081 | 0.960567 | 0.480283 | − | 0.877113i | \(-0.340534\pi\) | ||||
0.480283 | + | 0.877113i | \(0.340534\pi\) | |||||||
\(888\) | −90.5404 | −3.03834 | ||||||||
\(889\) | 1.14725 | 0.0384776 | ||||||||
\(890\) | −16.3550 | −0.548219 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 4.29213 | 0.143711 | ||||||||
\(893\) | 2.19855 | 0.0735716 | ||||||||
\(894\) | 21.0937 | 0.705479 | ||||||||
\(895\) | −6.52195 | −0.218005 | ||||||||
\(896\) | −129.858 | −4.33824 | ||||||||
\(897\) | 0.368551 | 0.0123056 | ||||||||
\(898\) | −34.4777 | −1.15054 | ||||||||
\(899\) | 12.4030 | 0.413663 | ||||||||
\(900\) | 5.68522 | 0.189507 | ||||||||
\(901\) | −54.1931 | −1.80543 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −15.9504 | −0.530794 | ||||||||
\(904\) | 1.45124 | 0.0482676 | ||||||||
\(905\) | −13.7522 | −0.457138 | ||||||||
\(906\) | −7.41362 | −0.246301 | ||||||||
\(907\) | 26.9693 | 0.895499 | 0.447750 | − | 0.894159i | \(-0.352226\pi\) | ||||
0.447750 | + | 0.894159i | \(0.352226\pi\) | |||||||
\(908\) | 47.0963 | 1.56295 | ||||||||
\(909\) | −5.68126 | −0.188436 | ||||||||
\(910\) | −2.75124 | −0.0912027 | ||||||||
\(911\) | 7.13660 | 0.236446 | 0.118223 | − | 0.992987i | \(-0.462280\pi\) | ||||
0.118223 | + | 0.992987i | \(0.462280\pi\) | |||||||
\(912\) | 79.6025 | 2.63590 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | −105.783 | −3.49900 | ||||||||
\(915\) | −2.96549 | −0.0980361 | ||||||||
\(916\) | −16.3519 | −0.540284 | ||||||||
\(917\) | −43.5243 | −1.43730 | ||||||||
\(918\) | 13.8611 | 0.457485 | ||||||||
\(919\) | −6.89424 | −0.227420 | −0.113710 | − | 0.993514i | \(-0.536273\pi\) | ||||
−0.113710 | + | 0.993514i | \(0.536273\pi\) | |||||||
\(920\) | 8.64102 | 0.284886 | ||||||||
\(921\) | 4.51902 | 0.148907 | ||||||||
\(922\) | 95.3219 | 3.13926 | ||||||||
\(923\) | 4.92992 | 0.162270 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −8.86239 | −0.291394 | ||||||||
\(926\) | −111.599 | −3.66737 | ||||||||
\(927\) | −1.29613 | −0.0425705 | ||||||||
\(928\) | −70.5735 | −2.31669 | ||||||||
\(929\) | −36.3816 | −1.19364 | −0.596821 | − | 0.802375i | \(-0.703570\pi\) | ||||
−0.596821 | + | 0.802375i | \(0.703570\pi\) | |||||||
\(930\) | 12.9403 | 0.424330 | ||||||||
\(931\) | −8.51179 | −0.278963 | ||||||||
\(932\) | −29.4420 | −0.964403 | ||||||||
\(933\) | 23.9970 | 0.785626 | ||||||||
\(934\) | 41.9052 | 1.37118 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −4.45160 | −0.145505 | ||||||||
\(937\) | 52.6934 | 1.72142 | 0.860710 | − | 0.509096i | \(-0.170020\pi\) | ||||
0.860710 | + | 0.509096i | \(0.170020\pi\) | |||||||
\(938\) | 15.5986 | 0.509312 | ||||||||
\(939\) | −25.8686 | −0.844190 | ||||||||
\(940\) | −2.66170 | −0.0868151 | ||||||||
\(941\) | −20.2984 | −0.661709 | −0.330854 | − | 0.943682i | \(-0.607337\pi\) | ||||
−0.330854 | + | 0.943682i | \(0.607337\pi\) | |||||||
\(942\) | 55.9988 | 1.82454 | ||||||||
\(943\) | 3.63206 | 0.118276 | ||||||||
\(944\) | 66.7199 | 2.17155 | ||||||||
\(945\) | 2.27759 | 0.0740900 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 14.5680 | 0.473395 | 0.236698 | − | 0.971583i | \(-0.423935\pi\) | ||||
0.236698 | + | 0.971583i | \(0.423935\pi\) | |||||||
\(948\) | −61.8022 | −2.00724 | ||||||||
\(949\) | −3.67287 | −0.119226 | ||||||||
\(950\) | 13.0182 | 0.422367 | ||||||||
\(951\) | 2.90319 | 0.0941425 | ||||||||
\(952\) | −116.342 | −3.77067 | ||||||||
\(953\) | −39.5054 | −1.27970 | −0.639852 | − | 0.768498i | \(-0.721004\pi\) | ||||
−0.639852 | + | 0.768498i | \(0.721004\pi\) | |||||||
\(954\) | −30.0471 | −0.972810 | ||||||||
\(955\) | 19.4360 | 0.628936 | ||||||||
\(956\) | 61.5867 | 1.99186 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −79.8524 | −2.57991 | ||||||||
\(959\) | −28.1164 | −0.907924 | ||||||||
\(960\) | −39.7283 | −1.28223 | ||||||||
\(961\) | −9.21120 | −0.297135 | ||||||||
\(962\) | 10.7054 | 0.345156 | ||||||||
\(963\) | −12.2008 | −0.393164 | ||||||||
\(964\) | −16.8581 | −0.542964 | ||||||||
\(965\) | −22.6124 | −0.727917 | ||||||||
\(966\) | 5.34044 | 0.171826 | ||||||||
\(967\) | −44.8051 | −1.44083 | −0.720417 | − | 0.693541i | \(-0.756050\pi\) | ||||
−0.720417 | + | 0.693541i | \(0.756050\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 23.4798 | 0.754279 | ||||||||
\(970\) | 23.9743 | 0.769767 | ||||||||
\(971\) | 18.1454 | 0.582313 | 0.291156 | − | 0.956675i | \(-0.405960\pi\) | ||||
0.291156 | + | 0.956675i | \(0.405960\pi\) | |||||||
\(972\) | 5.68522 | 0.182354 | ||||||||
\(973\) | 17.6111 | 0.564587 | ||||||||
\(974\) | 79.9856 | 2.56290 | ||||||||
\(975\) | −0.435737 | −0.0139547 | ||||||||
\(976\) | 50.2689 | 1.60907 | ||||||||
\(977\) | 51.9967 | 1.66352 | 0.831761 | − | 0.555134i | \(-0.187333\pi\) | ||||
0.831761 | + | 0.555134i | \(0.187333\pi\) | |||||||
\(978\) | −27.1562 | −0.868359 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 10.3049 | 0.329178 | ||||||||
\(981\) | −12.1644 | −0.388378 | ||||||||
\(982\) | −41.4079 | −1.32138 | ||||||||
\(983\) | 44.3322 | 1.41398 | 0.706989 | − | 0.707224i | \(-0.250053\pi\) | ||||
0.706989 | + | 0.707224i | \(0.250053\pi\) | |||||||
\(984\) | −43.8703 | −1.39854 | ||||||||
\(985\) | −23.0300 | −0.733797 | ||||||||
\(986\) | −36.8305 | −1.17292 | ||||||||
\(987\) | −1.06632 | −0.0339414 | ||||||||
\(988\) | −11.6331 | −0.370098 | ||||||||
\(989\) | −5.92336 | −0.188352 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 10.4084 | 0.330635 | 0.165317 | − | 0.986240i | \(-0.447135\pi\) | ||||
0.165317 | + | 0.986240i | \(0.447135\pi\) | |||||||
\(992\) | −123.979 | −3.93634 | ||||||||
\(993\) | 10.9837 | 0.348558 | ||||||||
\(994\) | 71.4364 | 2.26583 | ||||||||
\(995\) | 19.6216 | 0.622046 | ||||||||
\(996\) | −33.6593 | −1.06654 | ||||||||
\(997\) | 6.52202 | 0.206554 | 0.103277 | − | 0.994653i | \(-0.467067\pi\) | ||||
0.103277 | + | 0.994653i | \(0.467067\pi\) | |||||||
\(998\) | 61.5406 | 1.94803 | ||||||||
\(999\) | −8.86239 | −0.280394 |
(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 | 1815.2.a.x.1.4 | 4 | ||
3.2 | odd | 2 | 5445.2.a.be.1.1 | 4 | |||
5.4 | even | 2 | 9075.2.a.cl.1.1 | 4 | |||
11.5 | even | 5 | 165.2.m.a.91.1 | ✓ | 8 | ||
11.9 | even | 5 | 165.2.m.a.136.1 | yes | 8 | ||
11.10 | odd | 2 | 1815.2.a.o.1.1 | 4 | |||
33.5 | odd | 10 | 495.2.n.d.91.2 | 8 | |||
33.20 | odd | 10 | 495.2.n.d.136.2 | 8 | |||
33.32 | even | 2 | 5445.2.a.bv.1.4 | 4 | |||
55.9 | even | 10 | 825.2.n.k.301.2 | 8 | |||
55.27 | odd | 20 | 825.2.bx.h.124.1 | 16 | |||
55.38 | odd | 20 | 825.2.bx.h.124.4 | 16 | |||
55.42 | odd | 20 | 825.2.bx.h.499.4 | 16 | |||
55.49 | even | 10 | 825.2.n.k.751.2 | 8 | |||
55.53 | odd | 20 | 825.2.bx.h.499.1 | 16 | |||
55.54 | odd | 2 | 9075.2.a.dj.1.4 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
165.2.m.a.91.1 | ✓ | 8 | 11.5 | even | 5 | ||
165.2.m.a.136.1 | yes | 8 | 11.9 | even | 5 | ||
495.2.n.d.91.2 | 8 | 33.5 | odd | 10 | |||
495.2.n.d.136.2 | 8 | 33.20 | odd | 10 | |||
825.2.n.k.301.2 | 8 | 55.9 | even | 10 | |||
825.2.n.k.751.2 | 8 | 55.49 | even | 10 | |||
825.2.bx.h.124.1 | 16 | 55.27 | odd | 20 | |||
825.2.bx.h.124.4 | 16 | 55.38 | odd | 20 | |||
825.2.bx.h.499.1 | 16 | 55.53 | odd | 20 | |||
825.2.bx.h.499.4 | 16 | 55.42 | odd | 20 | |||
1815.2.a.o.1.1 | 4 | 11.10 | odd | 2 | |||
1815.2.a.x.1.4 | 4 | 1.1 | even | 1 | trivial | ||
5445.2.a.be.1.1 | 4 | 3.2 | odd | 2 | |||
5445.2.a.bv.1.4 | 4 | 33.32 | even | 2 | |||
9075.2.a.cl.1.1 | 4 | 5.4 | even | 2 | |||
9075.2.a.dj.1.4 | 4 | 55.54 | odd | 2 |