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 | \(-1.35567\) 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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.35567 | 1.66571 | 0.832857 | − | 0.553489i | \(-0.186704\pi\) | ||||
0.832857 | + | 0.553489i | \(0.186704\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 3.54920 | 1.77460 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 2.35567 | 0.961700 | ||||||||
\(7\) | −0.193527 | −0.0731464 | −0.0365732 | − | 0.999331i | \(-0.511644\pi\) | ||||
−0.0365732 | + | 0.999331i | \(0.511644\pi\) | |||||||
\(8\) | 3.64941 | 1.29026 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 2.35567 | 0.744930 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 3.54920 | 1.02457 | ||||||||
\(13\) | −0.973708 | −0.270058 | −0.135029 | − | 0.990842i | \(-0.543113\pi\) | ||||
−0.135029 | + | 0.990842i | \(0.543113\pi\) | |||||||
\(14\) | −0.455887 | −0.121841 | ||||||||
\(15\) | 1.00000 | 0.258199 | ||||||||
\(16\) | 1.49843 | 0.374607 | ||||||||
\(17\) | 2.67571 | 0.648954 | 0.324477 | − | 0.945894i | \(-0.394812\pi\) | ||||
0.324477 | + | 0.945894i | \(0.394812\pi\) | |||||||
\(18\) | 2.35567 | 0.555238 | ||||||||
\(19\) | 5.54920 | 1.27307 | 0.636537 | − | 0.771246i | \(-0.280366\pi\) | ||||
0.636537 | + | 0.771246i | \(0.280366\pi\) | |||||||
\(20\) | 3.54920 | 0.793626 | ||||||||
\(21\) | −0.193527 | −0.0422311 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −4.80040 | −1.00095 | −0.500476 | − | 0.865750i | \(-0.666842\pi\) | ||||
−0.500476 | + | 0.865750i | \(0.666842\pi\) | |||||||
\(24\) | 3.64941 | 0.744933 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | −2.29374 | −0.449839 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | −0.686867 | −0.129806 | ||||||||
\(29\) | 10.1178 | 1.87883 | 0.939414 | − | 0.342785i | \(-0.111370\pi\) | ||||
0.939414 | + | 0.342785i | \(0.111370\pi\) | |||||||
\(30\) | 2.35567 | 0.430085 | ||||||||
\(31\) | −2.50533 | −0.449970 | −0.224985 | − | 0.974362i | \(-0.572233\pi\) | ||||
−0.224985 | + | 0.974362i | \(0.572233\pi\) | |||||||
\(32\) | −3.76902 | −0.666275 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 6.30309 | 1.08097 | ||||||||
\(35\) | −0.193527 | −0.0327120 | ||||||||
\(36\) | 3.54920 | 0.591534 | ||||||||
\(37\) | 5.71217 | 0.939076 | 0.469538 | − | 0.882912i | \(-0.344421\pi\) | ||||
0.469538 | + | 0.882912i | \(0.344421\pi\) | |||||||
\(38\) | 13.0721 | 2.12058 | ||||||||
\(39\) | −0.973708 | −0.155918 | ||||||||
\(40\) | 3.64941 | 0.577023 | ||||||||
\(41\) | 8.27861 | 1.29290 | 0.646451 | − | 0.762956i | \(-0.276253\pi\) | ||||
0.646451 | + | 0.762956i | \(0.276253\pi\) | |||||||
\(42\) | −0.455887 | −0.0703449 | ||||||||
\(43\) | −5.11353 | −0.779807 | −0.389903 | − | 0.920856i | \(-0.627492\pi\) | ||||
−0.389903 | + | 0.920856i | \(0.627492\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.00000 | 0.149071 | ||||||||
\(46\) | −11.3082 | −1.66730 | ||||||||
\(47\) | −10.8523 | −1.58297 | −0.791485 | − | 0.611189i | \(-0.790692\pi\) | ||||
−0.791485 | + | 0.611189i | \(0.790692\pi\) | |||||||
\(48\) | 1.49843 | 0.216279 | ||||||||
\(49\) | −6.96255 | −0.994650 | ||||||||
\(50\) | 2.35567 | 0.333143 | ||||||||
\(51\) | 2.67571 | 0.374674 | ||||||||
\(52\) | −3.45589 | −0.479245 | ||||||||
\(53\) | −9.28879 | −1.27591 | −0.637956 | − | 0.770072i | \(-0.720220\pi\) | ||||
−0.637956 | + | 0.770072i | \(0.720220\pi\) | |||||||
\(54\) | 2.35567 | 0.320567 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −0.706260 | −0.0943780 | ||||||||
\(57\) | 5.54920 | 0.735010 | ||||||||
\(58\) | 23.8342 | 3.12959 | ||||||||
\(59\) | −11.2180 | −1.46046 | −0.730230 | − | 0.683201i | \(-0.760587\pi\) | ||||
−0.730230 | + | 0.683201i | \(0.760587\pi\) | |||||||
\(60\) | 3.54920 | 0.458200 | ||||||||
\(61\) | −1.20602 | −0.154415 | −0.0772077 | − | 0.997015i | \(-0.524600\pi\) | ||||
−0.0772077 | + | 0.997015i | \(0.524600\pi\) | |||||||
\(62\) | −5.90173 | −0.749521 | ||||||||
\(63\) | −0.193527 | −0.0243821 | ||||||||
\(64\) | −11.8754 | −1.48443 | ||||||||
\(65\) | −0.973708 | −0.120774 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 3.25922 | 0.398176 | 0.199088 | − | 0.979982i | \(-0.436202\pi\) | ||||
0.199088 | + | 0.979982i | \(0.436202\pi\) | |||||||
\(68\) | 9.49662 | 1.15163 | ||||||||
\(69\) | −4.80040 | −0.577900 | ||||||||
\(70\) | −0.455887 | −0.0544889 | ||||||||
\(71\) | 5.99078 | 0.710975 | 0.355488 | − | 0.934681i | \(-0.384315\pi\) | ||||
0.355488 | + | 0.934681i | \(0.384315\pi\) | |||||||
\(72\) | 3.64941 | 0.430088 | ||||||||
\(73\) | −3.30624 | −0.386966 | −0.193483 | − | 0.981104i | \(-0.561978\pi\) | ||||
−0.193483 | + | 0.981104i | \(0.561978\pi\) | |||||||
\(74\) | 13.4560 | 1.56423 | ||||||||
\(75\) | 1.00000 | 0.115470 | ||||||||
\(76\) | 19.6952 | 2.25920 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −2.29374 | −0.259715 | ||||||||
\(79\) | −10.1529 | −1.14229 | −0.571147 | − | 0.820848i | \(-0.693501\pi\) | ||||
−0.571147 | + | 0.820848i | \(0.693501\pi\) | |||||||
\(80\) | 1.49843 | 0.167529 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 19.5017 | 2.15360 | ||||||||
\(83\) | −8.31508 | −0.912698 | −0.456349 | − | 0.889801i | \(-0.650843\pi\) | ||||
−0.456349 | + | 0.889801i | \(0.650843\pi\) | |||||||
\(84\) | −0.686867 | −0.0749433 | ||||||||
\(85\) | 2.67571 | 0.290221 | ||||||||
\(86\) | −12.0458 | −1.29893 | ||||||||
\(87\) | 10.1178 | 1.08474 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 7.34270 | 0.778325 | 0.389163 | − | 0.921169i | \(-0.372764\pi\) | ||||
0.389163 | + | 0.921169i | \(0.372764\pi\) | |||||||
\(90\) | 2.35567 | 0.248310 | ||||||||
\(91\) | 0.188439 | 0.0197538 | ||||||||
\(92\) | −17.0376 | −1.77629 | ||||||||
\(93\) | −2.50533 | −0.259790 | ||||||||
\(94\) | −25.5645 | −2.63677 | ||||||||
\(95\) | 5.54920 | 0.569336 | ||||||||
\(96\) | −3.76902 | −0.384674 | ||||||||
\(97\) | −15.8523 | −1.60956 | −0.804778 | − | 0.593576i | \(-0.797716\pi\) | ||||
−0.804778 | + | 0.593576i | \(0.797716\pi\) | |||||||
\(98\) | −16.4015 | −1.65680 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 3.54920 | 0.354920 | ||||||||
\(101\) | −13.1591 | −1.30938 | −0.654692 | − | 0.755896i | \(-0.727201\pi\) | ||||
−0.654692 | + | 0.755896i | \(0.727201\pi\) | |||||||
\(102\) | 6.30309 | 0.624099 | ||||||||
\(103\) | 3.99737 | 0.393872 | 0.196936 | − | 0.980416i | \(-0.436901\pi\) | ||||
0.196936 | + | 0.980416i | \(0.436901\pi\) | |||||||
\(104\) | −3.55346 | −0.348446 | ||||||||
\(105\) | −0.193527 | −0.0188863 | ||||||||
\(106\) | −21.8814 | −2.12530 | ||||||||
\(107\) | −4.88682 | −0.472426 | −0.236213 | − | 0.971701i | \(-0.575906\pi\) | ||||
−0.236213 | + | 0.971701i | \(0.575906\pi\) | |||||||
\(108\) | 3.54920 | 0.341522 | ||||||||
\(109\) | 7.51977 | 0.720263 | 0.360131 | − | 0.932902i | \(-0.382732\pi\) | ||||
0.360131 | + | 0.932902i | \(0.382732\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 5.71217 | 0.542176 | ||||||||
\(112\) | −0.289986 | −0.0274011 | ||||||||
\(113\) | 20.2237 | 1.90249 | 0.951243 | − | 0.308442i | \(-0.0998076\pi\) | ||||
0.951243 | + | 0.308442i | \(0.0998076\pi\) | |||||||
\(114\) | 13.0721 | 1.22432 | ||||||||
\(115\) | −4.80040 | −0.447640 | ||||||||
\(116\) | 35.9101 | 3.33417 | ||||||||
\(117\) | −0.973708 | −0.0900194 | ||||||||
\(118\) | −26.4260 | −2.43271 | ||||||||
\(119\) | −0.517822 | −0.0474686 | ||||||||
\(120\) | 3.64941 | 0.333144 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | −2.84100 | −0.257212 | ||||||||
\(123\) | 8.27861 | 0.746457 | ||||||||
\(124\) | −8.89190 | −0.798517 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | −0.455887 | −0.0406136 | ||||||||
\(127\) | −7.10021 | −0.630042 | −0.315021 | − | 0.949085i | \(-0.602012\pi\) | ||||
−0.315021 | + | 0.949085i | \(0.602012\pi\) | |||||||
\(128\) | −20.4366 | −1.80636 | ||||||||
\(129\) | −5.11353 | −0.450222 | ||||||||
\(130\) | −2.29374 | −0.201174 | ||||||||
\(131\) | 2.50024 | 0.218447 | 0.109223 | − | 0.994017i | \(-0.465164\pi\) | ||||
0.109223 | + | 0.994017i | \(0.465164\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.07392 | −0.0931207 | ||||||||
\(134\) | 7.67765 | 0.663248 | ||||||||
\(135\) | 1.00000 | 0.0860663 | ||||||||
\(136\) | 9.76476 | 0.837321 | ||||||||
\(137\) | −15.2944 | −1.30669 | −0.653344 | − | 0.757061i | \(-0.726634\pi\) | ||||
−0.653344 | + | 0.757061i | \(0.726634\pi\) | |||||||
\(138\) | −11.3082 | −0.962616 | ||||||||
\(139\) | 19.6586 | 1.66742 | 0.833711 | − | 0.552202i | \(-0.186212\pi\) | ||||
0.833711 | + | 0.552202i | \(0.186212\pi\) | |||||||
\(140\) | −0.686867 | −0.0580508 | ||||||||
\(141\) | −10.8523 | −0.913928 | ||||||||
\(142\) | 14.1123 | 1.18428 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 1.49843 | 0.124869 | ||||||||
\(145\) | 10.1178 | 0.840237 | ||||||||
\(146\) | −7.78841 | −0.644574 | ||||||||
\(147\) | −6.96255 | −0.574261 | ||||||||
\(148\) | 20.2737 | 1.66648 | ||||||||
\(149\) | 10.1329 | 0.830122 | 0.415061 | − | 0.909794i | \(-0.363760\pi\) | ||||
0.415061 | + | 0.909794i | \(0.363760\pi\) | |||||||
\(150\) | 2.35567 | 0.192340 | ||||||||
\(151\) | −11.9632 | −0.973548 | −0.486774 | − | 0.873528i | \(-0.661826\pi\) | ||||
−0.486774 | + | 0.873528i | \(0.661826\pi\) | |||||||
\(152\) | 20.2513 | 1.64260 | ||||||||
\(153\) | 2.67571 | 0.216318 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −2.50533 | −0.201233 | ||||||||
\(156\) | −3.45589 | −0.276692 | ||||||||
\(157\) | −2.62605 | −0.209582 | −0.104791 | − | 0.994494i | \(-0.533417\pi\) | ||||
−0.104791 | + | 0.994494i | \(0.533417\pi\) | |||||||
\(158\) | −23.9170 | −1.90273 | ||||||||
\(159\) | −9.28879 | −0.736649 | ||||||||
\(160\) | −3.76902 | −0.297967 | ||||||||
\(161\) | 0.929007 | 0.0732160 | ||||||||
\(162\) | 2.35567 | 0.185079 | ||||||||
\(163\) | 23.7235 | 1.85817 | 0.929083 | − | 0.369872i | \(-0.120598\pi\) | ||||
0.929083 | + | 0.369872i | \(0.120598\pi\) | |||||||
\(164\) | 29.3825 | 2.29438 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −19.5876 | −1.52029 | ||||||||
\(167\) | −3.49175 | −0.270199 | −0.135100 | − | 0.990832i | \(-0.543135\pi\) | ||||
−0.135100 | + | 0.990832i | \(0.543135\pi\) | |||||||
\(168\) | −0.706260 | −0.0544892 | ||||||||
\(169\) | −12.0519 | −0.927069 | ||||||||
\(170\) | 6.30309 | 0.483425 | ||||||||
\(171\) | 5.54920 | 0.424358 | ||||||||
\(172\) | −18.1490 | −1.38385 | ||||||||
\(173\) | 20.3596 | 1.54791 | 0.773954 | − | 0.633241i | \(-0.218276\pi\) | ||||
0.773954 | + | 0.633241i | \(0.218276\pi\) | |||||||
\(174\) | 23.8342 | 1.80687 | ||||||||
\(175\) | −0.193527 | −0.0146293 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −11.2180 | −0.843197 | ||||||||
\(178\) | 17.2970 | 1.29647 | ||||||||
\(179\) | 3.85117 | 0.287850 | 0.143925 | − | 0.989589i | \(-0.454028\pi\) | ||||
0.143925 | + | 0.989589i | \(0.454028\pi\) | |||||||
\(180\) | 3.54920 | 0.264542 | ||||||||
\(181\) | −17.6151 | −1.30932 | −0.654660 | − | 0.755923i | \(-0.727188\pi\) | ||||
−0.654660 | + | 0.755923i | \(0.727188\pi\) | |||||||
\(182\) | 0.443901 | 0.0329041 | ||||||||
\(183\) | −1.20602 | −0.0891518 | ||||||||
\(184\) | −17.5186 | −1.29149 | ||||||||
\(185\) | 5.71217 | 0.419967 | ||||||||
\(186\) | −5.90173 | −0.432736 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | −38.5170 | −2.80914 | ||||||||
\(189\) | −0.193527 | −0.0140770 | ||||||||
\(190\) | 13.0721 | 0.948351 | ||||||||
\(191\) | 0.417099 | 0.0301802 | 0.0150901 | − | 0.999886i | \(-0.495196\pi\) | ||||
0.0150901 | + | 0.999886i | \(0.495196\pi\) | |||||||
\(192\) | −11.8754 | −0.857036 | ||||||||
\(193\) | −11.6965 | −0.841935 | −0.420967 | − | 0.907076i | \(-0.638309\pi\) | ||||
−0.420967 | + | 0.907076i | \(0.638309\pi\) | |||||||
\(194\) | −37.3428 | −2.68106 | ||||||||
\(195\) | −0.973708 | −0.0697287 | ||||||||
\(196\) | −24.7115 | −1.76511 | ||||||||
\(197\) | −21.5958 | −1.53864 | −0.769320 | − | 0.638863i | \(-0.779405\pi\) | ||||
−0.769320 | + | 0.638863i | \(0.779405\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 7.76028 | 0.550111 | 0.275056 | − | 0.961428i | \(-0.411304\pi\) | ||||
0.275056 | + | 0.961428i | \(0.411304\pi\) | |||||||
\(200\) | 3.64941 | 0.258053 | ||||||||
\(201\) | 3.25922 | 0.229887 | ||||||||
\(202\) | −30.9986 | −2.18106 | ||||||||
\(203\) | −1.95807 | −0.137429 | ||||||||
\(204\) | 9.49662 | 0.664896 | ||||||||
\(205\) | 8.27861 | 0.578203 | ||||||||
\(206\) | 9.41649 | 0.656078 | ||||||||
\(207\) | −4.80040 | −0.333651 | ||||||||
\(208\) | −1.45903 | −0.101166 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | −0.455887 | −0.0314592 | ||||||||
\(211\) | 12.5057 | 0.860926 | 0.430463 | − | 0.902608i | \(-0.358350\pi\) | ||||
0.430463 | + | 0.902608i | \(0.358350\pi\) | |||||||
\(212\) | −32.9678 | −2.26424 | ||||||||
\(213\) | 5.99078 | 0.410482 | ||||||||
\(214\) | −11.5117 | −0.786927 | ||||||||
\(215\) | −5.11353 | −0.348740 | ||||||||
\(216\) | 3.64941 | 0.248311 | ||||||||
\(217\) | 0.484848 | 0.0329137 | ||||||||
\(218\) | 17.7141 | 1.19975 | ||||||||
\(219\) | −3.30624 | −0.223415 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −2.60536 | −0.175255 | ||||||||
\(222\) | 13.4560 | 0.903109 | ||||||||
\(223\) | −5.37568 | −0.359982 | −0.179991 | − | 0.983668i | \(-0.557607\pi\) | ||||
−0.179991 | + | 0.983668i | \(0.557607\pi\) | |||||||
\(224\) | 0.729407 | 0.0487356 | ||||||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | 47.6405 | 3.16900 | ||||||||
\(227\) | 21.7529 | 1.44379 | 0.721895 | − | 0.692002i | \(-0.243271\pi\) | ||||
0.721895 | + | 0.692002i | \(0.243271\pi\) | |||||||
\(228\) | 19.6952 | 1.30435 | ||||||||
\(229\) | 2.67075 | 0.176488 | 0.0882441 | − | 0.996099i | \(-0.471874\pi\) | ||||
0.0882441 | + | 0.996099i | \(0.471874\pi\) | |||||||
\(230\) | −11.3082 | −0.745639 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 36.9240 | 2.42418 | ||||||||
\(233\) | 5.72699 | 0.375188 | 0.187594 | − | 0.982247i | \(-0.439931\pi\) | ||||
0.187594 | + | 0.982247i | \(0.439931\pi\) | |||||||
\(234\) | −2.29374 | −0.149946 | ||||||||
\(235\) | −10.8523 | −0.707925 | ||||||||
\(236\) | −39.8150 | −2.59173 | ||||||||
\(237\) | −10.1529 | −0.659504 | ||||||||
\(238\) | −1.21982 | −0.0790691 | ||||||||
\(239\) | 24.3680 | 1.57624 | 0.788118 | − | 0.615524i | \(-0.211056\pi\) | ||||
0.788118 | + | 0.615524i | \(0.211056\pi\) | |||||||
\(240\) | 1.49843 | 0.0967231 | ||||||||
\(241\) | 16.7082 | 1.07627 | 0.538135 | − | 0.842859i | \(-0.319129\pi\) | ||||
0.538135 | + | 0.842859i | \(0.319129\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | −4.28042 | −0.274026 | ||||||||
\(245\) | −6.96255 | −0.444821 | ||||||||
\(246\) | 19.5017 | 1.24338 | ||||||||
\(247\) | −5.40330 | −0.343804 | ||||||||
\(248\) | −9.14297 | −0.580579 | ||||||||
\(249\) | −8.31508 | −0.526947 | ||||||||
\(250\) | 2.35567 | 0.148986 | ||||||||
\(251\) | −16.0984 | −1.01612 | −0.508061 | − | 0.861321i | \(-0.669638\pi\) | ||||
−0.508061 | + | 0.861321i | \(0.669638\pi\) | |||||||
\(252\) | −0.686867 | −0.0432685 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −16.7258 | −1.04947 | ||||||||
\(255\) | 2.67571 | 0.167559 | ||||||||
\(256\) | −24.3912 | −1.52445 | ||||||||
\(257\) | 5.96875 | 0.372321 | 0.186160 | − | 0.982519i | \(-0.440396\pi\) | ||||
0.186160 | + | 0.982519i | \(0.440396\pi\) | |||||||
\(258\) | −12.0458 | −0.749940 | ||||||||
\(259\) | −1.10546 | −0.0686900 | ||||||||
\(260\) | −3.45589 | −0.214325 | ||||||||
\(261\) | 10.1178 | 0.626276 | ||||||||
\(262\) | 5.88974 | 0.363870 | ||||||||
\(263\) | 0.451149 | 0.0278190 | 0.0139095 | − | 0.999903i | \(-0.495572\pi\) | ||||
0.0139095 | + | 0.999903i | \(0.495572\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −9.28879 | −0.570606 | ||||||||
\(266\) | −2.52981 | −0.155112 | ||||||||
\(267\) | 7.34270 | 0.449366 | ||||||||
\(268\) | 11.5676 | 0.706604 | ||||||||
\(269\) | 14.7197 | 0.897477 | 0.448738 | − | 0.893663i | \(-0.351873\pi\) | ||||
0.448738 | + | 0.893663i | \(0.351873\pi\) | |||||||
\(270\) | 2.35567 | 0.143362 | ||||||||
\(271\) | −4.42787 | −0.268974 | −0.134487 | − | 0.990915i | \(-0.542939\pi\) | ||||
−0.134487 | + | 0.990915i | \(0.542939\pi\) | |||||||
\(272\) | 4.00935 | 0.243103 | ||||||||
\(273\) | 0.188439 | 0.0114048 | ||||||||
\(274\) | −36.0286 | −2.17657 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −17.0376 | −1.02554 | ||||||||
\(277\) | 0.0923299 | 0.00554757 | 0.00277378 | − | 0.999996i | \(-0.499117\pi\) | ||||
0.00277378 | + | 0.999996i | \(0.499117\pi\) | |||||||
\(278\) | 46.3093 | 2.77745 | ||||||||
\(279\) | −2.50533 | −0.149990 | ||||||||
\(280\) | −0.706260 | −0.0422071 | ||||||||
\(281\) | −5.18301 | −0.309192 | −0.154596 | − | 0.987978i | \(-0.549408\pi\) | ||||
−0.154596 | + | 0.987978i | \(0.549408\pi\) | |||||||
\(282\) | −25.5645 | −1.52234 | ||||||||
\(283\) | −1.56463 | −0.0930073 | −0.0465037 | − | 0.998918i | \(-0.514808\pi\) | ||||
−0.0465037 | + | 0.998918i | \(0.514808\pi\) | |||||||
\(284\) | 21.2625 | 1.26170 | ||||||||
\(285\) | 5.54920 | 0.328706 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −1.60214 | −0.0945710 | ||||||||
\(288\) | −3.76902 | −0.222092 | ||||||||
\(289\) | −9.84060 | −0.578859 | ||||||||
\(290\) | 23.8342 | 1.39959 | ||||||||
\(291\) | −15.8523 | −0.929278 | ||||||||
\(292\) | −11.7345 | −0.686709 | ||||||||
\(293\) | 23.1570 | 1.35285 | 0.676424 | − | 0.736512i | \(-0.263529\pi\) | ||||
0.676424 | + | 0.736512i | \(0.263529\pi\) | |||||||
\(294\) | −16.4015 | −0.956555 | ||||||||
\(295\) | −11.2180 | −0.653138 | ||||||||
\(296\) | 20.8461 | 1.21165 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 23.8699 | 1.38274 | ||||||||
\(299\) | 4.67419 | 0.270315 | ||||||||
\(300\) | 3.54920 | 0.204913 | ||||||||
\(301\) | 0.989607 | 0.0570400 | ||||||||
\(302\) | −28.1813 | −1.62165 | ||||||||
\(303\) | −13.1591 | −0.755973 | ||||||||
\(304\) | 8.31508 | 0.476902 | ||||||||
\(305\) | −1.20602 | −0.0690567 | ||||||||
\(306\) | 6.30309 | 0.360324 | ||||||||
\(307\) | 7.72480 | 0.440878 | 0.220439 | − | 0.975401i | \(-0.429251\pi\) | ||||
0.220439 | + | 0.975401i | \(0.429251\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 3.99737 | 0.227402 | ||||||||
\(310\) | −5.90173 | −0.335196 | ||||||||
\(311\) | −19.1209 | −1.08424 | −0.542122 | − | 0.840300i | \(-0.682379\pi\) | ||||
−0.542122 | + | 0.840300i | \(0.682379\pi\) | |||||||
\(312\) | −3.55346 | −0.201175 | ||||||||
\(313\) | 2.90307 | 0.164091 | 0.0820455 | − | 0.996629i | \(-0.473855\pi\) | ||||
0.0820455 | + | 0.996629i | \(0.473855\pi\) | |||||||
\(314\) | −6.18612 | −0.349103 | ||||||||
\(315\) | −0.193527 | −0.0109040 | ||||||||
\(316\) | −36.0348 | −2.02712 | ||||||||
\(317\) | 2.26153 | 0.127020 | 0.0635102 | − | 0.997981i | \(-0.479770\pi\) | ||||
0.0635102 | + | 0.997981i | \(0.479770\pi\) | |||||||
\(318\) | −21.8814 | −1.22705 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | −11.8754 | −0.663857 | ||||||||
\(321\) | −4.88682 | −0.272756 | ||||||||
\(322\) | 2.18844 | 0.121957 | ||||||||
\(323\) | 14.8480 | 0.826166 | ||||||||
\(324\) | 3.54920 | 0.197178 | ||||||||
\(325\) | −0.973708 | −0.0540116 | ||||||||
\(326\) | 55.8848 | 3.09517 | ||||||||
\(327\) | 7.51977 | 0.415844 | ||||||||
\(328\) | 30.2121 | 1.66818 | ||||||||
\(329\) | 2.10021 | 0.115788 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 6.02336 | 0.331074 | 0.165537 | − | 0.986204i | \(-0.447064\pi\) | ||||
0.165537 | + | 0.986204i | \(0.447064\pi\) | |||||||
\(332\) | −29.5119 | −1.61967 | ||||||||
\(333\) | 5.71217 | 0.313025 | ||||||||
\(334\) | −8.22542 | −0.450075 | ||||||||
\(335\) | 3.25922 | 0.178070 | ||||||||
\(336\) | −0.289986 | −0.0158201 | ||||||||
\(337\) | 14.5648 | 0.793393 | 0.396696 | − | 0.917950i | \(-0.370157\pi\) | ||||
0.396696 | + | 0.917950i | \(0.370157\pi\) | |||||||
\(338\) | −28.3903 | −1.54423 | ||||||||
\(339\) | 20.2237 | 1.09840 | ||||||||
\(340\) | 9.49662 | 0.515026 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 13.0721 | 0.706859 | ||||||||
\(343\) | 2.70213 | 0.145901 | ||||||||
\(344\) | −18.6614 | −1.00616 | ||||||||
\(345\) | −4.80040 | −0.258445 | ||||||||
\(346\) | 47.9605 | 2.57837 | ||||||||
\(347\) | −28.8351 | −1.54795 | −0.773976 | − | 0.633215i | \(-0.781735\pi\) | ||||
−0.773976 | + | 0.633215i | \(0.781735\pi\) | |||||||
\(348\) | 35.9101 | 1.92498 | ||||||||
\(349\) | 1.63234 | 0.0873771 | 0.0436886 | − | 0.999045i | \(-0.486089\pi\) | ||||
0.0436886 | + | 0.999045i | \(0.486089\pi\) | |||||||
\(350\) | −0.455887 | −0.0243682 | ||||||||
\(351\) | −0.973708 | −0.0519727 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 24.9297 | 1.32687 | 0.663437 | − | 0.748232i | \(-0.269097\pi\) | ||||
0.663437 | + | 0.748232i | \(0.269097\pi\) | |||||||
\(354\) | −26.4260 | −1.40452 | ||||||||
\(355\) | 5.99078 | 0.317958 | ||||||||
\(356\) | 26.0607 | 1.38122 | ||||||||
\(357\) | −0.517822 | −0.0274060 | ||||||||
\(358\) | 9.07211 | 0.479476 | ||||||||
\(359\) | −28.4409 | −1.50106 | −0.750528 | − | 0.660839i | \(-0.770201\pi\) | ||||
−0.750528 | + | 0.660839i | \(0.770201\pi\) | |||||||
\(360\) | 3.64941 | 0.192341 | ||||||||
\(361\) | 11.7936 | 0.620718 | ||||||||
\(362\) | −41.4955 | −2.18095 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0.668808 | 0.0350550 | ||||||||
\(365\) | −3.30624 | −0.173056 | ||||||||
\(366\) | −2.84100 | −0.148501 | ||||||||
\(367\) | −10.4413 | −0.545030 | −0.272515 | − | 0.962152i | \(-0.587855\pi\) | ||||
−0.272515 | + | 0.962152i | \(0.587855\pi\) | |||||||
\(368\) | −7.19305 | −0.374964 | ||||||||
\(369\) | 8.27861 | 0.430967 | ||||||||
\(370\) | 13.4560 | 0.699545 | ||||||||
\(371\) | 1.79763 | 0.0933284 | ||||||||
\(372\) | −8.89190 | −0.461024 | ||||||||
\(373\) | 2.81747 | 0.145883 | 0.0729416 | − | 0.997336i | \(-0.476761\pi\) | ||||
0.0729416 | + | 0.997336i | \(0.476761\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1.00000 | 0.0516398 | ||||||||
\(376\) | −39.6045 | −2.04245 | ||||||||
\(377\) | −9.85178 | −0.507393 | ||||||||
\(378\) | −0.455887 | −0.0234483 | ||||||||
\(379\) | 8.93319 | 0.458867 | 0.229434 | − | 0.973324i | \(-0.426313\pi\) | ||||
0.229434 | + | 0.973324i | \(0.426313\pi\) | |||||||
\(380\) | 19.6952 | 1.01034 | ||||||||
\(381\) | −7.10021 | −0.363755 | ||||||||
\(382\) | 0.982550 | 0.0502716 | ||||||||
\(383\) | −8.53279 | −0.436005 | −0.218003 | − | 0.975948i | \(-0.569954\pi\) | ||||
−0.218003 | + | 0.975948i | \(0.569954\pi\) | |||||||
\(384\) | −20.4366 | −1.04290 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −27.5532 | −1.40242 | ||||||||
\(387\) | −5.11353 | −0.259936 | ||||||||
\(388\) | −56.2630 | −2.85632 | ||||||||
\(389\) | 11.7757 | 0.597054 | 0.298527 | − | 0.954401i | \(-0.403505\pi\) | ||||
0.298527 | + | 0.954401i | \(0.403505\pi\) | |||||||
\(390\) | −2.29374 | −0.116148 | ||||||||
\(391\) | −12.8445 | −0.649572 | ||||||||
\(392\) | −25.4092 | −1.28336 | ||||||||
\(393\) | 2.50024 | 0.126120 | ||||||||
\(394\) | −50.8728 | −2.56293 | ||||||||
\(395\) | −10.1529 | −0.510849 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −1.41214 | −0.0708735 | −0.0354368 | − | 0.999372i | \(-0.511282\pi\) | ||||
−0.0354368 | + | 0.999372i | \(0.511282\pi\) | |||||||
\(398\) | 18.2807 | 0.916328 | ||||||||
\(399\) | −1.07392 | −0.0537633 | ||||||||
\(400\) | 1.49843 | 0.0749214 | ||||||||
\(401\) | 8.45917 | 0.422431 | 0.211215 | − | 0.977440i | \(-0.432258\pi\) | ||||
0.211215 | + | 0.977440i | \(0.432258\pi\) | |||||||
\(402\) | 7.67765 | 0.382926 | ||||||||
\(403\) | 2.43946 | 0.121518 | ||||||||
\(404\) | −46.7044 | −2.32363 | ||||||||
\(405\) | 1.00000 | 0.0496904 | ||||||||
\(406\) | −4.61257 | −0.228918 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 9.76476 | 0.483428 | ||||||||
\(409\) | −10.1255 | −0.500675 | −0.250337 | − | 0.968159i | \(-0.580542\pi\) | ||||
−0.250337 | + | 0.968159i | \(0.580542\pi\) | |||||||
\(410\) | 19.5017 | 0.963121 | ||||||||
\(411\) | −15.2944 | −0.754416 | ||||||||
\(412\) | 14.1875 | 0.698966 | ||||||||
\(413\) | 2.17099 | 0.106827 | ||||||||
\(414\) | −11.3082 | −0.555767 | ||||||||
\(415\) | −8.31508 | −0.408171 | ||||||||
\(416\) | 3.66993 | 0.179933 | ||||||||
\(417\) | 19.6586 | 0.962686 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 32.8019 | 1.60248 | 0.801240 | − | 0.598343i | \(-0.204174\pi\) | ||||
0.801240 | + | 0.598343i | \(0.204174\pi\) | |||||||
\(420\) | −0.686867 | −0.0335157 | ||||||||
\(421\) | −14.1293 | −0.688619 | −0.344309 | − | 0.938856i | \(-0.611887\pi\) | ||||
−0.344309 | + | 0.938856i | \(0.611887\pi\) | |||||||
\(422\) | 29.4593 | 1.43406 | ||||||||
\(423\) | −10.8523 | −0.527657 | ||||||||
\(424\) | −33.8986 | −1.64626 | ||||||||
\(425\) | 2.67571 | 0.129791 | ||||||||
\(426\) | 14.1123 | 0.683745 | ||||||||
\(427\) | 0.233398 | 0.0112949 | ||||||||
\(428\) | −17.3443 | −0.838368 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −12.0458 | −0.580901 | ||||||||
\(431\) | −19.1057 | −0.920291 | −0.460145 | − | 0.887844i | \(-0.652203\pi\) | ||||
−0.460145 | + | 0.887844i | \(0.652203\pi\) | |||||||
\(432\) | 1.49843 | 0.0720931 | ||||||||
\(433\) | 15.1200 | 0.726622 | 0.363311 | − | 0.931668i | \(-0.381646\pi\) | ||||
0.363311 | + | 0.931668i | \(0.381646\pi\) | |||||||
\(434\) | 1.14214 | 0.0548247 | ||||||||
\(435\) | 10.1178 | 0.485111 | ||||||||
\(436\) | 26.6892 | 1.27818 | ||||||||
\(437\) | −26.6384 | −1.27429 | ||||||||
\(438\) | −7.78841 | −0.372145 | ||||||||
\(439\) | −37.1642 | −1.77375 | −0.886876 | − | 0.462008i | \(-0.847129\pi\) | ||||
−0.886876 | + | 0.462008i | \(0.847129\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −6.96255 | −0.331550 | ||||||||
\(442\) | −6.13737 | −0.291925 | ||||||||
\(443\) | −2.76049 | −0.131155 | −0.0655775 | − | 0.997847i | \(-0.520889\pi\) | ||||
−0.0655775 | + | 0.997847i | \(0.520889\pi\) | |||||||
\(444\) | 20.2737 | 0.962145 | ||||||||
\(445\) | 7.34270 | 0.348078 | ||||||||
\(446\) | −12.6633 | −0.599627 | ||||||||
\(447\) | 10.1329 | 0.479271 | ||||||||
\(448\) | 2.29822 | 0.108581 | ||||||||
\(449\) | −17.8661 | −0.843156 | −0.421578 | − | 0.906792i | \(-0.638524\pi\) | ||||
−0.421578 | + | 0.906792i | \(0.638524\pi\) | |||||||
\(450\) | 2.35567 | 0.111048 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 71.7780 | 3.37615 | ||||||||
\(453\) | −11.9632 | −0.562078 | ||||||||
\(454\) | 51.2428 | 2.40494 | ||||||||
\(455\) | 0.188439 | 0.00883415 | ||||||||
\(456\) | 20.2513 | 0.948356 | ||||||||
\(457\) | 21.1621 | 0.989922 | 0.494961 | − | 0.868915i | \(-0.335182\pi\) | ||||
0.494961 | + | 0.868915i | \(0.335182\pi\) | |||||||
\(458\) | 6.29142 | 0.293979 | ||||||||
\(459\) | 2.67571 | 0.124891 | ||||||||
\(460\) | −17.0376 | −0.794382 | ||||||||
\(461\) | 34.3476 | 1.59973 | 0.799864 | − | 0.600181i | \(-0.204905\pi\) | ||||
0.799864 | + | 0.600181i | \(0.204905\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 10.4516 | 0.485727 | 0.242864 | − | 0.970060i | \(-0.421913\pi\) | ||||
0.242864 | + | 0.970060i | \(0.421913\pi\) | |||||||
\(464\) | 15.1608 | 0.703822 | ||||||||
\(465\) | −2.50533 | −0.116182 | ||||||||
\(466\) | 13.4909 | 0.624955 | ||||||||
\(467\) | 29.6434 | 1.37173 | 0.685866 | − | 0.727728i | \(-0.259424\pi\) | ||||
0.685866 | + | 0.727728i | \(0.259424\pi\) | |||||||
\(468\) | −3.45589 | −0.159748 | ||||||||
\(469\) | −0.630746 | −0.0291252 | ||||||||
\(470\) | −25.5645 | −1.17920 | ||||||||
\(471\) | −2.62605 | −0.121002 | ||||||||
\(472\) | −40.9392 | −1.88438 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | −23.9170 | −1.09854 | ||||||||
\(475\) | 5.54920 | 0.254615 | ||||||||
\(476\) | −1.83785 | −0.0842378 | ||||||||
\(477\) | −9.28879 | −0.425304 | ||||||||
\(478\) | 57.4031 | 2.62556 | ||||||||
\(479\) | 13.2186 | 0.603974 | 0.301987 | − | 0.953312i | \(-0.402350\pi\) | ||||
0.301987 | + | 0.953312i | \(0.402350\pi\) | |||||||
\(480\) | −3.76902 | −0.172031 | ||||||||
\(481\) | −5.56199 | −0.253605 | ||||||||
\(482\) | 39.3591 | 1.79276 | ||||||||
\(483\) | 0.929007 | 0.0422713 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −15.8523 | −0.719816 | ||||||||
\(486\) | 2.35567 | 0.106856 | ||||||||
\(487\) | −42.4976 | −1.92575 | −0.962875 | − | 0.269949i | \(-0.912993\pi\) | ||||
−0.962875 | + | 0.269949i | \(0.912993\pi\) | |||||||
\(488\) | −4.40128 | −0.199236 | ||||||||
\(489\) | 23.7235 | 1.07281 | ||||||||
\(490\) | −16.4015 | −0.740944 | ||||||||
\(491\) | 15.7457 | 0.710592 | 0.355296 | − | 0.934754i | \(-0.384380\pi\) | ||||
0.355296 | + | 0.934754i | \(0.384380\pi\) | |||||||
\(492\) | 29.3825 | 1.32466 | ||||||||
\(493\) | 27.0722 | 1.21927 | ||||||||
\(494\) | −12.7284 | −0.572679 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −3.75405 | −0.168562 | ||||||||
\(497\) | −1.15938 | −0.0520052 | ||||||||
\(498\) | −19.5876 | −0.877742 | ||||||||
\(499\) | −33.5279 | −1.50092 | −0.750458 | − | 0.660918i | \(-0.770167\pi\) | ||||
−0.750458 | + | 0.660918i | \(0.770167\pi\) | |||||||
\(500\) | 3.54920 | 0.158725 | ||||||||
\(501\) | −3.49175 | −0.156000 | ||||||||
\(502\) | −37.9226 | −1.69257 | ||||||||
\(503\) | 22.8163 | 1.01733 | 0.508664 | − | 0.860965i | \(-0.330139\pi\) | ||||
0.508664 | + | 0.860965i | \(0.330139\pi\) | |||||||
\(504\) | −0.706260 | −0.0314593 | ||||||||
\(505\) | −13.1591 | −0.585574 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −12.0519 | −0.535243 | ||||||||
\(508\) | −25.2001 | −1.11807 | ||||||||
\(509\) | 39.7166 | 1.76041 | 0.880204 | − | 0.474596i | \(-0.157406\pi\) | ||||
0.880204 | + | 0.474596i | \(0.157406\pi\) | |||||||
\(510\) | 6.30309 | 0.279106 | ||||||||
\(511\) | 0.639846 | 0.0283051 | ||||||||
\(512\) | −16.5844 | −0.732933 | ||||||||
\(513\) | 5.54920 | 0.245003 | ||||||||
\(514\) | 14.0604 | 0.620179 | ||||||||
\(515\) | 3.99737 | 0.176145 | ||||||||
\(516\) | −18.1490 | −0.798963 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | −2.60410 | −0.114418 | ||||||||
\(519\) | 20.3596 | 0.893686 | ||||||||
\(520\) | −3.55346 | −0.155830 | ||||||||
\(521\) | 25.5004 | 1.11719 | 0.558596 | − | 0.829440i | \(-0.311340\pi\) | ||||
0.558596 | + | 0.829440i | \(0.311340\pi\) | |||||||
\(522\) | 23.8342 | 1.04320 | ||||||||
\(523\) | 15.4304 | 0.674725 | 0.337363 | − | 0.941375i | \(-0.390465\pi\) | ||||
0.337363 | + | 0.941375i | \(0.390465\pi\) | |||||||
\(524\) | 8.87385 | 0.387656 | ||||||||
\(525\) | −0.193527 | −0.00844621 | ||||||||
\(526\) | 1.06276 | 0.0463385 | ||||||||
\(527\) | −6.70351 | −0.292010 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 0.0438407 | 0.00190612 | ||||||||
\(530\) | −21.8814 | −0.950465 | ||||||||
\(531\) | −11.2180 | −0.486820 | ||||||||
\(532\) | −3.81156 | −0.165252 | ||||||||
\(533\) | −8.06095 | −0.349159 | ||||||||
\(534\) | 17.2970 | 0.748515 | ||||||||
\(535\) | −4.88682 | −0.211276 | ||||||||
\(536\) | 11.8942 | 0.513752 | ||||||||
\(537\) | 3.85117 | 0.166190 | ||||||||
\(538\) | 34.6749 | 1.49494 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 3.54920 | 0.152733 | ||||||||
\(541\) | −27.6007 | −1.18665 | −0.593324 | − | 0.804964i | \(-0.702185\pi\) | ||||
−0.593324 | + | 0.804964i | \(0.702185\pi\) | |||||||
\(542\) | −10.4306 | −0.448033 | ||||||||
\(543\) | −17.6151 | −0.755937 | ||||||||
\(544\) | −10.0848 | −0.432382 | ||||||||
\(545\) | 7.51977 | 0.322111 | ||||||||
\(546\) | 0.443901 | 0.0189972 | ||||||||
\(547\) | −30.7685 | −1.31557 | −0.657784 | − | 0.753207i | \(-0.728506\pi\) | ||||
−0.657784 | + | 0.753207i | \(0.728506\pi\) | |||||||
\(548\) | −54.2828 | −2.31885 | ||||||||
\(549\) | −1.20602 | −0.0514718 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 56.1457 | 2.39189 | ||||||||
\(552\) | −17.5186 | −0.745643 | ||||||||
\(553\) | 1.96487 | 0.0835546 | ||||||||
\(554\) | 0.217499 | 0.00924065 | ||||||||
\(555\) | 5.71217 | 0.242468 | ||||||||
\(556\) | 69.7723 | 2.95901 | ||||||||
\(557\) | 13.9359 | 0.590482 | 0.295241 | − | 0.955423i | \(-0.404600\pi\) | ||||
0.295241 | + | 0.955423i | \(0.404600\pi\) | |||||||
\(558\) | −5.90173 | −0.249840 | ||||||||
\(559\) | 4.97909 | 0.210593 | ||||||||
\(560\) | −0.289986 | −0.0122542 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −12.2095 | −0.515026 | ||||||||
\(563\) | −5.83988 | −0.246122 | −0.123061 | − | 0.992399i | \(-0.539271\pi\) | ||||
−0.123061 | + | 0.992399i | \(0.539271\pi\) | |||||||
\(564\) | −38.5170 | −1.62186 | ||||||||
\(565\) | 20.2237 | 0.850818 | ||||||||
\(566\) | −3.68575 | −0.154924 | ||||||||
\(567\) | −0.193527 | −0.00812737 | ||||||||
\(568\) | 21.8628 | 0.917345 | ||||||||
\(569\) | 5.45394 | 0.228641 | 0.114321 | − | 0.993444i | \(-0.463531\pi\) | ||||
0.114321 | + | 0.993444i | \(0.463531\pi\) | |||||||
\(570\) | 13.0721 | 0.547530 | ||||||||
\(571\) | −40.2894 | −1.68606 | −0.843030 | − | 0.537866i | \(-0.819230\pi\) | ||||
−0.843030 | + | 0.537866i | \(0.819230\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0.417099 | 0.0174246 | ||||||||
\(574\) | −3.77411 | −0.157528 | ||||||||
\(575\) | −4.80040 | −0.200191 | ||||||||
\(576\) | −11.8754 | −0.494810 | ||||||||
\(577\) | −23.8236 | −0.991789 | −0.495894 | − | 0.868383i | \(-0.665160\pi\) | ||||
−0.495894 | + | 0.868383i | \(0.665160\pi\) | |||||||
\(578\) | −23.1812 | −0.964213 | ||||||||
\(579\) | −11.6965 | −0.486091 | ||||||||
\(580\) | 35.9101 | 1.49109 | ||||||||
\(581\) | 1.60919 | 0.0667606 | ||||||||
\(582\) | −37.3428 | −1.54791 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | −12.0658 | −0.499287 | ||||||||
\(585\) | −0.973708 | −0.0402579 | ||||||||
\(586\) | 54.5504 | 2.25346 | ||||||||
\(587\) | 19.6080 | 0.809307 | 0.404654 | − | 0.914470i | \(-0.367392\pi\) | ||||
0.404654 | + | 0.914470i | \(0.367392\pi\) | |||||||
\(588\) | −24.7115 | −1.01908 | ||||||||
\(589\) | −13.9026 | −0.572845 | ||||||||
\(590\) | −26.4260 | −1.08794 | ||||||||
\(591\) | −21.5958 | −0.888334 | ||||||||
\(592\) | 8.55928 | 0.351784 | ||||||||
\(593\) | −3.31095 | −0.135964 | −0.0679822 | − | 0.997687i | \(-0.521656\pi\) | ||||
−0.0679822 | + | 0.997687i | \(0.521656\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −0.517822 | −0.0212286 | ||||||||
\(596\) | 35.9638 | 1.47313 | ||||||||
\(597\) | 7.76028 | 0.317607 | ||||||||
\(598\) | 11.0109 | 0.450268 | ||||||||
\(599\) | 32.0710 | 1.31039 | 0.655193 | − | 0.755462i | \(-0.272587\pi\) | ||||
0.655193 | + | 0.755462i | \(0.272587\pi\) | |||||||
\(600\) | 3.64941 | 0.148987 | ||||||||
\(601\) | 29.2905 | 1.19478 | 0.597392 | − | 0.801950i | \(-0.296204\pi\) | ||||
0.597392 | + | 0.801950i | \(0.296204\pi\) | |||||||
\(602\) | 2.33119 | 0.0950123 | ||||||||
\(603\) | 3.25922 | 0.132725 | ||||||||
\(604\) | −42.4596 | −1.72766 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −30.9986 | −1.25923 | ||||||||
\(607\) | 39.0806 | 1.58623 | 0.793117 | − | 0.609070i | \(-0.208457\pi\) | ||||
0.793117 | + | 0.609070i | \(0.208457\pi\) | |||||||
\(608\) | −20.9151 | −0.848217 | ||||||||
\(609\) | −1.95807 | −0.0793449 | ||||||||
\(610\) | −2.84100 | −0.115029 | ||||||||
\(611\) | 10.5670 | 0.427494 | ||||||||
\(612\) | 9.49662 | 0.383878 | ||||||||
\(613\) | 12.7324 | 0.514256 | 0.257128 | − | 0.966377i | \(-0.417224\pi\) | ||||
0.257128 | + | 0.966377i | \(0.417224\pi\) | |||||||
\(614\) | 18.1971 | 0.734376 | ||||||||
\(615\) | 8.27861 | 0.333826 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −8.97789 | −0.361436 | −0.180718 | − | 0.983535i | \(-0.557842\pi\) | ||||
−0.180718 | + | 0.983535i | \(0.557842\pi\) | |||||||
\(618\) | 9.41649 | 0.378787 | ||||||||
\(619\) | −22.2121 | −0.892780 | −0.446390 | − | 0.894839i | \(-0.647290\pi\) | ||||
−0.446390 | + | 0.894839i | \(0.647290\pi\) | |||||||
\(620\) | −8.89190 | −0.357107 | ||||||||
\(621\) | −4.80040 | −0.192633 | ||||||||
\(622\) | −45.0425 | −1.80604 | ||||||||
\(623\) | −1.42101 | −0.0569316 | ||||||||
\(624\) | −1.45903 | −0.0584080 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 6.83868 | 0.273329 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −9.32038 | −0.371924 | ||||||||
\(629\) | 15.2841 | 0.609417 | ||||||||
\(630\) | −0.455887 | −0.0181630 | ||||||||
\(631\) | 26.7672 | 1.06559 | 0.532794 | − | 0.846245i | \(-0.321142\pi\) | ||||
0.532794 | + | 0.846245i | \(0.321142\pi\) | |||||||
\(632\) | −37.0522 | −1.47386 | ||||||||
\(633\) | 12.5057 | 0.497056 | ||||||||
\(634\) | 5.32744 | 0.211580 | ||||||||
\(635\) | −7.10021 | −0.281763 | ||||||||
\(636\) | −32.9678 | −1.30726 | ||||||||
\(637\) | 6.77949 | 0.268613 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 5.99078 | 0.236992 | ||||||||
\(640\) | −20.4366 | −0.807829 | ||||||||
\(641\) | 15.0726 | 0.595333 | 0.297666 | − | 0.954670i | \(-0.403792\pi\) | ||||
0.297666 | + | 0.954670i | \(0.403792\pi\) | |||||||
\(642\) | −11.5117 | −0.454332 | ||||||||
\(643\) | −39.2872 | −1.54934 | −0.774669 | − | 0.632367i | \(-0.782083\pi\) | ||||
−0.774669 | + | 0.632367i | \(0.782083\pi\) | |||||||
\(644\) | 3.29723 | 0.129929 | ||||||||
\(645\) | −5.11353 | −0.201345 | ||||||||
\(646\) | 34.9771 | 1.37616 | ||||||||
\(647\) | 23.8136 | 0.936208 | 0.468104 | − | 0.883673i | \(-0.344937\pi\) | ||||
0.468104 | + | 0.883673i | \(0.344937\pi\) | |||||||
\(648\) | 3.64941 | 0.143363 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | −2.29374 | −0.0899679 | ||||||||
\(651\) | 0.484848 | 0.0190027 | ||||||||
\(652\) | 84.1994 | 3.29750 | ||||||||
\(653\) | 6.90354 | 0.270156 | 0.135078 | − | 0.990835i | \(-0.456871\pi\) | ||||
0.135078 | + | 0.990835i | \(0.456871\pi\) | |||||||
\(654\) | 17.7141 | 0.692677 | ||||||||
\(655\) | 2.50024 | 0.0976924 | ||||||||
\(656\) | 12.4049 | 0.484330 | ||||||||
\(657\) | −3.30624 | −0.128989 | ||||||||
\(658\) | 4.94742 | 0.192870 | ||||||||
\(659\) | 20.3718 | 0.793571 | 0.396786 | − | 0.917911i | \(-0.370126\pi\) | ||||
0.396786 | + | 0.917911i | \(0.370126\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −19.7451 | −0.767994 | −0.383997 | − | 0.923334i | \(-0.625453\pi\) | ||||
−0.383997 | + | 0.923334i | \(0.625453\pi\) | |||||||
\(662\) | 14.1891 | 0.551474 | ||||||||
\(663\) | −2.60536 | −0.101184 | ||||||||
\(664\) | −30.3452 | −1.17762 | ||||||||
\(665\) | −1.07392 | −0.0416449 | ||||||||
\(666\) | 13.4560 | 0.521410 | ||||||||
\(667\) | −48.5695 | −1.88062 | ||||||||
\(668\) | −12.3929 | −0.479496 | ||||||||
\(669\) | −5.37568 | −0.207836 | ||||||||
\(670\) | 7.67765 | 0.296613 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0.729407 | 0.0281375 | ||||||||
\(673\) | −36.6132 | −1.41134 | −0.705669 | − | 0.708542i | \(-0.749353\pi\) | ||||
−0.705669 | + | 0.708542i | \(0.749353\pi\) | |||||||
\(674\) | 34.3098 | 1.32157 | ||||||||
\(675\) | 1.00000 | 0.0384900 | ||||||||
\(676\) | −42.7746 | −1.64518 | ||||||||
\(677\) | −7.37138 | −0.283305 | −0.141653 | − | 0.989916i | \(-0.545242\pi\) | ||||
−0.141653 | + | 0.989916i | \(0.545242\pi\) | |||||||
\(678\) | 47.6405 | 1.82962 | ||||||||
\(679\) | 3.06785 | 0.117733 | ||||||||
\(680\) | 9.76476 | 0.374461 | ||||||||
\(681\) | 21.7529 | 0.833573 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 24.5651 | 0.939959 | 0.469979 | − | 0.882677i | \(-0.344261\pi\) | ||||
0.469979 | + | 0.882677i | \(0.344261\pi\) | |||||||
\(684\) | 19.6952 | 0.753066 | ||||||||
\(685\) | −15.2944 | −0.584368 | ||||||||
\(686\) | 6.36534 | 0.243030 | ||||||||
\(687\) | 2.67075 | 0.101896 | ||||||||
\(688\) | −7.66226 | −0.292121 | ||||||||
\(689\) | 9.04457 | 0.344571 | ||||||||
\(690\) | −11.3082 | −0.430495 | ||||||||
\(691\) | 29.8435 | 1.13530 | 0.567651 | − | 0.823269i | \(-0.307852\pi\) | ||||
0.567651 | + | 0.823269i | \(0.307852\pi\) | |||||||
\(692\) | 72.2602 | 2.74692 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −67.9262 | −2.57844 | ||||||||
\(695\) | 19.6586 | 0.745693 | ||||||||
\(696\) | 36.9240 | 1.39960 | ||||||||
\(697\) | 22.1511 | 0.839033 | ||||||||
\(698\) | 3.84526 | 0.145545 | ||||||||
\(699\) | 5.72699 | 0.216615 | ||||||||
\(700\) | −0.686867 | −0.0259611 | ||||||||
\(701\) | 14.4189 | 0.544595 | 0.272297 | − | 0.962213i | \(-0.412217\pi\) | ||||
0.272297 | + | 0.962213i | \(0.412217\pi\) | |||||||
\(702\) | −2.29374 | −0.0865716 | ||||||||
\(703\) | 31.6980 | 1.19551 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −10.8523 | −0.408721 | ||||||||
\(706\) | 58.7263 | 2.21019 | ||||||||
\(707\) | 2.54665 | 0.0957766 | ||||||||
\(708\) | −39.8150 | −1.49634 | ||||||||
\(709\) | −44.5088 | −1.67156 | −0.835781 | − | 0.549063i | \(-0.814985\pi\) | ||||
−0.835781 | + | 0.549063i | \(0.814985\pi\) | |||||||
\(710\) | 14.1123 | 0.529626 | ||||||||
\(711\) | −10.1529 | −0.380765 | ||||||||
\(712\) | 26.7966 | 1.00424 | ||||||||
\(713\) | 12.0266 | 0.450398 | ||||||||
\(714\) | −1.21982 | −0.0456506 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 13.6686 | 0.510819 | ||||||||
\(717\) | 24.3680 | 0.910040 | ||||||||
\(718\) | −66.9976 | −2.50033 | ||||||||
\(719\) | 3.59345 | 0.134013 | 0.0670066 | − | 0.997753i | \(-0.478655\pi\) | ||||
0.0670066 | + | 0.997753i | \(0.478655\pi\) | |||||||
\(720\) | 1.49843 | 0.0558431 | ||||||||
\(721\) | −0.773598 | −0.0288103 | ||||||||
\(722\) | 27.7820 | 1.03394 | ||||||||
\(723\) | 16.7082 | 0.621385 | ||||||||
\(724\) | −62.5196 | −2.32352 | ||||||||
\(725\) | 10.1178 | 0.375766 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −39.0846 | −1.44957 | −0.724784 | − | 0.688976i | \(-0.758060\pi\) | ||||
−0.724784 | + | 0.688976i | \(0.758060\pi\) | |||||||
\(728\) | 0.687692 | 0.0254875 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −7.78841 | −0.288262 | ||||||||
\(731\) | −13.6823 | −0.506059 | ||||||||
\(732\) | −4.28042 | −0.158209 | ||||||||
\(733\) | −37.7065 | −1.39272 | −0.696360 | − | 0.717693i | \(-0.745198\pi\) | ||||
−0.696360 | + | 0.717693i | \(0.745198\pi\) | |||||||
\(734\) | −24.5962 | −0.907863 | ||||||||
\(735\) | −6.96255 | −0.256817 | ||||||||
\(736\) | 18.0928 | 0.666910 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 19.5017 | 0.717868 | ||||||||
\(739\) | −14.9324 | −0.549298 | −0.274649 | − | 0.961545i | \(-0.588562\pi\) | ||||
−0.274649 | + | 0.961545i | \(0.588562\pi\) | |||||||
\(740\) | 20.2737 | 0.745274 | ||||||||
\(741\) | −5.40330 | −0.198495 | ||||||||
\(742\) | 4.23463 | 0.155458 | ||||||||
\(743\) | −13.3680 | −0.490423 | −0.245211 | − | 0.969470i | \(-0.578857\pi\) | ||||
−0.245211 | + | 0.969470i | \(0.578857\pi\) | |||||||
\(744\) | −9.14297 | −0.335198 | ||||||||
\(745\) | 10.1329 | 0.371242 | ||||||||
\(746\) | 6.63705 | 0.243000 | ||||||||
\(747\) | −8.31508 | −0.304233 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0.945731 | 0.0345563 | ||||||||
\(750\) | 2.35567 | 0.0860171 | ||||||||
\(751\) | 40.4655 | 1.47661 | 0.738303 | − | 0.674469i | \(-0.235627\pi\) | ||||
0.738303 | + | 0.674469i | \(0.235627\pi\) | |||||||
\(752\) | −16.2614 | −0.592991 | ||||||||
\(753\) | −16.0984 | −0.586658 | ||||||||
\(754\) | −23.2076 | −0.845171 | ||||||||
\(755\) | −11.9632 | −0.435384 | ||||||||
\(756\) | −0.686867 | −0.0249811 | ||||||||
\(757\) | −8.53757 | −0.310303 | −0.155152 | − | 0.987891i | \(-0.549587\pi\) | ||||
−0.155152 | + | 0.987891i | \(0.549587\pi\) | |||||||
\(758\) | 21.0437 | 0.764341 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 20.2513 | 0.734593 | ||||||||
\(761\) | 21.2805 | 0.771416 | 0.385708 | − | 0.922621i | \(-0.373957\pi\) | ||||
0.385708 | + | 0.922621i | \(0.373957\pi\) | |||||||
\(762\) | −16.7258 | −0.605911 | ||||||||
\(763\) | −1.45528 | −0.0526846 | ||||||||
\(764\) | 1.48037 | 0.0535579 | ||||||||
\(765\) | 2.67571 | 0.0967403 | ||||||||
\(766\) | −20.1005 | −0.726260 | ||||||||
\(767\) | 10.9231 | 0.394409 | ||||||||
\(768\) | −24.3912 | −0.880140 | ||||||||
\(769\) | 24.4717 | 0.882471 | 0.441235 | − | 0.897391i | \(-0.354540\pi\) | ||||
0.441235 | + | 0.897391i | \(0.354540\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 5.96875 | 0.214959 | ||||||||
\(772\) | −41.5134 | −1.49410 | ||||||||
\(773\) | 13.6472 | 0.490855 | 0.245427 | − | 0.969415i | \(-0.421072\pi\) | ||||
0.245427 | + | 0.969415i | \(0.421072\pi\) | |||||||
\(774\) | −12.0458 | −0.432978 | ||||||||
\(775\) | −2.50533 | −0.0899940 | ||||||||
\(776\) | −57.8516 | −2.07675 | ||||||||
\(777\) | −1.10546 | −0.0396582 | ||||||||
\(778\) | 27.7398 | 0.994520 | ||||||||
\(779\) | 45.9397 | 1.64596 | ||||||||
\(780\) | −3.45589 | −0.123741 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | −30.2574 | −1.08200 | ||||||||
\(783\) | 10.1178 | 0.361581 | ||||||||
\(784\) | −10.4329 | −0.372603 | ||||||||
\(785\) | −2.62605 | −0.0937278 | ||||||||
\(786\) | 5.88974 | 0.210080 | ||||||||
\(787\) | 7.45709 | 0.265816 | 0.132908 | − | 0.991128i | \(-0.457568\pi\) | ||||
0.132908 | + | 0.991128i | \(0.457568\pi\) | |||||||
\(788\) | −76.6480 | −2.73047 | ||||||||
\(789\) | 0.451149 | 0.0160613 | ||||||||
\(790\) | −23.9170 | −0.850929 | ||||||||
\(791\) | −3.91383 | −0.139160 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1.17431 | 0.0417011 | ||||||||
\(794\) | −3.32655 | −0.118055 | ||||||||
\(795\) | −9.28879 | −0.329439 | ||||||||
\(796\) | 27.5428 | 0.976228 | ||||||||
\(797\) | 12.0347 | 0.426289 | 0.213145 | − | 0.977021i | \(-0.431629\pi\) | ||||
0.213145 | + | 0.977021i | \(0.431629\pi\) | |||||||
\(798\) | −2.52981 | −0.0895542 | ||||||||
\(799\) | −29.0375 | −1.02727 | ||||||||
\(800\) | −3.76902 | −0.133255 | ||||||||
\(801\) | 7.34270 | 0.259442 | ||||||||
\(802\) | 19.9270 | 0.703648 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 11.5676 | 0.407958 | ||||||||
\(805\) | 0.929007 | 0.0327432 | ||||||||
\(806\) | 5.74656 | 0.202414 | ||||||||
\(807\) | 14.7197 | 0.518159 | ||||||||
\(808\) | −48.0231 | −1.68945 | ||||||||
\(809\) | 50.0338 | 1.75909 | 0.879546 | − | 0.475813i | \(-0.157846\pi\) | ||||
0.879546 | + | 0.475813i | \(0.157846\pi\) | |||||||
\(810\) | 2.35567 | 0.0827700 | ||||||||
\(811\) | 11.2188 | 0.393944 | 0.196972 | − | 0.980409i | \(-0.436889\pi\) | ||||
0.196972 | + | 0.980409i | \(0.436889\pi\) | |||||||
\(812\) | −6.94958 | −0.243882 | ||||||||
\(813\) | −4.42787 | −0.155292 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 23.7235 | 0.830997 | ||||||||
\(816\) | 4.00935 | 0.140355 | ||||||||
\(817\) | −28.3760 | −0.992752 | ||||||||
\(818\) | −23.8524 | −0.833981 | ||||||||
\(819\) | 0.188439 | 0.00658459 | ||||||||
\(820\) | 29.3825 | 1.02608 | ||||||||
\(821\) | −7.37723 | −0.257467 | −0.128734 | − | 0.991679i | \(-0.541091\pi\) | ||||
−0.128734 | + | 0.991679i | \(0.541091\pi\) | |||||||
\(822\) | −36.0286 | −1.25664 | ||||||||
\(823\) | 35.6380 | 1.24226 | 0.621132 | − | 0.783706i | \(-0.286673\pi\) | ||||
0.621132 | + | 0.783706i | \(0.286673\pi\) | |||||||
\(824\) | 14.5880 | 0.508198 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 5.11414 | 0.177944 | ||||||||
\(827\) | 50.5291 | 1.75707 | 0.878535 | − | 0.477678i | \(-0.158522\pi\) | ||||
0.878535 | + | 0.477678i | \(0.158522\pi\) | |||||||
\(828\) | −17.0376 | −0.592097 | ||||||||
\(829\) | −6.14491 | −0.213422 | −0.106711 | − | 0.994290i | \(-0.534032\pi\) | ||||
−0.106711 | + | 0.994290i | \(0.534032\pi\) | |||||||
\(830\) | −19.5876 | −0.679896 | ||||||||
\(831\) | 0.0923299 | 0.00320289 | ||||||||
\(832\) | 11.5632 | 0.400882 | ||||||||
\(833\) | −18.6297 | −0.645482 | ||||||||
\(834\) | 46.3093 | 1.60356 | ||||||||
\(835\) | −3.49175 | −0.120837 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −2.50533 | −0.0865967 | ||||||||
\(838\) | 77.2707 | 2.66927 | ||||||||
\(839\) | −37.5230 | −1.29544 | −0.647719 | − | 0.761879i | \(-0.724277\pi\) | ||||
−0.647719 | + | 0.761879i | \(0.724277\pi\) | |||||||
\(840\) | −0.706260 | −0.0243683 | ||||||||
\(841\) | 73.3698 | 2.52999 | ||||||||
\(842\) | −33.2840 | −1.14704 | ||||||||
\(843\) | −5.18301 | −0.178512 | ||||||||
\(844\) | 44.3852 | 1.52780 | ||||||||
\(845\) | −12.0519 | −0.414598 | ||||||||
\(846\) | −25.5645 | −0.878924 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −13.9186 | −0.477966 | ||||||||
\(849\) | −1.56463 | −0.0536978 | ||||||||
\(850\) | 6.30309 | 0.216194 | ||||||||
\(851\) | −27.4207 | −0.939970 | ||||||||
\(852\) | 21.2625 | 0.728441 | ||||||||
\(853\) | 27.0122 | 0.924880 | 0.462440 | − | 0.886651i | \(-0.346974\pi\) | ||||
0.462440 | + | 0.886651i | \(0.346974\pi\) | |||||||
\(854\) | 0.549810 | 0.0188141 | ||||||||
\(855\) | 5.54920 | 0.189779 | ||||||||
\(856\) | −17.8340 | −0.609554 | ||||||||
\(857\) | 2.51515 | 0.0859159 | 0.0429580 | − | 0.999077i | \(-0.486322\pi\) | ||||
0.0429580 | + | 0.999077i | \(0.486322\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 6.70885 | 0.228903 | 0.114451 | − | 0.993429i | \(-0.463489\pi\) | ||||
0.114451 | + | 0.993429i | \(0.463489\pi\) | |||||||
\(860\) | −18.1490 | −0.618874 | ||||||||
\(861\) | −1.60214 | −0.0546006 | ||||||||
\(862\) | −45.0069 | −1.53294 | ||||||||
\(863\) | −3.30744 | −0.112586 | −0.0562932 | − | 0.998414i | \(-0.517928\pi\) | ||||
−0.0562932 | + | 0.998414i | \(0.517928\pi\) | |||||||
\(864\) | −3.76902 | −0.128225 | ||||||||
\(865\) | 20.3596 | 0.692246 | ||||||||
\(866\) | 35.6179 | 1.21034 | ||||||||
\(867\) | −9.84060 | −0.334204 | ||||||||
\(868\) | 1.72082 | 0.0584086 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 23.8342 | 0.808056 | ||||||||
\(871\) | −3.17352 | −0.107531 | ||||||||
\(872\) | 27.4427 | 0.929328 | ||||||||
\(873\) | −15.8523 | −0.536519 | ||||||||
\(874\) | −62.7514 | −2.12260 | ||||||||
\(875\) | −0.193527 | −0.00654241 | ||||||||
\(876\) | −11.7345 | −0.396472 | ||||||||
\(877\) | −32.1004 | −1.08395 | −0.541976 | − | 0.840394i | \(-0.682324\pi\) | ||||
−0.541976 | + | 0.840394i | \(0.682324\pi\) | |||||||
\(878\) | −87.5468 | −2.95456 | ||||||||
\(879\) | 23.1570 | 0.781067 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −35.2547 | −1.18776 | −0.593881 | − | 0.804553i | \(-0.702405\pi\) | ||||
−0.593881 | + | 0.804553i | \(0.702405\pi\) | |||||||
\(882\) | −16.4015 | −0.552267 | ||||||||
\(883\) | −0.455852 | −0.0153406 | −0.00767032 | − | 0.999971i | \(-0.502442\pi\) | ||||
−0.00767032 | + | 0.999971i | \(0.502442\pi\) | |||||||
\(884\) | −9.24694 | −0.311008 | ||||||||
\(885\) | −11.2180 | −0.377089 | ||||||||
\(886\) | −6.50282 | −0.218467 | ||||||||
\(887\) | 1.80160 | 0.0604918 | 0.0302459 | − | 0.999542i | \(-0.490371\pi\) | ||||
0.0302459 | + | 0.999542i | \(0.490371\pi\) | |||||||
\(888\) | 20.8461 | 0.699549 | ||||||||
\(889\) | 1.37408 | 0.0460853 | ||||||||
\(890\) | 17.2970 | 0.579797 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −19.0794 | −0.638824 | ||||||||
\(893\) | −60.2216 | −2.01524 | ||||||||
\(894\) | 23.8699 | 0.798328 | ||||||||
\(895\) | 3.85117 | 0.128731 | ||||||||
\(896\) | 3.95504 | 0.132129 | ||||||||
\(897\) | 4.67419 | 0.156067 | ||||||||
\(898\) | −42.0868 | −1.40446 | ||||||||
\(899\) | −25.3484 | −0.845416 | ||||||||
\(900\) | 3.54920 | 0.118307 | ||||||||
\(901\) | −24.8541 | −0.828009 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0.989607 | 0.0329321 | ||||||||
\(904\) | 73.8047 | 2.45471 | ||||||||
\(905\) | −17.6151 | −0.585546 | ||||||||
\(906\) | −28.1813 | −0.936261 | ||||||||
\(907\) | −35.3469 | −1.17367 | −0.586837 | − | 0.809705i | \(-0.699627\pi\) | ||||
−0.586837 | + | 0.809705i | \(0.699627\pi\) | |||||||
\(908\) | 77.2054 | 2.56215 | ||||||||
\(909\) | −13.1591 | −0.436461 | ||||||||
\(910\) | 0.443901 | 0.0147152 | ||||||||
\(911\) | −1.64877 | −0.0546262 | −0.0273131 | − | 0.999627i | \(-0.508695\pi\) | ||||
−0.0273131 | + | 0.999627i | \(0.508695\pi\) | |||||||
\(912\) | 8.31508 | 0.275340 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 49.8511 | 1.64893 | ||||||||
\(915\) | −1.20602 | −0.0398699 | ||||||||
\(916\) | 9.47903 | 0.313196 | ||||||||
\(917\) | −0.483864 | −0.0159786 | ||||||||
\(918\) | 6.30309 | 0.208033 | ||||||||
\(919\) | 0.318990 | 0.0105225 | 0.00526125 | − | 0.999986i | \(-0.498325\pi\) | ||||
0.00526125 | + | 0.999986i | \(0.498325\pi\) | |||||||
\(920\) | −17.5186 | −0.577573 | ||||||||
\(921\) | 7.72480 | 0.254541 | ||||||||
\(922\) | 80.9118 | 2.66469 | ||||||||
\(923\) | −5.83327 | −0.192005 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 5.71217 | 0.187815 | ||||||||
\(926\) | 24.6206 | 0.809082 | ||||||||
\(927\) | 3.99737 | 0.131291 | ||||||||
\(928\) | −38.1342 | −1.25182 | ||||||||
\(929\) | 56.1509 | 1.84225 | 0.921125 | − | 0.389267i | \(-0.127272\pi\) | ||||
0.921125 | + | 0.389267i | \(0.127272\pi\) | |||||||
\(930\) | −5.90173 | −0.193525 | ||||||||
\(931\) | −38.6366 | −1.26626 | ||||||||
\(932\) | 20.3262 | 0.665808 | ||||||||
\(933\) | −19.1209 | −0.625989 | ||||||||
\(934\) | 69.8301 | 2.28491 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −3.55346 | −0.116149 | ||||||||
\(937\) | −36.8424 | −1.20359 | −0.601795 | − | 0.798651i | \(-0.705547\pi\) | ||||
−0.601795 | + | 0.798651i | \(0.705547\pi\) | |||||||
\(938\) | −1.48583 | −0.0485142 | ||||||||
\(939\) | 2.90307 | 0.0947380 | ||||||||
\(940\) | −38.5170 | −1.25629 | ||||||||
\(941\) | 15.3105 | 0.499108 | 0.249554 | − | 0.968361i | \(-0.419716\pi\) | ||||
0.249554 | + | 0.968361i | \(0.419716\pi\) | |||||||
\(942\) | −6.18612 | −0.201555 | ||||||||
\(943\) | −39.7406 | −1.29413 | ||||||||
\(944\) | −16.8094 | −0.547099 | ||||||||
\(945\) | −0.193527 | −0.00629544 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −22.6654 | −0.736526 | −0.368263 | − | 0.929722i | \(-0.620047\pi\) | ||||
−0.368263 | + | 0.929722i | \(0.620047\pi\) | |||||||
\(948\) | −36.0348 | −1.17036 | ||||||||
\(949\) | 3.21931 | 0.104503 | ||||||||
\(950\) | 13.0721 | 0.424115 | ||||||||
\(951\) | 2.26153 | 0.0733353 | ||||||||
\(952\) | −1.88974 | −0.0612470 | ||||||||
\(953\) | −39.3324 | −1.27410 | −0.637051 | − | 0.770822i | \(-0.719846\pi\) | ||||
−0.637051 | + | 0.770822i | \(0.719846\pi\) | |||||||
\(954\) | −21.8814 | −0.708435 | ||||||||
\(955\) | 0.417099 | 0.0134970 | ||||||||
\(956\) | 86.4870 | 2.79719 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 31.1388 | 1.00605 | ||||||||
\(959\) | 2.95988 | 0.0955794 | ||||||||
\(960\) | −11.8754 | −0.383278 | ||||||||
\(961\) | −24.7233 | −0.797527 | ||||||||
\(962\) | −13.1022 | −0.422433 | ||||||||
\(963\) | −4.88682 | −0.157475 | ||||||||
\(964\) | 59.3008 | 1.90995 | ||||||||
\(965\) | −11.6965 | −0.376525 | ||||||||
\(966\) | 2.18844 | 0.0704119 | ||||||||
\(967\) | −3.06103 | −0.0984360 | −0.0492180 | − | 0.998788i | \(-0.515673\pi\) | ||||
−0.0492180 | + | 0.998788i | \(0.515673\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 14.8480 | 0.476987 | ||||||||
\(970\) | −37.3428 | −1.19901 | ||||||||
\(971\) | 32.0385 | 1.02816 | 0.514082 | − | 0.857741i | \(-0.328133\pi\) | ||||
0.514082 | + | 0.857741i | \(0.328133\pi\) | |||||||
\(972\) | 3.54920 | 0.113841 | ||||||||
\(973\) | −3.80447 | −0.121966 | ||||||||
\(974\) | −100.110 | −3.20775 | ||||||||
\(975\) | −0.973708 | −0.0311836 | ||||||||
\(976\) | −1.80714 | −0.0578451 | ||||||||
\(977\) | −53.1962 | −1.70190 | −0.850948 | − | 0.525250i | \(-0.823972\pi\) | ||||
−0.850948 | + | 0.525250i | \(0.823972\pi\) | |||||||
\(978\) | 55.8848 | 1.78700 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | −24.7115 | −0.789379 | ||||||||
\(981\) | 7.51977 | 0.240088 | ||||||||
\(982\) | 37.0916 | 1.18364 | ||||||||
\(983\) | −24.5004 | −0.781442 | −0.390721 | − | 0.920509i | \(-0.627774\pi\) | ||||
−0.390721 | + | 0.920509i | \(0.627774\pi\) | |||||||
\(984\) | 30.2121 | 0.963126 | ||||||||
\(985\) | −21.5958 | −0.688101 | ||||||||
\(986\) | 63.7734 | 2.03096 | ||||||||
\(987\) | 2.10021 | 0.0668505 | ||||||||
\(988\) | −19.1774 | −0.610115 | ||||||||
\(989\) | 24.5470 | 0.780549 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −6.34819 | −0.201657 | −0.100828 | − | 0.994904i | \(-0.532149\pi\) | ||||
−0.100828 | + | 0.994904i | \(0.532149\pi\) | |||||||
\(992\) | 9.44262 | 0.299804 | ||||||||
\(993\) | 6.02336 | 0.191146 | ||||||||
\(994\) | −2.73112 | −0.0866258 | ||||||||
\(995\) | 7.76028 | 0.246017 | ||||||||
\(996\) | −29.5119 | −0.935120 | ||||||||
\(997\) | 25.9460 | 0.821719 | 0.410860 | − | 0.911699i | \(-0.365229\pi\) | ||||
0.410860 | + | 0.911699i | \(0.365229\pi\) | |||||||
\(998\) | −78.9808 | −2.50010 | ||||||||
\(999\) | 5.71217 | 0.180725 |
(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.w.1.4 | 4 | ||
3.2 | odd | 2 | 5445.2.a.bf.1.1 | 4 | |||
5.4 | even | 2 | 9075.2.a.cm.1.1 | 4 | |||
11.2 | odd | 10 | 165.2.m.d.136.2 | yes | 8 | ||
11.6 | odd | 10 | 165.2.m.d.91.2 | ✓ | 8 | ||
11.10 | odd | 2 | 1815.2.a.p.1.1 | 4 | |||
33.2 | even | 10 | 495.2.n.a.136.1 | 8 | |||
33.17 | even | 10 | 495.2.n.a.91.1 | 8 | |||
33.32 | even | 2 | 5445.2.a.bt.1.4 | 4 | |||
55.2 | even | 20 | 825.2.bx.f.499.1 | 16 | |||
55.13 | even | 20 | 825.2.bx.f.499.4 | 16 | |||
55.17 | even | 20 | 825.2.bx.f.124.4 | 16 | |||
55.24 | odd | 10 | 825.2.n.g.301.1 | 8 | |||
55.28 | even | 20 | 825.2.bx.f.124.1 | 16 | |||
55.39 | odd | 10 | 825.2.n.g.751.1 | 8 | |||
55.54 | odd | 2 | 9075.2.a.di.1.4 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
165.2.m.d.91.2 | ✓ | 8 | 11.6 | odd | 10 | ||
165.2.m.d.136.2 | yes | 8 | 11.2 | odd | 10 | ||
495.2.n.a.91.1 | 8 | 33.17 | even | 10 | |||
495.2.n.a.136.1 | 8 | 33.2 | even | 10 | |||
825.2.n.g.301.1 | 8 | 55.24 | odd | 10 | |||
825.2.n.g.751.1 | 8 | 55.39 | odd | 10 | |||
825.2.bx.f.124.1 | 16 | 55.28 | even | 20 | |||
825.2.bx.f.124.4 | 16 | 55.17 | even | 20 | |||
825.2.bx.f.499.1 | 16 | 55.2 | even | 20 | |||
825.2.bx.f.499.4 | 16 | 55.13 | even | 20 | |||
1815.2.a.p.1.1 | 4 | 11.10 | odd | 2 | |||
1815.2.a.w.1.4 | 4 | 1.1 | even | 1 | trivial | ||
5445.2.a.bf.1.1 | 4 | 3.2 | odd | 2 | |||
5445.2.a.bt.1.4 | 4 | 33.32 | even | 2 | |||
9075.2.a.cm.1.1 | 4 | 5.4 | even | 2 | |||
9075.2.a.di.1.4 | 4 | 55.54 | odd | 2 |