Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1617,2,Mod(1,1617)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1617, 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("1617.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1617 = 3 \cdot 7^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1617.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: | \(12.9118100068\) |
Analytic rank: | \(0\) |
Dimension: | \(5\) |
Coefficient field: | 5.5.3676752.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{5} - 2x^{4} - 8x^{3} + 14x^{2} + 11x - 10 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 231) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(0.614936\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1617.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.614936 | 0.434825 | 0.217413 | − | 0.976080i | \(-0.430238\pi\) | ||||
0.217413 | + | 0.976080i | \(0.430238\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | −1.62185 | −0.810927 | ||||||||
\(5\) | 1.49597 | 0.669019 | 0.334509 | − | 0.942392i | \(-0.391429\pi\) | ||||
0.334509 | + | 0.942392i | \(0.391429\pi\) | |||||||
\(6\) | −0.614936 | −0.251047 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −2.22721 | −0.787437 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0.919926 | 0.290906 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | 1.62185 | 0.468189 | ||||||||
\(13\) | −1.27568 | −0.353810 | −0.176905 | − | 0.984228i | \(-0.556609\pi\) | ||||
−0.176905 | + | 0.984228i | \(0.556609\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.49597 | −0.386258 | ||||||||
\(16\) | 1.87412 | 0.468529 | ||||||||
\(17\) | 0.614936 | 0.149144 | 0.0745719 | − | 0.997216i | \(-0.476241\pi\) | ||||
0.0745719 | + | 0.997216i | \(0.476241\pi\) | |||||||
\(18\) | 0.614936 | 0.144942 | ||||||||
\(19\) | −2.66075 | −0.610417 | −0.305208 | − | 0.952286i | \(-0.598726\pi\) | ||||
−0.305208 | + | 0.952286i | \(0.598726\pi\) | |||||||
\(20\) | −2.42625 | −0.542525 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0.614936 | 0.131105 | ||||||||
\(23\) | 1.87412 | 0.390780 | 0.195390 | − | 0.980726i | \(-0.437403\pi\) | ||||
0.195390 | + | 0.980726i | \(0.437403\pi\) | |||||||
\(24\) | 2.22721 | 0.454627 | ||||||||
\(25\) | −2.76207 | −0.552414 | ||||||||
\(26\) | −0.784462 | −0.153846 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 8.44902 | 1.56894 | 0.784472 | − | 0.620164i | \(-0.212934\pi\) | ||||
0.784472 | + | 0.620164i | \(0.212934\pi\) | |||||||
\(30\) | −0.919926 | −0.167955 | ||||||||
\(31\) | 4.62185 | 0.830109 | 0.415055 | − | 0.909796i | \(-0.363762\pi\) | ||||
0.415055 | + | 0.909796i | \(0.363762\pi\) | |||||||
\(32\) | 5.60688 | 0.991165 | ||||||||
\(33\) | −1.00000 | −0.174078 | ||||||||
\(34\) | 0.378146 | 0.0648515 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −1.62185 | −0.270309 | ||||||||
\(37\) | 0.274157 | 0.0450711 | 0.0225356 | − | 0.999746i | \(-0.492826\pi\) | ||||
0.0225356 | + | 0.999746i | \(0.492826\pi\) | |||||||
\(38\) | −1.63619 | −0.265425 | ||||||||
\(39\) | 1.27568 | 0.204272 | ||||||||
\(40\) | −3.33184 | −0.526810 | ||||||||
\(41\) | −4.91993 | −0.768363 | −0.384182 | − | 0.923258i | \(-0.625516\pi\) | ||||
−0.384182 | + | 0.923258i | \(0.625516\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 9.42511 | 1.43732 | 0.718658 | − | 0.695364i | \(-0.244757\pi\) | ||||
0.718658 | + | 0.695364i | \(0.244757\pi\) | |||||||
\(44\) | −1.62185 | −0.244504 | ||||||||
\(45\) | 1.49597 | 0.223006 | ||||||||
\(46\) | 1.15246 | 0.169921 | ||||||||
\(47\) | −3.16211 | −0.461241 | −0.230621 | − | 0.973044i | \(-0.574076\pi\) | ||||
−0.230621 | + | 0.973044i | \(0.574076\pi\) | |||||||
\(48\) | −1.87412 | −0.270506 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −1.69850 | −0.240204 | ||||||||
\(51\) | −0.614936 | −0.0861083 | ||||||||
\(52\) | 2.06897 | 0.286914 | ||||||||
\(53\) | 6.18832 | 0.850031 | 0.425015 | − | 0.905186i | \(-0.360269\pi\) | ||||
0.425015 | + | 0.905186i | \(0.360269\pi\) | |||||||
\(54\) | −0.614936 | −0.0836822 | ||||||||
\(55\) | 1.49597 | 0.201717 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 2.66075 | 0.352424 | ||||||||
\(58\) | 5.19561 | 0.682217 | ||||||||
\(59\) | 1.87412 | 0.243989 | 0.121995 | − | 0.992531i | \(-0.461071\pi\) | ||||
0.121995 | + | 0.992531i | \(0.461071\pi\) | |||||||
\(60\) | 2.42625 | 0.313227 | ||||||||
\(61\) | −8.52643 | −1.09170 | −0.545849 | − | 0.837884i | \(-0.683793\pi\) | ||||
−0.545849 | + | 0.837884i | \(0.683793\pi\) | |||||||
\(62\) | 2.84214 | 0.360953 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −0.300364 | −0.0375455 | ||||||||
\(65\) | −1.90838 | −0.236706 | ||||||||
\(66\) | −0.614936 | −0.0756934 | ||||||||
\(67\) | 5.06243 | 0.618475 | 0.309237 | − | 0.950985i | \(-0.399926\pi\) | ||||
0.309237 | + | 0.950985i | \(0.399926\pi\) | |||||||
\(68\) | −0.997336 | −0.120945 | ||||||||
\(69\) | −1.87412 | −0.225617 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 16.0954 | 1.91018 | 0.955088 | − | 0.296322i | \(-0.0957600\pi\) | ||||
0.955088 | + | 0.296322i | \(0.0957600\pi\) | |||||||
\(72\) | −2.22721 | −0.262479 | ||||||||
\(73\) | 8.75732 | 1.02497 | 0.512483 | − | 0.858697i | \(-0.328726\pi\) | ||||
0.512483 | + | 0.858697i | \(0.328726\pi\) | |||||||
\(74\) | 0.168589 | 0.0195981 | ||||||||
\(75\) | 2.76207 | 0.318936 | ||||||||
\(76\) | 4.31534 | 0.495003 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0.784462 | 0.0888228 | ||||||||
\(79\) | 9.44966 | 1.06317 | 0.531585 | − | 0.847005i | \(-0.321597\pi\) | ||||
0.531585 | + | 0.847005i | \(0.321597\pi\) | |||||||
\(80\) | 2.80363 | 0.313455 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −3.02544 | −0.334104 | ||||||||
\(83\) | 9.00578 | 0.988513 | 0.494256 | − | 0.869316i | \(-0.335440\pi\) | ||||
0.494256 | + | 0.869316i | \(0.335440\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.919926 | 0.0997800 | ||||||||
\(86\) | 5.79584 | 0.624981 | ||||||||
\(87\) | −8.44902 | −0.905830 | ||||||||
\(88\) | −2.22721 | −0.237421 | ||||||||
\(89\) | 10.6762 | 1.13168 | 0.565839 | − | 0.824516i | \(-0.308552\pi\) | ||||
0.565839 | + | 0.824516i | \(0.308552\pi\) | |||||||
\(90\) | 0.919926 | 0.0969688 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −3.03954 | −0.316894 | ||||||||
\(93\) | −4.62185 | −0.479264 | ||||||||
\(94\) | −1.94450 | −0.200559 | ||||||||
\(95\) | −3.98040 | −0.408380 | ||||||||
\(96\) | −5.60688 | −0.572250 | ||||||||
\(97\) | −17.6881 | −1.79595 | −0.897977 | − | 0.440042i | \(-0.854964\pi\) | ||||
−0.897977 | + | 0.440042i | \(0.854964\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.00000 | 0.100504 | ||||||||
\(100\) | 4.47967 | 0.447967 | ||||||||
\(101\) | 4.70079 | 0.467746 | 0.233873 | − | 0.972267i | \(-0.424860\pi\) | ||||
0.233873 | + | 0.972267i | \(0.424860\pi\) | |||||||
\(102\) | −0.378146 | −0.0374421 | ||||||||
\(103\) | 17.5642 | 1.73065 | 0.865325 | − | 0.501211i | \(-0.167112\pi\) | ||||
0.865325 | + | 0.501211i | \(0.167112\pi\) | |||||||
\(104\) | 2.84121 | 0.278603 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 3.80542 | 0.369615 | ||||||||
\(107\) | 11.8341 | 1.14404 | 0.572022 | − | 0.820238i | \(-0.306159\pi\) | ||||
0.572022 | + | 0.820238i | \(0.306159\pi\) | |||||||
\(108\) | 1.62185 | 0.156063 | ||||||||
\(109\) | −1.02392 | −0.0980733 | −0.0490367 | − | 0.998797i | \(-0.515615\pi\) | ||||
−0.0490367 | + | 0.998797i | \(0.515615\pi\) | |||||||
\(110\) | 0.919926 | 0.0877115 | ||||||||
\(111\) | −0.274157 | −0.0260218 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 6.28526 | 0.591268 | 0.295634 | − | 0.955301i | \(-0.404469\pi\) | ||||
0.295634 | + | 0.955301i | \(0.404469\pi\) | |||||||
\(114\) | 1.63619 | 0.153243 | ||||||||
\(115\) | 2.80363 | 0.261439 | ||||||||
\(116\) | −13.7031 | −1.27230 | ||||||||
\(117\) | −1.27568 | −0.117937 | ||||||||
\(118\) | 1.15246 | 0.106093 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 3.33184 | 0.304154 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | −5.24321 | −0.474698 | ||||||||
\(123\) | 4.91993 | 0.443615 | ||||||||
\(124\) | −7.49597 | −0.673158 | ||||||||
\(125\) | −11.6118 | −1.03859 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −19.7328 | −1.75100 | −0.875500 | − | 0.483218i | \(-0.839468\pi\) | ||||
−0.875500 | + | 0.483218i | \(0.839468\pi\) | |||||||
\(128\) | −11.3985 | −1.00749 | ||||||||
\(129\) | −9.42511 | −0.829834 | ||||||||
\(130\) | −1.17353 | −0.102926 | ||||||||
\(131\) | −5.31572 | −0.464437 | −0.232218 | − | 0.972664i | \(-0.574598\pi\) | ||||
−0.232218 | + | 0.972664i | \(0.574598\pi\) | |||||||
\(132\) | 1.62185 | 0.141164 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 3.11307 | 0.268929 | ||||||||
\(135\) | −1.49597 | −0.128753 | ||||||||
\(136\) | −1.36959 | −0.117441 | ||||||||
\(137\) | 2.38817 | 0.204035 | 0.102017 | − | 0.994783i | \(-0.467470\pi\) | ||||
0.102017 | + | 0.994783i | \(0.467470\pi\) | |||||||
\(138\) | −1.15246 | −0.0981041 | ||||||||
\(139\) | 12.4948 | 1.05980 | 0.529899 | − | 0.848061i | \(-0.322230\pi\) | ||||
0.529899 | + | 0.848061i | \(0.322230\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 3.16211 | 0.266298 | ||||||||
\(142\) | 9.89766 | 0.830593 | ||||||||
\(143\) | −1.27568 | −0.106678 | ||||||||
\(144\) | 1.87412 | 0.156176 | ||||||||
\(145\) | 12.6395 | 1.04965 | ||||||||
\(146\) | 5.38519 | 0.445681 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −0.444643 | −0.0365494 | ||||||||
\(149\) | −6.70655 | −0.549422 | −0.274711 | − | 0.961527i | \(-0.588582\pi\) | ||||
−0.274711 | + | 0.961527i | \(0.588582\pi\) | |||||||
\(150\) | 1.69850 | 0.138682 | ||||||||
\(151\) | −10.1690 | −0.827544 | −0.413772 | − | 0.910381i | \(-0.635789\pi\) | ||||
−0.413772 | + | 0.910381i | \(0.635789\pi\) | |||||||
\(152\) | 5.92603 | 0.480665 | ||||||||
\(153\) | 0.614936 | 0.0497146 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 6.91416 | 0.555359 | ||||||||
\(156\) | −2.06897 | −0.165650 | ||||||||
\(157\) | 21.8764 | 1.74593 | 0.872964 | − | 0.487784i | \(-0.162195\pi\) | ||||
0.872964 | + | 0.487784i | \(0.162195\pi\) | |||||||
\(158\) | 5.81094 | 0.462293 | ||||||||
\(159\) | −6.18832 | −0.490765 | ||||||||
\(160\) | 8.38773 | 0.663108 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0.614936 | 0.0483139 | ||||||||
\(163\) | 17.2719 | 1.35284 | 0.676419 | − | 0.736517i | \(-0.263531\pi\) | ||||
0.676419 | + | 0.736517i | \(0.263531\pi\) | |||||||
\(164\) | 7.97940 | 0.623087 | ||||||||
\(165\) | −1.49597 | −0.116461 | ||||||||
\(166\) | 5.53798 | 0.429830 | ||||||||
\(167\) | −13.4655 | −1.04199 | −0.520997 | − | 0.853559i | \(-0.674440\pi\) | ||||
−0.520997 | + | 0.853559i | \(0.674440\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −11.3726 | −0.874818 | ||||||||
\(170\) | 0.565696 | 0.0433869 | ||||||||
\(171\) | −2.66075 | −0.203472 | ||||||||
\(172\) | −15.2861 | −1.16556 | ||||||||
\(173\) | −18.0559 | −1.37276 | −0.686382 | − | 0.727241i | \(-0.740802\pi\) | ||||
−0.686382 | + | 0.727241i | \(0.740802\pi\) | |||||||
\(174\) | −5.19561 | −0.393878 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 1.87412 | 0.141267 | ||||||||
\(177\) | −1.87412 | −0.140867 | ||||||||
\(178\) | 6.56520 | 0.492082 | ||||||||
\(179\) | −17.4693 | −1.30572 | −0.652860 | − | 0.757479i | \(-0.726431\pi\) | ||||
−0.652860 | + | 0.757479i | \(0.726431\pi\) | |||||||
\(180\) | −2.42625 | −0.180842 | ||||||||
\(181\) | −2.68530 | −0.199597 | −0.0997985 | − | 0.995008i | \(-0.531820\pi\) | ||||
−0.0997985 | + | 0.995008i | \(0.531820\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 8.52643 | 0.630292 | ||||||||
\(184\) | −4.17405 | −0.307715 | ||||||||
\(185\) | 0.410131 | 0.0301534 | ||||||||
\(186\) | −2.84214 | −0.208396 | ||||||||
\(187\) | 0.614936 | 0.0449686 | ||||||||
\(188\) | 5.12848 | 0.374033 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −2.44769 | −0.177574 | ||||||||
\(191\) | −18.8394 | −1.36317 | −0.681586 | − | 0.731738i | \(-0.738710\pi\) | ||||
−0.681586 | + | 0.731738i | \(0.738710\pi\) | |||||||
\(192\) | 0.300364 | 0.0216769 | ||||||||
\(193\) | 14.2427 | 1.02521 | 0.512606 | − | 0.858624i | \(-0.328680\pi\) | ||||
0.512606 | + | 0.858624i | \(0.328680\pi\) | |||||||
\(194\) | −10.8771 | −0.780927 | ||||||||
\(195\) | 1.90838 | 0.136662 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −13.5291 | −0.963908 | −0.481954 | − | 0.876196i | \(-0.660073\pi\) | ||||
−0.481954 | + | 0.876196i | \(0.660073\pi\) | |||||||
\(198\) | 0.614936 | 0.0437016 | ||||||||
\(199\) | 14.2356 | 1.00914 | 0.504569 | − | 0.863371i | \(-0.331651\pi\) | ||||
0.504569 | + | 0.863371i | \(0.331651\pi\) | |||||||
\(200\) | 6.15171 | 0.434991 | ||||||||
\(201\) | −5.06243 | −0.357077 | ||||||||
\(202\) | 2.89068 | 0.203388 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0.997336 | 0.0698275 | ||||||||
\(205\) | −7.36007 | −0.514049 | ||||||||
\(206\) | 10.8008 | 0.752531 | ||||||||
\(207\) | 1.87412 | 0.130260 | ||||||||
\(208\) | −2.39078 | −0.165770 | ||||||||
\(209\) | −2.66075 | −0.184048 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1.50124 | 0.103350 | 0.0516748 | − | 0.998664i | \(-0.483544\pi\) | ||||
0.0516748 | + | 0.998664i | \(0.483544\pi\) | |||||||
\(212\) | −10.0365 | −0.689313 | ||||||||
\(213\) | −16.0954 | −1.10284 | ||||||||
\(214\) | 7.27720 | 0.497459 | ||||||||
\(215\) | 14.0997 | 0.961591 | ||||||||
\(216\) | 2.22721 | 0.151542 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −0.629642 | −0.0426448 | ||||||||
\(219\) | −8.75732 | −0.591765 | ||||||||
\(220\) | −2.42625 | −0.163578 | ||||||||
\(221\) | −0.784462 | −0.0527686 | ||||||||
\(222\) | −0.168589 | −0.0113150 | ||||||||
\(223\) | 7.22937 | 0.484115 | 0.242057 | − | 0.970262i | \(-0.422178\pi\) | ||||
0.242057 | + | 0.970262i | \(0.422178\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −2.76207 | −0.184138 | ||||||||
\(226\) | 3.86503 | 0.257098 | ||||||||
\(227\) | −0.800079 | −0.0531031 | −0.0265516 | − | 0.999647i | \(-0.508453\pi\) | ||||
−0.0265516 | + | 0.999647i | \(0.508453\pi\) | |||||||
\(228\) | −4.31534 | −0.285790 | ||||||||
\(229\) | −8.54229 | −0.564490 | −0.282245 | − | 0.959342i | \(-0.591079\pi\) | ||||
−0.282245 | + | 0.959342i | \(0.591079\pi\) | |||||||
\(230\) | 1.72405 | 0.113680 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −18.8177 | −1.23544 | ||||||||
\(233\) | 1.83904 | 0.120480 | 0.0602398 | − | 0.998184i | \(-0.480813\pi\) | ||||
0.0602398 | + | 0.998184i | \(0.480813\pi\) | |||||||
\(234\) | −0.784462 | −0.0512819 | ||||||||
\(235\) | −4.73043 | −0.308579 | ||||||||
\(236\) | −3.03954 | −0.197857 | ||||||||
\(237\) | −9.44966 | −0.613822 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −8.71500 | −0.563726 | −0.281863 | − | 0.959455i | \(-0.590952\pi\) | ||||
−0.281863 | + | 0.959455i | \(0.590952\pi\) | |||||||
\(240\) | −2.80363 | −0.180973 | ||||||||
\(241\) | 1.08051 | 0.0696019 | 0.0348010 | − | 0.999394i | \(-0.488920\pi\) | ||||
0.0348010 | + | 0.999394i | \(0.488920\pi\) | |||||||
\(242\) | 0.614936 | 0.0395296 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 13.8286 | 0.885287 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 3.02544 | 0.192895 | ||||||||
\(247\) | 3.39426 | 0.215972 | ||||||||
\(248\) | −10.2938 | −0.653659 | ||||||||
\(249\) | −9.00578 | −0.570718 | ||||||||
\(250\) | −7.14053 | −0.451607 | ||||||||
\(251\) | −8.63296 | −0.544908 | −0.272454 | − | 0.962169i | \(-0.587835\pi\) | ||||
−0.272454 | + | 0.962169i | \(0.587835\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.87412 | 0.117825 | ||||||||
\(254\) | −12.1344 | −0.761379 | ||||||||
\(255\) | −0.919926 | −0.0576080 | ||||||||
\(256\) | −6.40860 | −0.400537 | ||||||||
\(257\) | 14.7115 | 0.917679 | 0.458839 | − | 0.888519i | \(-0.348265\pi\) | ||||
0.458839 | + | 0.888519i | \(0.348265\pi\) | |||||||
\(258\) | −5.79584 | −0.360833 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 3.09512 | 0.191951 | ||||||||
\(261\) | 8.44902 | 0.522981 | ||||||||
\(262\) | −3.26883 | −0.201949 | ||||||||
\(263\) | 30.9280 | 1.90710 | 0.953551 | − | 0.301232i | \(-0.0973978\pi\) | ||||
0.953551 | + | 0.301232i | \(0.0973978\pi\) | |||||||
\(264\) | 2.22721 | 0.137075 | ||||||||
\(265\) | 9.25754 | 0.568686 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −10.6762 | −0.653375 | ||||||||
\(268\) | −8.21053 | −0.501538 | ||||||||
\(269\) | −31.1163 | −1.89720 | −0.948598 | − | 0.316485i | \(-0.897497\pi\) | ||||
−0.948598 | + | 0.316485i | \(0.897497\pi\) | |||||||
\(270\) | −0.919926 | −0.0559849 | ||||||||
\(271\) | 2.76969 | 0.168247 | 0.0841233 | − | 0.996455i | \(-0.473191\pi\) | ||||
0.0841233 | + | 0.996455i | \(0.473191\pi\) | |||||||
\(272\) | 1.15246 | 0.0698783 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 1.46857 | 0.0887195 | ||||||||
\(275\) | −2.76207 | −0.166559 | ||||||||
\(276\) | 3.03954 | 0.182959 | ||||||||
\(277\) | 19.3029 | 1.15980 | 0.579900 | − | 0.814688i | \(-0.303092\pi\) | ||||
0.579900 | + | 0.814688i | \(0.303092\pi\) | |||||||
\(278\) | 7.68352 | 0.460827 | ||||||||
\(279\) | 4.62185 | 0.276703 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −7.96061 | −0.474890 | −0.237445 | − | 0.971401i | \(-0.576310\pi\) | ||||
−0.237445 | + | 0.971401i | \(0.576310\pi\) | |||||||
\(282\) | 1.94450 | 0.115793 | ||||||||
\(283\) | −8.55797 | −0.508718 | −0.254359 | − | 0.967110i | \(-0.581865\pi\) | ||||
−0.254359 | + | 0.967110i | \(0.581865\pi\) | |||||||
\(284\) | −26.1044 | −1.54901 | ||||||||
\(285\) | 3.98040 | 0.235778 | ||||||||
\(286\) | −0.784462 | −0.0463862 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 5.60688 | 0.330388 | ||||||||
\(289\) | −16.6219 | −0.977756 | ||||||||
\(290\) | 7.77248 | 0.456416 | ||||||||
\(291\) | 17.6881 | 1.03689 | ||||||||
\(292\) | −14.2031 | −0.831173 | ||||||||
\(293\) | −28.2280 | −1.64910 | −0.824548 | − | 0.565792i | \(-0.808571\pi\) | ||||
−0.824548 | + | 0.565792i | \(0.808571\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2.80363 | 0.163233 | ||||||||
\(296\) | −0.610605 | −0.0354907 | ||||||||
\(297\) | −1.00000 | −0.0580259 | ||||||||
\(298\) | −4.12410 | −0.238903 | ||||||||
\(299\) | −2.39078 | −0.138262 | ||||||||
\(300\) | −4.47967 | −0.258634 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −6.25330 | −0.359837 | ||||||||
\(303\) | −4.70079 | −0.270053 | ||||||||
\(304\) | −4.98655 | −0.285998 | ||||||||
\(305\) | −12.7553 | −0.730366 | ||||||||
\(306\) | 0.378146 | 0.0216172 | ||||||||
\(307\) | 8.29757 | 0.473568 | 0.236784 | − | 0.971562i | \(-0.423907\pi\) | ||||
0.236784 | + | 0.971562i | \(0.423907\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −17.5642 | −0.999191 | ||||||||
\(310\) | 4.25177 | 0.241484 | ||||||||
\(311\) | −34.7221 | −1.96891 | −0.984453 | − | 0.175646i | \(-0.943799\pi\) | ||||
−0.984453 | + | 0.175646i | \(0.943799\pi\) | |||||||
\(312\) | −2.84121 | −0.160852 | ||||||||
\(313\) | 32.1941 | 1.81972 | 0.909859 | − | 0.414918i | \(-0.136190\pi\) | ||||
0.909859 | + | 0.414918i | \(0.136190\pi\) | |||||||
\(314\) | 13.4526 | 0.759174 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −15.3260 | −0.862153 | ||||||||
\(317\) | −11.0109 | −0.618431 | −0.309216 | − | 0.950992i | \(-0.600067\pi\) | ||||
−0.309216 | + | 0.950992i | \(0.600067\pi\) | |||||||
\(318\) | −3.80542 | −0.213397 | ||||||||
\(319\) | 8.44902 | 0.473054 | ||||||||
\(320\) | −0.449336 | −0.0251186 | ||||||||
\(321\) | −11.8341 | −0.660514 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −1.63619 | −0.0910399 | ||||||||
\(324\) | −1.62185 | −0.0901030 | ||||||||
\(325\) | 3.52352 | 0.195450 | ||||||||
\(326\) | 10.6211 | 0.588248 | ||||||||
\(327\) | 1.02392 | 0.0566227 | ||||||||
\(328\) | 10.9577 | 0.605038 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −0.919926 | −0.0506403 | ||||||||
\(331\) | 14.4013 | 0.791567 | 0.395784 | − | 0.918344i | \(-0.370473\pi\) | ||||
0.395784 | + | 0.918344i | \(0.370473\pi\) | |||||||
\(332\) | −14.6061 | −0.801611 | ||||||||
\(333\) | 0.274157 | 0.0150237 | ||||||||
\(334\) | −8.28043 | −0.453085 | ||||||||
\(335\) | 7.57326 | 0.413771 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −19.0458 | −1.03749 | −0.518746 | − | 0.854928i | \(-0.673601\pi\) | ||||
−0.518746 | + | 0.854928i | \(0.673601\pi\) | |||||||
\(338\) | −6.99344 | −0.380393 | ||||||||
\(339\) | −6.28526 | −0.341369 | ||||||||
\(340\) | −1.49199 | −0.0809143 | ||||||||
\(341\) | 4.62185 | 0.250287 | ||||||||
\(342\) | −1.63619 | −0.0884749 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −20.9917 | −1.13180 | ||||||||
\(345\) | −2.80363 | −0.150942 | ||||||||
\(346\) | −11.1032 | −0.596913 | ||||||||
\(347\) | −17.4851 | −0.938651 | −0.469325 | − | 0.883025i | \(-0.655503\pi\) | ||||
−0.469325 | + | 0.883025i | \(0.655503\pi\) | |||||||
\(348\) | 13.7031 | 0.734562 | ||||||||
\(349\) | 31.9333 | 1.70935 | 0.854676 | − | 0.519162i | \(-0.173756\pi\) | ||||
0.854676 | + | 0.519162i | \(0.173756\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.27568 | 0.0680908 | ||||||||
\(352\) | 5.60688 | 0.298848 | ||||||||
\(353\) | −27.7531 | −1.47715 | −0.738574 | − | 0.674173i | \(-0.764500\pi\) | ||||
−0.738574 | + | 0.674173i | \(0.764500\pi\) | |||||||
\(354\) | −1.15246 | −0.0612527 | ||||||||
\(355\) | 24.0783 | 1.27794 | ||||||||
\(356\) | −17.3153 | −0.917708 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −10.7425 | −0.567760 | ||||||||
\(359\) | 6.60649 | 0.348677 | 0.174339 | − | 0.984686i | \(-0.444221\pi\) | ||||
0.174339 | + | 0.984686i | \(0.444221\pi\) | |||||||
\(360\) | −3.33184 | −0.175603 | ||||||||
\(361\) | −11.9204 | −0.627391 | ||||||||
\(362\) | −1.65129 | −0.0867898 | ||||||||
\(363\) | −1.00000 | −0.0524864 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 13.1007 | 0.685722 | ||||||||
\(366\) | 5.24321 | 0.274067 | ||||||||
\(367\) | −26.2452 | −1.36999 | −0.684995 | − | 0.728548i | \(-0.740196\pi\) | ||||
−0.684995 | + | 0.728548i | \(0.740196\pi\) | |||||||
\(368\) | 3.51232 | 0.183092 | ||||||||
\(369\) | −4.91993 | −0.256121 | ||||||||
\(370\) | 0.252204 | 0.0131115 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 7.49597 | 0.388648 | ||||||||
\(373\) | −7.76233 | −0.401918 | −0.200959 | − | 0.979600i | \(-0.564406\pi\) | ||||
−0.200959 | + | 0.979600i | \(0.564406\pi\) | |||||||
\(374\) | 0.378146 | 0.0195535 | ||||||||
\(375\) | 11.6118 | 0.599632 | ||||||||
\(376\) | 7.04268 | 0.363198 | ||||||||
\(377\) | −10.7783 | −0.555108 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 15.4636 | 0.794310 | 0.397155 | − | 0.917752i | \(-0.369998\pi\) | ||||
0.397155 | + | 0.917752i | \(0.369998\pi\) | |||||||
\(380\) | 6.45562 | 0.331166 | ||||||||
\(381\) | 19.7328 | 1.01094 | ||||||||
\(382\) | −11.5850 | −0.592742 | ||||||||
\(383\) | −26.7573 | −1.36724 | −0.683618 | − | 0.729840i | \(-0.739594\pi\) | ||||
−0.683618 | + | 0.729840i | \(0.739594\pi\) | |||||||
\(384\) | 11.3985 | 0.581675 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 8.75834 | 0.445788 | ||||||||
\(387\) | 9.42511 | 0.479105 | ||||||||
\(388\) | 28.6875 | 1.45639 | ||||||||
\(389\) | 19.7790 | 1.00283 | 0.501416 | − | 0.865206i | \(-0.332812\pi\) | ||||
0.501416 | + | 0.865206i | \(0.332812\pi\) | |||||||
\(390\) | 1.17353 | 0.0594241 | ||||||||
\(391\) | 1.15246 | 0.0582825 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 5.31572 | 0.268143 | ||||||||
\(394\) | −8.31953 | −0.419132 | ||||||||
\(395\) | 14.1364 | 0.711281 | ||||||||
\(396\) | −1.62185 | −0.0815012 | ||||||||
\(397\) | −0.248788 | −0.0124863 | −0.00624316 | − | 0.999981i | \(-0.501987\pi\) | ||||
−0.00624316 | + | 0.999981i | \(0.501987\pi\) | |||||||
\(398\) | 8.75401 | 0.438799 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −5.17644 | −0.258822 | ||||||||
\(401\) | 34.7875 | 1.73721 | 0.868603 | − | 0.495508i | \(-0.165018\pi\) | ||||
0.868603 | + | 0.495508i | \(0.165018\pi\) | |||||||
\(402\) | −3.11307 | −0.155266 | ||||||||
\(403\) | −5.89601 | −0.293701 | ||||||||
\(404\) | −7.62399 | −0.379308 | ||||||||
\(405\) | 1.49597 | 0.0743354 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0.274157 | 0.0135895 | ||||||||
\(408\) | 1.36959 | 0.0678048 | ||||||||
\(409\) | −1.80788 | −0.0893939 | −0.0446969 | − | 0.999001i | \(-0.514232\pi\) | ||||
−0.0446969 | + | 0.999001i | \(0.514232\pi\) | |||||||
\(410\) | −4.52597 | −0.223522 | ||||||||
\(411\) | −2.38817 | −0.117800 | ||||||||
\(412\) | −28.4865 | −1.40343 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 1.15246 | 0.0566404 | ||||||||
\(415\) | 13.4724 | 0.661333 | ||||||||
\(416\) | −7.15259 | −0.350684 | ||||||||
\(417\) | −12.4948 | −0.611875 | ||||||||
\(418\) | −1.63619 | −0.0800286 | ||||||||
\(419\) | 25.7007 | 1.25556 | 0.627780 | − | 0.778391i | \(-0.283964\pi\) | ||||
0.627780 | + | 0.778391i | \(0.283964\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 25.2666 | 1.23142 | 0.615710 | − | 0.787973i | \(-0.288869\pi\) | ||||
0.615710 | + | 0.787973i | \(0.288869\pi\) | |||||||
\(422\) | 0.923166 | 0.0449390 | ||||||||
\(423\) | −3.16211 | −0.153747 | ||||||||
\(424\) | −13.7827 | −0.669346 | ||||||||
\(425\) | −1.69850 | −0.0823892 | ||||||||
\(426\) | −9.89766 | −0.479543 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −19.1932 | −0.927736 | ||||||||
\(429\) | 1.27568 | 0.0615905 | ||||||||
\(430\) | 8.67040 | 0.418124 | ||||||||
\(431\) | 33.0300 | 1.59100 | 0.795499 | − | 0.605955i | \(-0.207209\pi\) | ||||
0.795499 | + | 0.605955i | \(0.207209\pi\) | |||||||
\(432\) | −1.87412 | −0.0901685 | ||||||||
\(433\) | 15.9029 | 0.764243 | 0.382122 | − | 0.924112i | \(-0.375194\pi\) | ||||
0.382122 | + | 0.924112i | \(0.375194\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −12.6395 | −0.606017 | ||||||||
\(436\) | 1.66064 | 0.0795303 | ||||||||
\(437\) | −4.98655 | −0.238539 | ||||||||
\(438\) | −5.38519 | −0.257314 | ||||||||
\(439\) | 4.47623 | 0.213639 | 0.106819 | − | 0.994278i | \(-0.465933\pi\) | ||||
0.106819 | + | 0.994278i | \(0.465933\pi\) | |||||||
\(440\) | −3.33184 | −0.158839 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −0.482394 | −0.0229451 | ||||||||
\(443\) | −1.63747 | −0.0777986 | −0.0388993 | − | 0.999243i | \(-0.512385\pi\) | ||||
−0.0388993 | + | 0.999243i | \(0.512385\pi\) | |||||||
\(444\) | 0.444643 | 0.0211018 | ||||||||
\(445\) | 15.9713 | 0.757114 | ||||||||
\(446\) | 4.44560 | 0.210505 | ||||||||
\(447\) | 6.70655 | 0.317209 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −2.45974 | −0.116082 | −0.0580412 | − | 0.998314i | \(-0.518485\pi\) | ||||
−0.0580412 | + | 0.998314i | \(0.518485\pi\) | |||||||
\(450\) | −1.69850 | −0.0800679 | ||||||||
\(451\) | −4.91993 | −0.231670 | ||||||||
\(452\) | −10.1938 | −0.479475 | ||||||||
\(453\) | 10.1690 | 0.477783 | ||||||||
\(454\) | −0.491998 | −0.0230906 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −5.92603 | −0.277512 | ||||||||
\(457\) | −30.9963 | −1.44994 | −0.724972 | − | 0.688778i | \(-0.758147\pi\) | ||||
−0.724972 | + | 0.688778i | \(0.758147\pi\) | |||||||
\(458\) | −5.25296 | −0.245455 | ||||||||
\(459\) | −0.614936 | −0.0287028 | ||||||||
\(460\) | −4.54707 | −0.212008 | ||||||||
\(461\) | −17.0555 | −0.794355 | −0.397177 | − | 0.917742i | \(-0.630010\pi\) | ||||
−0.397177 | + | 0.917742i | \(0.630010\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 13.9963 | 0.650461 | 0.325231 | − | 0.945635i | \(-0.394558\pi\) | ||||
0.325231 | + | 0.945635i | \(0.394558\pi\) | |||||||
\(464\) | 15.8345 | 0.735096 | ||||||||
\(465\) | −6.91416 | −0.320636 | ||||||||
\(466\) | 1.13089 | 0.0523876 | ||||||||
\(467\) | 37.6382 | 1.74169 | 0.870845 | − | 0.491558i | \(-0.163572\pi\) | ||||
0.870845 | + | 0.491558i | \(0.163572\pi\) | |||||||
\(468\) | 2.06897 | 0.0956381 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −2.90891 | −0.134178 | ||||||||
\(471\) | −21.8764 | −1.00801 | ||||||||
\(472\) | −4.17405 | −0.192126 | ||||||||
\(473\) | 9.42511 | 0.433367 | ||||||||
\(474\) | −5.81094 | −0.266905 | ||||||||
\(475\) | 7.34916 | 0.337203 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 6.18832 | 0.283344 | ||||||||
\(478\) | −5.35916 | −0.245122 | ||||||||
\(479\) | 34.4990 | 1.57630 | 0.788149 | − | 0.615484i | \(-0.211040\pi\) | ||||
0.788149 | + | 0.615484i | \(0.211040\pi\) | |||||||
\(480\) | −8.38773 | −0.382846 | ||||||||
\(481\) | −0.349737 | −0.0159466 | ||||||||
\(482\) | 0.664446 | 0.0302647 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −1.62185 | −0.0737206 | ||||||||
\(485\) | −26.4609 | −1.20153 | ||||||||
\(486\) | −0.614936 | −0.0278941 | ||||||||
\(487\) | −2.07482 | −0.0940192 | −0.0470096 | − | 0.998894i | \(-0.514969\pi\) | ||||
−0.0470096 | + | 0.998894i | \(0.514969\pi\) | |||||||
\(488\) | 18.9901 | 0.859643 | ||||||||
\(489\) | −17.2719 | −0.781061 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −29.9003 | −1.34938 | −0.674692 | − | 0.738100i | \(-0.735723\pi\) | ||||
−0.674692 | + | 0.738100i | \(0.735723\pi\) | |||||||
\(492\) | −7.97940 | −0.359739 | ||||||||
\(493\) | 5.19561 | 0.233998 | ||||||||
\(494\) | 2.08725 | 0.0939100 | ||||||||
\(495\) | 1.49597 | 0.0672389 | ||||||||
\(496\) | 8.66190 | 0.388931 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −5.53798 | −0.248163 | ||||||||
\(499\) | 1.37815 | 0.0616943 | 0.0308471 | − | 0.999524i | \(-0.490179\pi\) | ||||
0.0308471 | + | 0.999524i | \(0.490179\pi\) | |||||||
\(500\) | 18.8327 | 0.842224 | ||||||||
\(501\) | 13.4655 | 0.601595 | ||||||||
\(502\) | −5.30872 | −0.236940 | ||||||||
\(503\) | 34.3693 | 1.53245 | 0.766226 | − | 0.642571i | \(-0.222132\pi\) | ||||
0.766226 | + | 0.642571i | \(0.222132\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 7.03224 | 0.312931 | ||||||||
\(506\) | 1.15246 | 0.0512332 | ||||||||
\(507\) | 11.3726 | 0.505077 | ||||||||
\(508\) | 32.0037 | 1.41993 | ||||||||
\(509\) | −32.1962 | −1.42707 | −0.713536 | − | 0.700619i | \(-0.752907\pi\) | ||||
−0.713536 | + | 0.700619i | \(0.752907\pi\) | |||||||
\(510\) | −0.565696 | −0.0250494 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 18.8560 | 0.833327 | ||||||||
\(513\) | 2.66075 | 0.117475 | ||||||||
\(514\) | 9.04664 | 0.399030 | ||||||||
\(515\) | 26.2755 | 1.15784 | ||||||||
\(516\) | 15.2861 | 0.672935 | ||||||||
\(517\) | −3.16211 | −0.139069 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 18.0559 | 0.792566 | ||||||||
\(520\) | 4.25036 | 0.186391 | ||||||||
\(521\) | 27.1775 | 1.19067 | 0.595334 | − | 0.803479i | \(-0.297020\pi\) | ||||
0.595334 | + | 0.803479i | \(0.297020\pi\) | |||||||
\(522\) | 5.19561 | 0.227406 | ||||||||
\(523\) | −0.989920 | −0.0432862 | −0.0216431 | − | 0.999766i | \(-0.506890\pi\) | ||||
−0.0216431 | + | 0.999766i | \(0.506890\pi\) | |||||||
\(524\) | 8.62133 | 0.376624 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 19.0187 | 0.829256 | ||||||||
\(527\) | 2.84214 | 0.123806 | ||||||||
\(528\) | −1.87412 | −0.0815605 | ||||||||
\(529\) | −19.4877 | −0.847291 | ||||||||
\(530\) | 5.69280 | 0.247279 | ||||||||
\(531\) | 1.87412 | 0.0813298 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 6.27626 | 0.271855 | ||||||||
\(534\) | −6.56520 | −0.284104 | ||||||||
\(535\) | 17.7035 | 0.765387 | ||||||||
\(536\) | −11.2751 | −0.487010 | ||||||||
\(537\) | 17.4693 | 0.753858 | ||||||||
\(538\) | −19.1345 | −0.824949 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 2.42625 | 0.104409 | ||||||||
\(541\) | −25.5459 | −1.09830 | −0.549151 | − | 0.835723i | \(-0.685049\pi\) | ||||
−0.549151 | + | 0.835723i | \(0.685049\pi\) | |||||||
\(542\) | 1.70318 | 0.0731579 | ||||||||
\(543\) | 2.68530 | 0.115237 | ||||||||
\(544\) | 3.44787 | 0.147826 | ||||||||
\(545\) | −1.53175 | −0.0656129 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −5.97544 | −0.255491 | −0.127746 | − | 0.991807i | \(-0.540774\pi\) | ||||
−0.127746 | + | 0.991807i | \(0.540774\pi\) | |||||||
\(548\) | −3.87326 | −0.165457 | ||||||||
\(549\) | −8.52643 | −0.363899 | ||||||||
\(550\) | −1.69850 | −0.0724241 | ||||||||
\(551\) | −22.4807 | −0.957710 | ||||||||
\(552\) | 4.17405 | 0.177659 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 11.8701 | 0.504310 | ||||||||
\(555\) | −0.410131 | −0.0174091 | ||||||||
\(556\) | −20.2648 | −0.859419 | ||||||||
\(557\) | −14.9614 | −0.633933 | −0.316967 | − | 0.948437i | \(-0.602664\pi\) | ||||
−0.316967 | + | 0.948437i | \(0.602664\pi\) | |||||||
\(558\) | 2.84214 | 0.120318 | ||||||||
\(559\) | −12.0234 | −0.508537 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −0.614936 | −0.0259626 | ||||||||
\(562\) | −4.89527 | −0.206494 | ||||||||
\(563\) | −38.2276 | −1.61110 | −0.805551 | − | 0.592527i | \(-0.798130\pi\) | ||||
−0.805551 | + | 0.592527i | \(0.798130\pi\) | |||||||
\(564\) | −5.12848 | −0.215948 | ||||||||
\(565\) | 9.40257 | 0.395569 | ||||||||
\(566\) | −5.26260 | −0.221204 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −35.8479 | −1.50414 | ||||||||
\(569\) | 9.95889 | 0.417498 | 0.208749 | − | 0.977969i | \(-0.433061\pi\) | ||||
0.208749 | + | 0.977969i | \(0.433061\pi\) | |||||||
\(570\) | 2.44769 | 0.102522 | ||||||||
\(571\) | −26.2511 | −1.09858 | −0.549288 | − | 0.835633i | \(-0.685101\pi\) | ||||
−0.549288 | + | 0.835633i | \(0.685101\pi\) | |||||||
\(572\) | 2.06897 | 0.0865079 | ||||||||
\(573\) | 18.8394 | 0.787028 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −5.17644 | −0.215873 | ||||||||
\(576\) | −0.300364 | −0.0125152 | ||||||||
\(577\) | 11.5066 | 0.479024 | 0.239512 | − | 0.970893i | \(-0.423012\pi\) | ||||
0.239512 | + | 0.970893i | \(0.423012\pi\) | |||||||
\(578\) | −10.2214 | −0.425153 | ||||||||
\(579\) | −14.2427 | −0.591906 | ||||||||
\(580\) | −20.4994 | −0.851192 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 10.8771 | 0.450868 | ||||||||
\(583\) | 6.18832 | 0.256294 | ||||||||
\(584\) | −19.5044 | −0.807097 | ||||||||
\(585\) | −1.90838 | −0.0789019 | ||||||||
\(586\) | −17.3584 | −0.717069 | ||||||||
\(587\) | 21.1030 | 0.871013 | 0.435506 | − | 0.900186i | \(-0.356569\pi\) | ||||
0.435506 | + | 0.900186i | \(0.356569\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −12.2976 | −0.506713 | ||||||||
\(590\) | 1.72405 | 0.0709780 | ||||||||
\(591\) | 13.5291 | 0.556513 | ||||||||
\(592\) | 0.513802 | 0.0211171 | ||||||||
\(593\) | 19.4100 | 0.797074 | 0.398537 | − | 0.917152i | \(-0.369518\pi\) | ||||
0.398537 | + | 0.917152i | \(0.369518\pi\) | |||||||
\(594\) | −0.614936 | −0.0252311 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 10.8771 | 0.445541 | ||||||||
\(597\) | −14.2356 | −0.582626 | ||||||||
\(598\) | −1.47017 | −0.0601199 | ||||||||
\(599\) | 7.40460 | 0.302544 | 0.151272 | − | 0.988492i | \(-0.451663\pi\) | ||||
0.151272 | + | 0.988492i | \(0.451663\pi\) | |||||||
\(600\) | −6.15171 | −0.251142 | ||||||||
\(601\) | −11.5056 | −0.469322 | −0.234661 | − | 0.972077i | \(-0.575398\pi\) | ||||
−0.234661 | + | 0.972077i | \(0.575398\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 5.06243 | 0.206158 | ||||||||
\(604\) | 16.4927 | 0.671077 | ||||||||
\(605\) | 1.49597 | 0.0608199 | ||||||||
\(606\) | −2.89068 | −0.117426 | ||||||||
\(607\) | 45.0283 | 1.82764 | 0.913821 | − | 0.406118i | \(-0.133118\pi\) | ||||
0.913821 | + | 0.406118i | \(0.133118\pi\) | |||||||
\(608\) | −14.9185 | −0.605024 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −7.84369 | −0.317582 | ||||||||
\(611\) | 4.03384 | 0.163192 | ||||||||
\(612\) | −0.997336 | −0.0403149 | ||||||||
\(613\) | −17.8422 | −0.720638 | −0.360319 | − | 0.932829i | \(-0.617332\pi\) | ||||
−0.360319 | + | 0.932829i | \(0.617332\pi\) | |||||||
\(614\) | 5.10248 | 0.205919 | ||||||||
\(615\) | 7.36007 | 0.296787 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 11.7052 | 0.471235 | 0.235617 | − | 0.971846i | \(-0.424289\pi\) | ||||
0.235617 | + | 0.971846i | \(0.424289\pi\) | |||||||
\(618\) | −10.8008 | −0.434474 | ||||||||
\(619\) | −7.51913 | −0.302219 | −0.151110 | − | 0.988517i | \(-0.548285\pi\) | ||||
−0.151110 | + | 0.988517i | \(0.548285\pi\) | |||||||
\(620\) | −11.2138 | −0.450355 | ||||||||
\(621\) | −1.87412 | −0.0752057 | ||||||||
\(622\) | −21.3518 | −0.856131 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 2.39078 | 0.0957076 | ||||||||
\(625\) | −3.56062 | −0.142425 | ||||||||
\(626\) | 19.7973 | 0.791259 | ||||||||
\(627\) | 2.66075 | 0.106260 | ||||||||
\(628\) | −35.4804 | −1.41582 | ||||||||
\(629\) | 0.168589 | 0.00672208 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 27.1694 | 1.08159 | 0.540797 | − | 0.841153i | \(-0.318123\pi\) | ||||
0.540797 | + | 0.841153i | \(0.318123\pi\) | |||||||
\(632\) | −21.0464 | −0.837180 | ||||||||
\(633\) | −1.50124 | −0.0596689 | ||||||||
\(634\) | −6.77097 | −0.268910 | ||||||||
\(635\) | −29.5197 | −1.17145 | ||||||||
\(636\) | 10.0365 | 0.397975 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 5.19561 | 0.205696 | ||||||||
\(639\) | 16.0954 | 0.636725 | ||||||||
\(640\) | −17.0518 | −0.674030 | ||||||||
\(641\) | −12.3538 | −0.487945 | −0.243973 | − | 0.969782i | \(-0.578451\pi\) | ||||
−0.243973 | + | 0.969782i | \(0.578451\pi\) | |||||||
\(642\) | −7.27720 | −0.287208 | ||||||||
\(643\) | −21.3948 | −0.843728 | −0.421864 | − | 0.906659i | \(-0.638624\pi\) | ||||
−0.421864 | + | 0.906659i | \(0.638624\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −14.0997 | −0.555175 | ||||||||
\(646\) | −1.00615 | −0.0395865 | ||||||||
\(647\) | 2.75530 | 0.108322 | 0.0541609 | − | 0.998532i | \(-0.482752\pi\) | ||||
0.0541609 | + | 0.998532i | \(0.482752\pi\) | |||||||
\(648\) | −2.22721 | −0.0874930 | ||||||||
\(649\) | 1.87412 | 0.0735655 | ||||||||
\(650\) | 2.16674 | 0.0849865 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −28.0125 | −1.09705 | ||||||||
\(653\) | −8.66698 | −0.339165 | −0.169583 | − | 0.985516i | \(-0.554242\pi\) | ||||
−0.169583 | + | 0.985516i | \(0.554242\pi\) | |||||||
\(654\) | 0.629642 | 0.0246210 | ||||||||
\(655\) | −7.95217 | −0.310717 | ||||||||
\(656\) | −9.22052 | −0.360001 | ||||||||
\(657\) | 8.75732 | 0.341656 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −32.2924 | −1.25793 | −0.628967 | − | 0.777432i | \(-0.716522\pi\) | ||||
−0.628967 | + | 0.777432i | \(0.716522\pi\) | |||||||
\(660\) | 2.42625 | 0.0944415 | ||||||||
\(661\) | −12.7559 | −0.496146 | −0.248073 | − | 0.968741i | \(-0.579797\pi\) | ||||
−0.248073 | + | 0.968741i | \(0.579797\pi\) | |||||||
\(662\) | 8.85588 | 0.344194 | ||||||||
\(663\) | 0.784462 | 0.0304660 | ||||||||
\(664\) | −20.0577 | −0.778391 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0.168589 | 0.00653269 | ||||||||
\(667\) | 15.8345 | 0.613113 | ||||||||
\(668\) | 21.8391 | 0.844980 | ||||||||
\(669\) | −7.22937 | −0.279504 | ||||||||
\(670\) | 4.65707 | 0.179918 | ||||||||
\(671\) | −8.52643 | −0.329159 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 43.6075 | 1.68095 | 0.840473 | − | 0.541853i | \(-0.182277\pi\) | ||||
0.840473 | + | 0.541853i | \(0.182277\pi\) | |||||||
\(674\) | −11.7120 | −0.451128 | ||||||||
\(675\) | 2.76207 | 0.106312 | ||||||||
\(676\) | 18.4448 | 0.709414 | ||||||||
\(677\) | 2.16774 | 0.0833132 | 0.0416566 | − | 0.999132i | \(-0.486736\pi\) | ||||
0.0416566 | + | 0.999132i | \(0.486736\pi\) | |||||||
\(678\) | −3.86503 | −0.148436 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −2.04887 | −0.0785705 | ||||||||
\(681\) | 0.800079 | 0.0306591 | ||||||||
\(682\) | 2.84214 | 0.108831 | ||||||||
\(683\) | 23.9590 | 0.916767 | 0.458383 | − | 0.888755i | \(-0.348429\pi\) | ||||
0.458383 | + | 0.888755i | \(0.348429\pi\) | |||||||
\(684\) | 4.31534 | 0.165001 | ||||||||
\(685\) | 3.57263 | 0.136503 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 8.54229 | 0.325909 | ||||||||
\(688\) | 17.6638 | 0.673424 | ||||||||
\(689\) | −7.89432 | −0.300750 | ||||||||
\(690\) | −1.72405 | −0.0656335 | ||||||||
\(691\) | 5.05889 | 0.192449 | 0.0962246 | − | 0.995360i | \(-0.469323\pi\) | ||||
0.0962246 | + | 0.995360i | \(0.469323\pi\) | |||||||
\(692\) | 29.2840 | 1.11321 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −10.7522 | −0.408149 | ||||||||
\(695\) | 18.6919 | 0.709024 | ||||||||
\(696\) | 18.8177 | 0.713284 | ||||||||
\(697\) | −3.02544 | −0.114597 | ||||||||
\(698\) | 19.6370 | 0.743270 | ||||||||
\(699\) | −1.83904 | −0.0695589 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −21.7177 | −0.820265 | −0.410132 | − | 0.912026i | \(-0.634517\pi\) | ||||
−0.410132 | + | 0.912026i | \(0.634517\pi\) | |||||||
\(702\) | 0.784462 | 0.0296076 | ||||||||
\(703\) | −0.729462 | −0.0275122 | ||||||||
\(704\) | −0.300364 | −0.0113204 | ||||||||
\(705\) | 4.73043 | 0.178158 | ||||||||
\(706\) | −17.0664 | −0.642301 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 3.03954 | 0.114233 | ||||||||
\(709\) | 5.59190 | 0.210008 | 0.105004 | − | 0.994472i | \(-0.466514\pi\) | ||||
0.105004 | + | 0.994472i | \(0.466514\pi\) | |||||||
\(710\) | 14.8066 | 0.555682 | ||||||||
\(711\) | 9.44966 | 0.354390 | ||||||||
\(712\) | −23.7782 | −0.891125 | ||||||||
\(713\) | 8.66190 | 0.324391 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1.90838 | −0.0713694 | ||||||||
\(716\) | 28.3327 | 1.05884 | ||||||||
\(717\) | 8.71500 | 0.325467 | ||||||||
\(718\) | 4.06257 | 0.151614 | ||||||||
\(719\) | 7.72426 | 0.288066 | 0.144033 | − | 0.989573i | \(-0.453993\pi\) | ||||
0.144033 | + | 0.989573i | \(0.453993\pi\) | |||||||
\(720\) | 2.80363 | 0.104485 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −7.33030 | −0.272806 | ||||||||
\(723\) | −1.08051 | −0.0401847 | ||||||||
\(724\) | 4.35517 | 0.161859 | ||||||||
\(725\) | −23.3368 | −0.866707 | ||||||||
\(726\) | −0.614936 | −0.0228224 | ||||||||
\(727\) | −35.7990 | −1.32771 | −0.663855 | − | 0.747861i | \(-0.731081\pi\) | ||||
−0.663855 | + | 0.747861i | \(0.731081\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 8.05609 | 0.298169 | ||||||||
\(731\) | 5.79584 | 0.214367 | ||||||||
\(732\) | −13.8286 | −0.511121 | ||||||||
\(733\) | 16.2538 | 0.600347 | 0.300174 | − | 0.953885i | \(-0.402955\pi\) | ||||
0.300174 | + | 0.953885i | \(0.402955\pi\) | |||||||
\(734\) | −16.1391 | −0.595707 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 10.5079 | 0.387328 | ||||||||
\(737\) | 5.06243 | 0.186477 | ||||||||
\(738\) | −3.02544 | −0.111368 | ||||||||
\(739\) | 0.574082 | 0.0211179 | 0.0105590 | − | 0.999944i | \(-0.496639\pi\) | ||||
0.0105590 | + | 0.999944i | \(0.496639\pi\) | |||||||
\(740\) | −0.665172 | −0.0244522 | ||||||||
\(741\) | −3.39426 | −0.124691 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 25.6448 | 0.940818 | 0.470409 | − | 0.882449i | \(-0.344106\pi\) | ||||
0.470409 | + | 0.882449i | \(0.344106\pi\) | |||||||
\(744\) | 10.2938 | 0.377390 | ||||||||
\(745\) | −10.0328 | −0.367574 | ||||||||
\(746\) | −4.77333 | −0.174764 | ||||||||
\(747\) | 9.00578 | 0.329504 | ||||||||
\(748\) | −0.997336 | −0.0364662 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 7.14053 | 0.260735 | ||||||||
\(751\) | 29.9121 | 1.09151 | 0.545755 | − | 0.837945i | \(-0.316243\pi\) | ||||
0.545755 | + | 0.837945i | \(0.316243\pi\) | |||||||
\(752\) | −5.92617 | −0.216105 | ||||||||
\(753\) | 8.63296 | 0.314603 | ||||||||
\(754\) | −6.62794 | −0.241375 | ||||||||
\(755\) | −15.2126 | −0.553642 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 13.9358 | 0.506505 | 0.253252 | − | 0.967400i | \(-0.418500\pi\) | ||||
0.253252 | + | 0.967400i | \(0.418500\pi\) | |||||||
\(758\) | 9.50910 | 0.345386 | ||||||||
\(759\) | −1.87412 | −0.0680261 | ||||||||
\(760\) | 8.86517 | 0.321574 | ||||||||
\(761\) | −36.4563 | −1.32154 | −0.660770 | − | 0.750589i | \(-0.729770\pi\) | ||||
−0.660770 | + | 0.750589i | \(0.729770\pi\) | |||||||
\(762\) | 12.1344 | 0.439583 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 30.5548 | 1.10543 | ||||||||
\(765\) | 0.919926 | 0.0332600 | ||||||||
\(766\) | −16.4540 | −0.594509 | ||||||||
\(767\) | −2.39078 | −0.0863259 | ||||||||
\(768\) | 6.40860 | 0.231250 | ||||||||
\(769\) | −10.7416 | −0.387354 | −0.193677 | − | 0.981065i | \(-0.562041\pi\) | ||||
−0.193677 | + | 0.981065i | \(0.562041\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −14.7115 | −0.529822 | ||||||||
\(772\) | −23.0996 | −0.831372 | ||||||||
\(773\) | −1.82374 | −0.0655953 | −0.0327976 | − | 0.999462i | \(-0.510442\pi\) | ||||
−0.0327976 | + | 0.999462i | \(0.510442\pi\) | |||||||
\(774\) | 5.79584 | 0.208327 | ||||||||
\(775\) | −12.7659 | −0.458564 | ||||||||
\(776\) | 39.3951 | 1.41420 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 12.1628 | 0.436057 | ||||||||
\(779\) | 13.0907 | 0.469022 | ||||||||
\(780\) | −3.09512 | −0.110823 | ||||||||
\(781\) | 16.0954 | 0.575940 | ||||||||
\(782\) | 0.708690 | 0.0253427 | ||||||||
\(783\) | −8.44902 | −0.301943 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 32.7265 | 1.16806 | ||||||||
\(786\) | 3.26883 | 0.116595 | ||||||||
\(787\) | 24.9933 | 0.890916 | 0.445458 | − | 0.895303i | \(-0.353041\pi\) | ||||
0.445458 | + | 0.895303i | \(0.353041\pi\) | |||||||
\(788\) | 21.9422 | 0.781659 | ||||||||
\(789\) | −30.9280 | −1.10107 | ||||||||
\(790\) | 8.69300 | 0.309283 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −2.22721 | −0.0791404 | ||||||||
\(793\) | 10.8770 | 0.386254 | ||||||||
\(794\) | −0.152989 | −0.00542937 | ||||||||
\(795\) | −9.25754 | −0.328331 | ||||||||
\(796\) | −23.0881 | −0.818338 | ||||||||
\(797\) | −14.0330 | −0.497074 | −0.248537 | − | 0.968622i | \(-0.579950\pi\) | ||||
−0.248537 | + | 0.968622i | \(0.579950\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1.94450 | −0.0687913 | ||||||||
\(800\) | −15.4866 | −0.547534 | ||||||||
\(801\) | 10.6762 | 0.377226 | ||||||||
\(802\) | 21.3921 | 0.755381 | ||||||||
\(803\) | 8.75732 | 0.309039 | ||||||||
\(804\) | 8.21053 | 0.289563 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −3.62567 | −0.127709 | ||||||||
\(807\) | 31.1163 | 1.09535 | ||||||||
\(808\) | −10.4696 | −0.368320 | ||||||||
\(809\) | −39.5483 | −1.39045 | −0.695223 | − | 0.718795i | \(-0.744694\pi\) | ||||
−0.695223 | + | 0.718795i | \(0.744694\pi\) | |||||||
\(810\) | 0.919926 | 0.0323229 | ||||||||
\(811\) | 19.9504 | 0.700555 | 0.350277 | − | 0.936646i | \(-0.386087\pi\) | ||||
0.350277 | + | 0.936646i | \(0.386087\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −2.76969 | −0.0971372 | ||||||||
\(814\) | 0.168589 | 0.00590904 | ||||||||
\(815\) | 25.8382 | 0.905074 | ||||||||
\(816\) | −1.15246 | −0.0403442 | ||||||||
\(817\) | −25.0778 | −0.877361 | ||||||||
\(818\) | −1.11173 | −0.0388707 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 11.9370 | 0.416857 | ||||||||
\(821\) | 1.03529 | 0.0361319 | 0.0180659 | − | 0.999837i | \(-0.494249\pi\) | ||||
0.0180659 | + | 0.999837i | \(0.494249\pi\) | |||||||
\(822\) | −1.46857 | −0.0512222 | ||||||||
\(823\) | 7.90025 | 0.275386 | 0.137693 | − | 0.990475i | \(-0.456031\pi\) | ||||
0.137693 | + | 0.990475i | \(0.456031\pi\) | |||||||
\(824\) | −39.1191 | −1.36278 | ||||||||
\(825\) | 2.76207 | 0.0961629 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −19.4794 | −0.677364 | −0.338682 | − | 0.940901i | \(-0.609981\pi\) | ||||
−0.338682 | + | 0.940901i | \(0.609981\pi\) | |||||||
\(828\) | −3.03954 | −0.105631 | ||||||||
\(829\) | 25.5634 | 0.887854 | 0.443927 | − | 0.896063i | \(-0.353585\pi\) | ||||
0.443927 | + | 0.896063i | \(0.353585\pi\) | |||||||
\(830\) | 8.28465 | 0.287565 | ||||||||
\(831\) | −19.3029 | −0.669611 | ||||||||
\(832\) | 0.383168 | 0.0132840 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −7.68352 | −0.266059 | ||||||||
\(835\) | −20.1440 | −0.697113 | ||||||||
\(836\) | 4.31534 | 0.149249 | ||||||||
\(837\) | −4.62185 | −0.159755 | ||||||||
\(838\) | 15.8043 | 0.545949 | ||||||||
\(839\) | 29.1936 | 1.00787 | 0.503937 | − | 0.863740i | \(-0.331884\pi\) | ||||
0.503937 | + | 0.863740i | \(0.331884\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 42.3860 | 1.46159 | ||||||||
\(842\) | 15.5374 | 0.535453 | ||||||||
\(843\) | 7.96061 | 0.274178 | ||||||||
\(844\) | −2.43479 | −0.0838090 | ||||||||
\(845\) | −17.0131 | −0.585270 | ||||||||
\(846\) | −1.94450 | −0.0668531 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 11.5976 | 0.398264 | ||||||||
\(849\) | 8.55797 | 0.293709 | ||||||||
\(850\) | −1.04447 | −0.0358249 | ||||||||
\(851\) | 0.513802 | 0.0176129 | ||||||||
\(852\) | 26.1044 | 0.894323 | ||||||||
\(853\) | 3.81162 | 0.130507 | 0.0652536 | − | 0.997869i | \(-0.479214\pi\) | ||||
0.0652536 | + | 0.997869i | \(0.479214\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −3.98040 | −0.136127 | ||||||||
\(856\) | −26.3570 | −0.900863 | ||||||||
\(857\) | −34.6870 | −1.18488 | −0.592442 | − | 0.805613i | \(-0.701836\pi\) | ||||
−0.592442 | + | 0.805613i | \(0.701836\pi\) | |||||||
\(858\) | 0.784462 | 0.0267811 | ||||||||
\(859\) | −48.6058 | −1.65841 | −0.829205 | − | 0.558945i | \(-0.811206\pi\) | ||||
−0.829205 | + | 0.558945i | \(0.811206\pi\) | |||||||
\(860\) | −22.8676 | −0.779780 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 20.3113 | 0.691806 | ||||||||
\(863\) | 21.6564 | 0.737191 | 0.368596 | − | 0.929590i | \(-0.379839\pi\) | ||||
0.368596 | + | 0.929590i | \(0.379839\pi\) | |||||||
\(864\) | −5.60688 | −0.190750 | ||||||||
\(865\) | −27.0111 | −0.918405 | ||||||||
\(866\) | 9.77925 | 0.332312 | ||||||||
\(867\) | 16.6219 | 0.564508 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 9.44966 | 0.320558 | ||||||||
\(870\) | −7.77248 | −0.263512 | ||||||||
\(871\) | −6.45805 | −0.218823 | ||||||||
\(872\) | 2.28047 | 0.0772266 | ||||||||
\(873\) | −17.6881 | −0.598652 | ||||||||
\(874\) | −3.06641 | −0.103723 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 14.2031 | 0.479878 | ||||||||
\(877\) | −16.0026 | −0.540370 | −0.270185 | − | 0.962808i | \(-0.587085\pi\) | ||||
−0.270185 | + | 0.962808i | \(0.587085\pi\) | |||||||
\(878\) | 2.75260 | 0.0928956 | ||||||||
\(879\) | 28.2280 | 0.952106 | ||||||||
\(880\) | 2.80363 | 0.0945102 | ||||||||
\(881\) | −36.2250 | −1.22045 | −0.610226 | − | 0.792228i | \(-0.708921\pi\) | ||||
−0.610226 | + | 0.792228i | \(0.708921\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −4.78873 | −0.161154 | −0.0805768 | − | 0.996748i | \(-0.525676\pi\) | ||||
−0.0805768 | + | 0.996748i | \(0.525676\pi\) | |||||||
\(884\) | 1.27228 | 0.0427915 | ||||||||
\(885\) | −2.80363 | −0.0942428 | ||||||||
\(886\) | −1.00694 | −0.0338288 | ||||||||
\(887\) | −54.4131 | −1.82701 | −0.913507 | − | 0.406823i | \(-0.866636\pi\) | ||||
−0.913507 | + | 0.406823i | \(0.866636\pi\) | |||||||
\(888\) | 0.610605 | 0.0204906 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 9.82135 | 0.329212 | ||||||||
\(891\) | 1.00000 | 0.0335013 | ||||||||
\(892\) | −11.7250 | −0.392582 | ||||||||
\(893\) | 8.41357 | 0.281549 | ||||||||
\(894\) | 4.12410 | 0.137931 | ||||||||
\(895\) | −26.1336 | −0.873551 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 2.39078 | 0.0798257 | ||||||||
\(898\) | −1.51258 | −0.0504756 | ||||||||
\(899\) | 39.0501 | 1.30240 | ||||||||
\(900\) | 4.47967 | 0.149322 | ||||||||
\(901\) | 3.80542 | 0.126777 | ||||||||
\(902\) | −3.02544 | −0.100736 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −13.9986 | −0.465586 | ||||||||
\(905\) | −4.01713 | −0.133534 | ||||||||
\(906\) | 6.25330 | 0.207752 | ||||||||
\(907\) | 53.8600 | 1.78839 | 0.894196 | − | 0.447676i | \(-0.147748\pi\) | ||||
0.894196 | + | 0.447676i | \(0.147748\pi\) | |||||||
\(908\) | 1.29761 | 0.0430628 | ||||||||
\(909\) | 4.70079 | 0.155915 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −22.0506 | −0.730571 | −0.365285 | − | 0.930896i | \(-0.619029\pi\) | ||||
−0.365285 | + | 0.930896i | \(0.619029\pi\) | |||||||
\(912\) | 4.98655 | 0.165121 | ||||||||
\(913\) | 9.00578 | 0.298048 | ||||||||
\(914\) | −19.0607 | −0.630473 | ||||||||
\(915\) | 12.7553 | 0.421677 | ||||||||
\(916\) | 13.8543 | 0.457760 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −0.378146 | −0.0124807 | ||||||||
\(919\) | 6.34908 | 0.209437 | 0.104718 | − | 0.994502i | \(-0.466606\pi\) | ||||
0.104718 | + | 0.994502i | \(0.466606\pi\) | |||||||
\(920\) | −6.24426 | −0.205867 | ||||||||
\(921\) | −8.29757 | −0.273414 | ||||||||
\(922\) | −10.4880 | −0.345406 | ||||||||
\(923\) | −20.5326 | −0.675840 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −0.757241 | −0.0248979 | ||||||||
\(926\) | 8.60680 | 0.282837 | ||||||||
\(927\) | 17.5642 | 0.576883 | ||||||||
\(928\) | 47.3726 | 1.55508 | ||||||||
\(929\) | 57.8664 | 1.89854 | 0.949268 | − | 0.314469i | \(-0.101826\pi\) | ||||
0.949268 | + | 0.314469i | \(0.101826\pi\) | |||||||
\(930\) | −4.25177 | −0.139421 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −2.98266 | −0.0977001 | ||||||||
\(933\) | 34.7221 | 1.13675 | ||||||||
\(934\) | 23.1451 | 0.757331 | ||||||||
\(935\) | 0.919926 | 0.0300848 | ||||||||
\(936\) | 2.84121 | 0.0928678 | ||||||||
\(937\) | 16.1657 | 0.528110 | 0.264055 | − | 0.964508i | \(-0.414940\pi\) | ||||
0.264055 | + | 0.964508i | \(0.414940\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −32.1941 | −1.05061 | ||||||||
\(940\) | 7.67206 | 0.250235 | ||||||||
\(941\) | 53.1550 | 1.73280 | 0.866401 | − | 0.499348i | \(-0.166427\pi\) | ||||
0.866401 | + | 0.499348i | \(0.166427\pi\) | |||||||
\(942\) | −13.4526 | −0.438309 | ||||||||
\(943\) | −9.22052 | −0.300261 | ||||||||
\(944\) | 3.51232 | 0.114316 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 5.79584 | 0.188439 | ||||||||
\(947\) | −15.0920 | −0.490423 | −0.245211 | − | 0.969470i | \(-0.578857\pi\) | ||||
−0.245211 | + | 0.969470i | \(0.578857\pi\) | |||||||
\(948\) | 15.3260 | 0.497764 | ||||||||
\(949\) | −11.1715 | −0.362644 | ||||||||
\(950\) | 4.51927 | 0.146624 | ||||||||
\(951\) | 11.0109 | 0.357052 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −27.2774 | −0.883602 | −0.441801 | − | 0.897113i | \(-0.645660\pi\) | ||||
−0.441801 | + | 0.897113i | \(0.645660\pi\) | |||||||
\(954\) | 3.80542 | 0.123205 | ||||||||
\(955\) | −28.1832 | −0.911988 | ||||||||
\(956\) | 14.1344 | 0.457141 | ||||||||
\(957\) | −8.44902 | −0.273118 | ||||||||
\(958\) | 21.2147 | 0.685414 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0.449336 | 0.0145022 | ||||||||
\(961\) | −9.63847 | −0.310918 | ||||||||
\(962\) | −0.215066 | −0.00693400 | ||||||||
\(963\) | 11.8341 | 0.381348 | ||||||||
\(964\) | −1.75243 | −0.0564421 | ||||||||
\(965\) | 21.3067 | 0.685886 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 47.7400 | 1.53521 | 0.767607 | − | 0.640920i | \(-0.221447\pi\) | ||||
0.767607 | + | 0.640920i | \(0.221447\pi\) | |||||||
\(968\) | −2.22721 | −0.0715852 | ||||||||
\(969\) | 1.63619 | 0.0525619 | ||||||||
\(970\) | −16.2718 | −0.522455 | ||||||||
\(971\) | −27.6966 | −0.888826 | −0.444413 | − | 0.895822i | \(-0.646588\pi\) | ||||
−0.444413 | + | 0.895822i | \(0.646588\pi\) | |||||||
\(972\) | 1.62185 | 0.0520210 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −1.27588 | −0.0408819 | ||||||||
\(975\) | −3.52352 | −0.112843 | ||||||||
\(976\) | −15.9795 | −0.511492 | ||||||||
\(977\) | 17.9202 | 0.573318 | 0.286659 | − | 0.958033i | \(-0.407455\pi\) | ||||
0.286659 | + | 0.958033i | \(0.407455\pi\) | |||||||
\(978\) | −10.6211 | −0.339625 | ||||||||
\(979\) | 10.6762 | 0.341214 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1.02392 | −0.0326911 | ||||||||
\(982\) | −18.3868 | −0.586746 | ||||||||
\(983\) | 30.4192 | 0.970220 | 0.485110 | − | 0.874453i | \(-0.338779\pi\) | ||||
0.485110 | + | 0.874453i | \(0.338779\pi\) | |||||||
\(984\) | −10.9577 | −0.349319 | ||||||||
\(985\) | −20.2391 | −0.644873 | ||||||||
\(986\) | 3.19497 | 0.101748 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −5.50500 | −0.175137 | ||||||||
\(989\) | 17.6638 | 0.561675 | ||||||||
\(990\) | 0.919926 | 0.0292372 | ||||||||
\(991\) | 14.2095 | 0.451379 | 0.225689 | − | 0.974199i | \(-0.427537\pi\) | ||||
0.225689 | + | 0.974199i | \(0.427537\pi\) | |||||||
\(992\) | 25.9142 | 0.822776 | ||||||||
\(993\) | −14.4013 | −0.457012 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 21.2961 | 0.675132 | ||||||||
\(996\) | 14.6061 | 0.462811 | ||||||||
\(997\) | −0.997451 | −0.0315896 | −0.0157948 | − | 0.999875i | \(-0.505028\pi\) | ||||
−0.0157948 | + | 0.999875i | \(0.505028\pi\) | |||||||
\(998\) | 0.847472 | 0.0268262 | ||||||||
\(999\) | −0.274157 | −0.00867394 |
(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 | 1617.2.a.ba.1.3 | 5 | ||
3.2 | odd | 2 | 4851.2.a.ca.1.3 | 5 | |||
7.2 | even | 3 | 231.2.i.f.67.3 | ✓ | 10 | ||
7.4 | even | 3 | 231.2.i.f.100.3 | yes | 10 | ||
7.6 | odd | 2 | 1617.2.a.bb.1.3 | 5 | |||
21.2 | odd | 6 | 693.2.i.j.298.3 | 10 | |||
21.11 | odd | 6 | 693.2.i.j.100.3 | 10 | |||
21.20 | even | 2 | 4851.2.a.bz.1.3 | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
231.2.i.f.67.3 | ✓ | 10 | 7.2 | even | 3 | ||
231.2.i.f.100.3 | yes | 10 | 7.4 | even | 3 | ||
693.2.i.j.100.3 | 10 | 21.11 | odd | 6 | |||
693.2.i.j.298.3 | 10 | 21.2 | odd | 6 | |||
1617.2.a.ba.1.3 | 5 | 1.1 | even | 1 | trivial | ||
1617.2.a.bb.1.3 | 5 | 7.6 | odd | 2 | |||
4851.2.a.bz.1.3 | 5 | 21.20 | even | 2 | |||
4851.2.a.ca.1.3 | 5 | 3.2 | odd | 2 |