Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8004,2,Mod(1,8004)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8004, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("8004.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8004 = 2^{2} \cdot 3 \cdot 23 \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8004.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: | \(63.9122617778\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 3 x^{15} - 49 x^{14} + 130 x^{13} + 932 x^{12} - 2028 x^{11} - 8965 x^{10} + 14400 x^{9} + \cdots + 3888 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.10 | ||
Root | \(0.897331\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8004.1 |
$q$-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 | 0 | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.897331 | 0.401299 | 0.200649 | − | 0.979663i | \(-0.435695\pi\) | ||||
0.200649 | + | 0.979663i | \(0.435695\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.81467 | 1.44181 | 0.720905 | − | 0.693034i | \(-0.243726\pi\) | ||||
0.720905 | + | 0.693034i | \(0.243726\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 5.23385 | 1.57806 | 0.789032 | − | 0.614352i | \(-0.210583\pi\) | ||||
0.789032 | + | 0.614352i | \(0.210583\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.43366 | −0.952327 | −0.476164 | − | 0.879357i | \(-0.657973\pi\) | ||||
−0.476164 | + | 0.879357i | \(0.657973\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.897331 | 0.231690 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.92187 | 0.466122 | 0.233061 | − | 0.972462i | \(-0.425126\pi\) | ||||
0.233061 | + | 0.972462i | \(0.425126\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −7.80360 | −1.79027 | −0.895134 | − | 0.445796i | \(-0.852921\pi\) | ||||
−0.895134 | + | 0.445796i | \(0.852921\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 3.81467 | 0.832429 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.00000 | 0.208514 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.19480 | −0.838959 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.00000 | −0.185695 | ||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.73130 | 0.670162 | 0.335081 | − | 0.942189i | \(-0.391236\pi\) | ||||
0.335081 | + | 0.942189i | \(0.391236\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 5.23385 | 0.911096 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 3.42302 | 0.578596 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.939833 | 0.154508 | 0.0772538 | − | 0.997011i | \(-0.475385\pi\) | ||||
0.0772538 | + | 0.997011i | \(0.475385\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −3.43366 | −0.549826 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −5.90444 | −0.922119 | −0.461060 | − | 0.887369i | \(-0.652531\pi\) | ||||
−0.461060 | + | 0.887369i | \(0.652531\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.82368 | −0.430607 | −0.215303 | − | 0.976547i | \(-0.569074\pi\) | ||||
−0.215303 | + | 0.976547i | \(0.569074\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0.897331 | 0.133766 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 13.3375 | 1.94547 | 0.972734 | − | 0.231923i | \(-0.0745019\pi\) | ||||
0.972734 | + | 0.231923i | \(0.0745019\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 7.55171 | 1.07882 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.92187 | 0.269116 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 12.4108 | 1.70475 | 0.852377 | − | 0.522928i | \(-0.175160\pi\) | ||||
0.852377 | + | 0.522928i | \(0.175160\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 4.69649 | 0.633275 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −7.80360 | −1.03361 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −3.06388 | −0.398884 | −0.199442 | − | 0.979910i | \(-0.563913\pi\) | ||||
−0.199442 | + | 0.979910i | \(0.563913\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 9.88695 | 1.26589 | 0.632947 | − | 0.774195i | \(-0.281845\pi\) | ||||
0.632947 | + | 0.774195i | \(0.281845\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 3.81467 | 0.480603 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −3.08113 | −0.382168 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 14.3222 | 1.74973 | 0.874866 | − | 0.484365i | \(-0.160949\pi\) | ||||
0.874866 | + | 0.484365i | \(0.160949\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1.00000 | 0.120386 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 10.5787 | 1.25547 | 0.627733 | − | 0.778429i | \(-0.283983\pi\) | ||||
0.627733 | + | 0.778429i | \(0.283983\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −9.23222 | −1.08055 | −0.540275 | − | 0.841489i | \(-0.681680\pi\) | ||||
−0.540275 | + | 0.841489i | \(0.681680\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −4.19480 | −0.484373 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 19.9654 | 2.27527 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.22128 | 0.249914 | 0.124957 | − | 0.992162i | \(-0.460121\pi\) | ||||
0.124957 | + | 0.992162i | \(0.460121\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 2.48600 | 0.272874 | 0.136437 | − | 0.990649i | \(-0.456435\pi\) | ||||
0.136437 | + | 0.990649i | \(0.456435\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.72455 | 0.187054 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −1.00000 | −0.107211 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −13.2715 | −1.40678 | −0.703390 | − | 0.710804i | \(-0.748331\pi\) | ||||
−0.703390 | + | 0.710804i | \(0.748331\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −13.0983 | −1.37307 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 3.73130 | 0.386918 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −7.00241 | −0.718432 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −7.70919 | −0.782750 | −0.391375 | − | 0.920231i | \(-0.628000\pi\) | ||||
−0.391375 | + | 0.920231i | \(0.628000\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 5.23385 | 0.526021 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 13.1086 | 1.30435 | 0.652176 | − | 0.758068i | \(-0.273856\pi\) | ||||
0.652176 | + | 0.758068i | \(0.273856\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 18.5637 | 1.82913 | 0.914567 | − | 0.404435i | \(-0.132532\pi\) | ||||
0.914567 | + | 0.404435i | \(0.132532\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 3.42302 | 0.334053 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 12.8057 | 1.23797 | 0.618987 | − | 0.785401i | \(-0.287543\pi\) | ||||
0.618987 | + | 0.785401i | \(0.287543\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1.08922 | −0.104328 | −0.0521640 | − | 0.998639i | \(-0.516612\pi\) | ||||
−0.0521640 | + | 0.998639i | \(0.516612\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0.939833 | 0.0892050 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 15.8228 | 1.48849 | 0.744244 | − | 0.667908i | \(-0.232810\pi\) | ||||
0.744244 | + | 0.667908i | \(0.232810\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0.897331 | 0.0836765 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −3.43366 | −0.317442 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 7.33130 | 0.672059 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 16.3931 | 1.49029 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −5.90444 | −0.532386 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −8.25078 | −0.737972 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 20.9937 | 1.86289 | 0.931444 | − | 0.363885i | \(-0.118550\pi\) | ||||
0.931444 | + | 0.363885i | \(0.118550\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −2.82368 | −0.248611 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −11.8838 | −1.03829 | −0.519145 | − | 0.854686i | \(-0.673749\pi\) | ||||
−0.519145 | + | 0.854686i | \(0.673749\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −29.7682 | −2.58123 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0.897331 | 0.0772299 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −9.74379 | −0.832468 | −0.416234 | − | 0.909258i | \(-0.636650\pi\) | ||||
−0.416234 | + | 0.909258i | \(0.636650\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −21.7119 | −1.84158 | −0.920790 | − | 0.390060i | \(-0.872454\pi\) | ||||
−0.920790 | + | 0.390060i | \(0.872454\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 13.3375 | 1.12322 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −17.9713 | −1.50283 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −0.897331 | −0.0745193 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 7.55171 | 0.622854 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −0.0539251 | −0.00441771 | −0.00220886 | − | 0.999998i | \(-0.500703\pi\) | ||||
−0.00220886 | + | 0.999998i | \(0.500703\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −9.95429 | −0.810069 | −0.405034 | − | 0.914301i | \(-0.632740\pi\) | ||||
−0.405034 | + | 0.914301i | \(0.632740\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 1.92187 | 0.155374 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 3.34821 | 0.268935 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −5.32590 | −0.425053 | −0.212527 | − | 0.977155i | \(-0.568169\pi\) | ||||
−0.212527 | + | 0.977155i | \(0.568169\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 12.4108 | 0.984240 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 3.81467 | 0.300638 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 18.3644 | 1.43841 | 0.719206 | − | 0.694797i | \(-0.244506\pi\) | ||||
0.719206 | + | 0.694797i | \(0.244506\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 4.69649 | 0.365621 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −16.8360 | −1.30281 | −0.651405 | − | 0.758730i | \(-0.725820\pi\) | ||||
−0.651405 | + | 0.758730i | \(0.725820\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1.20995 | −0.0930729 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −7.80360 | −0.596756 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −22.0282 | −1.67478 | −0.837388 | − | 0.546609i | \(-0.815918\pi\) | ||||
−0.837388 | + | 0.546609i | \(0.815918\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −16.0018 | −1.20962 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −3.06388 | −0.230296 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 2.29809 | 0.171767 | 0.0858837 | − | 0.996305i | \(-0.472629\pi\) | ||||
0.0858837 | + | 0.996305i | \(0.472629\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1.94435 | 0.144522 | 0.0722611 | − | 0.997386i | \(-0.476979\pi\) | ||||
0.0722611 | + | 0.997386i | \(0.476979\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 9.88695 | 0.730865 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0.843341 | 0.0620037 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 10.0588 | 0.735570 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 3.81467 | 0.277476 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 13.7295 | 0.993430 | 0.496715 | − | 0.867914i | \(-0.334539\pi\) | ||||
0.496715 | + | 0.867914i | \(0.334539\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 13.9644 | 1.00518 | 0.502591 | − | 0.864524i | \(-0.332380\pi\) | ||||
0.502591 | + | 0.864524i | \(0.332380\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −3.08113 | −0.220645 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 6.85157 | 0.488154 | 0.244077 | − | 0.969756i | \(-0.421515\pi\) | ||||
0.244077 | + | 0.969756i | \(0.421515\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 14.0960 | 0.999240 | 0.499620 | − | 0.866245i | \(-0.333473\pi\) | ||||
0.499620 | + | 0.866245i | \(0.333473\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 14.3222 | 1.01021 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −3.81467 | −0.267737 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −5.29824 | −0.370045 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1.00000 | 0.0695048 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −40.8428 | −2.82516 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.38760 | −0.0955265 | −0.0477632 | − | 0.998859i | \(-0.515209\pi\) | ||||
−0.0477632 | + | 0.998859i | \(0.515209\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 10.5787 | 0.724844 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −2.53377 | −0.172802 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 14.2337 | 0.966246 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −9.23222 | −0.623856 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −6.59905 | −0.443900 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −8.82944 | −0.591263 | −0.295632 | − | 0.955302i | \(-0.595530\pi\) | ||||
−0.295632 | + | 0.955302i | \(0.595530\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −4.19480 | −0.279653 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 27.1801 | 1.80401 | 0.902004 | − | 0.431727i | \(-0.142096\pi\) | ||||
0.902004 | + | 0.431727i | \(0.142096\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −3.21756 | −0.212622 | −0.106311 | − | 0.994333i | \(-0.533904\pi\) | ||||
−0.106311 | + | 0.994333i | \(0.533904\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 19.9654 | 1.31363 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 2.82764 | 0.185245 | 0.0926225 | − | 0.995701i | \(-0.470475\pi\) | ||||
0.0926225 | + | 0.995701i | \(0.470475\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 11.9681 | 0.780714 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 2.22128 | 0.144288 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −25.8036 | −1.66909 | −0.834547 | − | 0.550937i | \(-0.814271\pi\) | ||||
−0.834547 | + | 0.550937i | \(0.814271\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −27.3656 | −1.76277 | −0.881387 | − | 0.472396i | \(-0.843389\pi\) | ||||
−0.881387 | + | 0.472396i | \(0.843389\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 6.77638 | 0.432927 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 26.7950 | 1.70492 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 2.48600 | 0.157544 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −2.14400 | −0.135328 | −0.0676639 | − | 0.997708i | \(-0.521555\pi\) | ||||
−0.0676639 | + | 0.997708i | \(0.521555\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 5.23385 | 0.329049 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 1.72455 | 0.107996 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −18.0033 | −1.12302 | −0.561508 | − | 0.827471i | \(-0.689779\pi\) | ||||
−0.561508 | + | 0.827471i | \(0.689779\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 3.58515 | 0.222771 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1.00000 | −0.0618984 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −10.5249 | −0.648991 | −0.324495 | − | 0.945887i | \(-0.605194\pi\) | ||||
−0.324495 | + | 0.945887i | \(0.605194\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 11.1366 | 0.684115 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −13.2715 | −0.812204 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 1.28161 | 0.0781413 | 0.0390706 | − | 0.999236i | \(-0.487560\pi\) | ||||
0.0390706 | + | 0.999236i | \(0.487560\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1.11624 | −0.0678070 | −0.0339035 | − | 0.999425i | \(-0.510794\pi\) | ||||
−0.0339035 | + | 0.999425i | \(0.510794\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −13.0983 | −0.792745 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −21.9549 | −1.32393 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 4.29599 | 0.258121 | 0.129061 | − | 0.991637i | \(-0.458804\pi\) | ||||
0.129061 | + | 0.991637i | \(0.458804\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 3.73130 | 0.223387 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −16.1931 | −0.965999 | −0.482999 | − | 0.875621i | \(-0.660453\pi\) | ||||
−0.482999 | + | 0.875621i | \(0.660453\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 4.02545 | 0.239288 | 0.119644 | − | 0.992817i | \(-0.461825\pi\) | ||||
0.119644 | + | 0.992817i | \(0.461825\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −7.00241 | −0.414787 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −22.5235 | −1.32952 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −13.3064 | −0.782731 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −7.70919 | −0.451921 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −21.5224 | −1.25735 | −0.628676 | − | 0.777667i | \(-0.716403\pi\) | ||||
−0.628676 | + | 0.777667i | \(0.716403\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −2.74932 | −0.160071 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 5.23385 | 0.303699 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −3.43366 | −0.198574 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −10.7714 | −0.620853 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 13.1086 | 0.753068 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 8.87187 | 0.508002 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 7.57632 | 0.432403 | 0.216202 | − | 0.976349i | \(-0.430633\pi\) | ||||
0.216202 | + | 0.976349i | \(0.430633\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 18.5637 | 1.05605 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −13.2050 | −0.748789 | −0.374394 | − | 0.927270i | \(-0.622149\pi\) | ||||
−0.374394 | + | 0.927270i | \(0.622149\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 23.9026 | 1.35105 | 0.675527 | − | 0.737336i | \(-0.263916\pi\) | ||||
0.675527 | + | 0.737336i | \(0.263916\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 3.42302 | 0.192865 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −3.42802 | −0.192537 | −0.0962683 | − | 0.995355i | \(-0.530691\pi\) | ||||
−0.0962683 | + | 0.995355i | \(0.530691\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −5.23385 | −0.293039 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 12.8057 | 0.714744 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −14.9975 | −0.834483 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 14.4035 | 0.798964 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −1.08922 | −0.0602338 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 50.8780 | 2.80499 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 19.5447 | 1.07428 | 0.537138 | − | 0.843494i | \(-0.319505\pi\) | ||||
0.537138 | + | 0.843494i | \(0.319505\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0.939833 | 0.0515025 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 12.8517 | 0.702165 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −27.5463 | −1.50054 | −0.750272 | − | 0.661129i | \(-0.770078\pi\) | ||||
−0.750272 | + | 0.661129i | \(0.770078\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 15.8228 | 0.859379 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 19.5291 | 1.05756 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 2.10458 | 0.113637 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0.897331 | 0.0483107 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 17.9600 | 0.964141 | 0.482070 | − | 0.876132i | \(-0.339885\pi\) | ||||
0.482070 | + | 0.876132i | \(0.339885\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −15.2215 | −0.814790 | −0.407395 | − | 0.913252i | \(-0.633563\pi\) | ||||
−0.407395 | + | 0.913252i | \(0.633563\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −3.43366 | −0.183275 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −30.5406 | −1.62551 | −0.812756 | − | 0.582604i | \(-0.802034\pi\) | ||||
−0.812756 | + | 0.582604i | \(0.802034\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 9.49263 | 0.503817 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 7.33130 | 0.388013 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −29.2887 | −1.54580 | −0.772900 | − | 0.634528i | \(-0.781195\pi\) | ||||
−0.772900 | + | 0.634528i | \(0.781195\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 41.8962 | 2.20506 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 16.3931 | 0.860417 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −8.28436 | −0.433623 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 5.83369 | 0.304516 | 0.152258 | − | 0.988341i | \(-0.451346\pi\) | ||||
0.152258 | + | 0.988341i | \(0.451346\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −5.90444 | −0.307373 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 47.3431 | 2.45793 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 6.18034 | 0.320006 | 0.160003 | − | 0.987117i | \(-0.448850\pi\) | ||||
0.160003 | + | 0.987117i | \(0.448850\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −8.25078 | −0.426068 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 3.43366 | 0.176843 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 28.9038 | 1.48469 | 0.742344 | − | 0.670019i | \(-0.233714\pi\) | ||||
0.742344 | + | 0.670019i | \(0.233714\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 20.9937 | 1.07554 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −3.03770 | −0.155219 | −0.0776096 | − | 0.996984i | \(-0.524729\pi\) | ||||
−0.0776096 | + | 0.996984i | \(0.524729\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 17.9156 | 0.913062 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −2.82368 | −0.143536 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −4.43947 | −0.225090 | −0.112545 | − | 0.993647i | \(-0.535900\pi\) | ||||
−0.112545 | + | 0.993647i | \(0.535900\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.92187 | 0.0971931 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −11.8838 | −0.599457 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 1.99322 | 0.100290 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −14.6535 | −0.735436 | −0.367718 | − | 0.929937i | \(-0.619861\pi\) | ||||
−0.367718 | + | 0.929937i | \(0.619861\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −29.7682 | −1.49027 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −5.70941 | −0.285115 | −0.142557 | − | 0.989787i | \(-0.545533\pi\) | ||||
−0.142557 | + | 0.989787i | \(0.545533\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −12.8120 | −0.638214 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0.897331 | 0.0445887 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 4.91894 | 0.243823 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −10.1737 | −0.503055 | −0.251527 | − | 0.967850i | \(-0.580933\pi\) | ||||
−0.251527 | + | 0.967850i | \(0.580933\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −9.74379 | −0.480626 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −11.6877 | −0.575115 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 2.23077 | 0.109504 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −21.7119 | −1.06324 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 26.3758 | 1.28854 | 0.644272 | − | 0.764796i | \(-0.277160\pi\) | ||||
0.644272 | + | 0.764796i | \(0.277160\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 38.1010 | 1.85693 | 0.928464 | − | 0.371422i | \(-0.121130\pi\) | ||||
0.928464 | + | 0.371422i | \(0.121130\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 13.3375 | 0.648489 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −8.06185 | −0.391057 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 37.7155 | 1.82518 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −17.9713 | −0.867661 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 4.20187 | 0.202397 | 0.101199 | − | 0.994866i | \(-0.467732\pi\) | ||||
0.101199 | + | 0.994866i | \(0.467732\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 27.2424 | 1.30918 | 0.654592 | − | 0.755982i | \(-0.272840\pi\) | ||||
0.654592 | + | 0.755982i | \(0.272840\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −0.897331 | −0.0430237 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −7.80360 | −0.373297 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −21.4883 | −1.02558 | −0.512791 | − | 0.858513i | \(-0.671389\pi\) | ||||
−0.512791 | + | 0.858513i | \(0.671389\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 7.55171 | 0.359605 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 12.1798 | 0.578681 | 0.289341 | − | 0.957226i | \(-0.406564\pi\) | ||||
0.289341 | + | 0.957226i | \(0.406564\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −11.9090 | −0.564539 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −0.0539251 | −0.00255057 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −8.96580 | −0.423122 | −0.211561 | − | 0.977365i | \(-0.567855\pi\) | ||||
−0.211561 | + | 0.977365i | \(0.567855\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −30.9029 | −1.45516 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −9.95429 | −0.467693 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −11.7535 | −0.551013 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 28.6575 | 1.34054 | 0.670271 | − | 0.742117i | \(-0.266178\pi\) | ||||
0.670271 | + | 0.742117i | \(0.266178\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 1.92187 | 0.0897052 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −14.1620 | −0.659590 | −0.329795 | − | 0.944053i | \(-0.606980\pi\) | ||||
−0.329795 | + | 0.944053i | \(0.606980\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −29.2565 | −1.35967 | −0.679833 | − | 0.733367i | \(-0.737948\pi\) | ||||
−0.679833 | + | 0.733367i | \(0.737948\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 3.34821 | 0.155270 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 31.1030 | 1.43927 | 0.719637 | − | 0.694351i | \(-0.244308\pi\) | ||||
0.719637 | + | 0.694351i | \(0.244308\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 54.6344 | 2.52278 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −5.32590 | −0.245405 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −14.7787 | −0.679525 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 32.7345 | 1.50196 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 12.4108 | 0.568251 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 3.86249 | 0.176482 | 0.0882409 | − | 0.996099i | \(-0.471875\pi\) | ||||
0.0882409 | + | 0.996099i | \(0.471875\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −3.22707 | −0.147142 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 3.81467 | 0.173573 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −6.91770 | −0.314116 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −16.7922 | −0.760929 | −0.380465 | − | 0.924795i | \(-0.624236\pi\) | ||||
−0.380465 | + | 0.924795i | \(0.624236\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 18.3644 | 0.830468 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −15.8110 | −0.713540 | −0.356770 | − | 0.934192i | \(-0.616122\pi\) | ||||
−0.356770 | + | 0.934192i | \(0.616122\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1.92187 | −0.0865566 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 4.69649 | 0.211092 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 40.3544 | 1.81014 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −34.0511 | −1.52433 | −0.762167 | − | 0.647380i | \(-0.775865\pi\) | ||||
−0.762167 | + | 0.647380i | \(0.775865\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −16.8360 | −0.752178 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 2.51408 | 0.112097 | 0.0560486 | − | 0.998428i | \(-0.482150\pi\) | ||||
0.0560486 | + | 0.998428i | \(0.482150\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 11.7627 | 0.523434 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −1.20995 | −0.0537356 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −17.5905 | −0.779686 | −0.389843 | − | 0.920881i | \(-0.627471\pi\) | ||||
−0.389843 | + | 0.920881i | \(0.627471\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −35.2179 | −1.55795 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −7.80360 | −0.344537 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 16.6578 | 0.734029 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 69.8062 | 3.07007 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −22.0282 | −0.966932 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 39.9368 | 1.74966 | 0.874832 | − | 0.484426i | \(-0.160972\pi\) | ||||
0.874832 | + | 0.484426i | \(0.160972\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −6.76095 | −0.295636 | −0.147818 | − | 0.989015i | \(-0.547225\pi\) | ||||
−0.147818 | + | 0.989015i | \(0.547225\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −16.0018 | −0.698374 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 7.17108 | 0.312377 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −3.06388 | −0.132961 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 20.2739 | 0.878159 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 11.4909 | 0.496797 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 2.29809 | 0.0991700 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 39.5245 | 1.70244 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −13.6532 | −0.586997 | −0.293498 | − | 0.955960i | \(-0.594820\pi\) | ||||
−0.293498 | + | 0.955960i | \(0.594820\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 1.94435 | 0.0834399 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −0.977388 | −0.0418667 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 27.3579 | 1.16974 | 0.584870 | − | 0.811127i | \(-0.301146\pi\) | ||||
0.584870 | + | 0.811127i | \(0.301146\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 9.88695 | 0.421965 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 7.80360 | 0.332445 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 8.47345 | 0.360328 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0.843341 | 0.0357978 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −21.0863 | −0.893456 | −0.446728 | − | 0.894670i | \(-0.647411\pi\) | ||||
−0.446728 | + | 0.894670i | \(0.647411\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 9.69556 | 0.410078 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 10.0588 | 0.424681 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −17.2843 | −0.728446 | −0.364223 | − | 0.931312i | \(-0.618665\pi\) | ||||
−0.364223 | + | 0.931312i | \(0.618665\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 14.1983 | 0.597328 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 3.81467 | 0.160201 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −14.4233 | −0.604658 | −0.302329 | − | 0.953204i | \(-0.597764\pi\) | ||||
−0.302329 | + | 0.953204i | \(0.597764\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −8.58461 | −0.359255 | −0.179627 | − | 0.983735i | \(-0.557489\pi\) | ||||
−0.179627 | + | 0.983735i | \(0.557489\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 13.7295 | 0.573557 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −4.19480 | −0.174935 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −11.1434 | −0.463907 | −0.231953 | − | 0.972727i | \(-0.574512\pi\) | ||||
−0.231953 | + | 0.972727i | \(0.574512\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 13.9644 | 0.580342 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 9.48328 | 0.393433 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 64.9562 | 2.69021 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −3.08113 | −0.127389 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −28.2597 | −1.16640 | −0.583200 | − | 0.812328i | \(-0.698200\pi\) | ||||
−0.583200 | + | 0.812328i | \(0.698200\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −29.1176 | −1.19977 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 6.85157 | 0.281836 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 25.4794 | 1.04631 | 0.523157 | − | 0.852236i | \(-0.324754\pi\) | ||||
0.523157 | + | 0.852236i | \(0.324754\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 6.57860 | 0.269696 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 14.0960 | 0.576911 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −39.7316 | −1.62339 | −0.811694 | − | 0.584082i | \(-0.801454\pi\) | ||||
−0.811694 | + | 0.584082i | \(0.801454\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −12.5941 | −0.513725 | −0.256863 | − | 0.966448i | \(-0.582689\pi\) | ||||
−0.256863 | + | 0.966448i | \(0.582689\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 14.3222 | 0.583244 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 14.7101 | 0.598049 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −35.7473 | −1.45094 | −0.725470 | − | 0.688254i | \(-0.758378\pi\) | ||||
−0.725470 | + | 0.688254i | \(0.758378\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −3.81467 | −0.154578 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −45.7964 | −1.85272 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −24.5319 | −0.990835 | −0.495418 | − | 0.868655i | \(-0.664985\pi\) | ||||
−0.495418 | + | 0.868655i | \(0.664985\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −5.29824 | −0.213646 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −31.9825 | −1.28757 | −0.643784 | − | 0.765207i | \(-0.722637\pi\) | ||||
−0.643784 | + | 0.765207i | \(0.722637\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −21.6271 | −0.869266 | −0.434633 | − | 0.900608i | \(-0.643122\pi\) | ||||
−0.434633 | + | 0.900608i | \(0.643122\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.00000 | 0.0401286 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −50.6265 | −2.02831 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 13.5703 | 0.542812 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −40.8428 | −1.63111 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 1.80624 | 0.0720194 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −2.28377 | −0.0909156 | −0.0454578 | − | 0.998966i | \(-0.514475\pi\) | ||||
−0.0454578 | + | 0.998966i | \(0.514475\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −1.38760 | −0.0551522 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 18.8383 | 0.747574 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −25.9300 | −1.02739 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 10.5787 | 0.418489 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 13.9618 | 0.551459 | 0.275730 | − | 0.961235i | \(-0.411081\pi\) | ||||
0.275730 | + | 0.961235i | \(0.411081\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −15.5694 | −0.613997 | −0.306999 | − | 0.951710i | \(-0.599325\pi\) | ||||
−0.306999 | + | 0.951710i | \(0.599325\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −2.53377 | −0.0997672 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −49.3101 | −1.93858 | −0.969289 | − | 0.245924i | \(-0.920909\pi\) | ||||
−0.969289 | + | 0.245924i | \(0.920909\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −16.0359 | −0.629464 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 14.2337 | 0.557863 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 7.26719 | 0.284387 | 0.142194 | − | 0.989839i | \(-0.454584\pi\) | ||||
0.142194 | + | 0.989839i | \(0.454584\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −10.6637 | −0.416664 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −9.23222 | −0.360183 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 8.90275 | 0.346802 | 0.173401 | − | 0.984851i | \(-0.444524\pi\) | ||||
0.173401 | + | 0.984851i | \(0.444524\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 4.56464 | 0.177544 | 0.0887720 | − | 0.996052i | \(-0.471706\pi\) | ||||
0.0887720 | + | 0.996052i | \(0.471706\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −6.59905 | −0.256286 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −26.7119 | −1.03584 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1.00000 | −0.0387202 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −8.82944 | −0.341366 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 51.7468 | 1.99766 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −5.28579 | −0.203752 | −0.101876 | − | 0.994797i | \(-0.532485\pi\) | ||||
−0.101876 | + | 0.994797i | \(0.532485\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −4.19480 | −0.161458 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 26.6869 | 1.02566 | 0.512831 | − | 0.858490i | \(-0.328597\pi\) | ||||
0.512831 | + | 0.858490i | \(0.328597\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −29.4080 | −1.12858 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 27.1801 | 1.04154 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −7.20362 | −0.275639 | −0.137819 | − | 0.990457i | \(-0.544009\pi\) | ||||
−0.137819 | + | 0.990457i | \(0.544009\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −8.74340 | −0.334068 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −3.21756 | −0.122758 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −42.6145 | −1.62348 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 30.4661 | 1.15898 | 0.579492 | − | 0.814978i | \(-0.303251\pi\) | ||||
0.579492 | + | 0.814978i | \(0.303251\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 19.9654 | 0.758423 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −19.4828 | −0.739023 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −11.3476 | −0.429820 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 2.82764 | 0.106951 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 20.7783 | 0.784784 | 0.392392 | − | 0.919798i | \(-0.371648\pi\) | ||||
0.392392 | + | 0.919798i | \(0.371648\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −7.33408 | −0.276610 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 11.9681 | 0.450745 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 50.0049 | 1.88063 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 19.4473 | 0.730359 | 0.365179 | − | 0.930937i | \(-0.381008\pi\) | ||||
0.365179 | + | 0.930937i | \(0.381008\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 2.22128 | 0.0833046 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 3.73130 | 0.139738 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −16.1262 | −0.603085 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −25.8036 | −0.963652 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 26.2733 | 0.979827 | 0.489914 | − | 0.871771i | \(-0.337028\pi\) | ||||
0.489914 | + | 0.871771i | \(0.337028\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 70.8143 | 2.63726 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −27.3656 | −1.01774 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 4.19480 | 0.155791 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 28.3921 | 1.05300 | 0.526502 | − | 0.850174i | \(-0.323503\pi\) | ||||
0.526502 | + | 0.850174i | \(0.323503\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −5.42674 | −0.200715 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 46.1551 | 1.70478 | 0.852389 | − | 0.522909i | \(-0.175153\pi\) | ||||
0.852389 | + | 0.522909i | \(0.175153\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 6.77638 | 0.249951 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 74.9600 | 2.76119 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −4.13404 | −0.152073 | −0.0760365 | − | 0.997105i | \(-0.524227\pi\) | ||||
−0.0760365 | + | 0.997105i | \(0.524227\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 26.7950 | 0.984337 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −31.3373 | −1.14965 | −0.574826 | − | 0.818276i | \(-0.694930\pi\) | ||||
−0.574826 | + | 0.818276i | \(0.694930\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −0.0483886 | −0.00177282 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 2.48600 | 0.0909581 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 48.8495 | 1.78492 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 15.2978 | 0.558226 | 0.279113 | − | 0.960258i | \(-0.409960\pi\) | ||||
0.279113 | + | 0.960258i | \(0.409960\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −2.14400 | −0.0781315 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −8.93229 | −0.325079 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −38.9382 | −1.41523 | −0.707617 | − | 0.706596i | \(-0.750230\pi\) | ||||
−0.707617 | + | 0.706596i | \(0.750230\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 5.23385 | 0.189977 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −16.3325 | −0.592054 | −0.296027 | − | 0.955180i | \(-0.595662\pi\) | ||||
−0.296027 | + | 0.955180i | \(0.595662\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −4.15500 | −0.150421 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 1.72455 | 0.0623513 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 10.5204 | 0.379868 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −52.3619 | −1.88822 | −0.944109 | − | 0.329634i | \(-0.893075\pi\) | ||||
−0.944109 | + | 0.329634i | \(0.893075\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −18.0033 | −0.648373 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −20.5849 | −0.740388 | −0.370194 | − | 0.928955i | \(-0.620709\pi\) | ||||
−0.370194 | + | 0.928955i | \(0.620709\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −15.6521 | −0.562239 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 3.58515 | 0.128617 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 46.0759 | 1.65084 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 55.3675 | 1.98121 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −1.00000 | −0.0357371 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −4.77910 | −0.170573 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −54.1435 | −1.93001 | −0.965003 | − | 0.262239i | \(-0.915539\pi\) | ||||
−0.965003 | + | 0.262239i | \(0.915539\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −10.5249 | −0.374695 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 60.3589 | 2.14612 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −33.9485 | −1.20555 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 11.1366 | 0.394974 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 50.2674 | 1.78056 | 0.890281 | − | 0.455412i | \(-0.150508\pi\) | ||||
0.890281 | + | 0.455412i | \(0.150508\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 25.6328 | 0.906825 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −13.2715 | −0.468926 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −48.3200 | −1.70518 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 3.42302 | 0.120646 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 1.28161 | 0.0451149 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 7.91149 | 0.278153 | 0.139077 | − | 0.990282i | \(-0.455587\pi\) | ||||
0.139077 | + | 0.990282i | \(0.455587\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −8.86464 | −0.311280 | −0.155640 | − | 0.987814i | \(-0.549744\pi\) | ||||
−0.155640 | + | 0.987814i | \(0.549744\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −1.11624 | −0.0391484 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 16.4790 | 0.577233 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 22.0349 | 0.770902 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −13.0983 | −0.457692 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −1.24346 | −0.0433970 | −0.0216985 | − | 0.999765i | \(-0.506907\pi\) | ||||
−0.0216985 | + | 0.999765i | \(0.506907\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −17.8486 | −0.622163 | −0.311081 | − | 0.950383i | \(-0.600691\pi\) | ||||
−0.311081 | + | 0.950383i | \(0.600691\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −21.9549 | −0.764372 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −14.7403 | −0.512570 | −0.256285 | − | 0.966601i | \(-0.582499\pi\) | ||||
−0.256285 | + | 0.966601i | \(0.582499\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −2.83338 | −0.0984075 | −0.0492038 | − | 0.998789i | \(-0.515668\pi\) | ||||
−0.0492038 | + | 0.998789i | \(0.515668\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 4.29599 | 0.149026 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 14.5134 | 0.502859 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −15.1075 | −0.522816 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 3.73130 | 0.128973 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −17.7053 | −0.611255 | −0.305627 | − | 0.952151i | \(-0.598866\pi\) | ||||
−0.305627 | + | 0.952151i | \(0.598866\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.00000 | 0.0344828 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −16.1931 | −0.557720 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −1.08572 | −0.0373500 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 62.5344 | 2.14871 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 4.02545 | 0.138153 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0.939833 | 0.0322171 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −9.48557 | −0.324780 | −0.162390 | − | 0.986727i | \(-0.551920\pi\) | ||||
−0.162390 | + | 0.986727i | \(0.551920\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −7.00241 | −0.239477 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 13.4094 | 0.458058 | 0.229029 | − | 0.973420i | \(-0.426445\pi\) | ||||
0.229029 | + | 0.973420i | \(0.426445\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −34.9045 | −1.19093 | −0.595463 | − | 0.803382i | \(-0.703031\pi\) | ||||
−0.595463 | + | 0.803382i | \(0.703031\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −22.5235 | −0.767599 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 38.8001 | 1.32077 | 0.660386 | − | 0.750926i | \(-0.270393\pi\) | ||||
0.660386 | + | 0.750926i | \(0.270393\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −19.7666 | −0.672085 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −13.3064 | −0.451910 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 11.6258 | 0.394380 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −49.1775 | −1.66632 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −7.70919 | −0.260917 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −31.4740 | −1.06401 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −22.4583 | −0.758365 | −0.379182 | − | 0.925322i | \(-0.623795\pi\) | ||||
−0.379182 | + | 0.925322i | \(0.623795\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −21.5224 | −0.725932 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 24.8079 | 0.835799 | 0.417900 | − | 0.908493i | \(-0.362766\pi\) | ||||
0.417900 | + | 0.908493i | \(0.362766\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1.03936 | 0.0349773 | 0.0174886 | − | 0.999847i | \(-0.494433\pi\) | ||||
0.0174886 | + | 0.999847i | \(0.494433\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −2.74932 | −0.0924173 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −5.32456 | −0.178781 | −0.0893906 | − | 0.995997i | \(-0.528492\pi\) | ||||
−0.0893906 | + | 0.995997i | \(0.528492\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 80.0840 | 2.68593 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 5.23385 | 0.175340 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −104.080 | −3.48291 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 2.06215 | 0.0689300 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −3.43366 | −0.114647 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −3.73130 | −0.124446 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 23.8519 | 0.794623 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −10.7714 | −0.358450 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 1.74472 | 0.0579965 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −25.7645 | −0.855497 | −0.427749 | − | 0.903898i | \(-0.640693\pi\) | ||||
−0.427749 | + | 0.903898i | \(0.640693\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 13.1086 | 0.434784 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −36.3906 | −1.20567 | −0.602837 | − | 0.797864i | \(-0.705963\pi\) | ||||
−0.602837 | + | 0.797864i | \(0.705963\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 13.0114 | 0.430613 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 8.87187 | 0.293295 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −45.3326 | −1.49702 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 30.3593 | 1.00146 | 0.500731 | − | 0.865603i | \(-0.333065\pi\) | ||||
0.500731 | + | 0.865603i | \(0.333065\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 7.57632 | 0.249648 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −36.3239 | −1.19561 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −3.94241 | −0.129626 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 18.5637 | 0.609711 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 8.91679 | 0.292550 | 0.146275 | − | 0.989244i | \(-0.453271\pi\) | ||||
0.146275 | + | 0.989244i | \(0.453271\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −58.9305 | −1.93137 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −13.2050 | −0.432313 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 9.02604 | 0.295183 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 30.9839 | 1.01220 | 0.506099 | − | 0.862475i | \(-0.331087\pi\) | ||||
0.506099 | + | 0.862475i | \(0.331087\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 23.9026 | 0.780031 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 53.3625 | 1.73957 | 0.869783 | − | 0.493434i | \(-0.164259\pi\) | ||||
0.869783 | + | 0.493434i | \(0.164259\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −5.90444 | −0.192275 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 3.42302 | 0.111351 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −45.6156 | −1.48231 | −0.741155 | − | 0.671334i | \(-0.765722\pi\) | ||||
−0.741155 | + | 0.671334i | \(0.765722\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 31.7003 | 1.02904 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −3.42802 | −0.111161 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 22.5093 | 0.729147 | 0.364574 | − | 0.931175i | \(-0.381215\pi\) | ||||
0.364574 | + | 0.931175i | \(0.381215\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 12.3199 | 0.398662 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −5.23385 | −0.169186 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −37.1693 | −1.20026 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −17.0774 | −0.550883 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 12.8057 | 0.412658 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 12.5307 | 0.403378 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −2.31451 | −0.0744295 | −0.0372147 | − | 0.999307i | \(-0.511849\pi\) | ||||
−0.0372147 | + | 0.999307i | \(0.511849\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −14.9975 | −0.481789 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 29.4829 | 0.946152 | 0.473076 | − | 0.881022i | \(-0.343144\pi\) | ||||
0.473076 | + | 0.881022i | \(0.343144\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −82.8237 | −2.65521 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 14.4035 | 0.461282 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 13.0559 | 0.417697 | 0.208848 | − | 0.977948i | \(-0.433029\pi\) | ||||
0.208848 | + | 0.977948i | \(0.433029\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −69.4611 | −2.21999 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1.08922 | −0.0347760 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −7.30342 | −0.232943 | −0.116471 | − | 0.993194i | \(-0.537158\pi\) | ||||
−0.116471 | + | 0.993194i | \(0.537158\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 6.14812 | 0.195895 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 50.8780 | 1.61946 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −2.82368 | −0.0897877 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 4.49027 | 0.142638 | 0.0713190 | − | 0.997454i | \(-0.477279\pi\) | ||||
0.0713190 | + | 0.997454i | \(0.477279\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 19.5447 | 0.620234 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 12.6488 | 0.400993 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 14.3467 | 0.454365 | 0.227183 | − | 0.973852i | \(-0.427049\pi\) | ||||
0.227183 | + | 0.973852i | \(0.427049\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0.939833 | 0.0297350 |
(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 | 8004.2.a.j.1.10 | ✓ | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8004.2.a.j.1.10 | ✓ | 16 | 1.1 | even | 1 | trivial |