Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4026,2,Mod(1,4026)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4026, 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("4026.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4026 = 2 \cdot 3 \cdot 11 \cdot 61 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4026.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: | \(32.1477718538\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.6809.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 5x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(2.29041\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4026.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 2.29041 | 1.02430 | 0.512151 | − | 0.858895i | \(-0.328849\pi\) | ||||
0.512151 | + | 0.858895i | \(0.328849\pi\) | |||||||
\(6\) | 1.00000 | 0.408248 | ||||||||
\(7\) | −0.955570 | −0.361172 | −0.180586 | − | 0.983559i | \(-0.557799\pi\) | ||||
−0.180586 | + | 0.983559i | \(0.557799\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −2.29041 | −0.724291 | ||||||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | −1.00000 | −0.288675 | ||||||||
\(13\) | 2.11919 | 0.587757 | 0.293878 | − | 0.955843i | \(-0.405054\pi\) | ||||
0.293878 | + | 0.955843i | \(0.405054\pi\) | |||||||
\(14\) | 0.955570 | 0.255387 | ||||||||
\(15\) | −2.29041 | −0.591381 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 4.97299 | 1.20613 | 0.603064 | − | 0.797693i | \(-0.293946\pi\) | ||||
0.603064 | + | 0.797693i | \(0.293946\pi\) | |||||||
\(18\) | −1.00000 | −0.235702 | ||||||||
\(19\) | 7.95360 | 1.82468 | 0.912340 | − | 0.409433i | \(-0.134274\pi\) | ||||
0.912340 | + | 0.409433i | \(0.134274\pi\) | |||||||
\(20\) | 2.29041 | 0.512151 | ||||||||
\(21\) | 0.955570 | 0.208523 | ||||||||
\(22\) | 1.00000 | 0.213201 | ||||||||
\(23\) | 7.11919 | 1.48445 | 0.742227 | − | 0.670149i | \(-0.233770\pi\) | ||||
0.742227 | + | 0.670149i | \(0.233770\pi\) | |||||||
\(24\) | 1.00000 | 0.204124 | ||||||||
\(25\) | 0.245981 | 0.0491962 | ||||||||
\(26\) | −2.11919 | −0.415607 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | −0.955570 | −0.180586 | ||||||||
\(29\) | −6.92856 | −1.28660 | −0.643301 | − | 0.765613i | \(-0.722436\pi\) | ||||
−0.643301 | + | 0.765613i | \(0.722436\pi\) | |||||||
\(30\) | 2.29041 | 0.418170 | ||||||||
\(31\) | 7.11721 | 1.27829 | 0.639145 | − | 0.769087i | \(-0.279289\pi\) | ||||
0.639145 | + | 0.769087i | \(0.279289\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 1.00000 | 0.174078 | ||||||||
\(34\) | −4.97299 | −0.852861 | ||||||||
\(35\) | −2.18865 | −0.369949 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | −10.7379 | −1.76531 | −0.882653 | − | 0.470024i | \(-0.844245\pi\) | ||||
−0.882653 | + | 0.470024i | \(0.844245\pi\) | |||||||
\(38\) | −7.95360 | −1.29024 | ||||||||
\(39\) | −2.11919 | −0.339341 | ||||||||
\(40\) | −2.29041 | −0.362146 | ||||||||
\(41\) | 7.66968 | 1.19780 | 0.598901 | − | 0.800823i | \(-0.295604\pi\) | ||||
0.598901 | + | 0.800823i | \(0.295604\pi\) | |||||||
\(42\) | −0.955570 | −0.147448 | ||||||||
\(43\) | −3.54400 | −0.540455 | −0.270227 | − | 0.962797i | \(-0.587099\pi\) | ||||
−0.270227 | + | 0.962797i | \(0.587099\pi\) | |||||||
\(44\) | −1.00000 | −0.150756 | ||||||||
\(45\) | 2.29041 | 0.341434 | ||||||||
\(46\) | −7.11919 | −1.04967 | ||||||||
\(47\) | −5.59372 | −0.815929 | −0.407964 | − | 0.912998i | \(-0.633761\pi\) | ||||
−0.407964 | + | 0.912998i | \(0.633761\pi\) | |||||||
\(48\) | −1.00000 | −0.144338 | ||||||||
\(49\) | −6.08689 | −0.869555 | ||||||||
\(50\) | −0.245981 | −0.0347869 | ||||||||
\(51\) | −4.97299 | −0.696358 | ||||||||
\(52\) | 2.11919 | 0.293878 | ||||||||
\(53\) | 8.21368 | 1.12824 | 0.564118 | − | 0.825694i | \(-0.309216\pi\) | ||||
0.564118 | + | 0.825694i | \(0.309216\pi\) | |||||||
\(54\) | 1.00000 | 0.136083 | ||||||||
\(55\) | −2.29041 | −0.308839 | ||||||||
\(56\) | 0.955570 | 0.127693 | ||||||||
\(57\) | −7.95360 | −1.05348 | ||||||||
\(58\) | 6.92856 | 0.909765 | ||||||||
\(59\) | 4.62525 | 0.602156 | 0.301078 | − | 0.953599i | \(-0.402653\pi\) | ||||
0.301078 | + | 0.953599i | \(0.402653\pi\) | |||||||
\(60\) | −2.29041 | −0.295691 | ||||||||
\(61\) | 1.00000 | 0.128037 | ||||||||
\(62\) | −7.11721 | −0.903887 | ||||||||
\(63\) | −0.955570 | −0.120391 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 4.85381 | 0.602041 | ||||||||
\(66\) | −1.00000 | −0.123091 | ||||||||
\(67\) | 12.3059 | 1.50340 | 0.751700 | − | 0.659505i | \(-0.229234\pi\) | ||||
0.751700 | + | 0.659505i | \(0.229234\pi\) | |||||||
\(68\) | 4.97299 | 0.603064 | ||||||||
\(69\) | −7.11919 | −0.857049 | ||||||||
\(70\) | 2.18865 | 0.261593 | ||||||||
\(71\) | −4.85183 | −0.575807 | −0.287903 | − | 0.957659i | \(-0.592958\pi\) | ||||
−0.287903 | + | 0.957659i | \(0.592958\pi\) | |||||||
\(72\) | −1.00000 | −0.117851 | ||||||||
\(73\) | −9.48633 | −1.11029 | −0.555145 | − | 0.831753i | \(-0.687337\pi\) | ||||
−0.555145 | + | 0.831753i | \(0.687337\pi\) | |||||||
\(74\) | 10.7379 | 1.24826 | ||||||||
\(75\) | −0.245981 | −0.0284034 | ||||||||
\(76\) | 7.95360 | 0.912340 | ||||||||
\(77\) | 0.955570 | 0.108897 | ||||||||
\(78\) | 2.11919 | 0.239951 | ||||||||
\(79\) | 6.68822 | 0.752483 | 0.376242 | − | 0.926522i | \(-0.377216\pi\) | ||||
0.376242 | + | 0.926522i | \(0.377216\pi\) | |||||||
\(80\) | 2.29041 | 0.256076 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −7.66968 | −0.846975 | ||||||||
\(83\) | −1.24401 | −0.136547 | −0.0682737 | − | 0.997667i | \(-0.521749\pi\) | ||||
−0.0682737 | + | 0.997667i | \(0.521749\pi\) | |||||||
\(84\) | 0.955570 | 0.104261 | ||||||||
\(85\) | 11.3902 | 1.23544 | ||||||||
\(86\) | 3.54400 | 0.382159 | ||||||||
\(87\) | 6.92856 | 0.742820 | ||||||||
\(88\) | 1.00000 | 0.106600 | ||||||||
\(89\) | −6.29041 | −0.666782 | −0.333391 | − | 0.942789i | \(-0.608193\pi\) | ||||
−0.333391 | + | 0.942789i | \(0.608193\pi\) | |||||||
\(90\) | −2.29041 | −0.241430 | ||||||||
\(91\) | −2.02503 | −0.212281 | ||||||||
\(92\) | 7.11919 | 0.742227 | ||||||||
\(93\) | −7.11721 | −0.738021 | ||||||||
\(94\) | 5.59372 | 0.576949 | ||||||||
\(95\) | 18.2170 | 1.86902 | ||||||||
\(96\) | 1.00000 | 0.102062 | ||||||||
\(97\) | −4.37166 | −0.443875 | −0.221938 | − | 0.975061i | \(-0.571238\pi\) | ||||
−0.221938 | + | 0.975061i | \(0.571238\pi\) | |||||||
\(98\) | 6.08689 | 0.614868 | ||||||||
\(99\) | −1.00000 | −0.100504 | ||||||||
\(100\) | 0.245981 | 0.0245981 | ||||||||
\(101\) | 17.8704 | 1.77817 | 0.889084 | − | 0.457744i | \(-0.151342\pi\) | ||||
0.889084 | + | 0.457744i | \(0.151342\pi\) | |||||||
\(102\) | 4.97299 | 0.492400 | ||||||||
\(103\) | 6.09868 | 0.600920 | 0.300460 | − | 0.953794i | \(-0.402860\pi\) | ||||
0.300460 | + | 0.953794i | \(0.402860\pi\) | |||||||
\(104\) | −2.11919 | −0.207803 | ||||||||
\(105\) | 2.18865 | 0.213590 | ||||||||
\(106\) | −8.21368 | −0.797783 | ||||||||
\(107\) | −16.4577 | −1.59102 | −0.795512 | − | 0.605937i | \(-0.792798\pi\) | ||||
−0.795512 | + | 0.605937i | \(0.792798\pi\) | |||||||
\(108\) | −1.00000 | −0.0962250 | ||||||||
\(109\) | 6.53528 | 0.625966 | 0.312983 | − | 0.949759i | \(-0.398672\pi\) | ||||
0.312983 | + | 0.949759i | \(0.398672\pi\) | |||||||
\(110\) | 2.29041 | 0.218382 | ||||||||
\(111\) | 10.7379 | 1.01920 | ||||||||
\(112\) | −0.955570 | −0.0902929 | ||||||||
\(113\) | −6.67079 | −0.627535 | −0.313768 | − | 0.949500i | \(-0.601591\pi\) | ||||
−0.313768 | + | 0.949500i | \(0.601591\pi\) | |||||||
\(114\) | 7.95360 | 0.744923 | ||||||||
\(115\) | 16.3059 | 1.52053 | ||||||||
\(116\) | −6.92856 | −0.643301 | ||||||||
\(117\) | 2.11919 | 0.195919 | ||||||||
\(118\) | −4.62525 | −0.425789 | ||||||||
\(119\) | −4.75205 | −0.435619 | ||||||||
\(120\) | 2.29041 | 0.209085 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | −1.00000 | −0.0905357 | ||||||||
\(123\) | −7.66968 | −0.691552 | ||||||||
\(124\) | 7.11721 | 0.639145 | ||||||||
\(125\) | −10.8887 | −0.973911 | ||||||||
\(126\) | 0.955570 | 0.0851290 | ||||||||
\(127\) | 9.31544 | 0.826612 | 0.413306 | − | 0.910592i | \(-0.364374\pi\) | ||||
0.413306 | + | 0.910592i | \(0.364374\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 3.54400 | 0.312032 | ||||||||
\(130\) | −4.85381 | −0.425707 | ||||||||
\(131\) | 6.88611 | 0.601642 | 0.300821 | − | 0.953681i | \(-0.402739\pi\) | ||||
0.300821 | + | 0.953681i | \(0.402739\pi\) | |||||||
\(132\) | 1.00000 | 0.0870388 | ||||||||
\(133\) | −7.60022 | −0.659023 | ||||||||
\(134\) | −12.3059 | −1.06306 | ||||||||
\(135\) | −2.29041 | −0.197127 | ||||||||
\(136\) | −4.97299 | −0.426431 | ||||||||
\(137\) | 12.8841 | 1.10077 | 0.550383 | − | 0.834912i | \(-0.314482\pi\) | ||||
0.550383 | + | 0.834912i | \(0.314482\pi\) | |||||||
\(138\) | 7.11919 | 0.606025 | ||||||||
\(139\) | −0.407623 | −0.0345742 | −0.0172871 | − | 0.999851i | \(-0.505503\pi\) | ||||
−0.0172871 | + | 0.999851i | \(0.505503\pi\) | |||||||
\(140\) | −2.18865 | −0.184975 | ||||||||
\(141\) | 5.59372 | 0.471077 | ||||||||
\(142\) | 4.85183 | 0.407157 | ||||||||
\(143\) | −2.11919 | −0.177215 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | −15.8693 | −1.31787 | ||||||||
\(146\) | 9.48633 | 0.785094 | ||||||||
\(147\) | 6.08689 | 0.502038 | ||||||||
\(148\) | −10.7379 | −0.882653 | ||||||||
\(149\) | −6.54169 | −0.535916 | −0.267958 | − | 0.963431i | \(-0.586349\pi\) | ||||
−0.267958 | + | 0.963431i | \(0.586349\pi\) | |||||||
\(150\) | 0.245981 | 0.0200842 | ||||||||
\(151\) | −23.2854 | −1.89493 | −0.947467 | − | 0.319852i | \(-0.896367\pi\) | ||||
−0.947467 | + | 0.319852i | \(0.896367\pi\) | |||||||
\(152\) | −7.95360 | −0.645122 | ||||||||
\(153\) | 4.97299 | 0.402043 | ||||||||
\(154\) | −0.955570 | −0.0770020 | ||||||||
\(155\) | 16.3013 | 1.30936 | ||||||||
\(156\) | −2.11919 | −0.169671 | ||||||||
\(157\) | −19.0675 | −1.52175 | −0.760876 | − | 0.648898i | \(-0.775230\pi\) | ||||
−0.760876 | + | 0.648898i | \(0.775230\pi\) | |||||||
\(158\) | −6.68822 | −0.532086 | ||||||||
\(159\) | −8.21368 | −0.651387 | ||||||||
\(160\) | −2.29041 | −0.181073 | ||||||||
\(161\) | −6.80288 | −0.536142 | ||||||||
\(162\) | −1.00000 | −0.0785674 | ||||||||
\(163\) | 14.3786 | 1.12622 | 0.563111 | − | 0.826381i | \(-0.309604\pi\) | ||||
0.563111 | + | 0.826381i | \(0.309604\pi\) | |||||||
\(164\) | 7.66968 | 0.598901 | ||||||||
\(165\) | 2.29041 | 0.178308 | ||||||||
\(166\) | 1.24401 | 0.0965537 | ||||||||
\(167\) | −9.78237 | −0.756983 | −0.378491 | − | 0.925605i | \(-0.623557\pi\) | ||||
−0.378491 | + | 0.925605i | \(0.623557\pi\) | |||||||
\(168\) | −0.955570 | −0.0737238 | ||||||||
\(169\) | −8.50905 | −0.654542 | ||||||||
\(170\) | −11.3902 | −0.873588 | ||||||||
\(171\) | 7.95360 | 0.608227 | ||||||||
\(172\) | −3.54400 | −0.270227 | ||||||||
\(173\) | 9.17089 | 0.697250 | 0.348625 | − | 0.937262i | \(-0.386649\pi\) | ||||
0.348625 | + | 0.937262i | \(0.386649\pi\) | |||||||
\(174\) | −6.92856 | −0.525253 | ||||||||
\(175\) | −0.235052 | −0.0177683 | ||||||||
\(176\) | −1.00000 | −0.0753778 | ||||||||
\(177\) | −4.62525 | −0.347655 | ||||||||
\(178\) | 6.29041 | 0.471486 | ||||||||
\(179\) | 9.93222 | 0.742369 | 0.371185 | − | 0.928559i | \(-0.378952\pi\) | ||||
0.371185 | + | 0.928559i | \(0.378952\pi\) | |||||||
\(180\) | 2.29041 | 0.170717 | ||||||||
\(181\) | 6.05093 | 0.449762 | 0.224881 | − | 0.974386i | \(-0.427801\pi\) | ||||
0.224881 | + | 0.974386i | \(0.427801\pi\) | |||||||
\(182\) | 2.02503 | 0.150105 | ||||||||
\(183\) | −1.00000 | −0.0739221 | ||||||||
\(184\) | −7.11919 | −0.524833 | ||||||||
\(185\) | −24.5943 | −1.80821 | ||||||||
\(186\) | 7.11721 | 0.521859 | ||||||||
\(187\) | −4.97299 | −0.363661 | ||||||||
\(188\) | −5.59372 | −0.407964 | ||||||||
\(189\) | 0.955570 | 0.0695075 | ||||||||
\(190\) | −18.2170 | −1.32160 | ||||||||
\(191\) | 19.3685 | 1.40145 | 0.700727 | − | 0.713429i | \(-0.252859\pi\) | ||||
0.700727 | + | 0.713429i | \(0.252859\pi\) | |||||||
\(192\) | −1.00000 | −0.0721688 | ||||||||
\(193\) | −0.00563344 | −0.000405504 0 | −0.000202752 | − | 1.00000i | \(-0.500065\pi\) | ||||
−0.000202752 | 1.00000i | \(0.500065\pi\) | ||||||||
\(194\) | 4.37166 | 0.313867 | ||||||||
\(195\) | −4.85381 | −0.347588 | ||||||||
\(196\) | −6.08689 | −0.434778 | ||||||||
\(197\) | −2.81665 | −0.200678 | −0.100339 | − | 0.994953i | \(-0.531993\pi\) | ||||
−0.100339 | + | 0.994953i | \(0.531993\pi\) | |||||||
\(198\) | 1.00000 | 0.0710669 | ||||||||
\(199\) | −5.67941 | −0.402603 | −0.201301 | − | 0.979529i | \(-0.564517\pi\) | ||||
−0.201301 | + | 0.979529i | \(0.564517\pi\) | |||||||
\(200\) | −0.245981 | −0.0173935 | ||||||||
\(201\) | −12.3059 | −0.867988 | ||||||||
\(202\) | −17.8704 | −1.25735 | ||||||||
\(203\) | 6.62073 | 0.464684 | ||||||||
\(204\) | −4.97299 | −0.348179 | ||||||||
\(205\) | 17.5667 | 1.22691 | ||||||||
\(206\) | −6.09868 | −0.424915 | ||||||||
\(207\) | 7.11919 | 0.494818 | ||||||||
\(208\) | 2.11919 | 0.146939 | ||||||||
\(209\) | −7.95360 | −0.550162 | ||||||||
\(210\) | −2.18865 | −0.151031 | ||||||||
\(211\) | 25.9408 | 1.78584 | 0.892921 | − | 0.450214i | \(-0.148652\pi\) | ||||
0.892921 | + | 0.450214i | \(0.148652\pi\) | |||||||
\(212\) | 8.21368 | 0.564118 | ||||||||
\(213\) | 4.85183 | 0.332442 | ||||||||
\(214\) | 16.4577 | 1.12502 | ||||||||
\(215\) | −8.11721 | −0.553589 | ||||||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | −6.80100 | −0.461682 | ||||||||
\(218\) | −6.53528 | −0.442625 | ||||||||
\(219\) | 9.48633 | 0.641027 | ||||||||
\(220\) | −2.29041 | −0.154419 | ||||||||
\(221\) | 10.5387 | 0.708910 | ||||||||
\(222\) | −10.7379 | −0.720684 | ||||||||
\(223\) | −13.9319 | −0.932948 | −0.466474 | − | 0.884535i | \(-0.654476\pi\) | ||||
−0.466474 | + | 0.884535i | \(0.654476\pi\) | |||||||
\(224\) | 0.955570 | 0.0638467 | ||||||||
\(225\) | 0.245981 | 0.0163987 | ||||||||
\(226\) | 6.67079 | 0.443735 | ||||||||
\(227\) | 26.5355 | 1.76122 | 0.880612 | − | 0.473837i | \(-0.157131\pi\) | ||||
0.880612 | + | 0.473837i | \(0.157131\pi\) | |||||||
\(228\) | −7.95360 | −0.526740 | ||||||||
\(229\) | −20.9876 | −1.38690 | −0.693449 | − | 0.720505i | \(-0.743910\pi\) | ||||
−0.693449 | + | 0.720505i | \(0.743910\pi\) | |||||||
\(230\) | −16.3059 | −1.07518 | ||||||||
\(231\) | −0.955570 | −0.0628719 | ||||||||
\(232\) | 6.92856 | 0.454883 | ||||||||
\(233\) | 27.3573 | 1.79223 | 0.896117 | − | 0.443817i | \(-0.146376\pi\) | ||||
0.896117 | + | 0.443817i | \(0.146376\pi\) | |||||||
\(234\) | −2.11919 | −0.138536 | ||||||||
\(235\) | −12.8119 | −0.835758 | ||||||||
\(236\) | 4.62525 | 0.301078 | ||||||||
\(237\) | −6.68822 | −0.434446 | ||||||||
\(238\) | 4.75205 | 0.308029 | ||||||||
\(239\) | 15.5679 | 1.00700 | 0.503502 | − | 0.863994i | \(-0.332044\pi\) | ||||
0.503502 | + | 0.863994i | \(0.332044\pi\) | |||||||
\(240\) | −2.29041 | −0.147845 | ||||||||
\(241\) | −19.3688 | −1.24766 | −0.623828 | − | 0.781562i | \(-0.714423\pi\) | ||||
−0.623828 | + | 0.781562i | \(0.714423\pi\) | |||||||
\(242\) | −1.00000 | −0.0642824 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 1.00000 | 0.0640184 | ||||||||
\(245\) | −13.9415 | −0.890688 | ||||||||
\(246\) | 7.66968 | 0.489001 | ||||||||
\(247\) | 16.8552 | 1.07247 | ||||||||
\(248\) | −7.11721 | −0.451943 | ||||||||
\(249\) | 1.24401 | 0.0788357 | ||||||||
\(250\) | 10.8887 | 0.688659 | ||||||||
\(251\) | −1.85183 | −0.116887 | −0.0584434 | − | 0.998291i | \(-0.518614\pi\) | ||||
−0.0584434 | + | 0.998291i | \(0.518614\pi\) | |||||||
\(252\) | −0.955570 | −0.0601953 | ||||||||
\(253\) | −7.11919 | −0.447579 | ||||||||
\(254\) | −9.31544 | −0.584503 | ||||||||
\(255\) | −11.3902 | −0.713282 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 29.4287 | 1.83571 | 0.917856 | − | 0.396913i | \(-0.129919\pi\) | ||||
0.917856 | + | 0.396913i | \(0.129919\pi\) | |||||||
\(258\) | −3.54400 | −0.220640 | ||||||||
\(259\) | 10.2609 | 0.637579 | ||||||||
\(260\) | 4.85381 | 0.301020 | ||||||||
\(261\) | −6.92856 | −0.428867 | ||||||||
\(262\) | −6.88611 | −0.425425 | ||||||||
\(263\) | 30.8588 | 1.90284 | 0.951418 | − | 0.307902i | \(-0.0996270\pi\) | ||||
0.951418 | + | 0.307902i | \(0.0996270\pi\) | |||||||
\(264\) | −1.00000 | −0.0615457 | ||||||||
\(265\) | 18.8127 | 1.15565 | ||||||||
\(266\) | 7.60022 | 0.465999 | ||||||||
\(267\) | 6.29041 | 0.384967 | ||||||||
\(268\) | 12.3059 | 0.751700 | ||||||||
\(269\) | −1.87321 | −0.114211 | −0.0571057 | − | 0.998368i | \(-0.518187\pi\) | ||||
−0.0571057 | + | 0.998368i | \(0.518187\pi\) | |||||||
\(270\) | 2.29041 | 0.139390 | ||||||||
\(271\) | −29.1719 | −1.77207 | −0.886035 | − | 0.463619i | \(-0.846551\pi\) | ||||
−0.886035 | + | 0.463619i | \(0.846551\pi\) | |||||||
\(272\) | 4.97299 | 0.301532 | ||||||||
\(273\) | 2.02503 | 0.122560 | ||||||||
\(274\) | −12.8841 | −0.778359 | ||||||||
\(275\) | −0.245981 | −0.0148332 | ||||||||
\(276\) | −7.11919 | −0.428525 | ||||||||
\(277\) | −15.3837 | −0.924317 | −0.462159 | − | 0.886797i | \(-0.652925\pi\) | ||||
−0.462159 | + | 0.886797i | \(0.652925\pi\) | |||||||
\(278\) | 0.407623 | 0.0244476 | ||||||||
\(279\) | 7.11721 | 0.426096 | ||||||||
\(280\) | 2.18865 | 0.130797 | ||||||||
\(281\) | 23.6753 | 1.41235 | 0.706175 | − | 0.708037i | \(-0.250419\pi\) | ||||
0.706175 | + | 0.708037i | \(0.250419\pi\) | |||||||
\(282\) | −5.59372 | −0.333101 | ||||||||
\(283\) | 7.17969 | 0.426788 | 0.213394 | − | 0.976966i | \(-0.431548\pi\) | ||||
0.213394 | + | 0.976966i | \(0.431548\pi\) | |||||||
\(284\) | −4.85183 | −0.287903 | ||||||||
\(285\) | −18.2170 | −1.07908 | ||||||||
\(286\) | 2.11919 | 0.125310 | ||||||||
\(287\) | −7.32892 | −0.432612 | ||||||||
\(288\) | −1.00000 | −0.0589256 | ||||||||
\(289\) | 7.73067 | 0.454745 | ||||||||
\(290\) | 15.8693 | 0.931875 | ||||||||
\(291\) | 4.37166 | 0.256271 | ||||||||
\(292\) | −9.48633 | −0.555145 | ||||||||
\(293\) | 14.8090 | 0.865153 | 0.432577 | − | 0.901597i | \(-0.357604\pi\) | ||||
0.432577 | + | 0.901597i | \(0.357604\pi\) | |||||||
\(294\) | −6.08689 | −0.354994 | ||||||||
\(295\) | 10.5937 | 0.616790 | ||||||||
\(296\) | 10.7379 | 0.624130 | ||||||||
\(297\) | 1.00000 | 0.0580259 | ||||||||
\(298\) | 6.54169 | 0.378950 | ||||||||
\(299\) | 15.0869 | 0.872497 | ||||||||
\(300\) | −0.245981 | −0.0142017 | ||||||||
\(301\) | 3.38654 | 0.195197 | ||||||||
\(302\) | 23.2854 | 1.33992 | ||||||||
\(303\) | −17.8704 | −1.02663 | ||||||||
\(304\) | 7.95360 | 0.456170 | ||||||||
\(305\) | 2.29041 | 0.131149 | ||||||||
\(306\) | −4.97299 | −0.284287 | ||||||||
\(307\) | 18.6245 | 1.06296 | 0.531478 | − | 0.847072i | \(-0.321637\pi\) | ||||
0.531478 | + | 0.847072i | \(0.321637\pi\) | |||||||
\(308\) | 0.955570 | 0.0544487 | ||||||||
\(309\) | −6.09868 | −0.346942 | ||||||||
\(310\) | −16.3013 | −0.925854 | ||||||||
\(311\) | 4.09647 | 0.232289 | 0.116145 | − | 0.993232i | \(-0.462946\pi\) | ||||
0.116145 | + | 0.993232i | \(0.462946\pi\) | |||||||
\(312\) | 2.11919 | 0.119975 | ||||||||
\(313\) | −19.5465 | −1.10484 | −0.552418 | − | 0.833567i | \(-0.686295\pi\) | ||||
−0.552418 | + | 0.833567i | \(0.686295\pi\) | |||||||
\(314\) | 19.0675 | 1.07604 | ||||||||
\(315\) | −2.18865 | −0.123316 | ||||||||
\(316\) | 6.68822 | 0.376242 | ||||||||
\(317\) | −7.28921 | −0.409403 | −0.204701 | − | 0.978824i | \(-0.565622\pi\) | ||||
−0.204701 | + | 0.978824i | \(0.565622\pi\) | |||||||
\(318\) | 8.21368 | 0.460600 | ||||||||
\(319\) | 6.92856 | 0.387925 | ||||||||
\(320\) | 2.29041 | 0.128038 | ||||||||
\(321\) | 16.4577 | 0.918578 | ||||||||
\(322\) | 6.80288 | 0.379110 | ||||||||
\(323\) | 39.5532 | 2.20080 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 0.521279 | 0.0289154 | ||||||||
\(326\) | −14.3786 | −0.796359 | ||||||||
\(327\) | −6.53528 | −0.361402 | ||||||||
\(328\) | −7.66968 | −0.423487 | ||||||||
\(329\) | 5.34520 | 0.294690 | ||||||||
\(330\) | −2.29041 | −0.126083 | ||||||||
\(331\) | 12.2209 | 0.671724 | 0.335862 | − | 0.941911i | \(-0.390972\pi\) | ||||
0.335862 | + | 0.941911i | \(0.390972\pi\) | |||||||
\(332\) | −1.24401 | −0.0682737 | ||||||||
\(333\) | −10.7379 | −0.588436 | ||||||||
\(334\) | 9.78237 | 0.535268 | ||||||||
\(335\) | 28.1855 | 1.53994 | ||||||||
\(336\) | 0.955570 | 0.0521306 | ||||||||
\(337\) | −15.3770 | −0.837636 | −0.418818 | − | 0.908070i | \(-0.637556\pi\) | ||||
−0.418818 | + | 0.908070i | \(0.637556\pi\) | |||||||
\(338\) | 8.50905 | 0.462831 | ||||||||
\(339\) | 6.67079 | 0.362308 | ||||||||
\(340\) | 11.3902 | 0.617720 | ||||||||
\(341\) | −7.11721 | −0.385419 | ||||||||
\(342\) | −7.95360 | −0.430081 | ||||||||
\(343\) | 12.5054 | 0.675230 | ||||||||
\(344\) | 3.54400 | 0.191080 | ||||||||
\(345\) | −16.3059 | −0.877878 | ||||||||
\(346\) | −9.17089 | −0.493030 | ||||||||
\(347\) | 20.4399 | 1.09727 | 0.548636 | − | 0.836061i | \(-0.315147\pi\) | ||||
0.548636 | + | 0.836061i | \(0.315147\pi\) | |||||||
\(348\) | 6.92856 | 0.371410 | ||||||||
\(349\) | 19.9050 | 1.06549 | 0.532744 | − | 0.846276i | \(-0.321161\pi\) | ||||
0.532744 | + | 0.846276i | \(0.321161\pi\) | |||||||
\(350\) | 0.235052 | 0.0125641 | ||||||||
\(351\) | −2.11919 | −0.113114 | ||||||||
\(352\) | 1.00000 | 0.0533002 | ||||||||
\(353\) | −26.1923 | −1.39408 | −0.697038 | − | 0.717034i | \(-0.745499\pi\) | ||||
−0.697038 | + | 0.717034i | \(0.745499\pi\) | |||||||
\(354\) | 4.62525 | 0.245829 | ||||||||
\(355\) | −11.1127 | −0.589800 | ||||||||
\(356\) | −6.29041 | −0.333391 | ||||||||
\(357\) | 4.75205 | 0.251505 | ||||||||
\(358\) | −9.93222 | −0.524934 | ||||||||
\(359\) | 29.1045 | 1.53608 | 0.768040 | − | 0.640402i | \(-0.221232\pi\) | ||||
0.768040 | + | 0.640402i | \(0.221232\pi\) | |||||||
\(360\) | −2.29041 | −0.120715 | ||||||||
\(361\) | 44.2597 | 2.32946 | ||||||||
\(362\) | −6.05093 | −0.318030 | ||||||||
\(363\) | −1.00000 | −0.0524864 | ||||||||
\(364\) | −2.02503 | −0.106140 | ||||||||
\(365\) | −21.7276 | −1.13727 | ||||||||
\(366\) | 1.00000 | 0.0522708 | ||||||||
\(367\) | 8.26229 | 0.431288 | 0.215644 | − | 0.976472i | \(-0.430815\pi\) | ||||
0.215644 | + | 0.976472i | \(0.430815\pi\) | |||||||
\(368\) | 7.11919 | 0.371113 | ||||||||
\(369\) | 7.66968 | 0.399268 | ||||||||
\(370\) | 24.5943 | 1.27860 | ||||||||
\(371\) | −7.84875 | −0.407487 | ||||||||
\(372\) | −7.11721 | −0.369010 | ||||||||
\(373\) | −24.0005 | −1.24270 | −0.621349 | − | 0.783534i | \(-0.713415\pi\) | ||||
−0.621349 | + | 0.783534i | \(0.713415\pi\) | |||||||
\(374\) | 4.97299 | 0.257147 | ||||||||
\(375\) | 10.8887 | 0.562288 | ||||||||
\(376\) | 5.59372 | 0.288474 | ||||||||
\(377\) | −14.6829 | −0.756209 | ||||||||
\(378\) | −0.955570 | −0.0491492 | ||||||||
\(379\) | −12.3500 | −0.634374 | −0.317187 | − | 0.948363i | \(-0.602738\pi\) | ||||
−0.317187 | + | 0.948363i | \(0.602738\pi\) | |||||||
\(380\) | 18.2170 | 0.934512 | ||||||||
\(381\) | −9.31544 | −0.477245 | ||||||||
\(382\) | −19.3685 | −0.990978 | ||||||||
\(383\) | −30.4079 | −1.55377 | −0.776884 | − | 0.629643i | \(-0.783201\pi\) | ||||
−0.776884 | + | 0.629643i | \(0.783201\pi\) | |||||||
\(384\) | 1.00000 | 0.0510310 | ||||||||
\(385\) | 2.18865 | 0.111544 | ||||||||
\(386\) | 0.00563344 | 0.000286734 0 | ||||||||
\(387\) | −3.54400 | −0.180152 | ||||||||
\(388\) | −4.37166 | −0.221938 | ||||||||
\(389\) | −24.1891 | −1.22644 | −0.613219 | − | 0.789913i | \(-0.710126\pi\) | ||||
−0.613219 | + | 0.789913i | \(0.710126\pi\) | |||||||
\(390\) | 4.85381 | 0.245782 | ||||||||
\(391\) | 35.4037 | 1.79044 | ||||||||
\(392\) | 6.08689 | 0.307434 | ||||||||
\(393\) | −6.88611 | −0.347358 | ||||||||
\(394\) | 2.81665 | 0.141901 | ||||||||
\(395\) | 15.3188 | 0.770771 | ||||||||
\(396\) | −1.00000 | −0.0502519 | ||||||||
\(397\) | 21.8667 | 1.09746 | 0.548729 | − | 0.836000i | \(-0.315112\pi\) | ||||
0.548729 | + | 0.836000i | \(0.315112\pi\) | |||||||
\(398\) | 5.67941 | 0.284683 | ||||||||
\(399\) | 7.60022 | 0.380487 | ||||||||
\(400\) | 0.245981 | 0.0122990 | ||||||||
\(401\) | 11.0868 | 0.553648 | 0.276824 | − | 0.960921i | \(-0.410718\pi\) | ||||
0.276824 | + | 0.960921i | \(0.410718\pi\) | |||||||
\(402\) | 12.3059 | 0.613761 | ||||||||
\(403\) | 15.0827 | 0.751323 | ||||||||
\(404\) | 17.8704 | 0.889084 | ||||||||
\(405\) | 2.29041 | 0.113811 | ||||||||
\(406\) | −6.62073 | −0.328581 | ||||||||
\(407\) | 10.7379 | 0.532260 | ||||||||
\(408\) | 4.97299 | 0.246200 | ||||||||
\(409\) | 6.66232 | 0.329431 | 0.164715 | − | 0.986341i | \(-0.447329\pi\) | ||||
0.164715 | + | 0.986341i | \(0.447329\pi\) | |||||||
\(410\) | −17.5667 | −0.867558 | ||||||||
\(411\) | −12.8841 | −0.635527 | ||||||||
\(412\) | 6.09868 | 0.300460 | ||||||||
\(413\) | −4.41975 | −0.217482 | ||||||||
\(414\) | −7.11919 | −0.349889 | ||||||||
\(415\) | −2.84929 | −0.139866 | ||||||||
\(416\) | −2.11919 | −0.103902 | ||||||||
\(417\) | 0.407623 | 0.0199614 | ||||||||
\(418\) | 7.95360 | 0.389023 | ||||||||
\(419\) | 16.5348 | 0.807776 | 0.403888 | − | 0.914809i | \(-0.367659\pi\) | ||||
0.403888 | + | 0.914809i | \(0.367659\pi\) | |||||||
\(420\) | 2.18865 | 0.106795 | ||||||||
\(421\) | 20.0115 | 0.975301 | 0.487650 | − | 0.873039i | \(-0.337854\pi\) | ||||
0.487650 | + | 0.873039i | \(0.337854\pi\) | |||||||
\(422\) | −25.9408 | −1.26278 | ||||||||
\(423\) | −5.59372 | −0.271976 | ||||||||
\(424\) | −8.21368 | −0.398892 | ||||||||
\(425\) | 1.22326 | 0.0593369 | ||||||||
\(426\) | −4.85183 | −0.235072 | ||||||||
\(427\) | −0.955570 | −0.0462433 | ||||||||
\(428\) | −16.4577 | −0.795512 | ||||||||
\(429\) | 2.11919 | 0.102315 | ||||||||
\(430\) | 8.11721 | 0.391447 | ||||||||
\(431\) | 1.25411 | 0.0604085 | 0.0302042 | − | 0.999544i | \(-0.490384\pi\) | ||||
0.0302042 | + | 0.999544i | \(0.490384\pi\) | |||||||
\(432\) | −1.00000 | −0.0481125 | ||||||||
\(433\) | −18.6548 | −0.896493 | −0.448246 | − | 0.893910i | \(-0.647951\pi\) | ||||
−0.448246 | + | 0.893910i | \(0.647951\pi\) | |||||||
\(434\) | 6.80100 | 0.326458 | ||||||||
\(435\) | 15.8693 | 0.760873 | ||||||||
\(436\) | 6.53528 | 0.312983 | ||||||||
\(437\) | 56.6231 | 2.70865 | ||||||||
\(438\) | −9.48633 | −0.453274 | ||||||||
\(439\) | 11.2330 | 0.536121 | 0.268061 | − | 0.963402i | \(-0.413617\pi\) | ||||
0.268061 | + | 0.963402i | \(0.413617\pi\) | |||||||
\(440\) | 2.29041 | 0.109191 | ||||||||
\(441\) | −6.08689 | −0.289852 | ||||||||
\(442\) | −10.5387 | −0.501275 | ||||||||
\(443\) | −39.3617 | −1.87013 | −0.935066 | − | 0.354475i | \(-0.884660\pi\) | ||||
−0.935066 | + | 0.354475i | \(0.884660\pi\) | |||||||
\(444\) | 10.7379 | 0.509600 | ||||||||
\(445\) | −14.4076 | −0.682987 | ||||||||
\(446\) | 13.9319 | 0.659694 | ||||||||
\(447\) | 6.54169 | 0.309411 | ||||||||
\(448\) | −0.955570 | −0.0451464 | ||||||||
\(449\) | 7.53196 | 0.355455 | 0.177728 | − | 0.984080i | \(-0.443125\pi\) | ||||
0.177728 | + | 0.984080i | \(0.443125\pi\) | |||||||
\(450\) | −0.245981 | −0.0115956 | ||||||||
\(451\) | −7.66968 | −0.361151 | ||||||||
\(452\) | −6.67079 | −0.313768 | ||||||||
\(453\) | 23.2854 | 1.09404 | ||||||||
\(454\) | −26.5355 | −1.24537 | ||||||||
\(455\) | −4.63815 | −0.217440 | ||||||||
\(456\) | 7.95360 | 0.372461 | ||||||||
\(457\) | 3.25494 | 0.152259 | 0.0761297 | − | 0.997098i | \(-0.475744\pi\) | ||||
0.0761297 | + | 0.997098i | \(0.475744\pi\) | |||||||
\(458\) | 20.9876 | 0.980685 | ||||||||
\(459\) | −4.97299 | −0.232119 | ||||||||
\(460\) | 16.3059 | 0.760265 | ||||||||
\(461\) | −10.6567 | −0.496332 | −0.248166 | − | 0.968718i | \(-0.579828\pi\) | ||||
−0.248166 | + | 0.968718i | \(0.579828\pi\) | |||||||
\(462\) | 0.955570 | 0.0444571 | ||||||||
\(463\) | −26.9484 | −1.25240 | −0.626200 | − | 0.779662i | \(-0.715391\pi\) | ||||
−0.626200 | + | 0.779662i | \(0.715391\pi\) | |||||||
\(464\) | −6.92856 | −0.321651 | ||||||||
\(465\) | −16.3013 | −0.755957 | ||||||||
\(466\) | −27.3573 | −1.26730 | ||||||||
\(467\) | −36.6878 | −1.69771 | −0.848855 | − | 0.528626i | \(-0.822708\pi\) | ||||
−0.848855 | + | 0.528626i | \(0.822708\pi\) | |||||||
\(468\) | 2.11919 | 0.0979594 | ||||||||
\(469\) | −11.7591 | −0.542985 | ||||||||
\(470\) | 12.8119 | 0.590970 | ||||||||
\(471\) | 19.0675 | 0.878583 | ||||||||
\(472\) | −4.62525 | −0.212894 | ||||||||
\(473\) | 3.54400 | 0.162953 | ||||||||
\(474\) | 6.68822 | 0.307200 | ||||||||
\(475\) | 1.95643 | 0.0897673 | ||||||||
\(476\) | −4.75205 | −0.217810 | ||||||||
\(477\) | 8.21368 | 0.376079 | ||||||||
\(478\) | −15.5679 | −0.712060 | ||||||||
\(479\) | 37.7824 | 1.72632 | 0.863160 | − | 0.504930i | \(-0.168482\pi\) | ||||
0.863160 | + | 0.504930i | \(0.168482\pi\) | |||||||
\(480\) | 2.29041 | 0.104542 | ||||||||
\(481\) | −22.7557 | −1.03757 | ||||||||
\(482\) | 19.3688 | 0.882226 | ||||||||
\(483\) | 6.80288 | 0.309542 | ||||||||
\(484\) | 1.00000 | 0.0454545 | ||||||||
\(485\) | −10.0129 | −0.454662 | ||||||||
\(486\) | 1.00000 | 0.0453609 | ||||||||
\(487\) | −29.7214 | −1.34681 | −0.673403 | − | 0.739275i | \(-0.735168\pi\) | ||||
−0.673403 | + | 0.739275i | \(0.735168\pi\) | |||||||
\(488\) | −1.00000 | −0.0452679 | ||||||||
\(489\) | −14.3786 | −0.650225 | ||||||||
\(490\) | 13.9415 | 0.629811 | ||||||||
\(491\) | 1.92302 | 0.0867846 | 0.0433923 | − | 0.999058i | \(-0.486183\pi\) | ||||
0.0433923 | + | 0.999058i | \(0.486183\pi\) | |||||||
\(492\) | −7.66968 | −0.345776 | ||||||||
\(493\) | −34.4557 | −1.55181 | ||||||||
\(494\) | −16.8552 | −0.758349 | ||||||||
\(495\) | −2.29041 | −0.102946 | ||||||||
\(496\) | 7.11721 | 0.319572 | ||||||||
\(497\) | 4.63627 | 0.207965 | ||||||||
\(498\) | −1.24401 | −0.0557453 | ||||||||
\(499\) | 7.49173 | 0.335376 | 0.167688 | − | 0.985840i | \(-0.446370\pi\) | ||||
0.167688 | + | 0.985840i | \(0.446370\pi\) | |||||||
\(500\) | −10.8887 | −0.486956 | ||||||||
\(501\) | 9.78237 | 0.437044 | ||||||||
\(502\) | 1.85183 | 0.0826514 | ||||||||
\(503\) | 20.4948 | 0.913820 | 0.456910 | − | 0.889513i | \(-0.348956\pi\) | ||||
0.456910 | + | 0.889513i | \(0.348956\pi\) | |||||||
\(504\) | 0.955570 | 0.0425645 | ||||||||
\(505\) | 40.9305 | 1.82138 | ||||||||
\(506\) | 7.11919 | 0.316486 | ||||||||
\(507\) | 8.50905 | 0.377900 | ||||||||
\(508\) | 9.31544 | 0.413306 | ||||||||
\(509\) | 13.9642 | 0.618952 | 0.309476 | − | 0.950907i | \(-0.399846\pi\) | ||||
0.309476 | + | 0.950907i | \(0.399846\pi\) | |||||||
\(510\) | 11.3902 | 0.504366 | ||||||||
\(511\) | 9.06485 | 0.401005 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −7.95360 | −0.351160 | ||||||||
\(514\) | −29.4287 | −1.29804 | ||||||||
\(515\) | 13.9685 | 0.615524 | ||||||||
\(516\) | 3.54400 | 0.156016 | ||||||||
\(517\) | 5.59372 | 0.246012 | ||||||||
\(518\) | −10.2609 | −0.450836 | ||||||||
\(519\) | −9.17089 | −0.402557 | ||||||||
\(520\) | −4.85381 | −0.212854 | ||||||||
\(521\) | 24.1931 | 1.05992 | 0.529959 | − | 0.848023i | \(-0.322207\pi\) | ||||
0.529959 | + | 0.848023i | \(0.322207\pi\) | |||||||
\(522\) | 6.92856 | 0.303255 | ||||||||
\(523\) | −2.36594 | −0.103455 | −0.0517277 | − | 0.998661i | \(-0.516473\pi\) | ||||
−0.0517277 | + | 0.998661i | \(0.516473\pi\) | |||||||
\(524\) | 6.88611 | 0.300821 | ||||||||
\(525\) | 0.235052 | 0.0102585 | ||||||||
\(526\) | −30.8588 | −1.34551 | ||||||||
\(527\) | 35.3939 | 1.54178 | ||||||||
\(528\) | 1.00000 | 0.0435194 | ||||||||
\(529\) | 27.6828 | 1.20360 | ||||||||
\(530\) | −18.8127 | −0.817171 | ||||||||
\(531\) | 4.62525 | 0.200719 | ||||||||
\(532\) | −7.60022 | −0.329511 | ||||||||
\(533\) | 16.2535 | 0.704017 | ||||||||
\(534\) | −6.29041 | −0.272213 | ||||||||
\(535\) | −37.6949 | −1.62969 | ||||||||
\(536\) | −12.3059 | −0.531532 | ||||||||
\(537\) | −9.93222 | −0.428607 | ||||||||
\(538\) | 1.87321 | 0.0807596 | ||||||||
\(539\) | 6.08689 | 0.262181 | ||||||||
\(540\) | −2.29041 | −0.0985636 | ||||||||
\(541\) | 3.12328 | 0.134280 | 0.0671402 | − | 0.997744i | \(-0.478613\pi\) | ||||
0.0671402 | + | 0.997744i | \(0.478613\pi\) | |||||||
\(542\) | 29.1719 | 1.25304 | ||||||||
\(543\) | −6.05093 | −0.259670 | ||||||||
\(544\) | −4.97299 | −0.213215 | ||||||||
\(545\) | 14.9685 | 0.641179 | ||||||||
\(546\) | −2.02503 | −0.0866634 | ||||||||
\(547\) | −20.0242 | −0.856171 | −0.428086 | − | 0.903738i | \(-0.640812\pi\) | ||||
−0.428086 | + | 0.903738i | \(0.640812\pi\) | |||||||
\(548\) | 12.8841 | 0.550383 | ||||||||
\(549\) | 1.00000 | 0.0426790 | ||||||||
\(550\) | 0.245981 | 0.0104887 | ||||||||
\(551\) | −55.1070 | −2.34764 | ||||||||
\(552\) | 7.11919 | 0.303013 | ||||||||
\(553\) | −6.39106 | −0.271776 | ||||||||
\(554\) | 15.3837 | 0.653591 | ||||||||
\(555\) | 24.5943 | 1.04397 | ||||||||
\(556\) | −0.407623 | −0.0172871 | ||||||||
\(557\) | 29.0440 | 1.23064 | 0.615318 | − | 0.788279i | \(-0.289028\pi\) | ||||
0.615318 | + | 0.788279i | \(0.289028\pi\) | |||||||
\(558\) | −7.11721 | −0.301296 | ||||||||
\(559\) | −7.51040 | −0.317656 | ||||||||
\(560\) | −2.18865 | −0.0924873 | ||||||||
\(561\) | 4.97299 | 0.209960 | ||||||||
\(562\) | −23.6753 | −0.998683 | ||||||||
\(563\) | −33.0798 | −1.39415 | −0.697073 | − | 0.717000i | \(-0.745515\pi\) | ||||
−0.697073 | + | 0.717000i | \(0.745515\pi\) | |||||||
\(564\) | 5.59372 | 0.235538 | ||||||||
\(565\) | −15.2789 | −0.642786 | ||||||||
\(566\) | −7.17969 | −0.301785 | ||||||||
\(567\) | −0.955570 | −0.0401302 | ||||||||
\(568\) | 4.85183 | 0.203578 | ||||||||
\(569\) | −38.4897 | −1.61357 | −0.806786 | − | 0.590844i | \(-0.798795\pi\) | ||||
−0.806786 | + | 0.590844i | \(0.798795\pi\) | |||||||
\(570\) | 18.2170 | 0.763026 | ||||||||
\(571\) | 14.9702 | 0.626482 | 0.313241 | − | 0.949674i | \(-0.398585\pi\) | ||||
0.313241 | + | 0.949674i | \(0.398585\pi\) | |||||||
\(572\) | −2.11919 | −0.0886076 | ||||||||
\(573\) | −19.3685 | −0.809130 | ||||||||
\(574\) | 7.32892 | 0.305903 | ||||||||
\(575\) | 1.75118 | 0.0730294 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | −26.9110 | −1.12032 | −0.560161 | − | 0.828384i | \(-0.689261\pi\) | ||||
−0.560161 | + | 0.828384i | \(0.689261\pi\) | |||||||
\(578\) | −7.73067 | −0.321554 | ||||||||
\(579\) | 0.00563344 | 0.000234118 0 | ||||||||
\(580\) | −15.8693 | −0.658935 | ||||||||
\(581\) | 1.18874 | 0.0493171 | ||||||||
\(582\) | −4.37166 | −0.181211 | ||||||||
\(583\) | −8.21368 | −0.340176 | ||||||||
\(584\) | 9.48633 | 0.392547 | ||||||||
\(585\) | 4.85381 | 0.200680 | ||||||||
\(586\) | −14.8090 | −0.611756 | ||||||||
\(587\) | 8.62130 | 0.355839 | 0.177920 | − | 0.984045i | \(-0.443063\pi\) | ||||
0.177920 | + | 0.984045i | \(0.443063\pi\) | |||||||
\(588\) | 6.08689 | 0.251019 | ||||||||
\(589\) | 56.6074 | 2.33247 | ||||||||
\(590\) | −10.5937 | −0.436137 | ||||||||
\(591\) | 2.81665 | 0.115861 | ||||||||
\(592\) | −10.7379 | −0.441327 | ||||||||
\(593\) | 17.9932 | 0.738893 | 0.369446 | − | 0.929252i | \(-0.379547\pi\) | ||||
0.369446 | + | 0.929252i | \(0.379547\pi\) | |||||||
\(594\) | −1.00000 | −0.0410305 | ||||||||
\(595\) | −10.8841 | −0.446206 | ||||||||
\(596\) | −6.54169 | −0.267958 | ||||||||
\(597\) | 5.67941 | 0.232443 | ||||||||
\(598\) | −15.0869 | −0.616949 | ||||||||
\(599\) | −7.62275 | −0.311457 | −0.155729 | − | 0.987800i | \(-0.549773\pi\) | ||||
−0.155729 | + | 0.987800i | \(0.549773\pi\) | |||||||
\(600\) | 0.245981 | 0.0100421 | ||||||||
\(601\) | 23.9940 | 0.978735 | 0.489368 | − | 0.872078i | \(-0.337228\pi\) | ||||
0.489368 | + | 0.872078i | \(0.337228\pi\) | |||||||
\(602\) | −3.38654 | −0.138025 | ||||||||
\(603\) | 12.3059 | 0.501133 | ||||||||
\(604\) | −23.2854 | −0.947467 | ||||||||
\(605\) | 2.29041 | 0.0931184 | ||||||||
\(606\) | 17.8704 | 0.725934 | ||||||||
\(607\) | 46.4708 | 1.88619 | 0.943096 | − | 0.332520i | \(-0.107899\pi\) | ||||
0.943096 | + | 0.332520i | \(0.107899\pi\) | |||||||
\(608\) | −7.95360 | −0.322561 | ||||||||
\(609\) | −6.62073 | −0.268286 | ||||||||
\(610\) | −2.29041 | −0.0927360 | ||||||||
\(611\) | −11.8541 | −0.479567 | ||||||||
\(612\) | 4.97299 | 0.201021 | ||||||||
\(613\) | 19.3828 | 0.782866 | 0.391433 | − | 0.920207i | \(-0.371980\pi\) | ||||
0.391433 | + | 0.920207i | \(0.371980\pi\) | |||||||
\(614\) | −18.6245 | −0.751623 | ||||||||
\(615\) | −17.5667 | −0.708358 | ||||||||
\(616\) | −0.955570 | −0.0385010 | ||||||||
\(617\) | 30.1621 | 1.21428 | 0.607141 | − | 0.794594i | \(-0.292316\pi\) | ||||
0.607141 | + | 0.794594i | \(0.292316\pi\) | |||||||
\(618\) | 6.09868 | 0.245325 | ||||||||
\(619\) | −8.45291 | −0.339751 | −0.169876 | − | 0.985466i | \(-0.554337\pi\) | ||||
−0.169876 | + | 0.985466i | \(0.554337\pi\) | |||||||
\(620\) | 16.3013 | 0.654678 | ||||||||
\(621\) | −7.11919 | −0.285683 | ||||||||
\(622\) | −4.09647 | −0.164253 | ||||||||
\(623\) | 6.01093 | 0.240823 | ||||||||
\(624\) | −2.11919 | −0.0848354 | ||||||||
\(625\) | −26.1694 | −1.04678 | ||||||||
\(626\) | 19.5465 | 0.781237 | ||||||||
\(627\) | 7.95360 | 0.317636 | ||||||||
\(628\) | −19.0675 | −0.760876 | ||||||||
\(629\) | −53.3997 | −2.12919 | ||||||||
\(630\) | 2.18865 | 0.0871978 | ||||||||
\(631\) | 19.3634 | 0.770846 | 0.385423 | − | 0.922740i | \(-0.374056\pi\) | ||||
0.385423 | + | 0.922740i | \(0.374056\pi\) | |||||||
\(632\) | −6.68822 | −0.266043 | ||||||||
\(633\) | −25.9408 | −1.03106 | ||||||||
\(634\) | 7.28921 | 0.289492 | ||||||||
\(635\) | 21.3362 | 0.846701 | ||||||||
\(636\) | −8.21368 | −0.325694 | ||||||||
\(637\) | −12.8992 | −0.511087 | ||||||||
\(638\) | −6.92856 | −0.274304 | ||||||||
\(639\) | −4.85183 | −0.191936 | ||||||||
\(640\) | −2.29041 | −0.0905364 | ||||||||
\(641\) | 10.1198 | 0.399706 | 0.199853 | − | 0.979826i | \(-0.435953\pi\) | ||||
0.199853 | + | 0.979826i | \(0.435953\pi\) | |||||||
\(642\) | −16.4577 | −0.649533 | ||||||||
\(643\) | 20.7190 | 0.817076 | 0.408538 | − | 0.912741i | \(-0.366039\pi\) | ||||
0.408538 | + | 0.912741i | \(0.366039\pi\) | |||||||
\(644\) | −6.80288 | −0.268071 | ||||||||
\(645\) | 8.11721 | 0.319615 | ||||||||
\(646\) | −39.5532 | −1.55620 | ||||||||
\(647\) | −37.3438 | −1.46814 | −0.734069 | − | 0.679075i | \(-0.762381\pi\) | ||||
−0.734069 | + | 0.679075i | \(0.762381\pi\) | |||||||
\(648\) | −1.00000 | −0.0392837 | ||||||||
\(649\) | −4.62525 | −0.181557 | ||||||||
\(650\) | −0.521279 | −0.0204463 | ||||||||
\(651\) | 6.80100 | 0.266552 | ||||||||
\(652\) | 14.3786 | 0.563111 | ||||||||
\(653\) | 21.0253 | 0.822783 | 0.411391 | − | 0.911459i | \(-0.365043\pi\) | ||||
0.411391 | + | 0.911459i | \(0.365043\pi\) | |||||||
\(654\) | 6.53528 | 0.255550 | ||||||||
\(655\) | 15.7720 | 0.616264 | ||||||||
\(656\) | 7.66968 | 0.299451 | ||||||||
\(657\) | −9.48633 | −0.370097 | ||||||||
\(658\) | −5.34520 | −0.208377 | ||||||||
\(659\) | 22.4802 | 0.875703 | 0.437852 | − | 0.899047i | \(-0.355740\pi\) | ||||
0.437852 | + | 0.899047i | \(0.355740\pi\) | |||||||
\(660\) | 2.29041 | 0.0891541 | ||||||||
\(661\) | 23.9508 | 0.931580 | 0.465790 | − | 0.884895i | \(-0.345770\pi\) | ||||
0.465790 | + | 0.884895i | \(0.345770\pi\) | |||||||
\(662\) | −12.2209 | −0.474981 | ||||||||
\(663\) | −10.5387 | −0.409289 | ||||||||
\(664\) | 1.24401 | 0.0482768 | ||||||||
\(665\) | −17.4076 | −0.675039 | ||||||||
\(666\) | 10.7379 | 0.416087 | ||||||||
\(667\) | −49.3257 | −1.90990 | ||||||||
\(668\) | −9.78237 | −0.378491 | ||||||||
\(669\) | 13.9319 | 0.538638 | ||||||||
\(670\) | −28.1855 | −1.08890 | ||||||||
\(671\) | −1.00000 | −0.0386046 | ||||||||
\(672\) | −0.955570 | −0.0368619 | ||||||||
\(673\) | −0.0441412 | −0.00170152 | −0.000850760 | − | 1.00000i | \(-0.500271\pi\) | ||||
−0.000850760 | 1.00000i | \(0.500271\pi\) | ||||||||
\(674\) | 15.3770 | 0.592298 | ||||||||
\(675\) | −0.245981 | −0.00946781 | ||||||||
\(676\) | −8.50905 | −0.327271 | ||||||||
\(677\) | −13.9598 | −0.536517 | −0.268258 | − | 0.963347i | \(-0.586448\pi\) | ||||
−0.268258 | + | 0.963347i | \(0.586448\pi\) | |||||||
\(678\) | −6.67079 | −0.256190 | ||||||||
\(679\) | 4.17743 | 0.160315 | ||||||||
\(680\) | −11.3902 | −0.436794 | ||||||||
\(681\) | −26.5355 | −1.01684 | ||||||||
\(682\) | 7.11721 | 0.272532 | ||||||||
\(683\) | −34.4615 | −1.31863 | −0.659317 | − | 0.751865i | \(-0.729154\pi\) | ||||
−0.659317 | + | 0.751865i | \(0.729154\pi\) | |||||||
\(684\) | 7.95360 | 0.304113 | ||||||||
\(685\) | 29.5100 | 1.12752 | ||||||||
\(686\) | −12.5054 | −0.477460 | ||||||||
\(687\) | 20.9876 | 0.800726 | ||||||||
\(688\) | −3.54400 | −0.135114 | ||||||||
\(689\) | 17.4063 | 0.663128 | ||||||||
\(690\) | 16.3059 | 0.620754 | ||||||||
\(691\) | −30.3959 | −1.15632 | −0.578158 | − | 0.815925i | \(-0.696228\pi\) | ||||
−0.578158 | + | 0.815925i | \(0.696228\pi\) | |||||||
\(692\) | 9.17089 | 0.348625 | ||||||||
\(693\) | 0.955570 | 0.0362991 | ||||||||
\(694\) | −20.4399 | −0.775889 | ||||||||
\(695\) | −0.933625 | −0.0354144 | ||||||||
\(696\) | −6.92856 | −0.262627 | ||||||||
\(697\) | 38.1413 | 1.44470 | ||||||||
\(698\) | −19.9050 | −0.753414 | ||||||||
\(699\) | −27.3573 | −1.03475 | ||||||||
\(700\) | −0.235052 | −0.00888413 | ||||||||
\(701\) | 15.7658 | 0.595466 | 0.297733 | − | 0.954649i | \(-0.403769\pi\) | ||||
0.297733 | + | 0.954649i | \(0.403769\pi\) | |||||||
\(702\) | 2.11919 | 0.0799835 | ||||||||
\(703\) | −85.4053 | −3.22112 | ||||||||
\(704\) | −1.00000 | −0.0376889 | ||||||||
\(705\) | 12.8119 | 0.482525 | ||||||||
\(706\) | 26.1923 | 0.985760 | ||||||||
\(707\) | −17.0764 | −0.642224 | ||||||||
\(708\) | −4.62525 | −0.173828 | ||||||||
\(709\) | 30.8310 | 1.15788 | 0.578941 | − | 0.815369i | \(-0.303466\pi\) | ||||
0.578941 | + | 0.815369i | \(0.303466\pi\) | |||||||
\(710\) | 11.1127 | 0.417052 | ||||||||
\(711\) | 6.68822 | 0.250828 | ||||||||
\(712\) | 6.29041 | 0.235743 | ||||||||
\(713\) | 50.6688 | 1.89756 | ||||||||
\(714\) | −4.75205 | −0.177841 | ||||||||
\(715\) | −4.85381 | −0.181522 | ||||||||
\(716\) | 9.93222 | 0.371185 | ||||||||
\(717\) | −15.5679 | −0.581395 | ||||||||
\(718\) | −29.1045 | −1.08617 | ||||||||
\(719\) | −25.2408 | −0.941324 | −0.470662 | − | 0.882314i | \(-0.655985\pi\) | ||||
−0.470662 | + | 0.882314i | \(0.655985\pi\) | |||||||
\(720\) | 2.29041 | 0.0853586 | ||||||||
\(721\) | −5.82771 | −0.217035 | ||||||||
\(722\) | −44.2597 | −1.64718 | ||||||||
\(723\) | 19.3688 | 0.720334 | ||||||||
\(724\) | 6.05093 | 0.224881 | ||||||||
\(725\) | −1.70429 | −0.0632959 | ||||||||
\(726\) | 1.00000 | 0.0371135 | ||||||||
\(727\) | −17.9477 | −0.665644 | −0.332822 | − | 0.942990i | \(-0.608001\pi\) | ||||
−0.332822 | + | 0.942990i | \(0.608001\pi\) | |||||||
\(728\) | 2.02503 | 0.0750527 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 21.7276 | 0.804174 | ||||||||
\(731\) | −17.6243 | −0.651858 | ||||||||
\(732\) | −1.00000 | −0.0369611 | ||||||||
\(733\) | −41.0507 | −1.51624 | −0.758122 | − | 0.652113i | \(-0.773883\pi\) | ||||
−0.758122 | + | 0.652113i | \(0.773883\pi\) | |||||||
\(734\) | −8.26229 | −0.304967 | ||||||||
\(735\) | 13.9415 | 0.514239 | ||||||||
\(736\) | −7.11919 | −0.262417 | ||||||||
\(737\) | −12.3059 | −0.453292 | ||||||||
\(738\) | −7.66968 | −0.282325 | ||||||||
\(739\) | −14.1410 | −0.520187 | −0.260093 | − | 0.965583i | \(-0.583753\pi\) | ||||
−0.260093 | + | 0.965583i | \(0.583753\pi\) | |||||||
\(740\) | −24.5943 | −0.904104 | ||||||||
\(741\) | −16.8552 | −0.619190 | ||||||||
\(742\) | 7.84875 | 0.288137 | ||||||||
\(743\) | 11.3843 | 0.417649 | 0.208824 | − | 0.977953i | \(-0.433036\pi\) | ||||
0.208824 | + | 0.977953i | \(0.433036\pi\) | |||||||
\(744\) | 7.11721 | 0.260930 | ||||||||
\(745\) | −14.9831 | −0.548940 | ||||||||
\(746\) | 24.0005 | 0.878720 | ||||||||
\(747\) | −1.24401 | −0.0455158 | ||||||||
\(748\) | −4.97299 | −0.181831 | ||||||||
\(749\) | 15.7265 | 0.574633 | ||||||||
\(750\) | −10.8887 | −0.397598 | ||||||||
\(751\) | 2.99596 | 0.109324 | 0.0546621 | − | 0.998505i | \(-0.482592\pi\) | ||||
0.0546621 | + | 0.998505i | \(0.482592\pi\) | |||||||
\(752\) | −5.59372 | −0.203982 | ||||||||
\(753\) | 1.85183 | 0.0674846 | ||||||||
\(754\) | 14.6829 | 0.534720 | ||||||||
\(755\) | −53.3330 | −1.94099 | ||||||||
\(756\) | 0.955570 | 0.0347538 | ||||||||
\(757\) | −33.5931 | −1.22096 | −0.610481 | − | 0.792031i | \(-0.709024\pi\) | ||||
−0.610481 | + | 0.792031i | \(0.709024\pi\) | |||||||
\(758\) | 12.3500 | 0.448570 | ||||||||
\(759\) | 7.11919 | 0.258410 | ||||||||
\(760\) | −18.2170 | −0.660800 | ||||||||
\(761\) | −4.80683 | −0.174247 | −0.0871237 | − | 0.996197i | \(-0.527768\pi\) | ||||
−0.0871237 | + | 0.996197i | \(0.527768\pi\) | |||||||
\(762\) | 9.31544 | 0.337463 | ||||||||
\(763\) | −6.24492 | −0.226081 | ||||||||
\(764\) | 19.3685 | 0.700727 | ||||||||
\(765\) | 11.3902 | 0.411814 | ||||||||
\(766\) | 30.4079 | 1.09868 | ||||||||
\(767\) | 9.80177 | 0.353921 | ||||||||
\(768\) | −1.00000 | −0.0360844 | ||||||||
\(769\) | −34.5793 | −1.24696 | −0.623481 | − | 0.781838i | \(-0.714282\pi\) | ||||
−0.623481 | + | 0.781838i | \(0.714282\pi\) | |||||||
\(770\) | −2.18865 | −0.0788734 | ||||||||
\(771\) | −29.4287 | −1.05985 | ||||||||
\(772\) | −0.00563344 | −0.000202752 0 | ||||||||
\(773\) | 12.5207 | 0.450340 | 0.225170 | − | 0.974320i | \(-0.427706\pi\) | ||||
0.225170 | + | 0.974320i | \(0.427706\pi\) | |||||||
\(774\) | 3.54400 | 0.127386 | ||||||||
\(775\) | 1.75070 | 0.0628869 | ||||||||
\(776\) | 4.37166 | 0.156934 | ||||||||
\(777\) | −10.2609 | −0.368106 | ||||||||
\(778\) | 24.1891 | 0.867222 | ||||||||
\(779\) | 61.0015 | 2.18561 | ||||||||
\(780\) | −4.85381 | −0.173794 | ||||||||
\(781\) | 4.85183 | 0.173612 | ||||||||
\(782\) | −35.4037 | −1.26603 | ||||||||
\(783\) | 6.92856 | 0.247607 | ||||||||
\(784\) | −6.08689 | −0.217389 | ||||||||
\(785\) | −43.6724 | −1.55873 | ||||||||
\(786\) | 6.88611 | 0.245619 | ||||||||
\(787\) | 15.9069 | 0.567021 | 0.283511 | − | 0.958969i | \(-0.408501\pi\) | ||||
0.283511 | + | 0.958969i | \(0.408501\pi\) | |||||||
\(788\) | −2.81665 | −0.100339 | ||||||||
\(789\) | −30.8588 | −1.09860 | ||||||||
\(790\) | −15.3188 | −0.545017 | ||||||||
\(791\) | 6.37441 | 0.226648 | ||||||||
\(792\) | 1.00000 | 0.0355335 | ||||||||
\(793\) | 2.11919 | 0.0752545 | ||||||||
\(794\) | −21.8667 | −0.776021 | ||||||||
\(795\) | −18.8127 | −0.667218 | ||||||||
\(796\) | −5.67941 | −0.201301 | ||||||||
\(797\) | −54.7388 | −1.93895 | −0.969473 | − | 0.245198i | \(-0.921147\pi\) | ||||
−0.969473 | + | 0.245198i | \(0.921147\pi\) | |||||||
\(798\) | −7.60022 | −0.269045 | ||||||||
\(799\) | −27.8176 | −0.984114 | ||||||||
\(800\) | −0.245981 | −0.00869674 | ||||||||
\(801\) | −6.29041 | −0.222261 | ||||||||
\(802\) | −11.0868 | −0.391488 | ||||||||
\(803\) | 9.48633 | 0.334765 | ||||||||
\(804\) | −12.3059 | −0.433994 | ||||||||
\(805\) | −15.5814 | −0.549172 | ||||||||
\(806\) | −15.0827 | −0.531266 | ||||||||
\(807\) | 1.87321 | 0.0659400 | ||||||||
\(808\) | −17.8704 | −0.628677 | ||||||||
\(809\) | −35.5247 | −1.24898 | −0.624492 | − | 0.781031i | \(-0.714694\pi\) | ||||
−0.624492 | + | 0.781031i | \(0.714694\pi\) | |||||||
\(810\) | −2.29041 | −0.0804768 | ||||||||
\(811\) | 11.4903 | 0.403478 | 0.201739 | − | 0.979439i | \(-0.435341\pi\) | ||||
0.201739 | + | 0.979439i | \(0.435341\pi\) | |||||||
\(812\) | 6.62073 | 0.232342 | ||||||||
\(813\) | 29.1719 | 1.02310 | ||||||||
\(814\) | −10.7379 | −0.376365 | ||||||||
\(815\) | 32.9330 | 1.15359 | ||||||||
\(816\) | −4.97299 | −0.174090 | ||||||||
\(817\) | −28.1875 | −0.986157 | ||||||||
\(818\) | −6.66232 | −0.232943 | ||||||||
\(819\) | −2.02503 | −0.0707603 | ||||||||
\(820\) | 17.5667 | 0.613456 | ||||||||
\(821\) | −18.9077 | −0.659884 | −0.329942 | − | 0.944001i | \(-0.607029\pi\) | ||||
−0.329942 | + | 0.944001i | \(0.607029\pi\) | |||||||
\(822\) | 12.8841 | 0.449386 | ||||||||
\(823\) | −20.2629 | −0.706320 | −0.353160 | − | 0.935563i | \(-0.614893\pi\) | ||||
−0.353160 | + | 0.935563i | \(0.614893\pi\) | |||||||
\(824\) | −6.09868 | −0.212457 | ||||||||
\(825\) | 0.245981 | 0.00856395 | ||||||||
\(826\) | 4.41975 | 0.153783 | ||||||||
\(827\) | 30.9597 | 1.07657 | 0.538287 | − | 0.842761i | \(-0.319071\pi\) | ||||
0.538287 | + | 0.842761i | \(0.319071\pi\) | |||||||
\(828\) | 7.11919 | 0.247409 | ||||||||
\(829\) | 3.63686 | 0.126313 | 0.0631566 | − | 0.998004i | \(-0.479883\pi\) | ||||
0.0631566 | + | 0.998004i | \(0.479883\pi\) | |||||||
\(830\) | 2.84929 | 0.0989002 | ||||||||
\(831\) | 15.3837 | 0.533655 | ||||||||
\(832\) | 2.11919 | 0.0734696 | ||||||||
\(833\) | −30.2700 | −1.04879 | ||||||||
\(834\) | −0.407623 | −0.0141148 | ||||||||
\(835\) | −22.4056 | −0.775379 | ||||||||
\(836\) | −7.95360 | −0.275081 | ||||||||
\(837\) | −7.11721 | −0.246007 | ||||||||
\(838\) | −16.5348 | −0.571184 | ||||||||
\(839\) | −19.3922 | −0.669492 | −0.334746 | − | 0.942308i | \(-0.608651\pi\) | ||||
−0.334746 | + | 0.942308i | \(0.608651\pi\) | |||||||
\(840\) | −2.18865 | −0.0755155 | ||||||||
\(841\) | 19.0050 | 0.655345 | ||||||||
\(842\) | −20.0115 | −0.689642 | ||||||||
\(843\) | −23.6753 | −0.815421 | ||||||||
\(844\) | 25.9408 | 0.892921 | ||||||||
\(845\) | −19.4892 | −0.670449 | ||||||||
\(846\) | 5.59372 | 0.192316 | ||||||||
\(847\) | −0.955570 | −0.0328338 | ||||||||
\(848\) | 8.21368 | 0.282059 | ||||||||
\(849\) | −7.17969 | −0.246406 | ||||||||
\(850\) | −1.22326 | −0.0419575 | ||||||||
\(851\) | −76.4454 | −2.62052 | ||||||||
\(852\) | 4.85183 | 0.166221 | ||||||||
\(853\) | 17.6487 | 0.604282 | 0.302141 | − | 0.953263i | \(-0.402299\pi\) | ||||
0.302141 | + | 0.953263i | \(0.402299\pi\) | |||||||
\(854\) | 0.955570 | 0.0326989 | ||||||||
\(855\) | 18.2170 | 0.623008 | ||||||||
\(856\) | 16.4577 | 0.562512 | ||||||||
\(857\) | −36.9544 | −1.26234 | −0.631169 | − | 0.775645i | \(-0.717425\pi\) | ||||
−0.631169 | + | 0.775645i | \(0.717425\pi\) | |||||||
\(858\) | −2.11919 | −0.0723478 | ||||||||
\(859\) | 34.9450 | 1.19231 | 0.596154 | − | 0.802870i | \(-0.296695\pi\) | ||||
0.596154 | + | 0.802870i | \(0.296695\pi\) | |||||||
\(860\) | −8.11721 | −0.276795 | ||||||||
\(861\) | 7.32892 | 0.249769 | ||||||||
\(862\) | −1.25411 | −0.0427152 | ||||||||
\(863\) | 12.2622 | 0.417410 | 0.208705 | − | 0.977979i | \(-0.433075\pi\) | ||||
0.208705 | + | 0.977979i | \(0.433075\pi\) | |||||||
\(864\) | 1.00000 | 0.0340207 | ||||||||
\(865\) | 21.0051 | 0.714195 | ||||||||
\(866\) | 18.6548 | 0.633916 | ||||||||
\(867\) | −7.73067 | −0.262547 | ||||||||
\(868\) | −6.80100 | −0.230841 | ||||||||
\(869\) | −6.68822 | −0.226882 | ||||||||
\(870\) | −15.8693 | −0.538018 | ||||||||
\(871\) | 26.0784 | 0.883633 | ||||||||
\(872\) | −6.53528 | −0.221312 | ||||||||
\(873\) | −4.37166 | −0.147958 | ||||||||
\(874\) | −56.6231 | −1.91531 | ||||||||
\(875\) | 10.4049 | 0.351749 | ||||||||
\(876\) | 9.48633 | 0.320513 | ||||||||
\(877\) | 11.7653 | 0.397285 | 0.198642 | − | 0.980072i | \(-0.436347\pi\) | ||||
0.198642 | + | 0.980072i | \(0.436347\pi\) | |||||||
\(878\) | −11.2330 | −0.379095 | ||||||||
\(879\) | −14.8090 | −0.499497 | ||||||||
\(880\) | −2.29041 | −0.0772097 | ||||||||
\(881\) | −9.14296 | −0.308034 | −0.154017 | − | 0.988068i | \(-0.549221\pi\) | ||||
−0.154017 | + | 0.988068i | \(0.549221\pi\) | |||||||
\(882\) | 6.08689 | 0.204956 | ||||||||
\(883\) | −34.9399 | −1.17582 | −0.587911 | − | 0.808926i | \(-0.700049\pi\) | ||||
−0.587911 | + | 0.808926i | \(0.700049\pi\) | |||||||
\(884\) | 10.5387 | 0.354455 | ||||||||
\(885\) | −10.5937 | −0.356104 | ||||||||
\(886\) | 39.3617 | 1.32238 | ||||||||
\(887\) | −42.2945 | −1.42011 | −0.710054 | − | 0.704147i | \(-0.751330\pi\) | ||||
−0.710054 | + | 0.704147i | \(0.751330\pi\) | |||||||
\(888\) | −10.7379 | −0.360342 | ||||||||
\(889\) | −8.90156 | −0.298549 | ||||||||
\(890\) | 14.4076 | 0.482945 | ||||||||
\(891\) | −1.00000 | −0.0335013 | ||||||||
\(892\) | −13.9319 | −0.466474 | ||||||||
\(893\) | −44.4902 | −1.48881 | ||||||||
\(894\) | −6.54169 | −0.218787 | ||||||||
\(895\) | 22.7489 | 0.760411 | ||||||||
\(896\) | 0.955570 | 0.0319234 | ||||||||
\(897\) | −15.0869 | −0.503736 | ||||||||
\(898\) | −7.53196 | −0.251345 | ||||||||
\(899\) | −49.3121 | −1.64465 | ||||||||
\(900\) | 0.245981 | 0.00819936 | ||||||||
\(901\) | 40.8466 | 1.36080 | ||||||||
\(902\) | 7.66968 | 0.255372 | ||||||||
\(903\) | −3.38654 | −0.112697 | ||||||||
\(904\) | 6.67079 | 0.221867 | ||||||||
\(905\) | 13.8591 | 0.460692 | ||||||||
\(906\) | −23.2854 | −0.773604 | ||||||||
\(907\) | 25.1262 | 0.834301 | 0.417150 | − | 0.908837i | \(-0.363029\pi\) | ||||
0.417150 | + | 0.908837i | \(0.363029\pi\) | |||||||
\(908\) | 26.5355 | 0.880612 | ||||||||
\(909\) | 17.8704 | 0.592723 | ||||||||
\(910\) | 4.63815 | 0.153753 | ||||||||
\(911\) | 38.5060 | 1.27576 | 0.637881 | − | 0.770135i | \(-0.279811\pi\) | ||||
0.637881 | + | 0.770135i | \(0.279811\pi\) | |||||||
\(912\) | −7.95360 | −0.263370 | ||||||||
\(913\) | 1.24401 | 0.0411706 | ||||||||
\(914\) | −3.25494 | −0.107664 | ||||||||
\(915\) | −2.29041 | −0.0757186 | ||||||||
\(916\) | −20.9876 | −0.693449 | ||||||||
\(917\) | −6.58016 | −0.217296 | ||||||||
\(918\) | 4.97299 | 0.164133 | ||||||||
\(919\) | 45.5184 | 1.50151 | 0.750757 | − | 0.660578i | \(-0.229689\pi\) | ||||
0.750757 | + | 0.660578i | \(0.229689\pi\) | |||||||
\(920\) | −16.3059 | −0.537588 | ||||||||
\(921\) | −18.6245 | −0.613697 | ||||||||
\(922\) | 10.6567 | 0.350959 | ||||||||
\(923\) | −10.2819 | −0.338434 | ||||||||
\(924\) | −0.955570 | −0.0314360 | ||||||||
\(925\) | −2.64133 | −0.0868463 | ||||||||
\(926\) | 26.9484 | 0.885581 | ||||||||
\(927\) | 6.09868 | 0.200307 | ||||||||
\(928\) | 6.92856 | 0.227441 | ||||||||
\(929\) | 32.5812 | 1.06895 | 0.534477 | − | 0.845183i | \(-0.320509\pi\) | ||||
0.534477 | + | 0.845183i | \(0.320509\pi\) | |||||||
\(930\) | 16.3013 | 0.534542 | ||||||||
\(931\) | −48.4126 | −1.58666 | ||||||||
\(932\) | 27.3573 | 0.896117 | ||||||||
\(933\) | −4.09647 | −0.134112 | ||||||||
\(934\) | 36.6878 | 1.20046 | ||||||||
\(935\) | −11.3902 | −0.372499 | ||||||||
\(936\) | −2.11919 | −0.0692678 | ||||||||
\(937\) | 20.5672 | 0.671901 | 0.335951 | − | 0.941880i | \(-0.390942\pi\) | ||||
0.335951 | + | 0.941880i | \(0.390942\pi\) | |||||||
\(938\) | 11.7591 | 0.383949 | ||||||||
\(939\) | 19.5465 | 0.637877 | ||||||||
\(940\) | −12.8119 | −0.417879 | ||||||||
\(941\) | 6.21893 | 0.202731 | 0.101366 | − | 0.994849i | \(-0.467679\pi\) | ||||
0.101366 | + | 0.994849i | \(0.467679\pi\) | |||||||
\(942\) | −19.0675 | −0.621252 | ||||||||
\(943\) | 54.6019 | 1.77808 | ||||||||
\(944\) | 4.62525 | 0.150539 | ||||||||
\(945\) | 2.18865 | 0.0711967 | ||||||||
\(946\) | −3.54400 | −0.115225 | ||||||||
\(947\) | −31.9775 | −1.03913 | −0.519565 | − | 0.854431i | \(-0.673906\pi\) | ||||
−0.519565 | + | 0.854431i | \(0.673906\pi\) | |||||||
\(948\) | −6.68822 | −0.217223 | ||||||||
\(949\) | −20.1033 | −0.652581 | ||||||||
\(950\) | −1.95643 | −0.0634750 | ||||||||
\(951\) | 7.28921 | 0.236369 | ||||||||
\(952\) | 4.75205 | 0.154015 | ||||||||
\(953\) | 6.81968 | 0.220911 | 0.110456 | − | 0.993881i | \(-0.464769\pi\) | ||||
0.110456 | + | 0.993881i | \(0.464769\pi\) | |||||||
\(954\) | −8.21368 | −0.265928 | ||||||||
\(955\) | 44.3618 | 1.43551 | ||||||||
\(956\) | 15.5679 | 0.503502 | ||||||||
\(957\) | −6.92856 | −0.223969 | ||||||||
\(958\) | −37.7824 | −1.22069 | ||||||||
\(959\) | −12.3117 | −0.397565 | ||||||||
\(960\) | −2.29041 | −0.0739227 | ||||||||
\(961\) | 19.6547 | 0.634023 | ||||||||
\(962\) | 22.7557 | 0.733673 | ||||||||
\(963\) | −16.4577 | −0.530342 | ||||||||
\(964\) | −19.3688 | −0.623828 | ||||||||
\(965\) | −0.0129029 | −0.000415359 0 | ||||||||
\(966\) | −6.80288 | −0.218879 | ||||||||
\(967\) | −32.2662 | −1.03761 | −0.518806 | − | 0.854892i | \(-0.673623\pi\) | ||||
−0.518806 | + | 0.854892i | \(0.673623\pi\) | |||||||
\(968\) | −1.00000 | −0.0321412 | ||||||||
\(969\) | −39.5532 | −1.27063 | ||||||||
\(970\) | 10.0129 | 0.321495 | ||||||||
\(971\) | −14.3665 | −0.461043 | −0.230522 | − | 0.973067i | \(-0.574043\pi\) | ||||
−0.230522 | + | 0.973067i | \(0.574043\pi\) | |||||||
\(972\) | −1.00000 | −0.0320750 | ||||||||
\(973\) | 0.389513 | 0.0124872 | ||||||||
\(974\) | 29.7214 | 0.952336 | ||||||||
\(975\) | −0.521279 | −0.0166943 | ||||||||
\(976\) | 1.00000 | 0.0320092 | ||||||||
\(977\) | −13.8643 | −0.443557 | −0.221778 | − | 0.975097i | \(-0.571186\pi\) | ||||
−0.221778 | + | 0.975097i | \(0.571186\pi\) | |||||||
\(978\) | 14.3786 | 0.459778 | ||||||||
\(979\) | 6.29041 | 0.201042 | ||||||||
\(980\) | −13.9415 | −0.445344 | ||||||||
\(981\) | 6.53528 | 0.208655 | ||||||||
\(982\) | −1.92302 | −0.0613660 | ||||||||
\(983\) | 22.0561 | 0.703480 | 0.351740 | − | 0.936098i | \(-0.385590\pi\) | ||||
0.351740 | + | 0.936098i | \(0.385590\pi\) | |||||||
\(984\) | 7.66968 | 0.244500 | ||||||||
\(985\) | −6.45128 | −0.205555 | ||||||||
\(986\) | 34.4557 | 1.09729 | ||||||||
\(987\) | −5.34520 | −0.170139 | ||||||||
\(988\) | 16.8552 | 0.536234 | ||||||||
\(989\) | −25.2304 | −0.802280 | ||||||||
\(990\) | 2.29041 | 0.0727940 | ||||||||
\(991\) | 36.7000 | 1.16581 | 0.582906 | − | 0.812539i | \(-0.301915\pi\) | ||||
0.582906 | + | 0.812539i | \(0.301915\pi\) | |||||||
\(992\) | −7.11721 | −0.225972 | ||||||||
\(993\) | −12.2209 | −0.387820 | ||||||||
\(994\) | −4.63627 | −0.147053 | ||||||||
\(995\) | −13.0082 | −0.412387 | ||||||||
\(996\) | 1.24401 | 0.0394179 | ||||||||
\(997\) | −22.7669 | −0.721036 | −0.360518 | − | 0.932752i | \(-0.617400\pi\) | ||||
−0.360518 | + | 0.932752i | \(0.617400\pi\) | |||||||
\(998\) | −7.49173 | −0.237146 | ||||||||
\(999\) | 10.7379 | 0.339733 |
(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 | 4026.2.a.q.1.4 | ✓ | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4026.2.a.q.1.4 | ✓ | 4 | 1.1 | even | 1 | trivial |