Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [5054,2,Mod(1,5054)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5054, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("5054.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 5054 = 2 \cdot 7 \cdot 19^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 5054.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: | \(40.3563931816\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{10})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(1.61803\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 5054.1 |
$q$-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 | ||||||||
\(3\) | −1.61803 | −0.934172 | −0.467086 | − | 0.884212i | \(-0.654696\pi\) | ||||
−0.467086 | + | 0.884212i | \(0.654696\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 1.00000 | 0.447214 | 0.223607 | − | 0.974679i | \(-0.428217\pi\) | ||||
0.223607 | + | 0.974679i | \(0.428217\pi\) | |||||||
\(6\) | 1.61803 | 0.660560 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | −0.381966 | −0.127322 | ||||||||
\(10\) | −1.00000 | −0.316228 | ||||||||
\(11\) | −5.00000 | −1.50756 | −0.753778 | − | 0.657129i | \(-0.771771\pi\) | ||||
−0.753778 | + | 0.657129i | \(0.771771\pi\) | |||||||
\(12\) | −1.61803 | −0.467086 | ||||||||
\(13\) | 1.85410 | 0.514235 | 0.257118 | − | 0.966380i | \(-0.417227\pi\) | ||||
0.257118 | + | 0.966380i | \(0.417227\pi\) | |||||||
\(14\) | 1.00000 | 0.267261 | ||||||||
\(15\) | −1.61803 | −0.417775 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 0.145898 | 0.0353855 | 0.0176927 | − | 0.999843i | \(-0.494368\pi\) | ||||
0.0176927 | + | 0.999843i | \(0.494368\pi\) | |||||||
\(18\) | 0.381966 | 0.0900303 | ||||||||
\(19\) | 0 | 0 | ||||||||
\(20\) | 1.00000 | 0.223607 | ||||||||
\(21\) | 1.61803 | 0.353084 | ||||||||
\(22\) | 5.00000 | 1.06600 | ||||||||
\(23\) | −8.23607 | −1.71734 | −0.858669 | − | 0.512530i | \(-0.828708\pi\) | ||||
−0.858669 | + | 0.512530i | \(0.828708\pi\) | |||||||
\(24\) | 1.61803 | 0.330280 | ||||||||
\(25\) | −4.00000 | −0.800000 | ||||||||
\(26\) | −1.85410 | −0.363619 | ||||||||
\(27\) | 5.47214 | 1.05311 | ||||||||
\(28\) | −1.00000 | −0.188982 | ||||||||
\(29\) | 3.76393 | 0.698945 | 0.349472 | − | 0.936947i | \(-0.386361\pi\) | ||||
0.349472 | + | 0.936947i | \(0.386361\pi\) | |||||||
\(30\) | 1.61803 | 0.295411 | ||||||||
\(31\) | −6.70820 | −1.20483 | −0.602414 | − | 0.798183i | \(-0.705795\pi\) | ||||
−0.602414 | + | 0.798183i | \(0.705795\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 8.09017 | 1.40832 | ||||||||
\(34\) | −0.145898 | −0.0250213 | ||||||||
\(35\) | −1.00000 | −0.169031 | ||||||||
\(36\) | −0.381966 | −0.0636610 | ||||||||
\(37\) | 11.9443 | 1.96363 | 0.981813 | − | 0.189850i | \(-0.0608002\pi\) | ||||
0.981813 | + | 0.189850i | \(0.0608002\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −3.00000 | −0.480384 | ||||||||
\(40\) | −1.00000 | −0.158114 | ||||||||
\(41\) | −10.0902 | −1.57582 | −0.787910 | − | 0.615791i | \(-0.788837\pi\) | ||||
−0.787910 | + | 0.615791i | \(0.788837\pi\) | |||||||
\(42\) | −1.61803 | −0.249668 | ||||||||
\(43\) | −0.145898 | −0.0222492 | −0.0111246 | − | 0.999938i | \(-0.503541\pi\) | ||||
−0.0111246 | + | 0.999938i | \(0.503541\pi\) | |||||||
\(44\) | −5.00000 | −0.753778 | ||||||||
\(45\) | −0.381966 | −0.0569401 | ||||||||
\(46\) | 8.23607 | 1.21434 | ||||||||
\(47\) | −9.94427 | −1.45052 | −0.725261 | − | 0.688474i | \(-0.758281\pi\) | ||||
−0.725261 | + | 0.688474i | \(0.758281\pi\) | |||||||
\(48\) | −1.61803 | −0.233543 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 4.00000 | 0.565685 | ||||||||
\(51\) | −0.236068 | −0.0330561 | ||||||||
\(52\) | 1.85410 | 0.257118 | ||||||||
\(53\) | −0.708204 | −0.0972793 | −0.0486396 | − | 0.998816i | \(-0.515489\pi\) | ||||
−0.0486396 | + | 0.998816i | \(0.515489\pi\) | |||||||
\(54\) | −5.47214 | −0.744663 | ||||||||
\(55\) | −5.00000 | −0.674200 | ||||||||
\(56\) | 1.00000 | 0.133631 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −3.76393 | −0.494228 | ||||||||
\(59\) | −11.0000 | −1.43208 | −0.716039 | − | 0.698060i | \(-0.754047\pi\) | ||||
−0.716039 | + | 0.698060i | \(0.754047\pi\) | |||||||
\(60\) | −1.61803 | −0.208887 | ||||||||
\(61\) | −1.47214 | −0.188488 | −0.0942438 | − | 0.995549i | \(-0.530043\pi\) | ||||
−0.0942438 | + | 0.995549i | \(0.530043\pi\) | |||||||
\(62\) | 6.70820 | 0.851943 | ||||||||
\(63\) | 0.381966 | 0.0481232 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 1.85410 | 0.229973 | ||||||||
\(66\) | −8.09017 | −0.995831 | ||||||||
\(67\) | −1.14590 | −0.139994 | −0.0699969 | − | 0.997547i | \(-0.522299\pi\) | ||||
−0.0699969 | + | 0.997547i | \(0.522299\pi\) | |||||||
\(68\) | 0.145898 | 0.0176927 | ||||||||
\(69\) | 13.3262 | 1.60429 | ||||||||
\(70\) | 1.00000 | 0.119523 | ||||||||
\(71\) | 10.0000 | 1.18678 | 0.593391 | − | 0.804914i | \(-0.297789\pi\) | ||||
0.593391 | + | 0.804914i | \(0.297789\pi\) | |||||||
\(72\) | 0.381966 | 0.0450151 | ||||||||
\(73\) | 5.56231 | 0.651019 | 0.325509 | − | 0.945539i | \(-0.394464\pi\) | ||||
0.325509 | + | 0.945539i | \(0.394464\pi\) | |||||||
\(74\) | −11.9443 | −1.38849 | ||||||||
\(75\) | 6.47214 | 0.747338 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 5.00000 | 0.569803 | ||||||||
\(78\) | 3.00000 | 0.339683 | ||||||||
\(79\) | 2.14590 | 0.241432 | 0.120716 | − | 0.992687i | \(-0.461481\pi\) | ||||
0.120716 | + | 0.992687i | \(0.461481\pi\) | |||||||
\(80\) | 1.00000 | 0.111803 | ||||||||
\(81\) | −7.70820 | −0.856467 | ||||||||
\(82\) | 10.0902 | 1.11427 | ||||||||
\(83\) | 11.4164 | 1.25311 | 0.626557 | − | 0.779376i | \(-0.284464\pi\) | ||||
0.626557 | + | 0.779376i | \(0.284464\pi\) | |||||||
\(84\) | 1.61803 | 0.176542 | ||||||||
\(85\) | 0.145898 | 0.0158249 | ||||||||
\(86\) | 0.145898 | 0.0157326 | ||||||||
\(87\) | −6.09017 | −0.652935 | ||||||||
\(88\) | 5.00000 | 0.533002 | ||||||||
\(89\) | 1.85410 | 0.196534 | 0.0982672 | − | 0.995160i | \(-0.468670\pi\) | ||||
0.0982672 | + | 0.995160i | \(0.468670\pi\) | |||||||
\(90\) | 0.381966 | 0.0402628 | ||||||||
\(91\) | −1.85410 | −0.194363 | ||||||||
\(92\) | −8.23607 | −0.858669 | ||||||||
\(93\) | 10.8541 | 1.12552 | ||||||||
\(94\) | 9.94427 | 1.02567 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 1.61803 | 0.165140 | ||||||||
\(97\) | 0.527864 | 0.0535965 | 0.0267982 | − | 0.999641i | \(-0.491469\pi\) | ||||
0.0267982 | + | 0.999641i | \(0.491469\pi\) | |||||||
\(98\) | −1.00000 | −0.101015 | ||||||||
\(99\) | 1.90983 | 0.191945 | ||||||||
\(100\) | −4.00000 | −0.400000 | ||||||||
\(101\) | 10.8541 | 1.08002 | 0.540012 | − | 0.841657i | \(-0.318420\pi\) | ||||
0.540012 | + | 0.841657i | \(0.318420\pi\) | |||||||
\(102\) | 0.236068 | 0.0233742 | ||||||||
\(103\) | 3.90983 | 0.385247 | 0.192624 | − | 0.981273i | \(-0.438300\pi\) | ||||
0.192624 | + | 0.981273i | \(0.438300\pi\) | |||||||
\(104\) | −1.85410 | −0.181810 | ||||||||
\(105\) | 1.61803 | 0.157904 | ||||||||
\(106\) | 0.708204 | 0.0687868 | ||||||||
\(107\) | −3.94427 | −0.381307 | −0.190654 | − | 0.981657i | \(-0.561061\pi\) | ||||
−0.190654 | + | 0.981657i | \(0.561061\pi\) | |||||||
\(108\) | 5.47214 | 0.526557 | ||||||||
\(109\) | −6.56231 | −0.628555 | −0.314277 | − | 0.949331i | \(-0.601762\pi\) | ||||
−0.314277 | + | 0.949331i | \(0.601762\pi\) | |||||||
\(110\) | 5.00000 | 0.476731 | ||||||||
\(111\) | −19.3262 | −1.83437 | ||||||||
\(112\) | −1.00000 | −0.0944911 | ||||||||
\(113\) | 2.85410 | 0.268491 | 0.134246 | − | 0.990948i | \(-0.457139\pi\) | ||||
0.134246 | + | 0.990948i | \(0.457139\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −8.23607 | −0.768017 | ||||||||
\(116\) | 3.76393 | 0.349472 | ||||||||
\(117\) | −0.708204 | −0.0654735 | ||||||||
\(118\) | 11.0000 | 1.01263 | ||||||||
\(119\) | −0.145898 | −0.0133745 | ||||||||
\(120\) | 1.61803 | 0.147706 | ||||||||
\(121\) | 14.0000 | 1.27273 | ||||||||
\(122\) | 1.47214 | 0.133281 | ||||||||
\(123\) | 16.3262 | 1.47209 | ||||||||
\(124\) | −6.70820 | −0.602414 | ||||||||
\(125\) | −9.00000 | −0.804984 | ||||||||
\(126\) | −0.381966 | −0.0340282 | ||||||||
\(127\) | −8.32624 | −0.738834 | −0.369417 | − | 0.929264i | \(-0.620443\pi\) | ||||
−0.369417 | + | 0.929264i | \(0.620443\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 0.236068 | 0.0207846 | ||||||||
\(130\) | −1.85410 | −0.162615 | ||||||||
\(131\) | −6.61803 | −0.578220 | −0.289110 | − | 0.957296i | \(-0.593359\pi\) | ||||
−0.289110 | + | 0.957296i | \(0.593359\pi\) | |||||||
\(132\) | 8.09017 | 0.704159 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 1.14590 | 0.0989905 | ||||||||
\(135\) | 5.47214 | 0.470966 | ||||||||
\(136\) | −0.145898 | −0.0125107 | ||||||||
\(137\) | −19.1246 | −1.63393 | −0.816963 | − | 0.576690i | \(-0.804344\pi\) | ||||
−0.816963 | + | 0.576690i | \(0.804344\pi\) | |||||||
\(138\) | −13.3262 | −1.13440 | ||||||||
\(139\) | 4.23607 | 0.359299 | 0.179649 | − | 0.983731i | \(-0.442504\pi\) | ||||
0.179649 | + | 0.983731i | \(0.442504\pi\) | |||||||
\(140\) | −1.00000 | −0.0845154 | ||||||||
\(141\) | 16.0902 | 1.35504 | ||||||||
\(142\) | −10.0000 | −0.839181 | ||||||||
\(143\) | −9.27051 | −0.775239 | ||||||||
\(144\) | −0.381966 | −0.0318305 | ||||||||
\(145\) | 3.76393 | 0.312578 | ||||||||
\(146\) | −5.56231 | −0.460340 | ||||||||
\(147\) | −1.61803 | −0.133453 | ||||||||
\(148\) | 11.9443 | 0.981813 | ||||||||
\(149\) | 3.61803 | 0.296401 | 0.148200 | − | 0.988957i | \(-0.452652\pi\) | ||||
0.148200 | + | 0.988957i | \(0.452652\pi\) | |||||||
\(150\) | −6.47214 | −0.528448 | ||||||||
\(151\) | 9.76393 | 0.794578 | 0.397289 | − | 0.917694i | \(-0.369951\pi\) | ||||
0.397289 | + | 0.917694i | \(0.369951\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −0.0557281 | −0.00450535 | ||||||||
\(154\) | −5.00000 | −0.402911 | ||||||||
\(155\) | −6.70820 | −0.538816 | ||||||||
\(156\) | −3.00000 | −0.240192 | ||||||||
\(157\) | 6.67376 | 0.532624 | 0.266312 | − | 0.963887i | \(-0.414195\pi\) | ||||
0.266312 | + | 0.963887i | \(0.414195\pi\) | |||||||
\(158\) | −2.14590 | −0.170718 | ||||||||
\(159\) | 1.14590 | 0.0908756 | ||||||||
\(160\) | −1.00000 | −0.0790569 | ||||||||
\(161\) | 8.23607 | 0.649093 | ||||||||
\(162\) | 7.70820 | 0.605614 | ||||||||
\(163\) | −8.47214 | −0.663589 | −0.331794 | − | 0.943352i | \(-0.607654\pi\) | ||||
−0.331794 | + | 0.943352i | \(0.607654\pi\) | |||||||
\(164\) | −10.0902 | −0.787910 | ||||||||
\(165\) | 8.09017 | 0.629819 | ||||||||
\(166\) | −11.4164 | −0.886085 | ||||||||
\(167\) | −24.1803 | −1.87113 | −0.935565 | − | 0.353153i | \(-0.885109\pi\) | ||||
−0.935565 | + | 0.353153i | \(0.885109\pi\) | |||||||
\(168\) | −1.61803 | −0.124834 | ||||||||
\(169\) | −9.56231 | −0.735562 | ||||||||
\(170\) | −0.145898 | −0.0111899 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −0.145898 | −0.0111246 | ||||||||
\(173\) | −6.23607 | −0.474119 | −0.237060 | − | 0.971495i | \(-0.576184\pi\) | ||||
−0.237060 | + | 0.971495i | \(0.576184\pi\) | |||||||
\(174\) | 6.09017 | 0.461695 | ||||||||
\(175\) | 4.00000 | 0.302372 | ||||||||
\(176\) | −5.00000 | −0.376889 | ||||||||
\(177\) | 17.7984 | 1.33781 | ||||||||
\(178\) | −1.85410 | −0.138971 | ||||||||
\(179\) | 20.0344 | 1.49744 | 0.748722 | − | 0.662884i | \(-0.230668\pi\) | ||||
0.748722 | + | 0.662884i | \(0.230668\pi\) | |||||||
\(180\) | −0.381966 | −0.0284701 | ||||||||
\(181\) | 20.2361 | 1.50414 | 0.752068 | − | 0.659086i | \(-0.229057\pi\) | ||||
0.752068 | + | 0.659086i | \(0.229057\pi\) | |||||||
\(182\) | 1.85410 | 0.137435 | ||||||||
\(183\) | 2.38197 | 0.176080 | ||||||||
\(184\) | 8.23607 | 0.607171 | ||||||||
\(185\) | 11.9443 | 0.878160 | ||||||||
\(186\) | −10.8541 | −0.795861 | ||||||||
\(187\) | −0.729490 | −0.0533456 | ||||||||
\(188\) | −9.94427 | −0.725261 | ||||||||
\(189\) | −5.47214 | −0.398039 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 25.1803 | 1.82199 | 0.910993 | − | 0.412422i | \(-0.135317\pi\) | ||||
0.910993 | + | 0.412422i | \(0.135317\pi\) | |||||||
\(192\) | −1.61803 | −0.116772 | ||||||||
\(193\) | −12.1803 | −0.876760 | −0.438380 | − | 0.898790i | \(-0.644448\pi\) | ||||
−0.438380 | + | 0.898790i | \(0.644448\pi\) | |||||||
\(194\) | −0.527864 | −0.0378984 | ||||||||
\(195\) | −3.00000 | −0.214834 | ||||||||
\(196\) | 1.00000 | 0.0714286 | ||||||||
\(197\) | 12.5623 | 0.895027 | 0.447514 | − | 0.894277i | \(-0.352310\pi\) | ||||
0.447514 | + | 0.894277i | \(0.352310\pi\) | |||||||
\(198\) | −1.90983 | −0.135726 | ||||||||
\(199\) | −16.0902 | −1.14060 | −0.570301 | − | 0.821436i | \(-0.693173\pi\) | ||||
−0.570301 | + | 0.821436i | \(0.693173\pi\) | |||||||
\(200\) | 4.00000 | 0.282843 | ||||||||
\(201\) | 1.85410 | 0.130778 | ||||||||
\(202\) | −10.8541 | −0.763692 | ||||||||
\(203\) | −3.76393 | −0.264176 | ||||||||
\(204\) | −0.236068 | −0.0165281 | ||||||||
\(205\) | −10.0902 | −0.704728 | ||||||||
\(206\) | −3.90983 | −0.272411 | ||||||||
\(207\) | 3.14590 | 0.218655 | ||||||||
\(208\) | 1.85410 | 0.128559 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | −1.61803 | −0.111655 | ||||||||
\(211\) | 21.9443 | 1.51071 | 0.755353 | − | 0.655318i | \(-0.227465\pi\) | ||||
0.755353 | + | 0.655318i | \(0.227465\pi\) | |||||||
\(212\) | −0.708204 | −0.0486396 | ||||||||
\(213\) | −16.1803 | −1.10866 | ||||||||
\(214\) | 3.94427 | 0.269625 | ||||||||
\(215\) | −0.145898 | −0.00995016 | ||||||||
\(216\) | −5.47214 | −0.372332 | ||||||||
\(217\) | 6.70820 | 0.455383 | ||||||||
\(218\) | 6.56231 | 0.444455 | ||||||||
\(219\) | −9.00000 | −0.608164 | ||||||||
\(220\) | −5.00000 | −0.337100 | ||||||||
\(221\) | 0.270510 | 0.0181965 | ||||||||
\(222\) | 19.3262 | 1.29709 | ||||||||
\(223\) | 25.6525 | 1.71782 | 0.858908 | − | 0.512129i | \(-0.171143\pi\) | ||||
0.858908 | + | 0.512129i | \(0.171143\pi\) | |||||||
\(224\) | 1.00000 | 0.0668153 | ||||||||
\(225\) | 1.52786 | 0.101858 | ||||||||
\(226\) | −2.85410 | −0.189852 | ||||||||
\(227\) | 9.76393 | 0.648055 | 0.324027 | − | 0.946048i | \(-0.394963\pi\) | ||||
0.324027 | + | 0.946048i | \(0.394963\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1.09017 | 0.0720405 | 0.0360202 | − | 0.999351i | \(-0.488532\pi\) | ||||
0.0360202 | + | 0.999351i | \(0.488532\pi\) | |||||||
\(230\) | 8.23607 | 0.543070 | ||||||||
\(231\) | −8.09017 | −0.532294 | ||||||||
\(232\) | −3.76393 | −0.247114 | ||||||||
\(233\) | 18.0344 | 1.18148 | 0.590738 | − | 0.806864i | \(-0.298837\pi\) | ||||
0.590738 | + | 0.806864i | \(0.298837\pi\) | |||||||
\(234\) | 0.708204 | 0.0462967 | ||||||||
\(235\) | −9.94427 | −0.648693 | ||||||||
\(236\) | −11.0000 | −0.716039 | ||||||||
\(237\) | −3.47214 | −0.225539 | ||||||||
\(238\) | 0.145898 | 0.00945716 | ||||||||
\(239\) | −17.8541 | −1.15489 | −0.577443 | − | 0.816431i | \(-0.695949\pi\) | ||||
−0.577443 | + | 0.816431i | \(0.695949\pi\) | |||||||
\(240\) | −1.61803 | −0.104444 | ||||||||
\(241\) | −19.0902 | −1.22971 | −0.614853 | − | 0.788642i | \(-0.710785\pi\) | ||||
−0.614853 | + | 0.788642i | \(0.710785\pi\) | |||||||
\(242\) | −14.0000 | −0.899954 | ||||||||
\(243\) | −3.94427 | −0.253025 | ||||||||
\(244\) | −1.47214 | −0.0942438 | ||||||||
\(245\) | 1.00000 | 0.0638877 | ||||||||
\(246\) | −16.3262 | −1.04092 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 6.70820 | 0.425971 | ||||||||
\(249\) | −18.4721 | −1.17062 | ||||||||
\(250\) | 9.00000 | 0.569210 | ||||||||
\(251\) | −2.47214 | −0.156040 | −0.0780199 | − | 0.996952i | \(-0.524860\pi\) | ||||
−0.0780199 | + | 0.996952i | \(0.524860\pi\) | |||||||
\(252\) | 0.381966 | 0.0240616 | ||||||||
\(253\) | 41.1803 | 2.58899 | ||||||||
\(254\) | 8.32624 | 0.522435 | ||||||||
\(255\) | −0.236068 | −0.0147832 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −25.9443 | −1.61836 | −0.809180 | − | 0.587561i | \(-0.800088\pi\) | ||||
−0.809180 | + | 0.587561i | \(0.800088\pi\) | |||||||
\(258\) | −0.236068 | −0.0146970 | ||||||||
\(259\) | −11.9443 | −0.742181 | ||||||||
\(260\) | 1.85410 | 0.114987 | ||||||||
\(261\) | −1.43769 | −0.0889910 | ||||||||
\(262\) | 6.61803 | 0.408864 | ||||||||
\(263\) | −2.81966 | −0.173868 | −0.0869338 | − | 0.996214i | \(-0.527707\pi\) | ||||
−0.0869338 | + | 0.996214i | \(0.527707\pi\) | |||||||
\(264\) | −8.09017 | −0.497916 | ||||||||
\(265\) | −0.708204 | −0.0435046 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −3.00000 | −0.183597 | ||||||||
\(268\) | −1.14590 | −0.0699969 | ||||||||
\(269\) | 13.1803 | 0.803620 | 0.401810 | − | 0.915723i | \(-0.368381\pi\) | ||||
0.401810 | + | 0.915723i | \(0.368381\pi\) | |||||||
\(270\) | −5.47214 | −0.333024 | ||||||||
\(271\) | −29.6525 | −1.80126 | −0.900630 | − | 0.434587i | \(-0.856894\pi\) | ||||
−0.900630 | + | 0.434587i | \(0.856894\pi\) | |||||||
\(272\) | 0.145898 | 0.00884637 | ||||||||
\(273\) | 3.00000 | 0.181568 | ||||||||
\(274\) | 19.1246 | 1.15536 | ||||||||
\(275\) | 20.0000 | 1.20605 | ||||||||
\(276\) | 13.3262 | 0.802145 | ||||||||
\(277\) | −8.00000 | −0.480673 | −0.240337 | − | 0.970690i | \(-0.577258\pi\) | ||||
−0.240337 | + | 0.970690i | \(0.577258\pi\) | |||||||
\(278\) | −4.23607 | −0.254062 | ||||||||
\(279\) | 2.56231 | 0.153401 | ||||||||
\(280\) | 1.00000 | 0.0597614 | ||||||||
\(281\) | 7.76393 | 0.463157 | 0.231579 | − | 0.972816i | \(-0.425611\pi\) | ||||
0.231579 | + | 0.972816i | \(0.425611\pi\) | |||||||
\(282\) | −16.0902 | −0.958156 | ||||||||
\(283\) | 26.5623 | 1.57897 | 0.789483 | − | 0.613773i | \(-0.210349\pi\) | ||||
0.789483 | + | 0.613773i | \(0.210349\pi\) | |||||||
\(284\) | 10.0000 | 0.593391 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 9.27051 | 0.548177 | ||||||||
\(287\) | 10.0902 | 0.595604 | ||||||||
\(288\) | 0.381966 | 0.0225076 | ||||||||
\(289\) | −16.9787 | −0.998748 | ||||||||
\(290\) | −3.76393 | −0.221026 | ||||||||
\(291\) | −0.854102 | −0.0500683 | ||||||||
\(292\) | 5.56231 | 0.325509 | ||||||||
\(293\) | −11.7639 | −0.687256 | −0.343628 | − | 0.939106i | \(-0.611656\pi\) | ||||
−0.343628 | + | 0.939106i | \(0.611656\pi\) | |||||||
\(294\) | 1.61803 | 0.0943657 | ||||||||
\(295\) | −11.0000 | −0.640445 | ||||||||
\(296\) | −11.9443 | −0.694247 | ||||||||
\(297\) | −27.3607 | −1.58763 | ||||||||
\(298\) | −3.61803 | −0.209587 | ||||||||
\(299\) | −15.2705 | −0.883116 | ||||||||
\(300\) | 6.47214 | 0.373669 | ||||||||
\(301\) | 0.145898 | 0.00840942 | ||||||||
\(302\) | −9.76393 | −0.561851 | ||||||||
\(303\) | −17.5623 | −1.00893 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −1.47214 | −0.0842943 | ||||||||
\(306\) | 0.0557281 | 0.00318576 | ||||||||
\(307\) | 12.9443 | 0.738769 | 0.369384 | − | 0.929277i | \(-0.379569\pi\) | ||||
0.369384 | + | 0.929277i | \(0.379569\pi\) | |||||||
\(308\) | 5.00000 | 0.284901 | ||||||||
\(309\) | −6.32624 | −0.359887 | ||||||||
\(310\) | 6.70820 | 0.381000 | ||||||||
\(311\) | 24.2361 | 1.37430 | 0.687151 | − | 0.726515i | \(-0.258861\pi\) | ||||
0.687151 | + | 0.726515i | \(0.258861\pi\) | |||||||
\(312\) | 3.00000 | 0.169842 | ||||||||
\(313\) | 30.0902 | 1.70080 | 0.850398 | − | 0.526139i | \(-0.176361\pi\) | ||||
0.850398 | + | 0.526139i | \(0.176361\pi\) | |||||||
\(314\) | −6.67376 | −0.376622 | ||||||||
\(315\) | 0.381966 | 0.0215213 | ||||||||
\(316\) | 2.14590 | 0.120716 | ||||||||
\(317\) | 18.4164 | 1.03437 | 0.517184 | − | 0.855874i | \(-0.326980\pi\) | ||||
0.517184 | + | 0.855874i | \(0.326980\pi\) | |||||||
\(318\) | −1.14590 | −0.0642588 | ||||||||
\(319\) | −18.8197 | −1.05370 | ||||||||
\(320\) | 1.00000 | 0.0559017 | ||||||||
\(321\) | 6.38197 | 0.356207 | ||||||||
\(322\) | −8.23607 | −0.458978 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | −7.70820 | −0.428234 | ||||||||
\(325\) | −7.41641 | −0.411388 | ||||||||
\(326\) | 8.47214 | 0.469228 | ||||||||
\(327\) | 10.6180 | 0.587179 | ||||||||
\(328\) | 10.0902 | 0.557136 | ||||||||
\(329\) | 9.94427 | 0.548245 | ||||||||
\(330\) | −8.09017 | −0.445349 | ||||||||
\(331\) | −3.52786 | −0.193909 | −0.0969545 | − | 0.995289i | \(-0.530910\pi\) | ||||
−0.0969545 | + | 0.995289i | \(0.530910\pi\) | |||||||
\(332\) | 11.4164 | 0.626557 | ||||||||
\(333\) | −4.56231 | −0.250013 | ||||||||
\(334\) | 24.1803 | 1.32309 | ||||||||
\(335\) | −1.14590 | −0.0626071 | ||||||||
\(336\) | 1.61803 | 0.0882710 | ||||||||
\(337\) | −22.4508 | −1.22298 | −0.611488 | − | 0.791254i | \(-0.709429\pi\) | ||||
−0.611488 | + | 0.791254i | \(0.709429\pi\) | |||||||
\(338\) | 9.56231 | 0.520121 | ||||||||
\(339\) | −4.61803 | −0.250817 | ||||||||
\(340\) | 0.145898 | 0.00791243 | ||||||||
\(341\) | 33.5410 | 1.81635 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 0.145898 | 0.00786629 | ||||||||
\(345\) | 13.3262 | 0.717461 | ||||||||
\(346\) | 6.23607 | 0.335253 | ||||||||
\(347\) | −22.9443 | −1.23171 | −0.615857 | − | 0.787858i | \(-0.711190\pi\) | ||||
−0.615857 | + | 0.787858i | \(0.711190\pi\) | |||||||
\(348\) | −6.09017 | −0.326467 | ||||||||
\(349\) | 6.70820 | 0.359082 | 0.179541 | − | 0.983750i | \(-0.442539\pi\) | ||||
0.179541 | + | 0.983750i | \(0.442539\pi\) | |||||||
\(350\) | −4.00000 | −0.213809 | ||||||||
\(351\) | 10.1459 | 0.541548 | ||||||||
\(352\) | 5.00000 | 0.266501 | ||||||||
\(353\) | 1.90983 | 0.101650 | 0.0508250 | − | 0.998708i | \(-0.483815\pi\) | ||||
0.0508250 | + | 0.998708i | \(0.483815\pi\) | |||||||
\(354\) | −17.7984 | −0.945973 | ||||||||
\(355\) | 10.0000 | 0.530745 | ||||||||
\(356\) | 1.85410 | 0.0982672 | ||||||||
\(357\) | 0.236068 | 0.0124940 | ||||||||
\(358\) | −20.0344 | −1.05885 | ||||||||
\(359\) | 10.0557 | 0.530721 | 0.265361 | − | 0.964149i | \(-0.414509\pi\) | ||||
0.265361 | + | 0.964149i | \(0.414509\pi\) | |||||||
\(360\) | 0.381966 | 0.0201314 | ||||||||
\(361\) | 0 | 0 | ||||||||
\(362\) | −20.2361 | −1.06358 | ||||||||
\(363\) | −22.6525 | −1.18895 | ||||||||
\(364\) | −1.85410 | −0.0971813 | ||||||||
\(365\) | 5.56231 | 0.291144 | ||||||||
\(366\) | −2.38197 | −0.124507 | ||||||||
\(367\) | 25.3262 | 1.32202 | 0.661009 | − | 0.750378i | \(-0.270128\pi\) | ||||
0.661009 | + | 0.750378i | \(0.270128\pi\) | |||||||
\(368\) | −8.23607 | −0.429335 | ||||||||
\(369\) | 3.85410 | 0.200637 | ||||||||
\(370\) | −11.9443 | −0.620953 | ||||||||
\(371\) | 0.708204 | 0.0367681 | ||||||||
\(372\) | 10.8541 | 0.562759 | ||||||||
\(373\) | 0.145898 | 0.00755431 | 0.00377716 | − | 0.999993i | \(-0.498798\pi\) | ||||
0.00377716 | + | 0.999993i | \(0.498798\pi\) | |||||||
\(374\) | 0.729490 | 0.0377210 | ||||||||
\(375\) | 14.5623 | 0.751994 | ||||||||
\(376\) | 9.94427 | 0.512837 | ||||||||
\(377\) | 6.97871 | 0.359422 | ||||||||
\(378\) | 5.47214 | 0.281456 | ||||||||
\(379\) | 17.0344 | 0.875001 | 0.437500 | − | 0.899218i | \(-0.355864\pi\) | ||||
0.437500 | + | 0.899218i | \(0.355864\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 13.4721 | 0.690198 | ||||||||
\(382\) | −25.1803 | −1.28834 | ||||||||
\(383\) | 11.9443 | 0.610324 | 0.305162 | − | 0.952300i | \(-0.401289\pi\) | ||||
0.305162 | + | 0.952300i | \(0.401289\pi\) | |||||||
\(384\) | 1.61803 | 0.0825700 | ||||||||
\(385\) | 5.00000 | 0.254824 | ||||||||
\(386\) | 12.1803 | 0.619963 | ||||||||
\(387\) | 0.0557281 | 0.00283282 | ||||||||
\(388\) | 0.527864 | 0.0267982 | ||||||||
\(389\) | 13.6180 | 0.690462 | 0.345231 | − | 0.938518i | \(-0.387801\pi\) | ||||
0.345231 | + | 0.938518i | \(0.387801\pi\) | |||||||
\(390\) | 3.00000 | 0.151911 | ||||||||
\(391\) | −1.20163 | −0.0607688 | ||||||||
\(392\) | −1.00000 | −0.0505076 | ||||||||
\(393\) | 10.7082 | 0.540157 | ||||||||
\(394\) | −12.5623 | −0.632880 | ||||||||
\(395\) | 2.14590 | 0.107972 | ||||||||
\(396\) | 1.90983 | 0.0959726 | ||||||||
\(397\) | 1.27051 | 0.0637651 | 0.0318825 | − | 0.999492i | \(-0.489850\pi\) | ||||
0.0318825 | + | 0.999492i | \(0.489850\pi\) | |||||||
\(398\) | 16.0902 | 0.806527 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −4.00000 | −0.200000 | ||||||||
\(401\) | 33.4164 | 1.66874 | 0.834368 | − | 0.551208i | \(-0.185833\pi\) | ||||
0.834368 | + | 0.551208i | \(0.185833\pi\) | |||||||
\(402\) | −1.85410 | −0.0924742 | ||||||||
\(403\) | −12.4377 | −0.619566 | ||||||||
\(404\) | 10.8541 | 0.540012 | ||||||||
\(405\) | −7.70820 | −0.383024 | ||||||||
\(406\) | 3.76393 | 0.186801 | ||||||||
\(407\) | −59.7214 | −2.96028 | ||||||||
\(408\) | 0.236068 | 0.0116871 | ||||||||
\(409\) | 34.2148 | 1.69181 | 0.845906 | − | 0.533332i | \(-0.179060\pi\) | ||||
0.845906 | + | 0.533332i | \(0.179060\pi\) | |||||||
\(410\) | 10.0902 | 0.498318 | ||||||||
\(411\) | 30.9443 | 1.52637 | ||||||||
\(412\) | 3.90983 | 0.192624 | ||||||||
\(413\) | 11.0000 | 0.541275 | ||||||||
\(414\) | −3.14590 | −0.154612 | ||||||||
\(415\) | 11.4164 | 0.560409 | ||||||||
\(416\) | −1.85410 | −0.0909048 | ||||||||
\(417\) | −6.85410 | −0.335647 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 16.7426 | 0.817932 | 0.408966 | − | 0.912550i | \(-0.365890\pi\) | ||||
0.408966 | + | 0.912550i | \(0.365890\pi\) | |||||||
\(420\) | 1.61803 | 0.0789520 | ||||||||
\(421\) | 25.9443 | 1.26445 | 0.632223 | − | 0.774786i | \(-0.282143\pi\) | ||||
0.632223 | + | 0.774786i | \(0.282143\pi\) | |||||||
\(422\) | −21.9443 | −1.06823 | ||||||||
\(423\) | 3.79837 | 0.184683 | ||||||||
\(424\) | 0.708204 | 0.0343934 | ||||||||
\(425\) | −0.583592 | −0.0283084 | ||||||||
\(426\) | 16.1803 | 0.783940 | ||||||||
\(427\) | 1.47214 | 0.0712417 | ||||||||
\(428\) | −3.94427 | −0.190654 | ||||||||
\(429\) | 15.0000 | 0.724207 | ||||||||
\(430\) | 0.145898 | 0.00703583 | ||||||||
\(431\) | 14.9443 | 0.719840 | 0.359920 | − | 0.932983i | \(-0.382804\pi\) | ||||
0.359920 | + | 0.932983i | \(0.382804\pi\) | |||||||
\(432\) | 5.47214 | 0.263278 | ||||||||
\(433\) | 25.3820 | 1.21978 | 0.609890 | − | 0.792486i | \(-0.291214\pi\) | ||||
0.609890 | + | 0.792486i | \(0.291214\pi\) | |||||||
\(434\) | −6.70820 | −0.322004 | ||||||||
\(435\) | −6.09017 | −0.292001 | ||||||||
\(436\) | −6.56231 | −0.314277 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 9.00000 | 0.430037 | ||||||||
\(439\) | 39.9443 | 1.90644 | 0.953218 | − | 0.302284i | \(-0.0977490\pi\) | ||||
0.953218 | + | 0.302284i | \(0.0977490\pi\) | |||||||
\(440\) | 5.00000 | 0.238366 | ||||||||
\(441\) | −0.381966 | −0.0181889 | ||||||||
\(442\) | −0.270510 | −0.0128668 | ||||||||
\(443\) | −34.2148 | −1.62559 | −0.812797 | − | 0.582547i | \(-0.802056\pi\) | ||||
−0.812797 | + | 0.582547i | \(0.802056\pi\) | |||||||
\(444\) | −19.3262 | −0.917183 | ||||||||
\(445\) | 1.85410 | 0.0878929 | ||||||||
\(446\) | −25.6525 | −1.21468 | ||||||||
\(447\) | −5.85410 | −0.276890 | ||||||||
\(448\) | −1.00000 | −0.0472456 | ||||||||
\(449\) | −0.180340 | −0.00851077 | −0.00425538 | − | 0.999991i | \(-0.501355\pi\) | ||||
−0.00425538 | + | 0.999991i | \(0.501355\pi\) | |||||||
\(450\) | −1.52786 | −0.0720242 | ||||||||
\(451\) | 50.4508 | 2.37564 | ||||||||
\(452\) | 2.85410 | 0.134246 | ||||||||
\(453\) | −15.7984 | −0.742272 | ||||||||
\(454\) | −9.76393 | −0.458244 | ||||||||
\(455\) | −1.85410 | −0.0869216 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −5.88854 | −0.275454 | −0.137727 | − | 0.990470i | \(-0.543980\pi\) | ||||
−0.137727 | + | 0.990470i | \(0.543980\pi\) | |||||||
\(458\) | −1.09017 | −0.0509403 | ||||||||
\(459\) | 0.798374 | 0.0372649 | ||||||||
\(460\) | −8.23607 | −0.384009 | ||||||||
\(461\) | −24.5410 | −1.14299 | −0.571495 | − | 0.820606i | \(-0.693636\pi\) | ||||
−0.571495 | + | 0.820606i | \(0.693636\pi\) | |||||||
\(462\) | 8.09017 | 0.376389 | ||||||||
\(463\) | 6.56231 | 0.304976 | 0.152488 | − | 0.988305i | \(-0.451271\pi\) | ||||
0.152488 | + | 0.988305i | \(0.451271\pi\) | |||||||
\(464\) | 3.76393 | 0.174736 | ||||||||
\(465\) | 10.8541 | 0.503347 | ||||||||
\(466\) | −18.0344 | −0.835429 | ||||||||
\(467\) | 24.5279 | 1.13501 | 0.567507 | − | 0.823369i | \(-0.307908\pi\) | ||||
0.567507 | + | 0.823369i | \(0.307908\pi\) | |||||||
\(468\) | −0.708204 | −0.0327367 | ||||||||
\(469\) | 1.14590 | 0.0529127 | ||||||||
\(470\) | 9.94427 | 0.458695 | ||||||||
\(471\) | −10.7984 | −0.497563 | ||||||||
\(472\) | 11.0000 | 0.506316 | ||||||||
\(473\) | 0.729490 | 0.0335420 | ||||||||
\(474\) | 3.47214 | 0.159480 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −0.145898 | −0.00668723 | ||||||||
\(477\) | 0.270510 | 0.0123858 | ||||||||
\(478\) | 17.8541 | 0.816628 | ||||||||
\(479\) | 22.1803 | 1.01345 | 0.506723 | − | 0.862109i | \(-0.330857\pi\) | ||||
0.506723 | + | 0.862109i | \(0.330857\pi\) | |||||||
\(480\) | 1.61803 | 0.0738528 | ||||||||
\(481\) | 22.1459 | 1.00977 | ||||||||
\(482\) | 19.0902 | 0.869533 | ||||||||
\(483\) | −13.3262 | −0.606365 | ||||||||
\(484\) | 14.0000 | 0.636364 | ||||||||
\(485\) | 0.527864 | 0.0239691 | ||||||||
\(486\) | 3.94427 | 0.178916 | ||||||||
\(487\) | 11.1803 | 0.506630 | 0.253315 | − | 0.967384i | \(-0.418479\pi\) | ||||
0.253315 | + | 0.967384i | \(0.418479\pi\) | |||||||
\(488\) | 1.47214 | 0.0666405 | ||||||||
\(489\) | 13.7082 | 0.619906 | ||||||||
\(490\) | −1.00000 | −0.0451754 | ||||||||
\(491\) | 29.5967 | 1.33568 | 0.667841 | − | 0.744304i | \(-0.267218\pi\) | ||||
0.667841 | + | 0.744304i | \(0.267218\pi\) | |||||||
\(492\) | 16.3262 | 0.736044 | ||||||||
\(493\) | 0.549150 | 0.0247325 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 1.90983 | 0.0858405 | ||||||||
\(496\) | −6.70820 | −0.301207 | ||||||||
\(497\) | −10.0000 | −0.448561 | ||||||||
\(498\) | 18.4721 | 0.827756 | ||||||||
\(499\) | −10.4164 | −0.466302 | −0.233151 | − | 0.972440i | \(-0.574904\pi\) | ||||
−0.233151 | + | 0.972440i | \(0.574904\pi\) | |||||||
\(500\) | −9.00000 | −0.402492 | ||||||||
\(501\) | 39.1246 | 1.74796 | ||||||||
\(502\) | 2.47214 | 0.110337 | ||||||||
\(503\) | −39.7771 | −1.77357 | −0.886786 | − | 0.462180i | \(-0.847068\pi\) | ||||
−0.886786 | + | 0.462180i | \(0.847068\pi\) | |||||||
\(504\) | −0.381966 | −0.0170141 | ||||||||
\(505\) | 10.8541 | 0.483001 | ||||||||
\(506\) | −41.1803 | −1.83069 | ||||||||
\(507\) | 15.4721 | 0.687142 | ||||||||
\(508\) | −8.32624 | −0.369417 | ||||||||
\(509\) | 25.4164 | 1.12656 | 0.563281 | − | 0.826265i | \(-0.309539\pi\) | ||||
0.563281 | + | 0.826265i | \(0.309539\pi\) | |||||||
\(510\) | 0.236068 | 0.0104533 | ||||||||
\(511\) | −5.56231 | −0.246062 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 25.9443 | 1.14435 | ||||||||
\(515\) | 3.90983 | 0.172288 | ||||||||
\(516\) | 0.236068 | 0.0103923 | ||||||||
\(517\) | 49.7214 | 2.18674 | ||||||||
\(518\) | 11.9443 | 0.524801 | ||||||||
\(519\) | 10.0902 | 0.442909 | ||||||||
\(520\) | −1.85410 | −0.0813077 | ||||||||
\(521\) | 5.65248 | 0.247639 | 0.123820 | − | 0.992305i | \(-0.460486\pi\) | ||||
0.123820 | + | 0.992305i | \(0.460486\pi\) | |||||||
\(522\) | 1.43769 | 0.0629262 | ||||||||
\(523\) | −34.1591 | −1.49367 | −0.746836 | − | 0.665009i | \(-0.768428\pi\) | ||||
−0.746836 | + | 0.665009i | \(0.768428\pi\) | |||||||
\(524\) | −6.61803 | −0.289110 | ||||||||
\(525\) | −6.47214 | −0.282467 | ||||||||
\(526\) | 2.81966 | 0.122943 | ||||||||
\(527\) | −0.978714 | −0.0426334 | ||||||||
\(528\) | 8.09017 | 0.352079 | ||||||||
\(529\) | 44.8328 | 1.94925 | ||||||||
\(530\) | 0.708204 | 0.0307624 | ||||||||
\(531\) | 4.20163 | 0.182335 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −18.7082 | −0.810342 | ||||||||
\(534\) | 3.00000 | 0.129823 | ||||||||
\(535\) | −3.94427 | −0.170526 | ||||||||
\(536\) | 1.14590 | 0.0494953 | ||||||||
\(537\) | −32.4164 | −1.39887 | ||||||||
\(538\) | −13.1803 | −0.568245 | ||||||||
\(539\) | −5.00000 | −0.215365 | ||||||||
\(540\) | 5.47214 | 0.235483 | ||||||||
\(541\) | 32.3050 | 1.38890 | 0.694449 | − | 0.719542i | \(-0.255648\pi\) | ||||
0.694449 | + | 0.719542i | \(0.255648\pi\) | |||||||
\(542\) | 29.6525 | 1.27368 | ||||||||
\(543\) | −32.7426 | −1.40512 | ||||||||
\(544\) | −0.145898 | −0.00625533 | ||||||||
\(545\) | −6.56231 | −0.281098 | ||||||||
\(546\) | −3.00000 | −0.128388 | ||||||||
\(547\) | 13.1803 | 0.563551 | 0.281775 | − | 0.959480i | \(-0.409077\pi\) | ||||
0.281775 | + | 0.959480i | \(0.409077\pi\) | |||||||
\(548\) | −19.1246 | −0.816963 | ||||||||
\(549\) | 0.562306 | 0.0239986 | ||||||||
\(550\) | −20.0000 | −0.852803 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | −13.3262 | −0.567202 | ||||||||
\(553\) | −2.14590 | −0.0912529 | ||||||||
\(554\) | 8.00000 | 0.339887 | ||||||||
\(555\) | −19.3262 | −0.820353 | ||||||||
\(556\) | 4.23607 | 0.179649 | ||||||||
\(557\) | −32.2361 | −1.36589 | −0.682943 | − | 0.730472i | \(-0.739300\pi\) | ||||
−0.682943 | + | 0.730472i | \(0.739300\pi\) | |||||||
\(558\) | −2.56231 | −0.108471 | ||||||||
\(559\) | −0.270510 | −0.0114413 | ||||||||
\(560\) | −1.00000 | −0.0422577 | ||||||||
\(561\) | 1.18034 | 0.0498340 | ||||||||
\(562\) | −7.76393 | −0.327502 | ||||||||
\(563\) | 22.0689 | 0.930093 | 0.465046 | − | 0.885286i | \(-0.346038\pi\) | ||||
0.465046 | + | 0.885286i | \(0.346038\pi\) | |||||||
\(564\) | 16.0902 | 0.677518 | ||||||||
\(565\) | 2.85410 | 0.120073 | ||||||||
\(566\) | −26.5623 | −1.11650 | ||||||||
\(567\) | 7.70820 | 0.323714 | ||||||||
\(568\) | −10.0000 | −0.419591 | ||||||||
\(569\) | −3.27051 | −0.137107 | −0.0685535 | − | 0.997647i | \(-0.521838\pi\) | ||||
−0.0685535 | + | 0.997647i | \(0.521838\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −45.0132 | −1.88374 | −0.941871 | − | 0.335975i | \(-0.890934\pi\) | ||||
−0.941871 | + | 0.335975i | \(0.890934\pi\) | |||||||
\(572\) | −9.27051 | −0.387619 | ||||||||
\(573\) | −40.7426 | −1.70205 | ||||||||
\(574\) | −10.0902 | −0.421156 | ||||||||
\(575\) | 32.9443 | 1.37387 | ||||||||
\(576\) | −0.381966 | −0.0159153 | ||||||||
\(577\) | −16.7082 | −0.695572 | −0.347786 | − | 0.937574i | \(-0.613066\pi\) | ||||
−0.347786 | + | 0.937574i | \(0.613066\pi\) | |||||||
\(578\) | 16.9787 | 0.706221 | ||||||||
\(579\) | 19.7082 | 0.819045 | ||||||||
\(580\) | 3.76393 | 0.156289 | ||||||||
\(581\) | −11.4164 | −0.473632 | ||||||||
\(582\) | 0.854102 | 0.0354037 | ||||||||
\(583\) | 3.54102 | 0.146654 | ||||||||
\(584\) | −5.56231 | −0.230170 | ||||||||
\(585\) | −0.708204 | −0.0292806 | ||||||||
\(586\) | 11.7639 | 0.485964 | ||||||||
\(587\) | −24.0557 | −0.992886 | −0.496443 | − | 0.868069i | \(-0.665361\pi\) | ||||
−0.496443 | + | 0.868069i | \(0.665361\pi\) | |||||||
\(588\) | −1.61803 | −0.0667266 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 11.0000 | 0.452863 | ||||||||
\(591\) | −20.3262 | −0.836110 | ||||||||
\(592\) | 11.9443 | 0.490907 | ||||||||
\(593\) | 25.5623 | 1.04972 | 0.524859 | − | 0.851189i | \(-0.324118\pi\) | ||||
0.524859 | + | 0.851189i | \(0.324118\pi\) | |||||||
\(594\) | 27.3607 | 1.12262 | ||||||||
\(595\) | −0.145898 | −0.00598124 | ||||||||
\(596\) | 3.61803 | 0.148200 | ||||||||
\(597\) | 26.0344 | 1.06552 | ||||||||
\(598\) | 15.2705 | 0.624458 | ||||||||
\(599\) | −17.0000 | −0.694601 | −0.347301 | − | 0.937754i | \(-0.612902\pi\) | ||||
−0.347301 | + | 0.937754i | \(0.612902\pi\) | |||||||
\(600\) | −6.47214 | −0.264224 | ||||||||
\(601\) | 26.1246 | 1.06565 | 0.532823 | − | 0.846227i | \(-0.321131\pi\) | ||||
0.532823 | + | 0.846227i | \(0.321131\pi\) | |||||||
\(602\) | −0.145898 | −0.00594636 | ||||||||
\(603\) | 0.437694 | 0.0178243 | ||||||||
\(604\) | 9.76393 | 0.397289 | ||||||||
\(605\) | 14.0000 | 0.569181 | ||||||||
\(606\) | 17.5623 | 0.713420 | ||||||||
\(607\) | 0.944272 | 0.0383268 | 0.0191634 | − | 0.999816i | \(-0.493900\pi\) | ||||
0.0191634 | + | 0.999816i | \(0.493900\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 6.09017 | 0.246786 | ||||||||
\(610\) | 1.47214 | 0.0596050 | ||||||||
\(611\) | −18.4377 | −0.745909 | ||||||||
\(612\) | −0.0557281 | −0.00225267 | ||||||||
\(613\) | 20.6525 | 0.834146 | 0.417073 | − | 0.908873i | \(-0.363056\pi\) | ||||
0.417073 | + | 0.908873i | \(0.363056\pi\) | |||||||
\(614\) | −12.9443 | −0.522388 | ||||||||
\(615\) | 16.3262 | 0.658337 | ||||||||
\(616\) | −5.00000 | −0.201456 | ||||||||
\(617\) | −8.67376 | −0.349193 | −0.174596 | − | 0.984640i | \(-0.555862\pi\) | ||||
−0.174596 | + | 0.984640i | \(0.555862\pi\) | |||||||
\(618\) | 6.32624 | 0.254479 | ||||||||
\(619\) | −10.2016 | −0.410038 | −0.205019 | − | 0.978758i | \(-0.565726\pi\) | ||||
−0.205019 | + | 0.978758i | \(0.565726\pi\) | |||||||
\(620\) | −6.70820 | −0.269408 | ||||||||
\(621\) | −45.0689 | −1.80855 | ||||||||
\(622\) | −24.2361 | −0.971778 | ||||||||
\(623\) | −1.85410 | −0.0742830 | ||||||||
\(624\) | −3.00000 | −0.120096 | ||||||||
\(625\) | 11.0000 | 0.440000 | ||||||||
\(626\) | −30.0902 | −1.20265 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 6.67376 | 0.266312 | ||||||||
\(629\) | 1.74265 | 0.0694838 | ||||||||
\(630\) | −0.381966 | −0.0152179 | ||||||||
\(631\) | −4.94427 | −0.196828 | −0.0984142 | − | 0.995146i | \(-0.531377\pi\) | ||||
−0.0984142 | + | 0.995146i | \(0.531377\pi\) | |||||||
\(632\) | −2.14590 | −0.0853592 | ||||||||
\(633\) | −35.5066 | −1.41126 | ||||||||
\(634\) | −18.4164 | −0.731409 | ||||||||
\(635\) | −8.32624 | −0.330417 | ||||||||
\(636\) | 1.14590 | 0.0454378 | ||||||||
\(637\) | 1.85410 | 0.0734622 | ||||||||
\(638\) | 18.8197 | 0.745077 | ||||||||
\(639\) | −3.81966 | −0.151103 | ||||||||
\(640\) | −1.00000 | −0.0395285 | ||||||||
\(641\) | −30.0902 | −1.18849 | −0.594245 | − | 0.804284i | \(-0.702549\pi\) | ||||
−0.594245 | + | 0.804284i | \(0.702549\pi\) | |||||||
\(642\) | −6.38197 | −0.251876 | ||||||||
\(643\) | −8.65248 | −0.341220 | −0.170610 | − | 0.985339i | \(-0.554574\pi\) | ||||
−0.170610 | + | 0.985339i | \(0.554574\pi\) | |||||||
\(644\) | 8.23607 | 0.324547 | ||||||||
\(645\) | 0.236068 | 0.00929517 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 46.1033 | 1.81251 | 0.906254 | − | 0.422733i | \(-0.138929\pi\) | ||||
0.906254 | + | 0.422733i | \(0.138929\pi\) | |||||||
\(648\) | 7.70820 | 0.302807 | ||||||||
\(649\) | 55.0000 | 2.15894 | ||||||||
\(650\) | 7.41641 | 0.290895 | ||||||||
\(651\) | −10.8541 | −0.425406 | ||||||||
\(652\) | −8.47214 | −0.331794 | ||||||||
\(653\) | −36.6869 | −1.43567 | −0.717835 | − | 0.696213i | \(-0.754867\pi\) | ||||
−0.717835 | + | 0.696213i | \(0.754867\pi\) | |||||||
\(654\) | −10.6180 | −0.415198 | ||||||||
\(655\) | −6.61803 | −0.258588 | ||||||||
\(656\) | −10.0902 | −0.393955 | ||||||||
\(657\) | −2.12461 | −0.0828890 | ||||||||
\(658\) | −9.94427 | −0.387668 | ||||||||
\(659\) | 33.5410 | 1.30657 | 0.653286 | − | 0.757111i | \(-0.273390\pi\) | ||||
0.653286 | + | 0.757111i | \(0.273390\pi\) | |||||||
\(660\) | 8.09017 | 0.314909 | ||||||||
\(661\) | −41.8328 | −1.62711 | −0.813554 | − | 0.581489i | \(-0.802470\pi\) | ||||
−0.813554 | + | 0.581489i | \(0.802470\pi\) | |||||||
\(662\) | 3.52786 | 0.137114 | ||||||||
\(663\) | −0.437694 | −0.0169986 | ||||||||
\(664\) | −11.4164 | −0.443043 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 4.56231 | 0.176786 | ||||||||
\(667\) | −31.0000 | −1.20032 | ||||||||
\(668\) | −24.1803 | −0.935565 | ||||||||
\(669\) | −41.5066 | −1.60474 | ||||||||
\(670\) | 1.14590 | 0.0442699 | ||||||||
\(671\) | 7.36068 | 0.284156 | ||||||||
\(672\) | −1.61803 | −0.0624170 | ||||||||
\(673\) | −32.0902 | −1.23699 | −0.618493 | − | 0.785791i | \(-0.712256\pi\) | ||||
−0.618493 | + | 0.785791i | \(0.712256\pi\) | |||||||
\(674\) | 22.4508 | 0.864774 | ||||||||
\(675\) | −21.8885 | −0.842490 | ||||||||
\(676\) | −9.56231 | −0.367781 | ||||||||
\(677\) | 9.70820 | 0.373117 | 0.186558 | − | 0.982444i | \(-0.440267\pi\) | ||||
0.186558 | + | 0.982444i | \(0.440267\pi\) | |||||||
\(678\) | 4.61803 | 0.177355 | ||||||||
\(679\) | −0.527864 | −0.0202576 | ||||||||
\(680\) | −0.145898 | −0.00559493 | ||||||||
\(681\) | −15.7984 | −0.605395 | ||||||||
\(682\) | −33.5410 | −1.28435 | ||||||||
\(683\) | −13.2705 | −0.507782 | −0.253891 | − | 0.967233i | \(-0.581710\pi\) | ||||
−0.253891 | + | 0.967233i | \(0.581710\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −19.1246 | −0.730714 | ||||||||
\(686\) | 1.00000 | 0.0381802 | ||||||||
\(687\) | −1.76393 | −0.0672982 | ||||||||
\(688\) | −0.145898 | −0.00556231 | ||||||||
\(689\) | −1.31308 | −0.0500245 | ||||||||
\(690\) | −13.3262 | −0.507321 | ||||||||
\(691\) | 0.527864 | 0.0200809 | 0.0100404 | − | 0.999950i | \(-0.496804\pi\) | ||||
0.0100404 | + | 0.999950i | \(0.496804\pi\) | |||||||
\(692\) | −6.23607 | −0.237060 | ||||||||
\(693\) | −1.90983 | −0.0725484 | ||||||||
\(694\) | 22.9443 | 0.870953 | ||||||||
\(695\) | 4.23607 | 0.160683 | ||||||||
\(696\) | 6.09017 | 0.230847 | ||||||||
\(697\) | −1.47214 | −0.0557611 | ||||||||
\(698\) | −6.70820 | −0.253909 | ||||||||
\(699\) | −29.1803 | −1.10370 | ||||||||
\(700\) | 4.00000 | 0.151186 | ||||||||
\(701\) | 35.2705 | 1.33215 | 0.666074 | − | 0.745885i | \(-0.267973\pi\) | ||||
0.666074 | + | 0.745885i | \(0.267973\pi\) | |||||||
\(702\) | −10.1459 | −0.382932 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | −5.00000 | −0.188445 | ||||||||
\(705\) | 16.0902 | 0.605991 | ||||||||
\(706\) | −1.90983 | −0.0718774 | ||||||||
\(707\) | −10.8541 | −0.408211 | ||||||||
\(708\) | 17.7984 | 0.668904 | ||||||||
\(709\) | 8.34752 | 0.313498 | 0.156749 | − | 0.987638i | \(-0.449899\pi\) | ||||
0.156749 | + | 0.987638i | \(0.449899\pi\) | |||||||
\(710\) | −10.0000 | −0.375293 | ||||||||
\(711\) | −0.819660 | −0.0307397 | ||||||||
\(712\) | −1.85410 | −0.0694854 | ||||||||
\(713\) | 55.2492 | 2.06910 | ||||||||
\(714\) | −0.236068 | −0.00883462 | ||||||||
\(715\) | −9.27051 | −0.346697 | ||||||||
\(716\) | 20.0344 | 0.748722 | ||||||||
\(717\) | 28.8885 | 1.07886 | ||||||||
\(718\) | −10.0557 | −0.375276 | ||||||||
\(719\) | −13.8328 | −0.515877 | −0.257938 | − | 0.966161i | \(-0.583043\pi\) | ||||
−0.257938 | + | 0.966161i | \(0.583043\pi\) | |||||||
\(720\) | −0.381966 | −0.0142350 | ||||||||
\(721\) | −3.90983 | −0.145610 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 30.8885 | 1.14876 | ||||||||
\(724\) | 20.2361 | 0.752068 | ||||||||
\(725\) | −15.0557 | −0.559156 | ||||||||
\(726\) | 22.6525 | 0.840712 | ||||||||
\(727\) | 48.1246 | 1.78484 | 0.892422 | − | 0.451203i | \(-0.149005\pi\) | ||||
0.892422 | + | 0.451203i | \(0.149005\pi\) | |||||||
\(728\) | 1.85410 | 0.0687176 | ||||||||
\(729\) | 29.5066 | 1.09284 | ||||||||
\(730\) | −5.56231 | −0.205870 | ||||||||
\(731\) | −0.0212862 | −0.000787300 0 | ||||||||
\(732\) | 2.38197 | 0.0880400 | ||||||||
\(733\) | 43.6525 | 1.61234 | 0.806170 | − | 0.591683i | \(-0.201536\pi\) | ||||
0.806170 | + | 0.591683i | \(0.201536\pi\) | |||||||
\(734\) | −25.3262 | −0.934808 | ||||||||
\(735\) | −1.61803 | −0.0596821 | ||||||||
\(736\) | 8.23607 | 0.303585 | ||||||||
\(737\) | 5.72949 | 0.211048 | ||||||||
\(738\) | −3.85410 | −0.141871 | ||||||||
\(739\) | −15.4164 | −0.567102 | −0.283551 | − | 0.958957i | \(-0.591512\pi\) | ||||
−0.283551 | + | 0.958957i | \(0.591512\pi\) | |||||||
\(740\) | 11.9443 | 0.439080 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −0.708204 | −0.0259990 | ||||||||
\(743\) | 12.4934 | 0.458339 | 0.229170 | − | 0.973387i | \(-0.426399\pi\) | ||||
0.229170 | + | 0.973387i | \(0.426399\pi\) | |||||||
\(744\) | −10.8541 | −0.397931 | ||||||||
\(745\) | 3.61803 | 0.132555 | ||||||||
\(746\) | −0.145898 | −0.00534171 | ||||||||
\(747\) | −4.36068 | −0.159549 | ||||||||
\(748\) | −0.729490 | −0.0266728 | ||||||||
\(749\) | 3.94427 | 0.144121 | ||||||||
\(750\) | −14.5623 | −0.531740 | ||||||||
\(751\) | 10.1803 | 0.371486 | 0.185743 | − | 0.982598i | \(-0.440531\pi\) | ||||
0.185743 | + | 0.982598i | \(0.440531\pi\) | |||||||
\(752\) | −9.94427 | −0.362630 | ||||||||
\(753\) | 4.00000 | 0.145768 | ||||||||
\(754\) | −6.97871 | −0.254150 | ||||||||
\(755\) | 9.76393 | 0.355346 | ||||||||
\(756\) | −5.47214 | −0.199020 | ||||||||
\(757\) | 29.8885 | 1.08632 | 0.543159 | − | 0.839630i | \(-0.317228\pi\) | ||||
0.543159 | + | 0.839630i | \(0.317228\pi\) | |||||||
\(758\) | −17.0344 | −0.618719 | ||||||||
\(759\) | −66.6312 | −2.41856 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −39.8328 | −1.44394 | −0.721969 | − | 0.691925i | \(-0.756763\pi\) | ||||
−0.721969 | + | 0.691925i | \(0.756763\pi\) | |||||||
\(762\) | −13.4721 | −0.488044 | ||||||||
\(763\) | 6.56231 | 0.237571 | ||||||||
\(764\) | 25.1803 | 0.910993 | ||||||||
\(765\) | −0.0557281 | −0.00201485 | ||||||||
\(766\) | −11.9443 | −0.431564 | ||||||||
\(767\) | −20.3951 | −0.736425 | ||||||||
\(768\) | −1.61803 | −0.0583858 | ||||||||
\(769\) | 12.5836 | 0.453776 | 0.226888 | − | 0.973921i | \(-0.427145\pi\) | ||||
0.226888 | + | 0.973921i | \(0.427145\pi\) | |||||||
\(770\) | −5.00000 | −0.180187 | ||||||||
\(771\) | 41.9787 | 1.51183 | ||||||||
\(772\) | −12.1803 | −0.438380 | ||||||||
\(773\) | −20.5623 | −0.739575 | −0.369787 | − | 0.929116i | \(-0.620569\pi\) | ||||
−0.369787 | + | 0.929116i | \(0.620569\pi\) | |||||||
\(774\) | −0.0557281 | −0.00200310 | ||||||||
\(775\) | 26.8328 | 0.963863 | ||||||||
\(776\) | −0.527864 | −0.0189492 | ||||||||
\(777\) | 19.3262 | 0.693325 | ||||||||
\(778\) | −13.6180 | −0.488230 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | −3.00000 | −0.107417 | ||||||||
\(781\) | −50.0000 | −1.78914 | ||||||||
\(782\) | 1.20163 | 0.0429701 | ||||||||
\(783\) | 20.5967 | 0.736068 | ||||||||
\(784\) | 1.00000 | 0.0357143 | ||||||||
\(785\) | 6.67376 | 0.238197 | ||||||||
\(786\) | −10.7082 | −0.381949 | ||||||||
\(787\) | 34.3262 | 1.22360 | 0.611799 | − | 0.791013i | \(-0.290446\pi\) | ||||
0.611799 | + | 0.791013i | \(0.290446\pi\) | |||||||
\(788\) | 12.5623 | 0.447514 | ||||||||
\(789\) | 4.56231 | 0.162422 | ||||||||
\(790\) | −2.14590 | −0.0763476 | ||||||||
\(791\) | −2.85410 | −0.101480 | ||||||||
\(792\) | −1.90983 | −0.0678629 | ||||||||
\(793\) | −2.72949 | −0.0969270 | ||||||||
\(794\) | −1.27051 | −0.0450887 | ||||||||
\(795\) | 1.14590 | 0.0406408 | ||||||||
\(796\) | −16.0902 | −0.570301 | ||||||||
\(797\) | 11.7984 | 0.417920 | 0.208960 | − | 0.977924i | \(-0.432992\pi\) | ||||
0.208960 | + | 0.977924i | \(0.432992\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1.45085 | −0.0513274 | ||||||||
\(800\) | 4.00000 | 0.141421 | ||||||||
\(801\) | −0.708204 | −0.0250232 | ||||||||
\(802\) | −33.4164 | −1.17997 | ||||||||
\(803\) | −27.8115 | −0.981448 | ||||||||
\(804\) | 1.85410 | 0.0653891 | ||||||||
\(805\) | 8.23607 | 0.290283 | ||||||||
\(806\) | 12.4377 | 0.438099 | ||||||||
\(807\) | −21.3262 | −0.750719 | ||||||||
\(808\) | −10.8541 | −0.381846 | ||||||||
\(809\) | −32.8541 | −1.15509 | −0.577544 | − | 0.816359i | \(-0.695989\pi\) | ||||
−0.577544 | + | 0.816359i | \(0.695989\pi\) | |||||||
\(810\) | 7.70820 | 0.270839 | ||||||||
\(811\) | −26.5410 | −0.931981 | −0.465991 | − | 0.884790i | \(-0.654302\pi\) | ||||
−0.465991 | + | 0.884790i | \(0.654302\pi\) | |||||||
\(812\) | −3.76393 | −0.132088 | ||||||||
\(813\) | 47.9787 | 1.68269 | ||||||||
\(814\) | 59.7214 | 2.09323 | ||||||||
\(815\) | −8.47214 | −0.296766 | ||||||||
\(816\) | −0.236068 | −0.00826403 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | −34.2148 | −1.19629 | ||||||||
\(819\) | 0.708204 | 0.0247466 | ||||||||
\(820\) | −10.0902 | −0.352364 | ||||||||
\(821\) | 14.2361 | 0.496842 | 0.248421 | − | 0.968652i | \(-0.420088\pi\) | ||||
0.248421 | + | 0.968652i | \(0.420088\pi\) | |||||||
\(822\) | −30.9443 | −1.07931 | ||||||||
\(823\) | −38.2361 | −1.33283 | −0.666413 | − | 0.745583i | \(-0.732171\pi\) | ||||
−0.666413 | + | 0.745583i | \(0.732171\pi\) | |||||||
\(824\) | −3.90983 | −0.136205 | ||||||||
\(825\) | −32.3607 | −1.12665 | ||||||||
\(826\) | −11.0000 | −0.382739 | ||||||||
\(827\) | −15.6180 | −0.543092 | −0.271546 | − | 0.962425i | \(-0.587535\pi\) | ||||
−0.271546 | + | 0.962425i | \(0.587535\pi\) | |||||||
\(828\) | 3.14590 | 0.109328 | ||||||||
\(829\) | 28.8885 | 1.00334 | 0.501670 | − | 0.865059i | \(-0.332719\pi\) | ||||
0.501670 | + | 0.865059i | \(0.332719\pi\) | |||||||
\(830\) | −11.4164 | −0.396269 | ||||||||
\(831\) | 12.9443 | 0.449032 | ||||||||
\(832\) | 1.85410 | 0.0642794 | ||||||||
\(833\) | 0.145898 | 0.00505507 | ||||||||
\(834\) | 6.85410 | 0.237338 | ||||||||
\(835\) | −24.1803 | −0.836795 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −36.7082 | −1.26882 | ||||||||
\(838\) | −16.7426 | −0.578365 | ||||||||
\(839\) | −18.8197 | −0.649727 | −0.324863 | − | 0.945761i | \(-0.605318\pi\) | ||||
−0.324863 | + | 0.945761i | \(0.605318\pi\) | |||||||
\(840\) | −1.61803 | −0.0558275 | ||||||||
\(841\) | −14.8328 | −0.511476 | ||||||||
\(842\) | −25.9443 | −0.894099 | ||||||||
\(843\) | −12.5623 | −0.432669 | ||||||||
\(844\) | 21.9443 | 0.755353 | ||||||||
\(845\) | −9.56231 | −0.328953 | ||||||||
\(846\) | −3.79837 | −0.130591 | ||||||||
\(847\) | −14.0000 | −0.481046 | ||||||||
\(848\) | −0.708204 | −0.0243198 | ||||||||
\(849\) | −42.9787 | −1.47503 | ||||||||
\(850\) | 0.583592 | 0.0200170 | ||||||||
\(851\) | −98.3738 | −3.37221 | ||||||||
\(852\) | −16.1803 | −0.554329 | ||||||||
\(853\) | −54.9574 | −1.88171 | −0.940853 | − | 0.338814i | \(-0.889974\pi\) | ||||
−0.940853 | + | 0.338814i | \(0.889974\pi\) | |||||||
\(854\) | −1.47214 | −0.0503755 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 3.94427 | 0.134812 | ||||||||
\(857\) | 24.7426 | 0.845193 | 0.422596 | − | 0.906318i | \(-0.361119\pi\) | ||||
0.422596 | + | 0.906318i | \(0.361119\pi\) | |||||||
\(858\) | −15.0000 | −0.512092 | ||||||||
\(859\) | 53.0689 | 1.81069 | 0.905343 | − | 0.424680i | \(-0.139613\pi\) | ||||
0.905343 | + | 0.424680i | \(0.139613\pi\) | |||||||
\(860\) | −0.145898 | −0.00497508 | ||||||||
\(861\) | −16.3262 | −0.556397 | ||||||||
\(862\) | −14.9443 | −0.509004 | ||||||||
\(863\) | 20.7082 | 0.704915 | 0.352458 | − | 0.935828i | \(-0.385346\pi\) | ||||
0.352458 | + | 0.935828i | \(0.385346\pi\) | |||||||
\(864\) | −5.47214 | −0.186166 | ||||||||
\(865\) | −6.23607 | −0.212033 | ||||||||
\(866\) | −25.3820 | −0.862514 | ||||||||
\(867\) | 27.4721 | 0.933003 | ||||||||
\(868\) | 6.70820 | 0.227691 | ||||||||
\(869\) | −10.7295 | −0.363973 | ||||||||
\(870\) | 6.09017 | 0.206476 | ||||||||
\(871\) | −2.12461 | −0.0719897 | ||||||||
\(872\) | 6.56231 | 0.222228 | ||||||||
\(873\) | −0.201626 | −0.00682401 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 9.00000 | 0.304256 | ||||||||
\(876\) | −9.00000 | −0.304082 | ||||||||
\(877\) | 10.3262 | 0.348692 | 0.174346 | − | 0.984684i | \(-0.444219\pi\) | ||||
0.174346 | + | 0.984684i | \(0.444219\pi\) | |||||||
\(878\) | −39.9443 | −1.34805 | ||||||||
\(879\) | 19.0344 | 0.642016 | ||||||||
\(880\) | −5.00000 | −0.168550 | ||||||||
\(881\) | 20.8541 | 0.702593 | 0.351296 | − | 0.936264i | \(-0.385741\pi\) | ||||
0.351296 | + | 0.936264i | \(0.385741\pi\) | |||||||
\(882\) | 0.381966 | 0.0128615 | ||||||||
\(883\) | −57.9787 | −1.95114 | −0.975570 | − | 0.219691i | \(-0.929495\pi\) | ||||
−0.975570 | + | 0.219691i | \(0.929495\pi\) | |||||||
\(884\) | 0.270510 | 0.00909823 | ||||||||
\(885\) | 17.7984 | 0.598286 | ||||||||
\(886\) | 34.2148 | 1.14947 | ||||||||
\(887\) | 32.8328 | 1.10242 | 0.551209 | − | 0.834367i | \(-0.314167\pi\) | ||||
0.551209 | + | 0.834367i | \(0.314167\pi\) | |||||||
\(888\) | 19.3262 | 0.648546 | ||||||||
\(889\) | 8.32624 | 0.279253 | ||||||||
\(890\) | −1.85410 | −0.0621496 | ||||||||
\(891\) | 38.5410 | 1.29117 | ||||||||
\(892\) | 25.6525 | 0.858908 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 5.85410 | 0.195790 | ||||||||
\(895\) | 20.0344 | 0.669678 | ||||||||
\(896\) | 1.00000 | 0.0334077 | ||||||||
\(897\) | 24.7082 | 0.824983 | ||||||||
\(898\) | 0.180340 | 0.00601802 | ||||||||
\(899\) | −25.2492 | −0.842109 | ||||||||
\(900\) | 1.52786 | 0.0509288 | ||||||||
\(901\) | −0.103326 | −0.00344227 | ||||||||
\(902\) | −50.4508 | −1.67983 | ||||||||
\(903\) | −0.236068 | −0.00785585 | ||||||||
\(904\) | −2.85410 | −0.0949260 | ||||||||
\(905\) | 20.2361 | 0.672670 | ||||||||
\(906\) | 15.7984 | 0.524866 | ||||||||
\(907\) | −32.3262 | −1.07338 | −0.536688 | − | 0.843781i | \(-0.680325\pi\) | ||||
−0.536688 | + | 0.843781i | \(0.680325\pi\) | |||||||
\(908\) | 9.76393 | 0.324027 | ||||||||
\(909\) | −4.14590 | −0.137511 | ||||||||
\(910\) | 1.85410 | 0.0614629 | ||||||||
\(911\) | 23.1591 | 0.767294 | 0.383647 | − | 0.923480i | \(-0.374668\pi\) | ||||
0.383647 | + | 0.923480i | \(0.374668\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −57.0820 | −1.88914 | ||||||||
\(914\) | 5.88854 | 0.194776 | ||||||||
\(915\) | 2.38197 | 0.0787454 | ||||||||
\(916\) | 1.09017 | 0.0360202 | ||||||||
\(917\) | 6.61803 | 0.218547 | ||||||||
\(918\) | −0.798374 | −0.0263503 | ||||||||
\(919\) | −19.0344 | −0.627888 | −0.313944 | − | 0.949441i | \(-0.601650\pi\) | ||||
−0.313944 | + | 0.949441i | \(0.601650\pi\) | |||||||
\(920\) | 8.23607 | 0.271535 | ||||||||
\(921\) | −20.9443 | −0.690137 | ||||||||
\(922\) | 24.5410 | 0.808215 | ||||||||
\(923\) | 18.5410 | 0.610285 | ||||||||
\(924\) | −8.09017 | −0.266147 | ||||||||
\(925\) | −47.7771 | −1.57090 | ||||||||
\(926\) | −6.56231 | −0.215651 | ||||||||
\(927\) | −1.49342 | −0.0490504 | ||||||||
\(928\) | −3.76393 | −0.123557 | ||||||||
\(929\) | 8.88854 | 0.291624 | 0.145812 | − | 0.989312i | \(-0.453421\pi\) | ||||
0.145812 | + | 0.989312i | \(0.453421\pi\) | |||||||
\(930\) | −10.8541 | −0.355920 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 18.0344 | 0.590738 | ||||||||
\(933\) | −39.2148 | −1.28383 | ||||||||
\(934\) | −24.5279 | −0.802576 | ||||||||
\(935\) | −0.729490 | −0.0238569 | ||||||||
\(936\) | 0.708204 | 0.0231484 | ||||||||
\(937\) | −33.3951 | −1.09097 | −0.545486 | − | 0.838120i | \(-0.683655\pi\) | ||||
−0.545486 | + | 0.838120i | \(0.683655\pi\) | |||||||
\(938\) | −1.14590 | −0.0374149 | ||||||||
\(939\) | −48.6869 | −1.58884 | ||||||||
\(940\) | −9.94427 | −0.324346 | ||||||||
\(941\) | 24.2148 | 0.789379 | 0.394690 | − | 0.918814i | \(-0.370852\pi\) | ||||
0.394690 | + | 0.918814i | \(0.370852\pi\) | |||||||
\(942\) | 10.7984 | 0.351830 | ||||||||
\(943\) | 83.1033 | 2.70622 | ||||||||
\(944\) | −11.0000 | −0.358020 | ||||||||
\(945\) | −5.47214 | −0.178009 | ||||||||
\(946\) | −0.729490 | −0.0237178 | ||||||||
\(947\) | 14.1115 | 0.458561 | 0.229280 | − | 0.973360i | \(-0.426363\pi\) | ||||
0.229280 | + | 0.973360i | \(0.426363\pi\) | |||||||
\(948\) | −3.47214 | −0.112770 | ||||||||
\(949\) | 10.3131 | 0.334777 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −29.7984 | −0.966278 | ||||||||
\(952\) | 0.145898 | 0.00472858 | ||||||||
\(953\) | −40.7771 | −1.32090 | −0.660450 | − | 0.750870i | \(-0.729634\pi\) | ||||
−0.660450 | + | 0.750870i | \(0.729634\pi\) | |||||||
\(954\) | −0.270510 | −0.00875808 | ||||||||
\(955\) | 25.1803 | 0.814817 | ||||||||
\(956\) | −17.8541 | −0.577443 | ||||||||
\(957\) | 30.4508 | 0.984336 | ||||||||
\(958\) | −22.1803 | −0.716614 | ||||||||
\(959\) | 19.1246 | 0.617566 | ||||||||
\(960\) | −1.61803 | −0.0522218 | ||||||||
\(961\) | 14.0000 | 0.451613 | ||||||||
\(962\) | −22.1459 | −0.714012 | ||||||||
\(963\) | 1.50658 | 0.0485488 | ||||||||
\(964\) | −19.0902 | −0.614853 | ||||||||
\(965\) | −12.1803 | −0.392099 | ||||||||
\(966\) | 13.3262 | 0.428765 | ||||||||
\(967\) | −21.7295 | −0.698773 | −0.349387 | − | 0.936979i | \(-0.613610\pi\) | ||||
−0.349387 | + | 0.936979i | \(0.613610\pi\) | |||||||
\(968\) | −14.0000 | −0.449977 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −0.527864 | −0.0169487 | ||||||||
\(971\) | 7.58359 | 0.243369 | 0.121685 | − | 0.992569i | \(-0.461170\pi\) | ||||
0.121685 | + | 0.992569i | \(0.461170\pi\) | |||||||
\(972\) | −3.94427 | −0.126513 | ||||||||
\(973\) | −4.23607 | −0.135802 | ||||||||
\(974\) | −11.1803 | −0.358241 | ||||||||
\(975\) | 12.0000 | 0.384308 | ||||||||
\(976\) | −1.47214 | −0.0471219 | ||||||||
\(977\) | −22.7771 | −0.728704 | −0.364352 | − | 0.931261i | \(-0.618709\pi\) | ||||
−0.364352 | + | 0.931261i | \(0.618709\pi\) | |||||||
\(978\) | −13.7082 | −0.438340 | ||||||||
\(979\) | −9.27051 | −0.296287 | ||||||||
\(980\) | 1.00000 | 0.0319438 | ||||||||
\(981\) | 2.50658 | 0.0800289 | ||||||||
\(982\) | −29.5967 | −0.944470 | ||||||||
\(983\) | −47.5066 | −1.51522 | −0.757612 | − | 0.652705i | \(-0.773634\pi\) | ||||
−0.757612 | + | 0.652705i | \(0.773634\pi\) | |||||||
\(984\) | −16.3262 | −0.520461 | ||||||||
\(985\) | 12.5623 | 0.400268 | ||||||||
\(986\) | −0.549150 | −0.0174885 | ||||||||
\(987\) | −16.0902 | −0.512156 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 1.20163 | 0.0382095 | ||||||||
\(990\) | −1.90983 | −0.0606984 | ||||||||
\(991\) | −1.41641 | −0.0449937 | −0.0224968 | − | 0.999747i | \(-0.507162\pi\) | ||||
−0.0224968 | + | 0.999747i | \(0.507162\pi\) | |||||||
\(992\) | 6.70820 | 0.212986 | ||||||||
\(993\) | 5.70820 | 0.181144 | ||||||||
\(994\) | 10.0000 | 0.317181 | ||||||||
\(995\) | −16.0902 | −0.510093 | ||||||||
\(996\) | −18.4721 | −0.585312 | ||||||||
\(997\) | 1.96556 | 0.0622499 | 0.0311249 | − | 0.999516i | \(-0.490091\pi\) | ||||
0.0311249 | + | 0.999516i | \(0.490091\pi\) | |||||||
\(998\) | 10.4164 | 0.329726 | ||||||||
\(999\) | 65.3607 | 2.06792 |
(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 | 5054.2.a.f.1.1 | ✓ | 2 | |
19.18 | odd | 2 | 5054.2.a.p.1.2 | yes | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
5054.2.a.f.1.1 | ✓ | 2 | 1.1 | even | 1 | trivial | |
5054.2.a.p.1.2 | yes | 2 | 19.18 | odd | 2 |