Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4015,2,Mod(1,4015)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4015, 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("4015.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4015 = 5 \cdot 11 \cdot 73 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4015.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: | \(32.0599364115\) |
Analytic rank: | \(1\) |
Dimension: | \(31\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.19 | ||
Character | \(\chi\) | \(=\) | 4015.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.416759 | 0.294693 | 0.147346 | − | 0.989085i | \(-0.452927\pi\) | ||||
0.147346 | + | 0.989085i | \(0.452927\pi\) | |||||||
\(3\) | 1.40268 | 0.809838 | 0.404919 | − | 0.914352i | \(-0.367300\pi\) | ||||
0.404919 | + | 0.914352i | \(0.367300\pi\) | |||||||
\(4\) | −1.82631 | −0.913156 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 0.584579 | 0.238654 | ||||||||
\(7\) | −1.52897 | −0.577898 | −0.288949 | − | 0.957345i | \(-0.593306\pi\) | ||||
−0.288949 | + | 0.957345i | \(0.593306\pi\) | |||||||
\(8\) | −1.59465 | −0.563793 | ||||||||
\(9\) | −1.03249 | −0.344162 | ||||||||
\(10\) | −0.416759 | −0.131791 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | −2.56173 | −0.739509 | ||||||||
\(13\) | 2.05922 | 0.571125 | 0.285563 | − | 0.958360i | \(-0.407820\pi\) | ||||
0.285563 | + | 0.958360i | \(0.407820\pi\) | |||||||
\(14\) | −0.637213 | −0.170302 | ||||||||
\(15\) | −1.40268 | −0.362171 | ||||||||
\(16\) | 2.98804 | 0.747010 | ||||||||
\(17\) | 6.91820 | 1.67791 | 0.838955 | − | 0.544200i | \(-0.183167\pi\) | ||||
0.838955 | + | 0.544200i | \(0.183167\pi\) | |||||||
\(18\) | −0.430297 | −0.101422 | ||||||||
\(19\) | −1.02478 | −0.235101 | −0.117551 | − | 0.993067i | \(-0.537504\pi\) | ||||
−0.117551 | + | 0.993067i | \(0.537504\pi\) | |||||||
\(20\) | 1.82631 | 0.408376 | ||||||||
\(21\) | −2.14466 | −0.468004 | ||||||||
\(22\) | 0.416759 | 0.0888532 | ||||||||
\(23\) | −0.555659 | −0.115863 | −0.0579314 | − | 0.998321i | \(-0.518450\pi\) | ||||
−0.0579314 | + | 0.998321i | \(0.518450\pi\) | |||||||
\(24\) | −2.23678 | −0.456581 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0.858198 | 0.168307 | ||||||||
\(27\) | −5.65629 | −1.08855 | ||||||||
\(28\) | 2.79238 | 0.527711 | ||||||||
\(29\) | 8.69161 | 1.61399 | 0.806996 | − | 0.590557i | \(-0.201092\pi\) | ||||
0.806996 | + | 0.590557i | \(0.201092\pi\) | |||||||
\(30\) | −0.584579 | −0.106729 | ||||||||
\(31\) | −9.18767 | −1.65015 | −0.825077 | − | 0.565021i | \(-0.808868\pi\) | ||||
−0.825077 | + | 0.565021i | \(0.808868\pi\) | |||||||
\(32\) | 4.43459 | 0.783932 | ||||||||
\(33\) | 1.40268 | 0.244175 | ||||||||
\(34\) | 2.88322 | 0.494468 | ||||||||
\(35\) | 1.52897 | 0.258444 | ||||||||
\(36\) | 1.88564 | 0.314274 | ||||||||
\(37\) | −10.0732 | −1.65603 | −0.828015 | − | 0.560706i | \(-0.810530\pi\) | ||||
−0.828015 | + | 0.560706i | \(0.810530\pi\) | |||||||
\(38\) | −0.427087 | −0.0692827 | ||||||||
\(39\) | 2.88843 | 0.462519 | ||||||||
\(40\) | 1.59465 | 0.252136 | ||||||||
\(41\) | 3.73463 | 0.583251 | 0.291625 | − | 0.956533i | \(-0.405804\pi\) | ||||
0.291625 | + | 0.956533i | \(0.405804\pi\) | |||||||
\(42\) | −0.893806 | −0.137917 | ||||||||
\(43\) | −7.10211 | −1.08306 | −0.541531 | − | 0.840681i | \(-0.682155\pi\) | ||||
−0.541531 | + | 0.840681i | \(0.682155\pi\) | |||||||
\(44\) | −1.82631 | −0.275327 | ||||||||
\(45\) | 1.03249 | 0.153914 | ||||||||
\(46\) | −0.231576 | −0.0341440 | ||||||||
\(47\) | 12.0692 | 1.76048 | 0.880240 | − | 0.474529i | \(-0.157381\pi\) | ||||
0.880240 | + | 0.474529i | \(0.157381\pi\) | |||||||
\(48\) | 4.19127 | 0.604958 | ||||||||
\(49\) | −4.66224 | −0.666034 | ||||||||
\(50\) | 0.416759 | 0.0589386 | ||||||||
\(51\) | 9.70403 | 1.35884 | ||||||||
\(52\) | −3.76078 | −0.521527 | ||||||||
\(53\) | −9.47032 | −1.30085 | −0.650424 | − | 0.759571i | \(-0.725409\pi\) | ||||
−0.650424 | + | 0.759571i | \(0.725409\pi\) | |||||||
\(54\) | −2.35731 | −0.320789 | ||||||||
\(55\) | −1.00000 | −0.134840 | ||||||||
\(56\) | 2.43817 | 0.325815 | ||||||||
\(57\) | −1.43744 | −0.190394 | ||||||||
\(58\) | 3.62230 | 0.475632 | ||||||||
\(59\) | −10.1112 | −1.31637 | −0.658183 | − | 0.752858i | \(-0.728675\pi\) | ||||
−0.658183 | + | 0.752858i | \(0.728675\pi\) | |||||||
\(60\) | 2.56173 | 0.330718 | ||||||||
\(61\) | −3.95339 | −0.506180 | −0.253090 | − | 0.967443i | \(-0.581447\pi\) | ||||
−0.253090 | + | 0.967443i | \(0.581447\pi\) | |||||||
\(62\) | −3.82904 | −0.486288 | ||||||||
\(63\) | 1.57864 | 0.198890 | ||||||||
\(64\) | −4.12793 | −0.515991 | ||||||||
\(65\) | −2.05922 | −0.255415 | ||||||||
\(66\) | 0.584579 | 0.0719567 | ||||||||
\(67\) | −1.23353 | −0.150700 | −0.0753501 | − | 0.997157i | \(-0.524007\pi\) | ||||
−0.0753501 | + | 0.997157i | \(0.524007\pi\) | |||||||
\(68\) | −12.6348 | −1.53219 | ||||||||
\(69\) | −0.779412 | −0.0938302 | ||||||||
\(70\) | 0.637213 | 0.0761615 | ||||||||
\(71\) | −3.25447 | −0.386235 | −0.193117 | − | 0.981176i | \(-0.561860\pi\) | ||||
−0.193117 | + | 0.981176i | \(0.561860\pi\) | |||||||
\(72\) | 1.64645 | 0.194036 | ||||||||
\(73\) | 1.00000 | 0.117041 | ||||||||
\(74\) | −4.19811 | −0.488020 | ||||||||
\(75\) | 1.40268 | 0.161968 | ||||||||
\(76\) | 1.87157 | 0.214684 | ||||||||
\(77\) | −1.52897 | −0.174243 | ||||||||
\(78\) | 1.20378 | 0.136301 | ||||||||
\(79\) | −8.38322 | −0.943186 | −0.471593 | − | 0.881816i | \(-0.656321\pi\) | ||||
−0.471593 | + | 0.881816i | \(0.656321\pi\) | |||||||
\(80\) | −2.98804 | −0.334073 | ||||||||
\(81\) | −4.83652 | −0.537391 | ||||||||
\(82\) | 1.55644 | 0.171880 | ||||||||
\(83\) | 15.2456 | 1.67343 | 0.836714 | − | 0.547641i | \(-0.184474\pi\) | ||||
0.836714 | + | 0.547641i | \(0.184474\pi\) | |||||||
\(84\) | 3.91682 | 0.427360 | ||||||||
\(85\) | −6.91820 | −0.750384 | ||||||||
\(86\) | −2.95986 | −0.319170 | ||||||||
\(87\) | 12.1916 | 1.30707 | ||||||||
\(88\) | −1.59465 | −0.169990 | ||||||||
\(89\) | −6.12001 | −0.648720 | −0.324360 | − | 0.945934i | \(-0.605149\pi\) | ||||
−0.324360 | + | 0.945934i | \(0.605149\pi\) | |||||||
\(90\) | 0.430297 | 0.0453573 | ||||||||
\(91\) | −3.14849 | −0.330052 | ||||||||
\(92\) | 1.01481 | 0.105801 | ||||||||
\(93\) | −12.8874 | −1.33636 | ||||||||
\(94\) | 5.02996 | 0.518801 | ||||||||
\(95\) | 1.02478 | 0.105141 | ||||||||
\(96\) | 6.22031 | 0.634858 | ||||||||
\(97\) | −12.1941 | −1.23813 | −0.619064 | − | 0.785341i | \(-0.712488\pi\) | ||||
−0.619064 | + | 0.785341i | \(0.712488\pi\) | |||||||
\(98\) | −1.94303 | −0.196276 | ||||||||
\(99\) | −1.03249 | −0.103769 | ||||||||
\(100\) | −1.82631 | −0.182631 | ||||||||
\(101\) | 19.2090 | 1.91136 | 0.955682 | − | 0.294402i | \(-0.0951206\pi\) | ||||
0.955682 | + | 0.294402i | \(0.0951206\pi\) | |||||||
\(102\) | 4.04424 | 0.400439 | ||||||||
\(103\) | −1.01096 | −0.0996125 | −0.0498062 | − | 0.998759i | \(-0.515860\pi\) | ||||
−0.0498062 | + | 0.998759i | \(0.515860\pi\) | |||||||
\(104\) | −3.28373 | −0.321997 | ||||||||
\(105\) | 2.14466 | 0.209298 | ||||||||
\(106\) | −3.94684 | −0.383351 | ||||||||
\(107\) | 0.0132951 | 0.00128528 | 0.000642642 | − | 1.00000i | \(-0.499795\pi\) | ||||
0.000642642 | 1.00000i | \(0.499795\pi\) | ||||||||
\(108\) | 10.3302 | 0.994020 | ||||||||
\(109\) | −17.2613 | −1.65333 | −0.826665 | − | 0.562694i | \(-0.809765\pi\) | ||||
−0.826665 | + | 0.562694i | \(0.809765\pi\) | |||||||
\(110\) | −0.416759 | −0.0397364 | ||||||||
\(111\) | −14.1295 | −1.34112 | ||||||||
\(112\) | −4.56863 | −0.431695 | ||||||||
\(113\) | −11.6377 | −1.09479 | −0.547393 | − | 0.836876i | \(-0.684380\pi\) | ||||
−0.547393 | + | 0.836876i | \(0.684380\pi\) | |||||||
\(114\) | −0.599067 | −0.0561078 | ||||||||
\(115\) | 0.555659 | 0.0518154 | ||||||||
\(116\) | −15.8736 | −1.47383 | ||||||||
\(117\) | −2.12612 | −0.196560 | ||||||||
\(118\) | −4.21393 | −0.387924 | ||||||||
\(119\) | −10.5777 | −0.969660 | ||||||||
\(120\) | 2.23678 | 0.204189 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | −1.64761 | −0.149168 | ||||||||
\(123\) | 5.23849 | 0.472339 | ||||||||
\(124\) | 16.7795 | 1.50685 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0.657913 | 0.0586116 | ||||||||
\(127\) | −15.5671 | −1.38136 | −0.690678 | − | 0.723163i | \(-0.742688\pi\) | ||||
−0.690678 | + | 0.723163i | \(0.742688\pi\) | |||||||
\(128\) | −10.5895 | −0.935991 | ||||||||
\(129\) | −9.96199 | −0.877104 | ||||||||
\(130\) | −0.858198 | −0.0752690 | ||||||||
\(131\) | −2.08978 | −0.182585 | −0.0912927 | − | 0.995824i | \(-0.529100\pi\) | ||||
−0.0912927 | + | 0.995824i | \(0.529100\pi\) | |||||||
\(132\) | −2.56173 | −0.222970 | ||||||||
\(133\) | 1.56687 | 0.135864 | ||||||||
\(134\) | −0.514086 | −0.0444103 | ||||||||
\(135\) | 5.65629 | 0.486816 | ||||||||
\(136\) | −11.0321 | −0.945995 | ||||||||
\(137\) | −18.4460 | −1.57594 | −0.787972 | − | 0.615711i | \(-0.788869\pi\) | ||||
−0.787972 | + | 0.615711i | \(0.788869\pi\) | |||||||
\(138\) | −0.324827 | −0.0276511 | ||||||||
\(139\) | −16.7729 | −1.42266 | −0.711328 | − | 0.702860i | \(-0.751906\pi\) | ||||
−0.711328 | + | 0.702860i | \(0.751906\pi\) | |||||||
\(140\) | −2.79238 | −0.235999 | ||||||||
\(141\) | 16.9293 | 1.42570 | ||||||||
\(142\) | −1.35633 | −0.113821 | ||||||||
\(143\) | 2.05922 | 0.172201 | ||||||||
\(144\) | −3.08511 | −0.257093 | ||||||||
\(145\) | −8.69161 | −0.721799 | ||||||||
\(146\) | 0.416759 | 0.0344912 | ||||||||
\(147\) | −6.53964 | −0.539380 | ||||||||
\(148\) | 18.3969 | 1.51221 | ||||||||
\(149\) | −15.0955 | −1.23667 | −0.618337 | − | 0.785913i | \(-0.712193\pi\) | ||||
−0.618337 | + | 0.785913i | \(0.712193\pi\) | |||||||
\(150\) | 0.584579 | 0.0477307 | ||||||||
\(151\) | 15.5459 | 1.26510 | 0.632552 | − | 0.774518i | \(-0.282007\pi\) | ||||
0.632552 | + | 0.774518i | \(0.282007\pi\) | |||||||
\(152\) | 1.63417 | 0.132549 | ||||||||
\(153\) | −7.14295 | −0.577473 | ||||||||
\(154\) | −0.637213 | −0.0513481 | ||||||||
\(155\) | 9.18767 | 0.737971 | ||||||||
\(156\) | −5.27518 | −0.422352 | ||||||||
\(157\) | −13.4904 | −1.07665 | −0.538324 | − | 0.842738i | \(-0.680942\pi\) | ||||
−0.538324 | + | 0.842738i | \(0.680942\pi\) | |||||||
\(158\) | −3.49378 | −0.277950 | ||||||||
\(159\) | −13.2838 | −1.05348 | ||||||||
\(160\) | −4.43459 | −0.350585 | ||||||||
\(161\) | 0.849587 | 0.0669569 | ||||||||
\(162\) | −2.01566 | −0.158365 | ||||||||
\(163\) | 20.5026 | 1.60589 | 0.802944 | − | 0.596054i | \(-0.203266\pi\) | ||||
0.802944 | + | 0.596054i | \(0.203266\pi\) | |||||||
\(164\) | −6.82059 | −0.532599 | ||||||||
\(165\) | −1.40268 | −0.109199 | ||||||||
\(166\) | 6.35375 | 0.493147 | ||||||||
\(167\) | 12.7938 | 0.990011 | 0.495005 | − | 0.868890i | \(-0.335166\pi\) | ||||
0.495005 | + | 0.868890i | \(0.335166\pi\) | |||||||
\(168\) | 3.41998 | 0.263857 | ||||||||
\(169\) | −8.75961 | −0.673816 | ||||||||
\(170\) | −2.88322 | −0.221133 | ||||||||
\(171\) | 1.05807 | 0.0809129 | ||||||||
\(172\) | 12.9707 | 0.989004 | ||||||||
\(173\) | 17.6575 | 1.34247 | 0.671237 | − | 0.741242i | \(-0.265763\pi\) | ||||
0.671237 | + | 0.741242i | \(0.265763\pi\) | |||||||
\(174\) | 5.08094 | 0.385185 | ||||||||
\(175\) | −1.52897 | −0.115580 | ||||||||
\(176\) | 2.98804 | 0.225232 | ||||||||
\(177\) | −14.1828 | −1.06604 | ||||||||
\(178\) | −2.55057 | −0.191173 | ||||||||
\(179\) | −12.9425 | −0.967370 | −0.483685 | − | 0.875242i | \(-0.660702\pi\) | ||||
−0.483685 | + | 0.875242i | \(0.660702\pi\) | |||||||
\(180\) | −1.88564 | −0.140547 | ||||||||
\(181\) | 2.58085 | 0.191833 | 0.0959166 | − | 0.995389i | \(-0.469422\pi\) | ||||
0.0959166 | + | 0.995389i | \(0.469422\pi\) | |||||||
\(182\) | −1.31216 | −0.0972639 | ||||||||
\(183\) | −5.54535 | −0.409924 | ||||||||
\(184\) | 0.886080 | 0.0653227 | ||||||||
\(185\) | 10.0732 | 0.740599 | ||||||||
\(186\) | −5.37092 | −0.393815 | ||||||||
\(187\) | 6.91820 | 0.505909 | ||||||||
\(188\) | −22.0422 | −1.60759 | ||||||||
\(189\) | 8.64832 | 0.629073 | ||||||||
\(190\) | 0.427087 | 0.0309842 | ||||||||
\(191\) | 15.4394 | 1.11715 | 0.558577 | − | 0.829453i | \(-0.311348\pi\) | ||||
0.558577 | + | 0.829453i | \(0.311348\pi\) | |||||||
\(192\) | −5.79017 | −0.417869 | ||||||||
\(193\) | −2.73093 | −0.196577 | −0.0982884 | − | 0.995158i | \(-0.531337\pi\) | ||||
−0.0982884 | + | 0.995158i | \(0.531337\pi\) | |||||||
\(194\) | −5.08201 | −0.364867 | ||||||||
\(195\) | −2.88843 | −0.206845 | ||||||||
\(196\) | 8.51471 | 0.608193 | ||||||||
\(197\) | −9.84862 | −0.701685 | −0.350842 | − | 0.936435i | \(-0.614105\pi\) | ||||
−0.350842 | + | 0.936435i | \(0.614105\pi\) | |||||||
\(198\) | −0.430297 | −0.0305799 | ||||||||
\(199\) | 16.6457 | 1.17998 | 0.589991 | − | 0.807410i | \(-0.299131\pi\) | ||||
0.589991 | + | 0.807410i | \(0.299131\pi\) | |||||||
\(200\) | −1.59465 | −0.112759 | ||||||||
\(201\) | −1.73026 | −0.122043 | ||||||||
\(202\) | 8.00550 | 0.563265 | ||||||||
\(203\) | −13.2892 | −0.932722 | ||||||||
\(204\) | −17.7226 | −1.24083 | ||||||||
\(205\) | −3.73463 | −0.260838 | ||||||||
\(206\) | −0.421325 | −0.0293551 | ||||||||
\(207\) | 0.573710 | 0.0398756 | ||||||||
\(208\) | 6.15304 | 0.426636 | ||||||||
\(209\) | −1.02478 | −0.0708857 | ||||||||
\(210\) | 0.893806 | 0.0616785 | ||||||||
\(211\) | 1.71690 | 0.118196 | 0.0590981 | − | 0.998252i | \(-0.481178\pi\) | ||||
0.0590981 | + | 0.998252i | \(0.481178\pi\) | |||||||
\(212\) | 17.2958 | 1.18788 | ||||||||
\(213\) | −4.56499 | −0.312788 | ||||||||
\(214\) | 0.00554083 | 0.000378764 0 | ||||||||
\(215\) | 7.10211 | 0.484360 | ||||||||
\(216\) | 9.01980 | 0.613719 | ||||||||
\(217\) | 14.0477 | 0.953620 | ||||||||
\(218\) | −7.19378 | −0.487225 | ||||||||
\(219\) | 1.40268 | 0.0947844 | ||||||||
\(220\) | 1.82631 | 0.123130 | ||||||||
\(221\) | 14.2461 | 0.958297 | ||||||||
\(222\) | −5.88860 | −0.395217 | ||||||||
\(223\) | 6.28221 | 0.420688 | 0.210344 | − | 0.977627i | \(-0.432542\pi\) | ||||
0.210344 | + | 0.977627i | \(0.432542\pi\) | |||||||
\(224\) | −6.78037 | −0.453032 | ||||||||
\(225\) | −1.03249 | −0.0688324 | ||||||||
\(226\) | −4.85012 | −0.322625 | ||||||||
\(227\) | 2.68694 | 0.178338 | 0.0891692 | − | 0.996016i | \(-0.471579\pi\) | ||||
0.0891692 | + | 0.996016i | \(0.471579\pi\) | |||||||
\(228\) | 2.62522 | 0.173859 | ||||||||
\(229\) | −20.8926 | −1.38062 | −0.690312 | − | 0.723512i | \(-0.742527\pi\) | ||||
−0.690312 | + | 0.723512i | \(0.742527\pi\) | |||||||
\(230\) | 0.231576 | 0.0152696 | ||||||||
\(231\) | −2.14466 | −0.141108 | ||||||||
\(232\) | −13.8601 | −0.909958 | ||||||||
\(233\) | −12.9315 | −0.847168 | −0.423584 | − | 0.905857i | \(-0.639228\pi\) | ||||
−0.423584 | + | 0.905857i | \(0.639228\pi\) | |||||||
\(234\) | −0.886078 | −0.0579247 | ||||||||
\(235\) | −12.0692 | −0.787311 | ||||||||
\(236\) | 18.4662 | 1.20205 | ||||||||
\(237\) | −11.7590 | −0.763828 | ||||||||
\(238\) | −4.40837 | −0.285752 | ||||||||
\(239\) | 10.4220 | 0.674143 | 0.337071 | − | 0.941479i | \(-0.390564\pi\) | ||||
0.337071 | + | 0.941479i | \(0.390564\pi\) | |||||||
\(240\) | −4.19127 | −0.270545 | ||||||||
\(241\) | −4.15242 | −0.267481 | −0.133740 | − | 0.991016i | \(-0.542699\pi\) | ||||
−0.133740 | + | 0.991016i | \(0.542699\pi\) | |||||||
\(242\) | 0.416759 | 0.0267903 | ||||||||
\(243\) | 10.1848 | 0.653354 | ||||||||
\(244\) | 7.22012 | 0.462221 | ||||||||
\(245\) | 4.66224 | 0.297860 | ||||||||
\(246\) | 2.18319 | 0.139195 | ||||||||
\(247\) | −2.11025 | −0.134272 | ||||||||
\(248\) | 14.6511 | 0.930345 | ||||||||
\(249\) | 21.3848 | 1.35521 | ||||||||
\(250\) | −0.416759 | −0.0263581 | ||||||||
\(251\) | −2.77030 | −0.174860 | −0.0874300 | − | 0.996171i | \(-0.527865\pi\) | ||||
−0.0874300 | + | 0.996171i | \(0.527865\pi\) | |||||||
\(252\) | −2.88310 | −0.181618 | ||||||||
\(253\) | −0.555659 | −0.0349340 | ||||||||
\(254\) | −6.48772 | −0.407076 | ||||||||
\(255\) | −9.70403 | −0.607690 | ||||||||
\(256\) | 3.84258 | 0.240161 | ||||||||
\(257\) | −9.79718 | −0.611131 | −0.305566 | − | 0.952171i | \(-0.598846\pi\) | ||||
−0.305566 | + | 0.952171i | \(0.598846\pi\) | |||||||
\(258\) | −4.15175 | −0.258476 | ||||||||
\(259\) | 15.4017 | 0.957015 | ||||||||
\(260\) | 3.76078 | 0.233234 | ||||||||
\(261\) | −8.97396 | −0.555474 | ||||||||
\(262\) | −0.870936 | −0.0538066 | ||||||||
\(263\) | −5.96549 | −0.367848 | −0.183924 | − | 0.982940i | \(-0.558880\pi\) | ||||
−0.183924 | + | 0.982940i | \(0.558880\pi\) | |||||||
\(264\) | −2.23678 | −0.137664 | ||||||||
\(265\) | 9.47032 | 0.581757 | ||||||||
\(266\) | 0.653005 | 0.0400383 | ||||||||
\(267\) | −8.58443 | −0.525358 | ||||||||
\(268\) | 2.25282 | 0.137613 | ||||||||
\(269\) | −6.16244 | −0.375731 | −0.187865 | − | 0.982195i | \(-0.560157\pi\) | ||||
−0.187865 | + | 0.982195i | \(0.560157\pi\) | |||||||
\(270\) | 2.35731 | 0.143461 | ||||||||
\(271\) | 22.2281 | 1.35026 | 0.675130 | − | 0.737699i | \(-0.264087\pi\) | ||||
0.675130 | + | 0.737699i | \(0.264087\pi\) | |||||||
\(272\) | 20.6719 | 1.25342 | ||||||||
\(273\) | −4.41633 | −0.267289 | ||||||||
\(274\) | −7.68751 | −0.464420 | ||||||||
\(275\) | 1.00000 | 0.0603023 | ||||||||
\(276\) | 1.42345 | 0.0856816 | ||||||||
\(277\) | 21.8299 | 1.31163 | 0.655816 | − | 0.754921i | \(-0.272325\pi\) | ||||
0.655816 | + | 0.754921i | \(0.272325\pi\) | |||||||
\(278\) | −6.99023 | −0.419246 | ||||||||
\(279\) | 9.48613 | 0.567920 | ||||||||
\(280\) | −2.43817 | −0.145709 | ||||||||
\(281\) | −31.3683 | −1.87128 | −0.935639 | − | 0.352960i | \(-0.885175\pi\) | ||||
−0.935639 | + | 0.352960i | \(0.885175\pi\) | |||||||
\(282\) | 7.05543 | 0.420145 | ||||||||
\(283\) | −21.0095 | −1.24888 | −0.624442 | − | 0.781071i | \(-0.714673\pi\) | ||||
−0.624442 | + | 0.781071i | \(0.714673\pi\) | |||||||
\(284\) | 5.94368 | 0.352693 | ||||||||
\(285\) | 1.43744 | 0.0851468 | ||||||||
\(286\) | 0.858198 | 0.0507463 | ||||||||
\(287\) | −5.71014 | −0.337059 | ||||||||
\(288\) | −4.57865 | −0.269800 | ||||||||
\(289\) | 30.8615 | 1.81538 | ||||||||
\(290\) | −3.62230 | −0.212709 | ||||||||
\(291\) | −17.1045 | −1.00268 | ||||||||
\(292\) | −1.82631 | −0.106877 | ||||||||
\(293\) | −0.276370 | −0.0161457 | −0.00807286 | − | 0.999967i | \(-0.502570\pi\) | ||||
−0.00807286 | + | 0.999967i | \(0.502570\pi\) | |||||||
\(294\) | −2.72545 | −0.158951 | ||||||||
\(295\) | 10.1112 | 0.588697 | ||||||||
\(296\) | 16.0633 | 0.933658 | ||||||||
\(297\) | −5.65629 | −0.328211 | ||||||||
\(298\) | −6.29119 | −0.364439 | ||||||||
\(299\) | −1.14422 | −0.0661722 | ||||||||
\(300\) | −2.56173 | −0.147902 | ||||||||
\(301\) | 10.8589 | 0.625898 | ||||||||
\(302\) | 6.47887 | 0.372817 | ||||||||
\(303\) | 26.9440 | 1.54790 | ||||||||
\(304\) | −3.06209 | −0.175623 | ||||||||
\(305\) | 3.95339 | 0.226370 | ||||||||
\(306\) | −2.97688 | −0.170177 | ||||||||
\(307\) | −7.33762 | −0.418780 | −0.209390 | − | 0.977832i | \(-0.567148\pi\) | ||||
−0.209390 | + | 0.977832i | \(0.567148\pi\) | |||||||
\(308\) | 2.79238 | 0.159111 | ||||||||
\(309\) | −1.41805 | −0.0806700 | ||||||||
\(310\) | 3.82904 | 0.217475 | ||||||||
\(311\) | −31.5817 | −1.79083 | −0.895417 | − | 0.445228i | \(-0.853122\pi\) | ||||
−0.895417 | + | 0.445228i | \(0.853122\pi\) | |||||||
\(312\) | −4.60603 | −0.260765 | ||||||||
\(313\) | 21.3123 | 1.20464 | 0.602320 | − | 0.798255i | \(-0.294243\pi\) | ||||
0.602320 | + | 0.798255i | \(0.294243\pi\) | |||||||
\(314\) | −5.62222 | −0.317280 | ||||||||
\(315\) | −1.57864 | −0.0889465 | ||||||||
\(316\) | 15.3104 | 0.861276 | ||||||||
\(317\) | 29.1322 | 1.63623 | 0.818114 | − | 0.575056i | \(-0.195020\pi\) | ||||
0.818114 | + | 0.575056i | \(0.195020\pi\) | |||||||
\(318\) | −5.53615 | −0.310452 | ||||||||
\(319\) | 8.69161 | 0.486637 | ||||||||
\(320\) | 4.12793 | 0.230758 | ||||||||
\(321\) | 0.0186487 | 0.00104087 | ||||||||
\(322\) | 0.354073 | 0.0197317 | ||||||||
\(323\) | −7.08965 | −0.394479 | ||||||||
\(324\) | 8.83299 | 0.490722 | ||||||||
\(325\) | 2.05922 | 0.114225 | ||||||||
\(326\) | 8.54464 | 0.473244 | ||||||||
\(327\) | −24.2121 | −1.33893 | ||||||||
\(328\) | −5.95542 | −0.328833 | ||||||||
\(329\) | −18.4536 | −1.01738 | ||||||||
\(330\) | −0.584579 | −0.0321800 | ||||||||
\(331\) | 3.65757 | 0.201038 | 0.100519 | − | 0.994935i | \(-0.467950\pi\) | ||||
0.100519 | + | 0.994935i | \(0.467950\pi\) | |||||||
\(332\) | −27.8433 | −1.52810 | ||||||||
\(333\) | 10.4005 | 0.569942 | ||||||||
\(334\) | 5.33191 | 0.291749 | ||||||||
\(335\) | 1.23353 | 0.0673952 | ||||||||
\(336\) | −6.40834 | −0.349603 | ||||||||
\(337\) | −2.52764 | −0.137689 | −0.0688445 | − | 0.997627i | \(-0.521931\pi\) | ||||
−0.0688445 | + | 0.997627i | \(0.521931\pi\) | |||||||
\(338\) | −3.65064 | −0.198569 | ||||||||
\(339\) | −16.3240 | −0.886599 | ||||||||
\(340\) | 12.6348 | 0.685218 | ||||||||
\(341\) | −9.18767 | −0.497540 | ||||||||
\(342\) | 0.440961 | 0.0238445 | ||||||||
\(343\) | 17.8313 | 0.962797 | ||||||||
\(344\) | 11.3254 | 0.610623 | ||||||||
\(345\) | 0.779412 | 0.0419621 | ||||||||
\(346\) | 7.35892 | 0.395618 | ||||||||
\(347\) | 28.6273 | 1.53679 | 0.768396 | − | 0.639974i | \(-0.221055\pi\) | ||||
0.768396 | + | 0.639974i | \(0.221055\pi\) | |||||||
\(348\) | −22.2656 | −1.19356 | ||||||||
\(349\) | 5.58630 | 0.299028 | 0.149514 | − | 0.988760i | \(-0.452229\pi\) | ||||
0.149514 | + | 0.988760i | \(0.452229\pi\) | |||||||
\(350\) | −0.637213 | −0.0340604 | ||||||||
\(351\) | −11.6476 | −0.621701 | ||||||||
\(352\) | 4.43459 | 0.236364 | ||||||||
\(353\) | −31.2555 | −1.66356 | −0.831781 | − | 0.555103i | \(-0.812679\pi\) | ||||
−0.831781 | + | 0.555103i | \(0.812679\pi\) | |||||||
\(354\) | −5.91080 | −0.314155 | ||||||||
\(355\) | 3.25447 | 0.172729 | ||||||||
\(356\) | 11.1771 | 0.592383 | ||||||||
\(357\) | −14.8372 | −0.785268 | ||||||||
\(358\) | −5.39391 | −0.285077 | ||||||||
\(359\) | −12.7143 | −0.671036 | −0.335518 | − | 0.942034i | \(-0.608911\pi\) | ||||
−0.335518 | + | 0.942034i | \(0.608911\pi\) | |||||||
\(360\) | −1.64645 | −0.0867756 | ||||||||
\(361\) | −17.9498 | −0.944727 | ||||||||
\(362\) | 1.07559 | 0.0565319 | ||||||||
\(363\) | 1.40268 | 0.0736217 | ||||||||
\(364\) | 5.75013 | 0.301389 | ||||||||
\(365\) | −1.00000 | −0.0523424 | ||||||||
\(366\) | −2.31107 | −0.120802 | ||||||||
\(367\) | 19.7409 | 1.03047 | 0.515234 | − | 0.857050i | \(-0.327705\pi\) | ||||
0.515234 | + | 0.857050i | \(0.327705\pi\) | |||||||
\(368\) | −1.66033 | −0.0865508 | ||||||||
\(369\) | −3.85595 | −0.200733 | ||||||||
\(370\) | 4.19811 | 0.218249 | ||||||||
\(371\) | 14.4799 | 0.751757 | ||||||||
\(372\) | 23.5364 | 1.22030 | ||||||||
\(373\) | −15.1098 | −0.782357 | −0.391178 | − | 0.920315i | \(-0.627932\pi\) | ||||
−0.391178 | + | 0.920315i | \(0.627932\pi\) | |||||||
\(374\) | 2.88322 | 0.149088 | ||||||||
\(375\) | −1.40268 | −0.0724341 | ||||||||
\(376\) | −19.2462 | −0.992547 | ||||||||
\(377\) | 17.8979 | 0.921791 | ||||||||
\(378\) | 3.60426 | 0.185383 | ||||||||
\(379\) | 3.96090 | 0.203458 | 0.101729 | − | 0.994812i | \(-0.467563\pi\) | ||||
0.101729 | + | 0.994812i | \(0.467563\pi\) | |||||||
\(380\) | −1.87157 | −0.0960097 | ||||||||
\(381\) | −21.8357 | −1.11867 | ||||||||
\(382\) | 6.43449 | 0.329217 | ||||||||
\(383\) | 14.4766 | 0.739721 | 0.369861 | − | 0.929087i | \(-0.379405\pi\) | ||||
0.369861 | + | 0.929087i | \(0.379405\pi\) | |||||||
\(384\) | −14.8537 | −0.758001 | ||||||||
\(385\) | 1.52897 | 0.0779237 | ||||||||
\(386\) | −1.13814 | −0.0579297 | ||||||||
\(387\) | 7.33282 | 0.372748 | ||||||||
\(388\) | 22.2703 | 1.13060 | ||||||||
\(389\) | 0.420250 | 0.0213075 | 0.0106538 | − | 0.999943i | \(-0.496609\pi\) | ||||
0.0106538 | + | 0.999943i | \(0.496609\pi\) | |||||||
\(390\) | −1.20378 | −0.0609557 | ||||||||
\(391\) | −3.84416 | −0.194408 | ||||||||
\(392\) | 7.43464 | 0.375506 | ||||||||
\(393\) | −2.93130 | −0.147865 | ||||||||
\(394\) | −4.10450 | −0.206781 | ||||||||
\(395\) | 8.38322 | 0.421806 | ||||||||
\(396\) | 1.88564 | 0.0947571 | ||||||||
\(397\) | 4.84757 | 0.243293 | 0.121646 | − | 0.992574i | \(-0.461183\pi\) | ||||
0.121646 | + | 0.992574i | \(0.461183\pi\) | |||||||
\(398\) | 6.93724 | 0.347732 | ||||||||
\(399\) | 2.19781 | 0.110028 | ||||||||
\(400\) | 2.98804 | 0.149402 | ||||||||
\(401\) | 14.4688 | 0.722539 | 0.361269 | − | 0.932461i | \(-0.382343\pi\) | ||||
0.361269 | + | 0.932461i | \(0.382343\pi\) | |||||||
\(402\) | −0.721099 | −0.0359651 | ||||||||
\(403\) | −18.9194 | −0.942444 | ||||||||
\(404\) | −35.0816 | −1.74537 | ||||||||
\(405\) | 4.83652 | 0.240328 | ||||||||
\(406\) | −5.53840 | −0.274866 | ||||||||
\(407\) | −10.0732 | −0.499312 | ||||||||
\(408\) | −15.4745 | −0.766103 | ||||||||
\(409\) | −0.859207 | −0.0424850 | −0.0212425 | − | 0.999774i | \(-0.506762\pi\) | ||||
−0.0212425 | + | 0.999774i | \(0.506762\pi\) | |||||||
\(410\) | −1.55644 | −0.0768670 | ||||||||
\(411\) | −25.8738 | −1.27626 | ||||||||
\(412\) | 1.84632 | 0.0909617 | ||||||||
\(413\) | 15.4598 | 0.760725 | ||||||||
\(414\) | 0.239098 | 0.0117510 | ||||||||
\(415\) | −15.2456 | −0.748379 | ||||||||
\(416\) | 9.13180 | 0.447723 | ||||||||
\(417\) | −23.5270 | −1.15212 | ||||||||
\(418\) | −0.427087 | −0.0208895 | ||||||||
\(419\) | −7.47353 | −0.365106 | −0.182553 | − | 0.983196i | \(-0.558436\pi\) | ||||
−0.182553 | + | 0.983196i | \(0.558436\pi\) | |||||||
\(420\) | −3.91682 | −0.191121 | ||||||||
\(421\) | −20.9877 | −1.02288 | −0.511439 | − | 0.859320i | \(-0.670887\pi\) | ||||
−0.511439 | + | 0.859320i | \(0.670887\pi\) | |||||||
\(422\) | 0.715533 | 0.0348316 | ||||||||
\(423\) | −12.4613 | −0.605890 | ||||||||
\(424\) | 15.1018 | 0.733410 | ||||||||
\(425\) | 6.91820 | 0.335582 | ||||||||
\(426\) | −1.90250 | −0.0921763 | ||||||||
\(427\) | 6.04463 | 0.292520 | ||||||||
\(428\) | −0.0242810 | −0.00117366 | ||||||||
\(429\) | 2.88843 | 0.139455 | ||||||||
\(430\) | 2.95986 | 0.142737 | ||||||||
\(431\) | 20.7998 | 1.00189 | 0.500947 | − | 0.865478i | \(-0.332985\pi\) | ||||
0.500947 | + | 0.865478i | \(0.332985\pi\) | |||||||
\(432\) | −16.9012 | −0.813161 | ||||||||
\(433\) | −6.88854 | −0.331042 | −0.165521 | − | 0.986206i | \(-0.552931\pi\) | ||||
−0.165521 | + | 0.986206i | \(0.552931\pi\) | |||||||
\(434\) | 5.85450 | 0.281025 | ||||||||
\(435\) | −12.1916 | −0.584540 | ||||||||
\(436\) | 31.5245 | 1.50975 | ||||||||
\(437\) | 0.569430 | 0.0272395 | ||||||||
\(438\) | 0.584579 | 0.0279323 | ||||||||
\(439\) | −26.9712 | −1.28726 | −0.643632 | − | 0.765335i | \(-0.722573\pi\) | ||||
−0.643632 | + | 0.765335i | \(0.722573\pi\) | |||||||
\(440\) | 1.59465 | 0.0760219 | ||||||||
\(441\) | 4.81370 | 0.229224 | ||||||||
\(442\) | 5.93719 | 0.282403 | ||||||||
\(443\) | 22.9865 | 1.09212 | 0.546062 | − | 0.837745i | \(-0.316126\pi\) | ||||
0.546062 | + | 0.837745i | \(0.316126\pi\) | |||||||
\(444\) | 25.8049 | 1.22465 | ||||||||
\(445\) | 6.12001 | 0.290116 | ||||||||
\(446\) | 2.61817 | 0.123974 | ||||||||
\(447\) | −21.1742 | −1.00151 | ||||||||
\(448\) | 6.31149 | 0.298190 | ||||||||
\(449\) | −3.74464 | −0.176721 | −0.0883603 | − | 0.996089i | \(-0.528163\pi\) | ||||
−0.0883603 | + | 0.996089i | \(0.528163\pi\) | |||||||
\(450\) | −0.430297 | −0.0202844 | ||||||||
\(451\) | 3.73463 | 0.175857 | ||||||||
\(452\) | 21.2541 | 0.999710 | ||||||||
\(453\) | 21.8059 | 1.02453 | ||||||||
\(454\) | 1.11980 | 0.0525550 | ||||||||
\(455\) | 3.14849 | 0.147604 | ||||||||
\(456\) | 2.29222 | 0.107343 | ||||||||
\(457\) | −4.95202 | −0.231646 | −0.115823 | − | 0.993270i | \(-0.536951\pi\) | ||||
−0.115823 | + | 0.993270i | \(0.536951\pi\) | |||||||
\(458\) | −8.70718 | −0.406860 | ||||||||
\(459\) | −39.1314 | −1.82650 | ||||||||
\(460\) | −1.01481 | −0.0473156 | ||||||||
\(461\) | 33.6844 | 1.56884 | 0.784419 | − | 0.620232i | \(-0.212961\pi\) | ||||
0.784419 | + | 0.620232i | \(0.212961\pi\) | |||||||
\(462\) | −0.893806 | −0.0415836 | ||||||||
\(463\) | −12.4478 | −0.578498 | −0.289249 | − | 0.957254i | \(-0.593406\pi\) | ||||
−0.289249 | + | 0.957254i | \(0.593406\pi\) | |||||||
\(464\) | 25.9709 | 1.20567 | ||||||||
\(465\) | 12.8874 | 0.597637 | ||||||||
\(466\) | −5.38929 | −0.249654 | ||||||||
\(467\) | 33.2477 | 1.53852 | 0.769260 | − | 0.638935i | \(-0.220625\pi\) | ||||
0.769260 | + | 0.638935i | \(0.220625\pi\) | |||||||
\(468\) | 3.88295 | 0.179490 | ||||||||
\(469\) | 1.88604 | 0.0870893 | ||||||||
\(470\) | −5.02996 | −0.232015 | ||||||||
\(471\) | −18.9227 | −0.871910 | ||||||||
\(472\) | 16.1238 | 0.742158 | ||||||||
\(473\) | −7.10211 | −0.326555 | ||||||||
\(474\) | −4.90066 | −0.225095 | ||||||||
\(475\) | −1.02478 | −0.0470203 | ||||||||
\(476\) | 19.3183 | 0.885451 | ||||||||
\(477\) | 9.77797 | 0.447702 | ||||||||
\(478\) | 4.34346 | 0.198665 | ||||||||
\(479\) | −23.1598 | −1.05820 | −0.529099 | − | 0.848560i | \(-0.677470\pi\) | ||||
−0.529099 | + | 0.848560i | \(0.677470\pi\) | |||||||
\(480\) | −6.22031 | −0.283917 | ||||||||
\(481\) | −20.7430 | −0.945800 | ||||||||
\(482\) | −1.73056 | −0.0788247 | ||||||||
\(483\) | 1.19170 | 0.0542242 | ||||||||
\(484\) | −1.82631 | −0.0830142 | ||||||||
\(485\) | 12.1941 | 0.553707 | ||||||||
\(486\) | 4.24460 | 0.192539 | ||||||||
\(487\) | −10.1003 | −0.457690 | −0.228845 | − | 0.973463i | \(-0.573495\pi\) | ||||
−0.228845 | + | 0.973463i | \(0.573495\pi\) | |||||||
\(488\) | 6.30427 | 0.285381 | ||||||||
\(489\) | 28.7586 | 1.30051 | ||||||||
\(490\) | 1.94303 | 0.0877771 | ||||||||
\(491\) | 27.5045 | 1.24126 | 0.620629 | − | 0.784104i | \(-0.286877\pi\) | ||||
0.620629 | + | 0.784104i | \(0.286877\pi\) | |||||||
\(492\) | −9.56712 | −0.431319 | ||||||||
\(493\) | 60.1303 | 2.70813 | ||||||||
\(494\) | −0.879467 | −0.0395691 | ||||||||
\(495\) | 1.03249 | 0.0464068 | ||||||||
\(496\) | −27.4531 | −1.23268 | ||||||||
\(497\) | 4.97600 | 0.223204 | ||||||||
\(498\) | 8.91229 | 0.399369 | ||||||||
\(499\) | −8.62750 | −0.386220 | −0.193110 | − | 0.981177i | \(-0.561857\pi\) | ||||
−0.193110 | + | 0.981177i | \(0.561857\pi\) | |||||||
\(500\) | 1.82631 | 0.0816752 | ||||||||
\(501\) | 17.9456 | 0.801749 | ||||||||
\(502\) | −1.15455 | −0.0515300 | ||||||||
\(503\) | −19.8170 | −0.883597 | −0.441799 | − | 0.897114i | \(-0.645659\pi\) | ||||
−0.441799 | + | 0.897114i | \(0.645659\pi\) | |||||||
\(504\) | −2.51738 | −0.112133 | ||||||||
\(505\) | −19.2090 | −0.854788 | ||||||||
\(506\) | −0.231576 | −0.0102948 | ||||||||
\(507\) | −12.2869 | −0.545682 | ||||||||
\(508\) | 28.4304 | 1.26139 | ||||||||
\(509\) | 42.0636 | 1.86444 | 0.932219 | − | 0.361895i | \(-0.117870\pi\) | ||||
0.932219 | + | 0.361895i | \(0.117870\pi\) | |||||||
\(510\) | −4.04424 | −0.179082 | ||||||||
\(511\) | −1.52897 | −0.0676378 | ||||||||
\(512\) | 22.7805 | 1.00676 | ||||||||
\(513\) | 5.79647 | 0.255920 | ||||||||
\(514\) | −4.08306 | −0.180096 | ||||||||
\(515\) | 1.01096 | 0.0445480 | ||||||||
\(516\) | 18.1937 | 0.800933 | ||||||||
\(517\) | 12.0692 | 0.530805 | ||||||||
\(518\) | 6.41879 | 0.282026 | ||||||||
\(519\) | 24.7678 | 1.08719 | ||||||||
\(520\) | 3.28373 | 0.144001 | ||||||||
\(521\) | −20.8980 | −0.915559 | −0.457780 | − | 0.889066i | \(-0.651355\pi\) | ||||
−0.457780 | + | 0.889066i | \(0.651355\pi\) | |||||||
\(522\) | −3.73998 | −0.163694 | ||||||||
\(523\) | −11.2086 | −0.490118 | −0.245059 | − | 0.969508i | \(-0.578807\pi\) | ||||
−0.245059 | + | 0.969508i | \(0.578807\pi\) | |||||||
\(524\) | 3.81660 | 0.166729 | ||||||||
\(525\) | −2.14466 | −0.0936007 | ||||||||
\(526\) | −2.48617 | −0.108402 | ||||||||
\(527\) | −63.5621 | −2.76881 | ||||||||
\(528\) | 4.19127 | 0.182402 | ||||||||
\(529\) | −22.6912 | −0.986576 | ||||||||
\(530\) | 3.94684 | 0.171440 | ||||||||
\(531\) | 10.4397 | 0.453043 | ||||||||
\(532\) | −2.86159 | −0.124065 | ||||||||
\(533\) | 7.69042 | 0.333109 | ||||||||
\(534\) | −3.57763 | −0.154819 | ||||||||
\(535\) | −0.0132951 | −0.000574796 0 | ||||||||
\(536\) | 1.96705 | 0.0849638 | ||||||||
\(537\) | −18.1542 | −0.783413 | ||||||||
\(538\) | −2.56825 | −0.110725 | ||||||||
\(539\) | −4.66224 | −0.200817 | ||||||||
\(540\) | −10.3302 | −0.444539 | ||||||||
\(541\) | −25.7007 | −1.10496 | −0.552479 | − | 0.833527i | \(-0.686318\pi\) | ||||
−0.552479 | + | 0.833527i | \(0.686318\pi\) | |||||||
\(542\) | 9.26375 | 0.397912 | ||||||||
\(543\) | 3.62011 | 0.155354 | ||||||||
\(544\) | 30.6794 | 1.31537 | ||||||||
\(545\) | 17.2613 | 0.739392 | ||||||||
\(546\) | −1.84054 | −0.0787680 | ||||||||
\(547\) | −19.8262 | −0.847707 | −0.423853 | − | 0.905731i | \(-0.639323\pi\) | ||||
−0.423853 | + | 0.905731i | \(0.639323\pi\) | |||||||
\(548\) | 33.6881 | 1.43908 | ||||||||
\(549\) | 4.08182 | 0.174208 | ||||||||
\(550\) | 0.416759 | 0.0177706 | ||||||||
\(551\) | −8.90701 | −0.379451 | ||||||||
\(552\) | 1.24289 | 0.0529008 | ||||||||
\(553\) | 12.8177 | 0.545065 | ||||||||
\(554\) | 9.09780 | 0.386529 | ||||||||
\(555\) | 14.1295 | 0.599765 | ||||||||
\(556\) | 30.6325 | 1.29911 | ||||||||
\(557\) | 30.8244 | 1.30607 | 0.653036 | − | 0.757327i | \(-0.273495\pi\) | ||||
0.653036 | + | 0.757327i | \(0.273495\pi\) | |||||||
\(558\) | 3.95343 | 0.167362 | ||||||||
\(559\) | −14.6248 | −0.618564 | ||||||||
\(560\) | 4.56863 | 0.193060 | ||||||||
\(561\) | 9.70403 | 0.409705 | ||||||||
\(562\) | −13.0730 | −0.551452 | ||||||||
\(563\) | −17.0695 | −0.719394 | −0.359697 | − | 0.933069i | \(-0.617120\pi\) | ||||
−0.359697 | + | 0.933069i | \(0.617120\pi\) | |||||||
\(564\) | −30.9182 | −1.30189 | ||||||||
\(565\) | 11.6377 | 0.489603 | ||||||||
\(566\) | −8.75588 | −0.368037 | ||||||||
\(567\) | 7.39490 | 0.310557 | ||||||||
\(568\) | 5.18974 | 0.217757 | ||||||||
\(569\) | −24.1003 | −1.01034 | −0.505170 | − | 0.863020i | \(-0.668570\pi\) | ||||
−0.505170 | + | 0.863020i | \(0.668570\pi\) | |||||||
\(570\) | 0.599067 | 0.0250922 | ||||||||
\(571\) | 11.6950 | 0.489420 | 0.244710 | − | 0.969596i | \(-0.421307\pi\) | ||||
0.244710 | + | 0.969596i | \(0.421307\pi\) | |||||||
\(572\) | −3.76078 | −0.157246 | ||||||||
\(573\) | 21.6565 | 0.904714 | ||||||||
\(574\) | −2.37975 | −0.0993289 | ||||||||
\(575\) | −0.555659 | −0.0231726 | ||||||||
\(576\) | 4.26203 | 0.177585 | ||||||||
\(577\) | 0.831618 | 0.0346207 | 0.0173104 | − | 0.999850i | \(-0.494490\pi\) | ||||
0.0173104 | + | 0.999850i | \(0.494490\pi\) | |||||||
\(578\) | 12.8618 | 0.534980 | ||||||||
\(579\) | −3.83062 | −0.159195 | ||||||||
\(580\) | 15.8736 | 0.659115 | ||||||||
\(581\) | −23.3102 | −0.967070 | ||||||||
\(582\) | −7.12844 | −0.295483 | ||||||||
\(583\) | −9.47032 | −0.392220 | ||||||||
\(584\) | −1.59465 | −0.0659870 | ||||||||
\(585\) | 2.12612 | 0.0879041 | ||||||||
\(586\) | −0.115180 | −0.00475803 | ||||||||
\(587\) | −36.3618 | −1.50081 | −0.750406 | − | 0.660978i | \(-0.770142\pi\) | ||||
−0.750406 | + | 0.660978i | \(0.770142\pi\) | |||||||
\(588\) | 11.9434 | 0.492538 | ||||||||
\(589\) | 9.41536 | 0.387953 | ||||||||
\(590\) | 4.21393 | 0.173485 | ||||||||
\(591\) | −13.8145 | −0.568251 | ||||||||
\(592\) | −30.0992 | −1.23707 | ||||||||
\(593\) | 37.0630 | 1.52199 | 0.760997 | − | 0.648756i | \(-0.224710\pi\) | ||||
0.760997 | + | 0.648756i | \(0.224710\pi\) | |||||||
\(594\) | −2.35731 | −0.0967215 | ||||||||
\(595\) | 10.5777 | 0.433645 | ||||||||
\(596\) | 27.5691 | 1.12928 | ||||||||
\(597\) | 23.3486 | 0.955595 | ||||||||
\(598\) | −0.476865 | −0.0195005 | ||||||||
\(599\) | 16.8635 | 0.689022 | 0.344511 | − | 0.938782i | \(-0.388045\pi\) | ||||
0.344511 | + | 0.938782i | \(0.388045\pi\) | |||||||
\(600\) | −2.23678 | −0.0913163 | ||||||||
\(601\) | 3.44336 | 0.140457 | 0.0702287 | − | 0.997531i | \(-0.477627\pi\) | ||||
0.0702287 | + | 0.997531i | \(0.477627\pi\) | |||||||
\(602\) | 4.52555 | 0.184448 | ||||||||
\(603\) | 1.27361 | 0.0518653 | ||||||||
\(604\) | −28.3916 | −1.15524 | ||||||||
\(605\) | −1.00000 | −0.0406558 | ||||||||
\(606\) | 11.2292 | 0.456154 | ||||||||
\(607\) | 3.14805 | 0.127775 | 0.0638877 | − | 0.997957i | \(-0.479650\pi\) | ||||
0.0638877 | + | 0.997957i | \(0.479650\pi\) | |||||||
\(608\) | −4.54449 | −0.184303 | ||||||||
\(609\) | −18.6406 | −0.755354 | ||||||||
\(610\) | 1.64761 | 0.0667097 | ||||||||
\(611\) | 24.8532 | 1.00545 | ||||||||
\(612\) | 13.0452 | 0.527323 | ||||||||
\(613\) | −40.4271 | −1.63283 | −0.816417 | − | 0.577463i | \(-0.804043\pi\) | ||||
−0.816417 | + | 0.577463i | \(0.804043\pi\) | |||||||
\(614\) | −3.05801 | −0.123411 | ||||||||
\(615\) | −5.23849 | −0.211236 | ||||||||
\(616\) | 2.43817 | 0.0982369 | ||||||||
\(617\) | −46.9003 | −1.88814 | −0.944068 | − | 0.329750i | \(-0.893036\pi\) | ||||
−0.944068 | + | 0.329750i | \(0.893036\pi\) | |||||||
\(618\) | −0.590984 | −0.0237729 | ||||||||
\(619\) | −26.1801 | −1.05227 | −0.526134 | − | 0.850401i | \(-0.676359\pi\) | ||||
−0.526134 | + | 0.850401i | \(0.676359\pi\) | |||||||
\(620\) | −16.7795 | −0.673883 | ||||||||
\(621\) | 3.14297 | 0.126123 | ||||||||
\(622\) | −13.1619 | −0.527746 | ||||||||
\(623\) | 9.35734 | 0.374894 | ||||||||
\(624\) | 8.63075 | 0.345507 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 8.88206 | 0.354999 | ||||||||
\(627\) | −1.43744 | −0.0574060 | ||||||||
\(628\) | 24.6376 | 0.983147 | ||||||||
\(629\) | −69.6887 | −2.77867 | ||||||||
\(630\) | −0.657913 | −0.0262119 | ||||||||
\(631\) | −19.7703 | −0.787042 | −0.393521 | − | 0.919316i | \(-0.628743\pi\) | ||||
−0.393521 | + | 0.919316i | \(0.628743\pi\) | |||||||
\(632\) | 13.3683 | 0.531762 | ||||||||
\(633\) | 2.40826 | 0.0957199 | ||||||||
\(634\) | 12.1411 | 0.482185 | ||||||||
\(635\) | 15.5671 | 0.617761 | ||||||||
\(636\) | 24.2604 | 0.961989 | ||||||||
\(637\) | −9.60059 | −0.380389 | ||||||||
\(638\) | 3.62230 | 0.143408 | ||||||||
\(639\) | 3.36020 | 0.132927 | ||||||||
\(640\) | 10.5895 | 0.418588 | ||||||||
\(641\) | 7.79782 | 0.307995 | 0.153998 | − | 0.988071i | \(-0.450785\pi\) | ||||
0.153998 | + | 0.988071i | \(0.450785\pi\) | |||||||
\(642\) | 0.00777202 | 0.000306737 0 | ||||||||
\(643\) | −1.37087 | −0.0540619 | −0.0270309 | − | 0.999635i | \(-0.508605\pi\) | ||||
−0.0270309 | + | 0.999635i | \(0.508605\pi\) | |||||||
\(644\) | −1.55161 | −0.0611421 | ||||||||
\(645\) | 9.96199 | 0.392253 | ||||||||
\(646\) | −2.95467 | −0.116250 | ||||||||
\(647\) | 45.6510 | 1.79473 | 0.897363 | − | 0.441292i | \(-0.145480\pi\) | ||||
0.897363 | + | 0.441292i | \(0.145480\pi\) | |||||||
\(648\) | 7.71254 | 0.302977 | ||||||||
\(649\) | −10.1112 | −0.396899 | ||||||||
\(650\) | 0.858198 | 0.0336613 | ||||||||
\(651\) | 19.7044 | 0.772278 | ||||||||
\(652\) | −37.4442 | −1.46643 | ||||||||
\(653\) | −21.6563 | −0.847476 | −0.423738 | − | 0.905785i | \(-0.639282\pi\) | ||||
−0.423738 | + | 0.905785i | \(0.639282\pi\) | |||||||
\(654\) | −10.0906 | −0.394573 | ||||||||
\(655\) | 2.08978 | 0.0816546 | ||||||||
\(656\) | 11.1592 | 0.435694 | ||||||||
\(657\) | −1.03249 | −0.0402811 | ||||||||
\(658\) | −7.69068 | −0.299814 | ||||||||
\(659\) | 22.5335 | 0.877780 | 0.438890 | − | 0.898541i | \(-0.355372\pi\) | ||||
0.438890 | + | 0.898541i | \(0.355372\pi\) | |||||||
\(660\) | 2.56173 | 0.0997153 | ||||||||
\(661\) | 11.5859 | 0.450639 | 0.225319 | − | 0.974285i | \(-0.427657\pi\) | ||||
0.225319 | + | 0.974285i | \(0.427657\pi\) | |||||||
\(662\) | 1.52432 | 0.0592445 | ||||||||
\(663\) | 19.9827 | 0.776066 | ||||||||
\(664\) | −24.3114 | −0.943467 | ||||||||
\(665\) | −1.56687 | −0.0607604 | ||||||||
\(666\) | 4.33449 | 0.167958 | ||||||||
\(667\) | −4.82957 | −0.187002 | ||||||||
\(668\) | −23.3654 | −0.904035 | ||||||||
\(669\) | 8.81194 | 0.340689 | ||||||||
\(670\) | 0.514086 | 0.0198609 | ||||||||
\(671\) | −3.95339 | −0.152619 | ||||||||
\(672\) | −9.51069 | −0.366883 | ||||||||
\(673\) | 26.4702 | 1.02035 | 0.510175 | − | 0.860070i | \(-0.329580\pi\) | ||||
0.510175 | + | 0.860070i | \(0.329580\pi\) | |||||||
\(674\) | −1.05341 | −0.0405760 | ||||||||
\(675\) | −5.65629 | −0.217711 | ||||||||
\(676\) | 15.9978 | 0.615299 | ||||||||
\(677\) | 0.369548 | 0.0142029 | 0.00710145 | − | 0.999975i | \(-0.497740\pi\) | ||||
0.00710145 | + | 0.999975i | \(0.497740\pi\) | |||||||
\(678\) | −6.80318 | −0.261274 | ||||||||
\(679\) | 18.6445 | 0.715511 | ||||||||
\(680\) | 11.0321 | 0.423062 | ||||||||
\(681\) | 3.76892 | 0.144425 | ||||||||
\(682\) | −3.82904 | −0.146621 | ||||||||
\(683\) | −38.6482 | −1.47883 | −0.739416 | − | 0.673249i | \(-0.764898\pi\) | ||||
−0.739416 | + | 0.673249i | \(0.764898\pi\) | |||||||
\(684\) | −1.93237 | −0.0738861 | ||||||||
\(685\) | 18.4460 | 0.704784 | ||||||||
\(686\) | 7.43133 | 0.283729 | ||||||||
\(687\) | −29.3057 | −1.11808 | ||||||||
\(688\) | −21.2214 | −0.809058 | ||||||||
\(689\) | −19.5015 | −0.742947 | ||||||||
\(690\) | 0.324827 | 0.0123659 | ||||||||
\(691\) | −3.42747 | −0.130387 | −0.0651936 | − | 0.997873i | \(-0.520767\pi\) | ||||
−0.0651936 | + | 0.997873i | \(0.520767\pi\) | |||||||
\(692\) | −32.2481 | −1.22589 | ||||||||
\(693\) | 1.57864 | 0.0599677 | ||||||||
\(694\) | 11.9307 | 0.452882 | ||||||||
\(695\) | 16.7729 | 0.636231 | ||||||||
\(696\) | −19.4412 | −0.736919 | ||||||||
\(697\) | 25.8369 | 0.978642 | ||||||||
\(698\) | 2.32814 | 0.0881213 | ||||||||
\(699\) | −18.1387 | −0.686069 | ||||||||
\(700\) | 2.79238 | 0.105542 | ||||||||
\(701\) | −23.9261 | −0.903677 | −0.451838 | − | 0.892100i | \(-0.649232\pi\) | ||||
−0.451838 | + | 0.892100i | \(0.649232\pi\) | |||||||
\(702\) | −4.85422 | −0.183211 | ||||||||
\(703\) | 10.3229 | 0.389335 | ||||||||
\(704\) | −4.12793 | −0.155577 | ||||||||
\(705\) | −16.9293 | −0.637594 | ||||||||
\(706\) | −13.0260 | −0.490240 | ||||||||
\(707\) | −29.3700 | −1.10457 | ||||||||
\(708\) | 25.9022 | 0.973464 | ||||||||
\(709\) | −32.3934 | −1.21656 | −0.608281 | − | 0.793722i | \(-0.708140\pi\) | ||||
−0.608281 | + | 0.793722i | \(0.708140\pi\) | |||||||
\(710\) | 1.35633 | 0.0509021 | ||||||||
\(711\) | 8.65556 | 0.324609 | ||||||||
\(712\) | 9.75927 | 0.365744 | ||||||||
\(713\) | 5.10521 | 0.191191 | ||||||||
\(714\) | −6.18353 | −0.231413 | ||||||||
\(715\) | −2.05922 | −0.0770105 | ||||||||
\(716\) | 23.6371 | 0.883360 | ||||||||
\(717\) | 14.6187 | 0.545947 | ||||||||
\(718\) | −5.29880 | −0.197749 | ||||||||
\(719\) | 20.9020 | 0.779513 | 0.389757 | − | 0.920918i | \(-0.372559\pi\) | ||||
0.389757 | + | 0.920918i | \(0.372559\pi\) | |||||||
\(720\) | 3.08511 | 0.114975 | ||||||||
\(721\) | 1.54572 | 0.0575658 | ||||||||
\(722\) | −7.48074 | −0.278404 | ||||||||
\(723\) | −5.82452 | −0.216616 | ||||||||
\(724\) | −4.71344 | −0.175174 | ||||||||
\(725\) | 8.69161 | 0.322798 | ||||||||
\(726\) | 0.584579 | 0.0216958 | ||||||||
\(727\) | −17.7799 | −0.659420 | −0.329710 | − | 0.944082i | \(-0.606951\pi\) | ||||
−0.329710 | + | 0.944082i | \(0.606951\pi\) | |||||||
\(728\) | 5.02074 | 0.186081 | ||||||||
\(729\) | 28.7956 | 1.06650 | ||||||||
\(730\) | −0.416759 | −0.0154249 | ||||||||
\(731\) | −49.1338 | −1.81728 | ||||||||
\(732\) | 10.1275 | 0.374324 | ||||||||
\(733\) | 18.1618 | 0.670822 | 0.335411 | − | 0.942072i | \(-0.391125\pi\) | ||||
0.335411 | + | 0.942072i | \(0.391125\pi\) | |||||||
\(734\) | 8.22720 | 0.303672 | ||||||||
\(735\) | 6.53964 | 0.241218 | ||||||||
\(736\) | −2.46412 | −0.0908286 | ||||||||
\(737\) | −1.23353 | −0.0454378 | ||||||||
\(738\) | −1.60700 | −0.0591545 | ||||||||
\(739\) | 15.6914 | 0.577218 | 0.288609 | − | 0.957447i | \(-0.406807\pi\) | ||||
0.288609 | + | 0.957447i | \(0.406807\pi\) | |||||||
\(740\) | −18.3969 | −0.676282 | ||||||||
\(741\) | −2.96001 | −0.108739 | ||||||||
\(742\) | 6.03461 | 0.221537 | ||||||||
\(743\) | 2.72073 | 0.0998141 | 0.0499070 | − | 0.998754i | \(-0.484107\pi\) | ||||
0.0499070 | + | 0.998754i | \(0.484107\pi\) | |||||||
\(744\) | 20.5508 | 0.753429 | ||||||||
\(745\) | 15.0955 | 0.553057 | ||||||||
\(746\) | −6.29715 | −0.230555 | ||||||||
\(747\) | −15.7409 | −0.575930 | ||||||||
\(748\) | −12.6348 | −0.461974 | ||||||||
\(749\) | −0.0203278 | −0.000742762 0 | ||||||||
\(750\) | −0.584579 | −0.0213458 | ||||||||
\(751\) | −18.6383 | −0.680120 | −0.340060 | − | 0.940404i | \(-0.610447\pi\) | ||||
−0.340060 | + | 0.940404i | \(0.610447\pi\) | |||||||
\(752\) | 36.0634 | 1.31510 | ||||||||
\(753\) | −3.88585 | −0.141608 | ||||||||
\(754\) | 7.45912 | 0.271645 | ||||||||
\(755\) | −15.5459 | −0.565772 | ||||||||
\(756\) | −15.7945 | −0.574441 | ||||||||
\(757\) | −41.0573 | −1.49225 | −0.746126 | − | 0.665805i | \(-0.768088\pi\) | ||||
−0.746126 | + | 0.665805i | \(0.768088\pi\) | |||||||
\(758\) | 1.65074 | 0.0599575 | ||||||||
\(759\) | −0.779412 | −0.0282909 | ||||||||
\(760\) | −1.63417 | −0.0592775 | ||||||||
\(761\) | 27.6541 | 1.00246 | 0.501229 | − | 0.865314i | \(-0.332881\pi\) | ||||
0.501229 | + | 0.865314i | \(0.332881\pi\) | |||||||
\(762\) | −9.10020 | −0.329665 | ||||||||
\(763\) | 26.3920 | 0.955456 | ||||||||
\(764\) | −28.1971 | −1.02014 | ||||||||
\(765\) | 7.14295 | 0.258254 | ||||||||
\(766\) | 6.03326 | 0.217990 | ||||||||
\(767\) | −20.8212 | −0.751810 | ||||||||
\(768\) | 5.38992 | 0.194492 | ||||||||
\(769\) | 39.9562 | 1.44086 | 0.720428 | − | 0.693530i | \(-0.243945\pi\) | ||||
0.720428 | + | 0.693530i | \(0.243945\pi\) | |||||||
\(770\) | 0.637213 | 0.0229636 | ||||||||
\(771\) | −13.7423 | −0.494917 | ||||||||
\(772\) | 4.98753 | 0.179505 | ||||||||
\(773\) | 28.0949 | 1.01050 | 0.505251 | − | 0.862973i | \(-0.331400\pi\) | ||||
0.505251 | + | 0.862973i | \(0.331400\pi\) | |||||||
\(774\) | 3.05602 | 0.109846 | ||||||||
\(775\) | −9.18767 | −0.330031 | ||||||||
\(776\) | 19.4454 | 0.698048 | ||||||||
\(777\) | 21.6037 | 0.775028 | ||||||||
\(778\) | 0.175143 | 0.00627918 | ||||||||
\(779\) | −3.82718 | −0.137123 | ||||||||
\(780\) | 5.27518 | 0.188882 | ||||||||
\(781\) | −3.25447 | −0.116454 | ||||||||
\(782\) | −1.60209 | −0.0572905 | ||||||||
\(783\) | −49.1623 | −1.75692 | ||||||||
\(784\) | −13.9310 | −0.497535 | ||||||||
\(785\) | 13.4904 | 0.481491 | ||||||||
\(786\) | −1.22164 | −0.0435746 | ||||||||
\(787\) | 44.8960 | 1.60037 | 0.800185 | − | 0.599753i | \(-0.204735\pi\) | ||||
0.800185 | + | 0.599753i | \(0.204735\pi\) | |||||||
\(788\) | 17.9866 | 0.640748 | ||||||||
\(789\) | −8.36768 | −0.297897 | ||||||||
\(790\) | 3.49378 | 0.124303 | ||||||||
\(791\) | 17.7938 | 0.632674 | ||||||||
\(792\) | 1.64645 | 0.0585041 | ||||||||
\(793\) | −8.14091 | −0.289092 | ||||||||
\(794\) | 2.02027 | 0.0716966 | ||||||||
\(795\) | 13.2838 | 0.471129 | ||||||||
\(796\) | −30.4003 | −1.07751 | ||||||||
\(797\) | −48.8760 | −1.73128 | −0.865639 | − | 0.500669i | \(-0.833087\pi\) | ||||
−0.865639 | + | 0.500669i | \(0.833087\pi\) | |||||||
\(798\) | 0.915957 | 0.0324245 | ||||||||
\(799\) | 83.4975 | 2.95393 | ||||||||
\(800\) | 4.43459 | 0.156786 | ||||||||
\(801\) | 6.31883 | 0.223265 | ||||||||
\(802\) | 6.03001 | 0.212927 | ||||||||
\(803\) | 1.00000 | 0.0352892 | ||||||||
\(804\) | 3.15999 | 0.111444 | ||||||||
\(805\) | −0.849587 | −0.0299440 | ||||||||
\(806\) | −7.88484 | −0.277732 | ||||||||
\(807\) | −8.64394 | −0.304281 | ||||||||
\(808\) | −30.6315 | −1.07761 | ||||||||
\(809\) | 56.5694 | 1.98887 | 0.994437 | − | 0.105335i | \(-0.0335914\pi\) | ||||
0.994437 | + | 0.105335i | \(0.0335914\pi\) | |||||||
\(810\) | 2.01566 | 0.0708230 | ||||||||
\(811\) | 41.6209 | 1.46151 | 0.730753 | − | 0.682642i | \(-0.239169\pi\) | ||||
0.730753 | + | 0.682642i | \(0.239169\pi\) | |||||||
\(812\) | 24.2703 | 0.851721 | ||||||||
\(813\) | 31.1789 | 1.09349 | ||||||||
\(814\) | −4.19811 | −0.147144 | ||||||||
\(815\) | −20.5026 | −0.718175 | ||||||||
\(816\) | 28.9960 | 1.01506 | ||||||||
\(817\) | 7.27812 | 0.254629 | ||||||||
\(818\) | −0.358082 | −0.0125200 | ||||||||
\(819\) | 3.25078 | 0.113591 | ||||||||
\(820\) | 6.82059 | 0.238185 | ||||||||
\(821\) | −40.4047 | −1.41013 | −0.705066 | − | 0.709141i | \(-0.749083\pi\) | ||||
−0.705066 | + | 0.709141i | \(0.749083\pi\) | |||||||
\(822\) | −10.7831 | −0.376105 | ||||||||
\(823\) | −43.1125 | −1.50281 | −0.751403 | − | 0.659843i | \(-0.770623\pi\) | ||||
−0.751403 | + | 0.659843i | \(0.770623\pi\) | |||||||
\(824\) | 1.61212 | 0.0561608 | ||||||||
\(825\) | 1.40268 | 0.0488351 | ||||||||
\(826\) | 6.44298 | 0.224180 | ||||||||
\(827\) | −25.7392 | −0.895041 | −0.447521 | − | 0.894274i | \(-0.647693\pi\) | ||||
−0.447521 | + | 0.894274i | \(0.647693\pi\) | |||||||
\(828\) | −1.04777 | −0.0364126 | ||||||||
\(829\) | 50.6863 | 1.76041 | 0.880204 | − | 0.474595i | \(-0.157405\pi\) | ||||
0.880204 | + | 0.474595i | \(0.157405\pi\) | |||||||
\(830\) | −6.35375 | −0.220542 | ||||||||
\(831\) | 30.6204 | 1.06221 | ||||||||
\(832\) | −8.50032 | −0.294696 | ||||||||
\(833\) | −32.2543 | −1.11755 | ||||||||
\(834\) | −9.80507 | −0.339522 | ||||||||
\(835\) | −12.7938 | −0.442746 | ||||||||
\(836\) | 1.87157 | 0.0647297 | ||||||||
\(837\) | 51.9681 | 1.79628 | ||||||||
\(838\) | −3.11466 | −0.107594 | ||||||||
\(839\) | −9.81138 | −0.338726 | −0.169363 | − | 0.985554i | \(-0.554171\pi\) | ||||
−0.169363 | + | 0.985554i | \(0.554171\pi\) | |||||||
\(840\) | −3.41998 | −0.118001 | ||||||||
\(841\) | 46.5441 | 1.60497 | ||||||||
\(842\) | −8.74680 | −0.301435 | ||||||||
\(843\) | −43.9997 | −1.51543 | ||||||||
\(844\) | −3.13560 | −0.107932 | ||||||||
\(845\) | 8.75961 | 0.301340 | ||||||||
\(846\) | −5.19336 | −0.178552 | ||||||||
\(847\) | −1.52897 | −0.0525361 | ||||||||
\(848\) | −28.2977 | −0.971747 | ||||||||
\(849\) | −29.4696 | −1.01139 | ||||||||
\(850\) | 2.88322 | 0.0988936 | ||||||||
\(851\) | 5.59728 | 0.191872 | ||||||||
\(852\) | 8.33709 | 0.285624 | ||||||||
\(853\) | −24.5647 | −0.841078 | −0.420539 | − | 0.907274i | \(-0.638159\pi\) | ||||
−0.420539 | + | 0.907274i | \(0.638159\pi\) | |||||||
\(854\) | 2.51915 | 0.0862035 | ||||||||
\(855\) | −1.05807 | −0.0361854 | ||||||||
\(856\) | −0.0212010 | −0.000724634 0 | ||||||||
\(857\) | −32.7436 | −1.11850 | −0.559250 | − | 0.828999i | \(-0.688911\pi\) | ||||
−0.559250 | + | 0.828999i | \(0.688911\pi\) | |||||||
\(858\) | 1.20378 | 0.0410963 | ||||||||
\(859\) | 19.4957 | 0.665184 | 0.332592 | − | 0.943071i | \(-0.392077\pi\) | ||||
0.332592 | + | 0.943071i | \(0.392077\pi\) | |||||||
\(860\) | −12.9707 | −0.442296 | ||||||||
\(861\) | −8.00951 | −0.272963 | ||||||||
\(862\) | 8.66851 | 0.295251 | ||||||||
\(863\) | −9.02807 | −0.307319 | −0.153660 | − | 0.988124i | \(-0.549106\pi\) | ||||
−0.153660 | + | 0.988124i | \(0.549106\pi\) | |||||||
\(864\) | −25.0833 | −0.853352 | ||||||||
\(865\) | −17.6575 | −0.600373 | ||||||||
\(866\) | −2.87086 | −0.0975558 | ||||||||
\(867\) | 43.2889 | 1.47017 | ||||||||
\(868\) | −25.6555 | −0.870804 | ||||||||
\(869\) | −8.38322 | −0.284381 | ||||||||
\(870\) | −5.08094 | −0.172260 | ||||||||
\(871\) | −2.54012 | −0.0860687 | ||||||||
\(872\) | 27.5257 | 0.932137 | ||||||||
\(873\) | 12.5903 | 0.426116 | ||||||||
\(874\) | 0.237315 | 0.00802729 | ||||||||
\(875\) | 1.52897 | 0.0516887 | ||||||||
\(876\) | −2.56173 | −0.0865530 | ||||||||
\(877\) | 29.9432 | 1.01111 | 0.505556 | − | 0.862794i | \(-0.331288\pi\) | ||||
0.505556 | + | 0.862794i | \(0.331288\pi\) | |||||||
\(878\) | −11.2405 | −0.379347 | ||||||||
\(879\) | −0.387659 | −0.0130754 | ||||||||
\(880\) | −2.98804 | −0.100727 | ||||||||
\(881\) | −38.3300 | −1.29137 | −0.645686 | − | 0.763603i | \(-0.723429\pi\) | ||||
−0.645686 | + | 0.763603i | \(0.723429\pi\) | |||||||
\(882\) | 2.00615 | 0.0675506 | ||||||||
\(883\) | −0.271994 | −0.00915331 | −0.00457666 | − | 0.999990i | \(-0.501457\pi\) | ||||
−0.00457666 | + | 0.999990i | \(0.501457\pi\) | |||||||
\(884\) | −26.0178 | −0.875075 | ||||||||
\(885\) | 14.1828 | 0.476749 | ||||||||
\(886\) | 9.57984 | 0.321841 | ||||||||
\(887\) | 22.6847 | 0.761679 | 0.380839 | − | 0.924641i | \(-0.375635\pi\) | ||||
0.380839 | + | 0.924641i | \(0.375635\pi\) | |||||||
\(888\) | 22.5316 | 0.756112 | ||||||||
\(889\) | 23.8017 | 0.798282 | ||||||||
\(890\) | 2.55057 | 0.0854952 | ||||||||
\(891\) | −4.83652 | −0.162029 | ||||||||
\(892\) | −11.4733 | −0.384154 | ||||||||
\(893\) | −12.3684 | −0.413891 | ||||||||
\(894\) | −8.82453 | −0.295136 | ||||||||
\(895\) | 12.9425 | 0.432621 | ||||||||
\(896\) | 16.1911 | 0.540907 | ||||||||
\(897\) | −1.60498 | −0.0535888 | ||||||||
\(898\) | −1.56061 | −0.0520783 | ||||||||
\(899\) | −79.8556 | −2.66333 | ||||||||
\(900\) | 1.88564 | 0.0628547 | ||||||||
\(901\) | −65.5176 | −2.18271 | ||||||||
\(902\) | 1.55644 | 0.0518237 | ||||||||
\(903\) | 15.2316 | 0.506876 | ||||||||
\(904\) | 18.5581 | 0.617233 | ||||||||
\(905\) | −2.58085 | −0.0857904 | ||||||||
\(906\) | 9.08779 | 0.301922 | ||||||||
\(907\) | −17.7568 | −0.589606 | −0.294803 | − | 0.955558i | \(-0.595254\pi\) | ||||
−0.294803 | + | 0.955558i | \(0.595254\pi\) | |||||||
\(908\) | −4.90719 | −0.162851 | ||||||||
\(909\) | −19.8330 | −0.657818 | ||||||||
\(910\) | 1.31216 | 0.0434977 | ||||||||
\(911\) | −1.46318 | −0.0484773 | −0.0242386 | − | 0.999706i | \(-0.507716\pi\) | ||||
−0.0242386 | + | 0.999706i | \(0.507716\pi\) | |||||||
\(912\) | −4.29514 | −0.142226 | ||||||||
\(913\) | 15.2456 | 0.504557 | ||||||||
\(914\) | −2.06380 | −0.0682644 | ||||||||
\(915\) | 5.54535 | 0.183323 | ||||||||
\(916\) | 38.1565 | 1.26072 | ||||||||
\(917\) | 3.19522 | 0.105516 | ||||||||
\(918\) | −16.3083 | −0.538255 | ||||||||
\(919\) | 32.9872 | 1.08815 | 0.544073 | − | 0.839038i | \(-0.316881\pi\) | ||||
0.544073 | + | 0.839038i | \(0.316881\pi\) | |||||||
\(920\) | −0.886080 | −0.0292132 | ||||||||
\(921\) | −10.2923 | −0.339144 | ||||||||
\(922\) | 14.0382 | 0.462325 | ||||||||
\(923\) | −6.70168 | −0.220589 | ||||||||
\(924\) | 3.91682 | 0.128854 | ||||||||
\(925\) | −10.0732 | −0.331206 | ||||||||
\(926\) | −5.18772 | −0.170479 | ||||||||
\(927\) | 1.04380 | 0.0342828 | ||||||||
\(928\) | 38.5437 | 1.26526 | ||||||||
\(929\) | 14.7059 | 0.482486 | 0.241243 | − | 0.970465i | \(-0.422445\pi\) | ||||
0.241243 | + | 0.970465i | \(0.422445\pi\) | |||||||
\(930\) | 5.37092 | 0.176119 | ||||||||
\(931\) | 4.77778 | 0.156586 | ||||||||
\(932\) | 23.6169 | 0.773596 | ||||||||
\(933\) | −44.2991 | −1.45029 | ||||||||
\(934\) | 13.8563 | 0.453391 | ||||||||
\(935\) | −6.91820 | −0.226249 | ||||||||
\(936\) | 3.39041 | 0.110819 | ||||||||
\(937\) | −8.40476 | −0.274572 | −0.137286 | − | 0.990531i | \(-0.543838\pi\) | ||||
−0.137286 | + | 0.990531i | \(0.543838\pi\) | |||||||
\(938\) | 0.786024 | 0.0256646 | ||||||||
\(939\) | 29.8943 | 0.975563 | ||||||||
\(940\) | 22.0422 | 0.718938 | ||||||||
\(941\) | 4.27537 | 0.139373 | 0.0696865 | − | 0.997569i | \(-0.477800\pi\) | ||||
0.0696865 | + | 0.997569i | \(0.477800\pi\) | |||||||
\(942\) | −7.88618 | −0.256946 | ||||||||
\(943\) | −2.07518 | −0.0675771 | ||||||||
\(944\) | −30.2127 | −0.983339 | ||||||||
\(945\) | −8.64832 | −0.281330 | ||||||||
\(946\) | −2.95986 | −0.0962335 | ||||||||
\(947\) | −0.339000 | −0.0110160 | −0.00550801 | − | 0.999985i | \(-0.501753\pi\) | ||||
−0.00550801 | + | 0.999985i | \(0.501753\pi\) | |||||||
\(948\) | 21.4756 | 0.697494 | ||||||||
\(949\) | 2.05922 | 0.0668452 | ||||||||
\(950\) | −0.427087 | −0.0138565 | ||||||||
\(951\) | 40.8632 | 1.32508 | ||||||||
\(952\) | 16.8678 | 0.546688 | ||||||||
\(953\) | −12.6535 | −0.409886 | −0.204943 | − | 0.978774i | \(-0.565701\pi\) | ||||
−0.204943 | + | 0.978774i | \(0.565701\pi\) | |||||||
\(954\) | 4.07505 | 0.131935 | ||||||||
\(955\) | −15.4394 | −0.499606 | ||||||||
\(956\) | −19.0338 | −0.615598 | ||||||||
\(957\) | 12.1916 | 0.394097 | ||||||||
\(958\) | −9.65205 | −0.311844 | ||||||||
\(959\) | 28.2034 | 0.910735 | ||||||||
\(960\) | 5.79017 | 0.186877 | ||||||||
\(961\) | 53.4132 | 1.72301 | ||||||||
\(962\) | −8.64483 | −0.278721 | ||||||||
\(963\) | −0.0137270 | −0.000442346 0 | ||||||||
\(964\) | 7.58362 | 0.244252 | ||||||||
\(965\) | 2.73093 | 0.0879118 | ||||||||
\(966\) | 0.496651 | 0.0159795 | ||||||||
\(967\) | −35.8135 | −1.15169 | −0.575843 | − | 0.817561i | \(-0.695326\pi\) | ||||
−0.575843 | + | 0.817561i | \(0.695326\pi\) | |||||||
\(968\) | −1.59465 | −0.0512539 | ||||||||
\(969\) | −9.94452 | −0.319464 | ||||||||
\(970\) | 5.08201 | 0.163174 | ||||||||
\(971\) | 35.3725 | 1.13516 | 0.567579 | − | 0.823319i | \(-0.307880\pi\) | ||||
0.567579 | + | 0.823319i | \(0.307880\pi\) | |||||||
\(972\) | −18.6006 | −0.596615 | ||||||||
\(973\) | 25.6453 | 0.822149 | ||||||||
\(974\) | −4.20940 | −0.134878 | ||||||||
\(975\) | 2.88843 | 0.0925038 | ||||||||
\(976\) | −11.8129 | −0.378121 | ||||||||
\(977\) | −23.2763 | −0.744676 | −0.372338 | − | 0.928097i | \(-0.621444\pi\) | ||||
−0.372338 | + | 0.928097i | \(0.621444\pi\) | |||||||
\(978\) | 11.9854 | 0.383251 | ||||||||
\(979\) | −6.12001 | −0.195596 | ||||||||
\(980\) | −8.51471 | −0.271992 | ||||||||
\(981\) | 17.8220 | 0.569013 | ||||||||
\(982\) | 11.4627 | 0.365790 | ||||||||
\(983\) | 47.3065 | 1.50884 | 0.754422 | − | 0.656390i | \(-0.227917\pi\) | ||||
0.754422 | + | 0.656390i | \(0.227917\pi\) | |||||||
\(984\) | −8.35355 | −0.266301 | ||||||||
\(985\) | 9.84862 | 0.313803 | ||||||||
\(986\) | 25.0598 | 0.798067 | ||||||||
\(987\) | −25.8844 | −0.823911 | ||||||||
\(988\) | 3.85398 | 0.122612 | ||||||||
\(989\) | 3.94635 | 0.125487 | ||||||||
\(990\) | 0.430297 | 0.0136757 | ||||||||
\(991\) | 15.6916 | 0.498461 | 0.249231 | − | 0.968444i | \(-0.419822\pi\) | ||||
0.249231 | + | 0.968444i | \(0.419822\pi\) | |||||||
\(992\) | −40.7435 | −1.29361 | ||||||||
\(993\) | 5.13040 | 0.162808 | ||||||||
\(994\) | 2.07379 | 0.0657767 | ||||||||
\(995\) | −16.6457 | −0.527704 | ||||||||
\(996\) | −39.0553 | −1.23751 | ||||||||
\(997\) | 26.7697 | 0.847804 | 0.423902 | − | 0.905708i | \(-0.360660\pi\) | ||||
0.423902 | + | 0.905708i | \(0.360660\pi\) | |||||||
\(998\) | −3.59558 | −0.113816 | ||||||||
\(999\) | 56.9772 | 1.80268 |
(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 | 4015.2.a.f.1.19 | ✓ | 31 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4015.2.a.f.1.19 | ✓ | 31 | 1.1 | even | 1 | trivial |