Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1875,2,Mod(1249,1875)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1875, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1875.1249");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1875 = 3 \cdot 5^{4} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1875.b (of order \(2\), degree \(1\), not minimal) |
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: | no |
Analytic conductor: | \(14.9719503790\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.6724000000.12 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 16x^{6} + 86x^{4} + 181x^{2} + 121 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 75) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1249.2 | ||
Root | \(-2.12233i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1875.1249 |
Dual form | 1875.2.b.c.1249.7 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1875\mathbb{Z}\right)^\times\).
\(n\) | \(626\) | \(1252\) |
\(\chi(n)\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − 2.12233i | − 1.50072i | −0.661031 | − | 0.750358i | \(-0.729881\pi\) | ||||
0.661031 | − | 0.750358i | \(-0.270119\pi\) | |||||||
\(3\) | 1.00000i | 0.577350i | ||||||||
\(4\) | −2.50430 | −1.25215 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 2.12233 | 0.866439 | ||||||||
\(7\) | − 4.35840i | − 1.64732i | −0.567083 | − | 0.823660i | \(-0.691928\pi\) | ||||
0.567083 | − | 0.823660i | \(-0.308072\pi\) | |||||||
\(8\) | 1.07029i | 0.378405i | ||||||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.57991 | −0.476360 | −0.238180 | − | 0.971221i | \(-0.576551\pi\) | ||||
−0.238180 | + | 0.971221i | \(0.576551\pi\) | |||||||
\(12\) | − 2.50430i | − 0.722929i | ||||||||
\(13\) | 1.19794i | 0.332249i | 0.986105 | + | 0.166124i | \(0.0531253\pi\) | ||||
−0.986105 | + | 0.166124i | \(0.946875\pi\) | |||||||
\(14\) | −9.24998 | −2.47216 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −2.73708 | −0.684271 | ||||||||
\(17\) | 1.12233i | 0.272206i | 0.990695 | + | 0.136103i | \(0.0434578\pi\) | ||||
−0.990695 | + | 0.136103i | \(0.956542\pi\) | |||||||
\(18\) | 2.12233i | 0.500239i | ||||||||
\(19\) | −7.67867 | −1.76161 | −0.880804 | − | 0.473480i | \(-0.842998\pi\) | ||||
−0.880804 | + | 0.473480i | \(0.842998\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 4.35840 | 0.951081 | ||||||||
\(22\) | 3.35309i | 0.714881i | ||||||||
\(23\) | − 2.32027i | − 0.483810i | −0.970300 | − | 0.241905i | \(-0.922228\pi\) | ||||
0.970300 | − | 0.241905i | \(-0.0777723\pi\) | |||||||
\(24\) | −1.07029 | −0.218472 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 2.54243 | 0.498611 | ||||||||
\(27\) | − 1.00000i | − 0.192450i | ||||||||
\(28\) | 10.9147i | 2.06269i | ||||||||
\(29\) | 5.50430 | 1.02212 | 0.511061 | − | 0.859544i | \(-0.329252\pi\) | ||||
0.511061 | + | 0.859544i | \(0.329252\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.80206 | 0.862475 | 0.431238 | − | 0.902238i | \(-0.358077\pi\) | ||||
0.431238 | + | 0.902238i | \(0.358077\pi\) | |||||||
\(32\) | 7.94959i | 1.40530i | ||||||||
\(33\) | − 1.57991i | − 0.275026i | ||||||||
\(34\) | 2.38197 | 0.408504 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 2.50430 | 0.417383 | ||||||||
\(37\) | 6.37232i | 1.04760i | 0.851841 | + | 0.523801i | \(0.175486\pi\) | ||||
−0.851841 | + | 0.523801i | \(0.824514\pi\) | |||||||
\(38\) | 16.2967i | 2.64368i | ||||||||
\(39\) | −1.19794 | −0.191824 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −7.47214 | −1.16695 | −0.583476 | − | 0.812131i | \(-0.698308\pi\) | ||||
−0.583476 | + | 0.812131i | \(0.698308\pi\) | |||||||
\(42\) | − 9.24998i | − 1.42730i | ||||||||
\(43\) | − 1.24998i | − 0.190620i | −0.995448 | − | 0.0953102i | \(-0.969616\pi\) | ||||
0.995448 | − | 0.0953102i | \(-0.0303843\pi\) | |||||||
\(44\) | 3.95656 | 0.596473 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −4.92439 | −0.726062 | ||||||||
\(47\) | − 4.12765i | − 0.602079i | −0.953612 | − | 0.301040i | \(-0.902666\pi\) | ||||
0.953612 | − | 0.301040i | \(-0.0973337\pi\) | |||||||
\(48\) | − 2.73708i | − 0.395064i | ||||||||
\(49\) | −11.9957 | −1.71367 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1.12233 | −0.157158 | ||||||||
\(52\) | − 3.00000i | − 0.416025i | ||||||||
\(53\) | 3.74568i | 0.514509i | 0.966344 | + | 0.257254i | \(0.0828179\pi\) | ||||
−0.966344 | + | 0.257254i | \(0.917182\pi\) | |||||||
\(54\) | −2.12233 | −0.288813 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 4.66476 | 0.623355 | ||||||||
\(57\) | − 7.67867i | − 1.01707i | ||||||||
\(58\) | − 11.6820i | − 1.53392i | ||||||||
\(59\) | −9.15613 | −1.19203 | −0.596013 | − | 0.802975i | \(-0.703249\pi\) | ||||
−0.596013 | + | 0.802975i | \(0.703249\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.39588 | 0.178724 | 0.0893620 | − | 0.995999i | \(-0.471517\pi\) | ||||
0.0893620 | + | 0.995999i | \(0.471517\pi\) | |||||||
\(62\) | − 10.1916i | − 1.29433i | ||||||||
\(63\) | 4.35840i | 0.549107i | ||||||||
\(64\) | 11.3975 | 1.42469 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −3.35309 | −0.412736 | ||||||||
\(67\) | 3.86270i | 0.471904i | 0.971765 | + | 0.235952i | \(0.0758208\pi\) | ||||
−0.971765 | + | 0.235952i | \(0.924179\pi\) | |||||||
\(68\) | − 2.81066i | − 0.340843i | ||||||||
\(69\) | 2.32027 | 0.279328 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −10.6051 | −1.25859 | −0.629297 | − | 0.777165i | \(-0.716657\pi\) | ||||
−0.629297 | + | 0.777165i | \(0.716657\pi\) | |||||||
\(72\) | − 1.07029i | − 0.126135i | ||||||||
\(73\) | 4.99672i | 0.584821i | 0.956293 | + | 0.292411i | \(0.0944574\pi\) | ||||
−0.956293 | + | 0.292411i | \(0.905543\pi\) | |||||||
\(74\) | 13.5242 | 1.57215 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 19.2297 | 2.20580 | ||||||||
\(77\) | 6.88586i | 0.784717i | ||||||||
\(78\) | 2.54243i | 0.287873i | ||||||||
\(79\) | −14.5531 | −1.63735 | −0.818673 | − | 0.574259i | \(-0.805290\pi\) | ||||
−0.818673 | + | 0.574259i | \(0.805290\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 15.8584i | 1.75126i | ||||||||
\(83\) | − 8.73603i | − 0.958904i | −0.877568 | − | 0.479452i | \(-0.840835\pi\) | ||||
0.877568 | − | 0.479452i | \(-0.159165\pi\) | |||||||
\(84\) | −10.9147 | −1.19090 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −2.65288 | −0.286067 | ||||||||
\(87\) | 5.50430i | 0.590123i | ||||||||
\(88\) | − 1.69096i | − 0.180257i | ||||||||
\(89\) | 10.0381 | 1.06404 | 0.532020 | − | 0.846732i | \(-0.321433\pi\) | ||||
0.532020 | + | 0.846732i | \(0.321433\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 5.22110 | 0.547320 | ||||||||
\(92\) | 5.81066i | 0.605803i | ||||||||
\(93\) | 4.80206i | 0.497950i | ||||||||
\(94\) | −8.76025 | −0.903550 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −7.94959 | −0.811351 | ||||||||
\(97\) | 7.49996i | 0.761506i | 0.924677 | + | 0.380753i | \(0.124335\pi\) | ||||
−0.924677 | + | 0.380753i | \(0.875665\pi\) | |||||||
\(98\) | 25.4588i | 2.57173i | ||||||||
\(99\) | 1.57991 | 0.158787 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −6.51821 | −0.648586 | −0.324293 | − | 0.945957i | \(-0.605126\pi\) | ||||
−0.324293 | + | 0.945957i | \(0.605126\pi\) | |||||||
\(102\) | 2.38197i | 0.235850i | ||||||||
\(103\) | 8.04876i | 0.793068i | 0.918020 | + | 0.396534i | \(0.129787\pi\) | ||||
−0.918020 | + | 0.396534i | \(0.870213\pi\) | |||||||
\(104\) | −1.28215 | −0.125725 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 7.94959 | 0.772132 | ||||||||
\(107\) | − 9.47745i | − 0.916220i | −0.888896 | − | 0.458110i | \(-0.848527\pi\) | ||||
0.888896 | − | 0.458110i | \(-0.151473\pi\) | |||||||
\(108\) | 2.50430i | 0.240976i | ||||||||
\(109\) | 11.6657 | 1.11738 | 0.558688 | − | 0.829378i | \(-0.311305\pi\) | ||||
0.558688 | + | 0.829378i | \(0.311305\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −6.37232 | −0.604833 | ||||||||
\(112\) | 11.9293i | 1.12721i | ||||||||
\(113\) | − 14.9254i | − 1.40406i | −0.712147 | − | 0.702030i | \(-0.752277\pi\) | ||||
0.712147 | − | 0.702030i | \(-0.247723\pi\) | |||||||
\(114\) | −16.2967 | −1.52633 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −13.7844 | −1.27985 | ||||||||
\(117\) | − 1.19794i | − 0.110750i | ||||||||
\(118\) | 19.4324i | 1.78889i | ||||||||
\(119\) | 4.89158 | 0.448410 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −8.50390 | −0.773082 | ||||||||
\(122\) | − 2.96252i | − 0.268214i | ||||||||
\(123\) | − 7.47214i | − 0.673740i | ||||||||
\(124\) | −12.0258 | −1.07995 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 9.24998 | 0.824054 | ||||||||
\(127\) | 16.9957i | 1.50812i | 0.656805 | + | 0.754061i | \(0.271908\pi\) | ||||
−0.656805 | + | 0.754061i | \(0.728092\pi\) | |||||||
\(128\) | − 8.29014i | − 0.732752i | ||||||||
\(129\) | 1.24998 | 0.110055 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −0.328872 | −0.0287337 | −0.0143669 | − | 0.999897i | \(-0.504573\pi\) | ||||
−0.0143669 | + | 0.999897i | \(0.504573\pi\) | |||||||
\(132\) | 3.95656i | 0.344374i | ||||||||
\(133\) | 33.4667i | 2.90194i | ||||||||
\(134\) | 8.19794 | 0.708194 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −1.20122 | −0.103004 | ||||||||
\(137\) | − 4.56271i | − 0.389818i | −0.980821 | − | 0.194909i | \(-0.937559\pi\) | ||||
0.980821 | − | 0.194909i | \(-0.0624412\pi\) | |||||||
\(138\) | − 4.92439i | − 0.419192i | ||||||||
\(139\) | 4.73400 | 0.401533 | 0.200766 | − | 0.979639i | \(-0.435657\pi\) | ||||
0.200766 | + | 0.979639i | \(0.435657\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 4.12765 | 0.347611 | ||||||||
\(142\) | 22.5076i | 1.88879i | ||||||||
\(143\) | − 1.89263i | − 0.158270i | ||||||||
\(144\) | 2.73708 | 0.228090 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 10.6047 | 0.877651 | ||||||||
\(147\) | − 11.9957i | − 0.989386i | ||||||||
\(148\) | − 15.9582i | − 1.31175i | ||||||||
\(149\) | −4.67644 | −0.383109 | −0.191555 | − | 0.981482i | \(-0.561353\pi\) | ||||
−0.191555 | + | 0.981482i | \(0.561353\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −6.54178 | −0.532362 | −0.266181 | − | 0.963923i | \(-0.585762\pi\) | ||||
−0.266181 | + | 0.963923i | \(0.585762\pi\) | |||||||
\(152\) | − 8.21842i | − 0.666602i | ||||||||
\(153\) | − 1.12233i | − 0.0907353i | ||||||||
\(154\) | 14.6141 | 1.17764 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 3.00000 | 0.240192 | ||||||||
\(157\) | − 3.99404i | − 0.318759i | −0.987217 | − | 0.159379i | \(-0.949051\pi\) | ||||
0.987217 | − | 0.159379i | \(-0.0509493\pi\) | |||||||
\(158\) | 30.8864i | 2.45719i | ||||||||
\(159\) | −3.74568 | −0.297052 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −10.1127 | −0.796991 | ||||||||
\(162\) | − 2.12233i | − 0.166746i | ||||||||
\(163\) | 4.80141i | 0.376075i | 0.982162 | + | 0.188038i | \(0.0602127\pi\) | ||||
−0.982162 | + | 0.188038i | \(0.939787\pi\) | |||||||
\(164\) | 18.7125 | 1.46120 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −18.5408 | −1.43904 | ||||||||
\(167\) | − 23.6600i | − 1.83087i | −0.402469 | − | 0.915434i | \(-0.631848\pi\) | ||||
0.402469 | − | 0.915434i | \(-0.368152\pi\) | |||||||
\(168\) | 4.66476i | 0.359894i | ||||||||
\(169\) | 11.5649 | 0.889611 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 7.67867 | 0.587203 | ||||||||
\(172\) | 3.13033i | 0.238685i | ||||||||
\(173\) | 14.5043i | 1.10274i | 0.834260 | + | 0.551371i | \(0.185895\pi\) | ||||
−0.834260 | + | 0.551371i | \(0.814105\pi\) | |||||||
\(174\) | 11.6820 | 0.885607 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 4.32433 | 0.325959 | ||||||||
\(177\) | − 9.15613i | − 0.688217i | ||||||||
\(178\) | − 21.3043i | − 1.59682i | ||||||||
\(179\) | −0.796746 | −0.0595516 | −0.0297758 | − | 0.999557i | \(-0.509479\pi\) | ||||
−0.0297758 | + | 0.999557i | \(0.509479\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −14.2185 | −1.05685 | −0.528425 | − | 0.848980i | \(-0.677217\pi\) | ||||
−0.528425 | + | 0.848980i | \(0.677217\pi\) | |||||||
\(182\) | − 11.0809i | − 0.821372i | ||||||||
\(183\) | 1.39588i | 0.103186i | ||||||||
\(184\) | 2.48337 | 0.183076 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 10.1916 | 0.747282 | ||||||||
\(187\) | − 1.77318i | − 0.129668i | ||||||||
\(188\) | 10.3369i | 0.753894i | ||||||||
\(189\) | −4.35840 | −0.317027 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −10.3697 | −0.750324 | −0.375162 | − | 0.926959i | \(-0.622413\pi\) | ||||
−0.375162 | + | 0.926959i | \(0.622413\pi\) | |||||||
\(192\) | 11.3975i | 0.822544i | ||||||||
\(193\) | 4.34712i | 0.312913i | 0.987685 | + | 0.156456i | \(0.0500071\pi\) | ||||
−0.987685 | + | 0.156456i | \(0.949993\pi\) | |||||||
\(194\) | 15.9174 | 1.14280 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 30.0407 | 2.14577 | ||||||||
\(197\) | − 1.87990i | − 0.133937i | −0.997755 | − | 0.0669686i | \(-0.978667\pi\) | ||||
0.997755 | − | 0.0669686i | \(-0.0213327\pi\) | |||||||
\(198\) | − 3.35309i | − 0.238294i | ||||||||
\(199\) | −4.26028 | −0.302003 | −0.151002 | − | 0.988534i | \(-0.548250\pi\) | ||||
−0.151002 | + | 0.988534i | \(0.548250\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −3.86270 | −0.272454 | ||||||||
\(202\) | 13.8338i | 0.973344i | ||||||||
\(203\) | − 23.9899i | − 1.68376i | ||||||||
\(204\) | 2.81066 | 0.196786 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 17.0821 | 1.19017 | ||||||||
\(207\) | 2.32027i | 0.161270i | ||||||||
\(208\) | − 3.27886i | − 0.227348i | ||||||||
\(209\) | 12.1316 | 0.839159 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −9.29671 | −0.640012 | −0.320006 | − | 0.947416i | \(-0.603685\pi\) | ||||
−0.320006 | + | 0.947416i | \(0.603685\pi\) | |||||||
\(212\) | − 9.38031i | − 0.644242i | ||||||||
\(213\) | − 10.6051i | − 0.726649i | ||||||||
\(214\) | −20.1143 | −1.37499 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 1.07029 | 0.0728241 | ||||||||
\(217\) | − 20.9293i | − 1.42077i | ||||||||
\(218\) | − 24.7586i | − 1.67686i | ||||||||
\(219\) | −4.99672 | −0.337647 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1.34449 | −0.0904400 | ||||||||
\(222\) | 13.5242i | 0.907683i | ||||||||
\(223\) | − 3.39758i | − 0.227519i | −0.993508 | − | 0.113759i | \(-0.963711\pi\) | ||||
0.993508 | − | 0.113759i | \(-0.0362893\pi\) | |||||||
\(224\) | 34.6475 | 2.31498 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −31.6766 | −2.10710 | ||||||||
\(227\) | − 26.7973i | − 1.77860i | −0.457324 | − | 0.889300i | \(-0.651192\pi\) | ||||
0.457324 | − | 0.889300i | \(-0.348808\pi\) | |||||||
\(228\) | 19.2297i | 1.27352i | ||||||||
\(229\) | 1.18200 | 0.0781085 | 0.0390543 | − | 0.999237i | \(-0.487565\pi\) | ||||
0.0390543 | + | 0.999237i | \(0.487565\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −6.88586 | −0.453057 | ||||||||
\(232\) | 5.89121i | 0.386777i | ||||||||
\(233\) | 7.09483i | 0.464798i | 0.972621 | + | 0.232399i | \(0.0746575\pi\) | ||||
−0.972621 | + | 0.232399i | \(0.925342\pi\) | |||||||
\(234\) | −2.54243 | −0.166204 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 22.9297 | 1.49260 | ||||||||
\(237\) | − 14.5531i | − 0.945323i | ||||||||
\(238\) | − 10.3816i | − 0.672937i | ||||||||
\(239\) | −0.0427926 | −0.00276802 | −0.00138401 | − | 0.999999i | \(-0.500441\pi\) | ||||
−0.00138401 | + | 0.999999i | \(0.500441\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −11.7711 | −0.758242 | −0.379121 | − | 0.925347i | \(-0.623774\pi\) | ||||
−0.379121 | + | 0.925347i | \(0.623774\pi\) | |||||||
\(242\) | 18.0481i | 1.16018i | ||||||||
\(243\) | 1.00000i | 0.0641500i | ||||||||
\(244\) | −3.49570 | −0.223789 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −15.8584 | −1.01109 | ||||||||
\(247\) | − 9.19859i | − 0.585292i | ||||||||
\(248\) | 5.13961i | 0.326365i | ||||||||
\(249\) | 8.73603 | 0.553623 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 17.4764 | 1.10310 | 0.551550 | − | 0.834142i | \(-0.314036\pi\) | ||||
0.551550 | + | 0.834142i | \(0.314036\pi\) | |||||||
\(252\) | − 10.9147i | − 0.687564i | ||||||||
\(253\) | 3.66581i | 0.230468i | ||||||||
\(254\) | 36.0705 | 2.26326 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 5.20057 | 0.325036 | ||||||||
\(257\) | − 15.4671i | − 0.964814i | −0.875947 | − | 0.482407i | \(-0.839763\pi\) | ||||
0.875947 | − | 0.482407i | \(-0.160237\pi\) | |||||||
\(258\) | − 2.65288i | − 0.165161i | ||||||||
\(259\) | 27.7731 | 1.72574 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −5.50430 | −0.340708 | ||||||||
\(262\) | 0.697977i | 0.0431211i | ||||||||
\(263\) | 1.44759i | 0.0892624i | 0.999004 | + | 0.0446312i | \(0.0142113\pi\) | ||||
−0.999004 | + | 0.0446312i | \(0.985789\pi\) | |||||||
\(264\) | 1.69096 | 0.104071 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 71.0276 | 4.35498 | ||||||||
\(267\) | 10.0381i | 0.614323i | ||||||||
\(268\) | − 9.67336i | − 0.590895i | ||||||||
\(269\) | 8.70617 | 0.530825 | 0.265412 | − | 0.964135i | \(-0.414492\pi\) | ||||
0.265412 | + | 0.964135i | \(0.414492\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −28.6338 | −1.73938 | −0.869689 | − | 0.493600i | \(-0.835681\pi\) | ||||
−0.869689 | + | 0.493600i | \(0.835681\pi\) | |||||||
\(272\) | − 3.07192i | − 0.186263i | ||||||||
\(273\) | 5.22110i | 0.315995i | ||||||||
\(274\) | −9.68359 | −0.585007 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −5.81066 | −0.349761 | ||||||||
\(277\) | − 5.30210i | − 0.318572i | −0.987232 | − | 0.159286i | \(-0.949081\pi\) | ||||
0.987232 | − | 0.159286i | \(-0.0509192\pi\) | |||||||
\(278\) | − 10.0471i | − 0.602587i | ||||||||
\(279\) | −4.80206 | −0.287492 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −24.0832 | −1.43668 | −0.718342 | − | 0.695691i | \(-0.755098\pi\) | ||||
−0.718342 | + | 0.695691i | \(0.755098\pi\) | |||||||
\(282\) | − 8.76025i | − 0.521665i | ||||||||
\(283\) | − 27.1143i | − 1.61178i | −0.592066 | − | 0.805889i | \(-0.701688\pi\) | ||||
0.592066 | − | 0.805889i | \(-0.298312\pi\) | |||||||
\(284\) | 26.5583 | 1.57595 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −4.01680 | −0.237518 | ||||||||
\(287\) | 32.5666i | 1.92234i | ||||||||
\(288\) | − 7.94959i | − 0.468434i | ||||||||
\(289\) | 15.7404 | 0.925904 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −7.49996 | −0.439656 | ||||||||
\(292\) | − 12.5133i | − 0.732284i | ||||||||
\(293\) | − 20.3016i | − 1.18603i | −0.805190 | − | 0.593017i | \(-0.797937\pi\) | ||||
0.805190 | − | 0.593017i | \(-0.202063\pi\) | |||||||
\(294\) | −25.4588 | −1.48479 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −6.82024 | −0.396418 | ||||||||
\(297\) | 1.57991i | 0.0916754i | ||||||||
\(298\) | 9.92497i | 0.574938i | ||||||||
\(299\) | 2.77955 | 0.160745 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −5.44792 | −0.314013 | ||||||||
\(302\) | 13.8838i | 0.798925i | ||||||||
\(303\) | − 6.51821i | − 0.374462i | ||||||||
\(304\) | 21.0172 | 1.20542 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −2.38197 | −0.136168 | ||||||||
\(307\) | 2.51330i | 0.143442i | 0.997425 | + | 0.0717208i | \(0.0228491\pi\) | ||||
−0.997425 | + | 0.0717208i | \(0.977151\pi\) | |||||||
\(308\) | − 17.2443i | − 0.982583i | ||||||||
\(309\) | −8.04876 | −0.457878 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 4.82417 | 0.273554 | 0.136777 | − | 0.990602i | \(-0.456326\pi\) | ||||
0.136777 | + | 0.990602i | \(0.456326\pi\) | |||||||
\(312\) | − 1.28215i | − 0.0725872i | ||||||||
\(313\) | − 5.98812i | − 0.338468i | −0.985576 | − | 0.169234i | \(-0.945871\pi\) | ||||
0.985576 | − | 0.169234i | \(-0.0541294\pi\) | |||||||
\(314\) | −8.47668 | −0.478366 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 36.4452 | 2.05020 | ||||||||
\(317\) | − 17.3531i | − 0.974646i | −0.873222 | − | 0.487323i | \(-0.837973\pi\) | ||||
0.873222 | − | 0.487323i | \(-0.162027\pi\) | |||||||
\(318\) | 7.94959i | 0.445791i | ||||||||
\(319\) | −8.69627 | −0.486898 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 9.47745 | 0.528980 | ||||||||
\(322\) | 21.4625i | 1.19606i | ||||||||
\(323\) | − 8.61803i | − 0.479520i | ||||||||
\(324\) | −2.50430 | −0.139128 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 10.1902 | 0.564383 | ||||||||
\(327\) | 11.6657i | 0.645117i | ||||||||
\(328\) | − 7.99737i | − 0.441581i | ||||||||
\(329\) | −17.9899 | −0.991818 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 20.3355 | 1.11774 | 0.558870 | − | 0.829255i | \(-0.311235\pi\) | ||||
0.558870 | + | 0.829255i | \(0.311235\pi\) | |||||||
\(332\) | 21.8776i | 1.20069i | ||||||||
\(333\) | − 6.37232i | − 0.349201i | ||||||||
\(334\) | −50.2145 | −2.74761 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −11.9293 | −0.650797 | ||||||||
\(337\) | − 34.2571i | − 1.86610i | −0.359741 | − | 0.933052i | \(-0.617135\pi\) | ||||
0.359741 | − | 0.933052i | \(-0.382865\pi\) | |||||||
\(338\) | − 24.5447i | − 1.33505i | ||||||||
\(339\) | 14.9254 | 0.810635 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −7.58680 | −0.410848 | ||||||||
\(342\) | − 16.2967i | − 0.881225i | ||||||||
\(343\) | 21.7731i | 1.17564i | ||||||||
\(344\) | 1.33784 | 0.0721318 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 30.7830 | 1.65490 | ||||||||
\(347\) | 0.0493616i | 0.00264987i | 0.999999 | + | 0.00132494i | \(0.000421740\pi\) | ||||
−0.999999 | + | 0.00132494i | \(0.999578\pi\) | |||||||
\(348\) | − 13.7844i | − 0.738922i | ||||||||
\(349\) | 7.47437 | 0.400094 | 0.200047 | − | 0.979786i | \(-0.435891\pi\) | ||||
0.200047 | + | 0.979786i | \(0.435891\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.19794 | 0.0639413 | ||||||||
\(352\) | − 12.5596i | − 0.669429i | ||||||||
\(353\) | − 18.5650i | − 0.988115i | −0.869429 | − | 0.494057i | \(-0.835513\pi\) | ||||
0.869429 | − | 0.494057i | \(-0.164487\pi\) | |||||||
\(354\) | −19.4324 | −1.03282 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −25.1385 | −1.33234 | ||||||||
\(357\) | 4.89158i | 0.258890i | ||||||||
\(358\) | 1.69096i | 0.0893700i | ||||||||
\(359\) | −10.6044 | −0.559681 | −0.279841 | − | 0.960046i | \(-0.590282\pi\) | ||||
−0.279841 | + | 0.960046i | \(0.590282\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 39.9620 | 2.10327 | ||||||||
\(362\) | 30.1763i | 1.58603i | ||||||||
\(363\) | − 8.50390i | − 0.446339i | ||||||||
\(364\) | −13.0752 | −0.685327 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 2.96252 | 0.154854 | ||||||||
\(367\) | 11.6176i | 0.606435i | 0.952921 | + | 0.303218i | \(0.0980609\pi\) | ||||
−0.952921 | + | 0.303218i | \(0.901939\pi\) | |||||||
\(368\) | 6.35078i | 0.331057i | ||||||||
\(369\) | 7.47214 | 0.388984 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 16.3252 | 0.847561 | ||||||||
\(372\) | − 12.0258i | − 0.623509i | ||||||||
\(373\) | − 23.1272i | − 1.19748i | −0.800942 | − | 0.598742i | \(-0.795668\pi\) | ||||
0.800942 | − | 0.598742i | \(-0.204332\pi\) | |||||||
\(374\) | −3.76328 | −0.194595 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 4.41779 | 0.227830 | ||||||||
\(377\) | 6.59382i | 0.339599i | ||||||||
\(378\) | 9.24998i | 0.475768i | ||||||||
\(379\) | −24.8912 | −1.27857 | −0.639287 | − | 0.768968i | \(-0.720770\pi\) | ||||
−0.639287 | + | 0.768968i | \(0.720770\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −16.9957 | −0.870714 | ||||||||
\(382\) | 22.0079i | 1.12602i | ||||||||
\(383\) | − 15.7221i | − 0.803363i | −0.915780 | − | 0.401681i | \(-0.868426\pi\) | ||||
0.915780 | − | 0.401681i | \(-0.131574\pi\) | |||||||
\(384\) | 8.29014 | 0.423054 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 9.22604 | 0.469593 | ||||||||
\(387\) | 1.24998i | 0.0635401i | ||||||||
\(388\) | − 18.7822i | − 0.953519i | ||||||||
\(389\) | 8.50633 | 0.431288 | 0.215644 | − | 0.976472i | \(-0.430815\pi\) | ||||
0.215644 | + | 0.976472i | \(0.430815\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.60412 | 0.131696 | ||||||||
\(392\) | − 12.8389i | − 0.648460i | ||||||||
\(393\) | − 0.328872i | − 0.0165894i | ||||||||
\(394\) | −3.98977 | −0.201002 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −3.95656 | −0.198824 | ||||||||
\(397\) | − 26.2549i | − 1.31770i | −0.752276 | − | 0.658848i | \(-0.771044\pi\) | ||||
0.752276 | − | 0.658848i | \(-0.228956\pi\) | |||||||
\(398\) | 9.04174i | 0.453222i | ||||||||
\(399\) | −33.4667 | −1.67543 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −25.2815 | −1.26250 | −0.631250 | − | 0.775579i | \(-0.717458\pi\) | ||||
−0.631250 | + | 0.775579i | \(0.717458\pi\) | |||||||
\(402\) | 8.19794i | 0.408876i | ||||||||
\(403\) | 5.75258i | 0.286556i | ||||||||
\(404\) | 16.3236 | 0.812127 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −50.9147 | −2.52685 | ||||||||
\(407\) | − 10.0677i | − 0.499035i | ||||||||
\(408\) | − 1.20122i | − 0.0594695i | ||||||||
\(409\) | −33.7932 | −1.67097 | −0.835483 | − | 0.549517i | \(-0.814812\pi\) | ||||
−0.835483 | + | 0.549517i | \(0.814812\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 4.56271 | 0.225062 | ||||||||
\(412\) | − 20.1565i | − 0.993039i | ||||||||
\(413\) | 39.9061i | 1.96365i | ||||||||
\(414\) | 4.92439 | 0.242021 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −9.52313 | −0.466910 | ||||||||
\(417\) | 4.73400i | 0.231825i | ||||||||
\(418\) | − 25.7473i | − 1.25934i | ||||||||
\(419\) | −7.93332 | −0.387568 | −0.193784 | − | 0.981044i | \(-0.562076\pi\) | ||||
−0.193784 | + | 0.981044i | \(0.562076\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 7.48795 | 0.364941 | 0.182470 | − | 0.983211i | \(-0.441591\pi\) | ||||
0.182470 | + | 0.983211i | \(0.441591\pi\) | |||||||
\(422\) | 19.7307i | 0.960476i | ||||||||
\(423\) | 4.12765i | 0.200693i | ||||||||
\(424\) | −4.00897 | −0.194693 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −22.5076 | −1.09049 | ||||||||
\(427\) | − 6.08380i | − 0.294416i | ||||||||
\(428\) | 23.7344i | 1.14724i | ||||||||
\(429\) | 1.89263 | 0.0913771 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 23.3470 | 1.12459 | 0.562294 | − | 0.826937i | \(-0.309919\pi\) | ||||
0.562294 | + | 0.826937i | \(0.309919\pi\) | |||||||
\(432\) | 2.73708i | 0.131688i | ||||||||
\(433\) | − 3.35677i | − 0.161316i | −0.996742 | − | 0.0806581i | \(-0.974298\pi\) | ||||
0.996742 | − | 0.0806581i | \(-0.0257022\pi\) | |||||||
\(434\) | −44.4190 | −2.13218 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −29.2145 | −1.39912 | ||||||||
\(437\) | 17.8166i | 0.852285i | ||||||||
\(438\) | 10.6047i | 0.506712i | ||||||||
\(439\) | 9.48402 | 0.452648 | 0.226324 | − | 0.974052i | \(-0.427329\pi\) | ||||
0.226324 | + | 0.974052i | \(0.427329\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 11.9957 | 0.571222 | ||||||||
\(442\) | 2.85345i | 0.135725i | ||||||||
\(443\) | 9.65446i | 0.458697i | 0.973344 | + | 0.229349i | \(0.0736596\pi\) | ||||
−0.973344 | + | 0.229349i | \(0.926340\pi\) | |||||||
\(444\) | 15.9582 | 0.757342 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −7.21080 | −0.341441 | ||||||||
\(447\) | − 4.67644i | − 0.221188i | ||||||||
\(448\) | − 49.6749i | − 2.34692i | ||||||||
\(449\) | −31.5260 | −1.48780 | −0.743902 | − | 0.668289i | \(-0.767027\pi\) | ||||
−0.743902 | + | 0.668289i | \(0.767027\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 11.8053 | 0.555888 | ||||||||
\(452\) | 37.3776i | 1.75809i | ||||||||
\(453\) | − 6.54178i | − 0.307360i | ||||||||
\(454\) | −56.8729 | −2.66918 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 8.21842 | 0.384863 | ||||||||
\(457\) | 9.94467i | 0.465192i | 0.972573 | + | 0.232596i | \(0.0747220\pi\) | ||||
−0.972573 | + | 0.232596i | \(0.925278\pi\) | |||||||
\(458\) | − 2.50859i | − 0.117219i | ||||||||
\(459\) | 1.12233 | 0.0523860 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −23.6836 | −1.10305 | −0.551527 | − | 0.834157i | \(-0.685955\pi\) | ||||
−0.551527 | + | 0.834157i | \(0.685955\pi\) | |||||||
\(462\) | 14.6141i | 0.679909i | ||||||||
\(463\) | 27.6504i | 1.28502i | 0.766277 | + | 0.642511i | \(0.222107\pi\) | ||||
−0.766277 | + | 0.642511i | \(0.777893\pi\) | |||||||
\(464\) | −15.0657 | −0.699409 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 15.0576 | 0.697530 | ||||||||
\(467\) | − 4.35840i | − 0.201683i | −0.994903 | − | 0.100841i | \(-0.967847\pi\) | ||||
0.994903 | − | 0.100841i | \(-0.0321535\pi\) | |||||||
\(468\) | 3.00000i | 0.138675i | ||||||||
\(469\) | 16.8352 | 0.777377 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 3.99404 | 0.184035 | ||||||||
\(472\) | − 9.79973i | − 0.451069i | ||||||||
\(473\) | 1.97485i | 0.0908038i | ||||||||
\(474\) | −30.8864 | −1.41866 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −12.2500 | −0.561477 | ||||||||
\(477\) | − 3.74568i | − 0.171503i | ||||||||
\(478\) | 0.0908201i | 0.00415401i | ||||||||
\(479\) | −12.8143 | −0.585499 | −0.292750 | − | 0.956189i | \(-0.594570\pi\) | ||||
−0.292750 | + | 0.956189i | \(0.594570\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −7.63365 | −0.348064 | ||||||||
\(482\) | 24.9822i | 1.13791i | ||||||||
\(483\) | − 10.1127i | − 0.460143i | ||||||||
\(484\) | 21.2963 | 0.968014 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 2.12233 | 0.0962710 | ||||||||
\(487\) | 6.92209i | 0.313670i | 0.987625 | + | 0.156835i | \(0.0501290\pi\) | ||||
−0.987625 | + | 0.156835i | \(0.949871\pi\) | |||||||
\(488\) | 1.49400i | 0.0676301i | ||||||||
\(489\) | −4.80141 | −0.217127 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 26.8161 | 1.21020 | 0.605098 | − | 0.796151i | \(-0.293134\pi\) | ||||
0.605098 | + | 0.796151i | \(0.293134\pi\) | |||||||
\(492\) | 18.7125i | 0.843623i | ||||||||
\(493\) | 6.17766i | 0.278228i | ||||||||
\(494\) | −19.5225 | −0.878358 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −13.1436 | −0.590167 | ||||||||
\(497\) | 46.2213i | 2.07331i | ||||||||
\(498\) | − 18.5408i | − 0.830832i | ||||||||
\(499\) | −2.75460 | −0.123313 | −0.0616565 | − | 0.998097i | \(-0.519638\pi\) | ||||
−0.0616565 | + | 0.998097i | \(0.519638\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 23.6600 | 1.05705 | ||||||||
\(502\) | − 37.0907i | − 1.65544i | ||||||||
\(503\) | 15.7102i | 0.700483i | 0.936659 | + | 0.350241i | \(0.113900\pi\) | ||||
−0.936659 | + | 0.350241i | \(0.886100\pi\) | |||||||
\(504\) | −4.66476 | −0.207785 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 7.78008 | 0.345867 | ||||||||
\(507\) | 11.5649i | 0.513617i | ||||||||
\(508\) | − 42.5622i | − 1.88839i | ||||||||
\(509\) | 41.0884 | 1.82121 | 0.910606 | − | 0.413277i | \(-0.135616\pi\) | ||||
0.910606 | + | 0.413277i | \(0.135616\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 21.7777 | 0.963388 | ||||||||
\(512\) | − 27.6176i | − 1.22054i | ||||||||
\(513\) | 7.67867i | 0.339022i | ||||||||
\(514\) | −32.8264 | −1.44791 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −3.13033 | −0.137805 | ||||||||
\(517\) | 6.52129i | 0.286806i | ||||||||
\(518\) | − 58.9438i | − 2.58984i | ||||||||
\(519\) | −14.5043 | −0.636668 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 36.1710 | 1.58468 | 0.792341 | − | 0.610079i | \(-0.208862\pi\) | ||||
0.792341 | + | 0.610079i | \(0.208862\pi\) | |||||||
\(522\) | 11.6820i | 0.511305i | ||||||||
\(523\) | 28.0490i | 1.22650i | 0.789891 | + | 0.613248i | \(0.210137\pi\) | ||||
−0.789891 | + | 0.613248i | \(0.789863\pi\) | |||||||
\(524\) | 0.823595 | 0.0359789 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 3.07228 | 0.133958 | ||||||||
\(527\) | 5.38951i | 0.234771i | ||||||||
\(528\) | 4.32433i | 0.188192i | ||||||||
\(529\) | 17.6163 | 0.765927 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 9.15613 | 0.397342 | ||||||||
\(532\) | − 83.8108i | − 3.63366i | ||||||||
\(533\) | − 8.95117i | − 0.387718i | ||||||||
\(534\) | 21.3043 | 0.921925 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −4.13422 | −0.178571 | ||||||||
\(537\) | − 0.796746i | − 0.0343821i | ||||||||
\(538\) | − 18.4774i | − 0.796617i | ||||||||
\(539\) | 18.9520 | 0.816321 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 3.45822 | 0.148681 | 0.0743403 | − | 0.997233i | \(-0.476315\pi\) | ||||
0.0743403 | + | 0.997233i | \(0.476315\pi\) | |||||||
\(542\) | 60.7704i | 2.61031i | ||||||||
\(543\) | − 14.2185i | − 0.610173i | ||||||||
\(544\) | −8.92209 | −0.382531 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 11.0809 | 0.474220 | ||||||||
\(547\) | − 13.9635i | − 0.597034i | −0.954404 | − | 0.298517i | \(-0.903508\pi\) | ||||
0.954404 | − | 0.298517i | \(-0.0964920\pi\) | |||||||
\(548\) | 11.4264i | 0.488111i | ||||||||
\(549\) | −1.39588 | −0.0595747 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −42.2657 | −1.80058 | ||||||||
\(552\) | 2.48337i | 0.105699i | ||||||||
\(553\) | 63.4281i | 2.69724i | ||||||||
\(554\) | −11.2528 | −0.478086 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −11.8554 | −0.502779 | ||||||||
\(557\) | 6.59585i | 0.279475i | 0.990189 | + | 0.139738i | \(0.0446259\pi\) | ||||
−0.990189 | + | 0.139738i | \(0.955374\pi\) | |||||||
\(558\) | 10.1916i | 0.431444i | ||||||||
\(559\) | 1.49740 | 0.0633334 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1.77318 | 0.0748638 | ||||||||
\(562\) | 51.1126i | 2.15605i | ||||||||
\(563\) | − 16.0218i | − 0.675238i | −0.941283 | − | 0.337619i | \(-0.890379\pi\) | ||||
0.941283 | − | 0.337619i | \(-0.109621\pi\) | |||||||
\(564\) | −10.3369 | −0.435261 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −57.5456 | −2.41882 | ||||||||
\(567\) | − 4.35840i | − 0.183036i | ||||||||
\(568\) | − 11.3505i | − 0.476258i | ||||||||
\(569\) | −23.0914 | −0.968042 | −0.484021 | − | 0.875056i | \(-0.660824\pi\) | ||||
−0.484021 | + | 0.875056i | \(0.660824\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −34.0102 | −1.42328 | −0.711640 | − | 0.702544i | \(-0.752047\pi\) | ||||
−0.711640 | + | 0.702544i | \(0.752047\pi\) | |||||||
\(572\) | 4.73972i | 0.198178i | ||||||||
\(573\) | − 10.3697i | − 0.433200i | ||||||||
\(574\) | 69.1171 | 2.88489 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −11.3975 | −0.474896 | ||||||||
\(577\) | 6.46727i | 0.269236i | 0.990898 | + | 0.134618i | \(0.0429807\pi\) | ||||
−0.990898 | + | 0.134618i | \(0.957019\pi\) | |||||||
\(578\) | − 33.4063i | − 1.38952i | ||||||||
\(579\) | −4.34712 | −0.180660 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −38.0751 | −1.57962 | ||||||||
\(582\) | 15.9174i | 0.659798i | ||||||||
\(583\) | − 5.91782i | − 0.245091i | ||||||||
\(584\) | −5.34794 | −0.221299 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −43.0868 | −1.77990 | ||||||||
\(587\) | − 38.5012i | − 1.58911i | −0.607189 | − | 0.794557i | \(-0.707703\pi\) | ||||
0.607189 | − | 0.794557i | \(-0.292297\pi\) | |||||||
\(588\) | 30.0407i | 1.23886i | ||||||||
\(589\) | −36.8735 | −1.51934 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 1.87990 | 0.0773287 | ||||||||
\(592\) | − 17.4416i | − 0.716843i | ||||||||
\(593\) | 4.93069i | 0.202479i | 0.994862 | + | 0.101240i | \(0.0322808\pi\) | ||||
−0.994862 | + | 0.101240i | \(0.967719\pi\) | |||||||
\(594\) | 3.35309 | 0.137579 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 11.7112 | 0.479710 | ||||||||
\(597\) | − 4.26028i | − 0.174362i | ||||||||
\(598\) | − 5.89913i | − 0.241233i | ||||||||
\(599\) | 35.0268 | 1.43116 | 0.715578 | − | 0.698533i | \(-0.246164\pi\) | ||||
0.715578 | + | 0.698533i | \(0.246164\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −4.90570 | −0.200108 | −0.100054 | − | 0.994982i | \(-0.531901\pi\) | ||||
−0.100054 | + | 0.994982i | \(0.531901\pi\) | |||||||
\(602\) | 11.5623i | 0.471244i | ||||||||
\(603\) | − 3.86270i | − 0.157301i | ||||||||
\(604\) | 16.3826 | 0.666597 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −13.8338 | −0.561961 | ||||||||
\(607\) | − 48.6955i | − 1.97649i | −0.152884 | − | 0.988244i | \(-0.548856\pi\) | ||||
0.152884 | − | 0.988244i | \(-0.451144\pi\) | |||||||
\(608\) | − 61.0423i | − 2.47559i | ||||||||
\(609\) | 23.9899 | 0.972122 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 4.94467 | 0.200040 | ||||||||
\(612\) | 2.81066i | 0.113614i | ||||||||
\(613\) | 17.2139i | 0.695262i | 0.937631 | + | 0.347631i | \(0.113014\pi\) | ||||
−0.937631 | + | 0.347631i | \(0.886986\pi\) | |||||||
\(614\) | 5.33406 | 0.215265 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −7.36988 | −0.296941 | ||||||||
\(617\) | 31.6092i | 1.27254i | 0.771468 | + | 0.636268i | \(0.219523\pi\) | ||||
−0.771468 | + | 0.636268i | \(0.780477\pi\) | |||||||
\(618\) | 17.0821i | 0.687145i | ||||||||
\(619\) | 22.8196 | 0.917198 | 0.458599 | − | 0.888643i | \(-0.348351\pi\) | ||||
0.458599 | + | 0.888643i | \(0.348351\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −2.32027 | −0.0931094 | ||||||||
\(622\) | − 10.2385i | − 0.410526i | ||||||||
\(623\) | − 43.7502i | − 1.75281i | ||||||||
\(624\) | 3.27886 | 0.131259 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −12.7088 | −0.507945 | ||||||||
\(627\) | 12.1316i | 0.484489i | ||||||||
\(628\) | 10.0023i | 0.399134i | ||||||||
\(629\) | −7.15186 | −0.285163 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 38.0499 | 1.51474 | 0.757372 | − | 0.652984i | \(-0.226483\pi\) | ||||
0.757372 | + | 0.652984i | \(0.226483\pi\) | |||||||
\(632\) | − 15.5760i | − 0.619581i | ||||||||
\(633\) | − 9.29671i | − 0.369511i | ||||||||
\(634\) | −36.8290 | −1.46267 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 9.38031 | 0.371953 | ||||||||
\(637\) | − 14.3701i | − 0.569363i | ||||||||
\(638\) | 18.4564i | 0.730696i | ||||||||
\(639\) | 10.6051 | 0.419531 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 26.5108 | 1.04711 | 0.523557 | − | 0.851991i | \(-0.324605\pi\) | ||||
0.523557 | + | 0.851991i | \(0.324605\pi\) | |||||||
\(642\) | − 20.1143i | − 0.793849i | ||||||||
\(643\) | − 36.0014i | − 1.41976i | −0.704324 | − | 0.709879i | \(-0.748750\pi\) | ||||
0.704324 | − | 0.709879i | \(-0.251250\pi\) | |||||||
\(644\) | 25.3252 | 0.997952 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −18.2903 | −0.719624 | ||||||||
\(647\) | − 41.7840i | − 1.64270i | −0.570426 | − | 0.821349i | \(-0.693222\pi\) | ||||
0.570426 | − | 0.821349i | \(-0.306778\pi\) | |||||||
\(648\) | 1.07029i | 0.0420450i | ||||||||
\(649\) | 14.4658 | 0.567833 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 20.9293 | 0.820284 | ||||||||
\(652\) | − 12.0242i | − 0.470903i | ||||||||
\(653\) | 21.4404i | 0.839027i | 0.907749 | + | 0.419513i | \(0.137799\pi\) | ||||
−0.907749 | + | 0.419513i | \(0.862201\pi\) | |||||||
\(654\) | 24.7586 | 0.968137 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 20.4519 | 0.798511 | ||||||||
\(657\) | − 4.99672i | − 0.194940i | ||||||||
\(658\) | 38.1807i | 1.48844i | ||||||||
\(659\) | 16.8319 | 0.655678 | 0.327839 | − | 0.944734i | \(-0.393680\pi\) | ||||
0.327839 | + | 0.944734i | \(0.393680\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 2.03846 | 0.0792868 | 0.0396434 | − | 0.999214i | \(-0.487378\pi\) | ||||
0.0396434 | + | 0.999214i | \(0.487378\pi\) | |||||||
\(662\) | − 43.1587i | − 1.67741i | ||||||||
\(663\) | − 1.34449i | − 0.0522156i | ||||||||
\(664\) | 9.35010 | 0.362854 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −13.5242 | −0.524051 | ||||||||
\(667\) | − 12.7715i | − 0.494514i | ||||||||
\(668\) | 59.2518i | 2.29252i | ||||||||
\(669\) | 3.39758 | 0.131358 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −2.20536 | −0.0851369 | ||||||||
\(672\) | 34.6475i | 1.33656i | ||||||||
\(673\) | 35.3776i | 1.36371i | 0.731489 | + | 0.681854i | \(0.238826\pi\) | ||||
−0.731489 | + | 0.681854i | \(0.761174\pi\) | |||||||
\(674\) | −72.7050 | −2.80049 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −28.9621 | −1.11393 | ||||||||
\(677\) | − 44.4173i | − 1.70710i | −0.521014 | − | 0.853548i | \(-0.674446\pi\) | ||||
0.521014 | − | 0.853548i | \(-0.325554\pi\) | |||||||
\(678\) | − 31.6766i | − 1.21653i | ||||||||
\(679\) | 32.6879 | 1.25444 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 26.7973 | 1.02688 | ||||||||
\(682\) | 16.1017i | 0.616567i | ||||||||
\(683\) | 42.4952i | 1.62603i | 0.582241 | + | 0.813016i | \(0.302176\pi\) | ||||
−0.582241 | + | 0.813016i | \(0.697824\pi\) | |||||||
\(684\) | −19.2297 | −0.735266 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 46.2098 | 1.76430 | ||||||||
\(687\) | 1.18200i | 0.0450960i | ||||||||
\(688\) | 3.42130i | 0.130436i | ||||||||
\(689\) | −4.48710 | −0.170945 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 28.0808 | 1.06825 | 0.534123 | − | 0.845407i | \(-0.320642\pi\) | ||||
0.534123 | + | 0.845407i | \(0.320642\pi\) | |||||||
\(692\) | − 36.3231i | − 1.38080i | ||||||||
\(693\) | − 6.88586i | − 0.261572i | ||||||||
\(694\) | 0.104762 | 0.00397671 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −5.89121 | −0.223306 | ||||||||
\(697\) | − 8.38623i | − 0.317651i | ||||||||
\(698\) | − 15.8631i | − 0.600427i | ||||||||
\(699\) | −7.09483 | −0.268351 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 46.4314 | 1.75369 | 0.876845 | − | 0.480772i | \(-0.159644\pi\) | ||||
0.876845 | + | 0.480772i | \(0.159644\pi\) | |||||||
\(702\) | − 2.54243i | − 0.0959578i | ||||||||
\(703\) | − 48.9309i | − 1.84547i | ||||||||
\(704\) | −18.0070 | −0.678664 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −39.4011 | −1.48288 | ||||||||
\(707\) | 28.4090i | 1.06843i | ||||||||
\(708\) | 22.9297i | 0.861750i | ||||||||
\(709\) | −48.6331 | −1.82646 | −0.913228 | − | 0.407450i | \(-0.866418\pi\) | ||||
−0.913228 | + | 0.407450i | \(0.866418\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 14.5531 | 0.545782 | ||||||||
\(712\) | 10.7437i | 0.402638i | ||||||||
\(713\) | − 11.1421i | − 0.417275i | ||||||||
\(714\) | 10.3816 | 0.388520 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 1.99529 | 0.0745675 | ||||||||
\(717\) | − 0.0427926i | − 0.00159812i | ||||||||
\(718\) | 22.5062i | 0.839923i | ||||||||
\(719\) | 21.1954 | 0.790456 | 0.395228 | − | 0.918583i | \(-0.370666\pi\) | ||||
0.395228 | + | 0.918583i | \(0.370666\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 35.0797 | 1.30644 | ||||||||
\(722\) | − 84.8128i | − 3.15641i | ||||||||
\(723\) | − 11.7711i | − 0.437771i | ||||||||
\(724\) | 35.6073 | 1.32333 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −18.0481 | −0.669828 | ||||||||
\(727\) | − 13.5911i | − 0.504066i | −0.967719 | − | 0.252033i | \(-0.918901\pi\) | ||||
0.967719 | − | 0.252033i | \(-0.0810992\pi\) | |||||||
\(728\) | 5.58810i | 0.207109i | ||||||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1.40290 | 0.0518880 | ||||||||
\(732\) | − 3.49570i | − 0.129205i | ||||||||
\(733\) | 18.6531i | 0.688967i | 0.938792 | + | 0.344484i | \(0.111946\pi\) | ||||
−0.938792 | + | 0.344484i | \(0.888054\pi\) | |||||||
\(734\) | 24.6565 | 0.910088 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 18.4452 | 0.679900 | ||||||||
\(737\) | − 6.10270i | − 0.224796i | ||||||||
\(738\) | − 15.8584i | − 0.583754i | ||||||||
\(739\) | −26.4452 | −0.972803 | −0.486401 | − | 0.873735i | \(-0.661691\pi\) | ||||
−0.486401 | + | 0.873735i | \(0.661691\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 9.19859 | 0.337919 | ||||||||
\(742\) | − 34.6475i | − 1.27195i | ||||||||
\(743\) | − 29.0191i | − 1.06461i | −0.846553 | − | 0.532304i | \(-0.821326\pi\) | ||||
0.846553 | − | 0.532304i | \(-0.178674\pi\) | |||||||
\(744\) | −5.13961 | −0.188427 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −49.0837 | −1.79708 | ||||||||
\(747\) | 8.73603i | 0.319635i | ||||||||
\(748\) | 4.44058i | 0.162364i | ||||||||
\(749\) | −41.3065 | −1.50931 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 15.9489 | 0.581985 | 0.290992 | − | 0.956725i | \(-0.406015\pi\) | ||||
0.290992 | + | 0.956725i | \(0.406015\pi\) | |||||||
\(752\) | 11.2977i | 0.411985i | ||||||||
\(753\) | 17.4764i | 0.636875i | ||||||||
\(754\) | 13.9943 | 0.509642 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 10.9147 | 0.396965 | ||||||||
\(757\) | 16.4183i | 0.596734i | 0.954451 | + | 0.298367i | \(0.0964419\pi\) | ||||
−0.954451 | + | 0.298367i | \(0.903558\pi\) | |||||||
\(758\) | 52.8274i | 1.91878i | ||||||||
\(759\) | −3.66581 | −0.133061 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −49.2715 | −1.78609 | −0.893045 | − | 0.449967i | \(-0.851436\pi\) | ||||
−0.893045 | + | 0.449967i | \(0.851436\pi\) | |||||||
\(762\) | 36.0705i | 1.30670i | ||||||||
\(763\) | − 50.8440i | − 1.84068i | ||||||||
\(764\) | 25.9688 | 0.939518 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −33.3676 | −1.20562 | ||||||||
\(767\) | − 10.9685i | − 0.396049i | ||||||||
\(768\) | 5.20057i | 0.187660i | ||||||||
\(769\) | −49.4236 | −1.78226 | −0.891129 | − | 0.453749i | \(-0.850086\pi\) | ||||
−0.891129 | + | 0.453749i | \(0.850086\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 15.4671 | 0.557036 | ||||||||
\(772\) | − 10.8865i | − 0.391814i | ||||||||
\(773\) | 25.9084i | 0.931860i | 0.884822 | + | 0.465930i | \(0.154280\pi\) | ||||
−0.884822 | + | 0.465930i | \(0.845720\pi\) | |||||||
\(774\) | 2.65288 | 0.0953557 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −8.02715 | −0.288158 | ||||||||
\(777\) | 27.7731i | 0.996355i | ||||||||
\(778\) | − 18.0533i | − 0.647241i | ||||||||
\(779\) | 57.3761 | 2.05571 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 16.7551 | 0.599543 | ||||||||
\(782\) | − 5.52681i | − 0.197638i | ||||||||
\(783\) | − 5.50430i | − 0.196708i | ||||||||
\(784\) | 32.8331 | 1.17261 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −0.697977 | −0.0248960 | ||||||||
\(787\) | − 30.7155i | − 1.09489i | −0.836842 | − | 0.547444i | \(-0.815601\pi\) | ||||
0.836842 | − | 0.547444i | \(-0.184399\pi\) | |||||||
\(788\) | 4.70783i | 0.167710i | ||||||||
\(789\) | −1.44759 | −0.0515357 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −65.0508 | −2.31294 | ||||||||
\(792\) | 1.69096i | 0.0600857i | ||||||||
\(793\) | 1.67218i | 0.0593808i | ||||||||
\(794\) | −55.7216 | −1.97749 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 10.6690 | 0.378154 | ||||||||
\(797\) | 33.7141i | 1.19421i | 0.802161 | + | 0.597107i | \(0.203683\pi\) | ||||
−0.802161 | + | 0.597107i | \(0.796317\pi\) | |||||||
\(798\) | 71.0276i | 2.51435i | ||||||||
\(799\) | 4.63260 | 0.163890 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −10.0381 | −0.354680 | ||||||||
\(802\) | 53.6559i | 1.89465i | ||||||||
\(803\) | − 7.89434i | − 0.278585i | ||||||||
\(804\) | 9.67336 | 0.341153 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 12.2089 | 0.430040 | ||||||||
\(807\) | 8.70617i | 0.306472i | ||||||||
\(808\) | − 6.97639i | − 0.245429i | ||||||||
\(809\) | 0.923014 | 0.0324514 | 0.0162257 | − | 0.999868i | \(-0.494835\pi\) | ||||
0.0162257 | + | 0.999868i | \(0.494835\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 26.7815 | 0.940424 | 0.470212 | − | 0.882553i | \(-0.344177\pi\) | ||||
0.470212 | + | 0.882553i | \(0.344177\pi\) | |||||||
\(812\) | 60.0780i | 2.10832i | ||||||||
\(813\) | − 28.6338i | − 1.00423i | ||||||||
\(814\) | −21.3669 | −0.748910 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 3.07192 | 0.107539 | ||||||||
\(817\) | 9.59820i | 0.335799i | ||||||||
\(818\) | 71.7204i | 2.50765i | ||||||||
\(819\) | −5.22110 | −0.182440 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −36.8489 | −1.28604 | −0.643018 | − | 0.765851i | \(-0.722318\pi\) | ||||
−0.643018 | + | 0.765851i | \(0.722318\pi\) | |||||||
\(822\) | − 9.68359i | − 0.337754i | ||||||||
\(823\) | 20.4262i | 0.712012i | 0.934484 | + | 0.356006i | \(0.115862\pi\) | ||||
−0.934484 | + | 0.356006i | \(0.884138\pi\) | |||||||
\(824\) | −8.61452 | −0.300101 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 84.6940 | 2.94688 | ||||||||
\(827\) | − 4.33017i | − 0.150575i | −0.997162 | − | 0.0752874i | \(-0.976013\pi\) | ||||
0.997162 | − | 0.0752874i | \(-0.0239874\pi\) | |||||||
\(828\) | − 5.81066i | − 0.201934i | ||||||||
\(829\) | 0.614348 | 0.0213372 | 0.0106686 | − | 0.999943i | \(-0.496604\pi\) | ||||
0.0106686 | + | 0.999943i | \(0.496604\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 5.30210 | 0.183928 | ||||||||
\(832\) | 13.6535i | 0.473351i | ||||||||
\(833\) | − 13.4631i | − 0.466470i | ||||||||
\(834\) | 10.0471 | 0.347904 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −30.3811 | −1.05075 | ||||||||
\(837\) | − 4.80206i | − 0.165983i | ||||||||
\(838\) | 16.8372i | 0.581630i | ||||||||
\(839\) | −5.39981 | −0.186422 | −0.0932111 | − | 0.995646i | \(-0.529713\pi\) | ||||
−0.0932111 | + | 0.995646i | \(0.529713\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.29731 | 0.0447349 | ||||||||
\(842\) | − 15.8919i | − 0.547672i | ||||||||
\(843\) | − 24.0832i | − 0.829469i | ||||||||
\(844\) | 23.2817 | 0.801391 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 8.76025 | 0.301183 | ||||||||
\(847\) | 37.0634i | 1.27351i | ||||||||
\(848\) | − 10.2522i | − 0.352063i | ||||||||
\(849\) | 27.1143 | 0.930561 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 14.7855 | 0.506841 | ||||||||
\(852\) | 26.5583i | 0.909874i | ||||||||
\(853\) | − 39.7935i | − 1.36250i | −0.732049 | − | 0.681252i | \(-0.761436\pi\) | ||||
0.732049 | − | 0.681252i | \(-0.238564\pi\) | |||||||
\(854\) | −12.9119 | −0.441835 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 10.1436 | 0.346702 | ||||||||
\(857\) | 42.8643i | 1.46422i | 0.681188 | + | 0.732109i | \(0.261464\pi\) | ||||
−0.681188 | + | 0.732109i | \(0.738536\pi\) | |||||||
\(858\) | − 4.01680i | − 0.137131i | ||||||||
\(859\) | 4.56494 | 0.155754 | 0.0778769 | − | 0.996963i | \(-0.475186\pi\) | ||||
0.0778769 | + | 0.996963i | \(0.475186\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −32.5666 | −1.10987 | ||||||||
\(862\) | − 49.5502i | − 1.68769i | ||||||||
\(863\) | − 37.6273i | − 1.28085i | −0.768022 | − | 0.640424i | \(-0.778759\pi\) | ||||
0.768022 | − | 0.640424i | \(-0.221241\pi\) | |||||||
\(864\) | 7.94959 | 0.270450 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −7.12419 | −0.242090 | ||||||||
\(867\) | 15.7404i | 0.534571i | ||||||||
\(868\) | 52.4133i | 1.77902i | ||||||||
\(869\) | 22.9925 | 0.779966 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −4.62728 | −0.156790 | ||||||||
\(872\) | 12.4857i | 0.422821i | ||||||||
\(873\) | − 7.49996i | − 0.253835i | ||||||||
\(874\) | 37.8128 | 1.27904 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 12.5133 | 0.422784 | ||||||||
\(877\) | − 52.4041i | − 1.76956i | −0.466008 | − | 0.884781i | \(-0.654308\pi\) | ||||
0.466008 | − | 0.884781i | \(-0.345692\pi\) | |||||||
\(878\) | − 20.1283i | − 0.679296i | ||||||||
\(879\) | 20.3016 | 0.684757 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −7.93778 | −0.267430 | −0.133715 | − | 0.991020i | \(-0.542691\pi\) | ||||
−0.133715 | + | 0.991020i | \(0.542691\pi\) | |||||||
\(882\) | − 25.4588i | − 0.857242i | ||||||||
\(883\) | 31.6919i | 1.06652i | 0.845952 | + | 0.533259i | \(0.179033\pi\) | ||||
−0.845952 | + | 0.533259i | \(0.820967\pi\) | |||||||
\(884\) | 3.36700 | 0.113244 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 20.4900 | 0.688374 | ||||||||
\(887\) | − 2.82104i | − 0.0947213i | −0.998878 | − | 0.0473606i | \(-0.984919\pi\) | ||||
0.998878 | − | 0.0473606i | \(-0.0150810\pi\) | |||||||
\(888\) | − 6.82024i | − 0.228872i | ||||||||
\(889\) | 74.0739 | 2.48436 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1.57991 | −0.0529288 | ||||||||
\(892\) | 8.50856i | 0.284888i | ||||||||
\(893\) | 31.6949i | 1.06063i | ||||||||
\(894\) | −9.92497 | −0.331941 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −36.1318 | −1.20708 | ||||||||
\(897\) | 2.77955i | 0.0928064i | ||||||||
\(898\) | 66.9087i | 2.23277i | ||||||||
\(899\) | 26.4320 | 0.881556 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −4.20390 | −0.140052 | ||||||||
\(902\) | − 25.0547i | − 0.834231i | ||||||||
\(903\) | − 5.44792i | − 0.181295i | ||||||||
\(904\) | 15.9745 | 0.531304 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −13.8838 | −0.461259 | ||||||||
\(907\) | 44.1799i | 1.46697i | 0.679705 | + | 0.733485i | \(0.262108\pi\) | ||||
−0.679705 | + | 0.733485i | \(0.737892\pi\) | |||||||
\(908\) | 67.1085i | 2.22707i | ||||||||
\(909\) | 6.51821 | 0.216195 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −34.5260 | −1.14390 | −0.571949 | − | 0.820289i | \(-0.693812\pi\) | ||||
−0.571949 | + | 0.820289i | \(0.693812\pi\) | |||||||
\(912\) | 21.0172i | 0.695948i | ||||||||
\(913\) | 13.8021i | 0.456783i | ||||||||
\(914\) | 21.1059 | 0.698122 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −2.96007 | −0.0978036 | ||||||||
\(917\) | 1.43336i | 0.0473336i | ||||||||
\(918\) | − 2.38197i | − 0.0786166i | ||||||||
\(919\) | 0.531075 | 0.0175185 | 0.00875927 | − | 0.999962i | \(-0.497212\pi\) | ||||
0.00875927 | + | 0.999962i | \(0.497212\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −2.51330 | −0.0828161 | ||||||||
\(922\) | 50.2645i | 1.65537i | ||||||||
\(923\) | − 12.7043i | − 0.418166i | ||||||||
\(924\) | 17.2443 | 0.567295 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 58.6833 | 1.92845 | ||||||||
\(927\) | − 8.04876i | − 0.264356i | ||||||||
\(928\) | 43.7569i | 1.43639i | ||||||||
\(929\) | −46.1961 | −1.51565 | −0.757823 | − | 0.652460i | \(-0.773737\pi\) | ||||
−0.757823 | + | 0.652460i | \(0.773737\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 92.1108 | 3.01881 | ||||||||
\(932\) | − 17.7676i | − 0.581997i | ||||||||
\(933\) | 4.82417i | 0.157936i | ||||||||
\(934\) | −9.24998 | −0.302669 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 1.28215 | 0.0419082 | ||||||||
\(937\) | 30.1220i | 0.984042i | 0.870583 | + | 0.492021i | \(0.163742\pi\) | ||||
−0.870583 | + | 0.492021i | \(0.836258\pi\) | |||||||
\(938\) | − 35.7299i | − 1.16662i | ||||||||
\(939\) | 5.98812 | 0.195415 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 57.0783 | 1.86070 | 0.930350 | − | 0.366672i | \(-0.119503\pi\) | ||||
0.930350 | + | 0.366672i | \(0.119503\pi\) | |||||||
\(942\) | − 8.47668i | − 0.276185i | ||||||||
\(943\) | 17.3374i | 0.564583i | ||||||||
\(944\) | 25.0611 | 0.815668 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 4.19130 | 0.136271 | ||||||||
\(947\) | 41.1250i | 1.33638i | 0.743989 | + | 0.668192i | \(0.232931\pi\) | ||||
−0.743989 | + | 0.668192i | \(0.767069\pi\) | |||||||
\(948\) | 36.4452i | 1.18369i | ||||||||
\(949\) | −5.98576 | −0.194306 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 17.3531 | 0.562712 | ||||||||
\(952\) | 5.23542i | 0.169681i | ||||||||
\(953\) | 34.8143i | 1.12775i | 0.825861 | + | 0.563873i | \(0.190689\pi\) | ||||
−0.825861 | + | 0.563873i | \(0.809311\pi\) | |||||||
\(954\) | −7.94959 | −0.257377 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0.107165 | 0.00346598 | ||||||||
\(957\) | − 8.69627i | − 0.281111i | ||||||||
\(958\) | 27.1962i | 0.878668i | ||||||||
\(959\) | −19.8861 | −0.642156 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −7.94022 | −0.256136 | ||||||||
\(962\) | 16.2012i | 0.522346i | ||||||||
\(963\) | 9.47745i | 0.305407i | ||||||||
\(964\) | 29.4783 | 0.949432 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −21.4625 | −0.690544 | ||||||||
\(967\) | 37.2697i | 1.19851i | 0.800557 | + | 0.599257i | \(0.204537\pi\) | ||||
−0.800557 | + | 0.599257i | \(0.795463\pi\) | |||||||
\(968\) | − 9.10165i | − 0.292538i | ||||||||
\(969\) | 8.61803 | 0.276851 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −26.0092 | −0.834677 | −0.417338 | − | 0.908751i | \(-0.637037\pi\) | ||||
−0.417338 | + | 0.908751i | \(0.637037\pi\) | |||||||
\(972\) | − 2.50430i | − 0.0803254i | ||||||||
\(973\) | − 20.6327i | − 0.661453i | ||||||||
\(974\) | 14.6910 | 0.470729 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −3.82064 | −0.122296 | ||||||||
\(977\) | − 0.458579i | − 0.0146712i | −0.999973 | − | 0.00733561i | \(-0.997665\pi\) | ||||
0.999973 | − | 0.00733561i | \(-0.00233502\pi\) | |||||||
\(978\) | 10.1902i | 0.325846i | ||||||||
\(979\) | −15.8593 | −0.506865 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −11.6657 | −0.372458 | ||||||||
\(982\) | − 56.9128i | − 1.81616i | ||||||||
\(983\) | 8.94565i | 0.285322i | 0.989772 | + | 0.142661i | \(0.0455659\pi\) | ||||
−0.989772 | + | 0.142661i | \(0.954434\pi\) | |||||||
\(984\) | 7.99737 | 0.254947 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 13.1111 | 0.417541 | ||||||||
\(987\) | − 17.9899i | − 0.572626i | ||||||||
\(988\) | 23.0360i | 0.732874i | ||||||||
\(989\) | −2.90030 | −0.0922241 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −56.5337 | −1.79585 | −0.897926 | − | 0.440147i | \(-0.854926\pi\) | ||||
−0.897926 | + | 0.440147i | \(0.854926\pi\) | |||||||
\(992\) | 38.1744i | 1.21204i | ||||||||
\(993\) | 20.3355i | 0.645327i | ||||||||
\(994\) | 98.0970 | 3.11145 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −21.8776 | −0.693219 | ||||||||
\(997\) | − 39.6114i | − 1.25451i | −0.778816 | − | 0.627253i | \(-0.784179\pi\) | ||||
0.778816 | − | 0.627253i | \(-0.215821\pi\) | |||||||
\(998\) | 5.84619i | 0.185058i | ||||||||
\(999\) | 6.37232 | 0.201611 |
(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 | 1875.2.b.c.1249.2 | 8 | ||
5.2 | odd | 4 | 1875.2.a.h.1.3 | 4 | |||
5.3 | odd | 4 | 1875.2.a.e.1.2 | 4 | |||
5.4 | even | 2 | inner | 1875.2.b.c.1249.7 | 8 | ||
15.2 | even | 4 | 5625.2.a.i.1.2 | 4 | |||
15.8 | even | 4 | 5625.2.a.n.1.3 | 4 | |||
25.2 | odd | 20 | 75.2.g.b.46.2 | yes | 8 | ||
25.9 | even | 10 | 375.2.i.b.349.1 | 16 | |||
25.11 | even | 5 | 375.2.i.b.274.1 | 16 | |||
25.12 | odd | 20 | 75.2.g.b.31.2 | ✓ | 8 | ||
25.13 | odd | 20 | 375.2.g.b.151.1 | 8 | |||
25.14 | even | 10 | 375.2.i.b.274.4 | 16 | |||
25.16 | even | 5 | 375.2.i.b.349.4 | 16 | |||
25.23 | odd | 20 | 375.2.g.b.226.1 | 8 | |||
75.2 | even | 20 | 225.2.h.c.46.1 | 8 | |||
75.62 | even | 20 | 225.2.h.c.181.1 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
75.2.g.b.31.2 | ✓ | 8 | 25.12 | odd | 20 | ||
75.2.g.b.46.2 | yes | 8 | 25.2 | odd | 20 | ||
225.2.h.c.46.1 | 8 | 75.2 | even | 20 | |||
225.2.h.c.181.1 | 8 | 75.62 | even | 20 | |||
375.2.g.b.151.1 | 8 | 25.13 | odd | 20 | |||
375.2.g.b.226.1 | 8 | 25.23 | odd | 20 | |||
375.2.i.b.274.1 | 16 | 25.11 | even | 5 | |||
375.2.i.b.274.4 | 16 | 25.14 | even | 10 | |||
375.2.i.b.349.1 | 16 | 25.9 | even | 10 | |||
375.2.i.b.349.4 | 16 | 25.16 | even | 5 | |||
1875.2.a.e.1.2 | 4 | 5.3 | odd | 4 | |||
1875.2.a.h.1.3 | 4 | 5.2 | odd | 4 | |||
1875.2.b.c.1249.2 | 8 | 1.1 | even | 1 | trivial | ||
1875.2.b.c.1249.7 | 8 | 5.4 | even | 2 | inner | ||
5625.2.a.i.1.2 | 4 | 15.2 | even | 4 | |||
5625.2.a.n.1.3 | 4 | 15.8 | even | 4 |