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 | 1249.5 | ||
Root | \(1.12233i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1875.1249 |
Dual form | 1875.2.b.c.1249.4 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.12233i | 0.793610i | 0.917903 | + | 0.396805i | \(0.129881\pi\) | ||||
−0.917903 | + | 0.396805i | \(0.870119\pi\) | |||||||
\(3\) | 1.00000i | 0.577350i | ||||||||
\(4\) | 0.740367 | 0.370184 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −1.12233 | −0.458191 | ||||||||
\(7\) | − 1.11373i | − 0.420952i | −0.977599 | − | 0.210476i | \(-0.932499\pi\) | ||||
0.977599 | − | 0.210476i | \(-0.0675014\pi\) | |||||||
\(8\) | 3.07561i | 1.08739i | ||||||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.67008 | 1.10657 | 0.553285 | − | 0.832992i | \(-0.313374\pi\) | ||||
0.553285 | + | 0.832992i | \(0.313374\pi\) | |||||||
\(12\) | 0.740367i | 0.213726i | ||||||||
\(13\) | − 4.05204i | − 1.12383i | −0.827194 | − | 0.561917i | \(-0.810064\pi\) | ||||
0.827194 | − | 0.561917i | \(-0.189936\pi\) | |||||||
\(14\) | 1.24998 | 0.334072 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −1.97112 | −0.492780 | ||||||||
\(17\) | − 2.12233i | − 0.514741i | −0.966313 | − | 0.257371i | \(-0.917144\pi\) | ||||
0.966313 | − | 0.257371i | \(-0.0828562\pi\) | |||||||
\(18\) | − 1.12233i | − 0.264537i | ||||||||
\(19\) | 4.06064 | 0.931575 | 0.465787 | − | 0.884897i | \(-0.345771\pi\) | ||||
0.465787 | + | 0.884897i | \(0.345771\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.11373 | 0.243037 | ||||||||
\(22\) | 4.11905i | 0.878184i | ||||||||
\(23\) | 6.17438i | 1.28745i | 0.765258 | + | 0.643723i | \(0.222611\pi\) | ||||
−0.765258 | + | 0.643723i | \(0.777389\pi\) | |||||||
\(24\) | −3.07561 | −0.627806 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 4.54774 | 0.891886 | ||||||||
\(27\) | − 1.00000i | − 0.192450i | ||||||||
\(28\) | − 0.824573i | − 0.155830i | ||||||||
\(29\) | 2.25963 | 0.419603 | 0.209802 | − | 0.977744i | \(-0.432718\pi\) | ||||
0.209802 | + | 0.977744i | \(0.432718\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 10.0520 | 1.80540 | 0.902700 | − | 0.430271i | \(-0.141582\pi\) | ||||
0.902700 | + | 0.430271i | \(0.141582\pi\) | |||||||
\(32\) | 3.93896i | 0.696316i | ||||||||
\(33\) | 3.67008i | 0.638878i | ||||||||
\(34\) | 2.38197 | 0.408504 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −0.740367 | −0.123395 | ||||||||
\(37\) | − 7.37232i | − 1.21200i | −0.795464 | − | 0.606001i | \(-0.792773\pi\) | ||||
0.795464 | − | 0.606001i | \(-0.207227\pi\) | |||||||
\(38\) | 4.55739i | 0.739307i | ||||||||
\(39\) | 4.05204 | 0.648846 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −7.47214 | −1.16695 | −0.583476 | − | 0.812131i | \(-0.698308\pi\) | ||||
−0.583476 | + | 0.812131i | \(0.698308\pi\) | |||||||
\(42\) | 1.24998i | 0.192876i | ||||||||
\(43\) | 9.24998i | 1.41061i | 0.708905 | + | 0.705304i | \(0.249190\pi\) | ||||
−0.708905 | + | 0.705304i | \(0.750810\pi\) | |||||||
\(44\) | 2.71720 | 0.409634 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −6.92971 | −1.02173 | ||||||||
\(47\) | 3.12765i | 0.456214i | 0.973636 | + | 0.228107i | \(0.0732537\pi\) | ||||
−0.973636 | + | 0.228107i | \(0.926746\pi\) | |||||||
\(48\) | − 1.97112i | − 0.284507i | ||||||||
\(49\) | 5.75960 | 0.822799 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 2.12233 | 0.297186 | ||||||||
\(52\) | − 3.00000i | − 0.416025i | ||||||||
\(53\) | − 3.50961i | − 0.482083i | −0.970515 | − | 0.241041i | \(-0.922511\pi\) | ||||
0.970515 | − | 0.241041i | \(-0.0774889\pi\) | |||||||
\(54\) | 1.12233 | 0.152730 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 3.42541 | 0.457739 | ||||||||
\(57\) | 4.06064i | 0.537845i | ||||||||
\(58\) | 2.53606i | 0.333001i | ||||||||
\(59\) | 6.59382 | 0.858442 | 0.429221 | − | 0.903199i | \(-0.358788\pi\) | ||||
0.429221 | + | 0.903199i | \(0.358788\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −9.10408 | −1.16566 | −0.582829 | − | 0.812595i | \(-0.698054\pi\) | ||||
−0.582829 | + | 0.812595i | \(0.698054\pi\) | |||||||
\(62\) | 11.2817i | 1.43278i | ||||||||
\(63\) | 1.11373i | 0.140317i | ||||||||
\(64\) | −8.36307 | −1.04538 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −4.11905 | −0.507020 | ||||||||
\(67\) | − 2.62663i | − 0.320894i | −0.987044 | − | 0.160447i | \(-0.948706\pi\) | ||||
0.987044 | − | 0.160447i | \(-0.0512936\pi\) | |||||||
\(68\) | − 1.57131i | − 0.190549i | ||||||||
\(69\) | −6.17438 | −0.743307 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0.660827 | 0.0784257 | 0.0392128 | − | 0.999231i | \(-0.487515\pi\) | ||||
0.0392128 | + | 0.999231i | \(0.487515\pi\) | |||||||
\(72\) | − 3.07561i | − 0.362464i | ||||||||
\(73\) | 7.47542i | 0.874932i | 0.899235 | + | 0.437466i | \(0.144124\pi\) | ||||
−0.899235 | + | 0.437466i | \(0.855876\pi\) | |||||||
\(74\) | 8.27420 | 0.961856 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 3.00637 | 0.344854 | ||||||||
\(77\) | − 4.08749i | − 0.465813i | ||||||||
\(78\) | 4.54774i | 0.514930i | ||||||||
\(79\) | −8.53711 | −0.960500 | −0.480250 | − | 0.877132i | \(-0.659454\pi\) | ||||
−0.480250 | + | 0.877132i | \(0.659454\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | − 8.38623i | − 0.926104i | ||||||||
\(83\) | 12.2639i | 1.34614i | 0.739580 | + | 0.673069i | \(0.235024\pi\) | ||||
−0.739580 | + | 0.673069i | \(0.764976\pi\) | |||||||
\(84\) | 0.824573 | 0.0899683 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −10.3816 | −1.11947 | ||||||||
\(87\) | 2.25963i | 0.242258i | ||||||||
\(88\) | 11.2877i | 1.20327i | ||||||||
\(89\) | 15.2881 | 1.62054 | 0.810268 | − | 0.586059i | \(-0.199321\pi\) | ||||
0.810268 | + | 0.586059i | \(0.199321\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −4.51290 | −0.473080 | ||||||||
\(92\) | 4.57131i | 0.476592i | ||||||||
\(93\) | 10.0520i | 1.04235i | ||||||||
\(94\) | −3.51026 | −0.362056 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −3.93896 | −0.402018 | ||||||||
\(97\) | − 13.5000i | − 1.37071i | −0.728207 | − | 0.685357i | \(-0.759646\pi\) | ||||
0.728207 | − | 0.685357i | \(-0.240354\pi\) | |||||||
\(98\) | 6.46419i | 0.652982i | ||||||||
\(99\) | −3.67008 | −0.368856 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 7.22642 | 0.719055 | 0.359528 | − | 0.933134i | \(-0.382938\pi\) | ||||
0.359528 | + | 0.933134i | \(0.382938\pi\) | |||||||
\(102\) | 2.38197i | 0.235850i | ||||||||
\(103\) | 5.27748i | 0.520006i | 0.965608 | + | 0.260003i | \(0.0837235\pi\) | ||||
−0.965608 | + | 0.260003i | \(0.916277\pi\) | |||||||
\(104\) | 12.4625 | 1.22205 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 3.93896 | 0.382585 | ||||||||
\(107\) | − 5.46682i | − 0.528498i | −0.964455 | − | 0.264249i | \(-0.914876\pi\) | ||||
0.964455 | − | 0.264249i | \(-0.0851240\pi\) | |||||||
\(108\) | − 0.740367i | − 0.0712419i | ||||||||
\(109\) | −11.3395 | −1.08613 | −0.543064 | − | 0.839692i | \(-0.682736\pi\) | ||||
−0.543064 | + | 0.839692i | \(0.682736\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 7.37232 | 0.699749 | ||||||||
\(112\) | 2.19531i | 0.207437i | ||||||||
\(113\) | 4.83520i | 0.454858i | 0.973795 | + | 0.227429i | \(0.0730319\pi\) | ||||
−0.973795 | + | 0.227429i | \(0.926968\pi\) | |||||||
\(114\) | −4.55739 | −0.426839 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 1.67296 | 0.155330 | ||||||||
\(117\) | 4.05204i | 0.374611i | ||||||||
\(118\) | 7.40046i | 0.681268i | ||||||||
\(119\) | −2.36372 | −0.216681 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 2.46946 | 0.224496 | ||||||||
\(122\) | − 10.2178i | − 0.925078i | ||||||||
\(123\) | − 7.47214i | − 0.673740i | ||||||||
\(124\) | 7.44220 | 0.668330 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −1.24998 | −0.111357 | ||||||||
\(127\) | − 0.759596i | − 0.0674032i | −0.999432 | − | 0.0337016i | \(-0.989270\pi\) | ||||
0.999432 | − | 0.0337016i | \(-0.0107296\pi\) | |||||||
\(128\) | − 1.50823i | − 0.133310i | ||||||||
\(129\) | −9.24998 | −0.814415 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 14.6551 | 1.28042 | 0.640211 | − | 0.768199i | \(-0.278847\pi\) | ||||
0.640211 | + | 0.768199i | \(0.278847\pi\) | |||||||
\(132\) | 2.71720i | 0.236502i | ||||||||
\(133\) | − 4.52248i | − 0.392148i | ||||||||
\(134\) | 2.94796 | 0.254665 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 6.52746 | 0.559725 | ||||||||
\(137\) | − 12.2914i | − 1.05012i | −0.851064 | − | 0.525062i | \(-0.824042\pi\) | ||||
0.851064 | − | 0.525062i | \(-0.175958\pi\) | |||||||
\(138\) | − 6.92971i | − 0.589896i | ||||||||
\(139\) | −14.7340 | −1.24972 | −0.624861 | − | 0.780736i | \(-0.714844\pi\) | ||||
−0.624861 | + | 0.780736i | \(0.714844\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −3.12765 | −0.263395 | ||||||||
\(142\) | 0.741668i | 0.0622394i | ||||||||
\(143\) | − 14.8713i | − 1.24360i | ||||||||
\(144\) | 1.97112 | 0.164260 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −8.38991 | −0.694354 | ||||||||
\(147\) | 5.75960i | 0.475043i | ||||||||
\(148\) | − 5.45822i | − 0.448663i | ||||||||
\(149\) | −15.6498 | −1.28208 | −0.641041 | − | 0.767507i | \(-0.721497\pi\) | ||||
−0.641041 | + | 0.767507i | \(0.721497\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 3.95819 | 0.322113 | 0.161056 | − | 0.986945i | \(-0.448510\pi\) | ||||
0.161056 | + | 0.986945i | \(0.448510\pi\) | |||||||
\(152\) | 12.4889i | 1.01299i | ||||||||
\(153\) | 2.12233i | 0.171580i | ||||||||
\(154\) | 4.58753 | 0.369673 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 3.00000 | 0.240192 | ||||||||
\(157\) | 4.50061i | 0.359188i | 0.983741 | + | 0.179594i | \(0.0574784\pi\) | ||||
−0.983741 | + | 0.179594i | \(0.942522\pi\) | |||||||
\(158\) | − 9.58149i | − 0.762262i | ||||||||
\(159\) | 3.50961 | 0.278330 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 6.87661 | 0.541953 | ||||||||
\(162\) | 1.12233i | 0.0881788i | ||||||||
\(163\) | − 2.45389i | − 0.192203i | −0.995372 | − | 0.0961016i | \(-0.969363\pi\) | ||||
0.995372 | − | 0.0961016i | \(-0.0306374\pi\) | |||||||
\(164\) | −5.53213 | −0.431987 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −13.7642 | −1.06831 | ||||||||
\(167\) | 3.06328i | 0.237043i | 0.992951 | + | 0.118522i | \(0.0378155\pi\) | ||||
−0.992951 | + | 0.118522i | \(0.962184\pi\) | |||||||
\(168\) | 3.42541i | 0.264276i | ||||||||
\(169\) | −3.41904 | −0.263003 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −4.06064 | −0.310525 | ||||||||
\(172\) | 6.84839i | 0.522185i | ||||||||
\(173\) | 11.2596i | 0.856054i | 0.903766 | + | 0.428027i | \(0.140791\pi\) | ||||
−0.903766 | + | 0.428027i | \(0.859209\pi\) | |||||||
\(174\) | −2.53606 | −0.192258 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −7.23416 | −0.545296 | ||||||||
\(177\) | 6.59382i | 0.495622i | ||||||||
\(178\) | 17.1584i | 1.28607i | ||||||||
\(179\) | −10.0574 | −0.751722 | −0.375861 | − | 0.926676i | \(-0.622653\pi\) | ||||
−0.375861 | + | 0.926676i | \(0.622653\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −19.4684 | −1.44708 | −0.723539 | − | 0.690283i | \(-0.757486\pi\) | ||||
−0.723539 | + | 0.690283i | \(0.757486\pi\) | |||||||
\(182\) | − 5.06498i | − 0.375441i | ||||||||
\(183\) | − 9.10408i | − 0.672993i | ||||||||
\(184\) | −18.9899 | −1.39996 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −11.2817 | −0.827218 | ||||||||
\(187\) | − 7.78912i | − 0.569597i | ||||||||
\(188\) | 2.31561i | 0.168883i | ||||||||
\(189\) | −1.11373 | −0.0810123 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −11.6090 | −0.840000 | −0.420000 | − | 0.907524i | \(-0.637970\pi\) | ||||
−0.420000 | + | 0.907524i | \(0.637970\pi\) | |||||||
\(192\) | − 8.36307i | − 0.603552i | ||||||||
\(193\) | − 3.38156i | − 0.243410i | −0.992566 | − | 0.121705i | \(-0.961164\pi\) | ||||
0.992566 | − | 0.121705i | \(-0.0388362\pi\) | |||||||
\(194\) | 15.1515 | 1.08781 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 4.26422 | 0.304587 | ||||||||
\(197\) | 17.5881i | 1.25310i | 0.779381 | + | 0.626550i | \(0.215534\pi\) | ||||
−0.779381 | + | 0.626550i | \(0.784466\pi\) | |||||||
\(198\) | − 4.11905i | − 0.292728i | ||||||||
\(199\) | −20.0102 | −1.41849 | −0.709244 | − | 0.704963i | \(-0.750963\pi\) | ||||
−0.709244 | + | 0.704963i | \(0.750963\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 2.62663 | 0.185268 | ||||||||
\(202\) | 8.11045i | 0.570649i | ||||||||
\(203\) | − 2.51663i | − 0.176633i | ||||||||
\(204\) | 1.57131 | 0.110013 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −5.92309 | −0.412681 | ||||||||
\(207\) | − 6.17438i | − 0.429149i | ||||||||
\(208\) | 7.98706i | 0.553803i | ||||||||
\(209\) | 14.9029 | 1.03085 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2.44261 | 0.168156 | 0.0840780 | − | 0.996459i | \(-0.473206\pi\) | ||||
0.0840780 | + | 0.996459i | \(0.473206\pi\) | |||||||
\(212\) | − 2.59840i | − 0.178459i | ||||||||
\(213\) | 0.660827i | 0.0452791i | ||||||||
\(214\) | 6.13560 | 0.419421 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 3.07561 | 0.209269 | ||||||||
\(217\) | − 11.1953i | − 0.759987i | ||||||||
\(218\) | − 12.7267i | − 0.861961i | ||||||||
\(219\) | −7.47542 | −0.505142 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −8.59978 | −0.578484 | ||||||||
\(222\) | 8.27420i | 0.555328i | ||||||||
\(223\) | − 25.6369i | − 1.71677i | −0.513005 | − | 0.858386i | \(-0.671468\pi\) | ||||
0.513005 | − | 0.858386i | \(-0.328532\pi\) | |||||||
\(224\) | 4.38695 | 0.293116 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −5.42671 | −0.360979 | ||||||||
\(227\) | − 6.56336i | − 0.435625i | −0.975991 | − | 0.217813i | \(-0.930108\pi\) | ||||
0.975991 | − | 0.217813i | \(-0.0698922\pi\) | |||||||
\(228\) | 3.00637i | 0.199101i | ||||||||
\(229\) | 7.96390 | 0.526269 | 0.263135 | − | 0.964759i | \(-0.415244\pi\) | ||||
0.263135 | + | 0.964759i | \(0.415244\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 4.08749 | 0.268937 | ||||||||
\(232\) | 6.94974i | 0.456273i | ||||||||
\(233\) | − 9.42107i | − 0.617195i | −0.951193 | − | 0.308597i | \(-0.900140\pi\) | ||||
0.951193 | − | 0.308597i | \(-0.0998596\pi\) | |||||||
\(234\) | −4.54774 | −0.297295 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 4.88185 | 0.317781 | ||||||||
\(237\) | − 8.53711i | − 0.554545i | ||||||||
\(238\) | − 2.65288i | − 0.171961i | ||||||||
\(239\) | 11.2231 | 0.725964 | 0.362982 | − | 0.931796i | \(-0.381759\pi\) | ||||
0.362982 | + | 0.931796i | \(0.381759\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 22.6809 | 1.46101 | 0.730503 | − | 0.682910i | \(-0.239286\pi\) | ||||
0.730503 | + | 0.682910i | \(0.239286\pi\) | |||||||
\(242\) | 2.77155i | 0.178162i | ||||||||
\(243\) | 1.00000i | 0.0641500i | ||||||||
\(244\) | −6.74037 | −0.431508 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 8.38623 | 0.534686 | ||||||||
\(247\) | − 16.4539i | − 1.04694i | ||||||||
\(248\) | 30.9161i | 1.96318i | ||||||||
\(249\) | −12.2639 | −0.777193 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −6.76819 | −0.427205 | −0.213602 | − | 0.976921i | \(-0.568520\pi\) | ||||
−0.213602 | + | 0.976921i | \(0.568520\pi\) | |||||||
\(252\) | 0.824573i | 0.0519432i | ||||||||
\(253\) | 22.6604i | 1.42465i | ||||||||
\(254\) | 0.852520 | 0.0534918 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −15.0334 | −0.939587 | ||||||||
\(257\) | 14.7934i | 0.922786i | 0.887196 | + | 0.461393i | \(0.152650\pi\) | ||||
−0.887196 | + | 0.461393i | \(0.847350\pi\) | |||||||
\(258\) | − 10.3816i | − 0.646328i | ||||||||
\(259\) | −8.21080 | −0.510194 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −2.25963 | −0.139868 | ||||||||
\(262\) | 16.4479i | 1.01616i | ||||||||
\(263\) | 19.9688i | 1.23133i | 0.788008 | + | 0.615665i | \(0.211113\pi\) | ||||
−0.788008 | + | 0.615665i | \(0.788887\pi\) | |||||||
\(264\) | −11.2877 | −0.694710 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 5.07573 | 0.311213 | ||||||||
\(267\) | 15.2881i | 0.935617i | ||||||||
\(268\) | − 1.94467i | − 0.118790i | ||||||||
\(269\) | 10.2381 | 0.624228 | 0.312114 | − | 0.950045i | \(-0.398963\pi\) | ||||
0.312114 | + | 0.950045i | \(0.398963\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 12.3075 | 0.747630 | 0.373815 | − | 0.927503i | \(-0.378050\pi\) | ||||
0.373815 | + | 0.927503i | \(0.378050\pi\) | |||||||
\(272\) | 4.18338i | 0.253654i | ||||||||
\(273\) | − 4.51290i | − 0.273133i | ||||||||
\(274\) | 13.7950 | 0.833389 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −4.57131 | −0.275160 | ||||||||
\(277\) | − 31.5520i | − 1.89578i | −0.318603 | − | 0.947888i | \(-0.603214\pi\) | ||||
0.318603 | − | 0.947888i | \(-0.396786\pi\) | |||||||
\(278\) | − 16.5365i | − 0.991791i | ||||||||
\(279\) | −10.0520 | −0.601800 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −21.3119 | −1.27136 | −0.635681 | − | 0.771952i | \(-0.719281\pi\) | ||||
−0.635681 | + | 0.771952i | \(0.719281\pi\) | |||||||
\(282\) | − 3.51026i | − 0.209033i | ||||||||
\(283\) | − 0.864403i | − 0.0513834i | −0.999670 | − | 0.0256917i | \(-0.991821\pi\) | ||||
0.999670 | − | 0.0256917i | \(-0.00817883\pi\) | |||||||
\(284\) | 0.489254 | 0.0290319 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 16.6906 | 0.986933 | ||||||||
\(287\) | 8.32198i | 0.491231i | ||||||||
\(288\) | − 3.93896i | − 0.232105i | ||||||||
\(289\) | 12.4957 | 0.735041 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 13.5000 | 0.791382 | ||||||||
\(292\) | 5.53456i | 0.323886i | ||||||||
\(293\) | 3.17701i | 0.185603i | 0.995685 | + | 0.0928014i | \(0.0295822\pi\) | ||||
−0.995685 | + | 0.0928014i | \(0.970418\pi\) | |||||||
\(294\) | −6.46419 | −0.376999 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 22.6743 | 1.31792 | ||||||||
\(297\) | − 3.67008i | − 0.212959i | ||||||||
\(298\) | − 17.5643i | − 1.01747i | ||||||||
\(299\) | 25.0188 | 1.44688 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 10.3020 | 0.593799 | ||||||||
\(302\) | 4.44240i | 0.255632i | ||||||||
\(303\) | 7.22642i | 0.415147i | ||||||||
\(304\) | −8.00401 | −0.459062 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −2.38197 | −0.136168 | ||||||||
\(307\) | 0.507986i | 0.0289923i | 0.999895 | + | 0.0144961i | \(0.00461443\pi\) | ||||
−0.999895 | + | 0.0144961i | \(0.995386\pi\) | |||||||
\(308\) | − 3.02624i | − 0.172436i | ||||||||
\(309\) | −5.27748 | −0.300225 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −14.6438 | −0.830375 | −0.415188 | − | 0.909736i | \(-0.636284\pi\) | ||||
−0.415188 | + | 0.909736i | \(0.636284\pi\) | |||||||
\(312\) | 12.4625i | 0.705549i | ||||||||
\(313\) | − 14.9562i | − 0.845372i | −0.906276 | − | 0.422686i | \(-0.861087\pi\) | ||||
0.906276 | − | 0.422686i | \(-0.138913\pi\) | |||||||
\(314\) | −5.05119 | −0.285055 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −6.32060 | −0.355562 | ||||||||
\(317\) | − 18.1190i | − 1.01767i | −0.860865 | − | 0.508834i | \(-0.830077\pi\) | ||||
0.860865 | − | 0.508834i | \(-0.169923\pi\) | |||||||
\(318\) | 3.93896i | 0.220886i | ||||||||
\(319\) | 8.29302 | 0.464320 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 5.46682 | 0.305128 | ||||||||
\(322\) | 7.71785i | 0.430099i | ||||||||
\(323\) | − 8.61803i | − 0.479520i | ||||||||
\(324\) | 0.740367 | 0.0411315 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 2.75408 | 0.152534 | ||||||||
\(327\) | − 11.3395i | − 0.627076i | ||||||||
\(328\) | − 22.9813i | − 1.26893i | ||||||||
\(329\) | 3.48337 | 0.192044 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 26.3514 | 1.44841 | 0.724203 | − | 0.689587i | \(-0.242208\pi\) | ||||
0.724203 | + | 0.689587i | \(0.242208\pi\) | |||||||
\(332\) | 9.07979i | 0.498318i | ||||||||
\(333\) | 7.37232i | 0.404000i | ||||||||
\(334\) | −3.43802 | −0.188120 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −2.19531 | −0.119764 | ||||||||
\(337\) | 10.6948i | 0.582584i | 0.956634 | + | 0.291292i | \(0.0940851\pi\) | ||||
−0.956634 | + | 0.291292i | \(0.905915\pi\) | |||||||
\(338\) | − 3.83731i | − 0.208722i | ||||||||
\(339\) | −4.83520 | −0.262612 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 36.8918 | 1.99780 | ||||||||
\(342\) | − 4.55739i | − 0.246436i | ||||||||
\(343\) | − 14.2108i | − 0.767311i | ||||||||
\(344\) | −28.4493 | −1.53388 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −12.6371 | −0.679373 | ||||||||
\(347\) | − 16.1740i | − 0.868264i | −0.900849 | − | 0.434132i | \(-0.857055\pi\) | ||||
0.900849 | − | 0.434132i | \(-0.142945\pi\) | |||||||
\(348\) | 1.67296i | 0.0896800i | ||||||||
\(349\) | −15.2383 | −0.815688 | −0.407844 | − | 0.913052i | \(-0.633719\pi\) | ||||
−0.407844 | + | 0.913052i | \(0.633719\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −4.05204 | −0.216282 | ||||||||
\(352\) | 14.4563i | 0.770522i | ||||||||
\(353\) | − 29.5383i | − 1.57217i | −0.618120 | − | 0.786084i | \(-0.712106\pi\) | ||||
0.618120 | − | 0.786084i | \(-0.287894\pi\) | |||||||
\(354\) | −7.40046 | −0.393330 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 11.3188 | 0.599896 | ||||||||
\(357\) | − 2.36372i | − 0.125101i | ||||||||
\(358\) | − 11.2877i | − 0.596574i | ||||||||
\(359\) | 13.1668 | 0.694915 | 0.347457 | − | 0.937696i | \(-0.387045\pi\) | ||||
0.347457 | + | 0.937696i | \(0.387045\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −2.51120 | −0.132168 | ||||||||
\(362\) | − 21.8501i | − 1.14842i | ||||||||
\(363\) | 2.46946i | 0.129613i | ||||||||
\(364\) | −3.34120 | −0.175127 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 10.2178 | 0.534094 | ||||||||
\(367\) | 3.88895i | 0.203001i | 0.994835 | + | 0.101501i | \(0.0323644\pi\) | ||||
−0.994835 | + | 0.101501i | \(0.967636\pi\) | |||||||
\(368\) | − 12.1704i | − 0.634428i | ||||||||
\(369\) | 7.47214 | 0.388984 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −3.90878 | −0.202934 | ||||||||
\(372\) | 7.44220i | 0.385860i | ||||||||
\(373\) | − 8.14326i | − 0.421642i | −0.977525 | − | 0.210821i | \(-0.932386\pi\) | ||||
0.977525 | − | 0.210821i | \(-0.0676138\pi\) | |||||||
\(374\) | 8.74200 | 0.452038 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −9.61941 | −0.496083 | ||||||||
\(377\) | − 9.15613i | − 0.471564i | ||||||||
\(378\) | − 1.24998i | − 0.0642921i | ||||||||
\(379\) | −9.90720 | −0.508898 | −0.254449 | − | 0.967086i | \(-0.581894\pi\) | ||||
−0.254449 | + | 0.967086i | \(0.581894\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0.759596 | 0.0389153 | ||||||||
\(382\) | − 13.0292i | − 0.666632i | ||||||||
\(383\) | − 5.22215i | − 0.266840i | −0.991060 | − | 0.133420i | \(-0.957404\pi\) | ||||
0.991060 | − | 0.133420i | \(-0.0425959\pi\) | |||||||
\(384\) | 1.50823 | 0.0769668 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 3.79524 | 0.193173 | ||||||||
\(387\) | − 9.24998i | − 0.470203i | ||||||||
\(388\) | − 9.99493i | − 0.507416i | ||||||||
\(389\) | 3.72974 | 0.189105 | 0.0945526 | − | 0.995520i | \(-0.469858\pi\) | ||||
0.0945526 | + | 0.995520i | \(0.469858\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 13.1041 | 0.662702 | ||||||||
\(392\) | 17.7142i | 0.894705i | ||||||||
\(393\) | 14.6551i | 0.739253i | ||||||||
\(394\) | −19.7397 | −0.994473 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −2.71720 | −0.136545 | ||||||||
\(397\) | − 4.01562i | − 0.201538i | −0.994910 | − | 0.100769i | \(-0.967870\pi\) | ||||
0.994910 | − | 0.100769i | \(-0.0321303\pi\) | |||||||
\(398\) | − 22.4581i | − 1.12573i | ||||||||
\(399\) | 4.52248 | 0.226407 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −24.9890 | −1.24789 | −0.623945 | − | 0.781468i | \(-0.714471\pi\) | ||||
−0.623945 | + | 0.781468i | \(0.714471\pi\) | |||||||
\(402\) | 2.94796i | 0.147031i | ||||||||
\(403\) | − 40.7313i | − 2.02897i | ||||||||
\(404\) | 5.35020 | 0.266183 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 2.82450 | 0.140178 | ||||||||
\(407\) | − 27.0570i | − 1.34116i | ||||||||
\(408\) | 6.52746i | 0.323158i | ||||||||
\(409\) | 25.3768 | 1.25480 | 0.627401 | − | 0.778697i | \(-0.284119\pi\) | ||||
0.627401 | + | 0.778697i | \(0.284119\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 12.2914 | 0.606290 | ||||||||
\(412\) | 3.90728i | 0.192498i | ||||||||
\(413\) | − 7.34376i | − 0.361363i | ||||||||
\(414\) | 6.92971 | 0.340577 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 15.9608 | 0.782544 | ||||||||
\(417\) | − 14.7340i | − 0.721527i | ||||||||
\(418\) | 16.7260i | 0.818094i | ||||||||
\(419\) | 30.8219 | 1.50575 | 0.752873 | − | 0.658165i | \(-0.228667\pi\) | ||||
0.752873 | + | 0.658165i | \(0.228667\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 8.54649 | 0.416530 | 0.208265 | − | 0.978072i | \(-0.433218\pi\) | ||||
0.208265 | + | 0.978072i | \(0.433218\pi\) | |||||||
\(422\) | 2.74142i | 0.133450i | ||||||||
\(423\) | − 3.12765i | − 0.152071i | ||||||||
\(424\) | 10.7942 | 0.524212 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −0.741668 | −0.0359339 | ||||||||
\(427\) | 10.1395i | 0.490686i | ||||||||
\(428\) | − 4.04746i | − 0.195641i | ||||||||
\(429\) | 14.8713 | 0.717993 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −26.3815 | −1.27075 | −0.635376 | − | 0.772203i | \(-0.719155\pi\) | ||||
−0.635376 | + | 0.772203i | \(0.719155\pi\) | |||||||
\(432\) | 1.97112i | 0.0948356i | ||||||||
\(433\) | − 9.37272i | − 0.450424i | −0.974310 | − | 0.225212i | \(-0.927693\pi\) | ||||
0.974310 | − | 0.225212i | \(-0.0723075\pi\) | |||||||
\(434\) | 12.5649 | 0.603133 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −8.39540 | −0.402067 | ||||||||
\(437\) | 25.0719i | 1.19935i | ||||||||
\(438\) | − 8.38991i | − 0.400886i | ||||||||
\(439\) | 0.515980 | 0.0246264 | 0.0123132 | − | 0.999924i | \(-0.496080\pi\) | ||||
0.0123132 | + | 0.999924i | \(0.496080\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −5.75960 | −0.274266 | ||||||||
\(442\) | − 9.65183i | − 0.459091i | ||||||||
\(443\) | − 17.8348i | − 0.847357i | −0.905813 | − | 0.423678i | \(-0.860739\pi\) | ||||
0.905813 | − | 0.423678i | \(-0.139261\pi\) | |||||||
\(444\) | 5.45822 | 0.259036 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 28.7731 | 1.36245 | ||||||||
\(447\) | − 15.6498i | − 0.740210i | ||||||||
\(448\) | 9.31423i | 0.440056i | ||||||||
\(449\) | 4.16533 | 0.196574 | 0.0982870 | − | 0.995158i | \(-0.468664\pi\) | ||||
0.0982870 | + | 0.995158i | \(0.468664\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −27.4233 | −1.29131 | ||||||||
\(452\) | 3.57983i | 0.168381i | ||||||||
\(453\) | 3.95819i | 0.185972i | ||||||||
\(454\) | 7.36628 | 0.345716 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −12.4889 | −0.584848 | ||||||||
\(457\) | 17.6734i | 0.826725i | 0.910567 | + | 0.413362i | \(0.135646\pi\) | ||||
−0.910567 | + | 0.413362i | \(0.864354\pi\) | |||||||
\(458\) | 8.93815i | 0.417652i | ||||||||
\(459\) | −2.12233 | −0.0990620 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −0.204956 | −0.00954577 | −0.00477288 | − | 0.999989i | \(-0.501519\pi\) | ||||
−0.00477288 | + | 0.999989i | \(0.501519\pi\) | |||||||
\(462\) | 4.58753i | 0.213431i | ||||||||
\(463\) | − 12.8176i | − 0.595682i | −0.954615 | − | 0.297841i | \(-0.903733\pi\) | ||||
0.954615 | − | 0.297841i | \(-0.0962666\pi\) | |||||||
\(464\) | −4.45401 | −0.206772 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 10.5736 | 0.489812 | ||||||||
\(467\) | − 1.11373i | − 0.0515375i | −0.999668 | − | 0.0257687i | \(-0.991797\pi\) | ||||
0.999668 | − | 0.0257687i | \(-0.00820335\pi\) | |||||||
\(468\) | 3.00000i | 0.138675i | ||||||||
\(469\) | −2.92537 | −0.135081 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −4.50061 | −0.207377 | ||||||||
\(472\) | 20.2800i | 0.933462i | ||||||||
\(473\) | 33.9481i | 1.56094i | ||||||||
\(474\) | 9.58149 | 0.440092 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −1.75002 | −0.0802120 | ||||||||
\(477\) | 3.50961i | 0.160694i | ||||||||
\(478\) | 12.5961i | 0.576132i | ||||||||
\(479\) | 25.1750 | 1.15027 | 0.575136 | − | 0.818057i | \(-0.304949\pi\) | ||||
0.575136 | + | 0.818057i | \(0.304949\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −29.8729 | −1.36209 | ||||||||
\(482\) | 25.4555i | 1.15947i | ||||||||
\(483\) | 6.87661i | 0.312897i | ||||||||
\(484\) | 1.82830 | 0.0831048 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −1.12233 | −0.0509101 | ||||||||
\(487\) | − 10.3598i | − 0.469447i | −0.972062 | − | 0.234723i | \(-0.924582\pi\) | ||||
0.972062 | − | 0.234723i | \(-0.0754184\pi\) | |||||||
\(488\) | − 28.0006i | − 1.26753i | ||||||||
\(489\) | 2.45389 | 0.110969 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −15.6571 | −0.706595 | −0.353297 | − | 0.935511i | \(-0.614940\pi\) | ||||
−0.353297 | + | 0.935511i | \(0.614940\pi\) | |||||||
\(492\) | − 5.53213i | − 0.249408i | ||||||||
\(493\) | − 4.79569i | − 0.215987i | ||||||||
\(494\) | 18.4667 | 0.830858 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −19.8138 | −0.889665 | ||||||||
\(497\) | − 0.735985i | − 0.0330135i | ||||||||
\(498\) | − 13.7642i | − 0.616788i | ||||||||
\(499\) | −35.7864 | −1.60202 | −0.801010 | − | 0.598651i | \(-0.795704\pi\) | ||||
−0.801010 | + | 0.598651i | \(0.795704\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −3.06328 | −0.136857 | ||||||||
\(502\) | − 7.59617i | − 0.339034i | ||||||||
\(503\) | − 11.7791i | − 0.525203i | −0.964904 | − | 0.262601i | \(-0.915420\pi\) | ||||
0.964904 | − | 0.262601i | \(-0.0845804\pi\) | |||||||
\(504\) | −3.42541 | −0.152580 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −25.4326 | −1.13061 | ||||||||
\(507\) | − 3.41904i | − 0.151845i | ||||||||
\(508\) | − 0.562380i | − 0.0249516i | ||||||||
\(509\) | −33.6507 | −1.49154 | −0.745771 | − | 0.666203i | \(-0.767918\pi\) | ||||
−0.745771 | + | 0.666203i | \(0.767918\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 8.32563 | 0.368304 | ||||||||
\(512\) | − 19.8889i | − 0.878976i | ||||||||
\(513\) | − 4.06064i | − 0.179282i | ||||||||
\(514\) | −16.6031 | −0.732332 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −6.84839 | −0.301483 | ||||||||
\(517\) | 11.4787i | 0.504833i | ||||||||
\(518\) | − 9.21526i | − 0.404895i | ||||||||
\(519\) | −11.2596 | −0.494243 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −11.8448 | −0.518929 | −0.259465 | − | 0.965753i | \(-0.583546\pi\) | ||||
−0.259465 | + | 0.965753i | \(0.583546\pi\) | |||||||
\(522\) | − 2.53606i | − 0.111000i | ||||||||
\(523\) | 4.09694i | 0.179147i | 0.995980 | + | 0.0895733i | \(0.0285503\pi\) | ||||
−0.995980 | + | 0.0895733i | \(0.971450\pi\) | |||||||
\(524\) | 10.8502 | 0.473992 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −22.4117 | −0.977195 | ||||||||
\(527\) | − 21.3338i | − 0.929314i | ||||||||
\(528\) | − 7.23416i | − 0.314827i | ||||||||
\(529\) | −15.1229 | −0.657518 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −6.59382 | −0.286147 | ||||||||
\(532\) | − 3.34829i | − 0.145167i | ||||||||
\(533\) | 30.2774i | 1.31146i | ||||||||
\(534\) | −17.1584 | −0.742515 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 8.07849 | 0.348938 | ||||||||
\(537\) | − 10.0574i | − 0.434007i | ||||||||
\(538\) | 11.4906i | 0.495393i | ||||||||
\(539\) | 21.1382 | 0.910485 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 13.9582 | 0.600109 | 0.300055 | − | 0.953922i | \(-0.402995\pi\) | ||||
0.300055 | + | 0.953922i | \(0.402995\pi\) | |||||||
\(542\) | 13.8132i | 0.593326i | ||||||||
\(543\) | − 19.4684i | − 0.835471i | ||||||||
\(544\) | 8.35978 | 0.358423 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 5.06498 | 0.216761 | ||||||||
\(547\) | 26.5045i | 1.13325i | 0.823976 | + | 0.566625i | \(0.191751\pi\) | ||||
−0.823976 | + | 0.566625i | \(0.808249\pi\) | |||||||
\(548\) | − 9.10015i | − 0.388739i | ||||||||
\(549\) | 9.10408 | 0.388553 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 9.17556 | 0.390892 | ||||||||
\(552\) | − 18.9899i | − 0.808266i | ||||||||
\(553\) | 9.50808i | 0.404325i | ||||||||
\(554\) | 35.4119 | 1.50451 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −10.9086 | −0.462627 | ||||||||
\(557\) | − 10.6860i | − 0.452781i | −0.974037 | − | 0.226391i | \(-0.927307\pi\) | ||||
0.974037 | − | 0.226391i | \(-0.0726926\pi\) | |||||||
\(558\) | − 11.2817i | − 0.477594i | ||||||||
\(559\) | 37.4813 | 1.58529 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 7.78912 | 0.328857 | ||||||||
\(562\) | − 23.9191i | − 1.00897i | ||||||||
\(563\) | − 25.5750i | − 1.07786i | −0.842352 | − | 0.538928i | \(-0.818829\pi\) | ||||
0.842352 | − | 0.538928i | \(-0.181171\pi\) | |||||||
\(564\) | −2.31561 | −0.0975047 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0.970149 | 0.0407784 | ||||||||
\(567\) | − 1.11373i | − 0.0467725i | ||||||||
\(568\) | 2.03244i | 0.0852794i | ||||||||
\(569\) | −6.10210 | −0.255813 | −0.127907 | − | 0.991786i | \(-0.540826\pi\) | ||||
−0.127907 | + | 0.991786i | \(0.540826\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 23.7396 | 0.993473 | 0.496737 | − | 0.867901i | \(-0.334532\pi\) | ||||
0.496737 | + | 0.867901i | \(0.334532\pi\) | |||||||
\(572\) | − 11.0102i | − 0.460361i | ||||||||
\(573\) | − 11.6090i | − 0.484974i | ||||||||
\(574\) | −9.34003 | −0.389845 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 8.36307 | 0.348461 | ||||||||
\(577\) | 44.1639i | 1.83857i | 0.393595 | + | 0.919284i | \(0.371231\pi\) | ||||
−0.393595 | + | 0.919284i | \(0.628769\pi\) | |||||||
\(578\) | 14.0243i | 0.583336i | ||||||||
\(579\) | 3.38156 | 0.140533 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 13.6587 | 0.566659 | ||||||||
\(582\) | 15.1515i | 0.628048i | ||||||||
\(583\) | − 12.8805i | − 0.533458i | ||||||||
\(584\) | −22.9915 | −0.951393 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −3.56566 | −0.147296 | ||||||||
\(587\) | − 0.511966i | − 0.0211311i | −0.999944 | − | 0.0105656i | \(-0.996637\pi\) | ||||
0.999944 | − | 0.0105656i | \(-0.00336318\pi\) | |||||||
\(588\) | 4.26422i | 0.175853i | ||||||||
\(589\) | 40.8177 | 1.68187 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −17.5881 | −0.723478 | ||||||||
\(592\) | 14.5317i | 0.597250i | ||||||||
\(593\) | − 18.8405i | − 0.773687i | −0.922145 | − | 0.386844i | \(-0.873565\pi\) | ||||
0.922145 | − | 0.386844i | \(-0.126435\pi\) | |||||||
\(594\) | 4.11905 | 0.169007 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −11.5866 | −0.474606 | ||||||||
\(597\) | − 20.0102i | − 0.818964i | ||||||||
\(598\) | 28.0795i | 1.14825i | ||||||||
\(599\) | −6.20712 | −0.253616 | −0.126808 | − | 0.991927i | \(-0.540473\pi\) | ||||
−0.126808 | + | 0.991927i | \(0.540473\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 34.0303 | 1.38813 | 0.694063 | − | 0.719915i | \(-0.255819\pi\) | ||||
0.694063 | + | 0.719915i | \(0.255819\pi\) | |||||||
\(602\) | 11.5623i | 0.471244i | ||||||||
\(603\) | 2.62663i | 0.106965i | ||||||||
\(604\) | 2.93051 | 0.119241 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −8.11045 | −0.329465 | ||||||||
\(607\) | − 16.2488i | − 0.659518i | −0.944065 | − | 0.329759i | \(-0.893032\pi\) | ||||
0.944065 | − | 0.329759i | \(-0.106968\pi\) | |||||||
\(608\) | 15.9947i | 0.648670i | ||||||||
\(609\) | 2.51663 | 0.101979 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 12.6734 | 0.512709 | ||||||||
\(612\) | 1.57131i | 0.0635163i | ||||||||
\(613\) | − 0.0679852i | − 0.00274590i | −0.999999 | − | 0.00137295i | \(-0.999563\pi\) | ||||
0.999999 | − | 0.00137295i | \(-0.000437023\pi\) | |||||||
\(614\) | −0.570130 | −0.0230086 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 12.5715 | 0.506521 | ||||||||
\(617\) | − 32.8108i | − 1.32091i | −0.750864 | − | 0.660456i | \(-0.770363\pi\) | ||||
0.750864 | − | 0.660456i | \(-0.229637\pi\) | |||||||
\(618\) | − 5.92309i | − 0.238262i | ||||||||
\(619\) | 6.77712 | 0.272395 | 0.136198 | − | 0.990682i | \(-0.456512\pi\) | ||||
0.136198 | + | 0.990682i | \(0.456512\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 6.17438 | 0.247769 | ||||||||
\(622\) | − 16.4353i | − 0.658994i | ||||||||
\(623\) | − 17.0269i | − 0.682168i | ||||||||
\(624\) | −7.98706 | −0.319738 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 16.7858 | 0.670895 | ||||||||
\(627\) | 14.9029i | 0.595163i | ||||||||
\(628\) | 3.33211i | 0.132966i | ||||||||
\(629\) | −15.6465 | −0.623867 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −7.66797 | −0.305257 | −0.152629 | − | 0.988284i | \(-0.548774\pi\) | ||||
−0.152629 | + | 0.988284i | \(0.548774\pi\) | |||||||
\(632\) | − 26.2568i | − 1.04444i | ||||||||
\(633\) | 2.44261i | 0.0970849i | ||||||||
\(634\) | 20.3356 | 0.807630 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 2.59840 | 0.103033 | ||||||||
\(637\) | − 23.3381i | − 0.924690i | ||||||||
\(638\) | 9.30754i | 0.368489i | ||||||||
\(639\) | −0.660827 | −0.0261419 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −23.6911 | −0.935744 | −0.467872 | − | 0.883796i | \(-0.654979\pi\) | ||||
−0.467872 | + | 0.883796i | \(0.654979\pi\) | |||||||
\(642\) | 6.13560i | 0.242153i | ||||||||
\(643\) | 2.16861i | 0.0855218i | 0.999085 | + | 0.0427609i | \(0.0136154\pi\) | ||||
−0.999085 | + | 0.0427609i | \(0.986385\pi\) | |||||||
\(644\) | 5.09122 | 0.200622 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 9.67231 | 0.380552 | ||||||||
\(647\) | − 2.55541i | − 0.100463i | −0.998738 | − | 0.0502317i | \(-0.984004\pi\) | ||||
0.998738 | − | 0.0502317i | \(-0.0159960\pi\) | |||||||
\(648\) | 3.07561i | 0.120821i | ||||||||
\(649\) | 24.1998 | 0.949926 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 11.1953 | 0.438779 | ||||||||
\(652\) | − 1.81678i | − 0.0711505i | ||||||||
\(653\) | 32.4137i | 1.26845i | 0.773150 | + | 0.634224i | \(0.218680\pi\) | ||||
−0.773150 | + | 0.634224i | \(0.781320\pi\) | |||||||
\(654\) | 12.7267 | 0.497653 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 14.7285 | 0.575051 | ||||||||
\(657\) | − 7.47542i | − 0.291644i | ||||||||
\(658\) | 3.90950i | 0.152408i | ||||||||
\(659\) | −0.449951 | −0.0175276 | −0.00876381 | − | 0.999962i | \(-0.502790\pi\) | ||||
−0.00876381 | + | 0.999962i | \(0.502790\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −26.9827 | −1.04951 | −0.524753 | − | 0.851254i | \(-0.675842\pi\) | ||||
−0.524753 | + | 0.851254i | \(0.675842\pi\) | |||||||
\(662\) | 29.5751i | 1.14947i | ||||||||
\(663\) | − 8.59978i | − 0.333988i | ||||||||
\(664\) | −37.7189 | −1.46378 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −8.27420 | −0.320619 | ||||||||
\(667\) | 13.9518i | 0.540217i | ||||||||
\(668\) | 2.26795i | 0.0877496i | ||||||||
\(669\) | 25.6369 | 0.991178 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −33.4127 | −1.28988 | ||||||||
\(672\) | 4.38695i | 0.169230i | ||||||||
\(673\) | 17.6224i | 0.679292i | 0.940553 | + | 0.339646i | \(0.110307\pi\) | ||||
−0.940553 | + | 0.339646i | \(0.889693\pi\) | |||||||
\(674\) | −12.0032 | −0.462344 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −2.53135 | −0.0973595 | ||||||||
\(677\) | 19.3484i | 0.743621i | 0.928309 | + | 0.371810i | \(0.121263\pi\) | ||||
−0.928309 | + | 0.371810i | \(0.878737\pi\) | |||||||
\(678\) | − 5.42671i | − 0.208412i | ||||||||
\(679\) | −15.0354 | −0.577005 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 6.56336 | 0.251508 | ||||||||
\(682\) | 41.4049i | 1.58547i | ||||||||
\(683\) | − 29.9460i | − 1.14585i | −0.819607 | − | 0.572926i | \(-0.805808\pi\) | ||||
0.819607 | − | 0.572926i | \(-0.194192\pi\) | |||||||
\(684\) | −3.00637 | −0.114951 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 15.9493 | 0.608946 | ||||||||
\(687\) | 7.96390i | 0.303842i | ||||||||
\(688\) | − 18.2328i | − 0.695120i | ||||||||
\(689\) | −14.2211 | −0.541781 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −19.9349 | −0.758361 | −0.379181 | − | 0.925323i | \(-0.623794\pi\) | ||||
−0.379181 | + | 0.925323i | \(0.623794\pi\) | |||||||
\(692\) | 8.33627i | 0.316897i | ||||||||
\(693\) | 4.08749i | 0.155271i | ||||||||
\(694\) | 18.1526 | 0.689063 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −6.94974 | −0.263429 | ||||||||
\(697\) | 15.8584i | 0.600678i | ||||||||
\(698\) | − 17.1025i | − 0.647337i | ||||||||
\(699\) | 9.42107 | 0.356338 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −49.0150 | −1.85127 | −0.925636 | − | 0.378415i | \(-0.876469\pi\) | ||||
−0.925636 | + | 0.378415i | \(0.876469\pi\) | |||||||
\(702\) | − 4.54774i | − 0.171643i | ||||||||
\(703\) | − 29.9363i | − 1.12907i | ||||||||
\(704\) | −30.6931 | −1.15679 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 33.1519 | 1.24769 | ||||||||
\(707\) | − 8.04831i | − 0.302688i | ||||||||
\(708\) | 4.88185i | 0.183471i | ||||||||
\(709\) | 4.81347 | 0.180774 | 0.0903868 | − | 0.995907i | \(-0.471190\pi\) | ||||
0.0903868 | + | 0.995907i | \(0.471190\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 8.53711 | 0.320167 | ||||||||
\(712\) | 47.0202i | 1.76216i | ||||||||
\(713\) | 62.0651i | 2.32436i | ||||||||
\(714\) | 2.65288 | 0.0992815 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −7.44614 | −0.278275 | ||||||||
\(717\) | 11.2231i | 0.419136i | ||||||||
\(718\) | 14.7775i | 0.551491i | ||||||||
\(719\) | −32.2512 | −1.20277 | −0.601383 | − | 0.798961i | \(-0.705383\pi\) | ||||
−0.601383 | + | 0.798961i | \(0.705383\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 5.87771 | 0.218897 | ||||||||
\(722\) | − 2.81840i | − 0.104890i | ||||||||
\(723\) | 22.6809i | 0.843512i | ||||||||
\(724\) | −14.4138 | −0.535685 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −2.77155 | −0.102862 | ||||||||
\(727\) | 29.1747i | 1.08203i | 0.841013 | + | 0.541015i | \(0.181960\pi\) | ||||
−0.841013 | + | 0.541015i | \(0.818040\pi\) | |||||||
\(728\) | − 13.8799i | − 0.514423i | ||||||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 19.6315 | 0.726099 | ||||||||
\(732\) | − 6.74037i | − 0.249131i | ||||||||
\(733\) | 5.20102i | 0.192104i | 0.995376 | + | 0.0960521i | \(0.0306215\pi\) | ||||
−0.995376 | + | 0.0960521i | \(0.969378\pi\) | |||||||
\(734\) | −4.36469 | −0.161104 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −24.3206 | −0.896469 | ||||||||
\(737\) | − 9.63994i | − 0.355092i | ||||||||
\(738\) | 8.38623i | 0.308701i | ||||||||
\(739\) | 16.3206 | 0.600363 | 0.300182 | − | 0.953882i | \(-0.402953\pi\) | ||||
0.300182 | + | 0.953882i | \(0.402953\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 16.4539 | 0.604449 | ||||||||
\(742\) | − 4.38695i | − 0.161050i | ||||||||
\(743\) | 53.4487i | 1.96084i | 0.196914 | + | 0.980421i | \(0.436908\pi\) | ||||
−0.196914 | + | 0.980421i | \(0.563092\pi\) | |||||||
\(744\) | −30.9161 | −1.13344 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 9.13946 | 0.334619 | ||||||||
\(747\) | − 12.2639i | − 0.448712i | ||||||||
\(748\) | − 5.76681i | − 0.210856i | ||||||||
\(749\) | −6.08859 | −0.222472 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −0.566970 | −0.0206890 | −0.0103445 | − | 0.999946i | \(-0.503293\pi\) | ||||
−0.0103445 | + | 0.999946i | \(0.503293\pi\) | |||||||
\(752\) | − 6.16497i | − 0.224813i | ||||||||
\(753\) | − 6.76819i | − 0.246647i | ||||||||
\(754\) | 10.2762 | 0.374238 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −0.824573 | −0.0299894 | ||||||||
\(757\) | − 53.0708i | − 1.92889i | −0.264282 | − | 0.964445i | \(-0.585135\pi\) | ||||
0.264282 | − | 0.964445i | \(-0.414865\pi\) | |||||||
\(758\) | − 11.1192i | − 0.403867i | ||||||||
\(759\) | −22.6604 | −0.822521 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −27.5056 | −0.997077 | −0.498539 | − | 0.866867i | \(-0.666130\pi\) | ||||
−0.498539 | + | 0.866867i | \(0.666130\pi\) | |||||||
\(762\) | 0.852520i | 0.0308835i | ||||||||
\(763\) | 12.6292i | 0.457208i | ||||||||
\(764\) | −8.59495 | −0.310954 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 5.86100 | 0.211766 | ||||||||
\(767\) | − 26.7184i | − 0.964747i | ||||||||
\(768\) | − 15.0334i | − 0.542471i | ||||||||
\(769\) | −14.9716 | −0.539889 | −0.269944 | − | 0.962876i | \(-0.587005\pi\) | ||||
−0.269944 | + | 0.962876i | \(0.587005\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −14.7934 | −0.532771 | ||||||||
\(772\) | − 2.50360i | − 0.0901065i | ||||||||
\(773\) | − 2.05427i | − 0.0738871i | −0.999317 | − | 0.0369436i | \(-0.988238\pi\) | ||||
0.999317 | − | 0.0369436i | \(-0.0117622\pi\) | |||||||
\(774\) | 10.3816 | 0.373158 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 41.5206 | 1.49050 | ||||||||
\(777\) | − 8.21080i | − 0.294561i | ||||||||
\(778\) | 4.18601i | 0.150076i | ||||||||
\(779\) | −30.3417 | −1.08710 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 2.42528 | 0.0867835 | ||||||||
\(782\) | 14.7072i | 0.525927i | ||||||||
\(783\) | − 2.25963i | − 0.0807527i | ||||||||
\(784\) | −11.3529 | −0.405459 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −16.4479 | −0.586678 | ||||||||
\(787\) | 16.8269i | 0.599815i | 0.953968 | + | 0.299908i | \(0.0969559\pi\) | ||||
−0.953968 | + | 0.299908i | \(0.903044\pi\) | |||||||
\(788\) | 13.0217i | 0.463877i | ||||||||
\(789\) | −19.9688 | −0.710909 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 5.38513 | 0.191473 | ||||||||
\(792\) | − 11.2877i | − 0.401091i | ||||||||
\(793\) | 36.8901i | 1.31001i | ||||||||
\(794\) | 4.50686 | 0.159942 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −14.8149 | −0.525101 | ||||||||
\(797\) | 0.208891i | 0.00739930i | 0.999993 | + | 0.00369965i | \(0.00117764\pi\) | ||||
−0.999993 | + | 0.00369965i | \(0.998822\pi\) | |||||||
\(798\) | 5.07573i | 0.179679i | ||||||||
\(799\) | 6.63791 | 0.234832 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −15.2881 | −0.540179 | ||||||||
\(802\) | − 28.0460i | − 0.990337i | ||||||||
\(803\) | 27.4354i | 0.968173i | ||||||||
\(804\) | 1.94467 | 0.0685834 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 45.7141 | 1.61021 | ||||||||
\(807\) | 10.2381i | 0.360398i | ||||||||
\(808\) | 22.2256i | 0.781894i | ||||||||
\(809\) | 16.9655 | 0.596476 | 0.298238 | − | 0.954491i | \(-0.403601\pi\) | ||||
0.298238 | + | 0.954491i | \(0.403601\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −20.4684 | −0.718742 | −0.359371 | − | 0.933195i | \(-0.617009\pi\) | ||||
−0.359371 | + | 0.933195i | \(0.617009\pi\) | |||||||
\(812\) | − 1.86323i | − 0.0653866i | ||||||||
\(813\) | 12.3075i | 0.431644i | ||||||||
\(814\) | 30.3669 | 1.06436 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −4.18338 | −0.146447 | ||||||||
\(817\) | 37.5609i | 1.31409i | ||||||||
\(818\) | 28.4812i | 0.995822i | ||||||||
\(819\) | 4.51290 | 0.157693 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 38.3636 | 1.33890 | 0.669449 | − | 0.742858i | \(-0.266530\pi\) | ||||
0.669449 | + | 0.742858i | \(0.266530\pi\) | |||||||
\(822\) | 13.7950i | 0.481157i | ||||||||
\(823\) | − 29.0098i | − 1.01122i | −0.862763 | − | 0.505609i | \(-0.831268\pi\) | ||||
0.862763 | − | 0.505609i | \(-0.168732\pi\) | |||||||
\(824\) | −16.2315 | −0.565449 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 8.24215 | 0.286781 | ||||||||
\(827\) | − 14.3567i | − 0.499233i | −0.968345 | − | 0.249616i | \(-0.919695\pi\) | ||||
0.968345 | − | 0.249616i | \(-0.0803045\pi\) | |||||||
\(828\) | − 4.57131i | − 0.158864i | ||||||||
\(829\) | −4.63563 | −0.161002 | −0.0805011 | − | 0.996755i | \(-0.525652\pi\) | ||||
−0.0805011 | + | 0.996755i | \(0.525652\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 31.5520 | 1.09453 | ||||||||
\(832\) | 33.8875i | 1.17484i | ||||||||
\(833\) | − 12.2238i | − 0.423529i | ||||||||
\(834\) | 16.5365 | 0.572611 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 11.0336 | 0.381605 | ||||||||
\(837\) | − 10.0520i | − 0.347449i | ||||||||
\(838\) | 34.5924i | 1.19498i | ||||||||
\(839\) | −4.92642 | −0.170079 | −0.0850395 | − | 0.996378i | \(-0.527102\pi\) | ||||
−0.0850395 | + | 0.996378i | \(0.527102\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −23.8941 | −0.823933 | ||||||||
\(842\) | 9.59201i | 0.330562i | ||||||||
\(843\) | − 21.3119i | − 0.734022i | ||||||||
\(844\) | 1.80843 | 0.0622486 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 3.51026 | 0.120685 | ||||||||
\(847\) | − 2.75032i | − 0.0945020i | ||||||||
\(848\) | 6.91787i | 0.237561i | ||||||||
\(849\) | 0.864403 | 0.0296662 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 45.5194 | 1.56039 | ||||||||
\(852\) | 0.489254i | 0.0167616i | ||||||||
\(853\) | 53.6476i | 1.83686i | 0.395584 | + | 0.918430i | \(0.370542\pi\) | ||||
−0.395584 | + | 0.918430i | \(0.629458\pi\) | |||||||
\(854\) | −11.3799 | −0.389413 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 16.8138 | 0.574684 | ||||||||
\(857\) | 27.1144i | 0.926210i | 0.886303 | + | 0.463105i | \(0.153265\pi\) | ||||
−0.886303 | + | 0.463105i | \(0.846735\pi\) | |||||||
\(858\) | 16.6906i | 0.569806i | ||||||||
\(859\) | −10.4190 | −0.355493 | −0.177747 | − | 0.984076i | \(-0.556881\pi\) | ||||
−0.177747 | + | 0.984076i | \(0.556881\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −8.32198 | −0.283612 | ||||||||
\(862\) | − 29.6088i | − 1.00848i | ||||||||
\(863\) | − 43.6432i | − 1.48563i | −0.669495 | − | 0.742816i | \(-0.733490\pi\) | ||||
0.669495 | − | 0.742816i | \(-0.266510\pi\) | |||||||
\(864\) | 3.93896 | 0.134006 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 10.5193 | 0.357461 | ||||||||
\(867\) | 12.4957i | 0.424376i | ||||||||
\(868\) | − 8.28864i | − 0.281335i | ||||||||
\(869\) | −31.3319 | −1.06286 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −10.6432 | −0.360632 | ||||||||
\(872\) | − 34.8758i | − 1.18105i | ||||||||
\(873\) | 13.5000i | 0.456905i | ||||||||
\(874\) | −28.1391 | −0.951818 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −5.53456 | −0.186995 | ||||||||
\(877\) | − 53.6435i | − 1.81141i | −0.423907 | − | 0.905706i | \(-0.639342\pi\) | ||||
0.423907 | − | 0.905706i | \(-0.360658\pi\) | |||||||
\(878\) | 0.579102i | 0.0195438i | ||||||||
\(879\) | −3.17701 | −0.107158 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −54.8950 | −1.84946 | −0.924730 | − | 0.380623i | \(-0.875710\pi\) | ||||
−0.924730 | + | 0.380623i | \(0.875710\pi\) | |||||||
\(882\) | − 6.46419i | − 0.217661i | ||||||||
\(883\) | − 19.0952i | − 0.642603i | −0.946977 | − | 0.321302i | \(-0.895880\pi\) | ||||
0.946977 | − | 0.321302i | \(-0.104120\pi\) | |||||||
\(884\) | −6.36700 | −0.214145 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 20.0166 | 0.672471 | ||||||||
\(887\) | 11.2162i | 0.376602i | 0.982111 | + | 0.188301i | \(0.0602980\pi\) | ||||
−0.982111 | + | 0.188301i | \(0.939702\pi\) | |||||||
\(888\) | 22.6743i | 0.760901i | ||||||||
\(889\) | −0.845988 | −0.0283735 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 3.67008 | 0.122952 | ||||||||
\(892\) | − 18.9807i | − 0.635521i | ||||||||
\(893\) | 12.7003i | 0.424998i | ||||||||
\(894\) | 17.5643 | 0.587438 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −1.67977 | −0.0561173 | ||||||||
\(897\) | 25.0188i | 0.835354i | ||||||||
\(898\) | 4.67489i | 0.156003i | ||||||||
\(899\) | 22.7139 | 0.757552 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −7.44857 | −0.248148 | ||||||||
\(902\) | − 30.7781i | − 1.02480i | ||||||||
\(903\) | 10.3020i | 0.342830i | ||||||||
\(904\) | −14.8712 | −0.494608 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −4.44240 | −0.147589 | ||||||||
\(907\) | 36.4513i | 1.21034i | 0.796095 | + | 0.605172i | \(0.206896\pi\) | ||||
−0.796095 | + | 0.605172i | \(0.793104\pi\) | |||||||
\(908\) | − 4.85930i | − 0.161261i | ||||||||
\(909\) | −7.22642 | −0.239685 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1.16533 | 0.0386091 | 0.0193045 | − | 0.999814i | \(-0.493855\pi\) | ||||
0.0193045 | + | 0.999814i | \(0.493855\pi\) | |||||||
\(912\) | − 8.00401i | − 0.265039i | ||||||||
\(913\) | 45.0094i | 1.48959i | ||||||||
\(914\) | −19.8354 | −0.656097 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 5.89621 | 0.194816 | ||||||||
\(917\) | − 16.3219i | − 0.538997i | ||||||||
\(918\) | − 2.38197i | − 0.0786166i | ||||||||
\(919\) | −43.9475 | −1.44969 | −0.724847 | − | 0.688910i | \(-0.758089\pi\) | ||||
−0.724847 | + | 0.688910i | \(0.758089\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −0.507986 | −0.0167387 | ||||||||
\(922\) | − 0.230029i | − 0.00757561i | ||||||||
\(923\) | − 2.67770i | − 0.0881375i | ||||||||
\(924\) | 3.02624 | 0.0995561 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 14.3856 | 0.472739 | ||||||||
\(927\) | − 5.27748i | − 0.173335i | ||||||||
\(928\) | 8.90060i | 0.292176i | ||||||||
\(929\) | −31.2121 | −1.02404 | −0.512019 | − | 0.858974i | \(-0.671102\pi\) | ||||
−0.512019 | + | 0.858974i | \(0.671102\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 23.3876 | 0.766499 | ||||||||
\(932\) | − 6.97506i | − 0.228476i | ||||||||
\(933\) | − 14.6438i | − 0.479418i | ||||||||
\(934\) | 1.24998 | 0.0409006 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −12.4625 | −0.407349 | ||||||||
\(937\) | 45.1060i | 1.47355i | 0.676139 | + | 0.736774i | \(0.263652\pi\) | ||||
−0.676139 | + | 0.736774i | \(0.736348\pi\) | |||||||
\(938\) | − 3.28324i | − 0.107202i | ||||||||
\(939\) | 14.9562 | 0.488076 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −39.1341 | −1.27573 | −0.637867 | − | 0.770146i | \(-0.720183\pi\) | ||||
−0.637867 | + | 0.770146i | \(0.720183\pi\) | |||||||
\(942\) | − 5.05119i | − 0.164577i | ||||||||
\(943\) | − 46.1358i | − 1.50239i | ||||||||
\(944\) | −12.9972 | −0.423023 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −38.1011 | −1.23877 | ||||||||
\(947\) | 48.8537i | 1.58753i | 0.608223 | + | 0.793766i | \(0.291883\pi\) | ||||
−0.608223 | + | 0.793766i | \(0.708117\pi\) | |||||||
\(948\) | − 6.32060i | − 0.205284i | ||||||||
\(949\) | 30.2907 | 0.983278 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 18.1190 | 0.587550 | ||||||||
\(952\) | − 7.26986i | − 0.235618i | ||||||||
\(953\) | 22.7824i | 0.737995i | 0.929430 | + | 0.368998i | \(0.120299\pi\) | ||||
−0.929430 | + | 0.368998i | \(0.879701\pi\) | |||||||
\(954\) | −3.93896 | −0.127528 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 8.30924 | 0.268740 | ||||||||
\(957\) | 8.29302i | 0.268075i | ||||||||
\(958\) | 28.2547i | 0.912868i | ||||||||
\(959\) | −13.6893 | −0.442052 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 70.0435 | 2.25947 | ||||||||
\(962\) | − 33.5274i | − 1.08097i | ||||||||
\(963\) | 5.46682i | 0.176166i | ||||||||
\(964\) | 16.7922 | 0.540841 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −7.71785 | −0.248318 | ||||||||
\(967\) | − 43.1927i | − 1.38898i | −0.719500 | − | 0.694492i | \(-0.755629\pi\) | ||||
0.719500 | − | 0.694492i | \(-0.244371\pi\) | |||||||
\(968\) | 7.59507i | 0.244115i | ||||||||
\(969\) | 8.61803 | 0.276851 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −32.0252 | −1.02774 | −0.513869 | − | 0.857869i | \(-0.671788\pi\) | ||||
−0.513869 | + | 0.857869i | \(0.671788\pi\) | |||||||
\(972\) | 0.740367i | 0.0237473i | ||||||||
\(973\) | 16.4098i | 0.526073i | ||||||||
\(974\) | 11.6271 | 0.372557 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 17.9452 | 0.574413 | ||||||||
\(977\) | 7.27011i | 0.232591i | 0.993215 | + | 0.116296i | \(0.0371020\pi\) | ||||
−0.993215 | + | 0.116296i | \(0.962898\pi\) | |||||||
\(978\) | 2.75408i | 0.0880657i | ||||||||
\(979\) | 56.1085 | 1.79324 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 11.3395 | 0.362042 | ||||||||
\(982\) | − 17.5725i | − 0.560760i | ||||||||
\(983\) | − 5.09155i | − 0.162395i | −0.996698 | − | 0.0811976i | \(-0.974126\pi\) | ||||
0.996698 | − | 0.0811976i | \(-0.0258745\pi\) | |||||||
\(984\) | 22.9813 | 0.732619 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 5.38237 | 0.171410 | ||||||||
\(987\) | 3.48337i | 0.110877i | ||||||||
\(988\) | − 12.1819i | − 0.387559i | ||||||||
\(989\) | −57.1129 | −1.81608 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −62.0762 | −1.97192 | −0.985958 | − | 0.166992i | \(-0.946594\pi\) | ||||
−0.985958 | + | 0.166992i | \(0.946594\pi\) | |||||||
\(992\) | 39.5946i | 1.25713i | ||||||||
\(993\) | 26.3514i | 0.836237i | ||||||||
\(994\) | 0.826021 | 0.0261998 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −9.07979 | −0.287704 | ||||||||
\(997\) | − 2.56895i | − 0.0813594i | −0.999172 | − | 0.0406797i | \(-0.987048\pi\) | ||||
0.999172 | − | 0.0406797i | \(-0.0129523\pi\) | |||||||
\(998\) | − 40.1643i | − 1.27138i | ||||||||
\(999\) | −7.37232 | −0.233250 |
(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.1249.5 | 8 | ||
5.2 | odd | 4 | 1875.2.a.h.1.2 | 4 | |||
5.3 | odd | 4 | 1875.2.a.e.1.3 | 4 | |||
5.4 | even | 2 | inner | 1875.2.b.c.1249.4 | 8 | ||
15.2 | even | 4 | 5625.2.a.i.1.3 | 4 | |||
15.8 | even | 4 | 5625.2.a.n.1.2 | 4 | |||
25.2 | odd | 20 | 75.2.g.b.46.1 | yes | 8 | ||
25.9 | even | 10 | 375.2.i.b.349.3 | 16 | |||
25.11 | even | 5 | 375.2.i.b.274.3 | 16 | |||
25.12 | odd | 20 | 75.2.g.b.31.1 | ✓ | 8 | ||
25.13 | odd | 20 | 375.2.g.b.151.2 | 8 | |||
25.14 | even | 10 | 375.2.i.b.274.2 | 16 | |||
25.16 | even | 5 | 375.2.i.b.349.2 | 16 | |||
25.23 | odd | 20 | 375.2.g.b.226.2 | 8 | |||
75.2 | even | 20 | 225.2.h.c.46.2 | 8 | |||
75.62 | even | 20 | 225.2.h.c.181.2 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
75.2.g.b.31.1 | ✓ | 8 | 25.12 | odd | 20 | ||
75.2.g.b.46.1 | yes | 8 | 25.2 | odd | 20 | ||
225.2.h.c.46.2 | 8 | 75.2 | even | 20 | |||
225.2.h.c.181.2 | 8 | 75.62 | even | 20 | |||
375.2.g.b.151.2 | 8 | 25.13 | odd | 20 | |||
375.2.g.b.226.2 | 8 | 25.23 | odd | 20 | |||
375.2.i.b.274.2 | 16 | 25.14 | even | 10 | |||
375.2.i.b.274.3 | 16 | 25.11 | even | 5 | |||
375.2.i.b.349.2 | 16 | 25.16 | even | 5 | |||
375.2.i.b.349.3 | 16 | 25.9 | even | 10 | |||
1875.2.a.e.1.3 | 4 | 5.3 | odd | 4 | |||
1875.2.a.h.1.2 | 4 | 5.2 | odd | 4 | |||
1875.2.b.c.1249.4 | 8 | 5.4 | even | 2 | inner | ||
1875.2.b.c.1249.5 | 8 | 1.1 | even | 1 | trivial | ||
5625.2.a.i.1.3 | 4 | 15.2 | even | 4 | |||
5625.2.a.n.1.2 | 4 | 15.8 | even | 4 |