Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [5265,2,Mod(1,5265)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5265, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("5265.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 5265 = 3^{4} \cdot 5 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 5265.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(42.0412366642\) |
Analytic rank: | \(1\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 3x^{7} - 8x^{6} + 31x^{5} - x^{4} - 70x^{3} + 66x^{2} - 19x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 585) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(0.494096\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 5265.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.494096 | 0.349379 | 0.174689 | − | 0.984624i | \(-0.444108\pi\) | ||||
0.174689 | + | 0.984624i | \(0.444108\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.75587 | −0.877935 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −4.28539 | −1.61972 | −0.809862 | − | 0.586621i | \(-0.800458\pi\) | ||||
−0.809862 | + | 0.586621i | \(0.800458\pi\) | |||||||
\(8\) | −1.85576 | −0.656110 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −0.494096 | −0.156247 | ||||||||
\(11\) | 4.48530 | 1.35237 | 0.676185 | − | 0.736732i | \(-0.263632\pi\) | ||||
0.676185 | + | 0.736732i | \(0.263632\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.00000 | −0.277350 | ||||||||
\(14\) | −2.11739 | −0.565897 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 2.59482 | 0.648704 | ||||||||
\(17\) | 1.57196 | 0.381256 | 0.190628 | − | 0.981662i | \(-0.438948\pi\) | ||||
0.190628 | + | 0.981662i | \(0.438948\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.86934 | 0.428857 | 0.214429 | − | 0.976740i | \(-0.431211\pi\) | ||||
0.214429 | + | 0.976740i | \(0.431211\pi\) | |||||||
\(20\) | 1.75587 | 0.392624 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 2.21617 | 0.472489 | ||||||||
\(23\) | −5.25780 | −1.09633 | −0.548163 | − | 0.836371i | \(-0.684673\pi\) | ||||
−0.548163 | + | 0.836371i | \(0.684673\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | −0.494096 | −0.0969002 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 7.52458 | 1.42201 | ||||||||
\(29\) | −0.750308 | −0.139329 | −0.0696644 | − | 0.997570i | \(-0.522193\pi\) | ||||
−0.0696644 | + | 0.997570i | \(0.522193\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 10.2013 | 1.83222 | 0.916108 | − | 0.400931i | \(-0.131313\pi\) | ||||
0.916108 | + | 0.400931i | \(0.131313\pi\) | |||||||
\(32\) | 4.99361 | 0.882753 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0.776699 | 0.133203 | ||||||||
\(35\) | 4.28539 | 0.724362 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.78257 | 0.457452 | 0.228726 | − | 0.973491i | \(-0.426544\pi\) | ||||
0.228726 | + | 0.973491i | \(0.426544\pi\) | |||||||
\(38\) | 0.923636 | 0.149833 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 1.85576 | 0.293421 | ||||||||
\(41\) | −6.36016 | −0.993289 | −0.496645 | − | 0.867954i | \(-0.665435\pi\) | ||||
−0.496645 | + | 0.867954i | \(0.665435\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 7.59324 | 1.15796 | 0.578979 | − | 0.815342i | \(-0.303451\pi\) | ||||
0.578979 | + | 0.815342i | \(0.303451\pi\) | |||||||
\(44\) | −7.87560 | −1.18729 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −2.59786 | −0.383033 | ||||||||
\(47\) | −8.27021 | −1.20633 | −0.603167 | − | 0.797615i | \(-0.706095\pi\) | ||||
−0.603167 | + | 0.797615i | \(0.706095\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 11.3645 | 1.62350 | ||||||||
\(50\) | 0.494096 | 0.0698757 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 1.75587 | 0.243495 | ||||||||
\(53\) | 0.0752567 | 0.0103373 | 0.00516865 | − | 0.999987i | \(-0.498355\pi\) | ||||
0.00516865 | + | 0.999987i | \(0.498355\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −4.48530 | −0.604798 | ||||||||
\(56\) | 7.95265 | 1.06272 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −0.370724 | −0.0486785 | ||||||||
\(59\) | 11.4407 | 1.48946 | 0.744728 | − | 0.667368i | \(-0.232579\pi\) | ||||
0.744728 | + | 0.667368i | \(0.232579\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −11.9600 | −1.53133 | −0.765663 | − | 0.643241i | \(-0.777589\pi\) | ||||
−0.765663 | + | 0.643241i | \(0.777589\pi\) | |||||||
\(62\) | 5.04044 | 0.640137 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −2.72231 | −0.340289 | ||||||||
\(65\) | 1.00000 | 0.124035 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −12.8975 | −1.57568 | −0.787839 | − | 0.615881i | \(-0.788800\pi\) | ||||
−0.787839 | + | 0.615881i | \(0.788800\pi\) | |||||||
\(68\) | −2.76016 | −0.334718 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 2.11739 | 0.253077 | ||||||||
\(71\) | 14.4466 | 1.71450 | 0.857250 | − | 0.514900i | \(-0.172171\pi\) | ||||
0.857250 | + | 0.514900i | \(0.172171\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 9.37293 | 1.09702 | 0.548509 | − | 0.836144i | \(-0.315196\pi\) | ||||
0.548509 | + | 0.836144i | \(0.315196\pi\) | |||||||
\(74\) | 1.37486 | 0.159824 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −3.28232 | −0.376508 | ||||||||
\(77\) | −19.2212 | −2.19046 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −6.09918 | −0.686212 | −0.343106 | − | 0.939297i | \(-0.611479\pi\) | ||||
−0.343106 | + | 0.939297i | \(0.611479\pi\) | |||||||
\(80\) | −2.59482 | −0.290109 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −3.14253 | −0.347034 | ||||||||
\(83\) | 0.612178 | 0.0671953 | 0.0335976 | − | 0.999435i | \(-0.489304\pi\) | ||||
0.0335976 | + | 0.999435i | \(0.489304\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.57196 | −0.170503 | ||||||||
\(86\) | 3.75179 | 0.404566 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −8.32364 | −0.887303 | ||||||||
\(89\) | −16.2485 | −1.72234 | −0.861169 | − | 0.508319i | \(-0.830267\pi\) | ||||
−0.861169 | + | 0.508319i | \(0.830267\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 4.28539 | 0.449230 | ||||||||
\(92\) | 9.23201 | 0.962503 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −4.08628 | −0.421467 | ||||||||
\(95\) | −1.86934 | −0.191791 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −14.9940 | −1.52241 | −0.761207 | − | 0.648509i | \(-0.775393\pi\) | ||||
−0.761207 | + | 0.648509i | \(0.775393\pi\) | |||||||
\(98\) | 5.61517 | 0.567218 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −1.75587 | −0.175587 | ||||||||
\(101\) | 10.8897 | 1.08357 | 0.541785 | − | 0.840517i | \(-0.317749\pi\) | ||||
0.541785 | + | 0.840517i | \(0.317749\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1.53733 | −0.151478 | −0.0757390 | − | 0.997128i | \(-0.524132\pi\) | ||||
−0.0757390 | + | 0.997128i | \(0.524132\pi\) | |||||||
\(104\) | 1.85576 | 0.181972 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0.0371840 | 0.00361163 | ||||||||
\(107\) | −5.43803 | −0.525715 | −0.262857 | − | 0.964835i | \(-0.584665\pi\) | ||||
−0.262857 | + | 0.964835i | \(0.584665\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1.44466 | 0.138374 | 0.0691868 | − | 0.997604i | \(-0.477960\pi\) | ||||
0.0691868 | + | 0.997604i | \(0.477960\pi\) | |||||||
\(110\) | −2.21617 | −0.211303 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −11.1198 | −1.05072 | ||||||||
\(113\) | 4.46478 | 0.420011 | 0.210006 | − | 0.977700i | \(-0.432652\pi\) | ||||
0.210006 | + | 0.977700i | \(0.432652\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 5.25780 | 0.490292 | ||||||||
\(116\) | 1.31744 | 0.122322 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 5.65282 | 0.520384 | ||||||||
\(119\) | −6.73645 | −0.617530 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 9.11794 | 0.828903 | ||||||||
\(122\) | −5.90941 | −0.535013 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −17.9122 | −1.60857 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −3.92097 | −0.347930 | −0.173965 | − | 0.984752i | \(-0.555658\pi\) | ||||
−0.173965 | + | 0.984752i | \(0.555658\pi\) | |||||||
\(128\) | −11.3323 | −1.00164 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0.494096 | 0.0433351 | ||||||||
\(131\) | 0.774428 | 0.0676620 | 0.0338310 | − | 0.999428i | \(-0.489229\pi\) | ||||
0.0338310 | + | 0.999428i | \(0.489229\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −8.01086 | −0.694630 | ||||||||
\(134\) | −6.37259 | −0.550508 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −2.91718 | −0.250146 | ||||||||
\(137\) | 4.70810 | 0.402240 | 0.201120 | − | 0.979567i | \(-0.435542\pi\) | ||||
0.201120 | + | 0.979567i | \(0.435542\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −6.96691 | −0.590926 | −0.295463 | − | 0.955354i | \(-0.595474\pi\) | ||||
−0.295463 | + | 0.955354i | \(0.595474\pi\) | |||||||
\(140\) | −7.52458 | −0.635943 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 7.13803 | 0.599010 | ||||||||
\(143\) | −4.48530 | −0.375080 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0.750308 | 0.0623097 | ||||||||
\(146\) | 4.63113 | 0.383275 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −4.88583 | −0.401613 | ||||||||
\(149\) | −8.23725 | −0.674822 | −0.337411 | − | 0.941357i | \(-0.609551\pi\) | ||||
−0.337411 | + | 0.941357i | \(0.609551\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −8.77188 | −0.713846 | −0.356923 | − | 0.934134i | \(-0.616174\pi\) | ||||
−0.356923 | + | 0.934134i | \(0.616174\pi\) | |||||||
\(152\) | −3.46905 | −0.281377 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −9.49714 | −0.765301 | ||||||||
\(155\) | −10.2013 | −0.819392 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −13.3937 | −1.06894 | −0.534468 | − | 0.845189i | \(-0.679488\pi\) | ||||
−0.534468 | + | 0.845189i | \(0.679488\pi\) | |||||||
\(158\) | −3.01358 | −0.239748 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −4.99361 | −0.394779 | ||||||||
\(161\) | 22.5317 | 1.77575 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −0.242444 | −0.0189897 | −0.00949486 | − | 0.999955i | \(-0.503022\pi\) | ||||
−0.00949486 | + | 0.999955i | \(0.503022\pi\) | |||||||
\(164\) | 11.1676 | 0.872043 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0.302475 | 0.0234766 | ||||||||
\(167\) | 5.08610 | 0.393575 | 0.196787 | − | 0.980446i | \(-0.436949\pi\) | ||||
0.196787 | + | 0.980446i | \(0.436949\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | −0.776699 | −0.0595701 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −13.3327 | −1.01661 | ||||||||
\(173\) | −23.1711 | −1.76166 | −0.880831 | − | 0.473430i | \(-0.843016\pi\) | ||||
−0.880831 | + | 0.473430i | \(0.843016\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −4.28539 | −0.323945 | ||||||||
\(176\) | 11.6385 | 0.877287 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −8.02832 | −0.601748 | ||||||||
\(179\) | 13.9237 | 1.04070 | 0.520352 | − | 0.853952i | \(-0.325801\pi\) | ||||
0.520352 | + | 0.853952i | \(0.325801\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 13.6884 | 1.01745 | 0.508725 | − | 0.860929i | \(-0.330117\pi\) | ||||
0.508725 | + | 0.860929i | \(0.330117\pi\) | |||||||
\(182\) | 2.11739 | 0.156951 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 9.75721 | 0.719311 | ||||||||
\(185\) | −2.78257 | −0.204579 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 7.05071 | 0.515599 | ||||||||
\(188\) | 14.5214 | 1.05908 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −0.923636 | −0.0670076 | ||||||||
\(191\) | −7.84336 | −0.567525 | −0.283763 | − | 0.958895i | \(-0.591583\pi\) | ||||
−0.283763 | + | 0.958895i | \(0.591583\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −20.6518 | −1.48655 | −0.743274 | − | 0.668987i | \(-0.766728\pi\) | ||||
−0.743274 | + | 0.668987i | \(0.766728\pi\) | |||||||
\(194\) | −7.40850 | −0.531899 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −19.9546 | −1.42533 | ||||||||
\(197\) | 4.38617 | 0.312502 | 0.156251 | − | 0.987717i | \(-0.450059\pi\) | ||||
0.156251 | + | 0.987717i | \(0.450059\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −13.3916 | −0.949304 | −0.474652 | − | 0.880174i | \(-0.657426\pi\) | ||||
−0.474652 | + | 0.880174i | \(0.657426\pi\) | |||||||
\(200\) | −1.85576 | −0.131222 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 5.38058 | 0.378576 | ||||||||
\(203\) | 3.21536 | 0.225674 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 6.36016 | 0.444213 | ||||||||
\(206\) | −0.759591 | −0.0529232 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −2.59482 | −0.179918 | ||||||||
\(209\) | 8.38458 | 0.579973 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −6.06986 | −0.417866 | −0.208933 | − | 0.977930i | \(-0.566999\pi\) | ||||
−0.208933 | + | 0.977930i | \(0.566999\pi\) | |||||||
\(212\) | −0.132141 | −0.00907547 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −2.68691 | −0.183673 | ||||||||
\(215\) | −7.59324 | −0.517855 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −43.7167 | −2.96768 | ||||||||
\(218\) | 0.713802 | 0.0483448 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 7.87560 | 0.530973 | ||||||||
\(221\) | −1.57196 | −0.105741 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −22.9881 | −1.53940 | −0.769700 | − | 0.638406i | \(-0.779594\pi\) | ||||
−0.769700 | + | 0.638406i | \(0.779594\pi\) | |||||||
\(224\) | −21.3995 | −1.42982 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 2.20603 | 0.146743 | ||||||||
\(227\) | −18.8346 | −1.25010 | −0.625050 | − | 0.780585i | \(-0.714921\pi\) | ||||
−0.625050 | + | 0.780585i | \(0.714921\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −5.40926 | −0.357454 | −0.178727 | − | 0.983899i | \(-0.557198\pi\) | ||||
−0.178727 | + | 0.983899i | \(0.557198\pi\) | |||||||
\(230\) | 2.59786 | 0.171298 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 1.39239 | 0.0914150 | ||||||||
\(233\) | −7.45934 | −0.488677 | −0.244339 | − | 0.969690i | \(-0.578571\pi\) | ||||
−0.244339 | + | 0.969690i | \(0.578571\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 8.27021 | 0.539489 | ||||||||
\(236\) | −20.0884 | −1.30765 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −3.32845 | −0.215752 | ||||||||
\(239\) | 7.68073 | 0.496825 | 0.248412 | − | 0.968654i | \(-0.420091\pi\) | ||||
0.248412 | + | 0.968654i | \(0.420091\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 29.2801 | 1.88610 | 0.943048 | − | 0.332657i | \(-0.107945\pi\) | ||||
0.943048 | + | 0.332657i | \(0.107945\pi\) | |||||||
\(242\) | 4.50514 | 0.289601 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 21.0003 | 1.34440 | ||||||||
\(245\) | −11.3645 | −0.726053 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1.86934 | −0.118944 | ||||||||
\(248\) | −18.9312 | −1.20214 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −0.494096 | −0.0312494 | ||||||||
\(251\) | −26.6402 | −1.68152 | −0.840758 | − | 0.541412i | \(-0.817890\pi\) | ||||
−0.840758 | + | 0.541412i | \(0.817890\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −23.5828 | −1.48264 | ||||||||
\(254\) | −1.93733 | −0.121559 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.154621 | −0.00966380 | ||||||||
\(257\) | −0.712283 | −0.0444310 | −0.0222155 | − | 0.999753i | \(-0.507072\pi\) | ||||
−0.0222155 | + | 0.999753i | \(0.507072\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −11.9244 | −0.740946 | ||||||||
\(260\) | −1.75587 | −0.108894 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0.382641 | 0.0236397 | ||||||||
\(263\) | −13.2030 | −0.814134 | −0.407067 | − | 0.913398i | \(-0.633448\pi\) | ||||
−0.407067 | + | 0.913398i | \(0.633448\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −0.0752567 | −0.00462298 | ||||||||
\(266\) | −3.95813 | −0.242689 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 22.6463 | 1.38334 | ||||||||
\(269\) | −18.3263 | −1.11737 | −0.558687 | − | 0.829379i | \(-0.688695\pi\) | ||||
−0.558687 | + | 0.829379i | \(0.688695\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −28.9102 | −1.75617 | −0.878084 | − | 0.478507i | \(-0.841178\pi\) | ||||
−0.878084 | + | 0.478507i | \(0.841178\pi\) | |||||||
\(272\) | 4.07894 | 0.247322 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 2.32625 | 0.140534 | ||||||||
\(275\) | 4.48530 | 0.270474 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 26.1305 | 1.57003 | 0.785014 | − | 0.619478i | \(-0.212656\pi\) | ||||
0.785014 | + | 0.619478i | \(0.212656\pi\) | |||||||
\(278\) | −3.44232 | −0.206457 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −7.95265 | −0.475261 | ||||||||
\(281\) | 27.6778 | 1.65112 | 0.825559 | − | 0.564315i | \(-0.190860\pi\) | ||||
0.825559 | + | 0.564315i | \(0.190860\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 26.1441 | 1.55411 | 0.777053 | − | 0.629436i | \(-0.216714\pi\) | ||||
0.777053 | + | 0.629436i | \(0.216714\pi\) | |||||||
\(284\) | −25.3664 | −1.50522 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −2.21617 | −0.131045 | ||||||||
\(287\) | 27.2557 | 1.60885 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −14.5289 | −0.854644 | ||||||||
\(290\) | 0.370724 | 0.0217697 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −16.4576 | −0.963111 | ||||||||
\(293\) | 4.01651 | 0.234647 | 0.117323 | − | 0.993094i | \(-0.462569\pi\) | ||||
0.117323 | + | 0.993094i | \(0.462569\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −11.4407 | −0.666105 | ||||||||
\(296\) | −5.16379 | −0.300139 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −4.06999 | −0.235768 | ||||||||
\(299\) | 5.25780 | 0.304066 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −32.5400 | −1.87557 | ||||||||
\(302\) | −4.33415 | −0.249402 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 4.85060 | 0.278201 | ||||||||
\(305\) | 11.9600 | 0.684830 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −7.51331 | −0.428807 | −0.214404 | − | 0.976745i | \(-0.568781\pi\) | ||||
−0.214404 | + | 0.976745i | \(0.568781\pi\) | |||||||
\(308\) | 33.7500 | 1.92308 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −5.04044 | −0.286278 | ||||||||
\(311\) | 21.0401 | 1.19307 | 0.596537 | − | 0.802586i | \(-0.296543\pi\) | ||||
0.596537 | + | 0.802586i | \(0.296543\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −6.50014 | −0.367410 | −0.183705 | − | 0.982981i | \(-0.558809\pi\) | ||||
−0.183705 | + | 0.982981i | \(0.558809\pi\) | |||||||
\(314\) | −6.61779 | −0.373463 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 10.7094 | 0.602449 | ||||||||
\(317\) | −11.4558 | −0.643422 | −0.321711 | − | 0.946838i | \(-0.604258\pi\) | ||||
−0.321711 | + | 0.946838i | \(0.604258\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −3.36536 | −0.188424 | ||||||||
\(320\) | 2.72231 | 0.152182 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 11.1328 | 0.620408 | ||||||||
\(323\) | 2.93853 | 0.163504 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1.00000 | −0.0554700 | ||||||||
\(326\) | −0.119791 | −0.00663460 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 11.8029 | 0.651707 | ||||||||
\(329\) | 35.4410 | 1.95393 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −24.3594 | −1.33891 | −0.669456 | − | 0.742852i | \(-0.733473\pi\) | ||||
−0.669456 | + | 0.742852i | \(0.733473\pi\) | |||||||
\(332\) | −1.07490 | −0.0589931 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 2.51302 | 0.137507 | ||||||||
\(335\) | 12.8975 | 0.704665 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 11.6002 | 0.631902 | 0.315951 | − | 0.948776i | \(-0.397677\pi\) | ||||
0.315951 | + | 0.948776i | \(0.397677\pi\) | |||||||
\(338\) | 0.494096 | 0.0268753 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 2.76016 | 0.149690 | ||||||||
\(341\) | 45.7561 | 2.47783 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −18.7037 | −1.00990 | ||||||||
\(344\) | −14.0912 | −0.759748 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −11.4487 | −0.615487 | ||||||||
\(347\) | −12.1820 | −0.653964 | −0.326982 | − | 0.945031i | \(-0.606032\pi\) | ||||
−0.326982 | + | 0.945031i | \(0.606032\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 7.91102 | 0.423467 | 0.211734 | − | 0.977327i | \(-0.432089\pi\) | ||||
0.211734 | + | 0.977327i | \(0.432089\pi\) | |||||||
\(350\) | −2.11739 | −0.113179 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 22.3978 | 1.19381 | ||||||||
\(353\) | 21.2588 | 1.13149 | 0.565747 | − | 0.824579i | \(-0.308588\pi\) | ||||
0.565747 | + | 0.824579i | \(0.308588\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −14.4466 | −0.766748 | ||||||||
\(356\) | 28.5302 | 1.51210 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 6.87962 | 0.363599 | ||||||||
\(359\) | −7.59638 | −0.400922 | −0.200461 | − | 0.979702i | \(-0.564244\pi\) | ||||
−0.200461 | + | 0.979702i | \(0.564244\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −15.5056 | −0.816082 | ||||||||
\(362\) | 6.76337 | 0.355475 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −7.52458 | −0.394395 | ||||||||
\(365\) | −9.37293 | −0.490602 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 21.6141 | 1.12825 | 0.564124 | − | 0.825690i | \(-0.309214\pi\) | ||||
0.564124 | + | 0.825690i | \(0.309214\pi\) | |||||||
\(368\) | −13.6430 | −0.711191 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −1.37486 | −0.0714754 | ||||||||
\(371\) | −0.322504 | −0.0167436 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −12.0134 | −0.622028 | −0.311014 | − | 0.950405i | \(-0.600669\pi\) | ||||
−0.311014 | + | 0.950405i | \(0.600669\pi\) | |||||||
\(374\) | 3.48373 | 0.180139 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 15.3475 | 0.791488 | ||||||||
\(377\) | 0.750308 | 0.0386429 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −3.44005 | −0.176704 | −0.0883518 | − | 0.996089i | \(-0.528160\pi\) | ||||
−0.0883518 | + | 0.996089i | \(0.528160\pi\) | |||||||
\(380\) | 3.28232 | 0.168380 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −3.87537 | −0.198281 | ||||||||
\(383\) | 26.8988 | 1.37446 | 0.687232 | − | 0.726438i | \(-0.258826\pi\) | ||||
0.687232 | + | 0.726438i | \(0.258826\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 19.2212 | 0.979606 | ||||||||
\(386\) | −10.2040 | −0.519368 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 26.3276 | 1.33658 | ||||||||
\(389\) | 3.33515 | 0.169099 | 0.0845494 | − | 0.996419i | \(-0.473055\pi\) | ||||
0.0845494 | + | 0.996419i | \(0.473055\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −8.26504 | −0.417981 | ||||||||
\(392\) | −21.0898 | −1.06520 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 2.16719 | 0.109181 | ||||||||
\(395\) | 6.09918 | 0.306883 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 0.768687 | 0.0385793 | 0.0192897 | − | 0.999814i | \(-0.493860\pi\) | ||||
0.0192897 | + | 0.999814i | \(0.493860\pi\) | |||||||
\(398\) | −6.61672 | −0.331666 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 2.59482 | 0.129741 | ||||||||
\(401\) | 29.6031 | 1.47831 | 0.739153 | − | 0.673537i | \(-0.235226\pi\) | ||||
0.739153 | + | 0.673537i | \(0.235226\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −10.2013 | −0.508165 | ||||||||
\(404\) | −19.1210 | −0.951303 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 1.58870 | 0.0788457 | ||||||||
\(407\) | 12.4807 | 0.618644 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −16.2011 | −0.801092 | −0.400546 | − | 0.916277i | \(-0.631180\pi\) | ||||
−0.400546 | + | 0.916277i | \(0.631180\pi\) | |||||||
\(410\) | 3.14253 | 0.155198 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 2.69936 | 0.132988 | ||||||||
\(413\) | −49.0279 | −2.41251 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −0.612178 | −0.0300506 | ||||||||
\(416\) | −4.99361 | −0.244832 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 4.14278 | 0.202630 | ||||||||
\(419\) | 11.4127 | 0.557546 | 0.278773 | − | 0.960357i | \(-0.410072\pi\) | ||||
0.278773 | + | 0.960357i | \(0.410072\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 10.3983 | 0.506784 | 0.253392 | − | 0.967364i | \(-0.418454\pi\) | ||||
0.253392 | + | 0.967364i | \(0.418454\pi\) | |||||||
\(422\) | −2.99909 | −0.145994 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −0.139658 | −0.00678241 | ||||||||
\(425\) | 1.57196 | 0.0762512 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 51.2534 | 2.48033 | ||||||||
\(428\) | 9.54848 | 0.461543 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −3.75179 | −0.180927 | ||||||||
\(431\) | −0.879972 | −0.0423868 | −0.0211934 | − | 0.999775i | \(-0.506747\pi\) | ||||
−0.0211934 | + | 0.999775i | \(0.506747\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 31.4562 | 1.51169 | 0.755845 | − | 0.654750i | \(-0.227226\pi\) | ||||
0.755845 | + | 0.654750i | \(0.227226\pi\) | |||||||
\(434\) | −21.6002 | −1.03684 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −2.53664 | −0.121483 | ||||||||
\(437\) | −9.82864 | −0.470167 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −5.76414 | −0.275108 | −0.137554 | − | 0.990494i | \(-0.543924\pi\) | ||||
−0.137554 | + | 0.990494i | \(0.543924\pi\) | |||||||
\(440\) | 8.32364 | 0.396814 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −0.776699 | −0.0369438 | ||||||||
\(443\) | 4.12846 | 0.196149 | 0.0980746 | − | 0.995179i | \(-0.468732\pi\) | ||||
0.0980746 | + | 0.995179i | \(0.468732\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 16.2485 | 0.770253 | ||||||||
\(446\) | −11.3583 | −0.537833 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 11.6661 | 0.551174 | ||||||||
\(449\) | −30.3402 | −1.43184 | −0.715921 | − | 0.698181i | \(-0.753993\pi\) | ||||
−0.715921 | + | 0.698181i | \(0.753993\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −28.5272 | −1.34329 | ||||||||
\(452\) | −7.83957 | −0.368742 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −9.30612 | −0.436758 | ||||||||
\(455\) | −4.28539 | −0.200902 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −8.46282 | −0.395874 | −0.197937 | − | 0.980215i | \(-0.563424\pi\) | ||||
−0.197937 | + | 0.980215i | \(0.563424\pi\) | |||||||
\(458\) | −2.67269 | −0.124887 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −9.23201 | −0.430444 | ||||||||
\(461\) | 17.6308 | 0.821149 | 0.410575 | − | 0.911827i | \(-0.365328\pi\) | ||||
0.410575 | + | 0.911827i | \(0.365328\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −1.25439 | −0.0582962 | −0.0291481 | − | 0.999575i | \(-0.509279\pi\) | ||||
−0.0291481 | + | 0.999575i | \(0.509279\pi\) | |||||||
\(464\) | −1.94691 | −0.0903831 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −3.68563 | −0.170733 | ||||||||
\(467\) | 11.3158 | 0.523634 | 0.261817 | − | 0.965117i | \(-0.415678\pi\) | ||||
0.261817 | + | 0.965117i | \(0.415678\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 55.2707 | 2.55216 | ||||||||
\(470\) | 4.08628 | 0.188486 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −21.2312 | −0.977247 | ||||||||
\(473\) | 34.0580 | 1.56599 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.86934 | 0.0857714 | ||||||||
\(476\) | 11.8283 | 0.542151 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 3.79502 | 0.173580 | ||||||||
\(479\) | −33.3836 | −1.52533 | −0.762667 | − | 0.646791i | \(-0.776111\pi\) | ||||
−0.762667 | + | 0.646791i | \(0.776111\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2.78257 | −0.126874 | ||||||||
\(482\) | 14.4672 | 0.658961 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −16.0099 | −0.727723 | ||||||||
\(485\) | 14.9940 | 0.680844 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −42.2806 | −1.91592 | −0.957959 | − | 0.286904i | \(-0.907374\pi\) | ||||
−0.957959 | + | 0.286904i | \(0.907374\pi\) | |||||||
\(488\) | 22.1950 | 1.00472 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −5.61517 | −0.253667 | ||||||||
\(491\) | 11.4657 | 0.517441 | 0.258720 | − | 0.965952i | \(-0.416699\pi\) | ||||
0.258720 | + | 0.965952i | \(0.416699\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1.17945 | −0.0531200 | ||||||||
\(494\) | −0.923636 | −0.0415563 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 26.4706 | 1.18857 | ||||||||
\(497\) | −61.9094 | −2.77702 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 6.70853 | 0.300315 | 0.150157 | − | 0.988662i | \(-0.452022\pi\) | ||||
0.150157 | + | 0.988662i | \(0.452022\pi\) | |||||||
\(500\) | 1.75587 | 0.0785249 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −13.1628 | −0.587485 | ||||||||
\(503\) | 13.1409 | 0.585925 | 0.292963 | − | 0.956124i | \(-0.405359\pi\) | ||||
0.292963 | + | 0.956124i | \(0.405359\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −10.8897 | −0.484587 | ||||||||
\(506\) | −11.6522 | −0.518002 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 6.88471 | 0.305459 | ||||||||
\(509\) | −31.1201 | −1.37937 | −0.689687 | − | 0.724107i | \(-0.742252\pi\) | ||||
−0.689687 | + | 0.724107i | \(0.742252\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −40.1666 | −1.77687 | ||||||||
\(512\) | 22.5882 | 0.998267 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −0.351936 | −0.0155232 | ||||||||
\(515\) | 1.53733 | 0.0677431 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −37.0944 | −1.63141 | ||||||||
\(518\) | −5.89179 | −0.258871 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −1.85576 | −0.0813804 | ||||||||
\(521\) | 10.6889 | 0.468287 | 0.234144 | − | 0.972202i | \(-0.424771\pi\) | ||||
0.234144 | + | 0.972202i | \(0.424771\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −22.8750 | −1.00025 | −0.500127 | − | 0.865952i | \(-0.666713\pi\) | ||||
−0.500127 | + | 0.865952i | \(0.666713\pi\) | |||||||
\(524\) | −1.35979 | −0.0594029 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −6.52357 | −0.284441 | ||||||||
\(527\) | 16.0361 | 0.698544 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 4.64444 | 0.201932 | ||||||||
\(530\) | −0.0371840 | −0.00161517 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 14.0660 | 0.609840 | ||||||||
\(533\) | 6.36016 | 0.275489 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 5.43803 | 0.235107 | ||||||||
\(536\) | 23.9346 | 1.03382 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −9.05495 | −0.390387 | ||||||||
\(539\) | 50.9733 | 2.19558 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −13.5880 | −0.584192 | −0.292096 | − | 0.956389i | \(-0.594353\pi\) | ||||
−0.292096 | + | 0.956389i | \(0.594353\pi\) | |||||||
\(542\) | −14.2844 | −0.613567 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 7.84975 | 0.336555 | ||||||||
\(545\) | −1.44466 | −0.0618825 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 23.9636 | 1.02461 | 0.512305 | − | 0.858804i | \(-0.328792\pi\) | ||||
0.512305 | + | 0.858804i | \(0.328792\pi\) | |||||||
\(548\) | −8.26680 | −0.353140 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 2.21617 | 0.0944978 | ||||||||
\(551\) | −1.40259 | −0.0597521 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 26.1374 | 1.11147 | ||||||||
\(554\) | 12.9110 | 0.548534 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 12.2330 | 0.518794 | ||||||||
\(557\) | 0.501996 | 0.0212702 | 0.0106351 | − | 0.999943i | \(-0.496615\pi\) | ||||
0.0106351 | + | 0.999943i | \(0.496615\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −7.59324 | −0.321160 | ||||||||
\(560\) | 11.1198 | 0.469897 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 13.6755 | 0.576866 | ||||||||
\(563\) | 16.9153 | 0.712893 | 0.356447 | − | 0.934316i | \(-0.383988\pi\) | ||||
0.356447 | + | 0.934316i | \(0.383988\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −4.46478 | −0.187835 | ||||||||
\(566\) | 12.9177 | 0.542971 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −26.8095 | −1.12490 | ||||||||
\(569\) | −24.1253 | −1.01139 | −0.505693 | − | 0.862714i | \(-0.668763\pi\) | ||||
−0.505693 | + | 0.862714i | \(0.668763\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −14.6557 | −0.613323 | −0.306661 | − | 0.951819i | \(-0.599212\pi\) | ||||
−0.306661 | + | 0.951819i | \(0.599212\pi\) | |||||||
\(572\) | 7.87560 | 0.329296 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 13.4669 | 0.562099 | ||||||||
\(575\) | −5.25780 | −0.219265 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 4.42835 | 0.184355 | 0.0921774 | − | 0.995743i | \(-0.470617\pi\) | ||||
0.0921774 | + | 0.995743i | \(0.470617\pi\) | |||||||
\(578\) | −7.17869 | −0.298594 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −1.31744 | −0.0547039 | ||||||||
\(581\) | −2.62342 | −0.108838 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0.337549 | 0.0139798 | ||||||||
\(584\) | −17.3939 | −0.719765 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 1.98454 | 0.0819806 | ||||||||
\(587\) | −6.81157 | −0.281143 | −0.140572 | − | 0.990071i | \(-0.544894\pi\) | ||||
−0.140572 | + | 0.990071i | \(0.544894\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 19.0698 | 0.785759 | ||||||||
\(590\) | −5.65282 | −0.232723 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 7.22026 | 0.296751 | ||||||||
\(593\) | 9.71004 | 0.398744 | 0.199372 | − | 0.979924i | \(-0.436110\pi\) | ||||
0.199372 | + | 0.979924i | \(0.436110\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 6.73645 | 0.276168 | ||||||||
\(596\) | 14.4635 | 0.592450 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 2.59786 | 0.106234 | ||||||||
\(599\) | 22.2733 | 0.910064 | 0.455032 | − | 0.890475i | \(-0.349628\pi\) | ||||
0.455032 | + | 0.890475i | \(0.349628\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 13.5423 | 0.552402 | 0.276201 | − | 0.961100i | \(-0.410924\pi\) | ||||
0.276201 | + | 0.961100i | \(0.410924\pi\) | |||||||
\(602\) | −16.0779 | −0.655285 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 15.4023 | 0.626710 | ||||||||
\(605\) | −9.11794 | −0.370697 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −4.76397 | −0.193364 | −0.0966818 | − | 0.995315i | \(-0.530823\pi\) | ||||
−0.0966818 | + | 0.995315i | \(0.530823\pi\) | |||||||
\(608\) | 9.33477 | 0.378575 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 5.90941 | 0.239265 | ||||||||
\(611\) | 8.27021 | 0.334577 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −7.58211 | −0.306238 | −0.153119 | − | 0.988208i | \(-0.548932\pi\) | ||||
−0.153119 | + | 0.988208i | \(0.548932\pi\) | |||||||
\(614\) | −3.71230 | −0.149816 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 35.6700 | 1.43719 | ||||||||
\(617\) | 14.5642 | 0.586331 | 0.293166 | − | 0.956062i | \(-0.405291\pi\) | ||||
0.293166 | + | 0.956062i | \(0.405291\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −42.7018 | −1.71633 | −0.858165 | − | 0.513374i | \(-0.828395\pi\) | ||||
−0.858165 | + | 0.513374i | \(0.828395\pi\) | |||||||
\(620\) | 17.9122 | 0.719373 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 10.3958 | 0.416835 | ||||||||
\(623\) | 69.6311 | 2.78971 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −3.21169 | −0.128365 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 23.5176 | 0.938456 | ||||||||
\(629\) | 4.37409 | 0.174406 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −35.7936 | −1.42492 | −0.712461 | − | 0.701712i | \(-0.752419\pi\) | ||||
−0.712461 | + | 0.701712i | \(0.752419\pi\) | |||||||
\(632\) | 11.3186 | 0.450231 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −5.66026 | −0.224798 | ||||||||
\(635\) | 3.92097 | 0.155599 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −11.3645 | −0.450279 | ||||||||
\(638\) | −1.66281 | −0.0658313 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 11.3323 | 0.447948 | ||||||||
\(641\) | 11.4684 | 0.452973 | 0.226486 | − | 0.974014i | \(-0.427276\pi\) | ||||
0.226486 | + | 0.974014i | \(0.427276\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −28.9956 | −1.14348 | −0.571738 | − | 0.820436i | \(-0.693731\pi\) | ||||
−0.571738 | + | 0.820436i | \(0.693731\pi\) | |||||||
\(644\) | −39.5627 | −1.55899 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 1.45192 | 0.0571249 | ||||||||
\(647\) | −11.2588 | −0.442630 | −0.221315 | − | 0.975202i | \(-0.571035\pi\) | ||||
−0.221315 | + | 0.975202i | \(0.571035\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 51.3151 | 2.01430 | ||||||||
\(650\) | −0.494096 | −0.0193800 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0.425701 | 0.0166717 | ||||||||
\(653\) | −34.4838 | −1.34946 | −0.674729 | − | 0.738066i | \(-0.735739\pi\) | ||||
−0.674729 | + | 0.738066i | \(0.735739\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −0.774428 | −0.0302594 | ||||||||
\(656\) | −16.5034 | −0.644351 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 17.5113 | 0.682660 | ||||||||
\(659\) | 30.4667 | 1.18682 | 0.593408 | − | 0.804902i | \(-0.297782\pi\) | ||||
0.593408 | + | 0.804902i | \(0.297782\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 21.4816 | 0.835538 | 0.417769 | − | 0.908553i | \(-0.362812\pi\) | ||||
0.417769 | + | 0.908553i | \(0.362812\pi\) | |||||||
\(662\) | −12.0359 | −0.467787 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −1.13606 | −0.0440875 | ||||||||
\(665\) | 8.01086 | 0.310648 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 3.94497 | 0.152750 | ||||||||
\(668\) | −8.93053 | −0.345533 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 6.37259 | 0.246195 | ||||||||
\(671\) | −53.6444 | −2.07092 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 9.10550 | 0.350991 | 0.175496 | − | 0.984480i | \(-0.443847\pi\) | ||||
0.175496 | + | 0.984480i | \(0.443847\pi\) | |||||||
\(674\) | 5.73160 | 0.220773 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −1.75587 | −0.0675334 | ||||||||
\(677\) | 3.44575 | 0.132431 | 0.0662155 | − | 0.997805i | \(-0.478908\pi\) | ||||
0.0662155 | + | 0.997805i | \(0.478908\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 64.2553 | 2.46589 | ||||||||
\(680\) | 2.91718 | 0.111869 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 22.6079 | 0.865702 | ||||||||
\(683\) | 36.2676 | 1.38774 | 0.693870 | − | 0.720100i | \(-0.255904\pi\) | ||||
0.693870 | + | 0.720100i | \(0.255904\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −4.70810 | −0.179887 | ||||||||
\(686\) | −9.24141 | −0.352839 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 19.7031 | 0.751172 | ||||||||
\(689\) | −0.0752567 | −0.00286705 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −38.2326 | −1.45444 | −0.727218 | − | 0.686407i | \(-0.759187\pi\) | ||||
−0.727218 | + | 0.686407i | \(0.759187\pi\) | |||||||
\(692\) | 40.6853 | 1.54662 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −6.01907 | −0.228481 | ||||||||
\(695\) | 6.96691 | 0.264270 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −9.99791 | −0.378698 | ||||||||
\(698\) | 3.90880 | 0.147950 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 7.52458 | 0.284402 | ||||||||
\(701\) | −2.09523 | −0.0791359 | −0.0395679 | − | 0.999217i | \(-0.512598\pi\) | ||||
−0.0395679 | + | 0.999217i | \(0.512598\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 5.20159 | 0.196182 | ||||||||
\(704\) | −12.2104 | −0.460196 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 10.5039 | 0.395320 | ||||||||
\(707\) | −46.6667 | −1.75508 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −19.8774 | −0.746511 | −0.373255 | − | 0.927729i | \(-0.621759\pi\) | ||||
−0.373255 | + | 0.927729i | \(0.621759\pi\) | |||||||
\(710\) | −7.13803 | −0.267885 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 30.1533 | 1.13004 | ||||||||
\(713\) | −53.6366 | −2.00871 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 4.48530 | 0.167741 | ||||||||
\(716\) | −24.4481 | −0.913669 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −3.75334 | −0.140073 | ||||||||
\(719\) | −15.9997 | −0.596687 | −0.298344 | − | 0.954459i | \(-0.596434\pi\) | ||||
−0.298344 | + | 0.954459i | \(0.596434\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 6.58807 | 0.245353 | ||||||||
\(722\) | −7.66123 | −0.285121 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −24.0350 | −0.893254 | ||||||||
\(725\) | −0.750308 | −0.0278658 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −30.5724 | −1.13387 | −0.566934 | − | 0.823763i | \(-0.691871\pi\) | ||||
−0.566934 | + | 0.823763i | \(0.691871\pi\) | |||||||
\(728\) | −7.95265 | −0.294745 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −4.63113 | −0.171406 | ||||||||
\(731\) | 11.9363 | 0.441479 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 27.6616 | 1.02170 | 0.510852 | − | 0.859669i | \(-0.329330\pi\) | ||||
0.510852 | + | 0.859669i | \(0.329330\pi\) | |||||||
\(734\) | 10.6795 | 0.394186 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −26.2554 | −0.967786 | ||||||||
\(737\) | −57.8491 | −2.13090 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −2.03805 | −0.0749710 | −0.0374855 | − | 0.999297i | \(-0.511935\pi\) | ||||
−0.0374855 | + | 0.999297i | \(0.511935\pi\) | |||||||
\(740\) | 4.88583 | 0.179607 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −0.159348 | −0.00584984 | ||||||||
\(743\) | 8.46498 | 0.310550 | 0.155275 | − | 0.987871i | \(-0.450374\pi\) | ||||
0.155275 | + | 0.987871i | \(0.450374\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 8.23725 | 0.301790 | ||||||||
\(746\) | −5.93575 | −0.217323 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −12.3801 | −0.452662 | ||||||||
\(749\) | 23.3041 | 0.851512 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −18.6979 | −0.682298 | −0.341149 | − | 0.940009i | \(-0.610816\pi\) | ||||
−0.341149 | + | 0.940009i | \(0.610816\pi\) | |||||||
\(752\) | −21.4597 | −0.782553 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0.370724 | 0.0135010 | ||||||||
\(755\) | 8.77188 | 0.319241 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −4.02963 | −0.146459 | −0.0732296 | − | 0.997315i | \(-0.523331\pi\) | ||||
−0.0732296 | + | 0.997315i | \(0.523331\pi\) | |||||||
\(758\) | −1.69972 | −0.0617365 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 3.46905 | 0.125836 | ||||||||
\(761\) | 16.4332 | 0.595704 | 0.297852 | − | 0.954612i | \(-0.403730\pi\) | ||||
0.297852 | + | 0.954612i | \(0.403730\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −6.19094 | −0.224127 | ||||||||
\(764\) | 13.7719 | 0.498250 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 13.2906 | 0.480208 | ||||||||
\(767\) | −11.4407 | −0.413101 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −27.0670 | −0.976062 | −0.488031 | − | 0.872826i | \(-0.662285\pi\) | ||||
−0.488031 | + | 0.872826i | \(0.662285\pi\) | |||||||
\(770\) | 9.49714 | 0.342253 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 36.2618 | 1.30509 | ||||||||
\(773\) | −50.3630 | −1.81143 | −0.905716 | − | 0.423886i | \(-0.860666\pi\) | ||||
−0.905716 | + | 0.423886i | \(0.860666\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 10.2013 | 0.366443 | ||||||||
\(776\) | 27.8253 | 0.998872 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 1.64788 | 0.0590795 | ||||||||
\(779\) | −11.8893 | −0.425979 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 64.7976 | 2.31864 | ||||||||
\(782\) | −4.08372 | −0.146034 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 29.4889 | 1.05317 | ||||||||
\(785\) | 13.3937 | 0.478043 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −35.9512 | −1.28152 | −0.640760 | − | 0.767741i | \(-0.721381\pi\) | ||||
−0.640760 | + | 0.767741i | \(0.721381\pi\) | |||||||
\(788\) | −7.70154 | −0.274356 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 3.01358 | 0.107218 | ||||||||
\(791\) | −19.1333 | −0.680302 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 11.9600 | 0.424714 | ||||||||
\(794\) | 0.379805 | 0.0134788 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 23.5139 | 0.833427 | ||||||||
\(797\) | −32.2790 | −1.14338 | −0.571690 | − | 0.820470i | \(-0.693712\pi\) | ||||
−0.571690 | + | 0.820470i | \(0.693712\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −13.0004 | −0.459922 | ||||||||
\(800\) | 4.99361 | 0.176551 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 14.6268 | 0.516489 | ||||||||
\(803\) | 42.0404 | 1.48357 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −22.5317 | −0.794138 | ||||||||
\(806\) | −5.04044 | −0.177542 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −20.2087 | −0.710941 | ||||||||
\(809\) | 42.4707 | 1.49319 | 0.746594 | − | 0.665279i | \(-0.231688\pi\) | ||||
0.746594 | + | 0.665279i | \(0.231688\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −14.1284 | −0.496116 | −0.248058 | − | 0.968745i | \(-0.579792\pi\) | ||||
−0.248058 | + | 0.968745i | \(0.579792\pi\) | |||||||
\(812\) | −5.64575 | −0.198127 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 6.16665 | 0.216141 | ||||||||
\(815\) | 0.242444 | 0.00849246 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 14.1944 | 0.496599 | ||||||||
\(818\) | −8.00489 | −0.279885 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −11.1676 | −0.389990 | ||||||||
\(821\) | −44.1796 | −1.54188 | −0.770939 | − | 0.636909i | \(-0.780213\pi\) | ||||
−0.770939 | + | 0.636909i | \(0.780213\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −26.3196 | −0.917443 | −0.458721 | − | 0.888580i | \(-0.651692\pi\) | ||||
−0.458721 | + | 0.888580i | \(0.651692\pi\) | |||||||
\(824\) | 2.85292 | 0.0993863 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −24.2245 | −0.842878 | ||||||||
\(827\) | −52.3359 | −1.81990 | −0.909949 | − | 0.414720i | \(-0.863879\pi\) | ||||
−0.909949 | + | 0.414720i | \(0.863879\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −44.0239 | −1.52901 | −0.764506 | − | 0.644617i | \(-0.777017\pi\) | ||||
−0.764506 | + | 0.644617i | \(0.777017\pi\) | |||||||
\(830\) | −0.302475 | −0.0104991 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 2.72231 | 0.0943791 | ||||||||
\(833\) | 17.8646 | 0.618971 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −5.08610 | −0.176012 | ||||||||
\(836\) | −14.7222 | −0.509179 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 5.63896 | 0.194795 | ||||||||
\(839\) | 7.99106 | 0.275882 | 0.137941 | − | 0.990440i | \(-0.455952\pi\) | ||||
0.137941 | + | 0.990440i | \(0.455952\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.4370 | −0.980587 | ||||||||
\(842\) | 5.13778 | 0.177059 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 10.6579 | 0.366859 | ||||||||
\(845\) | −1.00000 | −0.0344010 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −39.0739 | −1.34259 | ||||||||
\(848\) | 0.195277 | 0.00670585 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0.776699 | 0.0266405 | ||||||||
\(851\) | −14.6302 | −0.501517 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −16.7270 | −0.572723 | −0.286361 | − | 0.958122i | \(-0.592446\pi\) | ||||
−0.286361 | + | 0.958122i | \(0.592446\pi\) | |||||||
\(854\) | 25.3241 | 0.866573 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 10.0917 | 0.344927 | ||||||||
\(857\) | 23.5174 | 0.803339 | 0.401669 | − | 0.915785i | \(-0.368430\pi\) | ||||
0.401669 | + | 0.915785i | \(0.368430\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −19.8510 | −0.677307 | −0.338653 | − | 0.940911i | \(-0.609971\pi\) | ||||
−0.338653 | + | 0.940911i | \(0.609971\pi\) | |||||||
\(860\) | 13.3327 | 0.454643 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −0.434791 | −0.0148090 | ||||||||
\(863\) | 11.3010 | 0.384690 | 0.192345 | − | 0.981327i | \(-0.438391\pi\) | ||||
0.192345 | + | 0.981327i | \(0.438391\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 23.1711 | 0.787839 | ||||||||
\(866\) | 15.5424 | 0.528152 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 76.7608 | 2.60543 | ||||||||
\(869\) | −27.3567 | −0.928012 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 12.8975 | 0.437015 | ||||||||
\(872\) | −2.68095 | −0.0907883 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −4.85629 | −0.164266 | ||||||||
\(875\) | 4.28539 | 0.144872 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 47.2377 | 1.59510 | 0.797552 | − | 0.603250i | \(-0.206128\pi\) | ||||
0.797552 | + | 0.603250i | \(0.206128\pi\) | |||||||
\(878\) | −2.84804 | −0.0961167 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −11.6385 | −0.392335 | ||||||||
\(881\) | 5.64812 | 0.190290 | 0.0951450 | − | 0.995463i | \(-0.469669\pi\) | ||||
0.0951450 | + | 0.995463i | \(0.469669\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 16.3032 | 0.548645 | 0.274323 | − | 0.961638i | \(-0.411546\pi\) | ||||
0.274323 | + | 0.961638i | \(0.411546\pi\) | |||||||
\(884\) | 2.76016 | 0.0928341 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 2.03986 | 0.0685303 | ||||||||
\(887\) | −37.6918 | −1.26557 | −0.632783 | − | 0.774329i | \(-0.718087\pi\) | ||||
−0.632783 | + | 0.774329i | \(0.718087\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 16.8029 | 0.563550 | ||||||||
\(890\) | 8.02832 | 0.269110 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 40.3642 | 1.35149 | ||||||||
\(893\) | −15.4599 | −0.517345 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −13.9237 | −0.465417 | ||||||||
\(896\) | 48.5633 | 1.62238 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −14.9910 | −0.500255 | ||||||||
\(899\) | −7.65416 | −0.255280 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0.118300 | 0.00394116 | ||||||||
\(902\) | −14.0952 | −0.469318 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −8.28556 | −0.275574 | ||||||||
\(905\) | −13.6884 | −0.455017 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 23.8528 | 0.792019 | 0.396009 | − | 0.918246i | \(-0.370395\pi\) | ||||
0.396009 | + | 0.918246i | \(0.370395\pi\) | |||||||
\(908\) | 33.0712 | 1.09751 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −2.11739 | −0.0701908 | ||||||||
\(911\) | 46.7610 | 1.54926 | 0.774630 | − | 0.632414i | \(-0.217936\pi\) | ||||
0.774630 | + | 0.632414i | \(0.217936\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 2.74580 | 0.0908729 | ||||||||
\(914\) | −4.18145 | −0.138310 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 9.49795 | 0.313821 | ||||||||
\(917\) | −3.31872 | −0.109594 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −12.3909 | −0.408738 | −0.204369 | − | 0.978894i | \(-0.565514\pi\) | ||||
−0.204369 | + | 0.978894i | \(0.565514\pi\) | |||||||
\(920\) | −9.75721 | −0.321686 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 8.71132 | 0.286892 | ||||||||
\(923\) | −14.4466 | −0.475517 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 2.78257 | 0.0914904 | ||||||||
\(926\) | −0.619787 | −0.0203675 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −3.74675 | −0.122993 | ||||||||
\(929\) | 10.2213 | 0.335349 | 0.167674 | − | 0.985842i | \(-0.446374\pi\) | ||||
0.167674 | + | 0.985842i | \(0.446374\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 21.2442 | 0.696251 | ||||||||
\(932\) | 13.0976 | 0.429027 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 5.59111 | 0.182947 | ||||||||
\(935\) | −7.05071 | −0.230583 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 23.8520 | 0.779212 | 0.389606 | − | 0.920982i | \(-0.372611\pi\) | ||||
0.389606 | + | 0.920982i | \(0.372611\pi\) | |||||||
\(938\) | 27.3090 | 0.891671 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −14.5214 | −0.473636 | ||||||||
\(941\) | −25.3193 | −0.825385 | −0.412692 | − | 0.910870i | \(-0.635412\pi\) | ||||
−0.412692 | + | 0.910870i | \(0.635412\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 33.4404 | 1.08897 | ||||||||
\(944\) | 29.6866 | 0.966216 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 16.8279 | 0.547122 | ||||||||
\(947\) | −23.1019 | −0.750710 | −0.375355 | − | 0.926881i | \(-0.622479\pi\) | ||||
−0.375355 | + | 0.926881i | \(0.622479\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −9.37293 | −0.304258 | ||||||||
\(950\) | 0.923636 | 0.0299667 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 12.5012 | 0.405167 | ||||||||
\(953\) | 46.4511 | 1.50470 | 0.752350 | − | 0.658764i | \(-0.228920\pi\) | ||||
0.752350 | + | 0.658764i | \(0.228920\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 7.84336 | 0.253805 | ||||||||
\(956\) | −13.4864 | −0.436180 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −16.4947 | −0.532919 | ||||||||
\(959\) | −20.1760 | −0.651518 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 73.0675 | 2.35702 | ||||||||
\(962\) | −1.37486 | −0.0443272 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −51.4120 | −1.65587 | ||||||||
\(965\) | 20.6518 | 0.664804 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −7.74255 | −0.248984 | −0.124492 | − | 0.992221i | \(-0.539730\pi\) | ||||
−0.124492 | + | 0.992221i | \(0.539730\pi\) | |||||||
\(968\) | −16.9207 | −0.543852 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 7.40850 | 0.237872 | ||||||||
\(971\) | −2.78737 | −0.0894511 | −0.0447256 | − | 0.998999i | \(-0.514241\pi\) | ||||
−0.0447256 | + | 0.998999i | \(0.514241\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 29.8559 | 0.957136 | ||||||||
\(974\) | −20.8907 | −0.669381 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −31.0341 | −0.993378 | ||||||||
\(977\) | −11.4785 | −0.367231 | −0.183616 | − | 0.982998i | \(-0.558780\pi\) | ||||
−0.183616 | + | 0.982998i | \(0.558780\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −72.8794 | −2.32924 | ||||||||
\(980\) | 19.9546 | 0.637427 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 5.66517 | 0.180783 | ||||||||
\(983\) | −28.9499 | −0.923359 | −0.461679 | − | 0.887047i | \(-0.652753\pi\) | ||||
−0.461679 | + | 0.887047i | \(0.652753\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −4.38617 | −0.139755 | ||||||||
\(986\) | −0.582764 | −0.0185590 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 3.28232 | 0.104425 | ||||||||
\(989\) | −39.9237 | −1.26950 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −5.40688 | −0.171755 | −0.0858776 | − | 0.996306i | \(-0.527369\pi\) | ||||
−0.0858776 | + | 0.996306i | \(0.527369\pi\) | |||||||
\(992\) | 50.9415 | 1.61739 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −30.5892 | −0.970230 | ||||||||
\(995\) | 13.3916 | 0.424542 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −36.9243 | −1.16941 | −0.584703 | − | 0.811248i | \(-0.698789\pi\) | ||||
−0.584703 | + | 0.811248i | \(0.698789\pi\) | |||||||
\(998\) | 3.31466 | 0.104924 | ||||||||
\(999\) | 0 | 0 |
(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 | 5265.2.a.bf.1.4 | 8 | ||
3.2 | odd | 2 | 5265.2.a.ba.1.5 | 8 | |||
9.2 | odd | 6 | 1755.2.i.f.1171.4 | 16 | |||
9.4 | even | 3 | 585.2.i.e.196.5 | ✓ | 16 | ||
9.5 | odd | 6 | 1755.2.i.f.586.4 | 16 | |||
9.7 | even | 3 | 585.2.i.e.391.5 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
585.2.i.e.196.5 | ✓ | 16 | 9.4 | even | 3 | ||
585.2.i.e.391.5 | yes | 16 | 9.7 | even | 3 | ||
1755.2.i.f.586.4 | 16 | 9.5 | odd | 6 | |||
1755.2.i.f.1171.4 | 16 | 9.2 | odd | 6 | |||
5265.2.a.ba.1.5 | 8 | 3.2 | odd | 2 | |||
5265.2.a.bf.1.4 | 8 | 1.1 | even | 1 | trivial |