Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [475,3,Mod(151,475)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(475, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("475.151");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 475 = 5^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 475.c (of order \(2\), degree \(1\), 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: | \(12.9428125571\) |
Analytic rank: | \(0\) |
Dimension: | \(14\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{14} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{14} + 42x^{12} + 677x^{10} + 5313x^{8} + 21125x^{6} + 40138x^{4} + 30565x^{2} + 3675 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 151.9 | ||
Root | \(1.40632i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 475.151 |
Dual form | 475.3.c.h.151.6 |
$q$-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 \(\left(\mathbb{Z}/475\mathbb{Z}\right)^\times\).
\(n\) | \(77\) | \(401\) |
\(\chi(n)\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.40632i | 0.703162i | 0.936157 | + | 0.351581i | \(0.114356\pi\) | ||||
−0.936157 | + | 0.351581i | \(0.885644\pi\) | |||||||
\(3\) | − | 2.91656i | − | 0.972185i | −0.873907 | − | 0.486093i | \(-0.838422\pi\) | ||
0.873907 | − | 0.486093i | \(-0.161578\pi\) | |||||||
\(4\) | 2.02225 | 0.505563 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 4.10162 | 0.683604 | ||||||||
\(7\) | −11.7208 | −1.67441 | −0.837203 | − | 0.546893i | \(-0.815810\pi\) | ||||
−0.837203 | + | 0.546893i | \(0.815810\pi\) | |||||||
\(8\) | 8.46924i | 1.05865i | ||||||||
\(9\) | 0.493705 | 0.0548561 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −6.36259 | −0.578417 | −0.289209 | − | 0.957266i | \(-0.593392\pi\) | ||||
−0.289209 | + | 0.957266i | \(0.593392\pi\) | |||||||
\(12\) | − | 5.89801i | − | 0.491501i | ||||||
\(13\) | 17.7815i | 1.36781i | 0.729573 | + | 0.683903i | \(0.239719\pi\) | ||||
−0.729573 | + | 0.683903i | \(0.760281\pi\) | |||||||
\(14\) | − | 16.4833i | − | 1.17738i | ||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −3.82148 | −0.238842 | ||||||||
\(17\) | −17.5868 | −1.03452 | −0.517260 | − | 0.855828i | \(-0.673048\pi\) | ||||
−0.517260 | + | 0.855828i | \(0.673048\pi\) | |||||||
\(18\) | 0.694309i | 0.0385727i | ||||||||
\(19\) | −16.8066 | − | 8.86223i | −0.884557 | − | 0.466433i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 34.1845i | 1.62783i | ||||||||
\(22\) | − | 8.94786i | − | 0.406721i | ||||||
\(23\) | 1.53826 | 0.0668809 | 0.0334404 | − | 0.999441i | \(-0.489354\pi\) | ||||
0.0334404 | + | 0.999441i | \(0.489354\pi\) | |||||||
\(24\) | 24.7010 | 1.02921 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −25.0065 | −0.961789 | ||||||||
\(27\) | − | 27.6889i | − | 1.02552i | ||||||
\(28\) | −23.7025 | −0.846518 | ||||||||
\(29\) | 39.9749i | 1.37845i | 0.724549 | + | 0.689223i | \(0.242048\pi\) | ||||
−0.724549 | + | 0.689223i | \(0.757952\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 9.24369i | − | 0.298184i | −0.988823 | − | 0.149092i | \(-0.952365\pi\) | ||
0.988823 | − | 0.149092i | \(-0.0476350\pi\) | |||||||
\(32\) | 28.5027i | 0.890710i | ||||||||
\(33\) | 18.5568i | 0.562328i | ||||||||
\(34\) | − | 24.7328i | − | 0.727435i | ||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0.998396 | 0.0277332 | ||||||||
\(37\) | 56.4183i | 1.52482i | 0.647095 | + | 0.762410i | \(0.275984\pi\) | ||||
−0.647095 | + | 0.762410i | \(0.724016\pi\) | |||||||
\(38\) | 12.4632 | − | 23.6355i | 0.327978 | − | 0.621986i | ||||
\(39\) | 51.8607 | 1.32976 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 39.5382i | 0.964347i | 0.876076 | + | 0.482173i | \(0.160152\pi\) | ||||
−0.876076 | + | 0.482173i | \(0.839848\pi\) | |||||||
\(42\) | −48.0744 | −1.14463 | ||||||||
\(43\) | 18.4360 | 0.428744 | 0.214372 | − | 0.976752i | \(-0.431230\pi\) | ||||
0.214372 | + | 0.976752i | \(0.431230\pi\) | |||||||
\(44\) | −12.8668 | −0.292426 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 2.16329i | 0.0470281i | ||||||||
\(47\) | −61.5720 | −1.31004 | −0.655021 | − | 0.755610i | \(-0.727340\pi\) | ||||
−0.655021 | + | 0.755610i | \(0.727340\pi\) | |||||||
\(48\) | 11.1456i | 0.232199i | ||||||||
\(49\) | 88.3780 | 1.80363 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 51.2930i | 1.00574i | ||||||||
\(52\) | 35.9587i | 0.691513i | ||||||||
\(53\) | − | 66.5116i | − | 1.25494i | −0.778642 | − | 0.627468i | \(-0.784091\pi\) | ||
0.778642 | − | 0.627468i | \(-0.215909\pi\) | |||||||
\(54\) | 38.9396 | 0.721103 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | − | 99.2665i | − | 1.77262i | ||||||
\(57\) | −25.8472 | + | 49.0173i | −0.453459 | + | 0.859953i | ||||
\(58\) | −56.2177 | −0.969270 | ||||||||
\(59\) | 9.42839i | 0.159803i | 0.996803 | + | 0.0799016i | \(0.0254606\pi\) | ||||
−0.996803 | + | 0.0799016i | \(0.974539\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −36.5472 | −0.599134 | −0.299567 | − | 0.954075i | \(-0.596842\pi\) | ||||
−0.299567 | + | 0.954075i | \(0.596842\pi\) | |||||||
\(62\) | 12.9996 | 0.209671 | ||||||||
\(63\) | −5.78663 | −0.0918513 | ||||||||
\(64\) | −55.3700 | −0.865156 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −26.0969 | −0.395408 | ||||||||
\(67\) | 2.55637i | 0.0381548i | 0.999818 | + | 0.0190774i | \(0.00607289\pi\) | ||||
−0.999818 | + | 0.0190774i | \(0.993927\pi\) | |||||||
\(68\) | −35.5650 | −0.523015 | ||||||||
\(69\) | − | 4.48642i | − | 0.0650206i | ||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 53.8192i | 0.758017i | 0.925393 | + | 0.379008i | \(0.123735\pi\) | ||||
−0.925393 | + | 0.379008i | \(0.876265\pi\) | |||||||
\(72\) | 4.18130i | 0.0580737i | ||||||||
\(73\) | −115.725 | −1.58527 | −0.792636 | − | 0.609695i | \(-0.791292\pi\) | ||||
−0.792636 | + | 0.609695i | \(0.791292\pi\) | |||||||
\(74\) | −79.3424 | −1.07219 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −33.9871 | − | 17.9217i | −0.447199 | − | 0.235811i | ||||
\(77\) | 74.5748 | 0.968504 | ||||||||
\(78\) | 72.9329i | 0.935037i | ||||||||
\(79\) | − | 95.9222i | − | 1.21421i | −0.794623 | − | 0.607103i | \(-0.792332\pi\) | ||
0.794623 | − | 0.607103i | \(-0.207668\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −76.3129 | −0.942135 | ||||||||
\(82\) | −55.6035 | −0.678092 | ||||||||
\(83\) | 143.935 | 1.73416 | 0.867081 | − | 0.498168i | \(-0.165994\pi\) | ||||
0.867081 | + | 0.498168i | \(0.165994\pi\) | |||||||
\(84\) | 69.1296i | 0.822972i | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 25.9270i | 0.301476i | ||||||||
\(87\) | 116.589 | 1.34010 | ||||||||
\(88\) | − | 53.8863i | − | 0.612344i | ||||||
\(89\) | 19.4615i | 0.218668i | 0.994005 | + | 0.109334i | \(0.0348718\pi\) | ||||
−0.994005 | + | 0.109334i | \(0.965128\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 208.414i | − | 2.29026i | ||||||
\(92\) | 3.11075 | 0.0338125 | ||||||||
\(93\) | −26.9597 | −0.289890 | ||||||||
\(94\) | − | 86.5902i | − | 0.921172i | ||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 83.1297 | 0.865935 | ||||||||
\(97\) | − | 163.156i | − | 1.68202i | −0.541017 | − | 0.841012i | \(-0.681960\pi\) | ||
0.541017 | − | 0.841012i | \(-0.318040\pi\) | |||||||
\(98\) | 124.288i | 1.26825i | ||||||||
\(99\) | −3.14124 | −0.0317297 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −57.2111 | −0.566447 | −0.283223 | − | 0.959054i | \(-0.591404\pi\) | ||||
−0.283223 | + | 0.959054i | \(0.591404\pi\) | |||||||
\(102\) | −72.1346 | −0.707202 | ||||||||
\(103\) | 22.5345i | 0.218782i | 0.993999 | + | 0.109391i | \(0.0348900\pi\) | ||||
−0.993999 | + | 0.109391i | \(0.965110\pi\) | |||||||
\(104\) | −150.596 | −1.44803 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 93.5369 | 0.882424 | ||||||||
\(107\) | 68.7799i | 0.642803i | 0.946943 | + | 0.321401i | \(0.104154\pi\) | ||||
−0.946943 | + | 0.321401i | \(0.895846\pi\) | |||||||
\(108\) | − | 55.9940i | − | 0.518463i | ||||||
\(109\) | 79.5462i | 0.729781i | 0.931050 | + | 0.364891i | \(0.118894\pi\) | ||||
−0.931050 | + | 0.364891i | \(0.881106\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 164.547 | 1.48241 | ||||||||
\(112\) | 44.7909 | 0.399919 | ||||||||
\(113\) | − | 188.929i | − | 1.67193i | −0.548780 | − | 0.835967i | \(-0.684907\pi\) | ||
0.548780 | − | 0.835967i | \(-0.315093\pi\) | |||||||
\(114\) | −68.9342 | − | 36.3495i | −0.604686 | − | 0.318855i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 80.8394i | 0.696891i | ||||||||
\(117\) | 8.77880i | 0.0750325i | ||||||||
\(118\) | −13.2594 | −0.112368 | ||||||||
\(119\) | 206.132 | 1.73221 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −80.5175 | −0.665434 | ||||||||
\(122\) | − | 51.3972i | − | 0.421288i | ||||||
\(123\) | 115.315 | 0.937524 | ||||||||
\(124\) | − | 18.6931i | − | 0.150751i | ||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | − | 8.13788i | − | 0.0645864i | ||||||
\(127\) | 12.5720i | 0.0989923i | 0.998774 | + | 0.0494961i | \(0.0157616\pi\) | ||||
−0.998774 | + | 0.0494961i | \(0.984238\pi\) | |||||||
\(128\) | 36.1427i | 0.282365i | ||||||||
\(129\) | − | 53.7695i | − | 0.416818i | ||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 96.6711 | 0.737947 | 0.368974 | − | 0.929440i | \(-0.379709\pi\) | ||||
0.368974 | + | 0.929440i | \(0.379709\pi\) | |||||||
\(132\) | 37.5266i | 0.284293i | ||||||||
\(133\) | 196.987 | + | 103.873i | 1.48111 | + | 0.780998i | ||||
\(134\) | −3.59508 | −0.0268290 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | − | 148.947i | − | 1.09520i | ||||||
\(137\) | 219.187 | 1.59991 | 0.799954 | − | 0.600061i | \(-0.204857\pi\) | ||||
0.799954 | + | 0.600061i | \(0.204857\pi\) | |||||||
\(138\) | 6.30936 | 0.0457200 | ||||||||
\(139\) | −188.602 | −1.35685 | −0.678425 | − | 0.734669i | \(-0.737337\pi\) | ||||
−0.678425 | + | 0.734669i | \(0.737337\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 179.578i | 1.27360i | ||||||||
\(142\) | −75.6872 | −0.533008 | ||||||||
\(143\) | − | 113.136i | − | 0.791163i | ||||||
\(144\) | −1.88668 | −0.0131020 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | − | 162.747i | − | 1.11470i | ||||||
\(147\) | − | 257.759i | − | 1.75346i | ||||||
\(148\) | 114.092i | 0.770893i | ||||||||
\(149\) | 177.432 | 1.19082 | 0.595410 | − | 0.803422i | \(-0.296990\pi\) | ||||
0.595410 | + | 0.803422i | \(0.296990\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 9.49631i | 0.0628895i | 0.999505 | + | 0.0314447i | \(0.0100108\pi\) | ||||
−0.999505 | + | 0.0314447i | \(0.989989\pi\) | |||||||
\(152\) | 75.0563 | − | 142.339i | 0.493792 | − | 0.936440i | ||||
\(153\) | −8.68271 | −0.0567497 | ||||||||
\(154\) | 104.876i | 0.681016i | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 104.875 | 0.672278 | ||||||||
\(157\) | 27.3090 | 0.173943 | 0.0869715 | − | 0.996211i | \(-0.472281\pi\) | ||||
0.0869715 | + | 0.996211i | \(0.472281\pi\) | |||||||
\(158\) | 134.898 | 0.853783 | ||||||||
\(159\) | −193.985 | −1.22003 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −18.0297 | −0.111986 | ||||||||
\(162\) | − | 107.321i | − | 0.662473i | ||||||
\(163\) | 128.144 | 0.786161 | 0.393081 | − | 0.919504i | \(-0.371409\pi\) | ||||
0.393081 | + | 0.919504i | \(0.371409\pi\) | |||||||
\(164\) | 79.9563i | 0.487538i | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 202.420i | 1.21940i | ||||||||
\(167\) | 83.5190i | 0.500114i | 0.968231 | + | 0.250057i | \(0.0804493\pi\) | ||||
−0.968231 | + | 0.250057i | \(0.919551\pi\) | |||||||
\(168\) | −289.516 | −1.72331 | ||||||||
\(169\) | −147.181 | −0.870894 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −8.29749 | − | 4.37532i | −0.0485233 | − | 0.0255867i | ||||
\(172\) | 37.2822 | 0.216757 | ||||||||
\(173\) | 125.617i | 0.726110i | 0.931768 | + | 0.363055i | \(0.118266\pi\) | ||||
−0.931768 | + | 0.363055i | \(0.881734\pi\) | |||||||
\(174\) | 163.962i | 0.942310i | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 24.3145 | 0.138151 | ||||||||
\(177\) | 27.4984 | 0.155358 | ||||||||
\(178\) | −27.3691 | −0.153759 | ||||||||
\(179\) | − | 86.1103i | − | 0.481063i | −0.970641 | − | 0.240532i | \(-0.922678\pi\) | ||
0.970641 | − | 0.240532i | \(-0.0773218\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 299.094i | 1.65246i | 0.563336 | + | 0.826228i | \(0.309518\pi\) | ||||
−0.563336 | + | 0.826228i | \(0.690482\pi\) | |||||||
\(182\) | 293.097 | 1.61043 | ||||||||
\(183\) | 106.592i | 0.582469i | ||||||||
\(184\) | 13.0279i | 0.0708038i | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | − | 37.9141i | − | 0.203839i | ||||||
\(187\) | 111.898 | 0.598384 | ||||||||
\(188\) | −124.514 | −0.662309 | ||||||||
\(189\) | 324.537i | 1.71713i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −6.80277 | −0.0356166 | −0.0178083 | − | 0.999841i | \(-0.505669\pi\) | ||||
−0.0178083 | + | 0.999841i | \(0.505669\pi\) | |||||||
\(192\) | 161.490i | 0.841092i | ||||||||
\(193\) | − | 235.945i | − | 1.22251i | −0.791433 | − | 0.611256i | \(-0.790665\pi\) | ||
0.791433 | − | 0.611256i | \(-0.209335\pi\) | |||||||
\(194\) | 229.451 | 1.18274 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 178.723 | 0.911850 | ||||||||
\(197\) | 29.4014 | 0.149245 | 0.0746227 | − | 0.997212i | \(-0.476225\pi\) | ||||
0.0746227 | + | 0.997212i | \(0.476225\pi\) | |||||||
\(198\) | − | 4.41760i | − | 0.0223111i | ||||||
\(199\) | −65.6370 | −0.329834 | −0.164917 | − | 0.986307i | \(-0.552736\pi\) | ||||
−0.164917 | + | 0.986307i | \(0.552736\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 7.45579 | 0.0370935 | ||||||||
\(202\) | − | 80.4573i | − | 0.398304i | ||||||
\(203\) | − | 468.539i | − | 2.30808i | ||||||
\(204\) | 103.727i | 0.508468i | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −31.6909 | −0.153839 | ||||||||
\(207\) | 0.759447 | 0.00366882 | ||||||||
\(208\) | − | 67.9516i | − | 0.326690i | ||||||
\(209\) | 106.933 | + | 56.3867i | 0.511643 | + | 0.269793i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 45.4463i | 0.215385i | 0.994184 | + | 0.107693i | \(0.0343463\pi\) | ||||
−0.994184 | + | 0.107693i | \(0.965654\pi\) | |||||||
\(212\) | − | 134.503i | − | 0.634450i | ||||||
\(213\) | 156.967 | 0.736933 | ||||||||
\(214\) | −96.7268 | −0.451995 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 234.504 | 1.08567 | ||||||||
\(217\) | 108.344i | 0.499280i | ||||||||
\(218\) | −111.868 | −0.513154 | ||||||||
\(219\) | 337.518i | 1.54118i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 312.720i | − | 1.41502i | ||||||
\(222\) | 231.407i | 1.04237i | ||||||||
\(223\) | 236.447i | 1.06030i | 0.847904 | + | 0.530149i | \(0.177864\pi\) | ||||
−0.847904 | + | 0.530149i | \(0.822136\pi\) | |||||||
\(224\) | − | 334.076i | − | 1.49141i | ||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 265.695 | 1.17564 | ||||||||
\(227\) | 143.537i | 0.632323i | 0.948705 | + | 0.316162i | \(0.102394\pi\) | ||||
−0.948705 | + | 0.316162i | \(0.897606\pi\) | |||||||
\(228\) | −52.2695 | + | 99.1254i | −0.229252 | + | 0.434761i | ||||
\(229\) | −102.645 | −0.448230 | −0.224115 | − | 0.974563i | \(-0.571949\pi\) | ||||
−0.224115 | + | 0.974563i | \(0.571949\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | − | 217.502i | − | 0.941566i | ||||||
\(232\) | −338.557 | −1.45930 | ||||||||
\(233\) | 170.820 | 0.733132 | 0.366566 | − | 0.930392i | \(-0.380533\pi\) | ||||
0.366566 | + | 0.930392i | \(0.380533\pi\) | |||||||
\(234\) | −12.3458 | −0.0527600 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 19.0666i | 0.0807907i | ||||||||
\(237\) | −279.762 | −1.18043 | ||||||||
\(238\) | 289.889i | 1.21802i | ||||||||
\(239\) | 194.352 | 0.813186 | 0.406593 | − | 0.913609i | \(-0.366717\pi\) | ||||
0.406593 | + | 0.913609i | \(0.366717\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 457.159i | − | 1.89693i | −0.316888 | − | 0.948463i | \(-0.602638\pi\) | ||
0.316888 | − | 0.948463i | \(-0.397362\pi\) | |||||||
\(242\) | − | 113.234i | − | 0.467908i | ||||||
\(243\) | − | 26.6294i | − | 0.109586i | ||||||
\(244\) | −73.9076 | −0.302900 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 162.171i | 0.659231i | ||||||||
\(247\) | 157.584 | − | 298.846i | 0.637990 | − | 1.20990i | ||||
\(248\) | 78.2870 | 0.315674 | ||||||||
\(249\) | − | 419.796i | − | 1.68593i | ||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −345.070 | −1.37478 | −0.687391 | − | 0.726288i | \(-0.741244\pi\) | ||||
−0.687391 | + | 0.726288i | \(0.741244\pi\) | |||||||
\(252\) | −11.7020 | −0.0464367 | ||||||||
\(253\) | −9.78732 | −0.0386850 | ||||||||
\(254\) | −17.6803 | −0.0696076 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −272.308 | −1.06370 | ||||||||
\(257\) | 286.104i | 1.11324i | 0.830766 | + | 0.556622i | \(0.187903\pi\) | ||||
−0.830766 | + | 0.556622i | \(0.812097\pi\) | |||||||
\(258\) | 75.6174 | 0.293091 | ||||||||
\(259\) | − | 661.270i | − | 2.55317i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 19.7358i | 0.0756161i | ||||||||
\(262\) | 135.951i | 0.518896i | ||||||||
\(263\) | 203.484 | 0.773703 | 0.386851 | − | 0.922142i | \(-0.373563\pi\) | ||||
0.386851 | + | 0.922142i | \(0.373563\pi\) | |||||||
\(264\) | −157.162 | −0.595312 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −146.079 | + | 277.028i | −0.549168 | + | 1.04146i | ||||
\(267\) | 56.7604 | 0.212586 | ||||||||
\(268\) | 5.16963i | 0.0192896i | ||||||||
\(269\) | − | 420.928i | − | 1.56479i | −0.622783 | − | 0.782395i | \(-0.713998\pi\) | ||
0.622783 | − | 0.782395i | \(-0.286002\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −127.006 | −0.468655 | −0.234328 | − | 0.972158i | \(-0.575289\pi\) | ||||
−0.234328 | + | 0.972158i | \(0.575289\pi\) | |||||||
\(272\) | 67.2078 | 0.247087 | ||||||||
\(273\) | −607.850 | −2.22656 | ||||||||
\(274\) | 308.249i | 1.12499i | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | − | 9.07268i | − | 0.0328720i | ||||||
\(277\) | −342.553 | −1.23665 | −0.618327 | − | 0.785921i | \(-0.712189\pi\) | ||||
−0.618327 | + | 0.785921i | \(0.712189\pi\) | |||||||
\(278\) | − | 265.236i | − | 0.954086i | ||||||
\(279\) | − | 4.56366i | − | 0.0163572i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 151.942i | 0.540718i | 0.962760 | + | 0.270359i | \(0.0871424\pi\) | ||||
−0.962760 | + | 0.270359i | \(0.912858\pi\) | |||||||
\(282\) | −252.545 | −0.895550 | ||||||||
\(283\) | −240.982 | −0.851527 | −0.425764 | − | 0.904834i | \(-0.639994\pi\) | ||||
−0.425764 | + | 0.904834i | \(0.639994\pi\) | |||||||
\(284\) | 108.836i | 0.383225i | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 159.106 | 0.556315 | ||||||||
\(287\) | − | 463.421i | − | 1.61471i | ||||||
\(288\) | 14.0719i | 0.0488609i | ||||||||
\(289\) | 20.2970 | 0.0702317 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −475.854 | −1.63524 | ||||||||
\(292\) | −234.025 | −0.801455 | ||||||||
\(293\) | − | 7.05363i | − | 0.0240738i | −0.999928 | − | 0.0120369i | \(-0.996168\pi\) | ||
0.999928 | − | 0.0120369i | \(-0.00383156\pi\) | |||||||
\(294\) | 362.493 | 1.23297 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −477.820 | −1.61426 | ||||||||
\(297\) | 176.173i | 0.593176i | ||||||||
\(298\) | 249.527i | 0.837339i | ||||||||
\(299\) | 27.3526i | 0.0914801i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −216.085 | −0.717891 | ||||||||
\(302\) | −13.3549 | −0.0442215 | ||||||||
\(303\) | 166.859i | 0.550691i | ||||||||
\(304\) | 64.2260 | + | 33.8668i | 0.211270 | + | 0.111404i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | − | 12.2107i | − | 0.0399042i | ||||||
\(307\) | 44.7370i | 0.145723i | 0.997342 | + | 0.0728616i | \(0.0232131\pi\) | ||||
−0.997342 | + | 0.0728616i | \(0.976787\pi\) | |||||||
\(308\) | 150.809 | 0.489640 | ||||||||
\(309\) | 65.7232 | 0.212696 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −110.679 | −0.355883 | −0.177941 | − | 0.984041i | \(-0.556944\pi\) | ||||
−0.177941 | + | 0.984041i | \(0.556944\pi\) | |||||||
\(312\) | 439.220i | 1.40776i | ||||||||
\(313\) | −131.862 | −0.421286 | −0.210643 | − | 0.977563i | \(-0.567556\pi\) | ||||
−0.210643 | + | 0.977563i | \(0.567556\pi\) | |||||||
\(314\) | 38.4054i | 0.122310i | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | − | 193.979i | − | 0.613858i | ||||||
\(317\) | 309.486i | 0.976295i | 0.872761 | + | 0.488148i | \(0.162327\pi\) | ||||
−0.872761 | + | 0.488148i | \(0.837673\pi\) | |||||||
\(318\) | − | 272.806i | − | 0.857879i | ||||||
\(319\) | − | 254.344i | − | 0.797316i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 200.600 | 0.624923 | ||||||||
\(322\) | − | 25.3556i | − | 0.0787441i | ||||||
\(323\) | 295.575 | + | 155.859i | 0.915091 | + | 0.482534i | ||||
\(324\) | −154.324 | −0.476309 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 180.212i | 0.552799i | ||||||||
\(327\) | 232.001 | 0.709483 | ||||||||
\(328\) | −334.859 | −1.02091 | ||||||||
\(329\) | 721.675 | 2.19354 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 200.092i | − | 0.604508i | −0.953227 | − | 0.302254i | \(-0.902261\pi\) | ||
0.953227 | − | 0.302254i | \(-0.0977390\pi\) | |||||||
\(332\) | 291.074 | 0.876728 | ||||||||
\(333\) | 27.8540i | 0.0836456i | ||||||||
\(334\) | −117.455 | −0.351661 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | − | 130.635i | − | 0.388795i | ||||||
\(337\) | 425.356i | 1.26218i | 0.775708 | + | 0.631092i | \(0.217393\pi\) | ||||
−0.775708 | + | 0.631092i | \(0.782607\pi\) | |||||||
\(338\) | − | 206.984i | − | 0.612380i | ||||||
\(339\) | −551.021 | −1.62543 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 58.8138i | 0.172475i | ||||||||
\(342\) | 6.15312 | − | 11.6690i | 0.0179916 | − | 0.0341198i | ||||
\(343\) | −461.543 | −1.34561 | ||||||||
\(344\) | 156.139i | 0.453892i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −176.658 | −0.510573 | ||||||||
\(347\) | −553.742 | −1.59580 | −0.797900 | − | 0.602790i | \(-0.794056\pi\) | ||||
−0.797900 | + | 0.602790i | \(0.794056\pi\) | |||||||
\(348\) | 235.773 | 0.677508 | ||||||||
\(349\) | 273.499 | 0.783666 | 0.391833 | − | 0.920036i | \(-0.371841\pi\) | ||||
0.391833 | + | 0.920036i | \(0.371841\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 492.350 | 1.40271 | ||||||||
\(352\) | − | 181.351i | − | 0.515202i | ||||||
\(353\) | 545.758 | 1.54606 | 0.773028 | − | 0.634372i | \(-0.218741\pi\) | ||||
0.773028 | + | 0.634372i | \(0.218741\pi\) | |||||||
\(354\) | 38.6717i | 0.109242i | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 39.3560i | 0.110551i | ||||||||
\(357\) | − | 601.197i | − | 1.68402i | ||||||
\(358\) | 121.099 | 0.338265 | ||||||||
\(359\) | −73.9842 | −0.206084 | −0.103042 | − | 0.994677i | \(-0.532858\pi\) | ||||
−0.103042 | + | 0.994677i | \(0.532858\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 203.922 | + | 297.887i | 0.564881 | + | 0.825173i | ||||
\(362\) | −420.624 | −1.16194 | ||||||||
\(363\) | 234.834i | 0.646925i | ||||||||
\(364\) | − | 421.466i | − | 1.15787i | ||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −149.903 | −0.409570 | ||||||||
\(367\) | 397.670 | 1.08357 | 0.541785 | − | 0.840517i | \(-0.317749\pi\) | ||||
0.541785 | + | 0.840517i | \(0.317749\pi\) | |||||||
\(368\) | −5.87843 | −0.0159740 | ||||||||
\(369\) | 19.5202i | 0.0529003i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 779.572i | 2.10127i | ||||||||
\(372\) | −54.5194 | −0.146558 | ||||||||
\(373\) | − | 284.800i | − | 0.763538i | −0.924258 | − | 0.381769i | \(-0.875315\pi\) | ||
0.924258 | − | 0.381769i | \(-0.124685\pi\) | |||||||
\(374\) | 157.365i | 0.420761i | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | − | 521.468i | − | 1.38688i | ||||||
\(377\) | −710.813 | −1.88545 | ||||||||
\(378\) | −456.404 | −1.20742 | ||||||||
\(379\) | 543.499i | 1.43403i | 0.697055 | + | 0.717017i | \(0.254493\pi\) | ||||
−0.697055 | + | 0.717017i | \(0.745507\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 36.6670 | 0.0962388 | ||||||||
\(382\) | − | 9.56690i | − | 0.0250442i | ||||||
\(383\) | 598.496i | 1.56265i | 0.624123 | + | 0.781326i | \(0.285456\pi\) | ||||
−0.624123 | + | 0.781326i | \(0.714544\pi\) | |||||||
\(384\) | 105.412 | 0.274511 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 331.815 | 0.859624 | ||||||||
\(387\) | 9.10193 | 0.0235192 | ||||||||
\(388\) | − | 329.943i | − | 0.850369i | ||||||
\(389\) | 714.756 | 1.83742 | 0.918709 | − | 0.394935i | \(-0.129233\pi\) | ||||
0.918709 | + | 0.394935i | \(0.129233\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −27.0531 | −0.0691896 | ||||||||
\(392\) | 748.494i | 1.90942i | ||||||||
\(393\) | − | 281.947i | − | 0.717421i | ||||||
\(394\) | 41.3478i | 0.104944i | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −6.35238 | −0.0160414 | ||||||||
\(397\) | −375.385 | −0.945555 | −0.472777 | − | 0.881182i | \(-0.656749\pi\) | ||||
−0.472777 | + | 0.881182i | \(0.656749\pi\) | |||||||
\(398\) | − | 92.3068i | − | 0.231927i | ||||||
\(399\) | 302.950 | − | 574.524i | 0.759274 | − | 1.43991i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 261.219i | 0.651419i | 0.945470 | + | 0.325709i | \(0.105603\pi\) | ||||
−0.945470 | + | 0.325709i | \(0.894397\pi\) | |||||||
\(402\) | 10.4853i | 0.0260827i | ||||||||
\(403\) | 164.367 | 0.407858 | ||||||||
\(404\) | −115.695 | −0.286375 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 658.918 | 1.62295 | ||||||||
\(407\) | − | 358.966i | − | 0.881982i | ||||||
\(408\) | −434.413 | −1.06474 | ||||||||
\(409\) | 723.501i | 1.76895i | 0.466587 | + | 0.884475i | \(0.345484\pi\) | ||||
−0.466587 | + | 0.884475i | \(0.654516\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − | 639.272i | − | 1.55541i | ||||||
\(412\) | 45.5705i | 0.110608i | ||||||||
\(413\) | − | 110.509i | − | 0.267575i | ||||||
\(414\) | 1.06803i | 0.00257978i | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −506.821 | −1.21832 | ||||||||
\(417\) | 550.069i | 1.31911i | ||||||||
\(418\) | −79.2980 | + | 150.383i | −0.189708 | + | 0.359768i | ||||
\(419\) | −667.084 | −1.59209 | −0.796043 | − | 0.605240i | \(-0.793077\pi\) | ||||
−0.796043 | + | 0.605240i | \(0.793077\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 358.717i | 0.852059i | 0.904709 | + | 0.426030i | \(0.140088\pi\) | ||||
−0.904709 | + | 0.426030i | \(0.859912\pi\) | |||||||
\(422\) | −63.9123 | −0.151451 | ||||||||
\(423\) | −30.3984 | −0.0718638 | ||||||||
\(424\) | 563.303 | 1.32854 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 220.746i | 0.518183i | ||||||||
\(427\) | 428.363 | 1.00319 | ||||||||
\(428\) | 139.090i | 0.324978i | ||||||||
\(429\) | −329.968 | −0.769156 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 742.801i | 1.72344i | 0.507387 | + | 0.861718i | \(0.330611\pi\) | ||||
−0.507387 | + | 0.861718i | \(0.669389\pi\) | |||||||
\(432\) | 105.813i | 0.244937i | ||||||||
\(433\) | 802.697i | 1.85380i | 0.375304 | + | 0.926902i | \(0.377538\pi\) | ||||
−0.375304 | + | 0.926902i | \(0.622462\pi\) | |||||||
\(434\) | −152.366 | −0.351075 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 160.862i | 0.368951i | ||||||||
\(437\) | −25.8529 | − | 13.6324i | −0.0591599 | − | 0.0311955i | ||||
\(438\) | −474.660 | −1.08370 | ||||||||
\(439\) | 89.6015i | 0.204104i | 0.994779 | + | 0.102052i | \(0.0325408\pi\) | ||||
−0.994779 | + | 0.102052i | \(0.967459\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 43.6326 | 0.0989402 | ||||||||
\(442\) | 439.786 | 0.994990 | ||||||||
\(443\) | 541.058 | 1.22135 | 0.610675 | − | 0.791881i | \(-0.290898\pi\) | ||||
0.610675 | + | 0.791881i | \(0.290898\pi\) | |||||||
\(444\) | 332.756 | 0.749450 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −332.520 | −0.745561 | ||||||||
\(447\) | − | 517.490i | − | 1.15770i | ||||||
\(448\) | 648.982 | 1.44862 | ||||||||
\(449\) | 462.639i | 1.03038i | 0.857077 | + | 0.515188i | \(0.172278\pi\) | ||||
−0.857077 | + | 0.515188i | \(0.827722\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 251.565i | − | 0.557795i | ||||||
\(452\) | − | 382.061i | − | 0.845269i | ||||||
\(453\) | 27.6965 | 0.0611402 | ||||||||
\(454\) | −201.860 | −0.444626 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −415.139 | − | 218.906i | −0.910393 | − | 0.480057i | ||||
\(457\) | −668.815 | −1.46349 | −0.731745 | − | 0.681578i | \(-0.761294\pi\) | ||||
−0.731745 | + | 0.681578i | \(0.761294\pi\) | |||||||
\(458\) | − | 144.352i | − | 0.315178i | ||||||
\(459\) | 486.961i | 1.06092i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 317.165 | 0.687993 | 0.343996 | − | 0.938971i | \(-0.388219\pi\) | ||||
0.343996 | + | 0.938971i | \(0.388219\pi\) | |||||||
\(462\) | 305.878 | 0.662073 | ||||||||
\(463\) | −888.893 | −1.91985 | −0.959927 | − | 0.280250i | \(-0.909583\pi\) | ||||
−0.959927 | + | 0.280250i | \(0.909583\pi\) | |||||||
\(464\) | − | 152.763i | − | 0.329231i | ||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 240.228i | 0.515510i | ||||||||
\(467\) | 564.676 | 1.20916 | 0.604578 | − | 0.796546i | \(-0.293342\pi\) | ||||
0.604578 | + | 0.796546i | \(0.293342\pi\) | |||||||
\(468\) | 17.7530i | 0.0379337i | ||||||||
\(469\) | − | 29.9628i | − | 0.0638865i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | − | 79.6483i | − | 0.169105i | ||||||
\(472\) | −79.8513 | −0.169176 | ||||||||
\(473\) | −117.301 | −0.247993 | ||||||||
\(474\) | − | 393.437i | − | 0.830035i | ||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 416.852 | 0.875740 | ||||||||
\(477\) | − | 32.8371i | − | 0.0688409i | ||||||
\(478\) | 273.321i | 0.571802i | ||||||||
\(479\) | −535.419 | −1.11778 | −0.558892 | − | 0.829240i | \(-0.688773\pi\) | ||||
−0.558892 | + | 0.829240i | \(0.688773\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1003.20 | −2.08566 | ||||||||
\(482\) | 642.914 | 1.33385 | ||||||||
\(483\) | 52.5846i | 0.108871i | ||||||||
\(484\) | −162.827 | −0.336419 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 37.4496 | 0.0770567 | ||||||||
\(487\) | − | 396.046i | − | 0.813236i | −0.913598 | − | 0.406618i | \(-0.866708\pi\) | ||
0.913598 | − | 0.406618i | \(-0.133292\pi\) | |||||||
\(488\) | − | 309.527i | − | 0.634276i | ||||||
\(489\) | − | 373.740i | − | 0.764294i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 14.9147 | 0.0303763 | 0.0151881 | − | 0.999885i | \(-0.495165\pi\) | ||||
0.0151881 | + | 0.999885i | \(0.495165\pi\) | |||||||
\(492\) | 233.197 | 0.473977 | ||||||||
\(493\) | − | 703.033i | − | 1.42603i | ||||||
\(494\) | 420.274 | + | 221.613i | 0.850757 | + | 0.448610i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 35.3246i | 0.0712189i | ||||||||
\(497\) | − | 630.806i | − | 1.26923i | ||||||
\(498\) | 590.369 | 1.18548 | ||||||||
\(499\) | −437.113 | −0.875978 | −0.437989 | − | 0.898980i | \(-0.644309\pi\) | ||||
−0.437989 | + | 0.898980i | \(0.644309\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 243.588 | 0.486203 | ||||||||
\(502\) | − | 485.281i | − | 0.966694i | ||||||
\(503\) | 391.808 | 0.778942 | 0.389471 | − | 0.921039i | \(-0.372658\pi\) | ||||
0.389471 | + | 0.921039i | \(0.372658\pi\) | |||||||
\(504\) | − | 49.0084i | − | 0.0972388i | ||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | − | 13.7641i | − | 0.0272019i | ||||||
\(507\) | 429.262i | 0.846671i | ||||||||
\(508\) | 25.4238i | 0.0500469i | ||||||||
\(509\) | − | 83.4859i | − | 0.164020i | −0.996632 | − | 0.0820098i | \(-0.973866\pi\) | ||
0.996632 | − | 0.0820098i | \(-0.0261339\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1356.39 | 2.65439 | ||||||||
\(512\) | − | 238.383i | − | 0.465591i | ||||||
\(513\) | −245.385 | + | 465.356i | −0.478334 | + | 0.907126i | ||||
\(514\) | −402.354 | −0.782791 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | − | 108.736i | − | 0.210728i | ||||||
\(517\) | 391.757 | 0.757751 | ||||||||
\(518\) | 929.959 | 1.79529 | ||||||||
\(519\) | 366.369 | 0.705914 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 561.658i | − | 1.07804i | −0.842294 | − | 0.539019i | \(-0.818795\pi\) | ||
0.842294 | − | 0.539019i | \(-0.181205\pi\) | |||||||
\(522\) | −27.7549 | −0.0531704 | ||||||||
\(523\) | − | 941.358i | − | 1.79992i | −0.435973 | − | 0.899960i | \(-0.643596\pi\) | ||
0.435973 | − | 0.899960i | \(-0.356404\pi\) | |||||||
\(524\) | 195.493 | 0.373079 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 286.164i | 0.544038i | ||||||||
\(527\) | 162.567i | 0.308477i | ||||||||
\(528\) | − | 70.9146i | − | 0.134308i | ||||||
\(529\) | −526.634 | −0.995527 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 4.65484i | 0.00876618i | ||||||||
\(532\) | 398.358 | + | 210.057i | 0.748793 | + | 0.394844i | ||||
\(533\) | −703.048 | −1.31904 | ||||||||
\(534\) | 79.8236i | 0.149482i | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −21.6505 | −0.0403927 | ||||||||
\(537\) | −251.145 | −0.467682 | ||||||||
\(538\) | 591.962 | 1.10030 | ||||||||
\(539\) | −562.313 | −1.04325 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 890.685 | 1.64637 | 0.823184 | − | 0.567774i | \(-0.192195\pi\) | ||||
0.823184 | + | 0.567774i | \(0.192195\pi\) | |||||||
\(542\) | − | 178.611i | − | 0.329541i | ||||||
\(543\) | 872.326 | 1.60649 | ||||||||
\(544\) | − | 501.273i | − | 0.921457i | ||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | − | 854.835i | − | 1.56563i | ||||||
\(547\) | 374.919i | 0.685410i | 0.939443 | + | 0.342705i | \(0.111343\pi\) | ||||
−0.939443 | + | 0.342705i | \(0.888657\pi\) | |||||||
\(548\) | 443.252 | 0.808855 | ||||||||
\(549\) | −18.0435 | −0.0328662 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 354.267 | − | 671.841i | 0.642952 | − | 1.21931i | ||||
\(552\) | 37.9966 | 0.0688344 | ||||||||
\(553\) | 1124.29i | 2.03307i | ||||||||
\(554\) | − | 481.740i | − | 0.869568i | ||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −381.402 | −0.685974 | ||||||||
\(557\) | 93.1828 | 0.167294 | 0.0836470 | − | 0.996495i | \(-0.473343\pi\) | ||||
0.0836470 | + | 0.996495i | \(0.473343\pi\) | |||||||
\(558\) | 6.41798 | 0.0115018 | ||||||||
\(559\) | 327.819i | 0.586438i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | − | 326.356i | − | 0.581740i | ||||||
\(562\) | −213.679 | −0.380213 | ||||||||
\(563\) | − | 526.142i | − | 0.934533i | −0.884116 | − | 0.467267i | \(-0.845239\pi\) | ||
0.884116 | − | 0.467267i | \(-0.154761\pi\) | |||||||
\(564\) | 363.152i | 0.643887i | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | − | 338.899i | − | 0.598762i | ||||||
\(567\) | 894.451 | 1.57752 | ||||||||
\(568\) | −455.807 | −0.802478 | ||||||||
\(569\) | − | 320.890i | − | 0.563955i | −0.959421 | − | 0.281977i | \(-0.909010\pi\) | ||
0.959421 | − | 0.281977i | \(-0.0909903\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 649.237 | 1.13702 | 0.568508 | − | 0.822677i | \(-0.307521\pi\) | ||||
0.568508 | + | 0.822677i | \(0.307521\pi\) | |||||||
\(572\) | − | 228.790i | − | 0.399983i | ||||||
\(573\) | 19.8407i | 0.0346259i | ||||||||
\(574\) | 651.720 | 1.13540 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −27.3364 | −0.0474591 | ||||||||
\(577\) | −49.2538 | −0.0853618 | −0.0426809 | − | 0.999089i | \(-0.513590\pi\) | ||||
−0.0426809 | + | 0.999089i | \(0.513590\pi\) | |||||||
\(578\) | 28.5441i | 0.0493842i | ||||||||
\(579\) | −688.146 | −1.18851 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −1687.04 | −2.90369 | ||||||||
\(582\) | − | 669.205i | − | 1.14984i | ||||||
\(583\) | 423.186i | 0.725877i | ||||||||
\(584\) | − | 980.102i | − | 1.67826i | ||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 9.91968 | 0.0169278 | ||||||||
\(587\) | −194.238 | −0.330900 | −0.165450 | − | 0.986218i | \(-0.552908\pi\) | ||||
−0.165450 | + | 0.986218i | \(0.552908\pi\) | |||||||
\(588\) | − | 521.254i | − | 0.886487i | ||||||
\(589\) | −81.9197 | + | 155.355i | −0.139083 | + | 0.263760i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | − | 85.7507i | − | 0.145094i | ||||||
\(592\) | − | 215.601i | − | 0.364192i | ||||||
\(593\) | −284.628 | −0.479980 | −0.239990 | − | 0.970775i | \(-0.577144\pi\) | ||||
−0.239990 | + | 0.970775i | \(0.577144\pi\) | |||||||
\(594\) | −247.757 | −0.417099 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 358.813 | 0.602035 | ||||||||
\(597\) | 191.434i | 0.320660i | ||||||||
\(598\) | −38.4665 | −0.0643253 | ||||||||
\(599\) | 723.173i | 1.20730i | 0.797249 | + | 0.603650i | \(0.206288\pi\) | ||||
−0.797249 | + | 0.603650i | \(0.793712\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 194.647i | − | 0.323872i | −0.986801 | − | 0.161936i | \(-0.948226\pi\) | ||
0.986801 | − | 0.161936i | \(-0.0517739\pi\) | |||||||
\(602\) | − | 303.886i | − | 0.504793i | ||||||
\(603\) | 1.26209i | 0.00209302i | ||||||||
\(604\) | 19.2039i | 0.0317946i | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −234.658 | −0.387225 | ||||||||
\(607\) | − | 69.2294i | − | 0.114052i | −0.998373 | − | 0.0570259i | \(-0.981838\pi\) | ||
0.998373 | − | 0.0570259i | \(-0.0181618\pi\) | |||||||
\(608\) | 252.598 | − | 479.033i | 0.415456 | − | 0.787883i | ||||
\(609\) | −1366.52 | −2.24388 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 1094.84i | − | 1.79188i | ||||||
\(612\) | −17.5586 | −0.0286906 | ||||||||
\(613\) | −220.182 | −0.359187 | −0.179593 | − | 0.983741i | \(-0.557478\pi\) | ||||
−0.179593 | + | 0.983741i | \(0.557478\pi\) | |||||||
\(614\) | −62.9147 | −0.102467 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 631.592i | 1.02531i | ||||||||
\(617\) | 399.663 | 0.647753 | 0.323876 | − | 0.946099i | \(-0.395014\pi\) | ||||
0.323876 | + | 0.946099i | \(0.395014\pi\) | |||||||
\(618\) | 92.4281i | 0.149560i | ||||||||
\(619\) | 1061.05 | 1.71413 | 0.857067 | − | 0.515206i | \(-0.172284\pi\) | ||||
0.857067 | + | 0.515206i | \(0.172284\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | − | 42.5928i | − | 0.0685874i | ||||||
\(622\) | − | 155.651i | − | 0.250243i | ||||||
\(623\) | − | 228.105i | − | 0.366139i | ||||||
\(624\) | −198.185 | −0.317603 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | − | 185.441i | − | 0.296232i | ||||||
\(627\) | 164.455 | − | 311.877i | 0.262289 | − | 0.497411i | ||||
\(628\) | 55.2258 | 0.0879392 | ||||||||
\(629\) | − | 992.220i | − | 1.57746i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 374.486 | 0.593480 | 0.296740 | − | 0.954958i | \(-0.404101\pi\) | ||||
0.296740 | + | 0.954958i | \(0.404101\pi\) | |||||||
\(632\) | 812.388 | 1.28542 | ||||||||
\(633\) | 132.547 | 0.209395 | ||||||||
\(634\) | −435.237 | −0.686494 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −392.286 | −0.616803 | ||||||||
\(637\) | 1571.49i | 2.46702i | ||||||||
\(638\) | 357.690 | 0.560643 | ||||||||
\(639\) | 26.5708i | 0.0415818i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 1147.29i | 1.78984i | 0.446227 | + | 0.894920i | \(0.352767\pi\) | ||||
−0.446227 | + | 0.894920i | \(0.647233\pi\) | |||||||
\(642\) | 282.109i | 0.439422i | ||||||||
\(643\) | −824.922 | −1.28293 | −0.641463 | − | 0.767154i | \(-0.721672\pi\) | ||||
−0.641463 | + | 0.767154i | \(0.721672\pi\) | |||||||
\(644\) | −36.4606 | −0.0566159 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −219.188 | + | 415.674i | −0.339300 | + | 0.643457i | ||||
\(647\) | 153.175 | 0.236746 | 0.118373 | − | 0.992969i | \(-0.462232\pi\) | ||||
0.118373 | + | 0.992969i | \(0.462232\pi\) | |||||||
\(648\) | − | 646.312i | − | 0.997395i | ||||||
\(649\) | − | 59.9890i | − | 0.0924329i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 315.991 | 0.485393 | ||||||||
\(652\) | 259.140 | 0.397454 | ||||||||
\(653\) | −1120.33 | −1.71567 | −0.857833 | − | 0.513928i | \(-0.828190\pi\) | ||||
−0.857833 | + | 0.513928i | \(0.828190\pi\) | |||||||
\(654\) | 326.268i | 0.498881i | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | − | 151.095i | − | 0.230327i | ||||||
\(657\) | −57.1339 | −0.0869618 | ||||||||
\(658\) | 1014.91i | 1.54242i | ||||||||
\(659\) | 875.929i | 1.32918i | 0.747208 | + | 0.664590i | \(0.231394\pi\) | ||||
−0.747208 | + | 0.664590i | \(0.768606\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 283.488i | 0.428878i | 0.976737 | + | 0.214439i | \(0.0687923\pi\) | ||||
−0.976737 | + | 0.214439i | \(0.931208\pi\) | |||||||
\(662\) | 281.394 | 0.425067 | ||||||||
\(663\) | −912.066 | −1.37566 | ||||||||
\(664\) | 1219.02i | 1.83588i | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −39.1717 | −0.0588164 | ||||||||
\(667\) | 61.4918i | 0.0921917i | ||||||||
\(668\) | 168.897i | 0.252839i | ||||||||
\(669\) | 689.609 | 1.03081 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 232.535 | 0.346549 | ||||||||
\(672\) | −974.350 | −1.44993 | ||||||||
\(673\) | − | 373.637i | − | 0.555182i | −0.960699 | − | 0.277591i | \(-0.910464\pi\) | ||
0.960699 | − | 0.277591i | \(-0.0895360\pi\) | |||||||
\(674\) | −598.188 | −0.887520 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −297.638 | −0.440292 | ||||||||
\(677\) | 215.956i | 0.318990i | 0.987199 | + | 0.159495i | \(0.0509866\pi\) | ||||
−0.987199 | + | 0.159495i | \(0.949013\pi\) | |||||||
\(678\) | − | 774.913i | − | 1.14294i | ||||||
\(679\) | 1912.33i | 2.81639i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 418.635 | 0.614735 | ||||||||
\(682\) | −82.7113 | −0.121278 | ||||||||
\(683\) | 469.374i | 0.687224i | 0.939112 | + | 0.343612i | \(0.111650\pi\) | ||||
−0.939112 | + | 0.343612i | \(0.888350\pi\) | |||||||
\(684\) | −16.7796 | − | 8.84801i | −0.0245316 | − | 0.0129357i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | − | 649.079i | − | 0.946179i | ||||||
\(687\) | 299.369i | 0.435762i | ||||||||
\(688\) | −70.4527 | −0.102402 | ||||||||
\(689\) | 1182.68 | 1.71651 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −80.4567 | −0.116435 | −0.0582176 | − | 0.998304i | \(-0.518542\pi\) | ||||
−0.0582176 | + | 0.998304i | \(0.518542\pi\) | |||||||
\(692\) | 254.030i | 0.367095i | ||||||||
\(693\) | 36.8180 | 0.0531284 | ||||||||
\(694\) | − | 778.741i | − | 1.12211i | ||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 987.421i | 1.41871i | ||||||||
\(697\) | − | 695.352i | − | 0.997636i | ||||||
\(698\) | 384.629i | 0.551044i | ||||||||
\(699\) | − | 498.205i | − | 0.712740i | ||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 144.654 | 0.206353 | 0.103177 | − | 0.994663i | \(-0.467099\pi\) | ||||
0.103177 | + | 0.994663i | \(0.467099\pi\) | |||||||
\(702\) | 692.404i | 0.986330i | ||||||||
\(703\) | 499.992 | − | 948.199i | 0.711226 | − | 1.34879i | ||||
\(704\) | 352.296 | 0.500421 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 767.512i | 1.08713i | ||||||||
\(707\) | 670.562 | 0.948461 | ||||||||
\(708\) | 55.6088 | 0.0785435 | ||||||||
\(709\) | −108.558 | −0.153115 | −0.0765573 | − | 0.997065i | \(-0.524393\pi\) | ||||
−0.0765573 | + | 0.997065i | \(0.524393\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − | 47.3573i | − | 0.0666066i | ||||||
\(712\) | −164.824 | −0.231494 | ||||||||
\(713\) | − | 14.2192i | − | 0.0199428i | ||||||
\(714\) | 845.477 | 1.18414 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | − | 174.137i | − | 0.243208i | ||||||
\(717\) | − | 566.837i | − | 0.790568i | ||||||
\(718\) | − | 104.046i | − | 0.144911i | ||||||
\(719\) | 804.887 | 1.11945 | 0.559727 | − | 0.828677i | \(-0.310906\pi\) | ||||
0.559727 | + | 0.828677i | \(0.310906\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − | 264.124i | − | 0.366329i | ||||||
\(722\) | −418.926 | + | 286.780i | −0.580230 | + | 0.397202i | ||||
\(723\) | −1333.33 | −1.84416 | ||||||||
\(724\) | 604.845i | 0.835421i | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −330.252 | −0.454893 | ||||||||
\(727\) | 242.633 | 0.333746 | 0.166873 | − | 0.985978i | \(-0.446633\pi\) | ||||
0.166873 | + | 0.985978i | \(0.446633\pi\) | |||||||
\(728\) | 1765.11 | 2.42460 | ||||||||
\(729\) | −764.482 | −1.04867 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −324.231 | −0.443544 | ||||||||
\(732\) | 215.556i | 0.294475i | ||||||||
\(733\) | 577.444 | 0.787782 | 0.393891 | − | 0.919157i | \(-0.371129\pi\) | ||||
0.393891 | + | 0.919157i | \(0.371129\pi\) | |||||||
\(734\) | 559.253i | 0.761925i | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 43.8446i | 0.0595715i | ||||||||
\(737\) | − | 16.2651i | − | 0.0220694i | ||||||
\(738\) | −27.4517 | −0.0371975 | ||||||||
\(739\) | −482.046 | −0.652295 | −0.326148 | − | 0.945319i | \(-0.605751\pi\) | ||||
−0.326148 | + | 0.945319i | \(0.605751\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −871.600 | − | 459.601i | −1.17625 | − | 0.620244i | ||||
\(742\) | −1096.33 | −1.47753 | ||||||||
\(743\) | − | 713.547i | − | 0.960359i | −0.877170 | − | 0.480179i | \(-0.840572\pi\) | ||
0.877170 | − | 0.480179i | \(-0.159428\pi\) | |||||||
\(744\) | − | 228.328i | − | 0.306893i | ||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 400.521 | 0.536891 | ||||||||
\(747\) | 71.0616 | 0.0951293 | ||||||||
\(748\) | 226.286 | 0.302521 | ||||||||
\(749\) | − | 806.158i | − | 1.07631i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 1049.66i | − | 1.39768i | −0.715276 | − | 0.698842i | \(-0.753699\pi\) | ||
0.715276 | − | 0.698842i | \(-0.246301\pi\) | |||||||
\(752\) | 235.296 | 0.312894 | ||||||||
\(753\) | 1006.42i | 1.33654i | ||||||||
\(754\) | − | 999.634i | − | 1.32577i | ||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 656.296i | 0.868117i | ||||||||
\(757\) | −87.6677 | −0.115809 | −0.0579047 | − | 0.998322i | \(-0.518442\pi\) | ||||
−0.0579047 | + | 0.998322i | \(0.518442\pi\) | |||||||
\(758\) | −764.336 | −1.00836 | ||||||||
\(759\) | 28.5453i | 0.0376090i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 706.869 | 0.928869 | 0.464435 | − | 0.885607i | \(-0.346258\pi\) | ||||
0.464435 | + | 0.885607i | \(0.346258\pi\) | |||||||
\(762\) | 51.5657i | 0.0676715i | ||||||||
\(763\) | − | 932.348i | − | 1.22195i | ||||||
\(764\) | −13.7569 | −0.0180064 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −841.679 | −1.09880 | ||||||||
\(767\) | −167.651 | −0.218580 | ||||||||
\(768\) | 794.202i | 1.03412i | ||||||||
\(769\) | −69.6679 | −0.0905955 | −0.0452977 | − | 0.998974i | \(-0.514424\pi\) | ||||
−0.0452977 | + | 0.998974i | \(0.514424\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 834.437 | 1.08228 | ||||||||
\(772\) | − | 477.140i | − | 0.618057i | ||||||
\(773\) | 1236.62i | 1.59977i | 0.600153 | + | 0.799886i | \(0.295107\pi\) | ||||
−0.600153 | + | 0.799886i | \(0.704893\pi\) | |||||||
\(774\) | 12.8003i | 0.0165378i | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 1381.81 | 1.78068 | ||||||||
\(777\) | −1928.63 | −2.48215 | ||||||||
\(778\) | 1005.18i | 1.29200i | ||||||||
\(779\) | 350.397 | − | 664.502i | 0.449803 | − | 0.853019i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − | 342.429i | − | 0.438450i | ||||||
\(782\) | − | 38.0455i | − | 0.0486515i | ||||||
\(783\) | 1106.86 | 1.41362 | ||||||||
\(784\) | −337.735 | −0.430784 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 396.508 | 0.504463 | ||||||||
\(787\) | 962.806i | 1.22339i | 0.791095 | + | 0.611693i | \(0.209511\pi\) | ||||
−0.791095 | + | 0.611693i | \(0.790489\pi\) | |||||||
\(788\) | 59.4570 | 0.0754530 | ||||||||
\(789\) | − | 593.472i | − | 0.752182i | ||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 2214.40i | 2.79950i | ||||||||
\(792\) | − | 26.6039i | − | 0.0335908i | ||||||
\(793\) | − | 649.863i | − | 0.819499i | ||||||
\(794\) | − | 527.913i | − | 0.664878i | ||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −132.735 | −0.166752 | ||||||||
\(797\) | − | 412.057i | − | 0.517010i | −0.966010 | − | 0.258505i | \(-0.916770\pi\) | ||
0.966010 | − | 0.258505i | \(-0.0832298\pi\) | |||||||
\(798\) | 807.966 | + | 426.047i | 1.01249 | + | 0.533893i | ||||
\(799\) | 1082.86 | 1.35527 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 9.60822i | 0.0119953i | ||||||||
\(802\) | −367.358 | −0.458053 | ||||||||
\(803\) | 736.310 | 0.916949 | ||||||||
\(804\) | 15.0775 | 0.0187531 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 231.153i | 0.286790i | ||||||||
\(807\) | −1227.66 | −1.52126 | ||||||||
\(808\) | − | 484.535i | − | 0.599671i | ||||||
\(809\) | 445.562 | 0.550756 | 0.275378 | − | 0.961336i | \(-0.411197\pi\) | ||||
0.275378 | + | 0.961336i | \(0.411197\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 558.857i | − | 0.689096i | −0.938769 | − | 0.344548i | \(-0.888032\pi\) | ||
0.938769 | − | 0.344548i | \(-0.111968\pi\) | |||||||
\(812\) | − | 947.505i | − | 1.16688i | ||||||
\(813\) | 370.419i | 0.455620i | ||||||||
\(814\) | 504.823 | 0.620176 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | − | 196.015i | − | 0.240215i | ||||||
\(817\) | −309.846 | − | 163.384i | −0.379248 | − | 0.199980i | ||||
\(818\) | −1017.48 | −1.24386 | ||||||||
\(819\) | − | 102.895i | − | 0.125635i | ||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −1469.94 | −1.79043 | −0.895215 | − | 0.445634i | \(-0.852978\pi\) | ||||
−0.895215 | + | 0.445634i | \(0.852978\pi\) | |||||||
\(822\) | 899.024 | 1.09370 | ||||||||
\(823\) | −165.659 | −0.201287 | −0.100643 | − | 0.994923i | \(-0.532090\pi\) | ||||
−0.100643 | + | 0.994923i | \(0.532090\pi\) | |||||||
\(824\) | −190.850 | −0.231614 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 155.411 | 0.188149 | ||||||||
\(827\) | 503.503i | 0.608831i | 0.952539 | + | 0.304415i | \(0.0984610\pi\) | ||||
−0.952539 | + | 0.304415i | \(0.901539\pi\) | |||||||
\(828\) | 1.53579 | 0.00185482 | ||||||||
\(829\) | 156.053i | 0.188242i | 0.995561 | + | 0.0941211i | \(0.0300041\pi\) | ||||
−0.995561 | + | 0.0941211i | \(0.969996\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 999.075i | 1.20226i | ||||||||
\(832\) | − | 984.560i | − | 1.18337i | ||||||
\(833\) | −1554.29 | −1.86589 | ||||||||
\(834\) | −773.575 | −0.927548 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 216.246 | + | 114.028i | 0.258668 | + | 0.136397i | ||||
\(837\) | −255.948 | −0.305792 | ||||||||
\(838\) | − | 938.136i | − | 1.11949i | ||||||
\(839\) | − | 543.442i | − | 0.647725i | −0.946104 | − | 0.323863i | \(-0.895018\pi\) | ||
0.946104 | − | 0.323863i | \(-0.104982\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −756.994 | −0.900112 | ||||||||
\(842\) | −504.472 | −0.599136 | ||||||||
\(843\) | 443.147 | 0.525678 | ||||||||
\(844\) | 91.9040i | 0.108891i | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | − | 42.7500i | − | 0.0505319i | ||||||
\(847\) | 943.732 | 1.11421 | ||||||||
\(848\) | 254.173i | 0.299732i | ||||||||
\(849\) | 702.838i | 0.827842i | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 86.7861i | 0.101981i | ||||||||
\(852\) | 317.426 | 0.372566 | ||||||||
\(853\) | −788.764 | −0.924694 | −0.462347 | − | 0.886699i | \(-0.652993\pi\) | ||||
−0.462347 | + | 0.886699i | \(0.652993\pi\) | |||||||
\(854\) | 602.418i | 0.705407i | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −582.514 | −0.680506 | ||||||||
\(857\) | 387.309i | 0.451935i | 0.974135 | + | 0.225968i | \(0.0725544\pi\) | ||||
−0.974135 | + | 0.225968i | \(0.927446\pi\) | |||||||
\(858\) | − | 464.042i | − | 0.540842i | ||||||
\(859\) | −47.4552 | −0.0552447 | −0.0276224 | − | 0.999618i | \(-0.508794\pi\) | ||||
−0.0276224 | + | 0.999618i | \(0.508794\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −1351.59 | −1.56979 | ||||||||
\(862\) | −1044.62 | −1.21185 | ||||||||
\(863\) | 852.591i | 0.987938i | 0.869479 | + | 0.493969i | \(0.164454\pi\) | ||||
−0.869479 | + | 0.493969i | \(0.835546\pi\) | |||||||
\(864\) | 789.209 | 0.913437 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −1128.85 | −1.30352 | ||||||||
\(867\) | − | 59.1972i | − | 0.0682782i | ||||||
\(868\) | 219.099i | 0.252418i | ||||||||
\(869\) | 610.313i | 0.702317i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −45.4560 | −0.0521883 | ||||||||
\(872\) | −673.695 | −0.772587 | ||||||||
\(873\) | − | 80.5511i | − | 0.0922693i | ||||||
\(874\) | 19.1716 | − | 36.3575i | 0.0219355 | − | 0.0415990i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 682.547i | 0.779163i | ||||||||
\(877\) | 832.003i | 0.948692i | 0.880339 | + | 0.474346i | \(0.157315\pi\) | ||||
−0.880339 | + | 0.474346i | \(0.842685\pi\) | |||||||
\(878\) | −126.009 | −0.143518 | ||||||||
\(879\) | −20.5723 | −0.0234042 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −450.264 | −0.511083 | −0.255541 | − | 0.966798i | \(-0.582254\pi\) | ||||
−0.255541 | + | 0.966798i | \(0.582254\pi\) | |||||||
\(882\) | 61.3616i | 0.0695710i | ||||||||
\(883\) | 1035.05 | 1.17219 | 0.586096 | − | 0.810241i | \(-0.300664\pi\) | ||||
0.586096 | + | 0.810241i | \(0.300664\pi\) | |||||||
\(884\) | − | 632.399i | − | 0.715384i | ||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 760.903i | 0.858807i | ||||||||
\(887\) | − | 296.394i | − | 0.334153i | −0.985944 | − | 0.167077i | \(-0.946567\pi\) | ||
0.985944 | − | 0.167077i | \(-0.0534327\pi\) | |||||||
\(888\) | 1393.59i | 1.56936i | ||||||||
\(889\) | − | 147.355i | − | 0.165753i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 485.548 | 0.544947 | ||||||||
\(892\) | 478.155i | 0.536048i | ||||||||
\(893\) | 1034.81 | + | 545.665i | 1.15881 | + | 0.611047i | ||||
\(894\) | 727.759 | 0.814048 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | − | 423.623i | − | 0.472794i | ||||||
\(897\) | 79.7752 | 0.0889356 | ||||||||
\(898\) | −650.620 | −0.724521 | ||||||||
\(899\) | 369.516 | 0.411030 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1169.73i | 1.29826i | ||||||||
\(902\) | 353.782 | 0.392220 | ||||||||
\(903\) | 630.224i | 0.697922i | ||||||||
\(904\) | 1600.08 | 1.77000 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 38.9503i | 0.0429915i | ||||||||
\(907\) | 775.691i | 0.855227i | 0.903962 | + | 0.427614i | \(0.140646\pi\) | ||||
−0.903962 | + | 0.427614i | \(0.859354\pi\) | |||||||
\(908\) | 290.269i | 0.319679i | ||||||||
\(909\) | −28.2454 | −0.0310730 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1211.86i | 1.33025i | 0.746731 | + | 0.665126i | \(0.231622\pi\) | ||||
−0.746731 | + | 0.665126i | \(0.768378\pi\) | |||||||
\(912\) | 98.7745 | − | 187.319i | 0.108305 | − | 0.205393i | ||||
\(913\) | −915.802 | −1.00307 | ||||||||
\(914\) | − | 940.570i | − | 1.02907i | ||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −207.573 | −0.226609 | ||||||||
\(917\) | −1133.07 | −1.23562 | ||||||||
\(918\) | −684.824 | −0.745996 | ||||||||
\(919\) | −1413.02 | −1.53757 | −0.768784 | − | 0.639509i | \(-0.779138\pi\) | ||||
−0.768784 | + | 0.639509i | \(0.779138\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 130.478 | 0.141670 | ||||||||
\(922\) | 446.036i | 0.483770i | ||||||||
\(923\) | −956.985 | −1.03682 | ||||||||
\(924\) | − | 439.843i | − | 0.476021i | ||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | − | 1250.07i | − | 1.34997i | ||||||
\(927\) | 11.1254i | 0.0120015i | ||||||||
\(928\) | −1139.39 | −1.22780 | ||||||||
\(929\) | −775.131 | −0.834371 | −0.417185 | − | 0.908821i | \(-0.636983\pi\) | ||||
−0.417185 | + | 0.908821i | \(0.636983\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1485.33 | − | 783.226i | −1.59541 | − | 0.841274i | ||||
\(932\) | 345.441 | 0.370644 | ||||||||
\(933\) | 322.803i | 0.345984i | ||||||||
\(934\) | 794.117i | 0.850233i | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −74.3498 | −0.0794335 | ||||||||
\(937\) | −808.931 | −0.863320 | −0.431660 | − | 0.902036i | \(-0.642072\pi\) | ||||
−0.431660 | + | 0.902036i | \(0.642072\pi\) | |||||||
\(938\) | 42.1374 | 0.0449226 | ||||||||
\(939\) | 384.584i | 0.409568i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 1692.92i | − | 1.79906i | −0.436856 | − | 0.899532i | \(-0.643908\pi\) | ||
0.436856 | − | 0.899532i | \(-0.356092\pi\) | |||||||
\(942\) | 112.011 | 0.118908 | ||||||||
\(943\) | 60.8201i | 0.0644964i | ||||||||
\(944\) | − | 36.0304i | − | 0.0381678i | ||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | − | 164.963i | − | 0.174379i | ||||||
\(947\) | −1511.42 | −1.59601 | −0.798003 | − | 0.602654i | \(-0.794110\pi\) | ||||
−0.798003 | + | 0.602654i | \(0.794110\pi\) | |||||||
\(948\) | −565.750 | −0.596783 | ||||||||
\(949\) | − | 2057.76i | − | 2.16835i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 902.632 | 0.949140 | ||||||||
\(952\) | 1745.78i | 1.83381i | ||||||||
\(953\) | − | 305.820i | − | 0.320902i | −0.987044 | − | 0.160451i | \(-0.948705\pi\) | ||
0.987044 | − | 0.160451i | \(-0.0512949\pi\) | |||||||
\(954\) | 46.1796 | 0.0484063 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 393.028 | 0.411117 | ||||||||
\(957\) | −741.808 | −0.775139 | ||||||||
\(958\) | − | 752.972i | − | 0.785983i | ||||||
\(959\) | −2569.06 | −2.67889 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 875.554 | 0.911087 | ||||||||
\(962\) | − | 1410.83i | − | 1.46656i | ||||||
\(963\) | 33.9570i | 0.0352617i | ||||||||
\(964\) | − | 924.491i | − | 0.959016i | ||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −73.9510 | −0.0765538 | ||||||||
\(967\) | 188.075 | 0.194493 | 0.0972466 | − | 0.995260i | \(-0.468996\pi\) | ||||
0.0972466 | + | 0.995260i | \(0.468996\pi\) | |||||||
\(968\) | − | 681.922i | − | 0.704465i | ||||||
\(969\) | 454.570 | − | 862.059i | 0.469113 | − | 0.889638i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 1108.38i | − | 1.14148i | −0.821129 | − | 0.570742i | \(-0.806655\pi\) | ||
0.821129 | − | 0.570742i | \(-0.193345\pi\) | |||||||
\(972\) | − | 53.8514i | − | 0.0554027i | ||||||
\(973\) | 2210.58 | 2.27192 | ||||||||
\(974\) | 556.969 | 0.571836 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 139.664 | 0.143099 | ||||||||
\(977\) | − | 559.011i | − | 0.572171i | −0.958204 | − | 0.286086i | \(-0.907646\pi\) | ||
0.958204 | − | 0.286086i | \(-0.0923542\pi\) | |||||||
\(978\) | 525.599 | 0.537423 | ||||||||
\(979\) | − | 123.825i | − | 0.126481i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 39.2723i | 0.0400330i | ||||||||
\(982\) | 20.9750i | 0.0213594i | ||||||||
\(983\) | − | 1006.84i | − | 1.02425i | −0.858910 | − | 0.512126i | \(-0.828858\pi\) | ||
0.858910 | − | 0.512126i | \(-0.171142\pi\) | |||||||
\(984\) | 976.634i | 0.992514i | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 988.692 | 1.00273 | ||||||||
\(987\) | − | 2104.81i | − | 2.13253i | ||||||
\(988\) | 318.674 | − | 604.342i | 0.322544 | − | 0.611682i | ||||
\(989\) | 28.3593 | 0.0286748 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 999.726i | − | 1.00881i | −0.863468 | − | 0.504403i | \(-0.831713\pi\) | ||
0.863468 | − | 0.504403i | \(-0.168287\pi\) | |||||||
\(992\) | 263.470 | 0.265595 | ||||||||
\(993\) | −583.580 | −0.587693 | ||||||||
\(994\) | 887.117 | 0.892472 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | − | 848.933i | − | 0.852342i | ||||||
\(997\) | 1250.46 | 1.25422 | 0.627112 | − | 0.778929i | \(-0.284237\pi\) | ||||
0.627112 | + | 0.778929i | \(0.284237\pi\) | |||||||
\(998\) | − | 614.722i | − | 0.615954i | ||||||
\(999\) | 1562.16 | 1.56373 |
(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 | 475.3.c.h.151.9 | yes | 14 | |
5.2 | odd | 4 | 475.3.d.d.474.11 | 28 | |||
5.3 | odd | 4 | 475.3.d.d.474.18 | 28 | |||
5.4 | even | 2 | 475.3.c.i.151.6 | yes | 14 | ||
19.18 | odd | 2 | inner | 475.3.c.h.151.6 | ✓ | 14 | |
95.18 | even | 4 | 475.3.d.d.474.12 | 28 | |||
95.37 | even | 4 | 475.3.d.d.474.17 | 28 | |||
95.94 | odd | 2 | 475.3.c.i.151.9 | yes | 14 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
475.3.c.h.151.6 | ✓ | 14 | 19.18 | odd | 2 | inner | |
475.3.c.h.151.9 | yes | 14 | 1.1 | even | 1 | trivial | |
475.3.c.i.151.6 | yes | 14 | 5.4 | even | 2 | ||
475.3.c.i.151.9 | yes | 14 | 95.94 | odd | 2 | ||
475.3.d.d.474.11 | 28 | 5.2 | odd | 4 | |||
475.3.d.d.474.12 | 28 | 95.18 | even | 4 | |||
475.3.d.d.474.17 | 28 | 95.37 | even | 4 | |||
475.3.d.d.474.18 | 28 | 5.3 | odd | 4 |