Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [475,2,Mod(1,475)]
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, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("475.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 475 = 5^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 475.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: | \(3.79289409601\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.11344.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{4} - 2x^{3} - 4x^{2} + 4x + 3 \)
|
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 95) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(1.28734\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 475.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.63010 | 1.85976 | 0.929882 | − | 0.367859i | \(-0.119909\pi\) | ||||
0.929882 | + | 0.367859i | \(0.119909\pi\) | |||||||
\(3\) | −3.04306 | −1.75691 | −0.878455 | − | 0.477825i | \(-0.841425\pi\) | ||||
−0.878455 | + | 0.477825i | \(0.841425\pi\) | |||||||
\(4\) | 4.91744 | 2.45872 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −8.00355 | −3.26744 | ||||||||
\(7\) | 0.574672 | 0.217205 | 0.108603 | − | 0.994085i | \(-0.465362\pi\) | ||||
0.108603 | + | 0.994085i | \(0.465362\pi\) | |||||||
\(8\) | 7.67316 | 2.71287 | ||||||||
\(9\) | 6.26020 | 2.08673 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.57467 | 0.776293 | 0.388146 | − | 0.921598i | \(-0.373116\pi\) | ||||
0.388146 | + | 0.921598i | \(0.373116\pi\) | |||||||
\(12\) | −14.9641 | −4.31975 | ||||||||
\(13\) | 0.468387 | 0.129907 | 0.0649536 | − | 0.997888i | \(-0.479310\pi\) | ||||
0.0649536 | + | 0.997888i | \(0.479310\pi\) | |||||||
\(14\) | 1.51145 | 0.403951 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 10.3463 | 2.58658 | ||||||||
\(17\) | 4.08612 | 0.991029 | 0.495514 | − | 0.868600i | \(-0.334980\pi\) | ||||
0.495514 | + | 0.868600i | \(0.334980\pi\) | |||||||
\(18\) | 16.4650 | 3.88083 | ||||||||
\(19\) | 1.00000 | 0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.74876 | −0.381611 | ||||||||
\(22\) | 6.77165 | 1.44372 | ||||||||
\(23\) | −1.51145 | −0.315158 | −0.157579 | − | 0.987506i | \(-0.550369\pi\) | ||||
−0.157579 | + | 0.987506i | \(0.550369\pi\) | |||||||
\(24\) | −23.3499 | −4.76627 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 1.23191 | 0.241596 | ||||||||
\(27\) | −9.92099 | −1.90930 | ||||||||
\(28\) | 2.82591 | 0.534047 | ||||||||
\(29\) | −4.08612 | −0.758773 | −0.379386 | − | 0.925238i | \(-0.623865\pi\) | ||||
−0.379386 | + | 0.925238i | \(0.623865\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −9.92099 | −1.78186 | −0.890931 | − | 0.454138i | \(-0.849947\pi\) | ||||
−0.890931 | + | 0.454138i | \(0.849947\pi\) | |||||||
\(32\) | 11.8656 | 2.09755 | ||||||||
\(33\) | −7.83488 | −1.36388 | ||||||||
\(34\) | 10.7469 | 1.84308 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 30.7842 | 5.13069 | ||||||||
\(37\) | 8.30326 | 1.36505 | 0.682524 | − | 0.730863i | \(-0.260882\pi\) | ||||
0.682524 | + | 0.730863i | \(0.260882\pi\) | |||||||
\(38\) | 2.63010 | 0.426659 | ||||||||
\(39\) | −1.42533 | −0.228235 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.83488 | −0.286560 | −0.143280 | − | 0.989682i | \(-0.545765\pi\) | ||||
−0.143280 | + | 0.989682i | \(0.545765\pi\) | |||||||
\(42\) | −4.59942 | −0.709705 | ||||||||
\(43\) | 0.574672 | 0.0876366 | 0.0438183 | − | 0.999040i | \(-0.486048\pi\) | ||||
0.0438183 | + | 0.999040i | \(0.486048\pi\) | |||||||
\(44\) | 12.6608 | 1.90869 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −3.97526 | −0.586119 | ||||||||
\(47\) | −7.09508 | −1.03492 | −0.517462 | − | 0.855706i | \(-0.673123\pi\) | ||||
−0.517462 | + | 0.855706i | \(0.673123\pi\) | |||||||
\(48\) | −31.4845 | −4.54439 | ||||||||
\(49\) | −6.66975 | −0.952822 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −12.4343 | −1.74115 | ||||||||
\(52\) | 2.30326 | 0.319405 | ||||||||
\(53\) | −4.30326 | −0.591099 | −0.295549 | − | 0.955327i | \(-0.595503\pi\) | ||||
−0.295549 | + | 0.955327i | \(0.595503\pi\) | |||||||
\(54\) | −26.0932 | −3.55084 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 4.40955 | 0.589251 | ||||||||
\(57\) | −3.04306 | −0.403063 | ||||||||
\(58\) | −10.7469 | −1.41114 | ||||||||
\(59\) | −2.68553 | −0.349627 | −0.174813 | − | 0.984602i | \(-0.555932\pi\) | ||||
−0.174813 | + | 0.984602i | \(0.555932\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 12.4095 | 1.58888 | 0.794440 | − | 0.607343i | \(-0.207765\pi\) | ||||
0.794440 | + | 0.607343i | \(0.207765\pi\) | |||||||
\(62\) | −26.0932 | −3.31384 | ||||||||
\(63\) | 3.59756 | 0.453250 | ||||||||
\(64\) | 10.5150 | 1.31438 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −20.6065 | −2.53649 | ||||||||
\(67\) | 2.70570 | 0.330554 | 0.165277 | − | 0.986247i | \(-0.447148\pi\) | ||||
0.165277 | + | 0.986247i | \(0.447148\pi\) | |||||||
\(68\) | 20.0932 | 2.43666 | ||||||||
\(69\) | 4.59942 | 0.553705 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −7.40058 | −0.878288 | −0.439144 | − | 0.898417i | \(-0.644718\pi\) | ||||
−0.439144 | + | 0.898417i | \(0.644718\pi\) | |||||||
\(72\) | 48.0356 | 5.66104 | ||||||||
\(73\) | −12.0861 | −1.41457 | −0.707286 | − | 0.706927i | \(-0.750081\pi\) | ||||
−0.707286 | + | 0.706927i | \(0.750081\pi\) | |||||||
\(74\) | 21.8384 | 2.53867 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 4.91744 | 0.564069 | ||||||||
\(77\) | 1.47959 | 0.168615 | ||||||||
\(78\) | −3.74876 | −0.424463 | ||||||||
\(79\) | −6.68553 | −0.752181 | −0.376091 | − | 0.926583i | \(-0.622732\pi\) | ||||
−0.376091 | + | 0.926583i | \(0.622732\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 11.4095 | 1.26773 | ||||||||
\(82\) | −4.82591 | −0.532933 | ||||||||
\(83\) | 6.66079 | 0.731117 | 0.365558 | − | 0.930788i | \(-0.380878\pi\) | ||||
0.365558 | + | 0.930788i | \(0.380878\pi\) | |||||||
\(84\) | −8.59942 | −0.938273 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 1.51145 | 0.162983 | ||||||||
\(87\) | 12.4343 | 1.33310 | ||||||||
\(88\) | 19.7559 | 2.10598 | ||||||||
\(89\) | 14.6065 | 1.54829 | 0.774144 | − | 0.633009i | \(-0.218180\pi\) | ||||
0.774144 | + | 0.633009i | \(0.218180\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.269169 | 0.0282165 | ||||||||
\(92\) | −7.43244 | −0.774885 | ||||||||
\(93\) | 30.1902 | 3.13057 | ||||||||
\(94\) | −18.6608 | −1.92471 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −36.1076 | −3.68522 | ||||||||
\(97\) | −17.4526 | −1.77204 | −0.886022 | − | 0.463643i | \(-0.846542\pi\) | ||||
−0.886022 | + | 0.463643i | \(0.846542\pi\) | |||||||
\(98\) | −17.5421 | −1.77202 | ||||||||
\(99\) | 16.1180 | 1.61992 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 14.2831 | 1.42122 | 0.710611 | − | 0.703586i | \(-0.248419\pi\) | ||||
0.710611 | + | 0.703586i | \(0.248419\pi\) | |||||||
\(102\) | −32.7035 | −3.23813 | ||||||||
\(103\) | −4.79182 | −0.472152 | −0.236076 | − | 0.971735i | \(-0.575861\pi\) | ||||
−0.236076 | + | 0.971735i | \(0.575861\pi\) | |||||||
\(104\) | 3.59401 | 0.352421 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −11.3180 | −1.09930 | ||||||||
\(107\) | −9.22611 | −0.891922 | −0.445961 | − | 0.895052i | \(-0.647138\pi\) | ||||
−0.445961 | + | 0.895052i | \(0.647138\pi\) | |||||||
\(108\) | −48.7859 | −4.69442 | ||||||||
\(109\) | 4.89810 | 0.469153 | 0.234577 | − | 0.972098i | \(-0.424630\pi\) | ||||
0.234577 | + | 0.972098i | \(0.424630\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −25.2673 | −2.39827 | ||||||||
\(112\) | 5.94574 | 0.561819 | ||||||||
\(113\) | −1.61773 | −0.152183 | −0.0760916 | − | 0.997101i | \(-0.524244\pi\) | ||||
−0.0760916 | + | 0.997101i | \(0.524244\pi\) | |||||||
\(114\) | −8.00355 | −0.749602 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −20.0932 | −1.86561 | ||||||||
\(117\) | 2.93220 | 0.271082 | ||||||||
\(118\) | −7.06323 | −0.650223 | ||||||||
\(119\) | 2.34818 | 0.215257 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −4.37107 | −0.397370 | ||||||||
\(122\) | 32.6384 | 2.95494 | ||||||||
\(123\) | 5.58364 | 0.503459 | ||||||||
\(124\) | −48.7859 | −4.38110 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 9.46196 | 0.842938 | ||||||||
\(127\) | 13.1292 | 1.16503 | 0.582513 | − | 0.812821i | \(-0.302070\pi\) | ||||
0.582513 | + | 0.812821i | \(0.302070\pi\) | |||||||
\(128\) | 3.92440 | 0.346871 | ||||||||
\(129\) | −1.74876 | −0.153970 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −8.17223 | −0.714011 | −0.357006 | − | 0.934102i | \(-0.616202\pi\) | ||||
−0.357006 | + | 0.934102i | \(0.616202\pi\) | |||||||
\(132\) | −38.5275 | −3.35339 | ||||||||
\(133\) | 0.574672 | 0.0498304 | ||||||||
\(134\) | 7.11627 | 0.614752 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 31.3534 | 2.68853 | ||||||||
\(137\) | 14.6065 | 1.24792 | 0.623960 | − | 0.781456i | \(-0.285523\pi\) | ||||
0.623960 | + | 0.781456i | \(0.285523\pi\) | |||||||
\(138\) | 12.0969 | 1.02976 | ||||||||
\(139\) | −2.07219 | −0.175761 | −0.0878804 | − | 0.996131i | \(-0.528009\pi\) | ||||
−0.0878804 | + | 0.996131i | \(0.528009\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 21.5907 | 1.81827 | ||||||||
\(142\) | −19.4643 | −1.63341 | ||||||||
\(143\) | 1.20594 | 0.100846 | ||||||||
\(144\) | 64.7701 | 5.39751 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −31.7877 | −2.63077 | ||||||||
\(147\) | 20.2964 | 1.67402 | ||||||||
\(148\) | 40.8308 | 3.35627 | ||||||||
\(149\) | 8.91203 | 0.730102 | 0.365051 | − | 0.930988i | \(-0.381052\pi\) | ||||
0.365051 | + | 0.930988i | \(0.381052\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 11.4572 | 0.932372 | 0.466186 | − | 0.884687i | \(-0.345628\pi\) | ||||
0.466186 | + | 0.884687i | \(0.345628\pi\) | |||||||
\(152\) | 7.67316 | 0.622376 | ||||||||
\(153\) | 25.5799 | 2.06801 | ||||||||
\(154\) | 3.89148 | 0.313584 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −7.00896 | −0.561166 | ||||||||
\(157\) | 6.60653 | 0.527258 | 0.263629 | − | 0.964624i | \(-0.415081\pi\) | ||||
0.263629 | + | 0.964624i | \(0.415081\pi\) | |||||||
\(158\) | −17.5836 | −1.39888 | ||||||||
\(159\) | 13.0951 | 1.03851 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −0.868585 | −0.0684541 | ||||||||
\(162\) | 30.0083 | 2.35767 | ||||||||
\(163\) | −20.2444 | −1.58567 | −0.792833 | − | 0.609439i | \(-0.791395\pi\) | ||||
−0.792833 | + | 0.609439i | \(0.791395\pi\) | |||||||
\(164\) | −9.02289 | −0.704569 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 17.5186 | 1.35970 | ||||||||
\(167\) | 5.89372 | 0.456069 | 0.228035 | − | 0.973653i | \(-0.426770\pi\) | ||||
0.228035 | + | 0.973653i | \(0.426770\pi\) | |||||||
\(168\) | −13.4185 | −1.03526 | ||||||||
\(169\) | −12.7806 | −0.983124 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 6.26020 | 0.478730 | ||||||||
\(172\) | 2.82591 | 0.215474 | ||||||||
\(173\) | 3.53161 | 0.268504 | 0.134252 | − | 0.990947i | \(-0.457137\pi\) | ||||
0.134252 | + | 0.990947i | \(0.457137\pi\) | |||||||
\(174\) | 32.7035 | 2.47924 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 26.6384 | 2.00794 | ||||||||
\(177\) | 8.17223 | 0.614263 | ||||||||
\(178\) | 38.4167 | 2.87945 | ||||||||
\(179\) | 7.18801 | 0.537257 | 0.268629 | − | 0.963244i | \(-0.413430\pi\) | ||||
0.268629 | + | 0.963244i | \(0.413430\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 15.5433 | 1.15532 | 0.577662 | − | 0.816276i | \(-0.303965\pi\) | ||||
0.577662 | + | 0.816276i | \(0.303965\pi\) | |||||||
\(182\) | 0.707941 | 0.0524761 | ||||||||
\(183\) | −37.7630 | −2.79152 | ||||||||
\(184\) | −11.5976 | −0.854984 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 79.4032 | 5.82213 | ||||||||
\(187\) | 10.5204 | 0.769329 | ||||||||
\(188\) | −34.8896 | −2.54459 | ||||||||
\(189\) | −5.70131 | −0.414710 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 13.3216 | 0.963915 | 0.481958 | − | 0.876194i | \(-0.339926\pi\) | ||||
0.481958 | + | 0.876194i | \(0.339926\pi\) | |||||||
\(192\) | −31.9978 | −2.30924 | ||||||||
\(193\) | −18.9959 | −1.36736 | −0.683678 | − | 0.729784i | \(-0.739621\pi\) | ||||
−0.683678 | + | 0.729784i | \(0.739621\pi\) | |||||||
\(194\) | −45.9021 | −3.29558 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −32.7981 | −2.34272 | ||||||||
\(197\) | −2.17223 | −0.154765 | −0.0773826 | − | 0.997001i | \(-0.524656\pi\) | ||||
−0.0773826 | + | 0.997001i | \(0.524656\pi\) | |||||||
\(198\) | 42.3919 | 3.01266 | ||||||||
\(199\) | −1.87355 | −0.132812 | −0.0664061 | − | 0.997793i | \(-0.521153\pi\) | ||||
−0.0664061 | + | 0.997793i | \(0.521153\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −8.23361 | −0.580754 | ||||||||
\(202\) | 37.5660 | 2.64313 | ||||||||
\(203\) | −2.34818 | −0.164810 | ||||||||
\(204\) | −61.1449 | −4.28100 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −12.6030 | −0.878091 | ||||||||
\(207\) | −9.46196 | −0.657651 | ||||||||
\(208\) | 4.84608 | 0.336015 | ||||||||
\(209\) | 2.57467 | 0.178094 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −17.1090 | −1.17783 | −0.588916 | − | 0.808194i | \(-0.700445\pi\) | ||||
−0.588916 | + | 0.808194i | \(0.700445\pi\) | |||||||
\(212\) | −21.1610 | −1.45335 | ||||||||
\(213\) | 22.5204 | 1.54307 | ||||||||
\(214\) | −24.2656 | −1.65876 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −76.1254 | −5.17968 | ||||||||
\(217\) | −5.70131 | −0.387030 | ||||||||
\(218\) | 12.8825 | 0.872514 | ||||||||
\(219\) | 36.7788 | 2.48528 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.91388 | 0.128742 | ||||||||
\(222\) | −66.4556 | −4.46021 | ||||||||
\(223\) | −5.12918 | −0.343475 | −0.171737 | − | 0.985143i | \(-0.554938\pi\) | ||||
−0.171737 | + | 0.985143i | \(0.554938\pi\) | |||||||
\(224\) | 6.81880 | 0.455600 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −4.25480 | −0.283025 | ||||||||
\(227\) | 7.31223 | 0.485330 | 0.242665 | − | 0.970110i | \(-0.421978\pi\) | ||||
0.242665 | + | 0.970110i | \(0.421978\pi\) | |||||||
\(228\) | −14.9641 | −0.991019 | ||||||||
\(229\) | −8.40955 | −0.555719 | −0.277859 | − | 0.960622i | \(-0.589625\pi\) | ||||
−0.277859 | + | 0.960622i | \(0.589625\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −4.50248 | −0.296242 | ||||||||
\(232\) | −31.3534 | −2.05845 | ||||||||
\(233\) | 14.1722 | 0.928454 | 0.464227 | − | 0.885716i | \(-0.346332\pi\) | ||||
0.464227 | + | 0.885716i | \(0.346332\pi\) | |||||||
\(234\) | 7.71198 | 0.504148 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −13.2059 | −0.859634 | ||||||||
\(237\) | 20.3445 | 1.32152 | ||||||||
\(238\) | 6.17594 | 0.400327 | ||||||||
\(239\) | −14.1902 | −0.917885 | −0.458943 | − | 0.888466i | \(-0.651772\pi\) | ||||
−0.458943 | + | 0.888466i | \(0.651772\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 27.8807 | 1.79595 | 0.897976 | − | 0.440045i | \(-0.145038\pi\) | ||||
0.897976 | + | 0.440045i | \(0.145038\pi\) | |||||||
\(242\) | −11.4964 | −0.739013 | ||||||||
\(243\) | −4.95694 | −0.317988 | ||||||||
\(244\) | 61.0232 | 3.90661 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 14.6855 | 0.936315 | ||||||||
\(247\) | 0.468387 | 0.0298027 | ||||||||
\(248\) | −76.1254 | −4.83397 | ||||||||
\(249\) | −20.2692 | −1.28451 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −26.1902 | −1.65311 | −0.826554 | − | 0.562857i | \(-0.809702\pi\) | ||||
−0.826554 | + | 0.562857i | \(0.809702\pi\) | |||||||
\(252\) | 17.6908 | 1.11441 | ||||||||
\(253\) | −3.89148 | −0.244655 | ||||||||
\(254\) | 34.5311 | 2.16667 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −10.7084 | −0.669276 | ||||||||
\(257\) | −9.01831 | −0.562547 | −0.281273 | − | 0.959628i | \(-0.590757\pi\) | ||||
−0.281273 | + | 0.959628i | \(0.590757\pi\) | |||||||
\(258\) | −4.59942 | −0.286347 | ||||||||
\(259\) | 4.77165 | 0.296496 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −25.5799 | −1.58336 | ||||||||
\(262\) | −21.4938 | −1.32789 | ||||||||
\(263\) | 9.00896 | 0.555517 | 0.277758 | − | 0.960651i | \(-0.410409\pi\) | ||||
0.277758 | + | 0.960651i | \(0.410409\pi\) | |||||||
\(264\) | −60.1183 | −3.70002 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 1.51145 | 0.0926727 | ||||||||
\(267\) | −44.4485 | −2.72020 | ||||||||
\(268\) | 13.3051 | 0.812739 | ||||||||
\(269\) | −30.6136 | −1.86655 | −0.933273 | − | 0.359167i | \(-0.883061\pi\) | ||||
−0.933273 | + | 0.359167i | \(0.883061\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 24.1180 | 1.46506 | 0.732531 | − | 0.680733i | \(-0.238339\pi\) | ||||
0.732531 | + | 0.680733i | \(0.238339\pi\) | |||||||
\(272\) | 42.2763 | 2.56338 | ||||||||
\(273\) | −0.819096 | −0.0495739 | ||||||||
\(274\) | 38.4167 | 2.32084 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 22.6173 | 1.36140 | ||||||||
\(277\) | −4.56075 | −0.274029 | −0.137014 | − | 0.990569i | \(-0.543751\pi\) | ||||
−0.137014 | + | 0.990569i | \(0.543751\pi\) | |||||||
\(278\) | −5.45007 | −0.326874 | ||||||||
\(279\) | −62.1074 | −3.71828 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −6.11563 | −0.364828 | −0.182414 | − | 0.983222i | \(-0.558391\pi\) | ||||
−0.182414 | + | 0.983222i | \(0.558391\pi\) | |||||||
\(282\) | 56.7859 | 3.38155 | ||||||||
\(283\) | 19.0547 | 1.13269 | 0.566344 | − | 0.824169i | \(-0.308358\pi\) | ||||
0.566344 | + | 0.824169i | \(0.308358\pi\) | |||||||
\(284\) | −36.3919 | −2.15946 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 3.17175 | 0.187550 | ||||||||
\(287\) | −1.05445 | −0.0622423 | ||||||||
\(288\) | 74.2808 | 4.37704 | ||||||||
\(289\) | −0.303649 | −0.0178617 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 53.1093 | 3.11332 | ||||||||
\(292\) | −59.4327 | −3.47804 | ||||||||
\(293\) | 6.43887 | 0.376163 | 0.188081 | − | 0.982153i | \(-0.439773\pi\) | ||||
0.188081 | + | 0.982153i | \(0.439773\pi\) | |||||||
\(294\) | 53.3817 | 3.11329 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 63.7123 | 3.70320 | ||||||||
\(297\) | −25.5433 | −1.48217 | ||||||||
\(298\) | 23.4395 | 1.35782 | ||||||||
\(299\) | −0.707941 | −0.0409413 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0.330247 | 0.0190351 | ||||||||
\(302\) | 30.1336 | 1.73399 | ||||||||
\(303\) | −43.4643 | −2.49696 | ||||||||
\(304\) | 10.3463 | 0.593402 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 67.2778 | 3.84602 | ||||||||
\(307\) | 6.77389 | 0.386606 | 0.193303 | − | 0.981139i | \(-0.438080\pi\) | ||||
0.193303 | + | 0.981139i | \(0.438080\pi\) | |||||||
\(308\) | 7.27580 | 0.414577 | ||||||||
\(309\) | 14.5818 | 0.829529 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 20.6205 | 1.16928 | 0.584639 | − | 0.811293i | \(-0.301236\pi\) | ||||
0.584639 | + | 0.811293i | \(0.301236\pi\) | |||||||
\(312\) | −10.9368 | −0.619173 | ||||||||
\(313\) | −19.3711 | −1.09492 | −0.547459 | − | 0.836833i | \(-0.684405\pi\) | ||||
−0.547459 | + | 0.836833i | \(0.684405\pi\) | |||||||
\(314\) | 17.3758 | 0.980575 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −32.8757 | −1.84940 | ||||||||
\(317\) | −3.37360 | −0.189480 | −0.0947401 | − | 0.995502i | \(-0.530202\pi\) | ||||
−0.0947401 | + | 0.995502i | \(0.530202\pi\) | |||||||
\(318\) | 34.4414 | 1.93138 | ||||||||
\(319\) | −10.5204 | −0.589030 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 28.0756 | 1.56703 | ||||||||
\(322\) | −2.28447 | −0.127308 | ||||||||
\(323\) | 4.08612 | 0.227358 | ||||||||
\(324\) | 56.1057 | 3.11699 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −53.2449 | −2.94896 | ||||||||
\(327\) | −14.9052 | −0.824260 | ||||||||
\(328\) | −14.0793 | −0.777399 | ||||||||
\(329\) | −4.07734 | −0.224791 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −32.7788 | −1.80168 | −0.900842 | − | 0.434148i | \(-0.857050\pi\) | ||||
−0.900842 | + | 0.434148i | \(0.857050\pi\) | |||||||
\(332\) | 32.7540 | 1.79761 | ||||||||
\(333\) | 51.9801 | 2.84849 | ||||||||
\(334\) | 15.5011 | 0.848181 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −18.0932 | −0.987066 | ||||||||
\(337\) | −8.74915 | −0.476596 | −0.238298 | − | 0.971192i | \(-0.576590\pi\) | ||||
−0.238298 | + | 0.971192i | \(0.576590\pi\) | |||||||
\(338\) | −33.6143 | −1.82838 | ||||||||
\(339\) | 4.92285 | 0.267372 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −25.5433 | −1.38325 | ||||||||
\(342\) | 16.4650 | 0.890324 | ||||||||
\(343\) | −7.85562 | −0.424164 | ||||||||
\(344\) | 4.40955 | 0.237747 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 9.28850 | 0.499353 | ||||||||
\(347\) | 18.5028 | 0.993281 | 0.496640 | − | 0.867956i | \(-0.334567\pi\) | ||||
0.496640 | + | 0.867956i | \(0.334567\pi\) | |||||||
\(348\) | 61.1449 | 3.27771 | ||||||||
\(349\) | 3.54330 | 0.189668 | 0.0948342 | − | 0.995493i | \(-0.469768\pi\) | ||||
0.0948342 | + | 0.995493i | \(0.469768\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −4.64686 | −0.248031 | ||||||||
\(352\) | 30.5499 | 1.62832 | ||||||||
\(353\) | 3.41140 | 0.181571 | 0.0907853 | − | 0.995870i | \(-0.471062\pi\) | ||||
0.0907853 | + | 0.995870i | \(0.471062\pi\) | |||||||
\(354\) | 21.4938 | 1.14238 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 71.8267 | 3.80681 | ||||||||
\(357\) | −7.14564 | −0.378187 | ||||||||
\(358\) | 18.9052 | 0.999172 | ||||||||
\(359\) | −1.70609 | −0.0900438 | −0.0450219 | − | 0.998986i | \(-0.514336\pi\) | ||||
−0.0450219 | + | 0.998986i | \(0.514336\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 40.8805 | 2.14863 | ||||||||
\(363\) | 13.3014 | 0.698143 | ||||||||
\(364\) | 1.32362 | 0.0693765 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −99.3205 | −5.19157 | ||||||||
\(367\) | −37.6155 | −1.96351 | −0.981756 | − | 0.190144i | \(-0.939105\pi\) | ||||
−0.981756 | + | 0.190144i | \(0.939105\pi\) | |||||||
\(368\) | −15.6379 | −0.815182 | ||||||||
\(369\) | −11.4867 | −0.597974 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −2.47296 | −0.128390 | ||||||||
\(372\) | 148.458 | 7.69720 | ||||||||
\(373\) | −13.4031 | −0.693987 | −0.346994 | − | 0.937868i | \(-0.612797\pi\) | ||||
−0.346994 | + | 0.937868i | \(0.612797\pi\) | |||||||
\(374\) | 27.6698 | 1.43077 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −54.4417 | −2.80762 | ||||||||
\(377\) | −1.91388 | −0.0985700 | ||||||||
\(378\) | −14.9950 | −0.771262 | ||||||||
\(379\) | −9.37107 | −0.481359 | −0.240680 | − | 0.970605i | \(-0.577370\pi\) | ||||
−0.240680 | + | 0.970605i | \(0.577370\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −39.9528 | −2.04685 | ||||||||
\(382\) | 35.0371 | 1.79265 | ||||||||
\(383\) | 2.09917 | 0.107263 | 0.0536314 | − | 0.998561i | \(-0.482920\pi\) | ||||
0.0536314 | + | 0.998561i | \(0.482920\pi\) | |||||||
\(384\) | −11.9422 | −0.609422 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −49.9612 | −2.54296 | ||||||||
\(387\) | 3.59756 | 0.182874 | ||||||||
\(388\) | −85.8221 | −4.35696 | ||||||||
\(389\) | 1.07238 | 0.0543718 | 0.0271859 | − | 0.999630i | \(-0.491345\pi\) | ||||
0.0271859 | + | 0.999630i | \(0.491345\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −6.17594 | −0.312331 | ||||||||
\(392\) | −51.1781 | −2.58488 | ||||||||
\(393\) | 24.8686 | 1.25445 | ||||||||
\(394\) | −5.71320 | −0.287827 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 79.2591 | 3.98292 | ||||||||
\(397\) | 23.5341 | 1.18114 | 0.590572 | − | 0.806985i | \(-0.298902\pi\) | ||||
0.590572 | + | 0.806985i | \(0.298902\pi\) | |||||||
\(398\) | −4.92762 | −0.246999 | ||||||||
\(399\) | −1.74876 | −0.0875475 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 18.6469 | 0.931180 | 0.465590 | − | 0.885001i | \(-0.345842\pi\) | ||||
0.465590 | + | 0.885001i | \(0.345842\pi\) | |||||||
\(402\) | −21.6552 | −1.08006 | ||||||||
\(403\) | −4.64686 | −0.231477 | ||||||||
\(404\) | 70.2362 | 3.49438 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −6.17594 | −0.306507 | ||||||||
\(407\) | 21.3782 | 1.05968 | ||||||||
\(408\) | −95.4103 | −4.72351 | ||||||||
\(409\) | −6.88017 | −0.340203 | −0.170101 | − | 0.985427i | \(-0.554410\pi\) | ||||
−0.170101 | + | 0.985427i | \(0.554410\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −44.4485 | −2.19248 | ||||||||
\(412\) | −23.5635 | −1.16089 | ||||||||
\(413\) | −1.54330 | −0.0759408 | ||||||||
\(414\) | −24.8859 | −1.22308 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 5.55767 | 0.272487 | ||||||||
\(417\) | 6.30580 | 0.308796 | ||||||||
\(418\) | 6.77165 | 0.331212 | ||||||||
\(419\) | 13.4796 | 0.658521 | 0.329261 | − | 0.944239i | \(-0.393201\pi\) | ||||
0.329261 | + | 0.944239i | \(0.393201\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −5.83488 | −0.284374 | −0.142187 | − | 0.989840i | \(-0.545414\pi\) | ||||
−0.142187 | + | 0.989840i | \(0.545414\pi\) | |||||||
\(422\) | −44.9984 | −2.19049 | ||||||||
\(423\) | −44.4167 | −2.15961 | ||||||||
\(424\) | −33.0196 | −1.60357 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 59.2310 | 2.86975 | ||||||||
\(427\) | 7.13142 | 0.345113 | ||||||||
\(428\) | −45.3688 | −2.19298 | ||||||||
\(429\) | −3.66975 | −0.177177 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 29.2039 | 1.40670 | 0.703351 | − | 0.710843i | \(-0.251686\pi\) | ||||
0.703351 | + | 0.710843i | \(0.251686\pi\) | |||||||
\(432\) | −102.646 | −4.93855 | ||||||||
\(433\) | 12.5229 | 0.601814 | 0.300907 | − | 0.953653i | \(-0.402711\pi\) | ||||
0.300907 | + | 0.953653i | \(0.402711\pi\) | |||||||
\(434\) | −14.9950 | −0.719785 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 24.0861 | 1.15352 | ||||||||
\(437\) | −1.51145 | −0.0723022 | ||||||||
\(438\) | 96.7319 | 4.62203 | ||||||||
\(439\) | 15.6769 | 0.748216 | 0.374108 | − | 0.927385i | \(-0.377949\pi\) | ||||
0.374108 | + | 0.927385i | \(0.377949\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −41.7540 | −1.98829 | ||||||||
\(442\) | 5.03371 | 0.239429 | ||||||||
\(443\) | 29.8281 | 1.41717 | 0.708587 | − | 0.705624i | \(-0.249333\pi\) | ||||
0.708587 | + | 0.705624i | \(0.249333\pi\) | |||||||
\(444\) | −124.250 | −5.89667 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −13.4903 | −0.638782 | ||||||||
\(447\) | −27.1198 | −1.28272 | ||||||||
\(448\) | 6.04267 | 0.285489 | ||||||||
\(449\) | 29.9668 | 1.41422 | 0.707110 | − | 0.707104i | \(-0.249999\pi\) | ||||
0.707110 | + | 0.707104i | \(0.249999\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −4.72420 | −0.222454 | ||||||||
\(452\) | −7.95509 | −0.374176 | ||||||||
\(453\) | −34.8649 | −1.63809 | ||||||||
\(454\) | 19.2319 | 0.902598 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −23.3499 | −1.09346 | ||||||||
\(457\) | −17.6698 | −0.826556 | −0.413278 | − | 0.910605i | \(-0.635616\pi\) | ||||
−0.413278 | + | 0.910605i | \(0.635616\pi\) | |||||||
\(458\) | −22.1180 | −1.03350 | ||||||||
\(459\) | −40.5383 | −1.89217 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 22.3445 | 1.04069 | 0.520343 | − | 0.853957i | \(-0.325804\pi\) | ||||
0.520343 | + | 0.853957i | \(0.325804\pi\) | |||||||
\(462\) | −11.8420 | −0.550939 | ||||||||
\(463\) | 6.83302 | 0.317557 | 0.158779 | − | 0.987314i | \(-0.449244\pi\) | ||||
0.158779 | + | 0.987314i | \(0.449244\pi\) | |||||||
\(464\) | −42.2763 | −1.96263 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 37.2744 | 1.72670 | ||||||||
\(467\) | −9.00896 | −0.416885 | −0.208443 | − | 0.978035i | \(-0.566839\pi\) | ||||
−0.208443 | + | 0.978035i | \(0.566839\pi\) | |||||||
\(468\) | 14.4189 | 0.666514 | ||||||||
\(469\) | 1.55489 | 0.0717981 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −20.1040 | −0.926345 | ||||||||
\(472\) | −20.6065 | −0.948492 | ||||||||
\(473\) | 1.47959 | 0.0680317 | ||||||||
\(474\) | 53.5080 | 2.45771 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 11.5470 | 0.529256 | ||||||||
\(477\) | −26.9393 | −1.23347 | ||||||||
\(478\) | −37.3216 | −1.70705 | ||||||||
\(479\) | 9.26731 | 0.423434 | 0.211717 | − | 0.977331i | \(-0.432094\pi\) | ||||
0.211717 | + | 0.977331i | \(0.432094\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 3.88914 | 0.177329 | ||||||||
\(482\) | 73.3290 | 3.34004 | ||||||||
\(483\) | 2.64315 | 0.120268 | ||||||||
\(484\) | −21.4944 | −0.977020 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −13.0373 | −0.591382 | ||||||||
\(487\) | 38.7694 | 1.75681 | 0.878405 | − | 0.477917i | \(-0.158608\pi\) | ||||
0.878405 | + | 0.477917i | \(0.158608\pi\) | |||||||
\(488\) | 95.2205 | 4.31043 | ||||||||
\(489\) | 61.6050 | 2.78587 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 21.6877 | 0.978751 | 0.489376 | − | 0.872073i | \(-0.337225\pi\) | ||||
0.489376 | + | 0.872073i | \(0.337225\pi\) | |||||||
\(492\) | 27.4572 | 1.23787 | ||||||||
\(493\) | −16.6964 | −0.751966 | ||||||||
\(494\) | 1.23191 | 0.0554260 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −102.646 | −4.60893 | ||||||||
\(497\) | −4.25291 | −0.190769 | ||||||||
\(498\) | −53.3100 | −2.38888 | ||||||||
\(499\) | −27.8372 | −1.24616 | −0.623082 | − | 0.782156i | \(-0.714120\pi\) | ||||
−0.623082 | + | 0.782156i | \(0.714120\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −17.9349 | −0.801273 | ||||||||
\(502\) | −68.8828 | −3.07439 | ||||||||
\(503\) | 41.2449 | 1.83902 | 0.919510 | − | 0.393067i | \(-0.128586\pi\) | ||||
0.919510 | + | 0.393067i | \(0.128586\pi\) | |||||||
\(504\) | 27.6047 | 1.22961 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −10.2350 | −0.455000 | ||||||||
\(507\) | 38.8922 | 1.72726 | ||||||||
\(508\) | 64.5619 | 2.86447 | ||||||||
\(509\) | 0.416364 | 0.0184550 | 0.00922751 | − | 0.999957i | \(-0.497063\pi\) | ||||
0.00922751 | + | 0.999957i | \(0.497063\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −6.94555 | −0.307253 | ||||||||
\(512\) | −36.0131 | −1.59157 | ||||||||
\(513\) | −9.92099 | −0.438023 | ||||||||
\(514\) | −23.7191 | −1.04620 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −8.59942 | −0.378568 | ||||||||
\(517\) | −18.2675 | −0.803404 | ||||||||
\(518\) | 12.5499 | 0.551412 | ||||||||
\(519\) | −10.7469 | −0.471737 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 24.0458 | 1.05346 | 0.526732 | − | 0.850031i | \(-0.323417\pi\) | ||||
0.526732 | + | 0.850031i | \(0.323417\pi\) | |||||||
\(522\) | −67.2778 | −2.94467 | ||||||||
\(523\) | 5.19736 | 0.227265 | 0.113632 | − | 0.993523i | \(-0.463751\pi\) | ||||
0.113632 | + | 0.993523i | \(0.463751\pi\) | |||||||
\(524\) | −40.1865 | −1.75555 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 23.6945 | 1.03313 | ||||||||
\(527\) | −40.5383 | −1.76588 | ||||||||
\(528\) | −81.0621 | −3.52778 | ||||||||
\(529\) | −20.7155 | −0.900675 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −16.8120 | −0.729578 | ||||||||
\(532\) | 2.82591 | 0.122519 | ||||||||
\(533\) | −0.859432 | −0.0372261 | ||||||||
\(534\) | −116.904 | −5.05894 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 20.7613 | 0.896751 | ||||||||
\(537\) | −21.8735 | −0.943913 | ||||||||
\(538\) | −80.5170 | −3.47133 | ||||||||
\(539\) | −17.1724 | −0.739669 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −1.93863 | −0.0833481 | −0.0416741 | − | 0.999131i | \(-0.513269\pi\) | ||||
−0.0416741 | + | 0.999131i | \(0.513269\pi\) | |||||||
\(542\) | 63.4327 | 2.72467 | ||||||||
\(543\) | −47.2992 | −2.02980 | ||||||||
\(544\) | 48.4841 | 2.07874 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −2.15431 | −0.0921958 | ||||||||
\(547\) | 12.9075 | 0.551883 | 0.275941 | − | 0.961174i | \(-0.411010\pi\) | ||||
0.275941 | + | 0.961174i | \(0.411010\pi\) | |||||||
\(548\) | 71.8267 | 3.06828 | ||||||||
\(549\) | 77.6863 | 3.31557 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −4.08612 | −0.174074 | ||||||||
\(552\) | 35.2921 | 1.50213 | ||||||||
\(553\) | −3.84199 | −0.163378 | ||||||||
\(554\) | −11.9952 | −0.509628 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −10.1899 | −0.432147 | ||||||||
\(557\) | 34.1040 | 1.44503 | 0.722517 | − | 0.691353i | \(-0.242985\pi\) | ||||
0.722517 | + | 0.691353i | \(0.242985\pi\) | |||||||
\(558\) | −163.349 | −6.91511 | ||||||||
\(559\) | 0.269169 | 0.0113846 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −32.0142 | −1.35164 | ||||||||
\(562\) | −16.0847 | −0.678494 | ||||||||
\(563\) | 14.4911 | 0.610727 | 0.305363 | − | 0.952236i | \(-0.401222\pi\) | ||||
0.305363 | + | 0.952236i | \(0.401222\pi\) | |||||||
\(564\) | 106.171 | 4.47061 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 50.1159 | 2.10653 | ||||||||
\(567\) | 6.55674 | 0.275357 | ||||||||
\(568\) | −56.7859 | −2.38268 | ||||||||
\(569\) | −39.2110 | −1.64381 | −0.821906 | − | 0.569624i | \(-0.807089\pi\) | ||||
−0.821906 | + | 0.569624i | \(0.807089\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 21.9915 | 0.920316 | 0.460158 | − | 0.887837i | \(-0.347793\pi\) | ||||
0.460158 | + | 0.887837i | \(0.347793\pi\) | |||||||
\(572\) | 5.93015 | 0.247952 | ||||||||
\(573\) | −40.5383 | −1.69351 | ||||||||
\(574\) | −2.77331 | −0.115756 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 65.8261 | 2.74275 | ||||||||
\(577\) | −23.8735 | −0.993869 | −0.496934 | − | 0.867788i | \(-0.665541\pi\) | ||||
−0.496934 | + | 0.867788i | \(0.665541\pi\) | |||||||
\(578\) | −0.798628 | −0.0332185 | ||||||||
\(579\) | 57.8057 | 2.40232 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 3.82777 | 0.158803 | ||||||||
\(582\) | 139.683 | 5.79004 | ||||||||
\(583\) | −11.0795 | −0.458866 | ||||||||
\(584\) | −92.7387 | −3.83756 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 16.9349 | 0.699574 | ||||||||
\(587\) | −17.8281 | −0.735843 | −0.367921 | − | 0.929857i | \(-0.619930\pi\) | ||||
−0.367921 | + | 0.929857i | \(0.619930\pi\) | |||||||
\(588\) | 99.8065 | 4.11595 | ||||||||
\(589\) | −9.92099 | −0.408787 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 6.61023 | 0.271909 | ||||||||
\(592\) | 85.9082 | 3.53081 | ||||||||
\(593\) | 21.2446 | 0.872412 | 0.436206 | − | 0.899847i | \(-0.356322\pi\) | ||||
0.436206 | + | 0.899847i | \(0.356322\pi\) | |||||||
\(594\) | −67.1815 | −2.75649 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 43.8244 | 1.79512 | ||||||||
\(597\) | 5.70131 | 0.233339 | ||||||||
\(598\) | −1.86196 | −0.0761411 | ||||||||
\(599\) | 24.3374 | 0.994397 | 0.497199 | − | 0.867637i | \(-0.334362\pi\) | ||||
0.497199 | + | 0.867637i | \(0.334362\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 15.7891 | 0.644051 | 0.322025 | − | 0.946731i | \(-0.395636\pi\) | ||||
0.322025 | + | 0.946731i | \(0.395636\pi\) | |||||||
\(602\) | 0.868585 | 0.0354009 | ||||||||
\(603\) | 16.9382 | 0.689779 | ||||||||
\(604\) | 56.3400 | 2.29244 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −114.316 | −4.64375 | ||||||||
\(607\) | −7.81471 | −0.317189 | −0.158595 | − | 0.987344i | \(-0.550696\pi\) | ||||
−0.158595 | + | 0.987344i | \(0.550696\pi\) | |||||||
\(608\) | 11.8656 | 0.481212 | ||||||||
\(609\) | 7.14564 | 0.289556 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −3.32324 | −0.134444 | ||||||||
\(612\) | 125.788 | 5.08467 | ||||||||
\(613\) | −12.9547 | −0.523235 | −0.261618 | − | 0.965172i | \(-0.584256\pi\) | ||||
−0.261618 | + | 0.965172i | \(0.584256\pi\) | |||||||
\(614\) | 17.8160 | 0.718996 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 11.3531 | 0.457431 | ||||||||
\(617\) | −18.8873 | −0.760373 | −0.380187 | − | 0.924910i | \(-0.624140\pi\) | ||||
−0.380187 | + | 0.924910i | \(0.624140\pi\) | |||||||
\(618\) | 38.3516 | 1.54273 | ||||||||
\(619\) | 29.2673 | 1.17635 | 0.588176 | − | 0.808733i | \(-0.299846\pi\) | ||||
0.588176 | + | 0.808733i | \(0.299846\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 14.9950 | 0.601730 | ||||||||
\(622\) | 54.2339 | 2.17458 | ||||||||
\(623\) | 8.39396 | 0.336297 | ||||||||
\(624\) | −14.7469 | −0.590349 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −50.9479 | −2.03629 | ||||||||
\(627\) | −7.83488 | −0.312895 | ||||||||
\(628\) | 32.4872 | 1.29638 | ||||||||
\(629\) | 33.9281 | 1.35280 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −5.25309 | −0.209122 | −0.104561 | − | 0.994518i | \(-0.533344\pi\) | ||||
−0.104561 | + | 0.994518i | \(0.533344\pi\) | |||||||
\(632\) | −51.2992 | −2.04057 | ||||||||
\(633\) | 52.0637 | 2.06935 | ||||||||
\(634\) | −8.87291 | −0.352388 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 64.3942 | 2.55340 | ||||||||
\(637\) | −3.12402 | −0.123778 | ||||||||
\(638\) | −27.6698 | −1.09546 | ||||||||
\(639\) | −46.3292 | −1.83275 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −13.0021 | −0.513554 | −0.256777 | − | 0.966471i | \(-0.582661\pi\) | ||||
−0.256777 | + | 0.966471i | \(0.582661\pi\) | |||||||
\(642\) | 73.8417 | 2.91430 | ||||||||
\(643\) | 17.3534 | 0.684353 | 0.342176 | − | 0.939636i | \(-0.388836\pi\) | ||||
0.342176 | + | 0.939636i | \(0.388836\pi\) | |||||||
\(644\) | −4.27121 | −0.168309 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 10.7469 | 0.422831 | ||||||||
\(647\) | −12.4848 | −0.490830 | −0.245415 | − | 0.969418i | \(-0.578924\pi\) | ||||
−0.245415 | + | 0.969418i | \(0.578924\pi\) | |||||||
\(648\) | 87.5473 | 3.43918 | ||||||||
\(649\) | −6.91437 | −0.271413 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 17.3494 | 0.679978 | ||||||||
\(652\) | −99.5507 | −3.89871 | ||||||||
\(653\) | 28.3532 | 1.10955 | 0.554774 | − | 0.832001i | \(-0.312805\pi\) | ||||
0.554774 | + | 0.832001i | \(0.312805\pi\) | |||||||
\(654\) | −39.2022 | −1.53293 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −18.9842 | −0.741209 | ||||||||
\(657\) | −75.6616 | −2.95184 | ||||||||
\(658\) | −10.7238 | −0.418058 | ||||||||
\(659\) | 45.2202 | 1.76153 | 0.880764 | − | 0.473556i | \(-0.157030\pi\) | ||||
0.880764 | + | 0.473556i | \(0.157030\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −14.6086 | −0.568207 | −0.284104 | − | 0.958794i | \(-0.591696\pi\) | ||||
−0.284104 | + | 0.958794i | \(0.591696\pi\) | |||||||
\(662\) | −86.2115 | −3.35070 | ||||||||
\(663\) | −5.82406 | −0.226188 | ||||||||
\(664\) | 51.1093 | 1.98343 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 136.713 | 5.29752 | ||||||||
\(667\) | 6.17594 | 0.239133 | ||||||||
\(668\) | 28.9820 | 1.12135 | ||||||||
\(669\) | 15.6084 | 0.603455 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 31.9505 | 1.23344 | ||||||||
\(672\) | −20.7500 | −0.800449 | ||||||||
\(673\) | 0.440534 | 0.0169813 | 0.00849067 | − | 0.999964i | \(-0.497297\pi\) | ||||
0.00849067 | + | 0.999964i | \(0.497297\pi\) | |||||||
\(674\) | −23.0111 | −0.886356 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −62.8479 | −2.41723 | ||||||||
\(677\) | −32.8057 | −1.26083 | −0.630414 | − | 0.776259i | \(-0.717115\pi\) | ||||
−0.630414 | + | 0.776259i | \(0.717115\pi\) | |||||||
\(678\) | 12.9476 | 0.497249 | ||||||||
\(679\) | −10.0295 | −0.384898 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −22.2515 | −0.852681 | ||||||||
\(682\) | −67.1815 | −2.57251 | ||||||||
\(683\) | 39.6092 | 1.51561 | 0.757803 | − | 0.652484i | \(-0.226273\pi\) | ||||
0.757803 | + | 0.652484i | \(0.226273\pi\) | |||||||
\(684\) | 30.7842 | 1.17706 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −20.6611 | −0.788844 | ||||||||
\(687\) | 25.5907 | 0.976348 | ||||||||
\(688\) | 5.94574 | 0.226679 | ||||||||
\(689\) | −2.01559 | −0.0767879 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −19.8962 | −0.756889 | −0.378444 | − | 0.925624i | \(-0.623541\pi\) | ||||
−0.378444 | + | 0.925624i | \(0.623541\pi\) | |||||||
\(692\) | 17.3665 | 0.660175 | ||||||||
\(693\) | 9.26254 | 0.351855 | ||||||||
\(694\) | 48.6642 | 1.84727 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 95.4103 | 3.61652 | ||||||||
\(697\) | −7.49752 | −0.283989 | ||||||||
\(698\) | 9.31924 | 0.352738 | ||||||||
\(699\) | −43.1269 | −1.63121 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −14.1251 | −0.533497 | −0.266748 | − | 0.963766i | \(-0.585949\pi\) | ||||
−0.266748 | + | 0.963766i | \(0.585949\pi\) | |||||||
\(702\) | −12.2217 | −0.461279 | ||||||||
\(703\) | 8.30326 | 0.313163 | ||||||||
\(704\) | 27.0727 | 1.02034 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 8.97234 | 0.337678 | ||||||||
\(707\) | 8.20809 | 0.308697 | ||||||||
\(708\) | 40.1865 | 1.51030 | ||||||||
\(709\) | −41.1815 | −1.54660 | −0.773302 | − | 0.634038i | \(-0.781396\pi\) | ||||
−0.773302 | + | 0.634038i | \(0.781396\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −41.8528 | −1.56960 | ||||||||
\(712\) | 112.078 | 4.20031 | ||||||||
\(713\) | 14.9950 | 0.561569 | ||||||||
\(714\) | −18.7938 | −0.703338 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 35.3466 | 1.32097 | ||||||||
\(717\) | 43.1815 | 1.61264 | ||||||||
\(718\) | −4.48718 | −0.167460 | ||||||||
\(719\) | −18.0227 | −0.672133 | −0.336067 | − | 0.941838i | \(-0.609097\pi\) | ||||
−0.336067 | + | 0.941838i | \(0.609097\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −2.75372 | −0.102554 | ||||||||
\(722\) | 2.63010 | 0.0978823 | ||||||||
\(723\) | −84.8425 | −3.15533 | ||||||||
\(724\) | 76.4332 | 2.84062 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 34.9841 | 1.29838 | ||||||||
\(727\) | 21.1266 | 0.783544 | 0.391772 | − | 0.920062i | \(-0.371862\pi\) | ||||
0.391772 | + | 0.920062i | \(0.371862\pi\) | |||||||
\(728\) | 2.06537 | 0.0765479 | ||||||||
\(729\) | −19.1444 | −0.709051 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 2.34818 | 0.0868504 | ||||||||
\(732\) | −185.697 | −6.86356 | ||||||||
\(733\) | 27.6660 | 1.02187 | 0.510934 | − | 0.859620i | \(-0.329300\pi\) | ||||
0.510934 | + | 0.859620i | \(0.329300\pi\) | |||||||
\(734\) | −98.9326 | −3.65167 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −17.9341 | −0.661061 | ||||||||
\(737\) | 6.96629 | 0.256607 | ||||||||
\(738\) | −30.2112 | −1.11209 | ||||||||
\(739\) | −14.2987 | −0.525986 | −0.262993 | − | 0.964798i | \(-0.584710\pi\) | ||||
−0.262993 | + | 0.964798i | \(0.584710\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −1.42533 | −0.0523607 | ||||||||
\(742\) | −6.50415 | −0.238775 | ||||||||
\(743\) | −49.9438 | −1.83226 | −0.916130 | − | 0.400881i | \(-0.868704\pi\) | ||||
−0.916130 | + | 0.400881i | \(0.868704\pi\) | |||||||
\(744\) | 231.654 | 8.49285 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −35.2516 | −1.29065 | ||||||||
\(747\) | 41.6979 | 1.52565 | ||||||||
\(748\) | 51.7335 | 1.89156 | ||||||||
\(749\) | −5.30198 | −0.193730 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 9.69216 | 0.353672 | 0.176836 | − | 0.984240i | \(-0.443414\pi\) | ||||
0.176836 | + | 0.984240i | \(0.443414\pi\) | |||||||
\(752\) | −73.4080 | −2.67691 | ||||||||
\(753\) | 79.6982 | 2.90436 | ||||||||
\(754\) | −5.03371 | −0.183317 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −28.0359 | −1.01965 | ||||||||
\(757\) | −46.6889 | −1.69694 | −0.848469 | − | 0.529245i | \(-0.822475\pi\) | ||||
−0.848469 | + | 0.529245i | \(0.822475\pi\) | |||||||
\(758\) | −24.6469 | −0.895214 | ||||||||
\(759\) | 11.8420 | 0.429837 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −38.7361 | −1.40418 | −0.702091 | − | 0.712087i | \(-0.747750\pi\) | ||||
−0.702091 | + | 0.712087i | \(0.747750\pi\) | |||||||
\(762\) | −105.080 | −3.80665 | ||||||||
\(763\) | 2.81480 | 0.101903 | ||||||||
\(764\) | 65.5080 | 2.37000 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 5.52104 | 0.199483 | ||||||||
\(767\) | −1.25787 | −0.0454190 | ||||||||
\(768\) | 32.5864 | 1.17586 | ||||||||
\(769\) | −5.38666 | −0.194248 | −0.0971239 | − | 0.995272i | \(-0.530964\pi\) | ||||
−0.0971239 | + | 0.995272i | \(0.530964\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 27.4433 | 0.988345 | ||||||||
\(772\) | −93.4112 | −3.36194 | ||||||||
\(773\) | −7.20137 | −0.259015 | −0.129508 | − | 0.991578i | \(-0.541340\pi\) | ||||
−0.129508 | + | 0.991578i | \(0.541340\pi\) | |||||||
\(774\) | 9.46196 | 0.340103 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −133.917 | −4.80733 | ||||||||
\(777\) | −14.5204 | −0.520917 | ||||||||
\(778\) | 2.82047 | 0.101119 | ||||||||
\(779\) | −1.83488 | −0.0657413 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −19.0541 | −0.681808 | ||||||||
\(782\) | −16.2434 | −0.580861 | ||||||||
\(783\) | 40.5383 | 1.44872 | ||||||||
\(784\) | −69.0074 | −2.46455 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 65.4069 | 2.33299 | ||||||||
\(787\) | 33.5231 | 1.19497 | 0.597485 | − | 0.801880i | \(-0.296167\pi\) | ||||
0.597485 | + | 0.801880i | \(0.296167\pi\) | |||||||
\(788\) | −10.6818 | −0.380524 | ||||||||
\(789\) | −27.4148 | −0.975993 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −0.929664 | −0.0330550 | ||||||||
\(792\) | 123.676 | 4.39463 | ||||||||
\(793\) | 5.81247 | 0.206407 | ||||||||
\(794\) | 61.8972 | 2.19665 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −9.21305 | −0.326548 | ||||||||
\(797\) | 10.4979 | 0.371855 | 0.185927 | − | 0.982563i | \(-0.440471\pi\) | ||||
0.185927 | + | 0.982563i | \(0.440471\pi\) | |||||||
\(798\) | −4.59942 | −0.162818 | ||||||||
\(799\) | −28.9913 | −1.02564 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 91.4398 | 3.23087 | ||||||||
\(802\) | 49.0432 | 1.73177 | ||||||||
\(803\) | −31.1178 | −1.09812 | ||||||||
\(804\) | −40.4882 | −1.42791 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −12.2217 | −0.430492 | ||||||||
\(807\) | 93.1591 | 3.27936 | ||||||||
\(808\) | 109.596 | 3.85559 | ||||||||
\(809\) | −13.0724 | −0.459600 | −0.229800 | − | 0.973238i | \(-0.573807\pi\) | ||||
−0.229800 | + | 0.973238i | \(0.573807\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −10.0790 | −0.353922 | −0.176961 | − | 0.984218i | \(-0.556627\pi\) | ||||
−0.176961 | + | 0.984218i | \(0.556627\pi\) | |||||||
\(812\) | −11.5470 | −0.405221 | ||||||||
\(813\) | −73.3924 | −2.57398 | ||||||||
\(814\) | 56.2268 | 1.97075 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −128.649 | −4.50362 | ||||||||
\(817\) | 0.574672 | 0.0201052 | ||||||||
\(818\) | −18.0956 | −0.632697 | ||||||||
\(819\) | 1.68505 | 0.0588804 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 40.2987 | 1.40643 | 0.703217 | − | 0.710975i | \(-0.251746\pi\) | ||||
0.703217 | + | 0.710975i | \(0.251746\pi\) | |||||||
\(822\) | −116.904 | −4.07750 | ||||||||
\(823\) | 5.07715 | 0.176978 | 0.0884892 | − | 0.996077i | \(-0.471796\pi\) | ||||
0.0884892 | + | 0.996077i | \(0.471796\pi\) | |||||||
\(824\) | −36.7684 | −1.28089 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −4.05904 | −0.141232 | ||||||||
\(827\) | 42.8077 | 1.48857 | 0.744285 | − | 0.667862i | \(-0.232791\pi\) | ||||
0.744285 | + | 0.667862i | \(0.232791\pi\) | |||||||
\(828\) | −46.5286 | −1.61698 | ||||||||
\(829\) | 24.2018 | 0.840562 | 0.420281 | − | 0.907394i | \(-0.361932\pi\) | ||||
0.420281 | + | 0.907394i | \(0.361932\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 13.8786 | 0.481444 | ||||||||
\(832\) | 4.92509 | 0.170747 | ||||||||
\(833\) | −27.2534 | −0.944274 | ||||||||
\(834\) | 16.5849 | 0.574288 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 12.6608 | 0.437883 | ||||||||
\(837\) | 98.4261 | 3.40210 | ||||||||
\(838\) | 35.4527 | 1.22469 | ||||||||
\(839\) | −8.63975 | −0.298277 | −0.149139 | − | 0.988816i | \(-0.547650\pi\) | ||||
−0.149139 | + | 0.988816i | \(0.547650\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −12.3036 | −0.424264 | ||||||||
\(842\) | −15.3463 | −0.528869 | ||||||||
\(843\) | 18.6102 | 0.640971 | ||||||||
\(844\) | −84.1325 | −2.89596 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −116.820 | −4.01637 | ||||||||
\(847\) | −2.51193 | −0.0863109 | ||||||||
\(848\) | −44.5229 | −1.52892 | ||||||||
\(849\) | −57.9847 | −1.99003 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −12.5499 | −0.430206 | ||||||||
\(852\) | 110.743 | 3.79398 | ||||||||
\(853\) | 13.0229 | 0.445895 | 0.222948 | − | 0.974830i | \(-0.428432\pi\) | ||||
0.222948 | + | 0.974830i | \(0.428432\pi\) | |||||||
\(854\) | 18.7564 | 0.641829 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −70.7934 | −2.41967 | ||||||||
\(857\) | 2.82367 | 0.0964548 | 0.0482274 | − | 0.998836i | \(-0.484643\pi\) | ||||
0.0482274 | + | 0.998836i | \(0.484643\pi\) | |||||||
\(858\) | −9.65182 | −0.329508 | ||||||||
\(859\) | 24.1227 | 0.823057 | 0.411529 | − | 0.911397i | \(-0.364995\pi\) | ||||
0.411529 | + | 0.911397i | \(0.364995\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 3.20876 | 0.109354 | ||||||||
\(862\) | 76.8092 | 2.61613 | ||||||||
\(863\) | −32.7307 | −1.11417 | −0.557084 | − | 0.830456i | \(-0.688080\pi\) | ||||
−0.557084 | + | 0.830456i | \(0.688080\pi\) | |||||||
\(864\) | −117.718 | −4.00485 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 32.9366 | 1.11923 | ||||||||
\(867\) | 0.924022 | 0.0313814 | ||||||||
\(868\) | −28.0359 | −0.951599 | ||||||||
\(869\) | −17.2131 | −0.583913 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.26731 | 0.0429413 | ||||||||
\(872\) | 37.5839 | 1.27275 | ||||||||
\(873\) | −109.257 | −3.69779 | ||||||||
\(874\) | −3.97526 | −0.134465 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 180.857 | 6.11060 | ||||||||
\(877\) | 49.5072 | 1.67174 | 0.835869 | − | 0.548929i | \(-0.184964\pi\) | ||||
0.835869 | + | 0.548929i | \(0.184964\pi\) | |||||||
\(878\) | 41.2318 | 1.39150 | ||||||||
\(879\) | −19.5939 | −0.660884 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 40.3152 | 1.35826 | 0.679128 | − | 0.734020i | \(-0.262358\pi\) | ||||
0.679128 | + | 0.734020i | \(0.262358\pi\) | |||||||
\(882\) | −109.817 | −3.69774 | ||||||||
\(883\) | 29.3347 | 0.987192 | 0.493596 | − | 0.869691i | \(-0.335682\pi\) | ||||
0.493596 | + | 0.869691i | \(0.335682\pi\) | |||||||
\(884\) | 9.41140 | 0.316540 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 78.4508 | 2.63561 | ||||||||
\(887\) | −43.3214 | −1.45459 | −0.727295 | − | 0.686325i | \(-0.759223\pi\) | ||||
−0.727295 | + | 0.686325i | \(0.759223\pi\) | |||||||
\(888\) | −193.880 | −6.50619 | ||||||||
\(889\) | 7.54496 | 0.253050 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 29.3758 | 0.984128 | ||||||||
\(892\) | −25.2224 | −0.844508 | ||||||||
\(893\) | −7.09508 | −0.237428 | ||||||||
\(894\) | −71.3279 | −2.38556 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 2.25524 | 0.0753424 | ||||||||
\(897\) | 2.15431 | 0.0719302 | ||||||||
\(898\) | 78.8157 | 2.63011 | ||||||||
\(899\) | 40.5383 | 1.35203 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −17.5836 | −0.585796 | ||||||||
\(902\) | −12.4251 | −0.413712 | ||||||||
\(903\) | −1.00496 | −0.0334431 | ||||||||
\(904\) | −12.4131 | −0.412854 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −91.6982 | −3.04647 | ||||||||
\(907\) | −14.0731 | −0.467288 | −0.233644 | − | 0.972322i | \(-0.575065\pi\) | ||||
−0.233644 | + | 0.972322i | \(0.575065\pi\) | |||||||
\(908\) | 35.9574 | 1.19329 | ||||||||
\(909\) | 89.4151 | 2.96571 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 30.0725 | 0.996346 | 0.498173 | − | 0.867078i | \(-0.334004\pi\) | ||||
0.498173 | + | 0.867078i | \(0.334004\pi\) | |||||||
\(912\) | −31.4845 | −1.04255 | ||||||||
\(913\) | 17.1493 | 0.567560 | ||||||||
\(914\) | −46.4733 | −1.53720 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −41.3534 | −1.36636 | ||||||||
\(917\) | −4.69635 | −0.155087 | ||||||||
\(918\) | −106.620 | −3.51898 | ||||||||
\(919\) | 29.6518 | 0.978123 | 0.489062 | − | 0.872249i | \(-0.337339\pi\) | ||||
0.489062 | + | 0.872249i | \(0.337339\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −20.6133 | −0.679233 | ||||||||
\(922\) | 58.7682 | 1.93543 | ||||||||
\(923\) | −3.46634 | −0.114096 | ||||||||
\(924\) | −22.1407 | −0.728375 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 17.9715 | 0.590582 | ||||||||
\(927\) | −29.9978 | −0.985256 | ||||||||
\(928\) | −48.4841 | −1.59157 | ||||||||
\(929\) | 58.3803 | 1.91540 | 0.957698 | − | 0.287775i | \(-0.0929154\pi\) | ||||
0.957698 | + | 0.287775i | \(0.0929154\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −6.66975 | −0.218592 | ||||||||
\(932\) | 69.6911 | 2.28281 | ||||||||
\(933\) | −62.7492 | −2.05432 | ||||||||
\(934\) | −23.6945 | −0.775308 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 22.4992 | 0.735410 | ||||||||
\(937\) | 3.15850 | 0.103184 | 0.0515918 | − | 0.998668i | \(-0.483571\pi\) | ||||
0.0515918 | + | 0.998668i | \(0.483571\pi\) | |||||||
\(938\) | 4.08952 | 0.133528 | ||||||||
\(939\) | 58.9473 | 1.92367 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −9.66975 | −0.315225 | −0.157612 | − | 0.987501i | \(-0.550380\pi\) | ||||
−0.157612 | + | 0.987501i | \(0.550380\pi\) | |||||||
\(942\) | −52.8757 | −1.72278 | ||||||||
\(943\) | 2.77331 | 0.0903116 | ||||||||
\(944\) | −27.7854 | −0.904337 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 3.89148 | 0.126523 | ||||||||
\(947\) | −31.3714 | −1.01943 | −0.509716 | − | 0.860343i | \(-0.670250\pi\) | ||||
−0.509716 | + | 0.860343i | \(0.670250\pi\) | |||||||
\(948\) | 100.043 | 3.24923 | ||||||||
\(949\) | −5.66098 | −0.183763 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 10.2661 | 0.332900 | ||||||||
\(952\) | 18.0179 | 0.583964 | ||||||||
\(953\) | 13.1224 | 0.425075 | 0.212537 | − | 0.977153i | \(-0.431827\pi\) | ||||
0.212537 | + | 0.977153i | \(0.431827\pi\) | |||||||
\(954\) | −70.8531 | −2.29395 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −69.7792 | −2.25682 | ||||||||
\(957\) | 32.0142 | 1.03487 | ||||||||
\(958\) | 24.3740 | 0.787488 | ||||||||
\(959\) | 8.39396 | 0.271055 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 67.4261 | 2.17504 | ||||||||
\(962\) | 10.2288 | 0.329791 | ||||||||
\(963\) | −57.7573 | −1.86120 | ||||||||
\(964\) | 137.101 | 4.41574 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 6.95177 | 0.223669 | ||||||||
\(967\) | 44.4400 | 1.42910 | 0.714548 | − | 0.699587i | \(-0.246633\pi\) | ||||
0.714548 | + | 0.699587i | \(0.246633\pi\) | |||||||
\(968\) | −33.5399 | −1.07801 | ||||||||
\(969\) | −12.4343 | −0.399447 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −5.69927 | −0.182898 | −0.0914491 | − | 0.995810i | \(-0.529150\pi\) | ||||
−0.0914491 | + | 0.995810i | \(0.529150\pi\) | |||||||
\(972\) | −24.3755 | −0.781843 | ||||||||
\(973\) | −1.19083 | −0.0381762 | ||||||||
\(974\) | 101.968 | 3.26725 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 128.393 | 4.10977 | ||||||||
\(977\) | 23.9164 | 0.765154 | 0.382577 | − | 0.923924i | \(-0.375037\pi\) | ||||
0.382577 | + | 0.923924i | \(0.375037\pi\) | |||||||
\(978\) | 162.027 | 5.18106 | ||||||||
\(979\) | 37.6070 | 1.20193 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 30.6631 | 0.978998 | ||||||||
\(982\) | 57.0408 | 1.82025 | ||||||||
\(983\) | 45.5302 | 1.45219 | 0.726095 | − | 0.687595i | \(-0.241333\pi\) | ||||
0.726095 | + | 0.687595i | \(0.241333\pi\) | |||||||
\(984\) | 42.8441 | 1.36582 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −43.9131 | −1.39848 | ||||||||
\(987\) | 12.4076 | 0.394938 | ||||||||
\(988\) | 2.30326 | 0.0732766 | ||||||||
\(989\) | −0.868585 | −0.0276194 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 27.5521 | 0.875220 | 0.437610 | − | 0.899165i | \(-0.355825\pi\) | ||||
0.437610 | + | 0.899165i | \(0.355825\pi\) | |||||||
\(992\) | −117.718 | −3.73756 | ||||||||
\(993\) | 99.7477 | 3.16540 | ||||||||
\(994\) | −11.1856 | −0.354785 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −99.6724 | −3.15824 | ||||||||
\(997\) | −16.8557 | −0.533826 | −0.266913 | − | 0.963721i | \(-0.586004\pi\) | ||||
−0.266913 | + | 0.963721i | \(0.586004\pi\) | |||||||
\(998\) | −73.2147 | −2.31757 | ||||||||
\(999\) | −82.3766 | −2.60628 |
(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 | 475.2.a.i.1.4 | 4 | ||
3.2 | odd | 2 | 4275.2.a.bo.1.1 | 4 | |||
4.3 | odd | 2 | 7600.2.a.cf.1.4 | 4 | |||
5.2 | odd | 4 | 475.2.b.e.324.8 | 8 | |||
5.3 | odd | 4 | 475.2.b.e.324.1 | 8 | |||
5.4 | even | 2 | 95.2.a.b.1.1 | ✓ | 4 | ||
15.14 | odd | 2 | 855.2.a.m.1.4 | 4 | |||
19.18 | odd | 2 | 9025.2.a.bf.1.1 | 4 | |||
20.19 | odd | 2 | 1520.2.a.t.1.1 | 4 | |||
35.34 | odd | 2 | 4655.2.a.y.1.1 | 4 | |||
40.19 | odd | 2 | 6080.2.a.ch.1.4 | 4 | |||
40.29 | even | 2 | 6080.2.a.cc.1.1 | 4 | |||
95.94 | odd | 2 | 1805.2.a.p.1.4 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
95.2.a.b.1.1 | ✓ | 4 | 5.4 | even | 2 | ||
475.2.a.i.1.4 | 4 | 1.1 | even | 1 | trivial | ||
475.2.b.e.324.1 | 8 | 5.3 | odd | 4 | |||
475.2.b.e.324.8 | 8 | 5.2 | odd | 4 | |||
855.2.a.m.1.4 | 4 | 15.14 | odd | 2 | |||
1520.2.a.t.1.1 | 4 | 20.19 | odd | 2 | |||
1805.2.a.p.1.4 | 4 | 95.94 | odd | 2 | |||
4275.2.a.bo.1.1 | 4 | 3.2 | odd | 2 | |||
4655.2.a.y.1.1 | 4 | 35.34 | odd | 2 | |||
6080.2.a.cc.1.1 | 4 | 40.29 | even | 2 | |||
6080.2.a.ch.1.4 | 4 | 40.19 | odd | 2 | |||
7600.2.a.cf.1.4 | 4 | 4.3 | odd | 2 | |||
9025.2.a.bf.1.1 | 4 | 19.18 | odd | 2 |