Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8034,2,Mod(1,8034)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8034, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8034.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8034 = 2 \cdot 3 \cdot 13 \cdot 103 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8034.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: | \(64.1518129839\) |
Analytic rank: | \(0\) |
Dimension: | \(15\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{15} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{15} - x^{14} - 48 x^{13} + 44 x^{12} + 872 x^{11} - 707 x^{10} - 7580 x^{9} + 5112 x^{8} + \cdots + 2048 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(4.06882\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8034.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −4.06882 | −1.81963 | −0.909815 | − | 0.415015i | \(-0.863776\pi\) | ||||
−0.909815 | + | 0.415015i | \(0.863776\pi\) | |||||||
\(6\) | −1.00000 | −0.408248 | ||||||||
\(7\) | 4.31915 | 1.63249 | 0.816243 | − | 0.577708i | \(-0.196053\pi\) | ||||
0.816243 | + | 0.577708i | \(0.196053\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −4.06882 | −1.28667 | ||||||||
\(11\) | −3.45943 | −1.04306 | −0.521529 | − | 0.853234i | \(-0.674638\pi\) | ||||
−0.521529 | + | 0.853234i | \(0.674638\pi\) | |||||||
\(12\) | −1.00000 | −0.288675 | ||||||||
\(13\) | −1.00000 | −0.277350 | ||||||||
\(14\) | 4.31915 | 1.15434 | ||||||||
\(15\) | 4.06882 | 1.05056 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −7.56875 | −1.83569 | −0.917845 | − | 0.396938i | \(-0.870073\pi\) | ||||
−0.917845 | + | 0.396938i | \(0.870073\pi\) | |||||||
\(18\) | 1.00000 | 0.235702 | ||||||||
\(19\) | −1.84870 | −0.424120 | −0.212060 | − | 0.977257i | \(-0.568017\pi\) | ||||
−0.212060 | + | 0.977257i | \(0.568017\pi\) | |||||||
\(20\) | −4.06882 | −0.909815 | ||||||||
\(21\) | −4.31915 | −0.942517 | ||||||||
\(22\) | −3.45943 | −0.737553 | ||||||||
\(23\) | −8.50665 | −1.77376 | −0.886879 | − | 0.462001i | \(-0.847132\pi\) | ||||
−0.886879 | + | 0.462001i | \(0.847132\pi\) | |||||||
\(24\) | −1.00000 | −0.204124 | ||||||||
\(25\) | 11.5553 | 2.31105 | ||||||||
\(26\) | −1.00000 | −0.196116 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 4.31915 | 0.816243 | ||||||||
\(29\) | 6.61550 | 1.22847 | 0.614234 | − | 0.789124i | \(-0.289465\pi\) | ||||
0.614234 | + | 0.789124i | \(0.289465\pi\) | |||||||
\(30\) | 4.06882 | 0.742861 | ||||||||
\(31\) | −5.55957 | −0.998528 | −0.499264 | − | 0.866450i | \(-0.666396\pi\) | ||||
−0.499264 | + | 0.866450i | \(0.666396\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 3.45943 | 0.602210 | ||||||||
\(34\) | −7.56875 | −1.29803 | ||||||||
\(35\) | −17.5738 | −2.97052 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | 10.0080 | 1.64530 | 0.822652 | − | 0.568545i | \(-0.192493\pi\) | ||||
0.822652 | + | 0.568545i | \(0.192493\pi\) | |||||||
\(38\) | −1.84870 | −0.299898 | ||||||||
\(39\) | 1.00000 | 0.160128 | ||||||||
\(40\) | −4.06882 | −0.643336 | ||||||||
\(41\) | 0.695896 | 0.108681 | 0.0543403 | − | 0.998522i | \(-0.482694\pi\) | ||||
0.0543403 | + | 0.998522i | \(0.482694\pi\) | |||||||
\(42\) | −4.31915 | −0.666460 | ||||||||
\(43\) | −3.09807 | −0.472452 | −0.236226 | − | 0.971698i | \(-0.575910\pi\) | ||||
−0.236226 | + | 0.971698i | \(0.575910\pi\) | |||||||
\(44\) | −3.45943 | −0.521529 | ||||||||
\(45\) | −4.06882 | −0.606543 | ||||||||
\(46\) | −8.50665 | −1.25424 | ||||||||
\(47\) | −1.17792 | −0.171818 | −0.0859089 | − | 0.996303i | \(-0.527379\pi\) | ||||
−0.0859089 | + | 0.996303i | \(0.527379\pi\) | |||||||
\(48\) | −1.00000 | −0.144338 | ||||||||
\(49\) | 11.6551 | 1.66501 | ||||||||
\(50\) | 11.5553 | 1.63416 | ||||||||
\(51\) | 7.56875 | 1.05984 | ||||||||
\(52\) | −1.00000 | −0.138675 | ||||||||
\(53\) | 5.76954 | 0.792507 | 0.396253 | − | 0.918141i | \(-0.370310\pi\) | ||||
0.396253 | + | 0.918141i | \(0.370310\pi\) | |||||||
\(54\) | −1.00000 | −0.136083 | ||||||||
\(55\) | 14.0758 | 1.89798 | ||||||||
\(56\) | 4.31915 | 0.577171 | ||||||||
\(57\) | 1.84870 | 0.244866 | ||||||||
\(58\) | 6.61550 | 0.868657 | ||||||||
\(59\) | 6.88464 | 0.896303 | 0.448152 | − | 0.893958i | \(-0.352082\pi\) | ||||
0.448152 | + | 0.893958i | \(0.352082\pi\) | |||||||
\(60\) | 4.06882 | 0.525282 | ||||||||
\(61\) | 12.3520 | 1.58151 | 0.790755 | − | 0.612133i | \(-0.209688\pi\) | ||||
0.790755 | + | 0.612133i | \(0.209688\pi\) | |||||||
\(62\) | −5.55957 | −0.706066 | ||||||||
\(63\) | 4.31915 | 0.544162 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 4.06882 | 0.504674 | ||||||||
\(66\) | 3.45943 | 0.425827 | ||||||||
\(67\) | −14.3536 | −1.75357 | −0.876786 | − | 0.480881i | \(-0.840317\pi\) | ||||
−0.876786 | + | 0.480881i | \(0.840317\pi\) | |||||||
\(68\) | −7.56875 | −0.917845 | ||||||||
\(69\) | 8.50665 | 1.02408 | ||||||||
\(70\) | −17.5738 | −2.10048 | ||||||||
\(71\) | 4.40758 | 0.523083 | 0.261542 | − | 0.965192i | \(-0.415769\pi\) | ||||
0.261542 | + | 0.965192i | \(0.415769\pi\) | |||||||
\(72\) | 1.00000 | 0.117851 | ||||||||
\(73\) | −8.29562 | −0.970928 | −0.485464 | − | 0.874257i | \(-0.661349\pi\) | ||||
−0.485464 | + | 0.874257i | \(0.661349\pi\) | |||||||
\(74\) | 10.0080 | 1.16341 | ||||||||
\(75\) | −11.5553 | −1.33429 | ||||||||
\(76\) | −1.84870 | −0.212060 | ||||||||
\(77\) | −14.9418 | −1.70278 | ||||||||
\(78\) | 1.00000 | 0.113228 | ||||||||
\(79\) | 6.21617 | 0.699373 | 0.349687 | − | 0.936867i | \(-0.386288\pi\) | ||||
0.349687 | + | 0.936867i | \(0.386288\pi\) | |||||||
\(80\) | −4.06882 | −0.454907 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0.695896 | 0.0768488 | ||||||||
\(83\) | −11.6646 | −1.28036 | −0.640179 | − | 0.768226i | \(-0.721140\pi\) | ||||
−0.640179 | + | 0.768226i | \(0.721140\pi\) | |||||||
\(84\) | −4.31915 | −0.471258 | ||||||||
\(85\) | 30.7958 | 3.34028 | ||||||||
\(86\) | −3.09807 | −0.334074 | ||||||||
\(87\) | −6.61550 | −0.709256 | ||||||||
\(88\) | −3.45943 | −0.368777 | ||||||||
\(89\) | −2.88091 | −0.305375 | −0.152688 | − | 0.988274i | \(-0.548793\pi\) | ||||
−0.152688 | + | 0.988274i | \(0.548793\pi\) | |||||||
\(90\) | −4.06882 | −0.428891 | ||||||||
\(91\) | −4.31915 | −0.452770 | ||||||||
\(92\) | −8.50665 | −0.886879 | ||||||||
\(93\) | 5.55957 | 0.576501 | ||||||||
\(94\) | −1.17792 | −0.121494 | ||||||||
\(95\) | 7.52201 | 0.771742 | ||||||||
\(96\) | −1.00000 | −0.102062 | ||||||||
\(97\) | 4.85929 | 0.493386 | 0.246693 | − | 0.969094i | \(-0.420656\pi\) | ||||
0.246693 | + | 0.969094i | \(0.420656\pi\) | |||||||
\(98\) | 11.6551 | 1.17734 | ||||||||
\(99\) | −3.45943 | −0.347686 | ||||||||
\(100\) | 11.5553 | 1.15553 | ||||||||
\(101\) | 9.41575 | 0.936903 | 0.468451 | − | 0.883489i | \(-0.344812\pi\) | ||||
0.468451 | + | 0.883489i | \(0.344812\pi\) | |||||||
\(102\) | 7.56875 | 0.749418 | ||||||||
\(103\) | −1.00000 | −0.0985329 | ||||||||
\(104\) | −1.00000 | −0.0980581 | ||||||||
\(105\) | 17.5738 | 1.71503 | ||||||||
\(106\) | 5.76954 | 0.560387 | ||||||||
\(107\) | 3.81409 | 0.368722 | 0.184361 | − | 0.982859i | \(-0.440978\pi\) | ||||
0.184361 | + | 0.982859i | \(0.440978\pi\) | |||||||
\(108\) | −1.00000 | −0.0962250 | ||||||||
\(109\) | 18.7539 | 1.79630 | 0.898149 | − | 0.439691i | \(-0.144912\pi\) | ||||
0.898149 | + | 0.439691i | \(0.144912\pi\) | |||||||
\(110\) | 14.0758 | 1.34207 | ||||||||
\(111\) | −10.0080 | −0.949917 | ||||||||
\(112\) | 4.31915 | 0.408122 | ||||||||
\(113\) | −10.5876 | −0.995998 | −0.497999 | − | 0.867178i | \(-0.665932\pi\) | ||||
−0.497999 | + | 0.867178i | \(0.665932\pi\) | |||||||
\(114\) | 1.84870 | 0.173146 | ||||||||
\(115\) | 34.6120 | 3.22758 | ||||||||
\(116\) | 6.61550 | 0.614234 | ||||||||
\(117\) | −1.00000 | −0.0924500 | ||||||||
\(118\) | 6.88464 | 0.633782 | ||||||||
\(119\) | −32.6906 | −2.99674 | ||||||||
\(120\) | 4.06882 | 0.371430 | ||||||||
\(121\) | 0.967666 | 0.0879696 | ||||||||
\(122\) | 12.3520 | 1.11830 | ||||||||
\(123\) | −0.695896 | −0.0627468 | ||||||||
\(124\) | −5.55957 | −0.499264 | ||||||||
\(125\) | −26.6721 | −2.38563 | ||||||||
\(126\) | 4.31915 | 0.384781 | ||||||||
\(127\) | −21.5905 | −1.91585 | −0.957923 | − | 0.287026i | \(-0.907333\pi\) | ||||
−0.957923 | + | 0.287026i | \(0.907333\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 3.09807 | 0.272770 | ||||||||
\(130\) | 4.06882 | 0.356859 | ||||||||
\(131\) | −2.47190 | −0.215971 | −0.107985 | − | 0.994152i | \(-0.534440\pi\) | ||||
−0.107985 | + | 0.994152i | \(0.534440\pi\) | |||||||
\(132\) | 3.45943 | 0.301105 | ||||||||
\(133\) | −7.98481 | −0.692370 | ||||||||
\(134\) | −14.3536 | −1.23996 | ||||||||
\(135\) | 4.06882 | 0.350188 | ||||||||
\(136\) | −7.56875 | −0.649015 | ||||||||
\(137\) | 7.60382 | 0.649638 | 0.324819 | − | 0.945776i | \(-0.394697\pi\) | ||||
0.324819 | + | 0.945776i | \(0.394697\pi\) | |||||||
\(138\) | 8.50665 | 0.724134 | ||||||||
\(139\) | −0.701284 | −0.0594821 | −0.0297410 | − | 0.999558i | \(-0.509468\pi\) | ||||
−0.0297410 | + | 0.999558i | \(0.509468\pi\) | |||||||
\(140\) | −17.5738 | −1.48526 | ||||||||
\(141\) | 1.17792 | 0.0991990 | ||||||||
\(142\) | 4.40758 | 0.369876 | ||||||||
\(143\) | 3.45943 | 0.289292 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | −26.9172 | −2.23535 | ||||||||
\(146\) | −8.29562 | −0.686550 | ||||||||
\(147\) | −11.6551 | −0.961296 | ||||||||
\(148\) | 10.0080 | 0.822652 | ||||||||
\(149\) | 18.0995 | 1.48276 | 0.741382 | − | 0.671083i | \(-0.234171\pi\) | ||||
0.741382 | + | 0.671083i | \(0.234171\pi\) | |||||||
\(150\) | −11.5553 | −0.943483 | ||||||||
\(151\) | 16.5279 | 1.34502 | 0.672512 | − | 0.740086i | \(-0.265215\pi\) | ||||
0.672512 | + | 0.740086i | \(0.265215\pi\) | |||||||
\(152\) | −1.84870 | −0.149949 | ||||||||
\(153\) | −7.56875 | −0.611897 | ||||||||
\(154\) | −14.9418 | −1.20405 | ||||||||
\(155\) | 22.6209 | 1.81695 | ||||||||
\(156\) | 1.00000 | 0.0800641 | ||||||||
\(157\) | −8.57471 | −0.684336 | −0.342168 | − | 0.939639i | \(-0.611161\pi\) | ||||
−0.342168 | + | 0.939639i | \(0.611161\pi\) | |||||||
\(158\) | 6.21617 | 0.494532 | ||||||||
\(159\) | −5.76954 | −0.457554 | ||||||||
\(160\) | −4.06882 | −0.321668 | ||||||||
\(161\) | −36.7415 | −2.89564 | ||||||||
\(162\) | 1.00000 | 0.0785674 | ||||||||
\(163\) | −9.70287 | −0.759987 | −0.379994 | − | 0.924989i | \(-0.624074\pi\) | ||||
−0.379994 | + | 0.924989i | \(0.624074\pi\) | |||||||
\(164\) | 0.695896 | 0.0543403 | ||||||||
\(165\) | −14.0758 | −1.09580 | ||||||||
\(166\) | −11.6646 | −0.905350 | ||||||||
\(167\) | 13.4484 | 1.04067 | 0.520335 | − | 0.853962i | \(-0.325807\pi\) | ||||
0.520335 | + | 0.853962i | \(0.325807\pi\) | |||||||
\(168\) | −4.31915 | −0.333230 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 30.7958 | 2.36193 | ||||||||
\(171\) | −1.84870 | −0.141373 | ||||||||
\(172\) | −3.09807 | −0.236226 | ||||||||
\(173\) | 0.334934 | 0.0254646 | 0.0127323 | − | 0.999919i | \(-0.495947\pi\) | ||||
0.0127323 | + | 0.999919i | \(0.495947\pi\) | |||||||
\(174\) | −6.61550 | −0.501520 | ||||||||
\(175\) | 49.9089 | 3.77276 | ||||||||
\(176\) | −3.45943 | −0.260764 | ||||||||
\(177\) | −6.88464 | −0.517481 | ||||||||
\(178\) | −2.88091 | −0.215933 | ||||||||
\(179\) | 18.9801 | 1.41864 | 0.709321 | − | 0.704886i | \(-0.249002\pi\) | ||||
0.709321 | + | 0.704886i | \(0.249002\pi\) | |||||||
\(180\) | −4.06882 | −0.303272 | ||||||||
\(181\) | −4.69449 | −0.348938 | −0.174469 | − | 0.984663i | \(-0.555821\pi\) | ||||
−0.174469 | + | 0.984663i | \(0.555821\pi\) | |||||||
\(182\) | −4.31915 | −0.320157 | ||||||||
\(183\) | −12.3520 | −0.913085 | ||||||||
\(184\) | −8.50665 | −0.627118 | ||||||||
\(185\) | −40.7207 | −2.99385 | ||||||||
\(186\) | 5.55957 | 0.407647 | ||||||||
\(187\) | 26.1836 | 1.91473 | ||||||||
\(188\) | −1.17792 | −0.0859089 | ||||||||
\(189\) | −4.31915 | −0.314172 | ||||||||
\(190\) | 7.52201 | 0.545704 | ||||||||
\(191\) | 12.4462 | 0.900579 | 0.450289 | − | 0.892883i | \(-0.351321\pi\) | ||||
0.450289 | + | 0.892883i | \(0.351321\pi\) | |||||||
\(192\) | −1.00000 | −0.0721688 | ||||||||
\(193\) | 2.02744 | 0.145939 | 0.0729693 | − | 0.997334i | \(-0.476752\pi\) | ||||
0.0729693 | + | 0.997334i | \(0.476752\pi\) | |||||||
\(194\) | 4.85929 | 0.348877 | ||||||||
\(195\) | −4.06882 | −0.291374 | ||||||||
\(196\) | 11.6551 | 0.832507 | ||||||||
\(197\) | 16.8314 | 1.19919 | 0.599595 | − | 0.800303i | \(-0.295328\pi\) | ||||
0.599595 | + | 0.800303i | \(0.295328\pi\) | |||||||
\(198\) | −3.45943 | −0.245851 | ||||||||
\(199\) | −0.301529 | −0.0213748 | −0.0106874 | − | 0.999943i | \(-0.503402\pi\) | ||||
−0.0106874 | + | 0.999943i | \(0.503402\pi\) | |||||||
\(200\) | 11.5553 | 0.817080 | ||||||||
\(201\) | 14.3536 | 1.01243 | ||||||||
\(202\) | 9.41575 | 0.662490 | ||||||||
\(203\) | 28.5734 | 2.00546 | ||||||||
\(204\) | 7.56875 | 0.529918 | ||||||||
\(205\) | −2.83147 | −0.197759 | ||||||||
\(206\) | −1.00000 | −0.0696733 | ||||||||
\(207\) | −8.50665 | −0.591253 | ||||||||
\(208\) | −1.00000 | −0.0693375 | ||||||||
\(209\) | 6.39544 | 0.442382 | ||||||||
\(210\) | 17.5738 | 1.21271 | ||||||||
\(211\) | −3.92060 | −0.269905 | −0.134953 | − | 0.990852i | \(-0.543088\pi\) | ||||
−0.134953 | + | 0.990852i | \(0.543088\pi\) | |||||||
\(212\) | 5.76954 | 0.396253 | ||||||||
\(213\) | −4.40758 | −0.302002 | ||||||||
\(214\) | 3.81409 | 0.260726 | ||||||||
\(215\) | 12.6055 | 0.859687 | ||||||||
\(216\) | −1.00000 | −0.0680414 | ||||||||
\(217\) | −24.0126 | −1.63008 | ||||||||
\(218\) | 18.7539 | 1.27017 | ||||||||
\(219\) | 8.29562 | 0.560566 | ||||||||
\(220\) | 14.0758 | 0.948989 | ||||||||
\(221\) | 7.56875 | 0.509129 | ||||||||
\(222\) | −10.0080 | −0.671693 | ||||||||
\(223\) | 13.3625 | 0.894819 | 0.447410 | − | 0.894329i | \(-0.352347\pi\) | ||||
0.447410 | + | 0.894329i | \(0.352347\pi\) | |||||||
\(224\) | 4.31915 | 0.288586 | ||||||||
\(225\) | 11.5553 | 0.770351 | ||||||||
\(226\) | −10.5876 | −0.704277 | ||||||||
\(227\) | −1.25297 | −0.0831623 | −0.0415811 | − | 0.999135i | \(-0.513240\pi\) | ||||
−0.0415811 | + | 0.999135i | \(0.513240\pi\) | |||||||
\(228\) | 1.84870 | 0.122433 | ||||||||
\(229\) | 8.24201 | 0.544647 | 0.272324 | − | 0.962206i | \(-0.412208\pi\) | ||||
0.272324 | + | 0.962206i | \(0.412208\pi\) | |||||||
\(230\) | 34.6120 | 2.28225 | ||||||||
\(231\) | 14.9418 | 0.983099 | ||||||||
\(232\) | 6.61550 | 0.434329 | ||||||||
\(233\) | 12.8913 | 0.844538 | 0.422269 | − | 0.906471i | \(-0.361234\pi\) | ||||
0.422269 | + | 0.906471i | \(0.361234\pi\) | |||||||
\(234\) | −1.00000 | −0.0653720 | ||||||||
\(235\) | 4.79275 | 0.312645 | ||||||||
\(236\) | 6.88464 | 0.448152 | ||||||||
\(237\) | −6.21617 | −0.403783 | ||||||||
\(238\) | −32.6906 | −2.11902 | ||||||||
\(239\) | 20.1551 | 1.30373 | 0.651864 | − | 0.758336i | \(-0.273987\pi\) | ||||
0.651864 | + | 0.758336i | \(0.273987\pi\) | |||||||
\(240\) | 4.06882 | 0.262641 | ||||||||
\(241\) | −2.43963 | −0.157150 | −0.0785751 | − | 0.996908i | \(-0.525037\pi\) | ||||
−0.0785751 | + | 0.996908i | \(0.525037\pi\) | |||||||
\(242\) | 0.967666 | 0.0622039 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 12.3520 | 0.790755 | ||||||||
\(245\) | −47.4224 | −3.02971 | ||||||||
\(246\) | −0.695896 | −0.0443687 | ||||||||
\(247\) | 1.84870 | 0.117630 | ||||||||
\(248\) | −5.55957 | −0.353033 | ||||||||
\(249\) | 11.6646 | 0.739215 | ||||||||
\(250\) | −26.6721 | −1.68689 | ||||||||
\(251\) | −7.14154 | −0.450770 | −0.225385 | − | 0.974270i | \(-0.572364\pi\) | ||||
−0.225385 | + | 0.974270i | \(0.572364\pi\) | |||||||
\(252\) | 4.31915 | 0.272081 | ||||||||
\(253\) | 29.4282 | 1.85013 | ||||||||
\(254\) | −21.5905 | −1.35471 | ||||||||
\(255\) | −30.7958 | −1.92851 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 9.93685 | 0.619844 | 0.309922 | − | 0.950762i | \(-0.399697\pi\) | ||||
0.309922 | + | 0.950762i | \(0.399697\pi\) | |||||||
\(258\) | 3.09807 | 0.192878 | ||||||||
\(259\) | 43.2261 | 2.68594 | ||||||||
\(260\) | 4.06882 | 0.252337 | ||||||||
\(261\) | 6.61550 | 0.409489 | ||||||||
\(262\) | −2.47190 | −0.152715 | ||||||||
\(263\) | −24.6988 | −1.52299 | −0.761497 | − | 0.648168i | \(-0.775535\pi\) | ||||
−0.761497 | + | 0.648168i | \(0.775535\pi\) | |||||||
\(264\) | 3.45943 | 0.212913 | ||||||||
\(265\) | −23.4752 | −1.44207 | ||||||||
\(266\) | −7.98481 | −0.489580 | ||||||||
\(267\) | 2.88091 | 0.176309 | ||||||||
\(268\) | −14.3536 | −0.876786 | ||||||||
\(269\) | 25.6107 | 1.56151 | 0.780756 | − | 0.624836i | \(-0.214834\pi\) | ||||
0.780756 | + | 0.624836i | \(0.214834\pi\) | |||||||
\(270\) | 4.06882 | 0.247620 | ||||||||
\(271\) | −6.42255 | −0.390142 | −0.195071 | − | 0.980789i | \(-0.562494\pi\) | ||||
−0.195071 | + | 0.980789i | \(0.562494\pi\) | |||||||
\(272\) | −7.56875 | −0.458923 | ||||||||
\(273\) | 4.31915 | 0.261407 | ||||||||
\(274\) | 7.60382 | 0.459364 | ||||||||
\(275\) | −39.9746 | −2.41056 | ||||||||
\(276\) | 8.50665 | 0.512040 | ||||||||
\(277\) | 18.0070 | 1.08194 | 0.540969 | − | 0.841043i | \(-0.318058\pi\) | ||||
0.540969 | + | 0.841043i | \(0.318058\pi\) | |||||||
\(278\) | −0.701284 | −0.0420602 | ||||||||
\(279\) | −5.55957 | −0.332843 | ||||||||
\(280\) | −17.5738 | −1.05024 | ||||||||
\(281\) | −12.7632 | −0.761386 | −0.380693 | − | 0.924701i | \(-0.624315\pi\) | ||||
−0.380693 | + | 0.924701i | \(0.624315\pi\) | |||||||
\(282\) | 1.17792 | 0.0701443 | ||||||||
\(283\) | 10.4087 | 0.618732 | 0.309366 | − | 0.950943i | \(-0.399883\pi\) | ||||
0.309366 | + | 0.950943i | \(0.399883\pi\) | |||||||
\(284\) | 4.40758 | 0.261542 | ||||||||
\(285\) | −7.52201 | −0.445565 | ||||||||
\(286\) | 3.45943 | 0.204560 | ||||||||
\(287\) | 3.00568 | 0.177420 | ||||||||
\(288\) | 1.00000 | 0.0589256 | ||||||||
\(289\) | 40.2859 | 2.36976 | ||||||||
\(290\) | −26.9172 | −1.58063 | ||||||||
\(291\) | −4.85929 | −0.284857 | ||||||||
\(292\) | −8.29562 | −0.485464 | ||||||||
\(293\) | −13.9122 | −0.812758 | −0.406379 | − | 0.913705i | \(-0.633209\pi\) | ||||
−0.406379 | + | 0.913705i | \(0.633209\pi\) | |||||||
\(294\) | −11.6551 | −0.679739 | ||||||||
\(295\) | −28.0123 | −1.63094 | ||||||||
\(296\) | 10.0080 | 0.581703 | ||||||||
\(297\) | 3.45943 | 0.200737 | ||||||||
\(298\) | 18.0995 | 1.04847 | ||||||||
\(299\) | 8.50665 | 0.491952 | ||||||||
\(300\) | −11.5553 | −0.667143 | ||||||||
\(301\) | −13.3811 | −0.771271 | ||||||||
\(302\) | 16.5279 | 0.951076 | ||||||||
\(303\) | −9.41575 | −0.540921 | ||||||||
\(304\) | −1.84870 | −0.106030 | ||||||||
\(305\) | −50.2580 | −2.87776 | ||||||||
\(306\) | −7.56875 | −0.432676 | ||||||||
\(307\) | 7.65826 | 0.437080 | 0.218540 | − | 0.975828i | \(-0.429871\pi\) | ||||
0.218540 | + | 0.975828i | \(0.429871\pi\) | |||||||
\(308\) | −14.9418 | −0.851389 | ||||||||
\(309\) | 1.00000 | 0.0568880 | ||||||||
\(310\) | 22.6209 | 1.28478 | ||||||||
\(311\) | 8.22932 | 0.466642 | 0.233321 | − | 0.972400i | \(-0.425041\pi\) | ||||
0.233321 | + | 0.972400i | \(0.425041\pi\) | |||||||
\(312\) | 1.00000 | 0.0566139 | ||||||||
\(313\) | 0.937649 | 0.0529991 | 0.0264995 | − | 0.999649i | \(-0.491564\pi\) | ||||
0.0264995 | + | 0.999649i | \(0.491564\pi\) | |||||||
\(314\) | −8.57471 | −0.483899 | ||||||||
\(315\) | −17.5738 | −0.990174 | ||||||||
\(316\) | 6.21617 | 0.349687 | ||||||||
\(317\) | −13.7271 | −0.770991 | −0.385496 | − | 0.922710i | \(-0.625969\pi\) | ||||
−0.385496 | + | 0.922710i | \(0.625969\pi\) | |||||||
\(318\) | −5.76954 | −0.323540 | ||||||||
\(319\) | −22.8859 | −1.28136 | ||||||||
\(320\) | −4.06882 | −0.227454 | ||||||||
\(321\) | −3.81409 | −0.212882 | ||||||||
\(322\) | −36.7415 | −2.04752 | ||||||||
\(323\) | 13.9923 | 0.778553 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | −11.5553 | −0.640970 | ||||||||
\(326\) | −9.70287 | −0.537392 | ||||||||
\(327\) | −18.7539 | −1.03709 | ||||||||
\(328\) | 0.695896 | 0.0384244 | ||||||||
\(329\) | −5.08763 | −0.280490 | ||||||||
\(330\) | −14.0758 | −0.774847 | ||||||||
\(331\) | 33.3238 | 1.83164 | 0.915822 | − | 0.401585i | \(-0.131540\pi\) | ||||
0.915822 | + | 0.401585i | \(0.131540\pi\) | |||||||
\(332\) | −11.6646 | −0.640179 | ||||||||
\(333\) | 10.0080 | 0.548435 | ||||||||
\(334\) | 13.4484 | 0.735865 | ||||||||
\(335\) | 58.4022 | 3.19085 | ||||||||
\(336\) | −4.31915 | −0.235629 | ||||||||
\(337\) | −11.5951 | −0.631623 | −0.315811 | − | 0.948822i | \(-0.602277\pi\) | ||||
−0.315811 | + | 0.948822i | \(0.602277\pi\) | |||||||
\(338\) | 1.00000 | 0.0543928 | ||||||||
\(339\) | 10.5876 | 0.575040 | ||||||||
\(340\) | 30.7958 | 1.67014 | ||||||||
\(341\) | 19.2330 | 1.04152 | ||||||||
\(342\) | −1.84870 | −0.0999661 | ||||||||
\(343\) | 20.1061 | 1.08563 | ||||||||
\(344\) | −3.09807 | −0.167037 | ||||||||
\(345\) | −34.6120 | −1.86345 | ||||||||
\(346\) | 0.334934 | 0.0180062 | ||||||||
\(347\) | −11.6647 | −0.626192 | −0.313096 | − | 0.949721i | \(-0.601366\pi\) | ||||
−0.313096 | + | 0.949721i | \(0.601366\pi\) | |||||||
\(348\) | −6.61550 | −0.354628 | ||||||||
\(349\) | 9.80093 | 0.524632 | 0.262316 | − | 0.964982i | \(-0.415514\pi\) | ||||
0.262316 | + | 0.964982i | \(0.415514\pi\) | |||||||
\(350\) | 49.9089 | 2.66775 | ||||||||
\(351\) | 1.00000 | 0.0533761 | ||||||||
\(352\) | −3.45943 | −0.184388 | ||||||||
\(353\) | 6.38978 | 0.340094 | 0.170047 | − | 0.985436i | \(-0.445608\pi\) | ||||
0.170047 | + | 0.985436i | \(0.445608\pi\) | |||||||
\(354\) | −6.88464 | −0.365914 | ||||||||
\(355\) | −17.9336 | −0.951817 | ||||||||
\(356\) | −2.88091 | −0.152688 | ||||||||
\(357\) | 32.6906 | 1.73017 | ||||||||
\(358\) | 18.9801 | 1.00313 | ||||||||
\(359\) | −14.0791 | −0.743064 | −0.371532 | − | 0.928420i | \(-0.621167\pi\) | ||||
−0.371532 | + | 0.928420i | \(0.621167\pi\) | |||||||
\(360\) | −4.06882 | −0.214445 | ||||||||
\(361\) | −15.5823 | −0.820122 | ||||||||
\(362\) | −4.69449 | −0.246737 | ||||||||
\(363\) | −0.967666 | −0.0507893 | ||||||||
\(364\) | −4.31915 | −0.226385 | ||||||||
\(365\) | 33.7533 | 1.76673 | ||||||||
\(366\) | −12.3520 | −0.645649 | ||||||||
\(367\) | −25.9658 | −1.35540 | −0.677701 | − | 0.735338i | \(-0.737023\pi\) | ||||
−0.677701 | + | 0.735338i | \(0.737023\pi\) | |||||||
\(368\) | −8.50665 | −0.443440 | ||||||||
\(369\) | 0.695896 | 0.0362269 | ||||||||
\(370\) | −40.7207 | −2.11697 | ||||||||
\(371\) | 24.9195 | 1.29376 | ||||||||
\(372\) | 5.55957 | 0.288250 | ||||||||
\(373\) | 28.3171 | 1.46620 | 0.733101 | − | 0.680120i | \(-0.238072\pi\) | ||||
0.733101 | + | 0.680120i | \(0.238072\pi\) | |||||||
\(374\) | 26.1836 | 1.35392 | ||||||||
\(375\) | 26.6721 | 1.37734 | ||||||||
\(376\) | −1.17792 | −0.0607468 | ||||||||
\(377\) | −6.61550 | −0.340715 | ||||||||
\(378\) | −4.31915 | −0.222153 | ||||||||
\(379\) | 5.80714 | 0.298293 | 0.149146 | − | 0.988815i | \(-0.452347\pi\) | ||||
0.149146 | + | 0.988815i | \(0.452347\pi\) | |||||||
\(380\) | 7.52201 | 0.385871 | ||||||||
\(381\) | 21.5905 | 1.10611 | ||||||||
\(382\) | 12.4462 | 0.636805 | ||||||||
\(383\) | 22.5633 | 1.15293 | 0.576467 | − | 0.817121i | \(-0.304431\pi\) | ||||
0.576467 | + | 0.817121i | \(0.304431\pi\) | |||||||
\(384\) | −1.00000 | −0.0510310 | ||||||||
\(385\) | 60.7955 | 3.09843 | ||||||||
\(386\) | 2.02744 | 0.103194 | ||||||||
\(387\) | −3.09807 | −0.157484 | ||||||||
\(388\) | 4.85929 | 0.246693 | ||||||||
\(389\) | 23.6159 | 1.19737 | 0.598686 | − | 0.800984i | \(-0.295690\pi\) | ||||
0.598686 | + | 0.800984i | \(0.295690\pi\) | |||||||
\(390\) | −4.06882 | −0.206032 | ||||||||
\(391\) | 64.3847 | 3.25607 | ||||||||
\(392\) | 11.6551 | 0.588671 | ||||||||
\(393\) | 2.47190 | 0.124691 | ||||||||
\(394\) | 16.8314 | 0.847956 | ||||||||
\(395\) | −25.2924 | −1.27260 | ||||||||
\(396\) | −3.45943 | −0.173843 | ||||||||
\(397\) | 18.8538 | 0.946246 | 0.473123 | − | 0.880996i | \(-0.343127\pi\) | ||||
0.473123 | + | 0.880996i | \(0.343127\pi\) | |||||||
\(398\) | −0.301529 | −0.0151143 | ||||||||
\(399\) | 7.98481 | 0.399740 | ||||||||
\(400\) | 11.5553 | 0.577763 | ||||||||
\(401\) | 10.3423 | 0.516472 | 0.258236 | − | 0.966082i | \(-0.416859\pi\) | ||||
0.258236 | + | 0.966082i | \(0.416859\pi\) | |||||||
\(402\) | 14.3536 | 0.715893 | ||||||||
\(403\) | 5.55957 | 0.276942 | ||||||||
\(404\) | 9.41575 | 0.468451 | ||||||||
\(405\) | −4.06882 | −0.202181 | ||||||||
\(406\) | 28.5734 | 1.41807 | ||||||||
\(407\) | −34.6220 | −1.71615 | ||||||||
\(408\) | 7.56875 | 0.374709 | ||||||||
\(409\) | −18.2409 | −0.901956 | −0.450978 | − | 0.892535i | \(-0.648925\pi\) | ||||
−0.450978 | + | 0.892535i | \(0.648925\pi\) | |||||||
\(410\) | −2.83147 | −0.139836 | ||||||||
\(411\) | −7.60382 | −0.375069 | ||||||||
\(412\) | −1.00000 | −0.0492665 | ||||||||
\(413\) | 29.7358 | 1.46320 | ||||||||
\(414\) | −8.50665 | −0.418079 | ||||||||
\(415\) | 47.4612 | 2.32978 | ||||||||
\(416\) | −1.00000 | −0.0490290 | ||||||||
\(417\) | 0.701284 | 0.0343420 | ||||||||
\(418\) | 6.39544 | 0.312811 | ||||||||
\(419\) | −22.7734 | −1.11255 | −0.556277 | − | 0.830997i | \(-0.687771\pi\) | ||||
−0.556277 | + | 0.830997i | \(0.687771\pi\) | |||||||
\(420\) | 17.5738 | 0.857516 | ||||||||
\(421\) | 19.3529 | 0.943204 | 0.471602 | − | 0.881811i | \(-0.343676\pi\) | ||||
0.471602 | + | 0.881811i | \(0.343676\pi\) | |||||||
\(422\) | −3.92060 | −0.190852 | ||||||||
\(423\) | −1.17792 | −0.0572726 | ||||||||
\(424\) | 5.76954 | 0.280193 | ||||||||
\(425\) | −87.4588 | −4.24238 | ||||||||
\(426\) | −4.40758 | −0.213548 | ||||||||
\(427\) | 53.3501 | 2.58179 | ||||||||
\(428\) | 3.81409 | 0.184361 | ||||||||
\(429\) | −3.45943 | −0.167023 | ||||||||
\(430\) | 12.6055 | 0.607890 | ||||||||
\(431\) | −23.1867 | −1.11687 | −0.558433 | − | 0.829550i | \(-0.688597\pi\) | ||||
−0.558433 | + | 0.829550i | \(0.688597\pi\) | |||||||
\(432\) | −1.00000 | −0.0481125 | ||||||||
\(433\) | 5.73037 | 0.275384 | 0.137692 | − | 0.990475i | \(-0.456032\pi\) | ||||
0.137692 | + | 0.990475i | \(0.456032\pi\) | |||||||
\(434\) | −24.0126 | −1.15264 | ||||||||
\(435\) | 26.9172 | 1.29058 | ||||||||
\(436\) | 18.7539 | 0.898149 | ||||||||
\(437\) | 15.7262 | 0.752287 | ||||||||
\(438\) | 8.29562 | 0.396380 | ||||||||
\(439\) | −3.84780 | −0.183645 | −0.0918226 | − | 0.995775i | \(-0.529269\pi\) | ||||
−0.0918226 | + | 0.995775i | \(0.529269\pi\) | |||||||
\(440\) | 14.0758 | 0.671037 | ||||||||
\(441\) | 11.6551 | 0.555004 | ||||||||
\(442\) | 7.56875 | 0.360009 | ||||||||
\(443\) | 31.2358 | 1.48406 | 0.742029 | − | 0.670367i | \(-0.233864\pi\) | ||||
0.742029 | + | 0.670367i | \(0.233864\pi\) | |||||||
\(444\) | −10.0080 | −0.474959 | ||||||||
\(445\) | 11.7219 | 0.555670 | ||||||||
\(446\) | 13.3625 | 0.632733 | ||||||||
\(447\) | −18.0995 | −0.856075 | ||||||||
\(448\) | 4.31915 | 0.204061 | ||||||||
\(449\) | 3.02705 | 0.142855 | 0.0714277 | − | 0.997446i | \(-0.477244\pi\) | ||||
0.0714277 | + | 0.997446i | \(0.477244\pi\) | |||||||
\(450\) | 11.5553 | 0.544720 | ||||||||
\(451\) | −2.40740 | −0.113360 | ||||||||
\(452\) | −10.5876 | −0.497999 | ||||||||
\(453\) | −16.5279 | −0.776550 | ||||||||
\(454\) | −1.25297 | −0.0588046 | ||||||||
\(455\) | 17.5738 | 0.823874 | ||||||||
\(456\) | 1.84870 | 0.0865732 | ||||||||
\(457\) | −38.0751 | −1.78108 | −0.890540 | − | 0.454905i | \(-0.849673\pi\) | ||||
−0.890540 | + | 0.454905i | \(0.849673\pi\) | |||||||
\(458\) | 8.24201 | 0.385124 | ||||||||
\(459\) | 7.56875 | 0.353279 | ||||||||
\(460\) | 34.6120 | 1.61379 | ||||||||
\(461\) | −16.0253 | −0.746373 | −0.373186 | − | 0.927756i | \(-0.621735\pi\) | ||||
−0.373186 | + | 0.927756i | \(0.621735\pi\) | |||||||
\(462\) | 14.9418 | 0.695156 | ||||||||
\(463\) | −7.54870 | −0.350818 | −0.175409 | − | 0.984496i | \(-0.556125\pi\) | ||||
−0.175409 | + | 0.984496i | \(0.556125\pi\) | |||||||
\(464\) | 6.61550 | 0.307117 | ||||||||
\(465\) | −22.6209 | −1.04902 | ||||||||
\(466\) | 12.8913 | 0.597178 | ||||||||
\(467\) | −32.7890 | −1.51729 | −0.758646 | − | 0.651503i | \(-0.774139\pi\) | ||||
−0.758646 | + | 0.651503i | \(0.774139\pi\) | |||||||
\(468\) | −1.00000 | −0.0462250 | ||||||||
\(469\) | −61.9954 | −2.86268 | ||||||||
\(470\) | 4.79275 | 0.221073 | ||||||||
\(471\) | 8.57471 | 0.395102 | ||||||||
\(472\) | 6.88464 | 0.316891 | ||||||||
\(473\) | 10.7176 | 0.492794 | ||||||||
\(474\) | −6.21617 | −0.285518 | ||||||||
\(475\) | −21.3622 | −0.980164 | ||||||||
\(476\) | −32.6906 | −1.49837 | ||||||||
\(477\) | 5.76954 | 0.264169 | ||||||||
\(478\) | 20.1551 | 0.921874 | ||||||||
\(479\) | 38.4984 | 1.75904 | 0.879519 | − | 0.475863i | \(-0.157864\pi\) | ||||
0.879519 | + | 0.475863i | \(0.157864\pi\) | |||||||
\(480\) | 4.06882 | 0.185715 | ||||||||
\(481\) | −10.0080 | −0.456325 | ||||||||
\(482\) | −2.43963 | −0.111122 | ||||||||
\(483\) | 36.7415 | 1.67180 | ||||||||
\(484\) | 0.967666 | 0.0439848 | ||||||||
\(485\) | −19.7716 | −0.897781 | ||||||||
\(486\) | −1.00000 | −0.0453609 | ||||||||
\(487\) | −6.04136 | −0.273760 | −0.136880 | − | 0.990588i | \(-0.543707\pi\) | ||||
−0.136880 | + | 0.990588i | \(0.543707\pi\) | |||||||
\(488\) | 12.3520 | 0.559148 | ||||||||
\(489\) | 9.70287 | 0.438779 | ||||||||
\(490\) | −47.4224 | −2.14233 | ||||||||
\(491\) | 26.8174 | 1.21025 | 0.605126 | − | 0.796130i | \(-0.293123\pi\) | ||||
0.605126 | + | 0.796130i | \(0.293123\pi\) | |||||||
\(492\) | −0.695896 | −0.0313734 | ||||||||
\(493\) | −50.0710 | −2.25509 | ||||||||
\(494\) | 1.84870 | 0.0831768 | ||||||||
\(495\) | 14.0758 | 0.632660 | ||||||||
\(496\) | −5.55957 | −0.249632 | ||||||||
\(497\) | 19.0370 | 0.853926 | ||||||||
\(498\) | 11.6646 | 0.522704 | ||||||||
\(499\) | 8.59968 | 0.384975 | 0.192487 | − | 0.981299i | \(-0.438345\pi\) | ||||
0.192487 | + | 0.981299i | \(0.438345\pi\) | |||||||
\(500\) | −26.6721 | −1.19281 | ||||||||
\(501\) | −13.4484 | −0.600832 | ||||||||
\(502\) | −7.14154 | −0.318743 | ||||||||
\(503\) | 31.4358 | 1.40165 | 0.700827 | − | 0.713331i | \(-0.252814\pi\) | ||||
0.700827 | + | 0.713331i | \(0.252814\pi\) | |||||||
\(504\) | 4.31915 | 0.192390 | ||||||||
\(505\) | −38.3110 | −1.70482 | ||||||||
\(506\) | 29.4282 | 1.30824 | ||||||||
\(507\) | −1.00000 | −0.0444116 | ||||||||
\(508\) | −21.5905 | −0.957923 | ||||||||
\(509\) | 31.8853 | 1.41329 | 0.706646 | − | 0.707567i | \(-0.250207\pi\) | ||||
0.706646 | + | 0.707567i | \(0.250207\pi\) | |||||||
\(510\) | −30.7958 | −1.36366 | ||||||||
\(511\) | −35.8300 | −1.58503 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 1.84870 | 0.0816220 | ||||||||
\(514\) | 9.93685 | 0.438296 | ||||||||
\(515\) | 4.06882 | 0.179293 | ||||||||
\(516\) | 3.09807 | 0.136385 | ||||||||
\(517\) | 4.07494 | 0.179216 | ||||||||
\(518\) | 43.2261 | 1.89925 | ||||||||
\(519\) | −0.334934 | −0.0147020 | ||||||||
\(520\) | 4.06882 | 0.178429 | ||||||||
\(521\) | −10.1483 | −0.444606 | −0.222303 | − | 0.974978i | \(-0.571357\pi\) | ||||
−0.222303 | + | 0.974978i | \(0.571357\pi\) | |||||||
\(522\) | 6.61550 | 0.289552 | ||||||||
\(523\) | 27.9932 | 1.22406 | 0.612028 | − | 0.790836i | \(-0.290354\pi\) | ||||
0.612028 | + | 0.790836i | \(0.290354\pi\) | |||||||
\(524\) | −2.47190 | −0.107985 | ||||||||
\(525\) | −49.9089 | −2.17820 | ||||||||
\(526\) | −24.6988 | −1.07692 | ||||||||
\(527\) | 42.0790 | 1.83299 | ||||||||
\(528\) | 3.45943 | 0.150552 | ||||||||
\(529\) | 49.3630 | 2.14622 | ||||||||
\(530\) | −23.4752 | −1.01970 | ||||||||
\(531\) | 6.88464 | 0.298768 | ||||||||
\(532\) | −7.98481 | −0.346185 | ||||||||
\(533\) | −0.695896 | −0.0301426 | ||||||||
\(534\) | 2.88091 | 0.124669 | ||||||||
\(535\) | −15.5188 | −0.670937 | ||||||||
\(536\) | −14.3536 | −0.619981 | ||||||||
\(537\) | −18.9801 | −0.819053 | ||||||||
\(538\) | 25.6107 | 1.10416 | ||||||||
\(539\) | −40.3200 | −1.73670 | ||||||||
\(540\) | 4.06882 | 0.175094 | ||||||||
\(541\) | −31.0959 | −1.33692 | −0.668459 | − | 0.743749i | \(-0.733046\pi\) | ||||
−0.668459 | + | 0.743749i | \(0.733046\pi\) | |||||||
\(542\) | −6.42255 | −0.275872 | ||||||||
\(543\) | 4.69449 | 0.201460 | ||||||||
\(544\) | −7.56875 | −0.324507 | ||||||||
\(545\) | −76.3062 | −3.26860 | ||||||||
\(546\) | 4.31915 | 0.184843 | ||||||||
\(547\) | −13.9231 | −0.595311 | −0.297655 | − | 0.954673i | \(-0.596205\pi\) | ||||
−0.297655 | + | 0.954673i | \(0.596205\pi\) | |||||||
\(548\) | 7.60382 | 0.324819 | ||||||||
\(549\) | 12.3520 | 0.527170 | ||||||||
\(550\) | −39.9746 | −1.70452 | ||||||||
\(551\) | −12.2300 | −0.521018 | ||||||||
\(552\) | 8.50665 | 0.362067 | ||||||||
\(553\) | 26.8486 | 1.14172 | ||||||||
\(554\) | 18.0070 | 0.765045 | ||||||||
\(555\) | 40.7207 | 1.72850 | ||||||||
\(556\) | −0.701284 | −0.0297410 | ||||||||
\(557\) | 40.1013 | 1.69915 | 0.849573 | − | 0.527471i | \(-0.176860\pi\) | ||||
0.849573 | + | 0.527471i | \(0.176860\pi\) | |||||||
\(558\) | −5.55957 | −0.235355 | ||||||||
\(559\) | 3.09807 | 0.131034 | ||||||||
\(560\) | −17.5738 | −0.742630 | ||||||||
\(561\) | −26.1836 | −1.10547 | ||||||||
\(562\) | −12.7632 | −0.538382 | ||||||||
\(563\) | 16.0210 | 0.675204 | 0.337602 | − | 0.941289i | \(-0.390384\pi\) | ||||
0.337602 | + | 0.941289i | \(0.390384\pi\) | |||||||
\(564\) | 1.17792 | 0.0495995 | ||||||||
\(565\) | 43.0790 | 1.81235 | ||||||||
\(566\) | 10.4087 | 0.437510 | ||||||||
\(567\) | 4.31915 | 0.181387 | ||||||||
\(568\) | 4.40758 | 0.184938 | ||||||||
\(569\) | −0.0543899 | −0.00228014 | −0.00114007 | − | 0.999999i | \(-0.500363\pi\) | ||||
−0.00114007 | + | 0.999999i | \(0.500363\pi\) | |||||||
\(570\) | −7.52201 | −0.315062 | ||||||||
\(571\) | 3.23201 | 0.135256 | 0.0676278 | − | 0.997711i | \(-0.478457\pi\) | ||||
0.0676278 | + | 0.997711i | \(0.478457\pi\) | |||||||
\(572\) | 3.45943 | 0.144646 | ||||||||
\(573\) | −12.4462 | −0.519949 | ||||||||
\(574\) | 3.00568 | 0.125455 | ||||||||
\(575\) | −98.2965 | −4.09925 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | −17.2957 | −0.720029 | −0.360015 | − | 0.932947i | \(-0.617228\pi\) | ||||
−0.360015 | + | 0.932947i | \(0.617228\pi\) | |||||||
\(578\) | 40.2859 | 1.67567 | ||||||||
\(579\) | −2.02744 | −0.0842577 | ||||||||
\(580\) | −26.9172 | −1.11768 | ||||||||
\(581\) | −50.3813 | −2.09017 | ||||||||
\(582\) | −4.85929 | −0.201424 | ||||||||
\(583\) | −19.9593 | −0.826630 | ||||||||
\(584\) | −8.29562 | −0.343275 | ||||||||
\(585\) | 4.06882 | 0.168225 | ||||||||
\(586\) | −13.9122 | −0.574707 | ||||||||
\(587\) | −20.0181 | −0.826237 | −0.413119 | − | 0.910677i | \(-0.635561\pi\) | ||||
−0.413119 | + | 0.910677i | \(0.635561\pi\) | |||||||
\(588\) | −11.6551 | −0.480648 | ||||||||
\(589\) | 10.2780 | 0.423496 | ||||||||
\(590\) | −28.0123 | −1.15325 | ||||||||
\(591\) | −16.8314 | −0.692353 | ||||||||
\(592\) | 10.0080 | 0.411326 | ||||||||
\(593\) | 0.139648 | 0.00573467 | 0.00286733 | − | 0.999996i | \(-0.499087\pi\) | ||||
0.00286733 | + | 0.999996i | \(0.499087\pi\) | |||||||
\(594\) | 3.45943 | 0.141942 | ||||||||
\(595\) | 133.012 | 5.45296 | ||||||||
\(596\) | 18.0995 | 0.741382 | ||||||||
\(597\) | 0.301529 | 0.0123408 | ||||||||
\(598\) | 8.50665 | 0.347863 | ||||||||
\(599\) | −38.6375 | −1.57869 | −0.789343 | − | 0.613952i | \(-0.789579\pi\) | ||||
−0.789343 | + | 0.613952i | \(0.789579\pi\) | |||||||
\(600\) | −11.5553 | −0.471741 | ||||||||
\(601\) | 4.72512 | 0.192742 | 0.0963708 | − | 0.995346i | \(-0.469277\pi\) | ||||
0.0963708 | + | 0.995346i | \(0.469277\pi\) | |||||||
\(602\) | −13.3811 | −0.545371 | ||||||||
\(603\) | −14.3536 | −0.584524 | ||||||||
\(604\) | 16.5279 | 0.672512 | ||||||||
\(605\) | −3.93725 | −0.160072 | ||||||||
\(606\) | −9.41575 | −0.382489 | ||||||||
\(607\) | 13.3446 | 0.541639 | 0.270819 | − | 0.962630i | \(-0.412705\pi\) | ||||
0.270819 | + | 0.962630i | \(0.412705\pi\) | |||||||
\(608\) | −1.84870 | −0.0749746 | ||||||||
\(609\) | −28.5734 | −1.15785 | ||||||||
\(610\) | −50.2580 | −2.03489 | ||||||||
\(611\) | 1.17792 | 0.0476537 | ||||||||
\(612\) | −7.56875 | −0.305948 | ||||||||
\(613\) | −20.0161 | −0.808442 | −0.404221 | − | 0.914661i | \(-0.632457\pi\) | ||||
−0.404221 | + | 0.914661i | \(0.632457\pi\) | |||||||
\(614\) | 7.65826 | 0.309062 | ||||||||
\(615\) | 2.83147 | 0.114176 | ||||||||
\(616\) | −14.9418 | −0.602023 | ||||||||
\(617\) | −26.6433 | −1.07262 | −0.536309 | − | 0.844021i | \(-0.680182\pi\) | ||||
−0.536309 | + | 0.844021i | \(0.680182\pi\) | |||||||
\(618\) | 1.00000 | 0.0402259 | ||||||||
\(619\) | 35.7643 | 1.43749 | 0.718745 | − | 0.695274i | \(-0.244717\pi\) | ||||
0.718745 | + | 0.695274i | \(0.244717\pi\) | |||||||
\(620\) | 22.6209 | 0.908476 | ||||||||
\(621\) | 8.50665 | 0.341360 | ||||||||
\(622\) | 8.22932 | 0.329966 | ||||||||
\(623\) | −12.4431 | −0.498521 | ||||||||
\(624\) | 1.00000 | 0.0400320 | ||||||||
\(625\) | 50.7477 | 2.02991 | ||||||||
\(626\) | 0.937649 | 0.0374760 | ||||||||
\(627\) | −6.39544 | −0.255409 | ||||||||
\(628\) | −8.57471 | −0.342168 | ||||||||
\(629\) | −75.7480 | −3.02027 | ||||||||
\(630\) | −17.5738 | −0.700159 | ||||||||
\(631\) | 1.98763 | 0.0791262 | 0.0395631 | − | 0.999217i | \(-0.487403\pi\) | ||||
0.0395631 | + | 0.999217i | \(0.487403\pi\) | |||||||
\(632\) | 6.21617 | 0.247266 | ||||||||
\(633\) | 3.92060 | 0.155830 | ||||||||
\(634\) | −13.7271 | −0.545173 | ||||||||
\(635\) | 87.8477 | 3.48613 | ||||||||
\(636\) | −5.76954 | −0.228777 | ||||||||
\(637\) | −11.6551 | −0.461792 | ||||||||
\(638\) | −22.8859 | −0.906060 | ||||||||
\(639\) | 4.40758 | 0.174361 | ||||||||
\(640\) | −4.06882 | −0.160834 | ||||||||
\(641\) | 25.8792 | 1.02217 | 0.511084 | − | 0.859531i | \(-0.329244\pi\) | ||||
0.511084 | + | 0.859531i | \(0.329244\pi\) | |||||||
\(642\) | −3.81409 | −0.150530 | ||||||||
\(643\) | −14.3720 | −0.566778 | −0.283389 | − | 0.959005i | \(-0.591459\pi\) | ||||
−0.283389 | + | 0.959005i | \(0.591459\pi\) | |||||||
\(644\) | −36.7415 | −1.44782 | ||||||||
\(645\) | −12.6055 | −0.496340 | ||||||||
\(646\) | 13.9923 | 0.550520 | ||||||||
\(647\) | 42.4147 | 1.66749 | 0.833747 | − | 0.552147i | \(-0.186191\pi\) | ||||
0.833747 | + | 0.552147i | \(0.186191\pi\) | |||||||
\(648\) | 1.00000 | 0.0392837 | ||||||||
\(649\) | −23.8169 | −0.934896 | ||||||||
\(650\) | −11.5553 | −0.453235 | ||||||||
\(651\) | 24.0126 | 0.941130 | ||||||||
\(652\) | −9.70287 | −0.379994 | ||||||||
\(653\) | −9.61493 | −0.376261 | −0.188131 | − | 0.982144i | \(-0.560243\pi\) | ||||
−0.188131 | + | 0.982144i | \(0.560243\pi\) | |||||||
\(654\) | −18.7539 | −0.733336 | ||||||||
\(655\) | 10.0577 | 0.392987 | ||||||||
\(656\) | 0.695896 | 0.0271702 | ||||||||
\(657\) | −8.29562 | −0.323643 | ||||||||
\(658\) | −5.08763 | −0.198337 | ||||||||
\(659\) | 0.623573 | 0.0242910 | 0.0121455 | − | 0.999926i | \(-0.496134\pi\) | ||||
0.0121455 | + | 0.999926i | \(0.496134\pi\) | |||||||
\(660\) | −14.0758 | −0.547899 | ||||||||
\(661\) | −7.46895 | −0.290508 | −0.145254 | − | 0.989394i | \(-0.546400\pi\) | ||||
−0.145254 | + | 0.989394i | \(0.546400\pi\) | |||||||
\(662\) | 33.3238 | 1.29517 | ||||||||
\(663\) | −7.56875 | −0.293946 | ||||||||
\(664\) | −11.6646 | −0.452675 | ||||||||
\(665\) | 32.4887 | 1.25986 | ||||||||
\(666\) | 10.0080 | 0.387802 | ||||||||
\(667\) | −56.2757 | −2.17900 | ||||||||
\(668\) | 13.4484 | 0.520335 | ||||||||
\(669\) | −13.3625 | −0.516624 | ||||||||
\(670\) | 58.4022 | 2.25627 | ||||||||
\(671\) | −42.7309 | −1.64961 | ||||||||
\(672\) | −4.31915 | −0.166615 | ||||||||
\(673\) | 45.3201 | 1.74696 | 0.873481 | − | 0.486858i | \(-0.161857\pi\) | ||||
0.873481 | + | 0.486858i | \(0.161857\pi\) | |||||||
\(674\) | −11.5951 | −0.446625 | ||||||||
\(675\) | −11.5553 | −0.444762 | ||||||||
\(676\) | 1.00000 | 0.0384615 | ||||||||
\(677\) | 41.0621 | 1.57814 | 0.789072 | − | 0.614301i | \(-0.210562\pi\) | ||||
0.789072 | + | 0.614301i | \(0.210562\pi\) | |||||||
\(678\) | 10.5876 | 0.406614 | ||||||||
\(679\) | 20.9880 | 0.805447 | ||||||||
\(680\) | 30.7958 | 1.18097 | ||||||||
\(681\) | 1.25297 | 0.0480138 | ||||||||
\(682\) | 19.2330 | 0.736468 | ||||||||
\(683\) | −1.15076 | −0.0440324 | −0.0220162 | − | 0.999758i | \(-0.507009\pi\) | ||||
−0.0220162 | + | 0.999758i | \(0.507009\pi\) | |||||||
\(684\) | −1.84870 | −0.0706867 | ||||||||
\(685\) | −30.9385 | −1.18210 | ||||||||
\(686\) | 20.1061 | 0.767653 | ||||||||
\(687\) | −8.24201 | −0.314452 | ||||||||
\(688\) | −3.09807 | −0.118113 | ||||||||
\(689\) | −5.76954 | −0.219802 | ||||||||
\(690\) | −34.6120 | −1.31766 | ||||||||
\(691\) | 28.6259 | 1.08898 | 0.544490 | − | 0.838767i | \(-0.316723\pi\) | ||||
0.544490 | + | 0.838767i | \(0.316723\pi\) | |||||||
\(692\) | 0.334934 | 0.0127323 | ||||||||
\(693\) | −14.9418 | −0.567593 | ||||||||
\(694\) | −11.6647 | −0.442785 | ||||||||
\(695\) | 2.85339 | 0.108235 | ||||||||
\(696\) | −6.61550 | −0.250760 | ||||||||
\(697\) | −5.26706 | −0.199504 | ||||||||
\(698\) | 9.80093 | 0.370971 | ||||||||
\(699\) | −12.8913 | −0.487594 | ||||||||
\(700\) | 49.9089 | 1.88638 | ||||||||
\(701\) | −40.7619 | −1.53955 | −0.769777 | − | 0.638313i | \(-0.779633\pi\) | ||||
−0.769777 | + | 0.638313i | \(0.779633\pi\) | |||||||
\(702\) | 1.00000 | 0.0377426 | ||||||||
\(703\) | −18.5018 | −0.697807 | ||||||||
\(704\) | −3.45943 | −0.130382 | ||||||||
\(705\) | −4.79275 | −0.180505 | ||||||||
\(706\) | 6.38978 | 0.240482 | ||||||||
\(707\) | 40.6681 | 1.52948 | ||||||||
\(708\) | −6.88464 | −0.258740 | ||||||||
\(709\) | −32.4818 | −1.21988 | −0.609940 | − | 0.792448i | \(-0.708806\pi\) | ||||
−0.609940 | + | 0.792448i | \(0.708806\pi\) | |||||||
\(710\) | −17.9336 | −0.673037 | ||||||||
\(711\) | 6.21617 | 0.233124 | ||||||||
\(712\) | −2.88091 | −0.107966 | ||||||||
\(713\) | 47.2933 | 1.77115 | ||||||||
\(714\) | 32.6906 | 1.22341 | ||||||||
\(715\) | −14.0758 | −0.526405 | ||||||||
\(716\) | 18.9801 | 0.709321 | ||||||||
\(717\) | −20.1551 | −0.752707 | ||||||||
\(718\) | −14.0791 | −0.525426 | ||||||||
\(719\) | −36.3983 | −1.35743 | −0.678714 | − | 0.734403i | \(-0.737462\pi\) | ||||
−0.678714 | + | 0.734403i | \(0.737462\pi\) | |||||||
\(720\) | −4.06882 | −0.151636 | ||||||||
\(721\) | −4.31915 | −0.160854 | ||||||||
\(722\) | −15.5823 | −0.579914 | ||||||||
\(723\) | 2.43963 | 0.0907307 | ||||||||
\(724\) | −4.69449 | −0.174469 | ||||||||
\(725\) | 76.4438 | 2.83905 | ||||||||
\(726\) | −0.967666 | −0.0359134 | ||||||||
\(727\) | −27.7079 | −1.02763 | −0.513814 | − | 0.857902i | \(-0.671768\pi\) | ||||
−0.513814 | + | 0.857902i | \(0.671768\pi\) | |||||||
\(728\) | −4.31915 | −0.160079 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 33.7533 | 1.24927 | ||||||||
\(731\) | 23.4485 | 0.867275 | ||||||||
\(732\) | −12.3520 | −0.456543 | ||||||||
\(733\) | 31.1625 | 1.15101 | 0.575507 | − | 0.817797i | \(-0.304805\pi\) | ||||
0.575507 | + | 0.817797i | \(0.304805\pi\) | |||||||
\(734\) | −25.9658 | −0.958414 | ||||||||
\(735\) | 47.4224 | 1.74920 | ||||||||
\(736\) | −8.50665 | −0.313559 | ||||||||
\(737\) | 49.6553 | 1.82908 | ||||||||
\(738\) | 0.695896 | 0.0256163 | ||||||||
\(739\) | −11.1385 | −0.409736 | −0.204868 | − | 0.978790i | \(-0.565676\pi\) | ||||
−0.204868 | + | 0.978790i | \(0.565676\pi\) | |||||||
\(740\) | −40.7207 | −1.49692 | ||||||||
\(741\) | −1.84870 | −0.0679136 | ||||||||
\(742\) | 24.9195 | 0.914824 | ||||||||
\(743\) | −32.7056 | −1.19985 | −0.599925 | − | 0.800056i | \(-0.704803\pi\) | ||||
−0.599925 | + | 0.800056i | \(0.704803\pi\) | |||||||
\(744\) | 5.55957 | 0.203824 | ||||||||
\(745\) | −73.6433 | −2.69808 | ||||||||
\(746\) | 28.3171 | 1.03676 | ||||||||
\(747\) | −11.6646 | −0.426786 | ||||||||
\(748\) | 26.1836 | 0.957366 | ||||||||
\(749\) | 16.4736 | 0.601934 | ||||||||
\(750\) | 26.6721 | 0.973929 | ||||||||
\(751\) | 5.02809 | 0.183478 | 0.0917389 | − | 0.995783i | \(-0.470757\pi\) | ||||
0.0917389 | + | 0.995783i | \(0.470757\pi\) | |||||||
\(752\) | −1.17792 | −0.0429544 | ||||||||
\(753\) | 7.14154 | 0.260252 | ||||||||
\(754\) | −6.61550 | −0.240922 | ||||||||
\(755\) | −67.2491 | −2.44745 | ||||||||
\(756\) | −4.31915 | −0.157086 | ||||||||
\(757\) | 49.6215 | 1.80352 | 0.901762 | − | 0.432233i | \(-0.142274\pi\) | ||||
0.901762 | + | 0.432233i | \(0.142274\pi\) | |||||||
\(758\) | 5.80714 | 0.210925 | ||||||||
\(759\) | −29.4282 | −1.06817 | ||||||||
\(760\) | 7.52201 | 0.272852 | ||||||||
\(761\) | 53.9627 | 1.95615 | 0.978074 | − | 0.208258i | \(-0.0667793\pi\) | ||||
0.978074 | + | 0.208258i | \(0.0667793\pi\) | |||||||
\(762\) | 21.5905 | 0.782141 | ||||||||
\(763\) | 81.0010 | 2.93243 | ||||||||
\(764\) | 12.4462 | 0.450289 | ||||||||
\(765\) | 30.7958 | 1.11343 | ||||||||
\(766\) | 22.5633 | 0.815247 | ||||||||
\(767\) | −6.88464 | −0.248590 | ||||||||
\(768\) | −1.00000 | −0.0360844 | ||||||||
\(769\) | −26.3748 | −0.951098 | −0.475549 | − | 0.879689i | \(-0.657751\pi\) | ||||
−0.475549 | + | 0.879689i | \(0.657751\pi\) | |||||||
\(770\) | 60.7955 | 2.19092 | ||||||||
\(771\) | −9.93685 | −0.357867 | ||||||||
\(772\) | 2.02744 | 0.0729693 | ||||||||
\(773\) | −13.9060 | −0.500165 | −0.250083 | − | 0.968225i | \(-0.580458\pi\) | ||||
−0.250083 | + | 0.968225i | \(0.580458\pi\) | |||||||
\(774\) | −3.09807 | −0.111358 | ||||||||
\(775\) | −64.2423 | −2.30765 | ||||||||
\(776\) | 4.85929 | 0.174438 | ||||||||
\(777\) | −43.2261 | −1.55073 | ||||||||
\(778\) | 23.6159 | 0.846670 | ||||||||
\(779\) | −1.28650 | −0.0460937 | ||||||||
\(780\) | −4.06882 | −0.145687 | ||||||||
\(781\) | −15.2477 | −0.545606 | ||||||||
\(782\) | 64.3847 | 2.30239 | ||||||||
\(783\) | −6.61550 | −0.236419 | ||||||||
\(784\) | 11.6551 | 0.416253 | ||||||||
\(785\) | 34.8889 | 1.24524 | ||||||||
\(786\) | 2.47190 | 0.0881698 | ||||||||
\(787\) | −29.1344 | −1.03853 | −0.519265 | − | 0.854613i | \(-0.673794\pi\) | ||||
−0.519265 | + | 0.854613i | \(0.673794\pi\) | |||||||
\(788\) | 16.8314 | 0.599595 | ||||||||
\(789\) | 24.6988 | 0.879301 | ||||||||
\(790\) | −25.2924 | −0.899864 | ||||||||
\(791\) | −45.7295 | −1.62595 | ||||||||
\(792\) | −3.45943 | −0.122926 | ||||||||
\(793\) | −12.3520 | −0.438632 | ||||||||
\(794\) | 18.8538 | 0.669097 | ||||||||
\(795\) | 23.4752 | 0.832579 | ||||||||
\(796\) | −0.301529 | −0.0106874 | ||||||||
\(797\) | −0.139563 | −0.00494358 | −0.00247179 | − | 0.999997i | \(-0.500787\pi\) | ||||
−0.00247179 | + | 0.999997i | \(0.500787\pi\) | |||||||
\(798\) | 7.98481 | 0.282659 | ||||||||
\(799\) | 8.91540 | 0.315404 | ||||||||
\(800\) | 11.5553 | 0.408540 | ||||||||
\(801\) | −2.88091 | −0.101792 | ||||||||
\(802\) | 10.3423 | 0.365201 | ||||||||
\(803\) | 28.6981 | 1.01273 | ||||||||
\(804\) | 14.3536 | 0.506213 | ||||||||
\(805\) | 149.494 | 5.26899 | ||||||||
\(806\) | 5.55957 | 0.195828 | ||||||||
\(807\) | −25.6107 | −0.901540 | ||||||||
\(808\) | 9.41575 | 0.331245 | ||||||||
\(809\) | −32.0202 | −1.12577 | −0.562884 | − | 0.826536i | \(-0.690308\pi\) | ||||
−0.562884 | + | 0.826536i | \(0.690308\pi\) | |||||||
\(810\) | −4.06882 | −0.142964 | ||||||||
\(811\) | −40.4544 | −1.42055 | −0.710273 | − | 0.703926i | \(-0.751428\pi\) | ||||
−0.710273 | + | 0.703926i | \(0.751428\pi\) | |||||||
\(812\) | 28.5734 | 1.00273 | ||||||||
\(813\) | 6.42255 | 0.225249 | ||||||||
\(814\) | −34.6220 | −1.21350 | ||||||||
\(815\) | 39.4792 | 1.38290 | ||||||||
\(816\) | 7.56875 | 0.264959 | ||||||||
\(817\) | 5.72740 | 0.200376 | ||||||||
\(818\) | −18.2409 | −0.637779 | ||||||||
\(819\) | −4.31915 | −0.150923 | ||||||||
\(820\) | −2.83147 | −0.0988793 | ||||||||
\(821\) | −33.3453 | −1.16376 | −0.581880 | − | 0.813274i | \(-0.697683\pi\) | ||||
−0.581880 | + | 0.813274i | \(0.697683\pi\) | |||||||
\(822\) | −7.60382 | −0.265214 | ||||||||
\(823\) | −49.9130 | −1.73986 | −0.869928 | − | 0.493179i | \(-0.835835\pi\) | ||||
−0.869928 | + | 0.493179i | \(0.835835\pi\) | |||||||
\(824\) | −1.00000 | −0.0348367 | ||||||||
\(825\) | 39.9746 | 1.39174 | ||||||||
\(826\) | 29.7358 | 1.03464 | ||||||||
\(827\) | 10.8878 | 0.378606 | 0.189303 | − | 0.981919i | \(-0.439377\pi\) | ||||
0.189303 | + | 0.981919i | \(0.439377\pi\) | |||||||
\(828\) | −8.50665 | −0.295626 | ||||||||
\(829\) | 32.1946 | 1.11817 | 0.559083 | − | 0.829112i | \(-0.311153\pi\) | ||||
0.559083 | + | 0.829112i | \(0.311153\pi\) | |||||||
\(830\) | 47.4612 | 1.64740 | ||||||||
\(831\) | −18.0070 | −0.624657 | ||||||||
\(832\) | −1.00000 | −0.0346688 | ||||||||
\(833\) | −88.2144 | −3.05645 | ||||||||
\(834\) | 0.701284 | 0.0242835 | ||||||||
\(835\) | −54.7192 | −1.89364 | ||||||||
\(836\) | 6.39544 | 0.221191 | ||||||||
\(837\) | 5.55957 | 0.192167 | ||||||||
\(838\) | −22.7734 | −0.786695 | ||||||||
\(839\) | 19.0612 | 0.658065 | 0.329033 | − | 0.944319i | \(-0.393277\pi\) | ||||
0.329033 | + | 0.944319i | \(0.393277\pi\) | |||||||
\(840\) | 17.5738 | 0.606355 | ||||||||
\(841\) | 14.7648 | 0.509131 | ||||||||
\(842\) | 19.3529 | 0.666946 | ||||||||
\(843\) | 12.7632 | 0.439587 | ||||||||
\(844\) | −3.92060 | −0.134953 | ||||||||
\(845\) | −4.06882 | −0.139972 | ||||||||
\(846\) | −1.17792 | −0.0404978 | ||||||||
\(847\) | 4.17950 | 0.143609 | ||||||||
\(848\) | 5.76954 | 0.198127 | ||||||||
\(849\) | −10.4087 | −0.357225 | ||||||||
\(850\) | −87.4588 | −2.99981 | ||||||||
\(851\) | −85.1345 | −2.91837 | ||||||||
\(852\) | −4.40758 | −0.151001 | ||||||||
\(853\) | −6.03350 | −0.206583 | −0.103292 | − | 0.994651i | \(-0.532937\pi\) | ||||
−0.103292 | + | 0.994651i | \(0.532937\pi\) | |||||||
\(854\) | 53.3501 | 1.82560 | ||||||||
\(855\) | 7.52201 | 0.257247 | ||||||||
\(856\) | 3.81409 | 0.130363 | ||||||||
\(857\) | 39.3766 | 1.34508 | 0.672540 | − | 0.740061i | \(-0.265203\pi\) | ||||
0.672540 | + | 0.740061i | \(0.265203\pi\) | |||||||
\(858\) | −3.45943 | −0.118103 | ||||||||
\(859\) | −37.2844 | −1.27213 | −0.636063 | − | 0.771637i | \(-0.719438\pi\) | ||||
−0.636063 | + | 0.771637i | \(0.719438\pi\) | |||||||
\(860\) | 12.6055 | 0.429843 | ||||||||
\(861\) | −3.00568 | −0.102433 | ||||||||
\(862\) | −23.1867 | −0.789743 | ||||||||
\(863\) | −55.0793 | −1.87492 | −0.937461 | − | 0.348090i | \(-0.886830\pi\) | ||||
−0.937461 | + | 0.348090i | \(0.886830\pi\) | |||||||
\(864\) | −1.00000 | −0.0340207 | ||||||||
\(865\) | −1.36278 | −0.0463361 | ||||||||
\(866\) | 5.73037 | 0.194726 | ||||||||
\(867\) | −40.2859 | −1.36818 | ||||||||
\(868\) | −24.0126 | −0.815042 | ||||||||
\(869\) | −21.5044 | −0.729487 | ||||||||
\(870\) | 26.9172 | 0.912580 | ||||||||
\(871\) | 14.3536 | 0.486353 | ||||||||
\(872\) | 18.7539 | 0.635087 | ||||||||
\(873\) | 4.85929 | 0.164462 | ||||||||
\(874\) | 15.7262 | 0.531947 | ||||||||
\(875\) | −115.201 | −3.89451 | ||||||||
\(876\) | 8.29562 | 0.280283 | ||||||||
\(877\) | −17.2810 | −0.583539 | −0.291769 | − | 0.956489i | \(-0.594244\pi\) | ||||
−0.291769 | + | 0.956489i | \(0.594244\pi\) | |||||||
\(878\) | −3.84780 | −0.129857 | ||||||||
\(879\) | 13.9122 | 0.469246 | ||||||||
\(880\) | 14.0758 | 0.474495 | ||||||||
\(881\) | 2.51424 | 0.0847068 | 0.0423534 | − | 0.999103i | \(-0.486514\pi\) | ||||
0.0423534 | + | 0.999103i | \(0.486514\pi\) | |||||||
\(882\) | 11.6551 | 0.392447 | ||||||||
\(883\) | −46.5170 | −1.56542 | −0.782711 | − | 0.622385i | \(-0.786164\pi\) | ||||
−0.782711 | + | 0.622385i | \(0.786164\pi\) | |||||||
\(884\) | 7.56875 | 0.254565 | ||||||||
\(885\) | 28.0123 | 0.941624 | ||||||||
\(886\) | 31.2358 | 1.04939 | ||||||||
\(887\) | 50.6035 | 1.69910 | 0.849550 | − | 0.527508i | \(-0.176874\pi\) | ||||
0.849550 | + | 0.527508i | \(0.176874\pi\) | |||||||
\(888\) | −10.0080 | −0.335846 | ||||||||
\(889\) | −93.2526 | −3.12759 | ||||||||
\(890\) | 11.7219 | 0.392918 | ||||||||
\(891\) | −3.45943 | −0.115895 | ||||||||
\(892\) | 13.3625 | 0.447410 | ||||||||
\(893\) | 2.17762 | 0.0728714 | ||||||||
\(894\) | −18.0995 | −0.605336 | ||||||||
\(895\) | −77.2267 | −2.58140 | ||||||||
\(896\) | 4.31915 | 0.144293 | ||||||||
\(897\) | −8.50665 | −0.284029 | ||||||||
\(898\) | 3.02705 | 0.101014 | ||||||||
\(899\) | −36.7793 | −1.22666 | ||||||||
\(900\) | 11.5553 | 0.385175 | ||||||||
\(901\) | −43.6682 | −1.45480 | ||||||||
\(902\) | −2.40740 | −0.0801578 | ||||||||
\(903\) | 13.3811 | 0.445293 | ||||||||
\(904\) | −10.5876 | −0.352138 | ||||||||
\(905\) | 19.1010 | 0.634939 | ||||||||
\(906\) | −16.5279 | −0.549104 | ||||||||
\(907\) | −31.9748 | −1.06171 | −0.530853 | − | 0.847464i | \(-0.678128\pi\) | ||||
−0.530853 | + | 0.847464i | \(0.678128\pi\) | |||||||
\(908\) | −1.25297 | −0.0415811 | ||||||||
\(909\) | 9.41575 | 0.312301 | ||||||||
\(910\) | 17.5738 | 0.582567 | ||||||||
\(911\) | 39.0255 | 1.29297 | 0.646486 | − | 0.762926i | \(-0.276238\pi\) | ||||
0.646486 | + | 0.762926i | \(0.276238\pi\) | |||||||
\(912\) | 1.84870 | 0.0612165 | ||||||||
\(913\) | 40.3529 | 1.33549 | ||||||||
\(914\) | −38.0751 | −1.25941 | ||||||||
\(915\) | 50.2580 | 1.66148 | ||||||||
\(916\) | 8.24201 | 0.272324 | ||||||||
\(917\) | −10.6765 | −0.352570 | ||||||||
\(918\) | 7.56875 | 0.249806 | ||||||||
\(919\) | 31.8283 | 1.04992 | 0.524959 | − | 0.851127i | \(-0.324081\pi\) | ||||
0.524959 | + | 0.851127i | \(0.324081\pi\) | |||||||
\(920\) | 34.6120 | 1.14112 | ||||||||
\(921\) | −7.65826 | −0.252348 | ||||||||
\(922\) | −16.0253 | −0.527765 | ||||||||
\(923\) | −4.40758 | −0.145077 | ||||||||
\(924\) | 14.9418 | 0.491550 | ||||||||
\(925\) | 115.645 | 3.80238 | ||||||||
\(926\) | −7.54870 | −0.248066 | ||||||||
\(927\) | −1.00000 | −0.0328443 | ||||||||
\(928\) | 6.61550 | 0.217164 | ||||||||
\(929\) | 28.7737 | 0.944033 | 0.472017 | − | 0.881590i | \(-0.343526\pi\) | ||||
0.472017 | + | 0.881590i | \(0.343526\pi\) | |||||||
\(930\) | −22.6209 | −0.741767 | ||||||||
\(931\) | −21.5467 | −0.706166 | ||||||||
\(932\) | 12.8913 | 0.422269 | ||||||||
\(933\) | −8.22932 | −0.269416 | ||||||||
\(934\) | −32.7890 | −1.07289 | ||||||||
\(935\) | −106.536 | −3.48410 | ||||||||
\(936\) | −1.00000 | −0.0326860 | ||||||||
\(937\) | −52.1487 | −1.70362 | −0.851812 | − | 0.523847i | \(-0.824496\pi\) | ||||
−0.851812 | + | 0.523847i | \(0.824496\pi\) | |||||||
\(938\) | −61.9954 | −2.02422 | ||||||||
\(939\) | −0.937649 | −0.0305990 | ||||||||
\(940\) | 4.79275 | 0.156322 | ||||||||
\(941\) | −46.7160 | −1.52290 | −0.761449 | − | 0.648225i | \(-0.775512\pi\) | ||||
−0.761449 | + | 0.648225i | \(0.775512\pi\) | |||||||
\(942\) | 8.57471 | 0.279379 | ||||||||
\(943\) | −5.91974 | −0.192773 | ||||||||
\(944\) | 6.88464 | 0.224076 | ||||||||
\(945\) | 17.5738 | 0.571677 | ||||||||
\(946\) | 10.7176 | 0.348458 | ||||||||
\(947\) | 60.8358 | 1.97690 | 0.988450 | − | 0.151549i | \(-0.0484263\pi\) | ||||
0.988450 | + | 0.151549i | \(0.0484263\pi\) | |||||||
\(948\) | −6.21617 | −0.201892 | ||||||||
\(949\) | 8.29562 | 0.269287 | ||||||||
\(950\) | −21.3622 | −0.693080 | ||||||||
\(951\) | 13.7271 | 0.445132 | ||||||||
\(952\) | −32.6906 | −1.05951 | ||||||||
\(953\) | 18.6575 | 0.604375 | 0.302187 | − | 0.953249i | \(-0.402283\pi\) | ||||
0.302187 | + | 0.953249i | \(0.402283\pi\) | |||||||
\(954\) | 5.76954 | 0.186796 | ||||||||
\(955\) | −50.6415 | −1.63872 | ||||||||
\(956\) | 20.1551 | 0.651864 | ||||||||
\(957\) | 22.8859 | 0.739795 | ||||||||
\(958\) | 38.4984 | 1.24383 | ||||||||
\(959\) | 32.8421 | 1.06053 | ||||||||
\(960\) | 4.06882 | 0.131320 | ||||||||
\(961\) | −0.0911780 | −0.00294123 | ||||||||
\(962\) | −10.0080 | −0.322671 | ||||||||
\(963\) | 3.81409 | 0.122907 | ||||||||
\(964\) | −2.43963 | −0.0785751 | ||||||||
\(965\) | −8.24930 | −0.265554 | ||||||||
\(966\) | 36.7415 | 1.18214 | ||||||||
\(967\) | 22.4665 | 0.722474 | 0.361237 | − | 0.932474i | \(-0.382355\pi\) | ||||
0.361237 | + | 0.932474i | \(0.382355\pi\) | |||||||
\(968\) | 0.967666 | 0.0311020 | ||||||||
\(969\) | −13.9923 | −0.449498 | ||||||||
\(970\) | −19.7716 | −0.634827 | ||||||||
\(971\) | −60.8053 | −1.95133 | −0.975667 | − | 0.219258i | \(-0.929636\pi\) | ||||
−0.975667 | + | 0.219258i | \(0.929636\pi\) | |||||||
\(972\) | −1.00000 | −0.0320750 | ||||||||
\(973\) | −3.02895 | −0.0971037 | ||||||||
\(974\) | −6.04136 | −0.193578 | ||||||||
\(975\) | 11.5553 | 0.370064 | ||||||||
\(976\) | 12.3520 | 0.395378 | ||||||||
\(977\) | −18.3313 | −0.586471 | −0.293235 | − | 0.956040i | \(-0.594732\pi\) | ||||
−0.293235 | + | 0.956040i | \(0.594732\pi\) | |||||||
\(978\) | 9.70287 | 0.310263 | ||||||||
\(979\) | 9.96629 | 0.318524 | ||||||||
\(980\) | −47.4224 | −1.51485 | ||||||||
\(981\) | 18.7539 | 0.598766 | ||||||||
\(982\) | 26.8174 | 0.855778 | ||||||||
\(983\) | 18.8713 | 0.601902 | 0.300951 | − | 0.953640i | \(-0.402696\pi\) | ||||
0.300951 | + | 0.953640i | \(0.402696\pi\) | |||||||
\(984\) | −0.695896 | −0.0221843 | ||||||||
\(985\) | −68.4840 | −2.18208 | ||||||||
\(986\) | −50.0710 | −1.59459 | ||||||||
\(987\) | 5.08763 | 0.161941 | ||||||||
\(988\) | 1.84870 | 0.0588149 | ||||||||
\(989\) | 26.3542 | 0.838015 | ||||||||
\(990\) | 14.0758 | 0.447358 | ||||||||
\(991\) | 43.5025 | 1.38190 | 0.690951 | − | 0.722902i | \(-0.257192\pi\) | ||||
0.690951 | + | 0.722902i | \(0.257192\pi\) | |||||||
\(992\) | −5.55957 | −0.176517 | ||||||||
\(993\) | −33.3238 | −1.05750 | ||||||||
\(994\) | 19.0370 | 0.603817 | ||||||||
\(995\) | 1.22687 | 0.0388943 | ||||||||
\(996\) | 11.6646 | 0.369608 | ||||||||
\(997\) | −46.1647 | −1.46205 | −0.731025 | − | 0.682351i | \(-0.760958\pi\) | ||||
−0.731025 | + | 0.682351i | \(0.760958\pi\) | |||||||
\(998\) | 8.59968 | 0.272218 | ||||||||
\(999\) | −10.0080 | −0.316639 |
(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 | 8034.2.a.bc.1.1 | ✓ | 15 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8034.2.a.bc.1.1 | ✓ | 15 | 1.1 | even | 1 | trivial |