Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1338,2,Mod(1,1338)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1338, 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("1338.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1338 = 2 \cdot 3 \cdot 223 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1338.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: | \(10.6839837904\) |
Analytic rank: | \(1\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.10273.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 2x^{3} - 5x^{2} + x + 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(0.673533\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1338.1 |
$q$-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 | ||||||||
\(5\) | 0.326467 | 0.146000 | 0.0730002 | − | 0.997332i | \(-0.476743\pi\) | ||||
0.0730002 | + | 0.997332i | \(0.476743\pi\) | |||||||
\(6\) | 1.00000 | 0.408248 | ||||||||
\(7\) | −1.59754 | −0.603813 | −0.301906 | − | 0.953338i | \(-0.597623\pi\) | ||||
−0.301906 | + | 0.953338i | \(0.597623\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −0.326467 | −0.103238 | ||||||||
\(11\) | −2.21989 | −0.669321 | −0.334660 | − | 0.942339i | \(-0.608622\pi\) | ||||
−0.334660 | + | 0.942339i | \(0.608622\pi\) | |||||||
\(12\) | −1.00000 | −0.288675 | ||||||||
\(13\) | 2.49096 | 0.690867 | 0.345434 | − | 0.938443i | \(-0.387732\pi\) | ||||
0.345434 | + | 0.938443i | \(0.387732\pi\) | |||||||
\(14\) | 1.59754 | 0.426960 | ||||||||
\(15\) | −0.326467 | −0.0842933 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 6.46037 | 1.56687 | 0.783435 | − | 0.621473i | \(-0.213466\pi\) | ||||
0.783435 | + | 0.621473i | \(0.213466\pi\) | |||||||
\(18\) | −1.00000 | −0.235702 | ||||||||
\(19\) | −7.66776 | −1.75910 | −0.879552 | − | 0.475802i | \(-0.842158\pi\) | ||||
−0.879552 | + | 0.475802i | \(0.842158\pi\) | |||||||
\(20\) | 0.326467 | 0.0730002 | ||||||||
\(21\) | 1.59754 | 0.348611 | ||||||||
\(22\) | 2.21989 | 0.473281 | ||||||||
\(23\) | 2.91402 | 0.607615 | 0.303808 | − | 0.952733i | \(-0.401742\pi\) | ||||
0.303808 | + | 0.952733i | \(0.401742\pi\) | |||||||
\(24\) | 1.00000 | 0.204124 | ||||||||
\(25\) | −4.89342 | −0.978684 | ||||||||
\(26\) | −2.49096 | −0.488517 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | −1.59754 | −0.301906 | ||||||||
\(29\) | −4.18930 | −0.777934 | −0.388967 | − | 0.921252i | \(-0.627168\pi\) | ||||
−0.388967 | + | 0.921252i | \(0.627168\pi\) | |||||||
\(30\) | 0.326467 | 0.0596044 | ||||||||
\(31\) | 5.66776 | 1.01796 | 0.508980 | − | 0.860779i | \(-0.330023\pi\) | ||||
0.508980 | + | 0.860779i | \(0.330023\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 2.21989 | 0.386433 | ||||||||
\(34\) | −6.46037 | −1.10794 | ||||||||
\(35\) | −0.521543 | −0.0881568 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | −2.05540 | −0.337905 | −0.168952 | − | 0.985624i | \(-0.554038\pi\) | ||||
−0.168952 | + | 0.985624i | \(0.554038\pi\) | |||||||
\(38\) | 7.66776 | 1.24387 | ||||||||
\(39\) | −2.49096 | −0.398872 | ||||||||
\(40\) | −0.326467 | −0.0516189 | ||||||||
\(41\) | 12.2901 | 1.91939 | 0.959696 | − | 0.281040i | \(-0.0906794\pi\) | ||||
0.959696 | + | 0.281040i | \(0.0906794\pi\) | |||||||
\(42\) | −1.59754 | −0.246505 | ||||||||
\(43\) | −8.89342 | −1.35623 | −0.678117 | − | 0.734954i | \(-0.737204\pi\) | ||||
−0.678117 | + | 0.734954i | \(0.737204\pi\) | |||||||
\(44\) | −2.21989 | −0.334660 | ||||||||
\(45\) | 0.326467 | 0.0486668 | ||||||||
\(46\) | −2.91402 | −0.429649 | ||||||||
\(47\) | −8.26530 | −1.20562 | −0.602809 | − | 0.797886i | \(-0.705952\pi\) | ||||
−0.602809 | + | 0.797886i | \(0.705952\pi\) | |||||||
\(48\) | −1.00000 | −0.144338 | ||||||||
\(49\) | −4.44787 | −0.635410 | ||||||||
\(50\) | 4.89342 | 0.692034 | ||||||||
\(51\) | −6.46037 | −0.904633 | ||||||||
\(52\) | 2.49096 | 0.345434 | ||||||||
\(53\) | −6.20990 | −0.852996 | −0.426498 | − | 0.904489i | \(-0.640253\pi\) | ||||
−0.426498 | + | 0.904489i | \(0.640253\pi\) | |||||||
\(54\) | 1.00000 | 0.136083 | ||||||||
\(55\) | −0.724719 | −0.0977211 | ||||||||
\(56\) | 1.59754 | 0.213480 | ||||||||
\(57\) | 7.66776 | 1.01562 | ||||||||
\(58\) | 4.18930 | 0.550082 | ||||||||
\(59\) | −0.283381 | −0.0368930 | −0.0184465 | − | 0.999830i | \(-0.505872\pi\) | ||||
−0.0184465 | + | 0.999830i | \(0.505872\pi\) | |||||||
\(60\) | −0.326467 | −0.0421467 | ||||||||
\(61\) | −2.94460 | −0.377018 | −0.188509 | − | 0.982071i | \(-0.560365\pi\) | ||||
−0.188509 | + | 0.982071i | \(0.560365\pi\) | |||||||
\(62\) | −5.66776 | −0.719806 | ||||||||
\(63\) | −1.59754 | −0.201271 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0.813215 | 0.100867 | ||||||||
\(66\) | −2.21989 | −0.273249 | ||||||||
\(67\) | −5.67353 | −0.693132 | −0.346566 | − | 0.938026i | \(-0.612652\pi\) | ||||
−0.346566 | + | 0.938026i | \(0.612652\pi\) | |||||||
\(68\) | 6.46037 | 0.783435 | ||||||||
\(69\) | −2.91402 | −0.350807 | ||||||||
\(70\) | 0.521543 | 0.0623363 | ||||||||
\(71\) | 4.12141 | 0.489121 | 0.244560 | − | 0.969634i | \(-0.421356\pi\) | ||||
0.244560 | + | 0.969634i | \(0.421356\pi\) | |||||||
\(72\) | −1.00000 | −0.117851 | ||||||||
\(73\) | 7.69257 | 0.900347 | 0.450173 | − | 0.892941i | \(-0.351362\pi\) | ||||
0.450173 | + | 0.892941i | \(0.351362\pi\) | |||||||
\(74\) | 2.05540 | 0.238935 | ||||||||
\(75\) | 4.89342 | 0.565043 | ||||||||
\(76\) | −7.66776 | −0.879552 | ||||||||
\(77\) | 3.54635 | 0.404144 | ||||||||
\(78\) | 2.49096 | 0.282045 | ||||||||
\(79\) | −0.116565 | −0.0131146 | −0.00655732 | − | 0.999979i | \(-0.502087\pi\) | ||||
−0.00655732 | + | 0.999979i | \(0.502087\pi\) | |||||||
\(80\) | 0.326467 | 0.0365001 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −12.2901 | −1.35722 | ||||||||
\(83\) | −7.08850 | −0.778063 | −0.389032 | − | 0.921224i | \(-0.627190\pi\) | ||||
−0.389032 | + | 0.921224i | \(0.627190\pi\) | |||||||
\(84\) | 1.59754 | 0.174306 | ||||||||
\(85\) | 2.10910 | 0.228764 | ||||||||
\(86\) | 8.89342 | 0.959002 | ||||||||
\(87\) | 4.18930 | 0.449140 | ||||||||
\(88\) | 2.21989 | 0.236641 | ||||||||
\(89\) | 0.513252 | 0.0544046 | 0.0272023 | − | 0.999630i | \(-0.491340\pi\) | ||||
0.0272023 | + | 0.999630i | \(0.491340\pi\) | |||||||
\(90\) | −0.326467 | −0.0344126 | ||||||||
\(91\) | −3.97940 | −0.417154 | ||||||||
\(92\) | 2.91402 | 0.303808 | ||||||||
\(93\) | −5.66776 | −0.587719 | ||||||||
\(94\) | 8.26530 | 0.852500 | ||||||||
\(95\) | −2.50327 | −0.256830 | ||||||||
\(96\) | 1.00000 | 0.102062 | ||||||||
\(97\) | −6.38186 | −0.647980 | −0.323990 | − | 0.946061i | \(-0.605024\pi\) | ||||
−0.323990 | + | 0.946061i | \(0.605024\pi\) | |||||||
\(98\) | 4.44787 | 0.449303 | ||||||||
\(99\) | −2.21989 | −0.223107 | ||||||||
\(100\) | −4.89342 | −0.489342 | ||||||||
\(101\) | −12.2801 | −1.22192 | −0.610959 | − | 0.791662i | \(-0.709216\pi\) | ||||
−0.610959 | + | 0.791662i | \(0.709216\pi\) | |||||||
\(102\) | 6.46037 | 0.639672 | ||||||||
\(103\) | −19.4504 | −1.91650 | −0.958252 | − | 0.285926i | \(-0.907699\pi\) | ||||
−0.958252 | + | 0.285926i | \(0.907699\pi\) | |||||||
\(104\) | −2.49096 | −0.244258 | ||||||||
\(105\) | 0.521543 | 0.0508974 | ||||||||
\(106\) | 6.20990 | 0.603159 | ||||||||
\(107\) | −6.16028 | −0.595537 | −0.297768 | − | 0.954638i | \(-0.596242\pi\) | ||||
−0.297768 | + | 0.954638i | \(0.596242\pi\) | |||||||
\(108\) | −1.00000 | −0.0962250 | ||||||||
\(109\) | −9.68026 | −0.927201 | −0.463600 | − | 0.886044i | \(-0.653443\pi\) | ||||
−0.463600 | + | 0.886044i | \(0.653443\pi\) | |||||||
\(110\) | 0.724719 | 0.0690992 | ||||||||
\(111\) | 2.05540 | 0.195089 | ||||||||
\(112\) | −1.59754 | −0.150953 | ||||||||
\(113\) | 3.79915 | 0.357394 | 0.178697 | − | 0.983904i | \(-0.442812\pi\) | ||||
0.178697 | + | 0.983904i | \(0.442812\pi\) | |||||||
\(114\) | −7.66776 | −0.718151 | ||||||||
\(115\) | 0.951330 | 0.0887120 | ||||||||
\(116\) | −4.18930 | −0.388967 | ||||||||
\(117\) | 2.49096 | 0.230289 | ||||||||
\(118\) | 0.283381 | 0.0260873 | ||||||||
\(119\) | −10.3207 | −0.946096 | ||||||||
\(120\) | 0.326467 | 0.0298022 | ||||||||
\(121\) | −6.07211 | −0.552010 | ||||||||
\(122\) | 2.94460 | 0.266592 | ||||||||
\(123\) | −12.2901 | −1.10816 | ||||||||
\(124\) | 5.66776 | 0.508980 | ||||||||
\(125\) | −3.22987 | −0.288888 | ||||||||
\(126\) | 1.59754 | 0.142320 | ||||||||
\(127\) | −17.9861 | −1.59601 | −0.798005 | − | 0.602650i | \(-0.794111\pi\) | ||||
−0.798005 | + | 0.602650i | \(0.794111\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 8.89342 | 0.783022 | ||||||||
\(130\) | −0.813215 | −0.0713236 | ||||||||
\(131\) | 7.32898 | 0.640336 | 0.320168 | − | 0.947361i | \(-0.396261\pi\) | ||||
0.320168 | + | 0.947361i | \(0.396261\pi\) | |||||||
\(132\) | 2.21989 | 0.193216 | ||||||||
\(133\) | 12.2495 | 1.06217 | ||||||||
\(134\) | 5.67353 | 0.490119 | ||||||||
\(135\) | −0.326467 | −0.0280978 | ||||||||
\(136\) | −6.46037 | −0.553972 | ||||||||
\(137\) | −8.66776 | −0.740537 | −0.370268 | − | 0.928925i | \(-0.620734\pi\) | ||||
−0.370268 | + | 0.928925i | \(0.620734\pi\) | |||||||
\(138\) | 2.91402 | 0.248058 | ||||||||
\(139\) | 5.85706 | 0.496789 | 0.248395 | − | 0.968659i | \(-0.420097\pi\) | ||||
0.248395 | + | 0.968659i | \(0.420097\pi\) | |||||||
\(140\) | −0.521543 | −0.0440784 | ||||||||
\(141\) | 8.26530 | 0.696064 | ||||||||
\(142\) | −4.12141 | −0.345861 | ||||||||
\(143\) | −5.52964 | −0.462412 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | −1.36767 | −0.113579 | ||||||||
\(146\) | −7.69257 | −0.636641 | ||||||||
\(147\) | 4.44787 | 0.366854 | ||||||||
\(148\) | −2.05540 | −0.168952 | ||||||||
\(149\) | −15.7586 | −1.29099 | −0.645497 | − | 0.763763i | \(-0.723350\pi\) | ||||
−0.645497 | + | 0.763763i | \(0.723350\pi\) | |||||||
\(150\) | −4.89342 | −0.399546 | ||||||||
\(151\) | −7.78263 | −0.633341 | −0.316671 | − | 0.948536i | \(-0.602565\pi\) | ||||
−0.316671 | + | 0.948536i | \(0.602565\pi\) | |||||||
\(152\) | 7.66776 | 0.621937 | ||||||||
\(153\) | 6.46037 | 0.522290 | ||||||||
\(154\) | −3.54635 | −0.285773 | ||||||||
\(155\) | 1.85033 | 0.148622 | ||||||||
\(156\) | −2.49096 | −0.199436 | ||||||||
\(157\) | 3.52575 | 0.281386 | 0.140693 | − | 0.990053i | \(-0.455067\pi\) | ||||
0.140693 | + | 0.990053i | \(0.455067\pi\) | |||||||
\(158\) | 0.116565 | 0.00927345 | ||||||||
\(159\) | 6.20990 | 0.492477 | ||||||||
\(160\) | −0.326467 | −0.0258095 | ||||||||
\(161\) | −4.65526 | −0.366886 | ||||||||
\(162\) | −1.00000 | −0.0785674 | ||||||||
\(163\) | 0.0621204 | 0.00486564 | 0.00243282 | − | 0.999997i | \(-0.499226\pi\) | ||||
0.00243282 | + | 0.999997i | \(0.499226\pi\) | |||||||
\(164\) | 12.2901 | 0.959696 | ||||||||
\(165\) | 0.724719 | 0.0564193 | ||||||||
\(166\) | 7.08850 | 0.550174 | ||||||||
\(167\) | 2.08850 | 0.161613 | 0.0808063 | − | 0.996730i | \(-0.474250\pi\) | ||||
0.0808063 | + | 0.996730i | \(0.474250\pi\) | |||||||
\(168\) | −1.59754 | −0.123253 | ||||||||
\(169\) | −6.79513 | −0.522702 | ||||||||
\(170\) | −2.10910 | −0.161760 | ||||||||
\(171\) | −7.66776 | −0.586368 | ||||||||
\(172\) | −8.89342 | −0.678117 | ||||||||
\(173\) | −14.2597 | −1.08415 | −0.542073 | − | 0.840331i | \(-0.682360\pi\) | ||||
−0.542073 | + | 0.840331i | \(0.682360\pi\) | |||||||
\(174\) | −4.18930 | −0.317590 | ||||||||
\(175\) | 7.81742 | 0.590942 | ||||||||
\(176\) | −2.21989 | −0.167330 | ||||||||
\(177\) | 0.283381 | 0.0213002 | ||||||||
\(178\) | −0.513252 | −0.0384699 | ||||||||
\(179\) | 24.5192 | 1.83265 | 0.916327 | − | 0.400431i | \(-0.131140\pi\) | ||||
0.916327 | + | 0.400431i | \(0.131140\pi\) | |||||||
\(180\) | 0.326467 | 0.0243334 | ||||||||
\(181\) | −18.2125 | −1.35373 | −0.676864 | − | 0.736108i | \(-0.736661\pi\) | ||||
−0.676864 | + | 0.736108i | \(0.736661\pi\) | |||||||
\(182\) | 3.97940 | 0.294973 | ||||||||
\(183\) | 2.94460 | 0.217671 | ||||||||
\(184\) | −2.91402 | −0.214824 | ||||||||
\(185\) | −0.671018 | −0.0493342 | ||||||||
\(186\) | 5.66776 | 0.415580 | ||||||||
\(187\) | −14.3413 | −1.04874 | ||||||||
\(188\) | −8.26530 | −0.602809 | ||||||||
\(189\) | 1.59754 | 0.116204 | ||||||||
\(190\) | 2.50327 | 0.181606 | ||||||||
\(191\) | 21.0644 | 1.52417 | 0.762085 | − | 0.647477i | \(-0.224176\pi\) | ||||
0.762085 | + | 0.647477i | \(0.224176\pi\) | |||||||
\(192\) | −1.00000 | −0.0721688 | ||||||||
\(193\) | −27.0985 | −1.95059 | −0.975296 | − | 0.220901i | \(-0.929100\pi\) | ||||
−0.975296 | + | 0.220901i | \(0.929100\pi\) | |||||||
\(194\) | 6.38186 | 0.458191 | ||||||||
\(195\) | −0.813215 | −0.0582355 | ||||||||
\(196\) | −4.44787 | −0.317705 | ||||||||
\(197\) | 17.7547 | 1.26497 | 0.632485 | − | 0.774573i | \(-0.282035\pi\) | ||||
0.632485 | + | 0.774573i | \(0.282035\pi\) | |||||||
\(198\) | 2.21989 | 0.157760 | ||||||||
\(199\) | 20.2190 | 1.43328 | 0.716642 | − | 0.697442i | \(-0.245678\pi\) | ||||
0.716642 | + | 0.697442i | \(0.245678\pi\) | |||||||
\(200\) | 4.89342 | 0.346017 | ||||||||
\(201\) | 5.67353 | 0.400180 | ||||||||
\(202\) | 12.2801 | 0.864026 | ||||||||
\(203\) | 6.69257 | 0.469726 | ||||||||
\(204\) | −6.46037 | −0.452317 | ||||||||
\(205\) | 4.01231 | 0.280232 | ||||||||
\(206\) | 19.4504 | 1.35517 | ||||||||
\(207\) | 2.91402 | 0.202538 | ||||||||
\(208\) | 2.49096 | 0.172717 | ||||||||
\(209\) | 17.0216 | 1.17741 | ||||||||
\(210\) | −0.521543 | −0.0359899 | ||||||||
\(211\) | −11.3049 | −0.778264 | −0.389132 | − | 0.921182i | \(-0.627225\pi\) | ||||
−0.389132 | + | 0.921182i | \(0.627225\pi\) | |||||||
\(212\) | −6.20990 | −0.426498 | ||||||||
\(213\) | −4.12141 | −0.282394 | ||||||||
\(214\) | 6.16028 | 0.421108 | ||||||||
\(215\) | −2.90340 | −0.198011 | ||||||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | −9.05446 | −0.614657 | ||||||||
\(218\) | 9.68026 | 0.655630 | ||||||||
\(219\) | −7.69257 | −0.519816 | ||||||||
\(220\) | −0.724719 | −0.0488605 | ||||||||
\(221\) | 16.0925 | 1.08250 | ||||||||
\(222\) | −2.05540 | −0.137949 | ||||||||
\(223\) | −1.00000 | −0.0669650 | ||||||||
\(224\) | 1.59754 | 0.106740 | ||||||||
\(225\) | −4.89342 | −0.326228 | ||||||||
\(226\) | −3.79915 | −0.252716 | ||||||||
\(227\) | 18.8653 | 1.25214 | 0.626069 | − | 0.779768i | \(-0.284663\pi\) | ||||
0.626069 | + | 0.779768i | \(0.284663\pi\) | |||||||
\(228\) | 7.66776 | 0.507810 | ||||||||
\(229\) | 25.1506 | 1.66200 | 0.831000 | − | 0.556273i | \(-0.187769\pi\) | ||||
0.831000 | + | 0.556273i | \(0.187769\pi\) | |||||||
\(230\) | −0.951330 | −0.0627289 | ||||||||
\(231\) | −3.54635 | −0.233333 | ||||||||
\(232\) | 4.18930 | 0.275041 | ||||||||
\(233\) | −2.13736 | −0.140023 | −0.0700115 | − | 0.997546i | \(-0.522304\pi\) | ||||
−0.0700115 | + | 0.997546i | \(0.522304\pi\) | |||||||
\(234\) | −2.49096 | −0.162839 | ||||||||
\(235\) | −2.69834 | −0.176021 | ||||||||
\(236\) | −0.283381 | −0.0184465 | ||||||||
\(237\) | 0.116565 | 0.00757174 | ||||||||
\(238\) | 10.3207 | 0.668991 | ||||||||
\(239\) | 0.112547 | 0.00728005 | 0.00364003 | − | 0.999993i | \(-0.498841\pi\) | ||||
0.00364003 | + | 0.999993i | \(0.498841\pi\) | |||||||
\(240\) | −0.326467 | −0.0210733 | ||||||||
\(241\) | 13.8957 | 0.895104 | 0.447552 | − | 0.894258i | \(-0.352296\pi\) | ||||
0.447552 | + | 0.894258i | \(0.352296\pi\) | |||||||
\(242\) | 6.07211 | 0.390330 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | −2.94460 | −0.188509 | ||||||||
\(245\) | −1.45208 | −0.0927701 | ||||||||
\(246\) | 12.2901 | 0.783589 | ||||||||
\(247\) | −19.1001 | −1.21531 | ||||||||
\(248\) | −5.66776 | −0.359903 | ||||||||
\(249\) | 7.08850 | 0.449215 | ||||||||
\(250\) | 3.22987 | 0.204275 | ||||||||
\(251\) | 1.18698 | 0.0749213 | 0.0374607 | − | 0.999298i | \(-0.488073\pi\) | ||||
0.0374607 | + | 0.999298i | \(0.488073\pi\) | |||||||
\(252\) | −1.59754 | −0.100635 | ||||||||
\(253\) | −6.46879 | −0.406689 | ||||||||
\(254\) | 17.9861 | 1.12855 | ||||||||
\(255\) | −2.10910 | −0.132077 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −9.49749 | −0.592437 | −0.296219 | − | 0.955120i | \(-0.595726\pi\) | ||||
−0.296219 | + | 0.955120i | \(0.595726\pi\) | |||||||
\(258\) | −8.89342 | −0.553680 | ||||||||
\(259\) | 3.28357 | 0.204031 | ||||||||
\(260\) | 0.813215 | 0.0504334 | ||||||||
\(261\) | −4.18930 | −0.259311 | ||||||||
\(262\) | −7.32898 | −0.452786 | ||||||||
\(263\) | −20.2440 | −1.24830 | −0.624148 | − | 0.781306i | \(-0.714554\pi\) | ||||
−0.624148 | + | 0.781306i | \(0.714554\pi\) | |||||||
\(264\) | −2.21989 | −0.136625 | ||||||||
\(265\) | −2.02733 | −0.124538 | ||||||||
\(266\) | −12.2495 | −0.751067 | ||||||||
\(267\) | −0.513252 | −0.0314105 | ||||||||
\(268\) | −5.67353 | −0.346566 | ||||||||
\(269\) | −9.55885 | −0.582814 | −0.291407 | − | 0.956599i | \(-0.594123\pi\) | ||||
−0.291407 | + | 0.956599i | \(0.594123\pi\) | |||||||
\(270\) | 0.326467 | 0.0198681 | ||||||||
\(271\) | 24.0547 | 1.46122 | 0.730608 | − | 0.682797i | \(-0.239237\pi\) | ||||
0.730608 | + | 0.682797i | \(0.239237\pi\) | |||||||
\(272\) | 6.46037 | 0.391718 | ||||||||
\(273\) | 3.97940 | 0.240844 | ||||||||
\(274\) | 8.66776 | 0.523638 | ||||||||
\(275\) | 10.8628 | 0.655054 | ||||||||
\(276\) | −2.91402 | −0.175403 | ||||||||
\(277\) | 30.8702 | 1.85481 | 0.927405 | − | 0.374059i | \(-0.122034\pi\) | ||||
0.927405 | + | 0.374059i | \(0.122034\pi\) | |||||||
\(278\) | −5.85706 | −0.351283 | ||||||||
\(279\) | 5.66776 | 0.339320 | ||||||||
\(280\) | 0.521543 | 0.0311681 | ||||||||
\(281\) | 6.78665 | 0.404857 | 0.202429 | − | 0.979297i | \(-0.435117\pi\) | ||||
0.202429 | + | 0.979297i | \(0.435117\pi\) | |||||||
\(282\) | −8.26530 | −0.492191 | ||||||||
\(283\) | 12.2466 | 0.727984 | 0.363992 | − | 0.931402i | \(-0.381414\pi\) | ||||
0.363992 | + | 0.931402i | \(0.381414\pi\) | |||||||
\(284\) | 4.12141 | 0.244560 | ||||||||
\(285\) | 2.50327 | 0.148281 | ||||||||
\(286\) | 5.52964 | 0.326975 | ||||||||
\(287\) | −19.6339 | −1.15895 | ||||||||
\(288\) | −1.00000 | −0.0589256 | ||||||||
\(289\) | 24.7364 | 1.45508 | ||||||||
\(290\) | 1.36767 | 0.0803122 | ||||||||
\(291\) | 6.38186 | 0.374111 | ||||||||
\(292\) | 7.69257 | 0.450173 | ||||||||
\(293\) | −10.7176 | −0.626127 | −0.313064 | − | 0.949732i | \(-0.601355\pi\) | ||||
−0.313064 | + | 0.949732i | \(0.601355\pi\) | |||||||
\(294\) | −4.44787 | −0.259405 | ||||||||
\(295\) | −0.0925144 | −0.00538640 | ||||||||
\(296\) | 2.05540 | 0.119467 | ||||||||
\(297\) | 2.21989 | 0.128811 | ||||||||
\(298\) | 15.7586 | 0.912870 | ||||||||
\(299\) | 7.25870 | 0.419781 | ||||||||
\(300\) | 4.89342 | 0.282522 | ||||||||
\(301\) | 14.2076 | 0.818911 | ||||||||
\(302\) | 7.78263 | 0.447840 | ||||||||
\(303\) | 12.2801 | 0.705475 | ||||||||
\(304\) | −7.66776 | −0.439776 | ||||||||
\(305\) | −0.961315 | −0.0550447 | ||||||||
\(306\) | −6.46037 | −0.369315 | ||||||||
\(307\) | 6.39669 | 0.365078 | 0.182539 | − | 0.983199i | \(-0.441568\pi\) | ||||
0.182539 | + | 0.983199i | \(0.441568\pi\) | |||||||
\(308\) | 3.54635 | 0.202072 | ||||||||
\(309\) | 19.4504 | 1.10649 | ||||||||
\(310\) | −1.85033 | −0.105092 | ||||||||
\(311\) | −6.95535 | −0.394402 | −0.197201 | − | 0.980363i | \(-0.563185\pi\) | ||||
−0.197201 | + | 0.980363i | \(0.563185\pi\) | |||||||
\(312\) | 2.49096 | 0.141023 | ||||||||
\(313\) | 6.45365 | 0.364782 | 0.182391 | − | 0.983226i | \(-0.441616\pi\) | ||||
0.182391 | + | 0.983226i | \(0.441616\pi\) | |||||||
\(314\) | −3.52575 | −0.198970 | ||||||||
\(315\) | −0.521543 | −0.0293856 | ||||||||
\(316\) | −0.116565 | −0.00655732 | ||||||||
\(317\) | 5.56695 | 0.312671 | 0.156336 | − | 0.987704i | \(-0.450032\pi\) | ||||
0.156336 | + | 0.987704i | \(0.450032\pi\) | |||||||
\(318\) | −6.20990 | −0.348234 | ||||||||
\(319\) | 9.29977 | 0.520687 | ||||||||
\(320\) | 0.326467 | 0.0182500 | ||||||||
\(321\) | 6.16028 | 0.343833 | ||||||||
\(322\) | 4.65526 | 0.259427 | ||||||||
\(323\) | −49.5366 | −2.75629 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | −12.1893 | −0.676141 | ||||||||
\(326\) | −0.0621204 | −0.00344053 | ||||||||
\(327\) | 9.68026 | 0.535320 | ||||||||
\(328\) | −12.2901 | −0.678608 | ||||||||
\(329\) | 13.2041 | 0.727967 | ||||||||
\(330\) | −0.724719 | −0.0398945 | ||||||||
\(331\) | −24.9131 | −1.36935 | −0.684673 | − | 0.728850i | \(-0.740055\pi\) | ||||
−0.684673 | + | 0.728850i | \(0.740055\pi\) | |||||||
\(332\) | −7.08850 | −0.389032 | ||||||||
\(333\) | −2.05540 | −0.112635 | ||||||||
\(334\) | −2.08850 | −0.114277 | ||||||||
\(335\) | −1.85222 | −0.101198 | ||||||||
\(336\) | 1.59754 | 0.0871528 | ||||||||
\(337\) | 12.2978 | 0.669902 | 0.334951 | − | 0.942236i | \(-0.391280\pi\) | ||||
0.334951 | + | 0.942236i | \(0.391280\pi\) | |||||||
\(338\) | 6.79513 | 0.369606 | ||||||||
\(339\) | −3.79915 | −0.206341 | ||||||||
\(340\) | 2.10910 | 0.114382 | ||||||||
\(341\) | −12.5818 | −0.681341 | ||||||||
\(342\) | 7.66776 | 0.414625 | ||||||||
\(343\) | 18.2884 | 0.987481 | ||||||||
\(344\) | 8.89342 | 0.479501 | ||||||||
\(345\) | −0.951330 | −0.0512179 | ||||||||
\(346\) | 14.2597 | 0.766607 | ||||||||
\(347\) | −2.80103 | −0.150367 | −0.0751837 | − | 0.997170i | \(-0.523954\pi\) | ||||
−0.0751837 | + | 0.997170i | \(0.523954\pi\) | |||||||
\(348\) | 4.18930 | 0.224570 | ||||||||
\(349\) | 13.6847 | 0.732523 | 0.366262 | − | 0.930512i | \(-0.380638\pi\) | ||||
0.366262 | + | 0.930512i | \(0.380638\pi\) | |||||||
\(350\) | −7.81742 | −0.417859 | ||||||||
\(351\) | −2.49096 | −0.132957 | ||||||||
\(352\) | 2.21989 | 0.118320 | ||||||||
\(353\) | 19.7430 | 1.05081 | 0.525407 | − | 0.850851i | \(-0.323913\pi\) | ||||
0.525407 | + | 0.850851i | \(0.323913\pi\) | |||||||
\(354\) | −0.283381 | −0.0150615 | ||||||||
\(355\) | 1.34550 | 0.0714118 | ||||||||
\(356\) | 0.513252 | 0.0272023 | ||||||||
\(357\) | 10.3207 | 0.546229 | ||||||||
\(358\) | −24.5192 | −1.29588 | ||||||||
\(359\) | 9.56526 | 0.504835 | 0.252418 | − | 0.967618i | \(-0.418774\pi\) | ||||
0.252418 | + | 0.967618i | \(0.418774\pi\) | |||||||
\(360\) | −0.326467 | −0.0172063 | ||||||||
\(361\) | 39.7945 | 2.09445 | ||||||||
\(362\) | 18.2125 | 0.957230 | ||||||||
\(363\) | 6.07211 | 0.318703 | ||||||||
\(364\) | −3.97940 | −0.208577 | ||||||||
\(365\) | 2.51137 | 0.131451 | ||||||||
\(366\) | −2.94460 | −0.153917 | ||||||||
\(367\) | −24.7755 | −1.29327 | −0.646635 | − | 0.762800i | \(-0.723824\pi\) | ||||
−0.646635 | + | 0.762800i | \(0.723824\pi\) | |||||||
\(368\) | 2.91402 | 0.151904 | ||||||||
\(369\) | 12.2901 | 0.639797 | ||||||||
\(370\) | 0.671018 | 0.0348846 | ||||||||
\(371\) | 9.92055 | 0.515049 | ||||||||
\(372\) | −5.66776 | −0.293860 | ||||||||
\(373\) | 35.7002 | 1.84849 | 0.924244 | − | 0.381802i | \(-0.124696\pi\) | ||||
0.924244 | + | 0.381802i | \(0.124696\pi\) | |||||||
\(374\) | 14.3413 | 0.741571 | ||||||||
\(375\) | 3.22987 | 0.166790 | ||||||||
\(376\) | 8.26530 | 0.426250 | ||||||||
\(377\) | −10.4354 | −0.537449 | ||||||||
\(378\) | −1.59754 | −0.0821685 | ||||||||
\(379\) | −14.3802 | −0.738660 | −0.369330 | − | 0.929298i | \(-0.620413\pi\) | ||||
−0.369330 | + | 0.929298i | \(0.620413\pi\) | |||||||
\(380\) | −2.50327 | −0.128415 | ||||||||
\(381\) | 17.9861 | 0.921457 | ||||||||
\(382\) | −21.0644 | −1.07775 | ||||||||
\(383\) | −30.9671 | −1.58235 | −0.791173 | − | 0.611593i | \(-0.790529\pi\) | ||||
−0.791173 | + | 0.611593i | \(0.790529\pi\) | |||||||
\(384\) | 1.00000 | 0.0510310 | ||||||||
\(385\) | 1.15777 | 0.0590052 | ||||||||
\(386\) | 27.0985 | 1.37928 | ||||||||
\(387\) | −8.89342 | −0.452078 | ||||||||
\(388\) | −6.38186 | −0.323990 | ||||||||
\(389\) | 8.50767 | 0.431356 | 0.215678 | − | 0.976465i | \(-0.430804\pi\) | ||||
0.215678 | + | 0.976465i | \(0.430804\pi\) | |||||||
\(390\) | 0.813215 | 0.0411787 | ||||||||
\(391\) | 18.8257 | 0.952054 | ||||||||
\(392\) | 4.44787 | 0.224651 | ||||||||
\(393\) | −7.32898 | −0.369698 | ||||||||
\(394\) | −17.7547 | −0.894468 | ||||||||
\(395\) | −0.0380547 | −0.00191474 | ||||||||
\(396\) | −2.21989 | −0.111553 | ||||||||
\(397\) | −14.2651 | −0.715945 | −0.357973 | − | 0.933732i | \(-0.616532\pi\) | ||||
−0.357973 | + | 0.933732i | \(0.616532\pi\) | |||||||
\(398\) | −20.2190 | −1.01348 | ||||||||
\(399\) | −12.2495 | −0.613244 | ||||||||
\(400\) | −4.89342 | −0.244671 | ||||||||
\(401\) | 31.5109 | 1.57358 | 0.786791 | − | 0.617220i | \(-0.211741\pi\) | ||||
0.786791 | + | 0.617220i | \(0.211741\pi\) | |||||||
\(402\) | −5.67353 | −0.282970 | ||||||||
\(403\) | 14.1181 | 0.703275 | ||||||||
\(404\) | −12.2801 | −0.610959 | ||||||||
\(405\) | 0.326467 | 0.0162223 | ||||||||
\(406\) | −6.69257 | −0.332147 | ||||||||
\(407\) | 4.56274 | 0.226167 | ||||||||
\(408\) | 6.46037 | 0.319836 | ||||||||
\(409\) | −9.16293 | −0.453078 | −0.226539 | − | 0.974002i | \(-0.572741\pi\) | ||||
−0.226539 | + | 0.974002i | \(0.572741\pi\) | |||||||
\(410\) | −4.01231 | −0.198154 | ||||||||
\(411\) | 8.66776 | 0.427549 | ||||||||
\(412\) | −19.4504 | −0.958252 | ||||||||
\(413\) | 0.452712 | 0.0222765 | ||||||||
\(414\) | −2.91402 | −0.143216 | ||||||||
\(415\) | −2.31416 | −0.113598 | ||||||||
\(416\) | −2.49096 | −0.122129 | ||||||||
\(417\) | −5.85706 | −0.286821 | ||||||||
\(418\) | −17.0216 | −0.832551 | ||||||||
\(419\) | −29.4201 | −1.43727 | −0.718634 | − | 0.695389i | \(-0.755232\pi\) | ||||
−0.718634 | + | 0.695389i | \(0.755232\pi\) | |||||||
\(420\) | 0.521543 | 0.0254487 | ||||||||
\(421\) | 28.8396 | 1.40556 | 0.702778 | − | 0.711409i | \(-0.251943\pi\) | ||||
0.702778 | + | 0.711409i | \(0.251943\pi\) | |||||||
\(422\) | 11.3049 | 0.550315 | ||||||||
\(423\) | −8.26530 | −0.401872 | ||||||||
\(424\) | 6.20990 | 0.301579 | ||||||||
\(425\) | −31.6133 | −1.53347 | ||||||||
\(426\) | 4.12141 | 0.199683 | ||||||||
\(427\) | 4.70412 | 0.227648 | ||||||||
\(428\) | −6.16028 | −0.297768 | ||||||||
\(429\) | 5.52964 | 0.266974 | ||||||||
\(430\) | 2.90340 | 0.140015 | ||||||||
\(431\) | 29.9517 | 1.44272 | 0.721360 | − | 0.692560i | \(-0.243517\pi\) | ||||
0.721360 | + | 0.692560i | \(0.243517\pi\) | |||||||
\(432\) | −1.00000 | −0.0481125 | ||||||||
\(433\) | −11.1833 | −0.537437 | −0.268718 | − | 0.963219i | \(-0.586600\pi\) | ||||
−0.268718 | + | 0.963219i | \(0.586600\pi\) | |||||||
\(434\) | 9.05446 | 0.434628 | ||||||||
\(435\) | 1.36767 | 0.0655746 | ||||||||
\(436\) | −9.68026 | −0.463600 | ||||||||
\(437\) | −22.3440 | −1.06886 | ||||||||
\(438\) | 7.69257 | 0.367565 | ||||||||
\(439\) | −30.8644 | −1.47308 | −0.736539 | − | 0.676395i | \(-0.763541\pi\) | ||||
−0.736539 | + | 0.676395i | \(0.763541\pi\) | |||||||
\(440\) | 0.724719 | 0.0345496 | ||||||||
\(441\) | −4.44787 | −0.211803 | ||||||||
\(442\) | −16.0925 | −0.765443 | ||||||||
\(443\) | −35.8542 | −1.70349 | −0.851743 | − | 0.523960i | \(-0.824454\pi\) | ||||
−0.851743 | + | 0.523960i | \(0.824454\pi\) | |||||||
\(444\) | 2.05540 | 0.0975447 | ||||||||
\(445\) | 0.167560 | 0.00794309 | ||||||||
\(446\) | 1.00000 | 0.0473514 | ||||||||
\(447\) | 15.7586 | 0.745355 | ||||||||
\(448\) | −1.59754 | −0.0754766 | ||||||||
\(449\) | −15.7066 | −0.741242 | −0.370621 | − | 0.928784i | \(-0.620855\pi\) | ||||
−0.370621 | + | 0.928784i | \(0.620855\pi\) | |||||||
\(450\) | 4.89342 | 0.230678 | ||||||||
\(451\) | −27.2826 | −1.28469 | ||||||||
\(452\) | 3.79915 | 0.178697 | ||||||||
\(453\) | 7.78263 | 0.365660 | ||||||||
\(454\) | −18.8653 | −0.885395 | ||||||||
\(455\) | −1.29914 | −0.0609047 | ||||||||
\(456\) | −7.66776 | −0.359076 | ||||||||
\(457\) | −29.0459 | −1.35871 | −0.679355 | − | 0.733809i | \(-0.737741\pi\) | ||||
−0.679355 | + | 0.733809i | \(0.737741\pi\) | |||||||
\(458\) | −25.1506 | −1.17521 | ||||||||
\(459\) | −6.46037 | −0.301544 | ||||||||
\(460\) | 0.951330 | 0.0443560 | ||||||||
\(461\) | 21.5743 | 1.00482 | 0.502408 | − | 0.864631i | \(-0.332448\pi\) | ||||
0.502408 | + | 0.864631i | \(0.332448\pi\) | |||||||
\(462\) | 3.54635 | 0.164991 | ||||||||
\(463\) | 24.3686 | 1.13251 | 0.566253 | − | 0.824232i | \(-0.308393\pi\) | ||||
0.566253 | + | 0.824232i | \(0.308393\pi\) | |||||||
\(464\) | −4.18930 | −0.194483 | ||||||||
\(465\) | −1.85033 | −0.0858072 | ||||||||
\(466\) | 2.13736 | 0.0990111 | ||||||||
\(467\) | −32.4960 | −1.50374 | −0.751868 | − | 0.659314i | \(-0.770847\pi\) | ||||
−0.751868 | + | 0.659314i | \(0.770847\pi\) | |||||||
\(468\) | 2.49096 | 0.115145 | ||||||||
\(469\) | 9.06369 | 0.418522 | ||||||||
\(470\) | 2.69834 | 0.124465 | ||||||||
\(471\) | −3.52575 | −0.162458 | ||||||||
\(472\) | 0.283381 | 0.0130437 | ||||||||
\(473\) | 19.7424 | 0.907756 | ||||||||
\(474\) | −0.116565 | −0.00535403 | ||||||||
\(475\) | 37.5216 | 1.72161 | ||||||||
\(476\) | −10.3207 | −0.473048 | ||||||||
\(477\) | −6.20990 | −0.284332 | ||||||||
\(478\) | −0.112547 | −0.00514778 | ||||||||
\(479\) | 34.9175 | 1.59542 | 0.797710 | − | 0.603041i | \(-0.206044\pi\) | ||||
0.797710 | + | 0.603041i | \(0.206044\pi\) | |||||||
\(480\) | 0.326467 | 0.0149011 | ||||||||
\(481\) | −5.11990 | −0.233447 | ||||||||
\(482\) | −13.8957 | −0.632934 | ||||||||
\(483\) | 4.65526 | 0.211822 | ||||||||
\(484\) | −6.07211 | −0.276005 | ||||||||
\(485\) | −2.08346 | −0.0946053 | ||||||||
\(486\) | 1.00000 | 0.0453609 | ||||||||
\(487\) | −6.46037 | −0.292747 | −0.146374 | − | 0.989229i | \(-0.546760\pi\) | ||||
−0.146374 | + | 0.989229i | \(0.546760\pi\) | |||||||
\(488\) | 2.94460 | 0.133296 | ||||||||
\(489\) | −0.0621204 | −0.00280918 | ||||||||
\(490\) | 1.45208 | 0.0655984 | ||||||||
\(491\) | −0.708520 | −0.0319750 | −0.0159875 | − | 0.999872i | \(-0.505089\pi\) | ||||
−0.0159875 | + | 0.999872i | \(0.505089\pi\) | |||||||
\(492\) | −12.2901 | −0.554081 | ||||||||
\(493\) | −27.0644 | −1.21892 | ||||||||
\(494\) | 19.1001 | 0.859352 | ||||||||
\(495\) | −0.724719 | −0.0325737 | ||||||||
\(496\) | 5.66776 | 0.254490 | ||||||||
\(497\) | −6.58410 | −0.295337 | ||||||||
\(498\) | −7.08850 | −0.317643 | ||||||||
\(499\) | 20.2230 | 0.905304 | 0.452652 | − | 0.891687i | \(-0.350478\pi\) | ||||
0.452652 | + | 0.891687i | \(0.350478\pi\) | |||||||
\(500\) | −3.22987 | −0.144444 | ||||||||
\(501\) | −2.08850 | −0.0933071 | ||||||||
\(502\) | −1.18698 | −0.0529774 | ||||||||
\(503\) | −36.3380 | −1.62023 | −0.810116 | − | 0.586269i | \(-0.800596\pi\) | ||||
−0.810116 | + | 0.586269i | \(0.800596\pi\) | |||||||
\(504\) | 1.59754 | 0.0711600 | ||||||||
\(505\) | −4.00905 | −0.178400 | ||||||||
\(506\) | 6.46879 | 0.287573 | ||||||||
\(507\) | 6.79513 | 0.301782 | ||||||||
\(508\) | −17.9861 | −0.798005 | ||||||||
\(509\) | 4.16857 | 0.184769 | 0.0923844 | − | 0.995723i | \(-0.470551\pi\) | ||||
0.0923844 | + | 0.995723i | \(0.470551\pi\) | |||||||
\(510\) | 2.10910 | 0.0933923 | ||||||||
\(511\) | −12.2892 | −0.543641 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 7.66776 | 0.338540 | ||||||||
\(514\) | 9.49749 | 0.418916 | ||||||||
\(515\) | −6.34990 | −0.279810 | ||||||||
\(516\) | 8.89342 | 0.391511 | ||||||||
\(517\) | 18.3480 | 0.806945 | ||||||||
\(518\) | −3.28357 | −0.144272 | ||||||||
\(519\) | 14.2597 | 0.625932 | ||||||||
\(520\) | −0.813215 | −0.0356618 | ||||||||
\(521\) | −16.3684 | −0.717114 | −0.358557 | − | 0.933508i | \(-0.616731\pi\) | ||||
−0.358557 | + | 0.933508i | \(0.616731\pi\) | |||||||
\(522\) | 4.18930 | 0.183361 | ||||||||
\(523\) | 31.9673 | 1.39783 | 0.698916 | − | 0.715204i | \(-0.253666\pi\) | ||||
0.698916 | + | 0.715204i | \(0.253666\pi\) | |||||||
\(524\) | 7.32898 | 0.320168 | ||||||||
\(525\) | −7.81742 | −0.341180 | ||||||||
\(526\) | 20.2440 | 0.882678 | ||||||||
\(527\) | 36.6158 | 1.59501 | ||||||||
\(528\) | 2.21989 | 0.0966081 | ||||||||
\(529\) | −14.5085 | −0.630804 | ||||||||
\(530\) | 2.02733 | 0.0880614 | ||||||||
\(531\) | −0.283381 | −0.0122977 | ||||||||
\(532\) | 12.2495 | 0.531085 | ||||||||
\(533\) | 30.6141 | 1.32605 | ||||||||
\(534\) | 0.513252 | 0.0222106 | ||||||||
\(535\) | −2.01113 | −0.0869486 | ||||||||
\(536\) | 5.67353 | 0.245059 | ||||||||
\(537\) | −24.5192 | −1.05808 | ||||||||
\(538\) | 9.55885 | 0.412111 | ||||||||
\(539\) | 9.87377 | 0.425293 | ||||||||
\(540\) | −0.326467 | −0.0140489 | ||||||||
\(541\) | 31.0977 | 1.33700 | 0.668498 | − | 0.743714i | \(-0.266937\pi\) | ||||
0.668498 | + | 0.743714i | \(0.266937\pi\) | |||||||
\(542\) | −24.0547 | −1.03324 | ||||||||
\(543\) | 18.2125 | 0.781575 | ||||||||
\(544\) | −6.46037 | −0.276986 | ||||||||
\(545\) | −3.16028 | −0.135372 | ||||||||
\(546\) | −3.97940 | −0.170303 | ||||||||
\(547\) | −21.5025 | −0.919381 | −0.459691 | − | 0.888079i | \(-0.652040\pi\) | ||||
−0.459691 | + | 0.888079i | \(0.652040\pi\) | |||||||
\(548\) | −8.66776 | −0.370268 | ||||||||
\(549\) | −2.94460 | −0.125673 | ||||||||
\(550\) | −10.8628 | −0.463193 | ||||||||
\(551\) | 32.1225 | 1.36847 | ||||||||
\(552\) | 2.91402 | 0.124029 | ||||||||
\(553\) | 0.186218 | 0.00791879 | ||||||||
\(554\) | −30.8702 | −1.31155 | ||||||||
\(555\) | 0.671018 | 0.0284831 | ||||||||
\(556\) | 5.85706 | 0.248395 | ||||||||
\(557\) | 0.144826 | 0.00613649 | 0.00306824 | − | 0.999995i | \(-0.499023\pi\) | ||||
0.00306824 | + | 0.999995i | \(0.499023\pi\) | |||||||
\(558\) | −5.66776 | −0.239935 | ||||||||
\(559\) | −22.1531 | −0.936978 | ||||||||
\(560\) | −0.521543 | −0.0220392 | ||||||||
\(561\) | 14.3413 | 0.605490 | ||||||||
\(562\) | −6.78665 | −0.286277 | ||||||||
\(563\) | 26.8290 | 1.13071 | 0.565354 | − | 0.824849i | \(-0.308740\pi\) | ||||
0.565354 | + | 0.824849i | \(0.308740\pi\) | |||||||
\(564\) | 8.26530 | 0.348032 | ||||||||
\(565\) | 1.24030 | 0.0521796 | ||||||||
\(566\) | −12.2466 | −0.514762 | ||||||||
\(567\) | −1.59754 | −0.0670903 | ||||||||
\(568\) | −4.12141 | −0.172930 | ||||||||
\(569\) | −25.5083 | −1.06936 | −0.534682 | − | 0.845054i | \(-0.679569\pi\) | ||||
−0.534682 | + | 0.845054i | \(0.679569\pi\) | |||||||
\(570\) | −2.50327 | −0.104850 | ||||||||
\(571\) | 1.66059 | 0.0694937 | 0.0347468 | − | 0.999396i | \(-0.488938\pi\) | ||||
0.0347468 | + | 0.999396i | \(0.488938\pi\) | |||||||
\(572\) | −5.52964 | −0.231206 | ||||||||
\(573\) | −21.0644 | −0.879980 | ||||||||
\(574\) | 19.6339 | 0.819504 | ||||||||
\(575\) | −14.2595 | −0.594663 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | −9.53888 | −0.397109 | −0.198554 | − | 0.980090i | \(-0.563625\pi\) | ||||
−0.198554 | + | 0.980090i | \(0.563625\pi\) | |||||||
\(578\) | −24.7364 | −1.02890 | ||||||||
\(579\) | 27.0985 | 1.12618 | ||||||||
\(580\) | −1.36767 | −0.0567893 | ||||||||
\(581\) | 11.3241 | 0.469805 | ||||||||
\(582\) | −6.38186 | −0.264537 | ||||||||
\(583\) | 13.7853 | 0.570928 | ||||||||
\(584\) | −7.69257 | −0.318321 | ||||||||
\(585\) | 0.813215 | 0.0336223 | ||||||||
\(586\) | 10.7176 | 0.442739 | ||||||||
\(587\) | 13.8126 | 0.570107 | 0.285053 | − | 0.958512i | \(-0.407989\pi\) | ||||
0.285053 | + | 0.958512i | \(0.407989\pi\) | |||||||
\(588\) | 4.44787 | 0.183427 | ||||||||
\(589\) | −43.4590 | −1.79070 | ||||||||
\(590\) | 0.0925144 | 0.00380876 | ||||||||
\(591\) | −17.7547 | −0.730330 | ||||||||
\(592\) | −2.05540 | −0.0844762 | ||||||||
\(593\) | −9.72780 | −0.399473 | −0.199736 | − | 0.979850i | \(-0.564009\pi\) | ||||
−0.199736 | + | 0.979850i | \(0.564009\pi\) | |||||||
\(594\) | −2.21989 | −0.0910830 | ||||||||
\(595\) | −3.36936 | −0.138130 | ||||||||
\(596\) | −15.7586 | −0.645497 | ||||||||
\(597\) | −20.2190 | −0.827507 | ||||||||
\(598\) | −7.25870 | −0.296830 | ||||||||
\(599\) | 36.0854 | 1.47441 | 0.737204 | − | 0.675670i | \(-0.236146\pi\) | ||||
0.737204 | + | 0.675670i | \(0.236146\pi\) | |||||||
\(600\) | −4.89342 | −0.199773 | ||||||||
\(601\) | 11.5725 | 0.472054 | 0.236027 | − | 0.971747i | \(-0.424155\pi\) | ||||
0.236027 | + | 0.971747i | \(0.424155\pi\) | |||||||
\(602\) | −14.2076 | −0.579058 | ||||||||
\(603\) | −5.67353 | −0.231044 | ||||||||
\(604\) | −7.78263 | −0.316671 | ||||||||
\(605\) | −1.98234 | −0.0805936 | ||||||||
\(606\) | −12.2801 | −0.498846 | ||||||||
\(607\) | 13.4321 | 0.545193 | 0.272596 | − | 0.962129i | \(-0.412118\pi\) | ||||
0.272596 | + | 0.962129i | \(0.412118\pi\) | |||||||
\(608\) | 7.66776 | 0.310969 | ||||||||
\(609\) | −6.69257 | −0.271197 | ||||||||
\(610\) | 0.961315 | 0.0389225 | ||||||||
\(611\) | −20.5885 | −0.832922 | ||||||||
\(612\) | 6.46037 | 0.261145 | ||||||||
\(613\) | −11.7622 | −0.475072 | −0.237536 | − | 0.971379i | \(-0.576340\pi\) | ||||
−0.237536 | + | 0.971379i | \(0.576340\pi\) | |||||||
\(614\) | −6.39669 | −0.258149 | ||||||||
\(615\) | −4.01231 | −0.161792 | ||||||||
\(616\) | −3.54635 | −0.142887 | ||||||||
\(617\) | −42.4730 | −1.70990 | −0.854950 | − | 0.518711i | \(-0.826412\pi\) | ||||
−0.854950 | + | 0.518711i | \(0.826412\pi\) | |||||||
\(618\) | −19.4504 | −0.782409 | ||||||||
\(619\) | −43.7701 | −1.75927 | −0.879635 | − | 0.475649i | \(-0.842213\pi\) | ||||
−0.879635 | + | 0.475649i | \(0.842213\pi\) | |||||||
\(620\) | 1.85033 | 0.0743112 | ||||||||
\(621\) | −2.91402 | −0.116936 | ||||||||
\(622\) | 6.95535 | 0.278884 | ||||||||
\(623\) | −0.819940 | −0.0328502 | ||||||||
\(624\) | −2.49096 | −0.0997181 | ||||||||
\(625\) | 23.4127 | 0.936506 | ||||||||
\(626\) | −6.45365 | −0.257940 | ||||||||
\(627\) | −17.0216 | −0.679775 | ||||||||
\(628\) | 3.52575 | 0.140693 | ||||||||
\(629\) | −13.2786 | −0.529453 | ||||||||
\(630\) | 0.521543 | 0.0207788 | ||||||||
\(631\) | −38.5593 | −1.53502 | −0.767511 | − | 0.641036i | \(-0.778505\pi\) | ||||
−0.767511 | + | 0.641036i | \(0.778505\pi\) | |||||||
\(632\) | 0.116565 | 0.00463673 | ||||||||
\(633\) | 11.3049 | 0.449331 | ||||||||
\(634\) | −5.56695 | −0.221092 | ||||||||
\(635\) | −5.87187 | −0.233018 | ||||||||
\(636\) | 6.20990 | 0.246239 | ||||||||
\(637\) | −11.0795 | −0.438984 | ||||||||
\(638\) | −9.29977 | −0.368181 | ||||||||
\(639\) | 4.12141 | 0.163040 | ||||||||
\(640\) | −0.326467 | −0.0129047 | ||||||||
\(641\) | 47.9344 | 1.89330 | 0.946648 | − | 0.322268i | \(-0.104445\pi\) | ||||
0.946648 | + | 0.322268i | \(0.104445\pi\) | |||||||
\(642\) | −6.16028 | −0.243127 | ||||||||
\(643\) | −33.1025 | −1.30544 | −0.652718 | − | 0.757601i | \(-0.726371\pi\) | ||||
−0.652718 | + | 0.757601i | \(0.726371\pi\) | |||||||
\(644\) | −4.65526 | −0.183443 | ||||||||
\(645\) | 2.90340 | 0.114321 | ||||||||
\(646\) | 49.5366 | 1.94899 | ||||||||
\(647\) | 21.7062 | 0.853359 | 0.426680 | − | 0.904403i | \(-0.359683\pi\) | ||||
0.426680 | + | 0.904403i | \(0.359683\pi\) | |||||||
\(648\) | −1.00000 | −0.0392837 | ||||||||
\(649\) | 0.629073 | 0.0246933 | ||||||||
\(650\) | 12.1893 | 0.478104 | ||||||||
\(651\) | 9.05446 | 0.354872 | ||||||||
\(652\) | 0.0621204 | 0.00243282 | ||||||||
\(653\) | −32.0324 | −1.25352 | −0.626761 | − | 0.779211i | \(-0.715620\pi\) | ||||
−0.626761 | + | 0.779211i | \(0.715620\pi\) | |||||||
\(654\) | −9.68026 | −0.378528 | ||||||||
\(655\) | 2.39267 | 0.0934893 | ||||||||
\(656\) | 12.2901 | 0.479848 | ||||||||
\(657\) | 7.69257 | 0.300116 | ||||||||
\(658\) | −13.2041 | −0.514750 | ||||||||
\(659\) | −21.7155 | −0.845915 | −0.422958 | − | 0.906149i | \(-0.639008\pi\) | ||||
−0.422958 | + | 0.906149i | \(0.639008\pi\) | |||||||
\(660\) | 0.724719 | 0.0282096 | ||||||||
\(661\) | 17.2593 | 0.671310 | 0.335655 | − | 0.941985i | \(-0.391042\pi\) | ||||
0.335655 | + | 0.941985i | \(0.391042\pi\) | |||||||
\(662\) | 24.9131 | 0.968275 | ||||||||
\(663\) | −16.0925 | −0.624981 | ||||||||
\(664\) | 7.08850 | 0.275087 | ||||||||
\(665\) | 3.99906 | 0.155077 | ||||||||
\(666\) | 2.05540 | 0.0796449 | ||||||||
\(667\) | −12.2077 | −0.472684 | ||||||||
\(668\) | 2.08850 | 0.0808063 | ||||||||
\(669\) | 1.00000 | 0.0386622 | ||||||||
\(670\) | 1.85222 | 0.0715575 | ||||||||
\(671\) | 6.53669 | 0.252346 | ||||||||
\(672\) | −1.59754 | −0.0616264 | ||||||||
\(673\) | 22.1687 | 0.854541 | 0.427270 | − | 0.904124i | \(-0.359475\pi\) | ||||
0.427270 | + | 0.904124i | \(0.359475\pi\) | |||||||
\(674\) | −12.2978 | −0.473692 | ||||||||
\(675\) | 4.89342 | 0.188348 | ||||||||
\(676\) | −6.79513 | −0.261351 | ||||||||
\(677\) | 4.75877 | 0.182894 | 0.0914472 | − | 0.995810i | \(-0.470851\pi\) | ||||
0.0914472 | + | 0.995810i | \(0.470851\pi\) | |||||||
\(678\) | 3.79915 | 0.145905 | ||||||||
\(679\) | 10.1953 | 0.391258 | ||||||||
\(680\) | −2.10910 | −0.0808801 | ||||||||
\(681\) | −18.8653 | −0.722922 | ||||||||
\(682\) | 12.5818 | 0.481781 | ||||||||
\(683\) | 18.3973 | 0.703954 | 0.351977 | − | 0.936009i | \(-0.385510\pi\) | ||||
0.351977 | + | 0.936009i | \(0.385510\pi\) | |||||||
\(684\) | −7.66776 | −0.293184 | ||||||||
\(685\) | −2.82973 | −0.108119 | ||||||||
\(686\) | −18.2884 | −0.698255 | ||||||||
\(687\) | −25.1506 | −0.959556 | ||||||||
\(688\) | −8.89342 | −0.339058 | ||||||||
\(689\) | −15.4686 | −0.589307 | ||||||||
\(690\) | 0.951330 | 0.0362165 | ||||||||
\(691\) | 28.6842 | 1.09120 | 0.545598 | − | 0.838047i | \(-0.316302\pi\) | ||||
0.545598 | + | 0.838047i | \(0.316302\pi\) | |||||||
\(692\) | −14.2597 | −0.542073 | ||||||||
\(693\) | 3.54635 | 0.134715 | ||||||||
\(694\) | 2.80103 | 0.106326 | ||||||||
\(695\) | 1.91213 | 0.0725314 | ||||||||
\(696\) | −4.18930 | −0.158795 | ||||||||
\(697\) | 79.3987 | 3.00744 | ||||||||
\(698\) | −13.6847 | −0.517972 | ||||||||
\(699\) | 2.13736 | 0.0808423 | ||||||||
\(700\) | 7.81742 | 0.295471 | ||||||||
\(701\) | −49.5192 | −1.87032 | −0.935158 | − | 0.354231i | \(-0.884743\pi\) | ||||
−0.935158 | + | 0.354231i | \(0.884743\pi\) | |||||||
\(702\) | 2.49096 | 0.0940151 | ||||||||
\(703\) | 15.7603 | 0.594410 | ||||||||
\(704\) | −2.21989 | −0.0836651 | ||||||||
\(705\) | 2.69834 | 0.101625 | ||||||||
\(706\) | −19.7430 | −0.743038 | ||||||||
\(707\) | 19.6180 | 0.737809 | ||||||||
\(708\) | 0.283381 | 0.0106501 | ||||||||
\(709\) | −11.5396 | −0.433380 | −0.216690 | − | 0.976240i | \(-0.569526\pi\) | ||||
−0.216690 | + | 0.976240i | \(0.569526\pi\) | |||||||
\(710\) | −1.34550 | −0.0504958 | ||||||||
\(711\) | −0.116565 | −0.00437155 | ||||||||
\(712\) | −0.513252 | −0.0192349 | ||||||||
\(713\) | 16.5160 | 0.618528 | ||||||||
\(714\) | −10.3207 | −0.386242 | ||||||||
\(715\) | −1.80524 | −0.0675123 | ||||||||
\(716\) | 24.5192 | 0.916327 | ||||||||
\(717\) | −0.112547 | −0.00420314 | ||||||||
\(718\) | −9.56526 | −0.356972 | ||||||||
\(719\) | −4.75550 | −0.177350 | −0.0886750 | − | 0.996061i | \(-0.528263\pi\) | ||||
−0.0886750 | + | 0.996061i | \(0.528263\pi\) | |||||||
\(720\) | 0.326467 | 0.0121667 | ||||||||
\(721\) | 31.0727 | 1.15721 | ||||||||
\(722\) | −39.7945 | −1.48100 | ||||||||
\(723\) | −13.8957 | −0.516788 | ||||||||
\(724\) | −18.2125 | −0.676864 | ||||||||
\(725\) | 20.5000 | 0.761351 | ||||||||
\(726\) | −6.07211 | −0.225357 | ||||||||
\(727\) | 11.4025 | 0.422894 | 0.211447 | − | 0.977389i | \(-0.432182\pi\) | ||||
0.211447 | + | 0.977389i | \(0.432182\pi\) | |||||||
\(728\) | 3.97940 | 0.147486 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −2.51137 | −0.0929499 | ||||||||
\(731\) | −57.4548 | −2.12504 | ||||||||
\(732\) | 2.94460 | 0.108836 | ||||||||
\(733\) | 4.38123 | 0.161824 | 0.0809122 | − | 0.996721i | \(-0.474217\pi\) | ||||
0.0809122 | + | 0.996721i | \(0.474217\pi\) | |||||||
\(734\) | 24.7755 | 0.914480 | ||||||||
\(735\) | 1.45208 | 0.0535608 | ||||||||
\(736\) | −2.91402 | −0.107412 | ||||||||
\(737\) | 12.5946 | 0.463928 | ||||||||
\(738\) | −12.2901 | −0.452405 | ||||||||
\(739\) | 19.2143 | 0.706810 | 0.353405 | − | 0.935471i | \(-0.385024\pi\) | ||||
0.353405 | + | 0.935471i | \(0.385024\pi\) | |||||||
\(740\) | −0.671018 | −0.0246671 | ||||||||
\(741\) | 19.1001 | 0.701658 | ||||||||
\(742\) | −9.92055 | −0.364195 | ||||||||
\(743\) | 11.5536 | 0.423862 | 0.211931 | − | 0.977285i | \(-0.432025\pi\) | ||||
0.211931 | + | 0.977285i | \(0.432025\pi\) | |||||||
\(744\) | 5.66776 | 0.207790 | ||||||||
\(745\) | −5.14465 | −0.188485 | ||||||||
\(746\) | −35.7002 | −1.30708 | ||||||||
\(747\) | −7.08850 | −0.259354 | ||||||||
\(748\) | −14.3413 | −0.524370 | ||||||||
\(749\) | 9.84128 | 0.359593 | ||||||||
\(750\) | −3.22987 | −0.117938 | ||||||||
\(751\) | −28.3814 | −1.03565 | −0.517827 | − | 0.855486i | \(-0.673259\pi\) | ||||
−0.517827 | + | 0.855486i | \(0.673259\pi\) | |||||||
\(752\) | −8.26530 | −0.301404 | ||||||||
\(753\) | −1.18698 | −0.0432558 | ||||||||
\(754\) | 10.4354 | 0.380034 | ||||||||
\(755\) | −2.54077 | −0.0924680 | ||||||||
\(756\) | 1.59754 | 0.0581019 | ||||||||
\(757\) | −2.52311 | −0.0917039 | −0.0458520 | − | 0.998948i | \(-0.514600\pi\) | ||||
−0.0458520 | + | 0.998948i | \(0.514600\pi\) | |||||||
\(758\) | 14.3802 | 0.522311 | ||||||||
\(759\) | 6.46879 | 0.234802 | ||||||||
\(760\) | 2.50327 | 0.0908030 | ||||||||
\(761\) | −38.2137 | −1.38525 | −0.692623 | − | 0.721300i | \(-0.743545\pi\) | ||||
−0.692623 | + | 0.721300i | \(0.743545\pi\) | |||||||
\(762\) | −17.9861 | −0.651569 | ||||||||
\(763\) | 15.4646 | 0.559855 | ||||||||
\(764\) | 21.0644 | 0.762085 | ||||||||
\(765\) | 2.10910 | 0.0762545 | ||||||||
\(766\) | 30.9671 | 1.11889 | ||||||||
\(767\) | −0.705890 | −0.0254882 | ||||||||
\(768\) | −1.00000 | −0.0360844 | ||||||||
\(769\) | −18.2995 | −0.659898 | −0.329949 | − | 0.943999i | \(-0.607032\pi\) | ||||
−0.329949 | + | 0.943999i | \(0.607032\pi\) | |||||||
\(770\) | −1.15777 | −0.0417230 | ||||||||
\(771\) | 9.49749 | 0.342044 | ||||||||
\(772\) | −27.0985 | −0.975296 | ||||||||
\(773\) | −14.7714 | −0.531290 | −0.265645 | − | 0.964071i | \(-0.585585\pi\) | ||||
−0.265645 | + | 0.964071i | \(0.585585\pi\) | |||||||
\(774\) | 8.89342 | 0.319667 | ||||||||
\(775\) | −27.7347 | −0.996260 | ||||||||
\(776\) | 6.38186 | 0.229095 | ||||||||
\(777\) | −3.28357 | −0.117797 | ||||||||
\(778\) | −8.50767 | −0.305015 | ||||||||
\(779\) | −94.2376 | −3.37641 | ||||||||
\(780\) | −0.813215 | −0.0291178 | ||||||||
\(781\) | −9.14905 | −0.327379 | ||||||||
\(782\) | −18.8257 | −0.673204 | ||||||||
\(783\) | 4.18930 | 0.149713 | ||||||||
\(784\) | −4.44787 | −0.158853 | ||||||||
\(785\) | 1.15104 | 0.0410824 | ||||||||
\(786\) | 7.32898 | 0.261416 | ||||||||
\(787\) | −3.28144 | −0.116971 | −0.0584853 | − | 0.998288i | \(-0.518627\pi\) | ||||
−0.0584853 | + | 0.998288i | \(0.518627\pi\) | |||||||
\(788\) | 17.7547 | 0.632485 | ||||||||
\(789\) | 20.2440 | 0.720704 | ||||||||
\(790\) | 0.0380547 | 0.00135393 | ||||||||
\(791\) | −6.06928 | −0.215799 | ||||||||
\(792\) | 2.21989 | 0.0788802 | ||||||||
\(793\) | −7.33489 | −0.260469 | ||||||||
\(794\) | 14.2651 | 0.506250 | ||||||||
\(795\) | 2.02733 | 0.0719018 | ||||||||
\(796\) | 20.2190 | 0.716642 | ||||||||
\(797\) | 15.6573 | 0.554612 | 0.277306 | − | 0.960782i | \(-0.410558\pi\) | ||||
0.277306 | + | 0.960782i | \(0.410558\pi\) | |||||||
\(798\) | 12.2495 | 0.433629 | ||||||||
\(799\) | −53.3969 | −1.88905 | ||||||||
\(800\) | 4.89342 | 0.173009 | ||||||||
\(801\) | 0.513252 | 0.0181349 | ||||||||
\(802\) | −31.5109 | −1.11269 | ||||||||
\(803\) | −17.0766 | −0.602621 | ||||||||
\(804\) | 5.67353 | 0.200090 | ||||||||
\(805\) | −1.51979 | −0.0535654 | ||||||||
\(806\) | −14.1181 | −0.497290 | ||||||||
\(807\) | 9.55885 | 0.336488 | ||||||||
\(808\) | 12.2801 | 0.432013 | ||||||||
\(809\) | −31.0320 | −1.09103 | −0.545513 | − | 0.838102i | \(-0.683665\pi\) | ||||
−0.545513 | + | 0.838102i | \(0.683665\pi\) | |||||||
\(810\) | −0.326467 | −0.0114709 | ||||||||
\(811\) | 22.1470 | 0.777688 | 0.388844 | − | 0.921304i | \(-0.372875\pi\) | ||||
0.388844 | + | 0.921304i | \(0.372875\pi\) | |||||||
\(812\) | 6.69257 | 0.234863 | ||||||||
\(813\) | −24.0547 | −0.843633 | ||||||||
\(814\) | −4.56274 | −0.159924 | ||||||||
\(815\) | 0.0202802 | 0.000710385 0 | ||||||||
\(816\) | −6.46037 | −0.226158 | ||||||||
\(817\) | 68.1926 | 2.38576 | ||||||||
\(818\) | 9.16293 | 0.320374 | ||||||||
\(819\) | −3.97940 | −0.139051 | ||||||||
\(820\) | 4.01231 | 0.140116 | ||||||||
\(821\) | −7.24105 | −0.252715 | −0.126357 | − | 0.991985i | \(-0.540329\pi\) | ||||
−0.126357 | + | 0.991985i | \(0.540329\pi\) | |||||||
\(822\) | −8.66776 | −0.302323 | ||||||||
\(823\) | 12.0581 | 0.420319 | 0.210160 | − | 0.977667i | \(-0.432602\pi\) | ||||
0.210160 | + | 0.977667i | \(0.432602\pi\) | |||||||
\(824\) | 19.4504 | 0.677586 | ||||||||
\(825\) | −10.8628 | −0.378195 | ||||||||
\(826\) | −0.452712 | −0.0157519 | ||||||||
\(827\) | 28.5104 | 0.991403 | 0.495701 | − | 0.868493i | \(-0.334911\pi\) | ||||
0.495701 | + | 0.868493i | \(0.334911\pi\) | |||||||
\(828\) | 2.91402 | 0.101269 | ||||||||
\(829\) | 9.20256 | 0.319618 | 0.159809 | − | 0.987148i | \(-0.448912\pi\) | ||||
0.159809 | + | 0.987148i | \(0.448912\pi\) | |||||||
\(830\) | 2.31416 | 0.0803256 | ||||||||
\(831\) | −30.8702 | −1.07088 | ||||||||
\(832\) | 2.49096 | 0.0863584 | ||||||||
\(833\) | −28.7349 | −0.995606 | ||||||||
\(834\) | 5.85706 | 0.202813 | ||||||||
\(835\) | 0.681824 | 0.0235955 | ||||||||
\(836\) | 17.0216 | 0.588703 | ||||||||
\(837\) | −5.66776 | −0.195906 | ||||||||
\(838\) | 29.4201 | 1.01630 | ||||||||
\(839\) | −16.9775 | −0.586129 | −0.293064 | − | 0.956093i | \(-0.594675\pi\) | ||||
−0.293064 | + | 0.956093i | \(0.594675\pi\) | |||||||
\(840\) | −0.521543 | −0.0179949 | ||||||||
\(841\) | −11.4498 | −0.394819 | ||||||||
\(842\) | −28.8396 | −0.993878 | ||||||||
\(843\) | −6.78665 | −0.233745 | ||||||||
\(844\) | −11.3049 | −0.389132 | ||||||||
\(845\) | −2.21838 | −0.0763147 | ||||||||
\(846\) | 8.26530 | 0.284167 | ||||||||
\(847\) | 9.70042 | 0.333310 | ||||||||
\(848\) | −6.20990 | −0.213249 | ||||||||
\(849\) | −12.2466 | −0.420302 | ||||||||
\(850\) | 31.6133 | 1.08433 | ||||||||
\(851\) | −5.98946 | −0.205316 | ||||||||
\(852\) | −4.12141 | −0.141197 | ||||||||
\(853\) | 26.0908 | 0.893333 | 0.446666 | − | 0.894701i | \(-0.352611\pi\) | ||||
0.446666 | + | 0.894701i | \(0.352611\pi\) | |||||||
\(854\) | −4.70412 | −0.160972 | ||||||||
\(855\) | −2.50327 | −0.0856099 | ||||||||
\(856\) | 6.16028 | 0.210554 | ||||||||
\(857\) | −14.7870 | −0.505115 | −0.252558 | − | 0.967582i | \(-0.581272\pi\) | ||||
−0.252558 | + | 0.967582i | \(0.581272\pi\) | |||||||
\(858\) | −5.52964 | −0.188779 | ||||||||
\(859\) | 25.5670 | 0.872334 | 0.436167 | − | 0.899866i | \(-0.356336\pi\) | ||||
0.436167 | + | 0.899866i | \(0.356336\pi\) | |||||||
\(860\) | −2.90340 | −0.0990053 | ||||||||
\(861\) | 19.6339 | 0.669122 | ||||||||
\(862\) | −29.9517 | −1.02016 | ||||||||
\(863\) | 44.4272 | 1.51232 | 0.756159 | − | 0.654388i | \(-0.227074\pi\) | ||||
0.756159 | + | 0.654388i | \(0.227074\pi\) | |||||||
\(864\) | 1.00000 | 0.0340207 | ||||||||
\(865\) | −4.65532 | −0.158286 | ||||||||
\(866\) | 11.1833 | 0.380025 | ||||||||
\(867\) | −24.7364 | −0.840093 | ||||||||
\(868\) | −9.05446 | −0.307328 | ||||||||
\(869\) | 0.258762 | 0.00877790 | ||||||||
\(870\) | −1.36767 | −0.0463683 | ||||||||
\(871\) | −14.1325 | −0.478863 | ||||||||
\(872\) | 9.68026 | 0.327815 | ||||||||
\(873\) | −6.38186 | −0.215993 | ||||||||
\(874\) | 22.3440 | 0.755797 | ||||||||
\(875\) | 5.15984 | 0.174435 | ||||||||
\(876\) | −7.69257 | −0.259908 | ||||||||
\(877\) | −11.9340 | −0.402983 | −0.201491 | − | 0.979490i | \(-0.564579\pi\) | ||||
−0.201491 | + | 0.979490i | \(0.564579\pi\) | |||||||
\(878\) | 30.8644 | 1.04162 | ||||||||
\(879\) | 10.7176 | 0.361495 | ||||||||
\(880\) | −0.724719 | −0.0244303 | ||||||||
\(881\) | 34.8986 | 1.17576 | 0.587882 | − | 0.808947i | \(-0.299962\pi\) | ||||
0.587882 | + | 0.808947i | \(0.299962\pi\) | |||||||
\(882\) | 4.44787 | 0.149768 | ||||||||
\(883\) | −37.8330 | −1.27318 | −0.636591 | − | 0.771202i | \(-0.719656\pi\) | ||||
−0.636591 | + | 0.771202i | \(0.719656\pi\) | |||||||
\(884\) | 16.0925 | 0.541250 | ||||||||
\(885\) | 0.0925144 | 0.00310984 | ||||||||
\(886\) | 35.8542 | 1.20455 | ||||||||
\(887\) | −41.1789 | −1.38265 | −0.691326 | − | 0.722543i | \(-0.742973\pi\) | ||||
−0.691326 | + | 0.722543i | \(0.742973\pi\) | |||||||
\(888\) | −2.05540 | −0.0689745 | ||||||||
\(889\) | 28.7335 | 0.963691 | ||||||||
\(890\) | −0.167560 | −0.00561661 | ||||||||
\(891\) | −2.21989 | −0.0743690 | ||||||||
\(892\) | −1.00000 | −0.0334825 | ||||||||
\(893\) | 63.3763 | 2.12081 | ||||||||
\(894\) | −15.7586 | −0.527046 | ||||||||
\(895\) | 8.00471 | 0.267568 | ||||||||
\(896\) | 1.59754 | 0.0533700 | ||||||||
\(897\) | −7.25870 | −0.242361 | ||||||||
\(898\) | 15.7066 | 0.524137 | ||||||||
\(899\) | −23.7439 | −0.791905 | ||||||||
\(900\) | −4.89342 | −0.163114 | ||||||||
\(901\) | −40.1183 | −1.33653 | ||||||||
\(902\) | 27.2826 | 0.908412 | ||||||||
\(903\) | −14.2076 | −0.472799 | ||||||||
\(904\) | −3.79915 | −0.126358 | ||||||||
\(905\) | −5.94579 | −0.197645 | ||||||||
\(906\) | −7.78263 | −0.258561 | ||||||||
\(907\) | −53.0797 | −1.76248 | −0.881241 | − | 0.472668i | \(-0.843291\pi\) | ||||
−0.881241 | + | 0.472668i | \(0.843291\pi\) | |||||||
\(908\) | 18.8653 | 0.626069 | ||||||||
\(909\) | −12.2801 | −0.407306 | ||||||||
\(910\) | 1.29914 | 0.0430661 | ||||||||
\(911\) | 40.1408 | 1.32992 | 0.664961 | − | 0.746878i | \(-0.268448\pi\) | ||||
0.664961 | + | 0.746878i | \(0.268448\pi\) | |||||||
\(912\) | 7.66776 | 0.253905 | ||||||||
\(913\) | 15.7357 | 0.520774 | ||||||||
\(914\) | 29.0459 | 0.960754 | ||||||||
\(915\) | 0.961315 | 0.0317801 | ||||||||
\(916\) | 25.1506 | 0.831000 | ||||||||
\(917\) | −11.7083 | −0.386643 | ||||||||
\(918\) | 6.46037 | 0.213224 | ||||||||
\(919\) | −23.1072 | −0.762237 | −0.381118 | − | 0.924526i | \(-0.624461\pi\) | ||||
−0.381118 | + | 0.924526i | \(0.624461\pi\) | |||||||
\(920\) | −0.951330 | −0.0313644 | ||||||||
\(921\) | −6.39669 | −0.210778 | ||||||||
\(922\) | −21.5743 | −0.710512 | ||||||||
\(923\) | 10.2662 | 0.337918 | ||||||||
\(924\) | −3.54635 | −0.116666 | ||||||||
\(925\) | 10.0579 | 0.330702 | ||||||||
\(926\) | −24.3686 | −0.800802 | ||||||||
\(927\) | −19.4504 | −0.638835 | ||||||||
\(928\) | 4.18930 | 0.137521 | ||||||||
\(929\) | −1.79556 | −0.0589105 | −0.0294553 | − | 0.999566i | \(-0.509377\pi\) | ||||
−0.0294553 | + | 0.999566i | \(0.509377\pi\) | |||||||
\(930\) | 1.85033 | 0.0606748 | ||||||||
\(931\) | 34.1052 | 1.11775 | ||||||||
\(932\) | −2.13736 | −0.0700115 | ||||||||
\(933\) | 6.95535 | 0.227708 | ||||||||
\(934\) | 32.4960 | 1.06330 | ||||||||
\(935\) | −4.68195 | −0.153116 | ||||||||
\(936\) | −2.49096 | −0.0814195 | ||||||||
\(937\) | −9.00535 | −0.294192 | −0.147096 | − | 0.989122i | \(-0.546993\pi\) | ||||
−0.147096 | + | 0.989122i | \(0.546993\pi\) | |||||||
\(938\) | −9.06369 | −0.295940 | ||||||||
\(939\) | −6.45365 | −0.210607 | ||||||||
\(940\) | −2.69834 | −0.0880103 | ||||||||
\(941\) | −13.2698 | −0.432584 | −0.216292 | − | 0.976329i | \(-0.569396\pi\) | ||||
−0.216292 | + | 0.976329i | \(0.569396\pi\) | |||||||
\(942\) | 3.52575 | 0.114875 | ||||||||
\(943\) | 35.8136 | 1.16625 | ||||||||
\(944\) | −0.283381 | −0.00922326 | ||||||||
\(945\) | 0.521543 | 0.0169658 | ||||||||
\(946\) | −19.7424 | −0.641880 | ||||||||
\(947\) | 38.7970 | 1.26073 | 0.630366 | − | 0.776298i | \(-0.282905\pi\) | ||||
0.630366 | + | 0.776298i | \(0.282905\pi\) | |||||||
\(948\) | 0.116565 | 0.00378587 | ||||||||
\(949\) | 19.1619 | 0.622020 | ||||||||
\(950\) | −37.5216 | −1.21736 | ||||||||
\(951\) | −5.56695 | −0.180521 | ||||||||
\(952\) | 10.3207 | 0.334496 | ||||||||
\(953\) | 57.9423 | 1.87694 | 0.938468 | − | 0.345367i | \(-0.112246\pi\) | ||||
0.938468 | + | 0.345367i | \(0.112246\pi\) | |||||||
\(954\) | 6.20990 | 0.201053 | ||||||||
\(955\) | 6.87684 | 0.222529 | ||||||||
\(956\) | 0.112547 | 0.00364003 | ||||||||
\(957\) | −9.29977 | −0.300619 | ||||||||
\(958\) | −34.9175 | −1.12813 | ||||||||
\(959\) | 13.8471 | 0.447145 | ||||||||
\(960\) | −0.326467 | −0.0105367 | ||||||||
\(961\) | 1.12348 | 0.0362414 | ||||||||
\(962\) | 5.11990 | 0.165072 | ||||||||
\(963\) | −6.16028 | −0.198512 | ||||||||
\(964\) | 13.8957 | 0.447552 | ||||||||
\(965\) | −8.84675 | −0.284787 | ||||||||
\(966\) | −4.65526 | −0.149780 | ||||||||
\(967\) | 35.0066 | 1.12574 | 0.562868 | − | 0.826547i | \(-0.309698\pi\) | ||||
0.562868 | + | 0.826547i | \(0.309698\pi\) | |||||||
\(968\) | 6.07211 | 0.195165 | ||||||||
\(969\) | 49.5366 | 1.59134 | ||||||||
\(970\) | 2.08346 | 0.0668960 | ||||||||
\(971\) | 31.1405 | 0.999345 | 0.499672 | − | 0.866214i | \(-0.333454\pi\) | ||||
0.499672 | + | 0.866214i | \(0.333454\pi\) | |||||||
\(972\) | −1.00000 | −0.0320750 | ||||||||
\(973\) | −9.35688 | −0.299968 | ||||||||
\(974\) | 6.46037 | 0.207004 | ||||||||
\(975\) | 12.1893 | 0.390370 | ||||||||
\(976\) | −2.94460 | −0.0942545 | ||||||||
\(977\) | −9.44587 | −0.302200 | −0.151100 | − | 0.988518i | \(-0.548282\pi\) | ||||
−0.151100 | + | 0.988518i | \(0.548282\pi\) | |||||||
\(978\) | 0.0621204 | 0.00198639 | ||||||||
\(979\) | −1.13936 | −0.0364141 | ||||||||
\(980\) | −1.45208 | −0.0463850 | ||||||||
\(981\) | −9.68026 | −0.309067 | ||||||||
\(982\) | 0.708520 | 0.0226098 | ||||||||
\(983\) | −20.5690 | −0.656051 | −0.328025 | − | 0.944669i | \(-0.606383\pi\) | ||||
−0.328025 | + | 0.944669i | \(0.606383\pi\) | |||||||
\(984\) | 12.2901 | 0.391794 | ||||||||
\(985\) | 5.79631 | 0.184686 | ||||||||
\(986\) | 27.0644 | 0.861908 | ||||||||
\(987\) | −13.2041 | −0.420292 | ||||||||
\(988\) | −19.1001 | −0.607654 | ||||||||
\(989\) | −25.9156 | −0.824068 | ||||||||
\(990\) | 0.724719 | 0.0230331 | ||||||||
\(991\) | −7.89877 | −0.250913 | −0.125456 | − | 0.992099i | \(-0.540040\pi\) | ||||
−0.125456 | + | 0.992099i | \(0.540040\pi\) | |||||||
\(992\) | −5.66776 | −0.179951 | ||||||||
\(993\) | 24.9131 | 0.790593 | ||||||||
\(994\) | 6.58410 | 0.208835 | ||||||||
\(995\) | 6.60081 | 0.209260 | ||||||||
\(996\) | 7.08850 | 0.224608 | ||||||||
\(997\) | 6.14766 | 0.194698 | 0.0973492 | − | 0.995250i | \(-0.468964\pi\) | ||||
0.0973492 | + | 0.995250i | \(0.468964\pi\) | |||||||
\(998\) | −20.2230 | −0.640147 | ||||||||
\(999\) | 2.05540 | 0.0650298 |
(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 | 1338.2.a.g.1.2 | ✓ | 4 | |
3.2 | odd | 2 | 4014.2.a.q.1.3 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1338.2.a.g.1.2 | ✓ | 4 | 1.1 | even | 1 | trivial | |
4014.2.a.q.1.3 | 4 | 3.2 | odd | 2 |