Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2151,2,Mod(1,2151)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2151, 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("2151.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2151 = 3^{2} \cdot 239 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2151.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: | \(17.1758214748\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} - 4 x^{19} - 21 x^{18} + 96 x^{17} + 164 x^{16} - 936 x^{15} - 540 x^{14} + 4804 x^{13} + 229 x^{12} - 14020 x^{11} + 3356 x^{10} + 23404 x^{9} - 9429 x^{8} - 21252 x^{7} + \cdots + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.11 | ||
Root | \(0.244320\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2151.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.244320 | 0.172761 | 0.0863803 | − | 0.996262i | \(-0.472470\pi\) | ||||
0.0863803 | + | 0.996262i | \(0.472470\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.94031 | −0.970154 | ||||||||
\(5\) | 4.22460 | 1.88930 | 0.944649 | − | 0.328081i | \(-0.106402\pi\) | ||||
0.944649 | + | 0.328081i | \(0.106402\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.0748971 | 0.0283084 | 0.0141542 | − | 0.999900i | \(-0.495494\pi\) | ||||
0.0141542 | + | 0.999900i | \(0.495494\pi\) | |||||||
\(8\) | −0.962697 | −0.340365 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 1.03216 | 0.326396 | ||||||||
\(11\) | 3.64400 | 1.09871 | 0.549354 | − | 0.835590i | \(-0.314874\pi\) | ||||
0.549354 | + | 0.835590i | \(0.314874\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 6.36423 | 1.76512 | 0.882560 | − | 0.470200i | \(-0.155818\pi\) | ||||
0.882560 | + | 0.470200i | \(0.155818\pi\) | |||||||
\(14\) | 0.0182989 | 0.00489058 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 3.64541 | 0.911352 | ||||||||
\(17\) | −2.35633 | −0.571493 | −0.285747 | − | 0.958305i | \(-0.592242\pi\) | ||||
−0.285747 | + | 0.958305i | \(0.592242\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.06774 | 0.244956 | 0.122478 | − | 0.992471i | \(-0.460916\pi\) | ||||
0.122478 | + | 0.992471i | \(0.460916\pi\) | |||||||
\(20\) | −8.19702 | −1.83291 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0.890304 | 0.189813 | ||||||||
\(23\) | −1.33116 | −0.277566 | −0.138783 | − | 0.990323i | \(-0.544319\pi\) | ||||
−0.138783 | + | 0.990323i | \(0.544319\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 12.8473 | 2.56945 | ||||||||
\(26\) | 1.55491 | 0.304943 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −0.145323 | −0.0274635 | ||||||||
\(29\) | −8.25717 | −1.53332 | −0.766659 | − | 0.642054i | \(-0.778082\pi\) | ||||
−0.766659 | + | 0.642054i | \(0.778082\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −7.90166 | −1.41918 | −0.709590 | − | 0.704615i | \(-0.751120\pi\) | ||||
−0.709590 | + | 0.704615i | \(0.751120\pi\) | |||||||
\(32\) | 2.81604 | 0.497811 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −0.575699 | −0.0987315 | ||||||||
\(35\) | 0.316410 | 0.0534831 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2.87745 | −0.473050 | −0.236525 | − | 0.971625i | \(-0.576008\pi\) | ||||
−0.236525 | + | 0.971625i | \(0.576008\pi\) | |||||||
\(38\) | 0.260871 | 0.0423188 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −4.06701 | −0.643051 | ||||||||
\(41\) | 7.12557 | 1.11283 | 0.556414 | − | 0.830905i | \(-0.312177\pi\) | ||||
0.556414 | + | 0.830905i | \(0.312177\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 6.29063 | 0.959313 | 0.479656 | − | 0.877456i | \(-0.340761\pi\) | ||||
0.479656 | + | 0.877456i | \(0.340761\pi\) | |||||||
\(44\) | −7.07048 | −1.06592 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −0.325230 | −0.0479525 | ||||||||
\(47\) | 6.74450 | 0.983786 | 0.491893 | − | 0.870656i | \(-0.336305\pi\) | ||||
0.491893 | + | 0.870656i | \(0.336305\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.99439 | −0.999199 | ||||||||
\(50\) | 3.13884 | 0.443900 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −12.3486 | −1.71244 | ||||||||
\(53\) | 9.74812 | 1.33901 | 0.669504 | − | 0.742809i | \(-0.266507\pi\) | ||||
0.669504 | + | 0.742809i | \(0.266507\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 15.3945 | 2.07579 | ||||||||
\(56\) | −0.0721032 | −0.00963519 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −2.01739 | −0.264897 | ||||||||
\(59\) | −4.34109 | −0.565162 | −0.282581 | − | 0.959243i | \(-0.591191\pi\) | ||||
−0.282581 | + | 0.959243i | \(0.591191\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −13.4316 | −1.71974 | −0.859870 | − | 0.510513i | \(-0.829456\pi\) | ||||
−0.859870 | + | 0.510513i | \(0.829456\pi\) | |||||||
\(62\) | −1.93054 | −0.245178 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −6.60280 | −0.825350 | ||||||||
\(65\) | 26.8863 | 3.33484 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −4.26661 | −0.521249 | −0.260625 | − | 0.965440i | \(-0.583928\pi\) | ||||
−0.260625 | + | 0.965440i | \(0.583928\pi\) | |||||||
\(68\) | 4.57200 | 0.554436 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0.0773054 | 0.00923977 | ||||||||
\(71\) | −14.0313 | −1.66521 | −0.832604 | − | 0.553869i | \(-0.813151\pi\) | ||||
−0.832604 | + | 0.553869i | \(0.813151\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 6.66218 | 0.779749 | 0.389874 | − | 0.920868i | \(-0.372518\pi\) | ||||
0.389874 | + | 0.920868i | \(0.372518\pi\) | |||||||
\(74\) | −0.703019 | −0.0817243 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −2.07174 | −0.237645 | ||||||||
\(77\) | 0.272925 | 0.0311027 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 17.5165 | 1.97077 | 0.985383 | − | 0.170356i | \(-0.0544918\pi\) | ||||
0.985383 | + | 0.170356i | \(0.0544918\pi\) | |||||||
\(80\) | 15.4004 | 1.72182 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 1.74092 | 0.192253 | ||||||||
\(83\) | 11.0622 | 1.21423 | 0.607117 | − | 0.794613i | \(-0.292326\pi\) | ||||
0.607117 | + | 0.794613i | \(0.292326\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −9.95454 | −1.07972 | ||||||||
\(86\) | 1.53693 | 0.165731 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −3.50807 | −0.373961 | ||||||||
\(89\) | 10.5732 | 1.12075 | 0.560376 | − | 0.828238i | \(-0.310657\pi\) | ||||
0.560376 | + | 0.828238i | \(0.310657\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.476662 | 0.0499678 | ||||||||
\(92\) | 2.58286 | 0.269282 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 1.64782 | 0.169959 | ||||||||
\(95\) | 4.51078 | 0.462796 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 9.62047 | 0.976810 | 0.488405 | − | 0.872617i | \(-0.337579\pi\) | ||||
0.488405 | + | 0.872617i | \(0.337579\pi\) | |||||||
\(98\) | −1.70887 | −0.172622 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −24.9276 | −2.49276 | ||||||||
\(101\) | −8.02921 | −0.798936 | −0.399468 | − | 0.916747i | \(-0.630805\pi\) | ||||
−0.399468 | + | 0.916747i | \(0.630805\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1.57808 | 0.155493 | 0.0777465 | − | 0.996973i | \(-0.475228\pi\) | ||||
0.0777465 | + | 0.996973i | \(0.475228\pi\) | |||||||
\(104\) | −6.12683 | −0.600785 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 2.38166 | 0.231328 | ||||||||
\(107\) | −17.8549 | −1.72609 | −0.863047 | − | 0.505123i | \(-0.831447\pi\) | ||||
−0.863047 | + | 0.505123i | \(0.831447\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 3.68362 | 0.352827 | 0.176414 | − | 0.984316i | \(-0.443550\pi\) | ||||
0.176414 | + | 0.984316i | \(0.443550\pi\) | |||||||
\(110\) | 3.76118 | 0.358614 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0.273030 | 0.0257989 | ||||||||
\(113\) | 17.8113 | 1.67555 | 0.837775 | − | 0.546016i | \(-0.183856\pi\) | ||||
0.837775 | + | 0.546016i | \(0.183856\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −5.62362 | −0.524405 | ||||||||
\(116\) | 16.0215 | 1.48755 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −1.06062 | −0.0976377 | ||||||||
\(119\) | −0.176482 | −0.0161781 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 2.27875 | 0.207159 | ||||||||
\(122\) | −3.28161 | −0.297103 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 15.3316 | 1.37682 | ||||||||
\(125\) | 33.1515 | 2.96516 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −10.4238 | −0.924959 | −0.462479 | − | 0.886630i | \(-0.653040\pi\) | ||||
−0.462479 | + | 0.886630i | \(0.653040\pi\) | |||||||
\(128\) | −7.24528 | −0.640398 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 6.56888 | 0.576129 | ||||||||
\(131\) | −1.77066 | −0.154703 | −0.0773514 | − | 0.997004i | \(-0.524646\pi\) | ||||
−0.0773514 | + | 0.997004i | \(0.524646\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.0799706 | 0.00693433 | ||||||||
\(134\) | −1.04242 | −0.0900513 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 2.26843 | 0.194516 | ||||||||
\(137\) | 6.86164 | 0.586229 | 0.293115 | − | 0.956077i | \(-0.405308\pi\) | ||||
0.293115 | + | 0.956077i | \(0.405308\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 8.85784 | 0.751312 | 0.375656 | − | 0.926759i | \(-0.377417\pi\) | ||||
0.375656 | + | 0.926759i | \(0.377417\pi\) | |||||||
\(140\) | −0.613933 | −0.0518868 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −3.42813 | −0.287682 | ||||||||
\(143\) | 23.1913 | 1.93935 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −34.8832 | −2.89690 | ||||||||
\(146\) | 1.62770 | 0.134710 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 5.58314 | 0.458931 | ||||||||
\(149\) | 8.32832 | 0.682283 | 0.341141 | − | 0.940012i | \(-0.389187\pi\) | ||||
0.341141 | + | 0.940012i | \(0.389187\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −23.9749 | −1.95105 | −0.975527 | − | 0.219881i | \(-0.929433\pi\) | ||||
−0.975527 | + | 0.219881i | \(0.929433\pi\) | |||||||
\(152\) | −1.02791 | −0.0833746 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0.0666811 | 0.00537332 | ||||||||
\(155\) | −33.3813 | −2.68125 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −7.07989 | −0.565037 | −0.282518 | − | 0.959262i | \(-0.591170\pi\) | ||||
−0.282518 | + | 0.959262i | \(0.591170\pi\) | |||||||
\(158\) | 4.27965 | 0.340470 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 11.8967 | 0.940513 | ||||||||
\(161\) | −0.0997000 | −0.00785746 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −5.72901 | −0.448731 | −0.224366 | − | 0.974505i | \(-0.572031\pi\) | ||||
−0.224366 | + | 0.974505i | \(0.572031\pi\) | |||||||
\(164\) | −13.8258 | −1.07961 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 2.70272 | 0.209772 | ||||||||
\(167\) | −11.6739 | −0.903356 | −0.451678 | − | 0.892181i | \(-0.649174\pi\) | ||||
−0.451678 | + | 0.892181i | \(0.649174\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 27.5034 | 2.11565 | ||||||||
\(170\) | −2.43210 | −0.186533 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −12.2058 | −0.930681 | ||||||||
\(173\) | −4.00079 | −0.304174 | −0.152087 | − | 0.988367i | \(-0.548599\pi\) | ||||
−0.152087 | + | 0.988367i | \(0.548599\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0.962221 | 0.0727371 | ||||||||
\(176\) | 13.2839 | 1.00131 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 2.58324 | 0.193622 | ||||||||
\(179\) | 18.0881 | 1.35197 | 0.675985 | − | 0.736915i | \(-0.263718\pi\) | ||||
0.675985 | + | 0.736915i | \(0.263718\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 12.0863 | 0.898366 | 0.449183 | − | 0.893440i | \(-0.351715\pi\) | ||||
0.449183 | + | 0.893440i | \(0.351715\pi\) | |||||||
\(182\) | 0.116458 | 0.00863246 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 1.28150 | 0.0944738 | ||||||||
\(185\) | −12.1561 | −0.893732 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −8.58646 | −0.627904 | ||||||||
\(188\) | −13.0864 | −0.954424 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 1.10207 | 0.0799529 | ||||||||
\(191\) | −8.49649 | −0.614785 | −0.307392 | − | 0.951583i | \(-0.599456\pi\) | ||||
−0.307392 | + | 0.951583i | \(0.599456\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −14.8139 | −1.06633 | −0.533164 | − | 0.846012i | \(-0.678997\pi\) | ||||
−0.533164 | + | 0.846012i | \(0.678997\pi\) | |||||||
\(194\) | 2.35048 | 0.168754 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 13.5713 | 0.969376 | ||||||||
\(197\) | 3.15281 | 0.224629 | 0.112314 | − | 0.993673i | \(-0.464174\pi\) | ||||
0.112314 | + | 0.993673i | \(0.464174\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −16.0694 | −1.13913 | −0.569563 | − | 0.821947i | \(-0.692888\pi\) | ||||
−0.569563 | + | 0.821947i | \(0.692888\pi\) | |||||||
\(200\) | −12.3680 | −0.874551 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −1.96170 | −0.138025 | ||||||||
\(203\) | −0.618438 | −0.0434058 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 30.1027 | 2.10246 | ||||||||
\(206\) | 0.385557 | 0.0268630 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 23.2002 | 1.60865 | ||||||||
\(209\) | 3.89085 | 0.269136 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 16.8371 | 1.15912 | 0.579558 | − | 0.814931i | \(-0.303225\pi\) | ||||
0.579558 | + | 0.814931i | \(0.303225\pi\) | |||||||
\(212\) | −18.9144 | −1.29904 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −4.36231 | −0.298201 | ||||||||
\(215\) | 26.5754 | 1.81243 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −0.591811 | −0.0401747 | ||||||||
\(218\) | 0.899984 | 0.0609546 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −29.8700 | −2.01383 | ||||||||
\(221\) | −14.9962 | −1.00875 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −21.5486 | −1.44300 | −0.721502 | − | 0.692413i | \(-0.756548\pi\) | ||||
−0.721502 | + | 0.692413i | \(0.756548\pi\) | |||||||
\(224\) | 0.210913 | 0.0140922 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 4.35167 | 0.289469 | ||||||||
\(227\) | 17.1428 | 1.13781 | 0.568903 | − | 0.822405i | \(-0.307368\pi\) | ||||
0.568903 | + | 0.822405i | \(0.307368\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −13.0286 | −0.860956 | −0.430478 | − | 0.902601i | \(-0.641655\pi\) | ||||
−0.430478 | + | 0.902601i | \(0.641655\pi\) | |||||||
\(230\) | −1.37396 | −0.0905966 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 7.94915 | 0.521888 | ||||||||
\(233\) | 18.0528 | 1.18268 | 0.591338 | − | 0.806424i | \(-0.298600\pi\) | ||||
0.591338 | + | 0.806424i | \(0.298600\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 28.4928 | 1.85867 | ||||||||
\(236\) | 8.42305 | 0.548294 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −0.0431181 | −0.00279493 | ||||||||
\(239\) | 1.00000 | 0.0646846 | ||||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 14.9582 | 0.963542 | 0.481771 | − | 0.876297i | \(-0.339994\pi\) | ||||
0.481771 | + | 0.876297i | \(0.339994\pi\) | |||||||
\(242\) | 0.556744 | 0.0357889 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 26.0614 | 1.66841 | ||||||||
\(245\) | −29.5485 | −1.88778 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 6.79535 | 0.432378 | ||||||||
\(248\) | 7.60690 | 0.483039 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 8.09959 | 0.512263 | ||||||||
\(251\) | 15.6861 | 0.990098 | 0.495049 | − | 0.868865i | \(-0.335150\pi\) | ||||
0.495049 | + | 0.868865i | \(0.335150\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −4.85075 | −0.304964 | ||||||||
\(254\) | −2.54673 | −0.159796 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 11.4354 | 0.714715 | ||||||||
\(257\) | 25.8292 | 1.61118 | 0.805590 | − | 0.592474i | \(-0.201849\pi\) | ||||
0.805590 | + | 0.592474i | \(0.201849\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −0.215513 | −0.0133913 | ||||||||
\(260\) | −52.1678 | −3.23531 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −0.432607 | −0.0267266 | ||||||||
\(263\) | −19.4124 | −1.19702 | −0.598511 | − | 0.801115i | \(-0.704241\pi\) | ||||
−0.598511 | + | 0.801115i | \(0.704241\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 41.1819 | 2.52979 | ||||||||
\(266\) | 0.0195384 | 0.00119798 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 8.27853 | 0.505692 | ||||||||
\(269\) | 0.0307895 | 0.00187727 | 0.000938635 | − | 1.00000i | \(-0.499701\pi\) | ||||
0.000938635 | 1.00000i | \(0.499701\pi\) | ||||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −7.27426 | −0.441880 | −0.220940 | − | 0.975287i | \(-0.570912\pi\) | ||||
−0.220940 | + | 0.975287i | \(0.570912\pi\) | |||||||
\(272\) | −8.58978 | −0.520832 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 1.67644 | 0.101277 | ||||||||
\(275\) | 46.8154 | 2.82307 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2.12921 | 0.127932 | 0.0639659 | − | 0.997952i | \(-0.479625\pi\) | ||||
0.0639659 | + | 0.997952i | \(0.479625\pi\) | |||||||
\(278\) | 2.16415 | 0.129797 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −0.304607 | −0.0182038 | ||||||||
\(281\) | −12.3210 | −0.735007 | −0.367504 | − | 0.930022i | \(-0.619787\pi\) | ||||
−0.367504 | + | 0.930022i | \(0.619787\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −20.6645 | −1.22838 | −0.614189 | − | 0.789159i | \(-0.710517\pi\) | ||||
−0.614189 | + | 0.789159i | \(0.710517\pi\) | |||||||
\(284\) | 27.2250 | 1.61551 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 5.66610 | 0.335043 | ||||||||
\(287\) | 0.533684 | 0.0315024 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −11.4477 | −0.673395 | ||||||||
\(290\) | −8.52269 | −0.500469 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −12.9267 | −0.756476 | ||||||||
\(293\) | 25.1094 | 1.46691 | 0.733454 | − | 0.679740i | \(-0.237907\pi\) | ||||
0.733454 | + | 0.679740i | \(0.237907\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −18.3394 | −1.06776 | ||||||||
\(296\) | 2.77011 | 0.161010 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 2.03478 | 0.117872 | ||||||||
\(299\) | −8.47181 | −0.489938 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0.471150 | 0.0271566 | ||||||||
\(302\) | −5.85757 | −0.337065 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 3.89235 | 0.223242 | ||||||||
\(305\) | −56.7431 | −3.24910 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 14.4578 | 0.825151 | 0.412575 | − | 0.910924i | \(-0.364629\pi\) | ||||
0.412575 | + | 0.910924i | \(0.364629\pi\) | |||||||
\(308\) | −0.529558 | −0.0301744 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −8.15574 | −0.463215 | ||||||||
\(311\) | −26.3144 | −1.49215 | −0.746075 | − | 0.665861i | \(-0.768064\pi\) | ||||
−0.746075 | + | 0.665861i | \(0.768064\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −11.3681 | −0.642563 | −0.321281 | − | 0.946984i | \(-0.604114\pi\) | ||||
−0.321281 | + | 0.946984i | \(0.604114\pi\) | |||||||
\(314\) | −1.72976 | −0.0976161 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −33.9875 | −1.91195 | ||||||||
\(317\) | −21.3000 | −1.19633 | −0.598163 | − | 0.801374i | \(-0.704103\pi\) | ||||
−0.598163 | + | 0.801374i | \(0.704103\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −30.0891 | −1.68467 | ||||||||
\(320\) | −27.8942 | −1.55933 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −0.0243587 | −0.00135746 | ||||||||
\(323\) | −2.51595 | −0.139991 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 81.7629 | 4.53539 | ||||||||
\(326\) | −1.39971 | −0.0775230 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −6.85977 | −0.378767 | ||||||||
\(329\) | 0.505143 | 0.0278494 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 6.61971 | 0.363852 | 0.181926 | − | 0.983312i | \(-0.441767\pi\) | ||||
0.181926 | + | 0.983312i | \(0.441767\pi\) | |||||||
\(332\) | −21.4641 | −1.17799 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −2.85218 | −0.156064 | ||||||||
\(335\) | −18.0247 | −0.984795 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −10.0337 | −0.546572 | −0.273286 | − | 0.961933i | \(-0.588110\pi\) | ||||
−0.273286 | + | 0.961933i | \(0.588110\pi\) | |||||||
\(338\) | 6.71965 | 0.365501 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 19.3149 | 1.04750 | ||||||||
\(341\) | −28.7937 | −1.55926 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.04814 | −0.0565942 | ||||||||
\(344\) | −6.05598 | −0.326516 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −0.977474 | −0.0525493 | ||||||||
\(347\) | 3.07598 | 0.165127 | 0.0825636 | − | 0.996586i | \(-0.473689\pi\) | ||||
0.0825636 | + | 0.996586i | \(0.473689\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −6.65984 | −0.356493 | −0.178247 | − | 0.983986i | \(-0.557042\pi\) | ||||
−0.178247 | + | 0.983986i | \(0.557042\pi\) | |||||||
\(350\) | 0.235090 | 0.0125661 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 10.2617 | 0.546948 | ||||||||
\(353\) | −0.692908 | −0.0368798 | −0.0184399 | − | 0.999830i | \(-0.505870\pi\) | ||||
−0.0184399 | + | 0.999830i | \(0.505870\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −59.2766 | −3.14608 | ||||||||
\(356\) | −20.5152 | −1.08730 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 4.41930 | 0.233567 | ||||||||
\(359\) | −2.40470 | −0.126915 | −0.0634576 | − | 0.997985i | \(-0.520213\pi\) | ||||
−0.0634576 | + | 0.997985i | \(0.520213\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −17.8599 | −0.939996 | ||||||||
\(362\) | 2.95292 | 0.155202 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −0.924871 | −0.0484764 | ||||||||
\(365\) | 28.1450 | 1.47318 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −30.6458 | −1.59970 | −0.799848 | − | 0.600202i | \(-0.795087\pi\) | ||||
−0.799848 | + | 0.600202i | \(0.795087\pi\) | |||||||
\(368\) | −4.85262 | −0.252960 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −2.96998 | −0.154402 | ||||||||
\(371\) | 0.730106 | 0.0379052 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −25.7277 | −1.33213 | −0.666065 | − | 0.745894i | \(-0.732023\pi\) | ||||
−0.666065 | + | 0.745894i | \(0.732023\pi\) | |||||||
\(374\) | −2.09785 | −0.108477 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −6.49291 | −0.334846 | ||||||||
\(377\) | −52.5505 | −2.70649 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −28.5899 | −1.46856 | −0.734281 | − | 0.678845i | \(-0.762481\pi\) | ||||
−0.734281 | + | 0.678845i | \(0.762481\pi\) | |||||||
\(380\) | −8.75229 | −0.448983 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −2.07587 | −0.106211 | ||||||||
\(383\) | 5.30492 | 0.271069 | 0.135534 | − | 0.990773i | \(-0.456725\pi\) | ||||
0.135534 | + | 0.990773i | \(0.456725\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1.15300 | 0.0587623 | ||||||||
\(386\) | −3.61933 | −0.184219 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −18.6667 | −0.947656 | ||||||||
\(389\) | 7.61972 | 0.386335 | 0.193168 | − | 0.981166i | \(-0.438124\pi\) | ||||
0.193168 | + | 0.981166i | \(0.438124\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3.13665 | 0.158627 | ||||||||
\(392\) | 6.73348 | 0.340092 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0.770297 | 0.0388070 | ||||||||
\(395\) | 74.0004 | 3.72336 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 6.58074 | 0.330278 | 0.165139 | − | 0.986270i | \(-0.447193\pi\) | ||||
0.165139 | + | 0.986270i | \(0.447193\pi\) | |||||||
\(398\) | −3.92607 | −0.196796 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 46.8335 | 2.34167 | ||||||||
\(401\) | 10.2473 | 0.511727 | 0.255864 | − | 0.966713i | \(-0.417640\pi\) | ||||
0.255864 | + | 0.966713i | \(0.417640\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −50.2880 | −2.50502 | ||||||||
\(404\) | 15.5791 | 0.775091 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −0.151097 | −0.00749881 | ||||||||
\(407\) | −10.4854 | −0.519744 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 4.75187 | 0.234965 | 0.117483 | − | 0.993075i | \(-0.462518\pi\) | ||||
0.117483 | + | 0.993075i | \(0.462518\pi\) | |||||||
\(410\) | 7.35470 | 0.363223 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −3.06196 | −0.150852 | ||||||||
\(413\) | −0.325135 | −0.0159988 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 46.7334 | 2.29405 | ||||||||
\(416\) | 17.9219 | 0.878695 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0.950613 | 0.0464960 | ||||||||
\(419\) | −15.8353 | −0.773605 | −0.386803 | − | 0.922163i | \(-0.626421\pi\) | ||||
−0.386803 | + | 0.922163i | \(0.626421\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −20.4926 | −0.998749 | −0.499375 | − | 0.866386i | \(-0.666437\pi\) | ||||
−0.499375 | + | 0.866386i | \(0.666437\pi\) | |||||||
\(422\) | 4.11365 | 0.200250 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −9.38449 | −0.455751 | ||||||||
\(425\) | −30.2723 | −1.46842 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −1.00599 | −0.0486831 | ||||||||
\(428\) | 34.6439 | 1.67458 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 6.49291 | 0.313116 | ||||||||
\(431\) | 4.25692 | 0.205049 | 0.102524 | − | 0.994731i | \(-0.467308\pi\) | ||||
0.102524 | + | 0.994731i | \(0.467308\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −24.2092 | −1.16342 | −0.581710 | − | 0.813396i | \(-0.697616\pi\) | ||||
−0.581710 | + | 0.813396i | \(0.697616\pi\) | |||||||
\(434\) | −0.144591 | −0.00694061 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −7.14736 | −0.342297 | ||||||||
\(437\) | −1.42133 | −0.0679916 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −26.7197 | −1.27526 | −0.637630 | − | 0.770343i | \(-0.720085\pi\) | ||||
−0.637630 | + | 0.770343i | \(0.720085\pi\) | |||||||
\(440\) | −14.8202 | −0.706525 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −3.66388 | −0.174273 | ||||||||
\(443\) | −17.3125 | −0.822542 | −0.411271 | − | 0.911513i | \(-0.634915\pi\) | ||||
−0.411271 | + | 0.911513i | \(0.634915\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 44.6674 | 2.11744 | ||||||||
\(446\) | −5.26477 | −0.249294 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −0.494530 | −0.0233644 | ||||||||
\(449\) | 28.6843 | 1.35369 | 0.676847 | − | 0.736124i | \(-0.263346\pi\) | ||||
0.676847 | + | 0.736124i | \(0.263346\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 25.9656 | 1.22267 | ||||||||
\(452\) | −34.5595 | −1.62554 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 4.18833 | 0.196568 | ||||||||
\(455\) | 2.01371 | 0.0944040 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −20.0915 | −0.939841 | −0.469920 | − | 0.882709i | \(-0.655717\pi\) | ||||
−0.469920 | + | 0.882709i | \(0.655717\pi\) | |||||||
\(458\) | −3.18316 | −0.148739 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 10.9116 | 0.508754 | ||||||||
\(461\) | 1.64319 | 0.0765311 | 0.0382655 | − | 0.999268i | \(-0.487817\pi\) | ||||
0.0382655 | + | 0.999268i | \(0.487817\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 13.3260 | 0.619310 | 0.309655 | − | 0.950849i | \(-0.399786\pi\) | ||||
0.309655 | + | 0.950849i | \(0.399786\pi\) | |||||||
\(464\) | −30.1008 | −1.39739 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 4.41066 | 0.204320 | ||||||||
\(467\) | −3.59055 | −0.166151 | −0.0830755 | − | 0.996543i | \(-0.526474\pi\) | ||||
−0.0830755 | + | 0.996543i | \(0.526474\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −0.319556 | −0.0147557 | ||||||||
\(470\) | 6.96137 | 0.321104 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 4.17916 | 0.192361 | ||||||||
\(473\) | 22.9231 | 1.05400 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 13.7175 | 0.629403 | ||||||||
\(476\) | 0.342429 | 0.0156952 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0.244320 | 0.0111750 | ||||||||
\(479\) | −28.7910 | −1.31549 | −0.657747 | − | 0.753239i | \(-0.728490\pi\) | ||||
−0.657747 | + | 0.753239i | \(0.728490\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −18.3128 | −0.834990 | ||||||||
\(482\) | 3.65459 | 0.166462 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −4.42147 | −0.200976 | ||||||||
\(485\) | 40.6426 | 1.84549 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 8.43245 | 0.382111 | 0.191055 | − | 0.981579i | \(-0.438809\pi\) | ||||
0.191055 | + | 0.981579i | \(0.438809\pi\) | |||||||
\(488\) | 12.9306 | 0.585339 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −7.21930 | −0.326135 | ||||||||
\(491\) | −4.08991 | −0.184575 | −0.0922875 | − | 0.995732i | \(-0.529418\pi\) | ||||
−0.0922875 | + | 0.995732i | \(0.529418\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 19.4566 | 0.876281 | ||||||||
\(494\) | 1.66024 | 0.0746978 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −28.8048 | −1.29337 | ||||||||
\(497\) | −1.05090 | −0.0471394 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −6.56133 | −0.293725 | −0.146863 | − | 0.989157i | \(-0.546918\pi\) | ||||
−0.146863 | + | 0.989157i | \(0.546918\pi\) | |||||||
\(500\) | −64.3241 | −2.87666 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 3.83243 | 0.171050 | ||||||||
\(503\) | −9.32533 | −0.415796 | −0.207898 | − | 0.978151i | \(-0.566662\pi\) | ||||
−0.207898 | + | 0.978151i | \(0.566662\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −33.9202 | −1.50943 | ||||||||
\(506\) | −1.18514 | −0.0526858 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 20.2253 | 0.897352 | ||||||||
\(509\) | −8.28590 | −0.367266 | −0.183633 | − | 0.982995i | \(-0.558786\pi\) | ||||
−0.183633 | + | 0.982995i | \(0.558786\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0.498977 | 0.0220735 | ||||||||
\(512\) | 17.2845 | 0.763873 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 6.31059 | 0.278348 | ||||||||
\(515\) | 6.66676 | 0.293773 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 24.5770 | 1.08089 | ||||||||
\(518\) | −0.0526541 | −0.00231349 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −25.8834 | −1.13506 | ||||||||
\(521\) | −0.470820 | −0.0206270 | −0.0103135 | − | 0.999947i | \(-0.503283\pi\) | ||||
−0.0103135 | + | 0.999947i | \(0.503283\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 3.00357 | 0.131337 | 0.0656685 | − | 0.997841i | \(-0.479082\pi\) | ||||
0.0656685 | + | 0.997841i | \(0.479082\pi\) | |||||||
\(524\) | 3.43562 | 0.150086 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −4.74285 | −0.206798 | ||||||||
\(527\) | 18.6189 | 0.811052 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −21.2280 | −0.922957 | ||||||||
\(530\) | 10.0616 | 0.437047 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −0.155168 | −0.00672737 | ||||||||
\(533\) | 45.3488 | 1.96427 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −75.4297 | −3.26111 | ||||||||
\(536\) | 4.10745 | 0.177415 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0.00752251 | 0.000324318 0 | ||||||||
\(539\) | −25.4876 | −1.09783 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −1.18196 | −0.0508164 | −0.0254082 | − | 0.999677i | \(-0.508089\pi\) | ||||
−0.0254082 | + | 0.999677i | \(0.508089\pi\) | |||||||
\(542\) | −1.77725 | −0.0763394 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −6.63552 | −0.284495 | ||||||||
\(545\) | 15.5618 | 0.666596 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 32.8349 | 1.40392 | 0.701960 | − | 0.712217i | \(-0.252309\pi\) | ||||
0.701960 | + | 0.712217i | \(0.252309\pi\) | |||||||
\(548\) | −13.3137 | −0.568733 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 11.4380 | 0.487716 | ||||||||
\(551\) | −8.81651 | −0.375596 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1.31194 | 0.0557893 | ||||||||
\(554\) | 0.520209 | 0.0221016 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −17.1869 | −0.728888 | ||||||||
\(557\) | 15.9291 | 0.674938 | 0.337469 | − | 0.941337i | \(-0.390429\pi\) | ||||
0.337469 | + | 0.941337i | \(0.390429\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 40.0350 | 1.69330 | ||||||||
\(560\) | 1.15344 | 0.0487419 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −3.01026 | −0.126980 | ||||||||
\(563\) | −37.8619 | −1.59569 | −0.797844 | − | 0.602864i | \(-0.794026\pi\) | ||||
−0.797844 | + | 0.602864i | \(0.794026\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 75.2458 | 3.16561 | ||||||||
\(566\) | −5.04876 | −0.212215 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 13.5079 | 0.566778 | ||||||||
\(569\) | −25.3083 | −1.06098 | −0.530489 | − | 0.847692i | \(-0.677992\pi\) | ||||
−0.530489 | + | 0.847692i | \(0.677992\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 10.3713 | 0.434027 | 0.217013 | − | 0.976169i | \(-0.430369\pi\) | ||||
0.217013 | + | 0.976169i | \(0.430369\pi\) | |||||||
\(572\) | −44.9982 | −1.88147 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0.130390 | 0.00544237 | ||||||||
\(575\) | −17.1018 | −0.713192 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −31.2506 | −1.30098 | −0.650490 | − | 0.759515i | \(-0.725436\pi\) | ||||
−0.650490 | + | 0.759515i | \(0.725436\pi\) | |||||||
\(578\) | −2.79691 | −0.116336 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 67.6842 | 2.81043 | ||||||||
\(581\) | 0.828526 | 0.0343731 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 35.5222 | 1.47118 | ||||||||
\(584\) | −6.41366 | −0.265399 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 6.13474 | 0.253424 | ||||||||
\(587\) | −34.9885 | −1.44413 | −0.722066 | − | 0.691825i | \(-0.756807\pi\) | ||||
−0.722066 | + | 0.691825i | \(0.756807\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −8.43692 | −0.347637 | ||||||||
\(590\) | −4.48068 | −0.184467 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −10.4895 | −0.431115 | ||||||||
\(593\) | 1.74281 | 0.0715688 | 0.0357844 | − | 0.999360i | \(-0.488607\pi\) | ||||
0.0357844 | + | 0.999360i | \(0.488607\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −0.745566 | −0.0305652 | ||||||||
\(596\) | −16.1595 | −0.661919 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −2.06984 | −0.0846419 | ||||||||
\(599\) | 26.0525 | 1.06448 | 0.532238 | − | 0.846595i | \(-0.321351\pi\) | ||||
0.532238 | + | 0.846595i | \(0.321351\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −22.3167 | −0.910318 | −0.455159 | − | 0.890410i | \(-0.650418\pi\) | ||||
−0.455159 | + | 0.890410i | \(0.650418\pi\) | |||||||
\(602\) | 0.115112 | 0.00469160 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 46.5188 | 1.89282 | ||||||||
\(605\) | 9.62679 | 0.391385 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 40.8318 | 1.65731 | 0.828655 | − | 0.559760i | \(-0.189107\pi\) | ||||
0.828655 | + | 0.559760i | \(0.189107\pi\) | |||||||
\(608\) | 3.00680 | 0.121942 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −13.8635 | −0.561317 | ||||||||
\(611\) | 42.9235 | 1.73650 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 19.6260 | 0.792687 | 0.396344 | − | 0.918102i | \(-0.370279\pi\) | ||||
0.396344 | + | 0.918102i | \(0.370279\pi\) | |||||||
\(614\) | 3.53234 | 0.142553 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −0.262744 | −0.0105863 | ||||||||
\(617\) | 16.8830 | 0.679683 | 0.339841 | − | 0.940483i | \(-0.389627\pi\) | ||||
0.339841 | + | 0.940483i | \(0.389627\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 21.3216 | 0.856986 | 0.428493 | − | 0.903545i | \(-0.359045\pi\) | ||||
0.428493 | + | 0.903545i | \(0.359045\pi\) | |||||||
\(620\) | 64.7701 | 2.60123 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −6.42913 | −0.257785 | ||||||||
\(623\) | 0.791898 | 0.0317267 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 75.8156 | 3.03262 | ||||||||
\(626\) | −2.77746 | −0.111010 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 13.7372 | 0.548173 | ||||||||
\(629\) | 6.78021 | 0.270345 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 28.2400 | 1.12422 | 0.562109 | − | 0.827063i | \(-0.309990\pi\) | ||||
0.562109 | + | 0.827063i | \(0.309990\pi\) | |||||||
\(632\) | −16.8631 | −0.670779 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −5.20402 | −0.206678 | ||||||||
\(635\) | −44.0362 | −1.74752 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −44.5139 | −1.76371 | ||||||||
\(638\) | −7.35139 | −0.291044 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −30.6084 | −1.20990 | ||||||||
\(641\) | −33.9514 | −1.34100 | −0.670500 | − | 0.741910i | \(-0.733920\pi\) | ||||
−0.670500 | + | 0.741910i | \(0.733920\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −27.1751 | −1.07168 | −0.535841 | − | 0.844319i | \(-0.680005\pi\) | ||||
−0.535841 | + | 0.844319i | \(0.680005\pi\) | |||||||
\(644\) | 0.193449 | 0.00762294 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −0.614697 | −0.0241849 | ||||||||
\(647\) | −42.6110 | −1.67521 | −0.837606 | − | 0.546275i | \(-0.816045\pi\) | ||||
−0.837606 | + | 0.546275i | \(0.816045\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −15.8189 | −0.620948 | ||||||||
\(650\) | 19.9763 | 0.783536 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 11.1160 | 0.435338 | ||||||||
\(653\) | 19.5670 | 0.765715 | 0.382857 | − | 0.923807i | \(-0.374940\pi\) | ||||
0.382857 | + | 0.923807i | \(0.374940\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −7.48031 | −0.292280 | ||||||||
\(656\) | 25.9756 | 1.01418 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0.123417 | 0.00481128 | ||||||||
\(659\) | 24.6924 | 0.961878 | 0.480939 | − | 0.876754i | \(-0.340296\pi\) | ||||
0.480939 | + | 0.876754i | \(0.340296\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 31.9176 | 1.24145 | 0.620725 | − | 0.784028i | \(-0.286838\pi\) | ||||
0.620725 | + | 0.784028i | \(0.286838\pi\) | |||||||
\(662\) | 1.61733 | 0.0628593 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −10.6495 | −0.413283 | ||||||||
\(665\) | 0.337844 | 0.0131010 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 10.9916 | 0.425597 | ||||||||
\(668\) | 22.6510 | 0.876394 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −4.40380 | −0.170134 | ||||||||
\(671\) | −48.9448 | −1.88949 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 13.7390 | 0.529599 | 0.264799 | − | 0.964303i | \(-0.414694\pi\) | ||||
0.264799 | + | 0.964303i | \(0.414694\pi\) | |||||||
\(674\) | −2.45144 | −0.0944260 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −53.3651 | −2.05250 | ||||||||
\(677\) | 0.981890 | 0.0377371 | 0.0188685 | − | 0.999822i | \(-0.493994\pi\) | ||||
0.0188685 | + | 0.999822i | \(0.493994\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0.720545 | 0.0276520 | ||||||||
\(680\) | 9.58321 | 0.367499 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −7.03487 | −0.269379 | ||||||||
\(683\) | −19.2274 | −0.735716 | −0.367858 | − | 0.929882i | \(-0.619909\pi\) | ||||
−0.367858 | + | 0.929882i | \(0.619909\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 28.9877 | 1.10756 | ||||||||
\(686\) | −0.256082 | −0.00977724 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 22.9319 | 0.874272 | ||||||||
\(689\) | 62.0393 | 2.36351 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −27.3404 | −1.04008 | −0.520038 | − | 0.854143i | \(-0.674082\pi\) | ||||
−0.520038 | + | 0.854143i | \(0.674082\pi\) | |||||||
\(692\) | 7.76276 | 0.295096 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0.751524 | 0.0285275 | ||||||||
\(695\) | 37.4208 | 1.41945 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −16.7902 | −0.635973 | ||||||||
\(698\) | −1.62714 | −0.0615880 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −1.86701 | −0.0705662 | ||||||||
\(701\) | 4.84865 | 0.183131 | 0.0915654 | − | 0.995799i | \(-0.470813\pi\) | ||||
0.0915654 | + | 0.995799i | \(0.470813\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −3.07237 | −0.115877 | ||||||||
\(704\) | −24.0606 | −0.906819 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −0.169291 | −0.00637137 | ||||||||
\(707\) | −0.601364 | −0.0226166 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 42.1926 | 1.58457 | 0.792287 | − | 0.610148i | \(-0.208890\pi\) | ||||
0.792287 | + | 0.610148i | \(0.208890\pi\) | |||||||
\(710\) | −14.4825 | −0.543518 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −10.1787 | −0.381465 | ||||||||
\(713\) | 10.5184 | 0.393916 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 97.9738 | 3.66401 | ||||||||
\(716\) | −35.0965 | −1.31162 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −0.587517 | −0.0219259 | ||||||||
\(719\) | 33.7164 | 1.25741 | 0.628704 | − | 0.777645i | \(-0.283586\pi\) | ||||
0.628704 | + | 0.777645i | \(0.283586\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0.118194 | 0.00440176 | ||||||||
\(722\) | −4.36354 | −0.162394 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −23.4511 | −0.871553 | ||||||||
\(725\) | −106.082 | −3.93978 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −15.2627 | −0.566061 | −0.283030 | − | 0.959111i | \(-0.591340\pi\) | ||||
−0.283030 | + | 0.959111i | \(0.591340\pi\) | |||||||
\(728\) | −0.458881 | −0.0170073 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 6.87640 | 0.254507 | ||||||||
\(731\) | −14.8228 | −0.548241 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 1.87172 | 0.0691336 | 0.0345668 | − | 0.999402i | \(-0.488995\pi\) | ||||
0.0345668 | + | 0.999402i | \(0.488995\pi\) | |||||||
\(734\) | −7.48739 | −0.276364 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −3.74860 | −0.138175 | ||||||||
\(737\) | −15.5475 | −0.572700 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 11.6680 | 0.429214 | 0.214607 | − | 0.976701i | \(-0.431153\pi\) | ||||
0.214607 | + | 0.976701i | \(0.431153\pi\) | |||||||
\(740\) | 23.5865 | 0.867058 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0.178380 | 0.00654852 | ||||||||
\(743\) | 14.6237 | 0.536491 | 0.268245 | − | 0.963351i | \(-0.413556\pi\) | ||||
0.268245 | + | 0.963351i | \(0.413556\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 35.1838 | 1.28904 | ||||||||
\(746\) | −6.28580 | −0.230140 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 16.6604 | 0.609164 | ||||||||
\(749\) | −1.33728 | −0.0488630 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −47.4417 | −1.73117 | −0.865586 | − | 0.500761i | \(-0.833054\pi\) | ||||
−0.865586 | + | 0.500761i | \(0.833054\pi\) | |||||||
\(752\) | 24.5864 | 0.896575 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −12.8392 | −0.467575 | ||||||||
\(755\) | −101.285 | −3.68612 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 32.1954 | 1.17016 | 0.585082 | − | 0.810974i | \(-0.301062\pi\) | ||||
0.585082 | + | 0.810974i | \(0.301062\pi\) | |||||||
\(758\) | −6.98508 | −0.253710 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −4.34251 | −0.157519 | ||||||||
\(761\) | 25.0702 | 0.908794 | 0.454397 | − | 0.890799i | \(-0.349855\pi\) | ||||
0.454397 | + | 0.890799i | \(0.349855\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0.275893 | 0.00998798 | ||||||||
\(764\) | 16.4858 | 0.596436 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 1.29610 | 0.0468300 | ||||||||
\(767\) | −27.6277 | −0.997579 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 7.38439 | 0.266288 | 0.133144 | − | 0.991097i | \(-0.457493\pi\) | ||||
0.133144 | + | 0.991097i | \(0.457493\pi\) | |||||||
\(770\) | 0.281701 | 0.0101518 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 28.7435 | 1.03450 | ||||||||
\(773\) | 6.55568 | 0.235792 | 0.117896 | − | 0.993026i | \(-0.462385\pi\) | ||||
0.117896 | + | 0.993026i | \(0.462385\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −101.515 | −3.64651 | ||||||||
\(776\) | −9.26160 | −0.332472 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 1.86165 | 0.0667435 | ||||||||
\(779\) | 7.60826 | 0.272594 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −51.1300 | −1.82958 | ||||||||
\(782\) | 0.766347 | 0.0274045 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −25.4974 | −0.910622 | ||||||||
\(785\) | −29.9097 | −1.06752 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −37.9638 | −1.35326 | −0.676632 | − | 0.736321i | \(-0.736561\pi\) | ||||
−0.676632 | + | 0.736321i | \(0.736561\pi\) | |||||||
\(788\) | −6.11743 | −0.217924 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 18.0798 | 0.643250 | ||||||||
\(791\) | 1.33402 | 0.0474322 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −85.4818 | −3.03555 | ||||||||
\(794\) | 1.60781 | 0.0570590 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 31.1795 | 1.10513 | ||||||||
\(797\) | −7.47891 | −0.264917 | −0.132458 | − | 0.991189i | \(-0.542287\pi\) | ||||
−0.132458 | + | 0.991189i | \(0.542287\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −15.8922 | −0.562227 | ||||||||
\(800\) | 36.1784 | 1.27910 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 2.50363 | 0.0884062 | ||||||||
\(803\) | 24.2770 | 0.856716 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −0.421193 | −0.0148451 | ||||||||
\(806\) | −12.2864 | −0.432769 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 7.72970 | 0.271930 | ||||||||
\(809\) | −19.1096 | −0.671858 | −0.335929 | − | 0.941887i | \(-0.609050\pi\) | ||||
−0.335929 | + | 0.941887i | \(0.609050\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1.33294 | 0.0468057 | 0.0234028 | − | 0.999726i | \(-0.492550\pi\) | ||||
0.0234028 | + | 0.999726i | \(0.492550\pi\) | |||||||
\(812\) | 1.19996 | 0.0421103 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −2.56180 | −0.0897912 | ||||||||
\(815\) | −24.2028 | −0.847787 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 6.71676 | 0.234990 | ||||||||
\(818\) | 1.16098 | 0.0405927 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −58.4085 | −2.03971 | ||||||||
\(821\) | −27.6681 | −0.965623 | −0.482812 | − | 0.875724i | \(-0.660384\pi\) | ||||
−0.482812 | + | 0.875724i | \(0.660384\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −14.1900 | −0.494634 | −0.247317 | − | 0.968935i | \(-0.579549\pi\) | ||||
−0.247317 | + | 0.968935i | \(0.579549\pi\) | |||||||
\(824\) | −1.51921 | −0.0529243 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −0.0794371 | −0.00276397 | ||||||||
\(827\) | 20.9131 | 0.727220 | 0.363610 | − | 0.931551i | \(-0.381544\pi\) | ||||
0.363610 | + | 0.931551i | \(0.381544\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −11.6318 | −0.403989 | −0.201995 | − | 0.979387i | \(-0.564742\pi\) | ||||
−0.201995 | + | 0.979387i | \(0.564742\pi\) | |||||||
\(830\) | 11.4179 | 0.396321 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −42.0217 | −1.45684 | ||||||||
\(833\) | 16.4811 | 0.571035 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −49.3177 | −1.70671 | ||||||||
\(836\) | −7.54944 | −0.261103 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −3.86889 | −0.133648 | ||||||||
\(839\) | −11.9369 | −0.412107 | −0.206053 | − | 0.978541i | \(-0.566062\pi\) | ||||
−0.206053 | + | 0.978541i | \(0.566062\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 39.1809 | 1.35106 | ||||||||
\(842\) | −5.00676 | −0.172544 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −32.6692 | −1.12452 | ||||||||
\(845\) | 116.191 | 3.99709 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0.170671 | 0.00586434 | ||||||||
\(848\) | 35.5359 | 1.22031 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −7.39614 | −0.253686 | ||||||||
\(851\) | 3.83035 | 0.131303 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −19.2324 | −0.658506 | −0.329253 | − | 0.944242i | \(-0.606797\pi\) | ||||
−0.329253 | + | 0.944242i | \(0.606797\pi\) | |||||||
\(854\) | −0.245783 | −0.00841053 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 17.1888 | 0.587502 | ||||||||
\(857\) | −9.11993 | −0.311531 | −0.155765 | − | 0.987794i | \(-0.549784\pi\) | ||||
−0.155765 | + | 0.987794i | \(0.549784\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 41.6196 | 1.42004 | 0.710022 | − | 0.704180i | \(-0.248685\pi\) | ||||
0.710022 | + | 0.704180i | \(0.248685\pi\) | |||||||
\(860\) | −51.5645 | −1.75833 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 1.04005 | 0.0354243 | ||||||||
\(863\) | 30.3148 | 1.03193 | 0.515964 | − | 0.856610i | \(-0.327434\pi\) | ||||
0.515964 | + | 0.856610i | \(0.327434\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −16.9017 | −0.574676 | ||||||||
\(866\) | −5.91480 | −0.200993 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 1.14830 | 0.0389757 | ||||||||
\(869\) | 63.8303 | 2.16529 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −27.1537 | −0.920067 | ||||||||
\(872\) | −3.54621 | −0.120090 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −0.347261 | −0.0117463 | ||||||||
\(875\) | 2.48295 | 0.0839390 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 34.0049 | 1.14826 | 0.574131 | − | 0.818763i | \(-0.305340\pi\) | ||||
0.574131 | + | 0.818763i | \(0.305340\pi\) | |||||||
\(878\) | −6.52815 | −0.220315 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 56.1191 | 1.89177 | ||||||||
\(881\) | 33.5155 | 1.12917 | 0.564584 | − | 0.825376i | \(-0.309037\pi\) | ||||
0.564584 | + | 0.825376i | \(0.309037\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 3.58518 | 0.120651 | 0.0603255 | − | 0.998179i | \(-0.480786\pi\) | ||||
0.0603255 | + | 0.998179i | \(0.480786\pi\) | |||||||
\(884\) | 29.0973 | 0.978647 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −4.22980 | −0.142103 | ||||||||
\(887\) | 43.2091 | 1.45082 | 0.725410 | − | 0.688317i | \(-0.241650\pi\) | ||||
0.725410 | + | 0.688317i | \(0.241650\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −0.780708 | −0.0261841 | ||||||||
\(890\) | 10.9131 | 0.365809 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 41.8110 | 1.39994 | ||||||||
\(893\) | 7.20137 | 0.240985 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 76.4151 | 2.55428 | ||||||||
\(896\) | −0.542650 | −0.0181287 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 7.00815 | 0.233865 | ||||||||
\(899\) | 65.2453 | 2.17605 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −22.9698 | −0.765234 | ||||||||
\(902\) | 6.34392 | 0.211230 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −17.1469 | −0.570298 | ||||||||
\(905\) | 51.0597 | 1.69728 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 0.941818 | 0.0312726 | 0.0156363 | − | 0.999878i | \(-0.495023\pi\) | ||||
0.0156363 | + | 0.999878i | \(0.495023\pi\) | |||||||
\(908\) | −33.2622 | −1.10385 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0.491990 | 0.0163093 | ||||||||
\(911\) | 21.2909 | 0.705398 | 0.352699 | − | 0.935737i | \(-0.385264\pi\) | ||||
0.352699 | + | 0.935737i | \(0.385264\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 40.3107 | 1.33409 | ||||||||
\(914\) | −4.90876 | −0.162367 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 25.2795 | 0.835260 | ||||||||
\(917\) | −0.132617 | −0.00437940 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 3.97921 | 0.131262 | 0.0656310 | − | 0.997844i | \(-0.479094\pi\) | ||||
0.0656310 | + | 0.997844i | \(0.479094\pi\) | |||||||
\(920\) | 5.41384 | 0.178489 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0.401465 | 0.0132215 | ||||||||
\(923\) | −89.2984 | −2.93929 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −36.9673 | −1.21548 | ||||||||
\(926\) | 3.25580 | 0.106992 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −23.2525 | −0.763302 | ||||||||
\(929\) | 24.9145 | 0.817417 | 0.408709 | − | 0.912665i | \(-0.365979\pi\) | ||||
0.408709 | + | 0.912665i | \(0.365979\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −7.46819 | −0.244760 | ||||||||
\(932\) | −35.0279 | −1.14738 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −0.877245 | −0.0287043 | ||||||||
\(935\) | −36.2744 | −1.18630 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −7.37922 | −0.241069 | −0.120534 | − | 0.992709i | \(-0.538461\pi\) | ||||
−0.120534 | + | 0.992709i | \(0.538461\pi\) | |||||||
\(938\) | −0.0780741 | −0.00254921 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −55.2848 | −1.80319 | ||||||||
\(941\) | −19.7016 | −0.642255 | −0.321127 | − | 0.947036i | \(-0.604062\pi\) | ||||
−0.321127 | + | 0.947036i | \(0.604062\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −9.48528 | −0.308883 | ||||||||
\(944\) | −15.8251 | −0.515062 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 5.60057 | 0.182090 | ||||||||
\(947\) | 3.62801 | 0.117895 | 0.0589473 | − | 0.998261i | \(-0.481226\pi\) | ||||
0.0589473 | + | 0.998261i | \(0.481226\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 42.3996 | 1.37635 | ||||||||
\(950\) | 3.35147 | 0.108736 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0.169899 | 0.00550645 | ||||||||
\(953\) | −7.87411 | −0.255067 | −0.127534 | − | 0.991834i | \(-0.540706\pi\) | ||||
−0.127534 | + | 0.991834i | \(0.540706\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −35.8943 | −1.16151 | ||||||||
\(956\) | −1.94031 | −0.0627540 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −7.03422 | −0.227265 | ||||||||
\(959\) | 0.513917 | 0.0165952 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 31.4362 | 1.01407 | ||||||||
\(962\) | −4.47418 | −0.144253 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −29.0235 | −0.934784 | ||||||||
\(965\) | −62.5828 | −2.01461 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −21.9578 | −0.706116 | −0.353058 | − | 0.935601i | \(-0.614858\pi\) | ||||
−0.353058 | + | 0.935601i | \(0.614858\pi\) | |||||||
\(968\) | −2.19374 | −0.0705096 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 9.92982 | 0.318827 | ||||||||
\(971\) | −26.9544 | −0.865007 | −0.432504 | − | 0.901632i | \(-0.642370\pi\) | ||||
−0.432504 | + | 0.901632i | \(0.642370\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0.663426 | 0.0212685 | ||||||||
\(974\) | 2.06022 | 0.0660137 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −48.9637 | −1.56729 | ||||||||
\(977\) | 25.4387 | 0.813855 | 0.406927 | − | 0.913460i | \(-0.366600\pi\) | ||||
0.406927 | + | 0.913460i | \(0.366600\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 38.5286 | 1.23138 | ||||||||
\(980\) | 57.3332 | 1.83144 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −0.999247 | −0.0318873 | ||||||||
\(983\) | −3.71985 | −0.118645 | −0.0593224 | − | 0.998239i | \(-0.518894\pi\) | ||||
−0.0593224 | + | 0.998239i | \(0.518894\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 13.3194 | 0.424391 | ||||||||
\(986\) | 4.75364 | 0.151387 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −13.1851 | −0.419473 | ||||||||
\(989\) | −8.37384 | −0.266273 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 2.46785 | 0.0783938 | 0.0391969 | − | 0.999232i | \(-0.487520\pi\) | ||||
0.0391969 | + | 0.999232i | \(0.487520\pi\) | |||||||
\(992\) | −22.2514 | −0.706483 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −0.256757 | −0.00814383 | ||||||||
\(995\) | −67.8866 | −2.15215 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −57.3747 | −1.81708 | −0.908538 | − | 0.417803i | \(-0.862800\pi\) | ||||
−0.908538 | + | 0.417803i | \(0.862800\pi\) | |||||||
\(998\) | −1.60307 | −0.0507441 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 2151.2.a.k.1.11 | yes | 20 | |
3.2 | odd | 2 | 2151.2.a.j.1.10 | ✓ | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2151.2.a.j.1.10 | ✓ | 20 | 3.2 | odd | 2 | ||
2151.2.a.k.1.11 | yes | 20 | 1.1 | even | 1 | trivial |