Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [605,2,Mod(1,605)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(605, 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("605.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 605 = 5 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 605.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: | \(4.83094932229\) |
Analytic rank: | \(1\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.2525.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 2x^{3} - 4x^{2} + 5x + 5 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 55) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(-1.46673\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 605.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.0935099 | −0.0661215 | −0.0330607 | − | 0.999453i | \(-0.510525\pi\) | ||||
−0.0330607 | + | 0.999453i | \(0.510525\pi\) | |||||||
\(3\) | 1.46673 | 0.846818 | 0.423409 | − | 0.905939i | \(-0.360833\pi\) | ||||
0.423409 | + | 0.905939i | \(0.360833\pi\) | |||||||
\(4\) | −1.99126 | −0.995628 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | −0.137154 | −0.0559929 | ||||||||
\(7\) | −4.52452 | −1.71011 | −0.855055 | − | 0.518538i | \(-0.826477\pi\) | ||||
−0.855055 | + | 0.518538i | \(0.826477\pi\) | |||||||
\(8\) | 0.373222 | 0.131954 | ||||||||
\(9\) | −0.848698 | −0.282899 | ||||||||
\(10\) | −0.0935099 | −0.0295704 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | −2.92064 | −0.843116 | ||||||||
\(13\) | 1.14256 | 0.316889 | 0.158444 | − | 0.987368i | \(-0.449352\pi\) | ||||
0.158444 | + | 0.987368i | \(0.449352\pi\) | |||||||
\(14\) | 0.423088 | 0.113075 | ||||||||
\(15\) | 1.46673 | 0.378709 | ||||||||
\(16\) | 3.94761 | 0.986903 | ||||||||
\(17\) | −3.37322 | −0.818126 | −0.409063 | − | 0.912506i | \(-0.634144\pi\) | ||||
−0.409063 | + | 0.912506i | \(0.634144\pi\) | |||||||
\(18\) | 0.0793616 | 0.0187057 | ||||||||
\(19\) | −6.08477 | −1.39594 | −0.697971 | − | 0.716127i | \(-0.745913\pi\) | ||||
−0.697971 | + | 0.716127i | \(0.745913\pi\) | |||||||
\(20\) | −1.99126 | −0.445258 | ||||||||
\(21\) | −6.63626 | −1.44815 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −5.45258 | −1.13694 | −0.568471 | − | 0.822703i | \(-0.692465\pi\) | ||||
−0.568471 | + | 0.822703i | \(0.692465\pi\) | |||||||
\(24\) | 0.547416 | 0.111741 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | −0.106840 | −0.0209531 | ||||||||
\(27\) | −5.64501 | −1.08638 | ||||||||
\(28\) | 9.00949 | 1.70263 | ||||||||
\(29\) | −3.32083 | −0.616663 | −0.308332 | − | 0.951279i | \(-0.599771\pi\) | ||||
−0.308332 | + | 0.951279i | \(0.599771\pi\) | |||||||
\(30\) | −0.137154 | −0.0250408 | ||||||||
\(31\) | 1.79091 | 0.321656 | 0.160828 | − | 0.986982i | \(-0.448584\pi\) | ||||
0.160828 | + | 0.986982i | \(0.448584\pi\) | |||||||
\(32\) | −1.11558 | −0.197209 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0.315430 | 0.0540957 | ||||||||
\(35\) | −4.52452 | −0.764784 | ||||||||
\(36\) | 1.68997 | 0.281662 | ||||||||
\(37\) | 1.48881 | 0.244758 | 0.122379 | − | 0.992483i | \(-0.460948\pi\) | ||||
0.122379 | + | 0.992483i | \(0.460948\pi\) | |||||||
\(38\) | 0.568986 | 0.0923017 | ||||||||
\(39\) | 1.67583 | 0.268347 | ||||||||
\(40\) | 0.373222 | 0.0590116 | ||||||||
\(41\) | 1.74726 | 0.272876 | 0.136438 | − | 0.990649i | \(-0.456434\pi\) | ||||
0.136438 | + | 0.990649i | \(0.456434\pi\) | |||||||
\(42\) | 0.620556 | 0.0957539 | ||||||||
\(43\) | 0.263041 | 0.0401134 | 0.0200567 | − | 0.999799i | \(-0.493615\pi\) | ||||
0.0200567 | + | 0.999799i | \(0.493615\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −0.848698 | −0.126516 | ||||||||
\(46\) | 0.509871 | 0.0751763 | ||||||||
\(47\) | 6.92472 | 1.01007 | 0.505037 | − | 0.863098i | \(-0.331479\pi\) | ||||
0.505037 | + | 0.863098i | \(0.331479\pi\) | |||||||
\(48\) | 5.79009 | 0.835727 | ||||||||
\(49\) | 13.4713 | 1.92447 | ||||||||
\(50\) | −0.0935099 | −0.0132243 | ||||||||
\(51\) | −4.94761 | −0.692804 | ||||||||
\(52\) | −2.27513 | −0.315503 | ||||||||
\(53\) | −1.43976 | −0.197766 | −0.0988830 | − | 0.995099i | \(-0.531527\pi\) | ||||
−0.0988830 | + | 0.995099i | \(0.531527\pi\) | |||||||
\(54\) | 0.527864 | 0.0718332 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −1.68865 | −0.225656 | ||||||||
\(57\) | −8.92472 | −1.18211 | ||||||||
\(58\) | 0.310531 | 0.0407747 | ||||||||
\(59\) | −7.06810 | −0.920188 | −0.460094 | − | 0.887870i | \(-0.652184\pi\) | ||||
−0.460094 | + | 0.887870i | \(0.652184\pi\) | |||||||
\(60\) | −2.92064 | −0.377053 | ||||||||
\(61\) | −2.50245 | −0.320406 | −0.160203 | − | 0.987084i | \(-0.551215\pi\) | ||||
−0.160203 | + | 0.987084i | \(0.551215\pi\) | |||||||
\(62\) | −0.167467 | −0.0212684 | ||||||||
\(63\) | 3.83995 | 0.483789 | ||||||||
\(64\) | −7.79091 | −0.973863 | ||||||||
\(65\) | 1.14256 | 0.141717 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −0.516598 | −0.0631124 | −0.0315562 | − | 0.999502i | \(-0.510046\pi\) | ||||
−0.0315562 | + | 0.999502i | \(0.510046\pi\) | |||||||
\(68\) | 6.71695 | 0.814550 | ||||||||
\(69\) | −7.99748 | −0.962783 | ||||||||
\(70\) | 0.423088 | 0.0505687 | ||||||||
\(71\) | −10.7303 | −1.27345 | −0.636725 | − | 0.771091i | \(-0.719711\pi\) | ||||
−0.636725 | + | 0.771091i | \(0.719711\pi\) | |||||||
\(72\) | −0.316753 | −0.0373297 | ||||||||
\(73\) | 5.68123 | 0.664938 | 0.332469 | − | 0.943114i | \(-0.392118\pi\) | ||||
0.332469 | + | 0.943114i | \(0.392118\pi\) | |||||||
\(74\) | −0.139218 | −0.0161838 | ||||||||
\(75\) | 1.46673 | 0.169364 | ||||||||
\(76\) | 12.1163 | 1.38984 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −0.156706 | −0.0177435 | ||||||||
\(79\) | 11.3033 | 1.27173 | 0.635863 | − | 0.771802i | \(-0.280644\pi\) | ||||
0.635863 | + | 0.771802i | \(0.280644\pi\) | |||||||
\(80\) | 3.94761 | 0.441356 | ||||||||
\(81\) | −5.73362 | −0.637069 | ||||||||
\(82\) | −0.163386 | −0.0180430 | ||||||||
\(83\) | −4.48088 | −0.491840 | −0.245920 | − | 0.969290i | \(-0.579090\pi\) | ||||
−0.245920 | + | 0.969290i | \(0.579090\pi\) | |||||||
\(84\) | 13.2145 | 1.44182 | ||||||||
\(85\) | −3.37322 | −0.365877 | ||||||||
\(86\) | −0.0245970 | −0.00265236 | ||||||||
\(87\) | −4.87077 | −0.522202 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 13.2676 | 1.40637 | 0.703183 | − | 0.711009i | \(-0.251762\pi\) | ||||
0.703183 | + | 0.711009i | \(0.251762\pi\) | |||||||
\(90\) | 0.0793616 | 0.00836545 | ||||||||
\(91\) | −5.16953 | −0.541914 | ||||||||
\(92\) | 10.8575 | 1.13197 | ||||||||
\(93\) | 2.62678 | 0.272384 | ||||||||
\(94\) | −0.647530 | −0.0667876 | ||||||||
\(95\) | −6.08477 | −0.624284 | ||||||||
\(96\) | −1.63626 | −0.167000 | ||||||||
\(97\) | −3.35655 | −0.340806 | −0.170403 | − | 0.985374i | \(-0.554507\pi\) | ||||
−0.170403 | + | 0.985374i | \(0.554507\pi\) | |||||||
\(98\) | −1.25970 | −0.127249 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −1.99126 | −0.199126 | ||||||||
\(101\) | 9.33498 | 0.928865 | 0.464433 | − | 0.885608i | \(-0.346258\pi\) | ||||
0.464433 | + | 0.885608i | \(0.346258\pi\) | |||||||
\(102\) | 0.462651 | 0.0458092 | ||||||||
\(103\) | −13.9160 | −1.37118 | −0.685591 | − | 0.727987i | \(-0.740456\pi\) | ||||
−0.685591 | + | 0.727987i | \(0.740456\pi\) | |||||||
\(104\) | 0.426428 | 0.0418147 | ||||||||
\(105\) | −6.63626 | −0.647633 | ||||||||
\(106\) | 0.134632 | 0.0130766 | ||||||||
\(107\) | 16.7883 | 1.62299 | 0.811493 | − | 0.584362i | \(-0.198655\pi\) | ||||
0.811493 | + | 0.584362i | \(0.198655\pi\) | |||||||
\(108\) | 11.2407 | 1.08163 | ||||||||
\(109\) | 3.65293 | 0.349888 | 0.174944 | − | 0.984578i | \(-0.444026\pi\) | ||||
0.174944 | + | 0.984578i | \(0.444026\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 2.18368 | 0.207266 | ||||||||
\(112\) | −17.8611 | −1.68771 | ||||||||
\(113\) | −11.9023 | −1.11968 | −0.559839 | − | 0.828602i | \(-0.689137\pi\) | ||||
−0.559839 | + | 0.828602i | \(0.689137\pi\) | |||||||
\(114\) | 0.834550 | 0.0781627 | ||||||||
\(115\) | −5.45258 | −0.508456 | ||||||||
\(116\) | 6.61263 | 0.613967 | ||||||||
\(117\) | −0.969687 | −0.0896476 | ||||||||
\(118\) | 0.660937 | 0.0608442 | ||||||||
\(119\) | 15.2622 | 1.39909 | ||||||||
\(120\) | 0.547416 | 0.0499721 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | 0.234004 | 0.0211857 | ||||||||
\(123\) | 2.56276 | 0.231077 | ||||||||
\(124\) | −3.56615 | −0.320250 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | −0.359074 | −0.0319888 | ||||||||
\(127\) | −19.7627 | −1.75365 | −0.876826 | − | 0.480808i | \(-0.840344\pi\) | ||||
−0.876826 | + | 0.480808i | \(0.840344\pi\) | |||||||
\(128\) | 2.95970 | 0.261603 | ||||||||
\(129\) | 0.385811 | 0.0339688 | ||||||||
\(130\) | −0.106840 | −0.00937053 | ||||||||
\(131\) | 1.93479 | 0.169043 | 0.0845215 | − | 0.996422i | \(-0.473064\pi\) | ||||
0.0845215 | + | 0.996422i | \(0.473064\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 27.5307 | 2.38721 | ||||||||
\(134\) | 0.0483070 | 0.00417309 | ||||||||
\(135\) | −5.64501 | −0.485845 | ||||||||
\(136\) | −1.25896 | −0.107955 | ||||||||
\(137\) | −12.5353 | −1.07097 | −0.535483 | − | 0.844546i | \(-0.679870\pi\) | ||||
−0.535483 | + | 0.844546i | \(0.679870\pi\) | |||||||
\(138\) | 0.747843 | 0.0636606 | ||||||||
\(139\) | 11.2450 | 0.953793 | 0.476896 | − | 0.878960i | \(-0.341762\pi\) | ||||
0.476896 | + | 0.878960i | \(0.341762\pi\) | |||||||
\(140\) | 9.00949 | 0.761440 | ||||||||
\(141\) | 10.1567 | 0.855349 | ||||||||
\(142\) | 1.00339 | 0.0842024 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −3.35033 | −0.279194 | ||||||||
\(145\) | −3.32083 | −0.275780 | ||||||||
\(146\) | −0.531251 | −0.0439667 | ||||||||
\(147\) | 19.7588 | 1.62968 | ||||||||
\(148\) | −2.96459 | −0.243688 | ||||||||
\(149\) | 17.3337 | 1.42003 | 0.710014 | − | 0.704187i | \(-0.248688\pi\) | ||||
0.710014 | + | 0.704187i | \(0.248688\pi\) | |||||||
\(150\) | −0.137154 | −0.0111986 | ||||||||
\(151\) | 0.00540415 | 0.000439784 0 | 0.000219892 | − | 1.00000i | \(-0.499930\pi\) | ||||
0.000219892 | 1.00000i | \(0.499930\pi\) | ||||||||
\(152\) | −2.27097 | −0.184200 | ||||||||
\(153\) | 2.86285 | 0.231447 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1.79091 | 0.143849 | ||||||||
\(156\) | −3.33700 | −0.267174 | ||||||||
\(157\) | 0.554838 | 0.0442809 | 0.0221404 | − | 0.999755i | \(-0.492952\pi\) | ||||
0.0221404 | + | 0.999755i | \(0.492952\pi\) | |||||||
\(158\) | −1.05697 | −0.0840884 | ||||||||
\(159\) | −2.11174 | −0.167472 | ||||||||
\(160\) | −1.11558 | −0.0881947 | ||||||||
\(161\) | 24.6703 | 1.94430 | ||||||||
\(162\) | 0.536150 | 0.0421239 | ||||||||
\(163\) | −7.96428 | −0.623811 | −0.311905 | − | 0.950113i | \(-0.600967\pi\) | ||||
−0.311905 | + | 0.950113i | \(0.600967\pi\) | |||||||
\(164\) | −3.47924 | −0.271683 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0.419007 | 0.0325212 | ||||||||
\(167\) | −3.42643 | −0.265145 | −0.132572 | − | 0.991173i | \(-0.542324\pi\) | ||||
−0.132572 | + | 0.991173i | \(0.542324\pi\) | |||||||
\(168\) | −2.47680 | −0.191089 | ||||||||
\(169\) | −11.6946 | −0.899582 | ||||||||
\(170\) | 0.315430 | 0.0241923 | ||||||||
\(171\) | 5.16413 | 0.394911 | ||||||||
\(172\) | −0.523783 | −0.0399381 | ||||||||
\(173\) | −20.5669 | −1.56367 | −0.781836 | − | 0.623484i | \(-0.785717\pi\) | ||||
−0.781836 | + | 0.623484i | \(0.785717\pi\) | |||||||
\(174\) | 0.455465 | 0.0345287 | ||||||||
\(175\) | −4.52452 | −0.342022 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −10.3670 | −0.779231 | ||||||||
\(178\) | −1.24065 | −0.0929910 | ||||||||
\(179\) | −2.56432 | −0.191666 | −0.0958332 | − | 0.995397i | \(-0.530552\pi\) | ||||
−0.0958332 | + | 0.995397i | \(0.530552\pi\) | |||||||
\(180\) | 1.68997 | 0.125963 | ||||||||
\(181\) | 13.4169 | 0.997268 | 0.498634 | − | 0.866813i | \(-0.333835\pi\) | ||||
0.498634 | + | 0.866813i | \(0.333835\pi\) | |||||||
\(182\) | 0.483402 | 0.0358322 | ||||||||
\(183\) | −3.67042 | −0.271325 | ||||||||
\(184\) | −2.03502 | −0.150024 | ||||||||
\(185\) | 1.48881 | 0.109459 | ||||||||
\(186\) | −0.245630 | −0.0180104 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | −13.7889 | −1.00566 | ||||||||
\(189\) | 25.5410 | 1.85783 | ||||||||
\(190\) | 0.568986 | 0.0412786 | ||||||||
\(191\) | 18.1898 | 1.31617 | 0.658085 | − | 0.752944i | \(-0.271367\pi\) | ||||
0.658085 | + | 0.752944i | \(0.271367\pi\) | |||||||
\(192\) | −11.4272 | −0.824685 | ||||||||
\(193\) | −15.6887 | −1.12929 | −0.564647 | − | 0.825333i | \(-0.690988\pi\) | ||||
−0.564647 | + | 0.825333i | \(0.690988\pi\) | |||||||
\(194\) | 0.313871 | 0.0225346 | ||||||||
\(195\) | 1.67583 | 0.120008 | ||||||||
\(196\) | −26.8248 | −1.91606 | ||||||||
\(197\) | 21.8486 | 1.55665 | 0.778325 | − | 0.627862i | \(-0.216070\pi\) | ||||
0.778325 | + | 0.627862i | \(0.216070\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −4.55200 | −0.322683 | −0.161341 | − | 0.986899i | \(-0.551582\pi\) | ||||
−0.161341 | + | 0.986899i | \(0.551582\pi\) | |||||||
\(200\) | 0.373222 | 0.0263908 | ||||||||
\(201\) | −0.757710 | −0.0534448 | ||||||||
\(202\) | −0.872913 | −0.0614180 | ||||||||
\(203\) | 15.0252 | 1.05456 | ||||||||
\(204\) | 9.85196 | 0.689775 | ||||||||
\(205\) | 1.74726 | 0.122034 | ||||||||
\(206\) | 1.30128 | 0.0906646 | ||||||||
\(207\) | 4.62760 | 0.321640 | ||||||||
\(208\) | 4.51038 | 0.312738 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0.620556 | 0.0428225 | ||||||||
\(211\) | −18.9604 | −1.30529 | −0.652645 | − | 0.757664i | \(-0.726341\pi\) | ||||
−0.652645 | + | 0.757664i | \(0.726341\pi\) | |||||||
\(212\) | 2.86693 | 0.196901 | ||||||||
\(213\) | −15.7384 | −1.07838 | ||||||||
\(214\) | −1.56987 | −0.107314 | ||||||||
\(215\) | 0.263041 | 0.0179393 | ||||||||
\(216\) | −2.10684 | −0.143352 | ||||||||
\(217\) | −8.10300 | −0.550067 | ||||||||
\(218\) | −0.341585 | −0.0231351 | ||||||||
\(219\) | 8.33284 | 0.563081 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −3.85410 | −0.259255 | ||||||||
\(222\) | −0.204196 | −0.0137047 | ||||||||
\(223\) | 4.87952 | 0.326757 | 0.163378 | − | 0.986563i | \(-0.447761\pi\) | ||||
0.163378 | + | 0.986563i | \(0.447761\pi\) | |||||||
\(224\) | 5.04749 | 0.337250 | ||||||||
\(225\) | −0.848698 | −0.0565799 | ||||||||
\(226\) | 1.11299 | 0.0740347 | ||||||||
\(227\) | −16.3229 | −1.08339 | −0.541693 | − | 0.840577i | \(-0.682216\pi\) | ||||
−0.541693 | + | 0.840577i | \(0.682216\pi\) | |||||||
\(228\) | 17.7714 | 1.17694 | ||||||||
\(229\) | −4.83167 | −0.319286 | −0.159643 | − | 0.987175i | \(-0.551034\pi\) | ||||
−0.159643 | + | 0.987175i | \(0.551034\pi\) | |||||||
\(230\) | 0.509871 | 0.0336199 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −1.23941 | −0.0813711 | ||||||||
\(233\) | 8.41975 | 0.551596 | 0.275798 | − | 0.961216i | \(-0.411058\pi\) | ||||
0.275798 | + | 0.961216i | \(0.411058\pi\) | |||||||
\(234\) | 0.0906753 | 0.00592763 | ||||||||
\(235\) | 6.92472 | 0.451719 | ||||||||
\(236\) | 14.0744 | 0.916165 | ||||||||
\(237\) | 16.5790 | 1.07692 | ||||||||
\(238\) | −1.42717 | −0.0925096 | ||||||||
\(239\) | 22.6928 | 1.46787 | 0.733937 | − | 0.679218i | \(-0.237681\pi\) | ||||
0.733937 | + | 0.679218i | \(0.237681\pi\) | |||||||
\(240\) | 5.79009 | 0.373749 | ||||||||
\(241\) | −11.6065 | −0.747638 | −0.373819 | − | 0.927502i | \(-0.621952\pi\) | ||||
−0.373819 | + | 0.927502i | \(0.621952\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 8.52534 | 0.546901 | ||||||||
\(244\) | 4.98302 | 0.319005 | ||||||||
\(245\) | 13.4713 | 0.860651 | ||||||||
\(246\) | −0.239644 | −0.0152791 | ||||||||
\(247\) | −6.95220 | −0.442358 | ||||||||
\(248\) | 0.668405 | 0.0424438 | ||||||||
\(249\) | −6.57225 | −0.416499 | ||||||||
\(250\) | −0.0935099 | −0.00591408 | ||||||||
\(251\) | 3.31305 | 0.209118 | 0.104559 | − | 0.994519i | \(-0.466657\pi\) | ||||
0.104559 | + | 0.994519i | \(0.466657\pi\) | |||||||
\(252\) | −7.64633 | −0.481674 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 1.84800 | 0.115954 | ||||||||
\(255\) | −4.94761 | −0.309831 | ||||||||
\(256\) | 15.3051 | 0.956566 | ||||||||
\(257\) | −26.8466 | −1.67465 | −0.837323 | − | 0.546709i | \(-0.815880\pi\) | ||||
−0.837323 | + | 0.546709i | \(0.815880\pi\) | |||||||
\(258\) | −0.0360772 | −0.00224607 | ||||||||
\(259\) | −6.73614 | −0.418563 | ||||||||
\(260\) | −2.27513 | −0.141097 | ||||||||
\(261\) | 2.81838 | 0.174454 | ||||||||
\(262\) | −0.180922 | −0.0111774 | ||||||||
\(263\) | −12.1682 | −0.750324 | −0.375162 | − | 0.926959i | \(-0.622413\pi\) | ||||
−0.375162 | + | 0.926959i | \(0.622413\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1.43976 | −0.0884436 | ||||||||
\(266\) | −2.57439 | −0.157846 | ||||||||
\(267\) | 19.4601 | 1.19094 | ||||||||
\(268\) | 1.02868 | 0.0628365 | ||||||||
\(269\) | −2.09351 | −0.127644 | −0.0638218 | − | 0.997961i | \(-0.520329\pi\) | ||||
−0.0638218 | + | 0.997961i | \(0.520329\pi\) | |||||||
\(270\) | 0.527864 | 0.0321248 | ||||||||
\(271\) | −15.1428 | −0.919859 | −0.459930 | − | 0.887955i | \(-0.652125\pi\) | ||||
−0.459930 | + | 0.887955i | \(0.652125\pi\) | |||||||
\(272\) | −13.3162 | −0.807411 | ||||||||
\(273\) | −7.58232 | −0.458903 | ||||||||
\(274\) | 1.17218 | 0.0708138 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 15.9250 | 0.958574 | ||||||||
\(277\) | −8.27066 | −0.496936 | −0.248468 | − | 0.968640i | \(-0.579927\pi\) | ||||
−0.248468 | + | 0.968640i | \(0.579927\pi\) | |||||||
\(278\) | −1.05152 | −0.0630662 | ||||||||
\(279\) | −1.51994 | −0.0909963 | ||||||||
\(280\) | −1.68865 | −0.100916 | ||||||||
\(281\) | −2.44723 | −0.145989 | −0.0729947 | − | 0.997332i | \(-0.523256\pi\) | ||||
−0.0729947 | + | 0.997332i | \(0.523256\pi\) | |||||||
\(282\) | −0.949753 | −0.0565569 | ||||||||
\(283\) | −26.0948 | −1.55117 | −0.775586 | − | 0.631242i | \(-0.782546\pi\) | ||||
−0.775586 | + | 0.631242i | \(0.782546\pi\) | |||||||
\(284\) | 21.3667 | 1.26788 | ||||||||
\(285\) | −8.92472 | −0.528655 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −7.90553 | −0.466648 | ||||||||
\(288\) | 0.946794 | 0.0557904 | ||||||||
\(289\) | −5.62137 | −0.330669 | ||||||||
\(290\) | 0.310531 | 0.0182350 | ||||||||
\(291\) | −4.92316 | −0.288601 | ||||||||
\(292\) | −11.3128 | −0.662031 | ||||||||
\(293\) | −13.4529 | −0.785929 | −0.392965 | − | 0.919554i | \(-0.628551\pi\) | ||||
−0.392965 | + | 0.919554i | \(0.628551\pi\) | |||||||
\(294\) | −1.84764 | −0.107757 | ||||||||
\(295\) | −7.06810 | −0.411520 | ||||||||
\(296\) | 0.555655 | 0.0322968 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −1.62087 | −0.0938944 | ||||||||
\(299\) | −6.22989 | −0.360284 | ||||||||
\(300\) | −2.92064 | −0.168623 | ||||||||
\(301\) | −1.19014 | −0.0685984 | ||||||||
\(302\) | −0.000505342 0 | −2.90791e−5 0 | ||||||||
\(303\) | 13.6919 | 0.786580 | ||||||||
\(304\) | −24.0203 | −1.37766 | ||||||||
\(305\) | −2.50245 | −0.143290 | ||||||||
\(306\) | −0.267704 | −0.0153036 | ||||||||
\(307\) | −27.1844 | −1.55150 | −0.775748 | − | 0.631042i | \(-0.782627\pi\) | ||||
−0.775748 | + | 0.631042i | \(0.782627\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −20.4110 | −1.16114 | ||||||||
\(310\) | −0.167467 | −0.00951151 | ||||||||
\(311\) | −13.1990 | −0.748448 | −0.374224 | − | 0.927338i | \(-0.622091\pi\) | ||||
−0.374224 | + | 0.927338i | \(0.622091\pi\) | |||||||
\(312\) | 0.625455 | 0.0354094 | ||||||||
\(313\) | 16.1719 | 0.914090 | 0.457045 | − | 0.889443i | \(-0.348908\pi\) | ||||
0.457045 | + | 0.889443i | \(0.348908\pi\) | |||||||
\(314\) | −0.0518828 | −0.00292792 | ||||||||
\(315\) | 3.83995 | 0.216357 | ||||||||
\(316\) | −22.5079 | −1.26617 | ||||||||
\(317\) | −5.38115 | −0.302235 | −0.151118 | − | 0.988516i | \(-0.548287\pi\) | ||||
−0.151118 | + | 0.988516i | \(0.548287\pi\) | |||||||
\(318\) | 0.197469 | 0.0110735 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | −7.79091 | −0.435525 | ||||||||
\(321\) | 24.6239 | 1.37437 | ||||||||
\(322\) | −2.30692 | −0.128560 | ||||||||
\(323\) | 20.5253 | 1.14206 | ||||||||
\(324\) | 11.4171 | 0.634283 | ||||||||
\(325\) | 1.14256 | 0.0633777 | ||||||||
\(326\) | 0.744739 | 0.0412473 | ||||||||
\(327\) | 5.35787 | 0.296291 | ||||||||
\(328\) | 0.652116 | 0.0360071 | ||||||||
\(329\) | −31.3311 | −1.72734 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −18.5702 | −1.02071 | −0.510356 | − | 0.859963i | \(-0.670486\pi\) | ||||
−0.510356 | + | 0.859963i | \(0.670486\pi\) | |||||||
\(332\) | 8.92258 | 0.489690 | ||||||||
\(333\) | −1.26355 | −0.0692419 | ||||||||
\(334\) | 0.320405 | 0.0175318 | ||||||||
\(335\) | −0.516598 | −0.0282247 | ||||||||
\(336\) | −26.1974 | −1.42918 | ||||||||
\(337\) | −9.00615 | −0.490596 | −0.245298 | − | 0.969448i | \(-0.578886\pi\) | ||||
−0.245298 | + | 0.969448i | \(0.578886\pi\) | |||||||
\(338\) | 1.09356 | 0.0594817 | ||||||||
\(339\) | −17.4575 | −0.948163 | ||||||||
\(340\) | 6.71695 | 0.364278 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | −0.482897 | −0.0261121 | ||||||||
\(343\) | −29.2796 | −1.58095 | ||||||||
\(344\) | 0.0981728 | 0.00529312 | ||||||||
\(345\) | −7.99748 | −0.430570 | ||||||||
\(346\) | 1.92321 | 0.103392 | ||||||||
\(347\) | −10.2710 | −0.551374 | −0.275687 | − | 0.961247i | \(-0.588905\pi\) | ||||
−0.275687 | + | 0.961247i | \(0.588905\pi\) | |||||||
\(348\) | 9.69895 | 0.519919 | ||||||||
\(349\) | −17.2613 | −0.923974 | −0.461987 | − | 0.886887i | \(-0.652863\pi\) | ||||
−0.461987 | + | 0.886887i | \(0.652863\pi\) | |||||||
\(350\) | 0.423088 | 0.0226150 | ||||||||
\(351\) | −6.44975 | −0.344262 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −22.8096 | −1.21403 | −0.607017 | − | 0.794689i | \(-0.707634\pi\) | ||||
−0.607017 | + | 0.794689i | \(0.707634\pi\) | |||||||
\(354\) | 0.969417 | 0.0515239 | ||||||||
\(355\) | −10.7303 | −0.569504 | ||||||||
\(356\) | −26.4192 | −1.40022 | ||||||||
\(357\) | 22.3856 | 1.18477 | ||||||||
\(358\) | 0.239790 | 0.0126733 | ||||||||
\(359\) | 16.0747 | 0.848390 | 0.424195 | − | 0.905571i | \(-0.360557\pi\) | ||||
0.424195 | + | 0.905571i | \(0.360557\pi\) | |||||||
\(360\) | −0.316753 | −0.0166943 | ||||||||
\(361\) | 18.0244 | 0.948651 | ||||||||
\(362\) | −1.25461 | −0.0659408 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 10.2939 | 0.539545 | ||||||||
\(365\) | 5.68123 | 0.297369 | ||||||||
\(366\) | 0.343221 | 0.0179404 | ||||||||
\(367\) | 21.9975 | 1.14826 | 0.574129 | − | 0.818765i | \(-0.305341\pi\) | ||||
0.574129 | + | 0.818765i | \(0.305341\pi\) | |||||||
\(368\) | −21.5247 | −1.12205 | ||||||||
\(369\) | −1.48290 | −0.0771965 | ||||||||
\(370\) | −0.139218 | −0.00723761 | ||||||||
\(371\) | 6.51422 | 0.338202 | ||||||||
\(372\) | −5.23059 | −0.271193 | ||||||||
\(373\) | 20.2604 | 1.04905 | 0.524523 | − | 0.851396i | \(-0.324244\pi\) | ||||
0.524523 | + | 0.851396i | \(0.324244\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1.46673 | 0.0757417 | ||||||||
\(376\) | 2.58446 | 0.133283 | ||||||||
\(377\) | −3.79425 | −0.195414 | ||||||||
\(378\) | −2.38833 | −0.122843 | ||||||||
\(379\) | −3.72771 | −0.191480 | −0.0957398 | − | 0.995406i | \(-0.530522\pi\) | ||||
−0.0957398 | + | 0.995406i | \(0.530522\pi\) | |||||||
\(380\) | 12.1163 | 0.621554 | ||||||||
\(381\) | −28.9865 | −1.48502 | ||||||||
\(382\) | −1.70093 | −0.0870271 | ||||||||
\(383\) | −10.9974 | −0.561941 | −0.280970 | − | 0.959716i | \(-0.590656\pi\) | ||||
−0.280970 | + | 0.959716i | \(0.590656\pi\) | |||||||
\(384\) | 4.34108 | 0.221530 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 1.46704 | 0.0746706 | ||||||||
\(387\) | −0.223243 | −0.0113481 | ||||||||
\(388\) | 6.68375 | 0.339316 | ||||||||
\(389\) | 9.38220 | 0.475697 | 0.237848 | − | 0.971302i | \(-0.423558\pi\) | ||||
0.237848 | + | 0.971302i | \(0.423558\pi\) | |||||||
\(390\) | −0.156706 | −0.00793513 | ||||||||
\(391\) | 18.3928 | 0.930163 | ||||||||
\(392\) | 5.02779 | 0.253942 | ||||||||
\(393\) | 2.83781 | 0.143149 | ||||||||
\(394\) | −2.04306 | −0.102928 | ||||||||
\(395\) | 11.3033 | 0.568733 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 22.3136 | 1.11989 | 0.559945 | − | 0.828530i | \(-0.310822\pi\) | ||||
0.559945 | + | 0.828530i | \(0.310822\pi\) | |||||||
\(398\) | 0.425657 | 0.0213363 | ||||||||
\(399\) | 40.3801 | 2.02153 | ||||||||
\(400\) | 3.94761 | 0.197381 | ||||||||
\(401\) | −24.6822 | −1.23257 | −0.616285 | − | 0.787523i | \(-0.711363\pi\) | ||||
−0.616285 | + | 0.787523i | \(0.711363\pi\) | |||||||
\(402\) | 0.0708534 | 0.00353385 | ||||||||
\(403\) | 2.04621 | 0.101929 | ||||||||
\(404\) | −18.5883 | −0.924804 | ||||||||
\(405\) | −5.73362 | −0.284906 | ||||||||
\(406\) | −1.40500 | −0.0697292 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | −1.84656 | −0.0914182 | ||||||||
\(409\) | −29.5056 | −1.45896 | −0.729478 | − | 0.684004i | \(-0.760237\pi\) | ||||
−0.729478 | + | 0.684004i | \(0.760237\pi\) | |||||||
\(410\) | −0.163386 | −0.00806907 | ||||||||
\(411\) | −18.3860 | −0.906913 | ||||||||
\(412\) | 27.7103 | 1.36519 | ||||||||
\(413\) | 31.9798 | 1.57362 | ||||||||
\(414\) | −0.432726 | −0.0212673 | ||||||||
\(415\) | −4.48088 | −0.219958 | ||||||||
\(416\) | −1.27462 | −0.0624934 | ||||||||
\(417\) | 16.4935 | 0.807689 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 9.03564 | 0.441420 | 0.220710 | − | 0.975339i | \(-0.429163\pi\) | ||||
0.220710 | + | 0.975339i | \(0.429163\pi\) | |||||||
\(420\) | 13.2145 | 0.644802 | ||||||||
\(421\) | 14.2201 | 0.693047 | 0.346524 | − | 0.938041i | \(-0.387362\pi\) | ||||
0.346524 | + | 0.938041i | \(0.387362\pi\) | |||||||
\(422\) | 1.77299 | 0.0863077 | ||||||||
\(423\) | −5.87699 | −0.285749 | ||||||||
\(424\) | −0.537349 | −0.0260960 | ||||||||
\(425\) | −3.37322 | −0.163625 | ||||||||
\(426\) | 1.47170 | 0.0713041 | ||||||||
\(427\) | 11.3224 | 0.547929 | ||||||||
\(428\) | −33.4298 | −1.61589 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −0.0245970 | −0.00118617 | ||||||||
\(431\) | 1.73155 | 0.0834060 | 0.0417030 | − | 0.999130i | \(-0.486722\pi\) | ||||
0.0417030 | + | 0.999130i | \(0.486722\pi\) | |||||||
\(432\) | −22.2843 | −1.07215 | ||||||||
\(433\) | 18.4476 | 0.886535 | 0.443268 | − | 0.896389i | \(-0.353819\pi\) | ||||
0.443268 | + | 0.896389i | \(0.353819\pi\) | |||||||
\(434\) | 0.757710 | 0.0363713 | ||||||||
\(435\) | −4.87077 | −0.233536 | ||||||||
\(436\) | −7.27393 | −0.348358 | ||||||||
\(437\) | 33.1777 | 1.58710 | ||||||||
\(438\) | −0.779203 | −0.0372318 | ||||||||
\(439\) | 17.1704 | 0.819499 | 0.409750 | − | 0.912198i | \(-0.365616\pi\) | ||||
0.409750 | + | 0.912198i | \(0.365616\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −11.4331 | −0.544432 | ||||||||
\(442\) | 0.360397 | 0.0171423 | ||||||||
\(443\) | 36.5992 | 1.73888 | 0.869441 | − | 0.494037i | \(-0.164479\pi\) | ||||
0.869441 | + | 0.494037i | \(0.164479\pi\) | |||||||
\(444\) | −4.34827 | −0.206360 | ||||||||
\(445\) | 13.2676 | 0.628946 | ||||||||
\(446\) | −0.456283 | −0.0216056 | ||||||||
\(447\) | 25.4238 | 1.20251 | ||||||||
\(448\) | 35.2501 | 1.66541 | ||||||||
\(449\) | −16.6029 | −0.783540 | −0.391770 | − | 0.920063i | \(-0.628137\pi\) | ||||
−0.391770 | + | 0.920063i | \(0.628137\pi\) | |||||||
\(450\) | 0.0793616 | 0.00374114 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 23.7006 | 1.11478 | ||||||||
\(453\) | 0.00792644 | 0.000372417 0 | ||||||||
\(454\) | 1.52635 | 0.0716351 | ||||||||
\(455\) | −5.16953 | −0.242351 | ||||||||
\(456\) | −3.33090 | −0.155984 | ||||||||
\(457\) | 31.6653 | 1.48124 | 0.740620 | − | 0.671924i | \(-0.234532\pi\) | ||||
0.740620 | + | 0.671924i | \(0.234532\pi\) | |||||||
\(458\) | 0.451809 | 0.0211116 | ||||||||
\(459\) | 19.0419 | 0.888798 | ||||||||
\(460\) | 10.8575 | 0.506233 | ||||||||
\(461\) | 25.4351 | 1.18463 | 0.592315 | − | 0.805706i | \(-0.298214\pi\) | ||||
0.592315 | + | 0.805706i | \(0.298214\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −16.3319 | −0.759007 | −0.379503 | − | 0.925190i | \(-0.623905\pi\) | ||||
−0.379503 | + | 0.925190i | \(0.623905\pi\) | |||||||
\(464\) | −13.1094 | −0.608587 | ||||||||
\(465\) | 2.62678 | 0.121814 | ||||||||
\(466\) | −0.787330 | −0.0364723 | ||||||||
\(467\) | 8.52911 | 0.394680 | 0.197340 | − | 0.980335i | \(-0.436770\pi\) | ||||
0.197340 | + | 0.980335i | \(0.436770\pi\) | |||||||
\(468\) | 1.93089 | 0.0892556 | ||||||||
\(469\) | 2.33736 | 0.107929 | ||||||||
\(470\) | −0.647530 | −0.0298683 | ||||||||
\(471\) | 0.813798 | 0.0374978 | ||||||||
\(472\) | −2.63797 | −0.121422 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | −1.55030 | −0.0712076 | ||||||||
\(475\) | −6.08477 | −0.279188 | ||||||||
\(476\) | −30.3910 | −1.39297 | ||||||||
\(477\) | 1.22192 | 0.0559479 | ||||||||
\(478\) | −2.12200 | −0.0970580 | ||||||||
\(479\) | −29.9478 | −1.36835 | −0.684175 | − | 0.729318i | \(-0.739838\pi\) | ||||
−0.684175 | + | 0.729318i | \(0.739838\pi\) | |||||||
\(480\) | −1.63626 | −0.0746849 | ||||||||
\(481\) | 1.70105 | 0.0775611 | ||||||||
\(482\) | 1.08532 | 0.0494349 | ||||||||
\(483\) | 36.1848 | 1.64646 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −3.35655 | −0.152413 | ||||||||
\(486\) | −0.797204 | −0.0361619 | ||||||||
\(487\) | −19.6031 | −0.888300 | −0.444150 | − | 0.895952i | \(-0.646494\pi\) | ||||
−0.444150 | + | 0.895952i | \(0.646494\pi\) | |||||||
\(488\) | −0.933969 | −0.0422788 | ||||||||
\(489\) | −11.6815 | −0.528254 | ||||||||
\(490\) | −1.25970 | −0.0569075 | ||||||||
\(491\) | 15.7891 | 0.712553 | 0.356277 | − | 0.934381i | \(-0.384046\pi\) | ||||
0.356277 | + | 0.934381i | \(0.384046\pi\) | |||||||
\(492\) | −5.10312 | −0.230066 | ||||||||
\(493\) | 11.2019 | 0.504509 | ||||||||
\(494\) | 0.650099 | 0.0292494 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 7.06980 | 0.317443 | ||||||||
\(497\) | 48.5494 | 2.17774 | ||||||||
\(498\) | 0.614570 | 0.0275396 | ||||||||
\(499\) | 11.2081 | 0.501745 | 0.250872 | − | 0.968020i | \(-0.419283\pi\) | ||||
0.250872 | + | 0.968020i | \(0.419283\pi\) | |||||||
\(500\) | −1.99126 | −0.0890517 | ||||||||
\(501\) | −5.02565 | −0.224530 | ||||||||
\(502\) | −0.309803 | −0.0138272 | ||||||||
\(503\) | 0.342908 | 0.0152895 | 0.00764477 | − | 0.999971i | \(-0.497567\pi\) | ||||
0.00764477 | + | 0.999971i | \(0.497567\pi\) | |||||||
\(504\) | 1.43315 | 0.0638378 | ||||||||
\(505\) | 9.33498 | 0.415401 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −17.1528 | −0.761782 | ||||||||
\(508\) | 39.3525 | 1.74599 | ||||||||
\(509\) | −19.5626 | −0.867098 | −0.433549 | − | 0.901130i | \(-0.642739\pi\) | ||||
−0.433549 | + | 0.901130i | \(0.642739\pi\) | |||||||
\(510\) | 0.462651 | 0.0204865 | ||||||||
\(511\) | −25.7049 | −1.13712 | ||||||||
\(512\) | −7.35057 | −0.324852 | ||||||||
\(513\) | 34.3485 | 1.51653 | ||||||||
\(514\) | 2.51042 | 0.110730 | ||||||||
\(515\) | −13.9160 | −0.613211 | ||||||||
\(516\) | −0.768249 | −0.0338203 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0.629896 | 0.0276760 | ||||||||
\(519\) | −30.1661 | −1.32415 | ||||||||
\(520\) | 0.426428 | 0.0187001 | ||||||||
\(521\) | 42.0264 | 1.84121 | 0.920606 | − | 0.390493i | \(-0.127695\pi\) | ||||
0.920606 | + | 0.390493i | \(0.127695\pi\) | |||||||
\(522\) | −0.263547 | −0.0115351 | ||||||||
\(523\) | −30.0105 | −1.31227 | −0.656135 | − | 0.754644i | \(-0.727810\pi\) | ||||
−0.656135 | + | 0.754644i | \(0.727810\pi\) | |||||||
\(524\) | −3.85266 | −0.168304 | ||||||||
\(525\) | −6.63626 | −0.289630 | ||||||||
\(526\) | 1.13785 | 0.0496125 | ||||||||
\(527\) | −6.04112 | −0.263155 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 6.73067 | 0.292638 | ||||||||
\(530\) | 0.134632 | 0.00584802 | ||||||||
\(531\) | 5.99868 | 0.260320 | ||||||||
\(532\) | −54.8206 | −2.37677 | ||||||||
\(533\) | 1.99635 | 0.0864714 | ||||||||
\(534\) | −1.81971 | −0.0787464 | ||||||||
\(535\) | 16.7883 | 0.725822 | ||||||||
\(536\) | −0.192806 | −0.00832793 | ||||||||
\(537\) | −3.76117 | −0.162307 | ||||||||
\(538\) | 0.195764 | 0.00843998 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 11.2407 | 0.483721 | ||||||||
\(541\) | 10.3236 | 0.443846 | 0.221923 | − | 0.975064i | \(-0.428767\pi\) | ||||
0.221923 | + | 0.975064i | \(0.428767\pi\) | |||||||
\(542\) | 1.41600 | 0.0608225 | ||||||||
\(543\) | 19.6789 | 0.844504 | ||||||||
\(544\) | 3.76311 | 0.161342 | ||||||||
\(545\) | 3.65293 | 0.156474 | ||||||||
\(546\) | 0.709022 | 0.0303433 | ||||||||
\(547\) | −41.8168 | −1.78796 | −0.893979 | − | 0.448108i | \(-0.852098\pi\) | ||||
−0.893979 | + | 0.448108i | \(0.852098\pi\) | |||||||
\(548\) | 24.9611 | 1.06628 | ||||||||
\(549\) | 2.12382 | 0.0906426 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 20.2065 | 0.860826 | ||||||||
\(552\) | −2.98483 | −0.127043 | ||||||||
\(553\) | −51.1423 | −2.17479 | ||||||||
\(554\) | 0.773388 | 0.0328581 | ||||||||
\(555\) | 2.18368 | 0.0926920 | ||||||||
\(556\) | −22.3918 | −0.949622 | ||||||||
\(557\) | 38.4828 | 1.63057 | 0.815285 | − | 0.579060i | \(-0.196580\pi\) | ||||
0.815285 | + | 0.579060i | \(0.196580\pi\) | |||||||
\(558\) | 0.142129 | 0.00601681 | ||||||||
\(559\) | 0.300540 | 0.0127115 | ||||||||
\(560\) | −17.8611 | −0.754768 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0.228840 | 0.00965303 | ||||||||
\(563\) | −30.6864 | −1.29328 | −0.646639 | − | 0.762796i | \(-0.723826\pi\) | ||||
−0.646639 | + | 0.762796i | \(0.723826\pi\) | |||||||
\(564\) | −20.2246 | −0.851609 | ||||||||
\(565\) | −11.9023 | −0.500735 | ||||||||
\(566\) | 2.44012 | 0.102566 | ||||||||
\(567\) | 25.9419 | 1.08946 | ||||||||
\(568\) | −4.00478 | −0.168037 | ||||||||
\(569\) | −13.0485 | −0.547020 | −0.273510 | − | 0.961869i | \(-0.588185\pi\) | ||||
−0.273510 | + | 0.961869i | \(0.588185\pi\) | |||||||
\(570\) | 0.834550 | 0.0349554 | ||||||||
\(571\) | −16.1300 | −0.675018 | −0.337509 | − | 0.941322i | \(-0.609584\pi\) | ||||
−0.337509 | + | 0.941322i | \(0.609584\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 26.6796 | 1.11456 | ||||||||
\(574\) | 0.739245 | 0.0308555 | ||||||||
\(575\) | −5.45258 | −0.227388 | ||||||||
\(576\) | 6.61212 | 0.275505 | ||||||||
\(577\) | −14.5714 | −0.606617 | −0.303308 | − | 0.952892i | \(-0.598091\pi\) | ||||
−0.303308 | + | 0.952892i | \(0.598091\pi\) | |||||||
\(578\) | 0.525654 | 0.0218643 | ||||||||
\(579\) | −23.0110 | −0.956306 | ||||||||
\(580\) | 6.61263 | 0.274575 | ||||||||
\(581\) | 20.2738 | 0.841101 | ||||||||
\(582\) | 0.460364 | 0.0190827 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 2.12036 | 0.0877411 | ||||||||
\(585\) | −0.969687 | −0.0400916 | ||||||||
\(586\) | 1.25798 | 0.0519668 | ||||||||
\(587\) | −27.8742 | −1.15049 | −0.575246 | − | 0.817981i | \(-0.695094\pi\) | ||||
−0.575246 | + | 0.817981i | \(0.695094\pi\) | |||||||
\(588\) | −39.3448 | −1.62255 | ||||||||
\(589\) | −10.8972 | −0.449013 | ||||||||
\(590\) | 0.660937 | 0.0272103 | ||||||||
\(591\) | 32.0461 | 1.31820 | ||||||||
\(592\) | 5.87723 | 0.241553 | ||||||||
\(593\) | −15.1037 | −0.620236 | −0.310118 | − | 0.950698i | \(-0.600369\pi\) | ||||
−0.310118 | + | 0.950698i | \(0.600369\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 15.2622 | 0.625690 | ||||||||
\(596\) | −34.5158 | −1.41382 | ||||||||
\(597\) | −6.67657 | −0.273254 | ||||||||
\(598\) | 0.582557 | 0.0238225 | ||||||||
\(599\) | −25.8757 | −1.05725 | −0.528626 | − | 0.848855i | \(-0.677292\pi\) | ||||
−0.528626 | + | 0.848855i | \(0.677292\pi\) | |||||||
\(600\) | 0.547416 | 0.0223482 | ||||||||
\(601\) | 47.0268 | 1.91826 | 0.959132 | − | 0.282959i | \(-0.0913160\pi\) | ||||
0.959132 | + | 0.282959i | \(0.0913160\pi\) | |||||||
\(602\) | 0.111290 | 0.00453583 | ||||||||
\(603\) | 0.438435 | 0.0178545 | ||||||||
\(604\) | −0.0107610 | −0.000437861 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −1.28033 | −0.0520098 | ||||||||
\(607\) | 35.2239 | 1.42969 | 0.714847 | − | 0.699281i | \(-0.246496\pi\) | ||||
0.714847 | + | 0.699281i | \(0.246496\pi\) | |||||||
\(608\) | 6.78807 | 0.275293 | ||||||||
\(609\) | 22.0379 | 0.893022 | ||||||||
\(610\) | 0.234004 | 0.00947454 | ||||||||
\(611\) | 7.91189 | 0.320081 | ||||||||
\(612\) | −5.70066 | −0.230435 | ||||||||
\(613\) | 23.4117 | 0.945590 | 0.472795 | − | 0.881173i | \(-0.343245\pi\) | ||||
0.472795 | + | 0.881173i | \(0.343245\pi\) | |||||||
\(614\) | 2.54201 | 0.102587 | ||||||||
\(615\) | 2.56276 | 0.103341 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 22.8910 | 0.921557 | 0.460778 | − | 0.887515i | \(-0.347570\pi\) | ||||
0.460778 | + | 0.887515i | \(0.347570\pi\) | |||||||
\(618\) | 1.90863 | 0.0767764 | ||||||||
\(619\) | 2.12752 | 0.0855124 | 0.0427562 | − | 0.999086i | \(-0.486386\pi\) | ||||
0.0427562 | + | 0.999086i | \(0.486386\pi\) | |||||||
\(620\) | −3.56615 | −0.143220 | ||||||||
\(621\) | 30.7799 | 1.23515 | ||||||||
\(622\) | 1.23424 | 0.0494885 | ||||||||
\(623\) | −60.0297 | −2.40504 | ||||||||
\(624\) | 6.61551 | 0.264832 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −1.51223 | −0.0604410 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −1.10482 | −0.0440873 | ||||||||
\(629\) | −5.02207 | −0.200243 | ||||||||
\(630\) | −0.359074 | −0.0143058 | ||||||||
\(631\) | 15.4588 | 0.615404 | 0.307702 | − | 0.951483i | \(-0.400440\pi\) | ||||
0.307702 | + | 0.951483i | \(0.400440\pi\) | |||||||
\(632\) | 4.21866 | 0.167809 | ||||||||
\(633\) | −27.8099 | −1.10534 | ||||||||
\(634\) | 0.503191 | 0.0199843 | ||||||||
\(635\) | −19.7627 | −0.784257 | ||||||||
\(636\) | 4.20501 | 0.166740 | ||||||||
\(637\) | 15.3918 | 0.609844 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 9.10676 | 0.360258 | ||||||||
\(640\) | 2.95970 | 0.116992 | ||||||||
\(641\) | 14.1805 | 0.560096 | 0.280048 | − | 0.959986i | \(-0.409650\pi\) | ||||
0.280048 | + | 0.959986i | \(0.409650\pi\) | |||||||
\(642\) | −2.30258 | −0.0908757 | ||||||||
\(643\) | −12.3941 | −0.488774 | −0.244387 | − | 0.969678i | \(-0.578587\pi\) | ||||
−0.244387 | + | 0.969678i | \(0.578587\pi\) | |||||||
\(644\) | −49.1250 | −1.93580 | ||||||||
\(645\) | 0.385811 | 0.0151913 | ||||||||
\(646\) | −1.91932 | −0.0755145 | ||||||||
\(647\) | 33.2465 | 1.30705 | 0.653527 | − | 0.756903i | \(-0.273289\pi\) | ||||
0.653527 | + | 0.756903i | \(0.273289\pi\) | |||||||
\(648\) | −2.13991 | −0.0840637 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | −0.106840 | −0.00419063 | ||||||||
\(651\) | −11.8849 | −0.465807 | ||||||||
\(652\) | 15.8589 | 0.621083 | ||||||||
\(653\) | −34.8066 | −1.36209 | −0.681043 | − | 0.732243i | \(-0.738474\pi\) | ||||
−0.681043 | + | 0.732243i | \(0.738474\pi\) | |||||||
\(654\) | −0.501014 | −0.0195912 | ||||||||
\(655\) | 1.93479 | 0.0755984 | ||||||||
\(656\) | 6.89751 | 0.269303 | ||||||||
\(657\) | −4.82165 | −0.188110 | ||||||||
\(658\) | 2.92976 | 0.114214 | ||||||||
\(659\) | 34.4953 | 1.34375 | 0.671873 | − | 0.740666i | \(-0.265490\pi\) | ||||
0.671873 | + | 0.740666i | \(0.265490\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1.77827 | 0.0691668 | 0.0345834 | − | 0.999402i | \(-0.488990\pi\) | ||||
0.0345834 | + | 0.999402i | \(0.488990\pi\) | |||||||
\(662\) | 1.73650 | 0.0674910 | ||||||||
\(663\) | −5.65293 | −0.219542 | ||||||||
\(664\) | −1.67236 | −0.0649003 | ||||||||
\(665\) | 27.5307 | 1.06759 | ||||||||
\(666\) | 0.118154 | 0.00457838 | ||||||||
\(667\) | 18.1071 | 0.701111 | ||||||||
\(668\) | 6.82289 | 0.263986 | ||||||||
\(669\) | 7.15694 | 0.276703 | ||||||||
\(670\) | 0.0483070 | 0.00186626 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 7.40331 | 0.285589 | ||||||||
\(673\) | −19.2964 | −0.743823 | −0.371911 | − | 0.928268i | \(-0.621297\pi\) | ||||
−0.371911 | + | 0.928268i | \(0.621297\pi\) | |||||||
\(674\) | 0.842164 | 0.0324389 | ||||||||
\(675\) | −5.64501 | −0.217276 | ||||||||
\(676\) | 23.2869 | 0.895649 | ||||||||
\(677\) | 16.9101 | 0.649907 | 0.324953 | − | 0.945730i | \(-0.394651\pi\) | ||||
0.324953 | + | 0.945730i | \(0.394651\pi\) | |||||||
\(678\) | 1.63245 | 0.0626939 | ||||||||
\(679\) | 15.1868 | 0.582816 | ||||||||
\(680\) | −1.25896 | −0.0482789 | ||||||||
\(681\) | −23.9412 | −0.917430 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 4.14018 | 0.158420 | 0.0792098 | − | 0.996858i | \(-0.474760\pi\) | ||||
0.0792098 | + | 0.996858i | \(0.474760\pi\) | |||||||
\(684\) | −10.2831 | −0.393184 | ||||||||
\(685\) | −12.5353 | −0.478950 | ||||||||
\(686\) | 2.73794 | 0.104535 | ||||||||
\(687\) | −7.08676 | −0.270377 | ||||||||
\(688\) | 1.03839 | 0.0395881 | ||||||||
\(689\) | −1.64501 | −0.0626698 | ||||||||
\(690\) | 0.747843 | 0.0284699 | ||||||||
\(691\) | −46.3520 | −1.76331 | −0.881657 | − | 0.471891i | \(-0.843571\pi\) | ||||
−0.881657 | + | 0.471891i | \(0.843571\pi\) | |||||||
\(692\) | 40.9539 | 1.55684 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0.960437 | 0.0364577 | ||||||||
\(695\) | 11.2450 | 0.426549 | ||||||||
\(696\) | −1.81788 | −0.0689065 | ||||||||
\(697\) | −5.89390 | −0.223247 | ||||||||
\(698\) | 1.61410 | 0.0610945 | ||||||||
\(699\) | 12.3495 | 0.467101 | ||||||||
\(700\) | 9.00949 | 0.340527 | ||||||||
\(701\) | 45.4553 | 1.71682 | 0.858412 | − | 0.512961i | \(-0.171452\pi\) | ||||
0.858412 | + | 0.512961i | \(0.171452\pi\) | |||||||
\(702\) | 0.603115 | 0.0227631 | ||||||||
\(703\) | −9.05904 | −0.341668 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 10.1567 | 0.382524 | ||||||||
\(706\) | 2.13293 | 0.0802738 | ||||||||
\(707\) | −42.2364 | −1.58846 | ||||||||
\(708\) | 20.6434 | 0.775825 | ||||||||
\(709\) | −14.0241 | −0.526688 | −0.263344 | − | 0.964702i | \(-0.584825\pi\) | ||||
−0.263344 | + | 0.964702i | \(0.584825\pi\) | |||||||
\(710\) | 1.00339 | 0.0376565 | ||||||||
\(711\) | −9.59312 | −0.359770 | ||||||||
\(712\) | 4.95177 | 0.185575 | ||||||||
\(713\) | −9.76506 | −0.365704 | ||||||||
\(714\) | −2.09327 | −0.0783388 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 5.10622 | 0.190829 | ||||||||
\(717\) | 33.2842 | 1.24302 | ||||||||
\(718\) | −1.50314 | −0.0560968 | ||||||||
\(719\) | 13.1384 | 0.489980 | 0.244990 | − | 0.969526i | \(-0.421215\pi\) | ||||
0.244990 | + | 0.969526i | \(0.421215\pi\) | |||||||
\(720\) | −3.35033 | −0.124859 | ||||||||
\(721\) | 62.9632 | 2.34487 | ||||||||
\(722\) | −1.68546 | −0.0627262 | ||||||||
\(723\) | −17.0236 | −0.633113 | ||||||||
\(724\) | −26.7164 | −0.992908 | ||||||||
\(725\) | −3.32083 | −0.123333 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −18.3635 | −0.681063 | −0.340532 | − | 0.940233i | \(-0.610607\pi\) | ||||
−0.340532 | + | 0.940233i | \(0.610607\pi\) | |||||||
\(728\) | −1.92938 | −0.0715077 | ||||||||
\(729\) | 29.7052 | 1.10019 | ||||||||
\(730\) | −0.531251 | −0.0196625 | ||||||||
\(731\) | −0.887297 | −0.0328179 | ||||||||
\(732\) | 7.30875 | 0.270139 | ||||||||
\(733\) | 36.9977 | 1.36654 | 0.683270 | − | 0.730166i | \(-0.260557\pi\) | ||||
0.683270 | + | 0.730166i | \(0.260557\pi\) | |||||||
\(734\) | −2.05698 | −0.0759246 | ||||||||
\(735\) | 19.7588 | 0.728815 | ||||||||
\(736\) | 6.08282 | 0.224216 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0.138666 | 0.00510435 | ||||||||
\(739\) | −9.85033 | −0.362350 | −0.181175 | − | 0.983451i | \(-0.557990\pi\) | ||||
−0.181175 | + | 0.983451i | \(0.557990\pi\) | |||||||
\(740\) | −2.96459 | −0.108981 | ||||||||
\(741\) | −10.1970 | −0.374597 | ||||||||
\(742\) | −0.609144 | −0.0223624 | ||||||||
\(743\) | −27.4471 | −1.00694 | −0.503468 | − | 0.864014i | \(-0.667943\pi\) | ||||
−0.503468 | + | 0.864014i | \(0.667943\pi\) | |||||||
\(744\) | 0.980371 | 0.0359421 | ||||||||
\(745\) | 17.3337 | 0.635056 | ||||||||
\(746\) | −1.89455 | −0.0693645 | ||||||||
\(747\) | 3.80291 | 0.139141 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −75.9591 | −2.77549 | ||||||||
\(750\) | −0.137154 | −0.00500815 | ||||||||
\(751\) | 13.7284 | 0.500957 | 0.250479 | − | 0.968122i | \(-0.419412\pi\) | ||||
0.250479 | + | 0.968122i | \(0.419412\pi\) | |||||||
\(752\) | 27.3361 | 0.996845 | ||||||||
\(753\) | 4.85936 | 0.177085 | ||||||||
\(754\) | 0.354799 | 0.0129210 | ||||||||
\(755\) | 0.00540415 | 0.000196677 0 | ||||||||
\(756\) | −50.8586 | −1.84971 | ||||||||
\(757\) | −22.9299 | −0.833401 | −0.416701 | − | 0.909044i | \(-0.636814\pi\) | ||||
−0.416701 | + | 0.909044i | \(0.636814\pi\) | |||||||
\(758\) | 0.348578 | 0.0126609 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −2.27097 | −0.0823767 | ||||||||
\(761\) | 20.6818 | 0.749716 | 0.374858 | − | 0.927082i | \(-0.377692\pi\) | ||||
0.374858 | + | 0.927082i | \(0.377692\pi\) | |||||||
\(762\) | 2.71053 | 0.0981920 | ||||||||
\(763\) | −16.5278 | −0.598346 | ||||||||
\(764\) | −36.2206 | −1.31042 | ||||||||
\(765\) | 2.86285 | 0.103506 | ||||||||
\(766\) | 1.02837 | 0.0371564 | ||||||||
\(767\) | −8.07571 | −0.291597 | ||||||||
\(768\) | 22.4484 | 0.810037 | ||||||||
\(769\) | −38.4306 | −1.38584 | −0.692922 | − | 0.721013i | \(-0.743677\pi\) | ||||
−0.692922 | + | 0.721013i | \(0.743677\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −39.3768 | −1.41812 | ||||||||
\(772\) | 31.2401 | 1.12436 | ||||||||
\(773\) | 49.9406 | 1.79624 | 0.898120 | − | 0.439751i | \(-0.144933\pi\) | ||||
0.898120 | + | 0.439751i | \(0.144933\pi\) | |||||||
\(774\) | 0.0208754 | 0.000750351 0 | ||||||||
\(775\) | 1.79091 | 0.0643312 | ||||||||
\(776\) | −1.25274 | −0.0449707 | ||||||||
\(777\) | −9.88011 | −0.354447 | ||||||||
\(778\) | −0.877329 | −0.0314538 | ||||||||
\(779\) | −10.6317 | −0.380919 | ||||||||
\(780\) | −3.33700 | −0.119484 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | −1.71991 | −0.0615037 | ||||||||
\(783\) | 18.7461 | 0.669932 | ||||||||
\(784\) | 53.1795 | 1.89927 | ||||||||
\(785\) | 0.554838 | 0.0198030 | ||||||||
\(786\) | −0.265364 | −0.00946521 | ||||||||
\(787\) | 15.5540 | 0.554440 | 0.277220 | − | 0.960806i | \(-0.410587\pi\) | ||||
0.277220 | + | 0.960806i | \(0.410587\pi\) | |||||||
\(788\) | −43.5062 | −1.54984 | ||||||||
\(789\) | −17.8475 | −0.635388 | ||||||||
\(790\) | −1.05697 | −0.0376055 | ||||||||
\(791\) | 53.8524 | 1.91477 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −2.85919 | −0.101533 | ||||||||
\(794\) | −2.08655 | −0.0740488 | ||||||||
\(795\) | −2.11174 | −0.0748957 | ||||||||
\(796\) | 9.06420 | 0.321272 | ||||||||
\(797\) | 46.1068 | 1.63319 | 0.816593 | − | 0.577214i | \(-0.195860\pi\) | ||||
0.816593 | + | 0.577214i | \(0.195860\pi\) | |||||||
\(798\) | −3.77594 | −0.133667 | ||||||||
\(799\) | −23.3586 | −0.826368 | ||||||||
\(800\) | −1.11558 | −0.0394419 | ||||||||
\(801\) | −11.2602 | −0.397860 | ||||||||
\(802\) | 2.30803 | 0.0814994 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 1.50879 | 0.0532111 | ||||||||
\(805\) | 24.6703 | 0.869515 | ||||||||
\(806\) | −0.191341 | −0.00673971 | ||||||||
\(807\) | −3.07062 | −0.108091 | ||||||||
\(808\) | 3.48402 | 0.122567 | ||||||||
\(809\) | 37.5394 | 1.31981 | 0.659907 | − | 0.751347i | \(-0.270596\pi\) | ||||
0.659907 | + | 0.751347i | \(0.270596\pi\) | |||||||
\(810\) | 0.536150 | 0.0188384 | ||||||||
\(811\) | −7.20547 | −0.253018 | −0.126509 | − | 0.991965i | \(-0.540377\pi\) | ||||
−0.126509 | + | 0.991965i | \(0.540377\pi\) | |||||||
\(812\) | −29.9190 | −1.04995 | ||||||||
\(813\) | −22.2104 | −0.778953 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −7.96428 | −0.278977 | ||||||||
\(816\) | −19.5313 | −0.683731 | ||||||||
\(817\) | −1.60055 | −0.0559960 | ||||||||
\(818\) | 2.75906 | 0.0964684 | ||||||||
\(819\) | 4.38737 | 0.153307 | ||||||||
\(820\) | −3.47924 | −0.121500 | ||||||||
\(821\) | 8.63405 | 0.301331 | 0.150665 | − | 0.988585i | \(-0.451858\pi\) | ||||
0.150665 | + | 0.988585i | \(0.451858\pi\) | |||||||
\(822\) | 1.71927 | 0.0599664 | ||||||||
\(823\) | −25.0121 | −0.871865 | −0.435933 | − | 0.899979i | \(-0.643581\pi\) | ||||
−0.435933 | + | 0.899979i | \(0.643581\pi\) | |||||||
\(824\) | −5.19375 | −0.180933 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −2.99042 | −0.104050 | ||||||||
\(827\) | −48.8725 | −1.69946 | −0.849732 | − | 0.527216i | \(-0.823236\pi\) | ||||
−0.849732 | + | 0.527216i | \(0.823236\pi\) | |||||||
\(828\) | −9.21473 | −0.320234 | ||||||||
\(829\) | 5.29170 | 0.183788 | 0.0918941 | − | 0.995769i | \(-0.470708\pi\) | ||||
0.0918941 | + | 0.995769i | \(0.470708\pi\) | |||||||
\(830\) | 0.419007 | 0.0145439 | ||||||||
\(831\) | −12.1308 | −0.420814 | ||||||||
\(832\) | −8.90156 | −0.308606 | ||||||||
\(833\) | −45.4417 | −1.57446 | ||||||||
\(834\) | −1.54230 | −0.0534056 | ||||||||
\(835\) | −3.42643 | −0.118576 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −10.1097 | −0.349441 | ||||||||
\(838\) | −0.844922 | −0.0291873 | ||||||||
\(839\) | −13.2419 | −0.457160 | −0.228580 | − | 0.973525i | \(-0.573408\pi\) | ||||
−0.228580 | + | 0.973525i | \(0.573408\pi\) | |||||||
\(840\) | −2.47680 | −0.0854577 | ||||||||
\(841\) | −17.9721 | −0.619726 | ||||||||
\(842\) | −1.32972 | −0.0458253 | ||||||||
\(843\) | −3.58943 | −0.123626 | ||||||||
\(844\) | 37.7551 | 1.29958 | ||||||||
\(845\) | −11.6946 | −0.402305 | ||||||||
\(846\) | 0.549557 | 0.0188942 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −5.68361 | −0.195176 | ||||||||
\(849\) | −38.2740 | −1.31356 | ||||||||
\(850\) | 0.315430 | 0.0108191 | ||||||||
\(851\) | −8.11784 | −0.278276 | ||||||||
\(852\) | 31.3393 | 1.07367 | ||||||||
\(853\) | −2.21885 | −0.0759720 | −0.0379860 | − | 0.999278i | \(-0.512094\pi\) | ||||
−0.0379860 | + | 0.999278i | \(0.512094\pi\) | |||||||
\(854\) | −1.05876 | −0.0362299 | ||||||||
\(855\) | 5.16413 | 0.176609 | ||||||||
\(856\) | 6.26576 | 0.214159 | ||||||||
\(857\) | −31.4625 | −1.07474 | −0.537368 | − | 0.843348i | \(-0.680582\pi\) | ||||
−0.537368 | + | 0.843348i | \(0.680582\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 9.07676 | 0.309695 | 0.154848 | − | 0.987938i | \(-0.450511\pi\) | ||||
0.154848 | + | 0.987938i | \(0.450511\pi\) | |||||||
\(860\) | −0.523783 | −0.0178608 | ||||||||
\(861\) | −11.5953 | −0.395166 | ||||||||
\(862\) | −0.161917 | −0.00551493 | ||||||||
\(863\) | 42.4842 | 1.44618 | 0.723089 | − | 0.690755i | \(-0.242721\pi\) | ||||
0.723089 | + | 0.690755i | \(0.242721\pi\) | |||||||
\(864\) | 6.29748 | 0.214245 | ||||||||
\(865\) | −20.5669 | −0.699295 | ||||||||
\(866\) | −1.72503 | −0.0586190 | ||||||||
\(867\) | −8.24505 | −0.280017 | ||||||||
\(868\) | 16.1351 | 0.547662 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0.455465 | 0.0154417 | ||||||||
\(871\) | −0.590243 | −0.0199996 | ||||||||
\(872\) | 1.36335 | 0.0461690 | ||||||||
\(873\) | 2.84870 | 0.0964138 | ||||||||
\(874\) | −3.10244 | −0.104942 | ||||||||
\(875\) | −4.52452 | −0.152957 | ||||||||
\(876\) | −16.5928 | −0.560619 | ||||||||
\(877\) | 31.3101 | 1.05727 | 0.528634 | − | 0.848850i | \(-0.322704\pi\) | ||||
0.528634 | + | 0.848850i | \(0.322704\pi\) | |||||||
\(878\) | −1.60560 | −0.0541865 | ||||||||
\(879\) | −19.7319 | −0.665539 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 21.5189 | 0.724990 | 0.362495 | − | 0.931986i | \(-0.381925\pi\) | ||||
0.362495 | + | 0.931986i | \(0.381925\pi\) | |||||||
\(882\) | 1.06911 | 0.0359987 | ||||||||
\(883\) | −0.652552 | −0.0219601 | −0.0109801 | − | 0.999940i | \(-0.503495\pi\) | ||||
−0.0109801 | + | 0.999940i | \(0.503495\pi\) | |||||||
\(884\) | 7.67450 | 0.258121 | ||||||||
\(885\) | −10.3670 | −0.348483 | ||||||||
\(886\) | −3.42239 | −0.114977 | ||||||||
\(887\) | 14.6462 | 0.491771 | 0.245886 | − | 0.969299i | \(-0.420921\pi\) | ||||
0.245886 | + | 0.969299i | \(0.420921\pi\) | |||||||
\(888\) | 0.814997 | 0.0273495 | ||||||||
\(889\) | 89.4166 | 2.99894 | ||||||||
\(890\) | −1.24065 | −0.0415868 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −9.71637 | −0.325328 | ||||||||
\(893\) | −42.1353 | −1.41000 | ||||||||
\(894\) | −2.37738 | −0.0795115 | ||||||||
\(895\) | −2.56432 | −0.0857159 | ||||||||
\(896\) | −13.3912 | −0.447369 | ||||||||
\(897\) | −9.13758 | −0.305095 | ||||||||
\(898\) | 1.55254 | 0.0518088 | ||||||||
\(899\) | −5.94730 | −0.198354 | ||||||||
\(900\) | 1.68997 | 0.0563325 | ||||||||
\(901\) | 4.85662 | 0.161798 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −1.74561 | −0.0580903 | ||||||||
\(904\) | −4.44221 | −0.147746 | ||||||||
\(905\) | 13.4169 | 0.445992 | ||||||||
\(906\) | −0.000741201 0 | −2.46247e−5 0 | ||||||||
\(907\) | 28.7450 | 0.954461 | 0.477231 | − | 0.878778i | \(-0.341641\pi\) | ||||
0.477231 | + | 0.878778i | \(0.341641\pi\) | |||||||
\(908\) | 32.5030 | 1.07865 | ||||||||
\(909\) | −7.92258 | −0.262775 | ||||||||
\(910\) | 0.483402 | 0.0160246 | ||||||||
\(911\) | 17.2819 | 0.572573 | 0.286287 | − | 0.958144i | \(-0.407579\pi\) | ||||
0.286287 | + | 0.958144i | \(0.407579\pi\) | |||||||
\(912\) | −35.2313 | −1.16663 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | −2.96102 | −0.0979418 | ||||||||
\(915\) | −3.67042 | −0.121340 | ||||||||
\(916\) | 9.62109 | 0.317890 | ||||||||
\(917\) | −8.75399 | −0.289082 | ||||||||
\(918\) | −1.78060 | −0.0587686 | ||||||||
\(919\) | 2.19845 | 0.0725203 | 0.0362601 | − | 0.999342i | \(-0.488456\pi\) | ||||
0.0362601 | + | 0.999342i | \(0.488456\pi\) | |||||||
\(920\) | −2.03502 | −0.0670927 | ||||||||
\(921\) | −39.8723 | −1.31384 | ||||||||
\(922\) | −2.37843 | −0.0783295 | ||||||||
\(923\) | −12.2600 | −0.403542 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.48881 | 0.0489517 | ||||||||
\(926\) | 1.52719 | 0.0501866 | ||||||||
\(927\) | 11.8105 | 0.387906 | ||||||||
\(928\) | 3.70467 | 0.121612 | ||||||||
\(929\) | 24.2104 | 0.794317 | 0.397158 | − | 0.917750i | \(-0.369996\pi\) | ||||
0.397158 | + | 0.917750i | \(0.369996\pi\) | |||||||
\(930\) | −0.245630 | −0.00805452 | ||||||||
\(931\) | −81.9698 | −2.68645 | ||||||||
\(932\) | −16.7659 | −0.549184 | ||||||||
\(933\) | −19.3594 | −0.633799 | ||||||||
\(934\) | −0.797556 | −0.0260968 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −0.361908 | −0.0118293 | ||||||||
\(937\) | 20.8227 | 0.680249 | 0.340125 | − | 0.940380i | \(-0.389531\pi\) | ||||
0.340125 | + | 0.940380i | \(0.389531\pi\) | |||||||
\(938\) | −0.218566 | −0.00713644 | ||||||||
\(939\) | 23.7199 | 0.774068 | ||||||||
\(940\) | −13.7889 | −0.449744 | ||||||||
\(941\) | −34.2128 | −1.11530 | −0.557652 | − | 0.830075i | \(-0.688298\pi\) | ||||
−0.557652 | + | 0.830075i | \(0.688298\pi\) | |||||||
\(942\) | −0.0760982 | −0.00247941 | ||||||||
\(943\) | −9.52709 | −0.310245 | ||||||||
\(944\) | −27.9021 | −0.908136 | ||||||||
\(945\) | 25.5410 | 0.830848 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 33.8128 | 1.09877 | 0.549383 | − | 0.835570i | \(-0.314863\pi\) | ||||
0.549383 | + | 0.835570i | \(0.314863\pi\) | |||||||
\(948\) | −33.0130 | −1.07221 | ||||||||
\(949\) | 6.49114 | 0.210711 | ||||||||
\(950\) | 0.568986 | 0.0184603 | ||||||||
\(951\) | −7.89270 | −0.255938 | ||||||||
\(952\) | 5.69620 | 0.184615 | ||||||||
\(953\) | −25.5982 | −0.829206 | −0.414603 | − | 0.910002i | \(-0.636080\pi\) | ||||
−0.414603 | + | 0.910002i | \(0.636080\pi\) | |||||||
\(954\) | −0.114262 | −0.00369936 | ||||||||
\(955\) | 18.1898 | 0.588609 | ||||||||
\(956\) | −45.1871 | −1.46146 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 2.80042 | 0.0904774 | ||||||||
\(959\) | 56.7164 | 1.83147 | ||||||||
\(960\) | −11.4272 | −0.368810 | ||||||||
\(961\) | −27.7927 | −0.896537 | ||||||||
\(962\) | −0.159065 | −0.00512846 | ||||||||
\(963\) | −14.2482 | −0.459142 | ||||||||
\(964\) | 23.1114 | 0.744369 | ||||||||
\(965\) | −15.6887 | −0.505036 | ||||||||
\(966\) | −3.38363 | −0.108867 | ||||||||
\(967\) | −43.8942 | −1.41154 | −0.705772 | − | 0.708439i | \(-0.749400\pi\) | ||||
−0.705772 | + | 0.708439i | \(0.749400\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 30.1051 | 0.967114 | ||||||||
\(970\) | 0.313871 | 0.0100778 | ||||||||
\(971\) | 36.3707 | 1.16719 | 0.583596 | − | 0.812044i | \(-0.301645\pi\) | ||||
0.583596 | + | 0.812044i | \(0.301645\pi\) | |||||||
\(972\) | −16.9761 | −0.544510 | ||||||||
\(973\) | −50.8785 | −1.63109 | ||||||||
\(974\) | 1.83308 | 0.0587357 | ||||||||
\(975\) | 1.67583 | 0.0536694 | ||||||||
\(976\) | −9.87870 | −0.316209 | ||||||||
\(977\) | 10.3516 | 0.331177 | 0.165589 | − | 0.986195i | \(-0.447048\pi\) | ||||
0.165589 | + | 0.986195i | \(0.447048\pi\) | |||||||
\(978\) | 1.09233 | 0.0349289 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | −26.8248 | −0.856888 | ||||||||
\(981\) | −3.10024 | −0.0989830 | ||||||||
\(982\) | −1.47644 | −0.0471151 | ||||||||
\(983\) | −22.1158 | −0.705385 | −0.352693 | − | 0.935739i | \(-0.614734\pi\) | ||||
−0.352693 | + | 0.935739i | \(0.614734\pi\) | |||||||
\(984\) | 0.956480 | 0.0304915 | ||||||||
\(985\) | 21.8486 | 0.696155 | ||||||||
\(986\) | −1.04749 | −0.0333589 | ||||||||
\(987\) | −45.9543 | −1.46274 | ||||||||
\(988\) | 13.8436 | 0.440424 | ||||||||
\(989\) | −1.43426 | −0.0456067 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −55.5911 | −1.76591 | −0.882955 | − | 0.469457i | \(-0.844450\pi\) | ||||
−0.882955 | + | 0.469457i | \(0.844450\pi\) | |||||||
\(992\) | −1.99791 | −0.0634336 | ||||||||
\(993\) | −27.2376 | −0.864358 | ||||||||
\(994\) | −4.53985 | −0.143995 | ||||||||
\(995\) | −4.55200 | −0.144308 | ||||||||
\(996\) | 13.0870 | 0.414678 | ||||||||
\(997\) | −10.7911 | −0.341759 | −0.170879 | − | 0.985292i | \(-0.554661\pi\) | ||||
−0.170879 | + | 0.985292i | \(0.554661\pi\) | |||||||
\(998\) | −1.04807 | −0.0331761 | ||||||||
\(999\) | −8.40432 | −0.265901 |
(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 | 605.2.a.i.1.3 | 4 | ||
3.2 | odd | 2 | 5445.2.a.bu.1.2 | 4 | |||
4.3 | odd | 2 | 9680.2.a.cv.1.1 | 4 | |||
5.4 | even | 2 | 3025.2.a.be.1.2 | 4 | |||
11.2 | odd | 10 | 55.2.g.a.26.2 | ✓ | 8 | ||
11.3 | even | 5 | 605.2.g.g.251.2 | 8 | |||
11.4 | even | 5 | 605.2.g.g.511.2 | 8 | |||
11.5 | even | 5 | 605.2.g.n.366.1 | 8 | |||
11.6 | odd | 10 | 55.2.g.a.36.2 | yes | 8 | ||
11.7 | odd | 10 | 605.2.g.j.511.1 | 8 | |||
11.8 | odd | 10 | 605.2.g.j.251.1 | 8 | |||
11.9 | even | 5 | 605.2.g.n.81.1 | 8 | |||
11.10 | odd | 2 | 605.2.a.l.1.2 | 4 | |||
33.2 | even | 10 | 495.2.n.f.136.1 | 8 | |||
33.17 | even | 10 | 495.2.n.f.91.1 | 8 | |||
33.32 | even | 2 | 5445.2.a.bg.1.3 | 4 | |||
44.35 | even | 10 | 880.2.bo.e.81.1 | 8 | |||
44.39 | even | 10 | 880.2.bo.e.641.1 | 8 | |||
44.43 | even | 2 | 9680.2.a.cs.1.1 | 4 | |||
55.2 | even | 20 | 275.2.z.b.224.3 | 16 | |||
55.13 | even | 20 | 275.2.z.b.224.2 | 16 | |||
55.17 | even | 20 | 275.2.z.b.124.2 | 16 | |||
55.24 | odd | 10 | 275.2.h.b.26.1 | 8 | |||
55.28 | even | 20 | 275.2.z.b.124.3 | 16 | |||
55.39 | odd | 10 | 275.2.h.b.201.1 | 8 | |||
55.54 | odd | 2 | 3025.2.a.v.1.3 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
55.2.g.a.26.2 | ✓ | 8 | 11.2 | odd | 10 | ||
55.2.g.a.36.2 | yes | 8 | 11.6 | odd | 10 | ||
275.2.h.b.26.1 | 8 | 55.24 | odd | 10 | |||
275.2.h.b.201.1 | 8 | 55.39 | odd | 10 | |||
275.2.z.b.124.2 | 16 | 55.17 | even | 20 | |||
275.2.z.b.124.3 | 16 | 55.28 | even | 20 | |||
275.2.z.b.224.2 | 16 | 55.13 | even | 20 | |||
275.2.z.b.224.3 | 16 | 55.2 | even | 20 | |||
495.2.n.f.91.1 | 8 | 33.17 | even | 10 | |||
495.2.n.f.136.1 | 8 | 33.2 | even | 10 | |||
605.2.a.i.1.3 | 4 | 1.1 | even | 1 | trivial | ||
605.2.a.l.1.2 | 4 | 11.10 | odd | 2 | |||
605.2.g.g.251.2 | 8 | 11.3 | even | 5 | |||
605.2.g.g.511.2 | 8 | 11.4 | even | 5 | |||
605.2.g.j.251.1 | 8 | 11.8 | odd | 10 | |||
605.2.g.j.511.1 | 8 | 11.7 | odd | 10 | |||
605.2.g.n.81.1 | 8 | 11.9 | even | 5 | |||
605.2.g.n.366.1 | 8 | 11.5 | even | 5 | |||
880.2.bo.e.81.1 | 8 | 44.35 | even | 10 | |||
880.2.bo.e.641.1 | 8 | 44.39 | even | 10 | |||
3025.2.a.v.1.3 | 4 | 55.54 | odd | 2 | |||
3025.2.a.be.1.2 | 4 | 5.4 | even | 2 | |||
5445.2.a.bg.1.3 | 4 | 33.32 | even | 2 | |||
5445.2.a.bu.1.2 | 4 | 3.2 | odd | 2 | |||
9680.2.a.cs.1.1 | 4 | 44.43 | even | 2 | |||
9680.2.a.cv.1.1 | 4 | 4.3 | odd | 2 |