Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6561,2,Mod(1,6561)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6561, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6561.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6561 = 3^{8} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6561.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: | \(52.3898487662\) |
Analytic rank: | \(0\) |
Dimension: | \(72\) |
Twist minimal: | no (minimal twist has level 81) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.61 | ||
Character | \(\chi\) | \(=\) | 6561.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.11576 | 1.49607 | 0.748033 | − | 0.663662i | \(-0.230999\pi\) | ||||
0.748033 | + | 0.663662i | \(0.230999\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 2.47642 | 1.23821 | ||||||||
\(5\) | −3.89294 | −1.74098 | −0.870488 | − | 0.492190i | \(-0.836196\pi\) | ||||
−0.870488 | + | 0.492190i | \(0.836196\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −3.33519 | −1.26058 | −0.630292 | − | 0.776358i | \(-0.717065\pi\) | ||||
−0.630292 | + | 0.776358i | \(0.717065\pi\) | |||||||
\(8\) | 1.00799 | 0.356378 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −8.23651 | −2.60461 | ||||||||
\(11\) | −0.756735 | −0.228164 | −0.114082 | − | 0.993471i | \(-0.536393\pi\) | ||||
−0.114082 | + | 0.993471i | \(0.536393\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.48623 | 0.689557 | 0.344778 | − | 0.938684i | \(-0.387954\pi\) | ||||
0.344778 | + | 0.938684i | \(0.387954\pi\) | |||||||
\(14\) | −7.05645 | −1.88592 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −2.82018 | −0.705045 | ||||||||
\(17\) | −0.745917 | −0.180911 | −0.0904557 | − | 0.995900i | \(-0.528832\pi\) | ||||
−0.0904557 | + | 0.995900i | \(0.528832\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −4.48802 | −1.02962 | −0.514812 | − | 0.857303i | \(-0.672138\pi\) | ||||
−0.514812 | + | 0.857303i | \(0.672138\pi\) | |||||||
\(20\) | −9.64056 | −2.15569 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −1.60107 | −0.341348 | ||||||||
\(23\) | 2.28672 | 0.476814 | 0.238407 | − | 0.971165i | \(-0.423375\pi\) | ||||
0.238407 | + | 0.971165i | \(0.423375\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 10.1550 | 2.03100 | ||||||||
\(26\) | 5.26026 | 1.03162 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −8.25934 | −1.56087 | ||||||||
\(29\) | −0.463993 | −0.0861614 | −0.0430807 | − | 0.999072i | \(-0.513717\pi\) | ||||
−0.0430807 | + | 0.999072i | \(0.513717\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.94211 | −0.708025 | −0.354012 | − | 0.935241i | \(-0.615183\pi\) | ||||
−0.354012 | + | 0.935241i | \(0.615183\pi\) | |||||||
\(32\) | −7.98279 | −1.41117 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −1.57818 | −0.270655 | ||||||||
\(35\) | 12.9837 | 2.19465 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −4.75658 | −0.781977 | −0.390989 | − | 0.920395i | \(-0.627867\pi\) | ||||
−0.390989 | + | 0.920395i | \(0.627867\pi\) | |||||||
\(38\) | −9.49556 | −1.54038 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −3.92405 | −0.620446 | ||||||||
\(41\) | −4.89250 | −0.764081 | −0.382040 | − | 0.924146i | \(-0.624778\pi\) | ||||
−0.382040 | + | 0.924146i | \(0.624778\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5.94108 | 0.906006 | 0.453003 | − | 0.891509i | \(-0.350353\pi\) | ||||
0.453003 | + | 0.891509i | \(0.350353\pi\) | |||||||
\(44\) | −1.87399 | −0.282515 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 4.83814 | 0.713345 | ||||||||
\(47\) | 10.7663 | 1.57043 | 0.785217 | − | 0.619221i | \(-0.212552\pi\) | ||||
0.785217 | + | 0.619221i | \(0.212552\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 4.12352 | 0.589074 | ||||||||
\(50\) | 21.4854 | 3.03850 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 6.15696 | 0.853816 | ||||||||
\(53\) | 11.5059 | 1.58045 | 0.790227 | − | 0.612815i | \(-0.209963\pi\) | ||||
0.790227 | + | 0.612815i | \(0.209963\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.94592 | 0.397228 | ||||||||
\(56\) | −3.36184 | −0.449245 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −0.981696 | −0.128903 | ||||||||
\(59\) | 4.14919 | 0.540178 | 0.270089 | − | 0.962835i | \(-0.412947\pi\) | ||||
0.270089 | + | 0.962835i | \(0.412947\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.267217 | 0.0342136 | 0.0171068 | − | 0.999854i | \(-0.494554\pi\) | ||||
0.0171068 | + | 0.999854i | \(0.494554\pi\) | |||||||
\(62\) | −8.34055 | −1.05925 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −11.2493 | −1.40616 | ||||||||
\(65\) | −9.67875 | −1.20050 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.91755 | −0.234266 | −0.117133 | − | 0.993116i | \(-0.537370\pi\) | ||||
−0.117133 | + | 0.993116i | \(0.537370\pi\) | |||||||
\(68\) | −1.84720 | −0.224006 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 27.4703 | 3.28333 | ||||||||
\(71\) | −6.75379 | −0.801527 | −0.400764 | − | 0.916182i | \(-0.631255\pi\) | ||||
−0.400764 | + | 0.916182i | \(0.631255\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 7.93114 | 0.928269 | 0.464135 | − | 0.885765i | \(-0.346365\pi\) | ||||
0.464135 | + | 0.885765i | \(0.346365\pi\) | |||||||
\(74\) | −10.0638 | −1.16989 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −11.1142 | −1.27489 | ||||||||
\(77\) | 2.52386 | 0.287620 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 4.31679 | 0.485677 | 0.242838 | − | 0.970067i | \(-0.421922\pi\) | ||||
0.242838 | + | 0.970067i | \(0.421922\pi\) | |||||||
\(80\) | 10.9788 | 1.22747 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −10.3513 | −1.14311 | ||||||||
\(83\) | 2.54689 | 0.279558 | 0.139779 | − | 0.990183i | \(-0.455361\pi\) | ||||
0.139779 | + | 0.990183i | \(0.455361\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.90381 | 0.314962 | ||||||||
\(86\) | 12.5699 | 1.35544 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −0.762781 | −0.0813128 | ||||||||
\(89\) | 5.38761 | 0.571086 | 0.285543 | − | 0.958366i | \(-0.407826\pi\) | ||||
0.285543 | + | 0.958366i | \(0.407826\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −8.29206 | −0.869245 | ||||||||
\(92\) | 5.66288 | 0.590396 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 22.7790 | 2.34947 | ||||||||
\(95\) | 17.4716 | 1.79255 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 9.48838 | 0.963399 | 0.481700 | − | 0.876336i | \(-0.340020\pi\) | ||||
0.481700 | + | 0.876336i | \(0.340020\pi\) | |||||||
\(98\) | 8.72436 | 0.881293 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 25.1480 | 2.51480 | ||||||||
\(101\) | 12.3077 | 1.22466 | 0.612329 | − | 0.790603i | \(-0.290233\pi\) | ||||
0.612329 | + | 0.790603i | \(0.290233\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 16.6703 | 1.64257 | 0.821286 | − | 0.570516i | \(-0.193257\pi\) | ||||
0.821286 | + | 0.570516i | \(0.193257\pi\) | |||||||
\(104\) | 2.50610 | 0.245743 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 24.3436 | 2.36446 | ||||||||
\(107\) | 3.69388 | 0.357101 | 0.178550 | − | 0.983931i | \(-0.442859\pi\) | ||||
0.178550 | + | 0.983931i | \(0.442859\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −17.3392 | −1.66080 | −0.830398 | − | 0.557170i | \(-0.811887\pi\) | ||||
−0.830398 | + | 0.557170i | \(0.811887\pi\) | |||||||
\(110\) | 6.23285 | 0.594279 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 9.40585 | 0.888769 | ||||||||
\(113\) | 10.3090 | 0.969792 | 0.484896 | − | 0.874572i | \(-0.338857\pi\) | ||||
0.484896 | + | 0.874572i | \(0.338857\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −8.90206 | −0.830121 | ||||||||
\(116\) | −1.14904 | −0.106686 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 8.77867 | 0.808142 | ||||||||
\(119\) | 2.48778 | 0.228054 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.4274 | −0.947941 | ||||||||
\(122\) | 0.565366 | 0.0511858 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −9.76233 | −0.876683 | ||||||||
\(125\) | −20.0680 | −1.79494 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −13.2130 | −1.17246 | −0.586232 | − | 0.810143i | \(-0.699389\pi\) | ||||
−0.586232 | + | 0.810143i | \(0.699389\pi\) | |||||||
\(128\) | −7.83513 | −0.692534 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −20.4779 | −1.79603 | ||||||||
\(131\) | −10.0613 | −0.879064 | −0.439532 | − | 0.898227i | \(-0.644856\pi\) | ||||
−0.439532 | + | 0.898227i | \(0.644856\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 14.9684 | 1.29793 | ||||||||
\(134\) | −4.05706 | −0.350477 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −0.751877 | −0.0644729 | ||||||||
\(137\) | 9.46863 | 0.808960 | 0.404480 | − | 0.914547i | \(-0.367453\pi\) | ||||
0.404480 | + | 0.914547i | \(0.367453\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −10.5003 | −0.890627 | −0.445314 | − | 0.895375i | \(-0.646908\pi\) | ||||
−0.445314 | + | 0.895375i | \(0.646908\pi\) | |||||||
\(140\) | 32.1531 | 2.71744 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −14.2894 | −1.19914 | ||||||||
\(143\) | −1.88142 | −0.157332 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1.80630 | 0.150005 | ||||||||
\(146\) | 16.7803 | 1.38875 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −11.7793 | −0.968253 | ||||||||
\(149\) | −12.4294 | −1.01826 | −0.509128 | − | 0.860691i | \(-0.670032\pi\) | ||||
−0.509128 | + | 0.860691i | \(0.670032\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −18.2270 | −1.48329 | −0.741647 | − | 0.670791i | \(-0.765955\pi\) | ||||
−0.741647 | + | 0.670791i | \(0.765955\pi\) | |||||||
\(152\) | −4.52389 | −0.366936 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 5.33986 | 0.430299 | ||||||||
\(155\) | 15.3464 | 1.23265 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 23.3719 | 1.86528 | 0.932640 | − | 0.360809i | \(-0.117499\pi\) | ||||
0.932640 | + | 0.360809i | \(0.117499\pi\) | |||||||
\(158\) | 9.13327 | 0.726604 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 31.0765 | 2.45682 | ||||||||
\(161\) | −7.62665 | −0.601064 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 11.7238 | 0.918278 | 0.459139 | − | 0.888364i | \(-0.348158\pi\) | ||||
0.459139 | + | 0.888364i | \(0.348158\pi\) | |||||||
\(164\) | −12.1159 | −0.946093 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 5.38860 | 0.418237 | ||||||||
\(167\) | 24.2131 | 1.87366 | 0.936832 | − | 0.349780i | \(-0.113744\pi\) | ||||
0.936832 | + | 0.349780i | \(0.113744\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −6.81865 | −0.524512 | ||||||||
\(170\) | 6.14375 | 0.471204 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 14.7126 | 1.12183 | ||||||||
\(173\) | 15.5125 | 1.17939 | 0.589695 | − | 0.807626i | \(-0.299248\pi\) | ||||
0.589695 | + | 0.807626i | \(0.299248\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −33.8688 | −2.56024 | ||||||||
\(176\) | 2.13413 | 0.160866 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 11.3989 | 0.854382 | ||||||||
\(179\) | 7.18825 | 0.537275 | 0.268637 | − | 0.963241i | \(-0.413427\pi\) | ||||
0.268637 | + | 0.963241i | \(0.413427\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −7.73776 | −0.575143 | −0.287572 | − | 0.957759i | \(-0.592848\pi\) | ||||
−0.287572 | + | 0.957759i | \(0.592848\pi\) | |||||||
\(182\) | −17.5440 | −1.30045 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 2.30499 | 0.169926 | ||||||||
\(185\) | 18.5171 | 1.36140 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0.564461 | 0.0412775 | ||||||||
\(188\) | 26.6620 | 1.94453 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 36.9657 | 2.68177 | ||||||||
\(191\) | 10.0782 | 0.729230 | 0.364615 | − | 0.931158i | \(-0.381201\pi\) | ||||
0.364615 | + | 0.931158i | \(0.381201\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −15.9923 | −1.15115 | −0.575575 | − | 0.817749i | \(-0.695222\pi\) | ||||
−0.575575 | + | 0.817749i | \(0.695222\pi\) | |||||||
\(194\) | 20.0751 | 1.44131 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 10.2116 | 0.729398 | ||||||||
\(197\) | −10.9700 | −0.781578 | −0.390789 | − | 0.920480i | \(-0.627798\pi\) | ||||
−0.390789 | + | 0.920480i | \(0.627798\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 3.51072 | 0.248869 | 0.124434 | − | 0.992228i | \(-0.460288\pi\) | ||||
0.124434 | + | 0.992228i | \(0.460288\pi\) | |||||||
\(200\) | 10.2361 | 0.723803 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 26.0400 | 1.83217 | ||||||||
\(203\) | 1.54751 | 0.108614 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 19.0462 | 1.33025 | ||||||||
\(206\) | 35.2703 | 2.45740 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −7.01162 | −0.486169 | ||||||||
\(209\) | 3.39624 | 0.234923 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −7.68374 | −0.528971 | −0.264485 | − | 0.964390i | \(-0.585202\pi\) | ||||
−0.264485 | + | 0.964390i | \(0.585202\pi\) | |||||||
\(212\) | 28.4934 | 1.95693 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 7.81534 | 0.534246 | ||||||||
\(215\) | −23.1283 | −1.57733 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 13.1477 | 0.892525 | ||||||||
\(218\) | −36.6856 | −2.48466 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 7.29534 | 0.491852 | ||||||||
\(221\) | −1.85452 | −0.124749 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 10.8443 | 0.726186 | 0.363093 | − | 0.931753i | \(-0.381721\pi\) | ||||
0.363093 | + | 0.931753i | \(0.381721\pi\) | |||||||
\(224\) | 26.6242 | 1.77890 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 21.8114 | 1.45087 | ||||||||
\(227\) | 10.8613 | 0.720893 | 0.360446 | − | 0.932780i | \(-0.382624\pi\) | ||||
0.360446 | + | 0.932780i | \(0.382624\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2.28946 | 0.151292 | 0.0756460 | − | 0.997135i | \(-0.475898\pi\) | ||||
0.0756460 | + | 0.997135i | \(0.475898\pi\) | |||||||
\(230\) | −18.8346 | −1.24192 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −0.467701 | −0.0307060 | ||||||||
\(233\) | −17.8111 | −1.16684 | −0.583422 | − | 0.812169i | \(-0.698286\pi\) | ||||
−0.583422 | + | 0.812169i | \(0.698286\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −41.9127 | −2.73409 | ||||||||
\(236\) | 10.2751 | 0.668854 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 5.26353 | 0.341184 | ||||||||
\(239\) | 12.2663 | 0.793438 | 0.396719 | − | 0.917940i | \(-0.370149\pi\) | ||||
0.396719 | + | 0.917940i | \(0.370149\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 17.4995 | 1.12724 | 0.563620 | − | 0.826034i | \(-0.309408\pi\) | ||||
0.563620 | + | 0.826034i | \(0.309408\pi\) | |||||||
\(242\) | −22.0617 | −1.41818 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0.661742 | 0.0423637 | ||||||||
\(245\) | −16.0526 | −1.02556 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −11.1583 | −0.709984 | ||||||||
\(248\) | −3.97361 | −0.252325 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −42.4590 | −2.68534 | ||||||||
\(251\) | −18.8202 | −1.18792 | −0.593962 | − | 0.804493i | \(-0.702437\pi\) | ||||
−0.593962 | + | 0.804493i | \(0.702437\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.73044 | −0.108792 | ||||||||
\(254\) | −27.9555 | −1.75408 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 5.92133 | 0.370083 | ||||||||
\(257\) | −17.2431 | −1.07559 | −0.537797 | − | 0.843074i | \(-0.680743\pi\) | ||||
−0.537797 | + | 0.843074i | \(0.680743\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 15.8641 | 0.985749 | ||||||||
\(260\) | −23.9687 | −1.48647 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −21.2873 | −1.31514 | ||||||||
\(263\) | 24.6115 | 1.51761 | 0.758806 | − | 0.651317i | \(-0.225783\pi\) | ||||
0.758806 | + | 0.651317i | \(0.225783\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −44.7917 | −2.75153 | ||||||||
\(266\) | 31.6695 | 1.94178 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −4.74866 | −0.290070 | ||||||||
\(269\) | −10.6490 | −0.649279 | −0.324639 | − | 0.945838i | \(-0.605243\pi\) | ||||
−0.324639 | + | 0.945838i | \(0.605243\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −4.71634 | −0.286498 | −0.143249 | − | 0.989687i | \(-0.545755\pi\) | ||||
−0.143249 | + | 0.989687i | \(0.545755\pi\) | |||||||
\(272\) | 2.10362 | 0.127551 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 20.0333 | 1.21026 | ||||||||
\(275\) | −7.68462 | −0.463400 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −6.61161 | −0.397253 | −0.198627 | − | 0.980075i | \(-0.563648\pi\) | ||||
−0.198627 | + | 0.980075i | \(0.563648\pi\) | |||||||
\(278\) | −22.2162 | −1.33244 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 13.0875 | 0.782125 | ||||||||
\(281\) | 2.47619 | 0.147717 | 0.0738586 | − | 0.997269i | \(-0.476469\pi\) | ||||
0.0738586 | + | 0.997269i | \(0.476469\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 0.927155 | 0.0551137 | 0.0275568 | − | 0.999620i | \(-0.491227\pi\) | ||||
0.0275568 | + | 0.999620i | \(0.491227\pi\) | |||||||
\(284\) | −16.7252 | −0.992459 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −3.98062 | −0.235379 | ||||||||
\(287\) | 16.3174 | 0.963189 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.4436 | −0.967271 | ||||||||
\(290\) | 3.82168 | 0.224417 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 19.6408 | 1.14939 | ||||||||
\(293\) | −2.34506 | −0.137000 | −0.0684999 | − | 0.997651i | \(-0.521821\pi\) | ||||
−0.0684999 | + | 0.997651i | \(0.521821\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −16.1525 | −0.940437 | ||||||||
\(296\) | −4.79459 | −0.278680 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −26.2976 | −1.52338 | ||||||||
\(299\) | 5.68531 | 0.328790 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −19.8147 | −1.14210 | ||||||||
\(302\) | −38.5639 | −2.21910 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 12.6570 | 0.725931 | ||||||||
\(305\) | −1.04026 | −0.0595651 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −15.2577 | −0.870805 | −0.435403 | − | 0.900236i | \(-0.643394\pi\) | ||||
−0.435403 | + | 0.900236i | \(0.643394\pi\) | |||||||
\(308\) | 6.25013 | 0.356134 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 32.4692 | 1.84413 | ||||||||
\(311\) | 16.7436 | 0.949445 | 0.474722 | − | 0.880136i | \(-0.342549\pi\) | ||||
0.474722 | + | 0.880136i | \(0.342549\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 32.5733 | 1.84115 | 0.920577 | − | 0.390562i | \(-0.127719\pi\) | ||||
0.920577 | + | 0.390562i | \(0.127719\pi\) | |||||||
\(314\) | 49.4492 | 2.79058 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 10.6902 | 0.601370 | ||||||||
\(317\) | −21.6708 | −1.21716 | −0.608578 | − | 0.793494i | \(-0.708260\pi\) | ||||
−0.608578 | + | 0.793494i | \(0.708260\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0.351120 | 0.0196589 | ||||||||
\(320\) | 43.7928 | 2.44809 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −16.1361 | −0.899231 | ||||||||
\(323\) | 3.34769 | 0.186271 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 25.2476 | 1.40049 | ||||||||
\(326\) | 24.8047 | 1.37380 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −4.93160 | −0.272302 | ||||||||
\(329\) | −35.9079 | −1.97966 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 23.8122 | 1.30884 | 0.654419 | − | 0.756132i | \(-0.272913\pi\) | ||||
0.654419 | + | 0.756132i | \(0.272913\pi\) | |||||||
\(332\) | 6.30718 | 0.346151 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 51.2289 | 2.80312 | ||||||||
\(335\) | 7.46490 | 0.407851 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −18.3953 | −1.00205 | −0.501027 | − | 0.865432i | \(-0.667044\pi\) | ||||
−0.501027 | + | 0.865432i | \(0.667044\pi\) | |||||||
\(338\) | −14.4266 | −0.784704 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 7.19105 | 0.389990 | ||||||||
\(341\) | 2.98313 | 0.161546 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 9.59362 | 0.518007 | ||||||||
\(344\) | 5.98855 | 0.322881 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 32.8206 | 1.76444 | ||||||||
\(347\) | 16.9111 | 0.907836 | 0.453918 | − | 0.891043i | \(-0.350026\pi\) | ||||
0.453918 | + | 0.891043i | \(0.350026\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 8.16721 | 0.437181 | 0.218590 | − | 0.975817i | \(-0.429854\pi\) | ||||
0.218590 | + | 0.975817i | \(0.429854\pi\) | |||||||
\(350\) | −71.6581 | −3.83029 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 6.04086 | 0.321979 | ||||||||
\(353\) | −24.6144 | −1.31009 | −0.655047 | − | 0.755588i | \(-0.727351\pi\) | ||||
−0.655047 | + | 0.755588i | \(0.727351\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 26.2921 | 1.39544 | ||||||||
\(356\) | 13.3420 | 0.707125 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 15.2086 | 0.803798 | ||||||||
\(359\) | 12.6452 | 0.667390 | 0.333695 | − | 0.942681i | \(-0.391704\pi\) | ||||
0.333695 | + | 0.942681i | \(0.391704\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.14237 | 0.0601247 | ||||||||
\(362\) | −16.3712 | −0.860452 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −20.5346 | −1.07631 | ||||||||
\(365\) | −30.8754 | −1.61609 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −10.4942 | −0.547790 | −0.273895 | − | 0.961760i | \(-0.588312\pi\) | ||||
−0.273895 | + | 0.961760i | \(0.588312\pi\) | |||||||
\(368\) | −6.44896 | −0.336175 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 39.1776 | 2.03675 | ||||||||
\(371\) | −38.3743 | −1.99230 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 11.7964 | 0.610794 | 0.305397 | − | 0.952225i | \(-0.401211\pi\) | ||||
0.305397 | + | 0.952225i | \(0.401211\pi\) | |||||||
\(374\) | 1.19426 | 0.0617538 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 10.8524 | 0.559669 | ||||||||
\(377\) | −1.15359 | −0.0594131 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 18.1371 | 0.931639 | 0.465819 | − | 0.884880i | \(-0.345760\pi\) | ||||
0.465819 | + | 0.884880i | \(0.345760\pi\) | |||||||
\(380\) | 43.2671 | 2.21955 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 21.3229 | 1.09098 | ||||||||
\(383\) | −15.5176 | −0.792914 | −0.396457 | − | 0.918053i | \(-0.629760\pi\) | ||||
−0.396457 | + | 0.918053i | \(0.629760\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −9.82522 | −0.500740 | ||||||||
\(386\) | −33.8358 | −1.72219 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 23.4972 | 1.19289 | ||||||||
\(389\) | 15.4343 | 0.782551 | 0.391275 | − | 0.920274i | \(-0.372034\pi\) | ||||
0.391275 | + | 0.920274i | \(0.372034\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.70570 | −0.0862611 | ||||||||
\(392\) | 4.15647 | 0.209933 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −23.2098 | −1.16929 | ||||||||
\(395\) | −16.8050 | −0.845551 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 2.04261 | 0.102515 | 0.0512577 | − | 0.998685i | \(-0.483677\pi\) | ||||
0.0512577 | + | 0.998685i | \(0.483677\pi\) | |||||||
\(398\) | 7.42783 | 0.372324 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −28.6389 | −1.43194 | ||||||||
\(401\) | −14.9541 | −0.746774 | −0.373387 | − | 0.927676i | \(-0.621804\pi\) | ||||
−0.373387 | + | 0.927676i | \(0.621804\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −9.80101 | −0.488223 | ||||||||
\(404\) | 30.4790 | 1.51639 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 3.27415 | 0.162493 | ||||||||
\(407\) | 3.59947 | 0.178419 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 10.3886 | 0.513681 | 0.256841 | − | 0.966454i | \(-0.417318\pi\) | ||||
0.256841 | + | 0.966454i | \(0.417318\pi\) | |||||||
\(410\) | 40.2971 | 1.99013 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 41.2827 | 2.03385 | ||||||||
\(413\) | −13.8383 | −0.680940 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −9.91490 | −0.486703 | ||||||||
\(416\) | −19.8471 | −0.973083 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 7.18562 | 0.351460 | ||||||||
\(419\) | −0.530105 | −0.0258973 | −0.0129487 | − | 0.999916i | \(-0.504122\pi\) | ||||
−0.0129487 | + | 0.999916i | \(0.504122\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −32.0657 | −1.56279 | −0.781393 | − | 0.624039i | \(-0.785490\pi\) | ||||
−0.781393 | + | 0.624039i | \(0.785490\pi\) | |||||||
\(422\) | −16.2569 | −0.791374 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 11.5978 | 0.563239 | ||||||||
\(425\) | −7.57477 | −0.367430 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −0.891221 | −0.0431292 | ||||||||
\(428\) | 9.14760 | 0.442166 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −48.9337 | −2.35979 | ||||||||
\(431\) | −5.38293 | −0.259287 | −0.129643 | − | 0.991561i | \(-0.541383\pi\) | ||||
−0.129643 | + | 0.991561i | \(0.541383\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 33.2929 | 1.59996 | 0.799978 | − | 0.600029i | \(-0.204844\pi\) | ||||
0.799978 | + | 0.600029i | \(0.204844\pi\) | |||||||
\(434\) | 27.8173 | 1.33528 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −42.9392 | −2.05642 | ||||||||
\(437\) | −10.2629 | −0.490939 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −18.6820 | −0.891641 | −0.445820 | − | 0.895122i | \(-0.647088\pi\) | ||||
−0.445820 | + | 0.895122i | \(0.647088\pi\) | |||||||
\(440\) | 2.96946 | 0.141564 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −3.92371 | −0.186632 | ||||||||
\(443\) | 18.8705 | 0.896565 | 0.448282 | − | 0.893892i | \(-0.352036\pi\) | ||||
0.448282 | + | 0.893892i | \(0.352036\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −20.9737 | −0.994247 | ||||||||
\(446\) | 22.9438 | 1.08642 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 37.5185 | 1.77258 | ||||||||
\(449\) | 6.96621 | 0.328756 | 0.164378 | − | 0.986397i | \(-0.447438\pi\) | ||||
0.164378 | + | 0.986397i | \(0.447438\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 3.70233 | 0.174336 | ||||||||
\(452\) | 25.5295 | 1.20081 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 22.9800 | 1.07850 | ||||||||
\(455\) | 32.2805 | 1.51333 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 37.5977 | 1.75875 | 0.879373 | − | 0.476133i | \(-0.157962\pi\) | ||||
0.879373 | + | 0.476133i | \(0.157962\pi\) | |||||||
\(458\) | 4.84394 | 0.226343 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −22.0452 | −1.02786 | ||||||||
\(461\) | 27.6370 | 1.28719 | 0.643593 | − | 0.765368i | \(-0.277443\pi\) | ||||
0.643593 | + | 0.765368i | \(0.277443\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 24.5673 | 1.14174 | 0.570870 | − | 0.821040i | \(-0.306606\pi\) | ||||
0.570870 | + | 0.821040i | \(0.306606\pi\) | |||||||
\(464\) | 1.30854 | 0.0607477 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −37.6839 | −1.74567 | ||||||||
\(467\) | −7.86084 | −0.363756 | −0.181878 | − | 0.983321i | \(-0.558218\pi\) | ||||
−0.181878 | + | 0.983321i | \(0.558218\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 6.39540 | 0.295312 | ||||||||
\(470\) | −88.6771 | −4.09037 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 4.18234 | 0.192508 | ||||||||
\(473\) | −4.49582 | −0.206718 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −45.5758 | −2.09116 | ||||||||
\(476\) | 6.16078 | 0.282379 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 25.9524 | 1.18704 | ||||||||
\(479\) | 17.7116 | 0.809263 | 0.404632 | − | 0.914480i | \(-0.367400\pi\) | ||||
0.404632 | + | 0.914480i | \(0.367400\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −11.8260 | −0.539218 | ||||||||
\(482\) | 37.0246 | 1.68642 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −25.8225 | −1.17375 | ||||||||
\(485\) | −36.9377 | −1.67725 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −42.1146 | −1.90840 | −0.954198 | − | 0.299175i | \(-0.903289\pi\) | ||||
−0.954198 | + | 0.299175i | \(0.903289\pi\) | |||||||
\(488\) | 0.269352 | 0.0121930 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −33.9634 | −1.53431 | ||||||||
\(491\) | 7.27755 | 0.328431 | 0.164216 | − | 0.986424i | \(-0.447491\pi\) | ||||
0.164216 | + | 0.986424i | \(0.447491\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0.346100 | 0.0155876 | ||||||||
\(494\) | −23.6082 | −1.06218 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 11.1175 | 0.499189 | ||||||||
\(497\) | 22.5252 | 1.01039 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 16.1300 | 0.722078 | 0.361039 | − | 0.932551i | \(-0.382422\pi\) | ||||
0.361039 | + | 0.932551i | \(0.382422\pi\) | |||||||
\(500\) | −49.6968 | −2.22251 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −39.8190 | −1.77721 | ||||||||
\(503\) | 36.9391 | 1.64703 | 0.823517 | − | 0.567292i | \(-0.192009\pi\) | ||||
0.823517 | + | 0.567292i | \(0.192009\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −47.9130 | −2.13210 | ||||||||
\(506\) | −3.66119 | −0.162760 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −32.7209 | −1.45176 | ||||||||
\(509\) | −11.6819 | −0.517792 | −0.258896 | − | 0.965905i | \(-0.583359\pi\) | ||||
−0.258896 | + | 0.965905i | \(0.583359\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −26.4519 | −1.17016 | ||||||||
\(512\) | 28.1984 | 1.24620 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −36.4822 | −1.60916 | ||||||||
\(515\) | −64.8964 | −2.85968 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −8.14727 | −0.358317 | ||||||||
\(518\) | 33.5646 | 1.47474 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −9.75609 | −0.427833 | ||||||||
\(521\) | 0.861490 | 0.0377426 | 0.0188713 | − | 0.999822i | \(-0.493993\pi\) | ||||
0.0188713 | + | 0.999822i | \(0.493993\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −7.92246 | −0.346425 | −0.173212 | − | 0.984884i | \(-0.555415\pi\) | ||||
−0.173212 | + | 0.984884i | \(0.555415\pi\) | |||||||
\(524\) | −24.9161 | −1.08847 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 52.0720 | 2.27045 | ||||||||
\(527\) | 2.94049 | 0.128090 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −17.7709 | −0.772649 | ||||||||
\(530\) | −94.7682 | −4.11647 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 37.0681 | 1.60711 | ||||||||
\(533\) | −12.1639 | −0.526877 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −14.3800 | −0.621703 | ||||||||
\(536\) | −1.93287 | −0.0834873 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −22.5306 | −0.971363 | ||||||||
\(539\) | −3.12041 | −0.134406 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −12.0292 | −0.517176 | −0.258588 | − | 0.965988i | \(-0.583257\pi\) | ||||
−0.258588 | + | 0.965988i | \(0.583257\pi\) | |||||||
\(542\) | −9.97863 | −0.428619 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 5.95450 | 0.255297 | ||||||||
\(545\) | 67.5006 | 2.89141 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −6.38107 | −0.272835 | −0.136417 | − | 0.990651i | \(-0.543559\pi\) | ||||
−0.136417 | + | 0.990651i | \(0.543559\pi\) | |||||||
\(548\) | 23.4483 | 1.00166 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −16.2588 | −0.693277 | ||||||||
\(551\) | 2.08241 | 0.0887138 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −14.3973 | −0.612237 | ||||||||
\(554\) | −13.9886 | −0.594317 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −26.0033 | −1.10278 | ||||||||
\(557\) | 40.2925 | 1.70725 | 0.853623 | − | 0.520891i | \(-0.174400\pi\) | ||||
0.853623 | + | 0.520891i | \(0.174400\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 14.7709 | 0.624742 | ||||||||
\(560\) | −36.6164 | −1.54733 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 5.23902 | 0.220995 | ||||||||
\(563\) | 1.58567 | 0.0668279 | 0.0334139 | − | 0.999442i | \(-0.489362\pi\) | ||||
0.0334139 | + | 0.999442i | \(0.489362\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −40.1324 | −1.68838 | ||||||||
\(566\) | 1.96163 | 0.0824536 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −6.80775 | −0.285647 | ||||||||
\(569\) | −11.0442 | −0.462996 | −0.231498 | − | 0.972835i | \(-0.574363\pi\) | ||||
−0.231498 | + | 0.972835i | \(0.574363\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 7.90795 | 0.330937 | 0.165469 | − | 0.986215i | \(-0.447086\pi\) | ||||
0.165469 | + | 0.986215i | \(0.447086\pi\) | |||||||
\(572\) | −4.65918 | −0.194810 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 34.5237 | 1.44099 | ||||||||
\(575\) | 23.2216 | 0.968407 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −46.1655 | −1.92190 | −0.960948 | − | 0.276729i | \(-0.910749\pi\) | ||||
−0.960948 | + | 0.276729i | \(0.910749\pi\) | |||||||
\(578\) | −34.7907 | −1.44710 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 4.47315 | 0.185738 | ||||||||
\(581\) | −8.49438 | −0.352406 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −8.70690 | −0.360603 | ||||||||
\(584\) | 7.99451 | 0.330815 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −4.96157 | −0.204961 | ||||||||
\(587\) | −36.7605 | −1.51727 | −0.758633 | − | 0.651518i | \(-0.774133\pi\) | ||||
−0.758633 | + | 0.651518i | \(0.774133\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 17.6923 | 0.728999 | ||||||||
\(590\) | −34.1748 | −1.40695 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 13.4144 | 0.551329 | ||||||||
\(593\) | −14.3481 | −0.589207 | −0.294604 | − | 0.955620i | \(-0.595188\pi\) | ||||
−0.294604 | + | 0.955620i | \(0.595188\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −9.68477 | −0.397037 | ||||||||
\(596\) | −30.7804 | −1.26082 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 12.0287 | 0.491891 | ||||||||
\(599\) | 13.0159 | 0.531814 | 0.265907 | − | 0.963999i | \(-0.414329\pi\) | ||||
0.265907 | + | 0.963999i | \(0.414329\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −6.29784 | −0.256894 | −0.128447 | − | 0.991716i | \(-0.540999\pi\) | ||||
−0.128447 | + | 0.991716i | \(0.540999\pi\) | |||||||
\(602\) | −41.9230 | −1.70865 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −45.1378 | −1.83663 | ||||||||
\(605\) | 40.5931 | 1.65034 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 13.1496 | 0.533726 | 0.266863 | − | 0.963734i | \(-0.414013\pi\) | ||||
0.266863 | + | 0.963734i | \(0.414013\pi\) | |||||||
\(608\) | 35.8270 | 1.45298 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −2.20094 | −0.0891133 | ||||||||
\(611\) | 26.7676 | 1.08290 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −36.9849 | −1.49381 | −0.746903 | − | 0.664933i | \(-0.768460\pi\) | ||||
−0.746903 | + | 0.664933i | \(0.768460\pi\) | |||||||
\(614\) | −32.2817 | −1.30278 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 2.54402 | 0.102502 | ||||||||
\(617\) | −32.4778 | −1.30751 | −0.653753 | − | 0.756708i | \(-0.726807\pi\) | ||||
−0.653753 | + | 0.756708i | \(0.726807\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −42.9211 | −1.72514 | −0.862572 | − | 0.505934i | \(-0.831148\pi\) | ||||
−0.862572 | + | 0.505934i | \(0.831148\pi\) | |||||||
\(620\) | 38.0042 | 1.52628 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 35.4254 | 1.42043 | ||||||||
\(623\) | −17.9687 | −0.719902 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 27.3487 | 1.09395 | ||||||||
\(626\) | 68.9172 | 2.75449 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 57.8786 | 2.30961 | ||||||||
\(629\) | 3.54801 | 0.141469 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −13.9019 | −0.553424 | −0.276712 | − | 0.960953i | \(-0.589245\pi\) | ||||
−0.276712 | + | 0.960953i | \(0.589245\pi\) | |||||||
\(632\) | 4.35128 | 0.173085 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −45.8502 | −1.82094 | ||||||||
\(635\) | 51.4374 | 2.04123 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 10.2520 | 0.406200 | ||||||||
\(638\) | 0.742883 | 0.0294110 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 30.5017 | 1.20569 | ||||||||
\(641\) | 2.61962 | 0.103469 | 0.0517345 | − | 0.998661i | \(-0.483525\pi\) | ||||
0.0517345 | + | 0.998661i | \(0.483525\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −0.102506 | −0.00404244 | −0.00202122 | − | 0.999998i | \(-0.500643\pi\) | ||||
−0.00202122 | + | 0.999998i | \(0.500643\pi\) | |||||||
\(644\) | −18.8868 | −0.744244 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 7.08290 | 0.278673 | ||||||||
\(647\) | 25.1564 | 0.988998 | 0.494499 | − | 0.869178i | \(-0.335351\pi\) | ||||
0.494499 | + | 0.869178i | \(0.335351\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −3.13983 | −0.123249 | ||||||||
\(650\) | 53.4178 | 2.09522 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 29.0330 | 1.13702 | ||||||||
\(653\) | 7.45951 | 0.291913 | 0.145957 | − | 0.989291i | \(-0.453374\pi\) | ||||
0.145957 | + | 0.989291i | \(0.453374\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 39.1682 | 1.53043 | ||||||||
\(656\) | 13.7977 | 0.538711 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −75.9723 | −2.96171 | ||||||||
\(659\) | −16.2600 | −0.633399 | −0.316699 | − | 0.948526i | \(-0.602575\pi\) | ||||
−0.316699 | + | 0.948526i | \(0.602575\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 18.8700 | 0.733960 | 0.366980 | − | 0.930229i | \(-0.380392\pi\) | ||||
0.366980 | + | 0.930229i | \(0.380392\pi\) | |||||||
\(662\) | 50.3808 | 1.95811 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 2.56724 | 0.0996284 | ||||||||
\(665\) | −58.2712 | −2.25966 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1.06102 | −0.0410829 | ||||||||
\(668\) | 59.9618 | 2.31999 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 15.7939 | 0.610172 | ||||||||
\(671\) | −0.202212 | −0.00780632 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −8.18112 | −0.315359 | −0.157679 | − | 0.987490i | \(-0.550401\pi\) | ||||
−0.157679 | + | 0.987490i | \(0.550401\pi\) | |||||||
\(674\) | −38.9199 | −1.49914 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −16.8859 | −0.649456 | ||||||||
\(677\) | 23.0920 | 0.887497 | 0.443748 | − | 0.896151i | \(-0.353648\pi\) | ||||
0.443748 | + | 0.896151i | \(0.353648\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −31.6456 | −1.21445 | ||||||||
\(680\) | 2.92701 | 0.112246 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 6.31158 | 0.241683 | ||||||||
\(683\) | 18.7412 | 0.717112 | 0.358556 | − | 0.933508i | \(-0.383269\pi\) | ||||
0.358556 | + | 0.933508i | \(0.383269\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −36.8608 | −1.40838 | ||||||||
\(686\) | 20.2978 | 0.774972 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −16.7549 | −0.638775 | ||||||||
\(689\) | 28.6063 | 1.08981 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −6.64930 | −0.252951 | −0.126476 | − | 0.991970i | \(-0.540367\pi\) | ||||
−0.126476 | + | 0.991970i | \(0.540367\pi\) | |||||||
\(692\) | 38.4154 | 1.46033 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 35.7798 | 1.35818 | ||||||||
\(695\) | 40.8772 | 1.55056 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 3.64940 | 0.138231 | ||||||||
\(698\) | 17.2798 | 0.654051 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −83.8735 | −3.17012 | ||||||||
\(701\) | 24.2954 | 0.917625 | 0.458813 | − | 0.888533i | \(-0.348275\pi\) | ||||
0.458813 | + | 0.888533i | \(0.348275\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 21.3477 | 0.805142 | ||||||||
\(704\) | 8.51272 | 0.320835 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −52.0781 | −1.95999 | ||||||||
\(707\) | −41.0485 | −1.54379 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 29.9220 | 1.12375 | 0.561873 | − | 0.827224i | \(-0.310081\pi\) | ||||
0.561873 | + | 0.827224i | \(0.310081\pi\) | |||||||
\(710\) | 55.6276 | 2.08767 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 5.43066 | 0.203523 | ||||||||
\(713\) | −9.01451 | −0.337596 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 7.32425 | 0.273911 | ||||||||
\(716\) | 17.8011 | 0.665259 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 26.7542 | 0.998460 | ||||||||
\(719\) | 12.2598 | 0.457213 | 0.228607 | − | 0.973519i | \(-0.426583\pi\) | ||||
0.228607 | + | 0.973519i | \(0.426583\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −55.5987 | −2.07060 | ||||||||
\(722\) | 2.41697 | 0.0899504 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −19.1620 | −0.712149 | ||||||||
\(725\) | −4.71184 | −0.174993 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −49.0199 | −1.81805 | −0.909023 | − | 0.416745i | \(-0.863171\pi\) | ||||
−0.909023 | + | 0.416745i | \(0.863171\pi\) | |||||||
\(728\) | −8.35832 | −0.309780 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −65.3249 | −2.41778 | ||||||||
\(731\) | −4.43155 | −0.163907 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −20.1993 | −0.746080 | −0.373040 | − | 0.927815i | \(-0.621685\pi\) | ||||
−0.373040 | + | 0.927815i | \(0.621685\pi\) | |||||||
\(734\) | −22.2031 | −0.819530 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −18.2544 | −0.672866 | ||||||||
\(737\) | 1.45108 | 0.0534511 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 2.01212 | 0.0740170 | 0.0370085 | − | 0.999315i | \(-0.488217\pi\) | ||||
0.0370085 | + | 0.999315i | \(0.488217\pi\) | |||||||
\(740\) | 45.8561 | 1.68570 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −81.1907 | −2.98060 | ||||||||
\(743\) | −21.5721 | −0.791402 | −0.395701 | − | 0.918379i | \(-0.629498\pi\) | ||||
−0.395701 | + | 0.918379i | \(0.629498\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 48.3869 | 1.77276 | ||||||||
\(746\) | 24.9583 | 0.913788 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 1.39784 | 0.0511102 | ||||||||
\(749\) | −12.3198 | −0.450156 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −14.4775 | −0.528293 | −0.264147 | − | 0.964483i | \(-0.585090\pi\) | ||||
−0.264147 | + | 0.964483i | \(0.585090\pi\) | |||||||
\(752\) | −30.3631 | −1.10723 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −2.44072 | −0.0888859 | ||||||||
\(755\) | 70.9567 | 2.58238 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 10.5290 | 0.382684 | 0.191342 | − | 0.981523i | \(-0.438716\pi\) | ||||
0.191342 | + | 0.981523i | \(0.438716\pi\) | |||||||
\(758\) | 38.3736 | 1.39379 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 17.6112 | 0.638826 | ||||||||
\(761\) | 42.2753 | 1.53248 | 0.766240 | − | 0.642555i | \(-0.222125\pi\) | ||||
0.766240 | + | 0.642555i | \(0.222125\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 57.8297 | 2.09357 | ||||||||
\(764\) | 24.9578 | 0.902941 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −32.8315 | −1.18625 | ||||||||
\(767\) | 10.3158 | 0.372483 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −9.01925 | −0.325242 | −0.162621 | − | 0.986689i | \(-0.551995\pi\) | ||||
−0.162621 | + | 0.986689i | \(0.551995\pi\) | |||||||
\(770\) | −20.7878 | −0.749139 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −39.6036 | −1.42537 | ||||||||
\(773\) | −0.719581 | −0.0258815 | −0.0129408 | − | 0.999916i | \(-0.504119\pi\) | ||||
−0.0129408 | + | 0.999916i | \(0.504119\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −40.0321 | −1.43799 | ||||||||
\(776\) | 9.56420 | 0.343335 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 32.6552 | 1.17075 | ||||||||
\(779\) | 21.9577 | 0.786716 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 5.11083 | 0.182880 | ||||||||
\(782\) | −3.60885 | −0.129052 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −11.6291 | −0.415324 | ||||||||
\(785\) | −90.9853 | −3.24741 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 15.4274 | 0.549929 | 0.274964 | − | 0.961454i | \(-0.411334\pi\) | ||||
0.274964 | + | 0.961454i | \(0.411334\pi\) | |||||||
\(788\) | −27.1663 | −0.967758 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −35.5553 | −1.26500 | ||||||||
\(791\) | −34.3826 | −1.22251 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0.664364 | 0.0235922 | ||||||||
\(794\) | 4.32165 | 0.153370 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 8.69403 | 0.308152 | ||||||||
\(797\) | −13.9305 | −0.493444 | −0.246722 | − | 0.969086i | \(-0.579353\pi\) | ||||
−0.246722 | + | 0.969086i | \(0.579353\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −8.03080 | −0.284109 | ||||||||
\(800\) | −81.0651 | −2.86608 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −31.6393 | −1.11722 | ||||||||
\(803\) | −6.00177 | −0.211798 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 29.6901 | 1.04644 | ||||||||
\(806\) | −20.7365 | −0.730413 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 12.4060 | 0.436442 | ||||||||
\(809\) | 40.8781 | 1.43720 | 0.718599 | − | 0.695424i | \(-0.244784\pi\) | ||||
0.718599 | + | 0.695424i | \(0.244784\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 51.1039 | 1.79450 | 0.897250 | − | 0.441524i | \(-0.145562\pi\) | ||||
0.897250 | + | 0.441524i | \(0.145562\pi\) | |||||||
\(812\) | 3.83228 | 0.134487 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 7.61560 | 0.266927 | ||||||||
\(815\) | −45.6400 | −1.59870 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −26.6637 | −0.932845 | ||||||||
\(818\) | 21.9797 | 0.768501 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 47.1665 | 1.64712 | ||||||||
\(821\) | 48.5713 | 1.69515 | 0.847574 | − | 0.530677i | \(-0.178062\pi\) | ||||
0.847574 | + | 0.530677i | \(0.178062\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 27.0271 | 0.942107 | 0.471054 | − | 0.882105i | \(-0.343874\pi\) | ||||
0.471054 | + | 0.882105i | \(0.343874\pi\) | |||||||
\(824\) | 16.8035 | 0.585377 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −29.2786 | −1.01873 | ||||||||
\(827\) | −15.9406 | −0.554309 | −0.277155 | − | 0.960825i | \(-0.589391\pi\) | ||||
−0.277155 | + | 0.960825i | \(0.589391\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −1.69947 | −0.0590250 | −0.0295125 | − | 0.999564i | \(-0.509395\pi\) | ||||
−0.0295125 | + | 0.999564i | \(0.509395\pi\) | |||||||
\(830\) | −20.9775 | −0.728140 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −27.9683 | −0.969627 | ||||||||
\(833\) | −3.07580 | −0.106570 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −94.2600 | −3.26200 | ||||||||
\(836\) | 8.41053 | 0.290884 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −1.12157 | −0.0387441 | ||||||||
\(839\) | 46.3515 | 1.60023 | 0.800116 | − | 0.599845i | \(-0.204771\pi\) | ||||
0.800116 | + | 0.599845i | \(0.204771\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.7847 | −0.992576 | ||||||||
\(842\) | −67.8431 | −2.33803 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −19.0282 | −0.654977 | ||||||||
\(845\) | 26.5446 | 0.913162 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 34.7772 | 1.19496 | ||||||||
\(848\) | −32.4486 | −1.11429 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −16.0264 | −0.549699 | ||||||||
\(851\) | −10.8770 | −0.372858 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −24.1948 | −0.828413 | −0.414207 | − | 0.910183i | \(-0.635941\pi\) | ||||
−0.414207 | + | 0.910183i | \(0.635941\pi\) | |||||||
\(854\) | −1.88560 | −0.0645241 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 3.72339 | 0.127263 | ||||||||
\(857\) | 12.8286 | 0.438217 | 0.219109 | − | 0.975700i | \(-0.429685\pi\) | ||||
0.219109 | + | 0.975700i | \(0.429685\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 20.5200 | 0.700134 | 0.350067 | − | 0.936725i | \(-0.386159\pi\) | ||||
0.350067 | + | 0.936725i | \(0.386159\pi\) | |||||||
\(860\) | −57.2753 | −1.95307 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −11.3890 | −0.387910 | ||||||||
\(863\) | 37.0220 | 1.26024 | 0.630121 | − | 0.776497i | \(-0.283005\pi\) | ||||
0.630121 | + | 0.776497i | \(0.283005\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −60.3890 | −2.05329 | ||||||||
\(866\) | 70.4397 | 2.39364 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 32.5593 | 1.10513 | ||||||||
\(869\) | −3.26666 | −0.110814 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −4.76747 | −0.161540 | ||||||||
\(872\) | −17.4778 | −0.591872 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −21.7137 | −0.734476 | ||||||||
\(875\) | 66.9307 | 2.26267 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 43.3678 | 1.46443 | 0.732213 | − | 0.681076i | \(-0.238488\pi\) | ||||
0.732213 | + | 0.681076i | \(0.238488\pi\) | |||||||
\(878\) | −39.5264 | −1.33395 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −8.30803 | −0.280064 | ||||||||
\(881\) | −10.2812 | −0.346382 | −0.173191 | − | 0.984888i | \(-0.555408\pi\) | ||||
−0.173191 | + | 0.984888i | \(0.555408\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 7.85133 | 0.264218 | 0.132109 | − | 0.991235i | \(-0.457825\pi\) | ||||
0.132109 | + | 0.991235i | \(0.457825\pi\) | |||||||
\(884\) | −4.59258 | −0.154465 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 39.9254 | 1.34132 | ||||||||
\(887\) | 34.9936 | 1.17497 | 0.587485 | − | 0.809235i | \(-0.300118\pi\) | ||||
0.587485 | + | 0.809235i | \(0.300118\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 44.0679 | 1.47799 | ||||||||
\(890\) | −44.3751 | −1.48746 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 26.8550 | 0.899172 | ||||||||
\(893\) | −48.3196 | −1.61696 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −27.9834 | −0.935382 | ||||||||
\(896\) | 26.1317 | 0.872998 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 14.7388 | 0.491840 | ||||||||
\(899\) | 1.82911 | 0.0610044 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −8.58242 | −0.285922 | ||||||||
\(902\) | 7.83322 | 0.260818 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 10.3914 | 0.345613 | ||||||||
\(905\) | 30.1226 | 1.00131 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −50.2389 | −1.66815 | −0.834077 | − | 0.551648i | \(-0.813999\pi\) | ||||
−0.834077 | + | 0.551648i | \(0.813999\pi\) | |||||||
\(908\) | 26.8973 | 0.892617 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 68.2977 | 2.26405 | ||||||||
\(911\) | 24.6615 | 0.817073 | 0.408537 | − | 0.912742i | \(-0.366039\pi\) | ||||
0.408537 | + | 0.912742i | \(0.366039\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1.92732 | −0.0637851 | ||||||||
\(914\) | 79.5475 | 2.63120 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 5.66967 | 0.187331 | ||||||||
\(917\) | 33.5565 | 1.10813 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 8.25476 | 0.272300 | 0.136150 | − | 0.990688i | \(-0.456527\pi\) | ||||
0.136150 | + | 0.990688i | \(0.456527\pi\) | |||||||
\(920\) | −8.97319 | −0.295837 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 58.4732 | 1.92571 | ||||||||
\(923\) | −16.7915 | −0.552698 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −48.3030 | −1.58819 | ||||||||
\(926\) | 51.9785 | 1.70812 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 3.70396 | 0.121588 | ||||||||
\(929\) | 9.80781 | 0.321784 | 0.160892 | − | 0.986972i | \(-0.448563\pi\) | ||||
0.160892 | + | 0.986972i | \(0.448563\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −18.5065 | −0.606525 | ||||||||
\(932\) | −44.1078 | −1.44480 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −16.6316 | −0.544203 | ||||||||
\(935\) | −2.19741 | −0.0718631 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 44.1867 | 1.44352 | 0.721759 | − | 0.692145i | \(-0.243334\pi\) | ||||
0.721759 | + | 0.692145i | \(0.243334\pi\) | |||||||
\(938\) | 13.5311 | 0.441806 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −103.794 | −3.38537 | ||||||||
\(941\) | 10.6403 | 0.346864 | 0.173432 | − | 0.984846i | \(-0.444514\pi\) | ||||
0.173432 | + | 0.984846i | \(0.444514\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −11.1878 | −0.364324 | ||||||||
\(944\) | −11.7015 | −0.380850 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −9.51206 | −0.309264 | ||||||||
\(947\) | 10.9942 | 0.357263 | 0.178632 | − | 0.983916i | \(-0.442833\pi\) | ||||
0.178632 | + | 0.983916i | \(0.442833\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 19.7186 | 0.640094 | ||||||||
\(950\) | −96.4272 | −3.12851 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 2.50766 | 0.0812736 | ||||||||
\(953\) | 42.3248 | 1.37103 | 0.685517 | − | 0.728057i | \(-0.259576\pi\) | ||||
0.685517 | + | 0.728057i | \(0.259576\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −39.2337 | −1.26957 | ||||||||
\(956\) | 30.3764 | 0.982444 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 37.4734 | 1.21071 | ||||||||
\(959\) | −31.5797 | −1.01976 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −15.4597 | −0.498701 | ||||||||
\(962\) | −25.0209 | −0.806705 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 43.3361 | 1.39576 | ||||||||
\(965\) | 62.2570 | 2.00412 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −8.31143 | −0.267278 | −0.133639 | − | 0.991030i | \(-0.542666\pi\) | ||||
−0.133639 | + | 0.991030i | \(0.542666\pi\) | |||||||
\(968\) | −10.5107 | −0.337826 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −78.1511 | −2.50928 | ||||||||
\(971\) | 17.9539 | 0.576169 | 0.288084 | − | 0.957605i | \(-0.406982\pi\) | ||||
0.288084 | + | 0.957605i | \(0.406982\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 35.0207 | 1.12271 | ||||||||
\(974\) | −89.1043 | −2.85509 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −0.753600 | −0.0241222 | ||||||||
\(977\) | 24.4102 | 0.780952 | 0.390476 | − | 0.920613i | \(-0.372310\pi\) | ||||
0.390476 | + | 0.920613i | \(0.372310\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −4.07700 | −0.130301 | ||||||||
\(980\) | −39.7530 | −1.26986 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 15.3975 | 0.491355 | ||||||||
\(983\) | −46.6132 | −1.48673 | −0.743365 | − | 0.668886i | \(-0.766771\pi\) | ||||
−0.743365 | + | 0.668886i | \(0.766771\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 42.7054 | 1.36071 | ||||||||
\(986\) | 0.732263 | 0.0233200 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −27.6326 | −0.879109 | ||||||||
\(989\) | 13.5856 | 0.431996 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 58.8851 | 1.87055 | 0.935273 | − | 0.353926i | \(-0.115154\pi\) | ||||
0.935273 | + | 0.353926i | \(0.115154\pi\) | |||||||
\(992\) | 31.4691 | 0.999144 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 47.6578 | 1.51161 | ||||||||
\(995\) | −13.6670 | −0.433274 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 60.2906 | 1.90942 | 0.954712 | − | 0.297532i | \(-0.0961635\pi\) | ||||
0.954712 | + | 0.297532i | \(0.0961635\pi\) | |||||||
\(998\) | 34.1272 | 1.08028 | ||||||||
\(999\) | 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 | 6561.2.a.d.1.61 | 72 | ||
3.2 | odd | 2 | 6561.2.a.c.1.12 | 72 | |||
81.5 | odd | 54 | 81.2.g.a.25.2 | yes | 144 | ||
81.11 | odd | 54 | 729.2.g.d.514.7 | 144 | |||
81.16 | even | 27 | 243.2.g.a.10.7 | 144 | |||
81.22 | even | 27 | 729.2.g.a.217.2 | 144 | |||
81.32 | odd | 54 | 729.2.g.c.703.7 | 144 | |||
81.38 | odd | 54 | 729.2.g.c.28.7 | 144 | |||
81.43 | even | 27 | 729.2.g.b.28.2 | 144 | |||
81.49 | even | 27 | 729.2.g.b.703.2 | 144 | |||
81.59 | odd | 54 | 729.2.g.d.217.7 | 144 | |||
81.65 | odd | 54 | 81.2.g.a.13.2 | ✓ | 144 | ||
81.70 | even | 27 | 729.2.g.a.514.2 | 144 | |||
81.76 | even | 27 | 243.2.g.a.73.7 | 144 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
81.2.g.a.13.2 | ✓ | 144 | 81.65 | odd | 54 | ||
81.2.g.a.25.2 | yes | 144 | 81.5 | odd | 54 | ||
243.2.g.a.10.7 | 144 | 81.16 | even | 27 | |||
243.2.g.a.73.7 | 144 | 81.76 | even | 27 | |||
729.2.g.a.217.2 | 144 | 81.22 | even | 27 | |||
729.2.g.a.514.2 | 144 | 81.70 | even | 27 | |||
729.2.g.b.28.2 | 144 | 81.43 | even | 27 | |||
729.2.g.b.703.2 | 144 | 81.49 | even | 27 | |||
729.2.g.c.28.7 | 144 | 81.38 | odd | 54 | |||
729.2.g.c.703.7 | 144 | 81.32 | odd | 54 | |||
729.2.g.d.217.7 | 144 | 81.59 | odd | 54 | |||
729.2.g.d.514.7 | 144 | 81.11 | odd | 54 | |||
6561.2.a.c.1.12 | 72 | 3.2 | odd | 2 | |||
6561.2.a.d.1.61 | 72 | 1.1 | even | 1 | trivial |