Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3344,2,Mod(1,3344)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3344, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3344.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3344 = 2^{4} \cdot 11 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3344.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: | \(26.7019744359\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{6} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{6} - 2x^{5} - 12x^{4} + 28x^{3} + 16x^{2} - 60x + 27 \)
|
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 836) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Root | \(2.18868\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3344.1 |
$q$-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 | 0 | ||||||||
\(3\) | 2.18868 | 1.26363 | 0.631817 | − | 0.775118i | \(-0.282309\pi\) | ||||
0.631817 | + | 0.775118i | \(0.282309\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −3.62873 | −1.62282 | −0.811408 | − | 0.584480i | \(-0.801299\pi\) | ||||
−0.811408 | + | 0.584480i | \(0.801299\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 4.31127 | 1.62951 | 0.814753 | − | 0.579808i | \(-0.196872\pi\) | ||||
0.814753 | + | 0.579808i | \(0.196872\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.79031 | 0.596771 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −6.10370 | −1.69286 | −0.846431 | − | 0.532498i | \(-0.821253\pi\) | ||||
−0.846431 | + | 0.532498i | \(0.821253\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −7.94212 | −2.05065 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −0.694815 | −0.168517 | −0.0842587 | − | 0.996444i | \(-0.526852\pi\) | ||||
−0.0842587 | + | 0.996444i | \(0.526852\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.00000 | −0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 9.43598 | 2.05910 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 7.79640 | 1.62566 | 0.812830 | − | 0.582500i | \(-0.197926\pi\) | ||||
0.812830 | + | 0.582500i | \(0.197926\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 8.16767 | 1.63353 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −2.64762 | −0.509534 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 6.02709 | 1.11920 | 0.559602 | − | 0.828762i | \(-0.310954\pi\) | ||||
0.559602 | + | 0.828762i | \(0.310954\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.26529 | 1.12528 | 0.562639 | − | 0.826703i | \(-0.309786\pi\) | ||||
0.562639 | + | 0.826703i | \(0.309786\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −2.18868 | −0.381000 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −15.6444 | −2.64439 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 10.1139 | 1.66271 | 0.831354 | − | 0.555744i | \(-0.187566\pi\) | ||||
0.831354 | + | 0.555744i | \(0.187566\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −13.3590 | −2.13916 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −2.04380 | −0.319189 | −0.159594 | − | 0.987183i | \(-0.551019\pi\) | ||||
−0.159594 | + | 0.987183i | \(0.551019\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.16767 | 0.330566 | 0.165283 | − | 0.986246i | \(-0.447146\pi\) | ||||
0.165283 | + | 0.986246i | \(0.447146\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −6.49655 | −0.968449 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 10.2074 | 1.48890 | 0.744451 | − | 0.667677i | \(-0.232711\pi\) | ||||
0.744451 | + | 0.667677i | \(0.232711\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 11.5870 | 1.65529 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1.52073 | −0.212944 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −1.95798 | −0.268949 | −0.134475 | − | 0.990917i | \(-0.542935\pi\) | ||||
−0.134475 | + | 0.990917i | \(0.542935\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 3.62873 | 0.489298 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −2.18868 | −0.289897 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −5.89831 | −0.767895 | −0.383948 | − | 0.923355i | \(-0.625436\pi\) | ||||
−0.383948 | + | 0.923355i | \(0.625436\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 6.84803 | 0.876800 | 0.438400 | − | 0.898780i | \(-0.355545\pi\) | ||||
0.438400 | + | 0.898780i | \(0.355545\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 7.71852 | 0.972442 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 22.1487 | 2.74720 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 8.35725 | 1.02100 | 0.510501 | − | 0.859877i | \(-0.329460\pi\) | ||||
0.510501 | + | 0.859877i | \(0.329460\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 17.0638 | 2.05424 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −0.566034 | −0.0671759 | −0.0335880 | − | 0.999436i | \(-0.510693\pi\) | ||||
−0.0335880 | + | 0.999436i | \(0.510693\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 7.29948 | 0.854339 | 0.427170 | − | 0.904172i | \(-0.359511\pi\) | ||||
0.427170 | + | 0.904172i | \(0.359511\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 17.8764 | 2.06419 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −4.31127 | −0.491315 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 13.9103 | 1.56503 | 0.782513 | − | 0.622635i | \(-0.213938\pi\) | ||||
0.782513 | + | 0.622635i | \(0.213938\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −11.1657 | −1.24064 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 7.05772 | 0.774685 | 0.387343 | − | 0.921936i | \(-0.373393\pi\) | ||||
0.387343 | + | 0.921936i | \(0.373393\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.52129 | 0.273473 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 13.1914 | 1.41426 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −14.3590 | −1.52205 | −0.761027 | − | 0.648720i | \(-0.775305\pi\) | ||||
−0.761027 | + | 0.648720i | \(0.775305\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −26.3147 | −2.75853 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 13.7127 | 1.42194 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 3.62873 | 0.372300 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −2.89842 | −0.294290 | −0.147145 | − | 0.989115i | \(-0.547008\pi\) | ||||
−0.147145 | + | 0.989115i | \(0.547008\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −1.79031 | −0.179933 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −7.57491 | −0.753732 | −0.376866 | − | 0.926268i | \(-0.622998\pi\) | ||||
−0.376866 | + | 0.926268i | \(0.622998\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −3.29026 | −0.324199 | −0.162099 | − | 0.986774i | \(-0.551827\pi\) | ||||
−0.162099 | + | 0.986774i | \(0.551827\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −34.2406 | −3.34154 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −10.9079 | −1.05451 | −0.527255 | − | 0.849707i | \(-0.676779\pi\) | ||||
−0.527255 | + | 0.849707i | \(0.676779\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 5.42741 | 0.519852 | 0.259926 | − | 0.965629i | \(-0.416302\pi\) | ||||
0.259926 | + | 0.965629i | \(0.416302\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 22.1360 | 2.10105 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 11.9439 | 1.12359 | 0.561794 | − | 0.827277i | \(-0.310111\pi\) | ||||
0.561794 | + | 0.827277i | \(0.310111\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −28.2910 | −2.63815 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −10.9275 | −1.01025 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −2.99553 | −0.274600 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −4.47323 | −0.403337 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −11.4946 | −1.02811 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −7.72813 | −0.685761 | −0.342880 | − | 0.939379i | \(-0.611403\pi\) | ||||
−0.342880 | + | 0.939379i | \(0.611403\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 4.74433 | 0.417715 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 10.5909 | 0.925335 | 0.462668 | − | 0.886532i | \(-0.346892\pi\) | ||||
0.462668 | + | 0.886532i | \(0.346892\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −4.31127 | −0.373834 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 9.60749 | 0.826881 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −8.74829 | −0.747417 | −0.373708 | − | 0.927546i | \(-0.621914\pi\) | ||||
−0.373708 | + | 0.927546i | \(0.621914\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −10.2696 | −0.871055 | −0.435527 | − | 0.900175i | \(-0.643438\pi\) | ||||
−0.435527 | + | 0.900175i | \(0.643438\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 22.3407 | 1.88143 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 6.10370 | 0.510417 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −21.8707 | −1.81626 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 25.3603 | 2.09168 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −21.5725 | −1.76729 | −0.883643 | − | 0.468161i | \(-0.844917\pi\) | ||||
−0.883643 | + | 0.468161i | \(0.844917\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 0.461397 | 0.0375479 | 0.0187740 | − | 0.999824i | \(-0.494024\pi\) | ||||
0.0187740 | + | 0.999824i | \(0.494024\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −1.24394 | −0.100566 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −22.7350 | −1.82612 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −4.52449 | −0.361093 | −0.180547 | − | 0.983566i | \(-0.557787\pi\) | ||||
−0.180547 | + | 0.983566i | \(0.557787\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −4.28539 | −0.339853 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 33.6124 | 2.64903 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −11.9622 | −0.936953 | −0.468477 | − | 0.883476i | \(-0.655197\pi\) | ||||
−0.468477 | + | 0.883476i | \(0.655197\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 7.94212 | 0.618293 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 9.83576 | 0.761114 | 0.380557 | − | 0.924758i | \(-0.375732\pi\) | ||||
0.380557 | + | 0.924758i | \(0.375732\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 24.2552 | 1.86578 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.79031 | −0.136909 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −12.7818 | −0.971783 | −0.485891 | − | 0.874019i | \(-0.661505\pi\) | ||||
−0.485891 | + | 0.874019i | \(0.661505\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 35.2130 | 2.66185 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −12.9095 | −0.970338 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 8.13311 | 0.607897 | 0.303949 | − | 0.952688i | \(-0.401695\pi\) | ||||
0.303949 | + | 0.952688i | \(0.401695\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 18.5543 | 1.37913 | 0.689564 | − | 0.724225i | \(-0.257802\pi\) | ||||
0.689564 | + | 0.724225i | \(0.257802\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 14.9881 | 1.10795 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −36.7004 | −2.69827 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0.694815 | 0.0508099 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −11.4146 | −0.830290 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 10.6265 | 0.768910 | 0.384455 | − | 0.923144i | \(-0.374389\pi\) | ||||
0.384455 | + | 0.923144i | \(0.374389\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −0.759689 | −0.0546836 | −0.0273418 | − | 0.999626i | \(-0.508704\pi\) | ||||
−0.0273418 | + | 0.999626i | \(0.508704\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 48.4763 | 3.47146 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 1.68678 | 0.120178 | 0.0600891 | − | 0.998193i | \(-0.480862\pi\) | ||||
0.0600891 | + | 0.998193i | \(0.480862\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −24.2153 | −1.71658 | −0.858290 | − | 0.513166i | \(-0.828473\pi\) | ||||
−0.858290 | + | 0.513166i | \(0.828473\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 18.2913 | 1.29017 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 25.9844 | 1.82375 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 7.41641 | 0.517984 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 13.9580 | 0.970147 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1.00000 | 0.0691714 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 28.4049 | 1.95547 | 0.977735 | − | 0.209841i | \(-0.0672947\pi\) | ||||
0.977735 | + | 0.209841i | \(0.0672947\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −1.23887 | −0.0848858 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −7.86588 | −0.536448 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 27.0113 | 1.83365 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 15.9762 | 1.07957 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 4.24094 | 0.285277 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 8.82043 | 0.590660 | 0.295330 | − | 0.955395i | \(-0.404570\pi\) | ||||
0.295330 | + | 0.955395i | \(0.404570\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 14.6227 | 0.974845 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 17.2796 | 1.14689 | 0.573443 | − | 0.819246i | \(-0.305607\pi\) | ||||
0.573443 | + | 0.819246i | \(0.305607\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2.15539 | 0.142432 | 0.0712162 | − | 0.997461i | \(-0.477312\pi\) | ||||
0.0712162 | + | 0.997461i | \(0.477312\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −9.43598 | −0.620842 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 11.9733 | 0.784398 | 0.392199 | − | 0.919880i | \(-0.371715\pi\) | ||||
0.392199 | + | 0.919880i | \(0.371715\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −37.0399 | −2.41622 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 30.4451 | 1.97762 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −18.7692 | −1.21408 | −0.607038 | − | 0.794673i | \(-0.707643\pi\) | ||||
−0.607038 | + | 0.794673i | \(0.707643\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 14.9468 | 0.962807 | 0.481404 | − | 0.876499i | \(-0.340127\pi\) | ||||
0.481404 | + | 0.876499i | \(0.340127\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −16.4953 | −1.05817 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −42.0462 | −2.68624 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 6.10370 | 0.388369 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 15.4471 | 0.978918 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 12.1955 | 0.769771 | 0.384885 | − | 0.922964i | \(-0.374241\pi\) | ||||
0.384885 | + | 0.922964i | \(0.374241\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −7.79640 | −0.490155 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 5.51830 | 0.345569 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −6.96669 | −0.434570 | −0.217285 | − | 0.976108i | \(-0.569720\pi\) | ||||
−0.217285 | + | 0.976108i | \(0.569720\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 43.6036 | 2.70939 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 10.7904 | 0.667908 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −25.0396 | −1.54401 | −0.772005 | − | 0.635617i | \(-0.780746\pi\) | ||||
−0.772005 | + | 0.635617i | \(0.780746\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 7.10498 | 0.436455 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −31.4273 | −1.92332 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 1.58130 | 0.0964134 | 0.0482067 | − | 0.998837i | \(-0.484649\pi\) | ||||
0.0482067 | + | 0.998837i | \(0.484649\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −5.57867 | −0.338880 | −0.169440 | − | 0.985540i | \(-0.554196\pi\) | ||||
−0.169440 | + | 0.985540i | \(0.554196\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −57.5944 | −3.48577 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −8.16767 | −0.492529 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 30.5385 | 1.83488 | 0.917440 | − | 0.397874i | \(-0.130252\pi\) | ||||
0.917440 | + | 0.397874i | \(0.130252\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 11.2168 | 0.671533 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −15.0369 | −0.897029 | −0.448514 | − | 0.893776i | \(-0.648047\pi\) | ||||
−0.448514 | + | 0.893776i | \(0.648047\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −29.1158 | −1.73076 | −0.865378 | − | 0.501120i | \(-0.832921\pi\) | ||||
−0.865378 | + | 0.501120i | \(0.832921\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 7.94212 | 0.470450 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −8.81139 | −0.520120 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.5172 | −0.971602 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −6.34371 | −0.371875 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 5.88816 | 0.343990 | 0.171995 | − | 0.985098i | \(-0.444979\pi\) | ||||
0.171995 | + | 0.985098i | \(0.444979\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 21.4034 | 1.24615 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 2.64762 | 0.153630 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −47.5869 | −2.75202 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 9.34540 | 0.538660 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −16.5791 | −0.952442 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −24.8496 | −1.42289 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −19.2140 | −1.09660 | −0.548300 | − | 0.836282i | \(-0.684725\pi\) | ||||
−0.548300 | + | 0.836282i | \(0.684725\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −7.20132 | −0.409669 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −26.7459 | −1.51662 | −0.758310 | − | 0.651894i | \(-0.773975\pi\) | ||||
−0.758310 | + | 0.651894i | \(0.773975\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −16.0435 | −0.906834 | −0.453417 | − | 0.891298i | \(-0.649795\pi\) | ||||
−0.453417 | + | 0.891298i | \(0.649795\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −28.0084 | −1.57809 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 18.5664 | 1.04280 | 0.521398 | − | 0.853314i | \(-0.325411\pi\) | ||||
0.521398 | + | 0.853314i | \(0.325411\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −6.02709 | −0.337453 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −23.8739 | −1.33251 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0.694815 | 0.0386605 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −49.8530 | −2.76535 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 11.8789 | 0.656902 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 44.0069 | 2.42618 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 34.6196 | 1.90286 | 0.951431 | − | 0.307861i | \(-0.0996132\pi\) | ||||
0.951431 | + | 0.307861i | \(0.0996132\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 18.1070 | 0.992255 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −30.3262 | −1.65690 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2.84625 | 0.155045 | 0.0775224 | − | 0.996991i | \(-0.475299\pi\) | ||||
0.0775224 | + | 0.996991i | \(0.475299\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 26.1414 | 1.41980 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −6.26529 | −0.339284 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 19.7760 | 1.06780 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −61.9199 | −3.33366 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −10.0153 | −0.537651 | −0.268826 | − | 0.963189i | \(-0.586636\pi\) | ||||
−0.268826 | + | 0.963189i | \(0.586636\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −0.712288 | −0.0381279 | −0.0190640 | − | 0.999818i | \(-0.506069\pi\) | ||||
−0.0190640 | + | 0.999818i | \(0.506069\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 16.1603 | 0.862571 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 32.4528 | 1.72729 | 0.863645 | − | 0.504101i | \(-0.168176\pi\) | ||||
0.863645 | + | 0.504101i | \(0.168176\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 2.05398 | 0.109014 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −6.55626 | −0.346994 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −19.6749 | −1.03840 | −0.519200 | − | 0.854653i | \(-0.673770\pi\) | ||||
−0.519200 | + | 0.854653i | \(0.673770\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 2.18868 | 0.114876 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −26.4878 | −1.38644 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 31.5887 | 1.64891 | 0.824457 | − | 0.565924i | \(-0.191480\pi\) | ||||
0.824457 | + | 0.565924i | \(0.191480\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −3.65905 | −0.190482 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −8.44138 | −0.438255 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 20.4557 | 1.05916 | 0.529579 | − | 0.848260i | \(-0.322350\pi\) | ||||
0.529579 | + | 0.848260i | \(0.322350\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −25.1580 | −1.29915 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −36.7876 | −1.89466 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −6.22508 | −0.319761 | −0.159880 | − | 0.987136i | \(-0.551111\pi\) | ||||
−0.159880 | + | 0.987136i | \(0.551111\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −16.9144 | −0.866550 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 0.592813 | 0.0302913 | 0.0151457 | − | 0.999885i | \(-0.495179\pi\) | ||||
0.0151457 | + | 0.999885i | \(0.495179\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 15.6444 | 0.797314 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 3.88080 | 0.197272 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 32.2424 | 1.63475 | 0.817377 | − | 0.576103i | \(-0.195427\pi\) | ||||
0.817377 | + | 0.576103i | \(0.195427\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −5.41705 | −0.273952 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 23.1802 | 1.16929 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −50.4765 | −2.53975 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −25.1889 | −1.26420 | −0.632098 | − | 0.774888i | \(-0.717806\pi\) | ||||
−0.632098 | + | 0.774888i | \(0.717806\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −9.43598 | −0.472390 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −22.3272 | −1.11497 | −0.557484 | − | 0.830188i | \(-0.688233\pi\) | ||||
−0.557484 | + | 0.830188i | \(0.688233\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −38.2414 | −1.90494 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 40.5174 | 2.01332 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −10.1139 | −0.501325 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 24.1005 | 1.19169 | 0.595847 | − | 0.803098i | \(-0.296817\pi\) | ||||
0.595847 | + | 0.803098i | \(0.296817\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −19.1472 | −0.944461 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −25.4292 | −1.25129 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −25.6105 | −1.25717 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −22.4768 | −1.10069 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 17.0480 | 0.832851 | 0.416425 | − | 0.909170i | \(-0.363283\pi\) | ||||
0.416425 | + | 0.909170i | \(0.363283\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 4.12963 | 0.201266 | 0.100633 | − | 0.994924i | \(-0.467913\pi\) | ||||
0.100633 | + | 0.994924i | \(0.467913\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 18.2744 | 0.888533 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −5.67502 | −0.275279 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 29.5237 | 1.42875 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 13.3590 | 0.644980 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 5.86783 | 0.282643 | 0.141322 | − | 0.989964i | \(-0.454865\pi\) | ||||
0.141322 | + | 0.989964i | \(0.454865\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 15.5840 | 0.748920 | 0.374460 | − | 0.927243i | \(-0.377828\pi\) | ||||
0.374460 | + | 0.927243i | \(0.377828\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −47.8679 | −2.29509 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −7.79640 | −0.372952 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −13.1937 | −0.629699 | −0.314850 | − | 0.949142i | \(-0.601954\pi\) | ||||
−0.314850 | + | 0.949142i | \(0.601954\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 20.7444 | 0.987830 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 4.14411 | 0.196893 | 0.0984463 | − | 0.995142i | \(-0.468613\pi\) | ||||
0.0984463 | + | 0.995142i | \(0.468613\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 52.1050 | 2.47002 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −47.2152 | −2.23320 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −35.9971 | −1.69881 | −0.849405 | − | 0.527742i | \(-0.823039\pi\) | ||||
−0.849405 | + | 0.527742i | \(0.823039\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2.04380 | 0.0962390 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 1.00985 | 0.0474468 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 95.4889 | 4.47659 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 7.94870 | 0.371825 | 0.185912 | − | 0.982566i | \(-0.440476\pi\) | ||||
0.185912 | + | 0.982566i | \(0.440476\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 1.83960 | 0.0858654 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −9.33968 | −0.434992 | −0.217496 | − | 0.976061i | \(-0.569789\pi\) | ||||
−0.217496 | + | 0.976061i | \(0.569789\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −13.0328 | −0.605686 | −0.302843 | − | 0.953040i | \(-0.597936\pi\) | ||||
−0.302843 | + | 0.953040i | \(0.597936\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −49.7596 | −2.30755 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −17.1169 | −0.792076 | −0.396038 | − | 0.918234i | \(-0.629615\pi\) | ||||
−0.396038 | + | 0.918234i | \(0.629615\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 36.0304 | 1.66373 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −9.90264 | −0.456290 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −2.16767 | −0.0996695 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −8.16767 | −0.374758 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −3.50539 | −0.160501 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −39.8917 | −1.82270 | −0.911349 | − | 0.411635i | \(-0.864958\pi\) | ||||
−0.911349 | + | 0.411635i | \(0.864958\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −61.7319 | −2.81473 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 73.5666 | 3.34740 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 10.5176 | 0.477578 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 21.3504 | 0.967478 | 0.483739 | − | 0.875212i | \(-0.339278\pi\) | ||||
0.483739 | + | 0.875212i | \(0.339278\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −26.1814 | −1.18397 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 17.0293 | 0.768524 | 0.384262 | − | 0.923224i | \(-0.374456\pi\) | ||||
0.384262 | + | 0.923224i | \(0.374456\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −4.18771 | −0.188605 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 6.49655 | 0.291998 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −2.44033 | −0.109464 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 4.94667 | 0.221443 | 0.110722 | − | 0.993851i | \(-0.464684\pi\) | ||||
0.110722 | + | 0.993851i | \(0.464684\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 21.5273 | 0.961769 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 3.22196 | 0.143660 | 0.0718301 | − | 0.997417i | \(-0.477116\pi\) | ||||
0.0718301 | + | 0.997417i | \(0.477116\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 27.4873 | 1.22317 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 53.0868 | 2.35767 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 10.1751 | 0.451003 | 0.225502 | − | 0.974243i | \(-0.427598\pi\) | ||||
0.225502 | + | 0.974243i | \(0.427598\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 31.4700 | 1.39215 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 2.64762 | 0.116895 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 11.9395 | 0.526115 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −10.2074 | −0.448921 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −27.9753 | −1.22798 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −33.3792 | −1.46237 | −0.731186 | − | 0.682179i | \(-0.761033\pi\) | ||||
−0.731186 | + | 0.682179i | \(0.761033\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 2.17534 | 0.0951208 | 0.0475604 | − | 0.998868i | \(-0.484855\pi\) | ||||
0.0475604 | + | 0.998868i | \(0.484855\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 77.0700 | 3.36361 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −4.35321 | −0.189629 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 37.7838 | 1.64277 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −10.5598 | −0.458257 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 12.4748 | 0.540342 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 39.5819 | 1.71127 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 17.8008 | 0.768160 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −11.5870 | −0.499089 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 24.6958 | 1.06176 | 0.530878 | − | 0.847448i | \(-0.321862\pi\) | ||||
0.530878 | + | 0.847448i | \(0.321862\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 40.6093 | 1.74271 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −19.6946 | −0.843624 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 9.80330 | 0.419159 | 0.209579 | − | 0.977792i | \(-0.432791\pi\) | ||||
0.209579 | + | 0.977792i | \(0.432791\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 12.2601 | 0.523249 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −6.02709 | −0.256763 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 59.9708 | 2.55022 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −80.3254 | −3.40962 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −12.1796 | −0.516065 | −0.258033 | − | 0.966136i | \(-0.583074\pi\) | ||||
−0.258033 | + | 0.966136i | \(0.583074\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −13.2308 | −0.559603 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1.52073 | 0.0642051 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −10.6703 | −0.449698 | −0.224849 | − | 0.974394i | \(-0.572189\pi\) | ||||
−0.224849 | + | 0.974394i | \(0.572189\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −43.3412 | −1.82338 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −48.1384 | −2.02162 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −20.8260 | −0.873072 | −0.436536 | − | 0.899687i | \(-0.643795\pi\) | ||||
−0.436536 | + | 0.899687i | \(0.643795\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −21.5755 | −0.902907 | −0.451454 | − | 0.892295i | \(-0.649094\pi\) | ||||
−0.451454 | + | 0.892295i | \(0.649094\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 23.2581 | 0.971621 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 63.6784 | 2.65557 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 15.5212 | 0.646157 | 0.323079 | − | 0.946372i | \(-0.395282\pi\) | ||||
0.323079 | + | 0.946372i | \(0.395282\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −1.66272 | −0.0691001 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 30.4277 | 1.26235 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.95798 | 0.0810912 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 39.6530 | 1.63945 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −4.08383 | −0.168558 | −0.0842789 | − | 0.996442i | \(-0.526859\pi\) | ||||
−0.0842789 | + | 0.996442i | \(0.526859\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −6.26529 | −0.258157 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 3.69182 | 0.151861 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −45.1039 | −1.85220 | −0.926098 | − | 0.377283i | \(-0.876858\pi\) | ||||
−0.926098 | + | 0.377283i | \(0.876858\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 10.8700 | 0.445626 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −52.9996 | −2.16913 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 1.29026 | 0.0527186 | 0.0263593 | − | 0.999653i | \(-0.491609\pi\) | ||||
0.0263593 | + | 0.999653i | \(0.491609\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −29.0011 | −1.18298 | −0.591489 | − | 0.806313i | \(-0.701460\pi\) | ||||
−0.591489 | + | 0.806313i | \(0.701460\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 14.9621 | 0.609303 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −3.62873 | −0.147529 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 11.0119 | 0.446958 | 0.223479 | − | 0.974709i | \(-0.428259\pi\) | ||||
0.223479 | + | 0.974709i | \(0.428259\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 56.8715 | 2.30455 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −62.3029 | −2.52051 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 1.94010 | 0.0783600 | 0.0391800 | − | 0.999232i | \(-0.487525\pi\) | ||||
0.0391800 | + | 0.999232i | \(0.487525\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 16.2321 | 0.654543 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 15.1760 | 0.610964 | 0.305482 | − | 0.952198i | \(-0.401182\pi\) | ||||
0.305482 | + | 0.952198i | \(0.401182\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −35.8548 | −1.44113 | −0.720564 | − | 0.693389i | \(-0.756117\pi\) | ||||
−0.720564 | + | 0.693389i | \(0.756117\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −20.6419 | −0.828330 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −61.9057 | −2.48020 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0.872460 | 0.0348984 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 2.18868 | 0.0874074 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −7.02726 | −0.280195 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1.43092 | 0.0569640 | 0.0284820 | − | 0.999594i | \(-0.490933\pi\) | ||||
0.0284820 | + | 0.999594i | \(0.490933\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 62.1691 | 2.47100 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 28.0433 | 1.11286 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −70.7239 | −2.80218 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −1.01338 | −0.0400886 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −27.8685 | −1.10074 | −0.550369 | − | 0.834922i | \(-0.685513\pi\) | ||||
−0.550369 | + | 0.834922i | \(0.685513\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1.90753 | 0.0752256 | 0.0376128 | − | 0.999292i | \(-0.488025\pi\) | ||||
0.0376128 | + | 0.999292i | \(0.488025\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −17.2159 | −0.677874 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 44.9164 | 1.76584 | 0.882922 | − | 0.469519i | \(-0.155573\pi\) | ||||
0.882922 | + | 0.469519i | \(0.155573\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 5.89831 | 0.231529 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 59.1191 | 2.31706 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 23.6282 | 0.924642 | 0.462321 | − | 0.886713i | \(-0.347017\pi\) | ||||
0.462321 | + | 0.886713i | \(0.347017\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −38.4317 | −1.50165 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 13.0683 | 0.509844 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 10.7391 | 0.418334 | 0.209167 | − | 0.977880i | \(-0.432925\pi\) | ||||
0.209167 | + | 0.977880i | \(0.432925\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −46.0837 | −1.79245 | −0.896224 | − | 0.443603i | \(-0.853700\pi\) | ||||
−0.896224 | + | 0.443603i | \(0.853700\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 9.28206 | 0.360485 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 15.6444 | 0.606665 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 46.9896 | 1.81945 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 19.3051 | 0.746378 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −6.84803 | −0.264365 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −22.6538 | −0.873242 | −0.436621 | − | 0.899646i | \(-0.643825\pi\) | ||||
−0.436621 | + | 0.899646i | \(0.643825\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −21.6249 | −0.832341 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 24.3654 | 0.936438 | 0.468219 | − | 0.883613i | \(-0.344896\pi\) | ||||
0.468219 | + | 0.883613i | \(0.344896\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −12.4959 | −0.479547 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 37.8194 | 1.44924 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 26.6471 | 1.01962 | 0.509811 | − | 0.860286i | \(-0.329715\pi\) | ||||
0.509811 | + | 0.860286i | \(0.329715\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 31.7452 | 1.21292 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 4.71746 | 0.179982 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 11.9509 | 0.455294 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −39.6176 | −1.50713 | −0.753563 | − | 0.657376i | \(-0.771666\pi\) | ||||
−0.753563 | + | 0.657376i | \(0.771666\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −7.71852 | −0.293202 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 37.2655 | 1.41356 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.42007 | 0.0537888 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 26.2057 | 0.991192 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1.92410 | 0.0726722 | 0.0363361 | − | 0.999340i | \(-0.488431\pi\) | ||||
0.0363361 | + | 0.999340i | \(0.488431\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −10.1139 | −0.381451 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −81.0684 | −3.05321 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −32.6575 | −1.22821 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −6.91616 | −0.259742 | −0.129871 | − | 0.991531i | \(-0.541456\pi\) | ||||
−0.129871 | + | 0.991531i | \(0.541456\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 24.9037 | 0.933961 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 48.8466 | 1.82932 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −22.1487 | −0.828313 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −41.0797 | −1.53415 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 12.3035 | 0.458843 | 0.229422 | − | 0.973327i | \(-0.426317\pi\) | ||||
0.229422 | + | 0.973327i | \(0.426317\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −14.1852 | −0.528284 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 32.7137 | 1.21664 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 49.2273 | 1.82826 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 27.6098 | 1.02399 | 0.511995 | − | 0.858989i | \(-0.328907\pi\) | ||||
0.511995 | + | 0.858989i | \(0.328907\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −2.60577 | −0.0965099 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1.50613 | −0.0557062 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −45.0293 | −1.66319 | −0.831597 | − | 0.555380i | \(-0.812573\pi\) | ||||
−0.831597 | + | 0.555380i | \(0.812573\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −92.0257 | −3.39442 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −8.35725 | −0.307843 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −37.8963 | −1.39404 | −0.697018 | − | 0.717053i | \(-0.745490\pi\) | ||||
−0.697018 | + | 0.717053i | \(0.745490\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 13.3590 | 0.490757 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −23.3103 | −0.855172 | −0.427586 | − | 0.903975i | \(-0.640636\pi\) | ||||
−0.427586 | + | 0.903975i | \(0.640636\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 78.2807 | 2.86798 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 12.6355 | 0.462309 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −47.0270 | −1.71833 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 14.9643 | 0.546056 | 0.273028 | − | 0.962006i | \(-0.411975\pi\) | ||||
0.273028 | + | 0.962006i | \(0.411975\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 26.6919 | 0.972709 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −1.67428 | −0.0609334 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −13.3436 | −0.484980 | −0.242490 | − | 0.970154i | \(-0.577964\pi\) | ||||
−0.242490 | + | 0.970154i | \(0.577964\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −17.0638 | −0.619377 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −11.6962 | −0.423986 | −0.211993 | − | 0.977271i | \(-0.567995\pi\) | ||||
−0.211993 | + | 0.977271i | \(0.567995\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 23.3990 | 0.847102 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 4.51390 | 0.163200 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 36.0015 | 1.29994 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 41.2234 | 1.48655 | 0.743276 | − | 0.668985i | \(-0.233271\pi\) | ||||
0.743276 | + | 0.668985i | \(0.233271\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −15.2478 | −0.549137 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −12.9999 | −0.467574 | −0.233787 | − | 0.972288i | \(-0.575112\pi\) | ||||
−0.233787 | + | 0.972288i | \(0.575112\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 51.1728 | 1.83818 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 95.4341 | 3.42368 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 2.04380 | 0.0732269 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0.566034 | 0.0202543 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −15.9574 | −0.570273 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 16.4181 | 0.585988 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −4.63820 | −0.165334 | −0.0826669 | − | 0.996577i | \(-0.526344\pi\) | ||||
−0.0826669 | + | 0.996577i | \(0.526344\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −54.8037 | −1.95106 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 51.4934 | 1.83089 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −41.7983 | −1.48430 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 15.5505 | 0.551520 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −11.0271 | −0.390600 | −0.195300 | − | 0.980744i | \(-0.562568\pi\) | ||||
−0.195300 | + | 0.980744i | \(0.562568\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −7.09226 | −0.250906 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −25.7072 | −0.908318 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −7.29948 | −0.257593 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −121.970 | −4.29888 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 3.46095 | 0.121831 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −18.8659 | −0.663290 | −0.331645 | − | 0.943404i | \(-0.607604\pi\) | ||||
−0.331645 | + | 0.943404i | \(0.607604\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 13.9642 | 0.490348 | 0.245174 | − | 0.969479i | \(-0.421155\pi\) | ||||
0.245174 | + | 0.969479i | \(0.421155\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −12.2099 | −0.428221 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 43.4076 | 1.52050 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −2.16767 | −0.0758371 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −47.1115 | −1.64621 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −30.8485 | −1.07662 | −0.538310 | − | 0.842747i | \(-0.680937\pi\) | ||||
−0.538310 | + | 0.842747i | \(0.680937\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 9.48137 | 0.330500 | 0.165250 | − | 0.986252i | \(-0.447157\pi\) | ||||
0.165250 | + | 0.986252i | \(0.447157\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −17.8764 | −0.622376 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −16.7454 | −0.582296 | −0.291148 | − | 0.956678i | \(-0.594037\pi\) | ||||
−0.291148 | + | 0.956678i | \(0.594037\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1.59130 | 0.0552682 | 0.0276341 | − | 0.999618i | \(-0.491203\pi\) | ||||
0.0276341 | + | 0.999618i | \(0.491203\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 66.8389 | 2.31862 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −8.05085 | −0.278945 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −35.6913 | −1.23515 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −16.5881 | −0.573368 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 5.12222 | 0.176839 | 0.0884193 | − | 0.996083i | \(-0.471818\pi\) | ||||
0.0884193 | + | 0.996083i | \(0.471818\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 7.32587 | 0.252616 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −32.9110 | −1.13352 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −88.0154 | −3.02782 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 4.31127 | 0.148137 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −63.7251 | −2.18704 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 78.8516 | 2.70300 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −51.2020 | −1.75312 | −0.876561 | − | 0.481290i | \(-0.840168\pi\) | ||||
−0.876561 | + | 0.481290i | \(0.840168\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 6.49655 | 0.222177 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −7.92412 | −0.270683 | −0.135341 | − | 0.990799i | \(-0.543213\pi\) | ||||
−0.135341 | + | 0.990799i | \(0.543213\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 39.4668 | 1.34659 | 0.673296 | − | 0.739373i | \(-0.264878\pi\) | ||||
0.673296 | + | 0.739373i | \(0.264878\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −19.2853 | −0.657241 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 52.1231 | 1.77429 | 0.887145 | − | 0.461491i | \(-0.152685\pi\) | ||||
0.887145 | + | 0.461491i | \(0.152685\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 46.3817 | 1.57703 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −36.1509 | −1.22775 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −13.9103 | −0.471873 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −51.0102 | −1.72841 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −5.18907 | −0.175624 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −49.5563 | −1.67531 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 20.6344 | 0.696773 | 0.348386 | − | 0.937351i | \(-0.386730\pi\) | ||||
0.348386 | + | 0.937351i | \(0.386730\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 12.8873 | 0.434677 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 42.3008 | 1.42515 | 0.712574 | − | 0.701597i | \(-0.247529\pi\) | ||||
0.712574 | + | 0.701597i | \(0.247529\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 47.1397 | 1.58638 | 0.793188 | − | 0.608977i | \(-0.208420\pi\) | ||||
0.793188 | + | 0.608977i | \(0.208420\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 46.8451 | 1.57468 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −5.41860 | −0.181939 | −0.0909694 | − | 0.995854i | \(-0.528997\pi\) | ||||
−0.0909694 | + | 0.995854i | \(0.528997\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −33.3180 | −1.11745 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 11.1657 | 0.374066 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −10.2074 | −0.341578 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −29.5129 | −0.986506 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −104.152 | −3.47755 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 37.7615 | 1.25942 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.36043 | 0.0453226 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 20.4541 | 0.680669 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −67.3284 | −2.23807 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −22.1148 | −0.734309 | −0.367154 | − | 0.930160i | \(-0.619668\pi\) | ||||
−0.367154 | + | 0.930160i | \(0.619668\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −13.5615 | −0.449805 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −18.0321 | −0.597429 | −0.298715 | − | 0.954343i | \(-0.596558\pi\) | ||||
−0.298715 | + | 0.954343i | \(0.596558\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −7.05772 | −0.233576 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −54.3879 | −1.79801 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 45.6604 | 1.50784 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 36.9395 | 1.21852 | 0.609261 | − | 0.792970i | \(-0.291466\pi\) | ||||
0.609261 | + | 0.792970i | \(0.291466\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −42.0532 | −1.38570 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 3.45490 | 0.113720 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 82.6066 | 2.71609 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −5.89059 | −0.193472 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 10.2792 | 0.337250 | 0.168625 | − | 0.985680i | \(-0.446067\pi\) | ||||
0.168625 | + | 0.985680i | \(0.446067\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −11.5870 | −0.379750 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −58.5382 | −1.91645 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −2.52129 | −0.0824551 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1.42527 | 0.0465615 | 0.0232807 | − | 0.999729i | \(-0.492589\pi\) | ||||
0.0232807 | + | 0.999729i | \(0.492589\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −35.1141 | −1.14591 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 32.0967 | 1.04632 | 0.523161 | − | 0.852234i | \(-0.324753\pi\) | ||||
0.523161 | + | 0.852234i | \(0.324753\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −15.9343 | −0.518892 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 41.4205 | 1.34741 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 8.61405 | 0.279919 | 0.139959 | − | 0.990157i | \(-0.455303\pi\) | ||||
0.139959 | + | 0.990157i | \(0.455303\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −44.5538 | −1.44628 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 40.6360 | 1.31771 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 6.48103 | 0.209941 | 0.104971 | − | 0.994475i | \(-0.466525\pi\) | ||||
0.104971 | + | 0.994475i | \(0.466525\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −38.5609 | −1.24780 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −13.1914 | −0.426416 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −37.7162 | −1.21792 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 8.25380 | 0.266252 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −19.5286 | −0.629300 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 2.75671 | 0.0887415 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −55.2454 | −1.77657 | −0.888286 | − | 0.459292i | \(-0.848103\pi\) | ||||
−0.888286 | + | 0.459292i | \(0.848103\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 1.52073 | 0.0488528 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −30.1518 | −0.967618 | −0.483809 | − | 0.875174i | \(-0.660747\pi\) | ||||
−0.483809 | + | 0.875174i | \(0.660747\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −44.2750 | −1.41939 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −109.112 | −3.49439 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 22.6608 | 0.724984 | 0.362492 | − | 0.931987i | \(-0.381926\pi\) | ||||
0.362492 | + | 0.931987i | \(0.381926\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 14.3590 | 0.458917 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 9.71676 | 0.310232 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −17.3274 | −0.552658 | −0.276329 | − | 0.961063i | \(-0.589118\pi\) | ||||
−0.276329 | + | 0.961063i | \(0.589118\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −6.12087 | −0.195027 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 96.3169 | 3.06580 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 16.9000 | 0.537389 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −27.1931 | −0.863818 | −0.431909 | − | 0.901917i | \(-0.642160\pi\) | ||||
−0.431909 | + | 0.901917i | \(0.642160\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 75.7711 | 2.40452 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 87.8709 | 2.78569 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 21.0570 | 0.666881 | 0.333441 | − | 0.942771i | \(-0.391790\pi\) | ||||
0.333441 | + | 0.942771i | \(0.391790\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −26.7776 | −0.847207 |
(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 | 3344.2.a.x.1.5 | 6 | ||
4.3 | odd | 2 | 836.2.a.d.1.2 | ✓ | 6 | ||
12.11 | even | 2 | 7524.2.a.r.1.6 | 6 | |||
44.43 | even | 2 | 9196.2.a.k.1.2 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
836.2.a.d.1.2 | ✓ | 6 | 4.3 | odd | 2 | ||
3344.2.a.x.1.5 | 6 | 1.1 | even | 1 | trivial | ||
7524.2.a.r.1.6 | 6 | 12.11 | even | 2 | |||
9196.2.a.k.1.2 | 6 | 44.43 | even | 2 |